LMFDB - Embedded newform 680.2.h.b.509.27

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			509.27
Character	$\chi$	$=$	680.509
Dual form			680.2.h.b.509.26

$q$-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} +(-1.83508 + 2.57536i) 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} +(-4.46786 + 0.195600i) 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} +(8.00557 + 5.70440i) 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} +(-4.10625 - 4.81027i) 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} +(-6.68893 - 2.29307i) 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} +(0.608027 + 13.8884i) 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} +(-2.53785 + 3.56163i) 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} +(1.78868 - 8.76360i) q^{80} +15.4059 q^{81} +(5.29878 - 4.13669i) q^{82} -5.94240 q^{83} +(8.34101 + 2.08624i) q^{84} +(9.18551 + 0.791437i) q^{85} +(9.04371 + 11.5843i) q^{86} +5.31764i q^{87} +(-8.19515 + 3.63777i) q^{88} -8.65552 q^{89} +(12.2270 - 17.1594i) 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	$-0.645487\pi$
$3$		−	3.10853i		−	1.79471i	0.441311	−	0.897354i	$-0.354513\pi$
$4$	−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	$-0.415831\pi$
$7$	1.38296			0.522711			0.261356	+	0.965243i	$0.415831\pi$
$8$	−2.58518	+	1.14754i	−0.913999	+	0.405717i
$9$	−6.66293			−2.22098
$10$	−1.83508	+	2.57536i	−0.580304	+	0.814400i
$11$	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	$-0.274419\pi$
$13$	4.69324			1.30167			0.650835	+	0.759219i	$0.274419\pi$
$14$	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	$0.655311\pi$
$20$	−4.46786	+	0.195600i	−0.999043	+	0.0437374i
$21$		−	4.29898i		−	0.938114i
$22$	2.75878	+	3.53378i	0.588173	+	0.753405i
$23$	4.95047			1.03225			0.516123	−	0.856515i	$-0.327375\pi$
$23$	4.95047			1.03225			0.516123	+	0.856515i	$0.327375\pi$
$24$	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	$0.550772\pi$
$30$	8.00557	+	5.70440i	1.46161	+	1.04148i
$31$		−	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	$-0.893731\pi$
$37$		−	3.98650i		−	0.655376i	0.944786	−	0.327688i	$-0.106269\pi$
$38$	−8.58404	+	6.70145i	−1.39252	+	1.08712i
$39$		−	14.5891i		−	2.33612i
$40$	−4.10625	−	4.81027i	−0.649255	−	0.760571i
$41$		−	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	$-0.208843\pi$
$43$	10.3919			1.58475			0.792377	+	0.610031i	$0.208843\pi$
$44$	−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	$0.137777\pi$
$47$			5.75119i			0.838898i	−0.907779	+	0.419449i	$0.862223\pi$
$48$	−5.85378	+	10.9700i	−0.844921	+	1.58338i
$49$	−5.08741			−0.726773
$50$	−6.68893	−	2.29307i	−0.945958	−	0.324290i
$51$	−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	$-0.481261\pi$
$53$	0.856688			0.117675			0.0588376	+	0.998268i	$0.481261\pi$
$54$	−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	$0.928789\pi$
$60$	0.608027	+	13.8884i	0.0784959	+	1.79299i
$61$	−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	$-0.655345\pi$
$67$	−7.67601			−0.937774			−0.468887	+	0.883258i	$0.655345\pi$
$68$	6.71199	+	4.79054i	0.813948	+	0.580938i
$69$		−	15.3887i		−	1.85258i
$70$	−2.53785	+	3.56163i	−0.303331	+	0.425696i
$71$			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	$-0.661329\pi$
$73$	−8.29467			−0.970818			−0.485409	+	0.874287i	$0.661329\pi$
$74$	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	$-0.176883\pi$
$80$	1.78868	−	8.76360i	0.199981	−	0.979800i
$81$	15.4059			1.71176
$82$	5.29878	−	4.13669i	0.585152	−	0.456821i
$83$	−5.94240			−0.652263			−0.326131	−	0.945324i	$-0.605745\pi$
$83$	−5.94240			−0.652263			−0.326131	+	0.945324i	$0.605745\pi$
