LMFDB - Embedded newform 192.2.s.a.107.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(11,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 5, 8]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("192.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.s (of order $16$, degree $8$, 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:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			107.6
Character	$\chi$	$=$	192.107
Dual form			192.2.s.a.131.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13356 + 0.845597i) q^{2} +(-1.00574 + 1.41014i) q^{3} +(0.569932 - 1.91708i) q^{4} +(-0.908097 - 1.35906i) q^{5} +(-0.0523394 - 2.44893i) q^{6} +(1.44850 - 3.49700i) q^{7} +(0.975019 + 2.65506i) q^{8} +(-0.976978 - 2.83646i) q^{9} +O(q^{10})$	\(q+(-1.13356 + 0.845597i) q^{2} +(-1.00574 + 1.41014i) q^{3} +(0.569932 - 1.91708i) q^{4} +(-0.908097 - 1.35906i) q^{5} +(-0.0523394 - 2.44893i) q^{6} +(1.44850 - 3.49700i) q^{7} +(0.975019 + 2.65506i) q^{8} +(-0.976978 - 2.83646i) q^{9} +(2.17861 + 0.772701i) q^{10} +(3.39536 + 0.675380i) q^{11} +(2.13014 + 2.73176i) q^{12} +(-1.72260 - 1.15100i) q^{13} +(1.31508 + 5.18892i) q^{14} +(2.82978 + 0.0863210i) q^{15} +(-3.35036 - 2.18520i) q^{16} +(-1.04981 - 1.04981i) q^{17} +(3.50597 + 2.38918i) q^{18} +(6.92609 + 4.62786i) q^{19} +(-3.12298 + 0.966318i) q^{20} +(3.47443 + 5.55965i) q^{21} +(-4.41996 + 2.10552i) q^{22} +(-1.88173 - 4.54290i) q^{23} +(-4.72461 - 1.29538i) q^{24} +(0.891004 - 2.15107i) q^{25} +(2.92596 - 0.151889i) q^{26} +(4.98239 + 1.47507i) q^{27} +(-5.87846 - 4.76994i) q^{28} +(-1.76843 - 8.89050i) q^{29} +(-3.28072 + 2.29500i) q^{30} +2.37466 q^{31} +(5.64564 - 0.355984i) q^{32} +(-4.36723 + 4.10868i) q^{33} +(2.07775 + 0.302311i) q^{34} +(-6.06802 + 1.20700i) q^{35} +(-5.99452 + 0.256351i) q^{36} +(1.65056 + 2.47024i) q^{37} +(-11.7645 + 0.610702i) q^{38} +(3.35556 - 1.27149i) q^{39} +(2.72298 - 3.73617i) q^{40} +(-1.72291 + 0.713652i) q^{41} +(-8.63971 - 3.36425i) q^{42} +(-9.26200 - 1.84233i) q^{43} +(3.22988 - 6.12425i) q^{44} +(-2.96774 + 3.90356i) q^{45} +(5.97452 + 3.55848i) q^{46} +(0.0451118 - 0.0451118i) q^{47} +(6.45102 - 2.52672i) q^{48} +(-5.18107 - 5.18107i) q^{49} +(0.808932 + 3.19181i) q^{50} +(2.53622 - 0.424543i) q^{51} +(-3.18832 + 2.64636i) q^{52} +(-1.12932 + 5.67750i) q^{53} +(-6.89516 + 2.54101i) q^{54} +(-2.16544 - 5.22783i) q^{55} +(10.6970 + 0.436222i) q^{56} +(-13.4918 + 5.11231i) q^{57} +(9.52241 + 8.58257i) q^{58} +(5.63408 - 3.76457i) q^{59} +(1.77826 - 5.37570i) q^{60} +(1.08231 + 5.44112i) q^{61} +(-2.69183 + 2.00801i) q^{62} +(-11.3342 - 0.692136i) q^{63} +(-6.09867 + 5.17747i) q^{64} +3.38634i q^{65} +(1.47625 - 8.35036i) q^{66} +(-8.44485 + 1.67979i) q^{67} +(-2.61089 + 1.41425i) q^{68} +(8.29865 + 1.91547i) q^{69} +(5.85785 - 6.49932i) q^{70} +(7.65191 + 3.16953i) q^{71} +(6.57840 - 5.35954i) q^{72} +(6.47085 - 2.68031i) q^{73} +(-3.95985 - 1.40447i) q^{74} +(2.13719 + 3.41986i) q^{75} +(12.8194 - 10.6403i) q^{76} +(7.28000 - 10.8953i) q^{77} +(-2.72857 + 4.27877i) q^{78} +(-4.09884 + 4.09884i) q^{79} +(0.0726180 + 6.53773i) q^{80} +(-7.09103 + 5.54232i) q^{81} +(1.34956 - 2.26586i) q^{82} +(-3.39292 + 5.07787i) q^{83} +(12.6385 - 3.49212i) q^{84} +(-0.473430 + 2.38009i) q^{85} +(12.0569 - 5.74353i) q^{86} +(14.3154 + 6.44780i) q^{87} +(1.51737 + 9.67340i) q^{88} +(2.79449 + 1.15752i) q^{89} +(0.0632855 - 6.93444i) q^{90} +(-6.52024 + 4.35669i) q^{91} +(-9.78154 + 1.01828i) q^{92} +(-2.38829 + 3.34860i) q^{93} +(-0.0129907 + 0.0892834i) q^{94} -13.6155i q^{95} +(-5.17606 + 8.31916i) q^{96} -5.24368i q^{97} +(10.2542 + 1.49197i) q^{98} +(-1.40151 - 10.2907i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9}+O(q^{10}) $ 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9	$ 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28} - 88 q^{30} - 32 q^{31} - 16 q^{34} - 88 q^{36} - 16 q^{37} - 8 q^{39} - 16 q^{40} - 48 q^{42} - 16 q^{43} - 8 q^{45} - 16 q^{46} - 8 q^{48} - 16 q^{49} - 8 q^{51} + 32 q^{52} - 8 q^{54} - 80 q^{55} - 8 q^{57} + 128 q^{58} - 8 q^{60} - 16 q^{61} + 80 q^{64} - 24 q^{66} - 144 q^{67} - 8 q^{69} + 80 q^{70} - 8 q^{72} - 16 q^{73} - 8 q^{75} + 96 q^{76} + 16 q^{78} - 48 q^{79} - 8 q^{81} + 64 q^{82} + 104 q^{84} - 16 q^{85} - 8 q^{87} + 64 q^{88} + 136 q^{90} - 16 q^{91} - 32 q^{93} + 80 q^{94} + 128 q^{96} - 8 q^{99}+O(q^{100}) $ 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{16}\right)$

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 $

$2$	−1.13356	+	0.845597i	−0.801550	+	0.597927i
$2$	−1.13356	+	0.845597i	−0.801550	+	0.597927i
$3$	−1.00574	+	1.41014i	−0.580664	+	0.814144i
$3$	−1.00574	+	1.41014i	−0.580664	+	0.814144i
$4$	0.569932	−	1.91708i	0.284966	−	0.958538i
$5$	−0.908097	−	1.35906i	−0.406114	−	0.607792i	0.570887	−	0.821029i	$-0.306599\pi$
$5$	−0.908097	−	1.35906i	−0.406114	−	0.607792i	−0.977001	+	0.213237i	$0.931599\pi$
$6$	−0.0523394	−	2.44893i	−0.0213675	−	0.999772i
$7$	1.44850	−	3.49700i	0.547483	−	1.32174i	−0.371862	−	0.928288i	$-0.621281\pi$
$7$	1.44850	−	3.49700i	0.547483	−	1.32174i	0.919345	−	0.393452i	$-0.128719\pi$
$8$	0.975019	+	2.65506i	0.344721	+	0.938705i
$9$	−0.976978	−	2.83646i	−0.325659	−	0.945487i
$10$	2.17861	+	0.772701i	0.688936	+	0.244349i
$11$	3.39536	+	0.675380i	1.02374	+	0.203635i	0.678284	−	0.734800i	$-0.262724\pi$
$11$	3.39536	+	0.675380i	1.02374	+	0.203635i	0.345457	+	0.938435i	$0.387724\pi$
$12$	2.13014	+	2.73176i	0.614918	+	0.788591i
$13$	−1.72260	−	1.15100i	−0.477763	−	0.319231i	0.293266	−	0.956031i	$-0.405258\pi$
$13$	−1.72260	−	1.15100i	−0.477763	−	0.319231i	−0.771029	+	0.636800i	$0.780258\pi$
$14$	1.31508	+	5.18892i	0.351470	+	1.38680i
$15$	2.82978	+	0.0863210i	0.730645	+	0.0222880i
$16$	−3.35036	−	2.18520i	−0.837589	−	0.546301i
$17$	−1.04981	−	1.04981i	−0.254617	−	0.254617i	0.568244	−	0.822860i	$-0.307623\pi$
$17$	−1.04981	−	1.04981i	−0.254617	−	0.254617i	−0.822860	+	0.568244i	$0.807623\pi$
$18$	3.50597	+	2.38918i	0.826365	+	0.563135i
$19$	6.92609	+	4.62786i	1.58895	+	1.06170i	0.958349	+	0.285600i	$0.0921927\pi$
$19$	6.92609	+	4.62786i	1.58895	+	1.06170i	0.630604	+	0.776105i	$0.282807\pi$
$20$	−3.12298	+	0.966318i	−0.698320	+	0.216075i
$21$	3.47443	+	5.55965i	0.758183	+	1.21322i
$22$	−4.41996	+	2.10552i	−0.942339	+	0.448899i
$23$	−1.88173	−	4.54290i	−0.392368	−	0.947260i	−0.989423	−	0.145060i	$-0.953663\pi$
$23$	−1.88173	−	4.54290i	−0.392368	−	0.947260i	0.597055	−	0.802200i	$-0.296337\pi$
$24$	−4.72461	−	1.29538i	−0.964408	−	0.264419i
$25$	0.891004	−	2.15107i	0.178201	−	0.430215i
$26$	2.92596	−	0.151889i	0.573828	−	0.0297878i
$27$	4.98239	+	1.47507i	0.958861	+	0.283877i
$28$	−5.87846	−	4.76994i	−1.11092	−	0.901433i
$29$	−1.76843	−	8.89050i	−0.328389	−	1.65093i	−0.693866	−	0.720105i	$-0.744094\pi$
$29$	−1.76843	−	8.89050i	−0.328389	−	1.65093i	0.365476	−	0.930821i	$-0.380906\pi$
$30$	−3.28072	+	2.29500i	−0.598975	+	0.419008i
$31$	2.37466			0.426502			0.213251	−	0.976997i	$-0.431595\pi$
$31$	2.37466			0.426502			0.213251	+	0.976997i	$0.431595\pi$
$32$	5.64564	−	0.355984i	0.998018	−	0.0629296i
$33$	−4.36723	+	4.10868i	−0.760237	+	0.715229i
$34$	2.07775	+	0.302311i	0.356331	+	0.0518458i
$35$	−6.06802	+	1.20700i	−1.02568	+	0.204021i
$36$	−5.99452	+	0.256351i	−0.999087	+	0.0427251i
$37$	1.65056	+	2.47024i	0.271351	+	0.406106i	0.941970	−	0.335696i	$-0.108972\pi$
$37$	1.65056	+	2.47024i	0.271351	+	0.406106i	−0.670619	+	0.741802i	$0.733972\pi$
$38$	−11.7645	+	0.610702i	−1.90845	+	0.0990689i
$39$	3.35556	−	1.27149i	0.537319	−	0.203602i
$40$	2.72298	−	3.73617i	0.430541	−	0.590740i
$41$	−1.72291	+	0.713652i	−0.269073	+	0.111454i	−0.513141	−	0.858305i	$-0.671518\pi$
$41$	−1.72291	+	0.713652i	−0.269073	+	0.111454i	0.244068	+	0.969758i	$0.421518\pi$
$42$	−8.63971	−	3.36425i	−1.33314	−	0.519115i
$43$	−9.26200	−	1.84233i	−1.41244	−	0.280952i	−0.570845	−	0.821058i	$-0.693384\pi$
$43$	−9.26200	−	1.84233i	−1.41244	−	0.280952i	−0.841597	+	0.540106i	$0.818384\pi$
$44$	3.22988	−	6.12425i	0.486923	−	0.923265i
$45$	−2.96774	+	3.90356i	−0.442405	+	0.581908i
$46$	5.97452	+	3.55848i	0.880896	+	0.524669i
$47$	0.0451118	−	0.0451118i	0.00658023	−	0.00658023i	−0.703809	−	0.710389i	$-0.748519\pi$
$47$	0.0451118	−	0.0451118i	0.00658023	−	0.00658023i	0.710389	+	0.703809i	$0.248519\pi$
$48$	6.45102	−	2.52672i	0.931125	−	0.364700i
$49$	−5.18107	−	5.18107i	−0.740153	−	0.740153i
$50$	0.808932	+	3.19181i	0.114400	+	0.451390i
$51$	2.53622	−	0.424543i	0.355141	−	0.0594479i
$52$	−3.18832	+	2.64636i	−0.442141	+	0.366984i
$53$	−1.12932	+	5.67750i	−0.155125	+	0.779865i	0.822378	+	0.568942i	$0.192647\pi$
$53$	−1.12932	+	5.67750i	−0.155125	+	0.779865i	−0.977503	+	0.210923i	$0.932353\pi$
$54$	−6.89516	+	2.54101i	−0.938313	+	0.345788i
$55$	−2.16544	−	5.22783i	−0.291988	−	0.704920i
$56$	10.6970	+	0.436222i	1.42945	+	0.0582926i
$57$	−13.4918	+	5.11231i	−1.78703	+	0.677142i
$58$	9.52241	+	8.58257i	1.25035	+	1.12695i
$59$	5.63408	−	3.76457i	0.733495	−	0.490106i	−0.131858	−	0.991269i	$-0.542094\pi$
$59$	5.63408	−	3.76457i	0.733495	−	0.490106i	0.865353	+	0.501163i	$0.167094\pi$
$60$	1.77826	−	5.37570i	0.229573	−	0.694000i
$61$	1.08231	+	5.44112i	0.138575	+	0.696664i	0.986132	+	0.165960i	$0.0530724\pi$
$61$	1.08231	+	5.44112i	0.138575	+	0.696664i	−0.847557	+	0.530704i	$0.821928\pi$
$62$	−2.69183	+	2.00801i	−0.341863	+	0.255017i
$63$	−11.3342	−	0.692136i	−1.42798	−	0.0872009i
$64$	−6.09867	+	5.17747i	−0.762334	+	0.647183i
$65$			3.38634i			0.420024i
