LMFDB - Embedded newform 150.2.l.a.77.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(17,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("150.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.l (of order $20$, degree $8$, 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:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			77.6
Character	$\chi$	$=$	150.77
Dual form			150.2.l.a.113.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.156434 - 0.987688i) q^{2} +(-1.50729 + 0.853283i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(0.919260 + 2.03837i) q^{5} +(0.606986 + 1.62221i) q^{6} +(2.93554 + 2.93554i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(1.54382 - 2.57228i) q^{9} +O(q^{10})$	\(q+(0.156434 - 0.987688i) q^{2} +(-1.50729 + 0.853283i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(0.919260 + 2.03837i) q^{5} +(0.606986 + 1.62221i) q^{6} +(2.93554 + 2.93554i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(1.54382 - 2.57228i) q^{9} +(2.15708 - 0.589071i) q^{10} +(-0.613906 - 0.844968i) q^{11} +(1.69719 - 0.345744i) q^{12} +(0.542627 - 0.0859436i) q^{13} +(3.35862 - 2.44018i) q^{14} +(-3.12490 - 2.28802i) q^{15} +(0.809017 + 0.587785i) q^{16} +(4.43491 + 2.25970i) q^{17} +(-2.29911 - 1.92720i) q^{18} +(-5.82500 + 1.89266i) q^{19} +(-0.244377 - 2.22267i) q^{20} +(-6.92954 - 1.91985i) q^{21} +(-0.930602 + 0.474165i) q^{22} +(-0.754303 - 0.119470i) q^{23} +(-0.0759877 - 1.73038i) q^{24} +(-3.30992 + 3.74759i) q^{25} -0.549391i q^{26} +(-0.132087 + 5.19447i) q^{27} +(-1.88473 - 3.69899i) q^{28} +(2.30581 - 7.09654i) q^{29} +(-2.74869 + 2.72850i) q^{30} +(-0.786024 - 2.41913i) q^{31} +(0.707107 - 0.707107i) q^{32} +(1.64633 + 0.749773i) q^{33} +(2.92565 - 4.02682i) q^{34} +(-3.28520 + 8.68224i) q^{35} +(-2.26314 + 1.96932i) q^{36} +(-1.45972 - 9.21632i) q^{37} +(0.958124 + 6.04936i) q^{38} +(-0.744559 + 0.592556i) q^{39} +(-2.23354 - 0.106335i) q^{40} +(5.89166 - 8.10918i) q^{41} +(-2.98023 + 6.54389i) q^{42} +(0.405017 - 0.405017i) q^{43} +(0.322749 + 0.993320i) q^{44} +(6.66244 + 0.782276i) q^{45} +(-0.235998 + 0.726327i) q^{46} +(-0.320136 - 0.628302i) q^{47} +(-1.72097 - 0.195639i) q^{48} +10.2348i q^{49} +(3.18366 + 3.85542i) q^{50} +(-8.61284 + 0.378222i) q^{51} +(-0.542627 - 0.0859436i) q^{52} +(-6.82529 + 3.47766i) q^{53} +(5.10986 + 0.943055i) q^{54} +(1.15802 - 2.02811i) q^{55} +(-3.94829 + 1.28288i) q^{56} +(7.16496 - 7.82314i) q^{57} +(-6.64846 - 3.38756i) q^{58} +(-0.444196 - 0.322728i) q^{59} +(2.26492 + 3.14168i) q^{60} +(5.77332 - 4.19456i) q^{61} +(-2.51231 + 0.397911i) q^{62} +(12.0830 - 3.01910i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(0.674000 + 1.02707i) q^{65} +(0.998085 - 1.50877i) q^{66} +(4.27513 - 8.39042i) q^{67} +(-3.51957 - 3.51957i) q^{68} +(1.23889 - 0.463559i) q^{69} +(8.06143 + 4.60295i) q^{70} +(-4.73186 - 1.53747i) q^{71} +(1.59104 + 2.54334i) q^{72} +(-2.24264 + 14.1595i) q^{73} -9.33120 q^{74} +(1.79124 - 8.47298i) q^{75} +6.12476 q^{76} +(0.678294 - 4.28258i) q^{77} +(0.468786 + 0.828088i) q^{78} +(9.92188 + 3.22381i) q^{79} +(-0.454428 + 2.18941i) q^{80} +(-4.23326 - 7.94226i) q^{81} +(-7.08768 - 7.08768i) q^{82} +(1.84695 - 3.62484i) q^{83} +(5.99712 + 3.96723i) q^{84} +(-0.529273 + 11.1173i) q^{85} +(-0.336672 - 0.463389i) q^{86} +(2.57985 + 12.6640i) q^{87} +(1.03158 - 0.163386i) q^{88} +(7.67825 - 5.57858i) q^{89} +(1.81488 - 6.45803i) q^{90} +(1.84519 + 1.34061i) q^{91} +(0.680467 + 0.346715i) q^{92} +(3.24897 + 2.97562i) q^{93} +(-0.670646 + 0.217906i) q^{94} +(-9.21262 - 10.1337i) q^{95} +(-0.462449 + 1.66917i) q^{96} +(-1.77470 + 0.904255i) q^{97} +(10.1088 + 1.60107i) q^{98} +(-3.12125 + 0.274662i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q + 4 * q^3 + 4 * q^7	$ 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) $ 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{1}{20}\right)$

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 $

$2$	0.156434	−	0.987688i	0.110616	−	0.698401i
$2$	0.156434	−	0.987688i	0.110616	−	0.698401i
$3$	−1.50729	+	0.853283i	−0.870231	+	0.492643i
$3$	−1.50729	+	0.853283i	−0.870231	+	0.492643i
$4$	−0.951057	−	0.309017i	−0.475528	−	0.154508i
$5$	0.919260	+	2.03837i	0.411106	+	0.911588i
$5$	0.919260	+	2.03837i	0.411106	+	0.911588i
$6$	0.606986	+	1.62221i	0.247801	+	0.662265i
$7$	2.93554	+	2.93554i	1.10953	+	1.10953i	0.993212	+	0.116317i	$0.0371088\pi$
$7$	2.93554	+	2.93554i	1.10953	+	1.10953i	0.116317	+	0.993212i	$0.462891\pi$
$8$	−0.453990	+	0.891007i	−0.160510	+	0.315018i
$9$	1.54382	−	2.57228i	0.514605	−	0.857427i
$10$	2.15708	−	0.589071i	0.682129	−	0.186281i
$11$	−0.613906	−	0.844968i	−0.185099	−	0.254768i	0.706376	−	0.707837i	$-0.250329\pi$
$11$	−0.613906	−	0.844968i	−0.185099	−	0.254768i	−0.891475	+	0.453070i	$0.850329\pi$
$12$	1.69719	−	0.345744i	0.489937	−	0.0998076i
$13$	0.542627	−	0.0859436i	0.150498	−	0.0238365i	−0.0807310	−	0.996736i	$-0.525725\pi$
$13$	0.542627	−	0.0859436i	0.150498	−	0.0238365i	0.231229	+	0.972899i	$0.425725\pi$
$14$	3.35862	−	2.44018i	0.897628	−	0.652165i
$15$	−3.12490	−	2.28802i	−0.806845	−	0.590764i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	4.43491	+	2.25970i	1.07562	+	0.548058i	0.899773	−	0.436359i	$-0.143732\pi$
$17$	4.43491	+	2.25970i	1.07562	+	0.548058i	0.175851	+	0.984417i	$0.443732\pi$
$18$	−2.29911	−	1.92720i	−0.541905	−	0.454246i
$19$	−5.82500	+	1.89266i	−1.33635	+	0.434205i	−0.888077	−	0.459694i	$-0.847959\pi$
$19$	−5.82500	+	1.89266i	−1.33635	+	0.434205i	−0.448268	+	0.893899i	$0.647959\pi$
$20$	−0.244377	−	2.22267i	−0.0546443	−	0.497005i
$21$	−6.92954	−	1.91985i	−1.51215	−	0.418945i
$22$	−0.930602	+	0.474165i	−0.198405	+	0.101092i
$23$	−0.754303	−	0.119470i	−0.157283	−	0.0249112i	0.0772962	−	0.997008i	$-0.475371\pi$
$23$	−0.754303	−	0.119470i	−0.157283	−	0.0249112i	−0.234579	+	0.972097i	$0.575371\pi$
$24$	−0.0759877	−	1.73038i	−0.0155109	−	0.353213i
$25$	−3.30992	+	3.74759i	−0.661984	+	0.749518i
$26$		−	0.549391i		−	0.107744i
$27$	−0.132087	+	5.19447i	−0.0254201	+	0.999677i
$28$	−1.88473	−	3.69899i	−0.356181	−	0.699044i
$29$	2.30581	−	7.09654i	0.428177	−	1.31779i	−0.471741	−	0.881737i	$-0.656374\pi$
$29$	2.30581	−	7.09654i	0.428177	−	1.31779i	0.899919	−	0.436058i	$-0.143626\pi$
$30$	−2.74869	+	2.72850i	−0.501840	+	0.498153i
$31$	−0.786024	−	2.41913i	−0.141174	−	0.434489i	0.855325	−	0.518092i	$-0.173357\pi$
$31$	−0.786024	−	2.41913i	−0.141174	−	0.434489i	−0.996499	+	0.0836026i	$0.973357\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	1.64633	+	0.749773i	0.286589	+	0.130519i
$34$	2.92565	−	4.02682i	0.501745	−	0.690593i
$35$	−3.28520	+	8.68224i	−0.555299	+	1.46757i
$36$	−2.26314	+	1.96932i	−0.377189	+	0.328220i
$37$	−1.45972	−	9.21632i	−0.239977	−	1.51515i	−0.753712	−	0.657205i	$-0.771739\pi$
$37$	−1.45972	−	9.21632i	−0.239977	−	1.51515i	0.513735	−	0.857949i	$-0.328261\pi$
$38$	0.958124	+	6.04936i	0.155428	+	0.981335i
$39$	−0.744559	+	0.592556i	−0.119225	+	0.0948849i
$40$	−2.23354	−	0.106335i	−0.353153	−	0.0168130i
$41$	5.89166	−	8.10918i	0.920123	−	1.26644i	−0.0434660	−	0.999055i	$-0.513840\pi$
$41$	5.89166	−	8.10918i	0.920123	−	1.26644i	0.963589	−	0.267386i	$-0.0861600\pi$
$42$	−2.98023	+	6.54389i	−0.459859	+	1.00974i
$43$	0.405017	−	0.405017i	0.0617645	−	0.0617645i	−0.675550	−	0.737314i	$-0.736094\pi$
$43$	0.405017	−	0.405017i	0.0617645	−	0.0617645i	0.737314	+	0.675550i	$0.236094\pi$
$44$	0.322749	+	0.993320i	0.0486563	+	0.149749i
$45$	6.66244	+	0.782276i	0.993177	+	0.116615i
$46$	−0.235998	+	0.726327i	−0.0347960	+	0.107091i
$47$	−0.320136	−	0.628302i	−0.0466966	−	0.0916472i	0.866479	−	0.499213i	$-0.166378\pi$
$47$	−0.320136	−	0.628302i	−0.0466966	−	0.0916472i	−0.913176	+	0.407566i	$0.866378\pi$
$48$	−1.72097	−	0.195639i	−0.248400	−	0.0282381i
$49$			10.2348i			1.46211i
$50$	3.18366	+	3.85542i	0.450238	+	0.545239i
$51$	−8.61284	+	0.378222i	−1.20604	+	0.0529617i
$52$	−0.542627	−	0.0859436i	−0.0752488	−	0.0119182i
$53$	−6.82529	+	3.47766i	−0.937526	+	0.477693i	−0.854845	−	0.518883i	$-0.826348\pi$
$53$	−6.82529	+	3.47766i	−0.937526	+	0.477693i	−0.0826807	+	0.996576i	$0.526348\pi$
$54$	5.10986	+	0.943055i	0.695364	+	0.128334i
$55$	1.15802	−	2.02811i	0.156148	−	0.273471i
$56$	−3.94829	+	1.28288i	−0.527612	+	0.171432i
$57$	7.16496	−	7.82314i	0.949022	−	1.03620i
$58$	−6.64846	−	3.38756i	−0.872986	−	0.444809i
$59$	−0.444196	−	0.322728i	−0.0578294	−	0.0420156i	0.558495	−	0.829508i	$-0.311379\pi$
$59$	−0.444196	−	0.322728i	−0.0578294	−	0.0420156i	−0.616324	+	0.787492i	$0.711379\pi$
$60$	2.26492	+	3.14168i	0.292399	+	0.405589i
$61$	5.77332	−	4.19456i	0.739198	−	0.537059i	−0.153262	−	0.988186i	$-0.548978\pi$
$61$	5.77332	−	4.19456i	0.739198	−	0.537059i	0.892460	+	0.451127i	$0.148978\pi$
$62$	−2.51231	+	0.397911i	−0.319064	+	0.0505347i
$63$	12.0830	−	3.01910i	1.52231	−	0.380371i
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$	0.674000	+	1.02707i	0.0835994	+	0.127392i
$66$	0.998085	−	1.50877i	0.122856	−	0.185717i
$67$	4.27513	−	8.39042i	0.522290	−	1.02505i	−0.467696	−	0.883889i	$-0.654916\pi$
$67$	4.27513	−	8.39042i	0.522290	−	1.02505i	0.989986	−	0.141163i	$-0.0450843\pi$
$68$	−3.51957	−	3.51957i	−0.426810	−	0.426810i
$69$	1.23889	−	0.463559i	0.149145	−	0.0558059i
$70$	8.06143	+	4.60295i	0.963525	+	0.550158i
$71$	−4.73186	−	1.53747i	−0.561568	−	0.182465i	0.0144583	−	0.999895i	$-0.495398\pi$
$71$	−4.73186	−	1.53747i	−0.561568	−	0.182465i	−0.576027	+	0.817431i	$0.695398\pi$