$84$	8.34101	+	2.08624i	0.910079	+	0.227627i
$85$	9.18551	+	0.791437i	0.996309	+	0.0858434i
$86$	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	$0.651700\pi$
$90$	12.2270	−	17.1594i	1.28884	−	1.80876i
$91$	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	$-0.684037\pi$
$97$	−10.7647			−1.09299			−0.546493	+	0.837464i	$0.684037\pi$
$98$	−4.42738	−	5.67114i	−0.447233	−	0.572871i
$99$	−21.1218			−2.12283
$100$	−3.26495	−	9.45199i	−0.326495	−	0.945199i
$101$			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	$-0.750919\pi$
$103$		−	14.3112i		−	1.41013i	0.709145	−	0.705063i	$-0.249081\pi$
$104$	−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	$-0.939325\pi$
$107$		−	3.91968i		−	0.378930i	0.981887	−	0.189465i	$-0.0606754\pi$
$108$	−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	$0.489231\pi$
$110$	−5.81731	+	8.16402i	−0.554659	+	0.778409i
$111$	−12.3921			−1.17621
$112$	−4.88047	−	2.60431i	−0.461161	−	0.246084i
$113$	1.50130			0.141231			0.0706153	−	0.997504i	$-0.477504\pi$
$113$	1.50130			0.141231			0.0706153	+	0.997504i	$0.477504\pi$
$114$	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
$120$	−14.9529	+	12.7644i	−1.36500	+	1.16522i
$121$	−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	$-0.852863\pi$
$127$		−	10.0514i		−	0.891917i	0.895054	−	0.445958i	$-0.147137\pi$
$128$	11.2841	+	0.818582i	0.997379	+	0.0723531i
$129$		−	32.3036i		−	2.84417i
$130$	−8.61248	+	12.0868i	−0.755365	+	1.06008i
$131$	−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	$0.103956\pi$
$137$			7.51003i			0.641625i	−0.947143	+	0.320812i	$0.896044\pi$
$138$	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	$0.124761\pi$
$140$	−6.17888	+	0.270507i	−0.522211	+	0.0228620i
$141$	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	$0.767710\pi$
$150$	−7.12808	+	20.7927i	−0.582005	+	1.69772i
$151$	−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	$-0.403925\pi$
$157$	7.44951			0.594536			0.297268	+	0.954794i	$0.403925\pi$
$158$	10.4536	−	8.16101i	0.831646	−	0.649255i
$159$		−	2.66304i		−	0.211193i
$160$	11.3257	−	5.63271i	0.895379	−	0.445305i
$161$	6.84633			0.539566
$162$	13.4071	+	17.1735i	1.05336	+	1.34928i
$163$		−	3.76177i		−	0.294644i	−0.989089	−	0.147322i	$-0.952935\pi$
$163$		−	3.76177i		−	0.294644i	0.989089	−	0.147322i	$-0.0470654\pi$
$164$	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	$-0.691744\pi$
$167$	−14.6443			−1.13321			−0.566606	+	0.823989i	$0.691744\pi$
$168$	4.93326	+	11.1136i	0.380609	+	0.857435i
$169$	9.02650			0.694346
$170$	7.11156	+	10.9282i	0.545432	+	0.838155i
$171$		−	51.3079i		−	3.92361i
$172$	−5.04307	+	20.1627i	−0.384530	+	1.53740i
$173$			0.791181i			0.0601524i	0.999548	+	0.0300762i	$0.00957499\pi$
$173$			0.791181i			0.0601524i	−0.999548	+	0.0300762i	$0.990425\pi$
$174$	−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	$-0.0449894\pi$
$180$	29.7690	−	1.30327i	2.21885	−	0.0971398i
$181$	−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
$190$	−19.8315	−	14.1310i	−1.43873	−	1.02517i
$191$	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	$-0.526634\pi$
$193$	−2.32215			−0.167152			−0.0835759	+	0.996501i	$0.526634\pi$
$194$	−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	$-0.912964\pi$
$197$		−	7.58033i		−	0.540076i	0.962850	−	0.270038i	$-0.0870363\pi$
$198$	−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	$-0.00966060\pi$
$200$	7.69514	−	11.8653i	0.544129	−	0.839002i
$201$			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
$210$	11.0714	+	7.88898i	0.764000	+	0.544391i
$211$	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
$220$	−14.1633	+	0.620062i	−0.954892	+	0.0418045i
