LMFDB - Embedded newform 760.2.p.i.379.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [760,2,Mod(379,760)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(760, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))

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

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

chi := DirichletCharacter("760.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 760 = 2^{3} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	760.p (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.06863055362$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.13
Character	$\chi$	$=$	760.379
Dual form			760.2.p.i.379.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.23558 - 0.687996i) q^{2} +2.17214 q^{3} +(1.05332 + 1.70015i) q^{4} +(-2.19004 - 0.451368i) q^{5} +(-2.68385 - 1.49442i) q^{6} -2.03346 q^{7} +(-0.131770 - 2.82536i) q^{8} +1.71818 q^{9} +(2.39543 + 2.06444i) q^{10} +3.06284 q^{11} +(2.28796 + 3.69296i) q^{12} +6.48138i q^{13} +(2.51251 + 1.39901i) q^{14} +(-4.75706 - 0.980433i) q^{15} +(-1.78102 + 3.58162i) q^{16} -0.290473i q^{17} +(-2.12295 - 1.18210i) q^{18} +(2.28520 + 3.71186i) q^{19} +(-1.53942 - 4.19883i) q^{20} -4.41695 q^{21} +(-3.78439 - 2.10722i) q^{22} +7.22793 q^{23} +(-0.286223 - 6.13706i) q^{24} +(4.59253 + 1.97703i) q^{25} +(4.45916 - 8.00827i) q^{26} -2.78430 q^{27} +(-2.14189 - 3.45719i) q^{28} +7.49557 q^{29} +(5.20320 + 4.48424i) q^{30} +1.72538 q^{31} +(4.66473 - 3.20004i) q^{32} +6.65291 q^{33} +(-0.199844 + 0.358903i) q^{34} +(4.45336 + 0.917839i) q^{35} +(1.80979 + 2.92116i) q^{36} +0.791007i q^{37} +(-0.269805 - 6.15851i) q^{38} +14.0784i q^{39} +(-0.986693 + 6.24711i) q^{40} +8.58898i q^{41} +(5.45750 + 3.03885i) q^{42} -10.3417i q^{43} +(3.22617 + 5.20729i) q^{44} +(-3.76287 - 0.775530i) q^{45} +(-8.93069 - 4.97278i) q^{46} +0.0753866 q^{47} +(-3.86862 + 7.77976i) q^{48} -2.86504 q^{49} +(-4.31426 - 5.60242i) q^{50} -0.630947i q^{51} +(-11.0193 + 6.82699i) q^{52} +3.15587i q^{53} +(3.44023 + 1.91558i) q^{54} +(-6.70775 - 1.38247i) q^{55} +(0.267950 + 5.74525i) q^{56} +(4.96376 + 8.06266i) q^{57} +(-9.26139 - 5.15692i) q^{58} +6.29544i q^{59} +(-3.34384 - 9.12043i) q^{60} -6.53199i q^{61} +(-2.13185 - 1.18706i) q^{62} -3.49384 q^{63} +(-7.96527 + 0.744597i) q^{64} +(2.92549 - 14.1945i) q^{65} +(-8.22022 - 4.57718i) q^{66} -0.557751 q^{67} +(0.493847 - 0.305962i) q^{68} +15.7000 q^{69} +(-4.87101 - 4.19795i) q^{70} -13.0222 q^{71} +(-0.226405 - 4.85446i) q^{72} +10.7818i q^{73} +(0.544210 - 0.977354i) q^{74} +(9.97561 + 4.29437i) q^{75} +(-3.90366 + 7.79496i) q^{76} -6.22817 q^{77} +(9.68591 - 17.3951i) q^{78} +7.28720 q^{79} +(5.51713 - 7.03998i) q^{80} -11.2024 q^{81} +(5.90919 - 10.6124i) q^{82} +12.0125i q^{83} +(-4.65248 - 7.50948i) q^{84} +(-0.131110 + 0.636147i) q^{85} +(-7.11501 + 12.7780i) q^{86} +16.2814 q^{87} +(-0.403592 - 8.65363i) q^{88} -0.581069i q^{89} +(4.11577 + 3.54707i) q^{90} -13.1796i q^{91} +(7.61334 + 12.2886i) q^{92} +3.74777 q^{93} +(-0.0931463 - 0.0518657i) q^{94} +(-3.32925 - 9.16057i) q^{95} +(10.1324 - 6.95093i) q^{96} +3.90310 q^{97} +(3.53999 + 1.97114i) q^{98} +5.26251 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 16 q^{4} - 8 q^{6} + 88 q^{9} + 32 q^{11} + 48 q^{16} - 56 q^{19} + 4 q^{20} - 32 q^{24} + 80 q^{25} + 24 q^{26} + 24 q^{30} + 48 q^{35} - 96 q^{36} + 104 q^{44} - 72 q^{49} + 104 q^{54} + 16 q^{64}+ \cdots - 272 q^{99}+O(q^{100}) $ 56 * q + 16 * q^4 - 8 * q^6 + 88 * q^9 + 32 * q^11 + 48 * q^16 - 56 * q^19 + 4 * q^20 - 32 * q^24 + 80 * q^25 + 24 * q^26 + 24 * q^30 + 48 * q^35 - 96 * q^36 + 104 * q^44 - 72 * q^49 + 104 * q^54 + 16 * q^64 - 24 * q^66 + 64 * q^74 + 88 * q^76 + 128 * q^80 - 168 * q^81 - 96 * q^96 - 272 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/760\mathbb{Z}\right)^\times$.

$n$	$191$	$381$	$401$	$457$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.23558	−	0.687996i	−0.873688	−	0.486487i
$2$	−1.23558	−	0.687996i	−0.873688	−	0.486487i
$3$	2.17214			1.25408			0.627042	−	0.778986i	$-0.284266\pi$
$3$	2.17214			1.25408			0.627042	+	0.778986i	$0.284266\pi$
$4$	1.05332	+	1.70015i	0.526662	+	0.850075i
$5$	−2.19004	−	0.451368i	−0.979415	−	0.201858i
$5$	−2.19004	−	0.451368i	−0.979415	−	0.201858i
$6$	−2.68385	−	1.49442i	−1.09568	−	0.610095i
$7$	−2.03346			−0.768576			−0.384288	−	0.923213i	$-0.625553\pi$
$7$	−2.03346			−0.768576			−0.384288	+	0.923213i	$0.625553\pi$
$8$	−0.131770	−	2.82536i	−0.0465879	−	0.998914i
$9$	1.71818			0.572725
$10$	2.39543	+	2.06444i	0.757502	+	0.652833i
$11$	3.06284			0.923482			0.461741	−	0.887015i	$-0.347225\pi$
$11$	3.06284			0.923482			0.461741	+	0.887015i	$0.347225\pi$
$12$	2.28796	+	3.69296i	0.660478	+	1.06607i
$13$			6.48138i			1.79761i	0.438347	+	0.898806i	$0.355564\pi$
$13$			6.48138i			1.79761i	−0.438347	+	0.898806i	$0.644436\pi$
$14$	2.51251	+	1.39901i	0.671495	+	0.373902i
$15$	−4.75706	−	0.980433i	−1.22827	−	0.253147i
$16$	−1.78102	+	3.58162i	−0.445255	+	0.895404i
$17$		−	0.290473i		−	0.0704500i	−0.999379	−	0.0352250i	$-0.988785\pi$
$17$		−	0.290473i		−	0.0704500i	0.999379	−	0.0352250i	$-0.0112148\pi$
$18$	−2.12295	−	1.18210i	−0.500383	−	0.278623i
$19$	2.28520	+	3.71186i	0.524260	+	0.851558i
$19$	2.28520	+	3.71186i	0.524260	+	0.851558i
$20$	−1.53942	−	4.19883i	−0.344226	−	0.938887i
$21$	−4.41695			−0.963858
$22$	−3.78439	−	2.10722i	−0.806835	−	0.449262i
$23$	7.22793			1.50713			0.753563	−	0.657375i	$-0.228333\pi$
$23$	7.22793			1.50713			0.753563	+	0.657375i	$0.228333\pi$
$24$	−0.286223	−	6.13706i	−0.0584251	−	1.25272i
$25$	4.59253	+	1.97703i	0.918507	+	0.395405i
$26$	4.45916	−	8.00827i	0.874514	−	1.57055i
$27$	−2.78430			−0.535838
$28$	−2.14189	−	3.45719i	−0.404779	−	0.653347i
$29$	7.49557			1.39189			0.695946	−	0.718094i	$-0.254985\pi$
$29$	7.49557			1.39189			0.695946	+	0.718094i	$0.254985\pi$
$30$	5.20320	+	4.48424i	0.949971	+	0.818707i
$31$	1.72538			0.309888			0.154944	−	0.987923i	$-0.450480\pi$
$31$	1.72538			0.309888			0.154944	+	0.987923i	$0.450480\pi$
$32$	4.66473	−	3.20004i	0.824616	−	0.565693i
$33$	6.65291			1.15812
$34$	−0.199844	+	0.358903i	−0.0342730	+	0.0615513i
$35$	4.45336	+	0.917839i	0.752754	+	0.155143i
$36$	1.80979	+	2.92116i	0.301632	+	0.486860i
$37$			0.791007i			0.130041i	0.997884	+	0.0650204i	$0.0207112\pi$
$37$			0.791007i			0.130041i	−0.997884	+	0.0650204i	$0.979289\pi$
$38$	−0.269805	−	6.15851i	−0.0437682	−	0.999042i
$39$			14.0784i			2.25435i
$40$	−0.986693	+	6.24711i	−0.156010	+	0.987755i
$41$			8.58898i			1.34137i	0.741741	+	0.670687i	$0.234001\pi$
$41$			8.58898i			1.34137i	−0.741741	+	0.670687i	$0.765999\pi$
$42$	5.45750	+	3.03885i	0.842111	+	0.468904i
$43$		−	10.3417i		−	1.57709i	−0.614979	−	0.788544i	$-0.710835\pi$
$43$		−	10.3417i		−	1.57709i	0.614979	−	0.788544i	$-0.289165\pi$
$44$	3.22617	+	5.20729i	0.486363	+	0.785029i
$45$	−3.76287	−	0.775530i	−0.560936	−	0.115609i
$46$	−8.93069	−	4.97278i	−1.31676	−	0.733197i
$47$	0.0753866			0.0109963			0.00549813	−	0.999985i	$-0.498250\pi$
$47$	0.0753866			0.0109963			0.00549813	+	0.999985i	$0.498250\pi$
$48$	−3.86862	+	7.77976i	−0.558387	+	1.12291i
$49$	−2.86504			−0.409291
$50$	−4.31426	−	5.60242i	−0.610129	−	0.792302i
$51$		−	0.630947i		−	0.0883502i
$52$	−11.0193	+	6.82699i	−1.52810	+	0.946733i
$53$			3.15587i			0.433493i	0.976228	+	0.216746i	$0.0695444\pi$
$53$			3.15587i			0.433493i	−0.976228	+	0.216746i	$0.930456\pi$
$54$	3.44023	+	1.91558i	0.468155	+	0.260678i
$55$	−6.70775	−	1.38247i	−0.904472	−	0.186412i
$56$	0.267950	+	5.74525i	0.0358063	+	0.767741i
$57$	4.96376	+	8.06266i	0.657466	+	1.06793i
$58$	−9.26139	−	5.15692i	−1.21608	−	0.677137i
$59$			6.29544i			0.819597i	0.912176	+	0.409798i	$0.134401\pi$
$59$			6.29544i			0.819597i	−0.912176	+	0.409798i	$0.865599\pi$
$60$	−3.34384	−	9.12043i	−0.431688	−	1.17744i
$61$		−	6.53199i		−	0.836335i	−0.908370	−	0.418168i	$-0.862672\pi$
$61$		−	6.53199i		−	0.836335i	0.908370	−	0.418168i	$-0.137328\pi$
$62$	−2.13185	−	1.18706i	−0.270745	−	0.150756i
$63$	−3.49384			−0.440183
$64$	−7.96527	+	0.744597i	−0.995659	+	0.0930746i
$65$	2.92549	−	14.1945i	0.362862	−	1.76061i
$66$	−8.22022	−	4.57718i	−1.01184	−	0.563412i
