LMFDB - Embedded newform 680.2.h.b.509.14

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 = [40] 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:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			509.14
Character	$\chi$	$=$	680.509
Dual form			680.2.h.b.509.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.870262 - 1.11474i) q^{2} +3.10853i q^{3} +(-0.485287 + 1.94023i) q^{4} +(0.636925 - 2.14344i) q^{5} +(3.46520 - 2.70523i) q^{6} -1.38296 q^{7} +(2.58518 - 1.14754i) q^{8} -6.66293 q^{9} +(-2.94367 + 1.15535i) q^{10} +3.17005 q^{11} +(-6.03126 - 1.50853i) q^{12} -4.69324 q^{13} +(1.20354 + 1.54164i) q^{14} +(6.66293 + 1.97990i) q^{15} +(-3.52899 - 1.88314i) q^{16} +(-1.50938 + 3.83690i) q^{17} +(5.79850 + 7.42743i) q^{18} +7.70050i q^{19} +(3.84967 + 2.27596i) q^{20} -4.29898i q^{21} +(-2.75878 - 3.53378i) q^{22} -4.95047 q^{23} +(3.56716 + 8.03609i) q^{24} +(-4.18865 - 2.73042i) q^{25} +(4.08435 + 5.23174i) q^{26} -11.3863i q^{27} +(0.671134 - 2.68327i) q^{28} -1.71066 q^{29} +(-3.59143 - 9.15046i) q^{30} -6.13233i q^{31} +(0.971942 + 5.57273i) q^{32} +9.85419i q^{33} +(5.59069 - 1.65655i) q^{34} +(-0.880844 + 2.96430i) q^{35} +(3.23343 - 12.9276i) q^{36} +3.98650i q^{37} +(8.58404 - 6.70145i) q^{38} -14.5891i q^{39} +(-0.813118 - 6.27207i) q^{40} -4.75338i q^{41} +(-4.79224 + 3.74124i) q^{42} -10.3919 q^{43} +(-1.53839 + 6.15064i) q^{44} +(-4.24379 + 14.2816i) q^{45} +(4.30821 + 5.51849i) q^{46} -5.75119i q^{47} +(5.85378 - 10.9700i) q^{48} -5.08741 q^{49} +(0.601520 + 7.04544i) q^{50} +(-11.9271 - 4.69193i) q^{51} +(2.27757 - 9.10597i) q^{52} -0.856688 q^{53} +(-12.6928 + 9.90908i) q^{54} +(2.01909 - 6.79481i) q^{55} +(-3.57521 + 1.58701i) q^{56} -23.9372 q^{57} +(1.48872 + 1.90694i) q^{58} +3.40819i q^{59} +(-7.07490 + 11.9668i) q^{60} -4.33987 q^{61} +(-6.83595 + 5.33674i) q^{62} +9.21459 q^{63} +(5.36630 - 5.93320i) q^{64} +(-2.98924 + 10.0597i) q^{65} +(10.9849 - 8.57573i) q^{66} +7.67601 q^{67} +(-6.71199 - 4.79054i) q^{68} -15.3887i q^{69} +(4.07098 - 1.59780i) q^{70} +12.8320i q^{71} +(-17.2249 + 7.64599i) q^{72} +8.29467 q^{73} +(4.44390 - 3.46930i) q^{74} +(8.48758 - 13.0205i) q^{75} +(-14.9407 - 3.73695i) q^{76} -4.38407 q^{77} +(-16.2630 + 12.6963i) q^{78} -9.37764i q^{79} +(-6.28409 + 6.36476i) q^{80} +15.4059 q^{81} +(-5.29878 + 4.13669i) q^{82} +5.94240 q^{83} +(8.34101 + 2.08624i) q^{84} +(7.26279 + 5.67907i) q^{85} +(9.04371 + 11.5843i) q^{86} -5.31764i q^{87} +(8.19515 - 3.63777i) q^{88} -8.65552 q^{89} +(19.6134 - 7.69800i) q^{90} +6.49058 q^{91} +(2.40240 - 9.60506i) q^{92} +19.0625 q^{93} +(-6.41108 + 5.00505i) q^{94} +(16.5055 + 4.90464i) q^{95} +(-17.3230 + 3.02131i) q^{96} +10.7647 q^{97} +(4.42738 + 5.67114i) q^{98} -21.1218 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 12 q^{4} - 56 q^{9} + 56 q^{15} - 4 q^{16} - 36 q^{26} - 28 q^{30} + 24 q^{34} + 88 q^{36} + 8 q^{49} - 16 q^{50} - 88 q^{55} - 88 q^{60} - 132 q^{64} + 208 q^{66} + 72 q^{70} - 20 q^{76} - 56 q^{81}+ \cdots - 36 q^{94}+O(q^{100}) $ 40 * q + 12 * q^4 - 56 * q^9 + 56 * q^15 - 4 * q^16 - 36 * q^26 - 28 * q^30 + 24 * q^34 + 88 * q^36 + 8 * q^49 - 16 * q^50 - 88 * q^55 - 88 * q^60 - 132 * q^64 + 208 * q^66 + 72 * q^70 - 20 * q^76 - 56 * q^81 + 144 * q^84 + 256 * q^86 - 96 * q^89 - 36 * 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 $

$2$	−0.870262	−	1.11474i	−0.615368	−	0.788240i
$2$	−0.870262	−	1.11474i	−0.615368	−	0.788240i
$3$			3.10853i			1.79471i	0.441311	+	0.897354i	$0.354513\pi$
$3$			3.10853i			1.79471i	−0.441311	+	0.897354i	$0.645487\pi$
$4$	−0.485287	+	1.94023i	−0.242644	+	0.970116i
$5$	0.636925	−	2.14344i	0.284842	−	0.958575i
$5$	0.636925	−	2.14344i	0.284842	−	0.958575i
$6$	3.46520	−	2.70523i	1.41466	−	1.10441i
$7$	−1.38296			−0.522711			−0.261356	−	0.965243i	$-0.584169\pi$
$7$	−1.38296			−0.522711			−0.261356	+	0.965243i	$0.584169\pi$
$8$	2.58518	−	1.14754i	0.913999	−	0.405717i
$9$	−6.66293			−2.22098
$10$	−2.94367	+	1.15535i	−0.930869	+	0.365353i
$11$	3.17005			0.955807			0.477904	−	0.878412i	$-0.341397\pi$
$11$	3.17005			0.955807			0.477904	+	0.878412i	$0.341397\pi$
$12$	−6.03126	−	1.50853i	−1.74107	−	0.435474i
$13$	−4.69324			−1.30167			−0.650835	−	0.759219i	$-0.725581\pi$
$13$	−4.69324			−1.30167			−0.650835	+	0.759219i	$0.725581\pi$
$14$	1.20354	+	1.54164i	0.321660	+	0.412022i
$15$	6.66293	+	1.97990i	1.72036	+	0.511208i
$16$	−3.52899	−	1.88314i	−0.882248	−	0.470784i
$17$	−1.50938	+	3.83690i	−0.366077	+	0.930584i
$17$	−1.50938	+	3.83690i	−0.366077	+	0.930584i
$18$	5.79850	+	7.42743i	1.36672	+	1.75066i
$19$			7.70050i			1.76661i	0.468794	+	0.883307i	$0.344689\pi$
$19$			7.70050i			1.76661i	−0.468794	+	0.883307i	$0.655311\pi$
$20$	3.84967	+	2.27596i	0.860813	+	0.508921i
$21$		−	4.29898i		−	0.938114i
$22$	−2.75878	−	3.53378i	−0.588173	−	0.753405i
$23$	−4.95047			−1.03225			−0.516123	−	0.856515i	$-0.672625\pi$
$23$	−4.95047			−1.03225			−0.516123	+	0.856515i	$0.672625\pi$
$24$	3.56716	+	8.03609i	0.728144	+	1.64036i
$25$	−4.18865	−	2.73042i	−0.837730	−	0.546084i
$26$	4.08435	+	5.23174i	0.801007	+	1.02603i
$27$		−	11.3863i		−	2.19130i
$28$	0.671134	−	2.68327i	0.126832	−	0.507090i
$29$	−1.71066			−0.317662			−0.158831	−	0.987306i	$-0.550772\pi$
$29$	−1.71066			−0.317662			−0.158831	+	0.987306i	$0.550772\pi$
$30$	−3.59143	−	9.15046i	−0.655702	−	1.67064i
$31$		−	6.13233i		−	1.10140i	−0.834703	−	0.550700i	$-0.814361\pi$
$31$		−	6.13233i		−	1.10140i	0.834703	−	0.550700i	$-0.185639\pi$
$32$	0.971942	+	5.57273i	0.171817	+	0.985129i
$33$			9.85419i			1.71539i
$34$	5.59069	−	1.65655i	0.958796	−	0.284095i
$35$	−0.880844	+	2.96430i	−0.148890	+	0.501058i
$36$	3.23343	−	12.9276i	0.538906	−	2.15460i
$37$			3.98650i			0.655376i	0.944786	+	0.327688i	$0.106269\pi$
$37$			3.98650i			0.655376i	−0.944786	+	0.327688i	$0.893731\pi$
$38$	8.58404	−	6.70145i	1.39252	−	1.08712i
$39$		−	14.5891i		−	2.33612i
$40$	−0.813118	−	6.27207i	−0.128565	−	0.991701i
$41$		−	4.75338i		−	0.742353i	−0.928562	−	0.371176i	$-0.878954\pi$
$41$		−	4.75338i		−	0.742353i	0.928562	−	0.371176i	$-0.121046\pi$
$42$	−4.79224	+	3.74124i	−0.739458	+	0.577286i
$43$	−10.3919			−1.58475			−0.792377	−	0.610031i	$-0.791157\pi$
$43$	−10.3919			−1.58475			−0.792377	+	0.610031i	$0.791157\pi$
$44$	−1.53839	+	6.15064i	−0.231920	+	0.927243i
$45$	−4.24379	+	14.2816i	−0.632627	+	2.12897i
$46$	4.30821	+	5.51849i	0.635211	+	0.813657i
$47$		−	5.75119i		−	0.838898i	−0.907779	−	0.419449i	$-0.862223\pi$
$47$		−	5.75119i		−	0.838898i	0.907779	−	0.419449i	$-0.137777\pi$
$48$	5.85378	−	10.9700i	0.844921	−	1.58338i
$49$	−5.08741			−0.726773
$50$	0.601520	+	7.04544i	0.0850678	+	0.996375i
$51$	−11.9271	−	4.69193i	−1.67013	−	0.657002i
$52$	2.27757	−	9.10597i	0.315842	−	1.26277i
$53$	−0.856688			−0.117675			−0.0588376	−	0.998268i	$-0.518739\pi$
$53$	−0.856688			−0.117675			−0.0588376	+	0.998268i	$0.518739\pi$
$54$	−12.6928	+	9.90908i	−1.72727	+	1.34846i
$55$	2.01909	−	6.79481i	0.272254	−	0.916212i
$56$	−3.57521	+	1.58701i	−0.477757	+	0.212073i
$57$	−23.9372			−3.17056
$58$	1.48872	+	1.90694i	0.195479	+	0.250394i
$59$			3.40819i			0.443708i	0.975080	+	0.221854i	$0.0712109\pi$
$59$			3.40819i			0.443708i	−0.975080	+	0.221854i	$0.928789\pi$
$60$	−7.07490	+	11.9668i	−0.913365	+	1.54491i
$61$	−4.33987			−0.555663			−0.277832	−	0.960630i	$-0.589616\pi$
$61$	−4.33987			−0.555663			−0.277832	+	0.960630i	$0.589616\pi$
$62$	−6.83595	+	5.33674i	−0.868167	+	0.677767i
$63$	9.21459			1.16093
$64$	5.36630	−	5.93320i	0.670787	−	0.741650i
$65$	−2.98924	+	10.0597i	−0.370770	+	1.24775i
$66$	10.9849	−	8.57573i	1.35214	−	1.05560i
$67$	7.67601			0.937774			0.468887	−	0.883258i	$-0.344655\pi$
$67$	7.67601			0.937774			0.468887	+	0.883258i	$0.344655\pi$
$68$	−6.71199	−	4.79054i	−0.813948	−	0.580938i
$69$		−	15.3887i		−	1.85258i
$70$	4.07098	−	1.59780i	0.486576	−	0.190974i
$71$			12.8320i			1.52288i	0.648234	+	0.761441i	$0.275508\pi$
$71$			12.8320i			1.52288i	−0.648234	+	0.761441i	$0.724492\pi$
$72$	−17.2249	+	7.64599i	−2.02997	+	0.901089i
