LMFDB - Embedded newform 930.2.j.g.683.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [930,2,Mod(497,930)] 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("930.497"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(930, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [40,0,-4,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			683.12
Character	$\chi$	$=$	930.683
Dual form			930.2.j.g.497.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{2} +(-1.55395 + 0.765006i) q^{3} +1.00000i q^{4} +(-1.73301 + 1.41304i) q^{5} +(-1.63975 - 0.557869i) q^{6} +(1.07773 - 1.07773i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.82953 - 2.37756i) q^{9} +(-2.22459 - 0.226250i) q^{10} -5.88520i q^{11} +(-0.765006 - 1.55395i) q^{12} +(-2.66190 - 2.66190i) q^{13} +1.52413 q^{14} +(1.61202 - 3.52156i) q^{15} -1.00000 q^{16} +(4.04386 + 4.04386i) q^{17} +(2.97487 - 0.387518i) q^{18} -3.95873i q^{19} +(-1.41304 - 1.73301i) q^{20} +(-0.850267 + 2.49920i) q^{21} +(4.16146 - 4.16146i) q^{22} +(-1.71748 + 1.71748i) q^{23} +(0.557869 - 1.63975i) q^{24} +(1.00663 - 4.89762i) q^{25} -3.76449i q^{26} +(-1.02415 + 5.09422i) q^{27} +(1.07773 + 1.07773i) q^{28} +1.71299 q^{29} +(3.62999 - 1.35024i) q^{30} +1.00000 q^{31} +(-0.707107 - 0.707107i) q^{32} +(4.50221 + 9.14531i) q^{33} +5.71888i q^{34} +(-0.344835 + 3.39058i) q^{35} +(2.37756 + 1.82953i) q^{36} +(6.38692 - 6.38692i) q^{37} +(2.79924 - 2.79924i) q^{38} +(6.17283 + 2.10009i) q^{39} +(0.226250 - 2.22459i) q^{40} -2.84590i q^{41} +(-2.36843 + 1.16597i) q^{42} +(-0.535397 - 0.535397i) q^{43} +5.88520 q^{44} +(0.189005 + 6.70554i) q^{45} -2.42889 q^{46} +(1.30867 + 1.30867i) q^{47} +(1.55395 - 0.765006i) q^{48} +4.67702i q^{49} +(4.17494 - 2.75135i) q^{50} +(-9.37754 - 3.19039i) q^{51} +(2.66190 - 2.66190i) q^{52} +(-1.86090 + 1.86090i) q^{53} +(-4.32635 + 2.87797i) q^{54} +(8.31603 + 10.1991i) q^{55} +1.52413i q^{56} +(3.02845 + 6.15167i) q^{57} +(1.21127 + 1.21127i) q^{58} -6.57921 q^{59} +(3.52156 + 1.61202i) q^{60} +3.80070 q^{61} +(0.707107 + 0.707107i) q^{62} +(-0.590629 - 4.53409i) q^{63} -1.00000i q^{64} +(8.37446 + 0.851716i) q^{65} +(-3.28317 + 9.65026i) q^{66} +(8.88129 - 8.88129i) q^{67} +(-4.04386 + 4.04386i) q^{68} +(1.35500 - 3.98277i) q^{69} +(-2.64133 + 2.15366i) q^{70} -5.12798i q^{71} +(0.387518 + 2.97487i) q^{72} +(-5.41812 - 5.41812i) q^{73} +9.03246 q^{74} +(2.18246 + 8.38074i) q^{75} +3.95873 q^{76} +(-6.34263 - 6.34263i) q^{77} +(2.87986 + 5.84984i) q^{78} -16.1838i q^{79} +(1.73301 - 1.41304i) q^{80} +(-2.30563 - 8.69966i) q^{81} +(2.01236 - 2.01236i) q^{82} +(11.7132 - 11.7132i) q^{83} +(-2.49920 - 0.850267i) q^{84} +(-12.7222 - 1.29390i) q^{85} -0.757166i q^{86} +(-2.66190 + 1.31045i) q^{87} +(4.16146 + 4.16146i) q^{88} -1.16940 q^{89} +(-4.60789 + 4.87518i) q^{90} -5.73759 q^{91} +(-1.71748 - 1.71748i) q^{92} +(-1.55395 + 0.765006i) q^{93} +1.85073i q^{94} +(5.59384 + 6.86050i) q^{95} +(1.63975 + 0.557869i) q^{96} +(-9.95765 + 9.95765i) q^{97} +(-3.30715 + 3.30715i) q^{98} +(-13.9924 - 10.7672i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{3} - 8 q^{7} + 8 q^{10} + 4 q^{12} - 20 q^{13} - 44 q^{15} - 40 q^{16} + 16 q^{18} - 32 q^{21} - 4 q^{22} + 8 q^{25} + 8 q^{27} - 8 q^{28} - 4 q^{30} + 40 q^{31} + 48 q^{33} + 64 q^{37} - 4 q^{40}+ \cdots - 52 q^{97}+O(q^{100}) $ 40 * q - 4 * q^3 - 8 * q^7 + 8 * q^10 + 4 * q^12 - 20 * q^13 - 44 * q^15 - 40 * q^16 + 16 * q^18 - 32 * q^21 - 4 * q^22 + 8 * q^25 + 8 * q^27 - 8 * q^28 - 4 * q^30 + 40 * q^31 + 48 * q^33 + 64 * q^37 - 4 * q^40 - 20 * q^42 - 48 * q^43 - 4 * q^45 - 80 * q^46 + 4 * q^48 + 48 * q^51 + 20 * q^52 + 164 * q^55 + 40 * q^57 + 56 * q^58 + 24 * q^60 - 128 * q^61 + 56 * q^63 + 8 * q^66 - 4 * q^67 - 56 * q^70 - 16 * q^72 - 48 * q^73 - 48 * q^75 - 40 * q^76 - 36 * q^78 - 24 * q^81 - 16 * q^82 - 56 * q^85 - 12 * q^87 - 4 * q^88 - 28 * q^90 - 32 * q^91 - 4 * q^93 - 52 * q^97

Character values

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

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

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−1.55395	+	0.765006i	−0.897174	+	0.441676i
$3$	−1.55395	+	0.765006i	−0.897174	+	0.441676i
$4$			1.00000i			0.500000i
$5$	−1.73301	+	1.41304i	−0.775024	+	0.631931i
$5$	−1.73301	+	1.41304i	−0.775024	+	0.631931i
$6$	−1.63975	−	0.557869i	−0.669425	−	0.227749i
$7$	1.07773	−	1.07773i	0.407342	−	0.407342i	−0.473469	−	0.880811i	$-0.656998\pi$
$7$	1.07773	−	1.07773i	0.407342	−	0.407342i	0.880811	+	0.473469i	$0.156998\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	1.82953	−	2.37756i	0.609844	−	0.792522i
$10$	−2.22459	−	0.226250i	−0.703478	−	0.0715466i
$11$		−	5.88520i		−	1.77445i	−0.461333	−	0.887227i	$-0.652629\pi$
$11$		−	5.88520i		−	1.77445i	0.461333	−	0.887227i	$-0.347371\pi$
$12$	−0.765006	−	1.55395i	−0.220838	−	0.448587i
$13$	−2.66190	−	2.66190i	−0.738277	−	0.738277i	0.233967	−	0.972244i	$-0.424829\pi$
$13$	−2.66190	−	2.66190i	−0.738277	−	0.738277i	−0.972244	+	0.233967i	$0.924829\pi$
$14$	1.52413			0.407342
$15$	1.61202	−	3.52156i	0.416223	−	0.909263i
$16$	−1.00000			−0.250000
$17$	4.04386	+	4.04386i	0.980780	+	0.980780i	0.999819	−	0.0190383i	$-0.00606045\pi$
$17$	4.04386	+	4.04386i	0.980780	+	0.980780i	−0.0190383	+	0.999819i	$0.506060\pi$
$18$	2.97487	−	0.387518i	0.701183	−	0.0913388i
$19$		−	3.95873i		−	0.908194i	−0.890952	−	0.454097i	$-0.849962\pi$
$19$		−	3.95873i		−	0.908194i	0.890952	−	0.454097i	$-0.150038\pi$
$20$	−1.41304	−	1.73301i	−0.315966	−	0.387512i
$21$	−0.850267	+	2.49920i	−0.185543	+	0.545370i
$22$	4.16146	−	4.16146i	0.887227	−	0.887227i
$23$	−1.71748	+	1.71748i	−0.358120	+	0.358120i	−0.863120	−	0.505000i	$-0.831493\pi$
$23$	−1.71748	+	1.71748i	−0.358120	+	0.358120i	0.505000	+	0.863120i	$0.331493\pi$
$24$	0.557869	−	1.63975i	0.113875	−	0.334713i
$25$	1.00663	−	4.89762i	0.201326	−	0.979524i
$26$		−	3.76449i		−	0.738277i
$27$	−1.02415	+	5.09422i	−0.197098	+	0.980384i
$28$	1.07773	+	1.07773i	0.203671	+	0.203671i
$29$	1.71299			0.318094			0.159047	−	0.987271i	$-0.449158\pi$
$29$	1.71299			0.318094			0.159047	+	0.987271i	$0.449158\pi$
$30$	3.62999	−	1.35024i	0.662743	−	0.246520i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	4.50221	+	9.14531i	0.783734	+	1.59199i
$34$			5.71888i			0.980780i
$35$	−0.344835	+	3.39058i	−0.0582878	+	0.573112i
$36$	2.37756	+	1.82953i	0.396261	+	0.304922i
$37$	6.38692	−	6.38692i	1.05000	−	1.05000i	0.0513204	−	0.998682i	$-0.483657\pi$
$37$	6.38692	−	6.38692i	1.05000	−	1.05000i	0.998682	−	0.0513204i	$-0.0163430\pi$
$38$	2.79924	−	2.79924i	0.454097	−	0.454097i
$39$	6.17283	+	2.10009i	0.988443	+	0.336284i
$40$	0.226250	−	2.22459i	0.0357733	−	0.351739i
$41$		−	2.84590i		−	0.444455i	−0.974995	−	0.222228i	$-0.928667\pi$
$41$		−	2.84590i		−	0.444455i	0.974995	−	0.222228i	$-0.0713328\pi$
$42$	−2.36843	+	1.16597i	−0.365457	+	0.179913i
$43$	−0.535397	−	0.535397i	−0.0816473	−	0.0816473i	0.665104	−	0.746751i	$-0.268387\pi$
$43$	−0.535397	−	0.535397i	−0.0816473	−	0.0816473i	−0.746751	+	0.665104i	$0.768387\pi$
$44$	5.88520			0.887227
$45$	0.189005	+	6.70554i	0.0281752	+	0.999603i
$46$	−2.42889			−0.358120
$47$	1.30867	+	1.30867i	0.190888	+	0.190888i	0.796080	−	0.605191i	$-0.206903\pi$
$47$	1.30867	+	1.30867i	0.190888	+	0.190888i	−0.605191	+	0.796080i	$0.706903\pi$
$48$	1.55395	−	0.765006i	0.224294	−	0.110419i
$49$			4.67702i			0.668145i
$50$	4.17494	−	2.75135i	0.590425	−	0.389099i
$51$	−9.37754	−	3.19039i	−1.31312	−	0.446744i
$52$	2.66190	−	2.66190i	0.369139	−	0.369139i
$53$	−1.86090	+	1.86090i	−0.255614	+	0.255614i	−0.823268	−	0.567653i	$-0.807851\pi$
$53$	−1.86090	+	1.86090i	−0.255614	+	0.255614i	0.567653	+	0.823268i	$0.307851\pi$
$54$	−4.32635	+	2.87797i	−0.588741	+	0.391643i
$55$	8.31603	+	10.1991i	1.12133	+	1.37525i
$56$			1.52413i			0.203671i
$57$	3.02845	+	6.15167i	0.401128	+	0.814808i
$58$	1.21127	+	1.21127i	0.159047	+	0.159047i
$59$	−6.57921			−0.856541			−0.428270	−	0.903651i	$-0.640877\pi$
$59$	−6.57921			−0.856541			−0.428270	+	0.903651i	$0.640877\pi$
$60$	3.52156	+	1.61202i	0.454631	+	0.208111i
$61$	3.80070			0.486630			0.243315	−	0.969947i	$-0.421765\pi$
$61$	3.80070			0.486630			0.243315	+	0.969947i	$0.421765\pi$
$62$	0.707107	+	0.707107i	0.0898027	+	0.0898027i
$63$	−0.590629	−	4.53409i	−0.0744122	−	0.571242i
$64$		−	1.00000i		−	0.125000i
$65$	8.37446	+	0.851716i	1.03872	+	0.105642i
$66$	−3.28317	+	9.65026i	−0.404130	+	1.18786i
$67$	8.88129	−	8.88129i	1.08502	−	1.08502i	0.0889895	−	0.996033i	$-0.471636\pi$
$67$	8.88129	−	8.88129i	1.08502	−	1.08502i	0.996033	−	0.0889895i	$-0.0283637\pi$
$68$	−4.04386	+	4.04386i	−0.490390	+	0.490390i
