LMFDB - Embedded newform 380.2.k.c.267.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(267,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("380.267");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.k (of order $4$, degree $2$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			267.13
Character	$\chi$	$=$	380.267
Dual form			380.2.k.c.343.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.291109 - 1.38393i) q^{2} +(1.18694 + 1.18694i) q^{3} +(-1.83051 + 0.805748i) q^{4} +(1.27222 - 1.83887i) q^{5} +(1.29711 - 1.98816i) q^{6} +(-1.53689 + 1.53689i) q^{7} +(1.64798 + 2.29873i) q^{8} -0.182360i q^{9} +O(q^{10})$	\(q+(-0.291109 - 1.38393i) q^{2} +(1.18694 + 1.18694i) q^{3} +(-1.83051 + 0.805748i) q^{4} +(1.27222 - 1.83887i) q^{5} +(1.29711 - 1.98816i) q^{6} +(-1.53689 + 1.53689i) q^{7} +(1.64798 + 2.29873i) q^{8} -0.182360i q^{9} +(-2.91522 - 1.22536i) q^{10} -3.80154i q^{11} +(-3.12907 - 1.21633i) q^{12} +(4.33858 - 4.33858i) q^{13} +(2.57434 + 1.67954i) q^{14} +(3.69267 - 0.672572i) q^{15} +(2.70154 - 2.94986i) q^{16} +(3.54037 + 3.54037i) q^{17} +(-0.252372 + 0.0530865i) q^{18} +1.00000 q^{19} +(-0.847156 + 4.39116i) q^{20} -3.64838 q^{21} +(-5.26106 + 1.10666i) q^{22} +(3.11551 + 3.11551i) q^{23} +(-0.772410 + 4.68450i) q^{24} +(-1.76289 - 4.67891i) q^{25} +(-7.26728 - 4.74128i) q^{26} +(3.77726 - 3.77726i) q^{27} +(1.57495 - 4.05163i) q^{28} +3.00176i q^{29} +(-2.00576 - 4.91460i) q^{30} +8.41277i q^{31} +(-4.86884 - 2.88001i) q^{32} +(4.51219 - 4.51219i) q^{33} +(3.86898 - 5.93024i) q^{34} +(0.870870 + 4.78140i) q^{35} +(0.146936 + 0.333811i) q^{36} +(-8.05718 - 8.05718i) q^{37} +(-0.291109 - 1.38393i) q^{38} +10.2992 q^{39} +(6.32367 - 0.105905i) q^{40} -2.12365 q^{41} +(1.06208 + 5.04909i) q^{42} +(-2.98171 - 2.98171i) q^{43} +(3.06308 + 6.95876i) q^{44} +(-0.335336 - 0.232002i) q^{45} +(3.40469 - 5.21860i) q^{46} +(-2.50153 + 2.50153i) q^{47} +(6.70786 - 0.294740i) q^{48} +2.27595i q^{49} +(-5.96208 + 3.80178i) q^{50} +8.40439i q^{51} +(-4.44602 + 11.4376i) q^{52} +(-6.45515 + 6.45515i) q^{53} +(-6.32705 - 4.12786i) q^{54} +(-6.99054 - 4.83641i) q^{55} +(-6.06565 - 1.00014i) q^{56} +(1.18694 + 1.18694i) q^{57} +(4.15422 - 0.873840i) q^{58} -9.56354 q^{59} +(-6.21756 + 4.20652i) q^{60} -0.367160 q^{61} +(11.6427 - 2.44903i) q^{62} +(0.280266 + 0.280266i) q^{63} +(-2.56836 + 7.57651i) q^{64} +(-2.45844 - 13.4977i) q^{65} +(-7.55808 - 4.93100i) q^{66} +(6.11984 - 6.11984i) q^{67} +(-9.33332 - 3.62804i) q^{68} +7.39584i q^{69} +(6.36360 - 2.59713i) q^{70} +4.48386i q^{71} +(0.419196 - 0.300524i) q^{72} +(0.985330 - 0.985330i) q^{73} +(-8.80503 + 13.4961i) q^{74} +(3.46114 - 7.64601i) q^{75} +(-1.83051 + 0.805748i) q^{76} +(5.84254 + 5.84254i) q^{77} +(-2.99820 - 14.2534i) q^{78} -14.1049 q^{79} +(-1.98744 - 8.72067i) q^{80} +8.41967 q^{81} +(0.618215 + 2.93898i) q^{82} +(4.61568 + 4.61568i) q^{83} +(6.67840 - 2.93967i) q^{84} +(11.0144 - 2.00613i) q^{85} +(-3.25847 + 4.99447i) q^{86} +(-3.56290 + 3.56290i) q^{87} +(8.73873 - 6.26484i) q^{88} +10.7179i q^{89} +(-0.223455 + 0.531618i) q^{90} +13.3358i q^{91} +(-8.21330 - 3.19266i) q^{92} +(-9.98543 + 9.98543i) q^{93} +(4.19016 + 2.73372i) q^{94} +(1.27222 - 1.83887i) q^{95} +(-2.36062 - 9.19739i) q^{96} +(11.9851 + 11.9851i) q^{97} +(3.14975 - 0.662550i) q^{98} -0.693247 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8	$ 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 q^{98} + 128 q^{99}+O(q^{100}) $ 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.291109	−	1.38393i	−0.205845	−	0.978585i
$2$	−0.291109	−	1.38393i	−0.205845	−	0.978585i
$3$	1.18694	+	1.18694i	0.685279	+	0.685279i	0.961185	−	0.275906i	$-0.0889779\pi$
$3$	1.18694	+	1.18694i	0.685279	+	0.685279i	−0.275906	+	0.961185i	$0.588978\pi$
$4$	−1.83051	+	0.805748i	−0.915255	+	0.402874i
$5$	1.27222	−	1.83887i	0.568956	−	0.822368i
$5$	1.27222	−	1.83887i	0.568956	−	0.822368i
$6$	1.29711	−	1.98816i	0.529542	−	0.811664i
$7$	−1.53689	+	1.53689i	−0.580889	+	0.580889i	−0.935148	−	0.354259i	$-0.884733\pi$
$7$	−1.53689	+	1.53689i	−0.580889	+	0.580889i	0.354259	+	0.935148i	$0.384733\pi$
$8$	1.64798	+	2.29873i	0.582647	+	0.812725i
$9$		−	0.182360i		−	0.0607865i
$10$	−2.91522	−	1.22536i	−0.921873	−	0.387491i
$11$		−	3.80154i		−	1.14621i	−0.819483	−	0.573104i	$-0.805739\pi$
$11$		−	3.80154i		−	1.14621i	0.819483	−	0.573104i	$-0.194261\pi$
$12$	−3.12907	−	1.21633i	−0.903286	−	0.351124i
$13$	4.33858	−	4.33858i	1.20331	−	1.20331i	0.230151	−	0.973155i	$-0.426078\pi$
$13$	4.33858	−	4.33858i	1.20331	−	1.20331i	0.973155	−	0.230151i	$-0.0739219\pi$
$14$	2.57434	+	1.67954i	0.688022	+	0.448876i
$15$	3.69267	−	0.672572i	0.953445	−	0.173657i
$16$	2.70154	−	2.94986i	0.675385	−	0.737465i
$17$	3.54037	+	3.54037i	0.858665	+	0.858665i	0.991181	−	0.132516i	$-0.0423056\pi$
$17$	3.54037	+	3.54037i	0.858665	+	0.858665i	−0.132516	+	0.991181i	$0.542306\pi$
$18$	−0.252372	+	0.0530865i	−0.0594847	+	0.0125126i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	−0.847156	+	4.39116i	−0.189430	+	0.981894i
$21$	−3.64838			−0.796142
$22$	−5.26106	+	1.10666i	−1.12166	+	0.235941i
$23$	3.11551	+	3.11551i	0.649630	+	0.649630i	0.952903	−	0.303274i	$-0.0980797\pi$
$23$	3.11551	+	3.11551i	0.649630	+	0.649630i	−0.303274	+	0.952903i	$0.598080\pi$
$24$	−0.772410	+	4.68450i	−0.157668	+	0.956219i
$25$	−1.76289	−	4.67891i	−0.352577	−	0.935783i
$26$	−7.26728	−	4.74128i	−1.42523	−	0.929842i
$27$	3.77726	−	3.77726i	0.726934	−	0.726934i
$28$	1.57495	−	4.05163i	0.297637	−	0.765687i
$29$			3.00176i			0.557413i	0.960376	+	0.278706i	$0.0899056\pi$
$29$			3.00176i			0.557413i	−0.960376	+	0.278706i	$0.910094\pi$
$30$	−2.00576	−	4.91460i	−0.366201	−	0.897280i
$31$			8.41277i			1.51098i	0.655161	+	0.755489i	$0.272601\pi$
$31$			8.41277i			1.51098i	−0.655161	+	0.755489i	$0.727399\pi$
$32$	−4.86884	−	2.88001i	−0.860697	−	0.509118i
$33$	4.51219	−	4.51219i	0.785471	−	0.785471i
$34$	3.86898	−	5.93024i	0.663524	−	1.01703i
$35$	0.870870	+	4.78140i	0.147204	+	0.808205i
$36$	0.146936	+	0.333811i	0.0244893	+	0.0556352i
$37$	−8.05718	−	8.05718i	−1.32459	−	1.32459i	−0.910014	−	0.414578i	$-0.863929\pi$
$37$	−8.05718	−	8.05718i	−1.32459	−	1.32459i	−0.414578	−	0.910014i	$-0.636071\pi$
$38$	−0.291109	−	1.38393i	−0.0472241	−	0.224503i
$39$	10.2992			1.64920
$40$	6.32367	−	0.105905i	0.999860	−	0.0167451i
$41$	−2.12365			−0.331659			−0.165830	−	0.986154i	$-0.553030\pi$
$41$	−2.12365			−0.331659			−0.165830	+	0.986154i	$0.553030\pi$
$42$	1.06208	+	5.04909i	0.163882	+	0.779092i
$43$	−2.98171	−	2.98171i	−0.454706	−	0.454706i	0.442207	−	0.896913i	$-0.354196\pi$
$43$	−2.98171	−	2.98171i	−0.454706	−	0.454706i	−0.896913	+	0.442207i	$0.854196\pi$
$44$	3.06308	+	6.95876i	0.461777	+	1.04907i
$45$	−0.335336	−	0.232002i	−0.0499889	−	0.0345849i
$46$	3.40469	−	5.21860i	0.501994	−	0.769441i
$47$	−2.50153	+	2.50153i	−0.364886	+	0.364886i	−0.865608	−	0.500722i	$-0.833068\pi$
$47$	−2.50153	+	2.50153i	−0.364886	+	0.364886i	0.500722	+	0.865608i	$0.333068\pi$
$48$	6.70786	−	0.294740i	0.968196	−	0.0425420i
$49$			2.27595i			0.325136i
$50$	−5.96208	+	3.80178i	−0.843166	+	0.537653i
$51$			8.40439i			1.17685i
$52$	−4.44602	+	11.4376i	−0.616552	+	1.58611i
$53$	−6.45515	+	6.45515i	−0.886684	+	0.886684i	−0.994203	−	0.107519i	$-0.965709\pi$
$53$	−6.45515	+	6.45515i	−0.886684	+	0.886684i	0.107519	+	0.994203i	$0.465709\pi$
$54$	−6.32705	−	4.12786i	−0.861003	−	0.561731i
$55$	−6.99054	−	4.83641i	−0.942604	−	0.652142i
$56$	−6.06565	−	1.00014i	−0.810556	−	0.133650i
$57$	1.18694	+	1.18694i	0.157214	+	0.157214i
$58$	4.15422	−	0.873840i	0.545476	−	0.114741i
$59$	−9.56354			−1.24507			−0.622533	−	0.782593i	$-0.713897\pi$
$59$	−9.56354			−1.24507			−0.622533	+	0.782593i	$0.713897\pi$
$60$	−6.21756	+	4.20652i	−0.802683	+	0.543059i
$61$	−0.367160			−0.0470101			−0.0235050	−	0.999724i	$-0.507483\pi$
$61$	−0.367160			−0.0470101			−0.0235050	+	0.999724i	$0.507483\pi$
$62$	11.6427	−	2.44903i	1.47862	−	0.311028i
$63$	0.280266	+	0.280266i	0.0353102	+	0.0353102i
$64$	−2.56836	+	7.57651i	−0.321045	+	0.947064i
$65$	−2.45844	−	13.4977i	−0.304931	−	1.67419i
$66$	−7.55808	−	4.93100i	−0.930336	−	0.606965i
$67$	6.11984	−	6.11984i	0.747658	−	0.747658i	−0.226381	−	0.974039i	$-0.572689\pi$
$67$	6.11984	−	6.11984i	0.747658	−	0.747658i	0.974039	+	0.226381i	$0.0726894\pi$
$68$	−9.33332	−	3.62804i	−1.13183	−	0.439964i
$69$			7.39584i			0.890355i
$70$	6.36360	−	2.59713i	0.760596	−	0.310417i
$71$			4.48386i			0.532136i	0.963954	+	0.266068i	$0.0857245\pi$
$71$			4.48386i			0.532136i	−0.963954	+	0.266068i	$0.914275\pi$
$72$	0.419196	−	0.300524i	0.0494027	−	0.0354171i
$73$	0.985330	−	0.985330i	0.115324	−	0.115324i	−0.647090	−	0.762414i	$-0.724014\pi$