$72$	1.59104	+	2.54334i	0.187506	+	0.299736i
$73$	−2.24264	+	14.1595i	−0.262481	+	1.65724i	0.406268	+	0.913754i	$0.366830\pi$
$73$	−2.24264	+	14.1595i	−0.262481	+	1.65724i	−0.668749	+	0.743488i	$0.733170\pi$
$74$	−9.33120			−1.08473
$75$	1.79124	−	8.47298i	0.206835	−	0.978376i
$76$	6.12476			0.702558
$77$	0.678294	−	4.28258i	0.0772988	−	0.488045i
$78$	0.468786	+	0.828088i	0.0530795	+	0.0937625i
$79$	9.92188	+	3.22381i	1.11630	+	0.362708i	0.808354	−	0.588697i	$-0.200359\pi$
$79$	9.92188	+	3.22381i	1.11630	+	0.362708i	0.307945	+	0.951404i	$0.400359\pi$
$80$	−0.454428	+	2.18941i	−0.0508066	+	0.244783i
$81$	−4.23326	−	7.94226i	−0.470363	−	0.882473i
$82$	−7.08768	−	7.08768i	−0.782704	−	0.782704i
$83$	1.84695	−	3.62484i	0.202729	−	0.397878i	−0.767149	−	0.641469i	$-0.778325\pi$
$83$	1.84695	−	3.62484i	0.202729	−	0.397878i	0.969878	+	0.243591i	$0.0783254\pi$
$84$	5.99712	+	3.96723i	0.654339	+	0.432860i
$85$	−0.529273	+	11.1173i	−0.0574077	+	1.20584i
$86$	−0.336672	−	0.463389i	−0.0363043	−	0.0499685i
$87$	2.57985	+	12.6640i	0.276589	+	1.35773i
$88$	1.03158	−	0.163386i	0.109967	−	0.0174170i
$89$	7.67825	−	5.57858i	0.813893	−	0.591328i	−0.101064	−	0.994880i	$-0.532225\pi$
$89$	7.67825	−	5.57858i	0.813893	−	0.591328i	0.914957	+	0.403552i	$0.132225\pi$
$90$	1.81488	−	6.45803i	0.191305	−	0.680737i
$91$	1.84519	+	1.34061i	0.193429	+	0.140534i
$92$	0.680467	+	0.346715i	0.0709436	+	0.0361476i
$93$	3.24897	+	2.97562i	0.336902	+	0.308558i
$94$	−0.670646	+	0.217906i	−0.0691719	+	0.0224753i
$95$	−9.21262	−	10.1337i	−0.945195	−	1.03969i
$96$	−0.462449	+	1.66917i	−0.0471985	+	0.170359i
$97$	−1.77470	+	0.904255i	−0.180193	+	0.0918132i	−0.541760	−	0.840533i	$-0.682242\pi$
$97$	−1.77470	+	0.904255i	−0.180193	+	0.0918132i	0.361567	+	0.932346i	$0.382242\pi$
$98$	10.1088	+	1.60107i	1.02114	+	0.161732i
$99$	−3.12125	+	0.274662i	−0.313698	+	0.0276046i
$100$	4.30599	−	2.54135i	0.430599	−	0.254135i
$101$			13.1778i			1.31124i	0.755090	+	0.655621i	$0.227593\pi$
$101$			13.1778i			1.31124i	−0.755090	+	0.655621i	$0.772407\pi$
$102$	−0.973779	+	8.56597i	−0.0964185	+	0.848157i
$103$	−3.79637	−	7.45080i	−0.374068	−	0.734149i	0.624846	−	0.780748i	$-0.285162\pi$
$103$	−3.79637	−	7.45080i	−0.374068	−	0.734149i	−0.998914	+	0.0465989i	$0.985162\pi$
$104$	−0.169771	+	0.522502i	−0.0166474	+	0.0512355i
$105$	−2.45668	−	15.8898i	−0.239748	−	1.55069i
$106$	2.36713	+	7.28529i	0.229916	+	0.707610i
$107$	−7.96897	+	7.96897i	−0.770389	+	0.770389i	−0.978174	−	0.207785i	$-0.933374\pi$
$107$	−7.96897	+	7.96897i	−0.770389	+	0.770389i	0.207785	+	0.978174i	$0.433374\pi$
$108$	1.73080	−	4.89942i	0.166547	−	0.471447i
$109$	−6.82747	+	9.39721i	−0.653953	+	0.900089i	−0.999262	−	0.0383996i	$-0.987774\pi$
$109$	−6.82747	+	9.39721i	−0.653953	+	0.900089i	0.345309	+	0.938489i	$0.387774\pi$
$110$	−1.82199	−	1.46103i	−0.173720	−	0.139304i
$111$	10.0643	+	12.6461i	0.955266	+	1.20031i
$112$	0.649434	+	4.10037i	0.0613658	+	0.387448i
$113$	0.0791636	+	0.499819i	0.00744708	+	0.0470190i	0.991132	−	0.132881i	$-0.0424227\pi$
$113$	0.0791636	+	0.499819i	0.00744708	+	0.0470190i	−0.983685	+	0.179900i	$0.942423\pi$
$114$	−6.60598	−	8.30055i	−0.618707	−	0.777418i
$115$	−0.449877	−	1.64737i	−0.0419512	−	0.153618i
$116$	−4.38590	+	6.03668i	−0.407221	+	0.560492i
$117$	0.616645	−	1.52847i	0.0570088	−	0.141307i
$118$	−0.388242	+	0.388242i	−0.0357406	+	0.0357406i
$119$	6.38542	+	19.6523i	0.585350	+	1.80152i
$120$	3.45731	−	1.74556i	0.315608	−	0.159347i
$121$	3.06210	−	9.42416i	0.278372	−	0.856742i
$122$	−3.23977	−	6.35841i	−0.293315	−	0.575664i
$123$	−1.96099	+	17.2501i	−0.176817	+	1.55539i
$124$			2.54363i			0.228424i
$125$	−10.6817	−	3.30184i	−0.955397	−	0.295326i
$126$	−1.09174	−	12.4065i	−0.0972597	−	1.10526i
$127$	0.319989	+	0.0506813i	0.0283944	+	0.00449724i	0.170616	−	0.985338i	$-0.445424\pi$
$127$	0.319989	+	0.0506813i	0.0283944	+	0.00449724i	−0.142221	+	0.989835i	$0.545424\pi$
$128$	−0.891007	+	0.453990i	−0.0787546	+	0.0401275i
$129$	−0.264882	+	0.956070i	−0.0233215	+	0.0841773i
$130$	1.11986	−	0.505033i	0.0982184	−	0.0442943i
$131$	10.8014	−	3.50958i	0.943720	−	0.306633i	0.203559	−	0.979063i	$-0.434749\pi$
$131$	10.8014	−	3.50958i	0.943720	−	0.306633i	0.740161	+	0.672429i	$0.234749\pi$
$132$	−1.33406	−	1.22182i	−0.116115	−	0.106346i
$133$	−22.6555	−	11.5435i	−1.96448	−	1.00095i
$134$	−7.61834	−	5.53505i	−0.658124	−	0.478155i
$135$	−10.7097	+	4.50583i	−0.921743	+	0.387800i
$136$	−4.02682	+	2.92565i	−0.345297	+	0.250873i
$137$	−9.98531	+	1.58152i	−0.853102	+	0.135118i	−0.567645	−	0.823273i	$-0.692145\pi$
$137$	−9.98531	+	1.58152i	−0.853102	+	0.135118i	−0.285457	+	0.958391i	$0.592145\pi$
$138$	−0.264046	−	1.29616i	−0.0224771	−	0.110336i
$139$	−12.3527	−	17.0020i	−1.04774	−	1.44209i	−0.890751	−	0.454491i	$-0.849821\pi$
$139$	−12.3527	−	17.0020i	−1.04774	−	1.44209i	−0.156989	−	0.987600i	$-0.550179\pi$
$140$	5.80737	−	7.24212i	0.490812	−	0.612071i
$141$	1.01865	+	0.673863i	0.0857862	+	0.0567495i
$142$	−2.25877	+	4.43309i	−0.189552	+	0.372017i
$143$	−0.405741	−	0.405741i	−0.0339298	−	0.0339298i
$144$	2.76092	−	1.17359i	0.230077	−	0.0977989i
$145$	16.5850	−	1.82348i	1.37731	−	0.151432i
$146$	13.6343	+	4.43006i	1.12838	+	0.366634i
$147$	−8.73315	−	15.4267i	−0.720298	−	1.27237i
$148$	−1.45972	+	9.21632i	−0.119988	+	0.757577i
$149$	−13.3393			−1.09280			−0.546401	−	0.837524i	$-0.684003\pi$
$149$	−13.3393			−1.09280			−0.546401	+	0.837524i	$0.684003\pi$
$150$	−8.08846	−	3.09466i	−0.660420	−	0.252678i
$151$	5.12337			0.416934			0.208467	−	0.978029i	$-0.433153\pi$
$151$	5.12337			0.416934			0.208467	+	0.978029i	$0.433153\pi$
$152$	0.958124	−	6.04936i	0.0777141	−	0.490668i
$153$	12.6593	−	7.91928i	1.02344	−	0.640236i
$154$	−4.12375	−	1.33989i	−0.332301	−	0.107971i
$155$	4.20853	−	3.82602i	0.338037	−	0.307313i
$156$	0.891227	−	0.333473i	0.0713553	−	0.0266992i
$157$	3.63440	+	3.63440i	0.290057	+	0.290057i	0.837103	−	0.547046i	$-0.184248\pi$
$157$	3.63440	+	3.63440i	0.290057	+	0.290057i	−0.547046	+	0.837103i	$0.684248\pi$
$158$	4.73625	−	9.29541i	0.376796	−	0.739503i
$159$	7.32023	−	11.0657i	0.580532	−	0.877570i
$160$	2.09136	+	0.791332i	0.165337	+	0.0625603i
$161$	−1.86358	−	2.56499i	−0.146870	−	0.202150i
$162$	−8.50671	+	2.93870i	−0.668350	+	0.230886i
$163$	21.7604	−	3.44651i	1.70441	−	0.269952i	0.773126	−	0.634253i	$-0.218692\pi$
$163$	21.7604	−	3.44651i	1.70441	−	0.269952i	0.931281	+	0.364301i	$0.118692\pi$
$164$	−8.10918	+	5.89166i	−0.633221	+	0.460062i
$165$	−0.0149131	+	4.04507i	−0.00116098	+	0.314908i
$166$	−3.29129	−	2.39126i	−0.255453	−	0.185598i
$167$	−6.12488	−	3.12078i	−0.473957	−	0.241493i	0.200660	−	0.979661i	$-0.435691\pi$
$167$	−6.12488	−	3.12078i	−0.473957	−	0.241493i	−0.674617	+	0.738168i	$0.735691\pi$
$168$	4.85654	−	5.30267i	0.374690	−	0.409110i
$169$	−12.0767	+	3.92395i	−0.928975	+	0.301842i
$170$	10.8976	+	2.26188i	0.835807	+	0.173478i
$171$	−4.12428	+	17.9054i	−0.315391	+	1.36926i
$172$	−0.510351	+	0.260037i	−0.0389139	+	0.0198276i
$173$	−4.75334	−	0.752855i	−0.361390	−	0.0572385i	−0.0269007	−	0.999638i	$-0.508564\pi$
$173$	−4.75334	−	0.752855i	−0.361390	−	0.0572385i	−0.334489	+	0.942400i	$0.608564\pi$
$174$	12.9117	−	0.567001i	0.978832	−	0.0429842i
$175$	−20.7176	+	1.28479i	−1.56610	+	0.0971208i
$176$		−	1.04444i		−	0.0787275i
$177$	0.944909	+	0.107417i	0.0710237	+	0.00807397i
$178$	−4.30875	−	8.45640i	−0.322955	−	0.633834i
$179$	−4.01856	+	12.3679i	−0.300361	+	0.924417i	0.681006	+	0.732277i	$0.261543\pi$
$179$	−4.01856	+	12.3679i	−0.300361	+	0.924417i	−0.981368	+	0.192139i	$0.938457\pi$
$180$	−6.09462	−	2.80279i	−0.454266	−	0.208908i
$181$	2.06775	+	6.36388i	0.153695	+	0.473023i	0.998026	−	0.0627975i	$-0.0200022\pi$
$181$	2.06775	+	6.36388i	0.153695	+	0.473023i	−0.844332	+	0.535821i	$0.820002\pi$
$182$	1.61276	−	1.61276i	0.119546	−	0.119546i
$183$	−5.12289	+	11.2487i	−0.378695	+	0.831526i
$184$	0.448895	−	0.617851i	0.0330930	−	0.0455486i
$185$	17.4444	−	11.4477i	1.28254	−	0.841648i
$186$	3.44724	−	2.74348i	0.252764	−	0.201161i
$187$	−0.813241	−	5.13460i	−0.0594701	−	0.375479i
$188$	0.110311	+	0.696478i	0.00804527	+	0.0507959i
$189$	−15.6363	+	14.8608i	−1.13737	+	1.08097i
$190$	−11.4501	+	7.51395i	−0.830676	+	0.545119i
$191$	−2.80678	+	3.86321i	−0.203092	+	0.279532i	−0.898398	−	0.439181i	$-0.855269\pi$
$191$	−2.80678	+	3.86321i	−0.203092	+	0.279532i	0.695307	+	0.718713i	$0.255269\pi$
$192$	1.57628	+	0.717872i	0.113758	+	0.0518079i
$193$	4.29511	−	4.29511i	0.309169	−	0.309169i	−0.535418	−	0.844587i	$-0.679846\pi$
$193$	4.29511	−	4.29511i	0.309169	−	0.309169i	0.844587	+	0.535418i	$0.179846\pi$
$194$	0.615498	+	1.89431i	0.0441902	+	0.136003i
$195$	−1.89229	−	0.972975i	−0.135510	−	0.0696762i
$196$	3.16272	−	9.73384i	0.225908	−	0.695274i
$197$	6.07357	+	11.9200i	0.432724	+	0.849268i	0.999674	+	0.0255162i	$0.00812295\pi$
$197$	6.07357	+	11.9200i	0.432724	+	0.849268i	−0.566951	+	0.823752i	$0.691877\pi$
$198$	−0.216991	+	3.12579i	−0.0154209	+	0.222140i
$199$			3.34436i			0.237075i	0.992950	+	0.118538i	$0.0378206\pi$
$199$			3.34436i			0.237075i	−0.992950	+	0.118538i	$0.962179\pi$
$200$	−1.83645	−	4.65053i	−0.129857	−	0.328842i
$201$	0.715560	+	16.2946i	0.0504717	+	1.14934i
$202$	13.0156	+	2.06147i	0.915773	+	0.145044i
$203$	27.6009	−	14.0634i	1.93721	−	0.987056i
$204$	8.30818	+	2.30180i	0.581689	+	0.161158i
$205$	21.9455	+	4.55496i	1.53274	+	0.318132i
$206$	−7.95295	+	2.58407i	−0.554108	+	0.180041i
$207$	−1.47182	+	1.75584i	−0.102298	+	0.122039i