$66$	1.47625	−	8.35036i	0.181714	−	1.02786i
$67$	−8.44485	+	1.67979i	−1.03170	+	0.205218i	−0.681778	−	0.731559i	$-0.738793\pi$
$67$	−8.44485	+	1.67979i	−1.03170	+	0.205218i	−0.349925	+	0.936778i	$0.613793\pi$
$68$	−2.61089	+	1.41425i	−0.316617	+	0.171503i
$69$	8.29865	+	1.91547i	0.999040	+	0.230596i
$70$	5.85785	−	6.49932i	0.700147	−	0.776817i
$71$	7.65191	+	3.16953i	0.908115	+	0.376153i	0.787335	−	0.616526i	$-0.211460\pi$
$71$	7.65191	+	3.16953i	0.908115	+	0.376153i	0.120780	+	0.992679i	$0.461460\pi$
$72$	6.57840	−	5.35954i	0.775272	−	0.631628i
$73$	6.47085	−	2.68031i	0.757355	−	0.313707i	0.0296166	−	0.999561i	$-0.490571\pi$
$73$	6.47085	−	2.68031i	0.757355	−	0.313707i	0.727739	+	0.685855i	$0.240571\pi$
$74$	−3.95985	−	1.40447i	−0.460323	−	0.163266i
$75$	2.13719	+	3.41986i	0.246782	+	0.394891i
$76$	12.8194	−	10.6403i	1.47048	−	1.22052i
$77$	7.28000	−	10.8953i	0.829633	−	1.24163i
$78$	−2.72857	+	4.27877i	−0.308949	+	0.484475i
$79$	−4.09884	+	4.09884i	−0.461155	+	0.461155i	−0.899034	−	0.437879i	$-0.855730\pi$
$79$	−4.09884	+	4.09884i	−0.461155	+	0.461155i	0.437879	+	0.899034i	$0.355730\pi$
$80$	0.0726180	+	6.53773i	0.00811893	+	0.730940i
$81$	−7.09103	+	5.54232i	−0.787892	+	0.615813i
$82$	1.34956	−	2.26586i	0.149034	−	0.250222i
$83$	−3.39292	+	5.07787i	−0.372422	+	0.557369i	−0.969586	−	0.244750i	$-0.921294\pi$
$83$	−3.39292	+	5.07787i	−0.372422	+	0.557369i	0.597164	+	0.802119i	$0.296294\pi$
$84$	12.6385	−	3.49212i	1.37897	−	0.381022i
$85$	−0.473430	+	2.38009i	−0.0513507	+	0.258157i
$86$	12.0569	−	5.74353i	1.30013	−	0.619340i
$87$	14.3154	+	6.44780i	1.53477	+	0.691276i
$88$	1.51737	+	9.67340i	0.161752	+	1.03119i
$89$	2.79449	+	1.15752i	0.296215	+	0.122696i	0.525842	−	0.850582i	$-0.323750\pi$
$89$	2.79449	+	1.15752i	0.296215	+	0.122696i	−0.229626	+	0.973279i	$0.573750\pi$
$90$	0.0632855	−	6.93444i	0.00667087	−	0.730955i
$91$	−6.52024	+	4.35669i	−0.683507	+	0.456705i
$92$	−9.78154	+	1.01828i	−1.01980	+	0.106163i
$93$	−2.38829	+	3.34860i	−0.247654	+	0.347234i
$94$	−0.0129907	+	0.0892834i	−0.00133989	+	0.00920888i
$95$		−	13.6155i		−	1.39693i
$96$	−5.17606	+	8.31916i	−0.528279	+	0.849071i
$97$		−	5.24368i		−	0.532415i	−0.963916	−	0.266208i	$-0.914229\pi$
$97$		−	5.24368i		−	0.532415i	0.963916	−	0.266208i	$-0.0857707\pi$
$98$	10.2542	+	1.49197i	1.03583	+	0.150712i
$99$	−1.40151	−	10.2907i	−0.140857	−	1.03425i
$100$	−3.61596	−	2.93409i	−0.361596	−	0.293409i
$101$	2.00292	−	1.33831i	0.199298	−	0.133167i	−0.451917	−	0.892060i	$-0.649260\pi$
$101$	2.00292	−	1.33831i	0.199298	−	0.133167i	0.651215	+	0.758893i	$0.274260\pi$
$102$	−2.51597	+	2.62586i	−0.249118	+	0.259999i
$103$	12.3098	+	5.09889i	1.21292	+	0.502409i	0.895153	−	0.445759i	$-0.147066\pi$
$103$	12.3098	+	5.09889i	1.21292	+	0.502409i	0.317770	+	0.948168i	$0.397066\pi$
$104$	1.37642	−	5.69585i	0.134969	−	0.558524i
$105$	4.40080	−	9.77068i	0.429474	−	0.953521i
$106$	−3.52071	−	7.39076i	−0.341962	−	0.717854i
$107$	−1.54725	+	7.77853i	−0.149578	+	0.751979i	0.831065	+	0.556175i	$0.187732\pi$
$107$	−1.54725	+	7.77853i	−0.149578	+	0.751979i	−0.980643	+	0.195804i	$0.937268\pi$
$108$	5.66743	−	8.71092i	0.545349	−	0.838209i
$109$	0.951386	−	1.42385i	0.0911263	−	0.136380i	−0.783106	−	0.621889i	$-0.786366\pi$
$109$	0.951386	−	1.42385i	0.0911263	−	0.136380i	0.874232	+	0.485509i	$0.161366\pi$
$110$	6.87530	+	4.09499i	0.655534	+	0.390442i
$111$	−5.14342	−	0.156898i	−0.488192	−	0.0148921i
$112$	−12.4946	+	8.55090i	−1.18063	+	0.807985i
$113$	−1.49623	+	1.49623i	−0.140753	+	0.140753i	−0.773973	−	0.633219i	$-0.781733\pi$
$113$	−1.49623	+	1.49623i	−0.140753	+	0.140753i	0.633219	+	0.773973i	$0.281733\pi$
$114$	10.9708	−	17.2037i	1.02751	−	1.61128i
$115$	−4.46530	+	6.68279i	−0.416391	+	0.623173i
$116$	−18.0517	−	1.67676i	−1.67605	−	0.155684i
$117$	−1.58184	+	6.01059i	−0.146241	+	0.555679i
$118$	−3.20328	+	9.03155i	−0.294886	+	0.831421i
$119$	−5.19184	+	2.15053i	−0.475936	+	0.197139i
$120$	2.52990	+	7.59739i	0.230947	+	0.693543i
$121$	0.909689	+	0.376805i	0.0826990	+	0.0342550i
$122$	−5.82786	−	5.25266i	−0.527630	−	0.475554i
$123$	0.726448	−	3.14729i	0.0655016	−	0.283781i
$124$	1.35339	−	4.55240i	0.121538	−	0.408818i
$125$	−11.7482	+	2.33686i	−1.05079	+	0.209015i
$126$	13.4334	−	8.79963i	1.19674	−	0.783933i
$127$			14.4728i			1.28425i	0.766598	+	0.642127i	$0.221948\pi$
$127$			14.4728i			1.28425i	−0.766598	+	0.642127i	$0.778052\pi$
$128$	2.53518	−	11.0260i	0.224081	−	0.974571i
$129$	11.9131	−	11.2078i	1.04889	−	0.986792i
$130$	−2.86348	−	3.83864i	−0.251144	−	0.336671i
$131$	4.32387	+	21.7376i	0.377779	+	1.89922i	0.434204	+	0.900815i	$0.357030\pi$
$131$	4.32387	+	21.7376i	0.377779	+	1.89922i	−0.0564253	+	0.998407i	$0.517970\pi$
$132$	5.38762	+	10.7140i	0.468932	+	0.932532i
$133$	26.2161	−	17.5170i	2.27322	−	1.51892i
$134$	8.15235	−	9.04509i	0.704256	−	0.781376i
$135$	−2.51978	−	8.11089i	−0.216868	−	0.698074i
$136$	1.76373	−	3.81090i	0.151238	−	0.326782i
$137$	3.88223	+	9.37254i	0.331682	+	0.800750i	0.998459	+	0.0554933i	$0.0176731\pi$
$137$	3.88223	+	9.37254i	0.331682	+	0.800750i	−0.666778	+	0.745257i	$0.732327\pi$
$138$	−11.0268	+	4.84600i	−0.938660	+	0.412519i
$139$	2.91878	−	14.6737i	0.247568	−	1.24461i	−0.634291	−	0.773095i	$-0.718708\pi$
$139$	2.91878	−	14.6737i	0.247568	−	1.24461i	0.881859	−	0.471514i	$-0.156292\pi$
$140$	−1.14444	+	12.3208i	−0.0967227	+	1.04129i
$141$	0.0182431	+	0.108984i	0.00153635	+	0.00917815i
$142$	−11.3541	+	2.87757i	−0.952812	+	0.241481i
$143$	−5.07149	−	5.07149i	−0.424099	−	0.424099i
$144$	−2.92502	+	11.6381i	−0.243752	+	0.969838i
$145$	−10.4769	+	10.4769i	−0.870055	+	0.870055i
$146$	−5.06865	+	8.51003i	−0.419484	+	0.704295i
$147$	12.5168	−	2.09522i	1.03237	−	0.172811i
$148$	5.67635	−	1.75639i	0.466593	−	0.144374i
$149$	3.95335	+	0.786371i	0.323871	+	0.0644220i	0.354348	−	0.935113i	$-0.384703\pi$
$149$	3.95335	+	0.786371i	0.323871	+	0.0644220i	−0.0304772	+	0.999535i	$0.509703\pi$
$150$	−5.31446	−	2.06942i	−0.433924	−	0.168967i
$151$	−15.1163	+	6.26136i	−1.23014	+	0.509542i	−0.900621	−	0.434605i	$-0.856888\pi$
$151$	−15.1163	+	6.26136i	−1.23014	+	0.509542i	−0.329523	+	0.944148i	$0.606888\pi$
$152$	−5.53418	+	22.9014i	−0.448881	+	1.85755i
$153$	−1.95211	+	4.00340i	−0.157819	+	0.323655i
$154$	0.960682	+	18.5064i	0.0774140	+	1.49129i
$155$	−2.15642	−	3.22732i	−0.173208	−	0.259224i
$156$	−0.525108	−	7.15752i	−0.0420422	−	0.573060i
$157$	−8.64769	+	1.72013i	−0.690161	+	0.137282i	−0.527697	−	0.849433i	$-0.676944\pi$
$157$	−8.64769	+	1.72013i	−0.690161	+	0.137282i	−0.162464	+	0.986714i	$0.551944\pi$
$158$	1.18033	−	8.11225i	0.0939018	−	0.645376i
$159$	−6.87025	−	7.30259i	−0.544846	−	0.579133i
$160$	−5.61060	−	7.34952i	−0.443557	−	0.581031i
$161$	−18.6122			−1.46685
$162$	3.35156	−	12.2787i	0.263324	−	0.964708i
$163$	3.04203	+	15.2933i	0.238270	+	1.19786i	0.895807	+	0.444443i	$0.146598\pi$
$163$	3.04203	+	15.2933i	0.238270	+	1.19786i	−0.657537	+	0.753422i	$0.728402\pi$
$164$	0.386185	+	3.70968i	0.0301559	+	0.289677i
$165$	9.54982	+	2.20427i	0.743453	+	0.171602i
$166$	−0.447737	−	8.62513i	−0.0347511	−	0.669440i
$167$	8.75560	−	21.1379i	0.677529	−	1.63570i	−0.0909738	−	0.995853i	$-0.528998\pi$
$167$	8.75560	−	21.1379i	0.677529	−	1.63570i	0.768503	−	0.639846i	$-0.221002\pi$
$168$	−11.3736	+	14.6456i	−0.877490	+	1.12993i
$169$	−3.33235	−	8.04500i	−0.256334	−	0.618846i
$170$	−1.47594	−	3.09832i	−0.113199	−	0.237630i
$171$	6.36012	−	24.1669i	0.486371	−	1.84809i
$172$	−8.81059	+	16.7060i	−0.671801	+	1.27382i
$173$	12.1698	+	8.13161i	0.925254	+	0.618235i	0.924260	−	0.381765i	$-0.124683\pi$
$173$	12.1698	+	8.13161i	0.925254	+	0.618235i	0.000994366		1.00000i	$0.499683\pi$
$174$	−21.6797	+	4.79609i	−1.64353	+	0.363591i
$175$	−6.23167	−	6.23167i	−0.471070	−	0.471070i
$176$	−9.89984	−	9.68233i	−0.746228	−	0.729833i
$177$	−0.357849	+	11.7310i	−0.0268976	+	0.881757i
$178$	−4.14652	+	1.05089i	−0.310795	+	0.0787679i
$179$	−9.26280	−	6.18920i	−0.692334	−	0.462603i	0.158965	−	0.987284i	$-0.449184\pi$
$179$	−9.26280	−	6.18920i	−0.692334	−	0.462603i	−0.851299	+	0.524682i	$0.824184\pi$
$180$	5.79201	+	7.91415i	0.431711	+	0.589886i
$181$	−4.43070	−	0.881322i	−0.329332	−	0.0655081i	0.0276553	−	0.999618i	$-0.491196\pi$
$181$	−4.43070	−	0.881322i	−0.329332	−	0.0655081i	−0.356987	+	0.934109i	$0.616196\pi$
$182$	3.70711	−	10.4521i	0.274789	−	0.774760i
$183$	−8.76125	−	3.94615i	−0.647650	−	0.291708i
$184$	10.2269	−	9.42552i	0.753940	−	0.694859i
$185$	1.85835	−	4.48645i	0.136628	−	0.329850i
$186$	−0.124288	−	5.81538i	−0.00911325	−	0.426404i
$187$	−2.85547	−	4.27352i	−0.208813	−	0.312511i
$188$	−0.0607720	−	0.112193i	−0.00443226	−	0.00818254i
$189$	12.3753	−	15.2867i	0.900171	−	1.11195i
$190$	11.5133	+	15.4341i	0.835260	+	1.11971i
$191$	2.51135			0.181715			0.0908576	−	0.995864i	$-0.471039\pi$
$191$	2.51135			0.181715			0.0908576	+	0.995864i	$0.471039\pi$
$192$	−1.16727	−	13.8072i	−0.0842403	−	0.996445i
$193$	6.00321			0.432121			0.216060	−	0.976380i	$-0.430679\pi$
$193$	6.00321			0.432121			0.216060	+	0.976380i	$0.430679\pi$
$194$	4.43404	+	5.94405i	0.318346	+	0.426758i
$195$	−4.77521	−	3.40578i	−0.341960	−	0.243893i
$196$	−12.8854	+	6.97964i	−0.920382	+	0.498546i
$197$	−10.0186	−	14.9939i	−0.713798	−	1.06827i	−0.994111	−	0.108365i	$-0.965438\pi$
$197$	−10.0186	−	14.9939i	−0.713798	−	1.06827i	0.280313	−	0.959909i	$-0.409562\pi$
$198$	10.2904	+	10.4800i	0.731310	+	0.744781i
$199$	−4.17064	+	10.0688i	−0.295649	+	0.713759i	0.704344	+	0.709859i	$0.251241\pi$
