LMFDB - Embedded newform 345.2.t.a.4.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [345,2,Mod(4,345)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(345, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 4]))

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

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

chi := DirichletCharacter("345.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 345 = 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	345.t (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.75483886973$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			4.16
Character	$\chi$	$=$	345.4
Dual form			345.2.t.a.259.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.932222 - 0.425732i) q^{2} +(-0.281733 - 0.959493i) q^{3} +(-0.621931 + 0.717746i) q^{4} +(-2.06059 + 0.868302i) q^{5} +(-0.671124 - 0.774518i) q^{6} +(-3.06052 + 0.440036i) q^{7} +(-0.851669 + 2.90052i) q^{8} +(-0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(0.932222 - 0.425732i) q^{2} +(-0.281733 - 0.959493i) q^{3} +(-0.621931 + 0.717746i) q^{4} +(-2.06059 + 0.868302i) q^{5} +(-0.671124 - 0.774518i) q^{6} +(-3.06052 + 0.440036i) q^{7} +(-0.851669 + 2.90052i) q^{8} +(-0.841254 + 0.540641i) q^{9} +(-1.55127 + 1.68671i) q^{10} +(0.541626 - 1.18600i) q^{11} +(0.863891 + 0.394526i) q^{12} +(-0.774607 - 0.111372i) q^{13} +(-2.66575 + 1.71317i) q^{14} +(1.41367 + 1.73250i) q^{15} +(0.170580 + 1.18641i) q^{16} +(-4.83440 + 4.18903i) q^{17} +(-0.554067 + 0.862145i) q^{18} +(-1.16097 + 1.33983i) q^{19} +(0.658327 - 2.01901i) q^{20} +(1.28446 + 2.81258i) q^{21} -1.33620i q^{22} +(-2.16546 - 4.27911i) q^{23} +3.02297 q^{24} +(3.49210 - 3.57844i) q^{25} +(-0.769520 + 0.225952i) q^{26} +(0.755750 + 0.654861i) q^{27} +(1.58760 - 2.47035i) q^{28} +(3.28101 + 3.78648i) q^{29} +(2.05543 + 1.01323i) q^{30} +(8.23549 + 2.41816i) q^{31} +(-2.60457 - 4.05279i) q^{32} +(-1.29055 - 0.185553i) q^{33} +(-2.72333 + 5.96326i) q^{34} +(5.92441 - 3.56419i) q^{35} +(0.135158 - 0.940048i) q^{36} +(0.824607 + 1.28311i) q^{37} +(-0.511872 + 1.74328i) q^{38} +(0.111372 + 0.774607i) q^{39} +(-0.763582 - 6.71630i) q^{40} +(-9.67353 - 6.21680i) q^{41} +(2.39480 + 2.07511i) q^{42} +(-1.60487 - 5.46567i) q^{43} +(0.514391 + 1.12636i) q^{44} +(1.26404 - 1.84450i) q^{45} +(-3.84044 - 3.06717i) q^{46} +9.88097i q^{47} +(1.09030 - 0.497922i) q^{48} +(2.45671 - 0.721354i) q^{49} +(1.73196 - 4.82260i) q^{50} +(5.38135 + 3.45839i) q^{51} +(0.561689 - 0.486706i) q^{52} +(-5.21723 + 0.750125i) q^{53} +(0.983321 + 0.288729i) q^{54} +(-0.0862692 + 2.91415i) q^{55} +(1.33022 - 9.25186i) q^{56} +(1.61264 + 0.736466i) q^{57} +(4.67065 + 2.13301i) q^{58} +(-0.387020 + 2.69178i) q^{59} +(-2.12270 - 0.0628393i) q^{60} +(5.85465 + 1.71908i) q^{61} +(8.70679 - 1.25185i) q^{62} +(2.33677 - 2.02482i) q^{63} +(-6.17011 - 3.96529i) q^{64} +(1.69286 - 0.443101i) q^{65} +(-1.28207 + 0.376451i) q^{66} +(-5.80137 + 2.64940i) q^{67} -6.07516i q^{68} +(-3.49569 + 3.28331i) q^{69} +(4.00548 - 5.84483i) q^{70} +(-4.09711 - 8.97141i) q^{71} +(-0.851669 - 2.90052i) q^{72} +(6.68650 + 5.79389i) q^{73} +(1.31498 + 0.845085i) q^{74} +(-4.41733 - 2.34248i) q^{75} +(-0.239615 - 1.66656i) q^{76} +(-1.13578 + 3.86810i) q^{77} +(0.433598 + 0.674692i) q^{78} +(-0.946564 + 6.58349i) q^{79} +(-1.38166 - 