LMFDB - Embedded newform 336.2.bo.a.5.45

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(5,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 6, 10]))

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

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

chi := DirichletCharacter("336.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bo (of order $12$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$60$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			5.45
Character	$\chi$	$=$	336.5
Dual form			336.2.bo.a.269.45

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.902393 - 1.08889i) q^{2} +(-0.218562 + 1.71821i) q^{3} +(-0.371375 - 1.96522i) q^{4} +(-3.29199 + 0.882085i) q^{5} +(1.67371 + 1.78849i) q^{6} +(-2.31271 + 1.28506i) q^{7} +(-2.47504 - 1.36901i) q^{8} +(-2.90446 - 0.751070i) q^{9} +O(q^{10})$	\(q+(0.902393 - 1.08889i) q^{2} +(-0.218562 + 1.71821i) q^{3} +(-0.371375 - 1.96522i) q^{4} +(-3.29199 + 0.882085i) q^{5} +(1.67371 + 1.78849i) q^{6} +(-2.31271 + 1.28506i) q^{7} +(-2.47504 - 1.36901i) q^{8} +(-2.90446 - 0.751070i) q^{9} +(-2.01017 + 4.38061i) q^{10} +(-2.70922 - 0.725934i) q^{11} +(3.45782 - 0.208577i) q^{12} +(4.53845 + 4.53845i) q^{13} +(-0.687681 + 3.67792i) q^{14} +(-0.796100 - 5.84910i) q^{15} +(-3.72416 + 1.45967i) q^{16} +(-1.00283 - 1.73695i) q^{17} +(-3.43880 + 2.48489i) q^{18} +(-3.09875 + 0.830307i) q^{19} +(2.95605 + 6.14188i) q^{20} +(-1.70252 - 4.25458i) q^{21} +(-3.23525 + 2.29498i) q^{22} +(0.855139 - 1.48114i) q^{23} +(2.89319 - 3.95341i) q^{24} +(5.72897 - 3.30762i) q^{25} +(9.03734 - 0.846421i) q^{26} +(1.92530 - 4.82631i) q^{27} +(3.38430 + 4.06774i) q^{28} +(2.07878 + 2.07878i) q^{29} +(-7.08744 - 4.41132i) q^{30} +(-3.31731 + 1.91525i) q^{31} +(-1.77124 + 5.37240i) q^{32} +(1.83944 - 4.49634i) q^{33} +(-2.79630 - 0.475438i) q^{34} +(6.47988 - 6.27040i) q^{35} +(-0.397370 + 5.98683i) q^{36} +(-4.20434 + 1.12655i) q^{37} +(-1.89217 + 4.12347i) q^{38} +(-8.78992 + 6.80605i) q^{39} +(9.35537 + 2.32357i) q^{40} -8.67639i q^{41} +(-6.16912 - 1.98543i) q^{42} +(4.52927 + 4.52927i) q^{43} +(-0.420481 + 5.59381i) q^{44} +(10.2240 - 0.0894710i) q^{45} +(-0.841136 - 2.26773i) q^{46} +(-5.17739 + 8.96750i) q^{47} +(-1.69405 - 6.71790i) q^{48} +(3.69725 - 5.94393i) q^{49} +(1.56813 - 9.22301i) q^{50} +(3.20362 - 1.34343i) q^{51} +(7.23357 - 10.6045i) q^{52} +(5.54861 + 1.48675i) q^{53} +(-3.51796 - 6.45167i) q^{54} +9.55907 q^{55} +(7.48330 - 0.0144457i) q^{56} +(-0.749369 - 5.50576i) q^{57} +(4.13944 - 0.387693i) q^{58} +(-1.75857 + 6.56309i) q^{59} +(-11.1991 + 3.73672i) q^{60} +(2.03278 - 0.544681i) q^{61} +(-0.908015 + 5.34051i) q^{62} +(7.68234 - 1.99540i) q^{63} +(4.25162 + 6.77670i) q^{64} +(-18.9438 - 10.9372i) q^{65} +(-3.23614 - 6.06042i) q^{66} +(-3.10476 - 0.831917i) q^{67} +(-3.04106 + 2.61584i) q^{68} +(2.35801 + 1.79303i) q^{69} +(-0.980402 - 12.7143i) q^{70} -12.8919 q^{71} +(6.16043 + 5.83516i) q^{72} +(-0.0186751 - 0.0323462i) q^{73} +(-2.56727 + 5.59466i) q^{74} +(4.43104 + 10.5665i) q^{75} +(2.78253 + 5.78136i) q^{76} +(7.19852 - 1.80264i) q^{77} +(-0.520896 + 15.7130i) q^{78} +(1.41020 - 2.44253i) q^{79} +(10.9723 - 8.09023i) q^{80} +(7.87179 + 4.36290i) q^{81} +(-9.44766 - 7.82951i) q^{82} +(-5.54643 + 5.54643i) q^{83} +(-7.72889 + 4.92587i) q^{84} +(4.83344 + 4.83344i) q^{85} +(9.01907 - 0.844710i) q^{86} +(-4.02611 + 3.11743i) q^{87} +(5.71162 + 5.50567i) q^{88} +(-2.36808 - 1.36721i) q^{89} +(9.12860 - 11.2135i) q^{90} +(-16.3283 - 4.66394i) q^{91} +(-3.22835 - 1.13047i) q^{92} +(-2.56576 - 6.11843i) q^{93} +(5.09261 + 13.7298i) q^{94} +(9.46864 - 5.46672i) q^{95} +(-8.84377 - 4.21755i) q^{96} -2.90039i q^{97} +(-3.13594 - 9.38967i) q^{98} +(7.32361 + 4.14326i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 6 q^{3} - 4 q^{4}+O(q^{10}) $ 240 * q - 6 * q^3 - 4 * q^4	$ 240 q - 6 q^{3} - 4 q^{4} - 12 q^{10} - 6 q^{12} - 16 q^{15} - 20 q^{16} - 4 q^{18} - 12 q^{19} + 2 q^{21} - 40 q^{22} - 6 q^{24} - 12 q^{28} + 22 q^{30} - 24 q^{31} - 12 q^{33} - 64 q^{36} - 4 q^{37} + 48 q^{40} - 18 q^{42} - 16 q^{43} - 6 q^{45} + 12 q^{46} - 16 q^{49} - 10 q^{51} - 48 q^{52} - 90 q^{54} - 4 q^{58} - 18 q^{60} - 12 q^{61} - 36 q^{63} + 32 q^{64} - 66 q^{66} - 36 q^{67} - 76 q^{70} - 46 q^{72} + 24 q^{75} - 76 q^{78} - 8 q^{79} - 4 q^{81} + 72 q^{82} - 24 q^{84} + 24 q^{85} + 12 q^{88} - 88 q^{91} - 14 q^{93} + 24 q^{94} + 96 q^{96} + 28 q^{99}+O(q^{100}) $ 240 * q - 6 * q^3 - 4 * q^4 - 12 * q^10 - 6 * q^12 - 16 * q^15 - 20 * q^16 - 4 * q^18 - 12 * q^19 + 2 * q^21 - 40 * q^22 - 6 * q^24 - 12 * q^28 + 22 * q^30 - 24 * q^31 - 12 * q^33 - 64 * q^36 - 4 * q^37 + 48 * q^40 - 18 * q^42 - 16 * q^43 - 6 * q^45 + 12 * q^46 - 16 * q^49 - 10 * q^51 - 48 * q^52 - 90 * q^54 - 4 * q^58 - 18 * q^60 - 12 * q^61 - 36 * q^63 + 32 * q^64 - 66 * q^66 - 36 * q^67 - 76 * q^70 - 46 * q^72 + 24 * q^75 - 76 * q^78 - 8 * q^79 - 4 * q^81 + 72 * q^82 - 24 * q^84 + 24 * q^85 + 12 * q^88 - 88 * q^91 - 14 * q^93 + 24 * q^94 + 96 * q^96 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.902393	−	1.08889i	0.638088	−	0.769964i
$2$	0.902393	−	1.08889i	0.638088	−	0.769964i
$3$	−0.218562	+	1.71821i	−0.126187	+	0.992006i
$3$	−0.218562	+	1.71821i	−0.126187	+	0.992006i
$4$	−0.371375	−	1.96522i	−0.185688	−	0.982609i
$5$	−3.29199	+	0.882085i	−1.47222	+	0.394480i	−0.903692	−	0.428183i	$-0.859154\pi$
$5$	−3.29199	+	0.882085i	−1.47222	+	0.394480i	−0.568529	+	0.822663i	$0.692487\pi$
$6$	1.67371	+	1.78849i	0.683290	+	0.730147i
$7$	−2.31271	+	1.28506i	−0.874122	+	0.485706i
$7$	−2.31271	+	1.28506i	−0.874122	+	0.485706i
$8$	−2.47504	−	1.36901i	−0.875058	−	0.484018i
$9$	−2.90446	−	0.751070i	−0.968154	−	0.250357i
$10$	−2.01017	+	4.38061i	−0.635671	+	1.38527i
$11$	−2.70922	−	0.725934i	−0.816862	−	0.218877i	−0.173888	−	0.984765i	$-0.555633\pi$
$11$	−2.70922	−	0.725934i	−0.816862	−	0.218877i	−0.642974	+	0.765888i	$0.722300\pi$
$12$	3.45782	−	0.208577i	0.998186	−	0.0602109i
$13$	4.53845	+	4.53845i	1.25874	+	1.25874i	0.951696	+	0.307043i	$0.0993396\pi$
$13$	4.53845	+	4.53845i	1.25874	+	1.25874i	0.307043	+	0.951696i	$0.400660\pi$
$14$	−0.687681	+	3.67792i	−0.183790	+	0.982965i
$15$	−0.796100	−	5.84910i	−0.205552	−	1.51023i
$16$	−3.72416	+	1.45967i	−0.931040	+	0.364917i
$17$	−1.00283	−	1.73695i	−0.243222	−	0.421272i	0.718408	−	0.695622i	$-0.244871\pi$
$17$	−1.00283	−	1.73695i	−0.243222	−	0.421272i	−0.961630	+	0.274349i	$0.911538\pi$
$18$	−3.43880	+	2.48489i	−0.810533	+	0.585694i
$19$	−3.09875	+	0.830307i	−0.710902	+	0.190486i	−0.596109	−	0.802904i	$-0.703287\pi$
$19$	−3.09875	+	0.830307i	−0.710902	+	0.190486i	−0.114793	+	0.993389i	$0.536621\pi$
$20$	2.95605	+	6.14188i	0.660993	+	1.37337i
$21$	−1.70252	−	4.25458i	−0.371521	−	0.928424i
$22$	−3.23525	+	2.29498i	−0.689757	+	0.489291i
$23$	0.855139	−	1.48114i	0.178309	−	0.308840i	−0.762993	−	0.646407i	$-0.776271\pi$
$23$	0.855139	−	1.48114i	0.178309	−	0.308840i	0.941301	+	0.337567i	$0.109604\pi$
$24$	2.89319	−	3.95341i	0.590570	−	0.806986i
$25$	5.72897	−	3.30762i	1.14579	−	0.661525i
$26$	9.03734	−	0.846421i	1.77237	−	0.165997i
$27$	1.92530	−	4.82631i	0.370524	−	0.928823i
$28$	3.38430	+	4.06774i	0.639573	+	0.768730i
$29$	2.07878	+	2.07878i	0.386019	+	0.386019i	0.873265	−	0.487246i	$-0.161998\pi$
$29$	2.07878	+	2.07878i	0.386019	+	0.386019i	−0.487246	+	0.873265i	$0.661998\pi$
$30$	−7.08744	−	4.41132i	−1.29398	−	0.805393i
$31$	−3.31731	+	1.91525i	−0.595807	+	0.343989i	−0.767390	−	0.641180i	$-0.778445\pi$
$31$	−3.31731	+	1.91525i	−0.595807	+	0.343989i	0.171583	+	0.985170i	$0.445112\pi$
$32$	−1.77124	+	5.37240i	−0.313113	+	0.949716i
$33$	1.83944	−	4.49634i	0.320205	−	0.782713i
$34$	−2.79630	−	0.475438i	−0.479561	−	0.0815370i
$35$	6.47988	−	6.27040i	1.09530	−	1.05989i
$36$	−0.397370	+	5.98683i	−0.0662284	+	0.997804i
$37$	−4.20434	+	1.12655i	−0.691189	+	0.185203i	−0.587281	−	0.809383i	$-0.699801\pi$
$37$	−4.20434	+	1.12655i	−0.691189	+	0.185203i	−0.103908	+	0.994587i	$0.533135\pi$
$38$	−1.89217	+	4.12347i	−0.306951	+	0.668915i
$39$	−8.78992	+	6.80605i	−1.40751	+	1.08984i
$40$	9.35537	+	2.32357i	1.47921	+	0.367388i
$41$		−	8.67639i		−	1.35502i	−0.735512	−	0.677512i	$-0.763058\pi$
$41$		−	8.67639i		−	1.35502i	0.735512	−	0.677512i	$-0.236942\pi$
$42$	−6.16912	−	1.98543i	−0.951916	−	0.306359i
$43$	4.52927	+	4.52927i	0.690707	+	0.690707i	0.962388	−	0.271680i	$-0.0875794\pi$
$43$	4.52927	+	4.52927i	0.690707	+	0.690707i	−0.271680	+	0.962388i	$0.587579\pi$
$44$	−0.420481	+	5.59381i	−0.0633898	+	0.843299i
$45$	10.2240	−	0.0894710i	1.52410	−	0.0133376i
$46$	−0.841136	−	2.26773i	−0.124019	−	0.334358i
$47$	−5.17739	+	8.96750i	−0.755200	+	1.30804i	0.190075	+	0.981770i	$0.439127\pi$
$47$	−5.17739	+	8.96750i	−0.755200	+	1.30804i	−0.945275	+	0.326275i	$0.894206\pi$
$48$	−1.69405	−	6.71790i	−0.244514	−	0.969646i
$49$	3.69725	−	5.94393i	0.528178	−	0.849133i
$50$	1.56813	−	9.22301i	0.221768	−	1.30433i
$51$	3.20362	−	1.34343i	0.448596	−	0.188118i
$52$	7.23357	−	10.6045i	1.00312	−	1.47058i
$53$	5.54861	+	1.48675i	0.762161	+	0.204220i	0.618905	−	0.785465i	$-0.287576\pi$
$53$	5.54861	+	1.48675i	0.762161	+	0.204220i	0.143255	+	0.989686i	$0.454243\pi$
$54$	−3.51796	−	6.45167i	−0.478733	−	0.877960i
$55$	9.55907			1.28894
$56$	7.48330	−	0.0144457i	0.999998	−	0.00193039i
$57$	−0.749369	−	5.50576i	−0.0992564	−	0.729256i
$58$	4.13944	−	0.387693i	0.543535	−	0.0509065i
$59$	−1.75857	+	6.56309i	−0.228947	+	0.854441i	0.751838	+	0.659348i	$0.229168\pi$
$59$	−1.75857	+	6.56309i	−0.228947	+	0.854441i	−0.980785	+	0.195093i	$0.937499\pi$
$60$	−11.1991	+	3.73672i	−1.44580	+	0.482408i