$67$	−0.557751			−0.0681401			−0.0340700	−	0.999419i	$-0.510847\pi$
$67$	−0.557751			−0.0681401			−0.0340700	+	0.999419i	$0.510847\pi$
$68$	0.493847	−	0.305962i	0.0598878	−	0.0371033i
$69$	15.7000			1.89006
$70$	−4.87101	−	4.19795i	−0.582197	−	0.501752i
$71$	−13.0222			−1.54545			−0.772727	−	0.634738i	$-0.781108\pi$
$71$	−13.0222			−1.54545			−0.772727	+	0.634738i	$0.781108\pi$
$72$	−0.226405	−	4.85446i	−0.0266821	−	0.572103i
$73$			10.7818i			1.26192i	0.775816	+	0.630959i	$0.217338\pi$
$73$			10.7818i			1.26192i	−0.775816	+	0.630959i	$0.782662\pi$
$74$	0.544210	−	0.977354i	0.0632631	−	0.113615i
$75$	9.97561	+	4.29437i	1.15188	+	0.495871i
$76$	−3.90366	+	7.79496i	−0.447781	+	0.894143i
$77$	−6.22817			−0.709766
$78$	9.68591	−	17.3951i	1.09671	−	1.96960i
$79$	7.28720			0.819874			0.409937	−	0.912114i	$-0.365551\pi$
$79$	7.28720			0.819874			0.409937	+	0.912114i	$0.365551\pi$
$80$	5.51713	−	7.03998i	0.616834	−	0.787093i
$81$	−11.2024			−1.24471
$82$	5.90919	−	10.6124i	0.652560	−	1.17194i
$83$			12.0125i			1.31854i	0.751905	+	0.659272i	$0.229135\pi$
$83$			12.0125i			1.31854i	−0.751905	+	0.659272i	$0.770865\pi$
$84$	−4.65248	−	7.50948i	−0.507627	−	0.819352i
$85$	−0.131110	+	0.636147i	−0.0142209	+	0.0689998i
$86$	−7.11501	+	12.7780i	−0.767232	+	1.37788i
$87$	16.2814			1.74555
$88$	−0.403592	−	8.65363i	−0.0430231	−	0.922480i
$89$		−	0.581069i		−	0.0615932i	−0.999526	−	0.0307966i	$-0.990196\pi$
$89$		−	0.581069i		−	0.0615932i	0.999526	−	0.0307966i	$-0.00980441\pi$
$90$	4.11577	+	3.54707i	0.433841	+	0.373894i
$91$		−	13.1796i		−	1.38160i
$92$	7.61334	+	12.2886i	0.793746	+	1.28117i
$93$	3.74777			0.388625
$94$	−0.0931463	−	0.0518657i	−0.00960731	−	0.00534954i
$95$	−3.32925	−	9.16057i	−0.341574	−	0.939855i
$96$	10.1324	−	6.95093i	1.03414	−	0.709426i
$97$	3.90310			0.396300			0.198150	−	0.980172i	$-0.436507\pi$
$97$	3.90310			0.396300			0.198150	+	0.980172i	$0.436507\pi$
$98$	3.53999	+	1.97114i	0.357593	+	0.199115i
$99$	5.26251			0.528902
$100$	1.47618	+	9.89044i	0.147618	+	0.989044i
$101$		−	9.14908i		−	0.910367i	−0.890398	−	0.455184i	$-0.849574\pi$
$101$		−	9.14908i		−	0.910367i	0.890398	−	0.455184i	$-0.150426\pi$
$102$	−0.434089	+	0.779586i	−0.0429812	+	0.0771905i
$103$		−	0.434371i		−	0.0427999i	−0.999771	−	0.0213999i	$-0.993188\pi$
$103$		−	0.434371i		−	0.0427999i	0.999771	−	0.0213999i	$-0.00681233\pi$
$104$	18.3122	−	0.854055i	1.79566	−	0.0837469i
$105$	9.67329	+	1.99367i	0.944017	+	0.194562i
$106$	2.17123	−	3.89934i	0.210888	−	0.378737i
$107$	15.4877			1.49725			0.748626	−	0.662992i	$-0.230714\pi$
$107$	15.4877			1.49725			0.748626	+	0.662992i	$0.230714\pi$
$108$	−2.93276	−	4.73372i	−0.282205	−	0.455503i
$109$	−3.61452			−0.346208			−0.173104	−	0.984904i	$-0.555380\pi$
$109$	−3.61452			−0.346208			−0.173104	+	0.984904i	$0.555380\pi$
$110$	7.33683	+	6.32306i	0.699540	+	0.602880i
$111$			1.71818i			0.163082i
$112$	3.62163	−	7.28307i	0.342212	−	0.688186i
$113$	−6.05106			−0.569236			−0.284618	−	0.958641i	$-0.591867\pi$
$113$	−6.05106			−0.569236			−0.284618	+	0.958641i	$0.591867\pi$
$114$	−0.586053	−	13.3771i	−0.0548889	−	1.25288i
$115$	−15.8294	−	3.26245i	−1.47610	−	0.304225i
$116$	7.89526	+	12.7436i	0.733056	+	1.18321i
$117$			11.1362i			1.02954i
$118$	4.33124	−	7.77853i	0.398723	−	0.716072i
$119$			0.590665i			0.0541462i
$120$	−2.14323	+	13.5696i	−0.195649	+	1.23873i
$121$	−1.61899			−0.147181
$122$	−4.49398	+	8.07080i	−0.406866	+	0.730696i
$123$			18.6564i			1.68219i
$124$	1.81739	+	2.93341i	0.163206	+	0.263428i
$125$	−9.16546	−	6.40269i	−0.819783	−	0.572674i
$126$	4.31693	+	2.40375i	0.384582	+	0.214143i
$127$			4.05844i			0.360129i	0.983655	+	0.180064i	$0.0576306\pi$
$127$			4.05844i			0.360129i	−0.983655	+	0.180064i	$0.942369\pi$
$128$	10.3540	+	4.56006i	0.915175	+	0.403057i
$129$		−	22.4635i		−	1.97780i
$130$	−13.3804	+	15.5257i	−1.17354	+	1.36169i
$131$	14.9075			1.30248			0.651238	−	0.758874i	$-0.274250\pi$
$131$	14.9075			1.30248			0.651238	+	0.758874i	$0.274250\pi$
$132$	7.00767	+	11.3110i	0.609939	+	0.984492i
$133$	−4.64686	−	7.54791i	−0.402934	−	0.654487i
$134$	0.689146	+	0.383730i	0.0595332	+	0.0331492i
$135$	6.09772	+	1.25674i	0.524808	+	0.108163i
$136$	−0.820689	+	0.0382757i	−0.0703735	+	0.00328212i
$137$		−	23.3084i		−	1.99137i	−0.0927833	−	0.995686i	$-0.529576\pi$
$137$		−	23.3084i		−	1.99137i	0.0927833	−	0.995686i	$-0.470424\pi$
$138$	−19.3987	−	10.8016i	−1.65133	−	0.919490i
$139$	−10.0076			−0.848837			−0.424419	−	0.905466i	$-0.639521\pi$
$139$	−10.0076			−0.848837			−0.424419	+	0.905466i	$0.639521\pi$
$140$	3.13036	+	8.53815i	0.264564	+	0.721606i
$141$	0.163750			0.0137902
$142$	16.0900	+	8.95924i	1.35025	+	0.751843i
$143$			19.8515i			1.66006i
$144$	−3.06011	+	6.15385i	−0.255009	+	0.512820i
$145$	−16.4156	−	3.38326i	−1.36324	−	0.280964i
$146$	7.41785	−	13.3218i	0.613906	−	1.10252i
$147$	−6.22326			−0.513286
$148$	−1.34483	+	0.833186i	−0.110544	+	0.0684875i
$149$		−	17.0508i		−	1.39686i	−0.715679	−	0.698429i	$-0.753883\pi$
$149$		−	17.0508i		−	1.39686i	0.715679	−	0.698429i	$-0.246117\pi$
$150$	−9.37117	−	12.1692i	−0.765153	−	0.993613i
$151$	−17.0441			−1.38703			−0.693513	−	0.720445i	$-0.743938\pi$
$151$	−17.0441			−1.38703			−0.693513	+	0.720445i	$0.743938\pi$
$152$	10.1862	−	6.94561i	0.826209	−	0.563363i
$153$		−	0.499083i		−	0.0403485i
$154$	7.69541	+	4.28496i	0.620114	+	0.345292i
$155$	−3.77866	−	0.778783i	−0.303509	−	0.0625533i
$156$	−23.9355	+	14.8291i	−1.91637	+	1.18728i
$157$	7.59604			0.606230			0.303115	−	0.952954i	$-0.401973\pi$
$157$	7.59604			0.606230			0.303115	+	0.952954i	$0.401973\pi$
$158$	−9.00393	−	5.01356i	−0.716314	−	0.398858i
$159$			6.85499i			0.543636i
$160$	−11.6603	+	4.90270i	−0.921831	+	0.387593i
$161$	−14.6977			−1.15834
$162$	13.8415	+	7.70720i	1.08749	+	0.605535i
$163$			11.2751i			0.883137i	0.897227	+	0.441569i	$0.145578\pi$
$163$			11.2751i			0.883137i	−0.897227	+	0.441569i	$0.854422\pi$
$164$	−14.6026	+	9.04698i	−1.14027	+	0.706450i
$165$	−14.5701	−	3.00291i	−1.13428	−	0.233776i
$166$	8.26456	−	14.8424i	0.641454	−	1.15200i
$167$			10.6315i			0.822690i	0.911480	+	0.411345i	$0.134941\pi$
$167$			10.6315i			0.822690i	−0.911480	+	0.411345i	$0.865059\pi$
$168$	0.582024	+	12.4795i	0.0449041	+	0.962811i
$169$	−29.0083			−2.23141
$170$	0.599664	−	0.695808i	0.0459921	−	0.0533660i
$171$	3.92637	+	6.37762i	0.300257	+	0.487709i
$172$	17.5824	−	10.8931i	1.34064	−	0.830591i
$173$		−	14.8147i		−	1.12634i	−0.826341	−	0.563170i	$-0.809582\pi$
$173$		−	14.8147i		−	1.12634i	0.826341	−	0.563170i	$-0.190418\pi$
$174$	−20.1170	−	11.2015i	−1.52507	−	0.849186i
$175$	−9.33873	−	4.02020i	−0.705942	−	0.303899i
$176$	−5.45499	+	10.9699i	−0.411185	+	0.826890i
$177$			13.6746i			1.02784i
$178$	−0.399773	+	0.717958i	−0.0299643	+	0.0538132i
$179$		−	12.9138i		−	0.965220i	−0.875835	−	0.482610i	$-0.839689\pi$
$179$		−	12.9138i		−	0.965220i	0.875835	−	0.482610i	$-0.160311\pi$
$180$	−2.64500	−	7.21433i	−0.197147	−	0.537724i
$181$	15.6462			1.16297			0.581486	−	0.813556i	$-0.302471\pi$
$181$	15.6462			1.16297			0.581486	+	0.813556i	$0.302471\pi$
$182$	−9.06753	+	16.2845i	−0.672130	+	1.20709i
$183$		−	14.1884i		−	1.04883i
$184$	−0.952427	−	20.4215i	−0.0702139	−	1.50549i
$185$	0.357035	−	1.73234i	0.0262498	−	0.127364i
$186$	−4.63067	−	2.57845i	−0.339537	−	0.189061i
$187$		−	0.889673i		−	0.0650593i
$188$	0.0794065	+	0.128169i	0.00579131	+	0.00934765i
$189$	5.66176			0.411832
$190$	−2.18887	+	13.6091i	−0.158797	+	0.987311i
$191$		−	3.05943i		−	0.221372i	−0.993855	−	0.110686i	$-0.964695\pi$
$191$		−	3.05943i		−	0.221372i	0.993855	−	0.110686i	$-0.0353048\pi$
$192$	−17.3017	+	1.61737i	−1.24864	+	0.116723i
$193$	−3.71053			−0.267090			−0.133545	−	0.991043i	$-0.542636\pi$
$193$	−3.71053			−0.267090			−0.133545	+	0.991043i	$0.542636\pi$
$194$	−4.82260	−	2.68532i	−0.346242	−	0.192794i
$195$	6.35456	−	30.8323i	0.455059	−	2.20795i
$196$	−3.01781	−	4.87100i	−0.215558	−	0.347928i
$197$	16.5007			1.17563			0.587814	−	0.808996i	$-0.299989\pi$
$197$	16.5007			1.17563			0.587814	+	0.808996i	$0.299989\pi$
$198$	−6.50225	−	3.62058i	−0.462095	−	0.257304i
$199$			22.1764i			1.57204i	0.618201	+	0.786020i	$0.287862\pi$