$73$	8.29467			0.970818			0.485409	−	0.874287i	$-0.338671\pi$
$73$	8.29467			0.970818			0.485409	+	0.874287i	$0.338671\pi$
$74$	4.44390	−	3.46930i	0.516593	−	0.403298i
$75$	8.48758	−	13.0205i	0.980061	−	1.50348i
$76$	−14.9407	−	3.73695i	−1.71382	−	0.428658i
$77$	−4.38407			−0.499611
$78$	−16.2630	+	12.6963i	−1.84142	+	1.43757i
$79$		−	9.37764i		−	1.05507i	−0.849534	−	0.527534i	$-0.823117\pi$
$79$		−	9.37764i		−	1.05507i	0.849534	−	0.527534i	$-0.176883\pi$
$80$	−6.28409	+	6.36476i	−0.702583	+	0.711602i
$81$	15.4059			1.71176
$82$	−5.29878	+	4.13669i	−0.585152	+	0.456821i
$83$	5.94240			0.652263			0.326131	−	0.945324i	$-0.394255\pi$
$83$	5.94240			0.652263			0.326131	+	0.945324i	$0.394255\pi$
$84$	8.34101	+	2.08624i	0.910079	+	0.227627i
$85$	7.26279	+	5.67907i	0.787760	+	0.615982i
$86$	9.04371	+	11.5843i	0.975208	+	1.24917i
$87$		−	5.31764i		−	0.570111i
$88$	8.19515	−	3.63777i	0.873606	−	0.387787i
$89$	−8.65552			−0.917483			−0.458742	−	0.888570i	$-0.651700\pi$
$89$	−8.65552			−0.917483			−0.458742	+	0.888570i	$0.651700\pi$
$90$	19.6134	−	7.69800i	2.06744	−	0.811441i
$91$	6.49058			0.680398
$92$	2.40240	−	9.60506i	0.250468	−	1.00140i
$93$	19.0625			1.97669
$94$	−6.41108	+	5.00505i	−0.661252	+	0.516231i
$95$	16.5055	+	4.90464i	1.69343	+	0.503206i
$96$	−17.3230	+	3.02131i	−1.76802	+	0.308361i
$97$	10.7647			1.09299			0.546493	−	0.837464i	$-0.315963\pi$
$97$	10.7647			1.09299			0.546493	+	0.837464i	$0.315963\pi$
$98$	4.42738	+	5.67114i	0.447233	+	0.572871i
$99$	−21.1218			−2.12283
$100$	7.33034	−	6.80192i	0.733034	−	0.680192i
$101$			10.3161i			1.02649i	0.858242	+	0.513245i	$0.171557\pi$
$101$			10.3161i			1.02649i	−0.858242	+	0.513245i	$0.828443\pi$
$102$	5.14942	+	17.3788i	0.509868	+	1.72076i
$103$			14.3112i			1.41013i	0.709145	+	0.705063i	$0.249081\pi$
$103$			14.3112i			1.41013i	−0.709145	+	0.705063i	$0.750919\pi$
$104$	−12.1329	+	5.38569i	−1.18973	+	0.528110i
$105$	−9.21459	−	2.73813i	−0.899252	−	0.267214i
$106$	0.745543	+	0.954984i	0.0724136	+	0.0927562i
$107$			3.91968i			0.378930i	0.981887	+	0.189465i	$0.0606754\pi$
$107$			3.91968i			0.378930i	−0.981887	+	0.189465i	$0.939325\pi$
$108$	22.0921	+	5.52563i	2.12581	+	0.531704i
$109$	0.706273			0.0676487			0.0338243	−	0.999428i	$-0.489231\pi$
$109$	0.706273			0.0676487			0.0338243	+	0.999428i	$0.489231\pi$
$110$	−9.33158	+	3.66251i	−0.889731	+	0.349207i
$111$	−12.3921			−1.17621
$112$	4.88047	+	2.60431i	0.461161	+	0.246084i
$113$	−1.50130			−0.141231			−0.0706153	−	0.997504i	$-0.522496\pi$
$113$	−1.50130			−0.141231			−0.0706153	+	0.997504i	$0.522496\pi$
$114$	20.8316	+	26.6837i	1.95106	+	2.49916i
$115$	−3.15308	+	10.6110i	−0.294026	+	0.989484i
$116$	0.830162	−	3.31908i	0.0770786	−	0.308169i
$117$	31.2707			2.89098
$118$	3.79924	−	2.96602i	0.349749	−	0.273044i
$119$	2.08741	−	5.30629i	0.191353	−	0.486427i
$120$	19.4969	−	2.52760i	1.77981	−	0.230737i
$121$	−0.950762			−0.0864329
$122$	3.77682	+	4.83782i	0.341938	+	0.437996i
$123$	14.7760			1.33231
$124$	11.8981	+	2.97594i	1.06849	+	0.267248i
$125$	−8.52034	+	7.23904i	−0.762083	+	0.647480i
$126$	−8.01911	−	10.2719i	−0.714399	−	0.915091i
$127$			10.0514i			0.891917i	0.895054	+	0.445958i	$0.147137\pi$
$127$			10.0514i			0.891917i	−0.895054	+	0.445958i	$0.852863\pi$
$128$	−11.2841	−	0.818582i	−0.997379	−	0.0723531i
$129$		−	32.3036i		−	2.84417i
$130$	13.8153	−	5.42232i	1.21168	−	0.475569i
$131$	−16.3077			−1.42481			−0.712405	−	0.701769i	$-0.752394\pi$
$131$	−16.3077			−1.42481			−0.712405	+	0.701769i	$0.752394\pi$
$132$	−19.1194	−	4.78211i	−1.66413	−	0.416229i
$133$		−	10.6495i		−	0.923429i
$134$	−6.68014	−	8.55675i	−0.577076	−	0.739190i
$135$	−24.4059	−	7.25223i	−2.10052	−	0.624173i
$136$	0.500992	+	11.6511i	0.0429597	+	0.999077i
$137$		−	7.51003i		−	0.641625i	−0.947143	−	0.320812i	$-0.896044\pi$
$137$		−	7.51003i		−	0.641625i	0.947143	−	0.320812i	$-0.103956\pi$
$138$	−17.1544	+	13.3922i	−1.46028	+	1.14002i
$139$	21.7915			1.84833			0.924167	−	0.381989i	$-0.124761\pi$
$139$	21.7915			1.84833			0.924167	+	0.381989i	$0.124761\pi$
$140$	−5.32396	−	3.14758i	−0.449957	−	0.266019i
$141$	17.8777			1.50558
$142$	14.3044	−	11.1672i	1.20040	−	0.937134i
$143$	−14.8778			−1.24415
$144$	23.5134	+	12.5472i	1.95945	+	1.04560i
$145$	−1.08956	+	3.66670i	−0.0904834	+	0.304503i
$146$	−7.21854	−	9.24639i	−0.597410	−	0.765237i
$147$		−	15.8144i		−	1.30435i
$148$	−7.73472	−	1.93459i	−0.635790	−	0.159023i
$149$			16.2760i			1.33338i	0.745335	+	0.666691i	$0.232290\pi$
$149$			16.2760i			1.33338i	−0.745335	+	0.666691i	$0.767710\pi$
$150$	−21.9009	+	1.86984i	−1.78820	+	0.152672i
$151$	−2.67240			−0.217477			−0.108739	−	0.994070i	$-0.534681\pi$
$151$	−2.67240			−0.217477			−0.108739	+	0.994070i	$0.534681\pi$
$152$	8.83664	+	19.9072i	0.716746	+	1.61468i
$153$	10.0569	−	25.5650i	0.813050	−	2.06681i
$154$	3.81529	+	4.88709i	0.307445	+	0.393813i
$155$	−13.1443	−	3.90584i	−1.05577	−	0.313725i
$156$	28.3061	+	7.07988i	2.26630	+	0.566844i
$157$	−7.44951			−0.594536			−0.297268	−	0.954794i	$-0.596075\pi$
$157$	−7.44951			−0.594536			−0.297268	+	0.954794i	$0.596075\pi$
$158$	−10.4536	+	8.16101i	−0.831646	+	0.649255i
$159$		−	2.66304i		−	0.211193i
$160$	12.5639	+	1.46612i	0.993260	+	0.115907i
$161$	6.84633			0.539566
$162$	−13.4071	−	17.1735i	−1.05336	−	1.34928i
$163$			3.76177i			0.294644i	0.989089	+	0.147322i	$0.0470654\pi$
$163$			3.76177i			0.294644i	−0.989089	+	0.147322i	$0.952935\pi$
$164$	9.22265	+	2.30675i	0.720168	+	0.180127i
$165$	21.1218	+	6.27638i	1.64433	+	0.488616i
$166$	−5.17144	−	6.62422i	−0.401382	−	0.514139i
$167$	14.6443			1.13321			0.566606	−	0.823989i	$-0.308256\pi$
$167$	14.6443			1.13321			0.566606	+	0.823989i	$0.308256\pi$
$168$	−4.93326	−	11.1136i	−0.380609	−	0.857435i
$169$	9.02650			0.694346
$170$	0.0101492	−	13.0384i	0.000778411	−	1.00000i
$171$		−	51.3079i		−	3.92361i
$172$	5.04307	−	20.1627i	0.384530	−	1.53740i
$173$		−	0.791181i		−	0.0601524i	−0.999548	−	0.0300762i	$-0.990425\pi$
$173$		−	0.791181i		−	0.0601524i	0.999548	−	0.0300762i	$-0.00957499\pi$
$174$	−5.92778	+	4.62774i	−0.449384	+	0.350828i
$175$	5.79275	+	3.77607i	0.437891	+	0.285444i
$176$	−11.1871	−	5.96965i	−0.843259	−	0.449979i
$177$	−10.5944			−0.796327
$178$	7.53257	+	9.64865i	0.564590	+	0.723197i
$179$		−	3.76938i		−	0.281736i	−0.990028	−	0.140868i	$-0.955011\pi$
$179$		−	3.76938i		−	0.281736i	0.990028	−	0.140868i	$-0.0449894\pi$
$180$	−25.6501	−	15.1646i	−1.91185	−	1.13030i
$181$	−19.7192			−1.46571			−0.732857	−	0.680383i	$-0.761813\pi$
$181$	−19.7192			−1.46571			−0.732857	+	0.680383i	$0.761813\pi$
$182$	−5.64851	−	7.23530i	−0.418695	−	0.536316i
$183$		−	13.4906i		−	0.997253i
$184$	−12.7979	+	5.68087i	−0.943471	+	0.418800i
$185$	8.54481	+	2.53910i	0.628227	+	0.186678i
$186$	−16.5894	−	21.2497i	−1.21639	−	1.55811i
$187$	−4.78480	+	12.1632i	−0.349899	+	0.889459i
$188$	11.1586	+	2.79098i	0.813828	+	0.203553i
$189$			15.7469i			1.14542i
$190$	−8.89675	−	22.6677i	−0.645438	−	1.64449i
$191$	4.29510			0.310783			0.155391	−	0.987853i	$-0.450336\pi$
$191$	4.29510			0.310783			0.155391	+	0.987853i	$0.450336\pi$
$192$	18.4435	+	16.6813i	1.33105	+	1.20387i
$193$	2.32215			0.167152			0.0835759	−	0.996501i	$-0.473366\pi$
$193$	2.32215			0.167152			0.0835759	+	0.996501i	$0.473366\pi$
$194$	−9.36808	−	11.9998i	−0.672589	−	0.861535i
$195$	−31.2707	−	9.29214i	−2.23934	−	0.665424i
$196$	2.46885	−	9.87075i	0.176347	−	0.705054i
$197$			7.58033i			0.540076i	0.962850	+	0.270038i	$0.0870363\pi$
$197$			7.58033i			0.540076i	−0.962850	+	0.270038i	$0.912964\pi$
$198$	18.3815	+	23.5454i	1.30632	+	1.67330i
$199$		−	0.856138i		−	0.0606900i	−0.999539	−	0.0303450i	$-0.990339\pi$
$199$		−	0.856138i		−	0.0606900i	0.999539	−	0.0303450i	$-0.00966060\pi$
$200$	−13.9617	−	2.25197i	−0.987240	−	0.159238i
$201$			23.8611i			1.68303i
$202$	11.4998	−	8.97771i	0.809120	−	0.631670i
$203$	2.36578			0.166045
$204$	14.8915	−	20.8644i	1.04261	−	1.46080i
$205$	−10.1886	−	3.02755i	−0.711601	−	0.211453i
$206$	15.9533	−	12.4545i	1.11152	−	0.867747i
$207$	32.9847			2.29259