$61$	2.03278	−	0.544681i	0.260271	−	0.0697393i	−0.126324	−	0.991989i	$-0.540318\pi$
$61$	2.03278	−	0.544681i	0.260271	−	0.0697393i	0.386595	+	0.922250i	$0.373651\pi$
$62$	−0.908015	+	5.34051i	−0.115318	+	0.678245i
$63$	7.68234	−	1.99540i	0.967884	−	0.251396i
$64$	4.25162	+	6.77670i	0.531453	+	0.847088i
$65$	−18.9438	−	10.9372i	−2.34969	−	1.35659i
$66$	−3.23614	−	6.06042i	−0.398341	−	0.745986i
$67$	−3.10476	−	0.831917i	−0.379306	−	0.101635i	0.0641280	−	0.997942i	$-0.479573\pi$
$67$	−3.10476	−	0.831917i	−0.379306	−	0.101635i	−0.443434	+	0.896307i	$0.646240\pi$
$68$	−3.04106	+	2.61584i	−0.368783	+	0.317217i
$69$	2.35801	+	1.79303i	0.283871	+	0.215855i
$70$	−0.980402	−	12.7143i	−0.117181	−	1.51964i
$71$	−12.8919			−1.52999			−0.764995	−	0.644037i	$-0.777258\pi$
$71$	−12.8919			−1.52999			−0.764995	+	0.644037i	$0.777258\pi$
$72$	6.16043	+	5.83516i	0.726013	+	0.687680i
$73$	−0.0186751	−	0.0323462i	−0.00218575	−	0.00378583i	0.864930	−	0.501892i	$-0.167362\pi$
$73$	−0.0186751	−	0.0323462i	−0.00218575	−	0.00378583i	−0.867116	+	0.498106i	$0.834029\pi$
$74$	−2.56727	+	5.59466i	−0.298439	+	0.650366i
$75$	4.43104	+	10.5665i	0.511652	+	1.22011i
$76$	2.78253	+	5.78136i	0.319178	+	0.663167i
$77$	7.19852	−	1.80264i	0.820347	−	0.205429i
$78$	−0.520896	+	15.7130i	−0.0589798	+	1.77915i
$79$	1.41020	−	2.44253i	0.158660	−	0.274806i	−0.775726	−	0.631070i	$-0.782616\pi$
$79$	1.41020	−	2.44253i	0.158660	−	0.274806i	0.934386	+	0.356263i	$0.115949\pi$
$80$	10.9723	−	8.09023i	1.22674	−	0.904515i
$81$	7.87179	+	4.36290i	0.874643	+	0.484767i
$82$	−9.44766	−	7.82951i	−1.04332	−	0.864624i
$83$	−5.54643	+	5.54643i	−0.608800	+	0.608800i	−0.942632	−	0.333833i	$-0.891658\pi$
$83$	−5.54643	+	5.54643i	−0.608800	+	0.608800i	0.333833	+	0.942632i	$0.391658\pi$
$84$	−7.72889	+	4.92587i	−0.843291	+	0.537457i
$85$	4.83344	+	4.83344i	0.524260	+	0.524260i
$86$	9.01907	−	0.844710i	0.972551	−	0.0910874i
$87$	−4.02611	+	3.11743i	−0.431644	+	0.334223i
$88$	5.71162	+	5.50567i	0.608861	+	0.586906i
$89$	−2.36808	−	1.36721i	−0.251016	−	0.144924i	0.369214	−	0.929345i	$-0.379627\pi$
$89$	−2.36808	−	1.36721i	−0.251016	−	0.144924i	−0.620229	+	0.784421i	$0.712960\pi$
$90$	9.12860	−	11.2135i	0.962238	−	1.18201i
$91$	−16.3283	−	4.66394i	−1.71167	−	0.488914i
$92$	−3.22835	−	1.13047i	−0.336579	−	0.117860i
$93$	−2.56576	−	6.11843i	−0.266057	−	0.634452i
$94$	5.09261	+	13.7298i	0.525263	+	1.41612i
$95$	9.46864	−	5.46672i	0.971462	−	0.560874i
$96$	−8.84377	−	4.21755i	−0.902613	−	0.430452i
$97$		−	2.90039i		−	0.294490i	−0.989100	−	0.147245i	$-0.952959\pi$
$97$		−	2.90039i		−	0.294490i	0.989100	−	0.147245i	$-0.0470407\pi$
$98$	−3.13594	−	9.38967i	−0.316777	−	0.948500i
$99$	7.32361	+	4.14326i	0.736050	+	0.416414i
$100$	−8.62780	−	10.0303i	−0.862780	−	1.00303i
$101$	−4.44041	+	16.5718i	−0.441837	+	1.64896i	0.282317	+	0.959321i	$0.408897\pi$
$101$	−4.44041	+	16.5718i	−0.441837	+	1.64896i	−0.724154	+	0.689638i	$0.757770\pi$
$102$	1.42807	−	4.70070i	0.141400	−	0.465439i
$103$	−0.167609	+	0.290308i	−0.0165150	+	0.0286049i	−0.874165	−	0.485629i	$-0.838590\pi$
$103$	−0.167609	+	0.290308i	−0.0165150	+	0.0286049i	0.857650	+	0.514234i	$0.171924\pi$
$104$	−5.01965	−	17.4460i	−0.492217	−	1.71072i
$105$	9.35758	+	12.5042i	0.913207	+	1.22029i
$106$	6.62594	−	4.70022i	0.643568	−	0.456525i
$107$	−4.85598	−	18.1228i	−0.469445	−	1.75199i	−0.641715	−	0.766944i	$-0.721777\pi$
$107$	−4.85598	−	18.1228i	−0.469445	−	1.75199i	0.172269	−	0.985050i	$-0.444890\pi$
$108$	−10.1997	−	1.99126i	−0.981471	−	0.191609i
$109$	−8.77706	−	2.35180i	−0.840689	−	0.225262i	−0.187318	−	0.982299i	$-0.559979\pi$
$109$	−8.77706	−	2.35180i	−0.840689	−	0.225262i	−0.653372	+	0.757037i	$0.726646\pi$
$110$	8.62603	−	10.4088i	0.822460	−	0.992440i
$111$	−1.01673	−	7.47014i	−0.0965040	−	0.709034i
$112$	6.73715	−	8.16155i	0.636600	−	0.771194i
$113$			0.668582i			0.0628949i	0.999505	+	0.0314475i	$0.0100117\pi$
$113$			0.668582i			0.0628949i	−0.999505	+	0.0314475i	$0.989988\pi$
$114$	−6.67141	−	4.15238i	−0.624835	−	0.388906i
$115$	−1.50861	+	5.63021i	−0.140679	+	0.525020i
$116$	3.31324	−	4.85726i	0.307627	−	0.450985i
$117$	−9.77305	−	16.5904i	−0.903519	−	1.53379i
$118$	5.55958	+	7.83738i	0.511800	+	0.721489i
$119$	4.55133	+	2.72837i	0.417220	+	0.250109i
$120$	−6.03710	+	15.5666i	−0.551109	+	1.42103i
$121$	−2.71336	−	1.56656i	−0.246669	−	0.142415i
$122$	1.24126	−	2.70499i	0.112379	−	0.244899i
$123$	14.9078	+	1.89633i	1.34419	+	0.170986i
$124$	4.99586	+	5.80797i	0.448641	+	0.521571i
$125$	−3.89258	+	3.89258i	−0.348163	+	0.348163i
$126$	4.75972	−	10.1659i	0.424029	−	0.905649i
$127$	−0.163600			−0.0145171			−0.00725856	−	0.999974i	$-0.502310\pi$
$127$	−0.163600			−0.0145171			−0.00725856	+	0.999974i	$0.502310\pi$
$128$	11.2157	+	1.48569i	0.991340	+	0.131317i
$129$	−8.77214	+	6.79229i	−0.772344	+	0.598028i
$130$	−29.0042	+	10.7581i	−2.54384	+	0.943549i
$131$	4.16386	+	15.5397i	0.363798	+	1.35771i	0.869043	+	0.494737i	$0.164735\pi$
$131$	4.16386	+	15.5397i	0.363798	+	1.35771i	−0.505245	+	0.862976i	$0.668598\pi$
$132$	−9.51941	−	1.94507i	−0.828559	−	0.169296i
$133$	6.09951	−	5.90233i	0.528895	−	0.511797i
$134$	−3.70758	+	2.63003i	−0.320286	+	0.227200i
$135$	−2.08084	+	17.5864i	−0.179090	+	1.51360i
$136$	0.104136	+	5.67190i	0.00892962	+	0.486361i
$137$	0.568814	+	0.985215i	0.0485971	+	0.0841726i	0.889301	−	0.457323i	$-0.151192\pi$
$137$	0.568814	+	0.985215i	0.0485971	+	0.0841726i	−0.840704	+	0.541496i	$0.817858\pi$
$138$	4.08026	−	0.949605i	0.347335	−	0.0808358i
$139$	−4.36312	+	4.36312i	−0.370075	+	0.370075i	−0.867504	−	0.497430i	$-0.834277\pi$
$139$	−4.36312	+	4.36312i	−0.370075	+	0.370075i	0.497430	+	0.867504i	$0.334277\pi$
$140$	−14.7292	−	10.4057i	−1.24484	−	0.879442i
$141$	−14.2764	−	10.8558i	−1.20229	−	0.914221i
$142$	−11.6336	+	14.0379i	−0.976268	+	1.17804i
$143$	−9.00106	−	15.5903i	−0.752706	−	1.30373i
$144$	11.9130	−	1.44244i	0.992749	−	0.120203i
$145$	−8.67697	−	5.00965i	−0.720583	−	0.416029i
$146$	−0.0520737	−	0.00885379i	−0.00430965	−	0.000732745i
$147$	9.40482	+	7.65175i	0.775697	+	0.631106i
$148$	3.77530	+	7.84406i	0.310328	+	0.644778i
$149$	3.99255	+	14.9004i	0.327083	+	1.22069i	0.912202	+	0.409741i	$0.134381\pi$
$149$	3.99255	+	14.9004i	0.327083	+	1.22069i	−0.585119	+	0.810947i	$0.698952\pi$
$150$	15.5043	+	4.71018i	1.26592	+	0.384584i
$151$	2.15856	−	1.24625i	0.175661	−	0.101418i	−0.409591	−	0.912269i	$-0.634329\pi$
$151$	2.15856	−	1.24625i	0.175661	−	0.101418i	0.585253	+	0.810851i	$0.300995\pi$
$152$	8.80622	+	2.18718i	0.714279	+	0.177403i
$153$	1.60811	+	5.79810i	0.130008	+	0.468749i
$154$	4.53301	−	9.46510i	0.365280	−	0.762719i
$155$	9.23114	−	9.23114i	0.741463	−	0.741463i
$156$	16.6397	+	14.7465i	1.33224	+	1.18067i
$157$	6.08076	−	22.6937i	0.485297	−	1.81115i	−0.0934214	−	0.995627i	$-0.529780\pi$
$157$	6.08076	−	22.6937i	0.485297	−	1.81115i	0.578719	−	0.815527i	$-0.303553\pi$
$158$	−1.38710	−	3.73968i	−0.110352	−	0.297513i
$159$	−3.76725	+	9.20871i	−0.298763	+	0.730298i
$160$	1.09196	−	19.2483i	0.0863274	−	1.52171i
$161$	−0.0743310	+	4.52436i	−0.00585810	+	0.356569i
$162$	11.8542	−	4.63448i	0.931352	−	0.364119i
$163$	−2.06960	−	7.72387i	−0.162104	−	0.604980i	−0.998392	−	0.0566896i	$-0.981945\pi$
$163$	−2.06960	−	7.72387i	−0.162104	−	0.604980i	0.836288	−	0.548291i	$-0.184721\pi$
$164$	−17.0510	+	3.22219i	−1.33146	+	0.251611i
$165$	−2.08925	+	16.4244i	−0.162648	+	1.27864i
$166$	1.03441	+	11.0445i	0.0802858	+	0.857221i
$167$			21.7509i			1.68314i	0.540151	+	0.841568i	$0.318367\pi$
$167$			21.7509i			1.68314i	−0.540151	+	0.841568i	$0.681633\pi$
$168$	−1.61075	+	12.8610i	−0.124272	+	0.992248i
$169$			28.1950i			2.16885i
$170$	9.62475	−	0.901437i	0.738185	−	0.0691371i
$171$	9.62381	−	0.0842191i	0.735951	−	0.00644040i
$172$	7.21894	−	10.5831i	0.550439	−	0.806951i
$173$	3.39003	+	12.6518i	0.257739	+	0.961896i	0.966546	+	0.256493i	$0.0825672\pi$
$173$	3.39003	+	12.6518i	0.257739	+	0.961896i	−0.708807	+	0.705403i	$0.750766\pi$
$174$	−0.238590	+	7.19714i	−0.0180874	+	0.545614i
$175$	−8.99896	+	15.0116i	−0.680257	+	1.13477i
$176$	11.1492	−	1.25107i	0.840403	−	0.0943027i
$177$	−10.8924	−	4.45604i	−0.818721	−	0.334936i
$178$	−3.62568	+	1.34482i	−0.271756	+	0.100799i
$179$	0.516590	−	1.92794i	0.0386117	−	0.144101i	−0.943929	−	0.330149i	$-0.892901\pi$
$179$	0.516590	−	1.92794i	0.0386117	−	0.144101i	0.982541	+	0.186048i	$0.0595678\pi$
$180$	−3.97275	−	20.0591i	−0.296111	−	1.49511i
$181$	−6.81787	+	6.81787i	−0.506768	+	0.506768i	−0.913533	−	0.406765i	$-0.866657\pi$
$181$	−6.81787	+	6.81787i	−0.506768	+	0.506768i	0.406765	+	0.913533i	$0.366657\pi$
$182$	−19.8130	+	13.5710i	−1.46864	+	1.00595i
$183$	0.491586	+	3.61178i	0.0363391	+	0.266990i
$184$	−4.14420	+	2.49519i	−0.305515	+	0.183948i
$185$	12.8469	−	7.41716i	0.944523	−	0.545321i
$186$	−8.97763	−	2.72739i	−0.658272	−	0.199982i
$187$	1.45598	+	5.43378i	0.106472	+	0.397357i
$188$	19.5458	+	6.84439i	1.42553	+	0.499178i
$189$	1.74943	+	13.6360i	0.127252	+	0.991870i
$190$	2.59176	−	15.2435i	0.188026	−	1.10588i
$191$	12.5792	+	7.26260i	0.910198	+	0.525503i	0.880495	−	0.474056i	$-0.157210\pi$
$191$	12.5792	+	7.26260i	0.910198	+	0.525503i	0.0297031	+	0.999559i	$0.490544\pi$
$192$	−12.5730	+	5.82403i	−0.907379	+	0.420313i
$193$	11.9914	+	20.7697i	0.863160	+	1.49504i	0.868863	+	0.495053i	$0.164851\pi$
$193$	11.9914	+	20.7697i	0.863160	+	1.49504i	−0.00570281	+	0.999984i	$0.501815\pi$
$194$	−3.15822	−	2.61729i	−0.226747	−	0.187911i
$195$	22.9328	−	30.1589i	1.64225	−	2.15972i
$196$	−13.0542	−	5.05847i	−0.932442	−	0.361319i
$197$	4.27742	−	4.27742i	0.304754	−	0.304754i	−0.538117	−	0.842870i	$-0.680864\pi$
