LMFDB - Embedded newform 680.2.h.c.509.45

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(509,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.509"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.h (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			509.45
Character	$\chi$	$=$	680.509
Dual form			680.2.h.c.509.44

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.39273 + 0.245576i) q^{2} -3.26492i q^{3} +(1.87939 + 0.684040i) q^{4} +(1.77664 - 1.35778i) q^{5} +(0.801785 - 4.54715i) q^{6} -3.95202 q^{7} +(2.44949 + 1.41421i) q^{8} -7.65971 q^{9} +(2.80781 - 1.45471i) q^{10} -2.85688 q^{11} +(2.23334 - 6.13604i) q^{12} +2.44949 q^{13} +(-5.50409 - 0.970520i) q^{14} +(-4.43303 - 5.80059i) q^{15} +(3.06418 + 2.57115i) q^{16} +(2.47862 - 3.29491i) q^{17} +(-10.6679 - 1.88104i) q^{18} -3.93923i q^{19} +(4.26776 - 1.33649i) q^{20} +12.9030i q^{21} +(-3.97886 - 0.701580i) q^{22} +3.79746 q^{23} +(4.61730 - 7.99739i) q^{24} +(1.31289 - 4.82455i) q^{25} +(3.41147 + 0.601535i) q^{26} +15.2136i q^{27} +(-7.42737 - 2.70334i) q^{28} +3.04617 q^{29} +(-4.74952 - 9.16729i) q^{30} +5.69829i q^{31} +(3.63616 + 4.33340i) q^{32} +9.32749i q^{33} +(4.26119 - 3.98023i) q^{34} +(-7.02132 + 5.36596i) q^{35} +(-14.3955 - 5.23955i) q^{36} -2.83577i q^{37} +(0.967379 - 5.48628i) q^{38} -7.99739i q^{39} +(6.27204 - 0.813309i) q^{40} +8.36647i q^{41} +(-3.16867 + 17.9704i) q^{42} +1.30201 q^{43} +(-5.36918 - 1.95422i) q^{44} +(-13.6085 + 10.4002i) q^{45} +(5.28884 + 0.932564i) q^{46} -2.63968i q^{47} +(8.39460 - 10.0043i) q^{48} +8.61847 q^{49} +(3.01330 - 6.39688i) q^{50} +(-10.7576 - 8.09249i) q^{51} +(4.60353 + 1.67555i) q^{52} +2.80631 q^{53} +(-3.73609 + 21.1884i) q^{54} +(-5.07565 + 3.87900i) q^{55} +(-9.68044 - 5.58900i) q^{56} -12.8613 q^{57} +(4.24249 + 0.748066i) q^{58} +8.35170i q^{59} +(-4.36353 - 13.9339i) q^{60} +14.1216 q^{61} +(-1.39936 + 7.93617i) q^{62} +30.2713 q^{63} +(4.00000 + 6.92820i) q^{64} +(4.35186 - 3.32586i) q^{65} +(-2.29060 + 12.9907i) q^{66} +5.53763 q^{67} +(6.91213 - 4.49694i) q^{68} -12.3984i q^{69} +(-11.0965 + 5.74906i) q^{70} -11.9811i q^{71} +(-18.7624 - 10.8325i) q^{72} -3.64560 q^{73} +(0.696397 - 3.94946i) q^{74} +(-15.7518 - 4.28649i) q^{75} +(2.69459 - 7.40333i) q^{76} +11.2905 q^{77} +(1.96396 - 11.1382i) q^{78} -6.61063i q^{79} +(8.93498 + 0.407542i) q^{80} +26.6920 q^{81} +(-2.05460 + 11.6522i) q^{82} -16.8485 q^{83} +(-8.82620 + 24.2498i) q^{84} +(-0.0701406 - 9.21928i) q^{85} +(1.81335 + 0.319742i) q^{86} -9.94552i q^{87} +(-6.99790 - 4.04024i) q^{88} +4.40351 q^{89} +(-21.5070 + 11.1427i) q^{90} -9.68044 q^{91} +(7.13690 + 2.59762i) q^{92} +18.6045 q^{93} +(0.648241 - 3.67636i) q^{94} +(-5.34859 - 6.99859i) q^{95} +(14.1482 - 11.8718i) q^{96} -13.2445 q^{97} +(12.0032 + 2.11649i) q^{98} +21.8829 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 96 q^{9} - 48 q^{15} + 24 q^{34} - 96 q^{36} + 96 q^{49} + 48 q^{60} + 192 q^{64} - 144 q^{66} - 96 q^{70} + 96 q^{76} - 192 q^{84} - 192 q^{86} - 48 q^{89} - 144 q^{94}+O(q^{100}) $ 48 * q - 96 * q^9 - 48 * q^15 + 24 * q^34 - 96 * q^36 + 96 * q^49 + 48 * q^60 + 192 * q^64 - 144 * q^66 - 96 * q^70 + 96 * q^76 - 192 * q^84 - 192 * q^86 - 48 * q^89 - 144 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	1.39273	+	0.245576i	0.984808	+	0.173648i
$2$	1.39273	+	0.245576i	0.984808	+	0.173648i
$3$		−	3.26492i		−	1.88500i	−0.334202	−	0.942502i	$-0.608467\pi$
$3$		−	3.26492i		−	1.88500i	0.334202	−	0.942502i	$-0.391533\pi$
$4$	1.87939	+	0.684040i	0.939693	+	0.342020i
$5$	1.77664	−	1.35778i	0.794537	−	0.607216i
$5$	1.77664	−	1.35778i	0.794537	−	0.607216i
$6$	0.801785	−	4.54715i	0.327327	−	1.85637i
$7$	−3.95202			−1.49372			−0.746862	−	0.664979i	$-0.768440\pi$
$7$	−3.95202			−1.49372			−0.746862	+	0.664979i	$0.768440\pi$
$8$	2.44949	+	1.41421i	0.866025	+	0.500000i
$9$	−7.65971			−2.55324
$10$	2.80781	−	1.45471i	0.887908	−	0.460021i
$11$	−2.85688			−0.861382			−0.430691	−	0.902499i	$-0.641730\pi$
$11$	−2.85688			−0.861382			−0.430691	+	0.902499i	$0.641730\pi$
$12$	2.23334	−	6.13604i	0.644709	−	1.77132i
$13$	2.44949			0.679366			0.339683	−	0.940540i	$-0.389680\pi$
$13$	2.44949			0.679366			0.339683	+	0.940540i	$0.389680\pi$
$14$	−5.50409	−	0.970520i	−1.47103	−	0.259382i
$15$	−4.43303	−	5.80059i	−1.14460	−	1.49771i
$16$	3.06418	+	2.57115i	0.766044	+	0.642788i
$17$	2.47862	−	3.29491i	0.601153	−	0.799134i
$17$	2.47862	−	3.29491i	0.601153	−	0.799134i
$18$	−10.6679	−	1.88104i	−2.51445	−	0.443365i
$19$		−	3.93923i		−	0.903722i	−0.892088	−	0.451861i	$-0.850760\pi$
$19$		−	3.93923i		−	0.903722i	0.892088	−	0.451861i	$-0.149240\pi$
$20$	4.26776	−	1.33649i	0.954301	−	0.298848i
$21$			12.9030i			2.81567i
$22$	−3.97886	−	0.701580i	−0.848296	−	0.149577i
$23$	3.79746			0.791826			0.395913	−	0.918288i	$-0.370428\pi$
$23$	3.79746			0.791826			0.395913	+	0.918288i	$0.370428\pi$
$24$	4.61730	−	7.99739i	0.942502	−	1.63246i
$25$	1.31289	−	4.82455i	0.262579	−	0.964911i
$26$	3.41147	+	0.601535i	0.669045	+	0.117971i
$27$			15.2136i			2.92786i
$28$	−7.42737	−	2.70334i	−1.40364	−	0.510884i
$29$	3.04617			0.565660			0.282830	−	0.959170i	$-0.408727\pi$
$29$	3.04617			0.565660			0.282830	+	0.959170i	$0.408727\pi$
$30$	−4.74952	−	9.16729i	−0.867140	−	1.67371i
$31$			5.69829i			1.02344i	0.859151	+	0.511722i	$0.170992\pi$
$31$			5.69829i			1.02344i	−0.859151	+	0.511722i	$0.829008\pi$
$32$	3.63616	+	4.33340i	0.642788	+	0.766044i
$33$			9.32749i			1.62371i
$34$	4.26119	−	3.98023i	0.730788	−	0.682604i
$35$	−7.02132	+	5.36596i	−1.18682	+	0.907012i
$36$	−14.3955	−	5.23955i	−2.39926	−	0.873258i
$37$		−	2.83577i		−	0.466198i	−0.972453	−	0.233099i	$-0.925113\pi$
$37$		−	2.83577i		−	0.466198i	0.972453	−	0.233099i	$-0.0748867\pi$
$38$	0.967379	−	5.48628i	0.156930	−	0.889992i
$39$		−	7.99739i		−	1.28061i
$40$	6.27204	−	0.813309i	0.991697	−	0.128595i
$41$			8.36647i			1.30662i	0.757089	+	0.653311i	$0.226621\pi$
$41$			8.36647i			1.30662i	−0.757089	+	0.653311i	$0.773379\pi$
$42$	−3.16867	+	17.9704i	−0.488937	+	2.77290i
$43$	1.30201			0.198555			0.0992775	−	0.995060i	$-0.468347\pi$
$43$	1.30201			0.198555			0.0992775	+	0.995060i	$0.468347\pi$
$44$	−5.36918	−	1.95422i	−0.809434	−	0.294610i
$45$	−13.6085	+	10.4002i	−2.02864	+	1.55037i
$46$	5.28884	+	0.932564i	0.779796	+	0.137499i
$47$		−	2.63968i		−	0.385037i	−0.981293	−	0.192519i	$-0.938334\pi$
$47$		−	2.63968i		−	0.385037i	0.981293	−	0.192519i	$-0.0616656\pi$
$48$	8.39460	−	10.0043i	1.21166	−	1.44400i
$49$	8.61847			1.23121
$50$	3.01330	−	6.39688i	0.426144	−	0.904655i
$51$	−10.7576	−	8.09249i	−1.50637	−	1.13318i
$52$	4.60353	+	1.67555i	0.638395	+	0.232357i
$53$	2.80631			0.385476			0.192738	−	0.981250i	$-0.438263\pi$
$53$	2.80631			0.385476			0.192738	+	0.981250i	$0.438263\pi$
$54$	−3.73609	+	21.1884i	−0.508417	+	2.88338i
$55$	−5.07565	+	3.87900i	−0.684400	+	0.523045i
$56$	−9.68044	−	5.58900i	−1.29360	−	0.746862i
$57$	−12.8613			−1.70352
$58$	4.24249	+	0.748066i	0.557067	+	0.0982259i
$59$			8.35170i			1.08730i	0.839312	+	0.543650i	$0.182958\pi$
$59$			8.35170i			1.08730i	−0.839312	+	0.543650i	$0.817042\pi$
$60$	−4.36353	−	13.9339i	−0.563330	−	1.79886i
$61$	14.1216			1.80809			0.904044	−	0.427440i	$-0.140584\pi$
$61$	14.1216			1.80809			0.904044	+	0.427440i	$0.140584\pi$
$62$	−1.39936	+	7.93617i	−0.177719	+	1.00789i
$63$	30.2713			3.81383
$64$	4.00000	+	6.92820i	0.500000	+	0.866025i
$65$	4.35186	−	3.32586i	0.539782	−	0.412522i
$66$	−2.29060	+	12.9907i	−0.281954	+	1.59904i
$67$	5.53763			0.676530			0.338265	−	0.941051i	$-0.390160\pi$
$67$	5.53763			0.676530			0.338265	+	0.941051i	$0.390160\pi$
$68$	6.91213	−	4.49694i	0.838219	−	0.545334i
$69$		−	12.3984i		−	1.49259i
$70$	−11.0965	+	5.74906i	−1.32629	+	0.687144i
$71$		−	11.9811i		−	1.42189i	−0.703248	−	0.710945i	$-0.748268\pi$
$71$		−	11.9811i		−	1.42189i	0.703248	−	0.710945i	$-0.251732\pi$
$72$	−18.7624	−	10.8325i	−2.21117	−	1.27662i
$73$	−3.64560			−0.426685			−0.213343	−	0.976977i	$-0.568435\pi$
