LMFDB - Embedded newform 930.2.k.a.247.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(247,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("930.247");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			247.7
Character	$\chi$	$=$	930.247
Dual form			930.2.k.a.433.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(1.94894 - 1.09618i) q^{5} -1.00000i q^{6} +(-1.54434 - 1.54434i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(1.94894 - 1.09618i) q^{5} -1.00000i q^{6} +(-1.54434 - 1.54434i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(-2.15323 - 0.602992i) q^{10} +1.86765i q^{11} +(-0.707107 + 0.707107i) q^{12} +(1.01427 + 1.01427i) q^{13} +2.18403i q^{14} +(2.15323 + 0.602992i) q^{15} -1.00000 q^{16} +(4.64600 - 4.64600i) q^{17} +(0.707107 - 0.707107i) q^{18} -3.65522i q^{19} +(1.09618 + 1.94894i) q^{20} -2.18403i q^{21} +(1.32063 - 1.32063i) q^{22} +(2.46256 + 2.46256i) q^{23} +1.00000 q^{24} +(2.59676 - 4.27280i) q^{25} -1.43440i q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.54434 - 1.54434i) q^{28} -3.22584 q^{29} +(-1.09618 - 1.94894i) q^{30} +(5.27790 + 1.77308i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.32063 + 1.32063i) q^{33} -6.57044 q^{34} +(-4.70272 - 1.31695i) q^{35} -1.00000 q^{36} +(5.38089 - 5.38089i) q^{37} +(-2.58463 + 2.58463i) q^{38} +1.43440i q^{39} +(0.602992 - 2.15323i) q^{40} -5.91322 q^{41} +(-1.54434 + 1.54434i) q^{42} +(3.51374 + 3.51374i) q^{43} -1.86765 q^{44} +(1.09618 + 1.94894i) q^{45} -3.48259i q^{46} +(-5.19617 - 5.19617i) q^{47} +(-0.707107 - 0.707107i) q^{48} -2.23001i q^{49} +(-4.85751 + 1.18514i) q^{50} +6.57044 q^{51} +(-1.01427 + 1.01427i) q^{52} +(7.72298 + 7.72298i) q^{53} +1.00000 q^{54} +(2.04729 + 3.63995i) q^{55} -2.18403 q^{56} +(2.58463 - 2.58463i) q^{57} +(2.28101 + 2.28101i) q^{58} +4.31789i q^{59} +(-0.602992 + 2.15323i) q^{60} -9.74941i q^{61} +(-2.47828 - 4.98579i) q^{62} +(1.54434 - 1.54434i) q^{63} -1.00000i q^{64} +(3.08859 + 0.864931i) q^{65} +1.86765 q^{66} +(7.73177 + 7.73177i) q^{67} +(4.64600 + 4.64600i) q^{68} +3.48259i q^{69} +(2.39410 + 4.25655i) q^{70} -0.778659 q^{71} +(0.707107 + 0.707107i) q^{72} +(-1.92614 - 1.92614i) q^{73} -7.60973 q^{74} +(4.85751 - 1.18514i) q^{75} +3.65522 q^{76} +(2.88430 - 2.88430i) q^{77} +(1.01427 - 1.01427i) q^{78} +4.71035 q^{79} +(-1.94894 + 1.09618i) q^{80} -1.00000 q^{81} +(4.18128 + 4.18128i) q^{82} +(0.710451 + 0.710451i) q^{83} +2.18403 q^{84} +(3.96192 - 14.1477i) q^{85} -4.96918i q^{86} +(-2.28101 - 2.28101i) q^{87} +(1.32063 + 1.32063i) q^{88} +7.40439 q^{89} +(0.602992 - 2.15323i) q^{90} -3.13277i q^{91} +(-2.46256 + 2.46256i) q^{92} +(2.47828 + 4.98579i) q^{93} +7.34849i q^{94} +(-4.00680 - 7.12383i) q^{95} +1.00000i q^{96} +(-3.69010 - 3.69010i) q^{97} +(-1.57686 + 1.57686i) q^{98} -1.86765 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{7}+O(q^{10}) $ 32 * q - 4 * q^7	$ 32 q - 4 q^{7} + 4 q^{10} - 4 q^{15} - 32 q^{16} - 8 q^{17} + 4 q^{22} + 32 q^{24} + 8 q^{25} + 4 q^{28} - 8 q^{29} - 20 q^{31} - 4 q^{33} - 24 q^{35} - 32 q^{36} - 4 q^{37} + 16 q^{38} - 16 q^{41} - 4 q^{42} + 16 q^{43} + 8 q^{44} - 8 q^{47} - 16 q^{50} + 24 q^{53} + 32 q^{54} + 28 q^{55} - 16 q^{57} - 20 q^{58} + 16 q^{62} + 4 q^{63} - 56 q^{65} - 8 q^{66} + 32 q^{67} - 8 q^{68} - 28 q^{70} + 16 q^{71} + 20 q^{73} - 24 q^{74} + 16 q^{75} - 16 q^{76} + 40 q^{77} + 56 q^{79} - 32 q^{81} + 16 q^{82} - 72 q^{83} + 32 q^{85} + 20 q^{87} + 4 q^{88} + 64 q^{89} - 16 q^{93} + 32 q^{95} - 4 q^{97} + 16 q^{98} + 8 q^{99}+O(q^{100}) $ 32 * q - 4 * q^7 + 4 * q^10 - 4 * q^15 - 32 * q^16 - 8 * q^17 + 4 * q^22 + 32 * q^24 + 8 * q^25 + 4 * q^28 - 8 * q^29 - 20 * q^31 - 4 * q^33 - 24 * q^35 - 32 * q^36 - 4 * q^37 + 16 * q^38 - 16 * q^41 - 4 * q^42 + 16 * q^43 + 8 * q^44 - 8 * q^47 - 16 * q^50 + 24 * q^53 + 32 * q^54 + 28 * q^55 - 16 * q^57 - 20 * q^58 + 16 * q^62 + 4 * q^63 - 56 * q^65 - 8 * q^66 + 32 * q^67 - 8 * q^68 - 28 * q^70 + 16 * q^71 + 20 * q^73 - 24 * q^74 + 16 * q^75 - 16 * q^76 + 40 * q^77 + 56 * q^79 - 32 * q^81 + 16 * q^82 - 72 * q^83 + 32 * q^85 + 20 * q^87 + 4 * q^88 + 64 * q^89 - 16 * q^93 + 32 * q^95 - 4 * q^97 + 16 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$			1.00000i			0.500000i
$5$	1.94894	−	1.09618i	0.871594	−	0.490229i
$5$	1.94894	−	1.09618i	0.871594	−	0.490229i
$6$		−	1.00000i		−	0.408248i
$7$	−1.54434	−	1.54434i	−0.583707	−	0.583707i	0.352213	−	0.935920i	$-0.385429\pi$
$7$	−1.54434	−	1.54434i	−0.583707	−	0.583707i	−0.935920	+	0.352213i	$0.885429\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$			1.00000i			0.333333i
$10$	−2.15323	−	0.602992i	−0.680911	−	0.190683i
$11$			1.86765i			0.563118i	0.959544	+	0.281559i	$0.0908516\pi$
$11$			1.86765i			0.563118i	−0.959544	+	0.281559i	$0.909148\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	1.01427	+	1.01427i	0.281309	+	0.281309i	0.833631	−	0.552322i	$-0.186258\pi$
$13$	1.01427	+	1.01427i	0.281309	+	0.281309i	−0.552322	+	0.833631i	$0.686258\pi$
$14$			2.18403i			0.583707i
$15$	2.15323	+	0.602992i	0.555962	+	0.155692i
$16$	−1.00000			−0.250000
$17$	4.64600	−	4.64600i	1.12682	−	1.12682i	0.136129	−	0.990691i	$-0.456534\pi$
$17$	4.64600	−	4.64600i	1.12682	−	1.12682i	0.990691	−	0.136129i	$-0.0434662\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$		−	3.65522i		−	0.838566i	−0.907856	−	0.419283i	$-0.862281\pi$
$19$		−	3.65522i		−	0.838566i	0.907856	−	0.419283i	$-0.137719\pi$
$20$	1.09618	+	1.94894i	0.245114	+	0.435797i
$21$		−	2.18403i		−	0.476595i
$22$	1.32063	−	1.32063i	0.281559	−	0.281559i
$23$	2.46256	+	2.46256i	0.513480	+	0.513480i	0.915591	−	0.402111i	$-0.131723\pi$
$23$	2.46256	+	2.46256i	0.513480	+	0.513480i	−0.402111	+	0.915591i	$0.631723\pi$
$24$	1.00000			0.204124
$25$	2.59676	−	4.27280i	0.519352	−	0.854560i
$26$		−	1.43440i		−	0.281309i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	1.54434	−	1.54434i	0.291853	−	0.291853i
$29$	−3.22584			−0.599024			−0.299512	−	0.954093i	$-0.596824\pi$
$29$	−3.22584			−0.599024			−0.299512	+	0.954093i	$0.596824\pi$
$30$	−1.09618	−	1.94894i	−0.200135	−	0.355827i
$31$	5.27790	+	1.77308i	0.947938	+	0.318454i
$31$	5.27790	+	1.77308i	0.947938	+	0.318454i
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−1.32063	+	1.32063i	−0.229892	+	0.229892i
$34$	−6.57044			−1.12682
$35$	−4.70272	−	1.31695i	−0.794905	−	0.222606i
$36$	−1.00000			−0.166667
$37$	5.38089	−	5.38089i	0.884613	−	0.884613i	−0.109387	−	0.993999i	$-0.534889\pi$
$37$	5.38089	−	5.38089i	0.884613	−	0.884613i	0.993999	+	0.109387i	$0.0348887\pi$
$38$	−2.58463	+	2.58463i	−0.419283	+	0.419283i
$39$			1.43440i			0.229688i
$40$	0.602992	−	2.15323i	0.0953414	−	0.340456i
$41$	−5.91322			−0.923489			−0.461745	−	0.887013i	$-0.652776\pi$
$41$	−5.91322			−0.923489			−0.461745	+	0.887013i	$0.652776\pi$
$42$	−1.54434	+	1.54434i	−0.238297	+	0.238297i
$43$	3.51374	+	3.51374i	0.535841	+	0.535841i	0.922305	−	0.386464i	$-0.126304\pi$
$43$	3.51374	+	3.51374i	0.535841	+	0.535841i	−0.386464	+	0.922305i	$0.626304\pi$
$44$	−1.86765			−0.281559
$45$	1.09618	+	1.94894i	0.163410	+	0.290531i
$46$		−	3.48259i		−	0.513480i
$47$	−5.19617	−	5.19617i	−0.757939	−	0.757939i	0.218008	−	0.975947i	$-0.430044\pi$
$47$	−5.19617	−	5.19617i	−0.757939	−	0.757939i	−0.975947	+	0.218008i	$0.930044\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$		−	2.23001i		−	0.318573i
$50$	−4.85751	+	1.18514i	−0.686956	+	0.167604i
$51$	6.57044			0.920045
$52$	−1.01427	+	1.01427i	−0.140654	+	0.140654i
$53$	7.72298	+	7.72298i	1.06083	+	1.06083i	0.998026	+	0.0628073i	$0.0200054\pi$
$53$	7.72298	+	7.72298i	1.06083	+	1.06083i	0.0628073	+	0.998026i	$0.479995\pi$
$54$	1.00000			0.136083
$55$	2.04729	+	3.63995i	0.276057	+	0.490811i
$56$	−2.18403			−0.291853
$57$	2.58463	−	2.58463i	0.342343	−	0.342343i
$58$	2.28101	+	2.28101i	0.299512	+	0.299512i
$59$			4.31789i			0.562141i	0.959687	+	0.281071i	$0.0906895\pi$
$59$			4.31789i			0.562141i	−0.959687	+	0.281071i	$0.909310\pi$
$60$	−0.602992	+	2.15323i	−0.0778459	+	0.277981i
$61$		−	9.74941i		−	1.24828i	−0.781311	−	0.624142i	$-0.785449\pi$
$61$		−	9.74941i		−	1.24828i	0.781311	−	0.624142i	$-0.214551\pi$
$62$	−2.47828	−	4.98579i	−0.314742	−	0.633196i
$63$	1.54434	−	1.54434i	0.194569	−	0.194569i
$64$		−	1.00000i		−	0.125000i
$65$	3.08859	+	0.864931i	0.383093	+	0.107281i
$66$	1.86765			0.229892
$67$	7.73177	+	7.73177i	0.944587	+	0.944587i	0.998543	−	0.0539567i	$-0.0171833\pi$