$69$	1.35500	−	3.98277i	0.163123	−	0.479469i
$70$	−2.64133	+	2.15366i	−0.315700	+	0.257412i
$71$		−	5.12798i		−	0.608579i	−0.952580	−	0.304290i	$-0.901581\pi$
$71$		−	5.12798i		−	0.608579i	0.952580	−	0.304290i	$-0.0984191\pi$
$72$	0.387518	+	2.97487i	0.0456694	+	0.350591i
$73$	−5.41812	−	5.41812i	−0.634143	−	0.634143i	0.314962	−	0.949104i	$-0.398008\pi$
$73$	−5.41812	−	5.41812i	−0.634143	−	0.634143i	−0.949104	+	0.314962i	$0.898008\pi$
$74$	9.03246			1.05000
$75$	2.18246	+	8.38074i	0.252009	+	0.967725i
$76$	3.95873			0.454097
$77$	−6.34263	−	6.34263i	−0.722809	−	0.722809i
$78$	2.87986	+	5.84984i	0.326080	+	0.662364i
$79$		−	16.1838i		−	1.82082i	−0.413706	−	0.910411i	$-0.635766\pi$
$79$		−	16.1838i		−	1.82082i	0.413706	−	0.910411i	$-0.364234\pi$
$80$	1.73301	−	1.41304i	0.193756	−	0.157983i
$81$	−2.30563	−	8.69966i	−0.256181	−	0.966629i
$82$	2.01236	−	2.01236i	0.222228	−	0.222228i
$83$	11.7132	−	11.7132i	1.28569	−	1.28569i	0.348305	−	0.937381i	$-0.386758\pi$
$83$	11.7132	−	11.7132i	1.28569	−	1.28569i	0.937381	−	0.348305i	$-0.113242\pi$
$84$	−2.49920	−	0.850267i	−0.272685	−	0.0927717i
$85$	−12.7222	−	1.29390i	−1.37991	−	0.140343i
$86$		−	0.757166i		−	0.0816473i
$87$	−2.66190	+	1.31045i	−0.285386	+	0.140495i
$88$	4.16146	+	4.16146i	0.443613	+	0.443613i
$89$	−1.16940			−0.123956			−0.0619779	−	0.998078i	$-0.519741\pi$
$89$	−1.16940			−0.123956			−0.0619779	+	0.998078i	$0.519741\pi$
$90$	−4.60789	+	4.87518i	−0.485714	+	0.513889i
$91$	−5.73759			−0.601462
$92$	−1.71748	−	1.71748i	−0.179060	−	0.179060i
$93$	−1.55395	+	0.765006i	−0.161137	+	0.0793274i
$94$			1.85073i			0.190888i
$95$	5.59384	+	6.86050i	0.573916	+	0.703873i
$96$	1.63975	+	0.557869i	0.167356	+	0.0569373i
$97$	−9.95765	+	9.95765i	−1.01105	+	1.01105i	−0.0111079	+	0.999938i	$0.503536\pi$
$97$	−9.95765	+	9.95765i	−1.01105	+	1.01105i	−0.999938	+	0.0111079i	$0.996464\pi$
$98$	−3.30715	+	3.30715i	−0.334073	+	0.334073i
$99$	−13.9924	−	10.7672i	−1.40629	−	1.08214i
$100$	4.89762	+	1.00663i	0.489762	+	0.100663i
$101$		−	10.1399i		−	1.00895i	−0.863425	−	0.504477i	$-0.831685\pi$
$101$		−	10.1399i		−	1.00895i	0.863425	−	0.504477i	$-0.168315\pi$
$102$	−4.37498	−	8.88687i	−0.433188	−	0.879931i
$103$	12.1481	+	12.1481i	1.19699	+	1.19699i	0.975064	+	0.221924i	$0.0712336\pi$
$103$	12.1481	+	12.1481i	1.19699	+	1.19699i	0.221924	+	0.975064i	$0.428766\pi$
$104$	3.76449			0.369139
$105$	−2.05795	−	5.53259i	−0.200836	−	0.539926i
$106$	−2.63171			−0.255614
$107$	−6.82642	−	6.82642i	−0.659935	−	0.659935i	0.295430	−	0.955364i	$-0.404537\pi$
$107$	−6.82642	−	6.82642i	−0.659935	−	0.659935i	−0.955364	+	0.295430i	$0.904537\pi$
$108$	−5.09422	−	1.02415i	−0.490192	−	0.0985492i
$109$			14.5314i			1.39185i	0.718112	+	0.695927i	$0.245006\pi$
$109$			14.5314i			1.39185i	−0.718112	+	0.695927i	$0.754994\pi$
$110$	−1.33153	+	13.0922i	−0.126956	+	1.24829i
$111$	−5.03893	+	14.8110i	−0.478274	+	1.40580i
$112$	−1.07773	+	1.07773i	−0.101835	+	0.101835i
$113$	1.20082	−	1.20082i	0.112963	−	0.112963i	−0.648366	−	0.761329i	$-0.724547\pi$
$113$	1.20082	−	1.20082i	0.112963	−	0.112963i	0.761329	+	0.648366i	$0.224547\pi$
$114$	−2.20845	+	6.49132i	−0.206840	+	0.607968i
$115$	0.549536	−	5.40328i	0.0512445	−	0.503859i
$116$			1.71299i			0.159047i
$117$	−11.1989	+	1.45881i	−1.03533	+	0.134867i
$118$	−4.65221	−	4.65221i	−0.428270	−	0.428270i
$119$	8.71634			0.799026
$120$	1.35024	+	3.62999i	0.123260	+	0.331371i
$121$	−23.6355			−2.14869
$122$	2.68750	+	2.68750i	0.243315	+	0.243315i
$123$	2.17713	+	4.42239i	0.196305	+	0.398754i
$124$			1.00000i			0.0898027i
$125$	5.17605	+	9.91002i	0.462960	+	0.886379i
$126$	2.78845	−	3.62373i	0.248415	−	0.322827i
$127$	3.09845	−	3.09845i	0.274943	−	0.274943i	−0.556143	−	0.831086i	$-0.687720\pi$
$127$	3.09845	−	3.09845i	0.274943	−	0.274943i	0.831086	+	0.556143i	$0.187720\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	1.24156	+	0.422399i	0.109314	+	0.0371902i
$130$	5.31938	+	6.52389i	0.466541	+	0.572183i
$131$			5.24622i			0.458365i	0.973384	+	0.229182i	$0.0736052\pi$
$131$			5.24622i			0.458365i	−0.973384	+	0.229182i	$0.926395\pi$
$132$	−9.14531	+	4.50221i	−0.795997	+	0.391867i
$133$	−4.26642	−	4.26642i	−0.369945	−	0.369945i
$134$	12.5600			1.08502
$135$	−5.42348	−	10.2755i	−0.466779	−	0.884374i
$136$	−5.71888			−0.490390
$137$	−13.6538	−	13.6538i	−1.16652	−	1.16652i	−0.983019	−	0.183505i	$-0.941255\pi$
$137$	−13.6538	−	13.6538i	−1.16652	−	1.16652i	−0.183505	−	0.983019i	$-0.558745\pi$
$138$	3.77437	−	1.85811i	0.321296	−	0.158173i
$139$		−	23.1290i		−	1.96177i	−0.194577	−	0.980887i	$-0.562334\pi$
$139$		−	23.1290i		−	1.96177i	0.194577	−	0.980887i	$-0.437666\pi$
$140$	−3.39058	−	0.344835i	−0.286556	−	0.0291439i
$141$	−3.03474	−	1.03247i	−0.255571	−	0.0869493i
$142$	3.62603	−	3.62603i	0.304290	−	0.304290i
$143$	−15.6658	+	15.6658i	−1.31004	+	1.31004i
$144$	−1.82953	+	2.37756i	−0.152461	+	0.198130i
$145$	−2.96863	+	2.42053i	−0.246531	+	0.201014i
$146$		−	7.66238i		−	0.634143i
$147$	−3.57795	−	7.26786i	−0.295104	−	0.599443i
$148$	6.38692	+	6.38692i	0.525001	+	0.525001i
$149$	−17.1237			−1.40283			−0.701414	−	0.712754i	$-0.747447\pi$
$149$	−17.1237			−1.40283			−0.701414	+	0.712754i	$0.747447\pi$
$150$	−4.38285	+	7.46931i	−0.357858	+	0.609867i
$151$	8.82338			0.718036			0.359018	−	0.933331i	$-0.383112\pi$
$151$	8.82338			0.718036			0.359018	+	0.933331i	$0.383112\pi$
$152$	2.79924	+	2.79924i	0.227048	+	0.227048i
$153$	17.0129	−	2.21617i	1.37541	−	0.179167i
$154$		−	8.96983i		−	0.722809i
$155$	−1.73301	+	1.41304i	−0.139198	+	0.113498i
$156$	−2.10009	+	6.17283i	−0.168142	+	0.494222i
$157$	−3.93949	+	3.93949i	−0.314406	+	0.314406i	−0.846614	−	0.532208i	$-0.821362\pi$
$157$	−3.93949	+	3.93949i	−0.314406	+	0.314406i	0.532208	+	0.846614i	$0.321362\pi$
$158$	11.4437	−	11.4437i	0.910411	−	0.910411i
$159$	1.46815	−	4.31535i	0.116432	−	0.342230i
$160$	2.22459	+	0.226250i	0.175869	+	0.0178866i
$161$			3.70195i			0.291754i
$162$	4.52126	−	7.78191i	0.355224	−	0.611405i
$163$	14.1999	+	14.1999i	1.11222	+	1.11222i	0.992850	+	0.119369i	$0.0380871\pi$
$163$	14.1999	+	14.1999i	1.11222	+	1.11222i	0.119369	+	0.992850i	$0.461913\pi$
$164$	2.84590			0.222228
$165$	−20.7251	−	9.48708i	−1.61344	−	0.738568i
$166$	16.5649			1.28569
$167$	9.34843	+	9.34843i	0.723403	+	0.723403i	0.969297	−	0.245893i	$-0.0790813\pi$
$167$	9.34843	+	9.34843i	0.723403	+	0.723403i	−0.245893	+	0.969297i	$0.579081\pi$
$168$	−1.16597	−	2.36843i	−0.0899566	−	0.182728i
$169$			1.17139i			0.0901067i
$170$	−8.08102	−	9.91087i	−0.619786	−	0.760129i
$171$	−9.41213	−	7.24261i	−0.719763	−	0.553857i
$172$	0.535397	−	0.535397i	0.0408236	−	0.0408236i
$173$	−9.23238	+	9.23238i	−0.701925	+	0.701925i	−0.964824	−	0.262898i	$-0.915322\pi$
$173$	−9.23238	+	9.23238i	−0.701925	+	0.701925i	0.262898	+	0.964824i	$0.415322\pi$
$174$	−2.80888	−	0.955624i	−0.212940	−	0.0724457i
$175$	−4.19342	−	6.36316i	−0.316993	−	0.481010i
$176$			5.88520i			0.443613i
$177$	10.2238	−	5.03314i	0.768466	−	0.378314i
$178$	−0.826888	−	0.826888i	−0.0619779	−	0.0619779i
$179$	−10.6481			−0.795880			−0.397940	−	0.917412i	$-0.630275\pi$
$179$	−10.6481			−0.795880			−0.397940	+	0.917412i	$0.630275\pi$
$180$	−6.70554	+	0.189005i	−0.499802	+	0.0140876i
$181$	2.85916			0.212520			0.106260	−	0.994338i	$-0.466112\pi$
$181$	2.85916			0.212520			0.106260	+	0.994338i	$0.466112\pi$
$182$	−4.05709	−	4.05709i	−0.300731	−	0.300731i
$183$	−5.90611	+	2.90756i	−0.436592	+	0.214933i
$184$		−	2.42889i		−	0.179060i
$185$	−2.04360	+	20.0935i	−0.150248	+	1.47731i
$186$	−1.63975	−	0.557869i	−0.120232	−	0.0409049i
$187$	23.7989	−	23.7989i	1.74035	−	1.74035i
$188$	−1.30867	+	1.30867i	−0.0954442	+	0.0954442i
$189$	4.38642	+	6.59393i	0.319065	+	0.479638i
$190$	−0.895662	+	8.80655i	−0.0649782	+	0.638894i
$191$		−	12.5060i		−	0.904905i	−0.891789	−	0.452452i	$-0.850549\pi$
$191$		−	12.5060i		−	0.904905i	0.891789	−	0.452452i	$-0.149451\pi$
$192$	0.765006	+	1.55395i	0.0552095	+	0.112147i
$193$	15.0464	+	15.0464i	1.08306	+	1.08306i	0.996222	+	0.0868411i	$0.0276773\pi$
$193$	15.0464	+	15.0464i	1.08306	+	1.08306i	0.0868411	+	0.996222i	$0.472323\pi$
$194$	−14.0822			−1.01105
$195$	−13.6651	+	5.08298i	−0.978576	+	0.364000i
$196$	−4.67702			−0.334073
$197$	3.75213	+	3.75213i	0.267328	+	0.267328i	0.828023	−	0.560694i	$-0.189466\pi$
$197$	3.75213	+	3.75213i	0.267328	+	0.267328i	−0.560694	+	0.828023i	$0.689466\pi$
$198$	−2.28062	−	17.5077i	−0.162076	−	1.24422i
$199$		−	11.3351i		−	0.803526i	−0.915744	−	0.401763i	$-0.868398\pi$
$199$		−	11.3351i		−	0.803526i	0.915744	−	0.401763i	$-0.131602\pi$
$200$	2.75135	+	4.17494i	0.194550	+	0.295213i
$201$	−7.00685	+	20.5953i	−0.494225	+	1.45268i