$197$	4.27742	−	4.27742i	0.304754	−	0.304754i	0.842870	+	0.538117i	$0.180864\pi$
$198$	11.1203	−	4.23577i	0.790288	−	0.301023i
$199$	−9.49769	−	16.4505i	−0.673274	−	1.16614i	−0.976970	−	0.213375i	$-0.931554\pi$
$199$	−9.49769	−	16.4505i	−0.673274	−	1.16614i	0.303697	−	0.952769i	$-0.401779\pi$
$200$	−18.7076	+	0.343472i	−1.32283	+	0.0242871i
$201$	2.10799	−	5.15278i	0.148686	−	0.363449i
$202$	14.0380	+	19.7894i	0.987707	+	1.39238i
$203$	−7.47896	−	2.13626i	−0.524920	−	0.149936i
$204$	−3.82989	−	5.79689i	−0.268146	−	0.405863i
$205$	7.65331	+	28.5625i	0.534530	+	1.99489i
$206$	0.164865	+	0.444480i	0.0114867	+	0.0309684i
$207$	−3.59616	+	3.65966i	−0.249950	+	0.254364i
$208$	−23.5265	−	10.2773i	−1.63127	−	0.712602i
$209$	8.99795			0.622402
$210$	22.0600	+	1.09432i	1.52228	+	0.0755154i
$211$	−0.836426	+	0.836426i	−0.0575819	+	0.0575819i	−0.735311	−	0.677729i	$-0.762964\pi$
$211$	−0.836426	+	0.836426i	−0.0575819	+	0.0575819i	0.677729	+	0.735311i	$0.262964\pi$
$212$	0.861163	−	11.4564i	0.0591449	−	0.786827i
$213$	2.81769	−	22.1510i	0.193065	−	1.51776i
$214$	−24.1157	−	11.0662i	−1.64852	−	0.756470i
$215$	−18.9055	−	10.9151i	−1.28934	−	0.744403i
$216$	−11.3724	+	9.30954i	−0.773797	+	0.633434i
$217$	5.21077	−	8.69236i	0.353730	−	0.590076i
$218$	−10.4812	+	7.43502i	−0.709877	+	0.503563i
$219$	0.0596590	−	0.0250180i	0.00403138	−	0.00169056i
$220$	−3.55000	−	18.7856i	−0.239341	−	1.26653i
$221$	3.33177	−	12.4343i	0.224119	−	0.836424i
$222$	−9.05167	−	5.63388i	−0.607508	−	0.378121i
$223$		−	16.6515i		−	1.11506i	−0.830155	−	0.557532i	$-0.811748\pi$
$223$		−	16.6515i		−	1.11506i	0.830155	−	0.557532i	$-0.188252\pi$
$224$	−2.80750	−	14.7010i	−0.187584	−	0.982249i
$225$	−19.1238	+	5.30401i	−1.27492	+	0.353600i
$226$	0.728014	+	0.603324i	0.0484268	+	0.0401325i
$227$	−4.44054	−	1.18984i	−0.294729	−	0.0789724i	0.108425	−	0.994105i	$-0.465419\pi$
$227$	−4.44054	−	1.18984i	−0.294729	−	0.0789724i	−0.403154	+	0.915132i	$0.632086\pi$
$228$	−10.5417	+	3.51738i	−0.698143	+	0.232944i
$229$	4.36609	+	16.2945i	0.288519	+	1.07677i	0.946229	+	0.323497i	$0.104859\pi$
$229$	4.36609	+	16.2945i	0.288519	+	1.07677i	−0.657710	+	0.753271i	$0.728475\pi$
$230$	4.76934	+	6.72338i	0.314481	+	0.443326i
$231$	1.52398	+	12.7625i	0.100270	+	0.839712i
$232$	−2.29919	−	7.99092i	−0.150949	−	0.524630i
$233$	−1.10118	+	1.90731i	−0.0721410	+	0.124952i	−0.899839	−	0.436221i	$-0.856316\pi$
$233$	−1.10118	+	1.90731i	−0.0721410	+	0.124952i	0.827698	+	0.561173i	$0.189650\pi$
$234$	−26.8843	−	4.32928i	−1.75748	−	0.283014i
$235$	9.13380	−	34.0878i	0.595823	−	2.22364i
$236$	13.5510	+	1.01861i	0.882094	+	0.0663061i
$237$	3.88856	+	2.95685i	0.252589	+	0.192068i
$238$	7.07799	−	2.49386i	0.458798	−	0.161653i
$239$			7.87372i			0.509308i	0.967032	+	0.254654i	$0.0819616\pi$
$239$			7.87372i			0.509308i	−0.967032	+	0.254654i	$0.918038\pi$
$240$	11.5025	+	20.6209i	0.742486	+	1.33108i
$241$	16.1012	−	9.29604i	1.03717	−	0.598811i	0.118140	−	0.992997i	$-0.462307\pi$
$241$	16.1012	−	9.29604i	1.03717	−	0.598811i	0.919031	+	0.394186i	$0.128973\pi$
$242$	−4.15434	+	1.54091i	−0.267051	+	0.0990534i
$243$	−9.21684	+	12.5718i	−0.591261	+	0.806480i
$244$	−1.82534	−	3.79257i	−0.116855	−	0.242794i
$245$	−6.92824	+	22.8286i	−0.442629	+	1.45847i
$246$	15.5176	−	14.5218i	0.989366	−	0.925875i
$247$	−17.8318	−	10.2952i	−1.13461	−	0.655068i
$248$	10.8325	−	0.198885i	0.687863	−	0.0126292i
$249$	−8.31767	−	10.7421i	−0.527111	−	0.680756i
$250$	0.725968	+	7.75125i	0.0459142	+	0.490232i
$251$	1.66865	+	1.66865i	0.105324	+	0.105324i	0.757805	−	0.652481i	$-0.226272\pi$
$251$	1.66865	+	1.66865i	0.105324	+	0.105324i	−0.652481	+	0.757805i	$0.726272\pi$
$252$	−6.77442	−	14.3564i	−0.426748	−	0.904370i
$253$	−3.39198	+	3.39198i	−0.213252	+	0.213252i
$254$	−0.147631	+	0.178142i	−0.00926320	+	0.0111777i
$255$	−9.36124	+	7.24843i	−0.586224	+	0.453914i
$256$	11.7387	−	10.8721i	0.733672	−	0.679504i
$257$	0.169419	−	0.293443i	0.0105681	−	0.0183045i	−0.860693	−	0.509124i	$-0.829969\pi$
$257$	0.169419	−	0.293443i	0.0105681	−	0.0183045i	0.871261	+	0.490820i	$0.163303\pi$
$258$	−0.519842	+	15.6812i	−0.0323640	+	0.976271i
$259$	8.27573	−	8.00820i	0.514229	−	0.497605i
$260$	−14.4587	+	41.2905i	−0.896693	+	2.56073i
$261$	−4.47642	−	7.59904i	−0.277084	−	0.470369i
$262$	20.6785	+	9.48894i	1.27752	+	0.586229i
$263$	−10.8012	−	18.7081i	−0.666028	−	1.15359i	−0.979006	−	0.203833i	$-0.934660\pi$
$263$	−10.8012	−	18.7081i	−0.666028	−	1.15359i	0.312978	−	0.949760i	$-0.398673\pi$
$264$	−10.7082	+	8.61041i	−0.659045	+	0.529934i
$265$	−19.5774			−1.20263
$266$	−0.922853	−	11.9679i	−0.0565838	−	0.733801i
$267$	2.86672	−	3.77002i	0.175440	−	0.230722i
$268$	−0.481868	+	6.41048i	−0.0294348	+	0.391582i
$269$	−29.8955	−	8.01046i	−1.82276	−	0.488407i	−0.825635	−	0.564204i	$-0.809183\pi$
$269$	−29.8955	−	8.01046i	−1.82276	−	0.488407i	−0.997123	+	0.0757976i	$0.975850\pi$
$270$	17.2720	+	18.1357i	1.05114	+	1.10370i
$271$	4.95578	+	2.86122i	0.301042	+	0.173807i	0.642911	−	0.765941i	$-0.277726\pi$
$271$	4.95578	+	2.86122i	0.301042	+	0.173807i	−0.341869	+	0.939748i	$0.611060\pi$
$272$	6.27006	+	5.00489i	0.380178	+	0.303466i
$273$	11.5824	−	27.0360i	0.700996	−	1.63629i
$274$	1.58609	+	0.269673i	0.0958190	+	0.0162915i
$275$	−17.9222	+	4.80224i	−1.08075	+	0.289586i
$276$	2.64798	−	5.29989i	0.159390	−	0.319016i
$277$	2.93902	−	10.9686i	0.176588	−	0.659037i	−0.819687	−	0.572811i	$-0.805853\pi$
$277$	2.93902	−	10.9686i	0.176588	−	0.659037i	0.996276	−	0.0862254i	$-0.0274805\pi$
$278$	0.813722	+	8.68821i	0.0488038	+	0.521084i
$279$	11.0735	−	3.07124i	0.662953	−	0.183870i
$280$	−24.6222	+	6.64846i	−1.47146	+	0.397322i
$281$	15.3960			0.918448			0.459224	−	0.888321i	$-0.348128\pi$
$281$	15.3960			0.918448			0.459224	+	0.888321i	$0.348128\pi$
$282$	−24.7037	+	5.74933i	−1.47109	+	0.342368i
$283$	−7.84008	−	2.10074i	−0.466044	−	0.124876i	0.0181526	−	0.999835i	$-0.494222\pi$
$283$	−7.84008	−	2.10074i	−0.466044	−	0.124876i	−0.484197	+	0.874959i	$0.660888\pi$
$284$	4.78774	+	25.3354i	0.284100	+	1.50338i
$285$	7.32346	+	17.4639i	0.433804	+	1.03447i
$286$	−25.0986	−	4.26737i	−1.48411	−	0.252335i
$287$	11.1497	+	20.0660i	0.658144	+	1.18446i
$288$	9.17953	−	14.2736i	0.540909	−	0.841081i
$289$	6.48867	−	11.2387i	0.381686	−	0.661100i
$290$	−13.2850	+	4.92762i	−0.780122	+	0.289360i
$291$	4.98347	+	0.633917i	0.292136	+	0.0371609i
$292$	−0.0566318	+	0.0487131i	−0.00331413	+	0.00285072i
$293$	−15.8827	−	15.8827i	−0.927878	−	0.927878i	0.0696911	−	0.997569i	$-0.477799\pi$
$293$	−15.8827	−	15.8827i	−0.927878	−	0.927878i	−0.997569	+	0.0696911i	$0.977799\pi$
$294$	16.8188	−	3.33596i	0.980891	−	0.194557i
$295$		−	23.1568i		−	1.34824i
$296$	11.9481	+	2.96753i	0.694472	+	0.172484i
$297$	−8.71964	+	11.6779i	−0.505965	+	0.677621i
$298$	19.8278	+	9.09855i	1.14859	+	0.527065i
$299$	10.6031	−	2.84109i	0.613193	−	0.164305i
$300$	19.1198	−	12.6321i	1.10388	−	0.729314i
$301$	−16.2953	−	4.65451i	−0.939243	−	0.268281i
$302$	0.590842	−	3.47505i	0.0339991	−	0.199966i
$303$	−27.5033	−	11.2515i	−1.58002	−	0.646383i
$304$	10.3283	−	7.61534i	0.592367	−	0.436769i
$305$	−6.21142	+	3.58617i	−0.355665	+	0.205343i
$306$	7.76465	+	3.48111i	0.443876	+	0.199002i
$307$	8.94432	+	8.94432i	0.510479	+	0.510479i	0.914673	−	0.404194i	$-0.132448\pi$
$307$	8.94432	+	8.94432i	0.510479	+	0.510479i	−0.404194	+	0.914673i	$0.632448\pi$
$308$	−6.21592	−	13.4772i	−0.354185	−	0.767935i
$309$	−0.462175	−	0.351437i	−0.0262922	−	0.0199926i
$310$	−1.72161	−	18.3818i	−0.0977808	−	1.04402i
$311$	17.3250	−	10.0026i	0.982412	−	0.567196i	0.0794146	−	0.996842i	$-0.474695\pi$
$311$	17.3250	−	10.0026i	0.982412	−	0.567196i	0.902998	+	0.429646i	$0.141362\pi$
$312$	31.0729	−	4.81175i	1.75916	−	0.272412i
$313$	−4.02341	+	6.96875i	−0.227417	+	0.393897i	−0.957042	−	0.289950i	$-0.906361\pi$
$313$	−4.02341	+	6.96875i	−0.227417	+	0.393897i	0.729625	+	0.683847i	$0.239695\pi$
$314$	−19.2238	−	27.0999i	−1.08486	−	1.52934i
$315$	−23.5301	+	13.3453i	−1.32577	+	0.751922i
$316$	−5.32382	−	1.86425i	−0.299488	−	0.104872i
$317$	19.9146	−	5.33610i	1.11852	−	0.299705i	0.348233	−	0.937408i	$-0.386782\pi$
$317$	19.9146	−	5.33610i	1.11852	−	0.299705i	0.770282	+	0.637703i	$0.220115\pi$
$318$	6.62776	+	12.4120i	0.371666	+	0.696031i
$319$	−4.12282	−	7.14093i	−0.230834	−	0.399815i
$320$	−19.9739	−	18.5585i	−1.11658	−	1.03745i
$321$	32.2000	−	4.38262i	1.79723	−	0.244614i
$322$	4.85947	+	4.16369i	0.270808	+	0.232033i
$323$	4.54972	+	4.54972i	0.253153	+	0.253153i
$324$	5.65067	−	17.0901i	0.313926	−	0.949447i
$325$	41.0121	+	10.9892i	2.27494	+	0.609569i
$326$	−10.2781	−	4.71639i	−0.569249	−	0.261216i
$327$	5.95922	−	14.5668i	0.329545	−	0.805544i
$328$	−11.8781	+	21.4744i	−0.655856	+	1.18572i
$329$	0.450033	−	27.3925i	0.0248111	−	1.51020i
$330$	15.9991	+	17.0963i	0.880723	+	0.941118i
$331$	12.9717	−	3.47575i	0.712988	−	0.191045i	0.115947	−	0.993255i	$-0.463010\pi$
$331$	12.9717	−	3.47575i	0.712988	−	0.191045i	0.597041	+	0.802211i	$0.296343\pi$
$332$	12.9597	+	8.84013i	0.711259	+	0.485165i
$333$	13.0574	−	0.114267i	0.715544	−	0.00626181i
$334$	23.6844	+	19.6279i	1.29595	+	1.07399i
$335$	10.9546			0.598516
$336$	12.5507	+	13.3596i	0.684699	+	0.728826i
$337$	−1.65822			−0.0903291			−0.0451646	−	0.998980i	$-0.514381\pi$
$337$	−1.65822			−0.0903291			−0.0451646	+	0.998980i	$0.514381\pi$
$338$	30.7013	+	25.4430i	1.66993	+	1.38391i
$339$	−1.14876	−	0.146127i	−0.0623922	−	0.00793652i
$340$	7.70374	−	11.2938i	0.417794	−	0.612491i
$341$	10.3777	−	2.78070i	0.561984	−	0.150583i
$342$	8.59275	−	10.5553i	0.464643	−	0.570765i