$221$	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	$-0.978250\pi$
$223$		−	2.03912i		−	0.136550i	0.997667	−	0.0682749i	$-0.0217495\pi$
$224$	−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	$0.0157189\pi$
$227$			1.48744i			0.0987248i	−0.998781	+	0.0493624i	$0.984281\pi$
$228$	−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	$-0.136920\pi$
$230$	−9.08453	+	12.7492i	−0.599016	+	0.840661i
$231$		−	13.6280i		−	0.896656i
$232$	4.42237	−	1.96306i	0.290343	−	0.128881i
$233$	−3.82345			−0.250482			−0.125241	−	0.992126i	$-0.539970\pi$
$233$	−3.82345			−0.250482			−0.125241	+	0.992126i	$0.539970\pi$
$234$	−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	$0.472649\pi$
$240$	−27.2419	−	5.56017i	−1.75845	−	0.358907i
$241$		−	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
$250$	0.654710	−	15.7978i	0.0414075	−	0.999142i
$251$			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
$255$	2.46020	−	28.5534i	0.154064	−	1.78808i
$256$	8.90758	+	13.2912i	0.556724	+	0.830698i
$257$		−	6.10715i		−	0.380953i	−0.981692	−	0.190477i	$-0.938997\pi$
$257$		−	6.10715i		−	0.380953i	0.981692	−	0.190477i	$-0.0610034\pi$
$258$	36.0101	−	28.1126i	2.24189	−	1.75021i
$259$		−	5.51318i		−	0.342572i
$260$	−20.9687	+	0.917996i	−1.30042	+	0.0569317i
$261$	11.3980			0.705520
$262$	−14.1920	−	18.1788i	−0.876782	−	1.12309i
$263$		−	18.6270i		−	1.14859i	−0.818649	−	0.574294i	$-0.805277\pi$
$263$		−	18.6270i		−	1.14859i	0.818649	−	0.574294i	$-0.194723\pi$
$264$	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	$0.256614\pi$
$270$	−29.3239	−	20.8948i	−1.78459	−	1.27162i
$271$	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	$-0.766434\pi$
$277$		−	22.2912i		−	1.33935i	0.742655	−	0.669674i	$-0.233566\pi$
$278$	18.9644	+	24.2919i	1.13741	+	1.45693i
$279$			40.8593i			2.44618i
$280$	−5.67879	−	6.65243i	−0.339373	−	0.397559i
$281$	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	$-0.761722\pi$
$283$		−	22.8987i		−	1.36118i	0.732662	−	0.680592i	$-0.238278\pi$
$284$	−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
$290$	3.13921	−	4.40557i	0.184340	−	0.258704i
$291$			33.4622i			1.96159i
$292$	4.02529	−	16.0936i	0.235563	−	0.941805i
$293$	−2.83599			−0.165680			−0.0828400	−	0.996563i	$-0.526399\pi$
$293$	−2.83599			−0.165680			−0.0828400	+	0.996563i	$0.526399\pi$
$294$	−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
$300$	−29.3818	+	10.1492i	−1.69636	+	0.585963i
$301$	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	$-0.474049\pi$
$307$	2.85382			0.162876			0.0814380	+	0.996678i	$0.474049\pi$
$308$	−2.12753	+	8.50610i	−0.121227	+	0.484680i
$309$	−44.4868			−2.53077
$310$	15.7930	+	11.2533i	0.896980	+	0.639147i
$311$		−	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	$-0.387102\pi$
$313$	12.2883			0.694578			0.347289	+	0.937758i	$0.387102\pi$
$314$	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	$-0.959106\pi$
$317$		−	4.56223i		−	0.256240i	0.991759	−	0.128120i	$-0.0408943\pi$
$318$	2.96859	−	2.31754i	0.166470	−	0.129961i
$319$	−5.42289			−0.303624
$320$	16.1354	+	7.72332i	0.901995	+	0.431747i
$321$	−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
$330$	25.3781	+	18.0833i	1.39702	+	0.995450i
$331$			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	$-0.777704\pi$
$337$	−28.1199			−1.53179			−0.765895	+	0.642966i	$0.777704\pi$
$338$	7.85542	+	10.0622i	0.427279	+	0.547311i
$339$		−	4.66684i		−	0.253468i
$340$	−5.99318	+	17.4379i	−0.325026	+	0.945705i
$341$		−	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	$0.159280\pi$
$347$			17.8743i			0.959543i	−0.877394	+	0.479771i	$0.840720\pi$
