LMFDB - Embedded newform 775.2.bl.c.51.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [775,2,Mod(51,775)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("775.51"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(775, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.bl (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,2,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 155)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			51.1
Character	$\chi$	$=$	775.51
Dual form			775.2.bl.c.76.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.646517 - 1.98977i) q^{2} +(-1.02325 - 1.13643i) q^{3} +(-1.92319 + 1.39728i) q^{4} +(-1.59970 + 2.77076i) q^{6} +(0.316994 + 3.01600i) q^{7} +(0.638431 + 0.463847i) q^{8} +(0.0691433 - 0.657854i) q^{9} +(-5.57748 - 2.48326i) q^{11} +(3.55581 + 0.755811i) q^{12} +(-5.63533 + 1.19783i) q^{13} +(5.79622 - 2.58064i) q^{14} +(-0.958988 + 2.95146i) q^{16} +(5.25138 - 2.33807i) q^{17} +(-1.35368 + 0.287735i) q^{18} +(1.99768 + 0.424620i) q^{19} +(3.10312 - 3.44636i) q^{21} +(-1.33518 + 12.7034i) q^{22} +(4.95413 + 3.59938i) q^{23} +(-0.126143 - 1.20017i) q^{24} +(6.02674 + 10.4386i) q^{26} +(-4.52986 + 3.29114i) q^{27} +(-4.82382 - 5.35740i) q^{28} +(1.77750 + 5.47059i) q^{29} +(2.16791 + 5.12837i) q^{31} +8.07104 q^{32} +(2.88510 + 8.87943i) q^{33} +(-8.04733 - 8.93747i) q^{34} +(0.786229 + 1.36179i) q^{36} +(1.18290 - 2.04884i) q^{37} +(-0.446636 - 4.24946i) q^{38} +(7.12760 + 5.17850i) q^{39} +(0.618888 - 0.687345i) q^{41} +(-8.86371 - 3.94638i) q^{42} +(-4.17130 - 0.886637i) q^{43} +(14.1963 - 3.01752i) q^{44} +(3.95904 - 12.1847i) q^{46} +(-0.482864 + 1.48610i) q^{47} +(4.33543 - 1.93026i) q^{48} +(-2.14873 + 0.456727i) q^{49} +(-8.03053 - 3.57542i) q^{51} +(9.16409 - 10.1778i) q^{52} +(-0.300872 + 2.86260i) q^{53} +(9.47725 + 6.88563i) q^{54} +(-1.19658 + 2.07254i) q^{56} +(-1.56157 - 2.70472i) q^{57} +(9.73605 - 7.07365i) q^{58} +(0.130293 + 0.144705i) q^{59} -9.68296 q^{61} +(8.80271 - 7.62923i) q^{62} +2.00601 q^{63} +(-3.30009 - 10.1566i) q^{64} +(15.8028 - 11.4814i) q^{66} +(3.22324 + 5.58282i) q^{67} +(-6.83246 + 11.8342i) q^{68} +(-0.978847 - 9.31310i) q^{69} +(-0.100240 + 0.953724i) q^{71} +(0.349287 - 0.387923i) q^{72} +(0.985838 + 0.438923i) q^{73} +(-4.84150 - 1.02909i) q^{74} +(-4.43522 + 1.97469i) q^{76} +(5.72147 - 17.6089i) q^{77} +(5.69594 - 17.5303i) q^{78} +(-8.81227 + 3.92348i) q^{79} +(6.43427 + 1.36765i) q^{81} +(-1.76778 - 0.787068i) q^{82} +(-5.35103 + 5.94292i) q^{83} +(-1.15235 + 10.9639i) q^{84} +(0.932608 + 8.87317i) q^{86} +(4.39813 - 7.61779i) q^{87} +(-2.40899 - 4.17249i) q^{88} +(-8.64669 + 6.28219i) q^{89} +(-5.39901 - 16.6164i) q^{91} -14.5570 q^{92} +(3.60974 - 7.71129i) q^{93} +3.26919 q^{94} +(-8.25869 - 9.17220i) q^{96} +(1.95842 - 1.42288i) q^{97} +(2.29797 + 3.98021i) q^{98} +(-2.01927 + 3.49747i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 2 q^{2} + q^{3} - 10 q^{4} + 4 q^{6} - 4 q^{7} - 13 q^{8} + 2 q^{9} - 28 q^{11} + 13 q^{12} + 6 q^{13} - 6 q^{14} + 8 q^{16} + 10 q^{17} + 27 q^{18} - 13 q^{19} - 8 q^{21} - 2 q^{22} + 12 q^{23}+ \cdots + 53 q^{99}+O(q^{100}) $ 40 * q + 2 * q^2 + q^3 - 10 * q^4 + 4 * q^6 - 4 * q^7 - 13 * q^8 + 2 * q^9 - 28 * q^11 + 13 * q^12 + 6 * q^13 - 6 * q^14 + 8 * q^16 + 10 * q^17 + 27 * q^18 - 13 * q^19 - 8 * q^21 - 2 * q^22 + 12 * q^23 - 82 * q^24 + 32 * q^26 + q^27 - 22 * q^28 + 42 * q^29 - 10 * q^31 - 4 * q^32 - 13 * q^33 + 32 * q^34 - 13 * q^36 - 12 * q^37 - 30 * q^38 + 37 * q^39 + 36 * q^41 + 64 * q^42 + 78 * q^43 - 56 * q^44 + 18 * q^46 + 4 * q^47 + 41 * q^48 - 31 * q^49 - 2 * q^51 - 49 * q^52 + 11 * q^53 + 22 * q^54 + 9 * q^56 - 38 * q^57 - 11 * q^58 - q^59 - 100 * q^61 + 35 * q^62 - 110 * q^63 + 17 * q^64 - 40 * q^66 - 30 * q^67 + 34 * q^68 + 8 * q^69 - 2 * q^71 - 151 * q^72 + 23 * q^73 - 2 * q^74 + 2 * q^76 - 36 * q^77 + 2 * q^78 - 67 * q^79 - 83 * q^81 - 2 * q^82 + 26 * q^84 - 5 * q^86 + 46 * q^87 - 70 * q^88 + 20 * q^89 + 19 * q^91 + 10 * q^92 + 67 * q^93 + 130 * q^94 + 46 * q^96 + 18 * q^97 + 65 * q^98 + 53 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{4}{15}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.646517	−	1.98977i	−0.457157	−	1.40698i	−0.868585	−	0.495541i	$-0.834970\pi$
$2$	−0.646517	−	1.98977i	−0.457157	−	1.40698i	0.411428	−	0.911442i	$-0.365030\pi$
$3$	−1.02325	−	1.13643i	−0.590773	−	0.656120i	0.371427	−	0.928462i	$-0.378869\pi$
$3$	−1.02325	−	1.13643i	−0.590773	−	0.656120i	−0.962201	+	0.272342i	$0.912202\pi$
$4$	−1.92319	+	1.39728i	−0.961593	+	0.698638i
$5$		0			0
$5$		0			0
$6$	−1.59970	+	2.77076i	−0.653075	+	1.13116i
$7$	0.316994	+	3.01600i	0.119813	+	1.13994i	0.874896	+	0.484311i	$0.160930\pi$
$7$	0.316994	+	3.01600i	0.119813	+	1.13994i	−0.755083	+	0.655629i	$0.772404\pi$
$8$	0.638431	+	0.463847i	0.225720	+	0.163995i
$9$	0.0691433	−	0.657854i	0.0230478	−	0.219285i
$10$		0			0
$11$	−5.57748	−	2.48326i	−1.68167	−	0.748730i	−0.999852	−	0.0172126i	$-0.994521\pi$
$11$	−5.57748	−	2.48326i	−1.68167	−	0.748730i	−0.681823	−	0.731517i	$-0.738813\pi$
$12$	3.55581	+	0.755811i	1.02647	+	0.218184i
$13$	−5.63533	+	1.19783i	−1.56296	+	0.332217i	−0.906520	−	0.422163i	$-0.861271\pi$
$13$	−5.63533	+	1.19783i	−1.56296	+	0.332217i	−0.656438	+	0.754380i	$0.727938\pi$
$14$	5.79622	−	2.58064i	1.54910	−	0.689706i
$15$		0			0
$16$	−0.958988	+	2.95146i	−0.239747	+	0.737866i
$17$	5.25138	−	2.33807i	1.27365	−	0.567064i	0.345200	−	0.938529i	$-0.387811\pi$
$17$	5.25138	−	2.33807i	1.27365	−	0.567064i	0.928447	+	0.371465i	$0.121144\pi$
$18$	−1.35368	+	0.287735i	−0.319067	+	0.0678197i
$19$	1.99768	+	0.424620i	0.458299	+	0.0974145i	0.431276	−	0.902220i	$-0.358064\pi$
$19$	1.99768	+	0.424620i	0.458299	+	0.0974145i	0.0270238	+	0.999635i	$0.491397\pi$
$20$		0			0
$21$	3.10312	−	3.44636i	0.677156	−	0.752058i
$22$	−1.33518	+	12.7034i	−0.284662	+	2.70838i
$23$	4.95413	+	3.59938i	1.03301	+	0.750523i	0.968908	−	0.247420i	$-0.0795828\pi$
$23$	4.95413	+	3.59938i	1.03301	+	0.750523i	0.0640985	+	0.997944i	$0.479583\pi$
$24$	−0.126143	−	1.20017i	−0.0257487	−	0.244983i
$25$		0			0
$26$	6.02674	+	10.4386i	1.18194	+	2.04718i
$27$	−4.52986	+	3.29114i	−0.871772	+	0.633379i
$28$	−4.82382	−	5.35740i	−0.911617	−	1.01245i
$29$	1.77750	+	5.47059i	0.330074	+	1.01586i	0.969098	+	0.246676i	$0.0793383\pi$
$29$	1.77750	+	5.47059i	0.330074	+	1.01586i	−0.639024	+	0.769186i	$0.720662\pi$
$30$		0			0
$31$	2.16791	+	5.12837i	0.389368	+	0.921082i
$31$	2.16791	+	5.12837i	0.389368	+	0.921082i
$32$	8.07104			1.42677
$33$	2.88510	+	8.87943i	0.502232	+	1.54571i
$34$	−8.04733	−	8.93747i	−1.38011	−	1.53276i
$35$		0			0
$36$	0.786229	+	1.36179i	0.131038	+	0.226965i
$37$	1.18290	−	2.04884i	0.194468	−	0.336828i	−0.752258	−	0.658868i	$-0.771035\pi$
$37$	1.18290	−	2.04884i	0.194468	−	0.336828i	0.946726	+	0.322041i	$0.104369\pi$
$38$	−0.446636	−	4.24946i	−0.0724539	−	0.689353i
$39$	7.12760	+	5.17850i	1.14133	+	0.829224i
$40$		0			0
$41$	0.618888	−	0.687345i	0.0966541	−	0.107345i	−0.692877	−	0.721056i	$-0.743657\pi$
$41$	0.618888	−	0.687345i	0.0966541	−	0.107345i	0.789531	+	0.613711i	$0.210324\pi$
$42$	−8.86371	−	3.94638i	−1.36770	−	0.608939i
$43$	−4.17130	−	0.886637i	−0.636117	−	0.135211i	−0.121445	−	0.992598i	$-0.538753\pi$
$43$	−4.17130	−	0.886637i	−0.636117	−	0.135211i	−0.514672	+	0.857387i	$0.672086\pi$
$44$	14.1963	−	3.01752i	2.14018	−	0.454909i
$45$		0			0
$46$	3.95904	−	12.1847i	0.583728	−	1.79653i
$47$	−0.482864	+	1.48610i	−0.0704330	+	0.216770i	−0.980077	−	0.198619i	$-0.936355\pi$
$47$	−0.482864	+	1.48610i	−0.0704330	+	0.216770i	0.909644	+	0.415389i	$0.136355\pi$
$48$	4.33543	−	1.93026i	0.625765	−	0.278608i
$49$	−2.14873	+	0.456727i	−0.306961	+	0.0652466i
$50$		0			0
$51$	−8.03053	−	3.57542i	−1.12450	−	0.500659i
$52$	9.16409	−	10.1778i	1.27083	−	1.41140i
$53$	−0.300872	+	2.86260i	−0.0413279	+	0.393209i	0.954231	+	0.299070i	$0.0966764\pi$
$53$	−0.300872	+	2.86260i	−0.0413279	+	0.393209i	−0.995559	+	0.0941388i	$0.969990\pi$
$54$	9.47725	+	6.88563i	1.28969	+	0.937015i
$55$		0			0
$56$	−1.19658	+	2.07254i	−0.159900	+	0.276955i
$57$	−1.56157	−	2.70472i	−0.206835	−	0.358249i
$58$	9.73605	−	7.07365i	1.27841	−	0.928816i
$59$	0.130293	+	0.144705i	0.0169627	+	0.0188390i	0.751566	−	0.659657i	$-0.229299\pi$
$59$	0.130293	+	0.144705i	0.0169627	+	0.0188390i	−0.734604	+	0.678496i	$0.762632\pi$
$60$		0			0
$61$	−9.68296			−1.23978			−0.619888	−	0.784690i	$-0.712822\pi$
$61$	−9.68296			−1.23978			−0.619888	+	0.784690i	$0.712822\pi$
$62$	8.80271	−	7.62923i	1.11795	−	0.968913i
