LMFDB - Embedded newform 460.2.o.b.19.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(19,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 15]))

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

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

chi := DirichletCharacter("460.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.o (of order $22$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$64$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			19.19
Character	$\chi$	$=$	460.19
Dual form			460.2.o.b.339.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.925935 - 1.06895i) q^{2} +(-0.832655 + 0.244489i) q^{3} +(-0.285289 + 1.97955i) q^{4} +(0.527840 + 2.17287i) q^{5} +(1.03233 + 0.663681i) q^{6} +(3.68197 - 0.529388i) q^{7} +(2.38019 - 1.52797i) q^{8} +(-1.89022 + 1.21477i) q^{9} +O(q^{10})$	\(q+(-0.925935 - 1.06895i) q^{2} +(-0.832655 + 0.244489i) q^{3} +(-0.285289 + 1.97955i) q^{4} +(0.527840 + 2.17287i) q^{5} +(1.03233 + 0.663681i) q^{6} +(3.68197 - 0.529388i) q^{7} +(2.38019 - 1.52797i) q^{8} +(-1.89022 + 1.21477i) q^{9} +(1.83394 - 2.57617i) q^{10} +(-0.707471 + 1.54915i) q^{11} +(-0.246432 - 1.71803i) q^{12} +(-6.12035 - 0.879974i) q^{13} +(-3.97516 - 3.44565i) q^{14} +(-0.970754 - 1.68020i) q^{15} +(-3.83722 - 1.12949i) q^{16} +(3.22947 + 3.72701i) q^{17} +(3.04875 + 0.895744i) q^{18} +(-0.975396 + 1.12567i) q^{19} +(-4.45190 + 0.424989i) q^{20} +(-2.93638 + 1.34100i) q^{21} +(2.31103 - 0.678160i) q^{22} +(-3.18762 - 3.58316i) q^{23} +(-1.60830 + 1.85421i) q^{24} +(-4.44277 + 2.29386i) q^{25} +(4.72640 + 7.35712i) q^{26} +(2.98178 - 3.44116i) q^{27} +(-0.00247671 + 7.43967i) q^{28} +(4.63295 + 5.34670i) q^{29} +(-0.897190 + 2.59344i) q^{30} +(-1.44850 + 4.93313i) q^{31} +(2.34566 + 5.14761i) q^{32} +(0.210329 - 1.46287i) q^{33} +(0.993689 - 6.90310i) q^{34} +(3.09379 + 7.72104i) q^{35} +(-1.86544 - 4.08835i) q^{36} +(-6.77081 + 4.35133i) q^{37} +(2.10643 + 0.000350621i) q^{38} +(5.31128 - 0.763647i) q^{39} +(4.57646 + 4.36532i) q^{40} +(3.40582 + 2.18879i) q^{41} +(4.15236 + 1.89715i) q^{42} +(-0.475023 - 1.61778i) q^{43} +(-2.86478 - 1.84243i) q^{44} +(-3.63728 - 3.46601i) q^{45} +(-0.878674 + 6.72517i) q^{46} +7.96584 q^{47} +(3.47123 + 0.00231118i) q^{48} +(6.56023 - 1.92626i) q^{49} +(6.56573 + 2.62511i) q^{50} +(-3.60025 - 2.31374i) q^{51} +(3.48802 - 11.8645i) q^{52} +(-0.351223 - 2.44281i) q^{53} +(-6.43935 - 0.00107185i) q^{54} +(-3.73953 - 0.719545i) q^{55} +(7.95490 - 6.88601i) q^{56} +(0.536954 - 1.17577i) q^{57} +(1.42553 - 9.90307i) q^{58} +(-9.93615 - 1.42860i) q^{59} +(3.60299 - 1.44231i) q^{60} +(-2.63293 + 8.96693i) q^{61} +(6.61446 - 3.01939i) q^{62} +(-6.31666 + 5.47342i) q^{63} +(3.33059 - 7.27373i) q^{64} +(-1.31850 - 13.7632i) q^{65} +(-1.75848 + 1.12969i) q^{66} +(-5.02111 + 2.29306i) q^{67} +(-8.29913 + 5.32962i) q^{68} +(3.53024 + 2.20420i) q^{69} +(5.38872 - 10.4563i) q^{70} +(6.82651 - 3.11756i) q^{71} +(-2.64294 + 5.77960i) q^{72} +(7.36085 + 6.37821i) q^{73} +(10.9207 + 3.20857i) q^{74} +(3.13847 - 2.99620i) q^{75} +(-1.95004 - 2.25198i) q^{76} +(-1.78479 + 6.07844i) q^{77} +(-5.73420 - 4.97038i) q^{78} +(-0.882022 + 6.13460i) q^{79} +(0.428791 - 8.93399i) q^{80} +(1.15873 - 2.53728i) q^{81} +(-0.813873 - 5.66731i) q^{82} +(5.62706 + 8.75587i) q^{83} +(-1.81686 - 6.19528i) q^{84} +(-6.39368 + 8.98450i) q^{85} +(-1.28948 + 2.00573i) q^{86} +(-5.16486 - 3.31925i) q^{87} +(0.683142 + 4.76826i) q^{88} +(-0.297732 - 1.01398i) q^{89} +(-0.337089 + 7.09736i) q^{90} -23.0008 q^{91} +(8.00244 - 5.28782i) q^{92} -4.46173i q^{93} +(-7.37585 - 8.51504i) q^{94} +(-2.96079 - 1.52524i) q^{95} +(-3.21166 - 3.71269i) q^{96} +(-4.33652 - 2.78691i) q^{97} +(-8.13341 - 5.22894i) q^{98} +(-0.544581 - 3.78765i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9}+O(q^{10}) $ 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9	$ 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9} - 11 q^{10} - 22 q^{14} + 2 q^{16} - 11 q^{20} - 44 q^{21} - 8 q^{24} - 38 q^{25} - 46 q^{26} - 52 q^{29} - 11 q^{30} - 44 q^{34} + 18 q^{36} - 11 q^{40} - 76 q^{41} - 154 q^{44} - 30 q^{46} - 100 q^{49} + 21 q^{50} + 178 q^{54} + 242 q^{56} - 11 q^{60} - 44 q^{61} + 6 q^{64} - 22 q^{65} + 44 q^{66} - 12 q^{69} + 22 q^{70} - 22 q^{74} + 88 q^{76} - 110 q^{80} - 252 q^{81} - 374 q^{84} + 94 q^{85} - 198 q^{86} - 44 q^{89} - 242 q^{90} - 62 q^{94} + 372 q^{96}+O(q^{100}) $ 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9 - 11 * q^10 - 22 * q^14 + 2 * q^16 - 11 * q^20 - 44 * q^21 - 8 * q^24 - 38 * q^25 - 46 * q^26 - 52 * q^29 - 11 * q^30 - 44 * q^34 + 18 * q^36 - 11 * q^40 - 76 * q^41 - 154 * q^44 - 30 * q^46 - 100 * q^49 + 21 * q^50 + 178 * q^54 + 242 * q^56 - 11 * q^60 - 44 * q^61 + 6 * q^64 - 22 * q^65 + 44 * q^66 - 12 * q^69 + 22 * q^70 - 22 * q^74 + 88 * q^76 - 110 * q^80 - 252 * q^81 - 374 * q^84 + 94 * q^85 - 198 * q^86 - 44 * q^89 - 242 * q^90 - 62 * q^94 + 372 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{15}{22}\right)$

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 $

$2$	−0.925935	−	1.06895i	−0.654735	−	0.755859i
$2$	−0.925935	−	1.06895i	−0.654735	−	0.755859i
$3$	−0.832655	+	0.244489i	−0.480733	+	0.141156i	−0.513116	−	0.858319i	$-0.671509\pi$
$3$	−0.832655	+	0.244489i	−0.480733	+	0.141156i	0.0323822	+	0.999476i	$0.489691\pi$
$4$	−0.285289	+	1.97955i	−0.142644	+	0.989774i
$5$	0.527840	+	2.17287i	0.236057	+	0.971739i
$5$	0.527840	+	2.17287i	0.236057	+	0.971739i
$6$	1.03233	+	0.663681i	0.421447	+	0.270947i
$7$	3.68197	−	0.529388i	1.39166	−	0.200090i	0.594613	−	0.804012i	$-0.297305\pi$
$7$	3.68197	−	0.529388i	1.39166	−	0.200090i	0.797043	+	0.603923i	$0.206396\pi$
$8$	2.38019	−	1.52797i	0.841523	−	0.540221i
$9$	−1.89022	+	1.21477i	−0.630074	+	0.404924i
$10$	1.83394	−	2.57617i	0.579942	−	0.814658i
$11$	−0.707471	+	1.54915i	−0.213311	+	0.467085i	−0.985796	−	0.167948i	$-0.946286\pi$
$11$	−0.707471	+	1.54915i	−0.213311	+	0.467085i	0.772485	+	0.635033i	$0.219013\pi$
$12$	−0.246432	−	1.71803i	−0.0711387	−	0.495953i
$13$	−6.12035	−	0.879974i	−1.69748	−	0.244061i	−0.775514	−	0.631331i	$-0.782509\pi$
$13$	−6.12035	−	0.879974i	−1.69748	−	0.244061i	−0.921966	+	0.387270i	$0.873418\pi$
$14$	−3.97516	−	3.44565i	−1.06241	−	0.920889i
$15$	−0.970754	−	1.68020i	−0.250648	−	0.433827i
$16$	−3.83722	−	1.12949i	−0.959305	−	0.282371i
$17$	3.22947	+	3.72701i	0.783262	+	0.903933i	0.997340	−	0.0728839i	$-0.0232202\pi$
$17$	3.22947	+	3.72701i	0.783262	+	0.903933i	−0.214078	+	0.976816i	$0.568675\pi$
$18$	3.04875	+	0.895744i	0.718597	+	0.211129i
$19$	−0.975396	+	1.12567i	−0.223771	+	0.258246i	−0.856523	−	0.516109i	$-0.827380\pi$
$19$	−0.975396	+	1.12567i	−0.223771	+	0.258246i	0.632752	+	0.774355i	$0.281925\pi$
$20$	−4.45190	+	0.424989i	−0.995474	+	0.0950303i
$21$	−2.93638	+	1.34100i	−0.640771	+	0.292630i
$22$	2.31103	−	0.678160i	0.492712	−	0.144584i
$23$	−3.18762	−	3.58316i	−0.664665	−	0.747141i
$23$	−3.18762	−	3.58316i	−0.664665	−	0.747141i
$24$	−1.60830	+	1.85421i	−0.328293	+	0.378488i
$25$	−4.44277	+	2.29386i	−0.888554	+	0.458772i
$26$	4.72640	+	7.35712i	0.926924	+	1.44285i
$27$	2.98178	−	3.44116i	0.573844	−	0.662251i
$28$	−0.00247671	+	7.43967i	−0.000468054	+	1.40597i
$29$	4.63295	+	5.34670i	0.860316	+	0.992858i	0.999996	+	0.00266144i	$0.000847164\pi$
$29$	4.63295	+	5.34670i	0.860316	+	0.992858i	−0.139680	+	0.990197i	$0.544607\pi$
$30$	−0.897190	+	2.59344i	−0.163804	+	0.473495i
$31$	−1.44850	+	4.93313i	−0.260158	+	0.886016i	0.721021	+	0.692913i	$0.243673\pi$
$31$	−1.44850	+	4.93313i	−0.260158	+	0.886016i	−0.981179	+	0.193102i	$0.938145\pi$
$32$	2.34566	+	5.14761i	0.414658	+	0.909977i
$33$	0.210329	−	1.46287i	0.0366136	−	0.254654i
$34$	0.993689	−	6.90310i	0.170416	−	1.18387i
$35$	3.09379	+	7.72104i	0.522946	+	1.30509i
$36$	−1.86544	−	4.08835i	−0.310907	−	0.681391i
$37$	−6.77081	+	4.35133i	−1.11311	+	0.715355i	−0.961969	−	0.273157i	$-0.911932\pi$
$37$	−6.77081	+	4.35133i	−1.11311	+	0.715355i	−0.151144	+	0.988512i	$0.548296\pi$
$38$	2.10643		0.000350621i	0.341708		5.68782e-5i
$39$	5.31128	−	0.763647i	0.850486	−	0.122281i
$40$	4.57646	+	4.36532i	0.723601	+	0.690218i
$41$	3.40582	+	2.18879i	0.531900	+	0.341831i	0.778863	−	0.627194i	$-0.215796\pi$
$41$	3.40582	+	2.18879i	0.531900	+	0.341831i	−0.246964	+	0.969025i	$0.579433\pi$
$42$	4.15236	+	1.89715i	0.640723	+	0.292737i
$43$	−0.475023	−	1.61778i	−0.0724403	−	0.246709i	0.915310	−	0.402749i	$-0.131945\pi$
$43$	−0.475023	−	1.61778i	−0.0724403	−	0.246709i	−0.987751	+	0.156040i	$0.950127\pi$
$44$	−2.86478	−	1.84243i	−0.431881	−	0.277756i
$45$	−3.63728	−	3.46601i	−0.542214	−	0.516682i
$46$	−0.878674	+	6.72517i	−0.129553	+	0.991572i
$47$	7.96584			1.16194			0.580968	−	0.813926i	$-0.302674\pi$
$47$	7.96584			1.16194			0.580968	+	0.813926i	$0.302674\pi$
$48$	3.47123	+	0.00231118i	0.501028	+	0.000333590i
$49$	6.56023	−	1.92626i	0.937176	−	0.275180i
$50$	6.56573	+	2.62511i	0.928534	+	0.371247i
$51$	−3.60025	−	2.31374i	−0.504136	−	0.323988i
$52$	3.48802	−	11.8645i	0.483701	−	1.64531i
$53$	−0.351223	−	2.44281i	−0.0482442	−	0.335546i	−0.999621	−	0.0275173i	$-0.991240\pi$
$53$	−0.351223	−	2.44281i	−0.0482442	−	0.335546i	0.951377	−	0.308029i	$-0.0996692\pi$
$54$	−6.43935	−	0.00107185i	−0.876284	−	0.000145860i
$55$	−3.73953	−	0.719545i	−0.504238	−	0.0970234i
$56$	7.95490	−	6.88601i	1.06302	−	0.920181i
$57$	0.536954	−	1.17577i	0.0711213	−	0.155734i
$58$	1.42553	−	9.90307i	0.187181	−	1.30034i
$59$	−9.93615	−	1.42860i	−1.29358	−	0.185988i	−0.539059	−	0.842268i	$-0.681220\pi$
$59$	−9.93615	−	1.42860i	−1.29358	−	0.185988i	−0.754518	+	0.656280i	$0.772129\pi$
$60$	3.60299	−	1.44231i	0.465144	−	0.186201i
