LMFDB - Embedded newform 930.2.bf.a.377.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(377,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

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

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

chi := DirichletCharacter("930.377");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bf (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			377.15
Character	$\chi$	$=$	930.377
Dual form			930.2.bf.a.893.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.320052 + 1.70222i) q^{3} -1.00000i q^{4} +(1.97048 - 1.05698i) q^{5} +(-0.977343 - 1.42997i) q^{6} +(1.65949 - 0.444658i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.79513 - 1.08960i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.320052 + 1.70222i) q^{3} -1.00000i q^{4} +(1.97048 - 1.05698i) q^{5} +(-0.977343 - 1.42997i) q^{6} +(1.65949 - 0.444658i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.79513 - 1.08960i) q^{9} +(-0.645943 + 2.14074i) q^{10} +(3.05848 - 1.76581i) q^{11} +(1.70222 + 0.320052i) q^{12} +(-1.36225 - 0.365014i) q^{13} +(-0.859013 + 1.48785i) q^{14} +(1.16856 + 3.69249i) q^{15} -1.00000 q^{16} +(-1.90037 - 7.09227i) q^{17} +(2.74692 - 1.20599i) q^{18} +(5.33131 + 3.07803i) q^{19} +(-1.05698 - 1.97048i) q^{20} +(0.225785 + 2.96713i) q^{21} +(-0.914051 + 3.41129i) q^{22} +(-4.08541 - 4.08541i) q^{23} +(-1.42997 + 0.977343i) q^{24} +(2.76559 - 4.16551i) q^{25} +(1.22136 - 0.705153i) q^{26} +(2.74933 - 4.40921i) q^{27} +(-0.444658 - 1.65949i) q^{28} -0.557190 q^{29} +(-3.43728 - 1.78469i) q^{30} +(4.60155 - 3.13460i) q^{31} +(0.707107 - 0.707107i) q^{32} +(2.02693 + 5.77136i) q^{33} +(6.35875 + 3.67123i) q^{34} +(2.79999 - 2.63023i) q^{35} +(-1.08960 + 2.79513i) q^{36} +(-6.32534 + 1.69487i) q^{37} +(-5.94631 + 1.59331i) q^{38} +(1.05733 - 2.20203i) q^{39} +(2.14074 + 0.645943i) q^{40} +(7.97370 - 4.60362i) q^{41} +(-2.25773 - 1.93842i) q^{42} +(-1.80961 - 6.75357i) q^{43} +(-1.76581 - 3.05848i) q^{44} +(-6.65944 + 0.807359i) q^{45} +5.77764 q^{46} +(4.22749 - 4.22749i) q^{47} +(0.320052 - 1.70222i) q^{48} +(-3.50601 + 2.02419i) q^{49} +(0.989897 + 4.90103i) q^{50} +(12.6808 - 0.964954i) q^{51} +(-0.365014 + 1.36225i) q^{52} +(-2.51478 + 9.38527i) q^{53} +(1.17371 + 5.06186i) q^{54} +(4.16024 - 6.71224i) q^{55} +(1.48785 + 0.859013i) q^{56} +(-6.94580 + 8.08996i) q^{57} +(0.393993 - 0.393993i) q^{58} +(-3.91854 + 6.78711i) q^{59} +(3.69249 - 1.16856i) q^{60} +7.37809 q^{61} +(-1.03729 + 5.47029i) q^{62} +(-5.12298 - 0.565300i) q^{63} +1.00000i q^{64} +(-3.07010 + 0.720618i) q^{65} +(-5.51423 - 2.64771i) q^{66} +(-1.52752 + 5.70078i) q^{67} +(-7.09227 + 1.90037i) q^{68} +(8.26182 - 5.64673i) q^{69} +(-0.120038 + 3.83975i) q^{70} +(-8.39623 + 4.84757i) q^{71} +(-1.20599 - 2.74692i) q^{72} +(11.3822 + 3.04984i) q^{73} +(3.27424 - 5.67115i) q^{74} +(6.20551 + 6.04084i) q^{75} +(3.07803 - 5.33131i) q^{76} +(4.29031 - 4.29031i) q^{77} +(0.809429 + 2.30472i) q^{78} +(-0.336135 - 0.194068i) q^{79} +(-1.97048 + 1.05698i) q^{80} +(6.62554 + 6.09116i) q^{81} +(-2.38301 + 8.89350i) q^{82} +(-1.58924 + 5.93114i) q^{83} +(2.96713 - 0.225785i) q^{84} +(-11.2410 - 11.9665i) q^{85} +(6.05508 + 3.49590i) q^{86} +(0.178330 - 0.948463i) q^{87} +(3.41129 + 0.914051i) q^{88} +6.84912 q^{89} +(4.13805 - 5.27983i) q^{90} -2.42294 q^{91} +(-4.08541 + 4.08541i) q^{92} +(3.86306 + 8.83611i) q^{93} +5.97858i q^{94} +(13.7587 + 0.430121i) q^{95} +(0.977343 + 1.42997i) q^{96} +(5.85127 + 5.85127i) q^{97} +(1.04780 - 3.91044i) q^{98} +(-10.4729 + 1.60316i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 8 q^{3} - 4 q^{7}+O(q^{10}) $ 256 * q + 8 * q^3 - 4 * q^7	$ 256 q + 8 q^{3} - 4 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} - 256 q^{16} - 4 q^{22} - 16 q^{25} - 40 q^{27} - 4 q^{28} - 48 q^{30} + 32 q^{31} - 8 q^{33} + 8 q^{37} - 12 q^{42} - 40 q^{45} + 16 q^{46} - 8 q^{48} - 16 q^{51} + 20 q^{55} + 40 q^{57} + 56 q^{58} - 8 q^{60} - 32 q^{61} + 56 q^{63} + 32 q^{66} - 24 q^{67} + 24 q^{70} + 8 q^{73} - 4 q^{75} + 16 q^{76} - 88 q^{78} - 48 q^{81} + 64 q^{85} - 20 q^{87} - 4 q^{88} - 8 q^{90} - 68 q^{93} + 152 q^{97}+O(q^{100}) $ 256 * q + 8 * q^3 - 4 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 - 256 * q^16 - 4 * q^22 - 16 * q^25 - 40 * q^27 - 4 * q^28 - 48 * q^30 + 32 * q^31 - 8 * q^33 + 8 * q^37 - 12 * q^42 - 40 * q^45 + 16 * q^46 - 8 * q^48 - 16 * q^51 + 20 * q^55 + 40 * q^57 + 56 * q^58 - 8 * q^60 - 32 * q^61 + 56 * q^63 + 32 * q^66 - 24 * q^67 + 24 * q^70 + 8 * q^73 - 4 * q^75 + 16 * q^76 - 88 * q^78 - 48 * q^81 + 64 * q^85 - 20 * q^87 - 4 * q^88 - 8 * q^90 - 68 * q^93 + 152 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.320052	+	1.70222i	−0.184782	+	0.982779i
$3$	−0.320052	+	1.70222i	−0.184782	+	0.982779i
$4$		−	1.00000i		−	0.500000i
$5$	1.97048	−	1.05698i	0.881226	−	0.472696i
$5$	1.97048	−	1.05698i	0.881226	−	0.472696i
$6$	−0.977343	−	1.42997i	−0.398999	−	0.583781i
$7$	1.65949	−	0.444658i	0.627226	−	0.168065i	0.0688156	−	0.997629i	$-0.478078\pi$
$7$	1.65949	−	0.444658i	0.627226	−	0.168065i	0.558411	+	0.829565i	$0.311411\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.79513	−	1.08960i	−0.931711	−	0.363201i
$10$	−0.645943	+	2.14074i	−0.204265	+	0.676961i
$11$	3.05848	−	1.76581i	0.922165	−	0.532412i	0.0378399	−	0.999284i	$-0.487952\pi$
$11$	3.05848	−	1.76581i	0.922165	−	0.532412i	0.884325	+	0.466872i	$0.154619\pi$
$12$	1.70222	+	0.320052i	0.491390	+	0.0923911i
$13$	−1.36225	−	0.365014i	−0.377821	−	0.101237i	0.0649107	−	0.997891i	$-0.479324\pi$
$13$	−1.36225	−	0.365014i	−0.377821	−	0.101237i	−0.442731	+	0.896654i	$0.645990\pi$
$14$	−0.859013	+	1.48785i	−0.229581	+	0.397646i
$15$	1.16856	+	3.69249i	0.301721	+	0.953396i
$16$	−1.00000			−0.250000
$17$	−1.90037	−	7.09227i	−0.460907	−	1.72013i	−0.670116	−	0.742257i	$-0.733755\pi$
$17$	−1.90037	−	7.09227i	−0.460907	−	1.72013i	0.209209	−	0.977871i	$-0.432911\pi$
$18$	2.74692	−	1.20599i	0.647456	−	0.284255i
$19$	5.33131	+	3.07803i	1.22309	+	0.706150i	0.965575	−	0.260126i	$-0.0837639\pi$
$19$	5.33131	+	3.07803i	1.22309	+	0.706150i	0.257512	+	0.966275i	$0.417097\pi$
$20$	−1.05698	−	1.97048i	−0.236348	−	0.440613i
$21$	0.225785	+	2.96713i	0.0492703	+	0.647481i
$22$	−0.914051	+	3.41129i	−0.194876	+	0.727289i
$23$	−4.08541	−	4.08541i	−0.851866	−	0.851866i	0.138497	−	0.990363i	$-0.455773\pi$
$23$	−4.08541	−	4.08541i	−0.851866	−	0.851866i	−0.990363	+	0.138497i	$0.955773\pi$
$24$	−1.42997	+	0.977343i	−0.291890	+	0.199499i
$25$	2.76559	−	4.16551i	0.553118	−	0.833103i
$26$	1.22136	−	0.705153i	0.239529	−	0.138292i
$27$	2.74933	−	4.40921i	0.529110	−	0.848553i
$28$	−0.444658	−	1.65949i	−0.0840324	−	0.313613i
$29$	−0.557190			−0.103468			−0.0517338	−	0.998661i	$-0.516475\pi$
$29$	−0.557190			−0.103468			−0.0517338	+	0.998661i	$0.516475\pi$
$30$	−3.43728	−	1.78469i	−0.627558	−	0.325838i
$31$	4.60155	−	3.13460i	0.826463	−	0.562991i
$31$	4.60155	−	3.13460i	0.826463	−	0.562991i
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	2.02693	+	5.77136i	0.352844	+	1.00467i
$34$	6.35875	+	3.67123i	1.09052	+	0.629610i
$35$	2.79999	−	2.63023i	0.473285	−	0.444590i
$36$	−1.08960	+	2.79513i	−0.181600	+	0.465856i
$37$	−6.32534	+	1.69487i	−1.03988	+	0.278635i	−0.738064	−	0.674731i	$-0.764260\pi$
$37$	−6.32534	+	1.69487i	−1.03988	+	0.278635i	−0.301816	+	0.953366i	$0.597593\pi$
$38$	−5.94631	+	1.59331i	−0.964618	+	0.258469i
$39$	1.05733	−	2.20203i	0.169308	−	0.352608i
$40$	2.14074	+	0.645943i	0.338480	+	0.102133i
$41$	7.97370	−	4.60362i	1.24528	−	0.718964i	0.275118	−	0.961411i	$-0.411283\pi$
$41$	7.97370	−	4.60362i	1.24528	−	0.718964i	0.970165	+	0.242447i	$0.0779499\pi$
$42$	−2.25773	−	1.93842i	−0.348375	−	0.299105i
$43$	−1.80961	−	6.75357i	−0.275963	−	1.02991i	−0.955193	−	0.295984i	$-0.904353\pi$
$43$	−1.80961	−	6.75357i	−0.275963	−	1.02991i	0.679229	−	0.733926i	$-0.262314\pi$
$44$	−1.76581	−	3.05848i	−0.266206	−	0.461083i
$45$	−6.65944	+	0.807359i	−0.992731	+	0.120354i
$46$	5.77764			0.851866
$47$	4.22749	−	4.22749i	0.616643	−	0.616643i	−0.328026	−	0.944669i	$-0.606383\pi$
$47$	4.22749	−	4.22749i	0.616643	−	0.616643i	0.944669	+	0.328026i	$0.106383\pi$
$48$	0.320052	−	1.70222i	0.0461956	−	0.245695i
$49$	−3.50601	+	2.02419i	−0.500858	+	0.289171i
$50$	0.989897	+	4.90103i	0.139993	+	0.693110i
$51$	12.6808	−	0.964954i	1.77567	−	0.135121i
$52$	−0.365014	+	1.36225i	−0.0506184	+	0.188910i
$53$	−2.51478	+	9.38527i	−0.345431	+	1.28917i	0.546677	+	0.837344i	$0.315893\pi$
$53$	−2.51478	+	9.38527i	−0.345431	+	1.28917i	−0.892108	+	0.451822i	$0.850774\pi$
$54$	1.17371	+	5.06186i	0.159722	+	0.688832i
$55$	4.16024	−	6.71224i	0.560967	−	0.905079i
$56$	1.48785	+	0.859013i	0.198823	+	0.114790i
$57$	−6.94580	+	8.08996i	−0.919994	+	1.07154i
$58$	0.393993	−	0.393993i	0.0517338	−	0.0517338i
$59$	−3.91854	+	6.78711i	−0.510150	+	0.883606i	0.489781	+	0.871846i	$0.337077\pi$
$59$	−3.91854	+	6.78711i	−0.510150	+	0.883606i	−0.999931	+	0.0117603i	$0.996256\pi$
$60$	3.69249	−	1.16856i	0.476698	−	0.150860i
$61$	7.37809			0.944667			0.472334	−	0.881420i	$-0.343412\pi$
$61$	7.37809			0.944667			0.472334	+	0.881420i	$0.343412\pi$
$62$	−1.03729	+	5.47029i	−0.131736	+	0.694727i
$63$	−5.12298	−	0.565300i	−0.645435	−	0.0712211i
$64$			1.00000i			0.125000i
$65$	−3.07010	+	0.720618i	−0.380799	+	0.0893817i
$66$	−5.51423	−	2.64771i	−0.678755	−	0.325911i
$67$	−1.52752	+	5.70078i	−0.186616	+	0.696461i	0.807663	+	0.589645i	$0.200732\pi$
