LMFDB - Embedded newform 33.8.e.a.4.5

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			4.5
Character	$\chi$	$=$	33.4
Dual form			33.8.e.a.25.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.67280 + 4.84807i) q^{2} +(-8.34346 + 25.6785i) q^{3} +(-18.5317 - 57.0347i) q^{4} +(269.190 - 195.578i) q^{5} +(-180.166 + 130.898i) q^{6} +(-36.4929 - 112.314i) q^{7} +(479.095 - 1474.50i) q^{8} +(-589.773 - 428.495i) q^{9} +O(q^{10})$	\(q+(6.67280 + 4.84807i) q^{2} +(-8.34346 + 25.6785i) q^{3} +(-18.5317 - 57.0347i) q^{4} +(269.190 - 195.578i) q^{5} +(-180.166 + 130.898i) q^{6} +(-36.4929 - 112.314i) q^{7} +(479.095 - 1474.50i) q^{8} +(-589.773 - 428.495i) q^{9} +2744.43 q^{10} +(4083.84 - 1676.14i) q^{11} +1619.19 q^{12} +(6585.24 + 4784.46i) q^{13} +(300.995 - 926.366i) q^{14} +(2776.18 + 8544.19i) q^{15} +(4135.26 - 3004.45i) q^{16} +(1949.84 - 1416.64i) q^{17} +(-1858.06 - 5718.53i) q^{18} +(4248.60 - 13075.8i) q^{19} +(-16143.3 - 11728.8i) q^{20} +3188.52 q^{21} +(35376.7 + 8614.19i) q^{22} +20856.3 q^{23} +(33865.7 + 24604.9i) q^{24} +(10070.5 - 30993.8i) q^{25} +(20746.6 + 63851.5i) q^{26} +(15923.9 - 11569.4i) q^{27} +(-5729.50 + 4162.72i) q^{28} +(-40052.4 - 123269. i) q^{29} +(-22898.0 + 70472.8i) q^{30} +(-106523. - 77393.2i) q^{31} -156289. q^{32} +(8967.49 + 118852. i) q^{33} +19878.9 q^{34} +(-31789.5 - 23096.4i) q^{35} +(-13509.6 + 41578.3i) q^{36} +(11937.4 + 36739.6i) q^{37} +(91742.6 - 66654.9i) q^{38} +(-177802. + 129180. i) q^{39} +(-159412. - 490621. i) q^{40} +(-166928. + 513752. i) q^{41} +(21276.4 + 15458.2i) q^{42} -540279. q^{43} +(-171279. - 201859. i) q^{44} -242565. q^{45} +(139170. + 101113. i) q^{46} +(-325407. + 1.00150e6i) q^{47} +(42647.3 + 131255. i) q^{48} +(654978. - 475869. i) q^{49} +(217459. - 157993. i) q^{50} +(20108.9 + 61888.7i) q^{51} +(150845. - 464252. i) q^{52} +(1.05912e6 + 769495. i) q^{53} +162346. q^{54} +(771511. - 1.24991e6i) q^{55} -183090. q^{56} +(300320. + 218195. i) q^{57} +(330354. - 1.01672e6i) q^{58} +(510445. + 1.57099e6i) q^{59} +(435868. - 316677. i) q^{60} +(2.34594e6 - 1.70443e6i) q^{61} +(-335596. - 1.03286e6i) q^{62} +(-26603.3 + 81876.5i) q^{63} +(-1.57220e6 - 1.14227e6i) q^{64} +2.70841e6 q^{65} +(-516364. + 836549. i) q^{66} -3.29141e6 q^{67} +(-116932. - 84955.8i) q^{68} +(-174014. + 535560. i) q^{69} +(-100152. - 308236. i) q^{70} +(215363. - 156470. i) q^{71} +(-914374. + 664332. i) q^{72} +(1.26683e6 + 3.89890e6i) q^{73} +(-98460.2 + 303029. i) q^{74} +(711852. + 517191. i) q^{75} -824510. q^{76} +(-337284. - 397503. i) q^{77} -1.81271e6 q^{78} +(2.82550e6 + 2.05284e6i) q^{79} +(525568. - 1.61753e6i) q^{80} +(164224. + 505430. i) q^{81} +(-3.60459e6 + 2.61889e6i) q^{82} +(-4.86007e6 + 3.53105e6i) q^{83} +(-59088.8 - 181857. i) q^{84} +(247813. - 762691. i) q^{85} +(-3.60517e6 - 2.61931e6i) q^{86} +3.49953e6 q^{87} +(-514927. - 6.82465e6i) q^{88} -1.14935e7 q^{89} +(-1.61859e6 - 1.17597e6i) q^{90} +(297045. - 914211. i) q^{91} +(-386504. - 1.18954e6i) q^{92} +(2.87611e6 - 2.08962e6i) q^{93} +(-7.02672e6 + 5.10521e6i) q^{94} +(-1.41366e6 - 4.35081e6i) q^{95} +(1.30399e6 - 4.01328e6i) q^{96} +(1.26805e7 + 9.21294e6i) q^{97} +6.67759e6 q^{98} +(-3.12676e6 - 761363. i) 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 $

$2$	6.67280	+	4.84807i	0.589798	+	0.428513i	0.842243	−	0.539098i	$-0.181235\pi$
$2$	6.67280	+	4.84807i	0.589798	+	0.428513i	−0.252445	+	0.967611i	$0.581235\pi$
$3$	−8.34346	+	25.6785i	−0.178411	+	0.549093i
$3$	−8.34346	+	25.6785i	−0.178411	+	0.549093i
$4$	−18.5317	−	57.0347i	−0.144779	−	0.445584i
$5$	269.190	−	195.578i	0.963083	−	0.699720i	0.00921791	−	0.999958i	$-0.497066\pi$
$5$	269.190	−	195.578i	0.963083	−	0.699720i	0.953865	+	0.300237i	$0.0970658\pi$
$6$	−180.166	+	130.898i	−0.340520	+	0.247402i
$7$	−36.4929	−	112.314i	−0.0402129	−	0.123762i	0.928935	−	0.370243i	$-0.120726\pi$
$7$	−36.4929	−	112.314i	−0.0402129	−	0.123762i	−0.969148	+	0.246481i	$0.920726\pi$
$8$	479.095	−	1474.50i	0.330831	−	1.01819i
$9$	−589.773	−	428.495i	−0.269672	−	0.195928i
$10$	2744.43			0.867864
$11$	4083.84	−	1676.14i	0.925111	−	0.379696i
$11$	4083.84	−	1676.14i	0.925111	−	0.379696i
$12$	1619.19			0.270497
$13$	6585.24	+	4784.46i	0.831324	+	0.603992i	0.919934	−	0.392074i	$-0.128242\pi$
$13$	6585.24	+	4784.46i	0.831324	+	0.603992i	−0.0886098	+	0.996066i	$0.528242\pi$
$14$	300.995	−	926.366i	0.0293164	−	0.0902266i
$15$	2776.18	+	8544.19i	0.212387	+	0.653659i
$16$	4135.26	−	3004.45i	0.252397	−	0.183377i
$17$	1949.84	−	1416.64i	0.0962560	−	0.0699341i	−0.538616	−	0.842551i	$-0.681053\pi$
$17$	1949.84	−	1416.64i	0.0962560	−	0.0699341i	0.634872	+	0.772617i	$0.281053\pi$
$18$	−1858.06	−	5718.53i	−0.0750943	−	0.231116i
$19$	4248.60	−	13075.8i	0.142104	−	0.437353i	−0.854523	−	0.519414i	$-0.826150\pi$
$19$	4248.60	−	13075.8i	0.142104	−	0.437353i	0.996627	+	0.0820613i	$0.0261503\pi$
$20$	−16143.3	−	11728.8i	−0.451218	−	0.327829i
$21$	3188.52			0.0751315
$22$	35376.7	+	8614.19i	0.708334	+	0.172479i
$23$	20856.3			0.357430			0.178715	−	0.983901i	$-0.442806\pi$
$23$	20856.3			0.357430			0.178715	+	0.983901i	$0.442806\pi$
$24$	33865.7	+	24604.9i	0.500059	+	0.363314i
$25$	10070.5	−	30993.8i	0.128902	−	0.396720i
$26$	20746.6	+	63851.5i	0.231494	+	0.712467i
$27$	15923.9	−	11569.4i	0.155695	−	0.113119i
$28$	−5729.50	+	4162.72i	−0.0493246	+	0.0358364i
$29$	−40052.4	−	123269.i	−0.304955	−	0.938554i	−0.979694	−	0.200498i	$-0.935744\pi$
$29$	−40052.4	−	123269.i	−0.304955	−	0.938554i	0.674739	−	0.738056i	$-0.264256\pi$
$30$	−22898.0	+	70472.8i	−0.154836	+	0.476538i
$31$	−106523.	−	77393.2i	−0.642208	−	0.466591i	0.218400	−	0.975859i	$-0.429916\pi$
$31$	−106523.	−	77393.2i	−0.642208	−	0.466591i	−0.860608	+	0.509268i	$0.829916\pi$
$32$	−156289.			−0.843149
$33$	8967.49	+	118852.i	0.0434382	+	0.575714i
$34$	19878.9			0.0867392
$35$	−31789.5	−	23096.4i	−0.125327	−	0.0910557i
$36$	−13509.6	+	41578.3i	−0.0482597	+	0.148528i
$37$	11937.4	+	36739.6i	0.0387440	+	0.119242i	0.968558	−	0.248788i	$-0.0800324\pi$
$37$	11937.4	+	36739.6i	0.0387440	+	0.119242i	−0.929814	+	0.368030i	$0.880032\pi$
$38$	91742.6	−	66654.9i	0.271224	−	0.197056i
$39$	−177802.	+	129180.i	−0.479965	+	0.348715i
$40$	−159412.	−	490621.i	−0.393833	−	1.21209i
$41$	−166928.	+	513752.i	−0.378256	+	1.16415i	0.562999	+	0.826458i	$0.309648\pi$
$41$	−166928.	+	513752.i	−0.378256	+	1.16415i	−0.941255	+	0.337696i	$0.890352\pi$
$42$	21276.4	+	15458.2i	0.0443124	+	0.0321948i
$43$	−540279.			−1.03628			−0.518141	−	0.855295i	$-0.673376\pi$
$43$	−540279.			−1.03628			−0.518141	+	0.855295i	$0.673376\pi$
$44$	−171279.	−	201859.i	−0.303123	−	0.357243i
$45$	−242565.			−0.396812
$46$	139170.	+	101113.i	0.210811	+	0.153163i
$47$	−325407.	+	1.00150e6i	−0.457177	+	1.40705i	0.411383	+	0.911462i	$0.365046\pi$
$47$	−325407.	+	1.00150e6i	−0.457177	+	1.40705i	−0.868560	+	0.495583i	$0.834954\pi$
$48$	42647.3	+	131255.i	0.0556605	+	0.171306i
$49$	654978.	−	475869.i	0.795317	−	0.577832i
$50$	217459.	−	157993.i	0.246026	−	0.178749i
$51$	20108.9	+	61888.7i	0.0212272	+	0.0653305i
$52$	150845.	−	464252.i	0.148771	−	0.457870i
$53$	1.05912e6	+	769495.i	0.977191	+	0.709971i	0.957079	−	0.289827i	$-0.0935978\pi$
$53$	1.05912e6	+	769495.i	0.977191	+	0.709971i	0.0201116	+	0.999798i	$0.493598\pi$
$54$	162346.			0.140302
$55$	771511.	−	1.24991e6i	0.625278	−	1.01300i
$56$	−183090.			−0.139318
$57$	300320.	+	218195.i	0.214794	+	0.156057i
$58$	330354.	−	1.01672e6i	0.222321	−	0.684235i
$59$	510445.	+	1.57099e6i	0.323569	+	0.995844i	0.972082	+	0.234640i	$0.0753912\pi$
$59$	510445.	+	1.57099e6i	0.323569	+	0.995844i	−0.648513	+	0.761204i	$0.724609\pi$
$60$	435868.	−	316677.i	0.260511	−	0.189272i
$61$	2.34594e6	−	1.70443e6i	1.32331	−	0.961444i	0.323430	−	0.946252i	$-0.395164\pi$
$61$	2.34594e6	−	1.70443e6i	1.32331	−	0.961444i	0.999885	−	0.0151923i	$-0.00483605\pi$
$62$	−335596.	−	1.03286e6i	−0.178832	−	0.550389i
$63$	−26603.3	+	81876.5i	−0.0134043	+	0.0412541i
$64$	−1.57220e6	−	1.14227e6i	−0.749684	−	0.544678i
$65$	2.70841e6			1.22326
$66$	−516364.	+	836549.i	−0.221081	+	0.358169i
$67$	−3.29141e6			−1.33697			−0.668483	−	0.743727i	$-0.733056\pi$
$67$	−3.29141e6			−1.33697			−0.668483	+	0.743727i	$0.733056\pi$
$68$	−116932.	−	84955.8i	−0.0450973	−	0.0327651i
$69$	−174014.	+	535560.i	−0.0637694	+	0.196262i
$70$	−100152.	−	308236.i	−0.0348993	−	0.107409i
$71$	215363.	−	156470.i	0.0714113	−	0.0518834i	−0.551507	−	0.834170i	$-0.685947\pi$
$71$	215363.	−	156470.i	0.0714113	−	0.0518834i	0.622918	+	0.782287i	$0.285947\pi$
$72$	−914374.	+	664332.i	−0.288709	+	0.209759i
$73$	1.26683e6	+	3.89890e6i	0.381143	+	1.17304i	0.939240	+	0.343262i	$0.111532\pi$
$73$	1.26683e6	+	3.89890e6i	0.381143	+	1.17304i	−0.558097	+	0.829776i	$0.688468\pi$
$74$	−98460.2	+	303029.i	−0.0282455	+	0.0869308i
$75$	711852.	+	517191.i	0.194839	+	0.141559i
$76$	−824510.			−0.215451
$77$	−337284.	−	397503.i	−0.0841935	−	0.0992254i
$78$	−1.81271e6			−0.432511
$79$	2.82550e6	+	2.05284e6i	0.644763	+	0.468448i	0.861483	−	0.507786i	$-0.169536\pi$
$79$	2.82550e6	+	2.05284e6i	0.644763	+	0.468448i	−0.216720	+	0.976234i	$0.569536\pi$
$80$	525568.	−	1.61753e6i	0.114766	−	0.353214i
$81$	164224.	+	505430.i	0.0343352	+	0.105673i
$82$	−3.60459e6	+	2.61889e6i	−0.721950	+	0.524527i
$83$	−4.86007e6	+	3.53105e6i	−0.932974	+	0.677845i	−0.946719	−	0.322060i	$-0.895625\pi$
