LMFDB - Embedded newform 33.8.e.a.4.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,8,Mod(4,33)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("33.4");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	33.e (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.3087058410$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			4.7
Character	$\chi$	$=$	33.4
Dual form			33.8.e.a.25.7

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(15.4308 + 11.2111i) q^{2} +(-8.34346 + 25.6785i) q^{3} +(72.8662 + 224.259i) q^{4} +(0.205524 - 0.149322i) q^{5} +(-416.632 + 302.701i) q^{6} +(242.486 + 746.295i) q^{7} +(-635.379 + 1955.49i) q^{8} +(-589.773 - 428.495i) q^{9} +O(q^{10})$	\(q+(15.4308 + 11.2111i) q^{2} +(-8.34346 + 25.6785i) q^{3} +(72.8662 + 224.259i) q^{4} +(0.205524 - 0.149322i) q^{5} +(-416.632 + 302.701i) q^{6} +(242.486 + 746.295i) q^{7} +(-635.379 + 1955.49i) q^{8} +(-589.773 - 428.495i) q^{9} +4.84548 q^{10} +(-4411.63 - 157.205i) q^{11} -6366.60 q^{12} +(3855.23 + 2800.99i) q^{13} +(-4625.06 + 14234.5i) q^{14} +(2.11959 + 6.52342i) q^{15} +(-7309.67 + 5310.78i) q^{16} +(8292.40 - 6024.78i) q^{17} +(-4296.76 - 13224.1i) q^{18} +(4573.18 - 14074.8i) q^{19} +(48.4626 + 35.2102i) q^{20} -21186.9 q^{21} +(-66312.6 - 51885.2i) q^{22} +94090.2 q^{23} +(-44913.0 - 32631.2i) q^{24} +(-24141.9 + 74301.2i) q^{25} +(28087.0 + 86443.0i) q^{26} +(15923.9 - 11569.4i) q^{27} +(-149694. + 108759. i) q^{28} +(35729.6 + 109964. i) q^{29} +(-40.4281 + 124.425i) q^{30} +(36613.2 + 26601.0i) q^{31} +90850.3 q^{32} +(40845.0 - 111972. i) q^{33} +195503. q^{34} +(161.275 + 117.173i) q^{35} +(53119.5 - 163485. i) q^{36} +(-68461.0 - 210701. i) q^{37} +(228362. - 165915. i) q^{38} +(-104091. + 75626.6i) q^{39} +(161.413 + 496.778i) q^{40} +(165995. - 510881. i) q^{41} +(-326931. - 237530. i) q^{42} +579446. q^{43} +(-286204. - 1.00080e6i) q^{44} -185.197 q^{45} +(1.45189e6 + 1.05486e6i) q^{46} +(-18406.4 + 56649.1i) q^{47} +(-75385.2 - 232012. i) q^{48} +(168104. - 122135. i) q^{49} +(-1.20553e6 + 875870. i) q^{50} +(85520.2 + 263204. i) q^{51} +(-347231. + 1.06867e6i) q^{52} +(-1.37433e6 - 998512. i) q^{53} +375425. q^{54} +(-930.171 + 626.444i) q^{55} -1.61344e6 q^{56} +(323264. + 234865. i) q^{57} +(-681490. + 2.09741e6i) q^{58} +(-293330. - 902777. i) q^{59} +(-1308.49 + 950.674i) q^{60} +(-2.12593e6 + 1.54458e6i) q^{61} +(266743. + 820952. i) q^{62} +(176772. - 544049. i) q^{63} +(2.33753e6 + 1.69832e6i) q^{64} +1210.59 q^{65} +(1.88561e6 - 1.26991e6i) q^{66} -3.39507e6 q^{67} +(1.95535e6 + 1.42064e6i) q^{68} +(-785038. + 2.41610e6i) q^{69} +(1174.96 + 3616.16i) q^{70} +(-48918.8 + 35541.6i) q^{71} +(1.21265e6 - 881042. i) q^{72} +(-568125. - 1.74851e6i) q^{73} +(1.30579e6 - 4.01882e6i) q^{74} +(-1.70652e6 - 1.23986e6i) q^{75} +3.48963e6 q^{76} +(-952436. - 3.33049e6i) q^{77} -2.45407e6 q^{78} +(-3.05212e6 - 2.21749e6i) q^{79} +(-709.296 + 2182.99i) q^{80} +(164224. + 505430. i) q^{81} +(8.28901e6 - 6.02232e6i) q^{82} +(4.99755e6 - 3.63093e6i) q^{83} +(-1.54381e6 - 4.75136e6i) q^{84} +(804.656 - 2476.48i) q^{85} +(8.94132e6 + 6.49625e6i) q^{86} -3.12183e6 q^{87} +(3.11047e6 - 8.52703e6i) q^{88} -1.26434e7 q^{89} +(-2857.74 - 2076.27i) q^{90} +(-1.15552e6 + 3.55633e6i) q^{91} +(6.85600e6 + 2.11006e7i) q^{92} +(-988556. + 718228. i) q^{93} +(-919128. + 667785. i) q^{94} +(-1161.78 - 3575.59i) q^{95} +(-758005. + 2.33290e6i) q^{96} +(8.22406e6 + 5.97513e6i) q^{97} +3.96325e6 q^{98} +(2.53450e6 + 1.98308e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 22 q^{2} + 189 q^{3} - 692 q^{4} - 777 q^{5} + 594 q^{6} - 83 q^{7} + 3568 q^{8} - 5103 q^{9}+O(q^{10}) $ 28 * q - 22 * q^2 + 189 * q^3 - 692 * q^4 - 777 * q^5 + 594 * q^6 - 83 * q^7 + 3568 * q^8 - 5103 * q^9	\( 28 q - 22 q^{2} + 189 q^{3} - 692 q^{4} - 777 q^{5} + 594 q^{6} - 83 q^{7} + 3568 q^{8} - 5103 q^{9} - 1352 q^{10} - 18851 q^{11} - 60966 q^{12} + 14635 q^{13} + 62912 q^{14} - 22896 q^{15} - 36148 q^{16} - 10338 q^{17} + 9477 q^{18} + 90342 q^{19} - 289719 q^{20} + 28836 q^{21} - 202339 q^{22} + 138508 q^{23} + 187704 q^{24} - 174068 q^{25} + 466130 q^{26} + 137781 q^{27} - 640233 q^{28} - 487290 q^{29} - 372546 q^{30} - 388352 q^{31} + 2726322 q^{32} - 265923 q^{33} - 1543708 q^{34} + 742659 q^{35} - 504468 q^{36} + 670209 q^{37} + 2282072 q^{38} - 395145 q^{39} + 4641741 q^{40} - 2721357 q^{41} + 620676 q^{42} - 199784 q^{43} - 5887437 q^{44} - 103518 q^{45} + 3389447 q^{46} + 2112053 q^{47} + 2292111 q^{48} + 3927748 q^{49} - 3663090 q^{50} + 615681 q^{51} - 4343053 q^{52} - 1743854 q^{53} - 354294 q^{54} - 8387710 q^{55} - 6307818 q^{56} + 1223721 q^{57} + 546605 q^{58} - 218820 q^{59} + 7822413 q^{60} - 743157 q^{61} + 3996183 q^{62} - 60507 q^{63} - 21725666 q^{64} + 4895794 q^{65} - 8684037 q^{66} - 3235686 q^{67} + 961671 q^{68} + 4712499 q^{69} + 31155916 q^{70} + 9848757 q^{71} - 5068008 q^{72} - 6667768 q^{73} - 31115192 q^{74} - 2544939 q^{75} - 6535748 q^{76} + 8320585 q^{77} + 20060730 q^{78} - 10121851 q^{79} + 44592526 q^{80} - 3720087 q^{81} + 24927115 q^{82} + 13288897 q^{83} - 17477019 q^{84} - 28050005 q^{85} + 20937351 q^{86} - 22226400 q^{87} + 39687014 q^{88} - 40241460 q^{89} - 9565938 q^{90} + 8733043 q^{91} + 11607651 q^{92} + 10485504 q^{93} - 7877385 q^{94} + 14371097 q^{95} + 2790126 q^{96} + 30518151 q^{97} - 16954218 q^{98} + 11659626 q^{99}+O(q^{100}) \) 28 * q - 22 * q^2 + 189 * q^3 - 692 * q^4 - 777 * q^5 + 594 * q^6 - 83 * q^7 + 3568 * q^8 - 5103 * q^9 - 1352 * q^10 - 18851 * q^11 - 60966 * q^12 + 14635 * q^13 + 62912 * q^14 - 22896 * q^15 - 36148 * q^16 - 10338 * q^17 + 9477 * q^18 + 90342 * q^19 - 289719 * q^20 + 28836 * q^21 - 202339 * q^22 + 138508 * q^23 + 187704 * q^24 - 174068 * q^25 + 466130 * q^26 + 137781 * q^27 - 640233 * q^28 - 487290 * q^29 - 372546 * q^30 - 388352 * q^31 + 2726322 * q^32 - 265923 * q^33 - 1543708 * q^34 + 742659 * q^35 - 504468 * q^36 + 670209 * q^37 + 2282072 * q^38 - 395145 * q^39 + 4641741 * q^40 - 2721357 * q^41 + 620676 * q^42 - 199784 * q^43 - 5887437 * q^44 - 103518 * q^45 + 3389447 * q^46 + 2112053 * q^47 + 2292111 * q^48 + 3927748 * q^49 - 3663090 * q^50 + 615681 * q^51 - 4343053 * q^52 - 1743854 * q^53 - 354294 * q^54 - 8387710 * q^55 - 6307818 * q^56 + 1223721 * q^57 + 546605 * q^58 - 218820 * q^59 + 7822413 * q^60 - 743157 * q^61 + 3996183 * q^62 - 60507 * q^63 - 21725666 * q^64 + 4895794 * q^65 - 8684037 * q^66 - 3235686 * q^67 + 961671 * q^68 + 4712499 * q^69 + 31155916 * q^70 + 9848757 * q^71 - 5068008 * q^72 - 6667768 * q^73 - 31115192 * q^74 - 2544939 * q^75 - 6535748 * q^76 + 8320585 * q^77 + 20060730 * q^78 - 10121851 * q^79 + 44592526 * q^80 - 3720087 * q^81 + 24927115 * q^82 + 13288897 * q^83 - 17477019 * q^84 - 28050005 * q^85 + 20937351 * q^86 - 22226400 * q^87 + 39687014 * q^88 - 40241460 * q^89 - 9565938 * q^90 + 8733043 * q^91 + 11607651 * q^92 + 10485504 * q^93 - 7877385 * q^94 + 14371097 * q^95 + 2790126 * q^96 + 30518151 * q^97 - 16954218 * q^98 + 11659626 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	15.4308	+	11.2111i	1.36390	+	0.990935i	0.998186	+	0.0602094i	$0.0191768\pi$
$2$	15.4308	+	11.2111i	1.36390	+	0.990935i	0.365719	+	0.930725i	$0.380823\pi$
$3$	−8.34346	+	25.6785i	−0.178411	+	0.549093i
$3$	−8.34346	+	25.6785i	−0.178411	+	0.549093i
$4$	72.8662	+	224.259i	0.569267	+	1.75202i
$5$	0.205524	−	0.149322i	0.000735306	−	0.000534231i	−0.587418	−	0.809284i	$-0.699855\pi$
$5$	0.205524	−	0.149322i	0.000735306	−	0.000534231i	0.588153	+	0.808750i	$0.299855\pi$
$6$	−416.632	+	302.701i	−0.787451	+	0.572116i
$7$	242.486	+	746.295i	0.267204	+	0.822370i	0.991177	+	0.132542i	$0.0423139\pi$
$7$	242.486	+	746.295i	0.267204	+	0.822370i	−0.723973	+	0.689828i	$0.757686\pi$
$8$	−635.379	+	1955.49i	−0.438750	+	1.35034i
$9$	−589.773	−	428.495i	−0.269672	−	0.195928i
$10$	4.84548			0.00153228
$11$	−4411.63	−	157.205i	−0.999366	−	0.0356117i
$11$	−4411.63	−	157.205i	−0.999366	−	0.0356117i
$12$	−6366.60			−1.06359
$13$	3855.23	+	2800.99i	0.486685	+	0.353598i	0.803908	−	0.594753i	$-0.202750\pi$
$13$	3855.23	+	2800.99i	0.486685	+	0.353598i	−0.317223	+	0.948351i	$0.602750\pi$
$14$	−4625.06	+	14234.5i	−0.450474	+	1.38642i
$15$	2.11959	+	6.52342i	0.000162156	+	0.000499064i
$16$	−7309.67	+	5310.78i	−0.446147	+	0.324145i
$17$	8292.40	−	6024.78i	0.409363	−	0.297420i	−0.363981	−	0.931407i	$-0.618583\pi$
$17$	8292.40	−	6024.78i	0.409363	−	0.297420i	0.773344	+	0.633987i	$0.218583\pi$
$18$	−4296.76	−	13224.1i	−0.173655	−	0.534455i
$19$	4573.18	−	14074.8i	0.152961	−	0.470765i	−0.844988	−	0.534786i	$-0.820392\pi$
$19$	4573.18	−	14074.8i	0.152961	−	0.470765i	0.997949	+	0.0640205i	$0.0203923\pi$
$20$	48.4626	+	35.2102i	0.00135457	+	0.000984154i
$21$	−21186.9			−0.499229
$22$	−66312.6	−	51885.2i	−1.32775	−	1.03888i
$23$	94090.2			1.61249			0.806245	−	0.591581i	$-0.201496\pi$
$23$	94090.2			1.61249			0.806245	+	0.591581i	$0.201496\pi$
$24$	−44913.0	−	32631.2i	−0.663181	−	0.481829i
$25$	−24141.9	+	74301.2i	−0.309017	+	0.951056i
$26$	28087.0	+	86443.0i	0.313400	+	0.964547i
$27$	15923.9	−	11569.4i	0.155695	−	0.113119i
$28$	−149694.	+	108759.i	−1.28870	+	0.936296i
$29$	35729.6	+	109964.i	0.272041	+	0.837257i	0.989987	+	0.141158i	$0.0450826\pi$
$29$	35729.6	+	109964.i	0.272041	+	0.837257i	−0.717946	+	0.696099i	$0.754917\pi$
$30$	−40.4281	+	124.425i	−0.000273375	+	0.000841361i
$31$	36613.2	+	26601.0i	0.220735	+	0.160374i	0.692658	−	0.721267i	$-0.256440\pi$
$31$	36613.2	+	26601.0i	0.220735	+	0.160374i	−0.471922	+	0.881640i	$0.656440\pi$
$32$	90850.3			0.490119
$33$	40845.0	−	111972.i	0.197852	−	0.542391i
$34$	195503.			0.853056
$35$	161.275	+	117.173i	0.000635812	+	0.000461945i
$36$	53119.5	−	163485.i	0.189756	−	0.584008i
$37$	−68461.0	−	210701.i	−0.222196	−	0.683850i	−0.998564	−	0.0535700i	$-0.982940\pi$
$37$	−68461.0	−	210701.i	−0.222196	−	0.683850i	0.776368	−	0.630280i	$-0.217060\pi$
$38$	228362.	−	165915.i	0.675122	−	0.490505i
$39$	−104091.	+	75626.6i	−0.280988	+	0.204150i
$40$	161.413	+	496.778i	0.000398775	+	0.00122730i
$41$	165995.	−	510881.i	0.376143	−	1.15765i	−0.566562	−	0.824019i	$-0.691727\pi$
$41$	165995.	−	510881.i	0.376143	−	1.15765i	0.942705	−	0.333629i	$-0.108273\pi$
$42$	−326931.	−	237530.i	−0.680901	−	0.494704i
