LMFDB - Embedded newform 273.2.cd.e.44.4

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			44.4
Character	$\chi$	$=$	273.44
Dual form			273.2.cd.e.242.4

$q$-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 $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

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

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	−0.929540	−	0.368722i	$-0.879795\pi$
$2$	−2.19229	+	0.587422i	−1.55018	+	0.415370i	−0.620644	+	0.784093i	$0.713129\pi$
$3$	−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	−0.0377407	−	0.999288i	$-0.512016\pi$
$5$	0.959762	−	0.257167i	0.429219	−	0.115009i	0.466959	+	0.884279i	$0.345349\pi$
$6$	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	0.878147	−	0.478391i	$-0.158780\pi$
$11$	4.64145	+	1.24367i	1.39945	+	0.374981i	0.521302	+	0.853372i	$0.325447\pi$
$12$	−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	−0.956354	−	0.292210i	$-0.905609\pi$
$17$	−3.01497	−	5.22208i	−0.731238	−	1.26654i	0.225116	−	0.974332i	$-0.427724\pi$
$18$	−1.96818	+	6.51821i	−0.463904	+	1.53636i
$19$	0.269277	+	1.00496i	0.0617764	+	0.230553i	0.989911	−	0.141693i	$-0.0452545\pi$
$19$	0.269277	+	1.00496i	0.0617764	+	0.230553i	−0.928134	+	0.372246i	$0.878588\pi$
$20$	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	0.0437676	+	0.999042i	$0.486064\pi$
$23$	−4.04438	+	7.00507i	−0.843312	+	1.46066i	−0.887079	+	0.461617i	$0.847269\pi$
$24$	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	$0.296587\pi$
$29$			8.64500i			1.60534i	−0.596426	+	0.802668i	$0.703413\pi$
$30$	2.00595	−	3.35159i	0.366235	−	0.611914i
$31$	−4.64428	−	1.24443i	−0.834137	−	0.223506i	−0.183619	−	0.982997i	$-0.558781\pi$
$31$	−4.64428	−	1.24443i	−0.834137	−	0.223506i	−0.650518	+	0.759491i	$0.725448\pi$
$32$	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	0.0146086	−	0.999893i	$-0.495350\pi$
$37$	3.20687	−	0.859279i	0.527207	−	0.141265i	0.512598	+	0.858629i	$0.328683\pi$
$38$	−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	0.618098	−	0.786101i	$-0.287904\pi$
$41$	−1.07575	−	1.07575i	−0.168003	−	0.168003i	−0.786101	+	0.618098i	$0.787904\pi$
$42$	−1.88199	+	10.2290i	−0.290397	+	1.57838i
$43$			3.62015i			0.552068i	0.961148	+	0.276034i	$0.0890203\pi$
$43$			3.62015i			0.552068i	−0.961148	+	0.276034i	$0.910980\pi$
$44$	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	0.994271	+	0.106892i	$0.0340900\pi$
$47$	1.27963	+	4.77564i	0.186653	+	0.696599i	−0.807617	+	0.589707i	$0.799243\pi$
$48$	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	−0.572001	−	0.820253i	$-0.693833\pi$
$53$	−1.07485	+	0.620567i	−0.147643	+	0.0852415i	0.424359	+	0.905494i	$0.360499\pi$
$54$	−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	0.425912	−	0.904765i	$-0.359953\pi$
$59$	2.62988	+	0.704673i	0.342381	+	0.0917406i	−0.0835315	+	0.996505i	$0.526620\pi$
$60$	−1.48582	+	5.21570i	−0.191818	+	0.673344i
$61$	−1.70491	+	2.95300i	−0.218292	+	0.378093i	−0.954286	−	0.298896i	$-0.903382\pi$
$61$	−1.70491	+	2.95300i	−0.218292	+	0.378093i	0.735994	+	0.676988i	$0.236715\pi$
$62$	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	0.586820	−	0.809718i	$-0.300380\pi$
$67$	5.64922	+	1.51370i	0.690162	+	0.184928i	0.103342	+	0.994646i	$0.467046\pi$
$68$	−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	0.996166	−	0.0874786i	$-0.0278809\pi$
$71$	7.65674	+	7.65674i	0.908688	+	0.908688i	−0.0874786	+	0.996166i	$0.527881\pi$
$72$	1.78967	+	7.63134i	0.210915	+	0.899362i
$73$	−1.40500	+	5.24352i	−0.164442	+	0.613707i	0.833668	+	0.552266i	$0.186237\pi$
$73$	−1.40500	+	5.24352i	−0.164442	+	0.613707i	−0.998111	+	0.0614419i	$0.980430\pi$