$67$	−1.52752	+	5.70078i	−0.186616	+	0.696461i	−0.994279	+	0.106816i	$0.965934\pi$
$68$	−7.09227	+	1.90037i	−0.860064	+	0.230453i
$69$	8.26182	−	5.64673i	0.994606	−	0.679787i
$70$	−0.120038	+	3.83975i	−0.0143472	+	0.458937i
$71$	−8.39623	+	4.84757i	−0.996449	+	0.575300i	−0.907196	−	0.420709i	$-0.861781\pi$
$71$	−8.39623	+	4.84757i	−0.996449	+	0.575300i	−0.0892533	+	0.996009i	$0.528448\pi$
$72$	−1.20599	−	2.74692i	−0.142128	−	0.323728i
$73$	11.3822	+	3.04984i	1.33218	+	0.356957i	0.853528	−	0.521048i	$-0.174459\pi$
$73$	11.3822	+	3.04984i	1.33218	+	0.356957i	0.478653	+	0.878004i	$0.341125\pi$
$74$	3.27424	−	5.67115i	0.380622	−	0.659257i
$75$	6.20551	+	6.04084i	0.716550	+	0.697536i
$76$	3.07803	−	5.33131i	0.353075	−	0.611543i
$77$	4.29031	−	4.29031i	0.488927	−	0.488927i
$78$	0.809429	+	2.30472i	0.0916498	+	0.260958i
$79$	−0.336135	−	0.194068i	−0.0378181	−	0.0218343i	0.480972	−	0.876736i	$-0.340284\pi$
$79$	−0.336135	−	0.194068i	−0.0378181	−	0.0218343i	−0.518790	+	0.854902i	$0.673617\pi$
$80$	−1.97048	+	1.05698i	−0.220306	+	0.118174i
$81$	6.62554	+	6.09116i	0.736171	+	0.676796i
$82$	−2.38301	+	8.89350i	−0.263159	+	0.982123i
$83$	−1.58924	+	5.93114i	−0.174442	+	0.651027i	0.822204	+	0.569193i	$0.192744\pi$
$83$	−1.58924	+	5.93114i	−0.174442	+	0.651027i	−0.996646	+	0.0818340i	$0.973922\pi$
$84$	2.96713	−	0.225785i	0.323740	−	0.0246352i
$85$	−11.2410	−	11.9665i	−1.21926	−	1.29795i
$86$	6.05508	+	3.49590i	0.652937	+	0.376973i
$87$	0.178330	−	0.948463i	0.0191190	−	0.101686i
$88$	3.41129	+	0.914051i	0.363644	+	0.0974382i
$89$	6.84912			0.726005			0.363003	−	0.931788i	$-0.381752\pi$
$89$	6.84912			0.726005			0.363003	+	0.931788i	$0.381752\pi$
$90$	4.13805	−	5.27983i	0.436189	−	0.556542i
$91$	−2.42294			−0.253993
$92$	−4.08541	+	4.08541i	−0.425933	+	0.425933i
$93$	3.86306	+	8.83611i	0.400581	+	0.916261i
$94$			5.97858i			0.616643i
$95$	13.7587	+	0.430121i	1.41161	+	0.0441295i
$96$	0.977343	+	1.42997i	0.0997496	+	0.145945i
$97$	5.85127	+	5.85127i	0.594106	+	0.594106i	0.938738	−	0.344632i	$-0.111996\pi$
$97$	5.85127	+	5.85127i	0.594106	+	0.594106i	−0.344632	+	0.938738i	$0.611996\pi$
$98$	1.04780	−	3.91044i	0.105844	−	0.395014i
$99$	−10.4729	+	1.60316i	−1.05256	+	0.161124i
$100$	−4.16551	−	2.76559i	−0.416551	−	0.276559i
$101$			18.0451i			1.79555i	0.440455	+	0.897775i	$0.354817\pi$
$101$			18.0451i			1.79555i	−0.440455	+	0.897775i	$0.645183\pi$
$102$	−8.28439	+	9.64904i	−0.820277	+	0.955397i
$103$	−5.30028	−	1.42021i	−0.522253	−	0.139937i	−0.0119442	−	0.999929i	$-0.503802\pi$
$103$	−5.30028	−	1.42021i	−0.522253	−	0.139937i	−0.510308	+	0.859992i	$0.670469\pi$
$104$	−0.705153	−	1.22136i	−0.0691460	−	0.119764i
$105$	3.58110	+	5.60802i	0.349479	+	0.547287i
$106$	−4.85817	−	8.41460i	−0.471867	−	0.817298i
$107$	2.62897	+	9.81146i	0.254152	+	0.948509i	0.968560	+	0.248780i	$0.0800295\pi$
$107$	2.62897	+	9.81146i	0.254152	+	0.948509i	−0.714408	+	0.699730i	$0.753304\pi$
$108$	−4.40921	−	2.74933i	−0.424277	−	0.264555i
$109$			5.33687i			0.511180i	0.966785	+	0.255590i	$0.0822697\pi$
$109$			5.33687i			0.511180i	−0.966785	+	0.255590i	$0.917730\pi$
$110$	1.80454	+	7.68801i	0.172056	+	0.733023i
$111$	−0.860608	−	11.3096i	−0.0816853	−	1.07346i
$112$	−1.65949	+	0.444658i	−0.156807	+	0.0420162i
$113$	0.264962	−	0.988853i	0.0249256	−	0.0930234i	−0.952343	−	0.305031i	$-0.901333\pi$
$113$	0.264962	−	0.988853i	0.0249256	−	0.0930234i	0.977268	+	0.212007i	$0.0680000\pi$
$114$	−0.809038	−	10.6319i	−0.0757733	−	0.995767i
$115$	−12.3684	−	3.73202i	−1.15336	−	0.348013i
$116$			0.557190i			0.0517338i
$117$	3.40995	+	2.50457i	0.315250	+	0.231548i
$118$	−2.02838	−	7.57003i	−0.186728	−	0.696878i
$119$	−6.30726	−	10.9245i	−0.578186	−	1.00145i
$120$	−1.78469	+	3.43728i	−0.162919	+	0.313779i
$121$	0.736182	−	1.27510i	0.0669256	−	0.115919i
$122$	−5.21709	+	5.21709i	−0.472334	+	0.472334i
$123$	5.28439	+	15.0464i	0.476477	+	1.35669i
$124$	−3.13460	−	4.60155i	−0.281496	−	0.413231i
$125$	1.04668	−	11.1312i	0.0936177	−	0.995608i
$126$	4.02222	−	3.22277i	0.358328	−	0.287107i
$127$	15.9054	−	4.26184i	1.41138	−	0.378177i	0.528960	−	0.848647i	$-0.322582\pi$
$127$	15.9054	−	4.26184i	1.41138	−	0.378177i	0.882416	+	0.470470i	$0.155916\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	12.0753	−	0.918872i	1.06317	−	0.0809022i
$130$	1.66134	−	2.68044i	0.145709	−	0.235091i
$131$	−7.48795	−	4.32317i	−0.654225	−	0.377717i	0.135848	−	0.990730i	$-0.456624\pi$
$131$	−7.48795	−	4.32317i	−0.654225	−	0.377717i	−0.790073	+	0.613013i	$0.789958\pi$
$132$	5.77136	−	2.02693i	0.502333	−	0.176422i
$133$	10.2159	+	2.73734i	0.885831	+	0.237358i
$134$	−2.95094	−	5.11118i	−0.254922	−	0.441538i
$135$	0.757064	−	11.5943i	0.0651577	−	0.997875i
$136$	3.67123	−	6.35875i	0.314805	−	0.545259i
$137$	−13.1097	−	3.51275i	−1.12004	−	0.300114i	−0.349141	−	0.937070i	$-0.613527\pi$
$137$	−13.1097	−	3.51275i	−1.12004	−	0.300114i	−0.770900	+	0.636956i	$0.780193\pi$
$138$	−1.84915	+	9.83483i	−0.157410	+	0.837196i
$139$		−	17.6893i		−	1.50039i	−0.661217	−	0.750195i	$-0.729960\pi$
$139$		−	17.6893i		−	1.50039i	0.661217	−	0.750195i	$-0.270040\pi$
$140$	−2.63023	−	2.79999i	−0.222295	−	0.236642i
$141$	5.84312	+	8.54916i	0.492080	+	0.719969i
$142$	2.50928	−	9.36478i	0.210574	−	0.785875i
$143$	−4.81096	+	1.28909i	−0.402313	+	0.107799i
$144$	2.79513	+	1.08960i	0.232928	+	0.0908001i
$145$	−1.09793	+	0.588939i	−0.0911784	+	0.0489087i
$146$	−10.2050	+	5.89184i	−0.844568	+	0.487612i
$147$	−2.32353	−	6.61586i	−0.191641	−	0.545667i
$148$	1.69487	+	6.32534i	0.139317	+	0.519940i
$149$	−4.07428	+	7.05685i	−0.333778	+	0.578120i	−0.983249	−	0.182266i	$-0.941657\pi$
$149$	−4.07428	+	7.05685i	−0.333778	+	0.578120i	0.649472	+	0.760386i	$0.274990\pi$
$150$	−8.65947	+	0.116440i	−0.707043	+	0.00950726i
$151$	−3.22136			−0.262151			−0.131075	−	0.991372i	$-0.541843\pi$
$151$	−3.22136			−0.262151			−0.131075	+	0.991372i	$0.541843\pi$
$152$	1.59331	+	5.94631i	0.129234	+	0.482309i
$153$	−2.41597	+	21.8945i	−0.195319	+	1.77006i
$154$			6.06742i			0.488927i
$155$	5.75405	−	11.0404i	0.462177	−	0.886788i
$156$	−2.20203	−	1.05733i	−0.176304	−	0.0846540i
$157$	0.559717	+	0.559717i	0.0446702	+	0.0446702i	0.729089	−	0.684419i	$-0.239944\pi$
$157$	0.559717	+	0.559717i	0.0446702	+	0.0446702i	−0.684419	+	0.729089i	$0.739944\pi$
$158$	0.374910	−	0.100457i	0.0298262	−	0.00799191i
$159$	−15.1710	−	7.28449i	−1.20314	−	0.577698i
$160$	0.645943	−	2.14074i	0.0510663	−	0.169240i
$161$	−8.59628	−	4.96306i	−0.677481	−	0.391144i
$162$	−8.99206	+	0.377860i	−0.706483	+	0.0296875i
$163$	5.73757	−	5.73757i	0.449401	−	0.449401i	−0.445754	−	0.895155i	$-0.647064\pi$
$163$	5.73757	−	5.73757i	0.449401	−	0.449401i	0.895155	+	0.445754i	$0.147064\pi$
$164$	−4.60362	−	7.97370i	−0.359482	−	0.622641i
$165$	10.0942	+	9.22993i	0.785836	+	0.718549i
$166$	−3.07018	−	5.31772i	−0.238293	−	0.412735i
$167$	−0.530014	−	1.97804i	−0.0410137	−	0.153065i	0.942382	−	0.334538i	$-0.108580\pi$
$167$	−0.530014	−	1.97804i	−0.0410137	−	0.153065i	−0.983396	+	0.181473i	$0.941914\pi$
$168$	−1.93842	+	2.25773i	−0.149553	+	0.174188i
$169$	−9.53584	−	5.50552i	−0.733526	−	0.423501i
$170$	16.4102	+	0.513014i	1.25861	+	0.0393464i
$171$	−11.5479	−	14.4125i	−0.883090	−	1.10215i
$172$	−6.75357	+	1.80961i	−0.514955	+	0.137982i
$173$	−3.63917	+	13.5816i	−0.276681	+	1.03259i	0.678026	+	0.735038i	$0.262836\pi$
$173$	−3.63917	+	13.5816i	−0.276681	+	1.03259i	−0.954707	+	0.297548i	$0.903831\pi$
$174$	0.544566	+	0.796763i	0.0412834	+	0.0604024i
$175$	2.73723	−	8.14235i	0.206915	−	0.615504i
$176$	−3.05848	+	1.76581i	−0.230541	+	0.133103i
$177$	−10.2990	−	8.84246i	−0.774123	−	0.664640i
$178$	−4.84306	+	4.84306i	−0.363003	+	0.363003i
$179$	10.7605	−	18.6377i	0.804278	−	1.39305i	−0.112500	−	0.993652i	$-0.535886\pi$
$179$	10.7605	−	18.6377i	0.804278	−	1.39305i	0.916778	−	0.399398i	$-0.130781\pi$
$180$	0.807359	+	6.65944i	0.0601770	+	0.496366i
$181$	6.27698	+	10.8721i	0.466564	+	0.808113i	0.999271	−	0.0381870i	$-0.0121583\pi$
$181$	6.27698	+	10.8721i	0.466564	+	0.808113i	−0.532706	+	0.846300i	$0.678825\pi$
$182$	1.71328	−	1.71328i	0.126997	−	0.126997i
$183$	−2.36137	+	12.5592i	−0.174558	+	0.928399i
$184$		−	5.77764i		−	0.425933i
$185$	−10.6725	+	10.0255i	−0.784659	+	0.737087i
$186$	−8.97967	−	3.51647i	−0.658421	−	0.257840i
$187$	−18.3358	−	18.3358i	−1.34085	−	1.34085i
$188$	−4.22749	−	4.22749i	−0.308322	−	0.308322i
$189$	2.60189	−	8.53954i	0.189260	−	0.621160i
$190$	−10.0330	+	9.42471i	−0.727870	+	0.683740i
$191$	22.2007	−	12.8176i	1.60638	−	0.927446i	0.616214	−	0.787579i	$-0.288666\pi$
$191$	22.2007	−	12.8176i	1.60638	−	0.927446i	0.990170	−	0.139867i	$-0.0446676\pi$
$192$	−1.70222	−	0.320052i	−0.122847	−	0.0230978i
$193$	−5.34813	−	19.9595i	−0.384967	−	1.43671i	−0.838220	−	0.545333i	$-0.816403\pi$
$193$	−5.34813	−	19.9595i	−0.384967	−	1.43671i	0.453253	−	0.891382i	$-0.350263\pi$
$194$	−8.27494			−0.594106
$195$	−0.244060	−	5.45664i	−0.0174775	−	0.390758i
$196$	2.02419	+	3.50601i	0.144585	+	0.250429i
$197$	−15.7578	−	4.22228i	−1.12269	−	0.300825i	−0.350721	−	0.936480i	$-0.614064\pi$
$197$	−15.7578	−	4.22228i	−1.12269	−	0.300825i	−0.771973	+	0.635655i	$0.780730\pi$
$198$	6.27184	−	8.53905i	0.445720	−	0.606844i
$199$	3.24541	−	1.87374i	0.230061	−	0.132826i	−0.380539	−	0.924765i	$-0.624262\pi$
$199$	3.24541	−	1.87374i	0.230061	−	0.132826i	0.610600	+	0.791939i	$0.290928\pi$
$200$	4.90103	−	0.989897i	0.346555	−	0.0699963i
