LMFDB - Embedded newform 750.2.l.c.107.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(107,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("750.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.l (of order $20$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			107.2
Character	$\chi$	$=$	750.107
Dual form			750.2.l.c.743.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.891007 - 0.453990i) q^{2} +(-1.36935 + 1.06061i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.70160 - 0.323338i) q^{6} +(3.13589 + 3.13589i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(0.750223 - 2.90468i) q^{9} +O(q^{10})$	\(q+(-0.891007 - 0.453990i) q^{2} +(-1.36935 + 1.06061i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.70160 - 0.323338i) q^{6} +(3.13589 + 3.13589i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(0.750223 - 2.90468i) q^{9} +(3.57685 - 1.16219i) q^{11} +(-1.66293 - 0.484416i) q^{12} +(-1.78169 - 3.49677i) q^{13} +(-1.37043 - 4.21776i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(0.406920 - 0.0644499i) q^{17} +(-1.98715 + 2.24749i) q^{18} +(2.93913 - 4.04536i) q^{19} +(-7.62006 - 0.968173i) q^{21} +(-3.71462 - 0.588338i) q^{22} +(-2.28327 + 4.48117i) q^{23} +(1.26176 + 1.18657i) q^{24} +3.92451i q^{26} +(2.05341 + 4.77321i) q^{27} +(-0.693758 + 4.38021i) q^{28} +(1.49299 - 1.08472i) q^{29} +(2.69808 + 1.96027i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.66532 + 5.38508i) q^{33} +(-0.391828 - 0.127313i) q^{34} +(2.79091 - 1.10038i) q^{36} +(4.70465 - 2.39714i) q^{37} +(-4.45534 + 2.27011i) q^{38} +(6.14845 + 2.89861i) q^{39} +(-3.24600 - 1.05469i) q^{41} +(6.34998 + 4.32208i) q^{42} +(3.71639 - 3.71639i) q^{43} +(3.04265 + 2.21062i) q^{44} +(4.06882 - 2.95617i) q^{46} +(0.808572 - 5.10512i) q^{47} +(-0.585546 - 1.63007i) q^{48} +12.6676i q^{49} +(-0.488859 + 0.519837i) q^{51} +(1.78169 - 3.49677i) q^{52} +(8.20487 + 1.29952i) q^{53} +(0.337390 - 5.18519i) q^{54} +(2.60672 - 3.58784i) q^{56} +(0.265855 + 8.65677i) q^{57} +(-1.82271 + 0.288689i) q^{58} +(-1.73564 + 5.34175i) q^{59} +(4.43829 + 13.6596i) q^{61} +(-1.51406 - 2.97152i) q^{62} +(11.4614 - 6.75613i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(5.71060 - 3.13412i) q^{66} +(-0.968887 - 6.11731i) q^{67} +(0.291323 + 0.291323i) q^{68} +(-1.62617 - 8.55793i) q^{69} +(0.992045 + 1.36543i) q^{71} +(-2.98628 - 0.286595i) q^{72} +(3.19175 + 1.62628i) q^{73} -5.28015 q^{74} +5.00034 q^{76} +(14.8611 + 7.57211i) q^{77} +(-4.16237 - 5.37402i) q^{78} +(6.24842 + 8.60021i) q^{79} +(-7.87433 - 4.35832i) q^{81} +(2.41339 + 2.41339i) q^{82} +(1.10932 + 7.00394i) q^{83} +(-3.69569 - 6.73384i) q^{84} +(-4.99854 + 1.62412i) q^{86} +(-0.893957 + 3.06883i) q^{87} +(-1.70742 - 3.35101i) q^{88} +(0.324819 + 0.999689i) q^{89} +(5.37828 - 16.5526i) q^{91} +(-4.96742 + 0.786761i) q^{92} +(-5.77369 + 0.177314i) q^{93} +(-3.03812 + 4.18162i) q^{94} +(-0.218312 + 1.71824i) q^{96} +(-7.61627 - 1.20630i) q^{97} +(5.75096 - 11.2869i) q^{98} +(-0.692350 - 11.2615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q + 4 * q^3 + 4 * q^7	$ 80 q + 4 q^{3} + 4 q^{7} + 16 q^{12} + 20 q^{16} - 8 q^{18} + 40 q^{19} + 4 q^{22} - 56 q^{27} + 4 q^{28} - 96 q^{33} + 40 q^{34} - 64 q^{37} + 40 q^{39} - 4 q^{42} - 24 q^{43} + 16 q^{48} - 64 q^{57} + 20 q^{58} + 4 q^{63} - 104 q^{67} - 140 q^{69} + 8 q^{72} - 60 q^{73} - 60 q^{78} - 80 q^{79} - 40 q^{81} + 96 q^{82} - 60 q^{84} + 80 q^{87} + 24 q^{88} + 12 q^{93} - 12 q^{97}+O(q^{100}) $ 80 * q + 4 * q^3 + 4 * q^7 + 16 * q^12 + 20 * q^16 - 8 * q^18 + 40 * q^19 + 4 * q^22 - 56 * q^27 + 4 * q^28 - 96 * q^33 + 40 * q^34 - 64 * q^37 + 40 * q^39 - 4 * q^42 - 24 * q^43 + 16 * q^48 - 64 * q^57 + 20 * q^58 + 4 * q^63 - 104 * q^67 - 140 * q^69 + 8 * q^72 - 60 * q^73 - 60 * q^78 - 80 * q^79 - 40 * q^81 + 96 * q^82 - 60 * q^84 + 80 * q^87 + 24 * q^88 + 12 * q^93 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{13}{20}\right)$	$-1$

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 $

$2$	−0.891007	−	0.453990i	−0.630037	−	0.321020i
$2$	−0.891007	−	0.453990i	−0.630037	−	0.321020i
$3$	−1.36935	+	1.06061i	−0.790593	+	0.612342i
$3$	−1.36935	+	1.06061i	−0.790593	+	0.612342i
$4$	0.587785	+	0.809017i	0.293893	+	0.404508i
$5$		0			0
$5$		0			0
$6$	1.70160	−	0.323338i	0.694677	−	0.132002i
$7$	3.13589	+	3.13589i	1.18525	+	1.18525i	0.978364	+	0.206890i	$0.0663341\pi$
$7$	3.13589	+	3.13589i	1.18525	+	1.18525i	0.206890	+	0.978364i	$0.433666\pi$
$8$	−0.156434	−	0.987688i	−0.0553079	−	0.349201i
$9$	0.750223	−	2.90468i	0.250074	−	0.968227i
$10$		0			0
$11$	3.57685	−	1.16219i	1.07846	−	0.350413i	0.284684	−	0.958622i	$-0.408111\pi$
$11$	3.57685	−	1.16219i	1.07846	−	0.350413i	0.793778	+	0.608208i	$0.208111\pi$
$12$	−1.66293	−	0.484416i	−0.480047	−	0.139839i
$13$	−1.78169	−	3.49677i	−0.494152	−	0.969828i	−0.994573	−	0.104046i	$-0.966821\pi$
$13$	−1.78169	−	3.49677i	−0.494152	−	0.969828i	0.500420	−	0.865783i	$-0.333179\pi$
$14$	−1.37043	−	4.21776i	−0.366264	−	1.12724i
$15$		0			0
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	0.406920	−	0.0644499i	0.0986927	−	0.0156314i	−0.106893	−	0.994271i	$-0.534090\pi$
$17$	0.406920	−	0.0644499i	0.0986927	−	0.0156314i	0.205585	+	0.978639i	$0.434090\pi$
$18$	−1.98715	+	2.24749i	−0.468376	+	0.529739i
$19$	2.93913	−	4.04536i	0.674282	−	0.928070i	−0.325565	−	0.945520i	$-0.605555\pi$
$19$	2.93913	−	4.04536i	0.674282	−	0.928070i	0.999848	+	0.0174495i	$0.00555464\pi$
$20$		0			0
$21$	−7.62006	−	0.968173i	−1.66283	−	0.211273i
$22$	−3.71462	−	0.588338i	−0.791960	−	0.125434i
$23$	−2.28327	+	4.48117i	−0.476095	+	0.934389i	0.520650	+	0.853770i	$0.325690\pi$
$23$	−2.28327	+	4.48117i	−0.476095	+	0.934389i	−0.996745	+	0.0806186i	$0.974310\pi$
$24$	1.26176	+	1.18657i	0.257556	+	0.242208i
$25$		0			0
$26$			3.92451i			0.769660i
$27$	2.05341	+	4.77321i	0.395179	+	0.918604i
$28$	−0.693758	+	4.38021i	−0.131108	+	0.827783i
$29$	1.49299	−	1.08472i	0.277241	−	0.201427i	−0.440472	−	0.897766i	$-0.645189\pi$
$29$	1.49299	−	1.08472i	0.277241	−	0.201427i	0.717713	+	0.696339i	$0.245189\pi$
$30$		0			0
$31$	2.69808	+	1.96027i	0.484590	+	0.352075i	0.803100	−	0.595844i	$-0.203182\pi$
$31$	2.69808	+	1.96027i	0.484590	+	0.352075i	−0.318510	+	0.947920i	$0.603182\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−3.66532	+	5.38508i	−0.638051	+	0.937421i
$34$	−0.391828	−	0.127313i	−0.0671980	−	0.0218340i
$35$		0			0
$36$	2.79091	−	1.10038i	0.465151	−	0.183397i
$37$	4.70465	−	2.39714i	0.773440	−	0.394087i	−0.0222802	−	0.999752i	$-0.507093\pi$
$37$	4.70465	−	2.39714i	0.773440	−	0.394087i	0.795720	+	0.605664i	$0.207093\pi$
$38$	−4.45534	+	2.27011i	−0.722751	+	0.368260i
$39$	6.14845	+	2.89861i	0.984540	+	0.464149i
$40$		0			0
$41$	−3.24600	−	1.05469i	−0.506941	−	0.164715i	0.0443698	−	0.999015i	$-0.485872\pi$
$41$	−3.24600	−	1.05469i	−0.506941	−	0.164715i	−0.551310	+	0.834300i	$0.685872\pi$
$42$	6.34998	+	4.32208i	0.979824	+	0.666912i
$43$	3.71639	−	3.71639i	0.566745	−	0.566745i	−0.364470	−	0.931215i	$-0.618750\pi$
$43$	3.71639	−	3.71639i	0.566745	−	0.566745i	0.931215	+	0.364470i	$0.118750\pi$
$44$	3.04265	+	2.21062i	0.458697	+	0.333263i
$45$		0			0
$46$	4.06882	−	2.95617i	0.599914	−	0.435863i
$47$	0.808572	−	5.10512i	0.117942	−	0.744659i	−0.855851	−	0.517223i	$-0.826966\pi$
$47$	0.808572	−	5.10512i	0.117942	−	0.744659i	0.973793	−	0.227436i	$-0.0730342\pi$
$48$	−0.585546	−	1.63007i	−0.0845163	−	0.235281i
$49$			12.6676i			1.80965i
$50$		0			0
$51$	−0.488859	+	0.519837i	−0.0684540	+	0.0727917i
$52$	1.78169	−	3.49677i	0.247076	−	0.484914i
$53$	8.20487	+	1.29952i	1.12703	+	0.178503i	0.691988	−	0.721909i	$-0.256735\pi$
$53$	8.20487	+	1.29952i	1.12703	+	0.178503i	0.435037	+	0.900412i	$0.356735\pi$
$54$	0.337390	−	5.18519i	0.0459130	−	0.705615i
$55$		0			0
$56$	2.60672	−	3.58784i	0.348337	−	0.479445i
$57$	0.265855	+	8.65677i	0.0352134	+	1.14662i
$58$	−1.82271	+	0.288689i	−0.239334	+	0.0379068i
$59$	−1.73564	+	5.34175i	−0.225961	+	0.695437i	0.772231	+	0.635341i	$0.219141\pi$
$59$	−1.73564	+	5.34175i	−0.225961	+	0.695437i	−0.998193	+	0.0600956i	$0.980859\pi$
$60$		0			0
$61$	4.43829	+	13.6596i	0.568264	+	1.74894i	0.658047	+	0.752977i	$0.271383\pi$
$61$	4.43829	+	13.6596i	0.568264	+	1.74894i	−0.0897825	+	0.995961i	$0.528617\pi$
$62$	−1.51406	−	2.97152i	−0.192286	−	0.377383i
$63$	11.4614	−	6.75613i	1.44400	−	0.851193i
$64$	−0.951057	+	0.309017i	−0.118882	+	0.0386271i
$65$		0			0
$66$	5.71060	−	3.13412i	0.702926	−	0.385783i
$67$	−0.968887	−	6.11731i	−0.118368	−	0.747349i	−0.973458	−	0.228868i	$-0.926498\pi$