$199$			22.1764i			1.57204i	−0.618201	+	0.786020i	$0.712138\pi$
$200$	4.98064	−	13.2361i	0.352185	−	0.935931i
$201$	−1.21151			−0.0854533
$202$	−6.29453	+	11.3044i	−0.442881	+	0.795377i
$203$	−15.2419			−1.06977
$204$	1.07270	−	0.664591i	0.0751043	−	0.0465307i
$205$	3.87679	−	18.8102i	0.270767	−	1.31376i
$206$	−0.298846	+	0.536701i	−0.0208216	+	0.0373937i
$207$	12.4188			0.863170
$208$	−23.2138	−	11.5435i	−1.60959	−	0.800396i
$209$	6.99920	+	11.3688i	0.484145	+	0.786399i
$210$	−10.5805	−	9.11853i	−0.730124	−	0.629238i
$211$		−	11.1535i		−	0.767840i	−0.923366	−	0.383920i	$-0.874574\pi$
$211$		−	11.1535i		−	0.767840i	0.923366	−	0.383920i	$-0.125426\pi$
$212$	−5.36546	+	3.32416i	−0.368501	+	0.228304i
$213$	−28.2861			−1.93813
$214$	−19.1363	−	10.6555i	−1.30813	−	0.728393i
$215$	−4.66789	+	22.6486i	−0.318348	+	1.54462i
$216$	0.366888	+	7.86663i	0.0249636	+	0.535256i
$217$	−3.50850			−0.238172
$218$	4.46603	+	2.48677i	0.302478	+	0.168425i
$219$			23.4196i			1.58255i
$220$	−4.71502	−	12.8604i	−0.317886	−	0.867045i
$221$	1.88266			0.126642
$222$	1.18210	−	2.12295i	0.0793372	−	0.142483i
$223$			25.6400i			1.71698i	0.512832	+	0.858489i	$0.328597\pi$
$223$			25.6400i			1.71698i	−0.512832	+	0.858489i	$0.671403\pi$
$224$	−9.48555	+	6.50716i	−0.633780	+	0.434778i
$225$	7.89078	+	3.39688i	0.526052	+	0.226459i
$226$	7.47658	+	4.16311i	0.497335	+	0.276926i
$227$	−4.48894			−0.297942			−0.148971	−	0.988842i	$-0.547596\pi$
$227$	−4.48894			−0.297942			−0.148971	+	0.988842i	$0.547596\pi$
$228$	−8.47928	+	16.9317i	−0.561554	+	1.12133i
$229$			7.23271i			0.477951i	0.971026	+	0.238975i	$0.0768116\pi$
$229$			7.23271i			0.477951i	−0.971026	+	0.238975i	$0.923188\pi$
$230$	17.3140	+	14.9216i	1.14165	+	0.983902i
$231$	−13.5284			−0.890106
$232$	−0.987695	−	21.1777i	−0.0648453	−	1.39038i
$233$		−	18.7921i		−	1.23111i	−0.788093	−	0.615556i	$-0.788931\pi$
$233$		−	18.7921i		−	1.23111i	0.788093	−	0.615556i	$-0.211069\pi$
$234$	7.66163	−	13.7596i	0.500856	−	0.899495i
$235$	−0.165100	−	0.0340271i	−0.0107699	−	0.00221968i
$236$	−10.7032	+	6.63113i	−0.696719	+	0.431650i
$237$	15.8288			1.02819
$238$	0.406375	−	0.729815i	0.0263414	−	0.0473069i
$239$		−	7.26494i		−	0.469930i	−0.972004	−	0.234965i	$-0.924503\pi$
$239$		−	7.26494i		−	0.469930i	0.972004	−	0.234965i	$-0.0754975\pi$
$240$	11.9840	−	15.2918i	0.773561	−	0.987081i
$241$			0.854300i			0.0550303i	0.999621	+	0.0275152i	$0.00875945\pi$
$241$			0.854300i			0.0550303i	−0.999621	+	0.0275152i	$0.991241\pi$
$242$	2.00039	+	1.11386i	0.128590	+	0.0716013i
$243$	−15.9802			−1.02513
$244$	11.1054	−	6.88030i	0.710948	−	0.440466i
$245$	6.27455	+	1.29319i	0.400866	+	0.0826187i
$246$	12.8356	−	23.0516i	0.818365	−	1.46971i
$247$	−24.0580	+	14.8112i	−1.53077	+	0.942416i
$248$	−0.227355	−	4.87482i	−0.0144370	−	0.309552i
$249$			26.0928i			1.65356i
$250$	6.91965	+	14.2168i	0.437637	+	0.899152i
$251$	−5.55780			−0.350805			−0.175403	−	0.984497i	$-0.556123\pi$
$251$	−5.55780			−0.350805			−0.175403	+	0.984497i	$0.556123\pi$
$252$	−3.68015	−	5.94006i	−0.231827	−	0.374188i
$253$	22.1380			1.39180
$254$	2.79219	−	5.01454i	0.175198	−	0.314640i
$255$	−0.284789	+	1.38180i	−0.0178342	+	0.0865315i
$256$	−9.65593	−	12.7579i	−0.603496	−	0.797366i
$257$	−22.0409			−1.37488			−0.687438	−	0.726243i	$-0.741265\pi$
$257$	−22.0409			−1.37488			−0.687438	+	0.726243i	$0.741265\pi$
$258$	−15.4548	+	27.7555i	−0.962173	+	1.72798i
$259$		−	1.60848i		−	0.0999462i
$260$	27.2142	−	9.97760i	1.68775	−	0.618784i
$261$	12.8787			0.797172
$262$	−18.4194	−	10.2563i	−1.13796	−	0.633637i
$263$	16.7210			1.03106			0.515531	−	0.856871i	$-0.327595\pi$
$263$	16.7210			1.03106			0.515531	+	0.856871i	$0.327595\pi$
$264$	−0.876658	−	18.7969i	−0.0539546	−	1.15687i
$265$	1.42446	−	6.91148i	0.0875039	−	0.424569i
$266$	0.548638	+	12.5231i	0.0336391	+	0.767839i
$267$		−	1.26216i		−	0.0772430i
$268$	−0.587492	−	0.948260i	−0.0358868	−	0.0579242i
$269$	−12.5272			−0.763794			−0.381897	−	0.924205i	$-0.624729\pi$
$269$	−12.5272			−0.763794			−0.381897	+	0.924205i	$0.624729\pi$
$270$	−6.66959	−	5.74801i	−0.405898	−	0.349813i
$271$		−	6.43912i		−	0.391149i	−0.980689	−	0.195574i	$-0.937343\pi$
$271$		−	6.43912i		−	0.391149i	0.980689	−	0.195574i	$-0.0626571\pi$
$272$	1.04036	+	0.517338i	0.0630812	+	0.0313682i
$273$		−	28.6279i		−	1.73264i
$274$	−16.0361	+	28.7995i	−0.968776	+	1.73984i
$275$	14.0662	+	6.05532i	0.848225	+	0.365150i
$276$	16.5372	+	26.6924i	0.995424	+	1.60670i
$277$	−8.46422			−0.508566			−0.254283	−	0.967130i	$-0.581839\pi$
$277$	−8.46422			−0.508566			−0.254283	+	0.967130i	$0.581839\pi$
$278$	12.3653	+	6.88522i	0.741619	+	0.412948i
$279$	2.96451			0.177481
$280$	2.00640	−	12.7033i	0.119905	−	0.759165i
$281$		−	8.27869i		−	0.493865i	−0.969033	−	0.246933i	$-0.920577\pi$
$281$		−	8.27869i		−	0.493865i	0.969033	−	0.246933i	$-0.0794226\pi$
$282$	−0.202326	−	0.112659i	−0.0120484	−	0.00670876i
$283$		−	6.09490i		−	0.362304i	−0.983455	−	0.181152i	$-0.942017\pi$
$283$		−	6.09490i		−	0.362304i	0.983455	−	0.181152i	$-0.0579827\pi$
$284$	−13.7166	−	22.1397i	−0.813932	−	1.31375i
$285$	−7.23160	−	19.8980i	−0.428363	−	1.17866i
$286$	13.6577	−	24.5281i	0.807598	−	1.45038i
$287$		−	17.4654i		−	1.03095i
$288$	8.01483	−	5.49824i	0.472278	−	0.323987i
$289$	16.9156			0.995037
$290$	17.9551	+	15.4741i	1.05436	+	0.908673i
$291$	8.47806			0.496993
$292$	−18.3307	+	11.3568i	−1.07272	+	0.664604i
$293$		−	23.3576i		−	1.36456i	−0.731089	−	0.682282i	$-0.760988\pi$
$293$		−	23.3576i		−	1.36456i	0.731089	−	0.682282i	$-0.239012\pi$
$294$	7.68934	+	4.28158i	0.448452	+	0.249707i
$295$	2.84156	−	13.7873i	0.165442	−	0.802725i
$296$	2.23488	−	0.104231i	0.129900	−	0.00605833i
$297$	−8.52787			−0.494837
$298$	−11.7309	+	21.0677i	−0.679553	+	1.22042i
$299$			46.8469i			2.70923i
$300$	3.20647	+	21.4834i	0.185125	+	1.24034i
$301$			21.0293i			1.21211i
$302$	21.0593	+	11.7262i	1.21183	+	0.674769i
$303$		−	19.8730i		−	1.14168i
$304$	−17.3644	+	1.57380i	−0.995918	+	0.0902639i
$305$	−2.94833	+	14.3053i	−0.168821	+	0.819119i
$306$	−0.343367	+	0.616658i	−0.0196290	+	0.0352520i
$307$	27.5932			1.57483			0.787414	−	0.616424i	$-0.211419\pi$
$307$	27.5932			1.57483			0.787414	+	0.616424i	$0.211419\pi$
$308$	−6.56028	−	10.5888i	−0.373807	−	0.603354i
$309$		−	0.943514i		−	0.0536746i
$310$	4.13304	+	3.56195i	0.234741	+	0.202305i
$311$			11.7699i			0.667413i	0.942677	+	0.333706i	$0.108299\pi$
$311$			11.7699i			0.667413i	−0.942677	+	0.333706i	$0.891701\pi$
$312$	39.7766	−	1.85512i	2.25191	−	0.105026i
$313$			3.49384i			0.197484i	0.995113	+	0.0987418i	$0.0314818\pi$
$313$			3.49384i			0.197484i	−0.995113	+	0.0987418i	$0.968518\pi$
$314$	−9.38552	−	5.22604i	−0.529656	−	0.294923i
$315$	7.65165	+	1.57701i	0.431122	+	0.0888544i
$316$	7.67578	+	12.3893i	0.431796	+	0.696954i
$317$		−	25.6965i		−	1.44326i	−0.692280	−	0.721629i	$-0.743394\pi$
$317$		−	25.6965i		−	1.44326i	0.692280	−	0.721629i	$-0.256606\pi$
$318$	4.71620	−	8.46990i	0.264472	−	0.474968i
$319$	22.9578			1.28539
$320$	17.7803	+	1.96457i	0.993951	+	0.109823i
$321$	33.6414			1.87768
$322$	18.1602	+	10.1120i	1.01203	+	0.563517i
$323$	1.07819	−	0.663788i	0.0599923	−	0.0369341i
$324$	−11.7997	−	19.0458i	−0.655542	−	1.05810i
$325$	−12.8139	+	29.7660i	−0.710785	+	1.65112i
$326$	7.75725	−	13.9314i	0.429635	−	0.771587i
$327$	−7.85122			−0.434174
$328$	24.2669	−	1.13177i	1.33992	−	0.0624918i
$329$	−0.153296			−0.00845146
$330$	15.9366	+	13.7345i	0.877281	+	0.756061i
$331$		−	2.51332i		−	0.138144i	−0.997612	−	0.0690722i	$-0.977996\pi$
$331$		−	2.51332i		−	0.138144i	0.997612	−	0.0690722i	$-0.0220039\pi$
$332$	−20.4231	+	12.6531i	−1.12086	+	0.694427i
$333$			1.35909i			0.0744777i
$334$	7.31442	−	13.1361i	0.400227	−	0.718774i
$335$	1.22150	+	0.251751i	0.0667374	+	0.0137546i
$336$	7.86668	−	15.8198i	0.429163	−	0.863042i
$337$	1.48035			0.0806398			0.0403199	−	0.999187i	$-0.487162\pi$
$337$	1.48035			0.0806398			0.0403199	+	0.999187i	$0.487162\pi$
$338$	35.8421	+	19.9576i	1.94955	+	1.08555i
$339$	−13.1437			−0.713870
$340$	−1.21965	+	0.447161i	−0.0661446	+	0.0242507i
$341$	5.28458			0.286176
$342$	−0.463573	−	10.5814i	−0.0250671	−	0.572177i
$343$	20.0602			1.08315
$344$	−29.2188	+	1.36272i	−1.57537	+	0.0734732i
