LMFDB - Embedded newform 112.2.v.a.19.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [112,2,Mod(3,112)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(112, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("112.3"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	112.v (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.894324502638$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.10
Character	$\chi$	$=$	112.19
Dual form			112.2.v.a.59.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.699767 + 1.22895i) q^{2} +(0.524583 - 1.95777i) q^{3} +(-1.02065 + 1.71996i) q^{4} +(2.48890 - 0.666898i) q^{5} +(2.77309 - 0.725295i) q^{6} +(-2.38027 - 1.15512i) q^{7} +(-2.82797 - 0.0507629i) q^{8} +(-0.959602 - 0.554026i) q^{9} +(2.56123 + 2.59207i) q^{10} +(-1.35371 + 5.05213i) q^{11} +(2.83187 + 2.90047i) q^{12} +(0.848888 - 0.848888i) q^{13} +(-0.246053 - 3.73356i) q^{14} -5.22253i q^{15} +(-1.91654 - 3.51097i) q^{16} +(-2.23951 + 1.29298i) q^{17} +(0.00937511 - 1.56699i) q^{18} +(-4.72466 + 1.26597i) q^{19} +(-1.39326 + 4.96148i) q^{20} +(-3.51010 + 4.05408i) q^{21} +(-7.15612 + 1.87166i) q^{22} +(3.15967 - 5.47271i) q^{23} +(-1.58289 + 5.50989i) q^{24} +(1.41973 - 0.819681i) q^{25} +(1.63727 + 0.449220i) q^{26} +(2.71152 - 2.71152i) q^{27} +(4.41619 - 2.91501i) q^{28} +(-3.92758 - 3.92758i) q^{29} +(6.41825 - 3.65455i) q^{30} +(0.585390 + 1.01392i) q^{31} +(2.97369 - 4.81219i) q^{32} +(9.18077 + 5.30052i) q^{33} +(-3.15615 - 1.84747i) q^{34} +(-6.69460 - 1.28757i) q^{35} +(1.93232 - 1.08501i) q^{36} +(1.61869 + 6.04104i) q^{37} +(-4.86198 - 4.92051i) q^{38} +(-1.21662 - 2.10724i) q^{39} +(-7.07238 + 1.75962i) q^{40} +4.77063 q^{41} +(-7.43853 - 1.47685i) q^{42} +(4.80121 + 4.80121i) q^{43} +(-7.30780 - 7.48481i) q^{44} +(-2.75783 - 0.738958i) q^{45} +(8.93673 + 0.0534672i) q^{46} +(3.39263 - 5.87622i) q^{47} +(-7.87905 + 1.91034i) q^{48} +(4.33141 + 5.49899i) q^{49} +(2.00083 + 1.17120i) q^{50} +(1.35655 + 5.06272i) q^{51} +(0.593634 + 2.32647i) q^{52} +(-7.35887 - 1.97180i) q^{53} +(5.22975 + 1.43490i) q^{54} +13.4770i q^{55} +(6.67271 + 3.38747i) q^{56} +9.91391i q^{57} +(2.07842 - 7.57520i) q^{58} +(-0.809319 - 0.216856i) q^{59} +(8.98255 + 5.33039i) q^{60} +(1.17253 + 4.37595i) q^{61} +(-0.836430 + 1.42893i) q^{62} +(1.64415 + 2.42719i) q^{63} +(7.99485 + 0.287112i) q^{64} +(1.54667 - 2.67892i) q^{65} +(-0.0896943 + 14.9919i) q^{66} +(0.376913 + 0.100994i) q^{67} +(0.0618836 - 5.17155i) q^{68} +(-9.05679 - 9.05679i) q^{69} +(-3.10230 - 9.12835i) q^{70} +3.83330 q^{71} +(2.68560 + 1.61548i) q^{72} +(-4.84591 - 8.39335i) q^{73} +(-6.29145 + 6.21661i) q^{74} +(-0.859981 - 3.20949i) q^{75} +(2.64482 - 9.41835i) q^{76} +(9.05801 - 10.4618i) q^{77} +(1.73835 - 2.96974i) q^{78} +(0.954167 + 0.550889i) q^{79} +(-7.11152 - 7.46030i) q^{80} +(-5.54819 - 9.60974i) q^{81} +(3.33833 + 5.86288i) q^{82} +(9.73434 + 9.73434i) q^{83} +(-3.39026 - 10.1750i) q^{84} +(-4.71162 + 4.71162i) q^{85} +(-2.54074 + 9.26019i) q^{86} +(-9.74964 + 5.62896i) q^{87} +(4.08473 - 14.2186i) q^{88} +(7.91117 - 13.7025i) q^{89} +(-1.02169 - 3.90634i) q^{90} +(-3.00115 + 1.04002i) q^{91} +(6.18792 + 11.0202i) q^{92} +(2.29212 - 0.614171i) q^{93} +(9.59565 + 0.0574094i) q^{94} +(-10.9149 + 6.30174i) q^{95} +(-7.86122 - 8.34619i) q^{96} -1.12228i q^{97} +(-3.72702 + 9.17111i) q^{98} +(4.09804 - 4.09804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{2} - 6 q^{3} - 4 q^{4} - 6 q^{5} - 8 q^{7} + 4 q^{8} - 24 q^{10} + 2 q^{11} - 6 q^{12} + 16 q^{14} + 8 q^{16} - 12 q^{17} - 30 q^{18} - 6 q^{19} - 10 q^{21} - 28 q^{22} - 12 q^{23} - 6 q^{24}+ \cdots - 16 q^{99}+O(q^{100}) $ 56 * q - 2 * q^2 - 6 * q^3 - 4 * q^4 - 6 * q^5 - 8 * q^7 + 4 * q^8 - 24 * q^10 + 2 * q^11 - 6 * q^12 + 16 * q^14 + 8 * q^16 - 12 * q^17 - 30 * q^18 - 6 * q^19 - 10 * q^21 - 28 * q^22 - 12 * q^23 - 6 * q^24 - 6 * q^26 + 26 * q^28 - 24 * q^29 - 18 * q^30 - 12 * q^32 - 12 * q^33 - 2 * q^35 + 16 * q^36 + 6 * q^37 - 6 * q^38 - 4 * q^39 - 66 * q^40 + 70 * q^42 + 26 * q^44 + 12 * q^45 + 16 * q^46 - 8 * q^49 - 34 * q^51 + 84 * q^52 + 6 * q^53 + 42 * q^54 + 16 * q^56 + 18 * q^58 + 42 * q^59 + 78 * q^60 - 6 * q^61 - 16 * q^64 - 4 * q^65 + 126 * q^66 + 6 * q^67 + 24 * q^68 - 80 * q^70 - 80 * q^71 - 4 * q^72 + 62 * q^74 + 24 * q^75 + 10 * q^77 + 4 * q^78 + 12 * q^80 - 8 * q^81 + 42 * q^82 - 152 * q^84 - 28 * q^85 - 12 * q^87 + 30 * q^88 + 16 * q^91 - 20 * q^92 + 10 * q^93 - 42 * q^94 + 36 * q^96 - 108 * q^98 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.699767	+	1.22895i	0.494810	+	0.869001i
$2$	0.699767	+	1.22895i	0.494810	+	0.869001i
$3$	0.524583	−	1.95777i	0.302868	−	1.13032i	−0.631897	−	0.775053i	$-0.717723\pi$
$3$	0.524583	−	1.95777i	0.302868	−	1.13032i	0.934765	−	0.355267i	$-0.115610\pi$
$4$	−1.02065	+	1.71996i	−0.510326	+	0.859981i
$5$	2.48890	−	0.666898i	1.11307	−	0.298246i	0.344993	−	0.938605i	$-0.387881\pi$
$5$	2.48890	−	0.666898i	1.11307	−	0.298246i	0.768075	+	0.640359i	$0.221215\pi$
$6$	2.77309	−	0.725295i	1.13211	−	0.296100i
$7$	−2.38027	−	1.15512i	−0.899659	−	0.436593i
$7$	−2.38027	−	1.15512i	−0.899659	−	0.436593i
$8$	−2.82797	−	0.0507629i	−0.999839	−	0.0179474i
$9$	−0.959602	−	0.554026i	−0.319867	−	0.184675i
$10$	2.56123	+	2.59207i	0.809933	+	0.819683i
$11$	−1.35371	+	5.05213i	−0.408160	+	1.52327i	0.389992	+	0.920818i	$0.372478\pi$
$11$	−1.35371	+	5.05213i	−0.408160	+	1.52327i	−0.798152	+	0.602456i	$0.794189\pi$
$12$	2.83187	+	2.90047i	0.817491	+	0.837293i
$13$	0.848888	−	0.848888i	0.235439	−	0.235439i	−0.579519	−	0.814958i	$-0.696760\pi$
$13$	0.848888	−	0.848888i	0.235439	−	0.235439i	0.814958	+	0.579519i	$0.196760\pi$
$14$	−0.246053	−	3.73356i	−0.0657603	−	0.997835i
$15$		−	5.22253i		−	1.34845i
$16$	−1.91654	−	3.51097i	−0.479134	−	0.877742i
$17$	−2.23951	+	1.29298i	−0.543161	+	0.313594i	−0.746359	−	0.665544i	$-0.768200\pi$
$17$	−2.23951	+	1.29298i	−0.543161	+	0.313594i	0.203198	+	0.979138i	$0.434866\pi$
$18$	0.00937511	−	1.56699i	0.00220974	−	0.369344i
$19$	−4.72466	+	1.26597i	−1.08391	+	0.290433i	−0.756197	−	0.654343i	$-0.772945\pi$
$19$	−4.72466	+	1.26597i	−1.08391	+	0.290433i	−0.327714	+	0.944777i	$0.606278\pi$
$20$	−1.39326	+	4.96148i	−0.311543	+	1.10942i
$21$	−3.51010	+	4.05408i	−0.765968	+	0.884672i
$22$	−7.15612	+	1.87166i	−1.52569	+	0.399039i
$23$	3.15967	−	5.47271i	0.658836	−	1.14114i	−0.322081	−	0.946712i	$-0.604382\pi$
$23$	3.15967	−	5.47271i	0.658836	−	1.14114i	0.980917	−	0.194426i	$-0.0622844\pi$
$24$	−1.58289	+	5.50989i	−0.323106	+	1.12470i
$25$	1.41973	−	0.819681i	0.283946	−	0.163936i
$26$	1.63727	+	0.449220i	0.321094	+	0.0880993i
$27$	2.71152	−	2.71152i	0.521831	−	0.521831i
$28$	4.41619	−	2.91501i	0.834581	−	0.550885i
$29$	−3.92758	−	3.92758i	−0.729333	−	0.729333i	0.241154	−	0.970487i	$-0.422474\pi$
$29$	−3.92758	−	3.92758i	−0.729333	−	0.729333i	−0.970487	+	0.241154i	$0.922474\pi$
$30$	6.41825	−	3.65455i	1.17181	−	0.667227i
$31$	0.585390	+	1.01392i	0.105139	+	0.182106i	0.913795	−	0.406176i	$-0.133138\pi$
$31$	0.585390	+	1.01392i	0.105139	+	0.182106i	−0.808656	+	0.588282i	$0.799805\pi$
$32$	2.97369	−	4.81219i	0.525679	−	0.850683i
$33$	9.18077	+	5.30052i	1.59817	+	0.922703i
$34$	−3.15615	−	1.84747i	−0.541275	−	0.316838i
$35$	−6.69460	−	1.28757i	−1.13159	−	0.217638i
$36$	1.93232	−	1.08501i	0.322054	−	0.180835i
$37$	1.61869	+	6.04104i	0.266111	+	0.993141i	0.961567	+	0.274571i	$0.0885360\pi$
$37$	1.61869	+	6.04104i	0.266111	+	0.993141i	−0.695455	+	0.718569i	$0.744797\pi$
$38$	−4.86198	−	4.92051i	−0.788717	−	0.798212i
$39$	−1.21662	−	2.10724i	−0.194814	−	0.337428i
$40$	−7.07238	+	1.75962i	−1.11824	+	0.278221i
$41$	4.77063			0.745047			0.372523	−	0.928023i	$-0.378493\pi$
$41$	4.77063			0.745047			0.372523	+	0.928023i	$0.378493\pi$
$42$	−7.43853	−	1.47685i	−1.14779	−	0.227882i
$43$	4.80121	+	4.80121i	0.732177	+	0.732177i	0.971051	−	0.238873i	$-0.0767781\pi$
$43$	4.80121	+	4.80121i	0.732177	+	0.732177i	−0.238873	+	0.971051i	$0.576778\pi$
$44$	−7.30780	−	7.48481i	−1.10169	−	1.12838i
$45$	−2.75783	−	0.738958i	−0.411113	−	0.110157i
$46$	8.93673	+	0.0534672i	1.31765	+	0.00788331i
$47$	3.39263	−	5.87622i	0.494867	−	0.857134i	−0.505116	−	0.863052i	$-0.668550\pi$
$47$	3.39263	−	5.87622i	0.494867	−	0.857134i	0.999982	+	0.00591740i	$0.00188358\pi$
$48$	−7.87905	+	1.91034i	−1.13724	+	0.275734i
$49$	4.33141	+	5.49899i	0.618773	+	0.785570i
$50$	2.00083	+	1.17120i	0.282960	+	0.165632i
$51$	1.35655	+	5.06272i	0.189955	+	0.708923i
$52$	0.593634	+	2.32647i	0.0823223	+	0.322624i
$53$	−7.35887	−	1.97180i	−1.01082	−	0.270848i	−0.284847	−	0.958573i	$-0.591943\pi$
$53$	−7.35887	−	1.97180i	−1.01082	−	0.270848i	−0.725971	+	0.687725i	$0.758610\pi$
$54$	5.22975	+	1.43490i	0.711679	+	0.195265i
$55$			13.4770i			1.81724i
$56$	6.67271	+	3.38747i	0.891679	+	0.452669i
$57$			9.91391i			1.31313i
$58$	2.07842	−	7.57520i	0.272910	−	0.994673i
$59$	−0.809319	−	0.216856i	−0.105364	−	0.0282323i	0.205752	−	0.978604i	$-0.434036\pi$
$59$	−0.809319	−	0.216856i	−0.105364	−	0.0282323i	−0.311116	+	0.950372i	$0.600703\pi$
$60$	8.98255	+	5.33039i	1.15964	+	0.688151i
$61$	1.17253	+	4.37595i	0.150127	+	0.560283i	0.999473	+	0.0324466i	$0.0103299\pi$
$61$	1.17253	+	4.37595i	0.150127	+	0.560283i	−0.849346	+	0.527836i	$0.823003\pi$
$62$	−0.836430	+	1.42893i	−0.106227	+	0.181474i
$63$	1.64415	+	2.42719i	0.207143	+	0.305797i
$64$	7.99485	+	0.287112i	0.999356	+	0.0358890i
$65$	1.54667	−	2.67892i	0.191841	−	0.332279i
$66$	−0.0896943	+	14.9919i	−0.0110406	+	1.84537i
$67$	0.376913	+	0.100994i	0.0460473	+	0.0123383i	0.281769	−	0.959482i	$-0.409079\pi$