$67$	−0.968887	−	6.11731i	−0.118368	−	0.747349i	0.855089	−	0.518481i	$-0.173502\pi$
$68$	0.291323	+	0.291323i	0.0353281	+	0.0353281i
$69$	−1.62617	−	8.55793i	−0.195768	−	1.03025i
$70$		0			0
$71$	0.992045	+	1.36543i	0.117734	+	0.162047i	0.863817	−	0.503806i	$-0.168068\pi$
$71$	0.992045	+	1.36543i	0.117734	+	0.162047i	−0.746082	+	0.665854i	$0.768068\pi$
$72$	−2.98628	−	0.286595i	−0.351936	−	0.0337755i
$73$	3.19175	+	1.62628i	0.373567	+	0.190342i	0.630686	−	0.776038i	$-0.282773\pi$
$73$	3.19175	+	1.62628i	0.373567	+	0.190342i	−0.257120	+	0.966380i	$0.582773\pi$
$74$	−5.28015			−0.613805
$75$		0			0
$76$	5.00034			0.573579
$77$	14.8611	+	7.57211i	1.69358	+	0.862922i
$78$	−4.16237	−	5.37402i	−0.471295	−	0.608488i
$79$	6.24842	+	8.60021i	0.703002	+	0.967599i	0.999919	+	0.0126959i	$0.00404134\pi$
$79$	6.24842	+	8.60021i	0.703002	+	0.967599i	−0.296918	+	0.954903i	$0.595959\pi$
$80$		0			0
$81$	−7.87433	−	4.35832i	−0.874926	−	0.484258i
$82$	2.41339	+	2.41339i	0.266514	+	0.266514i
$83$	1.10932	+	7.00394i	0.121763	+	0.768782i	0.970701	+	0.240290i	$0.0772425\pi$
$83$	1.10932	+	7.00394i	0.121763	+	0.768782i	−0.848938	+	0.528493i	$0.822757\pi$
$84$	−3.69569	−	6.73384i	−0.403233	−	0.734722i
$85$		0			0
$86$	−4.99854	+	1.62412i	−0.539006	+	0.175134i
$87$	−0.893957	+	3.06883i	−0.0958423	+	0.329013i
$88$	−1.70742	−	3.35101i	−0.182012	−	0.357219i
$89$	0.324819	+	0.999689i	0.0344307	+	0.105967i	0.966795	−	0.255554i	$-0.0822577\pi$
$89$	0.324819	+	0.999689i	0.0344307	+	0.105967i	−0.932364	+	0.361521i	$0.882258\pi$
$90$		0			0
$91$	5.37828	−	16.5526i	0.563797	−	1.73519i
$92$	−4.96742	+	0.786761i	−0.517889	+	0.0820255i
$93$	−5.77369	+	0.177314i	−0.598704	+	0.0183866i
$94$	−3.03812	+	4.18162i	−0.313358	+	0.431301i
$95$		0			0
$96$	−0.218312	+	1.71824i	−0.0222814	+	0.175367i
$97$	−7.61627	−	1.20630i	−0.773315	−	0.122481i	−0.242709	−	0.970099i	$-0.578036\pi$
$97$	−7.61627	−	1.20630i	−0.773315	−	0.122481i	−0.530607	+	0.847618i	$0.678036\pi$
$98$	5.75096	−	11.2869i	0.580935	−	1.14015i
$99$	−0.692350	−	11.2615i	−0.0695838	−	1.13182i
$100$		0			0
$101$			11.0847i			1.10297i	0.834184	+	0.551487i	$0.185939\pi$
$101$			11.0847i			1.10297i	−0.834184	+	0.551487i	$0.814061\pi$
$102$	0.671578	−	0.241241i	0.0664961	−	0.0238864i
$103$	0.383628	−	2.42213i	0.0378000	−	0.238660i	−0.961553	−	0.274618i	$-0.911448\pi$
$103$	0.383628	−	2.42213i	0.0378000	−	0.238660i	0.999353	+	0.0359588i	$0.0114485\pi$
$104$	−3.17500	+	2.30677i	−0.311334	+	0.226197i
$105$		0			0
$106$	−6.72062	−	4.88282i	−0.652764	−	0.474261i
$107$	−4.30681	+	4.30681i	−0.416355	+	0.416355i	−0.883945	−	0.467590i	$-0.845122\pi$
$107$	−4.30681	+	4.30681i	−0.416355	+	0.416355i	0.467590	+	0.883945i	$0.345122\pi$
$108$	−2.65464	+	4.46686i	−0.255443	+	0.429824i
$109$	−4.46242	−	1.44993i	−0.427422	−	0.138878i	0.0874029	−	0.996173i	$-0.472143\pi$
$109$	−4.46242	−	1.44993i	−0.427422	−	0.138878i	−0.514825	+	0.857295i	$0.672143\pi$
$110$		0			0
$111$	−3.89988	+	8.27231i	−0.370160	+	0.785173i
$112$	−3.95145	+	2.01336i	−0.373377	+	0.190245i
$113$	−15.2342	+	7.76223i	−1.43312	+	0.730209i	−0.986384	−	0.164459i	$-0.947412\pi$
$113$	−15.2342	+	7.76223i	−1.43312	+	0.730209i	−0.446732	+	0.894668i	$0.647412\pi$
$114$	3.69321	−	7.83393i	0.345901	−	0.733715i
$115$		0			0
$116$	1.75511	+	0.570270i	0.162958	+	0.0529483i
$117$	−11.4937	+	2.55189i	−1.06259	+	0.235922i
$118$	3.97157	−	3.97157i	0.365613	−	0.365613i
$119$	1.47816	+	1.07395i	0.135503	+	0.0984487i
$120$		0			0
$121$	2.54399	−	1.84832i	0.231272	−	0.168029i
$122$	2.24681	−	14.1858i	0.203416	−	1.28432i
$123$	5.56352	−	1.99850i	0.501646	−	0.180199i
$124$			3.33501i			0.299493i
$125$		0			0
$126$	−13.2794	+	0.816407i	−1.18302	+	0.0727313i
$127$	8.90421	−	17.4755i	0.790121	−	1.55070i	−0.0439442	−	0.999034i	$-0.513992\pi$
$127$	8.90421	−	17.4755i	0.790121	−	1.55070i	0.834065	−	0.551666i	$-0.186008\pi$
$128$	0.987688	+	0.156434i	0.0873001	+	0.0138270i
$129$	−1.14740	+	9.03067i	−0.101023	+	0.795106i
$130$		0			0
$131$	12.0644	−	16.6052i	1.05407	−	1.45080i	0.168841	−	0.985643i	$-0.445998\pi$
$131$	12.0644	−	16.6052i	1.05407	−	1.45080i	0.885228	−	0.465158i	$-0.154002\pi$
$132$	−6.51104	+	0.199959i	−0.566713	+	0.0174042i
$133$	21.9026	−	3.46903i	1.89919	−	0.300803i
$134$	−1.91392	+	5.89043i	−0.165337	+	0.508856i
$135$		0			0
$136$	−0.127313	−	0.391828i	−0.0109170	−	0.0335990i
$137$	−3.28166	−	6.44062i	−0.280371	−	0.550259i	0.707279	−	0.706935i	$-0.249922\pi$
$137$	−3.28166	−	6.44062i	−0.280371	−	0.550259i	−0.987650	+	0.156675i	$0.949922\pi$
$138$	−2.43629	+	8.36344i	−0.207391	+	0.711943i
$139$	−9.21867	+	2.99533i	−0.781918	+	0.254060i	−0.672659	−	0.739953i	$-0.734848\pi$
$139$	−9.21867	+	2.99533i	−0.781918	+	0.254060i	−0.109259	+	0.994013i	$0.534848\pi$
$140$		0			0
$141$	4.30732	+	7.84827i	0.362742	+	0.660943i
$142$	−0.264025	−	1.66699i	−0.0221565	−	0.139891i
$143$	−10.4367	−	10.4367i	−0.872765	−	0.872765i
$144$	2.53068	+	1.61110i	0.210890	+	0.134258i
$145$		0			0
$146$	−2.10556	−	2.89805i	−0.174257	−	0.239845i
$147$	−13.4353	−	17.3463i	−1.10813	−	1.43070i
$148$	4.70465	+	2.39714i	0.386720	+	0.197044i
$149$	4.14920			0.339915			0.169958	−	0.985451i	$-0.445637\pi$
$149$	4.14920			0.339915			0.169958	+	0.985451i	$0.445637\pi$
$150$		0			0
$151$	−9.50070			−0.773156			−0.386578	−	0.922257i	$-0.626343\pi$
$151$	−9.50070			−0.773156			−0.386578	+	0.922257i	$0.626343\pi$
$152$	−4.45534	−	2.27011i	−0.361376	−	0.184130i
$153$	0.118075	−	1.23033i	0.00954580	−	0.0994659i
$154$	−9.80367	−	13.4936i	−0.790002	−	1.08734i
$155$		0			0
$156$	1.26894	+	6.67796i	0.101597	+	0.534665i
$157$	2.98265	+	2.98265i	0.238041	+	0.238041i	0.816039	−	0.577997i	$-0.196166\pi$
$157$	2.98265	+	2.98265i	0.238041	+	0.238041i	−0.577997	+	0.816039i	$0.696166\pi$
$158$	−1.66297	−	10.4996i	−0.132299	−	0.835300i
$159$	−12.6136	+	6.92265i	−1.00032	+	0.549002i
$160$		0			0
$161$	−21.2125	+	6.89237i	−1.67178	+	0.543195i
$162$	5.03744	+	7.45816i	0.395779	+	0.585968i
$163$	4.73142	+	9.28593i	0.370593	+	0.727330i	0.998709	−	0.0507896i	$-0.0161738\pi$
$163$	4.73142	+	9.28593i	0.370593	+	0.727330i	−0.628116	+	0.778119i	$0.716174\pi$
$164$	−1.05469	−	3.24600i	−0.0823575	−	0.253470i
$165$		0			0
$166$	2.19132	−	6.74418i	0.170079	−	0.523450i
$167$	−13.8268	+	2.18995i	−1.06995	+	0.169464i	−0.666476	−	0.745527i	$-0.732198\pi$
$167$	−13.8268	+	2.18995i	−1.06995	+	0.169464i	−0.403476	+	0.914990i	$0.632198\pi$
$168$	0.235788	+	7.67770i	0.0181914	+	0.592348i
$169$	−1.41174	+	1.94309i	−0.108595	+	0.149469i
$170$		0			0
$171$	−9.54548	−	11.5722i	−0.729961	−	0.884945i
$172$	5.19107	+	0.822184i	0.395815	+	0.0626910i
$173$	3.18237	−	6.24576i	0.241951	−	0.474856i	−0.737815	−	0.675003i	$-0.764142\pi$
$173$	3.18237	−	6.24576i	0.241951	−	0.474856i	0.979766	+	0.200147i	$0.0641421\pi$
$174$	2.18974	−	2.32850i	0.166004	−	0.176523i
$175$		0			0
$176$			3.76092i			0.283490i
$177$	−3.28881	−	9.15555i	−0.247202	−	0.688173i
$178$	0.164434	−	1.03819i	0.0123248	−	0.0778159i
$179$	2.28996	−	1.66375i	0.171159	−	0.124355i	−0.498908	−	0.866655i	$-0.666265\pi$
$179$	2.28996	−	1.66375i	0.171159	−	0.124355i	0.670067	+	0.742301i	$0.266265\pi$
$180$		0			0
$181$	−0.283169	−	0.205734i	−0.0210478	−	0.0152921i	0.577212	−	0.816595i	$-0.304141\pi$
$181$	−0.283169	−	0.205734i	−0.0210478	−	0.0152921i	−0.598259	+	0.801302i	$0.704141\pi$
$182$	−12.3068	+	12.3068i	−0.912243	+	0.912243i
$183$	−20.5651	−	13.9975i	−1.52021	−	1.03473i
$184$	4.78318	+	1.55415i	0.352621	+	0.114573i
$185$		0			0
$186$	5.22490	+	2.46321i	0.383108	+	0.180612i
$187$	1.38059	−	0.703446i	0.100959	−	0.0514411i
$188$	4.60540	−	2.34657i	0.335883	−	0.171141i
$189$	−8.52898	+	21.4075i	−0.620392	+	1.55717i
$190$		0			0
$191$	1.07980	+	0.350849i	0.0781318	+	0.0253866i	0.347822	−	0.937561i	$-0.386921\pi$
$191$	1.07980	+	0.350849i	0.0781318	+	0.0253866i	−0.269690	+	0.962947i	$0.586921\pi$
$192$	0.974581	−	1.43185i	0.0703343	−	0.103335i
$193$	4.16176	−	4.16176i	0.299570	−	0.299570i	−0.541275	−	0.840845i	$-0.682058\pi$
$193$	4.16176	−	4.16176i	0.299570	−	0.299570i	0.840845	+	0.541275i	$0.182058\pi$
$194$	6.23850	+	4.53254i	0.447898	+	0.325417i
$195$		0			0
$196$	−10.2483	+	7.44581i	−0.732020	+	0.531844i
$197$	−3.00593	+	18.9787i	−0.214164	+	1.35218i	0.612941	+	0.790129i	$0.289986\pi$
$197$	−3.00593	+	18.9787i	−0.214164	+	1.35218i	−0.827105	+	0.562048i	$0.810014\pi$
$198$	−4.49573	+	10.3484i	−0.319498	+	0.735429i
$199$		−	12.7124i		−	0.901157i	−0.892737	−	0.450579i	$-0.851218\pi$
$199$		−	12.7124i		−	0.901157i	0.892737	−	0.450579i	$-0.148782\pi$
$200$		0			0
$201$	7.81481	+	7.34912i	0.551214	+	0.518367i