$345$	−34.3837	−	7.08650i	−1.85116	−	0.381524i
$346$	−10.1924	+	18.3047i	−0.547949	+	0.984069i
$347$		−	20.7077i		−	1.11165i	−0.831301	−	0.555823i	$-0.812403\pi$
$347$		−	20.7077i		−	1.11165i	0.831301	−	0.555823i	$-0.187597\pi$
$348$	17.1496	+	27.6808i	0.919314	+	1.48385i
$349$		−	25.8876i		−	1.38573i	−0.721066	−	0.692867i	$-0.756347\pi$
$349$		−	25.8876i		−	1.38573i	0.721066	−	0.692867i	$-0.243653\pi$
$350$	8.77288	+	11.3923i	0.468930	+	0.608944i
$351$		−	18.0461i		−	0.963229i
$352$	14.2873	−	9.80123i	0.761518	−	0.522407i
$353$		−	21.8390i		−	1.16238i	−0.813770	−	0.581188i	$-0.802588\pi$
$353$		−	21.8390i		−	1.16238i	0.813770	−	0.581188i	$-0.197412\pi$
$354$	9.40804	−	16.8960i	0.500032	−	0.898014i
$355$	28.5192	+	5.87782i	1.51364	+	0.311962i
$356$	0.987904	−	0.612053i	0.0523588	−	0.0324388i
$357$			1.28300i			0.0679038i
$358$	−8.88462	+	15.9560i	−0.469567	+	0.843301i
$359$			13.6703i			0.721493i	0.932664	+	0.360747i	$0.117478\pi$
$359$			13.6703i			0.721493i	−0.932664	+	0.360747i	$0.882522\pi$
$360$	−1.69531	+	10.7336i	−0.0893508	+	0.565713i
$361$	−8.55575	+	16.9646i	−0.450303	+	0.892876i
$362$	−19.3322	−	10.7645i	−1.01608	−	0.565771i
$363$	−3.51666			−0.184577
$364$	22.4073	−	13.8824i	1.17446	−	0.727636i
$365$	4.86657	−	23.6126i	0.254728	−	1.23594i
$366$	−9.76154	+	17.5309i	−0.510244	+	0.916354i
$367$	4.92069			0.256858			0.128429	−	0.991719i	$-0.459007\pi$
$367$	4.92069			0.256858			0.128429	+	0.991719i	$0.459007\pi$
$368$	−12.8731	+	25.8877i	−0.671056	+	1.34949i
$369$			14.7574i			0.768239i
$370$	−1.63299	+	1.89480i	−0.0848949	+	0.0985061i
$371$		−	6.41734i		−	0.333172i
$372$	3.94761	+	6.37177i	0.204674	+	0.330361i
$373$			22.4580i			1.16283i	0.813607	+	0.581415i	$0.197501\pi$
$373$			22.4580i			1.16283i	−0.813607	+	0.581415i	$0.802499\pi$
$374$	−0.612091	+	1.09926i	−0.0316505	+	0.0568416i
$375$	−19.9086	−	13.9075i	−1.02808	−	0.718181i
$376$	−0.00993373	−	0.212994i	−0.000512293	−	0.0109843i
$377$			48.5816i			2.50208i
$378$	−6.99556	−	3.89526i	−0.359813	−	0.200351i
$379$		−	29.5964i		−	1.52027i	−0.649767	−	0.760133i	$-0.725134\pi$
$379$		−	29.5964i		−	1.52027i	0.649767	−	0.760133i	$-0.274866\pi$
$380$	12.0676	−	15.3093i	0.619053	−	0.785349i
$381$			8.81549i			0.451631i
$382$	−2.10487	+	3.78017i	−0.107695	+	0.193410i
$383$		−	14.9234i		−	0.762549i	−0.924462	−	0.381274i	$-0.875485\pi$
$383$		−	14.9234i		−	0.762549i	0.924462	−	0.381274i	$-0.124515\pi$
$384$	22.4904	+	9.90508i	1.14771	+	0.505467i
$385$	13.6399	+	2.81120i	0.695155	+	0.143272i
$386$	4.58466	+	2.55283i	0.233353	+	0.129936i
$387$		−	17.7688i		−	0.903238i
$388$	4.11123	+	6.63585i	0.208716	+	0.336884i
$389$			27.2805i			1.38318i	0.722292	+	0.691589i	$0.243089\pi$
$389$			27.2805i			1.38318i	−0.722292	+	0.691589i	$0.756911\pi$
$390$	−29.0641	+	33.7239i	−1.47172	+	1.70768i
$391$		−	2.09952i		−	0.106177i
$392$	0.377528	+	8.09476i	0.0190680	+	0.408847i
$393$	32.3811			1.63341
$394$	−20.3880	−	11.3524i	−1.02713	−	0.571927i
$395$	−15.9592	−	3.28921i	−0.802997	−	0.165498i
$396$	5.54312	+	8.94705i	0.278552	+	0.449606i
$397$	−0.925751			−0.0464621			−0.0232311	−	0.999730i	$-0.507395\pi$
$397$	−0.925751			−0.0464621			−0.0232311	+	0.999730i	$0.507395\pi$
$398$	15.2572	−	27.4007i	0.764777	−	1.37347i
$399$	−10.0936	−	16.3951i	−0.505312	−	0.820781i
$400$	−15.2603	+	12.9276i	−0.763017	+	0.646378i
$401$			24.5355i			1.22524i	0.790376	+	0.612622i	$0.209885\pi$
$401$			24.5355i			1.22524i	−0.790376	+	0.612622i	$0.790115\pi$
$402$	1.49692	+	0.833514i	0.0746596	+	0.0415719i
$403$			11.1829i			0.557058i
$404$	15.5548	−	9.63693i	0.773880	−	0.479455i
$405$	24.5337	+	5.05640i	1.21909	+	0.251255i
$406$	18.8327	+	10.4864i	0.934649	+	0.520431i
$407$			2.42273i			0.120090i
$408$	−1.78265	+	0.0831401i	−0.0882543	+	0.00411605i
$409$		−	10.3479i		−	0.511670i	−0.966720	−	0.255835i	$-0.917650\pi$
$409$		−	10.3479i		−	0.511670i	0.966720	−	0.255835i	$-0.0823505\pi$
$410$	−17.7314	+	20.5743i	−0.875693	+	1.01609i
$411$		−	50.6291i		−	2.49735i
$412$	0.738497	−	0.457534i	0.0363831	−	0.0225411i
$413$		−	12.8015i		−	0.629922i
$414$	−15.3445	−	8.54412i	−0.754141	−	0.419920i
$415$	5.42206	−	26.3078i	0.266159	−	1.29140i
$416$	20.7407	+	30.2339i	1.01690	+	1.48234i
$417$	−21.7380			−1.06451
$418$	−0.826371	−	18.8625i	−0.0404191	−	0.922597i
$419$	13.0061			0.635391			0.317695	−	0.948193i	$-0.397091\pi$
$419$	13.0061			0.635391			0.317695	+	0.948193i	$0.397091\pi$
$420$	6.79957	+	18.5460i	0.331785	+	0.904954i
$421$	−10.4954			−0.511517			−0.255758	−	0.966741i	$-0.582325\pi$
$421$	−10.4954			−0.511517			−0.255758	+	0.966741i	$0.582325\pi$
$422$	−7.67358	+	13.7811i	−0.373544	+	0.670853i
$423$	0.129527			0.00629784
$424$	8.91647	−	0.415851i	0.433022	−	0.0201955i
$425$	0.574272	−	1.33401i	0.0278563	−	0.0647088i
$426$	34.9497	+	19.4607i	1.69332	+	0.942874i
$427$			13.2825i			0.642787i
$428$	16.3136	+	26.3314i	0.788545	+	1.27278i
$429$			43.1201i			2.08186i
$430$	21.3497	−	24.7727i	1.02957	−	1.19465i
$431$	−6.15950			−0.296693			−0.148346	−	0.988935i	$-0.547395\pi$
$431$	−6.15950			−0.296693			−0.148346	+	0.988935i	$0.547395\pi$
$432$	4.95889	−	9.97228i	0.238585	−	0.479791i
$433$	27.7801			1.33503			0.667514	−	0.744597i	$-0.267359\pi$
$433$	27.7801			1.33503			0.667514	+	0.744597i	$0.267359\pi$
$434$	4.33504	+	2.41383i	0.208088	+	0.115868i
$435$	−35.6569	−	7.34890i	−1.70962	−	0.352353i
$436$	−3.80725	−	6.14522i	−0.182334	−	0.294303i
$437$	16.5172	+	26.8290i	0.790126	+	1.28341i
$438$	16.1126	−	28.9368i	0.769889	−	1.38266i
$439$	12.6703			0.604722			0.302361	−	0.953193i	$-0.402225\pi$
$439$	12.6703			0.604722			0.302361	+	0.953193i	$0.402225\pi$
$440$	−3.02209	+	19.1339i	−0.144072	+	0.912175i
$441$	−4.92264			−0.234412
$442$	−2.32619	−	1.29527i	−0.110645	−	0.0616095i
$443$			12.5615i			0.596817i	0.954438	+	0.298408i	$0.0964557\pi$
$443$			12.5615i			0.596817i	−0.954438	+	0.298408i	$0.903544\pi$
$444$	−2.92116	+	1.80979i	−0.138632	+	0.0858890i
$445$	−0.262276	+	1.27256i	−0.0124331	+	0.0603253i
$446$	17.6402	−	31.6803i	0.835287	−	1.50010i
$447$		−	37.0367i		−	1.75178i
$448$	16.1971	−	1.51411i	0.765239	−	0.0715349i
$449$		−	26.1401i		−	1.23363i	−0.787108	−	0.616815i	$-0.788423\pi$
$449$		−	26.1401i		−	1.23363i	0.787108	−	0.616815i	$-0.211577\pi$
$450$	−7.41266	−	9.62595i	−0.349436	−	0.453771i
$451$			26.3067i			1.23873i
$452$	−6.37373	−	10.2877i	−0.299795	−	0.483893i
$453$	−37.0220			−1.73945
$454$	5.54645	+	3.08837i	0.260308	+	0.144945i
$455$	−5.94886	+	28.8639i	−0.278887	+	1.35316i
$456$	22.1258	−	15.0868i	1.03614	−	0.706504i
$457$			20.4139i			0.954922i	0.878653	+	0.477461i	$0.158443\pi$
$457$			20.4139i			0.954922i	−0.878653	+	0.477461i	$0.841557\pi$
$458$	4.97607	−	8.93660i	0.232517	−	0.417580i
$459$			0.808762i			0.0377498i
$460$	−11.1268	−	30.3488i	−0.518792	−	1.41502i
$461$			3.75548i			0.174910i	0.996168	+	0.0874552i	$0.0278734\pi$
$461$			3.75548i			0.174910i	−0.996168	+	0.0874552i	$0.972127\pi$
$462$	16.7155	+	9.30751i	0.777675	+	0.433025i
$463$	−20.0853			−0.933445			−0.466722	−	0.884404i	$-0.654565\pi$
$463$	−20.0853			−0.933445			−0.466722	+	0.884404i	$0.654565\pi$
$464$	−13.3498	+	26.8462i	−0.619747	+	1.24631i
$465$	−8.20775	−	1.69162i	−0.380625	−	0.0784471i
$466$	−12.9289	+	23.2192i	−0.598920	+	1.07561i
$467$		−	35.3060i		−	1.63377i	−0.576802	−	0.816884i	$-0.695700\pi$
$467$		−	35.3060i		−	1.63377i	0.576802	−	0.816884i	$-0.304300\pi$
$468$	−18.9331	+	11.7300i	−0.875184	+	0.542218i
$469$	1.13416			0.0523708
$470$	0.180583	+	0.155631i	0.00832969	+	0.00717873i
$471$	16.4996			0.760263
$472$	17.7869	−	0.829553i	0.818707	−	0.0381833i
$473$		−	31.6749i		−	1.45641i
$474$	−19.5578	−	10.8901i	−0.898318	−	0.500201i
$475$	3.15641	+	21.5647i	0.144826	+	0.989457i
$476$	−1.00422	+	0.622161i	−0.0460283	+	0.0285167i
$477$			5.42235i			0.248272i
$478$	−4.99825	+	8.97642i	−0.228614	+	0.410572i
$479$		−	13.1322i		−	0.600027i	−0.953935	−	0.300014i	$-0.903009\pi$
$479$		−	13.1322i		−	0.600027i	0.953935	−	0.300014i	$-0.0969912\pi$
$480$	−25.3278	+	10.6493i	−1.15605	+	0.486074i
$481$	−5.12682			−0.233763
$482$	0.587755	−	1.05556i	0.0267715	−	0.0480793i
$483$	−31.9254			−1.45266
$484$	−1.70532	−	2.75252i	−0.0775143	−	0.125114i
