LMFDB - Embedded newform 150.6.g.c.91.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,6,Mod(31,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("150.31");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	150.g (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:	$24.0575729719$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.1
Character	$\chi$	$=$	150.91
Dual form			150.6.g.c.61.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.23607 + 2.35114i) q^{2} +(2.78115 + 8.55951i) q^{3} +(4.94427 + 15.2169i) q^{4} +(-41.7488 - 37.1757i) q^{5} +(-11.1246 + 34.2380i) q^{6} -164.912 q^{7} +(-19.7771 + 60.8676i) q^{8} +(-65.5304 + 47.6106i) q^{9} +O(q^{10})$	\(q+(3.23607 + 2.35114i) q^{2} +(2.78115 + 8.55951i) q^{3} +(4.94427 + 15.2169i) q^{4} +(-41.7488 - 37.1757i) q^{5} +(-11.1246 + 34.2380i) q^{6} -164.912 q^{7} +(-19.7771 + 60.8676i) q^{8} +(-65.5304 + 47.6106i) q^{9} +(-47.6968 - 218.461i) q^{10} +(213.032 + 154.777i) q^{11} +(-116.498 + 84.6411i) q^{12} +(689.248 - 500.768i) q^{13} +(-533.668 - 387.732i) q^{14} +(202.096 - 460.741i) q^{15} +(-207.108 + 150.473i) q^{16} +(334.923 - 1030.79i) q^{17} -324.000 q^{18} +(758.991 - 2335.94i) q^{19} +(359.282 - 819.095i) q^{20} +(-458.647 - 1411.57i) q^{21} +(325.484 + 1001.74i) q^{22} +(-877.198 - 637.322i) q^{23} -576.000 q^{24} +(360.932 + 3104.09i) q^{25} +3407.83 q^{26} +(-589.773 - 428.495i) q^{27} +(-815.372 - 2509.46i) q^{28} +(-2261.89 - 6961.39i) q^{29} +(1737.26 - 1015.83i) q^{30} +(-885.284 + 2724.62i) q^{31} -1024.00 q^{32} +(-732.340 + 2253.91i) q^{33} +(3507.36 - 2548.25i) q^{34} +(6884.90 + 6130.74i) q^{35} +(-1048.49 - 761.770i) q^{36} +(1264.90 - 919.004i) q^{37} +(7948.26 - 5774.75i) q^{38} +(6203.23 + 4506.91i) q^{39} +(3088.47 - 1805.93i) q^{40} +(10259.2 - 7453.76i) q^{41} +(1834.59 - 5646.28i) q^{42} -20890.5 q^{43} +(-1301.94 + 4006.95i) q^{44} +(4505.78 + 448.451i) q^{45} +(-1340.24 - 4124.83i) q^{46} +(-2194.21 - 6753.09i) q^{47} +(-1863.98 - 1354.26i) q^{48} +10389.1 q^{49} +(-6130.14 + 10893.6i) q^{50} +9754.51 q^{51} +(11028.0 + 8012.29i) q^{52} +(396.608 + 1220.63i) q^{53} +(-901.094 - 2773.28i) q^{54} +(-3139.90 - 14381.4i) q^{55} +(3261.49 - 10037.8i) q^{56} +22105.3 q^{57} +(9047.57 - 27845.6i) q^{58} +(-23044.4 + 16742.8i) q^{59} +(8010.27 + 797.246i) q^{60} +(-26406.3 - 19185.3i) q^{61} +(-9270.82 + 6735.64i) q^{62} +(10806.8 - 7851.58i) q^{63} +(-3313.73 - 2407.57i) q^{64} +(-47391.7 - 4716.80i) q^{65} +(-7669.16 + 5571.97i) q^{66} +(11658.9 - 35882.5i) q^{67} +17341.3 q^{68} +(3015.54 - 9280.88i) q^{69} +(7865.79 + 36026.9i) q^{70} +(10343.4 + 31833.6i) q^{71} +(-1601.94 - 4930.28i) q^{72} +(39112.1 + 28416.6i) q^{73} +6254.01 q^{74} +(-25565.6 + 11722.3i) q^{75} +39298.4 q^{76} +(-35131.7 - 25524.6i) q^{77} +(9477.70 + 29169.3i) q^{78} +(-10306.6 - 31720.5i) q^{79} +(14240.5 + 1417.33i) q^{80} +(2027.46 - 6239.88i) q^{81} +50724.4 q^{82} +(-4076.78 + 12547.1i) q^{83} +(19212.0 - 13958.4i) q^{84} +(-52302.9 + 30583.2i) q^{85} +(-67603.0 - 49116.5i) q^{86} +(53295.4 - 38721.4i) q^{87} +(-13634.1 + 9905.73i) q^{88} +(101880. + 74020.2i) q^{89} +(13526.6 + 12044.9i) q^{90} +(-113666. + 82582.9i) q^{91} +(5360.96 - 16499.3i) q^{92} -25783.6 q^{93} +(8776.85 - 27012.4i) q^{94} +(-118527. + 69306.6i) q^{95} +(-2847.90 - 8764.94i) q^{96} +(-41309.4 - 127137. i) q^{97} +(33619.9 + 24426.3i) q^{98} -21329.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{2} - 54 q^{3} - 96 q^{4} + 80 q^{5} + 216 q^{6} - 454 q^{7} + 384 q^{8} - 486 q^{9}+O(q^{10}) $ 24 * q + 24 * q^2 - 54 * q^3 - 96 * q^4 + 80 * q^5 + 216 * q^6 - 454 * q^7 + 384 * q^8 - 486 * q^9	\( 24 q + 24 q^{2} - 54 q^{3} - 96 q^{4} + 80 q^{5} + 216 q^{6} - 454 q^{7} + 384 q^{8} - 486 q^{9} + 120 q^{10} + 125 q^{11} - 864 q^{12} - 578 q^{13} - 344 q^{14} + 855 q^{15} - 1536 q^{16} - 2664 q^{17} - 7776 q^{18} + 1424 q^{19} + 1520 q^{20} + 1269 q^{21} + 1280 q^{22} - 4810 q^{23} - 13824 q^{24} - 10880 q^{25} + 6392 q^{26} - 4374 q^{27} + 2256 q^{28} - 1554 q^{29} + 4320 q^{30} - 24513 q^{31} - 24576 q^{32} - 2880 q^{33} - 4004 q^{34} + 15310 q^{35} - 7776 q^{36} - 28123 q^{37} + 8384 q^{38} - 5202 q^{39} + 7680 q^{40} - 17914 q^{41} - 5076 q^{42} + 1256 q^{43} - 5120 q^{44} - 2025 q^{45} - 13040 q^{46} + 930 q^{47} - 13824 q^{48} + 24606 q^{49} - 7880 q^{50} + 29934 q^{51} - 9248 q^{52} - 49701 q^{53} + 17496 q^{54} - 99060 q^{55} - 9024 q^{56} + 12096 q^{57} + 6216 q^{58} - 14465 q^{59} - 3600 q^{60} - 52750 q^{61} - 72528 q^{62} + 6966 q^{63} - 24576 q^{64} - 34885 q^{65} - 4500 q^{66} + 199846 q^{67} + 53216 q^{68} + 29340 q^{69} + 116820 q^{70} - 42880 q^{71} + 31104 q^{72} + 35852 q^{73} + 21832 q^{74} - 28620 q^{75} + 21504 q^{76} - 114745 q^{77} - 49572 q^{78} - 236128 q^{79} - 6400 q^{80} - 39366 q^{81} + 46216 q^{82} - 97273 q^{83} + 12384 q^{84} + 372975 q^{85} - 232304 q^{86} + 21609 q^{87} - 8000 q^{88} + 278147 q^{89} - 25920 q^{90} - 103052 q^{91} + 52160 q^{92} + 114858 q^{93} - 3720 q^{94} + 79590 q^{95} + 55296 q^{96} - 249803 q^{97} - 28164 q^{98} + 31590 q^{99}+O(q^{100}) \) 24 * q + 24 * q^2 - 54 * q^3 - 96 * q^4 + 80 * q^5 + 216 * q^6 - 454 * q^7 + 384 * q^8 - 486 * q^9 + 120 * q^10 + 125 * q^11 - 864 * q^12 - 578 * q^13 - 344 * q^14 + 855 * q^15 - 1536 * q^16 - 2664 * q^17 - 7776 * q^18 + 1424 * q^19 + 1520 * q^20 + 1269 * q^21 + 1280 * q^22 - 4810 * q^23 - 13824 * q^24 - 10880 * q^25 + 6392 * q^26 - 4374 * q^27 + 2256 * q^28 - 1554 * q^29 + 4320 * q^30 - 24513 * q^31 - 24576 * q^32 - 2880 * q^33 - 4004 * q^34 + 15310 * q^35 - 7776 * q^36 - 28123 * q^37 + 8384 * q^38 - 5202 * q^39 + 7680 * q^40 - 17914 * q^41 - 5076 * q^42 + 1256 * q^43 - 5120 * q^44 - 2025 * q^45 - 13040 * q^46 + 930 * q^47 - 13824 * q^48 + 24606 * q^49 - 7880 * q^50 + 29934 * q^51 - 9248 * q^52 - 49701 * q^53 + 17496 * q^54 - 99060 * q^55 - 9024 * q^56 + 12096 * q^57 + 6216 * q^58 - 14465 * q^59 - 3600 * q^60 - 52750 * q^61 - 72528 * q^62 + 6966 * q^63 - 24576 * q^64 - 34885 * q^65 - 4500 * q^66 + 199846 * q^67 + 53216 * q^68 + 29340 * q^69 + 116820 * q^70 - 42880 * q^71 + 31104 * q^72 + 35852 * q^73 + 21832 * q^74 - 28620 * q^75 + 21504 * q^76 - 114745 * q^77 - 49572 * q^78 - 236128 * q^79 - 6400 * q^80 - 39366 * q^81 + 46216 * q^82 - 97273 * q^83 + 12384 * q^84 + 372975 * q^85 - 232304 * q^86 + 21609 * q^87 - 8000 * q^88 + 278147 * q^89 - 25920 * q^90 - 103052 * q^91 + 52160 * q^92 + 114858 * q^93 - 3720 * q^94 + 79590 * q^95 + 55296 * q^96 - 249803 * q^97 - 28164 * q^98 + 31590 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	3.23607	+	2.35114i	0.572061	+	0.415627i
$2$	3.23607	+	2.35114i	0.572061	+	0.415627i
$3$	2.78115	+	8.55951i	0.178411	+	0.549093i
$3$	2.78115	+	8.55951i	0.178411	+	0.549093i
$4$	4.94427	+	15.2169i	0.154508	+	0.475528i
$5$	−41.7488	−	37.1757i	−0.746826	−	0.665019i
$5$	−41.7488	−	37.1757i	−0.746826	−	0.665019i
$6$	−11.1246	+	34.2380i	−0.126156	+	0.388267i
$7$	−164.912			−1.27206			−0.636031	−	0.771663i	$-0.719425\pi$
$7$	−164.912			−1.27206			−0.636031	+	0.771663i	$0.719425\pi$
$8$	−19.7771	+	60.8676i	−0.109254	+	0.336249i
$9$	−65.5304	+	47.6106i	−0.269672	+	0.195928i
$10$	−47.6968	−	218.461i	−0.150830	−	0.690833i
$11$	213.032	+	154.777i	0.530840	+	0.385678i	0.820672	−	0.571400i	$-0.193599\pi$
$11$	213.032	+	154.777i	0.530840	+	0.385678i	−0.289832	+	0.957078i	$0.593599\pi$
$12$	−116.498	+	84.6411i	−0.233543	+	0.169679i
$13$	689.248	−	500.768i	1.13114	−	0.821823i	0.145281	−	0.989390i	$-0.453591\pi$
$13$	689.248	−	500.768i	1.13114	−	0.821823i	0.985861	+	0.167568i	$0.0535912\pi$
$14$	−533.668	−	387.732i	−0.727698	−	0.528703i
$15$	202.096	−	460.741i	0.231915	−	0.528724i
$16$	−207.108	+	150.473i	−0.202254	+	0.146946i
$17$	334.923	−	1030.79i	0.281075	−	0.865061i	−0.706472	−	0.707741i	$-0.749714\pi$
$17$	334.923	−	1030.79i	0.281075	−	0.865061i	0.987548	−	0.157321i	$-0.0502856\pi$
$18$	−324.000			−0.235702
$19$	758.991	−	2335.94i	0.482340	−	1.48449i	−0.353458	−	0.935450i	$-0.614994\pi$
$19$	758.991	−	2335.94i	0.482340	−	1.48449i	0.835797	−	0.549038i	$-0.185006\pi$
$20$	359.282	−	819.095i	0.200845	−	0.457888i
$21$	−458.647	−	1411.57i	−0.226950	−	0.698480i
$22$	325.484	+	1001.74i	0.143375	+	0.441263i
$23$	−877.198	−	637.322i	−0.345763	−	0.251211i	0.401327	−	0.915935i	$-0.368549\pi$
$23$	−877.198	−	637.322i	−0.345763	−	0.251211i	−0.747089	+	0.664724i	$0.768549\pi$
$24$	−576.000			−0.204124
$25$	360.932	+	3104.09i	0.115498	+	0.993308i
$26$	3407.83			0.988654
$27$	−589.773	−	428.495i	−0.155695	−	0.113119i
$28$	−815.372	−	2509.46i	−0.196544	−	0.604902i
$29$	−2261.89	−	6961.39i	−0.499433	−	1.53710i	−0.809933	−	0.586523i	$-0.800496\pi$
$29$	−2261.89	−	6961.39i	−0.499433	−	1.53710i	0.310500	−	0.950574i	$-0.399504\pi$
$30$	1737.26	−	1015.83i	0.352422	−	0.206072i
$31$	−885.284	+	2724.62i	−0.165454	+	0.509216i	−0.999069	−	0.0431294i	$-0.986267\pi$
$31$	−885.284	+	2724.62i	−0.165454	+	0.509216i	0.833615	+	0.552346i	$0.186267\pi$
$32$	−1024.00			−0.176777
$33$	−732.340	+	2253.91i	−0.117065	+	0.360289i
$34$	3507.36	−	2548.25i	0.520335	−	0.378046i
$35$	6884.90	+	6130.74i	0.950009	+	0.845946i
$36$	−1048.49	−	761.770i	−0.134836	−	0.0979642i
$37$	1264.90	−	919.004i	0.151898	−	0.110360i	−0.509240	−	0.860624i	$-0.670074\pi$
$37$	1264.90	−	919.004i	0.151898	−	0.110360i	0.661138	+	0.750264i	$0.270074\pi$
$38$	7948.26	−	5774.75i	0.892921	−	0.648745i
$39$	6203.23	+	4506.91i	0.653065	+	0.474480i
$40$	3088.47	−	1805.93i	0.305206	−	0.178464i
$41$	10259.2	−	7453.76i	0.953136	−	0.692494i	0.00158963	−	0.999999i	$-0.499494\pi$
$41$	10259.2	−	7453.76i	0.953136	−	0.692494i	0.951547	+	0.307505i	$0.0994940\pi$
$42$	1834.59	−	5646.28i	0.160478	−	0.493900i
$43$	−20890.5			−1.72297			−0.861485	−	0.507784i	$-0.830465\pi$
$43$	−20890.5			−1.72297			−0.861485	+	0.507784i	$0.830465\pi$
$44$	−1301.94	+	4006.95i	−0.101381	+	0.312020i
$45$	4505.78	+	448.451i	0.331695	+	0.0330129i