$67$	0.376913	+	0.100994i	0.0460473	+	0.0123383i	−0.235722	+	0.971821i	$0.575745\pi$
$68$	0.0618836	−	5.17155i	0.00750449	−	0.627143i
$69$	−9.05679	−	9.05679i	−1.09031	−	1.09031i
$70$	−3.10230	−	9.12835i	−0.370796	−	1.09105i
$71$	3.83330			0.454929			0.227465	−	0.973786i	$-0.426956\pi$
$71$	3.83330			0.454929			0.227465	+	0.973786i	$0.426956\pi$
$72$	2.68560	+	1.61548i	0.316501	+	0.190386i
$73$	−4.84591	−	8.39335i	−0.567170	−	0.982368i	−0.996844	−	0.0793836i	$-0.974705\pi$
$73$	−4.84591	−	8.39335i	−0.567170	−	0.982368i	0.429674	−	0.902984i	$-0.358629\pi$
$74$	−6.29145	+	6.21661i	−0.731366	+	0.722667i
$75$	−0.859981	−	3.20949i	−0.0993021	−	0.370600i
$76$	2.64482	−	9.41835i	0.303382	−	1.08036i
$77$	9.05801	−	10.4618i	1.03226	−	1.19223i
$78$	1.73835	−	2.96974i	0.196830	−	0.336257i
$79$	0.954167	+	0.550889i	0.107352	+	0.0619798i	0.552715	−	0.833370i	$-0.313592\pi$
$79$	0.954167	+	0.550889i	0.107352	+	0.0619798i	−0.445363	+	0.895350i	$0.646925\pi$
$80$	−7.11152	−	7.46030i	−0.795092	−	0.834087i
$81$	−5.54819	−	9.60974i	−0.616465	−	1.06775i
$82$	3.33833	+	5.86288i	0.368656	+	0.647446i
$83$	9.73434	+	9.73434i	1.06848	+	1.06848i	0.997476	+	0.0710068i	$0.0226212\pi$
$83$	9.73434	+	9.73434i	1.06848	+	1.06848i	0.0710068	+	0.997476i	$0.477379\pi$
$84$	−3.39026	−	10.1750i	−0.369907	−	1.11019i
$85$	−4.71162	+	4.71162i	−0.511047	+	0.511047i
$86$	−2.54074	+	9.26019i	−0.273975	+	0.998552i
$87$	−9.74964	+	5.62896i	−1.04527	+	0.603488i
$88$	4.08473	−	14.2186i	0.435433	−	1.51570i
$89$	7.91117	−	13.7025i	0.838582	−	1.45247i	−0.0524979	−	0.998621i	$-0.516718\pi$
$89$	7.91117	−	13.7025i	0.838582	−	1.45247i	0.891080	−	0.453846i	$-0.149948\pi$
$90$	−1.02169	−	3.90634i	−0.107696	−	0.411764i
$91$	−3.00115	+	1.04002i	−0.314606	+	0.109024i
$92$	6.18792	+	11.0202i	0.645135	+	1.14894i
$93$	2.29212	−	0.614171i	0.237682	−	0.0636866i
$94$	9.59565	+	0.0574094i	0.989716	+	0.00592133i
$95$	−10.9149	+	6.30174i	−1.11985	+	0.646544i
$96$	−7.86122	−	8.34619i	−0.802332	−	0.851830i
$97$		−	1.12228i		−	0.113950i	−0.998376	−	0.0569750i	$-0.981854\pi$
$97$		−	1.12228i		−	0.113950i	0.998376	−	0.0569750i	$-0.0181455\pi$
$98$	−3.72702	+	9.17111i	−0.376486	+	0.926422i
$99$	4.09804	−	4.09804i	0.411868	−	0.411868i
$100$	−0.0392309	+	3.27849i	−0.00392309	+	0.327849i
$101$	3.75591	−	14.0172i	0.373727	−	1.39477i	−0.481470	−	0.876463i	$-0.659897\pi$
$101$	3.75591	−	14.0172i	0.373727	−	1.39477i	0.855196	−	0.518304i	$-0.173436\pi$
$102$	−5.27258	+	5.20986i	−0.522063	+	0.515853i
$103$	0.741916	+	0.428345i	0.0731031	+	0.0422061i	0.536106	−	0.844151i	$-0.319895\pi$
$103$	0.741916	+	0.428345i	0.0731031	+	0.0422061i	−0.463003	+	0.886357i	$0.653228\pi$
$104$	−2.44372	+	2.35754i	−0.239627	+	0.231176i
$105$	−6.03263	+	12.4311i	−0.588725	+	1.21315i
$106$	−2.72624	−	10.4235i	−0.264796	−	1.01242i
$107$	−5.09589	+	1.36544i	−0.492639	+	0.132002i	−0.496581	−	0.867990i	$-0.665412\pi$
$107$	−5.09589	+	1.36544i	−0.492639	+	0.132002i	0.00394288	+	0.999992i	$0.498745\pi$
$108$	1.89619	+	7.43122i	0.182461	+	0.715069i
$109$	−3.58485	+	13.3788i	−0.343367	+	1.28146i	0.551142	+	0.834411i	$0.314192\pi$
$109$	−3.58485	+	13.3788i	−0.343367	+	1.28146i	−0.894509	+	0.447050i	$0.852475\pi$
$110$	−16.5626	+	9.43077i	−1.57918	+	0.899189i
$111$	12.6761			1.20316
$112$	0.506304	+	10.5709i	0.0478412	+	0.998855i
$113$	−8.67774			−0.816333			−0.408167	−	0.912907i	$-0.633832\pi$
$113$	−8.67774			−0.816333			−0.408167	+	0.912907i	$0.633832\pi$
$114$	−12.1837	+	6.93743i	−1.14111	+	0.649749i
$115$	4.21435	−	15.7282i	0.392990	−	1.46666i
$116$	10.7640	−	2.74659i	0.999410	−	0.255014i
$117$	−1.28490	+	0.344288i	−0.118789	+	0.0318294i
$118$	−0.299828	−	1.14636i	−0.0276014	−	0.105531i
$119$	6.82419	−	0.490756i	0.625572	−	0.0449875i
$120$	−0.265111	+	14.7692i	−0.0242012	+	1.34823i
$121$	−14.1652	−	8.17828i	−1.28774	−	0.743480i
$122$	−4.55734	+	4.50313i	−0.412602	+	0.407694i
$123$	2.50259	−	9.33979i	0.225651	−	0.842141i
$124$	−2.34139	−	0.0280175i	−0.210263	−	0.00251604i
$125$	−6.12308	+	6.12308i	−0.547665	+	0.547665i
$126$	−1.83238	+	3.71905i	−0.163241	+	0.331319i
$127$		−	14.0559i		−	1.24726i	−0.781721	−	0.623628i	$-0.785658\pi$
$127$		−	14.0559i		−	1.24726i	0.781721	−	0.623628i	$-0.214342\pi$
$128$	5.24168	+	10.0262i	0.463303	+	0.886200i
$129$	11.9183	−	6.88103i	1.04935	−	0.605841i
$130$	4.37457	+	0.0261725i	0.383675	+	0.00229548i
$131$	−14.5921	+	3.90994i	−1.27492	+	0.341613i	−0.831913	−	0.554907i	$-0.812754\pi$
$131$	−14.5921	+	3.90994i	−1.27492	+	0.341613i	−0.443004	+	0.896520i	$0.646087\pi$
$132$	−18.4871	+	10.3806i	−1.60909	+	0.903514i
$133$	12.7083	+	2.44418i	1.10195	+	0.211937i
$134$	0.139635	+	0.533881i	0.0120626	+	0.0461203i
$135$	4.94038	−	8.55699i	0.425200	−	0.736468i
$136$	6.39890	−	3.54283i	0.548701	−	0.303795i
$137$	−4.37058	+	2.52336i	−0.373404	+	0.215585i	−0.674945	−	0.737868i	$-0.735832\pi$
$137$	−4.37058	+	2.52336i	−0.373404	+	0.215585i	0.301541	+	0.953453i	$0.402499\pi$
$138$	4.79273	−	17.4680i	0.407985	−	1.48698i
$139$	−3.77959	+	3.77959i	−0.320581	+	0.320581i	−0.848990	−	0.528409i	$-0.822789\pi$
$139$	−3.77959	+	3.77959i	−0.320581	+	0.320581i	0.528409	+	0.848990i	$0.322789\pi$
$140$	9.04743	−	10.2003i	0.764647	−	0.862083i
$141$	−9.72456	−	9.72456i	−0.818956	−	0.818956i
$142$	2.68242	+	4.71095i	0.225103	+	0.395334i
$143$	3.13954	+	5.43784i	0.262541	+	0.454735i
$144$	−0.106058	+	4.43094i	−0.00883815	+	0.369245i
$145$	−12.3946	−	7.15605i	−1.02932	−	0.594277i
$146$	6.92404	−	11.8288i	0.573037	−	0.978957i
$147$	13.0379	−	5.59523i	1.07535	−	0.461487i
$148$	−12.0425	−	3.38172i	−0.989885	−	0.277975i
$149$	0.0705758	+	0.263393i	0.00578180	+	0.0215780i	0.968756	−	0.248014i	$-0.0797779\pi$
$149$	0.0705758	+	0.263393i	0.00578180	+	0.0215780i	−0.962975	+	0.269592i	$0.913111\pi$
$150$	3.34253	−	3.30277i	0.272917	−	0.269670i
$151$	−4.58028	−	7.93328i	−0.372738	−	0.645601i	0.617248	−	0.786769i	$-0.288248\pi$
$151$	−4.58028	−	7.93328i	−0.372738	−	0.645601i	−0.989986	+	0.141168i	$0.954914\pi$
$152$	13.4255	−	3.34029i	1.08895	−	0.270933i
$153$	2.86538			0.231652
$154$	19.1955	+	3.81108i	1.54682	+	0.307106i
$155$	2.13316	+	2.13316i	0.171340	+	0.171340i
$156$	4.86611	+	0.0582286i	0.389601	+	0.00466202i
$157$	14.3922	+	3.85638i	1.14862	+	0.307772i	0.782413	−	0.622760i	$-0.213989\pi$
$157$	14.3922	+	3.85638i	1.14862	+	0.307772i	0.366209	+	0.930533i	$0.380655\pi$
$158$	−0.00932202	+	1.55812i	−0.000741620	+	0.123957i
$159$	−7.72068	+	13.3726i	−0.612290	+	1.06052i
$160$	4.19196	−	13.9602i	0.331404	−	1.10365i
$161$	−13.8425	+	9.37676i	−1.09094	+	0.738992i
$162$	7.92749	−	13.5430i	0.622842	−	1.06404i
$163$	4.99953	+	18.6585i	0.391593	+	1.46145i	0.827506	+	0.561457i	$0.189759\pi$
$163$	4.99953	+	18.6585i	0.391593	+	1.46145i	−0.435912	+	0.899989i	$0.643574\pi$
$164$	−4.86915	+	8.20529i	−0.380217	+	0.640726i
$165$	26.3849	+	7.06982i	2.05406	+	0.550384i
$166$	−5.15128	+	18.7748i	−0.399817	+	1.45721i
$167$		−	3.48341i		−	0.269554i	−0.990876	−	0.134777i	$-0.956968\pi$
$167$		−	3.48341i		−	0.269554i	0.990876	−	0.134777i	$-0.0430318\pi$
$168$	10.1323	−	11.2866i	0.781722	−	0.870782i
$169$			11.5588i			0.889137i
$170$	−9.08740	−	2.49333i	−0.696972	−	0.191229i
$171$	5.23517	+	1.40276i	0.400344	+	0.107272i
$172$	−13.1583	+	3.35753i	−1.00331	+	0.256009i
$173$	0.0189557	+	0.0707438i	0.00144118	+	0.00537855i	0.966643	−	0.256129i	$-0.0824471\pi$
$173$	0.0189557	+	0.0707438i	0.00144118	+	0.00537855i	−0.965201	+	0.261507i	$0.915780\pi$
$174$	−13.7402	−	8.04290i	−1.04164	−	0.609730i
$175$	−4.32617	+	0.311113i	−0.327028	+	0.0235179i
$176$	20.3323	−	4.92974i	1.53260	−	0.371593i
$177$	−0.849110	+	1.47070i	−0.0638230	+	0.110545i
$178$	22.3758	+	0.133871i	1.67713	+	0.0100341i
$179$	−3.00622	−	0.805515i	−0.224696	−	0.0602070i	0.144715	−	0.989473i	$-0.453774\pi$
$179$	−3.00622	−	0.805515i	−0.224696	−	0.0602070i	−0.369410	+	0.929266i	$0.620440\pi$
$180$	4.08576	−	3.98914i	0.304535	−	0.297333i
$181$	3.34414	+	3.34414i	0.248568	+	0.248568i	0.820383	−	0.571815i	$-0.193760\pi$
$181$	3.34414	+	3.34414i	0.248568	+	0.248568i	−0.571815	+	0.820383i	$0.693760\pi$
$182$	−3.37824	−	2.96050i	−0.250412	−	0.219447i
$183$	9.18219			0.678767
$184$	−9.21326	+	15.3163i	−0.679211	+	1.12913i
$185$	8.05751	+	13.9560i	0.592400	+	1.02607i
$186$	2.35874	+	2.38713i	0.172951	+	0.175033i
$187$	−3.50065	−	13.0646i	−0.255993	−	0.955379i
$188$	6.64416	+	11.8328i	0.484575	+	0.862994i
$189$	−9.58627	+	3.32203i	−0.697298	+	0.241642i
$190$	−15.3824	−	9.00419i	−1.11596	−	0.653233i
$191$	0.271101	+	0.156520i	0.0196162	+	0.0113254i	0.509776	−	0.860307i	$-0.329728\pi$
$191$	0.271101	+	0.156520i	0.0196162	+	0.0113254i	−0.490160	+	0.871633i	$0.663062\pi$
$192$	4.75606	−	15.5015i	0.343239	−	1.11872i
$193$	5.17806	+	8.96866i	0.372725	+	0.645578i	0.989984	−	0.141182i	$-0.0450902\pi$
$193$	5.17806	+	8.96866i	0.372725	+	0.645578i	−0.617259	+	0.786760i	$0.711757\pi$
$194$	1.37923	−	0.785332i	0.0990227	−	0.0563836i
$195$	−4.43334	−	4.43334i	−0.317478	−	0.317478i
$196$	−13.8789	+	1.83730i	−0.991351	+	0.131236i
$197$	0.112804	−	0.112804i	0.00803695	−	0.00803695i	−0.703077	−	0.711114i	$-0.748191\pi$
$197$	0.112804	−	0.112804i	0.00803695	−	0.00803695i	0.711114	+	0.703077i	$0.248191\pi$
$198$	7.90397	+	2.16863i	0.561711	+	0.154118i
$199$	−18.4737	+	10.6658i	−1.30957	+	0.756078i	−0.982023	−	0.188759i	$-0.939554\pi$
$199$	−18.4737	+	10.6658i	−1.30957	+	0.756078i	−0.327542	+	0.944837i	$0.606220\pi$
$200$	−4.05656	+	2.24596i	−0.286842	+	0.158814i
$201$	0.395444	−	0.684930i	0.0278925	−	0.0483112i
$202$	19.8548	−	5.19296i	1.39698	−	0.365375i
$203$	4.81190	+	13.8855i	0.337730	+	0.974573i