$67$	7.73177	+	7.73177i	0.944587	+	0.944587i	−0.0539567	+	0.998543i	$0.517183\pi$
$68$	4.64600	+	4.64600i	0.563410	+	0.563410i
$69$			3.48259i			0.419255i
$70$	2.39410	+	4.25655i	0.286150	+	0.508755i
$71$	−0.778659			−0.0924099			−0.0462049	−	0.998932i	$-0.514713\pi$
$71$	−0.778659			−0.0924099			−0.0462049	+	0.998932i	$0.514713\pi$
$72$	0.707107	+	0.707107i	0.0833333	+	0.0833333i
$73$	−1.92614	−	1.92614i	−0.225437	−	0.225437i	0.585346	−	0.810784i	$-0.300959\pi$
$73$	−1.92614	−	1.92614i	−0.225437	−	0.225437i	−0.810784	+	0.585346i	$0.800959\pi$
$74$	−7.60973			−0.884613
$75$	4.85751	−	1.18514i	0.560897	−	0.136848i
$76$	3.65522			0.419283
$77$	2.88430	−	2.88430i	0.328696	−	0.328696i
$78$	1.01427	−	1.01427i	0.114844	−	0.114844i
$79$	4.71035			0.529955			0.264978	−	0.964255i	$-0.414635\pi$
$79$	4.71035			0.529955			0.264978	+	0.964255i	$0.414635\pi$
$80$	−1.94894	+	1.09618i	−0.217898	+	0.122557i
$81$	−1.00000			−0.111111
$82$	4.18128	+	4.18128i	0.461745	+	0.461745i
$83$	0.710451	+	0.710451i	0.0779821	+	0.0779821i	0.745022	−	0.667040i	$-0.232439\pi$
$83$	0.710451	+	0.710451i	0.0779821	+	0.0779821i	−0.667040	+	0.745022i	$0.732439\pi$
$84$	2.18403			0.238297
$85$	3.96192	−	14.1477i	0.429730	−	1.53453i
$86$		−	4.96918i		−	0.535841i
$87$	−2.28101	−	2.28101i	−0.244550	−	0.244550i
$88$	1.32063	+	1.32063i	0.140780	+	0.140780i
$89$	7.40439			0.784864			0.392432	−	0.919781i	$-0.371634\pi$
$89$	7.40439			0.784864			0.392432	+	0.919781i	$0.371634\pi$
$90$	0.602992	−	2.15323i	0.0635609	−	0.226970i
$91$		−	3.13277i		−	0.328404i
$92$	−2.46256	+	2.46256i	−0.256740	+	0.256740i
$93$	2.47828	+	4.98579i	0.256986	+	0.517003i
$94$			7.34849i			0.757939i
$95$	−4.00680	−	7.12383i	−0.411089	−	0.730889i
$96$			1.00000i			0.102062i
$97$	−3.69010	−	3.69010i	−0.374673	−	0.374673i	0.494503	−	0.869176i	$-0.335350\pi$
$97$	−3.69010	−	3.69010i	−0.374673	−	0.374673i	−0.869176	+	0.494503i	$0.835350\pi$
$98$	−1.57686	+	1.57686i	−0.159286	+	0.159286i
$99$	−1.86765			−0.187706
$100$	4.27280	+	2.59676i	0.427280	+	0.259676i
$101$	−12.3553			−1.22939			−0.614697	−	0.788763i	$-0.710722\pi$
$101$	−12.3553			−1.22939			−0.614697	+	0.788763i	$0.710722\pi$
$102$	−4.64600	−	4.64600i	−0.460022	−	0.460022i
$103$	3.04612	−	3.04612i	0.300143	−	0.300143i	−0.540927	−	0.841070i	$-0.681926\pi$
$103$	3.04612	−	3.04612i	0.300143	−	0.300143i	0.841070	+	0.540927i	$0.181926\pi$
$104$	1.43440			0.140654
$105$	−2.39410	−	4.25655i	−0.233640	−	0.415397i
$106$		−	10.9219i		−	1.06083i
$107$	−2.84771	−	2.84771i	−0.275298	−	0.275298i	0.555930	−	0.831229i	$-0.312362\pi$
$107$	−2.84771	−	2.84771i	−0.275298	−	0.275298i	−0.831229	+	0.555930i	$0.812362\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$		−	8.57997i		−	0.821812i	−0.911678	−	0.410906i	$-0.865212\pi$
$109$		−	8.57997i		−	0.821812i	0.911678	−	0.410906i	$-0.134788\pi$
$110$	1.12618	−	4.02149i	0.107377	−	0.383434i
$111$	7.60973			0.722283
$112$	1.54434	+	1.54434i	0.145927	+	0.145927i
$113$	−4.97955	+	4.97955i	−0.468437	+	0.468437i	−0.901408	−	0.432971i	$-0.857465\pi$
$113$	−4.97955	+	4.97955i	−0.468437	+	0.468437i	0.432971	+	0.901408i	$0.357465\pi$
$114$	−3.65522			−0.342343
$115$	7.49882	+	2.09997i	0.699269	+	0.195824i
$116$		−	3.22584i		−	0.299512i
$117$	−1.01427	+	1.01427i	−0.0937696	+	0.0937696i
$118$	3.05321	−	3.05321i	0.281071	−	0.281071i
$119$	−14.3500			−1.31547
$120$	1.94894	−	1.09618i	0.177913	−	0.100067i
$121$	7.51187			0.682898
$122$	−6.89387	+	6.89387i	−0.624142	+	0.624142i
$123$	−4.18128	−	4.18128i	−0.377013	−	0.377013i
$124$	−1.77308	+	5.27790i	−0.159227	+	0.473969i
$125$	0.377160	−	11.1740i	0.0337342	−	0.999431i
$126$	−2.18403			−0.194569
$127$	−5.46441	+	5.46441i	−0.484888	+	0.484888i	−0.906689	−	0.421801i	$-0.861398\pi$
$127$	−5.46441	+	5.46441i	−0.484888	+	0.484888i	0.421801	+	0.906689i	$0.361398\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$			4.96918i			0.437512i
$130$	−1.57237	−	2.79556i	−0.137906	−	0.245187i
$131$	−15.3951			−1.34507			−0.672537	−	0.740063i	$-0.734795\pi$
$131$	−15.3951			−1.34507			−0.672537	+	0.740063i	$0.734795\pi$
$132$	−1.32063	−	1.32063i	−0.114946	−	0.114946i
$133$	−5.64492	+	5.64492i	−0.489477	+	0.489477i
$134$		−	10.9344i		−	0.944587i
$135$	−0.602992	+	2.15323i	−0.0518973	+	0.185321i
$136$		−	6.57044i		−	0.563410i
$137$	1.80311	−	1.80311i	0.154050	−	0.154050i	−0.625874	−	0.779924i	$-0.715258\pi$
$137$	1.80311	−	1.80311i	0.154050	−	0.154050i	0.779924	+	0.625874i	$0.215258\pi$
$138$	2.46256	−	2.46256i	0.209627	−	0.209627i
$139$	−8.56030			−0.726075			−0.363038	−	0.931774i	$-0.618260\pi$
$139$	−8.56030			−0.726075			−0.363038	+	0.931774i	$0.618260\pi$
$140$	1.31695	−	4.70272i	0.111303	−	0.397452i
$141$		−	7.34849i		−	0.618855i
$142$	0.550595	+	0.550595i	0.0462049	+	0.0462049i
$143$	−1.89431	+	1.89431i	−0.158410	+	0.158410i
$144$		−	1.00000i		−	0.0833333i
$145$	−6.28698	+	3.53612i	−0.522105	+	0.293658i
$146$			2.72397i			0.225437i
$147$	1.57686	−	1.57686i	0.130057	−	0.130057i
$148$	5.38089	+	5.38089i	0.442306	+	0.442306i
$149$			21.7052i			1.77816i	0.457756	+	0.889078i	$0.348653\pi$
$149$			21.7052i			1.77816i	−0.457756	+	0.889078i	$0.651347\pi$
$150$	−4.27280	−	2.59676i	−0.348873	−	0.212025i
$151$			12.9017i			1.04992i	0.851126	+	0.524961i	$0.175920\pi$
$151$			12.9017i			1.04992i	−0.851126	+	0.524961i	$0.824080\pi$
$152$	−2.58463	−	2.58463i	−0.209642	−	0.209642i
$153$	4.64600	+	4.64600i	0.375607	+	0.375607i
$154$	−4.07901			−0.328696
$155$	12.2299	−	2.32992i	0.982333	−	0.187144i
$156$	−1.43440			−0.114844
$157$	10.1673	+	10.1673i	0.811442	+	0.811442i	0.984850	−	0.173408i	$-0.0554780\pi$
$157$	10.1673	+	10.1673i	0.811442	+	0.811442i	−0.173408	+	0.984850i	$0.555478\pi$
$158$	−3.33072	−	3.33072i	−0.264978	−	0.264978i
$159$			10.9219i			0.866167i
$160$	2.15323	+	0.602992i	0.170228	+	0.0476707i
$161$		−	7.60609i		−	0.599443i
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	3.84676	−	3.84676i	0.301301	−	0.301301i	−0.540222	−	0.841523i	$-0.681660\pi$
$163$	3.84676	−	3.84676i	0.301301	−	0.301301i	0.841523	+	0.540222i	$0.181660\pi$
$164$		−	5.91322i		−	0.461745i
$165$	−1.12618	+	4.02149i	−0.0876729	+	0.313072i
$166$		−	1.00473i		−	0.0779821i
$167$	−13.5049	+	13.5049i	−1.04504	+	1.04504i	−0.0461057	+	0.998937i	$0.514681\pi$
$167$	−13.5049	+	13.5049i	−1.04504	+	1.04504i	−0.998937	+	0.0461057i	$0.985319\pi$
$168$	−1.54434	−	1.54434i	−0.119149	−	0.119149i
$169$		−	10.9425i		−	0.841731i
$170$	−12.8054	+	7.20241i	−0.982130	+	0.552399i
$171$	3.65522			0.279522
$172$	−3.51374	+	3.51374i	−0.267920	+	0.267920i
$173$	9.51835	−	9.51835i	0.723667	−	0.723667i	−0.245684	−	0.969350i	$-0.579012\pi$
$173$	9.51835	−	9.51835i	0.723667	−	0.723667i	0.969350	+	0.245684i	$0.0790124\pi$
$174$			3.22584i			0.244550i
$175$	−10.6090	+	2.58838i	−0.801962	+	0.195663i
$176$		−	1.86765i		−	0.140780i
$177$	−3.05321	+	3.05321i	−0.229493	+	0.229493i
$178$	−5.23570	−	5.23570i	−0.392432	−	0.392432i
$179$	−11.7843			−0.880803			−0.440401	−	0.897801i	$-0.645164\pi$
$179$	−11.7843			−0.880803			−0.440401	+	0.897801i	$0.645164\pi$
$180$	−1.94894	+	1.09618i	−0.145266	+	0.0817048i
$181$			23.0030i			1.70980i	0.518792	+	0.854901i	$0.326382\pi$
$181$			23.0030i			1.70980i	−0.518792	+	0.854901i	$0.673618\pi$
$182$	−2.21520	+	2.21520i	−0.164202	+	0.164202i
$183$	6.89387	−	6.89387i	0.509610	−	0.509610i
$184$	3.48259			0.256740
$185$	4.58860	−	16.3855i	0.337361	−	1.20469i
$186$	1.77308	−	5.27790i	0.130008	−	0.386994i
$187$	8.67711	+	8.67711i	0.634533	+	0.634533i
$188$	5.19617	−	5.19617i	0.378970	−	0.378970i
$189$	2.18403			0.158865
$190$	−2.20407	+	7.87054i	−0.159900	+	0.570989i
$191$	5.18365			0.375076			0.187538	−	0.982257i	$-0.439949\pi$
$191$	5.18365			0.375076			0.187538	+	0.982257i	$0.439949\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	11.7916	−	11.7916i	0.848776	−	0.848776i	−0.141204	−	0.989980i	$-0.545098\pi$
$193$	11.7916	−	11.7916i	0.848776	−	0.848776i	0.989980	+	0.141204i	$0.0450975\pi$
$194$			5.21859i			0.374673i
$195$	1.57237	+	2.79556i	0.112599	+	0.200194i
$196$	2.23001			0.159286
$197$	−15.5308	+	15.5308i	−1.10652	+	1.10652i	−0.112920	+	0.993604i	$0.536020\pi$
$197$	−15.5308	+	15.5308i	−1.10652	+	1.10652i	−0.993604	+	0.112920i	$0.963980\pi$
$198$	1.32063	+	1.32063i	0.0938531	+	0.0938531i
$199$	−23.5086			−1.66648			−0.833242	−	0.552909i	$-0.813518\pi$
$199$	−23.5086			−1.66648			−0.833242	+	0.552909i	$0.813518\pi$