$61$	−2.63293	+	8.96693i	−0.337112	+	1.14810i	0.600271	+	0.799797i	$0.295059\pi$
$61$	−2.63293	+	8.96693i	−0.337112	+	1.14810i	−0.937383	+	0.348301i	$0.886759\pi$
$62$	6.61446	−	3.01939i	0.840037	−	0.383463i
$63$	−6.31666	+	5.47342i	−0.795825	+	0.689586i
$64$	3.33059	−	7.27373i	0.416323	−	0.909217i
$65$	−1.31850	−	13.7632i	−0.163539	−	1.70712i
$66$	−1.75848	+	1.12969i	−0.216454	+	0.139056i
$67$	−5.02111	+	2.29306i	−0.613426	+	0.280142i	−0.697801	−	0.716292i	$-0.745838\pi$
$67$	−5.02111	+	2.29306i	−0.613426	+	0.280142i	0.0843747	+	0.996434i	$0.473111\pi$
$68$	−8.29913	+	5.32962i	−1.00642	+	0.646312i
$69$	3.53024	+	2.20420i	0.424990	+	0.265354i
$70$	5.38872	−	10.4563i	0.644075	−	1.24976i
$71$	6.82651	−	3.11756i	0.810158	−	0.369987i	0.0331288	−	0.999451i	$-0.489453\pi$
$71$	6.82651	−	3.11756i	0.810158	−	0.369987i	0.777029	+	0.629464i	$0.216726\pi$
$72$	−2.64294	+	5.77960i	−0.311474	+	0.681132i
$73$	7.36085	+	6.37821i	0.861522	+	0.746513i	0.968834	−	0.247712i	$-0.0796787\pi$
$73$	7.36085	+	6.37821i	0.861522	+	0.746513i	−0.107311	+	0.994225i	$0.534224\pi$
$74$	10.9207	+	3.20857i	1.26950	+	0.372989i
$75$	3.13847	−	2.99620i	0.362399	−	0.345972i
$76$	−1.95004	−	2.25198i	−0.223685	−	0.258320i
$77$	−1.78479	+	6.07844i	−0.203396	+	0.692703i
$78$	−5.73420	−	4.97038i	−0.649270	−	0.562785i
$79$	−0.882022	+	6.13460i	−0.0992353	+	0.690196i	0.878097	+	0.478483i	$0.158813\pi$
$79$	−0.882022	+	6.13460i	−0.0992353	+	0.690196i	−0.977332	+	0.211713i	$0.932096\pi$
$80$	0.428791	−	8.93399i	0.0479403	−	0.998850i
$81$	1.15873	−	2.53728i	0.128748	−	0.281920i
$82$	−0.813873	−	5.66731i	−0.0898773	−	0.625850i
$83$	5.62706	+	8.75587i	0.617650	+	0.961081i	0.999323	+	0.0367843i	$0.0117115\pi$
$83$	5.62706	+	8.75587i	0.617650	+	0.961081i	−0.381674	+	0.924297i	$0.624652\pi$
$84$	−1.81686	−	6.19528i	−0.198236	−	0.675961i
$85$	−6.39368	+	8.98450i	−0.693492	+	0.974506i
$86$	−1.28948	+	2.00573i	−0.139048	+	0.216284i
$87$	−5.16486	−	3.31925i	−0.553731	−	0.355861i
$88$	0.683142	+	4.76826i	0.0728231	+	0.508298i
$89$	−0.297732	−	1.01398i	−0.0315595	−	0.107482i	0.942207	−	0.335031i	$-0.108747\pi$
$89$	−0.297732	−	1.01398i	−0.0315595	−	0.107482i	−0.973767	+	0.227549i	$0.926929\pi$
$90$	−0.337089	+	7.09736i	−0.0355322	+	0.748127i
$91$	−23.0008			−2.41114
$92$	8.00244	−	5.28782i	0.834312	−	0.551293i
$93$		−	4.46173i		−	0.462660i
$94$	−7.37585	−	8.51504i	−0.760760	−	0.878260i
$95$	−2.96079	−	1.52524i	−0.303770	−	0.156486i
$96$	−3.21166	−	3.71269i	−0.327789	−	0.378925i
$97$	−4.33652	−	2.78691i	−0.440307	−	0.282968i	0.301646	−	0.953420i	$-0.402464\pi$
$97$	−4.33652	−	2.78691i	−0.440307	−	0.282968i	−0.741953	+	0.670452i	$0.766100\pi$
$98$	−8.13341	−	5.22894i	−0.821599	−	0.528203i
$99$	−0.544581	−	3.78765i	−0.0547325	−	0.380673i
$100$	−3.27334	−	9.44909i	−0.327334	−	0.944909i
$101$	1.74926	−	1.12418i	0.174058	−	0.111860i	−0.450711	−	0.892670i	$-0.648829\pi$
$101$	1.74926	−	1.12418i	0.174058	−	0.111860i	0.624769	+	0.780810i	$0.285193\pi$
$102$	0.860335	+	5.99084i	0.0851859	+	0.593182i
$103$	−10.5054	−	4.79766i	−1.03513	−	0.472728i	−0.175949	−	0.984399i	$-0.556299\pi$
$103$	−10.5054	−	4.79766i	−1.03513	−	0.472728i	−0.859181	+	0.511671i	$0.829027\pi$
$104$	−15.9122	+	7.25724i	−1.56032	+	0.711631i
$105$	−4.46377	−	5.67256i	−0.435619	−	0.553585i
$106$	−2.28602	+	2.63732i	−0.222038	+	0.256159i
$107$	3.77667	−	12.8622i	0.365105	−	1.24343i	−0.548266	−	0.836304i	$-0.684712\pi$
$107$	3.77667	−	12.8622i	0.365105	−	1.24343i	0.913371	−	0.407128i	$-0.133470\pi$
$108$	5.96127	+	6.88430i	0.573624	+	0.662442i
$109$	6.49200	−	5.62535i	0.621821	−	0.538811i	−0.285967	−	0.958239i	$-0.592315\pi$
$109$	6.49200	−	5.62535i	0.621821	−	0.538811i	0.907789	+	0.419428i	$0.137769\pi$
$110$	2.69341	+	4.66361i	0.256807	+	0.444658i
$111$	4.57389	−	5.27855i	0.434134	−	0.501018i
$112$	−14.7265	−	2.12736i	−1.39152	−	0.201016i
$113$	−0.171641	−	0.375842i	−0.0161466	−	0.0353562i	0.901387	−	0.433015i	$-0.142550\pi$
$113$	−0.171641	−	0.375842i	−0.0161466	−	0.0353562i	−0.917534	+	0.397658i	$0.869823\pi$
$114$	−1.75401	+	0.514708i	−0.164278	+	0.0482068i
$115$	6.10321	−	8.81764i	0.569127	−	0.822250i
$116$	−11.9058	+	7.64578i	−1.10542	+	0.709893i
$117$	12.6378	−	5.77149i	1.16836	−	0.533574i
$118$	7.67313	+	11.9440i	0.706369	+	1.09953i
$119$	13.8639	+	12.0131i	1.27090	+	1.10124i
$120$	−4.87788	−	2.51591i	−0.445288	−	0.229670i
$121$	5.30413	+	6.12129i	0.482194	+	0.556481i
$122$	12.0231	−	5.48834i	1.08852	−	0.496891i
$123$	−3.37101	−	0.989817i	−0.303953	−	0.0892488i
$124$	−9.35212	−	4.27473i	−0.839845	−	0.383883i
$125$	−7.32935	−	8.44279i	−0.655557	−	0.755146i
$126$	11.6996	+	1.68414i	1.04228	+	0.150035i
$127$	2.56977	−	5.62700i	0.228030	−	0.499316i	−0.760686	−	0.649120i	$-0.775137\pi$
$127$	2.56977	−	5.62700i	0.228030	−	0.499316i	0.988716	+	0.149805i	$0.0478644\pi$
$128$	−10.8591	+	3.17479i	−0.959821	+	0.280614i
$129$	0.791060	+	1.23091i	0.0696490	+	0.108376i
$130$	−13.4913	+	14.1533i	−1.18327	+	1.24132i
$131$	13.4413	−	1.93256i	1.17437	−	0.168849i	0.472615	−	0.881269i	$-0.343310\pi$
$131$	13.4413	−	1.93256i	1.17437	−	0.168849i	0.701753	+	0.712420i	$0.252401\pi$
$132$	2.83582	+	0.833698i	0.246827	+	0.0725641i
$133$	−2.99547	+	4.66104i	−0.259740	+	0.404163i
$134$	7.10038	+	3.24406i	0.613380	+	0.280244i
$135$	9.05111	+	4.66265i	0.778996	+	0.401297i
$136$	13.3815	+	3.93643i	1.14746	+	0.337546i
$137$	7.22301			0.617103			0.308551	−	0.951208i	$-0.400156\pi$
$137$	7.22301			0.617103			0.308551	+	0.951208i	$0.400156\pi$
$138$	−0.912602	−	5.81457i	−0.0776858	−	0.494969i
$139$		−	17.6544i		−	1.49743i	−0.662893	−	0.748714i	$-0.730671\pi$
$139$		−	17.6544i		−	1.49743i	0.662893	−	0.748714i	$-0.269329\pi$
$140$	−16.1668	+	3.92158i	−1.36634	+	0.331434i
$141$	−6.63279	+	1.94756i	−0.558582	+	0.164014i
$142$	−9.65342	−	4.41051i	−0.810097	−	0.370122i
$143$	5.69318	−	8.85876i	0.476088	−	0.740807i
$144$	8.62527	−	2.52637i	0.718772	−	0.210531i
$145$	−9.17226	+	12.8890i	−0.761715	+	1.07037i
$146$	0.00229275	−	13.7742i	0.000189749	−	1.13996i
$147$	−4.99146	+	3.20782i	−0.411689	+	0.264576i
$148$	−6.68204	−	14.6445i	−0.549260	−	1.20377i
$149$	5.48162	+	2.50337i	0.449072	+	0.205084i	0.627096	−	0.778942i	$-0.284243\pi$
$149$	5.48162	+	2.50337i	0.449072	+	0.205084i	−0.178024	+	0.984026i	$0.556971\pi$
$150$	−6.10880	−	0.580560i	−0.498781	−	0.0474025i
$151$	5.86534	+	0.843308i	0.477314	+	0.0686274i	0.376773	−	0.926305i	$-0.377034\pi$
$151$	5.86534	+	0.843308i	0.477314	+	0.0686274i	0.100541	+	0.994933i	$0.467943\pi$
$152$	−0.601634	+	4.16968i	−0.0487990	+	0.338205i
$153$	−10.6319	−	3.12180i	−0.859537	−	0.252383i
$154$	8.15013	−	3.72040i	0.656756	−	0.299798i
$155$	−11.4836	−	0.543499i	−0.922388	−	0.0436549i
$156$	−0.00357268	+	10.7318i	−0.000286043	+	0.859232i
$157$	12.7096	−	14.6677i	1.01434	−	1.17061i	0.0290697	−	0.999577i	$-0.490746\pi$
$157$	12.7096	−	14.6677i	1.01434	−	1.17061i	0.985266	−	0.171029i	$-0.0547090\pi$
$158$	7.37425	−	4.73741i	0.586664	−	0.376888i
$159$	0.889689	+	1.94815i	0.0705569	+	0.154498i
$160$	−9.94698	+	7.81394i	−0.786378	+	0.617746i
$161$	−13.6336	−	11.5056i	−1.07448	−	0.906770i
$162$	−3.78512	+	1.11073i	−0.297387	+	0.0872670i
$163$	4.49005	+	9.83184i	0.351688	+	0.770089i	0.999962	+	0.00868252i	$0.00276377\pi$
$163$	4.49005	+	9.83184i	0.351688	+	0.770089i	−0.648274	+	0.761407i	$0.724509\pi$
$164$	−5.30445	+	6.11755i	−0.414208	+	0.477700i
$165$	3.28966	−	0.315144i	0.256100	−	0.0245339i
$166$	4.14926	−	14.1224i	0.322045	−	1.09611i
$167$	−7.91019	−	9.12885i	−0.612109	−	0.706412i	0.362079	−	0.932147i	$-0.382067\pi$
$167$	−7.91019	−	9.12885i	−0.612109	−	0.706412i	−0.974189	+	0.225736i	$0.927521\pi$
$168$	−4.94013	+	7.67855i	−0.381139	+	0.592413i
$169$	24.2109	+	7.10897i	1.86238	+	0.546844i
$170$	15.5241	−	1.48457i	1.19064	−	0.113862i
$171$	0.476286	−	3.31264i	0.0364225	−	0.253324i
$172$	3.33799	−	0.478797i	0.254519	−	0.0365079i
$173$	15.0049	+	6.85250i	1.14080	+	0.520986i	0.893994	−	0.448079i	$-0.147892\pi$
$173$	15.0049	+	6.85250i	1.14080	+	0.520986i	0.246806	+	0.969065i	$0.420619\pi$
$174$	1.23422	+	8.59436i	0.0935662	+	0.651537i
$175$	−15.1438	+	10.7979i	−1.14477	+	0.816244i
$176$	4.46446	−	5.14534i	0.336521	−	0.387844i
$177$	8.62266	−	1.23975i	0.648119	−	0.0931855i
$178$	−0.808211	+	1.25714i	−0.0605780	+	0.0942267i
$179$	−12.9101	+	20.0885i	−0.964943	+	1.50148i	−0.102872	+	0.994695i	$0.532803\pi$
$179$	−12.9101	+	20.0885i	−0.964943	+	1.50148i	−0.862072	+	0.506787i	$0.830833\pi$
$180$	7.89881	−	6.21136i	0.588742	−	0.462968i
$181$	−4.30191	−	14.6510i	−0.319759	−	1.08900i	−0.949909	−	0.312526i	$-0.898825\pi$
$181$	−4.30191	−	14.6510i	−0.319759	−	1.08900i	0.630151	−	0.776473i	$-0.282993\pi$
$182$	21.2973	+	24.5866i	1.57866	+	1.82248i
$183$		−	8.11008i		−	0.599514i
$184$	−13.0621	−	3.65799i	−0.962953	−	0.269671i
$185$	−13.0288	−	12.4153i	−0.957897	−	0.912791i
$186$	−4.76935	+	4.13128i	−0.349706	+	0.302920i
$187$	−8.05844	+	2.36617i	−0.589292	+	0.173032i
$188$	−2.27256	+	15.7688i	−0.165744	+	1.15005i
$189$	9.15713	−	14.2488i	0.666083	−	1.03645i
$190$	1.11110	+	4.57719i	0.0806074	+	0.332064i
$191$	−0.0296783	−	0.206417i	−0.00214744	−	0.0149358i	0.988720	−	0.149779i	$-0.0478561\pi$
$191$	−0.0296783	−	0.206417i	−0.00214744	−	0.0149358i	−0.990867	+	0.134843i	$0.956947\pi$
$192$	−0.994877	+	6.87080i	−0.0717991	+	0.495857i
$193$	−9.91117	−	15.4221i	−0.713422	−	1.11011i	−0.988869	−	0.148790i	$-0.952462\pi$
$193$	−9.91117	−	15.4221i	−0.713422	−	1.11011i	0.275447	−	0.961316i	$-0.411174\pi$
$194$	1.03628	+	7.21600i	0.0744004	+	0.518078i
$195$	4.46282	+	11.1377i	0.319589	+	0.797585i
$196$	1.94156	+	13.5358i	0.138683	+	0.966845i
$197$	−3.15208	−	0.453201i	−0.224577	−	0.0322893i	0.0291078	−	0.999576i	$-0.490733\pi$
