LMFDB - Embedded newform 775.2.ck.c.174.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [775,2,Mod(49,775)] 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("775.49"); 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([15, 26])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.ck (of order $30$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [80,0,0,20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 155)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			174.7
Character	$\chi$	$=$	775.174
Dual form			775.2.ck.c.49.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.276293 - 0.380285i) q^{2} +(-0.673286 + 1.51222i) q^{3} +(0.549755 + 1.69197i) q^{4} +(0.389052 + 0.673858i) q^{6} +(-3.07510 - 2.76883i) q^{7} +(1.68943 + 0.548929i) q^{8} +(0.173882 + 0.193116i) q^{9} +(-2.87081 - 0.610210i) q^{11} +(-2.92878 - 0.307828i) q^{12} +(-2.02152 + 0.212471i) q^{13} +(-1.90257 + 0.404405i) q^{14} +(-2.20303 + 1.60059i) q^{16} +(-0.0399441 - 0.187922i) q^{17} +(0.121482 - 0.0127682i) q^{18} +(-0.712651 + 6.78042i) q^{19} +(6.25751 - 2.78602i) q^{21} +(-1.02524 + 0.923131i) q^{22} +(-2.38756 - 0.775764i) q^{23} +(-1.96757 + 2.18521i) q^{24} +(-0.477734 + 0.827460i) q^{26} +(-5.13206 + 1.66751i) q^{27} +(2.99423 - 6.72516i) q^{28} +(-4.63691 - 3.36892i) q^{29} +(-5.30321 - 1.69587i) q^{31} +4.83275i q^{32} +(2.85565 - 3.93047i) q^{33} +(-0.0825003 - 0.0367315i) q^{34} +(-0.231154 + 0.400371i) q^{36} +(6.80193 - 3.92710i) q^{37} +(2.38159 + 2.14440i) q^{38} +(1.03976 - 3.20005i) q^{39} +(8.04782 - 3.58312i) q^{41} +(0.669425 - 3.14940i) q^{42} +(-6.47245 - 0.680282i) q^{43} +(-0.545786 - 5.19280i) q^{44} +(-0.954677 + 0.693613i) q^{46} +(-4.13611 - 5.69287i) q^{47} +(-0.937190 - 4.40913i) q^{48} +(1.05811 + 10.0672i) q^{49} +(0.311074 + 0.0661209i) q^{51} +(-1.47084 - 3.30356i) q^{52} +(-5.80788 + 5.22944i) q^{53} +(-0.783826 + 2.41237i) q^{54} +(-3.67527 - 6.36575i) q^{56} +(-9.77371 - 5.64285i) q^{57} +(-2.56230 + 0.832541i) q^{58} +(-4.29740 - 1.91333i) q^{59} +2.19934 q^{61} +(-2.11015 + 1.54817i) q^{62} -1.07530i q^{63} +(-2.56823 - 1.86593i) q^{64} +(-0.705701 - 2.17192i) q^{66} +(1.41260 + 0.815567i) q^{67} +(0.296000 - 0.170895i) q^{68} +(2.78064 - 3.08821i) q^{69} +(9.25749 + 10.2815i) q^{71} +(0.187755 + 0.421705i) q^{72} +(-1.73920 + 8.18228i) q^{73} +(0.385912 - 3.67171i) q^{74} +(-11.8641 + 2.52179i) q^{76} +(7.13847 + 9.82525i) q^{77} +(-0.929653 - 1.27956i) q^{78} +(13.3534 - 2.83835i) q^{79} +(0.852208 - 8.10822i) q^{81} +(0.860951 - 4.05046i) q^{82} +(2.14076 + 4.80822i) q^{83} +(8.15398 + 9.05591i) q^{84} +(-2.04700 + 2.27342i) q^{86} +(8.21652 - 4.74381i) q^{87} +(-4.51507 - 2.60678i) q^{88} +(0.460162 + 1.41623i) q^{89} +(6.80468 + 4.94389i) q^{91} -4.46616i q^{92} +(6.13511 - 6.87784i) q^{93} -3.30769 q^{94} +(-7.30821 - 3.25382i) q^{96} +(-7.43435 + 2.41557i) q^{97} +(4.12075 + 2.37912i) q^{98} +(-0.381343 - 0.660505i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 20 q^{4} + 8 q^{6} - 4 q^{9} - 56 q^{11} + 12 q^{14} + 16 q^{16} + 26 q^{19} - 16 q^{21} + 164 q^{24} + 64 q^{26} - 84 q^{29} - 20 q^{31} - 64 q^{34} - 26 q^{36} - 74 q^{39} + 72 q^{41} + 112 q^{44}+ \cdots - 106 q^{99}+O(q^{100}) $ 80 * q + 20 * q^4 + 8 * q^6 - 4 * q^9 - 56 * q^11 + 12 * q^14 + 16 * q^16 + 26 * q^19 - 16 * q^21 + 164 * q^24 + 64 * q^26 - 84 * q^29 - 20 * q^31 - 64 * q^34 - 26 * q^36 - 74 * q^39 + 72 * q^41 + 112 * q^44 + 36 * q^46 + 62 * q^49 - 4 * q^51 - 44 * q^54 + 18 * q^56 + 2 * q^59 - 200 * q^61 - 34 * q^64 - 80 * q^66 - 16 * q^69 - 4 * q^71 + 4 * q^74 + 4 * q^76 + 134 * q^79 - 166 * q^81 - 52 * q^84 - 10 * q^86 - 40 * q^89 + 38 * q^91 - 260 * q^94 + 92 * q^96 - 106 * q^99

Character values

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

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{2}{15}\right)$	$-1$

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 $

$2$	0.276293	−	0.380285i	0.195369	−	0.268902i	−0.700082	−	0.714062i	$-0.746853\pi$
$2$	0.276293	−	0.380285i	0.195369	−	0.268902i	0.895451	+	0.445160i	$0.146853\pi$
$3$	−0.673286	+	1.51222i	−0.388722	+	0.873083i	0.608133	+	0.793835i	$0.291919\pi$
$3$	−0.673286	+	1.51222i	−0.388722	+	0.873083i	−0.996855	+	0.0792482i	$0.974748\pi$
$4$	0.549755	+	1.69197i	0.274878	+	0.845986i
$5$		0			0
$5$		0			0
$6$	0.389052	+	0.673858i	0.158830	+	0.275101i
$7$	−3.07510	−	2.76883i	−1.16228	−	1.04652i	−0.998194	−	0.0600733i	$-0.980867\pi$
$7$	−3.07510	−	2.76883i	−1.16228	−	1.04652i	−0.164084	−	0.986446i	$-0.552467\pi$
$8$	1.68943	+	0.548929i	0.597303	+	0.194076i
$9$	0.173882	+	0.193116i	0.0579608	+	0.0643720i
$10$		0			0
$11$	−2.87081	−	0.610210i	−0.865583	−	0.183985i	−0.246339	−	0.969184i	$-0.579228\pi$
$11$	−2.87081	−	0.610210i	−0.865583	−	0.183985i	−0.619244	+	0.785198i	$0.712561\pi$
$12$	−2.92878	−	0.307828i	−0.845467	−	0.0888622i
$13$	−2.02152	+	0.212471i	−0.560670	+	0.0589288i	−0.380625	−	0.924730i	$-0.624291\pi$
$13$	−2.02152	+	0.212471i	−0.560670	+	0.0589288i	−0.180045	+	0.983658i	$0.557624\pi$
$14$	−1.90257	+	0.404405i	−0.508484	+	0.108082i
$15$		0			0
$16$	−2.20303	+	1.60059i	−0.550757	+	0.400148i
$17$	−0.0399441	−	0.187922i	−0.00968786	−	0.0455778i	0.973038	−	0.230644i	$-0.0740833\pi$
$17$	−0.0399441	−	0.187922i	−0.00968786	−	0.0455778i	−0.982726	+	0.185066i	$0.940750\pi$
$18$	0.121482	−	0.0127682i	0.0286335	−	0.00300950i
$19$	−0.712651	+	6.78042i	−0.163493	+	1.55554i	0.538052	+	0.842911i	$0.319160\pi$
$19$	−0.712651	+	6.78042i	−0.163493	+	1.55554i	−0.701546	+	0.712624i	$0.747506\pi$
$20$		0			0
$21$	6.25751	−	2.78602i	1.36550	−	0.607960i
$22$	−1.02524	+	0.923131i	−0.218582	+	0.196812i
$23$	−2.38756	−	0.775764i	−0.497840	−	0.161758i	0.0493251	−	0.998783i	$-0.484293\pi$
$23$	−2.38756	−	0.775764i	−0.497840	−	0.161758i	−0.547165	+	0.837025i	$0.684293\pi$
$24$	−1.96757	+	2.18521i	−0.401629	+	0.446054i
$25$		0			0
$26$	−0.477734	+	0.827460i	−0.0936914	+	0.162278i
$27$	−5.13206	+	1.66751i	−0.987666	+	0.320912i
$28$	2.99423	−	6.72516i	0.565857	−	1.27094i
$29$	−4.63691	−	3.36892i	−0.861053	−	0.625592i	0.0671180	−	0.997745i	$-0.478620\pi$
$29$	−4.63691	−	3.36892i	−0.861053	−	0.625592i	−0.928171	+	0.372153i	$0.878620\pi$
$30$		0			0
$31$	−5.30321	−	1.69587i	−0.952485	−	0.304587i
$31$	−5.30321	−	1.69587i	−0.952485	−	0.304587i
$32$			4.83275i			0.854318i
$33$	2.85565	−	3.93047i	0.497105	−	0.684207i
$34$	−0.0825003	−	0.0367315i	−0.0141487	−	0.00629940i
$35$		0			0
$36$	−0.231154	+	0.400371i	−0.0385257	+	0.0667285i
$37$	6.80193	−	3.92710i	1.11823	−	0.645611i	0.177282	−	0.984160i	$-0.443269\pi$
$37$	6.80193	−	3.92710i	1.11823	−	0.645611i	0.940949	+	0.338549i	$0.109936\pi$
$38$	2.38159	+	2.14440i	0.386345	+	0.347867i
$39$	1.03976	−	3.20005i	0.166495	−	0.512418i
$40$		0			0
$41$	8.04782	−	3.58312i	1.25686	−	0.559589i	0.333218	−	0.942850i	$-0.391866\pi$
$41$	8.04782	−	3.58312i	1.25686	−	0.559589i	0.923640	+	0.383261i	$0.125199\pi$
$42$	0.669425	−	3.14940i	0.103295	−	0.485963i
$43$	−6.47245	−	0.680282i	−0.987040	−	0.103742i	−0.402770	−	0.915301i	$-0.631952\pi$
$43$	−6.47245	−	0.680282i	−0.987040	−	0.103742i	−0.584270	+	0.811559i	$0.698619\pi$
$44$	−0.545786	−	5.19280i	−0.0822803	−	0.782845i
$45$		0			0
$46$	−0.954677	+	0.693613i	−0.140759	+	0.102268i
$47$	−4.13611	−	5.69287i	−0.603314	−	0.830391i	0.392692	−	0.919670i	$-0.371544\pi$
$47$	−4.13611	−	5.69287i	−0.603314	−	0.830391i	−0.996007	+	0.0892791i	$0.971544\pi$
$48$	−0.937190	−	4.40913i	−0.135272	−	0.636403i
$49$	1.05811	+	10.0672i	0.151158	+	1.43817i
$50$		0			0
$51$	0.311074	+	0.0661209i	0.0435591	+	0.00925877i
$52$	−1.47084	−	3.30356i	−0.203969	−	0.458121i
$53$	−5.80788	+	5.22944i	−0.797774	+	0.718319i	−0.963458	−	0.267860i	$-0.913684\pi$
$53$	−5.80788	+	5.22944i	−0.797774	+	0.718319i	0.165684	+	0.986179i	$0.447017\pi$
$54$	−0.783826	+	2.41237i	−0.106665	+	0.328282i
$55$		0			0
$56$	−3.67527	−	6.36575i	−0.491129	−	0.850660i
$57$	−9.77371	−	5.64285i	−1.29456	−	0.747414i
$58$	−2.56230	+	0.832541i	−0.336446	+	0.109318i
$59$	−4.29740	−	1.91333i	−0.559474	−	0.249094i	0.107462	−	0.994209i	$-0.465728\pi$
$59$	−4.29740	−	1.91333i	−0.559474	−	0.249094i	−0.666936	+	0.745115i	$0.732394\pi$
$60$		0			0
$61$	2.19934			0.281597			0.140798	−	0.990038i	$-0.455033\pi$
$61$	2.19934			0.281597			0.140798	+	0.990038i	$0.455033\pi$
$62$	−2.11015	+	1.54817i	−0.267990	+	0.196618i
$63$		−	1.07530i		−	0.135475i
$64$	−2.56823	−	1.86593i	−0.321029	−	0.233241i
$65$		0			0
$66$	−0.705701	−	2.17192i	−0.0868658	−	0.267345i