$200$	−1.18514	−	4.85751i	−0.0838021	−	0.343478i
$201$			10.9344i			0.771252i
$202$	8.73649	+	8.73649i	0.614697	+	0.614697i
$203$	4.98180	+	4.98180i	0.349654	+	0.349654i
$204$			6.57044i			0.460022i
$205$	−11.5245	+	6.48198i	−0.804908	+	0.452721i
$206$	−4.30787			−0.300143
$207$	−2.46256	+	2.46256i	−0.171160	+	0.171160i
$208$	−1.01427	−	1.01427i	−0.0703272	−	0.0703272i
$209$	6.82669			0.472212
$210$	−1.31695	+	4.70272i	−0.0908783	+	0.324519i
$211$	−17.5886			−1.21085			−0.605426	−	0.795902i	$-0.706997\pi$
$211$	−17.5886			−1.21085			−0.605426	+	0.795902i	$0.706997\pi$
$212$	−7.72298	+	7.72298i	−0.530417	+	0.530417i
$213$	−0.550595	−	0.550595i	−0.0377262	−	0.0377262i
$214$			4.02727i			0.275298i
$215$	10.6998	+	2.99638i	0.729720	+	0.204351i
$216$			1.00000i			0.0680414i
$217$	−5.41264	−	10.8891i	−0.367434	−	0.739202i
$218$	−6.06695	+	6.06695i	−0.410906	+	0.410906i
$219$		−	2.72397i		−	0.184069i
$220$	−3.63995	+	2.04729i	−0.245405	+	0.138028i
$221$	9.42463			0.633969
$222$	−5.38089	−	5.38089i	−0.361142	−	0.361142i
$223$	14.3634	+	14.3634i	0.961843	+	0.961843i	0.999298	−	0.0374557i	$-0.0119253\pi$
$223$	14.3634	+	14.3634i	0.961843	+	0.961843i	−0.0374557	+	0.999298i	$0.511925\pi$
$224$		−	2.18403i		−	0.145927i
$225$	4.27280	+	2.59676i	0.284853	+	0.173117i
$226$	7.04215			0.468437
$227$	7.42490	+	7.42490i	0.492808	+	0.492808i	0.909190	−	0.416382i	$-0.136702\pi$
$227$	7.42490	+	7.42490i	0.492808	+	0.492808i	−0.416382	+	0.909190i	$0.636702\pi$
$228$	2.58463	+	2.58463i	0.171172	+	0.171172i
$229$	−29.3189			−1.93745			−0.968723	−	0.248146i	$-0.920179\pi$
$229$	−29.3189			−1.93745			−0.968723	+	0.248146i	$0.920179\pi$
$230$	−3.81756	−	6.78737i	−0.251723	−	0.447546i
$231$	4.07901			0.268379
$232$	−2.28101	+	2.28101i	−0.149756	+	0.149756i
$233$	0.365247	−	0.365247i	0.0239282	−	0.0239282i	−0.695041	−	0.718970i	$-0.744614\pi$
$233$	0.365247	−	0.365247i	0.0239282	−	0.0239282i	0.718970	+	0.695041i	$0.244614\pi$
$234$	1.43440			0.0937696
$235$	−15.8230	−	4.43108i	−1.03218	−	0.289052i
$236$	−4.31789			−0.281071
$237$	3.33072	+	3.33072i	0.216353	+	0.216353i
$238$	10.1470	+	10.1470i	0.657733	+	0.657733i
$239$	1.76680			0.114285			0.0571424	−	0.998366i	$-0.481801\pi$
$239$	1.76680			0.114285			0.0571424	+	0.998366i	$0.481801\pi$
$240$	−2.15323	−	0.602992i	−0.138990	−	0.0389229i
$241$		−	7.01509i		−	0.451882i	−0.974141	−	0.225941i	$-0.927454\pi$
$241$		−	7.01509i		−	0.451882i	0.974141	−	0.225941i	$-0.0725456\pi$
$242$	−5.31170	−	5.31170i	−0.341449	−	0.341449i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	9.74941			0.624142
$245$	−2.44450	−	4.34616i	−0.156174	−	0.277666i
$246$			5.91322i			0.377013i
$247$	3.70740	−	3.70740i	0.235896	−	0.235896i
$248$	4.98579	−	2.47828i	0.316598	−	0.157371i
$249$			1.00473i			0.0636721i
$250$	−8.16789	+	7.63450i	−0.516583	+	0.482848i
$251$			25.1973i			1.59044i	0.606322	+	0.795220i	$0.292644\pi$
$251$			25.1973i			1.59044i	−0.606322	+	0.795220i	$0.707356\pi$
$252$	1.54434	+	1.54434i	0.0972845	+	0.0972845i
$253$	−4.59921	+	4.59921i	−0.289150	+	0.289150i
$254$	7.72784			0.484888
$255$	12.8054	−	7.20241i	0.801906	−	0.451032i
$256$	1.00000			0.0625000
$257$	15.8089	+	15.8089i	0.986135	+	0.986135i	0.999905	−	0.0137701i	$-0.00438328\pi$
$257$	15.8089	+	15.8089i	0.986135	+	0.986135i	−0.0137701	+	0.999905i	$0.504383\pi$
$258$	3.51374	−	3.51374i	0.218756	−	0.218756i
$259$	−16.6199			−1.03271
$260$	−0.864931	+	3.08859i	−0.0536407	+	0.191546i
$261$		−	3.22584i		−	0.199675i
$262$	10.8860	+	10.8860i	0.672537	+	0.672537i
$263$	8.70851	+	8.70851i	0.536990	+	0.536990i	0.922644	−	0.385654i	$-0.126024\pi$
$263$	8.70851	+	8.70851i	0.536990	+	0.536990i	−0.385654	+	0.922644i	$0.626024\pi$
$264$			1.86765i			0.114946i
$265$	23.5175	+	6.58584i	1.44467	+	0.404565i
$266$	7.98312			0.489477
$267$	5.23570	+	5.23570i	0.320419	+	0.320419i
$268$	−7.73177	+	7.73177i	−0.472293	+	0.472293i
$269$	−20.4231			−1.24522			−0.622608	−	0.782534i	$-0.713927\pi$
$269$	−20.4231			−1.24522			−0.622608	+	0.782534i	$0.713927\pi$
$270$	1.94894	−	1.09618i	0.118609	−	0.0667116i
$271$		−	12.1313i		−	0.736925i	−0.929643	−	0.368463i	$-0.879884\pi$
$271$		−	12.1313i		−	0.736925i	0.929643	−	0.368463i	$-0.120116\pi$
$272$	−4.64600	+	4.64600i	−0.281705	+	0.281705i
$273$	2.21520	−	2.21520i	0.134070	−	0.134070i
$274$	−2.54998			−0.154050
$275$	7.98011	+	4.84985i	0.481219	+	0.292457i
$276$	−3.48259			−0.209627
$277$	−7.93626	+	7.93626i	−0.476844	+	0.476844i	−0.904121	−	0.427277i	$-0.859473\pi$
$277$	−7.93626	+	7.93626i	−0.476844	+	0.476844i	0.427277	+	0.904121i	$0.359473\pi$
$278$	6.05305	+	6.05305i	0.363038	+	0.363038i
$279$	−1.77308	+	5.27790i	−0.106151	+	0.315979i
$280$	−4.25655	+	2.39410i	−0.254378	+	0.143075i
$281$	1.76103			0.105054			0.0525272	−	0.998619i	$-0.483272\pi$
$281$	1.76103			0.105054			0.0525272	+	0.998619i	$0.483272\pi$
$282$	−5.19617	+	5.19617i	−0.309427	+	0.309427i
$283$	−5.08404	+	5.08404i	−0.302215	+	0.302215i	−0.841880	−	0.539665i	$-0.818551\pi$
$283$	−5.08404	+	5.08404i	−0.302215	+	0.302215i	0.539665	+	0.841880i	$0.318551\pi$
$284$		−	0.778659i		−	0.0462049i
$285$	2.20407	−	7.87054i	0.130558	−	0.466211i
$286$	2.67896			0.158410
$287$	9.13204	+	9.13204i	0.539047	+	0.539047i
$288$	−0.707107	+	0.707107i	−0.0416667	+	0.0416667i
$289$		−	26.1706i		−	1.53945i
$290$	6.94598	+	1.94516i	0.407882	+	0.114223i
$291$		−	5.21859i		−	0.305919i
$292$	1.92614	−	1.92614i	0.112719	−	0.112719i
$293$	−13.9336	+	13.9336i	−0.814012	+	0.814012i	−0.985233	−	0.171221i	$-0.945229\pi$
$293$	−13.9336	+	13.9336i	−0.814012	+	0.814012i	0.171221	+	0.985233i	$0.445229\pi$
$294$	−2.23001			−0.130057
$295$	4.73320	+	8.41532i	0.275578	+	0.489959i
$296$		−	7.60973i		−	0.442306i
$297$	−1.32063	−	1.32063i	−0.0766307	−	0.0766307i
$298$	15.3479	−	15.3479i	0.889078	−	0.889078i
$299$			4.99543i			0.288893i
$300$	1.18514	+	4.85751i	0.0684241	+	0.280449i
$301$		−	10.8528i		−	0.625548i
$302$	9.12285	−	9.12285i	0.524961	−	0.524961i
$303$	−8.73649	−	8.73649i	−0.501898	−	0.501898i
$304$			3.65522i			0.209642i
$305$	−10.6871	−	19.0010i	−0.611944	−	1.08800i
$306$		−	6.57044i		−	0.375607i
$307$	−13.1979	−	13.1979i	−0.753243	−	0.753243i	0.221840	−	0.975083i	$-0.428794\pi$
$307$	−13.1979	−	13.1979i	−0.753243	−	0.753243i	−0.975083	+	0.221840i	$0.928794\pi$
$308$	2.88430	+	2.88430i	0.164348	+	0.164348i
$309$	4.30787			0.245066
$310$	−10.2954	−	7.00037i	−0.584738	−	0.397594i
$311$	−20.2310			−1.14719			−0.573596	−	0.819138i	$-0.694452\pi$
$311$	−20.2310			−1.14719			−0.573596	+	0.819138i	$0.694452\pi$
$312$	1.01427	+	1.01427i	0.0574219	+	0.0574219i
$313$	−1.74424	−	1.74424i	−0.0985904	−	0.0985904i	0.656091	−	0.754682i	$-0.272209\pi$
$313$	−1.74424	−	1.74424i	−0.0985904	−	0.0985904i	−0.754682	+	0.656091i	$0.772209\pi$
$314$		−	14.3788i		−	0.811442i
$315$	1.31695	−	4.70272i	0.0742019	−	0.264968i
$316$			4.71035i			0.264978i
$317$	−4.48268	−	4.48268i	−0.251772	−	0.251772i	0.569925	−	0.821697i	$-0.306972\pi$
$317$	−4.48268	−	4.48268i	−0.251772	−	0.251772i	−0.821697	+	0.569925i	$0.806972\pi$
$318$	7.72298	−	7.72298i	0.433083	−	0.433083i
$319$		−	6.02475i		−	0.337321i
$320$	−1.09618	−	1.94894i	−0.0612786	−	0.108949i
$321$		−	4.02727i		−	0.224780i
$322$	−5.37831	+	5.37831i	−0.299722	+	0.299722i
$323$	−16.9822	−	16.9822i	−0.944913	−	0.944913i
$324$		−	1.00000i		−	0.0555556i
$325$	6.96761	−	1.69996i	0.386494	−	0.0942971i
$326$	−5.44014			−0.301301
$327$	6.06695	−	6.06695i	0.335503	−	0.335503i
$328$	−4.18128	+	4.18128i	−0.230872	+	0.230872i
$329$			16.0493i			0.884828i
$330$	3.63995	−	2.04729i	0.200373	−	0.112700i
$331$		−	8.23716i		−	0.452755i	−0.974040	−	0.226378i	$-0.927312\pi$
$331$		−	8.23716i		−	0.452755i	0.974040	−	0.226378i	$-0.0726883\pi$
$332$	−0.710451	+	0.710451i	−0.0389911	+	0.0389911i
$333$	5.38089	+	5.38089i	0.294871	+	0.294871i
$334$	19.0988			1.04504
$335$	23.5442	+	6.59334i	1.28636	+	0.360233i
$336$			2.18403i			0.119149i
$337$	−1.53632	+	1.53632i	−0.0836887	+	0.0836887i	−0.747712	−	0.664023i	$-0.768848\pi$
$337$	−1.53632	+	1.53632i	−0.0836887	+	0.0836887i	0.664023	+	0.747712i	$0.268848\pi$
$338$	−7.73752	+	7.73752i	−0.420865	+	0.420865i
$339$	−7.04215			−0.382477
$340$	14.1477	+	3.96192i	0.767265	+	0.214865i
$341$	−3.31149	+	9.85728i	−0.179327	+	0.533801i
$342$	−2.58463	−	2.58463i	−0.139761	−	0.139761i
$343$	−14.2543	+	14.2543i	−0.769660	+	0.769660i
$344$	4.96918			0.267920
$345$	3.81756	+	6.78737i	0.205531	+	0.365420i
$346$	−13.4610			−0.723667