$73$	0.985330	−	0.985330i	0.115324	−	0.115324i	0.762414	+	0.647090i	$0.224014\pi$
$74$	−8.80503	+	13.4961i	−1.02356	+	1.56889i
$75$	3.46114	−	7.64601i	0.399658	−	0.882886i
$76$	−1.83051	+	0.805748i	−0.209974	+	0.0924256i
$77$	5.84254	+	5.84254i	0.665819	+	0.665819i
$78$	−2.99820	−	14.2534i	−0.339480	−	1.61388i
$79$	−14.1049			−1.58693			−0.793463	−	0.608618i	$-0.791724\pi$
$79$	−14.1049			−1.58693			−0.793463	+	0.608618i	$0.791724\pi$
$80$	−1.98744	−	8.72067i	−0.222203	−	0.975000i
$81$	8.41967			0.935518
$82$	0.618215	+	2.93898i	0.0682704	+	0.324556i
$83$	4.61568	+	4.61568i	0.506637	+	0.506637i	0.913492	−	0.406856i	$-0.133375\pi$
$83$	4.61568	+	4.61568i	0.506637	+	0.506637i	−0.406856	+	0.913492i	$0.633375\pi$
$84$	6.67840	−	2.93967i	0.728673	−	0.320745i
$85$	11.0144	−	2.00613i	1.19468	−	0.217596i
$86$	−3.25847	+	4.99447i	−0.351369	+	0.538567i
$87$	−3.56290	+	3.56290i	−0.381983	+	0.381983i
$88$	8.73873	−	6.26484i	0.931552	−	0.667834i
$89$			10.7179i			1.13610i	0.822995	+	0.568049i	$0.192301\pi$
$89$			10.7179i			1.13610i	−0.822995	+	0.568049i	$0.807699\pi$
$90$	−0.223455	+	0.531618i	−0.0235543	+	0.0560375i
$91$			13.3358i			1.39797i
$92$	−8.21330	−	3.19266i	−0.856296	−	0.332858i
$93$	−9.98543	+	9.98543i	−1.03544	+	1.03544i
$94$	4.19016	+	2.73372i	0.432182	+	0.281962i
$95$	1.27222	−	1.83887i	0.130528	−	0.188664i
$96$	−2.36062	−	9.19739i	−0.240930	−	0.938705i
$97$	11.9851	+	11.9851i	1.21691	+	1.21691i	0.968709	+	0.248198i	$0.0798384\pi$
$97$	11.9851	+	11.9851i	1.21691	+	1.21691i	0.248198	+	0.968709i	$0.420162\pi$
$98$	3.14975	−	0.662550i	0.318173	−	0.0669277i
$99$	−0.693247			−0.0696740
$100$	6.99701	+	7.14436i	0.699701	+	0.714436i
$101$	−0.0884970			−0.00880578			−0.00440289	−	0.999990i	$-0.501401\pi$
$101$	−0.0884970			−0.00880578			−0.00440289	+	0.999990i	$0.501401\pi$
$102$	11.6311	−	2.44659i	1.15165	−	0.242249i
$103$	4.11374	+	4.11374i	0.405339	+	0.405339i	0.880110	−	0.474771i	$-0.157469\pi$
$103$	4.11374	+	4.11374i	0.405339	+	0.405339i	−0.474771	+	0.880110i	$0.657469\pi$
$104$	17.1231	+	2.82337i	1.67906	+	0.276854i
$105$	−4.64156	+	6.70890i	−0.452970	+	0.654721i
$106$	10.8126	+	7.05431i	1.05021	+	0.685175i
$107$	6.63747	−	6.63747i	0.641668	−	0.641668i	−0.309297	−	0.950965i	$-0.600094\pi$
$107$	6.63747	−	6.63747i	0.641668	−	0.641668i	0.950965	+	0.309297i	$0.100094\pi$
$108$	−3.87080	+	9.95784i	−0.372468	+	0.958193i
$109$			8.56202i			0.820093i	0.912065	+	0.410047i	$0.134488\pi$
$109$			8.56202i			0.820093i	−0.912065	+	0.410047i	$0.865512\pi$
$110$	−4.65824	+	11.0823i	−0.444145	+	1.05666i
$111$		−	19.1267i		−	1.81543i
$112$	0.381640	+	8.68557i	0.0360615	+	0.820709i
$113$	7.12934	−	7.12934i	0.670672	−	0.670672i	−0.287199	−	0.957871i	$-0.592724\pi$
$113$	7.12934	−	7.12934i	0.670672	−	0.670672i	0.957871	+	0.287199i	$0.0927241\pi$
$114$	1.29711	−	1.98816i	0.121485	−	0.186209i
$115$	9.69266	−	1.76539i	0.903845	−	0.164624i
$116$	−2.41866	−	5.49475i	−0.224567	−	0.510175i
$117$	−0.791182	−	0.791182i	−0.0731448	−	0.0731448i
$118$	2.78403	+	13.2352i	0.256291	+	1.21840i
$119$	−10.8823			−0.997578
$120$	7.63150	+	7.38010i	0.696658	+	0.673707i
$121$	−3.45170			−0.313791
$122$	0.106884	+	0.508123i	0.00967680	+	0.0460033i
$123$	−2.52064	−	2.52064i	−0.227279	−	0.227279i
$124$	−6.77857	−	15.3997i	−0.608734	−	1.38293i
$125$	−10.8467	−	2.71091i	−0.970159	−	0.242471i
$126$	0.306280	−	0.469456i	0.0272856	−	0.0418225i
$127$	2.39718	−	2.39718i	0.212715	−	0.212715i	−0.592705	−	0.805420i	$-0.701940\pi$
$127$	2.39718	−	2.39718i	0.212715	−	0.212715i	0.805420	+	0.592705i	$0.201940\pi$
$128$	11.2330	+	1.34883i	0.992868	+	0.119221i
$129$		−	7.07820i		−	0.623201i
$130$	−17.9642	+	7.33161i	−1.57557	+	0.643025i
$131$			2.44655i			0.213756i	0.994272	+	0.106878i	$0.0340855\pi$
$131$			2.44655i			0.213756i	−0.994272	+	0.106878i	$0.965915\pi$
$132$	−4.62393	+	11.8953i	−0.402461	+	1.03535i
$133$	−1.53689	+	1.53689i	−0.133265	+	0.133265i
$134$	−10.2510	−	6.68788i	−0.885548	−	0.577745i
$135$	−2.14037	−	11.7514i	−0.184213	−	1.01140i
$136$	−2.30392	+	13.9728i	−0.197560	+	1.19816i
$137$	−4.35212	−	4.35212i	−0.371827	−	0.371827i	0.496316	−	0.868142i	$-0.334686\pi$
$137$	−4.35212	−	4.35212i	−0.371827	−	0.371827i	−0.868142	+	0.496316i	$0.834686\pi$
$138$	10.2353	−	2.15300i	0.871287	−	0.183275i
$139$	−1.26585			−0.107368			−0.0536840	−	0.998558i	$-0.517096\pi$
$139$	−1.26585			−0.107368			−0.0536840	+	0.998558i	$0.517096\pi$
$140$	−5.44674	−	8.05071i	−0.460334	−	0.680409i
$141$	−5.93832			−0.500097
$142$	6.20533	−	1.30529i	0.520740	−	0.109538i
$143$	−16.4933	−	16.4933i	−1.37924	−	1.37924i
$144$	−0.537935	−	0.492652i	−0.0448279	−	0.0410543i
$145$	5.51985	+	3.81891i	0.458398	+	0.317144i
$146$	−1.65046	−	1.07679i	−0.136593	−	0.0891155i
$147$	−2.70141	+	2.70141i	−0.222809	+	0.222809i
$148$	21.2408	+	8.25670i	1.74598	+	0.678696i
$149$		−	6.85430i		−	0.561526i	−0.959777	−	0.280763i	$-0.909413\pi$
$149$		−	6.85430i		−	0.561526i	0.959777	−	0.280763i	$-0.0905875\pi$
$150$	−11.5891	−	2.56414i	−0.946246	−	0.209361i
$151$		−	3.69443i		−	0.300648i	−0.988637	−	0.150324i	$-0.951968\pi$
$151$		−	3.69443i		−	0.300648i	0.988637	−	0.150324i	$-0.0480318\pi$
$152$	1.64798	+	2.29873i	0.133668	+	0.186452i
$153$	0.645620	−	0.645620i	0.0521952	−	0.0521952i
$154$	6.38484	−	9.78647i	0.514505	−	0.788616i
$155$	15.4700	+	10.7029i	1.24258	+	0.859680i
$156$	−18.8529	+	8.29859i	−1.50944	+	0.664419i
$157$	13.2728	+	13.2728i	1.05929	+	1.05929i	0.998128	+	0.0611582i	$0.0194794\pi$
$157$	13.2728	+	13.2728i	1.05929	+	1.05929i	0.0611582	+	0.998128i	$0.480521\pi$
$158$	4.10607	+	19.5202i	0.326661	+	1.55294i
$159$	−15.3237			−1.21525
$160$	−11.4902	+	5.28914i	−0.908381	+	0.418144i
$161$	−9.57639			−0.754725
$162$	−2.45104	−	11.6522i	−0.192572	−	0.915484i
$163$	−17.1216	−	17.1216i	−1.34107	−	1.34107i	−0.894998	−	0.446069i	$-0.852823\pi$
$163$	−17.1216	−	17.1216i	−1.34107	−	1.34107i	−0.446069	−	0.894998i	$-0.647177\pi$
$164$	3.88737	−	1.71113i	0.303553	−	0.133617i
$165$	−2.55681	−	14.0379i	−0.199047	−	1.09285i
$166$	5.04410	−	7.73143i	0.391498	−	0.600076i
$167$	−14.2420	+	14.2420i	−1.10208	+	1.10208i	−0.107921	+	0.994159i	$0.534420\pi$
$167$	−14.2420	+	14.2420i	−1.10208	+	1.10208i	−0.994159	+	0.107921i	$0.965580\pi$
$168$	−6.01244	−	8.38665i	−0.463870	−	0.647044i
$169$		−	24.6466i		−	1.89589i
$170$	−5.98274	−	14.6591i	−0.458855	−	1.12431i
$171$		−	0.182360i		−	0.0139454i
$172$	7.86055	+	3.05554i	0.599362	+	0.232983i
$173$	−6.44735	+	6.44735i	−0.490183	+	0.490183i	−0.908364	−	0.418181i	$-0.862668\pi$
$173$	−6.44735	+	6.44735i	−0.490183	+	0.490183i	0.418181	+	0.908364i	$0.362668\pi$
$174$	5.96799	+	3.89360i	0.452432	+	0.295173i
$175$	9.90032	+	4.48160i	0.748394	+	0.338777i
$176$	−11.2140	−	10.2700i	−0.845288	−	0.774131i
$177$	−11.3513	−	11.3513i	−0.853218	−	0.853218i
$178$	14.8328	−	3.12008i	1.11177	−	0.233860i
$179$	2.58550			0.193249			0.0966246	−	0.995321i	$-0.469195\pi$
$179$	2.58550			0.193249			0.0966246	+	0.995321i	$0.469195\pi$
$180$	0.800771	+	0.154487i	0.0596859	+	0.0115148i
$181$	8.24031			0.612498			0.306249	−	0.951951i	$-0.400926\pi$
$181$	8.24031			0.612498			0.306249	+	0.951951i	$0.400926\pi$
$182$	18.4558	−	3.88218i	1.36804	−	0.287766i
$183$	−0.435796	−	0.435796i	−0.0322150	−	0.0322150i
$184$	−2.02745	+	12.2960i	−0.149466	+	0.906475i
$185$	−25.0666	+	4.56556i	−1.84294	+	0.335667i
$186$	16.7260	+	10.9123i	1.22641	+	0.800126i
$187$	13.4588	−	13.4588i	0.984208	−	0.984208i
$188$	2.56348	−	6.59469i	0.186961	−	0.480967i
$189$			11.6105i			0.844536i
$190$	−2.91522	−	1.22536i	−0.211492	−	0.0888966i
$191$			10.8399i			0.784350i	0.919891	+	0.392175i	$0.128277\pi$
$191$			10.8399i			0.784350i	−0.919891	+	0.392175i	$0.871723\pi$
$192$	−12.0413	+	5.94437i	−0.869008	+	0.428998i
$193$	2.23316	−	2.23316i	0.160746	−	0.160746i	−0.622151	−	0.782897i	$-0.713741\pi$
$193$	2.23316	−	2.23316i	0.160746	−	0.160746i	0.782897	+	0.622151i	$0.213741\pi$
$194$	13.0976	−	20.0756i	0.940352	−	1.44134i
$195$	13.1030	−	18.9390i	0.938322	−	1.35625i
$196$	−1.83384	−	4.16615i	−0.130989	−	0.297582i
$197$	−4.56128	−	4.56128i	−0.324978	−	0.324978i	0.525695	−	0.850673i	$-0.323805\pi$
$197$	−4.56128	−	4.56128i	−0.324978	−	0.324978i	−0.850673	+	0.525695i	$0.823805\pi$
$198$	0.201811	+	0.959404i	0.0143421	+	0.0681819i
$199$	−7.45582			−0.528529			−0.264264	−	0.964450i	$-0.585129\pi$
$199$	−7.45582			−0.528529			−0.264264	+	0.964450i	$0.585129\pi$
$200$	7.85038	−	11.7631i	0.555106	−	0.831780i
$201$	14.5277			1.02471
$202$	0.0257623	+	0.122473i	0.00181263	+	0.00861720i
$203$	−4.61337	−	4.61337i	−0.323795	−	0.323795i
$204$	−6.77182	−	15.3843i	−0.474122	−	1.07712i
$205$	−2.70177	+	3.90512i	−0.188700	+	0.272746i
$206$	4.49557	−	6.89067i	0.313221	−	0.480095i