$43$	579446.			1.11141			0.555704	−	0.831380i	$-0.312449\pi$
$43$	579446.			1.11141			0.555704	+	0.831380i	$0.312449\pi$
$44$	−286204.	−	1.00080e6i	−0.506514	−	1.77119i
$45$	−185.197			−0.000302963
$46$	1.45189e6	+	1.05486e6i	2.19928	+	1.59787i
$47$	−18406.4	+	56649.1i	−0.0258599	+	0.0795886i	−0.963154	−	0.268952i	$-0.913323\pi$
$47$	−18406.4	+	56649.1i	−0.0258599	+	0.0795886i	0.937294	+	0.348541i	$0.113323\pi$
$48$	−75385.2	−	232012.i	−0.0983879	−	0.302807i
$49$	168104.	−	122135.i	0.204123	−	0.148304i
$50$	−1.20553e6	+	875870.i	−1.36390	+	0.990934i
$51$	85520.2	+	263204.i	0.0902762	+	0.277841i
$52$	−347231.	+	1.06867e6i	−0.342458	+	1.05398i
$53$	−1.37433e6	−	998512.i	−1.26802	−	0.921271i	−0.268899	−	0.963168i	$-0.586660\pi$
$53$	−1.37433e6	−	998512.i	−1.26802	−	0.921271i	−0.999122	+	0.0418969i	$0.986660\pi$
$54$	375425.			0.324448
$55$	−930.171	+	626.444i	−0.000753864	+	0.000507707i
$56$	−1.61344e6			−1.22771
$57$	323264.	+	234865.i	0.231204	+	0.167979i
$58$	−681490.	+	2.09741e6i	−0.458629	+	1.41151i
$59$	−293330.	−	902777.i	−0.185941	−	0.572267i	0.814023	−	0.580833i	$-0.197273\pi$
$59$	−293330.	−	902777.i	−0.185941	−	0.572267i	−0.999963	+	0.00856657i	$0.997273\pi$
$60$	−1308.49	+	950.674i	−0.000782062	+	0.000568202i
$61$	−2.12593e6	+	1.54458e6i	−1.19921	+	0.871275i	−0.994207	−	0.107487i	$-0.965720\pi$
$61$	−2.12593e6	+	1.54458e6i	−1.19921	+	0.871275i	−0.205001	+	0.978762i	$0.565720\pi$
$62$	266743.	+	820952.i	0.142142	+	0.437468i
$63$	176772.	−	544049.i	0.0890680	−	0.274123i
$64$	2.33753e6	+	1.69832e6i	1.11462	+	0.809820i
$65$	1210.59			0.000546765
$66$	1.88561e6	−	1.26991e6i	0.807325	−	0.543711i
$67$	−3.39507e6			−1.37907			−0.689536	−	0.724252i	$-0.742185\pi$
$67$	−3.39507e6			−1.37907			−0.689536	+	0.724252i	$0.742185\pi$
$68$	1.95535e6	+	1.42064e6i	0.754124	+	0.547903i
$69$	−785038.	+	2.41610e6i	−0.287686	+	0.885407i
$70$	1174.96	+	3616.16i	0.000409430	+	0.00126010i
$71$	−48918.8	+	35541.6i	−0.0162208	+	0.0117851i	−0.595866	−	0.803084i	$-0.703191\pi$
$71$	−48918.8	+	35541.6i	−0.0162208	+	0.0117851i	0.579645	+	0.814869i	$0.303191\pi$
$72$	1.21265e6	−	881042.i	0.382888	−	0.278184i
$73$	−568125.	−	1.74851e6i	−0.170928	−	0.526063i	0.828496	−	0.559995i	$-0.189197\pi$
$73$	−568125.	−	1.74851e6i	−0.170928	−	0.526063i	−0.999424	+	0.0339322i	$0.989197\pi$
$74$	1.30579e6	−	4.01882e6i	0.374596	−	1.15289i
$75$	−1.70652e6	−	1.23986e6i	−0.467086	−	0.339358i
$76$	3.48963e6			0.911868
$77$	−952436.	−	3.33049e6i	−0.237749	−	0.831364i
$78$	−2.45407e6			−0.585540
$79$	−3.05212e6	−	2.21749e6i	−0.696477	−	0.506020i	0.182306	−	0.983242i	$-0.441644\pi$
$79$	−3.05212e6	−	2.21749e6i	−0.696477	−	0.506020i	−0.878783	+	0.477222i	$0.841644\pi$
$80$	−709.296	+	2182.99i	−0.000154886	+	0.000476691i
$81$	164224.	+	505430.i	0.0343352	+	0.105673i
$82$	8.28901e6	−	6.02232e6i	1.66018	−	1.20619i
$83$	4.99755e6	−	3.63093e6i	0.959365	−	0.697019i	0.00636158	−	0.999980i	$-0.497975\pi$
$83$	4.99755e6	−	3.63093e6i	0.959365	−	0.697019i	0.953003	+	0.302961i	$0.0979750\pi$
$84$	−1.54381e6	−	4.75136e6i	−0.284195	−	0.874662i
$85$	804.656	−	2476.48i	0.000142116	−	0.000437389i
$86$	8.94132e6	+	6.49625e6i	1.51585	+	1.10133i
$87$	−3.12183e6			−0.508267
$88$	3.11047e6	−	8.52703e6i	0.486560	−	1.33385i
$89$	−1.26434e7			−1.90107			−0.950537	−	0.310610i	$-0.899467\pi$
$89$	−1.26434e7			−1.90107			−0.950537	+	0.310610i	$0.899467\pi$
$90$	−2857.74	−	2076.27i	−0.000413212	−	0.000300216i
$91$	−1.15552e6	+	3.55633e6i	−0.160744	+	0.494718i
$92$	6.85600e6	+	2.11006e7i	0.917938	+	2.82512i
$93$	−988556.	+	718228.i	−0.127442	+	0.0925917i
$94$	−919128.	+	667785.i	−0.114137	+	0.0829257i
$95$	−1161.78	−	3575.59i	−0.000139024	−	0.000427873i
$96$	−758005.	+	2.33290e6i	−0.0874426	+	0.269121i
$97$	8.22406e6	+	5.97513e6i	0.914924	+	0.664731i	0.942255	−	0.334895i	$-0.108701\pi$
$97$	8.22406e6	+	5.97513e6i	0.914924	+	0.664731i	−0.0273313	+	0.999626i	$0.508701\pi$
$98$	3.96325e6			0.425364
$99$	2.53450e6	+	1.98308e6i	0.262524	+	0.205408i
$100$	−1.84219e7			−1.84219
$101$	1.26211e7	+	9.16977e6i	1.21891	+	0.885592i	0.996009	−	0.0892487i	$-0.0284466\pi$
$101$	1.26211e7	+	9.16977e6i	1.21891	+	0.885592i	0.222903	+	0.974841i	$0.428447\pi$
$102$	−1.63117e6	+	5.02023e6i	−0.152195	+	0.468407i
$103$	2.97093e6	+	9.14360e6i	0.267894	+	0.824493i	0.991013	+	0.133769i	$0.0427080\pi$
$103$	2.97093e6	+	9.14360e6i	0.267894	+	0.824493i	−0.723119	+	0.690724i	$0.757292\pi$
$104$	−7.92684e6	+	5.75919e6i	−0.691009	+	0.502047i
$105$	−4354.43	+	3163.68i	−0.000367086	+	0.000266704i
$106$	−1.00126e7	−	3.08157e7i	−0.816540	−	2.51305i
$107$	7.53829e6	−	2.32005e7i	0.594881	−	1.83085i	0.0395609	−	0.999217i	$-0.487404\pi$
$107$	7.53829e6	−	2.32005e7i	0.594881	−	1.83085i	0.555320	−	0.831637i	$-0.312596\pi$
$108$	3.75485e6	+	2.72806e6i	0.286820	+	0.208387i
$109$	−2.53071e7			−1.87176			−0.935878	−	0.352324i	$-0.885392\pi$
$109$	−2.53071e7			−1.87176			−0.935878	+	0.352324i	$0.885392\pi$
$110$	−21376.5	−	761.735i	−0.00153130	−	5.45669e-5i
$111$	5.98170e6			0.415140
$112$	−5.73590e6	−	4.16738e6i	−0.385779	−	0.280285i
$113$	6.89634e6	−	2.12248e7i	0.449618	−	1.38378i	−0.427720	−	0.903911i	$-0.640683\pi$
$113$	6.89634e6	−	2.12248e7i	0.449618	−	1.38378i	0.877339	−	0.479872i	$-0.159317\pi$
$114$	2.35512e6	+	7.24832e6i	0.148883	+	0.458216i
$115$	19337.8	−	14049.8i	0.00118567	−	0.000861443i
$116$	−2.20570e7	+	1.60254e7i	−1.31203	+	0.953246i
$117$	−1.07350e6	−	3.30389e6i	−0.0619657	−	0.190711i
$118$	5.59484e6	−	1.72192e7i	0.313473	−	0.964772i
$119$	6.50705e6	+	4.72765e6i	0.353973	+	0.257176i
$120$	−14103.3			−0.000745049
$121$	1.94377e7	+	1.38706e6i	0.997464	+	0.0711782i
$122$	−5.01213e7			−2.49898
$123$	1.17337e7	+	8.52503e6i	0.568548	+	0.413074i
$124$	−3.29766e6	+	1.01492e7i	−0.155321	+	0.478029i
$125$	12266.1	+	37751.3i	0.000561724	+	0.00172881i
$126$	8.82715e6	−	6.41330e6i	0.393119	−	0.285617i
$127$	876116.	−	636535.i	0.0379532	−	0.0275746i	−0.568647	−	0.822582i	$-0.692533\pi$
$127$	876116.	−	636535.i	0.0379532	−	0.0275746i	0.606600	+	0.795007i	$0.292533\pi$
$128$	1.34364e7	+	4.13531e7i	0.566304	+	1.74290i
$129$	−4.83458e6	+	1.48793e7i	−0.198287	+	0.610266i
$130$	18680.4	+	13572.1i	0.000745736	+	0.000541809i
$131$	2.23010e7			0.866712			0.433356	−	0.901223i	$-0.357329\pi$
$131$	2.23010e7			0.866712			0.433356	+	0.901223i	$0.357329\pi$
$132$	2.80871e7	+	1.00086e6i	1.06291	+	0.0378761i
$133$	1.16129e7			0.428015
$134$	−5.23887e7	−	3.80626e7i	−1.88092	−	1.36657i
$135$	1545.18	−	4755.58i	5.40519e−5	−	0.000166355i
$136$	6.51261e6	+	2.00438e7i	0.222008	+	0.683271i
$137$	1.02510e7	−	7.44780e6i	0.340600	−	0.247461i	−0.404315	−	0.914620i	$-0.632490\pi$
$137$	1.02510e7	−	7.44780e6i	0.340600	−	0.247461i	0.744915	+	0.667159i	$0.232490\pi$
$138$	−3.92010e7	+	2.84812e7i	−1.26976	+	0.922532i
$139$	1.07786e7	+	3.31731e7i	0.340417	+	1.04769i	0.963992	+	0.265931i	$0.0856795\pi$
$139$	1.07786e7	+	3.31731e7i	0.340417	+	1.04769i	−0.623575	+	0.781763i	$0.714321\pi$
$140$	−14525.7	+	44705.4i	−0.000447391	+	0.00137693i
$141$	−1.30109e6	−	945299.i	−0.0390878	−	0.0283990i
$142$	−1.15332e6			−0.0338018
$143$	−1.65675e7	−	1.29630e7i	−0.473784	−	0.370705i
$144$	6.58669e6			0.183823
$145$	23763.4	+	17265.1i	0.000647323	+	0.000470307i
$146$	1.08362e7	−	3.33502e7i	0.288164	−	0.886878i
$147$	1.73367e6	+	5.33569e6i	0.0450149	+	0.138542i
$148$	4.22632e7	−	3.07060e7i	1.07163	−	0.778587i
$149$	−9.94067e6	+	7.22232e6i	−0.246186	+	0.178865i	−0.704035	−	0.710165i	$-0.748620\pi$
$149$	−9.94067e6	+	7.22232e6i	−0.246186	+	0.178865i	0.457849	+	0.889030i	$0.348620\pi$
$150$	−1.24327e7	−	3.82641e7i	−0.300779	−	0.925703i
$151$	2.56212e6	−	7.88538e6i	0.0605591	−	0.186382i	−0.916200	−	0.400721i	$-0.868760\pi$
$151$	2.56212e6	−	7.88538e6i	0.0605591	−	0.186382i	0.976759	+	0.214339i	$0.0687597\pi$
$152$	2.46175e7	+	1.78856e7i	0.568579	+	0.413097i
$153$	−7.47223e6			−0.168667
$154$	2.26418e7	−	6.20701e7i	0.499561	−	1.36949i
$155$	11497.0			0.000247984
$156$	−2.45447e7	−	1.78328e7i	−0.517632	−	0.376082i
$157$	−2.65136e7	+	8.16003e7i	−0.546788	+	1.68284i	0.169911	+	0.985459i	$0.445652\pi$
$157$	−2.65136e7	+	8.16003e7i	−0.546788	+	1.68284i	−0.716700	+	0.697382i	$0.754348\pi$
$158$	−2.22360e7	−	6.84355e7i	−0.448495	−	1.38033i
$159$	3.71070e7	−	2.69598e7i	0.732092	−	0.531896i
$160$	18671.9	−	13566.0i	0.000360387	−	0.000261837i
$161$	2.28155e7	+	7.02190e7i	0.430864	+	1.32606i
$162$	−3.13234e6	+	9.64035e6i	−0.0578850	+	0.178152i
$163$	−4.34275e7	−	3.15519e7i	−0.785431	−	0.570649i	0.121173	−	0.992631i	$-0.461334\pi$
$163$	−4.34275e7	−	3.15519e7i	−0.785431	−	0.570649i	−0.906604	+	0.421983i	$0.861334\pi$
$164$	1.26665e8			2.24235
$165$	−8325.32	−	29112.1i	−0.000144280	−	0.000504522i
$166$	1.17823e8			1.99918
$167$	439941.	+	319636.i	0.00730949	+	0.00531066i	0.591434	−	0.806353i	$-0.298562\pi$
$167$	439941.	+	319636.i	0.00730949	+	0.00531066i	−0.584125	+	0.811664i	$0.698562\pi$
$168$	1.34617e7	−	4.14309e7i	0.219037	−	0.674127i
$169$	−1.23731e7	−	3.80805e7i	−0.197186	−	0.606875i
$170$	40180.7	−	29193.0i	0.000627257	−	0.000455729i
$171$	−8.72812e6	+	6.34135e6i	−0.133486	+	0.0969830i
$172$	4.22220e7	+	1.29946e8i	0.632688	+	1.94721i
$173$	−7.91856e6	+	2.43708e7i	−0.116275	+	0.357856i	−0.992211	−	0.124571i	$-0.960245\pi$
$173$	−7.91856e6	+	2.43708e7i	−0.116275	+	0.357856i	0.875936	+	0.482427i	$0.160245\pi$
$174$	−4.81724e7	−	3.49993e7i	−0.693228	−	0.503660i
$175$	−6.13047e7			−0.864690
$176$	3.30824e7	−	2.22801e7i	0.457407	−	0.308051i
$177$	2.56294e7			0.347401
$178$	−1.95098e8	−	1.41747e8i	−2.59288	−	1.88384i
$179$	2.71690e7	−	8.36175e7i	0.354069	−	1.08971i	−0.602478	−	0.798135i	$-0.705820\pi$
$179$	2.71690e7	−	8.36175e7i	0.354069	−	1.08971i	0.956547	−	0.291577i	$-0.0941800\pi$
$180$	−13494.6	−	41532.0i	−0.000172467	−	0.000530798i
$181$	−9.43783e6	+	6.85698e6i	−0.118303	+	0.0859524i	−0.645364	−	0.763875i	$-0.723294\pi$
$181$	−9.43783e6	+	6.85698e6i	−0.118303	+	0.0859524i	0.527060	+	0.849828i	$0.323294\pi$
$182$	−5.77013e7	+	4.19224e7i	−0.709472	+	0.515462i
$183$	−2.19249e7	−	6.74778e7i	−0.264459	−	0.813921i
$184$	−5.97829e7	+	1.83993e8i	−0.707481	+	2.17740i
$185$	−45532.7	−	33081.5i	−0.000528716	−	0.000384135i
$186$	−2.33064e7			−0.265570
$187$	−3.75301e7	+	2.52755e7i	−0.419695	+	0.282653i
$188$	−1.40453e7			−0.154162