$83$	−4.86007e6	+	3.53105e6i	−0.932974	+	0.677845i	0.0137451	+	0.999906i	$0.495625\pi$
$84$	−59088.8	−	181857.i	−0.0108775	−	0.0334774i
$85$	247813.	−	762691.i	0.0437682	−	0.134705i
$86$	−3.60517e6	−	2.61931e6i	−0.611197	−	0.444061i
$87$	3.49953e6			0.569761
$88$	−514927.	−	6.82465e6i	−0.0805483	−	1.06756i
$89$	−1.14935e7			−1.72818			−0.864089	−	0.503340i	$-0.832104\pi$
$89$	−1.14935e7			−1.72818			−0.864089	+	0.503340i	$0.832104\pi$
$90$	−1.61859e6	−	1.17597e6i	−0.234039	−	0.170039i
$91$	297045.	−	914211.i	0.0413216	−	0.127175i
$92$	−386504.	−	1.18954e6i	−0.0517483	−	0.159265i
$93$	2.87611e6	−	2.08962e6i	0.370779	−	0.269387i
$94$	−7.02672e6	+	5.10521e6i	−0.872580	+	0.633966i
$95$	−1.41366e6	−	4.35081e6i	−0.169166	−	0.520640i
$96$	1.30399e6	−	4.01328e6i	0.150427	−	0.462967i
$97$	1.26805e7	+	9.21294e6i	1.41071	+	1.02494i	0.993220	+	0.116254i	$0.0370887\pi$
$97$	1.26805e7	+	9.21294e6i	1.41071	+	1.02494i	0.417486	+	0.908683i	$0.362911\pi$
$98$	6.67759e6			0.716685
$99$	−3.12676e6	−	761363.i	−0.323870	−	0.0788621i
$100$	−1.95435e6			−0.195435
$101$	1.23772e6	+	899258.i	0.119536	+	0.0868479i	0.645947	−	0.763382i	$-0.276463\pi$
$101$	1.23772e6	+	899258.i	0.119536	+	0.0868479i	−0.526411	+	0.850230i	$0.676463\pi$
$102$	−165859.	+	510460.i	−0.0154752	+	0.0476279i
$103$	2.70839e6	+	8.33557e6i	0.244220	+	0.751631i	0.995764	+	0.0919484i	$0.0293095\pi$
$103$	2.70839e6	+	8.33557e6i	0.244220	+	0.751631i	−0.751544	+	0.659683i	$0.770691\pi$
$104$	1.02096e7	−	7.41774e6i	0.890008	−	0.646629i
$105$	858317.	−	623604.i	0.0723578	−	0.0525710i
$106$	3.33672e6	+	1.02694e7i	0.272113	+	0.837478i
$107$	3.99212e6	−	1.22865e7i	0.315036	−	0.969583i	−0.660703	−	0.750647i	$-0.729742\pi$
$107$	3.99212e6	−	1.22865e7i	0.315036	−	0.969583i	0.975739	−	0.218935i	$-0.0702583\pi$
$108$	−954953.	−	693814.i	−0.0729456	−	0.0529981i
$109$	−1.73849e7			−1.28582			−0.642908	−	0.765943i	$-0.722272\pi$
$109$	−1.73849e7			−1.28582			−0.642908	+	0.765943i	$0.722272\pi$
$110$	1.12078e7	−	4.60004e6i	0.802870	−	0.329524i
$111$	−1.04302e6			−0.0723871
$112$	−488347.	−	354805.i	−0.0328447	−	0.0238631i
$113$	−1.92391e6	+	5.92118e6i	−0.125432	+	0.386041i	−0.993980	−	0.109565i	$-0.965054\pi$
$113$	−1.92391e6	+	5.92118e6i	−0.125432	+	0.386041i	0.868547	+	0.495606i	$0.165054\pi$
$114$	946149.	+	2.91195e6i	0.0598126	+	0.184084i
$115$	5.61431e6	−	4.07904e6i	0.344234	−	0.250101i
$116$	−6.28835e6	+	4.56876e6i	−0.374054	+	0.271766i
$117$	−1.83368e6	−	5.64349e6i	−0.105846	−	0.325760i
$118$	−4.21017e6	+	1.29576e7i	−0.235892	+	0.726000i
$119$	−230263.	−	167296.i	−0.0125259	−	0.00910063i
$120$	1.39285e7			0.735816
$121$	1.38683e7	−	1.36902e7i	0.711662	−	0.702522i
$122$	2.39172e7			1.19248
$123$	−1.17996e7	−	8.57294e6i	−0.571743	−	0.415396i
$124$	−2.44005e6	+	7.50971e6i	−0.114927	+	0.353710i
$125$	4.68209e6	+	1.44100e7i	0.214415	+	0.659901i
$126$	−574462.	+	417371.i	−0.0255838	+	0.0185877i
$127$	−4.78309e6	+	3.47511e6i	−0.207203	+	0.150541i	−0.686547	−	0.727085i	$-0.740874\pi$
$127$	−4.78309e6	+	3.47511e6i	−0.207203	+	0.150541i	0.479345	+	0.877627i	$0.340874\pi$
$128$	1.22872e6	+	3.78162e6i	0.0517868	+	0.159383i
$129$	4.50779e6	−	1.38736e7i	0.184884	−	0.569015i
$130$	1.80727e7	+	1.31306e7i	0.721476	+	0.524183i
$131$	−2.57426e7			−1.00047			−0.500234	−	0.865890i	$-0.666753\pi$
$131$	−2.57426e7			−1.00047			−0.500234	+	0.865890i	$0.666753\pi$
$132$	6.61249e6	−	2.71398e6i	0.250240	−	0.102707i
$133$	−1.62364e6			−0.0598422
$134$	−2.19629e7	−	1.59570e7i	−0.788540	−	0.572908i
$135$	2.02383e6	−	6.22872e6i	0.0707956	−	0.217886i
$136$	−1.15468e6	−	3.55375e6i	−0.0393619	−	0.121144i
$137$	2.29758e7	−	1.66929e7i	0.763392	−	0.554637i	−0.136557	−	0.990632i	$-0.543604\pi$
$137$	2.29758e7	−	1.66929e7i	0.763392	−	0.554637i	0.899949	+	0.435995i	$0.143604\pi$
$138$	−3.75760e6	+	2.73005e6i	−0.121712	+	0.0884289i
$139$	−2.69431e6	−	8.29223e6i	−0.0850934	−	0.261890i	0.899452	−	0.437019i	$-0.143966\pi$
$139$	−2.69431e6	−	8.29223e6i	−0.0850934	−	0.261890i	−0.984546	+	0.175129i	$0.943966\pi$
$140$	−728186.	+	2.24112e6i	−0.0224282	+	0.0690268i
$141$	−2.30020e7	−	1.67119e7i	−0.691033	−	0.502065i
$142$	2.19566e6			0.0643510
$143$	3.49125e7	+	8.50116e6i	0.998400	+	0.243110i
$144$	−3.72626e6			−0.103993
$145$	−3.48903e7	−	2.53493e7i	−0.950422	−	0.690522i
$146$	−1.04489e7	+	3.21583e7i	−0.277865	+	0.855180i
$147$	6.75484e6	+	2.07893e7i	0.175390	+	0.539794i
$148$	1.87421e6	−	1.36169e6i	0.0475229	−	0.0345274i
$149$	−3.15611e7	+	2.29305e7i	−0.781627	+	0.567886i	−0.905467	−	0.424417i	$-0.860479\pi$
$149$	−3.15611e7	+	2.29305e7i	−0.781627	+	0.567886i	0.123840	+	0.992302i	$0.460479\pi$
$150$	2.24267e6	+	6.90222e6i	0.0542557	+	0.166982i
$151$	−7.67441e6	+	2.36194e7i	−0.181395	+	0.558277i	−0.999868	−	0.0162687i	$-0.994821\pi$
$151$	−7.67441e6	+	2.36194e7i	−0.181395	+	0.558277i	0.818472	+	0.574546i	$0.194821\pi$
$152$	−1.72449e7	−	1.25291e7i	−0.398297	−	0.289380i
$153$	−1.75699e6			−0.0396596
$154$	−323507.	−	4.28764e6i	−0.00713774	−	0.0946009i
$155$	−4.38112e7			−0.944983
$156$	1.06627e7	+	7.74694e6i	0.224871	+	0.163378i
$157$	2.70730e7	−	8.33222e7i	0.558326	−	1.71835i	−0.128667	−	0.991688i	$-0.541070\pi$
$157$	2.70730e7	−	8.33222e7i	0.558326	−	1.71835i	0.686993	−	0.726664i	$-0.258930\pi$
$158$	8.90164e6	+	2.73964e7i	0.179544	+	0.552579i
$159$	−2.85962e7	+	2.07764e7i	−0.564181	+	0.409902i
$160$	−4.20715e7	+	3.05667e7i	−0.812023	+	0.589969i
$161$	−761108.	−	2.34245e6i	−0.0143733	−	0.0442364i
$162$	−1.35453e6	+	4.16881e6i	−0.0250314	+	0.0770388i
$163$	4.20924e7	+	3.05820e7i	0.761285	+	0.553106i	0.899304	−	0.437323i	$-0.144073\pi$
$163$	4.20924e7	+	3.05820e7i	0.761285	+	0.553106i	−0.138019	+	0.990430i	$0.544073\pi$
$164$	3.23952e7			0.573492
$165$	2.56587e7	+	3.02398e7i	0.444673	+	0.524065i
$166$	−4.95491e7			−0.840732
$167$	−5.70315e7	−	4.14358e7i	−0.947561	−	0.688443i	0.00266782	−	0.999996i	$-0.499151\pi$
$167$	−5.70315e7	−	4.14358e7i	−0.947561	−	0.688443i	−0.950229	+	0.311553i	$0.899151\pi$
$168$	1.52760e6	−	4.70148e6i	0.0248558	−	0.0764984i
$169$	1.08403e6	+	3.33630e6i	0.0172758	+	0.0531694i
$170$	5.35119e6	−	3.88787e6i	0.0835371	−	0.0606932i
$171$	−8.10864e6	+	5.89127e6i	−0.124011	+	0.0900996i
$172$	1.00123e7	+	3.08147e7i	0.150032	+	0.461751i
$173$	−1.65296e7	+	5.08727e7i	−0.242717	+	0.747006i	0.753287	+	0.657692i	$0.228467\pi$
$173$	−1.65296e7	+	5.08727e7i	−0.242717	+	0.747006i	−0.996004	+	0.0893133i	$0.971533\pi$
$174$	2.33517e7	+	1.69660e7i	0.336044	+	0.244150i
$175$	−3.84852e6			−0.0542826
$176$	1.18519e7	−	1.92010e7i	0.163867	−	0.265478i
$177$	−4.45996e7			−0.604539
$178$	−7.66940e7	−	5.57215e7i	−1.01928	−	0.740547i
$179$	4.00754e7	−	1.23339e8i	0.522267	−	1.60737i	−0.247391	−	0.968916i	$-0.579573\pi$
$179$	4.00754e7	−	1.23339e8i	0.522267	−	1.60737i	0.769658	−	0.638457i	$-0.220427\pi$
$180$	4.49515e6	+	1.38346e7i	0.0574500	+	0.176813i
$181$	1.16862e8	−	8.49050e7i	1.46486	−	1.06429i	0.482800	−	0.875731i	$-0.339620\pi$
$181$	1.16862e8	−	8.49050e7i	1.46486	−	1.06429i	0.982063	−	0.188555i	$-0.0603803\pi$
$182$	6.41428e6	−	4.66025e6i	0.0788675	−	0.0573006i
$183$	2.41939e7	+	7.44612e7i	0.291828	+	0.898155i
$184$	9.99216e6	−	3.07527e7i	0.118249	−	0.363933i
$185$	1.03989e7	+	7.55522e6i	0.120749	+	0.0877296i
$186$	2.93223e7			0.334120
$187$	5.58834e6	−	9.05354e6i	0.0624938	−	0.101245i
$188$	6.31506e7			0.693147
$189$	−1.88051e6	−	1.36627e6i	−0.0202609	−	0.0147204i
$190$	1.16600e7	−	3.58856e7i	0.123327	−	0.379562i
$191$	2.92132e7	+	8.99089e7i	0.303363	+	0.933654i	0.980283	+	0.197598i	$0.0633141\pi$
$191$	2.92132e7	+	8.99089e7i	0.303363	+	0.933654i	−0.676920	+	0.736056i	$0.736686\pi$
$192$	4.24495e7	−	3.08413e7i	0.432830	−	0.314470i
$193$	1.22545e8	−	8.90342e7i	1.22700	−	0.891470i	0.230341	−	0.973110i	$-0.426016\pi$
$193$	1.22545e8	−	8.90342e7i	1.22700	−	0.891470i	0.996662	+	0.0816406i	$0.0260159\pi$
$194$	3.99496e7	+	1.22952e8i	0.392832	+	1.20901i
$195$	−2.25975e7	+	6.95481e7i	−0.218243	+	0.671683i
$196$	−3.92789e7	−	2.85378e7i	−0.372618	−	0.270723i
$197$	2.18409e7			0.203535			0.101768	−	0.994808i	$-0.467550\pi$
$197$	2.18409e7			0.203535			0.101768	+	0.994808i	$0.467550\pi$
$198$	−1.71731e7	−	2.02392e7i	−0.157225	−	0.185295i
$199$	9.24125e7			0.831276			0.415638	−	0.909530i	$-0.363558\pi$
$199$	9.24125e7			0.831276			0.415638	+	0.909530i	$0.363558\pi$
$200$	−4.08757e7	−	2.96979e7i	−0.361293	−	0.262495i
$201$	2.74618e7	−	8.45186e7i	0.238530	−	0.734118i
$202$	3.89941e6	+	1.20011e7i	0.0332866	+	0.102445i
$203$	−1.23831e7	+	8.99685e6i	−0.103895	+	0.0754839i
$204$	3.15715e6	−	2.29381e6i	0.0260370	−	0.0189170i
$205$	5.55432e7	+	1.70944e8i	0.450290	+	1.38585i
$206$	−2.23389e7	+	6.87521e7i	−0.178044	+	0.547962i
$207$	−1.23005e7	−	8.93685e6i	−0.0963889	−	0.0700307i
$208$	4.16064e7			0.320581
$209$	−4.56636e6	−	6.05208e7i	−0.0345986	−	0.458556i
$210$	8.75066e6			0.0652039
$211$	−2.12789e8	−	1.54600e8i	−1.55941	−	1.13298i	−0.936493	−	0.350687i	$-0.885948\pi$
$211$	−2.12789e8	−	1.54600e8i	−1.55941	−	1.13298i	−0.622915	−	0.782289i	$-0.714052\pi$
$212$	2.42607e7	−	7.46667e7i	0.174875	−	0.538209i
$213$	2.22106e6	+	6.83571e6i	0.0157482	+	0.0484680i
$214$	8.62045e7	−	6.26312e7i	0.601287	−	0.436861i
$215$	−1.45437e8	+	1.05666e8i	−0.998025	+	0.725108i
$216$	−9.43002e6	−	2.90226e7i	−0.0636685	−	0.195951i