$208$	16.5624	+	8.83802i	1.14840	+	0.612806i
$209$			24.4110i			1.68854i
$210$	4.96681	+	12.6548i	0.342743	+	0.873261i
$211$	8.34696			0.574628			0.287314	−	0.957836i	$-0.407238\pi$
$211$	8.34696			0.574628			0.287314	+	0.957836i	$0.407238\pi$
$212$	0.415740	−	1.66217i	0.0285531	−	0.114159i
$213$	−39.8887			−2.73313
$214$	4.36943	−	3.41115i	0.298688	−	0.233182i
$215$	−6.61888	+	22.2745i	−0.451404	+	1.51911i
$216$	−13.0663	−	29.4357i	−0.889047	−	2.00284i
$217$			8.48079i			0.575714i
$218$	−0.614643	−	0.787310i	−0.0416289	−	0.0533234i
$219$			25.7842i			1.74233i
$220$	12.2037	+	7.21493i	0.822771	+	0.486430i
$221$	7.08386	−	18.0075i	0.476512	−	1.21131i
$222$	10.7844	+	13.8140i	0.723802	+	0.927134i
$223$			2.03912i			0.136550i	0.997667	+	0.0682749i	$0.0217495\pi$
$223$			2.03912i			0.136550i	−0.997667	+	0.0682749i	$0.978250\pi$
$224$	−1.34416	−	7.70688i	−0.0898105	−	0.514938i
$225$	27.9087	+	18.1926i	1.86058	+	1.21284i
$226$	1.30653	+	1.67356i	0.0869089	+	0.111324i
$227$		−	1.48744i		−	0.0987248i	−0.998781	−	0.0493624i	$-0.984281\pi$
$227$		−	1.48744i		−	0.0987248i	0.998781	−	0.0493624i	$-0.0157189\pi$
$228$	11.6164	−	46.4437i	0.769315	−	3.07581i
$229$		−	12.6208i		−	0.834006i	−0.908905	−	0.417003i	$-0.863080\pi$
$229$		−	12.6208i		−	0.834006i	0.908905	−	0.417003i	$-0.136920\pi$
$230$	14.5725	−	5.71952i	0.960885	−	0.377134i
$231$		−	13.6280i		−	0.896656i
$232$	−4.42237	+	1.96306i	−0.290343	+	0.128881i
$233$	3.82345			0.250482			0.125241	−	0.992126i	$-0.460030\pi$
$233$	3.82345			0.250482			0.125241	+	0.992126i	$0.460030\pi$
$234$	−27.2137	−	34.8587i	−1.77902	−	2.27879i
$235$	−12.3273	−	3.66308i	−0.804146	−	0.238953i
$236$	−6.61267	−	1.65395i	−0.430448	−	0.107663i
$237$	29.1506			1.89354
$238$	−7.73172	+	2.29094i	−0.501173	+	0.148500i
$239$	2.65346			0.171638			0.0858190	−	0.996311i	$-0.472649\pi$
$239$	2.65346			0.171638			0.0858190	+	0.996311i	$0.472649\pi$
$240$	−19.7850	−	19.5343i	−1.27712	−	1.26093i
$241$		−	17.4604i		−	1.12473i	−0.826890	−	0.562363i	$-0.809892\pi$
$241$		−	17.4604i		−	1.12473i	0.826890	−	0.562363i	$-0.190108\pi$
$242$	0.827413	+	1.05985i	0.0531881	+	0.0681299i
$243$			13.7306i			0.880817i
$244$	2.10608	−	8.42035i	0.134828	−	0.539057i
$245$	−3.24030	+	10.9046i	−0.207015	+	0.696666i
$246$	−12.8590	−	16.4714i	−0.819860	−	1.05018i
$247$		−	36.1403i		−	2.29955i
$248$	−7.03711	−	15.8532i	−0.446857	−	1.00668i
$249$			18.4721i			1.17062i
$250$	15.4846	+	3.19810i	0.979331	+	0.202265i
$251$			5.05359i			0.318980i	0.987200	+	0.159490i	$0.0509849\pi$
$251$			5.05359i			0.318980i	−0.987200	+	0.159490i	$0.949015\pi$
$252$	−4.47172	+	17.8784i	−0.281692	+	1.12624i
$253$	−15.6933			−0.986627
$254$	11.2047	−	8.74734i	0.703044	−	0.548857i
$255$	−17.6535	+	22.5766i	−1.10551	+	1.41380i
$256$	8.90758	+	13.2912i	0.556724	+	0.830698i
$257$			6.10715i			0.380953i	0.981692	+	0.190477i	$0.0610034\pi$
$257$			6.10715i			0.380953i	−0.981692	+	0.190477i	$0.938997\pi$
$258$	−36.0101	+	28.1126i	−2.24189	+	1.75021i
$259$		−	5.51318i		−	0.342572i
$260$	−18.0674	−	10.6816i	−1.12049	−	0.662448i
$261$	11.3980			0.705520
$262$	14.1920	+	18.1788i	0.876782	+	1.12309i
$263$			18.6270i			1.14859i	0.818649	+	0.574294i	$0.194723\pi$
$263$			18.6270i			1.14859i	−0.818649	+	0.574294i	$0.805277\pi$
$264$	11.3081	+	25.4748i	0.695965	+	1.56787i
$265$	−0.545646	+	1.83626i	−0.0335188	+	0.112800i
$266$	−11.8714	+	9.26786i	−0.727883	+	0.568249i
$267$		−	26.9059i		−	1.64661i
$268$	−3.72507	+	14.8932i	−0.227545	+	0.909749i
$269$	22.7079			1.38452			0.692262	−	0.721647i	$-0.256614\pi$
$269$	22.7079			1.38452			0.692262	+	0.721647i	$0.256614\pi$
$270$	13.1552	+	33.5175i	0.800597	+	2.03981i
$271$	22.2596			1.35217			0.676087	−	0.736822i	$-0.263674\pi$
$271$	22.2596			1.35217			0.676087	+	0.736822i	$0.263674\pi$
$272$	12.5520	−	10.6980i	0.761076	−	0.648663i
$273$			20.1761i			1.22112i
$274$	−8.37172	+	6.53569i	−0.505754	+	0.394836i
$275$	−13.2783	−	8.65558i	−0.800709	−	0.521951i
$276$	29.8576	+	7.46792i	1.79722	+	0.449516i
$277$			22.2912i			1.33935i	0.742655	+	0.669674i	$0.233566\pi$
$277$			22.2912i			1.33935i	−0.742655	+	0.669674i	$0.766434\pi$
$278$	−18.9644	−	24.2919i	−1.13741	−	1.45693i
$279$			40.8593i			2.44618i
$280$	1.12451	+	8.67404i	0.0672025	+	0.518373i
$281$	15.8092			0.943098			0.471549	−	0.881840i	$-0.343695\pi$
$281$	15.8092			0.943098			0.471549	+	0.881840i	$0.343695\pi$
$282$	−15.5583	−	19.9290i	−0.926484	−	1.18675i
$283$			22.8987i			1.36118i	0.732662	+	0.680592i	$0.238278\pi$
$283$			22.8987i			1.36118i	−0.732662	+	0.680592i	$0.761722\pi$
$284$	−24.8971	−	6.22722i	−1.47737	−	0.369518i
$285$	−15.2462	+	51.3079i	−0.903107	+	3.03922i
$286$	12.9476	+	16.5849i	0.765608	+	0.980685i
$287$			6.57375i			0.388036i
$288$	−6.47598	−	37.1307i	−0.381601	−	2.18795i
$289$	−12.4436	−	11.5826i	−0.731975	−	0.681332i
$290$	5.03562	−	1.97641i	0.295702	−	0.116059i
$291$			33.4622i			1.96159i
$292$	−4.02529	+	16.0936i	−0.235563	+	0.941805i
$293$	2.83599			0.165680			0.0828400	−	0.996563i	$-0.473601\pi$
$293$	2.83599			0.165680			0.0828400	+	0.996563i	$0.473601\pi$
$294$	−17.6289	+	13.7626i	−1.02814	+	0.802653i
$295$	7.30524	+	2.17076i	0.425328	+	0.126387i
$296$	4.57467	+	10.3058i	0.265897	+	0.599013i
$297$		−	36.0952i		−	2.09446i
$298$	18.1435	−	14.1644i	1.05102	−	0.820521i
$299$	23.2338			1.34364
$300$	21.1439	+	22.7866i	1.22075	+	1.31558i
$301$	14.3717			0.828369
$302$	2.32569	+	2.97903i	0.133829	+	0.171424i
$303$	−32.0679			−1.84225
$304$	14.5011	−	27.1750i	0.831695	−	1.55859i
$305$	−2.76417	+	9.30224i	−0.158276	+	0.532645i
$306$	−37.2504	+	11.0375i	−2.12946	+	0.630969i
$307$	−2.85382			−0.162876			−0.0814380	−	0.996678i	$-0.525951\pi$
$307$	−2.85382			−0.162876			−0.0814380	+	0.996678i	$0.525951\pi$
$308$	2.12753	−	8.50610i	0.121227	−	0.484680i
$309$	−44.4868			−2.53077
$310$	7.08498	+	18.0515i	0.402400	+	1.02526i
$311$		−	1.91623i		−	0.108659i	−0.998523	−	0.0543297i	$-0.982698\pi$
$311$		−	1.91623i		−	0.108659i	0.998523	−	0.0543297i	$-0.0173022\pi$
$312$	−16.7415	−	37.7153i	−0.947803	−	2.13521i
$313$	−12.2883			−0.694578			−0.347289	−	0.937758i	$-0.612898\pi$
$313$	−12.2883			−0.694578			−0.347289	+	0.937758i	$0.612898\pi$
$314$	6.48303	+	8.30426i	0.365858	+	0.468637i
$315$	5.86901	−	19.7509i	0.330681	−	1.11284i
$316$	18.1948	+	4.55085i	1.02354	+	0.256005i
$317$			4.56223i			0.256240i	0.991759	+	0.128120i	$0.0408943\pi$
$317$			4.56223i			0.256240i	−0.991759	+	0.128120i	$0.959106\pi$
$318$	−2.96859	+	2.31754i	−0.166470	+	0.129961i
$319$	−5.42289			−0.303624
$320$	−9.29951	−	15.2813i	−0.519859	−	0.854252i
$321$	−12.1844			−0.680069
$322$	−5.95810	−	7.63187i	−0.332032	−	0.425307i
$323$	−29.5460	−	11.6229i	−1.64398	−	0.646718i
$324$	−7.47627	+	29.8909i	−0.415348	+	1.66061i
$325$	19.6583	+	12.8145i	1.09045	+	0.710821i
$326$	4.19339	−	3.27373i	0.232250	−	0.181315i
$327$			2.19547i			0.121410i
$328$	−5.45470	−	12.2883i	−0.301185	−	0.678510i
$329$			7.95369i			0.438501i
$330$	−11.3850	−	29.0075i	−0.626725	−	1.59681i
$331$			29.9051i			1.64373i	0.569681	+	0.821866i	$0.307067\pi$
$331$			29.9051i			1.64373i	−0.569681	+	0.821866i	$0.692933\pi$
$332$	−2.88377	+	11.5296i	−0.158267	+	0.632770i
$333$		−	26.5618i		−	1.45558i
$334$	−12.7444	−	16.3246i	−0.697342	−	0.893242i
$335$	4.88904	−	16.4530i	0.267117	−	0.898926i
$336$	−8.09557	+	15.1711i	−0.441649	+	0.827649i
$337$	28.1199			1.53179			0.765895	−	0.642966i	$-0.222296\pi$
$337$	28.1199			1.53179			0.765895	+	0.642966i	$0.222296\pi$
$338$	−7.85542	−	10.0622i	−0.427279	−	0.547311i
$339$		−	4.66684i		−	0.253468i
$340$	−14.5432	+	11.3355i	−0.788718	+	0.614755i
$341$		−	19.4398i		−	1.05273i
$342$	−57.1949	+	44.6513i	−3.09275	+	2.41447i
$343$	16.7164			0.902603
$344$	−26.8650	+	11.9252i	−1.44846	+	0.642962i
$345$	−32.9847	−	9.80144i	−1.77584	−	0.527692i
$346$	−0.881960	+	0.688535i	−0.0474145	+	0.0370159i
$347$		−	17.8743i		−	0.959543i	−0.877394	−	0.479771i	$-0.840720\pi$
$347$		−	17.8743i		−	0.959543i	0.877394	−	0.479771i	$-0.159280\pi$
$348$	10.3174	+	2.58058i	0.553073	+	0.138334i