$208$	0.489511	+	0.249418i	0.0339415	+	0.0172940i
$209$	5.17523	+	3.76003i	0.357978	+	0.260086i
$210$	−16.0785	−	0.0592771i	−1.10952	−	0.00409051i
$211$	−11.9355	+	8.67168i	−0.821677	+	0.596983i	−0.917192	−	0.398445i	$-0.869550\pi$
$211$	−11.9355	+	8.67168i	−0.821677	+	0.596983i	0.0955156	+	0.995428i	$0.469550\pi$
$212$	7.56590	−	1.19832i	0.519628	−	0.0823010i
$213$	8.44416	−	1.72020i	0.578584	−	0.117866i
$214$	6.62423	+	9.11748i	0.452823	+	0.623258i
$215$	1.19789	+	0.453259i	0.0816955	+	0.0309120i
$216$	−4.56834	−	2.47593i	−0.310836	−	0.168466i
$217$	4.79405	−	9.40886i	0.325441	−	0.638715i
$218$	8.21346	+	8.21346i	0.556286	+	0.556286i
$219$	−8.70174	−	23.2560i	−0.588009	−	1.57149i
$220$	−1.72807	+	1.57100i	−0.116506	+	0.105917i
$221$	2.60071	+	0.845022i	0.174943	+	0.0568423i
$222$	14.0648	−	7.96216i	0.943966	−	0.534385i
$223$	0.624895	−	3.94543i	0.0418460	−	0.264205i	−0.957891	−	0.287132i	$-0.907298\pi$
$223$	0.624895	−	3.94543i	0.0418460	−	0.264205i	0.999737	+	0.0229262i	$0.00729827\pi$
$224$	4.15148			0.277382
$225$	4.52994	+	14.2996i	0.301996	+	0.953309i
$226$	0.506049			0.0336619
$227$	−1.25853	+	7.94605i	−0.0835316	+	0.527398i	0.910070	+	0.414455i	$0.136028\pi$
$227$	−1.25853	+	7.94605i	−0.0835316	+	0.527398i	−0.993601	+	0.112943i	$0.963972\pi$
$228$	−9.23176	+	5.22616i	−0.611388	+	0.346111i
$229$	10.7327	+	3.48726i	0.709236	+	0.230445i	0.641350	−	0.767248i	$-0.278375\pi$
$229$	10.7327	+	3.48726i	0.709236	+	0.230445i	0.0678859	+	0.997693i	$0.478375\pi$
$230$	−1.69747	+	0.186632i	−0.111928	+	0.0123061i
$231$	2.63187	+	7.03384i	0.173164	+	0.462793i
$232$	5.27625	+	5.27625i	0.346403	+	0.346403i
$233$	−3.34738	+	6.56960i	−0.219294	+	0.430389i	−0.974276	−	0.225356i	$-0.927645\pi$
$233$	−3.34738	+	6.56960i	−0.219294	+	0.430389i	0.754982	+	0.655745i	$0.227645\pi$
$234$	−1.41319	−	0.848158i	−0.0923830	−	0.0554458i
$235$	0.986424	−	1.23013i	0.0643472	−	0.0802447i
$236$	0.322728	+	0.444196i	0.0210078	+	0.0289147i
$237$	−17.7059	+	3.60697i	−1.15012	+	0.234298i
$238$	20.4092	−	3.23251i	1.32293	−	0.209532i
$239$	15.6921	−	11.4010i	1.01504	−	0.737467i	0.0497763	−	0.998760i	$-0.484149\pi$
$239$	15.6921	−	11.4010i	1.01504	−	0.737467i	0.965259	+	0.261294i	$0.0841492\pi$
$240$	−1.18323	−	3.68781i	−0.0763772	−	0.238047i
$241$	−1.47476	−	1.07147i	−0.0949975	−	0.0690197i	0.539273	−	0.842131i	$-0.318699\pi$
$241$	−1.47476	−	1.07147i	−0.0949975	−	0.0690197i	−0.634270	+	0.773112i	$0.718699\pi$
$242$	−8.82912	−	4.49866i	−0.567557	−	0.289185i
$243$	13.1577	+	8.35908i	0.844069	+	0.536235i
$244$	−6.78694	+	2.20521i	−0.434489	+	0.141174i
$245$	−20.8623	+	9.40841i	−1.33284	+	0.601081i
$246$	16.7310	+	4.63536i	1.06673	+	0.295540i
$247$	−2.99814	+	1.52763i	−0.190767	+	0.0972006i
$248$	2.51231	+	0.397911i	0.159532	+	0.0252674i
$249$	0.309137	+	7.03964i	0.0195908	+	0.446119i
$250$	−4.93217	+	10.0336i	−0.311938	+	0.634582i
$251$		−	13.2082i		−	0.833692i	−0.908977	−	0.416846i	$-0.863135\pi$
$251$		−	13.2082i		−	0.833692i	0.908977	−	0.416846i	$-0.136865\pi$
$252$	−12.4245	−	0.862506i	−0.782672	−	0.0543328i
$253$	0.362123	+	0.710706i	0.0227665	+	0.0446817i
$254$	0.100115	−	0.308121i	0.00628175	−	0.0193332i
$255$	−8.68840	−	17.2085i	−0.544089	−	1.07764i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	1.31744	−	1.31744i	0.0821794	−	0.0821794i	−0.664822	−	0.747002i	$-0.731493\pi$
$257$	1.31744	−	1.31744i	0.0821794	−	0.0821794i	0.747002	+	0.664822i	$0.231493\pi$
$258$	0.902862	+	0.411183i	0.0562098	+	0.0255991i
$259$	22.7698	−	31.3399i	1.41485	−	1.94737i
$260$	−0.323630	−	1.18508i	−0.0200707	−	0.0734955i
$261$	−14.6946	−	16.8869i	−0.909571	−	1.04528i
$262$	−1.77666	−	11.2174i	−0.109763	−	0.693014i
$263$	−4.21352	−	26.6031i	−0.259817	−	1.64042i	−0.680167	−	0.733057i	$-0.738093\pi$
$263$	−4.21352	−	26.6031i	−0.259817	−	1.64042i	0.420351	−	0.907362i	$-0.361907\pi$
$264$	−1.41547	+	1.12650i	−0.0871162	+	0.0693312i
$265$	−13.3630	−	10.7156i	−0.820882	−	0.658255i
$266$	−14.9455	+	20.5707i	−0.916368	+	1.26127i
$267$	−6.81321	+	14.9602i	−0.416962	+	0.915551i
$268$	−6.65867	+	6.65867i	−0.406743	+	0.406743i
$269$	3.12783	+	9.62647i	0.190707	+	0.586936i	1.00000		0.000469431i	$-0.000149425\pi$
$269$	3.12783	+	9.62647i	0.190707	+	0.586936i	−0.809293	+	0.587405i	$0.800149\pi$
$270$	2.77499	+	11.2827i	0.168881	+	0.686644i
$271$	−0.130543	+	0.401771i	−0.00792994	+	0.0244058i	−0.954943	−	0.296789i	$-0.904084\pi$
$271$	−0.130543	+	0.401771i	−0.00792994	+	0.0244058i	0.947013	+	0.321194i	$0.104084\pi$
$272$	2.25970	+	4.43491i	0.137014	+	0.268906i
$273$	−3.92515	−	0.446211i	−0.237561	−	0.0270059i
$274$			10.1098i			0.610754i
$275$	5.19857	+	0.496114i	0.313486	+	0.0299168i
$276$	−1.32150	+	0.0580322i	−0.0795452	+	0.00349313i
$277$	−26.8065	−	4.24574i	−1.61065	−	0.255102i	−0.714757	−	0.699373i	$-0.753463\pi$
$277$	−26.8065	−	4.24574i	−1.61065	−	0.255102i	−0.895892	+	0.444271i	$0.853463\pi$
$278$	−18.7251	+	9.54090i	−1.12305	+	0.572225i
$279$	−7.43617	−	1.71282i	−0.445192	−	0.102544i
$280$	−6.24449	−	6.86879i	−0.373179	−	0.410488i
$281$	11.9782	−	3.89197i	0.714562	−	0.232175i	0.0708982	−	0.997484i	$-0.477413\pi$
$281$	11.9782	−	3.89197i	0.714562	−	0.232175i	0.643664	+	0.765308i	$0.277413\pi$
$282$	0.824920	−	0.900698i	0.0491232	−	0.0536358i
$283$	6.90768	+	3.51964i	0.410619	+	0.209221i	0.647083	−	0.762419i	$-0.275989\pi$
$283$	6.90768	+	3.51964i	0.410619	+	0.209221i	−0.236464	+	0.971640i	$0.575989\pi$
$284$	4.02516	+	2.92445i	0.238849	+	0.173534i
$285$	22.5329	+	7.41335i	1.33474	+	0.439129i
$286$	−0.464218	+	0.337274i	−0.0274498	+	0.0199434i
$287$	41.1000	−	6.50960i	2.42606	−	0.384250i
$288$	−0.727235	−	2.91052i	−0.0428527	−	0.171504i
$289$	4.56985	+	6.28986i	0.268815	+	0.369992i
$290$	0.793443	−	16.6661i	0.0465926	−	0.978667i
$291$	1.90339	−	2.87729i	0.111579	−	0.168670i
$292$	6.50840	−	12.7735i	0.380875	−	0.747510i
$293$	−3.01356	−	3.01356i	−0.176054	−	0.176054i	0.613579	−	0.789633i	$-0.289729\pi$
$293$	−3.01356	−	3.01356i	−0.176054	−	0.176054i	−0.789633	+	0.613579i	$0.789729\pi$
$294$	−16.6029	+	6.21236i	−0.968303	+	0.362312i
$295$	0.249507	−	1.20211i	0.0145269	−	0.0699894i
$296$	8.87450	+	2.88350i	0.515820	+	0.167600i
$297$	4.47026	−	3.07731i	0.259391	−	0.178563i
$298$	−2.08673	+	13.1751i	−0.120881	+	0.763214i
$299$	−0.419573			−0.0242645
$300$	−4.32187	+	7.50476i	−0.249523	+	0.433288i
$301$	2.37788			0.137059
$302$	0.801471	−	5.06029i	0.0461195	−	0.291187i
$303$	−11.2444	−	19.8627i	−0.645975	−	1.14108i
$304$	−5.82500	−	1.89266i	−0.334086	−	0.108551i
$305$	13.8573	+	7.91228i	0.793464	+	0.453056i
$306$	−5.84143	−	13.7423i	−0.333933	−	0.785593i
$307$	13.5058	+	13.5058i	0.770815	+	0.770815i	0.978249	−	0.207434i	$-0.0665113\pi$
$307$	13.5058	+	13.5058i	0.770815	+	0.770815i	−0.207434	+	0.978249i	$0.566511\pi$
$308$	−1.96849	+	3.86337i	−0.112165	+	0.220136i
$309$	12.0799	+	7.99110i	0.687199	+	0.454598i
$310$	−3.12056	−	4.75524i	−0.177236	−	0.270079i
$311$	−5.51649	−	7.59280i	−0.312811	−	0.430548i	0.623444	−	0.781868i	$-0.285733\pi$
$311$	−5.51649	−	7.59280i	−0.312811	−	0.430548i	−0.936255	+	0.351320i	$0.885733\pi$
$312$	−0.189948	−	0.932422i	−0.0107537	−	0.0527880i
$313$	−29.5807	+	4.68513i	−1.67200	+	0.264819i	−0.919304	−	0.393548i	$-0.871248\pi$
$313$	−29.5807	+	4.68513i	−1.67200	+	0.264819i	−0.752697	+	0.658367i	$0.771248\pi$
$314$	4.15820	−	3.02111i	0.234661	−	0.170491i
$315$	17.2614	+	21.8542i	0.972571	+	1.23135i
$316$	−8.44006	−	6.13206i	−0.474790	−	0.344955i
$317$	−10.3462	−	5.27165i	−0.581100	−	0.296085i	0.138624	−	0.990345i	$-0.455732\pi$
$317$	−10.3462	−	5.27165i	−0.581100	−	0.296085i	−0.719725	+	0.694260i	$0.755732\pi$
$318$	−9.78436	−	8.96117i	−0.548680	−	0.502518i
$319$	−7.41190	+	2.40827i	−0.414987	+	0.134837i
$320$	1.10875	−	1.94182i	0.0619810	−	0.108551i
$321$	5.21172	−	18.8113i	0.290890	−	1.04994i
$322$	−2.82494	+	1.43938i	−0.157428	+	0.0802135i
$323$	−30.1102	−	4.76898i	−1.67538	−	0.265353i
$324$	1.57178	+	8.86169i	0.0873211	+	0.492316i
$325$	−1.47397	+	2.31801i	−0.0817612	+	0.128580i
$326$		−	22.0317i		−	1.22022i
$327$	2.27247	−	19.9900i	0.125668	−	1.10545i
$328$	4.55057	+	8.93100i	0.251263	+	0.493132i
$329$	0.904633	−	2.78417i	0.0498740	−	0.153496i
$330$	3.99293	+	0.647517i	0.219804	+	0.0356446i
$331$	2.94074	+	9.05067i	0.161638	+	0.497470i	0.998773	−	0.0495264i	$-0.0157712\pi$
$331$	2.94074	+	9.05067i	0.161638	+	0.497470i	−0.837135	+	0.546996i	$0.815771\pi$
$332$	−2.87669	+	2.87669i	−0.157879	+	0.157879i
$333$	−25.9605	−	10.4735i	−1.42263	−	0.573944i
$334$	−4.04050	+	5.56128i	−0.221086	+	0.304299i
$335$	21.0328	+	1.00133i	1.14914	+	0.0547086i
$336$	−4.47765	−	5.62627i	−0.244276	−	0.306938i
$337$	0.877532	+	5.54052i	0.0478022	+	0.301811i	0.999993	−	0.00369222i	$-0.00117527\pi$
$337$	0.877532	+	5.54052i	0.0478022	+	0.301811i	−0.952191	+	0.305503i	$0.901175\pi$
$338$	1.98643	+	12.5418i	0.108048	+	0.682186i
$339$	−0.545809	−	0.685821i	−0.0296443	−	0.0372487i
$340$	3.93879	−	10.4096i	0.213611	−	0.564539i
$341$	−1.56155	+	2.14928i	−0.0845625	+	0.116390i
$342$	17.0398	+	6.87453i	0.921408	+	0.371732i
$343$	−9.49577	+	9.49577i	−0.512723	+	0.512723i
$344$	0.176999	+	0.544747i	0.00954314	+	0.0293708i
$345$	2.08377	+	2.09919i	0.112186	+	0.113017i
$346$	−1.48717	+	4.57705i	−0.0799509	+	0.246064i
$347$	12.4125	+	24.3609i	0.666339	+	1.30776i	0.938423	+	0.345490i	$0.112287\pi$
$347$	12.4125	+	24.3609i	0.666339	+	1.30776i	−0.272084	+	0.962274i	$0.587713\pi$
$348$	1.45981	−	12.8414i	0.0782541	−	0.688372i