$199$	−4.17064	+	10.0688i	−0.295649	+	0.713759i	−0.999992	+	0.00390010i	$0.998759\pi$
$200$	6.57997	+	0.268329i	0.465274	+	0.0189737i
$201$	6.12459	−	13.5978i	0.431995	−	0.959117i
$202$	−1.13877	+	3.21073i	−0.0801236	+	0.225906i
$203$	−33.6516	−	6.69373i	−2.36188	−	0.469807i
$204$	0.631590	−	5.10408i	0.0442201	−	0.357357i
$205$	2.53447	+	1.69348i	0.177015	+	0.118278i
$206$	−18.2656	+	4.62923i	−1.27262	+	0.322533i
$207$	−11.0474	+	9.77577i	−0.767844	+	0.679463i
$208$	3.25614	+	7.62050i	0.225773	+	0.528387i
$209$	20.3910	+	20.3910i	1.41048	+	1.41048i
$210$	3.27347	+	14.7970i	0.225891	+	1.02109i
$211$	8.95451	+	5.98321i	0.616454	+	0.411901i	0.824214	−	0.566278i	$-0.191617\pi$
$211$	8.95451	+	5.98321i	0.616454	+	0.411901i	−0.207760	+	0.978180i	$0.566617\pi$
$212$	10.2406	+	5.40079i	0.703324	+	0.370928i
$213$	−12.1653	+	7.60253i	−0.833552	+	0.520917i
$214$	−4.82360	−	10.1258i	−0.329734	−	0.692185i
$215$	5.90696	+	14.2607i	0.402851	+	0.972569i
$216$	0.941535	+	14.6667i	0.0640633	+	0.997946i
$217$	3.43970	−	8.30418i	0.233502	−	0.563724i
$218$	0.125547	+	2.41851i	0.00850310	+	0.163802i
$219$	−2.72837	+	11.8205i	−0.184366	+	0.798754i
$220$	−11.2563	+	1.17180i	−0.758899	+	0.0790029i
$221$	0.600067	+	3.01674i	0.0403649	+	0.202928i
$222$	5.96307	−	4.17141i	0.400215	−	0.279967i
$223$	15.0549			1.00815			0.504076	−	0.863659i	$-0.331833\pi$
$223$	15.0549			1.00815			0.504076	+	0.863659i	$0.331833\pi$
$224$	6.93286	−	20.2584i	0.463221	−	1.35357i
$225$	−6.97193	−	0.425747i	−0.464795	−	0.0283831i
$226$	0.430864	−	2.96128i	0.0286606	−	0.196981i
$227$	−3.59460	+	0.715010i	−0.238582	+	0.0474569i	−0.312933	−	0.949775i	$-0.601311\pi$
$227$	−3.59460	+	0.715010i	−0.238582	+	0.0474569i	0.0743510	+	0.997232i	$0.476311\pi$
$228$	2.11131	+	28.7784i	0.139825	+	1.90590i
$229$	6.31300	+	9.44807i	0.417175	+	0.624346i	0.979230	−	0.202754i	$-0.0649891\pi$
$229$	6.31300	+	9.44807i	0.417175	+	0.624346i	−0.562055	+	0.827100i	$0.689989\pi$
$230$	−0.589249	−	11.3512i	−0.0388539	−	0.748476i
$231$	8.04208	+	21.2236i	0.529130	+	1.39641i
$232$	21.8806	−	13.3637i	1.43653	−	0.877370i
$233$	22.3030	−	9.23819i	1.46112	−	0.605214i	0.496302	−	0.868150i	$-0.334691\pi$
$233$	22.3030	−	9.23819i	1.46112	−	0.605214i	0.964813	+	0.262936i	$0.0846908\pi$
$234$	−3.28942	−	8.15098i	−0.215036	−	0.532846i
$235$	−0.102276	−	0.0203439i	−0.00667173	−	0.00132709i
$236$	−4.00593	−	12.9465i	−0.260764	−	0.842746i
$237$	−1.65756	−	9.90228i	−0.107670	−	0.643222i
$238$	4.06680	−	6.82797i	0.263612	−	0.442592i
$239$	4.96424	−	4.96424i	0.321110	−	0.321110i	−0.528083	−	0.849193i	$-0.677089\pi$
$239$	4.96424	−	4.96424i	0.321110	−	0.321110i	0.849193	+	0.528083i	$0.177089\pi$
$240$	−9.29213	−	6.47284i	−0.599804	−	0.417820i
$241$	16.3360	+	16.3360i	1.05229	+	1.05229i	0.998555	+	0.0537389i	$0.0171139\pi$
$241$	16.3360	+	16.3360i	1.05229	+	1.05229i	0.0537389	+	0.998555i	$0.482886\pi$
$242$	−1.34982	+	0.342097i	−0.0867694	+	0.0219908i
$243$	−0.683711	−	15.5735i	−0.0438601	−	0.999038i
$244$	11.0479	+	1.02620i	0.707268	+	0.0656960i
$245$	−2.33649	+	11.7463i	−0.149273	+	0.750445i
$246$	1.83786	+	4.18193i	0.117178	+	0.266630i
$247$	−6.60418	−	15.9439i	−0.420214	−	1.01449i
$248$	2.31534	+	6.30486i	0.147024	+	0.400359i
$249$	−3.74810	−	9.89150i	−0.237526	−	0.626849i
$250$	11.3413	−	12.5832i	0.717285	−	0.795832i
$251$	19.1412	−	12.7898i	1.20818	−	0.807283i	0.222344	−	0.974968i	$-0.428629\pi$
$251$	19.1412	−	12.7898i	1.20818	−	0.807283i	0.985841	+	0.167685i	$0.0536292\pi$
$252$	−7.78662	+	21.3341i	−0.490511	+	1.34392i
$253$	−3.32098	−	16.6957i	−0.208788	−	1.04965i
$254$	−12.2382	−	16.4058i	−0.767891	−	1.02939i
$255$	−2.88011	−	3.06135i	−0.180360	−	0.191709i
$256$	6.44977	+	14.6424i	0.403111	+	0.915151i
$257$			5.49498i			0.342768i	0.985204	+	0.171384i	$0.0548238\pi$
$257$			5.49498i			0.342768i	−0.985204	+	0.171384i	$0.945176\pi$
$258$	−4.02696	+	22.7784i	−0.250708	+	1.41812i
$259$	11.0293	−	2.19386i	0.685326	−	0.136320i
$260$	6.49188	+	1.92999i	0.402609	+	0.119693i
$261$	−23.4899	+	13.7019i	−1.45399	+	0.848127i
$262$	−23.2826	−	20.9847i	−1.43840	−	1.29644i
$263$	19.7415	+	8.17718i	1.21731	+	0.504227i	0.896554	−	0.442935i	$-0.146063\pi$
$263$	19.7415	+	8.17718i	1.21731	+	0.504227i	0.320757	+	0.947161i	$0.396063\pi$
$264$	−15.1669	−	7.58921i	−0.933459	−	0.467084i
$265$	8.74162	−	3.62090i	0.536994	−	0.222430i
$266$	−14.9052	+	42.0249i	−0.913899	+	2.57671i
$267$	−4.44278	+	2.77646i	−0.271894	+	0.169916i
$268$	−1.59271	+	17.1468i	−0.0972904	+	1.04741i
$269$	3.23189	−	4.83687i	0.197052	−	0.294909i	−0.719764	−	0.694218i	$-0.755750\pi$
$269$	3.23189	−	4.83687i	0.197052	−	0.294909i	0.916816	+	0.399310i	$0.130750\pi$
$270$	9.71487	+	7.06348i	0.591228	+	0.429870i
$271$	−4.58692	+	4.58692i	−0.278636	+	0.278636i	−0.832564	−	0.553929i	$-0.813128\pi$
$271$	−4.58692	+	4.58692i	−0.278636	+	0.278636i	0.553929	+	0.832564i	$0.313128\pi$
$272$	1.22319	+	5.81130i	0.0741668	+	0.352362i
$273$	0.414134	−	13.5761i	0.0250645	−	0.821665i
$274$	−12.3261	−	7.34156i	−0.744650	−	0.443520i
$275$	4.47807	−	6.70191i	0.270038	−	0.404140i
$276$	8.40177	−	14.8174i	0.505727	−	0.891905i
$277$	5.93330	−	29.8287i	0.356497	−	1.79223i	−0.220393	−	0.975411i	$-0.570734\pi$
$277$	5.93330	−	29.8287i	0.356497	−	1.79223i	0.576891	−	0.816821i	$-0.304266\pi$
$278$	9.09943	+	19.1017i	0.545747	+	1.14564i
$279$	−2.31999	−	6.73563i	−0.138894	−	0.403252i
$280$	−9.12111	−	14.9341i	−0.545090	−	0.892483i
$281$	16.3507	+	6.77266i	0.975399	+	0.404023i	0.812719	−	0.582656i	$-0.197986\pi$
$281$	16.3507	+	6.77266i	0.975399	+	0.404023i	0.162679	+	0.986679i	$0.447986\pi$
$282$	−0.112837	−	0.108114i	−0.00671933	−	0.00643812i
$283$	1.96148	−	1.31062i	0.116598	−	0.0779083i	−0.495904	−	0.868377i	$-0.665163\pi$
$283$	1.96148	−	1.31062i	0.116598	−	0.0779083i	0.612502	+	0.790469i	$0.290163\pi$
$284$	10.4373	−	12.8629i	0.619339	−	0.763271i
$285$	19.1998	+	13.6937i	1.13730	+	0.811144i
$286$	10.0373	+	1.46042i	0.593517	+	0.0863563i
$287$			7.05873i			0.416664i
$288$	−6.52540	−	15.6659i	−0.384513	−	0.923120i
$289$		−	14.7958i		−	0.870341i
$290$	3.01698	−	20.7354i	0.177163	−	1.21762i
$291$	7.39432	+	5.27378i	0.433462	+	0.309154i
$292$	−1.45042	−	13.9327i	−0.0848794	−	0.815349i
$293$	−19.1040	+	12.7649i	−1.11607	+	0.745734i	−0.969895	−	0.243525i	$-0.921696\pi$
$293$	−19.1040	+	12.7649i	−1.11607	+	0.745734i	−0.146175	+	0.989259i	$0.546696\pi$
$294$	−12.4169	+	12.9593i	−0.724169	+	0.755799i
$295$	−10.2326	−	4.23848i	−0.595765	−	0.246774i
$296$	−4.94931	+	6.79088i	−0.287673	+	0.394712i
$297$	15.9208	+	8.37339i	0.923818	+	0.485874i
$298$	−5.14633	+	2.45154i	−0.298119	+	0.142014i
$299$	−1.98743	+	9.99147i	−0.114936	+	0.577822i
$300$	7.77418	−	2.14807i	0.448842	−	0.124019i
$301$	−19.8586	+	29.7206i	−1.14463	+	1.71306i
$302$	11.8407	−	19.8799i	0.681353	−	1.14396i
$303$	−0.127216	+	4.17039i	−0.00730836	+	0.239583i
$304$	−13.0920	−	30.6399i	−0.750879	−	1.75732i
$305$	6.41199	−	6.41199i	0.367150	−	0.367150i
$306$	−1.17242	−	6.18880i	−0.0670228	−	0.353790i
$307$	1.53667	−	2.29980i	0.0877026	−	0.131256i	−0.785024	−	0.619465i	$-0.787350\pi$
$307$	1.53667	−	2.29980i	0.0877026	−	0.131256i	0.872727	+	0.488209i	$0.162350\pi$
$308$	−16.7380	−	20.1659i	−0.953735	−	1.14906i
$309$	−19.5706	+	12.2304i	−1.11333	+	0.695762i
$310$	5.17345	+	1.83490i	0.293832	+	0.104215i
$311$	−16.6455	+	6.89481i	−0.943882	+	0.390969i	−0.800928	−	0.598761i	$-0.795660\pi$
$311$	−16.6455	+	6.89481i	−0.943882	+	0.390969i	−0.142954	+	0.989729i	$0.545660\pi$
$312$	6.64762	+	7.66948i	0.376347	+	0.434199i
$313$	−2.17680	−	0.901661i	−0.123040	−	0.0509649i	0.320314	−	0.947311i	$-0.396212\pi$
$313$	−2.17680	−	0.901661i	−0.123040	−	0.0509649i	−0.443354	+	0.896347i	$0.646212\pi$
$314$	8.34817	−	9.26234i	0.471114	−	0.522704i
$315$	9.35194	+	16.0325i	0.526922	+	0.903329i
$316$	5.52172	+	10.1938i	0.310621	+	0.573448i
$317$	−31.5144	+	6.26860i	−1.77002	+	0.352080i	−0.969096	−	0.246683i	$-0.920660\pi$
$317$	−31.5144	+	6.26860i	−1.77002	+	0.352080i	−0.800927	+	0.598762i	$0.795660\pi$
$318$	13.9629	+	2.46848i	0.783001	+	0.138426i
$319$		−	31.3809i		−	1.75699i
$320$	12.5747	+	3.58684i	0.702947	+	0.200511i
$321$	−9.41267	−	10.0050i	−0.525364	−	0.558425i
$322$	21.0981	−	15.7384i	1.17575	−	0.877068i
$323$	−2.41270	−	12.1295i	−0.134246	−	0.674902i
$324$	6.58364	+	16.7528i	0.365758	+	0.930710i
$325$	−4.01073	+	2.67989i	−0.222475	+	0.148653i
$326$	−16.3803	−	14.7636i	−0.907222	−	0.817681i
$327$	1.05098	+	2.77361i	0.0581193	+	0.153381i
$328$	−3.57466	−	3.87860i	−0.197377	−	0.214160i
$329$	−0.0924111	−	0.223100i	−0.00509479	−	0.0122999i
$330$	−12.6893	+	5.57663i	−0.698520	+	0.306983i
$331$	4.80427	−	24.1527i	0.264067	−	1.32755i	−0.590006	−	0.807399i	$-0.700875\pi$
$331$	4.80427	−	24.1527i	0.264067	−	1.32755i	0.854073	−	0.520154i	$-0.174125\pi$
$332$	7.80092	+	9.39853i	0.428131	+	0.515811i
$333$	5.39419	−	7.09514i	0.295600	−	0.388811i
$334$	7.94911	+	31.3649i	0.434956	+	1.71621i
$335$	9.95169	+	9.95169i	0.543719	+	0.543719i
$336$	0.508401	−	26.2192i	0.0277355	−	1.43037i
$337$	−9.43292	+	9.43292i	−0.513844	+	0.513844i	−0.915702	−	0.401858i	$-0.868365\pi$
$337$	−9.43292	+	9.43292i	−0.513844	+	0.513844i	0.401858	+	0.915702i	$0.368365\pi$
$338$	10.5803	+	6.30169i	0.575490	+	0.342767i
$339$	−0.605073	−	3.61471i	−0.0328631	−	0.196324i
$340$	4.29300	+	2.26409i	0.232820	+	0.122788i
$341$	8.06284	+	1.60380i	0.436627	+	0.0868506i
$342$	13.2259	+	32.7728i	0.715172	+	1.77215i
$343$	−1.14400	+	0.473860i	−0.0617702	+	0.0255861i
$344$	−4.13915	−	26.3875i	−0.223168	−	1.42272i