$347$	10.3701	−	10.3701i	0.556696	−	0.556696i	−0.371669	−	0.928365i	$-0.621214\pi$
$347$	10.3701	−	10.3701i	0.556696	−	0.556696i	0.928365	+	0.371669i	$0.121214\pi$
$348$	2.28101	−	2.28101i	0.122275	−	0.122275i
$349$			22.9750i			1.22982i	0.788596	+	0.614912i	$0.210809\pi$
$349$			22.9750i			1.22982i	−0.788596	+	0.614912i	$0.789191\pi$
$350$	9.33193	+	5.67140i	0.498813	+	0.303149i
$351$	−1.43440			−0.0765626
$352$	−1.32063	+	1.32063i	−0.0703898	+	0.0703898i
$353$	−15.2484	−	15.2484i	−0.811588	−	0.811588i	0.173283	−	0.984872i	$-0.444562\pi$
$353$	−15.2484	−	15.2484i	−0.811588	−	0.811588i	−0.984872	+	0.173283i	$0.944562\pi$
$354$	4.31789			0.229493
$355$	−1.51756	+	0.853554i	−0.0805439	+	0.0453020i
$356$			7.40439i			0.392432i
$357$	−10.1470	−	10.1470i	−0.537036	−	0.537036i
$358$	8.33278	+	8.33278i	0.440401	+	0.440401i
$359$		−	0.658683i		−	0.0347640i	−0.999849	−	0.0173820i	$-0.994467\pi$
$359$		−	0.658683i		−	0.0347640i	0.999849	−	0.0173820i	$-0.00553313\pi$
$360$	2.15323	+	0.602992i	0.113485	+	0.0317805i
$361$	5.63933			0.296807
$362$	16.2656	−	16.2656i	0.854901	−	0.854901i
$363$	5.31170	+	5.31170i	0.278792	+	0.278792i
$364$	3.13277			0.164202
$365$	−5.86534	−	1.64253i	−0.307006	−	0.0859740i
$366$	−9.74941			−0.509610
$367$	−20.1526	+	20.1526i	−1.05196	+	1.05196i	−0.0533820	+	0.998574i	$0.517000\pi$
$367$	−20.1526	+	20.1526i	−1.05196	+	1.05196i	−0.998574	+	0.0533820i	$0.983000\pi$
$368$	−2.46256	−	2.46256i	−0.128370	−	0.128370i
$369$		−	5.91322i		−	0.307830i
$370$	−14.8309	+	8.34166i	−0.771023	+	0.433662i
$371$		−	23.8539i		−	1.23843i
$372$	−4.98579	+	2.47828i	−0.258501	+	0.128493i
$373$	8.86555	−	8.86555i	0.459041	−	0.459041i	−0.439300	−	0.898340i	$-0.644773\pi$
$373$	8.86555	−	8.86555i	0.459041	−	0.459041i	0.898340	+	0.439300i	$0.144773\pi$
$374$		−	12.2713i		−	0.634533i
$375$	8.16789	−	7.63450i	0.421788	−	0.394244i
$376$	−7.34849			−0.378970
$377$	−3.27188	−	3.27188i	−0.168511	−	0.168511i
$378$	−1.54434	−	1.54434i	−0.0794324	−	0.0794324i
$379$		−	18.2672i		−	0.938325i	−0.883112	−	0.469163i	$-0.844556\pi$
$379$		−	18.2672i		−	0.938325i	0.883112	−	0.469163i	$-0.155444\pi$
$380$	7.12383	−	4.00680i	0.365445	−	0.205545i
$381$	−7.72784			−0.395909
$382$	−3.66540	−	3.66540i	−0.187538	−	0.187538i
$383$	1.57461	+	1.57461i	0.0804589	+	0.0804589i	0.746191	−	0.665732i	$-0.231881\pi$
$383$	1.57461	+	1.57461i	0.0804589	+	0.0804589i	−0.665732	+	0.746191i	$0.731881\pi$
$384$	−1.00000			−0.0510310
$385$	2.45961	−	8.78305i	0.125353	−	0.447626i
$386$	−16.6758			−0.848776
$387$	−3.51374	+	3.51374i	−0.178614	+	0.178614i
$388$	3.69010	−	3.69010i	0.187336	−	0.187336i
$389$	14.2498			0.722496			0.361248	−	0.932470i	$-0.382351\pi$
$389$	14.2498			0.722496			0.361248	+	0.932470i	$0.382351\pi$
$390$	0.864931	−	3.08859i	0.0437975	−	0.156397i
$391$	22.8821			1.15720
$392$	−1.57686	−	1.57686i	−0.0796432	−	0.0796432i
$393$	−10.8860	−	10.8860i	−0.549124	−	0.549124i
$394$	21.9639			1.10652
$395$	9.18020	−	5.16341i	0.461906	−	0.259799i
$396$		−	1.86765i		−	0.0938531i
$397$	−16.0461	−	16.0461i	−0.805333	−	0.805333i	0.178591	−	0.983923i	$-0.442846\pi$
$397$	−16.0461	−	16.0461i	−0.805333	−	0.805333i	−0.983923	+	0.178591i	$0.942846\pi$
$398$	16.6231	+	16.6231i	0.833242	+	0.833242i
$399$	−7.98312			−0.399656
$400$	−2.59676	+	4.27280i	−0.129838	+	0.213640i
$401$			22.8087i			1.13901i	0.821987	+	0.569507i	$0.192866\pi$
$401$			22.8087i			1.13901i	−0.821987	+	0.569507i	$0.807134\pi$
$402$	7.73177	−	7.73177i	0.385626	−	0.385626i
$403$	3.55484	+	7.15162i	0.177079	+	0.356247i
$404$		−	12.3553i		−	0.614697i
$405$	−1.94894	+	1.09618i	−0.0968438	+	0.0544698i
$406$		−	7.04533i		−	0.349654i
$407$	10.0496	+	10.0496i	0.498142	+	0.498142i
$408$	4.64600	−	4.64600i	0.230011	−	0.230011i
$409$	−18.8641			−0.932768			−0.466384	−	0.884582i	$-0.654443\pi$
$409$	−18.8641			−0.932768			−0.466384	+	0.884582i	$0.654443\pi$
$410$	12.7325	+	3.56562i	0.628814	+	0.176093i
$411$	2.54998			0.125781
$412$	3.04612	+	3.04612i	0.150072	+	0.150072i
$413$	6.66830	−	6.66830i	0.328126	−	0.328126i
$414$	3.48259			0.171160
$415$	2.16341	+	0.605844i	0.106198	+	0.0297397i
$416$			1.43440i			0.0703272i
$417$	−6.05305	−	6.05305i	−0.296419	−	0.296419i
$418$	−4.82720	−	4.82720i	−0.236106	−	0.236106i
$419$			21.0868i			1.03016i	0.857142	+	0.515080i	$0.172238\pi$
$419$			21.0868i			1.03016i	−0.857142	+	0.515080i	$0.827762\pi$
$420$	4.25655	−	2.39410i	0.207698	−	0.116820i
$421$	−9.01255			−0.439245			−0.219622	−	0.975585i	$-0.570482\pi$
$421$	−9.01255			−0.439245			−0.219622	+	0.975585i	$0.570482\pi$
$422$	12.4370	+	12.4370i	0.605426	+	0.605426i
$423$	5.19617	−	5.19617i	0.252646	−	0.252646i
$424$	10.9219			0.530417
$425$	−7.78689	−	31.9160i	−0.377720	−	1.54815i
$426$			0.778659i			0.0377262i
$427$	−15.0564	+	15.0564i	−0.728632	+	0.728632i
$428$	2.84771	−	2.84771i	0.137649	−	0.137649i
$429$	−2.67896			−0.129341
$430$	−5.44714	−	9.68466i	−0.262684	−	0.467036i
$431$	−7.33400			−0.353266			−0.176633	−	0.984277i	$-0.556521\pi$
$431$	−7.33400			−0.353266			−0.176633	+	0.984277i	$0.556521\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	−12.2251	−	12.2251i	−0.587500	−	0.587500i	0.349453	−	0.936954i	$-0.386367\pi$
$433$	−12.2251	−	12.2251i	−0.587500	−	0.587500i	−0.936954	+	0.349453i	$0.886367\pi$
$434$	−3.87246	+	11.5271i	−0.185884	+	0.553318i
$435$	−6.94598	−	1.94516i	−0.333034	−	0.0932631i
$436$	8.57997			0.410906
$437$	9.00122	−	9.00122i	0.430587	−	0.430587i
$438$	−1.92614	+	1.92614i	−0.0920344	+	0.0920344i
$439$			11.9831i			0.571924i	0.958241	+	0.285962i	$0.0923131\pi$
$439$			11.9831i			0.571924i	−0.958241	+	0.285962i	$0.907687\pi$
$440$	4.02149	+	1.12618i	0.191717	+	0.0536885i
$441$	2.23001			0.106191
$442$	−6.66422	−	6.66422i	−0.316984	−	0.316984i
$443$	26.1991	−	26.1991i	1.24476	−	1.24476i	0.286753	−	0.958005i	$-0.407424\pi$
$443$	26.1991	−	26.1991i	1.24476	−	1.24476i	0.958005	−	0.286753i	$-0.0925759\pi$
$444$			7.60973i			0.361142i
$445$	14.4307	−	8.11658i	0.684083	−	0.384763i
$446$		−	20.3129i		−	0.961843i
$447$	−15.3479	+	15.3479i	−0.725929	+	0.725929i
$448$	−1.54434	+	1.54434i	−0.0729633	+	0.0729633i
$449$	−0.227494			−0.0107361			−0.00536805	−	0.999986i	$-0.501709\pi$
$449$	−0.227494			−0.0107361			−0.00536805	+	0.999986i	$0.501709\pi$
$450$	−1.18514	−	4.85751i	−0.0558681	−	0.228985i
$451$		−	11.0438i		−	0.520034i
$452$	−4.97955	−	4.97955i	−0.234218	−	0.234218i
$453$	−9.12285	+	9.12285i	−0.428629	+	0.428629i
$454$		−	10.5004i		−	0.492808i
$455$	−3.43409	−	6.10559i	−0.160993	−	0.286235i
$456$		−	3.65522i		−	0.171172i
$457$	15.7591	−	15.7591i	0.737181	−	0.737181i	−0.234850	−	0.972032i	$-0.575460\pi$
$457$	15.7591	−	15.7591i	0.737181	−	0.737181i	0.972032	+	0.234850i	$0.0754600\pi$
$458$	20.7316	+	20.7316i	0.968723	+	0.968723i
$459$			6.57044i			0.306682i
$460$	−2.09997	+	7.49882i	−0.0979118	+	0.349634i
$461$		−	14.7187i		−	0.685516i	−0.939424	−	0.342758i	$-0.888639\pi$
$461$		−	14.7187i		−	0.685516i	0.939424	−	0.342758i	$-0.111361\pi$
$462$	−2.88430	−	2.88430i	−0.134190	−	0.134190i
$463$	−13.4138	−	13.4138i	−0.623393	−	0.623393i	0.323005	−	0.946397i	$-0.395307\pi$
$463$	−13.4138	−	13.4138i	−0.623393	−	0.623393i	−0.946397	+	0.323005i	$0.895307\pi$
$464$	3.22584			0.149756
$465$	10.2954	+	7.00037i	0.477437	+	0.324635i
$466$	−0.516538			−0.0239282
$467$	−1.03055	−	1.03055i	−0.0476881	−	0.0476881i	0.682861	−	0.730549i	$-0.260736\pi$
$467$	−1.03055	−	1.03055i	−0.0476881	−	0.0476881i	−0.730549	+	0.682861i	$0.760736\pi$
$468$	−1.01427	−	1.01427i	−0.0468848	−	0.0468848i
$469$		−	23.8810i		−	1.10272i
$470$	8.05530	+	14.3218i	0.371563	+	0.660615i
$471$			14.3788i			0.662540i
$472$	3.05321	+	3.05321i	0.140535	+	0.140535i
$473$	−6.56245	+	6.56245i	−0.301742	+	0.301742i
$474$		−	4.71035i		−	0.216353i
$475$	−15.6181	−	9.49174i	−0.716605	−	0.435511i
$476$		−	14.3500i		−	0.657733i
$477$	−7.72298	+	7.72298i	−0.353611	+	0.353611i
$478$	−1.24932	−	1.24932i	−0.0571424	−	0.0571424i
$479$		−	25.0465i		−	1.14440i	−0.820113	−	0.572202i	$-0.806089\pi$
$479$		−	25.0465i		−	1.14440i	0.820113	−	0.572202i	$-0.193911\pi$
$480$	1.09618	+	1.94894i	0.0500337	+	0.0889567i
$481$	10.9154			0.497699
$482$	−4.96042	+	4.96042i	−0.225941	+	0.225941i
$483$	5.37831	−	5.37831i	0.244722	−	0.244722i
$484$			7.51187i			0.341449i
$485$	−11.2368	−	3.14676i	−0.510238	−	0.142887i
$486$			1.00000i			0.0453609i
$487$	21.9807	−	21.9807i	0.996040	−	0.996040i	−0.00395184	−	0.999992i	$-0.501258\pi$