$204$	−10.0923	−	2.83406i	−0.706599	−	0.198424i
$205$	11.8736	−	3.18152i	0.829288	−	0.222207i
$206$	−0.00724837	+	1.21152i	−0.000505018	+	0.0844107i
$207$	−6.06405	+	3.50108i	−0.421480	+	0.243342i
$208$	−4.60734	−	1.35349i	−0.319462	−	0.0938479i
$209$		−	25.5834i		−	1.76964i
$210$	−19.4986	+	1.28502i	−1.34553	+	0.0886747i
$211$	7.71946	−	7.71946i	0.531430	−	0.531430i	−0.389568	−	0.920998i	$-0.627376\pi$
$211$	7.71946	−	7.71946i	0.531430	−	0.531430i	0.920998	+	0.389568i	$0.127376\pi$
$212$	10.9023	−	10.6444i	0.748772	−	0.731064i
$213$	2.01088	−	7.50472i	0.137784	−	0.514215i
$214$	−5.24400	−	5.30713i	−0.358472	−	0.362788i
$215$	15.1516	+	8.74780i	1.03333	+	0.596595i
$216$	−7.80573	+	7.53044i	−0.531113	+	0.512382i
$217$	−0.222187	−	3.08961i	−0.0150830	−	0.209737i
$218$	−18.9505	+	4.95646i	−1.28349	+	0.335694i
$219$	−18.9743	+	5.08416i	−1.28217	+	0.343556i
$220$	−23.1800	−	13.7554i	−1.56279	−	0.927386i
$221$	−0.803496	+	2.99869i	−0.0540490	+	0.201714i
$222$	8.87032	+	15.5783i	0.595337	+	1.04555i
$223$	−9.74121			−0.652319			−0.326160	−	0.945315i	$-0.605755\pi$
$223$	−9.74121			−0.652319			−0.326160	+	0.945315i	$0.605755\pi$
$224$	−12.6368	+	8.01938i	−0.844334	+	0.535817i
$225$	−1.81650			−0.121100
$226$	−6.07240	−	10.6645i	−0.403930	−	0.709395i
$227$	0.269850	−	1.00710i	0.0179106	−	0.0668433i	−0.956392	−	0.292086i	$-0.905651\pi$
$227$	0.269850	−	1.00710i	0.0179106	−	0.0668433i	0.974303	+	0.225242i	$0.0723174\pi$
$228$	−17.0515	−	10.1187i	−1.12927	−	0.670125i
$229$	−5.19372	+	1.39165i	−0.343210	+	0.0919630i	−0.426307	−	0.904579i	$-0.640186\pi$
$229$	−5.19372	+	1.39165i	−0.343210	+	0.0919630i	0.0830966	+	0.996541i	$0.473519\pi$
$230$	22.2783	−	5.82681i	1.46899	−	0.384209i
$231$	−15.7300	−	23.2216i	−1.03496	−	1.52787i
$232$	10.9077	+	11.3065i	0.716126	+	0.742305i
$233$	11.0720	+	6.39244i	0.725352	+	0.418782i	0.816720	−	0.577035i	$-0.195790\pi$
$233$	11.0720	+	6.39244i	0.725352	+	0.418782i	−0.0913671	+	0.995817i	$0.529124\pi$
$234$	−1.32224	−	1.33816i	−0.0864378	−	0.0874783i
$235$	4.52508	−	16.8878i	0.295184	−	1.10164i
$236$	1.19902	−	1.17066i	0.0780494	−	0.0762036i
$237$	1.57905	−	1.57905i	0.102571	−	0.102571i
$238$	5.37846	+	8.04320i	0.348634	+	0.521363i
$239$			26.2285i			1.69658i	0.529530	+	0.848291i	$0.322368\pi$
$239$			26.2285i			1.69658i	−0.529530	+	0.848291i	$0.677632\pi$
$240$	−18.3361	+	10.0092i	−1.18359	+	0.646089i
$241$	−19.0929	+	11.0233i	−1.22988	+	0.710072i	−0.967005	−	0.254758i	$-0.918004\pi$
$241$	−19.0929	+	11.0233i	−1.22988	+	0.710072i	−0.262875	+	0.964830i	$0.584671\pi$
$242$	0.138391	−	23.1312i	0.00889611	−	1.48693i
$243$	−10.6122	+	2.84352i	−0.680771	+	0.182412i
$244$	−8.72321	−	2.44962i	−0.558446	−	0.156821i
$245$	14.4477	+	10.7978i	0.923030	+	0.689846i
$246$	13.2294	−	3.46011i	0.843475	−	0.220609i
$247$	−2.93604	+	5.08537i	−0.186816	+	0.323575i
$248$	−1.60400	−	2.89707i	−0.101854	−	0.183964i
$249$	24.1641	−	13.9511i	1.53134	−	0.884117i
$250$	−11.8097	−	3.24025i	−0.746912	−	0.204932i
$251$	15.4991	−	15.4991i	0.978295	−	0.978295i	−0.0214744	−	0.999769i	$-0.506836\pi$
$251$	15.4991	−	15.4991i	0.978295	−	0.978295i	0.999769	+	0.0214744i	$0.00683604\pi$
$252$	−5.85277	+	0.350561i	−0.368690	+	0.0220832i
$253$	23.3715	+	23.3715i	1.46936	+	1.46936i
$254$	17.2740	−	9.83583i	1.08387	−	0.617155i
$255$	6.75264	+	11.6959i	0.422866	+	0.732426i
$256$	−8.65379	+	13.4578i	−0.540862	+	0.841112i
$257$	1.64001	+	0.946858i	0.102301	+	0.0590633i	0.550277	−	0.834982i	$-0.314522\pi$
$257$	1.64001	+	0.946858i	0.102301	+	0.0590633i	−0.447977	+	0.894045i	$0.647855\pi$
$258$	16.7965	+	9.83191i	1.04570	+	0.612108i
$259$	3.12517	−	16.2491i	0.194189	−	1.00967i
$260$	3.02902	+	5.39446i	0.187852	+	0.334550i
$261$	1.59293	+	5.94489i	0.0985998	+	0.367980i
$262$	−15.0162	−	15.1970i	−0.927703	−	0.938871i
$263$	4.67609	+	8.09923i	0.288340	+	0.499420i	0.973414	−	0.229054i	$-0.0735633\pi$
$263$	4.67609	+	8.09923i	0.288340	+	0.499420i	−0.685073	+	0.728474i	$0.740230\pi$
$264$	−25.6939	−	15.4558i	−1.58135	−	0.951237i
$265$	−19.6305			−1.20589
$266$	5.88909	+	17.3283i	0.361083	+	1.06247i
$267$	−22.6764	−	22.6764i	−1.38777	−	1.38777i
$268$	−0.558403	+	0.545197i	−0.0341099	+	0.0333032i
$269$	−25.7633	−	6.90325i	−1.57082	−	0.420899i	−0.634748	−	0.772719i	$-0.718896\pi$
$269$	−25.7633	−	6.90325i	−1.57082	−	0.420899i	−0.936067	+	0.351820i	$0.885563\pi$
$270$	13.9733	+	0.0836000i	0.850385	+	0.00508774i
$271$	−4.30075	+	7.44912i	−0.261252	+	0.452502i	−0.966575	−	0.256384i	$-0.917469\pi$
$271$	−4.30075	+	7.44912i	−0.261252	+	0.452502i	0.705323	+	0.708886i	$0.250802\pi$
$272$	8.83171	+	5.38480i	0.535501	+	0.326501i
$273$	0.461771	+	6.42114i	0.0279477	+	0.388625i
$274$	−6.15948	−	3.60548i	−0.372108	−	0.217815i
$275$	2.21923	+	8.28227i	0.133824	+	0.499440i
$276$	24.8212	−	6.33349i	1.49406	−	0.381232i
$277$	−24.7551	−	6.63310i	−1.48739	−	0.398544i	−0.578533	−	0.815659i	$-0.696375\pi$
$277$	−24.7551	−	6.63310i	−1.48739	−	0.398544i	−0.908854	+	0.417114i	$0.863041\pi$
$278$	−7.28977	−	2.00011i	−0.437211	−	0.119959i
$279$		−	1.29729i		−	0.0776664i
$280$	18.8668	+	3.98104i	1.12751	+	0.237912i
$281$		−	23.2859i		−	1.38912i	−0.719434	−	0.694561i	$-0.755599\pi$
$281$		−	23.2859i		−	1.38912i	0.719434	−	0.694561i	$-0.244401\pi$
$282$	5.14611	−	18.7560i	0.306446	−	1.11690i
$283$	9.80680	+	2.62772i	0.582954	+	0.156202i	0.538231	−	0.842797i	$-0.319093\pi$
$283$	9.80680	+	2.62772i	0.582954	+	0.156202i	0.0447228	+	0.998999i	$0.485760\pi$
$284$	−3.91247	+	6.59313i	−0.232162	+	0.391230i
$285$	6.61157	+	24.6747i	0.391635	+	1.46160i
$286$	−4.48591	+	7.66357i	−0.265257	+	0.453156i
$287$	−11.3554	−	5.51063i	−0.670288	−	0.325282i
$288$	−5.51964	+	2.97028i	−0.325248	+	0.175026i
$289$	−5.15640	+	8.93115i	−0.303318	+	0.525362i
$290$	0.121093	−	20.2400i	0.00711083	−	1.18853i
$291$	−2.19716	−	0.588728i	−0.128800	−	0.0345118i
$292$	19.3822	+	0.231931i	1.13426	+	0.0135727i
$293$	0.0961358	+	0.0961358i	0.00561631	+	0.00561631i	0.709909	−	0.704293i	$-0.248736\pi$
$293$	0.0961358	+	0.0961358i	0.00561631	+	0.00561631i	−0.704293	+	0.709909i	$0.748736\pi$
$294$	15.9998	+	12.1077i	0.933127	+	0.706133i
$295$	−2.15893			−0.125698
$296$	−4.27095	−	17.1661i	−0.248244	−	0.997757i
$297$	10.0283	+	17.3695i	0.581902	+	1.00788i
$298$	−0.274311	+	0.271048i	−0.0158904	+	0.0157014i
$299$	−1.96351	−	7.32792i	−0.113553	−	0.423784i
$300$	6.39795	+	1.79664i	0.369386	+	0.103729i
$301$	−5.88224	−	16.9741i	−0.339047	−	0.978374i
$302$	6.54450	−	11.1804i	0.376594	−	0.643360i
$303$	−25.4722	−	14.7064i	−1.46334	−	0.844861i
$304$	13.4998	+	14.1619i	0.774264	+	0.812238i
$305$	5.83662	+	10.1093i	0.334204	+	0.578858i
$306$	2.00510	+	3.52142i	0.114624	+	0.201306i
$307$	−16.2451	−	16.2451i	−0.927157	−	0.927157i	0.0703642	−	0.997521i	$-0.477584\pi$
$307$	−16.2451	−	16.2451i	−0.927157	−	0.927157i	−0.997521	+	0.0703642i	$0.977584\pi$
$308$	8.74874	+	26.2572i	0.498506	+	1.49615i
$309$	1.22780	−	1.22780i	0.0698470	−	0.0698470i
$310$	−1.12884	+	4.11427i	−0.0641138	+	0.233675i
$311$	12.3134	−	7.10914i	0.698228	−	0.403122i	−0.108459	−	0.994101i	$-0.534592\pi$
$311$	12.3134	−	7.10914i	0.698228	−	0.403122i	0.806687	+	0.590979i	$0.201258\pi$
$312$	3.33358	+	6.02097i	0.188727	+	0.340870i
$313$	13.4403	−	23.2792i	0.759689	−	1.31582i	−0.183321	−	0.983053i	$-0.558685\pi$
$313$	13.4403	−	23.2792i	0.759689	−	1.31582i	0.943009	−	0.332766i	$-0.107982\pi$
$314$	5.33187	+	20.3859i	0.300895	+	1.15044i
$315$	5.71081	+	4.94454i	0.321767	+	0.278593i
$316$	−1.92138	+	1.07886i	−0.108086	+	0.0606909i
$317$	15.4978	−	4.15263i	0.870445	−	0.233235i	0.204165	−	0.978936i	$-0.434552\pi$
$317$	15.4978	−	4.15263i	0.870445	−	0.233235i	0.666280	+	0.745701i	$0.267885\pi$
$318$	−21.8370	−	0.130648i	−1.22456	−	0.00732636i
$319$	25.1595	−	14.5258i	1.40866	−	0.813290i
$320$	20.0898	−	4.61715i	1.12306	−	0.258107i
$321$			10.6929i			0.596818i
$322$	−21.2101	−	10.4502i	−1.18199	−	0.582369i
$323$	8.94405	−	8.94405i	0.497660	−	0.497660i
$324$	22.1912	+	0.265543i	1.23284	+	0.0147524i
$325$	0.509373	−	1.90101i	0.0282549	−	0.105449i
$326$	−19.4319	+	19.2008i	−1.07623	+	1.06343i
$327$	24.3122	+	14.0366i	1.34447	+	0.776228i
$328$	−13.4912	−	0.242171i	−0.744927	−	0.0133717i
$329$	−14.8631	+	10.0681i	−0.819430	+	0.555073i
$330$	9.77481	+	37.3730i	0.538086	+	2.05732i
$331$	18.3460	−	4.91579i	1.00839	−	0.270196i	0.283431	−	0.958993i	$-0.408527\pi$
$331$	18.3460	−	4.91579i	1.00839	−	0.270196i	0.724955	+	0.688796i	$0.241861\pi$
$332$	−26.6781	+	6.80731i	−1.46415	+	0.373600i
$333$	1.79360	−	6.69379i	0.0982884	−	0.366817i
$334$	4.28095	−	2.43757i	0.234243	−	0.133378i
$335$	1.00545			0.0549336
$336$	20.9610	+	4.55408i	1.14351	+	0.248446i
$337$	15.6500			0.852513			0.426256	−	0.904602i	$-0.359832\pi$
$337$	15.6500			0.852513			0.426256	+	0.904602i	$0.359832\pi$
$338$	−14.2052	+	8.08845i	−0.772661	+	0.439954i
$339$	−4.55220	+	16.9890i	−0.247241	+	0.922717i
$340$	−3.29488	−	12.9127i	−0.178690	−	0.700291i
$341$	−5.91493	+	1.58490i	−0.320311	+	0.0858272i
$342$	1.93947	+	7.41539i	0.104875	+	0.400978i
$343$	−3.95798	−	18.0924i	−0.213711	−	0.976897i
$344$	−13.3340	−	13.8214i	−0.718919	−	0.745200i
$345$	−28.5814	−	16.5015i	−1.53877	−	0.888409i
$346$	−0.0736762	+	0.0727999i	−0.00396086	+	0.00391375i
$347$	−5.07381	+	18.9357i	−0.272376	+	1.01652i	0.685203	+	0.728352i	$0.259714\pi$
$347$	−5.07381	+	18.9357i	−0.272376	+	1.01652i	−0.957579	+	0.288170i	$0.906953\pi$
$348$	0.269409	−	22.5142i	0.0144418	−	1.20689i
$349$	−7.34147	+	7.34147i	−0.392980	+	0.392980i	−0.875748	−	0.482768i	$-0.839631\pi$