$348$	−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	$-0.307348\pi$
$350$	−9.25055	−	3.17124i	−0.494463	−	0.169510i
$351$			53.4387i			2.85235i
$352$	−3.08111	−	17.6659i	−0.164224	−	0.941593i
$353$		−	12.4620i		−	0.663287i	−0.943405	−	0.331643i	$-0.892397\pi$
$353$		−	12.4620i		−	0.663287i	0.943405	−	0.331643i	$-0.107603\pi$
$354$	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	$0.188149\pi$
$360$	27.3597	+	32.0505i	1.44198	+	1.68921i
$361$	−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	$-0.359859\pi$
$367$	16.3289			0.852360			0.426180	+	0.904638i	$0.359859\pi$
$368$	−17.4702	−	9.32243i	−0.910697	−	0.485965i
$369$			31.6714i			1.64875i
$370$	10.2667	+	7.31555i	0.533738	+	0.380317i
$371$	1.18477			0.0615101
$372$	9.25079	−	36.9857i	0.479631	−	1.91762i
$373$	12.0595			0.624415			0.312207	−	0.950014i	$-0.398932\pi$
$373$	12.0595			0.624415			0.312207	+	0.950014i	$0.398932\pi$
$374$	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	$0.694676\pi$
$380$	−1.50621	−	34.4047i	−0.0772672	−	1.76492i
$381$	−31.2450			−1.60073
$382$	3.73786	+	4.78792i	0.191246	+	0.244971i
$383$			23.7458i			1.21335i	0.794949	+	0.606676i	$0.207498\pi$
$383$			23.7458i			1.21335i	−0.794949	+	0.606676i	$0.792502\pi$
$384$	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	$0.838398\pi$
$390$	37.5721	+	26.7721i	1.90253	+	1.35566i
$391$	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	$0.319341\pi$
$397$			33.6020i			1.68643i	−0.537573	+	0.843217i	$0.680659\pi$
$398$	0.954371	−	0.745065i	0.0478383	−	0.0373467i
$399$	33.1043			1.65729
$400$	19.9235	−	1.74782i	0.996174	−	0.0873911i
$401$			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	$0.644614\pi$
$410$	12.2417	+	8.72284i	0.604572	+	0.430790i
$411$	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	$0.552758\pi$
$420$	0.840879	+	19.2072i	0.0410307	+	0.937216i
$421$		−	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
$425$	4.15409	+	20.1927i	0.201503	+	0.979488i
$426$	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
$430$	−19.0700	+	26.7630i	−0.919639	+	1.29062i
$431$		−	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	$0.0145911\pi$
$433$			1.90705i			0.0916468i	−0.998950	+	0.0458234i	$0.985409\pi$
$434$	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	$-0.0166884\pi$
$440$	−13.0170	−	15.2488i	−0.620563	−	0.726959i
$441$	33.8971			1.61415
$442$	26.2385	−	7.77457i	1.24804	−	0.369799i
$443$	−0.504565			−0.0239726			−0.0119863	−	0.999928i	$-0.503815\pi$
$443$	−0.504565			−0.0239726			−0.0119863	+	0.999928i	$0.503815\pi$
$444$	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	$0.829179\pi$
$450$	44.5679	+	15.2786i	2.10095	+	0.720240i
$451$		−	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	$0.269915\pi$
$457$			32.0636i			1.49987i	−0.661511	+	0.749935i	$0.730085\pi$
$458$	14.0689	−	10.9834i	0.657397	−	0.513221i
$459$	43.6881	+	17.1862i	2.03919	+	0.802185i
$460$	−22.1180	+	0.968311i	−1.03126	+	0.0451477i
$461$		−	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	$0.0676324\pi$
$463$			9.07513i			0.421757i	−0.977512	+	0.210878i	$0.932368\pi$
$464$	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	$-0.531257\pi$
$467$	−4.23729			−0.196078			−0.0980391	+	0.995183i	$0.531257\pi$
$468$	15.1753	−	60.6725i	0.701478	−	2.80459i
$469$	−10.6156			−0.490185
$470$	−14.8114	−	10.5539i	−0.683198	−	0.486816i
$471$		−	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	$0.675789\pi$
$480$	−17.5094	−	35.2064i	−0.799192	−	1.60694i
$481$		−	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	$-0.338010\pi$
$487$	21.5041			0.974446			0.487223	+	0.873278i	$0.338010\pi$
$488$	11.2193	−	4.98018i	0.507875	−	0.225442i