$63$	2.00601			0.252733
$64$	−3.30009	−	10.1566i	−0.412511	−	1.26958i
$65$		0			0
$66$	15.8028	−	11.4814i	1.94519	−	1.41326i
$67$	3.22324	+	5.58282i	0.393782	+	0.682050i	0.992945	−	0.118577i	$-0.0378332\pi$
$67$	3.22324	+	5.58282i	0.393782	+	0.682050i	−0.599163	+	0.800627i	$0.704500\pi$
$68$	−6.83246	+	11.8342i	−0.828558	+	1.43510i
$69$	−0.978847	−	9.31310i	−0.117839	−	1.12117i
$70$		0			0
$71$	−0.100240	+	0.953724i	−0.0118964	+	0.113186i	−0.998859	−	0.0477660i	$-0.984790\pi$
$71$	−0.100240	+	0.953724i	−0.0118964	+	0.113186i	0.986962	+	0.160952i	$0.0514565\pi$
$72$	0.349287	−	0.387923i	0.0411639	−	0.0457171i
$73$	0.985838	+	0.438923i	0.115384	+	0.0513721i	0.463617	−	0.886036i	$-0.346552\pi$
$73$	0.985838	+	0.438923i	0.115384	+	0.0513721i	−0.348233	+	0.937408i	$0.613218\pi$
$74$	−4.84150	−	1.02909i	−0.562813	−	0.119630i
$75$		0			0
$76$	−4.43522	+	1.97469i	−0.508755	+	0.226512i
$77$	5.72147	−	17.6089i	0.652022	−	2.00672i
$78$	5.69594	−	17.5303i	0.644938	−	1.98492i
$79$	−8.81227	+	3.92348i	−0.991458	+	0.441426i	−0.837373	−	0.546632i	$-0.815910\pi$
$79$	−8.81227	+	3.92348i	−0.991458	+	0.441426i	−0.154085	+	0.988058i	$0.549243\pi$
$80$		0			0
$81$	6.43427	+	1.36765i	0.714919	+	0.151961i
$82$	−1.76778	−	0.787068i	−0.195219	−	0.0869171i
$83$	−5.35103	+	5.94292i	−0.587352	+	0.652320i	−0.961421	−	0.275081i	$-0.911295\pi$
$83$	−5.35103	+	5.94292i	−0.587352	+	0.652320i	0.374070	+	0.927401i	$0.377962\pi$
$84$	−1.15235	+	10.9639i	−0.125732	+	1.19626i
$85$		0			0
$86$	0.932608	+	8.87317i	0.100566	+	0.956819i
$87$	4.39813	−	7.61779i	0.471529	−	0.816713i
$88$	−2.40899	−	4.17249i	−0.256799	−	0.444789i
$89$	−8.64669	+	6.28219i	−0.916548	+	0.665911i	−0.942662	−	0.333748i	$-0.891686\pi$
$89$	−8.64669	+	6.28219i	−0.916548	+	0.665911i	0.0261147	+	0.999659i	$0.491686\pi$
$90$		0			0
$91$	−5.39901	−	16.6164i	−0.565970	−	1.74188i
$92$	−14.5570			−1.51768
$93$	3.60974	−	7.71129i	0.374312	−	0.799623i
$94$	3.26919			0.337191
$95$		0			0
$96$	−8.25869	−	9.17220i	−0.842899	−	0.936134i
$97$	1.95842	−	1.42288i	0.198848	−	0.144471i	−0.483906	−	0.875120i	$-0.660782\pi$
$97$	1.95842	−	1.42288i	0.198848	−	0.144471i	0.682754	+	0.730649i	$0.260782\pi$
$98$	2.29797	+	3.98021i	0.232130	+	0.402062i
$99$	−2.01927	+	3.49747i	−0.202944	+	0.351509i
$100$		0			0
$101$	0.949838	+	0.690097i	0.0945124	+	0.0686673i	0.634038	−	0.773302i	$-0.281396\pi$
$101$	0.949838	+	0.690097i	0.0945124	+	0.0686673i	−0.539525	+	0.841969i	$0.681396\pi$
$102$	−1.92241	+	18.2905i	−0.190347	+	1.81103i
$103$	−8.05374	+	8.94458i	−0.793558	+	0.881336i	−0.995174	−	0.0981289i	$-0.968714\pi$
$103$	−8.05374	+	8.94458i	−0.793558	+	0.881336i	0.201615	+	0.979465i	$0.435381\pi$
$104$	−4.15338	−	1.84920i	−0.407272	−	0.181329i
$105$		0			0
$106$	5.89046	−	1.25206i	0.572132	−	0.121610i
$107$	3.33708	−	1.48576i	0.322607	−	0.143634i	−0.239042	−	0.971009i	$-0.576833\pi$
$107$	3.33708	−	1.48576i	0.322607	−	0.143634i	0.561650	+	0.827375i	$0.310167\pi$
$108$	4.11314	−	12.6589i	0.395787	−	1.21811i
$109$	−0.901993	+	2.77605i	−0.0863952	+	0.265897i	−0.984916	−	0.173034i	$-0.944643\pi$
$109$	−0.901993	+	2.77605i	−0.0863952	+	0.265897i	0.898521	+	0.438931i	$0.144643\pi$
$110$		0			0
$111$	−3.53878	+	0.752190i	−0.335886	+	0.0713947i
$112$	−9.20560	−	1.95671i	−0.869847	−	0.184892i
$113$	−15.7857	−	7.02825i	−1.48499	−	0.661162i	−0.505536	−	0.862806i	$-0.668705\pi$
$113$	−15.7857	−	7.02825i	−1.48499	−	0.661162i	−0.979459	+	0.201643i	$0.935372\pi$
$114$	−4.37221	+	4.85583i	−0.409495	+	0.454790i
$115$		0			0
$116$	−11.0624	−	8.03729i	−1.02712	−	0.746244i
$117$	0.398350	+	3.79005i	0.0368275	+	0.350390i
$118$	0.203694	−	0.352808i	0.0187516	−	0.0324786i
$119$	8.71626	+	15.0970i	0.799018	+	1.38394i
$120$		0			0
$121$	17.5813	+	19.5260i	1.59830	+	1.77510i
$122$	6.26020	+	19.2669i	0.566772	+	1.74434i
$123$	−1.41440			−0.127532
$124$	−11.3350	−	6.83364i	−1.01792	−	0.613679i
$125$		0			0
$126$	−1.29692	−	3.99150i	−0.115539	−	0.355591i
$127$	6.64696	+	7.38220i	0.589822	+	0.655064i	0.961985	−	0.273104i	$-0.0880502\pi$
$127$	6.64696	+	7.38220i	0.589822	+	0.655064i	−0.372162	+	0.928168i	$0.621384\pi$
$128$	−5.01662	+	3.64479i	−0.443411	+	0.322157i
$129$	3.26068	+	5.64766i	0.287087	+	0.497248i
$130$		0			0
$131$	−0.622368	−	5.92143i	−0.0543765	−	0.517358i	−0.987479	−	0.157748i	$-0.949577\pi$
$131$	−0.622368	−	5.92143i	−0.0543765	−	0.517358i	0.933103	−	0.359610i	$-0.117090\pi$
$132$	−17.9556	−	13.0455i	−1.56284	−	1.13547i
$133$	−0.647400	+	6.15960i	−0.0561367	+	0.534105i
$134$	9.02468	−	10.0229i	0.779613	−	0.865848i
$135$		0			0
$136$	4.43715	+	0.943146i	0.380483	+	0.0808741i
$137$	−21.8539	+	4.64520i	−1.86711	+	0.396866i	−0.995615	−	0.0935423i	$-0.970181\pi$
$137$	−21.8539	+	4.64520i	−1.86711	+	0.396866i	−0.871493	+	0.490408i	$0.836848\pi$
$138$	−17.8981	+	7.96877i	−1.52359	+	0.678346i
$139$	−2.09191	+	6.43825i	−0.177434	+	0.546085i	−0.999736	−	0.0229656i	$-0.992689\pi$
$139$	−2.09191	+	6.43825i	−0.177434	+	0.546085i	0.822302	+	0.569051i	$0.192689\pi$
$140$		0			0
$141$	2.18295	−	0.971911i	0.183837	−	0.0818497i
$142$	1.96250	−	0.417143i	0.164690	−	0.0350059i
$143$	34.4055	+	7.31311i	2.87713	+	0.611553i
$144$	1.87532	+	0.834948i	0.156277	+	0.0695790i
$145$		0			0
$146$	0.235998	−	2.24537i	0.0195313	−	0.185828i
$147$	2.71773	+	1.97454i	0.224154	+	0.162858i
$148$	0.587863	+	5.59314i	0.0483221	+	0.459754i
$149$	10.7029	−	18.5379i	0.876812	−	1.51868i	0.0219926	−	0.999758i	$-0.492999\pi$
$149$	10.7029	−	18.5379i	0.876812	−	1.51868i	0.854820	−	0.518925i	$-0.173668\pi$
$150$		0			0
$151$	2.75097	−	1.99870i	0.223871	−	0.162652i	−0.470196	−	0.882562i	$-0.655817\pi$
$151$	2.75097	−	1.99870i	0.223871	−	0.162652i	0.694067	+	0.719910i	$0.255817\pi$
$152$	1.07842	+	1.19771i	0.0874716	+	0.0971471i
$153$	−1.17501	−	3.61631i	−0.0949939	−	0.292361i
$154$	−38.7367			−3.12149
$155$		0			0
$156$	−20.9435			−1.67682
$157$	−2.90996	−	8.95594i	−0.232240	−	0.714762i	−0.997476	−	0.0710113i	$-0.977377\pi$
$157$	−2.90996	−	8.95594i	−0.232240	−	0.714762i	0.765235	−	0.643751i	$-0.222623\pi$
$158$	13.5041	+	14.9978i	1.07433	+	1.19316i
$159$	3.56103	−	2.58724i	0.282408	−	0.205181i
$160$		0			0
$161$	−9.28531	+	16.0826i	−0.731785	+	1.26749i
$162$	−1.43856	−	13.6870i	−0.113024	−	1.07535i
$163$	−9.25245	−	6.72230i	−0.724708	−	0.526531i	0.163177	−	0.986597i	$-0.447826\pi$
$163$	−9.25245	−	6.72230i	−0.724708	−	0.526531i	−0.887885	+	0.460066i	$0.847826\pi$
$164$	−0.229826	+	2.18665i	−0.0179464	+	0.170749i
$165$		0			0
$166$	15.2846	+	6.80514i	1.18632	+	0.528182i
$167$	7.54945	+	1.60468i	0.584194	+	0.124174i	0.490522	−	0.871429i	$-0.336806\pi$
$167$	7.54945	+	1.60468i	0.584194	+	0.124174i	0.0936719	+	0.995603i	$0.470140\pi$
$168$	3.57971	−	0.760892i	0.276181	−	0.0587041i
$169$	18.4460	−	8.21270i	1.41893	−	0.631747i
$170$		0			0
$171$	0.417464	−	1.28482i	0.0319243	−	0.0982529i
$172$	9.26106	−	4.12329i	0.706149	−	0.314398i
$173$	−4.55039	+	0.967215i	−0.345960	+	0.0735360i	−0.377615	−	0.925963i	$-0.623256\pi$
$173$	−4.55039	+	0.967215i	−0.345960	+	0.0735360i	0.0316548	+	0.999499i	$0.489922\pi$
$174$	−18.0012	−	3.82626i	−1.36466	−	0.290068i
$175$		0			0
$176$	12.6780	−	14.0803i	0.955639	−	1.06134i
$177$	0.0311255	−	0.296139i	0.00233953	−	0.0222592i
$178$	18.0904	+	13.1434i	1.35593	+	0.985142i
$179$	0.594181	+	5.65325i	0.0444111	+	0.422544i	0.994028	+	0.109129i	$0.0348063\pi$
$179$	0.594181	+	5.65325i	0.0444111	+	0.422544i	−0.949616	+	0.313415i	$0.898527\pi$
$180$		0			0
$181$	0.568358	+	0.984425i	0.0422457	+	0.0731718i	0.886375	−	0.462968i	$-0.153215\pi$
$181$	0.568358	+	0.984425i	0.0422457	+	0.0731718i	−0.844129	+	0.536140i	$0.819882\pi$
$182$	−29.5724	+	21.4856i	−2.19205	+	1.59262i
$183$	9.90809	+	11.0040i	0.732427	+	0.813442i
$184$	1.49330	+	4.59592i	0.110088	+	0.338816i
$185$		0			0
$186$	−17.6775	−	2.19709i	−1.29618	−	0.161098i
$187$	−35.0955			−2.56644
$188$	−1.14786	−	3.53275i	−0.0837162	−	0.257652i
$189$	−11.3620	−	12.6188i	−0.826464	−	0.917881i
$190$		0			0
$191$	9.70293	+	16.8060i	0.702079	+	1.21604i	0.967735	+	0.251969i	$0.0810782\pi$
$191$	9.70293	+	16.8060i	0.702079	+	1.21604i	−0.265656	+	0.964068i	$0.585589\pi$
$192$	−8.16552	+	14.1431i	−0.589295	+	1.02069i
$193$	−1.68977	−	16.0771i	−0.121632	−	1.15725i	−0.869683	−	0.493611i	$-0.835677\pi$
$193$	−1.68977	−	16.0771i	−0.121632	−	1.15725i	0.748051	−	0.663641i	$-0.230990\pi$
$194$	−4.09736	−	2.97691i	−0.294173	−	0.213729i
$195$		0			0
$196$	3.49423	−	3.88074i	0.249588	−	0.277196i
$197$	7.06835	+	3.14703i	0.503599	+	0.224217i	0.642781	−	0.766050i	$-0.277781\pi$