$349$	−7.34147	+	7.34147i	−0.392980	+	0.392980i	0.482768	+	0.875748i	$0.339631\pi$
$350$	−3.40965	−	5.09896i	−0.182254	−	0.272551i
$351$		−	4.60354i		−	0.245719i
$352$	20.2863	+	21.5378i	1.08126	+	1.14797i
$353$	10.4533	−	6.03519i	0.556371	−	0.321221i	−0.195317	−	0.980740i	$-0.562574\pi$
$353$	10.4533	−	6.03519i	0.556371	−	0.321221i	0.751687	+	0.659519i	$0.229240\pi$
$354$	−2.40160	−	0.0143685i	−0.127644	−	0.000763675i
$355$	9.54069	−	2.55642i	0.506367	−	0.135681i
$356$	15.4933	+	27.5925i	0.821143	+	1.46240i
$357$	2.61907	−	13.6176i	0.138616	−	0.720722i
$358$	−1.11371	−	4.25818i	−0.0588616	−	0.225052i
$359$	0.868374	−	1.50407i	0.0458310	−	0.0793816i	−0.842200	−	0.539165i	$-0.818740\pi$
$359$	0.868374	−	1.50407i	0.0458310	−	0.0793816i	0.888031	+	0.459784i	$0.152073\pi$
$360$	7.76155	+	2.22975i	0.409070	+	0.117518i
$361$	4.26528	−	2.46256i	0.224488	−	0.129608i
$362$	−1.76967	+	6.44991i	−0.0930120	+	0.339000i
$363$	−23.4420	+	23.4420i	−1.23039	+	1.23039i
$364$	1.27434	−	6.22336i	0.0667933	−	0.326193i
$365$	−17.6585	−	17.6585i	−0.924287	−	0.924287i
$366$	6.42539	+	11.2845i	0.335861	+	0.589850i
$367$	−5.21754	−	9.03704i	−0.272353	−	0.471730i	0.697111	−	0.716963i	$-0.254469\pi$
$367$	−5.21754	−	9.03704i	−0.272353	−	0.471730i	−0.969464	+	0.245234i	$0.921135\pi$
$368$	−25.2701	−	0.604859i	−1.31730	−	0.0315304i
$369$	−4.57790	−	2.64305i	−0.238316	−	0.137592i
$370$	−11.5129	+	19.6683i	−0.598528	+	1.02250i
$371$	15.2385	+	13.1938i	0.791142	+	0.684987i
$372$	−1.28311	+	4.56921i	−0.0665260	+	0.236903i
$373$	−2.84184	−	10.6059i	−0.147145	−	0.549153i	−0.999651	−	0.0264347i	$-0.991585\pi$
$373$	−2.84184	−	10.6059i	−0.147145	−	0.549153i	0.852505	−	0.522718i	$-0.175082\pi$
$374$	13.6062	−	13.4443i	0.703558	−	0.695189i
$375$	8.77552	+	15.1996i	0.453166	+	0.784907i
$376$	−9.89257	+	16.4456i	−0.510170	+	0.848115i
$377$	−6.66815			−0.343427
$378$	−10.7908	−	9.45643i	−0.555018	−	0.486386i
$379$	19.3486	+	19.3486i	0.993870	+	0.993870i	0.999981	−	0.00611151i	$-0.00194537\pi$
$379$	19.3486	+	19.3486i	0.993870	+	0.993870i	−0.00611151	+	0.999981i	$0.501945\pi$
$380$	0.301609	−	25.2051i	0.0154722	−	1.29300i
$381$	−27.5182	−	7.37347i	−1.40980	−	0.377754i
$382$	−0.00264861	+	0.442699i	−0.000135514	+	0.0226504i
$383$	8.91313	−	15.4380i	0.455440	−	0.788844i	−0.543274	−	0.839556i	$-0.682815\pi$
$383$	8.91313	−	15.4380i	0.455440	−	0.788844i	0.998713	+	0.0507112i	$0.0161488\pi$
$384$	22.3787	−	5.00243i	1.14201	−	0.255279i
$385$	15.5675	−	32.0790i	0.793395	−	1.63490i
$386$	−7.39863	+	12.6396i	−0.376581	+	0.643337i
$387$	−1.94725	−	7.26724i	−0.0989844	−	0.369415i
$388$	1.93027	+	1.14546i	0.0979948	+	0.0581517i
$389$	6.02818	+	1.61525i	0.305641	+	0.0818963i	0.408380	−	0.912812i	$-0.366094\pi$
$389$	6.02818	+	1.61525i	0.305641	+	0.0818963i	−0.102739	+	0.994708i	$0.532761\pi$
$390$	2.34607	−	8.55068i	0.118798	−	0.432980i
$391$			16.3416i			0.826429i
$392$	−11.9700	−	15.7709i	−0.604575	−	0.796549i
$393$			30.6190i			1.54453i
$394$	0.217567	+	0.0596943i	0.0109609	+	0.00300736i
$395$	2.74221	+	0.734773i	0.137976	+	0.0369705i
$396$	2.86579	+	11.2311i	0.144012	+	0.564386i
$397$	−1.82783	−	6.82155i	−0.0917361	−	0.342364i	0.904768	−	0.425904i	$-0.140044\pi$
$397$	−1.82783	−	6.82155i	−0.0917361	−	0.342364i	−0.996504	+	0.0835403i	$0.973377\pi$
$398$	−26.0350	−	15.2397i	−1.30502	−	0.763899i
$399$	11.4517	−	23.5978i	0.573303	−	1.18137i
$400$	−5.59883	−	3.41367i	−0.279942	−	0.170684i
$401$	10.4950	−	18.1779i	0.524096	−	0.907761i	−0.475510	−	0.879710i	$-0.657737\pi$
$401$	10.4950	−	18.1779i	0.524096	−	0.907761i	0.999606	−	0.0280512i	$-0.00893014\pi$
$402$	1.11847	+	0.00669163i	0.0557840	+	0.000333748i
$403$	1.35764	+	0.363778i	0.0676288	+	0.0181211i
$404$	20.2756	+	20.7667i	1.00875	+	1.03318i
$405$	−20.2176	−	20.2176i	−1.00462	−	1.00462i
$406$	−13.6975	+	15.6302i	−0.679793	+	0.775716i
$407$	−32.7114			−1.62144
$408$	−3.57929	−	14.3861i	−0.177201	−	0.712218i
$409$	18.0958	+	31.3428i	0.894780	+	1.54980i	0.834077	+	0.551648i	$0.186001\pi$
$409$	18.0958	+	31.3428i	0.894780	+	1.54980i	0.0607027	+	0.998156i	$0.480666\pi$
$410$	12.2187	+	12.3658i	0.603438	+	0.610702i
$411$	2.64742	+	9.88031i	0.130588	+	0.487360i
$412$	−1.49398	+	0.838875i	−0.0736029	+	0.0413284i
$413$	1.67591	+	1.45103i	0.0824660	+	0.0714008i
$414$	−8.54608	−	5.00249i	−0.420017	−	0.245859i
$415$	30.7196	+	17.7360i	1.50797	+	0.870624i
$416$	−1.56068	−	6.60934i	−0.0765188	−	0.324049i
$417$	5.41686	+	9.38228i	0.265265	+	0.459452i
$418$	31.4408	−	17.9024i	1.53782	−	0.875635i
$419$	5.15413	+	5.15413i	0.251796	+	0.251796i	0.821707	−	0.569911i	$-0.193022\pi$
$419$	5.15413	+	5.15413i	0.251796	+	0.251796i	−0.569911	+	0.821707i	$0.693022\pi$
$420$	−15.2237	−	23.0637i	−0.742842	−	1.12539i
$421$	−7.75876	+	7.75876i	−0.378139	+	0.378139i	−0.870430	−	0.492292i	$-0.836159\pi$
$421$	−7.75876	+	7.75876i	−0.378139	+	0.378139i	0.492292	+	0.870430i	$0.336159\pi$
$422$	14.8887	+	4.08504i	0.724770	+	0.198856i
$423$	−6.51116	+	3.75922i	−0.316583	+	0.182779i
$424$	20.7106	+	5.94976i	1.00579	+	0.288946i
$425$	−2.11966	+	3.67137i	−0.102819	+	0.178087i
$426$	10.6301	−	2.78027i	0.515030	−	0.134705i
$427$	2.26378	−	11.7704i	0.109552	−	0.569608i
$428$	2.85263	−	10.1584i	0.137887	−	0.491024i
$429$	12.2930	−	3.29390i	0.593511	−	0.159031i
$430$	−0.148028	+	24.7421i	−0.00713856	+	1.19317i
$431$	21.4746	−	12.3984i	1.03440	−	0.597209i	0.116156	−	0.993231i	$-0.462943\pi$
$431$	21.4746	−	12.3984i	1.03440	−	0.597209i	0.918241	+	0.396022i	$0.129609\pi$
$432$	−14.7168	−	4.32333i	−0.708060	−	0.208006i
$433$			4.84981i			0.233067i	0.993187	+	0.116534i	$0.0371782\pi$
$433$			4.84981i			0.233067i	−0.993187	+	0.116534i	$0.962822\pi$
$434$	3.64151	−	2.43507i	0.174798	−	0.116887i
$435$	−20.5119	+	20.5119i	−0.983471	+	0.983471i
$436$	−19.3522	−	19.8210i	−0.926803	−	0.949252i
$437$	−8.00009	+	29.8567i	−0.382696	+	1.42824i
$438$	−19.5258	−	19.7609i	−0.932979	−	0.944210i
$439$	−32.2458	−	18.6171i	−1.53901	−	0.888546i	−0.998897	−	0.0469506i	$-0.985050\pi$
$439$	−32.2458	−	18.6171i	−1.53901	−	0.888546i	−0.540109	−	0.841595i	$-0.681617\pi$
$440$	0.684133	−	38.1126i	0.0326148	−	1.81695i
$441$	−1.10985	−	7.67655i	−0.0528498	−	0.365550i
$442$	−4.24751	+	1.11092i	−0.202033	+	0.0528412i
$443$	−24.3077	+	6.51323i	−1.15489	+	0.309453i	−0.784925	−	0.619591i	$-0.787298\pi$
$443$	−24.3077	+	6.51323i	−1.15489	+	0.309453i	−0.369969	+	0.929044i	$0.620632\pi$
$444$	−12.9379	+	21.8024i	−0.614006	+	1.03470i
$445$	10.5519	−	39.3802i	0.500207	−	1.86680i
$446$	−6.81657	−	11.9715i	−0.322774	−	0.566866i
$447$	0.552685			0.0261411
$448$	−18.6983	−	9.91838i	−0.883411	−	0.468600i
$449$	0.885883			0.0418074			0.0209037	−	0.999781i	$-0.493346\pi$
$449$	0.885883			0.0418074			0.0209037	+	0.999781i	$0.493346\pi$
$450$	−1.27113	−	2.23239i	−0.0599214	−	0.105236i
$451$	−6.45806	+	24.1018i	−0.304098	+	1.13491i
$452$	8.85696	−	14.9254i	0.416597	−	0.702031i
$453$	−17.9343	+	4.80548i	−0.842626	+	0.225781i
$454$	1.42651	−	0.373098i	0.0669492	−	0.0175104i
$455$	−6.77596	+	4.58997i	−0.317662	+	0.215181i
$456$	0.503259	−	28.0363i	0.0235673	−	1.31292i
$457$	−30.0308	−	17.3383i	−1.40478	−	0.811052i	−0.409904	−	0.912129i	$-0.634438\pi$
$457$	−30.0308	−	17.3383i	−1.40478	−	0.811052i	−0.994879	+	0.101077i	$0.967771\pi$
$458$	−5.34467	−	5.40900i	−0.249740	−	0.252746i
$459$	−2.56653	+	9.57840i	−0.119795	+	0.447082i
$460$	22.7505	+	23.3015i	1.06075	+	1.08644i
$461$	4.11212	−	4.11212i	0.191520	−	0.191520i	−0.604832	−	0.796353i	$-0.706760\pi$
$461$	4.11212	−	4.11212i	0.191520	−	0.191520i	0.796353	+	0.604832i	$0.206760\pi$
$462$	17.5309	−	35.5812i	0.815609	−	1.65539i
$463$			11.6892i			0.543245i	0.962404	+	0.271623i	$0.0875603\pi$
$463$			11.6892i			0.543245i	−0.962404	+	0.271623i	$0.912440\pi$
$464$	−6.26226	+	21.3169i	−0.290718	+	0.989614i
$465$	5.29526	−	3.05722i	0.245562	−	0.141775i
$466$	−0.108171	+	18.0802i	−0.00501095	+	0.837550i
$467$	−24.3284	+	6.51878i	−1.12579	+	0.301653i	−0.773222	−	0.634135i	$-0.781356\pi$
$467$	−24.3284	+	6.51878i	−1.12579	+	0.301653i	−0.352563	+	0.935788i	$0.614690\pi$
$468$	0.719275	−	2.56138i	0.0332485	−	0.118400i
$469$	−0.780497	−	0.675771i	−0.0360400	−	0.0312042i
$470$	23.9209	−	6.25643i	1.10339	−	0.288588i
$471$	15.0998	−	26.1536i	0.695762	−	1.20509i
$472$	2.27772	+	0.654347i	0.104841	+	0.0301188i
$473$	−30.7558	+	17.7569i	−1.41415	+	0.816461i
$474$	3.04555	+	0.835614i	0.139887	+	0.0383810i
$475$	−5.67005	+	5.67005i	−0.260160	+	0.260160i
$476$	−6.12105	+	12.2382i	−0.280558	+	0.560939i
$477$	5.96915	+	5.96915i	0.273309	+	0.273309i
$478$	−32.2336	+	18.3538i	−1.47433	+	0.839485i
$479$	−12.1539	−	21.0512i	−0.555328	−	0.961856i	−0.997878	−	0.0651122i	$-0.979259\pi$
$479$	−12.1539	−	21.0512i	−0.555328	−	0.961856i	0.442550	−	0.896744i	$-0.354074\pi$
$480$	−25.1318	−	15.5302i	−1.14711	−	0.708853i
$481$	6.50225	+	3.75408i	0.296477	+	0.171171i
$482$	−26.9077	−	15.7505i	−1.22561	−	0.717417i
$483$	11.0960	+	32.0193i	0.504886	+	1.45693i
$484$	28.5241	−	16.0164i	1.29655	−	0.728018i
$485$	−0.748444	−	2.79323i	−0.0339851	−	0.126834i
$486$	−10.9206	−	11.0521i	−0.495368	−	0.501331i
$487$	15.5000	+	26.8468i	0.702373	+	1.21655i	0.967631	+	0.252369i	$0.0812095\pi$
$487$	15.5000	+	26.8468i	0.702373	+	1.21655i	−0.265258	+	0.964177i	$0.585457\pi$
$488$	−3.09375	−	12.4346i	−0.140048	−	0.562887i
$489$	39.1517			1.77050
$490$	−3.15998	+	25.3115i	−0.142753	+	1.14346i
$491$	8.29080	+	8.29080i	0.374159	+	0.374159i	0.868989	−	0.494831i	$-0.164770\pi$
$491$	8.29080	+	8.29080i	0.374159	+	0.374159i	−0.494831	+	0.868989i	$0.664770\pi$
$492$	13.5098	+	13.8370i	0.609069	+	0.623822i