$489$	−11.6936			−0.528801
$490$	9.33582	−	13.1019i	0.421749	−	0.591884i
$491$			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	$0.366992\pi$
$500$	18.1802	−	13.0184i	0.813044	−	0.582202i
$501$			45.5222i			2.03378i
$502$	−5.63344	+	4.39795i	−0.251433	+	0.196290i
$503$	30.9286			1.37904			0.689520	−	0.724267i	$-0.257821\pi$
$503$	30.9286			1.37904			0.689520	+	0.724267i	$0.257821\pi$
$504$	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	$-0.107715\pi$
$510$	33.9706	−	22.1065i	1.50424	−	0.978891i
$511$	−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
$520$	−19.2716	−	22.5758i	−0.845116	−	0.990012i
$521$		−	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	$-0.655166\pi$
$523$	−21.4234			−0.936781			−0.468390	+	0.883522i	$0.655166\pi$
$524$	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
$530$	−1.57209	+	2.20628i	−0.0682874	+	0.0958347i
$531$		−	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
$540$	−2.22716	−	50.8724i	−0.0958417	−	2.18920i
$541$	−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	$-0.888368\pi$
$547$		−	16.0703i		−	0.687115i	0.939132	−	0.343558i	$-0.111632\pi$
$548$	−14.5712	−	3.64452i	−0.622450	−	0.155686i
$549$	28.9162			1.23412
$550$	−21.2043	−	7.26916i	−0.904153	−	0.309958i
$551$		−	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	$-0.147009\pi$
$557$	42.2565			1.79047			0.895233	+	0.445598i	$0.147009\pi$
$558$	−45.5475	+	35.5583i	−1.92818	+	1.50530i
$559$	48.7718			2.06283
$560$	2.47368	−	12.1197i	0.104532	−	0.512152i
$561$	−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	$-0.433995\pi$
$563$	9.77006			0.411759			0.205879	+	0.978577i	$0.433995\pi$
$564$	−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	$0.818809\pi$
$570$	−43.9267	+	61.6469i	−1.83989	+	2.58210i
$571$	−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	$0.0365632\pi$
$577$			5.50626i			0.229229i	−0.993410	+	0.114614i	$0.963437\pi$
$578$	2.08246	−	23.9513i	0.0866189	−	0.996242i
$579$			7.21845i			0.299989i
$580$	7.64299	−	0.334605i	0.317358	−	0.0138937i
$581$	−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	$-0.828649\pi$
$587$	−41.6032			−1.71715			−0.858574	+	0.512690i	$0.828649\pi$
$588$	−30.6835	−	7.67450i	−1.26537	−	0.316491i
$589$	47.2220			1.94575
$590$	−8.77731	−	6.25431i	−0.361356	−	0.257486i
$591$	−23.5637			−0.969280
$592$	−7.50712	+	14.0683i	−0.308541	+	0.578204i
$593$			5.38912i			0.221305i	0.993859	+	0.110652i	$0.0352940\pi$
$593$			5.38912i			0.221305i	−0.993859	+	0.110652i	$0.964706\pi$
$594$	−40.2368	+	31.4123i	−1.65093	+	1.28886i
$595$	12.7032	+	1.09453i	0.520782	+	0.0448713i
$596$	−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	$0.481080\pi$
$600$	−36.8835	−	23.9206i	−1.50576	−	0.976552i
$601$		−	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	$-0.296358\pi$
$607$	29.4172			1.19401			0.597003	+	0.802239i	$0.296358\pi$
$608$	42.9128	−	7.48444i	1.74034	−	0.303534i
$609$			7.35410i			0.298003i
$610$	7.96401	−	11.1767i	0.322454	−	0.452532i
$611$			26.9917i			1.09197i
$612$	−44.7215	−	31.9190i	−1.80776	−	1.29025i
$613$	12.5726			0.507803			0.253901	−	0.967230i	$-0.418286\pi$
$613$	12.5726			0.507803			0.253901	+	0.967230i	$0.418286\pi$
$614$	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	$-0.284256\pi$
$617$	31.1520			1.25413			0.627065	+	0.778967i	$0.284256\pi$
$618$	−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	$0.515300\pi$
$620$	1.19948	+	27.3984i	0.0481724	+	1.10035i
$621$			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
$630$	16.9095	−	23.7309i	0.673692	−	0.945461i
$631$	−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