$197$	7.06835	+	3.14703i	0.503599	+	0.224217i	−0.139182	+	0.990267i	$0.544447\pi$
$198$	8.26467	+	1.75671i	0.587345	+	0.124844i
$199$	−25.9544	+	5.51677i	−1.83986	+	0.391074i	−0.990587	−	0.136884i	$-0.956291\pi$
$199$	−25.9544	+	5.51677i	−1.83986	+	0.391074i	−0.849271	+	0.527958i	$0.822958\pi$
$200$		0			0
$201$	3.04633	−	9.37562i	0.214871	−	0.661306i
$202$	0.759052	−	2.33612i	0.0534067	−	0.164369i
$203$	−15.9358	+	7.09509i	−1.11848	+	0.497977i
$204$	20.4401	−	4.34467i	1.43109	−	0.304188i
$205$		0			0
$206$	23.0046	+	10.2423i	1.60281	+	0.713615i
$207$	2.71041	−	3.01022i	0.188387	−	0.209225i
$208$	1.86887	−	17.7812i	0.129583	−	1.23290i
$209$	−10.0876	−	7.32906i	−0.697773	−	0.506962i
$210$		0			0
$211$	−8.12604	+	14.0747i	−0.559419	+	0.968943i	0.438125	+	0.898914i	$0.355643\pi$
$211$	−8.12604	+	14.0747i	−0.559419	+	0.968943i	−0.997545	+	0.0700292i	$0.977691\pi$
$212$	−3.42122	−	5.92572i	−0.234970	−	0.406980i
$213$	1.18642	−	0.861981i	0.0812918	−	0.0590620i
$214$	−5.11381	−	5.67946i	−0.349573	−	0.388240i
$215$		0			0
$216$	−4.41859			−0.300647
$217$	−14.7799	+	8.16408i	−1.00333	+	0.554214i
$218$	6.10686			0.413609
$219$	−0.509951	−	1.56947i	−0.0344593	−	0.106055i
$220$		0			0
$221$	−26.7927	+	19.4660i	−1.80227	+	1.30943i
$222$	3.78457	+	6.55507i	0.254004	+	0.439947i
$223$	−2.42908	+	4.20728i	−0.162663	+	0.281741i	−0.935823	−	0.352471i	$-0.885342\pi$
$223$	−2.42908	+	4.20728i	−0.162663	+	0.281741i	0.773160	+	0.634211i	$0.218675\pi$
$224$	2.55847	+	24.3422i	0.170945	+	1.62643i
$225$		0			0
$226$	−3.77891	+	35.9539i	−0.251369	+	2.39162i
$227$	−3.26879	+	3.63036i	−0.216957	+	0.240955i	−0.841793	−	0.539801i	$-0.818499\pi$
$227$	−3.26879	+	3.63036i	−0.216957	+	0.240955i	0.624835	+	0.780756i	$0.285166\pi$
$228$	6.78244	+	3.01974i	0.449178	+	0.199987i
$229$	−3.34903	−	0.711858i	−0.221310	−	0.0470409i	0.0959219	−	0.995389i	$-0.469420\pi$
$229$	−3.34903	−	0.711858i	−0.221310	−	0.0470409i	−0.317232	+	0.948348i	$0.602753\pi$
$230$		0			0
$231$	−25.8658	+	11.5162i	−1.70184	+	0.757710i
$232$	−1.40270	+	4.31708i	−0.0920921	+	0.283430i
$233$	−4.60780	+	14.1813i	−0.301867	+	0.929050i	0.678961	+	0.734174i	$0.262431\pi$
$233$	−4.60780	+	14.1813i	−0.301867	+	0.929050i	−0.980828	+	0.194876i	$0.937569\pi$
$234$	7.28380	−	3.24296i	0.476157	−	0.211999i
$235$		0			0
$236$	−0.452771	−	0.0962395i	−0.0294729	−	0.00626466i
$237$	13.4759	+	5.99987i	0.875356	+	0.389733i
$238$	24.4044	−	27.1039i	1.58190	−	1.75688i
$239$	0.784172	−	7.46090i	0.0507239	−	0.482605i	−0.939442	−	0.342708i	$-0.888656\pi$
$239$	0.784172	−	7.46090i	0.0507239	−	0.482605i	0.990166	−	0.139898i	$-0.0446773\pi$
$240$		0			0
$241$	0.637348	+	6.06396i	0.0410552	+	0.390614i	0.995683	+	0.0928139i	$0.0295862\pi$
$241$	0.637348	+	6.06396i	0.0410552	+	0.390614i	−0.954628	+	0.297800i	$0.903747\pi$
$242$	27.4858	−	47.6068i	1.76685	−	3.06028i
$243$	3.36920	+	5.83563i	0.216134	+	0.374356i
$244$	18.6221	−	13.5298i	1.19216	−	0.866155i
$245$		0			0
$246$	0.914433	+	2.81434i	0.0583021	+	0.179436i
$247$	−11.7662			−0.748666
$248$	−0.994719	+	4.27969i	−0.0631647	+	0.271761i
$249$	12.2292			0.774992
$250$		0			0
$251$	3.54377	+	3.93575i	0.223681	+	0.248422i	0.844531	−	0.535507i	$-0.179879\pi$
$251$	3.54377	+	3.93575i	0.223681	+	0.248422i	−0.620851	+	0.783929i	$0.713213\pi$
$252$	−3.85792	+	2.80295i	−0.243026	+	0.176569i
$253$	−18.6934	−	32.3779i	−1.17524	−	2.03558i
$254$	10.3915	−	17.9987i	0.652023	−	1.12934i
$255$		0			0
$256$	−6.78384	−	4.92875i	−0.423990	−	0.308047i
$257$	−0.766808	+	7.29569i	−0.0478321	+	0.455092i	0.944225	+	0.329302i	$0.106813\pi$
$257$	−0.766808	+	7.29569i	−0.0478321	+	0.455092i	−0.992057	+	0.125791i	$0.959853\pi$
$258$	9.12948	−	10.1393i	0.568377	−	0.631246i
$259$	6.55428	+	2.91815i	0.407263	+	0.181325i
$260$		0			0
$261$	3.72175	−	0.791083i	0.230371	−	0.0489668i
$262$	−11.3799	+	5.06668i	−0.703056	+	0.313021i
$263$	5.46518	−	16.8201i	0.336998	−	1.03717i	−0.628732	−	0.777622i	$-0.716426\pi$
$263$	5.46518	−	16.8201i	0.336998	−	1.03717i	0.965730	−	0.259550i	$-0.0835742\pi$
$264$	−2.27676	+	7.00715i	−0.140125	+	0.431261i
$265$		0			0
$266$	12.6748	−	2.69411i	0.777141	−	0.165186i
$267$	15.9870	+	3.39815i	0.978390	+	0.207963i
$268$	−13.9996	−	6.23304i	−0.855164	−	0.380744i
$269$	−9.87200	+	10.9640i	−0.601906	+	0.668485i	−0.964690	−	0.263389i	$-0.915160\pi$
$269$	−9.87200	+	10.9640i	−0.601906	+	0.668485i	0.362783	+	0.931873i	$0.381826\pi$
$270$		0			0
$271$	−9.47183	−	6.88169i	−0.575373	−	0.418033i	0.261680	−	0.965155i	$-0.415723\pi$
$271$	−9.47183	−	6.88169i	−0.575373	−	0.418033i	−0.837053	+	0.547122i	$0.815723\pi$
$272$	1.86470	+	17.7414i	0.113064	+	1.07573i
$273$	−13.3589	+	23.1384i	−0.808520	+	1.40040i
$274$	23.3718	+	40.4812i	1.41194	+	2.44556i
$275$		0			0
$276$	14.8955	+	16.5431i	0.896603	+	0.995778i
$277$	3.15910	+	9.72271i	0.189812	+	0.584181i	0.999998	−	0.00199166i	$-0.000633966\pi$
$277$	3.15910	+	9.72271i	0.189812	+	0.584181i	−0.810186	+	0.586173i	$0.800634\pi$
$278$	14.1631			0.849448
$279$	3.52362	−	1.07158i	0.210953	−	0.0641536i
$280$		0			0
$281$	−1.32233	−	4.06971i	−0.0788835	−	0.242779i	0.903836	−	0.427879i	$-0.140739\pi$
$281$	−1.32233	−	4.06971i	−0.0788835	−	0.242779i	−0.982720	+	0.185100i	$0.940739\pi$
$282$	−3.34520	−	3.71522i	−0.199204	−	0.221238i
$283$	−16.6406	+	12.0901i	−0.989180	+	0.718682i	−0.959741	−	0.280885i	$-0.909372\pi$
$283$	−16.6406	+	12.0901i	−0.989180	+	0.718682i	−0.0294389	+	0.999567i	$0.509372\pi$
$284$	−1.13984	−	1.97425i	−0.0676368	−	0.117150i
$285$		0			0
$286$	−7.69228	−	73.1872i	−0.454854	−	4.32765i
$287$	2.26922	+	1.64868i	0.133948	+	0.0973186i
$288$	0.558058	−	5.30957i	0.0328839	−	0.312869i
$289$	10.7352	−	11.9227i	0.631485	−	0.701335i
$290$		0			0
$291$	−3.62096	−	0.769659i	−0.212264	−	0.0451182i
$292$	−2.50925	+	0.533357i	−0.146843	+	0.0312123i
$293$	5.98353	−	2.66404i	0.349562	−	0.155635i	−0.224442	−	0.974487i	$-0.572056\pi$
$293$	5.98353	−	2.66404i	0.349562	−	0.155635i	0.574004	+	0.818853i	$0.305389\pi$
$294$	2.17184	−	6.68424i	0.126664	−	0.389833i
$295$		0			0
$296$	1.70555	−	0.759360i	0.0991331	−	0.0441369i
$297$	33.4380	−	7.10746i	1.94027	−	0.412416i
$298$	−43.8058	−	9.31121i	−2.53760	−	0.539384i
$299$	−32.2296	−	14.3495i	−1.86388	−	0.829854i
$300$		0			0
$301$	1.35182	−	12.8617i	0.0779175	−	0.741336i
$302$	−5.75551	−	4.18162i	−0.331192	−	0.240625i
$303$	−0.187671	−	1.78557i	−0.0107814	−	0.102578i
$304$	−3.16900	+	5.48887i	−0.181755	+	0.314808i
$305$		0			0
$306$	−6.43597	+	4.67601i	−0.367920	+	0.267310i
$307$	21.0413	+	23.3687i	1.20089	+	1.33372i	0.928407	+	0.371564i	$0.121178\pi$
$307$	21.0413	+	23.3687i	1.20089	+	1.33372i	0.272483	+	0.962161i	$0.412155\pi$
$308$	13.6010	+	41.8596i	0.774989	+	2.38517i
$309$	18.4059			1.04708
$310$		0			0
$311$	1.01917			0.0577920			0.0288960	−	0.999582i	$-0.490801\pi$
$311$	1.01917			0.0577920			0.0288960	+	0.999582i	$0.490801\pi$
$312$	2.14845	+	6.61223i	0.121632	+	0.374344i
$313$	1.18545	+	1.31658i	0.0670057	+	0.0744173i	0.775716	−	0.631083i	$-0.217389\pi$
$313$	1.18545	+	1.31658i	0.0670057	+	0.0744173i	−0.708710	+	0.705500i	$0.750722\pi$
$314$	−15.9390	+	11.5803i	−0.899488	+	0.653516i
$315$		0			0
$316$	11.4655	−	19.8588i	0.644982	−	1.11714i
$317$	−2.12894	−	20.2556i	−0.119573	−	1.13767i	−0.875570	−	0.483090i	$-0.839514\pi$
$317$	−2.12894	−	20.2556i	−0.119573	−	1.13767i	0.755997	−	0.654575i	$-0.227152\pi$
$318$	−7.45029	−	5.41295i	−0.417791	−	0.303543i
$319$	3.67088	−	34.9261i	0.205530	−	1.95549i
$320$		0			0
$321$	−5.10313	−	2.27206i	−0.284829	−	0.126814i
$322$	38.0039	+	8.07798i	2.11787	+	0.450168i
$323$	11.4834	−	2.44087i	0.638952	−	0.135813i
$324$	−14.2853	+	6.36021i	−0.793626	+	0.353345i
$325$		0			0
$326$	−7.39399	+	22.7564i	−0.409515	+	1.26036i
$327$	4.07776	−	1.81553i	0.225501	−	0.100399i
$328$	0.713941	−	0.151753i	0.0394208	−	0.00837915i
$329$	−4.63515	−	0.985232i	−0.255544	−	0.0543176i
$330$		0			0
$331$	12.0257	−	13.3559i	0.660991	−	0.734104i	−0.315676	−	0.948867i	$-0.602231\pi$
$331$	12.0257	−	13.3559i	0.660991	−	0.734104i	0.976666	+	0.214763i	$0.0688978\pi$
$332$	1.98712	−	18.9062i	0.109057	−	1.03761i
$333$	−1.26605	−	0.919840i	−0.0693792	−	0.0504069i
$334$	−1.68789	−	16.0592i	−0.0923570	−	0.878718i
$335$		0			0
$336$	7.19595	+	12.4638i	0.392572	+	0.679954i
$337$	7.33578	−	5.32976i	0.399606	−	0.290330i	−0.369775	−	0.929121i	$-0.620565\pi$
$337$	7.33578	−	5.32976i	0.399606	−	0.290330i	0.769380	+	0.638791i	$0.220565\pi$
$338$	−28.2671	−	31.3938i	−1.53753	−	1.70760i
$339$	8.16558	+	25.1311i	0.443494	+	1.36493i
$340$		0			0