$67$	1.41260	+	0.815567i	0.172577	+	0.0996373i	0.583800	−	0.811897i	$-0.301565\pi$
$67$	1.41260	+	0.815567i	0.172577	+	0.0996373i	−0.411223	+	0.911535i	$0.634898\pi$
$68$	0.296000	−	0.170895i	0.0358952	−	0.0207241i
$69$	2.78064	−	3.08821i	0.334749	−	0.371777i
$70$		0			0
$71$	9.25749	+	10.2815i	1.09866	+	1.22019i	0.973654	+	0.228032i	$0.0732290\pi$
$71$	9.25749	+	10.2815i	1.09866	+	1.22019i	0.125008	+	0.992156i	$0.460104\pi$
$72$	0.187755	+	0.421705i	0.0221272	+	0.0496984i
$73$	−1.73920	+	8.18228i	−0.203558	+	0.957663i	0.751153	+	0.660128i	$0.229498\pi$
$73$	−1.73920	+	8.18228i	−0.203558	+	0.957663i	−0.954711	+	0.297535i	$0.903835\pi$
$74$	0.385912	−	3.67171i	0.0448613	−	0.426827i
$75$		0			0
$76$	−11.8641	+	2.52179i	−1.36090	+	0.289269i
$77$	7.13847	+	9.82525i	0.813504	+	1.11969i
$78$	−0.929653	−	1.27956i	−0.105263	−	0.144881i
$79$	13.3534	−	2.83835i	1.50237	−	0.319340i	0.618023	−	0.786160i	$-0.287934\pi$
$79$	13.3534	−	2.83835i	1.50237	−	0.319340i	0.884352	+	0.466821i	$0.154601\pi$
$80$		0			0
$81$	0.852208	−	8.10822i	0.0946898	−	0.900913i
$82$	0.860951	−	4.05046i	0.0950761	−	0.447298i
$83$	2.14076	+	4.80822i	0.234979	+	0.527771i	0.992092	−	0.125513i	$-0.0400576\pi$
$83$	2.14076	+	4.80822i	0.234979	+	0.527771i	−0.757113	+	0.653284i	$0.773391\pi$
$84$	8.15398	+	9.05591i	0.889672	+	0.988081i
$85$		0			0
$86$	−2.04700	+	2.27342i	−0.220733	+	0.245149i
$87$	8.21652	−	4.74381i	0.880904	−	0.508590i
$88$	−4.51507	−	2.60678i	−0.481309	−	0.277884i
$89$	0.460162	+	1.41623i	0.0487771	+	0.150120i	0.972478	−	0.232993i	$-0.0748519\pi$
$89$	0.460162	+	1.41623i	0.0487771	+	0.150120i	−0.923701	+	0.383113i	$0.874852\pi$
$90$		0			0
$91$	6.80468	+	4.94389i	0.713324	+	0.518261i
$92$		−	4.46616i		−	0.465629i
$93$	6.13511	−	6.87784i	0.636181	−	0.713199i
$94$	−3.30769			−0.341163
$95$		0			0
$96$	−7.30821	−	3.25382i	−0.745891	−	0.332092i
$97$	−7.43435	+	2.41557i	−0.754844	+	0.245264i	−0.661064	−	0.750329i	$-0.729895\pi$
$97$	−7.43435	+	2.41557i	−0.754844	+	0.245264i	−0.0937795	+	0.995593i	$0.529895\pi$
$98$	4.12075	+	2.37912i	0.416259	+	0.240327i
$99$	−0.381343	−	0.660505i	−0.0383264	−	0.0663833i
$100$		0			0
$101$	−3.69501	+	11.3721i	−0.367667	+	1.13156i	0.580627	+	0.814170i	$0.302808\pi$
$101$	−3.69501	+	11.3721i	−0.367667	+	1.13156i	−0.948294	+	0.317394i	$0.897192\pi$
$102$	0.111093	−	0.100028i	0.0109998	−	0.00990426i
$103$	3.62407	+	8.13979i	0.357090	+	0.802037i	0.999367	+	0.0355650i	$0.0113231\pi$
$103$	3.62407	+	8.13979i	0.357090	+	0.802037i	−0.642277	+	0.766472i	$0.722010\pi$
$104$	−3.53185	−	0.750719i	−0.346327	−	0.0736140i
$105$		0			0
$106$	0.383999	+	3.65351i	0.0372973	+	0.354860i
$107$	3.18206	+	14.9704i	0.307621	+	1.44724i	0.811948	+	0.583730i	$0.198407\pi$
$107$	3.18206	+	14.9704i	0.307621	+	1.44724i	−0.504327	+	0.863513i	$0.668259\pi$
$108$	−5.64276	−	7.76659i	−0.542974	−	0.747340i
$109$	−4.08287	+	2.96638i	−0.391068	+	0.284127i	−0.765893	−	0.642968i	$-0.777703\pi$
$109$	−4.08287	+	2.96638i	−0.391068	+	0.284127i	0.374825	+	0.927096i	$0.377703\pi$
$110$		0			0
$111$	1.35901	+	12.9301i	0.128991	+	1.22727i
$112$	11.2063	+	1.17783i	1.05890	+	0.111294i
$113$	−0.730279	+	3.43569i	−0.0686989	+	0.323203i	−0.999055	−	0.0434532i	$-0.986164\pi$
$113$	−0.730279	+	3.43569i	−0.0686989	+	0.323203i	0.930357	+	0.366656i	$0.119497\pi$
$114$	−4.84630	+	2.15771i	−0.453898	+	0.202088i
$115$		0			0
$116$	3.15094	−	9.69761i	0.292558	−	0.900401i
$117$	−0.392539	−	0.353444i	−0.0362903	−	0.0326759i
$118$	−1.91495	+	1.10560i	−0.176286	+	0.101779i
$119$	−0.397493	+	0.688477i	−0.0364381	+	0.0631126i
$120$		0			0
$121$	−2.17978	−	0.970503i	−0.198162	−	0.0882275i
$122$	0.607663	−	0.836376i	0.0550152	−	0.0757220i
$123$			14.5826i			1.31487i
$124$	−0.0461062	−	9.90520i	−0.00414046	−	0.889513i
$125$		0			0
$126$	−0.408921	−	0.297099i	−0.0364296	−	0.0264677i
$127$	−5.74781	+	12.9098i	−0.510036	+	1.14556i	0.456663	+	0.889640i	$0.349045\pi$
$127$	−5.74781	+	12.9098i	−0.510036	+	1.14556i	−0.966698	+	0.255919i	$0.917622\pi$
$128$	−10.6116	+	3.44792i	−0.937943	+	0.304756i
$129$	5.38655	−	9.32978i	0.474259	−	0.821441i
$130$		0			0
$131$	−5.64304	+	6.26723i	−0.493034	+	0.547570i	−0.937391	−	0.348280i	$-0.886766\pi$
$131$	−5.64304	+	6.26723i	−0.493034	+	0.547570i	0.444356	+	0.895850i	$0.353432\pi$
$132$	8.22016	+	2.67089i	0.715473	+	0.232471i
$133$	20.9653	−	18.8773i	1.81792	−	1.63687i
$134$	0.700440	−	0.311856i	0.0605088	−	0.0269403i
$135$		0			0
$136$	0.0356732	−	0.339408i	0.00305895	−	0.0291040i
$137$	16.8514	−	1.77115i	1.43971	−	0.151320i	0.647733	−	0.761867i	$-0.275717\pi$
$137$	16.8514	−	1.77115i	1.43971	−	0.151320i	0.791980	+	0.610547i	$0.209050\pi$
$138$	−0.406129	−	1.91069i	−0.0345720	−	0.162648i
$139$	−10.3895	+	7.54843i	−0.881228	+	0.640250i	−0.933576	−	0.358379i	$-0.883329\pi$
$139$	−10.3895	+	7.54843i	−0.881228	+	0.640250i	0.0523481	+	0.998629i	$0.483329\pi$
$140$		0			0
$141$	11.3937	−	2.42180i	0.959522	−	0.203953i
$142$	6.46767	−	0.679780i	0.542755	−	0.0570459i
$143$	5.93307	+	0.623591i	0.496148	+	0.0521473i
$144$	−0.692168	−	0.147125i	−0.0576807	−	0.0122604i
$145$		0			0
$146$	2.63107	+	2.92210i	0.217749	+	0.241835i
$147$	−15.9363	−	5.17801i	−1.31440	−	0.427075i
$148$	10.3839	+	9.34974i	0.853555	+	0.768544i
$149$	1.11083	+	1.92401i	0.0910026	+	0.157621i	0.907933	−	0.419115i	$-0.137660\pi$
$149$	1.11083	+	1.92401i	0.0910026	+	0.157621i	−0.816931	+	0.576736i	$0.804326\pi$
$150$		0			0
$151$	−7.07903	−	21.7870i	−0.576083	−	1.77300i	−0.632460	−	0.774593i	$-0.717955\pi$
$151$	−7.07903	−	21.7870i	−0.576083	−	1.77300i	0.0563769	−	0.998410i	$-0.482045\pi$
$152$	−4.92594	+	11.0639i	−0.399547	+	0.897397i
$153$	0.0293452	−	0.0403902i	0.00237242	−	0.00326536i
$154$	5.70871			0.460021
$155$		0			0
$156$	5.98601			0.479265
$157$	−7.71578	+	10.6199i	−0.615786	+	0.847557i	−0.997038	−	0.0769142i	$-0.975493\pi$
$157$	−7.71578	+	10.6199i	−0.615786	+	0.847557i	0.381251	+	0.924471i	$0.375493\pi$
$158$	2.61007	−	5.86231i	0.207646	−	0.466381i
$159$	−3.99772	−	12.3037i	−0.317040	−	0.975749i
$160$		0			0
$161$	5.19401	+	8.99629i	0.409345	+	0.709007i
$162$	−2.84798	−	2.56433i	−0.223758	−	0.201473i
$163$	−12.7709	−	4.14953i	−1.00030	−	0.325016i	−0.237312	−	0.971433i	$-0.576267\pi$
$163$	−12.7709	−	4.14953i	−1.00030	−	0.325016i	−0.762984	+	0.646417i	$0.776267\pi$
$164$	10.4869	+	11.6468i	0.818887	+	0.909466i
$165$		0			0
$166$	2.41997	+	0.514381i	0.187826	+	0.0399237i
$167$	18.5908	+	1.95397i	1.43860	+	0.151203i	0.791485	−	0.611189i	$-0.209308\pi$
$167$	18.5908	+	1.95397i	1.43860	+	0.151203i	0.647115	+	0.762392i	$0.275975\pi$
$168$	12.1010	−	1.27186i	0.933609	−	0.0981263i
$169$	−8.67450	+	1.84382i	−0.667269	+	0.141832i
$170$		0			0
$171$	−1.43333	+	1.04137i	−0.109609	+	0.0796357i
$172$	−2.40725	−	11.3252i	−0.183551	−	0.863539i
$173$	12.5018	−	1.31399i	0.950496	−	0.0999011i	0.383427	−	0.923571i	$-0.374744\pi$
$173$	12.5018	−	1.31399i	0.950496	−	0.0999011i	0.567069	+	0.823670i	$0.308077\pi$
$174$	0.466169	−	4.43530i	0.0353402	−	0.336240i
$175$		0			0
$176$	7.30118	−	3.25070i	0.550347	−	0.245030i
$177$	5.78676	−	5.21042i	0.434959	−	0.391639i
$178$	0.665712	+	0.216303i	0.0498972	+	0.0162126i
$179$	11.1160	−	12.3455i	0.830847	−	0.922749i	−0.167155	−	0.985931i	$-0.553458\pi$
$179$	11.1160	−	12.3455i	0.830847	−	0.922749i	0.998002	+	0.0631814i	$0.0201247\pi$
$180$		0			0
$181$	−0.275725	+	0.477570i	−0.0204945	+	0.0354975i	−0.876091	−	0.482146i	$-0.839857\pi$
$181$	−0.275725	+	0.477570i	−0.0204945	+	0.0354975i	0.855596	+	0.517644i	$0.173191\pi$
$182$	3.76018	−	1.22176i	0.278723	−	0.0905625i
$183$	−1.48078	+	3.32590i	−0.109463	+	0.245857i
$184$	−3.60777	−	2.62120i	−0.265968	−	0.193237i
$185$		0			0
$186$	−0.920451	−	4.23339i	−0.0674907	−	0.310407i
$187$			0.563864i			0.0412338i
$188$	7.35833	−	10.1279i	0.536662	−	0.738651i
$189$	20.3986	+	9.08206i	1.48378	+	0.660623i
$190$		0			0
$191$	7.78153	−	13.4780i	0.563051	−	0.975234i	−0.434177	−	0.900828i	$-0.642961\pi$
$191$	7.78153	−	13.4780i	0.563051	−	0.975234i	0.997228	−	0.0744059i	$-0.0237060\pi$
$192$	4.55086	−	2.62744i	0.328430	−	0.189619i
$193$	−6.64851	−	5.98635i	−0.478571	−	0.430907i	0.394209	−	0.919021i	$-0.371018\pi$
$193$	−6.64851	−	5.98635i	−0.478571	−	0.430907i	−0.872780	+	0.488114i	$0.837685\pi$
$194$	−1.13546	+	3.49458i	−0.0815210	+	0.250896i
$195$		0			0
$196$	−16.4517	+	7.32478i	−1.17512	+	0.523199i
$197$	2.69890	−	12.6973i	0.192289	−	0.904649i	−0.771136	−	0.636670i	$-0.780311\pi$
$197$	2.69890	−	12.6973i	0.192289	−	0.904649i	0.963425	−	0.267978i	$-0.0863555\pi$
$198$	−0.356543	−	0.0374741i	−0.0253384	−	0.00266317i