$485$	−8.54794	−	1.76173i	−0.388142	−	0.0799962i
$486$	19.7449	+	10.9943i	0.895647	+	0.498714i
$487$			0.468139i			0.0212134i	0.999944	+	0.0106067i	$0.00337628\pi$
$487$			0.468139i			0.0212134i	−0.999944	+	0.0106067i	$0.996624\pi$
$488$	−18.4552	+	0.860723i	−0.835427	+	0.0389631i
$489$			24.4912i			1.10753i
$490$	−6.86301	−	5.91470i	−0.310039	−	0.267199i
$491$	16.1827			0.730315			0.365158	−	0.930946i	$-0.381015\pi$
$491$	16.1827			0.730315			0.365158	+	0.930946i	$0.381015\pi$
$492$	−31.7188	+	19.6513i	−1.42999	+	0.885947i
$493$		−	2.17726i		−	0.0980588i
$494$	39.9156	−	1.74871i	1.79589	−	0.0786781i
$495$	−11.5251	−	2.37533i	−0.518014	−	0.106763i
$496$	−3.07294	+	6.17966i	−0.137979	+	0.277475i
$497$	26.4802			1.18780
$498$	17.9517	−	32.2398i	0.804437	−	1.44470i
$499$	−33.8073			−1.51342			−0.756710	−	0.653750i	$-0.773195\pi$
$499$	−33.8073			−1.51342			−0.756710	+	0.653750i	$0.773195\pi$
$500$	1.23134	−	22.3268i	0.0550671	−	0.998483i
$501$			23.0930i			1.03172i
$502$	6.86712	+	3.82374i	0.306494	+	0.170662i
$503$	−20.7837			−0.926698			−0.463349	−	0.886176i	$-0.653352\pi$
$503$	−20.7837			−0.926698			−0.463349	+	0.886176i	$0.653352\pi$
$504$	0.460385	+	9.87135i	0.0205072	+	0.439705i
$505$	−4.12960	+	20.0368i	−0.183765	+	0.891627i
$506$	−27.3533	−	15.2309i	−1.21600	−	0.677094i
$507$	−63.0100			−2.79837
$508$	−6.89996	+	4.27485i	−0.306136	+	0.189666i
$509$	20.9109			0.926860			0.463430	−	0.886134i	$-0.346619\pi$
$509$	20.9109			0.926860			0.463430	+	0.886134i	$0.346619\pi$
$510$	1.30255	−	1.51139i	0.0576779	−	0.0669254i
$511$		−	21.9244i		−	0.969879i
$512$	3.15334	+	22.4066i	0.139359	+	0.990242i
$513$	−6.36267	−	10.3349i	−0.280919	−	0.456297i
$514$	27.2334	+	15.1641i	1.20121	+	0.668858i
$515$	−0.196061	+	0.951290i	−0.00863950	+	0.0419188i
$516$	38.1913	−	23.6613i	1.68128	−	1.04163i
$517$	0.230897			0.0101549
$518$	−1.10663	+	1.98741i	−0.0486225	+	0.0873218i
$519$		−	32.1795i		−	1.41252i
$520$	−40.4899	−	6.39513i	−1.77560	−	0.280445i
$521$		−	19.2274i		−	0.842366i	−0.906976	−	0.421183i	$-0.861615\pi$
$521$		−	19.2274i		−	0.842366i	0.906976	−	0.421183i	$-0.138385\pi$
$522$	−15.9127	−	8.86050i	−0.696480	−	0.387813i
$523$	30.2130			1.32112			0.660562	−	0.750772i	$-0.270318\pi$
$523$	30.2130			1.32112			0.660562	+	0.750772i	$0.270318\pi$
$524$	15.7024	+	25.3450i	0.685964	+	1.10720i
$525$	−20.2850	−	8.73243i	−0.885310	−	0.381115i
$526$	−20.6602	−	11.5040i	−0.900827	−	0.501598i
$527$		−	0.501177i		−	0.0218316i
$528$	−11.8490	+	23.8282i	−0.515660	+	1.03699i
$529$	29.2429			1.27143
$530$	−6.51511	+	7.55968i	−0.282998	+	0.328371i
$531$			10.8167i			0.469404i
$532$	7.93794	−	15.8507i	0.344153	−	0.687217i
$533$	−55.6685			−2.41127
$534$	−0.868362	+	1.55950i	−0.0375777	+	0.0674863i
$535$	−33.9186	−	6.99065i	−1.46643	−	0.302232i
$536$	0.0734951	+	1.57584i	0.00317450	+	0.0680661i
$537$		−	28.0505i		−	1.21047i
$538$	15.4783	+	8.61863i	0.667318	+	0.371576i
$539$	−8.77517			−0.377973
$540$	4.28621	+	11.6908i	0.184449	+	0.503091i
$541$		−	27.9086i		−	1.19988i	−0.800044	−	0.599942i	$-0.795190\pi$
$541$		−	27.9086i		−	1.19988i	0.800044	−	0.599942i	$-0.204810\pi$
$542$	−4.43009	+	7.95605i	−0.190289	+	0.341742i
$543$	33.9857			1.45846
$544$	−0.929526	−	1.35498i	−0.0398531	−	0.0580942i
$545$	7.91593	+	1.63148i	0.339081	+	0.0698848i
$546$	−19.6959	+	35.3722i	−0.842907	+	1.51379i
$547$	−19.9731			−0.853990			−0.426995	−	0.904254i	$-0.640428\pi$
$547$	−19.9731			−0.853990			−0.426995	+	0.904254i	$0.640428\pi$
$548$	39.6278	−	24.5513i	1.69282	−	1.04878i
$549$		−	11.2231i		−	0.478990i
$550$	−13.2139	−	17.1593i	−0.563443	−	0.731677i
$551$	17.1289	+	27.8225i	0.729714	+	1.18528i
$552$	−2.06880	−	44.3582i	−0.0880541	−	1.88801i
$553$	−14.8182			−0.630135
$554$	10.4582	+	5.82335i	0.444328	+	0.247410i
$555$	0.775530	−	3.76287i	0.0329194	−	0.159725i
$556$	−10.5413	−	17.0145i	−0.447050	−	0.721575i
$557$	−3.48721			−0.147758			−0.0738789	−	0.997267i	$-0.523538\pi$
$557$	−3.48721			−0.147758			−0.0738789	+	0.997267i	$0.523538\pi$
$558$	−3.66290	−	2.03957i	−0.155063	−	0.0863420i
$559$	67.0282			2.83499
$560$	−11.2189	+	14.3155i	−0.474083	+	0.604941i
$561$		−	1.93249i		−	0.0815898i
$562$	−5.69570	+	10.2290i	−0.240259	+	0.431484i
$563$	−29.6737			−1.25060			−0.625299	−	0.780385i	$-0.715023\pi$
$563$	−29.6737			−1.25060			−0.625299	+	0.780385i	$0.715023\pi$
$564$	0.172482	+	0.278400i	0.00726279	+	0.0117227i
$565$	13.2521	+	2.73126i	0.557518	+	0.114905i
$566$	−4.19327	+	7.53075i	−0.176256	+	0.316541i
$567$	22.7796			0.956655
$568$	1.71595	+	36.7924i	0.0719995	+	1.54378i
$569$			8.59891i			0.360485i	0.983622	+	0.180242i	$0.0576882\pi$
$569$			8.59891i			0.360485i	−0.983622	+	0.180242i	$0.942312\pi$
$570$	−4.75452	+	29.5609i	−0.199145	+	1.23817i
$571$	5.42526			0.227040			0.113520	−	0.993536i	$-0.463787\pi$
$571$	5.42526			0.227040			0.113520	+	0.993536i	$0.463787\pi$
$572$	−33.7505	+	20.9100i	−1.41118	+	0.874291i
$573$		−	6.64549i		−	0.277619i
$574$	−12.0161	+	21.5799i	−0.501542	+	0.900726i
$575$	33.1945	+	14.2898i	1.38431	+	0.595926i
$576$	−13.6857	+	1.27935i	−0.570239	+	0.0533062i
$577$		−	40.7260i		−	1.69545i	−0.530440	−	0.847723i	$-0.677973\pi$
$577$		−	40.7260i		−	1.69545i	0.530440	−	0.847723i	$-0.322027\pi$
$578$	−20.9006	−	11.6379i	−0.869352	−	0.484072i
$579$	−8.05978			−0.334953
$580$	−11.5389	−	31.4726i	−0.479125	−	1.30683i
$581$		−	24.4270i		−	1.01340i
$582$	−10.4753	−	5.83287i	−0.434217	−	0.241780i
$583$			9.66595i			0.400323i
$584$	30.4625	−	1.42073i	1.26055	−	0.0587901i
$585$	5.02650	−	24.3886i	0.207820	−	1.00834i
$586$	−16.0699	+	28.8602i	−0.663842	+	1.19220i
$587$			7.35706i			0.303659i	0.988407	+	0.151829i	$0.0485164\pi$
$587$			7.35706i			0.303659i	−0.988407	+	0.151829i	$0.951484\pi$
$588$	−6.55510	−	10.5805i	−0.270328	−	0.436331i
$589$	3.94284	+	6.40437i	0.162462	+	0.263888i
$590$	−12.9966	+	15.0803i	−0.535060	+	0.620846i
$591$	35.8418			1.47433
$592$	−2.83308	−	1.40880i	−0.116439	−	0.0579013i
$593$			13.7766i			0.565737i	0.959159	+	0.282868i	$0.0912859\pi$
$593$			13.7766i			0.565737i	−0.959159	+	0.282868i	$0.908714\pi$
$594$	10.5369	+	5.86714i	0.432333	+	0.240732i
$595$	0.266607	−	1.29358i	0.0109298	−	0.0530316i
$596$	28.9890	−	17.9600i	1.18743	−	0.735671i
$597$			48.1701i			1.97147i
$598$	32.2305	−	57.8832i	1.31800	−	2.36702i
$599$	−21.6806			−0.885847			−0.442924	−	0.896559i	$-0.646059\pi$
$599$	−21.6806			−0.885847			−0.442924	+	0.896559i	$0.646059\pi$
$600$	10.8186	−	28.7505i	0.441669	−	1.17374i
$601$		−	35.8998i		−	1.46438i	−0.681098	−	0.732192i	$-0.738497\pi$
$601$		−	35.8998i		−	1.46438i	0.681098	−	0.732192i	$-0.261503\pi$
$602$	14.4681	−	25.9835i	0.589676	−	1.05901i
$603$	−0.958314			−0.0390256
$604$	−17.9529	−	28.9774i	−0.730493	−	1.17908i
$605$	3.54564	+	0.730758i	0.144151	+	0.0297096i
$606$	−13.6726	+	24.5548i	−0.555410	+	0.997469i
$607$		−	17.8856i		−	0.725954i	−0.931798	−	0.362977i	$-0.881760\pi$
$607$		−	17.8856i		−	0.725954i	0.931798	−	0.362977i	$-0.118240\pi$
$608$	22.5379	+	10.0021i	0.914034	+	0.405638i
$609$	−33.1076			−1.34159
$610$	13.4849	−	15.6469i	0.545987	−	0.633526i
$611$			0.488609i			0.0197670i
$612$	0.848517	−	0.525696i	0.0342993	−	0.0212500i
$613$	−3.76326			−0.151997			−0.0759984	−	0.997108i	$-0.524214\pi$
$613$	−3.76326			−0.151997			−0.0759984	+	0.997108i	$0.524214\pi$
$614$	−34.0937	−	18.9840i	−1.37591	−	0.766133i
$615$	8.42092	−	40.8583i	0.339564	−	1.64757i
$616$	0.820689	+	17.5968i	0.0330665	+	0.708995i
$617$			7.29370i			0.293633i	0.989164	+	0.146817i	$0.0469027\pi$
$617$			7.29370i			0.293633i	−0.989164	+	0.146817i	$0.953097\pi$
$618$	−0.649134	+	1.16579i	−0.0261120	+	0.0468949i
$619$	−17.6571			−0.709699			−0.354850	−	0.934923i	$-0.615468\pi$
$619$	−17.6571			−0.709699			−0.354850	+	0.934923i	$0.615468\pi$
$620$	−2.65610	−	7.24459i	−0.106671	−	0.290950i
$621$	−20.1247			−0.807576
$622$	8.09768	−	14.5427i	0.324687	−	0.583110i
$623$			1.18158i			0.0473390i
$624$	−50.4236	−	25.0740i	−2.01856	−	1.00376i
$625$	17.1827	+	18.1591i	0.687309	+	0.726365i
$626$	2.40375	−	4.31693i	0.0960731	−	0.172539i
$627$	15.2032	+	24.6947i	0.607158	+	0.986210i
$628$	8.00108	+	12.9144i	0.319278	+	0.515341i