$73$	−3.64560			−0.426685			−0.213343	+	0.976977i	$0.568435\pi$
$74$	0.696397	−	3.94946i	0.0809545	−	0.459116i
$75$	−15.7518	−	4.28649i	−1.81886	−	0.494962i
$76$	2.69459	−	7.40333i	0.309091	−	0.849220i
$77$	11.2905			1.28667
$78$	1.96396	−	11.1382i	0.222375	−	1.26115i
$79$		−	6.61063i		−	0.743754i	−0.928282	−	0.371877i	$-0.878714\pi$
$79$		−	6.61063i		−	0.743754i	0.928282	−	0.371877i	$-0.121286\pi$
$80$	8.93498	+	0.407542i	0.998961	+	0.0455646i
$81$	26.6920			2.96578
$82$	−2.05460	+	11.6522i	−0.226893	+	1.28677i
$83$	−16.8485			−1.84936			−0.924680	−	0.380745i	$-0.875668\pi$
$83$	−16.8485			−1.84936			−0.924680	+	0.380745i	$0.875668\pi$
$84$	−8.82620	+	24.2498i	−0.963017	+	2.64587i
$85$	−0.0701406	−	9.21928i	−0.00760782	−	0.999971i
$86$	1.81335	+	0.319742i	0.195538	+	0.0344787i
$87$		−	9.94552i		−	1.06627i
$88$	−6.99790	−	4.04024i	−0.745979	−	0.430691i
$89$	4.40351			0.466771			0.233386	−	0.972384i	$-0.425020\pi$
$89$	4.40351			0.466771			0.233386	+	0.972384i	$0.425020\pi$
$90$	−21.5070	+	11.1427i	−2.26704	+	1.17454i
$91$	−9.68044			−1.01479
$92$	7.13690	+	2.59762i	0.744073	+	0.270820i
$93$	18.6045			1.92919
$94$	0.648241	−	3.67636i	0.0668610	−	0.379188i
$95$	−5.34859	−	6.99859i	−0.548754	−	0.718040i
$96$	14.1482	−	11.8718i	1.44400	−	1.21166i
$97$	−13.2445			−1.34477			−0.672387	−	0.740200i	$-0.734731\pi$
$97$	−13.2445			−1.34477			−0.672387	+	0.740200i	$0.734731\pi$
$98$	12.0032	+	2.11649i	1.21251	+	0.213797i
$99$	21.8829			2.19931
$100$	5.76762	−	8.16912i	0.576762	−	0.816912i
$101$			13.7178i			1.36497i	0.730900	+	0.682485i	$0.239101\pi$
$101$			13.7178i			1.36497i	−0.730900	+	0.682485i	$0.760899\pi$
$102$	−12.9951	−	13.9125i	−1.28671	−	1.37754i
$103$		−	0.784921i		−	0.0773406i	−0.999252	−	0.0386703i	$-0.987688\pi$
$103$		−	0.784921i		−	0.0773406i	0.999252	−	0.0386703i	$-0.0123122\pi$
$104$	6.00000	+	3.46410i	0.588348	+	0.339683i
$105$	17.5194	+	22.9240i	1.70972	+	2.23716i
$106$	3.90843	+	0.689161i	0.379620	+	0.0669372i
$107$			13.9864i			1.35211i	0.736849	+	0.676057i	$0.236313\pi$
$107$			13.9864i			1.35211i	−0.736849	+	0.676057i	$0.763687\pi$
$108$	−10.4067	+	28.5922i	−1.00139	+	2.75128i
$109$	−5.57034			−0.533542			−0.266771	−	0.963760i	$-0.585957\pi$
$109$	−5.57034			−0.533542			−0.266771	+	0.963760i	$0.585957\pi$
$110$	−8.02159	+	4.15594i	−0.764828	+	0.396254i
$111$	−9.25858			−0.878786
$112$	−12.1097	−	10.1612i	−1.14426	−	0.960147i
$113$	−2.81453			−0.264769			−0.132385	−	0.991198i	$-0.542263\pi$
$113$	−2.81453			−0.264769			−0.132385	+	0.991198i	$0.542263\pi$
$114$	−17.9123	−	3.15842i	−1.67764	−	0.295813i
$115$	6.74672	−	5.15610i	0.629135	−	0.480809i
$116$	5.72494	+	2.08371i	0.531547	+	0.193467i
$117$	−18.7624			−1.73458
$118$	−2.05097	+	11.6317i	−0.188808	+	1.07078i
$119$	−9.79555	+	13.0216i	−0.897957	+	1.19368i
$120$	−2.65539	−	20.4777i	−0.242403	−	1.86935i
$121$	−2.83823			−0.258021
$122$	19.6676	+	3.46792i	1.78062	+	0.313971i
$123$	27.3159			2.46299
$124$	−3.89786	+	10.7093i	−0.350038	+	0.961722i
$125$	−4.21812	−	10.3541i	−0.377280	−	0.926099i
$126$	42.1598	+	7.43390i	3.75589	+	0.662265i
$127$			4.98882i			0.442686i	0.975196	+	0.221343i	$0.0710440\pi$
$127$			4.98882i			0.442686i	−0.975196	+	0.221343i	$0.928956\pi$
$128$	3.86952	+	10.6314i	0.342020	+	0.939693i
$129$		−	4.25097i		−	0.374277i
$130$	6.87771	−	3.56330i	0.603215	−	0.312522i
$131$	14.6532			1.28025			0.640127	−	0.768269i	$-0.278882\pi$
$131$	14.6532			1.28025			0.640127	+	0.768269i	$0.278882\pi$
$132$	−6.38038	+	17.5300i	−0.555341	+	1.52579i
$133$			15.5679i			1.34991i
$134$	7.71242	+	1.35991i	0.666252	+	0.117478i
$135$	20.6566	+	27.0291i	1.77784	+	2.32629i
$136$	10.7311	−	4.56556i	0.920181	−	0.391494i
$137$			3.96246i			0.338536i	0.985570	+	0.169268i	$0.0541403\pi$
$137$			3.96246i			0.338536i	−0.985570	+	0.169268i	$0.945860\pi$
$138$	3.04475	−	17.2676i	0.259186	−	1.46992i
$139$	3.28155			0.278337			0.139169	−	0.990269i	$-0.455557\pi$
$139$	3.28155			0.278337			0.139169	+	0.990269i	$0.455557\pi$
$140$	−16.8663	+	5.28184i	−1.42546	+	0.446397i
$141$	−8.61835			−0.725796
$142$	2.94225	−	16.6864i	0.246908	−	1.40029i
$143$	−6.99790			−0.585194
$144$	−23.4707	−	19.6943i	−1.95589	−	1.64119i
$145$	5.41195	−	4.13602i	0.449438	−	0.343478i
$146$	−5.07733	−	0.895271i	−0.420203	−	0.0740931i
$147$		−	28.1386i		−	2.32083i
$148$	1.93978	−	5.32951i	0.159449	−	0.438083i
$149$			0.863462i			0.0707376i	0.999374	+	0.0353688i	$0.0112606\pi$
$149$			0.863462i			0.0707376i	−0.999374	+	0.0353688i	$0.988739\pi$
$150$	−20.8853	−	9.83817i	−1.70528	−	0.803284i
$151$	13.5986			1.10664			0.553318	−	0.832970i	$-0.313362\pi$
$151$	13.5986			1.10664			0.553318	+	0.832970i	$0.313362\pi$
$152$	5.57091	−	9.64911i	0.451861	−	0.782646i
$153$	−18.9855	+	25.2381i	−1.53489	+	2.04038i
$154$	15.7245	+	2.77266i	1.26712	+	0.223427i
$155$	7.73700	+	10.1238i	0.621451	+	0.813164i
$156$	5.47054	−	15.0302i	0.437994	−	1.20338i
$157$	−11.3414			−0.905146			−0.452573	−	0.891727i	$-0.649494\pi$
$157$	−11.3414			−0.905146			−0.452573	+	0.891727i	$0.649494\pi$
$158$	1.62341	−	9.20681i	0.129151	−	0.732454i
$159$		−	9.16238i		−	0.726624i
$160$	12.3439	+	2.76181i	0.975873	+	0.218340i
$161$	−15.0077			−1.18277
$162$	37.1748	+	6.55491i	2.92072	+	0.515003i
$163$			5.39441i			0.422523i	0.977430	+	0.211261i	$0.0677571\pi$
$163$			5.39441i			0.422523i	−0.977430	+	0.211261i	$0.932243\pi$
$164$	−5.72300	+	15.7238i	−0.446891	+	1.22782i
$165$	12.6646	+	16.5716i	0.985941	+	1.29010i
$166$	−23.4654	−	4.13757i	−1.82126	−	0.321138i
$167$	6.46743			0.500465			0.250233	−	0.968186i	$-0.419493\pi$
$167$	6.46743			0.500465			0.250233	+	0.968186i	$0.419493\pi$
$168$	−18.2477	+	31.6059i	−1.40784	+	2.43844i
$169$	−7.00000			−0.538462
$170$	2.16634	−	12.8572i	0.166151	−	0.986100i
$171$			30.1734i			2.30742i
$172$	2.44698	+	0.890629i	0.186581	+	0.0679098i
$173$		−	6.04537i		−	0.459621i	−0.973235	−	0.229810i	$-0.926189\pi$
$173$		−	6.04537i		−	0.459621i	0.973235	−	0.229810i	$-0.0738106\pi$
$174$	2.44238	−	13.8514i	0.185156	−	1.05007i
$175$	−5.18858	+	19.0667i	−0.392220	+	1.44131i
$176$	−8.75399	−	7.34547i	−0.659857	−	0.553686i
$177$	27.2677			2.04956
$178$	6.13289	+	1.08139i	0.459680	+	0.0810539i
$179$		−	12.6776i		−	0.947569i	−0.880641	−	0.473785i	$-0.842888\pi$
$179$		−	12.6776i		−	0.947569i	0.880641	−	0.473785i	$-0.157112\pi$
$180$	−32.6898	+	10.2371i	−2.43656	+	0.763030i
$181$	11.3106			0.840711			0.420355	−	0.907360i	$-0.361905\pi$
$181$	11.3106			0.840711			0.420355	+	0.907360i	$0.361905\pi$
$182$	−13.4822	−	2.37728i	−0.999368	−	0.176216i
$183$		−	46.1060i		−	3.40825i
$184$	9.30185	+	5.37042i	0.685741	+	0.395913i
$185$	−3.85034	−	5.03815i	−0.283083	−	0.370412i
$186$	25.9110	+	4.56880i	1.89988	+	0.335001i
$187$	−7.08112	+	9.41317i	−0.517823	+	0.688360i
$188$	1.80565	−	4.96098i	0.131690	−	0.361817i
$189$		−	60.1244i		−	4.37341i
$190$	−5.73045	−	11.0606i	−0.415731	−	0.802422i
$191$	−2.52037			−0.182368			−0.0911838	−	0.995834i	$-0.529065\pi$
$191$	−2.52037			−0.182368			−0.0911838	+	0.995834i	$0.529065\pi$
$192$	22.6200	−	13.0597i	1.63246	−	0.942502i
$193$	−12.2106			−0.878936			−0.439468	−	0.898258i	$-0.644833\pi$
$193$	−12.2106			−0.878936			−0.439468	+	0.898258i	$0.644833\pi$
$194$	−18.4460	−	3.25252i	−1.32434	−	0.233518i
$195$	−10.8587	−	14.2085i	−0.777605	−	1.01749i
$196$	16.1974	+	5.89538i	1.15696	+	0.421099i
$197$			8.55634i			0.609614i	0.952414	+	0.304807i	$0.0985920\pi$
$197$			8.55634i			0.609614i	−0.952414	+	0.304807i	$0.901408\pi$
$198$	30.4769	+	5.37390i	2.16590	+	0.381907i
$199$			17.2203i			1.22072i	0.792125	+	0.610358i	$0.208975\pi$
$199$			17.2203i			1.22072i	−0.792125	+	0.610358i	$0.791025\pi$
$200$	10.0389	−	9.96098i	0.709855	−	0.704348i
$201$		−	18.0799i		−	1.27526i
$202$	−3.36875	+	19.1051i	−0.237024	+	1.34423i
$203$	−12.0385			−0.844940
$204$	−14.6821	−	22.5676i	−1.02796	−	1.58005i
$205$	11.3598	+	14.8642i	0.793401	+	1.03816i
$206$	0.192757	−	1.09318i	0.0134300	−	0.0761656i
$207$	−29.0875			−2.02172
$208$	7.50567	+	6.29801i	0.520425	+	0.436688i