$349$		−	30.7262i		−	1.64474i	−0.568955	−	0.822369i	$-0.692652\pi$
$349$		−	30.7262i		−	1.64474i	0.568955	−	0.822369i	$-0.307348\pi$
$350$	−0.831880	−	9.74358i	−0.0444659	−	0.520816i
$351$			53.4387i			2.85235i
$352$	3.08111	+	17.6659i	0.164224	+	0.941593i
$353$			12.4620i			0.663287i	0.943405	+	0.331643i	$0.107603\pi$
$353$			12.4620i			0.663287i	−0.943405	+	0.331643i	$0.892397\pi$
$354$	9.21994	+	11.8100i	0.490035	+	0.627697i
$355$	27.5047	+	8.17305i	1.45980	+	0.433780i
$356$	4.20041	−	16.7937i	0.222621	−	0.890065i
$357$	16.4947	+	6.48877i	0.872994	+	0.343422i
$358$	−4.20187	+	3.28035i	−0.222076	+	0.173372i
$359$	31.4652			1.66067			0.830335	−	0.557265i	$-0.188149\pi$
$359$	31.4652			1.66067			0.830335	+	0.557265i	$0.188149\pi$
$360$	5.41775	+	41.7904i	0.285541	+	2.20255i
$361$	−40.2976			−2.12093
$362$	17.1608	+	21.9817i	0.901954	+	1.15533i
$363$		−	2.95547i		−	0.155122i
$364$	−3.14979	+	12.5932i	−0.165094	+	0.660064i
$365$	5.28308	−	17.7791i	0.276529	−	0.930601i
$366$	−15.0385	+	11.7404i	−0.786075	+	0.613678i
$367$	−16.3289			−0.852360			−0.426180	−	0.904638i	$-0.640141\pi$
$367$	−16.3289			−0.852360			−0.426180	+	0.904638i	$0.640141\pi$
$368$	17.4702	+	9.32243i	0.910697	+	0.485965i
$369$			31.6714i			1.64875i
$370$	−4.60579	−	11.7349i	−0.239444	−	0.610069i
$371$	1.18477			0.0615101
$372$	−9.25079	+	36.9857i	−0.479631	+	1.91762i
$373$	−12.0595			−0.624415			−0.312207	−	0.950014i	$-0.601068\pi$
$373$	−12.0595			−0.624415			−0.312207	+	0.950014i	$0.601068\pi$
$374$	17.7228	−	5.25134i	0.916424	−	0.271540i
$375$	−22.5027	−	26.4857i	−1.16204	−	1.36772i
$376$	−6.59973	−	14.8679i	−0.340355	−	0.766751i
$377$	8.02855			0.413491
$378$	17.5536	−	13.7039i	0.902862	−	0.704853i
$379$	−22.3559			−1.14834			−0.574172	−	0.818735i	$-0.694676\pi$
$379$	−22.3559			−1.14834			−0.574172	+	0.818735i	$0.694676\pi$
$380$	−17.5261	+	29.6444i	−0.899068	+	1.52073i
$381$	−31.2450			−1.60073
$382$	−3.73786	−	4.78792i	−0.191246	−	0.244971i
$383$		−	23.7458i		−	1.21335i	−0.794949	−	0.606676i	$-0.792502\pi$
$383$		−	23.7458i		−	1.21335i	0.794949	−	0.606676i	$-0.207498\pi$
$384$	2.54458	−	35.0768i	0.129853	−	1.79000i
$385$	−2.79232	+	9.39698i	−0.142310	+	0.478914i
$386$	−2.02088	−	2.58859i	−0.102860	−	0.131756i
$387$	69.2407			3.51970
$388$	−5.22395	+	20.8859i	−0.265206	+	1.06032i
$389$			19.1770i			0.972314i	0.873871	+	0.486157i	$0.161602\pi$
$389$			19.1770i			0.972314i	−0.873871	+	0.486157i	$0.838398\pi$
$390$	16.8554	+	42.9453i	0.853508	+	2.17462i
$391$	7.47213	−	18.9945i	0.377882	−	0.960591i
$392$	−13.1519	+	5.83802i	−0.664270	+	0.294864i
$393$		−	50.6929i		−	2.55712i
$394$	8.45010	−	6.59688i	0.425710	−	0.332346i
$395$	−20.1004	−	5.97286i	−1.01136	−	0.300527i
$396$	10.2502	−	40.9813i	0.515090	−	2.05939i
$397$		−	33.6020i		−	1.68643i	−0.537573	−	0.843217i	$-0.680659\pi$
$397$		−	33.6020i		−	1.68643i	0.537573	−	0.843217i	$-0.319341\pi$
$398$	−0.954371	+	0.745065i	−0.0478383	+	0.0373467i
$399$	33.1043			1.65729
$400$	9.63997	+	17.5234i	0.481998	+	0.876172i
$401$			26.1862i			1.30767i	0.756635	+	0.653837i	$0.226842\pi$
$401$			26.1862i			1.30767i	−0.756635	+	0.653837i	$0.773158\pi$
$402$	26.5989	−	20.7654i	1.32663	−	1.03568i
$403$			28.7805i			1.43366i
$404$	−20.0156	−	5.00627i	−0.995814	−	0.249071i
$405$	9.81239	−	33.0215i	0.487581	−	1.64085i
$406$	−2.05885	−	2.63723i	−0.102179	−	0.130884i
$407$			12.6374i			0.626413i
$408$	−36.2179	+	1.55735i	−1.79305	+	0.0771002i
$409$	−17.7503			−0.877698			−0.438849	−	0.898561i	$-0.644614\pi$
$409$	−17.7503			−0.877698			−0.438849	+	0.898561i	$0.644614\pi$
$410$	5.49180	+	13.9924i	0.271221	+	0.691033i
$411$	23.3451			1.15153
$412$	−27.7671	−	6.94505i	−1.36799	−	0.342158i
$413$		−	4.71340i		−	0.231931i
$414$	−28.7053	−	36.7693i	−1.41079	−	1.80711i
$415$	3.78486	−	12.7372i	0.185792	−	0.625243i
$416$	−4.56156	−	26.1542i	−0.223649	−	1.28231i
$417$			67.7396i			3.31722i
$418$	27.2119	−	21.2440i	1.33098	−	1.03908i
$419$	−6.75433			−0.329970			−0.164985	−	0.986296i	$-0.552758\pi$
$419$	−6.75433			−0.329970			−0.164985	+	0.986296i	$0.552758\pi$
$420$	9.78432	−	16.5497i	0.477426	−	0.807541i
$421$		−	16.0671i		−	0.783061i	−0.920165	−	0.391531i	$-0.871946\pi$
$421$		−	16.0671i		−	0.783061i	0.920165	−	0.391531i	$-0.128054\pi$
$422$	−7.26405	−	9.30468i	−0.353608	−	0.452945i
$423$			38.3198i			1.86317i
$424$	−2.21469	+	0.983085i	−0.107555	+	0.0477428i
$425$	16.7986	−	11.9502i	0.814851	−	0.579670i
$426$	34.7136	+	44.4655i	1.68188	+	2.15436i
$427$	6.00188			0.290451
$428$	−7.60509	−	1.90217i	−0.367606	−	0.0919449i
$429$		−	46.2481i		−	2.23288i
$430$	30.5904	−	12.0063i	1.47520	−	0.578995i
$431$		−	16.5890i		−	0.799062i	−0.916720	−	0.399531i	$-0.869173\pi$
$431$		−	16.5890i		−	0.799062i	0.916720	−	0.399531i	$-0.130827\pi$
$432$	−21.4420	+	40.1822i	−1.03163	+	1.93327i
$433$		−	1.90705i		−	0.0916468i	−0.998950	−	0.0458234i	$-0.985409\pi$
$433$		−	1.90705i		−	0.0916468i	0.998950	−	0.0458234i	$-0.0145911\pi$
$434$	9.45387	−	7.38052i	0.453801	−	0.354276i
$435$	−11.3980	−	3.38694i	−0.546493	−	0.162391i
$436$	−0.342745	+	1.37033i	−0.0164145	+	0.0656270i
$437$		−	38.1211i		−	1.82358i
$438$	28.7426	−	22.4390i	1.37338	−	1.07218i
$439$		−	2.19597i		−	0.104808i	−0.998626	−	0.0524041i	$-0.983312\pi$
$439$		−	2.19597i		−	0.104808i	0.998626	−	0.0524041i	$-0.0166884\pi$
$440$	−2.57763	−	19.8828i	−0.122884	−	0.947875i
$441$	33.8971			1.61415
$442$	−26.2385	+	7.77457i	−1.24804	+	0.369799i
$443$	0.504565			0.0239726			0.0119863	−	0.999928i	$-0.496185\pi$
$443$	0.504565			0.0239726			0.0119863	+	0.999928i	$0.496185\pi$
$444$	6.01374	−	24.0436i	0.285399	−	1.14106i
$445$	−5.51292	+	18.5526i	−0.261337	+	0.879476i
$446$	2.27309	−	1.77457i	0.107634	−	0.0840285i
$447$	−50.5943			−2.39303
$448$	−7.42139	+	8.20540i	−0.350628	+	0.387669i
$449$			21.6668i			1.02252i	0.859426	+	0.511260i	$0.170821\pi$
$449$			21.6668i			1.02252i	−0.859426	+	0.511260i	$0.829179\pi$
$450$	−4.00789	−	46.9433i	−0.188934	−	2.21293i
$451$		−	15.0685i		−	0.709546i
$452$	0.728562	−	2.91287i	0.0342687	−	0.137010i
$453$		−	8.30724i		−	0.390308i
$454$	−1.65811	+	1.29446i	−0.0778188	+	0.0607521i
$455$	4.13401	−	13.9122i	0.193806	−	0.652212i
$456$	−61.8819	+	27.4689i	−2.89789	+	1.28635i
$457$		−	32.0636i		−	1.49987i	−0.661511	−	0.749935i	$-0.730085\pi$
$457$		−	32.0636i		−	1.49987i	0.661511	−	0.749935i	$-0.269915\pi$
$458$	−14.0689	+	10.9834i	−0.657397	+	0.513221i
$459$	43.6881	+	17.1862i	2.03919	+	0.802185i
$460$	−19.0577	−	11.2671i	−0.888570	−	0.525332i
$461$		−	5.37334i		−	0.250261i	−0.992140	−	0.125131i	$-0.960065\pi$
$461$		−	5.37334i		−	0.250261i	0.992140	−	0.125131i	$-0.0399350\pi$
$462$	−15.1917	+	11.8599i	−0.706780	+	0.551774i
$463$		−	9.07513i		−	0.421757i	−0.977512	−	0.210878i	$-0.932368\pi$
$463$		−	9.07513i		−	0.421757i	0.977512	−	0.210878i	$-0.0676324\pi$
$464$	6.03691	+	3.22141i	0.280257	+	0.149550i
$465$	12.1414	−	40.8593i	0.563044	−	1.89481i
$466$	−3.32740	−	4.26215i	−0.154139	−	0.197440i
$467$	4.23729			0.196078			0.0980391	−	0.995183i	$-0.468743\pi$
$467$	4.23729			0.196078			0.0980391	+	0.995183i	$0.468743\pi$
$468$	−15.1753	+	60.6725i	−0.701478	+	2.80459i
$469$	−10.6156			−0.490185
$470$	6.64463	+	16.9296i	0.306494	+	0.780904i
$471$		−	23.1570i		−	1.06702i
$472$	3.91104	+	8.81078i	0.180020	+	0.405549i
$473$	−32.9430			−1.51472
$474$	−25.3687	−	32.4954i	−1.16522	−	1.49256i
$475$	21.0256	−	32.2547i	0.964720	−	1.47995i
$476$	9.28243	+	6.62513i	0.425460	+	0.303663i
$477$	5.70805			0.261354
$478$	−2.30921	−	2.95791i	−0.105621	−	0.135292i
$479$			37.2651i			1.70268i	0.524611	+	0.851342i	$0.324211\pi$
$479$			37.2651i			1.70268i	−0.524611	+	0.851342i	$0.675789\pi$
$480$	−4.55746	+	39.0551i	−0.208019	+	1.78261i
$481$		−	18.7096i		−	0.853084i
$482$	−19.4638	+	15.1952i	−0.886554	+	0.692121i
$483$			21.2820i			0.968363i
$484$	0.461393	−	1.84470i	0.0209724	−	0.0838499i
$485$	6.85629	−	23.0734i	0.311328	−	1.04771i
$486$	15.3060	−	11.9492i	0.694295	−	0.542027i
$487$	−21.5041			−0.974446			−0.487223	−	0.873278i	$-0.661990\pi$
$487$	−21.5041			−0.974446			−0.487223	+	0.873278i	$0.661990\pi$
