LMFDB - Embedded newform 273.2.cd.e.242.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(44,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 4, 9]))

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

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

chi := DirichletCharacter("273.44");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cd (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			242.4
Character	$\chi$	$=$	273.242
Dual form			273.2.cd.e.44.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.19229 - 0.587422i) q^{2} +(-1.51343 - 0.842335i) q^{3} +(2.72902 + 1.57560i) q^{4} +(0.959762 + 0.257167i) q^{5} +(2.82307 + 2.73567i) q^{6} +(-2.15459 - 1.53549i) q^{7} +(-1.84753 - 1.84753i) q^{8} +(1.58094 + 2.54963i) q^{9} +O(q^{10})$	\(q+(-2.19229 - 0.587422i) q^{2} +(-1.51343 - 0.842335i) q^{3} +(2.72902 + 1.57560i) q^{4} +(0.959762 + 0.257167i) q^{5} +(2.82307 + 2.73567i) q^{6} +(-2.15459 - 1.53549i) q^{7} +(-1.84753 - 1.84753i) q^{8} +(1.58094 + 2.54963i) q^{9} +(-1.95301 - 1.12757i) q^{10} +(4.64145 - 1.24367i) q^{11} +(-2.80300 - 4.68331i) q^{12} +(2.61037 - 2.48716i) q^{13} +(3.82151 + 4.63189i) q^{14} +(-1.23591 - 1.19765i) q^{15} +(-0.186167 - 0.322451i) q^{16} +(-3.01497 + 5.22208i) q^{17} +(-1.96818 - 6.51821i) q^{18} +(0.269277 - 1.00496i) q^{19} +(2.21402 + 2.21402i) q^{20} +(1.96743 + 4.13875i) q^{21} -10.9060 q^{22} +(-4.04438 - 7.00507i) q^{23} +(1.23987 + 4.35234i) q^{24} +(-3.47512 - 2.00636i) q^{25} +(-7.18370 + 3.91919i) q^{26} +(-0.245007 - 5.19037i) q^{27} +(-3.46061 - 7.58516i) q^{28} -8.64500i q^{29} +(2.00595 + 3.35159i) q^{30} +(-4.64428 + 1.24443i) q^{31} +(1.57120 + 5.86380i) q^{32} +(-8.07209 - 2.02744i) q^{33} +(9.67726 - 9.67726i) q^{34} +(-1.67302 - 2.02780i) q^{35} +(0.297229 + 9.44893i) q^{36} +(3.20687 + 0.859279i) q^{37} +(-1.18067 + 2.04498i) q^{38} +(-6.04563 + 1.56534i) q^{39} +(-1.29806 - 2.24831i) q^{40} +(-1.07575 + 1.07575i) q^{41} +(-1.88199 - 10.2290i) q^{42} -3.62015i q^{43} +(14.6261 + 3.91906i) q^{44} +(0.861648 + 2.85361i) q^{45} +(4.75152 + 17.7329i) q^{46} +(1.27963 - 4.77564i) q^{47} +(0.0101394 + 0.644823i) q^{48} +(2.28455 + 6.61671i) q^{49} +(6.43989 + 6.43989i) q^{50} +(8.96169 - 5.36365i) q^{51} +(11.0425 - 2.67462i) q^{52} +(-1.07485 - 0.620567i) q^{53} +(-2.51182 + 11.5227i) q^{54} +4.77451 q^{55} +(1.14381 + 6.81752i) q^{56} +(-1.25404 + 1.29411i) q^{57} +(-5.07827 + 18.9524i) q^{58} +(2.62988 - 0.704673i) q^{59} +(-1.48582 - 5.21570i) q^{60} +(-1.70491 - 2.95300i) q^{61} +10.9126 q^{62} +(0.508638 - 7.92094i) q^{63} -13.0334i q^{64} +(3.14495 - 1.71578i) q^{65} +(16.5054 + 9.18647i) q^{66} +(5.64922 - 1.51370i) q^{67} +(-16.4558 + 9.50078i) q^{68} +(0.220273 + 14.0084i) q^{69} +(2.47657 + 5.42828i) q^{70} +(7.65674 - 7.65674i) q^{71} +(1.78967 - 7.63134i) q^{72} +(-1.40500 - 5.24352i) q^{73} +(-6.52564 - 3.76758i) q^{74} +(3.56932 + 5.96370i) q^{75} +(2.31827 - 2.31827i) q^{76} +(-11.9101 - 4.44728i) q^{77} +(14.1733 + 0.119656i) q^{78} +(-4.42329 - 7.66137i) q^{79} +(-0.0957524 - 0.357353i) q^{80} +(-4.00123 + 8.06165i) q^{81} +(2.99027 - 1.72643i) q^{82} +(-3.07191 + 3.07191i) q^{83} +(-1.15185 + 14.3946i) q^{84} +(-4.23661 + 4.23661i) q^{85} +(-2.12656 + 7.93643i) q^{86} +(-7.28199 + 13.0836i) q^{87} +(-10.8729 - 6.27747i) q^{88} +(-1.08954 + 4.06621i) q^{89} +(-0.212711 - 6.76208i) q^{90} +(-9.44329 + 1.35063i) q^{91} -25.4893i q^{92} +(8.07702 + 2.02868i) q^{93} +(-5.61064 + 9.71791i) q^{94} +(0.516884 - 0.895270i) q^{95} +(2.56138 - 10.1979i) q^{96} +(6.16461 + 6.16461i) q^{97} +(-1.12158 - 15.8477i) q^{98} +(10.5088 + 9.86780i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9}+O(q^{10}) $ 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9	$ 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9} - 48 q^{13} - 12 q^{15} + 40 q^{16} - 26 q^{18} + 40 q^{19} - 10 q^{21} + 16 q^{22} + 32 q^{24} - 24 q^{27} - 52 q^{28} - 12 q^{31} - 44 q^{33} + 16 q^{34} - 8 q^{37} - 42 q^{39} - 160 q^{40} - 80 q^{42} + 6 q^{45} + 32 q^{46} + 72 q^{48} - 12 q^{52} + 34 q^{54} - 48 q^{55} - 24 q^{57} - 28 q^{58} + 44 q^{60} + 78 q^{63} + 4 q^{66} + 24 q^{67} - 12 q^{70} - 26 q^{72} - 40 q^{73} + 112 q^{76} + 32 q^{78} + 48 q^{79} + 128 q^{81} - 150 q^{84} + 160 q^{85} - 48 q^{87} + 24 q^{91} + 10 q^{93} - 8 q^{94} - 106 q^{96} + 56 q^{97} - 36 q^{99}+O(q^{100}) $ 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9 - 48 * q^13 - 12 * q^15 + 40 * q^16 - 26 * q^18 + 40 * q^19 - 10 * q^21 + 16 * q^22 + 32 * q^24 - 24 * q^27 - 52 * q^28 - 12 * q^31 - 44 * q^33 + 16 * q^34 - 8 * q^37 - 42 * q^39 - 160 * q^40 - 80 * q^42 + 6 * q^45 + 32 * q^46 + 72 * q^48 - 12 * q^52 + 34 * q^54 - 48 * q^55 - 24 * q^57 - 28 * q^58 + 44 * q^60 + 78 * q^63 + 4 * q^66 + 24 * q^67 - 12 * q^70 - 26 * q^72 - 40 * q^73 + 112 * q^76 + 32 * q^78 + 48 * q^79 + 128 * q^81 - 150 * q^84 + 160 * q^85 - 48 * q^87 + 24 * q^91 + 10 * q^93 - 8 * q^94 - 106 * q^96 + 56 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.19229	−	0.587422i	−1.55018	−	0.415370i	−0.620644	−	0.784093i	$-0.713129\pi$
$2$	−2.19229	−	0.587422i	−1.55018	−	0.415370i	−0.929540	+	0.368722i	$0.879795\pi$
$3$	−1.51343	−	0.842335i	−0.873780	−	0.486322i
$3$	−1.51343	−	0.842335i	−0.873780	−	0.486322i
$4$	2.72902	+	1.57560i	1.36451	+	0.787800i
$5$	0.959762	+	0.257167i	0.429219	+	0.115009i	0.466959	−	0.884279i	$-0.345349\pi$
$5$	0.959762	+	0.257167i	0.429219	+	0.115009i	−0.0377407	+	0.999288i	$0.512016\pi$
$6$	2.82307	+	2.73567i	1.15251	+	1.11683i
$7$	−2.15459	−	1.53549i	−0.814360	−	0.580360i
$7$	−2.15459	−	1.53549i	−0.814360	−	0.580360i
$8$	−1.84753	−	1.84753i	−0.653199	−	0.653199i
$9$	1.58094	+	2.54963i	0.526981	+	0.849877i
$10$	−1.95301	−	1.12757i	−0.617596	−	0.356569i
$11$	4.64145	−	1.24367i	1.39945	−	0.374981i	0.521302	−	0.853372i	$-0.325447\pi$
$11$	4.64145	−	1.24367i	1.39945	−	0.374981i	0.878147	+	0.478391i	$0.158780\pi$
$12$	−2.80300	−	4.68331i	−0.809156	−	1.35196i
$13$	2.61037	−	2.48716i	0.723986	−	0.689815i
$13$	2.61037	−	2.48716i	0.723986	−	0.689815i
$14$	3.82151	+	4.63189i	1.02134	+	1.23793i
$15$	−1.23591	−	1.19765i	−0.319111	−	0.309231i
$16$	−0.186167	−	0.322451i	−0.0465419	−	0.0806129i
$17$	−3.01497	+	5.22208i	−0.731238	+	1.26654i	0.225116	+	0.974332i	$0.427724\pi$
$17$	−3.01497	+	5.22208i	−0.731238	+	1.26654i	−0.956354	+	0.292210i	$0.905609\pi$
$18$	−1.96818	−	6.51821i	−0.463904	−	1.53636i
$19$	0.269277	−	1.00496i	0.0617764	−	0.230553i	−0.928134	−	0.372246i	$-0.878588\pi$
$19$	0.269277	−	1.00496i	0.0617764	−	0.230553i	0.989911	+	0.141693i	$0.0452545\pi$
$20$	2.21402	+	2.21402i	0.495069	+	0.495069i
$21$	1.96743	+	4.13875i	0.429329	+	0.903148i
$22$	−10.9060			−2.32516
$23$	−4.04438	−	7.00507i	−0.843312	−	1.46066i	−0.887079	−	0.461617i	$-0.847269\pi$
$23$	−4.04438	−	7.00507i	−0.843312	−	1.46066i	0.0437676	−	0.999042i	$-0.486064\pi$
$24$	1.23987	+	4.35234i	0.253087	+	0.888417i
$25$	−3.47512	−	2.00636i	−0.695024	−	0.401272i
$26$	−7.18370	+	3.91919i	−1.40884	+	0.768617i
$27$	−0.245007	−	5.19037i	−0.0471516	−	0.998888i
$28$	−3.46061	−	7.58516i	−0.653994	−	1.43346i
$29$		−	8.64500i		−	1.60534i	−0.596426	−	0.802668i	$-0.703413\pi$
$29$		−	8.64500i		−	1.60534i	0.596426	−	0.802668i	$-0.296587\pi$
$30$	2.00595	+	3.35159i	0.366235	+	0.611914i
$31$	−4.64428	+	1.24443i	−0.834137	+	0.223506i	−0.650518	−	0.759491i	$-0.725448\pi$
$31$	−4.64428	+	1.24443i	−0.834137	+	0.223506i	−0.183619	+	0.982997i	$0.558781\pi$
$32$	1.57120	+	5.86380i	0.277752	+	1.03658i
$33$	−8.07209	−	2.02744i	−1.40517	−	0.352932i
$34$	9.67726	−	9.67726i	1.65964	−	1.65964i
$35$	−1.67302	−	2.02780i	−0.282792	−	0.342760i
$36$	0.297229	+	9.44893i	0.0495382	+	1.57482i
$37$	3.20687	+	0.859279i	0.527207	+	0.141265i	0.512598	−	0.858629i	$-0.328683\pi$
$37$	3.20687	+	0.859279i	0.527207	+	0.141265i	0.0146086	+	0.999893i	$0.495350\pi$
$38$	−1.18067	+	2.04498i	−0.191530	+	0.331739i
$39$	−6.04563	+	1.56534i	−0.968076	+	0.250655i
$40$	−1.29806	−	2.24831i	−0.205241	−	0.355489i
$41$	−1.07575	+	1.07575i	−0.168003	+	0.168003i	−0.786101	−	0.618098i	$-0.787904\pi$
$41$	−1.07575	+	1.07575i	−0.168003	+	0.168003i	0.618098	+	0.786101i	$0.287904\pi$
$42$	−1.88199	−	10.2290i	−0.290397	−	1.57838i
$43$		−	3.62015i		−	0.552068i	−0.961148	−	0.276034i	$-0.910980\pi$
$43$		−	3.62015i		−	0.552068i	0.961148	−	0.276034i	$-0.0890203\pi$
$44$	14.6261	+	3.91906i	2.20497	+	0.590820i
$45$	0.861648	+	2.85361i	0.128447	+	0.425390i
$46$	4.75152	+	17.7329i	0.700573	+	2.61458i
$47$	1.27963	−	4.77564i	0.186653	−	0.696599i	−0.807617	−	0.589707i	$-0.799243\pi$
$47$	1.27963	−	4.77564i	0.186653	−	0.696599i	0.994271	−	0.106892i	$-0.0340900\pi$
$48$	0.0101394	+	0.644823i	0.00146350	+	0.0930722i
$49$	2.28455	+	6.61671i	0.326364	+	0.945244i
$50$	6.43989	+	6.43989i	0.910738	+	0.910738i
$51$	8.96169	−	5.36365i	1.25489	−	0.751061i
$52$	11.0425	−	2.67462i	1.53132	−	0.370903i
$53$	−1.07485	−	0.620567i	−0.147643	−	0.0852415i	0.424359	−	0.905494i	$-0.360499\pi$
$53$	−1.07485	−	0.620567i	−0.147643	−	0.0852415i	−0.572001	+	0.820253i	$0.693833\pi$
$54$	−2.51182	+	11.5227i	−0.341815	+	1.56804i
$55$	4.77451			0.643795
$56$	1.14381	+	6.81752i	0.152848	+	0.911029i
$57$	−1.25404	+	1.29411i	−0.166102	+	0.171409i
$58$	−5.07827	+	18.9524i	−0.666809	+	2.48857i
$59$	2.62988	−	0.704673i	0.342381	−	0.0917406i	−0.0835315	−	0.996505i	$-0.526620\pi$
$59$	2.62988	−	0.704673i	0.342381	−	0.0917406i	0.425912	+	0.904765i	$0.359953\pi$
$60$	−1.48582	−	5.21570i	−0.191818	−	0.673344i