$202$	7.16996	−	7.16996i	0.504477	−	0.504477i
$203$	1.84613	−	1.84613i	0.129573	−	0.129573i
$204$	3.19039	−	9.37754i	0.223372	−	0.656559i
$205$	4.02138	+	4.93197i	0.280865	+	0.344463i
$206$			17.1800i			1.19699i
$207$	0.941237	+	7.22562i	0.0654205	+	0.502215i
$208$	2.66190	+	2.66190i	0.184569	+	0.184569i
$209$	−23.2979			−1.61155
$210$	2.45694	−	5.36733i	0.169545	−	0.370381i
$211$	−13.5196			−0.930725			−0.465363	−	0.885120i	$-0.654076\pi$
$211$	−13.5196			−0.930725			−0.465363	+	0.885120i	$0.654076\pi$
$212$	−1.86090	−	1.86090i	−0.127807	−	0.127807i
$213$	3.92294	+	7.96863i	0.268795	+	0.546002i
$214$		−	9.65401i		−	0.659935i
$215$	1.68438	+	0.171309i	0.114874	+	0.0116832i
$216$	−2.87797	−	4.32635i	−0.195821	−	0.294371i
$217$	1.07773	−	1.07773i	0.0731608	−	0.0731608i
$218$	−10.2752	+	10.2752i	−0.695927	+	0.695927i
$219$	12.5644	+	4.27460i	0.849022	+	0.288851i
$220$	−10.1991	+	8.31603i	−0.687623	+	0.560666i
$221$		−	21.5287i		−	1.44818i
$222$	−14.0360	+	6.90989i	−0.942035	+	0.463761i
$223$	6.00939	+	6.00939i	0.402419	+	0.402419i	0.879084	−	0.476666i	$-0.158155\pi$
$223$	6.00939	+	6.00939i	0.402419	+	0.402419i	−0.476666	+	0.879084i	$0.658155\pi$
$224$	−1.52413			−0.101835
$225$	−9.80275	−	11.3537i	−0.653517	−	0.756912i
$226$	1.69821			0.112963
$227$	−16.1748	−	16.1748i	−1.07356	−	1.07356i	−0.997070	−	0.0764914i	$-0.975628\pi$
$227$	−16.1748	−	16.1748i	−1.07356	−	1.07356i	−0.0764914	−	0.997070i	$-0.524372\pi$
$228$	−6.15167	+	3.02845i	−0.407404	+	0.200564i
$229$		−	5.34021i		−	0.352891i	−0.984310	−	0.176446i	$-0.943540\pi$
$229$		−	5.34021i		−	0.352891i	0.984310	−	0.176446i	$-0.0564600\pi$
$230$	4.20928	−	3.43212i	0.277552	−	0.226307i
$231$	14.7083	+	5.00399i	0.967734	+	0.329238i
$232$	−1.21127	+	1.21127i	−0.0795236	+	0.0795236i
$233$	3.40443	−	3.40443i	0.223032	−	0.223032i	−0.586742	−	0.809774i	$-0.699590\pi$
$233$	3.40443	−	3.40443i	0.223032	−	0.223032i	0.809774	+	0.586742i	$0.199590\pi$
$234$	−8.95032	−	6.88725i	−0.585101	−	0.450234i
$235$	−4.11712	−	0.418728i	−0.268572	−	0.0273148i
$236$		−	6.57921i		−	0.428270i
$237$	12.3807	+	25.1489i	0.804214	+	1.63359i
$238$	6.16338	+	6.16338i	0.399513	+	0.399513i
$239$	2.52085			0.163061			0.0815303	−	0.996671i	$-0.474019\pi$
$239$	2.52085			0.163061			0.0815303	+	0.996671i	$0.474019\pi$
$240$	−1.61202	+	3.52156i	−0.104056	+	0.227316i
$241$	1.79206			0.115437			0.0577183	−	0.998333i	$-0.481617\pi$
$241$	1.79206			0.115437			0.0577183	+	0.998333i	$0.481617\pi$
$242$	−16.7129	−	16.7129i	−1.07434	−	1.07434i
$243$	10.2381	+	11.7550i	0.656776	+	0.754086i
$244$			3.80070i			0.243315i
$245$	−6.60882	−	8.10530i	−0.422222	−	0.517829i
$246$	−1.58764	+	4.66657i	−0.101224	+	0.297529i
$247$	−10.5377	+	10.5377i	−0.670499	+	0.670499i
$248$	−0.707107	+	0.707107i	−0.0449013	+	0.0449013i
$249$	−9.24105	+	27.1623i	−0.585627	+	1.72134i
$250$	−3.34743	+	10.6675i	−0.211710	+	0.674670i
$251$			6.83182i			0.431221i	0.976479	+	0.215610i	$0.0691741\pi$
$251$			6.83182i			0.431221i	−0.976479	+	0.215610i	$0.930826\pi$
$252$	4.53409	−	0.590629i	0.285621	−	0.0372061i
$253$	10.1077	+	10.1077i	0.635467	+	0.635467i
$254$	4.38187			0.274943
$255$	20.7595	−	7.72189i	1.30001	−	0.483564i
$256$	1.00000			0.0625000
$257$	7.63537	+	7.63537i	0.476281	+	0.476281i	0.903940	−	0.427659i	$-0.140662\pi$
$257$	7.63537	+	7.63537i	0.476281	+	0.476281i	−0.427659	+	0.903940i	$0.640662\pi$
$258$	0.579236	+	1.17660i	0.0360617	+	0.0732518i
$259$		−	13.7667i		−	0.855420i
$260$	−0.851716	+	8.37446i	−0.0528212	+	0.519362i
$261$	3.13397	−	4.07275i	0.193988	−	0.252097i
$262$	−3.70964	+	3.70964i	−0.229182	+	0.229182i
$263$	−18.0739	+	18.0739i	−1.11449	+	1.11449i	−0.121950	+	0.992536i	$0.538915\pi$
$263$	−18.0739	+	18.0739i	−1.11449	+	1.11449i	−0.992536	+	0.121950i	$0.961085\pi$
$264$	−9.65026	−	3.28317i	−0.593932	−	0.202065i
$265$	0.595425	−	5.85448i	0.0365767	−	0.359638i
$266$		−	6.03363i		−	0.369945i
$267$	1.81719	−	0.894595i	0.111210	−	0.0547483i
$268$	8.88129	+	8.88129i	0.542511	+	0.542511i
$269$	7.67463			0.467930			0.233965	−	0.972245i	$-0.424830\pi$
$269$	7.67463			0.467930			0.233965	+	0.972245i	$0.424830\pi$
$270$	3.43089	−	11.1009i	0.208797	−	0.675577i
$271$	18.7691			1.14014			0.570072	−	0.821595i	$-0.306915\pi$
$271$	18.7691			1.14014			0.570072	+	0.821595i	$0.306915\pi$
$272$	−4.04386	−	4.04386i	−0.245195	−	0.245195i
$273$	8.91593	−	4.38929i	0.539617	−	0.265652i
$274$		−	19.3094i		−	1.16652i
$275$	−28.8235	−	5.92421i	−1.73812	−	0.357243i
$276$	3.98277	+	1.35500i	0.239735	+	0.0815615i
$277$	3.61928	−	3.61928i	0.217462	−	0.217462i	−0.589966	−	0.807428i	$-0.700859\pi$
$277$	3.61928	−	3.61928i	0.217462	−	0.217462i	0.807428	+	0.589966i	$0.200859\pi$
$278$	16.3547	−	16.3547i	0.980887	−	0.980887i
$279$	1.82953	−	2.37756i	0.109531	−	0.142341i
$280$	−2.15366	−	2.64133i	−0.128706	−	0.157850i
$281$		−	12.1681i		−	0.725885i	−0.931812	−	0.362943i	$-0.881772\pi$
$281$		−	12.1681i		−	0.725885i	0.931812	−	0.362943i	$-0.118228\pi$
$282$	−1.41582	−	2.87595i	−0.0843109	−	0.171260i
$283$	−15.9927	−	15.9927i	−0.950666	−	0.950666i	0.0481726	−	0.998839i	$-0.484660\pi$
$283$	−15.9927	−	15.9927i	−0.950666	−	0.950666i	−0.998839	+	0.0481726i	$0.984660\pi$
$284$	5.12798			0.304290
$285$	−13.9409	−	6.38156i	−0.825787	−	0.378011i
$286$	−22.1548			−1.31004
$287$	−3.06710	−	3.06710i	−0.181045	−	0.181045i
$288$	−2.97487	+	0.387518i	−0.175296	+	0.0228347i
$289$			15.7056i			0.923861i
$290$	−3.81071	−	0.387564i	−0.223772	−	0.0227586i
$291$	7.85605	−	23.0914i	0.460530	−	1.35364i
$292$	5.41812	−	5.41812i	0.317071	−	0.317071i
$293$	6.25670	−	6.25670i	0.365520	−	0.365520i	−0.500320	−	0.865841i	$-0.666784\pi$
$293$	6.25670	−	6.25670i	0.365520	−	0.365520i	0.865841	+	0.500320i	$0.166784\pi$
$294$	2.60916	−	7.66914i	0.152169	−	0.447273i
$295$	11.4018	−	9.29670i	0.663840	−	0.541275i
$296$			9.03246i			0.525001i
$297$	29.9805	+	6.02734i	1.73965	+	0.349742i
$298$	−12.1083	−	12.1083i	−0.701414	−	0.701414i
$299$	9.14352			0.528784
$300$	−8.38074	+	2.18246i	−0.483863	+	0.126004i
$301$	−1.15402			−0.0665167
$302$	6.23907	+	6.23907i	0.359018	+	0.359018i
$303$	7.75705	+	15.7568i	0.445631	+	0.905207i
$304$			3.95873i			0.227048i
$305$	−6.58664	+	5.37055i	−0.377150	+	0.307517i
$306$	13.5970	+	10.4629i	0.777290	+	0.598123i
$307$	−10.7489	+	10.7489i	−0.613469	+	0.613469i	−0.943848	−	0.330379i	$-0.892823\pi$
$307$	−10.7489	+	10.7489i	−0.613469	+	0.613469i	0.330379	+	0.943848i	$0.392823\pi$
$308$	6.34263	−	6.34263i	0.361405	−	0.361405i
$309$	−28.1709	−	9.58419i	−1.60259	−	0.545226i
$310$	−2.22459	−	0.226250i	−0.126348	−	0.0128501i
$311$			5.04541i			0.286099i	0.989716	+	0.143049i	$0.0456908\pi$
$311$			5.04541i			0.286099i	−0.989716	+	0.143049i	$0.954309\pi$
$312$	−5.84984	+	2.87986i	−0.331182	+	0.163040i
$313$	−0.666018	−	0.666018i	−0.0376456	−	0.0376456i	0.688033	−	0.725679i	$-0.258474\pi$
$313$	−0.666018	−	0.666018i	−0.0376456	−	0.0376456i	−0.725679	+	0.688033i	$0.758474\pi$
$314$	−5.57128			−0.314406
$315$	7.43043	+	7.02303i	0.418657	+	0.395703i
$316$	16.1838			0.910411
$317$	0.0859022	+	0.0859022i	0.00482475	+	0.00482475i	0.709515	−	0.704690i	$-0.248914\pi$
$317$	0.0859022	+	0.0859022i	0.00482475	+	0.00482475i	−0.704690	+	0.709515i	$0.748914\pi$
$318$	4.08955	−	2.01327i	0.229331	−	0.112899i
$319$		−	10.0813i		−	0.564444i
$320$	1.41304	+	1.73301i	0.0789914	+	0.0968781i
$321$	15.8302	+	5.38567i	0.883554	+	0.300599i
$322$	−2.61767	+	2.61767i	−0.145877	+	0.145877i
$323$	16.0085	−	16.0085i	0.890739	−	0.890739i
$324$	8.69966	−	2.30563i	0.483314	−	0.128090i
$325$	−15.7165	+	10.3574i	−0.871795	+	0.574526i
$326$			20.0816i			1.11222i
$327$	−11.1166	−	22.5811i	−0.614749	−	1.24874i
$328$	2.01236	+	2.01236i	0.111114	+	0.111114i
$329$	2.82076			0.155514
$330$	−7.94646	−	21.3632i	−0.437438	−	1.17601i
$331$	14.5931			0.802107			0.401053	−	0.916055i	$-0.368644\pi$
$331$	14.5931			0.802107			0.401053	+	0.916055i	$0.368644\pi$
$332$	11.7132	+	11.7132i	0.642843	+	0.642843i
$333$	−3.50024	−	26.8704i	−0.191812	−	1.47249i
$334$			13.2207i			0.723403i
$335$	−2.84171	+	27.9410i	−0.155259	+	1.52658i
$336$	0.850267	−	2.49920i	0.0463859	−	0.136342i
$337$	11.9367	−	11.9367i	0.650236	−	0.650236i	−0.302814	−	0.953050i	$-0.597926\pi$
$337$	11.9367	−	11.9367i	0.650236	−	0.650236i	0.953050	+	0.302814i	$0.0979261\pi$
$338$	−0.828296	+	0.828296i	−0.0450534	+	0.0450534i
$339$	−0.947380	+	2.78465i	−0.0514546	+	0.151241i
$340$	1.29390	−	12.7222i	0.0701715	−	0.689957i
$341$		−	5.88520i		−	0.318701i
$342$	−1.53408	−	11.7767i	−0.0829533	−	0.636810i
$343$	12.5846	+	12.5846i	0.679505	+	0.679505i
$344$	0.757166			0.0408236
$345$	3.27959	+	8.81684i	0.176567	+	0.474683i