$207$	0.568144	−	0.568144i	0.0394887	−	0.0394887i
$208$	−1.07736	−	24.5191i	−0.0747011	−	1.70009i
$209$		−	3.80154i		−	0.262958i
$210$	10.6358	+	4.47056i	0.733942	+	0.308498i
$211$			6.58766i			0.453513i	0.973951	+	0.226757i	$0.0728122\pi$
$211$			6.58766i			0.453513i	−0.973951	+	0.226757i	$0.927188\pi$
$212$	6.61500	−	17.0175i	0.454320	−	1.16876i
$213$	−5.32206	+	5.32206i	−0.364661	+	0.364661i
$214$	−11.1180	−	7.25355i	−0.760011	−	0.495842i
$215$	−9.27638	+	1.68957i	−0.632644	+	0.115228i
$216$	14.9078	+	2.45809i	1.01434	+	0.167252i
$217$	−12.9295	−	12.9295i	−0.877710	−	0.877710i
$218$	11.8492	−	2.49248i	0.802531	−	0.168812i
$219$	2.33905			0.158058
$220$	16.6932	+	3.22050i	1.12545	+	0.217126i
$221$	30.7203			2.06647
$222$	−26.4700	+	5.56797i	−1.77655	+	0.373697i
$223$	8.47362	+	8.47362i	0.567435	+	0.567435i	0.931409	−	0.363974i	$-0.118580\pi$
$223$	8.47362	+	8.47362i	0.567435	+	0.567435i	−0.363974	+	0.931409i	$0.618580\pi$
$224$	11.9091	−	3.05661i	0.795710	−	0.204228i
$225$	−0.853245	+	0.321479i	−0.0568830	+	0.0214320i
$226$	−11.9419	−	7.79107i	−0.794364	−	0.518255i
$227$	4.59972	−	4.59972i	0.305294	−	0.305294i	−0.537787	−	0.843081i	$-0.680739\pi$
$227$	4.59972	−	4.59972i	0.305294	−	0.305294i	0.843081	+	0.537787i	$0.180739\pi$
$228$	−3.12907	−	1.21633i	−0.207228	−	0.0805534i
$229$		−	1.51885i		−	0.100369i	−0.998740	−	0.0501843i	$-0.984019\pi$
$229$		−	1.51885i		−	0.100369i	0.998740	−	0.0501843i	$-0.0159809\pi$
$230$	−5.26480	−	12.9000i	−0.347150	−	0.850602i
$231$			13.8695i			0.912543i
$232$	−6.90025	+	4.94683i	−0.453023	+	0.324775i
$233$	0.157673	−	0.157673i	0.0103295	−	0.0103295i	−0.701923	−	0.712253i	$-0.747675\pi$
$233$	0.157673	−	0.157673i	0.0103295	−	0.0103295i	0.712253	+	0.701923i	$0.247675\pi$
$234$	−0.864618	+	1.32526i	−0.0565218	+	0.0866348i
$235$	1.41748	+	7.78250i	0.0924663	+	0.507675i
$236$	17.5062	−	7.70580i	1.13955	−	0.501605i
$237$	−16.7416	−	16.7416i	−1.08749	−	1.08749i
$238$	3.16793	+	15.0603i	0.205347	+	0.976214i
$239$	−20.2669			−1.31096			−0.655480	−	0.755213i	$-0.727534\pi$
$239$	−20.2669			−1.31096			−0.655480	+	0.755213i	$0.727534\pi$
$240$	7.99192	−	12.7099i	0.515876	−	0.820418i
$241$	−11.9811			−0.771771			−0.385885	−	0.922547i	$-0.626104\pi$
$241$	−11.9811			−0.771771			−0.385885	+	0.922547i	$0.626104\pi$
$242$	1.00482	+	4.77691i	0.0645924	+	0.307071i
$243$	−1.33817	−	1.33817i	−0.0858435	−	0.0858435i
$244$	0.672091	−	0.295839i	0.0430262	−	0.0189391i
$245$	4.18518	+	2.89552i	0.267381	+	0.184988i
$246$	−2.75461	+	4.22217i	−0.175627	+	0.269196i
$247$	4.33858	−	4.33858i	0.276057	−	0.276057i
$248$	−19.3387	+	13.8640i	−1.22801	+	0.880367i
$249$			10.9570i			0.694375i
$250$	−0.594128	+	15.8002i	−0.0375759	+	0.999294i
$251$			2.88741i			0.182251i	0.995839	+	0.0911257i	$0.0290465\pi$
$251$			2.88741i			0.182251i	−0.995839	+	0.0911257i	$0.970953\pi$
$252$	−0.738854	−	0.287206i	−0.0465434	−	0.0180923i
$253$	11.8438	−	11.8438i	0.744610	−	0.744610i
$254$	−4.01537	−	2.61968i	−0.251946	−	0.164374i
$255$	15.4546	+	10.6923i	0.967803	+	0.669576i
$256$	−1.40335	−	15.9383i	−0.0877097	−	0.996146i
$257$	22.1754	+	22.1754i	1.38326	+	1.38326i	0.838756	+	0.544507i	$0.183283\pi$
$257$	22.1754	+	22.1754i	1.38326	+	1.38326i	0.544507	+	0.838756i	$0.316717\pi$
$258$	−9.79572	+	2.06053i	−0.609855	+	0.128283i
$259$	24.7660			1.53888
$260$	15.3760	+	22.7269i	0.953577	+	1.40946i
$261$	0.547400			0.0338832
$262$	3.38585	−	0.712214i	0.209179	−	0.0440007i
$263$	−10.6310	−	10.6310i	−0.655537	−	0.655537i	0.298784	−	0.954321i	$-0.403419\pi$
$263$	−10.6310	−	10.6310i	−0.655537	−	0.655537i	−0.954321	+	0.298784i	$0.903419\pi$
$264$	17.8083	+	2.93635i	1.09603	+	0.180720i
$265$	3.65778	+	20.0826i	0.224696	+	1.23366i
$266$	2.57434	+	1.67954i	0.157843	+	0.102979i
$267$	−12.7215	+	12.7215i	−0.778543	+	0.778543i
$268$	−6.27139	+	16.1335i	−0.383086	+	0.985510i
$269$			13.7693i			0.839531i	0.907633	+	0.419765i	$0.137888\pi$
$269$			13.7693i			0.839531i	−0.907633	+	0.419765i	$0.862112\pi$
$270$	−15.6400	+	6.38306i	−0.951822	+	0.388461i
$271$		−	22.8709i		−	1.38931i	−0.719345	−	0.694653i	$-0.755558\pi$
$271$		−	22.8709i		−	1.38931i	0.719345	−	0.694653i	$-0.244442\pi$
$272$	20.0080	−	0.879143i	1.21316	−	0.0533059i
$273$	−15.8288	+	15.8288i	−0.958002	+	0.958002i
$274$	−4.75608	+	7.28996i	−0.287325	+	0.440403i
$275$	−17.7871	+	6.70169i	−1.07260	+	0.404127i
$276$	−5.95918	−	13.5382i	−0.358701	−	0.814902i
$277$	−16.1699	−	16.1699i	−0.971556	−	0.971556i	0.0280505	−	0.999607i	$-0.491070\pi$
$277$	−16.1699	−	16.1699i	−0.971556	−	0.971556i	−0.999607	+	0.0280505i	$0.991070\pi$
$278$	0.368500	+	1.75184i	0.0221012	+	0.105069i
$279$	1.53415			0.0918471
$280$	−9.55600	+	9.88153i	−0.571081	+	0.590535i
$281$	−5.80090			−0.346052			−0.173026	−	0.984917i	$-0.555355\pi$
$281$	−5.80090			−0.346052			−0.173026	+	0.984917i	$0.555355\pi$
$282$	1.72870	+	8.21821i	0.102943	+	0.489387i
$283$	7.95528	+	7.95528i	0.472892	+	0.472892i	0.902849	−	0.429957i	$-0.141471\pi$
$283$	7.95528	+	7.95528i	0.472892	+	0.472892i	−0.429957	+	0.902849i	$0.641471\pi$
$284$	−3.61286	−	8.20775i	−0.214384	−	0.487040i
$285$	3.69267	−	0.672572i	0.218735	−	0.0398398i
$286$	−18.0242	+	27.6269i	−1.06579	+	1.63361i
$287$	3.26382	−	3.26382i	0.192657	−	0.192657i
$288$	−0.525197	+	0.887879i	−0.0309475	+	0.0523188i
$289$			8.06838i			0.474611i
$290$	3.67822	−	8.75079i	0.215993	−	0.513864i
$291$			28.4512i			1.66784i
$292$	−1.00973	+	2.59758i	−0.0590900	+	0.152012i
$293$	3.13243	−	3.13243i	0.182998	−	0.182998i	−0.609663	−	0.792661i	$-0.708695\pi$
$293$	3.13243	−	3.13243i	0.182998	−	0.182998i	0.792661	+	0.609663i	$0.208695\pi$
$294$	4.52496	+	2.95215i	0.263901	+	0.172173i
$295$	−12.1670	+	17.5861i	−0.708389	+	1.02390i
$296$	5.24328	−	31.7993i	0.304760	−	1.84830i
$297$	−14.3594	−	14.3594i	−0.833217	−	0.833217i
$298$	−9.48585	+	1.99535i	−0.549501	+	0.115587i
$299$	27.0338			1.56341
$300$	−0.174896	+	16.7849i	−0.0100976	+	0.969078i
$301$	9.16510			0.528268
$302$	−5.11282	+	1.07548i	−0.294210	+	0.0618870i
$303$	−0.105040	−	0.105040i	−0.00603442	−	0.00603442i
$304$	2.70154	−	2.94986i	0.154944	−	0.169186i
$305$	−0.467111	+	0.675160i	−0.0267467	+	0.0386596i
$306$	−1.08144	−	0.705545i	−0.0618216	−	0.0403333i
$307$	5.81276	−	5.81276i	0.331752	−	0.331752i	−0.521500	−	0.853251i	$-0.674627\pi$
$307$	5.81276	−	5.81276i	0.331752	−	0.331752i	0.853251	+	0.521500i	$0.174627\pi$
$308$	−15.4024	−	5.98722i	−0.877636	−	0.341153i
$309$			9.76550i			0.555540i
$310$	10.3086	−	24.5251i	0.585491	−	1.39293i
$311$			8.39347i			0.475950i	0.971271	+	0.237975i	$0.0764836\pi$
$311$			8.39347i			0.475950i	−0.971271	+	0.237975i	$0.923516\pi$
$312$	16.9729	+	23.6752i	0.960901	+	1.34035i
$313$	10.6331	−	10.6331i	0.601018	−	0.601018i	−0.339565	−	0.940583i	$-0.610280\pi$
$313$	10.6331	−	10.6331i	0.601018	−	0.601018i	0.940583	+	0.339565i	$0.110280\pi$
$314$	14.5048	−	22.2325i	0.818552	−	1.25465i
$315$	0.871935	−	0.158812i	0.0491280	−	0.00894801i
$316$	25.8192	−	11.3650i	1.45244	−	0.639331i
$317$	8.44977	+	8.44977i	0.474586	+	0.474586i	0.903395	−	0.428809i	$-0.141067\pi$
$317$	8.44977	+	8.44977i	0.474586	+	0.474586i	−0.428809	+	0.903395i	$0.641067\pi$
$318$	4.46088	+	21.2069i	0.250154	+	1.18923i
$319$	11.4113			0.638911
$320$	10.6647	+	14.3619i	0.596175	+	0.802855i
$321$	15.7565			0.879443
$322$	2.78777	+	13.2530i	0.155357	+	0.738563i
$323$	3.54037	+	3.54037i	0.196991	+	0.196991i
$324$	−15.4123	+	6.78413i	−0.856238	+	0.376896i
$325$	−27.9483	−	12.6514i	−1.55029	−	0.701774i
$326$	−18.7108	+	28.6793i	−1.03630	+	1.58840i
$327$	−10.1626	+	10.1626i	−0.561992	+	0.561992i
$328$	−3.49973	−	4.88172i	−0.193240	−	0.269548i
$329$		−	7.68915i		−	0.423916i
$330$	−18.6831	+	7.62499i	−1.02847	+	0.419742i
$331$		−	18.2260i		−	1.00179i	−0.865507	−	0.500896i	$-0.833004\pi$
$331$		−	18.2260i		−	1.00179i	0.865507	−	0.500896i	$-0.166996\pi$
$332$	−12.1681	−	4.72998i	−0.667813	−	0.259591i
$333$	−1.46930	+	1.46930i	−0.0805173	+	0.0805173i
$334$	23.8559	+	15.5639i	1.30534	+	0.851621i
$335$	−3.46778	−	19.0394i	−0.189465	−	1.04023i
$336$	−9.85625	+	10.7622i	−0.537702	+	0.587127i
$337$	13.3812	+	13.3812i	0.728918	+	0.728918i	0.970404	−	0.241486i	$-0.0776349\pi$
$337$	13.3812	+	13.3812i	0.728918	+	0.728918i	−0.241486	+	0.970404i	$0.577635\pi$
$338$	−34.1090	+	7.17484i	−1.85529	+	0.390260i
$339$	16.9242			0.919194
$340$	−18.5456	+	12.5471i	−1.00577	+	0.680461i
$341$	31.9815			1.73189
$342$	−0.252372	+	0.0530865i	−0.0136467	+	0.00287059i
$343$	−14.2561	−	14.2561i	−0.769757	−	0.769757i
$344$	1.94037	−	11.7679i	0.104618	−	0.634484i
$345$	13.6000	+	9.40917i	0.732199	+	0.506573i
$346$	10.7995	+	7.04578i	0.580587	+	0.378783i
