LMFDB - Embedded newform 336.2.bs.a.19.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(19,336)]

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([6, 9, 0, 10]))

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

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

chi := DirichletCharacter("336.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bs (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:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.11
Character	$\chi$	$=$	336.19
Dual form			336.2.bs.a.283.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.904988 - 1.08674i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(-0.361993 + 1.96697i) q^{4} +(-2.68161 + 0.718534i) q^{5} +(1.28394 - 0.592883i) q^{6} +(-0.164584 - 2.64063i) q^{7} +(2.46517 - 1.38669i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.904988 - 1.08674i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(-0.361993 + 1.96697i) q^{4} +(-2.68161 + 0.718534i) q^{5} +(1.28394 - 0.592883i) q^{6} +(-0.164584 - 2.64063i) q^{7} +(2.46517 - 1.38669i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(3.20768 + 2.26394i) q^{10} +(-0.476389 + 1.77791i) q^{11} +(-1.80625 - 0.858747i) q^{12} +(3.89320 - 3.89320i) q^{13} +(-2.72072 + 2.56860i) q^{14} -2.77620i q^{15} +(-3.73792 - 1.42406i) q^{16} +(1.76864 - 1.02112i) q^{17} +(0.240374 + 1.39364i) q^{18} +(7.81618 - 2.09434i) q^{19} +(-0.442611 - 5.53474i) q^{20} +(2.59325 + 0.524469i) q^{21} +(2.36325 - 1.09128i) q^{22} +(2.56511 - 4.44290i) q^{23} +(0.701407 + 2.74008i) q^{24} +(2.34460 - 1.35365i) q^{25} +(-7.75419 - 0.707584i) q^{26} +(0.707107 - 0.707107i) q^{27} +(5.25361 + 0.632158i) q^{28} +(-0.480330 - 0.480330i) q^{29} +(-3.01700 + 2.51243i) q^{30} +(-3.39359 - 5.87787i) q^{31} +(1.83520 + 5.35089i) q^{32} +(-1.59403 - 0.920314i) q^{33} +(-2.71028 - 0.997938i) q^{34} +(2.33873 + 6.96287i) q^{35} +(1.29698 - 1.52245i) q^{36} +(2.55419 + 9.53235i) q^{37} +(-9.34955 - 6.59878i) q^{38} +(2.75291 + 4.76818i) q^{39} +(-5.61424 + 5.48987i) q^{40} -9.53641 q^{41} +(-1.77690 - 3.29282i) q^{42} +(-3.82420 - 3.82420i) q^{43} +(-3.32464 - 1.58063i) q^{44} +(2.68161 + 0.718534i) q^{45} +(-7.14965 + 1.23317i) q^{46} +(6.70468 - 11.6128i) q^{47} +(2.34298 - 3.24198i) q^{48} +(-6.94582 + 0.869208i) q^{49} +(-3.59290 - 1.32292i) q^{50} +(0.528572 + 1.97266i) q^{51} +(6.24849 + 9.06711i) q^{52} +(-4.39093 - 1.17655i) q^{53} +(-1.40836 - 0.128516i) q^{54} -5.10996i q^{55} +(-4.06746 - 6.28138i) q^{56} +8.09191i q^{57} +(-0.0872993 + 0.956685i) q^{58} +(8.96747 + 2.40283i) q^{59} +(5.46070 + 1.00497i) q^{60} +(-0.502253 - 1.87444i) q^{61} +(-3.31654 + 9.00735i) q^{62} +(-1.17778 + 2.36914i) q^{63} +(4.15418 - 6.83687i) q^{64} +(-7.64264 + 13.2374i) q^{65} +(0.442440 + 2.56516i) q^{66} +(2.26490 + 0.606879i) q^{67} +(1.36828 + 3.84849i) q^{68} +(3.62761 + 3.62761i) q^{69} +(5.45028 - 8.84289i) q^{70} +4.35387 q^{71} +(-2.82825 - 0.0316777i) q^{72} +(2.93679 + 5.08666i) q^{73} +(8.04765 - 11.4024i) q^{74} +(0.700703 + 2.61506i) q^{75} +(1.29009 + 16.1323i) q^{76} +(4.77320 + 0.965352i) q^{77} +(2.69040 - 7.30683i) q^{78} +(-2.98280 - 1.72212i) q^{79} +(11.0469 + 1.13294i) q^{80} +(0.500000 + 0.866025i) q^{81} +(8.63034 + 10.3636i) q^{82} +(-3.24589 - 3.24589i) q^{83} +(-1.97035 + 4.91098i) q^{84} +(-4.00907 + 4.00907i) q^{85} +(-0.695042 + 7.61675i) q^{86} +(0.588282 - 0.339645i) q^{87} +(1.29103 + 5.04346i) q^{88} +(4.76354 - 8.25069i) q^{89} +(-1.64596 - 3.56447i) q^{90} +(-10.9213 - 9.63974i) q^{91} +(7.81048 + 6.65378i) q^{92} +(6.55592 - 1.75665i) q^{93} +(-18.6877 + 3.22326i) q^{94} +(-19.4551 + 11.2324i) q^{95} +(-5.64355 + 0.387755i) q^{96} +1.26255i q^{97} +(7.23049 + 6.76166i) q^{98} +(1.30152 - 1.30152i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{4} - 24 q^{8}+O(q^{10}) $ 128 * q + 4 * q^4 - 24 * q^8	$ 128 q + 4 q^{4} - 24 q^{8} + 36 q^{10} - 8 q^{11} - 32 q^{14} - 4 q^{16} + 4 q^{18} + 16 q^{22} + 16 q^{23} - 32 q^{28} + 32 q^{29} - 24 q^{35} - 16 q^{37} + 60 q^{40} - 20 q^{42} - 16 q^{43} - 12 q^{44} - 20 q^{46} - 32 q^{50} - 144 q^{52} - 16 q^{53} - 56 q^{56} - 40 q^{58} - 96 q^{59} - 24 q^{60} - 32 q^{64} - 72 q^{66} + 16 q^{67} - 60 q^{68} + 28 q^{70} + 128 q^{71} - 4 q^{72} - 72 q^{74} + 72 q^{78} - 36 q^{80} + 64 q^{81} - 60 q^{82} + 24 q^{84} - 44 q^{86} - 48 q^{88} - 8 q^{91} + 56 q^{92} + 36 q^{94} + 60 q^{96} + 148 q^{98} - 16 q^{99}+O(q^{100}) $ 128 * q + 4 * q^4 - 24 * q^8 + 36 * q^10 - 8 * q^11 - 32 * q^14 - 4 * q^16 + 4 * q^18 + 16 * q^22 + 16 * q^23 - 32 * q^28 + 32 * q^29 - 24 * q^35 - 16 * q^37 + 60 * q^40 - 20 * q^42 - 16 * q^43 - 12 * q^44 - 20 * q^46 - 32 * q^50 - 144 * q^52 - 16 * q^53 - 56 * q^56 - 40 * q^58 - 96 * q^59 - 24 * q^60 - 32 * q^64 - 72 * q^66 + 16 * q^67 - 60 * q^68 + 28 * q^70 + 128 * q^71 - 4 * q^72 - 72 * q^74 + 72 * q^78 - 36 * q^80 + 64 * q^81 - 60 * q^82 + 24 * q^84 - 44 * q^86 - 48 * q^88 - 8 * q^91 + 56 * q^92 + 36 * q^94 + 60 * q^96 + 148 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.904988	−	1.08674i	−0.639923	−	0.768439i
$2$	−0.904988	−	1.08674i	−0.639923	−	0.768439i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$4$	−0.361993	+	1.96697i	−0.180997	+	0.983484i
$5$	−2.68161	+	0.718534i	−1.19925	+	0.321338i	−0.802536	−	0.596604i	$-0.796517\pi$
$5$	−2.68161	+	0.718534i	−1.19925	+	0.321338i	−0.396715	+	0.917942i	$0.629850\pi$
$6$	1.28394	−	0.592883i	0.524164	−	0.242044i
$7$	−0.164584	−	2.64063i	−0.0622067	−	0.998063i
$7$	−0.164584	−	2.64063i	−0.0622067	−	0.998063i
$8$	2.46517	−	1.38669i	0.871571	−	0.490269i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	3.20768	+	2.26394i	1.01436	+	0.715919i
$11$	−0.476389	+	1.77791i	−0.143637	+	0.536060i	0.856175	+	0.516685i	$0.172834\pi$
$11$	−0.476389	+	1.77791i	−0.143637	+	0.536060i	−0.999812	+	0.0193747i	$0.993832\pi$
$12$	−1.80625	−	0.858747i	−0.521421	−	0.247899i
$13$	3.89320	−	3.89320i	1.07978	−	1.07978i	0.0832514	−	0.996529i	$-0.473470\pi$
$13$	3.89320	−	3.89320i	1.07978	−	1.07978i	0.996529	−	0.0832514i	$-0.0265305\pi$
$14$	−2.72072	+	2.56860i	−0.727143	+	0.686486i
$15$		−	2.77620i		−	0.716813i
$16$	−3.73792	−	1.42406i	−0.934481	−	0.356014i
$17$	1.76864	−	1.02112i	0.428957	−	0.247659i	−0.269945	−	0.962876i	$-0.587006\pi$
$17$	1.76864	−	1.02112i	0.428957	−	0.247659i	0.698902	+	0.715217i	$0.253672\pi$
$18$	0.240374	+	1.39364i	0.0566568	+	0.328483i
$19$	7.81618	−	2.09434i	1.79315	−	0.480474i	0.800279	−	0.599628i	$-0.204685\pi$
$19$	7.81618	−	2.09434i	1.79315	−	0.480474i	0.992876	+	0.119153i	$0.0380180\pi$
$20$	−0.442611	−	5.53474i	−0.0989708	−	1.23761i
$21$	2.59325	+	0.524469i	0.565893	+	0.114449i
$22$	2.36325	−	1.09128i	0.503846	−	0.232661i
$23$	2.56511	−	4.44290i	0.534862	−	0.926408i	−0.464308	−	0.885674i	$-0.653697\pi$
$23$	2.56511	−	4.44290i	0.534862	−	0.926408i	0.999170	−	0.0407343i	$-0.0129697\pi$
$24$	0.701407	+	2.74008i	0.143174	+	0.559316i
$25$	2.34460	−	1.35365i	0.468919	−	0.270731i
$26$	−7.75419	−	0.707584i	−1.52072	−	0.138769i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	5.25361	+	0.632158i	0.992838	+	0.119467i
$29$	−0.480330	−	0.480330i	−0.0891951	−	0.0891951i	0.661101	−	0.750297i	$-0.270089\pi$
$29$	−0.480330	−	0.480330i	−0.0891951	−	0.0891951i	−0.750297	+	0.661101i	$0.770089\pi$
$30$	−3.01700	+	2.51243i	−0.550827	+	0.458705i
$31$	−3.39359	−	5.87787i	−0.609507	−	1.05570i	−0.991322	−	0.131458i	$-0.958034\pi$
$31$	−3.39359	−	5.87787i	−0.609507	−	1.05570i	0.381814	−	0.924239i	$-0.375299\pi$
$32$	1.83520	+	5.35089i	0.324421	+	0.945913i
$33$	−1.59403	−	0.920314i	−0.277485	−	0.160206i
$34$	−2.71028	−	0.997938i	−0.464810	−	0.171145i
$35$	2.33873	+	6.96287i	0.395317	+	1.17694i
$36$	1.29698	−	1.52245i	0.216163	−	0.253741i
$37$	2.55419	+	9.53235i	0.419906	+	1.56711i	0.774802	+	0.632204i	$0.217849\pi$
$37$	2.55419	+	9.53235i	0.419906	+	1.56711i	−0.354897	+	0.934906i	$0.615484\pi$
$38$	−9.34955	−	6.59878i	−1.51670	−	1.07046i
$39$	2.75291	+	4.76818i	0.440818	+	0.763520i
$40$	−5.61424	+	5.48987i	−0.887690	+	0.868025i
$41$	−9.53641			−1.48934			−0.744669	−	0.667434i	$-0.767393\pi$
$41$	−9.53641			−1.48934			−0.744669	+	0.667434i	$0.767393\pi$
$42$	−1.77690	−	3.29282i	−0.274181	−	0.508092i
$43$	−3.82420	−	3.82420i	−0.583184	−	0.583184i	0.352593	−	0.935777i	$-0.385300\pi$
$43$	−3.82420	−	3.82420i	−0.583184	−	0.583184i	−0.935777	+	0.352593i	$0.885300\pi$
$44$	−3.32464	−	1.58063i	−0.501208	−	0.238289i
$45$	2.68161	+	0.718534i	0.399750	+	0.107113i
$46$	−7.14965	+	1.23317i	−1.05416	+	0.181821i
$47$	6.70468	−	11.6128i	0.977977	−	1.69391i	0.308240	−	0.951309i	$-0.400260\pi$
$47$	6.70468	−	11.6128i	0.977977	−	1.69391i	0.669737	−	0.742598i	$-0.266407\pi$
$48$	2.34298	−	3.24198i	0.338180	−	0.467940i
$49$	−6.94582	+	0.869208i	−0.992261	+	0.124173i
$50$	−3.59290	−	1.32292i	−0.508112	−	0.187089i
$51$	0.528572	+	1.97266i	0.0740148	+	0.276227i
$52$	6.24849	+	9.06711i	0.866510	+	1.25738i
$53$	−4.39093	−	1.17655i	−0.603141	−	0.161611i	−0.0556887	−	0.998448i	$-0.517735\pi$
$53$	−4.39093	−	1.17655i	−0.603141	−	0.161611i	−0.547452	+	0.836837i	$0.684402\pi$
$54$	−1.40836	−	0.128516i	−0.191654	−	0.0174888i
$55$		−	5.10996i		−	0.689026i
$56$	−4.06746	−	6.28138i	−0.543537	−	0.839385i
$57$			8.09191i			1.07180i
$58$	−0.0872993	+	0.956685i	−0.0114630	+	0.125619i
$59$	8.96747	+	2.40283i	1.16746	+	0.312821i	0.789943	−	0.613180i	$-0.210110\pi$
$59$	8.96747	+	2.40283i	1.16746	+	0.312821i	0.377521	+	0.926001i	$0.376776\pi$
$60$	5.46070	+	1.00497i	0.704974	+	0.129741i