$189$	1.24955e7	+	9.07850e6i	0.134628	+	0.0978132i
$190$	22159.2	−	68199.1i	0.000234378	−	0.000721342i
$191$	1.38504e7	+	4.26272e7i	0.143829	+	0.442660i	0.996859	−	0.0792027i	$-0.0252374\pi$
$191$	1.38504e7	+	4.26272e7i	0.143829	+	0.442660i	−0.853030	+	0.521862i	$0.825237\pi$
$192$	−6.31134e7	+	4.58545e7i	−0.643527	+	0.467550i
$193$	−6.45747e7	+	4.69162e7i	−0.646564	+	0.469756i	−0.862099	−	0.506740i	$-0.830850\pi$
$193$	−6.45747e7	+	4.69162e7i	−0.646564	+	0.469756i	0.215535	+	0.976496i	$0.430850\pi$
$194$	5.99159e7	+	1.84402e8i	0.589164	+	1.81326i
$195$	−10100.5	+	31086.2i	−9.75490e−5	+	0.000300225i
$196$	3.96389e7	+	2.87994e7i	0.376033	+	0.273204i
$197$	1.49991e7			0.139776			0.0698881	−	0.997555i	$-0.477736\pi$
$197$	1.49991e7			0.139776			0.0698881	+	0.997555i	$0.477736\pi$
$198$	1.68768e7	+	5.90152e7i	0.154512	+	0.540301i
$199$	1.17441e8			1.05641			0.528207	−	0.849115i	$-0.322864\pi$
$199$	1.17441e8			1.05641			0.528207	+	0.849115i	$0.322864\pi$
$200$	−1.29956e8	−	9.44188e7i	−1.14866	−	0.834552i
$201$	2.83266e7	−	8.71804e7i	0.246042	−	0.757238i
$202$	9.19504e7	+	2.82994e8i	0.784917	+	2.41573i
$203$	−7.34019e7	+	5.33296e7i	−0.615845	+	0.447437i
$204$	−5.27944e7	+	3.83574e7i	−0.435394	+	0.316332i
$205$	−42169.8	−	129785.i	−0.000341871	−	0.00105217i
$206$	−5.66662e7	+	1.74401e8i	−0.451637	+	1.38999i
$207$	−5.54919e7	−	4.03172e7i	−0.434844	−	0.315933i
$208$	−4.30559e7			−0.331750
$209$	−2.23878e7	+	6.13738e7i	−0.169629	+	0.465019i
$210$	−102661.			−0.000764957
$211$	−9.18736e7	−	6.67501e7i	−0.673290	−	0.489174i	0.197835	−	0.980235i	$-0.436609\pi$
$211$	−9.18736e7	−	6.67501e7i	−0.673290	−	0.489174i	−0.871125	+	0.491062i	$0.836609\pi$
$212$	1.23783e8	−	3.80965e8i	0.892247	−	2.74605i
$213$	−504504.	−	1.55270e6i	−0.00357714	−	0.0110093i
$214$	3.76426e8	−	2.73490e8i	2.62562	−	1.90762i
$215$	119090.	−	86524.1i	0.000817224	−	0.000593748i
$216$	1.25062e7	+	3.84900e7i	0.0844376	+	0.259872i
$217$	−1.09740e7	+	3.37746e7i	−0.0729050	+	0.224378i
$218$	−3.90509e8	−	2.83721e8i	−2.55290	−	1.85479i
$219$	4.96392e7			0.319353
$220$	−208264.	−	162953.i	−0.00131867	−	0.00103177i
$221$	4.88444e7			0.304398
$222$	9.23025e7	+	6.70617e7i	0.566211	+	0.411376i
$223$	5.62757e7	−	1.73199e8i	0.339824	−	1.04587i	−0.624473	−	0.781046i	$-0.714686\pi$
$223$	5.62757e7	−	1.73199e8i	0.339824	−	1.04587i	0.964297	−	0.264824i	$-0.0853138\pi$
$224$	2.20299e7	+	6.78011e7i	0.130962	+	0.403059i
$225$	4.60760e7	−	3.34762e7i	0.269672	−	0.195928i
$226$	3.44370e8	−	2.50199e8i	1.98448	−	1.44181i
$227$	−6.56206e7	−	2.01959e8i	−0.372349	−	1.14597i	−0.945250	−	0.326347i	$-0.894182\pi$
$227$	−6.56206e7	−	2.01959e8i	−0.372349	−	1.14597i	0.572901	−	0.819624i	$-0.305818\pi$
$228$	−2.91156e7	+	8.96086e7i	−0.162687	+	0.500700i
$229$	2.40869e8	+	1.75001e8i	1.32543	+	0.962979i	0.999847	+	0.0174647i	$0.00555947\pi$
$229$	2.40869e8	+	1.75001e8i	1.32543	+	0.962979i	0.325580	+	0.945515i	$0.394441\pi$
$230$	455912.			0.00247078
$231$	9.34688e7	+	3.33069e6i	0.498913	+	0.0177784i
$232$	−2.37736e8			−1.24994
$233$	−1.95090e6	−	1.41741e6i	−0.0101039	−	0.00734090i	0.582722	−	0.812672i	$-0.301988\pi$
$233$	−1.95090e6	−	1.41741e6i	−0.0101039	−	0.00734090i	−0.592826	+	0.805331i	$0.701988\pi$
$234$	2.04755e7	−	6.30170e7i	0.104467	−	0.321516i
$235$	4676.00	+	14391.3i	2.35037e−5	+	7.23371e-5i
$236$	1.81082e8	−	1.31564e8i	0.896775	−	0.651545i
$237$	8.24072e7	−	5.98723e7i	0.402111	−	0.292151i
$238$	4.74068e7	+	1.45903e8i	0.227940	+	0.701528i
$239$	−2.02731e6	+	6.23941e6i	−0.00960566	+	0.0295632i	−0.955744	−	0.294198i	$-0.904947\pi$
$239$	−2.02731e6	+	6.23941e6i	−0.00960566	+	0.0295632i	0.946139	+	0.323761i	$0.104947\pi$
$240$	−50138.0	−	36427.4i	−0.000234114	−	0.000170094i
$241$	−3.14700e8			−1.44823			−0.724114	−	0.689681i	$-0.757751\pi$
$241$	−3.14700e8			−1.44823			−0.724114	+	0.689681i	$0.757751\pi$
$242$	2.84390e8	+	2.39323e8i	1.28991	+	1.08550i
$243$	−1.43489e7			−0.0641500
$244$	−5.01294e8	−	3.64211e8i	−2.20916	−	1.60505i
$245$	16312.0	−	50203.3i	7.08642e−5	−	0.000218098i
$246$	8.54852e7	+	2.63096e8i	0.366116	+	1.12679i
$247$	5.70539e7	−	4.14521e7i	0.240905	−	0.175028i
$248$	−7.52814e7	+	5.46951e7i	−0.313406	+	0.227703i
$249$	5.15401e7	+	1.58624e8i	0.211567	+	0.651136i
$250$	−233959.	+	720051.i	−0.000946998	+	0.00291456i
$251$	1.24434e8	+	9.04067e7i	0.496686	+	0.360863i	0.807750	−	0.589526i	$-0.200685\pi$
$251$	1.24434e8	+	9.04067e7i	0.496686	+	0.360863i	−0.311064	+	0.950389i	$0.600685\pi$
$252$	1.34889e8			0.530974
$253$	−4.15091e8	−	1.47915e7i	−1.61147	−	0.0574235i
$254$	2.06555e7			0.0790892
$255$	56878.7	+	41324.8i	0.000214812	+	0.000156070i
$256$	−1.41995e8	+	4.37015e8i	−0.528972	+	1.62801i
$257$	1.09049e8	+	3.35619e8i	0.400734	+	1.23333i	0.924405	+	0.381412i	$0.124562\pi$
$257$	1.09049e8	+	3.35619e8i	0.400734	+	1.23333i	−0.523671	+	0.851921i	$0.675438\pi$
$258$	−2.41416e8	+	1.75399e8i	−0.875178	+	0.635854i
$259$	1.40644e8	−	1.02184e8i	0.503006	−	0.365455i
$260$	88211.2	+	271486.i	0.000311256	+	0.000957946i
$261$	2.60469e7	−	8.01640e7i	0.0906805	−	0.279086i
$262$	3.44123e8	+	2.50020e8i	1.18211	+	0.858855i
$263$	−2.96243e8			−1.00416			−0.502079	−	0.864822i	$-0.667431\pi$
$263$	−2.96243e8			−1.00416			−0.502079	+	0.864822i	$0.667431\pi$
$264$	1.93009e8	+	1.51017e8i	0.645602	+	0.505141i
$265$	−431559.			−0.00142456
$266$	1.79196e8	+	1.30194e8i	0.583772	+	0.424135i
$267$	1.05490e8	−	3.24664e8i	0.339173	−	1.04387i
$268$	−2.47386e8	−	7.61375e8i	−0.785060	−	2.41617i
$269$	−5.49384e7	+	3.99151e7i	−0.172085	+	0.125027i	−0.670494	−	0.741915i	$-0.733918\pi$
$269$	−5.49384e7	+	3.99151e7i	−0.172085	+	0.125027i	0.498409	+	0.866942i	$0.333918\pi$
$270$	77158.9	−	56059.2i	0.000238568	−	0.000173330i
$271$	−2.84994e7	−	8.77120e7i	−0.0869847	−	0.267711i	0.898097	−	0.439797i	$-0.144949\pi$
$271$	−2.84994e7	−	8.77120e7i	−0.0869847	−	0.267711i	−0.985082	+	0.172085i	$0.944949\pi$
$272$	−2.86184e7	+	8.80783e7i	−0.0862291	+	0.265386i
$273$	−8.16804e7	−	5.93443e7i	−0.242968	−	0.176526i
$274$	2.41680e8			0.709764
$275$	1.18186e8	−	3.23994e8i	0.342689	−	0.939448i
$276$	−5.99035e8			−1.71502
$277$	−1.59052e8	−	1.15558e8i	−0.449636	−	0.326680i	0.339816	−	0.940492i	$-0.389635\pi$
$277$	−1.59052e8	−	1.15558e8i	−0.449636	−	0.326680i	−0.789452	+	0.613812i	$0.789635\pi$
$278$	−2.05586e8	+	6.32729e8i	−0.573901	+	1.76629i
$279$	−1.01951e7	−	3.13772e7i	−0.0281045	−	0.0864966i
$280$	−331602.	+	240923.i	−0.000902743	+	0.000655881i
$281$	−3.75669e8	+	2.72939e8i	−1.01003	+	0.733827i	−0.964215	−	0.265123i	$-0.914587\pi$
$281$	−3.75669e8	+	2.72939e8i	−1.01003	+	0.733827i	−0.0458119	+	0.998950i	$0.514587\pi$
$282$	−9.47904e6	−	2.91735e7i	−0.0251705	−	0.0774669i
$283$	2.98612e7	−	9.19032e7i	0.0783167	−	0.241034i	−0.904231	−	0.427043i	$-0.859555\pi$
$283$	2.98612e7	−	9.19032e7i	0.0783167	−	0.241034i	0.982548	+	0.186009i	$0.0595553\pi$
$284$	−1.15351e7	−	8.38071e6i	−0.0298817	−	0.0217103i
$285$	101509.			0.000259745
$286$	−1.10320e8	−	3.85770e8i	−0.278852	−	0.975096i
$287$	4.21519e8			1.05252
$288$	−5.35811e7	−	3.89289e7i	−0.132171	−	0.0960282i
$289$	−9.43357e7	+	2.90336e8i	−0.229897	+	0.707551i
$290$	173127.	+	532830.i	0.000416842	+	0.00128291i
$291$	−2.22050e8	+	1.61328e8i	−0.528232	+	0.383783i
$292$	3.50722e8	−	2.54814e8i	0.824371	−	0.598941i
$293$	−6.57616e7	−	2.02393e8i	−0.152734	−	0.470067i	0.845190	−	0.534466i	$-0.179487\pi$
$293$	−6.57616e7	−	2.02393e8i	−0.152734	−	0.470067i	−0.997924	+	0.0643987i	$0.979487\pi$
$294$	−3.30672e7	+	1.01771e8i	−0.0758896	+	0.233564i
$295$	−195091.	−	141742.i	−0.000442446	−	0.000321456i
$296$	4.55524e8			1.02092
$297$	−7.20690e7	+	4.85365e7i	−0.159625	+	0.107503i
$298$	−2.34363e8			−0.513018
$299$	3.62739e8	+	2.63545e8i	0.784775	+	0.570173i
$300$	1.53702e8	−	4.73046e8i	0.328666	−	1.01153i
$301$	1.40507e8	+	4.32437e8i	0.296973	+	0.913988i
$302$	1.27940e8	−	9.29537e7i	0.267289	−	0.194197i
$303$	−3.40770e8	+	2.47584e8i	−0.703740	+	0.511297i
$304$	4.13198e7	+	1.27169e8i	0.0843530	+	0.259612i
$305$	−206290.	+	634896.i	−0.000416322	+	0.00128131i
$306$	−1.15303e8	−	8.37722e7i	−0.230046	−	0.167138i
$307$	−2.11257e8			−0.416704			−0.208352	−	0.978054i	$-0.566810\pi$
$307$	−2.11257e8			−0.416704			−0.208352	+	0.978054i	$0.566810\pi$
$308$	6.77493e8	−	4.56273e8i	1.32123	−	0.889810i
$309$	−2.59582e8			−0.500518
$310$	177408.	+	128895.i	0.000338227	+	0.000245736i
$311$	1.64015e8	−	5.04788e8i	0.309189	−	0.951585i	−0.668892	−	0.743359i	$-0.733231\pi$
$311$	1.64015e8	−	5.04788e8i	0.309189	−	0.951585i	0.978081	−	0.208225i	$-0.0667687\pi$
$312$	−8.17502e7	−	2.51601e8i	−0.152387	−	0.468999i
$313$	−4.05890e7	+	2.94896e7i	−0.0748174	+	0.0543580i	−0.624565	−	0.780973i	$-0.714724\pi$
$313$	−4.05890e7	+	2.94896e7i	−0.0748174	+	0.0543580i	0.549748	+	0.835331i	$0.314724\pi$
$314$	−1.32396e9	+	9.61913e8i	−2.41335	+	1.75340i
$315$	−44907.5	−	138211.i	−8.09529e−5	−	0.000249147i
$316$	2.74897e8	−	8.46046e8i	0.490078	−	1.50830i
$317$	−3.48799e8	−	2.53418e8i	−0.614990	−	0.446817i	0.236178	−	0.971710i	$-0.424105\pi$
$317$	−3.48799e8	−	2.53418e8i	−0.614990	−	0.446817i	−0.851168	+	0.524893i	$0.824105\pi$
$318$	8.74842e8			1.52558
$319$	−1.40339e8	−	4.90739e8i	−0.242053	−	0.846414i
$320$	734016.			0.00125222
$321$	5.32859e8	+	3.87145e8i	0.899175	+	0.653289i
$322$	−4.35173e8	+	1.33933e9i	−0.726385	+	2.23558i
$323$	−4.68749e7	−	1.44266e8i	−0.0773984	−	0.238208i
$324$	−1.01381e8	+	7.36576e7i	−0.165596	+	0.120312i
$325$	−3.01189e8	+	2.18827e8i	−0.486685	+	0.353597i
$326$	−3.16388e8	−	9.73743e8i	−0.505777	−	1.55662i
$327$	2.11149e8	−	6.49849e8i	0.333942	−	1.02777i
$328$	8.93555e8	+	6.49206e8i	1.39818	+	1.01584i
$329$	−4.67402e7			−0.0723611
$330$	197914.	−	542560.i	0.000303164	−	0.000831092i
$331$	−3.74479e7			−0.0567583			−0.0283791	−	0.999597i	$-0.509035\pi$
$331$	−3.74479e7			−0.0567583			−0.0283791	+	0.999597i	$0.509035\pi$
$332$	1.17842e9	+	8.56174e8i	1.76733	+	1.28404i
$333$	−4.99081e7	+	1.53601e8i	−0.0740655	+	0.227950i
$334$	3.20517e6	+	9.86450e6i	0.00470694	+	0.0144865i
$335$	−697769.	+	506959.i	−0.00101404	+	0.000736743i
$336$	1.54869e8	−	1.12519e8i	0.222730	−	0.161822i
$337$	3.46345e8	+	1.06594e9i	0.492952	+	1.51715i	0.820124	+	0.572186i	$0.193904\pi$
$337$	3.46345e8	+	1.06594e9i	0.492952	+	1.51715i	−0.327172	+	0.944965i	$0.606096\pi$