$61$	−1.70491	−	2.95300i	−0.218292	−	0.378093i	0.735994	−	0.676988i	$-0.236715\pi$
$61$	−1.70491	−	2.95300i	−0.218292	−	0.378093i	−0.954286	+	0.298896i	$0.903382\pi$
$62$	10.9126			1.38590
$63$	0.508638	−	7.92094i	0.0640824	−	0.997945i
$64$		−	13.0334i		−	1.62918i
$65$	3.14495	−	1.71578i	0.390083	−	0.212817i
$66$	16.5054	+	9.18647i	2.03168	+	1.13078i
$67$	5.64922	−	1.51370i	0.690162	−	0.184928i	0.103342	−	0.994646i	$-0.467046\pi$
$67$	5.64922	−	1.51370i	0.690162	−	0.184928i	0.586820	+	0.809718i	$0.300380\pi$
$68$	−16.4558	+	9.50078i	−1.99556	+	1.15214i
$69$	0.220273	+	14.0084i	0.0265177	+	1.68641i
$70$	2.47657	+	5.42828i	0.296007	+	0.648804i
$71$	7.65674	−	7.65674i	0.908688	−	0.908688i	−0.0874786	−	0.996166i	$-0.527881\pi$
$71$	7.65674	−	7.65674i	0.908688	−	0.908688i	0.996166	+	0.0874786i	$0.0278809\pi$
$72$	1.78967	−	7.63134i	0.210915	−	0.899362i
$73$	−1.40500	−	5.24352i	−0.164442	−	0.613707i	−0.998111	−	0.0614419i	$-0.980430\pi$
$73$	−1.40500	−	5.24352i	−0.164442	−	0.613707i	0.833668	−	0.552266i	$-0.186237\pi$
$74$	−6.52564	−	3.76758i	−0.758590	−	0.437972i
$75$	3.56932	+	5.96370i	0.412150	+	0.688629i
$76$	2.31827	−	2.31827i	0.265924	−	0.265924i
$77$	−11.9101	−	4.44728i	−1.35728	−	0.506815i
$78$	14.1733	+	0.119656i	1.60481	+	0.0135484i
$79$	−4.42329	−	7.66137i	−0.497660	−	0.861972i	0.502337	−	0.864672i	$-0.332474\pi$
$79$	−4.42329	−	7.66137i	−0.497660	−	0.861972i	−0.999996	+	0.00270045i	$0.999140\pi$
$80$	−0.0957524	−	0.357353i	−0.0107054	−	0.0399533i
$81$	−4.00123	+	8.06165i	−0.444581	+	0.895739i
$82$	2.99027	−	1.72643i	0.330220	−	0.190652i
$83$	−3.07191	+	3.07191i	−0.337186	+	0.337186i	−0.855307	−	0.518121i	$-0.826632\pi$
$83$	−3.07191	+	3.07191i	−0.337186	+	0.337186i	0.518121	+	0.855307i	$0.326632\pi$
$84$	−1.15185	+	14.3946i	−0.125677	+	1.57058i
$85$	−4.23661	+	4.23661i	−0.459524	+	0.459524i
$86$	−2.12656	+	7.93643i	−0.229313	+	0.855807i
$87$	−7.28199	+	13.0836i	−0.780711	+	1.40271i
$88$	−10.8729	−	6.27747i	−1.15906	−	0.669181i
$89$	−1.08954	+	4.06621i	−0.115491	+	0.431017i	−0.999323	−	0.0367864i	$-0.988288\pi$
$89$	−1.08954	+	4.06621i	−0.115491	+	0.431017i	0.883832	+	0.467804i	$0.154955\pi$
$90$	−0.212711	−	6.76208i	−0.0224217	−	0.712786i
$91$	−9.44329	+	1.35063i	−0.989926	+	0.141585i
$92$		−	25.4893i		−	2.65744i
$93$	8.07702	+	2.02868i	0.837548	+	0.210364i
$94$	−5.61064	+	9.71791i	−0.578693	+	1.00233i
$95$	0.516884	−	0.895270i	0.0530312	−	0.0918527i
$96$	2.56138	−	10.1979i	0.261420	−	1.04082i
$97$	6.16461	+	6.16461i	0.625922	+	0.625922i	0.947039	−	0.321118i	$-0.104059\pi$
$97$	6.16461	+	6.16461i	0.625922	+	0.625922i	−0.321118	+	0.947039i	$0.604059\pi$
$98$	−1.12158	−	15.8477i	−0.113297	−	1.60086i
$99$	10.5088	+	9.86780i	1.05617	+	0.991751i
$100$	−6.32245	−	10.9508i	−0.632245	−	1.09508i
$101$	1.32460	−	2.29428i	0.131803	−	0.228289i	−0.792569	−	0.609783i	$-0.791257\pi$
$101$	1.32460	−	2.29428i	0.131803	−	0.228289i	0.924372	+	0.381493i	$0.124590\pi$
$102$	−22.7974	+	6.49437i	−2.25728	+	0.643038i
$103$	8.18210	−	4.72394i	0.806206	−	0.465464i	−0.0394303	−	0.999222i	$-0.512554\pi$
$103$	8.18210	−	4.72394i	0.806206	−	0.465464i	0.845637	+	0.533759i	$0.179221\pi$
$104$	−9.41782	−	0.227627i	−0.923493	−	0.0223207i
$105$	0.823915	+	4.47817i	0.0804059	+	0.437025i
$106$	1.99186	+	1.99186i	0.193466	+	0.193466i
$107$	−4.82979	+	2.78848i	−0.466914	+	0.269573i	−0.714947	−	0.699179i	$-0.753549\pi$
$107$	−4.82979	+	2.78848i	−0.466914	+	0.269573i	0.248033	+	0.968752i	$0.420216\pi$
$108$	7.50933	−	14.5507i	0.722585	−	1.40014i
$109$	3.11104	−	0.833602i	0.297984	−	0.0798446i	−0.106730	−	0.994288i	$-0.534038\pi$
$109$	3.11104	−	0.833602i	0.297984	−	0.0798446i	0.404714	+	0.914444i	$0.367371\pi$
$110$	−10.4671	−	2.80466i	−0.998001	−	0.267414i
$111$	−4.12958	−	4.00172i	−0.391962	−	0.379826i
$112$	−0.0940056	+	0.980610i	−0.00888269	+	0.0926589i
$113$			5.11472i			0.481152i	0.970630	+	0.240576i	$0.0773363\pi$
$113$			5.11472i			0.481152i	−0.970630	+	0.240576i	$0.922664\pi$
$114$	3.50941	−	2.10041i	0.328687	−	0.196722i
$115$	−2.08017	−	7.76329i	−0.193976	−	0.723930i
$116$	13.6211	−	23.5924i	1.26468	−	2.19050i
$117$	10.4682	+	2.72341i	0.967785	+	0.251779i
$118$	−6.17939			−0.568859
$119$	14.5145	−	6.62201i	1.33054	−	0.607039i
$120$	0.0706974	+	4.49606i	0.00645376	+	0.410432i
$121$	10.4700	−	6.04487i	0.951820	−	0.549534i
$122$	2.00301	+	7.47533i	0.181344	+	0.676785i
$123$	2.53421	−	0.721929i	0.228502	−	0.0650942i
$124$	−14.6350	−	3.92145i	−1.31427	−	0.352157i
$125$	−6.33229	−	6.33229i	−0.566377	−	0.566377i
$126$	−5.76802	+	17.0662i	−0.513856	+	1.52038i
$127$			8.23094i			0.730378i	0.930933	+	0.365189i	$0.118996\pi$
$127$			8.23094i			0.730378i	−0.930933	+	0.365189i	$0.881004\pi$
$128$	−4.51373	+	16.8455i	−0.398961	+	1.48894i
$129$	−3.04938	+	5.47885i	−0.268483	+	0.482386i
$130$	−7.90253	+	1.91408i	−0.693098	+	0.167876i
$131$	−12.0285	+	6.94467i	−1.05094	+	0.606758i	−0.922911	−	0.385013i	$-0.874197\pi$
$131$	−12.0285	+	6.94467i	−1.05094	+	0.606758i	−0.128025	+	0.991771i	$0.540864\pi$
$132$	−18.8345	−	18.2513i	−1.63933	−	1.58857i
$133$	−2.12328	+	1.75180i	−0.184112	+	0.151900i
$134$	−13.2739			−1.14669
$135$	1.09965	−	5.04453i	0.0946425	−	0.434164i
$136$	15.2182	−	4.07770i	1.30495	−	0.349660i
$137$	10.3804	−	2.78142i	0.886858	−	0.237633i	0.213494	−	0.976944i	$-0.431516\pi$
$137$	10.3804	−	2.78142i	0.886858	−	0.237633i	0.673364	+	0.739311i	$0.264849\pi$
$138$	7.74595	−	30.8399i	0.659379	−	2.62527i
$139$	−22.6901			−1.92455			−0.962273	−	0.272085i	$-0.912287\pi$
$139$	−22.6901			−1.92455			−0.962273	+	0.272085i	$0.912287\pi$
$140$	−1.37071	−	8.16990i	−0.115846	−	0.690483i
$141$	−5.95932	+	6.14973i	−0.501865	+	0.517900i
$142$	−21.2835	+	12.2881i	−1.78607	+	1.03119i
$143$	9.02267	−	14.7905i	0.754514	−	1.23684i
$144$	0.527812	−	0.984436i	0.0439843	−	0.0820363i
$145$	2.22321	−	8.29714i	0.184628	−	0.689040i
$146$			12.3206i			1.01966i
$147$	2.11598	−	11.9383i	0.174523	−	0.984653i
$148$	7.39774	+	7.39774i	0.608091	+	0.608091i
$149$	−4.14885	−	1.11168i	−0.339887	−	0.0910725i	0.0848382	−	0.996395i	$-0.472963\pi$
$149$	−4.14885	−	1.11168i	−0.339887	−	0.0910725i	−0.424725	+	0.905322i	$0.639629\pi$
$150$	−4.32178	−	15.1709i	−0.352872	−	1.23870i
$151$	2.30084	+	8.58684i	0.187239	+	0.698787i	0.994140	+	0.108100i	$0.0344766\pi$
$151$	2.30084	+	8.58684i	0.187239	+	0.698787i	−0.806901	+	0.590687i	$0.798857\pi$
$152$	−2.35418	+	1.35919i	−0.190949	+	0.110245i
$153$	−18.0809	+	0.568760i	−1.46175	+	0.0459815i
$154$	23.4979	+	16.7460i	1.89351	+	1.34943i
$155$	−4.77743			−0.383732
$156$	−18.9650	−	5.25365i	−1.51842	−	0.420629i
$157$	2.93250	−	5.07924i	0.234039	−	0.405368i	−0.724954	−	0.688797i	$-0.758139\pi$
$157$	2.93250	−	5.07924i	0.234039	−	0.405368i	0.958993	+	0.283430i	$0.0914722\pi$
$158$	5.19668	+	19.3943i	0.413426	+	1.54293i
$159$	1.10399	+	1.84457i	0.0875522	+	0.146284i
$160$			6.03191i			0.476865i
$161$	−2.04222	+	21.3032i	−0.160949	+	1.67893i
$162$	13.5075	−	15.3231i	1.06125	−	1.20389i
$163$	17.3086	+	4.63783i	1.35571	+	0.363263i	0.862241	−	0.506498i	$-0.169060\pi$
$163$	17.3086	+	4.63783i	1.35571	+	0.363263i	0.493473	+	0.869761i	$0.335727\pi$
$164$	−4.63068	+	1.24079i	−0.361596	+	0.0968892i
$165$	−7.22590	−	4.02174i	−0.562535	−	0.313092i
$166$	8.53902	−	4.93000i	0.662756	−	0.382643i
$167$	−3.79103	−	3.79103i	−0.293359	−	0.293359i	0.545047	−	0.838406i	$-0.316512\pi$
$167$	−3.79103	−	3.79103i	−0.293359	−	0.293359i	−0.838406	+	0.545047i	$0.816512\pi$
$168$	4.01156	−	11.2813i	0.309498	−	0.870372i
$169$	0.628049	−	12.9848i	0.0483115	−	0.998832i
$170$	11.7765	−	6.79919i	0.903220	−	0.521474i
$171$	2.98798	−	0.902223i	0.228497	−	0.0689947i
$172$	5.70391	−	9.87947i	0.434919	−	0.753303i
$173$	5.84509	+	10.1240i	0.444394	+	0.769713i	0.998010	−	0.0630595i	$-0.0200858\pi$
$173$	5.84509	+	10.1240i	0.444394	+	0.769713i	−0.553616	+	0.832772i	$0.686752\pi$
$174$	23.6498	−	24.4055i	1.79289	−	1.85017i
$175$	4.40672	+	9.65890i	0.333117	+	0.730144i
$176$	−1.26511	−	1.26511i	−0.0953612	−	0.0953612i
$177$	−4.57371	−	1.14876i	−0.343781	−	0.0863463i
$178$	4.77716	−	8.27429i	0.358064	−	0.620184i
$179$	3.56463	−	6.17411i	0.266433	−	0.461475i	−0.701505	−	0.712664i	$-0.747488\pi$
$179$	3.56463	−	6.17411i	0.266433	−	0.461475i	0.967938	+	0.251189i	$0.0808217\pi$
$180$	−2.14469	+	9.14516i	−0.159856	+	0.681640i
$181$			13.2207i			0.982686i	0.870966	+	0.491343i	$0.163494\pi$
$181$			13.2207i			0.982686i	−0.870966	+	0.491343i	$0.836506\pi$
$182$	21.4958	+	2.58623i	1.59338	+	0.191704i
$183$	0.0928562	+	5.90526i	0.00686413	+	0.436530i
$184$	−5.46995	+	20.4141i	−0.403250	+	1.50495i
$185$	2.85686	+	1.64941i	0.210040	+	0.121267i
$186$	−16.5155	−	9.19207i	−1.21097	−	0.673995i
$187$	−7.49927	+	27.9877i	−0.548401	+	2.04666i
$188$	11.0166	−	11.0166i	0.803471	−	0.803471i
$189$	−7.44187	+	11.5593i	−0.541317	+	0.840819i
$190$	−1.65906	+	1.65906i	−0.120361	+	0.120361i
$191$	2.81669	−	1.62622i	0.203808	−	0.117669i	−0.394622	−	0.918843i	$-0.629125\pi$
$191$	2.81669	−	1.62622i	0.203808	−	0.117669i	0.598431	+	0.801175i	$0.295791\pi$
$192$	−10.9785	+	19.7252i	−0.792306	+	1.42354i
$193$	−6.49514	−	24.2402i	−0.467531	−	1.74485i	−0.648360	−	0.761334i	$-0.724545\pi$
$193$	−6.49514	−	24.2402i	−0.467531	−	1.74485i	0.180830	−	0.983514i	$-0.442122\pi$
$194$	−9.89339	−	17.1358i	−0.710304	−	1.23028i
$195$	−6.20493	−	0.0523841i	−0.444344	−	0.00375130i
$196$	−4.19072	+	21.6567i	−0.299337	+	1.54690i
$197$	2.04689	−	2.04689i	0.145835	−	0.145835i	−0.630420	−	0.776255i	$-0.717117\pi$