$487$	21.9807	−	21.9807i	0.996040	−	0.996040i	0.999992	+	0.00395184i	$0.00125791\pi$
$488$	−6.89387	−	6.89387i	−0.312071	−	0.312071i
$489$	5.44014			0.246011
$490$	−1.34468	+	4.80173i	−0.0607463	+	0.216920i
$491$			30.6331i			1.38245i	0.722637	+	0.691227i	$0.242930\pi$
$491$			30.6331i			1.38245i	−0.722637	+	0.691227i	$0.757070\pi$
$492$	4.18128	−	4.18128i	0.188506	−	0.188506i
$493$	−14.9873	+	14.9873i	−0.674992	+	0.674992i
$494$	−5.24305			−0.235896
$495$	−3.63995	+	2.04729i	−0.163604	+	0.0920189i
$496$	−5.27790	−	1.77308i	−0.236985	−	0.0796135i
$497$	1.20252	+	1.20252i	0.0539403	+	0.0539403i
$498$	0.710451	−	0.710451i	0.0318361	−	0.0318361i
$499$	32.3691			1.44904			0.724521	−	0.689253i	$-0.242061\pi$
$499$	32.3691			1.44904			0.724521	+	0.689253i	$0.242061\pi$
$500$	11.1740	+	0.377160i	0.499715	+	0.0168671i
$501$	−19.0988			−0.853273
$502$	17.8172	−	17.8172i	0.795220	−	0.795220i
$503$	−2.45641	+	2.45641i	−0.109526	+	0.109526i	−0.759746	−	0.650220i	$-0.774677\pi$
$503$	−2.45641	+	2.45641i	−0.109526	+	0.109526i	0.650220	+	0.759746i	$0.274677\pi$
$504$		−	2.18403i		−	0.0972845i
$505$	−24.0797	+	13.5436i	−1.07153	+	0.602684i
$506$	6.50427			0.289150
$507$	7.73752	−	7.73752i	0.343635	−	0.343635i
$508$	−5.46441	−	5.46441i	−0.242444	−	0.242444i
$509$	15.3382			0.679853			0.339927	−	0.940452i	$-0.389598\pi$
$509$	15.3382			0.679853			0.339927	+	0.940452i	$0.389598\pi$
$510$	−14.1477	−	3.96192i	−0.626469	−	0.175437i
$511$			5.94924i			0.263179i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	2.58463	+	2.58463i	0.114114	+	0.114114i
$514$		−	22.3572i		−	0.986135i
$515$	2.59761	−	9.27583i	0.114464	−	0.408742i
$516$	−4.96918			−0.218756
$517$	9.70464	−	9.70464i	0.426810	−	0.426810i
$518$	11.7520	+	11.7520i	0.516354	+	0.516354i
$519$	13.4610			0.590871
$520$	2.79556	−	1.57237i	0.122594	−	0.0689528i
$521$	20.4588			0.896318			0.448159	−	0.893954i	$-0.352080\pi$
$521$	20.4588			0.896318			0.448159	+	0.893954i	$0.352080\pi$
$522$	−2.28101	+	2.28101i	−0.0998373	+	0.0998373i
$523$	12.6091	+	12.6091i	0.551358	+	0.551358i	0.926833	−	0.375475i	$-0.122520\pi$
$523$	12.6091	+	12.6091i	0.551358	+	0.551358i	−0.375475	+	0.926833i	$0.622520\pi$
$524$		−	15.3951i		−	0.672537i
$525$	−9.33193	−	5.67140i	−0.407279	−	0.247520i
$526$		−	12.3157i		−	0.536990i
$527$	32.7588	−	16.2834i	1.42700	−	0.709315i
$528$	1.32063	−	1.32063i	0.0574730	−	0.0574730i
$529$		−	10.8716i		−	0.472677i
$530$	−11.9725	−	21.2863i	−0.520051	−	0.924616i
$531$	−4.31789			−0.187380
$532$	−5.64492	−	5.64492i	−0.244738	−	0.244738i
$533$	−5.99762	−	5.99762i	−0.259786	−	0.259786i
$534$		−	7.40439i		−	0.320419i
$535$	−8.67163	−	2.42841i	−0.374907	−	0.104989i
$536$	10.9344			0.472293
$537$	−8.33278	−	8.33278i	−0.359586	−	0.359586i
$538$	14.4413	+	14.4413i	0.622608	+	0.622608i
$539$	4.16488			0.179394
$540$	−2.15323	−	0.602992i	−0.0926603	−	0.0259486i
$541$	46.0012			1.97775			0.988873	−	0.148764i	$-0.0475295\pi$
$541$	46.0012			1.97775			0.988873	+	0.148764i	$0.0475295\pi$
$542$	−8.57814	+	8.57814i	−0.368463	+	0.368463i
$543$	−16.2656	+	16.2656i	−0.698023	+	0.698023i
$544$	6.57044			0.281705
$545$	−9.40523	−	16.7219i	−0.402876	−	0.716286i
$546$	−3.13277			−0.134070
$547$	3.47797	+	3.47797i	0.148707	+	0.148707i	0.777540	−	0.628833i	$-0.216467\pi$
$547$	3.47797	+	3.47797i	0.148707	+	0.148707i	−0.628833	+	0.777540i	$0.716467\pi$
$548$	1.80311	+	1.80311i	0.0770251	+	0.0770251i
$549$	9.74941			0.416095
$550$	−2.21343	−	9.07215i	−0.0943810	−	0.386838i
$551$			11.7912i			0.502321i
$552$	2.46256	+	2.46256i	0.104814	+	0.104814i
$553$	−7.27439	−	7.27439i	−0.309338	−	0.309338i
$554$	11.2236			0.476844
$555$	14.8309	−	8.34166i	0.629538	−	0.354084i
$556$		−	8.56030i		−	0.363038i
$557$	29.8683	−	29.8683i	1.26556	−	1.26556i	0.317205	−	0.948357i	$-0.397256\pi$
$557$	29.8683	−	29.8683i	1.26556	−	1.26556i	0.948357	−	0.317205i	$-0.102744\pi$
$558$	4.98579	−	2.47828i	0.211065	−	0.104914i
$559$			7.12779i			0.301473i
$560$	4.70272	+	1.31695i	0.198726	+	0.0556514i
$561$			12.2713i			0.518094i
$562$	−1.24524	−	1.24524i	−0.0525272	−	0.0525272i
$563$	26.4338	−	26.4338i	1.11405	−	1.11405i	0.121456	−	0.992597i	$-0.461244\pi$
$563$	26.4338	−	26.4338i	1.11405	−	1.11405i	0.992597	−	0.121456i	$-0.0387563\pi$
$564$	7.34849			0.309427
$565$	−4.24636	+	15.1634i	−0.178646	+	0.637928i
$566$	7.18992			0.302215
$567$	1.54434	+	1.54434i	0.0648563	+	0.0648563i
$568$	−0.550595	+	0.550595i	−0.0231025	+	0.0231025i
$569$	17.6443			0.739688			0.369844	−	0.929094i	$-0.379411\pi$
$569$	17.6443			0.739688			0.369844	+	0.929094i	$0.379411\pi$
$570$	−7.12383	+	4.00680i	−0.298384	+	0.167826i
$571$			19.0194i			0.795936i	0.917399	+	0.397968i	$0.130285\pi$
$571$			19.0194i			0.795936i	−0.917399	+	0.397968i	$0.869715\pi$
$572$	−1.89431	−	1.89431i	−0.0792051	−	0.0792051i
$573$	3.66540	+	3.66540i	0.153124	+	0.153124i
$574$		−	12.9146i		−	0.539047i
$575$	16.9167	−	4.12736i	0.705477	−	0.172123i
$576$	1.00000			0.0416667
$577$	10.4769	+	10.4769i	0.436160	+	0.436160i	0.890718	−	0.454557i	$-0.150203\pi$
$577$	10.4769	+	10.4769i	0.436160	+	0.436160i	−0.454557	+	0.890718i	$0.650203\pi$
$578$	−18.5054	+	18.5054i	−0.769724	+	0.769724i
$579$	16.6758			0.693023
$580$	−3.53612	−	6.28698i	−0.146829	−	0.261053i
$581$		−	2.19436i		−	0.0910374i
$582$	−3.69010	+	3.69010i	−0.152959	+	0.152959i
$583$	−14.4238	+	14.4238i	−0.597375	+	0.597375i
$584$	−2.72397			−0.112719
$585$	−0.864931	+	3.08859i	−0.0357605	+	0.127698i
$586$	19.7051			0.814012
$587$	−7.40949	+	7.40949i	−0.305822	+	0.305822i	−0.843287	−	0.537464i	$-0.819382\pi$
$587$	−7.40949	+	7.40949i	−0.305822	+	0.305822i	0.537464	+	0.843287i	$0.319382\pi$
$588$	1.57686	+	1.57686i	0.0650284	+	0.0650284i
$589$	6.48100	−	19.2919i	0.267045	−	0.794909i
$590$	2.60365	−	9.29741i	0.107191	−	0.382768i
$591$	−21.9639			−0.903473
$592$	−5.38089	+	5.38089i	−0.221153	+	0.221153i
$593$	−5.53779	+	5.53779i	−0.227410	+	0.227410i	−0.811610	−	0.584200i	$-0.801408\pi$
$593$	−5.53779	+	5.53779i	−0.227410	+	0.227410i	0.584200	+	0.811610i	$0.301408\pi$
$594$			1.86765i			0.0766307i
$595$	−27.9674	+	15.7303i	−1.14655	+	0.644879i
$596$	−21.7052			−0.889078
$597$	−16.6231	−	16.6231i	−0.680339	−	0.680339i
$598$	3.53230	−	3.53230i	0.144446	−	0.144446i
$599$			28.0156i			1.14469i	0.820015	+	0.572343i	$0.193965\pi$
$599$			28.0156i			1.14469i	−0.820015	+	0.572343i	$0.806035\pi$
$600$	2.59676	−	4.27280i	0.106012	−	0.174436i
$601$		−	5.51667i		−	0.225030i	−0.993650	−	0.112515i	$-0.964109\pi$
$601$		−	5.51667i		−	0.225030i	0.993650	−	0.112515i	$-0.0358906\pi$
$602$	−7.67412	+	7.67412i	−0.312774	+	0.312774i
$603$	−7.73177	+	7.73177i	−0.314862	+	0.314862i
$604$	−12.9017			−0.524961
$605$	14.6402	−	8.23440i	0.595209	−	0.334776i
$606$			12.3553i			0.501898i
$607$	−1.49773	−	1.49773i	−0.0607909	−	0.0607909i	0.676058	−	0.736849i	$-0.263687\pi$
$607$	−1.49773	−	1.49773i	−0.0607909	−	0.0607909i	−0.736849	+	0.676058i	$0.763687\pi$
$608$	2.58463	−	2.58463i	0.104821	−	0.104821i
$609$			7.04533i			0.285491i
$610$	−5.87881	+	20.9927i	−0.238026	+	0.849971i
$611$		−	10.5407i		−	0.426430i
$612$	−4.64600	+	4.64600i	−0.187803	+	0.187803i
$613$	−15.4778	−	15.4778i	−0.625144	−	0.625144i	0.321698	−	0.946842i	$-0.395746\pi$
$613$	−15.4778	−	15.4778i	−0.625144	−	0.625144i	−0.946842	+	0.321698i	$0.895746\pi$
$614$			18.6646i			0.753243i
$615$	−12.7325	−	3.56562i	−0.513425	−	0.143780i
$616$		−	4.07901i		−	0.164348i
$617$	1.15700	+	1.15700i	0.0465791	+	0.0465791i	0.730013	−	0.683434i	$-0.239514\pi$
$617$	1.15700	+	1.15700i	0.0465791	+	0.0465791i	−0.683434	+	0.730013i	$0.739514\pi$
$618$	−3.04612	−	3.04612i	−0.122533	−	0.122533i
$619$	45.7597			1.83924			0.919619	−	0.392812i	$-0.128498\pi$
$619$	45.7597			1.83924			0.919619	+	0.392812i	$0.128498\pi$
$620$	2.32992	+	12.2299i	0.0935718	+	0.491166i
$621$	−3.48259			−0.139752
$622$	14.3055	+	14.3055i	0.573596	+	0.573596i
$623$	−11.4349	−	11.4349i	−0.458131	−	0.458131i
$624$		−	1.43440i		−	0.0574219i
$625$	−11.5137	−	22.1909i	−0.460547	−	0.887635i
$626$			2.46673i			0.0985904i
$627$	4.82720	+	4.82720i	0.192780	+	0.192780i
$628$	−10.1673	+	10.1673i	−0.405721	+	0.405721i
$629$		−	49.9992i		−	1.99360i
$630$	−4.25655	+	2.39410i	−0.169585	+	0.0953832i
$631$			31.8101i			1.26634i	0.774013	+	0.633170i	$0.218247\pi$
$631$			31.8101i			1.26634i	−0.774013	+	0.633170i	$0.781753\pi$
$632$	3.33072	−	3.33072i	0.132489	−	0.132489i