$488$	−11.2193	+	4.98018i	−0.507875	+	0.225442i
$489$	−11.6936			−0.528801
$490$	14.9756	−	5.87773i	0.676531	−	0.265529i
$491$			12.5827i			0.567848i	0.958847	+	0.283924i	$0.0916363\pi$
$491$			12.5827i			0.567848i	−0.958847	+	0.283924i	$0.908364\pi$
$492$	−7.17060	+	28.6689i	−0.323276	+	1.29249i
$493$	2.58203	−	6.56364i	0.116289	−	0.295611i
$494$	−40.2870	+	31.4515i	−1.81260	+	1.41507i
$495$	−13.4530	+	45.2734i	−0.604669	+	2.03489i
$496$	−11.5480	+	21.6410i	−0.518522	+	0.971708i
$497$		−	17.7462i		−	0.796027i
$498$	20.5916	−	16.0756i	0.922730	−	0.720363i
$499$	18.1299			0.811606			0.405803	−	0.913961i	$-0.366992\pi$
$499$	18.1299			0.811606			0.405803	+	0.913961i	$0.366992\pi$
$500$	−9.91060	−	20.0444i	−0.443216	−	0.896415i
$501$			45.5222i			2.03378i
$502$	5.63344	−	4.39795i	0.251433	−	0.196290i
$503$	−30.9286			−1.37904			−0.689520	−	0.724267i	$-0.742179\pi$
$503$	−30.9286			−1.37904			−0.689520	+	0.724267i	$0.742179\pi$
$504$	23.8214	−	10.5741i	1.06109	−	0.471009i
$505$	22.1119	+	6.57059i	0.983968	+	0.292387i
$506$	13.6573	+	17.4939i	0.607139	+	0.777699i
$507$			28.0591i			1.24615i
$508$	−19.5020	−	4.87781i	−0.865262	−	0.216418i
$509$		−	14.9794i		−	0.663949i	−0.943288	−	0.331975i	$-0.892285\pi$
$509$		−	14.9794i		−	0.663949i	0.943288	−	0.331975i	$-0.107715\pi$
$510$	40.5302	+	0.0315492i	1.79471	+	0.00139702i
$511$	−11.4712			−0.507457
$512$	7.06424	−	21.4964i	0.312198	−	0.950017i
$513$	87.6803			3.87118
$514$	6.80788	−	5.31482i	0.300283	−	0.234427i
$515$	30.6752	+	9.11518i	1.35171	+	0.401663i
$516$	62.6764	+	15.6765i	2.75918	+	0.690120i
$517$		−	18.2316i		−	0.801824i
$518$	−6.14576	+	4.79791i	−0.270029	+	0.210808i
$519$	2.45941			0.107956
$520$	3.81616	+	29.4363i	0.167350	+	1.29087i
$521$		−	9.75940i		−	0.427567i	−0.976881	−	0.213784i	$-0.931421\pi$
$521$		−	9.75940i		−	0.427567i	0.976881	−	0.213784i	$-0.0685787\pi$
$522$	−9.91927	−	12.7058i	−0.434155	−	0.556119i
$523$	21.4234			0.936781			0.468390	−	0.883522i	$-0.344834\pi$
$523$	21.4234			0.936781			0.468390	+	0.883522i	$0.344834\pi$
$524$	7.91391	−	31.6407i	0.345721	−	1.38223i
$525$	−11.7380	+	18.0069i	−0.512289	+	0.785886i
$526$	20.7642	−	16.2104i	0.905363	−	0.706805i
$527$	23.5291	+	9.25600i	1.02495	+	0.403198i
$528$	18.5568	−	34.7754i	0.807581	−	1.51340i
$529$	1.50719			0.0655302
$530$	2.52180	−	0.989773i	0.109540	−	0.0429930i
$531$		−	22.7085i		−	0.985466i
$532$	20.6625	+	5.16807i	0.895833	+	0.224064i
$533$			22.3087i			0.966299i
$534$	−29.9931	+	23.4152i	−1.29793	+	1.01327i
$535$	8.40160	+	2.49655i	0.363233	+	0.107935i
$536$	19.8438	−	8.80854i	0.857124	−	0.380471i
$537$	11.7172			0.505635
$538$	−19.7618	−	25.3134i	−0.851992	−	1.09134i
$539$	−16.1274			−0.694655
$540$	25.9149	−	43.8336i	1.11520	−	1.88630i
$541$	−37.7525			−1.62310			−0.811552	−	0.584280i	$-0.801377\pi$
$541$	−37.7525			−1.62310			−0.811552	+	0.584280i	$0.801377\pi$
$542$	−19.3717	−	24.8136i	−0.832085	−	1.06584i
$543$		−	61.2975i		−	2.63053i
$544$	−22.8490	−	4.68210i	−0.979644	−	0.200744i
$545$	0.449843	−	1.51385i	0.0192692	−	0.0648463i
$546$	22.4911	−	17.5585i	0.962531	−	0.751436i
$547$			16.0703i			0.687115i	0.939132	+	0.343558i	$0.111632\pi$
$547$			16.0703i			0.687115i	−0.939132	+	0.343558i	$0.888368\pi$
$548$	14.5712	+	3.64452i	0.622450	+	0.155686i
$549$	28.9162			1.23412
$550$	1.90685	+	22.3344i	0.0813084	+	0.952342i
$551$		−	13.1729i		−	0.561186i
$552$	−17.6591	−	39.7825i	−0.751623	−	1.69325i
$553$			12.9689i			0.551495i
$554$	24.8489	−	19.3992i	1.05573	−	0.824193i
$555$	−7.89286	+	26.5618i	−0.335033	+	1.12748i
$556$	−10.5752	+	42.2806i	−0.448486	+	1.79310i
$557$	−42.2565			−1.79047			−0.895233	−	0.445598i	$-0.852991\pi$
$557$	−42.2565			−1.79047			−0.895233	+	0.445598i	$0.852991\pi$
$558$	45.5475	−	35.5583i	1.92818	−	1.50530i
$559$	48.7718			2.06283
$560$	8.69067	−	8.80223i	0.367248	−	0.371962i
$561$	−37.8095	−	14.8737i	−1.59632	−	0.627967i
$562$	−13.7581	−	17.6231i	−0.580352	−	0.743387i
$563$	−9.77006			−0.411759			−0.205879	−	0.978577i	$-0.566005\pi$
$563$	−9.77006			−0.411759			−0.205879	+	0.978577i	$0.566005\pi$
$564$	−8.67583	+	34.6869i	−0.365318	+	1.46058i
$565$	−0.956217	+	3.21795i	−0.0402284	+	0.135380i
$566$	25.5260	−	19.9279i	1.07294	−	0.837630i
$567$	−21.3057			−0.894757
$568$	14.7253	+	33.1731i	0.617860	+	1.39191i
$569$	−40.1848			−1.68463			−0.842317	−	0.538983i	$-0.818809\pi$
$569$	−40.1848			−1.68463			−0.842317	+	0.538983i	$0.818809\pi$
$570$	70.4631	−	27.6558i	2.95137	−	1.15837i
$571$	−20.3017			−0.849599			−0.424800	−	0.905287i	$-0.639655\pi$
$571$	−20.3017			−0.849599			−0.424800	+	0.905287i	$0.639655\pi$
$572$	7.22001	−	28.8664i	0.301884	−	1.20697i
$573$			13.3514i			0.557764i
$574$	7.32802	−	5.72089i	0.305865	−	0.238785i
$575$	20.7358	+	13.5169i	0.864743	+	0.563693i
$576$	−35.7553	+	39.5325i	−1.48980	+	1.64719i
$577$		−	5.50626i		−	0.229229i	−0.993410	−	0.114614i	$-0.963437\pi$
$577$		−	5.50626i		−	0.229229i	0.993410	−	0.114614i	$-0.0365632\pi$
$578$	−2.08246	+	23.9513i	−0.0866189	+	0.996242i
$579$			7.21845i			0.299989i
$580$	−6.58549	−	3.89341i	−0.273448	−	0.161665i
$581$	−8.21812			−0.340945
$582$	37.3017	−	29.1209i	1.54620	−	1.20710i
$583$	−2.71575			−0.112475
$584$	21.4432	−	9.51848i	0.887326	−	0.393877i
$585$	19.9171	−	67.0269i	0.823472	−	2.77122i
$586$	−2.46805	−	3.16138i	−0.101954	−	0.130596i
$587$	41.6032			1.71715			0.858574	−	0.512690i	$-0.171351\pi$
$587$	41.6032			1.71715			0.858574	+	0.512690i	$0.171351\pi$
$588$	30.6835	+	7.67450i	1.26537	+	0.316491i
$589$	47.2220			1.94575
$590$	−3.93764	−	10.0326i	−0.162110	−	0.413034i
$591$	−23.5637			−0.969280
$592$	7.50712	−	14.0683i	0.308541	−	0.578204i
$593$		−	5.38912i		−	0.221305i	−0.993859	−	0.110652i	$-0.964706\pi$
$593$		−	5.38912i		−	0.221305i	0.993859	−	0.110652i	$-0.0352940\pi$
$594$	−40.2368	+	31.4123i	−1.65093	+	1.28886i
$595$	−10.0442	−	7.85395i	−0.411771	−	0.321980i
$596$	−31.5792	−	7.89853i	−1.29353	−	0.323536i
$597$	2.66133			0.108921
$598$	−20.2195	−	25.8996i	−0.826836	−	1.05911i
$599$	2.90781			0.118810			0.0594050	−	0.998234i	$-0.481080\pi$
$599$	2.90781			0.118810			0.0594050	+	0.998234i	$0.481080\pi$
$600$	7.00031	−	43.4003i	0.285786	−	1.77181i
$601$		−	21.9861i		−	0.896833i	−0.893825	−	0.448417i	$-0.851988\pi$
$601$		−	21.9861i		−	0.896833i	0.893825	−	0.448417i	$-0.148012\pi$
$602$	−12.5071	−	16.0207i	−0.509752	−	0.652953i
$603$	−51.1447			−2.08277
$604$	1.29688	−	5.18508i	0.0527694	−	0.210978i
$605$	−0.605565	+	2.03790i	−0.0246197	+	0.0828524i
$606$	27.9075	+	35.7473i	1.13366	+	1.45213i
$607$	−29.4172			−1.19401			−0.597003	−	0.802239i	$-0.703642\pi$
$607$	−29.4172			−1.19401			−0.597003	+	0.802239i	$0.703642\pi$
$608$	−42.9128	+	7.48444i	−1.74034	+	0.303534i
$609$			7.35410i			0.298003i
$610$	12.7751	−	5.01406i	0.517250	−	0.203013i
$611$			26.9917i			1.09197i
$612$	44.7215	+	31.9190i	1.80776	+	1.29025i
$613$	−12.5726			−0.507803			−0.253901	−	0.967230i	$-0.581714\pi$
$613$	−12.5726			−0.507803			−0.253901	+	0.967230i	$0.581714\pi$
$614$	2.48357	+	3.18126i	0.100229	+	0.128385i
$615$	9.41121	−	31.6714i	0.379497	−	1.27712i
$616$	−11.3336	+	5.03090i	−0.456644	+	0.202701i
$617$	−31.1520			−1.25413			−0.627065	−	0.778967i	$-0.715744\pi$
$617$	−31.1520			−1.25413			−0.627065	+	0.778967i	$0.715744\pi$
$618$	38.7152	+	49.5912i	1.55735	+	1.99485i
$619$	−2.39088			−0.0960975			−0.0480487	−	0.998845i	$-0.515300\pi$
$619$	−2.39088			−0.0960975			−0.0480487	+	0.998845i	$0.515300\pi$
$620$	13.9570	−	23.6075i	0.560526	−	0.948099i
$621$			56.3677i			2.26196i
$622$	−2.13610	+	1.66762i	−0.0856496	+	0.0668655i
$623$	11.9703			0.479579
$624$	−27.4732	+	51.4847i	−1.09981	+	2.06104i
$625$	10.0896	+	22.8736i	0.403585	+	0.914942i
$626$	10.6941	+	13.6983i	0.427421	+	0.547494i
$627$	−75.8822			−3.03044
$628$	3.61515	−	14.4538i	0.144260	−	0.576768i
$629$	−15.2958	−	6.01712i	−0.609883	−	0.239918i
$630$	−27.1247	+	10.6461i	−1.08067	+	0.424149i
$631$	−12.5987			−0.501548			−0.250774	−	0.968046i	$-0.580685\pi$
$631$	−12.5987			−0.501548			−0.250774	+	0.968046i	$0.580685\pi$