$346$	−13.0566			−0.701925
$347$	10.9974	+	10.9974i	0.590371	+	0.590371i	0.937732	−	0.347361i	$-0.112922\pi$
$347$	10.9974	+	10.9974i	0.590371	+	0.590371i	−0.347361	+	0.937732i	$0.612922\pi$
$348$	−1.31045	−	2.66190i	−0.0702474	−	0.142693i
$349$			21.9906i			1.17713i	0.808449	+	0.588566i	$0.200307\pi$
$349$			21.9906i			1.17713i	−0.808449	+	0.588566i	$0.799693\pi$
$350$	1.53424	−	7.46463i	0.0820084	−	0.399001i
$351$	16.2865	−	10.8341i	0.869308	−	0.578282i
$352$	−4.16146	+	4.16146i	−0.221807	+	0.221807i
$353$	−22.1302	+	22.1302i	−1.17787	+	1.17787i	−0.197587	+	0.980285i	$0.563310\pi$
$353$	−22.1302	+	22.1302i	−1.17787	+	1.17787i	−0.980285	+	0.197587i	$0.936690\pi$
$354$	10.7883	+	3.67034i	0.573390	+	0.195076i
$355$	7.24605	+	8.88683i	0.384580	+	0.471664i
$356$		−	1.16940i		−	0.0619779i
$357$	−13.5448	+	6.66805i	−0.716866	+	0.352911i
$358$	−7.52937	−	7.52937i	−0.397940	−	0.397940i
$359$	−14.8084			−0.781558			−0.390779	−	0.920485i	$-0.627794\pi$
$359$	−14.8084			−0.781558			−0.390779	+	0.920485i	$0.627794\pi$
$360$	−4.87518	−	4.60789i	−0.256945	−	0.242857i
$361$	3.32849			0.175184
$362$	2.02173	+	2.02173i	0.106260	+	0.106260i
$363$	36.7285	−	18.0813i	1.92775	−	0.949024i
$364$		−	5.73759i		−	0.300731i
$365$	17.0457	+	1.73361i	0.892211	+	0.0907415i
$366$	−6.23220	−	2.12029i	−0.325763	−	0.110830i
$367$	0.143077	−	0.143077i	0.00746858	−	0.00746858i	−0.703363	−	0.710831i	$-0.748319\pi$
$367$	0.143077	−	0.143077i	0.00746858	−	0.00746858i	0.710831	+	0.703363i	$0.248319\pi$
$368$	1.71748	−	1.71748i	0.0895300	−	0.0895300i
$369$	−6.76631	−	5.20667i	−0.352240	−	0.271048i
$370$	−15.6533	+	12.7632i	−0.813778	+	0.663529i
$371$			4.01108i			0.208245i
$372$	−0.765006	−	1.55395i	−0.0396637	−	0.0805686i
$373$	−22.4080	−	22.4080i	−1.16024	−	1.16024i	−0.984423	−	0.175819i	$-0.943743\pi$
$373$	−22.4080	−	22.4080i	−1.16024	−	1.16024i	−0.175819	−	0.984423i	$-0.556257\pi$
$374$	33.6568			1.74035
$375$	−15.6246	−	11.4400i	−0.806848	−	0.590758i
$376$	−1.85073			−0.0954442
$377$	−4.55980	−	4.55980i	−0.234842	−	0.234842i
$378$	−1.56095	+	7.76428i	−0.0802864	+	0.399351i
$379$		−	23.1791i		−	1.19063i	−0.803492	−	0.595316i	$-0.797027\pi$
$379$		−	23.1791i		−	1.19063i	0.803492	−	0.595316i	$-0.202973\pi$
$380$	−6.86050	+	5.59384i	−0.351936	+	0.286958i
$381$	−2.44451	+	7.18517i	−0.125236	+	0.368107i
$382$	8.84310	−	8.84310i	0.452452	−	0.452452i
$383$	22.9626	−	22.9626i	1.17333	−	1.17333i	0.191925	−	0.981410i	$-0.438527\pi$
$383$	22.9626	−	22.9626i	1.17333	−	1.17333i	0.981410	−	0.191925i	$-0.0614729\pi$
$384$	−0.557869	+	1.63975i	−0.0284686	+	0.0836782i
$385$	19.9542	+	2.02942i	1.01696	+	0.103429i
$386$			21.2788i			1.08306i
$387$	−2.25247	+	0.293415i	−0.114499	+	0.0149151i
$388$	−9.95765	−	9.95765i	−0.505523	−	0.505523i
$389$	12.6552			0.641643			0.320822	−	0.947140i	$-0.396041\pi$
$389$	12.6552			0.641643			0.320822	+	0.947140i	$0.396041\pi$
$390$	−13.2569	−	6.06845i	−0.671288	−	0.307288i
$391$	−13.8905			−0.702474
$392$	−3.30715	−	3.30715i	−0.167036	−	0.167036i
$393$	−4.01339	−	8.15238i	−0.202449	−	0.411233i
$394$			5.30632i			0.267328i
$395$	22.8684	+	28.0467i	1.15063	+	1.41118i
$396$	10.7672	−	13.9924i	0.541070	−	0.703146i
$397$	−19.5158	+	19.5158i	−0.979468	+	0.979468i	−0.999793	−	0.0203254i	$-0.993530\pi$
$397$	−19.5158	+	19.5158i	−0.979468	+	0.979468i	0.0203254	+	0.999793i	$0.493530\pi$
$398$	8.01515	−	8.01515i	0.401763	−	0.401763i
$399$	9.89364	+	3.36597i	0.495302	+	0.168509i
$400$	−1.00663	+	4.89762i	−0.0503314	+	0.244881i
$401$			19.1422i			0.955914i	0.878383	+	0.477957i	$0.158622\pi$
$401$			19.1422i			0.955914i	−0.878383	+	0.477957i	$0.841378\pi$
$402$	−19.5177	+	9.60850i	−0.973454	+	0.479229i
$403$	−2.66190	−	2.66190i	−0.132599	−	0.132599i
$404$	10.1399			0.504477
$405$	16.2886	+	11.8186i	0.809389	+	0.587272i
$406$	2.61083			0.129573
$407$	−37.5883	−	37.5883i	−1.86318	−	1.86318i
$408$	8.88687	−	4.37498i	0.439966	−	0.216594i
$409$			24.1706i			1.19516i	0.801810	+	0.597579i	$0.203871\pi$
$409$			24.1706i			1.19516i	−0.801810	+	0.597579i	$0.796129\pi$
$410$	−0.643885	+	6.33097i	−0.0317992	+	0.312664i
$411$	31.6626	+	10.7721i	1.56180	+	0.531349i
$412$	−12.1481	+	12.1481i	−0.598494	+	0.598494i
$413$	−7.09058	+	7.09058i	−0.348905	+	0.348905i
$414$	−4.44373	+	5.77484i	−0.218397	+	0.283818i
$415$	−3.74781	+	36.8502i	−0.183973	+	1.80890i
$416$			3.76449i			0.184569i
$417$	17.6938	+	35.9413i	0.866469	+	1.76005i
$418$	−16.4741	−	16.4741i	−0.805774	−	0.805774i
$419$	17.7582			0.867547			0.433774	−	0.901022i	$-0.357182\pi$
$419$	17.7582			0.867547			0.433774	+	0.901022i	$0.357182\pi$
$420$	5.53259	−	2.05795i	0.269963	−	0.100418i
$421$	−2.93628			−0.143105			−0.0715527	−	0.997437i	$-0.522795\pi$
$421$	−2.93628			−0.143105			−0.0715527	+	0.997437i	$0.522795\pi$
$422$	−9.55977	−	9.55977i	−0.465363	−	0.465363i
$423$	5.50568	−	0.717191i	0.267695	−	0.0348710i
$424$		−	2.63171i		−	0.127807i
$425$	23.8760	−	15.7346i	1.15815	−	0.763242i
$426$	−2.86074	+	8.40861i	−0.138603	+	0.407398i
$427$	4.09611	−	4.09611i	0.198225	−	0.198225i
$428$	6.82642	−	6.82642i	0.329967	−	0.329967i
$429$	12.3595	−	36.3283i	0.596720	−	1.75395i
$430$	1.06991	+	1.31217i	0.0515955	+	0.0632786i
$431$			15.7850i			0.760336i	0.924917	+	0.380168i	$0.124134\pi$
$431$			15.7850i			0.760336i	−0.924917	+	0.380168i	$0.875866\pi$
$432$	1.02415	−	5.09422i	0.0492746	−	0.245096i
$433$	−13.1137	−	13.1137i	−0.630205	−	0.630205i	0.317915	−	0.948119i	$-0.397017\pi$
$433$	−13.1137	−	13.1137i	−0.630205	−	0.630205i	−0.948119	+	0.317915i	$0.897017\pi$
$434$	1.52413			0.0731608
$435$	2.76138	−	6.03240i	0.132398	−	0.289231i
$436$	−14.5314			−0.695927
$437$	6.79904	+	6.79904i	0.325242	+	0.325242i
$438$	5.86176	+	11.9070i	0.280086	+	0.568937i
$439$			39.0288i			1.86275i	0.364068	+	0.931373i	$0.381388\pi$
$439$			39.0288i			1.86275i	−0.364068	+	0.931373i	$0.618612\pi$
$440$	−13.0922	−	1.33153i	−0.624144	−	0.0634780i
$441$	11.1199	+	8.55675i	0.529520	+	0.407464i
$442$	15.2231	−	15.2231i	0.724088	−	0.724088i
$443$	−19.8465	+	19.8465i	−0.942936	+	0.942936i	−0.998457	−	0.0555220i	$-0.982318\pi$
$443$	−19.8465	+	19.8465i	−0.942936	+	0.942936i	0.0555220	+	0.998457i	$0.482318\pi$
$444$	−14.8110	−	5.03893i	−0.702898	−	0.239137i
$445$	2.02657	−	1.65241i	0.0960688	−	0.0783315i
$446$			8.49856i			0.402419i
$447$	26.6094	−	13.0997i	1.25858	−	0.619596i
$448$	−1.07773	−	1.07773i	−0.0509177	−	0.0509177i
$449$	11.8070			0.557205			0.278603	−	0.960406i	$-0.410129\pi$
$449$	11.8070			0.557205			0.278603	+	0.960406i	$0.410129\pi$
$450$	1.09667	−	14.9599i	0.0516975	−	0.705214i
$451$	−16.7487			−0.788665
$452$	1.20082	+	1.20082i	0.0564817	+	0.0564817i
$453$	−13.7111	+	6.74994i	−0.644204	+	0.317140i
$454$		−	22.8747i		−	1.07356i
$455$	9.94328	−	8.10745i	0.466148	−	0.380083i
$456$	−6.49132	−	2.20845i	−0.303984	−	0.103420i
$457$	−4.52375	+	4.52375i	−0.211612	+	0.211612i	−0.804952	−	0.593340i	$-0.797809\pi$
$457$	−4.52375	+	4.52375i	−0.211612	+	0.211612i	0.593340	+	0.804952i	$0.297809\pi$
$458$	3.77610	−	3.77610i	0.176446	−	0.176446i
$459$	−24.7419	+	16.4588i	−1.15485	+	0.768231i
$460$	5.40328	+	0.549536i	0.251929	+	0.0256223i
$461$		−	16.0944i		−	0.749592i	−0.927107	−	0.374796i	$-0.877713\pi$
$461$		−	16.0944i		−	0.749592i	0.927107	−	0.374796i	$-0.122287\pi$
$462$	6.86197	+	13.9387i	0.319248	+	0.648486i
$463$	5.96565	+	5.96565i	0.277247	+	0.277247i	0.832009	−	0.554762i	$-0.187191\pi$
$463$	5.96565	+	5.96565i	0.277247	+	0.277247i	−0.554762	+	0.832009i	$0.687191\pi$
$464$	−1.71299			−0.0795236
$465$	1.61202	−	3.52156i	0.0747559	−	0.163308i
$466$	4.81459			0.223032
$467$	25.3293	+	25.3293i	1.17210	+	1.17210i	0.981709	+	0.190390i	$0.0609751\pi$
$467$	25.3293	+	25.3293i	1.17210	+	1.17210i	0.190390	+	0.981709i	$0.439025\pi$
$468$	−1.45881	−	11.1989i	−0.0674334	−	0.517667i
$469$		−	19.1432i		−	0.883950i
$470$	−2.61516	−	3.20733i	−0.120628	−	0.147943i
$471$	3.10804	−	9.13551i	0.143211	−	0.420942i
$472$	4.65221	−	4.65221i	0.214135	−	0.214135i
$473$	−3.15092	+	3.15092i	−0.144879	+	0.144879i
$474$	−9.02845	+	26.5374i	−0.414690	+	1.21890i
$475$	−19.3883	−	3.98497i	−0.889598	−	0.182843i
$476$			8.71634i			0.399513i
$477$	1.01983	+	7.82899i	0.0466950	+	0.358465i
$478$	1.78251	+	1.78251i	0.0815303	+	0.0815303i
$479$	4.28019			0.195567			0.0977835	−	0.995208i	$-0.468825\pi$
$479$	4.28019			0.195567			0.0977835	+	0.995208i	$0.468825\pi$
$480$	−3.62999	+	1.35024i	−0.165686	+	0.0616300i
$481$	−34.0026			−1.55039
$482$	1.26718	+	1.26718i	0.0577183	+	0.0577183i
$483$	−2.83201	−	5.75265i	−0.128861	−	0.261755i
$484$		−	23.6355i		−	1.07434i
$485$	3.18611	−	31.3273i	0.144674	−	1.42250i