$46$	−1340.24	−	4124.83i	−0.0933873	−	0.287417i
$47$	−2194.21	−	6753.09i	−0.144888	−	0.445921i	0.852108	−	0.523366i	$-0.175324\pi$
$47$	−2194.21	−	6753.09i	−0.144888	−	0.445921i	−0.996997	+	0.0774448i	$0.975324\pi$
$48$	−1863.98	−	1354.26i	−0.116772	−	0.0848395i
$49$	10389.1			0.618142
$50$	−6130.14	+	10893.6i	−0.346773	+	0.616237i
$51$	9754.51			0.525146
$52$	11028.0	+	8012.29i	0.565571	+	0.410911i
$53$	396.608	+	1220.63i	0.0193942	+	0.0596892i	0.960285	−	0.279020i	$-0.0900096\pi$
$53$	396.608	+	1220.63i	0.0193942	+	0.0596892i	−0.940891	+	0.338709i	$0.890010\pi$
$54$	−901.094	−	2773.28i	−0.0420519	−	0.129422i
$55$	−3139.90	−	14381.4i	−0.139962	−	0.641053i
$56$	3261.49	−	10037.8i	0.138978	−	0.427730i
$57$	22105.3			0.901177
$58$	9047.57	−	27845.6i	0.353152	−	1.08689i
$59$	−23044.4	+	16742.8i	−0.861858	+	0.626177i	−0.928390	−	0.371608i	$-0.878807\pi$
$59$	−23044.4	+	16742.8i	−0.861858	+	0.626177i	0.0665317	+	0.997784i	$0.478807\pi$
$60$	8010.27	+	797.246i	0.287256	+	0.0285900i
$61$	−26406.3	−	19185.3i	−0.908621	−	0.660152i	0.0320445	−	0.999486i	$-0.489798\pi$
$61$	−26406.3	−	19185.3i	−0.908621	−	0.660152i	−0.940666	+	0.339334i	$0.889798\pi$
$62$	−9270.82	+	6735.64i	−0.306294	+	0.222536i
$63$	10806.8	−	7851.58i	0.343040	−	0.249233i
$64$	−3313.73	−	2407.57i	−0.101127	−	0.0734732i
$65$	−47391.7	−	4716.80i	−1.39129	−	0.138473i
$66$	−7669.16	+	5571.97i	−0.216714	+	0.157452i
$67$	11658.9	−	35882.5i	0.317301	−	0.976553i	−0.657496	−	0.753458i	$-0.728384\pi$
$67$	11658.9	−	35882.5i	0.317301	−	0.976553i	0.974797	−	0.223094i	$-0.0716158\pi$
$68$	17341.3			0.454790
$69$	3015.54	−	9280.88i	0.0762504	−	0.234675i
$70$	7865.79	+	36026.9i	0.191866	+	0.878783i
$71$	10343.4	+	31833.6i	0.243510	+	0.749446i	0.995878	+	0.0907032i	$0.0289115\pi$
$71$	10343.4	+	31833.6i	0.243510	+	0.749446i	−0.752368	+	0.658743i	$0.771089\pi$
$72$	−1601.94	−	4930.28i	−0.0364180	−	0.112083i
$73$	39112.1	+	28416.6i	0.859021	+	0.624115i	0.927618	−	0.373529i	$-0.121853\pi$
$73$	39112.1	+	28416.6i	0.859021	+	0.624115i	−0.0685978	+	0.997644i	$0.521853\pi$
$74$	6254.01			0.132764
$75$	−25565.6	+	11722.3i	−0.524812	+	0.240636i
$76$	39298.4			0.780442
$77$	−35131.7	−	25524.6i	−0.675261	−	0.490606i
$78$	9477.70	+	29169.3i	0.176387	+	0.542863i
$79$	−10306.6	−	31720.5i	−0.185801	−	0.571837i	0.814160	−	0.580640i	$-0.197198\pi$
$79$	−10306.6	−	31720.5i	−0.185801	−	0.571837i	−0.999961	+	0.00880363i	$0.997198\pi$
$80$	14240.5	+	1417.33i	0.248771	+	0.0247597i
$81$	2027.46	−	6239.88i	0.0343352	−	0.105673i
$82$	50724.4			0.833072
$83$	−4076.78	+	12547.1i	−0.0649565	+	0.199916i	−0.978267	−	0.207348i	$-0.933517\pi$
$83$	−4076.78	+	12547.1i	−0.0649565	+	0.199916i	0.913311	+	0.407263i	$0.133517\pi$
$84$	19212.0	−	13958.4i	0.297081	−	0.215842i
$85$	−52302.9	+	30583.2i	−0.785197	+	0.459130i
$86$	−67603.0	−	49116.5i	−0.985644	−	0.716112i
$87$	53295.4	−	38721.4i	0.754904	−	0.548470i
$88$	−13634.1	+	9905.73i	−0.187680	+	0.136358i
$89$	101880.	+	74020.2i	1.36337	+	0.990548i	0.998222	+	0.0595987i	$0.0189821\pi$
$89$	101880.	+	74020.2i	1.36337	+	0.990548i	0.365149	+	0.930949i	$0.381018\pi$
$90$	13526.6	+	12044.9i	0.176029	+	0.156747i
$91$	−113666.	+	82582.9i	−1.43888	+	1.04541i
$92$	5360.96	−	16499.3i	0.0660348	−	0.203234i
$93$	−25783.6			−0.309126
$94$	8776.85	−	27012.4i	0.102452	−	0.315314i
$95$	−118527.	+	69306.6i	−1.34744	+	0.787890i
$96$	−2847.90	−	8764.94i	−0.0315389	−	0.0970668i
$97$	−41309.4	−	127137.i	−0.445779	−	1.37197i	−0.881628	−	0.471946i	$-0.843552\pi$
$97$	−41309.4	−	127137.i	−0.445779	−	1.37197i	0.435849	−	0.900020i	$-0.356448\pi$
$98$	33619.9	+	24426.3i	0.353615	+	0.256917i
$99$	−21329.1			−0.218718
$100$	−45450.0	+	20839.7i	−0.454500	+	0.208397i
$101$	149100.			1.45437			0.727183	−	0.686444i	$-0.240829\pi$
$101$	149100.			1.45437			0.727183	+	0.686444i	$0.240829\pi$
$102$	31566.3	+	22934.2i	0.300416	+	0.218265i
$103$	−27531.4	−	84733.1i	−0.255703	−	0.786973i	−0.993690	−	0.112158i	$-0.964224\pi$
$103$	−27531.4	−	84733.1i	−0.255703	−	0.786973i	0.737987	−	0.674815i	$-0.235776\pi$
$104$	16849.2	+	51856.6i	0.152756	+	0.470133i
$105$	−33328.1	+	75981.9i	−0.295011	+	0.672569i
$106$	−1586.43	+	4882.54i	−0.0137138	+	0.0422067i
$107$	−117266.			−0.990179			−0.495089	−	0.868842i	$-0.664865\pi$
$107$	−117266.			−0.990179			−0.495089	+	0.868842i	$0.664865\pi$
$108$	3604.37	−	11093.1i	0.0297352	−	0.0915155i
$109$	−121048.	+	87946.4i	−0.975867	+	0.709009i	−0.956781	−	0.290809i	$-0.906076\pi$
$109$	−121048.	+	87946.4i	−0.975867	+	0.709009i	−0.0190861	+	0.999818i	$0.506076\pi$
$110$	23651.7	−	53921.5i	0.186372	−	0.424894i
$111$	11384.1	+	8271.04i	0.0876984	+	0.0637166i
$112$	34154.7	−	24814.9i	0.257280	−	0.186925i
$113$	−14414.7	+	10472.9i	−0.106196	+	0.0771562i	−0.639616	−	0.768695i	$-0.720907\pi$
$113$	−14414.7	+	10472.9i	−0.106196	+	0.0771562i	0.533420	+	0.845851i	$0.320907\pi$
$114$	71534.4	+	51972.8i	0.515528	+	0.374553i
$115$	12929.1	+	59217.9i	0.0911642	+	0.417550i
$116$	94747.4	−	68838.0i	0.653766	−	0.474989i
$117$	−21324.8	+	65631.0i	−0.144019	+	0.443246i
$118$	−113938.			−0.753292
$119$	−55233.0	+	169990.i	−0.357546	+	1.10041i
$120$	24047.3	+	21413.2i	0.152445	+	0.135747i
$121$	−28340.7	−	87223.7i	−0.175973	−	0.541590i
$122$	−40345.2	−	124170.i	−0.245410	−	0.755295i
$123$	92333.0	+	67083.9i	0.550293	+	0.399812i
$124$	−45837.4			−0.267711
$125$	100328.	−	143010.i	0.574312	−	0.818637i
$126$	53431.6			0.299828
$127$	−193407.	−	140518.i	−1.06405	−	0.773079i	−0.0892177	−	0.996012i	$-0.528437\pi$
$127$	−193407.	−	140518.i	−1.06405	−	0.773079i	−0.974834	+	0.222934i	$0.928437\pi$
$128$	−5062.93	−	15582.1i	−0.0273135	−	0.0840623i
$129$	−58099.6	−	178812.i	−0.307397	−	0.946070i
$130$	−142273.	−	126689.i	−0.738353	−	0.657474i
$131$	−100847.	+	310376.i	−0.513435	+	1.58019i	0.272677	+	0.962106i	$0.412091\pi$
$131$	−100847.	+	310376.i	−0.513435	+	1.58019i	−0.786112	+	0.618084i	$0.787909\pi$
$132$	−37918.4			−0.189415
$133$	−125167.	+	385225.i	−0.613566	+	1.88836i
$134$	122094.	−	88706.4i	0.587397	−	0.426769i
$135$	8692.73	+	39814.4i	0.0410508	+	0.188021i
$136$	56117.8	+	40772.0i	0.260168	+	0.189023i
$137$	91186.0	−	66250.5i	0.415075	−	0.301570i	−0.360578	−	0.932729i	$-0.617421\pi$
$137$	91186.0	−	66250.5i	0.415075	−	0.301570i	0.775653	+	0.631159i	$0.217421\pi$
$138$	31579.1	−	22943.6i	0.141157	−	0.102557i
$139$	−9866.32	−	7168.30i	−0.0433130	−	0.0314687i	0.565918	−	0.824461i	$-0.308522\pi$
$139$	−9866.32	−	7168.30i	−0.0433130	−	0.0314687i	−0.609231	+	0.792993i	$0.708522\pi$
$140$	−59250.0	+	135079.i	−0.255487	+	0.582462i
$141$	51700.7	−	37562.7i	0.219002	−	0.159114i
$142$	−41373.5	+	127335.i	−0.172187	+	0.529938i
$143$	224339.			0.917414
$144$	6407.78	−	19721.1i	0.0257514	−	0.0792547i
$145$	−164363.	+	374718.i	−0.649210	+	1.48008i
$146$	59757.9	+	183916.i	0.232014	+	0.714064i
$147$	28893.7	+	88925.8i	0.110283	+	0.339418i
$148$	20238.4	+	14704.1i	0.0759490	+	0.0551802i
$149$	254222.			0.938096			0.469048	−	0.883173i	$-0.344597\pi$
$149$	254222.			0.938096			0.469048	+	0.883173i	$0.344597\pi$
$150$	−110293.	−	22174.1i	−0.400240	−	0.0804672i
$151$	−237126.			−0.846323			−0.423161	−	0.906054i	$-0.639080\pi$
$151$	−237126.			−0.846323			−0.423161	+	0.906054i	$0.639080\pi$
$152$	127172.	+	92396.0i	0.446461	+	0.324373i
$153$	27128.8	+	83493.8i	0.0936918	+	0.288354i
$154$	−53676.4	−	165199.i	−0.182382	−	0.561314i
$155$	138249.	−	80838.9i	0.462205	−	0.270266i
$156$	−37910.8	+	116677.i	−0.124724	+	0.383862i
$157$	−361664.			−1.17100			−0.585500	−	0.810673i	$-0.699102\pi$
$157$	−361664.			−1.17100			−0.585500	+	0.810673i	$0.699102\pi$
$158$	41226.4	−	126882.i	0.131381	−	0.404350i
$159$	−9345.00	+	6789.54i	−0.0293148	+	0.0212984i
$160$	42750.8	+	38067.9i	0.132021	+	0.117560i
$161$	144661.	+	105102.i	0.439832	+	0.319556i
$162$	21231.8	−	15425.8i	0.0635624	−	0.0461808i
$163$	93181.5	−	67700.3i	0.274701	−	0.199582i	−0.441902	−	0.897063i	$-0.645696\pi$
$163$	93181.5	−	67700.3i	0.274701	−	0.199582i	0.716603	+	0.697481i	$0.245696\pi$
$164$	164148.	+	119260.i	0.476568	+	0.346247i
$165$	114365.	−	66872.9i	0.327027	−	0.191223i
$166$	−42692.6	+	31018.0i	−0.120249	+	0.0873663i
$167$	14632.7	−	45034.9i	0.0406008	−	0.124956i	−0.928702	−	0.370828i	$-0.879074\pi$
$167$	14632.7	−	45034.9i	0.0406008	−	0.124956i	0.969302	+	0.245871i	$0.0790741\pi$
$168$	94989.6			0.259659
$169$	109558.	−	337186.i	0.295073	−	0.908140i
$170$	−241161.	−	24002.3i	−0.640008	−	0.0636987i
$171$	61478.3	+	189211.i	0.160780	+	0.494830i
$172$	−103288.	−	317889.i	−0.266213	−	0.819320i
$173$	−67571.3	−	49093.4i	−0.171651	−	0.124712i	0.498643	−	0.866808i	$-0.333832\pi$
$173$	−67571.3	−	49093.4i	−0.171651	−	0.124712i	−0.670294	+	0.742096i	$0.733832\pi$
$174$	263507.			0.659810
$175$	−59522.2	−	511903.i	−0.146921	−	1.26355i
$176$	−67410.5			−0.164039
$177$	−207400.	−	150685.i	−0.497594	−	0.361523i
$178$	155659.	+	479069.i	0.368234	+	1.13331i
$179$	−55903.0	−	172052.i	−0.130407	−	0.401353i	0.864440	−	0.502736i	$-0.167673\pi$
$179$	−55903.0	−	172052.i	−0.130407	−	0.401353i	−0.994847	+	0.101383i	$0.967673\pi$
$180$	15453.7	+	70781.2i	0.0355511	+	0.162831i
$181$	172124.	−	529744.i	0.390522	−	1.20190i	−0.541873	−	0.840461i	$-0.682285\pi$
$181$	172124.	−	529744.i	0.390522	−	1.20190i	0.932395	−	0.361442i	$-0.117715\pi$
$182$	−561994.			−1.25763
$183$	90776.8	−	279382.i	0.200377	−	0.616696i
$184$	56140.7	−	40788.6i	0.122246	−	0.0888166i
$185$	−86972.8	−	8656.23i	−0.186833	−	0.0185951i
$186$	−83437.4	−	60620.8i	−0.176839	−	0.128481i
$187$	230892.	−	167753.i	0.482841	−	0.350805i
$188$	91912.3	−	66778.2i	0.189661	−	0.137797i
$189$	97261.0	+	70664.2i	0.198054	+	0.143895i
$190$	−546511.	−	54393.2i	−1.09829	−	0.109310i
$191$	670661.	−	487264.i	1.33021	−	0.966453i	0.330464	−	0.943818i	$-0.392795\pi$
$191$	670661.	−	487264.i	1.33021	−	0.966453i	0.999744	−	0.0226344i	$-0.00720535\pi$