$493$	13.8741	+	3.71756i	0.624860	+	0.167431i
$494$	−8.30423	−	0.0496831i	−0.373625	−	0.00223535i
$495$	7.46662	−	12.9326i	0.335600	−	0.581276i
$496$	2.43794	−	3.99851i	0.109467	−	0.179538i
$497$	−9.12431	−	4.42791i	−0.409281	−	0.198619i
$498$	34.0545	+	19.9340i	1.52602	+	0.893263i
$499$	−6.15379	−	22.9663i	−0.275482	−	1.02811i	−0.955518	−	0.294933i	$-0.904703\pi$
$499$	−6.15379	−	22.9663i	−0.275482	−	1.02811i	0.680036	−	0.733178i	$-0.261964\pi$
$500$	−4.28192	−	16.7810i	−0.191493	−	0.750469i
$501$	−6.81971	−	1.82734i	−0.304682	−	0.0816394i
$502$	29.8934	+	8.20192i	1.33421	+	0.366070i
$503$		−	3.42708i		−	0.152806i	−0.997077	−	0.0764029i	$-0.975656\pi$
$503$		−	3.42708i		−	0.152806i	0.997077	−	0.0764029i	$-0.0243435\pi$
$504$	−4.52640	−	6.94747i	−0.201622	−	0.309465i
$505$		−	37.3923i		−	1.66393i
$506$	−12.3679	+	45.0771i	−0.549820	+	2.00392i
$507$	22.6294	+	6.06354i	1.00501	+	0.269291i
$508$	24.1756	+	14.3462i	1.07262	+	0.636508i
$509$	9.52030	+	35.5302i	0.421980	+	1.57485i	0.770431	+	0.637523i	$0.220041\pi$
$509$	9.52030	+	35.5302i	0.421980	+	1.57485i	−0.348451	+	0.937327i	$0.613292\pi$
$510$	−9.64846	+	16.4831i	−0.427241	+	0.729883i
$511$	1.83928	+	25.5761i	0.0813651	+	1.13142i
$512$	−22.5946	−	1.21779i	−0.998551	−	0.0538191i
$513$	−9.37830	+	16.2437i	−0.414062	+	0.717177i
$514$	−0.0160225	+	2.67807i	−0.000706723	+	0.118125i
$515$	2.13221	+	0.571325i	0.0939566	+	0.0251756i
$516$	−0.329334	+	27.5222i	−0.0144981	+	1.21160i
$517$	25.0947	+	25.0947i	1.10367	+	1.10367i
$518$	22.1563	−	7.52989i	0.973491	−	0.330845i
$519$	0.148444			0.00651597
$520$	−4.50994	+	7.49738i	−0.197774	+	0.328782i
$521$	−6.82432	−	11.8201i	−0.298979	−	0.517846i	0.676924	−	0.736053i	$-0.263313\pi$
$521$	−6.82432	−	11.8201i	−0.298979	−	0.517846i	−0.975903	+	0.218207i	$0.929979\pi$
$522$	−6.19132	+	6.11767i	−0.270987	+	0.267763i
$523$	4.93451	+	18.4158i	0.215771	+	0.805269i	0.985894	+	0.167373i	$0.0535283\pi$
$523$	4.93451	+	18.4158i	0.215771	+	0.805269i	−0.770123	+	0.637896i	$0.779805\pi$
$524$	8.16851	−	29.0885i	0.356843	−	1.27074i
$525$	−1.66035	+	8.63285i	−0.0724635	+	0.376769i
$526$	−6.68140	+	11.4143i	−0.291323	+	0.497686i
$527$	−2.62197	−	1.51380i	−0.114215	−	0.0659420i
$528$	1.01468	−	42.3920i	0.0441585	−	1.84488i
$529$	−8.46701	−	14.6653i	−0.368131	−	0.637621i
$530$	−13.7367	−	24.1249i	−0.596686	−	1.04792i
$531$	0.656479	+	0.656479i	0.0284888	+	0.0284888i
$532$	−17.1747	+	19.3632i	−0.744618	+	0.839501i
$533$	4.04973	−	4.04973i	0.175413	−	0.175413i
$534$	12.0000	−	43.7364i	0.519292	−	1.89266i
$535$	−11.7725	+	6.79688i	−0.508971	+	0.293855i
$536$	−1.06077	−	0.304740i	−0.0458184	−	0.0131628i
$537$	−3.15403	+	5.46293i	−0.136106	+	0.235743i
$538$	−9.54452	−	36.4925i	−0.411493	−	1.57331i
$539$	−33.6451	+	14.4388i	−1.44920	+	0.621923i
$540$	9.67528	+	17.2310i	0.416358	+	0.741503i
$541$	0.455845	−	0.122143i	0.0195983	−	0.00525135i	−0.249007	−	0.968502i	$-0.580104\pi$
$541$	0.455845	−	0.122143i	0.0195983	−	0.00525135i	0.268605	+	0.963250i	$0.413437\pi$
$542$	−12.1641	−	0.0727764i	−0.522495	−	0.00312602i
$543$	8.30133	−	4.79278i	0.356244	−	0.205678i
$544$	−0.437528	+	14.6219i	−0.0187589	+	0.626907i
$545$			35.6893i			1.52876i
$546$	−7.56815	+	5.06080i	−0.323887	+	0.216582i
$547$	9.02908	−	9.02908i	0.386056	−	0.386056i	−0.487222	−	0.873278i	$-0.661990\pi$
$547$	9.02908	−	9.02908i	0.386056	−	0.386056i	0.873278	+	0.487222i	$0.161990\pi$
$548$	0.120771	−	10.0927i	0.00515908	−	0.431139i
$549$	1.29923	−	4.84878i	0.0554497	−	0.206941i
$550$	−8.62558	+	8.52298i	−0.367796	+	0.363421i
$551$	23.5287	+	13.5843i	1.00236	+	0.578710i
$552$	25.1526	+	26.0721i	1.07057	+	1.10970i
$553$	−1.63484	−	2.41344i	−0.0695204	−	0.102630i
$554$	−9.17100	−	35.0644i	−0.389638	−	1.48975i
$555$	31.5495	−	8.45367i	1.33920	−	0.358838i
$556$	−2.64310	−	10.3584i	−0.112092	−	0.439294i
$557$	1.79973	−	6.71669i	0.0762570	−	0.284595i	−0.917258	−	0.398293i	$-0.869603\pi$
$557$	1.79973	−	6.71669i	0.0762570	−	0.284595i	0.993515	+	0.113698i	$0.0362695\pi$
$558$	1.59430	−	0.907797i	0.0674922	−	0.0384301i
$559$	8.15137			0.344766
$560$	8.30984	+	25.9722i	0.351155	+	1.09753i
$561$	−27.4139			−1.15742
$562$	28.6173	−	16.2947i	1.20715	−	0.687351i
$563$	7.95972	−	29.7061i	0.335462	−	1.25196i	−0.567905	−	0.823094i	$-0.692246\pi$
$563$	7.95972	−	29.7061i	0.335462	−	1.25196i	0.903367	−	0.428868i	$-0.141087\pi$
$564$	26.6513	−	6.80047i	1.12222	−	0.286351i
$565$	−21.5980	+	5.78717i	−0.908635	+	0.243468i
$566$	3.63312	+	13.8909i	0.152711	+	0.583878i
$567$	2.10584	+	29.2826i	0.0884369	+	1.22975i
$568$	−10.8405	−	0.194590i	−0.454856	−	0.00816480i
$569$	33.8726	+	19.5564i	1.42002	+	0.819846i	0.996300	−	0.0859489i	$-0.0273922\pi$
$569$	33.8726	+	19.5564i	1.42002	+	0.819846i	0.423716	+	0.905795i	$0.360726\pi$
$570$	−25.6975	+	25.3918i	−1.07635	+	1.06355i
$571$	1.41986	−	5.29899i	0.0594193	−	0.221756i	−0.929831	−	0.367986i	$-0.880047\pi$
$571$	1.41986	−	5.29899i	0.0594193	−	0.221756i	0.989251	+	0.146230i	$0.0467141\pi$
$572$	−12.5573	−	0.150262i	−0.525045	−	0.00628277i
$573$	0.448646	−	0.448646i	0.0187425	−	0.0187425i
$574$	−1.17383	−	17.8114i	−0.0489945	−	0.743434i
$575$		−	10.3597i		−	0.432028i
$576$	−7.51280	−	4.70487i	−0.313033	−	0.196036i
$577$	30.0825	−	17.3681i	1.25235	−	0.723044i	0.280774	−	0.959774i	$-0.409409\pi$
$577$	30.0825	−	17.3681i	1.25235	−	0.723044i	0.971576	+	0.236729i	$0.0760755\pi$
$578$	−14.5842	−	0.0872555i	−0.606624	−	0.00362935i
$579$	20.2749	−	5.43264i	0.842596	−	0.225773i
$580$	24.9587	−	14.0145i	1.03636	−	0.581919i
$581$	−11.9261	−	34.4147i	−0.494778	−	1.42776i
$582$	−0.813982	−	3.11218i	−0.0337406	−	0.129004i
$583$	19.9236	−	34.5087i	0.825152	−	1.42920i
$584$	13.2780	+	23.9822i	0.549448	+	0.992389i
$585$	−2.96838	+	1.71379i	−0.122727	+	0.0708567i
$586$	−0.0508738	+	0.185419i	−0.00210158	+	0.00765959i
$587$	25.6897	−	25.6897i	1.06033	−	1.06033i	0.0622695	−	0.998059i	$-0.480166\pi$
$587$	25.6897	−	25.6897i	1.06033	−	1.06033i	0.998059	−	0.0622695i	$-0.0198338\pi$
$588$	−3.68362	+	28.1356i	−0.151910	+	1.16029i
$589$	−4.04937	−	4.04937i	−0.166851	−	0.166851i
$590$	−1.51075	−	2.65323i	−0.0621965	−	0.109232i
$591$	−0.161669	−	0.280019i	−0.00665018	−	0.0115185i
$592$	18.1076	−	17.2610i	0.744218	−	0.709424i
$593$	21.1335	+	12.2015i	0.867850	+	0.501054i	0.866633	−	0.498946i	$-0.166279\pi$
$593$	21.1335	+	12.2015i	0.867850	+	0.501054i	0.00121701	+	0.999999i	$0.499613\pi$
$594$	−14.3289	+	24.4790i	−0.587921	+	1.00438i
$595$	16.6574	−	5.77248i	0.682888	−	0.236649i
$596$	−0.525059	−	0.147445i	−0.0215072	−	0.00603957i
$597$	11.1902	+	41.7623i	0.457984	+	1.70922i
$598$	7.63167	−	7.54089i	0.312082	−	0.308370i
$599$	−13.3779	−	23.1712i	−0.546606	−	0.946750i	−0.998504	−	0.0546799i	$-0.982586\pi$
$599$	−13.3779	−	23.1712i	−0.546606	−	0.946750i	0.451898	−	0.892070i	$-0.350747\pi$
$600$	2.26908	+	9.12001i	0.0926348	+	0.372323i
$601$	16.1853			0.660212			0.330106	−	0.943944i	$-0.392915\pi$
$601$	16.1853			0.660212			0.330106	+	0.943944i	$0.392915\pi$
$602$	16.7442	−	19.1069i	0.682444	−	0.778741i
$603$	−0.305733	−	0.305733i	−0.0124504	−	0.0124504i
$604$	18.3198	+	0.219218i	0.745423	+	0.00891984i
$605$	−40.7098	−	10.9082i	−1.65509	−	0.443479i
$606$	0.248859	−	41.5952i	0.0101092	−	1.68969i
$607$	2.51647	−	4.35866i	0.102141	−	0.176913i	−0.810426	−	0.585841i	$-0.800764\pi$
$607$	2.51647	−	4.35866i	0.102141	−	0.176913i	0.912566	+	0.408929i	$0.134098\pi$
$608$	−7.95758	+	26.5006i	−0.322723	+	1.07474i
$609$	29.7089	−	2.13649i	1.20387	−	0.0865751i
$610$	−8.33962	+	14.2471i	−0.337661	+	0.576849i
$611$	−2.10828	−	7.86821i	−0.0852919	−	0.318314i
$612$	−2.92456	+	4.92835i	−0.118218	+	0.199217i
$613$	0.439011	+	0.117633i	0.0177315	+	0.00475113i	0.267674	−	0.963510i	$-0.413745\pi$
$613$	0.439011	+	0.117633i	0.0177315	+	0.00475113i	−0.249942	+	0.968261i	$0.580412\pi$
$614$	8.59669	−	31.3323i	0.346934	−	1.26447i
$615$		−	24.9147i		−	1.00466i
$616$	−26.1469	+	29.1257i	−1.05349	+	1.17351i
$617$			4.35363i			0.175271i	0.996153	+	0.0876353i	$0.0279310\pi$
$617$			4.35363i			0.175271i	−0.996153	+	0.0876353i	$0.972069\pi$
$618$	2.36808	+	0.649734i	0.0952581	+	0.0261361i
$619$	−4.74521	−	1.27148i	−0.190726	−	0.0511049i	0.162191	−	0.986759i	$-0.448144\pi$
$619$	−4.74521	−	1.27148i	−0.190726	−	0.0511049i	−0.352918	+	0.935654i	$0.614810\pi$
$620$	−5.84617	+	1.49174i	−0.234788	+	0.0599096i
$621$	−6.27184	−	23.4068i	−0.251680	−	0.939283i
$622$	17.3533	+	10.1578i	0.695804	+	0.407292i
$623$	−34.6588	+	23.4775i	−1.38858	+	0.940606i
$624$	−5.06676	+	8.31009i	−0.202833	+	0.332670i
$625$	−15.2547	+	26.4218i	−0.610186	+	1.05687i
$626$	38.0141	+	0.227433i	1.51935	+	0.00909006i
$627$	−50.0864	−	13.4206i	−2.00026	−	0.535967i
$628$	−21.3222	+	20.8180i	−0.850850	+	0.830728i
$629$	−11.4360	−	11.4360i	−0.455984	−	0.455984i
$630$	−2.08037	+	10.4783i	−0.0828840	+	0.417467i
$631$	−22.0158			−0.876434			−0.438217	−	0.898869i	$-0.644390\pi$
$631$	−22.0158			−0.876434			−0.438217	+	0.898869i	$0.644390\pi$
$632$	−2.67039	−	1.60633i	−0.106223	−	0.0638965i
$633$	−11.0634	−	19.1624i	−0.439732	−	0.761638i
$634$	15.9483	+	16.1402i	0.633387	+	0.641011i
$635$	−9.37383	−	34.9836i	−0.371989	−	1.38828i
$636$	−15.1202	−	26.9281i	−0.599556	−	1.06777i
$637$	8.34491	+	0.991141i	0.330637	+	0.0392704i
$638$	35.4573	+	20.7551i	1.40377	+	0.821703i
$639$	−3.67844	−	2.12375i	−0.145517	−	0.0840142i
$640$	19.7325	+	21.4585i	0.779994	+	0.848223i
$641$	11.9837	+	20.7564i	0.473328	+	0.819828i	0.999534	−	0.0305295i	$-0.00971934\pi$
$641$	11.9837	+	20.7564i	0.473328	+	0.819828i	−0.526206	+	0.850357i	$0.676386\pi$
$642$	−13.1410	+	7.48252i	−0.518636	+	0.295311i