$486$	−1.07262	+	15.5515i	−0.0486549	+	0.705431i
$487$	−10.4442	+	10.4442i	−0.473273	+	0.473273i	−0.902972	−	0.429699i	$-0.858620\pi$
$487$	−10.4442	+	10.4442i	−0.473273	+	0.473273i	0.429699	+	0.902972i	$0.358620\pi$
$488$	−2.68750	+	2.68750i	−0.121658	+	0.121658i
$489$	−32.9289	−	11.2029i	−1.48909	−	0.506613i
$490$	1.05818	−	10.4045i	0.0478035	−	0.470025i
$491$		−	15.1907i		−	0.685546i	−0.939418	−	0.342773i	$-0.888634\pi$
$491$		−	15.1907i		−	0.685546i	0.939418	−	0.342773i	$-0.111366\pi$
$492$	−4.42239	+	2.17713i	−0.199377	+	0.0981526i
$493$	6.92710	+	6.92710i	0.311981	+	0.311981i
$494$	−14.9026			−0.670499
$495$	39.4634	−	1.11233i	1.77375	−	0.0499956i
$496$	−1.00000			−0.0449013
$497$	−5.52655	−	5.52655i	−0.247900	−	0.247900i
$498$	−25.7411	+	12.6723i	−1.15348	+	0.567857i
$499$			12.0062i			0.537472i	0.963214	+	0.268736i	$0.0866060\pi$
$499$			12.0062i			0.537472i	−0.963214	+	0.268736i	$0.913394\pi$
$500$	−9.91002	+	5.17605i	−0.443190	+	0.231480i
$501$	−21.6786	−	7.37541i	−0.968529	−	0.329509i
$502$	−4.83083	+	4.83083i	−0.215610	+	0.215610i
$503$	−7.46239	+	7.46239i	−0.332731	+	0.332731i	−0.853623	−	0.520891i	$-0.825600\pi$
$503$	−7.46239	+	7.46239i	−0.332731	+	0.332731i	0.520891	+	0.853623i	$0.325600\pi$
$504$	3.62373	+	2.78845i	0.161414	+	0.124207i
$505$	14.3280	+	17.5724i	0.637589	+	0.781963i
$506$			14.2945i			0.635467i
$507$	−0.896118	−	1.82028i	−0.0397980	−	0.0808415i
$508$	3.09845	+	3.09845i	0.137471	+	0.137471i
$509$	29.9286			1.32656			0.663280	−	0.748371i	$-0.269164\pi$
$509$	29.9286			1.32656			0.663280	+	0.748371i	$0.269164\pi$
$510$	20.1394	+	9.21898i	0.891787	+	0.408223i
$511$	−11.6785			−0.516626
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	20.1666	+	4.05434i	0.890379	+	0.179004i
$514$			10.7980i			0.476281i
$515$	−38.2185	−	3.88698i	−1.68411	−	0.171281i
$516$	−0.422399	+	1.24156i	−0.0185951	+	0.0546568i
$517$	7.70175	−	7.70175i	0.338723	−	0.338723i
$518$	9.73451	−	9.73451i	0.427710	−	0.427710i
$519$	7.28385	−	21.4095i	0.319726	−	0.939773i
$520$	−6.52389	+	5.31938i	−0.286091	+	0.233270i
$521$			18.8758i			0.826966i	0.910512	+	0.413483i	$0.135688\pi$
$521$			18.8758i			0.826966i	−0.910512	+	0.413483i	$0.864312\pi$
$522$	5.09592	−	0.663814i	0.223042	−	0.0290544i
$523$	−17.7678	−	17.7678i	−0.776932	−	0.776932i	0.202376	−	0.979308i	$-0.435134\pi$
$523$	−17.7678	−	17.7678i	−0.776932	−	0.776932i	−0.979308	+	0.202376i	$0.935134\pi$
$524$	−5.24622			−0.229182
$525$	11.3842	+	6.68005i	0.496848	+	0.291541i
$526$	−25.5604			−1.11449
$527$	4.04386	+	4.04386i	0.176153	+	0.176153i
$528$	−4.50221	−	9.14531i	−0.195934	−	0.397999i
$529$			17.1005i			0.743500i
$530$	4.56077	−	3.71872i	0.198107	−	0.161531i
$531$	−12.0369	+	15.6425i	−0.522356	+	0.678827i
$532$	4.26642	−	4.26642i	0.184973	−	0.184973i
$533$	−7.57549	+	7.57549i	−0.328131	+	0.328131i
$534$	1.91752	+	0.652370i	0.0829792	+	0.0282308i
$535$	21.4762	+	2.18422i	0.928499	+	0.0944321i
$536$			12.5600i			0.542511i
$537$	16.5467	−	8.14589i	0.714043	−	0.351521i
$538$	5.42678	+	5.42678i	0.233965	+	0.233965i
$539$	27.5252			1.18559
$540$	10.2755	−	5.42348i	0.442187	−	0.233390i
$541$	15.1735			0.652361			0.326181	−	0.945307i	$-0.394238\pi$
$541$	15.1735			0.652361			0.326181	+	0.945307i	$0.394238\pi$
$542$	13.2718	+	13.2718i	0.570072	+	0.570072i
$543$	−4.44300	+	2.18728i	−0.190667	+	0.0938650i
$544$		−	5.71888i		−	0.245195i
$545$	−20.5335	−	25.1830i	−0.879557	−	1.07872i
$546$	9.40821	+	3.20082i	0.402634	+	0.136982i
$547$	29.2556	−	29.2556i	1.25088	−	1.25088i	0.295551	−	0.955327i	$-0.404497\pi$
$547$	29.2556	−	29.2556i	1.25088	−	1.25088i	0.955327	−	0.295551i	$-0.0955033\pi$
$548$	13.6538	−	13.6538i	0.583262	−	0.583262i
$549$	6.95351	−	9.03641i	0.296768	−	0.385665i
$550$	−16.1922	−	24.5703i	−0.690439	−	1.04768i
$551$		−	6.78126i		−	0.288891i
$552$	1.85811	+	3.77437i	0.0790866	+	0.160648i
$553$	−17.4417	−	17.4417i	−0.741697	−	0.741697i
$554$	5.11844			0.217462
$555$	−12.1960	−	32.7878i	−0.517693	−	1.39176i
$556$	23.1290			0.980887
$557$	19.8179	+	19.8179i	0.839712	+	0.839712i	0.988821	−	0.149109i	$-0.0476405\pi$
$557$	19.8179	+	19.8179i	0.839712	+	0.839712i	−0.149109	+	0.988821i	$0.547641\pi$
$558$	2.97487	−	0.387518i	0.125936	−	0.0164049i
$559$			2.85034i			0.120557i
$560$	0.344835	−	3.39058i	0.0145720	−	0.143278i
$561$	−18.7761	+	55.1887i	−0.792726	+	2.33007i
$562$	8.60411	−	8.60411i	0.362943	−	0.362943i
$563$	15.4555	−	15.4555i	0.651371	−	0.651371i	−0.301952	−	0.953323i	$-0.597638\pi$
$563$	15.4555	−	15.4555i	0.651371	−	0.651371i	0.953323	+	0.301952i	$0.0976383\pi$
$564$	1.03247	−	3.03474i	0.0434747	−	0.127786i
$565$	−0.384221	+	3.77783i	−0.0161643	+	0.158935i
$566$		−	22.6171i		−	0.950666i
$567$	−11.8607	−	6.89101i	−0.498102	−	0.289395i
$568$	3.62603	+	3.62603i	0.152145	+	0.152145i
$569$	−16.1031			−0.675076			−0.337538	−	0.941312i	$-0.609594\pi$
$569$	−16.1031			−0.675076			−0.337538	+	0.941312i	$0.609594\pi$
$570$	−5.34525	−	14.3701i	−0.223888	−	0.601899i
$571$	−13.0021			−0.544119			−0.272060	−	0.962280i	$-0.587705\pi$
$571$	−13.0021			−0.544119			−0.272060	+	0.962280i	$0.587705\pi$
$572$	−15.6658	−	15.6658i	−0.655019	−	0.655019i
$573$	9.56719	+	19.4338i	0.399675	+	0.811857i
$574$		−	4.33753i		−	0.181045i
$575$	6.68271	+	10.1404i	0.278688	+	0.422886i
$576$	−2.37756	−	1.82953i	−0.0990652	−	0.0762305i
$577$	16.5054	−	16.5054i	0.687130	−	0.687130i	−0.274467	−	0.961597i	$-0.588501\pi$
$577$	16.5054	−	16.5054i	0.687130	−	0.687130i	0.961597	+	0.274467i	$0.0885014\pi$
$578$	−11.1056	+	11.1056i	−0.461930	+	0.461930i
$579$	−34.8920	−	11.8708i	−1.45006	−	0.493333i
$580$	−2.42053	−	2.96863i	−0.100507	−	0.123265i
$581$		−	25.2471i		−	1.04743i
$582$	21.8831	−	10.7730i	0.907085	−	0.446555i
$583$	10.9518	+	10.9518i	0.453576	+	0.453576i
$584$	7.66238			0.317071
$585$	17.3463	−	18.3526i	0.717183	−	0.758785i
$586$	8.84831			0.365520
$587$	7.99099	+	7.99099i	0.329823	+	0.329823i	0.852519	−	0.522696i	$-0.175074\pi$
$587$	7.99099	+	7.99099i	0.329823	+	0.329823i	−0.522696	+	0.852519i	$0.675074\pi$
$588$	7.26786	−	3.57795i	0.299721	−	0.147552i
$589$		−	3.95873i		−	0.163116i
$590$	14.6361	+	1.48855i	0.602557	+	0.0612825i
$591$	−8.70103	−	2.96023i	−0.357913	−	0.121768i
$592$	−6.38692	+	6.38692i	−0.262501	+	0.262501i
$593$	−18.8701	+	18.8701i	−0.774901	+	0.774901i	−0.978959	−	0.204058i	$-0.934587\pi$
$593$	−18.8701	+	18.8701i	−0.774901	+	0.774901i	0.204058	+	0.978959i	$0.434587\pi$
$594$	16.9374	+	25.4614i	0.694952	+	1.04469i
$595$	−15.1055	+	12.3166i	−0.619264	+	0.504929i
$596$		−	17.1237i		−	0.701414i
$597$	8.67144	+	17.6142i	0.354898	+	0.720903i
$598$	6.46545	+	6.46545i	0.264392	+	0.264392i
$599$	10.2519			0.418880			0.209440	−	0.977822i	$-0.432836\pi$
$599$	10.2519			0.418880			0.209440	+	0.977822i	$0.432836\pi$
$600$	−7.46931	−	4.38285i	−0.304933	−	0.178929i
$601$	−30.1688			−1.23061			−0.615306	−	0.788288i	$-0.710968\pi$
$601$	−30.1688			−1.23061			−0.615306	+	0.788288i	$0.710968\pi$
$602$	−0.816016	−	0.816016i	−0.0332583	−	0.0332583i
$603$	−4.86724	−	37.3644i	−0.198209	−	1.52160i
$604$			8.82338i			0.359018i
$605$	40.9606	−	33.3980i	1.66528	−	1.35782i
$606$	−5.65671	+	16.6268i	−0.229788	+	0.675419i
$607$	−15.5467	+	15.5467i	−0.631021	+	0.631021i	−0.948324	−	0.317303i	$-0.897223\pi$
$607$	−15.5467	+	15.5467i	−0.631021	+	0.631021i	0.317303	+	0.948324i	$0.397223\pi$
$608$	−2.79924	+	2.79924i	−0.113524	+	0.113524i
$609$	−1.45650	+	4.28110i	−0.0590203	+	0.173479i
$610$	−8.45501	−	0.859909i	−0.342333	−	0.0348167i
$611$		−	6.96706i		−	0.281857i
$612$	2.21617	+	17.0129i	0.0895833	+	0.687706i
$613$	−4.00722	−	4.00722i	−0.161850	−	0.161850i	0.621536	−	0.783386i	$-0.286509\pi$
$613$	−4.00722	−	4.00722i	−0.161850	−	0.161850i	−0.783386	+	0.621536i	$0.786509\pi$
$614$	−15.2012			−0.613469
$615$	−10.0220	−	4.58766i	−0.404126	−	0.184992i
$616$	8.96983			0.361405
$617$	−5.30562	−	5.30562i	−0.213596	−	0.213596i	0.592197	−	0.805793i	$-0.298261\pi$
$617$	−5.30562	−	5.30562i	−0.213596	−	0.213596i	−0.805793	+	0.592197i	$0.798261\pi$
$618$	−13.1428	−	26.6969i	−0.528681	−	1.07391i
$619$			29.5505i			1.18774i	0.804562	+	0.593868i	$0.202400\pi$
$619$			29.5505i			1.18774i	−0.804562	+	0.593868i	$0.797600\pi$
$620$	−1.41304	−	1.73301i	−0.0567491	−	0.0695992i
$621$	−6.99028	−	10.5082i	−0.280510	−	0.421680i
$622$	−3.56764	+	3.56764i	−0.143049	+	0.143049i
$623$	−1.26029	+	1.26029i	−0.0504924	+	0.0504924i
$624$	−6.17283	−	2.10009i	−0.247111	−	0.0840710i
$625$	−22.9734	−	9.86017i	−0.918936	−	0.394407i
$626$		−	0.941892i		−	0.0376456i
$627$	36.2038	−	17.8230i	1.44584	−	0.711783i
$628$	−3.93949	−	3.93949i	−0.157203	−	0.157203i
$629$	51.6556			2.05964
$630$	0.288069	+	10.2201i	0.0114769	+	0.407180i