$632$	−10.7612	−	24.2429i	−0.428059	−	0.964330i
$633$			25.9467i			1.03129i
$634$	5.08569	−	3.97034i	0.201979	−	0.157682i
$635$	21.5445	+	6.40198i	0.854968	+	0.254055i
$636$	5.16691	+	1.29234i	0.204881	+	0.0512445i
$637$	23.8764			0.946019
$638$	4.71934	+	6.04511i	0.186840	+	0.239328i
$639$		−	85.4990i		−	3.38229i
$640$	−8.94168	+	23.6653i	−0.353451	+	0.935453i
$641$			1.97957i			0.0781885i	0.999236	+	0.0390942i	$0.0124473\pi$
$641$			1.97957i			0.0781885i	−0.999236	+	0.0390942i	$0.987553\pi$
$642$	10.6037	+	13.5825i	0.418493	+	0.536057i
$643$		−	33.0730i		−	1.30427i	−0.758102	−	0.652136i	$-0.773873\pi$
$643$		−	33.0730i		−	1.30427i	0.758102	−	0.652136i	$-0.226127\pi$
$644$	−3.32243	+	13.2835i	−0.130922	+	0.523441i
$645$	−69.2407	−	20.5750i	−2.72635	−	0.810139i
$646$	12.7562	+	43.0511i	0.501887	+	1.69382i
$647$			35.0894i			1.37951i	0.724044	+	0.689753i	$0.242281\pi$
$647$			35.0894i			1.37951i	−0.724044	+	0.689753i	$0.757719\pi$
$648$	39.8269	−	17.6789i	1.56455	−	0.694492i
$649$			10.8041i			0.424100i
$650$	−2.82308	−	33.0659i	−0.110730	−	1.29695i
$651$	−26.3628			−1.03324
$652$	−7.29870	−	1.82554i	−0.285839	−	0.0714936i
$653$		−	7.84685i		−	0.307071i	−0.988143	−	0.153535i	$-0.950934\pi$
$653$		−	7.84685i		−	0.307071i	0.988143	−	0.153535i	$-0.0490659\pi$
$654$	2.44737	−	1.91063i	0.0956999	−	0.0747117i
$655$	−10.3868	+	34.9545i	−0.405845	+	1.36579i
$656$	−8.95127	+	16.7746i	−0.349488	+	0.654940i
$657$	−55.2668			−2.15616
$658$	8.86629	−	6.92180i	0.345644	−	0.269840i
$659$			26.4942i			1.03207i	0.856569	+	0.516033i	$0.172592\pi$
$659$			26.4942i			1.03207i	−0.856569	+	0.516033i	$0.827408\pi$
$660$	−22.4278	+	37.9354i	−0.873001	+	1.47663i
$661$		−	0.681758i		−	0.0265173i	−0.999912	−	0.0132587i	$-0.995780\pi$
$661$		−	0.681758i		−	0.0265173i	0.999912	−	0.0132587i	$-0.00422049\pi$
$662$	33.3364	−	26.0253i	1.29565	−	1.01150i
$663$	55.9767	+	22.0204i	2.17396	+	0.855200i
$664$	15.3622	−	6.81915i	0.596167	−	0.264634i
$665$	−22.8266	−	6.78294i	−0.885176	−	0.263031i
$666$	−29.6094	+	23.1157i	−1.14734	+	0.895715i
$667$	8.46859			0.327905
$668$	−7.10670	+	28.4134i	−0.274966	+	1.09935i
$669$	−6.33867			−0.245067
$670$	−22.5956	+	8.86846i	−0.872944	+	0.342618i
$671$	−13.7576			−0.531107
$672$	23.9570	−	4.17836i	0.924163	−	0.161184i
$673$	−17.0552			−0.657431			−0.328715	−	0.944429i	$-0.606616\pi$
$673$	−17.0552			−0.657431			−0.328715	+	0.944429i	$0.606616\pi$
$674$	−24.4717	−	31.3464i	−0.942615	−	1.20742i
$675$	−31.0894	+	47.6933i	−1.19663	+	1.83572i
$676$	−4.38044	+	17.5135i	−0.168479	+	0.673596i
$677$			20.0992i			0.772476i	0.922399	+	0.386238i	$0.126226\pi$
$677$			20.0992i			0.772476i	−0.922399	+	0.386238i	$0.873774\pi$
$678$	−5.20231	+	4.06137i	−0.199793	+	0.155976i
$679$	−14.8871			−0.571316
$680$	25.2926	+	6.34706i	0.969926	+	0.243399i
$681$	4.62374			0.177182
$682$	−21.6703	+	16.9177i	−0.829800	+	0.647814i
$683$		−	21.4520i		−	0.820836i	−0.911897	−	0.410418i	$-0.865383\pi$
$683$		−	21.4520i		−	0.820836i	0.911897	−	0.410418i	$-0.134617\pi$
$684$	99.5491	+	24.8990i	3.80636	+	0.952039i
$685$	−16.0973	−	4.78333i	−0.615045	−	0.182762i
$686$	−14.5477	−	18.6345i	−0.555434	−	0.711468i
$687$	39.2321			1.49680
$688$	36.6731	+	19.5694i	1.39815	+	0.746078i
$689$	4.02064			0.153174
$690$	17.7793	+	45.2991i	0.676845	+	1.72451i
$691$	1.68049			0.0639289			0.0319645	−	0.999489i	$-0.489824\pi$
$691$	1.68049			0.0639289			0.0319645	+	0.999489i	$0.489824\pi$
$692$	1.53507	+	0.383950i	0.0583547	+	0.0145956i
$693$	29.2107			1.10962
$694$	−19.9252	+	15.5553i	−0.756350	+	0.590472i
$695$	13.8796	−	46.7088i	0.526483	−	1.77177i
$696$	−6.10221	−	13.7470i	−0.231304	−	0.521080i
$697$	18.2382	+	7.17464i	0.690822	+	0.271759i
$698$	−34.2517	+	26.7399i	−1.29645	+	1.01212i
$699$			11.8853i			0.449543i
$700$	−10.1376	+	9.40680i	−0.383165	+	0.355544i
$701$			40.1735i			1.51733i	0.651479	+	0.758667i	$0.274149\pi$
$701$			40.1735i			1.51733i	−0.651479	+	0.758667i	$0.725851\pi$
$702$	59.5702	−	46.5057i	2.24833	−	1.75524i
$703$	−30.6980			−1.15780
$704$	17.0114	−	18.8086i	0.641143	−	0.708874i
$705$	11.3868	−	38.3198i	0.428851	−	1.44321i
$706$	13.8919	−	10.8452i	0.522829	−	0.408166i
$707$		−	14.2668i		−	0.536558i
$708$	5.14135	−	20.5557i	0.193224	−	0.772529i
$709$	−36.6335			−1.37580			−0.687900	−	0.725806i	$-0.741467\pi$
$709$	−36.6335			−1.37580			−0.687900	+	0.725806i	$0.741467\pi$
$710$	−14.8255	−	37.7732i	−0.556390	−	1.41760i
$711$			62.4826i			2.34328i
$712$	−22.3761	+	9.93257i	−0.838579	+	0.372239i
$713$			30.3580i			1.13691i
$714$	−7.12146	−	24.0343i	−0.266514	−	0.899460i
$715$	−9.47606	+	31.8897i	−0.354385	+	1.19261i
$716$	7.31346	+	1.82923i	0.273317	+	0.0683615i
$717$			8.24835i			0.308040i
$718$	−27.3830	−	35.0755i	−1.02192	−	1.30901i
$719$			22.4385i			0.836817i	0.908259	+	0.418408i	$0.137412\pi$
$719$			22.4385i			0.836817i	−0.908259	+	0.418408i	$0.862588\pi$
$720$	41.8705	−	42.4080i	1.56042	−	1.58045i
$721$		−	19.7919i		−	0.737089i
$722$	35.0695	+	44.9214i	1.30515	+	1.67180i
$723$	54.2762			2.01856
$724$	9.56945	−	38.2597i	0.355646	−	1.42191i
$725$	7.16537	+	4.67083i	0.266115	+	0.173470i
$726$	−3.29458	+	2.57203i	−0.122273	+	0.0954571i
$727$		−	29.6872i		−	1.10104i	−0.834823	−	0.550519i	$-0.814430\pi$
$727$		−	29.6872i		−	1.10104i	0.834823	−	0.550519i	$-0.185570\pi$
$728$	16.7793	−	7.44821i	0.621882	−	0.276049i
$729$	3.53576			0.130954
$730$	−24.4167	+	9.58323i	−0.903704	+	0.354691i
$731$	15.6853	−	39.8728i	0.580143	−	1.47475i
$732$	26.1749	+	6.54681i	0.967451	+	0.241977i
$733$	30.5411			1.12806			0.564030	−	0.825754i	$-0.309250\pi$
$733$	30.5411			1.12806			0.564030	+	0.825754i	$0.309250\pi$
$734$	14.2104	+	18.2024i	0.524516	+	0.671864i
$735$	−33.8971	−	10.0726i	−1.25031	−	0.371532i
$736$	−4.81157	−	27.5877i	−0.177357	−	1.01689i
$737$	24.3334			0.896330
$738$	35.3054	−	27.5625i	1.29961	−	1.01459i
$739$		−	0.177926i		−	0.00654510i	−0.999995	−	0.00327255i	$-0.998958\pi$
$739$		−	0.177926i		−	0.00654510i	0.999995	−	0.00327255i	$-0.00104169\pi$
$740$	−9.07313	+	15.3467i	−0.333535	+	0.564156i
$741$	112.343			4.12702
$742$	−1.03106	−	1.32071i	−0.0378514	−	0.0484847i
$743$	39.2895			1.44139			0.720696	−	0.693251i	$-0.243822\pi$
$743$	39.2895			1.44139			0.720696	+	0.693251i	$0.243822\pi$
$744$	49.2800	−	21.8750i	1.80669	−	0.801978i
$745$	34.8866	+	10.3666i	1.27815	+	0.379803i
$746$	10.4949	+	13.4431i	0.384245	+	0.492188i
$747$	−39.5938			−1.44866
$748$	−21.2774	−	15.1863i	−0.777977	−	0.555264i
$749$		−	5.42078i		−	0.198071i
$750$	−9.94136	+	48.1342i	−0.363007	+	1.75761i
$751$			3.75737i			0.137108i	0.997647	+	0.0685541i	$0.0218386\pi$
$751$			3.75737i			0.137108i	−0.997647	+	0.0685541i	$0.978161\pi$
$752$	−10.8303	+	20.2959i	−0.394940	+	0.740116i
$753$	−15.7092			−0.572476
$754$	−6.98694	−	8.94974i	−0.254449	−	0.325930i
$755$	−1.70212	+	5.72813i	−0.0619466	+	0.208468i
$756$	−30.5525	−	7.64175i	−1.11119	−	0.277928i
$757$	−20.7558			−0.754384			−0.377192	−	0.926135i	$-0.623110\pi$
$757$	−20.7558			−0.754384			−0.377192	+	0.926135i	$0.623110\pi$
$758$	19.4555	+	24.9210i	0.706655	+	0.905171i
$759$		−	48.7829i		−	1.77071i
$760$	48.2980	−	6.26141i	1.75195	−	0.227125i
$761$	30.9329			1.12132			0.560659	−	0.828047i	$-0.310548\pi$
$761$	30.9329			1.12132			0.560659	+	0.828047i	$0.310548\pi$
$762$	27.1913	+	34.8300i	0.985039	+	1.26176i
$763$	−0.976750			−0.0353607
$764$	−2.08436	+	8.33349i	−0.0754094	+	0.301495i
$765$	−48.3915	−	37.8393i	−1.74960	−	1.36808i
$766$	−26.4704	+	20.6651i	−0.956413	+	0.746659i
$767$		−	15.9954i		−	0.577562i
$768$	−41.3159	+	27.6895i	−1.49086	+	0.999157i
$769$	26.4764			0.954763			0.477382	−	0.878696i	$-0.341586\pi$
$769$	26.4764			0.954763			0.477382	+	0.878696i	$0.341586\pi$
$770$	12.9052	−	5.06512i	0.465072	−	0.182534i
$771$	−18.9842			−0.683700
$772$	−1.12691	+	4.50550i	−0.0405583	+	0.162156i
$773$	16.9821			0.610805			0.305403	−	0.952223i	$-0.401209\pi$
$773$	16.9821			0.610805			0.305403	+	0.952223i	$0.401209\pi$
$774$	−60.2576	−	77.1854i	−2.16591	−	2.77437i
$775$	−16.7438	+	25.6862i	−0.601457	+	0.922676i