$61$	−0.502253	−	1.87444i	−0.0643070	−	0.239997i	0.926290	−	0.376812i	$-0.122980\pi$
$61$	−0.502253	−	1.87444i	−0.0643070	−	0.239997i	−0.990597	+	0.136816i	$0.956313\pi$
$62$	−3.31654	+	9.00735i	−0.421201	+	1.14393i
$63$	−1.17778	+	2.36914i	−0.148386	+	0.298484i
$64$	4.15418	−	6.83687i	0.519272	−	0.854609i
$65$	−7.64264	+	13.2374i	−0.947953	+	1.64190i
$66$	0.442440	+	2.56516i	0.0544606	+	0.315750i
$67$	2.26490	+	0.606879i	0.276702	+	0.0741421i	0.394501	−	0.918895i	$-0.370917\pi$
$67$	2.26490	+	0.606879i	0.276702	+	0.0741421i	−0.117799	+	0.993037i	$0.537584\pi$
$68$	1.36828	+	3.84849i	0.165928	+	0.466698i
$69$	3.62761	+	3.62761i	0.436713	+	0.436713i
$70$	5.45028	−	8.84289i	0.651433	−	1.05693i
$71$	4.35387			0.516709			0.258355	−	0.966050i	$-0.416820\pi$
$71$	4.35387			0.516709			0.258355	+	0.966050i	$0.416820\pi$
$72$	−2.82825	−	0.0316777i	−0.333312	−	0.00373326i
$73$	2.93679	+	5.08666i	0.343725	+	0.595349i	0.985121	−	0.171861i	$-0.0549779\pi$
$73$	2.93679	+	5.08666i	0.343725	+	0.595349i	−0.641396	+	0.767210i	$0.721645\pi$
$74$	8.04765	−	11.4024i	0.935520	−	1.32550i
$75$	0.700703	+	2.61506i	0.0809102	+	0.301961i
$76$	1.29009	+	16.1323i	0.147984	+	1.85050i
$77$	4.77320	+	0.965352i	0.543957	+	0.110012i
$78$	2.69040	−	7.30683i	0.304628	−	0.827336i
$79$	−2.98280	−	1.72212i	−0.335591	−	0.193753i	0.322730	−	0.946491i	$-0.395399\pi$
$79$	−2.98280	−	1.72212i	−0.335591	−	0.193753i	−0.658320	+	0.752738i	$0.728733\pi$
$80$	11.0469	+	1.13294i	1.23508	+	0.126666i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	8.63034	+	10.3636i	0.953062	+	1.14446i
$83$	−3.24589	−	3.24589i	−0.356283	−	0.356283i	0.506158	−	0.862441i	$-0.331065\pi$
$83$	−3.24589	−	3.24589i	−0.356283	−	0.356283i	−0.862441	+	0.506158i	$0.831065\pi$
$84$	−1.97035	+	4.91098i	−0.214983	+	0.535832i
$85$	−4.00907	+	4.00907i	−0.434845	+	0.434845i
$86$	−0.695042	+	7.61675i	−0.0749483	+	0.821335i
$87$	0.588282	−	0.339645i	0.0630704	−	0.0364137i
$88$	1.29103	+	5.04346i	0.137624	+	0.537635i
$89$	4.76354	−	8.25069i	0.504934	−	0.874572i	−0.495050	−	0.868865i	$-0.664850\pi$
$89$	4.76354	−	8.25069i	0.504934	−	0.874572i	0.999984	−	0.00570691i	$-0.00181658\pi$
$90$	−1.64596	−	3.56447i	−0.173500	−	0.375728i
$91$	−10.9213	−	9.63974i	−1.14486	−	1.01052i
$92$	7.81048	+	6.65378i	0.814299	+	0.693705i
$93$	6.55592	−	1.75665i	0.679817	−	0.182156i
$94$	−18.6877	+	3.22326i	−1.92749	+	0.332454i
$95$	−19.4551	+	11.2324i	−1.99605	+	1.15242i
$96$	−5.64355	+	0.387755i	−0.575992	+	0.0395751i
$97$			1.26255i			0.128192i	0.997944	+	0.0640962i	$0.0204164\pi$
$97$			1.26255i			0.128192i	−0.997944	+	0.0640962i	$0.979584\pi$
$98$	7.23049	+	6.76166i	0.730390	+	0.683031i
$99$	1.30152	−	1.30152i	0.130808	−	0.130808i
$100$	1.81386	+	5.10176i	0.181386	+	0.510176i
$101$	1.17524	−	4.38606i	0.116941	−	0.436430i	−0.882484	−	0.470343i	$-0.844130\pi$
$101$	1.17524	−	4.38606i	0.116941	−	0.436430i	0.999425	+	0.0339131i	$0.0107969\pi$
$102$	1.66541	−	2.35965i	0.164900	−	0.233640i
$103$	7.77116	+	4.48668i	0.765715	+	0.442086i	0.831344	−	0.555759i	$-0.187572\pi$
$103$	7.77116	+	4.48668i	0.765715	+	0.442086i	−0.0656291	+	0.997844i	$0.520905\pi$
$104$	4.19876	−	14.9961i	0.411722	−	1.47049i
$105$	−7.33092	+	0.456917i	−0.715424	+	0.0445906i
$106$	2.69514	+	5.83654i	0.261775	+	0.566895i
$107$	−4.25268	+	1.13950i	−0.411122	+	0.110160i	−0.458451	−	0.888719i	$-0.651596\pi$
$107$	−4.25268	+	1.13950i	−0.411122	+	0.110160i	0.0473292	+	0.998879i	$0.484929\pi$
$108$	1.13489	+	1.64682i	0.109205	+	0.158466i
$109$	−2.27022	+	8.47257i	−0.217447	+	0.811525i	0.767843	+	0.640638i	$0.221330\pi$
$109$	−2.27022	+	8.47257i	−0.217447	+	0.811525i	−0.985291	+	0.170887i	$0.945337\pi$
$110$	−5.55318	+	4.62445i	−0.529475	+	0.440924i
$111$	−9.86862			−0.936688
$112$	−3.14520	+	10.1048i	−0.297194	+	0.954817i
$113$	8.52426			0.801895			0.400947	−	0.916101i	$-0.368681\pi$
$113$	8.52426			0.801895			0.400947	+	0.916101i	$0.368681\pi$
$114$	8.79377	−	7.32308i	0.823612	−	0.685869i
$115$	−3.68624	+	13.7572i	−0.343743	+	1.28287i
$116$	1.11867	−	0.770918i	0.103866	−	0.0715779i
$117$	−5.31821	+	1.42501i	−0.491669	+	0.131742i
$118$	−5.50421	−	11.9198i	−0.506704	−	1.09731i
$119$	−2.98749	−	4.50225i	−0.273863	−	0.412720i
$120$	−3.84974	−	6.84383i	−0.351431	−	0.624753i
$121$	6.59226	+	3.80605i	0.599297	+	0.346004i
$122$	−1.58248	+	2.24216i	−0.143271	+	0.202996i
$123$	2.46821	−	9.21147i	0.222551	−	0.830570i
$124$	12.7900	−	4.54734i	1.14858	−	0.408363i
$125$	4.50072	−	4.50072i	0.402557	−	0.402557i
$126$	3.64051	−	0.864109i	0.324322	−	0.0769809i
$127$		−	5.73788i		−	0.509155i	−0.967052	−	0.254577i	$-0.918064\pi$
$127$		−	5.73788i		−	0.509155i	0.967052	−	0.254577i	$-0.0819364\pi$
$128$	−11.1894	+	1.67279i	−0.989009	+	0.147856i
$129$	4.68366	−	2.70411i	0.412374	−	0.238084i
$130$	21.3021	−	3.67419i	1.86832	−	0.322248i
$131$	−0.0124420	+	0.00333383i	−0.00108706	+	0.000291278i	−0.259363	−	0.965780i	$-0.583512\pi$
$131$	−0.0124420	+	0.00333383i	−0.00108706	+	0.000291278i	0.258275	+	0.966071i	$0.416846\pi$
$132$	2.38725	−	2.80226i	0.207784	−	0.243905i
$133$	−6.81678	−	20.2949i	−0.591090	−	1.75979i
$134$	−1.39019	−	3.01057i	−0.120094	−	0.260074i
$135$	−1.38810	+	2.40426i	−0.119469	+	0.206926i
$136$	2.94401	−	4.96980i	0.252447	−	0.426156i
$137$	−12.1045	+	6.98855i	−1.03416	+	0.597072i	−0.918174	−	0.396178i	$-0.870336\pi$
$137$	−12.1045	+	6.98855i	−1.03416	+	0.597072i	−0.115986	+	0.993251i	$0.537003\pi$
$138$	0.659313	−	7.22520i	0.0561244	−	0.615050i
$139$	0.127227	−	0.127227i	0.0107913	−	0.0107913i	−0.701691	−	0.712482i	$-0.747571\pi$
$139$	0.127227	−	0.127227i	0.0107913	−	0.0107913i	0.712482	+	0.701691i	$0.247571\pi$
$140$	−14.5423	+	2.07970i	−1.22905	+	0.175766i
$141$	9.48184	+	9.48184i	0.798515	+	0.798515i
$142$	−3.94020	−	4.73151i	−0.330654	−	0.397060i
$143$	5.06708	+	8.77644i	0.423731	+	0.733923i
$144$	2.52511	+	3.10223i	0.210426	+	0.258519i
$145$	1.63319	+	0.942923i	0.135629	+	0.0783055i
$146$	2.87011	−	7.79488i	0.237532	−	0.645109i
$147$	0.958122	−	6.93412i	0.0790245	−	0.571916i
$148$	−19.6744	+	1.57336i	−1.61723	+	0.129329i
$149$	0.857943	+	3.20189i	0.0702855	+	0.262309i	0.992123	−	0.125268i	$-0.0399790\pi$
$149$	0.857943	+	3.20189i	0.0702855	+	0.262309i	−0.921838	+	0.387577i	$0.873312\pi$
$150$	2.20775	−	3.12808i	0.180262	−	0.255406i
$151$	−10.6303	−	18.4122i	−0.865081	−	1.49837i	−0.866966	−	0.498367i	$-0.833933\pi$
$151$	−10.6303	−	18.4122i	−0.865081	−	1.49837i	0.00188478	−	0.999998i	$-0.499400\pi$
$152$	16.3641	−	16.0015i	1.32730	−	1.29790i
$153$	−2.04224			−0.165106
$154$	−3.27061	−	6.06085i	−0.263553	−	0.488397i
$155$	13.3237	+	13.3237i	1.07019	+	1.07019i
$156$	−10.3754	+	3.68884i	−0.830696	+	0.295343i
$157$	−7.14256	−	1.91384i	−0.570039	−	0.152741i	−0.0377243	−	0.999288i	$-0.512011\pi$
$157$	−7.14256	−	1.91384i	−0.570039	−	0.152741i	−0.532314	+	0.846547i	$0.678678\pi$
$158$	0.827906	+	4.80001i	0.0658647	+	0.381868i
$159$	2.27291	−	3.93680i	0.180254	−	0.312209i
$160$	−8.76609	−	13.0303i	−0.693020	−	1.03014i
$161$	−12.1542	−	6.04227i	−0.957886	−	0.476197i
$162$	0.488647	−	1.32711i	0.0383918	−	0.104268i
$163$	2.10330	+	7.84963i	0.164743	+	0.614830i	0.998073	+	0.0620537i	$0.0197650\pi$
$163$	2.10330	+	7.84963i	0.164743	+	0.614830i	−0.833330	+	0.552776i	$0.813568\pi$
$164$	3.45211	−	18.7578i	0.269565	−	1.46474i
$165$	4.93584	+	1.32255i	0.384255	+	0.102961i
$166$	−0.589935	+	6.46492i	−0.0457879	+	0.501775i
$167$			5.46606i			0.422976i	0.977381	+	0.211488i	$0.0678310\pi$
$167$			5.46606i			0.422976i	−0.977381	+	0.211488i	$0.932169\pi$
$168$	7.12009	−	2.30313i	0.549327	−	0.177690i
$169$		−	17.3140i		−	1.33185i
$170$	7.98497	+	0.728643i	0.612419	+	0.0558844i
$171$	−7.81618	−	2.09434i	−0.597718	−	0.160158i
$172$	8.90640	−	6.13774i	0.679107	−	0.467998i
$173$	0.864971	+	3.22811i	0.0657625	+	0.245429i	0.990980	−	0.134007i	$-0.0427846\pi$
$173$	0.864971	+	3.22811i	0.0657625	+	0.245429i	−0.925218	+	0.379436i	$0.876118\pi$
$174$	−0.901492	−	0.331933i	−0.0683420	−	0.0251638i
$175$	−3.96038	−	5.96842i	−0.299376	−	0.451170i
$176$	4.31255	−	5.96728i	0.325071	−	0.449801i
$177$	−4.64190	+	8.04001i	−0.348907	+	0.604324i
$178$	−13.2773	+	2.29007i	−0.995174	+	0.171648i
$179$	−1.22162	−	0.327333i	−0.0913085	−	0.0244660i	0.212876	−	0.977079i	$-0.431717\pi$
$179$	−1.22162	−	0.327333i	−0.0913085	−	0.0244660i	−0.304184	+	0.952613i	$0.598384\pi$
$180$	−2.38406	+	5.01453i	−0.177697	+	0.373761i
$181$	−13.4277	−	13.4277i	−0.998072	−	0.998072i	0.00192653	−	0.999998i	$-0.499387\pi$
$181$	−13.4277	−	13.4277i	−0.998072	−	0.998072i	−0.999998	+	0.00192653i	$0.999387\pi$
$182$	−0.592253	+	20.5924i	−0.0439007	+	1.52641i
$183$	1.94056			0.143450
$184$	0.162514	−	14.5095i	0.0119807	−	1.06966i
$185$	−13.6986	−	23.7268i	−1.00714	−	1.74443i
$186$	−7.84205	−	5.53481i	−0.575007	−	0.405832i
$187$	0.972904	+	3.63093i	0.0711458	+	0.265520i
$188$	20.4150	+	17.3916i	1.48892	+	1.26842i
$189$	−1.98358	−	1.75083i	−0.144284	−	0.127354i
$190$	29.8133	+	10.9774i	2.16288	+	0.796381i
$191$	17.6983	+	10.2181i	1.28060	+	0.739358i	0.976959	−	0.213427i	$-0.0684627\pi$
$191$	17.6983	+	10.2181i	1.28060	+	0.739358i	0.303646	+	0.952785i	$0.401796\pi$
$192$	5.52873	+	5.78214i	0.399002	+	0.417290i
$193$	−1.04540	−	1.81069i	−0.0752497	−	0.130336i	0.825945	−	0.563750i	$-0.190642\pi$
$193$	−1.04540	−	1.81069i	−0.0752497	−	0.130336i	−0.901195	+	0.433414i	$0.857309\pi$
$194$	1.37206	−	1.14259i	0.0985080	−	0.0820333i
$195$	−10.8083	−	10.8083i	−0.774000	−	0.774000i
$196$	0.804637	−	13.9769i	0.0574741	−	0.998347i