$209$			11.2539i			0.778450i
$210$	18.7702	+	36.2293i	1.29527	+	2.50006i
$211$	21.5114			1.48091			0.740454	−	0.672108i	$-0.234611\pi$
$211$	21.5114			1.48091			0.740454	+	0.672108i	$0.234611\pi$
$212$	5.27414	+	1.91963i	0.362229	+	0.131841i
$213$	−39.1172			−2.68027
$214$	−3.43471	+	19.4792i	−0.234792	+	1.33157i
$215$	2.31321	−	1.76784i	0.157759	−	0.120566i
$216$	−21.5153	+	37.2655i	−1.46393	+	2.53560i
$217$		−	22.5198i		−	1.52874i
$218$	−7.75797	−	1.36794i	−0.525436	−	0.0926485i
$219$			11.9026i			0.804303i
$220$	−12.1925	+	3.81819i	−0.822017	+	0.257423i
$221$	6.07135	−	8.07086i	0.408403	−	0.542904i
$222$	−12.8947	−	2.27368i	−0.865435	−	0.152600i
$223$			13.7954i			0.923806i	0.886931	+	0.461903i	$0.152833\pi$
$223$			13.7954i			0.923806i	−0.886931	+	0.461903i	$0.847167\pi$
$224$	−14.3702	−	17.1257i	−0.960147	−	1.14426i
$225$	−10.0564	+	36.9547i	−0.670425	+	2.46365i
$226$	−3.91988	−	0.691181i	−0.260747	−	0.0459767i
$227$		−	5.93315i		−	0.393797i	−0.980424	−	0.196898i	$-0.936913\pi$
$227$		−	5.93315i		−	0.393797i	0.980424	−	0.196898i	$-0.0630869\pi$
$228$	−24.1713	−	8.79763i	−1.60078	−	0.582637i
$229$			6.62811i			0.437998i	0.975725	+	0.218999i	$0.0702791\pi$
$229$			6.62811i			0.437998i	−0.975725	+	0.218999i	$0.929721\pi$
$230$	10.6626	−	5.52422i	0.703069	−	0.364256i
$231$		−	36.8624i		−	2.42537i
$232$	7.46157	+	4.30794i	0.489876	+	0.282830i
$233$	−27.0067			−1.76927			−0.884635	−	0.466285i	$-0.845592\pi$
$233$	−27.0067			−1.76927			−0.884635	+	0.466285i	$0.845592\pi$
$234$	−26.1309	−	4.60758i	−1.70823	−	0.301207i
$235$	−3.58409	−	4.68976i	−0.233801	−	0.305926i
$236$	−5.71290	+	15.6961i	−0.371878	+	1.02173i
$237$	−21.5832			−1.40198
$238$	−16.8403	+	15.7300i	−1.09160	+	1.01962i
$239$	−20.6172			−1.33362			−0.666808	−	0.745230i	$-0.732340\pi$
$239$	−20.6172			−1.33362			−0.666808	+	0.745230i	$0.732340\pi$
$240$	1.33059	−	29.1720i	0.0858894	−	1.88305i
$241$			8.33359i			0.536814i	0.963306	+	0.268407i	$0.0864972\pi$
$241$			8.33359i			0.536814i	−0.963306	+	0.268407i	$0.913503\pi$
$242$	−3.95288	−	0.697000i	−0.254101	−	0.0448049i
$243$		−	41.5066i		−	2.66265i
$244$	26.5400	+	9.65975i	1.69905	+	0.618402i
$245$	15.3119	−	11.7019i	0.978242	−	0.747610i
$246$	38.0436	+	6.70811i	2.42557	+	0.427693i
$247$		−	9.64911i		−	0.613958i
$248$	−8.05860	+	13.9579i	−0.511722	+	0.886328i
$249$			55.0089i			3.48605i
$250$	−3.33198	−	15.4563i	−0.210733	−	0.977544i
$251$		−	28.0495i		−	1.77047i	−0.465143	−	0.885235i	$-0.653997\pi$
$251$		−	28.0495i		−	1.77047i	0.465143	−	0.885235i	$-0.346003\pi$
$252$	56.8915	+	20.7068i	3.58383	+	1.30441i
$253$	−10.8489			−0.682065
$254$	−1.22513	+	6.94807i	−0.0768716	+	0.435961i
$255$	−30.1002	+	0.229004i	−1.88495	+	0.0143408i
$256$	2.77837	+	15.7569i	0.173648	+	0.984808i
$257$		−	3.18420i		−	0.198625i	−0.995056	−	0.0993126i	$-0.968336\pi$
$257$		−	3.18420i		−	0.198625i	0.995056	−	0.0993126i	$-0.0316644\pi$
$258$	1.04393	−	5.92044i	0.0649925	−	0.368591i
$259$			11.2070i			0.696372i
$260$	10.4538	−	3.27372i	0.648320	−	0.203027i
$261$	−23.3328			−1.44427
$262$	20.4079	+	3.59846i	1.26080	+	0.222314i
$263$		−	17.9996i		−	1.10990i	−0.831883	−	0.554950i	$-0.812737\pi$
$263$		−	17.9996i		−	1.10990i	0.831883	−	0.554950i	$-0.187263\pi$
$264$	−13.1911	+	22.8476i	−0.811854	+	1.40617i
$265$	4.98580	−	3.81034i	0.306275	−	0.234067i
$266$	−3.82310	+	21.6819i	−0.234409	+	1.32940i
$267$		−	14.3771i		−	0.879865i
$268$	10.4073	+	3.78796i	0.635730	+	0.231387i
$269$	−8.73894			−0.532822			−0.266411	−	0.963859i	$-0.585838\pi$
$269$	−8.73894			−0.532822			−0.266411	+	0.963859i	$0.585838\pi$
$270$	22.1314	+	42.7169i	1.34687	+	2.59967i
$271$	−9.20846			−0.559374			−0.279687	−	0.960091i	$-0.590231\pi$
$271$	−9.20846			−0.559374			−0.279687	+	0.960091i	$0.590231\pi$
$272$	16.0666	−	3.72330i	0.974183	−	0.225758i
$273$			31.6059i			1.91287i
$274$	−0.973083	+	5.51863i	−0.0587861	+	0.333392i
$275$	−3.75078	+	13.7832i	−0.226181	+	0.831157i
$276$	8.48102	−	23.3014i	0.510497	−	1.40258i
$277$			3.22987i			0.194064i	0.995281	+	0.0970321i	$0.0309349\pi$
$277$			3.22987i			0.194064i	−0.995281	+	0.0970321i	$0.969065\pi$
$278$	4.57030	+	0.805867i	0.274108	+	0.0483327i
$279$		−	43.6473i		−	2.61309i
$280$	−24.7872	+	3.21422i	−1.48132	+	0.192086i
$281$	−24.4823			−1.46049			−0.730247	−	0.683183i	$-0.760595\pi$
$281$	−24.4823			−1.46049			−0.730247	+	0.683183i	$0.760595\pi$
$282$	−12.0030	−	2.11646i	−0.714770	−	0.126033i
$283$			7.88131i			0.468495i	0.972177	+	0.234248i	$0.0752626\pi$
$283$			7.88131i			0.468495i	−0.972177	+	0.234248i	$0.924737\pi$
$284$	8.19552	−	22.5170i	0.486315	−	1.33614i
$285$	−22.8499	+	17.4627i	−1.35351	+	1.03440i
$286$	−9.74618	−	1.71851i	−0.576303	−	0.101618i
$287$		−	33.0645i		−	1.95173i
$288$	−27.8519	−	33.1926i	−1.64119	−	1.95589i
$289$	−4.71290	−	16.3337i	−0.277230	−	0.960804i
$290$	8.55309	−	4.43131i	0.502255	−	0.260215i
$291$			43.2422i			2.53490i
$292$	−6.85149	−	2.49374i	−0.400953	−	0.145935i
$293$	18.5741			1.08511			0.542555	−	0.840020i	$-0.317457\pi$
$293$	18.5741			1.08511			0.542555	+	0.840020i	$0.317457\pi$
$294$	6.91016	−	39.1895i	0.403009	−	2.28558i
$295$	11.3397	+	14.8380i	0.660225	+	0.863900i
$296$	4.01039	−	6.94620i	0.233099	−	0.403740i
$297$		−	43.4634i		−	2.52200i
$298$	−0.212045	+	1.20257i	−0.0122835	+	0.0696629i
$299$	9.30185			0.537940
$300$	−26.6715	−	18.8308i	−1.53988	−	1.08720i
$301$	−5.14558			−0.296586
$302$	18.9391	+	3.33947i	1.08982	+	0.192165i
$303$	44.7875			2.57297
$304$	10.1284	−	12.0705i	0.580901	−	0.692291i
$305$	25.0890	−	19.1740i	1.43659	−	1.09790i
$306$	−32.6395	+	30.4874i	−1.86588	+	1.74285i
$307$	14.0759			0.803355			0.401677	−	0.915781i	$-0.368427\pi$
$307$	14.0759			0.803355			0.401677	+	0.915781i	$0.368427\pi$
$308$	21.2191	+	7.72313i	1.20907	+	0.440066i
$309$	−2.56271			−0.145787
$310$	8.28938	+	15.9997i	0.470805	+	0.908724i
$311$			21.3760i			1.21212i	0.795418	+	0.606062i	$0.207252\pi$
$311$			21.3760i			1.21212i	−0.795418	+	0.606062i	$0.792748\pi$
$312$	11.3100	−	19.5895i	0.640304	−	1.10904i
$313$	16.6292			0.939936			0.469968	−	0.882684i	$-0.344266\pi$
$313$	16.6292			0.939936			0.469968	+	0.882684i	$0.344266\pi$
$314$	−15.7956	−	2.78518i	−0.891395	−	0.157177i
$315$	53.7812	−	41.1017i	3.03023	−	2.31582i
$316$	4.52193	−	12.4239i	0.254379	−	0.698900i
$317$		−	32.4847i		−	1.82452i	−0.409611	−	0.912260i	$-0.634336\pi$
$317$		−	32.4847i		−	1.82452i	0.409611	−	0.912260i	$-0.365664\pi$
$318$	2.25006	−	12.7607i	0.126177	−	0.715585i
$319$	−8.70256			−0.487250
$320$	16.5135	+	6.87782i	0.923133	+	0.384482i
$321$	45.6644			2.54874
$322$	−20.9016	−	3.68551i	−1.16480	−	0.205386i
$323$	−12.9794	−	9.76385i	−0.722194	−	0.543275i
$324$	50.1646	+	18.2584i	2.78692	+	1.01436i
$325$	3.21592	−	11.8177i	0.178387	−	0.655528i
$326$	−1.32473	+	7.51294i	−0.0733703	+	0.416103i
$327$			18.1867i			1.00573i
$328$	−11.8320	+	20.4936i	−0.653311	+	1.13157i
$329$			10.4321i			0.575139i
$330$	13.5688	+	26.1898i	0.746939	+	1.44170i
$331$			2.98608i			0.164130i	0.996627	+	0.0820649i	$0.0261515\pi$
$331$			2.98608i			0.164130i	−0.996627	+	0.0820649i	$0.973849\pi$
$332$	−31.6648	−	11.5250i	−1.73783	−	0.632519i
$333$			21.7212i			1.19032i
$334$	9.00738	+	1.58824i	0.492862	+	0.0869049i
$335$	9.83838	−	7.51886i	0.537528	−	0.410799i
$336$	−33.1757	+	39.5372i	−1.80988	+	2.15693i
$337$	−8.57588			−0.467158			−0.233579	−	0.972338i	$-0.575044\pi$
$337$	−8.57588			−0.467158			−0.233579	+	0.972338i	$0.575044\pi$
$338$	−9.74910	−	1.71903i	−0.530281	−	0.0935029i
$339$			9.18923i			0.499091i
$340$	6.17454	−	17.3746i	0.334861	−	0.942267i
$341$		−	16.2793i		−	0.881576i
$342$	−7.40984	+	42.0233i	−0.400678	+	2.27236i
$343$	−6.39623			−0.345364
$344$	3.18927	+	1.84132i	0.171954	+	0.0992775i
$345$	−16.8343	−	22.0275i	−0.906326	−	1.18592i
$346$	1.48459	−	8.41955i	0.0798123	−	0.452638i
$347$		−	9.22145i		−	0.495033i	−0.968884	−	0.247517i	$-0.920385\pi$
$347$		−	9.22145i		−	0.495033i	0.968884	−	0.247517i	$-0.0796145\pi$
$348$	6.80314	−	18.6915i	0.364686	−	1.00197i