$202$	5.03237	−	9.87658i	0.354076	−	0.694914i
$203$	8.08340	+	1.28028i	0.567343	+	0.0898583i
$204$	−0.707901	−	0.0899429i	−0.0495630	−	0.00629726i
$205$		0			0
$206$	−1.44144	+	1.98397i	−0.100430	+	0.138230i
$207$	11.3034	+	9.99405i	0.785641	+	0.694634i
$208$	3.87619	−	0.613929i	0.268766	−	0.0425683i
$209$	5.81135	−	17.8855i	0.401979	−	1.23716i
$210$		0			0
$211$	−5.38805	−	16.5827i	−0.370929	−	1.14160i	−0.946184	−	0.323628i	$-0.895097\pi$
$211$	−5.38805	−	16.5827i	−0.370929	−	1.14160i	0.575255	−	0.817974i	$-0.304903\pi$
$212$	3.77136	+	7.40172i	0.259018	+	0.508352i
$213$	−2.80664	−	0.817581i	−0.192308	−	0.0560198i
$214$	5.79265	−	1.88215i	0.395977	−	0.128661i
$215$		0			0
$216$	4.39322	−	2.77482i	0.298921	−	0.188803i
$217$	2.31369	+	14.6081i	0.157064	+	0.991661i
$218$	3.31779	+	3.31779i	0.224709	+	0.224709i
$219$	−6.09547	+	1.15826i	−0.411893	+	0.0782677i
$220$		0			0
$221$	−0.950373	−	1.30808i	−0.0639290	−	0.0879907i
$222$	7.23036	−	5.60017i	0.485270	−	0.375859i
$223$	−20.1688	−	10.2765i	−1.35060	−	0.688167i	−0.379136	−	0.925341i	$-0.623779\pi$
$223$	−20.1688	−	10.2765i	−1.35060	−	0.688167i	−0.971467	+	0.237174i	$0.923779\pi$
$224$	4.43481			0.296313
$225$		0			0
$226$	17.0978			1.13733
$227$	17.2036	+	8.76566i	1.14184	+	0.581797i	0.919468	−	0.393164i	$-0.128620\pi$
$227$	17.2036	+	8.76566i	1.14184	+	0.581797i	0.222373	+	0.974962i	$0.428620\pi$
$228$	−6.84721	+	5.30340i	−0.453467	+	0.351226i
$229$	−9.58051	−	13.1864i	−0.633098	−	0.871384i	0.365126	−	0.930958i	$-0.381026\pi$
$229$	−9.58051	−	13.1864i	−0.633098	−	0.871384i	−0.998224	+	0.0595738i	$0.981026\pi$
$230$		0			0
$231$	−28.3810	+	5.39295i	−1.86733	+	0.354830i
$232$	−1.30492	−	1.30492i	−0.0856721	−	0.0856721i
$233$	0.0952038	+	0.601093i	0.00623701	+	0.0393789i	0.990611	−	0.136714i	$-0.0436541\pi$
$233$	0.0952038	+	0.601093i	0.00623701	+	0.0393789i	−0.984374	+	0.176093i	$0.943654\pi$
$234$	11.3995	+	2.94426i	0.745205	+	0.192472i
$235$		0			0
$236$	−5.34175	+	1.73564i	−0.347718	+	0.112981i
$237$	−17.6777	−	5.14955i	−1.14829	−	0.334499i
$238$	−0.829491	−	1.62797i	−0.0537679	−	0.105525i
$239$	2.47857	+	7.62825i	0.160325	+	0.493430i	0.998661	−	0.0517231i	$-0.0164713\pi$
$239$	2.47857	+	7.62825i	0.160325	+	0.493430i	−0.838336	+	0.545154i	$0.816471\pi$
$240$		0			0
$241$	−2.23962	+	6.89284i	−0.144267	+	0.444007i	−0.996916	−	0.0784767i	$-0.974994\pi$
$241$	−2.23962	+	6.89284i	−0.144267	+	0.444007i	0.852649	+	0.522484i	$0.174994\pi$
$242$	−3.10583	+	0.491916i	−0.199650	+	0.0316215i
$243$	15.4052	−	2.38352i	0.988241	−	0.152903i
$244$	−8.44212	+	11.6196i	−0.540452	+	0.743868i
$245$		0			0
$246$	−5.86443	−	0.745110i	−0.373903	−	0.0475065i
$247$	−19.3823	−	3.06986i	−1.23327	−	0.195330i
$248$	1.51406	−	2.97152i	0.0961432	−	0.188692i
$249$	−8.94747	−	8.41428i	−0.567023	−	0.533233i
$250$		0			0
$251$			14.5520i			0.918511i	0.888304	+	0.459256i	$0.151884\pi$
$251$			14.5520i			0.918511i	−0.888304	+	0.459256i	$0.848116\pi$
$252$	12.2026	+	5.30128i	0.768694	+	0.333949i
$253$	−2.95895	+	18.6821i	−0.186028	+	1.17453i
$254$	−15.8674	+	11.5284i	−0.995611	+	0.723353i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−1.03830	+	1.03830i	−0.0647675	+	0.0647675i	−0.738749	−	0.673981i	$-0.764583\pi$
$257$	−1.03830	+	1.03830i	−0.0647675	+	0.0647675i	0.673981	+	0.738749i	$0.264583\pi$
$258$	5.12218	−	7.52548i	0.318893	−	0.468516i
$259$	22.2704	+	7.23610i	1.38382	+	0.449629i
$260$		0			0
$261$	−2.03069	−	5.15043i	−0.125696	−	0.318804i
$262$	−18.2880	+	9.31821i	−1.12984	+	0.575681i
$263$	19.8871	−	10.1330i	1.22629	−	0.624825i	0.283743	−	0.958901i	$-0.408424\pi$
$263$	19.8871	−	10.1330i	1.22629	−	0.624825i	0.942546	+	0.334075i	$0.108424\pi$
$264$	5.89216	+	2.77779i	0.362637	+	0.170961i
$265$		0			0
$266$	−21.0902	−	6.85264i	−1.29313	−	0.420162i
$267$	−1.50507	−	1.02442i	−0.0921086	−	0.0626933i
$268$	4.37951	−	4.37951i	0.267521	−	0.267521i
$269$	−20.2239	−	14.6936i	−1.23308	−	0.895882i	−0.235959	−	0.971763i	$-0.575823\pi$
$269$	−20.2239	−	14.6936i	−1.23308	−	0.895882i	−0.997117	+	0.0758813i	$0.975823\pi$
$270$		0			0
$271$	−13.1402	+	9.54690i	−0.798209	+	0.579933i	−0.910388	−	0.413755i	$-0.864217\pi$
$271$	−13.1402	+	9.54690i	−0.798209	+	0.579933i	0.112179	+	0.993688i	$0.464217\pi$
$272$	−0.0644499	+	0.406920i	−0.00390785	+	0.0246732i
$273$	10.1911	+	28.3706i	0.616795	+	1.71706i
$274$			7.22848i			0.436688i
$275$		0			0
$276$	5.96767	−	6.34583i	0.359212	−	0.381974i
$277$	3.12626	−	6.13564i	0.187839	−	0.368655i	−0.777812	−	0.628497i	$-0.783670\pi$
$277$	3.12626	−	6.13564i	0.187839	−	0.368655i	0.965651	+	0.259842i	$0.0836705\pi$
$278$	9.57375	+	1.51633i	0.574195	+	0.0909436i
$279$	7.71813	−	6.36643i	0.462072	−	0.381148i
$280$		0			0
$281$	14.3948	−	19.8128i	0.858723	−	1.18193i	−0.123150	−	0.992388i	$-0.539300\pi$
$281$	14.3948	−	19.8128i	0.858723	−	1.18193i	0.981873	−	0.189542i	$-0.0607004\pi$
$282$	−0.274810	−	8.94834i	−0.0163647	−	0.532866i
$283$	−7.23244	+	1.14551i	−0.429924	+	0.0680933i	−0.367646	−	0.929966i	$-0.619836\pi$
$283$	−7.23244	+	1.14551i	−0.429924	+	0.0680933i	−0.0622774	+	0.998059i	$0.519836\pi$
$284$	−0.521549	+	1.60516i	−0.0309482	+	0.0952489i
$285$		0			0
$286$	4.56103	+	14.0374i	0.269699	+	0.830049i
$287$	−6.87171	−	13.4865i	−0.405624	−	0.796083i
$288$	−1.52343	−	2.58441i	−0.0897690	−	0.152288i
$289$	−16.0065	+	5.20084i	−0.941561	+	0.305932i
$290$		0			0
$291$	11.7087	−	6.42603i	0.686378	−	0.376701i
$292$	0.560378	+	3.53809i	0.0327936	+	0.207051i
$293$	−1.14628	−	1.14628i	−0.0669662	−	0.0669662i	0.672830	−	0.739797i	$-0.265078\pi$
$293$	−1.14628	−	1.14628i	−0.0669662	−	0.0669662i	−0.739797	+	0.672830i	$0.765078\pi$
$294$	4.09590	+	21.5552i	0.238878	+	1.25712i
$295$		0			0
$296$	−3.10360	−	4.27173i	−0.180393	−	0.248290i
$297$	12.8921	+	14.6866i	0.748076	+	0.852203i
$298$	−3.69696	−	1.88370i	−0.214159	−	0.109120i
$299$	19.7377			1.14146
$300$		0			0
$301$	23.3084			1.34347
$302$	8.46519	+	4.31323i	0.487117	+	0.248198i
$303$	−11.7566	−	15.1789i	−0.675397	−	0.872003i
$304$	2.93913	+	4.04536i	0.168571	+	0.232018i
$305$		0			0
$306$	−0.663762	+	1.04262i	−0.0379447	+	0.0596028i
$307$	−8.29257	−	8.29257i	−0.473282	−	0.473282i	0.429693	−	0.902975i	$-0.358622\pi$
$307$	−8.29257	−	8.29257i	−0.473282	−	0.473282i	−0.902975	+	0.429693i	$0.858622\pi$
$308$	2.60917	+	16.4737i	0.148671	+	0.938673i
$309$	2.04361	+	3.72362i	0.116257	+	0.211829i
$310$		0			0
$311$	31.4637	−	10.2232i	1.78414	−	0.579703i	0.784937	−	0.619575i	$-0.212695\pi$
$311$	31.4637	−	10.2232i	1.78414	−	0.579703i	0.999205	+	0.0398725i	$0.0126952\pi$
$312$	1.90110	−	6.52620i	0.107628	−	0.369473i
$313$	−1.98845	−	3.90255i	−0.112394	−	0.220585i	0.827957	−	0.560791i	$-0.189503\pi$
$313$	−1.98845	−	3.90255i	−0.112394	−	0.220585i	−0.940351	+	0.340206i	$0.889503\pi$
$314$	−1.30346	−	4.01165i	−0.0735587	−	0.226391i
$315$		0			0
$316$	−3.28499	+	10.1102i	−0.184795	+	0.568740i
$317$	27.6572	−	4.38047i	1.55338	−	0.246032i	0.680053	−	0.733163i	$-0.261957\pi$
$317$	27.6572	−	4.38047i	1.55338	−	0.246032i	0.873329	+	0.487131i	$0.161957\pi$
$318$	14.3816	−	0.441669i	0.806481	−	0.0247676i
$319$	4.07954	−	5.61501i	0.228411	−	0.314380i
$320$		0			0
$321$	1.32968	−	10.4654i	0.0742157	−	0.584119i
$322$	22.0296	+	3.48914i	1.22766	+	0.194442i
$323$	0.935268	−	1.83557i	0.0520397	−	0.102134i
$324$	−1.10246	−	8.93222i	−0.0612479	−	0.496235i
$325$		0			0
$326$		−	10.4218i		−	0.577212i
$327$	7.64841	−	2.74742i	0.422958	−	0.151933i
$328$	−0.533919	+	3.37103i	−0.0294807	+	0.186134i
$329$	18.5447	−	13.4735i	1.02240	−	0.742818i
$330$		0			0
$331$	7.75360	+	5.63332i	0.426176	+	0.309635i	0.780118	−	0.625632i	$-0.215159\pi$
$331$	7.75360	+	5.63332i	0.426176	+	0.309635i	−0.353942	+	0.935267i	$0.615159\pi$
$332$	−5.01427	+	5.01427i	−0.275194	+	0.275194i
$333$	−3.43338	−	15.4639i	−0.188148	−	0.847416i
$334$	13.3140	+	4.32598i	0.728510	+	0.236707i
$335$		0			0
$336$	3.27552	−	6.94793i	0.178694	−	0.379041i
$337$	13.9578	−	7.11185i	0.760329	−	0.387407i	−0.0304279	−	0.999537i	$-0.509687\pi$
$337$	13.9578	−	7.11185i	0.760329	−	0.387407i	0.790757	+	0.612130i	$0.209687\pi$
$338$	2.14002	−	1.09039i	0.116401	−	0.0593095i
$339$	12.6283	−	26.7867i	0.685874	−	1.45485i
$340$		0			0
$341$	11.9289	+	3.87592i	0.645983	+	0.209893i
$342$	3.25144	+	14.6444i	0.175818	+	0.791880i
$343$	−17.7729	+	17.7729i	−0.959645	+	0.959645i
$344$	−4.25201	−	3.08927i	−0.229253	−	0.166562i
$345$		0			0
$346$	−5.67103	+	4.12024i	−0.304876	+	0.221506i
$347$	5.77593	−	36.4678i	0.310068	−	1.95769i	0.0231773	−	0.999731i	$-0.492622\pi$
$347$	5.77593	−	36.4678i	0.310068	−	1.95769i	0.286891	−	0.957963i	$-0.407378\pi$