$343$	−0.912360	+	18.4978i	−0.0492628	+	0.998786i
$344$	−5.00950	−	17.4107i	−0.270094	−	0.938724i
$345$	−9.34414	−	3.82265i	−0.503071	−	0.205805i
$346$	16.8356	+	7.72548i	0.905085	+	0.415324i
$347$	8.96682	+	2.40265i	0.481364	+	0.128981i	0.491338	−	0.870969i	$-0.336508\pi$
$347$	8.96682	+	2.40265i	0.481364	+	0.128981i	−0.00997366	+	0.999950i	$0.503175\pi$
$348$	7.62162	+	6.75445i	0.408562	+	0.362076i
$349$	−7.34726	−	7.34726i	−0.393290	−	0.393290i	0.482568	−	0.875858i	$-0.339704\pi$
$349$	−7.34726	−	7.34726i	−0.393290	−	0.393290i	−0.875858	+	0.482568i	$0.839704\pi$
$350$	8.22547	+	23.3453i	0.439670	+	1.24786i
$351$	30.6418	−	13.1661i	1.63554	−	0.702753i
$352$	8.69869	−	13.2692i	0.463642	−	0.707253i
$353$	−10.2706	−	17.7891i	−0.546647	−	0.946821i	−0.998501	−	0.0547287i	$-0.982571\pi$
$353$	−10.2706	−	17.7891i	−0.546647	−	0.946821i	0.451854	−	0.892092i	$-0.350763\pi$
$354$	−14.6813	+	7.83954i	−0.780305	+	0.416667i
$355$	42.4400	−	11.3718i	2.25248	−	0.603551i
$356$	−1.80742	+	5.16153i	−0.0957930	+	0.273561i
$357$	−5.68265	+	7.22381i	−0.300758	+	0.382325i
$358$	−1.63315	−	2.30227i	−0.0863148	−	0.121679i
$359$	8.60731	−	14.9083i	0.454277	−	0.786830i	−0.544370	−	0.838845i	$-0.683231\pi$
$359$	8.60731	−	14.9083i	0.454277	−	0.786830i	0.998646	+	0.0520153i	$0.0165645\pi$
$360$	−25.4272	−	13.7753i	−1.34013	−	0.726019i
$361$	−7.54165	+	4.35417i	−0.396929	+	0.229167i
$362$	1.27153	+	13.5763i	0.0668304	+	0.713556i
$363$	3.28471	−	4.31973i	0.172403	−	0.226727i
$364$	−3.10174	+	33.8207i	−0.162575	+	1.77269i
$365$	0.0900101	+	0.0900101i	0.00471135	+	0.00471135i
$366$	4.37644	+	2.72396i	0.228760	+	0.142384i
$367$	−22.2690	+	12.8570i	−1.16243	+	0.671132i	−0.951886	−	0.306452i	$-0.900858\pi$
$367$	−22.2690	+	12.8570i	−1.16243	+	0.671132i	−0.210548	+	0.977584i	$0.567525\pi$
$368$	−1.02270	+	6.76424i	−0.0533119	+	0.352610i
$369$	−6.51657	+	25.2002i	−0.339239	+	1.31187i
$370$	3.51646	−	20.6821i	0.182812	−	1.07521i
$371$	−14.7429	+	3.69188i	−0.765413	+	0.191673i
$372$	−11.0712	+	7.31450i	−0.574014	+	0.379239i
$373$	−16.9844	+	4.55097i	−0.879421	+	0.235640i	−0.670157	−	0.742219i	$-0.733773\pi$
$373$	−16.9844	+	4.55097i	−0.879421	+	0.235640i	−0.209264	+	0.977859i	$0.567107\pi$
$374$	7.23066	+	3.31800i	0.373889	+	0.171570i
$375$	−5.83749	−	7.53903i	−0.301447	−	0.389314i
$376$	25.0908	−	15.1070i	1.29396	−	0.779084i
$377$			18.8688i			0.971795i
$378$	16.4268	+	10.4000i	0.844902	+	0.534921i
$379$	−4.92976	−	4.92976i	−0.253225	−	0.253225i	0.569067	−	0.822291i	$-0.307305\pi$
$379$	−4.92976	−	4.92976i	−0.253225	−	0.253225i	−0.822291	+	0.569067i	$0.807305\pi$
$380$	−14.2597	−	16.5777i	−0.731508	−	0.850419i
$381$	0.0357567	−	0.281098i	0.00183187	−	0.0144011i
$382$	19.2596	−	7.14367i	0.985404	−	0.365502i
$383$	8.53248	−	14.7787i	0.435989	−	0.755156i	−0.561386	−	0.827554i	$-0.689732\pi$
$383$	8.53248	−	14.7787i	0.435989	−	0.755156i	0.997376	+	0.0723980i	$0.0230652\pi$
$384$	−5.00405	+	18.9462i	−0.255362	+	0.966846i
$385$	−22.1073	+	12.2840i	−1.12669	+	0.626048i
$386$	33.4369	+	5.68509i	1.70190	+	0.289363i
$387$	−9.75329	−	16.5569i	−0.495788	−	0.841634i
$388$	−5.69991	+	1.07713i	−0.289369	+	0.0546832i
$389$	22.3954	+	6.00083i	1.13549	+	0.304254i	0.777137	−	0.629331i	$-0.216671\pi$
$389$	22.3954	+	6.00083i	1.13549	+	0.304254i	0.358355	+	0.933585i	$0.383338\pi$
$390$	−12.1454	−	52.1865i	−0.615008	−	2.64257i
$391$	−3.43023			−0.173474
$392$	−17.2881	+	9.64989i	−0.873183	+	0.487393i
$393$	−27.6105	+	3.75797i	−1.39277	+	0.189564i
$394$	−0.797740	−	8.51757i	−0.0401896	−	0.429109i
$395$	−2.48783	+	9.28470i	−0.125176	+	0.467164i
$396$	5.42261	−	15.9312i	0.272496	−	0.800573i
$397$	−25.5598	+	6.84872i	−1.28281	+	0.343728i	−0.834925	−	0.550364i	$-0.814489\pi$
$397$	−25.5598	+	6.84872i	−1.28281	+	0.343728i	−0.447884	+	0.894092i	$0.647822\pi$
$398$	−26.4835	−	4.50283i	−1.32750	−	0.225706i
$399$	8.80830	+	11.7702i	0.440966	+	0.589249i
$400$	−16.5076	+	20.6805i	−0.825379	+	1.03403i
$401$	−17.4150	−	10.0545i	−0.869662	−	0.502100i	−0.00242636	−	0.999997i	$-0.500772\pi$
$401$	−17.4150	−	10.0545i	−0.869662	−	0.502100i	−0.867236	+	0.497897i	$0.834106\pi$
$402$	−3.70860	−	6.94521i	−0.184968	−	0.346395i
$403$	−23.7477	−	6.36318i	−1.18296	−	0.316973i
$404$	34.2163	+	2.57200i	1.70233	+	0.127962i
$405$	−29.7623	−	7.41903i	−1.47890	−	0.368655i
$406$	−9.07511	+	6.21604i	−0.450390	+	0.308497i
$407$	12.2083			0.605143
$408$	−9.76825	−	1.06074i	−0.483600	−	0.0525142i
$409$	10.7088	+	18.5481i	0.529514	+	0.917145i	0.999407	+	0.0344216i	$0.0109589\pi$
$409$	10.7088	+	18.5481i	0.529514	+	0.917145i	−0.469894	+	0.882723i	$0.655708\pi$
$410$	38.0078	+	17.4410i	1.87707	+	0.861349i
$411$	−1.81712	+	0.762009i	−0.0896321	+	0.0375871i
$412$	0.632763	+	0.221575i	0.0311740	+	0.0109162i
$413$	−4.36688	−	17.4384i	−0.214880	−	0.858087i
$414$	0.739826	+	7.21828i	0.0363604	+	0.354759i
$415$	13.3663	−	23.1512i	0.656128	−	1.13645i
$416$	−32.4210	+	16.3437i	−1.58957	+	0.801317i
$417$	−6.54312	−	8.45034i	−0.320418	−	0.413815i
$418$	8.11969	−	9.79781i	0.397147	−	0.479226i
$419$	−3.78223	+	3.78223i	−0.184774	+	0.184774i	−0.793432	−	0.608659i	$-0.791708\pi$
$419$	−3.78223	+	3.78223i	−0.184774	+	0.184774i	0.608659	+	0.793432i	$0.291708\pi$
$420$	21.0984	−	23.0334i	1.02949	−	1.12392i
$421$	−21.5539	−	21.5539i	−1.05047	−	1.05047i	−0.998657	−	0.0518156i	$-0.983499\pi$
$421$	−21.5539	−	21.5539i	−1.05047	−	1.05047i	−0.0518156	−	0.998657i	$-0.516501\pi$
$422$	0.155994	+	1.66556i	0.00759365	+	0.0810783i
$423$	21.7727	−	22.1572i	1.05863	−	1.07732i
$424$	−11.6977	−	11.2759i	−0.568088	−	0.547604i
$425$	−11.4904	−	6.63396i	−0.557364	−	0.321794i
$426$	−21.5774	−	23.0570i	−1.04543	−	1.11712i
$427$	−4.00128	+	3.87193i	−0.193635	+	0.187376i
$428$	−33.8118	+	16.2734i	−1.63435	+	0.786604i
$429$	28.7546	−	12.0582i	1.38829	−	0.582176i
$430$	−28.9455	+	10.7364i	−1.39588	+	0.517753i
$431$	9.70531	−	5.60337i	0.467488	−	0.269905i	−0.247699	−	0.968837i	$-0.579674\pi$
$431$	9.70531	−	5.60337i	0.467488	−	0.269905i	0.715188	+	0.698932i	$0.246341\pi$
$432$	−0.125322	+	20.7842i	−0.00602955	+	0.999982i
$433$			36.0374i			1.73185i	0.500178	+	0.865923i	$0.333268\pi$
$433$			36.0374i			1.73185i	−0.500178	+	0.865923i	$0.666732\pi$
$434$	−4.76289	−	13.5179i	−0.228626	−	0.648880i
$435$	10.5041	−	13.8139i	0.503631	−	0.662325i
$436$	−1.36223	+	18.1222i	−0.0652389	+	0.867897i
$437$	−1.42006	+	5.29972i	−0.0679305	+	0.253520i
$438$	0.0265940	−	0.0875383i	0.00127071	−	0.00418274i
$439$	−1.66600	+	2.88560i	−0.0795139	+	0.137722i	−0.903040	−	0.429556i	$-0.858670\pi$
$439$	−1.66600	+	2.88560i	−0.0795139	+	0.137722i	0.823526	+	0.567278i	$0.192003\pi$
$440$	−23.6590	−	13.0865i	−1.12790	−	0.623872i
$441$	−15.2028	+	14.4870i	−0.723944	+	0.689859i
$442$	−10.5331	−	14.8486i	−0.501008	−	0.706276i
$443$	2.03947	+	7.61140i	0.0968981	+	0.361629i	0.997300	−	0.0734297i	$-0.0233944\pi$
$443$	2.03947	+	7.61140i	0.0968981	+	0.361629i	−0.900402	+	0.435058i	$0.856728\pi$
$444$	−14.3029	+	4.77233i	−0.678783	+	0.226485i
$445$	9.00167	+	2.41199i	0.426720	+	0.114339i
$446$	−18.1317	−	15.0262i	−0.858559	−	0.711509i
$447$	−26.4746	+	3.60336i	−1.25220	+	0.170433i
$448$	−18.5412	−	10.2090i	−0.875991	−	0.482328i
$449$			23.0694i			1.08871i	0.838854	+	0.544357i	$0.183226\pi$
$449$			23.0694i			1.08871i	−0.838854	+	0.544357i	$0.816774\pi$
$450$	−11.4817	+	25.6101i	−0.541253	+	1.20727i
$451$	−6.29849	+	23.5063i	−0.296584	+	1.10687i
$452$	1.31391	−	0.248295i	0.0618011	−	0.0116788i
$453$	1.66953	+	3.98124i	0.0784413	+	0.187055i
$454$	−5.30272	+	3.76157i	−0.248869	+	0.176539i
$455$	57.8665	+	0.950692i	2.71282	+	0.0445691i
$456$	−5.68273	+	14.6529i	−0.266118	+	0.686183i
$457$	20.8225	+	12.0219i	0.974035	+	0.562360i	0.900464	−	0.434930i	$-0.143227\pi$
$457$	20.8225	+	12.0219i	0.974035	+	0.562360i	0.0735712	+	0.997290i	$0.476560\pi$
$458$	21.6829	+	9.94980i	1.01317	+	0.464924i
$459$	−10.3138	+	1.49581i	−0.481407	+	0.0698185i
$460$	11.6249	+	0.873827i	0.542011	+	0.0407424i
$461$	−15.4876	+	15.4876i	−0.721327	+	0.721327i	−0.968876	−	0.247548i	$-0.920375\pi$
$461$	−15.4876	+	15.4876i	−0.721327	+	0.721327i	0.247548	+	0.968876i	$0.420375\pi$
$462$	15.2722	+	9.85736i	0.710529	+	0.458606i
$463$	13.3594			0.620863			0.310431	−	0.950596i	$-0.399527\pi$
$463$	13.3594			0.620863			0.310431	+	0.950596i	$0.399527\pi$
$464$	−10.7760	−	4.70738i	−0.500264	−	0.218535i
$465$	13.8434	+	17.8786i	0.641973	+	0.829099i
$466$	1.08315	+	2.92021i	0.0501761	+	0.135276i
$467$	−6.51376	−	24.3097i	−0.301421	−	1.12492i	−0.935983	−	0.352046i	$-0.885486\pi$
$467$	−6.51376	−	24.3097i	−0.301421	−	1.12492i	0.634562	−	0.772872i	$-0.281181\pi$
$468$	−28.9743	+	25.3675i	−1.33934	+	1.17261i
$469$	8.24946	−	2.06581i	0.380925	−	0.0953903i
$470$	−28.8757	−	40.7063i	−1.33194	−	1.87764i
$471$	37.6634	+	15.4080i	1.73544	+	0.709962i
$472$	13.3375	−	13.8364i	0.613907	−	0.636871i
$473$	−8.98285	−	15.5588i	−0.413032	−	0.715393i
$474$	6.72870	−	1.56598i	0.309059	−	0.0719278i
$475$	−15.0063	+	15.0063i	−0.688536	+	0.688536i
$476$	3.67158	−	9.95761i	0.168287	−	0.456406i
$477$	−14.9991	−	8.48559i	−0.686761	−	0.388529i
$478$	8.57363	+	7.10518i	0.392149	+	0.324983i
$479$	5.69052	+	9.85626i	0.260006	+	0.450344i	0.966243	−	0.257631i	$-0.0829420\pi$
$479$	5.69052	+	9.85626i	0.260006	+	0.450344i	−0.706237	+	0.707975i	$0.749609\pi$
$480$	32.8338	+	6.08316i	1.49865	+	0.277657i
$481$	−24.1939	−	13.9684i	−1.10315	−	0.636903i
$482$	4.40723	−	25.9212i	0.200744	−	1.18068i
$483$	−7.75753	−	1.11657i	−0.352980	−	0.0508057i
$484$	−2.07096	+	5.91413i	−0.0941344	+	0.268824i
$485$	2.55839	+	9.54806i	0.116171	+	0.433555i