$640$	5.43252	+	24.7080i	0.214739	+	0.976671i
$641$			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	$0.226127\pi$
$643$			33.0730i			1.30427i	−0.758102	+	0.652136i	$0.773873\pi$
$644$	−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	$-0.757719\pi$
$647$		−	35.0894i		−	1.37951i	0.724044	−	0.689753i	$-0.242281\pi$
$648$	−39.8269	+	17.6789i	−1.56455	+	0.694492i
$649$			10.8041i			0.424100i
$650$	−31.3928	−	10.7619i	−1.23133	−	0.422118i
$651$	−26.3628			−1.03324
$652$	7.29870	+	1.82554i	0.285839	+	0.0714936i
$653$			7.84685i			0.307071i	0.988143	+	0.153535i	$0.0490659\pi$
$653$			7.84685i			0.307071i	−0.988143	+	0.153535i	$0.950934\pi$
$654$	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	$0.827408\pi$
$660$	1.92748	+	44.0271i	0.0750269	+	1.71375i
$661$		−	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
$670$	14.0861	−	19.7685i	0.544194	−	0.763723i
$671$	−13.7576			−0.531107
$672$	−23.9570	+	4.17836i	−0.924163	+	0.161184i
$673$	17.0552			0.657431			0.328715	−	0.944429i	$-0.393384\pi$
$673$	17.0552			0.657431			0.328715	+	0.944429i	$0.393384\pi$
$674$	−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	$-0.873774\pi$
$677$		−	20.0992i		−	0.772476i	0.922399	−	0.386238i	$-0.126226\pi$
$678$	5.20231	−	4.06137i	0.199793	−	0.155976i
$679$	−14.8871			−0.571316
$680$	−24.6544	+	8.49475i	−0.945453	+	0.325759i
$681$	4.62374			0.177182
$682$	21.6703	−	16.9177i	0.829800	−	0.647814i
$683$			21.4520i			0.820836i	0.911897	+	0.410418i	$0.134617\pi$
$683$			21.4520i			0.820836i	−0.911897	+	0.410418i	$0.865383\pi$
$684$	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
$690$	39.6314	+	28.2395i	1.50874	+	1.07506i
$691$	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
$700$	−4.51530	−	13.0718i	−0.170662	−	0.494066i
$701$			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	$0.741467\pi$
$710$	−33.0471	−	23.5478i	−1.24024	−	0.883735i
$711$			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	$0.862588\pi$
$720$	−11.9179	+	58.3912i	−0.444153	+	2.17611i
$721$		−	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	$0.185570\pi$
$727$			29.6872i			1.10104i	−0.834823	+	0.550519i	$0.814430\pi$
$728$	−16.7793	+	7.44821i	−0.621882	+	0.276049i
$729$	3.53576			0.130954
$730$	15.2214	−	21.3617i	0.563369	−	0.790634i
$731$	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	$-0.690750\pi$
$733$	−30.5411			−1.12806			−0.564030	+	0.825754i	$0.690750\pi$
$734$	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	$-0.00104169\pi$
$740$	0.779758	+	17.8111i	0.0286645	+	0.654749i
$741$	112.343			4.12702
$742$	1.03106	+	1.32071i	0.0378514	+	0.0484847i
$743$	−39.2895			−1.44139			−0.720696	−	0.693251i	$-0.756178\pi$
$743$	−39.2895			−1.44139			−0.720696	+	0.693251i	$0.756178\pi$
$744$	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
$750$	−49.1080	−	2.03518i	−1.79317	−	0.0743144i
$751$			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	$-0.376890\pi$
$757$	20.7558			0.754384			0.377192	+	0.926135i	$0.376890\pi$
$758$	−19.4555	−	24.9210i	−0.706655	−	0.905171i
$759$		−	48.7829i		−	1.77071i
$760$	37.0415	−	31.6202i	1.34364	−	1.14698i
$761$	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
$765$	−61.2024	−	5.27329i	−2.21278	−	0.190656i
$766$	−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	$0.341586\pi$
$770$	−8.04512	+	11.2905i	−0.289926	+	0.406883i
$771$	−18.9842			−0.683700
$772$	1.12691	−	4.50550i	0.0405583	−	0.162156i
$773$	−16.9821			−0.610805			−0.305403	−	0.952223i	$-0.598791\pi$
$773$	−16.9821			−0.610805			−0.305403	+	0.952223i	$0.598791\pi$
$774$	−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
$780$	2.85362	+	65.1818i	0.102176	+	2.33388i