$201$	−9.21511	−	4.42473i	−0.649984	−	0.312096i
$202$	−12.7598	−	12.7598i	−0.897775	−	0.897775i
$203$	−0.924649	+	0.247759i	−0.0648976	+	0.0173893i
$204$	−0.964954	−	12.6808i	−0.0675603	−	0.887837i
$205$	10.8461	−	17.4994i	0.757524	−	1.22221i
$206$	4.75211	−	2.74363i	0.331095	−	0.191158i
$207$	6.96779	+	15.8707i	0.484295	+	1.10309i
$208$	1.36225	+	0.365014i	0.0944551	+	0.0253092i
$209$	21.7409			1.50385
$210$	−6.49769	−	1.43325i	−0.448383	−	0.0989037i
$211$	−9.13212	+	15.8173i	−0.628681	+	1.08891i	0.359135	+	0.933285i	$0.383072\pi$
$211$	−9.13212	+	15.8173i	−0.628681	+	1.08891i	−0.987817	+	0.155622i	$0.950262\pi$
$212$	9.38527	+	2.51478i	0.644583	+	0.172715i
$213$	−5.56441	−	15.8437i	−0.381267	−	1.08559i
$214$	−8.79671	−	5.07878i	−0.601331	−	0.347178i
$215$	−10.7042	−	11.3951i	−0.730020	−	0.777136i
$216$	5.06186	−	1.17371i	0.344416	−	0.0798609i
$217$	6.24238	−	7.24794i	0.423760	−	0.492022i
$218$	−3.77374	−	3.77374i	−0.255590	−	0.255590i
$219$	−8.83439	+	18.3989i	−0.596973	+	1.24328i
$220$	−6.71224	−	4.16024i	−0.452539	−	0.280483i
$221$			10.3551i			0.696560i
$222$	8.60563	+	7.38855i	0.577572	+	0.495887i
$223$	5.60179	+	20.9062i	0.375124	+	1.39998i	0.853164	+	0.521643i	$0.174681\pi$
$223$	5.60179	+	20.9062i	0.375124	+	1.39998i	−0.478040	+	0.878338i	$0.658653\pi$
$224$	0.859013	−	1.48785i	0.0573952	−	0.0994114i
$225$	−12.2689	+	8.62978i	−0.817929	+	0.575319i
$226$	0.511868	+	0.886581i	0.0340489	+	0.0589745i
$227$	−14.0585	−	3.76696i	−0.933095	−	0.250022i	−0.239921	−	0.970792i	$-0.577122\pi$
$227$	−14.0585	−	3.76696i	−0.933095	−	0.250022i	−0.693174	+	0.720770i	$0.743788\pi$
$228$	8.08996	+	6.94580i	0.535770	+	0.459997i
$229$	6.06596	+	3.50218i	0.400850	+	0.231431i	0.686851	−	0.726799i	$-0.258993\pi$
$229$	6.06596	+	3.50218i	0.400850	+	0.231431i	−0.286001	+	0.958229i	$0.592326\pi$
$230$	11.3847	−	6.10684i	0.750686	−	0.402673i
$231$	5.92995	+	8.67620i	0.390162	+	0.570852i
$232$	−0.393993	−	0.393993i	−0.0258669	−	0.0258669i
$233$	13.0182	+	13.0182i	0.852847	+	0.852847i	0.990483	−	0.137636i	$-0.0439503\pi$
$233$	13.0182	+	13.0182i	0.852847	+	0.852847i	−0.137636	+	0.990483i	$0.543950\pi$
$234$	−4.18220	+	0.640200i	−0.273399	+	0.0418512i
$235$	3.86182	−	12.7986i	0.251917	−	0.834886i
$236$	6.78711	+	3.91854i	0.441803	+	0.255075i
$237$	0.437927	−	0.510065i	0.0284464	−	0.0331323i
$238$	12.1847	+	3.26488i	0.789817	+	0.211631i
$239$	−3.76330	−	6.51823i	−0.243428	−	0.421629i	0.718261	−	0.695774i	$-0.244939\pi$
$239$	−3.76330	−	6.51823i	−0.243428	−	0.421629i	−0.961688	+	0.274145i	$0.911605\pi$
$240$	−1.16856	−	3.69249i	−0.0754301	−	0.238349i
$241$	−1.56481	+	2.71033i	−0.100798	+	0.174588i	−0.912014	−	0.410159i	$-0.865473\pi$
$241$	−1.56481	+	2.71033i	−0.100798	+	0.174588i	0.811215	+	0.584747i	$0.198806\pi$
$242$	0.381076	+	1.42219i	0.0244965	+	0.0914221i
$243$	−12.4890	+	9.32866i	−0.801172	+	0.598434i
$244$		−	7.37809i		−	0.472334i
$245$	−4.76899	+	7.69441i	−0.304680	+	0.491578i
$246$	−14.3760	−	6.90280i	−0.916583	−	0.440106i
$247$	−6.13906	−	6.13906i	−0.390619	−	0.390619i
$248$	5.47029	+	1.03729i	0.347364	+	0.0658678i
$249$	−9.58749	−	4.60353i	−0.607582	−	0.291737i
$250$	7.13086	+	8.61109i	0.450995	+	0.544613i
$251$	5.74878	+	3.31906i	0.362860	+	0.209497i	0.670335	−	0.742059i	$-0.266151\pi$
$251$	5.74878	+	3.31906i	0.362860	+	0.209497i	−0.307475	+	0.951556i	$0.599484\pi$
$252$	−0.565300	+	5.12298i	−0.0356106	+	0.322717i
$253$	−19.7092	−	5.28106i	−1.23910	−	0.332017i
$254$	−8.23324	+	14.2604i	−0.516599	+	0.894776i
$255$	23.9674	−	15.3048i	1.50090	−	0.958425i
$256$	1.00000			0.0625000
$257$	−18.7436	−	5.02234i	−1.16920	−	0.313285i	−0.378563	−	0.925576i	$-0.623582\pi$
$257$	−18.7436	−	5.02234i	−1.16920	−	0.313285i	−0.790633	+	0.612291i	$0.790248\pi$
$258$	−7.88876	+	9.18824i	−0.491133	+	0.572035i
$259$	−9.74317	+	5.62522i	−0.605411	+	0.349534i
$260$	0.720618	+	3.07010i	0.0446908	+	0.190400i
$261$	1.55742	+	0.607115i	0.0964020	+	0.0375795i
$262$	8.35172	−	2.23784i	0.515971	−	0.138254i
$263$	6.08265	+	6.08265i	0.375072	+	0.375072i	0.869321	−	0.494248i	$-0.164557\pi$
$263$	6.08265	+	6.08265i	0.375072	+	0.375072i	−0.494248	+	0.869321i	$0.664557\pi$
$264$	−2.64771	+	5.51423i	−0.162955	+	0.339377i
$265$	4.96472	+	21.1516i	0.304980	+	1.29933i
$266$	−9.15933	+	5.28814i	−0.561595	+	0.324237i
$267$	−2.19208	+	11.6587i	−0.134153	+	0.713503i
$268$	5.70078	+	1.52752i	0.348230	+	0.0933081i
$269$	0.0543808	+	0.0941904i	0.00331566	+	0.00574289i	0.867678	−	0.497126i	$-0.165611\pi$
$269$	0.0543808	+	0.0941904i	0.00331566	+	0.00574289i	−0.864363	+	0.502869i	$0.832278\pi$
$270$	7.66305	+	8.73370i	0.466359	+	0.531516i
$271$	22.0860			1.34163			0.670816	−	0.741624i	$-0.265944\pi$
$271$	22.0860			1.34163			0.670816	+	0.741624i	$0.265944\pi$
$272$	1.90037	+	7.09227i	0.115227	+	0.430032i
$273$	0.775468	−	4.12439i	0.0469335	−	0.249619i
$274$	11.7539	−	6.78611i	0.710078	−	0.409964i
$275$	1.10297	−	17.6236i	0.0665118	−	1.06275i
$276$	−5.64673	−	8.26182i	−0.339893	−	0.497303i
$277$	−11.3361	−	11.3361i	−0.681121	−	0.681121i	0.279132	−	0.960253i	$-0.409953\pi$
$277$	−11.3361	−	11.3361i	−0.681121	−	0.681121i	−0.960253	+	0.279132i	$0.909953\pi$
$278$	12.5082	+	12.5082i	0.750195	+	0.750195i
$279$	−16.2774	+	3.74778i	−0.974503	+	0.224374i
$280$	3.83975	+	0.120038i	0.229469	+	0.00717362i
$281$			2.95794i			0.176456i	0.996100	+	0.0882280i	$0.0281204\pi$
$281$			2.95794i			0.176456i	−0.996100	+	0.0882280i	$0.971880\pi$
$282$	−10.1769	−	1.91346i	−0.606024	−	0.113945i
$283$	7.55010	−	7.55010i	0.448807	−	0.448807i	−0.446151	−	0.894958i	$-0.647206\pi$
$283$	7.55010	−	7.55010i	0.448807	−	0.448807i	0.894958	+	0.446151i	$0.147206\pi$
$284$	4.84757	+	8.39623i	0.287650	+	0.498225i
$285$	−5.13566	+	23.2827i	−0.304210	+	1.37915i
$286$	2.49034	−	4.31339i	0.147257	−	0.255056i
$287$	11.1852	−	11.1852i	0.660241	−	0.660241i
$288$	−2.74692	+	1.20599i	−0.161864	+	0.0710638i
$289$	−31.9664	+	18.4558i	−1.88038	+	1.08564i
$290$	0.359913	−	1.19280i	0.0211348	−	0.0700435i
$291$	−11.8329	+	8.08746i	−0.693656	+	0.474095i
$292$	3.04984	−	11.3822i	0.178478	−	0.666090i
$293$	−12.0356	+	3.22492i	−0.703126	+	0.188402i	−0.592630	−	0.805475i	$-0.701910\pi$
$293$	−12.0356	+	3.22492i	−0.703126	+	0.188402i	−0.110496	+	0.993877i	$0.535244\pi$
$294$	6.32110	+	3.03514i	0.368654	+	0.177013i
$295$	−0.547572	+	17.5157i	−0.0318809	+	1.01980i
$296$	−5.67115	−	3.27424i	−0.329629	−	0.190311i
$297$	0.622933	−	18.3403i	0.0361462	−	1.06421i
$298$	−2.10900	−	7.87090i	−0.122171	−	0.455949i
$299$	4.07412	+	7.05658i	0.235612	+	0.408093i
$300$	6.04084	−	6.20551i	0.348768	−	0.358275i
$301$	−6.00605	−	10.4028i	−0.346183	−	0.599607i
$302$	2.27785	−	2.27785i	0.131075	−	0.131075i
$303$	−30.7167	−	5.77536i	−1.76463	−	0.331786i
$304$	−5.33131	−	3.07803i	−0.305772	−	0.176537i
$305$	14.5384	−	7.79848i	0.832465	−	0.446540i
$306$	−13.7734	−	17.1901i	−0.787372	−	0.982691i
$307$	−15.0663	+	4.03701i	−0.859881	+	0.230404i	−0.661707	−	0.749763i	$-0.730168\pi$
$307$	−15.0663	+	4.03701i	−0.859881	+	0.230404i	−0.198174	+	0.980167i	$0.563501\pi$
$308$	−4.29031	−	4.29031i	−0.244463	−	0.244463i
$309$	4.11388	−	8.56773i	0.234030	−	0.487401i
$310$	3.73803	+	11.8755i	0.212306	+	0.674482i
$311$			0.984740i			0.0558395i	0.999610	+	0.0279197i	$0.00888828\pi$
$311$			0.984740i			0.0558395i	−0.999610	+	0.0279197i	$0.991112\pi$
$312$	2.30472	−	0.809429i	0.130479	−	0.0458249i
$313$	−2.41195	−	9.00152i	−0.136331	−	0.508796i	−0.999989	−	0.00471669i	$-0.998499\pi$
$313$	−2.41195	−	9.00152i	−0.136331	−	0.508796i	0.863657	−	0.504079i	$-0.168168\pi$
$314$	−0.791559			−0.0446702
$315$	−10.6922	+	4.30097i	−0.602440	+	0.242332i
$316$	−0.194068	+	0.336135i	−0.0109172	+	0.0189091i
$317$	8.83731	+	32.9813i	0.496353	+	1.85241i	0.522317	+	0.852751i	$0.325068\pi$
$317$	8.83731	+	32.9813i	0.496353	+	1.85241i	−0.0259644	+	0.999663i	$0.508266\pi$
$318$	15.8784	−	5.57659i	0.890417	−	0.312719i
$319$	−1.70415	+	0.983893i	−0.0954143	+	0.0550874i
$320$	1.05698	+	1.97048i	0.0590869	+	0.110153i
$321$	−17.5427	+	1.33492i	−0.979138	+	0.0745079i
$322$	9.58790	−	2.56907i	0.534313	−	0.143169i
$323$	11.6988	−	43.6605i	0.650938	−	2.42933i
$324$	6.09116	−	6.62554i	0.338398	−	0.368085i
$325$	−5.28790	+	4.66500i	−0.293320	+	0.258768i
$326$			8.11415i			0.449401i
$327$	−9.08455	−	1.70808i	−0.502377	−	0.0944569i
$328$	8.89350	+	2.38301i	0.491062	+	0.131580i
$329$	5.13567	−	8.89525i	0.283139	−	0.490411i
$330$	−13.6643	+	0.611163i	−0.752193	+	0.0336434i
$331$	−7.40251	−	12.8215i	−0.406879	−	0.704735i	0.587659	−	0.809109i	$-0.300050\pi$
$331$	−7.40251	−	12.8215i	−0.406879	−	0.704735i	−0.994538	+	0.104374i	$0.966716\pi$
$332$	5.93114	+	1.58924i	0.325514	+	0.0872211i
$333$	19.5269	+	2.15471i	1.07007	+	0.118078i
$334$	1.77346	+	1.02391i	0.0970394	+	0.0560257i
$335$	3.01566	+	12.8478i	0.164763	+	0.701952i
$336$	−0.225785	−	2.96713i	−0.0123176	−	0.161870i
$337$	19.6515	+	19.6515i	1.07048	+	1.07048i	0.997320	+	0.0731648i	$0.0233099\pi$
$337$	19.6515	+	19.6515i	1.07048	+	1.07048i	0.0731648	+	0.997320i	$0.476690\pi$
$338$	10.6358	−	2.84987i	0.578514	−	0.155012i
$339$	1.59845	+	0.767510i	0.0868157	+	0.0416854i
$340$	−11.9665	+	11.2410i	−0.648976	+	0.609630i
$341$	8.53861	−	17.7126i	0.462391	−	0.959190i
$342$	18.3568	+	2.02560i	0.992621	+	0.109532i
$343$	−13.4219	+	13.4219i	−0.724714	+	0.724714i
$344$	3.49590	−	6.05508i	0.188487	−	0.326468i
$345$	10.3113	−	19.8593i	0.555140	−	1.06919i