$349$			28.3199i			1.51593i	0.652295	+	0.757965i	$0.273806\pi$
$349$			28.3199i			1.51593i	−0.652295	+	0.757965i	$0.726194\pi$
$350$	−11.9086	+	25.2806i	−0.636542	+	1.35130i
$351$			37.2655i			1.98909i
$352$	−10.3881	−	12.3800i	−0.553686	−	0.659857i
$353$			23.4713i			1.24925i	0.780925	+	0.624625i	$0.214748\pi$
$353$			23.4713i			1.24925i	−0.780925	+	0.624625i	$0.785252\pi$
$354$	37.9764	+	6.69627i	2.01843	+	0.355903i
$355$	−16.2676	−	21.2860i	−0.863393	−	1.12974i
$356$	8.27589	+	3.01218i	0.438621	+	0.159645i
$357$	42.5144	+	31.9817i	2.25010	+	1.69265i
$358$	3.11331	−	17.6565i	0.164544	−	0.933173i
$359$	30.7669			1.62381			0.811907	−	0.583787i	$-0.198430\pi$
$359$	30.7669			1.62381			0.811907	+	0.583787i	$0.198430\pi$
$360$	−48.0420	+	6.22971i	−2.53204	+	0.328335i
$361$	3.48246			0.183287
$362$	15.7526	+	2.77761i	0.827938	+	0.145988i
$363$			9.26660i			0.486370i
$364$	−18.1933	−	6.62181i	−0.953586	−	0.347077i
$365$	−6.47692	+	4.94991i	−0.339017	+	0.259090i
$366$	11.3225	−	64.2131i	0.591837	−	3.35647i
$367$	−13.4873			−0.704032			−0.352016	−	0.935994i	$-0.614504\pi$
$367$	−13.4873			−0.704032			−0.352016	+	0.935994i	$0.614504\pi$
$368$	11.6361	+	9.76385i	0.606574	+	0.508976i
$369$		−	64.0847i		−	3.33612i
$370$	−4.12524	−	7.96232i	−0.214461	−	0.413941i
$371$	−11.0906			−0.575795
$372$	34.9650	+	12.7262i	1.81285	+	0.659823i
$373$	14.8935			0.771155			0.385578	−	0.922675i	$-0.374002\pi$
$373$	14.8935			0.771155			0.385578	+	0.922675i	$0.374002\pi$
$374$	−12.1737	+	11.3710i	−0.629488	+	0.587983i
$375$	−33.8053	+	13.7718i	−1.74570	+	0.711174i
$376$	3.73307	−	6.46587i	0.192519	−	0.333452i
$377$	7.46157			0.384291
$378$	14.7651	−	83.7370i	0.759434	−	4.30697i
$379$	−25.5257			−1.31117			−0.655583	−	0.755123i	$-0.727577\pi$
$379$	−25.5257			−1.31117			−0.655583	+	0.755123i	$0.727577\pi$
$380$	−5.26474	−	16.8117i	−0.270076	−	0.862422i
$381$	16.2881			0.834464
$382$	−3.51019	−	0.618941i	−0.179597	−	0.0316678i
$383$			31.0306i			1.58559i	0.609488	+	0.792795i	$0.291375\pi$
$383$			31.0306i			1.58559i	−0.609488	+	0.792795i	$0.708625\pi$
$384$	34.7107	−	12.6337i	1.77132	−	0.644709i
$385$	20.0591	−	15.3299i	1.02230	−	0.781284i
$386$	−17.0060	−	2.99862i	−0.865583	−	0.152626i
$387$	−9.97304			−0.506958
$388$	−24.8915	−	9.05976i	−1.26367	−	0.459940i
$389$			12.9639i			0.657295i	0.944453	+	0.328648i	$0.106593\pi$
$389$			12.9639i			0.657295i	−0.944453	+	0.328648i	$0.893407\pi$
$390$	−11.6339	−	22.4552i	−0.589106	−	1.13706i
$391$	9.41246	−	12.5123i	0.476009	−	0.632775i
$392$	21.1109	+	12.1884i	1.06626	+	0.615605i
$393$		−	47.8414i		−	2.41328i
$394$	−2.10123	+	11.9167i	−0.105858	+	0.600353i
$395$	−8.97574	−	11.7447i	−0.451619	−	0.590940i
$396$	41.1264	+	14.9688i	2.06668	+	0.752209i
$397$			8.48789i			0.425995i	0.977053	+	0.212997i	$0.0683226\pi$
$397$			8.48789i			0.425995i	−0.977053	+	0.212997i	$0.931677\pi$
$398$	−4.22889	+	23.9832i	−0.211975	+	1.20217i
$399$	50.8280			2.54459
$400$	16.4276	−	11.4076i	0.821379	−	0.570382i
$401$		−	2.48667i		−	0.124178i	−0.998071	−	0.0620891i	$-0.980224\pi$
$401$		−	2.48667i		−	0.124178i	0.998071	−	0.0620891i	$-0.0197763\pi$
$402$	4.43999	−	25.1804i	0.221447	−	1.25589i
$403$			13.9579i			0.695293i
$404$	−9.38351	+	25.7810i	−0.466847	+	1.28265i
$405$	47.4221	−	36.2418i	2.35642	−	1.80087i
$406$	−16.7664	−	2.95637i	−0.832104	−	0.146722i
$407$			8.10147i			0.401575i
$408$	−14.9062	−	35.0361i	−0.737967	−	1.73454i
$409$	−13.4539			−0.665255			−0.332627	−	0.943058i	$-0.607935\pi$
$409$	−13.4539			−0.665255			−0.332627	+	0.943058i	$0.607935\pi$
$410$	12.1708	+	23.4915i	0.601073	+	1.16016i
$411$	12.9371			0.638141
$412$	0.536918	−	1.47517i	0.0264520	−	0.0726764i
$413$		−	33.0061i		−	1.62412i
$414$	−40.5110	−	7.14317i	−1.99100	−	0.351068i
$415$	−29.9337	+	22.8764i	−1.46939	+	1.12296i
$416$	8.90673	+	10.6146i	0.436688	+	0.520425i
$417$		−	10.7140i		−	0.524666i
$418$	−2.76369	+	15.6736i	−0.135176	+	0.766623i
$419$	−16.7575			−0.818656			−0.409328	−	0.912387i	$-0.634237\pi$
$419$	−16.7575			−0.818656			−0.409328	+	0.912387i	$0.634237\pi$
$420$	17.2448	+	55.0671i	0.841459	+	2.68700i
$421$			2.77800i			0.135392i	0.997706	+	0.0676958i	$0.0215647\pi$
$421$			2.77800i			0.135392i	−0.997706	+	0.0676958i	$0.978435\pi$
$422$	29.9596	+	5.28268i	1.45841	+	0.257157i
$423$			20.2192i			0.983091i
$424$	6.87402	+	3.96872i	0.333832	+	0.192738i
$425$	−12.6423	−	16.2841i	−0.613243	−	0.789895i
$426$	−54.4796	−	9.60623i	−2.63955	−	0.465423i
$427$	−55.8089			−2.70078
$428$	−9.56724	+	26.2858i	−0.462450	+	1.27057i
$429$			22.8476i			1.10309i
$430$	3.65581	−	1.89405i	0.176299	−	0.0913394i
$431$		−	26.8983i		−	1.29564i	−0.761792	−	0.647822i	$-0.775680\pi$
$431$		−	26.8983i		−	1.29564i	0.761792	−	0.647822i	$-0.224320\pi$
$432$	−39.1164	+	46.6171i	−1.88199	+	2.24287i
$433$			7.26521i			0.349144i	0.984644	+	0.174572i	$0.0558541\pi$
$433$			7.26521i			0.349144i	−0.984644	+	0.174572i	$0.944146\pi$
$434$	5.53030	−	31.3639i	0.265463	−	1.50552i
$435$	−13.5038	−	17.6696i	−0.647457	−	0.847193i
$436$	−10.4688	−	3.81034i	−0.501365	−	0.182482i
$437$		−	14.9591i		−	0.715590i
$438$	−2.92299	+	16.5771i	−0.139666	+	0.792084i
$439$			20.9652i			1.00062i	0.865847	+	0.500308i	$0.166780\pi$
$439$			20.9652i			1.00062i	−0.865847	+	0.500308i	$0.833220\pi$
$440$	−17.9185	+	2.32353i	−0.854230	+	0.110770i
$441$	−66.0150			−3.14357
$442$	10.4377	−	9.74953i	0.496473	−	0.463738i
$443$	−9.47648			−0.450241			−0.225120	−	0.974331i	$-0.572278\pi$
$443$	−9.47648			−0.450241			−0.225120	+	0.974331i	$0.572278\pi$
$444$	−17.4004	−	6.33324i	−0.825788	−	0.300562i
$445$	7.82345	−	5.97898i	0.370867	−	0.283431i
$446$	−3.38780	+	19.2132i	−0.160417	+	0.909771i
$447$	2.81914			0.133341
$448$	−15.8081	−	27.3804i	−0.746862	−	1.29360i
$449$		−	6.27882i		−	0.296316i	−0.988964	−	0.148158i	$-0.952666\pi$
$449$		−	6.27882i		−	0.296316i	0.988964	−	0.148158i	$-0.0473344\pi$
$450$	−23.0810	+	48.9982i	−1.08805	+	2.30980i
$451$		−	23.9020i		−	1.12550i
$452$	−5.28960	−	1.92526i	−0.248802	−	0.0905564i
$453$		−	44.3982i		−	2.08601i
$454$	1.45704	−	8.26326i	0.0683821	−	0.387814i
$455$	−17.1986	+	13.1439i	−0.806285	+	0.616193i
$456$	−31.5036	−	18.1886i	−1.47529	−	0.851759i
$457$			3.84188i			0.179716i	0.995955	+	0.0898578i	$0.0286412\pi$
$457$			3.84188i			0.179716i	−0.995955	+	0.0898578i	$0.971359\pi$
$458$	−1.62770	+	9.23115i	−0.0760575	+	0.431343i
$459$	50.1274	+	37.7087i	2.33975	+	1.76009i
$460$	16.2067	−	5.07527i	0.755640	−	0.236636i
$461$		−	9.82683i		−	0.457681i	−0.973464	−	0.228841i	$-0.926507\pi$
$461$		−	9.82683i		−	0.457681i	0.973464	−	0.228841i	$-0.0734935\pi$
$462$	9.05252	−	51.3394i	0.421161	−	2.38852i
$463$			32.7468i			1.52187i	0.648828	+	0.760935i	$0.275260\pi$
$463$			32.7468i			1.52187i	−0.648828	+	0.760935i	$0.724740\pi$
$464$	9.33402	+	7.83217i	0.433321	+	0.363600i
$465$	33.0534	−	25.2607i	1.53282	−	1.17144i
$466$	−37.6130	−	6.63219i	−1.74239	−	0.307230i
$467$	−22.6029			−1.04594			−0.522968	−	0.852352i	$-0.675175\pi$
$467$	−22.6029			−1.04594			−0.522968	+	0.852352i	$0.675175\pi$
$468$	−35.2617	−	12.8342i	−1.62997	−	0.593262i
$469$	−21.8848			−1.01055
$470$	−3.83998	−	7.41173i	−0.177125	−	0.341878i
$471$			37.0289i			1.70620i
$472$	−11.8111	+	20.4574i	−0.543650	+	0.941629i
$473$	−3.71969			−0.171032
$474$	−30.0595	−	5.30030i	−1.38068	−	0.243451i
$475$	−19.0050	−	5.17179i	−0.872011	−	0.237298i
$476$	−27.3169	+	17.7720i	−1.25207	+	0.814578i
$477$	−21.4955			−0.984212
$478$	−28.7142	−	5.06308i	−1.31336	−	0.231580i
$479$			10.1653i			0.464467i	0.972660	+	0.232233i	$0.0746033\pi$
$479$			10.1653i			0.464467i	−0.972660	+	0.232233i	$0.925397\pi$
$480$	9.01709	−	40.3019i	0.411572	−	1.83952i
$481$		−	6.94620i		−	0.316720i
$482$	−2.04653	+	11.6064i	−0.0932168	+	0.528659i
$483$			48.9988i			2.22952i
$484$	−5.33413	−	1.94146i	−0.242460	−	0.0882484i
$485$	−23.5307	+	17.9830i	−1.06847	+	0.816568i
$486$	10.1930	−	57.8075i	0.462365	−	2.62220i
$487$	16.2908			0.738209			0.369104	−	0.929388i	$-0.379664\pi$
$487$	16.2908			0.738209			0.369104	+	0.929388i	$0.379664\pi$