$486$	5.37212	+	21.3808i	0.243684	+	0.969855i
$487$	22.3661	−	12.9131i	1.01350	−	0.585147i	0.101288	−	0.994857i	$-0.467704\pi$
$487$	22.3661	−	12.9131i	1.01350	−	0.585147i	0.912216	+	0.409710i	$0.134370\pi$
$488$	−5.77688	−	1.43479i	−0.261507	−	0.0649498i
$489$	13.7235	−	1.86786i	0.620600	−	0.0844676i
$490$	18.6059	+	28.1445i	0.840531	+	1.27144i
$491$	−18.7243	+	18.7243i	−0.845016	+	0.845016i	−0.989506	−	0.144490i	$-0.953846\pi$
$491$	−18.7243	+	18.7243i	−0.845016	+	0.845016i	0.144490	+	0.989506i	$0.453846\pi$
$492$	−1.80969	−	30.0014i	−0.0815872	−	1.35257i
$493$	1.52608	−	5.69539i	0.0687310	−	0.256508i
$494$	−27.3017	+	10.1266i	−1.22836	+	0.455618i
$495$	−27.7639	−	7.17952i	−1.24790	−	0.322696i
$496$	9.55858	−	11.9749i	0.429193	−	0.537688i
$497$	29.8153	−	16.5669i	1.33740	−	0.743126i
$498$	−19.2028	−	0.636586i	−0.860500	−	0.0285261i
$499$	7.68601	+	28.6846i	0.344073	+	1.28410i	0.893692	+	0.448682i	$0.148106\pi$
$499$	7.68601	+	28.6846i	0.344073	+	1.28410i	−0.549619	+	0.835416i	$0.685227\pi$
$500$	9.09539	+	6.20417i	0.406758	+	0.277459i
$501$	−37.3725	−	4.75393i	−1.66968	−	0.212390i
$502$	3.32276	−	0.311204i	0.148302	−	0.0138897i
$503$			6.45574i			0.287847i	0.989589	+	0.143924i	$0.0459719\pi$
$503$			6.45574i			0.287847i	−0.989589	+	0.143924i	$0.954028\pi$
$504$	−21.7458	−	5.57852i	−0.968635	−	0.248487i
$505$		−	58.4711i		−	2.60193i
$506$	0.632604	+	6.75439i	0.0281227	+	0.300269i
$507$	−48.4448	−	6.16236i	−2.15151	−	0.273680i
$508$	0.0607568	+	0.321509i	0.00269565	+	0.0142646i
$509$	3.77710	+	14.0963i	0.167417	+	0.624808i	0.997720	+	0.0674956i	$0.0215009\pi$
$509$	3.77710	+	14.0963i	0.167417	+	0.624808i	−0.830303	+	0.557313i	$0.811832\pi$
$510$	−0.554753	+	16.7343i	−0.0245649	+	0.741008i
$511$	0.0847567	+	0.0508087i	0.00374942	+	0.00224765i
$512$	−1.24555	−	22.5931i	−0.0550461	−	0.998484i
$513$	−1.95870	+	16.5541i	−0.0864785	+	0.730881i
$514$	−0.166645	−	0.449280i	−0.00735040	−	0.0198169i
$515$	0.295691	−	1.10353i	0.0130297	−	0.0486275i
$516$	16.6061	+	14.7167i	0.731042	+	0.647866i
$517$	20.5365	−	20.5365i	0.903195	−	0.903195i
$518$	−1.25211	−	16.2379i	−0.0550147	−	0.713453i
$519$	−22.4793	+	3.05957i	−0.986730	+	0.134300i
$520$	31.9135	+	53.0043i	1.39950	+	2.32439i
$521$	7.21181	−	4.16374i	0.315955	−	0.182417i	−0.333633	−	0.942703i	$-0.608275\pi$
$521$	7.21181	−	4.16374i	0.315955	−	0.182417i	0.649588	+	0.760286i	$0.274941\pi$
$522$	−12.3140	−	1.98297i	−0.538970	−	0.0867922i
$523$	−3.72384	−	13.8976i	−0.162832	−	0.607698i	−0.998307	−	0.0581689i	$-0.981474\pi$
$523$	−3.72384	−	13.8976i	−0.162832	−	0.607698i	0.835475	−	0.549529i	$-0.185193\pi$
$524$	28.9926	−	13.9540i	1.26655	−	0.609582i
$525$	−23.8262	−	18.7430i	−1.03986	−	0.818013i
$526$	−30.1180	−	5.12079i	−1.31321	−	0.223277i
$527$	6.65340	+	3.84134i	0.289826	+	0.167331i
$528$	−0.287207	+	19.4301i	−0.0124991	+	0.845585i
$529$	10.0375	+	17.3854i	0.436412	+	0.755888i
$530$	−17.6665	+	21.3177i	−0.767384	+	0.925981i
$531$	10.0370	−	17.7414i	0.435571	−	0.769912i
$532$	−13.8646	−	9.79489i	−0.601106	−	0.424662i
$533$	39.3773	−	39.3773i	1.70562	−	1.70562i
$534$	−1.51824	−	6.52359i	−0.0657008	−	0.282303i
$535$	31.9716	+	55.3765i	1.38225	+	2.39413i
$536$	6.54549	+	6.30947i	0.282722	+	0.272528i
$537$	3.19969	+	1.30898i	0.138077	+	0.0564868i
$538$	−35.7000	+	25.3244i	−1.53914	+	1.09181i
$539$	−14.3316	+	13.4195i	−0.617305	+	0.578018i
$540$	35.3339	−	2.44185i	1.52053	−	0.105081i
$541$	−0.810778	−	3.02586i	−0.0348581	−	0.130092i	0.946304	−	0.323278i	$-0.104785\pi$
$541$	−0.810778	−	3.02586i	−0.0348581	−	0.130092i	−0.981162	+	0.193186i	$0.938118\pi$
$542$	7.58763	−	2.81437i	0.325916	−	0.120888i
$543$	−10.2244	−	13.2046i	−0.438770	−	0.566665i
$544$	11.1078	−	2.31105i	0.476245	−	0.0990856i
$545$	30.9684			1.32654
$546$	−18.9875	−	37.0090i	−0.812588	−	1.58384i
$547$	6.31808	−	6.31808i	0.270142	−	0.270142i	−0.559015	−	0.829157i	$-0.688821\pi$
$547$	6.31808	−	6.31808i	0.270142	−	0.270142i	0.829157	+	0.559015i	$0.188821\pi$
$548$	1.72492	−	1.48373i	0.0736849	−	0.0633817i
$549$	−6.31322	+	0.0552477i	−0.269442	+	0.00235792i
$550$	−10.9437	+	23.8488i	−0.466642	+	1.01692i
$551$	−8.16763	−	4.71559i	−0.347953	−	0.200891i
$552$	−3.38149	−	7.66595i	−0.143926	−	0.326284i
$553$	−0.122578	+	7.46105i	−0.00521255	+	0.317276i
$554$	−9.29144	−	13.0982i	−0.394755	−	0.556490i
$555$	9.93637	+	23.6947i	0.421775	+	1.00579i
$556$	10.1948	+	6.95412i	0.432357	+	0.294920i
$557$	−5.59438	+	20.8785i	−0.237042	+	0.884651i	0.740176	+	0.672413i	$0.234742\pi$
$557$	−5.59438	+	20.8785i	−0.237042	+	0.884651i	−0.977218	+	0.212238i	$0.931925\pi$
$558$	6.64839	−	14.8293i	0.281449	−	0.627775i
$559$			41.1117i			1.73884i
$560$	−14.9794	+	32.8104i	−0.632996	+	1.38649i
$561$	−9.65457	+	1.31405i	−0.407616	+	0.0554791i
$562$	13.8932	−	16.7646i	0.586050	−	0.707171i
$563$	−23.2697	−	6.23509i	−0.980700	−	0.262778i	−0.267361	−	0.963596i	$-0.586152\pi$
$563$	−23.2697	−	6.23509i	−0.980700	−	0.262778i	−0.713340	+	0.700819i	$0.752818\pi$
$564$	−16.0321	+	32.0879i	−0.675071	+	1.35114i
$565$	−0.589746	−	2.20096i	−0.0248108	−	0.0925952i
$566$	−9.36232	+	6.64131i	−0.393528	+	0.279155i
$567$	−23.8117	+	0.0255787i	−0.999999	+	0.00107421i
$568$	31.9080	+	17.6492i	1.33883	+	0.740543i
$569$	−6.37298	+	11.0383i	−0.267169	+	0.462751i	−0.968130	−	0.250449i	$-0.919422\pi$
$569$	−6.37298	+	11.0383i	−0.267169	+	0.462751i	0.700960	+	0.713200i	$0.252755\pi$
$570$	25.6249	+	7.78481i	1.07331	+	0.326070i
$571$	−7.25992	+	27.0944i	−0.303818	+	1.13387i	0.630139	+	0.776482i	$0.282998\pi$
$571$	−7.25992	+	27.0944i	−0.303818	+	1.13387i	−0.933958	+	0.357384i	$0.883669\pi$
$572$	−27.2955	+	23.4789i	−1.14128	+	0.981701i
$573$	−15.2280	+	20.0263i	−0.636157	+	0.836611i
$574$	31.9111	+	5.96658i	1.33194	+	0.249040i
$575$		−	11.3139i		−	0.471823i
$576$	−7.25890	−	22.8759i	−0.302454	−	0.953164i
$577$	36.0326	−	20.8035i	1.50006	−	0.866059i	0.500059	−	0.865992i	$-0.333312\pi$
$577$	36.0326	−	20.8035i	1.50006	−	0.866059i	1.00000		6.77305e-5i	$-2.15593e-5\pi$
$578$	−6.38242	−	17.2072i	−0.265474	−	0.715725i
$579$	−38.3075	+	16.0642i	−1.59201	+	0.667606i
$580$	−6.62264	+	18.9126i	−0.274990	+	0.785302i
$581$	5.69979	−	19.9548i	0.236467	−	0.827863i
$582$	5.18732	−	4.85443i	0.215021	−	0.201223i
$583$	−13.9532	−	8.05586i	−0.577881	−	0.333640i
$584$	0.00193927	+	0.105624i	8.02474e−5	+	0.00437077i
$585$	46.8069	+	45.9948i	1.93523	+	1.90165i
$586$	−31.6270	+	2.96213i	−1.30650	+	0.122364i
$587$	−0.456777	−	0.456777i	−0.0188532	−	0.0188532i	0.697617	−	0.716471i	$-0.254244\pi$
$587$	−0.456777	−	0.456777i	−0.0188532	−	0.0188532i	−0.716471	+	0.697617i	$0.754244\pi$
$588$	11.5446	−	21.3242i	0.476093	−	0.879395i
$589$	8.68927	−	8.68927i	0.358035	−	0.358035i
$590$	−25.2153	−	20.8965i	−1.03810	−	0.860297i
$591$	6.41461	+	8.28437i	0.263862	+	0.340774i
$592$	14.0132	−	10.3324i	0.575941	−	0.424658i
$593$	10.3640	−	17.9510i	0.425599	−	0.737159i	−0.570877	−	0.821035i	$-0.693397\pi$
$593$	10.3640	−	17.9510i	0.425599	−	0.737159i	0.996476	+	0.0838764i	$0.0267301\pi$
$594$	4.84745	+	20.0328i	0.198893	+	0.821956i
$595$	−17.3896	−	4.96708i	−0.712903	−	0.203631i
$596$	27.7998	−	13.3799i	1.13872	−	0.548061i
$597$	30.3412	−	12.7235i	1.24178	−	0.520740i
$598$	6.47451	−	14.1094i	0.264763	−	0.576977i
$599$	5.41603	+	9.38085i	0.221293	+	0.383291i	0.955201	−	0.295958i	$-0.0956389\pi$
$599$	5.41603	+	9.38085i	0.221293	+	0.383291i	−0.733908	+	0.679249i	$0.762306\pi$
$600$	3.49862	−	32.2186i	0.142830	−	1.31532i
$601$	7.05897			0.287941			0.143971	−	0.989582i	$-0.454013\pi$
$601$	7.05897			0.287941			0.143971	+	0.989582i	$0.454013\pi$
$602$	−19.7730	+	13.5436i	−0.805887	+	0.551996i
$603$	8.39282	+	4.74816i	0.341782	+	0.193360i
$604$	−3.25078	−	3.77922i	−0.132272	−	0.153774i
$605$	10.3142	+	2.76368i	0.419332	+	0.112360i
$606$	−37.0705	+	19.7949i	−1.50589	+	0.804112i
$607$	23.3242	+	13.4662i	0.946699	+	0.546577i	0.892054	−	0.451929i	$-0.149264\pi$
$607$	23.3242	+	13.4662i	0.946699	+	0.546577i	0.0546450	+	0.998506i	$0.482597\pi$
$608$	1.02787	−	18.1184i	0.0416855	−	0.734798i
$609$	5.30515	−	12.3835i	0.214975	−	0.501804i
$610$	−1.70019	+	9.99970i	−0.0688387	+	0.404876i
$611$	−64.1958	+	17.2012i	−2.59709	+	0.695887i
$612$	10.7973	−	5.31355i	0.436456	−	0.214788i
$613$	−5.83769	+	21.7866i	−0.235782	+	0.879951i	0.742013	+	0.670386i	$0.233871\pi$
$613$	−5.83769	+	21.7866i	−0.235782	+	0.879951i	−0.977795	+	0.209565i	$0.932795\pi$
$614$	17.8107	−	1.66812i	0.718781	−	0.0673198i
$615$	−50.7490	+	6.90727i	−2.04640	+	0.278528i
$616$	−20.2844	−	5.39325i	−0.817283	−	0.217300i
$617$	4.73842			0.190761			0.0953807	−	0.995441i	$-0.469593\pi$
$617$	4.73842			0.190761			0.0953807	+	0.995441i	$0.469593\pi$
$618$	−0.799741	+	0.186125i	−0.0321703	+	0.00748704i
$619$	6.87961	+	1.84339i	0.276515	+	0.0740919i	0.394411	−	0.918934i	$-0.370948\pi$
$619$	6.87961	+	1.84339i	0.276515	+	0.0740919i	−0.117897	+	0.993026i	$0.537615\pi$
$620$	−21.5694	−	14.7130i	−0.866248	−	0.590887i
$621$	−5.50206	−	6.97881i	−0.220790	−	0.280050i
$622$	4.74221	−	27.8914i	0.190145	−	1.11834i
$623$	7.23362	+	0.118842i	0.289809	+	0.00476129i
$624$	22.8005	−	38.1772i	0.912751	−	1.52831i
$625$	−7.15737	+	12.3969i	−0.286295	+	0.495877i
$626$	3.95753	+	10.6696i	0.158175	+	0.426443i
$627$	−1.96661	+	15.4603i	−0.0785389	+	0.617426i
$628$	−46.8563	−	3.52214i	−1.86977	−	0.140549i
$629$	6.17299	+	6.17299i	0.246133	+	0.246133i
$630$	−6.70175	+	37.6644i	−0.267004	+	1.50059i
$631$			28.3799i			1.12979i	0.825164	+	0.564894i	$0.191083\pi$
$631$			28.3799i			1.12979i	−0.825164	+	0.564894i	$0.808917\pi$
$632$	−6.83414	+	4.11479i	−0.271848	+	0.163677i