$346$	−7.03033	−	12.1769i	−0.377953	−	0.654634i
$347$	−1.56660	−	5.84664i	−0.0840996	−	0.313864i	0.911043	−	0.412312i	$-0.135279\pi$
$347$	−1.56660	−	5.84664i	−0.0840996	−	0.313864i	−0.995142	+	0.0984484i	$0.968612\pi$
$348$	−0.948463	−	0.178330i	−0.0508429	−	0.00955950i
$349$			12.2829i			0.657488i	0.944419	+	0.328744i	$0.106625\pi$
$349$			12.2829i			0.657488i	−0.944419	+	0.328744i	$0.893375\pi$
$350$	3.82200	+	7.69302i	0.204295	+	0.411209i
$351$	−5.35471	+	5.00291i	−0.285813	+	0.267036i
$352$	0.914051	−	3.41129i	0.0487191	−	0.181822i
$353$	−31.9433	+	8.55919i	−1.70017	+	0.455560i	−0.972983	−	0.230877i	$-0.925841\pi$
$353$	−31.9433	+	8.55919i	−1.70017	+	0.455560i	−0.727190	+	0.686437i	$0.759174\pi$
$354$	13.5351	−	1.02996i	0.719381	−	0.0547416i
$355$	−11.4208	+	18.4267i	−0.606155	+	0.977986i
$356$		−	6.84912i		−	0.363003i
$357$	20.6146	−	7.23996i	1.09104	−	0.383179i
$358$	5.57005	+	20.7877i	0.294386	+	1.09866i
$359$	−9.51310	−	16.4772i	−0.502082	−	0.869632i	−0.999997	−	0.00240593i	$-0.999234\pi$
$359$	−9.51310	−	16.4772i	−0.502082	−	0.869632i	0.497915	−	0.867226i	$-0.334099\pi$
$360$	−5.27983	−	4.13805i	−0.278271	−	0.218094i
$361$	9.44859	+	16.3654i	0.497294	+	0.861339i
$362$	−12.1262	−	3.24920i	−0.637339	−	0.170774i
$363$	1.93490	+	1.66125i	0.101556	+	0.0871928i
$364$			2.42294i			0.126997i
$365$	25.6519	−	6.02105i	1.34268	−	0.315156i
$366$	−7.21092	−	10.5504i	−0.376921	−	0.551479i
$367$	−4.05504	+	15.1336i	−0.211672	+	0.789969i	0.775640	+	0.631175i	$0.217427\pi$
$367$	−4.05504	+	15.1336i	−0.211672	+	0.789969i	−0.987312	+	0.158794i	$0.949240\pi$
$368$	4.08541	+	4.08541i	0.212966	+	0.212966i
$369$	−27.3037	+	4.17957i	−1.42137	+	0.217580i
$370$	0.457539	−	14.6357i	0.0237863	−	0.760873i
$371$			16.6929i			0.866654i
$372$	8.83611	−	3.86306i	0.458131	−	0.200290i
$373$	16.3872	−	16.3872i	0.848498	−	0.848498i	−0.141447	−	0.989946i	$-0.545176\pi$
$373$	16.3872	−	16.3872i	0.848498	−	0.848498i	0.989946	+	0.141447i	$0.0451756\pi$
$374$	25.9308			1.34085
$375$	18.6129	+	5.34426i	0.961164	+	0.275976i
$376$	5.97858			0.308322
$377$	0.759033	+	0.203382i	0.0390922	+	0.0104747i
$378$	4.19855	+	7.87818i	0.215950	+	0.405210i
$379$	16.6000	+	9.58402i	0.852685	+	0.492298i	0.861556	−	0.507662i	$-0.169490\pi$
$379$	16.6000	+	9.58402i	0.852685	+	0.492298i	−0.00887058	+	0.999961i	$0.502824\pi$
$380$	0.430121	−	13.7587i	0.0220648	−	0.705805i
$381$	2.16404	+	28.4386i	0.110867	+	1.45695i
$382$	−6.63486	+	24.7616i	−0.339469	+	1.26692i
$383$	1.39966	−	5.22359i	0.0715191	−	0.266913i	−0.920902	−	0.389793i	$-0.872546\pi$
$383$	1.39966	−	5.22359i	0.0715191	−	0.266913i	0.992421	+	0.122880i	$0.0392132\pi$
$384$	1.42997	−	0.977343i	0.0729726	−	0.0498748i
$385$	3.91921	−	12.9888i	0.199741	−	0.661968i
$386$	17.8952	+	10.3318i	0.910841	+	0.525874i
$387$	−2.30059	+	20.8489i	−0.116946	+	1.05981i
$388$	5.85127	−	5.85127i	0.297053	−	0.297053i
$389$	2.57059	−	4.45240i	0.130334	−	0.225745i	−0.793471	−	0.608608i	$-0.791728\pi$
$389$	2.57059	−	4.45240i	0.130334	−	0.225745i	0.923805	+	0.382862i	$0.125062\pi$
$390$	4.03100	+	3.68585i	0.204118	+	0.186640i
$391$	−21.2110	+	36.7386i	−1.07269	+	1.85795i
$392$	−3.91044	−	1.04780i	−0.197507	−	0.0529219i
$393$	9.75554	−	11.3625i	0.492102	−	0.573164i
$394$	14.1280	−	8.15682i	0.711760	−	0.410935i
$395$	−0.867473	−	0.0271188i	−0.0436473	−	0.00136449i
$396$	1.60316	+	10.4729i	0.0805618	+	0.526282i
$397$	36.5319	−	9.78869i	1.83348	−	0.491280i	0.835206	−	0.549938i	$-0.185349\pi$
$397$	36.5319	−	9.78869i	1.83348	−	0.491280i	0.998278	+	0.0586574i	$0.0186820\pi$
$398$	−0.969917	+	3.61978i	−0.0486176	+	0.181443i
$399$	−7.92920	+	16.5137i	−0.396956	+	0.826717i
$400$	−2.76559	+	4.16551i	−0.138279	+	0.208276i
$401$		−	8.17998i		−	0.408489i	−0.978920	−	0.204244i	$-0.934526\pi$
$401$		−	8.17998i		−	0.408489i	0.978920	−	0.204244i	$-0.0654737\pi$
$402$	9.64482	−	3.38732i	0.481040	−	0.168944i
$403$	−7.41264	+	2.59049i	−0.369250	+	0.129041i
$404$	18.0451			0.897775
$405$	19.4937	+	4.99946i	0.968651	+	0.248425i
$406$	0.478634	−	0.829018i	0.0237542	−	0.0411435i
$407$	−16.3531	+	16.3531i	−0.810592	+	0.810592i
$408$	9.64904	+	8.28439i	0.477699	+	0.410138i
$409$	−34.6691	−	20.0162i	−1.71428	−	0.989738i	−0.928584	−	0.371122i	$-0.878973\pi$
$409$	−34.6691	−	20.0162i	−1.71428	−	0.989738i	−0.785693	−	0.618616i	$-0.787694\pi$
$410$	4.70458	+	20.0433i	0.232343	+	0.989866i
$411$	10.1753	−	21.1915i	0.501910	−	1.04530i
$412$	−1.42021	+	5.30028i	−0.0699686	+	0.261126i
$413$	−3.48482	+	13.0055i	−0.171477	+	0.639959i
$414$	−16.1493	−	6.29532i	−0.793693	−	0.309398i
$415$	3.13752	+	13.3670i	0.154015	+	0.656160i
$416$	−1.22136	+	0.705153i	−0.0598822	+	0.0345730i
$417$	30.1112	+	5.66151i	1.47455	+	0.277245i
$418$	−15.3732	+	15.3732i	−0.751925	+	0.751925i
$419$	18.6357			0.910413			0.455206	−	0.890386i	$-0.349565\pi$
$419$	18.6357			0.910413			0.455206	+	0.890386i	$0.349565\pi$
$420$	5.60802	−	3.58110i	0.273643	−	0.174740i
$421$	−2.39499	−	4.14824i	−0.116724	−	0.202173i	0.801743	−	0.597668i	$-0.203906\pi$
$421$	−2.39499	−	4.14824i	−0.116724	−	0.202173i	−0.918468	+	0.395496i	$0.870573\pi$
$422$	−4.72713	−	17.6419i	−0.230113	−	0.858794i
$423$	−16.4227	+	7.21012i	−0.798498	+	0.350568i
$424$	−8.41460	+	4.85817i	−0.408649	+	0.235934i
$425$	−34.7986	−	11.6983i	−1.68798	−	0.567451i
$426$	15.1378	+	7.26858i	0.733431	+	0.352164i
$427$	12.2438	−	3.28072i	0.592520	−	0.158765i
$428$	9.81146	−	2.62897i	0.474255	−	0.127076i
$429$	−0.654566	−	8.60191i	−0.0316027	−	0.415304i
$430$	15.6265	+	0.488514i	0.753578	+	0.0235582i
$431$	−8.42809	−	4.86596i	−0.405967	−	0.234385i	0.283089	−	0.959094i	$-0.408641\pi$
$431$	−8.42809	−	4.86596i	−0.405967	−	0.234385i	−0.689055	+	0.724709i	$0.741974\pi$
$432$	−2.74933	+	4.40921i	−0.132277	+	0.212138i
$433$	5.97307	−	5.97307i	0.287048	−	0.287048i	−0.548864	−	0.835912i	$-0.684940\pi$
$433$	5.97307	−	5.97307i	0.287048	−	0.287048i	0.835912	+	0.548864i	$0.184940\pi$
$434$	0.711042	+	9.53910i	0.0341311	+	0.457891i
$435$	−0.651110	−	2.05742i	−0.0312183	−	0.0986457i
$436$	5.33687			0.255590
$437$	−9.20555	−	34.3556i	−0.440361	−	1.64345i
$438$	−6.76310	−	19.2568i	−0.323154	−	0.920126i
$439$	−25.0924	+	14.4871i	−1.19760	+	0.691432i	−0.960018	−	0.279937i	$-0.909687\pi$
$439$	−25.0924	+	14.4871i	−1.19760	+	0.691432i	−0.237577	+	0.971369i	$0.576353\pi$
$440$	7.68801	−	1.80454i	0.366511	−	0.0860280i
$441$	12.0053	−	1.83774i	0.571682	−	0.0875115i
$442$	−7.32217	−	7.32217i	−0.348280	−	0.348280i
$443$	−3.51345	+	13.1124i	−0.166929	+	0.622987i	0.830857	+	0.556485i	$0.187851\pi$
$443$	−3.51345	+	13.1124i	−0.166929	+	0.622987i	−0.997786	+	0.0665019i	$0.978816\pi$
$444$	−11.3096	+	0.860608i	−0.536730	+	0.0408427i
$445$	13.4961	−	7.23938i	0.639774	−	0.343179i
$446$	−18.7440	−	10.8218i	−0.887552	−	0.512429i
$447$	−10.7084	−	9.19389i	−0.506488	−	0.434856i
$448$	0.444658	+	1.65949i	0.0210081	+	0.0784033i
$449$	−6.56999			−0.310057			−0.155029	−	0.987910i	$-0.549547\pi$
$449$	−6.56999			−0.310057			−0.155029	+	0.987910i	$0.549547\pi$
$450$	2.57328	−	14.7776i	0.121305	−	0.696624i
$451$	16.2582	−	28.1601i	0.765571	−	1.32601i
$452$	−0.988853	−	0.264962i	−0.0465117	−	0.0124628i
$453$	1.03100	−	5.48348i	0.0484408	−	0.257636i
$454$	12.6045	−	7.27721i	0.591559	−	0.341537i
$455$	−4.77436	+	2.56100i	−0.223825	+	0.120062i
$456$	−10.6319	+	0.809038i	−0.497884	+	0.0378867i
$457$	7.72162	+	7.72162i	0.361202	+	0.361202i	0.864255	−	0.503053i	$-0.167790\pi$
$457$	7.72162	+	7.72162i	0.361202	+	0.361202i	−0.503053	+	0.864255i	$0.667790\pi$
$458$	−6.76570	+	1.81286i	−0.316140	+	0.0847095i
$459$	−36.4961	−	11.1199i	−1.70349	−	0.519032i
$460$	−3.73202	+	12.3684i	−0.174007	+	0.576680i
$461$			10.8781i			0.506642i	0.967382	+	0.253321i	$0.0815228\pi$
$461$			10.8781i			0.506642i	−0.967382	+	0.253321i	$0.918477\pi$
$462$	−10.3281	−	1.94189i	−0.480507	−	0.0903450i
$463$	18.8185	−	18.8185i	0.874569	−	0.874569i	−0.118397	−	0.992966i	$-0.537776\pi$
$463$	18.8185	−	18.8185i	0.874569	−	0.874569i	0.992966	+	0.118397i	$0.0377756\pi$
$464$	0.557190			0.0258669
$465$	16.9517	+	13.3282i	0.786115	+	0.618080i
$466$	−18.4104			−0.852847
$467$	16.3474	−	16.3474i	0.756466	−	0.756466i	−0.219212	−	0.975677i	$-0.570349\pi$
$467$	16.3474	−	16.3474i	0.756466	−	0.756466i	0.975677	+	0.219212i	$0.0703486\pi$
$468$	2.50457	−	3.40995i	0.115774	−	0.157625i
$469$			10.1396i			0.468202i
$470$	6.31923	+	11.7807i	0.291484	+	0.543402i
$471$	−1.13190	+	0.773624i	−0.0521553	+	0.0356467i
$472$	−7.57003	+	2.02838i	−0.348439	+	0.0933640i
$473$	−17.4602	−	17.4602i	−0.802820	−	0.802820i
$474$	0.0510092	+	0.670332i	0.00234293	+	0.0307894i
$475$	27.5658	−	13.6951i	1.26481	−	0.628373i
$476$	−10.9245	+	6.30726i	−0.500724	+	0.289093i
$477$	17.2553	−	23.4930i	0.790068	−	1.07567i
$478$	7.27014	+	1.94803i	0.332529	+	0.0891008i
$479$	2.13984	−	3.70631i	0.0977717	−	0.169346i	−0.812990	−	0.582277i	$-0.802162\pi$
$479$	2.13984	−	3.70631i	0.0977717	−	0.169346i	0.910762	+	0.412932i	$0.135495\pi$
$480$	3.43728	+	1.78469i	0.156890	+	0.0814595i
$481$	9.23536			0.421096
$482$	−0.810006	−	3.02298i	−0.0368948	−	0.137693i
$483$	11.1995	−	13.0443i	0.509595	−	0.593538i
$484$	−1.27510	−	0.736182i	−0.0579593	−	0.0334628i
$485$	17.7145	+	5.34514i	0.804373	+	0.242710i
$486$	2.23473	−	15.4274i	0.101369	−	0.699803i
$487$	−4.36329	+	16.2840i	−0.197719	+	0.737899i	0.793827	+	0.608144i	$0.208086\pi$
$487$	−4.36329	+	16.2840i	−0.197719	+	0.737899i	−0.991546	+	0.129755i	$0.958581\pi$