$341$	0.643568	−	33.9869i	0.0348511	−	1.84049i
$342$	−2.82641			−0.152835
$343$	4.50128	+	13.8535i	0.243046	+	0.748019i
$344$	−2.25182	−	2.50090i	−0.121410	−	0.134840i
$345$		0			0
$346$	4.86645	+	8.42893i	0.261622	+	0.453142i
$347$	−4.80067	+	8.31501i	−0.257714	+	0.446373i	−0.965629	−	0.259924i	$-0.916302\pi$
$347$	−4.80067	+	8.31501i	−0.257714	+	0.446373i	0.707915	+	0.706297i	$0.249636\pi$
$348$	2.18573	+	20.7958i	0.117167	+	1.11477i
$349$	−7.35418	−	5.34313i	−0.393660	−	0.286011i	0.373293	−	0.927713i	$-0.378228\pi$
$349$	−7.35418	−	5.34313i	−0.393660	−	0.286011i	−0.766954	+	0.641702i	$0.778228\pi$
$350$		0			0
$351$	21.5850	−	23.9726i	1.15212	−	1.27956i
$352$	−45.0161	−	20.0424i	−2.39937	−	1.06827i
$353$	−1.18790	−	0.252497i	−0.0632257	−	0.0134390i	0.176190	−	0.984356i	$-0.443623\pi$
$353$	−1.18790	−	0.252497i	−0.0632257	−	0.0134390i	−0.239416	+	0.970917i	$0.576956\pi$
$354$	−0.609373	+	0.129526i	−0.0323878	+	0.00688424i
$355$		0			0
$356$	7.85124	−	24.1636i	0.416115	−	1.28067i
$357$	8.23784	−	25.3535i	0.435993	−	1.34185i
$358$	10.8645	−	4.83721i	0.574209	−	0.255654i
$359$	−1.53751	+	0.326807i	−0.0811465	+	0.0172482i	−0.248306	−	0.968682i	$-0.579874\pi$
$359$	−1.53751	+	0.326807i	−0.0811465	+	0.0172482i	0.167160	+	0.985930i	$0.446541\pi$
$360$		0			0
$361$	−13.5469	−	6.03149i	−0.712997	−	0.317447i
$362$	1.59133	−	1.76735i	0.0836385	−	0.0928900i
$363$	4.19997	−	39.9600i	0.220441	−	2.09736i
$364$	33.6011	+	24.4126i	1.76117	+	1.27957i
$365$		0			0
$366$	15.4898	−	26.8292i	0.809666	−	1.40238i
$367$	1.15727	+	2.00445i	0.0604091	+	0.104632i	0.894648	−	0.446771i	$-0.147426\pi$
$367$	1.15727	+	2.00445i	0.0604091	+	0.104632i	−0.834239	+	0.551403i	$0.814093\pi$
$368$	−15.3744	+	11.1701i	−0.801446	+	0.582284i
$369$	−0.409381	−	0.454664i	−0.0213115	−	0.0236688i
$370$		0			0
$371$	−8.72898			−0.453186
$372$	3.83260	+	19.8740i	0.198711	+	1.03042i
$373$	30.7941			1.59446			0.797230	−	0.603676i	$-0.206298\pi$
$373$	30.7941			1.59446			0.797230	+	0.603676i	$0.206298\pi$
$374$	22.6899	+	69.8322i	1.17326	+	3.61094i
$375$		0			0
$376$	−0.997601	+	0.724799i	−0.0514473	+	0.0373787i
$377$	−16.5696	−	28.6994i	−0.853378	−	1.47809i
$378$	−17.7628	+	30.7661i	−0.913620	+	1.58244i
$379$	0.209001	+	1.98851i	0.0107357	+	0.102143i	0.998578	−	0.0533190i	$-0.0169800\pi$
$379$	0.209001	+	1.98851i	0.0107357	+	0.102143i	−0.987842	+	0.155462i	$0.950313\pi$
$380$		0			0
$381$	1.58788	−	15.1077i	0.0813495	−	0.773989i
$382$	27.1670	−	30.1720i	1.38998	−	1.54373i
$383$	−13.8994	−	6.18843i	−0.710228	−	0.316214i	0.0196351	−	0.999807i	$-0.493750\pi$
$383$	−13.8994	−	6.18843i	−0.710228	−	0.316214i	−0.729863	+	0.683593i	$0.760416\pi$
$384$	9.27531	+	1.97153i	0.473329	+	0.100609i
$385$		0			0
$386$	−30.8973	+	13.7563i	−1.57263	+	0.700180i
$387$	−0.871695	+	2.68280i	−0.0443108	+	0.136375i
$388$	−1.77826	+	5.47291i	−0.0902774	+	0.277845i
$389$	−20.1871	+	8.98788i	−1.02353	+	0.455704i	−0.848688	−	0.528893i	$-0.822607\pi$
$389$	−20.1871	+	8.98788i	−1.02353	+	0.455704i	−0.174839	+	0.984597i	$0.555941\pi$
$390$		0			0
$391$	34.4316	+	7.31866i	1.74128	+	0.370121i
$392$	−1.58367	−	0.705094i	−0.0799873	−	0.0356126i
$393$	−6.09248	+	6.76639i	−0.307325	+	0.341319i
$394$	1.69208	−	16.0990i	0.0852456	−	0.811058i
$395$		0			0
$396$	−1.00351	−	9.54776i	−0.0504283	−	0.479793i
$397$	−2.95954	+	5.12607i	−0.148535	+	0.257270i	−0.930686	−	0.365818i	$-0.880789\pi$
$397$	−2.95954	+	5.12607i	−0.148535	+	0.257270i	0.782151	+	0.623089i	$0.214122\pi$
$398$	27.7571	+	48.0767i	1.39134	+	2.40987i
$399$	7.66244	−	5.56708i	0.383602	−	0.278703i
$400$		0			0
$401$	6.80958	+	20.9577i	0.340054	+	1.04658i	0.964178	+	0.265254i	$0.0854560\pi$
$401$	6.80958	+	20.9577i	0.340054	+	1.04658i	−0.624124	+	0.781325i	$0.714544\pi$
$402$	−20.6249			−1.02868
$403$	−18.3598	−	26.3033i	−0.914566	−	1.31026i
$404$	−2.79097			−0.138856
$405$		0			0
$406$	24.4204	+	27.1216i	1.21196	+	1.34602i
$407$	−11.6854	+	8.48995i	−0.579224	+	0.420831i
$408$	−3.46849	−	6.00760i	−0.171716	−	0.297421i
$409$	15.7750	−	27.3232i	0.780026	−	1.35104i	−0.151900	−	0.988396i	$-0.548539\pi$
$409$	15.7750	−	27.3232i	0.780026	−	1.35104i	0.931926	−	0.362648i	$-0.118127\pi$
$410$		0			0
$411$	27.6410	+	20.0824i	1.36343	+	0.990590i
$412$	2.99078	−	28.4554i	0.147345	−	1.40190i
$413$	−0.395128	+	0.438835i	−0.0194430	+	0.0215936i
$414$	−7.74199	−	3.44696i	−0.380498	−	0.169409i
$415$		0			0
$416$	−45.4829	+	9.66770i	−2.22998	+	0.473998i
$417$	9.45719	−	4.21061i	0.463121	−	0.206195i
$418$	−8.06139	+	24.8104i	−0.394295	+	1.21352i
$419$	1.30801	−	4.02565i	0.0639007	−	0.196666i	−0.914009	−	0.405694i	$-0.867030\pi$
$419$	1.30801	−	4.02565i	0.0639007	−	0.196666i	0.977910	+	0.209028i	$0.0670299\pi$
$420$		0			0
$421$	−0.803249	+	0.170736i	−0.0391479	+	0.00832115i	−0.227444	−	0.973791i	$-0.573037\pi$
$421$	−0.803249	+	0.170736i	−0.0391479	+	0.00832115i	0.188296	+	0.982112i	$0.439704\pi$
$422$	33.2591	+	7.06945i	1.61903	+	0.344135i
$423$	0.944253	+	0.420408i	0.0459111	+	0.0204410i
$424$	−1.51990	+	1.68802i	−0.0738127	+	0.0819774i
$425$		0			0
$426$	−2.48219	−	1.80341i	−0.120262	−	0.0873757i
$427$	−3.06944	−	29.2038i	−0.148541	−	1.41327i
$428$	−4.34180	+	7.52022i	−0.209869	+	0.363503i
$429$	−26.8945	−	46.5827i	−1.29848	−	2.24903i
$430$		0			0
$431$	24.6170	+	27.3399i	1.18576	+	1.31692i	0.937402	+	0.348249i	$0.113223\pi$
$431$	24.6170	+	27.3399i	1.18576	+	1.31692i	0.248356	+	0.968669i	$0.420110\pi$
$432$	−5.36958	−	16.5259i	−0.258344	−	0.795101i
$433$	8.37708			0.402577			0.201288	−	0.979532i	$-0.435487\pi$
$433$	8.37708			0.402577			0.201288	+	0.979532i	$0.435487\pi$
$434$	25.8002	+	24.1305i	1.23845	+	1.15830i
$435$		0			0
$436$	−2.14421	−	6.59919i	−0.102689	−	0.316044i
$437$	8.36839	+	9.29404i	0.400314	+	0.444594i
$438$	−2.79320	+	2.02937i	−0.133464	+	0.0969673i
$439$	19.1752	+	33.2125i	0.915184	+	1.58515i	0.806632	+	0.591054i	$0.201288\pi$
$439$	19.1752	+	33.2125i	0.915184	+	1.58515i	0.108552	+	0.994091i	$0.465379\pi$
$440$		0			0
$441$	0.151889	+	1.44513i	0.00723283	+	0.0688157i
$442$	56.0549	+	40.7263i	2.66626	+	1.93715i
$443$	1.44602	−	13.7580i	0.0687027	−	0.653662i	−0.904933	−	0.425554i	$-0.860079\pi$
$443$	1.44602	−	13.7580i	0.0687027	−	0.653662i	0.973636	−	0.228108i	$-0.0732541\pi$
$444$	5.75471	−	6.39125i	0.273106	−	0.303315i
$445$		0			0
$446$	9.94199	+	2.11323i	0.470767	+	0.100065i
$447$	−32.0188	+	6.80580i	−1.51444	+	0.321903i
$448$	29.5863	−	13.1726i	1.39782	−	0.622349i
$449$	7.32528	−	22.5449i	0.345701	−	1.06396i	−0.615506	−	0.788132i	$-0.711048\pi$
$449$	7.32528	−	22.5449i	0.345701	−	1.06396i	0.961207	−	0.275827i	$-0.0889517\pi$
$450$		0			0
$451$	−5.15869	+	2.29680i	−0.242913	+	0.108152i
$452$	40.1793	−	8.54037i	1.88987	−	0.401705i
$453$	−5.08632	−	1.08113i	−0.238976	−	0.0507959i
$454$	9.33692	+	4.15706i	0.438203	+	0.195101i
$455$		0			0
$456$	0.257622	−	2.45111i	0.0120643	−	0.114784i
$457$	−23.6411	−	17.1763i	−1.10588	−	0.803472i	−0.123874	−	0.992298i	$-0.539532\pi$
$457$	−23.6411	−	17.1763i	−1.10588	−	0.803472i	−0.982011	+	0.188826i	$0.939532\pi$
$458$	0.748767	+	7.12404i	0.0349876	+	0.332885i
$459$	−16.0931	+	27.8741i	−0.751163	+	1.30105i
$460$		0			0
$461$	18.9530	−	13.7701i	0.882728	−	0.641340i	−0.0512435	−	0.998686i	$-0.516318\pi$
$461$	18.9530	−	13.7701i	0.882728	−	0.641340i	0.933972	+	0.357346i	$0.116318\pi$
$462$	39.6373	+	44.0217i	1.84409	+	2.04807i
$463$	−7.42425	−	22.8495i	−0.345034	−	1.06191i	−0.961566	−	0.274576i	$-0.911463\pi$
$463$	−7.42425	−	22.8495i	−0.345034	−	1.06191i	0.616531	−	0.787330i	$-0.288537\pi$
$464$	−17.8508			−0.828704
$465$		0			0
$466$	31.1967			1.44516
$467$	6.92278	+	21.3061i	0.320348	+	0.985930i	0.973497	+	0.228701i	$0.0734477\pi$
$467$	6.92278	+	21.3061i	0.320348	+	0.985930i	−0.653149	+	0.757230i	$0.726552\pi$
$468$	−6.06184	−	6.73236i	−0.280209	−	0.311203i
$469$	−15.8160	+	11.4910i	−0.730317	+	0.530606i
$470$		0			0
$471$	−7.20022	+	12.4711i	−0.331769	+	0.574640i
$472$	0.0160621	+	0.152820i	0.000739317	+	0.00703413i
$473$	21.0636	+	15.3036i	0.968506	+	0.703661i
$474$	3.22597	−	30.6931i	0.148174	−	1.40978i
$475$		0			0
$476$	−37.8577	−	16.8553i	−1.73520	−	0.772563i
$477$	1.86237	+	0.395860i	0.0852722	+	0.0181252i
$478$	−15.3525	+	3.26327i	−0.702206	+	0.149259i
$479$	20.2792	−	9.02888i	0.926580	−	0.412540i	0.112737	−	0.993625i	$-0.464038\pi$
$479$	20.2792	−	9.02888i	0.926580	−	0.412540i	0.813843	+	0.581085i	$0.197372\pi$
$480$		0			0
$481$	−4.21187	+	12.9628i	−0.192045	+	0.591053i
$482$	11.6539	−	5.18863i	0.530819	−	0.236336i
$483$	27.7780	−	5.90440i	1.26394	−	0.268660i