$192$	11391.6	−	35059.7i	0.0223014	−	0.0686366i
$193$	441629.			0.853423			0.426711	−	0.904388i	$-0.359672\pi$
$193$	441629.			0.853423			0.426711	+	0.904388i	$0.359672\pi$
$194$	165237.	−	508549.i	0.315213	−	0.970126i
$195$	−91430.1	−	418768.i	−0.172188	−	0.788655i
$196$	51366.6	+	158090.i	0.0955083	+	0.293944i
$197$	−217508.	−	669422.i	−0.399310	−	1.22895i	−0.925554	−	0.378616i	$-0.876400\pi$
$197$	−217508.	−	669422.i	−0.399310	−	1.22895i	0.526244	−	0.850334i	$-0.323600\pi$
$198$	−69022.4	−	50147.7i	−0.125120	−	0.0909051i
$199$	602859.			1.07915			0.539577	−	0.841936i	$-0.318584\pi$
$199$	602859.			1.07915			0.539577	+	0.841936i	$0.318584\pi$
$200$	−196077.	−	39420.7i	−0.346618	−	0.0696866i
$201$	339562.			0.592828
$202$	482497.	+	350555.i	0.831986	+	0.604474i
$203$	373014.	+	1.14802e6i	0.635310	+	1.95528i
$204$	48228.9	+	148433.i	0.0811395	+	0.249722i
$205$	−705410.	−	70208.0i	−1.17235	−	0.116682i
$206$	110126.	−	338932.i	0.180809	−	0.556474i
$207$	87826.4			0.142462
$208$	−67396.9	+	207426.i	−0.108014	+	0.332434i
$209$	523239.	−	380155.i	0.828579	−	0.601998i
$210$	−286496.	+	167524.i	−0.448302	+	0.262137i
$211$	517627.	+	376078.i	0.800406	+	0.581529i	0.911033	−	0.412333i	$-0.135286\pi$
$211$	517627.	+	376078.i	0.800406	+	0.581529i	−0.110627	+	0.993862i	$0.535286\pi$
$212$	−16613.3	+	12070.3i	−0.0253873	+	0.0184450i
$213$	−243714.	+	177068.i	−0.368071	+	0.267419i
$214$	−379482.	−	275710.i	−0.566443	−	0.411545i
$215$	872154.	+	776619.i	1.28676	+	1.14581i
$216$	37745.5	−	27423.7i	0.0550466	−	0.0399937i
$217$	145994.	−	449325.i	0.210468	−	0.647755i
$218$	−598493.			−0.852939
$219$	−134455.	+	413811.i	−0.189438	+	0.583031i
$220$	203316.	−	118885.i	0.283214	−	0.165604i
$221$	−285340.	−	878187.i	−0.392991	−	1.20950i
$222$	17393.4	+	53531.3i	0.0236865	+	0.0728996i
$223$	−235686.	−	171236.i	−0.317374	−	0.230585i	0.417680	−	0.908594i	$-0.362843\pi$
$223$	−235686.	−	171236.i	−0.317374	−	0.230585i	−0.735054	+	0.678009i	$0.762843\pi$
$224$	168870.			0.224871
$225$	−171439.	−	186228.i	−0.225764	−	0.245238i
$226$	−71270.3			−0.0928191
$227$	−211359.	−	153561.i	−0.272242	−	0.197796i	0.443284	−	0.896381i	$-0.353813\pi$
$227$	−211359.	−	153561.i	−0.272242	−	0.197796i	−0.715527	+	0.698585i	$0.753813\pi$
$228$	109295.	+	336375.i	0.139239	+	0.428535i
$229$	−360664.	−	1.11001e6i	−0.454479	−	1.39874i	−0.871746	−	0.489959i	$-0.837012\pi$
$229$	−360664.	−	1.11001e6i	−0.454479	−	1.39874i	0.417266	−	0.908784i	$-0.362988\pi$
$230$	−97390.2	+	222031.i	−0.121394	+	0.276755i
$231$	120772.	−	371698.i	0.148914	−	0.458311i
$232$	468457.			0.571413
$233$	−371179.	+	1.14237e6i	−0.447913	+	1.37854i	0.431343	+	0.902188i	$0.358040\pi$
$233$	−371179.	+	1.14237e6i	−0.447913	+	1.37854i	−0.879257	+	0.476348i	$0.841960\pi$
$234$	−223316.	+	162249.i	−0.266613	+	0.193705i
$235$	−159445.	+	363505.i	−0.188340	+	0.429379i
$236$	−368711.	−	267884.i	−0.430929	−	0.313088i
$237$	242847.	−	176439.i	0.280842	−	0.204044i
$238$	−578408.	+	420238.i	−0.661899	+	0.480898i
$239$	1.09990e6	+	799127.i	1.24555	+	0.904943i	0.997955	−	0.0639212i	$-0.0203606\pi$
$239$	1.09990e6	+	799127.i	1.24555	+	0.904943i	0.247592	+	0.968864i	$0.420361\pi$
$240$	27473.3	+	125833.i	0.0307881	+	0.141016i
$241$	−803188.	+	583550.i	−0.890788	+	0.647196i	−0.936083	−	0.351778i	$-0.885577\pi$
$241$	−803188.	+	583550.i	−0.890788	+	0.647196i	0.0452950	+	0.998974i	$0.485577\pi$
$242$	113363.	−	348895.i	0.124432	−	0.382962i
$243$	59049.0			0.0641500
$244$	161381.	−	496679.i	0.173531	−	0.534074i
$245$	−433734.	−	386223.i	−0.461645	−	0.411077i
$246$	141072.	+	434176.i	0.148629	+	0.457434i
$247$	−646628.	−	1.99012e6i	−0.674392	−	2.07557i
$248$	−148333.	−	107770.i	−0.153147	−	0.111268i
$249$	−118735.			−0.121361
$250$	660905.	−	226904.i	0.668789	−	0.229611i
$251$	1.72783e6			1.73108			0.865540	−	0.500839i	$-0.166975\pi$
$251$	1.72783e6			1.73108			0.865540	+	0.500839i	$0.166975\pi$
$252$	172908.	+	125625.i	0.171520	+	0.124617i
$253$	−88228.8	−	271540.i	−0.0866580	−	0.266706i
$254$	−295499.	−	909454.i	−0.287390	−	0.884497i
$255$	−407240.	−	362631.i	−0.392193	−	0.349232i
$256$	20251.7	−	62328.4i	0.0193136	−	0.0594410i
$257$	419054.			0.395765			0.197882	−	0.980226i	$-0.436594\pi$
$257$	419054.			0.395765			0.197882	+	0.980226i	$0.436594\pi$
$258$	232399.	−	715249.i	0.217362	−	0.668972i
$259$	−208598.	+	151555.i	−0.193224	+	0.140385i
$260$	−162542.	−	744476.i	−0.149119	−	0.682995i
$261$	479659.	+	348493.i	0.435844	+	0.316659i
$262$	−1.05609e6	+	767291.i	−0.950486	+	0.690568i
$263$	−221353.	+	160822.i	−0.197331	+	0.143369i	−0.682063	−	0.731293i	$-0.738917\pi$
$263$	−221353.	+	160822.i	−0.197331	+	0.143369i	0.484732	+	0.874663i	$0.338917\pi$
$264$	−122707.	−	89151.5i	−0.108357	−	0.0787261i
$265$	28820.0	−	65704.3i	0.0252104	−	0.0574750i
$266$	−1.31077e6	+	952328.i	−1.13585	+	0.825244i
$267$	−350233.	+	1.07791e6i	−0.300662	+	0.925342i
$268$	603665.			0.513404
$269$	513120.	−	1.57922e6i	0.432353	−	1.33065i	−0.463422	−	0.886138i	$-0.653379\pi$
$269$	513120.	−	1.57922e6i	0.432353	−	1.33065i	0.895775	−	0.444508i	$-0.146621\pi$
$270$	−65479.1	+	149280.i	−0.0546630	+	0.124621i
$271$	674576.	+	2.07613e6i	0.557966	+	1.71724i	0.687980	+	0.725730i	$0.258498\pi$
$271$	674576.	+	2.07613e6i	0.557966	+	1.71724i	−0.130014	+	0.991512i	$0.541502\pi$
$272$	85740.3	+	263882.i	0.0702689	+	0.216265i
$273$	−1.02299e6	−	743246.i	−0.830740	−	0.603568i
$274$	450848.			0.362789
$275$	−403551.	+	717134.i	−0.321786	+	0.571832i
$276$	156136.			0.123376
$277$	654497.	+	475520.i	0.512517	+	0.372365i	0.813777	−	0.581177i	$-0.197407\pi$
$277$	654497.	+	475520.i	0.512517	+	0.372365i	−0.301261	+	0.953542i	$0.597407\pi$
$278$	−15074.4	−	46394.2i	−0.0116984	−	0.0360041i
$279$	−71708.0	−	220695.i	−0.0551515	−	0.169739i
$280$	−509327.	+	297820.i	−0.388241	+	0.227017i
$281$	−602953.	+	1.85570e6i	−0.455531	+	1.40198i	0.414980	+	0.909830i	$0.363788\pi$
$281$	−602953.	+	1.85570e6i	−0.455531	+	1.40198i	−0.870511	+	0.492149i	$0.836212\pi$
$282$	255622.			0.191415
$283$	−741218.	+	2.28123e6i	−0.550149	+	1.69318i	0.158275	+	0.987395i	$0.449407\pi$
$283$	−741218.	+	2.28123e6i	−0.550149	+	1.69318i	−0.708423	+	0.705788i	$0.750593\pi$
$284$	−433269.	+	314788.i	−0.318758	+	0.231592i
$285$	−922872.	−	821782.i	−0.673022	−	0.599300i
$286$	725977.	+	527453.i	0.524817	+	0.381302i
$287$	−1.69187e6	+	1.22922e6i	−1.21245	+	0.880895i
$288$	67103.1	−	48753.3i	0.0476718	−	0.0346356i
$289$	198339.	+	144101.i	0.139689	+	0.101490i
$290$	−1.41290e6	+	826170.i	−0.986547	+	0.576866i
$291$	973344.	−	707176.i	0.673804	−	0.489548i
$292$	−239032.	+	735664.i	−0.164058	+	0.504920i
$293$	−1.84048e6			−1.25245			−0.626227	−	0.779641i	$-0.715401\pi$
$293$	−1.84048e6			−1.25245			−0.626227	+	0.779641i	$0.715401\pi$
$294$	−115575.	+	355703.i	−0.0779822	+	0.240004i
$295$	1.58450e6	+	157702.i	1.06008	+	0.105507i
$296$	30921.5	+	95166.7i	0.0205131	+	0.0631329i
$297$	−59319.5	−	182567.i	−0.0390217	−	0.120096i
$298$	822679.	+	597711.i	0.536648	+	0.389898i
$299$	−923758.			−0.597558
$300$	−304781.	−	331072.i	−0.195517	−	0.212383i
$301$	3.44510e6			2.19172
$302$	−767355.	−	557516.i	−0.484149	−	0.351755i
$303$	414669.	+	1.27622e6i	0.259475	+	0.798582i
$304$	194302.	+	598000.i	0.120585	+	0.371122i
$305$	389205.	+	1.78264e6i	0.239568	+	1.09727i
$306$	−108515.	+	333975.i	−0.0662501	+	0.203897i
$307$	−23469.5			−0.0142121			−0.00710604	−	0.999975i	$-0.502262\pi$
$307$	−23469.5			−0.0142121			−0.00710604	+	0.999975i	$0.502262\pi$
$308$	214706.	−	660796.i	0.128963	−	0.396909i
$309$	648704.	−	471311.i	0.386501	−	0.280809i
$310$	637448.	+	63443.9i	0.376739	+	0.0374961i
$311$	1.44015e6	+	1.04633e6i	0.844320	+	0.613435i	0.923574	−	0.383420i	$-0.125254\pi$
$311$	1.44015e6	+	1.04633e6i	0.844320	+	0.613435i	−0.0792539	+	0.996854i	$0.525254\pi$
$312$	−397007.	+	288442.i	−0.230893	+	0.167754i
$313$	−2.71048e6	+	1.96928e6i	−1.56382	+	1.13618i	−0.631026	+	0.775762i	$0.717366\pi$
$313$	−2.71048e6	+	1.96928e6i	−1.56382	+	1.13618i	−0.932791	+	0.360417i	$0.882634\pi$
$314$	−1.17037e6	−	850324.i	−0.669884	−	0.486699i
$315$	−743059.	−	73955.1i	−0.421936	−	0.0419945i
$316$	431729.	−	313669.i	0.243217	−	0.176707i
$317$	−217633.	+	669806.i	−0.121640	+	0.374370i	−0.993274	−	0.115788i	$-0.963061\pi$
$317$	−217633.	+	669806.i	−0.121640	+	0.374370i	0.871634	+	0.490158i	$0.163061\pi$
$318$	−46204.2			−0.0256221
$319$	595607.	−	1.83309e6i	0.327705	−	1.00857i
$320$	48841.5	+	223704.i	0.0266633	+	0.122123i
$321$	−326135.	−	1.00374e6i	−0.176659	−	0.543700i
$322$	221022.	+	680237.i	0.118794	+	0.365612i
$323$	−2.15365e6	−	1.56472e6i	−1.14860	−	0.834507i
$324$	104976.			0.0555556
$325$	1.80320e6	+	1.95874e6i	0.946968	+	1.02865i
$326$	460715.			0.240098
$327$	−1.08943e6	−	791518.i	−0.563417	−	0.409347i
$328$	250795.	+	771868.i	0.128717	+	0.396149i
$329$	361853.	+	1.11367e6i	0.184307	+	0.567239i
$330$	527321.	+	52483.2i	0.266557	+	0.0265299i
$331$	570238.	−	1.75501e6i	0.286079	−	0.880460i	−0.699994	−	0.714148i	$-0.746814\pi$
$331$	570238.	−	1.75501e6i	0.286079	−	0.880460i	0.986073	−	0.166312i	$-0.0531858\pi$
$332$	−211084.			−0.105102
$333$	−39135.1	+	120445.i	−0.0193400	+	0.0595223i
$334$	153236.	−	111332.i	0.0751613	−	0.0546079i
$335$	−1.82070e6	+	1.06462e6i	−0.886395	+	0.518303i
$336$	307393.	+	223334.i	0.148541	+	0.107921i
$337$	2.21388e6	−	1.60848e6i	1.06189	−	0.771508i	0.0874529	−	0.996169i	$-0.472127\pi$
$337$	2.21388e6	−	1.60848e6i	1.06189	−	0.771508i	0.974437	+	0.224660i	$0.0721273\pi$
$338$	1.14731e6	−	833570.i	0.546247	−	0.396872i
$339$	−129732.	−	94256.1i	−0.0613125	−	0.0445462i
$340$	−723981.	−	644677.i	−0.339649	−	0.302444i
$341$	−610303.	+	443411.i	−0.284223	+	0.206500i
$342$	−245913.	+	756843.i	−0.113689	+	0.349897i
$343$	1.05839e6			0.485747
$344$	413153.	−	1.27155e6i	0.188241	−	0.579347i
$345$	−470919.	+	275361.i	−0.213009	+	0.124553i
$346$	−103240.	−	317739.i	−0.0463614	−	0.142686i