$633$	−12.4370	−	12.4370i	−0.494328	−	0.494328i
$634$			6.33947i			0.251772i
$635$	−4.65982	+	16.6398i	−0.184919	+	0.660331i
$636$	−10.9219			−0.433083
$637$	2.26184	−	2.26184i	0.0896174	−	0.0896174i
$638$	−4.26014	+	4.26014i	−0.168661	+	0.168661i
$639$		−	0.778659i		−	0.0308033i
$640$	−0.602992	+	2.15323i	−0.0238353	+	0.0851139i
$641$			12.9392i			0.511067i	0.966800	+	0.255534i	$0.0822512\pi$
$641$			12.9392i			0.511067i	−0.966800	+	0.255534i	$0.917749\pi$
$642$	−2.84771	+	2.84771i	−0.112390	+	0.112390i
$643$	26.2347	+	26.2347i	1.03459	+	1.03459i	0.999380	+	0.0352139i	$0.0112113\pi$
$643$	26.2347	+	26.2347i	1.03459	+	1.03459i	0.0352139	+	0.999380i	$0.488789\pi$
$644$	7.60609			0.299722
$645$	5.44714	+	9.68466i	0.214481	+	0.381333i
$646$			24.0164i			0.944913i
$647$	−21.1855	+	21.1855i	−0.832888	+	0.832888i	−0.987911	−	0.155023i	$-0.950455\pi$
$647$	−21.1855	+	21.1855i	−0.832888	+	0.832888i	0.155023	+	0.987911i	$0.450455\pi$
$648$	−0.707107	+	0.707107i	−0.0277778	+	0.0277778i
$649$	−8.06432			−0.316552
$650$	−6.12890	−	3.72479i	−0.240395	−	0.146098i
$651$	3.87246	−	11.5271i	0.151774	−	0.451782i
$652$	3.84676	+	3.84676i	0.150651	+	0.150651i
$653$	1.11145	−	1.11145i	0.0434942	−	0.0434942i	−0.685025	−	0.728519i	$-0.740209\pi$
$653$	1.11145	−	1.11145i	0.0434942	−	0.0434942i	0.728519	+	0.685025i	$0.240209\pi$
$654$	−8.57997			−0.335503
$655$	−30.0041	+	16.8758i	−1.17236	+	0.659394i
$656$	5.91322			0.230872
$657$	1.92614	−	1.92614i	0.0751458	−	0.0751458i
$658$	11.3486	−	11.3486i	0.442414	−	0.442414i
$659$			32.1006i			1.25046i	0.780439	+	0.625231i	$0.214995\pi$
$659$			32.1006i			1.25046i	−0.780439	+	0.625231i	$0.785005\pi$
$660$	−4.02149	−	1.12618i	−0.156536	−	0.0438365i
$661$	27.0522			1.05221			0.526105	−	0.850420i	$-0.323652\pi$
$661$	27.0522			1.05221			0.526105	+	0.850420i	$0.323652\pi$
$662$	−5.82455	+	5.82455i	−0.226378	+	0.226378i
$663$	6.66422	+	6.66422i	0.258817	+	0.258817i
$664$	1.00473			0.0389911
$665$	−4.81376	+	17.1895i	−0.186669	+	0.666580i
$666$		−	7.60973i		−	0.294871i
$667$	−7.94384	−	7.94384i	−0.307587	−	0.307587i
$668$	−13.5049	−	13.5049i	−0.522521	−	0.522521i
$669$			20.3129i			0.785341i
$670$	−11.9861	−	21.3105i	−0.463063	−	0.823296i
$671$	18.2085			0.702932
$672$	1.54434	−	1.54434i	0.0595743	−	0.0595743i
$673$	−7.62528	−	7.62528i	−0.293933	−	0.293933i	0.544699	−	0.838632i	$-0.316644\pi$
$673$	−7.62528	−	7.62528i	−0.293933	−	0.293933i	−0.838632	+	0.544699i	$0.816644\pi$
$674$	2.17268			0.0836887
$675$	1.18514	+	4.85751i	0.0456161	+	0.186966i
$676$	10.9425			0.420865
$677$	−20.0859	+	20.0859i	−0.771963	+	0.771963i	−0.978449	−	0.206487i	$-0.933797\pi$
$677$	−20.0859	+	20.0859i	−0.771963	+	0.771963i	0.206487	+	0.978449i	$0.433797\pi$
$678$	4.97955	+	4.97955i	0.191239	+	0.191239i
$679$			11.3976i			0.437398i
$680$	−7.20241	−	12.8054i	−0.276200	−	0.491065i
$681$			10.5004i			0.402376i
$682$	9.31173	−	4.62857i	0.356564	−	0.177237i
$683$	16.9034	−	16.9034i	0.646792	−	0.646792i	−0.305424	−	0.952216i	$-0.598798\pi$
$683$	16.9034	−	16.9034i	0.646792	−	0.646792i	0.952216	+	0.305424i	$0.0987982\pi$
$684$			3.65522i			0.139761i
$685$	1.53762	−	5.49070i	0.0587494	−	0.209789i
$686$	20.1586			0.769660
$687$	−20.7316	−	20.7316i	−0.790959	−	0.790959i
$688$	−3.51374	−	3.51374i	−0.133960	−	0.133960i
$689$			15.6664i			0.596843i
$690$	2.09997	−	7.49882i	0.0799446	−	0.285475i
$691$	−16.3872			−0.623398			−0.311699	−	0.950181i	$-0.600898\pi$
$691$	−16.3872			−0.623398			−0.311699	+	0.950181i	$0.600898\pi$
$692$	9.51835	+	9.51835i	0.361833	+	0.361833i
$693$	2.88430	+	2.88430i	0.109565	+	0.109565i
$694$	−14.6655			−0.556696
$695$	−16.6835	+	9.38367i	−0.632843	+	0.355943i
$696$	−3.22584			−0.122275
$697$	−27.4728	+	27.4728i	−1.04061	+	1.04061i
$698$	16.2458	−	16.2458i	0.614912	−	0.614912i
$699$	0.516538			0.0195373
$700$	−2.58838	−	10.6090i	−0.0978317	−	0.400981i
$701$	−42.6327			−1.61021			−0.805107	−	0.593130i	$-0.797892\pi$
$701$	−42.6327			−1.61021			−0.805107	+	0.593130i	$0.797892\pi$
$702$	1.01427	+	1.01427i	0.0382813	+	0.0382813i
$703$	−19.6684	−	19.6684i	−0.741806	−	0.741806i
$704$	1.86765			0.0703898
$705$	−8.05530	−	14.3218i	−0.303380	−	0.539390i
$706$			21.5644i			0.811588i
$707$	19.0808	+	19.0808i	0.717606	+	0.717606i
$708$	−3.05321	−	3.05321i	−0.114747	−	0.114747i
$709$	14.7931			0.555568			0.277784	−	0.960644i	$-0.410400\pi$
$709$	14.7931			0.555568			0.277784	+	0.960644i	$0.410400\pi$
$710$	1.67663	+	0.469525i	0.0629229	+	0.0176210i
$711$			4.71035i			0.176652i
$712$	5.23570	−	5.23570i	0.196216	−	0.196216i
$713$	8.63084	+	17.3635i	0.323227	+	0.650267i
$714$			14.3500i			0.537036i
$715$	−1.61539	+	5.76842i	−0.0604122	+	0.215727i
$716$		−	11.7843i		−	0.440401i
$717$	1.24932	+	1.24932i	0.0466566	+	0.0466566i
$718$	−0.465759	+	0.465759i	−0.0173820	+	0.0173820i
$719$	−49.6784			−1.85269			−0.926345	−	0.376676i	$-0.877067\pi$
$719$	−49.6784			−1.85269			−0.926345	+	0.376676i	$0.877067\pi$
$720$	−1.09618	−	1.94894i	−0.0408524	−	0.0726328i
$721$	−9.40851			−0.350391
$722$	−3.98761	−	3.98761i	−0.148403	−	0.148403i
$723$	4.96042	−	4.96042i	0.184480	−	0.184480i
$724$	−23.0030			−0.854901
$725$	−8.37673	+	13.7834i	−0.311104	+	0.511902i
$726$		−	7.51187i		−	0.278792i
$727$	21.5766	+	21.5766i	0.800230	+	0.800230i	0.983131	−	0.182901i	$-0.0585489\pi$
$727$	21.5766	+	21.5766i	0.800230	+	0.800230i	−0.182901	+	0.983131i	$0.558549\pi$
$728$	−2.21520	−	2.21520i	−0.0821009	−	0.0821009i
$729$		−	1.00000i		−	0.0370370i
$730$	2.98597	+	5.30886i	0.110516	+	0.196490i
$731$	32.6497			1.20759
$732$	6.89387	+	6.89387i	0.254805	+	0.254805i
$733$	−7.54400	+	7.54400i	−0.278644	+	0.278644i	−0.832568	−	0.553923i	$-0.813130\pi$
$733$	−7.54400	+	7.54400i	−0.278644	+	0.278644i	0.553923	+	0.832568i	$0.313130\pi$
$734$	28.5001			1.05196
$735$	1.34468	−	4.80173i	0.0495992	−	0.177114i
$736$			3.48259i			0.128370i
$737$	−14.4403	+	14.4403i	−0.531914	+	0.531914i
$738$	−4.18128	+	4.18128i	−0.153915	+	0.153915i
$739$	−21.6305			−0.795689			−0.397845	−	0.917453i	$-0.630242\pi$
$739$	−21.6305			−0.795689			−0.397845	+	0.917453i	$0.630242\pi$
$740$	16.3855	+	4.58860i	0.602343	+	0.168680i
$741$	5.24305			0.192608
$742$	−16.8672	+	16.8672i	−0.619215	+	0.619215i
$743$	−29.6241	−	29.6241i	−1.08680	−	1.08680i	−0.995856	−	0.0909490i	$-0.971010\pi$
$743$	−29.6241	−	29.6241i	−1.08680	−	1.08680i	−0.0909490	−	0.995856i	$-0.528990\pi$
$744$	5.27790	+	1.77308i	0.193497	+	0.0650042i
$745$	23.7929	+	42.3021i	0.871703	+	1.54983i
$746$	−12.5378			−0.459041
$747$	−0.710451	+	0.710451i	−0.0259940	+	0.0259940i
$748$	−8.67711	+	8.67711i	−0.317267	+	0.317267i
$749$			8.79568i			0.321387i
$750$	−11.1740	−	0.377160i	−0.408016	−	0.0137719i
$751$	17.7787			0.648755			0.324377	−	0.945928i	$-0.394845\pi$
$751$	17.7787			0.648755			0.324377	+	0.945928i	$0.394845\pi$
$752$	5.19617	+	5.19617i	0.189485	+	0.189485i
$753$	−17.8172	+	17.8172i	−0.649294	+	0.649294i
$754$			4.62714i			0.168511i
$755$	14.1426	+	25.1446i	0.514702	+	0.915105i
$756$			2.18403i			0.0794324i
$757$	−26.6118	+	26.6118i	−0.967221	+	0.967221i	−0.999480	−	0.0322590i	$-0.989730\pi$
$757$	−26.6118	+	26.6118i	−0.967221	+	0.967221i	0.0322590	+	0.999480i	$0.489730\pi$
$758$	−12.9169	+	12.9169i	−0.469163	+	0.469163i
$759$	−6.50427			−0.236090
$760$	−7.87054	−	2.20407i	−0.285495	−	0.0799500i
$761$		−	10.8003i		−	0.391512i	−0.980653	−	0.195756i	$-0.937284\pi$
$761$		−	10.8003i		−	0.391512i	0.980653	−	0.195756i	$-0.0627161\pi$
$762$	5.46441	+	5.46441i	0.197955	+	0.197955i
$763$	−13.2504	+	13.2504i	−0.479697	+	0.479697i
$764$			5.18365i			0.187538i
$765$	14.1477	+	3.96192i	0.511510	+	0.143243i
$766$		−	2.22684i		−	0.0804589i
$767$	−4.37952	+	4.37952i	−0.158135	+	0.158135i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$		−	49.1797i		−	1.77347i	−0.462281	−	0.886733i	$-0.652969\pi$
$769$		−	49.1797i		−	1.77347i	0.462281	−	0.886733i	$-0.347031\pi$
$770$	−7.94976	+	4.47135i	−0.286489	+	0.161136i
$771$			22.3572i			0.805176i
$772$	11.7916	+	11.7916i	0.424388	+	0.424388i
$773$	−27.2433	−	27.2433i	−0.979872	−	0.979872i	0.0199289	−	0.999801i	$-0.493656\pi$
$773$	−27.2433	−	27.2433i	−0.979872	−	0.979872i	−0.999801	+	0.0199289i	$0.993656\pi$
$774$	4.96918			0.178614
$775$	21.2814	−	17.9471i	0.764452	−	0.644681i
$776$	−5.21859			−0.187336
$777$	−11.7520	−	11.7520i	−0.421602	−	0.421602i
$778$	−10.0762	−	10.0762i	−0.361248	−	0.361248i
$779$			21.6141i			0.774407i