$484$	−61.0955	−	12.9862i	−2.77707	−	0.590284i
$485$		0			0
$486$	9.43334	−	10.4768i	0.427905	−	0.475236i
$487$	−2.19255	+	20.8608i	−0.0993541	+	0.945291i	0.825354	+	0.564615i	$0.190975\pi$
$487$	−2.19255	+	20.8608i	−0.0993541	+	0.945291i	−0.924709	+	0.380676i	$0.875691\pi$
$488$	−6.18190	−	4.49142i	−0.279842	−	0.203317i
$489$	1.82812	+	17.3934i	0.0826704	+	0.786556i
$490$		0			0
$491$	−11.3850	−	19.7194i	−0.513798	−	0.889925i	−0.999872	−	0.0160069i	$-0.994905\pi$
$491$	−11.3850	−	19.7194i	−0.513798	−	0.889925i	0.486074	−	0.873918i	$-0.338429\pi$
$492$	2.72015	−	1.97631i	0.122634	−	0.0890988i
$493$	22.1249	+	24.5722i	0.996457	+	1.10668i
$494$	7.60705	+	23.4121i	0.342257	+	1.05336i
$495$		0			0
$496$	−17.2152	+	1.48046i	−0.772985	+	0.0664746i
$497$	−2.90821			−0.130451
$498$	−7.90637	−	24.3333i	−0.354293	−	1.09040i
$499$	4.53741	+	5.03931i	0.203123	+	0.225590i	0.836096	−	0.548583i	$-0.184833\pi$
$499$	4.53741	+	5.03931i	0.203123	+	0.225590i	−0.632974	+	0.774173i	$0.718166\pi$
$500$		0			0
$501$	−5.90135	−	10.2214i	−0.263653	−	0.456660i
$502$	5.54015	−	9.59583i	0.247269	−	0.428283i
$503$	−1.94958	−	18.5490i	−0.0869275	−	0.827060i	−0.947934	−	0.318466i	$-0.896832\pi$
$503$	−1.94958	−	18.5490i	−0.0869275	−	0.827060i	0.861007	−	0.508594i	$-0.169834\pi$
$504$	1.28070	+	0.930481i	0.0570468	+	0.0414469i
$505$		0			0
$506$	−52.3391	+	58.1284i	−2.32676	+	2.58412i
$507$	−28.2081	−	12.5591i	−1.25277	−	0.557767i
$508$	−23.0983	−	4.90970i	−1.02482	−	0.217833i
$509$	18.9298	−	4.02366i	0.839051	−	0.178346i	0.231708	−	0.972785i	$-0.425569\pi$
$509$	18.9298	−	4.02366i	0.839051	−	0.178346i	0.607343	+	0.794440i	$0.292235\pi$
$510$		0			0
$511$	−1.01129	+	3.11242i	−0.0447367	+	0.137685i
$512$	−9.25359	+	28.4796i	−0.408955	+	1.25863i
$513$	−10.4467	+	4.65117i	−0.461233	+	0.205354i
$514$	15.0125	−	3.19101i	0.662174	−	0.140749i
$515$		0			0
$516$	−14.1622	−	6.30543i	−0.623457	−	0.277581i
$517$	6.38354	−	7.08964i	0.280748	−	0.311802i
$518$	1.56901	−	14.9282i	0.0689386	−	0.655907i
$519$	5.75536	+	4.18152i	0.252632	+	0.183548i
$520$		0			0
$521$	17.8991	−	31.0021i	0.784172	−	1.35823i	−0.145320	−	0.989385i	$-0.546421\pi$
$521$	17.8991	−	31.0021i	0.784172	−	1.35823i	0.929492	−	0.368842i	$-0.120246\pi$
$522$	−3.98025	−	6.89400i	−0.174211	−	0.301742i
$523$	−13.4111	+	9.74371i	−0.586425	+	0.426063i	−0.841035	−	0.540981i	$-0.818053\pi$
$523$	−13.4111	+	9.74371i	−0.586425	+	0.426063i	0.254610	+	0.967044i	$0.418053\pi$
$524$	9.47081	+	10.5184i	0.413734	+	0.459498i
$525$		0			0
$526$	−37.0016			−1.61334
$527$	23.3750	+	21.8623i	1.01823	+	0.952337i
$528$	−28.9741			−1.26094
$529$	4.48041	+	13.7893i	0.194801	+	0.599535i
$530$		0			0
$531$	0.104204	−	0.0757085i	0.00452206	−	0.00328547i
$532$	−7.36160	−	12.7507i	−0.319166	−	0.552811i
$533$	−2.66432	+	4.61473i	−0.115404	+	0.199886i
$534$	−3.57434	−	34.0075i	−0.154677	−	1.47165i
$535$		0			0
$536$	−0.531758	+	5.05934i	−0.0229685	+	0.218530i
$537$	5.81655	−	6.45993i	0.251003	−	0.278767i
$538$	28.1982	+	12.5547i	1.21571	+	0.541270i
$539$	13.1187	+	2.78846i	0.565061	+	0.120107i
$540$		0			0
$541$	−18.3608	+	8.17474i	−0.789391	+	0.351460i	−0.761511	−	0.648152i	$-0.775542\pi$
$541$	−18.3608	+	8.17474i	−0.789391	+	0.351460i	−0.0278800	+	0.999611i	$0.508876\pi$
$542$	−7.56931	+	23.2959i	−0.325130	+	1.00065i
$543$	0.537162	−	1.65321i	0.0230518	−	0.0709462i
$544$	42.3841	−	18.8706i	1.81720	−	0.809071i
$545$		0			0
$546$	54.6770	+	11.6219i	2.33996	+	0.497373i
$547$	−9.58694	−	4.26838i	−0.409908	−	0.182503i	0.191414	−	0.981509i	$-0.438693\pi$
$547$	−9.58694	−	4.26838i	−0.409908	−	0.182503i	−0.601322	+	0.799007i	$0.705359\pi$
$548$	35.5386	−	39.4696i	1.51813	−	1.68606i
$549$	−0.669512	+	6.36998i	−0.0285741	+	0.271864i
$550$		0			0
$551$	1.22796	+	11.6832i	0.0523128	+	0.497723i
$552$	3.69493	−	6.39981i	0.157267	−	0.272394i
$553$	−14.6266	−	25.3341i	−0.621988	−	1.07731i
$554$	17.3036	−	12.5718i	0.735159	−	0.534125i
$555$		0			0
$556$	−4.97287	−	15.3049i	−0.210897	−	0.649074i
$557$	−30.1350			−1.27686			−0.638431	−	0.769679i	$-0.720416\pi$
$557$	−30.1350			−1.27686			−0.638431	+	0.769679i	$0.720416\pi$
$558$	−4.41028	−	6.31841i	−0.186702	−	0.267480i
$559$	24.5687			1.03914
$560$		0			0
$561$	35.9115	+	39.8837i	1.51618	+	1.68389i
$562$	−7.24290	+	5.26227i	−0.305523	+	0.221976i
$563$	20.5872	+	35.6581i	0.867648	+	1.50281i	0.864394	+	0.502815i	$0.167702\pi$
$563$	20.5872	+	35.6581i	0.867648	+	1.50281i	0.00325339	+	0.999995i	$0.498964\pi$
$564$	−2.84019	+	4.91935i	−0.119593	+	0.207142i
$565$		0			0
$566$	34.8150	+	25.2946i	1.46338	+	1.06321i
$567$	−2.08519	+	19.8393i	−0.0875698	+	0.833171i
$568$	−0.506379	+	0.562391i	−0.0212472	+	0.0235974i
$569$	−34.8431	−	15.5131i	−1.46070	−	0.650344i	−0.486017	−	0.873949i	$-0.661551\pi$
$569$	−34.8431	−	15.5131i	−1.46070	−	0.650344i	−0.974680	+	0.223605i	$0.928217\pi$
$570$		0			0
$571$	−12.4274	+	2.64152i	−0.520069	+	0.110544i	−0.460465	−	0.887678i	$-0.652317\pi$
$571$	−12.4274	+	2.64152i	−0.520069	+	0.110544i	−0.0596044	+	0.998222i	$0.518984\pi$
$572$	−76.3865	+	34.0095i	−3.19388	+	1.42201i
$573$	9.17035	−	28.2234i	0.383097	−	1.17905i
$574$	1.81342	−	5.58113i	0.0756906	−	0.232952i
$575$		0			0
$576$	−6.90976	+	1.46871i	−0.287907	+	0.0611964i
$577$	−9.42440	−	2.00322i	−0.392343	−	0.0833951i	0.00751594	−	0.999972i	$-0.497608\pi$
$577$	−9.42440	−	2.00322i	−0.392343	−	0.0833951i	−0.399859	+	0.916577i	$0.630941\pi$
$578$	−30.6640	−	13.6525i	−1.27545	−	0.567869i
$579$	−16.5415	+	18.3712i	−0.687440	+	0.763479i
$580$		0			0
$581$	−19.6201	−	14.2548i	−0.813978	−	0.591390i
$582$	0.809565	+	7.70249i	0.0335575	+	0.319279i
$583$	8.78669	−	15.2190i	0.363907	−	0.630306i
$584$	0.425796	+	0.737501i	0.0176196	+	0.0305180i
$585$		0			0
$586$	−9.16929	−	10.1835i	−0.378780	−	0.420678i
$587$	−11.2747	−	34.7001i	−0.465359	−	1.43223i	−0.858531	−	0.512762i	$-0.828622\pi$
$587$	−11.2747	−	34.7001i	−0.465359	−	1.43223i	0.393173	−	0.919465i	$-0.371378\pi$
$588$	−7.98568			−0.329324
$589$	2.15318	+	11.1654i	0.0887204	+	0.460061i
$590$		0			0
$591$	−3.65629	−	11.2529i	−0.150400	−	0.462883i
$592$	4.91270	+	5.45610i	0.201911	+	0.224244i
$593$	−22.7074	+	16.4979i	−0.932482	+	0.677488i	−0.946599	−	0.322413i	$-0.895506\pi$
$593$	−22.7074	+	16.4979i	−0.932482	+	0.677488i	0.0141175	+	0.999900i	$0.495506\pi$
$594$	−35.7605	−	61.9389i	−1.46727	−	2.54138i
$595$		0			0
$596$	5.31898	+	50.6067i	0.217874	+	2.07293i
$597$	32.8273	+	23.8504i	1.34353	+	0.976132i
$598$	−7.71536	+	73.4068i	−0.315505	+	3.00183i
$599$	−9.33989	+	10.3730i	−0.381618	+	0.423829i	−0.903098	−	0.429434i	$-0.858713\pi$
$599$	−9.33989	+	10.3730i	−0.381618	+	0.423829i	0.521481	+	0.853263i	$0.325380\pi$
$600$		0			0
$601$	−28.2285	−	6.00014i	−1.15146	−	0.244751i	−0.407649	−	0.913139i	$-0.633651\pi$
$601$	−28.2285	−	6.00014i	−1.15146	−	0.244751i	−0.743813	+	0.668388i	$0.766985\pi$
$602$	−26.4658	+	5.62549i	−1.07867	+	0.229278i
$603$	3.89555	−	1.73441i	0.158639	−	0.0706307i
$604$	−2.49790	+	7.68774i	−0.101638	+	0.312810i
$605$		0			0
$606$	−3.43155	+	1.52782i	−0.139397	+	0.0620636i
$607$	15.8258	−	3.36388i	0.642350	−	0.136536i	0.124791	−	0.992183i	$-0.460174\pi$
$607$	15.8258	−	3.36388i	0.642350	−	0.136536i	0.517559	+	0.855647i	$0.326841\pi$
$608$	16.1234	+	3.42712i	0.653888	+	0.138988i
$609$	24.3694	+	10.8500i	0.987499	+	0.439663i
$610$		0			0
$611$	0.941005	−	8.95307i	0.0380690	−	0.362202i
$612$	7.31274	+	5.31302i	0.295600	+	0.214766i
$613$	1.05171	+	10.0063i	0.0424781	+	0.404152i	0.995015	+	0.0997283i	$0.0317973\pi$
$613$	1.05171	+	10.0063i	0.0424781	+	0.404152i	−0.952537	+	0.304424i	$0.901536\pi$
$614$	32.8950	−	56.9757i	1.32753	−	2.29935i
$615$		0			0
$616$	11.8206	−	8.58816i	0.476265	−	0.346027i
$617$	−21.2109	−	23.5571i	−0.853921	−	0.948375i	0.145238	−	0.989397i	$-0.453605\pi$
$617$	−21.2109	−	23.5571i	−0.853921	−	0.948375i	−0.999158	+	0.0410218i	$0.986939\pi$
$618$	−11.8997	−	36.6236i	−0.478678	−	1.47322i
$619$	−8.46480			−0.340229			−0.170114	−	0.985424i	$-0.554414\pi$
$619$	−8.46480			−0.340229			−0.170114	+	0.985424i	$0.554414\pi$
$620$		0			0
$621$	−34.2876			−1.37591
$622$	−0.658913	−	2.02793i	−0.0264200	−	0.0813124i
$623$	−21.6880	−	24.0870i	−0.868912	−	0.965025i
$624$	−22.1194	+	16.0707i	−0.885486	+	0.643343i
$625$		0			0
$626$	1.85328	−	3.20997i	0.0740719	−	0.128296i
$627$	1.99313	+	18.9633i	0.0795979	+	0.757323i
$628$	18.1103	+	13.1579i	0.722681	+	0.525058i
$629$	1.42153	−	13.5250i	0.0566801	−	0.539275i
$630$		0			0
$631$	−42.3260	−	18.8448i	−1.68497	−	0.750198i	−0.999761	−	0.0218541i	$-0.993043\pi$