$347$	−78680.0	−	242152.i	−0.0350785	−	0.107960i	0.931984	−	0.362499i	$-0.118076\pi$
$347$	−78680.0	−	242152.i	−0.0350785	−	0.107960i	−0.967063	+	0.254539i	$0.918076\pi$
$348$	852727.	+	619542.i	0.377452	+	0.274235i
$349$	−2.61743e6			−1.15030			−0.575150	−	0.818048i	$-0.695056\pi$
$349$	−2.61743e6			−1.15030			−0.575150	+	0.818048i	$0.695056\pi$
$350$	1.01094e6	−	1.79650e6i	0.441117	−	0.783892i
$351$	−621077.			−0.269078
$352$	−218145.	−	158492.i	−0.0938401	−	0.0681788i
$353$	−439882.	−	1.35382e6i	−0.187888	−	0.578260i	0.812098	−	0.583521i	$-0.198325\pi$
$353$	−439882.	−	1.35382e6i	−0.187888	−	0.578260i	−0.999986	+	0.00526070i	$0.998325\pi$
$354$	−316879.	−	975252.i	−0.134396	−	0.413627i
$355$	751614.	−	1.71354e6i	0.316537	−	0.721645i
$356$	−622636.	+	1.91628e6i	−0.260381	+	0.801370i
$357$	−1.60864e6			−0.668018
$358$	223612.	−	688207.i	0.0922120	−	0.283799i
$359$	−1.06955e6	+	777075.i	−0.437992	+	0.318219i	−0.784836	−	0.619703i	$-0.787253\pi$
$359$	−1.06955e6	+	777075.i	−0.437992	+	0.318219i	0.346845	+	0.937923i	$0.387253\pi$
$360$	−116407.	+	265387.i	−0.0473395	+	0.107925i
$361$	−2.87732e6	−	2.09050e6i	−1.16204	−	0.844270i
$362$	1.80251e6	−	1.30960e6i	0.722945	−	0.525251i
$363$	667772.	−	485165.i	0.265988	−	0.193251i
$364$	−1.81865e6	−	1.32133e6i	−0.719442	−	0.522705i
$365$	−576477.	−	2.64038e6i	−0.226490	−	1.03737i
$366$	950627.	−	690671.i	0.370943	−	0.269506i
$367$	240128.	−	739039.i	0.0930633	−	0.286419i	−0.893681	−	0.448703i	$-0.851886\pi$
$367$	240128.	−	739039.i	0.0930633	−	0.286419i	0.986744	+	0.162284i	$0.0518860\pi$
$368$	277575.			0.106847
$369$	−317413.	+	976896.i	−0.121355	+	0.373493i
$370$	−261098.	−	232497.i	−0.0991514	−	0.0882905i
$371$	−65405.6	−	201298.i	−0.0246706	−	0.0759284i
$372$	−127481.	−	392346.i	−0.0477626	−	0.146998i
$373$	495916.	+	360304.i	0.184559	+	0.134090i	0.676229	−	0.736692i	$-0.263613\pi$
$373$	495916.	+	360304.i	0.184559	+	0.134090i	−0.491669	+	0.870782i	$0.663613\pi$
$374$	1.14159e6			0.422019
$375$	1.50312e6	+	461027.i	0.551971	+	0.169297i
$376$	454440.			0.165770
$377$	−5.04505e6	−	3.66544e6i	−1.82815	−	1.32823i
$378$	148602.	+	457349.i	0.0534926	+	0.164633i
$379$	1.21962e6	+	3.75361e6i	0.436142	+	1.34231i	0.891912	+	0.452209i	$0.149364\pi$
$379$	1.21962e6	+	3.75361e6i	0.436142	+	1.34231i	−0.455770	+	0.890097i	$0.650636\pi$
$380$	−1.64066e6	−	1.46094e6i	−0.582854	−	0.519009i
$381$	664874.	−	2.04627e6i	0.234653	−	0.722189i
$382$	3.31593e6			1.16264
$383$	927719.	−	2.85523e6i	0.323161	−	0.994589i	−0.649102	−	0.760701i	$-0.724855\pi$
$383$	927719.	−	2.85523e6i	0.323161	−	0.994589i	0.972264	−	0.233887i	$-0.0751447\pi$
$384$	119294.	−	86672.5i	0.0412850	−	0.0299953i
$385$	517809.	+	2.37167e6i	0.178040	+	0.815459i
$386$	1.42914e6	+	1.03833e6i	0.488210	+	0.354705i
$387$	1.36896e6	−	994609.i	0.464637	−	0.337579i
$388$	1.73039e6	−	1.25720e6i	0.583532	−	0.423961i
$389$	2.63908e6	+	1.91740e6i	0.884256	+	0.642449i	0.934374	−	0.356294i	$-0.115960\pi$
$389$	2.63908e6	+	1.91740e6i	0.884256	+	0.642449i	−0.0501181	+	0.998743i	$0.515960\pi$
$390$	688709.	−	1.57013e6i	0.229284	−	0.522725i
$391$	−950738.	+	690751.i	−0.314499	+	0.228497i
$392$	−205467.	+	632361.i	−0.0675345	+	0.207850i
$393$	−2.93713e6			−0.959273
$394$	870033.	−	2.67769e6i	0.282355	−	0.868999i
$395$	−748942.	+	1.70745e6i	−0.241521	+	0.550624i
$396$	−105457.	−	324563.i	−0.0337938	−	0.104007i
$397$	−590622.	−	1.81775e6i	−0.188076	−	0.578838i	0.811912	−	0.583780i	$-0.198427\pi$
$397$	−590622.	−	1.81775e6i	−0.188076	−	0.578838i	−0.999988	+	0.00494181i	$0.998427\pi$
$398$	1.95089e6	+	1.41741e6i	0.617342	+	0.448525i
$399$	−3.64544e6			−1.14635
$400$	−541833.	−	588572.i	−0.169323	−	0.183929i
$401$	1.81214e6			0.562770			0.281385	−	0.959595i	$-0.409206\pi$
$401$	1.81214e6			0.562770			0.281385	+	0.959595i	$0.409206\pi$
$402$	1.09885e6	+	798358.i	0.339134	+	0.246395i
$403$	754224.	+	2.32126e6i	0.231333	+	0.711970i
$404$	737190.	+	2.26884e6i	0.224712	+	0.691592i
$405$	−316616.	+	185136.i	−0.0959170	+	0.0560857i
$406$	−1.49206e6	+	4.59208e6i	−0.449232	+	1.38259i
$407$	411705.			0.123197
$408$	−192916.	+	593734.i	−0.0573743	+	0.176580i
$409$	−319057.	+	231808.i	−0.0943105	+	0.0685206i	−0.633941	−	0.773381i	$-0.718564\pi$
$409$	−319057.	+	231808.i	−0.0943105	+	0.0685206i	0.539631	+	0.841902i	$0.318564\pi$
$410$	−2.11769e6	−	1.88572e6i	−0.622160	−	0.554009i
$411$	820674.	+	596254.i	0.239644	+	0.174111i
$412$	1.15325e6	−	837887.i	0.334720	−	0.243188i
$413$	3.80031e6	−	2.76109e6i	1.09634	−	0.796536i
$414$	284212.	+	206492.i	0.0814971	+	0.0592111i
$415$	636647.	−	372268.i	0.181459	−	0.106105i
$416$	−705790.	+	512786.i	−0.199960	+	0.145279i
$417$	33917.4	−	104387.i	0.00955173	−	0.0293972i
$418$	2.58703e6			0.724205
$419$	45393.3	−	139706.i	0.0126315	−	0.0388759i	−0.944542	−	0.328390i	$-0.893494\pi$
$419$	45393.3	−	139706.i	0.0126315	−	0.0388759i	0.957174	+	0.289514i	$0.0934938\pi$
$420$	−1.32099e6	−	131476.i	−0.365407	−	0.0363683i
$421$	−2.08491e6	−	6.41670e6i	−0.573301	−	1.76444i	−0.641893	−	0.766795i	$-0.721851\pi$
$421$	−2.08491e6	−	6.41670e6i	−0.573301	−	1.76444i	0.0685915	−	0.997645i	$-0.478149\pi$
$422$	790863.	+	2.43403e6i	0.216182	+	0.665341i
$423$	465306.	+	338065.i	0.126441	+	0.0918648i
$424$	−82140.9			−0.0221894
$425$	3.32054e6	+	667586.i	0.891736	+	0.179281i
$426$	−1.20499e6			−0.321705
$427$	4.35473e6	+	3.16389e6i	1.15582	+	0.839754i
$428$	−579796.	−	1.78443e6i	−0.152991	−	0.470858i
$429$	623922.	+	1.92023e6i	0.163677	+	0.503745i
$430$	996408.	+	4.56375e6i	0.259876	+	1.19028i
$431$	−21558.0	+	66348.6i	−0.00559003	+	0.0172044i	−0.953813	−	0.300402i	$-0.902879\pi$
$431$	−21558.0	+	66348.6i	−0.00559003	+	0.0172044i	0.948223	+	0.317607i	$0.102879\pi$
$432$	186624.			0.0481125
$433$	153607.	−	472754.i	0.0393724	−	0.121176i	−0.929438	−	0.368977i	$-0.879708\pi$
$433$	153607.	−	472754.i	0.0393724	−	0.121176i	0.968811	+	0.247801i	$0.0797081\pi$
$434$	1.52887e6	−	1.11079e6i	0.389625	−	0.283079i
$435$	−3.66452e6	−	364722.i	−0.928525	−	0.0924143i
$436$	−1.93677e6	−	1.40714e6i	−0.487934	−	0.354505i
$437$	−2.15453e6	+	1.56536e6i	−0.539695	+	0.392112i
$438$	−1.40803e6	+	1.02300e6i	−0.350694	+	0.254794i
$439$	−976563.	−	709515.i	−0.241846	−	0.175711i	0.460259	−	0.887785i	$-0.347756\pi$
$439$	−976563.	−	709515.i	−0.241846	−	0.175711i	−0.702105	+	0.712073i	$0.747756\pi$
$440$	937459.	+	93303.4i	0.230845	+	0.0229755i
$441$	−680803.	+	494632.i	−0.166696	+	0.121112i
$442$	1.14136e6	−	3.51275e6i	0.277887	−	0.855247i
$443$	5.99904e6			1.45235			0.726177	−	0.687507i	$-0.241295\pi$
$443$	5.99904e6			1.45235			0.726177	+	0.687507i	$0.241295\pi$
$444$	−69573.5	+	214125.i	−0.0167489	+	0.0515478i
$445$	−1.50162e6	−	6.87772e6i	−0.359468	−	1.64644i
$446$	−360096.	−	1.10826e6i	−0.0857197	−	0.263818i
$447$	707030.	+	2.17601e6i	0.167367	+	0.515102i
$448$	546476.	+	397038.i	0.128640	+	0.0934624i
$449$	1.51038e6			0.353567			0.176783	−	0.984250i	$-0.443431\pi$
$449$	1.51038e6			0.353567			0.176783	+	0.984250i	$0.443431\pi$
$450$	−116942.	−	1.00572e6i	−0.0272232	−	0.234125i
$451$	3.33922e6			0.773042
$452$	−230635.	−	167566.i	−0.0530982	−	0.0385781i
$453$	−659483.	−	2.02968e6i	−0.150993	−	0.464710i
$454$	−322927.	−	993868.i	−0.0735301	−	0.226302i
$455$	7.81548e6	+	777860.i	1.76981	+	0.176146i
$456$	−437179.	+	1.34550e6i	−0.0984572	+	0.303020i
$457$	3.55430e6			0.796092			0.398046	−	0.917365i	$-0.369688\pi$
$457$	3.55430e6			0.796092			0.398046	+	0.917365i	$0.369688\pi$
$458$	1.44266e6	−	4.44004e6i	0.321365	−	0.989061i
$459$	−639217.	+	464418.i	−0.141617	+	0.102891i
$460$	−837189.	+	489531.i	−0.184471	+	0.107866i
$461$	−4.62836e6	−	3.36270e6i	−1.01432	−	0.736946i	−0.0492084	−	0.998789i	$-0.515670\pi$
$461$	−4.62836e6	−	3.36270e6i	−1.01432	−	0.736946i	−0.965111	+	0.261843i	$0.915670\pi$
$462$	1.26474e6	−	918887.i	0.275674	−	0.200289i
$463$	−4.26984e6	+	3.10222e6i	−0.925676	+	0.672543i	−0.944930	−	0.327272i	$-0.893871\pi$
$463$	−4.26984e6	+	3.10222e6i	−0.925676	+	0.672543i	0.0192546	+	0.999815i	$0.493871\pi$
$464$	1.51596e6	+	1.10141e6i	0.326883	+	0.237494i
$465$	1.07643e6	+	958522.i	0.230863	+	0.205575i
$466$	−3.88704e6	+	2.82410e6i	−0.829191	+	0.602442i
$467$	−562004.	+	1.72967e6i	−0.119247	+	0.367005i	−0.992809	−	0.119708i	$-0.961804\pi$
$467$	−562004.	+	1.72967e6i	−0.119247	+	0.367005i	0.873562	+	0.486713i	$0.161804\pi$
$468$	−1.10414e6			−0.233028
$469$	−1.92270e6	+	5.91747e6i	−0.403627	+	1.24224i
$470$	−1.37063e6	+	801449.i	−0.286203	+	0.167352i
$471$	−1.00584e6	−	3.09567e6i	−0.208919	−	0.642987i
$472$	−563340.	−	1.73378e6i	−0.116390	−	0.358211i
$473$	−4.45035e6	−	3.23337e6i	−0.914621	−	0.664511i
$474$	1.20070e6			0.245465
$475$	7.52489e6	+	1.51286e6i	1.53026	+	0.307656i
$476$	−2.85980e6			−0.578521
$477$	−84105.0	−	61105.9i	−0.0169249	−	0.0122967i
$478$	1.68050e6	+	5.17206e6i	0.336411	+	1.03537i
$479$	2.20545e6	+	6.78769e6i	0.439197	+	1.35171i	0.888724	+	0.458442i	$0.151592\pi$
$479$	2.20545e6	+	6.78769e6i	0.439197	+	1.35171i	−0.449528	+	0.893266i	$0.648408\pi$
$480$	−206946.	+	471799.i	−0.0409972	+	0.0934660i
$481$	411622.	−	1.26684e6i	0.0811216	−	0.249667i
$482$	−3.97118e6			−0.778578
$483$	−497300.	+	1.53053e6i	−0.0969953	+	0.298521i
$484$	1.18715e6	−	862515.i	0.230352	−	0.167361i
$485$	−3.00180e6	+	6.84354e6i	−0.579465	+	1.32107i
$486$	191087.	+	138833.i	0.0366978	+	0.0266625i
$487$	−5.89279e6	+	4.28136e6i	−1.12590	+	0.818011i	−0.985092	−	0.172026i	$-0.944969\pi$
$487$	−5.89279e6	+	4.28136e6i	−1.12590	+	0.818011i	−0.140804	+	0.990038i	$0.544969\pi$
$488$	1.69000e6	−	1.22786e6i	0.321246	−	0.233399i
$489$	838633.	+	609303.i	0.158599	+	0.115229i
$490$	−495527.	−	2.26961e6i	−0.0932347	−	0.427033i
$491$	933493.	−	678222.i	0.174746	−	0.126960i	−0.496974	−	0.867765i	$-0.665556\pi$
$491$	933493.	−	678222.i	0.174746	−	0.126960i	0.671720	+	0.740805i	$0.265556\pi$
$492$	−564289.	+	1.73670e6i	−0.105097	+	0.323454i