$197$	−3.15208	−	0.453201i	−0.224577	−	0.0322893i	−0.253684	+	0.967287i	$0.581642\pi$
$198$	−3.54454	+	4.08924i	−0.251900	+	0.290610i
$199$	25.8275	+	7.58365i	1.83087	+	0.537591i	0.999827	−	0.0186242i	$-0.00592861\pi$
$199$	25.8275	+	7.58365i	1.83087	+	0.537591i	0.831039	+	0.556215i	$0.187747\pi$
$200$	−7.06966	+	12.2483i	−0.499901	+	0.866083i
$201$	3.62022	−	3.13694i	0.255351	−	0.221263i
$202$	−2.82139	−	0.828946i	−0.198513	−	0.0583245i
$203$	19.8889	+	17.2338i	1.39593	+	1.20958i
$204$	5.60727	−	6.46678i	0.392587	−	0.452765i
$205$	−2.95823	+	8.55575i	−0.206612	+	0.597560i
$206$	4.59889	+	15.6720i	0.320420	+	1.09192i
$207$	10.3780	+	2.90074i	0.721324	+	0.201615i
$208$	22.4912	+	10.2895i	1.55949	+	0.713449i
$209$	−1.05376	−	2.30741i	−0.0728899	−	0.159607i
$210$	−1.93050	+	10.0239i	−0.133217	+	0.691718i
$211$	6.23919	+	5.40629i	0.429523	+	0.372184i	0.842625	−	0.538501i	$-0.181009\pi$
$211$	6.23919	+	5.40629i	0.429523	+	0.372184i	−0.413102	+	0.910685i	$0.635555\pi$
$212$	4.93586	+	0.00164318i	0.338996	+	0.000112854i
$213$	−4.92192	+	4.26487i	−0.337244	+	0.292224i
$214$	−17.2459	+	7.87247i	−1.17891	+	0.538151i
$215$	3.26450	−	1.88609i	0.222637	−	0.128631i
$216$	1.83919	−	12.7467i	0.125141	−	0.867302i
$217$	−2.72179	+	18.9305i	−0.184767	+	1.28508i
$218$	−12.0244	−	1.73089i	−0.814393	−	0.117230i
$219$	−7.68845	−	3.51120i	−0.519537	−	0.237265i
$220$	2.49122	−	7.19731i	0.167958	−	0.485242i
$221$	−16.4858	−	25.6525i	−1.10896	−	1.72557i
$222$	−9.87760	−	0.00164415i	−0.662941	−	0.000110348i
$223$	−2.14927	−	14.9485i	−0.143925	−	1.00102i	−0.925915	−	0.377732i	$-0.876704\pi$
$223$	−2.14927	−	14.9485i	−0.143925	−	1.00102i	0.781990	−	0.623292i	$-0.214205\pi$
$224$	11.3617	+	17.7116i	0.759138	+	1.18341i
$225$	5.61130	−	9.73286i	0.374087	−	0.648857i
$226$	−0.242826	+	0.531480i	−0.0161525	+	0.0353535i
$227$	4.30377	+	14.6573i	0.285651	+	0.972839i	0.969882	+	0.243574i	$0.0783197\pi$
$227$	4.30377	+	14.6573i	0.285651	+	0.972839i	−0.684231	+	0.729265i	$0.739862\pi$
$228$	2.17430	+	1.39836i	0.143996	+	0.0926086i
$229$		−	3.08895i		−	0.204124i	−0.994778	−	0.102062i	$-0.967456\pi$
$229$		−	3.08895i		−	0.204124i	0.994778	−	0.102062i	$-0.0325440\pi$
$230$	−15.0768	+	1.64057i	−0.994132	+	0.108176i
$231$		−	5.49761i		−	0.361716i
$232$	19.1969	+	5.64714i	1.26034	+	0.370753i
$233$	3.30145	+	11.2437i	0.216285	+	0.736600i	0.994135	+	0.108149i	$0.0344925\pi$
$233$	3.30145	+	11.2437i	0.216285	+	0.736600i	−0.777849	+	0.628451i	$0.783689\pi$
$234$	−17.8712	−	8.16509i	−1.16828	−	0.533769i
$235$	4.20469	+	17.3088i	0.274284	+	1.12910i
$236$	5.66266	−	19.2615i	0.368608	−	1.25382i
$237$	−0.765425	−	5.32365i	−0.0497197	−	0.345808i
$238$	0.00431830	−	25.9431i	0.000279914	−	1.68164i
$239$	−10.1436	−	15.7837i	−0.656132	−	1.02096i	−0.996734	−	0.0807542i	$-0.974267\pi$
$239$	−10.1436	−	15.7837i	−0.656132	−	1.02096i	0.340602	−	0.940208i	$-0.389369\pi$
$240$	1.82723	+	7.54376i	0.117947	+	0.486948i
$241$	−0.934104	−	0.426591i	−0.0601709	−	0.0274791i	0.385102	−	0.922874i	$-0.374166\pi$
$241$	−0.934104	−	0.426591i	−0.0601709	−	0.0274791i	−0.445273	+	0.895395i	$0.646893\pi$
$242$	1.63205	−	11.3377i	0.104912	−	0.728818i
$243$	−2.28850	+	15.9169i	−0.146807	+	1.02107i
$244$	−16.9993	−	7.77017i	−1.08827	−	0.497434i
$245$	7.64827	+	13.2378i	0.488630	+	0.845733i
$246$	2.06327	+	4.51993i	0.131550	+	0.288180i
$247$	6.96032	−	6.03115i	0.442875	−	0.383753i
$248$	4.09000	+	13.9550i	0.259715	+	0.886146i
$249$	−6.82611	−	5.91486i	−0.432587	−	0.374839i
$250$	−2.23838	+	15.6521i	−0.141568	+	0.989929i
$251$	9.47331	+	20.7437i	0.597950	+	1.30933i	0.930517	+	0.366248i	$0.119358\pi$
$251$	9.47331	+	20.7437i	0.597950	+	1.30933i	−0.332567	+	0.943080i	$0.607915\pi$
$252$	−9.03282	−	14.0656i	−0.569014	−	0.886052i
$253$	7.80600	−	2.40311i	0.490759	−	0.151082i
$254$	−8.39440	+	2.46330i	−0.526711	+	0.154561i
$255$	3.12711	−	9.04418i	0.195827	−	0.566368i
$256$	13.4485	+	8.66817i	0.840533	+	0.541761i
$257$	9.10216	+	7.88707i	0.567777	+	0.491982i	0.890792	−	0.454412i	$-0.150151\pi$
$257$	9.10216	+	7.88707i	0.567777	+	0.491982i	−0.323014	+	0.946394i	$0.604696\pi$
$258$	0.583309	−	1.98535i	0.0363152	−	0.123602i
$259$	−22.6264	+	19.6059i	−1.40594	+	1.21825i
$260$	27.6212	+	1.31647i	1.71299	+	0.0816442i
$261$	−15.2523	−	4.47849i	−0.944095	−	0.277211i
$262$	−14.5115	−	12.5785i	−0.896526	−	0.777105i
$263$	21.6053	+	3.10638i	1.33224	+	0.191547i	0.771387	−	0.636366i	$-0.219563\pi$
$263$	21.6053	+	3.10638i	1.33224	+	0.191547i	0.560855	+	0.827914i	$0.310472\pi$
$264$	−1.73461	−	3.80329i	−0.106758	−	0.234076i
$265$	5.12253	−	2.05258i	0.314675	−	0.126089i
$266$	7.75600	−	1.11383i	0.475551	−	0.0682931i
$267$	0.495816	+	0.771505i	0.0303434	+	0.0472153i
$268$	−3.10676	−	10.5937i	−0.189776	−	0.647114i
$269$	2.54603	+	17.7080i	0.155234	+	1.07968i	0.907268	+	0.420553i	$0.138164\pi$
$269$	2.54603	+	17.7080i	0.155234	+	1.07968i	−0.752034	+	0.659125i	$0.770927\pi$
$270$	−3.39662	−	13.9925i	−0.206712	−	0.851554i
$271$	14.8771	−	23.1492i	0.903718	−	1.40621i	−0.0100390	−	0.999950i	$-0.503196\pi$
$271$	14.8771	−	23.1492i	0.903718	−	1.40621i	0.913756	−	0.406262i	$-0.133168\pi$
$272$	−8.18260	−	17.9490i	−0.496143	−	1.08832i
$273$	19.1517	−	5.62346i	1.15912	−	0.340347i
$274$	−6.68803	−	7.72100i	−0.404039	−	0.466443i
$275$	−0.410395	−	8.50534i	−0.0247477	−	0.512891i
$276$	−5.37045	+	6.35944i	−0.323263	+	0.382793i
$277$			2.95716i			0.177679i	0.996046	+	0.0888393i	$0.0283157\pi$
$277$			2.95716i			0.177679i	−0.996046	+	0.0888393i	$0.971684\pi$
$278$	−18.8716	+	16.3468i	−1.13184	+	0.980419i
$279$	−3.25464	−	11.0843i	−0.194850	−	0.663600i
$280$	19.1613	+	13.6503i	1.14511	+	0.815761i
$281$	−7.36375	+	11.4582i	−0.439285	+	0.683540i	−0.988343	−	0.152244i	$-0.951350\pi$
$281$	−7.36375	+	11.4582i	−0.439285	+	0.683540i	0.549058	+	0.835784i	$0.314986\pi$
$282$	8.22337	+	5.28677i	0.489695	+	0.314823i
$283$	−22.7878	+	3.27639i	−1.35460	+	0.194761i	−0.781079	−	0.624433i	$-0.785330\pi$
$283$	−22.7878	+	3.27639i	−1.35460	+	0.194761i	−0.573516	+	0.819194i	$0.694421\pi$
$284$	4.22384	+	14.4028i	0.250639	+	0.854650i
$285$	2.83822	+	0.546118i	0.168121	+	0.0323492i
$286$	−14.7411	+	2.11694i	−0.871657	+	0.125177i
$287$	13.6989	+	6.25606i	0.808618	+	0.369284i
$288$	−10.6870	−	6.88068i	−0.629737	−	0.405448i
$289$	−1.04176	+	7.24559i	−0.0612799	+	0.426211i
$290$	22.2706	−	2.12974i	1.30777	−	0.125063i
$291$	4.29219	+	1.26030i	0.251613	+	0.0738801i
$292$	−14.7259	+	12.7515i	−0.861771	+	0.746226i
$293$	−2.37300	−	2.73859i	−0.138632	−	0.159990i	0.682188	−	0.731177i	$-0.261029\pi$
$293$	−2.37300	−	2.73859i	−0.138632	−	0.159990i	−0.820820	+	0.571187i	$0.806483\pi$
$294$	8.05075	+	2.36537i	0.469529	+	0.137951i
$295$	−2.14053	−	22.3441i	−0.124626	−	1.30092i
$296$	−9.46706	+	20.7026i	−0.550262	+	1.20331i
$297$	3.22133	+	7.05374i	0.186921	+	0.409299i
$298$	−2.39966	−	8.17752i	−0.139008	−	0.473711i
$299$	16.3563	+	24.7352i	0.945908	+	1.43048i
$300$	5.03576	+	7.06753i	0.290740	+	0.408044i
$301$	−2.60546	−	5.70515i	−0.150176	−	0.328839i
$302$	−4.52947	−	7.05057i	−0.260642	−	0.405715i
$303$	−1.18168	+	1.36373i	−0.0678858	+	0.0783444i
$304$	5.01423	−	3.21774i	0.287586	−	0.184550i
$305$	−20.8738	−	0.987916i	−1.19523	−	0.0565679i
$306$	6.50740	+	14.2555i	0.372003	+	0.814932i
$307$	3.53187	+	1.03705i	0.201575	+	0.0591876i	0.380961	−	0.924591i	$-0.375593\pi$
$307$	3.53187	+	1.03705i	0.201575	+	0.0591876i	−0.179387	+	0.983779i	$0.557411\pi$
$308$	−11.5234	−	5.26719i	−0.656606	−	0.300126i
$309$	9.92037	+	1.42633i	0.564350	+	0.0811413i
$310$	10.0521	+	12.7786i	0.570923	+	0.725778i
$311$	−3.28161	−	1.49866i	−0.186083	−	0.0849813i	0.320195	−	0.947352i	$-0.396252\pi$
$311$	−3.28161	−	1.49866i	−0.186083	−	0.0849813i	−0.506278	+	0.862370i	$0.668979\pi$
$312$	11.4750	−	9.93313i	0.649645	−	0.562353i
$313$	−2.66993	+	1.71586i	−0.150913	+	0.0969861i	−0.613918	−	0.789370i	$-0.710408\pi$
$313$	−2.66993	+	1.71586i	−0.150913	+	0.0969861i	0.463005	+	0.886356i	$0.346771\pi$
$314$	−27.4472	−	0.00456866i	−1.54893	−	0.000257824i
$315$	−15.2272	−	10.8362i	−0.857958	−	0.610552i
$316$	−11.8921	−	3.49614i	−0.668983	−	0.196673i
$317$	−7.57325	+	11.7842i	−0.425356	+	0.661867i	−0.986106	−	0.166118i	$-0.946877\pi$
$317$	−7.57325	+	11.7842i	−0.425356	+	0.661867i	0.560750	+	0.827985i	$0.310513\pi$
$318$	1.25867	−	2.75489i	0.0705826	−	0.154486i
$319$	−11.5605	+	3.39447i	−0.647264	+	0.190054i
$320$	17.5629	+	3.39758i	0.981798	+	0.189930i
$321$			11.6331i			0.649296i
$322$	0.324971	+	25.2271i	0.0181099	+	1.40585i
$323$	−7.34538			−0.408708
$324$	4.69208	+	3.01763i	0.260671	+	0.167646i
$325$	29.2098	−	10.1297i	1.62027	−	0.561896i
$326$	6.35221	−	13.9033i	0.351816	−	0.770031i
$327$	−4.03026	+	6.27120i	−0.222874	+	0.346798i
$328$	11.4509	+	0.00571810i	0.632270	+	0.000315729i
$329$	29.3300	−	4.21702i	1.61702	−	0.232492i
$330$	−3.38288	−	3.22466i	−0.186222	−	0.177512i
$331$	−11.0407	−	17.1796i	−0.606851	−	0.944278i	−0.999696	−	0.0246736i	$-0.992145\pi$
$331$	−11.0407	−	17.1796i	−0.606851	−	0.944278i	0.392845	−	0.919605i	$-0.371491\pi$
$332$	−18.9380	+	8.64108i	−1.03936	+	0.474241i
$333$	7.51245	−	16.4500i	0.411680	−	0.901453i
$334$	−2.43392	+	16.9083i	−0.133178	+	0.925180i
$335$	−7.63289	−	9.69987i	−0.417029	−	0.529961i
$336$	12.7822	−	1.82912i	0.697326	−	0.0997865i
$337$	−24.3685	−	7.15523i	−1.32744	−	0.389770i	−0.460265	−	0.887781i	$-0.652246\pi$
$337$	−24.3685	−	7.15523i	−1.32744	−	0.389770i	−0.867171	+	0.498011i	$0.834064\pi$
$338$	−14.8187	−	32.4626i	−0.806029	−	1.76573i
$339$	0.234807	+	0.270982i	0.0127530	+	0.0147177i
$340$	−15.9612	−	15.2198i	−0.865618	−	0.825408i
$341$	−6.61737	−	5.73398i	−0.358350	−	0.310512i