$488$	34.5908	+	19.9710i	1.56585	+	0.904044i
$489$	17.6123			0.796456
$490$	24.1990	−	12.5374i	1.09320	−	0.566382i
$491$		−	28.6143i		−	1.29135i	−0.763613	−	0.645674i	$-0.776577\pi$
$491$		−	28.6143i		−	1.29135i	0.763613	−	0.645674i	$-0.223423\pi$
$492$	51.3370	+	18.6851i	2.31445	+	0.842391i
$493$	7.55030	−	10.0369i	0.340049	−	0.452038i
$494$	2.36959	−	13.4386i	0.106613	−	0.604631i
$495$	38.8780	−	29.7120i	1.74744	−	1.33546i
$496$	−14.6512	+	17.4606i	−0.657857	+	0.784003i
$497$			47.3494i			2.12391i
$498$	−13.5089	+	76.6125i	−0.605346	+	3.43309i
$499$	−4.03677			−0.180711			−0.0903554	−	0.995910i	$-0.528800\pi$
$499$	−4.03677			−0.180711			−0.0903554	+	0.995910i	$0.528800\pi$
$500$	−0.844850	−	22.3447i	−0.0377828	−	0.999286i
$501$		−	21.1157i		−	0.943378i
$502$	6.88828	−	39.0654i	0.307439	−	1.74357i
$503$	−4.83145			−0.215424			−0.107712	−	0.994182i	$-0.534352\pi$
$503$	−4.83145			−0.215424			−0.107712	+	0.994182i	$0.534352\pi$
$504$	74.1493	+	42.8101i	3.30287	+	1.90692i
$505$	18.6257	+	24.3715i	0.828831	+	1.08452i
$506$	−15.1096	−	2.66423i	−0.671703	−	0.118439i
$507$			22.8544i			1.01500i
$508$	−3.41255	+	9.37591i	−0.151408	+	0.415989i
$509$		−	31.8045i		−	1.40971i	−0.709352	−	0.704855i	$-0.751012\pi$
$509$		−	31.8045i		−	1.40971i	0.709352	−	0.704855i	$-0.248988\pi$
$510$	−41.9777	−	7.07294i	−1.85880	−	0.313195i
$511$	14.4075			0.637350
$512$			22.6274i			1.00000i
$513$	59.9298			2.64597
$514$	0.781963	−	4.43473i	0.0344909	−	0.195608i
$515$	−1.06575	−	1.39452i	−0.0469624	−	0.0614500i
$516$	2.90783	−	7.98920i	0.128010	−	0.351705i
$517$			7.54126i			0.331664i
$518$	−2.75218	+	15.6084i	−0.120924	+	0.685792i
$519$	−19.7376			−0.866386
$520$	15.3633	−	1.99219i	0.673726	−	0.0873634i
$521$		−	36.9770i		−	1.61999i	−0.586435	−	0.809996i	$-0.699469\pi$
$521$		−	36.9770i		−	1.61999i	0.586435	−	0.809996i	$-0.300531\pi$
$522$	−32.4963	−	5.72997i	−1.42232	−	0.250794i
$523$	43.2268			1.89018			0.945089	−	0.326813i	$-0.105975\pi$
$523$	43.2268			1.89018			0.945089	+	0.326813i	$0.105975\pi$
$524$	27.5389	+	10.0234i	1.20304	+	0.437872i
$525$	62.2514	+	16.9403i	2.71687	+	0.739336i
$526$	4.42025	−	25.0685i	0.192732	−	1.09304i
$527$	18.7754	+	14.1239i	0.817868	+	0.615246i
$528$	−23.9824	+	28.5811i	−1.04370	+	1.24383i
$529$	−8.57927			−0.373012
$530$	7.87959	−	4.08237i	0.342267	−	0.177327i
$531$		−	63.9716i		−	2.77613i
$532$	−10.6491	+	29.2581i	−0.461696	+	1.26850i
$533$			20.4936i			0.887675i
$534$	3.53067	−	20.0234i	0.152787	−	0.866498i
$535$	18.9903	+	24.8487i	0.821024	+	1.07430i
$536$	13.5644	+	7.83140i	0.585892	+	0.338265i
$537$	−41.3914			−1.78617
$538$	−12.1710	−	2.14607i	−0.524728	−	0.0925236i
$539$	−24.6219			−1.06054
$540$	20.3328	+	64.9280i	0.874985	+	2.79406i
$541$	−11.0064			−0.473203			−0.236602	−	0.971607i	$-0.576034\pi$
$541$	−11.0064			−0.473203			−0.236602	+	0.971607i	$0.576034\pi$
$542$	−12.8249	−	2.26137i	−0.550876	−	0.0971343i
$543$		−	36.9282i		−	1.58474i
$544$	23.2908	−	1.23997i	0.998586	−	0.0531632i
$545$	−9.89648	+	7.56327i	−0.423919	+	0.323975i
$546$	−7.76163	+	44.0184i	−0.332167	+	1.88381i
$547$			35.1638i			1.50350i	0.659450	+	0.751748i	$0.270789\pi$
$547$			35.1638i			1.50350i	−0.659450	+	0.751748i	$0.729211\pi$
$548$	−2.71048	+	7.44698i	−0.115786	+	0.318119i
$549$	−108.167			−4.61648
$550$	−8.60863	+	18.2751i	−0.367073	+	0.779254i
$551$		−	11.9996i		−	0.511200i
$552$	17.5340	−	30.3698i	0.746297	−	1.29262i
$553$			26.1253i			1.11096i
$554$	−0.793178	+	4.49833i	−0.0336989	+	0.191116i
$555$	−16.4492	+	12.5711i	−0.698228	+	0.533612i
$556$	6.16729	+	2.24471i	0.261551	+	0.0951969i
$557$	6.13236			0.259837			0.129918	−	0.991525i	$-0.458528\pi$
$557$	6.13236			0.259837			0.129918	+	0.991525i	$0.458528\pi$
$558$	10.7187	−	60.7888i	0.453759	−	2.57339i
$559$	3.18927			0.134892
$560$	−35.3112	−	1.61061i	−1.49217	−	0.0680609i
$561$	30.7333	+	23.1193i	1.29756	+	0.976097i
$562$	−34.0973	−	6.01227i	−1.43831	−	0.253612i
$563$	−1.47960			−0.0623578			−0.0311789	−	0.999514i	$-0.509926\pi$
$563$	−1.47960			−0.0623578			−0.0311789	+	0.999514i	$0.509926\pi$
$564$	−16.1972	−	5.89530i	−0.682025	−	0.248237i
$565$	−5.00041	+	3.82151i	−0.210369	+	0.160772i
$566$	−1.93546	+	10.9765i	−0.0813533	+	0.461378i
$567$	−105.487			−4.43006
$568$	16.9438	−	29.3475i	0.710945	−	1.23139i
$569$	21.4439			0.898974			0.449487	−	0.893287i	$-0.351607\pi$
$569$	21.4439			0.898974			0.449487	+	0.893287i	$0.351607\pi$
$570$	−36.1121	+	18.7095i	−1.51257	+	0.783653i
$571$	26.4859			1.10840			0.554201	−	0.832383i	$-0.313024\pi$
$571$	26.4859			1.10840			0.554201	+	0.832383i	$0.313024\pi$
$572$	−13.1518	−	4.78685i	−0.549902	−	0.200148i
$573$			8.22881i			0.343763i
$574$	8.11982	−	46.0498i	0.338915	−	1.92208i
$575$	4.98566	−	18.3211i	0.207917	−	0.764041i
$576$	−30.6388	−	53.0680i	−1.27662	−	2.21117i
$577$		−	27.1774i		−	1.13141i	−0.824607	−	0.565706i	$-0.808604\pi$
$577$		−	27.1774i		−	1.13141i	0.824607	−	0.565706i	$-0.191396\pi$
$578$	−2.55264	−	23.9057i	−0.106176	−	0.994347i
$579$			39.8666i			1.65680i
$580$	13.0003	−	4.07118i	0.539810	−	0.169047i
$581$	66.5855			2.76243
$582$	−10.6192	+	60.2246i	−0.440181	+	2.49639i
$583$	−8.01729			−0.332042
$584$	−8.92986	−	5.15566i	−0.369520	−	0.213343i
$585$	−33.3340	+	25.4751i	−1.37819	+	1.05327i
$586$	25.8687	+	4.56135i	1.06863	+	0.188428i
$587$	−21.7425			−0.897408			−0.448704	−	0.893680i	$-0.648114\pi$
$587$	−21.7425			−0.897408			−0.448704	+	0.893680i	$0.648114\pi$
$588$	19.2480	−	52.8833i	0.793772	−	2.18087i
$589$	22.4469			0.924908
$590$	12.1493	+	23.4500i	0.500180	+	0.965422i
$591$	27.9358			1.14912
$592$	7.29120	−	8.68932i	0.299667	−	0.357129i
$593$		−	47.9889i		−	1.97067i	−0.170639	−	0.985334i	$-0.554583\pi$
$593$		−	47.9889i		−	1.97067i	0.170639	−	0.985334i	$-0.445417\pi$
$594$	10.6736	−	60.5327i	0.437941	−	2.48369i
$595$	0.277197	+	36.4348i	0.0113640	+	1.49368i
$596$	−0.590643	+	1.62278i	−0.0241937	+	0.0664716i
$597$	56.2230			2.30106
$598$	12.9549	+	2.28431i	0.529767	+	0.0934123i
$599$	−19.4099			−0.793066			−0.396533	−	0.918020i	$-0.629787\pi$
$599$	−19.4099			−0.793066			−0.396533	+	0.918020i	$0.629787\pi$
$600$	−32.5218	−	32.7761i	−1.32770	−	1.33808i
$601$			12.8704i			0.524994i	0.964933	+	0.262497i	$0.0845460\pi$
$601$			12.8704i			0.524994i	−0.964933	+	0.262497i	$0.915454\pi$
$602$	−7.16639	−	1.26363i	−0.292080	−	0.0515017i
$603$	−42.4167			−1.72734
$604$	25.5569	+	9.30196i	1.03990	+	0.378492i
$605$	−5.04251	+	3.85368i	−0.205007	+	0.156674i
$606$	62.3768	+	10.9987i	2.53388	+	0.446792i
$607$	−2.76842			−0.112367			−0.0561834	−	0.998420i	$-0.517893\pi$
$607$	−2.76842			−0.112367			−0.0561834	+	0.998420i	$0.517893\pi$
$608$	17.0703	−	14.3237i	0.692291	−	0.580901i
$609$			39.3049i			1.59272i
$610$	39.6508	−	20.5429i	1.60542	−	0.831758i
$611$		−	6.46587i		−	0.261581i
$612$	−52.9449	+	34.4452i	−2.14017	+	1.39237i
$613$	40.3681			1.63045			0.815225	−	0.579144i	$-0.196613\pi$
$613$	40.3681			1.63045			0.815225	+	0.579144i	$0.196613\pi$
$614$	19.6039	+	3.45670i	0.791150	+	0.139501i
$615$	48.5304	−	37.0888i	1.95694	−	1.49556i
$616$	27.6559	+	15.9671i	1.11429	+	0.643333i
$617$	−32.2833			−1.29968			−0.649839	−	0.760072i	$-0.725163\pi$
$617$	−32.2833			−1.29968			−0.649839	+	0.760072i	$0.725163\pi$
$618$	−3.56915	−	0.629338i	−0.143572	−	0.0253157i
$619$	−3.28155			−0.131896			−0.0659482	−	0.997823i	$-0.521007\pi$
$619$	−3.28155			−0.131896			−0.0659482	+	0.997823i	$0.521007\pi$
$620$	7.61571	+	24.3189i	0.305854	+	0.976673i
$621$			57.7730i			2.31835i
$622$	−5.24943	+	29.7710i	−0.210483	+	1.19371i
$623$	−17.4028			−0.697227
$624$	20.5625	−	24.5054i	0.823159	−	0.981002i
$625$	−21.5526	−	12.6682i	−0.862105	−	0.506730i
$626$	23.1599	+	4.08372i	0.925656	+	0.163218i
$627$	36.7431			1.46738
$628$	−21.3149	−	7.75800i	−0.850559	−	0.309578i
$629$	−9.34363	−	7.02880i	−0.372555	−	0.280257i
$630$	84.9962	−	44.0361i	3.38633	−	1.75444i
$631$	−20.8075			−0.828335			−0.414167	−	0.910201i	$-0.635927\pi$
$631$	−20.8075			−0.828335			−0.414167	+	0.910201i	$0.635927\pi$
