LMFDB - Embedded newform 150.2.l.a.77.5

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			77.5
Character	$\chi$	$=$	150.77
Dual form			150.2.l.a.113.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.156434 + 0.987688i) q^{2} +(1.57628 - 0.717872i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(-0.919260 - 2.03837i) q^{5} +(0.462449 + 1.66917i) q^{6} +(2.93554 + 2.93554i) q^{7} +(0.453990 - 0.891007i) q^{8} +(1.96932 - 2.26314i) q^{9} +O(q^{10})$	\(q+(-0.156434 + 0.987688i) q^{2} +(1.57628 - 0.717872i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(-0.919260 - 2.03837i) q^{5} +(0.462449 + 1.66917i) q^{6} +(2.93554 + 2.93554i) q^{7} +(0.453990 - 0.891007i) q^{8} +(1.96932 - 2.26314i) q^{9} +(2.15708 - 0.589071i) q^{10} +(0.613906 + 0.844968i) q^{11} +(-1.72097 + 0.195639i) q^{12} +(0.542627 - 0.0859436i) q^{13} +(-3.35862 + 2.44018i) q^{14} +(-2.91230 - 2.55313i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-4.43491 - 2.25970i) q^{17} +(1.92720 + 2.29911i) q^{18} +(-5.82500 + 1.89266i) q^{19} +(0.244377 + 2.22267i) q^{20} +(6.73457 + 2.51989i) 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} +(1.47956 - 4.98105i) q^{27} +(-1.88473 - 3.69899i) q^{28} +(-2.30581 + 7.09654i) q^{29} +(2.97729 - 2.47705i) q^{30} +(-0.786024 - 2.41913i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(1.57427 + 0.891202i) q^{33} +(2.92565 - 4.02682i) q^{34} +(3.28520 - 8.68224i) q^{35} +(-2.57228 + 1.54382i) q^{36} +(-1.45972 - 9.21632i) q^{37} +(-0.958124 - 6.04936i) q^{38} +(0.793635 - 0.525008i) q^{39} +(-2.23354 - 0.106335i) q^{40} +(-5.89166 + 8.10918i) q^{41} +(-3.54239 + 6.25746i) q^{42} +(0.405017 - 0.405017i) q^{43} +(-0.322749 - 0.993320i) q^{44} +(-6.42343 - 1.93380i) q^{45} +(-0.235998 + 0.726327i) q^{46} +(0.320136 + 0.628302i) q^{47} +(1.69719 + 0.345744i) 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} +(4.68828 + 2.24055i) q^{54} +(1.15802 - 2.02811i) q^{55} +(3.94829 - 1.28288i) q^{56} +(-7.82314 + 7.16496i) q^{57} +(-6.64846 - 3.38756i) q^{58} +(0.444196 + 0.322728i) q^{59} +(1.98080 + 3.32813i) q^{60} +(5.77332 - 4.19456i) q^{61} +(2.51231 - 0.397911i) q^{62} +(12.4245 - 0.862506i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-0.674000 - 1.02707i) q^{65} +(-1.12650 + 1.41547i) q^{66} +(4.27513 - 8.39042i) q^{67} +(3.51957 + 3.51957i) q^{68} +(1.27476 - 0.353175i) q^{69} +(8.06143 + 4.60295i) q^{70} +(4.73186 + 1.53747i) q^{71} +(-1.12242 - 2.78212i) q^{72} +(-2.24264 + 14.1595i) q^{73} +9.33120 q^{74} +(-2.52708 + 8.28335i) q^{75} +6.12476 q^{76} +(-0.678294 + 4.28258i) q^{77} +(0.394392 + 0.865994i) q^{78} +(9.92188 + 3.22381i) q^{79} +(0.454428 - 2.18941i) q^{80} +(-1.24356 - 8.91367i) q^{81} +(-7.08768 - 7.08768i) q^{82} +(-1.84695 + 3.62484i) q^{83} +(-5.62627 - 4.47765i) q^{84} +(-0.529273 + 11.1173i) q^{85} +(0.336672 + 0.463389i) q^{86} +(1.45981 + 12.8414i) q^{87} +(1.03158 - 0.163386i) q^{88} +(-7.67825 + 5.57858i) q^{89} +(2.91483 - 6.04183i) q^{90} +(1.84519 + 1.34061i) q^{91} +(-0.680467 - 0.346715i) q^{92} +(-2.97562 - 3.24897i) q^{93} +(-0.670646 + 0.217906i) q^{94} +(9.21262 + 10.1337i) q^{95} +(-0.606986 + 1.62221i) 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
$3$	1.57628	−	0.717872i	0.910066	−	0.414464i
$3$	1.57628	−	0.717872i	0.910066	−	0.414464i
$4$	−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
$6$	0.462449	+	1.66917i	0.188794	+	0.681437i
$7$	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
$9$	1.96932	−	2.26314i	0.656440	−	0.754378i
$10$	2.15708	−	0.589071i	0.682129	−	0.186281i
$11$	0.613906	+	0.844968i	0.185099	+	0.254768i	0.891475	−	0.453070i	$-0.149671\pi$
$11$	0.613906	+	0.844968i	0.185099	+	0.254768i	−0.706376	+	0.707837i	$0.749671\pi$
$12$	−1.72097	+	0.195639i	−0.496800	+	0.0564762i
$13$	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
$15$	−2.91230	−	2.55313i	−0.751953	−	0.659217i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	−4.43491	−	2.25970i	−1.07562	−	0.548058i	−0.175851	−	0.984417i	$-0.556268\pi$
$17$	−4.43491	−	2.25970i	−1.07562	−	0.548058i	−0.899773	+	0.436359i	$0.856268\pi$
$18$	1.92720	+	2.29911i	0.454246	+	0.541905i
$19$	−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
$21$	6.73457	+	2.51989i	1.46960	+	0.549885i
$22$	−0.930602	+	0.474165i	−0.198405	+	0.101092i
$23$	0.754303	+	0.119470i	0.157283	+	0.0249112i	0.234579	−	0.972097i	$-0.424629\pi$
$23$	0.754303	+	0.119470i	0.157283	+	0.0249112i	−0.0772962	+	0.997008i	$0.524629\pi$
$24$	0.0759877	−	1.73038i	0.0155109	−	0.353213i
$25$	−3.30992	+	3.74759i	−0.661984	+	0.749518i
$26$			0.549391i			0.107744i
$27$	1.47956	−	4.98105i	0.284741	−	0.958604i
$28$	−1.88473	−	3.69899i	−0.356181	−	0.699044i
$29$	−2.30581	+	7.09654i	−0.428177	+	1.31779i	0.471741	+	0.881737i	$0.343626\pi$
$29$	−2.30581	+	7.09654i	−0.428177	+	1.31779i	−0.899919	+	0.436058i	$0.856374\pi$
$30$	2.97729	−	2.47705i	0.543576	−	0.452245i
$31$	−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
$33$	1.57427	+	0.891202i	0.274045	+	0.155138i
$34$	2.92565	−	4.02682i	0.501745	−	0.690593i
$35$	3.28520	−	8.68224i	0.555299	−	1.46757i
$36$	−2.57228	+	1.54382i	−0.428714	+	0.257303i
$37$	−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
$39$	0.793635	−	0.525008i	0.127083	−	0.0840685i
$40$	−2.23354	−	0.106335i	−0.353153	−	0.0168130i
$41$	−5.89166	+	8.10918i	−0.920123	+	1.26644i	0.0434660	+	0.999055i	$0.486160\pi$
$41$	−5.89166	+	8.10918i	−0.920123	+	1.26644i	−0.963589	+	0.267386i	$0.913840\pi$
$42$	−3.54239	+	6.25746i	−0.546602	+	0.965547i
$43$	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
$45$	−6.42343	−	1.93380i	−0.957548	−	0.288273i
$46$	−0.235998	+	0.726327i	−0.0347960	+	0.107091i
$47$	0.320136	+	0.628302i	0.0466966	+	0.0916472i	0.913176	−	0.407566i	$-0.133622\pi$
$47$	0.320136	+	0.628302i	0.0466966	+	0.0916472i	−0.866479	+	0.499213i	$0.833622\pi$
$48$	1.69719	+	0.345744i	0.244969	+	0.0499038i
$49$			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	0.0826807	−	0.996576i	$-0.473652\pi$
$53$	6.82529	−	3.47766i	0.937526	−	0.477693i	0.854845	+	0.518883i	$0.173652\pi$
$54$	4.68828	+	2.24055i	0.637994	+	0.304900i
$55$	1.15802	−	2.02811i	0.156148	−	0.273471i
$56$	3.94829	−	1.28288i	0.527612	−	0.171432i
$57$	−7.82314	+	7.16496i	−1.03620	+	0.949022i
$58$	−6.64846	−	3.38756i	−0.872986	−	0.444809i
$59$	0.444196	+	0.322728i	0.0578294	+	0.0420156i	0.616324	−	0.787492i	$-0.288621\pi$
$59$	0.444196	+	0.322728i	0.0578294	+	0.0420156i	−0.558495	+	0.829508i	$0.688621\pi$
$60$	1.98080	+	3.32813i	0.255720	+	0.429659i
$61$	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
$63$	12.4245	−	0.862506i	1.56534	−	0.108666i
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$	−0.674000	−	1.02707i	−0.0835994	−	0.127392i
$66$	−1.12650	+	1.41547i	−0.138662	+	0.174232i
$67$	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
$69$	1.27476	−	0.353175i	0.153463	−	0.0425173i
$70$	8.06143	+	4.60295i	0.963525	+	0.550158i
$71$	4.73186	+	1.53747i	0.561568	+	0.182465i	0.576027	−	0.817431i	$-0.304602\pi$
$71$	4.73186	+	1.53747i	0.561568	+	0.182465i	−0.0144583	+	0.999895i	$0.504602\pi$
$72$	−1.12242	−	2.78212i	−0.132278	−	0.327876i
$73$	−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
$75$	−2.52708	+	8.28335i	−0.291802	+	0.956479i