$197$	2.04689	−	2.04689i	0.145835	−	0.145835i	0.776255	+	0.630420i	$0.217117\pi$
$198$	−17.2417	−	27.8062i	−1.22531	−	1.97610i
$199$	4.07388	+	2.35206i	0.288790	+	0.166733i	0.637396	−	0.770536i	$-0.280012\pi$
$199$	4.07388	+	2.35206i	0.288790	+	0.166733i	−0.348606	+	0.937269i	$0.613345\pi$
$200$	2.71357	+	10.1272i	0.191878	+	0.716099i
$201$	−9.82474	−	2.46765i	−0.692984	−	0.174054i
$202$	−4.25162	+	4.25162i	−0.299143	+	0.299143i
$203$	−13.2743	+	18.6265i	−0.931674	+	1.30732i
$204$	32.9076	−	0.517449i	2.30399	−	0.0362287i
$205$	−1.30911	+	0.755814i	−0.0914321	+	0.0527883i
$206$	−20.7125	+	5.54989i	−1.44311	+	0.386679i
$207$	11.4664	−	21.3863i	0.796970	−	1.48645i
$208$	−1.28795	−	0.378689i	−0.0893036	−	0.0262573i
$209$		−	4.99934i		−	0.345812i
$210$	0.824315	−	10.3014i	0.0568832	−	0.710866i
$211$	18.9964			1.30776			0.653881	−	0.756597i	$-0.273140\pi$
$211$	18.9964			1.30776			0.653881	+	0.756597i	$0.273140\pi$
$212$	−1.95553	−	3.38708i	−0.134306	−	0.232626i
$213$	−18.0375	+	5.13841i	−1.23591	+	0.352078i
$214$	12.2263	−	3.27603i	0.835774	−	0.223945i
$215$	0.930986	−	3.47449i	0.0634927	−	0.236958i
$216$	−9.13669	+	10.0420i	−0.621673	+	0.683272i
$217$	11.9173	+	4.45000i	0.809002	+	0.302085i
$218$	−7.30999			−0.495095
$219$	−2.29043	+	9.11918i	−0.154773	+	0.616217i
$220$	13.0297	+	7.52273i	0.878465	+	0.507182i
$221$	5.11798	+	21.1303i	0.344273	+	1.42138i
$222$	6.70254	+	11.1987i	0.449845	+	0.751610i
$223$	7.56742	+	7.56742i	0.506752	+	0.506752i	0.913528	−	0.406776i	$-0.133347\pi$
$223$	7.56742	+	7.56742i	0.506752	+	0.506752i	−0.406776	+	0.913528i	$0.633347\pi$
$224$	5.61850	−	15.0467i	0.375402	−	1.00535i
$225$	−0.378490	−	12.0322i	−0.0252327	−	0.802148i
$226$	3.00450	−	11.2129i	0.199856	−	0.745874i
$227$	−0.368103	−	1.37378i	−0.0244318	−	0.0911808i	0.952633	−	0.304121i	$-0.0983627\pi$
$227$	−0.368103	−	1.37378i	−0.0244318	−	0.0911808i	−0.977065	+	0.212940i	$0.931696\pi$
$228$	−5.46131	+	1.55578i	−0.361684	+	0.103034i
$229$	19.6652	+	5.26927i	1.29951	+	0.348203i	0.841266	−	0.540621i	$-0.181811\pi$
$229$	19.6652	+	5.26927i	1.29951	+	0.348203i	0.458247	+	0.888825i	$0.348478\pi$
$230$			18.2413i			1.20280i
$231$	14.2790	+	16.7629i	0.939487	+	1.10292i
$232$	−15.9719	+	15.9719i	−1.04860	+	1.04860i
$233$	0.464344	+	0.804267i	0.0304202	+	0.0526893i	0.880835	−	0.473424i	$-0.156982\pi$
$233$	0.464344	+	0.804267i	0.0304202	+	0.0526893i	−0.850415	+	0.526113i	$0.823649\pi$
$234$	−21.3495	−	12.1198i	−1.39566	−	0.792293i
$235$	2.45628	−	4.25440i	0.160230	−	0.277526i
$236$	8.28727	+	2.22057i	0.539455	+	0.144547i
$237$	0.240910	+	15.3208i	0.0156488	+	0.995196i
$238$	−35.7099	+	5.99123i	−2.31473	+	0.388354i
$239$	−11.6696	+	11.6696i	−0.754842	+	0.754842i	−0.975379	−	0.220537i	$-0.929219\pi$
$239$	−11.6696	+	11.6696i	−0.754842	+	0.754842i	0.220537	+	0.975379i	$0.429219\pi$
$240$	−0.156096	+	0.621484i	−0.0100760	+	0.0401166i
$241$	0.469356	+	1.75166i	0.0302339	+	0.112834i	0.979394	−	0.201960i	$-0.0647311\pi$
$241$	0.469356	+	1.75166i	0.0302339	+	0.112834i	−0.949160	+	0.314794i	$0.898064\pi$
$242$	−26.5042	+	7.10178i	−1.70376	+	0.456520i
$243$	12.8462	−	8.83037i	0.824084	−	0.566468i
$244$		−	10.7450i		−	0.687881i
$245$	0.491018	+	6.93798i	0.0313700	+	0.443251i
$246$	−5.97980	+	0.0940282i	−0.381258	+	0.00599502i
$247$	−1.79658	−	3.29304i	−0.114313	−	0.209531i
$248$	10.8795	+	6.28130i	0.690851	+	0.398863i
$249$	7.23669	−	2.06154i	0.458607	−	0.130645i
$250$	10.1625	+	17.6019i	0.642732	+	1.11324i
$251$	21.3956			1.35048			0.675239	−	0.737599i	$-0.264040\pi$
$251$	21.3956			1.35048			0.675239	+	0.737599i	$0.264040\pi$
$252$	13.8683	−	20.8150i	0.873622	−	1.31122i
$253$	−27.4838	−	27.4838i	−1.72789	−	1.72789i
$254$	4.83504	−	18.0446i	0.303377	−	1.13222i
$255$	9.98045	−	2.84317i	0.625000	−	0.178046i
$256$	6.75738	−	11.7041i	0.422336	−	0.731508i
$257$	10.6034	+	18.3657i	0.661423	+	1.14562i	0.980242	+	0.197803i	$0.0633806\pi$
$257$	10.6034	+	18.3657i	0.661423	+	1.14562i	−0.318818	+	0.947816i	$0.603286\pi$
$258$	9.90353	−	10.2200i	0.616567	−	0.636267i
$259$	−5.59009	−	6.77552i	−0.347352	−	0.421010i
$260$	11.2860	+	0.272781i	0.699929	+	0.0169172i
$261$	22.0416	−	13.6673i	1.36434	−	0.845983i
$262$	30.4494	−	8.15890i	1.88117	−	0.504059i
$263$	19.5351	+	11.2786i	1.20458	+	0.695467i	0.961571	−	0.274556i	$-0.0885307\pi$
$263$	19.5351	+	11.2786i	1.20458	+	0.695467i	0.243013	+	0.970023i	$0.421864\pi$
$264$	11.1676	+	18.6591i	0.687321	+	1.14839i
$265$	−0.872014	−	0.872014i	−0.0535674	−	0.0535674i
$266$	5.68390	−	2.59319i	0.348502	−	0.158999i
$267$	5.07405	−	5.23617i	0.310527	−	0.320448i
$268$	17.8018	+	4.76998i	1.08742	+	0.291373i
$269$	−1.28942	−	0.744445i	−0.0786171	−	0.0453896i	0.460176	−	0.887828i	$-0.347786\pi$
$269$	−1.28942	−	0.744445i	−0.0786171	−	0.0453896i	−0.538793	+	0.842438i	$0.681120\pi$
$270$	−5.37401	+	10.4131i	−0.327052	+	0.633722i
$271$	−26.7952	−	7.17977i	−1.62770	−	0.436140i	−0.674446	−	0.738324i	$-0.735617\pi$
$271$	−26.7952	−	7.17977i	−1.62770	−	0.436140i	−0.953249	+	0.302185i	$0.902284\pi$
$272$	2.24516			0.136133
$273$	15.4295	+	5.91033i	0.933833	+	0.357709i
$274$	−24.3907			−1.47350
$275$	−18.6248	−	4.99051i	−1.12312	−	0.300939i
$276$	−21.4705	+	38.5763i	−1.29237	+	2.32202i
$277$	10.5726	+	6.10411i	0.635248	+	0.366761i	0.782782	−	0.622296i	$-0.213800\pi$
$277$	10.5726	+	6.10411i	0.635248	+	0.366761i	−0.147534	+	0.989057i	$0.547133\pi$
$278$	49.7432	+	13.3287i	2.98340	+	0.799400i
$279$	−10.5152	−	9.87381i	−0.629527	−	0.591130i
$280$	−0.655458	+	6.83735i	−0.0391711	+	0.408610i
$281$	9.09057	+	9.09057i	0.542298	+	0.542298i	0.924202	−	0.381904i	$-0.124731\pi$
$281$	9.09057	+	9.09057i	0.542298	+	0.542298i	−0.381904	+	0.924202i	$0.624731\pi$
$282$	16.6770	−	9.98135i	0.993103	−	0.594380i
$283$	−19.2533	−	11.1159i	−1.14449	−	0.660772i	−0.196952	−	0.980413i	$-0.563104\pi$
$283$	−19.2533	−	11.1159i	−1.14449	−	0.660772i	−0.947539	+	0.319641i	$0.896438\pi$
$284$	32.9594	−	8.83143i	1.95578	−	0.524049i
$285$	−1.53639	+	0.919539i	−0.0910076	+	0.0544688i
$286$	−28.4686	+	27.1249i	−1.68338	+	1.60393i
$287$	3.96960	−	0.666000i	0.234318	−	0.0393127i
$288$	−12.4665	+	13.2763i	−0.734598	+	0.782315i
$289$	−9.68011	−	16.7664i	−0.569418	−	0.986262i
$290$	−9.74786	+	16.8838i	−0.572414	+	0.991450i
$291$	−4.13705	−	14.5224i	−0.242518	−	0.851317i
$292$	4.42743	−	16.5234i	0.259096	−	0.966958i
$293$	14.7365	+	14.7365i	0.860914	+	0.860914i	0.991444	−	0.130530i	$-0.0416680\pi$
$293$	14.7365	+	14.7365i	0.860914	+	0.860914i	−0.130530	+	0.991444i	$0.541668\pi$
$294$	−11.6517	+	24.9292i	−0.679539	+	1.45390i
$295$	2.70527			0.157507
$296$	−4.33724	−	7.51232i	−0.252097	−	0.436645i
$297$	−7.59230	−	23.7861i	−0.440550	−	1.38021i
$298$	8.44246	+	4.87425i	0.489058	+	0.282358i
$299$	−27.9801	−	8.22679i	−1.61813	−	0.475768i
$300$	0.344345	+	21.8989i	0.0198808	+	1.26433i
$301$	−5.55871	+	7.79996i	−0.320398	+	0.449582i
$302$		−	20.1764i		−	1.16102i
$303$	−3.93724	+	2.35647i	−0.226189	+	0.135376i
$304$	−0.374180	+	0.100261i	−0.0214607	+	0.00575038i
$305$	−0.876897	−	3.27262i	−0.0502109	−	0.187390i
$306$	39.9727	+	9.37423i	2.28508	+	0.535889i
$307$	−12.0170	+	12.0170i	−0.685847	+	0.685847i	−0.961311	−	0.275464i	$-0.911168\pi$
$307$	−12.0170	+	12.0170i	−0.685847	+	0.685847i	0.275464	+	0.961311i	$0.411168\pi$
$308$	−25.4957	−	30.9022i	−1.45275	−	1.76082i
$309$	−16.3622	+	0.257284i	−0.930812	+	0.0146364i
$310$	10.4735	+	2.80637i	0.594855	+	0.159391i
$311$	−7.65781	+	13.2637i	−0.434235	+	0.752116i	−0.997233	−	0.0743417i	$-0.976314\pi$
$311$	−7.65781	+	13.2637i	−0.434235	+	0.752116i	0.562998	+	0.826458i	$0.309648\pi$
$312$	14.0615	+	8.27745i	0.796074	+	0.468618i
$313$	−9.95534	−	17.2432i	−0.562709	−	0.974641i	−0.997259	−	0.0739928i	$-0.976426\pi$
$313$	−9.95534	−	17.2432i	−0.562709	−	0.974641i	0.434550	−	0.900648i	$-0.356908\pi$
$314$	−9.41256	+	9.41256i	−0.531181	+	0.531181i
$315$	2.52518	−	7.47141i	0.142278	−	0.420966i
$316$		−	27.8774i		−	1.56823i
$317$	4.17789	+	1.11946i	0.234654	+	0.0628752i	0.374229	−	0.927336i	$-0.377907\pi$
$317$	4.17789	+	1.11946i	0.234654	+	0.0628752i	−0.139576	+	0.990211i	$0.544574\pi$
$318$	−1.33673	−	4.69235i	−0.0749599	−	0.263134i
$319$	−10.7515	−	40.1253i	−0.601971	−	2.24659i
$320$	3.35178	−	12.5090i	0.187370	−	0.699274i
$321$	9.65839	−	0.151872i	0.539079	−	0.00847664i
$322$	16.9911	−	45.5031i	0.946877	−	2.53579i
$323$	4.43610	+	4.43610i	0.246831	+	0.246831i
$324$	−23.6214	+	15.6961i	−1.31230	+	0.872003i
$325$	−14.0615	+	3.40584i	−0.779991	+	0.188922i
$326$	−35.2211	−	20.3349i	−1.95072	−	1.12625i
$327$	−5.41052	−	1.35894i	−0.299203	−	0.0751497i
$328$	3.97494			0.219479
$329$	−10.0900	+	8.32471i	−0.556281	+	0.458956i
$330$	13.4788	+	13.0615i	0.741984	+	0.719011i
$331$	1.22136	−	4.55817i	0.0671319	−	0.250540i	−0.924202	−	0.381903i	$-0.875269\pi$
$331$	1.22136	−	4.55817i	0.0671319	−	0.250540i	0.991334	+	0.131363i	$0.0419355\pi$
$332$	−13.2234	+	3.54320i	−0.725728	+	0.194458i
$333$	2.87904	+	9.53481i	0.157771	+	0.522505i
$334$	6.08411	+	10.5380i	0.332907	+	0.576613i
$335$	5.81118			0.317499
$336$	0.968273	−	1.40490i	0.0528236	−	0.0766436i
$337$			20.0045i			1.08971i	0.838529	+	0.544856i	$0.183416\pi$
$337$			20.0045i			1.08971i	−0.838529	+	0.544856i	$0.816584\pi$
$338$	−9.00444	+	28.0976i	−0.489777	+	1.52831i
$339$	4.30830	−	7.74077i	0.233995	−	0.420421i
$340$	−18.2370	+	4.88658i	−0.989039	+	0.265012i
$341$	−20.0085	+	11.5519i	−1.08352	+	0.625571i
$342$	−7.08051	+	0.222727i	−0.382870	+	0.0120437i