$633$	−1.25434	−	1.61996i	−0.0498555	−	0.0643877i
$634$	12.1603	−	26.5001i	0.482949	−	1.05245i
$635$	0.538568	−	0.144309i	0.0213724	−	0.00572672i
$636$	19.4962	+	3.98359i	0.773074	+	0.157959i
$637$	43.7560	−	10.1965i	1.73368	−	0.403998i
$638$	−11.4961	−	1.95462i	−0.455135	−	0.0773840i
$639$	37.4441	+	9.68273i	1.48126	+	0.383043i
$640$	−38.2325	+	5.00238i	−1.51127	+	0.197736i
$641$	−34.7860	+	20.0837i	−1.37396	+	0.793258i	−0.991424	−	0.130681i	$-0.958284\pi$
$641$	−34.7860	+	20.0837i	−1.37396	+	0.793258i	−0.382539	+	0.923939i	$0.624950\pi$
$642$	24.2848	−	39.0172i	0.958445	−	1.53988i
$643$	−19.0526	−	19.0526i	−0.751361	−	0.751361i	0.223372	−	0.974733i	$-0.428293\pi$
$643$	−19.0526	−	19.0526i	−0.751361	−	0.751361i	−0.974733	+	0.223372i	$0.928293\pi$
$644$	8.91896	−	1.53416i	0.351456	−	0.0604543i
$645$	22.8864	−	30.0979i	0.901151	−	1.18510i
$646$	9.05978	−	0.848523i	0.356452	−	0.0333847i
$647$	6.05127	−	3.49370i	0.237900	−	0.137352i	−0.376311	−	0.926493i	$-0.622808\pi$
$647$	6.05127	−	3.49370i	0.237900	−	0.137352i	0.614211	+	0.789142i	$0.289474\pi$
$648$	−13.5101	−	21.5749i	−0.530727	−	0.847543i
$649$	9.52875	−	16.5043i	0.374036	−	0.647849i
$650$	48.9750	−	34.7413i	1.92096	−	1.36266i
$651$	13.7964	+	10.8530i	0.540723	+	0.425363i
$652$	−14.4105	+	6.93568i	−0.564358	+	0.271622i
$653$	−23.8185	+	6.38215i	−0.932091	+	0.249753i	−0.692746	−	0.721182i	$-0.743599\pi$
$653$	−23.8185	+	6.38215i	−0.932091	+	0.249753i	−0.239345	+	0.970935i	$0.576933\pi$
$654$	−10.4841	−	19.6339i	−0.409961	−	0.767746i
$655$	−27.4147	−	47.4837i	−1.07118	−	1.85534i
$656$	12.6646	+	32.3123i	0.494471	+	1.26158i
$657$	0.0299468	+	0.107974i	0.00116834	+	0.00421248i
$658$	−29.4214	−	25.2088i	−1.14696	−	0.982741i
$659$	29.4051	+	29.4051i	1.14546	+	1.14546i	0.987435	+	0.158024i	$0.0505123\pi$
$659$	29.4051	+	29.4051i	1.14546	+	1.14546i	0.158024	+	0.987435i	$0.449488\pi$
$660$	33.0535	−	1.99380i	1.28661	−	0.0776085i
$661$	−28.5894	−	7.66050i	−1.11200	−	0.297959i	−0.344357	−	0.938839i	$-0.611903\pi$
$661$	−28.5894	−	7.66050i	−1.11200	−	0.297959i	−0.767641	+	0.640880i	$0.778570\pi$
$662$	7.92083	−	17.2613i	0.307852	−	0.670878i
$663$	20.6366	+	8.44235i	0.801457	+	0.327874i
$664$	21.3207	−	6.13450i	0.827405	−	0.238065i
$665$	−14.8731	+	24.8107i	−0.576756	+	0.962117i
$666$	11.6585	−	14.3213i	0.451758	−	0.554938i
$667$	4.85661	−	1.30133i	0.188049	−	0.0503875i
$668$	42.7453	−	8.07775i	1.65386	−	0.312538i
$669$	28.6106	+	3.63938i	1.10615	+	0.140707i
$670$	9.88538	−	11.9284i	0.381906	−	0.460835i
$671$	−5.90266			−0.227869
$672$	25.8729	−	1.61079i	0.998068	−	0.0621377i
$673$	−25.1018			−0.967605			−0.483802	−	0.875177i	$-0.660745\pi$
$673$	−25.1018			−0.967605			−0.483802	+	0.875177i	$0.660745\pi$
$674$	−1.49637	+	1.80563i	−0.0576379	+	0.0695501i
$675$	−4.93363	−	34.0179i	−0.189895	−	1.30935i
$676$	55.4093	−	10.4709i	2.13113	−	0.402728i
$677$	−15.4714	+	4.14554i	−0.594612	+	0.159326i	−0.543560	−	0.839370i	$-0.682924\pi$
$677$	−15.4714	+	4.14554i	−0.594612	+	0.159326i	−0.0510520	+	0.998696i	$0.516257\pi$
$678$	−1.19575	+	1.11901i	−0.0459225	+	0.0429755i
$679$	3.72718	+	6.70777i	0.143036	+	0.257421i
$680$	−5.34591	−	18.5800i	−0.205006	−	0.712509i
$681$	3.01492	−	7.36971i	0.115532	−	0.282408i
$682$	6.33688	−	13.8095i	0.242652	−	0.528792i
$683$	32.7109	+	8.76487i	1.25165	+	0.335378i	0.822973	−	0.568080i	$-0.192314\pi$
$683$	32.7109	+	8.76487i	1.25165	+	0.335378i	0.428676	+	0.903458i	$0.358980\pi$
$684$	−3.73955	−	18.8816i	−0.142985	−	0.721956i
$685$	−2.74157	−	2.74157i	−0.104750	−	0.104750i
$686$	19.3188	+	17.6857i	0.737595	+	0.675244i
$687$	−28.9515	+	3.94048i	−1.10457	+	0.150339i
$688$	−23.4790	−	10.2565i	−0.895127	−	0.391026i
$689$	18.4346	+	31.9296i	0.702301	+	1.21642i
$690$	−12.5945	+	6.72523i	−0.479466	+	0.256025i
$691$	9.45931	−	2.53461i	0.359849	−	0.0964212i	−0.0743648	−	0.997231i	$-0.523693\pi$
$691$	9.45931	−	2.53461i	0.359849	−	0.0964212i	0.434214	+	0.900810i	$0.357026\pi$
$692$	23.6045	−	11.3607i	0.897309	−	0.431869i
$693$	−22.2617	−	0.170900i	−0.845653	−	0.00649194i
$694$	10.7078	−	7.59577i	0.406463	−	0.288331i
$695$	10.5147	−	18.2120i	0.398844	−	0.690819i
$696$	14.2326	−	2.20396i	0.539484	−	0.0835409i
$697$	−15.0705	+	8.70093i	−0.570834	+	0.329571i
$698$	−14.6305	+	1.37027i	−0.553772	+	0.0518653i
$699$	−3.03647	−	2.30893i	−0.114850	−	0.0873316i
$700$	32.8431	+	12.1100i	1.24135	+	0.457713i
$701$	−19.2823	−	19.2823i	−0.728284	−	0.728284i	0.241994	−	0.970278i	$-0.422199\pi$
$701$	−19.2823	−	19.2823i	−0.728284	−	0.728284i	−0.970278	+	0.241994i	$0.922199\pi$
$702$	13.3145	−	45.2466i	0.502523	−	1.70772i
$703$	12.0928	−	6.98178i	0.456089	−	0.263323i
$704$	−6.59916	−	21.4460i	−0.248715	−	0.808277i
$705$	56.5735	+	23.1440i	2.13068	+	0.871655i
$706$	−28.6386	−	4.86925i	−1.07783	−	0.183256i
$707$	−11.0264	−	44.0320i	−0.414690	−	1.65599i
$708$	−4.71192	+	23.0608i	−0.177085	+	0.866676i
$709$	−12.5961	+	3.37513i	−0.473058	+	0.126756i	−0.487468	−	0.873141i	$-0.662080\pi$
$709$	−12.5961	+	3.37513i	−0.473058	+	0.126756i	0.0144103	+	0.999896i	$0.495413\pi$
$710$	25.9149	−	56.4744i	0.972570	−	2.11945i
$711$	−5.93037	+	6.03508i	−0.222406	+	0.226333i
$712$	3.98935	+	6.62582i	0.149507	+	0.248313i
$713$			6.55123i			0.245345i
$714$	2.73798	+	12.7065i	0.102466	+	0.475529i
$715$	43.3833	+	43.3833i	1.62244	+	1.62244i
$716$	−3.98067	−	0.299223i	−0.148765	−	0.0111825i
$717$	−13.5287	−	1.72090i	−0.505237	−	0.0642681i
$718$	−8.46637	−	22.8256i	−0.315962	−	0.851843i
$719$	4.51352	−	7.81765i	0.168326	−	0.291549i	−0.769505	−	0.638640i	$-0.779497\pi$
$719$	4.51352	−	7.81765i	0.168326	−	0.291549i	0.937831	+	0.347091i	$0.112831\pi$
$720$	−37.9450	+	15.2568i	−1.41413	+	0.568586i
$721$	0.0145690	−	0.886785i	0.000542579	−	0.0330256i
$722$	−2.06430	+	12.1412i	−0.0768253	+	0.451849i
$723$	12.4534	+	29.6970i	0.463147	+	1.10444i
$724$	15.9306	+	10.8666i	0.592056	+	0.403854i
$725$	18.7851	+	5.03345i	0.697660	+	0.186937i
$726$	−1.73962	−	7.47479i	−0.0645633	−	0.277415i
$727$	−29.3525			−1.08863			−0.544313	−	0.838882i	$-0.683210\pi$
$727$	−29.3525			−1.08863			−0.544313	+	0.838882i	$0.683210\pi$
$728$	34.0281	+	33.8970i	1.26117	+	1.25631i
$729$	−19.5865	−	18.5841i	−0.725424	−	0.688302i
$730$	0.179236	−	0.0167869i	0.00663382	−	0.000621311i
$731$	3.32503	−	12.4092i	0.122981	−	0.458971i
$732$	6.91537	−	2.30740i	0.255599	−	0.0852839i
$733$	11.2515	−	3.01482i	0.415582	−	0.111355i	−0.0449684	−	0.998988i	$-0.514319\pi$
$733$	11.2515	−	3.01482i	0.415582	−	0.111355i	0.460550	+	0.887634i	$0.347652\pi$
$734$	−6.09548	+	35.8507i	−0.224988	+	1.32327i
$735$	−37.7100	−	16.8936i	−1.39096	−	0.623130i
$736$	6.44265	+	7.21761i	0.237479	+	0.266045i
$737$	7.80757	+	4.50770i	0.287595	+	0.166043i
$738$	21.5598	+	29.8363i	0.793629	+	1.09829i
$739$	−30.2876	−	8.11553i	−1.11415	−	0.298535i	−0.345634	−	0.938369i	$-0.612336\pi$
$739$	−30.2876	−	8.11553i	−1.11415	−	0.298535i	−0.768513	+	0.639835i	$0.779003\pi$
$740$	−19.3474	−	22.4924i	−0.711223	−	0.826838i
$741$	21.5866	−	28.3886i	0.793005	−	1.04288i
$742$	−9.28381	+	19.3849i	−0.340819	+	0.711644i
$743$	−20.7045			−0.759575			−0.379788	−	0.925074i	$-0.624003\pi$
$743$	−20.7045			−0.759575			−0.379788	+	0.925074i	$0.624003\pi$
$744$	−2.02584	+	18.6559i	−0.0742711	+	0.683958i
$745$	−26.2868	−	45.5301i	−0.963075	−	1.66810i
$746$	−10.3711	+	22.6010i	−0.379714	+	0.827481i
$747$	20.2751	−	11.9436i	0.741829	−	0.436995i
$748$	10.1378	−	4.87928i	0.370676	−	0.178404i
$749$	34.5193	+	35.6725i	1.26131	+	1.30344i
$750$	−13.4769	−	0.446767i	−0.492107	−	0.0163136i
$751$	−10.5912	+	18.3445i	−0.386479	+	0.669400i	−0.991973	−	0.126449i	$-0.959642\pi$
$751$	−10.5912	+	18.3445i	−0.386479	+	0.669400i	0.605495	+	0.795849i	$0.292975\pi$
$752$	6.19187	−	40.9537i	0.225794	−	1.49343i
$753$	−3.23179	+	2.50238i	−0.117773	+	0.0911919i
$754$	20.5462	+	17.0271i	0.748247	+	0.620091i
$755$	−6.00666	+	6.00666i	−0.218605	+	0.218605i
$756$	26.1479	−	8.50207i	0.950991	−	0.309217i
$757$	−16.8514	−	16.8514i	−0.612476	−	0.612476i	0.331114	−	0.943591i	$-0.392575\pi$
$757$	−16.8514	−	16.8514i	−0.612476	−	0.612476i	−0.943591	+	0.331114i	$0.892575\pi$
$758$	−9.81655	+	0.919400i	−0.356553	+	0.0333941i
$759$	−5.08676	−	6.56947i	−0.184638	−	0.238457i
$760$	−30.9192	+	0.567678i	−1.12156	+	0.0205919i
$761$	7.91897	+	4.57202i	0.287062	+	0.165736i	0.636616	−	0.771181i	$-0.280334\pi$
$761$	7.91897	+	4.57202i	0.287062	+	0.165736i	−0.349554	+	0.936916i	$0.613667\pi$
$762$	−0.273819	−	0.292596i	−0.00991941	−	0.0105996i
$763$	23.3210	−	5.83999i	0.844276	−	0.211422i
$764$	9.60098	−	27.4180i	0.347351	−	0.991948i
$765$	−10.4083	−	17.6688i	−0.376312	−	0.638816i
$766$	−8.39276	−	22.6271i	−0.303243	−	0.817552i
$767$	−37.7674	+	21.8050i	−1.36370	+	0.787334i
$768$	16.1148	+	22.5458i	0.581493	+	0.813552i
$769$		−	34.7218i		−	1.25210i	−0.779783	−	0.626050i	$-0.784670\pi$
$769$		−	34.7218i		−	1.25210i	0.779783	−	0.626050i	$-0.215330\pi$
$770$	−6.57359	+	35.1575i	−0.236896	+	1.26699i
$771$	0.467166	+	0.355233i	0.0168246	+	0.0127934i
$772$	36.3637	−	31.2791i	1.30876	−	1.12576i
$773$	−7.12294	+	26.5832i	−0.256194	+	0.956130i	0.711228	+	0.702962i	$0.248139\pi$
$773$	−7.12294	+	26.5832i	−0.256194	+	0.956130i	−0.967422	+	0.253169i	$0.918527\pi$
$774$	−26.8300	−	4.32052i	−0.964383	−	0.155298i
$775$	−12.6699	+	21.9449i	−0.455115	+	0.788282i
$776$	−3.97067	+	7.17859i	−0.142539	+	0.257696i
$777$	11.9510	+	15.9697i	0.428739	+	0.572910i
$778$	26.7437	−	18.9711i	0.958809	−	0.680147i
$779$	7.20407	+	26.8859i	0.258112	+	0.963289i
$780$	−67.7854	−	33.8676i	−2.42711	−	1.21266i
$781$	34.9271	+	9.35869i	1.24979	+	0.334880i
$782$	−3.09542	+	3.73515i	−0.110692	+	0.133569i