$348$	−3.00819	+	1.08059i	−0.161256	+	0.0579255i
$349$		−	15.0145i		−	0.803705i	−0.915704	−	0.401853i	$-0.868366\pi$
$349$		−	15.0145i		−	0.803705i	0.915704	−	0.401853i	$-0.131634\pi$
$350$		0			0
$351$	13.0322	−	15.6847i	0.695610	−	0.837186i
$352$	1.70742	−	3.35101i	0.0910060	−	0.178609i
$353$	−29.7348	−	4.70953i	−1.58263	−	0.250663i	−0.697698	−	0.716392i	$-0.745792\pi$
$353$	−29.7348	−	4.70953i	−1.58263	−	0.250663i	−0.884927	+	0.465729i	$0.845792\pi$
$354$	−1.22618	+	9.65074i	−0.0651708	+	0.512931i
$355$		0			0
$356$	−0.617842	+	0.850386i	−0.0327456	+	0.0450704i
$357$	−3.16316	+	0.0971428i	−0.167412	+	0.00514134i
$358$	−2.79569	+	0.442795i	−0.147757	+	0.0234024i
$359$	−1.07807	+	3.31797i	−0.0568986	+	0.175116i	−0.975467	−	0.220147i	$-0.929346\pi$
$359$	−1.07807	+	3.31797i	−0.0568986	+	0.175116i	0.918568	+	0.395263i	$0.129346\pi$
$360$		0			0
$361$	−1.85517	−	5.70961i	−0.0976403	−	0.300506i
$362$	0.158904	+	0.311866i	0.00835180	+	0.0163913i
$363$	−1.52327	+	5.22917i	−0.0799508	+	0.274460i
$364$	16.5526	−	5.37828i	0.867594	−	0.281898i
$365$		0			0
$366$	11.9689	+	21.8082i	0.625623	+	1.13993i
$367$	2.44988	+	15.4679i	0.127882	+	0.807418i	0.965355	+	0.260939i	$0.0840322\pi$
$367$	2.44988	+	15.4679i	0.127882	+	0.807418i	−0.837473	+	0.546479i	$0.815968\pi$
$368$	−3.55628	−	3.55628i	−0.185384	−	0.185384i
$369$	−5.49877	+	8.63735i	−0.286254	+	0.449642i
$370$		0			0
$371$	21.6544	+	29.8047i	1.12424	+	1.54738i
$372$	−3.53714	−	4.56679i	−0.183392	−	0.236777i
$373$	−5.68352	−	2.89590i	−0.294282	−	0.149944i	0.300616	−	0.953745i	$-0.402808\pi$
$373$	−5.68352	−	2.89590i	−0.294282	−	0.149944i	−0.594898	+	0.803801i	$0.702808\pi$
$374$	−1.54947			−0.0801213
$375$		0			0
$376$	−5.16876			−0.266558
$377$	−6.45305	−	3.28799i	−0.332349	−	0.169340i
$378$	17.3182	−	15.2021i	0.890751	−	0.781914i
$379$	15.8374	+	21.7983i	0.813510	+	1.11970i	0.990772	+	0.135537i	$0.0432760\pi$
$379$	15.8374	+	21.7983i	0.813510	+	1.11970i	−0.177262	+	0.984164i	$0.556724\pi$
$380$		0			0
$381$	6.34169	+	33.3739i	0.324895	+	1.70980i
$382$	−0.802829	−	0.802829i	−0.0410763	−	0.0410763i
$383$	4.68475	+	29.5784i	0.239380	+	1.51138i	0.755660	+	0.654964i	$0.227316\pi$
$383$	4.68475	+	29.5784i	0.239380	+	1.51138i	−0.516280	+	0.856420i	$0.672684\pi$
$384$	−1.51840	+	0.833337i	−0.0774857	+	0.0425260i
$385$		0			0
$386$	−5.59756	+	1.81876i	−0.284908	+	0.0925723i
$387$	−8.00681	−	13.5831i	−0.407009	−	0.690466i
$388$	−3.50082	−	6.87074i	−0.177727	−	0.348809i
$389$	−3.57268	−	10.9956i	−0.181142	−	0.557497i	0.818719	−	0.574195i	$-0.194685\pi$
$389$	−3.57268	−	10.9956i	−0.181142	−	0.557497i	−0.999861	+	0.0166975i	$0.994685\pi$
$390$		0			0
$391$	−0.640299	+	1.97064i	−0.0323813	+	0.0996594i
$392$	12.5116	−	1.98165i	0.631932	−	0.100088i
$393$	1.09127	+	35.5338i	0.0550472	+	1.79244i
$394$	11.2945	−	15.5455i	0.569007	−	0.783170i
$395$		0			0
$396$	8.70380	−	7.17947i	0.437382	−	0.360782i
$397$	−13.2341	−	2.09608i	−0.664203	−	0.105199i	−0.184775	−	0.982781i	$-0.559156\pi$
$397$	−13.2341	−	2.09608i	−0.664203	−	0.105199i	−0.479427	+	0.877581i	$0.659156\pi$
$398$	−5.77130	+	11.3268i	−0.289289	+	0.567762i
$399$	−26.3130	+	27.9803i	−1.31730	+	1.40077i
$400$		0			0
$401$		−	22.2904i		−	1.11313i	−0.830804	−	0.556565i	$-0.812119\pi$
$401$		−	22.2904i		−	1.11313i	0.830804	−	0.556565i	$-0.187881\pi$
$402$	−3.62662	−	10.0960i	−0.180879	−	0.503541i
$403$	2.04746	−	12.9272i	0.101991	−	0.643948i
$404$	−8.96775	+	6.51545i	−0.446162	+	0.324156i
$405$		0			0
$406$	−6.62112	−	4.81053i	−0.328601	−	0.238742i
$407$	14.0419	−	14.0419i	0.696032	−	0.696032i
$408$	0.589911	+	0.401520i	0.0292050	+	0.0198782i
$409$	−13.3939	−	4.35194i	−0.662285	−	0.215190i	−0.0414620	−	0.999140i	$-0.513202\pi$
$409$	−13.3939	−	4.35194i	−0.662285	−	0.215190i	−0.620823	+	0.783951i	$0.713202\pi$
$410$		0			0
$411$	11.3247	+	5.33889i	0.558606	+	0.263348i
$412$	2.18504	−	1.11333i	0.107649	−	0.0548499i
$413$	−22.1939	+	11.3084i	−1.09209	+	0.556448i
$414$	−5.53420	−	14.0364i	−0.271991	−	0.689851i
$415$		0			0
$416$	−3.73243	−	1.21274i	−0.182998	−	0.0594595i
$417$	9.44670	−	13.8790i	0.462607	−	0.679660i
$418$	−13.2978	+	13.2978i	−0.650416	+	0.650416i
$419$	4.58918	+	3.33423i	0.224196	+	0.162888i	0.694213	−	0.719769i	$-0.255752\pi$
$419$	4.58918	+	3.33423i	0.224196	+	0.162888i	−0.470017	+	0.882657i	$0.655752\pi$
$420$		0			0
$421$	5.16685	−	3.75393i	0.251817	−	0.182956i	−0.454715	−	0.890637i	$-0.650259\pi$
$421$	5.16685	−	3.75393i	0.251817	−	0.182956i	0.706532	+	0.707682i	$0.250259\pi$
$422$	−2.72761	+	17.2214i	−0.132778	+	0.838327i
$423$	−14.2221	−	6.17863i	−0.691504	−	0.300415i
$424$		−	8.30714i		−	0.403431i
$425$		0			0
$426$	2.12956	+	2.00266i	0.103178	+	0.0970292i
$427$	−28.9171	+	56.7531i	−1.39940	+	2.74647i
$428$	−6.01577	−	0.952804i	−0.290783	−	0.0460555i
$429$	25.3608	+	3.22224i	1.22443	+	0.155571i
$430$		0			0
$431$	11.7415	−	16.1608i	0.565568	−	0.778437i	−0.426453	−	0.904510i	$-0.640237\pi$
$431$	11.7415	−	16.1608i	0.565568	−	0.778437i	0.992021	+	0.126072i	$0.0402371\pi$
$432$	−5.17413	+	0.477906i	−0.248940	+	0.0229932i
$433$	−22.9138	+	3.62919i	−1.10117	+	0.174408i	−0.680458	−	0.732787i	$-0.738219\pi$
$433$	−22.9138	+	3.62919i	−1.10117	+	0.174408i	−0.420710	+	0.907195i	$0.638219\pi$
$434$	4.57041	−	14.0663i	0.219387	−	0.675203i
$435$		0			0
$436$	−1.44993	−	4.46242i	−0.0694390	−	0.213711i
$437$	11.4171	+	22.4074i	0.546156	+	1.07189i
$438$	5.95694	+	1.73527i	0.284633	+	0.0829144i
$439$	−10.7777	+	3.50189i	−0.514393	+	0.167136i	−0.554699	−	0.832051i	$-0.687167\pi$
$439$	−10.7777	+	3.50189i	−0.514393	+	0.167136i	0.0403065	+	0.999187i	$0.487167\pi$
$440$		0			0
$441$	36.7952	+	9.50351i	1.75215	+	0.452548i
$442$	0.252934	+	1.59696i	0.0120309	+	0.0759598i
$443$	5.43418	+	5.43418i	0.258186	+	0.258186i	0.824316	−	0.566130i	$-0.191560\pi$
$443$	5.43418	+	5.43418i	0.258186	+	0.258186i	−0.566130	+	0.824316i	$0.691560\pi$
$444$	−8.98473	+	1.70727i	−0.426396	+	0.0810236i
$445$		0			0
$446$	13.3051	+	18.3129i	0.630015	+	0.867141i
$447$	−5.68169	+	4.40067i	−0.268735	+	0.208144i
$448$	−3.95145	−	2.01336i	−0.186688	−	0.0951225i
$449$	−26.9459			−1.27165			−0.635827	−	0.771831i	$-0.719341\pi$
$449$	−26.9459			−1.27165			−0.635827	+	0.771831i	$0.719341\pi$
$450$		0			0
$451$	−12.8362			−0.604434
$452$	−15.2342	−	7.76223i	−0.716558	−	0.365104i
$453$	13.0098	−	10.0765i	0.611252	−	0.473436i
$454$	−11.3490	−	15.6205i	−0.532634	−	0.733108i
$455$		0			0
$456$	8.50860	−	1.61680i	0.398452	−	0.0757136i
$457$	24.1951	+	24.1951i	1.13180	+	1.13180i	0.989878	+	0.141919i	$0.0453271\pi$
$457$	24.1951	+	24.1951i	1.13180	+	1.13180i	0.141919	+	0.989878i	$0.454673\pi$
$458$	2.54978	+	16.0987i	0.119143	+	0.752241i
$459$	1.14321	+	1.80997i	0.0533603	+	0.0844823i
$460$		0			0
$461$	−35.3066	+	11.4718i	−1.64439	+	0.534295i	−0.977513	−	0.210873i	$-0.932369\pi$
$461$	−35.3066	+	11.4718i	−1.64439	+	0.534295i	−0.666877	+	0.745168i	$0.732369\pi$
$462$	27.7360	+	8.07957i	1.29040	+	0.375896i
$463$	−3.18828	−	6.25735i	−0.148172	−	0.290804i	0.804977	−	0.593307i	$-0.202178\pi$
$463$	−3.18828	−	6.25735i	−0.148172	−	0.290804i	−0.953149	+	0.302503i	$0.902178\pi$
$464$	0.570270	+	1.75511i	0.0264741	+	0.0814790i
$465$		0			0
$466$	0.188063	−	0.578799i	0.00871187	−	0.0268124i
$467$	−28.3424	+	4.48899i	−1.31153	+	0.207726i	−0.772744	−	0.634718i	$-0.781116\pi$
$467$	−28.3424	+	4.48899i	−1.31153	+	0.207726i	−0.538785	+	0.842444i	$0.681116\pi$
$468$	−8.82032	−	7.79860i	−0.407719	−	0.360490i
$469$	16.1449	−	22.2215i	0.745502	−	1.02609i
$470$		0			0
$471$	−7.24770	−	0.920861i	−0.333956	−	0.0424310i
$472$	5.54750	+	0.878638i	0.255344	+	0.0404426i
$473$	8.97383	−	17.6121i	0.412617	−	0.809807i
$474$	13.4131	+	12.6138i	0.616084	+	0.579371i
$475$		0			0
$476$			1.82711i			0.0837455i
$477$	9.93018	−	22.8576i	0.454672	−	1.04658i
$478$	1.25473	−	7.92207i	0.0573901	−	0.362347i
$479$	10.3928	−	7.55082i	0.474860	−	0.345006i	−0.324473	−	0.945895i	$-0.605187\pi$
$479$	10.3928	−	7.55082i	0.474860	−	0.345006i	0.799332	+	0.600889i	$0.205187\pi$
$480$		0			0
$481$	−16.7645	−	12.1801i	−0.764394	−	0.555365i
$482$	5.12480	−	5.12480i	0.233428	−	0.233428i
$483$	21.7372	−	31.9362i	0.989077	−	1.45315i
$484$	2.99064	+	0.971718i	0.135938	+	0.0441690i
$485$		0			0
$486$	−14.8082	−	4.87006i	−0.671713	−	0.220910i
$487$	−18.4423	+	9.39682i	−0.835700	+	0.425810i	−0.818822	−	0.574047i	$-0.805373\pi$
$487$	−18.4423	+	9.39682i	−0.835700	+	0.425810i	−0.0168777	+	0.999858i	$0.505373\pi$
$488$	12.7972	−	6.52048i	0.579301	−	0.295168i
$489$	−16.3277	−	7.69748i	−0.738363	−	0.348092i