$349$		−	10.5897i		−	0.566853i	−0.958994	−	0.283426i	$-0.908529\pi$
$349$		−	10.5897i		−	0.566853i	0.958994	−	0.283426i	$-0.0914711\pi$
$350$	−1.97198	+	20.6635i	−0.105407	+	1.10451i
$351$	0.374758	+	2.83001i	0.0200031	+	0.151055i
$352$	−1.03158	−	0.163386i	−0.0549834	−	0.00870851i
$353$	−1.13374	+	0.577670i	−0.0603430	+	0.0307463i	−0.483902	−	0.875122i	$-0.660781\pi$
$353$	−1.13374	+	0.577670i	−0.0603430	+	0.0307463i	0.423559	+	0.905869i	$0.360781\pi$
$354$	0.253911	−	0.916471i	0.0134952	−	0.0487099i
$355$	−1.21586	−	11.0586i	−0.0645314	−	0.586931i
$356$	−9.02633	+	2.93283i	−0.478394	+	0.155440i
$357$	−26.3936	−	24.1730i	−1.39690	−	1.27937i
$358$	11.5869	+	5.90384i	0.612389	+	0.312028i
$359$	−23.0178	−	16.7234i	−1.21483	−	0.882626i	−0.219170	−	0.975687i	$-0.570335\pi$
$359$	−23.0178	−	16.7234i	−1.21483	−	0.882626i	−0.995660	+	0.0930604i	$0.970335\pi$
$360$	−3.72170	+	5.58113i	−0.196151	+	0.294151i
$361$	14.9771	−	10.8815i	0.788269	−	0.572711i
$362$	6.60900	−	1.04676i	0.347361	−	0.0550166i
$363$	3.42603	+	16.8177i	0.179820	+	0.882702i
$364$	−1.34061	−	1.84519i	−0.0702671	−	0.0967143i
$365$	−30.9239	+	8.44491i	−1.61863	+	0.442027i
$366$	10.3088	+	6.81950i	0.538849	+	0.356461i
$367$	−14.8476	+	29.1400i	−0.775036	+	1.52109i	0.0766594	+	0.997057i	$0.475575\pi$
$367$	−14.8476	+	29.1400i	−0.775036	+	1.52109i	−0.851696	+	0.524037i	$0.824425\pi$
$368$	−0.540022	−	0.540022i	−0.0281506	−	0.0281506i
$369$	−11.7634	−	27.6741i	−0.612381	−	1.44066i
$370$	−8.57780	−	19.0205i	−0.445939	−	0.988827i
$371$	−30.2447	−	9.82710i	−1.57023	−	0.510198i
$372$	−2.17043	−	3.83397i	−0.112532	−	0.198782i
$373$	−1.19865	+	7.56799i	−0.0620639	+	0.391856i	0.937028	+	0.349254i	$0.113565\pi$
$373$	−1.19865	+	7.56799i	−0.0620639	+	0.391856i	−0.999092	+	0.0426023i	$0.986435\pi$
$374$	−5.19861			−0.268814
$375$	18.9177	−	4.13766i	0.976906	−	0.213668i
$376$	0.705159			0.0363658
$377$	0.641290	−	4.04894i	0.0330281	−	0.208531i
$378$	12.2318	+	17.7686i	0.629136	+	0.913916i
$379$	9.97124	+	3.23985i	0.512188	+	0.166420i	0.553697	−	0.832718i	$-0.313217\pi$
$379$	9.97124	+	3.23985i	0.512188	+	0.166420i	−0.0415090	+	0.999138i	$0.513217\pi$
$380$	5.63025	+	12.4845i	0.288826	+	0.640444i
$381$	−0.525560	+	0.196650i	−0.0269253	+	0.0100747i
$382$	3.37657	+	3.37657i	0.172760	+	0.172760i
$383$	−12.1180	+	23.7829i	−0.619200	+	1.21525i	0.342079	+	0.939671i	$0.388869\pi$
$383$	−12.1180	+	23.7829i	−0.619200	+	1.21525i	−0.961279	+	0.275577i	$0.911131\pi$
$384$	0.955618	−	1.44457i	0.0487662	−	0.0737181i
$385$	9.35302	−	2.55419i	0.476674	−	0.130174i
$386$	−3.57033	−	4.91413i	−0.181725	−	0.250123i
$387$	−0.416546	−	1.66709i	−0.0211742	−	0.0847429i
$388$	1.96727	−	0.311585i	0.0998730	−	0.0158183i
$389$	5.65060	−	4.10540i	0.286497	−	0.208152i	−0.435249	−	0.900310i	$-0.643340\pi$
$389$	5.65060	−	4.10540i	0.286497	−	0.208152i	0.721746	+	0.692158i	$0.243340\pi$
$390$	−1.25702	+	1.71679i	−0.0636515	+	0.0869330i
$391$	−3.07530	−	2.23434i	−0.155525	−	0.112995i
$392$	−9.11924	−	4.64649i	−0.460591	−	0.234683i
$393$	−13.2861	+	14.5066i	−0.670194	+	0.731759i
$394$	12.7234	−	4.13408i	0.640996	−	0.208272i
$395$	2.54946	+	23.1880i	0.128277	+	1.16672i
$396$	3.05336	+	0.703302i	0.153437	+	0.0353422i
$397$	−16.3171	+	8.31400i	−0.818934	+	0.417268i	−0.812678	−	0.582713i	$-0.801991\pi$
$397$	−16.3171	+	8.31400i	−0.818934	+	0.417268i	−0.00625557	+	0.999980i	$0.501991\pi$
$398$	3.30318	+	0.523173i	0.165574	+	0.0262243i
$399$	43.9981	−	1.93212i	2.20266	−	0.0967272i
$400$	−4.88056	+	1.08634i	−0.244028	+	0.0543170i
$401$		−	1.24697i		−	0.0622709i	−0.999515	−	0.0311355i	$-0.990088\pi$
$401$		−	1.24697i		−	0.0622709i	0.999515	−	0.0311355i	$-0.00991233\pi$
$402$	16.2060	+	1.84229i	0.808280	+	0.0918853i
$403$	−0.634427	−	1.24513i	−0.0316030	−	0.0620245i
$404$	4.07217	−	12.5329i	0.202598	−	0.623533i
$405$	12.2978	−	15.9300i	0.611083	−	0.791566i
$406$	−9.57250	−	29.4611i	−0.475075	−	1.46213i
$407$	−6.89137	+	6.89137i	−0.341593	+	0.341593i
$408$	3.57315	−	7.84581i	0.176897	−	0.388425i
$409$	−4.28708	+	5.90066i	−0.211982	+	0.291769i	−0.901746	−	0.432266i	$-0.857714\pi$
$409$	−4.28708	+	5.90066i	−0.211982	+	0.291769i	0.689764	+	0.724034i	$0.257714\pi$
$410$	7.93191	−	20.9628i	0.391729	−	1.03528i
$411$	13.7012	−	10.9041i	0.675832	−	0.537859i
$412$	1.30814	+	8.25928i	0.0644475	+	0.406905i
$413$	−0.356576	−	2.25133i	−0.0175460	−	0.110781i
$414$	1.50398	+	1.72837i	0.0739166	+	0.0849447i
$415$	9.08660	+	0.432597i	0.446044	+	0.0212353i
$416$	0.322924	−	0.444466i	0.0158326	−	0.0217918i
$417$	33.1265	+	15.0865i	1.62221	+	0.738791i
$418$	4.52332	−	4.52332i	0.221243	−	0.221243i
$419$	−5.54251	−	17.0581i	−0.270769	−	0.833343i	−0.990308	−	0.138890i	$-0.955647\pi$
$419$	−5.54251	−	17.0581i	−0.270769	−	0.833343i	0.719538	−	0.694453i	$-0.244353\pi$
$420$	−2.57378	+	15.8713i	−0.125587	+	0.774439i
$421$	−9.83501	+	30.2690i	−0.479329	+	1.47522i	0.360700	+	0.932682i	$0.382538\pi$
$421$	−9.83501	+	30.2690i	−0.479329	+	1.47522i	−0.840029	+	0.542541i	$0.817462\pi$
$422$	6.69779	+	13.1451i	0.326043	+	0.639896i
$423$	−2.11040	−	0.146503i	−0.102611	−	0.00712323i
$424$		−	7.66021i		−	0.372012i
$425$	−23.1476	+	9.14079i	−1.12283	+	0.443394i
$426$	−0.378067	−	8.60930i	−0.0183174	−	0.417122i
$427$	29.2611	+	4.63450i	1.41604	+	0.224279i
$428$	10.0415	−	5.11639i	0.485373	−	0.247310i
$429$	0.957780	+	0.265356i	0.0462420	+	0.0128115i
$430$	0.635070	−	1.11224i	0.0306258	−	0.0536369i
$431$	−9.09895	+	2.95643i	−0.438281	+	0.142406i	−0.519842	−	0.854262i	$-0.674009\pi$
$431$	−9.09895	+	2.95643i	−0.438281	+	0.142406i	0.0815614	+	0.996668i	$0.474009\pi$
$432$	−3.16010	+	4.12478i	−0.152040	+	0.198453i
$433$	15.4738	+	7.88429i	0.743622	+	0.378895i	0.784385	−	0.620274i	$-0.212979\pi$
$433$	15.4738	+	7.88429i	0.743622	+	0.378895i	−0.0407625	+	0.999169i	$0.512979\pi$
$434$	−8.54306	−	6.20690i	−0.410080	−	0.297941i
$435$	−23.4424	+	16.9002i	−1.12398	+	0.810304i
$436$	9.39721	−	6.82747i	0.450045	−	0.326977i
$437$	4.61993	−	0.731725i	0.221001	−	0.0350031i
$438$	−24.3309	+	4.95657i	−1.16258	+	0.236834i
$439$	−13.1783	−	18.1384i	−0.628967	−	0.865699i	0.369000	−	0.929429i	$-0.379700\pi$
$439$	−13.1783	−	18.1384i	−0.628967	−	0.865699i	−0.997967	+	0.0637305i	$0.979700\pi$
$440$	1.28133	+	1.95255i	0.0610851	+	0.0930841i
$441$	26.3267	+	15.8006i	1.25365	+	0.752409i
$442$	1.24146	−	2.43650i	0.0590502	−	0.115892i
$443$	6.92607	+	6.92607i	0.329068	+	0.329068i	0.852232	−	0.523164i	$-0.175249\pi$
$443$	6.92607	+	6.92607i	0.329068	+	0.329068i	−0.523164	+	0.852232i	$0.675249\pi$
$444$	−5.66391	−	15.1372i	−0.268797	−	0.718379i
$445$	18.4295	+	10.5230i	0.873643	+	0.498837i
$446$	−3.79910	−	1.23440i	−0.179893	−	0.0584506i
$447$	20.1062	−	11.3822i	0.950991	−	0.538361i
$448$	0.649434	−	4.10037i	0.0306829	−	0.193724i
$449$	24.5105			1.15672			0.578362	−	0.815780i	$-0.303692\pi$
$449$	24.5105			1.15672			0.578362	+	0.815780i	$0.303692\pi$
$450$	14.8322	−	2.23721i	0.699198	−	0.105463i
$451$	−10.4689			−0.492963
$452$	0.0791636	−	0.499819i	0.00372354	−	0.0235095i
$453$	−7.72237	+	4.37168i	−0.362829	+	0.205400i
$454$	7.65134	+	2.48607i	0.359095	+	0.116677i
$455$	−1.03645	+	4.99356i	−0.0485896	+	0.234102i
$456$	3.71765	+	9.93566i	0.174095	+	0.465280i
$457$	−10.0260	−	10.0260i	−0.468998	−	0.468998i	0.432592	−	0.901590i	$-0.357599\pi$
$457$	−10.0260	−	10.0260i	−0.468998	−	0.468998i	−0.901590	+	0.432592i	$0.857599\pi$
$458$	5.12329	−	10.0550i	0.239396	−	0.469840i
$459$	−12.3237	+	22.7386i	−0.575223	+	1.06134i
$460$	−0.0812085	+	1.70577i	−0.00378637	+	0.0795318i
$461$	12.2612	+	16.8761i	0.571060	+	0.785996i	0.992680	−	0.120776i	$-0.0385384\pi$
$461$	12.2612	+	16.8761i	0.571060	+	0.785996i	−0.421620	+	0.906773i	$0.638538\pi$
$462$	7.35896	−	1.49913i	0.342370	−	0.0697459i
$463$	19.2040	−	3.04161i	0.892485	−	0.141356i	0.306685	−	0.951811i	$-0.400780\pi$
$463$	19.2040	−	3.04161i	0.892485	−	0.141356i	0.585800	+	0.810456i	$0.300780\pi$
$464$	6.03668	−	4.38590i	0.280246	−	0.203610i
$465$	−3.07878	+	9.35797i	−0.142775	+	0.433966i
$466$	5.96507	+	4.33388i	0.276327	+	0.200763i
$467$	−12.2941	−	6.26414i	−0.568902	−	0.289870i	0.145783	−	0.989317i	$-0.453430\pi$
$467$	−12.2941	−	6.26414i	−0.568902	−	0.289870i	−0.714685	+	0.699447i	$0.753430\pi$
$468$	−1.05879	+	1.26311i	−0.0489425	+	0.0583872i
$469$	37.1802	−	12.0806i	1.71682	−	0.557829i
$470$	−1.06067	−	1.16671i	−0.0489252	−	0.0538165i
$471$	−8.57924	−	2.37690i	−0.395311	−	0.109522i
$472$	0.489213	−	0.249267i	0.0225179	−	0.0114734i
$473$	−0.590869	−	0.0935844i	−0.0271682	−	0.00430302i
$474$	0.792740	+	18.0522i	0.0364118	+	0.829165i
$475$	12.1874	−	28.0942i	0.559196	−	1.28905i
$476$		−	20.6636i		−	0.947116i
$477$	−1.59148	+	22.9254i	−0.0728687	+	1.04968i
$478$	−8.80581	−	17.2824i	−0.402768	−	0.790477i
$479$	−2.22757	+	6.85575i	−0.101780	+	0.313247i	−0.988961	−	0.148174i	$-0.952660\pi$
$479$	−2.22757	+	6.85575i	−0.101780	+	0.313247i	0.887181	+	0.461421i	$0.152660\pi$
$480$	−3.82751	+	0.591761i	−0.174701	+	0.0270101i
$481$	−1.58417	−	4.87557i	−0.0722319	−	0.222307i
$482$	−1.28899	+	1.28899i	−0.0587117	+	0.0587117i
$483$	4.99761	+	2.27602i	0.227399	+	0.103562i
$484$	−5.82445	+	8.01667i	−0.264748	+	0.364394i
$485$	−3.47462	−	2.78625i	−0.157774	−	0.126517i
$486$	10.3145	−	11.6881i	0.467875	−	0.530182i
$487$	2.37355	+	14.9860i	0.107556	+	0.679080i	0.981270	+	0.192640i	$0.0617048\pi$
$487$	2.37355	+	14.9860i	0.107556	+	0.679080i	−0.873714	+	0.486440i	$0.838295\pi$