$74$	−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	−0.999996	−	0.00270045i	$-0.999140\pi$
$79$	−4.42329	+	7.66137i	−0.497660	+	0.861972i	0.502337	+	0.864672i	$0.332474\pi$
$80$	−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	0.518121	−	0.855307i	$-0.326632\pi$
$83$	−3.07191	−	3.07191i	−0.337186	−	0.337186i	−0.855307	+	0.518121i	$0.826632\pi$
$84$	−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	0.883832	−	0.467804i	$-0.154955\pi$
$89$	−1.08954	−	4.06621i	−0.115491	−	0.431017i	−0.999323	+	0.0367864i	$0.988288\pi$
$90$	−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	−0.321118	−	0.947039i	$-0.604059\pi$
$97$	6.16461	−	6.16461i	0.625922	−	0.625922i	0.947039	+	0.321118i	$0.104059\pi$
$98$	−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	0.924372	−	0.381493i	$-0.124590\pi$
$101$	1.32460	+	2.29428i	0.131803	+	0.228289i	−0.792569	+	0.609783i	$0.791257\pi$
$102$	−22.7974	−	6.49437i	−2.25728	−	0.643038i
$103$	8.18210	+	4.72394i	0.806206	+	0.465464i	0.845637	−	0.533759i	$-0.179221\pi$
$103$	8.18210	+	4.72394i	0.806206	+	0.465464i	−0.0394303	+	0.999222i	$0.512554\pi$
$104$	−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	0.248033	−	0.968752i	$-0.420216\pi$
$107$	−4.82979	−	2.78848i	−0.466914	−	0.269573i	−0.714947	+	0.699179i	$0.753549\pi$
$108$	7.50933	+	14.5507i	0.722585	+	1.40014i
$109$	3.11104	+	0.833602i	0.297984	+	0.0798446i	0.404714	−	0.914444i	$-0.367371\pi$
$109$	3.11104	+	0.833602i	0.297984	+	0.0798446i	−0.106730	+	0.994288i	$0.534038\pi$
$110$	−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	$-0.922664\pi$
$113$		−	5.11472i		−	0.481152i	0.970630	−	0.240576i	$-0.0773363\pi$
$114$	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	$-0.881004\pi$
$127$		−	8.23094i		−	0.730378i	0.930933	−	0.365189i	$-0.118996\pi$
$128$	−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	−0.128025	−	0.991771i	$-0.540864\pi$
$131$	−12.0285	−	6.94467i	−1.05094	−	0.606758i	−0.922911	+	0.385013i	$0.874197\pi$
$132$	−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	0.673364	−	0.739311i	$-0.264849\pi$
$137$	10.3804	+	2.78142i	0.886858	+	0.237633i	0.213494	+	0.976944i	$0.431516\pi$
$138$	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	−0.424725	−	0.905322i	$-0.639629\pi$
$149$	−4.14885	+	1.11168i	−0.339887	+	0.0910725i	0.0848382	+	0.996395i	$0.472963\pi$
$150$	−4.32178	+	15.1709i	−0.352872	+	1.23870i
$151$	2.30084	−	8.58684i	0.187239	−	0.698787i	−0.806901	−	0.590687i	$-0.798857\pi$
$151$	2.30084	−	8.58684i	0.187239	−	0.698787i	0.994140	−	0.108100i	$-0.0344766\pi$
$152$	−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	0.958993	−	0.283430i	$-0.0914722\pi$
$157$	2.93250	+	5.07924i	0.234039	+	0.405368i	−0.724954	+	0.688797i	$0.758139\pi$
$158$	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	0.493473	−	0.869761i	$-0.335727\pi$
$163$	17.3086	−	4.63783i	1.35571	−	0.363263i	0.862241	+	0.506498i	$0.169060\pi$
$164$	−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	−0.838406	−	0.545047i	$-0.816512\pi$
$167$	−3.79103	+	3.79103i	−0.293359	+	0.293359i	0.545047	+	0.838406i	$0.316512\pi$
$168$	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	−0.553616	−	0.832772i	$-0.686752\pi$
$173$	5.84509	−	10.1240i	0.444394	−	0.769713i	0.998010	+	0.0630595i	$0.0200858\pi$
$174$	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	0.967938	−	0.251189i	$-0.0808217\pi$
$179$	3.56463	+	6.17411i	0.266433	+	0.461475i	−0.701505	+	0.712664i	$0.747488\pi$
$180$	−2.14469	−	9.14516i	−0.159856	−	0.681640i
$181$		−	13.2207i		−	0.982686i	−0.870966	−	0.491343i	$-0.836506\pi$
$181$		−	13.2207i		−	0.982686i	0.870966	−	0.491343i	$-0.163494\pi$
$182$	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	0.598431	−	0.801175i	$-0.295791\pi$