$776$	27.8286	−	12.3529i	0.998988	−	0.443443i
$777$	17.1379			0.614817
$778$	21.3774	−	16.6891i	0.766417	−	0.598332i
$779$	36.6034			1.31145
$780$	33.2042	−	56.1631i	1.18890	−	2.01096i
$781$			40.6782i			1.45558i
$782$	−27.6766	+	8.20069i	−0.989713	+	0.293256i
$783$			19.4781i			0.696092i
$784$	17.9534	+	9.58030i	0.641194	+	0.342154i
$785$	−4.74478	+	15.9676i	−0.169349	+	0.569907i
$786$	−56.5093	+	44.1161i	−2.01562	+	1.57357i
$787$			51.6950i			1.84273i	0.388703	+	0.921363i	$0.372923\pi$
$787$			51.6950i			1.84273i	−0.388703	+	0.921363i	$0.627077\pi$
$788$	−14.7076	−	3.67864i	−0.523937	−	0.131046i
$789$	−57.9024			−2.06138
$790$	10.8344	+	27.6046i	0.385472	+	0.982129i
$791$	2.07625			0.0738228
$792$	−54.6038	+	24.2382i	−1.94026	+	0.861267i
$793$	20.3680			0.723290
$794$	−37.4574	+	29.2425i	−1.32931	+	1.03778i
$795$	−5.70805	−	1.69616i	−0.202444	−	0.0601564i
$796$	1.66111	+	0.415473i	0.0588764	+	0.0147260i
$797$	11.8705			0.420476			0.210238	−	0.977650i	$-0.432576\pi$
$797$	11.8705			0.420476			0.210238	+	0.977650i	$0.432576\pi$
$798$	−28.8094	−	36.9026i	−1.01984	−	1.30634i
$799$	22.0667	+	8.68071i	0.780665	+	0.307102i
$800$	11.1448	−	25.9960i	0.394027	−	0.919099i
$801$	57.6711			2.03771
$802$	29.1907	−	22.7888i	1.03076	−	0.804701i
$803$	26.2945			0.927914
$804$	−46.2960	−	11.5795i	−1.63273	−	0.408376i
$805$	4.36060	−	14.6747i	0.153691	−	0.517214i
$806$	32.0828	−	25.0466i	1.13007	−	0.882229i
$807$			70.5880i			2.48481i
$808$	11.8382	+	26.6690i	0.416465	+	0.938211i
$809$			1.09134i			0.0383693i	0.999816	+	0.0191847i	$0.00610704\pi$
$809$			1.09134i			0.0383693i	−0.999816	+	0.0191847i	$0.993893\pi$
$810$	−45.3497	+	17.7991i	−1.59343	+	0.625398i
$811$	5.52216			0.193909			0.0969546	−	0.995289i	$-0.469090\pi$
$811$	5.52216			0.193909			0.0969546	+	0.995289i	$0.469090\pi$
$812$	−1.14808	+	4.59017i	−0.0402898	+	0.161083i
$813$			69.1945i			2.42676i
$814$	14.0874	−	10.9979i	0.493764	−	0.385475i
$815$	8.06312	+	2.39597i	0.282439	+	0.0839270i
$816$	33.2551	+	39.0182i	1.16416	+	1.36591i
$817$		−	80.0230i		−	2.79965i
$818$	15.4475	+	19.7870i	0.540108	+	0.691836i
$819$	−43.2463			−1.51115
$820$	10.8185	−	18.2990i	0.377799	−	0.639027i
$821$	14.8268			0.517458			0.258729	−	0.965950i	$-0.416696\pi$
$821$	14.8268			0.517458			0.258729	+	0.965950i	$0.416696\pi$
$822$	−20.3164	−	26.0237i	−0.708615	−	0.907681i
$823$	−25.8182			−0.899966			−0.449983	−	0.893037i	$-0.648570\pi$
$823$	−25.8182			−0.899966			−0.449983	+	0.893037i	$0.648570\pi$
$824$	16.4227	+	36.9971i	0.572112	+	1.28885i
$825$	26.9061	−	41.2758i	0.936749	−	1.43704i
$826$	−5.25421	+	4.10190i	−0.182817	+	0.142723i
$827$			26.3763i			0.917193i	0.888645	+	0.458596i	$0.151648\pi$
$827$			26.3763i			0.917193i	−0.888645	+	0.458596i	$0.848352\pi$
$828$	−16.0070	+	63.9979i	−0.556283	+	2.22408i
$829$			9.59045i			0.333090i	0.986034	+	0.166545i	$0.0532611\pi$
$829$			9.59045i			0.333090i	−0.986034	+	0.166545i	$0.946739\pi$
$830$	−17.4924	+	6.86553i	−0.607171	+	0.238306i
$831$	−69.2928			−2.40374
$832$	−25.1853	+	27.8459i	−0.873144	+	0.965384i
$833$	7.67882	−	19.5199i	0.266055	−	0.676324i
$834$	75.5119	−	58.9512i	2.61476	−	2.04131i
$835$	9.32734	−	31.3892i	0.322786	−	1.08627i
$836$	−47.3629	−	11.8463i	−1.63808	−	0.409714i
$837$	−69.8247			−2.41350
$838$	5.87803	+	7.52931i	0.203053	+	0.260096i
$839$			10.3436i			0.357099i	0.983931	+	0.178550i	$0.0571405\pi$
$839$			10.3436i			0.357099i	−0.983931	+	0.178550i	$0.942859\pi$
$840$	−26.9635	+	3.49558i	−0.930328	+	0.120609i
$841$	−26.0736			−0.899091
$842$	−17.9106	+	13.9826i	−0.617240	+	0.481871i
$843$			49.1433i			1.69258i
$844$	−4.05067	+	16.1950i	−0.139430	+	0.557456i
$845$	5.74921	−	19.3477i	0.197779	−	0.665582i
$846$	42.7166	−	33.3483i	1.46863	−	1.14654i
$847$	1.31487			0.0451795
$848$	3.02325	+	1.61326i	0.103819	+	0.0553996i
$849$	−71.1811			−2.44293
$850$	−27.9405	−	8.32624i	−0.958353	−	0.285588i
$851$		−	19.7350i		−	0.676509i
$852$	19.3575	−	77.3933i	0.663176	−	2.65145i
$853$		−	40.4041i		−	1.38341i	−0.722180	−	0.691705i	$-0.756860\pi$
$853$		−	40.4041i		−	1.38341i	0.722180	−	0.691705i	$-0.243140\pi$
$854$	−5.22321	−	6.69053i	−0.178735	−	0.228945i
$855$	−109.975	−	32.6793i	−3.76107	−	1.11761i
$856$	4.49800	+	10.1331i	0.153738	+	0.346342i
$857$	29.9227			1.02214			0.511071	−	0.859539i	$-0.329249\pi$
$857$	29.9227			1.02214			0.511071	+	0.859539i	$0.329249\pi$
$858$	−51.5546	+	40.2480i	−1.76004	+	1.37404i
$859$		−	7.12681i		−	0.243164i	−0.992581	−	0.121582i	$-0.961203\pi$
$859$		−	7.12681i		−	0.243164i	0.992581	−	0.121582i	$-0.0387967\pi$
$860$	−40.0055	−	23.6517i	−1.36418	−	0.806515i
$861$	−20.4347			−0.696412
$862$	−18.4924	+	14.4367i	−0.629852	+	0.491717i
$863$		−	19.4379i		−	0.661674i	−0.943688	−	0.330837i	$-0.892669\pi$
$863$		−	19.4379i		−	0.661674i	0.943688	−	0.330837i	$-0.107331\pi$
$864$	63.4529	−	11.0668i	2.15871	−	0.376502i
$865$	−1.69585	−	0.503923i	−0.0576605	−	0.0171339i
$866$	−2.12586	+	1.65963i	−0.0722396	+	0.0563965i
$867$	36.0049	−	38.6811i	1.22279	−	1.31368i
$868$	−16.4547	−	4.11562i	−0.558509	−	0.139693i
$869$		−	29.7276i		−	1.00844i
$870$	6.14372	+	15.6533i	0.208292	+	0.530698i
$871$	−36.0253			−1.22067
$872$	1.82584	−	0.810478i	0.0618308	−	0.0274462i
$873$	−71.7242			−2.42750
$874$	−42.4951	+	33.1754i	−1.43742	+	1.12217i
$875$	11.7833	−	10.0113i	0.398349	−	0.338445i
$876$	−50.0273	−	12.5127i	−1.69027	−	0.422766i
$877$		−	54.0672i		−	1.82572i	−0.408272	−	0.912860i	$-0.633869\pi$
$877$		−	54.0672i		−	1.82572i	0.408272	−	0.912860i	$-0.366131\pi$
$878$	−2.44794	+	1.91107i	−0.0826139	+	0.0644956i
$879$			8.81573i			0.297347i
$880$	−19.9209	+	20.1766i	−0.671534	+	0.680154i
$881$		−	42.3386i		−	1.42642i	−0.700948	−	0.713212i	$-0.747240\pi$
$881$		−	42.3386i		−	1.42642i	0.700948	−	0.713212i	$-0.252760\pi$
$882$	−29.4994	−	37.7864i	−0.993295	−	1.27233i
$883$	20.6175			0.693833			0.346917	−	0.937896i	$-0.387229\pi$
$883$	20.6175			0.693833			0.346917	+	0.937896i	$0.387229\pi$
$884$	31.5010	+	22.4831i	1.05949	+	0.756189i
$885$	−6.74787	+	22.7085i	−0.226827	+	0.763339i
$886$	−0.439104	−	0.562458i	−0.0147520	−	0.0188962i
$887$	−42.1816			−1.41632			−0.708159	−	0.706053i	$-0.750474\pi$
$887$	−42.1816			−1.41632			−0.708159	+	0.706053i	$0.750474\pi$
$888$	−32.0359	+	14.2205i	−1.07505	+	0.477208i
$889$		−	13.9007i		−	0.466215i
$890$	25.4790	−	10.0001i	0.854057	−	0.335205i
$891$	48.8374			1.63611
$892$	−3.95637	−	0.989561i	−0.132469	−	0.0331329i
$893$	44.2870			1.48201
$894$	44.0304	+	56.3995i	1.47260	+	1.88628i
$895$	−8.07943	−	2.40081i	−0.270065	−	0.0802503i
$896$	15.6054	+	1.13207i	0.521341	+	0.0378198i
$897$			72.2227i			2.41145i
$898$	24.1529	−	18.8558i	0.805991	−	0.629227i
$899$			10.4904i			0.349873i
$900$	−48.8416	+	45.3207i	−1.62805	+	1.51069i
$901$	1.29306	−	3.28702i	0.0430782	−	0.109507i
$902$	−16.7974	+	13.1135i	−0.559292	+	0.436632i
$903$			44.6747i			1.48668i
$904$	−3.88113	+	1.72281i	−0.129085	+	0.0572997i
$905$	−12.5596	+	42.2668i	−0.417496	+	1.40500i
$906$	−9.26040	+	7.22948i	−0.307656	+	0.240183i
$907$		−	8.18606i		−	0.271814i	−0.990722	−	0.135907i	$-0.956605\pi$
$907$		−	8.18606i		−	0.271814i	0.990722	−	0.135907i	$-0.0433948\pi$
$908$	2.88597	+	0.721835i	0.0957744	+	0.0239549i
$909$		−	68.7355i		−	2.27981i
$910$	−19.1061	+	7.49887i	−0.633361	+	0.248585i
$911$		−	56.9039i		−	1.88531i	−0.333770	−	0.942655i	$-0.608321\pi$
$911$		−	56.9039i		−	1.88531i	0.333770	−	0.942655i	$-0.391679\pi$
$912$	84.4742	+	45.0770i	2.79722	+	1.49265i
$913$	18.8377			0.623437
$914$	−35.7425	+	27.9037i	−1.18226	+	0.922973i
$915$	−28.9162	−	8.59250i	−0.955942	−	0.284059i
$916$	24.4873	+	6.12471i	0.809082	+	0.202366i
$917$	22.5529			0.744763
$918$	−18.8620	−	63.6574i	−0.622538	−	2.10101i
$919$	13.0090			0.429126			0.214563	−	0.976710i	$-0.431167\pi$
$919$	13.0090			0.429126			0.214563	+	0.976710i	$0.431167\pi$
$920$	4.02532	+	31.0497i	0.132711	+	1.02368i
$921$		−	8.87117i		−	0.292315i
$922$	−5.98987	+	4.67621i	−0.197266	+	0.154003i
$923$		−	60.2238i		−	1.98229i
$924$	26.4414	+	6.61349i	0.869860	+	0.217568i