$197$	−1.32672	+	1.32672i	−0.0945247	+	0.0945247i	−0.752788	−	0.658263i	$-0.771291\pi$
$197$	−1.32672	+	1.32672i	−0.0945247	+	0.0945247i	0.658263	+	0.752788i	$0.271291\pi$
$198$	−2.59227	−	0.236549i	−0.184225	−	0.0168108i
$199$	−6.96496	+	4.02122i	−0.493733	+	0.285057i	−0.726122	−	0.687566i	$-0.758679\pi$
$199$	−6.96496	+	4.02122i	−0.493733	+	0.285057i	0.232389	+	0.972623i	$0.425346\pi$
$200$	3.90274	−	6.58822i	0.275966	−	0.465858i
$201$	−1.17240	+	2.03066i	−0.0826948	+	0.143232i
$202$	−5.83008	+	2.69216i	−0.410203	+	0.189419i
$203$	−1.18932	+	1.34743i	−0.0834738	+	0.0945709i
$204$	−4.07149	+	0.325596i	−0.285061	+	0.0227962i
$205$	25.5729	−	6.85224i	1.78609	−	0.478581i
$206$	−2.15697	−	12.5056i	−0.150283	−	0.871306i
$207$	−4.44290	+	2.56511i	−0.308803	+	0.178287i
$208$	−20.0966	+	9.00834i	−1.39345	+	0.624616i
$209$			14.8942i			1.03025i
$210$	7.13094	+	7.55327i	0.492082	+	0.521225i
$211$	−6.04852	+	6.04852i	−0.416398	+	0.416398i	−0.883960	−	0.467563i	$-0.845132\pi$
$211$	−6.04852	+	6.04852i	−0.416398	+	0.416398i	0.467563	+	0.883960i	$0.345132\pi$
$212$	3.90371	−	8.21091i	0.268108	−	0.563928i
$213$	−1.12686	+	4.20552i	−0.0772115	+	0.288157i
$214$	5.08696	+	3.59031i	0.347738	+	0.245428i
$215$	13.0028	+	7.50717i	0.886784	+	0.511985i
$216$	0.762603	−	2.72368i	0.0518886	−	0.185323i
$217$	−14.9627	+	9.92861i	−1.01574	+	0.673998i
$218$	11.2620	−	5.20044i	0.762757	−	0.352219i
$219$	−5.67344	+	1.52019i	−0.383375	+	0.102725i
$220$	10.0511	+	1.84977i	0.677646	+	0.124711i
$221$	2.91022	−	10.8611i	0.195763	−	0.730596i
$222$	8.93098	+	10.7246i	0.599408	+	0.719787i
$223$	−0.122649			−0.00821321			−0.00410660	−	0.999992i	$-0.501307\pi$
$223$	−0.122649			−0.00821321			−0.00410660	+	0.999992i	$0.501307\pi$
$224$	13.8277	−	5.72675i	0.923900	−	0.382634i
$225$	−2.70731			−0.180487
$226$	−7.71435	−	9.26363i	−0.513151	−	0.616207i
$227$	−5.70069	+	21.2753i	−0.378368	+	1.41209i	0.469993	+	0.882670i	$0.344256\pi$
$227$	−5.70069	+	21.2753i	−0.378368	+	1.41209i	−0.848361	+	0.529418i	$0.822410\pi$
$228$	−15.9165	−	2.92921i	−1.05410	−	0.193992i
$229$	−7.25903	+	1.94505i	−0.479690	+	0.128533i	−0.490558	−	0.871408i	$-0.663207\pi$
$229$	−7.25903	+	1.94505i	−0.479690	+	0.128533i	0.0108681	+	0.999941i	$0.496541\pi$
$230$	18.2865	−	8.44415i	1.20577	−	0.556791i
$231$	−2.16785	+	4.36071i	−0.142634	+	0.286913i
$232$	−1.85017	−	0.518028i	−0.121469	−	0.0340102i
$233$	8.81183	+	5.08751i	0.577282	+	0.333294i	0.760052	−	0.649862i	$-0.225173\pi$
$233$	8.81183	+	5.08751i	0.577282	+	0.333294i	−0.182771	+	0.983156i	$0.558507\pi$
$234$	6.36153	+	4.48988i	0.415866	+	0.293513i
$235$	−9.63508	+	35.9586i	−0.628523	+	2.34568i
$236$	−7.97244	+	16.7689i	−0.518962	+	1.09156i
$237$	2.43544	−	2.43544i	0.158199	−	0.158199i
$238$	−2.18911	+	7.32110i	−0.141899	+	0.474556i
$239$		−	7.71316i		−	0.498923i	−0.968385	−	0.249461i	$-0.919746\pi$
$239$		−	7.71316i		−	0.498923i	0.968385	−	0.249461i	$-0.0802536\pi$
$240$	−3.95347	+	10.3772i	−0.255196	+	0.669848i
$241$	−0.751865	+	0.434090i	−0.0484319	+	0.0279622i	−0.524020	−	0.851706i	$-0.675568\pi$
$241$	−0.751865	+	0.434090i	−0.0484319	+	0.0279622i	0.475589	+	0.879668i	$0.342235\pi$
$242$	−1.82975	−	10.6085i	−0.117621	−	0.681939i
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$	3.86877	−	0.309384i	0.247672	−	0.0198063i
$245$	18.0014	−	7.32169i	1.15007	−	0.467765i
$246$	−12.2441	+	5.65398i	−0.780658	+	0.360485i
$247$	22.2763	−	38.5837i	1.41741	−	2.45502i
$248$	−16.5166	−	9.78412i	−1.04880	−	0.621293i
$249$	3.97539	−	2.29519i	0.251930	−	0.145452i
$250$	−8.96420	−	0.818000i	−0.566946	−	0.0517348i
$251$	13.4432	−	13.4432i	0.848529	−	0.848529i	−0.141421	−	0.989950i	$-0.545167\pi$
$251$	13.4432	−	13.4432i	0.848529	−	0.848529i	0.989950	+	0.141421i	$0.0451671\pi$
$252$	−4.23368	−	3.17427i	−0.266697	−	0.199960i
$253$	6.67708	+	6.67708i	0.419784	+	0.419784i
$254$	−6.23557	+	5.19272i	−0.391254	+	0.325820i
$255$	−2.83484	−	4.91009i	−0.177525	−	0.307482i
$256$	11.9441	+	10.6460i	0.746508	+	0.665377i
$257$	−5.20491	−	3.00506i	−0.324673	−	0.187450i	0.328800	−	0.944399i	$-0.393356\pi$
$257$	−5.20491	−	3.00506i	−0.324673	−	0.187450i	−0.653474	+	0.756949i	$0.726689\pi$
$258$	−7.17732	−	2.64272i	−0.446841	−	0.164528i
$259$	24.7510	−	8.31352i	1.53795	−	0.516577i
$260$	−23.2710	−	19.8247i	−1.44321	−	1.22947i
$261$	0.175813	+	0.656143i	0.0108826	+	0.0406142i
$262$	0.0148829	+	0.0105041i	0.000919467	+	0.000648947i
$263$	−3.40907	−	5.90468i	−0.210212	−	0.364098i	0.741569	−	0.670877i	$-0.234082\pi$
$263$	−3.40907	−	5.90468i	−0.210212	−	0.364098i	−0.951781	+	0.306779i	$0.900749\pi$
$264$	−5.20575	−	0.0583069i	−0.320392	−	0.00358854i
$265$	12.6201			0.775249
$266$	−15.8861	+	25.7747i	−0.974041	+	1.58035i
$267$	6.73666	+	6.73666i	0.412277	+	0.412277i
$268$	−2.01359	+	4.23531i	−0.123000	+	0.258713i
$269$	−18.7573	−	5.02599i	−1.14365	−	0.306440i	−0.363232	−	0.931699i	$-0.618327\pi$
$269$	−18.7573	−	5.02599i	−1.14365	−	0.306440i	−0.780418	+	0.625259i	$0.784994\pi$
$270$	3.86902	−	0.667328i	0.235461	−	0.0406123i
$271$	−5.53173	+	9.58124i	−0.336029	+	0.582019i	−0.983682	−	0.179916i	$-0.942417\pi$
$271$	−5.53173	+	9.58124i	−0.336029	+	0.582019i	0.647653	+	0.761935i	$0.275751\pi$
$272$	−8.06516	+	1.29824i	−0.489022	+	0.0787172i
$273$	12.1379	−	8.05417i	0.734619	−	0.487461i
$274$	18.5492	+	6.82988i	1.12060	+	0.412608i
$275$	1.28973	+	4.81335i	0.0777738	+	0.290256i
$276$	−8.44856	+	5.82222i	−0.508544	+	0.350457i
$277$	26.9278	+	7.21529i	1.61794	+	0.433525i	0.950394	−	0.311048i	$-0.100680\pi$
$277$	26.9278	+	7.21529i	1.61794	+	0.433525i	0.667542	+	0.744572i	$0.267347\pi$
$278$	−0.253402	−	0.0231234i	−0.0151980	−	0.00138685i
$279$			6.78718i			0.406338i
$280$	15.4207	+	13.9216i	0.921564	+	0.831974i
$281$			9.53041i			0.568536i	0.958745	+	0.284268i	$0.0917506\pi$
$281$			9.53041i			0.568536i	−0.958745	+	0.284268i	$0.908249\pi$
$282$	1.72331	−	18.8852i	0.102622	−	1.12460i
$283$	7.13162	+	1.91091i	0.423931	+	0.113592i	0.464476	−	0.885586i	$-0.346243\pi$
$283$	7.13162	+	1.91091i	0.423931	+	0.113592i	−0.0405451	+	0.999178i	$0.512909\pi$
$284$	−1.57607	+	8.56392i	−0.0935226	+	0.508175i
$285$	−5.81431	−	21.6993i	−0.344410	−	1.28536i
$286$	4.95203	−	13.4492i	0.292820	−	0.795265i
$287$	1.56954	+	25.1821i	0.0926468	+	1.48645i
$288$	1.08612	−	5.55161i	0.0640000	−	0.327132i
$289$	−6.41462	+	11.1104i	−0.377331	+	0.653556i
$290$	−0.453309	−	2.62818i	−0.0266192	−	0.154332i
$291$	−1.21953	−	0.326772i	−0.0714900	−	0.0191557i
$292$	−11.0684	+	3.93523i	−0.647729	+	0.230292i
$293$	21.0562	+	21.0562i	1.23012	+	1.23012i	0.963919	+	0.266196i	$0.0857670\pi$
$293$	21.0562	+	21.0562i	1.23012	+	1.23012i	0.266196	+	0.963919i	$0.414233\pi$
$294$	−8.40265	+	5.23407i	−0.490052	+	0.305257i
$295$	−25.7737			−1.50060
$296$	19.5149	+	19.9570i	1.13428	+	1.15998i
$297$	0.920314	+	1.59403i	0.0534020	+	0.0924950i
$298$	2.70318	−	3.83003i	0.156591	−	0.221868i
$299$	−7.31061	−	27.2836i	−0.422784	−	1.57785i
$300$	−5.39738	+	0.431627i	−0.311618	+	0.0249200i
$301$	−9.46888	+	10.7277i	−0.545777	+	0.618333i
$302$	−10.3889	+	28.2152i	−0.597816	+	1.62360i
$303$	3.93244	+	2.27039i	0.225913	+	0.130431i
$304$	−32.1987	−	3.30221i	−1.84672	−	0.189395i
$305$	2.69369	+	4.66561i	0.154240	+	0.267152i
$306$	1.84821	+	2.21938i	0.105655	+	0.126874i
$307$	14.7959	+	14.7959i	0.844449	+	0.844449i	0.989434	−	0.144985i	$-0.0463132\pi$
$307$	14.7959	+	14.7959i	0.844449	+	0.844449i	−0.144985	+	0.989434i	$0.546313\pi$
$308$	−3.62668	+	9.03928i	−0.206649	+	0.515061i
$309$	−6.34512	+	6.34512i	−0.360961	+	0.360961i
$310$	2.42157	−	26.5372i	0.137536	−	1.50721i
$311$	3.48684	−	2.01313i	0.197720	−	0.114154i	−0.397871	−	0.917441i	$-0.630251\pi$
$311$	3.48684	−	2.01313i	0.197720	−	0.114154i	0.595592	+	0.803287i	$0.296918\pi$
$312$	13.3984	+	7.93696i	0.758535	+	0.449342i
$313$	6.98128	−	12.0919i	0.394605	−	0.683476i	−0.598446	−	0.801163i	$-0.704215\pi$
$313$	6.98128	−	12.0919i	0.394605	−	0.683476i	0.993051	+	0.117687i	$0.0375480\pi$
$314$	4.38409	+	9.49409i	0.247409	+	0.535783i
$315$	1.45603	−	7.19938i	0.0820382	−	0.405639i
$316$	4.46710	−	5.24367i	0.251294	−	0.294979i
$317$	0.595693	−	0.159615i	0.0334574	−	0.00896489i	−0.242052	−	0.970263i	$-0.577820\pi$
$317$	0.595693	−	0.159615i	0.0334574	−	0.00896489i	0.275509	+	0.961299i	$0.411154\pi$
$318$	−6.33522	+	1.09270i	−0.355262	+	0.0612756i
$319$	1.08281	−	0.625159i	0.0606256	−	0.0350022i
$320$	−6.22734	+	21.3187i	−0.348119	+	1.19175i
$321$		−	4.40270i		−	0.245735i
$322$	4.43306	+	18.6766i	0.247045	+	1.04081i
$323$	11.6854	−	11.6854i	0.650193	−	0.650193i
$324$	−1.88444	+	0.669989i	−0.104691	+	0.0372216i
$325$	3.85794	−	14.3980i	0.214000	−	0.798659i
$326$	6.62701	−	9.38955i	0.367036	−	0.520039i
$327$	−7.59630	−	4.38572i	−0.420076	−	0.242531i
$328$	−23.5089	+	13.2241i	−1.29806	+	0.730177i
$329$	−31.7687	−	15.7933i	−1.75146	−	0.870711i
$330$	−3.02961	−	6.56085i	−0.166774	−	0.361163i
$331$	−24.2504	+	6.49787i	−1.33292	+	0.357155i	−0.853804	−	0.520595i	$-0.825710\pi$
$331$	−24.2504	+	6.49787i	−1.33292	+	0.357155i	−0.479118	+	0.877751i	$0.659043\pi$
$332$	7.55955	−	5.20957i	0.414884	−	0.285912i
$333$	2.55419	−	9.53235i	0.139969	−	0.522370i
$334$	5.94016	−	4.94672i	0.325031	−	0.270672i
$335$	−6.50965			−0.355660
$336$	−8.94648	−	5.65336i	−0.488071	−	0.308416i
$337$	13.5982			0.740739			0.370369	−	0.928885i	$-0.379231\pi$
$337$	13.5982			0.740739			0.370369	+	0.928885i	$0.379231\pi$
$338$	−18.8158	+	15.6690i	−1.02345	+	0.852282i
$339$	−2.20624	+	8.23380i	−0.119827	+	0.447199i
$340$	−6.43446	−	9.33697i	−0.348958	−	0.506369i