$488$	5.21709	+	5.21709i	0.236167	+	0.236167i
$489$	7.93030	+	11.6029i	0.358621	+	0.524703i
$490$	−2.06859	−	8.81296i	−0.0934493	−	0.398129i
$491$	−0.129542	+	0.0747912i	−0.00584615	+	0.00337528i	−0.502920	−	0.864333i	$-0.667741\pi$
$491$	−0.129542	+	0.0747912i	−0.00584615	+	0.00337528i	0.497074	+	0.867708i	$0.334408\pi$
$492$	15.0464	−	5.28439i	0.678345	−	0.238239i
$493$	1.05887	+	3.95174i	0.0476889	+	0.177978i
$494$	8.68194			0.390619
$495$	−18.9421	+	14.2286i	−0.851384	+	0.639528i
$496$	−4.60155	+	3.13460i	−0.206616	+	0.140748i
$497$	−11.7779	+	11.7779i	−0.528311	+	0.528311i
$498$	10.0346	−	3.52419i	0.449660	−	0.157923i
$499$	31.4303	+	18.1463i	1.40701	+	0.812339i	0.995099	−	0.0988846i	$-0.0315275\pi$
$499$	31.4303	+	18.1463i	1.40701	+	0.812339i	0.411913	+	0.911223i	$0.364861\pi$
$500$	−11.1312	−	1.04668i	−0.497804	−	0.0468089i
$501$	3.53670	−	0.269126i	0.158008	−	0.0120237i
$502$	−6.41193	+	1.71807i	−0.286179	+	0.0766813i
$503$	28.4378	−	7.61988i	1.26798	−	0.339754i	0.438722	−	0.898623i	$-0.355431\pi$
$503$	28.4378	−	7.61988i	1.26798	−	0.339754i	0.829256	+	0.558869i	$0.188765\pi$
$504$	−3.22277	−	4.02222i	−0.143553	−	0.179164i
$505$	19.0732	+	35.5574i	0.848748	+	1.58228i
$506$	17.6708	−	10.2022i	0.785561	−	0.453544i
$507$	12.4236	−	14.4701i	0.551751	−	0.642639i
$508$	−4.26184	−	15.9054i	−0.189088	−	0.705688i
$509$	10.3671	+	17.9564i	0.459515	+	0.795904i	0.998935	−	0.0461330i	$-0.0146898\pi$
$509$	10.3671	+	17.9564i	0.459515	+	0.795904i	−0.539420	+	0.842037i	$0.681356\pi$
$510$	−6.12539	+	27.7697i	−0.271237	+	1.22966i
$511$	20.2446			0.895570
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	28.2293	−	15.0443i	1.24635	−	0.664224i
$514$	16.8051	−	9.70242i	0.741240	−	0.427955i
$515$	−11.9452	+	2.80380i	−0.526370	+	0.123550i
$516$	−0.918872	−	12.0753i	−0.0404511	−	0.531584i
$517$	5.46473	−	20.3946i	0.240338	−	0.896955i
$518$	2.91183	−	10.8671i	0.127938	−	0.477473i
$519$	−21.9541	−	10.5415i	−0.963679	−	0.462720i
$520$	−2.68044	−	1.66134i	−0.117545	−	0.0728544i
$521$	−6.96288	−	4.02002i	−0.305049	−	0.176120i	0.339660	−	0.940548i	$-0.389688\pi$
$521$	−6.96288	−	4.02002i	−0.305049	−	0.176120i	−0.644709	+	0.764428i	$0.723021\pi$
$522$	−1.53056	+	0.671968i	−0.0669907	+	0.0294112i
$523$	−2.99814	+	2.99814i	−0.131099	+	0.131099i	−0.769612	−	0.638512i	$-0.779550\pi$
$523$	−2.99814	+	2.99814i	−0.131099	+	0.131099i	0.638512	+	0.769612i	$0.279550\pi$
$524$	−4.32317	+	7.48795i	−0.188859	+	0.327113i
$525$	12.9840	+	7.26535i	0.566670	+	0.317086i
$526$	−8.60217			−0.375072
$527$	−30.9761	−	26.6785i	−1.34934	−	1.16213i
$528$	−2.02693	−	5.77136i	−0.0882110	−	0.251166i
$529$			10.3811i			0.451351i
$530$	−18.4670	−	11.4458i	−0.802155	−	0.497175i
$531$	18.3481	−	14.7012i	0.796239	−	0.637979i
$532$	2.73734	−	10.2159i	0.118679	−	0.442916i
$533$	−12.5426	+	3.36077i	−0.543279	+	0.145571i
$534$	−6.69394	−	9.79400i	−0.289675	−	0.423828i
$535$	15.5508	+	16.5545i	0.672322	+	0.715714i
$536$	−5.11118	+	2.95094i	−0.220769	+	0.127461i
$537$	28.2817	+	24.2818i	1.22044	+	1.04784i
$538$	−0.105056	−	0.0281496i	−0.00452927	−	0.00121362i
$539$	−7.14869	+	12.3819i	−0.307916	+	0.533326i
$540$	−11.5943	−	0.757064i	−0.498937	−	0.0325789i
$541$	−22.3158	+	38.6521i	−0.959432	+	1.66178i	−0.235548	+	0.971863i	$0.575688\pi$
$541$	−22.3158	+	38.6521i	−0.959432	+	1.66178i	−0.723884	+	0.689922i	$0.757645\pi$
$542$	−15.6172	+	15.6172i	−0.670816	+	0.670816i
$543$	−20.5156	+	7.20520i	−0.880410	+	0.309205i
$544$	−6.35875	−	3.67123i	−0.272629	−	0.157403i
$545$	5.64096	+	10.5162i	0.241632	+	0.450465i
$546$	2.36805	+	3.46472i	0.101343	+	0.148276i
$547$	−9.49425	+	35.4330i	−0.405945	+	1.51501i	0.396362	+	0.918094i	$0.370273\pi$
$547$	−9.49425	+	35.4330i	−0.405945	+	1.51501i	−0.802307	+	0.596912i	$0.796394\pi$
$548$	−3.51275	+	13.1097i	−0.150057	+	0.560021i
$549$	−20.6227	−	8.03917i	−0.880157	−	0.343104i
$550$	11.6819	+	13.2417i	0.498117	+	0.564629i
$551$	−2.97056	−	1.71505i	−0.126550	−	0.0730636i
$552$	9.83483	+	1.84915i	0.418598	+	0.0787049i
$553$	−0.644104	−	0.172587i	−0.0273901	−	0.00733916i
$554$	16.0317			0.681121
$555$	−13.6498	−	21.3757i	−0.579403	−	0.907348i
$556$	−17.6893			−0.750195
$557$	−20.4567	+	20.4567i	−0.866779	+	0.866779i	−0.992114	−	0.125335i	$-0.959999\pi$
$557$	−20.4567	+	20.4567i	−0.866779	+	0.866779i	0.125335	+	0.992114i	$0.459999\pi$
$558$	8.85979	−	14.1599i	0.375065	−	0.599438i
$559$			9.86059i			0.417059i
$560$	−2.79999	+	2.63023i	−0.118321	+	0.111148i
$561$	37.0801	−	25.3433i	1.56552	−	1.06999i
$562$	−2.09158	−	2.09158i	−0.0882280	−	0.0882280i
$563$	−4.45625	+	16.6309i	−0.187809	+	0.700911i	0.806203	+	0.591639i	$0.201519\pi$
$563$	−4.45625	+	16.6309i	−0.187809	+	0.700911i	−0.994012	+	0.109272i	$0.965148\pi$
$564$	8.54916	−	5.84312i	0.359985	−	0.246040i
$565$	−0.523094	−	2.22857i	−0.0220067	−	0.0937569i
$566$			10.6774i			0.448807i
$567$	13.7035	+	7.16210i	0.575491	+	0.300780i
$568$	−9.36478	−	2.50928i	−0.392937	−	0.105287i
$569$	−7.75405	−	13.4304i	−0.325067	−	0.563032i	0.656459	−	0.754362i	$-0.272053\pi$
$569$	−7.75405	−	13.4304i	−0.325067	−	0.563032i	−0.981526	+	0.191329i	$0.938720\pi$
$570$	−12.8319	−	20.0948i	−0.537468	−	0.841678i
$571$	−12.7861	−	22.1462i	−0.535083	−	0.926791i	−0.999159	−	0.0409956i	$-0.986947\pi$
$571$	−12.7861	−	22.1462i	−0.535083	−	0.926791i	0.464076	−	0.885795i	$-0.346386\pi$
$572$	1.28909	+	4.81096i	0.0538997	+	0.201156i
$573$	14.7130	+	41.8928i	0.614644	+	1.75010i
$574$			15.8183i			0.660241i
$575$	−28.3164	+	5.71926i	−1.18087	+	0.238510i
$576$	1.08960	−	2.79513i	0.0454001	−	0.116464i
$577$	−41.2709	+	11.0585i	−1.71813	+	0.460372i	−0.977395	−	0.211423i	$-0.932190\pi$
$577$	−41.2709	+	11.0585i	−1.71813	+	0.460372i	−0.740737	+	0.671795i	$0.765524\pi$
$578$	9.55344	−	35.6539i	0.397371	−	1.48301i
$579$	35.6872	−	2.71563i	1.48311	−	0.112858i
$580$	0.588939	+	1.09793i	0.0244543	+	0.0455892i
$581$			10.5493i			0.437659i
$582$	2.64841	−	14.0858i	0.109780	−	0.583875i
$583$	8.88124	+	33.1452i	0.367823	+	1.37274i
$584$	5.89184	+	10.2050i	0.243806	+	0.422284i
$585$	9.36653	+	1.33096i	0.387258	+	0.0550286i
$586$	6.23007	−	10.7908i	0.257362	−	0.445764i
$587$	−3.93581	+	3.93581i	−0.162448	+	0.162448i	−0.783650	−	0.621202i	$-0.786645\pi$
$587$	−3.93581	+	3.93581i	−0.162448	+	0.162448i	0.621202	+	0.783650i	$0.286645\pi$
$588$	−6.61586	+	2.32353i	−0.272833	+	0.0958206i
$589$	34.1807	−	2.54782i	1.40839	−	0.104981i
$590$	−11.9983	−	12.7726i	−0.493961	−	0.525842i
$591$	12.2306	−	25.4719i	0.503099	−	1.04777i
$592$	6.32534	−	1.69487i	0.259970	−	0.0696587i
$593$	−7.62372	−	7.62372i	−0.313069	−	0.313069i	0.533029	−	0.846097i	$-0.321054\pi$
$593$	−7.62372	−	7.62372i	−0.313069	−	0.313069i	−0.846097	+	0.533029i	$0.821054\pi$
$594$	12.5281	+	13.4090i	0.514032	+	0.550179i
$595$	−23.9753	−	14.8599i	−0.982892	−	0.609195i
$596$	7.05685	+	4.07428i	0.289060	+	0.166889i
$597$	2.15082	+	6.12410i	0.0880272	+	0.250643i
$598$	−7.87059	−	2.10892i	−0.321852	−	0.0862401i
$599$	12.5466	+	21.7314i	0.512642	+	0.887922i	0.999893	+	0.0146595i	$0.00466643\pi$
$599$	12.5466	+	21.7314i	0.512642	+	0.887922i	−0.487251	+	0.873262i	$0.662000\pi$
$600$	0.116440	+	8.65947i	0.00475363	+	0.353521i
$601$	6.80744	−	11.7908i	0.277681	−	0.480958i	−0.693127	−	0.720816i	$-0.743767\pi$
$601$	6.80744	−	11.7908i	0.277681	−	0.480958i	0.970808	+	0.239858i	$0.0771008\pi$
$602$	11.6028	+	3.10896i	0.472895	+	0.126712i
$603$	10.4812	−	14.2700i	0.426827	−	0.581121i
$604$			3.22136i			0.131075i
$605$	0.102873	−	3.29070i	0.00418240	−	0.133786i
$606$	25.8038	−	17.6362i	1.04821	−	0.716422i
$607$	6.17942	−	23.0619i	0.250815	−	0.936054i	−0.719556	−	0.694434i	$-0.755655\pi$
$607$	6.17942	−	23.0619i	0.250815	−	0.936054i	0.970371	−	0.241620i	$-0.0776786\pi$
$608$	5.94631	−	1.59331i	0.241155	−	0.0646172i
$609$	−0.125805	−	1.65326i	−0.00509788	−	0.0669933i
$610$	−4.76582	+	15.7945i	−0.192963	+	0.639502i
$611$	−7.30200	+	4.21581i	−0.295407	+	0.170554i
$612$	21.8945	+	2.41597i	0.885032	+	0.0976596i
$613$	6.18029	+	23.0651i	0.249619	+	0.931592i	0.971005	+	0.239059i	$0.0768388\pi$
$613$	6.18029	+	23.0651i	0.249619	+	0.931592i	−0.721386	+	0.692533i	$0.756494\pi$
$614$	7.79890	−	13.5081i	0.314738	−	0.545142i
$615$	26.3165	+	24.0632i	1.06118	+	0.970321i
$616$	6.06742			0.244463
$617$	7.69574	+	28.7209i	0.309819	+	1.15626i	0.928717	+	0.370788i	$0.120912\pi$
$617$	7.69574	+	28.7209i	0.309819	+	1.15626i	−0.618899	+	0.785471i	$0.712421\pi$
$618$	3.14935	+	8.96725i	0.126685	+	0.360716i
$619$		−	37.8962i		−	1.52318i	−0.648060	−	0.761589i	$-0.724419\pi$
$619$		−	37.8962i		−	1.52318i	0.648060	−	0.761589i	$-0.275581\pi$
$620$	−11.0404	−	5.75405i	−0.443394	−	0.231088i
$621$	−29.2456	+	6.78128i	−1.17358	+	0.272123i
$622$	−0.696316	−	0.696316i	−0.0279197	−	0.0279197i
$623$	11.3660	−	3.04551i	0.455370	−	0.122016i
$624$	−1.05733	+	2.20203i	−0.0423270	+	0.0881519i
$625$	−9.70303	−	23.0402i	−0.388121	−	0.921608i
$626$	8.07054	+	4.65953i	0.322564	+	0.186232i
$627$	−6.95823	+	37.0079i	−0.277885	+	1.47795i
$628$	0.559717	−	0.559717i	0.0223351	−	0.0223351i
$629$	24.0409	+	41.6401i	0.958575	+	1.66030i
$630$	4.51931	−	10.6018i	0.180054	−	0.422386i
$631$	13.0490	+	22.6015i	0.519471	+	0.899750i	0.999744	+	0.0226307i	$0.00720420\pi$
$631$	13.0490	+	22.6015i	0.519471	+	0.899750i	−0.480273	+	0.877119i	$0.659462\pi$
$632$	−0.100457	−	0.374910i	−0.00399595	−	0.0149131i
$633$	−24.0018	−	20.6073i	−0.953987	−	0.819066i
$634$	−29.5702	−	17.0724i	−1.17438	−	0.678031i