$781$			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	$-0.627077\pi$
$787$		−	51.6950i		−	1.84273i	0.388703	−	0.921363i	$-0.372923\pi$
$788$	14.7076	+	3.67864i	0.523937	+	0.131046i
$789$	−57.9024			−2.06138
$790$	24.1508	+	17.2087i	0.859247	+	0.612260i
$791$	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	$-0.567424\pi$
$797$	−11.8705			−0.420476			−0.210238	+	0.977650i	$0.567424\pi$
$798$	28.8094	+	36.9026i	1.01984	+	1.30634i
$799$	22.0667	+	8.68071i	0.780665	+	0.307102i
$800$	19.2870	+	20.6884i	0.681899	+	0.731446i
$801$	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	$0.993893\pi$
$810$	−28.2710	+	39.6756i	−0.993343	+	1.39406i
$811$	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
$820$	0.929759	+	21.2374i	0.0324686	+	0.741643i
$821$	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	$-0.351430\pi$
$823$	25.8182			0.899966			0.449983	+	0.893037i	$0.351430\pi$
$824$	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	$-0.848352\pi$
$827$		−	26.3763i		−	0.917193i	0.888645	−	0.458596i	$-0.151648\pi$
$828$	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	$0.946739\pi$
$830$	10.9048	−	15.3038i	0.378511	−	0.531203i
$831$	−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	$0.942859\pi$
$840$	−20.6792	+	17.6527i	−0.713502	+	0.609075i
$841$	−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
$850$	−18.8944	+	22.2036i	−0.648073	+	0.761579i
$851$		−	19.7350i		−	0.676509i
$852$	−19.3575	+	77.3933i	−0.663176	+	2.65145i
$853$			40.4041i			1.38341i	0.722180	+	0.691705i	$0.243140\pi$
$853$			40.4041i			1.38341i	−0.722180	+	0.691705i	$0.756860\pi$
$854$	−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	$-0.670751\pi$
$857$	−29.9227			−1.02214			−0.511071	+	0.859539i	$0.670751\pi$
$858$	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	$-0.0387967\pi$
$860$	−46.4297	+	2.03266i	−1.58324	+	0.0693131i
$861$	−20.4347			−0.696412
$862$	18.4924	−	14.4367i	0.629852	−	0.491717i
$863$			19.4379i			0.661674i	0.943688	+	0.330837i	$0.107331\pi$
$863$			19.4379i			0.661674i	−0.943688	+	0.330837i	$0.892669\pi$
$864$	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
$870$	−13.6948	−	9.75830i	−0.464298	−	0.330837i
$871$	−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	$0.366131\pi$
$877$			54.0672i			1.82572i	−0.408272	+	0.912860i	$0.633869\pi$
$878$	2.44794	−	1.91107i	0.0826139	−	0.0644956i
$879$			8.81573i			0.297347i
$880$	5.67022	−	27.7811i	0.191143	−	0.936500i
$881$		−	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	$-0.612771\pi$
$883$	−20.6175			−0.693833			−0.346917	+	0.937896i	$0.612771\pi$
$884$	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	$-0.249526\pi$
$887$	42.1816			1.41632			0.708159	+	0.706053i	$0.249526\pi$
$888$	32.0359	−	14.2205i	1.07505	−	0.477208i
$889$		−	13.9007i		−	0.466215i
$890$	15.8836	−	22.2911i	0.532419	−	0.747198i
$891$	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
$900$	21.7541	+	62.9780i	0.725137	+	2.09927i
$901$	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	$0.0433948\pi$
$907$			8.18606i			0.271814i	−0.990722	+	0.135907i	$0.956605\pi$
$908$	−2.88597	−	0.721835i	−0.0957744	−	0.0239549i
$909$		−	68.7355i		−	2.27981i
$910$	−11.9107	+	16.7156i	−0.394837	+	0.554116i
$911$		−	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	$0.431167\pi$
$920$	−20.3279	−	23.8131i	−0.670190	−	0.785096i
$921$		−	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	$-0.00416171\pi$
$930$	34.9813	−	49.0928i	1.14708	−	1.60982i
$931$		−	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
$935$	29.1186	+	2.50890i	0.952279	+	0.0820497i
$936$	80.8404	−	35.8845i	2.64235	−	1.17292i