$343$	5.23762	−	17.7642i	0.282805	−	0.959177i
$344$	−6.68832	+	6.68832i	−0.360610	+	0.360610i
$345$	−3.39110	+	13.5014i	−0.182571	+	0.726890i
$346$	−6.86707	−	25.6283i	−0.369176	−	1.37778i
$347$	−20.8286	−	12.0254i	−1.11814	−	0.645558i	−0.177214	−	0.984172i	$-0.556708\pi$
$347$	−20.8286	−	12.0254i	−1.11814	−	0.645558i	−0.940925	+	0.338615i	$0.890042\pi$
$348$	−40.4872	+	24.2319i	−2.17034	+	1.29897i
$349$	7.22449	−	7.22449i	0.386718	−	0.386718i	−0.486797	−	0.873515i	$-0.661835\pi$
$349$	7.22449	−	7.22449i	0.386718	−	0.386718i	0.873515	+	0.486797i	$0.161835\pi$
$350$	−3.98696	−	23.7637i	−0.213112	−	1.27022i
$351$	−13.5489	−	12.9394i	−0.723184	−	0.690655i
$352$	14.5853	+	25.2624i	0.777398	+	1.34649i
$353$	−4.84966	−	18.0992i	−0.258121	−	0.963322i	−0.966327	−	0.257316i	$-0.917162\pi$
$353$	−4.84966	−	18.0992i	−0.258121	−	0.963322i	0.708206	−	0.706006i	$-0.249505\pi$
$354$	9.35208	+	5.20512i	0.497058	+	0.276649i
$355$	9.31771	−	5.37958i	0.494533	−	0.285519i
$356$	−9.38009	+	9.38009i	−0.497144	+	0.497144i
$357$	−27.5446	−	2.20411i	−1.45782	−	0.116654i
$358$	−11.4415	+	11.4415i	−0.604702	+	0.604702i
$359$	3.90265	−	14.5649i	0.205974	−	0.768706i	−0.783176	−	0.621800i	$-0.786402\pi$
$359$	3.90265	−	14.5649i	0.205974	−	0.768706i	0.989150	−	0.146906i	$-0.0469316\pi$
$360$	3.68019	−	6.86402i	0.193963	−	0.361766i
$361$	15.5171	+	8.95878i	0.816687	+	0.471515i
$362$	7.76612	−	28.9836i	0.408178	−	1.52334i
$363$	−20.9375	+	0.329227i	−1.09893	+	0.0172799i
$364$	−27.8990	−	11.1930i	−1.46230	−	0.586671i
$365$		−	5.39385i		−	0.282327i
$366$	3.26532	−	13.0006i	0.170681	−	0.679552i
$367$	−17.3258	+	30.0091i	−0.904399	+	1.56646i	−0.0826766	+	0.996576i	$0.526347\pi$
$367$	−17.3258	+	30.0091i	−0.904399	+	1.56646i	−0.821722	+	0.569888i	$0.806986\pi$
$368$	−1.50586	+	2.60823i	−0.0784986	+	0.135964i
$369$	−4.44345	−	1.04206i	−0.231317	−	0.0542476i
$370$	−5.29416	−	5.29416i	−0.275230	−	0.275230i
$371$	1.36300	+	2.98750i	0.0707634	+	0.155103i
$372$	18.8460	+	18.2625i	0.977117	+	0.946864i
$373$	5.86713	+	10.1622i	0.303788	+	0.526177i	0.976991	−	0.213281i	$-0.0684151\pi$
$373$	5.86713	+	10.1622i	0.303788	+	0.526177i	−0.673202	+	0.739458i	$0.735082\pi$
$374$	32.8812	−	56.9518i	1.70024	−	2.94491i
$375$	4.24957	+	14.9174i	0.219447	+	0.770331i
$376$	−11.1873	+	6.45897i	−0.576939	+	0.333096i
$377$	−21.5015	−	22.5666i	−1.10738	−	1.16224i
$378$	23.1050	−	20.9699i	1.18839	−	1.07858i
$379$	17.2711	+	17.2711i	0.887155	+	0.887155i	0.994249	−	0.107094i	$-0.0341547\pi$
$379$	17.2711	+	17.2711i	0.887155	+	0.887155i	−0.107094	+	0.994249i	$0.534155\pi$
$380$	2.82117	−	1.62881i	0.144723	−	0.0835560i
$381$	6.93320	−	12.4570i	0.355199	−	0.638189i
$382$	−7.13027	+	1.91055i	−0.364817	+	0.0977523i
$383$	32.4642	+	8.69875i	1.65884	+	0.444486i	0.962069	−	0.272806i	$-0.0879516\pi$
$383$	32.4642	+	8.69875i	1.65884	+	0.444486i	0.696773	+	0.717291i	$0.254618\pi$
$384$	21.0207	−	21.6924i	1.07271	−	1.10698i
$385$	−10.2871	−	7.33122i	−0.524281	−	0.373633i
$386$			56.9569i			2.89903i
$387$	9.23005	−	5.72326i	0.469190	−	0.290930i
$388$	7.11038	+	26.5363i	0.360975	+	1.34718i
$389$	0.501908	−	0.869331i	0.0254478	−	0.0440768i	−0.853021	−	0.521876i	$-0.825232\pi$
$389$	0.501908	−	0.869331i	0.0254478	−	0.0440768i	0.878469	+	0.477800i	$0.158566\pi$
$390$	13.5722	+	3.75975i	0.687256	+	0.190383i
$391$	48.7748			2.46665
$392$	8.00378	−	16.4453i	0.404252	−	0.830613i
$393$	24.0541	−	0.378233i	1.21337	−	0.0190794i
$394$	−5.68977	+	3.28499i	−0.286646	+	0.165495i
$395$	−2.27505	−	8.49062i	−0.114470	−	0.427209i
$396$	13.1309	+	43.4870i	0.659854	+	2.18531i
$397$	3.94963	+	1.05830i	0.198226	+	0.0531145i	0.356566	−	0.934270i	$-0.383947\pi$
$397$	3.94963	+	1.05830i	0.198226	+	0.0531145i	−0.158340	+	0.987385i	$0.550614\pi$
$398$	−7.54948	−	7.54948i	−0.378421	−	0.378421i
$399$	4.68904	−	0.862713i	0.234746	−	0.0431897i
$400$			1.49408i			0.0747038i
$401$	0.698135	−	2.60547i	0.0348632	−	0.130111i	−0.946301	−	0.323287i	$-0.895212\pi$
$401$	0.698135	−	2.60547i	0.0348632	−	0.130111i	0.981164	+	0.193176i	$0.0618788\pi$
$402$	20.0891	+	11.1811i	1.00195	+	0.557661i
$403$	−9.02817	+	14.7995i	−0.449725	+	0.737215i
$404$	7.22973	−	4.17409i	0.359693	−	0.207669i
$405$	−5.91342	+	6.70828i	−0.293840	+	0.333337i
$406$	40.0427	−	33.0370i	1.98729	−	1.63960i
$407$	15.9532			0.790770
$408$	−26.4664	−	6.64748i	−1.31028	−	0.329099i
$409$	27.5114	−	7.37165i	1.36035	−	0.364505i	0.496405	−	0.868091i	$-0.334653\pi$
$409$	27.5114	−	7.37165i	1.36035	−	0.364505i	0.863945	+	0.503586i	$0.167986\pi$
$410$	3.31393	−	0.887964i	0.163663	−	0.0438534i
$411$	−18.0529	−	4.53429i	−0.890485	−	0.223660i
$412$	29.7722			1.46677
$413$	−6.74833	−	2.51986i	−0.332064	−	0.123994i
$414$	−37.7005	+	40.1494i	−1.85288	+	1.97323i
$415$	−3.73829	+	2.15830i	−0.183506	+	0.105947i
$416$	18.6856	+	11.3988i	0.916138	+	0.558874i
$417$	34.3398	+	19.1126i	1.68163	+	0.935950i
$418$	−2.93673	+	10.9600i	−0.143640	+	0.536072i
$419$		−	20.1844i		−	0.986074i	−0.870008	−	0.493037i	$-0.835887\pi$
$419$		−	20.1844i		−	0.986074i	0.870008	−	0.493037i	$-0.164113\pi$
$420$	−4.80732	+	13.5192i	−0.234573	+	0.659668i
$421$	−16.5214	−	16.5214i	−0.805204	−	0.805204i	0.178700	−	0.983904i	$-0.442811\pi$
$421$	−16.5214	−	16.5214i	−0.805204	−	0.805204i	−0.983904	+	0.178700i	$0.942811\pi$
$422$	−41.6455	−	11.1589i	−2.02727	−	0.543206i
$423$	14.1991	−	4.28744i	0.690386	−	0.208463i
$424$	0.839306	+	3.13233i	0.0407603	+	0.152120i
$425$	20.9548	−	12.0982i	1.01646	−	0.586851i
$426$	42.5618	−	0.669255i	2.06213	−	0.0324255i
$427$	−0.860899	+	8.98038i	−0.0416618	+	0.434591i
$428$	−17.5741			−0.849478
$429$	−26.1137	+	14.7842i	−1.26078	+	0.713790i
$430$	−4.08198	+	7.07020i	−0.196851	+	0.340955i
$431$	3.86107	+	14.4097i	0.185981	+	0.694091i	0.994418	+	0.105509i	$0.0336471\pi$
$431$	3.86107	+	14.4097i	0.185981	+	0.694091i	−0.808437	+	0.588583i	$0.799686\pi$
$432$	−1.62803	+	1.04528i	−0.0783287	+	0.0502911i
$433$		−	22.6270i		−	1.08738i	−0.839285	−	0.543691i	$-0.817026\pi$
$433$		−	22.6270i		−	1.08738i	0.839285	−	0.543691i	$-0.182974\pi$
$434$	−23.5122	−	16.7562i	−1.12862	−	0.804323i
$435$	−10.3537	+	10.6845i	−0.496420	+	0.512281i
$436$	9.80353	+	2.62685i	0.469504	+	0.125803i
$437$	−8.12885	+	2.17812i	−0.388856	+	0.104194i
$438$	10.3781	−	18.6464i	0.495885	−	0.890961i
$439$	15.1987	−	8.77496i	0.725393	−	0.418806i	−0.0913414	−	0.995820i	$-0.529115\pi$
$439$	15.1987	−	8.77496i	0.725393	−	0.418806i	0.816734	+	0.577014i	$0.195782\pi$
$440$	−8.82104	−	8.82104i	−0.420526	−	0.420526i
$441$	−13.2584	+	16.2854i	−0.631354	+	0.775495i
$442$	1.19230	−	49.3301i	0.0567120	−	2.34640i
$443$	−18.5620	+	10.7168i	−0.881908	+	0.509170i	−0.871287	−	0.490774i	$-0.836714\pi$
$443$	−18.5620	+	10.7168i	−0.881908	+	0.509170i	−0.0106206	+	0.999944i	$0.503381\pi$
$444$	−4.96459	−	17.4273i	−0.235609	−	0.827065i
$445$	−2.09139	+	3.62240i	−0.0991415	+	0.171718i
$446$	−12.1447	−	21.0353i	−0.575069	−	0.996048i
$447$	5.34259	+	5.17717i	0.252696	+	0.244872i
$448$	−20.0127	+	28.0818i	−0.945511	+	1.32674i
$449$	4.61199	+	4.61199i	0.217653	+	0.217653i	0.807509	−	0.589855i	$-0.200815\pi$
$449$	4.61199	+	4.61199i	0.217653	+	0.217653i	−0.589855	+	0.807509i	$0.700815\pi$
$450$	−6.23823	+	26.6004i	−0.294073	+	1.25396i
$451$	−3.65515	+	6.33090i	−0.172114	+	0.298110i
$452$	−8.05875	+	13.9582i	−0.379052	+	0.656537i
$453$	3.75084	−	14.9337i	0.176230	−	0.701644i
$454$			3.22795i			0.151495i
$455$	−9.41065	−	1.13222i	−0.441178	−	0.0530795i
$456$	4.70778	−	0.0740265i	0.220462	−	0.00346661i
$457$	−4.27001	+	15.9359i	−0.199743	+	0.745451i	0.791245	+	0.611499i	$0.209433\pi$
$457$	−4.27001	+	15.9359i	−0.199743	+	0.745451i	−0.990988	+	0.133951i	$0.957233\pi$
$458$	−40.0165	−	23.1036i	−1.86985	−	1.07956i
$459$	27.8433	+	14.3694i	1.29961	+	0.670705i
$460$	6.55502	−	24.4637i	0.305629	−	1.14062i
$461$	−16.5408	+	16.5408i	−0.770382	+	0.770382i	−0.978173	−	0.207791i	$-0.933373\pi$
$461$	−16.5408	+	16.5408i	−0.770382	+	0.770382i	0.207791	+	0.978173i	$0.433373\pi$
$462$	−21.4567	−	45.1370i	−0.998257	−	2.09996i
$463$	−21.2860	+	21.2860i	−0.989246	+	0.989246i	−0.999943	−	0.0106969i	$-0.996595\pi$
$463$	−21.2860	+	21.2860i	−0.989246	+	0.989246i	0.0106969	+	0.999943i	$0.496595\pi$
$464$	−2.78759	+	1.60942i	−0.129411	+	0.0747154i
$465$	7.23030	+	4.02419i	0.335297	+	0.186617i
$466$	−0.545532	−	2.03595i	−0.0252713	−	0.0943137i
$467$	12.2928	+	21.2917i	0.568842	+	0.985263i	0.996681	+	0.0814080i	$0.0259417\pi$
$467$	12.2928	+	21.2917i	0.568842	+	0.985263i	−0.427839	+	0.903855i	$0.640725\pi$
$468$	24.2769	+	23.9259i	1.12220	+	1.10598i
$469$	−14.4960	−	5.41290i	−0.669365	−	0.249944i
$470$	−7.88401	+	7.88401i	−0.363662	+	0.363662i
$471$	−8.71656	+	5.21693i	−0.401638	+	0.240384i
$472$	−6.16066	−	3.55686i	−0.283568	−	0.163718i
$473$	−4.50228	−	16.8027i	−0.207015	−	0.772591i
$474$	8.47166	−	33.7293i	0.389116	−	1.54924i
$475$	−2.95208	+	2.95208i	−0.135451	+	0.135451i
$476$	50.0440	+	4.79744i	2.29376	+	0.219890i
$477$	−0.117067	−	3.72156i	−0.00536013	−	0.170399i
$478$	32.4380	−	18.7281i	1.48368	−	0.856604i
$479$	17.2167	−	4.61320i	0.786650	−	0.210782i	0.156936	−	0.987609i	$-0.449838\pi$
$479$	17.2167	−	4.61320i	0.786650	−	0.210782i	0.629715	+	0.776826i	$0.283172\pi$
$480$	5.08089	−	9.12888i	0.231910	−	0.416674i
$481$	10.5083	−	5.73298i	0.479137	−	0.261401i
$482$		−	4.11586i		−	0.187472i
$483$	21.0352	−	30.5207i	0.957133	−	1.38874i
$484$	38.0972			1.73169
$485$	4.33122	+	7.50190i	0.196671	+	0.340644i