$631$	20.0250			0.797182			0.398591	−	0.917129i	$-0.369499\pi$
$631$	20.0250			0.797182			0.398591	+	0.917129i	$0.369499\pi$
$632$	11.4437	+	11.4437i	0.455205	+	0.455205i
$633$	21.0087	−	10.3425i	0.835023	−	0.411079i
$634$			0.121484i			0.00482475i
$635$	−0.991398	+	9.74787i	−0.0393424	+	0.386832i
$636$	4.31535	+	1.46815i	0.171115	+	0.0582159i
$637$	12.4497	−	12.4497i	0.493276	−	0.493276i
$638$	7.12855	−	7.12855i	0.282222	−	0.282222i
$639$	−12.1921	−	9.38180i	−0.482312	−	0.371138i
$640$	−0.226250	+	2.22459i	−0.00894332	+	0.0879347i
$641$		−	11.9695i		−	0.472766i	−0.971660	−	0.236383i	$-0.924038\pi$
$641$		−	11.9695i		−	0.472766i	0.971660	−	0.236383i	$-0.0759620\pi$
$642$	7.38538	+	15.0019i	0.291478	+	0.592077i
$643$	5.02495	+	5.02495i	0.198165	+	0.198165i	0.799213	−	0.601048i	$-0.205250\pi$
$643$	5.02495	+	5.02495i	0.198165	+	0.198165i	−0.601048	+	0.799213i	$0.705250\pi$
$644$	−3.70195			−0.145877
$645$	−2.74850	+	1.02236i	−0.108222	+	0.0402553i
$646$	22.6395			0.890739
$647$	−29.4564	−	29.4564i	−1.15805	−	1.15805i	−0.984895	−	0.173155i	$-0.944604\pi$
$647$	−29.4564	−	29.4564i	−1.15805	−	1.15805i	−0.173155	−	0.984895i	$-0.555396\pi$
$648$	7.78191	+	4.52126i	0.305702	+	0.177612i
$649$			38.7200i			1.51989i
$650$	−18.4370	−	3.78944i	−0.723161	−	0.148634i
$651$	−0.850267	+	2.49920i	−0.0333246	+	0.0979513i
$652$	−14.1999	+	14.1999i	−0.556109	+	0.556109i
$653$	12.7404	−	12.7404i	0.498570	−	0.498570i	−0.412423	−	0.910993i	$-0.635317\pi$
$653$	12.7404	−	12.7404i	0.498570	−	0.498570i	0.910993	+	0.412423i	$0.135317\pi$
$654$	8.10661	−	23.8279i	0.316994	−	0.931743i
$655$	−7.41313	−	9.09174i	−0.289655	−	0.355244i
$656$			2.84590i			0.111114i
$657$	−22.7945	+	2.96931i	−0.889300	+	0.115844i
$658$	1.99458	+	1.99458i	0.0777568	+	0.0777568i
$659$	−38.2781			−1.49110			−0.745551	−	0.666448i	$-0.767814\pi$
$659$	−38.2781			−1.49110			−0.745551	+	0.666448i	$0.767814\pi$
$660$	9.48708	−	20.7251i	0.369284	−	0.806722i
$661$	10.2605			0.399087			0.199544	−	0.979889i	$-0.436054\pi$
$661$	10.2605			0.399087			0.199544	+	0.979889i	$0.436054\pi$
$662$	10.3188	+	10.3188i	0.401053	+	0.401053i
$663$	16.4696	+	33.4545i	0.639625	+	1.29927i
$664$			16.5649i			0.642843i
$665$	13.4224	+	1.36511i	0.520497	+	0.0529366i
$666$	16.5252	−	21.4753i	0.640338	−	0.832150i
$667$	−2.94203	+	2.94203i	−0.113916	+	0.113916i
$668$	−9.34843	+	9.34843i	−0.361702	+	0.361702i
$669$	−13.9355	−	4.74108i	−0.538778	−	0.183301i
$670$	−21.7666	+	17.7479i	−0.840919	+	0.685659i
$671$		−	22.3679i		−	0.863503i
$672$	2.36843	−	1.16597i	0.0913642	−	0.0449783i
$673$	30.9343	+	30.9343i	1.19243	+	1.19243i	0.976383	+	0.216046i	$0.0693160\pi$
$673$	30.9343	+	30.9343i	1.19243	+	1.19243i	0.216046	+	0.976383i	$0.430684\pi$
$674$	16.8811			0.650236
$675$	23.9186	+	10.1439i	0.920629	+	0.390439i
$676$	−1.17139			−0.0450534
$677$	23.6196	+	23.6196i	0.907776	+	0.907776i	0.996092	−	0.0883164i	$-0.0281487\pi$
$677$	23.6196	+	23.6196i	0.907776	+	0.907776i	−0.0883164	+	0.996092i	$0.528149\pi$
$678$	−2.63894	+	1.29914i	−0.101348	+	0.0498933i
$679$			21.4632i			0.823683i
$680$	9.91087	−	8.08102i	0.380064	−	0.309893i
$681$	37.5088	+	12.7611i	1.43734	+	0.489005i
$682$	4.16146	−	4.16146i	0.159351	−	0.159351i
$683$	−30.8937	+	30.8937i	−1.18211	+	1.18211i	−0.202917	+	0.979196i	$0.565042\pi$
$683$	−30.8937	+	30.8937i	−1.18211	+	1.18211i	−0.979196	+	0.202917i	$0.934958\pi$
$684$	7.24261	−	9.41213i	0.276928	−	0.359882i
$685$	42.9556	+	4.36876i	1.64125	+	0.166922i
$686$			17.7973i			0.679505i
$687$	4.08529	+	8.29843i	0.155864	+	0.316605i
$688$	0.535397	+	0.535397i	0.0204118	+	0.0204118i
$689$	9.90705			0.377429
$690$	−3.91543	+	8.55347i	−0.149058	+	0.325625i
$691$	28.5957			1.08783			0.543915	−	0.839140i	$-0.316941\pi$
$691$	28.5957			1.08783			0.543915	+	0.839140i	$0.316941\pi$
$692$	−9.23238	−	9.23238i	−0.350963	−	0.350963i
$693$	−26.6840	+	3.47597i	−1.01364	+	0.132041i
$694$			15.5527i			0.590371i
$695$	32.6822	+	40.0827i	1.23971	+	1.52042i
$696$	0.955624	−	2.80888i	0.0362228	−	0.106470i
$697$	11.5084	−	11.5084i	0.435913	−	0.435913i
$698$	−15.5497	+	15.5497i	−0.588566	+	0.588566i
$699$	−2.68591	+	7.89473i	−0.101590	+	0.298606i
$700$	6.36316	−	4.19342i	0.240505	−	0.158496i
$701$		−	28.2214i		−	1.06591i	−0.846145	−	0.532953i	$-0.821082\pi$
$701$		−	28.2214i		−	1.06591i	0.846145	−	0.532953i	$-0.178918\pi$
$702$	19.1772	+	3.85541i	0.723795	+	0.145513i
$703$	−25.2841	−	25.2841i	−0.953606	−	0.953606i
$704$	−5.88520			−0.221807
$705$	6.71814	−	2.49894i	0.253020	−	0.0941156i
$706$	−31.2968			−1.17787
$707$	−10.9280	−	10.9280i	−0.410989	−	0.410989i
$708$	5.03314	+	10.2238i	0.189157	+	0.384233i
$709$			48.6154i			1.82579i	0.408194	+	0.912895i	$0.366159\pi$
$709$			48.6154i			1.82579i	−0.408194	+	0.912895i	$0.633841\pi$
$710$	−1.16021	+	11.4077i	−0.0435418	+	0.428122i
$711$	−38.4781	−	29.6088i	−1.44304	−	1.11042i
$712$	0.826888	−	0.826888i	0.0309889	−	0.0309889i
$713$	−1.71748	+	1.71748i	−0.0643202	+	0.0643202i
$714$	−14.2926	−	4.86258i	−0.534888	−	0.181977i
$715$	5.01252	−	49.2853i	0.187458	−	1.84317i
$716$		−	10.6481i		−	0.397940i
$717$	−3.91729	+	1.92847i	−0.146294	+	0.0720200i
$718$	−10.4711	−	10.4711i	−0.390779	−	0.390779i
$719$	−23.9331			−0.892553			−0.446276	−	0.894895i	$-0.647250\pi$
$719$	−23.9331			−0.892553			−0.446276	+	0.894895i	$0.647250\pi$
$720$	−0.189005	−	6.70554i	−0.00704380	−	0.249901i
$721$	26.1846			0.975166
$722$	2.35360	+	2.35360i	0.0875918	+	0.0875918i
$723$	−2.78477	+	1.37094i	−0.103567	+	0.0509857i
$724$			2.85916i			0.106260i
$725$	1.72435	−	8.38958i	0.0640406	−	0.311581i
$726$	38.7564	+	13.1855i	1.43839	+	0.489361i
$727$	−2.96197	+	2.96197i	−0.109854	+	0.109854i	−0.759897	−	0.650043i	$-0.774751\pi$
$727$	−2.96197	+	2.96197i	−0.109854	+	0.109854i	0.650043	+	0.759897i	$0.274751\pi$
$728$	4.05709	−	4.05709i	0.150366	−	0.150366i
$729$	−24.9022	−	10.4345i	−0.922304	−	0.386464i
$730$	10.8273	+	13.2790i	0.400735	+	0.491476i
$731$		−	4.33014i		−	0.160156i
$732$	−2.90756	−	5.90611i	−0.107466	−	0.218296i
$733$	−16.0878	−	16.0878i	−0.594217	−	0.594217i	0.344551	−	0.938768i	$-0.388031\pi$
$733$	−16.0878	−	16.0878i	−0.594217	−	0.594217i	−0.938768	+	0.344551i	$0.888031\pi$
$734$	0.202342			0.00746858
$735$	16.4704	+	7.53947i	0.607520	+	0.278097i
$736$	2.42889			0.0895300
$737$	−52.2681	−	52.2681i	−1.92532	−	1.92532i
$738$	−1.10284	−	8.46617i	−0.0405960	−	0.311644i
$739$		−	12.7994i		−	0.470833i	−0.971895	−	0.235416i	$-0.924355\pi$
$739$		−	12.7994i		−	0.470833i	0.971895	−	0.235416i	$-0.0756454\pi$
$740$	−20.0935	−	2.04360i	−0.738654	−	0.0751241i
$741$	8.31369	−	24.4365i	0.305411	−	0.897698i
$742$	−2.83626	+	2.83626i	−0.104122	+	0.104122i
$743$	20.7857	−	20.7857i	0.762553	−	0.762553i	−0.214230	−	0.976783i	$-0.568724\pi$
$743$	20.7857	−	20.7857i	0.762553	−	0.762553i	0.976783	+	0.214230i	$0.0687243\pi$
$744$	0.557869	−	1.63975i	0.0204525	−	0.0601162i
$745$	29.6755	−	24.1965i	1.08723	−	0.886491i
$746$		−	31.6897i		−	1.16024i
$747$	−6.41919	−	49.2784i	−0.234866	−	1.80300i
$748$	23.7989	+	23.7989i	0.870175	+	0.870175i
$749$	−14.7140			−0.537638
$750$	−2.95893	−	19.1375i	−0.108045	−	0.698803i
$751$	24.8859			0.908099			0.454049	−	0.890977i	$-0.349979\pi$
$751$	24.8859			0.908099			0.454049	+	0.890977i	$0.349979\pi$
$752$	−1.30867	−	1.30867i	−0.0477221	−	0.0477221i
$753$	−5.22638	−	10.6163i	−0.190460	−	0.386880i
$754$		−	6.44854i		−	0.234842i
$755$	−15.2910	+	12.4678i	−0.556496	+	0.453750i
$756$	−6.59393	+	4.38642i	−0.239819	+	0.159532i
$757$	−24.2813	+	24.2813i	−0.882520	+	0.882520i	−0.993790	−	0.111270i	$-0.964508\pi$
$757$	−24.2813	+	24.2813i	−0.882520	+	0.882520i	0.111270	+	0.993790i	$0.464508\pi$
$758$	16.3901	−	16.3901i	0.595316	−	0.595316i
$759$	−23.4394	−	7.97445i	−0.850796	−	0.289454i
$760$	−8.80655	−	0.895662i	−0.319447	−	0.0324891i
$761$			30.1048i			1.09130i	0.838013	+	0.545650i	$0.183717\pi$
$761$			30.1048i			1.09130i	−0.838013	+	0.545650i	$0.816283\pi$
$762$	−6.80921	+	3.35215i	−0.246672	+	0.121436i
$763$	15.6608	+	15.6608i	0.566961	+	0.566961i
$764$	12.5060			0.452452
$765$	−26.3520	+	27.8806i	−0.952757	+	1.00802i
$766$	32.4740			1.17333
$767$	17.5132	+	17.5132i	0.632364	+	0.632364i
$768$	−1.55395	+	0.765006i	−0.0560734	+	0.0276048i
$769$		−	34.5113i		−	1.24451i	−0.782814	−	0.622255i	$-0.786217\pi$
$769$		−	34.5113i		−	1.24451i	0.782814	−	0.622255i	$-0.213783\pi$
$770$	12.6747	+	15.5448i	0.456766	+	0.560195i
$771$	−17.7061	−	6.02389i	−0.637670	−	0.216945i
$772$	−15.0464	+	15.0464i	−0.541532	+	0.541532i
$773$	25.5174	−	25.5174i	0.917796	−	0.917796i	−0.0790733	−	0.996869i	$-0.525196\pi$