$76$	6.12476			0.702558
$77$	−0.678294	+	4.28258i	−0.0772988	+	0.488045i
$78$	0.394392	+	0.865994i	0.0446561	+	0.0980545i
$79$	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
$81$	−1.24356	−	8.91367i	−0.138173	−	0.990408i
$82$	−7.08768	−	7.08768i	−0.782704	−	0.782704i
$83$	−1.84695	+	3.62484i	−0.202729	+	0.397878i	−0.969878	−	0.243591i	$-0.921675\pi$
$83$	−1.84695	+	3.62484i	−0.202729	+	0.397878i	0.767149	+	0.641469i	$0.221675\pi$
$84$	−5.62627	−	4.47765i	−0.613876	−	0.488552i
$85$	−0.529273	+	11.1173i	−0.0574077	+	1.20584i
$86$	0.336672	+	0.463389i	0.0363043	+	0.0499685i
$87$	1.45981	+	12.8414i	0.156508	+	1.37674i
$88$	1.03158	−	0.163386i	0.109967	−	0.0174170i
$89$	−7.67825	+	5.57858i	−0.813893	+	0.591328i	−0.914957	−	0.403552i	$-0.867775\pi$
$89$	−7.67825	+	5.57858i	−0.813893	+	0.591328i	0.101064	+	0.994880i	$0.467775\pi$
$90$	2.91483	−	6.04183i	0.307250	−	0.636865i
$91$	1.84519	+	1.34061i	0.193429	+	0.140534i
$92$	−0.680467	−	0.346715i	−0.0709436	−	0.0361476i
$93$	−2.97562	−	3.24897i	−0.308558	−	0.336902i
$94$	−0.670646	+	0.217906i	−0.0691719	+	0.0224753i
$95$	9.21262	+	10.1337i	0.945195	+	1.03969i
$96$	−0.606986	+	1.62221i	−0.0619503	+	0.165566i
$97$	−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	$-0.772407\pi$
$101$		−	13.1778i		−	1.31124i	0.755090	−	0.655621i	$-0.227593\pi$
$102$	1.72091	−	8.44764i	0.170396	−	0.836441i
$103$	−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
$105$	−1.05435	−	16.0440i	−0.102894	−	1.56573i
$106$	2.36713	+	7.28529i	0.229916	+	0.707610i
$107$	7.96897	−	7.96897i	0.770389	−	0.770389i	−0.207785	−	0.978174i	$-0.566626\pi$
$107$	7.96897	−	7.96897i	0.770389	−	0.770389i	0.978174	+	0.207785i	$0.0666256\pi$
$108$	−2.94637	+	4.28006i	−0.283515	+	0.411849i
$109$	−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
$111$	−8.91707	−	13.4796i	−0.846371	−	1.27943i
$112$	0.649434	+	4.10037i	0.0613658	+	0.387448i
$113$	−0.0791636	−	0.499819i	−0.00744708	−	0.0470190i	0.983685	−	0.179900i	$-0.0575773\pi$
$113$	−0.0791636	−	0.499819i	−0.00744708	−	0.0470190i	−0.991132	+	0.132881i	$0.957577\pi$
$114$	−5.85294	−	8.84767i	−0.548178	−	0.828660i
$115$	−0.449877	−	1.64737i	−0.0419512	−	0.153618i
$116$	4.38590	−	6.03668i	0.407221	−	0.560492i
$117$	0.874103	−	1.39729i	0.0808109	−	0.129179i
$118$	−0.388242	+	0.388242i	−0.0357406	+	0.0357406i
$119$	−6.38542	−	19.6523i	−0.585350	−	1.80152i
$120$	−3.59702	+	1.43578i	−0.328361	+	0.131068i
$121$	3.06210	−	9.42416i	0.278372	−	0.856742i
$122$	3.23977	+	6.35841i	0.293315	+	0.575664i
$123$	−3.46556	+	17.0118i	−0.312479	+	1.53390i
$124$			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
$129$	0.347670	−	0.929170i	0.0306106	−	0.0818089i
$130$	1.11986	−	0.505033i	0.0982184	−	0.0442943i
$131$	−10.8014	+	3.50958i	−0.943720	+	0.306633i	−0.740161	−	0.672429i	$-0.765251\pi$
$131$	−10.8014	+	3.50958i	−0.943720	+	0.306633i	−0.203559	+	0.979063i	$0.565251\pi$
$132$	−1.22182	−	1.33406i	−0.106346	−	0.116115i
$133$	−22.6555	−	11.5435i	−1.96448	−	1.00095i
$134$	7.61834	+	5.53505i	0.658124	+	0.478155i
$135$	−11.5133	+	1.56299i	−0.990911	+	0.134521i
$136$	−4.02682	+	2.92565i	−0.345297	+	0.250873i
$137$	9.98531	−	1.58152i	0.853102	−	0.135118i	0.285457	−	0.958391i	$-0.407855\pi$
$137$	9.98531	−	1.58152i	0.853102	−	0.135118i	0.567645	+	0.823273i	$0.307855\pi$
$138$	0.149411	+	1.31431i	0.0127187	+	0.111882i
$139$	−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
$141$	0.955664	+	0.760563i	0.0804814	+	0.0640510i
$142$	−2.25877	+	4.43309i	−0.189552	+	0.372017i
$143$	0.405741	+	0.405741i	0.0339298	+	0.0339298i
$144$	2.92345	−	0.673378i	0.243621	−	0.0561148i
$145$	16.5850	−	1.82348i	1.37731	−	0.151432i
$146$	−13.6343	−	4.43006i	−1.12838	−	0.366634i
$147$	7.34725	+	16.1329i	0.605991	+	1.33062i
$148$	−1.45972	+	9.21632i	−0.119988	+	0.757577i
$149$	13.3393			1.09280			0.546401	−	0.837524i	$-0.315997\pi$
$149$	13.3393			1.09280			0.546401	+	0.837524i	$0.315997\pi$
$150$	−7.78605	−	3.79176i	−0.635728	−	0.309596i
$151$	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
$153$	−13.8478	+	5.58673i	−1.11953	+	0.451661i
$154$	−4.12375	−	1.33989i	−0.332301	−	0.107971i
$155$	−4.20853	+	3.82602i	−0.338037	+	0.307313i
$156$	−0.917028	+	0.254065i	−0.0734210	+	0.0203415i
$157$	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
$159$	8.26206	−	10.3815i	0.655224	−	0.823303i
$160$	2.09136	+	0.791332i	0.165337	+	0.0625603i
$161$	1.86358	+	2.56499i	0.146870	+	0.202150i
$162$	8.99847	+	0.166155i	0.706986	+	0.0130544i
$163$	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
$165$	0.369440	−	4.02819i	0.0287609	−	0.313594i
$166$	−3.29129	−	2.39126i	−0.255453	−	0.185598i
$167$	6.12488	+	3.12078i	0.473957	+	0.241493i	0.674617	−	0.738168i	$-0.264309\pi$
$167$	6.12488	+	3.12078i	0.473957	+	0.241493i	−0.200660	+	0.979661i	$0.564309\pi$
$168$	5.30267	−	4.85654i	0.409110	−	0.374690i
$169$	−12.0767	+	3.92395i	−0.928975	+	0.301842i
$170$	−10.8976	−	2.26188i	−0.835807	−	0.173478i
$171$	−7.18794	+	16.9100i	−0.549676	+	1.29314i
$172$	−0.510351	+	0.260037i	−0.0389139	+	0.0198276i
$173$	4.75334	+	0.752855i	0.361390	+	0.0572385i	0.334489	−	0.942400i	$-0.391436\pi$
$173$	4.75334	+	0.752855i	0.361390	+	0.0572385i	0.0269007	+	0.999638i	$0.491436\pi$
$174$	−12.9117	−	0.567001i	−0.978832	−	0.0429842i
$175$	−20.7176	+	1.28479i	−1.56610	+	0.0971208i
$176$			1.04444i			0.0787275i
$177$	0.931855	+	0.189833i	0.0700425	+	0.0142687i
$178$	−4.30875	−	8.45640i	−0.322955	−	0.633834i
$179$	4.01856	−	12.3679i	0.300361	−	0.924417i	−0.681006	−	0.732277i	$-0.738457\pi$
$179$	4.01856	−	12.3679i	0.300361	−	0.924417i	0.981368	−	0.192139i	$-0.0615425\pi$
$180$	5.51147	+	3.82410i	0.410801	+	0.285031i
$181$	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
$183$	6.08921	−	10.7563i	0.450127	−	0.795129i
$184$	0.448895	−	0.617851i	0.0330930	−	0.0455486i
$185$	−17.4444	+	11.4477i	−1.28254	+	0.841648i
$186$	3.67446	−	2.43074i	0.269424	−	0.178230i
$187$	−0.813241	−	5.13460i	−0.0594701	−	0.375479i
$188$	−0.110311	−	0.696478i	−0.00804527	−	0.0507959i
$189$	18.9654	−	10.2788i	1.37953	−	0.747671i
$190$	−11.4501	+	7.51395i	−0.830676	+	0.545119i
$191$	2.80678	−	3.86321i	0.203092	−	0.279532i	−0.695307	−	0.718713i	$-0.744731\pi$
$191$	2.80678	−	3.86321i	0.203092	−	0.279532i	0.898398	+	0.439181i	$0.144731\pi$
$192$	−1.50729	−	0.853283i	−0.108779	−	0.0615804i
$193$	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
$195$	−1.79972	−	1.13511i	−0.128881	−	0.0812866i
$196$	3.16272	−	9.73384i	0.225908	−	0.695274i
$197$	−6.07357	−	11.9200i	−0.432724	−	0.849268i	−0.999674	−	0.0255162i	$-0.991877\pi$
$197$	−6.07357	−	11.9200i	−0.432724	−	0.849268i	0.566951	−	0.823752i	$-0.308123\pi$
$198$	−0.759552	+	3.03986i	−0.0539790	+	0.216033i
$199$			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
$204$	8.07442	+	3.02123i	0.565323	+	0.211528i
$205$	21.9455	+	4.55496i	1.53274	+	0.318132i
$206$	7.95295	−	2.58407i	0.554108	−	0.180041i
$207$	1.75584	−	1.47182i	0.122039	−	0.102298i
$208$	0.489511	+	0.249418i	0.0339415	+	0.0172940i
$209$	−5.17523	−	3.76003i	−0.357978	−	0.260086i
$210$	16.0114	+	1.46847i	1.10489	+	0.101334i
$211$	−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
$213$	8.56245	−	0.973379i	0.586689	−	0.0666948i
$214$	6.62423	+	9.11748i	0.452823	+	0.623258i