$347$	−8.82149	+	8.82149i	−0.473562	+	0.473562i	−0.903065	−	0.429503i	$-0.858689\pi$
$347$	−8.82149	+	8.82149i	−0.473562	+	0.473562i	0.429503	+	0.903065i	$0.358689\pi$
$348$	3.65113	−	9.39273i	0.195721	−	0.503503i
$349$		−	25.6800i		−	1.37462i	−0.726365	−	0.687309i	$-0.758792\pi$
$349$		−	25.6800i		−	1.37462i	0.726365	−	0.687309i	$-0.241208\pi$
$350$	3.32014	−	15.0060i	0.177469	−	0.802103i
$351$		−	32.7759i		−	1.74945i
$352$	−10.9485	+	18.5091i	−0.583555	+	0.986537i
$353$	−11.0134	+	11.0134i	−0.586184	+	0.586184i	−0.936596	−	0.350412i	$-0.886042\pi$
$353$	−11.0134	+	11.0134i	−0.586184	+	0.586184i	0.350412	+	0.936596i	$0.386042\pi$
$354$	−12.4049	+	19.0139i	−0.659315	+	1.01058i
$355$	8.24523	+	5.70447i	0.437611	+	0.302762i
$356$	−8.63594	−	19.6193i	−0.457704	−	1.03982i
$357$	−12.9166	−	12.9166i	−0.683619	−	0.683619i
$358$	−0.752662	−	3.57814i	−0.0397794	−	0.189111i
$359$	4.14442			0.218734			0.109367	−	0.994001i	$-0.465118\pi$
$359$	4.14442			0.218734			0.109367	+	0.994001i	$0.465118\pi$
$360$	−0.0193129	−	1.15318i	−0.00101788	−	0.0607780i
$361$	1.00000			0.0526316
$362$	−2.39883	−	11.4040i	−0.126080	−	0.599381i
$363$	−4.09696	−	4.09696i	−0.215034	−	0.215034i
$364$	−10.7453	−	24.4114i	−0.563207	−	1.27950i
$365$	−0.558333	−	3.06546i	−0.0292245	−	0.160453i
$366$	−0.476246	+	0.729975i	−0.0248938	+	0.0381564i
$367$	21.3402	−	21.3402i	1.11395	−	1.11395i	0.121341	−	0.992611i	$-0.461281\pi$
$367$	21.3402	−	21.3402i	1.11395	−	1.11395i	0.992611	−	0.121341i	$-0.0387194\pi$
$368$	17.6070	−	0.773644i	0.917829	−	0.0403290i
$369$			0.387269i			0.0201604i
$370$	13.6155	+	33.3613i	0.707838	+	1.73437i
$371$		−	19.8417i		−	1.03013i
$372$	10.2327	−	26.3242i	0.530541	−	1.36484i
$373$	−7.48124	+	7.48124i	−0.387364	+	0.387364i	−0.873746	−	0.486382i	$-0.838316\pi$
$373$	−7.48124	+	7.48124i	−0.387364	+	0.387364i	0.486382	+	0.873746i	$0.338316\pi$
$374$	−22.5441	−	14.7081i	−1.16573	−	0.760536i
$375$	−9.65668	−	16.0920i	−0.498669	−	0.830989i
$376$	−9.87282	−	1.62789i	−0.509152	−	0.0839522i
$377$	13.0234	+	13.0234i	0.670738	+	0.670738i
$378$	16.0680	−	3.37991i	0.826450	−	0.173844i
$379$	−25.6659			−1.31837			−0.659184	−	0.751982i	$-0.729098\pi$
$379$	−25.6659			−1.31837			−0.659184	+	0.751982i	$0.729098\pi$
$380$	−0.847156	+	4.39116i	−0.0434582	+	0.225262i
$381$	5.69061			0.291539
$382$	15.0017	−	3.15560i	0.767553	−	0.161455i
$383$	0.0728818	+	0.0728818i	0.00372408	+	0.00372408i	0.708966	−	0.705242i	$-0.249162\pi$
$383$	0.0728818	+	0.0728818i	0.00372408	+	0.00372408i	−0.705242	+	0.708966i	$0.749162\pi$
$384$	11.7319	+	14.9339i	0.598692	+	0.762090i
$385$	18.1767	−	3.31065i	0.926370	−	0.168726i
$386$	−3.74062	−	2.44044i	−0.190393	−	0.124215i
$387$	−0.543743	+	0.543743i	−0.0276400	+	0.0276400i
$388$	−31.5960	−	12.2819i	−1.60404	−	0.623521i
$389$			28.4889i			1.44445i	0.691660	+	0.722223i	$0.256880\pi$
$389$			28.4889i			1.44445i	−0.691660	+	0.722223i	$0.743120\pi$
$390$	−30.0246	−	12.6202i	−1.52035	−	0.639050i
$391$			22.0601i			1.11563i
$392$	−5.23181	+	3.75071i	−0.264246	+	0.189440i
$393$	−2.90391	+	2.90391i	−0.146483	+	0.146483i
$394$	−4.98465	+	7.64031i	−0.251123	+	0.384913i
$395$	−17.9446	+	25.9371i	−0.902892	+	1.30504i
$396$	1.26900	−	0.558582i	0.0637695	−	0.0280698i
$397$	−14.0781	−	14.0781i	−0.706561	−	0.706561i	0.259249	−	0.965810i	$-0.416525\pi$
$397$	−14.0781	−	14.0781i	−0.706561	−	0.706561i	−0.965810	+	0.259249i	$0.916525\pi$
$398$	2.17046	+	10.3183i	0.108795	+	0.517210i
$399$	−3.64838			−0.182647
$400$	−18.5647	−	7.44000i	−0.928233	−	0.372000i
$401$	13.1548			0.656917			0.328459	−	0.944518i	$-0.393471\pi$
$401$	13.1548			0.656917			0.328459	+	0.944518i	$0.393471\pi$
$402$	−4.22916	−	20.1053i	−0.210931	−	1.00276i
$403$	36.4995	+	36.4995i	1.81817	+	1.81817i
$404$	0.161995	−	0.0713063i	0.00805954	−	0.00354762i
$405$	10.7117	−	15.4827i	0.532269	−	0.769340i
$406$	−5.04157	+	7.72756i	−0.250209	+	0.383512i
$407$	−30.6297	+	30.6297i	−1.51826	+	1.51826i
$408$	−19.3194	+	13.8502i	−0.956455	+	0.685688i
$409$			18.3619i			0.907938i	0.891018	+	0.453969i	$0.149992\pi$
$409$			18.3619i			0.907938i	−0.891018	+	0.453969i	$0.850008\pi$
$410$	6.19092	+	2.60223i	0.305748	+	0.128515i
$411$		−	10.3314i		−	0.509610i
$412$	−10.8449	−	4.21561i	−0.534289	−	0.207688i
$413$	14.6981	−	14.6981i	0.723246	−	0.723246i
$414$	−0.951662	−	0.620878i	−0.0467716	−	0.0305145i
$415$	14.3598	−	2.61545i	0.704896	−	0.128388i
$416$	−33.6190	+	8.62870i	−1.64831	+	0.423057i
$417$	−1.50248	−	1.50248i	−0.0735769	−	0.0735769i
$418$	−5.26106	+	1.10666i	−0.257327	+	0.0541286i
$419$	19.6007			0.957557			0.478778	−	0.877936i	$-0.341080\pi$
$419$	19.6007			0.957557			0.478778	+	0.877936i	$0.341080\pi$
$420$	3.09075	−	16.0206i	0.150813	−	0.781727i
$421$	8.18578			0.398950			0.199475	−	0.979903i	$-0.436076\pi$
$421$	8.18578			0.398950			0.199475	+	0.979903i	$0.436076\pi$
$422$	9.11685	−	1.91773i	0.443801	−	0.0933536i
$423$	0.456178	+	0.456178i	0.0221801	+	0.0221801i
$424$	−25.4766	−	4.20075i	−1.23725	−	0.204006i
$425$	10.3238	−	22.8063i	0.500778	−	1.10627i
$426$	8.91464	+	5.81604i	0.431916	+	0.281788i
$427$	0.564284	−	0.564284i	0.0273076	−	0.0273076i
$428$	−6.80183	+	17.4981i	−0.328779	+	0.845802i
$429$		−	39.1530i		−	1.89032i
$430$	5.03868	+	12.3460i	0.242987	+	0.595376i
$431$			22.2804i			1.07321i	0.843834	+	0.536605i	$0.180293\pi$
$431$			22.2804i			1.07321i	−0.843834	+	0.536605i	$0.819707\pi$
$432$	−0.937969	−	21.3468i	−0.0451280	−	1.02705i
$433$	−14.6905	+	14.6905i	−0.705980	+	0.705980i	−0.965687	−	0.259707i	$-0.916374\pi$
$433$	−14.6905	+	14.6905i	−0.705980	+	0.705980i	0.259707	+	0.965687i	$0.416374\pi$
$434$	−14.1296	+	21.6574i	−0.678241	+	1.03959i
$435$	2.01890	+	11.0845i	0.0967989	+	0.531462i
$436$	−6.89883	−	15.6729i	−0.330394	−	0.750595i
$437$	3.11551	+	3.11551i	0.149035	+	0.149035i
$438$	−0.680919	−	3.23708i	−0.0325356	−	0.154673i
$439$	−32.1489			−1.53438			−0.767191	−	0.641419i	$-0.778346\pi$
$439$	−32.1489			−1.53438			−0.767191	+	0.641419i	$0.778346\pi$
$440$	−0.402604	−	24.0397i	−0.0191934	−	1.14605i
$441$	0.415041			0.0197639
$442$	−8.94297	−	42.5147i	−0.425374	−	2.02222i
$443$	3.60072	+	3.60072i	0.171076	+	0.171076i	0.787452	−	0.616376i	$-0.211400\pi$
$443$	3.60072	+	3.60072i	0.171076	+	0.171076i	−0.616376	+	0.787452i	$0.711400\pi$
$444$	15.4113	+	35.0117i	0.731389	+	1.66158i
$445$	19.7089	+	13.6356i	0.934290	+	0.646390i
$446$	9.26013	−	14.1936i	0.438480	−	0.672087i
$447$	8.13562	−	8.13562i	0.384802	−	0.384802i
$448$	−7.69697	−	15.5915i	−0.363648	−	0.736630i
$449$		−	20.0423i		−	0.945855i	−0.881101	−	0.472927i	$-0.843197\pi$
$449$		−	20.0423i		−	0.945855i	0.881101	−	0.472927i	$-0.156803\pi$
$450$	0.693291	+	1.08724i	0.0326821	+	0.0512531i
$451$			8.07316i			0.380150i
$452$	−7.30589	+	18.7948i	−0.343640	+	0.884032i
$453$	4.38506	−	4.38506i	0.206028	−	0.206028i
$454$	−7.70471	−	5.02666i	−0.361600	−	0.235913i
$455$	24.5228	+	16.9662i	1.14965	+	0.795386i
$456$	−0.772410	+	4.68450i	−0.0361714	+	0.219372i
$457$	−10.0424	−	10.0424i	−0.469765	−	0.469765i	0.432073	−	0.901839i	$-0.357782\pi$
$457$	−10.0424	−	10.0424i	−0.469765	−	0.469765i	−0.901839	+	0.432073i	$0.857782\pi$
$458$	−2.10198	+	0.442152i	−0.0982192	+	0.0206604i
$459$	26.7458			1.24839
$460$	−16.3201	+	11.0414i	−0.760927	+	0.514808i
$461$	−13.0150			−0.606168			−0.303084	−	0.952964i	$-0.598016\pi$
$461$	−13.0150			−0.606168			−0.303084	+	0.952964i	$0.598016\pi$
$462$	19.1943	−	4.03753i	0.893001	−	0.187843i
$463$	−10.0773	−	10.0773i	−0.468334	−	0.468334i	0.433041	−	0.901374i	$-0.357441\pi$
$463$	−10.0773	−	10.0773i	−0.468334	−	0.468334i	−0.901374	+	0.433041i	$0.857441\pi$
$464$	8.85477	+	8.10938i	0.411073	+	0.376468i
$465$	5.65820	+	31.0656i	0.262393	+	1.44063i
$466$	−0.264108	−	0.172308i	−0.0122346	−	0.00798202i
$467$	16.3296	−	16.3296i	0.755643	−	0.755643i	−0.219883	−	0.975526i	$-0.570568\pi$
$467$	16.3296	−	16.3296i	0.755643	−	0.755643i	0.975526	+	0.219883i	$0.0705676\pi$
$468$	2.08576	+	0.810774i	0.0964143	+	0.0374780i
$469$			18.8110i			0.868613i
$470$	10.3578	−	4.22725i	0.477769	−	0.194988i
$471$			31.5080i			1.45181i
$472$	−15.7605	−	21.9840i	−0.725435	−	1.01190i
$473$	−11.3351	+	11.3351i	−0.521188	+	0.521188i
$474$	−18.2956	+	28.0429i	−0.840344	+	1.28805i
$475$	−1.76289	−	4.67891i	−0.0808868	−	0.214683i
$476$	19.9202	−	8.76838i	0.913039	−	0.401898i
$477$	1.17716	+	1.17716i	0.0538984	+	0.0538984i
$478$	5.89989	+	28.0480i	0.269855	+	1.28289i
$479$	−6.20061			−0.283313			−0.141657	−	0.989916i	$-0.545243\pi$
$479$	−6.20061			−0.283313			−0.141657	+	0.989916i	$0.545243\pi$
$480$	−19.9160	−	7.36028i	−0.909039	−	0.335949i
$481$	−69.9134			−3.18778
$482$	3.48781	+	16.5810i	0.158865	+	0.755243i
$483$	−11.3666	−	11.3666i	−0.517197	−	0.517197i
$484$	6.31838	−	2.78120i	0.287199	−	0.126418i