$773$	25.5174	−	25.5174i	0.917796	−	0.917796i	0.996869	+	0.0790733i	$0.0251961\pi$
$774$	−1.80021	−	1.38526i	−0.0647072	−	0.0497921i
$775$	1.00663	−	4.89762i	0.0361592	−	0.175928i
$776$		−	14.0822i		−	0.505523i
$777$	10.5316	+	21.3928i	0.377819	+	0.767461i
$778$	8.94856	+	8.94856i	0.320822	+	0.320822i
$779$	−11.2661			−0.403651
$780$	−5.08298	−	13.6651i	−0.182000	−	0.489288i
$781$	−30.1792			−1.07990
$782$	−9.82208	−	9.82208i	−0.351237	−	0.351237i
$783$	−1.75436	+	8.72636i	−0.0626959	+	0.311855i
$784$		−	4.67702i		−	0.167036i
$785$	1.26050	−	12.3938i	0.0449893	−	0.442355i
$786$	2.92670	−	8.60250i	0.104392	−	0.306841i
$787$	−29.5518	+	29.5518i	−1.05341	+	1.05341i	−0.0549181	+	0.998491i	$0.517490\pi$
$787$	−29.5518	+	29.5518i	−1.05341	+	1.05341i	−0.998491	+	0.0549181i	$0.982510\pi$
$788$	−3.75213	+	3.75213i	−0.133664	+	0.133664i
$789$	14.2593	−	41.9127i	0.507646	−	1.49213i
$790$	−3.66159	+	36.0024i	−0.130274	+	1.28091i
$791$		−	2.58830i		−	0.0920295i
$792$	17.5077	−	2.28062i	0.622108	−	0.0810382i
$793$	−10.1171	−	10.1171i	−0.359268	−	0.359268i
$794$	−27.5995			−0.979468
$795$	3.55345	+	9.55309i	0.126028	+	0.338813i
$796$	11.3351			0.401763
$797$	−11.3248	−	11.3248i	−0.401145	−	0.401145i	0.477491	−	0.878636i	$-0.341546\pi$
$797$	−11.3248	−	11.3248i	−0.401145	−	0.401145i	−0.878636	+	0.477491i	$0.841546\pi$
$798$	4.61576	+	9.37596i	0.163396	+	0.331906i
$799$			10.5841i			0.374439i
$800$	−4.17494	+	2.75135i	−0.147606	+	0.0972748i
$801$	−2.13945	+	2.78032i	−0.0755937	+	0.0982376i
$802$	−13.5355	+	13.5355i	−0.477957	+	0.477957i
$803$	−31.8867	+	31.8867i	−1.12526	+	1.12526i
$804$	−20.5953	−	7.00685i	−0.726341	−	0.247113i
$805$	−5.23101	−	6.41550i	−0.184369	−	0.226117i
$806$		−	3.76449i		−	0.132599i
$807$	−11.9260	+	5.87114i	−0.419815	+	0.206674i
$808$	7.16996	+	7.16996i	0.252238	+	0.252238i
$809$	29.3613			1.03229			0.516143	−	0.856502i	$-0.327367\pi$
$809$	29.3613			1.03229			0.516143	+	0.856502i	$0.327367\pi$
$810$	3.16078	+	19.8748i	0.111059	+	0.698331i
$811$	−5.16605			−0.181405			−0.0907023	−	0.995878i	$-0.528911\pi$
$811$	−5.16605			−0.181405			−0.0907023	+	0.995878i	$0.528911\pi$
$812$	1.84613	+	1.84613i	0.0647866	+	0.0647866i
$813$	−29.1663	+	14.3585i	−1.02291	+	0.503574i
$814$		−	53.1578i		−	1.86318i
$815$	−44.6734	−	4.54347i	−1.56484	−	0.159151i
$816$	9.37754	+	3.19039i	0.328280	+	0.111686i
$817$	−2.11949	+	2.11949i	−0.0741516	+	0.0741516i
$818$	−17.0912	+	17.0912i	−0.597579	+	0.597579i
$819$	−10.4971	+	13.6415i	−0.366798	+	0.476672i
$820$	−4.93197	+	4.02138i	−0.172232	+	0.140433i
$821$			0.234824i			0.00819543i	0.999992	+	0.00409771i	$0.00130435\pi$
$821$			0.234824i			0.00819543i	−0.999992	+	0.00409771i	$0.998696\pi$
$822$	14.7718	+	30.0059i	0.515226	+	1.04658i
$823$	1.63126	+	1.63126i	0.0568623	+	0.0568623i	0.734966	−	0.678104i	$-0.237198\pi$
$823$	1.63126	+	1.63126i	0.0568623	+	0.0568623i	−0.678104	+	0.734966i	$0.737198\pi$
$824$	−17.1800			−0.598494
$825$	49.3223	−	12.8442i	1.71718	−	0.447177i
$826$	−10.0276			−0.348905
$827$	−0.735311	−	0.735311i	−0.0255693	−	0.0255693i	0.694207	−	0.719776i	$-0.255755\pi$
$827$	−0.735311	−	0.735311i	−0.0255693	−	0.0255693i	−0.719776	+	0.694207i	$0.755755\pi$
$828$	−7.22562	+	0.941237i	−0.251108	+	0.0327102i
$829$			20.7527i			0.720771i	0.932803	+	0.360386i	$0.117355\pi$
$829$			20.7527i			0.720771i	−0.932803	+	0.360386i	$0.882645\pi$
$830$	−28.7071	+	23.4069i	−0.996438	+	0.812465i
$831$	−2.85542	+	8.39297i	−0.0990534	+	0.291149i
$832$	−2.66190	+	2.66190i	−0.0922847	+	0.0922847i
$833$	−18.9132	+	18.9132i	−0.655304	+	0.655304i
$834$	−12.9029	+	37.9258i	−0.446792	+	1.31326i
$835$	−29.4106	−	2.99118i	−1.01780	−	0.103514i
$836$		−	23.2979i		−	0.805774i
$837$	−1.02415	+	5.09422i	−0.0353999	+	0.176082i
$838$	12.5570	+	12.5570i	0.433774	+	0.433774i
$839$	46.9394			1.62053			0.810264	−	0.586065i	$-0.199323\pi$
$839$	46.9394			1.62053			0.810264	+	0.586065i	$0.199323\pi$
$840$	5.36733	+	2.45694i	0.185190	+	0.0847725i
$841$	−26.0657			−0.898816
$842$	−2.07626	−	2.07626i	−0.0715527	−	0.0715527i
$843$	9.30863	+	18.9086i	0.320606	+	0.651246i
$844$		−	13.5196i		−	0.465363i
$845$	−1.65522	−	2.03002i	−0.0569413	−	0.0698349i
$846$	4.40023	+	3.38597i	0.151283	+	0.116412i
$847$	−25.4726	+	25.4726i	−0.875250	+	0.875250i
$848$	1.86090	−	1.86090i	0.0639036	−	0.0639036i
$849$	37.0864	+	12.6174i	1.27280	+	0.433027i
$850$	28.0089	+	5.75679i	0.960698	+	0.197456i
$851$			21.9388i			0.752054i
$852$	−7.96863	+	3.92294i	−0.273001	+	0.134398i
$853$	−19.2000	−	19.2000i	−0.657397	−	0.657397i	0.297367	−	0.954763i	$-0.403892\pi$
$853$	−19.2000	−	19.2000i	−0.657397	−	0.657397i	−0.954763	+	0.297367i	$0.903892\pi$
$854$	5.79278			0.198225
$855$	26.5454	−	0.748219i	0.907833	−	0.0255886i
$856$	9.65401			0.329967
$857$	22.1292	+	22.1292i	0.755919	+	0.755919i	0.975577	−	0.219658i	$-0.0704941\pi$
$857$	22.1292	+	22.1292i	0.755919	+	0.755919i	−0.219658	+	0.975577i	$0.570494\pi$
$858$	34.4274	−	16.9485i	1.17533	−	0.578613i
$859$		−	19.2083i		−	0.655377i	−0.944786	−	0.327689i	$-0.893730\pi$
$859$		−	19.2083i		−	0.655377i	0.944786	−	0.327689i	$-0.106270\pi$
$860$	−0.171309	+	1.68438i	−0.00584158	+	0.0574370i
$861$	7.11247	+	2.41977i	0.242392	+	0.0824657i
$862$	−11.1617	+	11.1617i	−0.380168	+	0.380168i
$863$	−4.98167	+	4.98167i	−0.169578	+	0.169578i	−0.786794	−	0.617216i	$-0.788261\pi$
$863$	−4.98167	+	4.98167i	−0.169578	+	0.169578i	0.617216	+	0.786794i	$0.288261\pi$
$864$	4.32635	−	2.87797i	0.147185	−	0.0979107i
$865$	2.95405	−	29.0455i	0.100441	−	0.987577i
$866$		−	18.5456i		−	0.630205i
$867$	−12.0149	−	24.4058i	−0.408047	−	0.828864i
$868$	1.07773	+	1.07773i	0.0365804	+	0.0365804i
$869$	−95.2449			−3.23096
$870$	6.21814	−	2.31296i	0.210815	−	0.0784166i
$871$	−47.2821			−1.60209
$872$	−10.2752	−	10.2752i	−0.347964	−	0.347964i
$873$	5.45712	+	41.8928i	0.184695	+	1.41786i
$874$			9.61530i			0.325242i
$875$	16.2586	+	5.10192i	0.549642	+	0.172476i
$876$	−4.27460	+	12.5644i	−0.144425	+	0.424511i
$877$	−15.3604	+	15.3604i	−0.518683	+	0.518683i	−0.917173	−	0.398490i	$-0.869534\pi$
$877$	−15.3604	+	15.3604i	−0.518683	+	0.518683i	0.398490	+	0.917173i	$0.369534\pi$
$878$	−27.5976	+	27.5976i	−0.931373	+	0.931373i
$879$	−4.93620	+	14.5090i	−0.166494	+	0.489377i
$880$	−8.31603	−	10.1991i	−0.280333	−	0.343811i
$881$		−	32.6789i		−	1.10098i	−0.834842	−	0.550490i	$-0.814441\pi$
$881$		−	32.6789i		−	1.10098i	0.834842	−	0.550490i	$-0.185559\pi$
$882$	1.81243	+	13.9135i	0.0610276	+	0.468492i
$883$	−22.0645	−	22.0645i	−0.742530	−	0.742530i	0.230534	−	0.973064i	$-0.425953\pi$
$883$	−22.0645	−	22.0645i	−0.742530	−	0.742530i	−0.973064	+	0.230534i	$0.925953\pi$
$884$	21.5287			0.724088
$885$	−10.6059	+	23.1691i	−0.356512	+	0.778820i
$886$	−28.0672			−0.942936
$887$	−10.9781	−	10.9781i	−0.368607	−	0.368607i	0.498362	−	0.866969i	$-0.333935\pi$
$887$	−10.9781	−	10.9781i	−0.368607	−	0.368607i	−0.866969	+	0.498362i	$0.833935\pi$
$888$	−6.90989	−	14.0360i	−0.231881	−	0.471018i
$889$		−	6.67855i		−	0.223991i
$890$	2.60143	+	0.264576i	0.0872002	+	0.00886861i
$891$	−51.1992	+	13.5691i	−1.71524	+	0.454581i
$892$	−6.00939	+	6.00939i	−0.201209	+	0.201209i
$893$	5.18065	−	5.18065i	0.173364	−	0.173364i
$894$	28.0786	+	9.55278i	0.939089	+	0.319493i
$895$	18.4533	−	15.0463i	0.616826	−	0.502941i
$896$		−	1.52413i		−	0.0509177i
$897$	−14.2086	+	6.99485i	−0.474411	+	0.233551i
$898$	8.34879	+	8.34879i	0.278603	+	0.278603i
$899$	1.71299			0.0571314
$900$	11.3537	−	9.80275i	0.378456	−	0.326758i
$901$	−15.0505			−0.501403
$902$	−11.8431	−	11.8431i	−0.394332	−	0.394332i
$903$	1.79329	−	0.882833i	0.0596771	−	0.0293789i
$904$			1.69821i			0.0564817i
$905$	−4.95495	+	4.04011i	−0.164708	+	0.134298i
$906$	−14.4681	−	4.92229i	−0.480672	−	0.163532i
$907$	−13.5200	+	13.5200i	−0.448924	+	0.448924i	−0.894997	−	0.446073i	$-0.852822\pi$
$907$	−13.5200	+	13.5200i	−0.448924	+	0.448924i	0.446073	+	0.894997i	$0.352822\pi$
$908$	16.1748	−	16.1748i	0.536781	−	0.536781i
$909$	−24.1082	−	18.5512i	−0.799617	−	0.615304i
$910$	12.7638	+	1.29813i	0.423116	+	0.0430326i
$911$		−	48.3234i		−	1.60103i	−0.599315	−	0.800513i	$-0.704560\pi$
$911$		−	48.3234i		−	1.60103i	0.599315	−	0.800513i	$-0.295440\pi$
$912$	−3.02845	−	6.15167i	−0.100282	−	0.203702i
$913$	−68.9342	−	68.9342i	−2.28139	−	2.28139i
$914$	−6.39755			−0.211612
$915$	6.12683	−	13.3844i	0.202547	−	0.442474i
$916$	5.34021			0.176446
$917$	5.65399	+	5.65399i	0.186711	+	0.186711i
$918$	−29.1333	−	5.85701i	−0.961541	−	0.193310i
$919$			48.5166i			1.60041i	0.599724	+	0.800207i	$0.295277\pi$
$919$			48.5166i			1.60041i	−0.599724	+	0.800207i	$0.704723\pi$
$920$	3.43212	+	4.20928i	0.113154	+	0.138776i
$921$	8.48026	−	24.9261i	0.279434	−	0.821344i