$341$	12.0670	−	3.23334i	0.653465	−	0.175095i
$342$	4.79756	+	10.3895i	0.259422	+	0.561799i
$343$	3.43842	+	18.1983i	0.185657	+	0.982615i
$344$	−14.7303	−	4.12433i	−0.794204	−	0.222369i
$345$	−12.3344	−	7.12126i	−0.664061	−	0.383396i
$346$	2.72532	−	3.86140i	0.146514	−	0.207590i
$347$	5.95727	−	22.2328i	0.319803	−	1.19352i	−0.599631	−	0.800277i	$-0.704686\pi$
$347$	5.95727	−	22.2328i	0.319803	−	1.19352i	0.919434	−	0.393244i	$-0.128647\pi$
$348$	0.455116	+	1.28008i	0.0243968	+	0.0686195i
$349$	−15.3660	+	15.3660i	−0.822525	+	0.822525i	−0.986470	−	0.163945i	$-0.947578\pi$
$349$	−15.3660	+	15.3660i	−0.822525	+	0.822525i	0.163945	+	0.986470i	$0.447578\pi$
$350$	−2.90200	+	9.70523i	−0.155119	+	0.518766i
$351$		−	5.50582i		−	0.293879i
$352$	−10.3877	+	0.713712i	−0.553665	+	0.0380410i
$353$	5.00015	−	2.88684i	0.266131	−	0.153651i	−0.360997	−	0.932567i	$-0.617564\pi$
$353$	5.00015	−	2.88684i	0.266131	−	0.153651i	0.627128	+	0.778916i	$0.284230\pi$
$354$	12.9382	−	2.23159i	0.687660	−	0.118608i
$355$	−11.6754	+	3.12841i	−0.619664	+	0.166039i
$356$	14.5045	+	12.3564i	0.768736	+	0.654889i
$357$	5.12206	−	1.72043i	0.271088	−	0.0910547i
$358$	0.749831	+	1.62382i	0.0396298	+	0.0858214i
$359$	−15.3406	+	26.5707i	−0.809645	+	1.40235i	0.103466	+	0.994633i	$0.467007\pi$
$359$	−15.3406	+	26.5707i	−0.809645	+	1.40235i	−0.913110	+	0.407713i	$0.866327\pi$
$360$	7.60702	−	1.94725i	0.400925	−	0.102629i
$361$	40.2519	−	23.2395i	2.11852	−	1.22313i
$362$	−2.44046	+	26.7442i	−0.128268	+	1.40565i
$363$	−5.38256	+	5.38256i	−0.282511	+	0.282511i
$364$	22.9145	−	17.9922i	1.20104	−	0.943049i
$365$	−11.5303	−	11.5303i	−0.603521	−	0.603521i
$366$	−1.75618	−	2.10888i	−0.0917971	−	0.110233i
$367$	10.9890	+	19.0335i	0.573621	+	0.993541i	0.996190	+	0.0872102i	$0.0277952\pi$
$367$	10.9890	+	19.0335i	0.573621	+	0.993541i	−0.422569	+	0.906331i	$0.638872\pi$
$368$	−15.9151	+	12.9543i	−0.829633	+	0.675292i
$369$	8.25878	+	4.76821i	0.429935	+	0.248223i
$370$	−13.3876	+	36.3592i	−0.695989	+	1.89023i
$371$	−2.38414	+	11.7884i	−0.123779	+	0.612026i
$372$	1.08208	+	13.5312i	0.0561034	+	0.701559i
$373$	−6.09639	−	22.7520i	−0.315659	−	1.17806i	−0.923375	−	0.383900i	$-0.874581\pi$
$373$	−6.09639	−	22.7520i	−0.315659	−	1.17806i	0.607716	−	0.794155i	$-0.292086\pi$
$374$	3.06539	−	4.34323i	0.158508	−	0.224583i
$375$	3.18249	+	5.51224i	0.164343	+	0.284651i
$376$	0.424778	−	37.9250i	0.0219062	−	1.95583i
$377$	−3.74004			−0.192622
$378$	−0.107569	+	3.74011i	−0.00553273	+	0.192371i
$379$	12.0328	+	12.0328i	0.618085	+	0.618085i	0.945040	−	0.326955i	$-0.106022\pi$
$379$	12.0328	+	12.0328i	0.618085	+	0.618085i	−0.326955	+	0.945040i	$0.606022\pi$
$380$	−15.0511	−	42.3335i	−0.772108	−	2.17166i
$381$	5.54237	+	1.48507i	0.283944	+	0.0760826i
$382$	−4.91235	−	28.4807i	−0.251338	−	1.45720i
$383$	12.2449	−	21.2088i	0.625685	−	1.08372i	−0.362724	−	0.931897i	$-0.618153\pi$
$383$	12.2449	−	21.2088i	0.625685	−	1.08372i	0.988408	−	0.151821i	$-0.0485136\pi$
$384$	1.28022	−	11.2410i	0.0653312	−	0.573642i
$385$	−13.4935	+	0.841015i	−0.687692	+	0.0428621i
$386$	−1.02167	+	2.77473i	−0.0520014	+	0.141230i
$387$	1.39975	+	5.22395i	0.0711534	+	0.265548i
$388$	−2.48339	−	0.457034i	−0.126075	−	0.0232024i
$389$	−1.50508	−	0.403284i	−0.0763104	−	0.0204473i	0.220462	−	0.975396i	$-0.429244\pi$
$389$	−1.50508	−	0.403284i	−0.0763104	−	0.0204473i	−0.296772	+	0.954948i	$0.595910\pi$
$390$	−1.96440	+	21.5272i	−0.0994711	+	1.09007i
$391$		−	10.4772i		−	0.529852i
$392$	−15.9174	+	11.7745i	−0.803948	+	0.594700i
$393$		−	0.0128809i		−	0.000649757i
$394$	2.64245	+	0.241129i	0.133125	+	0.0121479i
$395$	9.23609	+	2.47480i	0.464718	+	0.124521i
$396$	2.08891	+	3.03119i	0.104971	+	0.152323i
$397$	2.27666	+	8.49660i	0.114262	+	0.426432i	0.999231	−	0.0392189i	$-0.0124870\pi$
$397$	2.27666	+	8.49660i	0.114262	+	0.426432i	−0.884969	+	0.465651i	$0.845820\pi$
$398$	10.6732	+	3.92992i	0.535000	+	0.196989i
$399$	21.3677	−	1.33179i	1.06972	−	0.0666731i
$400$	−10.6916	+	1.72101i	−0.534580	+	0.0860506i
$401$	19.8143	−	34.3194i	0.989479	−	1.71383i	0.369446	−	0.929252i	$-0.379547\pi$
$401$	19.8143	−	34.3194i	0.989479	−	1.71383i	0.620033	−	0.784576i	$-0.287119\pi$
$402$	3.26780	−	0.563630i	0.162983	−	0.0281113i
$403$	−36.0957	−	9.67181i	−1.79805	−	0.481787i
$404$	8.20182	+	3.89939i	0.408056	+	0.194002i
$405$	−1.96307	−	1.96307i	−0.0975459	−	0.0975459i
$406$	2.54062	+	0.0730702i	0.126089	+	0.00362641i
$407$	−18.1644			−0.900378
$408$	4.03849	+	4.12998i	0.199935	+	0.204464i
$409$	16.2655	+	28.1726i	0.804276	+	1.39305i	0.916778	+	0.399396i	$0.130780\pi$
$409$	16.2655	+	28.1726i	0.804276	+	1.39305i	−0.112502	+	0.993651i	$0.535887\pi$
$410$	−30.5898	−	21.5898i	−1.51072	−	1.06625i
$411$	−3.61754	−	13.5008i	−0.178440	−	0.665948i
$412$	−11.6383	+	13.6615i	−0.573376	+	0.673052i
$413$	4.86907	−	24.0752i	0.239591	−	1.18466i
$414$	6.80837	+	2.50687i	0.334613	+	0.123206i
$415$	11.0365	+	6.37191i	0.541759	+	0.312785i
$416$	27.9769	+	13.6873i	1.37168	+	0.671075i
$417$	0.0899633	+	0.155821i	0.00440552	+	0.00763059i
$418$	16.1861	−	13.4791i	0.791686	−	0.659282i
$419$	−13.0545	−	13.0545i	−0.637755	−	0.637755i	0.312246	−	0.950001i	$-0.398919\pi$
$419$	−13.0545	−	13.0545i	−0.637755	−	0.637755i	−0.950001	+	0.312246i	$0.898919\pi$
$420$	1.75500	−	14.5851i	0.0856352	−	0.711679i
$421$	−28.2316	+	28.2316i	−1.37593	+	1.37593i	−0.524540	+	0.851386i	$0.675763\pi$
$421$	−28.2316	+	28.2316i	−1.37593	+	1.37593i	−0.851386	+	0.524540i	$0.824237\pi$
$422$	12.0470	+	1.09931i	0.586438	+	0.0535136i
$423$	−11.6128	+	6.70468i	−0.564636	+	0.325992i
$424$	−12.4559	+	3.18847i	−0.604913	+	0.154846i
$425$	2.76449	−	4.78824i	0.134098	−	0.232264i
$426$	5.59009	−	2.58134i	0.270841	−	0.125066i
$427$	−4.86702	+	1.63477i	−0.235532	+	0.0791118i
$428$	−0.701923	−	8.77738i	−0.0339288	−	0.424271i
$429$	−9.78885	+	2.62291i	−0.472610	+	0.126635i
$430$	−3.60906	−	20.9245i	−0.174045	−	1.00907i
$431$	−13.9810	+	8.07196i	−0.673443	+	0.388812i	−0.797380	−	0.603478i	$-0.793781\pi$
$431$	−13.9810	+	8.07196i	−0.673443	+	0.388812i	0.123937	+	0.992290i	$0.460448\pi$
$432$	−3.65007	+	1.63615i	−0.175614	+	0.0787193i
$433$		−	28.5121i		−	1.37021i	−0.728447	−	0.685103i	$-0.759757\pi$
$433$		−	28.5121i		−	1.37021i	0.728447	−	0.685103i	$-0.240243\pi$
$434$	24.3309	+	7.27529i	1.16792	+	0.349225i
$435$	−1.33349	+	1.33349i	−0.0639362	+	0.0639362i
$436$	−15.8435	−	7.53245i	−0.758764	−	0.360739i
$437$	10.7444	−	40.0987i	0.513975	−	1.91818i
$438$	6.78644	+	4.78978i	0.324269	+	0.228864i
$439$	−13.7356	−	7.93025i	−0.655564	−	0.378490i	0.135021	−	0.990843i	$-0.456890\pi$
$439$	−13.7356	−	7.93025i	−0.655564	−	0.378490i	−0.790585	+	0.612353i	$0.790223\pi$
$440$	−7.08593	−	12.5969i	−0.337809	−	0.600535i
$441$	6.44986	+	2.72016i	0.307136	+	0.129531i
$442$	−14.4369	+	6.66651i	−0.686691	+	0.317094i
$443$	−5.46080	+	1.46322i	−0.259451	+	0.0695196i	−0.386200	−	0.922415i	$-0.626212\pi$
$443$	−5.46080	+	1.46322i	−0.259451	+	0.0695196i	0.126749	+	0.991935i	$0.459546\pi$
$444$	3.57237	−	19.4112i	0.169537	−	0.921217i
$445$	−6.84553	+	25.5479i	−0.324509	+	1.21109i
$446$	0.110996	+	0.133287i	0.00525582	+	0.00631135i
$447$	−3.31484			−0.156786
$448$	−18.7373	−	9.84439i	−0.885256	−	0.465104i
$449$	−7.40443			−0.349437			−0.174718	−	0.984618i	$-0.555901\pi$
$449$	−7.40443			−0.349437			−0.174718	+	0.984618i	$0.555901\pi$
$450$	2.45008	+	2.94213i	0.115498	+	0.138693i
$451$	4.54305	−	16.9549i	0.213924	−	0.798374i
$452$	−3.08572	+	16.7669i	−0.145140	+	0.788651i
$453$	20.5362	−	5.50265i	0.964873	−	0.258537i
$454$	28.2797	−	13.0587i	1.32723	−	0.612875i
$455$	36.2130	+	18.0027i	1.69769	+	0.843979i
$456$	11.2210	+	19.9480i	0.525470	+	0.934149i
$457$	21.1446	+	12.2078i	0.989103	+	0.571059i	0.905006	−	0.425399i	$-0.139866\pi$
$457$	21.1446	+	12.2078i	0.989103	+	0.571059i	0.0840969	+	0.996458i	$0.473199\pi$
$458$	8.68310	+	6.12841i	0.405734	+	0.286362i
$459$	0.528572	−	1.97266i	0.0246716	−	0.0920757i
$460$	−25.7256	−	12.2307i	−1.19946	−	0.570260i
$461$	−10.6706	+	10.6706i	−0.496981	+	0.496981i	−0.910497	−	0.413516i	$-0.864301\pi$
$461$	−10.6706	+	10.6706i	−0.496981	+	0.496981i	0.413516	+	0.910497i	$0.364301\pi$
$462$	6.70082	−	1.59050i	0.311750	−	0.0739968i
$463$		−	20.3520i		−	0.945839i	−0.881106	−	0.472919i	$-0.843200\pi$
$463$		−	20.3520i		−	0.945839i	0.881106	−	0.472919i	$-0.156800\pi$
$464$	1.11142	+	2.47945i	0.0515963	+	0.115106i
$465$	−16.3182	+	9.42130i	−0.756737	+	0.436903i
$466$	−2.44581	−	14.1803i	−0.113300	−	0.656888i
$467$	−6.46219	+	1.73154i	−0.299034	+	0.0801260i	−0.405217	−	0.914221i	$-0.632804\pi$
$467$	−6.46219	+	1.73154i	−0.299034	+	0.0801260i	0.106182	+	0.994347i	$0.466137\pi$
$468$	−0.877794	−	10.9766i	−0.0405760	−	0.507393i
$469$	1.22978	−	6.08065i	0.0567858	−	0.280778i
$470$	47.7972	−	22.0713i	2.20472	−	1.01807i
$471$	3.69726	−	6.40385i	0.170361	−	0.295074i
$472$	25.4384	−	6.51172i	1.17090	−	0.299726i
$473$	8.62088	−	4.97727i	0.396389	−	0.228855i
$474$	−4.85073	−	0.442638i	−0.222801	−	0.0203310i
$475$	15.4908	−	15.4908i	0.710766	−	0.710766i
$476$	9.93722	−	4.24652i	0.455472	−	0.194639i
$477$	3.21438	+	3.21438i	0.147177	+	0.147177i
$478$	−8.38218	+	6.98032i	−0.383392	+	0.319272i
$479$	8.38510	+	14.5234i	0.383125	+	0.663592i	0.991507	−	0.130052i	$-0.0415145\pi$
$479$	8.38510	+	14.5234i	0.383125	+	0.663592i	−0.608382	+	0.793644i	$0.708181\pi$
$480$	14.8552	−	5.09489i	0.678042	−	0.232549i
$481$	47.0553	+	27.1674i	2.14554	+	1.23873i
$482$	1.15217	+	0.424234i	0.0524799	+	0.0193233i