$342$	−3.98204	+	2.55817i	−0.215324	+	0.138330i
$343$	−0.550906	+	0.251590i	−0.0297461	+	0.0135846i
$344$	−3.60257	−	3.12480i	−0.194238	−	0.168478i
$345$	−2.92604	+	8.83422i	−0.157533	+	0.475619i
$346$	−6.56860	−	22.3844i	−0.353130	−	1.20339i
$347$	−6.50603	−	14.2462i	−0.349262	−	0.764777i	−0.999985	−	0.00546207i	$-0.998261\pi$
$347$	−6.50603	−	14.2462i	−0.349262	−	0.764777i	0.650723	−	0.759315i	$-0.274466\pi$
$348$	8.04409	−	9.27714i	0.431209	−	0.497307i
$349$	4.33011	−	4.99721i	0.231785	−	0.267495i	−0.627928	−	0.778272i	$-0.716097\pi$
$349$	4.33011	−	4.99721i	0.231785	−	0.267495i	0.859713	+	0.510777i	$0.170642\pi$
$350$	25.5645	+	6.18978i	1.36648	+	0.330857i
$351$	−21.2777	+	18.4372i	−1.13572	+	0.984106i
$352$	−9.63389	−	0.00801794i	−0.513488	−	0.000427357i
$353$	2.83148	−	9.64315i	0.150705	−	0.513253i	−0.849185	−	0.528095i	$-0.822906\pi$
$353$	2.83148	−	9.64315i	0.150705	−	0.513253i	0.999890	+	0.0148423i	$0.00472462\pi$
$354$	−9.30925	−	8.06923i	−0.494781	−	0.428875i
$355$	10.3774	+	13.1876i	0.550775	+	0.699924i
$356$	2.09217	−	0.300097i	0.110885	−	0.0159051i
$357$	−14.4809	−	6.61320i	−0.766410	−	0.350008i
$358$	33.4273	−	4.80045i	1.76669	−	0.253711i
$359$	−1.36445	+	0.876878i	−0.0720129	+	0.0462799i	−0.576152	−	0.817343i	$-0.695446\pi$
$359$	−1.36445	+	0.876878i	−0.0720129	+	0.0462799i	0.504139	+	0.863623i	$0.331810\pi$
$360$	−13.9534	−	2.69208i	−0.735408	−	0.141885i
$361$	2.38825	+	16.6107i	0.125698	+	0.874246i
$362$	−11.6778	+	18.1644i	−0.613772	+	0.954698i
$363$	−5.91310	−	3.80012i	−0.310357	−	0.199455i
$364$	6.56188	−	45.5312i	0.343936	−	2.38649i
$365$	−9.97370	+	19.3609i	−0.522048	+	1.01339i
$366$	−8.66923	+	7.50940i	−0.453148	+	0.392523i
$367$			19.8068i			1.03391i	0.856014	+	0.516953i	$0.172934\pi$
$367$			19.8068i			1.03391i	−0.856014	+	0.516953i	$0.827066\pi$
$368$	8.18448	+	17.3498i	0.426646	+	0.904419i
$369$	−9.09663			−0.473552
$370$	−1.20746	+	25.4228i	−0.0627727	+	1.32167i
$371$	−2.58639	−	8.80843i	−0.134279	−	0.457311i
$372$	8.83222	+	1.27288i	0.457929	+	0.0659959i
$373$	16.9023	+	10.8625i	0.875169	+	0.562437i	0.899330	−	0.437271i	$-0.144055\pi$
$373$	16.9023	+	10.8625i	0.875169	+	0.562437i	−0.0241610	+	0.999708i	$0.507691\pi$
$374$	9.99090	+	6.42311i	0.516617	+	0.332131i
$375$	8.16699	+	5.23798i	0.421741	+	0.270488i
$376$	18.9602	−	12.1716i	0.977797	−	0.627702i
$377$	−23.6503	−	36.8006i	−1.21805	−	1.89533i
$378$	−23.7101	+	3.40497i	−1.21951	+	0.175133i
$379$	8.79662	−	19.2619i	0.451852	−	0.989418i	−0.537418	−	0.843316i	$-0.680600\pi$
$379$	8.79662	−	19.2619i	0.451852	−	0.989418i	0.989270	−	0.146101i	$-0.0466726\pi$
$380$	3.86397	−	5.42588i	0.198217	−	0.278342i
$381$	−0.763985	+	5.31363i	−0.0391401	+	0.272226i
$382$	−0.193168	+	0.222853i	−0.00988335	+	0.0114022i
$383$	4.57582	−	15.5838i	0.233814	−	0.796296i	−0.756079	−	0.654480i	$-0.772888\pi$
$383$	4.57582	−	15.5838i	0.233814	−	0.796296i	0.989893	−	0.141816i	$-0.0452942\pi$
$384$	8.26570	−	5.29845i	0.421807	−	0.270385i
$385$	−14.1498	−	0.669682i	−0.721140	−	0.0341302i
$386$	−7.30826	+	24.8743i	−0.371981	+	1.26607i
$387$	2.86313	+	2.48092i	0.145541	+	0.126112i
$388$	6.75398	−	7.78927i	0.342881	−	0.395440i
$389$	−19.8433	+	9.06213i	−1.00609	+	0.459468i	−0.849157	−	0.528140i	$-0.822889\pi$
$389$	−19.8433	+	9.06213i	−1.00609	+	0.459468i	−0.156938	+	0.987608i	$0.550162\pi$
$390$	7.77328	−	15.0833i	0.393615	−	0.763771i
$391$	3.06014	−	23.4520i	0.154758	−	1.18602i
$392$	12.6713	−	14.6087i	0.639998	−	0.737852i
$393$	−10.7194	+	4.89540i	−0.540724	+	0.246940i
$394$	2.43418	+	3.78904i	0.122632	+	0.190889i
$395$	−13.7953	+	1.32156i	−0.694116	+	0.0664951i
$396$	7.65319	+	0.00254779i	0.384587	+	0.000128031i
$397$	4.07513	−	3.53112i	0.204525	−	0.177222i	−0.546576	−	0.837410i	$-0.684069\pi$
$397$	4.07513	−	3.53112i	0.204525	−	0.177222i	0.751100	+	0.660188i	$0.229523\pi$
$398$	−15.8081	−	34.6302i	−0.792389	−	1.73585i
$399$	1.35462	−	4.61340i	0.0678156	−	0.230959i
$400$	19.6388	−	3.78401i	0.981938	−	0.189200i
$401$	12.6205	+	1.81455i	0.630236	+	0.0906142i	0.450028	−	0.893014i	$-0.351414\pi$
$401$	12.6205	+	1.81455i	0.630236	+	0.0906142i	0.180208	+	0.983629i	$0.442323\pi$
$402$	−6.70531	−	0.965217i	−0.334430	−	0.0481406i
$403$	13.2063	−	28.9178i	0.657854	−	1.44050i
$404$	1.72633	+	3.78347i	0.0858881	+	0.188235i
$405$	6.12481	+	1.17851i	0.304344	+	0.0585606i
$406$	0.00619496	−	37.2175i	0.000307451	−	1.84707i
$407$	−1.95070	−	13.5674i	−0.0966926	−	0.672512i
$408$	−12.1046	−	0.00604454i	−0.599267	−	0.000299249i
$409$	23.3175	+	14.9852i	1.15297	+	0.740972i	0.970229	−	0.242189i	$-0.0778653\pi$
$409$	23.3175	+	14.9852i	1.15297	+	0.740972i	0.182745	+	0.983160i	$0.441502\pi$
$410$	11.8848	−	4.75988i	0.586947	−	0.235074i
$411$	−6.01427	+	1.76595i	−0.296662	+	0.0871078i
$412$	12.4943	−	19.4273i	0.615549	−	0.957113i
$413$	−37.3410			−1.83743
$414$	−6.50866	−	13.7795i	−0.319883	−	0.677223i
$415$	−16.0552	+	16.8486i	−0.788120	+	0.827065i
$416$	−9.82650	−	33.5693i	−0.481784	−	1.64587i
$417$	4.31632	+	14.7000i	0.211371	+	0.719864i
$418$	−1.49078	+	3.26292i	−0.0729165	+	0.159595i
$419$	−9.33923	−	6.00196i	−0.456251	−	0.293215i	0.292258	−	0.956340i	$-0.405594\pi$
$419$	−9.33923	−	6.00196i	−0.456251	−	0.293215i	−0.748509	+	0.663125i	$0.769230\pi$
$420$	12.5026	−	7.21793i	0.610063	−	0.352199i
$421$	10.7015	−	1.53865i	0.521560	−	0.0749890i	0.123493	−	0.992345i	$-0.460590\pi$
$421$	10.7015	−	1.53865i	0.521560	−	0.0749890i	0.398067	+	0.917356i	$0.369681\pi$
$422$	0.00194337	−	11.6752i	9.46019e−5	−	0.568341i
$423$	−15.0572	+	9.67667i	−0.732106	+	0.470496i
$424$	−4.56853	−	5.27769i	−0.221867	−	0.256307i
$425$	−22.8970	−	9.15028i	−1.11067	−	0.443854i
$426$	9.11628	+	1.31227i	0.441685	+	0.0635798i
$427$	−4.94739	+	34.4098i	−0.239421	+	1.66521i
$428$	24.3838	+	11.1455i	1.17864	+	0.538740i
$429$	−2.57458	+	8.76821i	−0.124302	+	0.423333i
$430$	−5.03884	−	1.74317i	−0.242995	−	0.0840630i
$431$	7.64970	+	8.82823i	0.368473	+	0.425241i	0.909461	−	0.415790i	$-0.136495\pi$
$431$	7.64970	+	8.82823i	0.368473	+	0.425241i	−0.540988	+	0.841031i	$0.681949\pi$
$432$	−15.3285	+	9.83661i	−0.737492	+	0.473264i
$433$	−2.99946	+	3.46156i	−0.144145	+	0.166352i	−0.823231	−	0.567707i	$-0.807831\pi$
$433$	−2.99946	+	3.46156i	−0.144145	+	0.166352i	0.679086	+	0.734058i	$0.262376\pi$
$434$	22.7558	−	14.6189i	1.09232	−	0.701731i
$435$	4.48610	−	12.9746i	0.215092	−	0.622086i
$436$	9.28356	+	14.4561i	0.444602	+	0.692321i
$437$	7.14264	−	0.0931994i	0.341679	−	0.00445833i
$438$	3.36573	+	11.4697i	0.160821	+	0.548042i
$439$	12.5508	−	5.73178i	0.599019	−	0.273563i	−0.0927408	−	0.995690i	$-0.529563\pi$
$439$	12.5508	−	5.73178i	0.599019	−	0.273563i	0.691760	+	0.722127i	$0.256836\pi$
$440$	−10.0002	+	4.00126i	−0.476742	+	0.190753i
$441$	−10.0603	+	11.6102i	−0.479063	+	0.552869i
$442$	−12.1563	+	41.3750i	−0.578215	+	1.96801i
$443$	17.7112	+	20.4398i	0.841485	+	0.971125i	0.999868	−	0.0162525i	$-0.00517356\pi$
$443$	17.7112	+	20.4398i	0.841485	+	0.971125i	−0.158383	+	0.987378i	$0.550628\pi$
$444$	9.14426	+	10.5601i	0.433967	+	0.501162i
$445$	2.04610	−	1.18216i	0.0969945	−	0.0560395i
$446$	−13.9890	+	16.1388i	−0.662399	+	0.764192i
$447$	−5.17635	−	0.744246i	−0.244833	−	0.0352016i
$448$	8.41251	−	28.5449i	0.397454	−	1.34862i
$449$	−0.590347	+	1.29268i	−0.0278602	+	0.0610053i	−0.923051	−	0.384679i	$-0.874312\pi$
$449$	−0.590347	+	1.29268i	−0.0278602	+	0.0610053i	0.895190	+	0.445684i	$0.147040\pi$
$450$	−15.5996	+	3.01382i	−0.735372	+	0.142073i
$451$	−5.80027	+	3.72761i	−0.273124	+	0.175526i
$452$	0.792964	−	0.232548i	0.0372979	−	0.0109382i
$453$	−5.08998	+	0.731829i	−0.239148	+	0.0343843i
$454$	11.6828	−	18.1722i	0.548303	−	0.852863i
$455$	−12.1408	−	49.9779i	−0.569168	−	2.34300i
$456$	−0.518488	−	3.61899i	−0.0242804	−	0.169475i
$457$	−26.7443	+	7.85283i	−1.25104	+	0.367340i	−0.839154	−	0.543894i	$-0.816949\pi$
$457$	−26.7443	+	7.85283i	−1.25104	+	0.367340i	−0.411890	+	0.911233i	$0.635131\pi$
$458$	−3.30192	+	2.86017i	−0.154289	+	0.133647i
$459$	22.4548			1.04810
$460$	15.7138	+	14.5972i	0.732658	+	0.680597i
$461$	23.8805			1.11223			0.556114	−	0.831106i	$-0.312292\pi$
$461$	23.8805			1.11223			0.556114	+	0.831106i	$0.312292\pi$
$462$	−5.87664	+	5.09043i	−0.273406	+	0.236828i
$463$	−15.3924	+	4.51962i	−0.715347	+	0.210045i	−0.619099	−	0.785313i	$-0.712502\pi$
$463$	−15.3924	+	4.51962i	−0.715347	+	0.210045i	−0.0962473	+	0.995357i	$0.530684\pi$
$464$	−11.7386	−	25.7493i	−0.544951	−	1.19538i
$465$	9.69479	−	2.35508i	0.449585	−	0.109214i
$466$	8.96199	−	13.9400i	0.415156	−	0.645759i
$467$	−11.8223	+	1.69979i	−0.547071	+	0.0786570i	−0.410308	−	0.911947i	$-0.634579\pi$
$467$	−11.8223	+	1.69979i	−0.547071	+	0.0786570i	−0.136763	+	0.990604i	$0.543670\pi$
$468$	7.81951	+	26.6637i	0.361457	+	1.23253i
$469$	−17.2737	+	11.1011i	−0.797624	+	0.512602i
$470$	14.6089	−	20.5214i	0.673856	−	0.946580i
$471$	−6.99661	+	15.3204i	−0.322387	+	0.705929i
$472$	−25.8328	+	11.7818i	−1.18905	+	0.542304i
$473$	2.84224	+	0.408653i	0.130686	+	0.0187899i
$474$	−4.98196	+	5.74755i	−0.228829	+	0.263994i
$475$	1.75133	−	7.23850i	0.0803567	−	0.332125i
$476$	−27.7357	+	24.0170i	−1.27127	+	1.10082i
$477$	3.63135	+	4.19080i	0.166268	+	0.191883i
$478$	−7.47962	+	25.4576i	−0.342110	+	1.16440i
$479$	−1.40899	+	1.62606i	−0.0643782	+	0.0742964i	−0.787025	−	0.616921i	$-0.788380\pi$
$479$	−1.40899	+	1.62606i	−0.0643782	+	0.0742964i	0.722647	+	0.691217i	$0.242925\pi$
$480$	6.37197	−	8.93824i	0.290839	−	0.407973i
$481$	45.2688	−	20.6736i	2.06408	−	0.942633i
$482$	0.408917	+	1.39350i	0.0186257	+	0.0634723i
$483$	14.1651	+	6.24693i	0.644535	+	0.284245i
$484$	−13.6306	+	8.75344i	−0.619573	+	0.397884i
$485$	3.76662	−	10.8937i	0.171033	−	0.494660i