$217$	−4.80498e6	+	1.47882e7i	−0.0319215	+	0.0982442i
$218$	−1.16006e8	−	8.42832e7i	−0.758372	−	0.550989i
$219$	−1.10688e8			−0.712107
$220$	−8.55856e7	−	2.08400e7i	−0.541903	−	0.131953i
$221$	1.96180e7			0.122259
$222$	−6.95985e6	−	5.05662e6i	−0.0426937	−	0.0310188i
$223$	−7.12192e7	+	2.19190e8i	−0.430061	+	1.32359i	0.468003	+	0.883727i	$0.344974\pi$
$223$	−7.12192e7	+	2.19190e8i	−0.430061	+	1.32359i	−0.898064	+	0.439865i	$0.855026\pi$
$224$	5.70345e6	+	1.75534e7i	0.0339054	+	0.104350i
$225$	−1.92200e7	+	1.39641e7i	−0.112490	+	0.0817289i
$226$	−4.15442e7	+	3.01836e7i	−0.239404	+	0.173937i
$227$	1.17600e7	+	3.61934e7i	0.0667291	+	0.205371i	0.978861	−	0.204525i	$-0.0655650\pi$
$227$	1.17600e7	+	3.61934e7i	0.0667291	+	0.205371i	−0.912132	+	0.409896i	$0.865565\pi$
$228$	6.87927e6	−	2.11722e7i	0.0384388	−	0.118303i
$229$	−7.39998e7	−	5.37640e7i	−0.407199	−	0.295847i	0.365268	−	0.930902i	$-0.380977\pi$
$229$	−7.39998e7	−	5.37640e7i	−0.407199	−	0.295847i	−0.772467	+	0.635055i	$0.780977\pi$
$230$	5.72387e7			0.310200
$231$	1.30214e7	−	5.34441e6i	0.0695050	−	0.0285271i
$232$	−2.00949e8			−1.05652
$233$	4.06263e7	+	2.95168e7i	0.210408	+	0.152870i	0.687998	−	0.725712i	$-0.258490\pi$
$233$	4.06263e7	+	2.95168e7i	0.210408	+	0.152870i	−0.477590	+	0.878583i	$0.658490\pi$
$234$	1.51243e7	−	4.65478e7i	0.0771648	−	0.237489i
$235$	1.08275e8	+	3.33236e8i	0.544240	+	1.67500i
$236$	8.01416e7	−	5.82262e7i	0.396886	−	0.288355i
$237$	−7.62884e7	+	5.54268e7i	−0.372254	+	0.270458i
$238$	−725437.	−	2.23267e6i	−0.00348803	−	0.0107351i
$239$	−7.05255e7	+	2.17055e8i	−0.334159	+	1.02844i	0.632975	+	0.774172i	$0.281834\pi$
$239$	−7.05255e7	+	2.17055e8i	−0.334159	+	1.02844i	−0.967135	+	0.254265i	$0.918166\pi$
$240$	3.71508e7	+	2.69916e7i	0.173472	+	0.126035i
$241$	−7.77523e7			−0.357811			−0.178905	−	0.983866i	$-0.557256\pi$
$241$	−7.77523e7			−0.357811			−0.178905	+	0.983866i	$0.557256\pi$
$242$	1.58911e8	−	2.41173e7i	0.720777	−	0.109390i
$243$	−1.43489e7			−0.0641500
$244$	−1.40686e8	−	1.02214e8i	−0.619992	−	0.450451i
$245$	8.32438e7	−	2.56198e8i	0.361635	−	1.11300i
$246$	−3.71744e7	−	1.14411e8i	−0.159210	−	0.489999i
$247$	9.05388e7	−	6.57803e7i	0.382292	−	0.277752i
$248$	−1.65151e8	+	1.19989e8i	−0.687542	+	0.499529i
$249$	−5.01223e7	−	1.54261e8i	−0.205747	−	0.633224i
$250$	−3.86181e7	+	1.18854e8i	−0.156315	+	0.481088i
$251$	7.36789e7	+	5.35308e7i	0.294093	+	0.213671i	0.725041	−	0.688706i	$-0.241821\pi$
$251$	7.36789e7	+	5.35308e7i	0.294093	+	0.213671i	−0.430948	+	0.902377i	$0.641821\pi$
$252$	5.16281e6			0.0203228
$253$	8.51739e7	−	3.49582e7i	0.330662	−	0.135715i
$254$	−4.87642e7			−0.186717
$255$	1.75172e7	+	1.27270e7i	0.0661566	+	0.0480656i
$256$	−8.70021e7	+	2.67765e8i	−0.324108	+	0.997502i
$257$	−8.24502e7	−	2.53755e8i	−0.302988	−	0.932501i	−0.980420	−	0.196916i	$-0.936907\pi$
$257$	−8.24502e7	−	2.53755e8i	−0.302988	−	0.932501i	0.677432	−	0.735585i	$-0.263093\pi$
$258$	9.73396e7	−	7.07214e7i	0.352875	−	0.256379i
$259$	3.69072e6	−	2.68146e6i	0.0131996	−	0.00959009i
$260$	−5.01916e7	−	1.54474e8i	−0.177102	−	0.545065i
$261$	−2.91982e7	+	8.98628e7i	−0.101652	+	0.312851i
$262$	−1.71775e8	−	1.24802e8i	−0.590074	−	0.428714i
$263$	1.08839e6			0.00368925			0.00184462	−	0.999998i	$-0.499413\pi$
$263$	1.08839e6			0.00368925			0.00184462	+	0.999998i	$0.499413\pi$
$264$	1.79543e8	+	4.37186e7i	0.600559	+	0.146236i
$265$	4.35600e8			1.43790
$266$	−1.08342e7	−	7.87151e6i	−0.0352948	−	0.0256432i
$267$	9.58958e7	−	2.95137e8i	0.308326	−	0.948930i
$268$	6.09955e7	+	1.87725e8i	0.193565	+	0.595731i
$269$	2.01265e8	−	1.46228e8i	0.630429	−	0.458033i	−0.226120	−	0.974099i	$-0.572604\pi$
$269$	2.01265e8	−	1.46228e8i	0.630429	−	0.458033i	0.856549	+	0.516066i	$0.172604\pi$
$270$	4.37019e7	−	3.17513e7i	0.135122	−	0.0981721i
$271$	2.05919e7	+	6.33754e7i	0.0628498	+	0.193432i	0.977551	−	0.210699i	$-0.0675740\pi$
$271$	2.05919e7	+	6.33754e7i	0.0628498	+	0.193432i	−0.914701	+	0.404131i	$0.867574\pi$
$272$	3.80688e6	−	1.17164e7i	0.0114704	−	0.0353022i
$273$	2.09972e7	+	1.52554e7i	0.0624586	+	0.0453788i
$274$	2.34241e8			0.687917
$275$	−1.08237e7	−	1.43453e8i	−0.0313842	−	0.415954i
$276$	3.37703e7			0.0966837
$277$	5.46448e7	+	3.97017e7i	0.154479	+	0.112236i	0.662340	−	0.749204i	$-0.269564\pi$
$277$	5.46448e7	+	3.97017e7i	0.154479	+	0.112236i	−0.507861	+	0.861439i	$0.669564\pi$
$278$	2.22228e7	−	6.83947e7i	0.0620357	−	0.190926i
$279$	2.96615e7	+	9.12888e7i	0.0817672	+	0.251654i
$280$	−4.92859e7	+	3.58083e7i	−0.134174	+	0.0974835i
$281$	−2.59267e8	+	1.88368e8i	−0.697068	+	0.506449i	−0.878976	−	0.476866i	$-0.841773\pi$
$281$	−2.59267e8	+	1.88368e8i	−0.697068	+	0.506449i	0.181908	+	0.983316i	$0.441773\pi$
$282$	−7.24671e7	−	2.23031e8i	−0.192428	−	0.592234i
$283$	4.64877e7	−	1.43074e8i	0.121923	−	0.375240i	−0.871405	−	0.490564i	$-0.836791\pi$
$283$	4.64877e7	−	1.43074e8i	0.121923	−	0.375240i	0.993328	+	0.115324i	$0.0367907\pi$
$284$	−1.29153e7	−	9.38352e6i	−0.0334573	−	0.0243081i
$285$	1.23517e8			0.316061
$286$	1.91750e8	+	2.25985e8i	0.484679	+	0.571213i
$287$	6.37930e7			0.159289
$288$	9.21753e7	+	6.69693e7i	0.227374	+	0.165197i
$289$	−1.25007e8	+	3.84731e8i	−0.304643	+	0.937593i
$290$	−1.09921e8	−	3.38302e8i	−0.264659	−	0.814537i
$291$	−3.42374e8	+	2.48749e8i	−0.814471	+	0.591748i
$292$	1.98896e8	−	1.44507e8i	0.467505	−	0.339662i
$293$	1.26478e8	+	3.89258e8i	0.293749	+	0.904067i	0.983639	+	0.180152i	$0.0576591\pi$
$293$	1.26478e8	+	3.89258e8i	0.293749	+	0.904067i	−0.689890	+	0.723915i	$0.742341\pi$
$294$	−5.57142e7	+	1.71471e8i	−0.127864	+	0.393526i
$295$	4.44657e8	+	3.23062e8i	1.00844	+	0.732672i
$296$	5.98917e7			0.134229
$297$	4.56386e7	−	7.39381e7i	0.101085	−	0.163765i
$298$	−3.21769e8			−0.704349
$299$	1.37344e8	+	9.97864e7i	0.297140	+	0.215885i
$300$	1.63060e7	−	5.01847e7i	0.0348677	−	0.107312i
$301$	1.97163e7	+	6.06806e7i	0.0416719	+	0.128253i
$302$	−1.65719e8	+	1.20402e8i	−0.346216	+	0.251540i
$303$	−3.34185e7	+	2.42800e7i	−0.0690141	+	0.0501417i
$304$	−2.17166e7	−	6.68367e7i	−0.0443336	−	0.136445i
$305$	2.98156e8	−	9.17629e8i	0.601719	−	1.85190i
$306$	−1.17240e7	−	8.51801e6i	−0.0233912	−	0.0169947i
$307$	−6.15229e8			−1.21354			−0.606768	−	0.794879i	$-0.707534\pi$
$307$	−6.15229e8			−1.21354			−0.606768	+	0.794879i	$0.707534\pi$
$308$	−1.64210e7	+	2.66033e7i	−0.0320238	+	0.0518810i
$309$	−2.36642e8			−0.456287
$310$	−2.92343e8	−	2.12400e8i	−0.557349	−	0.404938i
$311$	−1.07589e8	+	3.31126e8i	−0.202818	+	0.624211i	0.796977	+	0.604009i	$0.206431\pi$
$311$	−1.07589e8	+	3.31126e8i	−0.202818	+	0.624211i	−0.999796	+	0.0202020i	$0.993569\pi$
$312$	1.05293e8	+	3.24058e8i	0.196272	+	0.604063i
$313$	1.50210e8	−	1.09134e8i	0.276882	−	0.201167i	−0.440674	−	0.897667i	$-0.645261\pi$
$313$	1.50210e8	−	1.09134e8i	0.276882	−	0.201167i	0.717556	+	0.696500i	$0.245261\pi$
$314$	5.84605e8	−	4.24741e8i	1.06564	−	0.774230i
$315$	8.85190e6	+	2.72433e7i	0.0159569	+	0.0491104i
$316$	6.47221e7	−	1.99194e8i	0.115385	−	0.355117i
$317$	5.53841e6	+	4.02389e6i	0.00976512	+	0.00709477i	0.592657	−	0.805455i	$-0.298079\pi$
$317$	5.53841e6	+	4.02389e6i	0.00976512	+	0.00709477i	−0.582892	+	0.812550i	$0.698079\pi$
$318$	−2.91542e8			−0.508401
$319$	−3.70183e8	−	4.36275e8i	−0.638483	−	0.752477i
$320$	−6.46624e8			−1.10313
$321$	2.82191e8	+	2.05024e8i	0.476185	+	0.345968i
$322$	6.27765e6	−	1.93206e7i	0.0104786	−	0.0322497i
$323$	−1.02397e7	−	3.15145e7i	−0.0169074	−	0.0520357i
$324$	2.57837e7	−	1.87330e7i	0.0421152	−	0.0305984i
$325$	2.14605e8	−	1.55920e8i	0.346776	−	0.251947i
$326$	1.32611e8	+	4.08135e8i	0.211991	+	0.652442i
$327$	1.45050e8	−	4.46418e8i	0.229404	−	0.706032i
$328$	6.77554e8	+	4.92272e8i	1.06019	+	0.770276i
$329$	1.24357e8			0.192524
$330$	2.46106e7	+	3.26180e8i	0.0376985	+	0.499641i
$331$	−4.60634e8			−0.698165			−0.349082	−	0.937092i	$-0.613507\pi$
$331$	−4.60634e8			−0.698165			−0.349082	+	0.937092i	$0.613507\pi$
$332$	2.91458e8	+	2.11757e8i	0.437112	+	0.317581i
$333$	8.70237e6	−	2.67831e7i	0.0129147	−	0.0397472i
$334$	−1.79676e8	−	5.52986e8i	−0.263862	−	0.812085i
$335$	−8.86014e8	+	6.43727e8i	−1.28761	+	0.935503i
$336$	1.31854e7	−	9.57974e6i	0.0189629	−	0.0137774i
$337$	−3.41318e8	−	1.05047e9i	−0.485797	−	1.49513i	−0.830823	−	0.556537i	$-0.812130\pi$
$337$	−3.41318e8	−	1.05047e9i	−0.485797	−	1.49513i	0.345026	−	0.938593i	$-0.387870\pi$
$338$	−8.94111e6	+	2.75179e7i	−0.0125946	+	0.0387621i
$339$	−1.35995e8	−	9.88062e7i	−0.189594	−	0.137748i
$340$	−4.80923e7			−0.0663589
$341$	−5.64742e8	−	1.37514e8i	−0.771277	−	0.187805i
$342$	−8.26687e7			−0.111751
$343$	−1.56029e8	−	1.13362e8i	−0.208774	−	0.151683i
$344$	−2.58845e8	+	7.96642e8i	−0.342834	+	1.05514i
$345$	5.79009e7	+	1.78201e8i	0.0759134	+	0.233637i
$346$	−3.56933e8	+	2.59327e8i	−0.463256	+	0.336575i
$347$	−1.21062e9	+	8.79565e8i	−1.55544	+	1.13010i	−0.615818	+	0.787889i	$0.711174\pi$
$347$	−1.21062e9	+	8.79565e8i	−1.55544	+	1.13010i	−0.939625	+	0.342206i	$0.888826\pi$
$348$	−6.48523e7	−	1.99595e8i	−0.0824894	−	0.253876i
$349$	3.11192e8	−	9.57749e8i	0.391867	−	1.20604i	−0.539507	−	0.841981i	$-0.681389\pi$
$349$	3.11192e8	−	9.57749e8i	0.391867	−	1.20604i	0.931375	−	0.364062i	$-0.118611\pi$
$350$	−2.56804e7	−	1.86579e7i	−0.0320158	−	0.0232608i
$351$	1.60216e8			0.197756
$352$	−6.38260e8	+	2.61963e8i	−0.780007	+	0.320140i
$353$	5.17028e8			0.625609			0.312805	−	0.949818i	$-0.398732\pi$