$783$	14.0351	−	6.03055i	0.501573	−	0.215514i
$784$	−5.09299	+	27.5329i	−0.181893	+	0.983318i
$785$			80.0711i			2.85786i
$786$	−20.8235	+	33.4561i	−0.742750	+	1.19334i
$787$	−7.64339	+	28.5255i	−0.272458	+	1.01683i	0.685068	+	0.728479i	$0.259772\pi$
$787$	−7.64339	+	28.5255i	−0.272458	+	1.01683i	−0.957526	+	0.288347i	$0.906894\pi$
$788$	−9.99459	−	6.81754i	−0.356043	−	0.242865i
$789$	34.5052	−	14.4697i	1.22842	−	0.515135i
$790$	7.86504	+	11.0874i	0.279826	+	0.394473i
$791$	−0.859167	−	1.54624i	−0.0305485	−	0.0549778i
$792$	−12.4540	−	20.2808i	−0.442535	−	0.720648i
$793$	11.6977	+	6.75365i	0.415396	+	0.239829i
$794$	−15.6074	+	34.0121i	−0.553887	+	1.20704i
$795$	4.27888	−	33.6380i	0.151756	−	1.19302i
$796$	−28.8016	+	24.7743i	−1.02084	+	0.878103i
$797$	−25.3019	+	25.3019i	−0.896238	+	0.896238i	−0.995101	−	0.0988633i	$-0.968479\pi$
$797$	−25.3019	+	25.3019i	−0.896238	+	0.896238i	0.0988633	+	0.995101i	$0.468479\pi$
$798$	20.7651	+	1.03009i	0.735076	+	0.0364647i
$799$	20.7681			0.734724
$800$	7.62253	+	36.6369i	0.269497	+	1.29531i
$801$	5.85112	+	5.74960i	0.206739	+	0.203152i
$802$	−26.6635	+	9.88990i	−0.941520	+	0.349224i
$803$	0.0271137	+	0.101190i	0.000956823	+	0.00357091i
$804$	−10.9092	−	2.22904i	−0.384738	−	0.0786121i
$805$	−3.74617	−	14.9597i	−0.132035	−	0.527260i
$806$	−28.3586	+	20.1166i	−0.998889	+	0.708578i
$807$	20.2976	−	49.6158i	0.714511	−	1.74656i
$808$	33.6772	−	34.9369i	1.18476	−	1.22908i
$809$	−17.7443	−	30.7340i	−0.623856	−	1.08055i	−0.988761	−	0.149505i	$-0.952232\pi$
$809$	−17.7443	−	30.7340i	−0.623856	−	1.08055i	0.364905	−	0.931045i	$-0.381101\pi$
$810$	−34.9358	+	25.7130i	−1.22752	+	0.903464i
$811$	26.7105	−	26.7105i	0.937931	−	0.937931i	−0.0602522	−	0.998183i	$-0.519191\pi$
$811$	26.7105	−	26.7105i	0.937931	−	0.937931i	0.998183	+	0.0602522i	$0.0191905\pi$
$812$	−1.42071	+	15.4911i	−0.0498572	+	0.543632i
$813$	−5.99932	+	7.88970i	−0.210405	+	0.276704i
$814$	11.0167	−	13.2935i	0.386134	−	0.465938i
$815$	13.6262	+	23.6013i	0.477306	+	0.826718i
$816$	−9.96982	+	9.67938i	−0.349014	+	0.338846i
$817$	−17.7958	−	10.2744i	−0.622595	−	0.359455i
$818$	29.8604	+	5.07699i	1.04404	+	0.177513i
$819$	43.9219	+	25.8099i	1.53476	+	0.901871i
$820$	53.2894	−	25.6478i	1.86095	−	0.895661i
$821$	6.69070	+	24.9700i	0.233507	+	0.871460i	0.978816	+	0.204741i	$0.0656351\pi$
$821$	6.69070	+	24.9700i	0.233507	+	0.871460i	−0.745309	+	0.666719i	$0.767698\pi$
$822$	−0.810013	+	2.66628i	−0.0282524	+	0.0929973i
$823$	19.7290	−	11.3906i	0.687711	−	0.397050i	−0.115043	−	0.993360i	$-0.536701\pi$
$823$	19.7290	−	11.3906i	0.687711	−	0.397050i	0.802754	+	0.596311i	$0.203367\pi$
$824$	0.812273	−	0.489064i	0.0282969	−	0.0170373i
$825$	−4.33412	−	31.8436i	−0.150895	−	1.10865i
$826$	−22.9292	−	10.9812i	−0.797808	−	0.382085i
$827$	25.6580	−	25.6580i	0.892217	−	0.892217i	−0.102515	−	0.994731i	$-0.532689\pi$
$827$	25.6580	−	25.6580i	0.892217	−	0.892217i	0.994731	+	0.102515i	$0.0326888\pi$
$828$	8.52755	+	5.70813i	0.296353	+	0.198371i
$829$	−4.46193	+	16.6522i	−0.154969	+	0.578353i	0.844139	+	0.536125i	$0.180112\pi$
$829$	−4.46193	+	16.6522i	−0.154969	+	0.578353i	−0.999108	+	0.0422283i	$0.986554\pi$
$830$	−13.1475	−	35.4460i	−0.456355	−	1.23035i
$831$	18.2039	+	7.44715i	0.631485	+	0.258339i
$832$	−11.4599	+	50.0515i	−0.397302	+	1.73522i
$833$	−14.0320	−	0.461191i	−0.486181	−	0.0159793i
$834$	−15.1060	−	0.500772i	−0.523077	−	0.0173403i
$835$	−19.1862	−	71.6037i	−0.663964	−	2.47795i
$836$	−3.34162	−	17.6829i	−0.115572	−	0.611577i
$837$	2.85678	+	19.6978i	0.0987447	+	0.680856i
$838$	0.705386	+	7.53149i	0.0243672	+	0.260171i
$839$		−	16.6615i		−	0.575220i	−0.957748	−	0.287610i	$-0.907139\pi$
$839$		−	16.6615i		−	0.575220i	0.957748	−	0.287610i	$-0.0928607\pi$
$840$	−6.04195	−	43.7591i	−0.208467	−	1.50983i
$841$		−	20.3574i		−	0.701978i
$842$	−42.9199	+	4.01981i	−1.47912	+	0.138532i
$843$	−3.36498	+	26.4535i	−0.115896	+	0.911106i
$844$	1.95439	+	1.33313i	0.0672727	+	0.0458882i
$845$	−24.8704	−	92.8176i	−0.855568	−	3.19302i
$846$	−4.47923	−	43.7027i	−0.153999	−	1.50253i
$847$	8.28834	+	0.136170i	0.284791	+	0.00467885i
$848$	−22.8341	+	2.56224i	−0.784126	+	0.0879877i
$849$	5.32305	−	13.0117i	0.182687	−	0.446561i
$850$	−17.5925	+	6.52533i	−0.603417	+	0.223817i
$851$	−1.92671	+	7.19058i	−0.0660468	+	0.246490i
$852$	−44.5779	+	2.68895i	−1.52721	+	0.0921220i
$853$	−15.2587	+	15.2587i	−0.522449	+	0.522449i	−0.918310	−	0.395861i	$-0.870446\pi$
$853$	−15.2587	+	15.2587i	−0.522449	+	0.522449i	0.395861	+	0.918310i	$0.370446\pi$
$854$	0.605392	+	7.85096i	0.0207161	+	0.268654i
$855$	−31.6072	+	8.76627i	−1.08094	+	0.299800i
$856$	−12.7915	+	51.5024i	−0.437205	+	1.76032i
$857$	19.5856	−	11.3078i	0.669033	−	0.386266i	−0.126677	−	0.991944i	$-0.540431\pi$
$857$	19.5856	−	11.3078i	0.669033	−	0.386266i	0.795710	+	0.605678i	$0.207098\pi$
$858$	12.8178	−	42.1919i	0.437594	−	1.44041i
$859$	1.69243	+	6.31625i	0.0577451	+	0.215508i	0.988769	−	0.149450i	$-0.0477502\pi$
$859$	1.69243	+	6.31625i	0.0577451	+	0.215508i	−0.931024	+	0.364957i	$0.881084\pi$
$860$	−14.4295	+	41.2070i	−0.492042	+	1.40515i
$861$	−36.9143	+	14.7718i	−1.25804	+	0.503420i
$862$	2.65654	−	15.6245i	0.0904821	−	0.532172i
$863$	4.92065	+	2.84094i	0.167501	+	0.0967068i	0.581407	−	0.813613i	$-0.302502\pi$
$863$	4.92065	+	2.84094i	0.167501	+	0.0967068i	−0.413906	+	0.910320i	$0.635836\pi$
$864$	22.5187	+	18.8920i	0.766102	+	0.642719i
$865$	−22.3199	−	38.6591i	−0.758898	−	1.31445i
$866$	39.2408	+	32.5199i	1.33346	+	1.10507i
$867$	17.8922	+	13.6052i	0.607652	+	0.462058i
$868$	−19.0175	−	7.01217i	−0.645497	−	0.238009i
$869$	−5.59366	+	5.59366i	−0.189752	+	0.189752i
$870$	−5.56306	−	23.9034i	−0.188605	−	0.810400i
$871$	−10.3152	−	17.8664i	−0.349516	−	0.605379i
$872$	18.5039	+	17.8367i	0.626621	+	0.604026i
$873$	−2.17840	+	8.42408i	−0.0737276	+	0.285112i
$874$	4.48938	+	6.32872i	0.151856	+	0.214072i
$875$	4.00022	−	14.0046i	0.135232	−	0.473442i
$876$	−0.0713216	−	0.107952i	−0.00240973	−	0.00364736i
$877$	7.78392	+	29.0500i	0.262844	+	0.980949i	0.963557	+	0.267505i	$0.0861990\pi$
$877$	7.78392	+	29.0500i	0.262844	+	0.980949i	−0.700712	+	0.713444i	$0.747134\pi$
$878$	1.63872	+	4.41804i	0.0553041	+	0.149102i
$879$	30.7611	−	23.8184i	1.03755	−	0.803375i
$880$	−35.5995	+	13.9530i	−1.20006	+	0.470357i
$881$	−8.04969			−0.271201			−0.135600	−	0.990764i	$-0.543296\pi$
$881$	−8.04969			−0.271201			−0.135600	+	0.990764i	$0.543296\pi$
$882$	2.05591	+	29.6272i	0.0692261	+	0.997601i
$883$	−18.1256	+	18.1256i	−0.609975	+	0.609975i	−0.942939	−	0.332964i	$-0.891951\pi$
$883$	−18.1256	+	18.1256i	−0.609975	+	0.609975i	0.332964	+	0.942939i	$0.391951\pi$
$884$	−25.6735	−	1.92985i	−0.863494	−	0.0649079i
$885$	39.7882	+	5.06120i	1.33746	+	0.170130i
$886$	10.1284	+	4.64771i	0.340270	+	0.156143i
$887$	−3.40816	−	1.96770i	−0.114435	−	0.0660689i	0.441690	−	0.897168i	$-0.354379\pi$
$887$	−3.40816	−	1.96770i	−0.114435	−	0.0660689i	−0.556125	+	0.831099i	$0.687712\pi$
$888$	−7.71024	+	19.8808i	−0.258739	+	0.667155i
$889$	0.378358	−	0.210235i	0.0126897	−	0.00705106i
$890$	10.7494	−	7.62529i	0.360322	−	0.255600i
$891$	−18.1593	−	17.5345i	−0.608358	−	0.587428i
$892$	−32.7238	+	6.18394i	−1.09567	+	0.207054i
$893$	8.59765	−	32.0869i	0.287709	−	1.07375i
$894$	−19.9668	+	32.0796i	−0.667789	+	1.07290i
$895$			6.80243i			0.227380i
$896$	−27.8479	+	10.9769i	−0.930334	+	0.366713i
$897$	2.56414	+	18.8393i	0.0856142	+	0.629024i
$898$	25.1201	+	20.8177i	0.838270	+	0.694695i
$899$	−10.8773	−	2.91458i	−0.362780	−	0.0972065i
$900$	17.5256	+	35.6127i	0.584188	+	1.18709i
$901$	−2.98190	−	11.1286i	−0.0993416	−	0.370748i
$902$	19.9121	+	28.0703i	0.663001	+	0.934638i
$903$	11.5589	−	26.9813i	0.384657	−	0.897882i
$904$	0.915296	−	1.65477i	0.0304423	−	0.0550367i
$905$	16.4304	−	28.4583i	0.546165	−	0.945985i
$906$	5.84171	+	1.77470i	0.194078	+	0.0589605i
$907$	−13.5852	+	50.7005i	−0.451088	+	1.68348i	0.248252	+	0.968695i	$0.420144\pi$
$907$	−13.5852	+	50.7005i	−0.451088	+	1.68348i	−0.699341	+	0.714789i	$0.746523\pi$
$908$	−0.689187	+	9.16851i	−0.0228715	+	0.304268i
$909$	25.3436	−	44.7972i	0.840594	−	1.48583i
$910$	53.2535	−	62.1525i	1.76534	−	2.06033i
$911$			0.0313447i			0.00103850i	1.00000		0.000519248i	$0.000165282\pi$
$911$			0.0313447i			0.00103850i	−1.00000		0.000519248i	$0.999835\pi$
$912$	10.8273	+	19.4105i	0.358529	+	0.642746i
$913$	19.0529	−	11.0002i	0.630558	−	0.364053i
$914$	31.8806	−	11.8250i	1.05452	−	0.391137i
$915$	−4.80419	−	11.4563i	−0.158822	−	0.378734i
$916$	30.4007	−	14.6317i	1.00447	−	0.483444i
$917$	−29.5993	−	30.5881i	−0.977454	−	1.01011i
$918$	−7.67831	+	12.5804i	−0.253422	+	0.415216i
$919$	0.884482	+	0.510656i	0.0291764	+	0.0168450i	0.514517	−	0.857480i	$-0.327971\pi$
$919$	0.884482	+	0.510656i	0.0291764	+	0.0168450i	−0.485341	+	0.874325i	$0.661304\pi$
$920$	11.4417	−	11.8697i	0.377221	−	0.391332i
$921$	−17.3231	+	13.4133i	−0.570815	+	0.441983i
$922$	2.88843	+	30.8401i	0.0951255	+	1.01567i
$923$	−58.5093	−	58.5093i	−1.92586	−	1.92586i
$924$	24.5152	−	7.73463i	0.806490	−	0.254451i
$925$	−20.3603	+	20.3603i	−0.669443	+	0.669443i
$926$	12.0554	−	14.5469i	0.396165	−	0.478042i
$927$	0.704855	−	0.717301i	0.0231505	−	0.0235593i
$928$	−14.8500	+	7.48603i	−0.487476	+	0.245741i
$929$	−5.43822	+	9.41926i	−0.178422	+	0.309036i	−0.941340	−	0.337459i	$-0.890433\pi$
$929$	−5.43822	+	9.41926i	−0.178422	+	0.309036i	0.762918	+	0.646495i	$0.223766\pi$
$930$	31.9600	+	1.05949i	1.04801	+	0.0347422i
$931$	−6.52155	+	21.4886i	−0.213735	+	0.704261i
$932$	4.15723	+	1.45574i	0.136174	+	0.0476844i
$933$	13.3999	+	31.9542i	0.438694	+	1.04613i