$486$	19.1332	−	12.2917i	0.867902	−	0.557562i
$487$	0.164674	−	0.190044i	0.00746211	−	0.00861173i	−0.752006	−	0.659156i	$-0.770914\pi$
$487$	0.164674	−	0.190044i	0.00746211	−	0.00861173i	0.759468	+	0.650544i	$0.225459\pi$
$488$	7.43438	+	25.3660i	0.336538	+	1.14827i
$489$	−6.14245	−	7.08876i	−0.277771	−	0.320565i
$490$	7.06869	−	20.4329i	0.319331	−	0.923066i
$491$	2.11904	−	7.21677i	0.0956307	−	0.325688i	−0.897758	−	0.440490i	$-0.854805\pi$
$491$	2.11904	−	7.21677i	0.0956307	−	0.325688i	0.993388	+	0.114801i	$0.0366231\pi$
$492$	2.92110	−	6.39069i	0.131693	−	0.288114i
$493$	−4.96525	+	34.5341i	−0.223624	+	1.55534i
$494$	−12.8918	−	1.85575i	−0.580029	−	0.0834941i
$495$	7.94263	−	3.18258i	0.356995	−	0.143046i
$496$	11.1301	−	17.2934i	0.499756	−	0.776498i
$497$	23.4847	−	15.0927i	1.05343	−	0.676999i
$498$	−0.00212619	+	12.7735i	−9.52767e−5	+	0.572395i
$499$	−9.21010	+	1.32421i	−0.412301	+	0.0592799i	−0.345344	−	0.938476i	$-0.612238\pi$
$499$	−9.21010	+	1.32421i	−0.412301	+	0.0592799i	−0.0669563	+	0.997756i	$0.521329\pi$
$500$	18.8039	−	12.1002i	0.840935	−	0.541136i
$501$	8.81837	+	5.66722i	0.393976	+	0.253193i
$502$	13.4022	−	29.3337i	0.598168	−	1.30923i
$503$	−10.4837	−	35.7043i	−0.467447	−	1.59198i	−0.769474	−	0.638679i	$-0.779481\pi$
$503$	−10.4837	−	35.7043i	−0.467447	−	1.59198i	0.302027	−	0.953300i	$-0.402337\pi$
$504$	−6.67160	+	22.6795i	−0.297177	+	1.01022i
$505$	3.36604	+	3.20754i	0.149787	+	0.142734i
$506$	−9.79664	−	6.11906i	−0.435514	−	0.272025i
$507$	−21.8974			−0.972499
$508$	10.4058	+	6.69230i	0.461683	+	0.296923i
$509$	26.1038	−	7.66477i	1.15703	−	0.339735i	0.353753	−	0.935339i	$-0.384905\pi$
$509$	26.1038	−	7.66477i	1.15703	−	0.339735i	0.803278	+	0.595604i	$0.203087\pi$
$510$	−12.5632	+	5.03161i	−0.556309	+	0.222803i
$511$	30.4790	+	19.5877i	1.34831	+	0.866507i
$512$	−3.18666	−	22.4019i	−0.140832	−	0.990034i
$513$	0.965181	+	6.71298i	0.0426138	+	0.296385i
$514$	0.00283513	−	17.0326i	0.000125052	−	0.751277i
$515$	4.87954	−	25.3594i	0.215018	−	1.11747i
$516$	−2.66233	+	1.21478i	−0.117203	+	0.0534775i
$517$	−5.63560	+	12.3402i	−0.247853	+	0.542723i
$518$	41.9082	+	6.03261i	1.84134	+	0.265058i
$519$	−14.1693	−	2.03723i	−0.621961	−	0.0894245i
$520$	−24.1682	−	30.7445i	−1.05984	−	1.34823i
$521$	1.34603	−	4.58416i	0.0589707	−	0.200836i	−0.924738	−	0.380603i	$-0.875716\pi$
$521$	1.34603	−	4.58416i	0.0589707	−	0.200836i	0.983709	+	0.179768i	$0.0575346\pi$
$522$	9.33540	+	20.4507i	0.408599	+	0.895102i
$523$	16.8633	−	14.6121i	0.737380	−	0.638943i	−0.202957	−	0.979188i	$-0.565055\pi$
$523$	16.8633	−	14.6121i	0.737380	−	0.638943i	0.940337	+	0.340244i	$0.110510\pi$
$524$	−0.00904137	+	27.1590i	−0.000394974	+	1.18644i
$525$	9.96960	−	12.6934i	0.435109	−	0.553986i
$526$	−16.6846	−	25.9712i	−0.727483	−	1.13240i
$527$	−23.0637	+	10.5328i	−1.00467	+	0.458818i
$528$	−2.45937	+	5.37580i	−0.107031	+	0.233952i
$529$	−2.67811	+	22.8435i	−0.116440	+	0.993198i
$530$	−6.93722	−	3.57515i	−0.301334	−	0.155295i
$531$	20.5170	−	9.36978i	0.890360	−	0.406614i
$532$	−8.37218	−	7.25941i	−0.362980	−	0.314735i
$533$	−18.9187	−	16.3932i	−0.819462	−	0.710068i
$534$	0.365603	−	1.24436i	0.0158212	−	0.0538489i
$535$	29.9413	+	1.41707i	1.29448	+	0.0612652i
$536$	−8.44744	+	13.1301i	−0.364874	+	0.567132i
$537$	5.83821	−	19.8831i	0.251937	−	0.858020i
$538$	16.5715	−	19.1181i	0.714446	−	0.824238i
$539$	−1.65712	+	11.5255i	−0.0713773	+	0.496440i
$540$	−11.8121	+	16.5869i	−0.508313	+	0.713787i
$541$	−16.4225	+	35.9603i	−0.706060	+	1.54606i	0.126405	+	0.991979i	$0.459656\pi$
$541$	−16.4225	+	35.9603i	−0.706060	+	1.54606i	−0.832465	+	0.554077i	$0.813071\pi$
$542$	−38.5204	+	5.53185i	−1.65459	+	0.237613i
$543$	7.16402	+	11.1474i	0.307437	+	0.478382i
$544$	−11.6100	+	25.3664i	−0.497773	+	1.08757i
$545$	15.6499	+	11.1370i	0.670369	+	0.477058i
$546$	−23.7444	−	15.2652i	−1.01617	−	0.653291i
$547$	−25.7882	−	16.5730i	−1.10262	−	0.708612i	−0.142949	−	0.989730i	$-0.545658\pi$
$547$	−25.7882	−	16.5730i	−1.10262	−	0.708612i	−0.959673	+	0.281118i	$0.909295\pi$
$548$	−2.06064	+	14.2983i	−0.0880263	+	0.610792i
$549$	−5.91595	−	20.1479i	−0.252487	−	0.859891i
$550$	−8.71175	+	8.31408i	−0.371470	+	0.354514i
$551$	−10.5376			−0.448915
$552$	11.7706	−	0.147708i	0.500989	−	0.00628685i
$553$			23.0544i			0.980372i
$554$	3.16104	−	2.73814i	0.134300	−	0.116332i
$555$	13.8839	+	7.15225i	0.589339	+	0.303596i
$556$	34.9478	+	5.03661i	1.48212	+	0.213600i
$557$	−2.06015	−	1.32398i	−0.0872915	−	0.0560988i	0.496267	−	0.868170i	$-0.334704\pi$
$557$	−2.06015	−	1.32398i	−0.0872915	−	0.0560988i	−0.583558	+	0.812071i	$0.698340\pi$
$558$	−8.83492	+	13.7424i	−0.374012	+	0.581761i
$559$	1.48370	+	10.3194i	0.0627540	+	0.436464i
$560$	−3.15075	−	33.1217i	−0.133143	−	1.39965i
$561$	6.13139	−	3.94041i	0.258868	−	0.166364i
$562$	19.0666	−	2.73812i	0.804275	−	0.115501i
$563$	−3.96001	−	1.80848i	−0.166895	−	0.0762183i	0.330216	−	0.943905i	$-0.392878\pi$
$563$	−3.96001	−	1.80848i	−0.166895	−	0.0762183i	−0.497111	+	0.867687i	$0.665606\pi$
$564$	−1.96303	−	13.6855i	−0.0826587	−	0.576265i
$565$	0.726058	−	0.571339i	0.0305455	−	0.0240364i
$566$	24.6023	+	21.3252i	1.03411	+	0.896365i
$567$	2.92323	−	9.95560i	0.122764	−	0.418096i
$568$	11.4848	−	17.8511i	0.481893	−	0.749017i
$569$	−3.04268	+	2.63650i	−0.127556	+	0.110528i	−0.716303	−	0.697790i	$-0.754167\pi$
$569$	−3.04268	+	2.63650i	−0.127556	+	0.110528i	0.588747	+	0.808317i	$0.299621\pi$
$570$	−2.04423	−	3.53957i	−0.0856236	−	0.148256i
$571$	−22.8225	+	26.3386i	−0.955092	+	1.10224i	0.0395871	+	0.999216i	$0.487396\pi$
$571$	−22.8225	+	26.3386i	−0.955092	+	1.10224i	−0.994679	+	0.103019i	$0.967150\pi$
$572$	15.9121	+	13.7972i	0.665320	+	0.576891i
$573$	0.0751785	+	0.164618i	0.00314063	+	0.00687701i
$574$	−5.99687	−	20.4360i	−0.250304	−	0.852984i
$575$	22.3812	+	8.60720i	0.933359	+	0.358945i
$576$	2.54038	+	17.7949i	0.105849	+	0.741453i
$577$	27.3578	−	12.4939i	1.13892	−	0.520128i	0.245522	−	0.969391i	$-0.421041\pi$
$577$	27.3578	−	12.4939i	1.13892	−	0.520128i	0.893399	+	0.449263i	$0.148314\pi$
$578$	8.70974	−	5.59536i	0.362277	−	0.232736i
$579$	12.0231	+	10.4181i	0.499664	+	0.432961i
$580$	−22.8977	−	21.8340i	−0.950775	−	0.906609i
$581$	25.3539	+	29.2600i	1.05186	+	1.21391i
$582$	−2.62710	−	5.75507i	−0.108897	−	0.238555i
$583$	4.03275	+	1.18412i	0.167019	+	0.0490413i
$584$	27.2659	+	3.93415i	1.12827	+	0.162796i
$585$	19.2114	+	24.4139i	0.794296	+	1.00939i
$586$	−0.730157	+	5.07236i	−0.0301625	+	0.209537i
$587$	−18.1145	+	39.6652i	−0.747666	+	1.63716i	0.0228506	+	0.999739i	$0.492726\pi$
$587$	−18.1145	+	39.6652i	−0.747666	+	1.63716i	−0.770516	+	0.637420i	$0.780001\pi$
$588$	−4.92602	−	10.7960i	−0.203146	−	0.445219i
$589$	−4.14020	−	6.44228i	−0.170594	−	0.265449i
$590$	−21.9026	+	22.9773i	−0.901717	+	0.945960i
$591$	2.73540	−	0.393291i	0.112519	−	0.0161778i
$592$	30.8958	−	9.04950i	1.26981	−	0.371932i
$593$	−4.06734	+	6.32890i	−0.167026	+	0.259897i	−0.914669	−	0.404203i	$-0.867549\pi$
$593$	−4.06734	+	6.32890i	−0.167026	+	0.259897i	0.747644	+	0.664100i	$0.231185\pi$
$594$	4.55731	−	9.97473i	0.186989	−	0.409268i
$595$	−18.7851	+	36.4655i	−0.770113	+	1.49494i
$596$	−6.51939	+	10.1370i	−0.267045	+	0.415226i
$597$	−23.3595			−0.956042
$598$	11.2958	−	40.3872i	0.461918	−	1.65156i
$599$		−	26.1128i		−	1.06694i	−0.845819	−	0.533470i	$-0.820888\pi$
$599$		−	26.1128i		−	1.06694i	0.845819	−	0.533470i	$-0.179112\pi$
$600$	2.89202	−	11.9270i	0.118066	−	0.486919i
$601$	−31.8969	+	9.36576i	−1.30110	+	0.382037i	−0.857637	−	0.514255i	$-0.828068\pi$
$601$	−31.8969	+	9.36576i	−1.30110	+	0.382037i	−0.443463	+	0.896293i	$0.646250\pi$
$602$	−3.68601	+	8.06769i	−0.150231	+	0.328814i
$603$	6.70546	−	10.4339i	0.273068	−	0.424901i
$604$	−3.34268	+	11.3701i	−0.136012	+	0.462644i
$605$	−10.5011	+	14.7563i	−0.426929	+	0.599928i
$606$	2.55192		0.000424774i	0.103665		1.72552e-5i
$607$	15.0229	−	9.65460i	0.609759	−	0.391868i	−0.199008	−	0.979998i	$-0.563772\pi$
$607$	15.0229	−	9.65460i	0.609759	−	0.391868i	0.808767	+	0.588130i	$0.200136\pi$
$608$	−8.08244	−	2.38053i	−0.327786	−	0.0965431i
$609$	−20.7740	−	9.48719i	−0.841807	−	0.384440i
$610$	18.2717	+	23.2277i	0.739801	+	0.940461i
$611$	−48.7537	−	7.00973i	−1.97236	−	0.283583i
$612$	9.21292	−	20.1557i	0.372410	−	0.814746i
$613$	46.1788	+	13.5593i	1.86514	+	0.547656i	0.998841	+	0.0481362i	$0.0153281\pi$
$613$	46.1788	+	13.5593i	1.86514	+	0.547656i	0.866303	+	0.499519i	$0.166490\pi$
$614$	−2.16173	−	4.73562i	−0.0872404	−	0.191114i
$615$	0.371395	−	7.84724i	0.0149761	−	0.316431i
$616$	5.03957	+	17.1950i	0.203050	+	0.692804i
$617$	−15.5479	+	17.9432i	−0.625935	+	0.722367i	−0.976823	−	0.214050i	$-0.931334\pi$
$617$	−15.5479	+	17.9432i	−0.625935	+	0.722367i	0.350888	+	0.936418i	$0.385880\pi$
$618$	−7.66094	−	11.9250i	−0.308168	−	0.479695i
$619$	−14.1331	−	30.9472i	−0.568057	−	1.24387i	−0.947825	−	0.318790i	$-0.896724\pi$
$619$	−14.1331	−	30.9472i	−0.568057	−	1.24387i	0.379769	−	0.925082i	$-0.376004\pi$
$620$	4.35204	−	22.5774i	0.174782	−	0.906729i
$621$	−21.8350	+	0.284910i	−0.876210	+	0.0114331i
$622$	1.43657	+	4.89553i	0.0576013	+	0.196293i
$623$	−1.63303	−	3.57584i	−0.0654260	−	0.143263i
$624$	−21.2431	−	3.06873i	−0.850404	−	0.122848i
$625$	14.4764	−	20.3822i	0.579056	−	0.815288i
$626$	4.30634	+	1.26523i	0.172116	+	0.0505689i
$627$	1.44155	+	1.66364i	0.0575701	+	0.0664394i
$628$	25.4094	+	29.3438i	1.01395	+	1.17094i
$629$	−38.0836	−	11.1823i	−1.51849	−	0.445869i
$630$	2.51610	+	26.3107i	0.100244	+	1.04824i
$631$	−6.81334	+	47.3878i	−0.271235	+	1.88648i	0.164460	+	0.986384i	$0.447412\pi$
$631$	−6.81334	+	47.3878i	−0.271235	+	1.88648i	−0.435695	+	0.900094i	$0.643497\pi$