$486$	−33.3497	+	11.8126i	−1.51277	+	0.535830i
$487$	−20.4704	+	5.48504i	−0.927604	+	0.248551i	−0.690833	−	0.723015i	$-0.742756\pi$
$487$	−20.4704	+	5.48504i	−0.927604	+	0.248551i	−0.236771	+	0.971565i	$0.576089\pi$
$488$	−2.30587	+	8.60561i	−0.104382	+	0.389557i
$489$	−22.2888	−	21.5987i	−1.00793	−	0.976725i
$490$	2.99907	−	15.4985i	0.135484	−	0.700151i
$491$	13.7884			0.622260			0.311130	−	0.950367i	$-0.399292\pi$
$491$	13.7884			0.622260			0.311130	+	0.950367i	$0.399292\pi$
$492$	8.05337	+	2.02274i	0.363074	+	0.0911921i
$493$	45.1449	+	26.0644i	2.03323	+	1.17388i
$494$	2.00421	+	8.27466i	0.0901737	+	0.372294i
$495$	7.54824	+	12.1732i	0.339268	+	0.547147i
$496$	1.26588	+	1.26588i	0.0568398	+	0.0568398i
$497$	−28.2540	+	4.74032i	−1.26737	+	0.212632i
$498$	−17.0759	+	0.268507i	−0.765190	+	0.0120321i
$499$	1.27846	−	4.77127i	0.0572317	−	0.213592i	−0.931388	−	0.364028i	$-0.881401\pi$
$499$	1.27846	−	4.77127i	0.0572317	−	0.213592i	0.988620	+	0.150436i	$0.0480679\pi$
$500$	−7.30379	−	27.2581i	−0.326635	−	1.21902i
$501$	2.54415	+	8.93078i	0.113664	+	0.398998i
$502$	−46.9054	−	12.5683i	−2.09349	−	0.560949i
$503$		−	42.1587i		−	1.87976i	−0.341500	−	0.939882i	$-0.610935\pi$
$503$		−	42.1587i		−	1.87976i	0.341500	−	0.939882i	$-0.389065\pi$
$504$	−15.5739	+	13.6944i	−0.693715	+	0.609998i
$505$	1.86132	−	1.86132i	0.0828275	−	0.0828275i
$506$	44.1078	+	76.3970i	1.96083	+	3.39626i
$507$	−11.8881	+	19.1226i	−0.527968	+	0.849264i
$508$	−12.9687	+	22.4624i	−0.575392	+	0.996607i
$509$	10.1298	+	2.71428i	0.448996	+	0.120308i	0.476230	−	0.879321i	$-0.342003\pi$
$509$	10.1298	+	2.71428i	0.448996	+	0.120308i	−0.0272334	+	0.999629i	$0.508670\pi$
$510$	−23.5502	+	0.370310i	−1.04282	+	0.0163976i
$511$	−5.02417	+	13.4550i	−0.222256	+	0.595215i
$512$	2.97408	−	2.97408i	0.131437	−	0.131437i
$513$	−5.28207	−	1.15143i	−0.233209	−	0.0508368i
$514$	−12.4574	−	46.4916i	−0.549471	−	2.05065i
$515$	9.06771	−	2.42969i	0.399571	−	0.107065i
$516$	−16.9543	+	10.1473i	−0.746371	+	0.446709i
$517$		−	23.7573i		−	1.04485i
$518$	8.27502	+	18.1376i	0.363583	+	0.796922i
$519$	−0.318346	−	20.2455i	−0.0139738	−	0.888678i
$520$	−8.98032	−	2.64042i	−0.393813	−	0.115790i
$521$	−9.14126	−	5.27771i	−0.400486	−	0.231221i	0.286208	−	0.958168i	$-0.407605\pi$
$521$	−9.14126	−	5.27771i	−0.400486	−	0.231221i	−0.686694	+	0.726947i	$0.740939\pi$
$522$	−56.3500	+	17.0149i	−2.46637	+	0.744722i
$523$	−3.18635	−	5.51892i	−0.139329	−	0.241325i	0.787914	−	0.615786i	$-0.211161\pi$
$523$	−3.18635	−	5.51892i	−0.139329	−	0.241325i	−0.927243	+	0.374460i	$0.877828\pi$
$524$	−43.7681			−1.91202
$525$	1.46676	−	18.3300i	0.0640146	−	0.799987i
$526$	−36.2013	−	36.2013i	−1.57845	−	1.57845i
$527$	7.50384	−	28.0047i	0.326873	−	1.21991i
$528$	0.849010	+	2.98030i	0.0369484	+	0.129701i
$529$	−21.2140	+	36.7438i	−0.922349	+	1.59756i
$530$	1.39947	+	2.42395i	0.0607890	+	0.105290i
$531$	5.95434	+	5.59116i	0.258397	+	0.242636i
$532$	−8.55462	+	1.43525i	−0.370890	+	0.0622261i
$533$	−0.132539	+	5.48365i	−0.00574091	+	0.237523i
$534$	−14.1996	+	8.49859i	−0.614478	+	0.367770i
$535$	−5.35256	+	1.43421i	−0.231411	+	0.0620065i
$536$	−13.2337	−	7.64046i	−0.571608	−	0.330018i
$537$	−10.5955	+	6.34148i	−0.457229	+	0.273655i
$538$	2.38947	+	2.38947i	0.103017	+	0.103017i
$539$	18.8326	+	27.8699i	0.811178	+	1.20044i
$540$	10.9491	−	12.0340i	0.471175	−	0.517862i
$541$	26.9379	+	7.21799i	1.15815	+	0.310326i	0.786227	−	0.617938i	$-0.212032\pi$
$541$	26.9379	+	7.21799i	1.15815	+	0.310326i	0.371924	+	0.928263i	$0.378698\pi$
$542$	54.5254	+	31.4803i	2.34207	+	1.35219i
$543$	11.1362	−	20.0086i	0.477902	−	0.858651i
$544$	−35.3584	−	9.47425i	−1.51598	−	0.406205i
$545$	3.20024			0.137083
$546$	−30.3540	−	22.0208i	−1.29903	−	0.942402i
$547$	−10.7569			−0.459932			−0.229966	−	0.973199i	$-0.573861\pi$
$547$	−10.7569			−0.459932			−0.229966	+	0.973199i	$0.573861\pi$
$548$	32.7107	+	8.76482i	1.39733	+	0.374414i
$549$	4.83368	−	9.01542i	0.206296	−	0.384769i
$550$	37.8995	+	21.8813i	1.61604	+	0.933021i
$551$	−8.68785	−	2.32790i	−0.370115	−	0.0991720i
$552$	25.4739	−	26.2879i	1.08424	−	1.11889i
$553$	−2.23355	+	23.2991i	−0.0949802	+	0.990777i
$554$	−19.5926	−	19.5926i	−0.832409	−	0.832409i
$555$	−2.93430	−	4.90269i	−0.124554	−	0.208108i
$556$	−61.9217	−	35.7505i	−2.62606	−	1.51616i
$557$	−22.7193	+	6.08763i	−0.962649	+	0.257941i	−0.705721	−	0.708490i	$-0.749377\pi$
$557$	−22.7193	+	6.08763i	−0.962649	+	0.257941i	−0.256928	+	0.966431i	$0.582710\pi$
$558$	17.2522	+	27.8231i	0.730345	+	1.17785i
$559$	−9.00391	−	9.44993i	−0.380825	−	0.399690i
$560$	−0.342404	+	0.916977i	−0.0144692	+	0.0387493i
$561$	34.9246	−	36.0405i	1.47452	−	1.52163i
$562$	−14.5892	−	25.2692i	−0.615407	−	1.06592i
$563$	−7.39506	+	12.8086i	−0.311665	+	0.539819i	−0.978723	−	0.205187i	$-0.934220\pi$
$563$	−7.39506	+	12.8086i	−0.311665	+	0.539819i	0.667058	+	0.745006i	$0.267553\pi$
$564$	−25.9526	+	7.39322i	−1.09280	+	0.311311i
$565$	−1.31534	+	4.90891i	−0.0553367	+	0.206519i
$566$	35.6791	+	35.6791i	1.49970	+	1.49970i
$567$	20.9996	−	11.2257i	0.881900	−	0.471436i
$568$	−28.2920			−1.18711
$569$	−9.27745	−	16.0690i	−0.388931	−	0.673648i	0.603375	−	0.797458i	$-0.293822\pi$
$569$	−9.27745	−	16.0690i	−0.388931	−	0.673648i	−0.992306	+	0.123809i	$0.960489\pi$
$570$	3.90836	−	1.11339i	0.163703	−	0.0466347i
$571$	−8.05438	−	4.65020i	−0.337065	−	0.194605i	0.321908	−	0.946771i	$-0.395676\pi$
$571$	−8.05438	−	4.65020i	−0.337065	−	0.194605i	−0.658974	+	0.752166i	$0.729009\pi$
$572$	47.9269	−	26.1474i	2.00393	−	1.09328i
$573$	−5.63268	+	0.0885700i	−0.235309	+	0.00370007i
$574$	−9.09373	−	0.871765i	−0.379565	−	0.0363868i
$575$			32.4580i			1.35359i
$576$	33.2304	−	20.6051i	1.38460	−	0.858547i
$577$	8.05655	−	2.15875i	0.335399	−	0.0898698i	−0.0871893	−	0.996192i	$-0.527788\pi$
$577$	8.05655	−	2.15875i	0.335399	−	0.0898698i	0.422588	+	0.906322i	$0.361122\pi$
$578$	11.3726	+	42.4432i	0.473039	+	1.76541i
$579$	−10.5884	+	42.1569i	−0.440040	+	1.75198i
$580$	19.1402	−	19.1402i	0.794753	−	0.794753i
$581$	11.3356	−	1.90183i	0.470280	−	0.0789012i
$582$	0.538832	+	34.2675i	0.0223353	+	1.42043i
$583$	−5.76066	−	1.54356i	−0.238582	−	0.0639279i
$584$	−7.09177	+	12.2833i	−0.293459	+	0.508287i
$585$	9.34660	+	5.30590i	0.386434	+	0.219372i
$586$	−23.6501	−	40.9632i	−0.976976	−	1.69217i
$587$	−4.74425	+	4.74425i	−0.195816	+	0.195816i	−0.798204	−	0.602387i	$-0.794216\pi$
$587$	−4.74425	+	4.74425i	−0.195816	+	0.195816i	0.602387	+	0.798204i	$0.294216\pi$
$588$	24.5845	−	29.2459i	1.01385	−	1.20608i
$589$			5.00239i			0.206120i
$590$	−5.93075	−	1.58914i	−0.244165	−	0.0654238i
$591$	−4.82200	+	1.37366i	−0.198350	+	0.0565048i
$592$	−0.319940	−	1.19403i	−0.0131494	−	0.0490744i
$593$	3.97846	−	14.8478i	0.163376	−	0.609726i	−0.834866	−	0.550453i	$-0.814455\pi$
$593$	3.97846	−	14.8478i	0.163376	−	0.609726i	0.998242	−	0.0592732i	$-0.0188783\pi$
$594$	2.67203	+	56.6060i	0.109635	+	2.32257i
$595$	15.6334	−	2.62290i	0.640908	−	0.107528i
$596$	−9.57073	−	9.57073i	−0.392032	−	0.392032i
$597$	−4.18432	−	6.99124i	−0.171253	−	0.286133i
$598$	56.5078	+	34.4716i	2.31078	+	1.40965i
$599$	−3.91492	−	2.26028i	−0.159959	−	0.0923525i	0.417884	−	0.908501i	$-0.362772\pi$
$599$	−3.91492	−	2.26028i	−0.159959	−	0.0923525i	−0.577843	+	0.816148i	$0.696105\pi$
$600$	4.42367	−	17.6125i	0.180596	−	0.719027i
$601$	−7.57081			−0.308820			−0.154410	−	0.988007i	$-0.549348\pi$
$601$	−7.57081			−0.308820			−0.154410	+	0.988007i	$0.549348\pi$
$602$	16.7682	−	13.8345i	0.683419	−	0.563851i
$603$	12.7905	+	12.0103i	0.520868	+	0.489099i
$604$	−7.25040	+	27.0588i	−0.295014	+	1.10101i
$605$	11.6033	−	3.10909i	0.471740	−	0.126402i
$606$	10.0158	−	2.85325i	0.406865	−	0.115905i
$607$	19.9004	+	34.4684i	0.807731	+	1.39903i	0.914432	+	0.404740i	$0.132638\pi$
$607$	19.9004	+	34.4684i	0.807731	+	1.39903i	−0.106701	+	0.994291i	$0.534029\pi$
$608$	6.31595			0.256146
$609$	35.7795	−	17.0085i	1.44986	−	0.689217i
$610$			7.68965i			0.311345i
$611$	−8.53749	−	15.6488i	−0.345390	−	0.633084i
$612$	−50.2392	−	26.9361i	−2.03080	−	1.08883i
$613$	17.6644	−	4.73317i	0.713460	−	0.191171i	0.116208	−	0.993225i	$-0.462926\pi$
$613$	17.6644	−	4.73317i	0.713460	−	0.191171i	0.597252	+	0.802054i	$0.296259\pi$
$614$	33.4038	−	19.2857i	1.34807	−	0.778308i
$615$	2.61789	−	0.0411646i	0.105564	−	0.00165992i
$616$	13.7877	+	30.2206i	0.555522	+	1.21762i
$617$	4.21321	−	4.21321i	0.169617	−	0.169617i	−0.617194	−	0.786811i	$-0.711731\pi$
$617$	4.21321	−	4.21321i	0.169617	−	0.169617i	0.786811	+	0.617194i	$0.211731\pi$
$618$	36.0218	+	9.04747i	1.44901	+	0.363943i
$619$	−4.46679	−	16.6703i	−0.179535	−	0.670035i	−0.995735	−	0.0922644i	$-0.970590\pi$
$619$	−4.46679	−	16.6703i	−0.179535	−	0.670035i	0.816199	−	0.577771i	$-0.196077\pi$
$620$	−13.0377	−	7.52732i	−0.523606	−	0.302304i
$621$	−35.3680	+	22.7081i	−1.41927	+	0.911246i
$622$	24.5795	−	24.5795i	0.985550	−	0.985550i
$623$	8.59113	−	7.08805i	0.344196	−	0.283977i
$624$	1.63025	+	1.65801i	0.0652621	+	0.0663734i
$625$	5.58277	+	9.66965i	0.223311	+	0.386786i
$626$	11.6960	+	43.6500i	0.467465	+	1.74460i
$627$	−4.21112	+	7.56616i	−0.168176	+	0.302163i
$628$	16.0057	−	9.24091i	0.638698	−	0.368752i
$629$	−14.1559	+	14.1559i	−0.564431	+	0.564431i
$630$	−9.92480	+	14.8962i	−0.395413	+	0.593477i
$631$	−16.3421	+	16.3421i	−0.650569	+	0.650569i	−0.953130	−	0.302561i	$-0.902158\pi$
$631$	−16.3421	+	16.3421i	−0.650569	+	0.650569i	0.302561	+	0.953130i	$0.402158\pi$
$632$	−5.98243	+	22.3267i	−0.237968	+	0.888109i