$490$		0			0
$491$	−26.5707	−	8.63333i	−1.19912	−	0.389617i	−0.359681	−	0.933075i	$-0.617114\pi$
$491$	−26.5707	−	8.63333i	−1.19912	−	0.389617i	−0.839436	+	0.543459i	$0.817114\pi$
$492$	4.88697	+	3.32629i	0.220322	+	0.149961i
$493$	0.537617	−	0.537617i	0.0242131	−	0.0242131i
$494$	15.8761	+	11.5346i	0.714298	+	0.518968i
$495$		0			0
$496$	−2.69808	+	1.96027i	−0.121148	+	0.0880188i
$497$	−1.17090	+	7.39279i	−0.0525221	+	0.331612i
$498$	4.15225	+	11.5592i	0.186067	+	0.517982i
$499$		−	0.405848i		−	0.0181683i	−0.999959	−	0.00908413i	$-0.997108\pi$
$499$		−	0.405848i		−	0.0181683i	0.999959	−	0.00908413i	$-0.00289161\pi$
$500$		0			0
$501$	16.6110	−	17.6636i	0.742126	−	0.789153i
$502$	6.60645	−	12.9659i	0.294860	−	0.578696i
$503$	5.98816	+	0.948431i	0.266999	+	0.0422885i	0.288498	−	0.957480i	$-0.406844\pi$
$503$	5.98816	+	0.948431i	0.266999	+	0.0422885i	−0.0214995	+	0.999769i	$0.506844\pi$
$504$	−8.46590	−	10.2634i	−0.377101	−	0.457167i
$505$		0			0
$506$	11.1179	−	15.3025i	0.494252	−	0.680280i
$507$	−0.127697	−	4.15807i	−0.00567123	−	0.184666i
$508$	19.3717	−	3.06818i	0.859482	−	0.136129i
$509$	−1.17675	+	3.62167i	−0.0521586	+	0.160528i	−0.973743	−	0.227651i	$-0.926896\pi$
$509$	−1.17675	+	3.62167i	−0.0521586	+	0.160528i	0.921584	+	0.388178i	$0.126896\pi$
$510$		0			0
$511$	4.90915	+	15.1088i	0.217168	+	0.668375i
$512$	0.453990	+	0.891007i	0.0200637	+	0.0393773i
$513$	25.3446	+	5.72229i	1.11899	+	0.252645i
$514$	1.39651	−	0.453755i	0.0615976	−	0.0200143i
$515$		0			0
$516$	−7.98039	+	4.37983i	−0.351317	+	0.192811i
$517$	−3.04098	−	19.2000i	−0.133742	−	0.844414i
$518$	−16.5580	−	16.5580i	−0.727515	−	0.727515i
$519$	2.26652	+	11.9279i	0.0994894	+	0.523575i
$520$		0			0
$521$	−1.70955	−	2.35299i	−0.0748966	−	0.103086i	0.769925	−	0.638134i	$-0.220294\pi$
$521$	−1.70955	−	2.35299i	−0.0748966	−	0.103086i	−0.844822	+	0.535048i	$0.820294\pi$
$522$	−0.528892	+	5.51098i	−0.0231490	+	0.241209i
$523$	−7.89460	−	4.02250i	−0.345207	−	0.175892i	0.272787	−	0.962074i	$-0.412054\pi$
$523$	−7.89460	−	4.02250i	−0.345207	−	0.175892i	−0.617994	+	0.786183i	$0.712054\pi$
$524$	20.5251			0.896645
$525$		0			0
$526$	−22.3198			−0.973188
$527$	1.22424	+	0.623784i	0.0533289	+	0.0271724i
$528$	−3.98886	−	5.15001i	−0.173593	−	0.224125i
$529$	−1.34851	−	1.85606i	−0.0586307	−	0.0806982i
$530$		0			0
$531$	14.2140	+	9.04899i	0.616833	+	0.392693i
$532$	15.6805	+	15.6805i	0.679837	+	0.679837i
$533$	2.09537	+	13.2296i	0.0907606	+	0.573040i
$534$	0.875950	+	1.59605i	0.0379060	+	0.0690678i
$535$		0			0
$536$	−5.89043	+	1.91392i	−0.254428	+	0.0826686i
$537$	−1.37116	+	4.70700i	−0.0591699	+	0.203122i
$538$	11.3489	+	22.2735i	0.489287	+	0.960280i
$539$	14.7221	+	45.3100i	0.634127	+	1.95164i
$540$		0			0
$541$	−11.3923	+	35.0618i	−0.489792	+	1.50742i	0.335128	+	0.942173i	$0.391221\pi$
$541$	−11.3923	+	35.0618i	−0.489792	+	1.50742i	−0.824919	+	0.565251i	$0.808779\pi$
$542$	16.0422	−	2.54083i	0.689071	−	0.109138i
$543$	0.605959	−	0.0186094i	0.0260042	−	0.000798607i
$544$	0.242163	−	0.333309i	0.0103827	−	0.0142905i
$545$		0			0
$546$	3.79961	−	29.9050i	0.162608	−	1.27982i
$547$	26.2003	+	4.14971i	1.12024	+	0.177429i	0.688968	−	0.724792i	$-0.258064\pi$
$547$	26.2003	+	4.14971i	1.12024	+	0.177429i	0.431274	+	0.902221i	$0.358064\pi$
$548$	3.28166	−	6.44062i	0.140186	−	0.275130i
$549$	43.0066	−	2.64402i	1.83548	−	0.112844i
$550$		0			0
$551$		−	9.22780i		−	0.393118i
$552$	−8.19818	+	2.94491i	−0.348938	+	0.125344i
$553$	−7.37495	+	46.5636i	−0.313615	+	1.98009i
$554$	−5.57104	+	4.04760i	−0.236691	+	0.171966i
$555$		0			0
$556$	−7.84187	−	5.69745i	−0.332569	−	0.241626i
$557$	20.9449	−	20.9449i	0.887465	−	0.887465i	−0.106814	−	0.994279i	$-0.534065\pi$
$557$	20.9449	−	20.9449i	0.887465	−	0.887465i	0.994279	+	0.106814i	$0.0340648\pi$
$558$	−9.76720	+	2.16857i	−0.413479	+	0.0918029i
$559$	−19.6168	−	6.37389i	−0.829703	−	0.269587i
$560$		0			0
$561$	−1.14443	+	2.42753i	−0.0483178	+	0.102490i
$562$	−21.8207	+	11.1182i	−0.920450	+	0.468993i
$563$	−13.4464	+	6.85128i	−0.566698	+	0.288747i	−0.713772	−	0.700378i	$-0.753015\pi$
$563$	−13.4464	+	6.85128i	−0.566698	+	0.288747i	0.147073	+	0.989126i	$0.453015\pi$
$564$	−3.81760	+	8.09779i	−0.160750	+	0.340978i
$565$		0			0
$566$	6.96420	+	2.26281i	0.292727	+	0.0951128i
$567$	−11.0258	−	38.3602i	−0.463041	−	1.61098i
$568$	1.19343	−	1.19343i	0.0500753	−	0.0500753i
$569$	−7.06373	−	5.13210i	−0.296127	−	0.215149i	0.429794	−	0.902927i	$-0.358586\pi$
$569$	−7.06373	−	5.13210i	−0.296127	−	0.215149i	−0.725921	+	0.687778i	$0.758586\pi$
$570$		0			0
$571$	19.6305	−	14.2624i	0.821513	−	0.596864i	−0.0956328	−	0.995417i	$-0.530487\pi$
$571$	19.6305	−	14.2624i	0.821513	−	0.596864i	0.917145	+	0.398553i	$0.130487\pi$
$572$	2.30894	−	14.5781i	0.0965416	−	0.609540i
$573$	−1.85074	+	0.664813i	−0.0773157	+	0.0277730i
$574$			15.1362i			0.631775i
$575$		0			0
$576$	0.184091	+	2.99435i	0.00767044	+	0.124764i
$577$	−16.6187	+	32.6160i	−0.691845	+	1.35782i	0.231114	+	0.972927i	$0.425763\pi$
$577$	−16.6187	+	32.6160i	−0.691845	+	1.35782i	−0.922960	+	0.384896i	$0.874237\pi$
$578$	16.6231	+	2.63283i	0.691428	+	0.109511i
$579$	−1.28490	+	10.1129i	−0.0533987	+	0.420277i
$580$		0			0
$581$	−18.4849	+	25.4423i	−0.766882	+	1.05552i
$582$	−13.3499	+	0.409985i	−0.553372	+	0.0169944i
$583$	30.8579	−	4.88741i	1.27800	−	0.202416i
$584$	1.10696	−	3.40687i	0.0458062	−	0.140977i
$585$		0			0
$586$	0.500941	+	1.54174i	0.0206937	+	0.0636887i
$587$	5.16169	+	10.1304i	0.213046	+	0.418126i	0.972655	−	0.232254i	$-0.0746099\pi$
$587$	5.16169	+	10.1304i	0.213046	+	0.418126i	−0.759609	+	0.650379i	$0.774610\pi$
$588$	6.13637	−	21.0653i	0.253060	−	0.868719i
$589$	15.8600	−	5.15324i	0.653501	−	0.212335i
$590$		0			0
$591$	−16.0128	−	29.1766i	−0.658678	−	1.20016i
$592$	0.825998	+	5.21515i	0.0339483	+	0.214341i
$593$	−16.4362	−	16.4362i	−0.674952	−	0.674952i	0.283901	−	0.958854i	$-0.408371\pi$
$593$	−16.4362	−	16.4362i	−0.674952	−	0.674952i	−0.958854	+	0.283901i	$0.908371\pi$
$594$	−4.81937	−	18.9388i	−0.197741	−	0.777066i
$595$		0			0
$596$	2.43884	+	3.35677i	0.0998986	+	0.137499i
$597$	13.4829	+	17.4077i	0.551817	+	0.712449i
$598$	−17.5864	−	8.96072i	−0.719162	−	0.366431i
$599$	−16.9386			−0.692094			−0.346047	−	0.938217i	$-0.612476\pi$
$599$	−16.9386			−0.692094			−0.346047	+	0.938217i	$0.612476\pi$
$600$		0			0
$601$	−26.0220			−1.06146			−0.530730	−	0.847541i	$-0.678082\pi$
$601$	−26.0220			−1.06146			−0.530730	+	0.847541i	$0.678082\pi$
$602$	−20.7679	−	10.5818i	−0.846437	−	0.431281i
$603$	−18.4957	−	1.77504i	−0.753204	−	0.0722854i
$604$	−5.58437	−	7.68623i	−0.227225	−	0.312748i
$605$		0			0
$606$	3.58411	+	18.8618i	0.145595	+	0.766210i
$607$	−29.4219	−	29.4219i	−1.19420	−	1.19420i	−0.975877	−	0.218322i	$-0.929942\pi$
$607$	−29.4219	−	29.4219i	−1.19420	−	1.19420i	−0.218322	−	0.975877i	$-0.570058\pi$
$608$	−0.782226	−	4.93878i	−0.0317235	−	0.200294i
$609$	−12.4269	+	6.82016i	−0.503562	+	0.276367i
$610$		0			0
$611$	−19.2921	+	6.26837i	−0.780473	+	0.253591i
$612$	1.06476	−	0.627642i	0.0430402	−	0.0253709i
$613$	−2.55565	−	5.01575i	−0.103222	−	0.202584i	0.833619	−	0.552339i	$-0.186265\pi$
$613$	−2.55565	−	5.01575i	−0.103222	−	0.202584i	−0.936841	+	0.349755i	$0.886265\pi$
$614$	3.62398	+	11.1535i	0.146252	+	0.450118i
$615$		0			0
$616$	5.15409	−	15.8627i	0.207664	−	0.639125i
$617$	−35.1967	+	5.57460i	−1.41696	+	0.224425i	−0.817478	−	0.575960i	$-0.804628\pi$
$617$	−35.1967	+	5.57460i	−1.41696	+	0.224425i	−0.599486	+	0.800385i	$0.704628\pi$
$618$	−0.130384	−	4.24555i	−0.00524480	−	0.170781i
$619$	20.2991	−	27.9393i	0.815889	−	1.12297i	−0.174499	−	0.984657i	$-0.555831\pi$
$619$	20.2991	−	27.9393i	0.815889	−	1.12297i	0.990388	−	0.138317i	$-0.0441694\pi$
$620$		0			0
$621$	−26.0780	−	1.69685i	−1.04648	−	0.0680922i
$622$	−32.6756	−	5.17530i	−1.31017	−	0.207511i
$623$	−2.11632	+	4.15351i	−0.0847885	+	0.166407i
$624$	−4.65672	+	4.95180i	−0.186418	+	0.198231i
$625$		0			0
$626$			4.37993i			0.175057i
$627$	11.0117	+	30.6550i	0.439766	+	1.22424i
$628$	−0.659856	+	4.16617i	−0.0263311	+	0.166248i
$629$	1.75992	−	1.27866i	0.0701727	−	0.0509835i
$630$		0			0
$631$	−6.95722	−	5.05472i	−0.276963	−	0.201225i	0.440629	−	0.897689i	$-0.354755\pi$
$631$	−6.95722	−	5.05472i	−0.276963	−	0.201225i	−0.717591	+	0.696464i	$0.754755\pi$
$632$	7.51686	−	7.51686i	0.299005	−	0.299005i
$633$	24.9659	+	16.9929i	0.992305	+	0.675407i
$634$	−26.6314	−	8.65307i	−1.05767	−	0.343657i
$635$		0			0
$636$	−13.0146	−	6.13559i	−0.516063	−	0.243292i
$637$	44.2955	−	22.5697i	1.75505	−	0.894244i