$191$	2.81669	+	1.62622i	0.203808	+	0.117669i	−0.394622	+	0.918843i	$0.629125\pi$
$192$	−10.9785	−	19.7252i	−0.792306	−	1.42354i
$193$	−6.49514	+	24.2402i	−0.467531	+	1.74485i	0.180830	+	0.983514i	$0.442122\pi$
$193$	−6.49514	+	24.2402i	−0.467531	+	1.74485i	−0.648360	+	0.761334i	$0.724545\pi$
$194$	−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	0.776255	−	0.630420i	$-0.217117\pi$
$197$	2.04689	+	2.04689i	0.145835	+	0.145835i	−0.630420	+	0.776255i	$0.717117\pi$
$198$	−17.2417	+	27.8062i	−1.22531	+	1.97610i
$199$	4.07388	−	2.35206i	0.288790	−	0.166733i	−0.348606	−	0.937269i	$-0.613345\pi$
$199$	4.07388	−	2.35206i	0.288790	−	0.166733i	0.637396	+	0.770536i	$0.280012\pi$
$200$	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	−0.406776	−	0.913528i	$-0.633347\pi$
$223$	7.56742	−	7.56742i	0.506752	−	0.506752i	0.913528	+	0.406776i	$0.133347\pi$
$224$	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	−0.977065	−	0.212940i	$-0.931696\pi$
$227$	−0.368103	+	1.37378i	−0.0244318	+	0.0911808i	0.952633	+	0.304121i	$0.0983627\pi$
$228$	−5.46131	−	1.55578i	−0.361684	−	0.103034i
$229$	19.6652	−	5.26927i	1.29951	−	0.348203i	0.458247	−	0.888825i	$-0.348478\pi$
$229$	19.6652	−	5.26927i	1.29951	−	0.348203i	0.841266	+	0.540621i	$0.181811\pi$
$230$		−	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	−0.850415	−	0.526113i	$-0.823649\pi$
$233$	0.464344	−	0.804267i	0.0304202	−	0.0526893i	0.880835	+	0.473424i	$0.156982\pi$
$234$	−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	0.220537	−	0.975379i	$-0.429219\pi$
$239$	−11.6696	−	11.6696i	−0.754842	−	0.754842i	−0.975379	+	0.220537i	$0.929219\pi$
$240$	−0.156096	−	0.621484i	−0.0100760	−	0.0401166i
$241$	0.469356	−	1.75166i	0.0302339	−	0.112834i	−0.949160	−	0.314794i	$-0.898064\pi$
$241$	0.469356	−	1.75166i	0.0302339	−	0.112834i	0.979394	+	0.201960i	$0.0647311\pi$
$242$	−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	−0.318818	−	0.947816i	$-0.603286\pi$
$257$	10.6034	−	18.3657i	0.661423	−	1.14562i	0.980242	−	0.197803i	$-0.0633806\pi$
$258$	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	0.243013	−	0.970023i	$-0.421864\pi$
$263$	19.5351	−	11.2786i	1.20458	−	0.695467i	0.961571	+	0.274556i	$0.0885307\pi$
$264$	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	−0.538793	−	0.842438i	$-0.681120\pi$
$269$	−1.28942	+	0.744445i	−0.0786171	+	0.0453896i	0.460176	+	0.887828i	$0.347786\pi$
$270$	−5.37401	−	10.4131i	−0.327052	−	0.633722i
$271$	−26.7952	+	7.17977i	−1.62770	+	0.436140i	−0.953249	−	0.302185i	$-0.902284\pi$
$271$	−26.7952	+	7.17977i	−1.62770	+	0.436140i	−0.674446	+	0.738324i	$0.735617\pi$
$272$	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	−0.147534	−	0.989057i	$-0.547133\pi$
$277$	10.5726	−	6.10411i	0.635248	−	0.366761i	0.782782	+	0.622296i	$0.213800\pi$
$278$	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	−0.381904	−	0.924202i	$-0.624731\pi$
$281$	9.09057	−	9.09057i	0.542298	−	0.542298i	0.924202	+	0.381904i	$0.124731\pi$
$282$	16.6770	+	9.98135i	0.993103	+	0.594380i
$283$	−19.2533	+	11.1159i	−1.14449	+	0.660772i	−0.947539	−	0.319641i	$-0.896438\pi$
$283$	−19.2533	+	11.1159i	−1.14449	+	0.660772i	−0.196952	+	0.980413i	$0.563104\pi$
$284$	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	−0.130530	−	0.991444i	$-0.541668\pi$
$293$	14.7365	−	14.7365i	0.860914	−	0.860914i	0.991444	+	0.130530i	$0.0416680\pi$
$294$	−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	0.275464	−	0.961311i	$-0.411168\pi$
$307$	−12.0170	−	12.0170i	−0.685847	−	0.685847i	−0.961311	+	0.275464i	$0.911168\pi$
$308$	−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	0.562998	−	0.826458i	$-0.309648\pi$