$199$	−0.367816	−	3.49954i	−0.0260738	−	0.248076i	−0.999793	−	0.0203255i	$-0.993530\pi$
$199$	−0.367816	−	3.49954i	−0.0260738	−	0.248076i	0.973720	−	0.227750i	$-0.0731369\pi$
$200$		0			0
$201$	−2.18440	+	1.58706i	−0.154076	+	0.111943i
$202$	3.30372	+	4.54718i	0.232449	+	0.319939i
$203$	4.93101	+	23.1986i	0.346089	+	1.62822i
$204$	0.0591400	+	0.562679i	0.00414063	+	0.0393954i
$205$		0			0
$206$	4.09675	+	0.870790i	0.285434	+	0.0606708i
$207$	−0.265342	−	0.595967i	−0.0184425	−	0.0414226i
$208$	4.11340	−	3.70372i	0.285213	−	0.256807i
$209$	6.18337	−	19.0305i	0.427713	−	1.31636i
$210$		0			0
$211$	−5.04331	−	8.73527i	−0.347196	−	0.601361i	0.638554	−	0.769577i	$-0.279533\pi$
$211$	−5.04331	−	8.73527i	−0.347196	−	0.601361i	−0.985750	+	0.168216i	$0.946199\pi$
$212$	−12.0410	−	6.95186i	−0.826978	−	0.477456i
$213$	−21.7808	+	7.07702i	−1.49240	+	0.484910i
$214$	6.57220	+	2.92613i	0.449266	+	0.200026i
$215$		0			0
$216$	−9.58560			−0.652217
$217$	11.6123	+	19.8986i	0.788296	+	1.35081i
$218$			2.37224i			0.160669i
$219$	−11.2025	−	8.13907i	−0.756992	−	0.549987i
$220$		0			0
$221$	0.120676	+	0.371402i	0.00811754	+	0.0249832i
$222$	5.29261	+	3.05569i	0.355217	+	0.205085i
$223$	−12.0643	+	6.96535i	−0.807889	+	0.466435i	−0.846222	−	0.532830i	$-0.821128\pi$
$223$	−12.0643	+	6.96535i	−0.807889	+	0.466435i	0.0383336	+	0.999265i	$0.487795\pi$
$224$	13.3811	−	14.8612i	0.894061	−	0.992955i
$225$		0			0
$226$	1.10477	+	1.22697i	0.0734883	+	0.0816170i
$227$	8.41245	+	18.8947i	0.558354	+	1.25408i	0.943544	+	0.331247i	$0.107469\pi$
$227$	8.41245	+	18.8947i	0.558354	+	1.25408i	−0.385190	+	0.922837i	$0.625864\pi$
$228$	4.17440	−	19.6390i	0.276457	−	1.30063i
$229$	2.09921	−	19.9726i	0.138719	−	1.31983i	−0.674675	−	0.738115i	$-0.735716\pi$
$229$	2.09921	−	19.9726i	0.138719	−	1.31983i	0.813395	−	0.581712i	$-0.197617\pi$
$230$		0			0
$231$	−19.6642	+	4.17976i	−1.29381	+	0.275008i
$232$	−5.98444	−	8.23688i	−0.392898	−	0.540778i
$233$	10.6205	+	14.6179i	0.695774	+	0.957651i	0.999987	+	0.00504685i	$0.00160647\pi$
$233$	10.6205	+	14.6179i	0.695774	+	0.957651i	−0.304213	+	0.952604i	$0.598394\pi$
$234$	−0.242865	+	0.0516226i	−0.0158766	+	0.00337468i
$235$		0			0
$236$	0.874777	−	8.32294i	0.0569431	−	0.541777i
$237$	−4.69843	+	22.1044i	−0.305196	+	1.43583i
$238$	0.151993	+	0.341382i	0.00985225	+	0.0221285i
$239$	13.3887	+	14.8696i	0.866040	+	0.961835i	0.999573	−	0.0292090i	$-0.00929884\pi$
$239$	13.3887	+	14.8696i	0.866040	+	0.961835i	−0.133533	+	0.991044i	$0.542632\pi$
$240$		0			0
$241$	−5.06259	+	5.62258i	−0.326110	+	0.362182i	−0.883798	−	0.467869i	$-0.845022\pi$
$241$	−5.06259	+	5.62258i	−0.326110	+	0.362182i	0.557688	+	0.830051i	$0.311689\pi$
$242$	−0.971328	+	0.560796i	−0.0624393	+	0.0360493i
$243$	−2.33199	−	1.34637i	−0.149597	−	0.0863700i
$244$	1.20910	+	3.72122i	0.0774046	+	0.238227i
$245$		0			0
$246$	5.54553	+	4.02907i	0.353570	+	0.256884i
$247$		−	13.8582i		−	0.881777i
$248$	−8.02849	−	5.77613i	−0.509809	−	0.366785i
$249$	−8.71245			−0.552129
$250$		0			0
$251$	−15.3427	−	6.83101i	−0.968423	−	0.431170i	−0.139309	−	0.990249i	$-0.544488\pi$
$251$	−15.3427	−	6.83101i	−0.968423	−	0.431170i	−0.829114	+	0.559079i	$0.811155\pi$
$252$	1.81938	−	0.591153i	0.114610	−	0.0372391i
$253$	6.38085	+	3.68398i	0.401161	+	0.231610i
$254$	3.32132	+	5.75269i	0.208398	+	0.360956i
$255$		0			0
$256$	0.341231	−	1.05020i	0.0213269	−	0.0656375i
$257$	4.03285	−	3.63120i	0.251562	−	0.226508i	−0.533695	−	0.845677i	$-0.679197\pi$
$257$	4.03285	−	3.63120i	0.251562	−	0.226508i	0.785258	+	0.619169i	$0.212530\pi$
$258$	−2.05971	−	4.62618i	−0.128232	−	0.288013i
$259$	−31.7901	−	6.75719i	−1.97534	−	0.419871i
$260$		0			0
$261$	−0.155686	−	1.48126i	−0.00963675	−	0.0916876i
$262$	0.824200	+	3.87755i	0.0509192	+	0.239556i
$263$	−11.9483	−	16.4454i	−0.736763	−	1.01407i	−0.998798	−	0.0490087i	$-0.984394\pi$
$263$	−11.9483	−	16.4454i	−0.736763	−	1.01407i	0.262036	−	0.965058i	$-0.415606\pi$
$264$	6.98197	−	5.07270i	0.429711	−	0.312203i
$265$		0			0
$266$	−1.38616	−	13.1885i	−0.0849911	−	0.808636i
$267$	−2.45148	−	0.257661i	−0.150028	−	0.0157686i
$268$	−0.603331	+	2.83845i	−0.0368543	+	0.173386i
$269$	−14.2060	+	6.32491i	−0.866154	+	0.385636i	−0.791205	−	0.611551i	$-0.790546\pi$
$269$	−14.2060	+	6.32491i	−0.866154	+	0.385636i	−0.0749486	+	0.997187i	$0.523879\pi$
$270$		0			0
$271$	−4.00648	+	12.3307i	−0.243377	+	0.749036i	0.752523	+	0.658566i	$0.228837\pi$
$271$	−4.00648	+	12.3307i	−0.243377	+	0.749036i	−0.995899	+	0.0904697i	$0.971163\pi$
$272$	0.388785	+	0.350064i	0.0235736	+	0.0212257i
$273$	−12.0578	+	6.96156i	−0.729769	+	0.421333i
$274$	3.98239	−	6.89770i	0.240585	−	0.416705i
$275$		0			0
$276$	6.75384	+	3.00700i	0.406533	+	0.181000i
$277$	1.63427	−	2.24938i	0.0981937	−	0.135152i	−0.757093	−	0.653307i	$-0.773381\pi$
$277$	1.63427	−	2.24938i	0.0981937	−	0.135152i	0.855287	+	0.518155i	$0.173381\pi$
$278$			6.03656i			0.362049i
$279$	−0.594636	−	1.31902i	−0.0355999	−	0.0789675i
$280$		0			0
$281$	5.78584	+	4.20366i	0.345154	+	0.250769i	0.746833	−	0.665011i	$-0.231573\pi$
$281$	5.78584	+	4.20366i	0.345154	+	0.250769i	−0.401679	+	0.915780i	$0.631573\pi$
$282$	2.22702	−	5.00198i	0.132617	−	0.297863i
$283$	−5.54082	+	1.80032i	−0.329367	+	0.107018i	−0.469033	−	0.883181i	$-0.655397\pi$
$283$	−5.54082	+	1.80032i	−0.329367	+	0.107018i	0.139665	+	0.990199i	$0.455397\pi$
$284$	−12.3066	+	21.3157i	−0.730264	+	1.26485i
$285$		0			0
$286$	1.87641	−	2.08396i	0.110954	−	0.123227i
$287$	−34.6689	−	11.2646i	−2.04644	−	0.664928i
$288$	−0.933282	+	0.840331i	−0.0549942	+	0.0495170i
$289$	15.4966	−	6.89951i	0.911562	−	0.405854i
$290$		0			0
$291$	1.35256	−	12.8688i	0.0792886	−	0.754381i
$292$	−14.8003	+	1.55558i	−0.866123	+	0.0910332i
$293$	4.93683	+	23.2260i	0.288413	+	1.35688i	0.848830	+	0.528665i	$0.177307\pi$
$293$	4.93683	+	23.2260i	0.288413	+	1.35688i	−0.560418	+	0.828210i	$0.689359\pi$
$294$	−6.37220	+	4.62968i	−0.371634	+	0.270008i
$295$		0			0
$296$	13.6471	−	2.90078i	0.793221	−	0.168604i
$297$	15.7507	−	1.65547i	0.913950	−	0.0960600i
$298$	1.03859	+	0.109160i	0.0601637	+	0.00632346i
$299$	4.99133	+	1.06094i	0.288656	+	0.0613557i
$300$		0			0
$301$	18.0198	+	20.0131i	1.03865	+	1.15353i
$302$	−10.2412	−	3.32756i	−0.589313	−	0.191479i
$303$	−14.7093	−	13.2443i	−0.845029	−	0.760867i
$304$	−9.28271	−	16.0781i	−0.532400	−	0.922144i
$305$		0			0
$306$	−0.00725191	−	0.0223191i	−0.000414564	−	0.00127590i
$307$	5.22601	−	11.7378i	0.298264	−	0.669912i	−0.700791	−	0.713366i	$-0.747170\pi$
$307$	5.22601	−	11.7378i	0.298264	−	0.669912i	0.999055	+	0.0434544i	$0.0138363\pi$
$308$	−12.6997	+	17.4796i	−0.723630	+	0.995991i
$309$	−14.7492			−0.839054
$310$		0			0
$311$	35.0877			1.98964			0.994819	−	0.101659i	$-0.0324152\pi$
$311$	35.0877			1.98964			0.994819	+	0.101659i	$0.0324152\pi$
$312$	3.51320	−	4.83551i	0.198896	−	0.273757i
$313$	8.07908	−	18.1459i	0.456657	−	1.02567i	−0.527692	−	0.849436i	$-0.676943\pi$
$313$	8.07908	−	18.1459i	0.456657	−	1.02567i	0.984349	−	0.176232i	$-0.0563908\pi$
$314$	1.90676	+	5.86839i	0.107604	+	0.331173i
$315$		0			0
$316$	12.1435	+	21.0332i	0.683126	+	1.18321i
$317$	4.01112	+	3.61163i	0.225287	+	0.202849i	0.774043	−	0.633133i	$-0.218232\pi$
$317$	4.01112	+	3.61163i	0.225287	+	0.202849i	−0.548756	+	0.835983i	$0.684898\pi$
$318$	−5.78347	−	1.87916i	−0.324321	−	0.105378i
$319$	11.2560	+	12.5010i	0.630213	+	0.699923i
$320$		0			0
$321$	−24.7810	−	5.26737i	−1.38314	−	0.293996i
$322$	4.85622	+	0.510410i	0.270627	+	0.0284440i
$323$	1.30266	−	0.136915i	0.0724818	−	0.00761815i
$324$	14.1874	−	3.01562i	0.788188	−	0.167535i
$325$		0			0
$326$	−5.10652	+	3.71011i	−0.282824	+	0.205484i
$327$	−1.73689	−	8.17143i	−0.0960503	−	0.451881i
$328$	15.5631	−	1.63575i	0.859328	−	0.0903190i
$329$	−3.04364	+	28.9583i	−0.167802	+	1.59653i
$330$		0			0
$331$	6.89017	−	3.06770i	0.378718	−	0.168616i	−0.208544	−	0.978013i	$-0.566872\pi$
$331$	6.89017	−	3.06770i	0.378718	−	0.168616i	0.587262	+	0.809397i	$0.300206\pi$
$332$	−6.95849	+	6.26545i	−0.381897	+	0.343861i
$333$	1.94112	+	0.630709i	0.106373	+	0.0345626i
$334$	5.87958	−	6.52994i	0.321716	−	0.357302i
$335$		0			0
$336$	−9.32619	+	16.1534i	−0.508785	+	0.881242i
$337$	1.78047	−	0.578511i	0.0969886	−	0.0315135i	−0.260121	−	0.965576i	$-0.583762\pi$
$337$	1.78047	−	0.578511i	0.0969886	−	0.0315135i	0.357109	+	0.934063i	$0.383762\pi$
$338$	−1.69553	+	3.80822i	−0.0922246	+	0.207140i
$339$	−4.70385	−	3.41755i	−0.255478	−	0.185616i
$340$		0			0
$341$	14.1897	+	8.10459i	0.768415	+	0.438888i