$922$	11.3805	−	11.3805i	0.374796	−	0.374796i
$923$	−13.6502	+	13.6502i	−0.449300	+	0.449300i
$924$	−5.00399	+	14.7083i	−0.164619	+	0.483867i
$925$	−24.8514	−	37.7100i	−0.817111	−	1.23990i
$926$			8.43671i			0.277247i
$927$	51.1082	−	6.65756i	1.67861	−	0.218663i
$928$	−1.21127	−	1.21127i	−0.0397618	−	0.0397618i
$929$	19.1173			0.627219			0.313610	−	0.949552i	$-0.398462\pi$
$929$	19.1173			0.627219			0.313610	+	0.949552i	$0.398462\pi$
$930$	3.62999	−	1.35024i	0.119032	−	0.0442763i
$931$	18.5150			0.606806
$932$	3.40443	+	3.40443i	0.111516	+	0.111516i
$933$	−3.85977	−	7.84032i	−0.126363	−	0.256681i
$934$			35.8210i			1.17210i
$935$	−7.61485	+	74.8726i	−0.249032	+	2.44859i
$936$	6.88725	−	8.95032i	0.225117	−	0.292550i
$937$	37.6734	−	37.6734i	1.23074	−	1.23074i	0.267054	−	0.963682i	$-0.413950\pi$
$937$	37.6734	−	37.6734i	1.23074	−	1.23074i	0.963682	−	0.267054i	$-0.0860501\pi$
$938$	13.5363	−	13.5363i	0.441975	−	0.441975i
$939$	1.54447	+	0.525452i	0.0504018	+	0.0171475i
$940$	0.418728	−	4.11712i	0.0136574	−	0.134286i
$941$			27.8989i			0.909477i	0.890625	+	0.454738i	$0.150267\pi$
$941$			27.8989i			0.909477i	−0.890625	+	0.454738i	$0.849733\pi$
$942$	8.65750	−	4.26206i	0.282077	−	0.138866i
$943$	4.88779	+	4.88779i	0.159168	+	0.159168i
$944$	6.57921			0.214135
$945$	−16.9192	−	5.22914i	−0.550381	−	0.170104i
$946$	−4.45607			−0.144879
$947$	−41.7393	−	41.7393i	−1.35635	−	1.35635i	−0.878376	−	0.477971i	$-0.841373\pi$
$947$	−41.7393	−	41.7393i	−1.35635	−	1.35635i	−0.477971	−	0.878376i	$-0.658627\pi$
$948$	−25.1489	+	12.3807i	−0.816797	+	0.402107i
$949$			28.8449i			0.936346i
$950$	−10.8918	−	16.5274i	−0.353378	−	0.536220i
$951$	−0.199204	−	0.0677722i	−0.00645962	−	0.00219766i
$952$	−6.16338	+	6.16338i	−0.199756	+	0.199756i
$953$	18.8803	−	18.8803i	0.611594	−	0.611594i	−0.331767	−	0.943361i	$-0.607645\pi$
$953$	18.8803	−	18.8803i	0.611594	−	0.611594i	0.943361	+	0.331767i	$0.107645\pi$
$954$	−4.81480	+	6.25706i	−0.155885	+	0.202580i
$955$	17.6715	+	21.6730i	0.571837	+	0.701323i
$956$			2.52085i			0.0815303i
$957$	7.71224	+	15.6658i	0.249301	+	0.506404i
$958$	3.02655	+	3.02655i	0.0977835	+	0.0977835i
$959$	−29.4301			−0.950348
$960$	−3.52156	−	1.61202i	−0.113658	−	0.0520279i
$961$	1.00000			0.0322581
$962$	−24.0435	−	24.0435i	−0.775193	−	0.775193i
$963$	−28.7194	+	3.74110i	−0.925470	+	0.120555i
$964$			1.79206i			0.0577183i
$965$	−47.3367	−	4.81433i	−1.52382	−	0.154979i
$966$	2.06520	−	6.07027i	0.0664468	−	0.195308i
$967$	43.1363	−	43.1363i	1.38717	−	1.38717i	0.555967	−	0.831205i	$-0.312348\pi$
$967$	43.1363	−	43.1363i	1.38717	−	1.38717i	0.831205	−	0.555967i	$-0.187652\pi$
$968$	16.7129	−	16.7129i	0.537172	−	0.537172i
$969$	−12.6299	+	37.1231i	−0.405730	+	1.19257i
$970$	24.4046	−	19.8988i	0.783585	−	0.638912i
$971$			3.26395i			0.104745i	0.998628	+	0.0523725i	$0.0166783\pi$
$971$			3.26395i			0.104745i	−0.998628	+	0.0523725i	$0.983322\pi$
$972$	−11.7550	+	10.2381i	−0.377043	+	0.328388i
$973$	−24.9267	−	24.9267i	−0.799113	−	0.799113i
$974$	−14.7704			−0.473273
$975$	16.4992	−	28.1182i	0.528397	−	0.900502i
$976$	−3.80070			−0.121658
$977$	5.20121	+	5.20121i	0.166401	+	0.166401i	0.785396	−	0.618994i	$-0.212460\pi$
$977$	5.20121	+	5.20121i	0.166401	+	0.166401i	−0.618994	+	0.785396i	$0.712460\pi$
$978$	−15.3626	−	31.2059i	−0.491241	−	0.997854i
$979$			6.88213i			0.219954i
$980$	8.10530	−	6.60882i	0.258914	−	0.211111i
$981$	34.5493	+	26.5856i	1.10307	+	0.848814i
$982$	10.7414	−	10.7414i	0.342773	−	0.342773i
$983$	−36.7462	+	36.7462i	−1.17202	+	1.17202i	−0.190295	+	0.981727i	$0.560944\pi$
$983$	−36.7462	+	36.7462i	−1.17202	+	1.17202i	−0.981727	+	0.190295i	$0.939056\pi$
$984$	−4.66657	−	1.58764i	−0.148765	−	0.0506121i
$985$	−11.8044	−	1.20055i	−0.376119	−	0.0382528i
$986$			9.79639i			0.311981i
$987$	−4.38333	+	2.15790i	−0.139523	+	0.0686867i
$988$	−10.5377	−	10.5377i	−0.335250	−	0.335250i
$989$	1.83907			0.0584790
$990$	28.6914	+	27.1183i	0.911872	+	0.861877i
$991$	57.5096			1.82685			0.913426	−	0.407006i	$-0.133427\pi$
$991$	57.5096			1.82685			0.913426	+	0.407006i	$0.133427\pi$
$992$	−0.707107	−	0.707107i	−0.0224507	−	0.0224507i
$993$	−22.6769	+	11.1638i	−0.719630	+	0.354272i
$994$		−	7.81573i		−	0.247900i
$995$	16.0170	+	19.6439i	0.507773	+	0.622752i
$996$	−27.1623	−	9.24105i	−0.860671	−	0.292814i
$997$	−17.7135	+	17.7135i	−0.560993	+	0.560993i	−0.929590	−	0.368596i	$-0.879839\pi$
$997$	−17.7135	+	17.7135i	−0.560993	+	0.560993i	0.368596	+	0.929590i	$0.379839\pi$
$998$	−8.48968	+	8.48968i	−0.268736	+	0.268736i
$999$	25.9952	+	39.0776i	0.822452	+	1.23636i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.g.683.12	yes	40
3.2	odd	2	inner	930.2.j.g.683.7	yes	40
5.2	odd	4	inner	930.2.j.g.497.7	✓	40
15.2	even	4	inner	930.2.j.g.497.12	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.g.497.7	✓	40	5.2	odd	4	inner
930.2.j.g.497.12	yes	40	15.2	even	4	inner
930.2.j.g.683.7	yes	40	3.2	odd	2	inner
930.2.j.g.683.12	yes	40	1.1	even	1	trivial

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

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.55395 + 0.765006i) q^{3} +1.00000i q^{4} +(-1.73301 + 1.41304i) q^{5} +(-1.63975 - 0.557869i) q^{6} +(1.07773 - 1.07773i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.82953 - 2.37756i) q^{9} +(-2.22459 - 0.226250i) q^{10} -5.88520i q^{11} +(-0.765006 - 1.55395i) q^{12} +(-2.66190 - 2.66190i) q^{13} +1.52413 q^{14} +(1.61202 - 3.52156i) q^{15} -1.00000 q^{16} +(4.04386 + 4.04386i) q^{17} +(2.97487 - 0.387518i) q^{18} -3.95873i q^{19} +(-1.41304 - 1.73301i) q^{20} +(-0.850267 + 2.49920i) q^{21} +(4.16146 - 4.16146i) q^{22} +(-1.71748 + 1.71748i) q^{23} +(0.557869 - 1.63975i) q^{24} +(1.00663 - 4.89762i) q^{25} -3.76449i q^{26} +(-1.02415 + 5.09422i) q^{27} +(1.07773 + 1.07773i) q^{28} +1.71299 q^{29} +(3.62999 - 1.35024i) q^{30} +1.00000 q^{31} +(-0.707107 - 0.707107i) q^{32} +(4.50221 + 9.14531i) q^{33} +5.71888i q^{34} +(-0.344835 + 3.39058i) q^{35} +(2.37756 + 1.82953i) q^{36} +(6.38692 - 6.38692i) q^{37} +(2.79924 - 2.79924i) q^{38} +(6.17283 + 2.10009i) q^{39} +(0.226250 - 2.22459i) q^{40} -2.84590i q^{41} +(-2.36843 + 1.16597i) q^{42} +(-0.535397 - 0.535397i) q^{43} +5.88520 q^{44} +(0.189005 + 6.70554i) q^{45} -2.42889 q^{46} +(1.30867 + 1.30867i) q^{47} +(1.55395 - 0.765006i) q^{48} +4.67702i q^{49} +(4.17494 - 2.75135i) q^{50} +(-9.37754 - 3.19039i) q^{51} +(2.66190 - 2.66190i) q^{52} +(-1.86090 + 1.86090i) q^{53} +(-4.32635 + 2.87797i) q^{54} +(8.31603 + 10.1991i) q^{55} +1.52413i q^{56} +(3.02845 + 6.15167i) q^{57} +(1.21127 + 1.21127i) q^{58} -6.57921 q^{59} +(3.52156 + 1.61202i) q^{60} +3.80070 q^{61} +(0.707107 + 0.707107i) q^{62} +(-0.590629 - 4.53409i) q^{63} -1.00000i q^{64} +(8.37446 + 0.851716i) q^{65} +(-3.28317 + 9.65026i) q^{66} +(8.88129 - 8.88129i) q^{67} +(-4.04386 + 4.04386i) q^{68} +(1.35500 - 3.98277i) q^{69} +(-2.64133 + 2.15366i) q^{70} -5.12798i q^{71} +(0.387518 + 2.97487i) q^{72} +(-5.41812 - 5.41812i) q^{73} +9.03246 q^{74} +(2.18246 + 8.38074i) q^{75} +3.95873 q^{76} +(-6.34263 - 6.34263i) q^{77} +(2.87986 + 5.84984i) q^{78} -16.1838i q^{79} +(1.73301 - 1.41304i) q^{80} +(-2.30563 - 8.69966i) q^{81} +(2.01236 - 2.01236i) q^{82} +(11.7132 - 11.7132i) q^{83} +(-2.49920 - 0.850267i) q^{84} +(-12.7222 - 1.29390i) q^{85} -0.757166i q^{86} +(-2.66190 + 1.31045i) q^{87} +(4.16146 + 4.16146i) q^{88} -1.16940 q^{89} +(-4.60789 + 4.87518i) q^{90} -5.73759 q^{91} +(-1.71748 - 1.71748i) q^{92} +(-1.55395 + 0.765006i) q^{93} +1.85073i q^{94} +(5.59384 + 6.86050i) q^{95} +(1.63975 + 0.557869i) q^{96} +(-9.95765 + 9.95765i) q^{97} +(-3.30715 + 3.30715i) q^{98} +(-13.9924 - 10.7672i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} - 8 q^{7} + 8 q^{10} + 4 q^{12} - 20 q^{13} - 44 q^{15} - 40 q^{16} + 16 q^{18} - 32 q^{21} - 4 q^{22} + 8 q^{25} + 8 q^{27} - 8 q^{28} - 4 q^{30} + 40 q^{31} + 48 q^{33} + 64 q^{37} - 4 q^{40}+ \cdots - 52 q^{97}+O(q^{100}) \) 40 * q - 4 * q^3 - 8 * q^7 + 8 * q^10 + 4 * q^12 - 20 * q^13 - 44 * q^15 - 40 * q^16 + 16 * q^18 - 32 * q^21 - 4 * q^22 + 8 * q^25 + 8 * q^27 - 8 * q^28 - 4 * q^30 + 40 * q^31 + 48 * q^33 + 64 * q^37 - 4 * q^40 - 20 * q^42 - 48 * q^43 - 4 * q^45 - 80 * q^46 + 4 * q^48 + 48 * q^51 + 20 * q^52 + 164 * q^55 + 40 * q^57 + 56 * q^58 + 24 * q^60 - 128 * q^61 + 56 * q^63 + 8 * q^66 - 4 * q^67 - 56 * q^70 - 16 * q^72 - 48 * q^73 - 48 * q^75 - 40 * q^76 - 36 * q^78 - 24 * q^81 - 16 * q^82 - 56 * q^85 - 12 * q^87 - 4 * q^88 - 28 * q^90 - 32 * q^91 - 4 * q^93 - 52 * q^97

Introduction

L-functions

Modular forms

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