$631$	−42.3260	−	18.8448i	−1.68497	−	0.750198i	−0.685212	−	0.728344i	$-0.740290\pi$
$632$	−7.44592	−	1.58268i	−0.296183	−	0.0629556i
$633$	24.3099	−	5.16724i	0.966233	−	0.205379i
$634$	−38.9276	+	17.3317i	−1.54601	+	0.688329i
$635$		0			0
$636$	−3.23343	+	9.95148i	−0.128214	+	0.394602i
$637$	11.5617	−	5.14761i	0.458092	−	0.203956i
$638$	−71.8684	+	15.2761i	−2.84530	+	0.604786i
$639$	0.620481	+	0.131887i	0.0245458	+	0.00521738i
$640$		0			0
$641$	18.1485	−	20.1560i	0.716824	−	0.796114i	−0.269134	−	0.963103i	$-0.586738\pi$
$641$	18.1485	−	20.1560i	0.716824	−	0.796114i	0.985959	+	0.166989i	$0.0534043\pi$
$642$	−1.22163	+	11.6230i	−0.0482138	+	0.458724i
$643$	2.65807	+	1.93120i	0.104824	+	0.0761590i	0.638962	−	0.769238i	$-0.279364\pi$
$643$	2.65807	+	1.93120i	0.104824	+	0.0761590i	−0.534139	+	0.845397i	$0.679364\pi$
$644$	−4.61450	−	43.9040i	−0.181837	−	1.73006i
$645$		0			0
$646$	−12.2810	−	21.2713i	−0.483188	−	0.836907i
$647$	40.1839	−	29.1953i	1.57979	−	1.14779i	0.662861	−	0.748742i	$-0.269342\pi$
$647$	40.1839	−	29.1953i	1.57979	−	1.14779i	0.916932	−	0.399045i	$-0.130658\pi$
$648$	3.47346	+	3.85767i	0.136450	+	0.151543i
$649$	−0.367368	−	1.13064i	−0.0144204	−	0.0443816i
$650$		0			0
$651$	24.4015	+	8.44253i	0.956370	+	0.330889i
$652$	27.1871			1.06473
$653$	3.38743	+	10.4254i	0.132560	+	0.407978i	0.995203	−	0.0978360i	$-0.0311921\pi$
$653$	3.38743	+	10.4254i	0.132560	+	0.407978i	−0.862642	+	0.505814i	$0.831192\pi$
$654$	−6.24885	−	6.94005i	−0.244349	−	0.271377i
$655$		0			0
$656$	1.43517	+	2.48578i	0.0560338	+	0.0970534i
$657$	0.356912	−	0.618189i	0.0139244	−	0.0241179i
$658$	1.03631	+	9.85988i	0.0403998	+	0.384378i
$659$	−36.2046	−	26.3042i	−1.41033	−	1.02466i	−0.993275	−	0.115783i	$-0.963062\pi$
$659$	−36.2046	−	26.3042i	−1.41033	−	1.02466i	−0.417055	−	0.908881i	$-0.636938\pi$
$660$		0			0
$661$	14.3179	−	15.9017i	0.556904	−	0.618504i	−0.397290	−	0.917693i	$-0.630049\pi$
$661$	14.3179	−	15.9017i	0.556904	−	0.618504i	0.954194	+	0.299189i	$0.0967161\pi$
$662$	−34.3500	−	15.2936i	−1.33505	−	0.594402i
$663$	49.5374	+	10.5295i	1.92387	+	0.408932i
$664$	−6.17287	+	1.31208i	−0.239554	+	0.0509187i
$665$		0			0
$666$	−1.01175	+	3.11385i	−0.0392045	+	0.120659i
$667$	−10.8848	+	33.4999i	−0.421460	+	1.29712i
$668$	−16.7612	+	7.46256i	−0.648509	+	0.288735i
$669$	7.26685	−	1.54462i	0.280953	−	0.0597183i
$670$		0			0
$671$	54.0066	+	24.0453i	2.08490	+	0.928257i
$672$	25.0454	−	27.8157i	0.966147	−	1.07301i
$673$	−3.99345	+	37.9951i	−0.153936	+	1.46460i	0.595942	+	0.803027i	$0.296779\pi$
$673$	−3.99345	+	37.9951i	−0.153936	+	1.46460i	−0.749878	+	0.661576i	$0.769888\pi$
$674$	−15.3477	−	11.1508i	−0.591172	−	0.429512i
$675$		0			0
$676$	−23.9997	+	41.5688i	−0.923067	+	1.59880i
$677$	18.8406	+	32.6330i	0.724105	+	1.25419i	0.959341	+	0.282248i	$0.0910802\pi$
$677$	18.8406	+	32.6330i	0.724105	+	1.25419i	−0.235236	+	0.971938i	$0.575586\pi$
$678$	44.7260	−	32.4953i	1.71769	−	1.24798i
$679$	4.91220	+	5.45555i	0.188513	+	0.209365i
$680$		0			0
$681$	7.47045			0.286268
$682$	−68.0423	+	20.6925i	−2.60547	+	0.792358i
$683$	−1.48318			−0.0567524			−0.0283762	−	0.999597i	$-0.509034\pi$
$683$	−1.48318			−0.0567524			−0.0283762	+	0.999597i	$0.509034\pi$
$684$	0.992392	+	3.05427i	0.0379450	+	0.116783i
$685$		0			0
$686$	24.6552	−	17.9131i	0.941340	−	0.683924i
$687$	2.61791	+	4.53436i	0.0998796	+	0.172997i
$688$	6.61710	−	11.4612i	0.252275	−	0.436952i
$689$	−1.73339	−	16.4921i	−0.0660369	−	0.628299i
$690$		0			0
$691$	−3.43812	+	32.7115i	−0.130792	+	1.24440i	0.710451	+	0.703747i	$0.248491\pi$
$691$	−3.43812	+	32.7115i	−0.130792	+	1.24440i	−0.841243	+	0.540658i	$0.818175\pi$
$692$	7.39978	−	8.21829i	0.281297	−	0.312413i
$693$	−11.1885	−	4.98143i	−0.425015	−	0.189229i
$694$	19.6487	+	4.17646i	0.745855	+	0.158536i
$695$		0			0
$696$	6.34140	−	2.82337i	0.240370	−	0.107020i
$697$	1.64296	−	5.05651i	0.0622316	−	0.191529i
$698$	−5.87701	+	18.0876i	−0.222448	+	0.684625i
$699$	20.8311	−	9.27460i	0.787904	−	0.350797i
$700$		0			0
$701$	−3.29647	−	0.700686i	−0.124506	−	0.0264646i	0.145237	−	0.989397i	$-0.453605\pi$
$701$	−3.29647	−	0.700686i	−0.124506	−	0.0264646i	−0.269743	+	0.962932i	$0.586939\pi$
$702$	−61.6552	−	27.4507i	−2.32703	−	1.03606i
$703$	3.23304	−	3.59065i	0.121936	−	0.135424i
$704$	−6.81531	+	64.8434i	−0.256862	+	2.44388i
$705$		0			0
$706$	0.265588	+	2.52690i	0.00999554	+	0.0951012i
$707$	−1.78024	+	3.08347i	−0.0669528	+	0.115966i
$708$	0.353928	+	0.613021i	0.0133014	+	0.0230388i
$709$	11.8802	−	8.63149i	0.446172	−	0.324163i	−0.341911	−	0.939732i	$-0.611074\pi$
$709$	11.8802	−	8.63149i	0.446172	−	0.324163i	0.788082	+	0.615570i	$0.211074\pi$
$710$		0			0
$711$	1.97177	+	6.06847i	0.0739470	+	0.227586i
$712$	−8.43430			−0.316089
$713$	−7.71886	+	33.2097i	−0.289074	+	1.24371i
$714$	−55.7736			−2.08727
$715$		0			0
$716$	−9.04188	−	10.0420i	−0.337911	−	0.375288i
$717$	−9.28122	+	6.74320i	−0.346613	+	0.251829i
$718$	1.64430	+	2.84800i	0.0613646	+	0.106287i
$719$	−26.6781	+	46.2078i	−0.994924	+	1.72326i	−0.410316	+	0.911943i	$0.634582\pi$
$719$	−26.6781	+	46.2078i	−0.994924	+	1.72326i	−0.584608	+	0.811316i	$0.698752\pi$
$720$		0			0
$721$	−29.5298	−	21.4547i	−1.09975	−	0.799014i
$722$	−3.24297	+	30.8548i	−0.120691	+	1.14830i
$723$	6.23912	−	6.92925i	0.232035	−	0.257701i
$724$	−2.46857	−	1.09908i	−0.0917438	−	0.0408470i
$725$		0			0
$726$	−82.2269	+	17.4779i	−3.05172	+	0.648664i
$727$	−22.9289	+	10.2086i	−0.850387	+	0.378617i	−0.785189	−	0.619256i	$-0.787434\pi$
$727$	−22.9289	+	10.2086i	−0.850387	+	0.378617i	−0.0651976	+	0.997872i	$0.520768\pi$
$728$	4.26060	−	13.1128i	0.157908	−	0.485991i
$729$	9.28242	−	28.5684i	0.343793	−	1.05809i
$730$		0			0
$731$	−23.9781	+	5.09670i	−0.886862	+	0.188508i
$732$	−34.4308	−	7.31849i	−1.27260	−	0.270499i
$733$	47.0408	+	20.9439i	1.73749	+	0.773582i	0.994554	+	0.104222i	$0.0332352\pi$
$733$	47.0408	+	20.9439i	1.73749	+	0.773582i	0.742938	+	0.669360i	$0.233432\pi$
$734$	3.24021	−	3.59862i	0.119599	−	0.132828i
$735$		0			0
$736$	39.9849	+	29.0508i	1.47386	+	1.07083i
$737$	−4.11402	−	39.1422i	−0.151542	−	1.44182i
$738$	−0.640007	+	1.10852i	−0.0235590	+	0.0408053i
$739$	19.2463	+	33.3355i	0.707985	+	1.22627i	0.965603	+	0.260019i	$0.0837288\pi$
$739$	19.2463	+	33.3355i	0.707985	+	1.22627i	−0.257619	+	0.966247i	$0.582938\pi$
$740$		0			0
$741$	12.0398	+	13.3715i	0.442292	+	0.491215i
$742$	5.64344	+	17.3687i	0.207177	+	0.637626i
$743$	14.9183			0.547299			0.273650	−	0.961829i	$-0.411769\pi$
$743$	14.9183			0.547299			0.273650	+	0.961829i	$0.411769\pi$
$744$	5.88143	−	3.24876i	0.215624	−	0.119105i
$745$		0			0
$746$	−19.9089	−	61.2734i	−0.728918	−	2.24338i
$747$	3.53959	+	3.93111i	0.129507	+	0.143832i
$748$	67.4952	−	49.0381i	2.46787	−	1.79301i
$749$	5.53889	+	9.59364i	0.202387	+	0.350544i
$750$		0			0
$751$	−0.461597	−	4.39180i	−0.0168439	−	0.160259i	0.982867	−	0.184318i	$-0.0590077\pi$
$751$	−0.461597	−	4.39180i	−0.0168439	−	0.160259i	−0.999711	+	0.0240591i	$0.992341\pi$
$752$	−3.92312	−	2.85031i	−0.143061	−	0.103940i
$753$	0.846563	−	8.05451i	0.0308505	−	0.293523i
$754$	−46.3928	+	51.5245i	−1.68953	+	1.87641i
$755$		0			0
$756$	39.4832	+	8.39241i	1.43599	+	0.305229i
$757$	25.4464	−	5.40879i	0.924863	−	0.196586i	0.279222	−	0.960227i	$-0.409923\pi$
$757$	25.4464	−	5.40879i	0.924863	−	0.196586i	0.645641	+	0.763641i	$0.276590\pi$
$758$	3.82157	−	1.70147i	0.138806	−	0.0618002i
$759$	−17.6673	+	54.3744i	−0.641283	+	1.97367i
$760$		0			0
$761$	37.3942	−	16.6490i	1.35554	−	0.603525i	0.405053	−	0.914293i	$-0.367253\pi$
$761$	37.3942	−	16.6490i	1.35554	−	0.603525i	0.950486	+	0.310769i	$0.100586\pi$
$762$	−31.0874	+	6.60784i	−1.12618	+	0.239377i
$763$	−8.65848	−	1.84042i	−0.313458	−	0.0666276i
$764$	−42.1431	−	18.7633i	−1.52468	−	0.678833i
$765$		0			0
$766$	−3.32736	+	31.6577i	−0.120222	+	1.14384i
$767$	−0.907576	−	0.659393i	−0.0327707	−	0.0238093i
$768$	1.34037	+	12.7527i	0.0483663	+	0.460174i
$769$	−13.8277	+	23.9503i	−0.498641	+	0.863671i	−0.999999	−	0.00156868i	$-0.999501\pi$
$769$	−13.8277	+	23.9503i	−0.498641	+	0.863671i	0.501358	+	0.865240i	$0.332834\pi$
$770$		0			0
$771$	9.07570	−	6.59388i	0.326853	−	0.237473i
$772$	25.7138	+	28.5581i	0.925461	+	1.02783i
$773$	−9.88207	−	30.4139i	−0.355433	−	1.09391i	−0.955758	−	0.294155i	$-0.904962\pi$
$773$	−9.88207	−	30.4139i	−0.355433	−	1.09391i	0.600324	−	0.799757i	$-0.295038\pi$
$774$	5.90174			0.212134
$775$		0			0
$776$	1.91032			0.0685763
$777$	−3.39038	−	10.4345i	−0.121629	−	0.374336i