$632$	9.34884	−	16.1927i	0.371877	−	0.644109i
$633$		−	70.2331i		−	2.79151i
$634$	7.97744	−	45.2423i	0.316825	−	1.79680i
$635$	6.77369	+	8.86333i	0.268806	+	0.351730i
$636$	6.26743	−	17.2196i	0.248520	−	0.682803i
$637$	21.1109			0.836443
$638$	−12.1203	−	2.13714i	−0.479847	−	0.0846100i
$639$			91.7714i			3.63042i
$640$	21.3098	+	13.6342i	0.842344	+	0.538941i
$641$			12.7879i			0.505091i	0.967585	+	0.252545i	$0.0812677\pi$
$641$			12.7879i			0.505091i	−0.967585	+	0.252545i	$0.918732\pi$
$642$	63.5981	+	11.2141i	2.51002	+	0.442584i
$643$		−	3.01560i		−	0.118924i	−0.998231	−	0.0594619i	$-0.981062\pi$
$643$		−	3.01560i		−	0.118924i	0.998231	−	0.0594619i	$-0.0189385\pi$
$644$	−28.2052	−	10.2658i	−1.11144	−	0.404531i
$645$	−5.77186	−	7.55243i	−0.227267	−	0.297377i
$646$	−15.6790	−	16.7858i	−0.616884	−	0.660429i
$647$		−	9.06560i		−	0.356405i	−0.983994	−	0.178203i	$-0.942972\pi$
$647$		−	9.06560i		−	0.356405i	0.983994	−	0.178203i	$-0.0570283\pi$
$648$	65.3819	+	37.7482i	2.56844	+	1.48289i
$649$		−	23.8598i		−	0.936580i
$650$	7.38104	−	15.6691i	0.289508	−	0.614592i
$651$	−73.5253			−2.88168
$652$	−3.68999	+	10.1382i	−0.144511	+	0.397041i
$653$			30.8227i			1.20618i	0.797672	+	0.603092i	$0.206065\pi$
$653$			30.8227i			1.20618i	−0.797672	+	0.603092i	$0.793935\pi$
$654$	−4.46621	+	25.3292i	−0.174643	+	0.990449i
$655$	26.0334	−	19.8957i	1.01721	−	0.777390i
$656$	−21.5114	+	25.6363i	−0.839881	+	1.00093i
$657$	27.9243			1.08943
$658$	−2.56186	+	14.5291i	−0.0998719	+	0.566401i
$659$		−	17.6434i		−	0.687290i	−0.939100	−	0.343645i	$-0.888338\pi$
$659$		−	17.6434i		−	0.687290i	0.939100	−	0.343645i	$-0.111662\pi$
$660$	12.4661	+	39.8075i	0.485242	+	1.54951i
$661$		−	24.6247i		−	0.957791i	−0.877872	−	0.478895i	$-0.841037\pi$
$661$		−	24.6247i		−	0.957791i	0.877872	−	0.478895i	$-0.158963\pi$
$662$	−0.733309	+	4.15880i	−0.0285009	+	0.161636i
$663$	−26.3507	−	19.8225i	−1.02338	−	0.769841i
$664$	−41.2702	−	23.8273i	−1.60159	−	0.924680i
$665$	21.1377	+	27.6586i	0.819686	+	1.07255i
$666$	−5.33420	+	30.2518i	−0.206696	+	1.17223i
$667$	11.5677			0.447905
$668$	12.1548	+	4.42399i	0.470283	+	0.171169i
$669$	45.0408			1.74138
$670$	15.5486	−	8.05567i	0.600696	−	0.311218i
$671$	−40.3438			−1.55745
$672$	−55.9140	+	46.9175i	−2.15693	+	1.80988i
$673$	15.4632			0.596064			0.298032	−	0.954556i	$-0.403670\pi$
$673$	15.4632			0.596064			0.298032	+	0.954556i	$0.403670\pi$
$674$	−11.9439	−	2.10603i	−0.460061	−	0.0811211i
$675$	73.3988	+	19.9738i	2.82512	+	0.768793i
$676$	−13.1557	−	4.78828i	−0.505988	−	0.184165i
$677$		−	2.81894i		−	0.108341i	−0.998532	−	0.0541703i	$-0.982749\pi$
$677$		−	2.81894i		−	0.108341i	0.998532	−	0.0541703i	$-0.0172514\pi$
$678$	−2.25665	+	12.7981i	−0.0866662	+	0.491508i
$679$	52.3425			2.00872
$680$	12.8662	−	22.6817i	0.493397	−	0.869804i
$681$	−19.3713			−0.742308
$682$	3.99781	−	22.6727i	0.153084	−	0.868183i
$683$		−	31.9818i		−	1.22375i	−0.790955	−	0.611874i	$-0.790416\pi$
$683$		−	31.9818i		−	1.22375i	0.790955	−	0.611874i	$-0.209584\pi$
$684$	−20.6398	+	56.7074i	−0.789182	+	2.16826i
$685$	5.38013	+	7.03986i	0.205564	+	0.268979i
$686$	−8.90821	−	1.57076i	−0.340117	−	0.0599718i
$687$	21.6402			0.825627
$688$	3.98960	+	3.34767i	0.152102	+	0.127629i
$689$	6.87402			0.261879
$690$	−18.0361	−	34.8124i	−0.686624	−	1.32529i
$691$	−5.42424			−0.206348			−0.103174	−	0.994663i	$-0.532900\pi$
$691$	−5.42424			−0.206348			−0.103174	+	0.994663i	$0.532900\pi$
$692$	4.13527	−	11.3616i	0.157200	−	0.431902i
$693$	−86.4816			−3.28516
$694$	2.26456	−	12.8430i	0.0859616	−	0.487513i
$695$	5.83012	−	4.45560i	0.221149	−	0.169011i
$696$	14.0651	−	24.3615i	0.533136	−	0.923418i
$697$	27.5668	+	20.7373i	1.04417	+	0.785480i
$698$	−6.95468	+	39.4420i	−0.263239	+	1.49290i
$699$			88.1748i			3.33508i
$700$	−22.7938	+	32.2845i	−0.861523	+	1.22024i
$701$			34.2006i			1.29174i	0.763448	+	0.645870i	$0.223505\pi$
$701$			34.2006i			1.29174i	−0.763448	+	0.645870i	$0.776495\pi$
$702$	−9.15150	+	51.9008i	−0.345401	+	1.95887i
$703$	−11.1708			−0.421314
$704$	−11.4275	−	19.7931i	−0.430691	−	0.745979i
$705$	−15.3117	+	11.7018i	−0.576672	+	0.440715i
$706$	−5.76397	+	32.6891i	−0.216930	+	1.23027i
$707$		−	54.2129i		−	2.03889i
$708$	51.2464	+	18.6522i	1.92596	+	0.700992i
$709$	−6.49760			−0.244023			−0.122011	−	0.992529i	$-0.538934\pi$
$709$	−6.49760			−0.244023			−0.122011	+	0.992529i	$0.538934\pi$
$710$	−17.4290	−	33.6405i	−0.654098	−	1.26251i
$711$			50.6355i			1.89898i
$712$	10.7864	+	6.22750i	0.404236	+	0.233386i
$713$			21.6391i			0.810389i
$714$	51.3571	+	54.9823i	1.92199	+	2.05766i
$715$	−12.4327	+	9.50158i	−0.464958	+	0.355339i
$716$	8.67200	−	23.8261i	0.324088	−	0.890424i
$717$			67.3135i			2.51387i
$718$	42.8499	+	7.55559i	1.59914	+	0.281972i
$719$		−	27.9732i		−	1.04323i	−0.853182	−	0.521613i	$-0.825331\pi$
$719$		−	27.9732i		−	1.04323i	0.853182	−	0.521613i	$-0.174669\pi$
$720$	−68.4394	−	3.12165i	−2.55059	−	0.116337i
$721$			3.10202i			0.115525i
$722$	4.85012	+	0.855207i	0.180503	+	0.0318275i
$723$	27.2085			1.01190
$724$	21.2570	+	7.73691i	0.790010	+	0.287540i
$725$	3.99930	−	14.6964i	0.148530	−	0.545812i
$726$	−2.27565	+	12.9059i	−0.0844573	+	0.478981i
$727$		−	19.8801i		−	0.737313i	−0.929566	−	0.368656i	$-0.879818\pi$
$727$		−	19.8801i		−	0.737313i	0.929566	−	0.368656i	$-0.120182\pi$
$728$	−23.7121	−	13.6902i	−0.878830	−	0.507393i
$729$	−55.4398			−2.05332
$730$	−10.2362	+	5.30330i	−0.378857	+	0.196284i
$731$	3.22719	−	4.29002i	0.119362	−	0.158672i
$732$	31.5383	−	86.6509i	1.16569	−	3.20271i
$733$	−15.3589			−0.567293			−0.283647	−	0.958929i	$-0.591544\pi$
$733$	−15.3589			−0.567293			−0.283647	+	0.958929i	$0.591544\pi$
$734$	−18.7842	−	3.31215i	−0.693336	−	0.122254i
$735$	−38.2059	−	49.9922i	−1.40925	−	1.84399i
$736$	13.8082	+	16.4559i	0.508976	+	0.606574i
$737$	−15.8204			−0.582750
$738$	15.7376	−	89.2526i	0.579311	−	3.28543i
$739$			5.22655i			0.192262i	0.995369	+	0.0961310i	$0.0306468\pi$
$739$			5.22655i			0.192262i	−0.995369	+	0.0961310i	$0.969353\pi$
$740$	−3.78998	−	12.1024i	−0.139323	−	0.444894i
$741$	−31.5036			−1.15731
$742$	−15.4462	−	2.72358i	−0.567047	−	0.0999857i
$743$	−21.3385			−0.782833			−0.391417	−	0.920214i	$-0.628015\pi$
$743$	−21.3385			−0.782833			−0.391417	+	0.920214i	$0.628015\pi$
$744$	45.5715	+	26.3107i	1.67073	+	0.964597i
$745$	1.17239	+	1.53406i	0.0429530	+	0.0562037i
$746$	20.7426	+	3.65748i	0.759440	+	0.133910i
$747$	129.054			4.72186
$748$	−19.7471	+	12.8472i	−0.722027	+	0.469741i
$749$		−	55.2744i		−	2.01968i
$750$	−50.4637	+	10.8787i	−1.84267	+	0.397232i
$751$			37.0942i			1.35359i	0.736173	+	0.676793i	$0.236631\pi$
$751$			37.0942i			1.35359i	−0.736173	+	0.676793i	$0.763369\pi$
$752$	6.78702	−	8.08845i	0.247497	−	0.294956i
$753$	−91.5795			−3.33734
$754$	10.3919	+	1.83238i	0.378452	+	0.0667314i
$755$	24.1597	−	18.4638i	0.879263	−	0.671966i
$756$	41.1275	−	112.997i	1.49579	−	4.10966i
$757$	16.9302			0.615339			0.307670	−	0.951493i	$-0.400451\pi$
$757$	16.9302			0.615339			0.307670	+	0.951493i	$0.400451\pi$
$758$	−35.5503	−	6.26848i	−1.29125	−	0.227682i
$759$			35.4208i			1.28569i
$760$	−3.20381	−	24.7070i	−0.116215	−	0.896218i
$761$	42.5037			1.54076			0.770380	−	0.637586i	$-0.220067\pi$
$761$	42.5037			1.54076			0.770380	+	0.637586i	$0.220067\pi$
$762$	22.6849	+	3.99996i	0.821787	+	0.144903i
$763$	22.0141			0.796964
$764$	−4.73674	−	1.72403i	−0.171369	−	0.0623734i
$765$	0.537257	+	70.6170i	0.0194246	+	2.55316i
$766$	−7.62036	+	43.2172i	−0.275335	+	1.56150i
$767$			20.4574i			0.738674i
$768$	51.4451	−	9.07116i	1.85637	−	0.327327i
$769$	−25.0458			−0.903173			−0.451586	−	0.892227i	$-0.649142\pi$
$769$	−25.0458			−0.903173			−0.451586	+	0.892227i	$0.649142\pi$
$770$	31.7015	−	16.4244i	1.14244	−	0.591893i
$771$	−10.3962			−0.374409
$772$	−22.9484	−	8.35253i	−0.825930	−	0.300614i
$773$	6.52248			0.234597			0.117299	−	0.993097i	$-0.462577\pi$
$773$	6.52248			0.234597			0.117299	+	0.993097i	$0.462577\pi$
$774$	−13.8897	−	2.44913i	−0.499256	−	0.0880323i