$311$	−7.65781	−	13.2637i	−0.434235	−	0.752116i	−0.997233	+	0.0743417i	$0.976314\pi$
$312$	14.0615	−	8.27745i	0.796074	−	0.468618i
$313$	−9.95534	+	17.2432i	−0.562709	+	0.974641i	0.434550	+	0.900648i	$0.356908\pi$
$313$	−9.95534	+	17.2432i	−0.562709	+	0.974641i	−0.997259	+	0.0739928i	$0.976426\pi$
$314$	−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	−0.139576	−	0.990211i	$-0.544574\pi$
$317$	4.17789	−	1.11946i	0.234654	−	0.0628752i	0.374229	+	0.927336i	$0.377907\pi$
$318$	−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	0.991334	−	0.131363i	$-0.0419355\pi$
$331$	1.22136	+	4.55817i	0.0671319	+	0.250540i	−0.924202	+	0.381903i	$0.875269\pi$
$332$	−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	$-0.816584\pi$
$337$		−	20.0045i		−	1.08971i	0.838529	−	0.544856i	$-0.183416\pi$
$338$	−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	−0.940925	−	0.338615i	$-0.890042\pi$
$347$	−20.8286	+	12.0254i	−1.11814	+	0.645558i	−0.177214	+	0.984172i	$0.556708\pi$
$348$	−40.4872	−	24.2319i	−2.17034	−	1.29897i
$349$	7.22449	+	7.22449i	0.386718	+	0.386718i	0.873515	−	0.486797i	$-0.161835\pi$
$349$	7.22449	+	7.22449i	0.386718	+	0.386718i	−0.486797	+	0.873515i	$0.661835\pi$
$350$	−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	0.708206	+	0.706006i	$0.249505\pi$
$353$	−4.84966	+	18.0992i	−0.258121	+	0.963322i	−0.966327	+	0.257316i	$0.917162\pi$
$354$	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	0.989150	+	0.146906i	$0.0469316\pi$
$359$	3.90265	+	14.5649i	0.205974	+	0.768706i	−0.783176	+	0.621800i	$0.786402\pi$
$360$	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	−0.821722	−	0.569888i	$-0.806986\pi$
$367$	−17.3258	−	30.0091i	−0.904399	−	1.56646i	−0.0826766	−	0.996576i	$-0.526347\pi$
$368$	−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	−0.673202	−	0.739458i	$-0.735082\pi$
$373$	5.86713	−	10.1622i	0.303788	−	0.526177i	0.976991	+	0.213281i	$0.0684151\pi$
$374$	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	−0.107094	−	0.994249i	$-0.534155\pi$
$379$	17.2711	−	17.2711i	0.887155	−	0.887155i	0.994249	+	0.107094i	$0.0341547\pi$
$380$	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	0.696773	−	0.717291i	$-0.254618\pi$
$383$	32.4642	−	8.69875i	1.65884	−	0.444486i	0.962069	+	0.272806i	$0.0879516\pi$
$384$	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	0.878469	−	0.477800i	$-0.158566\pi$
$389$	0.501908	+	0.869331i	0.0254478	+	0.0440768i	−0.853021	+	0.521876i	$0.825232\pi$
$390$	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	−0.158340	−	0.987385i	$-0.550614\pi$
$397$	3.94963	−	1.05830i	0.198226	−	0.0531145i	0.356566	+	0.934270i	$0.383947\pi$
$398$	−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	0.981164	−	0.193176i	$-0.0618788\pi$
$401$	0.698135	+	2.60547i	0.0348632	+	0.130111i	−0.946301	+	0.323287i	$0.895212\pi$
$402$	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	0.863945	−	0.503586i	$-0.167986\pi$
$409$	27.5114	+	7.37165i	1.36035	+	0.364505i	0.496405	+	0.868091i	$0.334653\pi$
$410$	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	$0.164113\pi$
$419$			20.1844i			0.986074i	−0.870008	+	0.493037i	$0.835887\pi$
$420$	−4.80732	−	13.5192i	−0.234573	−	0.659668i
$421$	−16.5214	+	16.5214i	−0.805204	+	0.805204i	−0.983904	−	0.178700i	$-0.942811\pi$
$421$	−16.5214	+	16.5214i	−0.805204	+	0.805204i	0.178700	+	0.983904i	$0.442811\pi$
$422$	−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	−0.808437	−	0.588583i	$-0.799686\pi$
$431$	3.86107	−	14.4097i	0.185981	−	0.694091i	0.994418	−	0.105509i	$-0.0336471\pi$
$432$	−1.62803	−	1.04528i	−0.0783287	−	0.0502911i
$433$			22.6270i			1.08738i	0.839285	+	0.543691i	$0.182974\pi$