$629$	0.229766			0.00916137
$630$	−8.36926	−	7.21283i	−0.333439	−	0.287366i
$631$			11.9122i			0.474216i	0.971483	+	0.237108i	$0.0761995\pi$
$631$			11.9122i			0.474216i	−0.971483	+	0.237108i	$0.923801\pi$
$632$	−0.960238	−	20.5889i	−0.0381962	−	0.818984i
$633$		−	24.2270i		−	0.962936i
$634$	−17.6791	+	31.7501i	−0.702126	+	1.26096i
$635$	1.83185	−	8.88815i	0.0726948	−	0.352715i
$636$	−11.6545	+	7.22052i	−0.462131	+	0.286312i
$637$		−	18.5694i		−	0.735747i
$638$	−28.3662	−	15.7948i	−1.12303	−	0.625324i
$639$	−22.3745			−0.885121
$640$	−20.6174	−	14.6602i	−0.814976	−	0.579495i
$641$			21.1484i			0.835313i	0.908605	+	0.417656i	$0.137148\pi$
$641$			21.1484i			0.835313i	−0.908605	+	0.417656i	$0.862852\pi$
$642$	−41.5667	−	23.1451i	−1.64051	−	0.913466i
$643$			36.8041i			1.45141i	0.688004	+	0.725707i	$0.258487\pi$
$643$			36.8041i			1.45141i	−0.688004	+	0.725707i	$0.741513\pi$
$644$	−15.4814	−	24.9883i	−0.610054	−	0.984677i
$645$	−10.1393	+	49.1959i	−0.399234	+	1.93709i
$646$	−1.78888	+	0.0783710i	−0.0703825	+	0.00308347i
$647$	−22.1511			−0.870851			−0.435426	−	0.900225i	$-0.643402\pi$
$647$	−22.1511			−0.870851			−0.435426	+	0.900225i	$0.643402\pi$
$648$	1.47615	+	31.6508i	0.0579885	+	1.24336i
$649$			19.2820i			0.756883i
$650$	36.3114	−	27.9624i	1.42425	−	1.09677i
$651$	−7.62094			−0.298688
$652$	−19.1694	+	11.8764i	−0.750733	+	0.465115i
$653$	46.7051			1.82771			0.913857	−	0.406037i	$-0.133090\pi$
$653$	46.7051			1.82771			0.913857	+	0.406037i	$0.133090\pi$
$654$	9.70083	+	5.40161i	0.379332	+	0.211220i
$655$	−32.6480	−	6.72877i	−1.27566	−	0.262915i
$656$	−30.7624	−	15.2972i	−1.20107	−	0.597253i
$657$			18.5251i			0.722732i
$658$	0.189409	+	0.105467i	0.00738394	+	0.00411152i
$659$			16.9399i			0.659886i	0.944001	+	0.329943i	$0.107029\pi$
$659$			16.9399i			0.659886i	−0.944001	+	0.329943i	$0.892971\pi$
$660$	−10.2417	−	27.9345i	−0.398656	−	1.08735i
$661$	0.654810			0.0254692			0.0127346	−	0.999919i	$-0.495946\pi$
$661$	0.654810			0.0254692			0.0127346	+	0.999919i	$0.495946\pi$
$662$	−1.72915	+	3.10541i	−0.0672054	+	0.120695i
$663$	4.08940			0.158819
$664$	33.9396	−	1.58289i	1.31711	−	0.0614282i
$665$	6.76991	+	18.6277i	0.262526	+	0.722349i
$666$	0.935048	−	1.67927i	0.0362324	−	0.0650702i
$667$	54.1774			2.09776
$668$	−18.0751	+	11.1984i	−0.699348	+	0.433279i
$669$			55.6935i			2.15323i
$670$	−1.33605	−	1.15144i	−0.0516162	−	0.0444841i
$671$		−	20.0065i		−	0.772341i
$672$	−20.6039	+	14.1344i	−0.794813	+	0.545248i
$673$	34.6820			1.33689			0.668446	−	0.743761i	$-0.266960\pi$
$673$	34.6820			1.33689			0.668446	+	0.743761i	$0.266960\pi$
$674$	−1.82909	−	1.01847i	−0.0704540	−	0.0392302i
$675$	−12.7870	−	5.50463i	−0.492171	−	0.211873i
$676$	−30.5551	−	49.3184i	−1.17520	−	1.89686i
$677$		−	1.21723i		−	0.0467821i	−0.999726	−	0.0233911i	$-0.992554\pi$
$677$		−	1.21723i		−	0.0467821i	0.999726	−	0.0233911i	$-0.00744628\pi$
$678$	16.2402	+	9.04283i	0.623699	+	0.347288i
$679$	−7.93680			−0.304586
$680$	1.81462	+	0.286608i	0.0695874	+	0.0109909i
$681$	−9.75059			−0.373644
$682$	−6.52953	−	3.63577i	−0.250029	−	0.139221i
$683$	19.2304			0.735829			0.367915	−	0.929860i	$-0.380072\pi$
$683$	19.2304			0.735829			0.367915	+	0.929860i	$0.380072\pi$
$684$	−6.70718	+	13.3931i	−0.256455	+	0.512099i
$685$	−10.5207	+	51.0463i	−0.401974	+	1.95038i
$686$	−24.7860	−	13.8013i	−0.946333	−	0.526937i
$687$			15.7104i			0.599390i
$688$	37.0398	+	18.4187i	1.41213	+	0.702206i
$689$	−20.4544			−0.779251
$690$	37.6084	+	32.4118i	1.43173	+	1.23390i
$691$	−5.75832			−0.219057			−0.109528	−	0.993984i	$-0.534934\pi$
$691$	−5.75832			−0.219057			−0.109528	+	0.993984i	$0.534934\pi$
$692$	25.1872	−	15.6046i	0.957473	−	0.593200i
$693$	−10.7011			−0.406501
$694$	−14.2468	+	25.5860i	−0.540800	+	0.971231i
$695$	21.9171	+	4.51713i	0.831364	+	0.171344i
$696$	−2.14541	−	46.0007i	−0.0813215	−	1.74365i
$697$	2.49487			0.0944998
$698$	−17.8106	+	31.9863i	−0.674141	+	1.21070i
$699$		−	40.8191i		−	1.54392i
$700$	−3.00176	−	20.1118i	−0.113456	−	0.760155i
$701$		−	7.41147i		−	0.279928i	−0.990157	−	0.139964i	$-0.955301\pi$
$701$		−	7.41147i		−	0.279928i	0.990157	−	0.139964i	$-0.0446986\pi$
$702$	−12.4156	+	22.2974i	−0.468598	+	0.841561i
$703$	−2.93611	+	1.80761i	−0.110737	+	0.0681752i
$704$	−24.3964	+	2.28058i	−0.919474	+	0.0859528i
$705$	−0.358619	−	0.0739115i	−0.0135064	−	0.00278367i
$706$	−15.0252	+	26.9839i	−0.565480	+	1.01555i
$707$			18.6043i			0.699686i
$708$	−23.2488	+	14.4037i	−0.873743	+	0.541325i
$709$			37.2505i			1.39897i	0.714646	+	0.699486i	$0.246588\pi$
$709$			37.2505i			1.39897i	−0.714646	+	0.699486i	$0.753412\pi$
$710$	−31.1939	−	26.8836i	−1.17068	−	1.00892i
$711$	12.5207			0.469563
$712$	−1.64173	+	0.0765677i	−0.0615263	+	0.00286950i
$713$	12.4709			0.467041
$714$	0.882702	−	1.58526i	0.0330343	−	0.0593267i
$715$	8.96031	−	43.4754i	0.335097	−	1.62589i
$716$	21.9553	−	13.6024i	0.820510	−	0.508344i
$717$		−	15.7804i		−	0.589331i
$718$	9.40514	−	16.8908i	0.350997	−	0.630360i
$719$			9.61636i			0.358630i	0.983792	+	0.179315i	$0.0573881\pi$
$719$			9.61636i			0.358630i	−0.983792	+	0.179315i	$0.942612\pi$
$720$	9.47940	−	12.0959i	0.353276	−	0.450788i
$721$			0.883277i			0.0328950i
$722$	22.2429	−	15.0749i	0.827796	−	0.561029i
$723$			1.85566i			0.0690126i
$724$	16.4805	+	26.6009i	0.612493	+	0.988614i
$725$	34.4237	+	14.8189i	1.27846	+	0.550362i
$726$	4.34512	+	2.41945i	0.161262	+	0.0897941i
$727$	10.6440			0.394764			0.197382	−	0.980327i	$-0.436756\pi$
$727$	10.6440			0.394764			0.197382	+	0.980327i	$0.436756\pi$
$728$	−37.2371	+	1.73669i	−1.38010	+	0.0643659i
$729$	−1.10408			−0.0408919
$730$	−22.2584	+	25.8271i	−0.823821	+	0.955905i
$731$	−3.00397			−0.111106
$732$	24.1224	−	14.9449i	0.891588	−	0.552381i
$733$	−14.9199			−0.551079			−0.275540	−	0.961290i	$-0.588857\pi$
$733$	−14.9199			−0.551079			−0.275540	+	0.961290i	$0.588857\pi$
$734$	−6.07991	−	3.38541i	−0.224413	−	0.124958i
$735$	13.6292	+	2.80898i	0.502720	+	0.103611i
$736$	33.7163	−	23.1297i	1.24280	−	0.852571i
$737$	−1.70830			−0.0629262
$738$	10.1530	−	18.2340i	0.373738	−	0.671201i
$739$	40.6736			1.49620			0.748101	−	0.663585i	$-0.230966\pi$
$739$	40.6736			1.49620			0.748101	+	0.663585i	$0.230966\pi$
$740$	3.32130	−	1.21770i	0.122094	−	0.0447634i
$741$	−52.2571	+	32.1720i	−1.91971	+	1.18187i
$742$	−4.41511	+	7.92915i	−0.162084	+	0.291088i
$743$			8.58103i			0.314808i	0.987534	+	0.157404i	$0.0503124\pi$
$743$			8.58103i			0.314808i	−0.987534	+	0.157404i	$0.949688\pi$
$744$	−0.493845	−	10.5888i	−0.0181052	−	0.388203i
$745$	−7.69620	+	37.3420i	−0.281967	+	1.36810i
$746$	15.4510	−	27.7487i	0.565701	−	1.01595i
$747$			20.6396i			0.755164i
$748$	1.51258	−	0.937113i	0.0553053	−	0.0342643i
$749$	−31.4936			−1.15075
$750$	15.0304	+	30.8809i	0.548833	+	1.12761i
$751$	−45.2216			−1.65016			−0.825080	−	0.565017i	$-0.808870\pi$
$751$	−45.2216			−1.65016			−0.825080	+	0.565017i	$0.808870\pi$
$752$	−0.134265	+	0.270006i	−0.00489614	+	0.00984610i
$753$	−12.0723			−0.439939
$754$	33.4240	−	60.0266i	1.21723	−	2.18604i
$755$	37.3271	+	7.69314i	1.35847	+	0.279982i
$756$	5.96366	+	9.62583i	0.216896	+	0.350088i
$757$	−51.2933			−1.86429			−0.932143	−	0.362089i	$-0.882063\pi$
$757$	−51.2933			−1.86429			−0.932143	+	0.362089i	$0.882063\pi$
$758$	−20.3622	+	36.5688i	−0.739589	+	1.32824i
$759$	48.0868			1.74544
$760$	−25.4432	+	10.6134i	−0.922921	+	0.384989i
$761$	32.7176			1.18601			0.593006	−	0.805198i	$-0.297941\pi$
$761$	32.7176			1.18601			0.593006	+	0.805198i	$0.297941\pi$
$762$	6.06502	−	10.8923i	0.219713	−	0.394585i
$763$	7.34998			0.266087
$764$	5.20148	−	3.22256i	0.188183	−	0.116588i
$765$	−0.225270	+	1.09301i	−0.00814467	+	0.0395179i
$766$	−10.2672	+	18.4390i	−0.370970	+	0.666230i
$767$	−40.8031			−1.47332
$768$	−20.9740	−	27.7118i	−0.756834	−	0.999964i
$769$	20.1957			0.728276			0.364138	−	0.931345i	$-0.381364\pi$
$769$	20.1957			0.728276			0.364138	+	0.931345i	$0.381364\pi$
$770$	−14.9192	−	12.8577i	−0.537649	−	0.463359i
$771$	−47.8759			−1.72421
$772$	−3.90839	−	6.30846i	−0.140666	−	0.227046i
$773$			10.9936i			0.395412i	0.980261	+	0.197706i	$0.0633491\pi$
$773$			10.9936i			0.395412i	−0.980261	+	0.197706i	$0.936651\pi$