$925$	10.8848	−	16.6980i	0.357890	−	0.549028i
$926$	−10.1164	+	7.89774i	−0.332446	+	0.259536i
$927$		−	95.3547i		−	3.13186i
$928$	−1.66266	−	9.53306i	−0.0545796	−	0.312938i
$929$		−	0.796980i		−	0.0261481i	−0.999915	−	0.0130740i	$-0.995838\pi$
$929$		−	0.796980i		−	0.0261481i	0.999915	−	0.0130740i	$-0.00416171\pi$
$930$	−56.1137	+	22.0238i	−1.84004	+	0.722190i
$931$		−	39.1756i		−	1.28393i
$932$	−1.85547	+	7.41837i	−0.0607779	+	0.242997i
$933$	5.95665			0.195012
$934$	−3.68755	−	4.72347i	−0.120660	−	0.154557i
$935$	23.0234	+	18.0030i	0.752947	+	0.588760i
$936$	80.8404	−	35.8845i	2.64235	−	1.17292i
$937$			15.8558i			0.517985i	0.965879	+	0.258992i	$0.0833905\pi$
$937$			15.8558i			0.517985i	−0.965879	+	0.258992i	$0.916610\pi$
$938$	9.23839	+	11.8337i	0.301644	+	0.386383i
$939$		−	38.1986i		−	1.24656i
$940$	13.0895	−	22.1402i	0.426933	−	0.722134i
$941$	−32.1862			−1.04924			−0.524620	−	0.851337i	$-0.675793\pi$
$941$	−32.1862			−1.04924			−0.524620	+	0.851337i	$0.675793\pi$
$942$	−25.8140	+	20.1527i	−0.841066	+	0.656609i
$943$			23.5315i			0.766290i
$944$	6.41809	−	12.0275i	0.208891	−	0.391461i
$945$	33.7524	+	10.0296i	1.09797	+	0.326262i
$946$	28.6690	+	36.7228i	0.932111	+	1.19396i
$947$			49.5549i			1.61032i	0.593058	+	0.805159i	$0.297920\pi$
$947$			49.5549i			1.61032i	−0.593058	+	0.805159i	$0.702080\pi$
$948$	−14.1464	+	56.5590i	−0.459455	+	1.83695i
$949$	−38.9289			−1.26368
$950$	−54.2534	+	4.63200i	−1.76021	+	0.150282i
$951$	−14.1818			−0.459876
$952$	−0.692854	−	16.1131i	−0.0224555	−	0.522228i
$953$			2.51887i			0.0815941i	0.999167	+	0.0407970i	$0.0129897\pi$
$953$			2.51887i			0.0815941i	−0.999167	+	0.0407970i	$0.987010\pi$
$954$	−4.96750	−	6.36299i	−0.160829	−	0.206009i
$955$	2.73566	−	9.20628i	0.0885238	−	0.297908i
$956$	−1.28769	+	5.14832i	−0.0416468	+	0.166509i
$957$		−	16.8572i		−	0.544916i
$958$	41.5408	−	32.4304i	1.34212	−	1.04778i
$959$			10.3861i			0.335384i
$960$	47.5024	−	28.9078i	1.53313	−	0.932995i
$961$	−6.60553			−0.213082
$962$	−20.8563	+	16.2822i	−0.672434	+	0.524961i
$963$		−	26.1166i		−	0.841595i
$964$	33.8773	+	8.47333i	1.09111	+	0.272907i
$965$	1.47903	−	4.97738i	0.0476118	−	0.160227i
$966$	23.7239	−	18.5209i	0.763302	−	0.595900i
$967$			19.8500i			0.638334i	0.947698	+	0.319167i	$0.103403\pi$
$967$			19.8500i			0.638334i	−0.947698	+	0.319167i	$0.896597\pi$
$968$	−2.45789	+	1.09104i	−0.0789996	+	0.0350673i
$969$	36.1302	−	91.8445i	1.16067	−	2.95047i
$970$	−31.6876	+	12.4369i	−1.01743	+	0.399326i
$971$		−	45.1544i		−	1.44907i	−0.689236	−	0.724537i	$-0.742054\pi$
$971$		−	45.1544i		−	1.44907i	0.689236	−	0.724537i	$-0.257946\pi$
$972$	−26.6405	−	6.66327i	−0.854494	−	0.213724i
$973$	−30.1369			−0.966145
$974$	18.7142	+	23.9715i	0.599643	+	0.768097i
$975$	−39.8342	+	61.1085i	−1.27572	+	1.95704i
$976$	15.3154	+	8.17257i	0.490233	+	0.261598i
$977$		−	22.4461i		−	0.718115i	−0.933315	−	0.359057i	$-0.883098\pi$
$977$		−	22.4461i		−	0.718115i	0.933315	−	0.359057i	$-0.116902\pi$
$978$	10.1765	+	13.0353i	0.325407	+	0.416822i
$979$	−27.4385			−0.876937
$980$	−19.5849	−	11.5788i	−0.625616	−	0.369870i
$981$	−4.70585			−0.150246
$982$	14.0264	−	10.9502i	0.447600	−	0.349436i
$983$	9.53411			0.304091			0.152045	−	0.988373i	$-0.451414\pi$
$983$	9.53411			0.304091			0.152045	+	0.988373i	$0.451414\pi$
$984$	38.1986	−	16.9561i	1.21773	−	0.540540i
$985$	16.2480	+	4.82811i	0.517704	+	0.153836i
$986$	−9.56379	+	2.83379i	−0.304573	+	0.0902463i
$987$	−24.7242			−0.786981
$988$	70.1205	+	17.5384i	2.23083	+	0.557971i
$989$	51.4450			1.63586
$990$	62.1757	−	24.4031i	1.97607	−	0.775581i
$991$		−	20.1528i		−	0.640176i	−0.947388	−	0.320088i	$-0.896287\pi$
$991$		−	20.1528i		−	0.640176i	0.947388	−	0.320088i	$-0.103713\pi$
$992$	34.1739	−	5.96027i	1.08502	−	0.189239i
$993$	−92.9607			−2.95002
$994$	−19.7824	+	15.4439i	−0.627460	+	0.489850i
$995$	−1.83508	−	0.545296i	−0.0581759	−	0.0172871i
$996$	−35.8401	−	8.96427i	−1.13564	−	0.284044i
$997$		−	57.3800i		−	1.81724i	−0.417622	−	0.908621i	$-0.637136\pi$
$997$		−	57.3800i		−	1.81724i	0.417622	−	0.908621i	$-0.362864\pi$
$998$	−15.7778	−	20.2101i	−0.499437	−	0.639740i
$999$	45.3915			1.43612

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.h.b.509.14	yes	40
5.4	even	2	inner	680.2.h.b.509.27	yes	40
8.5	even	2	inner	680.2.h.b.509.25	yes	40
17.16	even	2	inner	680.2.h.b.509.13	✓	40
40.29	even	2	inner	680.2.h.b.509.16	yes	40
85.84	even	2	inner	680.2.h.b.509.28	yes	40
136.101	even	2	inner	680.2.h.b.509.26	yes	40
680.509	even	2	inner	680.2.h.b.509.15	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.h.b.509.13	✓	40	17.16	even	2	inner
680.2.h.b.509.14	yes	40	1.1	even	1	trivial
680.2.h.b.509.15	yes	40	680.509	even	2	inner
680.2.h.b.509.16	yes	40	40.29	even	2	inner
680.2.h.b.509.25	yes	40	8.5	even	2	inner
680.2.h.b.509.26	yes	40	136.101	even	2	inner
680.2.h.b.509.27	yes	40	5.4	even	2	inner
680.2.h.b.509.28	yes	40	85.84	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+(-0.870262 - 1.11474i) q^{2} +3.10853i q^{3} +(-0.485287 + 1.94023i) q^{4} +(0.636925 - 2.14344i) q^{5} +(3.46520 - 2.70523i) q^{6} -1.38296 q^{7} +(2.58518 - 1.14754i) q^{8} -6.66293 q^{9} +(-2.94367 + 1.15535i) q^{10} +3.17005 q^{11} +(-6.03126 - 1.50853i) q^{12} -4.69324 q^{13} +(1.20354 + 1.54164i) q^{14} +(6.66293 + 1.97990i) q^{15} +(-3.52899 - 1.88314i) q^{16} +(-1.50938 + 3.83690i) q^{17} +(5.79850 + 7.42743i) q^{18} +7.70050i q^{19} +(3.84967 + 2.27596i) q^{20} -4.29898i q^{21} +(-2.75878 - 3.53378i) q^{22} -4.95047 q^{23} +(3.56716 + 8.03609i) q^{24} +(-4.18865 - 2.73042i) q^{25} +(4.08435 + 5.23174i) q^{26} -11.3863i q^{27} +(0.671134 - 2.68327i) q^{28} -1.71066 q^{29} +(-3.59143 - 9.15046i) q^{30} -6.13233i q^{31} +(0.971942 + 5.57273i) q^{32} +9.85419i q^{33} +(5.59069 - 1.65655i) q^{34} +(-0.880844 + 2.96430i) q^{35} +(3.23343 - 12.9276i) q^{36} +3.98650i q^{37} +(8.58404 - 6.70145i) q^{38} -14.5891i q^{39} +(-0.813118 - 6.27207i) q^{40} -4.75338i q^{41} +(-4.79224 + 3.74124i) q^{42} -10.3919 q^{43} +(-1.53839 + 6.15064i) q^{44} +(-4.24379 + 14.2816i) q^{45} +(4.30821 + 5.51849i) q^{46} -5.75119i q^{47} +(5.85378 - 10.9700i) q^{48} -5.08741 q^{49} +(0.601520 + 7.04544i) q^{50} +(-11.9271 - 4.69193i) q^{51} +(2.27757 - 9.10597i) q^{52} -0.856688 q^{53} +(-12.6928 + 9.90908i) q^{54} +(2.01909 - 6.79481i) q^{55} +(-3.57521 + 1.58701i) q^{56} -23.9372 q^{57} +(1.48872 + 1.90694i) q^{58} +3.40819i q^{59} +(-7.07490 + 11.9668i) q^{60} -4.33987 q^{61} +(-6.83595 + 5.33674i) q^{62} +9.21459 q^{63} +(5.36630 - 5.93320i) q^{64} +(-2.98924 + 10.0597i) q^{65} +(10.9849 - 8.57573i) q^{66} +7.67601 q^{67} +(-6.71199 - 4.79054i) q^{68} -15.3887i q^{69} +(4.07098 - 1.59780i) q^{70} +12.8320i q^{71} +(-17.2249 + 7.64599i) q^{72} +8.29467 q^{73} +(4.44390 - 3.46930i) q^{74} +(8.48758 - 13.0205i) q^{75} +(-14.9407 - 3.73695i) q^{76} -4.38407 q^{77} +(-16.2630 + 12.6963i) q^{78} -9.37764i q^{79} +(-6.28409 + 6.36476i) q^{80} +15.4059 q^{81} +(-5.29878 + 4.13669i) q^{82} +5.94240 q^{83} +(8.34101 + 2.08624i) q^{84} +(7.26279 + 5.67907i) q^{85} +(9.04371 + 11.5843i) q^{86} -5.31764i q^{87} +(8.19515 - 3.63777i) q^{88} -8.65552 q^{89} +(19.6134 - 7.69800i) q^{90} +6.49058 q^{91} +(2.40240 - 9.60506i) q^{92} +19.0625 q^{93} +(-6.41108 + 5.00505i) q^{94} +(16.5055 + 4.90464i) q^{95} +(-17.3230 + 3.02131i) q^{96} +10.7647 q^{97} +(4.42738 + 5.67114i) q^{98} -21.1218 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 12 q^{4} - 56 q^{9} + 56 q^{15} - 4 q^{16} - 36 q^{26} - 28 q^{30} + 24 q^{34} + 88 q^{36} + 8 q^{49} - 16 q^{50} - 88 q^{55} - 88 q^{60} - 132 q^{64} + 208 q^{66} + 72 q^{70} - 20 q^{76} - 56 q^{81}+ \cdots - 36 q^{94}+O(q^{100}) \) 40 * q + 12 * q^4 - 56 * q^9 + 56 * q^15 - 4 * q^16 - 36 * q^26 - 28 * q^30 + 24 * q^34 + 88 * q^36 + 8 * q^49 - 16 * q^50 - 88 * q^55 - 88 * q^60 - 132 * q^64 + 208 * q^66 + 72 * q^70 - 20 * q^76 - 56 * q^81 + 144 * q^84 + 256 * q^86 - 96 * q^89 - 36 * q^94

Introduction

L-functions

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