$775$	27.4917	+	7.48125i	0.987531	+	0.268734i
$776$	−32.4422	−	18.7305i	−1.16461	−	0.672387i
$777$	36.5901			1.31266
$778$	−3.18362	+	18.0552i	−0.114138	+	0.647310i
$779$	32.9574			1.18082
$780$	−10.6884	−	34.1310i	−0.382707	−	1.22208i
$781$			34.2284i			1.22479i
$782$	16.1817	−	15.1148i	0.578657	−	0.540503i
$783$			46.3432i			1.65617i
$784$	26.4085	+	22.1594i	0.943162	+	0.791407i
$785$	−20.1497	+	15.3991i	−0.719172	+	0.549619i
$786$	11.7487	−	66.6301i	0.419062	−	2.37662i
$787$		−	2.17067i		−	0.0773759i	−0.999251	−	0.0386879i	$-0.987682\pi$
$787$		−	2.17067i		−	0.0773759i	0.999251	−	0.0386879i	$-0.0123178\pi$
$788$	−5.85288	+	16.0807i	−0.208500	+	0.572850i
$789$	−58.7672			−2.09217
$790$	−9.61656	−	18.5614i	−0.342142	−	0.660385i
$791$	11.1231			0.395492
$792$	53.6019	+	30.9471i	1.90466	+	1.09966i
$793$	34.5908			1.22835
$794$	−2.08442	+	11.8213i	−0.0739732	+	0.419523i
$795$	−12.4404	−	16.2782i	−0.441217	−	0.577330i
$796$	−11.7794	+	32.3636i	−0.417510	+	1.14710i
$797$	−42.4909			−1.50510			−0.752552	−	0.658533i	$-0.771177\pi$
$797$	−42.4909			−1.50510			−0.752552	+	0.658533i	$0.771177\pi$
$798$	70.7897	+	12.4821i	2.50593	+	0.441863i
$799$	−8.69752	−	6.54276i	−0.307696	−	0.231466i
$800$	25.6806	−	11.8535i	0.907947	−	0.419086i
$801$	−33.7296			−1.19178
$802$	0.610664	−	3.46325i	0.0215633	−	0.122292i
$803$	10.4151			0.367539
$804$	12.3674	−	33.9792i	0.436165	−	1.19835i
$805$	−26.6632	+	20.3770i	−0.939754	+	0.718196i
$806$	−3.42772	+	19.4396i	−0.120736	+	0.684730i
$807$			28.5319i			1.00437i
$808$	−19.3999	+	33.6015i	−0.682485	+	1.18210i
$809$		−	36.0820i		−	1.26858i	−0.773097	−	0.634288i	$-0.781294\pi$
$809$		−	36.0820i		−	1.26858i	0.773097	−	0.634288i	$-0.218706\pi$
$810$	74.9462	−	38.8292i	2.63334	−	1.36432i
$811$	−24.9763			−0.877038			−0.438519	−	0.898722i	$-0.644497\pi$
$811$	−24.9763			−0.877038			−0.438519	+	0.898722i	$0.644497\pi$
$812$	−22.6251	−	8.23485i	−0.793984	−	0.288987i
$813$			30.0649i			1.05442i
$814$	−1.98952	+	11.2831i	−0.0697328	+	0.395474i
$815$	7.32439	+	9.58391i	0.256562	+	0.335710i
$816$	−12.1563	−	52.4563i	−0.425555	−	1.83634i
$817$		−	5.12893i		−	0.179438i
$818$	−18.7377	−	3.30396i	−0.655148	−	0.115520i
$819$	74.1493			2.59099
$820$	11.1817	+	35.7061i	0.390482	+	1.24691i
$821$	43.1631			1.50640			0.753202	−	0.657789i	$-0.228508\pi$
$821$	43.1631			1.50640			0.753202	+	0.657789i	$0.228508\pi$
$822$	18.0179	+	3.17704i	0.628446	+	0.110812i
$823$	−22.0577			−0.768882			−0.384441	−	0.923149i	$-0.625606\pi$
$823$	−22.0577			−0.768882			−0.384441	+	0.923149i	$0.625606\pi$
$824$	1.11005	−	1.92266i	0.0386703	−	0.0669789i
$825$	45.0010	+	12.2460i	1.56673	+	0.426351i
$826$	8.10550	−	45.9686i	0.282026	−	1.59945i
$827$			21.9044i			0.761690i	0.924639	+	0.380845i	$0.124367\pi$
$827$			21.9044i			0.761690i	−0.924639	+	0.380845i	$0.875633\pi$
$828$	−54.6666	−	19.8970i	−1.89979	−	0.691469i
$829$			19.6328i			0.681874i	0.940086	+	0.340937i	$0.110744\pi$
$829$			19.6328i			0.681874i	−0.940086	+	0.340937i	$0.889256\pi$
$830$	−47.3074	+	24.5097i	−1.64206	+	0.850744i
$831$	10.5453			0.365812
$832$	9.79796	+	16.9706i	0.339683	+	0.588348i
$833$	21.3619	−	28.3971i	0.740146	−	0.983902i
$834$	2.63109	−	14.9217i	0.0911073	−	0.516695i
$835$	11.4903	−	8.78132i	0.397638	−	0.303890i
$836$	−7.69813	+	21.1504i	−0.266245	+	0.731503i
$837$	−86.6914			−2.99649
$838$	−23.3386	−	4.11523i	−0.806219	−	0.142158i
$839$		−	19.2806i		−	0.665640i	−0.942990	−	0.332820i	$-0.892000\pi$
$839$		−	19.2806i		−	0.665640i	0.942990	−	0.332820i	$-0.108000\pi$
$840$	10.4942	+	80.9284i	0.362083	+	2.79230i
$841$	−19.7208			−0.680028
$842$	−0.682210	+	3.86900i	−0.0235105	+	0.133335i
$843$			79.9329i			2.75304i
$844$	40.4282	+	14.7147i	1.39160	+	0.506500i
$845$	−12.4365	+	9.50443i	−0.427828	+	0.326962i
$846$	−4.96534	+	28.1599i	−0.170712	+	0.968156i
$847$	11.2167			0.385412
$848$	8.59903	+	7.21544i	0.295292	+	0.247779i
$849$	25.7319			0.883115
$850$	−13.6083	−	25.7840i	−0.466762	−	0.884383i
$851$		−	10.7688i		−	0.369148i
$852$	−73.5163	−	26.7577i	−2.51863	−	0.916705i
$853$		−	29.2235i		−	1.00059i	−0.865854	−	0.500297i	$-0.833224\pi$
$853$		−	29.2235i		−	1.00059i	0.865854	−	0.500297i	$-0.166776\pi$
$854$	−77.7267	−	13.7053i	−2.65975	−	0.468986i
$855$	40.9687	+	53.6072i	1.40110	+	1.83333i
$856$	−19.7797	+	34.2595i	−0.676057	+	1.17096i
$857$	1.09290			0.0373329			0.0186665	−	0.999826i	$-0.494058\pi$
$857$	1.09290			0.0373329			0.0186665	+	0.999826i	$0.494058\pi$
$858$	−5.61081	+	31.8205i	−0.191550	+	1.08633i
$859$			27.3477i			0.933093i	0.884497	+	0.466547i	$0.154502\pi$
$859$			27.3477i			0.933093i	−0.884497	+	0.466547i	$0.845498\pi$
$860$	5.55668	−	1.74013i	0.189481	−	0.0593378i
$861$	−107.953			−3.67902
$862$	6.60556	−	37.4620i	0.224986	−	1.27596i
$863$			19.9736i			0.679909i	0.940442	+	0.339955i	$0.110412\pi$
$863$			19.9736i			0.679909i	−0.940442	+	0.339955i	$0.889588\pi$
$864$	−65.9266	+	55.3190i	−2.24287	+	1.88199i
$865$	−8.20825	−	10.7404i	−0.279089	−	0.365186i
$866$	−1.78416	+	10.1185i	−0.0606282	+	0.343839i
$867$	−53.3281	+	15.3873i	−1.81112	+	0.522579i
$868$	15.4044	−	42.3233i	0.522860	−	1.43655i
$869$			18.8858i			0.640656i
$870$	−14.4679	−	27.9252i	−0.490507	−	0.946751i
$871$	13.5644			0.459611
$872$	−13.6445	−	7.87765i	−0.462061	−	0.266771i
$873$	101.449			3.43353
$874$	3.67359	−	20.8339i	0.124261	−	0.704719i
$875$	16.6701	+	40.9196i	0.563552	+	1.38334i
$876$	−8.14186	+	22.3696i	−0.275088	+	0.755798i
$877$		−	32.4128i		−	1.09450i	−0.836969	−	0.547251i	$-0.815674\pi$
$877$		−	32.4128i		−	1.09450i	0.836969	−	0.547251i	$-0.184326\pi$
$878$	−5.14855	+	29.1989i	−0.173755	+	0.985415i
$879$		−	60.6430i		−	2.04544i
$880$	−25.5262	−	1.16430i	−0.860487	−	0.0392485i
$881$		−	13.0253i		−	0.438833i	−0.975631	−	0.219417i	$-0.929585\pi$
$881$		−	13.0253i		−	0.438833i	0.975631	−	0.219417i	$-0.0704154\pi$
$882$	−91.9410	−	16.2117i	−3.09581	−	0.545875i
$883$	7.08631			0.238473			0.119237	−	0.992866i	$-0.461955\pi$
$883$	7.08631			0.238473			0.119237	+	0.992866i	$0.461955\pi$
$884$	16.9312	−	11.0152i	0.569458	−	0.370481i
$885$	48.4448	−	37.0233i	1.62845	−	1.24453i
$886$	−13.1982	−	2.32719i	−0.443401	−	0.0781835i
$887$	53.7005			1.80309			0.901543	−	0.432690i	$-0.142436\pi$
$887$	53.7005			1.80309			0.901543	+	0.432690i	$0.142436\pi$
$888$	−22.6788	−	13.0936i	−0.761051	−	0.439393i
$889$		−	19.7159i		−	0.661250i
$890$	12.3642	−	6.40584i	0.414450	−	0.214724i
$891$	−76.2560			−2.55467
$892$	−9.43658	+	25.9268i	−0.315960	+	0.868093i
$893$	−10.3983			−0.347966
$894$	3.92629	+	0.692311i	0.131315	+	0.0231544i
$895$	−17.2133	−	22.5235i	−0.575379	−	0.752879i
$896$	−15.2924	−	42.0156i	−0.510884	−	1.40364i
$897$		−	30.3698i		−	1.01402i
$898$	1.54193	−	8.74470i	0.0514547	−	0.291814i
$899$			17.3580i			0.578921i
$900$	−44.1783	+	62.5731i	−1.47261	+	2.08577i
$901$	6.95577	−	9.24654i	0.231730	−	0.308047i
$902$	5.86975	−	33.2890i	0.195441	−	1.10840i
$903$			16.7999i			0.559066i
$904$	−6.89417	−	3.98035i	−0.229297	−	0.132385i
$905$	20.0949	−	15.3573i	0.667976	−	0.510493i
$906$	10.9031	−	61.8347i	0.362232	−	2.05432i
$907$		−	8.46087i		−	0.280939i	−0.990085	−	0.140469i	$-0.955139\pi$
$907$		−	8.46087i		−	0.280939i	0.990085	−	0.140469i	$-0.0448611\pi$
$908$	4.05851	−	11.1507i	0.134686	−	0.370048i
$909$		−	105.074i		−	3.48509i
$910$	−27.1808	+	14.0823i	−0.901036	+	0.466822i
$911$		−	15.7340i		−	0.521292i	−0.965434	−	0.260646i	$-0.916064\pi$
$911$		−	15.7340i		−	0.521292i	0.965434	−	0.260646i	$-0.0839356\pi$
$912$	−39.4092	−	33.0683i	−1.30497	−	1.09500i
$913$	48.1341			1.59301
$914$	−0.943472	+	5.35069i	−0.0312073	+	0.176985i
$915$	−62.6015	−	81.9137i	−2.06954	−	2.70798i
$916$	−4.53389	+	12.4568i	−0.149804	+	0.411583i
$917$	−57.9096			−1.91234
$918$	60.5536	+	64.8280i	1.99857	+	2.13964i
$919$	26.9250			0.888173			0.444087	−	0.895984i	$-0.353528\pi$
$919$	26.9250			0.888173			0.444087	+	0.895984i	$0.353528\pi$
$920$	23.8179	−	3.08851i	0.785251	−	0.101825i
$921$		−	45.9567i		−	1.51433i