$353$	5.17028e8			0.625609			0.312805	+	0.949818i	$0.398732\pi$
$354$	−2.97604e8	−	2.16222e8i	−0.356556	−	0.259053i
$355$	2.73714e7	−	8.42405e7i	0.0324712	−	0.0999359i
$356$	2.12995e8	+	6.55530e8i	0.250204	+	0.770048i
$357$	6.21711e6	−	4.51699e6i	0.00723185	−	0.00525425i
$358$	8.65375e8	−	6.28731e8i	0.996813	−	0.724227i
$359$	5.10746e7	+	1.57191e8i	0.0582605	+	0.179307i	0.975952	−	0.217987i	$-0.0699491\pi$
$359$	5.10746e7	+	1.57191e8i	0.0582605	+	0.179307i	−0.917691	+	0.397295i	$0.869949\pi$
$360$	−1.16212e8	+	3.57663e8i	−0.131278	+	0.404031i
$361$	5.70231e8	+	4.14297e8i	0.637933	+	0.463486i
$362$	1.19142e9			1.32003
$363$	2.35834e8	+	4.70340e8i	0.258781	+	0.516106i
$364$	−5.76465e7			−0.0626496
$365$	1.10356e9	+	8.01780e8i	1.18787	+	0.863038i
$366$	−1.99552e8	+	6.14159e8i	−0.212752	+	0.654782i
$367$	−3.15141e8	−	9.69904e8i	−0.332793	−	1.02423i	−0.967799	−	0.251723i	$-0.919003\pi$
$367$	−3.15141e8	−	9.69904e8i	−0.332793	−	1.02423i	0.635007	−	0.772507i	$-0.280997\pi$
$368$	8.62465e7	−	6.26618e7i	0.0902140	−	0.0655443i
$369$	3.18590e8	−	2.31469e8i	0.330096	−	0.239829i
$370$	3.27613e7	+	1.00829e8i	0.0336245	+	0.103485i
$371$	4.77744e7	−	1.47034e8i	0.0485721	−	0.149489i
$372$	−1.72480e8	−	1.25314e8i	−0.173715	−	0.126212i
$373$	−1.03538e9			−1.03304			−0.516520	−	0.856275i	$-0.672773\pi$
$373$	−1.03538e9			−1.03304			−0.516520	+	0.856275i	$0.672773\pi$
$374$	8.11821e7	−	3.33198e7i	0.0802435	−	0.0329345i
$375$	−4.09092e8			−0.400601
$376$	1.32081e9	+	9.59626e8i	1.28140	+	0.930989i
$377$	3.26019e8	−	1.00338e9i	0.313363	−	0.964433i
$378$	−5.92448e6	−	1.82337e7i	−0.00564194	−	0.0173641i
$379$	3.85692e8	−	2.80221e8i	0.363918	−	0.264402i	−0.390767	−	0.920490i	$-0.627790\pi$
$379$	3.85692e8	−	2.80221e8i	0.363918	−	0.264402i	0.754684	+	0.656088i	$0.227790\pi$
$380$	−2.21950e8	+	1.61256e8i	−0.207497	+	0.150755i
$381$	−4.93284e7	−	1.51817e8i	−0.0456940	−	0.140632i
$382$	−2.40951e8	+	7.41572e8i	−0.221161	+	0.680662i
$383$	−1.06247e9	−	7.71926e8i	−0.966316	−	0.702069i	−0.0117067	−	0.999931i	$-0.503726\pi$
$383$	−1.06247e9	−	7.71926e8i	−0.966316	−	0.702069i	−0.954609	+	0.297862i	$0.903726\pi$
$384$	−1.07358e8			−0.0967556
$385$	−1.68536e8	−	4.10384e7i	−0.150515	−	0.0366503i
$386$	1.24936e9			1.10569
$387$	3.18642e8	+	2.31507e8i	0.279457	+	0.203037i
$388$	2.90466e8	−	8.93962e8i	0.252455	−	0.776977i
$389$	−4.82151e8	−	1.48391e9i	−0.415298	−	1.27816i	−0.911984	−	0.410225i	$-0.865450\pi$
$389$	−4.82151e8	−	1.48391e9i	−0.415298	−	1.27816i	0.496686	−	0.867930i	$-0.334550\pi$
$390$	−4.87963e8	+	3.54526e8i	−0.416544	+	0.302637i
$391$	4.06665e7	−	2.95460e7i	0.0344048	−	0.0249965i
$392$	−3.87873e8	−	1.19375e9i	−0.325229	−	1.00095i
$393$	2.14782e8	−	6.61032e8i	0.178494	−	0.549349i
$394$	1.45740e8	+	1.05887e8i	0.120045	+	0.0872176i
$395$	1.16209e9			0.948742
$396$	1.45200e7	+	1.92443e8i	0.0117499	+	0.155729i
$397$	1.42889e9			1.14612			0.573062	−	0.819512i	$-0.305755\pi$
$397$	1.42889e9			1.14612			0.573062	+	0.819512i	$0.305755\pi$
$398$	6.16651e8	+	4.48023e8i	0.490285	+	0.356213i
$399$	1.35467e7	−	4.16926e7i	0.0106765	−	0.0328589i
$400$	−5.14750e7	−	1.58424e8i	−0.0402148	−	0.123769i
$401$	−1.05345e9	+	7.65376e8i	−0.815847	+	0.592747i	−0.915520	−	0.402273i	$-0.868220\pi$
$401$	−1.05345e9	+	7.65376e8i	−0.815847	+	0.592747i	0.0996731	+	0.995020i	$0.468220\pi$
$402$	5.92999e8	−	4.30839e8i	0.455264	−	0.330769i
$403$	−3.31193e8	−	1.01931e9i	−0.252065	−	0.775777i
$404$	2.83518e7	−	8.72580e7i	0.0213918	−	0.0658371i
$405$	1.43058e8	+	1.03938e8i	0.107009	+	0.0777467i
$406$	−1.26247e8			−0.0936227
$407$	1.10331e8	+	1.30030e8i	0.0811180	+	0.0956009i
$408$	1.00889e8			0.0735416
$409$	9.47796e8	+	6.88614e8i	0.684988	+	0.497673i	0.875009	−	0.484107i	$-0.160855\pi$
$409$	9.47796e8	+	6.88614e8i	0.684988	+	0.497673i	−0.190021	+	0.981780i	$0.560855\pi$
$410$	−4.58122e8	+	1.40995e9i	−0.328275	+	1.01033i
$411$	2.36951e8	+	7.29260e8i	0.168350	+	0.518127i
$412$	4.25226e8	−	3.08945e8i	0.299557	−	0.217641i
$413$	1.57816e8	−	1.14660e8i	0.110236	−	0.0800914i
$414$	−3.87524e7	−	1.19268e8i	−0.0268409	−	0.0826079i
$415$	−6.17687e8	+	1.90105e9i	−0.424229	+	1.30564i
$416$	−1.02920e9	−	7.47760e8i	−0.700930	−	0.509256i
$417$	2.35412e8			0.158984
$418$	2.62939e8	−	4.25981e8i	0.176091	−	0.285282i
$419$	1.60317e9			1.06471			0.532353	−	0.846523i	$-0.321308\pi$
$419$	1.60317e9			1.06471			0.532353	+	0.846523i	$0.321308\pi$
$420$	−5.14732e7	−	3.73975e7i	−0.0339007	−	0.0246303i
$421$	−7.70699e8	+	2.37197e9i	−0.503382	+	1.54925i	0.300093	+	0.953910i	$0.402982\pi$
$421$	−7.70699e8	+	2.37197e9i	−0.503382	+	1.54925i	−0.803475	+	0.595339i	$0.797018\pi$
$422$	−6.70384e8	−	2.06323e9i	−0.434240	−	1.33645i
$423$	6.21054e8	−	4.51222e8i	0.398968	−	0.289867i
$424$	1.64204e9	−	1.19301e9i	1.04617	−	0.760089i
$425$	−2.42712e7	−	7.46992e7i	−0.0153367	−	0.0472014i
$426$	−1.83194e7	+	5.63812e7i	−0.0114809	+	0.0353347i
$427$	−2.77040e8	−	2.01282e8i	−0.172205	−	0.125114i
$428$	−7.74738e8			−0.477641
$429$	−5.09588e8	+	8.25572e8i	−0.311615	+	0.504841i
$430$	−1.48275e9			−0.899352
$431$	6.91131e8	+	5.02136e8i	0.415805	+	0.302100i	0.775948	−	0.630797i	$-0.217272\pi$
$431$	6.91131e8	+	5.02136e8i	0.415805	+	0.302100i	−0.360143	+	0.932897i	$0.617272\pi$
$432$	3.10899e7	−	9.56849e7i	0.0185535	−	0.0571018i
$433$	−1.13668e7	−	3.49834e7i	−0.00672869	−	0.0207088i	0.947636	−	0.319353i	$-0.103466\pi$
$433$	−1.13668e7	−	3.49834e7i	−0.00672869	−	0.0207088i	−0.954364	+	0.298644i	$0.903466\pi$
$434$	−1.03757e8	+	7.53839e7i	−0.0609261	+	0.0442654i
$435$	9.42038e8	−	6.84431e8i	0.548727	−	0.398673i
$436$	3.22172e8	+	9.91542e8i	0.186159	+	0.572939i
$437$	8.86102e7	−	2.72714e8i	0.0507924	−	0.156323i
$438$	−7.38597e8	−	5.36622e8i	−0.419999	−	0.305147i
$439$	−3.18813e9			−1.79850			−0.899251	−	0.437434i	$-0.855888\pi$
$439$	−3.18813e9			−1.79850			−0.899251	+	0.437434i	$0.855888\pi$
$440$	−1.47336e9	−	1.73642e9i	−0.824566	−	0.971785i
$441$	−5.90196e8			−0.327689
$442$	1.30907e8	+	9.51097e7i	0.0721084	+	0.0523898i
$443$	−7.13725e8	+	2.19662e9i	−0.390048	+	1.20044i	0.542704	+	0.839924i	$0.317400\pi$
$443$	−7.13725e8	+	2.19662e9i	−0.390048	+	1.20044i	−0.932752	+	0.360519i	$0.882600\pi$
$444$	1.93289e7	+	5.94882e7i	0.0104801	+	0.0322545i
$445$	−3.09394e9	+	2.24788e9i	−1.66438	+	1.20924i
$446$	−1.53788e9	+	1.11734e9i	−0.820826	+	0.596365i
$447$	−3.25492e8	−	1.00176e9i	−0.172371	−	0.530503i
$448$	−7.09184e7	+	2.18264e8i	−0.0372637	+	0.114686i
$449$	−1.38797e9	−	1.00842e9i	−0.723632	−	0.525749i	0.163911	−	0.986475i	$-0.447589\pi$
$449$	−1.38797e9	−	1.00842e9i	−0.723632	−	0.525749i	−0.887543	+	0.460726i	$0.847589\pi$
$450$	−1.95951e8			−0.101368
$451$	1.79413e8	+	2.37788e9i	0.0920951	+	1.22059i
$452$	3.73366e8			0.190174
$453$	−5.42481e8	−	3.94135e8i	−0.274183	−	0.199206i
$454$	−9.69965e7	+	2.98525e8i	−0.0486475	+	0.149722i
$455$	−9.88378e7	−	3.04192e8i	−0.0491907	−	0.151393i
$456$	4.65611e8	−	3.38286e8i	0.229957	−	0.167073i
$457$	3.80586e8	−	2.76512e8i	0.186529	−	0.135521i	−0.490602	−	0.871384i	$-0.663223\pi$
$457$	3.80586e8	−	2.76512e8i	0.186529	−	0.135521i	0.677131	+	0.735863i	$0.263223\pi$
$458$	−2.33134e8	−	7.17513e8i	−0.113390	−	0.348980i
$459$	1.46594e7	−	4.51169e7i	0.00707572	−	0.0217768i
$460$	−3.36690e8	−	2.44619e8i	−0.161279	−	0.117176i
$461$	4.79746e8			0.228065			0.114032	−	0.993477i	$-0.463623\pi$
$461$	4.79746e8			0.228065			0.114032	+	0.993477i	$0.463623\pi$
$462$	1.12799e8	+	2.74665e7i	0.0532181	+	0.0129586i
$463$	1.49854e9			0.701672			0.350836	−	0.936437i	$-0.385897\pi$
$463$	1.49854e9			0.701672			0.350836	+	0.936437i	$0.385897\pi$
$464$	−5.35981e8	−	3.89413e8i	−0.249079	−	0.180966i
$465$	3.65537e8	−	1.12501e9i	0.168595	−	0.518883i
$466$	1.27992e8	+	3.93919e8i	0.0585912	+	0.180325i
$467$	3.14715e9	−	2.28654e9i	1.42991	−	1.03889i	0.439876	−	0.898058i	$-0.355022\pi$
$467$	3.14715e9	−	2.28654e9i	1.42991	−	1.03889i	0.990034	−	0.140832i	$-0.0449776\pi$
$468$	−2.87894e8	+	2.09167e8i	−0.129829	+	0.0943264i
$469$	1.20113e8	+	3.69670e8i	0.0537632	+	0.165466i
$470$	−8.93055e8	+	2.74854e9i	−0.396767	+	1.22112i
$471$	1.91371e9	+	1.39039e9i	0.843923	+	0.613146i
$472$	2.56098e9			1.12101
$473$	−2.20641e9	+	9.05583e8i	−0.958677	+	0.393472i
$474$	−7.77771e8			−0.335450
$475$	−3.62484e8	−	2.63360e8i	−0.155189	−	0.112751i
$476$	−5.27451e6	+	1.62333e7i	−0.00224160	+	0.00689894i
$477$	−2.94915e8	−	9.07655e8i	−0.124418	−	0.382919i
$478$	−1.52290e9	+	1.10645e9i	−0.637786	+	0.463378i
$479$	9.68720e8	−	7.03816e8i	0.402739	−	0.292607i	−0.367916	−	0.929859i	$-0.619929\pi$
$479$	9.68720e8	−	7.03816e8i	0.402739	−	0.292607i	0.770656	+	0.637252i	$0.219929\pi$
$480$	−4.33887e8	−	1.33537e9i	−0.179074	−	0.551133i
$481$	−9.71682e7	+	2.99053e8i	−0.0398122	+	0.122529i
$482$	−5.18826e8	−	3.76949e8i	−0.211036	−	0.153327i
$483$	6.65009e7			0.0268542
$484$	−1.03782e9	−	5.37271e8i	−0.416066	−	0.215395i
$485$	5.21532e9			2.07580
$486$	−9.57474e7	−	6.95646e7i	−0.0378356	−	0.0274891i
$487$	1.09575e9	−	3.37237e9i	0.429893	−	1.32307i	−0.468338	−	0.883549i	$-0.655147\pi$
$487$	1.09575e9	−	3.37237e9i	0.429893	−	1.32307i	0.898231	−	0.439524i	$-0.144853\pi$
$488$	−1.38925e9	−	4.27568e9i	−0.541143	−	1.66547i
$489$	−1.13650e9	+	8.25713e8i	−0.439528	+	0.319336i
$490$	1.79754e9	−	1.30599e9i	0.690227	−	0.501479i