$485$	37.2869	−	6.79133i	1.69311	−	0.308378i
$486$	−1.46237	+	2.24148i	−0.0663347	+	0.101676i
$487$	12.2791	−	12.2791i	0.556418	−	0.556418i	−0.371868	−	0.928286i	$-0.621283\pi$
$487$	12.2791	−	12.2791i	0.556418	−	0.556418i	0.928286	+	0.371868i	$0.121283\pi$
$488$	−0.605071	−	0.844004i	−0.0273903	−	0.0382063i
$489$		−	40.6445i		−	1.83801i
$490$	2.78885	−	6.63490i	0.125987	−	0.299734i
$491$			10.5091i			0.474267i	0.971477	+	0.237134i	$0.0762079\pi$
$491$			10.5091i			0.474267i	−0.971477	+	0.237134i	$0.923792\pi$
$492$	6.64507	+	2.58306i	0.299583	+	0.116453i
$493$	−10.6273	+	10.6273i	−0.478631	+	0.478631i
$494$	−7.26728	−	4.74128i	−0.326970	−	0.213320i
$495$	−0.881966	+	1.27479i	−0.0396414	+	0.0572976i
$496$	24.8165	+	22.7274i	1.11429	+	1.02049i
$497$	−6.89118	−	6.89118i	−0.309112	−	0.309112i
$498$	15.1638	−	3.18970i	0.679504	−	0.142934i
$499$	21.2547			0.951490			0.475745	−	0.879583i	$-0.342179\pi$
$499$	21.2547			0.951490			0.475745	+	0.879583i	$0.342179\pi$
$500$	22.0393	−	3.77736i	0.985628	−	0.168929i
$501$	−33.8088			−1.51046
$502$	3.99596	−	0.840550i	0.178348	−	0.0375156i
$503$	14.1016	+	14.1016i	0.628761	+	0.628761i	0.947756	−	0.318995i	$-0.103345\pi$
$503$	14.1016	+	14.1016i	0.628761	+	0.628761i	−0.318995	+	0.947756i	$0.603345\pi$
$504$	−0.182386	+	1.10613i	−0.00812411	+	0.0492709i
$505$	−0.112588	+	0.162735i	−0.00501011	+	0.00724159i
$506$	−19.8387	−	12.9431i	−0.881939	−	0.575390i
$507$	29.2539	−	29.2539i	1.29921	−	1.29921i
$508$	−2.45654	+	6.31959i	−0.108991	+	0.280386i
$509$		−	10.3767i		−	0.459939i	−0.973198	−	0.229969i	$-0.926137\pi$
$509$		−	10.3767i		−	0.459939i	0.973198	−	0.229969i	$-0.0738626\pi$
$510$	10.2984	−	24.5006i	0.456019	−	1.08491i
$511$			3.02868i			0.133981i
$512$	−21.6490	+	6.58194i	−0.956759	+	0.290883i
$513$	3.77726	−	3.77726i	0.166770	−	0.166770i
$514$	24.2337	−	37.1446i	1.06890	−	1.63838i
$515$	12.7982	−	2.33103i	0.563958	−	0.102718i
$516$	5.70324	+	12.9567i	0.251071	+	0.570388i
$517$	9.50967	+	9.50967i	0.418235	+	0.418235i
$518$	−7.20960	−	34.2743i	−0.316771	−	1.50593i
$519$	−15.3052			−0.671823
$520$	26.9763	−	27.8952i	1.18299	−	1.22329i
$521$	−7.61874			−0.333783			−0.166891	−	0.985975i	$-0.553373\pi$
$521$	−7.61874			−0.333783			−0.166891	+	0.985975i	$0.553373\pi$
$522$	−0.159353	−	0.757561i	−0.00697469	−	0.0331576i
$523$	14.6526	+	14.6526i	0.640715	+	0.640715i	0.950731	−	0.310016i	$-0.100334\pi$
$523$	14.6526	+	14.6526i	0.640715	+	0.640715i	−0.310016	+	0.950731i	$0.600334\pi$
$524$	−1.97131	−	4.47844i	−0.0861169	−	0.195642i
$525$	6.43168	+	17.0704i	0.280702	+	0.745015i
$526$	−11.6178	+	17.8073i	−0.506559	+	0.776437i
$527$	−29.7843	+	29.7843i	−1.29742	+	1.29742i
$528$	−1.12047	−	25.5002i	−0.0487620	−	1.10975i
$529$		−	3.58714i		−	0.155963i
$530$	26.7281	−	10.9083i	1.16099	−	0.473828i
$531$			1.74400i			0.0756833i
$532$	1.57495	−	4.05163i	0.0682826	−	0.175661i
$533$	−9.21364	+	9.21364i	−0.399087	+	0.399087i
$534$	21.3090	+	13.9023i	0.922130	+	0.601611i
$535$	−3.76109	−	20.6498i	−0.162606	−	0.892769i
$536$	24.1532	+	3.98254i	1.04326	+	0.172020i
$537$	3.06882	+	3.06882i	0.132430	+	0.132430i
$538$	19.0558	−	4.00838i	0.821552	−	0.172813i
$539$	8.65212			0.372673
$540$	13.3866	+	19.7865i	0.576070	+	0.851476i
$541$	−2.98167			−0.128192			−0.0640961	−	0.997944i	$-0.520416\pi$
$541$	−2.98167			−0.128192			−0.0640961	+	0.997944i	$0.520416\pi$
$542$	−31.6516	+	6.65792i	−1.35955	+	0.285982i
$543$	9.78074	+	9.78074i	0.419732	+	0.419732i
$544$	−7.04119	−	27.4337i	−0.301889	−	1.17621i
$545$	15.7445	+	10.8928i	0.674418	+	0.466597i
$546$	26.5138	+	17.2980i	1.13469	+	0.740286i
$547$	−22.4853	+	22.4853i	−0.961401	+	0.961401i	−0.999282	−	0.0378814i	$-0.987939\pi$
$547$	−22.4853	+	22.4853i	−0.961401	+	0.961401i	0.0378814	+	0.999282i	$0.487939\pi$
$548$	11.4733	+	4.45989i	0.490116	+	0.190517i
$549$			0.0669552i			0.00285758i
$550$	14.4526	+	22.6651i	0.616262	+	0.966443i
$551$			3.00176i			0.127879i
$552$	−17.0011	+	12.1882i	−0.723614	+	0.518763i
$553$	21.6777	−	21.6777i	0.921828	−	0.921828i
$554$	−17.6708	+	27.0852i	−0.750760	+	1.15074i
$555$	−35.1716	−	24.3335i	−1.49295	−	1.03290i
$556$	2.31715	−	1.01996i	0.0982691	−	0.0432557i
$557$	−1.94430	−	1.94430i	−0.0823826	−	0.0823826i	0.664715	−	0.747097i	$-0.268553\pi$
$557$	−1.94430	−	1.94430i	−0.0823826	−	0.0823826i	−0.747097	+	0.664715i	$0.768553\pi$
$558$	−0.446605	−	2.12315i	−0.0189063	−	0.0898801i
$559$	−25.8728			−1.09430
$560$	16.4572	+	10.3482i	0.695442	+	0.437292i
$561$	31.9496			1.34891
$562$	1.68869	+	8.02802i	0.0712332	+	0.338642i
$563$	−33.3549	−	33.3549i	−1.40574	−	1.40574i	−0.780163	−	0.625577i	$-0.784864\pi$
$563$	−33.3549	−	33.3549i	−1.40574	−	1.40574i	−0.625577	−	0.780163i	$-0.715136\pi$
$564$	10.8702	−	4.78479i	0.457717	−	0.201476i
$565$	−4.03981	−	22.1801i	−0.169956	−	0.933122i
$566$	8.69368	−	13.3254i	0.365422	−	0.560108i
$567$	−12.9401	+	12.9401i	−0.543432	+	0.543432i
$568$	−10.3072	+	7.38928i	−0.432480	+	0.310047i
$569$		−	5.38489i		−	0.225746i	−0.993609	−	0.112873i	$-0.963995\pi$
$569$		−	5.38489i		−	0.225746i	0.993609	−	0.112873i	$-0.0360054\pi$
$570$	−2.00576	−	4.91460i	−0.0840122	−	0.205850i
$571$		−	27.7359i		−	1.16071i	−0.814363	−	0.580356i	$-0.802913\pi$
$571$		−	27.7359i		−	1.16071i	0.814363	−	0.580356i	$-0.197087\pi$
$572$	43.4806	+	16.9017i	1.81801	+	0.706696i
$573$	−12.8663	+	12.8663i	−0.537498	+	0.537498i
$574$	−5.46702	−	3.56676i	−0.228189	−	0.148874i
$575$	9.08492	−	20.0695i	0.378867	−	0.836957i
$576$	1.38165	+	0.468364i	0.0575687	+	0.0195152i
$577$	−6.92326	−	6.92326i	−0.288219	−	0.288219i	0.548157	−	0.836376i	$-0.315330\pi$
$577$	−6.92326	−	6.92326i	−0.288219	−	0.288219i	−0.836376	+	0.548157i	$0.815330\pi$
$578$	11.1661	−	2.34878i	0.464447	−	0.0976964i
$579$	5.30124			0.220312
$580$	−13.1812	−	2.54296i	−0.547320	−	0.105591i
$581$	−14.1876			−0.588599
$582$	39.3745	−	8.28242i	1.63212	−	0.343317i
$583$	24.5395	+	24.5395i	1.01632	+	1.01632i
$584$	3.88881	+	0.641212i	0.160920	+	0.0265336i
$585$	−2.46144	+	0.448319i	−0.101768	+	0.0185357i
$586$	−5.24693	−	3.42317i	−0.216749	−	0.141410i
$587$	10.8409	−	10.8409i	0.447453	−	0.447453i	−0.447054	−	0.894507i	$-0.647527\pi$
$587$	10.8409	−	10.8409i	0.447453	−	0.447453i	0.894507	+	0.447054i	$0.147527\pi$
$588$	2.76831	−	7.12162i	0.114163	−	0.293691i
$589$			8.41277i			0.346642i
$590$	27.8798	+	11.7187i	1.14779	+	0.482453i
$591$		−	10.8279i		−	0.445400i
$592$	−45.5343	+	2.00076i	−1.87145	+	0.0822306i
$593$	26.9019	−	26.9019i	1.10473	−	1.10473i	0.110895	−	0.993832i	$-0.464628\pi$
$593$	26.9019	−	26.9019i	1.10473	−	1.10473i	0.993832	−	0.110895i	$-0.0353718\pi$
$594$	−15.6922	+	24.0525i	−0.643860	+	0.986888i
$595$	−13.8447	+	20.0111i	−0.567578	+	0.820376i
$596$	5.52284	+	12.5469i	0.226224	+	0.513940i
$597$	−8.84959	−	8.84959i	−0.362190	−	0.362190i
$598$	−7.86979	−	37.4128i	−0.321820	−	1.52992i
$599$	40.6502			1.66092			0.830462	−	0.557076i	$-0.188077\pi$
$599$	40.6502			1.66092			0.830462	+	0.557076i	$0.188077\pi$
$600$	23.2800	−	4.64420i	0.950403	−	0.189599i
$601$	−25.6431			−1.04600			−0.523001	−	0.852332i	$-0.675188\pi$
$601$	−25.6431			−1.04600			−0.523001	+	0.852332i	$0.675188\pi$
$602$	−2.66804	−	12.6838i	−0.108741	−	0.516955i
$603$	−1.11601	−	1.11601i	−0.0454475	−	0.0454475i
$604$	2.97678	+	6.76269i	0.121123	+	0.275170i
$605$	−4.39134	+	6.34723i	−0.178534	+	0.258052i
$606$	−0.114790	+	0.175947i	−0.00466303	+	0.00714734i
$607$	9.68289	−	9.68289i	0.393016	−	0.393016i	−0.482745	−	0.875761i	$-0.660360\pi$
$607$	9.68289	−	9.68289i	0.393016	−	0.393016i	0.875761	+	0.482745i	$0.160360\pi$
$608$	−4.86884	−	2.88001i	−0.197457	−	0.116800i
$609$		−	10.9516i		−	0.443780i
$610$	1.07035	+	0.449902i	0.0433373	+	0.0182160i
$611$			21.7062i			0.878139i
$612$	−0.661607	+	1.70202i	−0.0267439	+	0.0688001i
$613$	14.9284	−	14.9284i	0.602952	−	0.602952i	−0.338143	−	0.941095i	$-0.609799\pi$
$613$	14.9284	−	14.9284i	0.602952	−	0.602952i	0.941095	+	0.338143i	$0.109799\pi$
$614$	−9.73658	−	6.35229i	−0.392937	−	0.256358i
$615$	−7.84196	+	1.42831i	−0.316219	+	0.0575951i
$616$	−3.80209	+	23.0588i	−0.153190	+	0.929066i
$617$	12.4652	+	12.4652i	0.501830	+	0.501830i	0.912006	−	0.410176i	$-0.134533\pi$
$617$	12.4652	+	12.4652i	0.501830	+	0.501830i	−0.410176	+	0.912006i	$0.634533\pi$
$618$	13.5147	−	2.84283i	0.543643	−	0.114355i
$619$	−0.783581			−0.0314948			−0.0157474	−	0.999876i	$-0.505013\pi$
$619$	−0.783581			−0.0314948			−0.0157474	+	0.999876i	$0.505013\pi$
$620$	−36.9418	−	7.12693i	−1.48362	−	0.286224i
$621$	23.5362			0.944476
$622$	11.6159	−	2.44341i	0.465757	−	0.0979720i
$623$	−16.4722	−	16.4722i	−0.659946	−	0.659946i
$624$	27.8238	−	30.3813i	1.11384	−	1.21623i
$625$	−18.7845	+	16.4968i	−0.751378	+	0.659872i