$338$	2.35999e8	−	7.26330e8i	0.332431	−	1.02312i
$339$	4.87481e8	+	3.54176e8i	0.679608	+	0.493764i
$340$	614005.			0.000847219
$341$	−1.57342e8	−	1.23110e8i	−0.214884	−	0.168133i
$342$	−2.05776e8			−0.278165
$343$	6.54726e8	+	4.75686e8i	0.876053	+	0.636490i
$344$	−3.68167e8	+	1.13310e9i	−0.487630	+	1.50077i
$345$	199433.	+	613790.i	0.000261475	+	0.000804736i
$346$	−3.95415e8	+	2.87285e8i	−0.513200	+	0.372861i
$347$	−3.98861e8	+	2.89790e8i	−0.512470	+	0.372332i	−0.813760	−	0.581201i	$-0.802583\pi$
$347$	−3.98861e8	+	2.89790e8i	−0.512470	+	0.372332i	0.301289	+	0.953533i	$0.402583\pi$
$348$	−2.27476e8	−	7.00099e8i	−0.289340	−	0.890496i
$349$	3.69345e8	−	1.13673e9i	0.465097	−	1.43142i	−0.393765	−	0.919211i	$-0.628827\pi$
$349$	3.69345e8	−	1.13673e9i	0.465097	−	1.43142i	0.858861	−	0.512209i	$-0.171173\pi$
$350$	−9.45981e8	−	6.87296e8i	−1.17935	−	0.856851i
$351$	9.37958e7			0.115773
$352$	−4.00798e8	−	1.42821e7i	−0.489808	−	0.0174540i
$353$	1.31885e9			1.59582			0.797911	−	0.602775i	$-0.205938\pi$
$353$	1.31885e9			1.59582			0.797911	+	0.602775i	$0.205938\pi$
$354$	3.95482e8	+	2.87335e8i	0.473822	+	0.344252i
$355$	−4746.85	+	14609.3i	−5.63127e−6	+	1.73313e-5i
$356$	−9.21277e8	−	2.83540e9i	−1.08222	−	3.33073i
$357$	−1.75690e8	+	1.27647e8i	−0.204366	+	0.148481i
$358$	1.35669e9	−	9.85692e8i	1.56275	−	1.13540i
$359$	−3.57367e8	−	1.09986e9i	−0.407647	−	1.25461i	−0.918665	−	0.395038i	$-0.870731\pi$
$359$	−3.57367e8	−	1.09986e9i	−0.407647	−	1.25461i	0.511018	−	0.859570i	$-0.329269\pi$
$360$	117670.	−	362151.i	0.000132925	−	0.000409101i
$361$	5.45972e8	+	3.96672e8i	0.610794	+	0.443768i
$362$	−2.22508e8			−0.246528
$363$	−1.97796e8	+	4.87560e8i	−0.217042	+	0.535001i
$364$	−8.81739e8			−0.958264
$365$	−377854.	−	274527.i	−0.000406724	−	0.000295502i
$366$	4.18185e8	−	1.28704e9i	0.445846	−	1.37217i
$367$	5.02508e8	+	1.54656e9i	0.530654	+	1.63319i	0.752857	+	0.658185i	$0.228675\pi$
$367$	5.02508e8	+	1.54656e9i	0.530654	+	1.63319i	−0.222203	+	0.975001i	$0.571325\pi$
$368$	−6.87768e8	+	4.99693e8i	−0.719407	+	0.522680i
$369$	−3.16810e8	+	2.30176e8i	−0.328251	+	0.238489i
$370$	−331726.	−	1.02095e6i	−0.000340466	−	0.00104785i
$371$	4.11927e8	−	1.26778e9i	0.418805	−	1.28895i
$372$	−2.33102e8	−	1.69358e8i	−0.234771	−	0.170571i
$373$	−9.00198e8			−0.898168			−0.449084	−	0.893490i	$-0.648250\pi$
$373$	−9.00198e8			−0.898168			−0.449084	+	0.893490i	$0.648250\pi$
$374$	−8.62487e8	−	3.07341e7i	−0.852515	−	0.0303788i
$375$	−1.07174e6			−0.00104949
$376$	−9.90820e7	−	7.19873e7i	−0.0961252	−	0.0698390i
$377$	−1.70263e8	+	5.24016e8i	−0.163654	+	0.503674i
$378$	9.10351e7	+	2.80177e8i	0.0866937	+	0.266816i
$379$	1.10014e9	−	7.99295e8i	1.03803	−	0.754171i	0.0681283	−	0.997677i	$-0.478297\pi$
$379$	1.10014e9	−	7.99295e8i	1.03803	−	0.754171i	0.969900	+	0.243505i	$0.0782973\pi$
$380$	717204.	−	521079.i	0.000670502	−	0.000487148i
$381$	9.03545e6	+	2.78083e7i	0.00836975	+	0.0257594i
$382$	−2.64176e8	+	8.13052e8i	−0.242478	+	0.746271i
$383$	3.31591e8	+	2.40915e8i	0.301583	+	0.219113i	0.728277	−	0.685283i	$-0.240322\pi$
$383$	3.31591e8	+	2.40915e8i	0.301583	+	0.219113i	−0.426693	+	0.904396i	$0.640322\pi$
$384$	−1.17399e9			−1.05805
$385$	−693065.	−	542278.i	−0.000618958	−	0.000484294i
$386$	−1.52242e9			−1.34735
$387$	−3.41742e8	−	2.48290e8i	−0.299716	−	0.217756i
$388$	−7.40721e8	+	2.27971e9i	−0.643789	+	1.98138i
$389$	5.08719e8	+	1.56568e9i	0.438182	+	1.34858i	0.889791	+	0.456369i	$0.150850\pi$
$389$	5.08719e8	+	1.56568e9i	0.438182	+	1.34858i	−0.451609	+	0.892216i	$0.649150\pi$
$390$	−504371.	+	366447.i	−0.000430551	+	0.000312813i
$391$	7.80234e8	−	5.66873e8i	0.660094	−	0.479587i
$392$	1.32024e8	+	4.06328e8i	0.110701	+	0.340703i
$393$	−1.86068e8	+	5.72657e8i	−0.154631	+	0.475905i
$394$	2.31448e8	+	1.68157e8i	0.190641	+	0.138509i
$395$	−958405.			−0.000782455
$396$	−2.60044e8	+	7.12884e8i	−0.210433	+	0.576880i
$397$	9.12158e8			0.731650			0.365825	−	0.930684i	$-0.380787\pi$
$397$	9.12158e8			0.731650			0.365825	+	0.930684i	$0.380787\pi$
$398$	1.81221e9	+	1.31665e9i	1.44085	+	1.04684i
$399$	−9.68915e7	+	2.98201e8i	−0.0763626	+	0.235020i
$400$	−2.18128e8	−	6.71330e8i	−0.170413	−	0.524476i
$401$	−3.05111e7	+	2.21676e7i	−0.0236294	+	0.0171677i	−0.599537	−	0.800347i	$-0.704649\pi$
$401$	−3.05111e7	+	2.21676e7i	−0.0236294	+	0.0171677i	0.575908	+	0.817515i	$0.304649\pi$
$402$	1.41449e9	−	1.02769e9i	1.08595	−	0.788990i
$403$	6.66430e7	+	2.05106e8i	0.0507209	+	0.156103i
$404$	−1.13675e9	+	3.49856e9i	−0.857692	+	2.63970i
$405$	109224.	+	79355.9i	8.17007e−5	+	5.93590e-5i
$406$	−1.73054e9			−1.28333
$407$	2.68901e8	+	9.40298e8i	0.197702	+	0.691329i
$408$	−5.69032e8			−0.414788
$409$	−6.37661e8	−	4.63288e8i	−0.460849	−	0.334826i	0.333015	−	0.942921i	$-0.391934\pi$
$409$	−6.37661e8	−	4.63288e8i	−0.460849	−	0.334826i	−0.793864	+	0.608095i	$0.791934\pi$
$410$	804327.	−	2.47546e6i	0.000576354	−	0.00177383i
$411$	1.05720e8	+	3.25372e8i	0.0751120	+	0.231171i
$412$	−1.83405e9	+	1.33252e9i	−1.29203	+	0.938713i
$413$	6.02609e8	−	4.37821e8i	0.420931	−	0.305824i
$414$	−4.04283e8	−	1.24426e9i	−0.280017	−	0.861804i
$415$	484939.	−	1.49249e6i	0.000333057	−	0.00102504i
$416$	3.50248e8	+	2.54470e8i	0.238534	+	0.173305i
$417$	−9.41768e8			−0.636016
$418$	−1.03353e9	+	6.96056e8i	−0.692161	+	0.466151i
$419$	−9.23114e8			−0.613065			−0.306532	−	0.951860i	$-0.599169\pi$
$419$	−9.23114e8			−0.613065			−0.306532	+	0.951860i	$0.599169\pi$
$420$	−1.02677e6	−	745995.i	−0.000676242	−	0.000491319i
$421$	3.14331e8	−	9.67410e8i	0.205305	−	0.631864i	−0.794396	−	0.607400i	$-0.792212\pi$
$421$	3.14331e8	−	9.67410e8i	0.205305	−	0.631864i	0.999701	−	0.0244632i	$-0.00778765\pi$
$422$	−6.69340e8	−	2.06002e9i	−0.433564	−	1.33437i
$423$	3.51295e7	−	2.55231e7i	0.0225674	−	0.0163961i
$424$	2.82581e9	−	2.05307e9i	1.80037	−	1.30805i
$425$	2.47454e8	+	7.61585e8i	0.156363	+	0.481235i
$426$	9.62267e6	−	2.96155e7i	0.00603062	−	0.0185603i
$427$	−1.66822e9	−	1.21203e9i	−1.03694	−	0.753384i
$428$	5.75221e9			3.54635
$429$	4.71100e8	−	3.17273e8i	0.288080	−	0.194014i
$430$	2.80769e6			0.00170298
$431$	−6.66112e8	−	4.83959e8i	−0.400753	−	0.291164i	0.369094	−	0.929392i	$-0.379668\pi$
$431$	−6.66112e8	−	4.83959e8i	−0.400753	−	0.291164i	−0.769848	+	0.638228i	$0.779668\pi$
$432$	−5.49558e7	+	1.69137e8i	−0.0327960	+	0.100936i
$433$	−5.62891e8	−	1.73240e9i	−0.333209	−	1.02551i	−0.967597	−	0.252498i	$-0.918748\pi$
$433$	−5.62891e8	−	1.73240e9i	−0.333209	−	1.02551i	0.634388	−	0.773015i	$-0.281252\pi$
$434$	−5.47990e8	+	3.98138e8i	−0.321780	+	0.233787i
$435$	−641612.	+	466158.i	−0.000373732	+	0.000271532i
$436$	−1.84403e9	−	5.67534e9i	−1.06553	−	3.27936i
$437$	4.30291e8	−	1.32430e9i	0.246648	−	0.759104i
$438$	7.65974e8	+	5.56513e8i	0.435567	+	0.316458i
$439$	−8.61615e8			−0.486057			−0.243029	−	0.970019i	$-0.578141\pi$
$439$	−8.61615e8			−0.486057			−0.243029	+	0.970019i	$0.578141\pi$
$440$	−633997.	−	2.21697e6i	−0.000354816	−	0.00124073i
$441$	−1.51477e8			−0.0841033
$442$	7.53709e8	+	5.47602e8i	0.415170	+	0.301639i
$443$	7.93867e8	−	2.44327e9i	0.433845	−	1.33524i	−0.460420	−	0.887701i	$-0.652301\pi$
$443$	7.93867e8	−	2.44327e9i	0.433845	−	1.33524i	0.894265	−	0.447537i	$-0.147699\pi$
$444$	4.35864e8	+	1.34145e9i	0.236325	+	0.727335i
$445$	−2.59853e6	+	1.88794e6i	−0.00139787	+	0.00101561i
$446$	2.81014e9	−	2.04168e9i	1.49988	−	1.08972i
$447$	−1.02519e8	−	3.15521e8i	−0.0542910	−	0.167091i
$448$	−7.00626e8	+	2.15630e9i	−0.368140	+	1.13302i
$449$	1.37851e8	+	1.00155e8i	0.0718701	+	0.0522167i	0.623140	−	0.782110i	$-0.285857\pi$
$449$	1.37851e8	+	1.00155e8i	0.0718701	+	0.0522167i	−0.551270	+	0.834327i	$0.685857\pi$
$450$	1.08630e9			0.561959
$451$	−8.12623e8	+	2.22772e9i	−0.417130	+	1.14352i
$452$	5.26235e9			2.68038
$453$	1.81108e8	+	1.31583e8i	0.0915365	+	0.0665051i
$454$	1.25162e9	−	3.85208e9i	0.627735	−	1.93197i
$455$	293551.	+	903458.i	0.000146098	+	0.000449643i
$456$	−6.64672e8	+	4.82912e8i	−0.328269	+	0.238502i
$457$	−1.19618e8	+	8.69073e7i	−0.0586257	+	0.0425941i	−0.616712	−	0.787189i	$-0.711536\pi$
$457$	−1.19618e8	+	8.69073e7i	−0.0586257	+	0.0425941i	0.558086	+	0.829783i	$0.311536\pi$
$458$	1.75483e9	+	5.40083e9i	0.853507	+	2.62682i
$459$	6.23442e7	−	1.91876e8i	0.0300921	−	0.0926138i
$460$	4.55986e6	+	3.31293e6i	0.00218423	+	0.00158694i
$461$	−2.86691e9			−1.36289			−0.681444	−	0.731870i	$-0.738648\pi$
$461$	−2.86691e9			−1.36289			−0.681444	+	0.731870i	$0.738648\pi$
$462$	1.40496e9	+	1.09929e9i	0.662852	+	0.518638i
$463$	2.35389e9			1.10218			0.551090	−	0.834446i	$-0.314212\pi$
$463$	2.35389e9			1.10218			0.551090	+	0.834446i	$0.314212\pi$
$464$	−8.45168e8	−	6.14051e8i	−0.392763	−	0.285359i
$465$	−95924.9	+	295227.i	−4.42432e−5	+	0.000136166i
$466$	−1.42131e7	−	4.37435e7i	−0.00650638	−	0.0200246i
$467$	−2.74445e9	+	1.99396e9i	−1.24694	+	0.905958i	−0.998041	−	0.0625703i	$-0.980070\pi$
$467$	−2.74445e9	+	1.99396e9i	−1.24694	+	0.905958i	−0.248904	+	0.968528i	$0.580070\pi$
$468$	6.62707e8	−	4.81485e8i	0.298855	−	0.217131i
$469$	−8.23256e8	−	2.53372e9i	−0.368494	−	1.13411i
$470$	−89187.9	+	274492.i	−3.96245e−5	+	0.000121952i
$471$	−1.87416e9	−	1.36166e9i	−0.826483	−	0.600475i
$472$	1.95175e9			0.854333
$473$	−2.55630e9	−	9.10919e7i	−1.11070	−	0.0395791i
$474$	1.94285e9			0.837943
$475$	9.35369e8	+	6.79585e8i	0.400457	+	0.290949i
$476$	−5.86074e8	+	1.80375e9i	−0.249074	+	0.766571i
$477$	3.82688e8	+	1.17779e9i	0.161447	+	0.496883i
$478$	−1.01234e8	+	7.35508e7i	−0.0423964	+	0.0308028i
$479$	−3.23658e9	+	2.35151e9i	−1.34559	+	0.977626i	−0.346368	+	0.938099i	$0.612585\pi$
$479$	−3.23658e9	+	2.35151e9i	−1.34559	+	0.977626i	−0.999219	+	0.0395267i	$0.987415\pi$
$480$	192565.	+	592655.i	7.94755e−5	+	0.000244601i
$481$	3.26239e8	−	1.00406e9i	0.133668	−	0.411388i
$482$	−4.85608e9	−	3.52815e9i	−1.97524	−	1.43510i
$483$	−1.99348e9			−0.805003
$484$	1.10529e9	+	4.46016e9i	0.443117	+	1.78810i
$485$	2.58246e6			0.00102787
$486$	−2.21415e8	−	1.60868e8i	−0.0874945	−	0.0635685i
$487$	2.50748e8	−	7.71724e8i	0.0983754	−	0.302768i	−0.889743	−	0.456461i	$-0.849117\pi$
$487$	2.50748e8	−	7.71724e8i	0.0983754	−	0.302768i	0.988119	+	0.153693i	$0.0491167\pi$
$488$	−1.66964e9	−	5.13863e9i	−0.650361	−	2.00160i
$489$	1.17254e9	−	8.51901e8i	0.453469	−	0.329464i
$490$	814545.	−	591802.i	0.000312773	−	0.000227243i