$345$	−4.93273	−	13.0178i	−0.265569	−	0.700856i
$346$	−20.6713	+	1.07306i	−1.11130	+	0.0576882i
$347$	9.97350	+	14.9264i	0.535406	+	0.801291i	0.996280	−	0.0861742i	$-0.0274642\pi$
$347$	9.97350	+	14.9264i	0.535406	+	0.801291i	−0.460874	+	0.887465i	$0.652464\pi$
$348$	20.5197	−	23.7689i	1.09997	−	1.27415i
$349$	−22.7251	+	4.52030i	−1.21644	+	0.241966i	−0.761269	−	0.648436i	$-0.775423\pi$
$349$	−22.7251	+	4.52030i	−1.21644	+	0.241966i	−0.455175	+	0.890402i	$0.650423\pi$
$350$	12.3335	+	1.79451i	0.659252	+	0.0959207i
$351$	−6.88485	−	8.27569i	−0.367486	−	0.441724i
$352$	19.4094	+	2.60426i	1.03453	+	0.138808i
$353$	−3.10641			−0.165338			−0.0826688	−	0.996577i	$-0.526344\pi$
$353$	−3.10641			−0.165338			−0.0826688	+	0.996577i	$0.526344\pi$
$354$	−9.51407	−	13.6004i	−0.505667	−	0.722856i
$355$	−2.64109	−	13.2777i	−0.140175	−	0.704706i
$356$	3.81171	−	4.69754i	0.202020	−	0.248969i
$357$	2.18909	−	9.48409i	0.115859	−	0.501951i
$358$	15.7335	−	0.816739i	0.831543	−	0.0431660i
$359$	−7.94887	+	19.1903i	−0.419525	+	1.01282i	0.562960	+	0.826484i	$0.309663\pi$
$359$	−7.94887	+	19.1903i	−0.419525	+	1.01282i	−0.982485	+	0.186340i	$0.940337\pi$
$360$	−13.2578	−	4.07348i	−0.698747	−	0.214691i
$361$	19.2826	+	46.5522i	1.01487	+	2.45012i
$362$	5.76773	−	2.74756i	0.303145	−	0.144408i
$363$	−1.44626	+	0.903819i	−0.0759088	+	0.0474382i
$364$	4.63600	+	14.9828i	0.242993	+	0.785313i
$365$	−9.51887	−	6.36031i	−0.498241	−	0.332914i
$366$	13.2683	−	2.93528i	0.693544	−	0.153429i
$367$	11.6388	+	11.6388i	0.607541	+	0.607541i	0.942303	−	0.334762i	$-0.108656\pi$
$367$	11.6388	+	11.6388i	0.607541	+	0.607541i	−0.334762	+	0.942303i	$0.608656\pi$
$368$	−3.62270	+	19.3323i	−0.188846	+	1.00777i
$369$	3.70749	+	4.18974i	0.193004	+	0.218109i
$370$	1.68717	+	6.65708i	0.0877118	+	0.346085i
$371$	18.2184	+	12.1731i	0.945850	+	0.631997i
$372$	5.05836	+	6.48700i	0.262264	+	0.336335i
$373$	−7.84233	−	1.55994i	−0.406060	−	0.0807704i	−0.0121657	−	0.999926i	$-0.503873\pi$
$373$	−7.84233	−	1.55994i	−0.406060	−	0.0807704i	−0.393895	+	0.919156i	$0.628873\pi$
$374$	6.85053	+	2.42972i	0.354233	+	0.125638i
$375$	8.52032	−	18.9168i	0.439987	−	0.976861i
$376$	0.163759	+	0.0757896i	0.00844524	+	0.00390855i
$377$	−7.18670	+	17.3502i	−0.370134	+	0.893583i
$378$	−1.10177	+	27.7930i	−0.0566687	+	1.42952i
$379$	3.34562	+	5.00707i	0.171853	+	0.257196i	0.907391	−	0.420287i	$-0.138071\pi$
$379$	3.34562	+	5.00707i	0.171853	+	0.257196i	−0.735538	+	0.677483i	$0.763071\pi$
$380$	−26.1020	−	7.75993i	−1.33901	−	0.398076i
$381$	−20.4087	−	14.5559i	−1.04557	−	0.745720i
$382$	−2.84678	+	2.12359i	−0.145654	+	0.108653i
$383$	4.78786			0.244648			0.122324	−	0.992490i	$-0.460965\pi$
$383$	4.78786			0.244648			0.122324	+	0.992490i	$0.460965\pi$
$384$	12.9985	+	14.6642i	0.663325	+	0.748332i
$385$	−21.4183			−1.09158
$386$	−6.80502	+	5.07630i	−0.346367	+	0.258377i
$387$	3.82308	+	28.0712i	0.194338	+	1.42694i
$388$	−10.0525	−	2.98854i	−0.510340	−	0.151720i
$389$	−1.44268	−	2.15912i	−0.0731468	−	0.109472i	0.793093	−	0.609101i	$-0.208470\pi$
$389$	−1.44268	−	2.15912i	−0.0731468	−	0.109472i	−0.866239	+	0.499629i	$0.833470\pi$
$390$	8.29292	−	0.177239i	0.419928	−	0.00897485i
$391$	−2.79373	+	6.74466i	−0.141285	+	0.341092i
$392$	8.70440	−	18.8077i	0.439639	−	0.949932i
$393$	−35.0017	−	15.7651i	−1.76560	−	0.795243i
$394$	24.0356	+	8.52486i	1.21090	+	0.429476i
$395$	9.29272	+	1.84844i	0.467568	+	0.0930050i
$396$	−20.5267	−	3.17818i	−1.03151	−	0.159709i
$397$	6.83928	+	4.56986i	0.343253	+	0.229355i	0.715233	−	0.698886i	$-0.246321\pi$
$397$	6.83928	+	4.56986i	0.343253	+	0.229355i	−0.371979	+	0.928241i	$0.621321\pi$
$398$	−3.78647	−	14.9403i	−0.189799	−	0.748890i
$399$	−1.66511	+	54.5858i	−0.0833600	+	2.73271i
$400$	−7.68571	+	5.25984i	−0.384286	+	0.262992i
$401$	−0.714056	−	0.714056i	−0.0356583	−	0.0356583i	0.689053	−	0.724711i	$-0.258027\pi$
$401$	−0.714056	−	0.714056i	−0.0356583	−	0.0356583i	−0.724711	+	0.689053i	$0.758027\pi$
$402$	4.55568	+	20.5929i	0.227217	+	1.02708i
$403$	−4.09059	−	2.73324i	−0.203767	−	0.136153i
$404$	−1.42411	−	4.60250i	−0.0708523	−	0.228983i
$405$	13.9717	+	4.60419i	0.694260	+	0.228784i
$406$	43.8064	−	20.8680i	2.17408	−	1.03566i
$407$	3.93591	+	9.50214i	0.195096	+	0.471004i
$408$	3.60005	+	6.31987i	0.178229	+	0.312880i
$409$	−4.86109	+	11.7357i	−0.240365	+	0.580294i	−0.997319	−	0.0731750i	$-0.976687\pi$
$409$	−4.86109	+	11.7357i	−0.240365	+	0.580294i	0.756954	+	0.653469i	$0.226687\pi$
$410$	−4.30498	+	0.223474i	−0.212608	+	0.0110366i
$411$	−17.1211	−	3.95185i	−0.844521	−	0.194930i
$412$	16.7907	−	20.6928i	0.827219	−	1.01946i
$413$	−5.00371	−	25.1554i	−0.246217	−	1.23781i
$414$	4.25651	−	20.4231i	0.209196	−	1.00374i
$415$	9.98225			0.490010
$416$	−10.1349	−	5.88494i	−0.496905	−	0.288533i
$417$	17.7564	+	18.8738i	0.869536	+	0.924255i
$418$	−40.3571	−	5.87193i	−1.97393	−	0.287205i
$419$	−35.6710	+	7.09541i	−1.74264	+	0.346633i	−0.960885	−	0.276947i	$-0.910677\pi$
$419$	−35.6710	+	7.09541i	−1.74264	+	0.346633i	−0.781759	+	0.623581i	$0.785677\pi$
$420$	−16.2230	−	14.0053i	−0.791600	−	0.683388i
$421$	−11.0019	−	16.4655i	−0.536200	−	0.802479i	0.460150	−	0.887841i	$-0.347795\pi$
$421$	−11.0019	−	16.4655i	−0.536200	−	0.802479i	−0.996350	+	0.0853616i	$0.972795\pi$
$422$	−15.2099	+	0.789556i	−0.740406	+	0.0384350i
$423$	−0.172031	−	0.0838846i	−0.00836443	−	0.00407861i
$424$	−16.1752	+	2.53725i	−0.785538	+	0.123220i
$425$	−3.19361	+	1.32284i	−0.154913	+	0.0641670i
$426$	7.36145	−	18.9049i	0.356663	−	0.915945i
$427$	20.5953	+	4.09666i	0.996677	+	0.198251i
$428$	14.0302	+	7.39942i	0.678175	+	0.357664i
$429$	12.2521	−	2.05090i	0.591536	−	0.0990185i
$430$	−18.7547	−	11.1705i	−0.904431	−	0.538687i
$431$	−0.0952141	+	0.0952141i	−0.00458630	+	0.00458630i	−0.709396	−	0.704810i	$-0.751032\pi$
$431$	−0.0952141	+	0.0952141i	−0.00458630	+	0.00458630i	0.704810	+	0.709396i	$0.251032\pi$
$432$	−13.4694	−	15.8295i	−0.648049	−	0.761599i
$433$	−16.1388	−	16.1388i	−0.775580	−	0.775580i	0.203496	−	0.979076i	$-0.434770\pi$
$433$	−16.1388	−	16.1388i	−0.775580	−	0.775580i	−0.979076	+	0.203496i	$0.934770\pi$
$434$	3.12287	+	12.3219i	0.149902	+	0.591471i
$435$	−4.23683	−	25.3108i	−0.203140	−	1.21356i
$436$	−2.18740	−	2.63538i	−0.104758	−	0.126212i
$437$	7.99089	−	40.1729i	0.382256	−	1.92173i
$438$	−6.90258	−	15.7064i	−0.329818	−	0.750479i
$439$	10.1203	+	24.4326i	0.483015	+	1.16610i	0.958170	+	0.286200i	$0.0923922\pi$
$439$	10.1203	+	24.4326i	0.483015	+	1.16610i	−0.475154	+	0.879902i	$0.657608\pi$
$440$	11.7688	−	10.8466i	0.561058	−	0.517091i
$441$	−9.63411	+	19.7577i	−0.458767	+	0.940843i
$442$	−3.23116	−	2.91225i	−0.153691	−	0.138522i
$443$	−23.0385	+	15.3939i	−1.09459	+	0.731384i	−0.965540	−	0.260254i	$-0.916194\pi$
$443$	−23.0385	+	15.3939i	−1.09459	+	0.731384i	−0.129053	+	0.991638i	$0.541194\pi$
$444$	−3.23218	+	9.77091i	−0.153393	+	0.463707i
$445$	−0.964531	−	4.84902i	−0.0457232	−	0.229866i
$446$	−17.0657	+	12.7304i	−0.808084	+	0.602801i
$447$	−5.08493	+	4.78389i	−0.240509	+	0.226270i
$448$	9.27163	+	28.8266i	0.438044	+	1.36193i
$449$		−	37.8987i		−	1.78855i	−0.447518	−	0.894275i	$-0.647692\pi$
$449$		−	37.8987i		−	1.78855i	0.447518	−	0.894275i	$-0.352308\pi$
$450$	8.26313	−	5.41283i	0.389528	−	0.255163i
$451$	−6.33189	+	1.25949i	−0.298157	+	0.0593071i
$452$	2.01564	+	3.72113i	0.0948075	+	0.175027i
$453$	6.37363	−	27.6133i	0.299459	−	1.29739i
$454$	3.47009	−	3.85009i	0.162860	−	0.180694i
$455$	11.8420	+	4.90513i	0.555163	+	0.229956i
$456$	−26.7282	−	30.8368i	−1.25166	−	1.44407i
$457$	−9.25868	+	3.83507i	−0.433103	+	0.179397i	−0.588574	−	0.808443i	$-0.700310\pi$
$457$	−9.25868	+	3.83507i	−0.433103	+	0.179397i	0.155471	+	0.987840i	$0.450310\pi$
$458$	−15.1454	−	5.37173i	−0.707700	−	0.251005i
$459$	−3.68203	−	6.77911i	−0.171862	−	0.316422i
$460$	10.2665	+	12.3690i	0.478678	+	0.576710i
$461$	−14.5105	+	21.7165i	−0.675822	+	1.01144i	0.322081	+	0.946712i	$0.395618\pi$
$461$	−14.5105	+	21.7165i	−0.675822	+	1.01144i	−0.997903	+	0.0647269i	$0.979382\pi$
$462$	−27.0628	−	17.2580i	−1.25908	−	0.802913i
$463$	4.16586	−	4.16586i	0.193604	−	0.193604i	−0.603647	−	0.797251i	$-0.706287\pi$
$463$	4.16586	−	4.16586i	0.193604	−	0.193604i	0.797251	+	0.603647i	$0.206287\pi$
$464$	−13.5027	+	33.6507i	−0.626847	+	1.56220i
$465$	6.71976	+	0.204983i	0.311621	+	0.00950586i
$466$	−17.4700	+	29.3314i	−0.809284	+	1.35875i
$467$	19.6360	−	29.3873i	0.908644	−	1.35988i	−0.0242401	−	0.999706i	$-0.507717\pi$
$467$	19.6360	−	29.3873i	0.908644	−	1.35988i	0.932884	−	0.360176i	$-0.117283\pi$
$468$	10.6212	+	6.45813i	0.490966	+	0.298527i
$469$	−6.35819	+	31.9648i	−0.293594	+	1.47600i
$470$	0.133139	−	0.0634229i	0.00614123	−	0.00292548i
$471$	6.27170	−	13.9244i	0.288985	−	0.641604i
$472$	15.4885	+	11.2883i	0.712916	+	0.519586i
$473$	−30.2036	−	12.5107i	−1.38876	−	0.575245i
$474$	10.2523	+	9.82323i	0.470903	+	0.451196i
$475$	16.1260	−	10.7751i	0.739913	−	0.494394i
$476$	1.16374	+	11.1788i	0.0533398	+	0.512380i
$477$	17.2073	−	2.34350i	0.787870	−	0.107302i
$478$	−1.42953	+	9.82503i	−0.0653854	+	0.449386i
$479$			14.4391i			0.659737i	0.944027	+	0.329869i	$0.107004\pi$
$479$			14.4391i			0.659737i	−0.944027	+	0.329869i	$0.892996\pi$
$480$	16.0066	−	0.520017i	0.730600	−	0.0237354i
$481$		−	6.15504i		−	0.280646i
$482$	−32.3316	−	4.70422i	−1.47266	−	0.214271i
$483$	18.7190	−	26.2458i	0.851745	−	1.19422i
$484$	1.24082	−	1.52919i	0.0564011	−	0.0695086i
$485$	−7.12650	+	4.76178i	−0.323598	+	0.216221i
$486$	13.9439	+	17.0754i	0.632508	+	0.774554i