$483$	8.98212	−	10.1762i	0.408701	−	0.463034i
$484$	−9.87272	+	11.5890i	−0.448760	+	0.526773i
$485$	−0.907185	−	3.38566i	−0.0411931	−	0.153735i
$486$	1.15542	+	0.815479i	0.0524109	+	0.0369909i
$487$	10.4571	+	18.1121i	0.473854	+	0.820740i	0.999552	−	0.0299319i	$-0.00952903\pi$
$487$	10.4571	+	18.1121i	0.473854	+	0.820740i	−0.525698	+	0.850671i	$0.676196\pi$
$488$	−3.83741	−	3.92434i	−0.173711	−	0.177647i
$489$	−8.12653			−0.367494
$490$	−24.2478	−	12.9368i	−1.09540	−	0.584423i
$491$	4.47715	+	4.47715i	0.202051	+	0.202051i	0.800878	−	0.598827i	$-0.204366\pi$
$491$	4.47715	+	4.47715i	0.202051	+	0.202051i	−0.598827	+	0.800878i	$0.704366\pi$
$492$	17.2252	+	8.18937i	0.776571	+	0.369205i
$493$	−1.34000	−	0.359053i	−0.0603508	−	0.0161709i
$494$	−62.0901	+	10.7093i	−2.79356	+	0.481834i
$495$	−2.55498	+	4.42535i	−0.114838	+	0.198905i
$496$	4.31456	+	26.8037i	0.193729	+	1.20352i
$497$	−0.716575	−	11.4969i	−0.0321428	−	0.515709i
$498$	−6.09194	−	2.24308i	−0.272986	−	0.100515i
$499$	3.28627	+	12.2645i	0.147114	+	0.549036i	0.999652	+	0.0263716i	$0.00839531\pi$
$499$	3.28627	+	12.2645i	0.147114	+	0.549036i	−0.852538	+	0.522665i	$0.824938\pi$
$500$	7.22354	+	10.4820i	0.323047	+	0.468770i
$501$	−5.27981	−	1.41472i	−0.235884	−	0.0632050i
$502$	−26.7752	−	2.44329i	−1.19504	−	0.109049i
$503$			28.2260i			1.25853i	0.777189	+	0.629267i	$0.216645\pi$
$503$			28.2260i			1.25853i	−0.777189	+	0.629267i	$0.783355\pi$
$504$	0.381834	+	7.47357i	0.0170083	+	0.332899i
$505$			12.6062i			0.560966i
$506$	1.21355	−	13.2989i	0.0539488	−	0.591208i
$507$	16.7241	+	4.48120i	0.742743	+	0.199017i
$508$	11.2862	+	2.07707i	0.500746	+	0.0921553i
$509$	6.42663	+	23.9845i	0.284855	+	1.06309i	0.948945	+	0.315442i	$0.102153\pi$
$509$	6.42663	+	23.9845i	0.284855	+	1.06309i	−0.664089	+	0.747653i	$0.731181\pi$
$510$	−2.77048	+	7.52430i	−0.122679	+	0.333182i
$511$	12.9486	−	8.59214i	0.572814	−	0.380094i
$512$	0.760138	−	22.6146i	0.0335937	−	0.999436i
$513$	4.04595	−	7.00780i	0.178633	−	0.309402i
$514$	1.44468	+	8.37591i	0.0637220	+	0.369446i
$515$	−24.0630	−	6.44767i	−1.06034	−	0.284118i
$516$	3.62345	+	10.1915i	0.159514	+	0.448655i
$517$	17.4525	+	17.4525i	0.767562	+	0.767562i
$518$	−31.4340	−	19.3742i	−1.38113	−	0.851253i
$519$	−3.34199			−0.146697
$520$	−0.484203	+	43.2306i	−0.0212337	+	1.89579i
$521$	−1.13672	−	1.96885i	−0.0498004	−	0.0862568i	0.840051	−	0.542508i	$-0.182525\pi$
$521$	−1.13672	−	1.96885i	−0.0498004	−	0.0862568i	−0.889851	+	0.456251i	$0.849192\pi$
$522$	0.553946	−	0.784864i	0.0242456	−	0.0343526i
$523$	4.68590	+	17.4880i	0.204900	+	0.764697i	0.989480	+	0.144670i	$0.0462120\pi$
$523$	4.68590	+	17.4880i	0.204900	+	0.764697i	−0.784580	+	0.620028i	$0.787121\pi$
$524$	−0.00205361	−	0.0256799i	−8.97124e−5	−	0.00112183i
$525$	6.79007	−	2.28069i	0.296343	−	0.0995375i
$526$	−3.33167	+	9.04843i	−0.145268	+	0.394530i
$527$	−12.0041	−	6.93054i	−0.522905	−	0.301899i
$528$	4.64778	+	5.71005i	0.202269	+	0.248498i
$529$	−1.65956	−	2.87444i	−0.0721546	−	0.124975i
$530$	−11.4211	−	13.7148i	−0.496100	−	0.595731i
$531$	−6.56464	−	6.56464i	−0.284881	−	0.284881i
$532$	42.3871	−	6.06177i	1.83771	−	0.262811i
$533$	−37.1272	+	37.1272i	−1.60816	+	1.60816i
$534$	1.22438	−	13.4176i	0.0529840	−	0.580635i
$535$	10.5852	−	6.11140i	0.457640	−	0.264219i
$536$	6.42494	−	1.64466i	0.277515	−	0.0710385i
$537$	0.632360	−	1.09528i	0.0272883	−	0.0472648i
$538$	11.5132	+	24.9327i	0.496368	+	1.07492i
$539$	1.76354	−	12.7631i	0.0759613	−	0.549747i
$540$	−4.22662	−	3.60068i	−0.181885	−	0.154948i
$541$	−36.7088	+	9.83611i	−1.57824	+	0.422887i	−0.938379	−	0.345607i	$-0.887673\pi$
$541$	−36.7088	+	9.83611i	−1.57824	+	0.422887i	−0.639857	+	0.768494i	$0.721006\pi$
$542$	15.4184	−	2.65937i	0.662279	−	0.114230i
$543$	16.4455	−	9.49480i	0.705743	−	0.407461i
$544$	8.70971	+	7.58981i	0.373426	+	0.325411i
$545$		−	24.3513i		−	1.04310i
$546$	−19.7374	−	5.90177i	−0.844684	−	0.252572i
$547$	17.5002	−	17.5002i	0.748254	−	0.748254i	−0.225897	−	0.974151i	$-0.572531\pi$
$547$	17.5002	−	17.5002i	0.748254	−	0.748254i	0.974151	+	0.225897i	$0.0725312\pi$
$548$	−9.36450	−	26.3390i	−0.400032	−	1.12515i
$549$	−0.502253	+	1.87444i	−0.0214357	+	0.0799989i
$550$	4.06365	−	5.75762i	0.173275	−	0.245506i
$551$	−4.76032	−	2.74837i	−0.202797	−	0.117085i
$552$	13.9731	+	3.91232i	0.594733	+	0.166519i
$553$	−4.05655	+	8.15988i	−0.172502	+	0.346994i
$554$	−16.5282	−	35.7932i	−0.702218	−	1.52071i
$555$	26.4638	−	7.09094i	1.12332	−	0.300994i
$556$	0.204197	+	0.296308i	0.00865987	+	0.0125662i
$557$	−3.35039	+	12.5038i	−0.141961	+	0.529804i	0.857911	+	0.513798i	$0.171762\pi$
$557$	−3.35039	+	12.5038i	−0.141961	+	0.529804i	−0.999872	+	0.0160062i	$0.994905\pi$
$558$	7.37588	−	6.14232i	0.312246	−	0.260025i
$559$	−29.7767			−1.25942
$560$	1.17353	−	29.3571i	0.0495905	−	1.24057i
$561$	−3.75901			−0.158706
$562$	10.3570	−	8.62490i	0.436885	−	0.363820i
$563$	11.0154	−	41.1101i	0.464245	−	1.73259i	−0.195136	−	0.980776i	$-0.562515\pi$
$563$	11.0154	−	41.1101i	0.464245	−	1.73259i	0.659381	−	0.751809i	$-0.270819\pi$
$564$	−22.0828	+	15.2181i	−0.929855	+	0.640798i
$565$	−22.8587	+	6.12497i	−0.961673	+	0.257680i
$566$	−4.37737	−	9.47954i	−0.183995	−	0.398455i
$567$	2.20456	−	1.46285i	0.0925828	−	0.0614338i
$568$	10.7331	−	6.03747i	0.450349	−	0.253327i
$569$	30.9761	+	17.8840i	1.29858	+	0.749738i	0.980159	−	0.198210i	$-0.0635129\pi$
$569$	30.9761	+	17.8840i	1.29858	+	0.749738i	0.318424	+	0.947948i	$0.396846\pi$
$570$	−18.3196	+	25.9562i	−0.767322	+	1.08719i
$571$	−5.34978	+	19.9656i	−0.223881	+	0.835536i	0.758968	+	0.651127i	$0.225704\pi$
$571$	−5.34978	+	19.9656i	−0.223881	+	0.835536i	−0.982850	+	0.184409i	$0.940963\pi$
$572$	−19.0972	+	6.78977i	−0.798495	+	0.283895i
$573$	−14.4506	+	14.4506i	−0.603683	+	0.603683i
$574$	25.9459	−	24.4952i	1.08296	−	1.02241i
$575$		−	13.8891i		−	0.579214i
$576$	−7.01606	+	3.84382i	−0.292336	+	0.160159i
$577$	32.8375	−	18.9587i	1.36704	−	0.789263i	0.376494	−	0.926419i	$-0.377130\pi$
$577$	32.8375	−	18.9587i	1.36704	−	0.789263i	0.990549	+	0.137156i	$0.0437962\pi$
$578$	17.8793	−	3.08382i	0.743680	−	0.128270i
$579$	2.01956	−	0.541140i	0.0839301	−	0.0224890i
$580$	−2.44590	+	2.87110i	−0.101561	+	0.119216i
$581$	−8.03696	+	9.10540i	−0.333429	+	0.377756i
$582$	0.748544	+	1.62103i	0.0310281	+	0.0671939i
$583$	4.18358	−	7.24618i	0.173266	−	0.300106i
$584$	14.2933	+	8.46710i	0.591462	+	0.350371i
$585$	13.2374	−	7.64264i	0.547301	−	0.315984i
$586$	3.82693	−	41.9381i	0.158089	−	1.73245i
$587$	−0.303911	+	0.303911i	−0.0125438	+	0.0125438i	−0.713351	−	0.700807i	$-0.752823\pi$
$587$	−0.303911	+	0.303911i	−0.0125438	+	0.0125438i	0.700807	+	0.713351i	$0.252823\pi$
$588$	13.2924	+	4.39470i	0.548167	+	0.181234i
$589$	−38.8352	−	38.8352i	−1.60018	−	1.60018i
$590$	23.3249	+	28.0093i	0.960272	+	1.15312i
$591$	−0.938130	−	1.62489i	−0.0385895	−	0.0668390i
$592$	4.02726	−	39.2685i	0.165520	−	1.61393i
$593$	−24.7998	−	14.3182i	−1.01841	−	0.587977i	−0.104764	−	0.994497i	$-0.533409\pi$
$593$	−24.7998	−	14.3182i	−1.01841	−	0.587977i	−0.913642	+	0.406520i	$0.866742\pi$
$594$	0.899418	−	2.44272i	0.0369036	−	0.100226i
$595$	11.2463	+	9.92664i	0.461053	+	0.406953i
$596$	−6.60858	+	0.528486i	−0.270698	+	0.0216476i
$597$	−2.08154	−	7.76841i	−0.0851917	−	0.317940i
$598$	−23.0340	+	32.6360i	−0.941932	+	1.33459i
$599$	−19.1600	−	33.1861i	−0.782856	−	1.35595i	−0.930272	−	0.366872i	$-0.880429\pi$
$599$	−19.1600	−	33.1861i	−0.782856	−	1.35595i	0.147416	−	0.989075i	$-0.452905\pi$
$600$	5.35363	+	5.47492i	0.218561	+	0.223513i
$601$	4.60200			0.187720			0.0938598	−	0.995585i	$-0.470079\pi$
$601$	4.60200			0.187720			0.0938598	+	0.995585i	$0.470079\pi$
$602$	20.2274	+	0.581756i	0.824406	+	0.0237106i
$603$	−1.65803	−	1.65803i	−0.0675200	−	0.0675200i
$604$	40.0643	−	14.2444i	1.63019	−	0.579595i
$605$	−20.4126	−	5.46955i	−0.829892	−	0.222369i
$606$	−1.09149	−	6.32820i	−0.0443387	−	0.257066i
$607$	−5.30207	+	9.18346i	−0.215204	+	0.372745i	−0.953336	−	0.301912i	$-0.902375\pi$
$607$	−5.30207	+	9.18346i	−0.215204	+	0.372745i	0.738131	+	0.674657i	$0.235708\pi$
$608$	25.5508	+	37.9800i	1.03622	+	1.54029i
$609$	−0.993697	−	1.49753i	−0.0402666	−	0.0606831i
$610$	2.63253	−	7.14966i	0.106588	−	0.289481i
$611$	−19.1085	−	71.3138i	−0.773046	−	2.88505i
$612$	0.739278	−	4.01703i	0.0298835	−	0.162379i
$613$	−44.5312	−	11.9321i	−1.79860	−	0.481932i	−0.804839	−	0.593493i	$-0.797748\pi$
$613$	−44.5312	−	11.9321i	−1.79860	−	0.481932i	−0.993758	+	0.111561i	$0.964415\pi$
$614$	2.68914	−	29.4695i	0.108525	−	1.18929i
$615$			26.4750i			1.06758i
$616$	13.1054	−	4.23919i	0.528033	−	0.170802i
$617$			18.7866i			0.756318i	0.925741	+	0.378159i	$0.123443\pi$
$617$			18.7866i			0.756318i	−0.925741	+	0.378159i	$0.876557\pi$
$618$	12.6377	+	1.15322i	0.508364	+	0.0463892i
$619$	−22.2946	−	5.97382i	−0.896096	−	0.240108i	−0.218757	−	0.975779i	$-0.570200\pi$
$619$	−22.2946	−	5.97382i	−0.896096	−	0.240108i	−0.677339	+	0.735671i	$0.736867\pi$
$620$	−31.0305	+	21.3843i	−1.24621	+	0.858812i
$621$	−1.32780	−	4.95541i	−0.0532827	−	0.198854i
$622$	−5.34329	−	1.96742i	−0.214246	−	0.0788863i
$623$	−22.5710	−	11.2208i	−0.904288	−	0.449552i
$624$	−3.50000	−	21.7434i	−0.140112	−	0.870432i
$625$	−15.6035	+	27.0261i	−0.624140	+	1.08104i
$626$	−19.4587	+	3.35624i	−0.777727	+	0.134142i
$627$	−14.3867	−	3.85490i	−0.574549	−	0.153950i
$628$	6.35003	−	13.3564i	0.253394	−	0.532978i
$629$	14.2511	+	14.2511i	0.568229	+	0.568229i
$630$	−9.14153	+	4.93303i	−0.364207	+	0.196537i
$631$	10.9811			0.437151			0.218575	−	0.975820i	$-0.429859\pi$