$342$			0.832797i			0.0450325i
$343$	7.59500	−	10.4536i	0.410092	−	0.564443i
$344$	−10.5613	−	4.70220i	−0.569428	−	0.253526i
$345$		0			0
$346$	2.95448	−	5.11730i	0.158834	−	0.275108i
$347$	−16.1824	+	9.34290i	−0.868716	+	0.501553i	−0.866921	−	0.498445i	$-0.833905\pi$
$347$	−16.1824	+	9.34290i	−0.868716	+	0.501553i	−0.00179443	+	0.999998i	$0.500571\pi$
$348$	12.5435	+	11.2942i	0.672401	+	0.605433i
$349$	−0.461299	+	1.41973i	−0.0246928	+	0.0759965i	−0.962644	−	0.270772i	$-0.912721\pi$
$349$	−0.461299	+	1.41973i	−0.0246928	+	0.0759965i	0.937951	+	0.346768i	$0.112721\pi$
$350$		0			0
$351$	10.0203	−	4.46132i	0.534844	−	0.238128i
$352$	2.94900	−	13.8739i	0.157182	−	0.739483i
$353$	−6.33709	−	0.666055i	−0.337289	−	0.0354505i	−0.0656301	−	0.997844i	$-0.520906\pi$
$353$	−6.33709	−	0.666055i	−0.337289	−	0.0354505i	−0.271659	+	0.962393i	$0.587572\pi$
$354$	−0.382603	−	3.64022i	−0.0203351	−	0.193476i
$355$		0			0
$356$	−2.14325	+	1.55716i	−0.113592	+	0.0825295i
$357$	−0.773506	−	1.06464i	−0.0409383	−	0.0563467i
$358$	−1.62356	−	7.63823i	−0.0858076	−	0.403693i
$359$	2.09759	+	19.9572i	0.110707	+	1.05330i	0.898984	+	0.437982i	$0.144307\pi$
$359$	2.09759	+	19.9572i	0.110707	+	1.05330i	−0.788277	+	0.615320i	$0.789027\pi$
$360$		0			0
$361$	−26.8815	−	5.71383i	−1.41481	−	0.300728i
$362$	0.105432	+	0.236804i	0.00554137	+	0.0124461i
$363$	2.93524	−	2.64290i	0.154060	−	0.138716i
$364$	−4.62402	+	14.2313i	−0.242364	+	0.745921i
$365$		0			0
$366$	0.855658	+	1.48204i	0.0447260	+	0.0774676i
$367$	−26.3963	−	15.2399i	−1.37788	−	0.795517i	−0.385973	−	0.922510i	$-0.626134\pi$
$367$	−26.3963	−	15.2399i	−1.37788	−	0.795517i	−0.991904	+	0.126993i	$0.959467\pi$
$368$	6.50154	−	2.11248i	0.338916	−	0.110120i
$369$	2.09133	+	0.931121i	0.108870	+	0.0484722i
$370$		0			0
$371$	32.3392			1.67897
$372$	15.0099	+	6.59931i	0.778228	+	0.342158i
$373$		−	29.9469i		−	1.55059i	−0.631600	−	0.775295i	$-0.717601\pi$
$373$		−	29.9469i		−	1.55059i	0.631600	−	0.775295i	$-0.282399\pi$
$374$	0.214429	+	0.155792i	0.0110879	+	0.00805580i
$375$		0			0
$376$	−3.86269	−	11.8881i	−0.199203	−	0.613084i
$377$	10.0894	+	5.82514i	0.519632	+	0.300010i
$378$	9.08978	−	5.24799i	0.467528	−	0.269927i
$379$	−16.7750	+	18.6305i	−0.861675	+	0.956987i	−0.999439	−	0.0334783i	$-0.989342\pi$
$379$	−16.7750	+	18.6305i	−0.861675	+	0.956987i	0.137765	+	0.990465i	$0.456008\pi$
$380$		0			0
$381$	−15.6526	−	17.3840i	−0.801906	−	0.890607i
$382$	−2.97550	−	6.68308i	−0.152240	−	0.341936i
$383$	0.717708	−	3.37655i	0.0366732	−	0.172534i	−0.955999	−	0.293368i	$-0.905224\pi$
$383$	0.717708	−	3.37655i	0.0366732	−	0.172534i	0.992673	+	0.120835i	$0.0385571\pi$
$384$	1.93062	−	18.3686i	0.0985213	−	0.937368i
$385$		0			0
$386$	−4.11346	+	0.874343i	−0.209370	+	0.0445029i
$387$	−0.994073	−	1.36822i	−0.0505316	−	0.0695507i
$388$	−8.17414	−	11.2507i	−0.414979	−	0.571170i
$389$	−30.2488	+	6.42958i	−1.53368	+	0.325993i	−0.895909	−	0.444237i	$-0.853475\pi$
$389$	−30.2488	+	6.42958i	−1.53368	+	0.325993i	−0.637766	+	0.770230i	$0.720141\pi$
$390$		0			0
$391$	−0.0504145	+	0.479662i	−0.00254957	+	0.0242575i
$392$	−3.73858	+	17.5886i	−0.188827	+	0.888361i
$393$	−5.67808	−	12.7532i	−0.286421	−	0.643312i
$394$	−4.08292	−	4.53454i	−0.205695	−	0.228447i
$395$		0			0
$396$	0.907911	−	1.00834i	0.0456243	−	0.0506709i
$397$	0.708339	−	0.408960i	0.0355505	−	0.0205251i	−0.482119	−	0.876106i	$-0.660133\pi$
$397$	0.708339	−	0.408960i	0.0355505	−	0.0205251i	0.517670	+	0.855580i	$0.326800\pi$
$398$	−1.43245	−	0.827023i	−0.0718021	−	0.0414549i
$399$	14.4310	+	44.4141i	0.722454	+	2.22348i
$400$		0			0
$401$	−13.3225	−	9.67939i	−0.665296	−	0.483366i	0.203151	−	0.979147i	$-0.434882\pi$
$401$	−13.3225	−	9.67939i	−0.665296	−	0.483366i	−0.868447	+	0.495782i	$0.834882\pi$
$402$			1.26919i			0.0633015i
$403$	11.0809	+	2.30146i	0.551978	+	0.114644i
$404$	−21.2726			−1.05835
$405$		0			0
$406$	10.1845	+	4.53442i	0.505447	+	0.225040i
$407$	−21.9234	+	7.12336i	−1.08670	+	0.353092i
$408$	0.489242	+	0.282464i	0.0242211	+	0.0139841i
$409$	18.7941	+	32.5524i	0.929309	+	1.60961i	0.784481	+	0.620153i	$0.212930\pi$
$409$	18.7941	+	32.5524i	0.929309	+	1.60961i	0.144828	+	0.989457i	$0.453737\pi$
$410$		0			0
$411$	−8.66743	+	26.6756i	−0.427533	+	1.31581i
$412$	−11.7800	+	10.6067i	−0.580357	+	0.522555i
$413$	7.91725	+	17.7824i	0.389582	+	0.875016i
$414$	−0.299949	−	0.0637562i	−0.0147417	−	0.00313345i
$415$		0			0
$416$	−1.02682	−	9.76953i	−0.0503439	−	0.478991i
$417$	−4.41980	−	20.7935i	−0.216439	−	1.01826i
$418$	−5.52858	−	7.60943i	−0.270412	−	0.372190i
$419$	−6.80968	+	4.94752i	−0.332674	+	0.241702i	−0.741565	−	0.670881i	$-0.765916\pi$
$419$	−6.80968	+	4.94752i	−0.332674	+	0.241702i	0.408890	+	0.912584i	$0.365916\pi$
$420$		0			0
$421$	0.556276	+	5.29261i	0.0271112	+	0.257946i	0.999679	+	0.0253272i	$0.00806277\pi$
$421$	0.556276	+	5.29261i	0.0271112	+	0.257946i	−0.972568	+	0.232619i	$0.925271\pi$
$422$	−4.71533	−	0.495601i	−0.229538	−	0.0241255i
$423$	0.380187	−	1.78864i	0.0184853	−	0.0869667i
$424$	−12.6826	+	5.64666i	−0.615921	+	0.274226i
$425$		0			0
$426$	−3.32661	+	10.2383i	−0.161175	+	0.496045i
$427$	−6.76319	−	6.08960i	−0.327294	−	0.294697i
$428$	−23.5801	+	13.6140i	−1.13979	+	0.658058i
$429$	−4.93766	+	8.55228i	−0.238393	+	0.412908i
$430$		0			0
$431$	−18.8226	−	8.38035i	−0.906651	−	0.403667i	−0.100200	−	0.994967i	$-0.531948\pi$
$431$	−18.8226	−	8.38035i	−0.906651	−	0.403667i	−0.806452	+	0.591300i	$0.798615\pi$
$432$	8.63707	−	11.8879i	0.415551	−	0.571957i
$433$			20.6799i			0.993814i	0.867804	+	0.496907i	$0.165531\pi$
$433$			20.6799i			0.993814i	−0.867804	+	0.496907i	$0.834469\pi$
$434$	10.7756	+	1.08187i	0.517244	+	0.0519315i
$435$		0			0
$436$	−7.26361	−	5.27732i	−0.347864	−	0.252738i
$437$	6.96150	−	15.6358i	0.333014	−	0.747961i
$438$	−6.19033	+	2.01136i	−0.295785	+	0.0961065i
$439$	9.83969	−	17.0428i	0.469623	−	0.813410i	−0.529774	−	0.848139i	$-0.677723\pi$
$439$	9.83969	−	17.0428i	0.469623	−	0.813410i	0.999397	+	0.0347286i	$0.0110567\pi$
$440$		0			0
$441$	−1.76015	+	1.95485i	−0.0838168	+	0.0930879i
$442$	0.174581	+	0.0567247i	0.00830396	+	0.00269812i
$443$	−4.98434	+	4.48792i	−0.236813	+	0.213228i	−0.778989	−	0.627037i	$-0.784267\pi$
$443$	−4.98434	+	4.48792i	−0.236813	+	0.213228i	0.542176	+	0.840265i	$0.317601\pi$
$444$	−21.1303	+	9.40780i	−1.00280	+	0.446475i
$445$		0			0
$446$	−0.684478	+	6.51237i	−0.0324110	+	0.308370i
$447$	−3.65744	+	0.384413i	−0.172991	+	0.0181821i
$448$	2.73112	+	12.8489i	0.129033	+	0.607054i
$449$	24.7774	−	18.0018i	1.16932	−	0.849560i	0.178391	−	0.983960i	$-0.442911\pi$
$449$	24.7774	−	18.0018i	1.16932	−	0.849560i	0.990927	+	0.134400i	$0.0429107\pi$
$450$		0			0
$451$	−25.2902	+	5.37561i	−1.19087	+	0.253127i
$452$	−6.21457	+	0.653178i	−0.292309	+	0.0307229i
$453$	37.7131	+	3.96380i	1.77191	+	0.186236i
$454$	9.50967	+	2.02134i	0.446311	+	0.0948663i
$455$		0			0
$456$	−13.4145	−	14.8983i	−0.628190	−	0.697675i
$457$	8.71783	+	2.83259i	0.407803	+	0.132503i	0.505733	−	0.862690i	$-0.331222\pi$
$457$	8.71783	+	2.83259i	0.407803	+	0.132503i	−0.0979301	+	0.995193i	$0.531222\pi$
$458$	−7.01529	−	6.31659i	−0.327803	−	0.295155i
$459$	0.518357	+	0.897821i	0.0241948	+	0.0419067i
$460$		0			0
$461$	1.42697	+	4.39178i	0.0664608	+	0.204545i	0.978772	−	0.204952i	$-0.0657040\pi$
$461$	1.42697	+	4.39178i	0.0664608	+	0.204545i	−0.912311	+	0.409498i	$0.865704\pi$
$462$	−3.84359	+	8.63285i	−0.178820	+	0.401636i
$463$	10.1809	−	14.0128i	0.473148	−	0.651232i	−0.504022	−	0.863691i	$-0.668147\pi$
$463$	10.1809	−	14.0128i	0.473148	−	0.651232i	0.977170	+	0.212458i	$0.0681470\pi$
$464$	15.6075			0.724561
$465$		0			0
$466$	8.49335			0.393447
$467$	9.70326	−	13.3554i	0.449013	−	0.618014i	−0.523172	−	0.852227i	$-0.675251\pi$
$467$	9.70326	−	13.3554i	0.449013	−	0.618014i	0.972185	+	0.234214i	$0.0752515\pi$
$468$	0.382217	−	0.858473i	0.0176680	−	0.0396829i
$469$	−2.08573	−	6.41920i	−0.0963099	−	0.296411i
$470$		0			0
$471$	−10.8647	−	18.8182i	−0.500619	−	0.867097i
$472$	−6.20987	−	5.59140i	−0.285833	−	0.257365i
$473$	18.1661	+	5.90252i	0.835278	+	0.271398i
$474$	7.10781	+	7.89403i	0.326473	+	0.362585i
$475$		0			0
$476$	−1.38341	−	0.294053i	−0.0634084	−	0.0134779i
$477$	−2.01978	−	0.212287i	−0.0924793	−	0.00971996i
$478$	9.35389	−	0.983133i	0.427837	−	0.0449675i
$479$	−23.8502	+	5.06952i	−1.08975	+	0.231633i	−0.717540	−	0.696518i	$-0.754732\pi$
$479$	−23.8502	+	5.06952i	−1.08975	+	0.231633i	−0.372206	+	0.928150i	$0.621398\pi$
$480$		0			0
$481$	−12.9159	+	9.38394i	−0.588914	+	0.427871i