$626$	−17.8108	−	11.6200i	−0.711864	−	0.464430i
$627$	4.51219	−	4.51219i	0.180199	−	0.180199i
$628$	−34.9906	−	13.6015i	−1.39628	−	0.542759i
$629$		−	57.0507i		−	2.27476i
$630$	−0.473612	−	1.16046i	−0.0188691	−	0.0462340i
$631$		−	36.7340i		−	1.46236i	−0.682186	−	0.731179i	$-0.738971\pi$
$631$		−	36.7340i		−	1.46236i	0.682186	−	0.731179i	$-0.261029\pi$
$632$	−23.2445	−	32.4234i	−0.924618	−	1.28973i
$633$	−7.81914	+	7.81914i	−0.310783	+	0.310783i
$634$	9.23406	−	14.1537i	0.366731	−	0.562114i
$635$	−1.35835	−	7.45786i	−0.0539045	−	0.295956i
$636$	28.0503	−	12.3471i	1.11226	−	0.489593i
$637$	9.87440	+	9.87440i	0.391238	+	0.391238i
$638$	−3.32194	−	15.7924i	−0.131517	−	0.625228i
$639$	0.817674			0.0323467
$640$	16.7712	−	18.9400i	0.662942	−	0.748671i
$641$	−30.6773			−1.21168			−0.605840	−	0.795586i	$-0.707163\pi$
$641$	−30.6773			−1.21168			−0.605840	+	0.795586i	$0.707163\pi$
$642$	−4.58687	−	21.8059i	−0.181029	−	0.860609i
$643$	−13.0109	−	13.0109i	−0.513098	−	0.513098i	0.402376	−	0.915474i	$-0.368184\pi$
$643$	−13.0109	−	13.0109i	−0.513098	−	0.513098i	−0.915474	+	0.402376i	$0.868184\pi$
$644$	17.5297	−	7.71616i	0.690767	−	0.304059i
$645$	−13.0159	−	9.00506i	−0.512500	−	0.354574i
$646$	3.86898	−	5.93024i	0.152223	−	0.233322i
$647$	26.5081	−	26.5081i	1.04214	−	1.04214i	0.0430687	−	0.999072i	$-0.486287\pi$
$647$	26.5081	−	26.5081i	1.04214	−	1.04214i	0.999072	−	0.0430687i	$-0.0137134\pi$
$648$	13.8754	+	19.3546i	0.545077	+	0.760319i
$649$			36.3562i			1.42710i
$650$	−9.37264	+	42.3613i	−0.367625	+	1.66155i
$651$		−	30.6930i		−	1.20295i
$652$	45.1370	+	17.5456i	1.76770	+	0.687138i
$653$	−3.96735	+	3.96735i	−0.155255	+	0.155255i	−0.780460	−	0.625206i	$-0.785015\pi$
$653$	−3.96735	+	3.96735i	−0.155255	+	0.155255i	0.625206	+	0.780460i	$0.285015\pi$
$654$	17.0227	+	11.1059i	0.665640	+	0.434274i
$655$	4.49890	+	3.11257i	0.175786	+	0.121618i
$656$	−5.73714	+	6.26448i	−0.223998	+	0.244587i
$657$	−0.179684	−	0.179684i	−0.00701015	−	0.00701015i
$658$	−10.6412	+	2.23838i	−0.414838	+	0.0872612i
$659$	−28.2509			−1.10050			−0.550250	−	0.835000i	$-0.685468\pi$
$659$	−28.2509			−1.10050			−0.550250	+	0.835000i	$0.685468\pi$
$660$	15.9912	+	23.6363i	0.622458	+	0.920042i
$661$	1.71072			0.0665392			0.0332696	−	0.999446i	$-0.489408\pi$
$661$	1.71072			0.0665392			0.0332696	+	0.999446i	$0.489408\pi$
$662$	−25.2235	+	5.30576i	−0.980339	+	0.206214i
$663$	36.4631	+	36.4631i	1.41611	+	1.41611i
$664$	−3.00370	+	18.2167i	−0.116566	+	0.706947i
$665$	0.870870	+	4.78140i	0.0337709	+	0.185415i
$666$	2.46114	+	1.60568i	0.0953671	+	0.0622189i
$667$	−9.35203	+	9.35203i	−0.362112	+	0.362112i
$668$	14.5947	−	37.5457i	0.564686	−	1.45269i
$669$			20.1153i			0.777703i
$670$	−25.3397	+	10.3417i	−0.978957	+	0.399535i
$671$			1.39577i			0.0538833i
$672$	17.7634	+	10.5074i	0.685237	+	0.405330i
$673$	7.10338	−	7.10338i	0.273815	−	0.273815i	−0.556819	−	0.830634i	$-0.687978\pi$
$673$	7.10338	−	7.10338i	0.273815	−	0.273815i	0.830634	+	0.556819i	$0.187978\pi$
$674$	14.6232	−	22.4139i	0.563264	−	0.863352i
$675$	−24.3324	−	11.0146i	−0.936553	−	0.423952i
$676$	19.8589	+	45.1158i	0.763804	+	1.73522i
$677$	13.1079	+	13.1079i	0.503779	+	0.503779i	0.912610	−	0.408831i	$-0.134063\pi$
$677$	13.1079	+	13.1079i	0.503779	+	0.503779i	−0.408831	+	0.912610i	$0.634063\pi$
$678$	−4.92678	−	23.4218i	−0.189212	−	0.899509i
$679$	−36.8397			−1.41378
$680$	22.7630	+	22.0132i	0.872923	+	0.844166i
$681$	10.9192			0.418423
$682$	−9.31010	−	44.2600i	−0.356502	−	1.69480i
$683$	−23.7689	−	23.7689i	−0.909491	−	0.909491i	0.0867400	−	0.996231i	$-0.472355\pi$
$683$	−23.7689	−	23.7689i	−0.909491	−	0.909491i	−0.996231	+	0.0867400i	$0.972355\pi$
$684$	0.146936	+	0.333811i	0.00561823	+	0.0127636i
$685$	−13.5399	+	2.46611i	−0.517331	+	0.0942251i
$686$	−15.5793	+	23.8795i	−0.594821	+	0.911723i
$687$	1.80278	−	1.80278i	0.0687805	−	0.0687805i
$688$	−16.8508	+	0.740417i	−0.642432	+	0.0282281i
$689$			56.0124i			2.13390i
$690$	9.06253	−	21.5605i	0.345005	−	0.820794i
$691$			20.3717i			0.774975i	0.921875	+	0.387488i	$0.126657\pi$
$691$			20.3717i			0.774975i	−0.921875	+	0.387488i	$0.873343\pi$
$692$	6.60700	−	16.9969i	0.251161	−	0.646124i
$693$	1.06544	−	1.06544i	0.0404728	−	0.0404728i
$694$	14.7763	+	9.64029i	0.560901	+	0.365940i
$695$	−1.61044	+	2.32773i	−0.0610876	+	0.0882959i
$696$	−14.0617	−	2.31859i	−0.533009	−	0.0878859i
$697$	−7.51851	−	7.51851i	−0.284784	−	0.284784i
$698$	−35.5393	+	7.47568i	−1.34518	+	0.282959i
$699$	0.374296			0.0141572
$700$	−21.7337	−	0.226461i	−0.821457	−	0.00855942i
$701$	−15.4547			−0.583718			−0.291859	−	0.956461i	$-0.594274\pi$
$701$	−15.4547			−0.583718			−0.291859	+	0.956461i	$0.594274\pi$
$702$	−45.3595	+	9.54136i	−1.71198	+	0.360116i
$703$	−8.05718	−	8.05718i	−0.303882	−	0.303882i
$704$	28.8024	+	9.76371i	1.08553	+	0.367984i
$705$	−7.55488	+	10.9198i	−0.284533	+	0.411264i
$706$	18.4479	+	12.0356i	0.694294	+	0.452968i
$707$	0.136010	−	0.136010i	0.00511518	−	0.00511518i
$708$	29.9250	+	11.6324i	1.12465	+	0.437173i
$709$			37.3153i			1.40141i	0.713454	+	0.700703i	$0.247130\pi$
$709$			37.3153i			1.40141i	−0.713454	+	0.700703i	$0.752870\pi$
$710$	5.49432	−	13.0714i	0.206198	−	0.490562i
$711$			2.57216i			0.0964637i
$712$	−24.6376	+	17.6629i	−0.923335	+	0.661944i
$713$	−26.2101	+	26.2101i	−0.981576	+	0.981576i
$714$	−14.1155	+	21.6358i	−0.528259	+	0.809699i
$715$	−51.3122	+	9.34584i	−1.91897	+	0.349515i
$716$	−4.73278	+	2.08326i	−0.176872	+	0.0778550i
$717$	−24.0556	−	24.0556i	−0.898373	−	0.898373i
$718$	−1.20648	−	5.73557i	−0.0450253	−	0.214050i
$719$	20.7971			0.775602			0.387801	−	0.921743i	$-0.373235\pi$
$719$	20.7971			0.775602			0.387801	+	0.921743i	$0.373235\pi$
$720$	−1.59030	+	0.362429i	−0.0592669	+	0.0135069i
$721$	−12.6447			−0.470914
$722$	−0.291109	−	1.38393i	−0.0108340	−	0.0515045i
$723$	−14.2208	−	14.2208i	−0.528878	−	0.528878i
$724$	−15.0840	+	6.63961i	−0.560592	+	0.246759i
$725$	14.0450	−	5.29176i	0.521617	−	0.196531i
$726$	−4.47723	+	6.86255i	−0.166166	+	0.254693i
$727$	12.6284	−	12.6284i	0.468361	−	0.468361i	−0.433022	−	0.901383i	$-0.642553\pi$
$727$	12.6284	−	12.6284i	0.468361	−	0.468361i	0.901383	+	0.433022i	$0.142553\pi$
$728$	−30.6555	+	21.9771i	−1.13617	+	0.814526i
$729$		−	28.4356i		−	1.05317i
$730$	−4.07983	+	1.66507i	−0.151001	+	0.0616271i
$731$		−	21.1127i		−	0.780880i
$732$	1.14887	+	0.446588i	0.0424635	+	0.0165064i
$733$	−0.538751	+	0.538751i	−0.0198992	+	0.0198992i	−0.716986	−	0.697087i	$-0.754479\pi$
$733$	−0.538751	+	0.538751i	−0.0198992	+	0.0198992i	0.697087	+	0.716986i	$0.254479\pi$
$734$	−35.7457	−	23.3210i	−1.31940	−	0.860794i
$735$	1.53074	+	8.40435i	0.0564623	+	0.309999i
$736$	−6.19623	−	24.1416i	−0.228396	−	0.889872i
$737$	−23.2648	−	23.2648i	−0.856971	−	0.856971i
$738$	0.535952	−	0.112737i	0.0197287	−	0.00414992i
$739$	7.58704			0.279094			0.139547	−	0.990215i	$-0.455435\pi$
$739$	7.58704			0.279094			0.139547	+	0.990215i	$0.455435\pi$
$740$	42.2061	−	28.5547i	1.55153	−	1.04969i
$741$	10.2992			0.378352
$742$	−27.4595	+	5.77610i	−1.00807	+	0.212047i
$743$	35.1805	+	35.1805i	1.29065	+	1.29065i	0.934387	+	0.356259i	$0.115948\pi$
$743$	35.1805	+	35.1805i	1.29065	+	1.29065i	0.356259	+	0.934387i	$0.384052\pi$
$744$	−39.4096	−	6.49811i	−1.44483	−	0.238232i
$745$	−12.6042	−	8.72021i	−0.461781	−	0.319484i
$746$	12.5314	+	8.17564i	0.458806	+	0.299331i
$747$	0.841713	−	0.841713i	0.0307967	−	0.0307967i
$748$	−13.7921	+	35.4810i	−0.504290	+	1.29731i
$749$			20.4021i			0.745476i
$750$	−19.4591	+	18.0487i	−0.710545	+	0.659045i
$751$		−	36.7777i		−	1.34204i	−0.741441	−	0.671018i	$-0.765857\pi$
$751$		−	36.7777i		−	1.34204i	0.741441	−	0.671018i	$-0.234143\pi$
$752$	0.621180	+	14.1372i	0.0226521	+	0.515529i
$753$	−3.42717	+	3.42717i	−0.124893	+	0.124893i
$754$	14.2322	−	21.8146i	0.518306	−	0.794442i
$755$	−6.79358	−	4.70015i	−0.247244	−	0.171056i
$756$	−9.35510	−	21.2531i	−0.340242	−	0.772966i
$757$	25.0633	+	25.0633i	0.910942	+	0.910942i	0.996346	−	0.0854047i	$-0.0272183\pi$
$757$	25.0633	+	25.0633i	0.910942	+	0.910942i	−0.0854047	+	0.996346i	$0.527218\pi$
$758$	7.47157	+	35.5197i	0.271380	+	1.29013i
$759$	28.1156			1.02053
$760$	6.32367	−	0.105905i	0.229384	−	0.00384160i
$761$	1.70937			0.0619646			0.0309823	−	0.999520i	$-0.490136\pi$
$761$	1.70937			0.0619646			0.0309823	+	0.999520i	$0.490136\pi$
$762$	−1.65659	−	7.87539i	−0.0600118	−	0.285295i
$763$	−13.1589	−	13.1589i	−0.476383	−	0.476383i
$764$	−8.73426	−	19.8426i	−0.315994	−	0.717881i
$765$	−0.365837	−	2.00858i	−0.0132269	−	0.0726205i
$766$	0.0796466	−	0.122080i	0.00287775	−	0.00441092i
$767$	−41.4922	+	41.4922i	−1.49820	+	1.49820i
$768$	17.2521	−	20.5835i	0.622532	−	0.742743i