$488$	1.11635	+	7.04836i	0.0505348	+	0.319064i
$489$	−29.8583	+	23.7627i	−1.35024	+	1.07458i
$490$	6.02900	+	22.0772i	0.272362	+	0.997347i
$491$	15.9838	−	21.9998i	0.721340	−	0.992839i	−0.278139	−	0.960541i	$-0.589717\pi$
$491$	15.9838	−	21.9998i	0.721340	−	0.992839i	0.999478	−	0.0322980i	$-0.0102826\pi$
$492$	7.19559	−	15.7998i	0.324402	−	0.712312i
$493$	26.2621	−	26.2621i	1.18279	−	1.18279i
$494$	1.03981	+	3.20020i	0.0467831	+	0.143984i
$495$	−3.42911	−	6.10979i	−0.154127	−	0.274615i
$496$	0.786024	−	2.41913i	0.0352935	−	0.108622i
$497$	−9.37724	−	18.4039i	−0.420627	−	0.825526i
$498$	7.00133	+	0.795911i	0.313737	+	0.0356656i
$499$			7.08605i			0.317215i	0.987342	+	0.158608i	$0.0507005\pi$
$499$			7.08605i			0.317215i	−0.987342	+	0.158608i	$0.949300\pi$
$500$	9.13854	+	6.44105i	0.408688	+	0.288053i
$501$	11.8949	−	0.522348i	0.531423	−	0.0233368i
$502$	−13.0456	−	2.06621i	−0.582252	−	0.0922196i
$503$	−35.4598	+	18.0677i	−1.58108	+	0.805598i	−0.999966	−	0.00822664i	$-0.997381\pi$
$503$	−35.4598	+	18.0677i	−1.58108	+	0.805598i	−0.581110	+	0.813825i	$0.697381\pi$
$504$	−2.79551	+	12.1366i	−0.124522	+	0.540609i
$505$	−26.8613	+	12.1138i	−1.19531	+	0.539059i
$506$	0.758604	−	0.246485i	0.0337241	−	0.0109576i
$507$	14.8548	−	16.2193i	0.659723	−	0.720326i
$508$	−0.288666	−	0.147083i	−0.0128075	−	0.00652575i
$509$	12.2593	+	8.90692i	0.543385	+	0.394792i	0.825341	−	0.564635i	$-0.190983\pi$
$509$	12.2593	+	8.90692i	0.543385	+	0.394792i	−0.281956	+	0.959427i	$0.590983\pi$
$510$	−18.3558	+	5.88943i	−0.812808	+	0.260788i
$511$	−48.1490	+	34.9823i	−2.12999	+	1.54753i
$512$	0.987688	−	0.156434i	0.0436501	−	0.00691349i
$513$	−9.06194	−	30.5078i	−0.400095	−	1.34695i
$514$	−1.09512	−	1.50731i	−0.0483038	−	0.0664845i
$515$	11.6976	−	14.5876i	0.515460	−	0.642808i
$516$	0.547359	−	0.827424i	0.0240962	−	0.0364253i
$517$	−0.334362	+	0.656222i	−0.0147052	+	0.0288606i
$518$	−27.3921	−	27.3921i	−1.20354	−	1.20354i
$519$	7.80704	−	2.92118i	0.342691	−	0.128225i
$520$	−1.22112	+	0.134258i	−0.0535495	+	0.00588762i
$521$	−8.21939	−	2.67064i	−0.360098	−	0.117003i	0.123380	−	0.992360i	$-0.460627\pi$
$521$	−8.21939	−	2.67064i	−0.360098	−	0.117003i	−0.483478	+	0.875357i	$0.660627\pi$
$522$	−18.9778	+	11.8719i	−0.830634	+	0.519621i
$523$	5.18122	−	32.7129i	0.226559	−	1.43044i	−0.567890	−	0.823105i	$-0.692240\pi$
$523$	5.18122	−	32.7129i	0.226559	−	1.43044i	0.794448	−	0.607332i	$-0.207760\pi$
$524$	−11.3572			−0.496143
$525$	30.1310	−	19.6145i	1.31503	−	0.856047i
$526$	−26.9347			−1.17441
$527$	1.98057	−	12.5048i	0.0862749	−	0.544718i
$528$	0.891202	+	1.57427i	0.0387846	+	0.0685112i
$529$	−21.3196	−	6.92716i	−0.926939	−	0.301181i
$530$	−12.6741	+	11.5222i	−0.550528	+	0.500491i
$531$	−1.51590	+	0.644366i	−0.0657846	+	0.0279631i
$532$	17.9795	+	17.9795i	0.779509	+	0.779509i
$533$	2.50004	−	4.90661i	0.108289	−	0.212529i
$534$	13.7102	+	9.06962i	0.593299	+	0.392481i
$535$	−23.5693	−	8.91817i	−1.01899	−	0.385566i
$536$	5.53505	+	7.61834i	0.239078	+	0.329062i
$537$	−4.49616	−	22.0708i	−0.194024	−	0.952427i
$538$	9.99725	−	1.58341i	0.431012	−	0.0682656i
$539$	8.64805	−	6.28318i	0.372498	−	0.270636i
$540$	11.5779	−	0.975822i	0.498233	−	0.0419927i
$541$	−22.5154	−	16.3584i	−0.968012	−	0.703302i	−0.0130143	−	0.999915i	$-0.504143\pi$
$541$	−22.5154	−	16.3584i	−0.968012	−	0.703302i	−0.954998	+	0.296613i	$0.904143\pi$
$542$	0.376403	+	0.191787i	0.0161679	+	0.00823795i
$543$	−8.54688	−	7.82780i	−0.366782	−	0.335923i
$544$	4.73381	−	1.53811i	0.202960	−	0.0659458i
$545$	−25.4312	−	5.27845i	−1.08935	−	0.226104i
$546$	−1.05475	+	3.80702i	−0.0451390	+	0.162926i
$547$	−25.7853	+	13.1383i	−1.10250	+	0.561752i	−0.907924	−	0.419135i	$-0.862333\pi$
$547$	−25.7853	+	13.1383i	−1.10250	+	0.561752i	−0.194577	+	0.980887i	$0.562333\pi$
$548$	9.98531	+	1.58152i	0.426551	+	0.0675591i
$549$	−1.87665	−	21.3262i	−0.0800935	−	0.910181i
$550$	1.30324	−	5.05696i	0.0555704	−	0.215630i
$551$			45.7014i			1.94695i
$552$	−0.149411	+	1.31431i	−0.00635935	+	0.0559408i
$553$	19.6624	+	38.5897i	0.836131	+	1.64100i
$554$	−8.38693	+	25.8123i	−0.356327	+	1.09666i
$555$	−16.5256	+	32.1399i	−0.701474	+	1.36426i
$556$	6.49419	+	19.9871i	0.275415	+	0.847640i
$557$	2.89425	−	2.89425i	0.122633	−	0.122633i	−0.643127	−	0.765760i	$-0.722363\pi$
$557$	2.89425	−	2.89425i	0.122633	−	0.122633i	0.765760	+	0.643127i	$0.222363\pi$
$558$	−2.85501	+	7.07667i	−0.120862	+	0.299579i
$559$	0.184964	−	0.254582i	0.00782316	−	0.0107677i
$560$	−7.76107	+	5.09309i	−0.327965	+	0.215222i
$561$	5.60706	+	7.04539i	0.236730	+	0.297456i
$562$	−1.97024	−	12.4396i	−0.0831096	−	0.524733i
$563$	2.55888	+	16.1561i	0.107844	+	0.680900i	0.981080	+	0.193603i	$0.0620172\pi$
$563$	2.55888	+	16.1561i	0.107844	+	0.680900i	−0.873236	+	0.487297i	$0.837983\pi$
$564$	−0.760563	−	0.955664i	−0.0320255	−	0.0402407i
$565$	−0.946045	+	0.620829i	−0.0398004	+	0.0261185i
$566$	4.55691	−	6.27205i	0.191541	−	0.263634i
$567$	10.8879	−	35.7417i	0.457249	−	1.50101i
$568$	3.51812	−	3.51812i	0.147617	−	0.147617i
$569$	7.86991	+	24.2211i	0.329924	+	1.01540i	0.969169	+	0.246398i	$0.0792470\pi$
$569$	7.86991	+	24.2211i	0.329924	+	1.01540i	−0.639245	+	0.769003i	$0.720753\pi$
$570$	10.8470	−	21.0958i	0.454331	−	0.883606i
$571$	7.91581	−	24.3624i	0.331266	−	1.01953i	−0.637266	−	0.770644i	$-0.719935\pi$
$571$	7.91581	−	24.3624i	0.331266	−	1.01953i	0.968532	−	0.248889i	$-0.0800653\pi$
$572$	0.260502	+	0.511264i	0.0108921	+	0.0213770i
$573$	0.934215	−	8.21793i	0.0390274	−	0.343309i
$574$		−	41.6123i		−	1.73686i
$575$	2.94441	−	2.43138i	0.122790	−	0.101396i
$576$	−2.98845	+	0.262976i	−0.124519	+	0.0109573i
$577$	32.5663	+	5.15800i	1.35575	+	0.214730i	0.791651	−	0.610974i	$-0.209222\pi$
$577$	32.5663	+	5.15800i	1.35575	+	0.214730i	0.564103	+	0.825704i	$0.309222\pi$
$578$	6.92730	−	3.52964i	0.288138	−	0.146814i
$579$	−2.80901	+	10.1389i	−0.116738	+	0.421358i
$580$	−16.3368	−	3.39083i	−0.678348	−	0.140796i
$581$	16.0626	−	5.21907i	0.666391	−	0.216523i
$582$	−2.54411	−	2.33007i	−0.105457	−	0.0965844i
$583$	7.12860	+	3.63220i	0.295236	+	0.150430i
$584$	−11.5981	−	8.42648i	−0.479931	−	0.348690i
$585$	3.68245	−	0.148110i	0.152250	−	0.00612360i
$586$	−3.44789	+	2.50504i	−0.142431	+	0.103482i
$587$	−3.14939	+	0.498814i	−0.129989	+	0.0205882i	−0.221090	−	0.975253i	$-0.570961\pi$
$587$	−3.14939	+	0.498814i	−0.129989	+	0.0205882i	0.0911008	+	0.995842i	$0.470961\pi$
$588$	3.53860	+	17.3704i	0.145930	+	0.716342i
$589$	9.15717	+	12.6038i	0.377315	+	0.519329i
$590$	−1.14828	−	0.434486i	−0.0472738	−	0.0178875i
$591$	−19.3258	−	12.7844i	−0.794956	−	0.525881i
$592$	4.23628	−	8.31416i	0.174110	−	0.341710i
$593$	24.3096	+	24.3096i	0.998277	+	0.998277i	0.999999	−	0.00172155i	$-0.000547985\pi$
$593$	24.3096	+	24.3096i	0.998277	+	0.998277i	−0.00172155	+	0.999999i	$0.500548\pi$
$594$	−2.34012	−	4.89662i	−0.0960162	−	0.200911i
$595$	−34.1888	+	31.0814i	−1.40160	+	1.27421i
$596$	12.6865	+	4.12209i	0.519658	+	0.168847i
$597$	−2.85368	−	5.04090i	−0.116793	−	0.206310i
$598$	−0.0656357	+	0.414407i	−0.00268404	+	0.0169464i
$599$	−19.8769			−0.812148			−0.406074	−	0.913840i	$-0.633103\pi$
$599$	−19.8769			−0.812148			−0.406074	+	0.913840i	$0.633103\pi$
$600$	6.73628	+	5.44266i	0.275007	+	0.222196i
$601$	9.21318			0.375814			0.187907	−	0.982187i	$-0.439830\pi$
$601$	9.21318			0.375814			0.187907	+	0.982187i	$0.439830\pi$
$602$	0.371983	−	2.34861i	0.0151609	−	0.0957222i
$603$	−14.9825	−	23.9501i	−0.610135	−	0.975324i
$604$	−4.87261	−	1.58321i	−0.198264	−	0.0644198i
$605$	22.0248	−	2.42157i	0.895436	−	0.0984506i
$606$	−21.3772	+	7.99876i	−0.868389	+	0.324927i
$607$	−10.0691	−	10.0691i	−0.408693	−	0.408693i	0.472589	−	0.881283i	$-0.343319\pi$
$607$	−10.0691	−	10.0691i	−0.408693	−	0.408693i	−0.881283	+	0.472589i	$0.843319\pi$
$608$	−2.78058	+	5.45720i	−0.112768	+	0.221319i
$609$	−29.6024	+	44.7490i	−1.19955	+	1.81332i
$610$	9.98262	−	12.4489i	0.404184	−	0.504041i
$611$	−0.227713	−	0.313420i	−0.00921227	−	0.0126796i
$612$	−14.4869	+	3.61975i	−0.585597	+	0.146320i
$613$	−35.4154	+	5.60925i	−1.43042	+	0.226556i	−0.823096	−	0.567902i	$-0.807755\pi$
$613$	−35.4154	+	5.60925i	−1.43042	+	0.226556i	−0.607320	+	0.794458i	$0.707755\pi$
$614$	15.4523	−	11.2267i	0.623602	−	0.453074i
$615$	−36.9648	+	11.8601i	−1.49056	+	0.478245i
$616$	3.50787	+	2.54861i	0.141336	+	0.102687i
$617$	−26.2483	−	13.3742i	−1.05671	−	0.538423i	−0.162800	−	0.986659i	$-0.552052\pi$
$617$	−26.2483	−	13.3742i	−1.05671	−	0.538423i	−0.893915	+	0.448236i	$0.852052\pi$
$618$	9.78242	−	10.6810i	0.393507	−	0.429655i
$619$	8.70767	−	2.82929i	0.349991	−	0.113719i	−0.128745	−	0.991678i	$-0.541095\pi$
$619$	8.70767	−	2.82929i	0.349991	−	0.113719i	0.478736	+	0.877959i	$0.341095\pi$
$620$	−5.18486	+	2.33825i	−0.208229	+	0.0939066i
$621$	0.720217	−	3.90243i	0.0289013	−	0.156599i
$622$	−8.36229	+	4.26080i	−0.335297	+	0.170842i
$623$	38.9159	+	6.16368i	1.55913	+	0.246942i
$624$	−0.950656	+	0.0417469i	−0.0380567	+	0.00167121i
$625$	−3.08884	−	24.8084i	−0.123554	−	0.992338i
$626$			29.9495i			1.19702i
$627$	−11.0089	−	1.25149i	−0.439654	−	0.0499798i
$628$	−2.33343	−	4.57961i	−0.0931139	−	0.182746i
$629$	14.3524	−	44.1721i	0.572267	−	1.76126i
$630$	24.2855	−	13.6302i	0.967556	−	0.543038i
$631$	4.36435	+	13.4321i	0.173742	+	0.534723i	0.999574	−	0.0291939i	$-0.00929402\pi$
$631$	4.36435	+	13.4321i	0.173742	+	0.534723i	−0.825832	+	0.563916i	$0.809294\pi$
$632$	−7.37688	+	7.37688i	−0.293437	+	0.293437i
$633$	10.5909	−	23.2551i	0.420949	−	0.924307i