$482$	0.739423	+	3.47871i	0.0336798	+	0.158451i
$483$	−17.1015	+	1.79744i	−0.778143	+	0.0817862i
$484$	0.443716	−	4.22168i	0.0201689	−	0.191894i
$485$		0			0
$486$	−1.15632	+	0.514826i	−0.0524517	+	0.0233530i
$487$	3.66540	−	3.30034i	0.166095	−	0.149553i	−0.581892	−	0.813266i	$-0.697687\pi$
$487$	3.66540	−	3.30034i	0.166095	−	0.149553i	0.747987	+	0.663713i	$0.231021\pi$
$488$	3.71563	+	1.20728i	0.168199	+	0.0546511i
$489$	14.8735	−	16.5187i	0.672603	−	0.747001i
$490$		0			0
$491$	6.10250	−	10.5698i	0.275402	−	0.477010i	−0.694834	−	0.719170i	$-0.744522\pi$
$491$	6.10250	−	10.5698i	0.275402	−	0.477010i	0.970236	+	0.242159i	$0.0778557\pi$
$492$	−24.6733	+	8.01684i	−1.11236	+	0.361427i
$493$	−0.447877	+	1.00595i	−0.0201713	+	0.0453056i
$494$	−5.27007	−	3.82893i	−0.237112	−	0.172272i
$495$		0			0
$496$	14.3975	−	4.75224i	0.646468	−	0.213382i
$497$		−	57.2490i		−	2.56797i
$498$	−2.40719	+	3.31322i	−0.107869	+	0.148469i
$499$	13.7476	+	6.12082i	0.615427	+	0.274006i	0.690682	−	0.723159i	$-0.257310\pi$
$499$	13.7476	+	6.12082i	0.615427	+	0.274006i	−0.0752551	+	0.997164i	$0.523977\pi$
$500$		0			0
$501$	−15.4718	+	26.7979i	−0.691228	+	1.19724i
$502$	−6.83682	+	3.94724i	−0.305142	+	0.176174i
$503$	−11.0371	−	9.93783i	−0.492119	−	0.443106i	0.385328	−	0.922780i	$-0.374088\pi$
$503$	−11.0371	−	9.93783i	−0.492119	−	0.443106i	−0.877447	+	0.479674i	$0.840755\pi$
$504$	0.590264	−	1.81665i	0.0262925	−	0.0809199i
$505$		0			0
$506$	3.16395	−	1.40868i	0.140655	−	0.0626235i
$507$	3.05214	−	14.3592i	0.135551	−	0.637715i
$508$	−25.0029	−	2.62791i	−1.10932	−	0.116595i
$509$	−4.03529	−	38.3932i	−0.178861	−	1.70175i	−0.604295	−	0.796760i	$-0.706545\pi$
$509$	−4.03529	−	38.3932i	−0.178861	−	1.70175i	0.425434	−	0.904989i	$-0.360121\pi$
$510$		0			0
$511$	28.0035	−	20.3458i	1.23880	−	0.900044i
$512$	−13.4218	−	18.4735i	−0.593164	−	0.816421i
$513$	−7.64904	−	35.9859i	−0.337713	−	1.58882i
$514$	−0.266640	−	2.53691i	−0.0117610	−	0.111898i
$515$		0			0
$516$	18.7470	+	3.98480i	0.825291	+	0.175421i
$517$	8.40016	+	18.8671i	0.369439	+	0.829773i
$518$	−11.3530	+	10.2223i	−0.498824	+	0.449143i
$519$	−6.43024	+	19.7903i	−0.282256	+	0.868696i
$520$		0			0
$521$	6.04097	+	10.4633i	0.264660	+	0.458404i	0.967474	−	0.252969i	$-0.0814070\pi$
$521$	6.04097	+	10.4633i	0.264660	+	0.458404i	−0.702815	+	0.711373i	$0.748074\pi$
$522$	−0.606315	−	0.350056i	−0.0265377	−	0.0153215i
$523$	−6.83569	+	2.22105i	−0.298904	+	0.0971197i	−0.454630	−	0.890681i	$-0.650228\pi$
$523$	−6.83569	+	2.22105i	−0.298904	+	0.0971197i	0.155726	+	0.987800i	$0.450228\pi$
$524$	−13.7063	−	6.10242i	−0.598761	−	0.266586i
$525$		0			0
$526$	−9.55517			−0.416625
$527$	−0.106859	+	1.06433i	−0.00465486	+	0.0463630i
$528$			13.2297i			0.575748i
$529$	−13.5088	−	9.81470i	−0.587338	−	0.426726i
$530$		0			0
$531$	−0.377749	−	1.16259i	−0.0163929	−	0.0504521i
$532$	43.4656	+	25.0949i	1.88447	+	1.08800i
$533$	−15.5075	+	8.95329i	−0.671707	+	0.387810i
$534$	−0.775313	+	0.861073i	−0.0335511	+	0.0372623i
$535$		0			0
$536$	1.93880	+	2.15326i	0.0837436	+	0.0930067i
$537$	11.1850	+	25.1219i	0.482669	+	1.08409i
$538$	−1.51975	+	7.14985i	−0.0655210	+	0.308252i
$539$	3.10549	−	29.5467i	0.133763	−	1.27267i
$540$		0			0
$541$	42.1938	−	8.96857i	1.81405	−	0.385589i	0.829196	−	0.558958i	$-0.188799\pi$
$541$	42.1938	−	8.96857i	1.81405	−	0.385589i	0.984857	+	0.173370i	$0.0554656\pi$
$542$	3.58221	+	4.93049i	0.153869	+	0.211783i
$543$	−0.536551	−	0.738500i	−0.0230256	−	0.0316921i
$544$	0.908182	−	0.193040i	0.0389380	−	0.00827652i
$545$		0			0
$546$	−0.684105	+	6.50882i	−0.0292770	+	0.278552i
$547$	4.81664	−	22.6605i	0.205945	−	0.968893i	−0.746783	−	0.665068i	$-0.768403\pi$
$547$	4.81664	−	22.6605i	0.205945	−	0.968893i	0.952728	−	0.303825i	$-0.0982639\pi$
$548$	12.2609	+	27.5384i	0.523760	+	1.17638i
$549$	0.382427	+	0.424728i	0.0163216	+	0.0181270i
$550$		0			0
$551$	26.1472	−	29.0394i	1.11391	−	1.23712i
$552$	6.39290	−	3.69094i	0.272100	−	0.157097i
$553$	−48.9219	−	28.2451i	−2.08037	−	1.20110i
$554$	−0.403867	−	1.24298i	−0.0171587	−	0.0528090i
$555$		0			0
$556$	−18.4834	−	13.4290i	−0.783872	−	0.569516i
$557$			8.14169i			0.344975i	0.985012	+	0.172487i	$0.0551804\pi$
$557$			8.14169i			0.344975i	−0.985012	+	0.172487i	$0.944820\pi$
$558$	−0.665896	−	0.138304i	−0.0281896	−	0.00585488i
$559$	13.2288			0.559517
$560$		0			0
$561$	−0.852689	−	0.379641i	−0.0360005	−	0.0160285i
$562$	3.19718	−	1.03883i	0.134865	−	0.0438202i
$563$	3.04172	+	1.75614i	0.128193	+	0.0740124i	0.562725	−	0.826644i	$-0.309753\pi$
$563$	3.04172	+	1.75614i	0.128193	+	0.0740124i	−0.434532	+	0.900656i	$0.643086\pi$
$564$	10.3614	+	17.9464i	0.436292	+	0.755680i
$565$		0			0
$566$	−0.846255	+	2.60451i	−0.0355708	+	0.109476i
$567$	−25.0709	+	22.5739i	−1.05288	+	0.948017i
$568$	9.99607	+	22.4515i	0.419426	+	0.942046i
$569$	−21.0750	−	4.47963i	−0.883510	−	0.187796i	−0.256254	−	0.966609i	$-0.582489\pi$
$569$	−21.0750	−	4.47963i	−0.883510	−	0.187796i	−0.627256	+	0.778814i	$0.715822\pi$
$570$		0			0
$571$	0.179305	+	1.70597i	0.00750368	+	0.0713928i	0.997633	−	0.0687647i	$-0.0219058\pi$
$571$	0.179305	+	1.70597i	0.00750368	+	0.0713928i	−0.990129	+	0.140157i	$0.955239\pi$
$572$	2.20664	+	10.3814i	0.0922642	+	0.434069i
$573$	15.1426	+	20.8420i	0.632590	+	0.870685i
$574$	−13.8625	+	10.0717i	−0.578611	+	0.420386i
$575$		0			0
$576$	−0.0862296	−	0.820420i	−0.00359290	−	0.0341841i
$577$	−11.9040	−	1.25116i	−0.495568	−	0.0520863i	−0.146552	−	0.989203i	$-0.546818\pi$
$577$	−11.9040	−	1.25116i	−0.495568	−	0.0520863i	−0.349016	+	0.937117i	$0.613484\pi$
$578$	1.65781	−	7.79940i	0.0689559	−	0.324412i
$579$	13.5291	−	6.02352i	0.562248	−	0.250329i
$580$		0			0
$581$	6.73011	−	20.7132i	0.279212	−	0.859326i
$582$	−4.52010	−	4.06991i	−0.187364	−	0.168703i
$583$	19.8644	−	11.4687i	0.822700	−	0.474986i
$584$	−7.42974	+	12.8687i	−0.307445	+	0.532510i
$585$		0			0
$586$	10.1965	+	4.53977i	0.421213	+	0.187536i
$587$	−25.3329	+	34.8677i	−1.04560	+	1.43914i	−0.153037	+	0.988220i	$0.548905\pi$
$587$	−25.3329	+	34.8677i	−1.04560	+	1.43914i	−0.892563	+	0.450924i	$0.851095\pi$
$588$		−	29.8104i		−	1.22936i
$589$	15.2780	−	34.7494i	0.629521	−	1.43183i
$590$		0			0
$591$	17.3841	+	12.6303i	0.715087	+	0.519541i
$592$	−8.69917	+	19.5386i	−0.357534	+	0.803033i
$593$	13.4182	−	4.35984i	0.551020	−	0.179037i	−0.0202567	−	0.999795i	$-0.506448\pi$
$593$	13.4182	−	4.35984i	0.551020	−	0.179037i	0.571277	+	0.820758i	$0.306448\pi$
$594$	3.72227	−	6.44716i	0.152727	−	0.264530i
$595$		0			0
$596$	−2.64469	+	2.93723i	−0.108331	+	0.120313i
$597$	5.53973	+	1.79997i	0.226726	+	0.0736678i
$598$	1.78253	−	1.60500i	0.0728931	−	0.0656332i
$599$	29.1370	−	12.9726i	1.19051	−	0.530047i	0.286712	−	0.958017i	$-0.407438\pi$
$599$	29.1370	−	12.9726i	1.19051	−	0.530047i	0.903793	+	0.427970i	$0.140771\pi$
$600$		0			0
$601$	0.814514	−	7.74958i	0.0332247	−	0.316112i	−0.965270	−	0.261256i	$-0.915863\pi$
$601$	0.814514	−	7.74958i	0.0332247	−	0.316112i	0.998494	−	0.0548560i	$-0.0174700\pi$
$602$	12.5894	−	1.32320i	0.513107	−	0.0539297i
$603$	0.0881279	+	0.414609i	0.00358884	+	0.0168842i
$604$	32.9713	−	23.9551i	1.34158	−	0.974717i
$605$		0			0
$606$	−9.10071	+	1.93442i	−0.369691	+	0.0785803i
$607$	−31.2237	+	3.28174i	−1.26733	+	0.133202i	−0.714229	−	0.699912i	$-0.753223\pi$
$607$	−31.2237	+	3.28174i	−1.26733	+	0.133202i	−0.553102	+	0.833114i	$0.686556\pi$
$608$	−32.7681	−	3.44407i	−1.32892	−	0.139675i
$609$	−38.4014	−	8.16248i	−1.55610	−	0.330760i
$610$		0			0
$611$	9.57082	+	10.6295i	0.387194	+	0.430023i
$612$	0.0844718	+	0.0274466i	0.00341457	+	0.00110946i
$613$	7.47353	+	6.72920i	0.301853	+	0.271790i	0.806112	−	0.591763i	$-0.201568\pi$
$613$	7.47353	+	6.72920i	0.301853	+	0.271790i	−0.504259	+	0.863552i	$0.668234\pi$
$614$	−3.01980	−	5.23045i	−0.121869	−	0.211084i
$615$		0			0
$616$	6.66657	+	20.5176i	0.268604	+	0.826677i
$617$	11.7101	−	26.3014i	0.471432	−	1.05885i	−0.508779	−	0.860897i	$-0.669903\pi$
$617$	11.7101	−	26.3014i	0.471432	−	1.05885i	0.980211	−	0.197956i	$-0.0634304\pi$
$618$	−4.07511	+	5.60891i	−0.163925	+	0.225623i
$619$	−5.49470			−0.220851			−0.110425	−	0.993884i	$-0.535221\pi$
$619$	−5.49470			−0.220851			−0.110425	+	0.993884i	$0.535221\pi$
$620$		0			0
$621$	13.5467			0.543609
$622$	9.69448	−	13.3433i	0.388713	−	0.535018i
$623$	2.50627	−	5.62917i	0.100411	−	0.225528i
$624$	2.83136	+	8.71404i	0.113345	+	0.348841i
$625$		0			0
$626$	−4.66842	−	8.08595i	−0.186588	−	0.323179i
$627$	24.6152	+	22.1636i	0.983035	+	0.885129i
$628$	−22.2103	−	7.21657i	−0.886288	−	0.287972i