$633$	−28.7497	−	16.0013i	−1.14270	−	0.635994i
$634$	−8.50155	−	4.90837i	−0.337640	−	0.194936i
$635$	−2.11673	+	7.89974i	−0.0839998	+	0.313492i
$636$	0.106506	+	6.77332i	0.00422323	+	0.268580i
$637$	22.4203	+	11.5900i	0.888326	+	0.459213i
$638$			94.2820i			3.73266i
$639$	31.6267	+	7.41698i	1.25113	+	0.293411i
$640$	−8.66422	+	15.0069i	−0.342483	+	0.593198i
$641$	7.76733	−	13.4534i	0.306791	−	0.531378i	−0.670867	−	0.741577i	$-0.734078\pi$
$641$	7.76733	−	13.4534i	0.306791	−	0.531378i	0.977658	+	0.210200i	$0.0674114\pi$
$642$	−21.2632	−	5.34061i	−0.839192	−	0.210777i
$643$	6.92255	+	6.92255i	0.272999	+	0.272999i	0.830306	−	0.557307i	$-0.188166\pi$
$643$	6.92255	+	6.92255i	0.272999	+	0.272999i	−0.557307	+	0.830306i	$0.688166\pi$
$644$	−39.1386	+	54.9191i	−1.54228	+	2.16412i
$645$	−4.33566	+	4.47419i	−0.170717	+	0.176171i
$646$	−7.11936	−	12.3311i	−0.280108	−	0.485160i
$647$	−13.6167	+	23.5847i	−0.535326	+	0.927212i	0.463821	+	0.885929i	$0.346478\pi$
$647$	−13.6167	+	23.5847i	−0.535326	+	0.927212i	−0.999147	+	0.0412834i	$0.986855\pi$
$648$	22.2865	−	7.50172i	0.875495	−	0.294695i
$649$	11.3300	−	6.54141i	0.444743	−	0.256773i
$650$	32.8275	+	0.793437i	1.28760	+	0.0311211i
$651$	−14.2877	−	16.7731i	−0.559978	−	0.657391i
$652$	39.9282	+	39.9282i	1.56371	+	1.56371i
$653$	30.9656	−	17.8780i	1.21178	−	0.699621i	0.248632	−	0.968598i	$-0.420019\pi$
$653$	30.9656	−	17.8780i	1.21178	−	0.699621i	0.963146	+	0.268977i	$0.0866857\pi$
$654$	11.0632	+	6.15746i	0.432604	+	0.240776i
$655$	−13.3305	+	3.57188i	−0.520864	+	0.139565i
$656$	0.547145	+	0.146607i	0.0213624	+	0.00572405i
$657$	11.1478	−	11.8719i	0.434918	−	0.463168i
$658$	27.0104	−	12.3231i	1.05297	−	0.480403i
$659$		−	29.5283i		−	1.15026i	−0.818062	−	0.575130i	$-0.804951\pi$
$659$		−	29.5283i		−	1.15026i	0.818062	−	0.575130i	$-0.195049\pi$
$660$	−13.3830	−	22.3605i	−0.520931	−	0.870383i
$661$	−4.04655	−	15.1019i	−0.157393	−	0.587398i	−0.998889	−	0.0471340i	$-0.984991\pi$
$661$	−4.04655	−	15.1019i	−0.157393	−	0.587398i	0.841496	−	0.540264i	$-0.181675\pi$
$662$	−5.35514	+	9.27538i	−0.208134	+	0.360498i
$663$	10.0531	−	36.2903i	0.390429	−	1.40940i
$664$	11.3508			0.440498
$665$	−2.48835	+	1.13527i	−0.0964942	+	0.0440240i
$666$	−0.710735	−	22.5943i	−0.0275404	−	0.875511i
$667$	−60.5589	+	34.9637i	−2.34485	+	1.35380i
$668$	−4.37265	−	16.3190i	−0.169183	−	0.631399i
$669$	−5.07846	−	17.8271i	−0.196345	−	0.689234i
$670$	−12.7398	−	3.41362i	−0.492181	−	0.131879i
$671$	−11.5858	−	11.5858i	−0.447266	−	0.447266i
$672$	−21.1775	+	18.0394i	−0.816941	+	0.695886i
$673$			21.7075i			0.836764i	0.908271	+	0.418382i	$0.137403\pi$
$673$			21.7075i			0.836764i	−0.908271	+	0.418382i	$0.862597\pi$
$674$	11.7511	−	43.8556i	0.452634	−	1.68925i
$675$	−9.56233	+	18.5287i	−0.368054	+	0.713171i
$676$	22.1728	−	34.4463i	0.852802	−	1.32486i
$677$	10.6143	−	6.12816i	0.407940	−	0.235524i	−0.281964	−	0.959425i	$-0.590986\pi$
$677$	10.6143	−	6.12816i	0.407940	−	0.235524i	0.689904	+	0.723901i	$0.257653\pi$
$678$	−13.9922	+	14.4392i	−0.537365	+	0.554535i
$679$	−3.81654	−	22.7479i	−0.146465	−	0.872985i
$680$	15.6545			0.600322
$681$	−0.600083	+	2.38918i	−0.0229952	+	0.0915537i
$682$	50.6503	−	13.5717i	1.93950	−	0.519687i
$683$	−28.5278	+	7.64399i	−1.09158	+	0.292489i	−0.759333	−	0.650702i	$-0.774475\pi$
$683$	−28.5278	+	7.64399i	−1.09158	+	0.292489i	−0.332251	+	0.943191i	$0.607808\pi$
$684$	9.57580	+	2.24568i	0.366140	+	0.0858657i
$685$	10.6780			0.407986
$686$	−21.9175	+	35.8676i	−0.836813	+	1.36943i
$687$	−25.3234	−	24.5394i	−0.966149	−	0.936235i
$688$	−1.16732	+	0.673955i	−0.0445038	+	0.0256943i
$689$	−4.34922	+	1.05343i	−0.165692	+	0.0401324i
$690$	15.3653	−	27.6070i	0.584947	−	1.05098i
$691$	2.56670	−	9.57906i	0.0976419	−	0.364404i	−0.899765	−	0.436375i	$-0.856262\pi$
$691$	2.56670	−	9.57906i	0.0976419	−	0.364404i	0.997407	+	0.0719706i	$0.0229288\pi$
$692$			36.8381i			1.40037i
$693$	−7.49023	−	37.3972i	−0.284530	−	1.42060i
$694$	38.5984	+	38.5984i	1.46517	+	1.46517i
$695$	−21.7771	−	5.83515i	−0.826051	−	0.221340i
$696$	37.6260	−	10.7186i	1.42621	−	0.406289i
$697$	−2.37429	−	8.86099i	−0.0899328	−	0.335634i
$698$	−20.0820	+	11.5944i	−0.760115	+	0.438853i
$699$	−0.0252900	−	1.60834i	−0.000956554	−	0.0608328i
$700$	−3.19253	+	33.3026i	−0.120666	+	1.25872i
$701$	−5.11295			−0.193113			−0.0965567	−	0.995327i	$-0.530783\pi$
$701$	−5.11295			−0.193113			−0.0965567	+	0.995327i	$0.530783\pi$
$702$	22.1021	+	36.3259i	0.834191	+	1.37103i
$703$	1.72708	−	2.99138i	0.0651379	−	0.112822i
$704$	−16.2093	−	60.4940i	−0.610912	−	2.27995i
$705$	−7.30104	+	4.36973i	−0.274973	+	0.164574i
$706$			42.5274i			1.60054i
$707$	−6.37682	+	2.90933i	−0.239825	+	0.109416i
$708$	−10.6717	−	10.3413i	−0.401069	−	0.388651i
$709$	−20.7911	−	5.57096i	−0.780826	−	0.209222i	−0.153677	−	0.988121i	$-0.549112\pi$
$709$	−20.7911	−	5.57096i	−0.780826	−	0.209222i	−0.627149	+	0.778899i	$0.715778\pi$
$710$	−23.5872	+	6.32018i	−0.885212	+	0.237192i
$711$	12.5407	−	23.3900i	0.470312	−	0.877192i
$712$	9.52537	−	5.49947i	0.356978	−	0.206102i
$713$	27.5005	+	27.5005i	1.02990	+	1.02990i
$714$	59.0911	+	21.0124i	2.21143	+	0.786368i
$715$	12.4632	−	11.8750i	0.466099	−	0.444100i
$716$	19.4559	−	11.2329i	0.727100	−	0.419791i
$717$	27.4908	−	7.83140i	1.02666	−	0.292469i
$718$	−17.1115	+	29.6380i	−0.638595	+	1.10608i
$719$	−0.465006	−	0.805414i	−0.0173418	−	0.0300369i	0.857224	−	0.514943i	$-0.172187\pi$
$719$	−0.465006	−	0.805414i	−0.0173418	−	0.0300369i	−0.874566	+	0.484906i	$0.838854\pi$
$720$	0.759739	−	0.809088i	0.0283138	−	0.0301529i
$721$	−24.8827	−	2.38536i	−0.926679	−	0.0888355i
$722$	−28.7553	−	28.7553i	−1.07016	−	1.07016i
$723$	0.765147	−	3.04637i	0.0284561	−	0.113296i
$724$	−20.8305	+	36.0795i	−0.774160	+	1.34088i
$725$	−17.3450	+	30.0424i	−0.644177	+	1.11575i
$726$	46.0944	+	11.5774i	1.71072	+	0.429676i
$727$		−	43.5352i		−	1.61463i	−0.590119	−	0.807316i	$-0.700919\pi$
$727$		−	43.5352i		−	1.61463i	0.590119	−	0.807316i	$-0.299081\pi$
$728$	19.9420	+	14.9514i	0.739101	+	0.554136i
$729$	−26.8799	+	2.54335i	−0.995553	+	0.0941982i
$730$	−3.16847	+	11.8249i	−0.117270	+	0.437659i
$731$	18.9047	+	10.9147i	0.699217	+	0.403693i
$732$	−9.05093	+	16.2619i	−0.334532	+	0.601057i
$733$	−1.72840	+	6.45047i	−0.0638399	+	0.238254i	−0.990472	−	0.137716i	$-0.956024\pi$
$733$	−1.72840	+	6.45047i	−0.0638399	+	0.238254i	0.926632	+	0.375970i	$0.122690\pi$
$734$	55.6112	−	55.6112i	2.05265	−	2.05265i
$735$	5.10098	−	10.9137i	0.188152	−	0.402560i
$736$	34.7218	−	34.7218i	1.27986	−	1.27986i
$737$	24.3380	−	14.0515i	0.896501	−	0.517595i
$738$	9.12921	+	4.89468i	0.336051	+	0.180176i
$739$	9.70997	+	36.2381i	0.357187	+	1.33304i	0.877710	+	0.479193i	$0.159070\pi$
$739$	9.70997	+	36.2381i	0.357187	+	1.33304i	−0.520523	+	0.853848i	$0.674263\pi$
$740$	5.19761	+	9.00253i	0.191068	+	0.330940i
$741$	−0.0548508	+	6.49711i	−0.00201499	+	0.238677i
$742$	−1.23317	−	7.35011i	−0.0452710	−	0.269831i
$743$	−7.89935	+	7.89935i	−0.289799	+	0.289799i	−0.837001	−	0.547202i	$-0.815693\pi$
$743$	−7.89935	+	7.89935i	−0.289799	+	0.289799i	0.547202	+	0.837001i	$0.315693\pi$
$744$	−11.1745	−	18.6705i	−0.409676	−	0.684495i
$745$	−3.69602	−	2.13390i	−0.135412	−	0.0781800i
$746$	−6.89297	−	25.7249i	−0.252369	−	0.941855i
$747$	−12.6887	−	2.97571i	−0.464257	−	0.108876i
$748$	−64.5630	+	64.5630i	−2.36066	+	2.36066i
$749$	14.6879	+	1.40805i	0.536685	+	0.0514490i
$750$	−0.553488	−	35.1995i	−0.0202105	−	1.28531i
$751$	5.11674	−	2.95415i	0.186712	−	0.107798i	−0.403730	−	0.914878i	$-0.632287\pi$
$751$	5.11674	−	2.95415i	0.186712	−	0.107798i	0.590443	+	0.807080i	$0.298953\pi$
$752$	−1.77814	+	0.476451i	−0.0648420	+	0.0173744i
$753$	−32.3807	−	18.0223i	−1.18002	−	0.656767i
$754$	33.8814	+	62.1031i	1.23389	+	2.26166i
$755$			8.83302i			0.321466i
$756$	−38.5219	+	19.8203i	−1.40103	+	0.720857i
$757$	49.8366			1.81134			0.905671	−	0.423981i	$-0.139368\pi$
$757$	49.8366			1.81134			0.905671	+	0.423981i	$0.139368\pi$
$758$	−27.7178	−	48.0086i	−1.00675	−	1.74375i
$759$	18.4443	+	64.7453i	0.669484	+	2.35011i
$760$	−2.60899	+	0.699077i	−0.0946380	+	0.0253582i
$761$	2.05353	−	7.66389i	0.0744405	−	0.277816i	−0.918665	−	0.395037i	$-0.870732\pi$
$761$	2.05353	−	7.66389i	0.0744405	−	0.277816i	0.993106	+	0.117221i	$0.0373986\pi$
$762$	−22.5171	+	23.2365i	−0.815708	+	0.841771i
$763$	−7.98302	−	2.98090i	−0.289005	−	0.107916i
$764$	10.2491			0.370798
$765$	−17.4996	−	4.10394i	−0.632700	−	0.148378i
$766$	−66.0611	−	38.1404i	−2.38688	−	1.37807i
$767$	5.11231	−	8.38039i	0.184595	−	0.302598i
$768$	−20.0856	+	12.0214i	−0.724777	+	0.433785i
$769$	−28.3896	−	28.3896i	−1.02375	−	1.02375i	−0.999711	−	0.0240438i	$-0.992346\pi$
$769$	−28.3896	−	28.3896i	−1.02375	−	1.02375i	−0.0240438	−	0.999711i	$-0.507654\pi$
$770$	18.2459	+	22.1150i	0.657536	+	0.796971i
$771$	−0.577503	−	36.7268i	−0.0207983	−	1.32268i
$772$	20.4675	−	76.3857i	0.736641	−	2.74918i
$773$	−10.3303	−	38.5532i	−0.371555	−	1.38666i	−0.858314	−	0.513125i	$-0.828488\pi$
$773$	−10.3303	−	38.5532i	−0.371555	−	1.38666i	0.486759	−	0.873536i	$-0.338179\pi$
$774$	−23.5969	+	7.12511i	−0.848174	+	0.256107i
$775$	18.6362	+	4.99355i	0.669432	+	0.179374i
$776$		−	22.7786i		−	0.817702i
$777$	2.75297	+	14.9630i	0.0987621	+	0.536795i
$778$	−1.61099	+	1.61099i	−0.0577569	+	0.0577569i
$779$	0.791405	+	1.37075i	0.0283550	+	0.0491123i
$780$	−16.8508	−	9.91944i	−0.603356	−	0.355173i
$781$	26.0159	−	45.0608i	0.930921	−	1.61240i