$780$	−2.79556	+	1.57237i	−0.100097	+	0.0562997i
$781$		−	1.45427i		−	0.0520377i
$782$	−16.1801	−	16.1801i	−0.578600	−	0.578600i
$783$	2.28101	−	2.28101i	0.0815168	−	0.0815168i
$784$			2.23001i			0.0796432i
$785$	30.9608	+	8.67029i	1.10504	+	0.309456i
$786$			15.3951i			0.549124i
$787$	29.0473	−	29.0473i	1.03542	−	1.03542i	0.0360759	−	0.999349i	$-0.488514\pi$
$787$	29.0473	−	29.0473i	1.03542	−	1.03542i	0.999349	−	0.0360759i	$-0.0114858\pi$
$788$	−15.5308	−	15.5308i	−0.553262	−	0.553262i
$789$			12.3157i			0.438450i
$790$	−10.1425	−	2.84030i	−0.360853	−	0.101053i
$791$	15.3803			0.546859
$792$	−1.32063	+	1.32063i	−0.0469265	+	0.0469265i
$793$	9.88857	−	9.88857i	0.351153	−	0.351153i
$794$			22.6927i			0.805333i
$795$	11.9725	+	21.2863i	0.424620	+	0.754946i
$796$		−	23.5086i		−	0.833242i
$797$	16.6727	−	16.6727i	0.590577	−	0.590577i	−0.347211	−	0.937787i	$-0.612871\pi$
$797$	16.6727	−	16.6727i	0.590577	−	0.590577i	0.937787	+	0.347211i	$0.112871\pi$
$798$	5.64492	+	5.64492i	0.199828	+	0.199828i
$799$	−48.2828			−1.70812
$800$	4.85751	−	1.18514i	0.171739	−	0.0419010i
$801$			7.40439i			0.261621i
$802$	16.1282	−	16.1282i	0.569507	−	0.569507i
$803$	3.59736	−	3.59736i	0.126948	−	0.126948i
$804$	−10.9344			−0.385626
$805$	−8.33767	−	14.8238i	−0.293864	−	0.522471i
$806$	2.54330	−	7.57061i	0.0895840	−	0.266663i
$807$	−14.4413	−	14.4413i	−0.508358	−	0.508358i
$808$	−8.73649	+	8.73649i	−0.307349	+	0.307349i
$809$	47.1253			1.65684			0.828419	−	0.560108i	$-0.189241\pi$
$809$	47.1253			1.65684			0.828419	+	0.560108i	$0.189241\pi$
$810$	2.15323	+	0.602992i	0.0756568	+	0.0211870i
$811$	3.30151			0.115932			0.0579659	−	0.998319i	$-0.481539\pi$
$811$	3.30151			0.115932			0.0579659	+	0.998319i	$0.481539\pi$
$812$	−4.98180	+	4.98180i	−0.174827	+	0.174827i
$813$	8.57814	−	8.57814i	0.300848	−	0.300848i
$814$		−	14.2123i		−	0.498142i
$815$	3.28036	−	11.7139i	0.114906	−	0.410319i
$816$	−6.57044			−0.230011
$817$	12.8435	−	12.8435i	0.449338	−	0.449338i
$818$	13.3389	+	13.3389i	0.466384	+	0.466384i
$819$	3.13277			0.109468
$820$	−6.48198	−	11.5245i	−0.226360	−	0.402454i
$821$			37.5712i			1.31124i	0.755089	+	0.655622i	$0.227593\pi$
$821$			37.5712i			1.31124i	−0.755089	+	0.655622i	$0.772407\pi$
$822$	−1.80311	−	1.80311i	−0.0628907	−	0.0628907i
$823$	−25.1625	−	25.1625i	−0.877111	−	0.877111i	0.116123	−	0.993235i	$-0.462953\pi$
$823$	−25.1625	−	25.1625i	−0.877111	−	0.877111i	−0.993235	+	0.116123i	$0.962953\pi$
$824$		−	4.30787i		−	0.150072i
$825$	2.21343	+	9.07215i	0.0770618	+	0.315852i
$826$	−9.43040			−0.328126
$827$	35.3564	−	35.3564i	1.22946	−	1.22946i	0.265296	−	0.964167i	$-0.414530\pi$
$827$	35.3564	−	35.3564i	1.22946	−	1.22946i	0.964167	−	0.265296i	$-0.0854698\pi$
$828$	−2.46256	−	2.46256i	−0.0855800	−	0.0855800i
$829$	42.0139			1.45920			0.729601	−	0.683873i	$-0.239706\pi$
$829$	42.0139			1.45920			0.729601	+	0.683873i	$0.239706\pi$
$830$	−1.10137	−	1.95816i	−0.0382291	−	0.0679688i
$831$	−11.2236			−0.389341
$832$	1.01427	−	1.01427i	0.0351636	−	0.0351636i
$833$	−10.3606	−	10.3606i	−0.358974	−	0.358974i
$834$			8.56030i			0.296419i
$835$	−11.5164	+	41.1242i	−0.398543	+	1.42316i
$836$			6.82669i			0.236106i
$837$	−4.98579	+	2.47828i	−0.172334	+	0.0856619i
$838$	14.9106	−	14.9106i	0.515080	−	0.515080i
$839$			9.57891i			0.330701i	0.986235	+	0.165350i	$0.0528755\pi$
$839$			9.57891i			0.330701i	−0.986235	+	0.165350i	$0.947125\pi$
$840$	−4.70272	−	1.31695i	−0.162259	−	0.0454392i
$841$	−18.5940			−0.641171
$842$	6.37283	+	6.37283i	0.219622	+	0.219622i
$843$	1.24524	+	1.24524i	0.0428883	+	0.0428883i
$844$		−	17.5886i		−	0.605426i
$845$	−11.9950	−	21.3263i	−0.412640	−	0.733647i
$846$	−7.34849			−0.252646
$847$	−11.6009	−	11.6009i	−0.398612	−	0.398612i
$848$	−7.72298	−	7.72298i	−0.265208	−	0.265208i
$849$	−7.18992			−0.246757
$850$	−17.0618	+	28.0742i	−0.585216	+	0.962936i
$851$	26.5016			0.908462
$852$	0.550595	−	0.550595i	0.0188631	−	0.0188631i
$853$	−13.7084	+	13.7084i	−0.469366	+	0.469366i	−0.901709	−	0.432343i	$-0.857687\pi$
$853$	−13.7084	+	13.7084i	−0.469366	+	0.469366i	0.432343	+	0.901709i	$0.357687\pi$
$854$	21.2930			0.728632
$855$	7.12383	−	4.00680i	0.243630	−	0.137030i
$856$	−4.02727			−0.137649
$857$	−5.24670	−	5.24670i	−0.179224	−	0.179224i	0.611794	−	0.791017i	$-0.290448\pi$
$857$	−5.24670	−	5.24670i	−0.179224	−	0.179224i	−0.791017	+	0.611794i	$0.790448\pi$
$858$	1.89431	+	1.89431i	0.0646707	+	0.0646707i
$859$	−29.2574			−0.998251			−0.499125	−	0.866530i	$-0.666345\pi$
$859$	−29.2574			−0.998251			−0.499125	+	0.866530i	$0.666345\pi$
$860$	−2.99638	+	10.6998i	−0.102176	+	0.364860i
$861$			12.9146i			0.440130i
$862$	5.18592	+	5.18592i	0.176633	+	0.176633i
$863$	−0.790006	−	0.790006i	−0.0268921	−	0.0268921i	0.693533	−	0.720425i	$-0.256053\pi$
$863$	−0.790006	−	0.790006i	−0.0268921	−	0.0268921i	−0.720425	+	0.693533i	$0.756053\pi$
$864$	−1.00000			−0.0340207
$865$	8.11686	−	28.9846i	0.275981	−	0.985505i
$866$			17.2889i			0.587500i
$867$	18.5054	−	18.5054i	0.628477	−	0.628477i
$868$	10.8891	−	5.41264i	0.369601	−	0.183717i
$869$			8.79729i			0.298428i
$870$	3.53612	+	6.28698i	0.119886	+	0.213149i
$871$			15.6843i			0.531441i
$872$	−6.06695	−	6.06695i	−0.205453	−	0.205453i
$873$	3.69010	−	3.69010i	0.124891	−	0.124891i
$874$	−12.7297			−0.430587
$875$	−17.8389	+	16.6740i	−0.603065	+	0.563684i
$876$	2.72397			0.0920344
$877$	−21.8970	−	21.8970i	−0.739410	−	0.739410i	0.233054	−	0.972464i	$-0.425128\pi$
$877$	−21.8970	−	21.8970i	−0.739410	−	0.739410i	−0.972464	+	0.233054i	$0.925128\pi$
$878$	8.47336	−	8.47336i	0.285962	−	0.285962i
$879$	−19.7051			−0.664638
$880$	−2.04729	−	3.63995i	−0.0690142	−	0.122703i
$881$			47.0574i			1.58541i	0.609608	+	0.792703i	$0.291327\pi$
$881$			47.0574i			1.58541i	−0.609608	+	0.792703i	$0.708673\pi$
$882$	−1.57686	−	1.57686i	−0.0530955	−	0.0530955i
$883$	30.1977	+	30.1977i	1.01623	+	1.01623i	0.999866	+	0.0163658i	$0.00520964\pi$
$883$	30.1977	+	30.1977i	1.01623	+	1.01623i	0.0163658	+	0.999866i	$0.494790\pi$
$884$			9.42463i			0.316984i
$885$	−2.60365	+	9.29741i	−0.0875208	+	0.312529i
$886$	−37.0511			−1.24476
$887$	−33.2322	−	33.2322i	−1.11583	−	1.11583i	−0.992347	−	0.123480i	$-0.960595\pi$
$887$	−33.2322	−	33.2322i	−1.11583	−	1.11583i	−0.123480	−	0.992347i	$-0.539405\pi$
$888$	5.38089	−	5.38089i	0.180571	−	0.180571i
$889$	16.8778			0.566065
$890$	−15.9434	−	4.46479i	−0.534423	−	0.149660i
$891$		−	1.86765i		−	0.0625687i
$892$	−14.3634	+	14.3634i	−0.480921	+	0.480921i
$893$	−18.9932	+	18.9932i	−0.635582	+	0.635582i
$894$	21.7052			0.725929
$895$	−22.9670	+	12.9178i	−0.767702	+	0.431795i
$896$	2.18403			0.0729633
$897$	−3.53230	+	3.53230i	−0.117940	+	0.117940i
$898$	0.160863	+	0.160863i	0.00536805	+	0.00536805i
$899$	−17.0257	−	5.71967i	−0.567837	−	0.190762i
$900$	−2.59676	+	4.27280i	−0.0865587	+	0.142427i
$901$	71.7619			2.39074
$902$	−7.80917	+	7.80917i	−0.260017	+	0.260017i
$903$	7.67412	−	7.67412i	0.255379	−	0.255379i
$904$			7.04215i			0.234218i
$905$	25.2155	+	44.8316i	0.838193	+	1.49025i
$906$	12.9017			0.428629
$907$	−14.2494	−	14.2494i	−0.473142	−	0.473142i	0.429788	−	0.902930i	$-0.358588\pi$
$907$	−14.2494	−	14.2494i	−0.473142	−	0.473142i	−0.902930	+	0.429788i	$0.858588\pi$
$908$	−7.42490	+	7.42490i	−0.246404	+	0.246404i
$909$		−	12.3553i		−	0.409798i
$910$	−1.88904	+	6.74558i	−0.0626209	+	0.223614i
$911$		−	10.2920i		−	0.340990i	−0.985359	−	0.170495i	$-0.945463\pi$
$911$		−	10.2920i		−	0.340990i	0.985359	−	0.170495i	$-0.0545367\pi$
$912$	−2.58463	+	2.58463i	−0.0855858	+	0.0855858i
$913$	−1.32688	+	1.32688i	−0.0439132	+	0.0439132i
$914$	−22.2868			−0.737181
$915$	5.87881	−	20.9927i	0.194348	−	0.693998i
$916$		−	29.3189i		−	0.968723i
$917$	23.7753	+	23.7753i	0.785129	+	0.785129i
$918$	4.64600	−	4.64600i	0.153341	−	0.153341i
$919$		−	20.6370i		−	0.680750i	−0.940290	−	0.340375i	$-0.889446\pi$
$919$		−	20.6370i		−	0.680750i	0.940290	−	0.340375i	$-0.110554\pi$
$920$	6.78737	−	3.81756i	0.223773	−	0.125861i
$921$		−	18.6646i		−	0.615020i
$922$	−10.4077	+	10.4077i	−0.342758	+	0.342758i
$923$	−0.789774	−	0.789774i	−0.0259957	−	0.0259957i
$924$			4.07901i			0.134190i
$925$	−9.01859	−	36.9643i	−0.296530	−	1.21538i
$926$			18.9700i			0.623393i
$927$	3.04612	+	3.04612i	0.100048	+	0.100048i
$928$	−2.28101	−	2.28101i	−0.0748779	−	0.0748779i
$929$	44.9134			1.47356			0.736780	−	0.676133i	$-0.236345\pi$
$929$	44.9134			1.47356			0.736780	+	0.676133i	$0.236345\pi$