$629$	−1.00969	−	1.12137i	−0.0402588	−	0.0447119i
$630$		0			0
$631$	17.9688	+	3.81939i	0.715327	+	0.152048i	0.551178	−	0.834388i	$-0.314179\pi$
$631$	17.9688	+	3.81939i	0.715327	+	0.152048i	0.164150	+	0.986435i	$0.447512\pi$
$632$	24.1177	+	2.53487i	0.959350	+	0.100832i
$633$	16.6053	−	1.74529i	0.660001	−	0.0693689i
$634$	2.48170	−	0.527501i	0.0985607	−	0.0209497i
$635$		0			0
$636$	18.6198	−	13.5281i	0.738323	−	0.536423i
$637$	−4.27797	−	20.1263i	−0.169499	−	0.797432i
$638$	7.86390	−	0.826529i	0.311335	−	0.0327226i
$639$	−0.375804	+	3.57554i	−0.0148666	+	0.141446i
$640$		0			0
$641$	−33.5694	+	14.9461i	−1.32591	+	0.590334i	−0.942797	−	0.333367i	$-0.891815\pi$
$641$	−33.5694	+	14.9461i	−1.32591	+	0.590334i	−0.383115	+	0.923701i	$0.625149\pi$
$642$	−8.84993	+	7.96852i	−0.349279	+	0.314492i
$643$	−31.7175	−	10.3056i	−1.25081	−	0.406414i	−0.392602	−	0.919709i	$-0.628425\pi$
$643$	−31.7175	−	10.3056i	−1.25081	−	0.406414i	−0.858213	+	0.513294i	$0.828425\pi$
$644$	−12.3660	+	13.7339i	−0.487290	+	0.541191i
$645$		0			0
$646$	0.307849	−	0.533210i	0.0121122	−	0.0209789i
$647$	−38.2080	+	12.4145i	−1.50211	+	0.488066i	−0.940633	−	0.339424i	$-0.889768\pi$
$647$	−38.2080	+	12.4145i	−1.50211	+	0.488066i	−0.561480	+	0.827490i	$0.689768\pi$
$648$	5.89058	−	13.2305i	0.231404	−	0.519742i
$649$	11.1695	+	8.11512i	0.438441	+	0.318546i
$650$		0			0
$651$	−37.9096	+	4.16296i	−1.48580	+	0.163159i
$652$		−	23.8893i		−	0.935577i
$653$	10.0217	−	13.7937i	0.392180	−	0.539789i	−0.566580	−	0.824007i	$-0.691734\pi$
$653$	10.0217	−	13.7937i	0.392180	−	0.539789i	0.958760	+	0.284217i	$0.0917337\pi$
$654$	−3.58737	−	1.59720i	−0.140277	−	0.0624554i
$655$		0			0
$656$	−11.9945	+	20.7750i	−0.468305	+	0.811127i
$657$	−1.88254	+	1.08689i	−0.0734451	+	0.0424035i
$658$	10.1715	+	9.15845i	0.396526	+	0.357033i
$659$	−1.80245	+	5.54737i	−0.0702134	+	0.216095i	−0.980006	−	0.198969i	$-0.936241\pi$
$659$	−1.80245	+	5.54737i	−0.0702134	+	0.216095i	0.909792	+	0.415064i	$0.136241\pi$
$660$		0			0
$661$	−23.8585	+	10.6225i	−0.927989	+	0.413167i	−0.814363	−	0.580356i	$-0.802913\pi$
$661$	−23.8585	+	10.6225i	−0.927989	+	0.413167i	−0.113626	+	0.993524i	$0.536247\pi$
$662$	0.737107	−	3.46781i	0.0286485	−	0.134780i
$663$	−0.642893	−	0.0675708i	−0.0249679	−	0.00262423i
$664$	0.977288	+	9.29828i	0.0379261	+	0.360843i
$665$		0			0
$666$	0.776168	−	0.563919i	0.0300759	−	0.0218514i
$667$	8.45741	+	11.6406i	0.327472	+	0.450727i
$668$	6.91433	+	32.5293i	0.267523	+	1.25860i
$669$	−2.41043	−	22.9337i	−0.0931925	−	0.886667i
$670$		0			0
$671$	−6.31390	−	1.34206i	−0.243745	−	0.0518097i
$672$	13.4642	+	30.2410i	0.519392	+	1.16657i
$673$	1.22624	−	1.10411i	0.0472680	−	0.0425603i	−0.645158	−	0.764049i	$-0.723209\pi$
$673$	1.22624	−	1.10411i	0.0472680	−	0.0425603i	0.692426	+	0.721489i	$0.256542\pi$
$674$	0.271934	−	0.836926i	0.0104745	−	0.0322372i
$675$		0			0
$676$	−7.88855	−	13.6634i	−0.303406	−	0.525514i
$677$	37.7718	+	21.8076i	1.45169	+	0.838133i	0.998577	−	0.0533208i	$-0.0169806\pi$
$677$	37.7718	+	21.8076i	1.45169	+	0.838133i	0.453112	+	0.891454i	$0.350314\pi$
$678$	−2.59929	+	0.844559i	−0.0998250	+	0.0324351i
$679$	29.5496	+	13.1563i	1.13401	+	0.504894i
$680$		0			0
$681$	−34.2370			−1.31196
$682$	7.00257	−	3.15688i	0.268142	−	0.120883i
$683$		−	16.6116i		−	0.635627i	−0.948153	−	0.317814i	$-0.897051\pi$
$683$		−	16.6116i		−	0.635627i	0.948153	−	0.317814i	$-0.102949\pi$
$684$	−2.54995	−	1.85265i	−0.0974999	−	0.0708378i
$685$		0			0
$686$	−1.87691	−	5.77653i	−0.0716607	−	0.220549i
$687$	28.7897	+	16.6217i	1.09840	+	0.634159i
$688$	15.3479	−	8.86109i	0.585131	−	0.337826i
$689$	10.6297	−	11.8054i	0.404958	−	0.449752i
$690$		0			0
$691$	−18.4384	−	20.4780i	−0.701432	−	0.779019i	0.282172	−	0.959364i	$-0.408945\pi$
$691$	−18.4384	−	20.4780i	−0.701432	−	0.779019i	−0.983603	+	0.180345i	$0.942279\pi$
$692$	9.09618	+	20.4304i	0.345785	+	0.776646i
$693$	−0.656160	+	3.08699i	−0.0249255	+	0.117265i
$694$	−0.918117	+	8.73530i	−0.0348512	+	0.331587i
$695$		0			0
$696$	16.4853	−	3.50405i	0.624872	−	0.132821i
$697$	−0.994810	−	1.36924i	−0.0376811	−	0.0518636i
$698$	0.412449	+	0.567687i	0.0156114	+	0.0214873i
$699$	−29.2562	+	6.21860i	−1.10657	+	0.235209i
$700$		0			0
$701$	−1.86978	+	17.7898i	−0.0706206	+	0.671910i	0.900750	+	0.434339i	$0.143018\pi$
$701$	−1.86978	+	17.7898i	−0.0706206	+	0.671910i	−0.971370	+	0.237571i	$0.923649\pi$
$702$	1.07197	−	5.04320i	0.0404587	−	0.190343i
$703$	21.7800	+	48.9187i	0.821448	+	1.84500i
$704$	6.23431	+	6.92390i	0.234964	+	0.260954i
$705$		0			0
$706$	−2.00419	+	2.22588i	−0.0754286	+	0.0837719i
$707$	42.8499	−	24.7394i	1.61154	−	0.930420i
$708$	11.9972	+	6.92658i	0.450882	+	0.260317i
$709$	−1.19405	−	3.67492i	−0.0448436	−	0.138014i	0.926128	−	0.377210i	$-0.123116\pi$
$709$	−1.19405	−	3.67492i	−0.0448436	−	0.138014i	−0.970971	+	0.239195i	$0.923116\pi$
$710$		0			0
$711$	2.87005	+	2.08522i	0.107635	+	0.0782017i
$712$			2.64522i			0.0991339i
$713$	11.3461	+	8.16302i	0.424915	+	0.305707i
$714$	−0.618581			−0.0231498
$715$		0			0
$716$	26.9994	+	12.0209i	1.00901	+	0.449242i
$717$	−31.5006	+	10.2352i	−1.17641	+	0.382239i
$718$	8.16898	+	4.71637i	0.304864	+	0.176013i
$719$	−18.5818	−	32.1846i	−0.692984	−	1.20028i	−0.970856	−	0.239665i	$-0.922962\pi$
$719$	−18.5818	−	32.1846i	−0.692984	−	1.20028i	0.277872	−	0.960618i	$-0.410371\pi$
$720$		0			0
$721$	11.3933	−	35.0651i	0.424310	−	1.30589i
$722$	−9.60005	+	8.64393i	−0.357277	+	0.321694i
$723$	−5.09403	−	11.4414i	−0.189449	−	0.425510i
$724$	−0.959617	−	0.203973i	−0.0356639	−	0.00758059i
$725$		0			0
$726$	−0.194069	−	1.84644i	−0.00720257	−	0.0685279i
$727$	5.67306	+	26.6896i	0.210402	+	0.989863i	0.948892	+	0.315600i	$0.102206\pi$
$727$	5.67306	+	26.6896i	0.210402	+	0.989863i	−0.738491	+	0.674264i	$0.764461\pi$
$728$	8.78218	+	12.0876i	0.325489	+	0.447998i
$729$	23.3936	−	16.9964i	0.866429	−	0.629497i
$730$		0			0
$731$	0.130696	+	1.24349i	0.00483397	+	0.0459922i
$732$	−6.44140	−	0.677018i	−0.238081	−	0.0250233i
$733$	−6.03998	+	28.4159i	−0.223092	+	1.04956i	0.713910	+	0.700238i	$0.246923\pi$
$733$	−6.03998	+	28.4159i	−0.223092	+	1.04956i	−0.937001	+	0.349326i	$0.886411\pi$
$734$	−13.0886	+	5.82744i	−0.483110	+	0.215095i
$735$		0			0
$736$	3.74908	−	11.5385i	0.138193	−	0.425314i
$737$	−3.55765	−	3.20332i	−0.131048	−	0.117996i
$738$	0.931912	−	0.538040i	0.0343042	−	0.0198055i
$739$	−19.8898	+	34.4501i	−0.731658	+	1.26727i	0.224516	+	0.974470i	$0.427920\pi$
$739$	−19.8898	+	34.4501i	−0.731658	+	1.26727i	−0.956174	+	0.292799i	$0.905413\pi$
$740$		0			0
$741$	20.9567	+	9.33054i	0.769865	+	0.342766i
$742$	8.93511	−	12.2981i	0.328018	−	0.451479i
$743$		−	31.2123i		−	1.14507i	−0.819880	−	0.572535i	$-0.805960\pi$
$743$		−	31.2123i		−	1.14507i	0.819880	−	0.572535i	$-0.194040\pi$
$744$	14.1403	−	8.25189i	0.518408	−	0.302529i
$745$		0			0
$746$	−11.3883	−	8.27411i	−0.416957	−	0.302937i
$747$	−0.556304	+	1.24948i	−0.0203541	+	0.0457161i
$748$	−0.954042	+	0.309987i	−0.0348832	+	0.0113342i
$749$	31.6654	−	54.8460i	1.15703	−	2.00403i
$750$		0			0
$751$	−12.3876	+	13.7579i	−0.452031	+	0.502031i	−0.925483	−	0.378788i	$-0.876341\pi$
$751$	−12.3876	+	13.7579i	−0.452031	+	0.502031i	0.473452	+	0.880819i	$0.343008\pi$
$752$	18.2240	+	5.92132i	0.664559	+	0.215928i
$753$	20.6600	−	18.6024i	0.752894	−	0.677909i
$754$	5.00285	−	2.22741i	0.182193	−	0.0811176i
$755$		0			0
$756$	−4.15234	+	39.5068i	−0.151019	+	1.43685i
$757$	28.8703	−	3.03439i	1.04931	−	0.110287i	0.435855	−	0.900017i	$-0.356446\pi$
$757$	28.8703	−	3.03439i	1.04931	−	0.110287i	0.613455	+	0.789730i	$0.289779\pi$
$758$	2.45009	+	11.5268i	0.0889914	+	0.418672i
$759$	−9.86715	+	7.16890i	−0.358155	+	0.260215i
$760$		0			0
$761$	−35.9040	+	7.63164i	−1.30152	+	0.276647i	−0.805982	−	0.591940i	$-0.798362\pi$
$761$	−35.9040	+	7.63164i	−1.30152	+	0.276647i	−0.495538	+	0.868586i	$0.665029\pi$
$762$	−10.9356	+	1.14937i	−0.396154	+	0.0416374i
$763$	20.7686	+	2.18287i	0.751874	+	0.0790252i
$764$	27.0823	+	5.75653i	0.979805	+	0.208264i
$765$		0			0
$766$	−1.08575	−	1.20585i	−0.0392299	−	0.0435692i
$767$	9.09382	+	2.95476i	0.328359	+	0.106690i
$768$	1.35839	+	1.22310i	0.0490168	+	0.0441349i
$769$	−8.18667	−	14.1797i	−0.295219	−	0.511334i	0.679817	−	0.733382i	$-0.262059\pi$
$769$	−8.18667	−	14.1797i	−0.295219	−	0.511334i	−0.975036	+	0.222048i	$0.928726\pi$
$770$		0			0
$771$	2.77592	+	8.54341i	0.0999724	+	0.307683i
$772$	6.47368	−	14.5401i	0.232993	−	0.523311i
$773$	−9.36312	+	12.8872i	−0.336768	+	0.463521i	−0.943494	−	0.331390i	$-0.892482\pi$