$769$		−	21.7516i		−	0.784384i	−0.919883	−	0.392192i	$-0.871717\pi$
$769$		−	21.7516i		−	0.784384i	0.919883	−	0.392192i	$-0.128283\pi$
$770$	−9.87310	−	24.1915i	−0.355802	−	0.871800i
$771$			52.6416i			1.89584i
$772$	−2.28846	+	5.88719i	−0.0823635	+	0.211884i
$773$	−7.92601	+	7.92601i	−0.285079	+	0.285079i	−0.835131	−	0.550052i	$-0.814608\pi$
$773$	−7.92601	+	7.92601i	−0.285079	+	0.285079i	0.550052	+	0.835131i	$0.314608\pi$
$774$	0.910789	+	0.594212i	0.0327376	+	0.0213585i
$775$	39.3626	−	14.8308i	1.41395	−	0.532737i
$776$	−7.79944	+	47.3019i	−0.279984	+	1.69804i
$777$	29.3956	+	29.3956i	1.05456	+	1.05456i
$778$	39.4266	−	8.29339i	1.41351	−	0.297332i
$779$	−2.12365			−0.0760878
$780$	−8.72507	+	45.2257i	−0.312408	+	1.61934i
$781$	17.0456			0.609938
$782$	30.5296	−	6.42190i	1.09174	−	0.229647i
$783$	11.3384	+	11.3384i	0.405203	+	0.405203i
$784$	6.71374	+	6.14858i	0.239776	+	0.219592i
$785$	41.2930	−	7.52098i	1.47381	−	0.268435i
$786$	4.86415	+	3.17344i	0.173498	+	0.113193i
$787$	−16.2001	+	16.2001i	−0.577472	+	0.577472i	−0.934206	−	0.356734i	$-0.883890\pi$
$787$	−16.2001	+	16.2001i	−0.577472	+	0.577472i	0.356734	+	0.934206i	$0.383890\pi$
$788$	12.0247	+	4.67423i	0.428363	+	0.166513i
$789$		−	25.2367i		−	0.898450i
$790$	41.1189	+	17.2835i	1.46294	+	0.614920i
$791$			21.9140i			0.779172i
$792$	−1.14245	−	1.59359i	−0.0405953	−	0.0566258i
$793$	−1.59295	+	1.59295i	−0.0565675	+	0.0565675i
$794$	−15.3848	+	23.5814i	−0.545988	+	0.836872i
$795$	−19.4952	+	28.1783i	−0.691425	+	0.999383i
$796$	13.6480	−	6.00751i	0.483739	−	0.212931i
$797$	30.5067	+	30.5067i	1.08060	+	1.08060i	0.996453	+	0.0841479i	$0.0268168\pi$
$797$	30.5067	+	30.5067i	1.08060	+	1.08060i	0.0841479	+	0.996453i	$0.473183\pi$
$798$	1.06208	+	5.04909i	0.0375971	+	0.178736i
$799$	−17.7127			−0.626629
$800$	−4.89209	+	27.8580i	−0.172961	+	0.984929i
$801$	1.95451			0.0690594
$802$	−3.82947	−	18.2052i	−0.135223	−	0.642849i
$803$	−3.74577	−	3.74577i	−0.132185	−	0.132185i
$804$	−26.5932	+	11.7057i	−0.937870	+	0.412828i
$805$	−12.1833	+	17.6097i	−0.429406	+	0.620662i
$806$	39.8873	−	61.1379i	1.40497	−	2.15349i
$807$	−16.3433	+	16.3433i	−0.575312	+	0.575312i
$808$	−0.145841	−	0.203431i	−0.00513067	−	0.00715668i
$809$		−	40.5074i		−	1.42417i	−0.702096	−	0.712083i	$-0.747752\pi$
$809$		−	40.5074i		−	1.42417i	0.702096	−	0.712083i	$-0.252248\pi$
$810$	−24.5452	−	10.3171i	−0.862430	−	0.362505i
$811$		−	55.0958i		−	1.93468i	−0.253489	−	0.967338i	$-0.581578\pi$
$811$		−	55.0958i		−	1.93468i	0.253489	−	0.967338i	$-0.418422\pi$
$812$	12.1620	+	4.72761i	0.426804	+	0.165907i
$813$	27.1463	−	27.1463i	0.952062	−	0.952062i
$814$	51.3058	+	33.4727i	1.79827	+	1.17322i
$815$	−53.2669	+	9.70188i	−1.86586	+	0.339842i
$816$	24.7918	+	22.7048i	0.867885	+	0.794827i
$817$	−2.98171	−	2.98171i	−0.104317	−	0.104317i
$818$	25.4115	−	5.34532i	0.888494	−	0.186895i
$819$	2.43191			0.0849780
$820$	1.79907	−	9.32531i	0.0628261	−	0.325654i
$821$	−33.8381			−1.18096			−0.590478	−	0.807053i	$-0.701061\pi$
$821$	−33.8381			−1.18096			−0.590478	+	0.807053i	$0.701061\pi$
$822$	−14.2979	+	3.00756i	−0.498696	+	0.104901i
$823$	−20.4825	−	20.4825i	−0.713975	−	0.713975i	0.253390	−	0.967364i	$-0.418455\pi$
$823$	−20.4825	−	20.4825i	−0.713975	−	0.713975i	−0.967364	+	0.253390i	$0.918455\pi$
$824$	−2.67705	+	16.2357i	−0.0932596	+	0.565599i
$825$	−29.0666	−	13.1577i	−1.01197	−	0.458091i
$826$	−24.6198	−	16.0623i	−0.856634	−	0.558880i
$827$	32.1825	−	32.1825i	1.11910	−	1.11910i	0.127221	−	0.991874i	$-0.459394\pi$
$827$	32.1825	−	32.1825i	1.11910	−	1.11910i	0.991874	−	0.127221i	$-0.0406058\pi$
$828$	−0.582213	+	1.49777i	−0.0202333	+	0.0520512i
$829$		−	17.4030i		−	0.604432i	−0.953239	−	0.302216i	$-0.902274\pi$
$829$		−	17.4030i		−	0.604432i	0.953239	−	0.302216i	$-0.0977264\pi$
$830$	−7.79987	−	19.1116i	−0.270738	−	0.663372i
$831$		−	38.3854i		−	1.33157i
$832$	21.7283	+	44.0143i	0.753293	+	1.52592i
$833$	−8.05770	+	8.05770i	−0.279183	+	0.279183i
$834$	−1.64194	+	2.51671i	−0.0568558	+	0.0871467i
$835$	8.07018	+	44.3083i	0.279280	+	1.53335i
$836$	3.06308	+	6.95876i	0.105939	+	0.240674i
$837$	31.7772	+	31.7772i	1.09838	+	1.09838i
$838$	−5.70594	−	27.1259i	−0.197108	−	0.937050i
$839$	−15.7546			−0.543908			−0.271954	−	0.962310i	$-0.587670\pi$
$839$	−15.7546			−0.543908			−0.271954	+	0.962310i	$0.587670\pi$
$840$	−23.0711	+	0.386383i	−0.796030	+	0.0133315i
$841$	19.9894			0.689291
$842$	−2.38295	−	11.3285i	−0.0821220	−	0.390407i
$843$	−6.88530	−	6.88530i	−0.237142	−	0.237142i
$844$	−5.30800	−	12.0588i	−0.182709	−	0.415081i
$845$	−45.3218	−	31.3560i	−1.55912	−	1.07868i
$846$	0.498520	−	0.764115i	0.0171395	−	0.0262708i
$847$	5.30488	−	5.30488i	0.182278	−	0.182278i
$848$	1.60294	+	36.4807i	0.0550453	+	1.25275i
$849$			18.8848i			0.648126i
$850$	−34.5677	−	7.64826i	−1.18566	−	0.262333i
$851$		−	50.2045i		−	1.72099i
$852$	5.45385	−	14.0303i	0.186846	−	0.480671i
$853$	18.6933	−	18.6933i	0.640046	−	0.640046i	−0.310521	−	0.950567i	$-0.600503\pi$
$853$	18.6933	−	18.6933i	0.640046	−	0.640046i	0.950567	+	0.310521i	$0.100503\pi$
$854$	−0.945197	−	0.616660i	−0.0323440	−	0.0211017i
$855$	−0.335336	−	0.232002i	−0.0114682	−	0.00793431i
$856$	26.1962	+	4.31939i	0.895366	+	0.147634i
$857$	21.0431	+	21.0431i	0.718820	+	0.718820i	0.968363	−	0.249544i	$-0.0802807\pi$
$857$	21.0431	+	21.0431i	0.718820	+	0.718820i	−0.249544	+	0.968363i	$0.580281\pi$
$858$	−54.1849	+	11.3978i	−1.84984	+	0.389114i
$859$	−17.5794			−0.599802			−0.299901	−	0.953970i	$-0.596954\pi$
$859$	−17.5794			−0.599802			−0.299901	+	0.953970i	$0.596954\pi$
$860$	15.6191	−	10.5672i	0.532608	−	0.360338i
$861$	7.74790			0.264048
$862$	30.8345	−	6.48603i	1.05023	−	0.220915i
$863$	8.22730	+	8.22730i	0.280061	+	0.280061i	0.833133	−	0.553073i	$-0.186545\pi$
$863$	8.22730	+	8.22730i	0.280061	+	0.280061i	−0.553073	+	0.833133i	$0.686545\pi$
$864$	−29.2694	+	7.51233i	−0.995765	+	0.255575i
$865$	3.65336	+	20.0583i	0.124218	+	0.682003i
$866$	24.6071	+	16.0541i	0.836184	+	0.545539i
$867$	−9.57666	+	9.57666i	−0.325241	+	0.325241i
$868$	34.0855	+	13.2497i	1.15694	+	0.449723i
$869$			53.6204i			1.81895i
$870$	14.7525	−	6.02082i	0.500155	−	0.204125i
$871$		−	53.1029i		−	1.79932i
$872$	−19.6818	+	14.1100i	−0.666510	+	0.477825i
$873$	2.18561	−	2.18561i	0.0739716	−	0.0739716i
$874$	3.40469	−	5.21860i	0.115165	−	0.176522i
$875$	20.8365	−	12.5038i	0.704403	−	0.422706i
$876$	−4.28166	+	1.88468i	−0.144664	+	0.0636776i
$877$	33.8945	+	33.8945i	1.14454	+	1.14454i	0.987610	+	0.156927i	$0.0501588\pi$
$877$	33.8945	+	33.8945i	1.14454	+	1.14454i	0.156927	+	0.987610i	$0.449841\pi$
$878$	9.35883	+	44.4917i	0.315845	+	1.50152i
$879$	7.43599			0.250810
$880$	−33.1520	+	7.55534i	−1.11755	+	0.254691i
$881$	−11.0878			−0.373559			−0.186779	−	0.982402i	$-0.559805\pi$
$881$	−11.0878			−0.373559			−0.186779	+	0.982402i	$0.559805\pi$
$882$	−0.120822	−	0.574387i	−0.00406830	−	0.0193406i
$883$	31.6330	+	31.6330i	1.06453	+	1.06453i	0.997769	+	0.0667658i	$0.0212680\pi$
$883$	31.6330	+	31.6330i	1.06453	+	1.06453i	0.0667658	+	0.997769i	$0.478732\pi$
$884$	−56.2339	+	24.7528i	−1.89135	+	0.832528i
$885$	−35.3150	+	6.43217i	−1.18710	+	0.216215i
$886$	3.93494	−	6.03134i	0.132197	−	0.202627i
$887$	−31.7740	+	31.7740i	−1.06687	+	1.06687i	−0.0692669	+	0.997598i	$0.522066\pi$
$887$	−31.7740	+	31.7740i	−1.06687	+	1.06687i	−0.997598	+	0.0692669i	$0.977934\pi$
$888$	43.9673	−	31.5204i	1.47544	−	1.05775i
$889$			7.36840i			0.247128i
$890$	13.1333	−	31.2451i	0.440228	−	1.04734i
$891$		−	32.0077i		−	1.07230i
$892$	−22.3387	−	8.68345i	−0.747953	−	0.290743i
$893$	−2.50153	+	2.50153i	−0.0837106	+	0.0837106i
$894$	−13.6275	−	8.89076i	−0.455771	−	0.297351i
$895$	3.28933	−	4.75439i	0.109950	−	0.158922i
$896$	−19.3369	+	15.1909i	−0.646000	+	0.507492i
$897$	32.0874	+	32.0874i	1.07137	+	1.07137i
$898$	−27.7371	+	5.83450i	−0.925599	+	0.194700i
$899$	−25.2531			−0.842238
$900$	1.30284	−	1.27597i	0.0434281	−	0.0425324i
$901$	−45.7072			−1.52273
$902$	11.1727	−	2.35017i	0.372009	−	0.0782521i
$903$	10.8784	+	10.8784i	0.362010	+	0.362010i
$904$	28.1374	+	4.63948i	0.935837	+	0.154307i
$905$	10.4835	−	15.1529i	0.348484	−	0.503698i
$906$	−7.34513	−	4.79207i	−0.244026	−	0.159206i
$907$	8.88234	−	8.88234i	0.294933	−	0.294933i	−0.544092	−	0.839025i	$-0.683126\pi$
$907$	8.88234	−	8.88234i	0.294933	−	0.294933i	0.839025	+	0.544092i	$0.183126\pi$
$908$	−4.71363	+	12.1261i	−0.156427	+	0.402417i
$909$			0.0161383i			0.000535273i
$910$	16.3411	−	38.8768i	0.541703	−	1.28875i
$911$		−	31.0677i		−	1.02932i	−0.857395	−	0.514659i	$-0.827919\pi$
$911$		−	31.0677i		−	1.02932i	0.857395	−	0.514659i	$-0.172081\pi$
$912$	6.70786	−	0.294740i	0.222119	−	0.00975982i
$913$	17.5467	−	17.5467i	0.580711	−	0.580711i