$635$	26.8366	−	25.2095i	1.06498	−	1.00041i
$636$	−7.28449	+	15.1710i	−0.288849	+	0.601568i
$637$	5.51492	−	1.47772i	0.218509	−	0.0585494i
$638$	0.509301	−	1.90074i	0.0201634	−	0.0752509i
$639$	28.7505	−	4.40105i	1.13735	−	0.174103i
$640$	−2.14074	−	0.645943i	−0.0846201	−	0.0255331i
$641$	27.1052	−	15.6492i	1.07059	−	0.618106i	0.142249	−	0.989831i	$-0.454567\pi$
$641$	27.1052	−	15.6492i	1.07059	−	0.618106i	0.928343	+	0.371725i	$0.121233\pi$
$642$	11.4606	−	13.3485i	0.452315	−	0.526823i
$643$	6.60271	−	6.60271i	0.260386	−	0.260386i	−0.564825	−	0.825211i	$-0.691056\pi$
$643$	6.60271	−	6.60271i	0.260386	−	0.260386i	0.825211	+	0.564825i	$0.191056\pi$
$644$	−4.96306	+	8.59628i	−0.195572	+	0.338741i
$645$	22.8228	−	14.5739i	0.898648	−	0.573847i
$646$	22.6003	+	39.1449i	0.889198	+	1.54014i
$647$	−0.321359	+	0.321359i	−0.0126339	+	0.0126339i	−0.713396	−	0.700762i	$-0.752844\pi$
$647$	−0.321359	+	0.321359i	−0.0126339	+	0.0126339i	0.700762	+	0.713396i	$0.252844\pi$
$648$	0.377860	+	8.99206i	0.0148437	+	0.353242i
$649$			27.6776i			1.08644i
$650$	0.440457	−	7.03776i	0.0172762	−	0.276044i
$651$	10.3397	+	12.9456i	0.405246	+	0.507380i
$652$	−5.73757	−	5.73757i	−0.224701	−	0.224701i
$653$	−18.2782	−	18.2782i	−0.715282	−	0.715282i	0.252353	−	0.967635i	$-0.418796\pi$
$653$	−18.2782	−	18.2782i	−0.715282	−	0.715282i	−0.967635	+	0.252353i	$0.918796\pi$
$654$	7.63154	−	5.21595i	0.298417	−	0.203960i
$655$	−19.3244	−	0.604115i	−0.755065	−	0.0236047i
$656$	−7.97370	+	4.60362i	−0.311321	+	0.179741i
$657$	−28.4915	−	20.9267i	−1.11156	−	0.816429i
$658$	2.65842	+	9.92136i	0.103636	+	0.386775i
$659$	18.5334			0.721960			0.360980	−	0.932574i	$-0.382442\pi$
$659$	18.5334			0.721960			0.360980	+	0.932574i	$0.382442\pi$
$660$	9.22993	−	10.0942i	0.359275	−	0.392918i
$661$	−17.9342	−	31.0629i	−0.697559	−	1.20821i	−0.969310	−	0.245840i	$-0.920936\pi$
$661$	−17.9342	−	31.0629i	−0.697559	−	1.20821i	0.271751	−	0.962367i	$-0.412397\pi$
$662$	14.3006	+	3.83182i	0.555807	+	0.148928i
$663$	−17.6267	−	3.31418i	−0.684565	−	0.128712i
$664$	−5.31772	+	3.07018i	−0.206367	+	0.119146i
$665$	23.0236	−	5.40412i	0.892815	−	0.209563i
$666$	−15.3312	+	12.2840i	−0.594073	+	0.475995i
$667$	2.27635	+	2.27635i	0.0881406	+	0.0881406i
$668$	−1.97804	+	0.530014i	−0.0765326	+	0.0205068i
$669$	−37.3799	+	2.84444i	−1.44519	+	0.109972i
$670$	−11.2172	−	6.95239i	−0.433357	−	0.268594i
$671$	22.5657	−	13.0283i	0.871139	−	0.502952i
$672$	2.25773	+	1.93842i	0.0870939	+	0.0747763i
$673$	14.3001	+	3.83170i	0.551228	+	0.147701i	0.523673	−	0.851919i	$-0.324561\pi$
$673$	14.3001	+	3.83170i	0.551228	+	0.147701i	0.0275546	+	0.999620i	$0.491228\pi$
$674$	−27.7914			−1.07048
$675$	−10.7631	−	23.6465i	−0.414272	−	0.910153i
$676$	−5.50552	+	9.53584i	−0.211751	+	0.366763i
$677$	3.19798	+	0.856897i	0.122908	+	0.0329332i	0.319749	−	0.947502i	$-0.396401\pi$
$677$	3.19798	+	0.856897i	0.122908	+	0.0329332i	−0.196840	+	0.980436i	$0.563068\pi$
$678$	−1.67298	+	0.587561i	−0.0642506	+	0.0225652i
$679$	12.3119	+	7.10828i	0.472487	+	0.272791i
$680$	0.513014	−	16.4102i	0.0196732	−	0.629303i
$681$	10.9117	−	22.7251i	0.418136	−	0.870827i
$682$	6.48698	+	18.5624i	0.248399	+	0.710791i
$683$	−3.39275	−	3.39275i	−0.129820	−	0.129820i	0.639211	−	0.769031i	$-0.279261\pi$
$683$	−3.39275	−	3.39275i	−0.129820	−	0.129820i	−0.769031	+	0.639211i	$0.779261\pi$
$684$	−14.4125	+	11.5479i	−0.551077	+	0.441545i
$685$	−29.5454	+	6.93493i	−1.12887	+	0.264970i
$686$		−	18.9814i		−	0.724714i
$687$	−7.90292	+	9.20474i	−0.301515	+	0.351183i
$688$	1.80961	+	6.75357i	0.0689909	+	0.257477i
$689$	6.85151	−	11.8672i	0.261022	−	0.452103i
$690$	6.75151	+	21.3339i	0.257025	+	0.812166i
$691$	3.75965	+	6.51190i	0.143024	+	0.247724i	0.928634	−	0.370998i	$-0.120984\pi$
$691$	3.75965	+	6.51190i	0.143024	+	0.247724i	−0.785610	+	0.618722i	$0.787651\pi$
$692$	13.5816	+	3.63917i	0.516293	+	0.138340i
$693$	−16.6667	+	7.31726i	−0.633117	+	0.277960i
$694$	5.24195	+	3.02644i	0.198982	+	0.114882i
$695$	−18.6973	−	34.8565i	−0.709227	−	1.32218i
$696$	0.796763	−	0.544566i	0.0302012	−	0.0206417i
$697$	−47.8030	−	47.8030i	−1.81067	−	1.81067i
$698$	−8.68532	−	8.68532i	−0.328744	−	0.328744i
$699$	−26.3263	+	17.9933i	−0.995752	+	0.680570i
$700$	−8.14235	−	2.73723i	−0.307752	−	0.103457i
$701$	−16.1546	−	9.32688i	−0.610152	−	0.352271i	0.162873	−	0.986647i	$-0.447924\pi$
$701$	−16.1546	−	9.32688i	−0.610152	−	0.352271i	−0.773025	+	0.634376i	$0.781257\pi$
$702$	0.248760	−	7.32394i	0.00938884	−	0.276424i
$703$	−38.9392	−	10.4337i	−1.46862	−	0.393516i
$704$	1.76581	+	3.05848i	0.0665515	+	0.115271i
$705$	20.5500	+	10.6699i	0.773959	+	0.401852i
$706$	16.5351	−	28.6396i	0.622306	−	1.07787i
$707$	8.02387	+	29.9455i	0.301769	+	1.12622i
$708$	−8.84246	+	10.2990i	−0.332320	+	0.387062i
$709$			25.1538i			0.944672i	0.881419	+	0.472336i	$0.156589\pi$
$709$			25.1538i			0.944672i	−0.881419	+	0.472336i	$0.843411\pi$
$710$	−4.95388	−	21.1054i	−0.185916	−	0.792071i
$711$	0.728085	+	0.908698i	0.0273053	+	0.0340788i
$712$	4.84306	+	4.84306i	0.181501	+	0.181501i
$713$	−31.6053	−	5.99307i	−1.18363	−	0.224442i
$714$	−9.45730	+	19.6962i	−0.353930	+	0.737110i
$715$	−8.11736	+	7.62522i	−0.303572	+	0.285167i
$716$	−18.6377	−	10.7605i	−0.696525	−	0.402139i
$717$	12.2999	−	4.31981i	0.459350	−	0.161326i
$718$	18.3779	+	4.92434i	0.685857	+	0.183775i
$719$	−12.8144	+	22.1952i	−0.477897	+	0.827742i	−0.999679	−	0.0253368i	$-0.991934\pi$
$719$	−12.8144	+	22.1952i	−0.477897	+	0.827742i	0.521782	+	0.853079i	$0.325268\pi$
$720$	6.65944	−	0.807359i	0.248183	−	0.0300885i
$721$	−9.42725			−0.351089
$722$	−18.2533	−	4.89095i	−0.679317	−	0.182022i
$723$	−4.11277	−	3.53111i	−0.152956	−	0.131323i
$724$	10.8721	−	6.27698i	0.404057	−	0.233282i
$725$	−1.54096	+	2.32098i	−0.0572298	+	0.0861992i
$726$	−2.54286	+	0.193500i	−0.0943743	+	0.00718145i
$727$	−27.3455	+	7.32720i	−1.01419	+	0.271751i	−0.727378	−	0.686237i	$-0.759261\pi$
$727$	−27.3455	+	7.32720i	−1.01419	+	0.271751i	−0.286810	+	0.957988i	$0.592595\pi$
$728$	−1.71328	−	1.71328i	−0.0634983	−	0.0634983i
$729$	−11.8823	−	24.2448i	−0.440086	−	0.897956i
$730$	−13.8811	+	22.3962i	−0.513764	+	0.828920i
$731$	−44.4592	+	25.6685i	−1.64438	+	0.949385i
$732$	12.5592	+	2.36137i	0.464200	+	0.0872789i
$733$	20.8565	+	5.58848i	0.770353	+	0.206415i	0.622527	−	0.782598i	$-0.286106\pi$
$733$	20.8565	+	5.58848i	0.770353	+	0.206415i	0.147825	+	0.989013i	$0.452773\pi$
$734$	−7.83374	−	13.5684i	−0.289149	−	0.500820i
$735$	−11.5713	−	10.5805i	−0.426813	−	0.390268i
$736$	−5.77764			−0.212966
$737$	5.39462	+	20.1330i	0.198713	+	0.741609i
$738$	16.3512	−	22.2620i	0.601896	−	0.819475i
$739$	−23.6458	+	13.6519i	−0.869824	+	0.502193i	−0.867290	−	0.497804i	$-0.834140\pi$
$739$	−23.6458	+	13.6519i	−0.869824	+	0.502193i	−0.00253424	+	0.999997i	$0.500807\pi$
$740$	10.0255	+	10.6725i	0.368543	+	0.392330i
$741$	12.4149	−	8.48524i	0.456072	−	0.311713i
$742$	−11.8037	−	11.8037i	−0.433327	−	0.433327i
$743$	−14.2044	−	14.2044i	−0.521111	−	0.521111i	0.396796	−	0.917907i	$-0.370122\pi$
$743$	−14.2044	−	14.2044i	−0.521111	−	0.521111i	−0.917907	+	0.396796i	$0.870122\pi$
$744$	−3.51647	+	8.97967i	−0.128920	+	0.329211i
$745$	−0.569335	+	18.2118i	−0.0208588	+	0.667229i
$746$			23.1750i			0.848498i
$747$	10.9047	−	14.8467i	0.398983	−	0.543212i
$748$	−18.3358	+	18.3358i	−0.670425	+	0.670425i
$749$	8.72548	+	15.1130i	0.318822	+	0.552216i
$750$	−16.9402	+	9.38232i	−0.618570	+	0.342594i
$751$	−5.24988	+	9.09305i	−0.191571	+	0.331810i	−0.945771	−	0.324834i	$-0.894691\pi$
$751$	−5.24988	+	9.09305i	−0.191571	+	0.331810i	0.754200	+	0.656644i	$0.228025\pi$
$752$	−4.22749	+	4.22749i	−0.154161	+	0.154161i
$753$	−7.48970	+	8.72344i	−0.272940	+	0.317900i
$754$	−0.680531	+	0.392905i	−0.0247835	+	0.0143087i
$755$	−6.34763	+	3.40491i	−0.231014	+	0.123917i
$756$	−8.53954	−	2.60189i	−0.310580	−	0.0946298i
$757$	7.14572	−	26.6682i	0.259715	−	0.969271i	−0.705691	−	0.708520i	$-0.749363\pi$
$757$	7.14572	−	26.6682i	0.259715	−	0.969271i	0.965406	−	0.260751i	$-0.0839702\pi$
$758$	−18.5149	+	4.96106i	−0.672492	+	0.180194i
$759$	15.2975	−	31.8592i	0.555264	−	1.15642i
$760$	9.42471	+	10.0330i	0.341870	+	0.363935i
$761$	−8.03101	−	4.63671i	−0.291124	−	0.168080i	0.347325	−	0.937745i	$-0.387090\pi$
$761$	−8.03101	−	4.63671i	−0.291124	−	0.168080i	−0.638449	+	0.769664i	$0.720424\pi$
$762$	−21.6393	−	18.5789i	−0.783909	−	0.673042i
$763$	2.37308	+	8.85646i	0.0859113	+	0.320625i
$764$	−12.8176	−	22.2007i	−0.463723	−	0.803192i
$765$	18.3814	+	45.6963i	0.664581	+	1.65215i
$766$	2.70393	+	4.68334i	0.0976969	+	0.169216i
$767$	7.81542	−	7.81542i	0.282199	−	0.282199i
$768$	−0.320052	+	1.70222i	−0.0115489	+	0.0614237i
$769$	−12.7665	−	7.37075i	−0.460372	−	0.265796i	0.251828	−	0.967772i	$-0.418968\pi$
$769$	−12.7665	−	7.37075i	−0.460372	−	0.265796i	−0.712201	+	0.701976i	$0.752301\pi$
$770$	6.41314	+	11.9557i	0.231113	+	0.430855i
$771$	14.5481	−	30.2984i	0.523937	−	1.09117i
$772$	−19.9595	+	5.34813i	−0.718357	+	0.192483i
$773$	−19.0110	−	19.0110i	−0.683779	−	0.683779i	0.277070	−	0.960850i	$-0.410636\pi$
$773$	−19.0110	−	19.0110i	−0.683779	−	0.683779i	−0.960850	+	0.277070i	$0.910636\pi$
$774$	−13.1156	−	16.3691i	−0.471431	−	0.588377i
$775$	−0.331243	−	27.8369i	−0.0118986	−	0.999929i
$776$			8.27494i			0.297053i
$777$	−6.45707	−	18.3854i	−0.231646	−	0.659574i
$778$	1.33064	+	4.96600i	0.0477056	+	0.178040i
$779$	56.6804			2.03078
$780$	−5.45664	+	0.244060i	−0.195379	+	0.00873875i