$631$	10.9811			0.437151			0.218575	+	0.975820i	$0.429859\pi$
$632$	−9.74116	−	0.109106i	−0.387482	−	0.00433999i
$633$	−4.27695	−	7.40790i	−0.169994	−	0.294437i
$634$	−0.712555	−	0.502911i	−0.0282992	−	0.0199732i
$635$	4.12287	+	15.3867i	0.163611	+	0.610605i
$636$	6.92078	+	5.89584i	0.274427	+	0.233785i
$637$	−23.6575	+	30.4255i	−0.937344	+	1.20550i
$638$	−1.65931	−	0.610965i	−0.0656928	−	0.0241883i
$639$	−3.77056	−	2.17694i	−0.149161	−	0.0861182i
$640$	28.8035	−	12.5257i	1.13856	−	0.495122i
$641$	18.8302	+	32.6149i	0.743748	+	1.28821i	0.950777	+	0.309875i	$0.100287\pi$
$641$	18.8302	+	32.6149i	0.743748	+	1.28821i	−0.207029	+	0.978335i	$0.566379\pi$
$642$	−4.78457	+	3.98439i	−0.188832	+	0.157251i
$643$	−9.96576	−	9.96576i	−0.393011	−	0.393011i	0.482748	−	0.875759i	$-0.339639\pi$
$643$	−9.96576	−	9.96576i	−0.393011	−	0.393011i	−0.875759	+	0.482748i	$0.839639\pi$
$644$	16.2847	−	21.7197i	0.641706	−	0.855875i
$645$	−10.6167	+	10.6167i	−0.418034	+	0.418034i
$646$	−23.2741	−	2.12380i	−0.915707	−	0.0835599i
$647$	−26.6441	+	15.3830i	−1.04749	+	0.604768i	−0.921945	−	0.387320i	$-0.873401\pi$
$647$	−26.6441	+	15.3830i	−1.04749	+	0.604768i	−0.125544	+	0.992088i	$0.540067\pi$
$648$	2.43350	+	1.44156i	0.0955968	+	0.0566298i
$649$	−8.54401	+	14.7987i	−0.335382	+	0.580898i
$650$	−19.1383	+	8.83748i	−0.750664	+	0.346635i
$651$	−5.71766	−	17.0226i	−0.224093	−	0.667169i
$652$	−16.2013	+	1.29561i	−0.634493	+	0.0507402i
$653$	26.3997	−	7.07378i	1.03310	−	0.276818i	0.297849	−	0.954613i	$-0.403731\pi$
$653$	26.3997	−	7.07378i	1.03310	−	0.276818i	0.735251	+	0.677794i	$0.237064\pi$
$654$	2.10843	+	12.2242i	0.0824462	+	0.478004i
$655$	0.0309691	−	0.0178800i	0.00121006	−	0.000698631i
$656$	35.6464	+	13.5804i	1.39176	+	0.530225i
$657$		−	5.87357i		−	0.229150i
$658$	11.5871	+	48.8169i	0.451714	+	1.90308i
$659$	−5.34039	+	5.34039i	−0.208032	+	0.208032i	−0.803431	−	0.595398i	$-0.796994\pi$
$659$	−5.34039	+	5.34039i	−0.208032	+	0.208032i	0.595398	+	0.803431i	$0.296994\pi$
$660$	−4.38816	+	9.22988i	−0.170809	+	0.359273i
$661$	−3.25911	+	12.1632i	−0.126765	+	0.473092i	−0.999896	−	0.0143922i	$-0.995419\pi$
$661$	−3.25911	+	12.1632i	−0.126765	+	0.473092i	0.873132	+	0.487484i	$0.162085\pi$
$662$	29.0078	+	20.4733i	1.12742	+	0.795717i
$663$	9.73779	+	5.62211i	0.378184	+	0.218345i
$664$	−12.5027	−	3.50064i	−0.485200	−	0.135851i
$665$	32.8625	+	49.5249i	1.27435	+	1.92049i
$666$	−12.6707	+	5.85094i	−0.490978	+	0.226719i
$667$	−3.36616	+	0.901959i	−0.130338	+	0.0349240i
$668$	−10.7516	−	1.97867i	−0.415990	−	0.0765572i
$669$	0.0317440	−	0.118470i	0.00122729	−	0.00458032i
$670$	5.89115	+	7.07427i	0.227595	+	0.273303i
$671$	3.57184			0.137890
$672$	1.95275	+	14.8387i	0.0753290	+	0.572415i
$673$	−24.8040			−0.956124			−0.478062	−	0.878326i	$-0.658660\pi$
$673$	−24.8040			−0.956124			−0.478062	+	0.878326i	$0.658660\pi$
$674$	−12.3062	−	14.7776i	−0.474016	−	0.569212i
$675$	0.700703	−	2.61506i	0.0269701	−	0.100654i
$676$	34.0562	+	6.26756i	1.30985	+	0.241060i
$677$	−42.6123	+	11.4179i	−1.63772	+	0.438827i	−0.956140	−	0.292912i	$-0.905376\pi$
$677$	−42.6123	+	11.4179i	−1.63772	+	0.438827i	−0.681585	+	0.731739i	$0.738709\pi$
$678$	10.9446	−	5.05389i	0.420325	−	0.194094i
$679$	3.33392	−	0.207795i	0.127944	−	0.00797443i
$680$	−4.32372	+	15.4424i	−0.165807	+	0.592190i
$681$	−19.0749	−	11.0129i	−0.730951	−	0.422015i
$682$	−14.4343	−	10.1875i	−0.552717	−	0.390100i
$683$	−7.94930	+	29.6672i	−0.304171	+	1.13518i	0.629485	+	0.777013i	$0.283266\pi$
$683$	−7.94930	+	29.6672i	−0.304171	+	1.13518i	−0.933656	+	0.358170i	$0.883401\pi$
$684$	6.94890	−	14.6160i	0.265698	−	0.558858i
$685$	27.4381	−	27.4381i	1.04835	−	1.04835i
$686$	16.6650	−	20.2059i	0.636273	−	0.771464i
$687$		−	7.51510i		−	0.286719i
$688$	8.84867	+	19.7404i	0.337353	+	0.752596i
$689$	−21.6753	+	12.5142i	−0.825763	+	0.476755i
$690$	3.42354	+	19.8489i	0.130332	+	0.755634i
$691$	37.8465	−	10.1409i	1.43975	−	0.385779i	0.547303	−	0.836935i	$-0.315655\pi$
$691$	37.8465	−	10.1409i	1.43975	−	0.385779i	0.892446	+	0.451155i	$0.148988\pi$
$692$	−6.66271	+	0.532814i	−0.253278	+	0.0202546i
$693$	−3.65104	−	3.22262i	−0.138691	−	0.122417i
$694$	−29.5525	+	13.6465i	−1.12180	+	0.518013i
$695$	−0.249757	+	0.432591i	−0.00947381	+	0.0164091i
$696$	0.979235	−	1.65305i	0.0371178	−	0.0626587i
$697$	−16.8664	+	9.73784i	−0.638862	+	0.368847i
$698$	30.6049	+	2.79275i	1.15841	+	0.105707i
$699$	−7.19483	+	7.19483i	−0.272133	+	0.272133i
$700$	13.1733	−	5.62941i	0.497904	−	0.212772i
$701$	20.2522	+	20.2522i	0.764913	+	0.764913i	0.977206	−	0.212293i	$-0.0680931\pi$
$701$	20.2522	+	20.2522i	0.764913	+	0.764913i	−0.212293	+	0.977206i	$0.568093\pi$
$702$	−5.98338	+	4.98270i	−0.225828	+	0.188060i
$703$	39.9280	+	69.1573i	1.50591	+	2.60832i
$704$	10.1763	+	10.6428i	0.383535	+	0.401114i
$705$	−32.2396	−	18.6135i	−1.21421	−	0.701027i
$706$	−7.66231	−	2.82129i	−0.288375	−	0.106181i
$707$	−11.7754	−	2.38150i	−0.442859	−	0.0895656i
$708$	−14.1341	−	12.0409i	−0.531192	−	0.452525i
$709$	−8.96584	−	33.4610i	−0.336719	−	1.25665i	−0.901993	−	0.431750i	$-0.857896\pi$
$709$	−8.96584	−	33.4610i	−0.336719	−	1.25665i	0.565274	−	0.824903i	$-0.308770\pi$
$710$	13.9658	+	9.85688i	0.524128	+	0.369922i
$711$	1.72212	+	2.98280i	0.0645845	+	0.111864i
$712$	0.301796	−	26.9450i	0.0113103	−	1.00981i
$713$	−34.8197			−1.30401
$714$	−6.50505	−	4.00936i	−0.243445	−	0.150047i
$715$	−19.8941	−	19.8941i	−0.743997	−	0.743997i
$716$	1.08607	−	2.28440i	0.0405885	−	0.0853722i
$717$	7.45034	+	1.99631i	0.278238	+	0.0745537i
$718$	42.7583	−	7.37496i	1.59573	−	0.275231i
$719$	15.0728	−	26.1069i	0.562121	−	0.973622i	−0.435190	−	0.900339i	$-0.643319\pi$
$719$	15.0728	−	26.1069i	0.562121	−	0.973622i	0.997311	−	0.0732836i	$-0.0233478\pi$
$720$	−9.00040	−	6.50459i	−0.335425	−	0.242412i
$721$	10.5686	−	21.2592i	0.393597	−	0.791732i
$722$	−61.6827	−	22.7118i	−2.29559	−	0.845246i
$723$	−0.224701	−	0.838597i	−0.00835673	−	0.0311877i
$724$	31.2725	−	21.5511i	1.16223	−	0.800940i
$725$	−1.77638	−	0.475980i	−0.0659731	−	0.0176774i
$726$	10.7206	+	0.978272i	0.397878	+	0.0363071i
$727$			30.4180i			1.12814i	0.825726	+	0.564071i	$0.190766\pi$
$727$			30.4180i			1.12814i	−0.825726	+	0.564071i	$0.809234\pi$
$728$	−40.2901	−	8.61924i	−1.49325	−	0.319450i
$729$		−	1.00000i		−	0.0370370i
$730$	−2.09561	+	22.9651i	−0.0775619	+	0.849976i
$731$	−10.6686	−	2.85864i	−0.394592	−	0.105731i
$732$	−0.702468	+	3.81701i	−0.0259640	+	0.141081i
$733$	−0.255632	−	0.954032i	−0.00944199	−	0.0352380i	0.961044	−	0.276395i	$-0.0891398\pi$
$733$	−0.255632	−	0.954032i	−0.00944199	−	0.0352380i	−0.970486	+	0.241157i	$0.922473\pi$
$734$	10.7395	−	29.1672i	0.396402	−	1.07658i
$735$	2.41310	+	19.2830i	0.0890084	+	0.711265i
$736$	28.4809	+	5.57201i	1.04982	+	0.205387i
$737$	−2.15795	+	3.73768i	−0.0794892	+	0.137679i
$738$	−2.29231	−	13.2903i	−0.0843811	−	0.489222i
$739$	−4.41418	−	1.18278i	−0.162378	−	0.0435091i	0.176714	−	0.984262i	$-0.443453\pi$
$739$	−4.41418	−	1.18278i	−0.162378	−	0.0435091i	−0.339092	+	0.940753i	$0.610120\pi$
$740$	51.6286	−	18.3559i	1.89790	−	0.674775i
$741$	31.5034	+	31.5034i	1.15731	+	1.15731i
$742$	14.9686	−	8.07747i	0.549513	−	0.296533i
$743$	13.8598			0.508467			0.254234	−	0.967143i	$-0.418177\pi$
$743$	13.8598			0.508467			0.254234	+	0.967143i	$0.418177\pi$
$744$	13.7255	−	13.4215i	0.503203	−	0.492056i
$745$	−4.60133	−	7.96974i	−0.168580	−	0.291989i
$746$	−19.2083	+	27.2155i	−0.703266	+	0.996429i
$747$	1.18808	+	4.43397i	0.0434695	+	0.162230i
$748$	−7.49410	+	0.599300i	−0.274011	+	0.0219126i
$749$	3.70892	+	11.0422i	0.135521	+	0.403473i
$750$	3.11023	−	8.44704i	0.113570	−	0.308442i
$751$	6.93018	+	4.00114i	0.252886	+	0.146004i	0.621085	−	0.783743i	$-0.286692\pi$
$751$	6.93018	+	4.00114i	0.252886	+	0.146004i	−0.368199	+	0.929747i	$0.620026\pi$
$752$	−41.5989	+	33.8600i	−1.51696	+	1.23475i
$753$	9.50579	+	16.4645i	0.346410	+	0.600000i
$754$	3.38470	+	4.06444i	0.123263	+	0.148018i
$755$	41.7361	+	41.7361i	1.51893	+	1.51893i
$756$	4.16186	−	3.26786i	0.151366	−	0.118851i
$757$	14.3545	−	14.3545i	0.521724	−	0.521724i	−0.396368	−	0.918092i	$-0.629730\pi$
$757$	14.3545	−	14.3545i	0.521724	−	0.521724i	0.918092	+	0.396368i	$0.129730\pi$
$758$	2.18695	−	23.9661i	0.0794336	−	0.870488i
$759$	−8.17772	+	4.72141i	−0.296832	+	0.171376i
$760$	−32.3843	+	54.6680i	−1.17470	+	1.98302i
$761$	−6.93048	+	12.0039i	−0.251230	+	0.435142i	−0.963865	−	0.266393i	$-0.914168\pi$
$761$	−6.93048	+	12.0039i	−0.251230	+	0.435142i	0.712635	+	0.701535i	$0.247502\pi$
$762$	−3.40190	−	7.36707i	−0.123238	−	0.266881i
$763$	22.7465	+	4.60035i	0.823480	+	0.166544i
$764$	−26.5054	+	31.1131i	−0.958931	+	1.12563i
$765$	5.47650	−	1.46742i	0.198003	−	0.0530548i
$766$	−34.1298	+	5.88671i	−1.23316	+	0.212696i
$767$	44.2668	−	25.5575i	1.59838	−	0.922827i
$768$	−13.3746	+	8.78174i	−0.482616	+	0.316884i
$769$		−	17.2769i		−	0.623023i	−0.950242	−	0.311511i	$-0.899165\pi$
$769$		−	17.2769i		−	0.623023i	0.950242	−	0.311511i	$-0.100835\pi$
$770$	13.1254	+	13.9028i	0.473007	+	0.501021i
$771$	4.24979	−	4.24979i	0.153053	−	0.153053i
$772$	3.93999	−	1.40081i	0.141803	−	0.0504164i
$773$	10.4880	−	39.1418i	0.377228	−	1.40783i	−0.472834	−	0.881152i	$-0.656769\pi$
$773$	10.4880	−	39.1418i	0.377228	−	1.40783i	0.850062	−	0.526683i	$-0.176564\pi$
$774$	4.41030	−	6.24877i	0.158525	−	0.224608i
$775$	−15.9132	−	9.18750i	−0.571619	−	0.330025i
$776$	1.75077	+	3.11240i	0.0628488	+	0.111729i
$777$	1.62421	+	26.0593i	0.0582683	+	0.934874i