$433$			22.6270i			1.08738i	−0.839285	+	0.543691i	$0.817026\pi$
$434$	−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	0.816734	−	0.577014i	$-0.195782\pi$
$439$	15.1987	+	8.77496i	0.725393	+	0.418806i	−0.0913414	+	0.995820i	$0.529115\pi$
$440$	−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	−0.0106206	−	0.999944i	$-0.503381\pi$
$443$	−18.5620	−	10.7168i	−0.881908	−	0.509170i	−0.871287	+	0.490774i	$0.836714\pi$
$444$	−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	−0.589855	−	0.807509i	$-0.700815\pi$
$449$	4.61199	−	4.61199i	0.217653	−	0.217653i	0.807509	+	0.589855i	$0.200815\pi$
$450$	−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	−0.990988	−	0.133951i	$-0.957233\pi$
$457$	−4.27001	−	15.9359i	−0.199743	−	0.745451i	0.791245	−	0.611499i	$-0.209433\pi$
$458$	−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	0.207791	−	0.978173i	$-0.433373\pi$
$461$	−16.5408	−	16.5408i	−0.770382	−	0.770382i	−0.978173	+	0.207791i	$0.933373\pi$
$462$	−21.4567	+	45.1370i	−0.998257	+	2.09996i
$463$	−21.2860	−	21.2860i	−0.989246	−	0.989246i	0.0106969	−	0.999943i	$-0.496595\pi$
$463$	−21.2860	−	21.2860i	−0.989246	−	0.989246i	−0.999943	+	0.0106969i	$0.996595\pi$
$464$	−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	−0.427839	−	0.903855i	$-0.640725\pi$
$467$	12.2928	−	21.2917i	0.568842	−	0.985263i	0.996681	−	0.0814080i	$-0.0259417\pi$
$468$	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	0.629715	−	0.776826i	$-0.283172\pi$
$479$	17.2167	+	4.61320i	0.786650	+	0.210782i	0.156936	+	0.987609i	$0.449838\pi$
$480$	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	−0.236771	−	0.971565i	$-0.576089\pi$
$487$	−20.4704	−	5.48504i	−0.927604	−	0.248551i	−0.690833	+	0.723015i	$0.742756\pi$
$488$	−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	0.988620	−	0.150436i	$-0.0480679\pi$
$499$	1.27846	+	4.77127i	0.0572317	+	0.213592i	−0.931388	+	0.364028i	$0.881401\pi$
$500$	−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	$0.389065\pi$
$503$			42.1587i			1.87976i	−0.341500	+	0.939882i	$0.610935\pi$
$504$	−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	−0.0272334	−	0.999629i	$-0.508670\pi$
$509$	10.1298	−	2.71428i	0.448996	−	0.120308i	0.476230	+	0.879321i	$0.342003\pi$
$510$	−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	−0.686694	−	0.726947i	$-0.740939\pi$
$521$	−9.14126	+	5.27771i	−0.400486	+	0.231221i	0.286208	+	0.958168i	$0.407605\pi$
$522$	−56.3500	−	17.0149i	−2.46637	−	0.744722i
$523$	−3.18635	+	5.51892i	−0.139329	+	0.241325i	−0.927243	−	0.374460i	$-0.877828\pi$
$523$	−3.18635	+	5.51892i	−0.139329	+	0.241325i	0.787914	+	0.615786i	$0.211161\pi$
$524$	−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	0.371924	−	0.928263i	$-0.378698\pi$
$541$	26.9379	−	7.21799i	1.15815	−	0.310326i	0.786227	+	0.617938i	$0.212032\pi$
$542$	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	−0.256928	−	0.966431i	$-0.582710\pi$
$557$	−22.7193	−	6.08763i	−0.962649	−	0.257941i	−0.705721	+	0.708490i	$0.749377\pi$
$558$	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	0.667058	−	0.745006i	$-0.267553\pi$
$563$	−7.39506	−	12.8086i	−0.311665	−	0.539819i	−0.978723	+	0.205187i	$0.934220\pi$
$564$	−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	−0.992306	−	0.123809i	$-0.960489\pi$
$569$	−9.27745	+	16.0690i	−0.388931	+	0.673648i	0.603375	+	0.797458i	$0.293822\pi$
$570$	3.90836	+	1.11339i	0.163703	+	0.0466347i
$571$	−8.05438	+	4.65020i	−0.337065	+	0.194605i	−0.658974	−	0.752166i	$-0.729009\pi$
$571$	−8.05438	+	4.65020i	−0.337065	+	0.194605i	0.321908	+	0.946771i	$0.395676\pi$
$572$	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	0.422588	−	0.906322i	$-0.361122\pi$