$781$	−17.1198	+	29.6523i	−0.612594	+	1.06104i
$782$	−10.9796	−	40.9765i	−0.392631	−	1.46532i
$783$	−1.53190	+	2.45677i	−0.0547457	+	0.0877978i
$784$	3.50601	−	2.02419i	0.125215	−	0.0722927i
$785$	1.69452	+	0.511302i	0.0604800	+	0.0182491i
$786$	1.13631	+	14.9327i	0.0405309	+	0.532633i
$787$	0.317981	−	0.0852027i	0.0113348	−	0.00303715i	−0.253147	−	0.967428i	$-0.581466\pi$
$787$	0.317981	−	0.0852027i	0.0113348	−	0.00303715i	0.264482	+	0.964391i	$0.414799\pi$
$788$	−4.22228	+	15.7578i	−0.150413	+	0.561347i
$789$	−12.3008	+	8.40727i	−0.437920	+	0.299307i
$790$	0.632572	−	0.594220i	0.0225059	−	0.0211414i
$791$		−	1.75880i		−	0.0625359i
$792$	−8.53905	−	6.27184i	−0.303422	−	0.222860i
$793$	−10.0508	−	2.69311i	−0.356915	−	0.0956350i
$794$	−18.9103	+	32.7536i	−0.671102	+	1.16238i
$795$	−37.5937	+	1.68146i	−1.33331	+	0.0596352i
$796$	−1.87374	−	3.24541i	−0.0664128	−	0.115030i
$797$	13.9848	+	3.74723i	0.495368	+	0.132734i	0.497850	−	0.867263i	$-0.334123\pi$
$797$	13.9848	+	3.74723i	0.495368	+	0.132734i	−0.00248125	+	0.999997i	$0.500790\pi$
$798$	−6.07014	−	17.2837i	−0.214881	−	0.611837i
$799$	−38.0163	−	21.9487i	−1.34492	−	0.776490i
$800$	−0.989897	−	4.90103i	−0.0349981	−	0.173278i
$801$	−19.1442	−	7.46281i	−0.676427	−	0.263685i
$802$	5.78412	+	5.78412i	0.204244	+	0.204244i
$803$	40.1975	−	10.7709i	1.41854	−	0.380096i
$804$	−4.42473	+	9.21511i	−0.156048	+	0.324992i
$805$	−22.1847	−	0.693533i	−0.781906	−	0.0244438i
$806$	3.40978	−	7.07328i	0.120104	−	0.249146i
$807$	−0.177738	+	0.0624225i	−0.00625667	+	0.00219738i
$808$	−12.7598	+	12.7598i	−0.448887	+	0.448887i
$809$	−2.84165	+	4.92189i	−0.0999072	+	0.173044i	−0.911646	−	0.410976i	$-0.865188\pi$
$809$	−2.84165	+	4.92189i	−0.0999072	+	0.173044i	0.811739	+	0.584021i	$0.198521\pi$
$810$	−17.3193	+	10.2490i	−0.608538	+	0.360113i
$811$	3.43565	+	5.95073i	0.120642	+	0.208958i	0.920021	−	0.391869i	$-0.128171\pi$
$811$	3.43565	+	5.95073i	0.120642	+	0.208958i	−0.799379	+	0.600827i	$0.794838\pi$
$812$	0.247759	+	0.924649i	0.00869464	+	0.0324488i
$813$	−7.06869	+	37.5954i	−0.247910	+	1.31853i
$814$		−	23.1268i		−	0.810592i
$815$	5.24128	−	17.3703i	0.183594	−	0.608454i
$816$	−12.6808	+	0.964954i	−0.443918	+	0.0337802i
$817$	11.1401	−	41.5754i	0.389743	−	1.45454i
$818$	38.6684	−	10.3612i	1.35201	−	0.362269i
$819$	6.77245	+	2.64004i	0.236648	+	0.0922505i
$820$	−17.4994	−	10.8461i	−0.611105	−	0.378762i
$821$			44.5711i			1.55554i	0.628549	+	0.777770i	$0.283649\pi$
$821$			44.5711i			1.55554i	−0.628549	+	0.777770i	$0.716351\pi$
$822$	7.78962	+	22.1796i	0.271694	+	0.773604i
$823$	−4.71309	−	17.5895i	−0.164288	−	0.613131i	−0.998130	−	0.0611278i	$-0.980530\pi$
$823$	−4.71309	−	17.5895i	−0.164288	−	0.613131i	0.833842	−	0.552003i	$-0.186136\pi$
$824$	−2.74363	−	4.75211i	−0.0955789	−	0.165547i
$825$	29.6464	+	7.51799i	1.03215	+	0.261743i
$826$	−6.73215	−	11.6604i	−0.234241	−	0.405718i
$827$	6.33052	+	1.69626i	0.220134	+	0.0589846i	0.367200	−	0.930142i	$-0.380316\pi$
$827$	6.33052	+	1.69626i	0.220134	+	0.0589846i	−0.147066	+	0.989127i	$0.546983\pi$
$828$	15.8707	−	6.96779i	0.551545	−	0.242147i
$829$			0.640683i			0.0222518i	0.999938	+	0.0111259i	$0.00354156\pi$
$829$			0.640683i			0.0222518i	−0.999938	+	0.0111259i	$0.996458\pi$
$830$	−11.6705	−	7.23334i	−0.405087	−	0.251073i
$831$	22.9248	−	15.6685i	0.795251	−	0.543533i
$832$	0.365014	−	1.36225i	0.0126546	−	0.0472276i
$833$	21.0188	+	21.0188i	0.728259	+	0.728259i
$834$	−25.2951	+	17.2885i	−0.875899	+	0.598653i
$835$	−3.13513	−	3.33747i	−0.108496	−	0.115498i
$836$		−	21.7409i		−	0.751925i
$837$	−1.16994	−	28.9073i	−0.0404389	−	0.999182i
$838$	−13.1774	+	13.1774i	−0.455206	+	0.455206i
$839$	−23.0308			−0.795113			−0.397556	−	0.917578i	$-0.630142\pi$
$839$	−23.0308			−0.795113			−0.397556	+	0.917578i	$0.630142\pi$
$840$	−1.43325	+	6.49769i	−0.0494518	+	0.224192i
$841$	−28.6895			−0.989294
$842$	4.62676	+	1.23974i	0.159449	+	0.0427241i
$843$	−5.03508	−	0.946696i	−0.173417	−	0.0326060i
$844$	15.8173	+	9.13212i	0.544454	+	0.314341i
$845$	−24.6094	−	0.769335i	−0.846589	−	0.0264659i
$846$	6.51427	−	16.7109i	0.223965	−	0.574533i
$847$	0.654698	−	2.44337i	0.0224957	−	0.0839550i
$848$	2.51478	−	9.38527i	0.0863577	−	0.322291i
$849$	10.4355	+	15.2684i	0.358146	+	0.524010i
$850$	32.8783	−	16.3344i	1.12771	−	0.560264i
$851$	32.7658	+	18.9174i	1.12320	+	0.648479i
$852$	−15.8437	+	5.56441i	−0.542797	+	0.190634i
$853$	28.7965	−	28.7965i	0.985972	−	0.985972i	−0.0139311	−	0.999903i	$-0.504435\pi$
$853$	28.7965	−	28.7965i	0.985972	−	0.985972i	0.999903	+	0.0139311i	$0.00443456\pi$
$854$	−6.33787	+	10.9775i	−0.216877	+	0.375643i
$855$	−37.9886	−	16.1937i	−1.29918	−	0.553813i
$856$	−5.07878	+	8.79671i	−0.173589	+	0.300665i
$857$	22.7739	+	6.10226i	0.777943	+	0.208449i	0.625878	−	0.779921i	$-0.284741\pi$
$857$	22.7739	+	6.10226i	0.777943	+	0.208449i	0.152066	+	0.988370i	$0.451408\pi$
$858$	6.54531	+	5.61962i	0.223453	+	0.191851i
$859$	−1.24788	+	0.720464i	−0.0425771	+	0.0245819i	−0.521137	−	0.853473i	$-0.674492\pi$
$859$	−1.24788	+	0.720464i	−0.0425771	+	0.0245819i	0.478560	+	0.878055i	$0.341159\pi$
$860$	−11.3951	+	10.7042i	−0.388568	+	0.365010i
$861$	15.4599	+	22.6196i	0.526871	+	0.770873i
$862$	9.40031	−	2.51881i	0.320176	−	0.0857909i
$863$	9.40321	−	35.0933i	0.320089	−	1.19459i	−0.599068	−	0.800698i	$-0.704462\pi$
$863$	9.40321	−	35.0933i	0.320089	−	1.19459i	0.919157	−	0.393891i	$-0.128871\pi$
$864$	−1.17371	−	5.06186i	−0.0399305	−	0.172208i
$865$	7.18451	+	30.6087i	0.244281	+	1.04073i
$866$			8.44720i			0.287048i
$867$	−21.1850	−	60.3209i	−0.719481	−	2.04860i
$868$	−7.24794	−	6.24238i	−0.246011	−	0.211880i
$869$	−1.37075			−0.0464994
$870$	1.91522	+	0.994411i	0.0649320	+	0.0337137i
$871$	4.16173	−	7.20833i	0.141015	−	0.244245i
$872$	−3.77374	+	3.77374i	−0.127795	+	0.127795i
$873$	−9.97952	−	22.7306i	−0.337756	−	0.769315i
$874$	30.8024	+	17.7838i	1.04191	+	0.601545i
$875$	−3.21264	−	18.9375i	−0.108607	−	0.640206i
$876$	18.3989	+	8.83439i	0.621640	+	0.298486i
$877$	8.70832	−	32.4999i	0.294059	−	1.09744i	−0.647903	−	0.761723i	$-0.724354\pi$
$877$	8.70832	−	32.4999i	0.294059	−	1.09744i	0.941962	−	0.335720i	$-0.108980\pi$
$878$	7.49908	−	27.9869i	0.253082	−	0.944514i
$879$	−1.63753	−	21.5194i	−0.0552324	−	0.725831i
$880$	−4.16024	+	6.71224i	−0.140242	+	0.226270i
$881$	−23.1238	+	13.3505i	−0.779061	+	0.449791i	−0.836098	−	0.548581i	$-0.815168\pi$
$881$	−23.1238	+	13.3505i	−0.779061	+	0.449791i	0.0570361	+	0.998372i	$0.481835\pi$
$882$	−7.18957	+	9.78852i	−0.242085	+	0.329597i
$883$	−29.7427	+	29.7427i	−1.00092	+	1.00092i	−0.000921154		1.00000i	$0.500293\pi$
$883$	−29.7427	+	29.7427i	−1.00092	+	1.00092i	−1.00000		0.000921154i	$0.999707\pi$
$884$	10.3551			0.348280
$885$	−29.6404	−	6.53802i	−0.996350	−	0.219773i
$886$	−6.78746	−	11.7562i	−0.228029	−	0.394958i
$887$	9.55464	+	35.6584i	0.320813	+	1.19729i	0.918454	+	0.395528i	$0.129438\pi$
$887$	9.55464	+	35.6584i	0.320813	+	1.19729i	−0.597641	+	0.801764i	$0.703895\pi$
$888$	7.38855	−	8.60563i	0.247944	−	0.288786i
$889$	24.4997	−	14.1449i	0.821694	−	0.474405i
$890$	−4.42414	+	14.6622i	−0.148298	+	0.491477i
$891$	31.0199	+	6.93022i	1.03921	+	0.232171i
$892$	20.9062	−	5.60179i	0.699991	−	0.187562i
$893$	35.5505	−	9.52572i	1.18965	−	0.318766i
$894$	14.0730	−	1.07089i	0.470672	−	0.0358160i
$895$	1.50366	−	48.0989i	0.0502619	−	1.60777i
$896$	−1.48785	−	0.859013i	−0.0497057	−	0.0286976i
$897$	−13.3158	+	4.67659i	−0.444602	+	0.156147i
$898$	4.64569	−	4.64569i	0.155029	−	0.155029i
$899$	−2.56394	+	1.74657i	−0.0855122	+	0.0582514i
$900$	8.62978	+	12.2689i	0.287659	+	0.408965i
$901$	71.3418			2.37674
$902$	8.41588	+	31.4085i	0.280218	+	1.04579i
$903$	19.6301	−	6.89421i	0.653250	−	0.229425i
$904$	0.886581	−	0.511868i	0.0294872	−	0.0170245i
$905$	23.8602	+	14.7885i	0.793140	+	0.491587i
$906$	3.14838	+	4.60644i	0.104598	+	0.153039i
$907$	14.3192	+	14.3192i	0.475461	+	0.475461i	0.903677	−	0.428215i	$-0.140858\pi$
$907$	14.3192	+	14.3192i	0.475461	+	0.475461i	−0.428215	+	0.903677i	$0.640858\pi$
$908$	−3.76696	+	14.0585i	−0.125011	+	0.466548i
$909$	19.6619	−	50.4383i	0.652145	−	1.67293i
$910$	1.56508	−	5.18688i	0.0518820	−	0.171944i
$911$	10.0276	+	5.78945i	0.332230	+	0.191813i	0.656831	−	0.754038i	$-0.271897\pi$
$911$	10.0276	+	5.78945i	0.332230	+	0.191813i	−0.324601	+	0.945851i	$0.605230\pi$
$912$	6.94580	−	8.08996i	0.229999	−	0.267885i
$913$	5.61261	+	20.9466i	0.185750	+	0.693230i
$914$	−10.9200			−0.361202
$915$	8.62173	+	27.2435i	0.285025	+	0.900642i
$916$	3.50218	−	6.06596i	0.115715	−	0.200425i
$917$	−14.3485	−	3.84466i	−0.473828	−	0.126962i
$918$	33.6696	−	17.9437i	1.11126	−	0.592229i
$919$	13.2733	−	7.66331i	0.437844	−	0.252789i	−0.264839	−	0.964293i	$-0.585319\pi$
$919$	13.2733	−	7.66331i	0.437844	−	0.252789i	0.702683	+	0.711503i	$0.251985\pi$
$920$	−6.10684	−	11.3847i	−0.201337	−	0.375343i
$921$	−2.04988	−	26.9383i	−0.0675459	−	0.887648i
$922$	−7.69195	−	7.69195i	−0.253321	−	0.253321i
$923$	13.2072	−	3.53886i	0.434720	−	0.116483i
$924$	8.67620	−	5.92995i	0.285426	−	0.195081i
$925$	−10.4333	+	31.0356i	−0.343045	+	1.02044i
$926$			26.6134i			0.874569i
$927$	13.2675	+	9.74487i	0.435763	+	0.320063i
$928$	−0.393993	+	0.393993i	−0.0129335	+	0.0129335i
$929$	16.0924			0.527973			0.263986	−	0.964526i	$-0.414963\pi$
$929$	16.0924			0.527973			0.263986	+	0.964526i	$0.414963\pi$
$930$	−21.4111	+	2.56218i	−0.702098	+	0.0840172i
$931$	−24.9222			−0.816791