$487$	−18.1952	−	7.53672i	−0.824505	−	0.341521i	−0.0697800	−	0.997562i	$-0.522230\pi$
$487$	−18.1952	−	7.53672i	−0.824505	−	0.341521i	−0.754725	+	0.656041i	$0.772230\pi$
$488$	−13.3912	+	8.17879i	−0.606193	+	0.370236i
$489$	−24.6252	−	11.0914i	−1.11359	−	0.501571i
$490$	−7.28409	−	15.2909i	−0.329062	−	0.690774i
$491$	−2.66821	+	13.4140i	−0.120414	+	0.605365i	0.872704	+	0.488250i	$0.162365\pi$
$491$	−2.66821	+	13.4140i	−0.120414	+	0.605365i	−0.993118	+	0.117115i	$0.962635\pi$
$492$	−5.61956	−	3.18639i	−0.253349	−	0.143654i
$493$	−7.47684	+	11.1899i	−0.336740	+	0.503967i
$494$	20.9684	+	12.4889i	0.943411	+	0.561904i
$495$	−12.7129	+	11.2497i	−0.571405	+	0.505634i
$496$	−7.95596	−	5.18912i	−0.357233	−	0.232998i
$497$	22.1676	−	22.1676i	0.994354	−	0.994354i
$498$	12.6129	+	8.04326i	0.565199	+	0.360427i
$499$	7.27621	−	10.8896i	0.325728	−	0.487487i	−0.632077	−	0.774906i	$-0.717797\pi$
$499$	7.27621	−	10.8896i	0.325728	−	0.487487i	0.957805	+	0.287419i	$0.0927973\pi$
$500$	−2.21573	+	23.8540i	−0.0990904	+	1.06678i
$501$	21.0015	+	33.6058i	0.938278	+	1.50140i
$502$	−10.8828	+	30.6838i	−0.485724	+	1.36948i
$503$	−0.384619	+	0.159314i	−0.0171493	+	0.00710348i	−0.391242	−	0.920288i	$-0.627954\pi$
$503$	−0.384619	+	0.159314i	−0.0171493	+	0.00710348i	0.374092	+	0.927391i	$0.377954\pi$
$504$	−9.21345	−	30.7679i	−0.410400	−	1.37051i
$505$	−3.63770	−	1.50679i	−0.161876	−	0.0670511i
$506$	17.8824	+	16.1174i	0.794968	+	0.716506i
$507$	14.6960	+	3.39210i	0.652674	+	0.150648i
$508$	27.7455	+	8.24851i	1.23101	+	0.365969i
$509$	7.98294	−	1.58791i	0.353838	−	0.0703827i	−0.0149713	−	0.999888i	$-0.504766\pi$
$509$	7.98294	−	1.58791i	0.353838	−	0.0703827i	0.368809	+	0.929505i	$0.379766\pi$
$510$	5.85346	+	1.03482i	0.259196	+	0.0458228i
$511$		−	26.5110i		−	1.17278i
$512$	−19.6928	−	11.1442i	−0.870307	−	0.492509i
$513$	27.6820	+	33.2742i	1.22219	+	1.46909i
$514$	−4.64654	−	6.22891i	−0.204950	−	0.274746i
$515$	−4.24879	−	21.3601i	−0.187224	−	0.941239i
$516$	−14.6966	−	29.2260i	−0.646980	−	1.28660i
$517$	0.183639	−	0.122703i	0.00807641	−	0.00539649i
$518$	−10.6473	+	11.8132i	−0.467814	+	0.519042i
$519$	−23.7064	+	8.98284i	−1.04059	+	0.394303i
$520$	−8.99094	+	3.30175i	−0.394279	+	0.144791i
$521$	5.62098	+	13.5703i	0.246260	+	0.594524i	0.997881	−	0.0650718i	$-0.0207276\pi$
$521$	5.62098	+	13.5703i	0.246260	+	0.594524i	−0.751621	+	0.659595i	$0.770728\pi$
$522$	15.0409	−	35.3949i	0.658324	−	1.54919i
$523$	2.24424	−	11.2826i	0.0981340	−	0.493353i	−0.900191	−	0.435496i	$-0.856573\pi$
$523$	2.24424	−	11.2826i	0.0981340	−	0.493353i	0.998325	−	0.0578573i	$-0.0184268\pi$
$524$	44.1369	+	4.09974i	1.92813	+	0.179098i
$525$	15.0550	−	2.52008i	0.657052	−	0.109985i
$526$	−29.2928	+	7.42397i	−1.27723	+	0.323700i
$527$	−2.49295	−	2.49295i	−0.108595	−	0.108595i
$528$	23.6101	−	4.22224i	1.02750	−	0.183749i
$529$	−0.833580	+	0.833580i	−0.0362426	+	0.0362426i
$530$	−6.84736	+	11.4964i	−0.297430	+	0.499372i
$531$	−16.1824	−	12.3030i	−0.702258	−	0.533903i
$532$	−18.6401	−	60.2417i	−0.808150	−	2.61181i
$533$	3.78929	+	0.753737i	0.164133	+	0.0326480i
$534$	2.68841	−	6.90409i	0.116339	−	0.298769i
$535$	11.9766	−	4.96086i	0.517792	−	0.214477i
$536$	−12.6938	−	20.7838i	−0.548290	−	0.897722i
$537$	18.0436	−	6.83710i	0.778638	−	0.295042i
$538$	0.426486	+	8.21577i	0.0183871	+	0.354207i
$539$	−14.0924	−	21.0908i	−0.607004	−	0.908445i
$540$	−16.9853	+	0.207963i	−0.730930	+	0.00894929i
$541$	21.3611	−	4.24899i	0.918386	−	0.182678i	0.286806	−	0.957989i	$-0.407407\pi$
$541$	21.3611	−	4.24899i	0.918386	−	0.182678i	0.631580	+	0.775310i	$0.282407\pi$
$542$	1.32088	−	9.07826i	0.0567366	−	0.389944i
$543$	5.69892	−	5.36152i	0.244564	−	0.230085i
$544$	−6.30058	−	5.55315i	−0.270135	−	0.238089i
$545$	−2.79906			−0.119898
$546$	11.0105	+	15.7396i	0.471205	+	0.673593i
$547$	3.04023	+	15.2843i	0.129991	+	0.653509i	0.989750	+	0.142809i	$0.0456136\pi$
$547$	3.04023	+	15.2843i	0.129991	+	0.653509i	−0.859759	+	0.510700i	$0.829386\pi$
$548$	20.1805	−	2.10083i	0.862067	−	0.0897429i
$549$	14.3761	−	8.38578i	0.613559	−	0.357896i
$550$	0.590935	+	11.3837i	0.0251976	+	0.485402i
$551$	28.8957	−	69.7604i	1.23100	−	2.97189i
$552$	3.00565	+	23.9010i	0.127929	+	1.01729i
$553$	8.39643	+	20.2708i	0.357053	+	0.862001i
$554$	18.4973	+	38.8299i	0.785874	+	1.64972i
$555$	4.45749	+	7.13272i	0.189210	+	0.302767i
$556$	−26.4671	−	13.9585i	−1.12246	−	0.591974i
$557$	26.9912	+	18.0350i	1.14366	+	0.764166i	0.975153	−	0.221535i	$-0.0711066\pi$
$557$	26.9912	+	18.0350i	1.14366	+	0.764166i	0.168503	+	0.985701i	$0.446107\pi$
$558$	8.32549	+	5.67349i	0.352446	+	0.240178i
$559$	13.8342	+	13.8342i	0.585124	+	0.585124i
$560$	22.9676	+	9.21597i	0.970558	+	0.389446i
$561$	8.89811	+	0.271433i	0.375678	+	0.0114599i
$562$	−24.2615	+	6.14882i	−1.02341	+	0.259372i
$563$	8.22994	+	5.49907i	0.346851	+	0.231758i	0.716776	−	0.697303i	$-0.245617\pi$
$563$	8.22994	+	5.49907i	0.346851	+	0.231758i	−0.369926	+	0.929061i	$0.620617\pi$
$564$	0.219329	+	0.0271402i	0.00923541	+	0.00114281i
$565$	3.39219	+	0.674749i	0.142711	+	0.0283869i
$566$	−1.11521	+	3.14430i	−0.0468757	+	0.132165i
$567$	9.11009	+	32.8254i	0.382588	+	1.37854i
$568$	−0.954514	+	23.4066i	−0.0400505	+	0.982120i
$569$	0.962112	−	2.32274i	0.0403338	−	0.0973745i	−0.902429	−	0.430839i	$-0.858218\pi$
$569$	0.962112	−	2.32274i	0.0403338	−	0.0973745i	0.942763	+	0.333464i	$0.108218\pi$
$570$	−33.3435	+	0.712629i	−1.39661	+	0.0298487i
$571$	−2.20047	−	3.29324i	−0.0920869	−	0.137818i	0.782566	−	0.622568i	$-0.213911\pi$
$571$	−2.20047	−	3.29324i	−0.0920869	−	0.137818i	−0.874653	+	0.484750i	$0.838911\pi$
$572$	−12.6128	+	6.83202i	−0.527369	+	0.285661i
$573$	−2.52577	+	3.54136i	−0.105515	+	0.147942i
$574$	−5.96884	−	8.00151i	−0.249134	−	0.333977i
$575$	−11.4487			−0.477445
$576$	20.6440	+	12.2404i	0.860165	+	0.510016i
$577$	−21.1934			−0.882293			−0.441147	−	0.897435i	$-0.645428\pi$
$577$	−21.1934			−0.882293			−0.441147	+	0.897435i	$0.645428\pi$
$578$	12.5113	+	16.7720i	0.520400	+	0.697622i
$579$	−6.03767	+	8.46536i	−0.250917	+	0.351808i
$580$	14.1138	+	26.0560i	0.586045	+	1.08192i
$581$	12.8426	+	19.2203i	0.532802	+	0.797394i
$582$	−12.8414	+	0.274451i	−0.532294	+	0.0113764i
$583$	−7.66894	+	18.5145i	−0.317615	+	0.766791i
$584$	13.4256	+	14.5671i	0.555555	+	0.602792i
$585$	9.60524	−	3.30838i	0.397128	−	0.136785i
$586$	10.8617	−	30.6241i	0.448691	−	1.26507i
$587$	10.8843	+	2.16502i	0.449243	+	0.0893600i	0.414527	−	0.910037i	$-0.363947\pi$
$587$	10.8843	+	2.16502i	0.449243	+	0.0893600i	0.0347166	+	0.999397i	$0.488947\pi$
$588$	3.11704	−	25.1898i	0.128545	−	1.03881i
$589$	16.4471	+	10.9896i	0.677691	+	0.452819i
$590$	15.1833	−	3.84807i	0.625088	−	0.158422i
$591$	31.2197	+	0.952341i	1.28420	+	0.0391741i
$592$	−0.131991	−	11.8830i	−0.00542479	−	0.488389i
$593$	14.8720	+	14.8720i	0.610720	+	0.610720i	0.943134	−	0.332414i	$-0.107863\pi$
$593$	14.8720	+	14.8720i	0.610720	+	0.610720i	−0.332414	+	0.943134i	$0.607863\pi$
$594$	−25.1277	+	3.97080i	−1.03100	+	0.162924i
$595$	7.63741	+	5.10316i	0.313103	+	0.209209i
$596$	3.76067	−	7.13070i	0.154043	−	0.292085i
$597$	−10.0038	−	16.0078i	−0.409430	−	0.655155i
$598$	−6.19588	−	13.0065i	−0.253369	−	0.531877i
$599$	−14.6514	−	35.3715i	−0.598638	−	1.44524i	−0.874970	−	0.484178i	$-0.839119\pi$
$599$	−14.6514	−	35.3715i	−0.598638	−	1.44524i	0.276331	−	0.961062i	$-0.410881\pi$
$600$	−6.99611	+	9.00880i	−0.285615	+	0.367783i
$601$	−4.29088	+	10.3591i	−0.175029	+	0.422557i	−0.986911	−	0.161264i	$-0.948443\pi$
$601$	−4.29088	+	10.3591i	−0.175029	+	0.422557i	0.811883	+	0.583821i	$0.198443\pi$
$602$	−2.62059	−	50.4826i	−0.106807	−	2.05752i
$603$	13.0151	+	22.3124i	0.530015	+	0.908631i
$604$	3.38826	+	32.5476i	0.137867	+	1.32434i
$605$	−0.313983	−	1.57850i	−0.0127652	−	0.0641752i
$606$	−3.38226	−	4.83498i	−0.137395	−	0.196408i
$607$	18.9171			0.767822			0.383911	−	0.923370i	$-0.374577\pi$
$607$	18.9171			0.767822			0.383911	+	0.923370i	$0.374577\pi$
$608$	40.7496	+	23.6617i	1.65262	+	0.959608i
$609$	43.2838	−	40.7213i	1.75395	−	1.65011i
$610$	−1.84644	+	12.6904i	−0.0747601	+	0.513818i
$611$	−0.129633	+	0.0257857i	−0.00524440	+	0.00104318i
$612$	6.56224	+	6.02400i	0.265263	+	0.243506i
$613$	−13.6747	−	20.4657i	−0.552316	−	0.826600i	0.445316	−	0.895374i	$-0.353091\pi$
$613$	−13.6747	−	20.4657i	−0.552316	−	0.826600i	−0.997632	+	0.0687736i	$0.978091\pi$
$614$	0.202782	+	3.90637i	0.00818363	+	0.157648i
$615$	−4.93705	+	1.87075i	−0.199081	+	0.0754360i
$616$	36.0258	+	8.70570i	1.45152	+	0.350763i
$617$	−11.7405	+	4.86308i	−0.472655	+	0.195780i	−0.606279	−	0.795252i	$-0.707339\pi$
$617$	−11.7405	+	4.86308i	−0.472655	+	0.195780i	0.133624	+	0.991032i	$0.457339\pi$
$618$	11.8425	−	30.4128i	0.476377	−	1.22338i
$619$	−3.98600	−	0.792865i	−0.160211	−	0.0318679i	0.114333	−	0.993442i	$-0.463527\pi$
$619$	−3.98600	−	0.792865i	−0.160211	−	0.0318679i	−0.274544	+	0.961575i	$0.588527\pi$
$620$	−7.41602	+	2.29468i	−0.297835	+	0.0921564i
$621$	−2.67443	−	25.4102i	−0.107321	−	1.01967i
$622$	13.0385	−	21.8911i	0.522798	−	0.877754i
$623$	8.09565	−	8.09565i	0.324345	−	0.324345i
$624$	−14.0208	−	3.07263i	−0.561281	−	0.123004i
$625$	5.61264	+	5.61264i	0.224506	+	0.224506i
$626$	3.22999	−	0.818608i	0.129096	−	0.0327181i
$627$	−49.2622	+	8.24610i	−1.96734	+	0.329318i
$628$	−1.63097	+	17.5586i	−0.0650827	+	0.700666i
$629$	0.860510	−	4.32608i	0.0343108	−	0.172492i
$630$	−24.1580	−	10.2659i	−0.962480	−	0.409002i
$631$	−10.1275	−	24.4500i	−0.403170	−	0.973338i	−0.986892	−	0.161384i	$-0.948404\pi$