$778$	30.9352	+	34.3570i	1.10908	+	1.23176i
$779$	1.52820	−	1.11030i	0.0547535	−	0.0397807i
$780$		0			0
$781$	2.92743	−	5.07046i	0.104752	−	0.181435i
$782$	−7.69813	−	73.2428i	−0.275284	−	2.61916i
$783$	−26.0563	−	18.9310i	−0.931175	−	0.676538i
$784$	0.712595	−	6.77989i	0.0254498	−	0.242139i
$785$		0			0
$786$	17.4025	+	7.74808i	0.620726	+	0.276365i
$787$	−41.0761	−	8.73099i	−1.46420	−	0.311226i	−0.594219	−	0.804304i	$-0.702539\pi$
$787$	−41.0761	−	8.73099i	−1.46420	−	0.311226i	−0.869985	+	0.493077i	$0.835872\pi$
$788$	−17.9910	+	3.82411i	−0.640904	+	0.136228i
$789$	−24.7072	+	11.0003i	−0.879599	+	0.391623i
$790$		0			0
$791$	16.1932	−	49.8376i	0.575765	−	1.77202i
$792$	−2.91146	+	1.29626i	−0.103454	+	0.0460607i
$793$	54.5666	−	11.5985i	1.93772	−	0.411875i
$794$	12.1131	+	2.57472i	0.429879	+	0.0913735i
$795$		0			0
$796$	42.2067	−	46.8752i	1.49598	−	1.66145i
$797$	2.44204	−	23.2345i	0.0865015	−	0.823007i	−0.862144	−	0.506664i	$-0.830878\pi$
$797$	2.44204	−	23.2345i	0.0865015	−	0.823007i	0.948645	−	0.316343i	$-0.102455\pi$
$798$	−16.0311	−	11.6473i	−0.567496	−	0.412310i
$799$	0.938903	+	8.93306i	0.0332160	+	0.316029i
$800$		0			0
$801$	3.53491	+	6.12264i	0.124900	+	0.216333i
$802$	37.2987	−	27.0991i	1.31706	−	0.956902i
$803$	−4.40854	−	4.89617i	−0.155574	−	0.172782i
$804$	7.24169	+	22.2876i	0.255395	+	0.786024i
$805$		0			0
$806$	−40.4677	+	53.5373i	−1.42541	+	1.88577i
$807$	22.5613			0.794197
$808$	0.286306	+	0.881159i	0.0100722	+	0.0309991i
$809$	33.0587	+	36.7154i	1.16228	+	1.29085i	0.949507	+	0.313745i	$0.101584\pi$
$809$	33.0587	+	36.7154i	1.16228	+	1.29085i	0.212776	+	0.977101i	$0.431749\pi$
$810$		0			0
$811$	−15.1368	−	26.2176i	−0.531524	−	0.920626i	−0.999323	−	0.0367913i	$-0.988286\pi$
$811$	−15.1368	−	26.2176i	−0.531524	−	0.920626i	0.467799	−	0.883835i	$-0.345047\pi$
$812$	20.7338	−	35.9119i	0.727612	−	1.26026i
$813$	1.87146	+	17.8058i	0.0656351	+	0.624477i
$814$	24.4479	+	17.7624i	0.856898	+	0.622573i
$815$		0			0
$816$	18.2539	−	20.2730i	0.639015	−	0.709698i
$817$	−7.95644	−	3.54243i	−0.278361	−	0.123934i
$818$	−64.5658	−	13.7239i	−2.25749	−	0.479844i
$819$	−11.3045	+	2.40285i	−0.395011	+	0.0839622i
$820$		0			0
$821$	3.54582	−	10.9129i	0.123750	−	0.380863i	−0.869921	−	0.493190i	$-0.835831\pi$
$821$	3.54582	−	10.9129i	0.123750	−	0.380863i	0.993671	+	0.112328i	$0.0358306\pi$
$822$	22.0890	−	67.9830i	0.770442	−	2.37118i
$823$	−17.4335	+	7.76188i	−0.607692	+	0.270562i	−0.687426	−	0.726254i	$-0.741260\pi$
$823$	−17.4335	+	7.76188i	−0.607692	+	0.270562i	0.0797341	+	0.996816i	$0.474593\pi$
$824$	−9.29068	+	1.97479i	−0.323656	+	0.0687952i
$825$		0			0
$826$	1.12864	+	0.502503i	0.0392704	+	0.0174843i
$827$	10.5375	−	11.7031i	0.366425	−	0.406957i	−0.531533	−	0.847038i	$-0.678384\pi$
$827$	10.5375	−	11.7031i	0.366425	−	0.406957i	0.897958	+	0.440081i	$0.145050\pi$
$828$	−1.00652	+	9.57641i	−0.0349790	+	0.332803i
$829$	2.42911	+	1.76485i	0.0843666	+	0.0612959i	0.629169	−	0.777269i	$-0.283395\pi$
$829$	2.42911	+	1.76485i	0.0843666	+	0.0612959i	−0.544802	+	0.838564i	$0.683395\pi$
$830$		0			0
$831$	7.81667	−	13.5389i	0.271157	−	0.469658i
$832$	30.7629	+	53.2830i	1.06651	+	1.84725i
$833$	−10.2159	+	7.42232i	−0.353961	+	0.257168i
$834$	−14.4924	−	16.0955i	−0.501831	−	0.557340i
$835$		0			0
$836$	29.6410			1.02516
$837$	−26.6985	−	16.0959i	−0.922835	−	0.556356i
$838$	−8.85580			−0.305918
$839$	−11.8376	−	36.4324i	−0.408680	−	1.25779i	−0.917783	−	0.397082i	$-0.870023\pi$
$839$	−11.8376	−	36.4324i	−0.408680	−	1.25779i	0.509104	−	0.860705i	$-0.329977\pi$
$840$		0			0
$841$	−3.30631	+	2.40217i	−0.114011	+	0.0828336i
$842$	0.859040	+	1.48790i	0.0296045	+	0.0512764i
$843$	−3.27188	+	5.66707i	−0.112690	+	0.195184i
$844$	−4.03838	−	38.4226i	−0.139007	−	1.32256i
$845$		0			0
$846$	0.226043	−	2.15065i	0.00777150	−	0.0739409i
$847$	−53.3174	+	59.2149i	−1.83201	+	2.03465i
$848$	−8.16033	−	3.63322i	−0.280227	−	0.124765i
$849$	30.7671	+	6.53974i	1.05592	+	0.224443i
$850$		0			0
$851$	13.2348	−	5.89252i	0.453683	−	0.201993i
$852$	−1.07727	+	3.31550i	−0.0369067	+	0.113587i
$853$	−3.44891	+	10.6147i	−0.118089	+	0.363439i	−0.992579	−	0.121604i	$-0.961196\pi$
$853$	−3.44891	+	10.6147i	−0.118089	+	0.363439i	0.874490	+	0.485043i	$0.161196\pi$
$854$	−56.1245	+	24.9883i	−1.92054	+	0.855080i
$855$		0			0
$856$	2.81966	+	0.599337i	0.0963740	+	0.0204849i
$857$	35.8317	+	15.9533i	1.22399	+	0.544955i	0.913973	−	0.405776i	$-0.132999\pi$
$857$	35.8317	+	15.9533i	1.22399	+	0.544955i	0.310017	+	0.950731i	$0.399665\pi$
$858$	−75.3013	+	83.6305i	−2.57074	+	2.85510i
$859$	2.95115	−	28.0783i	0.100692	−	0.958020i	−0.821218	−	0.570615i	$-0.806705\pi$
$859$	2.95115	−	28.0783i	0.100692	−	0.958020i	0.921910	−	0.387405i	$-0.126628\pi$
$860$		0			0
$861$	−0.448356	−	4.26583i	−0.0152799	−	0.145379i
$862$	38.4850	−	66.6580i	1.31080	−	2.27038i
$863$	−13.9747	−	24.2050i	−0.475706	−	0.823947i	0.523907	−	0.851776i	$-0.324474\pi$
$863$	−13.9747	−	24.2050i	−0.475706	−	0.823947i	−0.999613	+	0.0278288i	$0.991141\pi$
$864$	−36.5607	+	26.5629i	−1.24382	+	0.903688i
$865$		0			0
$866$	−5.41592	−	16.6685i	−0.184041	−	0.566419i
$867$	−24.5342			−0.833225
$868$	17.0171	−	36.3527i	0.577598	−	1.23389i
$869$	58.8933			1.99782
$870$		0			0
$871$	−24.8513	−	27.6001i	−0.842054	−	0.935195i
$872$	−1.86352	+	1.35393i	−0.0631068	+	0.0458498i
$873$	−0.800634	−	1.38674i	−0.0270974	−	0.0469340i
$874$	13.0827	−	22.6600i	0.442530	−	0.766485i
$875$		0			0
$876$	3.17371	+	2.30584i	0.107230	+	0.0779070i
$877$	−4.38832	+	41.7521i	−0.148183	+	1.40987i	0.627437	+	0.778668i	$0.284104\pi$
$877$	−4.38832	+	41.7521i	−0.148183	+	1.40987i	−0.775620	+	0.631200i	$0.782563\pi$
$878$	53.6882	−	59.6268i	1.81189	−	2.01231i
$879$	−9.15015	−	4.07391i	−0.308627	−	0.137410i
$880$		0			0
$881$	51.0170	−	10.8440i	1.71881	−	0.365344i	0.760115	−	0.649789i	$-0.225143\pi$
$881$	51.0170	−	10.8440i	1.71881	−	0.365344i	0.958692	+	0.284445i	$0.0918095\pi$
$882$	2.77729	−	1.23653i	0.0935161	−	0.0416360i
$883$	2.45425	−	7.55342i	0.0825923	−	0.254193i	−0.901230	−	0.433342i	$-0.857334\pi$
$883$	2.45425	−	7.55342i	0.0825923	−	0.254193i	0.983822	+	0.179149i	$0.0573344\pi$
$884$	24.3279	−	74.8735i	0.818235	−	2.51827i
$885$		0			0
$886$	−28.3102	+	6.01752i	−0.951100	+	0.202163i
$887$	7.87730	+	1.67437i	0.264494	+	0.0562199i	0.338250	−	0.941056i	$-0.390165\pi$
$887$	7.87730	+	1.67437i	0.264494	+	0.0562199i	−0.0737558	+	0.997276i	$0.523499\pi$
$888$	−2.60817	−	1.16123i	−0.0875243	−	0.0389684i
$889$	−20.1576	+	22.3873i	−0.676066	+	0.750847i
$890$		0			0
$891$	−32.4908	−	23.6060i	−1.08848	−	0.790829i
$892$	−1.20717	−	11.4855i	−0.0404191	−	0.384562i
$893$	−1.59564	+	2.76373i	−0.0533960	+	0.0924845i
$894$	34.2427	+	59.3101i	1.14525	+	1.98363i
$895$		0			0
$896$	−12.5829	−	13.9747i	−0.420366	−	0.466863i
$897$	16.6716	+	51.3099i	0.556648	+	1.71319i
$898$	−49.5952			−1.65501
$899$	−24.2017	+	20.9754i	−0.807173	+	0.699569i
$900$		0			0
$901$	5.11296	+	15.7361i	0.170338	+	0.524245i
$902$	7.90529	+	8.77972i	0.263218	+	0.292333i
$903$	−15.9997	+	11.6245i	−0.532437	+	0.386838i
$904$	−6.81805	−	11.8092i	−0.226765	−	0.392769i
$905$		0			0
$906$	1.13719	+	10.8196i	0.0377805	+	0.359457i
$907$	−17.4168	−	12.6541i	−0.578317	−	0.420172i	0.259800	−	0.965662i	$-0.416343\pi$
$907$	−17.4168	−	12.6541i	−0.578317	−	0.420172i	−0.838117	+	0.545491i	$0.816343\pi$
$908$	1.21388	−	11.5493i	0.0402839	−	0.383275i
$909$	0.519659	−	0.577139i	0.0172360	−	0.0191425i
$910$		0			0
$911$	5.36767	+	1.14093i	0.177839	+	0.0378008i	0.295970	−	0.955197i	$-0.404357\pi$
$911$	5.36767	+	1.14093i	0.177839	+	0.0378008i	−0.118131	+	0.992998i	$0.537690\pi$
$912$	9.48042	−	2.01513i	0.313928	−	0.0667275i
$913$	44.6031	−	19.8586i	1.47615	−	0.657222i
$914$	−18.8925	+	58.1452i	−0.624909	+	1.92327i
$915$		0			0
$916$	7.43547	−	3.31048i	0.245675	−	0.109382i
$917$	17.6618	−	3.75412i	0.583242	−	0.123972i
$918$	65.8677	+	14.0006i	2.17396	+	0.462089i
$919$	−39.3196	−	17.5062i	−1.29703	−	0.577477i	−0.362048	−	0.932160i	$-0.617922\pi$
$919$	−39.3196	−	17.5062i	−1.29703	−	0.577477i	−0.934987	+	0.354683i	$0.884589\pi$
$920$		0			0
$921$	5.02652	−	47.8241i	0.165629	−	1.57586i
$922$	−39.6529	−	28.8095i	−1.30590	−	0.948791i
$923$	−0.577508	−	5.49462i	−0.0190089	−	0.180858i
$924$	33.6534	−	58.2895i	1.10712	−	1.91758i
$925$		0			0
$926$	−40.6654	+	29.5452i	−1.33635	+	0.970915i
$927$	5.32737	+	5.91664i	0.174974	+	0.194328i
$928$	14.3463	+	44.1533i	0.470940	+	1.44940i
$929$	1.87481			0.0615104			0.0307552	−	0.999527i	$-0.490209\pi$