$937$		−	15.8558i		−	0.517985i	−0.965879	−	0.258992i	$-0.916610\pi$
$937$		−	15.8558i		−	0.517985i	0.965879	−	0.258992i	$-0.0833905\pi$
$938$	−9.23839	−	11.8337i	−0.301644	−	0.386383i
$939$		−	38.1986i		−	1.24656i
$940$	−1.12493	−	25.6955i	−0.0366912	−	0.838095i
$941$	−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	$-0.702080\pi$
$947$		−	49.5549i		−	1.61032i	0.593058	−	0.805159i	$-0.297920\pi$
$948$	14.1464	−	56.5590i	0.459455	−	1.83695i
$949$	−38.9289			−1.26368
$950$	17.6578	−	51.5081i	0.572895	−	1.67114i
$951$	−14.1818			−0.459876
$952$	0.692854	+	16.1131i	0.0224555	+	0.522228i
$953$		−	2.51887i		−	0.0815941i	−0.999167	−	0.0407970i	$-0.987010\pi$
$953$		−	2.51887i		−	0.0815941i	0.999167	−	0.0407970i	$-0.0129897\pi$
$954$	−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
$960$	24.0081	−	50.1572i	0.774859	−	1.61882i
$961$	−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	$-0.896597\pi$
$967$		−	19.8500i		−	0.638334i	0.947698	−	0.319167i	$-0.103403\pi$
$968$	2.45789	−	1.09104i	0.0789996	−	0.0350673i
$969$	36.1302	−	91.8445i	1.16067	−	2.95047i
$970$	19.7540	−	27.7229i	0.634264	−	0.890128i
$971$		−	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	$0.116902\pi$
$977$			22.4461i			0.718115i	−0.933315	+	0.359057i	$0.883098\pi$
$978$	−10.1765	−	13.0353i	−0.325407	−	0.416822i
$979$	−27.4385			−0.876937
$980$	22.7298	−	0.995096i	0.726078	−	0.0317872i
$981$	−4.70585			−0.150246
$982$	−14.0264	+	10.9502i	−0.447600	+	0.349436i
$983$	−9.53411			−0.304091			−0.152045	−	0.988373i	$-0.548586\pi$
$983$	−9.53411			−0.304091			−0.152045	+	0.988373i	$0.548586\pi$
$984$	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
$990$	38.7603	−	54.3963i	1.23188	−	1.72883i
$991$		−	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	$0.362864\pi$
$997$			57.3800i			1.81724i	−0.417622	+	0.908621i	$0.637136\pi$
$998$	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.509.27	yes	40
5.4	even	2	inner	680.2.h.b.509.14	yes	40
8.5	even	2	inner	680.2.h.b.509.16	yes	40
17.16	even	2	inner	680.2.h.b.509.28	yes	40
40.29	even	2	inner	680.2.h.b.509.25	yes	40
85.84	even	2	inner	680.2.h.b.509.13	✓	40
136.101	even	2	inner	680.2.h.b.509.15	yes	40
680.509	even	2	inner	680.2.h.b.509.26	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.h.b.509.13	✓	40	85.84	even	2	inner
680.2.h.b.509.14	yes	40	5.4	even	2	inner
680.2.h.b.509.15	yes	40	136.101	even	2	inner
680.2.h.b.509.16	yes	40	8.5	even	2	inner
680.2.h.b.509.25	yes	40	40.29	even	2	inner
680.2.h.b.509.26	yes	40	680.509	even	2	inner
680.2.h.b.509.27	yes	40	1.1	even	1	trivial
680.2.h.b.509.28	yes	40	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+(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} +(-1.83508 + 2.57536i) 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} +(-4.46786 + 0.195600i) 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} +(8.00557 + 5.70440i) 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} +(-4.10625 - 4.81027i) 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} +(-6.68893 - 2.29307i) 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} +(0.608027 + 13.8884i) 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} +(-2.53785 + 3.56163i) 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} +(1.78868 - 8.76360i) q^{80} +15.4059 q^{81} +(5.29878 - 4.13669i) q^{82} -5.94240 q^{83} +(8.34101 + 2.08624i) q^{84} +(9.18551 + 0.791437i) q^{85} +(9.04371 + 11.5843i) q^{86} +5.31764i q^{87} +(-8.19515 + 3.63777i) q^{88} -8.65552 q^{89} +(12.2270 - 17.1594i) 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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