$577$	8.05655	+	2.15875i	0.335399	+	0.0898698i	−0.0871893	+	0.996192i	$0.527788\pi$
$578$	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	0.602387	−	0.798204i	$-0.294216\pi$
$587$	−4.74425	−	4.74425i	−0.195816	−	0.195816i	−0.798204	+	0.602387i	$0.794216\pi$
$588$	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	0.998242	+	0.0592732i	$0.0188783\pi$
$593$	3.97846	+	14.8478i	0.163376	+	0.609726i	−0.834866	+	0.550453i	$0.814455\pi$
$594$	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	−0.577843	−	0.816148i	$-0.696105\pi$
$599$	−3.91492	+	2.26028i	−0.159959	+	0.0923525i	0.417884	+	0.908501i	$0.362772\pi$
$600$	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	−0.106701	−	0.994291i	$-0.534029\pi$
$607$	19.9004	−	34.4684i	0.807731	−	1.39903i	0.914432	−	0.404740i	$-0.132638\pi$
$608$	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	0.597252	−	0.802054i	$-0.296259\pi$
$613$	17.6644	+	4.73317i	0.713460	+	0.191171i	0.116208	+	0.993225i	$0.462926\pi$
$614$	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	0.786811	−	0.617194i	$-0.211731\pi$
$617$	4.21321	+	4.21321i	0.169617	+	0.169617i	−0.617194	+	0.786811i	$0.711731\pi$
$618$	36.0218	−	9.04747i	1.44901	−	0.363943i
$619$	−4.46679	+	16.6703i	−0.179535	+	0.670035i	0.816199	+	0.577771i	$0.196077\pi$
$619$	−4.46679	+	16.6703i	−0.179535	+	0.670035i	−0.995735	+	0.0922644i	$0.970590\pi$
$620$	−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	0.302561	−	0.953130i	$-0.402158\pi$
$631$	−16.3421	−	16.3421i	−0.650569	−	0.650569i	−0.953130	+	0.302561i	$0.902158\pi$
$632$	−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	0.977658	−	0.210200i	$-0.0674114\pi$
$641$	7.76733	+	13.4534i	0.306791	+	0.531378i	−0.670867	+	0.741577i	$0.734078\pi$
$642$	−21.2632	+	5.34061i	−0.839192	+	0.210777i
$643$	6.92255	−	6.92255i	0.272999	−	0.272999i	−0.557307	−	0.830306i	$-0.688166\pi$
$643$	6.92255	−	6.92255i	0.272999	−	0.272999i	0.830306	+	0.557307i	$0.188166\pi$
$644$	−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	−0.999147	−	0.0412834i	$-0.986855\pi$
$647$	−13.6167	−	23.5847i	−0.535326	−	0.927212i	0.463821	−	0.885929i	$-0.346478\pi$
$648$	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	0.963146	−	0.268977i	$-0.0866857\pi$
$653$	30.9656	+	17.8780i	1.21178	+	0.699621i	0.248632	+	0.968598i	$0.420019\pi$
$654$	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	$0.195049\pi$
$659$			29.5283i			1.15026i	−0.818062	+	0.575130i	$0.804951\pi$
$660$	−13.3830	+	22.3605i	−0.520931	+	0.870383i
$661$	−4.04655	+	15.1019i	−0.157393	+	0.587398i	0.841496	+	0.540264i	$0.181675\pi$
$661$	−4.04655	+	15.1019i	−0.157393	+	0.587398i	−0.998889	+	0.0471340i	$0.984991\pi$
$662$	−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	$-0.862597\pi$
$673$		−	21.7075i		−	0.836764i	0.908271	−	0.418382i	$-0.137403\pi$
$674$	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	0.689904	−	0.723901i	$-0.257653\pi$
$677$	10.6143	+	6.12816i	0.407940	+	0.235524i	−0.281964	+	0.959425i	$0.590986\pi$
$678$	−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	−0.332251	−	0.943191i	$-0.607808\pi$
$683$	−28.5278	−	7.64399i	−1.09158	−	0.292489i	−0.759333	+	0.650702i	$0.774475\pi$
$684$	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	0.997407	−	0.0719706i	$-0.0229288\pi$
$691$	2.56670	+	9.57906i	0.0976419	+	0.364404i	−0.899765	+	0.436375i	$0.856262\pi$
$692$		−	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	−0.627149	−	0.778899i	$-0.715778\pi$
$709$	−20.7911	+	5.57096i	−0.780826	+	0.209222i	−0.153677	+	0.988121i	$0.549112\pi$
$710$	−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	−0.874566	−	0.484906i	$-0.838854\pi$