$491$	1.54249e9	+	4.74730e9i	0.588082	+	1.80993i	0.586525	+	0.809931i	$0.300496\pi$
$491$	1.54249e9	+	4.74730e9i	0.588082	+	1.80993i	0.00155730	+	0.999999i	$0.499504\pi$
$492$	−2.70288e8	+	8.31861e8i	−0.102317	+	0.314900i
$493$	−2.52723e8	−	1.83614e8i	−0.0949906	−	0.0690147i
$494$	9.23056e8			0.344495
$495$	−9.90597e8	+	4.06573e8i	−0.367095	+	0.150668i
$496$	−6.73022e8			−0.247653
$497$	−2.54330e7	−	1.84781e7i	−0.00929286	−	0.00675166i
$498$	4.13411e8	−	1.27235e9i	0.149996	−	0.461640i
$499$	1.18700e9	+	3.65322e9i	0.427661	+	1.31621i	0.900423	+	0.435015i	$0.143257\pi$
$499$	1.18700e9	+	3.65322e9i	0.427661	+	1.31621i	−0.472762	+	0.881190i	$0.656743\pi$
$500$	7.35104e8	−	5.34084e8i	0.262999	−	0.191080i
$501$	1.53985e9	−	1.11877e9i	0.547075	−	0.397473i
$502$	2.32123e8	+	7.14401e8i	0.0818946	+	0.252046i
$503$	1.52711e9	−	4.69997e9i	0.535036	−	1.64667i	−0.208535	−	0.978015i	$-0.566869\pi$
$503$	1.52711e9	−	4.69997e9i	0.535036	−	1.64667i	0.743571	−	0.668657i	$-0.233131\pi$
$504$	1.07982e8	+	7.84532e7i	0.0375701	+	0.0272963i
$505$	5.09057e8			0.175892
$506$	7.37828e8	+	1.79661e8i	0.253180	+	0.0616490i
$507$	−9.47158e7			−0.0322771
$508$	2.86841e8	+	2.08402e8i	0.0970774	+	0.0705309i
$509$	−1.23825e8	+	3.81093e8i	−0.0416193	+	0.128091i	−0.969707	−	0.244270i	$-0.921452\pi$
$509$	−1.23825e8	+	3.81093e8i	−0.0416193	+	0.128091i	0.928088	+	0.372361i	$0.121452\pi$
$510$	5.51873e7	+	1.69849e8i	0.0184223	+	0.0566979i
$511$	3.91669e8	−	2.84564e8i	0.129851	−	0.0943424i
$512$	−1.46694e9	+	1.06579e9i	−0.483022	+	0.350936i
$513$	−8.36251e7	−	2.57372e8i	−0.0273480	−	0.0841685i
$514$	6.80052e8	−	2.09298e9i	0.220888	−	0.679822i
$515$	2.35932e9	+	1.71415e9i	0.761136	+	0.552997i
$516$	−8.74812e8			−0.280311
$517$	3.49745e8	+	4.63539e9i	0.111310	+	1.47526i
$518$	3.76274e7			0.0118946
$519$	−1.16842e9	−	8.48909e8i	−0.366872	−	0.266548i
$520$	1.29759e9	−	3.99356e9i	0.404692	−	1.24551i
$521$	−1.18053e8	−	3.63329e8i	−0.0365717	−	0.112556i	0.931104	−	0.364753i	$-0.118847\pi$
$521$	−1.18053e8	−	3.63329e8i	−0.0365717	−	0.112556i	−0.967676	+	0.252198i	$0.918847\pi$
$522$	−6.30495e8	+	4.58082e8i	−0.194015	+	0.140960i
$523$	6.33472e8	−	4.60244e8i	0.193629	−	0.140680i	−0.486747	−	0.873543i	$-0.661816\pi$
$523$	6.33472e8	−	4.60244e8i	0.193629	−	0.140680i	0.680376	+	0.732863i	$0.261816\pi$
$524$	4.77055e8	+	1.46822e9i	0.144847	+	0.445792i
$525$	3.21100e7	−	9.88244e7i	0.00968462	−	0.0298062i
$526$	7.26259e6	+	5.27658e6i	0.00217591	+	0.00158089i
$527$	−3.17340e8			−0.0944470
$528$	3.94166e8	+	4.64541e8i	0.116536	+	0.137343i
$529$	−2.96984e9			−0.872244
$530$	2.90667e9	+	2.11182e9i	0.848068	+	0.616158i
$531$	3.72115e8	−	1.14525e9i	0.107856	−	0.331948i
$532$	3.00888e7	+	9.26037e7i	0.00866390	+	0.0266647i
$533$	−3.55729e9	+	2.58452e9i	−1.01759	+	0.739325i
$534$	2.07074e9	−	1.50448e9i	0.588479	−	0.427555i
$535$	−1.32833e9	−	4.08817e9i	−0.375031	−	1.15423i
$536$	−1.57690e9	+	4.85319e9i	−0.442310	+	1.36129i
$537$	2.83281e9	+	2.05816e9i	0.789418	+	0.573546i
$538$	2.05193e9			0.568099
$539$	1.87720e9	−	3.04121e9i	0.516356	−	0.836537i
$540$	−3.92758e8			−0.107336
$541$	−1.72795e9	−	1.25543e9i	−0.469182	−	0.340880i	0.327941	−	0.944698i	$-0.393645\pi$
$541$	−1.72795e9	−	1.25543e9i	−0.469182	−	0.340880i	−0.797122	+	0.603818i	$0.793645\pi$
$542$	−1.69843e8	+	5.22723e8i	−0.0458194	+	0.141018i
$543$	1.20520e9	+	3.70924e9i	0.323044	+	0.994226i
$544$	−3.04739e8	+	2.21406e8i	−0.0811582	+	0.0589649i
$545$	−4.67983e9	+	3.40010e9i	−1.23835	+	0.899712i
$546$	6.61510e7	+	2.03592e8i	0.0173925	+	0.0535287i
$547$	1.63502e9	−	5.03209e9i	0.427139	−	1.31460i	−0.473793	−	0.880636i	$-0.657116\pi$
$547$	1.63502e9	−	5.03209e9i	0.427139	−	1.31460i	0.900932	−	0.433961i	$-0.142884\pi$
$548$	−1.37785e9	−	1.00107e9i	−0.357661	−	0.259856i
$549$	−2.11391e9			−0.545236
$550$	6.23247e8	−	1.00971e9i	0.159732	−	0.258778i
$551$	−1.78201e9			−0.453815
$552$	7.06315e8	+	5.13168e8i	0.178736	+	0.129859i
$553$	1.27452e8	−	3.92256e8i	0.0320485	−	0.0986350i
$554$	1.72157e8	+	5.29844e8i	0.0430170	+	0.132393i
$555$	−2.80769e8	+	2.03991e8i	−0.0697147	+	0.0506507i
$556$	−4.23015e8	+	3.07339e8i	−0.104374	+	0.0758325i
$557$	2.10205e8	+	6.46944e8i	0.0515406	+	0.158626i	0.973514	−	0.228628i	$-0.0734238\pi$
$557$	2.10205e8	+	6.46944e8i	0.0515406	+	0.158626i	−0.921973	+	0.387253i	$0.873424\pi$
$558$	−2.44650e8	+	7.52954e8i	−0.0596108	+	0.183463i
$559$	−3.55787e9	−	2.58494e9i	−0.861486	−	0.625906i
$560$	−2.00850e8			−0.0483297
$561$	1.85855e8	+	2.19038e8i	0.0444432	+	0.0523781i
$562$	−2.64326e9			−0.628149
$563$	−5.00859e9	−	3.63895e9i	−1.18287	−	0.859404i	−0.190375	−	0.981711i	$-0.560971\pi$
$563$	−5.00859e9	−	3.63895e9i	−1.18287	−	0.859404i	−0.992492	+	0.122308i	$0.960971\pi$
$564$	−5.26895e8	+	1.62161e9i	−0.123665	+	0.380602i
$565$	6.40155e8	+	1.97019e9i	0.149319	+	0.459557i
$566$	1.00384e9	−	7.29331e8i	0.232705	−	0.169070i
$567$	5.07736e7	−	3.68892e7i	0.0116976	−	0.00849882i
$568$	−1.27537e8	−	3.92517e8i	−0.0292022	−	0.0898752i
$569$	7.77589e8	−	2.39317e9i	0.176953	−	0.544604i	−0.822765	−	0.568382i	$-0.807569\pi$
$569$	7.77589e8	−	2.39317e9i	0.176953	−	0.544604i	0.999717	+	0.0237779i	$0.00756946\pi$
$570$	8.24206e8	+	5.98821e8i	0.186412	+	0.135436i
$571$	4.85010e7			0.0109025			0.00545123	−	0.999985i	$-0.498265\pi$
$571$	4.85010e7			0.0109025			0.00545123	+	0.999985i	$0.498265\pi$
$572$	−1.62127e8	−	2.14877e9i	−0.0362217	−	0.480068i
$573$	−2.55247e9			−0.566786
$574$	4.25678e8	+	3.09273e8i	0.0939485	+	0.0682576i
$575$	2.10034e8	−	6.46417e8i	0.0460735	−	0.141800i
$576$	4.37785e8	+	1.34736e9i	0.0954513	+	0.293769i
$577$	4.54771e8	−	3.30411e8i	0.0985548	−	0.0716042i	−0.537416	−	0.843317i	$-0.680600\pi$
$577$	4.54771e8	−	3.30411e8i	0.0985548	−	0.0716042i	0.635971	+	0.771713i	$0.280600\pi$
$578$	−2.69935e9	+	1.96119e9i	−0.581449	+	0.422447i
$579$	1.26382e9	+	3.88963e9i	0.270589	+	0.832786i
$580$	−7.99213e8	+	2.45972e9i	−0.170084	+	0.523466i
$581$	5.73943e8	+	4.16994e8i	0.121409	+	0.0882090i
$582$	−3.49055e9			−0.733945
$583$	5.61505e9	+	1.36726e9i	1.17358	+	0.285766i
$584$	6.35586e9			1.32047
$585$	−1.59735e9	−	1.16054e9i	−0.329879	−	0.239671i
$586$	−1.04319e9	+	3.21061e9i	−0.214152	+	0.659092i
$587$	−1.88194e9	−	5.79203e9i	−0.384037	−	1.18195i	−0.937176	−	0.348856i	$-0.886570\pi$
$587$	−1.88194e9	−	5.79203e9i	−0.384037	−	1.18195i	0.553139	−	0.833089i	$-0.313430\pi$
$588$	1.06053e9	−	7.70521e8i	0.215131	−	0.156302i
$589$	−1.46455e9	+	1.06406e9i	−0.295326	+	0.214567i
$590$	1.40088e9	+	4.31146e9i	0.280814	+	0.864257i
$591$	−1.82229e8	+	5.60843e8i	−0.0363129	+	0.111760i
$592$	1.59746e8	+	1.16063e8i	0.0316450	+	0.0229914i
$593$	−9.82867e8			−0.193554			−0.0967772	−	0.995306i	$-0.530853\pi$
$593$	−9.82867e8			−0.193554			−0.0967772	+	0.995306i	$0.530853\pi$
$594$	6.62995e8	−	2.72115e8i	0.129795	−	0.0532721i
$595$	−9.47039e7			−0.0184314
$596$	1.89271e9	+	1.37514e9i	0.366204	+	0.266063i
$597$	−7.71040e8	+	2.37302e9i	−0.148309	+	0.456447i
$598$	4.32699e8	+	1.33171e9i	0.0827430	+	0.254657i
$599$	1.18514e9	−	8.61055e8i	0.225308	−	0.163696i	−0.469405	−	0.882983i	$-0.655532\pi$
$599$	1.18514e9	−	8.61055e8i	0.225308	−	0.163696i	0.694713	+	0.719287i	$0.255532\pi$
$600$	1.10364e9	−	8.01844e8i	0.208593	−	0.151552i
$601$	−1.99894e9	−	6.15211e9i	−0.375612	−	1.15601i	−0.943065	−	0.332608i	$-0.892071\pi$
$601$	−1.99894e9	−	6.15211e9i	−0.375612	−	1.15601i	0.567453	−	0.823406i	$-0.307929\pi$
$602$	−1.62621e8	+	5.00496e8i	−0.0303801	+	0.0935002i
$603$	1.94119e9	+	1.41036e9i	0.360543	+	0.261950i
$604$	1.48935e9			0.275022
$605$	1.05571e9	−	6.39758e9i	0.193820	−	1.17455i
$606$	−3.40706e8			−0.0621908
$607$	−8.77787e9	−	6.37749e9i	−1.59305	−	1.15742i	−0.899423	−	0.437080i	$-0.856013\pi$
$607$	−8.77787e9	−	6.37749e9i	−1.59305	−	1.15742i	−0.693624	−	0.720337i	$-0.743987\pi$
$608$	−6.64010e8	+	2.04361e9i	−0.119815	+	0.368754i
$609$	−1.27708e8	−	3.93045e8i	−0.0229117	−	0.0705150i
$610$	6.43827e9	−	4.67768e9i	1.14846	−	0.834403i
$611$	−6.93452e9	+	5.03822e9i	−1.22991	+	0.893579i
$612$	3.25600e7	+	1.00209e8i	0.00574188	+	0.0176717i
$613$	−3.34123e8	+	1.02833e9i	−0.0585862	+	0.180310i	−0.976067	−	0.217471i	$-0.930219\pi$
$613$	−3.34123e8	+	1.02833e9i	−0.0585862	+	0.180310i	0.917481	+	0.397780i	$0.130219\pi$
$614$	−4.10530e9	−	2.98268e9i	−0.715741	−	0.520016i
$615$	−4.85302e9			−0.841297
$616$	−7.47710e8	+	3.06884e8i	−0.128884	+	0.0528984i
$617$	−1.00156e9			−0.171664			−0.0858318	−	0.996310i	$-0.527355\pi$
$617$	−1.00156e9			−0.171664			−0.0858318	+	0.996310i	$0.527355\pi$
$618$	−1.57907e9	−	1.14726e9i	−0.269117	−	0.195525i
$619$	1.02646e9	−	3.15912e9i	0.173950	−	0.535364i	−0.825634	−	0.564207i	$-0.809182\pi$
$619$	1.02646e9	−	3.15912e9i	0.173950	−	0.535364i	0.999584	+	0.0288425i	$0.00918212\pi$
$620$	8.11896e8	+	2.49876e9i	0.136814	+	0.421069i
$621$	3.32114e8	−	2.41295e8i	0.0556502	−	0.0404322i
$622$	−2.32324e9	+	1.68794e9i	−0.387105	+	0.281248i
$623$	4.19432e8	+	1.29088e9i	0.0694949	+	0.213883i
$624$	−3.47141e8	+	1.06839e9i	−0.0571953	+	0.176029i
$625$	6.13840e9	+	4.45981e9i	1.00572	+	0.730696i
$626$	1.53142e9			0.249507
$627$	1.59218e9	+	3.87695e8i	0.257963	+	0.0628137i
$628$	−5.25397e9			−0.846504
$629$	7.53228e7	+	5.47252e7i	0.0120684	+	0.00876820i
$630$	−7.30108e7	+	2.24704e8i	−0.0116331	+	0.0358030i
$631$	3.02137e8	+	9.29882e8i	0.0478741	+	0.147341i	0.972136	−	0.234418i	$-0.0753184\pi$