$774$	−12.2248	+	21.9548i	−0.439413	+	0.789148i
$775$	7.92388	+	3.41113i	0.284634	+	0.122531i
$776$	−0.514313	−	11.0276i	−0.0184628	−	0.395869i
$777$		−	3.49384i		−	0.125341i
$778$	18.7689	−	33.7073i	0.672897	−	1.20847i
$779$	−31.8811	+	19.6275i	−1.14226	+	0.703229i
$780$	59.1130	−	21.6727i	2.11658	−	0.776007i
$781$	−39.8851			−1.42720
$782$	−1.44446	+	2.59412i	−0.0516537	+	0.0927657i
$783$	−20.8699			−0.745829
$784$	5.10269	−	10.2615i	0.182239	−	0.366481i
$785$	−16.6356	−	3.42861i	−0.593751	−	0.122372i
$786$	−40.0095	−	22.2781i	−1.42709	−	0.794633i
$787$	14.0613			0.501233			0.250616	−	0.968086i	$-0.419367\pi$
$787$	14.0613			0.501233			0.250616	+	0.968086i	$0.419367\pi$
$788$	17.3806	+	28.0537i	0.619158	+	0.999371i
$789$	36.3203			1.29304
$790$	17.4560	+	15.0440i	0.621056	+	0.535241i
$791$	12.3046			0.437501
$792$	−0.693443	−	14.8685i	−0.0246404	−	0.528327i
$793$	42.3363			1.50341
$794$	1.14384	+	0.636913i	0.0405934	+	0.0226032i
$795$	3.09412	−	15.0127i	0.109737	−	0.532445i
$796$	−37.7031	+	23.3589i	−1.33635	+	0.827933i
$797$		−	33.4826i		−	1.18602i	−0.805197	−	0.593008i	$-0.797940\pi$
$797$		−	33.4826i		−	1.18602i	0.805197	−	0.593008i	$-0.202060\pi$
$798$	1.19172	+	27.2018i	0.0421863	+	0.962934i
$799$		−	0.0218978i		−	0.000774687i
$800$	27.7495	−	5.47401i	0.981093	−	0.193535i
$801$		−	0.998379i		−	0.0352760i
$802$	16.8803	−	30.3156i	0.596064	−	1.07048i
$803$			33.0231i			1.16536i
$804$	−1.27611	−	2.05975i	−0.0450050	−	0.0726418i
$805$	32.1885	+	6.63407i	1.13450	+	0.233820i
$806$	7.69377	−	13.8173i	0.271001	−	0.486695i
$807$	−27.2107			−0.957862
$808$	−25.8494	+	1.20558i	−0.909379	+	0.0424121i
$809$	51.4477			1.80881			0.904403	−	0.426679i	$-0.140317\pi$
$809$	51.4477			1.80881			0.904403	+	0.426679i	$0.140317\pi$
$810$	−26.8346	−	23.1267i	−0.942871	−	0.812588i
$811$		−	7.74569i		−	0.271988i	−0.990710	−	0.135994i	$-0.956577\pi$
$811$		−	7.74569i		−	0.271988i	0.990710	−	0.135994i	$-0.0434228\pi$
$812$	−16.0547	−	25.9136i	−0.563409	−	0.909389i
$813$		−	13.9866i		−	0.490533i
$814$	1.66683	−	2.99348i	0.0584223	−	0.104922i
$815$	5.08924	−	24.6930i	0.178268	−	0.864958i
$816$	2.25981	+	1.12373i	0.0791091	+	0.0393384i
$817$	38.3867	−	23.6327i	1.34298	−	0.826804i
$818$	−7.11931	+	12.7857i	−0.248921	+	0.447040i
$819$		−	22.6449i		−	0.791278i
$820$	36.0637	−	13.2221i	1.25940	−	0.461736i
$821$			21.3518i			0.745182i	0.927996	+	0.372591i	$0.121531\pi$
$821$			21.3518i			0.745182i	−0.927996	+	0.372591i	$0.878469\pi$
$822$	−34.8326	+	62.5563i	−1.21493	+	2.18190i
$823$	−2.37327			−0.0827268			−0.0413634	−	0.999144i	$-0.513170\pi$
$823$	−2.37327			−0.0827268			−0.0413634	+	0.999144i	$0.513170\pi$
$824$	−1.22725	+	0.0572373i	−0.0427534	+	0.00199396i
$825$	30.5537	+	13.1530i	1.06374	+	0.457928i
$826$	−8.80740	+	15.8173i	−0.306449	+	0.550355i
$827$	17.0213			0.591887			0.295944	−	0.955205i	$-0.404366\pi$
$827$	17.0213			0.591887			0.295944	+	0.955205i	$0.404366\pi$
$828$	13.0811	+	21.1139i	0.454598	+	0.733759i
$829$	2.33355			0.0810476			0.0405238	−	0.999179i	$-0.487097\pi$
$829$	2.33355			0.0810476			0.0405238	+	0.999179i	$0.487097\pi$
$830$	−24.7991	+	28.7751i	−0.860789	+	0.998799i
$831$	−18.3854			−0.637784
$832$	−4.82602	−	51.6260i	−0.167312	−	1.78981i
$833$			0.832216i			0.0288346i
$834$	26.8590	+	14.9556i	0.930052	+	0.517871i
$835$	4.79872	−	23.2834i	0.166066	−	0.805754i
$836$	−11.9563	+	23.8748i	−0.413517	+	0.825726i
$837$	−4.80398			−0.166050
$838$	−16.0701	−	8.94816i	−0.555133	−	0.309109i
$839$	0.690090			0.0238246			0.0119123	−	0.999929i	$-0.496208\pi$
$839$	0.690090			0.0238246			0.0119123	+	0.999929i	$0.496208\pi$
$840$	4.35818	−	27.5932i	0.150371	−	0.952056i
$841$	27.1836			0.937364
$842$	12.9680	+	7.22083i	0.446906	+	0.248846i
$843$		−	17.9824i		−	0.619348i
$844$	18.9627	−	11.7483i	0.652722	−	0.404392i
$845$	63.5293	+	13.0934i	2.18547	+	0.450427i
$846$	−0.160042	−	0.0891144i	−0.00550235	−	0.00306381i
$847$	3.29214			0.113119
$848$	−11.3031	−	5.62068i	−0.388151	−	0.193015i
$849$		−	13.2390i		−	0.454360i
$850$	−1.62735	+	1.25318i	−0.0558177	+	0.0429836i
$851$			5.71734i			0.195988i
$852$	−29.7944	−	48.0905i	−1.02074	−	1.64755i
$853$	44.6873			1.53006			0.765032	−	0.643993i	$-0.222723\pi$
$853$	44.6873			1.53006			0.765032	+	0.643993i	$0.222723\pi$
$854$	9.13833	−	16.4117i	0.312707	−	0.561595i
$855$	−5.72025	−	15.7395i	−0.195628	−	0.538279i
$856$	−2.04082	−	43.7583i	−0.0697538	−	1.49563i
$857$	−14.1036			−0.481771			−0.240885	−	0.970554i	$-0.577438\pi$
$857$	−14.1036			−0.481771			−0.240885	+	0.970554i	$0.577438\pi$
$858$	29.6664	−	53.2784i	1.01280	−	1.81889i
$859$	32.1458			1.09680			0.548400	−	0.836216i	$-0.315237\pi$
$859$	32.1458			1.09680			0.548400	+	0.836216i	$0.315237\pi$
$860$	−43.4228	+	15.9202i	−1.48071	+	0.542874i
$861$		−	37.9371i		−	1.29289i
$862$	7.61057	+	4.23771i	0.259217	+	0.144337i
$863$		−	30.6899i		−	1.04470i	−0.852733	−	0.522348i	$-0.825056\pi$
$863$		−	30.6899i		−	1.04470i	0.852733	−	0.522348i	$-0.174944\pi$
$864$	−12.9880	+	8.90987i	−0.441861	+	0.303120i
$865$	−6.68687	+	32.4447i	−0.227360	+	1.10315i
$866$	−34.3246	−	19.1126i	−1.16640	−	0.649473i
$867$	36.7430			1.24786
$868$	−3.69558	−	5.96497i	−0.125436	−	0.202464i
$869$	22.3196			0.757139
$870$	39.0010	+	33.6120i	1.32226	+	1.13955i
$871$		−	3.61499i		−	0.122489i
$872$	0.476287	+	10.2123i	0.0161291	+	0.345832i
$873$	6.70621			0.226971
$874$	−1.95013	−	44.5132i	−0.0659642	−	1.50568i
$875$	18.6376	+	13.0196i	0.630066	+	0.440143i
$876$	−39.8168	+	24.6684i	−1.34529	+	0.833468i
$877$		−	18.6438i		−	0.629556i	−0.949165	−	0.314778i	$-0.898070\pi$
$877$		−	18.6438i		−	0.629556i	0.949165	−	0.314778i	$-0.101930\pi$
$878$	−15.6552	−	8.71714i	−0.528339	−	0.294189i
$879$		−	50.7359i		−	1.71128i
$880$	16.8981	−	21.5624i	0.569635	−	0.726867i
$881$	−18.8284			−0.634343			−0.317172	−	0.948368i	$-0.602733\pi$
$881$	−18.8284			−0.634343			−0.317172	+	0.948368i	$0.602733\pi$
$882$	6.08233	+	3.38676i	0.204803	+	0.114038i
$883$			41.8176i			1.40727i	0.710559	+	0.703637i	$0.248442\pi$
$883$			41.8176i			1.40727i	−0.710559	+	0.703637i	$0.751558\pi$
$884$	1.98305	+	3.20081i	0.0666973	+	0.107655i
$885$	6.17226	−	29.9478i	0.207478	−	1.00668i
$886$	8.64229	−	15.5208i	0.290343	−	0.521432i
$887$			29.0431i			0.975172i	0.873075	+	0.487586i	$0.162122\pi$
$887$			29.0431i			0.975172i	−0.873075	+	0.487586i	$0.837878\pi$
$888$	4.85446	−	0.226405i	0.162905	−	0.00759765i
$889$		−	8.25269i		−	0.276786i
$890$	1.19958	−	1.39191i	0.0402101	−	0.0466570i
$891$	−34.3112			−1.14947
$892$	−43.5918	+	27.0072i	−1.45956	+	0.904267i
$893$	0.172273	+	0.279824i	0.00576490	+	0.00936396i
$894$	−25.4811	+	45.7619i	−0.852216	+	1.53051i
$895$	−5.82886	+	28.2816i	−0.194837	+	0.945351i
$896$	−21.0545	−	9.27271i	−0.703381	−	0.309779i
$897$			101.758i			3.39760i
$898$	−17.9843	+	32.2983i	−0.600144	+	1.07781i
$899$	12.9327			0.431331
$900$	2.53634	+	16.9935i	0.0845446	+	0.566451i
$901$	0.916696			0.0305396
$902$	18.0989	−	32.5041i	0.602628	−	1.08227i
$903$			45.6786i			1.52009i
$904$	0.797351	+	17.0964i	0.0265195	+	0.568618i
$905$	−34.2658	−	7.06219i	−1.13903	−	0.234755i
$906$	45.7437	+	25.4710i	1.51973	+	0.846217i
$907$	−28.7443			−0.954439			−0.477219	−	0.878784i	$-0.658355\pi$
$907$	−28.7443			−0.954439			−0.477219	+	0.878784i	$0.658355\pi$
$908$	−4.72831	−	7.63187i	−0.156914	−	0.253273i
$909$		−	15.7197i		−	0.521390i
$910$	27.2085	−	31.5709i	0.901954	−	1.04656i
$911$	28.2251			0.935138			0.467569	−	0.883957i	$-0.345130\pi$
$911$	28.2251			0.935138			0.467569	+	0.883957i	$0.345130\pi$
$912$	−37.7179	+	3.41852i	−1.24896	+	0.113198i
$913$			36.7924i			1.21765i
$914$	14.0447	−	25.2230i	0.464557	−	0.834304i
$915$	−6.40418	+	31.0731i	−0.211716	+	1.02724i
$916$	−12.2967	+	7.61838i	−0.406294	+	0.251718i
$917$	−30.3138			−1.00105
$918$	0.556425	−	0.999292i	0.0183648	−	0.0329815i
$919$			17.0496i			0.562413i	0.959647	+	0.281207i	$0.0907347\pi$
$919$			17.0496i			0.562413i	−0.959647	+	0.281207i	$0.909265\pi$
$920$	−7.13174	+	45.1537i	−0.235127	+	1.48867i
$921$	59.9363			1.97497
$922$	2.58376	−	4.64021i	0.0850915	−	0.152817i
$923$		−	84.4020i		−	2.77813i
$924$	−14.2498	−	23.0004i	−0.468785	−	0.756657i
$925$	−1.56384	+	3.63273i	−0.0514188	+	0.119443i