$932$	13.0182	−	13.0182i	0.426424	−	0.426424i
$933$	−1.67625	−	0.315168i	−0.0548779	−	0.0103181i
$934$			23.1187i			0.756466i
$935$	−55.5110	−	16.7498i	−1.81540	−	0.547778i
$936$	0.640200	+	4.18220i	0.0209256	+	0.136700i
$937$	3.57365	−	0.957555i	0.116746	−	0.0312820i	−0.199973	−	0.979801i	$-0.564085\pi$
$937$	3.57365	−	0.957555i	0.116746	−	0.0312820i	0.316719	+	0.948519i	$0.397419\pi$
$938$	−7.16976	−	7.16976i	−0.234101	−	0.234101i
$939$	16.0946	−	1.22472i	0.525226	−	0.0399673i
$940$	−12.7986	−	3.86182i	−0.417443	−	0.125959i
$941$	−42.7651	+	24.6904i	−1.39410	+	0.804886i	−0.993766	−	0.111483i	$-0.964440\pi$
$941$	−42.7651	+	24.6904i	−1.39410	+	0.804886i	−0.400336	+	0.916368i	$0.631107\pi$
$942$	0.253340	−	1.34741i	0.00825427	−	0.0439010i
$943$	−51.3834	−	13.7681i	−1.67327	−	0.448353i
$944$	3.91854	−	6.78711i	0.127538	−	0.220902i
$945$	−3.89914	−	19.5771i	−0.126839	−	0.636844i
$946$	24.6924			0.802820
$947$	−6.49466	−	24.2384i	−0.211048	−	0.787642i	−0.987520	−	0.157491i	$-0.949660\pi$
$947$	−6.49466	−	24.2384i	−0.211048	−	0.787642i	0.776472	−	0.630151i	$-0.217007\pi$
$948$	−0.510065	−	0.437927i	−0.0165661	−	0.0142232i
$949$	−14.3921	−	8.30929i	−0.467188	−	0.269731i
$950$	−9.80809	+	29.1759i	−0.318217	+	0.946590i
$951$	−58.9700	+	4.48734i	−1.91223	+	0.145512i
$952$	3.26488	−	12.1847i	0.105815	−	0.394908i
$953$	−0.493128	−	0.493128i	−0.0159740	−	0.0159740i	0.699075	−	0.715049i	$-0.253595\pi$
$953$	−0.493128	−	0.493128i	−0.0159740	−	0.0159740i	−0.715049	+	0.699075i	$0.753595\pi$
$954$	4.41068	+	28.8134i	0.142801	+	0.932868i
$955$	30.1981	−	48.7224i	0.977187	−	1.57662i
$956$	−6.51823	+	3.76330i	−0.210815	+	0.121714i
$957$	−1.12939	−	3.21575i	−0.0365079	−	0.103950i
$958$	1.10766	+	4.13385i	0.0357869	+	0.133559i
$959$	−23.3174			−0.752958
$960$	−3.69249	+	1.16856i	−0.119175	+	0.0377151i
$961$	11.3485	−	28.8481i	0.366081	−	0.930583i
$962$	−6.53038	+	6.53038i	−0.210548	+	0.210548i
$963$	3.34225	−	30.2889i	0.107703	−	0.976045i
$964$	2.71033	+	1.56481i	0.0872939	+	0.0503992i
$965$	−31.6351	−	33.6769i	−1.01837	−	1.08410i
$966$	1.30450	+	17.1430i	0.0419717	+	0.551567i
$967$	4.06373	−	1.08887i	0.130681	−	0.0350158i	−0.192886	−	0.981221i	$-0.561785\pi$
$967$	4.06373	−	1.08887i	0.130681	−	0.0350158i	0.323566	+	0.946205i	$0.395118\pi$
$968$	1.42219	−	0.381076i	0.0457111	−	0.0122482i
$969$	70.5757	+	33.8876i	2.26722	+	1.08863i
$970$	−16.3056	+	8.74644i	−0.523542	+	0.280831i
$971$	44.7703	−	25.8482i	1.43675	−	0.829507i	0.439126	−	0.898426i	$-0.355288\pi$
$971$	44.7703	−	25.8482i	1.43675	−	0.829507i	0.997622	+	0.0689188i	$0.0219549\pi$
$972$	9.32866	+	12.4890i	0.299217	+	0.400586i
$973$	−7.86570	−	29.3552i	−0.252163	−	0.941084i
$974$	−8.42923	−	14.5998i	−0.270090	−	0.467809i
$975$	−6.24847	−	10.4942i	−0.200111	−	0.336084i
$976$	−7.37809			−0.236167
$977$	−6.08272	+	6.08272i	−0.194604	+	0.194604i	−0.797682	−	0.603078i	$-0.793941\pi$
$977$	−6.08272	+	6.08272i	−0.194604	+	0.194604i	0.603078	+	0.797682i	$0.293941\pi$
$978$	−13.8121	−	2.59695i	−0.441662	−	0.0830414i
$979$	20.9479	−	12.0943i	0.669497	−	0.386534i
$980$	7.69441	+	4.76899i	0.245789	+	0.152340i
$981$	5.81506	−	14.9173i	0.185661	−	0.476272i
$982$	0.0387148	−	0.144485i	0.00123544	−	0.00461072i
$983$	−13.7028	+	51.1395i	−0.437051	+	1.63110i	0.299059	+	0.954235i	$0.403327\pi$
$983$	−13.7028	+	51.1395i	−0.437051	+	1.63110i	−0.736110	+	0.676862i	$0.763339\pi$
$984$	−6.90280	+	14.3760i	−0.220053	+	0.458292i
$985$	−35.5132	+	8.33571i	−1.13155	+	0.265598i
$986$	−3.54304	−	2.04557i	−0.112833	−	0.0651443i
$987$	13.4980	+	11.5890i	0.429647	+	0.368882i
$988$	−6.13906	+	6.13906i	−0.195310	+	0.195310i
$989$	−20.1981	+	34.9841i	−0.642261	+	1.11243i
$990$	3.33294	−	23.4552i	0.105928	−	0.745456i
$991$	−59.0660			−1.87629			−0.938147	−	0.346238i	$-0.887459\pi$
$991$	−59.0660			−1.87629			−0.938147	+	0.346238i	$0.887459\pi$
$992$	1.03729	−	5.47029i	0.0329339	−	0.173682i
$993$	24.1943	−	8.49717i	0.767783	−	0.269650i
$994$		−	16.6565i		−	0.528311i
$995$	4.41451	−	7.12249i	0.139949	−	0.225798i
$996$	−4.60353	+	9.58749i	−0.145868	+	0.303791i
$997$	−12.1201	+	45.2327i	−0.383847	+	1.43253i	0.456131	+	0.889913i	$0.349235\pi$
$997$	−12.1201	+	45.2327i	−0.383847	+	1.43253i	−0.839977	+	0.542622i	$0.817432\pi$
$998$	−35.0559	+	9.39320i	−1.10968	+	0.297337i
$999$	−9.91744	+	32.5495i	−0.313774	+	1.02982i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bf.a.377.15	✓	256
3.2	odd	2	inner	930.2.bf.a.377.55	yes	256
5.3	odd	4	inner	930.2.bf.a.563.34	yes	256
15.8	even	4	inner	930.2.bf.a.563.7	yes	256
31.25	even	3	inner	930.2.bf.a.707.7	yes	256
93.56	odd	6	inner	930.2.bf.a.707.34	yes	256
155.118	odd	12	inner	930.2.bf.a.893.55	yes	256
465.428	even	12	inner	930.2.bf.a.893.15	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bf.a.377.15	✓	256	1.1	even	1	trivial
930.2.bf.a.377.55	yes	256	3.2	odd	2	inner
930.2.bf.a.563.7	yes	256	15.8	even	4	inner
930.2.bf.a.563.34	yes	256	5.3	odd	4	inner
930.2.bf.a.707.7	yes	256	31.25	even	3	inner
930.2.bf.a.707.34	yes	256	93.56	odd	6	inner
930.2.bf.a.893.15	yes	256	465.428	even	12	inner
930.2.bf.a.893.55	yes	256	155.118	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.320052 + 1.70222i) q^{3} -1.00000i q^{4} +(1.97048 - 1.05698i) q^{5} +(-0.977343 - 1.42997i) q^{6} +(1.65949 - 0.444658i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.79513 - 1.08960i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.320052 + 1.70222i) q^{3} -1.00000i q^{4} +(1.97048 - 1.05698i) q^{5} +(-0.977343 - 1.42997i) q^{6} +(1.65949 - 0.444658i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.79513 - 1.08960i) q^{9} +(-0.645943 + 2.14074i) q^{10} +(3.05848 - 1.76581i) q^{11} +(1.70222 + 0.320052i) q^{12} +(-1.36225 - 0.365014i) q^{13} +(-0.859013 + 1.48785i) q^{14} +(1.16856 + 3.69249i) q^{15} -1.00000 q^{16} +(-1.90037 - 7.09227i) q^{17} +(2.74692 - 1.20599i) q^{18} +(5.33131 + 3.07803i) q^{19} +(-1.05698 - 1.97048i) q^{20} +(0.225785 + 2.96713i) q^{21} +(-0.914051 + 3.41129i) q^{22} +(-4.08541 - 4.08541i) q^{23} +(-1.42997 + 0.977343i) q^{24} +(2.76559 - 4.16551i) q^{25} +(1.22136 - 0.705153i) q^{26} +(2.74933 - 4.40921i) q^{27} +(-0.444658 - 1.65949i) q^{28} -0.557190 q^{29} +(-3.43728 - 1.78469i) q^{30} +(4.60155 - 3.13460i) q^{31} +(0.707107 - 0.707107i) q^{32} +(2.02693 + 5.77136i) q^{33} +(6.35875 + 3.67123i) q^{34} +(2.79999 - 2.63023i) q^{35} +(-1.08960 + 2.79513i) q^{36} +(-6.32534 + 1.69487i) q^{37} +(-5.94631 + 1.59331i) q^{38} +(1.05733 - 2.20203i) q^{39} +(2.14074 + 0.645943i) q^{40} +(7.97370 - 4.60362i) q^{41} +(-2.25773 - 1.93842i) q^{42} +(-1.80961 - 6.75357i) q^{43} +(-1.76581 - 3.05848i) q^{44} +(-6.65944 + 0.807359i) q^{45} +5.77764 q^{46} +(4.22749 - 4.22749i) q^{47} +(0.320052 - 1.70222i) q^{48} +(-3.50601 + 2.02419i) q^{49} +(0.989897 + 4.90103i) q^{50} +(12.6808 - 0.964954i) q^{51} +(-0.365014 + 1.36225i) q^{52} +(-2.51478 + 9.38527i) q^{53} +(1.17371 + 5.06186i) q^{54} +(4.16024 - 6.71224i) q^{55} +(1.48785 + 0.859013i) q^{56} +(-6.94580 + 8.08996i) q^{57} +(0.393993 - 0.393993i) q^{58} +(-3.91854 + 6.78711i) q^{59} +(3.69249 - 1.16856i) q^{60} +7.37809 q^{61} +(-1.03729 + 5.47029i) q^{62} +(-5.12298 - 0.565300i) q^{63} +1.00000i q^{64} +(-3.07010 + 0.720618i) q^{65} +(-5.51423 - 2.64771i) q^{66} +(-1.52752 + 5.70078i) q^{67} +(-7.09227 + 1.90037i) q^{68} +(8.26182 - 5.64673i) q^{69} +(-0.120038 + 3.83975i) q^{70} +(-8.39623 + 4.84757i) q^{71} +(-1.20599 - 2.74692i) q^{72} +(11.3822 + 3.04984i) q^{73} +(3.27424 - 5.67115i) q^{74} +(6.20551 + 6.04084i) q^{75} +(3.07803 - 5.33131i) q^{76} +(4.29031 - 4.29031i) q^{77} +(0.809429 + 2.30472i) q^{78} +(-0.336135 - 0.194068i) q^{79} +(-1.97048 + 1.05698i) q^{80} +(6.62554 + 6.09116i) q^{81} +(-2.38301 + 8.89350i) q^{82} +(-1.58924 + 5.93114i) q^{83} +(2.96713 - 0.225785i) q^{84} +(-11.2410 - 11.9665i) q^{85} +(6.05508 + 3.49590i) q^{86} +(0.178330 - 0.948463i) q^{87} +(3.41129 + 0.914051i) q^{88} +6.84912 q^{89} +(4.13805 - 5.27983i) q^{90} -2.42294 q^{91} +(-4.08541 + 4.08541i) q^{92} +(3.86306 + 8.83611i) q^{93} +5.97858i q^{94} +(13.7587 + 0.430121i) q^{95} +(0.977343 + 1.42997i) q^{96} +(5.85127 + 5.85127i) q^{97} +(1.04780 - 3.91044i) q^{98} +(-10.4729 + 1.60316i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 8 q^{3} - 4 q^{7}+O(q^{10}) \) 256 * q + 8 * q^3 - 4 * q^7	\( 256 q + 8 q^{3} - 4 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} - 256 q^{16} - 4 q^{22} - 16 q^{25} - 40 q^{27} - 4 q^{28} - 48 q^{30} + 32 q^{31} - 8 q^{33} + 8 q^{37} - 12 q^{42} - 40 q^{45} + 16 q^{46} - 8 q^{48} - 16 q^{51} + 20 q^{55} + 40 q^{57} + 56 q^{58} - 8 q^{60} - 32 q^{61} + 56 q^{63} + 32 q^{66} - 24 q^{67} + 24 q^{70} + 8 q^{73} - 4 q^{75} + 16 q^{76} - 88 q^{78} - 48 q^{81} + 64 q^{85} - 20 q^{87} - 4 q^{88} - 8 q^{90} - 68 q^{93} + 152 q^{97}+O(q^{100}) \) 256 * q + 8 * q^3 - 4 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 - 256 * q^16 - 4 * q^22 - 16 * q^25 - 40 * q^27 - 4 * q^28 - 48 * q^30 + 32 * q^31 - 8 * q^33 + 8 * q^37 - 12 * q^42 - 40 * q^45 + 16 * q^46 - 8 * q^48 - 16 * q^51 + 20 * q^55 + 40 * q^57 + 56 * q^58 - 8 * q^60 - 32 * q^61 + 56 * q^63 + 32 * q^66 - 24 * q^67 + 24 * q^70 + 8 * q^73 - 4 * q^75 + 16 * q^76 - 88 * q^78 - 48 * q^81 + 64 * q^85 - 20 * q^87 - 4 * q^88 - 8 * q^90 - 68 * q^93 + 152 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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