$631$	3.02137e8	+	9.29882e8i	0.0478741	+	0.147341i	−0.924262	+	0.381759i	$0.875318\pi$
$632$	4.38060e9	−	3.18269e9i	0.690278	−	0.501516i
$633$	5.74529e9	−	4.17420e9i	0.900325	−	0.654124i
$634$	1.74486e7	+	5.37012e7i	0.00271924	+	0.00836896i
$635$	−6.07902e8	+	1.87093e9i	−0.0942162	+	0.289968i
$636$	1.71491e9	+	1.24596e9i	0.264327	+	0.192045i
$637$	6.58997e9			1.01017
$638$	−3.55062e8	−	4.70585e9i	−0.0541292	−	0.717408i
$639$	−1.94062e8			−0.0294231
$640$	1.07036e9	+	7.77662e8i	0.161399	+	0.117263i
$641$	−3.57848e9	+	1.10134e10i	−0.536655	+	1.65166i	0.203389	+	0.979098i	$0.434804\pi$
$641$	−3.57848e9	+	1.10134e10i	−0.536655	+	1.65166i	−0.740045	+	0.672558i	$0.765196\pi$
$642$	8.89034e8	+	2.73617e9i	0.132601	+	0.408103i
$643$	5.72684e9	−	4.16080e9i	0.849527	−	0.617217i	−0.0754888	−	0.997147i	$-0.524052\pi$
$643$	5.72684e9	−	4.16080e9i	0.849527	−	0.617217i	0.925015	+	0.379929i	$0.124052\pi$
$644$	−1.19496e8	+	8.68192e7i	−0.0176301	+	0.0128090i
$645$	−1.49991e9	−	4.61624e9i	−0.220093	−	0.677376i
$646$	8.44573e7	−	2.59933e8i	0.0123260	−	0.0379356i
$647$	2.55352e9	+	1.85524e9i	0.370658	+	0.269299i	0.757484	−	0.652854i	$-0.226428\pi$
$647$	2.55352e9	+	1.85524e9i	0.370658	+	0.269299i	−0.386826	+	0.922153i	$0.626428\pi$
$648$	8.23937e8			0.118955
$649$	4.71777e9	+	5.56009e9i	0.677455	+	0.798408i
$650$	2.18793e9			0.312490
$651$	−3.39649e8	−	2.46770e8i	−0.0482500	−	0.0350557i
$652$	9.64189e8	−	2.96747e9i	0.136237	−	0.419295i
$653$	1.15964e9	+	3.56899e9i	0.162977	+	0.501591i	0.998882	−	0.0472837i	$-0.0150565\pi$
$653$	1.15964e9	+	3.56899e9i	0.162977	+	0.501591i	−0.835905	+	0.548875i	$0.815056\pi$
$654$	3.13216e9	−	2.27565e9i	0.437846	−	0.318114i
$655$	−6.92965e9	+	5.03468e9i	−0.963533	+	0.700048i
$656$	8.53248e8	+	2.62603e9i	0.118008	+	0.363192i
$657$	9.23518e8	−	2.84230e9i	0.127048	−	0.391013i
$658$	8.29809e8	+	6.02892e8i	0.113550	+	0.0824990i
$659$	1.21512e10			1.65394			0.826972	−	0.562243i	$-0.190062\pi$
$659$	1.21512e10			1.65394			0.826972	+	0.562243i	$0.190062\pi$
$660$	1.24922e9	−	2.02383e9i	0.169136	−	0.274013i
$661$	−2.32661e9			−0.313341			−0.156671	−	0.987651i	$-0.550076\pi$
$661$	−2.32661e9			−0.313341			−0.156671	+	0.987651i	$0.550076\pi$
$662$	−3.07372e9	−	2.23319e9i	−0.411776	−	0.299173i
$663$	−1.63682e8	+	5.03762e8i	−0.0218124	+	0.0671318i
$664$	2.87810e9	+	8.85789e9i	0.381521	+	1.17420i
$665$	−4.37066e8	+	3.17547e8i	−0.0576330	+	0.0418728i
$666$	1.87916e8	−	1.36529e8i	0.0246492	−	0.0179087i
$667$	−8.35347e8	−	2.57093e9i	−0.109000	−	0.335467i
$668$	−1.30639e9	+	4.02065e9i	−0.169572	+	0.521890i
$669$	−5.03427e9	−	3.65761e9i	−0.650047	−	0.472287i
$670$	−9.03304e9			−1.16030
$671$	6.72359e9	−	1.08927e10i	0.859157	−	1.39190i
$672$	−4.98332e8			−0.0633471
$673$	8.22673e9	+	5.97707e9i	1.04034	+	0.755849i	0.970351	−	0.241698i	$-0.0777045\pi$
$673$	8.22673e9	+	5.97707e9i	1.04034	+	0.755849i	0.0699862	+	0.997548i	$0.477704\pi$
$674$	2.81521e9	−	8.66431e9i	0.354161	−	1.09000i
$675$	−1.98217e8	−	6.10051e8i	−0.0248073	−	0.0763489i
$676$	1.70196e8	−	1.23655e8i	0.0211903	−	0.0153956i
$677$	−4.25644e9	+	3.09248e9i	−0.527213	+	0.383042i	−0.819314	−	0.573345i	$-0.805646\pi$
$677$	−4.25644e9	+	3.09248e9i	−0.527213	+	0.383042i	0.292101	+	0.956387i	$0.405646\pi$
$678$	−4.28449e8	−	1.31863e9i	−0.0527952	−	0.162487i
$679$	5.71989e8	−	1.76040e9i	0.0701203	−	0.215808i
$680$	−1.00586e9	−	7.30802e8i	−0.122675	−	0.0891289i
$681$	−1.02751e9			−0.124673
$682$	−3.10174e9	−	3.65552e9i	−0.374420	−	0.441269i
$683$	1.17784e9			0.141454			0.0707269	−	0.997496i	$-0.477468\pi$
$683$	1.17784e9			0.141454			0.0707269	+	0.997496i	$0.477468\pi$
$684$	4.86274e8	+	3.53299e8i	0.0581012	+	0.0422130i
$685$	2.92008e9	−	8.98710e9i	0.347119	−	1.06832i
$686$	−4.91566e8	−	1.51289e9i	−0.0581363	−	0.178925i
$687$	1.99799e9	−	1.45163e9i	0.235096	−	0.170807i
$688$	−2.23419e9	+	1.62324e9i	−0.261554	+	0.190030i
$689$	3.29294e9	+	1.01346e10i	0.383545	+	1.18043i
$690$	−4.77569e8	+	1.46981e9i	−0.0553432	+	0.170329i
$691$	−4.21554e8	−	3.06277e8i	−0.0486050	−	0.0353136i	0.563218	−	0.826309i	$-0.309563\pi$
$691$	−4.21554e8	−	3.06277e8i	−0.0486050	−	0.0353136i	−0.611822	+	0.790995i	$0.709563\pi$
$692$	3.20784e9			0.367994
$693$	2.85930e7	+	3.78961e8i	0.00326358	+	0.0432542i
$694$	−1.23424e10			−1.40166
$695$	−2.34706e9	−	1.70524e9i	−0.265202	−	0.192681i
$696$	1.67661e9	−	5.16006e9i	0.188495	−	0.580127i
$697$	4.02319e8	+	1.23821e9i	0.0450045	+	0.138510i
$698$	6.71976e9	−	4.88219e9i	0.747928	−	0.543402i
$699$	−1.09691e9	+	7.96952e8i	−0.121479	+	0.0882597i
$700$	7.13197e7	+	2.19499e8i	0.00785898	+	0.0241875i
$701$	4.73467e9	−	1.45718e10i	0.519130	−	1.59772i	−0.256509	−	0.966542i	$-0.582572\pi$
$701$	4.73467e9	−	1.45718e10i	0.519130	−	1.59772i	0.775639	−	0.631177i	$-0.217428\pi$
$702$	1.06909e9	+	7.76739e8i	0.116636	+	0.0847413i
$703$	5.31118e8			0.0576563
$704$	−8.33522e9	−	2.02962e9i	−0.900353	−	0.219235i
$705$	−9.46039e9			−1.01683
$706$	3.45003e9	+	2.50659e9i	0.368983	+	0.268082i
$707$	5.58308e7	−	1.71829e8i	0.00594163	−	0.0182865i
$708$	8.26506e8	+	2.54373e9i	0.0875245	+	0.269373i
$709$	−1.25092e10	+	9.08847e9i	−1.31816	+	0.957699i	−0.318206	+	0.948022i	$0.603080\pi$
$709$	−1.25092e10	+	9.08847e9i	−1.31816	+	0.957699i	−0.999953	+	0.00967726i	$0.996920\pi$
$710$	5.91048e8	−	4.29422e8i	0.0619753	−	0.0450277i
$711$	−7.86769e8	−	2.42143e9i	−0.0820925	−	0.252655i
$712$	−5.50649e9	+	1.69472e10i	−0.571735	+	1.75962i
$713$	−2.22167e9	−	1.61414e9i	−0.229544	−	0.166774i
$714$	6.33842e7			0.00651685
$715$	1.10607e10	−	4.53968e9i	1.13165	−	0.464466i
$716$	−7.77730e9			−0.791833
$717$	−4.98523e9	−	3.62198e9i	−0.505090	−	0.366969i
$718$	−4.21265e8	+	1.29652e9i	−0.0424737	+	0.130720i
$719$	−3.80208e8	−	1.17016e9i	−0.0381478	−	0.117407i	0.930169	−	0.367131i	$-0.119660\pi$
$719$	−3.80208e8	−	1.17016e9i	−0.0381478	−	0.117407i	−0.968317	+	0.249724i	$0.919660\pi$
$720$	−1.00307e9	+	7.28774e8i	−0.100154	+	0.0727661i
$721$	8.37360e8	−	6.08378e8i	0.0832030	−	0.0604505i
$722$	1.79649e9	+	5.52904e9i	0.177642	+	0.546726i
$723$	6.48723e8	−	1.99656e9i	0.0638374	−	0.196471i
$724$	−7.00818e9	−	5.09174e9i	−0.686310	−	0.498633i
$725$	−4.22391e9			−0.411653
$726$	−7.06572e8	+	4.28183e9i	−0.0685296	+	0.415290i
$727$	9.50393e8			0.0917345			0.0458673	−	0.998948i	$-0.485395\pi$
$727$	9.50393e8			0.0917345			0.0458673	+	0.998948i	$0.485395\pi$
$728$	−1.20569e9	−	8.75987e8i	−0.115818	−	0.0841468i
$729$	1.19720e8	−	3.68459e8i	0.0114451	−	0.0352243i
$730$	3.47672e9	+	1.07002e10i	0.330780	+	1.01804i
$731$	−1.05346e9	+	7.65381e8i	−0.0997484	+	0.0724714i
$732$	3.79852e9	−	2.75979e9i	0.357953	−	0.260068i
$733$	6.10539e9	+	1.87905e10i	0.572597	+	1.76227i	0.644219	+	0.764841i	$0.277183\pi$
$733$	6.10539e9	+	1.87905e10i	0.572597	+	1.76227i	−0.0716212	+	0.997432i	$0.522817\pi$
$734$	2.59929e9	−	7.99980e9i	0.242616	−	0.746695i
$735$	5.88425e9	+	4.27516e9i	0.546620	+	0.397143i
$736$	−3.25963e9			−0.301367
$737$	−1.34416e10	+	5.51687e9i	−1.23684	+	0.507641i
$738$	3.24807e9			0.297460
$739$	−4.19887e9	−	3.05066e9i	−0.382716	−	0.278060i	0.379748	−	0.925090i	$-0.376011\pi$
$739$	−4.19887e9	−	3.05066e9i	−0.382716	−	0.278060i	−0.762464	+	0.647030i	$0.776011\pi$
$740$	2.38201e8	−	7.33108e8i	0.0216089	−	0.0665054i
$741$	9.33734e8	+	2.87374e9i	0.0843062	+	0.259468i
$742$	1.03162e9	−	7.49518e8i	0.0927059	−	0.0673548i
$743$	−1.59540e10	+	1.15913e10i	−1.42695	+	1.03674i	−0.436377	+	0.899764i	$0.643739\pi$
$743$	−1.59540e10	+	1.15913e10i	−1.42695	+	1.03674i	−0.990574	+	0.136977i	$0.956261\pi$
$744$	−1.70321e9	−	5.24195e9i	−0.151622	−	0.466646i
$745$	−4.01123e9	+	1.23453e10i	−0.355411	+	1.09384i
$746$	−6.90886e9	−	5.01958e9i	−0.609285	−	0.442671i
$747$	4.37938e9			0.384406
$748$	−6.19928e8	−	1.50952e8i	−0.0541608	−	0.0131881i
$749$	−1.52562e9			−0.132666
$750$	−2.72979e9	−	1.98331e9i	−0.236274	−	0.171663i
$751$	3.14588e9	−	9.68202e9i	0.271021	−	0.834116i	−0.719224	−	0.694778i	$-0.755503\pi$
$751$	3.14588e9	−	9.68202e9i	0.271021	−	0.834116i	0.990245	−	0.139338i	$-0.0444973\pi$
$752$	1.66331e9	+	5.11913e9i	0.142630	+	0.438969i
$753$	−1.98933e9	+	1.44533e9i	−0.169795	+	0.123363i
$754$	7.03994e9	−	5.11481e9i	0.598093	−	0.434540i
$755$	2.55356e9	+	7.85905e9i	0.215939	+	0.664593i
$756$	−4.30757e7	+	1.32573e8i	−0.00362582	+	0.0111591i
$757$	6.15260e9	+	4.47013e9i	0.515494	+	0.374528i	0.814904	−	0.579597i	$-0.196790\pi$
$757$	6.15260e9	+	4.47013e9i	0.515494	+	0.374528i	−0.299410	+	0.954125i	$0.596790\pi$
$758$	3.93218e9			0.327937
$759$	1.87029e8	+	2.47881e9i	0.0155261	+	0.205777i
$760$	−7.09256e9			−0.586078
$761$	−1.05246e10	−	7.64659e9i	−0.865686	−	0.628958i	0.0637399	−	0.997967i	$-0.479697\pi$
$761$	−1.05246e10	−	7.64659e9i	−0.865686	−	0.628958i	−0.929426	+	0.369009i	$0.879697\pi$
$762$	4.06862e8	−	1.25219e9i	0.0333123	−	0.102525i
$763$	6.34424e8	+	1.95256e9i	0.0517063	+	0.159136i
$764$	4.58656e9	−	3.33233e9i	0.372101	−	0.270347i
$765$	−4.72963e8	+	3.43628e8i	−0.0381955	+	0.0277507i
$766$	−3.34726e9	−	1.03018e10i	−0.269085	−	0.828158i
$767$	−4.15493e9	+	1.27876e10i	−0.332491	+	1.02330i
$768$	−6.14991e9	−	4.46817e9i	−0.489897	−	0.355931i
$769$	−8.20374e8			−0.0650533			−0.0325267	−	0.999471i	$-0.510355\pi$
$769$	−8.20374e8			−0.0650533			−0.0325267	+	0.999471i	$0.510355\pi$
$770$	−9.25651e8	−	1.09092e9i	−0.0730684	−	0.0861141i
$771$	7.20399e9			0.566086