$632$	7.27414	+	15.9492i	0.289350	+	0.634425i
$633$	−6.51687	−	2.97615i	−0.259022	−	0.118292i
$634$	19.6090	−	2.81602i	0.778774	−	0.111838i
$635$	13.5832	+	2.61362i	0.539033	+	0.103718i
$636$	−4.11027	+	1.20540i	−0.162983	+	0.0477971i
$637$	−41.8460	+	6.01655i	−1.65800	+	0.238384i
$638$	14.3328	+	9.21449i	0.567440	+	0.364805i
$639$	−9.11650	+	14.1855i	−0.360643	+	0.561172i
$640$	−12.6303	−	21.9197i	−0.499257	−	0.866454i
$641$	2.57601	+	8.77310i	0.101746	+	0.346517i	0.994594	−	0.103843i	$-0.0331140\pi$
$641$	2.57601	+	8.77310i	0.101746	+	0.346517i	−0.892847	+	0.450360i	$0.851296\pi$
$642$	12.4351	−	10.7715i	0.490776	−	0.425117i
$643$			10.9430i			0.431550i	0.976443	+	0.215775i	$0.0692278\pi$
$643$			10.9430i			0.431550i	−0.976443	+	0.215775i	$0.930772\pi$
$644$	26.6655	−	23.7060i	1.05077	−	0.934147i
$645$	−2.25707	+	2.36860i	−0.0888720	+	0.0932635i
$646$	6.80135	+	7.85181i	0.267595	+	0.308925i
$647$	0.848598	−	0.249171i	0.0333618	−	0.00979592i	−0.265009	−	0.964246i	$-0.585375\pi$
$647$	0.848598	−	0.249171i	0.0333618	−	0.00979592i	0.298371	+	0.954450i	$0.403557\pi$
$648$	−1.11889	−	7.80971i	−0.0439540	−	0.306794i
$649$	9.24266	−	14.3819i	0.362806	−	0.564537i
$650$	−37.8745	−	21.8443i	−1.48556	−	0.856803i
$651$	−2.36199	−	16.4280i	−0.0925736	−	0.643864i
$652$	−20.7436	+	6.08336i	−0.812381	+	0.238243i
$653$	−7.01078	−	10.9090i	−0.274353	−	0.426901i	0.676547	−	0.736399i	$-0.263475\pi$
$653$	−7.01078	−	10.9090i	−0.274353	−	0.426901i	−0.950900	+	0.309498i	$0.899839\pi$
$654$	10.4353	−	1.49860i	0.408054	−	0.0586000i
$655$	11.2941	+	28.1861i	0.441295	+	1.10132i
$656$	−10.5967	−	12.2457i	−0.413731	−	0.478114i
$657$	−21.6617	−	3.11448i	−0.845104	−	0.121508i
$658$	−31.6654	−	27.4475i	−1.23445	−	1.07001i
$659$	13.8791	+	4.07527i	0.540653	+	0.158750i	0.540646	−	0.841250i	$-0.318180\pi$
$659$	13.8791	+	4.07527i	0.540653	+	0.158750i	6.61127e−6		1.00000i	$0.499998\pi$
$660$	−0.314660	+	6.60195i	−0.0122481	+	0.256980i
$661$	8.15757	−	7.06858i	0.317293	−	0.274936i	−0.481623	−	0.876378i	$-0.659953\pi$
$661$	8.15757	−	7.06858i	0.317293	−	0.274936i	0.798916	+	0.601443i	$0.205407\pi$
$662$	−8.14114	+	27.7091i	−0.316414	+	1.07695i
$663$	19.9988	+	17.3290i	0.776688	+	0.673004i
$664$	26.7722	+	12.2426i	1.03896	+	0.475106i
$665$	−11.7090	−	4.04849i	−0.454055	−	0.156994i
$666$	−24.5402	+	7.20120i	−0.950912	+	0.279041i
$667$	4.39003	−	33.6439i	0.169983	−	1.30270i
$668$	20.3277	−	13.0543i	0.786502	−	0.505084i
$669$	5.44434	+	11.9214i	0.210490	+	0.460909i
$670$	−3.30108	+	17.1406i	−0.127532	+	0.662199i
$671$	−12.0284	−	10.4226i	−0.464350	−	0.402361i
$672$	−13.7907	−	11.9698i	−0.531988	−	0.461746i
$673$	−21.6104	+	18.7255i	−0.833018	+	0.721815i	−0.962942	−	0.269710i	$-0.913072\pi$
$673$	−21.6104	+	18.7255i	−0.833018	+	0.721815i	0.129923	+	0.991524i	$0.458527\pi$
$674$	14.9151	+	32.6739i	0.574507	+	1.25855i
$675$	−5.35382	+	22.1281i	−0.206069	+	0.851710i
$676$	−20.9797	+	45.8986i	−0.806910	+	1.76533i
$677$	4.49437	−	31.2590i	0.172733	−	1.20138i	−0.700346	−	0.713804i	$-0.746971\pi$
$677$	4.49437	−	31.2590i	0.172733	−	1.20138i	0.873079	−	0.487579i	$-0.162120\pi$
$678$	0.0722487	−	0.501907i	0.00277469	−	0.0192756i
$679$	−17.4423	−	7.96563i	−0.669374	−	0.305693i
$680$	−1.49006	+	31.1542i	−0.0571412	+	1.19471i
$681$	−7.16711	−	11.1522i	−0.274644	−	0.427355i
$682$	−0.00206117	+	12.3829i	−7.89262e−5	+	0.474166i
$683$	2.34043	+	16.2780i	0.0895540	+	0.622862i	0.984329	+	0.176344i	$0.0564271\pi$
$683$	2.34043	+	16.2780i	0.0895540	+	0.622862i	−0.894775	+	0.446518i	$0.852664\pi$
$684$	6.42166	+	1.88789i	0.245538	+	0.0721853i
$685$	3.81259	+	15.6947i	0.145672	+	0.599663i
$686$	0.779039	+	0.355932i	0.0297438	+	0.0135895i
$687$	0.755217	+	2.57203i	0.0288133	+	0.0981291i
$688$	−0.00449044	+	6.74431i	−0.000171196	+	0.257124i
$689$			15.2599i			0.581357i
$690$	12.1526	−	5.05213i	0.462643	−	0.192331i
$691$			2.26060i			0.0859973i	0.999075	+	0.0429987i	$0.0136911\pi$
$691$			2.26060i			0.0859973i	−0.999075	+	0.0429987i	$0.986309\pi$
$692$	−17.8456	+	27.7480i	−0.678387	+	1.05482i
$693$	−4.01027	−	13.6577i	−0.152338	−	0.518814i
$694$	−9.20427	+	20.1457i	−0.349389	+	0.764719i
$695$	38.3609	−	9.31872i	1.45511	−	0.353479i
$696$	−17.3651	−	0.00867139i	−0.658221	−	0.000328688i
$697$	2.84137	+	19.7622i	0.107625	+	0.748545i
$698$	−9.35115	−	0.00155652i	−0.353946	−	5.89153e-5i
$699$	−5.49794	−	8.55496i	−0.207951	−	0.323578i
$700$	−17.0546	−	33.0584i	−0.644602	−	1.24949i
$701$	40.0342	+	18.2830i	1.51207	+	0.690540i	0.987030	−	0.160537i	$-0.0513226\pi$
$701$	40.0342	+	18.2830i	1.51207	+	0.690540i	0.525041	+	0.851077i	$0.324050\pi$
$702$	39.4101	+	5.67302i	1.48744	+	0.214114i
$703$	1.70606	−	11.8659i	0.0643454	−	0.447532i
$704$	8.91178	+	10.3055i	0.335875	+	0.388404i
$705$	−7.73286	−	13.3842i	−0.291237	−	0.504079i
$706$	−12.9298	+	5.90223i	−0.486618	+	0.222133i
$707$	5.84561	−	5.06525i	0.219847	−	0.190498i
$708$	−0.00580010	+	17.4227i	−0.000217981	+	0.654784i
$709$	−2.38518	−	2.06677i	−0.0895773	−	0.0776192i	0.608921	−	0.793231i	$-0.291603\pi$
$709$	−2.38518	−	2.06677i	−0.0895773	−	0.0776192i	−0.698498	+	0.715612i	$0.746148\pi$
$710$	4.48802	−	23.3037i	0.168433	−	0.874573i
$711$	−5.78492	−	12.6672i	−0.216952	−	0.475058i
$712$	−2.25800	−	1.95854i	−0.0846220	−	0.0733994i
$713$	22.2935	−	10.5348i	0.834897	−	0.394530i
$714$	6.33921	+	21.6027i	0.237239	+	0.808460i
$715$	22.2541	+	7.69456i	0.832255	+	0.287760i
$716$	−36.0830	−	31.2871i	−1.34848	−	1.16925i
$717$	12.3050	+	10.6624i	0.459540	+	0.398193i
$718$	2.20073	+	0.646589i	0.0821304	+	0.0241305i
$719$	13.8742	−	12.0221i	0.517421	−	0.448348i	−0.356585	−	0.934263i	$-0.616059\pi$
$719$	13.8742	−	12.0221i	0.517421	−	0.448348i	0.874006	+	0.485915i	$0.161514\pi$
$720$	10.0422	+	17.4081i	0.374252	+	0.648762i
$721$	−41.2205	−	12.1034i	−1.53513	−	0.450755i
$722$	15.5445	−	17.9333i	0.578507	−	0.667409i
$723$	0.882083	+	0.126824i	0.0328050	+	0.00471665i
$724$	30.2296	−	4.33609i	1.12347	−	0.161149i
$725$	−32.8477	−	13.1268i	−1.21993	−	0.487519i
$726$	1.41303	+	9.83944i	0.0524423	+	0.365176i
$727$	12.8282	+	19.9610i	0.475770	+	0.740313i	0.993326	−	0.115336i	$-0.0367946\pi$
$727$	12.8282	+	19.9610i	0.475770	+	0.740313i	−0.517556	+	0.855649i	$0.673158\pi$
$728$	−54.7463	+	35.1447i	−2.02903	+	1.30255i
$729$	−0.795080	−	5.52990i	−0.0294474	−	0.204811i
$730$	29.9307	−	7.26557i	1.10779	−	0.268911i
$731$	4.49541	−	6.99499i	0.166269	−	0.258719i
$732$	16.0543	+	2.31371i	0.593384	+	0.0855173i
$733$	3.04214	−	0.893253i	0.112364	−	0.0329931i	−0.225067	−	0.974343i	$-0.572260\pi$
$733$	3.04214	−	0.893253i	0.112364	−	0.0329931i	0.337431	+	0.941350i	$0.390442\pi$
$734$	21.1724	−	18.3398i	0.781486	−	0.676934i
$735$	−9.60488	−	9.15260i	−0.354281	−	0.337599i
$736$	10.9676	−	24.8135i	0.404273	−	0.914638i
$737$		−	9.40071i		−	0.346280i
$738$	8.42289	+	9.72380i	0.310051	+	0.357938i
$739$	7.80496	+	26.5813i	0.287110	+	0.977807i	0.969146	+	0.246488i	$0.0792767\pi$
$739$	7.80496	+	26.5813i	0.287110	+	0.977807i	−0.682036	+	0.731319i	$0.738905\pi$
$740$	28.2937	−	22.2492i	1.04010	−	0.817897i
$741$	−4.32099	+	6.72359i	−0.158736	+	0.246997i
$742$	−7.02090	+	10.9207i	−0.257746	+	0.400913i
$743$	−44.8312	+	6.44575i	−1.64470	+	0.236472i	−0.901556	−	0.432663i	$-0.857574\pi$
$743$	−44.8312	+	6.44575i	−1.64470	+	0.236472i	−0.743141	+	0.669135i	$0.766665\pi$
$744$	−6.81742	−	10.6198i	−0.249939	−	0.389339i
$745$	−2.54610	+	13.2323i	−0.0932817	+	0.484792i
$746$	−4.03907	−	28.1256i	−0.147881	−	1.02975i
$747$	−21.2728	−	9.71495i	−0.778330	−	0.355451i
$748$	−2.38497	−	16.6271i	−0.0872031	−	0.607948i
$749$	7.09653	−	49.3575i	0.259302	−	1.80348i
$750$	−1.96299	−	13.5801i	−0.0716781	−	0.495875i
$751$	14.8585	+	4.36283i	0.542193	+	0.159202i	0.541350	−	0.840798i	$-0.317914\pi$
$751$	14.8585	+	4.36283i	0.542193	+	0.159202i	0.000842863		1.00000i	$0.499732\pi$
$752$	−30.5667	−	8.99729i	−1.11465	−	0.328098i
$753$	−12.9596	−	14.9562i	−0.472274	−	0.545033i
$754$	−17.4392	+	59.3558i	−0.635097	+	2.16161i
$755$	1.26356	+	13.1898i	0.0459856	+	0.480025i
$756$	25.5937	+	22.1920i	0.930834	+	0.807115i
$757$	0.185735	+	0.406703i	0.00675066	+	0.0147819i	0.912977	−	0.408010i	$-0.133777\pi$
$757$	0.185735	+	0.406703i	0.00675066	+	0.0147819i	−0.906227	+	0.422792i	$0.861050\pi$
$758$	−28.7350	+	8.43217i	−1.04370	+	0.306270i
$759$	−5.91216	+	3.90944i	−0.214598	+	0.141904i
$760$	−9.37775	+	0.893647i	−0.340167	+	0.0324160i
$761$	−19.0928	−	41.8073i	−0.692112	−	1.51551i	−0.849280	−	0.527943i	$-0.822964\pi$
$761$	−19.0928	−	41.8073i	−0.692112	−	1.51551i	0.157167	−	0.987572i	$-0.449764\pi$
$762$	6.38738	−	4.10342i	0.231390	−	0.148651i
$763$	20.9254	−	24.1492i	0.757550	−	0.874260i
$764$	0.417079		0.000138848i	0.0150894		5.02334e-6i
$765$	1.17135	−	24.7496i	0.0423503	−	0.894823i
$766$	−20.8952	+	9.53830i	−0.754973	+	0.344633i
$767$	59.5556	+	17.4871i	2.15043	+	0.631423i
$768$	−13.3173	−	3.92957i	−0.480545	−	0.141796i
$769$	−41.9438	−	6.03061i	−1.51253	−	0.217469i	−0.664450	−	0.747333i	$-0.731334\pi$
$769$	−41.9438	−	6.03061i	−1.51253	−	0.217469i	−0.848083	+	0.529863i	$0.822243\pi$
$770$	12.3859	+	15.7454i	0.446358	+	0.567426i
$771$	−9.50726	−	4.34182i	−0.342396	−	0.156367i
$772$	33.3563	−	15.2199i	1.20052	−	0.547776i
$773$	31.5566	−	20.2802i	1.13501	−	0.729429i	0.168413	−	0.985717i	$-0.446136\pi$
$773$	31.5566	−	20.2802i	1.13501	−	0.729429i	0.966600	+	0.256288i	$0.0824995\pi$
$774$	0.000891804	−	5.35770i	3.20552e−5	−	0.192579i
$775$	−4.88057	−	25.2394i	−0.175315	−	0.906626i
$776$	−14.5800	−	0.00728067i	−0.523393	−	0.000261361i
$777$	14.0465	−	21.8568i	0.503917	−	0.784110i
$778$	28.0605	+	12.8205i	1.00602	+	0.459636i
$779$	−5.78587	+	1.69888i	−0.207300	+	0.0608688i