$778$	0.923812	+	2.00059i	0.0331203	+	0.0717245i
$779$	−74.5383	+	19.9725i	−2.67061	+	0.715589i
$780$	25.1722	−	17.3471i	0.901308	−	0.621125i
$781$	−2.07414	+	7.74079i	−0.0742185	+	0.276987i
$782$	−11.3859	+	9.48170i	−0.407159	+	0.339065i
$783$	−0.679289			−0.0242758
$784$	27.2008	+	6.64222i	0.971455	+	0.237222i
$785$	20.5287			0.732701
$786$	−0.0139982	+	0.0116571i	−0.000499299	+	0.000415795i
$787$	−2.38110	+	8.88638i	−0.0848770	+	0.316765i	−0.995291	−	0.0969334i	$-0.969097\pi$
$787$	−2.38110	+	8.88638i	−0.0848770	+	0.316765i	0.910414	+	0.413699i	$0.135763\pi$
$788$	−2.12935	−	3.08987i	−0.0758548	−	0.110072i
$789$	6.58582	−	1.76466i	0.234461	−	0.0628237i
$790$	−5.66909	−	12.2769i	−0.201697	−	0.436791i
$791$	−1.40295	−	22.5094i	−0.0498833	−	0.800342i
$792$	1.40367	−	5.01328i	0.0498772	−	0.178139i
$793$	−9.25293	−	5.34218i	−0.328581	−	0.189706i
$794$	7.17322	−	10.1634i	0.254568	−	0.360687i
$795$	−3.26633	+	12.1901i	−0.115845	+	0.432339i
$796$	−5.38835	−	15.1555i	−0.190985	−	0.537173i
$797$	−16.7457	+	16.7457i	−0.593164	+	0.593164i	−0.938485	−	0.345321i	$-0.887770\pi$
$797$	−16.7457	+	16.7457i	−0.593164	+	0.593164i	0.345321	+	0.938485i	$0.387770\pi$
$798$	−20.7848	−	22.0158i	−0.735775	−	0.779351i
$799$		−	27.3852i		−	0.968818i
$800$	11.5461	+	10.0615i	0.408215	+	0.355726i
$801$	−8.25069	+	4.76354i	−0.291524	+	0.168311i
$802$	−55.2278	+	9.52570i	−1.95016	+	0.336364i
$803$	−10.4427	+	2.79811i	−0.368514	+	0.0987431i
$804$	−3.56984	−	3.04116i	−0.125898	−	0.107253i
$805$	36.9344	+	7.46976i	1.30177	+	0.263275i
$806$	22.1555	+	47.9794i	0.780393	+	1.69000i
$807$	9.70947	−	16.8173i	0.341789	−	0.591997i
$808$	−3.18494	−	12.4421i	−0.112046	−	0.437712i
$809$	9.26704	−	5.35033i	0.325812	−	0.188107i	−0.328168	−	0.944619i	$-0.606431\pi$
$809$	9.26704	−	5.35033i	0.325812	−	0.188107i	0.653980	+	0.756512i	$0.273098\pi$
$810$	−0.356785	+	3.90990i	−0.0125362	+	0.137380i
$811$	38.0038	−	38.0038i	1.33449	−	1.33449i	0.433193	−	0.901301i	$-0.357387\pi$
$811$	38.0038	−	38.0038i	1.33449	−	1.33449i	0.901301	−	0.433193i	$-0.142613\pi$
$812$	−2.21982	−	2.82711i	−0.0779004	−	0.0992121i
$813$	−7.82305	−	7.82305i	−0.274366	−	0.274366i
$814$	16.4386	+	19.7400i	0.576173	+	0.691886i
$815$	−11.2805	−	19.5383i	−0.395137	−	0.684397i
$816$	0.833415	−	8.12635i	0.0291754	−	0.284479i
$817$	−37.8998	−	21.8814i	−1.32595	−	0.765535i
$818$	15.8962	−	43.1722i	0.555797	−	1.50948i
$819$	4.63821	+	13.8089i	0.162072	+	0.482521i
$820$	4.22092	+	52.7815i	0.147401	+	1.84321i
$821$	11.8054	+	44.0582i	0.412010	+	1.53764i	0.790750	+	0.612139i	$0.209691\pi$
$821$	11.8054	+	44.0582i	0.412010	+	1.53764i	−0.378740	+	0.925503i	$0.623643\pi$
$822$	−11.3980	+	16.1494i	−0.397552	+	0.563276i
$823$	−3.99738	−	6.92366i	−0.139340	−	0.241344i	0.787907	−	0.615794i	$-0.211165\pi$
$823$	−3.99738	−	6.92366i	−0.139340	−	0.241344i	−0.927247	+	0.374450i	$0.877831\pi$
$824$	25.3789	+	0.284256i	0.884116	+	0.00990251i
$825$	−4.98314			−0.173491
$826$	−30.5699	+	16.4964i	−1.06366	+	0.573982i
$827$	10.5806	+	10.5806i	0.367922	+	0.367922i	0.866719	−	0.498797i	$-0.166225\pi$
$827$	10.5806	+	10.5806i	0.367922	+	0.367922i	−0.498797	+	0.866719i	$0.666225\pi$
$828$	−3.43719	−	9.66759i	−0.119450	−	0.335972i
$829$	28.1921	+	7.55404i	0.979151	+	0.262363i	0.712687	−	0.701482i	$-0.247478\pi$
$829$	28.1921	+	7.55404i	0.979151	+	0.262363i	0.266464	+	0.963845i	$0.414145\pi$
$830$	−3.06329	−	17.7603i	−0.106328	−	0.616467i
$831$	−13.9389	+	24.1428i	−0.483534	+	0.837505i
$832$	−10.4443	−	42.7904i	−0.362090	−	1.48349i
$833$	−11.3971	+	8.62985i	−0.394885	+	0.299006i
$834$	0.0879207	−	0.238783i	0.00304445	−	0.00826837i
$835$	−3.92755	−	14.6578i	−0.135918	−	0.507255i
$836$	−29.2964	−	5.39159i	−1.01324	−	0.186472i
$837$	−6.55592	−	1.75665i	−0.226606	−	0.0607188i
$838$	−2.37264	+	26.0010i	−0.0819615	+	0.898191i
$839$			28.7459i			0.992418i	0.868203	+	0.496209i	$0.165275\pi$
$839$			28.7459i			0.992418i	−0.868203	+	0.496209i	$0.834725\pi$
$840$	−17.4384	+	11.2921i	−0.601682	+	0.389615i
$841$		−	28.5386i		−	0.984088i
$842$	56.2297	+	5.13106i	1.93780	+	0.176828i
$843$	−9.20567	−	2.46665i	−0.317060	−	0.0849560i
$844$	−9.70773	−	14.0868i	−0.334154	−	0.484887i
$845$	12.4407	+	46.4295i	0.427974	+	1.59722i
$846$	17.7957	+	6.55245i	0.611829	+	0.225278i
$847$	8.96537	−	18.0341i	0.308054	−	0.619660i
$848$	14.7375	+	10.6508i	0.506087	+	0.365749i
$849$	−3.69160	+	6.39403i	−0.126695	+	0.219443i
$850$	−7.70539	+	1.32903i	−0.264293	+	0.0455852i
$851$	48.9030	+	13.1035i	1.67637	+	0.449183i
$852$	−7.86420	−	3.73887i	−0.269423	−	0.128092i
$853$	19.5710	+	19.5710i	0.670099	+	0.670099i	0.957739	−	0.287640i	$-0.0928706\pi$
$853$	19.5710	+	19.5710i	0.670099	+	0.670099i	−0.287640	+	0.957739i	$0.592871\pi$
$854$	6.18116	+	3.80973i	0.211515	+	0.130366i
$855$	22.4648			0.768279
$856$	−8.90346	+	8.70623i	−0.304314	+	0.297573i
$857$	1.69064	+	2.92827i	0.0577510	+	0.100028i	0.893456	−	0.449152i	$-0.148274\pi$
$857$	1.69064	+	2.92827i	0.0577510	+	0.100028i	−0.835705	+	0.549179i	$0.814940\pi$
$858$	11.7092	+	8.26419i	0.399746	+	0.282135i
$859$	7.22244	+	26.9545i	0.246426	+	0.919676i	0.972661	+	0.232229i	$0.0746019\pi$
$859$	7.22244	+	26.9545i	0.246426	+	0.919676i	−0.726235	+	0.687447i	$0.758731\pi$
$860$	−19.4733	+	22.8586i	−0.664034	+	0.779470i
$861$	−24.7303	−	5.00155i	−0.842806	−	0.170453i
$862$	21.4248	+	7.88868i	0.729730	+	0.268690i
$863$	−15.5339	−	8.96851i	−0.528781	−	0.305292i	0.211739	−	0.977326i	$-0.432087\pi$
$863$	−15.5339	−	8.96851i	−0.528781	−	0.305292i	−0.740520	+	0.672035i	$0.765421\pi$
$864$	5.08133	+	2.48597i	0.172871	+	0.0845744i
$865$	−4.63902	−	8.03502i	−0.157732	−	0.273199i
$866$	−30.9852	+	25.8031i	−1.05292	+	0.876826i
$867$	−9.07164	−	9.07164i	−0.308089	−	0.308089i
$868$	−14.1129	−	33.0253i	−0.479021	−	1.12095i
$869$	4.48274	−	4.48274i	0.152067	−	0.152067i
$870$	2.65595	+	0.242361i	0.0900453	+	0.00821679i
$871$	11.1804	−	6.45503i	0.378835	−	0.218720i
$872$	6.15235	+	24.0345i	0.208345	+	0.813909i
$873$	0.631274	−	1.09340i	0.0213654	−	0.0370060i
$874$	−53.3003	+	24.6125i	−1.80291	+	0.832530i
$875$	−12.6255	−	11.1440i	−0.426819	−	0.376735i
$876$	−0.936425	−	11.7098i	−0.0316389	−	0.395636i
$877$	−22.0927	+	5.91972i	−0.746017	+	0.199895i	−0.611751	−	0.791051i	$-0.709534\pi$
$877$	−22.0927	+	5.91972i	−0.746017	+	0.199895i	−0.134266	+	0.990945i	$0.542868\pi$
$878$	3.81246	+	22.1037i	0.128664	+	0.745965i
$879$	−25.7884	+	14.8890i	−0.869823	+	0.502192i
$880$	−7.27687	+	19.1006i	−0.245303	+	0.643882i
$881$		−	25.9051i		−	0.872766i	−0.899761	−	0.436383i	$-0.856259\pi$
$881$		−	25.9051i		−	0.872766i	0.899761	−	0.436383i	$-0.143741\pi$
$882$	−2.88096	−	9.47101i	−0.0970069	−	0.318906i
$883$	20.8312	−	20.8312i	0.701026	−	0.701026i	−0.263605	−	0.964631i	$-0.584911\pi$
$883$	20.8312	−	20.8312i	0.701026	−	0.701026i	0.964631	+	0.263605i	$0.0849114\pi$
$884$	20.3099	+	9.65595i	0.683097	+	0.324765i
$885$	6.67073	−	24.8955i	0.224234	−	0.836854i
$886$	6.53210	+	4.61026i	0.219450	+	0.154885i
$887$	1.09658	+	0.633108i	0.0368194	+	0.0212577i	0.518297	−	0.855201i	$-0.326566\pi$
$887$	1.09658	+	0.633108i	0.0368194	+	0.0212577i	−0.481477	+	0.876459i	$0.659900\pi$
$888$	−24.3279	+	13.6847i	−0.816390	+	0.459229i
$889$	−15.1516	+	0.944361i	−0.508169	+	0.0316729i
$890$	33.9589	−	15.6812i	1.13831	−	0.525636i
$891$	−1.77791	+	0.476389i	−0.0595622	+	0.0159596i
$892$	0.0443982	−	0.241247i	0.00148656	−	0.00807755i
$893$	28.0837	−	104.810i	0.939786	−	3.50733i
$894$	2.99989	+	3.60236i	0.100331	+	0.120481i
$895$	3.51112			0.117364
$896$	6.25881	+	29.2716i	0.209092	+	0.977896i
$897$	28.2460			0.943108
$898$	6.70092	+	8.04667i	0.223613	+	0.268521i
$899$	−1.19328	+	4.45337i	−0.0397980	+	0.148528i
$900$	0.980026	−	5.32518i	0.0326675	−	0.177506i
$901$	−8.96735	+	2.40279i	−0.298746	+	0.0800487i
$902$	−22.5369	+	10.4069i	−0.750396	+	0.346511i
$903$	−7.91141	−	11.9228i	−0.263275	−	0.396765i
$904$	21.0138	−	11.8205i	0.698908	−	0.393145i
$905$	45.6560	+	26.3595i	1.51766	+	0.876220i
$906$	−24.5649	−	17.3376i	−0.816114	−	0.576002i
$907$	7.92002	−	29.5579i	0.262980	−	0.981455i	−0.700495	−	0.713657i	$-0.747037\pi$
$907$	7.92002	−	29.5579i	0.262980	−	0.981455i	0.963475	−	0.267798i	$-0.0862959\pi$
$908$	−39.7841	−	18.9146i	−1.32028	−	0.627702i
$909$	−3.21082	+	3.21082i	−0.106496	+	0.106496i
$910$	−13.2081	−	55.6462i	−0.437846	−	1.84465i
$911$			9.20311i			0.304913i	0.988310	+	0.152456i	$0.0487184\pi$
$911$			9.20311i			0.304913i	−0.988310	+	0.152456i	$0.951282\pi$
$912$	11.5233	−	30.2469i	0.381576	−	1.00158i
$913$	7.31720	−	4.22459i	0.242164	−	0.139813i
$914$	−5.86891	−	34.0266i	−0.194126	−	1.12550i
$915$	−5.20381	+	1.39436i	−0.172033	+	0.0460960i
$916$	−1.19813	−	14.9824i	−0.0395875	−	0.495032i
$917$	0.0108512	+	0.0323061i	0.000358337	+	0.00106684i
$918$	−2.62211	+	1.21081i	−0.0865425	+	0.0399628i
$919$	−0.912455	+	1.58042i	−0.0300991	+	0.0521332i	−0.880683	−	0.473707i	$-0.842916\pi$
$919$	−0.912455	+	1.58042i	−0.0300991	+	0.0521332i	0.850583	+	0.525840i	$0.176249\pi$
$920$	9.98980	+	39.0256i	0.329354	+	1.28664i
$921$	−18.1213	+	10.4623i	−0.597116	+	0.344745i
$922$	21.2530	+	1.93937i	0.699929	+	0.0638698i
$923$	16.9505	−	16.9505i	0.557932	−	0.557932i
$924$	−7.79262	−	5.84264i	−0.256358	−	0.192209i
$925$	18.8920	+	18.8920i	0.621166	+	0.621166i
$926$	−22.1173	+	18.4183i	−0.726819	+	0.605264i
$927$	−4.48668	−	7.77116i	−0.147362	−	0.255238i
$928$	1.68869	−	3.45170i	0.0554340	−	0.113307i
$929$	32.4848	+	18.7551i	1.06579	+	0.615335i	0.927029	−	0.374990i	$-0.122354\pi$