$493$	−7.93328e6			−1.47006
$494$	2.58651e6	−	7.96047e6i	0.476867	−	1.46765i
$495$	890466.	+	792925.i	0.163344	+	0.145452i
$496$	−226633.	−	697504.i	−0.0413636	−	0.127304i
$497$	−1.70575e6	−	5.24976e6i	−0.309760	−	0.953342i
$498$	−384234.	−	279162.i	−0.0694260	−	0.0504410i
$499$	−502514.			−0.0903435			−0.0451718	−	0.998979i	$-0.514384\pi$
$499$	−502514.			−0.0903435			−0.0451718	+	0.998979i	$0.514384\pi$
$500$	2.67222e6	+	819604.i	0.478021	+	0.146615i
$501$	426172.			0.0758562
$502$	5.59138e6	+	4.06238e6i	0.990284	+	0.719484i
$503$	−621270.	−	1.91207e6i	−0.109486	−	0.336964i	0.881271	−	0.472612i	$-0.156689\pi$
$503$	−621270.	−	1.91207e6i	−0.109486	−	0.336964i	−0.990757	+	0.135647i	$0.956689\pi$
$504$	264181.	+	813064.i	0.0463260	+	0.142577i
$505$	−6.22474e6	−	5.54289e6i	−1.08616	−	0.967181i
$506$	352915.	−	1.08616e6i	0.0612765	−	0.188590i
$507$	3.19085e6			0.551297
$508$	1.18200e6	−	3.63781e6i	0.203216	−	0.625434i
$509$	1.27241e6	−	924460.i	0.217687	−	0.158159i	−0.473598	−	0.880741i	$-0.657045\pi$
$509$	1.27241e6	−	924460.i	0.217687	−	0.158159i	0.691285	+	0.722582i	$0.257045\pi$
$510$	−465258.	−	2.13098e6i	−0.0792080	−	0.362788i
$511$	−6.45007e6	−	4.68625e6i	−1.09273	−	0.793913i
$512$	212079.	−	154084.i	0.0357538	−	0.0259767i
$513$	−1.44857e6	+	1.05245e6i	−0.243022	+	0.176566i
$514$	1.35609e6	+	985255.i	0.226402	+	0.164490i
$515$	−2.00061e6	+	4.56101e6i	−0.332387	+	0.757780i
$516$	2.43371e6	−	1.76819e6i	0.402388	−	0.292352i
$517$	577785.	−	1.77824e6i	0.0950692	−	0.292593i
$518$	−1.03136e6			−0.168884
$519$	232289.	−	714913.i	0.0378539	−	0.116502i
$520$	1.22437e6	−	2.79134e6i	0.198566	−	0.452693i
$521$	2.49577e6	+	7.68118e6i	0.402819	+	1.23975i	0.922703	+	0.385512i	$0.125975\pi$
$521$	2.49577e6	+	7.68118e6i	0.402819	+	1.23975i	−0.519884	+	0.854237i	$0.674025\pi$
$522$	732854.	+	2.25549e6i	0.117717	+	0.362297i
$523$	−3.11751e6	−	2.26501e6i	−0.498373	−	0.362089i	0.310022	−	0.950729i	$-0.399663\pi$
$523$	−3.11751e6	−	2.26501e6i	−0.498373	−	0.362089i	−0.808395	+	0.588640i	$0.799663\pi$
$524$	−5.22157e6			−0.830755
$525$	4.21609e6	−	1.93316e6i	0.667593	−	0.306104i
$526$	−1.09443e6			−0.172474
$527$	2.51201e6	+	1.82508e6i	0.393998	+	0.286257i
$528$	−187479.	−	577001.i	−0.0292663	−	0.0900724i
$529$	−1.62564e6	−	5.00321e6i	−0.252572	−	0.777337i
$530$	247744.	−	144864.i	0.0383101	−	0.0224011i
$531$	712977.	−	2.19432e6i	0.109734	−	0.337725i
$532$	−6.48079e6			−0.992771
$533$	3.33854e6	−	1.02750e7i	0.509025	−	1.56662i
$534$	−3.66768e6	+	2.66473e6i	−0.556594	+	0.404389i
$535$	4.89573e6	+	4.35946e6i	0.739491	+	0.658488i
$536$	1.95350e6	+	1.41930e6i	0.293699	+	0.213385i
$537$	1.31720e6	−	957004.i	0.197114	−	0.143212i
$538$	5.37347e6	−	3.90405e6i	0.800385	−	0.581514i
$539$	2.21322e6	+	1.60800e6i	0.328135	+	0.238404i
$540$	−562873.	+	329130.i	−0.0830666	+	0.0485717i
$541$	−4.69448e6	+	3.41074e6i	−0.689596	+	0.501021i	−0.876527	−	0.481352i	$-0.840146\pi$
$541$	−4.69448e6	+	3.41074e6i	−0.689596	+	0.501021i	0.186932	+	0.982373i	$0.440146\pi$
$542$	−2.69830e6	+	8.30452e6i	−0.394541	+	1.21427i
$543$	5.01305e6			0.729629
$544$	−342961.	+	1.05553e6i	−0.0496876	+	0.152923i
$545$	8.32308e6	+	828379.i	1.20031	+	0.119464i
$546$	−1.56299e6	−	4.81039e6i	−0.224375	−	0.690555i
$547$	−216440.	−	666135.i	−0.0309293	−	0.0951905i	0.934400	−	0.356225i	$-0.115936\pi$
$547$	−216440.	−	666135.i	−0.0309293	−	0.0951905i	−0.965329	+	0.261035i	$0.915936\pi$
$548$	1.45898e6	+	1.06001e6i	0.207538	+	0.150785i
$549$	2.64384e6			0.374373
$550$	−2.99200e6	+	1.37189e6i	−0.421750	+	0.193381i
$551$	−1.79781e7			−2.52270
$552$	505266.	+	367097.i	0.0705785	+	0.0512783i
$553$	1.69969e6	+	5.23110e6i	0.236350	+	0.727412i
$554$	999982.	+	3.07763e6i	0.138426	+	0.426032i
$555$	−167792.	−	768519.i	−0.0231227	−	0.105906i
$556$	60297.6	−	185577.i	0.00827204	−	0.0254587i
$557$	−8.58329e6			−1.17224			−0.586119	−	0.810225i	$-0.699345\pi$
$557$	−8.58329e6			−1.17224			−0.586119	+	0.810225i	$0.699345\pi$
$558$	286832.	−	882778.i	0.0389980	−	0.120023i
$559$	−1.43987e7	+	1.04613e7i	−1.94892	+	1.41598i
$560$	−2.34843e6	−	233735.i	−0.316452	−	0.0314958i
$561$	2.07802e6	+	1.50977e6i	0.278768	+	0.202537i
$562$	−6.31421e6	+	4.58754e6i	−0.843292	+	0.612687i
$563$	−1.81010e6	+	1.31511e6i	−0.240675	+	0.174861i	−0.701584	−	0.712587i	$-0.747523\pi$
$563$	−1.81010e6	+	1.31511e6i	−0.240675	+	0.174861i	0.460909	+	0.887447i	$0.347523\pi$
$564$	827211.	+	601004.i	0.109501	+	0.0795572i
$565$	991135.	+	98645.7i	0.130621	+	0.0130004i
$566$	−7.76214e6	+	5.63952e6i	−1.01845	+	0.739948i
$567$	−334353.	+	1.02903e6i	−0.0436765	+	0.134423i
$568$	−2.14220e6			−0.278605
$569$	177572.	−	546511.i	0.0229929	−	0.0707649i	−0.938902	−	0.344186i	$-0.888155\pi$
$569$	177572.	−	546511.i	0.0229929	−	0.0707649i	0.961895	+	0.273421i	$0.0881551\pi$
$570$	−1.05435e6	−	4.82914e6i	−0.135925	−	0.622563i
$571$	−859950.	−	2.64665e6i	−0.110378	−	0.339709i	0.880577	−	0.473903i	$-0.157155\pi$
$571$	−859950.	−	2.64665e6i	−0.110378	−	0.339709i	−0.990955	+	0.134194i	$0.957155\pi$
$572$	1.10919e6	+	3.41375e6i	0.141748	+	0.436256i
$573$	6.03595e6	+	4.38537e6i	0.767996	+	0.557982i
$574$	−8.36509e6			−1.05972
$575$	1.66169e6	−	2.95293e6i	0.209595	−	0.372463i
$576$	331776.			0.0416667
$577$	6.58650e6	+	4.78537e6i	0.823598	+	0.598379i	0.917741	−	0.397180i	$-0.130011\pi$
$577$	6.58650e6	+	4.78537e6i	0.823598	+	0.598379i	−0.0941429	+	0.995559i	$0.530011\pi$
$578$	303035.	+	932644.i	0.0377288	+	0.116117i
$579$	1.22824e6	+	3.78013e6i	0.152260	+	0.468608i
$580$	−6.51470e6	−	648395.i	−0.804127	−	0.0800331i
$581$	672313.	−	2.06917e6i	0.0826287	−	0.254305i
$582$	4.81248e6			0.588927
$583$	−104436.	+	321420.i	−0.0127256	+	0.0391653i
$584$	−2.50317e6	+	1.81866e6i	−0.303710	+	0.220658i
$585$	3.33017e6	−	1.94725e6i	0.402324	−	0.235252i
$586$	−5.95591e6	−	4.32722e6i	−0.716480	−	0.520553i
$587$	9.56474e6	−	6.94919e6i	1.14572	−	0.832413i	0.157813	−	0.987469i	$-0.449556\pi$
$587$	9.56474e6	−	6.94919e6i	1.14572	−	0.832413i	0.987906	+	0.155056i	$0.0495558\pi$
$588$	−1.21032e6	+	879346.i	−0.144363	+	0.104886i
$589$	5.69262e6	+	4.13593e6i	0.676121	+	0.491231i
$590$	4.75678e6	+	4.23572e6i	0.562578	+	0.500954i
$591$	5.12500e6	−	3.72353e6i	0.603566	−	0.438516i
$592$	−123686.	+	380667.i	−0.0145050	+	0.0446417i
$593$	4.79946e6			0.560474			0.280237	−	0.959931i	$-0.409587\pi$
$593$	4.79946e6			0.560474			0.280237	+	0.959931i	$0.409587\pi$
$594$	237278.	−	730267.i	0.0275925	−	0.0849210i
$595$	8.62540e6	−	5.04355e6i	0.998820	−	0.584042i
$596$	1.25694e6	+	3.86847e6i	0.144944	+	0.446091i
$597$	1.67664e6	+	5.16018e6i	0.192533	+	0.592555i
$598$	−2.98934e6	−	2.17188e6i	−0.341840	−	0.248361i
$599$	1.16050e7			1.32153			0.660767	−	0.750591i	$-0.270231\pi$
$599$	1.16050e7			1.32153			0.660767	+	0.750591i	$0.270231\pi$
$600$	−207897.	−	1.78795e6i	−0.0235760	−	0.202758i
$601$	−1.04995e6			−0.118572			−0.0592859	−	0.998241i	$-0.518882\pi$
$601$	−1.04995e6			−0.118572			−0.0592859	+	0.998241i	$0.518882\pi$
$602$	1.11486e7	+	8.09992e6i	1.25380	+	0.910939i
$603$	944373.	+	2.90648e6i	0.105767	+	0.325518i
$604$	−1.17241e6	−	3.60832e6i	−0.130764	−	0.402450i
$605$	−2.05941e6	+	4.69507e6i	−0.228747	+	0.521499i
$606$	−1.65868e6	+	5.10488e6i	−0.183476	+	0.564682i
$607$	−4.45769e6			−0.491064			−0.245532	−	0.969388i	$-0.578963\pi$
$607$	−4.45769e6			−0.491064			−0.245532	+	0.969388i	$0.578963\pi$
$608$	−777207.	+	2.39200e6i	−0.0852664	+	0.262423i
$609$	−8.78908e6	+	6.38564e6i	−0.960285	+	0.697688i
$610$	−2.93174e6	+	6.68381e6i	−0.319007	+	0.727277i
$611$	−4.89409e6	−	3.55576e6i	−0.530357	−	0.385327i
$612$	−1.13639e6	+	825632.i	−0.122644	+	0.0891062i
$613$	1.12521e7	−	8.17515e6i	1.20944	−	0.878707i	0.214258	−	0.976777i	$-0.431267\pi$
$613$	1.12521e7	−	8.17515e6i	1.20944	−	0.878707i	0.995180	+	0.0980697i	$0.0312668\pi$
$614$	−75948.9	−	55180.1i	−0.00813019	−	0.00590693i
$615$	−1.36091e6	−	6.23322e6i	−0.145091	−	0.664546i
$616$	2.24843e6	−	1.63358e6i	0.238741	−	0.173455i
$617$	2.02946e6	−	6.24603e6i	0.214619	−	0.660528i	−0.784562	−	0.620051i	$-0.787112\pi$
$617$	2.02946e6	−	6.24603e6i	0.214619	−	0.660528i	0.999180	−	0.0404775i	$-0.0128879\pi$
$618$	3.20737e6			0.337814
$619$	1.86016e6	−	5.72499e6i	0.195130	−	0.600549i	−0.804845	−	0.593485i	$-0.797752\pi$
$619$	1.86016e6	−	5.72499e6i	0.195130	−	0.600549i	0.999975	−	0.00706359i	$-0.00224843\pi$
$620$	1.91366e6	+	1.70404e6i	0.199934	+	0.178033i
$621$	244259.	+	751751.i	0.0254168	+	0.0782249i
$622$	2.20036e6	+	6.77200e6i	0.228043	+	0.701844i
$623$	−1.68013e7	−	1.22069e7i	−1.73429	−	1.26004i
$624$	−1.96291e6			−0.201808
$625$	−9.50508e6	+	2.24073e6i	−0.973320	+	0.229451i
$626$	−1.34014e7			−1.36683
$627$	4.70915e6	+	3.42140e6i	0.478380	+	0.347564i
$628$	−1.78817e6	−	5.50341e6i	−0.180929	−	0.556843i
$629$	−523654.	−	1.61164e6i	−0.0527737	−	0.162421i
$630$	−2.23071e6	−	1.98636e6i	−0.223919	−	0.199391i
$631$	3.48624e6	−	1.07296e7i	0.348566	−	1.07277i	−0.611082	−	0.791568i	$-0.709265\pi$
$631$	3.48624e6	−	1.07296e7i	0.348566	−	1.07277i	0.959647	−	0.281207i	$-0.0907347\pi$
$632$	2.13458e6			0.212579
$633$	−1.77944e6	+	5.47656e6i	−0.176512	+	0.543248i
$634$	−2.27908e6	+	1.65585e6i	−0.225184	+	0.163606i
$635$	2.85064e6	+	1.30565e7i	0.280549	+	1.28497i
$636$	−149520.	−	108633.i	−0.0146574	−	0.0106492i
$637$	7.16068e6	−	5.20254e6i	0.699207	−	0.508004i
$638$	6.23728e6	−	4.53165e6i	0.606657	−	0.440762i
$639$	−2.19342e6	−	1.59362e6i	−0.212506	−	0.154394i
$640$	−367904.	+	838753.i	−0.0355046	+	0.0809439i
$641$	−5.13777e6	+	3.73281e6i	−0.493889	+	0.358832i	−0.806678	−	0.590991i	$-0.798737\pi$
$641$	−5.13777e6	+	3.73281e6i	−0.493889	+	0.358832i	0.312789	+	0.949823i	$0.398737\pi$
$642$	1.30454e6	−	4.01497e6i	0.124917	−	0.384454i
$643$	−1.45000e7			−1.38306			−0.691530	−	0.722348i	$-0.743063\pi$
$643$	−1.45000e7			−1.38306			−0.691530	+	0.722348i	$0.743063\pi$
$644$	−884089.	+	2.72095e6i	−0.0840004	+	0.258527i