$780$	−23.3207	+	5.65691i	−0.835017	+	0.202550i
$781$			12.7809i			0.457335i
$782$	−27.9024	+	18.4439i	−0.997789	+	0.659554i
$783$	32.2133			1.15121
$784$	−27.3487	−	0.0182091i	−0.976741	−	0.000650325i
$785$	38.5796	+	19.8742i	1.37696	+	0.709340i
$786$	15.1584	+	6.92567i	0.540683	+	0.247030i
$787$	−22.4282	+	34.8990i	−0.799480	+	1.24402i	0.166664	+	0.986014i	$0.446701\pi$
$787$	−22.4282	+	34.8990i	−0.799480	+	1.24402i	−0.966144	+	0.258002i	$0.916936\pi$
$788$	1.79639	−	6.11041i	0.0639937	−	0.217674i
$789$	−18.7493	+	2.69574i	−0.667491	+	0.0959708i
$790$	14.1862	+	13.5227i	0.504723	+	0.481117i
$791$	−0.830944	−	1.29297i	−0.0295450	−	0.0459729i
$792$	−7.08363	−	8.18320i	−0.251706	−	0.290777i
$793$	24.0051	−	52.5638i	0.852446	−	1.86660i
$794$	−7.54788	−	1.08650i	−0.267864	−	0.0385586i
$795$	−3.76347	+	2.96149i	−0.133476	+	0.105033i
$796$	−22.3805	+	48.9633i	−0.793256	+	1.73546i
$797$	48.8748	+	14.3509i	1.73123	+	0.508336i	0.987156	−	0.159756i	$-0.0510708\pi$
$797$	48.8748	+	14.3509i	1.73123	+	0.508336i	0.744078	+	0.668093i	$0.232889\pi$
$798$	−6.18575	+	2.82369i	−0.218973	+	0.0999577i
$799$	25.7254	+	29.6887i	0.910101	+	1.05031i
$800$	−22.2291	−	17.4890i	−0.785918	−	0.618330i
$801$	1.79454	+	1.55497i	0.0634068	+	0.0549423i
$802$	−9.74608	−	15.1707i	−0.344146	−	0.535698i
$803$	−15.0884	+	6.89063i	−0.532457	+	0.243165i
$804$	5.17691	+	8.06133i	0.182576	+	0.284301i
$805$	17.8039	−	35.6973i	0.627505	−	1.25816i
$806$	−43.1398	+	12.6592i	−1.51953	+	0.445901i
$807$	−6.44939	−	14.1222i	−0.227029	−	0.497125i
$808$	2.44585	−	5.34860i	0.0860447	−	0.188163i
$809$	−13.8736	+	16.0109i	−0.487768	+	0.562915i	−0.945268	−	0.326295i	$-0.894200\pi$
$809$	−13.8736	+	16.0109i	−0.487768	+	0.562915i	0.457500	+	0.889210i	$0.348745\pi$
$810$	−4.41141	−	7.63831i	−0.155001	−	0.268383i
$811$	−2.66020	+	2.30508i	−0.0934123	+	0.0809422i	−0.700315	−	0.713834i	$-0.746957\pi$
$811$	−2.66020	+	2.30508i	−0.0934123	+	0.0809422i	0.606903	+	0.794776i	$0.292412\pi$
$812$	−39.7892	+	34.4544i	−1.39633	+	1.20911i
$813$	−6.72773	+	22.9126i	−0.235952	+	0.803578i
$814$	−12.6966	+	14.6477i	−0.445016	+	0.513403i
$815$	−18.9933	+	14.9460i	−0.665307	+	0.523534i
$816$	11.2016	+	12.9448i	0.392135	+	0.453157i
$817$	2.28442	+	1.04326i	0.0799216	+	0.0364990i
$818$	−5.57207	−	38.8004i	−0.194823	−	1.35663i
$819$	43.4767	−	27.9408i	1.51920	−	0.976329i
$820$	−16.0926	−	8.29682i	−0.561977	−	0.289738i
$821$	−6.92378	−	48.1560i	−0.241642	−	1.68066i	−0.643885	−	0.765122i	$-0.722678\pi$
$821$	−6.92378	−	48.1560i	−0.241642	−	1.68066i	0.402243	−	0.915533i	$-0.368231\pi$
$822$	7.45653	+	4.79377i	0.260076	+	0.167202i
$823$	−39.0805	−	25.1155i	−1.36226	−	0.875472i	−0.363830	−	0.931465i	$-0.618531\pi$
$823$	−39.0805	−	25.1155i	−1.36226	−	0.875472i	−0.998431	+	0.0559932i	$0.982167\pi$
$824$	−32.3356	+	4.63268i	−1.12646	+	0.161387i
$825$	2.42118	+	6.98167i	0.0842948	+	0.243071i
$826$	34.5753	+	39.9154i	1.20303	+	1.38884i
$827$		−	25.6156i		−	0.890742i	−0.895346	−	0.445371i	$-0.853072\pi$
$827$		−	25.6156i		−	0.890742i	0.895346	−	0.445371i	$-0.146928\pi$
$828$	−8.70289	+	19.7163i	−0.302446	+	0.685188i
$829$	−7.46956			−0.259429			−0.129714	−	0.991551i	$-0.541406\pi$
$829$	−7.46956			−0.259429			−0.129714	+	0.991551i	$0.541406\pi$
$830$	32.8763	+	1.56146i	1.14115	+	0.0541990i
$831$	−0.722994	−	2.46229i	−0.0250804	−	0.0854160i
$832$	−26.7851	+	41.5870i	−0.928605	+	1.44177i
$833$	28.3653	+	18.2293i	0.982799	+	0.631606i
$834$	11.7169	−	18.2252i	0.405723	−	0.631087i
$835$	15.6605	−	22.0064i	0.541955	−	0.761564i
$836$	4.86825	−	1.42769i	0.168372	−	0.0493776i
$837$	12.6566	+	19.6940i	0.437475	+	0.680725i
$838$	2.23175	+	15.5406i	0.0770947	+	0.536840i
$839$	2.51592	−	5.50909i	0.0868591	−	0.190195i	−0.861218	−	0.508236i	$-0.830298\pi$
$839$	2.51592	−	5.50909i	0.0868591	−	0.190195i	0.948077	+	0.318041i	$0.103025\pi$
$840$	−19.2921	−	6.68123i	−0.665642	−	0.230524i
$841$	−2.99593	+	20.8372i	−0.103308	+	0.718523i
$842$	−11.5536	−	10.0147i	−0.398165	−	0.345128i
$843$	3.33005	−	11.3411i	0.114693	−	0.390608i
$844$	−12.4820	+	10.8084i	−0.429647	+	0.372041i
$845$	−2.66740	+	56.3598i	−0.0917614	+	1.93883i
$846$	24.2858	+	7.13535i	0.834964	+	0.245318i
$847$	22.7702	+	19.7305i	0.782394	+	0.677948i
$848$	−1.41140	+	9.77030i	−0.0484676	+	0.335514i
$849$	18.1733	−	8.29949i	0.623707	−	0.284838i
$850$	11.4200	+	32.9483i	0.391704	+	1.13012i
$851$	37.1743	+	10.3905i	1.27432	+	0.356181i
$852$	−7.03834	−	10.9599i	−0.241130	−	0.375480i
$853$	16.2921	−	7.44035i	0.557830	−	0.254753i	−0.116490	−	0.993192i	$-0.537164\pi$
$853$	16.2921	−	7.44035i	0.557830	−	0.254753i	0.674320	+	0.738439i	$0.264437\pi$
$854$	41.3632	−	26.5728i	1.41542	−	0.909302i
$855$	7.44936	−	0.713636i	0.254763	−	0.0244058i
$856$	−10.6639	−	36.3850i	−0.364484	−	1.24361i
$857$	7.60118	−	6.58646i	0.259652	−	0.224989i	−0.515300	−	0.857010i	$-0.672320\pi$
$857$	7.60118	−	6.58646i	0.259652	−	0.224989i	0.774952	+	0.632020i	$0.217774\pi$
$858$	11.7566	−	5.36671i	0.401365	−	0.183216i
$859$	3.73355	−	12.7153i	0.127387	−	0.433841i	−0.870957	−	0.491359i	$-0.836500\pi$
$859$	3.73355	−	12.7153i	0.127387	−	0.433841i	0.998344	+	0.0575178i	$0.0183186\pi$
$860$	2.80229	+	7.00031i	0.0955573	+	0.238709i
$861$	−12.9360	−	1.85991i	−0.440856	−	0.0633856i
$862$	2.35377	−	16.3515i	0.0801696	−	0.556934i
$863$	−13.3130	+	29.1513i	−0.453179	+	0.992323i	0.535811	+	0.844338i	$0.320006\pi$
$863$	−13.3130	+	29.1513i	−0.453179	+	0.992323i	−0.988990	+	0.147985i	$0.952721\pi$
$864$	24.7080	+	7.27726i	0.840583	+	0.247577i
$865$	−6.96945	+	36.2208i	−0.236968	+	1.23154i
$866$	6.47752	+	0.00107820i	0.220115	+	3.66387e-5i
$867$	−0.904045	−	6.28777i	−0.0307030	−	0.213544i
$868$	−36.6973	−	10.7886i	−1.24559	−	0.366188i
$869$	−8.87939	−	5.70644i	−0.301213	−	0.193578i
$870$	−18.0230	+	7.21826i	−0.611037	+	0.244722i
$871$	32.7488	−	9.61592i	1.10965	−	0.325823i
$872$	6.85679	−	23.3090i	0.232200	−	0.789343i
$873$	11.5824			0.392006
$874$	−6.71325	−	7.54880i	−0.227079	−	0.255342i
$875$	−31.4560	−	27.2061i	−1.06341	−	0.919733i
$876$	9.14401	−	14.2180i	0.308948	−	0.480380i
$877$	2.13659	+	7.27655i	0.0721475	+	0.245712i	0.987669	−	0.156558i	$-0.0500397\pi$
$877$	2.13659	+	7.27655i	0.0721475	+	0.245712i	−0.915521	+	0.402269i	$0.868222\pi$
$878$	−17.7482	−	8.10892i	−0.598974	−	0.273663i
$879$	2.64544	+	1.70012i	0.0892286	+	0.0573437i
$880$	13.5367	+	6.98480i	0.456322	+	0.235458i
$881$	40.9039	−	5.88109i	1.37809	−	0.198139i	0.586873	−	0.809679i	$-0.300359\pi$
$881$	40.9039	−	5.88109i	1.37809	−	0.198139i	0.791213	+	0.611540i	$0.209450\pi$
$882$	21.7259	+	0.00361634i	0.731550	+	0.000121769i
$883$	−12.4834	+	8.02257i	−0.420098	+	0.269981i	−0.733566	−	0.679618i	$-0.762146\pi$
$883$	−12.4834	+	8.02257i	−0.420098	+	0.269981i	0.313468	+	0.949599i	$0.398509\pi$
$884$	55.4835	−	25.3161i	1.86611	−	0.851474i
$885$	7.24521	+	18.0816i	0.243545	+	0.607806i
$886$	5.44963	−	37.8583i	0.183084	−	1.27187i
$887$	−4.55568	+	31.6855i	−0.152965	+	1.06389i	0.758251	+	0.651963i	$0.226054\pi$
$887$	−4.55568	+	31.6855i	−0.152965	+	1.06389i	−0.911215	+	0.411930i	$0.864855\pi$
$888$	2.82122	−	19.5527i	0.0946740	−	0.656146i
$889$	6.48295	−	22.0789i	0.217431	−	0.740502i
$890$	−3.15822	−	1.09257i	−0.105864	−	0.0366231i
$891$	3.11084	+	3.59010i	0.104217	+	0.120273i
$892$	30.2044	+	0.0100552i	1.01132	+	0.000336673i
$893$	−7.76984	+	8.96687i	−0.260008	+	0.300065i
$894$	3.99740	+	6.22236i	0.133693	+	0.208107i
$895$	−50.4641	−	17.4485i	−1.68683	−	0.583238i
$896$	−38.3023	+	17.4382i	−1.27959	+	0.582569i
$897$	−19.6666	−	16.5970i	−0.656650	−	0.554157i
$898$	1.92843	−	0.565888i	0.0643524	−	0.0188839i
$899$	−33.0868	+	15.1102i	−1.10351	+	0.503954i
$900$	17.6658	+	13.8845i	0.588861	+	0.462817i
$901$	7.97011	−	9.19800i	0.265523	−	0.306430i
$902$	9.35528	+	2.74865i	0.311497	+	0.0915201i
$903$	3.56429	+	4.11341i	0.118612	+	0.136886i
$904$	−0.982814	−	0.632310i	−0.0326879	−	0.0210303i
$905$	29.5640	−	17.0809i	0.982741	−	0.567788i
$906$	5.49528	+	4.76328i	0.182568	+	0.158250i
$907$	−0.842536	−	0.121138i	−0.0279759	−	0.00402233i	0.128313	−	0.991734i	$-0.459044\pi$
$907$	−0.842536	−	0.121138i	−0.0279759	−	0.00402233i	−0.156289	+	0.987711i	$0.549953\pi$
$908$	−30.2426	+	4.33796i	−1.00364	+	0.143960i
$909$	−1.94087	+	4.24991i	−0.0643746	+	0.140961i
$910$	−42.1821	+	59.2541i	−1.39832	+	1.96425i
$911$	10.1136	−	6.49959i	0.335077	−	0.215341i	−0.362272	−	0.932072i	$-0.617999\pi$
$911$	10.1136	−	6.49959i	0.335077	−	0.215341i	0.697349	+	0.716731i	$0.254363\pi$
$912$	−3.38842	+	3.90519i	−0.112202	+	0.129314i
$913$	−17.5451	+	2.52260i	−0.580658	+	0.0834860i
$914$	33.1577	+	21.3170i	1.09676	+	0.705102i
$915$	17.6222	−	4.28083i	0.582571	−	0.141520i
$916$	6.11473	+	0.881244i	0.202036	+	0.0291171i
$917$	48.4673	−	14.2313i	1.60053	−	0.469958i
$918$	−20.7917	−	24.0030i	−0.686228	−	0.792216i
$919$	−0.531098			−0.0175193			−0.00875966	−	0.999962i	$-0.502788\pi$
$919$	−0.531098			−0.0175193			−0.00875966	+	0.999962i	$0.502788\pi$
$920$	1.05364	−	30.3132i	0.0347376	−	0.999396i
$921$	−3.19438			−0.105258
$922$	−22.1118	−	25.5270i	−0.728214	−	0.840687i
$923$	−44.5240	+	13.0734i	−1.46553	+	0.430318i
$924$	10.8828	+	1.56841i	0.358017	+	0.0515967i
$925$	20.0998	−	34.8633i	0.660876	−	1.14630i
$926$	19.0836	+	12.2688i	0.627126	+	0.403177i
$927$	25.6856	−	3.69304i	0.843627	−	0.121295i
$928$	−16.6554	+	36.3901i	−0.546742	+	1.19456i
$929$	−40.9273	+	26.3024i	−1.34278	+	0.862954i	−0.997152	−	0.0754165i	$-0.975971\pi$
$929$	−40.9273	+	26.3024i	−1.34278	+	0.862954i	−0.345631	+	0.938371i	$0.612335\pi$
$930$	−11.4942	−	8.18255i	−0.376910	−	0.268316i
$931$	−4.23050	+	9.26350i	−0.138649	+	0.303599i
$932$	−23.1993	+	3.32768i	−0.759920	+	0.109002i