$773$	−9.36312	+	12.8872i	−0.336768	+	0.463521i	0.606726	+	0.794911i	$0.292482\pi$
$774$	−0.794971			−0.0285746
$775$		0			0
$776$	−13.8858			−0.498470
$777$	31.6222	−	43.5242i	1.13444	−	1.56142i
$778$	−5.91247	+	13.2796i	−0.211972	+	0.476098i
$779$	18.5598	+	57.1211i	0.664973	+	2.04658i
$780$		0			0
$781$	−20.3027	−	35.1652i	−0.726486	−	1.25831i
$782$	0.168479	+	0.151699i	0.00602480	+	0.00542475i
$783$	29.4146	+	9.55739i	1.05119	+	0.341553i
$784$	−18.4445	−	20.4847i	−0.658733	−	0.731597i
$785$		0			0
$786$	−6.41866	−	1.36433i	−0.228946	−	0.0486639i
$787$	26.2854	+	2.76271i	0.936974	+	0.0984800i	0.560691	−	0.828025i	$-0.310535\pi$
$787$	26.2854	+	2.76271i	0.936974	+	0.0984800i	0.376283	+	0.926505i	$0.377202\pi$
$788$	22.9673	−	2.41396i	0.818176	−	0.0859938i
$789$	32.9137	−	6.99603i	1.17176	−	0.249065i
$790$		0			0
$791$	11.7585	−	8.54307i	0.418085	−	0.303757i
$792$	−0.281681	−	1.32521i	−0.0100091	−	0.0470892i
$793$	−4.44602	+	0.467296i	−0.157883	+	0.0165942i
$794$	0.0401880	−	0.382363i	0.00142622	−	0.0135696i
$795$		0			0
$796$	5.71891	−	2.54622i	0.202701	−	0.0902485i
$797$	−7.69252	+	6.92638i	−0.272483	+	0.245345i	−0.794031	−	0.607877i	$-0.792021\pi$
$797$	−7.69252	+	6.92638i	−0.272483	+	0.245345i	0.521548	+	0.853222i	$0.325355\pi$
$798$	20.8772	+	6.78341i	0.739045	+	0.240130i
$799$	−0.904604	+	1.00466i	−0.0320026	+	0.0355425i
$800$		0			0
$801$	−0.193483	+	0.335123i	−0.00683640	+	0.0118410i
$802$	−7.36185	+	2.39201i	−0.259956	+	0.0844649i
$803$	9.98582	−	22.4285i	0.352392	−	0.791485i
$804$	−3.88616	−	2.82346i	−0.137054	−	0.0995757i
$805$		0			0
$806$	3.93679	−	3.57802i	0.138667	−	0.126030i
$807$		−	25.7411i		−	0.906130i
$808$	−12.4849	+	17.1840i	−0.439218	+	0.604532i
$809$	22.7087	+	10.1106i	0.798396	+	0.355469i	0.765047	−	0.643975i	$-0.222716\pi$
$809$	22.7087	+	10.1106i	0.798396	+	0.355469i	0.0333497	+	0.999444i	$0.489382\pi$
$810$		0			0
$811$	−18.6645	+	32.3279i	−0.655400	+	1.13519i	0.326393	+	0.945234i	$0.394167\pi$
$811$	−18.6645	+	32.3279i	−0.655400	+	1.13519i	−0.981793	+	0.189952i	$0.939167\pi$
$812$	−36.5405	+	21.0967i	−1.28232	+	0.740348i
$813$	−15.9493	−	14.3608i	−0.559365	−	0.503655i
$814$	−3.34839	+	10.3053i	−0.117361	+	0.361200i
$815$		0			0
$816$	−0.791138	+	0.352237i	−0.0276954	+	0.0123308i
$817$	9.22520	−	43.4012i	0.322749	−	1.51841i
$818$	17.5719	+	1.84688i	0.614386	+	0.0645745i
$819$	0.228470	+	2.17375i	0.00798340	+	0.0759569i
$820$		0			0
$821$	8.62910	−	6.26941i	0.301158	−	0.218804i	−0.426935	−	0.904282i	$-0.640407\pi$
$821$	8.62910	−	6.26941i	0.301158	−	0.218804i	0.728093	+	0.685478i	$0.240407\pi$
$822$	7.74958	+	10.6664i	0.270298	+	0.372033i
$823$	−7.31302	−	34.4050i	−0.254916	−	1.19928i	−0.900246	−	0.435381i	$-0.856614\pi$
$823$	−7.31302	−	34.4050i	−0.254916	−	1.19928i	0.645331	−	0.763903i	$-0.276720\pi$
$824$	1.65444	+	15.7410i	0.0576352	+	0.548362i
$825$		0			0
$826$	8.94988	+	1.90236i	0.311406	+	0.0661914i
$827$	−16.3023	−	36.6155i	−0.566886	−	1.27325i	−0.938635	−	0.344913i	$-0.887908\pi$
$827$	−16.3023	−	36.6155i	−0.566886	−	1.27325i	0.371749	−	0.928333i	$-0.378758\pi$
$828$	0.862487	−	0.776587i	0.0299735	−	0.0269883i
$829$	−6.63136	+	20.4092i	−0.230317	+	0.708842i	0.767392	+	0.641179i	$0.221554\pi$
$829$	−6.63136	+	20.4092i	−0.230317	+	0.708842i	−0.997708	+	0.0676630i	$0.978446\pi$
$830$		0			0
$831$	2.30123	+	3.98585i	0.0798289	+	0.138268i
$832$	5.58820	+	3.22635i	0.193736	+	0.111854i
$833$	1.84958	−	0.600966i	0.0640843	−	0.0208223i
$834$	−9.12864	−	4.06433i	−0.316099	−	0.140736i
$835$		0			0
$836$	35.5984			1.23120
$837$	30.0443	−	0.139849i	1.03848	−	0.00483387i
$838$			3.95658i			0.136678i
$839$	30.4163	+	22.0987i	1.05009	+	0.762933i	0.972229	−	0.234031i	$-0.0751918\pi$
$839$	30.4163	+	22.0987i	1.05009	+	0.762933i	0.0778583	+	0.996964i	$0.475192\pi$
$840$		0			0
$841$	1.18989	+	3.66211i	0.0410307	+	0.126279i
$842$	2.16640	+	1.25077i	0.0746589	+	0.0431043i
$843$	−10.2524	+	5.91922i	−0.353111	+	0.203869i
$844$	12.0073	−	13.3354i	0.413307	−	0.459024i
$845$		0			0
$846$	−0.575150	−	0.638769i	−0.0197741	−	0.0219613i
$847$	4.01589	+	9.01985i	0.137988	+	0.309926i
$848$	4.42472	−	20.8167i	0.151945	−	0.714847i
$849$	1.00806	−	9.59109i	0.0345967	−	0.329165i
$850$		0			0
$851$	−19.2865	+	4.09947i	−0.661133	+	0.140528i
$852$	−23.9483	−	32.9620i	−0.820454	−	1.12926i
$853$	−7.58739	−	10.4431i	−0.259787	−	0.357566i	0.659122	−	0.752036i	$-0.270928\pi$
$853$	−7.58739	−	10.4431i	−0.259787	−	0.357566i	−0.918909	+	0.394470i	$0.870928\pi$
$854$	−4.18441	+	0.889423i	−0.143188	+	0.0304354i
$855$		0			0
$856$	−2.84182	+	27.0381i	−0.0971315	+	0.924145i
$857$	−3.58211	+	16.8525i	−0.122363	+	0.575671i	0.873658	+	0.486541i	$0.161742\pi$
$857$	−3.58211	+	16.8525i	−0.122363	+	0.575671i	−0.996020	+	0.0891292i	$0.971592\pi$
$858$	1.88806	+	4.24066i	0.0644574	+	0.144774i
$859$	24.8392	+	27.5867i	0.847501	+	0.941246i	0.998884	−	0.0472295i	$-0.0150392\pi$
$859$	24.8392	+	27.5867i	0.847501	+	0.941246i	−0.151383	+	0.988475i	$0.548373\pi$
$860$		0			0
$861$	40.3767	−	44.8428i	1.37603	−	1.52824i
$862$	−8.38747	+	4.84251i	−0.285678	+	0.164936i
$863$	32.3554	+	18.6804i	1.10139	+	0.635888i	0.936586	−	0.350438i	$-0.113967\pi$
$863$	32.3554	+	18.6804i	1.10139	+	0.635888i	0.164805	+	0.986326i	$0.447301\pi$
$864$	−8.05866	−	24.8020i	−0.274161	−	0.843781i
$865$		0			0
$866$	7.86427	+	5.71373i	0.267239	+	0.194160i
$867$			28.0796i			0.953634i
$868$	−27.2840	+	30.5871i	−0.926081	+	1.03819i
$869$	−40.0671			−1.35918
$870$		0			0
$871$	−3.02889	−	1.34855i	−0.102630	−	0.0456939i
$872$	−8.52605	+	2.77028i	−0.288728	+	0.0938136i
$873$	−1.75919	−	1.01567i	−0.0595395	−	0.0343751i
$874$	−4.02264	−	6.96742i	−0.136068	−	0.235676i
$875$		0			0
$876$	7.61246	−	23.4288i	0.257201	−	0.791584i
$877$	−29.5901	+	26.6431i	−0.999187	+	0.899672i	−0.994955	−	0.100319i	$-0.968014\pi$
$877$	−29.5901	+	26.6431i	−0.999187	+	0.899672i	−0.00423173	+	0.999991i	$0.501347\pi$
$878$	−3.76250	−	8.45071i	−0.126978	−	0.285198i
$879$	−38.4468	−	8.17211i	−1.29678	−	0.275639i
$880$		0			0
$881$	1.99969	+	19.0258i	0.0673712	+	0.640994i	0.975150	+	0.221545i	$0.0711101\pi$
$881$	1.99969	+	19.0258i	0.0673712	+	0.640994i	−0.907779	+	0.419449i	$0.862223\pi$
$882$	0.257081	+	1.20947i	0.00865636	+	0.0407250i
$883$	−15.9477	−	21.9502i	−0.536684	−	0.738682i	0.451447	−	0.892298i	$-0.350908\pi$
$883$	−15.9477	−	21.9502i	−0.536684	−	0.738682i	−0.988131	+	0.153616i	$0.950908\pi$
$884$	−0.562060	+	0.408361i	−0.0189041	+	0.0137347i
$885$		0			0
$886$	0.329549	+	3.13545i	0.0110714	+	0.105338i
$887$	33.2023	+	3.48970i	1.11482	+	0.117173i	0.643978	−	0.765044i	$-0.277283\pi$
$887$	33.2023	+	3.48970i	1.11482	+	0.117173i	0.470844	+	0.882216i	$0.343949\pi$
$888$	−4.80176	+	22.5905i	−0.161137	+	0.758088i
$889$	53.4201	−	23.7842i	1.79165	−	0.797695i
$890$		0			0
$891$	−7.39425	+	22.7572i	−0.247717	+	0.762394i
$892$	−18.4176	−	16.5833i	−0.616668	−	0.555250i
$893$	41.5477	−	23.9876i	1.39034	−	0.802714i
$894$	−0.864340	+	1.49708i	−0.0289078	+	0.0500699i
$895$		0			0
$896$	42.1785	+	18.7791i	1.40908	+	0.627365i
$897$	−4.96497	+	6.83370i	−0.165776	+	0.228170i
$898$		−	14.3963i		−	0.480410i
$899$	18.8773	+	25.7297i	0.629593	+	0.858132i
$900$		0			0
$901$	1.21472	+	0.882544i	0.0404681	+	0.0294018i
$902$	−4.94326	+	11.1027i	−0.164593	+	0.369681i
$903$	−42.3967	+	13.7755i	−1.41088	+	0.458421i
$904$	−3.11971	+	5.40349i	−0.103760	+	0.179717i
$905$		0			0
$906$	11.9272	−	13.2465i	0.396256	−	0.440087i
$907$	11.6469	+	3.78431i	0.386729	+	0.125656i	0.495927	−	0.868364i	$-0.334828\pi$
$907$	11.6469	+	3.78431i	0.386729	+	0.125656i	−0.109198	+	0.994020i	$0.534828\pi$
$908$	−27.3445	+	24.6211i	−0.907459	+	0.817080i
$909$	−2.83863	+	1.26384i	−0.0941513	+	0.0419189i
$910$		0			0
$911$	−0.769337	+	7.31975i	−0.0254893	+	0.242514i	0.974357	+	0.225006i	$0.0722401\pi$
$911$	−0.769337	+	7.31975i	−0.0254893	+	0.242514i	−0.999847	+	0.0175085i	$0.994427\pi$
$912$	30.5637	−	3.21237i	1.01206	−	0.106372i
$913$	−3.21169	−	15.1098i	−0.106291	−	0.500062i
$914$	3.48587	−	2.53263i	0.115302	−	0.0837720i
$915$		0			0
$916$	34.9471	−	7.42825i	1.15469	−	0.245436i
$917$	34.7058	−	3.64772i	1.14609	−	0.120458i
$918$	0.484646	+	0.0509384i	0.0159957	+	0.00168122i
$919$	−28.3046	−	6.01632i	−0.933682	−	0.198460i	−0.284137	−	0.958784i	$-0.591707\pi$
$919$	−28.3046	−	6.01632i	−0.933682	−	0.198460i	−0.649545	+	0.760323i	$0.725040\pi$
$920$		0			0
$921$	14.2316	+	15.8058i	0.468947	+	0.520819i
$922$	2.06439	+	0.670761i	0.0679871	+	0.0220903i
$923$	−20.8988	−	18.8173i	−0.687891	−	0.619380i