$645$	−4.22188e6	+	9.62510e6i	−0.399583	+	0.910974i
$646$	−3.29048e6	−	1.01271e7i	−0.310226	−	0.954778i
$647$	1.66452e6	+	5.12288e6i	0.156325	+	0.481120i	0.998293	−	0.0584085i	$-0.0186026\pi$
$647$	1.66452e6	+	5.12288e6i	0.156325	+	0.481120i	−0.841967	+	0.539528i	$0.818603\pi$
$648$	339709.	+	246813.i	0.0317812	+	0.0230904i
$649$	−7.50060e6			−0.699011
$650$	1.23000e6	+	1.05782e7i	0.114188	+	0.982038i
$651$	4.25203e6			0.393227
$652$	1.49090e6	+	1.08320e6i	0.137351	+	0.0997910i
$653$	1.34236e6	+	4.13135e6i	0.123193	+	0.379148i	0.993567	−	0.113242i	$-0.0361234\pi$
$653$	1.34236e6	+	4.13135e6i	0.123193	+	0.379148i	−0.870375	+	0.492390i	$0.836123\pi$
$654$	−1.66450e6	−	5.12281e6i	−0.152174	−	0.468343i
$655$	1.57487e7	−	9.20876e6i	1.43430	−	0.838683i
$656$	−1.00318e6	+	3.08747e6i	−0.0910164	+	0.280120i
$657$	−3.91596e6			−0.353936
$658$	−1.44741e6	+	4.45467e6i	−0.130325	+	0.401099i
$659$	−1.27658e7	+	9.27492e6i	−1.14508	+	0.831949i	−0.987819	−	0.155608i	$-0.950266\pi$
$659$	−1.27658e7	+	9.27492e6i	−1.14508	+	0.831949i	−0.157261	+	0.987557i	$0.550266\pi$
$660$	1.58305e6	+	1.40964e6i	0.141460	+	0.125965i
$661$	1.78389e7	+	1.29608e7i	1.58805	+	1.15379i	0.906651	+	0.421882i	$0.138630\pi$
$661$	1.78389e7	+	1.29608e7i	1.58805	+	1.15379i	0.681404	+	0.731908i	$0.261370\pi$
$662$	5.97160e6	−	4.33862e6i	0.529598	−	0.384775i
$663$	6.72328e6	−	4.88475e6i	0.594015	−	0.431577i
$664$	−683082.	−	496288.i	−0.0601247	−	0.0436831i
$665$	1.95466e7	−	1.14295e7i	1.71402	−	1.00224i
$666$	−409828.	+	297757.i	−0.0358027	+	0.0260122i
$667$	−2.45252e6	+	7.54808e6i	−0.213451	+	0.656934i
$668$	757640.			0.0656934
$669$	810215.	−	2.49359e6i	0.0699898	−	0.215407i
$670$	−8.39500e6	−	835538.i	−0.722493	−	0.0719083i
$671$	−2.65595e6	−	8.17417e6i	−0.227726	−	0.700870i
$672$	469654.	+	1.44545e6i	0.0401195	+	0.123475i
$673$	3.97865e6	+	2.89066e6i	0.338608	+	0.246013i	0.744074	−	0.668097i	$-0.232891\pi$
$673$	3.97865e6	+	2.89066e6i	0.338608	+	0.246013i	−0.405466	+	0.914110i	$0.632891\pi$
$674$	1.09460e7			0.928126
$675$	1.11722e6	−	1.98537e6i	0.0943797	−	0.167719i
$676$	5.67261e6			0.477438
$677$	−1.64474e7	−	1.19497e7i	−1.37919	−	1.00204i	−0.996955	−	0.0779760i	$-0.975154\pi$
$677$	−1.64474e7	−	1.19497e7i	−1.37919	−	1.00204i	−0.382236	−	0.924065i	$-0.624846\pi$
$678$	−198213.	−	610038.i	−0.0165599	−	0.0509663i
$679$	6.81243e6	+	2.09665e7i	0.567058	+	1.74523i
$680$	−827126.	−	3.78840e6i	−0.0685961	−	0.314184i
$681$	726587.	−	2.23620e6i	0.0600371	−	0.184775i
$682$	−3.01750e6			−0.248420
$683$	1.47068e6	−	4.52627e6i	0.120633	−	0.371269i	−0.872447	−	0.488708i	$-0.837468\pi$
$683$	1.47068e6	−	4.52627e6i	0.120633	−	0.371269i	0.993080	+	0.117439i	$0.0374683\pi$
$684$	−2.57524e6	+	1.87102e6i	−0.210464	+	0.152911i
$685$	−6.26982e6	−	624022.i	−0.510539	−	0.0508129i
$686$	3.42502e6	+	2.48842e6i	0.277877	+	0.201889i
$687$	8.49807e6	−	6.17421e6i	0.686956	−	0.499102i
$688$	4.32659e6	−	3.14346e6i	0.348478	−	0.253184i
$689$	884616.	+	642711.i	0.0709916	+	0.0515784i
$690$	−2.17134e6	−	216109.i	−0.173622	−	0.0172802i
$691$	1.05555e7	−	7.66905e6i	0.840980	−	0.611008i	−0.0816643	−	0.996660i	$-0.526024\pi$
$691$	1.05555e7	−	7.66905e6i	0.840980	−	0.611008i	0.922644	+	0.385652i	$0.126024\pi$
$692$	412959.	−	1.27096e6i	0.0327825	−	0.100894i
$693$	3.51744e6			0.278223
$694$	314720.	−	968608.i	0.0248042	−	0.0763395i
$695$	145421.	+	666056.i	0.0114200	+	0.0523056i
$696$	1.30285e6	+	4.00976e6i	0.101946	+	0.313759i
$697$	−4.24720e6	−	1.30715e7i	−0.331147	−	1.01916i
$698$	−8.47018e6	−	6.15395e6i	−0.658043	−	0.478096i
$699$	−1.08105e7			−0.836857
$700$	7.49528e6	−	3.43673e6i	0.578153	−	0.265094i
$701$	1.23990e7			0.953000			0.476500	−	0.879174i	$-0.341905\pi$
$701$	1.23990e7			0.953000			0.476500	+	0.879174i	$0.341905\pi$
$702$	−2.00985e6	−	1.46024e6i	−0.153929	−	0.111836i
$703$	−1.18669e6	−	3.65224e6i	−0.0905623	−	0.278722i
$704$	−333296.	−	1.02578e6i	−0.0253453	−	0.0780050i
$705$	−3.55487e6	−	353809.i	−0.269371	−	0.0268099i
$706$	1.75953e6	−	5.41527e6i	0.132857	−	0.408892i
$707$	−2.45884e7			−1.85004
$708$	1.26751e6	−	3.90101e6i	0.0950320	−	0.292478i
$709$	−2.06930e7	+	1.50343e7i	−1.54599	+	1.12323i	−0.599560	+	0.800330i	$0.704658\pi$
$709$	−2.06930e7	+	1.50343e7i	−1.54599	+	1.12323i	−0.946433	+	0.322900i	$0.895342\pi$
$710$	6.46105e6	−	3.77798e6i	0.481013	−	0.281264i
$711$	2.18563e6	+	1.58795e6i	0.162144	+	0.117805i
$712$	−6.52033e6	+	4.73729e6i	−0.482025	+	0.350211i
$713$	2.51303e6	−	1.82583e6i	0.185129	−	0.134504i
$714$	−5.20567e6	−	3.78214e6i	−0.382147	−	0.277646i
$715$	−9.36591e6	−	8.33998e6i	−0.685149	−	0.610098i
$716$	2.34170e6	−	1.70134e6i	0.170706	−	0.124025i
$717$	−3.78114e6	+	1.16371e7i	−0.274678	+	0.845373i
$718$	−5.28815e6			−0.382819
$719$	5.56324e6	−	1.71219e7i	0.401334	−	1.23518i	−0.522585	−	0.852587i	$-0.675032\pi$
$719$	5.56324e6	−	1.71219e7i	0.401334	−	1.23518i	0.923918	−	0.382590i	$-0.124968\pi$
$720$	−1.00066e6	+	585120.i	−0.0719378	+	0.0420643i
$721$	4.54028e6	+	1.39735e7i	0.325270	+	1.00108i
$722$	−4.39615e6	−	1.35300e7i	−0.313856	−	0.965948i
$723$	−7.22869e6	−	5.25195e6i	−0.514297	−	0.373659i
$724$	8.91209e6			0.631878
$725$	2.07924e7	−	9.53371e6i	1.46913	−	0.673623i
$726$	3.30165e6			0.232482
$727$	1.06528e7	+	7.73974e6i	0.747532	+	0.543114i	0.895061	−	0.445944i	$-0.147132\pi$
$727$	1.06528e7	+	7.73974e6i	0.747532	+	0.543114i	−0.147529	+	0.989058i	$0.547132\pi$
$728$	−2.77865e6	−	8.55180e6i	−0.194315	−	0.598039i
$729$	164224.	+	505430.i	0.0114451	+	0.0352243i
$730$	4.34238e6	−	9.89982e6i	0.301593	−	0.687575i
$731$	−6.99671e6	+	2.15337e7i	−0.484284	+	1.49047i
$732$	4.70016e6			0.324216
$733$	3.94622e6	−	1.21452e7i	0.271282	−	0.834921i	−0.718897	−	0.695117i	$-0.755353\pi$
$733$	3.94622e6	−	1.21452e7i	0.271282	−	0.834921i	0.990179	−	0.139804i	$-0.0446474\pi$
$734$	2.51466e6	−	1.82700e6i	0.172281	−	0.125170i
$735$	2.09960e6	−	4.78669e6i	0.143357	−	0.326826i
$736$	898251.	+	652618.i	0.0611228	+	0.0444083i
$737$	8.03751e6	−	5.83959e6i	0.545071	−	0.396017i
$738$	−3.32399e6	+	2.41502e6i	−0.224656	+	0.163222i
$739$	−9.61445e6	−	6.98531e6i	−0.647610	−	0.470516i	0.214846	−	0.976648i	$-0.431075\pi$
$739$	−9.61445e6	−	6.98531e6i	−0.647610	−	0.470516i	−0.862456	+	0.506132i	$0.831075\pi$
$740$	−298296.	−	1.36626e6i	−0.0200248	−	0.0917176i
$741$	1.52361e7	−	1.10696e7i	1.01936	−	0.740607i
$742$	261623.	−	805191.i	0.0174448	−	0.0536895i
$743$	−1.53927e7			−1.02292			−0.511461	−	0.859307i	$-0.670895\pi$
$743$	−1.53927e7			−1.02292			−0.511461	+	0.859307i	$0.670895\pi$
$744$	509924.	−	1.56938e6i	0.0337733	−	0.103943i
$745$	−1.06135e7	−	9.45088e6i	−0.700594	−	0.623852i
$746$	757692.	+	2.33194e6i	0.0498477	+	0.153416i
$747$	−330220.	−	1.01631e6i	−0.0216522	−	0.0666385i
$748$	3.69427e6	+	2.68404e6i	0.241421	+	0.175402i
$749$	1.93387e7			1.25957
$750$	3.78027e6	+	5.02597e6i	0.245397	+	0.326262i
$751$	−2.57476e6			−0.166586			−0.0832928	−	0.996525i	$-0.526544\pi$
$751$	−2.57476e6			−0.166586			−0.0832928	+	0.996525i	$0.526544\pi$
$752$	1.47060e6	+	1.06845e6i	0.0948307	+	0.0688986i
$753$	4.80537e6	+	1.47894e7i	0.308844	+	0.950524i
$754$	−7.70815e6	−	2.37232e7i	−0.493767	−	1.51966i
$755$	9.89972e6	+	8.81531e6i	0.632056	+	0.562821i
$756$	−594406.	+	1.82939e6i	−0.0378250	+	0.116413i
$757$	2.02440e7			1.28398			0.641989	−	0.766714i	$-0.278110\pi$
$757$	2.02440e7			1.28398			0.641989	+	0.766714i	$0.278110\pi$
$758$	−4.87849e6	+	1.50145e7i	−0.308399	+	0.949154i
$759$	2.07887e6	−	1.51039e6i	0.130986	−	0.0951666i
$760$	−1.87440e6	−	8.58514e6i	−0.117714	−	0.539155i
$761$	−1.13970e7	−	8.28043e6i	−0.713395	−	0.518312i	0.170872	−	0.985293i	$-0.445342\pi$
$761$	−1.13970e7	−	8.28043e6i	−0.713395	−	0.518312i	−0.884267	+	0.466981i	$0.845342\pi$
$762$	6.96265e6	−	5.05866e6i	0.434397	−	0.315608i
$763$	1.99623e7	−	1.45035e7i	1.24136	−	0.901904i
$764$	1.07306e7	+	7.79622e6i	0.665104	+	0.483226i
$765$	1.97135e6	−	4.49430e6i	0.121789	−	0.277657i
$766$	9.71520e6	−	7.05851e6i	0.598246	−	0.434651i
$767$	−7.49909e6	+	2.30798e7i	−0.460278	+	1.41659i
$768$	589824.			0.0360844
$769$	5.06643e6	−	1.55929e7i	0.308948	−	0.950846i	−0.669226	−	0.743059i	$-0.733374\pi$
$769$	5.06643e6	−	1.55929e7i	0.308948	−	0.950846i	0.978174	−	0.207786i	$-0.0666259\pi$
$770$	−3.90046e6	+	8.89233e6i	−0.237077	+	0.540491i
$771$	1.16545e6	+	3.58689e6i	0.0706088	+	0.217311i
$772$	2.18353e6	+	6.72022e6i	0.131861	+	0.405827i
$773$	−5.73963e6	−	4.17009e6i	−0.345490	−	0.251013i	0.401485	−	0.915866i	$-0.368494\pi$
$773$	−5.73963e6	−	4.17009e6i	−0.345490	−	0.251013i	−0.746975	+	0.664853i	$0.768494\pi$
$774$	6.76852e6			0.406108
$775$	−8.77700e6	−	1.76459e6i	−0.524918	−	0.105534i
$776$	8.55552e6			0.510025
$777$	−1.87738e6	−	1.36400e6i	−0.111558	−	0.0810515i
$778$	4.03215e6	+	1.24097e7i	0.238829	+	0.735041i
$779$	−9.62485e6	−	2.96222e7i	−0.568264	−	1.74894i
$780$	5.92030e6	−	3.46179e6i	0.348423	−	0.203734i
$781$	−2.72364e6	+	8.38251e6i	−0.159780	+	0.491752i
$782$	−4.70071e6			−0.274882
$783$	−1.64892e6	+	5.07486e6i	−0.0961159	+	0.295814i
$784$	−2.15167e6	+	1.56328e6i	−0.125022	+	0.0908337i
$785$	1.50991e7	+	1.34451e7i	0.874533	+	0.778737i
$786$	−9.50477e6	−	6.90562e6i	−0.548763	−	0.398700i
$787$	2.27065e7	−	1.64973e7i	1.30681	−	0.949456i	0.306817	−	0.951768i	$-0.400736\pi$
$787$	2.27065e7	−	1.64973e7i	1.30681	−	0.949456i	0.999997	+	0.00231213i	$0.000735976\pi$
$788$	9.11110e6	−	6.61960e6i	0.522704	−	0.379766i
$789$	−1.99217e6	−	1.44740e6i	−0.113929	−	0.0827743i
$790$	−6.43808e6	+	3.76455e6i	−0.367019	+	0.214608i
$791$	2.37717e6	−	1.72711e6i	0.135088	−	0.0981475i
$792$	421828.	−	1.29825e6i	0.0238958	−	0.0735438i
$793$	−2.78079e7			−1.57031
$794$	2.36249e6	−	7.27099e6i	0.132990	−	0.409300i
$795$	642549.	+	63951.6i	0.0360569	+	0.00358867i
$796$	2.98070e6	+	9.17365e6i	0.166738	+	0.513168i
$797$	−988325.	−	3.04175e6i	−0.0551130	−	0.169620i	0.919711	−	0.392596i	$-0.128423\pi$