$638$	−6.18406	+	3.15094i	−0.244829	+	0.124747i
$639$	4.71040	−	1.85719i	0.186341	−	0.0734695i
$640$		0			0
$641$	−12.9664	−	4.21305i	−0.512144	−	0.166406i	0.0415332	−	0.999137i	$-0.486776\pi$
$641$	−12.9664	−	4.21305i	−0.512144	−	0.166406i	−0.553677	+	0.832732i	$0.686776\pi$
$642$	−5.93593	+	8.72104i	−0.234273	+	0.344192i
$643$	−11.4059	+	11.4059i	−0.449806	+	0.449806i	−0.895290	−	0.445484i	$-0.853032\pi$
$643$	−11.4059	+	11.4059i	−0.449806	+	0.449806i	0.445484	+	0.895290i	$0.353032\pi$
$644$	−18.0445	−	13.1101i	−0.711051	−	0.516609i
$645$		0			0
$646$	−1.66666	+	1.21090i	−0.0655739	+	0.0476422i
$647$	−4.90280	+	30.9551i	−0.192749	+	1.21697i	0.681619	+	0.731707i	$0.261276\pi$
$647$	−4.90280	+	30.9551i	−0.192749	+	1.21697i	−0.874368	+	0.485263i	$0.838724\pi$
$648$	−3.07284	+	8.45917i	−0.120713	+	0.332308i
$649$			21.1238i			0.829181i
$650$		0			0
$651$	−18.6617	−	17.5496i	−0.731409	−	0.687823i
$652$	−4.73142	+	9.28593i	−0.185297	+	0.363665i
$653$	37.8061	+	5.98789i	1.47947	+	0.234324i	0.843390	−	0.537302i	$-0.180556\pi$
$653$	37.8061	+	5.98789i	1.47947	+	0.234324i	0.636076	+	0.771626i	$0.280556\pi$
$654$	−8.06209	−	1.02433i	−0.315253	−	0.0400546i
$655$		0			0
$656$	2.00614	−	2.76122i	0.0783266	−	0.107807i
$657$	7.11835	−	8.05095i	0.277713	−	0.314098i
$658$	−22.6403	+	3.58587i	−0.882610	+	0.139792i
$659$	−6.33270	+	19.4901i	−0.246687	+	0.759225i	0.748667	+	0.662946i	$0.230694\pi$
$659$	−6.33270	+	19.4901i	−0.246687	+	0.759225i	−0.995354	+	0.0962789i	$0.969306\pi$
$660$		0			0
$661$	−13.4948	−	41.5327i	−0.524887	−	1.61544i	−0.764539	−	0.644577i	$-0.777033\pi$
$661$	−13.4948	−	41.5327i	−0.524887	−	1.61544i	0.239652	−	0.970859i	$-0.422967\pi$
$662$	−4.35103	−	8.53939i	−0.169108	−	0.331893i
$663$	2.68874	+	0.783237i	0.104422	+	0.0304184i
$664$	6.74418	−	2.19132i	0.261725	−	0.0850395i
$665$		0			0
$666$	−3.96130	+	15.3372i	−0.153497	+	0.594303i
$667$	1.45192	+	9.16704i	0.0562184	+	0.354949i
$668$	−9.89891	−	9.89891i	−0.383000	−	0.383000i
$669$	38.5175	−	7.31907i	1.48917	−	0.282971i
$670$		0			0
$671$	31.7502	+	43.7004i	1.22570	+	1.68703i
$672$	−6.07280	+	4.70360i	−0.234263	+	0.181445i
$673$	33.0273	+	16.8283i	1.27311	+	0.648681i	0.954219	−	0.299110i	$-0.0966898\pi$
$673$	33.0273	+	16.8283i	1.27311	+	0.648681i	0.318890	+	0.947792i	$0.396690\pi$
$674$	−15.6652			−0.603401
$675$		0			0
$676$	−2.40180			−0.0923767
$677$	−37.1946	−	18.9516i	−1.42951	−	0.728369i	−0.443686	−	0.896182i	$-0.646330\pi$
$677$	−37.1946	−	18.9516i	−1.42951	−	0.728369i	−0.985819	+	0.167813i	$0.946330\pi$
$678$	−23.4128	+	18.1340i	−0.899163	+	0.696433i
$679$	−20.1010	−	27.6666i	−0.771404	−	1.06175i
$680$		0			0
$681$	−32.8546	+	6.24301i	−1.25899	+	0.239233i
$682$	−8.86905	−	8.86905i	−0.339614	−	0.339614i
$683$	−7.96066	−	50.2616i	−0.304606	−	1.92321i	−0.377793	−	0.925890i	$-0.623317\pi$
$683$	−7.96066	−	50.2616i	−0.304606	−	1.92321i	0.0731865	−	0.997318i	$-0.476683\pi$
$684$	3.75138	−	14.5244i	0.143437	−	0.555354i
$685$		0			0
$686$	23.9045	−	7.76703i	0.912677	−	0.296547i
$687$	27.1047	+	7.89565i	1.03411	+	0.301238i
$688$	2.38607	+	4.68293i	0.0909681	+	0.178535i
$689$	−10.0744	−	31.0059i	−0.383805	−	1.18123i
$690$		0			0
$691$	−9.91187	+	30.5056i	−0.377065	+	1.16049i	0.565010	+	0.825084i	$0.308872\pi$
$691$	−9.91187	+	30.5056i	−0.377065	+	1.16049i	−0.942075	+	0.335403i	$0.891128\pi$
$692$	6.92347	−	1.09657i	0.263191	−	0.0416854i
$693$	33.1437	−	37.4860i	1.25902	−	1.42397i
$694$	−21.7024	+	29.8708i	−0.823813	+	1.13388i
$695$		0			0
$696$	3.17089	+	0.402880i	0.120192	+	0.0152711i
$697$	−1.38884	−	0.219971i	−0.0526061	−	0.00833198i
$698$	−6.81642	+	13.3780i	−0.258005	+	0.506364i
$699$	−0.767891	−	0.722131i	−0.0290443	−	0.0273135i
$700$		0			0
$701$			32.1785i			1.21536i	0.794180	+	0.607682i	$0.207900\pi$
$701$			32.1785i			1.21536i	−0.794180	+	0.607682i	$0.792100\pi$
$702$	−18.7325	+	8.05863i	−0.707013	+	0.304153i
$703$	4.13027	−	26.0775i	0.155776	−	0.983533i
$704$	−3.04265	+	2.21062i	−0.114674	+	0.0833157i
$705$		0			0
$706$	24.3558	+	17.6956i	0.916644	+	0.665981i
$707$	−34.7605	+	34.7605i	−1.30730	+	1.30730i
$708$	5.47388	−	8.04220i	0.205721	−	0.302244i
$709$	2.62130	+	0.851713i	0.0984451	+	0.0319867i	0.357825	−	0.933789i	$-0.383518\pi$
$709$	2.62130	+	0.851713i	0.0984451	+	0.0319867i	−0.259380	+	0.965775i	$0.583518\pi$
$710$		0			0
$711$	29.6686	−	11.6976i	1.11266	−	0.438693i
$712$	0.936569	−	0.477205i	0.0350994	−	0.0178840i
$713$	−14.9448	+	7.61474i	−0.559686	+	0.285174i
$714$	2.86250	+	1.34949i	0.107126	+	0.0505033i
$715$		0			0
$716$	2.69201	+	0.874686i	0.100605	+	0.0326886i
$717$	−11.4846	−	7.81693i	−0.428900	−	0.291929i
$718$	2.46690	−	2.46690i	0.0920639	−	0.0920639i
$719$	6.94235	+	5.04392i	0.258906	+	0.188106i	0.709665	−	0.704540i	$-0.248846\pi$
$719$	6.94235	+	5.04392i	0.258906	+	0.188106i	−0.450759	+	0.892646i	$0.648846\pi$
$720$		0			0
$721$	8.79854	−	6.39251i	0.327675	−	0.238070i
$722$	−0.939145	+	5.92953i	−0.0349514	+	0.220674i
$723$	−4.24378	−	11.8140i	−0.157828	−	0.439369i
$724$		−	0.350016i		−	0.0130082i
$725$		0			0
$726$	3.73123	−	3.96767i	0.138479	−	0.147254i
$727$	15.5376	−	30.4942i	0.576257	−	1.13097i	−0.400435	−	0.916325i	$-0.631141\pi$
$727$	15.5376	−	30.4942i	0.576257	−	1.13097i	0.976692	−	0.214644i	$-0.0688590\pi$
$728$	−17.1902	−	2.72266i	−0.637111	−	0.100909i
$729$	−18.5670	+	19.6027i	−0.687668	+	0.726026i
$730$		0			0
$731$	1.27276	−	1.75180i	0.0470746	−	0.0647926i
$732$	−0.763622	−	24.8650i	−0.0282243	−	0.919038i
$733$	−39.3201	+	6.22770i	−1.45232	+	0.230025i	−0.832198	−	0.554478i	$-0.812918\pi$
$733$	−39.3201	+	6.22770i	−1.45232	+	0.230025i	−0.620124	+	0.784504i	$0.712918\pi$
$734$	4.83943	−	14.8942i	0.178627	−	0.549756i
$735$		0			0
$736$	1.55415	+	4.78318i	0.0572867	+	0.176310i
$737$	−10.5750	−	20.7547i	−0.389537	−	0.764509i
$738$	8.82071	−	5.19955i	0.324695	−	0.191398i
$739$	−19.6010	+	6.36874i	−0.721033	+	0.234278i	−0.646471	−	0.762939i	$-0.723756\pi$
$739$	−19.6010	+	6.36874i	−0.721033	+	0.234278i	−0.0745620	+	0.997216i	$0.523756\pi$
$740$		0			0
$741$	29.7970	−	16.3533i	1.09462	−	0.600754i
$742$	−5.76314	−	36.3871i	−0.211572	−	1.33581i
$743$	25.7253	+	25.7253i	0.943771	+	0.943771i	0.998501	−	0.0547306i	$-0.0174300\pi$
$743$	25.7253	+	25.7253i	0.943771	+	0.943771i	−0.0547306	+	0.998501i	$0.517430\pi$
$744$	1.07834	+	5.67487i	0.0395337	+	0.208051i
$745$		0			0
$746$	3.74935	+	5.16053i	0.137273	+	0.188940i
$747$	21.1764	+	2.03232i	0.774806	+	0.0743585i
$748$	1.38059	+	0.703446i	0.0504794	+	0.0257205i
$749$	−27.0114			−0.986973
$750$		0			0
$751$	−13.8571			−0.505654			−0.252827	−	0.967511i	$-0.581360\pi$
$751$	−13.8571			−0.505654			−0.252827	+	0.967511i	$0.581360\pi$
$752$	4.60540	+	2.34657i	0.167942	+	0.0855705i
$753$	−15.4339	−	19.9267i	−0.562443	−	0.726169i
$754$	4.25699	+	5.85925i	0.155031	+	0.213381i
$755$		0			0
$756$	−22.3322	+	5.68292i	−0.812216	+	0.206686i
$757$	−28.7075	−	28.7075i	−1.04339	−	1.04339i	−0.999015	−	0.0443764i	$-0.985870\pi$
$757$	−28.7075	−	28.7075i	−1.04339	−	1.04339i	−0.0443764	−	0.999015i	$-0.514130\pi$
$758$	−4.21499	−	26.6124i	−0.153095	−	0.966606i
$759$	−15.7625	−	28.7205i	−0.572143	−	1.04249i
$760$		0			0
$761$	36.3818	−	11.8212i	1.31884	−	0.428517i	0.436744	−	0.899586i	$-0.356132\pi$
$761$	36.3818	−	11.8212i	1.31884	−	0.428517i	0.882096	+	0.471069i	$0.156132\pi$
$762$	9.50095	−	32.6154i	0.344183	−	1.18153i
$763$	−9.44684	−	18.5405i	−0.341998	−	0.671210i
$764$	0.350849	+	1.07980i	0.0126933	+	0.0390659i
$765$		0			0
$766$	9.25415	−	28.4814i	0.334366	−	1.02907i
$767$	21.7712	−	3.44822i	0.786114	−	0.124508i
$768$	1.73123	−	0.0531674i	0.0624705	−	0.00191851i
$769$	−23.2438	+	31.9924i	−0.838194	+	1.15368i	0.148148	+	0.988965i	$0.452669\pi$
$769$	−23.2438	+	31.9924i	−0.838194	+	1.15368i	−0.986342	+	0.164710i	$0.947331\pi$
$770$		0			0
$771$	0.320565	−	2.52303i	0.0115449	−	0.0908646i
$772$	5.81316	+	0.920714i	0.209220	+	0.0331372i
$773$	16.3075	−	32.0052i	0.586539	−	1.15115i	−0.386883	−	0.922129i	$-0.626448\pi$
$773$	16.3075	−	32.0052i	0.586539	−	1.15115i	0.973422	−	0.229019i	$-0.0735518\pi$
$774$	0.967539	+	15.7376i	0.0347775	+	0.565677i
$775$		0			0
$776$			7.71121i			0.276816i
$777$	−38.1706	+	13.7114i	−1.36936	+	0.491895i
$778$	−1.80860	+	11.4191i	−0.0648416	+	0.409394i
$779$	−13.8070	+	10.0314i	−0.494688	+	0.359412i
$780$		0			0
$781$	5.13529	+	3.73101i	0.183755	+	0.133506i
$782$	1.46516	−	1.46516i	0.0523940	−	0.0523940i
$783$	8.24330	+	4.89897i	0.294592	+	0.175075i
$784$	−12.0476	−	3.91450i	−0.430271	−	0.139803i
$785$		0			0
$786$	15.1597	−	32.1563i	0.540728	−	1.14698i