$782$	−106.928	−	28.6514i	−3.82375	−	1.02457i
$783$	−44.8708	+	2.11808i	−1.60355	+	0.0756941i
$784$	1.70826	−	1.96847i	0.0610093	−	0.0703025i
$785$	4.12072	−	4.12072i	0.147075	−	0.147075i
$786$	−52.9556	−	13.3007i	−1.88887	−	0.474420i
$787$	7.98595	+	29.8040i	0.284668	+	1.06240i	0.949081	+	0.315031i	$0.102015\pi$
$787$	7.98595	+	29.8040i	0.284668	+	1.06240i	−0.664413	+	0.747366i	$0.731318\pi$
$788$	8.81109	−	2.36092i	0.313882	−	0.0841045i
$789$	−20.0646	−	33.5244i	−0.714320	−	1.19350i
$790$			19.9503i			0.709801i
$791$	7.85359	−	11.0201i	0.279242	−	0.391831i
$792$	−1.18421	−	37.6462i	−0.0420792	−	1.33770i
$793$	−11.7950	−	3.46801i	−0.418854	−	0.123153i
$794$	−8.03706	−	4.64020i	−0.285225	−	0.164674i
$795$	0.585205	+	2.05426i	0.0207551	+	0.0728571i
$796$	7.41180	+	12.8376i	0.262704	+	0.455017i
$797$	37.3935			1.32454			0.662272	−	0.749263i	$-0.269592\pi$
$797$	37.3935			1.32454			0.662272	+	0.749263i	$0.269592\pi$
$798$	−10.7865	−	0.863132i	−0.381839	−	0.0305545i
$799$	21.0808	+	21.0808i	0.745784	+	0.745784i
$800$	6.30479	−	23.5298i	0.222908	−	0.831904i
$801$	−12.0898	+	3.65053i	−0.427173	+	0.128985i
$802$	−3.06103	+	5.30185i	−0.108089	+	0.187215i
$803$	−13.0424	−	22.5902i	−0.460257	−	0.797189i
$804$	−22.9239	−	22.2141i	−0.808463	−	0.783432i
$805$	−7.43853	+	19.9208i	−0.262174	+	0.702116i
$806$	28.4859	−	27.1414i	1.00337	−	0.956016i
$807$	1.32437	+	2.21279i	0.0466200	+	0.0778937i
$808$	−6.68597	+	1.79150i	−0.235212	+	0.0630248i
$809$	21.9528	+	12.6745i	0.771821	+	0.445611i	0.833524	−	0.552483i	$-0.186320\pi$
$809$	21.9528	+	12.6745i	0.771821	+	0.445611i	−0.0617028	+	0.998095i	$0.519653\pi$
$810$	16.9045	−	11.2328i	0.593965	−	0.394681i
$811$	−9.32142	−	9.32142i	−0.327319	−	0.327319i	0.524247	−	0.851566i	$-0.324347\pi$
$811$	−9.32142	−	9.32142i	−0.327319	−	0.327319i	−0.851566	+	0.524247i	$0.824347\pi$
$812$	−65.5737	+	29.9170i	−2.30119	+	1.04988i
$813$	34.5050	+	33.4366i	1.21014	+	1.17267i
$814$	−34.9740	−	9.37126i	−1.22584	−	0.328463i
$815$	15.4194	+	8.90242i	0.540119	+	0.311838i
$816$	−3.39789	−	1.89118i	−0.118950	−	0.0662044i
$817$	−3.63810	−	0.974825i	−0.127281	−	0.0341048i
$818$	−64.6432			−2.26020
$819$	−18.3729	−	21.9416i	−0.642002	−	0.766703i
$820$	−4.76344			−0.166347
$821$	−32.5179	−	8.71315i	−1.13488	−	0.304091i	−0.357992	−	0.933725i	$-0.616538\pi$
$821$	−32.5179	−	8.71315i	−1.13488	−	0.304091i	−0.776892	+	0.629634i	$0.783205\pi$
$822$	36.9137	+	20.5452i	1.28751	+	0.716595i
$823$	−21.9119	−	12.6508i	−0.763801	−	0.440981i	0.0668577	−	0.997763i	$-0.478703\pi$
$823$	−21.9119	−	12.6508i	−0.763801	−	0.440981i	−0.830659	+	0.556782i	$0.812036\pi$
$824$	−23.8442	−	6.38904i	−0.830653	−	0.222573i
$825$	23.9837	+	23.2411i	0.835006	+	0.809152i
$826$	13.3141	+	9.48839i	0.463256	+	0.330143i
$827$	16.9964	+	16.9964i	0.591022	+	0.591022i	0.937907	−	0.346886i	$-0.112761\pi$
$827$	16.9964	+	16.9964i	0.591022	+	0.591022i	−0.346886	+	0.937907i	$0.612761\pi$
$828$	64.9883	−	40.2972i	2.25850	−	1.40042i
$829$	14.9313	+	8.62060i	0.518586	+	0.299406i	0.736356	−	0.676594i	$-0.236545\pi$
$829$	14.9313	+	8.62060i	0.518586	+	0.299406i	−0.217770	+	0.976000i	$0.569878\pi$
$830$	9.46326	−	2.53567i	0.328475	−	0.0880145i
$831$	−10.8592	−	18.1439i	−0.376703	−	0.629403i
$832$	−32.4163	−	34.0221i	−1.12383	−	1.17950i
$833$	−41.4409	−	8.01910i	−1.43584	−	0.277845i
$834$	−64.0557	−	62.0724i	−2.21807	−	2.14939i
$835$	−2.66356	−	4.61342i	−0.0921763	−	0.159654i
$836$	7.87697	−	13.6433i	0.272431	−	0.471864i
$837$	7.59694	+	23.8006i	0.262588	+	0.822670i
$838$	−11.8568	+	44.2501i	−0.409586	+	1.52860i
$839$	−6.75391	−	6.75391i	−0.233171	−	0.233171i	0.580844	−	0.814015i	$-0.302723\pi$
$839$	−6.75391	−	6.75391i	−0.233171	−	0.233171i	−0.814015	+	0.580844i	$0.802723\pi$
$840$	6.75133	−	9.79574i	0.232943	−	0.337985i
$841$	−45.7361			−1.57711
$842$	26.5147	+	45.9247i	0.913755	+	1.58267i
$843$	−6.10065	−	21.4153i	−0.210117	−	0.737581i
$844$	51.8414	+	29.9307i	1.78446	+	1.03026i
$845$	3.94205	−	12.3008i	0.135611	−	0.423161i
$846$	−33.6472	+	1.05842i	−1.15681	+	0.0363892i
$847$	−31.8405	−	3.05237i	−1.09405	−	0.104881i
$848$			0.462118i			0.0158692i
$849$	19.7752	+	33.0409i	0.678684	+	1.13396i
$850$	−53.0457	+	14.2136i	−1.81945	+	0.487521i
$851$	−6.95050	−	25.9396i	−0.238260	−	0.889199i
$852$	−57.3207	−	14.3971i	−1.96378	−	0.493235i
$853$	−6.27369	+	6.27369i	−0.214807	+	0.214807i	−0.806306	−	0.591499i	$-0.798536\pi$
$853$	−6.27369	+	6.27369i	−0.214807	+	0.214807i	0.591499	+	0.806306i	$0.298536\pi$
$854$	7.16262	−	19.1819i	0.245100	−	0.656391i
$855$	3.09977	−	0.0975077i	0.106010	−	0.00333469i
$856$	14.0750	+	3.77137i	0.481072	+	0.128903i
$857$	26.1786	−	45.3427i	0.894245	−	1.54888i	0.0595090	−	0.998228i	$-0.481046\pi$
$857$	26.1786	−	45.3427i	0.894245	−	1.54888i	0.834736	−	0.550650i	$-0.185620\pi$
$858$	65.9334	−	17.0716i	2.25093	−	0.582813i
$859$	17.1641	+	29.7290i	0.585630	+	1.01434i	0.994797	+	0.101881i	$0.0324861\pi$
$859$	17.1641	+	29.7290i	0.585630	+	1.01434i	−0.409167	+	0.912460i	$0.634181\pi$
$860$	8.01508	−	8.01508i	0.273312	−	0.273312i
$861$	−6.56870	−	2.33578i	−0.223861	−	0.0796033i
$862$		−	33.8583i		−	1.15322i
$863$	−32.5628	−	8.72519i	−1.10845	−	0.297009i	−0.342250	−	0.939609i	$-0.611189\pi$
$863$	−32.5628	−	8.72519i	−1.10845	−	0.297009i	−0.766202	+	0.642600i	$0.777856\pi$
$864$	30.0503	−	9.59178i	1.02233	−	0.326319i
$865$	3.00633	+	11.2198i	0.102218	+	0.381484i
$866$	−13.2916	+	49.6049i	−0.451667	+	1.68564i
$867$	0.527216	+	33.5288i	0.0179052	+	1.13870i
$868$	25.5112	+	30.9211i	0.865908	+	1.04953i
$869$	−30.0587	−	30.0587i	−1.01967	−	1.01967i
$870$	28.9745	−	17.3415i	0.982328	−	0.587931i
$871$	10.9817	−	18.0018i	0.372101	−	0.609969i
$872$	−7.28783	−	4.20763i	−0.246797	−	0.142488i
$873$	−5.97158	+	25.4634i	−0.202107	+	0.861805i
$874$	19.1003			0.646077
$875$	3.92035	+	23.3667i	0.132532	+	0.789938i
$876$	−20.6188	+	21.2776i	−0.696645	+	0.718904i
$877$	−10.7508	+	40.1224i	−0.363028	+	1.35484i	0.507047	+	0.861919i	$0.330737\pi$
$877$	−10.7508	+	40.1224i	−0.363028	+	1.35484i	−0.870075	+	0.492920i	$0.835929\pi$
$878$	−38.4745	+	10.3092i	−1.29845	+	0.347919i
$879$	−9.88958	−	34.7157i	−0.333567	−	1.17093i
$880$	−0.888859	−	1.53955i	−0.0299634	−	0.0518982i
$881$	−24.8500			−0.837219			−0.418610	−	0.908166i	$-0.637482\pi$
$881$	−24.8500			−0.837219			−0.418610	+	0.908166i	$0.637482\pi$
$882$	38.6327	−	27.9140i	1.30083	−	0.939914i
$883$		−	20.5434i		−	0.691339i	−0.938356	−	0.345669i	$-0.887652\pi$
$883$		−	20.5434i		−	0.691339i	0.938356	−	0.345669i	$-0.112348\pi$
$884$	−19.3258	+	65.7289i	−0.649998	+	2.21070i
$885$	−4.09424	−	2.27875i	−0.137627	−	0.0765992i
$886$	46.9886	−	12.5906i	1.57861	−	0.422988i
$887$	28.3691	−	16.3789i	0.952543	−	0.549951i	0.0586728	−	0.998277i	$-0.481313\pi$
$887$	28.3691	−	16.3789i	0.952543	−	0.549951i	0.893870	+	0.448327i	$0.147980\pi$
$888$	0.236223	+	15.0228i	0.00792712	+	0.504132i
$889$	12.6385	−	17.7343i	0.423882	−	0.594790i
$890$	6.71282	−	6.71282i	0.225014	−	0.225014i
$891$	−8.54546	+	42.3939i	−0.286284	+	1.42025i
$892$	8.72841	+	32.5749i	0.292249	+	1.09069i
$893$	−4.45474	−	2.57194i	−0.149072	−	0.0860668i
$894$	−8.67132	−	14.4882i	−0.290012	−	0.484559i
$895$	5.00897	−	5.00897i	0.167431	−	0.167431i
$896$	35.5913	−	29.3644i	1.18902	−	0.980995i
$897$	35.4162	+	36.0193i	1.18251	+	1.20265i
$898$	−7.40164	−	12.8200i	−0.246996	−	0.427809i
$899$	10.7581	+	40.1498i	0.358803	+	1.33907i
$900$	17.9251	−	33.4325i	0.597502	−	1.11442i
$901$	6.48131	−	3.74199i	0.215924	−	0.124664i
$902$	11.7320	−	11.7320i	0.390635	−	0.390635i
$903$	14.9829	−	7.12240i	0.498599	−	0.237019i
$904$	9.44957	−	9.44957i	0.314288	−	0.314288i
$905$	−3.39993	+	12.6887i	−0.113017	+	0.421787i
$906$	−16.9953	+	30.5356i	−0.564630	+	1.01448i
$907$	−35.3946	−	20.4351i	−1.17526	−	0.678536i	−0.220346	−	0.975422i	$-0.570719\pi$
$907$	−35.3946	−	20.4351i	−1.17526	−	0.678536i	−0.954913	+	0.296886i	$0.904052\pi$
$908$	1.15997	−	4.32905i	0.0384948	−	0.143665i
$909$	7.94369	−	0.249880i	0.263475	−	0.00828799i
$910$	19.9658	+	8.01019i	0.661859	+	0.265535i
$911$		−	30.0686i		−	0.996218i	−0.867115	−	0.498109i	$-0.834028\pi$
$911$		−	30.0686i		−	0.996218i	0.867115	−	0.498109i	$-0.165972\pi$
$912$	0.650750	+	0.163447i	0.0215485	+	0.00541226i
$913$	−10.4376	+	18.0785i	−0.345436	+	0.598312i
$914$	18.7222	−	32.4278i	0.619276	−	1.07262i
$915$	−1.42952	+	5.69153i	−0.0472585	+	0.188156i
$916$	45.3645	+	45.3645i	1.49888	+	1.49888i
$917$	36.5800	+	3.50672i	1.20798	+	0.115802i
$918$	−52.5996	−	47.8576i	−1.73605	−	1.57954i
$919$	−25.1688	−	43.5937i	−0.830244	−	1.43802i	−0.897845	−	0.440312i	$-0.854868\pi$
$919$	−25.1688	−	43.5937i	−0.830244	−	1.43802i	0.0676011	−	0.997712i	$-0.478465\pi$
$920$	−10.4997	+	18.1860i	−0.346165	+	0.599575i
$921$	28.3093	−	8.06457i	0.932822	−	0.265737i
$922$	45.9787	−	26.5458i	1.51423	−	0.874239i
$923$	0.943361	−	39.0305i	0.0310511	−	1.28470i
$924$	12.5559	+	68.2443i	0.413059	+	2.24507i
$925$	−9.42024	−	9.42024i	−0.309736	−	0.309736i
$926$	59.1691	−	34.1613i	1.94442	−	1.12261i
$927$	24.9797	+	13.3931i	0.820442	+	0.439886i
$928$	50.6926	−	13.5830i	1.66406	−	0.445885i
$929$	39.3606	+	10.5466i	1.29138	+	0.346024i	0.838184	−	0.545388i	$-0.183618\pi$
$929$	39.3606	+	10.5466i	1.29138	+	0.346024i	0.453195	+	0.891412i	$0.350284\pi$
$930$	−13.4870	−	13.0694i	−0.442257	−	0.428564i
$931$	7.26468	−	0.514140i	0.238090	−	0.0168502i
$932$			2.92648i			0.0958601i
$933$	22.7621	−	13.6233i	0.745196	−	0.446006i
$934$	−14.4421	−	53.8987i	−0.472560	−	1.76362i