$643$	−30.4232	−	30.4232i	−1.19977	−	1.19977i	−0.974235	−	0.225537i	$-0.927586\pi$
$643$	−30.4232	−	30.4232i	−1.19977	−	1.19977i	−0.225537	−	0.974235i	$-0.572414\pi$
$644$	−1.99928	−	33.3790i	−0.0787828	−	1.31532i
$645$	25.0745	−	25.0745i	0.987306	−	0.987306i
$646$	17.2506	+	4.73307i	0.678715	+	0.186220i
$647$	5.45353	−	3.14859i	0.214400	−	0.123784i	−0.388954	−	0.921257i	$-0.627164\pi$
$647$	5.45353	−	3.14859i	0.214400	−	0.123784i	0.603355	+	0.797473i	$0.293830\pi$
$648$	15.2023	+	27.4577i	0.597203	+	1.07864i
$649$	2.19117	−	3.79522i	0.0860110	−	0.148975i
$650$	2.69269	−	0.704266i	0.105616	−	0.0276236i
$651$	−6.16531	−	1.18577i	−0.241638	−	0.0464739i
$652$	−37.1947	−	10.4449i	−1.45666	−	0.409052i
$653$	−30.7763	+	8.24649i	−1.20437	+	0.322710i	−0.804551	−	0.593884i	$-0.797594\pi$
$653$	−30.7763	+	8.24649i	−1.20437	+	0.322710i	−0.399819	+	0.916594i	$0.630927\pi$
$654$	−0.237525	+	39.7009i	−0.00928796	+	1.55243i
$655$	−33.7107	+	19.4629i	−1.31719	+	0.760477i
$656$	−9.14307	−	16.7495i	−0.356977	−	0.653959i
$657$			10.7390i			0.418970i
$658$	−22.7740	−	11.2207i	−0.887821	−	0.437430i
$659$	−3.27251	+	3.27251i	−0.127479	+	0.127479i	−0.767968	−	0.640489i	$-0.778732\pi$
$659$	−3.27251	+	3.27251i	−0.127479	+	0.127479i	0.640489	+	0.767968i	$0.278732\pi$
$660$	−39.0896	+	38.1652i	−1.52156	+	1.48558i
$661$	−3.83925	+	14.3283i	−0.149329	+	0.557305i	0.850195	+	0.526468i	$0.176484\pi$
$661$	−3.83925	+	14.3283i	−0.149329	+	0.557305i	−0.999524	+	0.0308372i	$0.990183\pi$
$662$	18.8792	+	19.1064i	0.733760	+	0.742593i
$663$	5.44924	+	3.14612i	0.211631	+	0.122185i
$664$	−27.0343	−	28.0226i	−1.04913	−	1.08749i
$665$	33.2598	−	2.39185i	1.28976	−	0.0927519i
$666$	9.48145	−	2.47985i	0.367399	−	0.0960921i
$667$	−33.9043	+	9.08464i	−1.31278	+	0.351759i
$668$	5.99133	+	3.55535i	0.231811	+	0.137561i
$669$	−5.11007	+	19.0710i	−0.197567	+	0.737329i
$670$	0.703581	+	1.23565i	0.0271817	+	0.0477374i
$671$	−23.6951			−0.914740
$672$	9.07104	+	28.9468i	0.349923	+	1.11665i
$673$	1.09724			0.0422955			0.0211478	−	0.999776i	$-0.493268\pi$
$673$	1.09724			0.0422955			0.0211478	+	0.999776i	$0.493268\pi$
$674$	10.9514	+	19.2332i	0.421832	+	0.740834i
$675$	1.62704	−	6.07219i	0.0626248	−	0.233719i
$676$	−19.8807	−	11.7975i	−0.764641	−	0.453750i
$677$	16.0585	−	4.30288i	0.617180	−	0.165373i	0.0633346	−	0.997992i	$-0.479826\pi$
$677$	16.0585	−	4.30288i	0.617180	−	0.165373i	0.553846	+	0.832619i	$0.313160\pi$
$678$	−24.0642	+	6.29392i	−0.924180	+	0.241717i
$679$	−1.29636	+	2.67133i	−0.0497498	+	0.102516i
$680$	13.5635	−	13.0852i	0.520137	−	0.501793i
$681$	−1.83010	−	1.05661i	−0.0701297	−	0.0404894i
$682$	−6.08684	−	6.16011i	−0.233077	−	0.235883i
$683$	5.03528	−	18.7919i	0.192670	−	0.719053i	−0.800188	−	0.599749i	$-0.795267\pi$
$683$	5.03528	−	18.7919i	0.192670	−	0.719053i	0.992858	−	0.119304i	$-0.0380663\pi$
$684$	−7.75599	+	7.57257i	−0.296558	+	0.289544i
$685$	−9.19511	+	9.19511i	−0.351327	+	0.351327i
$686$	19.4650	−	17.5246i	0.743179	−	0.669093i
$687$			10.8981i			0.415790i
$688$	7.65520	−	26.0586i	0.291852	−	0.993474i
$689$	−7.92069	+	4.57301i	−0.301754	+	0.174218i
$690$	0.279234	−	46.6724i	0.0106303	−	1.77679i
$691$	−1.24774	+	0.334331i	−0.0474663	+	0.0127186i	−0.282474	−	0.959275i	$-0.591155\pi$
$691$	−1.24774	+	0.334331i	−0.0474663	+	0.0127186i	0.235008	+	0.971993i	$0.424488\pi$
$692$	−0.141024	−	0.0396017i	−0.00536092	−	0.00150543i
$693$	−14.4882	+	5.02074i	−0.550360	+	0.190722i
$694$	−26.8216	+	7.01511i	−1.01813	+	0.266290i
$695$	−6.88641	+	11.9276i	−0.261216	+	0.452440i
$696$	27.8574	−	15.4236i	1.05593	−	0.584630i
$697$	−10.6839	+	6.16833i	−0.404680	+	0.233642i
$698$	−14.1596	−	3.88501i	−0.535950	−	0.147050i
$699$	18.3231	−	18.3231i	0.693044	−	0.693044i
$700$	3.88042	−	7.75839i	0.146666	−	0.293239i
$701$	4.42004	+	4.42004i	0.166942	+	0.166942i	0.785634	−	0.618692i	$-0.212337\pi$
$701$	4.42004	+	4.42004i	0.166942	+	0.166942i	−0.618692	+	0.785634i	$0.712337\pi$
$702$	5.65754	−	3.22141i	0.213530	−	0.121584i
$703$	−15.2955	−	26.4927i	−0.576882	−	0.999189i
$704$	−12.2733	+	40.0023i	−0.462566	+	1.50764i
$705$	−30.6887	−	17.7181i	−1.15580	−	0.667304i
$706$	14.7318	+	8.62334i	0.554439	+	0.324544i
$707$	−25.1316	+	29.0263i	−0.945172	+	1.09165i
$708$	−1.66290	−	2.96151i	−0.0624957	−	0.111300i
$709$	5.94273	+	22.1786i	0.223184	+	0.832934i	0.983124	+	0.182941i	$0.0585616\pi$
$709$	5.94273	+	22.1786i	0.223184	+	0.832934i	−0.759940	+	0.649993i	$0.774772\pi$
$710$	9.81798	+	9.93617i	0.368462	+	0.372898i
$711$	−0.610414	−	1.05727i	−0.0228923	−	0.0396506i
$712$	−23.0681	+	38.3488i	−0.864515	+	1.43718i
$713$	7.39855			0.277078
$714$	18.5682	−	6.31046i	0.694897	−	0.236163i
$715$	11.4405	+	11.4405i	0.427849	+	0.427849i
$716$	4.45377	−	4.34844i	0.166445	−	0.162509i
$717$	51.3494	+	13.7590i	1.91768	+	0.513841i
$718$	2.45609	+	0.0146944i	0.0916604	+	0.000548391i
$719$	3.53562	−	6.12387i	0.131856	−	0.228382i	−0.792536	−	0.609825i	$-0.791240\pi$
$719$	3.53562	−	6.12387i	0.131856	−	0.228382i	0.924392	+	0.381444i	$0.124573\pi$
$720$	2.69102	+	11.0989i	0.100288	+	0.413631i
$721$	−1.27117	−	1.87658i	−0.0473410	−	0.0698874i
$722$	6.01107	+	3.51861i	0.223709	+	0.130949i
$723$	11.5652	+	43.1621i	0.430116	+	1.60522i
$724$	−9.16500	+	2.33859i	−0.340614	+	0.0869128i
$725$	−8.79546	−	2.35674i	−0.326655	−	0.0875270i
$726$	−45.2131	−	12.4052i	−1.67801	−	0.460400i
$727$			21.2964i			0.789838i	0.918716	+	0.394919i	$0.129227\pi$
$727$			21.2964i			0.789838i	−0.918716	+	0.394919i	$0.870773\pi$
$728$	8.53996	−	2.78880i	0.316512	−	0.103360i
$729$		−	11.0213i		−	0.408196i
$730$	9.34463	−	34.0582i	0.345860	−	1.26055i
$731$	−16.9602	−	4.54448i	−0.627296	−	0.168084i
$732$	−9.37183	+	15.7930i	−0.346393	+	0.583727i
$733$	−7.20760	−	26.8991i	−0.266219	−	0.993543i	−0.961500	−	0.274805i	$-0.911387\pi$
$733$	−7.20760	−	26.8991i	−0.266219	−	0.993543i	0.695281	−	0.718738i	$-0.255280\pi$
$734$	7.45504	−	12.7359i	0.275171	−	0.470092i
$735$	28.7186	−	22.6209i	1.05930	−	0.834386i
$736$	−16.9398	−	31.4790i	−0.624411	−	1.16033i
$737$	−1.02047	+	1.76750i	−0.0375893	+	0.0651066i
$738$	0.0447252	−	7.47555i	0.00164636	−	0.275179i
$739$	26.8289	+	7.18877i	0.986916	+	0.264443i	0.715954	−	0.698147i	$-0.245992\pi$
$739$	26.8289	+	7.18877i	0.986916	+	0.264443i	0.270961	+	0.962590i	$0.412658\pi$
$740$	−32.2277	−	0.385642i	−1.18472	−	0.0141765i
$741$	8.41580	+	8.41580i	0.309162	+	0.309162i
$742$	−5.55117	+	27.9599i	−0.203790	+	1.02644i
$743$	−4.98267			−0.182796			−0.0913982	−	0.995814i	$-0.529134\pi$
$743$	−4.98267			−0.182796			−0.0913982	+	0.995814i	$0.529134\pi$
$744$	−6.51322	+	1.62050i	−0.238786	+	0.0594106i
$745$	0.351312	+	0.608490i	0.0128711	+	0.0222934i
$746$	11.0455	−	10.9142i	0.404406	−	0.399596i
$747$	−3.94801	−	14.7342i	−0.144450	−	0.539095i
$748$	26.0436	+	7.31345i	0.952248	+	0.267406i
$749$	13.7069	+	2.63623i	0.500838	+	0.0963256i
$750$	−12.5388	+	21.4209i	−0.457854	+	0.782181i
$751$	−14.1452	−	8.16676i	−0.516167	−	0.298009i	0.219198	−	0.975680i	$-0.429656\pi$
$751$	−14.1452	−	8.16676i	−0.516167	−	0.298009i	−0.735365	+	0.677671i	$0.762989\pi$
$752$	−27.1333	−	0.649456i	−0.989450	−	0.0236832i
$753$	−22.2131	−	38.4743i	−0.809491	−	1.40208i
$754$	−4.66615	−	8.19484i	−0.169931	−	0.298439i
$755$	−16.6905	−	16.6905i	−0.607431	−	0.607431i
$756$	4.07048	−	19.8787i	0.148042	−	0.722980i
$757$	38.1458	−	38.1458i	1.38643	−	1.38643i	0.553747	−	0.832685i	$-0.313198\pi$
$757$	38.1458	−	38.1458i	1.38643	−	1.38643i	0.832685	−	0.553747i	$-0.186802\pi$
$758$	−10.2390	+	37.3180i	−0.371898	+	1.35545i
$759$	58.0164	−	33.4958i	2.10586	−	1.21582i
$760$	31.1870	−	17.2671i	1.13127	−	0.626342i
$761$	−16.5068	+	28.5906i	−0.598371	+	1.03641i	0.394690	+	0.918814i	$0.370852\pi$
$761$	−16.5068	+	28.5906i	−0.598371	+	1.03641i	−0.993062	+	0.117595i	$0.962481\pi$
$762$	−10.1946	−	38.9782i	−0.369313	−	1.41203i
$763$	23.9871	−	27.7044i	0.868390	−	1.00297i
$764$	−0.545909	+	0.306531i	−0.0197503	+	0.0110899i
$765$	7.13164	−	1.91092i	0.257845	−	0.0690894i
$766$	25.2097	+	0.150826i	0.910863	+	0.00544957i
$767$	−0.871107	+	0.502934i	−0.0314539	+	0.0181599i
$768$	21.8076	+	24.0019i	0.786915	+	0.866092i
$769$		−	18.6850i		−	0.673800i	−0.941540	−	0.336900i	$-0.890622\pi$
$769$		−	18.6850i		−	0.673800i	0.941540	−	0.336900i	$-0.109378\pi$
$770$	50.3172	−	3.31606i	1.81331	−	0.119502i
$771$	2.71405	−	2.71405i	0.0977441	−	0.0977441i
$772$	−20.7108	−	0.247828i	−0.745396	−	0.00891953i
$773$	9.03958	−	33.7362i	0.325131	−	1.21341i	−0.589049	−	0.808097i	$-0.700497\pi$
$773$	9.03958	−	33.7362i	0.325131	−	1.21341i	0.914180	−	0.405309i	$-0.132836\pi$
$774$	7.56848	−	7.47846i	0.272043	−	0.268808i
$775$	1.66219	+	0.959666i	0.0597076	+	0.0344722i
$776$	−0.0569701	+	3.17377i	−0.00204511	+	0.113932i
$777$	−30.1726	−	14.6424i	−1.08244	−	0.525292i
$778$	2.23326	+	8.53865i	0.0800662	+	0.306126i
$779$	−22.5396	+	6.03947i	−0.807565	+	0.216386i
$780$	12.1501	−	3.10028i	0.435043	−	0.111008i
$781$	−5.18919	+	19.3663i	−0.185684	+	0.692982i
$782$	−20.0830	+	11.4353i	−0.718168	+	0.408925i
$783$	−21.2994			−0.761178
$784$	11.0055	−	25.7465i	0.393052	−	0.919516i
$785$	38.3925			1.37029
$786$	−37.6294	+	21.4262i	−1.34220	+	0.764247i
$787$	6.30807	−	23.5420i	0.224858	−	0.839183i	−0.757603	−	0.652716i	$-0.773630\pi$
$787$	6.30807	−	23.5420i	0.224858	−	0.839183i	0.982461	−	0.186467i	$-0.0597038\pi$
$788$	0.0788847	+	0.309152i	0.00281015	+	0.0110131i
$789$	18.3094	−	4.90600i	0.651833	−	0.174658i
$790$	1.01591	+	3.88422i	0.0361443	+	0.138194i
$791$	20.6554	+	10.0238i	0.734422	+	0.356405i
$792$	−11.7972	+	11.3811i	−0.419194	+	0.404410i