$215$	−1.19789	−	0.453259i	−0.0816955	−	0.0309120i
$216$	−3.76645	−	3.57965i	−0.256274	−	0.243564i
$217$	4.79405	−	9.40886i	0.325441	−	0.638715i
$218$	−8.21346	−	8.21346i	−0.556286	−	0.556286i
$219$	6.62966	+	23.9292i	0.447991	+	1.61699i
$220$	−1.72807	+	1.57100i	−0.116506	+	0.105917i
$221$	−2.60071	−	0.845022i	−0.174943	−	0.0568423i
$222$	14.7086	−	6.69861i	0.987176	−	0.449581i
$223$	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
$225$	1.96301	+	14.8710i	0.130867	+	0.991400i
$226$	0.506049			0.0336619
$227$	1.25853	−	7.94605i	0.0835316	−	0.527398i	−0.910070	−	0.414455i	$-0.863972\pi$
$227$	1.25853	−	7.94605i	0.0835316	−	0.527398i	0.993601	−	0.112943i	$-0.0360277\pi$
$228$	9.65434	−	4.39680i	0.639374	−	0.291185i
$229$	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
$231$	2.00516	+	7.23747i	0.131930	+	0.476191i
$232$	5.27625	+	5.27625i	0.346403	+	0.346403i
$233$	3.34738	−	6.56960i	0.219294	−	0.430389i	−0.754982	−	0.655745i	$-0.772355\pi$
$233$	3.34738	−	6.56960i	0.219294	−	0.430389i	0.974276	+	0.225356i	$0.0723546\pi$
$234$	1.24335	+	1.08193i	0.0812800	+	0.0707277i
$235$	0.986424	−	1.23013i	0.0643472	−	0.0802447i
$236$	−0.322728	−	0.444196i	−0.0210078	−	0.0289147i
$237$	17.9540	−	2.04101i	1.16623	−	0.132578i
$238$	20.4092	−	3.23251i	1.32293	−	0.209532i
$239$	−15.6921	+	11.4010i	−1.01504	+	0.737467i	−0.965259	−	0.261294i	$-0.915851\pi$
$239$	−15.6921	+	11.4010i	−1.01504	+	0.737467i	−0.0497763	+	0.998760i	$0.515851\pi$
$240$	−0.855407	−	3.77734i	−0.0552163	−	0.243826i
$241$	−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
$243$	−8.35908	−	13.1577i	−0.536235	−	0.844069i
$244$	−6.78694	+	2.20521i	−0.434489	+	0.141174i
$245$	20.8623	−	9.40841i	1.33284	−	0.601081i
$246$	−16.2602	−	6.08413i	−1.03671	−	0.387910i
$247$	−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	$0.136865\pi$
$251$			13.2082i			0.833692i	−0.908977	+	0.416846i	$0.863135\pi$
$252$	−12.0830	−	3.01910i	−0.761155	−	0.190185i
$253$	0.362123	+	0.710706i	0.0227665	+	0.0446817i
$254$	−0.100115	+	0.308121i	−0.00628175	+	0.0193332i
$255$	7.14648	+	17.9039i	0.447530	+	1.12118i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−1.31744	+	1.31744i	−0.0821794	+	0.0821794i	−0.747002	−	0.664822i	$-0.768507\pi$
$257$	−1.31744	+	1.31744i	−0.0821794	+	0.0821794i	0.664822	+	0.747002i	$0.268507\pi$
$258$	0.863343	+	0.488744i	0.0537494	+	0.0304279i
$259$	22.7698	−	31.3399i	1.41485	−	1.94737i
$260$	0.323630	+	1.18508i	0.0200707	+	0.0734955i
$261$	11.5196	+	19.1937i	0.713043	+	1.18806i
$262$	−1.77666	−	11.2174i	−0.109763	−	0.693014i
$263$	4.21352	+	26.6031i	0.259817	+	1.64042i	0.680167	+	0.733057i	$0.261907\pi$
$263$	4.21352	+	26.6031i	0.259817	+	1.64042i	−0.420351	+	0.907362i	$0.638093\pi$
$264$	1.50877	−	0.998085i	0.0928583	−	0.0614279i
$265$	−13.3630	−	10.7156i	−0.820882	−	0.658255i
$266$	14.9455	−	20.5707i	0.916368	−	1.26127i
$267$	−8.09837	+	14.3054i	−0.495612	+	0.875477i
$268$	−6.65867	+	6.65867i	−0.406743	+	0.406743i
$269$	−3.12783	−	9.62647i	−0.190707	−	0.586936i	0.809293	−	0.587405i	$-0.199851\pi$
$269$	−3.12783	−	9.62647i	−0.190707	−	0.586936i	−1.00000		0.000469431i	$0.999851\pi$
$270$	0.257332	−	11.6161i	0.0156607	−	0.706933i
$271$	−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
$273$	3.87093	+	0.788566i	0.234279	+	0.0477262i
$274$			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
$279$	−7.02276	−	2.98517i	−0.420441	−	0.178717i
$280$	−6.24449	−	6.86879i	−0.373179	−	0.410488i
$281$	−11.9782	+	3.89197i	−0.714562	+	0.232175i	−0.643664	−	0.765308i	$-0.722587\pi$
$281$	−11.9782	+	3.89197i	−0.714562	+	0.232175i	−0.0708982	+	0.997484i	$0.522587\pi$
$282$	−0.900698	+	0.824920i	−0.0536358	+	0.0491232i
$283$	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
$285$	21.7964	+	9.36001i	1.29110	+	0.554439i
$286$	−0.464218	+	0.337274i	−0.0274498	+	0.0199434i
$287$	−41.1000	+	6.50960i	−2.42606	+	0.384250i
$288$	0.207759	+	2.99280i	0.0122423	+	0.176352i
$289$	4.56985	+	6.28986i	0.268815	+	0.369992i
$290$	−0.793443	+	16.6661i	−0.0465926	+	0.978667i
$291$	−2.14829	+	2.69937i	−0.125935	+	0.158240i
$292$	6.50840	−	12.7735i	0.380875	−	0.747510i
$293$	3.01356	+	3.01356i	0.176054	+	0.176054i	0.789633	−	0.613579i	$-0.210271\pi$
$293$	3.01356	+	3.01356i	0.176054	+	0.176054i	−0.613579	+	0.789633i	$0.710271\pi$
$294$	−17.0836	+	4.73306i	−0.996336	+	0.276038i
$295$	0.249507	−	1.20211i	0.0145269	−	0.0699894i
$296$	−8.87450	−	2.88350i	−0.515820	−	0.167600i
$297$	5.11714	−	1.80772i	0.296927	−	0.104894i
$298$	−2.08673	+	13.1751i	−0.120881	+	0.763214i
$299$	0.419573			0.0242645
$300$	4.96309	−	7.09702i	0.286544	−	0.409747i
$301$	2.37788			0.137059
$302$	−0.801471	+	5.06029i	−0.0461195	+	0.291187i
$303$	−9.45999	−	20.7719i	−0.543462	−	1.19332i
$304$	−5.82500	−	1.89266i	−0.334086	−	0.108551i
$305$	−13.8573	−	7.91228i	−0.793464	−	0.453056i
$306$	−3.35168	−	14.5512i	−0.191603	−	0.831839i
$307$	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
$309$	−11.3329	−	9.01924i	−0.644704	−	0.513087i
$310$	−3.12056	−	4.75524i	−0.177236	−	0.270079i
$311$	5.51649	+	7.59280i	0.312811	+	0.430548i	0.936255	−	0.351320i	$-0.114267\pi$
$311$	5.51649	+	7.59280i	0.312811	+	0.430548i	−0.623444	+	0.781868i	$0.714267\pi$
$312$	−0.107482	−	0.945483i	−0.00608500	−	0.0535274i
$313$	−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
$315$	−13.1795	−	24.5329i	−0.742580	−	1.38228i
$316$	−8.44006	−	6.13206i	−0.474790	−	0.344955i
$317$	10.3462	+	5.27165i	0.581100	+	0.296085i	0.719725	−	0.694260i	$-0.244268\pi$
$317$	10.3462	+	5.27165i	0.581100	+	0.296085i	−0.138624	+	0.990345i	$0.544268\pi$
$318$	8.96117	+	9.78436i	0.502518	+	0.548680i
$319$	−7.41190	+	2.40827i	−0.414987	+	0.134837i
$320$	−1.10875	+	1.94182i	−0.0619810	+	0.108551i
$321$	6.84063	−	18.2820i	0.381807	−	1.02040i
$322$	−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
$327$	−4.01602	+	19.7139i	−0.222086	+	1.09018i
$328$	4.55057	+	8.93100i	0.251263	+	0.493132i
$329$	−0.904633	+	2.78417i	−0.0498740	+	0.153496i
$330$	3.92080	+	0.995039i	0.215833	+	0.0547751i
$331$	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
$333$	−23.7324	−	14.8463i	−1.30053	−	0.813574i
$334$	−4.04050	+	5.56128i	−0.221086	+	0.304299i
$335$	−21.0328	−	1.00133i	−1.14914	−	0.0547086i
$336$	3.96723	+	5.99712i	0.216430	+	0.327169i
$337$	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
$339$	−0.483590	−	0.731026i	−0.0262650	−	0.0397039i
$340$	3.93879	−	10.4096i	0.213611	−	0.564539i
$341$	1.56155	−	2.14928i	0.0845625	−	0.116390i
$342$	−15.5774	−	9.74475i	−0.842327	−	0.526936i
$343$	−9.49577	+	9.49577i	−0.512723	+	0.512723i
$344$	−0.176999	−	0.544747i	−0.00954314	−	0.0293708i
$345$	−1.89174	−	2.27377i	−0.101848	−	0.122416i
$346$	−1.48717	+	4.57705i	−0.0799509	+	0.246064i
$347$	−12.4125	−	24.3609i	−0.666339	−	1.30776i	−0.938423	−	0.345490i	$-0.887713\pi$
$347$	−12.4125	−	24.3609i	−0.666339	−	1.30776i	0.272084	−	0.962274i	$-0.412287\pi$
$348$	2.57985	−	12.6640i	0.138295	−	0.678863i
$349$		−	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	−0.423559	−	0.905869i	$-0.639219\pi$
$353$	1.13374	−	0.577670i	0.0603430	−	0.0307463i	0.483902	+	0.875122i	$0.339219\pi$
$354$	−0.333270	+	0.890686i	−0.0177131	+	0.0473394i
$355$	−1.21586	−	11.0586i	−0.0645314	−	0.586931i