$631$	−10.1275	−	24.4500i	−0.403170	−	0.973338i	0.583722	−	0.811954i	$-0.301596\pi$
$632$	−14.8791	−	6.88621i	−0.591859	−	0.273919i
$633$	−17.4431	+	6.60955i	−0.693299	+	0.262706i
$634$	30.4228	−	33.7543i	1.20824	−	1.34055i
$635$	19.6695	−	13.1427i	0.780559	−	0.521553i
$636$	−17.9152	+	9.00881i	−0.710383	+	0.357223i
$637$	2.96147	+	14.8883i	0.117338	+	0.589897i
$638$	26.5356	+	35.5722i	1.05055	+	1.40832i
$639$	1.51449	−	24.8009i	0.0599123	−	0.981109i
$640$	−17.2872	+	6.56721i	−0.683338	+	0.259592i
$641$			17.2479i			0.681253i	0.940199	+	0.340627i	$0.110639\pi$
$641$			17.2479i			0.681253i	−0.940199	+	0.340627i	$0.889361\pi$
$642$	19.1301	+	3.38197i	0.755003	+	0.133476i
$643$	−2.82948	+	0.562819i	−0.111584	+	0.0221954i	−0.250566	−	0.968099i	$-0.580617\pi$
$643$	−2.82948	+	0.562819i	−0.111584	+	0.0221954i	0.138982	+	0.990295i	$0.455617\pi$
$644$	−10.6077	+	35.6810i	−0.418001	+	1.40603i
$645$	−26.0504	−	6.01288i	−1.02573	−	0.236757i
$646$	12.9916	+	11.7094i	0.511148	+	0.460698i
$647$	−42.3867	−	17.5572i	−1.66639	−	0.690243i	−0.667855	−	0.744291i	$-0.732787\pi$
$647$	−42.3867	−	17.5572i	−1.66639	−	0.690243i	−0.998538	+	0.0540484i	$0.982787\pi$
$648$	−21.6291	−	13.4232i	−0.849670	−	0.527314i
$649$	21.6723	−	8.97696i	0.850712	−	0.352376i
$650$	2.28032	−	6.42929i	0.0894414	−	0.252177i
$651$	8.25059	+	13.2023i	0.323366	+	0.517439i
$652$	31.0522	+	2.88434i	1.21610	+	0.112960i
$653$	1.02429	−	1.53296i	0.0400837	−	0.0599895i	−0.810887	−	0.585203i	$-0.801015\pi$
$653$	1.02429	−	1.53296i	0.0400837	−	0.0599895i	0.850970	+	0.525214i	$0.176015\pi$
$654$	−3.53671	−	2.25536i	−0.138296	−	0.0881914i
$655$	25.6163	−	25.6163i	1.00091	−	1.00091i
$656$	7.33183	+	1.37392i	0.286260	+	0.0536425i
$657$	−13.9245	−	15.7357i	−0.543246	−	0.613908i
$658$	0.293407	+	0.174756i	0.0114382	+	0.00681268i
$659$	−9.68153	+	14.4894i	−0.377139	+	0.564428i	−0.970680	−	0.240376i	$-0.922729\pi$
$659$	−9.68153	+	14.4894i	−0.377139	+	0.564428i	0.593541	+	0.804804i	$0.297729\pi$
$660$	9.66849	−	17.0515i	0.376345	−	0.663727i
$661$	1.87032	−	9.40275i	0.0727472	−	0.365725i	−0.927214	−	0.374532i	$-0.877803\pi$
$661$	1.87032	−	9.40275i	0.0727472	−	0.365725i	0.999961	+	0.00880715i	$0.00280344\pi$
$662$	14.9775	+	31.4411i	0.582117	+	1.22199i
$663$	−4.85753	−	2.18788i	−0.188651	−	0.0849701i
$664$	−16.7902	−	4.05739i	−0.651586	−	0.157457i
$665$	−47.6135	−	19.7222i	−1.84637	−	0.764792i
$666$	−0.115028	+	12.6041i	−0.00445725	+	0.488399i
$667$	−37.0610	+	24.7633i	−1.43501	+	0.958841i
$668$	−35.5328	−	28.8323i	−1.37481	−	1.11556i
$669$	−15.1413	+	21.2295i	−0.585397	+	0.820780i
$670$	−19.6960	−	2.86575i	−0.760922	−	0.110714i
$671$			19.2056i			0.741423i
$672$	21.5945	+	30.1510i	0.833027	+	1.16310i
$673$		−	3.94418i		−	0.152037i	−0.997106	−	0.0760185i	$-0.975779\pi$
$673$		−	3.94418i		−	0.152037i	0.997106	−	0.0760185i	$-0.0242208\pi$
$674$	2.71637	−	18.6693i	0.104630	−	0.719113i
$675$	7.61230	−	9.40319i	0.292998	−	0.361929i
$676$	−17.3221	+	1.80326i	−0.666234	+	0.0693562i
$677$	23.1753	−	15.4852i	0.890698	−	0.595145i	−0.0238088	−	0.999717i	$-0.507579\pi$
$677$	23.1753	−	15.4852i	0.890698	−	0.595145i	0.914506	+	0.404571i	$0.132579\pi$
$678$	3.74247	+	3.58585i	0.143729	+	0.137714i
$679$	−18.3371	−	7.59549i	−0.703715	−	0.291488i
$680$	−6.78089	+	1.06365i	−0.260035	+	0.0407892i
$681$	2.60696	−	5.78799i	0.0998991	−	0.221796i
$682$	−10.4959	+	4.99991i	−0.401909	+	0.191456i
$683$	2.94755	−	14.8183i	0.112785	−	0.567007i	−0.882525	−	0.470266i	$-0.844158\pi$
$683$	2.94755	−	14.8183i	0.112785	−	0.567007i	0.995310	−	0.0967412i	$-0.0308419\pi$
$684$	−42.7049	−	25.9663i	−1.63286	−	0.992847i
$685$	9.21243	−	13.7874i	0.351989	−	0.526789i
$686$	0.896102	−	1.50451i	0.0342133	−	0.0574426i
$687$	−19.6723	−	0.600094i	−0.750545	−	0.0228950i
$688$	27.0051	+	26.4118i	1.02956	+	1.00694i
$689$	8.48020	−	8.48020i	0.323070	−	0.323070i
$690$	16.5994	+	10.5854i	0.631928	+	0.402980i
$691$	−12.1384	+	18.1664i	−0.461767	+	0.691083i	−0.987152	−	0.159781i	$-0.948921\pi$
$691$	−12.1384	+	18.1664i	−0.461767	+	0.691083i	0.525385	+	0.850864i	$0.323921\pi$
$692$	22.5249	−	18.6960i	0.856267	−	0.710715i
$693$	−38.0165	−	10.0050i	−1.44413	−	0.380058i
$694$	−23.9273	−	8.48646i	−0.908268	−	0.322142i
$695$	−22.5931	+	9.35835i	−0.857004	+	0.354983i
$696$	−3.16147	+	44.2950i	−0.119835	+	1.67900i
$697$	2.55793	+	1.05953i	0.0968885	+	0.0401325i
$698$	21.9380	−	24.3403i	0.830364	−	0.921293i
$699$	−9.40384	+	40.7415i	−0.355686	+	1.54098i
$700$	−15.4982	+	8.39496i	−0.585777	+	0.317300i
$701$	23.1472	−	4.60426i	0.874257	−	0.173901i	0.262487	−	0.964936i	$-0.415457\pi$
$701$	23.1472	−	4.60426i	0.874257	−	0.173901i	0.611771	+	0.791035i	$0.290457\pi$
$702$	14.8023	+	3.55922i	0.558677	+	0.134334i
$703$			24.7477i			0.933377i
$704$	−24.2040	+	13.4605i	−0.912222	+	0.507310i
$705$	0.131550	−	0.123762i	0.00495447	−	0.00466115i
$706$	3.52132	−	2.62677i	0.132526	−	0.0988599i
$707$	−1.77883	−	8.94277i	−0.0668997	−	0.336327i
$708$	22.2853	+	7.37190i	0.837533	+	0.277053i
$709$	−27.8807	+	18.6293i	−1.04708	+	0.699638i	−0.955149	−	0.296127i	$-0.904305\pi$
$709$	−27.8807	+	18.6293i	−1.04708	+	0.699638i	−0.0919343	+	0.995765i	$0.529305\pi$
$710$	14.2214	+	12.8178i	0.533720	+	0.481043i
$711$	15.6307	+	7.62172i	0.586196	+	0.285837i
$712$	−0.348590	+	8.54813i	−0.0130640	+	0.320355i
$713$	−4.46847	−	10.7878i	−0.167346	−	0.404008i
$714$	5.53824	+	12.6019i	0.207264	+	0.471615i
$715$	−2.28707	+	11.4979i	−0.0855316	+	0.429996i
$716$	−17.1443	+	14.2301i	−0.640714	+	0.531802i
$717$	2.00753	+	11.9930i	0.0749727	+	0.447887i
$718$	−7.21669	−	28.4749i	−0.269324	−	1.06268i
$719$	−13.0487	−	13.0487i	−0.486635	−	0.486635i	0.420607	−	0.907243i	$-0.361817\pi$
$719$	−13.0487	−	13.0487i	−0.486635	−	0.486635i	−0.907243	+	0.420607i	$0.861817\pi$
$720$	18.4731	−	6.59319i	0.688450	−	0.245714i
$721$	35.6616	−	35.6616i	1.32811	−	1.32811i
$722$	−61.2224	−	36.4646i	−2.27846	−	1.35707i
$723$	−39.4658	+	6.60626i	−1.46775	+	0.245689i
$724$	−4.21476	+	7.99170i	−0.156640	+	0.297009i
$725$	−20.6998	−	4.11745i	−0.768771	−	0.152918i
$726$	0.875158	−	2.24749i	0.0324802	−	0.0834120i
$727$	−12.9789	+	5.37605i	−0.481362	+	0.199387i	−0.610151	−	0.792285i	$-0.708891\pi$
$727$	−12.9789	+	5.37605i	−0.481362	+	0.199387i	0.128789	+	0.991672i	$0.458891\pi$
$728$	−17.9246	−	13.0638i	−0.664331	−	0.484176i
$729$	22.6484	+	14.6987i	0.838828	+	0.544397i
$730$	16.1685	−	0.839318i	0.598423	−	0.0310646i
$731$	7.78927	+	11.6575i	0.288096	+	0.431167i
$732$	−12.5584	+	14.5469i	−0.464171	+	0.537671i
$733$	3.69934	−	0.735845i	0.136638	−	0.0271790i	−0.126297	−	0.991992i	$-0.540309\pi$
$733$	3.69934	−	0.735845i	0.136638	−	0.0271790i	0.262936	+	0.964813i	$0.415309\pi$
$734$	−23.0351	−	3.35159i	−0.850240	−	0.123709i
$735$	−14.2140	−	15.1085i	−0.524292	−	0.557286i
$736$	−12.2408	−	24.9777i	−0.451201	−	0.920691i
$737$	−29.8079			−1.09799
$738$	−7.74550	−	1.61429i	−0.285116	−	0.0594230i
$739$	3.39301	+	17.0578i	0.124814	+	0.627483i	0.991657	+	0.128902i	$0.0411452\pi$
$739$	3.39301	+	17.0578i	0.124814	+	0.627483i	−0.866843	+	0.498581i	$0.833855\pi$
$740$	−7.54172	−	6.11956i	−0.277239	−	0.224959i
$741$	29.1252	+	6.72260i	1.06994	+	0.246961i
$742$	−30.9452	+	1.60639i	−1.13603	+	0.0589724i
$743$	−7.26490	+	17.5390i	−0.266523	+	0.643444i	−0.999315	−	0.0370089i	$-0.988217\pi$
$743$	−7.26490	+	17.5390i	−0.266523	+	0.643444i	0.732792	+	0.680453i	$0.238217\pi$
$744$	−11.2194	−	3.07610i	−0.411322	−	0.112775i
$745$	−2.52130	−	6.08696i	−0.0923733	−	0.223009i
$746$	10.2089	−	4.86316i	0.373773	−	0.178053i
$747$	17.7180	+	4.66293i	0.648267	+	0.170608i
$748$	−9.82008	+	3.03854i	−0.359058	+	0.111100i
$749$	24.9603	+	16.6779i	0.912029	+	0.609398i
$750$	6.33770	+	28.6482i	0.231420	+	1.04608i
$751$	−11.0906	−	11.0906i	−0.404702	−	0.404702i	0.475184	−	0.879886i	$-0.342381\pi$
$751$	−11.0906	−	11.0906i	−0.404702	−	0.404702i	−0.879886	+	0.475184i	$0.842381\pi$
$752$	−0.249719	+	0.0525621i	−0.00910631	+	0.00191674i
$753$	−1.21576	+	39.8550i	−0.0443046	+	1.45240i
$754$	−6.52472	−	25.7447i	−0.237616	−	0.937565i
$755$	22.2366	+	14.8580i	0.809274	+	0.540739i
$756$	−22.2528	−	32.4368i	−0.809325	−	1.17971i
$757$	8.89513	+	1.76935i	0.323299	+	0.0643081i	0.354072	−	0.935218i	$-0.384797\pi$
$757$	8.89513	+	1.76935i	0.323299	+	0.0643081i	−0.0307729	+	0.999526i	$0.509797\pi$
$758$	−8.02643	−	2.84679i	−0.291533	−	0.103400i
$759$	26.8833	+	12.1085i	0.975801	+	0.439510i
$760$	36.1501	−	13.2754i	1.31130	−	0.481550i
$761$	8.35579	−	20.1727i	0.302897	−	0.731258i	−0.697002	−	0.717069i	$-0.745483\pi$
$761$	8.35579	−	20.1727i	0.302897	−	0.731258i	0.999899	−	0.0141893i	$-0.00451675\pi$
$762$	35.4429	−	0.757498i	1.28396	−	0.0274412i
$763$	−3.60111	−	5.38945i	−0.130369	−	0.195111i
$764$	1.43130	−	4.81446i	0.0517826	−	0.174181i
$765$	7.21357	−	0.982432i	0.260807	−	0.0355199i
$766$	−5.42735	+	4.04860i	−0.196098	+	0.146282i
$767$	−14.0383			−0.506894
$768$	−27.1346	−	5.63139i	−0.979136	−	0.203205i
$769$	33.3185			1.20150			0.600748	−	0.799438i	$-0.294869\pi$
$769$	33.3185			1.20150			0.600748	+	0.799438i	$0.294869\pi$
$770$	24.2790	−	18.1113i	0.874956	−	0.652685i
$771$	−7.74868	−	5.52652i	−0.279062	−	0.199033i
$772$	3.42142	−	11.5086i	0.123140	−	0.414204i
$773$	7.89191	+	11.8111i	0.283852	+	0.424815i	0.945807	−	0.324729i	$-0.105273\pi$
$773$	7.89191	+	11.8111i	0.283852	+	0.424815i	−0.661955	+	0.749544i	$0.730273\pi$
$774$	−28.0707	−	28.5877i	−1.00898	−	1.02756i
$775$	2.11583	−	5.10807i	0.0760029	−	0.183487i