$922$	2.41323	−	13.6861i	0.0794755	−	0.450728i
$923$		−	29.3475i		−	0.965983i
$924$	25.2154	−	69.2787i	0.829526	−	2.27910i
$925$	−13.6813	−	3.72307i	−0.449840	−	0.122414i
$926$	−8.04180	+	45.6073i	−0.264270	+	1.49875i
$927$			6.01227i			0.197469i
$928$	11.0764	+	13.2003i	0.363600	+	0.433321i
$929$			47.2412i			1.54993i	0.632003	+	0.774966i	$0.282233\pi$
$929$			47.2412i			1.54993i	−0.632003	+	0.774966i	$0.717767\pi$
$930$	52.2379	−	27.0642i	1.71295	−	0.887469i
$931$		−	33.9501i		−	1.11267i
$932$	−50.7560	−	18.4737i	−1.66257	−	0.605126i
$933$	69.7911			2.28486
$934$	−31.4797	−	5.55072i	−1.03005	−	0.181625i
$935$	0.200383	+	26.3384i	0.00655324	+	0.861357i
$936$	−45.9583	−	26.5340i	−1.50219	−	0.867291i
$937$			0.449610i			0.0146881i	0.999973	+	0.00734406i	$0.00233771\pi$
$937$			0.449610i			0.0146881i	−0.999973	+	0.00734406i	$0.997662\pi$
$938$	−30.4796	−	5.37438i	−0.995196	−	0.175480i
$939$		−	54.2929i		−	1.77178i
$940$	−3.52791	−	11.2655i	−0.115068	−	0.367441i
$941$	1.88584			0.0614767			0.0307384	−	0.999527i	$-0.490214\pi$
$941$	1.88584			0.0614767			0.0307384	+	0.999527i	$0.490214\pi$
$942$	−9.09340	+	51.5712i	−0.296279	+	1.68028i
$943$			31.7714i			1.03462i
$944$	−21.4735	+	25.5911i	−0.698903	+	0.832920i
$945$	−81.6354	−	106.819i	−2.65560	−	3.47484i
$946$	−5.18052	−	0.913466i	−0.168433	−	0.0296993i
$947$			34.0760i			1.10732i	0.832742	+	0.553661i	$0.186769\pi$
$947$			34.0760i			1.10732i	−0.832742	+	0.553661i	$0.813231\pi$
$948$	−40.5631	−	14.7638i	−1.31743	−	0.479505i
$949$	−8.92986			−0.289876
$950$	−25.1988	−	11.8701i	−0.817556	−	0.385116i
$951$	−106.060			−3.43923
$952$	−42.4094	+	18.0432i	−1.37450	+	0.584783i
$953$		−	21.0994i		−	0.683476i	−0.939795	−	0.341738i	$-0.888984\pi$
$953$		−	21.0994i		−	0.683476i	0.939795	−	0.341738i	$-0.111016\pi$
$954$	−29.9374	−	5.27877i	−0.969259	−	0.170907i
$955$	−4.47779	+	3.42209i	−0.144898	+	0.110736i
$956$	−38.7477	−	14.1030i	−1.25319	−	0.456124i
$957$			28.4132i			0.918467i
$958$	−2.49636	+	14.1576i	−0.0806538	+	0.457410i
$959$		−	15.6597i		−	0.505679i
$960$	22.4555	−	53.9153i	0.724749	−	1.74011i
$961$	−1.47052			−0.0474360
$962$	1.70582	−	9.67417i	0.0549978	−	0.311908i
$963$		−	107.132i		−	3.45227i
$964$	−5.70051	+	15.6620i	−0.183601	+	0.504440i
$965$	−21.6938	+	16.5792i	−0.698348	+	0.533704i
$966$	−12.0329	+	68.2420i	−0.387153	+	2.19565i
$967$		−	44.9475i		−	1.44541i	−0.691155	−	0.722706i	$-0.742898\pi$
$967$		−	44.9475i		−	1.44541i	0.691155	−	0.722706i	$-0.257102\pi$
$968$	−6.95222	−	4.01386i	−0.223453	−	0.129010i
$969$	−31.8782	+	42.3768i	−1.02408	+	1.36134i
$970$	−37.1880	+	19.2669i	−1.19404	+	0.618624i
$971$			16.0267i			0.514320i	0.966369	+	0.257160i	$0.0827868\pi$
$971$			16.0267i			0.514320i	−0.966369	+	0.257160i	$0.917213\pi$
$972$	28.3922	−	78.0069i	0.910680	−	2.50207i
$973$	−12.9687			−0.415759
$974$	22.6887	+	4.00063i	0.726994	+	0.128189i
$975$	−38.5838	−	10.4997i	−1.23567	−	0.336260i
$976$	43.2711	+	36.3088i	1.38508	+	1.16222i
$977$			20.5970i			0.658955i	0.944163	+	0.329478i	$0.106873\pi$
$977$			20.5970i			0.658955i	−0.944163	+	0.329478i	$0.893127\pi$
$978$	24.5292	+	4.32515i	0.784356	+	0.138303i
$979$	−12.5803			−0.402068
$980$	36.7816	−	11.5185i	1.17494	−	0.367945i
$981$	42.6672			1.36226
$982$	7.02699	−	39.8520i	0.224240	−	1.27173i
$983$	−18.8102			−0.599952			−0.299976	−	0.953947i	$-0.596979\pi$
$983$	−18.8102			−0.599952			−0.299976	+	0.953947i	$0.596979\pi$
$984$	66.9099	+	38.6305i	2.13301	+	1.23149i
$985$	11.6176	+	15.2015i	0.370167	+	0.484361i
$986$	12.9803	−	12.1245i	0.413378	−	0.386122i
$987$	34.0599			1.08414
$988$	6.60038	−	18.1344i	0.209986	−	0.576932i
$989$	4.94434			0.157221
$990$	61.4430	−	31.8333i	1.95279	−	1.01173i
$991$		−	4.34248i		−	0.137943i	−0.997619	−	0.0689717i	$-0.978028\pi$
$991$		−	4.34248i		−	0.137943i	0.997619	−	0.0689717i	$-0.0219718\pi$
$992$	−24.6930	+	20.7199i	−0.784003	+	0.657857i
$993$	9.74932			0.309385
$994$	−11.6278	+	65.9448i	−0.368813	+	2.09164i
$995$	23.3813	+	30.5943i	0.741238	+	0.969905i
$996$	−37.6283	+	103.383i	−1.19230	+	3.27582i
$997$			32.7246i			1.03640i	0.855260	+	0.518199i	$0.173397\pi$
$997$			32.7246i			1.03640i	−0.855260	+	0.518199i	$0.826603\pi$
$998$	−5.62213	−	0.991333i	−0.177965	−	0.0313801i
$999$	43.1423			1.36496

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.h.c.509.45	yes	48
5.4	even	2	inner	680.2.h.c.509.4	yes	48
8.5	even	2	inner	680.2.h.c.509.8	yes	48
17.16	even	2	inner	680.2.h.c.509.48	yes	48
40.29	even	2	inner	680.2.h.c.509.41	yes	48
85.84	even	2	inner	680.2.h.c.509.1	✓	48
136.101	even	2	inner	680.2.h.c.509.5	yes	48
680.509	even	2	inner	680.2.h.c.509.44	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.h.c.509.1	✓	48	85.84	even	2	inner
680.2.h.c.509.4	yes	48	5.4	even	2	inner
680.2.h.c.509.5	yes	48	136.101	even	2	inner
680.2.h.c.509.8	yes	48	8.5	even	2	inner
680.2.h.c.509.41	yes	48	40.29	even	2	inner
680.2.h.c.509.44	yes	48	680.509	even	2	inner
680.2.h.c.509.45	yes	48	1.1	even	1	trivial
680.2.h.c.509.48	yes	48	17.16	even	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39273 + 0.245576i) q^{2} -3.26492i q^{3} +(1.87939 + 0.684040i) q^{4} +(1.77664 - 1.35778i) q^{5} +(0.801785 - 4.54715i) q^{6} -3.95202 q^{7} +(2.44949 + 1.41421i) q^{8} -7.65971 q^{9} +(2.80781 - 1.45471i) q^{10} -2.85688 q^{11} +(2.23334 - 6.13604i) q^{12} +2.44949 q^{13} +(-5.50409 - 0.970520i) q^{14} +(-4.43303 - 5.80059i) q^{15} +(3.06418 + 2.57115i) q^{16} +(2.47862 - 3.29491i) q^{17} +(-10.6679 - 1.88104i) q^{18} -3.93923i q^{19} +(4.26776 - 1.33649i) q^{20} +12.9030i q^{21} +(-3.97886 - 0.701580i) q^{22} +3.79746 q^{23} +(4.61730 - 7.99739i) q^{24} +(1.31289 - 4.82455i) q^{25} +(3.41147 + 0.601535i) q^{26} +15.2136i q^{27} +(-7.42737 - 2.70334i) q^{28} +3.04617 q^{29} +(-4.74952 - 9.16729i) q^{30} +5.69829i q^{31} +(3.63616 + 4.33340i) q^{32} +9.32749i q^{33} +(4.26119 - 3.98023i) q^{34} +(-7.02132 + 5.36596i) q^{35} +(-14.3955 - 5.23955i) q^{36} -2.83577i q^{37} +(0.967379 - 5.48628i) q^{38} -7.99739i q^{39} +(6.27204 - 0.813309i) q^{40} +8.36647i q^{41} +(-3.16867 + 17.9704i) q^{42} +1.30201 q^{43} +(-5.36918 - 1.95422i) q^{44} +(-13.6085 + 10.4002i) q^{45} +(5.28884 + 0.932564i) q^{46} -2.63968i q^{47} +(8.39460 - 10.0043i) q^{48} +8.61847 q^{49} +(3.01330 - 6.39688i) q^{50} +(-10.7576 - 8.09249i) q^{51} +(4.60353 + 1.67555i) q^{52} +2.80631 q^{53} +(-3.73609 + 21.1884i) q^{54} +(-5.07565 + 3.87900i) q^{55} +(-9.68044 - 5.58900i) q^{56} -12.8613 q^{57} +(4.24249 + 0.748066i) q^{58} +8.35170i q^{59} +(-4.36353 - 13.9339i) q^{60} +14.1216 q^{61} +(-1.39936 + 7.93617i) q^{62} +30.2713 q^{63} +(4.00000 + 6.92820i) q^{64} +(4.35186 - 3.32586i) q^{65} +(-2.29060 + 12.9907i) q^{66} +5.53763 q^{67} +(6.91213 - 4.49694i) q^{68} -12.3984i q^{69} +(-11.0965 + 5.74906i) q^{70} -11.9811i q^{71} +(-18.7624 - 10.8325i) q^{72} -3.64560 q^{73} +(0.696397 - 3.94946i) q^{74} +(-15.7518 - 4.28649i) q^{75} +(2.69459 - 7.40333i) q^{76} +11.2905 q^{77} +(1.96396 - 11.1382i) q^{78} -6.61063i q^{79} +(8.93498 + 0.407542i) q^{80} +26.6920 q^{81} +(-2.05460 + 11.6522i) q^{82} -16.8485 q^{83} +(-8.82620 + 24.2498i) q^{84} +(-0.0701406 - 9.21928i) q^{85} +(1.81335 + 0.319742i) q^{86} -9.94552i q^{87} +(-6.99790 - 4.04024i) q^{88} +4.40351 q^{89} +(-21.5070 + 11.1427i) q^{90} -9.68044 q^{91} +(7.13690 + 2.59762i) q^{92} +18.6045 q^{93} +(0.648241 - 3.67636i) q^{94} +(-5.34859 - 6.99859i) q^{95} +(14.1482 - 11.8718i) q^{96} -13.2445 q^{97} +(12.0032 + 2.11649i) q^{98} +21.8829 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 96 q^{9} - 48 q^{15} + 24 q^{34} - 96 q^{36} + 96 q^{49} + 48 q^{60} + 192 q^{64} - 144 q^{66} - 96 q^{70} + 96 q^{76} - 192 q^{84} - 192 q^{86} - 48 q^{89} - 144 q^{94}+O(q^{100}) \) 48 * q - 96 * q^9 - 48 * q^15 + 24 * q^34 - 96 * q^36 + 96 * q^49 + 48 * q^60 + 192 * q^64 - 144 * q^66 - 96 * q^70 + 96 * q^76 - 192 * q^84 - 192 * q^86 - 48 * q^89 - 144 * q^94

Introduction

L-functions

Modular forms

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