$356$	9.02633	−	2.93283i	0.478394	−	0.155440i
$357$	−24.1730	−	26.3936i	−1.27937	−	1.39690i
$358$	11.5869	+	5.90384i	0.612389	+	0.312028i
$359$	23.0178	+	16.7234i	1.21483	+	0.882626i	0.995660	−	0.0930604i	$-0.0296650\pi$
$359$	23.0178	+	16.7234i	1.21483	+	0.882626i	0.219170	+	0.975687i	$0.429665\pi$
$360$	−4.63920	+	4.84539i	−0.244507	+	0.255375i
$361$	14.9771	−	10.8815i	0.788269	−	0.572711i
$362$	−6.60900	+	1.04676i	−0.347361	+	0.0550166i
$363$	−1.93862	−	17.0533i	−0.101751	−	0.895067i
$364$	−1.34061	−	1.84519i	−0.0702671	−	0.0967143i
$365$	30.9239	−	8.44491i	1.61863	−	0.442027i
$366$	9.67132	+	7.69690i	0.505528	+	0.402323i
$367$	−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
$369$	6.74960	+	29.3032i	0.351370	+	1.52546i
$370$	−8.57780	−	19.0205i	−0.445939	−	0.988827i
$371$	30.2447	+	9.82710i	1.57023	+	0.510198i
$372$	1.82600	+	4.00947i	0.0946736	+	0.207881i
$373$	−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
$375$	19.2076	−	2.46343i	0.991876	−	0.127211i
$376$	0.705159			0.0363658
$377$	−0.641290	+	4.04894i	−0.0330281	+	0.208531i
$378$	7.18539	+	20.3398i	0.369576	+	1.04617i
$379$	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
$381$	0.540775	−	0.149823i	0.0277048	−	0.00767568i
$382$	3.37657	+	3.37657i	0.172760	+	0.172760i
$383$	12.1180	−	23.7829i	0.619200	−	1.21525i	−0.342079	−	0.939671i	$-0.611131\pi$
$383$	12.1180	−	23.7829i	0.619200	−	1.21525i	0.961279	−	0.275577i	$-0.0888689\pi$
$384$	1.07857	−	1.35524i	0.0550405	−	0.0691596i
$385$	9.35302	−	2.55419i	0.476674	−	0.130174i
$386$	3.57033	+	4.91413i	0.181725	+	0.250123i
$387$	−0.119000	−	1.71422i	−0.00604912	−	0.0871385i
$388$	1.96727	−	0.311585i	0.0998730	−	0.0158183i
$389$	−5.65060	+	4.10540i	−0.286497	+	0.208152i	−0.721746	−	0.692158i	$-0.756660\pi$
$389$	−5.65060	+	4.10540i	−0.286497	+	0.208152i	0.435249	+	0.900310i	$0.356660\pi$
$390$	1.40267	−	1.59999i	0.0710269	−	0.0810187i
$391$	−3.07530	−	2.23434i	−0.155525	−	0.112995i
$392$	9.11924	+	4.64649i	0.460591	+	0.234683i
$393$	−14.5066	+	13.2861i	−0.731759	+	0.670194i
$394$	12.7234	−	4.13408i	0.640996	−	0.208272i
$395$	−2.54946	−	23.1880i	−0.128277	−	1.16672i
$396$	−2.88361	−	1.22574i	−0.144907	−	0.0615957i
$397$	−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	$0.00991233\pi$
$401$			1.24697i			0.0622709i	−0.999515	+	0.0311355i	$0.990088\pi$
$402$	15.9821	+	3.25579i	0.797115	+	0.162384i
$403$	−0.634427	−	1.24513i	−0.0316030	−	0.0620245i
$404$	−4.07217	+	12.5329i	−0.202598	+	0.623533i
$405$	−17.0262	+	10.7288i	−0.846040	+	0.533120i
$406$	−9.57250	−	29.4611i	−0.475075	−	1.46213i
$407$	6.89137	−	6.89137i	0.341593	−	0.341593i
$408$	−4.24715	+	7.50239i	−0.210265	+	0.371424i
$409$	−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
$411$	14.6043	−	9.66109i	0.720378	−	0.476546i
$412$	1.30814	+	8.25928i	0.0644475	+	0.406905i
$413$	0.356576	+	2.25133i	0.0175460	+	0.110781i
$414$	1.17902	+	1.96447i	0.0579457	+	0.0965483i
$415$	9.08660	+	0.432597i	0.446044	+	0.0212353i
$416$	−0.322924	+	0.444466i	−0.0158326	+	0.0217918i
$417$	−31.6765	−	17.9323i	−1.55121	−	0.878148i
$418$	4.52332	−	4.52332i	0.221243	−	0.221243i
$419$	5.54251	+	17.0581i	0.270769	+	0.833343i	0.990308	+	0.138890i	$0.0443534\pi$
$419$	5.54251	+	17.0581i	0.270769	+	0.833343i	−0.719538	+	0.694453i	$0.755647\pi$
$420$	−3.95512	+	15.5846i	−0.192990	+	0.760449i
$421$	−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
$423$	2.05238	+	0.512816i	0.0997902	+	0.0249340i
$424$		−	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
$429$	0.930832	+	0.348292i	0.0449410	+	0.0168157i
$430$	0.635070	−	1.11224i	0.0306258	−	0.0536369i
$431$	9.09895	−	2.95643i	0.438281	−	0.142406i	−0.0815614	−	0.996668i	$-0.525991\pi$
$431$	9.09895	−	2.95643i	0.438281	−	0.142406i	0.519842	+	0.854262i	$0.325991\pi$
$432$	4.12478	−	3.16010i	0.198453	−	0.152040i
$433$	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
$435$	24.8336	−	14.7802i	1.19068	−	0.708658i
$436$	9.39721	−	6.82747i	0.450045	−	0.326977i
$437$	−4.61993	+	0.731725i	−0.221001	+	0.0350031i
$438$	−24.6717	+	2.80468i	−1.17886	+	0.134013i
$439$	−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
$441$	23.1627	+	20.1555i	1.10298	+	0.959787i
$442$	1.24146	−	2.43650i	0.0590502	−	0.115892i
$443$	−6.92607	−	6.92607i	−0.329068	−	0.329068i	0.523164	−	0.852232i	$-0.324751\pi$
$443$	−6.92607	−	6.92607i	−0.329068	−	0.329068i	−0.852232	+	0.523164i	$0.824751\pi$
$444$	4.31521	+	15.5754i	0.204791	+	0.739176i
$445$	18.4295	+	10.5230i	0.873643	+	0.498837i
$446$	3.79910	+	1.23440i	0.179893	+	0.0584506i
$447$	21.0266	−	9.57594i	0.994522	−	0.452927i
$448$	0.649434	−	4.10037i	0.0306829	−	0.193724i
$449$	−24.5105			−1.15672			−0.578362	−	0.815780i	$-0.696308\pi$
$449$	−24.5105			−1.15672			−0.578362	+	0.815780i	$0.696308\pi$
$450$	−14.9950	−	0.387499i	−0.706871	−	0.0182669i
$451$	−10.4689			−0.492963
$452$	−0.0791636	+	0.499819i	−0.00372354	+	0.0235095i
$453$	8.07586	−	3.67792i	0.379437	−	0.172804i
$454$	7.65134	+	2.48607i	0.359095	+	0.116677i
$455$	1.03645	−	4.99356i	0.0485896	−	0.234102i
$456$	2.83239	+	10.2233i	0.132639	+	0.478750i
$457$	−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
$459$	−17.8174	+	18.7472i	−0.831645	+	0.875043i
$460$	−0.0812085	+	1.70577i	−0.00378637	+	0.0795318i
$461$	−12.2612	−	16.8761i	−0.571060	−	0.785996i	0.421620	−	0.906773i	$-0.361462\pi$
$461$	−12.2612	−	16.8761i	−0.571060	−	0.785996i	−0.992680	+	0.120776i	$0.961462\pi$
$462$	−7.46205	+	0.848285i	−0.347166	+	0.0394658i
$463$	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
$465$	−3.88723	+	9.05207i	−0.180266	+	0.419780i
$466$	5.96507	+	4.33388i	0.276327	+	0.200763i
$467$	12.2941	+	6.26414i	0.568902	+	0.289870i	0.714685	−	0.699447i	$-0.246570\pi$
$467$	12.2941	+	6.26414i	0.568902	+	0.289870i	−0.145783	+	0.989317i	$0.546570\pi$
$468$	−1.26311	+	1.05879i	−0.0583872	+	0.0489425i
$469$	37.1802	−	12.0806i	1.71682	−	0.557829i
$470$	1.06067	+	1.16671i	0.0489252	+	0.0538165i
$471$	8.33786	+	3.11980i	0.384188	+	0.143753i
$472$	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
$477$	5.57077	−	22.2952i	0.255068	−	1.02083i
$478$	−8.80581	−	17.2824i	−0.402768	−	0.790477i
$479$	2.22757	−	6.85575i	0.101780	−	0.313247i	−0.887181	−	0.461421i	$-0.847340\pi$
$479$	2.22757	−	6.85575i	0.101780	−	0.313247i	0.988961	+	0.148174i	$0.0473396\pi$
$480$	3.86465	−	0.253970i	0.176396	−	0.0115921i
$481$	−1.58417	−	4.87557i	−0.0722319	−	0.222307i
$482$	1.28899	−	1.28899i	0.0587117	−	0.0587117i
$483$	4.77886	+	2.70534i	0.217446	+	0.123097i
$484$	−5.82445	+	8.01667i	−0.264748	+	0.364394i
$485$	3.47462	+	2.78625i	0.157774	+	0.126517i
$486$	14.3034	−	6.19784i	0.648815	−	0.281140i
$487$	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
$489$	31.8264	−	21.0539i	1.43924	−	0.952088i
$490$	6.02900	+	22.0772i	0.272362	+	0.997347i
$491$	−15.9838	+	21.9998i	−0.721340	+	0.992839i	0.278139	+	0.960541i	$0.410283\pi$
$491$	−15.9838	+	21.9998i	−0.721340	+	0.992839i	−0.999478	+	0.0322980i	$0.989717\pi$
$492$	8.55288	−	15.1083i	0.385594	−	0.681133i
$493$	26.2621	−	26.2621i	1.18279	−	1.18279i
$494$	−1.03981	−	3.20020i	−0.0467831	−	0.143984i
$495$	−2.30938	−	6.61476i	−0.103799	−	0.297311i
$496$	0.786024	−	2.41913i	0.0352935	−	0.108622i
$497$	9.37724	+	18.4039i	0.420627	+	0.825526i