$929$	32.4848	+	18.7551i	1.06579	+	0.615335i	0.138763	+	0.990326i	$0.455687\pi$
$930$	25.0062	+	9.20739i	0.819987	+	0.301922i
$931$	−52.4694	+	21.3408i	−1.71962	+	0.699416i
$932$	−13.1968	+	15.4909i	−0.432275	+	0.507422i
$933$	1.04207	+	3.88906i	0.0341159	+	0.127322i
$934$	7.72993	+	5.45568i	0.252931	+	0.178515i
$935$	−5.21789	−	9.03765i	−0.170643	−	0.295563i
$936$	−11.1343	+	10.8876i	−0.363935	+	0.355873i
$937$	1.40264			0.0458223			0.0229112	−	0.999738i	$-0.492707\pi$
$937$	1.40264			0.0458223			0.0229112	+	0.999738i	$0.492707\pi$
$938$	−7.72100	+	4.16647i	−0.252100	+	0.136040i
$939$	9.87302	+	9.87302i	0.322194	+	0.322194i
$940$	−67.2416	−	31.9687i	−2.19318	−	1.04270i
$941$	27.7691	+	7.44071i	0.905246	+	0.242560i	0.681268	−	0.732034i	$-0.261429\pi$
$941$	27.7691	+	7.44071i	0.905246	+	0.242560i	0.223978	+	0.974594i	$0.428095\pi$
$942$	−10.3053	+	1.77745i	−0.335764	+	0.0579126i
$943$	−24.4619	+	42.3693i	−0.796590	+	1.37973i
$944$	−30.0979	−	21.7518i	−0.979604	−	0.707959i
$945$	6.57722	+	3.26976i	0.213957	+	0.106365i
$946$	−13.2108	−	4.86426i	−0.429519	−	0.158151i
$947$	−8.92728	−	33.3171i	−0.290098	−	1.08266i	−0.945033	−	0.326974i	$-0.893971\pi$
$947$	−8.92728	−	33.3171i	−0.290098	−	1.08266i	0.654936	−	0.755685i	$-0.272696\pi$
$948$	3.90882	+	5.67205i	0.126953	+	0.184220i
$949$	31.2369	+	8.36991i	1.01399	+	0.271699i
$950$	−30.8534	−	2.81543i	−1.00102	−	0.0913445i
$951$			0.616707i			0.0199981i
$952$	−13.6079	−	6.95610i	−0.441035	−	0.225448i
$953$		−	38.7939i		−	1.25666i	−0.777948	−	0.628329i	$-0.783739\pi$
$953$		−	38.7939i		−	1.25666i	0.777948	−	0.628329i	$-0.216261\pi$
$954$	0.584209	−	6.40217i	0.0189145	−	0.207278i
$955$	−54.8020	−	14.6841i	−1.77335	−	0.475168i
$956$	15.1715	+	2.79211i	0.490683	+	0.0903033i
$957$	0.323606	+	1.20772i	0.0104607	+	0.0390399i
$958$	8.19472	−	22.2559i	0.264759	−	0.719056i
$959$	20.4464	+	30.8133i	0.660248	+	0.995015i
$960$	−18.9806	−	11.5328i	−0.612595	−	0.372221i
$961$	−7.53294	+	13.0474i	−0.242998	+	0.420885i
$962$	−13.0607	−	75.7229i	−0.421094	−	2.44141i
$963$	4.25268	+	1.13950i	0.137041	+	0.0367200i
$964$	−0.581670	−	1.63603i	−0.0187343	−	0.0526930i
$965$	4.10440	+	4.10440i	0.132125	+	0.132125i
$966$	−19.1876	−	0.551850i	−0.617350	−	0.0177555i
$967$	−22.0005			−0.707490			−0.353745	−	0.935342i	$-0.615092\pi$
$967$	−22.0005			−0.707490			−0.353745	+	0.935342i	$0.615092\pi$
$968$	21.5289	+	0.241134i	0.691965	+	0.00775033i
$969$	8.26282	+	14.3116i	0.265440	+	0.459756i
$970$	−2.85833	+	4.04985i	−0.0917754	+	0.130033i
$971$	−12.9868	−	48.4673i	−0.416765	−	1.55539i	−0.781273	−	0.624189i	$-0.785429\pi$
$971$	−12.9868	−	48.4673i	−0.416765	−	1.55539i	0.364508	−	0.931200i	$-0.381237\pi$
$972$	−0.159430	−	1.99364i	−0.00511373	−	0.0639459i
$973$	−0.356900	−	0.315021i	−0.0114417	−	0.0100991i
$974$	10.2196	−	27.7553i	0.327458	−	0.889338i
$975$	12.9089	+	7.45297i	0.413416	+	0.238686i
$976$	−0.791918	+	7.72173i	−0.0253487	+	0.247167i
$977$	21.4119	+	37.0865i	0.685027	+	1.18650i	0.973428	+	0.228993i	$0.0735432\pi$
$977$	21.4119	+	37.0865i	0.685027	+	1.18650i	−0.288401	+	0.957510i	$0.593124\pi$
$978$	7.35441	+	8.83140i	0.235168	+	0.282397i
$979$	12.3997	+	12.3997i	0.396296	+	0.396296i
$980$	7.88513	+	38.0586i	0.251881	+	1.21574i
$981$	6.20235	−	6.20235i	0.198026	−	0.198026i
$982$	0.813715	−	8.91725i	0.0259667	−	0.284561i
$983$	23.3323	−	13.4709i	0.744185	−	0.429655i	−0.0794040	−	0.996843i	$-0.525302\pi$
$983$	23.3323	−	13.4709i	0.744185	−	0.429655i	0.823589	+	0.567187i	$0.191968\pi$
$984$	−6.68890	−	26.1305i	−0.213234	−	0.833011i
$985$	2.60444	−	4.51102i	0.0829844	−	0.143733i
$986$	0.822492	+	1.78117i	0.0261935	+	0.0567240i
$987$	23.4775	−	26.5986i	0.747296	−	0.846642i
$988$	67.8289	+	57.7837i	2.15793	+	1.83835i
$989$	−26.8000	+	7.18103i	−0.852190	+	0.228344i
$990$	7.12142	−	1.22830i	0.226333	−	0.0390380i
$991$	42.2604	−	24.3991i	1.34245	−	0.775062i	0.355280	−	0.934760i	$-0.384385\pi$
$991$	42.2604	−	24.3991i	1.34245	−	0.775062i	0.987166	+	0.159698i	$0.0510521\pi$
$992$	25.2239	−	28.9458i	0.800861	−	0.919031i
$993$		−	25.1058i		−	0.796710i
$994$	−11.8457	+	11.1833i	−0.375722	+	0.354714i
$995$	15.7879	−	15.7879i	0.500510	−	0.500510i
$996$	3.07550	+	8.65030i	0.0974510	+	0.274095i
$997$	2.44342	−	9.11898i	0.0773840	−	0.288801i	−0.916379	−	0.400311i	$-0.868902\pi$
$997$	2.44342	−	9.11898i	0.0773840	−	0.288801i	0.993763	+	0.111510i	$0.0355687\pi$
$998$	10.3543	−	14.6706i	0.327759	−	0.464389i
$999$	8.54647	+	4.93431i	0.270398	+	0.156115i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bs.a.19.11	✓	128
7.3	odd	6	inner	336.2.bs.a.115.31	yes	128
16.11	odd	4	inner	336.2.bs.a.187.31	yes	128
112.59	even	12	inner	336.2.bs.a.283.11	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bs.a.19.11	✓	128	1.1	even	1	trivial
336.2.bs.a.115.31	yes	128	7.3	odd	6	inner
336.2.bs.a.187.31	yes	128	16.11	odd	4	inner
336.2.bs.a.283.11	yes	128	112.59	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.bs (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.904988 - 1.08674i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(-0.361993 + 1.96697i) q^{4} +(-2.68161 + 0.718534i) q^{5} +(1.28394 - 0.592883i) q^{6} +(-0.164584 - 2.64063i) q^{7} +(2.46517 - 1.38669i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.904988 - 1.08674i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(-0.361993 + 1.96697i) q^{4} +(-2.68161 + 0.718534i) q^{5} +(1.28394 - 0.592883i) q^{6} +(-0.164584 - 2.64063i) q^{7} +(2.46517 - 1.38669i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(3.20768 + 2.26394i) q^{10} +(-0.476389 + 1.77791i) q^{11} +(-1.80625 - 0.858747i) q^{12} +(3.89320 - 3.89320i) q^{13} +(-2.72072 + 2.56860i) q^{14} -2.77620i q^{15} +(-3.73792 - 1.42406i) q^{16} +(1.76864 - 1.02112i) q^{17} +(0.240374 + 1.39364i) q^{18} +(7.81618 - 2.09434i) q^{19} +(-0.442611 - 5.53474i) q^{20} +(2.59325 + 0.524469i) q^{21} +(2.36325 - 1.09128i) q^{22} +(2.56511 - 4.44290i) q^{23} +(0.701407 + 2.74008i) q^{24} +(2.34460 - 1.35365i) q^{25} +(-7.75419 - 0.707584i) q^{26} +(0.707107 - 0.707107i) q^{27} +(5.25361 + 0.632158i) q^{28} +(-0.480330 - 0.480330i) q^{29} +(-3.01700 + 2.51243i) q^{30} +(-3.39359 - 5.87787i) q^{31} +(1.83520 + 5.35089i) q^{32} +(-1.59403 - 0.920314i) q^{33} +(-2.71028 - 0.997938i) q^{34} +(2.33873 + 6.96287i) q^{35} +(1.29698 - 1.52245i) q^{36} +(2.55419 + 9.53235i) q^{37} +(-9.34955 - 6.59878i) q^{38} +(2.75291 + 4.76818i) q^{39} +(-5.61424 + 5.48987i) q^{40} -9.53641 q^{41} +(-1.77690 - 3.29282i) q^{42} +(-3.82420 - 3.82420i) q^{43} +(-3.32464 - 1.58063i) q^{44} +(2.68161 + 0.718534i) q^{45} +(-7.14965 + 1.23317i) q^{46} +(6.70468 - 11.6128i) q^{47} +(2.34298 - 3.24198i) q^{48} +(-6.94582 + 0.869208i) q^{49} +(-3.59290 - 1.32292i) q^{50} +(0.528572 + 1.97266i) q^{51} +(6.24849 + 9.06711i) q^{52} +(-4.39093 - 1.17655i) q^{53} +(-1.40836 - 0.128516i) q^{54} -5.10996i q^{55} +(-4.06746 - 6.28138i) q^{56} +8.09191i q^{57} +(-0.0872993 + 0.956685i) q^{58} +(8.96747 + 2.40283i) q^{59} +(5.46070 + 1.00497i) q^{60} +(-0.502253 - 1.87444i) q^{61} +(-3.31654 + 9.00735i) q^{62} +(-1.17778 + 2.36914i) q^{63} +(4.15418 - 6.83687i) q^{64} +(-7.64264 + 13.2374i) q^{65} +(0.442440 + 2.56516i) q^{66} +(2.26490 + 0.606879i) q^{67} +(1.36828 + 3.84849i) q^{68} +(3.62761 + 3.62761i) q^{69} +(5.45028 - 8.84289i) q^{70} +4.35387 q^{71} +(-2.82825 - 0.0316777i) q^{72} +(2.93679 + 5.08666i) q^{73} +(8.04765 - 11.4024i) q^{74} +(0.700703 + 2.61506i) q^{75} +(1.29009 + 16.1323i) q^{76} +(4.77320 + 0.965352i) q^{77} +(2.69040 - 7.30683i) q^{78} +(-2.98280 - 1.72212i) q^{79} +(11.0469 + 1.13294i) q^{80} +(0.500000 + 0.866025i) q^{81} +(8.63034 + 10.3636i) q^{82} +(-3.24589 - 3.24589i) q^{83} +(-1.97035 + 4.91098i) q^{84} +(-4.00907 + 4.00907i) q^{85} +(-0.695042 + 7.61675i) q^{86} +(0.588282 - 0.339645i) q^{87} +(1.29103 + 5.04346i) q^{88} +(4.76354 - 8.25069i) q^{89} +(-1.64596 - 3.56447i) q^{90} +(-10.9213 - 9.63974i) q^{91} +(7.81048 + 6.65378i) q^{92} +(6.55592 - 1.75665i) q^{93} +(-18.6877 + 3.22326i) q^{94} +(-19.4551 + 11.2324i) q^{95} +(-5.64355 + 0.387755i) q^{96} +1.26255i q^{97} +(7.23049 + 6.76166i) q^{98} +(1.30152 - 1.30152i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{4} - 24 q^{8}+O(q^{10}) \) 128 * q + 4 * q^4 - 24 * q^8	\( 128 q + 4 q^{4} - 24 q^{8} + 36 q^{10} - 8 q^{11} - 32 q^{14} - 4 q^{16} + 4 q^{18} + 16 q^{22} + 16 q^{23} - 32 q^{28} + 32 q^{29} - 24 q^{35} - 16 q^{37} + 60 q^{40} - 20 q^{42} - 16 q^{43} - 12 q^{44} - 20 q^{46} - 32 q^{50} - 144 q^{52} - 16 q^{53} - 56 q^{56} - 40 q^{58} - 96 q^{59} - 24 q^{60} - 32 q^{64} - 72 q^{66} + 16 q^{67} - 60 q^{68} + 28 q^{70} + 128 q^{71} - 4 q^{72} - 72 q^{74} + 72 q^{78} - 36 q^{80} + 64 q^{81} - 60 q^{82} + 24 q^{84} - 44 q^{86} - 48 q^{88} - 8 q^{91} + 56 q^{92} + 36 q^{94} + 60 q^{96} + 148 q^{98} - 16 q^{99}+O(q^{100}) \) 128 * q + 4 * q^4 - 24 * q^8 + 36 * q^10 - 8 * q^11 - 32 * q^14 - 4 * q^16 + 4 * q^18 + 16 * q^22 + 16 * q^23 - 32 * q^28 + 32 * q^29 - 24 * q^35 - 16 * q^37 + 60 * q^40 - 20 * q^42 - 16 * q^43 - 12 * q^44 - 20 * q^46 - 32 * q^50 - 144 * q^52 - 16 * q^53 - 56 * q^56 - 40 * q^58 - 96 * q^59 - 24 * q^60 - 32 * q^64 - 72 * q^66 + 16 * q^67 - 60 * q^68 + 28 * q^70 + 128 * q^71 - 4 * q^72 - 72 * q^74 + 72 * q^78 - 36 * q^80 + 64 * q^81 - 60 * q^82 + 24 * q^84 - 44 * q^86 - 48 * q^88 - 8 * q^91 + 56 * q^92 + 36 * q^94 + 60 * q^96 + 148 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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