$914$	−10.9746	+	16.8214i	−0.363006	+	0.556404i
$915$	−1.35580	+	0.246942i	−0.0448215	+	0.00816365i
$916$	1.22381	+	2.78028i	0.0404359	+	0.0918629i
$917$	−3.76008	−	3.76008i	−0.124169	−	0.124169i
$918$	−7.78594	−	37.0142i	−0.256974	−	1.22165i
$919$	34.0309			1.12257			0.561287	−	0.827621i	$-0.310306\pi$
$919$	34.0309			1.12257			0.561287	+	0.827621i	$0.310306\pi$
$920$	20.0314	+	19.3715i	0.660417	+	0.638660i
$921$	13.7988			0.454685
$922$	3.78878	+	18.0118i	0.124777	+	0.593187i
$923$	19.4536	+	19.4536i	0.640322	+	0.640322i
$924$	−11.1753	−	25.3882i	−0.367640	−	0.835210i
$925$	−23.4949	+	51.9027i	−0.772509	+	1.70655i
$926$	−11.0127	+	16.8799i	−0.361900	+	0.554709i
$927$	0.750180	−	0.750180i	0.0246391	−	0.0246391i
$928$	8.64509	−	14.6151i	0.283789	−	0.479763i
$929$		−	10.0530i		−	0.329830i	−0.986308	−	0.164915i	$-0.947265\pi$
$929$		−	10.0530i		−	0.329830i	0.986308	−	0.164915i	$-0.0527349\pi$
$930$	41.3454	−	16.8740i	1.35577	−	0.553321i
$931$			2.27595i			0.0745913i
$932$	−0.161578	+	0.415667i	−0.00529265	+	0.0136156i
$933$	−9.96252	+	9.96252i	−0.326158	+	0.326158i
$934$	−27.3527	−	17.8453i	−0.895006	−	0.583915i
$935$	−7.62639	−	41.8717i	−0.249410	−	1.36935i
$936$	0.514868	−	3.12256i	0.0168290	−	0.102064i
$937$	−32.7057	−	32.7057i	−1.06845	−	1.06845i	−0.997479	−	0.0709685i	$-0.977391\pi$
$937$	−32.7057	−	32.7057i	−1.06845	−	1.06845i	−0.0709685	−	0.997479i	$-0.522609\pi$
$938$	26.0331	−	5.47606i	0.850011	−	0.178800i
$939$	25.2416			0.823730
$940$	−8.86545	−	13.1038i	−0.289159	−	0.427400i
$941$	−38.2144			−1.24575			−0.622876	−	0.782320i	$-0.714036\pi$
$941$	−38.2144			−1.24575			−0.622876	+	0.782320i	$0.714036\pi$
$942$	43.6048	−	9.17227i	1.42072	−	0.298849i
$943$	−6.61627	−	6.61627i	−0.215456	−	0.215456i
$944$	−25.8363	+	28.2111i	−0.840900	+	0.918193i
$945$	21.3501	+	14.7711i	0.694519	+	0.480504i
$946$	18.9867	+	12.3872i	0.617310	+	0.402742i
$947$	−36.5561	+	36.5561i	−1.18791	+	1.18791i	−0.210269	+	0.977643i	$0.567434\pi$
$947$	−36.5561	+	36.5561i	−1.18791	+	1.18791i	−0.977643	+	0.210269i	$0.932566\pi$
$948$	44.1353	+	17.1562i	1.43345	+	0.557208i
$949$		−	8.54987i		−	0.277540i
$950$	−5.96208	+	3.80178i	−0.193436	+	0.123346i
$951$			20.0587i			0.650447i
$952$	−17.9337	−	25.0155i	−0.581236	−	0.810757i
$953$	−10.1647	+	10.1647i	−0.329266	+	0.329266i	−0.852307	−	0.523041i	$-0.824797\pi$
$953$	−10.1647	+	10.1647i	−0.329266	+	0.329266i	0.523041	+	0.852307i	$0.324797\pi$
$954$	1.28642	−	1.97178i	0.0416494	−	0.0638389i
$955$	19.9332	+	13.7908i	0.645024	+	0.446261i
$956$	37.0989	−	16.3300i	1.19986	−	0.528152i
$957$	13.5445	+	13.5445i	0.437832	+	0.437832i
$958$	1.80506	+	8.58120i	0.0583187	+	0.277246i
$959$	13.3774			0.431980
$960$	−4.38835	+	29.7050i	−0.141633	+	0.958725i
$961$	−39.7747			−1.28305
$962$	20.3524	+	96.7551i	0.656189	+	3.11951i
$963$	−1.21041	−	1.21041i	−0.0390048	−	0.0390048i
$964$	21.9315	−	9.65375i	0.706367	−	0.310926i
$965$	−1.26541	−	6.94757i	−0.0407350	−	0.223650i
$966$	−12.4216	+	19.0394i	−0.399659	+	0.612584i
$967$	13.7685	−	13.7685i	0.442765	−	0.442765i	−0.450175	−	0.892940i	$-0.648638\pi$
$967$	13.7685	−	13.7685i	0.442765	−	0.442765i	0.892940	+	0.450175i	$0.148638\pi$
$968$	−5.68832	−	7.93455i	−0.182830	−	0.255026i
$969$			8.40439i			0.269988i
$970$	−20.2533	−	49.6254i	−0.650293	−	1.59338i
$971$			37.2214i			1.19449i	0.802058	+	0.597246i	$0.203738\pi$
$971$			37.2214i			1.19449i	−0.802058	+	0.597246i	$0.796262\pi$
$972$	3.52776	+	1.37131i	0.113153	+	0.0439846i
$973$	1.94547	−	1.94547i	0.0623688	−	0.0623688i
$974$	−20.5679	−	13.4188i	−0.659038	−	0.429966i
$975$	−18.1564	−	48.1893i	−0.581470	−	1.54329i
$976$	−0.991899	+	1.08307i	−0.0317499	+	0.0346683i
$977$	−7.39190	−	7.39190i	−0.236488	−	0.236488i	0.578906	−	0.815394i	$-0.303480\pi$
$977$	−7.39190	−	7.39190i	−0.236488	−	0.236488i	−0.815394	+	0.578906i	$0.803480\pi$
$978$	−56.2491	+	11.8320i	−1.79865	+	0.378346i
$979$	40.7446			1.30220
$980$	−9.99408	−	1.92809i	−0.319249	−	0.0615904i
$981$	1.56137			0.0498506
$982$	14.5438	−	3.05928i	0.464111	−	0.0976257i
$983$	35.0965	+	35.0965i	1.11940	+	1.11940i	0.991829	+	0.127575i	$0.0407195\pi$
$983$	35.0965	+	35.0965i	1.11940	+	1.11940i	0.127575	+	0.991829i	$0.459281\pi$
$984$	1.64033	−	9.94825i	0.0522919	−	0.317139i
$985$	−14.1906	+	2.58463i	−0.452149	+	0.0823531i
$986$	17.8012	+	11.6137i	0.566905	+	0.369857i
$987$	9.12654	−	9.12654i	0.290501	−	0.290501i
$988$	−4.44602	+	11.4376i	−0.141447	+	0.363879i
$989$		−	18.5791i		−	0.590781i
$990$	2.02097	+	0.849474i	0.0642306	+	0.0269981i
$991$			18.6058i			0.591033i	0.955338	+	0.295516i	$0.0954917\pi$
$991$			18.6058i			0.591033i	−0.955338	+	0.295516i	$0.904508\pi$
$992$	24.2288	−	40.9604i	0.769266	−	1.30049i
$993$	21.6331	−	21.6331i	0.686507	−	0.686507i
$994$	−7.53081	+	11.5430i	−0.238863	+	0.366121i
$995$	−9.48548	+	13.7103i	−0.300710	+	0.434645i
$996$	−8.82862	−	20.0570i	−0.279745	−	0.635530i
$997$	−38.0763	−	38.0763i	−1.20589	−	1.20589i	−0.972347	−	0.233541i	$-0.924969\pi$
$997$	−38.0763	−	38.0763i	−1.20589	−	1.20589i	−0.233541	−	0.972347i	$-0.575031\pi$
$998$	−6.18743	−	29.4149i	−0.195860	−	0.931113i
$999$	−60.8681			−1.92578

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.k.c.267.13	✓	52
4.3	odd	2		380.2.k.d.267.1	yes	52
5.3	odd	4		380.2.k.d.343.1	yes	52
20.3	even	4	inner	380.2.k.c.343.13	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.k.c.267.13	✓	52	1.1	even	1	trivial
380.2.k.c.343.13	yes	52	20.3	even	4	inner
380.2.k.d.267.1	yes	52	4.3	odd	2
380.2.k.d.343.1	yes	52	5.3	odd	4

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.291109 - 1.38393i) q^{2} +(1.18694 + 1.18694i) q^{3} +(-1.83051 + 0.805748i) q^{4} +(1.27222 - 1.83887i) q^{5} +(1.29711 - 1.98816i) q^{6} +(-1.53689 + 1.53689i) q^{7} +(1.64798 + 2.29873i) q^{8} -0.182360i q^{9} +O(q^{10})\)	\(q+(-0.291109 - 1.38393i) q^{2} +(1.18694 + 1.18694i) q^{3} +(-1.83051 + 0.805748i) q^{4} +(1.27222 - 1.83887i) q^{5} +(1.29711 - 1.98816i) q^{6} +(-1.53689 + 1.53689i) q^{7} +(1.64798 + 2.29873i) q^{8} -0.182360i q^{9} +(-2.91522 - 1.22536i) q^{10} -3.80154i q^{11} +(-3.12907 - 1.21633i) q^{12} +(4.33858 - 4.33858i) q^{13} +(2.57434 + 1.67954i) q^{14} +(3.69267 - 0.672572i) q^{15} +(2.70154 - 2.94986i) q^{16} +(3.54037 + 3.54037i) q^{17} +(-0.252372 + 0.0530865i) q^{18} +1.00000 q^{19} +(-0.847156 + 4.39116i) q^{20} -3.64838 q^{21} +(-5.26106 + 1.10666i) q^{22} +(3.11551 + 3.11551i) q^{23} +(-0.772410 + 4.68450i) q^{24} +(-1.76289 - 4.67891i) q^{25} +(-7.26728 - 4.74128i) q^{26} +(3.77726 - 3.77726i) q^{27} +(1.57495 - 4.05163i) q^{28} +3.00176i q^{29} +(-2.00576 - 4.91460i) q^{30} +8.41277i q^{31} +(-4.86884 - 2.88001i) q^{32} +(4.51219 - 4.51219i) q^{33} +(3.86898 - 5.93024i) q^{34} +(0.870870 + 4.78140i) q^{35} +(0.146936 + 0.333811i) q^{36} +(-8.05718 - 8.05718i) q^{37} +(-0.291109 - 1.38393i) q^{38} +10.2992 q^{39} +(6.32367 - 0.105905i) q^{40} -2.12365 q^{41} +(1.06208 + 5.04909i) q^{42} +(-2.98171 - 2.98171i) q^{43} +(3.06308 + 6.95876i) q^{44} +(-0.335336 - 0.232002i) q^{45} +(3.40469 - 5.21860i) q^{46} +(-2.50153 + 2.50153i) q^{47} +(6.70786 - 0.294740i) q^{48} +2.27595i q^{49} +(-5.96208 + 3.80178i) q^{50} +8.40439i q^{51} +(-4.44602 + 11.4376i) q^{52} +(-6.45515 + 6.45515i) q^{53} +(-6.32705 - 4.12786i) q^{54} +(-6.99054 - 4.83641i) q^{55} +(-6.06565 - 1.00014i) q^{56} +(1.18694 + 1.18694i) q^{57} +(4.15422 - 0.873840i) q^{58} -9.56354 q^{59} +(-6.21756 + 4.20652i) q^{60} -0.367160 q^{61} +(11.6427 - 2.44903i) q^{62} +(0.280266 + 0.280266i) q^{63} +(-2.56836 + 7.57651i) q^{64} +(-2.45844 - 13.4977i) q^{65} +(-7.55808 - 4.93100i) q^{66} +(6.11984 - 6.11984i) q^{67} +(-9.33332 - 3.62804i) q^{68} +7.39584i q^{69} +(6.36360 - 2.59713i) q^{70} +4.48386i q^{71} +(0.419196 - 0.300524i) q^{72} +(0.985330 - 0.985330i) q^{73} +(-8.80503 + 13.4961i) q^{74} +(3.46114 - 7.64601i) q^{75} +(-1.83051 + 0.805748i) q^{76} +(5.84254 + 5.84254i) q^{77} +(-2.99820 - 14.2534i) q^{78} -14.1049 q^{79} +(-1.98744 - 8.72067i) q^{80} +8.41967 q^{81} +(0.618215 + 2.93898i) q^{82} +(4.61568 + 4.61568i) q^{83} +(6.67840 - 2.93967i) q^{84} +(11.0144 - 2.00613i) q^{85} +(-3.25847 + 4.99447i) q^{86} +(-3.56290 + 3.56290i) q^{87} +(8.73873 - 6.26484i) q^{88} +10.7179i q^{89} +(-0.223455 + 0.531618i) q^{90} +13.3358i q^{91} +(-8.21330 - 3.19266i) q^{92} +(-9.98543 + 9.98543i) q^{93} +(4.19016 + 2.73372i) q^{94} +(1.27222 - 1.83887i) q^{95} +(-2.36062 - 9.19739i) q^{96} +(11.9851 + 11.9851i) q^{97} +(3.14975 - 0.662550i) q^{98} -0.693247 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8	\( 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 q^{98} + 128 q^{99}+O(q^{100}) \) 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more