$498$	−6.90461	−	1.40657i	−0.309403	−	0.0630300i
$499$			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	0.581110	−	0.813825i	$-0.302619\pi$
$503$	35.4598	−	18.0677i	1.58108	−	0.805598i	0.999966	+	0.00822664i	$0.00261865\pi$
$504$	4.87212	−	11.4619i	0.217021	−	0.510554i
$505$	−26.8613	+	12.1138i	−1.19531	+	0.539059i
$506$	−0.758604	+	0.246485i	−0.0337241	+	0.0109576i
$507$	−16.2193	+	14.8548i	−0.720326	+	0.659723i
$508$	−0.288666	−	0.147083i	−0.0128075	−	0.00652575i
$509$	−12.2593	−	8.90692i	−0.543385	−	0.394792i	0.281956	−	0.959427i	$-0.409017\pi$
$509$	−12.2593	−	8.90692i	−0.543385	−	0.394792i	−0.825341	+	0.564635i	$0.809017\pi$
$510$	−18.8014	+	4.25772i	−0.832540	+	0.188535i
$511$	−48.1490	+	34.9823i	−2.12999	+	1.54753i
$512$	−0.987688	+	0.156434i	−0.0436501	+	0.00691349i
$513$	0.809001	+	31.8149i	0.0357182	+	1.40466i
$514$	−1.09512	−	1.50731i	−0.0483038	−	0.0664845i
$515$	−11.6976	+	14.5876i	−0.515460	+	0.642808i
$516$	−0.617783	+	0.776258i	−0.0271964	+	0.0341728i
$517$	−0.334362	+	0.656222i	−0.0147052	+	0.0288606i
$518$	27.3921	+	27.3921i	1.20354	+	1.20354i
$519$	8.03305	−	2.22558i	0.352612	−	0.0976921i
$520$	−1.22112	+	0.134258i	−0.0535495	+	0.00588762i
$521$	8.21939	+	2.67064i	0.360098	+	0.117003i	0.483478	−	0.875357i	$-0.339373\pi$
$521$	8.21939	+	2.67064i	0.360098	+	0.117003i	−0.123380	+	0.992360i	$0.539373\pi$
$522$	−20.7595	+	8.37518i	−0.908617	+	0.366572i
$523$	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
$525$	−31.7344	+	16.8978i	−1.38500	+	0.737479i
$526$	−26.9347			−1.17441
$527$	−1.98057	+	12.5048i	−0.0862749	+	0.544718i
$528$	0.749773	+	1.64633i	0.0326297	+	0.0716472i
$529$	−21.3196	−	6.92716i	−0.926939	−	0.301181i
$530$	12.6741	−	11.5222i	0.550528	−	0.500491i
$531$	1.60514	−	0.369723i	0.0696572	−	0.0160446i
$532$	17.9795	+	17.9795i	0.779509	+	0.779509i
$533$	−2.50004	+	4.90661i	−0.108289	+	0.212529i
$534$	−12.8624	−	10.2365i	−0.556611	−	0.442978i
$535$	−23.5693	−	8.91817i	−1.01899	−	0.385566i
$536$	−5.53505	−	7.61834i	−0.239078	−	0.329062i
$537$	−2.54416	−	22.3800i	−0.109789	−	0.965769i
$538$	9.99725	−	1.58341i	0.431012	−	0.0682656i
$539$	−8.64805	+	6.28318i	−0.372498	+	0.270636i
$540$	11.4328	+	2.07132i	0.491991	+	0.0891355i
$541$	−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
$543$	7.82780	+	8.54688i	0.335923	+	0.366782i
$544$	4.73381	−	1.53811i	0.202960	−	0.0659458i
$545$	25.4312	+	5.27845i	1.08935	+	0.226104i
$546$	−1.38440	+	3.69991i	−0.0592470	+	0.158342i
$547$	−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
$552$	0.264046	−	1.29616i	0.0112386	−	0.0551680i
$553$	19.6624	+	38.5897i	0.836131	+	1.64100i
$554$	8.38693	−	25.8123i	0.356327	−	1.09666i
$555$	−19.2794	+	30.5676i	−0.818363	+	1.29752i
$556$	6.49419	+	19.9871i	0.275415	+	0.847640i
$557$	−2.89425	+	2.89425i	−0.122633	+	0.122633i	−0.765760	−	0.643127i	$-0.777637\pi$
$557$	−2.89425	+	2.89425i	−0.122633	+	0.122633i	0.643127	+	0.765760i	$0.277637\pi$
$558$	4.04702	−	6.46931i	0.171324	−	0.273868i
$559$	0.184964	−	0.254582i	0.00782316	−	0.0107677i
$560$	7.76107	−	5.09309i	0.327965	−	0.215222i
$561$	−4.96788	−	7.50977i	−0.209744	−	0.317063i
$562$	−1.97024	−	12.4396i	−0.0831096	−	0.524733i
$563$	−2.55888	−	16.1561i	−0.107844	−	0.680900i	−0.981080	−	0.193603i	$-0.937983\pi$
$563$	−2.55888	−	16.1561i	−0.107844	−	0.680900i	0.873236	−	0.487297i	$-0.162017\pi$
$564$	−0.673863	−	1.01865i	−0.0283748	−	0.0428931i
$565$	−0.946045	+	0.620829i	−0.0398004	+	0.0261185i
$566$	−4.55691	+	6.27205i	−0.191541	+	0.263634i
$567$	22.5159	−	29.8169i	0.945579	−	1.25219i
$568$	3.51812	−	3.51812i	0.147617	−	0.147617i
$569$	−7.86991	−	24.2211i	−0.329924	−	1.01540i	−0.969169	−	0.246398i	$-0.920753\pi$
$569$	−7.86991	−	24.2211i	−0.329924	−	1.01540i	0.639245	−	0.769003i	$-0.279247\pi$
$570$	−12.6545	+	20.0638i	−0.530038	+	0.840379i
$571$	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
$573$	1.65099	−	8.10441i	0.0689711	−	0.338566i
$574$		−	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
$579$	3.68696	−	9.85364i	0.153225	−	0.409503i
$580$	−16.3368	−	3.39083i	−0.678348	−	0.140796i
$581$	−16.0626	+	5.21907i	−0.666391	+	0.216523i
$582$	−2.33007	−	2.54411i	−0.0965844	−	0.105457i
$583$	7.12860	+	3.63220i	0.295236	+	0.150430i
$584$	11.5981	+	8.42648i	0.479931	+	0.348690i
$585$	−3.65172	−	0.497277i	−0.150980	−	0.0205599i
$586$	−3.44789	+	2.50504i	−0.142431	+	0.103482i
$587$	3.14939	−	0.498814i	0.129989	−	0.0205882i	−0.0911008	−	0.995842i	$-0.529039\pi$
$587$	3.14939	−	0.498814i	0.129989	−	0.0205882i	0.221090	+	0.975253i	$0.429039\pi$
$588$	−2.00232	−	17.6137i	−0.0825744	−	0.726376i
$589$	9.15717	+	12.6038i	0.377315	+	0.519329i
$590$	1.14828	+	0.434486i	0.0472738	+	0.0178875i
$591$	−18.1307	−	14.4293i	−0.745798	−	0.593542i
$592$	4.23628	−	8.31416i	0.174110	−	0.341710i
$593$	−24.3096	−	24.3096i	−0.998277	−	0.998277i	0.00172155	−	0.999999i	$-0.499452\pi$
$593$	−24.3096	−	24.3096i	−0.998277	−	0.998277i	−0.999999	+	0.00172155i	$0.999452\pi$
$594$	0.984963	+	5.33693i	0.0404135	+	0.218977i
$595$	−34.1888	+	31.0814i	−1.40160	+	1.27421i
$596$	−12.6865	−	4.12209i	−0.519658	−	0.168847i
$597$	2.40082	+	5.27164i	0.0982590	+	0.215754i
$598$	−0.0656357	+	0.414407i	−0.00268404	+	0.0169464i
$599$	19.8769			0.812148			0.406074	−	0.913840i	$-0.366897\pi$
$599$	19.8769			0.812148			0.406074	+	0.913840i	$0.366897\pi$
$600$	6.23325	+	6.01220i	0.254471	+	0.245447i
$601$	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
$603$	−10.5695	−	26.1986i	−0.430425	−	1.06689i
$604$	−4.87261	−	1.58321i	−0.198264	−	0.0644198i
$605$	−22.0248	+	2.42157i	−0.895436	+	0.0984506i
$606$	21.9961	−	6.09407i	0.893529	−	0.247555i
$607$	−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
$609$	−33.4111	+	41.9818i	−1.35389	+	1.70119i
$610$	9.98262	−	12.4489i	0.404184	−	0.504041i
$611$	0.227713	+	0.313420i	0.00921227	+	0.0126796i
$612$	14.8964	−	1.03410i	0.602151	−	0.0418011i
$613$	−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
$615$	37.8621	−	8.57417i	1.52675	−	0.345744i
$616$	3.50787	+	2.54861i	0.141336	+	0.102687i
$617$	26.2483	+	13.3742i	1.05671	+	0.538423i	0.893915	−	0.448236i	$-0.147948\pi$
$617$	26.2483	+	13.3742i	1.05671	+	0.538423i	0.162800	+	0.986659i	$0.447948\pi$
$618$	10.6810	−	9.78242i	0.429655	−	0.393507i
$619$	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
$621$	1.71112	−	3.58046i	0.0686650	−	0.143679i
$622$	−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
$627$	−10.8568	−	2.21170i	−0.433580	−	0.0883268i
$628$	−2.33343	−	4.57961i	−0.0931139	−	0.182746i
$629$	−14.3524	+	44.1721i	−0.572267	+	1.76126i
$630$	26.2926	−	9.17942i	1.04752	−	0.365717i
$631$	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
$633$	−12.5886	+	22.2372i	−0.500352	+	0.883849i
$634$	−6.82525	+	9.39415i	−0.271065	+	0.373089i
$635$	−0.190846	−	0.698846i	−0.00757349	−	0.0277329i
$636$	−11.0657	+	7.32023i	−0.438785	+	0.290266i
$637$	0.879613	+	5.55366i	0.0348515	+	0.220044i
$638$	−1.21915	−	7.69739i	−0.0482665	−	0.304742i
$639$	12.7981	−	7.68106i	0.506283	−	0.303858i
$640$	−1.74447	−	1.39887i	−0.0689562	−	0.0552951i
$641$	−18.7007	+	25.7393i	−0.738632	+	1.01664i	0.260064	+	0.965591i	$0.416256\pi$
$641$	−18.7007	+	25.7393i	−0.738632	+	1.01664i	−0.998696	+	0.0510482i	$0.983744\pi$