$772$	−7.34902e9	−	5.33937e9i	−0.574869	−	0.417667i
$773$	−4.01188e8	+	1.23473e9i	−0.0312406	+	0.0961487i	−0.965461	−	0.260548i	$-0.916097\pi$
$773$	−4.01188e8	+	1.23473e9i	−0.0312406	+	0.0961487i	0.934220	+	0.356696i	$0.116097\pi$
$774$	1.00387e9	+	3.08960e9i	0.0778189	+	0.239502i
$775$	−3.47144e9	+	2.52215e9i	−0.267888	+	0.194632i
$776$	1.96597e10	−	1.42836e10i	1.51029	−	1.09729i
$777$	3.80627e7	+	1.17145e8i	0.00291089	+	0.00895880i
$778$	3.97680e9	−	1.22393e10i	0.302765	−	0.931814i
$779$	6.00853e9	+	4.36545e9i	0.455394	+	0.330863i
$780$	4.38543e9			0.330888
$781$	6.17241e8	−	9.99979e8i	0.0463635	−	0.0751125i
$782$	4.14601e8			0.0310032
$783$	−2.06393e9	−	1.49953e9i	−0.153649	−	0.111632i
$784$	1.27878e9	−	3.93569e9i	0.0947743	−	0.291685i
$785$	−9.00820e9	−	2.77244e10i	−0.664652	−	2.04559i
$786$	4.63793e9	−	3.36966e9i	0.340679	−	0.247518i
$787$	1.00519e10	−	7.30315e9i	0.735085	−	0.534070i	−0.156083	−	0.987744i	$-0.549887\pi$
$787$	1.00519e10	−	7.30315e9i	0.735085	−	0.534070i	0.891168	+	0.453674i	$0.149887\pi$
$788$	−4.04750e8	−	1.24569e9i	−0.0294676	−	0.0906920i
$789$	−9.08090e6	+	2.79482e7i	−0.000658203	+	0.00202574i
$790$	7.75437e9	+	5.63388e9i	0.559566	+	0.406549i
$791$	7.35237e8			0.0528214
$792$	−2.62064e9	+	4.24564e9i	−0.187443	+	0.303672i
$793$	2.36034e10			1.68081
$794$	9.53470e9	+	6.92736e9i	0.675982	+	0.491130i
$795$	−3.63441e9	+	1.11856e10i	−0.256537	+	0.789538i
$796$	−1.71256e9	−	5.27073e9i	−0.120351	−	0.370403i
$797$	1.45577e10	−	1.05768e10i	1.01856	−	0.740030i	0.0525757	−	0.998617i	$-0.483257\pi$
$797$	1.45577e10	−	1.05768e10i	1.01856	−	0.740030i	0.965988	+	0.258587i	$0.0832569\pi$
$798$	2.92523e8	−	2.12531e8i	0.0203775	−	0.0148051i
$799$	7.84274e8	+	2.41375e9i	0.0543944	+	0.167409i
$800$	−1.57391e9	+	4.84400e9i	−0.108684	+	0.334495i
$801$	6.77858e9	+	4.92492e9i	0.466042	+	0.338599i
$802$	−1.07401e10			−0.735185
$803$	1.17086e10	+	1.37991e10i	0.797997	+	0.940472i
$804$	−5.32941e9			−0.361646
$805$	−6.63013e8	−	4.81707e8i	−0.0447957	−	0.0325460i
$806$	2.73169e9	−	8.40727e9i	0.183763	−	0.565565i
$807$	2.07567e9	+	6.38825e9i	0.139027	+	0.427882i
$808$	1.91894e9	−	1.39419e9i	0.127974	−	0.0929787i
$809$	−7.71914e9	+	5.60828e9i	−0.512565	+	0.372400i	−0.813796	−	0.581151i	$-0.802603\pi$
$809$	−7.71914e9	+	5.60828e9i	−0.512565	+	0.372400i	0.301231	+	0.953551i	$0.402603\pi$
$810$	4.50701e8	+	1.38712e9i	0.0297983	+	0.0917097i
$811$	4.76627e9	−	1.46691e10i	0.313766	−	0.965671i	−0.662494	−	0.749067i	$-0.730502\pi$
$811$	4.76627e9	−	1.46691e10i	0.313766	−	0.965671i	0.976260	−	0.216604i	$-0.0694980\pi$
$812$	7.42613e8	+	5.39540e8i	0.0486762	+	0.0353653i
$813$	−1.79919e9			−0.117425
$814$	1.05824e8	+	1.40256e9i	0.00687701	+	0.0911454i
$815$	1.73120e10			1.12020
$816$	2.69097e8	+	1.95510e8i	0.0173378	+	0.0125966i
$817$	−2.29542e9	+	7.06459e9i	−0.147260	+	0.453221i
$818$	2.98600e9	+	9.18997e9i	0.190745	+	0.587053i
$819$	−5.66924e8	+	4.11895e8i	−0.0360605	+	0.0261995i
$820$	8.72045e9	−	6.33578e9i	0.552320	−	0.401284i
$821$	−3.80367e9	−	1.17065e10i	−0.239884	−	0.738288i	−0.996436	−	0.0843537i	$-0.973117\pi$
$821$	−3.80367e9	−	1.17065e10i	−0.239884	−	0.738288i	0.756552	−	0.653934i	$-0.226883\pi$
$822$	−1.95438e9	+	6.01496e9i	−0.122732	+	0.377730i
$823$	2.08497e9	+	1.51482e9i	0.130377	+	0.0947241i	0.651062	−	0.759024i	$-0.274324\pi$
$823$	2.08497e9	+	1.51482e9i	0.130377	+	0.0947241i	−0.520686	+	0.853748i	$0.674324\pi$
$824$	1.35884e10			0.846102
$825$	3.77397e9	+	9.18959e8i	0.233997	+	0.0569780i
$826$	1.60895e9			0.0993374
$827$	−1.10840e9	−	8.05298e8i	−0.0681438	−	0.0495093i	0.553192	−	0.833054i	$-0.313410\pi$
$827$	−1.10840e9	−	8.05298e8i	−0.0681438	−	0.0495093i	−0.621336	+	0.783545i	$0.713410\pi$
$828$	−2.81761e8	+	8.67172e8i	−0.0172494	+	0.0530883i
$829$	−6.99727e9	−	2.15354e10i	−0.426567	−	1.31284i	−0.901485	−	0.432809i	$-0.857522\pi$
$829$	−6.99727e9	−	2.15354e10i	−0.426567	−	1.31284i	0.474918	−	0.880030i	$-0.342478\pi$
$830$	−1.33381e10	+	9.69071e9i	−0.809694	+	0.588277i
$831$	−1.47541e9	+	1.07195e9i	−0.0891885	+	0.0647992i
$832$	−4.88818e9	−	1.50443e10i	−0.294249	−	0.905607i
$833$	6.02966e8	−	1.85574e9i	0.0361439	−	0.111239i
$834$	1.57086e9	+	1.14130e9i	0.0937683	+	0.0681267i
$835$	−2.34562e10			−1.39430
$836$	−3.36717e9	+	1.38200e9i	−0.199316	+	0.0818059i
$837$	−2.59164e9			−0.152769
$838$	1.06976e10	+	7.77227e9i	0.627961	+	0.456240i
$839$	−4.62567e9	+	1.42364e10i	−0.270401	+	0.832208i	0.719999	+	0.693975i	$0.244142\pi$
$839$	−4.62567e9	+	1.42364e10i	−0.270401	+	0.832208i	−0.990400	+	0.138233i	$0.955858\pi$
$840$	−5.08290e8	−	1.56436e9i	−0.0295893	−	0.0910664i
$841$	3.64490e8	−	2.64817e8i	0.0211300	−	0.0153518i
$842$	−1.66422e10	+	1.20913e10i	−0.960767	+	0.698038i
$843$	−2.67384e9	−	8.22924e9i	−0.153723	−	0.473111i
$844$	−4.87423e9	+	1.50013e10i	−0.279067	+	0.858878i
$845$	9.44316e8	+	6.86085e8i	0.0538417	+	0.0391183i
$846$	6.33173e9			0.359523
$847$	−2.04368e9	−	1.05800e9i	−0.115564	−	0.0598266i
$848$	6.69164e9			0.376832
$849$	3.28607e9	+	2.38747e9i	0.184289	+	0.133894i
$850$	2.00190e8	−	6.16122e8i	0.0111809	−	0.0344112i
$851$	2.48971e8	+	7.66253e8i	0.0138482	+	0.0426205i
$852$	3.48713e8	−	2.53355e8i	0.0193166	−	0.0140343i
$853$	1.65280e10	−	1.20083e10i	0.911797	−	0.662459i	−0.0296716	−	0.999560i	$-0.509446\pi$
$853$	1.65280e10	−	1.20083e10i	0.911797	−	0.662459i	0.941469	+	0.337100i	$0.109446\pi$
$854$	−8.72808e8	−	2.68623e9i	−0.0479530	−	0.147584i
$855$	−1.03056e9	+	3.17174e9i	−0.0563887	+	0.173547i
$856$	−1.62039e10	−	1.17728e10i	−0.882999	−	0.641536i
$857$	5.33937e9			0.289772			0.144886	−	0.989448i	$-0.453718\pi$
$857$	5.33937e9			0.289772			0.144886	+	0.989448i	$0.453718\pi$
$858$	−7.40282e9	+	3.03836e9i	−0.400121	+	0.164223i
$859$	1.03612e10			0.557741			0.278871	−	0.960329i	$-0.410040\pi$
$859$	1.03612e10			0.557741			0.278871	+	0.960329i	$0.410040\pi$
$860$	8.72187e9	+	6.33681e9i	0.467590	+	0.339724i
$861$	−5.32254e8	+	1.63811e9i	−0.0284190	+	0.0874646i
$862$	2.17739e9	+	6.70131e9i	0.115787	+	0.356356i
$863$	−2.55089e10	+	1.85333e10i	−1.35099	+	0.981554i	−0.352032	+	0.935988i	$0.614509\pi$
$863$	−2.55089e10	+	1.85333e10i	−1.35099	+	0.981554i	−0.998961	+	0.0455662i	$0.985491\pi$
$864$	−2.48873e9	+	1.80817e9i	−0.131274	+	0.0953765i
$865$	5.49999e9	+	1.69272e10i	0.288939	+	0.889262i
$866$	9.37538e7	−	2.88545e8i	0.00490542	−	0.0150973i
$867$	−8.83633e9	−	6.41997e9i	−0.460474	−	0.334554i
$868$	9.32487e8			0.0483976
$869$	1.49797e10	+	3.64755e9i	0.774345	+	0.188552i
$870$	9.60420e9			0.494475
$871$	−2.16748e10	−	1.57476e10i	−1.11145	−	0.807517i
$872$	−8.32900e9	+	2.56340e10i	−0.425388	+	1.30921i
$873$	−3.53093e9	−	1.08671e10i	−0.179614	−	0.552795i
$874$	1.91342e9	−	1.39018e9i	0.0969437	−	0.0704337i
$875$	1.44757e9	−	1.05172e9i	0.0730488	−	0.0530730i
$876$	2.05123e9	+	6.31305e9i	0.103098	+	0.317303i
$877$	5.08665e9	−	1.56551e10i	0.254644	−	0.783713i	−0.739256	−	0.673425i	$-0.764823\pi$
$877$	5.08665e9	−	1.56551e10i	0.254644	−	0.783713i	0.993900	−	0.110288i	$-0.0351774\pi$
$878$	−2.12738e10	−	1.54563e10i	−1.06075	−	0.770682i
$879$	−1.10508e10			−0.548825
$880$	−5.64877e8	−	7.48666e9i	−0.0279424	−	0.370339i
$881$	1.03263e10			0.508780			0.254390	−	0.967102i	$-0.418125\pi$
$881$	1.03263e10			0.508780			0.254390	+	0.967102i	$0.418125\pi$
$882$	−3.93826e9	−	2.86132e9i	−0.193270	−	0.140419i
$883$	−1.67338e9	+	5.15015e9i	−0.0817962	+	0.251743i	−0.983588	−	0.180427i	$-0.942252\pi$
$883$	−1.67338e9	+	5.15015e9i	−0.0817962	+	0.251743i	0.901792	+	0.432170i	$0.142252\pi$
$884$	−3.63556e8	−	1.11891e9i	−0.0177006	−	0.0544769i
$885$	−1.20057e10	+	8.72269e9i	−0.582221	+	0.423008i
$886$	−1.54119e10	+	1.11974e10i	−0.744455	+	0.540878i
$887$	1.15848e9	+	3.56545e9i	0.0557387	+	0.171546i	0.975050	−	0.221985i	$-0.0712535\pi$
$887$	1.15848e9	+	3.56545e9i	0.0557387	+	0.171546i	−0.919311	+	0.393531i	$0.871253\pi$
$888$	−4.99704e8	+	1.53793e9i	−0.0239479	+	0.0737040i
$889$	5.64851e8	+	4.10388e8i	0.0269636	+	0.0195902i
$890$	−3.15431e10			−1.49982
$891$	1.51784e9	+	1.78883e9i	0.0718875	+	0.0847223i
$892$	1.38213e10			0.652035
$893$	1.17129e10	+	8.50993e9i	0.550408	+	0.399895i
$894$	2.68467e9	−	8.26256e9i	0.125664	−	0.386753i
$895$	−1.33346e10	−	4.10396e10i	−0.621725	−	1.91347i
$896$	3.79887e8	−	2.76004e8i	0.0176432	−	0.0128185i
$897$	−3.70829e9	+	2.69423e9i	−0.171554	+	0.124641i
$898$	−4.37276e9	−	1.34580e10i	−0.201506	−	0.620172i
$899$	−5.27366e9	+	1.62307e10i	−0.242077	+	0.745036i
$900$	1.15262e9	+	8.37428e8i	0.0527033	+	0.0382912i
$901$	3.15521e9			0.143712
$902$	−1.03309e10	+	1.67369e10i	−0.468723	+	0.759368i
$903$	−1.72269e9			−0.0778574
$904$	7.80905e9	+	5.67361e9i	0.351568	+	0.255429i
$905$	1.48524e10	−	4.57111e10i	0.666082	−	2.04999i
$906$	−1.70907e9	−	5.25997e9i	−0.0763503	−	0.234982i
$907$	−1.92752e10	+	1.40042e10i	−0.857773	+	0.623209i	−0.927278	−	0.374373i	$-0.877858\pi$
$907$	−1.92752e10	+	1.40042e10i	−0.857773	+	0.623209i	0.0695051	+	0.997582i	$0.477858\pi$
$908$	1.84635e9	−	1.34145e9i	0.0818490	−	0.0594668i
$909$	−3.44648e8	−	1.06072e9i	−0.0152196	−	0.0468410i
$910$	8.15218e8	−	2.50898e9i	0.0358615	−	0.110370i
$911$	−6.67803e9	−	4.85187e9i	−0.292640	−	0.212615i	0.431772	−	0.901983i	$-0.357889\pi$
$911$	−6.67803e9	−	4.85187e9i	−0.292640	−	0.212615i	−0.724412	+	0.689367i	$0.757889\pi$
$912$	1.89746e9			0.0828305