$719$	−0.465006	+	0.805414i	−0.0173418	+	0.0300369i	0.857224	+	0.514943i	$0.172187\pi$
$720$	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	$0.299081\pi$
$727$			43.5352i			1.61463i	−0.590119	+	0.807316i	$0.700919\pi$
$728$	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	0.926632	−	0.375970i	$-0.122690\pi$
$733$	−1.72840	−	6.45047i	−0.0638399	−	0.238254i	−0.990472	+	0.137716i	$0.956024\pi$
$734$	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	−0.520523	−	0.853848i	$-0.674263\pi$
$739$	9.70997	−	36.2381i	0.357187	−	1.33304i	0.877710	−	0.479193i	$-0.159070\pi$
$740$	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	0.547202	−	0.837001i	$-0.315693\pi$
$743$	−7.89935	−	7.89935i	−0.289799	−	0.289799i	−0.837001	+	0.547202i	$0.815693\pi$
$744$	−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	0.590443	−	0.807080i	$-0.298953\pi$
$751$	5.11674	+	2.95415i	0.186712	+	0.107798i	−0.403730	+	0.914878i	$0.632287\pi$
$752$	−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	0.993106	−	0.117221i	$-0.0373986\pi$
$761$	2.05353	+	7.66389i	0.0744405	+	0.277816i	−0.918665	+	0.395037i	$0.870732\pi$
$762$	−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	−0.0240438	+	0.999711i	$0.507654\pi$
$769$	−28.3896	+	28.3896i	−1.02375	+	1.02375i	−0.999711	+	0.0240438i	$0.992346\pi$
$770$	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	0.486759	+	0.873536i	$0.338179\pi$
$773$	−10.3303	+	38.5532i	−0.371555	+	1.38666i	−0.858314	+	0.513125i	$0.828488\pi$
$774$	−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	−0.664413	−	0.747366i	$-0.731318\pi$
$787$	7.98595	−	29.8040i	0.284668	−	1.06240i	0.949081	−	0.315031i	$-0.102015\pi$
$788$	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	−0.0617028	−	0.998095i	$-0.519653\pi$
$809$	21.9528	−	12.6745i	0.771821	−	0.445611i	0.833524	+	0.552483i	$0.186320\pi$
$810$	16.9045	+	11.2328i	0.593965	+	0.394681i
$811$	−9.32142	+	9.32142i	−0.327319	+	0.327319i	−0.851566	−	0.524247i	$-0.824347\pi$
$811$	−9.32142	+	9.32142i	−0.327319	+	0.327319i	0.524247	+	0.851566i	$0.324347\pi$
$812$	−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	−0.776892	−	0.629634i	$-0.783205\pi$
$821$	−32.5179	+	8.71315i	−1.13488	+	0.304091i	−0.357992	+	0.933725i	$0.616538\pi$
$822$	36.9137	−	20.5452i	1.28751	−	0.716595i
$823$	−21.9119	+	12.6508i	−0.763801	+	0.440981i	−0.830659	−	0.556782i	$-0.812036\pi$
$823$	−21.9119	+	12.6508i	−0.763801	+	0.440981i	0.0668577	+	0.997763i	$0.478703\pi$
$824$	−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	−0.346886	−	0.937907i	$-0.612761\pi$
$827$	16.9964	−	16.9964i	0.591022	−	0.591022i	0.937907	+	0.346886i	$0.112761\pi$
$828$	64.9883	+	40.2972i	2.25850	+	1.40042i
$829$	14.9313	−	8.62060i	0.518586	−	0.299406i	−0.217770	−	0.976000i	$-0.569878\pi$
$829$	14.9313	−	8.62060i	0.518586	−	0.299406i	0.736356	+	0.676594i	$0.236545\pi$
$830$	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	−0.814015	−	0.580844i	$-0.802723\pi$
$839$	−6.75391	+	6.75391i	−0.233171	+	0.233171i	0.580844	+	0.814015i	$0.302723\pi$
$840$	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	0.591499	−	0.806306i	$-0.298536\pi$
$853$	−6.27369	−	6.27369i	−0.214807	−	0.214807i	−0.806306	+	0.591499i	$0.798536\pi$
$854$	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	0.834736	+	0.550650i	$0.185620\pi$
$857$	26.1786	+	45.3427i	0.894245	+	1.54888i	0.0595090	+	0.998228i	$0.481046\pi$
$858$	65.9334	+	17.0716i	2.25093	+	0.582813i
$859$	17.1641	−	29.7290i	0.585630	−	1.01434i	−0.409167	−	0.912460i	$-0.634181\pi$
$859$	17.1641	−	29.7290i	0.585630	−	1.01434i	0.994797	−	0.101881i	$-0.0324861\pi$
$860$	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	−0.766202	−	0.642600i	$-0.777856\pi$