$930$	−2.32992	−	12.2299i	−0.0764011	−	0.401036i
$931$	−8.15119			−0.267144
$932$	0.365247	+	0.365247i	0.0119641	+	0.0119641i
$933$	−14.3055	−	14.3055i	−0.468340	−	0.468340i
$934$			1.45741i			0.0476881i
$935$	26.4229	+	7.39949i	0.864122	+	0.241989i
$936$			1.43440i			0.0468848i
$937$	−5.38387	−	5.38387i	−0.175883	−	0.175883i	0.613675	−	0.789559i	$-0.289690\pi$
$937$	−5.38387	−	5.38387i	−0.175883	−	0.175883i	−0.789559	+	0.613675i	$0.789690\pi$
$938$	−16.8864	+	16.8864i	−0.551362	+	0.551362i
$939$		−	2.46673i		−	0.0804987i
$940$	4.43108	−	15.8230i	0.144526	−	0.516089i
$941$		−	54.4448i		−	1.77485i	−0.460953	−	0.887424i	$-0.652492\pi$
$941$		−	54.4448i		−	1.77485i	0.460953	−	0.887424i	$-0.347508\pi$
$942$	10.1673	−	10.1673i	0.331270	−	0.331270i
$943$	−14.5617	−	14.5617i	−0.474193	−	0.474193i
$944$		−	4.31789i		−	0.140535i
$945$	4.25655	−	2.39410i	0.138466	−	0.0778801i
$946$	9.28071			0.301742
$947$	−7.87387	+	7.87387i	−0.255866	+	0.255866i	−0.823371	−	0.567504i	$-0.807909\pi$
$947$	−7.87387	+	7.87387i	−0.255866	+	0.255866i	0.567504	+	0.823371i	$0.307909\pi$
$948$	−3.33072	+	3.33072i	−0.108177	+	0.108177i
$949$		−	3.90726i		−	0.126835i
$950$	4.33196	+	17.7553i	0.140547	+	0.576058i
$951$		−	6.33947i		−	0.205571i
$952$	−10.1470	+	10.1470i	−0.328866	+	0.328866i
$953$	−0.479006	−	0.479006i	−0.0155165	−	0.0155165i	0.699306	−	0.714822i	$-0.253493\pi$
$953$	−0.479006	−	0.479006i	−0.0155165	−	0.0155165i	−0.714822	+	0.699306i	$0.753493\pi$
$954$	10.9219			0.353611
$955$	10.1026	−	5.68224i	0.326914	−	0.183873i
$956$			1.76680i			0.0571424i
$957$	4.26014	−	4.26014i	0.137711	−	0.137711i
$958$	−17.7106	+	17.7106i	−0.572202	+	0.572202i
$959$	−5.56924			−0.179840
$960$	0.602992	−	2.15323i	0.0194615	−	0.0694952i
$961$	24.7124	+	18.7162i	0.797174	+	0.603750i
$962$	−7.71834	−	7.71834i	−0.248849	−	0.248849i
$963$	2.84771	−	2.84771i	0.0917661	−	0.0917661i
$964$	7.01509			0.225941
$965$	10.0554	−	35.9068i	0.323694	−	1.15588i
$966$	−7.60609			−0.244722
$967$	23.5728	−	23.5728i	0.758051	−	0.758051i	−0.217916	−	0.975968i	$-0.569926\pi$
$967$	23.5728	−	23.5728i	0.758051	−	0.758051i	0.975968	+	0.217916i	$0.0699259\pi$
$968$	5.31170	−	5.31170i	0.170724	−	0.170724i
$969$		−	24.0164i		−	0.771519i
$970$	5.72053	+	10.1707i	0.183675	+	0.326562i
$971$	−45.9352			−1.47413			−0.737065	−	0.675822i	$-0.763789\pi$
$971$	−45.9352			−1.47413			−0.737065	+	0.675822i	$0.763789\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	13.2200	+	13.2200i	0.423815	+	0.423815i
$974$	−31.0854			−0.996040
$975$	6.12890	+	3.72479i	0.196282	+	0.119289i
$976$			9.74941i			0.312071i
$977$	4.99445	+	4.99445i	0.159786	+	0.159786i	0.782472	−	0.622686i	$-0.213958\pi$
$977$	4.99445	+	4.99445i	0.159786	+	0.159786i	−0.622686	+	0.782472i	$0.713958\pi$
$978$	−3.84676	−	3.84676i	−0.123006	−	0.123006i
$979$			13.8288i			0.441972i
$980$	4.34616	−	2.44450i	0.138833	−	0.0780868i
$981$	8.57997			0.273937
$982$	21.6609	−	21.6609i	0.691227	−	0.691227i
$983$	−7.87879	−	7.87879i	−0.251294	−	0.251294i	0.570207	−	0.821501i	$-0.306863\pi$
$983$	−7.87879	−	7.87879i	−0.251294	−	0.251294i	−0.821501	+	0.570207i	$0.806863\pi$
$984$	−5.91322			−0.188506
$985$	−13.2440	+	47.2933i	−0.421990	+	1.50689i
$986$	21.1952			0.674992
$987$	−11.3486	+	11.3486i	−0.361230	+	0.361230i
$988$	3.70740	+	3.70740i	0.117948	+	0.117948i
$989$			17.3056i			0.550287i
$990$	4.02149	+	1.12618i	0.127811	+	0.0357923i
$991$		−	21.0639i		−	0.669115i	−0.942375	−	0.334558i	$-0.891413\pi$
$991$		−	21.0639i		−	0.669115i	0.942375	−	0.334558i	$-0.108587\pi$
$992$	2.47828	+	4.98579i	0.0786855	+	0.158299i
$993$	5.82455	−	5.82455i	0.184837	−	0.184837i
$994$		−	1.70062i		−	0.0539403i
$995$	−45.8170	+	25.7698i	−1.45250	+	0.816958i
$996$	−1.00473			−0.0318361
$997$	42.3741	+	42.3741i	1.34200	+	1.34200i	0.894065	+	0.447937i	$0.147841\pi$
$997$	42.3741	+	42.3741i	1.34200	+	1.34200i	0.447937	+	0.894065i	$0.352159\pi$
$998$	−22.8884	−	22.8884i	−0.724521	−	0.724521i
$999$			7.60973i			0.240761i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.k.a.247.7	✓	32
5.3	odd	4		930.2.k.b.433.7	yes	32
31.30	odd	2		930.2.k.b.247.7	yes	32
155.123	even	4	inner	930.2.k.a.433.7	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.k.a.247.7	✓	32	1.1	even	1	trivial
930.2.k.a.433.7	yes	32	155.123	even	4	inner
930.2.k.b.247.7	yes	32	31.30	odd	2
930.2.k.b.433.7	yes	32	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(1.94894 - 1.09618i) q^{5} -1.00000i q^{6} +(-1.54434 - 1.54434i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(1.94894 - 1.09618i) q^{5} -1.00000i q^{6} +(-1.54434 - 1.54434i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(-2.15323 - 0.602992i) q^{10} +1.86765i q^{11} +(-0.707107 + 0.707107i) q^{12} +(1.01427 + 1.01427i) q^{13} +2.18403i q^{14} +(2.15323 + 0.602992i) q^{15} -1.00000 q^{16} +(4.64600 - 4.64600i) q^{17} +(0.707107 - 0.707107i) q^{18} -3.65522i q^{19} +(1.09618 + 1.94894i) q^{20} -2.18403i q^{21} +(1.32063 - 1.32063i) q^{22} +(2.46256 + 2.46256i) q^{23} +1.00000 q^{24} +(2.59676 - 4.27280i) q^{25} -1.43440i q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.54434 - 1.54434i) q^{28} -3.22584 q^{29} +(-1.09618 - 1.94894i) q^{30} +(5.27790 + 1.77308i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.32063 + 1.32063i) q^{33} -6.57044 q^{34} +(-4.70272 - 1.31695i) q^{35} -1.00000 q^{36} +(5.38089 - 5.38089i) q^{37} +(-2.58463 + 2.58463i) q^{38} +1.43440i q^{39} +(0.602992 - 2.15323i) q^{40} -5.91322 q^{41} +(-1.54434 + 1.54434i) q^{42} +(3.51374 + 3.51374i) q^{43} -1.86765 q^{44} +(1.09618 + 1.94894i) q^{45} -3.48259i q^{46} +(-5.19617 - 5.19617i) q^{47} +(-0.707107 - 0.707107i) q^{48} -2.23001i q^{49} +(-4.85751 + 1.18514i) q^{50} +6.57044 q^{51} +(-1.01427 + 1.01427i) q^{52} +(7.72298 + 7.72298i) q^{53} +1.00000 q^{54} +(2.04729 + 3.63995i) q^{55} -2.18403 q^{56} +(2.58463 - 2.58463i) q^{57} +(2.28101 + 2.28101i) q^{58} +4.31789i q^{59} +(-0.602992 + 2.15323i) q^{60} -9.74941i q^{61} +(-2.47828 - 4.98579i) q^{62} +(1.54434 - 1.54434i) q^{63} -1.00000i q^{64} +(3.08859 + 0.864931i) q^{65} +1.86765 q^{66} +(7.73177 + 7.73177i) q^{67} +(4.64600 + 4.64600i) q^{68} +3.48259i q^{69} +(2.39410 + 4.25655i) q^{70} -0.778659 q^{71} +(0.707107 + 0.707107i) q^{72} +(-1.92614 - 1.92614i) q^{73} -7.60973 q^{74} +(4.85751 - 1.18514i) q^{75} +3.65522 q^{76} +(2.88430 - 2.88430i) q^{77} +(1.01427 - 1.01427i) q^{78} +4.71035 q^{79} +(-1.94894 + 1.09618i) q^{80} -1.00000 q^{81} +(4.18128 + 4.18128i) q^{82} +(0.710451 + 0.710451i) q^{83} +2.18403 q^{84} +(3.96192 - 14.1477i) q^{85} -4.96918i q^{86} +(-2.28101 - 2.28101i) q^{87} +(1.32063 + 1.32063i) q^{88} +7.40439 q^{89} +(0.602992 - 2.15323i) q^{90} -3.13277i q^{91} +(-2.46256 + 2.46256i) q^{92} +(2.47828 + 4.98579i) q^{93} +7.34849i q^{94} +(-4.00680 - 7.12383i) q^{95} +1.00000i q^{96} +(-3.69010 - 3.69010i) q^{97} +(-1.57686 + 1.57686i) q^{98} -1.86765 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{7}+O(q^{10}) \) 32 * q - 4 * q^7	\( 32 q - 4 q^{7} + 4 q^{10} - 4 q^{15} - 32 q^{16} - 8 q^{17} + 4 q^{22} + 32 q^{24} + 8 q^{25} + 4 q^{28} - 8 q^{29} - 20 q^{31} - 4 q^{33} - 24 q^{35} - 32 q^{36} - 4 q^{37} + 16 q^{38} - 16 q^{41} - 4 q^{42} + 16 q^{43} + 8 q^{44} - 8 q^{47} - 16 q^{50} + 24 q^{53} + 32 q^{54} + 28 q^{55} - 16 q^{57} - 20 q^{58} + 16 q^{62} + 4 q^{63} - 56 q^{65} - 8 q^{66} + 32 q^{67} - 8 q^{68} - 28 q^{70} + 16 q^{71} + 20 q^{73} - 24 q^{74} + 16 q^{75} - 16 q^{76} + 40 q^{77} + 56 q^{79} - 32 q^{81} + 16 q^{82} - 72 q^{83} + 32 q^{85} + 20 q^{87} + 4 q^{88} + 64 q^{89} - 16 q^{93} + 32 q^{95} - 4 q^{97} + 16 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - 4 * q^7 + 4 * q^10 - 4 * q^15 - 32 * q^16 - 8 * q^17 + 4 * q^22 + 32 * q^24 + 8 * q^25 + 4 * q^28 - 8 * q^29 - 20 * q^31 - 4 * q^33 - 24 * q^35 - 32 * q^36 - 4 * q^37 + 16 * q^38 - 16 * q^41 - 4 * q^42 + 16 * q^43 + 8 * q^44 - 8 * q^47 - 16 * q^50 + 24 * q^53 + 32 * q^54 + 28 * q^55 - 16 * q^57 - 20 * q^58 + 16 * q^62 + 4 * q^63 - 56 * q^65 - 8 * q^66 + 32 * q^67 - 8 * q^68 - 28 * q^70 + 16 * q^71 + 20 * q^73 - 24 * q^74 + 16 * q^75 - 16 * q^76 + 40 * q^77 + 56 * q^79 - 32 * q^81 + 16 * q^82 - 72 * q^83 + 32 * q^85 + 20 * q^87 + 4 * q^88 + 64 * q^89 - 16 * q^93 + 32 * q^95 - 4 * q^97 + 16 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

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Database

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