$642$	16.9868	+	9.61635i	0.670417	+	0.379527i
$643$	−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
$645$	−2.21359	+	0.145469i	−0.0871602	+	0.00572783i
$646$	−9.42054	+	28.9934i	−0.370646	+	1.14073i
$647$	−14.2920	−	28.0496i	−0.561876	−	1.10274i	−0.980854	−	0.194747i	$-0.937612\pi$
$647$	−14.2920	−	28.0496i	−0.561876	−	1.10274i	0.418978	−	0.907996i	$-0.362388\pi$
$648$	−8.50671	−	2.93870i	−0.334175	−	0.115443i
$649$			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	−0.961503	−	0.274794i	$-0.911390\pi$
$653$	−33.3311	+	16.9830i	−1.30435	+	0.664598i	−0.342844	+	0.939392i	$0.611390\pi$
$654$	−18.8429	−	7.05050i	−0.736817	−	0.275697i
$655$	17.0831	+	18.7910i	0.667492	+	0.734225i
$656$	−9.53291	+	3.09743i	−0.372198	+	0.120934i
$657$	27.6283	+	32.9599i	1.07788	+	1.28589i
$658$	−2.60838	−	1.32904i	−0.101685	−	0.0518112i
$659$	26.8536	+	19.5103i	1.04607	+	0.760012i	0.971460	−	0.237201i	$-0.0762301\pi$
$659$	26.8536	+	19.5103i	1.04607	+	0.760012i	0.0746059	+	0.997213i	$0.476230\pi$
$660$	−1.59614	+	3.71687i	−0.0621295	+	0.144679i
$661$	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
$663$	−4.70606	+	0.534985i	−0.182768	+	0.0207771i
$664$	2.39126	+	3.29129i	0.0927988	+	0.127727i
$665$	−2.70375	+	56.7918i	−0.104847	+	2.20229i
$666$	18.3761	−	21.1178i	0.712060	−	0.818297i
$667$	−2.58710	+	5.07747i	−0.100173	+	0.196600i
$668$	−4.86073	−	4.86073i	−0.188067	−	0.188067i
$669$	−1.84730	−	6.66770i	−0.0714209	−	0.257788i
$670$	4.27925	−	20.6172i	0.165322	−	0.796510i
$671$	7.08854	+	2.30321i	0.273650	+	0.0889143i
$672$	−6.54389	+	2.98023i	−0.252436	+	0.114965i
$673$	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
$675$	13.7697	+	22.0317i	0.529997	+	0.848000i
$676$	12.6982			0.488391
$677$	−4.04016	+	25.5085i	−0.155276	+	0.980373i	0.779827	+	0.625996i	$0.215307\pi$
$677$	−4.04016	+	25.5085i	−0.155276	+	0.980373i	−0.935102	+	0.354378i	$0.884693\pi$
$678$	0.797676	−	0.363279i	0.0306345	−	0.0139516i
$679$	−7.86417	−	2.55522i	−0.301799	−	0.0980605i
$680$	9.66526	+	5.51871i	0.370646	+	0.211633i
$681$	−3.72045	−	13.4287i	−0.142568	−	0.514588i
$682$	1.87854	+	1.87854i	0.0719331	+	0.0719331i
$683$	−21.7746	+	42.7351i	−0.833183	+	1.63521i	−0.0624575	+	0.998048i	$0.519894\pi$
$683$	−21.7746	+	42.7351i	−0.833183	+	1.63521i	−0.770726	+	0.637167i	$0.780106\pi$
$684$	12.0616	−	13.8612i	0.461187	−	0.529995i
$685$	−12.4028	−	18.8999i	−0.473887	−	0.722130i
$686$	−7.89339	−	10.8643i	−0.301371	−	0.414802i
$687$	19.4211	−	2.20779i	0.740962	−	0.0842326i
$688$	0.565729	−	0.0896026i	0.0215682	−	0.00341607i
$689$	3.40470	−	2.47366i	0.129709	−	0.0942390i
$690$	2.54171	−	1.51275i	0.0967612	−	0.0575894i
$691$	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
$693$	8.35628	+	9.96884i	0.317429	+	0.378685i
$694$	26.0028	−	8.44881i	0.987051	−	0.320712i
$695$	−23.3011	+	40.8086i	−0.883861	+	1.54796i
$696$	12.1045	+	4.52918i	0.458821	+	0.171678i
$697$	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	$-0.990513\pi$
$701$		−	1.57804i		−	0.0596019i	0.999556	−	0.0298009i	$-0.00948734\pi$
$702$	2.73655	+	0.812856i	0.103284	+	0.0306793i
$703$	25.9462	+	50.9223i	0.978579	+	1.92057i
$704$	0.322749	−	0.993320i	0.0121641	−	0.0374372i
$705$	0.671807	−	2.64715i	0.0253017	−	0.0996976i
$706$	0.393202	+	1.21015i	0.0147983	+	0.0455446i
$707$	38.6840	−	38.6840i	1.45486	−	1.45486i
$708$	−0.827585	−	0.468501i	−0.0311026	−	0.0176073i
$709$	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
$711$	26.8353	−	16.1058i	1.00640	−	0.604016i
$712$	1.48469	+	9.37399i	0.0556413	+	0.351305i
$713$	−0.303887	−	1.91867i	−0.0113807	−	0.0718546i
$714$	29.8502	−	19.7466i	1.11711	−	0.738996i
$715$	0.454070	−	1.20003i	0.0169813	−	0.0448787i
$716$	−7.64375	+	10.5207i	−0.285660	+	0.393178i
$717$	−16.5507	+	29.2360i	−0.618096	+	1.09184i
$718$	−20.1183	+	20.1183i	−0.750807	+	0.750807i
$719$	−12.0633	−	37.1272i	−0.449887	−	1.38461i	−0.877035	−	0.480427i	$-0.840482\pi$
$719$	−12.0633	−	37.1272i	−0.449887	−	1.38461i	0.427148	−	0.904182i	$-0.359518\pi$
$720$	−4.06001	−	5.34007i	−0.151307	−	0.199013i
$721$	10.7277	−	33.0165i	0.399521	−	1.22960i
$722$	8.40460	+	16.4950i	0.312787	+	0.613879i
$723$	−3.09381	−	0.630257i	−0.115060	−	0.0234395i
$724$		−	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
$729$	−22.6218	−	14.7395i	−0.837845	−	0.545908i
$730$	3.50338	+	31.8642i	0.129666	+	1.17935i
$731$	−2.71143	+	0.880997i	−0.100286	+	0.0325849i
$732$	−9.11506	+	8.34819i	−0.336902	+	0.308558i
$733$	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
$735$	26.1307	−	29.8067i	0.963846	−	1.09944i
$736$	−0.617851	+	0.448895i	−0.0227743	+	0.0165465i
$737$	9.71417	−	1.53857i	0.357826	−	0.0566741i
$738$	−29.9983	+	2.08247i	−1.10425	+	0.0766568i
$739$	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
$741$	−3.62926	+	4.56025i	−0.133324	+	0.167525i
$742$	−14.4374	+	28.3350i	−0.530015	+	1.04021i
$743$	6.31364	+	6.31364i	0.231625	+	0.231625i	0.813371	−	0.581746i	$-0.197630\pi$
$743$	6.31364	+	6.31364i	0.231625	+	0.231625i	−0.581746	+	0.813371i	$0.697630\pi$
$744$	−4.24575	+	1.17630i	−0.155657	+	0.0431252i
$745$	−12.2623	−	27.1906i	−0.449257	−	0.996185i
$746$	−7.28731	−	2.36779i	−0.266807	−	0.0866910i
$747$	4.56627	+	11.3184i	0.167071	+	0.414117i
$748$	−0.813241	+	5.13460i	−0.0297350	+	0.187740i
$749$	46.7864			1.70954
$750$	−0.571625	+	19.3565i	−0.0208728	+	0.706799i
$751$	−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
$753$	9.48178	+	20.8198i	0.345535	+	0.758715i
$754$	−3.89877	−	1.26679i	−0.141985	−	0.0461337i
$755$	−4.70971	−	10.4433i	−0.171404	−	0.380072i
$756$	−21.2135	+	3.91507i	−0.771526	+	0.142390i
$757$	−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
$759$	1.08100	+	0.860314i	0.0392379	+	0.0312274i
$760$	13.2116	−	3.60792i	0.479235	−	0.130873i
$761$	−28.8681	−	39.7336i	−1.04647	−	1.44034i	−0.891830	−	0.452370i	$-0.850579\pi$
$761$	−28.8681	−	39.7336i	−1.04647	−	1.44034i	−0.154638	−	0.987971i	$-0.549421\pi$
$762$	0.0633828	+	0.557555i	0.00229612	+	0.0201981i
$763$	−47.6282	+	7.54356i	−1.72426	+	0.273095i
$764$	−3.86321	+	2.80678i	−0.139766	+	0.101546i
$765$	24.1175	+	23.0912i	0.871971	+	0.834866i
$766$	21.5944	+	15.6892i	0.780237	+	0.566876i
$767$	0.268769	+	0.136945i	0.00970469	+	0.00494479i
$768$	1.16983	+	1.27730i	0.0422128	+	0.0460905i
$769$	−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
$771$	−1.13090	+	3.02240i	−0.0407283	+	0.108849i
$772$	−5.41215	+	2.75763i	−0.194788	+	0.0992493i
$773$	−13.6137	−	2.15619i	−0.489650	−	0.0775529i	−0.0932724	−	0.995641i	$-0.529733\pi$
$773$	−13.6137	−	2.15619i	−0.489650	−	0.0775529i	−0.396377	+	0.918088i	$0.629733\pi$
$774$	1.71173	+	0.150627i	0.0615267	+	0.00541418i
$775$	11.6676	+	5.06145i	0.419112	+	0.181812i
$776$			1.99179i			0.0715012i
$777$	13.3935	−	65.7463i	0.480490	−	2.35864i
$778$	−3.17091	−	6.22326i	−0.113683	−	0.223115i
$779$	18.9710	−	58.3868i	0.679708	−	2.09193i
$780$	1.36087	+	1.63569i	0.0487269	+	0.0585672i
$781$	1.60580	+	4.94214i	0.0574599	+	0.176844i
$782$	2.68791	−	2.68791i	0.0961196	−	0.0961196i
$783$	31.9367	+	21.9851i	1.14132	+	0.785683i
$784$	−6.01584	+	8.28010i	−0.214852	+	0.295718i
$785$	4.06730	−	10.7492i	0.145168	−	0.383656i
$786$	−10.8532	−	16.4064i	−0.387120	−	0.585196i
$787$	−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