$926$	24.8171	+	13.8186i	0.815539	+	0.454108i
$927$		−	0.746327i		−	0.0245126i
$928$	34.9648	−	23.9861i	1.14778	−	0.787384i
$929$	−20.5289			−0.673530			−0.336765	−	0.941589i	$-0.609333\pi$
$929$	−20.5289			−0.673530			−0.336765	+	0.941589i	$0.609333\pi$
$930$	8.97752	+	7.73704i	0.294384	+	0.253708i
$931$	−6.54718	−	10.6346i	−0.214575	−	0.348535i
$932$	31.9494	−	19.7942i	1.04654	−	0.648380i
$933$			25.5659i			0.836991i
$934$	−24.2904	+	43.6235i	−0.794806	+	1.42740i
$935$	−0.401570	+	1.94842i	−0.0131327	+	0.0637201i
$936$	31.4636	−	1.46742i	1.02842	−	0.0479640i
$937$		−	22.6949i		−	0.741410i	−0.928751	−	0.370705i	$-0.879116\pi$
$937$		−	22.6949i		−	0.741410i	0.928751	−	0.370705i	$-0.120884\pi$
$938$	−1.40135	−	0.780300i	−0.0457557	−	0.0254777i
$939$			7.58910i			0.247661i
$940$	−0.116052	−	0.316536i	−0.00378520	−	0.0103243i
$941$	26.8804			0.876276			0.438138	−	0.898908i	$-0.355638\pi$
$941$	26.8804			0.876276			0.438138	+	0.898908i	$0.355638\pi$
$942$	−20.3866	−	11.3517i	−0.664233	−	0.369858i
$943$			62.0805i			2.02162i
$944$	−22.5478	−	11.2123i	−0.733870	−	0.364930i
$945$	−12.3995	−	2.55554i	−0.403354	−	0.0831316i
$946$	−21.7922	+	39.1369i	−0.708525	+	1.27245i
$947$		−	50.2685i		−	1.63351i	−0.576988	−	0.816753i	$-0.695772\pi$
$947$		−	50.2685i		−	1.63351i	0.576988	−	0.816753i	$-0.304228\pi$
$948$	16.6728	+	26.9113i	0.541508	+	0.874039i
$949$	−69.8811			−2.26844
$950$	10.9364	−	28.8166i	0.354825	−	0.934933i
$951$		−	55.8163i		−	1.80997i
$952$	1.66884	−	0.0778322i	0.0540874	−	0.00252256i
$953$	−27.9136			−0.904211			−0.452106	−	0.891964i	$-0.649327\pi$
$953$	−27.9136			−0.904211			−0.452106	+	0.891964i	$0.649327\pi$
$954$	3.73055	−	6.69975i	0.120781	−	0.216912i
$955$	−1.38093	+	6.70026i	−0.0446857	+	0.216815i
$956$	12.3515	−	7.65233i	0.399475	−	0.247494i
$957$	49.8674			1.61198
$958$	−9.03492	+	16.2259i	−0.291905	+	0.524237i
$959$			47.3967i			1.53052i
$960$	38.6213	+	4.26732i	1.24650	+	0.137727i
$961$	−28.0231			−0.903969
$962$	6.33460	+	3.52723i	0.204236	+	0.113722i
$963$	26.6106			0.857514
$964$	−1.45244	+	0.899854i	−0.0467799	+	0.0289824i
$965$	8.12620	+	1.67481i	0.261592	+	0.0539142i
$966$	39.4464	+	21.9645i	1.26917	+	0.706698i
$967$	−33.0906			−1.06412			−0.532061	−	0.846706i	$-0.678582\pi$
$967$	−33.0906			−1.06412			−0.532061	+	0.846706i	$0.678582\pi$
$968$	0.213335	+	4.57421i	0.00685683	+	0.147021i
$969$	2.34198	−	1.44184i	0.0752353	−	0.0463185i
$970$	9.34961	+	8.05771i	0.300198	+	0.258718i
$971$			29.4204i			0.944145i	0.881560	+	0.472073i	$0.156494\pi$
$971$			29.4204i			0.944145i	−0.881560	+	0.472073i	$0.843506\pi$
$972$	−16.8324	−	27.1688i	−0.539898	−	0.871440i
$973$	20.3501			0.652395
$974$	0.322078	−	0.578424i	0.0103200	−	0.0185339i
$975$	−27.8334	+	64.6557i	−0.891384	+	2.07064i
$976$	23.3951	+	11.6336i	0.748858	+	0.372383i
$977$	−55.0893			−1.76246			−0.881232	−	0.472684i	$-0.843285\pi$
$977$	−55.0893			−1.76246			−0.881232	+	0.472684i	$0.843285\pi$
$978$	16.8498	−	30.2608i	0.538798	−	0.967634i
$979$		−	1.77972i		−	0.0568802i
$980$	4.41051	+	12.0298i	0.140889	+	0.384278i
$981$	−6.21038			−0.198282
$982$	−19.9951	−	11.1336i	−0.638068	−	0.355289i
$983$		−	10.4969i		−	0.334798i	−0.985889	−	0.167399i	$-0.946463\pi$
$983$		−	10.4969i		−	0.334798i	0.985889	−	0.167399i	$-0.0535368\pi$
$984$	52.7111	−	2.45837i	1.68037	−	0.0783699i
$985$	−36.1372	−	7.44789i	−1.15143	−	0.237310i
$986$	−1.49795	+	2.69018i	−0.0477043	+	0.0856728i
$987$	−0.332979			−0.0105988
$988$	−50.5221	−	25.3011i	−1.60732	−	0.804936i
$989$		−	74.7487i		−	2.37687i
$990$	12.6060	+	10.8641i	0.400644	+	0.345284i
$991$	2.34744			0.0745688			0.0372844	−	0.999305i	$-0.488129\pi$
$991$	2.34744			0.0745688			0.0372844	+	0.999305i	$0.488129\pi$
$992$	8.04845	−	5.52130i	0.255539	−	0.175301i
$993$		−	5.45927i		−	0.173245i
$994$	−32.7184	−	18.2183i	−1.03777	−	0.577848i
$995$	10.0097	−	48.5671i	0.317329	−	1.53968i
$996$	−44.3617	+	27.4842i	−1.40565	+	0.870869i
$997$	−14.6836			−0.465033			−0.232516	−	0.972592i	$-0.574696\pi$
$997$	−14.6836			−0.465033			−0.232516	+	0.972592i	$0.574696\pi$
$998$	41.7716	+	23.2593i	1.32226	+	0.736259i
$999$		−	2.20240i		−	0.0696808i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	760.2.p.i.379.13	✓	56
5.4	even	2	inner	760.2.p.i.379.44	yes	56
8.3	odd	2	inner	760.2.p.i.379.16	yes	56
19.18	odd	2	inner	760.2.p.i.379.43	yes	56
40.19	odd	2	inner	760.2.p.i.379.41	yes	56
95.94	odd	2	inner	760.2.p.i.379.14	yes	56
152.75	even	2	inner	760.2.p.i.379.42	yes	56
760.379	even	2	inner	760.2.p.i.379.15	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
760.2.p.i.379.13	✓	56	1.1	even	1	trivial
760.2.p.i.379.14	yes	56	95.94	odd	2	inner
760.2.p.i.379.15	yes	56	760.379	even	2	inner
760.2.p.i.379.16	yes	56	8.3	odd	2	inner
760.2.p.i.379.41	yes	56	40.19	odd	2	inner
760.2.p.i.379.42	yes	56	152.75	even	2	inner
760.2.p.i.379.43	yes	56	19.18	odd	2	inner
760.2.p.i.379.44	yes	56	5.4	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	760.p (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23558 - 0.687996i) q^{2} +2.17214 q^{3} +(1.05332 + 1.70015i) q^{4} +(-2.19004 - 0.451368i) q^{5} +(-2.68385 - 1.49442i) q^{6} -2.03346 q^{7} +(-0.131770 - 2.82536i) q^{8} +1.71818 q^{9} +(2.39543 + 2.06444i) q^{10} +3.06284 q^{11} +(2.28796 + 3.69296i) q^{12} +6.48138i q^{13} +(2.51251 + 1.39901i) q^{14} +(-4.75706 - 0.980433i) q^{15} +(-1.78102 + 3.58162i) q^{16} -0.290473i q^{17} +(-2.12295 - 1.18210i) q^{18} +(2.28520 + 3.71186i) q^{19} +(-1.53942 - 4.19883i) q^{20} -4.41695 q^{21} +(-3.78439 - 2.10722i) q^{22} +7.22793 q^{23} +(-0.286223 - 6.13706i) q^{24} +(4.59253 + 1.97703i) q^{25} +(4.45916 - 8.00827i) q^{26} -2.78430 q^{27} +(-2.14189 - 3.45719i) q^{28} +7.49557 q^{29} +(5.20320 + 4.48424i) q^{30} +1.72538 q^{31} +(4.66473 - 3.20004i) q^{32} +6.65291 q^{33} +(-0.199844 + 0.358903i) q^{34} +(4.45336 + 0.917839i) q^{35} +(1.80979 + 2.92116i) q^{36} +0.791007i q^{37} +(-0.269805 - 6.15851i) q^{38} +14.0784i q^{39} +(-0.986693 + 6.24711i) q^{40} +8.58898i q^{41} +(5.45750 + 3.03885i) q^{42} -10.3417i q^{43} +(3.22617 + 5.20729i) q^{44} +(-3.76287 - 0.775530i) q^{45} +(-8.93069 - 4.97278i) q^{46} +0.0753866 q^{47} +(-3.86862 + 7.77976i) q^{48} -2.86504 q^{49} +(-4.31426 - 5.60242i) q^{50} -0.630947i q^{51} +(-11.0193 + 6.82699i) q^{52} +3.15587i q^{53} +(3.44023 + 1.91558i) q^{54} +(-6.70775 - 1.38247i) q^{55} +(0.267950 + 5.74525i) q^{56} +(4.96376 + 8.06266i) q^{57} +(-9.26139 - 5.15692i) q^{58} +6.29544i q^{59} +(-3.34384 - 9.12043i) q^{60} -6.53199i q^{61} +(-2.13185 - 1.18706i) q^{62} -3.49384 q^{63} +(-7.96527 + 0.744597i) q^{64} +(2.92549 - 14.1945i) q^{65} +(-8.22022 - 4.57718i) q^{66} -0.557751 q^{67} +(0.493847 - 0.305962i) q^{68} +15.7000 q^{69} +(-4.87101 - 4.19795i) q^{70} -13.0222 q^{71} +(-0.226405 - 4.85446i) q^{72} +10.7818i q^{73} +(0.544210 - 0.977354i) q^{74} +(9.97561 + 4.29437i) q^{75} +(-3.90366 + 7.79496i) q^{76} -6.22817 q^{77} +(9.68591 - 17.3951i) q^{78} +7.28720 q^{79} +(5.51713 - 7.03998i) q^{80} -11.2024 q^{81} +(5.90919 - 10.6124i) q^{82} +12.0125i q^{83} +(-4.65248 - 7.50948i) q^{84} +(-0.131110 + 0.636147i) q^{85} +(-7.11501 + 12.7780i) q^{86} +16.2814 q^{87} +(-0.403592 - 8.65363i) q^{88} -0.581069i q^{89} +(4.11577 + 3.54707i) q^{90} -13.1796i q^{91} +(7.61334 + 12.2886i) q^{92} +3.74777 q^{93} +(-0.0931463 - 0.0518657i) q^{94} +(-3.32925 - 9.16057i) q^{95} +(10.1324 - 6.95093i) q^{96} +3.90310 q^{97} +(3.53999 + 1.97114i) q^{98} +5.26251 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 16 q^{4} - 8 q^{6} + 88 q^{9} + 32 q^{11} + 48 q^{16} - 56 q^{19} + 4 q^{20} - 32 q^{24} + 80 q^{25} + 24 q^{26} + 24 q^{30} + 48 q^{35} - 96 q^{36} + 104 q^{44} - 72 q^{49} + 104 q^{54} + 16 q^{64}+ \cdots - 272 q^{99}+O(q^{100}) \) 56 * q + 16 * q^4 - 8 * q^6 + 88 * q^9 + 32 * q^11 + 48 * q^16 - 56 * q^19 + 4 * q^20 - 32 * q^24 + 80 * q^25 + 24 * q^26 + 24 * q^30 + 48 * q^35 - 96 * q^36 + 104 * q^44 - 72 * q^49 + 104 * q^54 + 16 * q^64 - 24 * q^66 + 64 * q^74 + 88 * q^76 + 128 * q^80 - 168 * q^81 - 96 * q^96 - 272 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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