$491$	1.04970e9	+	3.23064e9i	0.400203	+	1.23170i	0.924835	+	0.380368i	$0.124203\pi$
$491$	1.04970e9	+	3.23064e9i	0.400203	+	1.23170i	−0.524632	+	0.851329i	$0.675797\pi$
$492$	−1.05683e9	+	3.25258e9i	−0.400060	+	1.23126i
$493$	9.58795e8	+	6.96605e8i	0.360381	+	0.261832i
$494$	1.34511e9			0.502013
$495$	817018.	+	29113.9i	0.000302771	+	1.07890e-5i
$496$	−4.08903e8			−0.150464
$497$	−3.83866e7	−	2.78895e7i	−0.0140260	−	0.0101905i
$498$	−9.83053e8	+	3.02553e9i	−0.356676	+	1.09774i
$499$	−4.34452e8	−	1.33711e9i	−0.156527	−	0.481742i	0.841785	−	0.539813i	$-0.181505\pi$
$499$	−4.34452e8	−	1.33711e9i	−0.156527	−	0.481742i	−0.998312	+	0.0580712i	$0.981505\pi$
$500$	−7.57228e6	+	5.50159e6i	−0.00270914	+	0.00196831i
$501$	−1.18784e7	+	8.63018e6i	−0.00422014	+	0.00306611i
$502$	9.06558e8	+	2.79010e9i	0.319840	+	0.984366i
$503$	−4.45184e7	+	1.37014e8i	−0.0155974	+	0.0480038i	−0.958552	−	0.284917i	$-0.908034\pi$
$503$	−4.45184e7	+	1.37014e8i	−0.0155974	+	0.0480038i	0.942955	+	0.332920i	$0.108034\pi$
$504$	9.51567e8	+	6.91354e8i	0.331080	+	0.240543i
$505$	3.96319e6			0.00136938
$506$	−6.23937e9	−	4.88189e9i	−2.14099	−	1.67518i
$507$	1.08109e9			0.368411
$508$	2.06588e8	+	1.50095e8i	0.0699169	+	0.0507976i
$509$	−6.58037e7	+	2.02523e8i	−0.0221176	+	0.0680710i	−0.961506	−	0.274784i	$-0.911394\pi$
$509$	−6.58037e7	+	2.02523e8i	−0.0221176	+	0.0680710i	0.939388	+	0.342855i	$0.111394\pi$
$510$	414386.	+	1.27535e6i	0.000138328	+	0.000425730i
$511$	1.16714e9	−	8.47977e8i	0.386946	−	0.281132i
$512$	−2.58788e9	+	1.88020e9i	−0.852116	+	0.619098i
$513$	−9.00138e7	−	2.77034e8i	−0.0294373	−	0.0905988i
$514$	−2.07995e9	+	6.40144e9i	−0.675589	+	2.07925i
$515$	1.97594e6	+	1.43560e6i	0.000637454	+	0.000463137i
$516$	−3.68910e9			−1.18208
$517$	9.01078e7	−	2.47021e8i	0.0286778	−	0.0786172i
$518$	3.31586e9			1.04819
$519$	−5.59738e8	−	4.06674e8i	−0.175752	−	0.127691i
$520$	−769184.	+	2.36731e6i	−0.000239894	+	0.000738316i
$521$	−1.35743e8	−	4.17775e8i	−0.0420519	−	0.129423i	0.927826	−	0.373012i	$-0.121675\pi$
$521$	−1.35743e8	−	4.17775e8i	−0.0420519	−	0.129423i	−0.969878	+	0.243590i	$0.921675\pi$
$522$	1.30066e9	−	9.44981e8i	0.400235	−	0.290788i
$523$	−3.68648e9	+	2.67839e9i	−1.12682	+	0.818686i	−0.985230	−	0.171239i	$-0.945223\pi$
$523$	−3.68648e9	+	2.67839e9i	−1.12682	+	0.818686i	−0.141595	+	0.989925i	$0.545223\pi$
$524$	1.62499e9	+	5.00121e9i	0.493391	+	1.51850i
$525$	5.11493e8	−	1.57421e9i	0.154270	−	0.474795i
$526$	−4.57127e9	−	3.32122e9i	−1.36958	−	0.995056i
$527$	4.63877e8			0.138059
$528$	2.96098e8	+	1.03540e9i	0.0875420	+	0.306119i
$529$	5.44815e9			1.60013
$530$	−6.65930e6	−	4.83827e6i	−0.00194296	−	0.00141164i
$531$	−2.13838e8	+	6.58124e8i	−0.0619802	+	0.190756i
$532$	8.46186e8	+	2.60429e9i	0.243655	+	0.749893i
$533$	2.07092e9	−	1.50461e9i	0.592404	−	0.430407i
$534$	5.26765e9	−	3.82717e9i	1.49700	−	1.08764i
$535$	−1.91504e6	−	5.89390e6i	−0.000540680	−	0.00166404i
$536$	2.15715e9	−	6.63904e9i	0.605068	−	1.86221i
$537$	1.92049e9	+	1.39532e9i	0.535183	+	0.388833i
$538$	−1.29524e9			−0.358601
$539$	−7.60813e8	+	5.12386e8i	−0.209275	+	0.140941i
$540$	1.17907e6			0.000322227
$541$	−3.96576e9	−	2.88130e9i	−1.07680	−	0.782344i	−0.0996809	−	0.995019i	$-0.531782\pi$
$541$	−3.96576e9	−	2.88130e9i	−1.07680	−	0.782344i	−0.977123	+	0.212676i	$0.931782\pi$
$542$	5.43584e8	−	1.67298e9i	0.146646	−	0.451329i
$543$	−9.73331e7	−	2.99560e8i	−0.0260892	−	0.0802944i
$544$	7.53367e8	−	5.47353e8i	0.200637	−	0.145771i
$545$	−5.20122e6	+	3.77891e6i	−0.00137631	+	0.000999950i
$546$	−5.95078e8	−	1.83146e9i	−0.156459	−	0.481530i
$547$	8.72624e8	−	2.68566e9i	0.227967	−	0.701609i	−0.770010	−	0.638032i	$-0.779749\pi$
$547$	8.72624e8	−	2.68566e9i	0.227967	−	0.701609i	0.997977	−	0.0635777i	$-0.0202511\pi$
$548$	2.41719e9	+	1.75619e9i	0.627450	+	0.455869i
$549$	1.91566e9			0.494101
$550$	5.45605e9	−	3.67450e9i	1.39833	−	0.941734i
$551$	1.71112e9			0.435763
$552$	−4.22587e9	−	3.07027e9i	−1.06937	−	0.776945i
$553$	9.14808e8	−	2.81549e9i	0.230034	−	0.707972i
$554$	−1.15877e9	−	3.56632e9i	−0.289542	−	0.891120i
$555$	1.22938e6	−	893200.i	0.000305255	−	0.000221780i
$556$	−6.65398e9	+	4.83440e9i	−1.64180	+	1.19284i
$557$	1.42536e9	+	4.38682e9i	0.349488	+	1.07561i	0.959137	+	0.282943i	$0.0913107\pi$
$557$	1.42536e9	+	4.38682e9i	0.349488	+	1.07561i	−0.609648	+	0.792672i	$0.708689\pi$
$558$	1.94456e8	−	5.98474e8i	0.0473807	−	0.145823i
$559$	2.23389e9	+	1.62302e9i	0.540905	+	0.392991i
$560$	−1.80115e6			−0.000433402
$561$	−3.35906e8	−	1.17460e9i	−0.0803245	−	0.280880i
$562$	−8.85684e9			−2.10475
$563$	−7.29673e8	−	5.30139e8i	−0.172325	−	0.125202i	0.498279	−	0.867016i	$-0.333965\pi$
$563$	−7.29673e8	−	5.30139e8i	−0.172325	−	0.125202i	−0.670605	+	0.741815i	$0.733965\pi$
$564$	1.17186e8	−	3.60662e8i	0.0275043	−	0.0846494i
$565$	−1.75196e6	−	5.39198e6i	−0.000408653	−	0.00125770i
$566$	1.49112e9	−	1.08336e9i	0.345665	−	0.251141i
$567$	−3.37378e8	+	2.45119e8i	−0.0777277	+	0.0564725i
$568$	−3.84194e7	−	1.18243e8i	−0.00879694	−	0.0270742i
$569$	1.54803e9	−	4.76435e9i	0.352279	−	1.08420i	−0.605292	−	0.796004i	$-0.706944\pi$
$569$	1.54803e9	−	4.76435e9i	0.352279	−	1.08420i	0.957571	−	0.288199i	$-0.0930564\pi$
$570$	1.56637e6	+	1.13803e6i	0.000354268	+	0.000257391i
$571$	3.39121e9			0.762304			0.381152	−	0.924512i	$-0.375527\pi$
$571$	3.39121e9			0.762304			0.381152	+	0.924512i	$0.375527\pi$
$572$	1.69985e9	−	4.65997e9i	0.379774	−	1.04111i
$573$	−1.21016e9			−0.268722
$574$	6.50439e9	+	4.72572e9i	1.43554	+	1.04298i
$575$	−2.27152e9	+	6.99102e9i	−0.498287	+	1.53357i
$576$	−6.50893e8	−	2.00324e9i	−0.141916	−	0.436772i
$577$	−5.41308e9	+	3.93284e9i	−1.17308	+	0.852296i	−0.991375	−	0.131056i	$-0.958163\pi$
$577$	−5.41308e9	+	3.93284e9i	−1.17308	+	0.852296i	−0.181710	+	0.983352i	$0.558163\pi$
$578$	−4.71067e9	+	3.42250e9i	−1.01469	+	0.737219i
$579$	−6.65964e8	−	2.04963e9i	−0.142586	−	0.438833i
$580$	−2.14031e6	+	6.58721e6i	−0.000455491	+	0.00140186i
$581$	3.92158e9	+	2.84919e9i	0.829554	+	0.602706i
$582$	−5.23508e9			−1.10076
$583$	5.90608e9	+	4.62111e9i	1.23441	+	0.965843i
$584$	3.78017e9			0.785356
$585$	−713975.	−	518733.i	−0.000147447	−	0.000107127i
$586$	1.25431e9	−	3.86036e9i	0.257491	−	0.792476i
$587$	1.22144e9	+	3.75921e9i	0.249252	+	0.767120i	0.994908	+	0.100789i	$0.0321365\pi$
$587$	1.22144e9	+	3.75921e9i	0.249252	+	0.767120i	−0.745655	+	0.666332i	$0.767863\pi$
$588$	−1.07025e9	+	7.77583e8i	−0.217103	+	0.157734i
$589$	5.41843e8	−	3.93672e8i	0.109262	−	0.0793836i
$590$	−1.42132e6	−	4.37439e6i	−0.000284912	−	0.000876870i
$591$	−1.25144e8	+	3.85154e8i	−0.0249376	+	0.0767501i
$592$	1.61942e9	+	1.17657e9i	0.320799	+	0.233074i
$593$	8.76962e9			1.72699			0.863494	−	0.504359i	$-0.168271\pi$
$593$	8.76962e9			1.72699			0.863494	+	0.504359i	$0.168271\pi$
$594$	−1.65623e9	−	5.90187e7i	−0.324242	−	0.0115541i
$595$	2.04330e6			0.000397670
$596$	−2.34401e9	−	1.70302e9i	−0.453521	−	0.329503i
$597$	−9.79865e8	+	3.01572e9i	−0.188476	+	0.580070i
$598$	2.64272e9	+	8.13344e9i	0.505355	+	1.55532i
$599$	2.03954e9	−	1.48181e9i	0.387738	−	0.281708i	−0.376790	−	0.926299i	$-0.622972\pi$
$599$	2.03954e9	−	1.48181e9i	0.387738	−	0.281708i	0.764528	+	0.644590i	$0.222972\pi$
$600$	3.50882e9	−	2.54931e9i	0.663181	−	0.481829i
$601$	−1.28858e9	−	3.96585e9i	−0.242132	−	0.745204i	−0.996095	−	0.0882879i	$-0.971860\pi$
$601$	−1.28858e9	−	3.96585e9i	−0.242132	−	0.745204i	0.753963	−	0.656916i	$-0.228140\pi$
$602$	−2.67997e9	+	8.24811e9i	−0.500660	+	1.54087i
$603$	2.00232e9	+	1.45477e9i	0.371897	+	0.270199i
$604$	1.95506e9			0.361020
$605$	4.20205e6	−	2.61741e6i	0.000771467	−	0.000480538i
$606$	−8.03406e9			−1.46650
$607$	3.52861e9	+	2.56369e9i	0.640388	+	0.465269i	0.859984	−	0.510322i	$-0.170474\pi$
$607$	3.52861e9	+	2.56369e9i	0.640388	+	0.465269i	−0.219595	+	0.975591i	$0.570474\pi$
$608$	4.15474e8	−	1.27870e9i	0.0749690	−	0.230731i
$609$	−7.57000e8	−	2.32981e9i	−0.135811	−	0.417984i
$610$	−1.03011e7	+	7.48422e6i	−0.00183752	+	0.00133503i
$611$	−2.29634e8	+	1.66839e8i	−0.0407279	+	0.0295906i
$612$	−5.44473e8	−	1.67572e9i	−0.0960166	−	0.295509i
$613$	9.61500e8	−	2.95919e9i	0.168592	−	0.518874i	−0.830691	−	0.556734i	$-0.812054\pi$
$613$	9.61500e8	−	2.95919e9i	0.168592	−	0.518874i	0.999283	+	0.0378604i	$0.0120542\pi$
$614$	−3.25988e9	−	2.36844e9i	−0.568345	−	0.412927i
$615$	3.68454e6			0.000638734
$616$	7.11792e9	+	2.53642e8i	1.22693	+	0.0437208i
$617$	−3.75705e9			−0.643944			−0.321972	−	0.946749i	$-0.604346\pi$
$617$	−3.75705e9			−0.643944			−0.321972	+	0.946749i	$0.604346\pi$
$618$	−4.00556e9	−	2.91021e9i	−0.682659	−	0.495981i
$619$	1.00671e9	−	3.09833e9i	0.170603	−	0.525062i	−0.828802	−	0.559542i	$-0.810977\pi$
$619$	1.00671e9	−	3.09833e9i	0.170603	−	0.525062i	0.999405	+	0.0344791i	$0.0109772\pi$
$620$	837745.	+	2.57831e6i	0.000141169	+	0.000434475i
$621$	1.49828e9	−	1.08857e9i	0.251057	−	0.182404i
$622$	8.19014e9	−	5.95049e9i	1.36466	−	0.991485i
$623$	−3.06585e9	−	9.43571e9i	−0.507975	−	1.56339i
$624$	3.59235e8	−	1.10561e9i	0.0591878	−	0.182161i
$625$	−4.93784e9	−	3.58755e9i	−0.809015	−	0.587784i
$626$	−9.56933e8			−0.155909
$627$	−1.38920e9	−	1.08696e9i	−0.225075	−	0.176106i
$628$	−2.02316e10			−3.25965
$629$	−1.83713e9	−	1.33476e9i	−0.294350	−	0.213858i
$630$	856546.	−	2.63618e6i	0.000136477	−	0.000420032i
$631$	2.53923e9	+	7.81496e9i	0.402346	+	1.23829i	0.923091	+	0.384582i	$0.125654\pi$
$631$	2.53923e9	+	7.81496e9i	0.402346	+	1.23829i	−0.520745	+	0.853713i	$0.674346\pi$
$632$	6.27555e9	−	4.55945e9i	0.988876	−	0.718460i
$633$	2.48059e9	−	1.80225e9i	0.388724	−	0.282425i
$634$	−2.54116e9	−	7.82088e9i	−0.396022	−	1.21883i
$635$	85014.2	−	261647.i	1.31760e−5	−	4.05516e-5i
$636$	8.74983e9	+	6.35712e9i	1.34865	+	0.979853i
$637$	9.90177e8			0.151784
$638$	3.33620e9	−	9.14586e9i	0.508604	−	1.39429i
$639$	4.40804e7			0.00668333
$640$	8.93646e6	+	6.49271e6i	0.00134752	+	0.000979031i
$641$	−2.36906e8	+	7.29123e8i	−0.0355282	+	0.109345i	−0.967248	−	0.253834i	$-0.918308\pi$
$641$	−2.36906e8	+	7.29123e8i	−0.0355282	+	0.109345i	0.931720	+	0.363178i	$0.118308\pi$
$642$	3.88211e9	+	1.19479e10i	0.579023	+	1.78205i
$643$	−9.37186e9	+	6.80905e9i	−1.39023	+	1.01006i	−0.394392	+	0.918942i	$0.629045\pi$
$643$	−9.37186e9	+	6.80905e9i	−1.39023	+	1.01006i	−0.995840	+	0.0911204i	$0.970955\pi$