$787$	25.5543	−	13.0206i	0.910913	−	0.464133i	0.0652610	−	0.997868i	$-0.479212\pi$
$787$	25.5543	−	13.0206i	0.910913	−	0.464133i	0.845652	+	0.533735i	$0.179212\pi$
$788$	−17.1209	+	8.72355i	−0.609908	+	0.310764i
$789$	−16.4852	+	34.9679i	−0.586889	+	1.24489i
$790$		0			0
$791$	−72.1143	−	23.4314i	−2.56409	−	0.833123i
$792$	−11.0146	+	2.44551i	−0.391385	+	0.0868976i
$793$	39.8569	−	39.8569i	1.41536	−	1.41536i
$794$	10.8401	+	7.87580i	0.384701	+	0.279502i
$795$		0			0
$796$	10.2845	−	7.47216i	0.364526	−	0.264844i
$797$	−1.51547	+	9.56827i	−0.0536805	+	0.338926i	0.946202	+	0.323578i	$0.104886\pi$
$797$	−1.51547	+	9.56827i	−0.0536805	+	0.338926i	−0.999882	+	0.0153481i	$0.995114\pi$
$798$	36.1478	−	12.9848i	1.27962	−	0.459658i
$799$		−	2.12949i		−	0.0753360i
$800$		0			0
$801$	3.14746	−	0.193504i	0.111210	−	0.00683713i
$802$	−10.1196	+	19.8609i	−0.357337	+	0.701313i
$803$	13.3065	+	2.10754i	0.469575	+	0.0743734i
$804$	−1.35213	+	10.6420i	−0.0476859	+	0.375315i
$805$		0			0
$806$	−7.69311	+	10.5887i	−0.270978	+	0.372970i
$807$	43.2777	−	1.32909i	1.52345	−	0.0467861i
$808$	10.9483	−	1.73404i	0.385159	−	0.0610032i
$809$	−17.2607	+	53.1231i	−0.606855	+	1.86771i	−0.123359	+	0.992362i	$0.539367\pi$
$809$	−17.2607	+	53.1231i	−0.606855	+	1.86771i	−0.483496	+	0.875346i	$0.660633\pi$
$810$		0			0
$811$	−6.13462	−	18.8804i	−0.215416	−	0.662981i	−0.999124	−	0.0418519i	$-0.986674\pi$
$811$	−6.13462	−	18.8804i	−0.215416	−	0.662981i	0.783708	−	0.621129i	$-0.213326\pi$
$812$	3.71553	+	7.29214i	0.130390	+	0.255904i
$813$	7.86795	−	27.0096i	0.275941	−	0.947268i
$814$	−18.8863	+	6.13654i	−0.661965	+	0.215086i
$815$		0			0
$816$	−0.343329	−	0.625571i	−0.0120189	−	0.0218994i
$817$	−4.11120	−	25.9571i	−0.143833	−	0.908125i
$818$	9.95831	+	9.95831i	0.348184	+	0.348184i
$819$	−44.0452	−	28.0404i	−1.53906	−	0.979810i
$820$		0			0
$821$	−22.0314	−	30.3236i	−0.768899	−	1.05830i	−0.996421	−	0.0845263i	$-0.973062\pi$
$821$	−22.0314	−	30.3236i	−0.768899	−	1.05830i	0.227522	−	0.973773i	$-0.426938\pi$
$822$	−7.66658	−	9.89830i	−0.267403	−	0.345243i
$823$	35.1647	+	17.9173i	1.22577	+	0.624559i	0.942411	−	0.334456i	$-0.108553\pi$
$823$	35.1647	+	17.9173i	1.22577	+	0.624559i	0.283355	+	0.959015i	$0.408553\pi$
$824$	−2.45232			−0.0854307
$825$		0			0
$826$	24.9088			0.866688
$827$	−22.4561	−	11.4419i	−0.780874	−	0.397875i	0.0176456	−	0.999844i	$-0.494383\pi$
$827$	−22.4561	−	11.4419i	−0.780874	−	0.397875i	−0.798519	+	0.601969i	$0.794383\pi$
$828$	−1.44138	+	15.0190i	−0.0500915	+	0.521946i
$829$	22.7111	+	31.2592i	0.788791	+	1.08568i	0.994258	+	0.107013i	$0.0341287\pi$
$829$	22.7111	+	31.2592i	0.788791	+	1.08568i	−0.205467	+	0.978664i	$0.565871\pi$
$830$		0			0
$831$	2.22656	+	11.7176i	0.0772386	+	0.406478i
$832$	2.77505	+	2.77505i	0.0962075	+	0.0962075i
$833$	0.816423	+	5.15469i	0.0282874	+	0.178600i
$834$	−14.7180	+	8.07760i	−0.509643	+	0.279705i
$835$		0			0
$836$	17.8855	−	5.81135i	0.618582	−	0.200990i
$837$	−3.81652	+	16.9038i	−0.131918	+	0.584279i
$838$	−2.57528	−	5.05427i	−0.0889615	−	0.174597i
$839$	−1.11037	−	3.41736i	−0.0383342	−	0.117980i	0.930058	−	0.367412i	$-0.119756\pi$
$839$	−1.11037	−	3.41736i	−0.0383342	−	0.117980i	−0.968392	+	0.249432i	$0.919756\pi$
$840$		0			0
$841$	−7.90910	+	24.3417i	−0.272727	+	0.839369i
$842$	−6.30794	+	0.999080i	−0.217386	+	0.0344306i
$843$	1.30207	+	42.3978i	0.0448455	+	1.46026i
$844$	10.2487	−	14.1061i	0.352774	−	0.485552i
$845$		0			0
$846$	9.86698	+	11.9619i	0.339234	+	0.411259i
$847$	13.7738	+	2.18155i	0.473273	+	0.0749591i
$848$	−3.77136	+	7.40172i	−0.129509	+	0.254176i
$849$	8.68879	−	9.23937i	0.298198	−	0.317095i
$850$		0			0
$851$			26.5557i			0.910317i
$852$	−0.988266	−	2.75118i	−0.0338574	−	0.0942540i
$853$	7.10018	−	44.8288i	0.243106	−	1.53491i	−0.500172	−	0.865926i	$-0.666730\pi$
$853$	7.10018	−	44.8288i	0.243106	−	1.53491i	0.743278	−	0.668983i	$-0.233270\pi$
$854$	51.5307	−	37.4393i	1.76334	−	1.28114i
$855$		0			0
$856$	4.92752	+	3.58005i	0.168419	+	0.122364i
$857$	5.49063	−	5.49063i	0.187556	−	0.187556i	−0.607082	−	0.794639i	$-0.707660\pi$
$857$	5.49063	−	5.49063i	0.187556	−	0.187556i	0.794639	+	0.607082i	$0.207660\pi$
$858$	−21.1338	−	14.3846i	−0.721496	−	0.491082i
$859$	−10.7387	−	3.48922i	−0.366400	−	0.119051i	0.120030	−	0.992770i	$-0.461701\pi$
$859$	−10.7387	−	3.48922i	−0.366400	−	0.119051i	−0.486430	+	0.873720i	$0.661701\pi$
$860$		0			0
$861$	23.7136	+	11.1795i	0.808159	+	0.380996i
$862$	−17.7986	+	9.06883i	−0.606222	+	0.308886i
$863$	−10.3665	+	5.28199i	−0.352880	+	0.179801i	−0.621440	−	0.783462i	$-0.713452\pi$
$863$	−10.3665	+	5.28199i	−0.352880	+	0.179801i	0.268560	+	0.963263i	$0.413452\pi$
$864$	4.82715	+	1.92319i	0.164223	+	0.0654282i
$865$		0			0
$866$	22.0640	+	7.16903i	0.749765	+	0.243613i
$867$	16.4025	−	24.0984i	0.557056	−	0.818424i
$868$	−10.4582	+	10.4582i	−0.354975	+	0.354975i
$869$	32.3447	+	23.4998i	1.09722	+	0.797177i
$870$		0			0
$871$	−19.6646	+	14.2871i	−0.666308	+	0.484101i
$872$	−0.734001	+	4.63430i	−0.0248564	+	0.156937i
$873$	−9.21782	+	21.2178i	−0.311976	+	0.718115i
$874$		−	25.1484i		−	0.850658i
$875$		0			0
$876$	−4.51987	−	4.25053i	−0.152712	−	0.143612i
$877$	−11.2271	+	22.0344i	−0.379112	+	0.744049i	−0.999180	−	0.0404992i	$-0.987105\pi$
$877$	−11.2271	+	22.0344i	−0.379112	+	0.744049i	0.620068	+	0.784548i	$0.287105\pi$
$878$	11.1928	+	1.77277i	0.377740	+	0.0598282i
$879$	2.78540	+	0.353901i	0.0939492	+	0.0119368i
$880$		0			0
$881$	7.08613	−	9.75322i	0.238738	−	0.328594i	−0.672790	−	0.739834i	$-0.734904\pi$
$881$	7.08613	−	9.75322i	0.238738	−	0.328594i	0.911527	+	0.411240i	$0.134904\pi$
$882$	−28.4703	−	25.1724i	−0.958645	−	0.847598i
$883$	7.05614	−	1.11758i	0.237458	−	0.0376097i	−0.0365710	−	0.999331i	$-0.511644\pi$
$883$	7.05614	−	1.11758i	0.237458	−	0.0376097i	0.274029	+	0.961721i	$0.411644\pi$
$884$	0.499640	−	1.53774i	0.0168047	−	0.0517196i
$885$		0			0
$886$	−2.37482	−	7.30895i	−0.0797837	−	0.245549i
$887$	1.61555	+	3.17069i	0.0542448	+	0.106461i	0.916537	−	0.399949i	$-0.130972\pi$
$887$	1.61555	+	3.17069i	0.0542448	+	0.106461i	−0.862293	+	0.506410i	$0.830972\pi$
$888$	8.78054	+	2.55779i	0.294655	+	0.0858338i
$889$	82.7238	−	26.8786i	2.77447	−	0.901479i
$890$		0			0
$891$	−33.2305	−	6.43759i	−1.11326	−	0.215667i
$892$	−3.54105	−	22.3573i	−0.118563	−	0.748578i
$893$	−18.2756	−	18.2756i	−0.611569	−	0.611569i
$894$	7.06028	−	1.34159i	0.236131	−	0.0448695i
$895$		0			0
$896$	2.60672	+	3.58784i	0.0870843	+	0.119861i
$897$	−27.0277	+	20.9339i	−0.902430	+	0.698964i
$898$	24.0090	+	12.2332i	0.801189	+	0.408226i
$899$	6.15455			0.205266
$900$		0			0
$901$	3.42248			0.114019
$902$	11.4372	+	5.82752i	0.380816	+	0.194035i
$903$	−31.9173	+	24.7210i	−1.06214	+	0.822665i
$904$	10.0498	+	13.8324i	0.334252	+	0.460058i
$905$		0			0
$906$	−16.1664	+	3.07193i	−0.537093	+	0.102058i
$907$	1.89862	+	1.89862i	0.0630427	+	0.0630427i	0.737925	−	0.674883i	$-0.235806\pi$
$907$	1.89862	+	1.89862i	0.0630427	+	0.0630427i	−0.674883	+	0.737925i	$0.735806\pi$
$908$	3.02044	+	19.0703i	0.100237	+	0.632871i
$909$	32.1976	+	8.31603i	1.06793	+	0.275825i
$910$		0			0
$911$	2.38886	−	0.776187i	0.0791464	−	0.0257162i	−0.269176	−	0.963091i	$-0.586751\pi$
$911$	2.38886	−	0.776187i	0.0791464	−	0.0257162i	0.348323	+	0.937375i	$0.386751\pi$
$912$	−8.31523	−	2.42225i	−0.275345	−	0.0802086i
$913$	12.1078	+	23.7628i	0.400708	+	0.786435i
$914$	−10.5736	−	32.5423i	−0.349744	−	1.07640i
$915$		0			0
$916$	5.03677	−	15.5016i	0.166420	−	0.512187i
$917$	89.9045	−	14.2395i	2.96891	−	0.470229i
$918$	−0.196894	−	2.13170i	−0.00649846	−	0.0703567i
$919$	5.62589	−	7.74338i	0.185581	−	0.255430i	−0.706082	−	0.708130i	$-0.749539\pi$
$919$	5.62589	−	7.74338i	0.185581	−	0.255430i	0.891663	+	0.452700i	$0.149539\pi$
$920$		0			0
$921$	20.1506	+	2.56024i	0.663983	+	0.0843629i
$922$	36.6665	+	5.80740i	1.20755	+	0.191256i
$923$	3.00708	−	5.90173i	0.0989793	−	0.194258i
$924$	−21.0449	−	19.7908i	−0.692328	−	0.651071i
$925$		0			0
$926$			7.02279i			0.230783i
$927$	−6.74771	−	2.93145i	−0.221624	−	0.0962816i
$928$	0.288689	−	1.82271i	0.00947670	−	0.0598335i
$929$	−28.0139	+	20.3533i	−0.919106	+	0.667770i	−0.943301	−	0.331938i	$-0.892298\pi$
$929$	−28.0139	+	20.3533i	−0.919106	+	0.667770i	0.0241953	+	0.999707i	$0.492298\pi$
$930$		0			0
$931$	51.2449	+	37.2316i	1.67949	+	1.22022i
$932$	−0.430335	+	0.430335i	−0.0140961	+	0.0140961i
$933$	−32.2419	+	47.3697i	−1.05555	+	1.55081i
$934$	27.2912	+	8.86745i	0.892995	+	0.290152i
$935$		0			0
$936$	4.31847	+	10.9529i	0.141154	+	0.358008i
$937$	−13.6302	+	6.94494i	−0.445280	+	0.226881i	−0.662229	−	0.749302i	$-0.730389\pi$