$935$	−14.3950	+	24.9329i	−0.470768	+	0.815394i
$936$	−14.3087	−	24.3718i	−0.467694	−	0.796618i
$937$	−39.5445			−1.29186			−0.645932	−	0.763395i	$-0.723531\pi$
$937$	−39.5445			−1.29186			−0.645932	+	0.763395i	$0.723531\pi$
$938$	28.5999	+	20.3819i	0.933819	+	0.665494i
$939$	0.542206	+	34.4820i	0.0176942	+	1.12528i
$940$	13.4065	−	7.74023i	0.437271	−	0.252458i
$941$	−12.3233	−	45.9911i	−0.401727	−	1.49927i	−0.810012	−	0.586413i	$-0.800540\pi$
$941$	−12.3233	−	45.9911i	−0.401727	−	1.49927i	0.408285	−	0.912855i	$-0.366127\pi$
$942$	22.1738	−	6.31673i	0.722461	−	0.205810i
$943$	11.8864	+	3.18496i	0.387075	+	0.103716i
$944$	−0.716820	−	0.716820i	−0.0233305	−	0.0233305i
$945$	−10.1151	+	9.18042i	−0.329045	+	0.298639i
$946$			39.4812i			1.28365i
$947$	−11.5273	+	43.0207i	−0.374589	+	1.39798i	0.479357	+	0.877620i	$0.340870\pi$
$947$	−11.5273	+	43.0207i	−0.374589	+	1.39798i	−0.853945	+	0.520363i	$0.825797\pi$
$948$	−23.4821	+	42.1905i	−0.762663	+	1.37028i
$949$	−16.7090	−	10.1931i	−0.542398	−	0.330881i
$950$	8.20592	−	4.73769i	0.266235	−	0.153711i
$951$	−5.37998	−	5.21341i	−0.174458	−	0.169056i
$952$	−39.0502	−	14.5816i	−1.26563	−	0.472591i
$953$	2.53748			0.0821970			0.0410985	−	0.999155i	$-0.486914\pi$
$953$	2.53748			0.0821970			0.0410985	+	0.999155i	$0.486914\pi$
$954$	−1.92948	+	8.22751i	−0.0624694	+	0.266376i
$955$	3.12156	−	0.836420i	0.101011	−	0.0270659i
$956$	−50.2331	+	13.4599i	−1.62465	+	0.435324i
$957$	−17.5272	+	69.7833i	−0.566575	+	2.25577i
$958$	−40.4539			−1.30701
$959$	−26.6364	−	9.94617i	−0.860134	−	0.321179i
$960$	−15.6094	+	16.1082i	−0.503793	+	0.519889i
$961$	−6.82609	+	3.94104i	−0.220196	+	0.127130i
$962$	−26.4049	+	6.39555i	−0.851328	+	0.206201i
$963$	−14.7452	−	7.90575i	−0.475158	−	0.254759i
$964$	−1.47904	+	5.51984i	−0.0476365	+	0.177782i
$965$		−	24.9352i		−	0.802691i
$966$	−64.0437	+	54.5536i	−2.06057	+	1.75523i
$967$	23.5554	+	23.5554i	0.757491	+	0.757491i	0.975865	−	0.218374i	$-0.0700752\pi$
$967$	23.5554	+	23.5554i	0.757491	+	0.757491i	−0.218374	+	0.975865i	$0.570075\pi$
$968$	−30.5117	−	8.17558i	−0.980682	−	0.262773i
$969$	−2.97705	−	10.4504i	−0.0956367	−	0.335716i
$970$	−5.08851	−	18.9906i	−0.163382	−	0.609751i
$971$	−46.1540	+	26.6470i	−1.48115	+	0.855144i	−0.999772	−	0.0213673i	$-0.993198\pi$
$971$	−46.1540	+	26.6470i	−1.48115	+	0.855144i	−0.481381	+	0.876511i	$0.659865\pi$
$972$	48.9706	−	3.85778i	1.57073	−	0.123738i
$973$	48.8879	+	34.8404i	1.56727	+	1.11693i
$974$	48.0992			1.54120
$975$	24.1499	+	6.68997i	0.773417	+	0.214251i
$976$	−0.634799	+	1.09950i	−0.0203194	+	0.0351943i
$977$	−11.6729	−	43.5640i	−0.373451	−	1.39374i	−0.855595	−	0.517645i	$-0.826809\pi$
$977$	−11.6729	−	43.5640i	−0.373451	−	1.39374i	0.482145	−	0.876091i	$-0.339858\pi$
$978$	36.1759	+	60.4435i	1.15678	+	1.93277i
$979$			20.2281i			0.646493i
$980$	−9.59148	+	19.7075i	−0.306389	+	0.629534i
$981$	7.04377	+	6.61414i	0.224890	+	0.211173i
$982$	−30.2281	−	8.09959i	−0.964617	−	0.258468i
$983$	37.0028	−	9.91487i	1.18021	−	0.316235i	0.385198	−	0.922834i	$-0.374133\pi$
$983$	37.0028	−	9.91487i	1.18021	−	0.316235i	0.795008	+	0.606599i	$0.207467\pi$
$984$	−6.01579	−	3.34823i	−0.191777	−	0.106738i
$985$	2.49092	−	1.43813i	0.0793674	−	0.0458228i
$986$	−83.6600	−	83.6600i	−2.66428	−	2.66428i
$987$	22.2827	−	4.09969i	0.709268	−	0.130495i
$988$	0.285626	−	11.8175i	0.00908699	−	0.375964i
$989$	−25.3594	+	14.6413i	−0.806383	+	0.465566i
$990$	−9.39710	−	31.1213i	−0.298659	−	0.989100i
$991$	3.00477	−	5.20441i	0.0954496	−	0.165324i	−0.814347	−	0.580379i	$-0.802904\pi$
$991$	3.00477	−	5.20441i	0.0954496	−	0.165324i	0.909796	+	0.415055i	$0.136238\pi$
$992$	−14.5942	−	25.2779i	−0.463366	−	0.802573i
$993$	−5.68795	+	5.86968i	−0.180502	+	0.186269i
$994$	64.7255	+	6.20488i	2.05297	+	0.196807i
$995$	3.30508	+	3.30508i	0.104778	+	0.104778i
$996$	22.9972	+	5.77614i	0.728696	+	0.183024i
$997$	26.4390	−	45.7936i	0.837331	−	1.45030i	−0.0547879	−	0.998498i	$-0.517448\pi$
$997$	26.4390	−	45.7936i	0.837331	−	1.45030i	0.892119	−	0.451801i	$-0.149218\pi$
$998$	−5.60551	+	9.70902i	−0.177439	+	0.307334i
$999$	3.67427	−	16.8554i	0.116249	−	0.533281i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cd.e.242.4	yes	112
3.2	odd	2	inner	273.2.cd.e.242.25	yes	112
7.2	even	3	inner	273.2.cd.e.86.25	yes	112
13.5	odd	4	inner	273.2.cd.e.200.4	yes	112
21.2	odd	6	inner	273.2.cd.e.86.4	yes	112
39.5	even	4	inner	273.2.cd.e.200.25	yes	112
91.44	odd	12	inner	273.2.cd.e.44.25	yes	112
273.44	even	12	inner	273.2.cd.e.44.4	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.cd.e.44.4	✓	112	273.44	even	12	inner
273.2.cd.e.44.25	yes	112	91.44	odd	12	inner
273.2.cd.e.86.4	yes	112	21.2	odd	6	inner
273.2.cd.e.86.25	yes	112	7.2	even	3	inner
273.2.cd.e.200.4	yes	112	13.5	odd	4	inner
273.2.cd.e.200.25	yes	112	39.5	even	4	inner
273.2.cd.e.242.4	yes	112	1.1	even	1	trivial
273.2.cd.e.242.25	yes	112	3.2	odd	2	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.19229 - 0.587422i) q^{2} +(-1.51343 - 0.842335i) q^{3} +(2.72902 + 1.57560i) q^{4} +(0.959762 + 0.257167i) q^{5} +(2.82307 + 2.73567i) q^{6} +(-2.15459 - 1.53549i) q^{7} +(-1.84753 - 1.84753i) q^{8} +(1.58094 + 2.54963i) q^{9} +O(q^{10})\)	\(q+(-2.19229 - 0.587422i) q^{2} +(-1.51343 - 0.842335i) q^{3} +(2.72902 + 1.57560i) q^{4} +(0.959762 + 0.257167i) q^{5} +(2.82307 + 2.73567i) q^{6} +(-2.15459 - 1.53549i) q^{7} +(-1.84753 - 1.84753i) q^{8} +(1.58094 + 2.54963i) q^{9} +(-1.95301 - 1.12757i) q^{10} +(4.64145 - 1.24367i) q^{11} +(-2.80300 - 4.68331i) q^{12} +(2.61037 - 2.48716i) q^{13} +(3.82151 + 4.63189i) q^{14} +(-1.23591 - 1.19765i) q^{15} +(-0.186167 - 0.322451i) q^{16} +(-3.01497 + 5.22208i) q^{17} +(-1.96818 - 6.51821i) q^{18} +(0.269277 - 1.00496i) q^{19} +(2.21402 + 2.21402i) q^{20} +(1.96743 + 4.13875i) q^{21} -10.9060 q^{22} +(-4.04438 - 7.00507i) q^{23} +(1.23987 + 4.35234i) q^{24} +(-3.47512 - 2.00636i) q^{25} +(-7.18370 + 3.91919i) q^{26} +(-0.245007 - 5.19037i) q^{27} +(-3.46061 - 7.58516i) q^{28} -8.64500i q^{29} +(2.00595 + 3.35159i) q^{30} +(-4.64428 + 1.24443i) q^{31} +(1.57120 + 5.86380i) q^{32} +(-8.07209 - 2.02744i) q^{33} +(9.67726 - 9.67726i) q^{34} +(-1.67302 - 2.02780i) q^{35} +(0.297229 + 9.44893i) q^{36} +(3.20687 + 0.859279i) q^{37} +(-1.18067 + 2.04498i) q^{38} +(-6.04563 + 1.56534i) q^{39} +(-1.29806 - 2.24831i) q^{40} +(-1.07575 + 1.07575i) q^{41} +(-1.88199 - 10.2290i) q^{42} -3.62015i q^{43} +(14.6261 + 3.91906i) q^{44} +(0.861648 + 2.85361i) q^{45} +(4.75152 + 17.7329i) q^{46} +(1.27963 - 4.77564i) q^{47} +(0.0101394 + 0.644823i) q^{48} +(2.28455 + 6.61671i) q^{49} +(6.43989 + 6.43989i) q^{50} +(8.96169 - 5.36365i) q^{51} +(11.0425 - 2.67462i) q^{52} +(-1.07485 - 0.620567i) q^{53} +(-2.51182 + 11.5227i) q^{54} +4.77451 q^{55} +(1.14381 + 6.81752i) q^{56} +(-1.25404 + 1.29411i) q^{57} +(-5.07827 + 18.9524i) q^{58} +(2.62988 - 0.704673i) q^{59} +(-1.48582 - 5.21570i) q^{60} +(-1.70491 - 2.95300i) q^{61} +10.9126 q^{62} +(0.508638 - 7.92094i) q^{63} -13.0334i q^{64} +(3.14495 - 1.71578i) q^{65} +(16.5054 + 9.18647i) q^{66} +(5.64922 - 1.51370i) q^{67} +(-16.4558 + 9.50078i) q^{68} +(0.220273 + 14.0084i) q^{69} +(2.47657 + 5.42828i) q^{70} +(7.65674 - 7.65674i) q^{71} +(1.78967 - 7.63134i) q^{72} +(-1.40500 - 5.24352i) q^{73} +(-6.52564 - 3.76758i) q^{74} +(3.56932 + 5.96370i) q^{75} +(2.31827 - 2.31827i) q^{76} +(-11.9101 - 4.44728i) q^{77} +(14.1733 + 0.119656i) q^{78} +(-4.42329 - 7.66137i) q^{79} +(-0.0957524 - 0.357353i) q^{80} +(-4.00123 + 8.06165i) q^{81} +(2.99027 - 1.72643i) q^{82} +(-3.07191 + 3.07191i) q^{83} +(-1.15185 + 14.3946i) q^{84} +(-4.23661 + 4.23661i) q^{85} +(-2.12656 + 7.93643i) q^{86} +(-7.28199 + 13.0836i) q^{87} +(-10.8729 - 6.27747i) q^{88} +(-1.08954 + 4.06621i) q^{89} +(-0.212711 - 6.76208i) q^{90} +(-9.44329 + 1.35063i) q^{91} -25.4893i q^{92} +(8.07702 + 2.02868i) q^{93} +(-5.61064 + 9.71791i) q^{94} +(0.516884 - 0.895270i) q^{95} +(2.56138 - 10.1979i) q^{96} +(6.16461 + 6.16461i) q^{97} +(-1.12158 - 15.8477i) q^{98} +(10.5088 + 9.86780i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9}+O(q^{10}) \) 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9	\( 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9} - 48 q^{13} - 12 q^{15} + 40 q^{16} - 26 q^{18} + 40 q^{19} - 10 q^{21} + 16 q^{22} + 32 q^{24} - 24 q^{27} - 52 q^{28} - 12 q^{31} - 44 q^{33} + 16 q^{34} - 8 q^{37} - 42 q^{39} - 160 q^{40} - 80 q^{42} + 6 q^{45} + 32 q^{46} + 72 q^{48} - 12 q^{52} + 34 q^{54} - 48 q^{55} - 24 q^{57} - 28 q^{58} + 44 q^{60} + 78 q^{63} + 4 q^{66} + 24 q^{67} - 12 q^{70} - 26 q^{72} - 40 q^{73} + 112 q^{76} + 32 q^{78} + 48 q^{79} + 128 q^{81} - 150 q^{84} + 160 q^{85} - 48 q^{87} + 24 q^{91} + 10 q^{93} - 8 q^{94} - 106 q^{96} + 56 q^{97} - 36 q^{99}+O(q^{100}) \) 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9 - 48 * q^13 - 12 * q^15 + 40 * q^16 - 26 * q^18 + 40 * q^19 - 10 * q^21 + 16 * q^22 + 32 * q^24 - 24 * q^27 - 52 * q^28 - 12 * q^31 - 44 * q^33 + 16 * q^34 - 8 * q^37 - 42 * q^39 - 160 * q^40 - 80 * q^42 + 6 * q^45 + 32 * q^46 + 72 * q^48 - 12 * q^52 + 34 * q^54 - 48 * q^55 - 24 * q^57 - 28 * q^58 + 44 * q^60 + 78 * q^63 + 4 * q^66 + 24 * q^67 - 12 * q^70 - 26 * q^72 - 40 * q^73 + 112 * q^76 + 32 * q^78 + 48 * q^79 + 128 * q^81 - 150 * q^84 + 160 * q^85 - 48 * q^87 + 24 * q^91 + 10 * q^93 - 8 * q^94 - 106 * q^96 + 56 * q^97 - 36 * q^99

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