$913$	−1.39292e10	+	2.25664e10i	−0.605730	+	0.981329i
$914$	3.88013e9			0.168087
$915$	2.10757e10	+	1.53124e10i	0.909512	+	0.660799i
$916$	−1.69507e9	+	5.21690e9i	−0.0728709	+	0.224274i
$917$	9.39422e8	+	2.89124e9i	0.0402317	+	0.123820i
$918$	3.16549e8	−	2.29986e8i	0.0135049	−	0.00981189i
$919$	−1.10570e9	+	8.03334e8i	−0.0469928	+	0.0341422i	−0.611034	−	0.791605i	$-0.709246\pi$
$919$	−1.10570e9	+	8.03334e8i	−0.0469928	+	0.0341422i	0.564041	+	0.825747i	$0.309246\pi$
$920$	−3.32476e9	−	1.02326e10i	−0.140768	−	0.433238i
$921$	5.13314e9	−	1.57982e10i	0.216508	−	0.666344i
$922$	3.20125e9	+	2.32584e9i	0.134512	+	0.0977287i
$923$	2.16685e9			0.0907031
$924$	−5.46126e8	−	6.43631e8i	−0.0227741	−	0.0268402i
$925$	1.25891e9			0.0522998
$926$	9.99945e9	+	7.26502e9i	0.413845	+	0.300676i
$927$	1.97442e9	−	6.07663e9i	0.0814066	−	0.250544i
$928$	6.25976e9	+	1.92656e10i	0.257122	+	0.791342i
$929$	−2.61680e10	+	1.90121e10i	−1.07082	+	0.777993i	−0.976059	−	0.217507i	$-0.930208\pi$
$929$	−2.61680e10	+	1.90121e10i	−1.07082	+	0.777993i	−0.0947574	+	0.995500i	$0.530208\pi$
$930$	7.89327e9	−	5.73479e9i	0.321785	−	0.233791i
$931$	−3.43965e9	−	1.05862e10i	−0.139698	−	0.429946i
$932$	9.30605e8	−	2.86411e9i	0.0376539	−	0.115887i
$933$	−7.60515e9	−	5.52547e9i	−0.306565	−	0.222732i
$934$	3.20856e10			1.28854
$935$	−2.66348e8	−	3.53007e9i	−0.0106564	−	0.141235i
$936$	−9.19985e9			−0.366704
$937$	2.07752e9	+	1.50940e9i	0.0825004	+	0.0599400i	0.628271	−	0.777995i	$-0.283763\pi$
$937$	2.07752e9	+	1.50940e9i	0.0825004	+	0.0599400i	−0.545771	+	0.837935i	$0.683763\pi$
$938$	−9.90697e8	+	3.04905e9i	−0.0391950	+	0.120630i
$939$	1.54913e9	+	4.76774e9i	0.0610603	+	0.187924i
$940$	1.69995e10	−	1.23509e10i	0.667557	−	0.485009i
$941$	2.98686e10	−	2.17008e10i	1.16856	−	0.849009i	0.177725	−	0.984080i	$-0.443126\pi$
$941$	2.98686e10	−	2.17008e10i	1.16856	−	0.849009i	0.990836	+	0.135071i	$0.0431262\pi$
$942$	6.02908e9	+	1.85556e10i	0.235003	+	0.723264i
$943$	−3.48151e9	+	1.07150e10i	−0.135200	+	0.416103i
$944$	6.83078e9	+	4.96285e9i	0.264282	+	0.192012i
$945$	−7.73424e8			−0.0298131
$946$	−1.91133e10	−	4.65406e9i	−0.734034	−	0.178737i
$947$	1.22679e10			0.469403			0.234702	−	0.972067i	$-0.424589\pi$
$947$	1.22679e10			0.469403			0.234702	+	0.972067i	$0.424589\pi$
$948$	4.57501e9	+	3.32394e9i	0.174406	+	0.126714i
$949$	−1.03117e10	+	3.17363e10i	−0.391652	+	1.20538i
$950$	−1.14200e9	−	3.51470e9i	−0.0432147	−	0.133001i
$951$	−1.49537e8	+	1.08645e8i	−0.00563789	+	0.00409617i
$952$	−3.56996e8	+	2.59373e8i	−0.0134102	+	0.00974305i
$953$	−1.04733e10	−	3.22334e10i	−0.391973	−	1.20637i	−0.931294	−	0.364269i	$-0.881319\pi$
$953$	−1.04733e10	−	3.22334e10i	−0.391973	−	1.20637i	0.539321	−	0.842100i	$-0.318681\pi$
$954$	2.43247e9	−	7.48638e9i	0.0907044	−	0.279159i
$955$	2.54481e10	+	1.84891e10i	0.945460	+	0.686917i
$956$	1.36867e10			0.506634
$957$	1.42915e10	−	5.86571e9i	0.527092	−	0.216336i
$958$	9.87623e9			0.362921
$959$	−2.71329e9	−	1.97132e9i	−0.0993414	−	0.0721758i
$960$	5.39508e9	−	1.66043e10i	0.196811	−	0.605721i
$961$	−3.14451e9	−	9.67782e9i	−0.114294	−	0.351759i
$962$	−2.09822e9	+	1.52444e9i	−0.0759867	+	0.0552075i
$963$	−7.61916e9	+	5.53564e9i	−0.274925	+	0.199745i
$964$	1.44088e9	+	4.43458e9i	0.0518035	+	0.159435i
$965$	1.55748e10	−	4.79342e10i	0.557925	−	1.71712i
$966$	4.43747e8	+	3.22401e8i	0.0158386	+	0.0115074i
$967$	−7.02638e9			−0.249884			−0.124942	−	0.992164i	$-0.539875\pi$
$967$	−7.02638e9			−0.249884			−0.124942	+	0.992164i	$0.539875\pi$
$968$	−1.35420e10	−	2.70077e10i	−0.479863	−	0.957026i
$969$	8.94681e8			0.0315889
$970$	3.48008e10	+	2.52842e10i	1.22430	+	0.889506i
$971$	−9.15598e9	+	2.81792e10i	−0.320950	+	0.987783i	0.652286	+	0.757973i	$0.273810\pi$
$971$	−9.15598e9	+	2.81792e10i	−0.320950	+	0.987783i	−0.973236	+	0.229809i	$0.926190\pi$
$972$	2.65910e8	+	8.18386e8i	0.00928758	+	0.0285842i
$973$	−8.33007e8	+	6.05215e8i	−0.0289904	+	0.0210627i
$974$	2.36612e10	−	1.71909e10i	0.820505	−	0.596132i
$975$	2.21324e9	+	6.81166e9i	0.0764738	+	0.235362i
$976$	4.58024e9	−	1.40965e10i	0.157693	−	0.485330i
$977$	2.36109e10	+	1.71543e10i	0.809995	+	0.588496i	0.913829	−	0.406099i	$-0.133111\pi$
$977$	2.36109e10	+	1.71543e10i	0.809995	+	0.588496i	−0.103834	+	0.994595i	$0.533111\pi$
$978$	−1.15867e10			−0.396073
$979$	−4.69377e10	+	1.92648e10i	−1.59876	+	0.656182i
$980$	−1.61548e10			−0.548292
$981$	1.02531e10	+	7.44934e9i	0.346749	+	0.251928i
$982$	−1.27225e10	+	3.91559e10i	−0.428730	+	1.31949i
$983$	−9.44685e9	−	2.90744e10i	−0.317212	−	0.976279i	−0.974834	−	0.222931i	$-0.928438\pi$
$983$	−9.44685e9	−	2.90744e10i	−0.317212	−	0.976279i	0.657622	−	0.753348i	$-0.271562\pi$
$984$	−1.82940e10	+	1.32913e10i	−0.612103	+	0.444719i
$985$	5.87936e9	−	4.27160e9i	0.196021	−	0.142418i
$986$	−7.96197e8	−	2.45044e9i	−0.0264516	−	0.0814095i
$987$	−1.03757e9	+	3.19330e9i	−0.0343484	+	0.105713i
$988$	−5.42960e9	−	3.94484e9i	−0.179110	−	0.130131i
$989$	−1.12682e10			−0.370398
$990$	−8.58115e9	−	2.08950e9i	−0.281075	−	0.0684415i
$991$	−5.02608e10			−1.64048			−0.820241	−	0.572018i	$-0.806161\pi$
$991$	−5.02608e10			−1.64048			−0.820241	+	0.572018i	$0.806161\pi$
$992$	1.66483e10	+	1.20957e10i	0.541477	+	0.393406i
$993$	3.84328e9	−	1.18284e10i	0.124560	−	0.383357i
$994$	−8.01258e7	−	2.46602e8i	−0.00258774	−	0.00796423i
$995$	2.48765e10	−	1.80738e10i	0.800587	−	0.581661i
$996$	−7.86937e9	+	5.71743e9i	−0.252367	+	0.183355i
$997$	1.13045e10	+	3.47916e10i	0.361258	+	1.11184i	0.952291	+	0.305191i	$0.0987203\pi$
$997$	1.13045e10	+	3.47916e10i	0.361258	+	1.11184i	−0.591033	+	0.806647i	$0.701280\pi$
$998$	−9.79044e9	+	3.01319e10i	−0.311778	+	0.959554i
$999$	6.15144e8	+	4.46928e8i	0.0195208	+	0.0141827i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.8.e.a.4.5	✓	28
3.2	odd	2		99.8.f.c.37.3		28
11.3	even	5	inner	33.8.e.a.25.5	yes	28
11.5	even	5		363.8.a.q.1.5		14
11.6	odd	10		363.8.a.p.1.10		14
33.14	odd	10		99.8.f.c.91.3		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.8.e.a.4.5	✓	28	1.1	even	1	trivial
33.8.e.a.25.5	yes	28	11.3	even	5	inner
99.8.f.c.37.3		28	3.2	odd	2
99.8.f.c.91.3		28	33.14	odd	10
363.8.a.p.1.10		14	11.6	odd	10
363.8.a.q.1.5		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)

\(f(q)\)	\(=\)	\(q+(6.67280 + 4.84807i) q^{2} +(-8.34346 + 25.6785i) q^{3} +(-18.5317 - 57.0347i) q^{4} +(269.190 - 195.578i) q^{5} +(-180.166 + 130.898i) q^{6} +(-36.4929 - 112.314i) q^{7} +(479.095 - 1474.50i) q^{8} +(-589.773 - 428.495i) q^{9} +O(q^{10})\)	\(q+(6.67280 + 4.84807i) q^{2} +(-8.34346 + 25.6785i) q^{3} +(-18.5317 - 57.0347i) q^{4} +(269.190 - 195.578i) q^{5} +(-180.166 + 130.898i) q^{6} +(-36.4929 - 112.314i) q^{7} +(479.095 - 1474.50i) q^{8} +(-589.773 - 428.495i) q^{9} +2744.43 q^{10} +(4083.84 - 1676.14i) q^{11} +1619.19 q^{12} +(6585.24 + 4784.46i) q^{13} +(300.995 - 926.366i) q^{14} +(2776.18 + 8544.19i) q^{15} +(4135.26 - 3004.45i) q^{16} +(1949.84 - 1416.64i) q^{17} +(-1858.06 - 5718.53i) q^{18} +(4248.60 - 13075.8i) q^{19} +(-16143.3 - 11728.8i) q^{20} +3188.52 q^{21} +(35376.7 + 8614.19i) q^{22} +20856.3 q^{23} +(33865.7 + 24604.9i) q^{24} +(10070.5 - 30993.8i) q^{25} +(20746.6 + 63851.5i) q^{26} +(15923.9 - 11569.4i) q^{27} +(-5729.50 + 4162.72i) q^{28} +(-40052.4 - 123269. i) q^{29} +(-22898.0 + 70472.8i) q^{30} +(-106523. - 77393.2i) q^{31} -156289. q^{32} +(8967.49 + 118852. i) q^{33} +19878.9 q^{34} +(-31789.5 - 23096.4i) q^{35} +(-13509.6 + 41578.3i) q^{36} +(11937.4 + 36739.6i) q^{37} +(91742.6 - 66654.9i) q^{38} +(-177802. + 129180. i) q^{39} +(-159412. - 490621. i) q^{40} +(-166928. + 513752. i) q^{41} +(21276.4 + 15458.2i) q^{42} -540279. q^{43} +(-171279. - 201859. i) q^{44} -242565. q^{45} +(139170. + 101113. i) q^{46} +(-325407. + 1.00150e6i) q^{47} +(42647.3 + 131255. i) q^{48} +(654978. - 475869. i) q^{49} +(217459. - 157993. i) q^{50} +(20108.9 + 61888.7i) q^{51} +(150845. - 464252. i) q^{52} +(1.05912e6 + 769495. i) q^{53} +162346. q^{54} +(771511. - 1.24991e6i) q^{55} -183090. q^{56} +(300320. + 218195. i) q^{57} +(330354. - 1.01672e6i) q^{58} +(510445. + 1.57099e6i) q^{59} +(435868. - 316677. i) q^{60} +(2.34594e6 - 1.70443e6i) q^{61} +(-335596. - 1.03286e6i) q^{62} +(-26603.3 + 81876.5i) q^{63} +(-1.57220e6 - 1.14227e6i) q^{64} +2.70841e6 q^{65} +(-516364. + 836549. i) q^{66} -3.29141e6 q^{67} +(-116932. - 84955.8i) q^{68} +(-174014. + 535560. i) q^{69} +(-100152. - 308236. i) q^{70} +(215363. - 156470. i) q^{71} +(-914374. + 664332. i) q^{72} +(1.26683e6 + 3.89890e6i) q^{73} +(-98460.2 + 303029. i) q^{74} +(711852. + 517191. i) q^{75} -824510. q^{76} +(-337284. - 397503. i) q^{77} -1.81271e6 q^{78} +(2.82550e6 + 2.05284e6i) q^{79} +(525568. - 1.61753e6i) q^{80} +(164224. + 505430. i) q^{81} +(-3.60459e6 + 2.61889e6i) q^{82} +(-4.86007e6 + 3.53105e6i) q^{83} +(-59088.8 - 181857. i) q^{84} +(247813. - 762691. i) q^{85} +(-3.60517e6 - 2.61931e6i) q^{86} +3.49953e6 q^{87} +(-514927. - 6.82465e6i) q^{88} -1.14935e7 q^{89} +(-1.61859e6 - 1.17597e6i) q^{90} +(297045. - 914211. i) q^{91} +(-386504. - 1.18954e6i) q^{92} +(2.87611e6 - 2.08962e6i) q^{93} +(-7.02672e6 + 5.10521e6i) q^{94} +(-1.41366e6 - 4.35081e6i) q^{95} +(1.30399e6 - 4.01328e6i) q^{96} +(1.26805e7 + 9.21294e6i) q^{97} +6.67759e6 q^{98} +(-3.12676e6 - 761363. i) 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