$929$	1.87481			0.0615104			0.0307552	+	0.999527i	$0.490209\pi$
$930$		0			0
$931$	−4.48641			−0.147036
$932$	−10.9536	−	33.7117i	−0.358797	−	1.10426i
$933$	−1.04287	−	1.15822i	−0.0341420	−	0.0379185i
$934$	37.9187	−	27.5496i	1.24074	−	0.901449i
$935$		0			0
$936$	−1.50368	+	2.60446i	−0.0491495	+	0.0851294i
$937$	−5.69083	−	54.1446i	−0.185911	−	1.76883i	−0.547803	−	0.836607i	$-0.684536\pi$
$937$	−5.69083	−	54.1446i	−0.185911	−	1.76883i	0.361892	−	0.932220i	$-0.382131\pi$
$938$	33.0899	+	24.0412i	1.08042	+	0.784973i
$939$	0.283190	−	2.69437i	0.00924156	−	0.0879276i
$940$		0			0
$941$	−22.6214	−	10.0717i	−0.737438	−	0.328328i	0.00341667	−	0.999994i	$-0.498912\pi$
$941$	−22.6214	−	10.0717i	−0.737438	−	0.328328i	−0.740854	+	0.671666i	$0.765579\pi$
$942$	29.4698	+	6.26401i	0.960179	+	0.204092i
$943$	5.54007	−	1.17758i	0.180409	−	0.0383472i
$944$	−0.552041	+	0.245785i	−0.0179674	+	0.00799961i
$945$		0			0
$946$	16.8328	−	51.8059i	0.547280	−	1.68435i
$947$	−13.1677	+	5.86266i	−0.427894	+	0.190511i	−0.609372	−	0.792884i	$-0.708579\pi$
$947$	−13.1677	+	5.86266i	−0.427894	+	0.190511i	0.181478	+	0.983395i	$0.441912\pi$
$948$	−34.3002	+	7.29073i	−1.11402	+	0.236792i
$949$	−6.08127	−	1.29261i	−0.197406	−	0.0419600i
$950$		0			0
$951$	−20.8407	+	23.1459i	−0.675805	+	0.750557i
$952$	−1.43797	+	13.6814i	−0.0466050	+	0.443417i
$953$	23.2462	+	16.8894i	0.753018	+	0.547100i	0.896761	−	0.442515i	$-0.145914\pi$
$953$	23.2462	+	16.8894i	0.753018	+	0.547100i	−0.143743	+	0.989615i	$0.545914\pi$
$954$	−0.416384	−	3.96163i	−0.0134809	−	0.128263i
$955$		0			0
$956$	8.91683	+	15.4444i	0.288391	+	0.499507i
$957$	−43.4474	+	31.5664i	−1.40446	+	1.02040i
$958$	−31.0763	−	34.5137i	−1.00403	−	1.11509i
$959$	−20.9375	−	64.4390i	−0.676107	−	2.08084i
$960$		0			0
$961$	−21.6003	+	22.2357i	−0.696785	+	0.717280i
$962$	28.5161			0.919397
$963$	−0.746679	−	2.29804i	−0.0240614	−	0.0740533i
$964$	−9.69876	−	10.7716i	−0.312376	−	0.346929i
$965$		0			0
$966$	−29.7074	−	51.4547i	−0.955820	−	1.65553i
$967$	14.9726	−	25.9332i	0.481485	−	0.833956i	−0.518289	−	0.855205i	$-0.673431\pi$
$967$	14.9726	−	25.9332i	0.481485	−	0.833956i	0.999774	+	0.0212492i	$0.00676434\pi$
$968$	2.16736	+	20.6211i	0.0696617	+	0.662787i
$969$	−14.5242	−	10.5525i	−0.466586	−	0.338995i
$970$		0			0
$971$	0.206211	−	0.229021i	0.00661763	−	0.00734963i	−0.739827	−	0.672797i	$-0.765093\pi$
$971$	0.206211	−	0.229021i	0.00661763	−	0.00734963i	0.746445	+	0.665448i	$0.231759\pi$
$972$	−14.6336	−	6.51529i	−0.469372	−	0.208978i
$973$	−20.0809	−	4.26832i	−0.643763	−	0.136836i
$974$	42.9257	−	9.12414i	1.37543	−	0.292356i
$975$		0			0
$976$	9.28584	−	28.5789i	0.297233	−	0.914788i
$977$	8.44141	−	25.9800i	0.270065	−	0.831173i	−0.720419	−	0.693539i	$-0.756050\pi$
$977$	8.44141	−	25.9800i	0.270065	−	0.831173i	0.990483	−	0.137634i	$-0.0439497\pi$
$978$	33.4270	−	14.8827i	1.06888	−	0.475895i
$979$	63.8271	−	13.5669i	2.03992	−	0.433599i
$980$		0			0
$981$	1.76387	+	0.785325i	0.0563160	+	0.0250735i
$982$	−31.8766	+	35.4025i	−1.01722	+	1.12974i
$983$	1.53616	−	14.6156i	0.0489960	−	0.466166i	−0.942325	−	0.334700i	$-0.891365\pi$
$983$	1.53616	−	14.6156i	0.0489960	−	0.466166i	0.991321	−	0.131466i	$-0.0419684\pi$
$984$	−0.902997	−	0.656066i	−0.0287865	−	0.0209146i
$985$		0			0
$986$	34.5891	−	59.9100i	1.10154	−	1.90792i
$987$	3.62327	+	6.27568i	0.115330	+	0.199757i
$988$	22.6286	−	16.4406i	0.719912	−	0.523046i
$989$	−17.4738	−	19.4066i	−0.555634	−	0.617094i
$990$		0			0
$991$	23.9105			0.759542			0.379771	−	0.925081i	$-0.376003\pi$
$991$	23.9105			0.759542			0.379771	+	0.925081i	$0.376003\pi$
$992$	17.4973	+	41.3913i	0.555539	+	1.31417i
$993$	−27.4833			−0.872157
$994$	1.88020	+	5.78668i	0.0596365	+	0.183542i
$995$		0			0
$996$	−23.5190	+	17.0875i	−0.745227	+	0.541439i
$997$	11.6392	+	20.1597i	0.368618	+	0.638465i	0.989350	−	0.145558i	$-0.0464977\pi$
$997$	11.6392	+	20.1597i	0.368618	+	0.638465i	−0.620732	+	0.784023i	$0.713164\pi$
$998$	7.09357	−	12.2864i	0.224543	−	0.388920i
$999$	1.38465	+	13.1741i	0.0438084	+	0.416809i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.bl.c.51.1		40
5.2	odd	4		775.2.ck.c.299.10		80
5.3	odd	4		775.2.ck.c.299.1		80
5.4	even	2		155.2.q.a.51.5	✓	40
31.14	even	15	inner	775.2.bl.c.76.1		40
155.14	even	30		155.2.q.a.76.5	yes	40
155.44	odd	30		4805.2.a.y.1.17		20
155.49	even	30		4805.2.a.x.1.17		20
155.107	odd	60		775.2.ck.c.324.1		80
155.138	odd	60		775.2.ck.c.324.10		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.q.a.51.5	✓	40	5.4	even	2
155.2.q.a.76.5	yes	40	155.14	even	30
775.2.bl.c.51.1		40	1.1	even	1	trivial
775.2.bl.c.76.1		40	31.14	even	15	inner
775.2.ck.c.299.1		80	5.3	odd	4
775.2.ck.c.299.10		80	5.2	odd	4
775.2.ck.c.324.1		80	155.107	odd	60
775.2.ck.c.324.10		80	155.138	odd	60
4805.2.a.x.1.17		20	155.49	even	30
4805.2.a.y.1.17		20	155.44	odd	30

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.bl (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.646517 - 1.98977i) q^{2} +(-1.02325 - 1.13643i) q^{3} +(-1.92319 + 1.39728i) q^{4} +(-1.59970 + 2.77076i) q^{6} +(0.316994 + 3.01600i) q^{7} +(0.638431 + 0.463847i) q^{8} +(0.0691433 - 0.657854i) q^{9} +(-5.57748 - 2.48326i) q^{11} +(3.55581 + 0.755811i) q^{12} +(-5.63533 + 1.19783i) q^{13} +(5.79622 - 2.58064i) q^{14} +(-0.958988 + 2.95146i) q^{16} +(5.25138 - 2.33807i) q^{17} +(-1.35368 + 0.287735i) q^{18} +(1.99768 + 0.424620i) q^{19} +(3.10312 - 3.44636i) q^{21} +(-1.33518 + 12.7034i) q^{22} +(4.95413 + 3.59938i) q^{23} +(-0.126143 - 1.20017i) q^{24} +(6.02674 + 10.4386i) q^{26} +(-4.52986 + 3.29114i) q^{27} +(-4.82382 - 5.35740i) q^{28} +(1.77750 + 5.47059i) q^{29} +(2.16791 + 5.12837i) q^{31} +8.07104 q^{32} +(2.88510 + 8.87943i) q^{33} +(-8.04733 - 8.93747i) q^{34} +(0.786229 + 1.36179i) q^{36} +(1.18290 - 2.04884i) q^{37} +(-0.446636 - 4.24946i) q^{38} +(7.12760 + 5.17850i) q^{39} +(0.618888 - 0.687345i) q^{41} +(-8.86371 - 3.94638i) q^{42} +(-4.17130 - 0.886637i) q^{43} +(14.1963 - 3.01752i) q^{44} +(3.95904 - 12.1847i) q^{46} +(-0.482864 + 1.48610i) q^{47} +(4.33543 - 1.93026i) q^{48} +(-2.14873 + 0.456727i) q^{49} +(-8.03053 - 3.57542i) q^{51} +(9.16409 - 10.1778i) q^{52} +(-0.300872 + 2.86260i) q^{53} +(9.47725 + 6.88563i) q^{54} +(-1.19658 + 2.07254i) q^{56} +(-1.56157 - 2.70472i) q^{57} +(9.73605 - 7.07365i) q^{58} +(0.130293 + 0.144705i) q^{59} -9.68296 q^{61} +(8.80271 - 7.62923i) q^{62} +2.00601 q^{63} +(-3.30009 - 10.1566i) q^{64} +(15.8028 - 11.4814i) q^{66} +(3.22324 + 5.58282i) q^{67} +(-6.83246 + 11.8342i) q^{68} +(-0.978847 - 9.31310i) q^{69} +(-0.100240 + 0.953724i) q^{71} +(0.349287 - 0.387923i) q^{72} +(0.985838 + 0.438923i) q^{73} +(-4.84150 - 1.02909i) q^{74} +(-4.43522 + 1.97469i) q^{76} +(5.72147 - 17.6089i) q^{77} +(5.69594 - 17.5303i) q^{78} +(-8.81227 + 3.92348i) q^{79} +(6.43427 + 1.36765i) q^{81} +(-1.76778 - 0.787068i) q^{82} +(-5.35103 + 5.94292i) q^{83} +(-1.15235 + 10.9639i) q^{84} +(0.932608 + 8.87317i) q^{86} +(4.39813 - 7.61779i) q^{87} +(-2.40899 - 4.17249i) q^{88} +(-8.64669 + 6.28219i) q^{89} +(-5.39901 - 16.6164i) q^{91} -14.5570 q^{92} +(3.60974 - 7.71129i) q^{93} +3.26919 q^{94} +(-8.25869 - 9.17220i) q^{96} +(1.95842 - 1.42288i) q^{97} +(2.29797 + 3.98021i) q^{98} +(-2.01927 + 3.49747i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 2 q^{2} + q^{3} - 10 q^{4} + 4 q^{6} - 4 q^{7} - 13 q^{8} + 2 q^{9} - 28 q^{11} + 13 q^{12} + 6 q^{13} - 6 q^{14} + 8 q^{16} + 10 q^{17} + 27 q^{18} - 13 q^{19} - 8 q^{21} - 2 q^{22} + 12 q^{23}+ \cdots + 53 q^{99}+O(q^{100}) \) 40 * q + 2 * q^2 + q^3 - 10 * q^4 + 4 * q^6 - 4 * q^7 - 13 * q^8 + 2 * q^9 - 28 * q^11 + 13 * q^12 + 6 * q^13 - 6 * q^14 + 8 * q^16 + 10 * q^17 + 27 * q^18 - 13 * q^19 - 8 * q^21 - 2 * q^22 + 12 * q^23 - 82 * q^24 + 32 * q^26 + q^27 - 22 * q^28 + 42 * q^29 - 10 * q^31 - 4 * q^32 - 13 * q^33 + 32 * q^34 - 13 * q^36 - 12 * q^37 - 30 * q^38 + 37 * q^39 + 36 * q^41 + 64 * q^42 + 78 * q^43 - 56 * q^44 + 18 * q^46 + 4 * q^47 + 41 * q^48 - 31 * q^49 - 2 * q^51 - 49 * q^52 + 11 * q^53 + 22 * q^54 + 9 * q^56 - 38 * q^57 - 11 * q^58 - q^59 - 100 * q^61 + 35 * q^62 - 110 * q^63 + 17 * q^64 - 40 * q^66 - 30 * q^67 + 34 * q^68 + 8 * q^69 - 2 * q^71 - 151 * q^72 + 23 * q^73 - 2 * q^74 + 2 * q^76 - 36 * q^77 + 2 * q^78 - 67 * q^79 - 83 * q^81 - 2 * q^82 + 26 * q^84 - 5 * q^86 + 46 * q^87 - 70 * q^88 + 20 * q^89 + 19 * q^91 + 10 * q^92 + 67 * q^93 + 130 * q^94 + 46 * q^96 + 18 * q^97 + 65 * q^98 + 53 * q^99

Introduction

L-functions

Modular forms

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