$797$	−988325.	−	3.04175e6i	−0.0551130	−	0.169620i	−0.974824	+	0.222976i	$0.928423\pi$
$798$	−1.17969e7	−	8.57095e6i	−0.655784	−	0.476455i
$799$	−7.69589e6			−0.426474
$800$	−369595.	−	3.17858e6i	−0.0204174	−	0.175594i
$801$	−1.02004e7			−0.561740
$802$	5.86421e6	+	4.26060e6i	0.321939	+	0.233902i
$803$	3.93390e6	+	1.21073e7i	0.215295	+	0.662610i
$804$	1.67889e6	+	5.16708e6i	0.0915970	+	0.281906i
$805$	−2.13217e6	−	9.76577e6i	−0.115967	−	0.531150i
$806$	−3.01690e6	+	9.28506e6i	−0.163577	+	0.503439i
$807$	1.49444e7			0.807784
$808$	−2.94876e6	+	9.07535e6i	−0.158895	+	0.489029i
$809$	−1.14474e6	+	831701.i	−0.0614943	+	0.0446782i	−0.618108	−	0.786093i	$-0.712100\pi$
$809$	−1.14474e6	+	831701.i	−0.0614943	+	0.0446782i	0.556613	+	0.830772i	$0.312100\pi$
$810$	−1.45987e6	−	145298.i	−0.0781812	−	0.00778121i
$811$	9.43205e6	+	6.85279e6i	0.503563	+	0.365860i	0.810376	−	0.585910i	$-0.199263\pi$
$811$	9.43205e6	+	6.85279e6i	0.503563	+	0.365860i	−0.306813	+	0.951770i	$0.599263\pi$
$812$	−1.56250e7	+	1.13523e7i	−0.831631	+	0.604216i
$813$	−1.58946e7	+	1.15481e7i	−0.843378	+	0.612750i
$814$	1.33231e6	+	967977.i	0.0704763	+	0.0512040i
$815$	−6.40703e6	−	637678.i	−0.337880	−	0.0336285i
$816$	−2.02024e6	+	1.46779e6i	−0.106213	+	0.0771683i
$817$	−1.58557e7	+	4.87988e7i	−0.831056	+	2.55773i
$818$	−1.57750e6			−0.0824304
$819$	3.51673e6	−	1.08234e7i	0.183201	−	0.563836i
$820$	−2.41939e6	−	1.10813e7i	−0.125652	−	0.575513i
$821$	2.53056e6	+	7.78826e6i	0.131026	+	0.403258i	0.994951	−	0.100364i	$-0.0320007\pi$
$821$	2.53056e6	+	7.78826e6i	0.131026	+	0.403258i	−0.863924	+	0.503621i	$0.832001\pi$
$822$	1.25388e6	+	3.85904e6i	0.0647255	+	0.199205i
$823$	−3.62966e6	−	2.63710e6i	−0.186795	−	0.135715i	0.490458	−	0.871465i	$-0.336830\pi$
$823$	−3.62966e6	−	2.63710e6i	−0.186795	−	0.135715i	−0.677253	+	0.735750i	$0.736830\pi$
$824$	5.70199e6			0.292556
$825$	−7.26065e6	−	1.45974e6i	−0.371399	−	0.0746689i
$826$	1.87898e7			0.958234
$827$	−1.58142e7	−	1.14897e7i	−0.804053	−	0.584179i	0.108047	−	0.994146i	$-0.465540\pi$
$827$	−1.58142e7	−	1.14897e7i	−0.804053	−	0.584179i	−0.912100	+	0.409967i	$0.865540\pi$
$828$	434238.	+	1.33645e6i	0.0220116	+	0.0677448i
$829$	7.93497e6	+	2.44213e7i	0.401014	+	1.23419i	0.924178	+	0.381961i	$0.124751\pi$
$829$	7.93497e6	+	2.44213e7i	0.401014	+	1.23419i	−0.523165	+	0.852232i	$0.675249\pi$
$830$	2.93549e6	+	292163.i	0.147906	+	0.0147208i
$831$	−2.24996e6	+	6.92466e6i	−0.113024	+	0.347853i
$832$	−3.48962e6			−0.174771
$833$	3.47956e6	−	1.07090e7i	0.173745	−	0.534731i
$834$	355187.	−	258059.i	0.0176824	−	0.0128471i
$835$	−2.28510e6	+	1.33617e6i	−0.113420	+	0.0663203i
$836$	8.37182e6	+	6.08248e6i	0.414290	+	0.300999i
$837$	1.68961e6	−	1.22757e6i	0.0833627	−	0.0605666i
$838$	475365.	−	345373.i	0.0233839	−	0.0169894i
$839$	−1.90484e7	−	1.38394e7i	−0.934228	−	0.678756i	0.0127965	−	0.999918i	$-0.495927\pi$
$839$	−1.90484e7	−	1.38394e7i	−0.934228	−	0.678756i	−0.947024	+	0.321162i	$0.895927\pi$
$840$	−3.96571e6	−	3.53131e6i	−0.193920	−	0.172678i
$841$	−2.67510e7	+	1.94357e7i	−1.30422	+	0.947568i
$842$	8.33965e6	−	2.56668e7i	0.405385	−	1.24765i
$843$	−1.75608e7			−0.851088
$844$	−3.16345e6	+	9.73610e6i	−0.152864	+	0.470467i
$845$	−1.71091e7	+	1.00042e7i	−0.824299	+	0.481994i
$846$	710925.	+	2.18800e6i	0.0341505	+	0.105105i
$847$	4.67373e6	+	1.43843e7i	0.223849	+	0.688937i
$848$	−265813.	−	193125.i	−0.0126937	−	0.00922249i
$849$	−2.15877e7			−1.02787
$850$	9.17590e6	+	9.96741e6i	0.435614	+	0.473189i
$851$	−1.69527e6			−0.0802445
$852$	−3.89942e6	−	2.83309e6i	−0.184035	−	0.133709i
$853$	6.36453e6	+	1.95880e7i	0.299498	+	0.921760i	0.981673	+	0.190571i	$0.0610340\pi$
$853$	6.36453e6	+	1.95880e7i	0.299498	+	0.921760i	−0.682176	+	0.731188i	$0.738966\pi$
$854$	6.65343e6	+	2.04772e7i	0.312177	+	0.960782i
$855$	4.46740e6	−	1.01848e7i	0.208997	−	0.476473i
$856$	2.31919e6	−	7.13772e6i	0.108181	−	0.332947i
$857$	−2.68938e7			−1.25084			−0.625418	−	0.780290i	$-0.715071\pi$
$857$	−2.68938e7			−1.25084			−0.625418	+	0.780290i	$0.715071\pi$
$858$	−2.49569e6	+	7.68094e6i	−0.115737	+	0.356202i
$859$	3.10362e7	−	2.25491e7i	1.43511	−	1.04267i	0.446074	−	0.894996i	$-0.352822\pi$
$859$	3.10362e7	−	2.25491e7i	1.43511	−	1.04267i	0.989036	−	0.147673i	$-0.0471783\pi$
$860$	−7.50557e6	+	1.71113e7i	−0.346049	+	0.788927i
$861$	−1.52269e7	−	1.10630e7i	−0.700008	−	0.508585i
$862$	−225758.	+	164023.i	−0.0103484	+	0.00751858i
$863$	3.02517e7	−	2.19792e7i	1.38268	−	1.00458i	0.386061	−	0.922473i	$-0.373836\pi$
$863$	3.02517e7	−	2.19792e7i	1.38268	−	1.00458i	0.996624	−	0.0821054i	$-0.0261644\pi$
$864$	603928.	+	438779.i	0.0275233	+	0.0199969i
$865$	995940.	+	4.56160e6i	0.0452577	+	0.207289i
$866$	1.60859e6	−	1.16871e6i	0.0728873	−	0.0529557i
$867$	−681828.	+	2.09845e6i	−0.0308054	+	0.0948093i
$868$	7.55916e6			0.340545
$869$	2.71396e6	−	8.35271e6i	0.121914	−	0.375213i
$870$	−1.10011e7	−	9.79607e6i	−0.492764	−	0.438787i
$871$	−9.93291e6	−	3.05704e7i	−0.443640	−	1.36539i
$872$	−2.95911e6	−	9.10722e6i	−0.131786	−	0.405597i
$873$	8.76010e6	+	6.36458e6i	0.389021	+	0.282640i
$874$	−1.06526e7			−0.471711
$875$	−1.65454e7	+	2.35841e7i	−0.730560	+	1.04136i
$876$	−6.96170e6			−0.306518
$877$	−4.49402e6	−	3.26509e6i	−0.197304	−	0.143350i	0.484747	−	0.874654i	$-0.338912\pi$
$877$	−4.49402e6	−	3.26509e6i	−0.197304	−	0.143350i	−0.682051	+	0.731305i	$0.738912\pi$
$878$	−1.49206e6	−	4.59207e6i	−0.0653204	−	0.201035i
$879$	−5.11865e6	−	1.57536e7i	−0.223451	−	0.687713i
$880$	2.81431e6	+	2.50603e6i	0.122508	+	0.109089i
$881$	5.65065e6	−	1.73909e7i	0.245278	−	0.754888i	−0.750313	−	0.661083i	$-0.770097\pi$
$881$	5.65065e6	−	1.73909e7i	0.245278	−	0.754888i	0.995591	−	0.0938048i	$-0.0299030\pi$
$882$	−3.36607e6			−0.145698
$883$	−1.10765e7	+	3.40899e7i	−0.478079	+	1.47138i	0.363680	+	0.931524i	$0.381520\pi$
$883$	−1.10765e7	+	3.40899e7i	−0.478079	+	1.47138i	−0.841759	+	0.539853i	$0.818480\pi$
$884$	1.19525e7	−	8.68399e6i	0.514432	−	0.373757i
$885$	3.05689e6	+	1.40012e7i	0.131196	+	0.600905i
$886$	1.94133e7	+	1.41046e7i	0.830836	+	0.603638i
$887$	−2.57094e7	+	1.86789e7i	−1.09719	+	0.797156i	−0.980599	−	0.196024i	$-0.937197\pi$
$887$	−2.57094e7	+	1.86789e7i	−1.09719	+	0.797156i	−0.116592	+	0.993180i	$0.537197\pi$
$888$	−728583.	+	529346.i	−0.0310061	+	0.0225272i
$889$	3.18952e7	+	2.31732e7i	1.35354	+	0.983404i
$890$	1.13111e7	−	2.57873e7i	0.478665	−	1.09127i
$891$	1.39770e6	−	1.01549e6i	0.0589822	−	0.0428531i
$892$	1.44038e6	−	4.43304e6i	0.0606130	−	0.186548i
$893$	−1.74402e7			−0.731850
$894$	−2.82812e6	+	8.70406e6i	−0.118346	+	0.364232i
$895$	−4.06226e6	+	9.26120e6i	−0.169516	+	0.386464i
$896$	834941.	+	2.56968e6i	0.0347445	+	0.106932i
$897$	−2.56911e6	−	7.90691e6i	−0.106611	−	0.328115i
$898$	4.88770e6	+	3.55112e6i	0.202262	+	0.146952i
$899$	2.09696e7			0.865348
$900$	1.98617e6	−	3.52954e6i	0.0817352	−	0.145249i
$901$	1.39105e6			0.0570861
$902$	1.08059e7	+	7.85097e6i	0.442228	+	0.321297i
$903$	9.58136e6	+	2.94884e7i	0.391028	+	1.20346i
$904$	−352380.	−	1.08451e6i	−0.0143413	−	0.0441381i
$905$	−2.68796e7	+	1.57173e7i	−1.09094	+	0.637908i
$906$	2.63793e6	−	8.11871e6i	0.106768	−	0.328599i
$907$	−1.84762e7			−0.745753			−0.372877	−	0.927881i	$-0.621629\pi$
$907$	−1.84762e7			−0.745753			−0.372877	+	0.927881i	$0.621629\pi$
$908$	1.29171e6	−	3.97547e6i	0.0519936	−	0.160020i
$909$	−9.77057e6	+	7.09873e6i	−0.392202	+	0.284952i
$910$	2.34626e7	+	2.08925e7i	0.939231	+	0.836348i
$911$	1.60654e7	+	1.16722e7i	0.641351	+	0.465968i	0.860314	−	0.509765i	$-0.170268\pi$
$911$	1.60654e7	+	1.16722e7i	0.641351	+	0.465968i	−0.218963	+	0.975733i	$0.570268\pi$
$912$	−4.57820e6	+	3.32626e6i	−0.182267	+	0.132425i
$913$	−2.81048e6	+	2.04193e6i	−0.111584	+	0.0810709i
$914$	1.15019e7	+	8.35665e6i	0.455413	+	0.330877i
$915$	−1.41761e7	+	8.28919e6i	−0.559761	+	0.327310i
$916$	1.51077e7	−	1.09764e7i	0.594921	−	0.432235i
$917$	1.66310e7	−	5.11848e7i	0.653121	−	2.01010i
$918$	−3.16046e6			−0.123778
$919$	−4.42266e6	+	1.36116e7i	−0.172741	+	0.531642i	−0.999523	−	0.0308805i	$-0.990169\pi$
$919$	−4.42266e6	+	1.36116e7i	−0.172741	+	0.531642i	0.826782	+	0.562522i	$0.190169\pi$
$920$	−3.86015e6	−	384193.i	−0.150361	−	0.0149651i
$921$	−65272.3	−	200887.i	−0.00253559	−	0.00780375i
$922$	−7.07150e6	−	2.17638e7i	−0.273958	−	0.843157i
$923$	2.30704e7	+	1.67616e7i	0.891356	+	0.647608i
$924$	6.25322e6			0.240948
$925$	3.30921e6	+	3.59466e6i	0.127166	+	0.138135i
$926$	−2.11112e7			−0.809070
$927$	5.83834e6	+	4.24180e6i	0.223146	+	0.162125i
$928$	2.31618e6	+	7.12847e6i	0.0882881	+	0.271723i
$929$	371533.	+	1.14346e6i	0.0141240	+	0.0434692i	0.957870	−	0.287202i	$-0.0927250\pi$
$929$	371533.	+	1.14346e6i	0.0141240	+	0.0434692i	−0.943746	+	0.330671i	$0.892725\pi$
$930$	1.22979e6	+	5.63269e6i	0.0466256	+	0.213554i
$931$	7.88525e6	−	2.42683e7i	0.298155	−	0.917625i
$932$	−1.92186e7			−0.724739
$933$	−4.95080e6	+	1.52370e7i	−0.186196	+	0.573054i
$934$	−5.88539e6	+	4.27598e6i	−0.220754	+	0.160387i
$935$	−1.58758e7	−	1.58008e6i	−0.593890	−	0.0591087i
$936$	−3.57306e6	−	2.59598e6i	−0.133306	−	0.0968527i
$937$	−5.51883e6	+	4.00967e6i	−0.205352	+	0.149197i	−0.685708	−	0.727877i	$-0.740507\pi$
$937$	−5.51883e6	+	4.00967e6i	−0.205352	+	0.149197i	0.480356	+	0.877073i	$0.340507\pi$
$938$	−2.01348e7	+	1.46288e7i	−0.747206	+	0.542877i
$939$	−2.43943e7	−	1.77235e7i	−0.902870	−	0.655973i
$940$	−6.31976e6	−	628993.i	−0.233282	−	0.0232181i
$941$	−8.47492e6	+	6.15739e6i	−0.312005	+	0.226685i	−0.732756	−	0.680491i	$-0.761767\pi$
$941$	−8.47492e6	+	6.15739e6i	−0.312005	+	0.226685i	0.420751	+	0.907176i	$0.361767\pi$
$942$	4.02338e6	−	1.23827e7i	0.147728	−	0.454661i
$943$	−1.37498e7			−0.503521
$944$	2.25336e6	−	6.93513e6i	0.0823001	−	0.253294i
$945$	−1.43354e6	−	6.56590e6i	−0.0522192	−	0.239174i
$946$	−6.79953e6	−	2.09268e7i	−0.247031	−	0.760282i
$947$	2.28443e6	+	7.03077e6i	0.0827759	+	0.254758i	0.983876	−	0.178854i	$-0.0572389\pi$