$793$	4.71004	+	2.71934i	0.167258	+	0.0965666i
$794$	7.10431	−	7.01981i	0.252123	−	0.249124i
$795$	−10.2978	+	38.4319i	−0.365226	+	1.36304i
$796$	0.510477	−	42.6601i	0.0180934	−	1.51205i
$797$	25.8769	−	25.8769i	0.916608	−	0.916608i	−0.0801732	−	0.996781i	$-0.525547\pi$
$797$	25.8769	−	25.8769i	0.916608	−	0.916608i	0.996781	+	0.0801732i	$0.0255473\pi$
$798$	37.0142	−	2.43934i	1.31029	−	0.0863519i
$799$			17.5465i			0.620749i
$800$	0.277370	−	9.26948i	0.00980650	−	0.327726i
$801$	−15.1831	+	8.76599i	−0.536470	+	0.309731i
$802$	29.6839	+	0.177595i	1.04817	+	0.00627108i
$803$	48.9643	−	13.1199i	1.72791	−	0.462993i
$804$	0.774442	+	1.37922i	0.0273124	+	0.0486415i
$805$	−28.1992	+	32.5693i	−0.993891	+	1.14792i
$806$	0.502964	+	1.92303i	0.0177162	+	0.0677360i
$807$	−27.0300	+	46.8173i	−0.951500	+	1.64805i
$808$	−11.3332	+	39.4497i	−0.398699	+	1.38783i
$809$	19.9357	−	11.5099i	0.700901	−	0.404665i	−0.106782	−	0.994282i	$-0.534055\pi$
$809$	19.9357	−	11.5099i	0.700901	−	0.404665i	0.807683	+	0.589617i	$0.200721\pi$
$810$	10.6989	−	38.9941i	0.375920	−	1.37011i
$811$	−8.31612	+	8.31612i	−0.292019	+	0.292019i	−0.837877	−	0.545859i	$-0.816204\pi$
$811$	−8.31612	+	8.31612i	−0.292019	+	0.292019i	0.545859	+	0.837877i	$0.316204\pi$
$812$	−28.7939	−	5.89601i	−1.01047	−	0.206909i
$813$	12.3276	+	12.3276i	0.432347	+	0.432347i
$814$	−22.8903	−	40.2007i	−0.802305	−	1.40903i
$815$	24.8866	+	43.1049i	0.871741	+	1.50990i
$816$	15.1752	−	14.4657i	0.531237	−	0.506401i
$817$	−28.7623	−	16.6059i	−1.00626	−	0.580967i
$818$	−25.8561	+	44.1716i	−0.904036	+	1.54442i
$819$	3.45611	+	0.664709i	0.120766	+	0.0232268i
$820$	−6.64673	+	23.6694i	−0.232114	+	0.826570i
$821$	−0.583745	−	2.17857i	−0.0203728	−	0.0760325i	0.954991	−	0.296635i	$-0.0958644\pi$
$821$	−0.583745	−	2.17857i	−0.0203728	−	0.0760325i	−0.975364	+	0.220602i	$0.929198\pi$
$822$	−10.2899	+	10.1675i	−0.358900	+	0.354631i
$823$	−4.37272	−	7.57377i	−0.152423	−	0.264005i	0.779694	−	0.626160i	$-0.215374\pi$
$823$	−4.37272	−	7.57377i	−0.152423	−	0.264005i	−0.932118	+	0.362155i	$0.882041\pi$
$824$	−2.07637	−	1.24901i	−0.0723339	−	0.0435113i
$825$	17.3789			0.605057
$826$	−0.610511	+	3.07500i	−0.0212424	+	0.106993i
$827$	−2.25129	−	2.25129i	−0.0782850	−	0.0782850i	0.666880	−	0.745165i	$-0.267629\pi$
$827$	−2.25129	−	2.25129i	−0.0782850	−	0.0782850i	−0.745165	+	0.666880i	$0.767629\pi$
$828$	0.167566	−	14.0033i	0.00582331	−	0.486649i
$829$	−6.26518	−	1.67875i	−0.217599	−	0.0583054i	0.148373	−	0.988932i	$-0.452597\pi$
$829$	−6.26518	−	1.67875i	−0.217599	−	0.0583054i	−0.365971	+	0.930626i	$0.619263\pi$
$830$	−0.300124	+	50.1640i	−0.0104175	+	1.74122i
$831$	−25.9722	+	44.9851i	−0.900965	+	1.56052i
$832$	7.03045	−	6.54300i	0.243737	−	0.226838i
$833$	−16.8103	−	6.71460i	−0.582443	−	0.232647i
$834$	−7.73984	+	13.2225i	−0.268009	+	0.457857i
$835$	−2.32308	−	8.66985i	−0.0803934	−	0.300032i
$836$	44.0024	+	26.1117i	1.52186	+	0.903093i
$837$	4.33657	+	1.16198i	0.149894	+	0.0401639i
$838$	−2.72750	+	9.94087i	−0.0942198	+	0.343402i
$839$		−	15.8804i		−	0.548253i	−0.961694	−	0.274126i	$-0.911611\pi$
$839$		−	15.8804i		−	0.548253i	0.961694	−	0.274126i	$-0.0883886\pi$
$840$	17.6912	−	34.8485i	0.610403	−	1.20239i
$841$			1.85175i			0.0638536i
$842$	−14.9645	−	4.10583i	−0.515710	−	0.141496i
$843$	−45.5885	−	12.2154i	−1.57015	−	0.420721i
$844$	5.39829	+	21.1561i	0.185817	+	0.728222i
$845$	7.70853	+	28.7686i	0.265181	+	0.989670i
$846$	−9.17619	−	5.37133i	−0.315484	−	0.184670i
$847$	24.2702	+	35.8290i	0.833933	+	1.23110i
$848$	7.18060	+	29.6158i	0.246583	+	1.01701i
$849$	10.2890	−	17.8210i	0.353116	−	0.611615i
$850$	−5.99521	−	0.0358685i	−0.205634	−	0.00123028i
$851$	38.1754	+	10.2291i	1.30863	+	0.350648i
$852$	10.8554	+	11.1184i	0.371901	+	0.380909i
$853$	31.2018	+	31.2018i	1.06833	+	1.06833i	0.997488	+	0.0708400i	$0.0225680\pi$
$853$	31.2018	+	31.2018i	1.06833	+	1.06833i	0.0708400	+	0.997488i	$0.477432\pi$
$854$	16.0494	−	5.45443i	0.549198	−	0.186647i
$855$	13.9653			0.477603
$856$	14.4804	−	3.60274i	0.494928	−	0.123139i
$857$	0.256772	+	0.444743i	0.00877118	+	0.0151921i	0.870378	−	0.492385i	$-0.163875\pi$
$857$	0.256772	+	0.444743i	0.00877118	+	0.0151921i	−0.861607	+	0.507577i	$0.830541\pi$
$858$	12.6503	+	12.8026i	0.431873	+	0.437072i
$859$	5.48453	+	20.4685i	0.187130	+	0.698377i	0.994165	+	0.107874i	$0.0344042\pi$
$859$	5.48453	+	20.4685i	0.187130	+	0.698377i	−0.807035	+	0.590504i	$0.798929\pi$
$860$	−30.5104	+	17.1318i	−1.04040	+	0.584188i
$861$	−16.7454	+	19.3405i	−0.570682	+	0.659122i
$862$	30.2643	+	17.7154i	1.03081	+	0.603387i
$863$	41.4589	+	23.9363i	1.41128	+	0.814801i	0.995509	−	0.0946697i	$-0.0301795\pi$
$863$	41.4589	+	23.9363i	1.41128	+	0.814801i	0.415768	+	0.909471i	$0.363513\pi$
$864$	−4.98513	−	21.1115i	−0.169598	−	0.718229i
$865$	0.0943578	+	0.163433i	0.00320826	+	0.00555687i
$866$	−5.96019	+	3.39374i	−0.202536	+	0.115324i
$867$	14.7802	+	14.7802i	0.501961	+	0.501961i
$868$	5.54079	+	2.77127i	0.188067	+	0.0940630i
$869$	−4.07483	+	4.07483i	−0.138229	+	0.138229i
$870$	−39.5617	−	10.8546i	−1.34127	−	0.368006i
$871$	0.405689	−	0.234225i	0.0137463	−	0.00793640i
$872$	10.8170	−	37.6530i	0.366310	−	1.27509i
$873$	−0.621771	+	1.07694i	−0.0210438	+	0.0364489i
$874$	−42.2907	+	11.0610i	−1.43051	+	0.374144i
$875$	21.6475	−	7.50174i	0.731818	−	0.253605i
$876$	10.6217	−	37.8243i	0.358873	−	1.27796i
$877$	−21.8607	+	5.85755i	−0.738182	+	0.197795i	−0.608270	−	0.793730i	$-0.708136\pi$
$877$	−21.8607	+	5.85755i	−0.738182	+	0.197795i	−0.129912	+	0.991525i	$0.541470\pi$
$878$	0.315035	−	52.6562i	0.0106319	−	1.77706i
$879$	0.238643	−	0.137781i	0.00804923	−	0.00464722i
$880$	47.3174	−	25.8292i	1.59507	−	0.870702i
$881$			17.7026i			0.596417i	0.954501	+	0.298209i	$0.0963891\pi$
$881$			17.7026i			0.596417i	−0.954501	+	0.298209i	$0.903611\pi$
$882$	8.65749	−	6.73575i	0.291513	−	0.226804i
$883$	−13.2141	+	13.2141i	−0.444691	+	0.444691i	−0.893585	−	0.448894i	$-0.851818\pi$
$883$	−13.2141	+	13.2141i	−0.444691	+	0.444691i	0.448894	+	0.893585i	$0.351818\pi$
$884$	−4.33754	−	4.44260i	−0.145887	−	0.149421i
$885$	−1.13254	+	4.22669i	−0.0380699	+	0.142079i
$886$	−25.0142	−	25.3153i	−0.840368	−	0.850484i
$887$	−44.3615	−	25.6121i	−1.48951	−	0.859970i	−0.489584	−	0.871956i	$-0.662851\pi$
$887$	−44.3615	−	25.6121i	−1.48951	−	0.859970i	−0.999928	+	0.0119857i	$0.996185\pi$
$888$	−35.8477	−	0.643476i	−1.20297	−	0.0215937i
$889$	−16.2362	+	33.4568i	−0.544543	+	1.12211i
$890$	55.7803	−	14.5892i	1.86976	−	0.489030i
$891$	56.0603	−	15.0213i	1.87809	−	0.503233i
$892$	9.94239	−	16.7545i	0.332896	−	0.560982i
$893$	−8.58994	+	32.0581i	−0.287452	+	1.07278i
$894$	0.386751	+	0.679224i	0.0129349	+	0.0227167i
$895$	−8.01938			−0.268058
$896$	−0.895203	−	29.9199i	−0.0299066	−	0.999553i
$897$	−15.3764			−0.513403
$898$	0.619911	+	1.08871i	0.0206867	+	0.0363307i
$899$	1.68311	−	6.28144i	0.0561347	−	0.209498i
$900$	1.85401	−	3.12431i	0.0618005	−	0.104144i
$901$	19.0298	−	5.09901i	0.633973	−	0.169873i
$902$	−34.1391	+	8.92899i	−1.13671	+	0.297303i
$903$	−36.3172	+	2.61172i	−1.20856	+	0.0869127i
$904$	24.5404	+	0.440508i	0.816202	+	0.0146511i
$905$	10.5534	+	6.09302i	0.350807	+	0.202539i
$906$	−18.4555	−	18.6777i	−0.613144	−	0.620524i
$907$	−2.19909	+	8.20711i	−0.0730195	+	0.272512i	−0.992777	−	0.119975i	$-0.961719\pi$
$907$	−2.19909	+	8.20711i	−0.0730195	+	0.272512i	0.919757	+	0.392487i	$0.128385\pi$
$908$	1.45674	+	1.49203i	0.0483437	+	0.0495147i
$909$	−11.3701	+	11.3701i	−0.377122	+	0.377122i
$910$	−10.3824	−	5.11544i	−0.344175	−	0.169575i
$911$		−	19.6850i		−	0.652192i	−0.945337	−	0.326096i	$-0.894267\pi$
$911$		−	19.6850i		−	0.652192i	0.945337	−	0.326096i	$-0.105733\pi$
$912$	34.8074	−	19.0004i	1.15259	−	0.629165i
$913$	−62.3567	+	36.0016i	−2.06370	+	1.19148i
$914$	0.293395	−	49.0392i	0.00970465	−	1.62207i
$915$	22.8535	−	6.12359i	0.755515	−	0.202440i
$916$	2.90739	−	10.3534i	0.0960630	−	0.342086i
$917$	39.2496	+	7.54884i	1.29614	+	0.249285i
$918$	−13.5674	+	3.54851i	−0.447790	+	0.117118i
$919$	−17.7313	+	30.7116i	−0.584903	+	1.01308i	0.409985	+	0.912092i	$0.365534\pi$
$919$	−17.7313	+	30.7116i	−0.584903	+	1.01308i	−0.994888	+	0.100989i	$0.967799\pi$
$920$	−12.7165	+	44.2649i	−0.419250	+	1.45937i
$921$	−40.3261	+	23.2823i	−1.32879	+	0.767177i
$922$	7.93112	+	2.17608i	0.261198	+	0.0716653i
$923$	3.25404	−	3.25404i	0.107108	−	0.107108i
$924$	55.9951	−	3.35391i	1.84210	−	0.110336i
$925$	7.24983	+	7.24983i	0.238373	+	0.238373i
$926$	−14.3655	+	8.17975i	−0.472081	+	0.268803i
$927$	−0.474629	−	0.822082i	−0.0155889	−	0.0270007i
$928$	−30.5797	+	7.22087i	−1.00383	+	0.237037i
$929$	−38.0765	−	21.9835i	−1.24925	−	0.721255i	−0.278290	−	0.960497i	$-0.589768\pi$
$929$	−38.0765	−	21.9835i	−1.24925	−	0.721255i	−0.970960	+	0.239242i	$0.923101\pi$
$930$	7.46262	+	4.36828i	0.244709	+	0.143242i
$931$	−27.4260	−	20.4974i	−0.898851	−	0.671776i
$932$	−22.2954	+	12.5190i	−0.730311	+	0.410073i
$933$	−7.45867	−	27.8361i	−0.244186	−	0.911314i
$934$	−25.0355	−	25.3369i	−0.819186	−	0.829048i
$935$	−17.4255	−	30.1819i	−0.569876	−	0.987054i
$936$	3.65114	−	0.908411i	0.119341	−	0.0296923i
$937$	−32.7634			−1.07033			−0.535167	−	0.844746i	$-0.679751\pi$
$937$	−32.7634			−1.07033			−0.535167	+	0.844746i	$0.679751\pi$
$938$	0.284325	−	1.43208i	0.00928354	−	0.0467590i
$939$	−38.5248	−	38.5248i	−1.25721	−	1.25721i
$940$	24.4279	+	25.0196i	0.796750	+	0.816049i
$941$	29.6051	+	7.93265i	0.965098	+	0.258597i	0.706757	−	0.707457i	$-0.250158\pi$
$941$	29.6051	+	7.93265i	0.965098	+	0.258597i	0.258341	+	0.966054i	$0.416824\pi$
$942$	42.7079	+	0.255516i	1.39150	+	0.00832515i