$644$	−1.40848e10	+	1.02332e10i	−2.07802	+	1.50977i
$645$	1.22819e6	+	3.77997e6i	0.000180221	+	0.000554663i
$646$	8.94071e8	−	2.75167e9i	0.130484	−	0.401589i
$647$	3.42071e9	+	2.48529e9i	0.496537	+	0.360755i	0.807693	−	0.589604i	$-0.200716\pi$
$647$	3.42071e9	+	2.48529e9i	0.496537	+	0.360755i	−0.311155	+	0.950359i	$0.600716\pi$
$648$	−1.09271e9			−0.157758
$649$	1.15214e9	+	4.02883e9i	0.165443	+	0.578525i
$650$	−7.10090e9			−1.01418
$651$	−7.75721e8	−	5.63594e8i	−0.110198	−	0.0800632i
$652$	3.91141e9	−	1.20381e10i	0.552671	−	1.70095i
$653$	−1.23299e9	−	3.79474e9i	−0.173286	−	0.533318i	0.826265	−	0.563281i	$-0.190461\pi$
$653$	−1.23299e9	−	3.79474e9i	−0.173286	−	0.533318i	−0.999551	+	0.0299629i	$0.990461\pi$
$654$	1.05437e10	−	7.66048e9i	1.47392	−	1.07086i
$655$	4.58340e6	−	3.33003e6i	0.000637299	−	0.000463025i
$656$	1.49981e9	+	4.61594e9i	0.207430	+	0.638405i
$657$	−4.14163e8	+	1.27466e9i	−0.0569761	+	0.175354i
$658$	−7.21240e8	−	5.24011e8i	−0.0986936	−	0.0717051i
$659$	−8.90217e9			−1.21171			−0.605853	−	0.795577i	$-0.707168\pi$
$659$	−8.90217e9			−1.21171			−0.605853	+	0.795577i	$0.707168\pi$
$660$	5.92203e6	−	3.98832e6i	0.000801801	−	0.000539991i
$661$	−1.02809e10			−1.38461			−0.692305	−	0.721605i	$-0.743405\pi$
$661$	−1.02809e10			−1.38461			−0.692305	+	0.721605i	$0.743405\pi$
$662$	−5.77852e8	−	4.19834e8i	−0.0774129	−	0.0562438i
$663$	−4.07531e8	+	1.25425e9i	−0.0543080	+	0.167143i
$664$	3.92493e9	+	1.20797e10i	0.520288	+	1.60128i
$665$	2.38673e6	−	1.73406e6i	0.000314722	−	0.000228659i
$666$	−2.49217e9	+	1.81067e9i	−0.326902	+	0.237508i
$667$	3.36181e9	+	1.03466e10i	0.438664	+	1.35007i
$668$	−3.96245e7	+	1.21952e8i	−0.00514335	+	0.0158296i
$669$	3.97795e9	+	2.89015e9i	0.513651	+	0.373190i
$670$	−1.64507e7			−0.00211312
$671$	9.62162e9	−	6.47989e9i	1.22947	−	0.828017i
$672$	−1.92484e9			−0.244682
$673$	−8.84394e9	−	6.42550e9i	−1.11839	−	0.812558i	−0.134425	−	0.990924i	$-0.542919\pi$
$673$	−8.84394e9	−	6.42550e9i	−1.11839	−	0.812558i	−0.983964	+	0.178366i	$0.942919\pi$
$674$	−6.60603e9	+	2.03313e10i	−0.831058	+	2.55773i
$675$	4.75186e8	+	1.46247e9i	0.0594703	+	0.183031i
$676$	7.63832e9	−	5.54957e9i	0.951009	−	0.690948i
$677$	2.34183e9	−	1.70144e9i	0.290064	−	0.210744i	−0.433231	−	0.901283i	$-0.642627\pi$
$677$	2.34183e9	−	1.70144e9i	0.290064	−	0.210744i	0.723295	+	0.690539i	$0.242627\pi$
$678$	3.55152e9	+	1.09304e10i	0.437633	+	1.34690i
$679$	−2.46499e9	+	7.58645e9i	−0.302183	+	0.930025i
$680$	4.33148e6	+	3.14700e6i	0.000528268	+	0.000383809i
$681$	5.73352e9			0.695676
$682$	−1.04771e9	−	3.66367e9i	−0.126473	−	0.442253i
$683$	−7.76079e9			−0.932038			−0.466019	−	0.884775i	$-0.654312\pi$
$683$	−7.76079e9			−0.932038			−0.466019	+	0.884775i	$0.654312\pi$
$684$	−2.05809e9	−	1.49529e9i	−0.245906	−	0.178661i
$685$	994712.	−	3.06141e6i	0.000118244	−	0.000363919i
$686$	4.76997e9	+	1.46805e10i	0.564133	+	1.73622i
$687$	−6.50345e9	+	4.72503e9i	−0.765236	+	0.555976i
$688$	−4.23556e9	+	3.07731e9i	−0.495851	+	0.360257i
$689$	−2.50155e9	−	7.69898e9i	−0.291368	−	0.896738i
$690$	−3.80389e6	+	1.17072e7i	−0.000440814	+	0.00135669i
$691$	4.50675e9	+	3.27435e9i	0.519626	+	0.377530i	0.816463	−	0.577398i	$-0.195932\pi$
$691$	4.50675e9	+	3.27435e9i	0.519626	+	0.377530i	−0.296837	+	0.954928i	$0.595932\pi$
$692$	−6.04237e9			−0.693164
$693$	−8.65380e8	+	2.37235e9i	−0.0987735	+	0.270778i
$694$	−9.40363e9			−1.06792
$695$	7.16875e6	+	5.20840e6i	0.000810022	+	0.000588515i
$696$	1.98354e9	−	6.10472e9i	0.223002	−	0.686331i
$697$	−1.70145e9	−	5.23652e9i	−0.190328	−	0.585771i
$698$	1.84433e10	−	1.33998e10i	2.05279	−	1.49144i
$699$	5.26742e7	−	3.82700e7i	0.00583348	−	0.00423827i
$700$	−4.46704e9	−	1.37481e10i	−0.492240	−	1.51496i
$701$	2.48702e9	−	7.65427e9i	0.272689	−	0.839249i	−0.717133	−	0.696936i	$-0.754546\pi$
$701$	2.48702e9	−	7.65427e9i	0.272689	−	0.839249i	0.989822	−	0.142313i	$-0.0454539\pi$
$702$	1.44735e9	+	1.05156e9i	0.157904	+	0.114724i
$703$	−3.27866e9			−0.355920
$704$	−1.00453e10	−	7.85981e9i	−1.08508	−	0.849000i
$705$	−408560.			−4.39131e−5
$706$	2.03510e10	+	1.47858e10i	2.17655	+	1.58136i
$707$	−3.78291e9	+	1.16426e10i	−0.402585	+	1.23903i
$708$	1.86751e9	+	5.74762e9i	0.197764	+	0.608656i
$709$	−4.20923e9	+	3.05818e9i	−0.443548	+	0.322256i	−0.787043	−	0.616898i	$-0.788389\pi$
$709$	−4.20923e9	+	3.05818e9i	−0.443548	+	0.322256i	0.343495	+	0.939154i	$0.388389\pi$
$710$	−237035.	+	172216.i	−2.48547e−5	+	1.80580e-5i
$711$	8.49872e8	+	2.61564e9i	0.0886768	+	0.272919i
$712$	8.03335e9	−	2.47241e10i	0.834097	−	2.56709i
$713$	3.44494e9	+	2.50290e9i	0.355933	+	0.258601i
$714$	−4.14211e9			−0.425871
$715$	−5.34068e6	−	190311.i	−0.000546419	−	1.94712e-5i
$716$	2.07317e10			2.11076
$717$	−1.43304e8	−	1.04117e8i	−0.0145192	−	0.0105488i
$718$	6.81626e9	−	2.09783e10i	0.687243	−	2.11512i
$719$	−5.85218e9	−	1.80112e10i	−0.587174	−	1.80714i	−0.590360	−	0.807140i	$-0.701014\pi$
$719$	−5.85218e9	−	1.80112e10i	−0.587174	−	1.80714i	0.00318617	−	0.999995i	$-0.498986\pi$
$720$	1.35373e6	−	983539.i	0.000135166	−	9.82037e-5i
$721$	−6.10341e9	+	4.43438e9i	−0.606455	+	0.440616i
$722$	3.97765e9	+	1.22419e10i	0.393320	+	1.21051i
$723$	2.62568e9	−	8.08103e9i	0.258380	−	0.795211i
$724$	−2.22544e9	−	1.61688e9i	−0.217937	−	0.158340i
$725$	−9.03307e9			−0.880344
$726$	−8.51825e9	+	5.30593e9i	−0.826176	+	0.514616i
$727$	1.67908e10			1.62070			0.810348	−	0.585949i	$-0.199278\pi$
$727$	1.67908e10			1.62070			0.810348	+	0.585949i	$0.199278\pi$
$728$	−6.22020e9	−	4.51924e9i	−0.597509	−	0.434115i
$729$	1.19720e8	−	3.68459e8i	0.0114451	−	0.0352243i
$730$	−2.75284e6	−	8.47236e6i	−0.000261909	−	0.000806073i
$731$	4.80500e9	−	3.49103e9i	0.454969	−	0.330555i
$732$	1.35349e10	−	9.83371e9i	1.27546	−	0.926677i
$733$	2.46721e9	+	7.59329e9i	0.231389	+	0.712141i	0.997580	+	0.0695284i	$0.0221495\pi$
$733$	2.46721e9	+	7.59329e9i	0.231389	+	0.712141i	−0.766191	+	0.642612i	$0.777851\pi$
$734$	−9.58460e9	+	2.94984e10i	−0.894618	+	2.75335i
$735$	1.15305e6	+	837739.i	0.000107113	+	7.78221e-5i
$736$	8.54812e9			0.790312
$737$	1.49778e10	+	5.33722e8i	1.37820	+	0.0491111i
$738$	−7.46917e9			−0.684030
$739$	−8.58151e9	−	6.23483e9i	−0.782182	−	0.568289i	0.123451	−	0.992351i	$-0.460604\pi$
$739$	−8.58151e9	−	6.23483e9i	−0.782182	−	0.568289i	−0.905633	+	0.424062i	$0.860604\pi$
$740$	4.10103e6	−	1.26217e7i	0.000372033	−	0.00114500i
$741$	5.88402e8	+	1.81091e9i	0.0531264	+	0.163506i
$742$	2.05697e10	−	1.49447e10i	1.84848	−	1.34300i
$743$	3.74757e8	−	2.72277e8i	0.0335188	−	0.0243528i	−0.570900	−	0.821020i	$-0.693405\pi$
$743$	3.74757e8	−	2.72277e8i	0.0335188	−	0.0243528i	0.604419	+	0.796667i	$0.293405\pi$
$744$	−7.76383e8	−	2.38946e9i	−0.0691148	−	0.212713i
$745$	−964597.	+	2.96872e6i	−8.54671e−5	+	0.000263041i
$746$	−1.38908e10	−	1.00923e10i	−1.22501	−	0.890025i
$747$	−4.50326e9			−0.395280
$748$	−8.40293e9	−	6.57474e9i	−0.734134	−	0.574411i
$749$	1.91423e10			1.66459
$750$	−1.65378e7	−	1.20154e7i	−0.00143141	−	0.00103998i
$751$	−4.92577e8	+	1.51600e9i	−0.0424360	+	0.130605i	−0.970030	−	0.242985i	$-0.921873\pi$
$751$	−4.92577e8	+	1.51600e9i	−0.0424360	+	0.130605i	0.927594	+	0.373590i	$0.121873\pi$
$752$	−1.66306e8	−	5.11839e8i	−0.0142609	−	0.0438905i
$753$	−3.35972e9	+	2.44098e9i	−0.286762	+	0.208345i
$754$	−8.50211e9	+	6.17715e9i	−0.722316	+	0.524793i
$755$	−650885.	−	2.00322e6i	−5.50415e−5	−	0.000169400i
$756$	−1.12544e9	+	3.46374e9i	−0.0947317	+	0.291554i
$757$	−7.08563e9	−	5.14801e9i	−0.593667	−	0.431324i	0.249958	−	0.968257i	$-0.419583\pi$
$757$	−7.08563e9	−	5.14801e9i	−0.593667	−	0.431324i	−0.843625	+	0.536932i	$0.819583\pi$
$758$	2.59370e10			2.16311
$759$	3.84312e9	−	1.05355e10i	0.319034	−	0.874600i
$760$	7.73021e6			0.000638769
$761$	3.42608e9	+	2.48919e9i	0.281807	+	0.204745i	0.719705	−	0.694280i	$-0.244277\pi$
$761$	3.42608e9	+	2.48919e9i	0.281807	+	0.204745i	−0.437898	+	0.899025i	$0.644277\pi$
$762$	−1.72338e8	+	5.30402e8i	−0.0141104	+	0.0434273i
$763$	−6.13661e9	−	1.88865e10i	−0.500141	−	1.53928i
$764$	−8.55031e9	+	6.21216e9i	−0.693674	+	0.503983i
$765$	−1.53572e6	+	1.11577e6i	−0.000124022	+	9.01071e-5i
$766$	2.41579e9	+	7.43503e9i	0.194204	+	0.597699i
$767$	1.39781e9	−	4.30202e9i	0.111857	−	0.344262i
$768$	−1.00372e10	−	7.29244e9i	−0.799554	−	0.580910i
$769$	7.89481e9			0.626036			0.313018	−	0.949747i	$-0.398660\pi$
$769$	7.89481e9			0.626036			0.313018	+	0.949747i	$0.398660\pi$
$770$	−4.61501e6	−	1.61378e7i	−0.000364296	−	0.00127388i
$771$	−9.52804e9			−0.748709
$772$	−1.52267e10	−	1.10628e10i	−1.19109	−	0.865379i
$773$	2.38100e9	−	7.32798e9i	0.185409	−	0.570632i	−0.814546	−	0.580099i	$-0.803014\pi$
$773$	2.38100e9	−	7.32798e9i	0.185409	−	0.570632i	0.999955	+	0.00946767i	$0.00301370\pi$
$774$	−2.48974e9	−	7.66263e9i	−0.193001	−	0.593998i
$775$	−2.86040e9	+	2.07820e9i	−0.220735	+	0.160373i
$776$	−1.69097e10	+	1.22856e10i	−1.29903	+	0.943803i
$777$	1.45048e9	+	4.46411e9i	0.110927	+	0.341398i
$778$	−9.70307e9	+	2.98630e10i	−0.738721	+	2.27355i
$779$	−6.43142e9	−	4.67270e9i	−0.487445	−	0.354150i
$780$	−7.70735e6			−0.000581533
$781$	2.21399e8	−	1.49106e8i	0.0166302	−	0.0112000i
$782$	1.83949e10			1.37555
$783$	1.84117e9	+	1.33769e9i	0.137066	+	0.0995840i
$784$	−5.80154e8	+	1.78553e9i	−0.0429969	+	0.132331i
$785$	6.73556e6	+	2.07299e7i	0.000496969	+	0.00152951i
$786$	−9.29132e9	+	6.75054e9i	−0.682493	+	0.495860i
$787$	−4.40720e9	+	3.20202e9i	−0.322293	+	0.234160i	−0.737153	−	0.675725i	$-0.763831\pi$
$787$	−4.40720e9	+	3.20202e9i	−0.322293	+	0.234160i	0.414860	+	0.909885i	$0.363831\pi$
$788$	1.09293e9	+	3.36368e9i	0.0795700	+	0.244891i
$789$	2.47169e9	−	7.60707e9i	0.179153	−	0.551376i
$790$	−1.47890e7	−	1.07448e7i	−0.00106719	−	0.000775362i
$791$	1.75122e10			1.25812
$792$	−5.48826e9	+	3.69619e9i	−0.392552	+	0.264373i
$793$	−1.25223e10			−0.891717
$794$	1.40753e10	+	1.02263e10i	0.997900	+	0.725017i
$795$	3.60069e6	−	1.10818e7i	0.000254156	−	0.000782213i
$796$	8.55749e9	+	2.63373e10i	0.601382	+	1.85086i
$797$	−1.14965e10	+	8.35272e9i	−0.804383	+	0.584419i	−0.912197	−	0.409753i	$-0.865615\pi$
$797$	−1.14965e10	+	8.35272e9i	−0.804383	+	0.584419i	0.107814	+	0.994171i	$0.465615\pi$
$798$	−4.83830e9	+	3.51523e9i	−0.337041	+	0.244874i
$799$	1.88665e8	+	5.80652e8i	0.0130851	+	0.0402719i