$634$	−6.82525	+	9.39415i	−0.271065	+	0.373089i
$635$	0.190846	+	0.698846i	0.00757349	+	0.0277329i
$636$	−10.3815	+	8.26206i	−0.411651	+	0.327612i
$637$	0.879613	+	5.55366i	0.0348515	+	0.220044i
$638$	1.21915	+	7.69739i	0.0482665	+	0.304742i
$639$	−11.2599	+	9.79810i	−0.445436	+	0.387607i
$640$	−1.74447	−	1.39887i	−0.0689562	−	0.0552951i
$641$	18.7007	−	25.7393i	0.738632	−	1.01664i	−0.260064	−	0.965591i	$-0.583744\pi$
$641$	18.7007	−	25.7393i	0.738632	−	1.01664i	0.998696	−	0.0510482i	$-0.0162562\pi$
$642$	−17.7644	−	8.09029i	−0.701105	−	0.319298i
$643$	−7.12848	+	7.12848i	−0.281120	+	0.281120i	−0.833556	−	0.552436i	$-0.813698\pi$
$643$	−7.12848	+	7.12848i	−0.281120	+	0.281120i	0.552436	+	0.833556i	$0.313698\pi$
$644$	0.979741	+	3.01533i	0.0386072	+	0.118821i
$645$	−2.19232	+	0.338949i	−0.0863226	+	0.0133461i
$646$	−9.42054	+	28.9934i	−0.370646	+	1.14073i
$647$	14.2920	+	28.0496i	0.561876	+	1.10274i	0.980854	+	0.194747i	$0.0623885\pi$
$647$	14.2920	+	28.0496i	0.561876	+	1.10274i	−0.418978	+	0.907996i	$0.637612\pi$
$648$	8.99847	−	0.166155i	0.353493	−	0.00652719i
$649$			0.573456i			0.0225101i
$650$	2.05889	+	1.81844i	0.0807563	+	0.0713251i
$651$	0.802415	+	18.2725i	0.0314491	+	0.716156i
$652$	−21.7604	−	3.44651i	−0.852203	−	0.134976i
$653$	33.3311	−	16.9830i	1.30435	−	0.664598i	0.342844	−	0.939392i	$-0.388610\pi$
$653$	33.3311	−	16.9830i	1.30435	−	0.664598i	0.961503	+	0.274794i	$0.0886098\pi$
$654$	−19.3884	−	5.37162i	−0.758148	−	0.210047i
$655$	17.0831	+	18.7910i	0.667492	+	0.734225i
$656$	9.53291	−	3.09743i	0.372198	−	0.120934i
$657$	32.9599	+	27.6283i	1.28589	+	1.07788i
$658$	−2.60838	−	1.32904i	−0.101685	−	0.0518112i
$659$	−26.8536	−	19.5103i	−1.04607	−	0.760012i	−0.0746059	−	0.997213i	$-0.523770\pi$
$659$	−26.8536	−	19.5103i	−1.04607	−	0.760012i	−0.971460	+	0.237201i	$0.923770\pi$
$660$	1.26418	−	3.84248i	0.0492080	−	0.149568i
$661$	1.18106	−	0.858090i	0.0459379	−	0.0333758i	−0.564579	−	0.825379i	$-0.690962\pi$
$661$	1.18106	−	0.858090i	0.0459379	−	0.0333758i	0.610517	+	0.792003i	$0.290962\pi$
$662$	9.39927	−	1.48870i	0.365313	−	0.0578599i
$663$	−4.64105	+	0.945452i	−0.180244	+	0.0367183i
$664$	2.39126	+	3.29129i	0.0927988	+	0.127727i
$665$	2.70375	−	56.7918i	0.104847	−	2.20229i
$666$	−14.4057	+	24.0025i	−0.558208	+	0.930077i
$667$	−2.58710	+	5.07747i	−0.100173	+	0.196600i
$668$	4.86073	+	4.86073i	0.188067	+	0.188067i
$669$	2.42467	+	6.48010i	0.0937433	+	0.250535i
$670$	4.27925	−	20.6172i	0.165322	−	0.796510i
$671$	−7.08854	−	2.30321i	−0.273650	−	0.0889143i
$672$	−6.25746	+	3.54239i	−0.241387	+	0.136650i
$673$	4.34867	−	27.4564i	0.167629	−	1.05837i	−0.750148	−	0.661270i	$-0.770018\pi$
$673$	4.34867	−	27.4564i	0.167629	−	1.05837i	0.917777	−	0.397097i	$-0.129982\pi$
$674$	5.60958			0.216073
$675$	−19.0296	−	17.6883i	−0.732448	−	0.680823i
$676$	12.6982			0.488391
$677$	4.04016	−	25.5085i	0.155276	−	0.980373i	−0.779827	−	0.625996i	$-0.784693\pi$
$677$	4.04016	−	25.5085i	0.155276	−	0.980373i	0.935102	−	0.354378i	$-0.115307\pi$
$678$	−0.762761	+	0.431803i	−0.0292936	+	0.0165833i
$679$	−7.86417	−	2.55522i	−0.301799	−	0.0980605i
$680$	−9.66526	−	5.51871i	−0.370646	−	0.211633i
$681$	−4.88326	−	13.0508i	−0.187127	−	0.500109i
$682$	1.87854	+	1.87854i	0.0719331	+	0.0719331i
$683$	21.7746	−	42.7351i	0.833183	−	1.63521i	0.0624575	−	0.998048i	$-0.480106\pi$
$683$	21.7746	−	42.7351i	0.833183	−	1.63521i	0.770726	−	0.637167i	$-0.219894\pi$
$684$	9.45551	−	15.7546i	0.361540	−	0.602393i
$685$	−12.4028	−	18.8999i	−0.473887	−	0.722130i
$686$	7.89339	+	10.8643i	0.301371	+	0.414802i
$687$	−19.1528	+	3.90172i	−0.730727	+	0.148860i
$688$	0.565729	−	0.0896026i	0.0215682	−	0.00341607i
$689$	−3.40470	+	2.47366i	−0.129709	+	0.0942390i
$690$	2.39932	−	1.72973i	0.0913405	−	0.0658497i
$691$	18.5633	+	13.4870i	0.706182	+	0.513071i	0.881940	−	0.471362i	$-0.156237\pi$
$691$	18.5633	+	13.4870i	0.706182	+	0.513071i	−0.175758	+	0.984433i	$0.556237\pi$
$692$	4.28805	+	2.18487i	0.163007	+	0.0830563i
$693$	−9.96884	−	8.35628i	−0.378685	−	0.317429i
$694$	26.0028	−	8.44881i	0.987051	−	0.320712i
$695$	23.3011	−	40.8086i	0.883861	−	1.54796i
$696$	−12.4550	−	3.45068i	−0.472104	−	0.130798i
$697$	44.4533	−	22.6501i	1.68379	−	0.857934i
$698$	−10.4593	−	1.65659i	−0.395891	−	0.0627029i
$699$	−0.560275	−	12.7585i	−0.0211916	−	0.482572i
$700$	20.1006	+	5.18018i	0.759732	+	0.195792i
$701$			1.57804i			0.0596019i	0.999556	+	0.0298009i	$0.00948734\pi$
$701$			1.57804i			0.0596019i	−0.999556	+	0.0298009i	$0.990513\pi$
$702$	2.85380	+	0.0725673i	0.107710	+	0.00273888i
$703$	25.9462	+	50.9223i	0.978579	+	1.92057i
$704$	−0.322749	+	0.993320i	−0.0121641	+	0.0374372i
$705$	−0.437175	+	2.69585i	−0.0164650	+	0.101532i
$706$	0.393202	+	1.21015i	0.0147983	+	0.0455446i
$707$	−38.6840	+	38.6840i	−1.45486	+	1.45486i
$708$	−0.865468	−	0.394153i	−0.0325263	−	0.0148132i
$709$	18.8054	−	25.8834i	0.706250	−	0.972070i	−0.293619	−	0.955922i	$-0.594860\pi$
$709$	18.8054	−	25.8834i	0.706250	−	0.972070i	0.999870	−	0.0161478i	$-0.00514022\pi$
$710$	−11.1127	−	0.529055i	−0.417052	−	0.0198551i
$711$	23.6101	−	20.5449i	0.885449	−	0.770494i
$712$	1.48469	+	9.37399i	0.0556413	+	0.351305i
$713$	0.303887	+	1.91867i	0.0113807	+	0.0718546i
$714$	−28.0043	+	22.2872i	−1.04803	+	0.834076i
$715$	0.454070	−	1.20003i	0.0169813	−	0.0448787i
$716$	7.64375	−	10.5207i	0.285660	−	0.393178i
$717$	−13.9242	+	30.5743i	−0.520008	+	1.14182i
$718$	−20.1183	+	20.1183i	−0.750807	+	0.750807i
$719$	12.0633	+	37.1272i	0.449887	+	1.38461i	0.877035	+	0.480427i	$0.159518\pi$
$719$	12.0633	+	37.1272i	0.449887	+	1.38461i	−0.427148	+	0.904182i	$0.640482\pi$
$720$	4.93021	+	4.54896i	0.183738	+	0.169530i
$721$	10.7277	−	33.0165i	0.399521	−	1.22960i
$722$	−8.40460	−	16.4950i	−0.312787	−	0.613879i
$723$	3.13715	+	0.356631i	0.116672	+	0.0132633i
$724$		−	6.69138i		−	0.248683i
$725$	18.9629	+	32.1302i	0.704264	+	1.19329i
$726$	17.1466	−	0.752973i	0.636371	−	0.0279455i
$727$	−3.64942	−	0.578012i	−0.135350	−	0.0214373i	0.0883920	−	0.996086i	$-0.471827\pi$
$727$	−3.64942	−	0.578012i	−0.135350	−	0.0214373i	−0.223742	+	0.974648i	$0.571827\pi$
$728$	−2.03219	+	1.03545i	−0.0753181	+	0.0383765i
$729$	−26.9651	−	1.37224i	−0.998708	−	0.0508238i
$730$	3.50338	+	31.8642i	0.129666	+	1.17935i
$731$	2.71143	−	0.880997i	0.100286	−	0.0325849i
$732$	8.34819	−	9.11506i	0.308558	−	0.336902i
$733$	29.0433	+	14.7983i	1.07274	+	0.546588i	0.898885	−	0.438184i	$-0.144378\pi$
$733$	29.0433	+	14.7983i	1.07274	+	0.546588i	0.173854	+	0.984772i	$0.444378\pi$
$734$	26.4585	+	19.2233i	0.976603	+	0.709543i
$735$	23.4173	−	31.9826i	0.863761	−	1.17969i
$736$	−0.617851	+	0.448895i	−0.0227743	+	0.0165465i
$737$	−9.71417	+	1.53857i	−0.357826	+	0.0566741i
$738$	−29.1736	+	7.28944i	−1.07389	+	0.268328i
$739$	24.9769	+	34.3778i	0.918792	+	1.26461i	0.964074	+	0.265634i	$0.0855813\pi$
$739$	24.9769	+	34.3778i	0.918792	+	1.26461i	−0.0452823	+	0.998974i	$0.514419\pi$
$740$	−20.1282	+	5.49674i	−0.739926	+	0.202064i
$741$	3.21555	−	4.86083i	0.118126	−	0.178567i
$742$	−14.4374	+	28.3350i	−0.530015	+	1.04021i
$743$	−6.31364	−	6.31364i	−0.231625	−	0.231625i	0.581746	−	0.813371i	$-0.302370\pi$
$743$	−6.31364	−	6.31364i	−0.231625	−	0.231625i	−0.813371	+	0.581746i	$0.802370\pi$
$744$	−4.12630	+	1.54395i	−0.151277	+	0.0566038i
$745$	−12.2623	−	27.1906i	−0.449257	−	0.996185i
$746$	7.28731	+	2.36779i	0.266807	+	0.0866910i
$747$	−6.47276	−	10.3470i	−0.236826	−	0.378575i
$748$	−0.813241	+	5.13460i	−0.0297350	+	0.187740i
$749$	−46.7864			−1.70954
$750$	−1.12734	−	19.3321i	−0.0411645	−	0.705908i
$751$	−0.00251959			−9.19412e−5			−4.59706e−5	−	1.00000i	$-0.500015\pi$
$751$	−0.00251959			−9.19412e−5			−4.59706e−5		1.00000i	$0.500015\pi$
$752$	0.110311	−	0.696478i	0.00402264	−	0.0253979i
$753$	11.2703	+	19.9085i	0.410713	+	0.725505i
$754$	−3.89877	−	1.26679i	−0.141985	−	0.0461337i
$755$	4.70971	+	10.4433i	0.171404	+	0.380072i
$756$	19.4633	−	9.30160i	0.707872	−	0.338296i
$757$	−3.39223	−	3.39223i	−0.123293	−	0.123293i	0.642768	−	0.766061i	$-0.277786\pi$
$757$	−3.39223	−	3.39223i	−0.123293	−	0.123293i	−0.766061	+	0.642768i	$0.777786\pi$
$758$	4.75981	−	9.34165i	0.172884	−	0.339304i
$759$	−1.15226	−	0.762243i	−0.0418242	−	0.0276677i
$760$	13.2116	−	3.60792i	0.479235	−	0.130873i
$761$	28.8681	+	39.7336i	1.04647	+	1.44034i	0.891830	+	0.452370i	$0.149421\pi$
$761$	28.8681	+	39.7336i	1.04647	+	1.44034i	0.154638	+	0.987971i	$0.450579\pi$
$762$	0.112013	+	0.549853i	0.00405781	+	0.0199191i
$763$	−47.6282	+	7.54356i	−1.72426	+	0.273095i
$764$	3.86321	−	2.80678i	0.139766	−	0.101546i
$765$	27.7796	+	18.5244i	1.00437	+	0.669752i
$766$	21.5944	+	15.6892i	0.780237	+	0.566876i
$767$	−0.268769	−	0.136945i	−0.00970469	−	0.00494479i
$768$	−1.27730	−	1.16983i	−0.0460905	−	0.0422128i
$769$	−38.8030	+	12.6079i	−1.39927	+	0.454651i	−0.908956	−	0.416893i	$-0.863119\pi$
$769$	−38.8030	+	12.6079i	−1.39927	+	0.454651i	−0.490317	+	0.871544i	$0.663119\pi$
$770$	−1.05961	−	9.63743i	−0.0381856	−	0.347309i
$771$	−0.861606	+	3.10990i	−0.0310300	+	0.112000i
$772$	−5.41215	+	2.75763i	−0.194788	+	0.0992493i
$773$	13.6137	+	2.15619i	0.489650	+	0.0775529i	0.396377	−	0.918088i	$-0.370267\pi$
$773$	13.6137	+	2.15619i	0.489650	+	0.0775529i	0.0932724	+	0.995641i	$0.470267\pi$
$774$	−1.71173	+	0.150627i	−0.0615267	+	0.00541418i
$775$	11.6676	+	5.06145i	0.419112	+	0.181812i
$776$		−	1.99179i		−	0.0715012i
$777$	−7.57873	+	66.6673i	−0.271886	+	2.39168i