$943$	15.0736	−	26.1082i	0.490864	−	0.850201i
$944$	0.789712	+	3.25710i	0.0257029	+	0.106010i
$945$	−21.6438	+	14.6613i	−0.704072	+	0.476931i
$946$	−43.3442	−	25.3718i	−1.40924	−	0.824907i
$947$	−2.97785	−	11.1135i	−0.0967672	−	0.361140i	0.900514	−	0.434826i	$-0.143190\pi$
$947$	−2.97785	−	11.1135i	−0.0967672	−	0.361140i	−0.997281	+	0.0736863i	$0.976524\pi$
$948$	1.10425	+	4.32758i	0.0358642	+	0.140553i
$949$	−11.2386	−	3.01139i	−0.364822	−	0.0977537i
$950$	−10.9359	−	3.00051i	−0.354809	−	0.0973495i
$951$		−	32.5196i		−	1.05452i
$952$	−19.3235	+	1.04143i	−0.626279	+	0.0337529i
$953$			31.6828i			1.02631i	0.858297	+	0.513153i	$0.171523\pi$
$953$			31.6828i			1.02631i	−0.858297	+	0.513153i	$0.828477\pi$
$954$	−3.15880	+	11.5128i	−0.102270	+	0.372742i
$955$	0.779126	+	0.208766i	0.0252119	+	0.00675552i
$956$	−45.1120	−	26.7702i	−1.45903	−	0.865811i
$957$	−15.2400	−	56.8764i	−0.492639	−	1.83855i
$958$	17.3661	−	29.6676i	0.561072	−	0.958516i
$959$	13.3180	−	0.957750i	0.430059	−	0.0309274i
$960$	1.49945	−	41.7533i	0.0483946	−	1.34758i
$961$	14.8146	−	25.6597i	0.477892	−	0.827732i
$962$	−0.0635257	+	10.6179i	−0.00204815	+	0.342336i
$963$	5.64652	+	1.51298i	0.181956	+	0.0487551i
$964$	0.527587	−	44.0900i	0.0169924	−	1.42004i
$965$	18.8688	+	18.8688i	0.607409	+	0.607409i
$966$	−31.5856	+	36.0425i	−1.01625	+	1.15965i
$967$	15.2574			0.490645			0.245322	−	0.969442i	$-0.421106\pi$
$967$	15.2574			0.490645			0.245322	+	0.969442i	$0.421106\pi$
$968$	39.6436	+	23.8470i	1.27419	+	0.766472i
$969$	−12.8185	−	22.2023i	−0.411790	−	0.713240i
$970$	2.90902	−	2.87441i	0.0934029	−	0.0922919i
$971$	7.84283	+	29.2698i	0.251688	+	0.939314i	0.969903	+	0.243492i	$0.0782930\pi$
$971$	7.84283	+	29.2698i	0.251688	+	0.939314i	−0.718215	+	0.695822i	$0.755040\pi$
$972$	5.94059	−	21.1548i	0.190544	−	0.678539i
$973$	13.3623	−	4.63059i	0.428377	−	0.148450i
$974$	−22.1471	+	37.8353i	−0.709639	+	1.21232i
$975$	−3.45453	−	1.99447i	−0.110633	−	0.0638742i
$976$	13.1166	−	12.5034i	0.419853	−	0.400223i
$977$	−25.1720	−	43.5992i	−0.805325	−	1.39486i	−0.916072	−	0.401015i	$-0.868658\pi$
$977$	−25.1720	−	43.5992i	−0.805325	−	1.39486i	0.110747	−	0.993849i	$-0.464676\pi$
$978$	27.3971	+	48.1156i	0.876062	+	1.53857i
$979$	58.5176	+	58.5176i	1.87023	+	1.87023i
$980$	−33.3179	+	13.8287i	−1.06430	+	0.441741i
$981$	10.8523	−	10.8523i	0.346486	−	0.346486i
$982$	−4.38738	+	15.9906i	−0.140007	+	0.510282i
$983$	8.64540	−	4.99143i	0.275746	−	0.159202i	−0.355750	−	0.934581i	$-0.615775\pi$
$983$	8.64540	−	4.99143i	0.275746	−	0.159202i	0.631496	+	0.775379i	$0.282441\pi$
$984$	−7.55137	+	26.2856i	−0.240729	+	0.837955i
$985$	0.205529	−	0.355986i	0.00654869	−	0.0113427i
$986$	5.13995	+	19.6521i	0.163689	+	0.625850i
$987$	11.9141	+	34.3801i	0.379231	+	1.09433i
$988$	−5.74997	−	10.2403i	−0.182931	−	0.325787i
$989$	41.4458	−	11.1054i	1.31790	−	0.353130i
$990$	21.1184	+	0.126349i	0.671187	+	0.00401562i
$991$	−40.8868	+	23.6060i	−1.29881	+	0.749869i	−0.980199	−	0.198016i	$-0.936550\pi$
$991$	−40.8868	+	23.6060i	−1.29881	+	0.749869i	−0.318612	+	0.947885i	$0.603217\pi$
$992$	6.61997	+	0.198088i	0.210184	+	0.00628932i
$993$		−	38.4959i		−	1.22163i
$994$	−0.943194	−	14.3119i	−0.0299163	−	0.453944i
$995$	−38.8661	+	38.8661i	−1.23214	+	1.23214i
$996$	−0.667718	+	55.8005i	−0.0211574	+	1.76811i
$997$	9.00216	−	33.5965i	0.285101	−	1.06401i	−0.663664	−	0.748031i	$-0.730999\pi$
$997$	9.00216	−	33.5965i	0.285101	−	1.06401i	0.948765	−	0.315982i	$-0.102334\pi$
$998$	23.9183	−	23.6338i	0.757119	−	0.748114i
$999$	20.7695	+	11.9913i	0.657117	+	0.379387i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.2.v.a.19.10	yes	56
4.3	odd	2		448.2.z.a.47.3		56
7.2	even	3		784.2.j.a.195.18		56
7.3	odd	6	inner	112.2.v.a.3.1	✓	56
7.4	even	3		784.2.w.f.227.1		56
7.5	odd	6		784.2.j.a.195.17		56
7.6	odd	2		784.2.w.f.19.10		56
8.3	odd	2		896.2.z.a.607.12		56
8.5	even	2		896.2.z.b.607.3		56
16.3	odd	4		896.2.z.b.159.3		56
16.5	even	4		448.2.z.a.271.3		56
16.11	odd	4	inner	112.2.v.a.75.1	yes	56
16.13	even	4		896.2.z.a.159.12		56
28.3	even	6		448.2.z.a.367.3		56
56.3	even	6		896.2.z.a.479.12		56
56.45	odd	6		896.2.z.b.479.3		56
112.3	even	12		896.2.z.b.31.3		56
112.11	odd	12		784.2.w.f.619.10		56
112.27	even	4		784.2.w.f.411.1		56
112.45	odd	12		896.2.z.a.31.12		56
112.59	even	12	inner	112.2.v.a.59.10	yes	56
112.75	even	12		784.2.j.a.587.18		56
112.101	odd	12		448.2.z.a.143.3		56
112.107	odd	12		784.2.j.a.587.17		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.1	✓	56	7.3	odd	6	inner
112.2.v.a.19.10	yes	56	1.1	even	1	trivial
112.2.v.a.59.10	yes	56	112.59	even	12	inner
112.2.v.a.75.1	yes	56	16.11	odd	4	inner
448.2.z.a.47.3		56	4.3	odd	2
448.2.z.a.143.3		56	112.101	odd	12
448.2.z.a.271.3		56	16.5	even	4
448.2.z.a.367.3		56	28.3	even	6
784.2.j.a.195.17		56	7.5	odd	6
784.2.j.a.195.18		56	7.2	even	3
784.2.j.a.587.17		56	112.107	odd	12
784.2.j.a.587.18		56	112.75	even	12
784.2.w.f.19.10		56	7.6	odd	2
784.2.w.f.227.1		56	7.4	even	3
784.2.w.f.411.1		56	112.27	even	4
784.2.w.f.619.10		56	112.11	odd	12
896.2.z.a.31.12		56	112.45	odd	12
896.2.z.a.159.12		56	16.13	even	4
896.2.z.a.479.12		56	56.3	even	6
896.2.z.a.607.12		56	8.3	odd	2
896.2.z.b.31.3		56	112.3	even	12
896.2.z.b.159.3		56	16.3	odd	4
896.2.z.b.479.3		56	56.45	odd	6
896.2.z.b.607.3		56	8.5	even	2

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:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	112.v (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.699767 + 1.22895i) q^{2} +(0.524583 - 1.95777i) q^{3} +(-1.02065 + 1.71996i) q^{4} +(2.48890 - 0.666898i) q^{5} +(2.77309 - 0.725295i) q^{6} +(-2.38027 - 1.15512i) q^{7} +(-2.82797 - 0.0507629i) q^{8} +(-0.959602 - 0.554026i) q^{9} +(2.56123 + 2.59207i) q^{10} +(-1.35371 + 5.05213i) q^{11} +(2.83187 + 2.90047i) q^{12} +(0.848888 - 0.848888i) q^{13} +(-0.246053 - 3.73356i) q^{14} -5.22253i q^{15} +(-1.91654 - 3.51097i) q^{16} +(-2.23951 + 1.29298i) q^{17} +(0.00937511 - 1.56699i) q^{18} +(-4.72466 + 1.26597i) q^{19} +(-1.39326 + 4.96148i) q^{20} +(-3.51010 + 4.05408i) q^{21} +(-7.15612 + 1.87166i) q^{22} +(3.15967 - 5.47271i) q^{23} +(-1.58289 + 5.50989i) q^{24} +(1.41973 - 0.819681i) q^{25} +(1.63727 + 0.449220i) q^{26} +(2.71152 - 2.71152i) q^{27} +(4.41619 - 2.91501i) q^{28} +(-3.92758 - 3.92758i) q^{29} +(6.41825 - 3.65455i) q^{30} +(0.585390 + 1.01392i) q^{31} +(2.97369 - 4.81219i) q^{32} +(9.18077 + 5.30052i) q^{33} +(-3.15615 - 1.84747i) q^{34} +(-6.69460 - 1.28757i) q^{35} +(1.93232 - 1.08501i) q^{36} +(1.61869 + 6.04104i) q^{37} +(-4.86198 - 4.92051i) q^{38} +(-1.21662 - 2.10724i) q^{39} +(-7.07238 + 1.75962i) q^{40} +4.77063 q^{41} +(-7.43853 - 1.47685i) q^{42} +(4.80121 + 4.80121i) q^{43} +(-7.30780 - 7.48481i) q^{44} +(-2.75783 - 0.738958i) q^{45} +(8.93673 + 0.0534672i) q^{46} +(3.39263 - 5.87622i) q^{47} +(-7.87905 + 1.91034i) q^{48} +(4.33141 + 5.49899i) q^{49} +(2.00083 + 1.17120i) q^{50} +(1.35655 + 5.06272i) q^{51} +(0.593634 + 2.32647i) q^{52} +(-7.35887 - 1.97180i) q^{53} +(5.22975 + 1.43490i) q^{54} +13.4770i q^{55} +(6.67271 + 3.38747i) q^{56} +9.91391i q^{57} +(2.07842 - 7.57520i) q^{58} +(-0.809319 - 0.216856i) q^{59} +(8.98255 + 5.33039i) q^{60} +(1.17253 + 4.37595i) q^{61} +(-0.836430 + 1.42893i) q^{62} +(1.64415 + 2.42719i) q^{63} +(7.99485 + 0.287112i) q^{64} +(1.54667 - 2.67892i) q^{65} +(-0.0896943 + 14.9919i) q^{66} +(0.376913 + 0.100994i) q^{67} +(0.0618836 - 5.17155i) q^{68} +(-9.05679 - 9.05679i) q^{69} +(-3.10230 - 9.12835i) q^{70} +3.83330 q^{71} +(2.68560 + 1.61548i) q^{72} +(-4.84591 - 8.39335i) q^{73} +(-6.29145 + 6.21661i) q^{74} +(-0.859981 - 3.20949i) q^{75} +(2.64482 - 9.41835i) q^{76} +(9.05801 - 10.4618i) q^{77} +(1.73835 - 2.96974i) q^{78} +(0.954167 + 0.550889i) q^{79} +(-7.11152 - 7.46030i) q^{80} +(-5.54819 - 9.60974i) q^{81} +(3.33833 + 5.86288i) q^{82} +(9.73434 + 9.73434i) q^{83} +(-3.39026 - 10.1750i) q^{84} +(-4.71162 + 4.71162i) q^{85} +(-2.54074 + 9.26019i) q^{86} +(-9.74964 + 5.62896i) q^{87} +(4.08473 - 14.2186i) q^{88} +(7.91117 - 13.7025i) q^{89} +(-1.02169 - 3.90634i) q^{90} +(-3.00115 + 1.04002i) q^{91} +(6.18792 + 11.0202i) q^{92} +(2.29212 - 0.614171i) q^{93} +(9.59565 + 0.0574094i) q^{94} +(-10.9149 + 6.30174i) q^{95} +(-7.86122 - 8.34619i) q^{96} -1.12228i q^{97} +(-3.72702 + 9.17111i) q^{98} +(4.09804 - 4.09804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{2} - 6 q^{3} - 4 q^{4} - 6 q^{5} - 8 q^{7} + 4 q^{8} - 24 q^{10} + 2 q^{11} - 6 q^{12} + 16 q^{14} + 8 q^{16} - 12 q^{17} - 30 q^{18} - 6 q^{19} - 10 q^{21} - 28 q^{22} - 12 q^{23} - 6 q^{24}+ \cdots - 16 q^{99}+O(q^{100}) \) 56 * q - 2 * q^2 - 6 * q^3 - 4 * q^4 - 6 * q^5 - 8 * q^7 + 4 * q^8 - 24 * q^10 + 2 * q^11 - 6 * q^12 + 16 * q^14 + 8 * q^16 - 12 * q^17 - 30 * q^18 - 6 * q^19 - 10 * q^21 - 28 * q^22 - 12 * q^23 - 6 * q^24 - 6 * q^26 + 26 * q^28 - 24 * q^29 - 18 * q^30 - 12 * q^32 - 12 * q^33 - 2 * q^35 + 16 * q^36 + 6 * q^37 - 6 * q^38 - 4 * q^39 - 66 * q^40 + 70 * q^42 + 26 * q^44 + 12 * q^45 + 16 * q^46 - 8 * q^49 - 34 * q^51 + 84 * q^52 + 6 * q^53 + 42 * q^54 + 16 * q^56 + 18 * q^58 + 42 * q^59 + 78 * q^60 - 6 * q^61 - 16 * q^64 - 4 * q^65 + 126 * q^66 + 6 * q^67 + 24 * q^68 - 80 * q^70 - 80 * q^71 - 4 * q^72 + 62 * q^74 + 24 * q^75 + 10 * q^77 + 4 * q^78 + 12 * q^80 - 8 * q^81 + 42 * q^82 - 152 * q^84 - 28 * q^85 - 12 * q^87 + 30 * q^88 + 16 * q^91 - 20 * q^92 + 10 * q^93 - 42 * q^94 + 36 * q^96 - 108 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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