$934$	−32.3486	−	14.8441i	−1.05848	−	0.485714i
$935$	−9.58611	−	16.6036i	−0.313499	−	0.542996i
$936$	1.47621	+	54.4414i	0.0482513	+	1.77947i
$937$	17.2886			0.564792			0.282396	−	0.959298i	$-0.408871\pi$
$937$	17.2886			0.564792			0.282396	+	0.959298i	$0.408871\pi$
$938$	5.19481	−	10.8470i	0.169616	−	0.354166i
$939$	−11.0944	−	8.43615i	−0.362051	−	0.275303i
$940$	−70.3820	−	5.29054i	−2.29561	−	0.172558i
$941$	28.1656	+	7.54696i	0.918174	+	0.246024i	0.686805	−	0.726842i	$-0.259013\pi$
$941$	28.1656	+	7.54696i	0.918174	+	0.246024i	0.231369	+	0.972866i	$0.425679\pi$
$942$	50.7648	−	27.1074i	1.65401	−	0.883206i
$943$	−12.8510	−	7.41952i	−0.418485	−	0.241613i
$944$	−3.03070	−	27.0089i	−0.0986410	−	0.879066i
$945$	−17.7872	−	43.3463i	−0.578617	−	1.41005i
$946$	−25.0479	−	4.25874i	−0.814377	−	0.138464i
$947$	45.0321	−	12.0663i	1.46335	−	0.392103i	0.562703	−	0.826659i	$-0.309762\pi$
$947$	45.0321	−	12.0663i	1.46335	−	0.392103i	0.900644	+	0.434557i	$0.143095\pi$
$948$	4.36675	−	8.73996i	0.141825	−	0.283861i
$949$	0.0620456	−	0.231557i	0.00201408	−	0.00751666i
$950$	2.79868	+	29.8818i	0.0908011	+	0.969494i
$951$	4.81594	+	35.3836i	0.156168	+	1.14739i
$952$	−7.52956	−	12.9836i	−0.244034	−	0.420802i
$953$	7.91438			0.256372			0.128186	−	0.991750i	$-0.459085\pi$
$953$	7.91438			0.256372			0.128186	+	0.991750i	$0.459085\pi$
$954$	−22.7750	+	8.67506i	−0.737367	+	0.280865i
$955$	−47.8167	−	12.8125i	−1.54731	−	0.414601i
$956$	15.4736	−	2.92410i	0.500451	−	0.0945722i
$957$	13.1707	−	5.52311i	0.425748	−	0.178537i
$958$	15.8675	+	2.69786i	0.512655	+	0.0871638i
$959$	−2.58156	−	1.54756i	−0.0833629	−	0.0499732i
$960$	36.2529	−	30.2631i	1.17006	−	0.976737i
$961$	−8.16362	+	14.1398i	−0.263343	+	0.456123i
$962$	−37.0425	+	13.7396i	−1.19430	+	0.442984i
$963$	0.492548	+	56.2840i	0.0158721	+	1.81373i
$964$	−24.2483	−	28.1901i	−0.780987	−	0.907942i
$965$	−57.7962	−	57.7962i	−1.86052	−	1.86052i
$966$	−8.21617	+	7.43954i	−0.264351	+	0.239363i
$967$			3.71172i			0.119361i	0.998218	+	0.0596804i	$0.0190082\pi$
$967$			3.71172i			0.119361i	−0.998218	+	0.0596804i	$0.980992\pi$
$968$	4.57104	+	7.59192i	0.146919	+	0.244014i
$969$	−8.81174	+	6.82295i	−0.283074	+	0.219185i
$970$	12.7055	+	5.83028i	0.407949	+	0.187199i
$971$	−21.1039	+	5.65478i	−0.677257	+	0.181470i	−0.581021	−	0.813888i	$-0.697347\pi$
$971$	−21.1039	+	5.65478i	−0.677257	+	0.181470i	−0.0962352	+	0.995359i	$0.530680\pi$
$972$	28.1292	+	13.4443i	0.902245	+	0.431225i
$973$	4.48376	−	15.6975i	0.143743	−	0.503238i
$974$	6.12205	−	36.0069i	0.196163	−	1.15374i
$975$	−27.8453	+	68.0654i	−0.891764	+	2.17984i
$976$	−6.77534	+	4.99566i	−0.216873	+	0.159907i
$977$	35.9079	−	20.7314i	1.14879	−	0.663257i	0.200201	−	0.979755i	$-0.435840\pi$
$977$	35.9079	−	20.7314i	1.14879	−	0.663257i	0.948593	+	0.316498i	$0.102507\pi$
$978$	10.3501	−	16.6290i	0.330960	−	0.531737i
$979$	5.42315	+	5.42315i	0.173324	+	0.173324i
$980$	47.4362	+	5.13751i	1.51529	+	0.164112i
$981$	23.7262	+	13.4229i	0.757521	+	0.428560i
$982$	3.49209	+	37.2854i	0.111437	+	1.18983i
$983$	−31.9359	+	18.4382i	−1.01860	+	0.588087i	−0.913697	−	0.406396i	$-0.866785\pi$
$983$	−31.9359	+	18.4382i	−1.01860	+	0.588087i	−0.104899	+	0.994483i	$0.533452\pi$
$984$	−34.3013	−	25.1024i	−1.09349	−	0.800237i
$985$	−10.3082	+	17.8543i	−0.328445	+	0.568884i
$986$	−4.82455	−	6.80121i	−0.153645	−	0.216595i
$987$	46.9675	+	6.76021i	1.49499	+	0.215180i
$988$	−13.6100	+	38.8668i	−0.432992	+	1.23652i
$989$	10.5817	−	2.83535i	0.336477	−	0.0901588i
$990$	−32.8717	+	23.7532i	−1.04473	+	0.754926i
$991$	22.8914	+	39.6490i	0.727168	+	1.25949i	0.958075	+	0.286517i	$0.0924974\pi$
$991$	22.8914	+	39.6490i	0.727168	+	1.25949i	−0.230907	+	0.972976i	$0.574169\pi$
$992$	−4.41376	−	21.2143i	−0.140137	−	0.673555i
$993$	3.13694	+	23.0477i	0.0995477	+	0.731396i
$994$	8.86552	−	47.4154i	0.281197	−	1.50393i
$995$	45.7770	+	45.7770i	1.45123	+	1.45123i
$996$	−18.0217	+	20.3354i	−0.571039	+	0.644352i
$997$	−9.57074	−	2.56447i	−0.303108	−	0.0812176i	0.104059	−	0.994571i	$-0.466817\pi$
$997$	−9.57074	−	2.56447i	−0.303108	−	0.0812176i	−0.407168	+	0.913353i	$0.633484\pi$
$998$	38.1702	+	17.5155i	1.20826	+	0.554444i
$999$	−2.65753	+	22.4604i	−0.0840805	+	0.710614i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bo.a.5.45	yes	240
3.2	odd	2	inner	336.2.bo.a.5.16	✓	240
7.3	odd	6	inner	336.2.bo.a.101.37	yes	240
16.13	even	4	inner	336.2.bo.a.173.24	yes	240
21.17	even	6	inner	336.2.bo.a.101.24	yes	240
48.29	odd	4	inner	336.2.bo.a.173.37	yes	240
112.45	odd	12	inner	336.2.bo.a.269.16	yes	240
336.269	even	12	inner	336.2.bo.a.269.45	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bo.a.5.16	✓	240	3.2	odd	2	inner
336.2.bo.a.5.45	yes	240	1.1	even	1	trivial
336.2.bo.a.101.24	yes	240	21.17	even	6	inner
336.2.bo.a.101.37	yes	240	7.3	odd	6	inner
336.2.bo.a.173.24	yes	240	16.13	even	4	inner
336.2.bo.a.173.37	yes	240	48.29	odd	4	inner
336.2.bo.a.269.16	yes	240	112.45	odd	12	inner
336.2.bo.a.269.45	yes	240	336.269	even	12	inner

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.902393 - 1.08889i) q^{2} +(-0.218562 + 1.71821i) q^{3} +(-0.371375 - 1.96522i) q^{4} +(-3.29199 + 0.882085i) q^{5} +(1.67371 + 1.78849i) q^{6} +(-2.31271 + 1.28506i) q^{7} +(-2.47504 - 1.36901i) q^{8} +(-2.90446 - 0.751070i) q^{9} +O(q^{10})\)	\(q+(0.902393 - 1.08889i) q^{2} +(-0.218562 + 1.71821i) q^{3} +(-0.371375 - 1.96522i) q^{4} +(-3.29199 + 0.882085i) q^{5} +(1.67371 + 1.78849i) q^{6} +(-2.31271 + 1.28506i) q^{7} +(-2.47504 - 1.36901i) q^{8} +(-2.90446 - 0.751070i) q^{9} +(-2.01017 + 4.38061i) q^{10} +(-2.70922 - 0.725934i) q^{11} +(3.45782 - 0.208577i) q^{12} +(4.53845 + 4.53845i) q^{13} +(-0.687681 + 3.67792i) q^{14} +(-0.796100 - 5.84910i) q^{15} +(-3.72416 + 1.45967i) q^{16} +(-1.00283 - 1.73695i) q^{17} +(-3.43880 + 2.48489i) q^{18} +(-3.09875 + 0.830307i) q^{19} +(2.95605 + 6.14188i) q^{20} +(-1.70252 - 4.25458i) q^{21} +(-3.23525 + 2.29498i) q^{22} +(0.855139 - 1.48114i) q^{23} +(2.89319 - 3.95341i) q^{24} +(5.72897 - 3.30762i) q^{25} +(9.03734 - 0.846421i) q^{26} +(1.92530 - 4.82631i) q^{27} +(3.38430 + 4.06774i) q^{28} +(2.07878 + 2.07878i) q^{29} +(-7.08744 - 4.41132i) q^{30} +(-3.31731 + 1.91525i) q^{31} +(-1.77124 + 5.37240i) q^{32} +(1.83944 - 4.49634i) q^{33} +(-2.79630 - 0.475438i) q^{34} +(6.47988 - 6.27040i) q^{35} +(-0.397370 + 5.98683i) q^{36} +(-4.20434 + 1.12655i) q^{37} +(-1.89217 + 4.12347i) q^{38} +(-8.78992 + 6.80605i) q^{39} +(9.35537 + 2.32357i) q^{40} -8.67639i q^{41} +(-6.16912 - 1.98543i) q^{42} +(4.52927 + 4.52927i) q^{43} +(-0.420481 + 5.59381i) q^{44} +(10.2240 - 0.0894710i) q^{45} +(-0.841136 - 2.26773i) q^{46} +(-5.17739 + 8.96750i) q^{47} +(-1.69405 - 6.71790i) q^{48} +(3.69725 - 5.94393i) q^{49} +(1.56813 - 9.22301i) q^{50} +(3.20362 - 1.34343i) q^{51} +(7.23357 - 10.6045i) q^{52} +(5.54861 + 1.48675i) q^{53} +(-3.51796 - 6.45167i) q^{54} +9.55907 q^{55} +(7.48330 - 0.0144457i) q^{56} +(-0.749369 - 5.50576i) q^{57} +(4.13944 - 0.387693i) q^{58} +(-1.75857 + 6.56309i) q^{59} +(-11.1991 + 3.73672i) q^{60} +(2.03278 - 0.544681i) q^{61} +(-0.908015 + 5.34051i) q^{62} +(7.68234 - 1.99540i) q^{63} +(4.25162 + 6.77670i) q^{64} +(-18.9438 - 10.9372i) q^{65} +(-3.23614 - 6.06042i) q^{66} +(-3.10476 - 0.831917i) q^{67} +(-3.04106 + 2.61584i) q^{68} +(2.35801 + 1.79303i) q^{69} +(-0.980402 - 12.7143i) q^{70} -12.8919 q^{71} +(6.16043 + 5.83516i) q^{72} +(-0.0186751 - 0.0323462i) q^{73} +(-2.56727 + 5.59466i) q^{74} +(4.43104 + 10.5665i) q^{75} +(2.78253 + 5.78136i) q^{76} +(7.19852 - 1.80264i) q^{77} +(-0.520896 + 15.7130i) q^{78} +(1.41020 - 2.44253i) q^{79} +(10.9723 - 8.09023i) q^{80} +(7.87179 + 4.36290i) q^{81} +(-9.44766 - 7.82951i) q^{82} +(-5.54643 + 5.54643i) q^{83} +(-7.72889 + 4.92587i) q^{84} +(4.83344 + 4.83344i) q^{85} +(9.01907 - 0.844710i) q^{86} +(-4.02611 + 3.11743i) q^{87} +(5.71162 + 5.50567i) q^{88} +(-2.36808 - 1.36721i) q^{89} +(9.12860 - 11.2135i) q^{90} +(-16.3283 - 4.66394i) q^{91} +(-3.22835 - 1.13047i) q^{92} +(-2.56576 - 6.11843i) q^{93} +(5.09261 + 13.7298i) q^{94} +(9.46864 - 5.46672i) q^{95} +(-8.84377 - 4.21755i) q^{96} -2.90039i q^{97} +(-3.13594 - 9.38967i) q^{98} +(7.32361 + 4.14326i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 6 q^{3} - 4 q^{4}+O(q^{10}) \) 240 * q - 6 * q^3 - 4 * q^4	\( 240 q - 6 q^{3} - 4 q^{4} - 12 q^{10} - 6 q^{12} - 16 q^{15} - 20 q^{16} - 4 q^{18} - 12 q^{19} + 2 q^{21} - 40 q^{22} - 6 q^{24} - 12 q^{28} + 22 q^{30} - 24 q^{31} - 12 q^{33} - 64 q^{36} - 4 q^{37} + 48 q^{40} - 18 q^{42} - 16 q^{43} - 6 q^{45} + 12 q^{46} - 16 q^{49} - 10 q^{51} - 48 q^{52} - 90 q^{54} - 4 q^{58} - 18 q^{60} - 12 q^{61} - 36 q^{63} + 32 q^{64} - 66 q^{66} - 36 q^{67} - 76 q^{70} - 46 q^{72} + 24 q^{75} - 76 q^{78} - 8 q^{79} - 4 q^{81} + 72 q^{82} - 24 q^{84} + 24 q^{85} + 12 q^{88} - 88 q^{91} - 14 q^{93} + 24 q^{94} + 96 q^{96} + 28 q^{99}+O(q^{100}) \) 240 * q - 6 * q^3 - 4 * q^4 - 12 * q^10 - 6 * q^12 - 16 * q^15 - 20 * q^16 - 4 * q^18 - 12 * q^19 + 2 * q^21 - 40 * q^22 - 6 * q^24 - 12 * q^28 + 22 * q^30 - 24 * q^31 - 12 * q^33 - 64 * q^36 - 4 * q^37 + 48 * q^40 - 18 * q^42 - 16 * q^43 - 6 * q^45 + 12 * q^46 - 16 * q^49 - 10 * q^51 - 48 * q^52 - 90 * q^54 - 4 * q^58 - 18 * q^60 - 12 * q^61 - 36 * q^63 + 32 * q^64 - 66 * q^66 - 36 * q^67 - 76 * q^70 - 46 * q^72 + 24 * q^75 - 76 * q^78 - 8 * q^79 - 4 * q^81 + 72 * q^82 - 24 * q^84 + 24 * q^85 + 12 * q^88 - 88 * q^91 - 14 * q^93 + 24 * q^94 + 96 * q^96 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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