$776$	13.9223	−	5.11269i	0.499781	−	0.183535i
$777$	−7.99893	+	17.7593i	−0.286960	+	0.637110i
$778$	3.46112	+	1.22758i	0.124087	+	0.0440108i
$779$	−15.2357	−	3.03057i	−0.545875	−	0.108581i
$780$	−9.25068	+	7.21338i	−0.331227	+	0.258281i
$781$	23.8404	+	15.9296i	0.853076	+	0.570007i
$782$	−2.53639	−	10.0079i	−0.0907012	−	0.357880i
$783$	4.30308	−	46.9045i	0.153779	−	1.67623i
$784$	6.03673	+	28.6801i	0.215598	+	1.02429i
$785$	10.1907	+	10.1907i	0.363722	+	0.363722i
$786$	53.0075	−	11.7266i	1.89072	−	0.418274i
$787$	−6.49735	−	4.34139i	−0.231606	−	0.154754i	0.434353	−	0.900743i	$-0.356977\pi$
$787$	−6.49735	−	4.34139i	−0.231606	−	0.154754i	−0.665958	+	0.745989i	$0.731977\pi$
$788$	−34.4544	+	10.6609i	−1.22739	+	0.379781i
$789$	−31.3857	+	19.6141i	−1.11736	+	0.698280i
$790$	−12.0969	+	5.76258i	−0.430389	+	0.205023i
$791$	3.06501	+	7.39960i	0.108979	+	0.263099i
$792$	25.9558	−	13.7547i	0.922299	−	0.488751i
$793$	4.39837	−	10.6186i	0.156191	−	0.377078i
$794$	−11.6170	+	0.603047i	−0.412272	+	0.0214013i
$795$	−3.68582	+	15.9686i	−0.130723	+	0.566347i
$796$	16.9257	+	13.7340i	0.599915	+	0.486787i
$797$	3.32636	+	16.7228i	0.117826	+	0.592350i	0.993910	+	0.110193i	$0.0351468\pi$
$797$	3.32636	+	16.7228i	0.117826	+	0.592350i	−0.876084	+	0.482158i	$0.839853\pi$
$798$	−44.2701	−	63.2845i	−1.56714	−	2.24025i
$799$	−0.0947178			−0.00335087
$800$	4.26454	−	12.4614i	0.150774	−	0.440576i
$801$	0.553094	−	9.05733i	0.0195426	−	0.320025i
$802$	1.41323	+	0.205624i	0.0499030	+	0.00726084i
$803$	23.7811	−	4.73036i	0.839217	−	0.166931i
$804$	−22.5775	−	19.4911i	−0.796246	−	0.687399i
$805$	16.9017	+	25.2952i	0.595706	+	0.891537i
$806$	6.94816	−	0.360684i	0.244739	−	0.0127046i
$807$	3.57021	+	9.42204i	0.125677	+	0.331671i
$808$	5.50619	+	4.01300i	0.193707	+	0.141177i
$809$	−39.4599	+	16.3448i	−1.38734	+	0.574654i	−0.946433	−	0.322900i	$-0.895342\pi$
$809$	−39.4599	+	16.3448i	−1.38734	+	0.574654i	−0.440904	+	0.897554i	$0.645342\pi$
$810$	−19.7311	+	6.59529i	−0.693281	+	0.231735i
$811$	−16.4745	−	3.27698i	−0.578498	−	0.115070i	−0.102835	−	0.994698i	$-0.532791\pi$
$811$	−16.4745	−	3.27698i	−0.578498	−	0.115070i	−0.475662	+	0.879628i	$0.657791\pi$
$812$	−32.0115	+	60.6977i	−1.12338	+	2.13007i
$813$	−1.85495	−	11.0814i	−0.0650558	−	0.388643i
$814$	−12.4966	−	7.44308i	−0.438005	−	0.260880i
$815$	18.0221	−	18.0221i	0.631288	−	0.631288i
$816$	−9.42494	−	4.11978i	−0.329939	−	0.144221i
$817$	−55.6234	−	55.6234i	−1.94602	−	1.94602i
$818$	−4.41333	−	17.4137i	−0.154308	−	0.608856i
$819$	18.7277	+	14.2380i	0.654399	+	0.497517i
$820$	4.69099	−	3.89360i	0.163817	−	0.135970i
$821$	6.13741	−	30.8549i	0.214197	−	1.07684i	−0.712683	−	0.701486i	$-0.752520\pi$
$821$	6.13741	−	30.8549i	0.214197	−	1.07684i	0.926881	−	0.375356i	$-0.122480\pi$
$822$	22.7495	−	9.99787i	0.793480	−	0.348716i
$823$	−6.50835	−	15.7125i	−0.226867	−	0.547705i	0.768926	−	0.639338i	$-0.220791\pi$
$823$	−6.50835	−	15.7125i	−0.226867	−	0.547705i	−0.995793	+	0.0916330i	$0.970791\pi$
$824$	−1.53555	+	37.6548i	−0.0534934	+	1.31177i
$825$	4.94685	+	13.0551i	0.172227	+	0.454519i
$826$	26.9433	+	24.2841i	0.937478	+	0.844951i
$827$	−3.14692	+	2.10271i	−0.109429	+	0.0731183i	−0.609081	−	0.793108i	$-0.708461\pi$
$827$	−3.14692	+	2.10271i	−0.109429	+	0.0731183i	0.499651	+	0.866227i	$0.333461\pi$
$828$	12.4447	+	26.7501i	0.432482	+	0.929631i
$829$	1.61511	+	8.11973i	0.0560952	+	0.282010i	0.998644	−	0.0520587i	$-0.0165783\pi$
$829$	1.61511	+	8.11973i	0.0560952	+	0.282010i	−0.942549	+	0.334069i	$0.891578\pi$
$830$	−11.3155	+	8.44096i	−0.392767	+	0.292990i
$831$	36.0952	+	38.3666i	1.25213	+	1.33092i
$832$	16.4649	−	1.89910i	0.570816	−	0.0658395i
$833$			10.8783i			0.376911i
$834$	−36.0877	−	6.37989i	−1.24961	−	0.220917i
$835$	−36.6787	+	7.29585i	−1.26932	+	0.252483i
$836$	50.7126	−	27.4696i	1.75393	−	0.950057i
$837$	11.8315	+	3.50278i	0.408956	+	0.121074i
$838$	34.4355	−	38.2064i	1.18956	−	1.31982i
$839$	2.71572	+	1.12489i	0.0937569	+	0.0388354i	0.429069	−	0.903272i	$-0.358842\pi$
$839$	2.71572	+	1.12489i	0.0937569	+	0.0388354i	−0.335312	+	0.942107i	$0.608842\pi$
$840$	30.2326	+	2.15779i	1.04312	+	0.0744508i
$841$	−49.1212	+	20.3467i	−1.69383	+	0.701609i
$842$	26.3945	+	9.36152i	0.909615	+	0.322619i
$843$	−25.9949	+	16.2452i	−0.895311	+	0.559513i
$844$	16.5737	−	13.7565i	0.570491	−	0.473517i
$845$	−7.90757	+	11.8345i	−0.272029	+	0.407120i
$846$	0.265941	−	0.0503804i	0.00914323	−	0.00173211i
$847$	2.63537	−	2.63537i	0.0905525	−	0.0905525i
$848$	16.1901	−	16.5538i	0.555971	−	0.568461i
$849$	−0.124584	+	4.08410i	−0.00427570	+	0.140166i
$850$	2.50157	−	4.20002i	0.0858032	−	0.144060i
$851$	8.11616	−	12.1467i	0.278218	−	0.416383i
$852$	7.64125	+	27.6547i	0.261785	+	0.947435i
$853$	−0.670496	+	3.37081i	−0.0229574	+	0.115414i	−0.990565	−	0.137045i	$-0.956239\pi$
$853$	−0.670496	+	3.37081i	−0.0229574	+	0.115414i	0.967607	+	0.252460i	$0.0812395\pi$
$854$	−26.8102	+	12.7715i	−0.917427	+	0.437032i
$855$	−38.6200	+	13.3021i	−1.32077	+	0.454922i
$856$	−22.1610	+	3.47619i	−0.757449	+	0.118814i
$857$	44.6410	+	18.4909i	1.52491	+	0.631637i	0.978568	−	0.205926i	$-0.0660207\pi$
$857$	44.6410	+	18.4909i	1.52491	+	0.631637i	0.546340	+	0.837563i	$0.316021\pi$
$858$	−12.1543	+	12.6852i	−0.414940	+	0.433064i
$859$	22.9633	−	15.3436i	0.783497	−	0.523516i	−0.0982936	−	0.995157i	$-0.531338\pi$
$859$	22.9633	−	15.3436i	0.783497	−	0.523516i	0.881790	+	0.471642i	$0.156338\pi$
$860$	30.7053	−	3.19648i	1.04704	−	0.108999i
$861$	−9.95378	−	7.09924i	−0.339224	−	0.241941i
$862$	0.0274185	−	0.188444i	0.000933877	−	0.00641843i
$863$			33.5051i			1.14053i	0.821462	+	0.570264i	$0.193159\pi$
$863$			33.5051i			1.14053i	−0.821462	+	0.570264i	$0.806841\pi$
$864$	28.6539	+	6.55405i	0.974825	+	0.222973i
$865$		−	23.9239i		−	0.813435i
$866$	31.9412	+	4.64742i	1.08541	+	0.157926i
$867$	20.8641	+	14.8807i	0.708582	+	0.505375i
$868$	−13.9593	−	11.3270i	−0.473811	−	0.384463i
$869$	−16.6853	+	11.1488i	−0.566011	+	0.378196i
$870$	26.2054	+	25.1087i	0.888448	+	0.851266i
$871$	16.4805	+	6.82646i	0.558421	+	0.231306i
$872$	4.70803	+	1.13771i	0.159434	+	0.0385276i
$873$	−14.8735	+	5.12296i	−0.503392	+	0.173386i
$874$	24.9119	+	52.2956i	0.842658	+	1.76893i
$875$	−8.84530	+	44.4683i	−0.299026	+	1.50330i
$876$	21.1058	+	11.9674i	0.713098	+	0.404340i
$877$	9.10376	−	13.6247i	0.307412	−	0.460075i	−0.645309	−	0.763922i	$-0.723271\pi$
$877$	9.10376	−	13.6247i	0.307412	−	0.460075i	0.952721	+	0.303847i	$0.0982712\pi$
$878$	−32.1321	−	19.1382i	−1.08441	−	0.645882i
$879$	1.21339	−	39.7775i	0.0409267	−	1.34166i
$880$	−4.16888	+	22.2470i	−0.140533	+	0.749946i
$881$	−17.3846	+	17.3846i	−0.585702	+	0.585702i	−0.936464	−	0.350763i	$-0.885922\pi$
$881$	−17.3846	+	17.3846i	−0.585702	+	0.585702i	0.350763	+	0.936464i	$0.385922\pi$
$882$	−5.78617	−	30.5432i	−0.194830	−	1.02844i
$883$	13.3527	−	19.9837i	0.449354	−	0.672506i	−0.535767	−	0.844366i	$-0.679978\pi$
$883$	13.3527	−	19.9837i	0.449354	−	0.672506i	0.985121	+	0.171860i	$0.0549775\pi$
$884$	6.12532	+	0.568963i	0.206017	+	0.0191363i
$885$	16.2682	−	10.1666i	0.546848	−	0.341745i
$886$	13.0986	−	36.9312i	0.440057	−	1.24073i
$887$	−42.0010	+	17.3974i	−1.41026	+	0.584147i	−0.952392	−	0.304876i	$-0.901385\pi$
$887$	−42.0010	+	17.3974i	−1.41026	+	0.584147i	−0.457863	+	0.889023i	$0.651385\pi$
$888$	−4.59836	−	13.8091i	−0.154311	−	0.463402i
$889$	50.6114	+	20.9639i	1.69745	+	0.703107i
$890$	5.19368	+	4.68107i	0.174092	+	0.156910i
$891$	−27.8198	+	14.0291i	−0.931998	+	0.469991i
$892$	8.58027	−	28.8614i	0.287289	−	0.966351i
$893$	0.521219	−	0.103677i	0.0174419	−	0.00346942i
$894$	1.71885	−	9.72264i	0.0574870	−	0.325174i
$895$			18.2091i			0.608664i
$896$	−34.8857	−	24.8367i	−1.16545	−	0.829737i
$897$	−12.0905	−	12.8514i	−0.403691	−	0.429094i
$898$	32.0470	+	42.9606i	1.06942	+	1.43361i
$899$	−4.19942	−	21.1119i	−0.140059	−	0.704122i
$900$	−4.78971	+	13.1231i	−0.159657	+	0.437435i
$901$	7.14589	−	4.77473i	0.238064	−	0.159069i
$902$	6.11257	−	6.78194i	0.203526	−	0.225814i
$903$	−21.9375	−	57.8946i	−0.730034	−	1.92661i
$904$	−5.43143	−	2.51372i	−0.180647	−	0.0836052i
$905$	2.82574	+	6.82194i	0.0939307	+	0.226769i
$906$	16.1248	+	36.6910i	0.535711	+	1.21898i
$907$	−8.09098	+	40.6761i	−0.268657	+	1.35063i	0.576932	+	0.816792i	$0.304250\pi$
$907$	−8.09098	+	40.6761i	−0.268657	+	1.35063i	−0.845588	+	0.533835i	$0.820750\pi$
$908$	−0.677947	+	7.29862i	−0.0224985	+	0.242213i
$909$	−5.75288	−	4.37372i	−0.190811	−	0.145067i
$910$	−17.5715	+	4.45331i	−0.582488	+	0.147626i
$911$	−1.23068	−	1.23068i	−0.0407742	−	0.0407742i	0.686426	−	0.727200i	$-0.259179\pi$
$911$	−1.23068	−	1.23068i	−0.0407742	−	0.0407742i	−0.727200	+	0.686426i	$0.759179\pi$
$912$	56.3736	+	12.3542i	1.86672	+	0.409088i
$913$	−14.9497	+	14.9497i	−0.494763	+	0.494763i
$914$	7.25238	−	12.1764i	0.239887	−	0.402760i
$915$	2.59300	+	15.4906i	0.0857220	+	0.512103i
$916$	21.7106	−	6.71774i	0.717339	−	0.221960i
$917$	82.2794	+	16.3664i	2.71710	+	0.540466i
$918$	9.90621	+	4.57104i	0.326954	+	0.150867i
$919$	−16.4068	+	6.79591i	−0.541210	+	0.224176i	−0.636505	−	0.771273i	$-0.719620\pi$
$919$	−16.4068	+	6.79591i	−0.541210	+	0.224176i	0.0952952	+	0.995449i	$0.469620\pi$
$920$	−22.0969	−	5.33978i	−0.728515	−	0.176047i
$921$	1.69754	+	4.47992i	0.0559357	+	0.147618i
$922$	−1.91483	−	36.8871i	−0.0630617	−	1.21481i
$923$	−9.53304	−	14.2672i	−0.313784	−	0.469610i
$924$	45.2707	−	3.32126i	1.48930	−	0.109261i
$925$	6.78433	−	1.34949i	0.223068	−	0.0443709i