$778$	−3.17091	−	6.22326i	−0.113683	−	0.223115i
$779$	−18.9710	+	58.3868i	−0.679708	+	2.09193i
$780$	1.49901	+	1.51011i	0.0536732	+	0.0540704i
$781$	1.60580	+	4.94214i	0.0574599	+	0.176844i
$782$	−2.68791	+	2.68791i	−0.0961196	+	0.0961196i
$783$	36.5582	+	12.9148i	1.30648	+	0.461538i
$784$	−6.01584	+	8.28010i	−0.214852	+	0.295718i
$785$	−4.06730	+	10.7492i	−0.145168	+	0.383656i
$786$	12.2496	+	15.3918i	0.436927	+	0.549009i
$787$	−3.68284	−	23.2525i	−0.131279	−	0.828864i	−0.962174	−	0.272435i	$-0.912171\pi$
$787$	−3.68284	−	23.2525i	−0.131279	−	0.828864i	0.830895	−	0.556429i	$-0.187829\pi$
$788$	−2.09281	−	13.2135i	−0.0745532	−	0.470710i
$789$	29.0510	+	36.5032i	1.03424	+	1.29955i
$790$	23.3014	+	1.10934i	0.829025	+	0.0394684i
$791$	−1.23485	+	1.69963i	−0.0439062	+	0.0604317i
$792$	1.17229	−	2.90575i	0.0416557	−	0.103251i
$793$	2.77226	−	2.77226i	0.0984459	−	0.0984459i
$794$	5.65908	+	17.4168i	0.200833	+	0.618101i
$795$	29.2853	+	4.74907i	1.03864	+	0.168432i
$796$	1.03346	−	3.18067i	0.0366301	−	0.112736i
$797$	−19.5456	−	38.3603i	−0.692339	−	1.35879i	−0.922636	−	0.385672i	$-0.873970\pi$
$797$	−19.5456	−	38.3603i	−0.692339	−	1.35879i	0.230297	−	0.973120i	$-0.426030\pi$
$798$	4.97449	−	43.7587i	0.176095	−	1.54904i
$799$		−	3.50987i		−	0.124170i
$800$	0.309477	+	4.99041i	0.0109417	+	0.176438i
$801$	−2.49586	−	28.3629i	−0.0881869	−	1.00215i
$802$	−1.23162	−	0.195070i	−0.0434901	−	0.00688815i
$803$	13.3411	−	6.79762i	0.470797	−	0.239883i
$804$	4.35479	−	15.7183i	0.153581	−	0.554340i
$805$	3.51530	−	6.15656i	0.123898	−	0.216990i
$806$	−1.32905	+	0.431834i	−0.0468138	+	0.0152107i
$807$	−12.9286	−	11.8409i	−0.455109	−	0.416820i
$808$	−11.7415	−	5.98261i	−0.413065	−	0.210467i
$809$	7.45131	+	5.41369i	0.261974	+	0.190335i	0.711017	−	0.703175i	$-0.248235\pi$
$809$	7.45131	+	5.41369i	0.261974	+	0.190335i	−0.449043	+	0.893510i	$0.648235\pi$
$810$	−13.8100	−	14.6384i	−0.485235	−	0.514341i
$811$	34.8513	−	25.3210i	1.22380	−	0.889140i	0.227386	−	0.973805i	$-0.426982\pi$
$811$	34.8513	−	25.3210i	1.22380	−	0.889140i	0.996409	+	0.0846648i	$0.0269820\pi$
$812$	−30.5959	+	4.84591i	−1.07371	+	0.170058i
$813$	−0.146058	−	0.716974i	−0.00512249	−	0.0251454i
$814$	5.72848	+	7.88457i	0.200783	+	0.276354i
$815$	27.0287	+	41.1876i	0.946776	+	1.44274i
$816$	−7.19025	−	4.75651i	−0.251709	−	0.166511i
$817$	−1.59266	+	3.12578i	−0.0557203	+	0.109357i
$818$	5.15736	+	5.15736i	0.180323	+	0.180323i
$819$	6.29706	−	2.67670i	0.220037	−	0.0935314i
$820$	−19.4639	−	11.1136i	−0.679707	−	0.388102i
$821$	3.34850	+	1.08799i	0.116863	+	0.0379712i	0.366865	−	0.930274i	$-0.380431\pi$
$821$	3.34850	+	1.08799i	0.116863	+	0.0379712i	−0.250001	+	0.968245i	$0.580431\pi$
$822$	−8.62650	−	15.2383i	−0.300884	−	0.531497i
$823$	−0.768705	+	4.85341i	−0.0267954	+	0.169179i	−0.997457	−	0.0712700i	$-0.977295\pi$
$823$	−0.768705	+	4.85341i	−0.0267954	+	0.169179i	0.970662	+	0.240449i	$0.0772948\pi$
$824$	8.36223			0.291312
$825$	−8.25906	+	3.68807i	−0.287543	+	0.128402i
$826$	−2.27940			−0.0793104
$827$	6.37481	−	40.2490i	0.221674	−	1.39959i	−0.586165	−	0.810192i	$-0.699363\pi$
$827$	6.37481	−	40.2490i	0.221674	−	1.39959i	0.807839	−	0.589403i	$-0.200637\pi$
$828$	1.94236	−	1.21509i	0.0675018	−	0.0422272i
$829$	−19.6622	−	6.38863i	−0.682896	−	0.221886i	−0.0530331	−	0.998593i	$-0.516889\pi$
$829$	−19.6622	−	6.38863i	−0.682896	−	0.221886i	−0.629863	+	0.776706i	$0.716889\pi$
$830$	1.84873	−	8.90705i	0.0641703	−	0.309168i
$831$	44.0279	−	16.4740i	1.52731	−	0.571478i
$832$	−0.388478	−	0.388478i	−0.0134680	−	0.0134680i
$833$	−23.1275	+	45.3903i	−0.801320	+	1.57268i
$834$	20.0829	−	30.3586i	0.695415	−	1.05123i
$835$	0.730958	−	15.3536i	0.0252958	−	0.531333i
$836$	−3.76003	−	5.17523i	−0.130043	−	0.178989i
$837$	12.6699	−	3.76344i	0.437937	−	0.130084i
$838$	−17.7151	+	2.80580i	−0.611959	+	0.0969248i
$839$	7.65838	−	5.56414i	0.264397	−	0.192095i	−0.447686	−	0.894191i	$-0.647752\pi$
$839$	7.65838	−	5.56414i	0.264397	−	0.192095i	0.712083	+	0.702095i	$0.247752\pi$
$840$	15.2732	+	5.02490i	0.526977	+	0.173376i
$841$	−21.5827	−	15.6807i	−0.744230	−	0.540715i
$842$	28.3578	+	14.4490i	0.977276	+	0.497947i
$843$	−14.7337	+	16.0871i	−0.507455	+	0.554070i
$844$	14.0311	−	4.55897i	0.482969	−	0.156926i
$845$	−19.1001	−	21.0096i	−0.657063	−	0.722753i
$846$	−0.474839	+	2.06150i	−0.0163253	+	0.0708758i
$847$	36.6539	−	18.6761i	1.25944	−	0.641718i
$848$	−7.56590	−	1.19832i	−0.259814	−	0.0411505i
$849$	−13.4151	+	0.589108i	−0.460405	+	0.0202181i
$850$	5.40717	+	24.2926i	0.185464	+	0.833229i
$851$			7.12629i			0.244286i
$852$	−8.56245	−	0.973379i	−0.293345	−	0.0333474i
$853$	−5.01168	−	9.83597i	−0.171597	−	0.336777i	0.789152	−	0.614198i	$-0.210520\pi$
$853$	−5.01168	−	9.83597i	−0.171597	−	0.336777i	−0.960749	+	0.277421i	$0.910520\pi$
$854$	9.15488	−	28.1758i	0.313274	−	0.964157i
$855$	−40.2892	+	8.05294i	−1.37786	+	0.275405i
$856$	−3.48257	−	10.7182i	−0.119032	−	0.366342i
$857$	10.2021	−	10.2021i	0.348497	−	0.348497i	−0.511053	−	0.859549i	$-0.670744\pi$
$857$	10.2021	−	10.2021i	0.348497	−	0.348497i	0.859549	+	0.511053i	$0.170744\pi$
$858$	0.411918	−	0.904477i	0.0140627	−	0.0308783i
$859$	−19.1249	+	26.3231i	−0.652532	+	0.898133i	−0.999206	−	0.0398530i	$-0.987311\pi$
$859$	−19.1249	+	26.3231i	−0.652532	+	0.898133i	0.346674	+	0.937986i	$0.387311\pi$
$860$	−0.999197	−	0.801244i	−0.0340723	−	0.0273222i
$861$	−56.3949	+	44.8818i	−1.92193	+	1.52957i
$862$	1.49664	+	9.44941i	0.0509758	+	0.321848i
$863$	−3.14654	−	19.8665i	−0.107109	−	0.676262i	−0.981561	−	0.191149i	$-0.938779\pi$
$863$	−3.14654	−	19.8665i	−0.107109	−	0.676262i	0.874452	−	0.485113i	$-0.161221\pi$
$864$	3.57965	+	3.76645i	0.121782	+	0.128137i
$865$	−2.83496	−	10.3811i	−0.0963915	−	0.352970i
$866$	10.2078	−	14.0499i	0.346877	−	0.477435i
$867$	−12.2551	−	5.58123i	−0.416205	−	0.189549i
$868$	−7.46691	+	7.46691i	−0.253444	+	0.253444i
$869$	−3.36708	−	10.3628i	−0.114220	−	0.351534i
$870$	13.0250	+	25.7976i	0.441587	+	0.874620i
$871$	1.59870	−	4.92029i	0.0541698	−	0.166718i
$872$	−5.27337	−	10.3496i	−0.178579	−	0.350480i
$873$	−0.413813	+	5.96103i	−0.0140054	+	0.201750i
$874$		−	4.67752i		−	0.158219i
$875$	−21.6637	−	41.0491i	−0.732368	−	1.38771i
$876$	1.08936	+	24.8067i	0.0368060	+	0.838142i
$877$	−30.9405	−	4.90050i	−1.04479	−	0.165478i	−0.389631	−	0.920971i	$-0.627397\pi$
$877$	−30.9405	−	4.90050i	−1.04479	−	0.165478i	−0.655157	+	0.755493i	$0.727397\pi$
$878$	−19.9766	+	10.1786i	−0.674179	+	0.343511i
$879$	7.11373	+	1.97088i	0.239940	+	0.0664760i
$880$	2.12895	−	0.960111i	0.0717670	−	0.0323653i
$881$	−53.5974	+	17.4149i	−1.80574	+	0.586722i	−0.999985	−	0.00552165i	$-0.998242\pi$
$881$	−53.5974	+	17.4149i	−1.80574	+	0.586722i	−0.805759	+	0.592243i	$0.798242\pi$
$882$	19.7245	−	23.5308i	0.664157	−	0.792324i
$883$	17.7557	+	9.04697i	0.597526	+	0.304455i	0.726471	−	0.687197i	$-0.241159\pi$
$883$	17.7557	+	9.04697i	0.597526	+	0.304455i	−0.128945	+	0.991652i	$0.541159\pi$
$884$	−2.21230	−	1.60733i	−0.0744075	−	0.0540602i
$885$	0.649661	+	2.02482i	0.0218381	+	0.0680636i
$886$	7.92428	−	5.75733i	0.266221	−	0.193421i
$887$	−26.4392	+	4.18756i	−0.887741	+	0.140604i	−0.583618	−	0.812028i	$-0.698363\pi$
$887$	−26.4392	+	4.18756i	−0.887741	+	0.140604i	−0.304123	+	0.952633i	$0.598363\pi$
$888$	−15.8368	+	3.22620i	−0.531450	+	0.108264i
$889$	0.790563	+	1.08812i	0.0265146	+	0.0364943i
$890$	13.2764	−	16.5565i	0.445027	−	0.554974i
$891$	−4.11213	+	8.45277i	−0.137762	+	0.283178i
$892$	−1.81351	+	3.55922i	−0.0607210	+	0.119172i
$893$	3.05395	+	3.05395i	0.102196	+	0.102196i
$894$	−8.09680	−	21.6392i	−0.270798	−	0.723724i
$895$	−28.9044	+	3.17796i	−0.966167	+	0.106227i
$896$	−3.94829	−	1.28288i	−0.131903	−	0.0428579i
$897$	0.632416	−	0.358014i	0.0211158	−	0.0119538i
$898$	3.83429	−	24.2088i	0.127952	−	0.807857i
$899$	−18.9799			−0.633015
$900$	0.110601	−	14.9996i	0.00368668	−	0.499986i
$901$	−38.1280			−1.27023
$902$	−1.63770	+	10.3400i	−0.0545295	+	0.344286i
$903$	−3.58415	+	2.02901i	−0.119273	+	0.0675212i
$904$	−0.481282	−	0.156378i	−0.0160072	−	0.00520105i
$905$	−11.0712	+	10.0649i	−0.368018	+	0.334569i
$906$	3.10981	+	8.31118i	0.103317	+	0.276120i
$907$	−19.5694	−	19.5694i	−0.649791	−	0.649791i	0.303151	−	0.952942i	$-0.401961\pi$
$907$	−19.5694	−	19.5694i	−0.649791	−	0.649791i	−0.952942	+	0.303151i	$0.901961\pi$
$908$	3.65240	−	7.16823i	0.121209	−	0.237886i
$909$	33.8971	+	20.3441i	1.12429	+	0.674772i
$910$	4.76994	+	1.80486i	0.158122	+	0.0598304i
$911$	−15.3895	−	21.1818i	−0.509877	−	0.701786i	0.474021	−	0.880513i	$-0.342802\pi$
$911$	−15.3895	−	21.1818i	−0.509877	−	0.701786i	−0.983899	+	0.178728i	$0.942802\pi$
$912$	10.3949	−	2.11760i	0.344210	−	0.0701207i
$913$	−4.19673	+	0.664696i	−0.138891	+	0.0219982i
$914$	−11.4710	+	8.33418i	−0.379428	+	0.275670i
$915$	−27.6382	−	0.101895i	−0.913692	−	0.00336854i
$916$	−9.12977	−	6.63317i	−0.301656	−	0.219166i
$917$	42.0103	+	21.4053i	1.38730	+	0.706866i
$918$	20.5307	+	15.7291i	0.677616	+	0.519138i
$919$	−24.1173	+	7.83618i	−0.795555	+	0.258492i	−0.678468	−	0.734630i	$-0.737356\pi$
$919$	−24.1173	+	7.83618i	−0.795555	+	0.258492i	−0.117087	+	0.993122i	$0.537356\pi$
$920$	1.67206	+	0.347049i	0.0551262	+	0.0114419i
$921$	−31.8813	−	8.83280i	−1.05052	−	0.291051i
$922$	18.5864	−	9.47022i	0.612109	−	0.311885i
$923$	−2.69977	−	0.427602i	−0.0888640	−	0.0140747i
$924$	−0.329480	−	7.50288i	−0.0108391	−	0.246827i
$925$	39.3705	+	25.0349i	1.29450	+	0.823141i
$926$		−	19.4434i		−	0.638949i