$789$	25.7393	+	38.9092i	0.916344	+	1.38520i
$790$	23.3014	+	1.10934i	0.829025	+	0.0394684i
$791$	1.23485	−	1.69963i	0.0439062	−	0.0604317i
$792$	1.66175	−	2.65636i	0.0590475	−	0.0943898i
$793$	2.77226	−	2.77226i	0.0984459	−	0.0984459i
$794$	−5.65908	−	17.4168i	−0.200833	−	0.618101i
$795$	−28.7563	−	7.29790i	−1.01988	−	0.258830i
$796$	1.03346	−	3.18067i	0.0366301	−	0.112736i
$797$	19.5456	+	38.3603i	0.692339	+	1.35879i	0.922636	+	0.385672i	$0.126030\pi$
$797$	19.5456	+	38.3603i	0.692339	+	1.35879i	−0.230297	+	0.973120i	$0.573970\pi$
$798$	8.79116	−	43.1542i	0.311204	−	1.52764i
$799$		−	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
$804$	−5.71586	+	15.2760i	−0.201583	+	0.538743i
$805$	3.51530	−	6.15656i	0.123898	−	0.216990i
$806$	1.32905	−	0.431834i	0.0468138	−	0.0152107i
$807$	−11.8409	−	12.9286i	−0.416820	−	0.455109i
$808$	−11.7415	−	5.98261i	−0.413065	−	0.210467i
$809$	−7.45131	−	5.41369i	−0.261974	−	0.190335i	0.449043	−	0.893510i	$-0.351765\pi$
$809$	−7.45131	−	5.41369i	−0.261974	−	0.190335i	−0.711017	+	0.703175i	$0.751765\pi$
$810$	−7.93325	−	18.4950i	−0.278746	−	0.649847i
$811$	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
$813$	0.0826473	+	0.727017i	0.00289857	+	0.0254976i
$814$	5.72848	+	7.88457i	0.200783	+	0.276354i
$815$	−27.0287	−	41.1876i	−0.946776	−	1.44274i
$816$	−6.74562	−	5.36849i	−0.236144	−	0.187935i
$817$	−1.59266	+	3.12578i	−0.0557203	+	0.109357i
$818$	−5.15736	−	5.15736i	−0.180323	−	0.180323i
$819$	6.66776	−	1.53583i	0.232990	−	0.0536662i
$820$	−19.4639	−	11.1136i	−0.679707	−	0.388102i
$821$	−3.34850	−	1.08799i	−0.116863	−	0.0379712i	0.250001	−	0.968245i	$-0.419569\pi$
$821$	−3.34850	−	1.08799i	−0.116863	−	0.0379712i	−0.366865	+	0.930274i	$0.619569\pi$
$822$	7.25753	+	15.9358i	0.253135	+	0.555826i
$823$	−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
$825$	−8.55056	+	2.94990i	−0.297692	+	0.102702i
$826$	−2.27940			−0.0793104
$827$	−6.37481	+	40.2490i	−0.221674	+	1.39959i	0.586165	+	0.810192i	$0.300637\pi$
$827$	−6.37481	+	40.2490i	−0.221674	+	1.39959i	−0.807839	+	0.589403i	$0.799363\pi$
$828$	−2.12472	+	0.857195i	−0.0738391	+	0.0297896i
$829$	−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
$831$	−45.3025	+	12.5512i	−1.57153	+	0.435396i
$832$	−0.388478	−	0.388478i	−0.0134680	−	0.0134680i
$833$	23.1275	−	45.3903i	0.801320	−	1.57268i
$834$	22.6668	−	28.4813i	0.784887	−	0.986228i
$835$	0.730958	−	15.3536i	0.0252958	−	0.531333i
$836$	3.76003	+	5.17523i	0.130043	+	0.178989i
$837$	−13.2128	+	0.335980i	−0.456701	+	0.0116132i
$838$	−17.7151	+	2.80580i	−0.611959	+	0.0969248i
$839$	−7.65838	+	5.56414i	−0.264397	+	0.192095i	−0.712083	−	0.702095i	$-0.752248\pi$
$839$	−7.65838	+	5.56414i	−0.264397	+	0.192095i	0.447686	+	0.894191i	$0.352248\pi$
$840$	−14.7740	−	6.34439i	−0.509750	−	0.218902i
$841$	−21.5827	−	15.6807i	−0.744230	−	0.540715i
$842$	−28.3578	−	14.4490i	−0.977276	−	0.497947i
$843$	−16.0871	+	14.7337i	−0.554070	+	0.507455i
$844$	14.0311	−	4.55897i	0.482969	−	0.156926i
$845$	19.1001	+	21.0096i	0.657063	+	0.722753i
$846$	−0.827566	+	1.94689i	−0.0284523	+	0.0669355i
$847$	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
$852$	−8.44416	−	1.72020i	−0.289292	−	0.0589332i
$853$	−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
$855$	41.0765	−	0.892984i	1.40479	−	0.0305394i
$856$	−3.48257	−	10.7182i	−0.119032	−	0.366342i
$857$	−10.2021	+	10.2021i	−0.348497	+	0.348497i	−0.859549	−	0.511053i	$-0.829256\pi$
$857$	−10.2021	+	10.2021i	−0.348497	+	0.348497i	0.511053	+	0.859549i	$0.329256\pi$
$858$	−0.489618	+	0.864887i	−0.0167153	+	0.0295268i
$859$	−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
$861$	−60.1121	+	39.7655i	−2.04861	+	1.35520i
$862$	1.49664	+	9.44941i	0.0509758	+	0.321848i
$863$	3.14654	+	19.8665i	0.107109	+	0.676262i	0.981561	+	0.191149i	$0.0612215\pi$
$863$	3.14654	+	19.8665i	0.107109	+	0.676262i	−0.874452	+	0.485113i	$0.838779\pi$
$864$	2.47593	+	4.56834i	0.0842329	+	0.155418i
$865$	−2.83496	−	10.3811i	−0.0963915	−	0.352970i
$866$	−10.2078	+	14.0499i	−0.346877	+	0.477435i
$867$	11.7187	+	6.63401i	0.397987	+	0.225303i
$868$	−7.46691	+	7.46691i	−0.253444	+	0.253444i
$869$	3.36708	+	10.3628i	0.114220	+	0.351534i
$870$	10.7134	+	26.8400i	0.363219	+	0.909962i
$871$	1.59870	−	4.92029i	0.0541698	−	0.166718i
$872$	5.27337	+	10.3496i	0.178579	+	0.350480i
$873$	−1.44850	+	5.79715i	−0.0490243	+	0.196204i
$874$		−	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
$879$	6.91358	+	2.58687i	0.233189	+	0.0872529i
$880$	2.12895	−	0.960111i	0.0717670	−	0.0323653i
$881$	53.5974	−	17.4149i	1.80574	−	0.586722i	0.805759	−	0.592243i	$-0.201758\pi$
$881$	53.5974	−	17.4149i	1.80574	−	0.586722i	0.999985	+	0.00552165i	$0.00175761\pi$
$882$	−23.5308	+	19.7245i	−0.792324	+	0.664157i
$883$	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
$885$	−0.469667	−	2.07397i	−0.0157877	−	0.0697159i
$886$	7.92428	−	5.75733i	0.266221	−	0.193421i
$887$	26.4392	−	4.18756i	0.887741	−	0.140604i	0.304123	−	0.952633i	$-0.401637\pi$
$887$	26.4392	−	4.18756i	0.887741	−	0.140604i	0.583618	+	0.812028i	$0.301637\pi$
$888$	−16.0587	+	1.82555i	−0.538894	+	0.0612615i
$889$	0.790563	+	1.08812i	0.0265146	+	0.0364943i
$890$	−13.2764	+	16.5565i	−0.445027	+	0.554974i
$891$	6.76834	−	6.52292i	0.226748	−	0.218526i
$892$	−1.81351	+	3.55922i	−0.0607210	+	0.119172i
$893$	−3.05395	−	3.05395i	−0.102196	−	0.102196i
$894$	6.16877	+	22.2657i	0.206315	+	0.744676i
$895$	−28.9044	+	3.17796i	−0.966167	+	0.106227i
$896$	3.94829	+	1.28288i	0.131903	+	0.0428579i
$897$	0.661364	−	0.301200i	0.0220823	−	0.0100568i
$898$	3.83429	−	24.2088i	0.127952	−	0.807857i
$899$	18.9799			0.633015
$900$	2.72846	−	14.7498i	0.0909487	−	0.491659i
$901$	−38.1280			−1.27023
$902$	1.63770	−	10.3400i	0.0545295	−	0.344286i
$903$	3.74821	−	1.70702i	0.124733	−	0.0568060i
$904$	−0.481282	−	0.156378i	−0.0160072	−	0.00520105i
$905$	11.0712	−	10.0649i	0.368018	−	0.334569i
$906$	2.36930	+	8.55179i	0.0787146	+	0.284114i
$907$	−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
$909$	−29.8232	−	25.9513i	−0.989173	−	0.860752i
$910$	4.76994	+	1.80486i	0.158122	+	0.0598304i
$911$	15.3895	+	21.1818i	0.509877	+	0.701786i	0.983899	−	0.178728i	$-0.0571981\pi$
$911$	15.3895	+	21.1818i	0.509877	+	0.701786i	−0.474021	+	0.880513i	$0.657198\pi$
$912$	−10.5405	+	1.19825i	−0.349031	+	0.0396779i
$913$	−4.19673	+	0.664696i	−0.138891	+	0.0219982i
$914$	11.4710	−	8.33418i	0.379428	−	0.275670i
$915$	−27.5229	−	2.52423i	−0.909880	−	0.0834485i
$916$	−9.12977	−	6.63317i	−0.301656	−	0.219166i
$917$	−42.0103	−	21.4053i	−1.38730	−	0.706866i
$918$	−15.7291	−	20.5307i	−0.519138	−	0.677616i
$919$	−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
$921$	30.9843	+	11.5935i	1.02097	+	0.382018i
$922$	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
$927$	−24.3384	−	6.08130i	−0.799379	−	0.199736i
$928$	−3.38756	−	6.64846i	−0.111202	−	0.218247i
$929$	−12.4755	+	38.3955i	−0.409307	+	1.25972i	0.507938	+	0.861393i	$0.330408\pi$
$929$	−12.4755	+	38.3955i	−0.409307	+	1.25972i	−0.917245	+	0.398323i	$0.869592\pi$
$930$	−8.33253	−	5.25543i	−0.273234	−	0.172332i
$931$	−19.3709	−	59.6174i	−0.634855	−	1.95388i
$932$	−5.21367	+	5.21367i	−0.170779	+	0.170779i
$933$	14.1462	+	8.00824i	0.463126	+	0.262178i