$924$	−17.8825	−	30.9735i	−0.588292	−	1.01895i
$925$		0			0
$926$	−2.51595	−	7.74331i	−0.0826794	−	0.254461i
$927$	−0.941762	+	2.11523i	−0.0309315	+	0.0694734i
$928$	16.2811	−	22.4091i	0.534455	−	0.735614i
$929$	−11.9900			−0.393378			−0.196689	−	0.980466i	$-0.563019\pi$
$929$	−11.9900			−0.393378			−0.196689	+	0.980466i	$0.563019\pi$
$930$		0			0
$931$	−69.0139			−2.26184
$932$	−18.8944	+	26.0059i	−0.618907	+	0.851852i
$933$	−23.6240	+	53.0604i	−0.773416	+	1.73712i
$934$	−2.39791	−	7.38001i	−0.0784620	−	0.241481i
$935$		0			0
$936$	−0.469152	−	0.812595i	−0.0153347	−	0.0265605i
$937$	20.9351	+	18.8501i	0.683920	+	0.615804i	0.936041	−	0.351891i	$-0.114461\pi$
$937$	20.9351	+	18.8501i	0.683920	+	0.615804i	−0.252121	+	0.967696i	$0.581128\pi$
$938$	−3.01740	−	0.980413i	−0.0985216	−	0.0320116i
$939$	22.0012	+	24.4348i	0.717981	+	0.797398i
$940$		0			0
$941$	0.265776	+	0.0564923i	0.00866404	+	0.00184160i	0.212242	−	0.977217i	$-0.431924\pi$
$941$	0.265776	+	0.0564923i	0.00866404	+	0.00184160i	−0.203578	+	0.979059i	$0.565257\pi$
$942$	−10.1581	−	1.06766i	−0.330969	−	0.0347863i
$943$	−21.9943	+	2.31169i	−0.716232	+	0.0752790i
$944$	12.5298	−	2.66328i	0.407809	−	0.0866824i
$945$		0			0
$946$	7.26381	−	5.27747i	0.236167	−	0.171585i
$947$	6.66928	+	31.3765i	0.216722	+	1.01960i	0.943153	+	0.332359i	$0.107844\pi$
$947$	6.66928	+	31.3765i	0.216722	+	1.01960i	−0.726431	+	0.687240i	$0.758822\pi$
$948$	−39.9830	+	4.20238i	−1.29859	+	0.136487i
$949$	1.77733	−	16.9102i	0.0576947	−	0.548928i
$950$		0			0
$951$	−8.16223	+	3.63406i	−0.264678	+	0.117842i
$952$	−1.04946	+	0.944939i	−0.0340132	+	0.0306256i
$953$	−32.3171	−	10.5005i	−1.04685	−	0.340144i	−0.265421	−	0.964133i	$-0.585511\pi$
$953$	−32.3171	−	10.5005i	−1.04685	−	0.340144i	−0.781433	+	0.623989i	$0.785511\pi$
$954$	−0.638781	+	0.709438i	−0.0206813	+	0.0229689i
$955$		0			0
$956$	−17.7985	+	30.8279i	−0.575644	+	0.997045i
$957$	−26.4828	+	8.60480i	−0.856069	+	0.278154i
$958$	−4.66180	+	10.4706i	−0.150616	+	0.338289i
$959$	−56.7238	−	41.2122i	−1.83171	−	1.33081i
$960$		0			0
$961$	25.2481	+	17.9871i	0.814454	+	0.580228i
$962$			7.50444i			0.241953i
$963$	−2.33772	+	3.21760i	−0.0753320	+	0.103686i
$964$	−12.2964	−	5.47473i	−0.396042	−	0.176329i
$965$		0			0
$966$	−4.04148	+	7.00005i	−0.130032	+	0.225223i
$967$	−34.4182	+	19.8713i	−1.10681	+	0.639019i	−0.938002	−	0.346629i	$-0.887326\pi$
$967$	−34.4182	+	19.8713i	−1.10681	+	0.639019i	−0.168811	+	0.985648i	$0.553993\pi$
$968$	−3.14986	−	2.83614i	−0.101240	−	0.0911571i
$969$	−0.670015	+	2.06209i	−0.0215240	+	0.0662440i
$970$		0			0
$971$	12.2536	−	5.45567i	0.393238	−	0.175081i	−0.200586	−	0.979676i	$-0.564284\pi$
$971$	12.2536	−	5.45567i	0.393238	−	0.175081i	0.593823	+	0.804595i	$0.297618\pi$
$972$	0.996006	−	4.68584i	0.0319469	−	0.150298i
$973$	52.8491	+	5.55467i	1.69427	+	0.178074i
$974$	−0.242345	−	2.30576i	−0.00776524	−	0.0738813i
$975$		0			0
$976$	−4.84521	+	3.52025i	−0.155091	+	0.112681i
$977$	7.15755	+	9.85153i	0.228990	+	0.315178i	0.908015	−	0.418937i	$-0.137597\pi$
$977$	7.15755	+	9.85153i	0.228990	+	0.315178i	−0.679025	+	0.734115i	$0.737597\pi$
$978$	−2.17237	−	10.2202i	−0.0694646	−	0.326805i
$979$	−0.456840	−	4.34654i	−0.0146007	−	0.138916i
$980$		0			0
$981$	−1.28279	−	0.272666i	−0.0409565	−	0.00870557i
$982$	−2.33347	−	5.24107i	−0.0744641	−	0.167249i
$983$	29.0697	−	26.1745i	0.927179	−	0.834835i	−0.0593813	−	0.998235i	$-0.518913\pi$
$983$	29.0697	−	26.1745i	0.927179	−	0.834835i	0.986560	+	0.163400i	$0.0522461\pi$
$984$	−8.00479	+	24.6362i	−0.255183	+	0.785374i
$985$		0			0
$986$	0.258801	+	0.448257i	0.00824192	+	0.0142754i
$987$	−41.7423	−	24.0999i	−1.32867	−	0.767109i
$988$	23.4477	−	7.61862i	0.745971	−	0.242381i
$989$	14.9256	+	6.64531i	0.474607	+	0.211308i
$990$		0			0
$991$	0.867505			0.0275572			0.0137786	−	0.999905i	$-0.495614\pi$
$991$	0.867505			0.0275572			0.0137786	+	0.999905i	$0.495614\pi$
$992$	8.19571	−	25.6291i	0.260214	−	0.813725i
$993$			12.4849i			0.396197i
$994$	−21.7709	−	15.8175i	−0.690532	−	0.501701i
$995$		0			0
$996$	−4.78972	−	14.7412i	−0.151768	−	0.467094i
$997$	0.916838	+	0.529337i	0.0290365	+	0.0167643i	0.514448	−	0.857522i	$-0.327997\pi$
$997$	0.916838	+	0.529337i	0.0290365	+	0.0167643i	−0.485411	+	0.874286i	$0.661330\pi$
$998$	6.12603	−	3.53686i	0.193916	−	0.111957i
$999$	−28.3595	+	31.4964i	−0.897254	+	0.996502i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.ck.c.174.7		80
5.2	odd	4		775.2.bl.c.701.4		40
5.3	odd	4		155.2.q.a.81.2	✓	40
5.4	even	2	inner	775.2.ck.c.174.4		80
31.18	even	15	inner	775.2.ck.c.49.4		80
155.18	odd	60		155.2.q.a.111.2	yes	40
155.38	odd	60		4805.2.a.x.1.13		20
155.49	even	30	inner	775.2.ck.c.49.7		80
155.142	odd	60		775.2.bl.c.576.4		40
155.148	even	60		4805.2.a.y.1.13		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.q.a.81.2	✓	40	5.3	odd	4
155.2.q.a.111.2	yes	40	155.18	odd	60
775.2.bl.c.576.4		40	155.142	odd	60
775.2.bl.c.701.4		40	5.2	odd	4
775.2.ck.c.49.4		80	31.18	even	15	inner
775.2.ck.c.49.7		80	155.49	even	30	inner
775.2.ck.c.174.4		80	5.4	even	2	inner
775.2.ck.c.174.7		80	1.1	even	1	trivial
4805.2.a.x.1.13		20	155.38	odd	60
4805.2.a.y.1.13		20	155.148	even	60

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.ck (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.276293 - 0.380285i) q^{2} +(-0.673286 + 1.51222i) q^{3} +(0.549755 + 1.69197i) q^{4} +(0.389052 + 0.673858i) q^{6} +(-3.07510 - 2.76883i) q^{7} +(1.68943 + 0.548929i) q^{8} +(0.173882 + 0.193116i) q^{9} +(-2.87081 - 0.610210i) q^{11} +(-2.92878 - 0.307828i) q^{12} +(-2.02152 + 0.212471i) q^{13} +(-1.90257 + 0.404405i) q^{14} +(-2.20303 + 1.60059i) q^{16} +(-0.0399441 - 0.187922i) q^{17} +(0.121482 - 0.0127682i) q^{18} +(-0.712651 + 6.78042i) q^{19} +(6.25751 - 2.78602i) q^{21} +(-1.02524 + 0.923131i) q^{22} +(-2.38756 - 0.775764i) q^{23} +(-1.96757 + 2.18521i) q^{24} +(-0.477734 + 0.827460i) q^{26} +(-5.13206 + 1.66751i) q^{27} +(2.99423 - 6.72516i) q^{28} +(-4.63691 - 3.36892i) q^{29} +(-5.30321 - 1.69587i) q^{31} +4.83275i q^{32} +(2.85565 - 3.93047i) q^{33} +(-0.0825003 - 0.0367315i) q^{34} +(-0.231154 + 0.400371i) q^{36} +(6.80193 - 3.92710i) q^{37} +(2.38159 + 2.14440i) q^{38} +(1.03976 - 3.20005i) q^{39} +(8.04782 - 3.58312i) q^{41} +(0.669425 - 3.14940i) q^{42} +(-6.47245 - 0.680282i) q^{43} +(-0.545786 - 5.19280i) q^{44} +(-0.954677 + 0.693613i) q^{46} +(-4.13611 - 5.69287i) q^{47} +(-0.937190 - 4.40913i) q^{48} +(1.05811 + 10.0672i) q^{49} +(0.311074 + 0.0661209i) q^{51} +(-1.47084 - 3.30356i) q^{52} +(-5.80788 + 5.22944i) q^{53} +(-0.783826 + 2.41237i) q^{54} +(-3.67527 - 6.36575i) q^{56} +(-9.77371 - 5.64285i) q^{57} +(-2.56230 + 0.832541i) q^{58} +(-4.29740 - 1.91333i) q^{59} +2.19934 q^{61} +(-2.11015 + 1.54817i) q^{62} -1.07530i q^{63} +(-2.56823 - 1.86593i) q^{64} +(-0.705701 - 2.17192i) q^{66} +(1.41260 + 0.815567i) q^{67} +(0.296000 - 0.170895i) q^{68} +(2.78064 - 3.08821i) q^{69} +(9.25749 + 10.2815i) q^{71} +(0.187755 + 0.421705i) q^{72} +(-1.73920 + 8.18228i) q^{73} +(0.385912 - 3.67171i) q^{74} +(-11.8641 + 2.52179i) q^{76} +(7.13847 + 9.82525i) q^{77} +(-0.929653 - 1.27956i) q^{78} +(13.3534 - 2.83835i) q^{79} +(0.852208 - 8.10822i) q^{81} +(0.860951 - 4.05046i) q^{82} +(2.14076 + 4.80822i) q^{83} +(8.15398 + 9.05591i) q^{84} +(-2.04700 + 2.27342i) q^{86} +(8.21652 - 4.74381i) q^{87} +(-4.51507 - 2.60678i) q^{88} +(0.460162 + 1.41623i) q^{89} +(6.80468 + 4.94389i) q^{91} -4.46616i q^{92} +(6.13511 - 6.87784i) q^{93} -3.30769 q^{94} +(-7.30821 - 3.25382i) q^{96} +(-7.43435 + 2.41557i) q^{97} +(4.12075 + 2.37912i) q^{98} +(-0.381343 - 0.660505i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 20 q^{4} + 8 q^{6} - 4 q^{9} - 56 q^{11} + 12 q^{14} + 16 q^{16} + 26 q^{19} - 16 q^{21} + 164 q^{24} + 64 q^{26} - 84 q^{29} - 20 q^{31} - 64 q^{34} - 26 q^{36} - 74 q^{39} + 72 q^{41} + 112 q^{44}+ \cdots - 106 q^{99}+O(q^{100}) \) 80 * q + 20 * q^4 + 8 * q^6 - 4 * q^9 - 56 * q^11 + 12 * q^14 + 16 * q^16 + 26 * q^19 - 16 * q^21 + 164 * q^24 + 64 * q^26 - 84 * q^29 - 20 * q^31 - 64 * q^34 - 26 * q^36 - 74 * q^39 + 72 * q^41 + 112 * q^44 + 36 * q^46 + 62 * q^49 - 4 * q^51 - 44 * q^54 + 18 * q^56 + 2 * q^59 - 200 * q^61 - 34 * q^64 - 80 * q^66 - 16 * q^69 - 4 * q^71 + 4 * q^74 + 4 * q^76 + 134 * q^79 - 166 * q^81 - 52 * q^84 - 10 * q^86 - 40 * q^89 + 38 * q^91 - 260 * q^94 + 92 * q^96 - 106 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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