$927$	−25.0265	−	1.73733i	−0.821977	−	0.0570613i
$928$	−3.38756	−	6.64846i	−0.111202	−	0.218247i
$929$	12.4755	−	38.3955i	0.409307	−	1.25972i	−0.507938	−	0.861393i	$-0.669592\pi$
$929$	12.4755	−	38.3955i	0.409307	−	1.25972i	0.917245	−	0.398323i	$-0.130408\pi$
$930$	8.76113	+	4.50478i	0.287289	+	0.147718i
$931$	−19.3709	−	59.6174i	−0.634855	−	1.95388i
$932$	5.21367	−	5.21367i	0.170779	−	0.170779i
$933$	14.7937	+	6.73738i	0.484325	+	0.220572i
$934$	−8.11024	+	11.1628i	−0.265375	+	0.365258i
$935$	9.71865	−	6.37772i	0.317834	−	0.208574i
$936$	1.08193	+	1.24335i	0.0353639	+	0.0406400i
$937$	3.76729	+	23.7857i	0.123072	+	0.777046i	0.969599	+	0.244700i	$0.0786895\pi$
$937$	3.76729	+	23.7857i	0.123072	+	0.777046i	−0.846527	+	0.532346i	$0.821310\pi$
$938$	−6.11558	−	38.6123i	−0.199681	−	1.26074i
$939$	40.5888	−	32.3025i	1.32457	−	1.05415i
$940$	−1.31828	+	0.865099i	−0.0429974	+	0.0282164i
$941$	−24.5801	+	33.8316i	−0.801288	+	1.10288i	0.191322	+	0.981527i	$0.438723\pi$
$941$	−24.5801	+	33.8316i	−0.801288	+	1.10288i	−0.992610	+	0.121351i	$0.961277\pi$
$942$	−3.68973	+	8.10179i	−0.120218	+	0.263971i
$943$	−5.41291	+	5.41291i	−0.176268	+	0.176268i
$944$	−0.169668	−	0.522184i	−0.00552222	−	0.0169956i
$945$	−44.6657	−	18.2117i	−1.45298	−	0.592426i
$946$	−0.184864	+	0.568954i	−0.00601046	+	0.0184983i
$947$	20.9731	+	41.1619i	0.681533	+	1.33758i	0.929503	+	0.368816i	$0.120237\pi$
$947$	20.9731	+	41.1619i	0.681533	+	1.33758i	−0.247970	+	0.968768i	$0.579763\pi$
$948$	17.9540	+	2.04101i	0.583117	+	0.0662888i
$949$			7.87605i			0.255668i
$950$	−25.8418	−	16.4322i	−0.838419	−	0.533132i
$951$	20.0929	−	0.882355i	0.651556	−	0.0286123i
$952$	−20.4092	−	3.23251i	−0.661467	−	0.104766i
$953$	−22.1963	+	11.3096i	−0.719009	+	0.366354i	−0.774900	−	0.632083i	$-0.782200\pi$
$953$	−22.1963	+	11.3096i	−0.719009	+	0.366354i	0.0558911	+	0.998437i	$0.482200\pi$
$954$	22.3942	+	5.15821i	0.725040	+	0.167003i
$955$	−10.4548	−	2.16998i	−0.338310	−	0.0702188i
$956$	−18.4471	+	5.99384i	−0.596623	+	0.193855i
$957$	9.11691	−	9.95440i	0.294708	−	0.321780i
$958$	6.42288	+	3.27262i	0.207514	+	0.105734i
$959$	−33.9549	−	24.6696i	−1.09646	−	0.796624i
$960$	−0.0142786	+	3.87296i	−0.000460839	+	0.124999i
$961$	19.8452	−	14.4184i	0.640166	−	0.465108i
$962$	−5.06336	+	0.801958i	−0.163249	+	0.0258562i
$963$	8.19581	+	32.8010i	0.264106	+	1.05700i
$964$	1.07147	+	1.47476i	0.0345099	+	0.0474988i
$965$	12.7034	+	4.80671i	0.408935	+	0.154733i
$966$	3.02980	−	4.58003i	0.0974821	−	0.147360i
$967$	20.6107	−	40.4508i	0.662796	−	1.30081i	−0.277590	−	0.960700i	$-0.589536\pi$
$967$	20.6107	−	40.4508i	0.662796	−	1.30081i	0.940386	−	0.340110i	$-0.110464\pi$
$968$	7.00683	+	7.00683i	0.225208	+	0.225208i
$969$	49.4539	−	18.5043i	1.58869	−	0.594443i
$970$	−3.29550	+	2.99597i	−0.105812	+	0.0961949i
$971$	47.1650	+	15.3248i	1.51360	+	0.491798i	0.943949	−	0.330091i	$-0.107079\pi$
$971$	47.1650	+	15.3248i	1.51360	+	0.491798i	0.569648	+	0.821889i	$0.307079\pi$
$972$	−9.93065	−	12.0159i	−0.318526	−	0.385411i
$973$	13.6483	−	86.1718i	0.437543	−	2.76254i
$974$	15.1728			0.486167
$975$	0.243777	−	4.75161i	0.00780710	−	0.152173i
$976$	7.13621			0.228425
$977$	−3.69043	+	23.3005i	−0.118067	+	0.745448i	0.855628	+	0.517592i	$0.173172\pi$
$977$	−3.69043	+	23.3005i	−0.118067	+	0.745448i	−0.973695	+	0.227856i	$0.926828\pi$
$978$	18.7992	+	33.2080i	0.601133	+	1.06187i
$979$	−9.42744	−	3.06316i	−0.301302	−	0.0978991i
$980$	22.7485	−	2.50114i	0.726676	−	0.0798959i
$981$	13.6319	+	32.0697i	0.435233	+	1.02391i
$982$	−19.2286	−	19.2286i	−0.613608	−	0.613608i
$983$	−3.32022	+	6.51631i	−0.105899	+	0.207838i	−0.937875	−	0.346973i	$-0.887209\pi$
$983$	−3.32022	+	6.51631i	−0.105899	+	0.207838i	0.831976	+	0.554811i	$0.187209\pi$
$984$	−14.4797	−	9.57864i	−0.461595	−	0.305356i
$985$	−18.7143	+	23.3378i	−0.596287	+	0.743604i
$986$	−21.8305	−	30.0471i	−0.695224	−	0.956894i
$987$	1.01215	+	4.96845i	0.0322170	+	0.158148i
$988$	3.32346	−	0.526384i	0.105733	−	0.0167465i
$989$	−0.353893	+	0.257118i	−0.0112531	+	0.00817589i
$990$	−6.57100	+	2.43111i	−0.208840	+	0.0772657i
$991$	2.22201	+	1.61438i	0.0705844	+	0.0512826i	0.622518	−	0.782606i	$-0.286110\pi$
$991$	2.22201	+	1.61438i	0.0705844	+	0.0512826i	−0.551934	+	0.833888i	$0.686110\pi$
$992$	−2.26639	−	1.15478i	−0.0719579	−	0.0366644i
$993$	−12.1553	−	11.1327i	−0.385737	−	0.353284i
$994$	−19.6442	+	6.38279i	−0.623076	+	0.202450i
$995$	−6.81704	+	3.07433i	−0.216115	+	0.0974629i
$996$	1.88136	−	6.79062i	0.0596132	−	0.215169i
$997$	−7.46783	+	3.80505i	−0.236508	+	0.120507i	−0.568229	−	0.822871i	$-0.692371\pi$
$997$	−7.46783	+	3.80505i	−0.236508	+	0.120507i	0.331720	+	0.943378i	$0.392371\pi$
$998$	6.99881	+	1.10850i	0.221543	+	0.0350890i
$999$	48.0667	−	6.36513i	1.52076	−	0.201384i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.l.a.77.6	yes	80
3.2	odd	2	inner	150.2.l.a.77.5	✓	80
5.2	odd	4		750.2.l.a.593.9		80
5.3	odd	4		750.2.l.c.593.2		80
5.4	even	2		750.2.l.b.407.5		80
15.2	even	4		750.2.l.a.593.3		80
15.8	even	4		750.2.l.c.593.8		80
15.14	odd	2		750.2.l.b.407.6		80
25.9	even	10		750.2.l.a.707.3		80
25.12	odd	20		750.2.l.b.293.6		80
25.13	odd	20	inner	150.2.l.a.113.5	yes	80
25.16	even	5		750.2.l.c.707.8		80
75.38	even	20	inner	150.2.l.a.113.6	yes	80
75.41	odd	10		750.2.l.c.707.2		80
75.59	odd	10		750.2.l.a.707.9		80
75.62	even	20		750.2.l.b.293.5		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.77.5	✓	80	3.2	odd	2	inner
150.2.l.a.77.6	yes	80	1.1	even	1	trivial
150.2.l.a.113.5	yes	80	25.13	odd	20	inner
150.2.l.a.113.6	yes	80	75.38	even	20	inner
750.2.l.a.593.3		80	15.2	even	4
750.2.l.a.593.9		80	5.2	odd	4
750.2.l.a.707.3		80	25.9	even	10
750.2.l.a.707.9		80	75.59	odd	10
750.2.l.b.293.5		80	75.62	even	20
750.2.l.b.293.6		80	25.12	odd	20
750.2.l.b.407.5		80	5.4	even	2
750.2.l.b.407.6		80	15.14	odd	2
750.2.l.c.593.2		80	5.3	odd	4
750.2.l.c.593.8		80	15.8	even	4
750.2.l.c.707.2		80	75.41	odd	10
750.2.l.c.707.8		80	25.16	even	5

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.156434 - 0.987688i) q^{2} +(-1.50729 + 0.853283i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(0.919260 + 2.03837i) q^{5} +(0.606986 + 1.62221i) q^{6} +(2.93554 + 2.93554i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(1.54382 - 2.57228i) q^{9} +O(q^{10})\)	\(q+(0.156434 - 0.987688i) q^{2} +(-1.50729 + 0.853283i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(0.919260 + 2.03837i) q^{5} +(0.606986 + 1.62221i) q^{6} +(2.93554 + 2.93554i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(1.54382 - 2.57228i) q^{9} +(2.15708 - 0.589071i) q^{10} +(-0.613906 - 0.844968i) q^{11} +(1.69719 - 0.345744i) q^{12} +(0.542627 - 0.0859436i) q^{13} +(3.35862 - 2.44018i) q^{14} +(-3.12490 - 2.28802i) q^{15} +(0.809017 + 0.587785i) q^{16} +(4.43491 + 2.25970i) q^{17} +(-2.29911 - 1.92720i) q^{18} +(-5.82500 + 1.89266i) q^{19} +(-0.244377 - 2.22267i) q^{20} +(-6.92954 - 1.91985i) q^{21} +(-0.930602 + 0.474165i) q^{22} +(-0.754303 - 0.119470i) q^{23} +(-0.0759877 - 1.73038i) q^{24} +(-3.30992 + 3.74759i) q^{25} -0.549391i q^{26} +(-0.132087 + 5.19447i) q^{27} +(-1.88473 - 3.69899i) q^{28} +(2.30581 - 7.09654i) q^{29} +(-2.74869 + 2.72850i) q^{30} +(-0.786024 - 2.41913i) q^{31} +(0.707107 - 0.707107i) q^{32} +(1.64633 + 0.749773i) q^{33} +(2.92565 - 4.02682i) q^{34} +(-3.28520 + 8.68224i) q^{35} +(-2.26314 + 1.96932i) q^{36} +(-1.45972 - 9.21632i) q^{37} +(0.958124 + 6.04936i) q^{38} +(-0.744559 + 0.592556i) q^{39} +(-2.23354 - 0.106335i) q^{40} +(5.89166 - 8.10918i) q^{41} +(-2.98023 + 6.54389i) q^{42} +(0.405017 - 0.405017i) q^{43} +(0.322749 + 0.993320i) q^{44} +(6.66244 + 0.782276i) q^{45} +(-0.235998 + 0.726327i) q^{46} +(-0.320136 - 0.628302i) q^{47} +(-1.72097 - 0.195639i) q^{48} +10.2348i q^{49} +(3.18366 + 3.85542i) q^{50} +(-8.61284 + 0.378222i) q^{51} +(-0.542627 - 0.0859436i) q^{52} +(-6.82529 + 3.47766i) q^{53} +(5.10986 + 0.943055i) q^{54} +(1.15802 - 2.02811i) q^{55} +(-3.94829 + 1.28288i) q^{56} +(7.16496 - 7.82314i) q^{57} +(-6.64846 - 3.38756i) q^{58} +(-0.444196 - 0.322728i) q^{59} +(2.26492 + 3.14168i) q^{60} +(5.77332 - 4.19456i) q^{61} +(-2.51231 + 0.397911i) q^{62} +(12.0830 - 3.01910i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(0.674000 + 1.02707i) q^{65} +(0.998085 - 1.50877i) q^{66} +(4.27513 - 8.39042i) q^{67} +(-3.51957 - 3.51957i) q^{68} +(1.23889 - 0.463559i) q^{69} +(8.06143 + 4.60295i) q^{70} +(-4.73186 - 1.53747i) q^{71} +(1.59104 + 2.54334i) q^{72} +(-2.24264 + 14.1595i) q^{73} -9.33120 q^{74} +(1.79124 - 8.47298i) q^{75} +6.12476 q^{76} +(0.678294 - 4.28258i) q^{77} +(0.468786 + 0.828088i) q^{78} +(9.92188 + 3.22381i) q^{79} +(-0.454428 + 2.18941i) q^{80} +(-4.23326 - 7.94226i) q^{81} +(-7.08768 - 7.08768i) q^{82} +(1.84695 - 3.62484i) q^{83} +(5.99712 + 3.96723i) q^{84} +(-0.529273 + 11.1173i) q^{85} +(-0.336672 - 0.463389i) q^{86} +(2.57985 + 12.6640i) q^{87} +(1.03158 - 0.163386i) q^{88} +(7.67825 - 5.57858i) q^{89} +(1.81488 - 6.45803i) q^{90} +(1.84519 + 1.34061i) q^{91} +(0.680467 + 0.346715i) q^{92} +(3.24897 + 2.97562i) q^{93} +(-0.670646 + 0.217906i) q^{94} +(-9.21262 - 10.1337i) q^{95} +(-0.462449 + 1.66917i) q^{96} +(-1.77470 + 0.904255i) q^{97} +(10.1088 + 1.60107i) q^{98} +(-3.12125 + 0.274662i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q + 4 * q^3 + 4 * q^7	\( 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) \) 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more