$934$	−8.11024	+	11.1628i	−0.265375	+	0.365258i
$935$	−9.71865	+	6.37772i	−0.317834	+	0.208574i
$936$	−0.848158	−	1.41319i	−0.0277229	−	0.0461915i
$937$	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
$939$	−43.2642	+	28.6202i	−1.41187	+	0.933986i
$940$	−1.31828	+	0.865099i	−0.0429974	+	0.0282164i
$941$	24.5801	−	33.8316i	0.801288	−	1.10288i	−0.191322	−	0.981527i	$-0.561277\pi$
$941$	24.5801	−	33.8316i	0.801288	−	1.10288i	0.992610	−	0.121351i	$-0.0387226\pi$
$942$	−4.38572	+	7.74717i	−0.142894	+	0.252416i
$943$	−5.41291	+	5.41291i	−0.176268	+	0.176268i
$944$	0.169668	+	0.522184i	0.00552222	+	0.0169956i
$945$	−38.3861	−	29.2096i	−1.24870	−	0.950189i
$946$	−0.184864	+	0.568954i	−0.00601046	+	0.0184983i
$947$	−20.9731	−	41.1619i	−0.681533	−	1.33758i	−0.929503	−	0.368816i	$-0.879763\pi$
$947$	−20.9731	−	41.1619i	−0.681533	−	1.33758i	0.247970	−	0.968768i	$-0.420237\pi$
$948$	−17.7059	−	3.60697i	−0.575062	−	0.117149i
$949$			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	−0.0558911	−	0.998437i	$-0.517800\pi$
$953$	22.1963	−	11.3096i	0.719009	−	0.366354i	0.774900	+	0.632083i	$0.217800\pi$
$954$	21.1492	+	8.98992i	0.684732	+	0.291059i
$955$	−10.4548	−	2.16998i	−0.338310	−	0.0702188i
$956$	18.4471	−	5.99384i	0.596623	−	0.193855i
$957$	−9.95440	+	9.11691i	−0.321780	+	0.294708i
$958$	6.42288	+	3.27262i	0.207514	+	0.105734i
$959$	33.9549	+	24.6696i	1.09646	+	0.796624i
$960$	−0.353721	+	3.85680i	−0.0114163	+	0.124478i
$961$	19.8452	−	14.4184i	0.640166	−	0.465108i
$962$	5.06336	−	0.801958i	0.163249	−	0.0258562i
$963$	−2.34141	−	33.7283i	−0.0754507	−	1.08688i
$964$	1.07147	+	1.47476i	0.0345099	+	0.0474988i
$965$	−12.7034	−	4.80671i	−0.408935	−	0.154733i
$966$	−3.41961	+	4.29681i	−0.110024	+	0.138248i
$967$	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
$969$	50.8856	−	14.0980i	1.63468	−	0.452893i
$970$	−3.29550	+	2.99597i	−0.105812	+	0.0961949i
$971$	−47.1650	−	15.3248i	−1.51360	−	0.491798i	−0.569648	−	0.821889i	$-0.692921\pi$
$971$	−47.1650	−	15.3248i	−1.51360	−	0.491798i	−0.943949	+	0.330091i	$0.892921\pi$
$972$	3.88399	+	15.0968i	0.124579	+	0.484231i
$973$	13.6483	−	86.1718i	0.437543	−	2.76254i
$974$	−15.1728			−0.486167
$975$	−0.659358	+	4.71195i	−0.0211163	+	0.150903i
$976$	7.13621			0.228425
$977$	3.69043	−	23.3005i	0.118067	−	0.745448i	−0.855628	−	0.517592i	$-0.826828\pi$
$977$	3.69043	−	23.3005i	0.118067	−	0.745448i	0.973695	−	0.227856i	$-0.0731715\pi$
$978$	15.8159	+	34.7281i	0.505737	+	1.11048i
$979$	−9.42744	−	3.06316i	−0.301302	−	0.0978991i
$980$	−22.7485	+	2.50114i	−0.726676	+	0.0798959i
$981$	7.82168	+	33.9576i	0.249727	+	1.08418i
$982$	−19.2286	−	19.2286i	−0.613608	−	0.613608i
$983$	3.32022	−	6.51631i	0.105899	−	0.207838i	−0.831976	−	0.554811i	$-0.812791\pi$
$983$	3.32022	−	6.51631i	0.105899	−	0.207838i	0.937875	+	0.346973i	$0.112791\pi$
$984$	13.5843	+	10.8110i	0.433052	+	0.344643i
$985$	−18.7143	+	23.3378i	−0.596287	+	0.743604i
$986$	21.8305	+	30.0471i	0.695224	+	0.956894i
$987$	0.572725	+	5.03805i	0.0182300	+	0.160363i
$988$	3.32346	−	0.526384i	0.105733	−	0.0167465i
$989$	0.353893	−	0.257118i	0.0112531	−	0.00817589i
$990$	6.89459	−	1.24617i	0.219124	−	0.0396060i
$991$	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
$993$	11.1327	+	12.1553i	0.353284	+	0.385737i
$994$	−19.6442	+	6.38279i	−0.623076	+	0.202450i
$995$	6.81704	−	3.07433i	0.216115	−	0.0974629i
$996$	2.46937	−	6.59956i	0.0782451	−	0.209115i
$997$	−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.77.5	✓	80
3.2	odd	2	inner	150.2.l.a.77.6	yes	80
5.2	odd	4		750.2.l.a.593.3		80
5.3	odd	4		750.2.l.c.593.8		80
5.4	even	2		750.2.l.b.407.6		80
15.2	even	4		750.2.l.a.593.9		80
15.8	even	4		750.2.l.c.593.2		80
15.14	odd	2		750.2.l.b.407.5		80
25.9	even	10		750.2.l.a.707.9		80
25.12	odd	20		750.2.l.b.293.5		80
25.13	odd	20	inner	150.2.l.a.113.6	yes	80
25.16	even	5		750.2.l.c.707.2		80
75.38	even	20	inner	150.2.l.a.113.5	yes	80
75.41	odd	10		750.2.l.c.707.8		80
75.59	odd	10		750.2.l.a.707.3		80
75.62	even	20		750.2.l.b.293.6		80

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

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)

\(f(q)\)	\(=\)	\(q+(-0.156434 + 0.987688i) q^{2} +(1.57628 - 0.717872i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(-0.919260 - 2.03837i) q^{5} +(0.462449 + 1.66917i) q^{6} +(2.93554 + 2.93554i) q^{7} +(0.453990 - 0.891007i) q^{8} +(1.96932 - 2.26314i) q^{9} +O(q^{10})\)	\(q+(-0.156434 + 0.987688i) q^{2} +(1.57628 - 0.717872i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(-0.919260 - 2.03837i) q^{5} +(0.462449 + 1.66917i) q^{6} +(2.93554 + 2.93554i) q^{7} +(0.453990 - 0.891007i) q^{8} +(1.96932 - 2.26314i) q^{9} +(2.15708 - 0.589071i) q^{10} +(0.613906 + 0.844968i) q^{11} +(-1.72097 + 0.195639i) q^{12} +(0.542627 - 0.0859436i) q^{13} +(-3.35862 + 2.44018i) q^{14} +(-2.91230 - 2.55313i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-4.43491 - 2.25970i) q^{17} +(1.92720 + 2.29911i) q^{18} +(-5.82500 + 1.89266i) q^{19} +(0.244377 + 2.22267i) q^{20} +(6.73457 + 2.51989i) 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} +(1.47956 - 4.98105i) q^{27} +(-1.88473 - 3.69899i) q^{28} +(-2.30581 + 7.09654i) q^{29} +(2.97729 - 2.47705i) q^{30} +(-0.786024 - 2.41913i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(1.57427 + 0.891202i) q^{33} +(2.92565 - 4.02682i) q^{34} +(3.28520 - 8.68224i) q^{35} +(-2.57228 + 1.54382i) q^{36} +(-1.45972 - 9.21632i) q^{37} +(-0.958124 - 6.04936i) q^{38} +(0.793635 - 0.525008i) q^{39} +(-2.23354 - 0.106335i) q^{40} +(-5.89166 + 8.10918i) q^{41} +(-3.54239 + 6.25746i) q^{42} +(0.405017 - 0.405017i) q^{43} +(-0.322749 - 0.993320i) q^{44} +(-6.42343 - 1.93380i) q^{45} +(-0.235998 + 0.726327i) q^{46} +(0.320136 + 0.628302i) q^{47} +(1.69719 + 0.345744i) 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} +(4.68828 + 2.24055i) q^{54} +(1.15802 - 2.02811i) q^{55} +(3.94829 - 1.28288i) q^{56} +(-7.82314 + 7.16496i) q^{57} +(-6.64846 - 3.38756i) q^{58} +(0.444196 + 0.322728i) q^{59} +(1.98080 + 3.32813i) q^{60} +(5.77332 - 4.19456i) q^{61} +(2.51231 - 0.397911i) q^{62} +(12.4245 - 0.862506i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-0.674000 - 1.02707i) q^{65} +(-1.12650 + 1.41547i) q^{66} +(4.27513 - 8.39042i) q^{67} +(3.51957 + 3.51957i) q^{68} +(1.27476 - 0.353175i) q^{69} +(8.06143 + 4.60295i) q^{70} +(4.73186 + 1.53747i) q^{71} +(-1.12242 - 2.78212i) q^{72} +(-2.24264 + 14.1595i) q^{73} +9.33120 q^{74} +(-2.52708 + 8.28335i) q^{75} +6.12476 q^{76} +(-0.678294 + 4.28258i) q^{77} +(0.394392 + 0.865994i) q^{78} +(9.92188 + 3.22381i) q^{79} +(0.454428 - 2.18941i) q^{80} +(-1.24356 - 8.91367i) q^{81} +(-7.08768 - 7.08768i) q^{82} +(-1.84695 + 3.62484i) q^{83} +(-5.62627 - 4.47765i) q^{84} +(-0.529273 + 11.1173i) q^{85} +(0.336672 + 0.463389i) q^{86} +(1.45981 + 12.8414i) q^{87} +(1.03158 - 0.163386i) q^{88} +(-7.67825 + 5.57858i) q^{89} +(2.91483 - 6.04183i) q^{90} +(1.84519 + 1.34061i) q^{91} +(-0.680467 - 0.346715i) q^{92} +(-2.97562 - 3.24897i) q^{93} +(-0.670646 + 0.217906i) q^{94} +(9.21262 + 10.1337i) q^{95} +(-0.606986 + 1.62221i) 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

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