$947$	2.28443e6	+	7.03077e6i	0.0827759	+	0.254758i	−0.901100	+	0.433612i	$0.857239\pi$
$948$	3.88556e6	+	2.82302e6i	0.140421	+	0.102022i
$949$	4.11880e7			1.48459
$950$	2.07941e7	+	2.25878e7i	0.747535	+	0.812017i
$951$	−6.33848e6			−0.227266
$952$	−9.25452e6	−	6.72380e6i	−0.330949	−	0.240449i
$953$	1.18660e7	+	3.65198e7i	0.423226	+	1.30256i	0.904682	+	0.426086i	$0.140108\pi$
$953$	1.18660e7	+	3.65198e7i	0.423226	+	1.30256i	−0.481456	+	0.876470i	$0.659892\pi$
$954$	−128501.	−	395486.i	−0.00457126	−	0.0140689i
$955$	−4.61137e7	−	4.58960e6i	−1.63614	−	0.162842i
$956$	−6.72202e6	+	2.06882e7i	−0.237878	+	0.732114i
$957$	1.73468e7			0.612266
$958$	−8.82181e6	+	2.71507e7i	−0.310559	+	0.955802i
$959$	−1.50377e7	+	1.09255e7i	−0.528001	+	0.383615i
$960$	−1.77896e6	+	1.04021e6i	−0.0622999	+	0.0364287i
$961$	1.65216e7	+	1.20037e7i	0.577091	+	0.419281i
$962$	4.31057e6	−	3.13181e6i	0.150175	−	0.109108i
$963$	7.68450e6	−	5.58312e6i	0.267024	−	0.194004i
$964$	−1.28510e7	−	9.33680e6i	−0.445394	−	0.323598i
$965$	−1.84375e7	−	1.64179e7i	−0.637358	−	0.567543i
$966$	−5.20779e6	+	3.78368e6i	−0.179561	+	0.130458i
$967$	1.59796e7	−	4.91801e7i	0.549540	−	1.69131i	−0.160403	−	0.987052i	$-0.551279\pi$
$967$	1.59796e7	−	4.91801e7i	0.549540	−	1.69131i	0.709943	−	0.704259i	$-0.248721\pi$
$968$	5.86959e6			0.201335
$969$	7.40359e6	−	2.27859e7i	0.253299	−	0.779573i
$970$	−2.58041e7	+	1.50885e7i	−0.880562	+	0.514893i
$971$	1.67480e7	+	5.15449e7i	0.570051	+	1.75444i	0.652443	+	0.757838i	$0.273744\pi$
$971$	1.67480e7	+	5.15449e7i	0.570051	+	1.75444i	−0.0823913	+	0.996600i	$0.526256\pi$
$972$	291954.	+	898543.i	0.00991172	+	0.0305052i
$973$	1.62708e6	+	1.18214e6i	0.0550968	+	0.0400302i
$974$	−2.91355e7			−0.984069
$975$	−1.17509e7	+	2.08821e7i	−0.395876	+	0.703496i
$976$	8.35583e6			0.280779
$977$	9.99827e6	+	7.26417e6i	0.335111	+	0.243472i	0.742596	−	0.669740i	$-0.233594\pi$
$977$	9.99827e6	+	7.26417e6i	0.335111	+	0.243472i	−0.407485	+	0.913212i	$0.633594\pi$
$978$	1.28132e6	+	3.94349e6i	0.0428361	+	0.131836i
$979$	1.02471e7	+	3.15374e7i	0.341700	+	1.05164i
$980$	3.73262e6	−	8.50968e6i	0.124151	−	0.283040i
$981$	3.74513e6	−	1.15263e7i	0.124249	−	0.382400i
$982$	4.61544e6			0.152734
$983$	490956.	−	1.51101e6i	0.0162053	−	0.0498749i	−0.942627	−	0.333848i	$-0.891653\pi$
$983$	490956.	−	1.51101e6i	0.0162053	−	0.0498749i	0.958832	+	0.283973i	$0.0916527\pi$
$984$	−5.90931e6	+	4.29337e6i	−0.194558	+	0.141355i
$985$	−1.58055e7	+	3.60336e7i	−0.519060	+	1.18336i
$986$	−2.56726e7	−	1.86523e7i	−0.840965	−	0.610997i
$987$	−8.52609e6	+	6.19457e6i	−0.278584	+	0.202403i
$988$	2.70863e7	−	1.96794e7i	0.882791	−	0.641385i
$989$	1.83251e7	+	1.33140e7i	0.595739	+	0.432829i
$990$	1.01733e6	+	4.65957e6i	0.0329893	+	0.151098i
$991$	1.55807e7	−	1.13201e7i	0.503969	−	0.366155i	−0.306562	−	0.951851i	$-0.599179\pi$
$991$	1.55807e7	−	1.13201e7i	0.503969	−	0.366155i	0.810531	+	0.585696i	$0.199179\pi$
$992$	906531.	−	2.79002e6i	0.0292485	−	0.0900176i
$993$	1.66079e7			0.534494
$994$	6.82301e6	−	2.09991e7i	0.219033	−	0.674115i
$995$	−2.51687e7	−	2.24117e7i	−0.805940	−	0.717658i
$996$	−587057.	−	1.80678e6i	−0.0187513	−	0.0577106i
$997$	4.59742e6	+	1.41494e7i	0.146479	+	0.450816i	0.997198	−	0.0748041i	$-0.0238332\pi$
$997$	4.59742e6	+	1.41494e7i	0.146479	+	0.450816i	−0.850719	+	0.525621i	$0.823833\pi$
$998$	−1.62617e6	−	1.18148e6i	−0.0516820	−	0.0375492i
$999$	−1.13979e6			−0.0361337

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.6.g.c.91.1	yes	24
25.11	even	5	inner	150.6.g.c.61.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.6.g.c.61.1	✓	24	25.11	even	5	inner
150.6.g.c.91.1	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	150.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.23607 + 2.35114i) q^{2} +(2.78115 + 8.55951i) q^{3} +(4.94427 + 15.2169i) q^{4} +(-41.7488 - 37.1757i) q^{5} +(-11.1246 + 34.2380i) q^{6} -164.912 q^{7} +(-19.7771 + 60.8676i) q^{8} +(-65.5304 + 47.6106i) q^{9} +O(q^{10})\)	\(q+(3.23607 + 2.35114i) q^{2} +(2.78115 + 8.55951i) q^{3} +(4.94427 + 15.2169i) q^{4} +(-41.7488 - 37.1757i) q^{5} +(-11.1246 + 34.2380i) q^{6} -164.912 q^{7} +(-19.7771 + 60.8676i) q^{8} +(-65.5304 + 47.6106i) q^{9} +(-47.6968 - 218.461i) q^{10} +(213.032 + 154.777i) q^{11} +(-116.498 + 84.6411i) q^{12} +(689.248 - 500.768i) q^{13} +(-533.668 - 387.732i) q^{14} +(202.096 - 460.741i) q^{15} +(-207.108 + 150.473i) q^{16} +(334.923 - 1030.79i) q^{17} -324.000 q^{18} +(758.991 - 2335.94i) q^{19} +(359.282 - 819.095i) q^{20} +(-458.647 - 1411.57i) q^{21} +(325.484 + 1001.74i) q^{22} +(-877.198 - 637.322i) q^{23} -576.000 q^{24} +(360.932 + 3104.09i) q^{25} +3407.83 q^{26} +(-589.773 - 428.495i) q^{27} +(-815.372 - 2509.46i) q^{28} +(-2261.89 - 6961.39i) q^{29} +(1737.26 - 1015.83i) q^{30} +(-885.284 + 2724.62i) q^{31} -1024.00 q^{32} +(-732.340 + 2253.91i) q^{33} +(3507.36 - 2548.25i) q^{34} +(6884.90 + 6130.74i) q^{35} +(-1048.49 - 761.770i) q^{36} +(1264.90 - 919.004i) q^{37} +(7948.26 - 5774.75i) q^{38} +(6203.23 + 4506.91i) q^{39} +(3088.47 - 1805.93i) q^{40} +(10259.2 - 7453.76i) q^{41} +(1834.59 - 5646.28i) q^{42} -20890.5 q^{43} +(-1301.94 + 4006.95i) q^{44} +(4505.78 + 448.451i) q^{45} +(-1340.24 - 4124.83i) q^{46} +(-2194.21 - 6753.09i) q^{47} +(-1863.98 - 1354.26i) q^{48} +10389.1 q^{49} +(-6130.14 + 10893.6i) q^{50} +9754.51 q^{51} +(11028.0 + 8012.29i) q^{52} +(396.608 + 1220.63i) q^{53} +(-901.094 - 2773.28i) q^{54} +(-3139.90 - 14381.4i) q^{55} +(3261.49 - 10037.8i) q^{56} +22105.3 q^{57} +(9047.57 - 27845.6i) q^{58} +(-23044.4 + 16742.8i) q^{59} +(8010.27 + 797.246i) q^{60} +(-26406.3 - 19185.3i) q^{61} +(-9270.82 + 6735.64i) q^{62} +(10806.8 - 7851.58i) q^{63} +(-3313.73 - 2407.57i) q^{64} +(-47391.7 - 4716.80i) q^{65} +(-7669.16 + 5571.97i) q^{66} +(11658.9 - 35882.5i) q^{67} +17341.3 q^{68} +(3015.54 - 9280.88i) q^{69} +(7865.79 + 36026.9i) q^{70} +(10343.4 + 31833.6i) q^{71} +(-1601.94 - 4930.28i) q^{72} +(39112.1 + 28416.6i) q^{73} +6254.01 q^{74} +(-25565.6 + 11722.3i) q^{75} +39298.4 q^{76} +(-35131.7 - 25524.6i) q^{77} +(9477.70 + 29169.3i) q^{78} +(-10306.6 - 31720.5i) q^{79} +(14240.5 + 1417.33i) q^{80} +(2027.46 - 6239.88i) q^{81} +50724.4 q^{82} +(-4076.78 + 12547.1i) q^{83} +(19212.0 - 13958.4i) q^{84} +(-52302.9 + 30583.2i) q^{85} +(-67603.0 - 49116.5i) q^{86} +(53295.4 - 38721.4i) q^{87} +(-13634.1 + 9905.73i) q^{88} +(101880. + 74020.2i) q^{89} +(13526.6 + 12044.9i) q^{90} +(-113666. + 82582.9i) q^{91} +(5360.96 - 16499.3i) q^{92} -25783.6 q^{93} +(8776.85 - 27012.4i) q^{94} +(-118527. + 69306.6i) q^{95} +(-2847.90 - 8764.94i) q^{96} +(-41309.4 - 127137. i) q^{97} +(33619.9 + 24426.3i) q^{98} -21329.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{2} - 54 q^{3} - 96 q^{4} + 80 q^{5} + 216 q^{6} - 454 q^{7} + 384 q^{8} - 486 q^{9}+O(q^{10}) \) 24 * q + 24 * q^2 - 54 * q^3 - 96 * q^4 + 80 * q^5 + 216 * q^6 - 454 * q^7 + 384 * q^8 - 486 * q^9	\( 24 q + 24 q^{2} - 54 q^{3} - 96 q^{4} + 80 q^{5} + 216 q^{6} - 454 q^{7} + 384 q^{8} - 486 q^{9} + 120 q^{10} + 125 q^{11} - 864 q^{12} - 578 q^{13} - 344 q^{14} + 855 q^{15} - 1536 q^{16} - 2664 q^{17} - 7776 q^{18} + 1424 q^{19} + 1520 q^{20} + 1269 q^{21} + 1280 q^{22} - 4810 q^{23} - 13824 q^{24} - 10880 q^{25} + 6392 q^{26} - 4374 q^{27} + 2256 q^{28} - 1554 q^{29} + 4320 q^{30} - 24513 q^{31} - 24576 q^{32} - 2880 q^{33} - 4004 q^{34} + 15310 q^{35} - 7776 q^{36} - 28123 q^{37} + 8384 q^{38} - 5202 q^{39} + 7680 q^{40} - 17914 q^{41} - 5076 q^{42} + 1256 q^{43} - 5120 q^{44} - 2025 q^{45} - 13040 q^{46} + 930 q^{47} - 13824 q^{48} + 24606 q^{49} - 7880 q^{50} + 29934 q^{51} - 9248 q^{52} - 49701 q^{53} + 17496 q^{54} - 99060 q^{55} - 9024 q^{56} + 12096 q^{57} + 6216 q^{58} - 14465 q^{59} - 3600 q^{60} - 52750 q^{61} - 72528 q^{62} + 6966 q^{63} - 24576 q^{64} - 34885 q^{65} - 4500 q^{66} + 199846 q^{67} + 53216 q^{68} + 29340 q^{69} + 116820 q^{70} - 42880 q^{71} + 31104 q^{72} + 35852 q^{73} + 21832 q^{74} - 28620 q^{75} + 21504 q^{76} - 114745 q^{77} - 49572 q^{78} - 236128 q^{79} - 6400 q^{80} - 39366 q^{81} + 46216 q^{82} - 97273 q^{83} + 12384 q^{84} + 372975 q^{85} - 232304 q^{86} + 21609 q^{87} - 8000 q^{88} + 278147 q^{89} - 25920 q^{90} - 103052 q^{91} + 52160 q^{92} + 114858 q^{93} - 3720 q^{94} + 79590 q^{95} + 55296 q^{96} - 249803 q^{97} - 28164 q^{98} + 31590 q^{99}+O(q^{100}) \) 24 * q + 24 * q^2 - 54 * q^3 - 96 * q^4 + 80 * q^5 + 216 * q^6 - 454 * q^7 + 384 * q^8 - 486 * q^9 + 120 * q^10 + 125 * q^11 - 864 * q^12 - 578 * q^13 - 344 * q^14 + 855 * q^15 - 1536 * q^16 - 2664 * q^17 - 7776 * q^18 + 1424 * q^19 + 1520 * q^20 + 1269 * q^21 + 1280 * q^22 - 4810 * q^23 - 13824 * q^24 - 10880 * q^25 + 6392 * q^26 - 4374 * q^27 + 2256 * q^28 - 1554 * q^29 + 4320 * q^30 - 24513 * q^31 - 24576 * q^32 - 2880 * q^33 - 4004 * q^34 + 15310 * q^35 - 7776 * q^36 - 28123 * q^37 + 8384 * q^38 - 5202 * q^39 + 7680 * q^40 - 17914 * q^41 - 5076 * q^42 + 1256 * q^43 - 5120 * q^44 - 2025 * q^45 - 13040 * q^46 + 930 * q^47 - 13824 * q^48 + 24606 * q^49 - 7880 * q^50 + 29934 * q^51 - 9248 * q^52 - 49701 * q^53 + 17496 * q^54 - 99060 * q^55 - 9024 * q^56 + 12096 * q^57 + 6216 * q^58 - 14465 * q^59 - 3600 * q^60 - 52750 * q^61 - 72528 * q^62 + 6966 * q^63 - 24576 * q^64 - 34885 * q^65 - 4500 * q^66 + 199846 * q^67 + 53216 * q^68 + 29340 * q^69 + 116820 * q^70 - 42880 * q^71 + 31104 * q^72 + 35852 * q^73 + 21832 * q^74 - 28620 * q^75 + 21504 * q^76 - 114745 * q^77 - 49572 * q^78 - 236128 * q^79 - 6400 * q^80 - 39366 * q^81 + 46216 * q^82 - 97273 * q^83 + 12384 * q^84 + 372975 * q^85 - 232304 * q^86 + 21609 * q^87 - 8000 * q^88 + 278147 * q^89 - 25920 * q^90 - 103052 * q^91 + 52160 * q^92 + 114858 * q^93 - 3720 * q^94 + 79590 * q^95 + 55296 * q^96 - 249803 * q^97 - 28164 * q^98 + 31590 * q^99

Introduction

L-functions

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