$926$	−1.19963	+	8.24490i	−0.0394222	+	0.270944i
$927$	2.43640	−	39.8978i	0.0800218	−	1.31042i
$928$	−13.1488	−	49.5631i	−0.431631	−	1.62699i
$929$	−43.9055			−1.44049			−0.720246	−	0.693719i	$-0.755971\pi$
$929$	−43.9055			−1.44049			−0.720246	+	0.693719i	$0.755971\pi$
$930$	−7.79061	+	5.44985i	−0.255464	+	0.178708i
$931$	−11.9073	−	59.8618i	−0.390244	−	1.96189i
$932$	−4.99914	−	48.0216i	−0.163752	−	1.57300i
$933$	7.01844	−	30.4069i	0.229773	−	0.995477i
$934$	2.59120	+	49.9165i	0.0847867	+	1.63332i
$935$	−3.21494	+	7.76154i	−0.105140	+	0.253830i
$936$	−17.5008	+	1.66057i	−0.572031	+	0.0542775i
$937$	−20.9744	−	50.6366i	−0.685203	−	1.65423i	−0.754229	−	0.656612i	$-0.771989\pi$
$937$	−20.9744	−	50.6366i	−0.685203	−	1.65423i	0.0690257	−	0.997615i	$-0.478011\pi$
$938$	−19.8219	−	41.6106i	−0.647208	−	1.35863i
$939$	3.46076	−	2.16276i	0.112938	−	0.0705789i
$940$	−0.0972909	+	0.184476i	−0.00317328	+	0.00601693i
$941$	−22.0612	−	14.7408i	−0.719174	−	0.480536i	0.141342	−	0.989961i	$-0.454858\pi$
$941$	−22.0612	−	14.7408i	−0.719174	−	0.480536i	−0.860515	+	0.509424i	$0.829858\pi$
$942$	4.66510	+	21.0876i	0.151997	+	0.687070i
$943$	6.48410	+	6.48410i	0.211151	+	0.211151i
$944$	−27.1026	+	0.301042i	−0.882113	+	0.00979809i
$945$	−32.0136	−	2.93697i	−1.04140	−	0.0955398i
$946$	44.8167	−	11.3584i	1.45712	−	0.369292i
$947$	29.5490	+	19.7440i	0.960214	+	0.641594i	0.933701	−	0.358054i	$-0.116560\pi$
$947$	29.5490	+	19.7440i	0.960214	+	0.641594i	0.0265131	+	0.999648i	$0.491560\pi$
$948$	−19.9281	−	2.46595i	−0.647235	−	0.0800903i
$949$	−14.2317	−	2.83087i	−0.461981	−	0.0918938i
$950$	−9.16851	+	25.8504i	−0.297466	+	0.838696i
$951$	22.8556	−	50.7442i	0.741145	−	1.64549i
$952$	−10.7719	−	11.6878i	−0.349121	−	0.378805i
$953$	18.7182	−	45.1898i	0.606342	−	1.46384i	−0.260608	−	0.965445i	$-0.583923\pi$
$953$	18.7182	−	45.1898i	0.606342	−	1.46384i	0.866950	−	0.498395i	$-0.166077\pi$
$954$	−17.5239	+	17.2070i	−0.567359	+	0.557097i
$955$	−2.28055	−	3.41309i	−0.0737970	−	0.110445i
$956$	−6.68754	−	12.3461i	−0.216291	−	0.399301i
$957$	44.2514	+	31.5610i	1.43044	+	1.02022i
$958$	−12.2096	−	16.3676i	−0.394475	−	0.528813i
$959$	38.3992			1.23997
$960$	−17.7048	+	14.1246i	−0.571420	+	0.455871i
$961$	−25.3610			−0.818096
$962$	5.20469	+	6.97713i	0.167806	+	0.224952i
$963$	23.5751	−	3.21075i	0.759698	−	0.103465i
$964$	40.6277	−	22.0069i	1.30853	−	0.708796i
$965$	−5.45150	−	8.15875i	−0.175490	−	0.262639i
$966$	0.974150	+	45.5800i	0.0313428	+	1.46651i
$967$	12.1593	−	29.3552i	0.391018	−	0.944000i	−0.598701	−	0.800973i	$-0.704316\pi$
$967$	12.1593	−	29.3552i	0.391018	−	0.944000i	0.989719	−	0.143027i	$-0.0456837\pi$
$968$	−0.113476	+	2.78267i	−0.00364727	+	0.0894384i
$969$	19.5308	+	8.79684i	0.627419	+	0.282595i
$970$	4.05180	−	11.4239i	0.130095	−	0.366800i
$971$	−1.21433	−	0.241545i	−0.0389696	−	0.00775154i	0.175567	−	0.984467i	$-0.443824\pi$
$971$	−1.21433	−	0.241545i	−0.0389696	−	0.00775154i	−0.214537	+	0.976716i	$0.568824\pi$
$972$	−30.2452	−	7.56508i	−0.970114	−	0.242650i
$973$	−47.0861	−	31.4619i	−1.50951	−	1.00862i
$974$	26.9985	−	6.84250i	0.865087	−	0.219248i
$975$	0.254742	−	8.35096i	0.00815827	−	0.267445i
$976$	8.26385	−	20.5948i	0.264519	−	0.659222i
$977$	15.9315	+	15.9315i	0.509695	+	0.509695i	0.914433	−	0.404738i	$-0.132637\pi$
$977$	15.9315	+	15.9315i	0.509695	+	0.509695i	−0.404738	+	0.914433i	$0.632637\pi$
$978$	37.2930	−	8.25016i	1.19250	−	0.263811i
$979$	8.70655	+	5.81753i	0.278262	+	0.185929i
$980$	21.1869	+	11.1738i	0.676792	+	0.356935i
$981$	−4.96818	−	1.30750i	−0.158622	−	0.0417453i
$982$	−8.31824	−	17.4618i	−0.265446	−	0.557229i
$983$	8.57077	+	20.6917i	0.273365	+	0.659962i	0.999623	−	0.0274605i	$-0.00874205\pi$
$983$	8.57077	+	20.6917i	0.273365	+	0.659962i	−0.726258	+	0.687423i	$0.758742\pi$
$984$	9.06453	−	1.13990i	0.288967	−	0.0363387i
$985$	−11.2798	+	27.2319i	−0.359405	+	0.867681i
$986$	−0.986658	−	19.0068i	−0.0314216	−	0.605301i
$987$	0.407544	+	0.0940681i	0.0129723	+	0.00299422i
$988$	−34.3296	+	3.57378i	−1.09217	+	0.113697i
$989$	9.05909	+	45.5431i	0.288062	+	1.44819i
$990$	4.89826	−	23.5022i	0.155677	−	0.746950i
$991$	−10.2331			−0.325066			−0.162533	−	0.986703i	$-0.551966\pi$
$991$	−10.2331			−0.325066			−0.162533	+	0.986703i	$0.551966\pi$
$992$	13.4065	−	0.845340i	0.425656	−	0.0268396i
$993$	29.2268	+	31.0660i	0.927485	+	0.985850i
$994$	−6.38353	+	43.8733i	−0.202473	+	1.39158i
$995$	17.4715	−	3.47530i	0.553884	−	0.110174i
$996$	−21.0989	+	1.54791i	−0.668545	+	0.0490474i
$997$	−9.87796	−	14.7834i	−0.312838	−	0.468196i	0.641415	−	0.767194i	$-0.278348\pi$
$997$	−9.87796	−	14.7834i	−0.312838	−	0.468196i	−0.954254	+	0.298998i	$0.903348\pi$
$998$	0.960183	+	18.4968i	0.0303941	+	0.585507i
$999$	4.57998	+	14.7424i	0.144904	+	0.466429i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.s.a.107.6	✓	240
3.2	odd	2	inner	192.2.s.a.107.25	yes	240
4.3	odd	2		768.2.s.a.335.21		240
12.11	even	2		768.2.s.a.335.25		240
64.3	odd	16	inner	192.2.s.a.131.25	yes	240
64.61	even	16		768.2.s.a.431.25		240
192.125	odd	16		768.2.s.a.431.21		240
192.131	even	16	inner	192.2.s.a.131.6	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.s.a.107.6	✓	240	1.1	even	1	trivial
192.2.s.a.107.25	yes	240	3.2	odd	2	inner
192.2.s.a.131.6	yes	240	192.131	even	16	inner
192.2.s.a.131.25	yes	240	64.3	odd	16	inner
768.2.s.a.335.21		240	4.3	odd	2
768.2.s.a.335.25		240	12.11	even	2
768.2.s.a.431.21		240	192.125	odd	16
768.2.s.a.431.25		240	64.61	even	16

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.s (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13356 + 0.845597i) q^{2} +(-1.00574 + 1.41014i) q^{3} +(0.569932 - 1.91708i) q^{4} +(-0.908097 - 1.35906i) q^{5} +(-0.0523394 - 2.44893i) q^{6} +(1.44850 - 3.49700i) q^{7} +(0.975019 + 2.65506i) q^{8} +(-0.976978 - 2.83646i) q^{9} +O(q^{10})\)	\(q+(-1.13356 + 0.845597i) q^{2} +(-1.00574 + 1.41014i) q^{3} +(0.569932 - 1.91708i) q^{4} +(-0.908097 - 1.35906i) q^{5} +(-0.0523394 - 2.44893i) q^{6} +(1.44850 - 3.49700i) q^{7} +(0.975019 + 2.65506i) q^{8} +(-0.976978 - 2.83646i) q^{9} +(2.17861 + 0.772701i) q^{10} +(3.39536 + 0.675380i) q^{11} +(2.13014 + 2.73176i) q^{12} +(-1.72260 - 1.15100i) q^{13} +(1.31508 + 5.18892i) q^{14} +(2.82978 + 0.0863210i) q^{15} +(-3.35036 - 2.18520i) q^{16} +(-1.04981 - 1.04981i) q^{17} +(3.50597 + 2.38918i) q^{18} +(6.92609 + 4.62786i) q^{19} +(-3.12298 + 0.966318i) q^{20} +(3.47443 + 5.55965i) q^{21} +(-4.41996 + 2.10552i) q^{22} +(-1.88173 - 4.54290i) q^{23} +(-4.72461 - 1.29538i) q^{24} +(0.891004 - 2.15107i) q^{25} +(2.92596 - 0.151889i) q^{26} +(4.98239 + 1.47507i) q^{27} +(-5.87846 - 4.76994i) q^{28} +(-1.76843 - 8.89050i) q^{29} +(-3.28072 + 2.29500i) q^{30} +2.37466 q^{31} +(5.64564 - 0.355984i) q^{32} +(-4.36723 + 4.10868i) q^{33} +(2.07775 + 0.302311i) q^{34} +(-6.06802 + 1.20700i) q^{35} +(-5.99452 + 0.256351i) q^{36} +(1.65056 + 2.47024i) q^{37} +(-11.7645 + 0.610702i) q^{38} +(3.35556 - 1.27149i) q^{39} +(2.72298 - 3.73617i) q^{40} +(-1.72291 + 0.713652i) q^{41} +(-8.63971 - 3.36425i) q^{42} +(-9.26200 - 1.84233i) q^{43} +(3.22988 - 6.12425i) q^{44} +(-2.96774 + 3.90356i) q^{45} +(5.97452 + 3.55848i) q^{46} +(0.0451118 - 0.0451118i) q^{47} +(6.45102 - 2.52672i) q^{48} +(-5.18107 - 5.18107i) q^{49} +(0.808932 + 3.19181i) q^{50} +(2.53622 - 0.424543i) q^{51} +(-3.18832 + 2.64636i) q^{52} +(-1.12932 + 5.67750i) q^{53} +(-6.89516 + 2.54101i) q^{54} +(-2.16544 - 5.22783i) q^{55} +(10.6970 + 0.436222i) q^{56} +(-13.4918 + 5.11231i) q^{57} +(9.52241 + 8.58257i) q^{58} +(5.63408 - 3.76457i) q^{59} +(1.77826 - 5.37570i) q^{60} +(1.08231 + 5.44112i) q^{61} +(-2.69183 + 2.00801i) q^{62} +(-11.3342 - 0.692136i) q^{63} +(-6.09867 + 5.17747i) q^{64} +3.38634i q^{65} +(1.47625 - 8.35036i) q^{66} +(-8.44485 + 1.67979i) q^{67} +(-2.61089 + 1.41425i) q^{68} +(8.29865 + 1.91547i) q^{69} +(5.85785 - 6.49932i) q^{70} +(7.65191 + 3.16953i) q^{71} +(6.57840 - 5.35954i) q^{72} +(6.47085 - 2.68031i) q^{73} +(-3.95985 - 1.40447i) q^{74} +(2.13719 + 3.41986i) q^{75} +(12.8194 - 10.6403i) q^{76} +(7.28000 - 10.8953i) q^{77} +(-2.72857 + 4.27877i) q^{78} +(-4.09884 + 4.09884i) q^{79} +(0.0726180 + 6.53773i) q^{80} +(-7.09103 + 5.54232i) q^{81} +(1.34956 - 2.26586i) q^{82} +(-3.39292 + 5.07787i) q^{83} +(12.6385 - 3.49212i) q^{84} +(-0.473430 + 2.38009i) q^{85} +(12.0569 - 5.74353i) q^{86} +(14.3154 + 6.44780i) q^{87} +(1.51737 + 9.67340i) q^{88} +(2.79449 + 1.15752i) q^{89} +(0.0632855 - 6.93444i) q^{90} +(-6.52024 + 4.35669i) q^{91} +(-9.78154 + 1.01828i) q^{92} +(-2.38829 + 3.34860i) q^{93} +(-0.0129907 + 0.0892834i) q^{94} -13.6155i q^{95} +(-5.17606 + 8.31916i) q^{96} -5.24368i q^{97} +(10.2542 + 1.49197i) q^{98} +(-1.40151 - 10.2907i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9}+O(q^{10}) \) 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9	\( 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28} - 88 q^{30} - 32 q^{31} - 16 q^{34} - 88 q^{36} - 16 q^{37} - 8 q^{39} - 16 q^{40} - 48 q^{42} - 16 q^{43} - 8 q^{45} - 16 q^{46} - 8 q^{48} - 16 q^{49} - 8 q^{51} + 32 q^{52} - 8 q^{54} - 80 q^{55} - 8 q^{57} + 128 q^{58} - 8 q^{60} - 16 q^{61} + 80 q^{64} - 24 q^{66} - 144 q^{67} - 8 q^{69} + 80 q^{70} - 8 q^{72} - 16 q^{73} - 8 q^{75} + 96 q^{76} + 16 q^{78} - 48 q^{79} - 8 q^{81} + 64 q^{82} + 104 q^{84} - 16 q^{85} - 8 q^{87} + 64 q^{88} + 136 q^{90} - 16 q^{91} - 32 q^{93} + 80 q^{94} + 128 q^{96} - 8 q^{99}+O(q^{100}) \) 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more