$800$	−2.19330e9	+	6.75029e9i	−0.151455	+	0.466130i
$801$	7.45675e9	+	5.41764e9i	0.512667	+	0.372475i
$802$	−7.19335e8			−0.0492403
$803$	2.23148e9	+	7.80308e9i	0.152086	+	0.531816i
$804$	2.16150e10			1.46676
$805$	1.51744e7	+	1.10248e7i	0.00102524	+	0.000744881i
$806$	−1.27112e9	+	3.91210e9i	−0.0855093	+	0.263171i
$807$	−5.66584e8	−	1.74377e9i	−0.0379496	−	0.116797i
$808$	−2.59506e10	+	1.88542e10i	−1.73064	+	1.25739i
$809$	−7.34275e9	+	5.33482e9i	−0.487572	+	0.354242i	−0.804250	−	0.594291i	$-0.797433\pi$
$809$	−7.34275e9	+	5.33482e9i	−0.487572	+	0.354242i	0.316678	+	0.948533i	$0.397433\pi$
$810$	795746.	+	2.44905e6i	5.26110e−5	+	0.000161920i
$811$	−6.47284e9	+	1.99214e10i	−0.426110	+	1.31143i	0.475817	+	0.879544i	$0.342152\pi$
$811$	−6.47284e9	+	1.99214e10i	−0.426110	+	1.31143i	−0.901927	+	0.431888i	$0.857848\pi$
$812$	−1.73082e10	−	1.25751e10i	−1.13450	−	0.824263i
$813$	2.49010e9			0.162517
$814$	−6.39245e9	+	1.75243e10i	−0.415415	+	1.13882i
$815$	−1.36368e7			−0.000882390
$816$	−2.02294e9	−	1.46975e9i	−0.130337	−	0.0946955i
$817$	2.64991e9	−	8.15558e9i	0.170002	−	0.523212i
$818$	−4.64565e9	−	1.42978e10i	−0.296763	−	0.913342i
$819$	2.20537e9	−	1.60229e9i	0.140277	−	0.101918i
$820$	2.60328e7	−	1.89139e7i	0.00164882	−	0.00119793i
$821$	6.72861e9	+	2.07085e10i	0.424350	+	1.30602i	0.903615	+	0.428345i	$0.140903\pi$
$821$	6.72861e9	+	2.07085e10i	0.424350	+	1.30602i	−0.479265	+	0.877670i	$0.659097\pi$
$822$	−2.01645e9	+	6.20599e9i	−0.126630	+	0.389726i
$823$	6.84594e9	+	4.97387e9i	0.428089	+	0.311025i	0.780884	−	0.624676i	$-0.214769\pi$
$823$	6.84594e9	+	4.97387e9i	0.428089	+	0.311025i	−0.352796	+	0.935700i	$0.614769\pi$
$824$	−1.97679e10			−1.23088
$825$	7.33361e9	+	5.73807e9i	0.454704	+	0.355776i
$826$	1.42072e10			0.877161
$827$	−2.10846e10	−	1.53189e10i	−1.29627	−	0.941797i	−0.296361	−	0.955076i	$-0.595773\pi$
$827$	−2.10846e10	−	1.53189e10i	−1.29627	−	0.941797i	−0.999912	+	0.0132785i	$0.995773\pi$
$828$	4.99802e9	−	1.53823e10i	0.305979	−	0.941708i
$829$	−6.44255e9	−	1.98281e10i	−0.392751	−	1.20876i	−0.930700	−	0.365785i	$-0.880801\pi$
$829$	−6.44255e9	−	1.98281e10i	−0.392751	−	1.20876i	0.537949	−	0.842977i	$-0.319199\pi$
$830$	2.42155e7	−	1.75936e7i	0.00147001	−	0.00106803i
$831$	4.29441e9	−	3.12007e9i	0.259597	−	0.188609i
$832$	4.25475e9	+	1.30948e10i	0.256120	+	0.788255i
$833$	6.58151e8	−	2.02558e9i	0.0394519	−	0.121420i
$834$	−1.45323e10	−	1.05583e10i	−0.867465	−	0.630250i
$835$	138147.			8.21183e−6
$836$	−1.53950e10	−	5.48588e8i	−0.911289	−	0.0324731i
$837$	8.90782e8			0.0525088
$838$	−1.42444e10	−	1.03492e10i	−0.836162	−	0.607507i
$839$	−1.08644e9	+	3.34372e9i	−0.0635095	+	0.195462i	−0.977776	−	0.209650i	$-0.932768\pi$
$839$	−1.08644e9	+	3.34372e9i	−0.0635095	+	0.195462i	0.914267	+	0.405112i	$0.132768\pi$
$840$	−3.41984e6	−	1.05252e7i	−0.000199080	−	0.000612706i
$841$	3.13989e9	−	2.28126e9i	0.182024	−	0.132248i
$842$	1.56962e10	−	1.14039e10i	0.906152	−	0.658358i
$843$	−3.87430e9	−	1.19239e10i	−0.222739	−	0.685521i
$844$	8.27483e9	−	2.54673e10i	0.473763	−	1.45809i
$845$	−8.22924e6	−	5.97889e6i	−0.000469203	−	0.000340896i
$846$	8.28220e8			0.0470272
$847$	3.67822e9	+	1.48426e10i	0.207992	+	0.839303i
$848$	1.53488e10			0.864349
$849$	2.11079e9	+	1.53358e9i	0.118377	+	0.0860063i
$850$	−4.71983e9	+	1.45261e10i	−0.263609	+	0.811304i
$851$	−6.44151e9	−	1.98249e10i	−0.358290	−	1.10270i
$852$	3.11446e8	−	2.26279e8i	0.0172522	−	0.0125345i
$853$	2.27906e10	−	1.65583e10i	1.25729	−	0.913472i	0.258665	−	0.965967i	$-0.416717\pi$
$853$	2.27906e10	−	1.65583e10i	1.25729	−	0.913472i	0.998621	+	0.0524950i	$0.0167174\pi$
$854$	−1.21537e10	−	3.74053e10i	−0.667738	−	2.05509i
$855$	−846937.	+	2.60660e6i	−4.63415e−5	+	0.000142624i
$856$	4.05787e10	+	2.94822e10i	2.21126	+	1.60658i
$857$	−1.42192e10			−0.771692			−0.385846	−	0.922563i	$-0.626090\pi$
$857$	−1.42192e10			−0.771692			−0.385846	+	0.922563i	$0.626090\pi$
$858$	1.08265e10	+	3.85793e8i	0.585168	+	0.0208520i
$859$	2.92967e10			1.57704			0.788519	−	0.615011i	$-0.210848\pi$
$859$	2.92967e10			1.57704			0.788519	+	0.615011i	$0.210848\pi$
$860$	2.80815e7	+	2.04024e7i	0.00150548	+	0.00109380i
$861$	−3.51693e9	+	1.08240e10i	−0.187781	+	0.577932i
$862$	−4.85293e9	−	1.49358e10i	−0.258064	−	0.794241i
$863$	−4.89314e9	+	3.55507e9i	−0.259149	+	0.188283i	−0.709772	−	0.704432i	$-0.751202\pi$
$863$	−4.89314e9	+	3.55507e9i	−0.259149	+	0.188283i	0.450623	+	0.892714i	$0.351202\pi$
$864$	1.44669e9	−	1.05108e9i	0.0763092	−	0.0554419i
$865$	2.01165e6	+	6.19121e6i	0.000105681	+	0.000325251i
$866$	1.07363e10	−	3.30430e10i	0.561750	−	1.72889i
$867$	−6.66830e9	−	4.84480e9i	−0.347495	−	0.252470i
$868$	−8.37390e9			−0.434619
$869$	1.31162e10	+	1.02626e10i	0.678015	+	0.530502i
$870$	−1.51268e7			−0.000778805
$871$	−1.30888e10	−	9.50954e9i	−0.671174	−	0.487636i
$872$	1.60796e10	−	4.94878e10i	0.821234	−	2.52750i
$873$	−2.29002e9	−	7.04794e9i	−0.116490	−	0.358519i
$874$	2.14867e10	−	1.56110e10i	1.08863	−	0.790934i
$875$	−2.51992e7	+	1.83083e7i	−0.00127162	+	0.000923889i
$876$	3.61702e9	+	1.11321e10i	0.181797	+	0.559514i
$877$	−1.00631e10	+	3.09711e10i	−0.503771	+	1.55045i	0.299055	+	0.954236i	$0.403329\pi$
$877$	−1.00631e10	+	3.09711e10i	−0.503771	+	1.55045i	−0.802826	+	0.596213i	$0.796671\pi$
$878$	−1.32954e10	−	9.65969e9i	−0.662936	−	0.481651i
$879$	5.74584e9			0.285360
$880$	3.47233e6	−	9.51903e6i	0.000171764	−	0.000470873i
$881$	−3.04620e10			−1.50087			−0.750435	−	0.660945i	$-0.770156\pi$
$881$	−3.04620e10			−1.50087			−0.750435	+	0.660945i	$0.770156\pi$
$882$	−2.33742e9	−	1.69824e9i	−0.114709	−	0.0833409i
$883$	−5.69283e9	+	1.75207e10i	−0.278269	+	0.856425i	0.710066	+	0.704135i	$0.248665\pi$
$883$	−5.69283e9	+	1.75207e10i	−0.278269	+	0.856425i	−0.988336	+	0.152291i	$0.951335\pi$
$884$	3.55911e9	+	1.09538e10i	0.173284	+	0.533313i
$885$	5.26746e6	−	3.82703e6i	0.000255446	−	0.000185593i
$886$	3.96419e10	−	2.88015e10i	1.91486	−	1.39123i
$887$	1.22976e9	+	3.78480e9i	0.0591679	+	0.182100i	0.976272	−	0.216548i	$-0.0694796\pi$
$887$	1.22976e9	+	3.78480e9i	0.0591679	+	0.182100i	−0.917104	+	0.398648i	$0.869480\pi$
$888$	−3.80064e9	+	1.16972e10i	−0.182143	+	0.560577i
$889$	6.87488e8	+	4.99490e8i	0.0328178	+	0.0238435i
$890$	−6.12634e7			−0.00291297
$891$	−6.45040e8	−	2.25559e9i	−0.0305503	−	0.106829i
$892$	4.29420e10			2.02584
$893$	7.13149e8	+	5.18133e8i	0.0335120	+	0.0243479i
$894$	1.95540e9	−	6.01810e9i	0.0915281	−	0.281694i
$895$	−6.90206e6	−	2.12424e7i	−0.000321809	−	0.000990427i
$896$	−2.76035e10	+	2.00551e10i	−1.28199	+	0.931423i
$897$	−9.79396e9	+	7.11573e9i	−0.453090	+	0.329189i
$898$	1.00431e9	+	3.09094e9i	0.0462806	+	0.142437i
$899$	−1.61699e9	+	4.97659e9i	−0.0742248	+	0.228440i
$900$	1.08647e10	+	7.89368e9i	0.496787	+	0.360937i
$901$	−1.74123e10			−0.793086
$902$	−3.75148e10	+	2.52651e10i	−1.70208	+	1.14630i
$903$	−1.22767e10			−0.554847
$904$	3.71231e10	+	2.69715e10i	1.67130	+	1.21427i
$905$	−915803.	+	2.81855e6i	−4.10707e−5	+	0.000126403i
$906$	1.31945e9	+	4.06086e9i	0.0589448	+	0.181413i
$907$	−3.63518e9	+	2.64111e9i	−0.161771	+	0.117533i	−0.665725	−	0.746197i	$-0.731878\pi$
$907$	−3.63518e9	+	2.64111e9i	−0.161771	+	0.117533i	0.503955	+	0.863730i	$0.331878\pi$
$908$	4.05097e10	−	2.94320e10i	1.79580	−	1.30473i
$909$	−3.51439e9	−	1.08162e10i	−0.155194	−	0.477639i
$910$	−5.59906e6	+	1.72321e7i	−0.000246303	+	0.000758044i
$911$	2.94627e10	+	2.14059e10i	1.29110	+	0.938037i	0.999827	−	0.0186045i	$-0.00592234\pi$
$911$	2.94627e10	+	2.14059e10i	1.29110	+	0.938037i	0.291270	+	0.956641i	$0.405922\pi$
$912$	−3.61027e9			−0.157600
$913$	−2.26181e10	+	1.52327e10i	−0.983578	+	0.662413i
$914$	−2.82013e9			−0.122168
$915$	−1.45820e7	−	1.05945e7i	−0.000629280	−	0.000457199i
$916$	−2.16944e10	+	6.67687e10i	−0.932641	+	2.87037i
$917$	5.40768e9	+	1.66431e10i	0.231589	+	0.712758i
$918$	3.11317e9	−	2.26185e9i	0.132817	−	0.0964971i
$919$	3.42606e10	−	2.48918e10i	1.45610	−	1.05792i	0.471739	−	0.881738i	$-0.343627\pi$
$919$	3.42606e10	−	2.48918e10i	1.45610	−	1.05792i	0.984358	−	0.176178i	$-0.0563734\pi$
$920$	1.51874e7	+	4.67419e7i	0.000643021	+	0.00197902i
$921$	1.76262e9	−	5.42478e9i	0.0743446	−	0.228809i
$922$	−4.42387e10	−	3.21413e10i	−1.85885	−	1.35053i
$923$	−2.88145e8			−0.0120616
$924$	6.06378e9	+	2.12039e10i	0.252867	+	0.884228i
$925$	1.73081e10			0.719042
$926$	3.63225e10	+	2.63898e10i	1.50327	+	1.09219i
$927$	2.16581e9	−	6.66568e9i	0.0892980	−	0.274831i
$928$	3.24604e9	+	9.99029e9i	0.133333	+	0.410355i
$929$	−1.16834e10	+	8.48852e9i	−0.478097	+	0.347358i	−0.800588	−	0.599215i	$-0.795480\pi$
$929$	−1.16834e10	+	8.48852e9i	−0.478097	+	0.347358i	0.322492	+	0.946572i	$0.395480\pi$
$930$	−4.79003e6	+	3.48016e6i	−0.000195276	+	0.000141876i
$931$	−9.50252e8	−	2.92457e9i	−0.0385936	−	0.118779i
$932$	1.75712e8	−	5.40787e8i	0.00710963	−	0.0218812i
$933$	1.15937e10	+	8.42335e9i	0.467346	+	0.339546i
$934$	−6.47038e10			−2.59846
$935$	−3.93916e6	+	1.07988e7i	−0.000157602	+	0.000432051i
$936$	7.14282e9			0.284711
$937$	−1.48937e10	−	1.08209e10i	−0.591443	−	0.429708i	0.251388	−	0.967886i	$-0.419113\pi$
$937$	−1.48937e10	−	1.08209e10i	−0.591443	−	0.429708i	−0.842831	+	0.538178i	$0.819113\pi$
$938$	1.57024e10	−	4.83270e10i	0.621236	−	1.91197i
$939$	−4.18597e8	−	1.28831e9i	−0.0164993	−	0.0507798i
$940$	−2.88665e6	+	2.09727e6i	−0.000113356	+	8.23583e-5i
$941$	−1.67819e10	+	1.21927e10i	−0.656563	+	0.477021i	−0.865501	−	0.500908i	$-0.833000\pi$
$941$	−1.67819e10	+	1.21927e10i	−0.656563	+	0.477021i	0.208937	+	0.977929i	$0.433000\pi$
$942$	−1.36541e10	−	4.20230e10i	−0.532212	−	1.63798i
$943$	1.56185e10	−	4.80689e10i	0.606526	−	1.86670i
$944$	6.93860e9	+	5.04119e9i	0.268454	+	0.195043i
$945$	3.92374e6			0.000151248
$946$	−3.84245e10	−	3.00647e10i	−1.47567	−	1.15462i
$947$	−2.37611e10			−0.909162			−0.454581	−	0.890705i	$-0.650211\pi$
$947$	−2.37611e10			−0.909162			−0.454581	+	0.890705i	$0.650211\pi$
$948$	1.94316e10	+	1.41179e10i	0.740764	+	0.538196i
$949$	2.70730e9	−	8.33221e9i	0.102826	−	0.316467i
$950$	6.81458e9	+	2.09731e10i	0.257873	+	0.793653i
$951$	9.41758e9	−	6.84227e9i	0.355065	−	0.257970i
$952$	−1.33793e10	+	9.72065e9i	−0.502580	+	0.365146i
$953$	9.62752e9	+	2.96304e10i	0.360321	+	1.10895i	0.952860	+	0.303411i	$0.0981255\pi$