$933$	3.09886	+	0.445548i	0.101452	+	0.0145866i
$934$	12.7637	+	11.0635i	0.417640	+	0.362009i
$935$	−9.39497	−	16.2610i	−0.307248	−	0.531792i
$936$	21.2616	−	33.0474i	0.694958	−	1.08019i
$937$	6.42532	+	7.41521i	0.209906	+	0.242244i	0.850933	−	0.525274i	$-0.176037\pi$
$937$	6.42532	+	7.41521i	0.209906	+	0.242244i	−0.641027	+	0.767518i	$0.721492\pi$
$938$	27.8608	+	8.18571i	0.909687	+	0.267273i
$939$	1.80362	−	2.08149i	0.0588589	−	0.0679268i
$940$	−35.4631	+	3.38539i	−1.15668	+	0.110419i
$941$	45.7388	−	20.8882i	1.49104	−	0.680936i	0.507506	−	0.861648i	$-0.330567\pi$
$941$	45.7388	−	20.8882i	1.49104	−	0.680936i	0.983536	+	0.180712i	$0.0578401\pi$
$942$	22.8551	−	6.70674i	0.744660	−	0.218517i
$943$	−3.01369	−	19.1806i	−0.0981392	−	0.624608i
$944$	36.5136	+	16.7046i	1.18842	+	0.543689i
$945$	35.7943	+	12.3762i	1.16439	+	0.402599i
$946$	−2.19490	−	3.41659i	−0.0713625	−	0.111083i
$947$	26.5496	−	30.6399i	0.862747	−	0.995664i	−0.137239	−	0.990538i	$-0.543823\pi$
$947$	26.5496	−	30.6399i	0.862747	−	0.995664i	0.999987	−	0.00512574i	$-0.00163158\pi$
$948$	10.7568	+	0.00358099i	0.349364	+	0.000116305i
$949$	−39.4383	−	45.5143i	−1.28022	−	1.47746i
$950$	−9.35918	+	4.83030i	−0.303652	+	0.156716i
$951$	3.42479	−	11.6638i	0.111056	−	0.378223i
$952$	51.3543	+	7.40982i	1.66440	+	0.240154i
$953$	1.07915	−	7.50565i	0.0349571	−	0.243132i	−0.964849	−	0.262803i	$-0.915353\pi$
$953$	1.07915	−	7.50565i	0.0349571	−	0.243132i	0.999806	+	0.0196715i	$0.00626203\pi$
$954$	1.11734	−	7.76212i	0.0361753	−	0.251308i
$955$	0.432853	−	0.173442i	0.0140068	−	0.00561246i
$956$	34.1384	−	15.5768i	1.10412	−	0.503788i
$957$	8.79599	−	5.65284i	0.284334	−	0.182730i
$958$	3.04279		0.000506482i	0.0983082		1.63637e-5i
$959$	26.5949	−	3.82377i	0.858795	−	0.123476i
$960$	−15.4545	+	1.46494i	−0.498793	+	0.0472808i
$961$	3.84126	+	2.46863i	0.123912	+	0.0796331i
$962$	−64.0148	−	29.2475i	−2.06392	−	0.942976i
$963$	8.48585	+	28.9001i	0.273453	+	0.931294i
$964$	1.11095	−	1.72740i	0.0357812	−	0.0556359i
$965$	28.2787	−	29.6761i	0.910325	−	0.955308i
$966$	−6.43834	−	20.9260i	−0.207150	−	0.673283i
$967$	32.9757			1.06043			0.530214	−	0.847864i	$-0.322112\pi$
$967$	32.9757			1.06043			0.530214	+	0.847864i	$0.322112\pi$
$968$	21.9780	+	6.46525i	0.706400	+	0.207801i
$969$	6.11617	−	1.79587i	0.196480	−	0.0576916i
$970$	−15.1325	+	6.06059i	−0.485874	+	0.194594i
$971$	−11.1105	−	7.14030i	−0.356553	−	0.229143i	0.350085	−	0.936718i	$-0.386153\pi$
$971$	−11.1105	−	7.14030i	−0.356553	−	0.229143i	−0.706638	+	0.707575i	$0.749789\pi$
$972$	−30.8553	−	9.07109i	−0.989684	−	0.290955i
$973$	−9.34604	−	65.0031i	−0.299620	−	2.08390i
$974$	−0.355625		5.91947e-5i	−0.0113950		1.89672e-6i
$975$	−21.8451	+	15.5761i	−0.699603	+	0.498833i
$976$	20.2311	−	31.4342i	0.647583	−	1.00619i
$977$	−20.1031	+	44.0196i	−0.643154	+	1.40831i	0.254265	+	0.967134i	$0.418166\pi$
$977$	−20.1031	+	44.0196i	−0.643154	+	1.40831i	−0.897420	+	0.441177i	$0.854561\pi$
$978$	−1.88999	+	13.1297i	−0.0604353	+	0.419841i
$979$	1.78144	+	0.256133i	0.0569352	+	0.00818604i
$980$	−28.3868	+	11.3635i	−0.906784	+	0.362995i
$981$	−5.43781	+	18.5195i	−0.173616	+	0.591281i
$982$	−9.67643	+	4.41713i	−0.308787	+	0.140956i
$983$	−30.8624	+	26.7424i	−0.984356	+	0.852950i	−0.989131	−	0.147039i	$-0.953026\pi$
$983$	−30.8624	+	26.7424i	−0.984356	+	0.852950i	0.00477445	+	0.999989i	$0.498480\pi$
$984$	−9.53605	+	2.79486i	−0.303998	+	0.0890970i
$985$	−0.679047	−	7.08830i	−0.0216362	−	0.225852i
$986$	41.5125	−	26.6687i	1.32203	−	0.849305i
$987$	−23.3907	+	10.6822i	−0.744536	+	0.340018i
$988$	9.95326	+	15.4989i	0.316655	+	0.493086i
$989$	−4.28257	+	6.85896i	−0.136178	+	0.218102i
$990$	−10.7564	−	5.54338i	−0.341860	−	0.176180i
$991$	10.4590	−	4.77644i	0.332240	−	0.151729i	−0.242309	−	0.970199i	$-0.577905\pi$
$991$	10.4590	−	4.77644i	0.332240	−	0.151729i	0.574549	+	0.818470i	$0.305178\pi$
$992$	−28.7915	+	4.11514i	−0.914131	+	0.130656i
$993$	13.3933	+	11.6054i	0.425024	+	0.368286i
$994$	−37.8785	−	11.1290i	−1.20143	−	0.352990i
$995$	−2.84551	+	60.1229i	−0.0902086	+	1.90603i
$996$	13.6562	−	11.8252i	0.432712	−	0.374695i
$997$	−0.733341	+	2.49753i	−0.0232252	+	0.0790976i	−0.970290	−	0.241944i	$-0.922215\pi$
$997$	−0.733341	+	2.49753i	−0.0232252	+	0.0790976i	0.947065	+	0.321042i	$0.104033\pi$
$998$	9.94347	+	8.61896i	0.314755	+	0.272828i
$999$	−5.21543	+	36.2741i	−0.165009	+	1.14766i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.o.b.19.19	✓	640
4.3	odd	2	inner	460.2.o.b.19.34	yes	640
5.4	even	2	inner	460.2.o.b.19.46	yes	640
20.19	odd	2	inner	460.2.o.b.19.31	yes	640
23.17	odd	22	inner	460.2.o.b.339.31	yes	640
92.63	even	22	inner	460.2.o.b.339.46	yes	640
115.109	odd	22	inner	460.2.o.b.339.34	yes	640
460.339	even	22	inner	460.2.o.b.339.19	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.o.b.19.19	✓	640	1.1	even	1	trivial
460.2.o.b.19.31	yes	640	20.19	odd	2	inner
460.2.o.b.19.34	yes	640	4.3	odd	2	inner
460.2.o.b.19.46	yes	640	5.4	even	2	inner
460.2.o.b.339.19	yes	640	460.339	even	22	inner
460.2.o.b.339.31	yes	640	23.17	odd	22	inner
460.2.o.b.339.34	yes	640	115.109	odd	22	inner
460.2.o.b.339.46	yes	640	92.63	even	22	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.925935 - 1.06895i) q^{2} +(-0.832655 + 0.244489i) q^{3} +(-0.285289 + 1.97955i) q^{4} +(0.527840 + 2.17287i) q^{5} +(1.03233 + 0.663681i) q^{6} +(3.68197 - 0.529388i) q^{7} +(2.38019 - 1.52797i) q^{8} +(-1.89022 + 1.21477i) q^{9} +O(q^{10})\)	\(q+(-0.925935 - 1.06895i) q^{2} +(-0.832655 + 0.244489i) q^{3} +(-0.285289 + 1.97955i) q^{4} +(0.527840 + 2.17287i) q^{5} +(1.03233 + 0.663681i) q^{6} +(3.68197 - 0.529388i) q^{7} +(2.38019 - 1.52797i) q^{8} +(-1.89022 + 1.21477i) q^{9} +(1.83394 - 2.57617i) q^{10} +(-0.707471 + 1.54915i) q^{11} +(-0.246432 - 1.71803i) q^{12} +(-6.12035 - 0.879974i) q^{13} +(-3.97516 - 3.44565i) q^{14} +(-0.970754 - 1.68020i) q^{15} +(-3.83722 - 1.12949i) q^{16} +(3.22947 + 3.72701i) q^{17} +(3.04875 + 0.895744i) q^{18} +(-0.975396 + 1.12567i) q^{19} +(-4.45190 + 0.424989i) q^{20} +(-2.93638 + 1.34100i) q^{21} +(2.31103 - 0.678160i) q^{22} +(-3.18762 - 3.58316i) q^{23} +(-1.60830 + 1.85421i) q^{24} +(-4.44277 + 2.29386i) q^{25} +(4.72640 + 7.35712i) q^{26} +(2.98178 - 3.44116i) q^{27} +(-0.00247671 + 7.43967i) q^{28} +(4.63295 + 5.34670i) q^{29} +(-0.897190 + 2.59344i) q^{30} +(-1.44850 + 4.93313i) q^{31} +(2.34566 + 5.14761i) q^{32} +(0.210329 - 1.46287i) q^{33} +(0.993689 - 6.90310i) q^{34} +(3.09379 + 7.72104i) q^{35} +(-1.86544 - 4.08835i) q^{36} +(-6.77081 + 4.35133i) q^{37} +(2.10643 + 0.000350621i) q^{38} +(5.31128 - 0.763647i) q^{39} +(4.57646 + 4.36532i) q^{40} +(3.40582 + 2.18879i) q^{41} +(4.15236 + 1.89715i) q^{42} +(-0.475023 - 1.61778i) q^{43} +(-2.86478 - 1.84243i) q^{44} +(-3.63728 - 3.46601i) q^{45} +(-0.878674 + 6.72517i) q^{46} +7.96584 q^{47} +(3.47123 + 0.00231118i) q^{48} +(6.56023 - 1.92626i) q^{49} +(6.56573 + 2.62511i) q^{50} +(-3.60025 - 2.31374i) q^{51} +(3.48802 - 11.8645i) q^{52} +(-0.351223 - 2.44281i) q^{53} +(-6.43935 - 0.00107185i) q^{54} +(-3.73953 - 0.719545i) q^{55} +(7.95490 - 6.88601i) q^{56} +(0.536954 - 1.17577i) q^{57} +(1.42553 - 9.90307i) q^{58} +(-9.93615 - 1.42860i) q^{59} +(3.60299 - 1.44231i) q^{60} +(-2.63293 + 8.96693i) q^{61} +(6.61446 - 3.01939i) q^{62} +(-6.31666 + 5.47342i) q^{63} +(3.33059 - 7.27373i) q^{64} +(-1.31850 - 13.7632i) q^{65} +(-1.75848 + 1.12969i) q^{66} +(-5.02111 + 2.29306i) q^{67} +(-8.29913 + 5.32962i) q^{68} +(3.53024 + 2.20420i) q^{69} +(5.38872 - 10.4563i) q^{70} +(6.82651 - 3.11756i) q^{71} +(-2.64294 + 5.77960i) q^{72} +(7.36085 + 6.37821i) q^{73} +(10.9207 + 3.20857i) q^{74} +(3.13847 - 2.99620i) q^{75} +(-1.95004 - 2.25198i) q^{76} +(-1.78479 + 6.07844i) q^{77} +(-5.73420 - 4.97038i) q^{78} +(-0.882022 + 6.13460i) q^{79} +(0.428791 - 8.93399i) q^{80} +(1.15873 - 2.53728i) q^{81} +(-0.813873 - 5.66731i) q^{82} +(5.62706 + 8.75587i) q^{83} +(-1.81686 - 6.19528i) q^{84} +(-6.39368 + 8.98450i) q^{85} +(-1.28948 + 2.00573i) q^{86} +(-5.16486 - 3.31925i) q^{87} +(0.683142 + 4.76826i) q^{88} +(-0.297732 - 1.01398i) q^{89} +(-0.337089 + 7.09736i) q^{90} -23.0008 q^{91} +(8.00244 - 5.28782i) q^{92} -4.46173i q^{93} +(-7.37585 - 8.51504i) q^{94} +(-2.96079 - 1.52524i) q^{95} +(-3.21166 - 3.71269i) q^{96} +(-4.33652 - 2.78691i) q^{97} +(-8.13341 - 5.22894i) q^{98} +(-0.544581 - 3.78765i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9}+O(q^{10}) \) 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9	\( 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9} - 11 q^{10} - 22 q^{14} + 2 q^{16} - 11 q^{20} - 44 q^{21} - 8 q^{24} - 38 q^{25} - 46 q^{26} - 52 q^{29} - 11 q^{30} - 44 q^{34} + 18 q^{36} - 11 q^{40} - 76 q^{41} - 154 q^{44} - 30 q^{46} - 100 q^{49} + 21 q^{50} + 178 q^{54} + 242 q^{56} - 11 q^{60} - 44 q^{61} + 6 q^{64} - 22 q^{65} + 44 q^{66} - 12 q^{69} + 22 q^{70} - 22 q^{74} + 88 q^{76} - 110 q^{80} - 252 q^{81} - 374 q^{84} + 94 q^{85} - 198 q^{86} - 44 q^{89} - 242 q^{90} - 62 q^{94} + 372 q^{96}+O(q^{100}) \) 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9 - 11 * q^10 - 22 * q^14 + 2 * q^16 - 11 * q^20 - 44 * q^21 - 8 * q^24 - 38 * q^25 - 46 * q^26 - 52 * q^29 - 11 * q^30 - 44 * q^34 + 18 * q^36 - 11 * q^40 - 76 * q^41 - 154 * q^44 - 30 * q^46 - 100 * q^49 + 21 * q^50 + 178 * q^54 + 242 * q^56 - 11 * q^60 - 44 * q^61 + 6 * q^64 - 22 * q^65 + 44 * q^66 - 12 * q^69 + 22 * q^70 - 22 * q^74 + 88 * q^76 - 110 * q^80 - 252 * q^81 - 374 * q^84 + 94 * q^85 - 198 * q^86 - 44 * q^89 - 242 * q^90 - 62 * q^94 + 372 * q^96

Introduction

L-functions

Modular forms

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