$863$	−32.5628	+	8.72519i	−1.10845	+	0.297009i	−0.342250	+	0.939609i	$0.611189\pi$
$864$	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	−0.870075	−	0.492920i	$-0.835929\pi$
$877$	−10.7508	−	40.1224i	−0.363028	−	1.35484i	0.507047	−	0.861919i	$-0.330737\pi$
$878$	−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	$0.112348\pi$
$883$			20.5434i			0.691339i	−0.938356	+	0.345669i	$0.887652\pi$
$884$	−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	0.893870	−	0.448327i	$-0.147980\pi$
$887$	28.3691	+	16.3789i	0.952543	+	0.549951i	0.0586728	+	0.998277i	$0.481313\pi$
$888$	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	−0.954913	−	0.296886i	$-0.904052\pi$
$907$	−35.3946	+	20.4351i	−1.17526	+	0.678536i	−0.220346	+	0.975422i	$0.570719\pi$
$908$	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	$0.165972\pi$
$911$			30.0686i			0.996218i	−0.867115	+	0.498109i	$0.834028\pi$
$912$	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	0.0676011	+	0.997712i	$0.478465\pi$
$919$	−25.1688	+	43.5937i	−0.830244	+	1.43802i	−0.897845	+	0.440312i	$0.854868\pi$
$920$	−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	0.453195	−	0.891412i	$-0.350284\pi$
$929$	39.3606	−	10.5466i	1.29138	−	0.346024i	0.838184	+	0.545388i	$0.183618\pi$
$930$	−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	0.408285	+	0.912855i	$0.366127\pi$
$941$	−12.3233	+	45.9911i	−0.401727	+	1.49927i	−0.810012	+	0.586413i	$0.800540\pi$
$942$	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	−0.853945	−	0.520363i	$-0.825797\pi$
$947$	−11.5273	−	43.0207i	−0.374589	−	1.39798i	0.479357	−	0.877620i	$-0.340870\pi$
$948$	−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	−0.218374	−	0.975865i	$-0.570075\pi$
$967$	23.5554	−	23.5554i	0.757491	−	0.757491i	0.975865	+	0.218374i	$0.0700752\pi$
$968$	−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	−0.481381	−	0.876511i	$-0.659865\pi$
$971$	−46.1540	−	26.6470i	−1.48115	−	0.855144i	−0.999772	+	0.0213673i	$0.993198\pi$
$972$	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	0.482145	+	0.876091i	$0.339858\pi$
$977$	−11.6729	+	43.5640i	−0.373451	+	1.39374i	−0.855595	+	0.517645i	$0.826809\pi$
$978$	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	0.795008	−	0.606599i	$-0.207467\pi$
$983$	37.0028	+	9.91487i	1.18021	+	0.316235i	0.385198	+	0.922834i	$0.374133\pi$
$984$	−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	0.909796	−	0.415055i	$-0.136238\pi$
$991$	3.00477	+	5.20441i	0.0954496	+	0.165324i	−0.814347	+	0.580379i	$0.802904\pi$
$992$	−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	0.892119	+	0.451801i	$0.149218\pi$
$997$	26.4390	+	45.7936i	0.837331	+	1.45030i	−0.0547879	+	0.998498i	$0.517448\pi$
$998$	−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.44.4	✓	112
3.2	odd	2	inner	273.2.cd.e.44.25	yes	112
7.4	even	3	inner	273.2.cd.e.200.25	yes	112
13.8	odd	4	inner	273.2.cd.e.86.4	yes	112
21.11	odd	6	inner	273.2.cd.e.200.4	yes	112
39.8	even	4	inner	273.2.cd.e.86.25	yes	112
91.60	odd	12	inner	273.2.cd.e.242.25	yes	112
273.242	even	12	inner	273.2.cd.e.242.4	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.cd.e.44.4	✓	112	1.1	even	1	trivial
273.2.cd.e.44.25	yes	112	3.2	odd	2	inner
273.2.cd.e.86.4	yes	112	13.8	odd	4	inner
273.2.cd.e.86.25	yes	112	39.8	even	4	inner
273.2.cd.e.200.4	yes	112	21.11	odd	6	inner
273.2.cd.e.200.25	yes	112	7.4	even	3	inner
273.2.cd.e.242.4	yes	112	273.242	even	12	inner
273.2.cd.e.242.25	yes	112	91.60	odd	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
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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