$937$	−13.6302	+	6.94494i	−0.445280	+	0.226881i	0.216949	+	0.976183i	$0.430389\pi$
$938$	−24.4736	+	12.4699i	−0.799090	+	0.407157i
$939$	6.86194	+	3.23498i	0.223931	+	0.105570i
$940$		0			0
$941$	−27.0255	−	8.78112i	−0.881006	−	0.286256i	−0.166631	−	0.986019i	$-0.553289\pi$
$941$	−27.0255	−	8.78112i	−0.881006	−	0.286256i	−0.714375	+	0.699763i	$0.753289\pi$
$942$	6.03968	+	4.11088i	0.196783	+	0.133940i
$943$	12.1378	−	12.1378i	0.395260	−	0.395260i
$944$	−4.54397	−	3.30138i	−0.147893	−	0.107451i
$945$		0			0
$946$	−15.9915	+	11.6185i	−0.519928	+	0.377750i
$947$	−5.88298	+	37.1437i	−0.191171	+	1.20701i	0.686279	+	0.727339i	$0.259243\pi$
$947$	−5.88298	+	37.1437i	−0.191171	+	1.20701i	−0.877450	+	0.479669i	$0.840757\pi$
$948$	−6.22461	−	17.3284i	−0.202166	−	0.562800i
$949$		−	14.0583i		−	0.456353i
$950$		0			0
$951$	−33.2263	+	35.3318i	−1.07744	+	1.14571i
$952$	0.829491	−	1.62797i	0.0268840	−	0.0527627i
$953$	26.3120	+	4.16742i	0.852331	+	0.134996i	0.567289	−	0.823519i	$-0.307992\pi$
$953$	26.3120	+	4.16742i	0.852331	+	0.134996i	0.285042	+	0.958515i	$0.407992\pi$
$954$	−19.2250	+	15.8580i	−0.622432	+	0.513423i
$955$		0			0
$956$	−4.71452	+	6.48898i	−0.152478	+	0.209868i
$957$	0.369010	+	12.0157i	0.0119284	+	0.388412i
$958$	−12.6881	+	2.00959i	−0.409933	+	0.0649269i
$959$	9.90614	−	30.4880i	0.319886	−	0.984508i
$960$		0			0
$961$	−6.14254	−	18.9048i	−0.198146	−	0.609832i
$962$	9.40760	+	18.4635i	0.303313	+	0.595286i
$963$	9.27884	+	15.7410i	0.299006	+	0.507246i
$964$	−6.89284	+	2.23962i	−0.222003	+	0.0721333i
$965$		0			0
$966$	−33.8667	+	18.5869i	−1.08964	+	0.598023i
$967$	6.56982	+	41.4802i	0.211271	+	1.33391i	0.834125	+	0.551576i	$0.185973\pi$
$967$	6.56982	+	41.4802i	0.211271	+	1.33391i	−0.622853	+	0.782339i	$0.714027\pi$
$968$	−2.22353	−	2.22353i	−0.0714670	−	0.0714670i
$969$	0.666109	+	3.50548i	0.0213985	+	0.112612i
$970$		0			0
$971$	−8.52779	−	11.7375i	−0.273670	−	0.376674i	0.649955	−	0.759973i	$-0.274788\pi$
$971$	−8.52779	−	11.7375i	−0.273670	−	0.376674i	−0.923624	+	0.383299i	$0.874788\pi$
$972$	10.9832	+	11.0620i	0.352287	+	0.354815i
$973$	−38.3017	−	19.5157i	−1.22790	−	0.625645i
$974$	20.6983			0.663215
$975$		0			0
$976$	−14.3626			−0.459736
$977$	−1.06999	−	0.545186i	−0.0342319	−	0.0174420i	0.436791	−	0.899563i	$-0.356115\pi$
$977$	−1.06999	−	0.545186i	−0.0342319	−	0.0174420i	−0.471023	+	0.882121i	$0.656115\pi$
$978$	11.0535	+	14.2711i	0.353451	+	0.456340i
$979$	2.32366	+	3.19824i	0.0742644	+	0.102216i
$980$		0			0
$981$	−7.55939	+	11.8741i	−0.241353	+	0.379112i
$982$	19.7552	+	19.7552i	0.630413	+	0.630413i
$983$	2.80520	+	17.7113i	0.0894719	+	0.564903i	0.991176	+	0.132550i	$0.0423165\pi$
$983$	2.80520	+	17.7113i	0.0894719	+	0.564903i	−0.901704	+	0.432353i	$0.857683\pi$
$984$	−2.84422	−	5.18239i	−0.0906704	−	0.165209i
$985$		0			0
$986$	−0.723093	+	0.234947i	−0.0230280	+	0.00748224i
$987$	−11.1040	+	38.1185i	−0.353445	+	1.21333i
$988$	−8.90907	−	17.4850i	−0.283435	−	0.556273i
$989$	8.16826	+	25.1393i	0.259736	+	0.799384i
$990$		0			0
$991$	14.9087	−	45.8841i	0.473589	−	1.45756i	−0.374262	−	0.927323i	$-0.622104\pi$
$991$	14.9087	−	45.8841i	0.473589	−	1.45756i	0.847851	−	0.530234i	$-0.177896\pi$
$992$	3.29395	−	0.521711i	0.104583	−	0.0165643i
$993$	−16.5921	+	0.509555i	−0.526535	+	0.0161702i
$994$	4.39954	−	6.05544i	0.139545	−	0.192067i
$995$		0			0
$996$	1.54810	−	12.1844i	0.0490535	−	0.386079i
$997$	21.3791	+	3.38611i	0.677082	+	0.107239i	0.485499	−	0.874237i	$-0.338638\pi$
$997$	21.3791	+	3.38611i	0.677082	+	0.107239i	0.191583	+	0.981476i	$0.438638\pi$
$998$	−0.184251	+	0.361613i	−0.00583237	+	0.0114467i
$999$	21.1026	+	17.5340i	0.667657	+	0.554750i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.l.c.107.2		80
3.2	odd	2	inner	750.2.l.c.107.9		80
5.2	odd	4		750.2.l.b.143.9		80
5.3	odd	4		150.2.l.a.83.2	yes	80
5.4	even	2		750.2.l.a.107.9		80
15.2	even	4		750.2.l.b.143.5		80
15.8	even	4		150.2.l.a.83.6	yes	80
15.14	odd	2		750.2.l.a.107.2		80
25.3	odd	20	inner	750.2.l.c.743.9		80
25.4	even	10		750.2.l.b.257.5		80
25.21	even	5		150.2.l.a.47.6	yes	80
25.22	odd	20		750.2.l.a.743.2		80
75.29	odd	10		750.2.l.b.257.9		80
75.47	even	20		750.2.l.a.743.9		80
75.53	even	20	inner	750.2.l.c.743.2		80
75.71	odd	10		150.2.l.a.47.2	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.47.2	✓	80	75.71	odd	10
150.2.l.a.47.6	yes	80	25.21	even	5
150.2.l.a.83.2	yes	80	5.3	odd	4
150.2.l.a.83.6	yes	80	15.8	even	4
750.2.l.a.107.2		80	15.14	odd	2
750.2.l.a.107.9		80	5.4	even	2
750.2.l.a.743.2		80	25.22	odd	20
750.2.l.a.743.9		80	75.47	even	20
750.2.l.b.143.5		80	15.2	even	4
750.2.l.b.143.9		80	5.2	odd	4
750.2.l.b.257.5		80	25.4	even	10
750.2.l.b.257.9		80	75.29	odd	10
750.2.l.c.107.2		80	1.1	even	1	trivial
750.2.l.c.107.9		80	3.2	odd	2	inner
750.2.l.c.743.2		80	75.53	even	20	inner
750.2.l.c.743.9		80	25.3	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.l (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.891007 - 0.453990i) q^{2} +(-1.36935 + 1.06061i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.70160 - 0.323338i) q^{6} +(3.13589 + 3.13589i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(0.750223 - 2.90468i) q^{9} +O(q^{10})\)	\(q+(-0.891007 - 0.453990i) q^{2} +(-1.36935 + 1.06061i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.70160 - 0.323338i) q^{6} +(3.13589 + 3.13589i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(0.750223 - 2.90468i) q^{9} +(3.57685 - 1.16219i) q^{11} +(-1.66293 - 0.484416i) q^{12} +(-1.78169 - 3.49677i) q^{13} +(-1.37043 - 4.21776i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(0.406920 - 0.0644499i) q^{17} +(-1.98715 + 2.24749i) q^{18} +(2.93913 - 4.04536i) q^{19} +(-7.62006 - 0.968173i) q^{21} +(-3.71462 - 0.588338i) q^{22} +(-2.28327 + 4.48117i) q^{23} +(1.26176 + 1.18657i) q^{24} +3.92451i q^{26} +(2.05341 + 4.77321i) q^{27} +(-0.693758 + 4.38021i) q^{28} +(1.49299 - 1.08472i) q^{29} +(2.69808 + 1.96027i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.66532 + 5.38508i) q^{33} +(-0.391828 - 0.127313i) q^{34} +(2.79091 - 1.10038i) q^{36} +(4.70465 - 2.39714i) q^{37} +(-4.45534 + 2.27011i) q^{38} +(6.14845 + 2.89861i) q^{39} +(-3.24600 - 1.05469i) q^{41} +(6.34998 + 4.32208i) q^{42} +(3.71639 - 3.71639i) q^{43} +(3.04265 + 2.21062i) q^{44} +(4.06882 - 2.95617i) q^{46} +(0.808572 - 5.10512i) q^{47} +(-0.585546 - 1.63007i) q^{48} +12.6676i q^{49} +(-0.488859 + 0.519837i) q^{51} +(1.78169 - 3.49677i) q^{52} +(8.20487 + 1.29952i) q^{53} +(0.337390 - 5.18519i) q^{54} +(2.60672 - 3.58784i) q^{56} +(0.265855 + 8.65677i) q^{57} +(-1.82271 + 0.288689i) q^{58} +(-1.73564 + 5.34175i) q^{59} +(4.43829 + 13.6596i) q^{61} +(-1.51406 - 2.97152i) q^{62} +(11.4614 - 6.75613i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(5.71060 - 3.13412i) q^{66} +(-0.968887 - 6.11731i) q^{67} +(0.291323 + 0.291323i) q^{68} +(-1.62617 - 8.55793i) q^{69} +(0.992045 + 1.36543i) q^{71} +(-2.98628 - 0.286595i) q^{72} +(3.19175 + 1.62628i) q^{73} -5.28015 q^{74} +5.00034 q^{76} +(14.8611 + 7.57211i) q^{77} +(-4.16237 - 5.37402i) q^{78} +(6.24842 + 8.60021i) q^{79} +(-7.87433 - 4.35832i) q^{81} +(2.41339 + 2.41339i) q^{82} +(1.10932 + 7.00394i) q^{83} +(-3.69569 - 6.73384i) q^{84} +(-4.99854 + 1.62412i) q^{86} +(-0.893957 + 3.06883i) q^{87} +(-1.70742 - 3.35101i) q^{88} +(0.324819 + 0.999689i) q^{89} +(5.37828 - 16.5526i) q^{91} +(-4.96742 + 0.786761i) q^{92} +(-5.77369 + 0.177314i) q^{93} +(-3.03812 + 4.18162i) q^{94} +(-0.218312 + 1.71824i) q^{96} +(-7.61627 - 1.20630i) q^{97} +(5.75096 - 11.2869i) q^{98} +(-0.692350 - 11.2615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q + 4 * q^3 + 4 * q^7	\( 80 q + 4 q^{3} + 4 q^{7} + 16 q^{12} + 20 q^{16} - 8 q^{18} + 40 q^{19} + 4 q^{22} - 56 q^{27} + 4 q^{28} - 96 q^{33} + 40 q^{34} - 64 q^{37} + 40 q^{39} - 4 q^{42} - 24 q^{43} + 16 q^{48} - 64 q^{57} + 20 q^{58} + 4 q^{63} - 104 q^{67} - 140 q^{69} + 8 q^{72} - 60 q^{73} - 60 q^{78} - 80 q^{79} - 40 q^{81} + 96 q^{82} - 60 q^{84} + 80 q^{87} + 24 q^{88} + 12 q^{93} - 12 q^{97}+O(q^{100}) \) 80 * q + 4 * q^3 + 4 * q^7 + 16 * q^12 + 20 * q^16 - 8 * q^18 + 40 * q^19 + 4 * q^22 - 56 * q^27 + 4 * q^28 - 96 * q^33 + 40 * q^34 - 64 * q^37 + 40 * q^39 - 4 * q^42 - 24 * q^43 + 16 * q^48 - 64 * q^57 + 20 * q^58 + 4 * q^63 - 104 * q^67 - 140 * q^69 + 8 * q^72 - 60 * q^73 - 60 * q^78 - 80 * q^79 - 40 * q^81 + 96 * q^82 - 60 * q^84 + 80 * q^87 + 24 * q^88 + 12 * q^93 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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