$953$	9.62752e9	+	2.96304e10i	0.360321	+	1.10895i	−0.592539	+	0.805542i	$0.701874\pi$
$954$	−7.29921e9	+	2.24646e10i	−0.272180	+	0.837684i
$955$	9.21178e6	+	6.69275e6i	0.000342241	+	0.000248652i
$956$	−1.54697e9			−0.0572636
$957$	1.37724e10	+	4.90768e8i	0.507945	+	0.0181002i
$958$	−7.63061e10			−2.80401
$959$	8.04398e9	+	5.84430e9i	0.294514	+	0.213977i
$960$	−6.12423e6	+	1.88484e7i	−0.000223410	+	0.000687585i
$961$	−7.86895e9	−	2.42182e10i	−0.286013	−	0.880256i
$962$	1.62908e10	−	1.18359e10i	0.589969	−	0.428638i
$963$	−1.43872e10	+	1.04529e10i	−0.519139	+	0.377177i
$964$	−2.29310e10	−	7.05743e10i	−0.824428	−	2.53733i
$965$	−6.26603e6	+	1.92849e7i	−0.000224464	+	0.000690829i
$966$	−3.07611e10	−	2.23492e10i	−1.09795	−	0.797705i
$967$	3.51839e9			0.125127			0.0625636	−	0.998041i	$-0.480072\pi$
$967$	3.51839e9			0.125127			0.0625636	+	0.998041i	$0.480072\pi$
$968$	−1.50627e10	+	3.71291e10i	−0.533752	+	1.31568i
$969$	4.09564e9			0.144607
$970$	3.98495e7	+	2.89524e7i	0.00140192	+	0.00101855i
$971$	4.96374e9	−	1.52768e10i	0.173997	−	0.535507i	−0.825589	−	0.564271i	$-0.809157\pi$
$971$	4.96374e9	−	1.52768e10i	0.173997	−	0.535507i	0.999586	+	0.0287641i	$0.00915718\pi$
$972$	−1.04555e9	−	3.21787e9i	−0.0365185	−	0.112392i
$973$	−2.21433e10	+	1.60880e10i	−0.770632	+	0.559897i
$974$	1.25212e10	−	9.09715e9i	0.434198	−	0.315464i
$975$	−3.10619e9	−	9.55987e9i	−0.107328	−	0.330321i
$976$	7.33691e9	−	2.25807e10i	0.252603	−	0.777433i
$977$	3.43718e10	+	2.49726e10i	1.17916	+	0.856708i	0.992076	−	0.125637i	$-0.0400974\pi$
$977$	3.43718e10	+	2.49726e10i	1.17916	+	0.856708i	0.187081	+	0.982345i	$0.440097\pi$
$978$	2.76441e10			0.944965
$979$	5.57780e10	+	1.98761e9i	1.89987	+	0.0677005i
$980$	1.24471e7			0.000422453
$981$	1.49254e10	+	1.08440e10i	0.504761	+	0.366730i
$982$	−2.00215e10	+	6.16198e10i	−0.674693	+	2.07649i
$983$	1.18674e9	+	3.65241e9i	0.0398490	+	0.122643i	0.969002	−	0.247053i	$-0.0794621\pi$
$983$	1.18674e9	+	3.65241e9i	0.0398490	+	0.122643i	−0.929153	+	0.369695i	$0.879462\pi$
$984$	−2.41260e10	+	1.75286e10i	−0.807239	+	0.586494i
$985$	3.08268e6	−	2.23970e6i	0.000102778	−	7.46728e-5i
$986$	6.98525e9	+	2.14984e10i	0.232067	+	0.714228i
$987$	3.89975e8	−	1.20022e9i	0.0129100	−	0.0397330i
$988$	1.34533e10	+	9.77441e9i	0.443793	+	0.322434i
$989$	5.45202e10			1.79213
$990$	1.22809e7	+	9.60896e6i	0.000402259	+	0.000314741i
$991$	3.66875e10			1.19746			0.598730	−	0.800951i	$-0.295672\pi$
$991$	3.66875e10			1.19746			0.598730	+	0.800951i	$0.295672\pi$
$992$	3.32632e9	+	2.41671e9i	0.108186	+	0.0786021i
$993$	3.12445e8	−	9.61607e8i	0.0101263	−	0.0311656i
$994$	−2.79663e8	−	8.60716e8i	−0.00903199	−	0.0277976i
$995$	2.41370e7	−	1.75366e7i	0.000776788	−	0.000564370i
$996$	−3.18174e10	+	2.31167e10i	−1.02037	+	0.741341i
$997$	7.43096e9	+	2.28701e10i	0.237472	+	0.730863i	0.996784	+	0.0801362i	$0.0255355\pi$
$997$	7.43096e9	+	2.28701e10i	0.237472	+	0.730863i	−0.759312	+	0.650726i	$0.774464\pi$
$998$	8.28654e9	−	2.55034e10i	0.263886	−	0.812158i
$999$	−3.52785e9	−	2.56313e9i	−0.111952	−	0.0813376i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.8.e.a.4.7	✓	28
3.2	odd	2		99.8.f.c.37.1		28
11.3	even	5	inner	33.8.e.a.25.7	yes	28
11.5	even	5		363.8.a.q.1.3		14
11.6	odd	10		363.8.a.p.1.12		14
33.14	odd	10		99.8.f.c.91.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.8.e.a.4.7	✓	28	1.1	even	1	trivial
33.8.e.a.25.7	yes	28	11.3	even	5	inner
99.8.f.c.37.1		28	3.2	odd	2
99.8.f.c.91.1		28	33.14	odd	10
363.8.a.p.1.12		14	11.6	odd	10
363.8.a.q.1.3		14	11.5	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	33.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(15.4308 + 11.2111i) q^{2} +(-8.34346 + 25.6785i) q^{3} +(72.8662 + 224.259i) q^{4} +(0.205524 - 0.149322i) q^{5} +(-416.632 + 302.701i) q^{6} +(242.486 + 746.295i) q^{7} +(-635.379 + 1955.49i) q^{8} +(-589.773 - 428.495i) q^{9} +O(q^{10})\)	\(q+(15.4308 + 11.2111i) q^{2} +(-8.34346 + 25.6785i) q^{3} +(72.8662 + 224.259i) q^{4} +(0.205524 - 0.149322i) q^{5} +(-416.632 + 302.701i) q^{6} +(242.486 + 746.295i) q^{7} +(-635.379 + 1955.49i) q^{8} +(-589.773 - 428.495i) q^{9} +4.84548 q^{10} +(-4411.63 - 157.205i) q^{11} -6366.60 q^{12} +(3855.23 + 2800.99i) q^{13} +(-4625.06 + 14234.5i) q^{14} +(2.11959 + 6.52342i) q^{15} +(-7309.67 + 5310.78i) q^{16} +(8292.40 - 6024.78i) q^{17} +(-4296.76 - 13224.1i) q^{18} +(4573.18 - 14074.8i) q^{19} +(48.4626 + 35.2102i) q^{20} -21186.9 q^{21} +(-66312.6 - 51885.2i) q^{22} +94090.2 q^{23} +(-44913.0 - 32631.2i) q^{24} +(-24141.9 + 74301.2i) q^{25} +(28087.0 + 86443.0i) q^{26} +(15923.9 - 11569.4i) q^{27} +(-149694. + 108759. i) q^{28} +(35729.6 + 109964. i) q^{29} +(-40.4281 + 124.425i) q^{30} +(36613.2 + 26601.0i) q^{31} +90850.3 q^{32} +(40845.0 - 111972. i) q^{33} +195503. q^{34} +(161.275 + 117.173i) q^{35} +(53119.5 - 163485. i) q^{36} +(-68461.0 - 210701. i) q^{37} +(228362. - 165915. i) q^{38} +(-104091. + 75626.6i) q^{39} +(161.413 + 496.778i) q^{40} +(165995. - 510881. i) q^{41} +(-326931. - 237530. i) q^{42} +579446. q^{43} +(-286204. - 1.00080e6i) q^{44} -185.197 q^{45} +(1.45189e6 + 1.05486e6i) q^{46} +(-18406.4 + 56649.1i) q^{47} +(-75385.2 - 232012. i) q^{48} +(168104. - 122135. i) q^{49} +(-1.20553e6 + 875870. i) q^{50} +(85520.2 + 263204. i) q^{51} +(-347231. + 1.06867e6i) q^{52} +(-1.37433e6 - 998512. i) q^{53} +375425. q^{54} +(-930.171 + 626.444i) q^{55} -1.61344e6 q^{56} +(323264. + 234865. i) q^{57} +(-681490. + 2.09741e6i) q^{58} +(-293330. - 902777. i) q^{59} +(-1308.49 + 950.674i) q^{60} +(-2.12593e6 + 1.54458e6i) q^{61} +(266743. + 820952. i) q^{62} +(176772. - 544049. i) q^{63} +(2.33753e6 + 1.69832e6i) q^{64} +1210.59 q^{65} +(1.88561e6 - 1.26991e6i) q^{66} -3.39507e6 q^{67} +(1.95535e6 + 1.42064e6i) q^{68} +(-785038. + 2.41610e6i) q^{69} +(1174.96 + 3616.16i) q^{70} +(-48918.8 + 35541.6i) q^{71} +(1.21265e6 - 881042. i) q^{72} +(-568125. - 1.74851e6i) q^{73} +(1.30579e6 - 4.01882e6i) q^{74} +(-1.70652e6 - 1.23986e6i) q^{75} +3.48963e6 q^{76} +(-952436. - 3.33049e6i) q^{77} -2.45407e6 q^{78} +(-3.05212e6 - 2.21749e6i) q^{79} +(-709.296 + 2182.99i) q^{80} +(164224. + 505430. i) q^{81} +(8.28901e6 - 6.02232e6i) q^{82} +(4.99755e6 - 3.63093e6i) q^{83} +(-1.54381e6 - 4.75136e6i) q^{84} +(804.656 - 2476.48i) q^{85} +(8.94132e6 + 6.49625e6i) q^{86} -3.12183e6 q^{87} +(3.11047e6 - 8.52703e6i) q^{88} -1.26434e7 q^{89} +(-2857.74 - 2076.27i) q^{90} +(-1.15552e6 + 3.55633e6i) q^{91} +(6.85600e6 + 2.11006e7i) q^{92} +(-988556. + 718228. i) q^{93} +(-919128. + 667785. i) q^{94} +(-1161.78 - 3575.59i) q^{95} +(-758005. + 2.33290e6i) q^{96} +(8.22406e6 + 5.97513e6i) q^{97} +3.96325e6 q^{98} +(2.53450e6 + 1.98308e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 22 q^{2} + 189 q^{3} - 692 q^{4} - 777 q^{5} + 594 q^{6} - 83 q^{7} + 3568 q^{8} - 5103 q^{9}+O(q^{10}) \) 28 * q - 22 * q^2 + 189 * q^3 - 692 * q^4 - 777 * q^5 + 594 * q^6 - 83 * q^7 + 3568 * q^8 - 5103 * q^9	\( 28 q - 22 q^{2} + 189 q^{3} - 692 q^{4} - 777 q^{5} + 594 q^{6} - 83 q^{7} + 3568 q^{8} - 5103 q^{9} - 1352 q^{10} - 18851 q^{11} - 60966 q^{12} + 14635 q^{13} + 62912 q^{14} - 22896 q^{15} - 36148 q^{16} - 10338 q^{17} + 9477 q^{18} + 90342 q^{19} - 289719 q^{20} + 28836 q^{21} - 202339 q^{22} + 138508 q^{23} + 187704 q^{24} - 174068 q^{25} + 466130 q^{26} + 137781 q^{27} - 640233 q^{28} - 487290 q^{29} - 372546 q^{30} - 388352 q^{31} + 2726322 q^{32} - 265923 q^{33} - 1543708 q^{34} + 742659 q^{35} - 504468 q^{36} + 670209 q^{37} + 2282072 q^{38} - 395145 q^{39} + 4641741 q^{40} - 2721357 q^{41} + 620676 q^{42} - 199784 q^{43} - 5887437 q^{44} - 103518 q^{45} + 3389447 q^{46} + 2112053 q^{47} + 2292111 q^{48} + 3927748 q^{49} - 3663090 q^{50} + 615681 q^{51} - 4343053 q^{52} - 1743854 q^{53} - 354294 q^{54} - 8387710 q^{55} - 6307818 q^{56} + 1223721 q^{57} + 546605 q^{58} - 218820 q^{59} + 7822413 q^{60} - 743157 q^{61} + 3996183 q^{62} - 60507 q^{63} - 21725666 q^{64} + 4895794 q^{65} - 8684037 q^{66} - 3235686 q^{67} + 961671 q^{68} + 4712499 q^{69} + 31155916 q^{70} + 9848757 q^{71} - 5068008 q^{72} - 6667768 q^{73} - 31115192 q^{74} - 2544939 q^{75} - 6535748 q^{76} + 8320585 q^{77} + 20060730 q^{78} - 10121851 q^{79} + 44592526 q^{80} - 3720087 q^{81} + 24927115 q^{82} + 13288897 q^{83} - 17477019 q^{84} - 28050005 q^{85} + 20937351 q^{86} - 22226400 q^{87} + 39687014 q^{88} - 40241460 q^{89} - 9565938 q^{90} + 8733043 q^{91} + 11607651 q^{92} + 10485504 q^{93} - 7877385 q^{94} + 14371097 q^{95} + 2790126 q^{96} + 30518151 q^{97} - 16954218 q^{98} + 11659626 q^{99}+O(q^{100}) \) 28 * q - 22 * q^2 + 189 * q^3 - 692 * q^4 - 777 * q^5 + 594 * q^6 - 83 * q^7 + 3568 * q^8 - 5103 * q^9 - 1352 * q^10 - 18851 * q^11 - 60966 * q^12 + 14635 * q^13 + 62912 * q^14 - 22896 * q^15 - 36148 * q^16 - 10338 * q^17 + 9477 * q^18 + 90342 * q^19 - 289719 * q^20 + 28836 * q^21 - 202339 * q^22 + 138508 * q^23 + 187704 * q^24 - 174068 * q^25 + 466130 * q^26 + 137781 * q^27 - 640233 * q^28 - 487290 * q^29 - 372546 * q^30 - 388352 * q^31 + 2726322 * q^32 - 265923 * q^33 - 1543708 * q^34 + 742659 * q^35 - 504468 * q^36 + 670209 * q^37 + 2282072 * q^38 - 395145 * q^39 + 4641741 * q^40 - 2721357 * q^41 + 620676 * q^42 - 199784 * q^43 - 5887437 * q^44 - 103518 * q^45 + 3389447 * q^46 + 2112053 * q^47 + 2292111 * q^48 + 3927748 * q^49 - 3663090 * q^50 + 615681 * q^51 - 4343053 * q^52 - 1743854 * q^53 - 354294 * q^54 - 8387710 * q^55 - 6307818 * q^56 + 1223721 * q^57 + 546605 * q^58 - 218820 * q^59 + 7822413 * q^60 - 743157 * q^61 + 3996183 * q^62 - 60507 * q^63 - 21725666 * q^64 + 4895794 * q^65 - 8684037 * q^66 - 3235686 * q^67 + 961671 * q^68 + 4712499 * q^69 + 31155916 * q^70 + 9848757 * q^71 - 5068008 * q^72 - 6667768 * q^73 - 31115192 * q^74 - 2544939 * q^75 - 6535748 * q^76 + 8320585 * q^77 + 20060730 * q^78 - 10121851 * q^79 + 44592526 * q^80 - 3720087 * q^81 + 24927115 * q^82 + 13288897 * q^83 - 17477019 * q^84 - 28050005 * q^85 + 20937351 * q^86 - 22226400 * q^87 + 39687014 * q^88 - 40241460 * q^89 - 9565938 * q^90 + 8733043 * q^91 + 11607651 * q^92 + 10485504 * q^93 - 7877385 * q^94 + 14371097 * q^95 + 2790126 * q^96 + 30518151 * q^97 - 16954218 * q^98 + 11659626 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more