2.29660i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-11.6646 - 1.67711i) q^{82} +(1.64055 + 2.55274i) q^{83} +(-2.81756 - 0.827311i) q^{84} +(6.32439 - 12.8296i) q^{85} +(-3.82300 - 4.41198i) q^{86} +(2.70874 - 4.21488i) q^{87} +(2.97872 + 2.58107i) q^{88} +(-14.0339 + 4.12073i) q^{89} +(0.393105 - 2.25763i) q^{90} +2.41971 q^{91} +(4.41808 + 1.10706i) q^{92} -8.58316i q^{93} +(4.20664 + 9.21126i) q^{94} +(1.22891 - 3.76891i) q^{95} +(-3.15483 + 3.64087i) q^{96} +(-1.61434 + 2.51196i) q^{97} +(1.98309 - 1.71836i) q^{98} +(0.185553 + 1.29055i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 28 q^{4} - 4 q^{5} - 4 q^{6} + 24 q^{9}+O(q^{10}) $ 240 * q + 28 * q^4 - 4 * q^5 - 4 * q^6 + 24 * q^9	$ 240 q + 28 q^{4} - 4 q^{5} - 4 q^{6} + 24 q^{9} + 8 q^{14} + 4 q^{15} - 36 q^{16} - 8 q^{19} - 92 q^{20} + 8 q^{21} + 12 q^{24} - 44 q^{25} + 32 q^{26} - 12 q^{29} + 8 q^{30} - 20 q^{31} - 54 q^{34} + 36 q^{35} - 28 q^{36} - 36 q^{39} - 24 q^{40} - 28 q^{41} - 224 q^{44} + 4 q^{45} - 8 q^{46} + 52 q^{49} - 48 q^{50} - 18 q^{54} - 22 q^{55} - 56 q^{59} - 36 q^{60} + 44 q^{61} + 12 q^{64} - 16 q^{65} + 8 q^{66} + 8 q^{69} - 152 q^{70} + 4 q^{71} + 88 q^{74} - 8 q^{75} - 100 q^{76} - 84 q^{79} + 122 q^{80} - 24 q^{81} - 56 q^{84} + 186 q^{85} - 392 q^{86} + 48 q^{89} - 304 q^{91} + 80 q^{94} + 190 q^{95} + 16 q^{96} + 44 q^{99}+O(q^{100}) $ 240 * q + 28 * q^4 - 4 * q^5 - 4 * q^6 + 24 * q^9 + 8 * q^14 + 4 * q^15 - 36 * q^16 - 8 * q^19 - 92 * q^20 + 8 * q^21 + 12 * q^24 - 44 * q^25 + 32 * q^26 - 12 * q^29 + 8 * q^30 - 20 * q^31 - 54 * q^34 + 36 * q^35 - 28 * q^36 - 36 * q^39 - 24 * q^40 - 28 * q^41 - 224 * q^44 + 4 * q^45 - 8 * q^46 + 52 * q^49 - 48 * q^50 - 18 * q^54 - 22 * q^55 - 56 * q^59 - 36 * q^60 + 44 * q^61 + 12 * q^64 - 16 * q^65 + 8 * q^66 + 8 * q^69 - 152 * q^70 + 4 * q^71 + 88 * q^74 - 8 * q^75 - 100 * q^76 - 84 * q^79 + 122 * q^80 - 24 * q^81 - 56 * q^84 + 186 * q^85 - 392 * q^86 + 48 * q^89 - 304 * q^91 + 80 * q^94 + 190 * q^95 + 16 * q^96 + 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$1$	$e\left(\frac{2}{11}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.932222	−	0.425732i	0.659181	−	0.301038i	−0.0575966	−	0.998340i	$-0.518344\pi$
$2$	0.932222	−	0.425732i	0.659181	−	0.301038i	0.716777	+	0.697302i	$0.245616\pi$
$3$	−0.281733	−	0.959493i	−0.162658	−	0.553964i
$3$	−0.281733	−	0.959493i	−0.162658	−	0.553964i
$4$	−0.621931	+	0.717746i	−0.310965	+	0.358873i
$5$	−2.06059	+	0.868302i	−0.921526	+	0.388317i
$5$	−2.06059	+	0.868302i	−0.921526	+	0.388317i
$6$	−0.671124	−	0.774518i	−0.273985	−	0.316196i
$7$	−3.06052	+	0.440036i	−1.15677	+	0.166318i	−0.693875	−	0.720096i	$-0.744098\pi$
$7$	−3.06052	+	0.440036i	−1.15677	+	0.166318i	−0.462894	+	0.886414i	$0.653189\pi$
$8$	−0.851669	+	2.90052i	−0.301110	+	1.02549i
$9$	−0.841254	+	0.540641i	−0.280418	+	0.180214i
$10$	−1.55127	+	1.68671i	−0.490554	+	0.533385i
$11$	0.541626	−	1.18600i	0.163307	−	0.357591i	−0.810234	−	0.586107i	$-0.800660\pi$
$11$	0.541626	−	1.18600i	0.163307	−	0.357591i	0.973540	+	0.228515i	$0.0733871\pi$
$12$	0.863891	+	0.394526i	0.249384	+	0.113890i
$13$	−0.774607	−	0.111372i	−0.214837	−	0.0308890i	0.0340556	−	0.999420i	$-0.489158\pi$
$13$	−0.774607	−	0.111372i	−0.214837	−	0.0308890i	−0.248893	+	0.968531i	$0.580067\pi$
$14$	−2.66575	+	1.71317i	−0.712451	+	0.457865i
$15$	1.41367	+	1.73250i	0.365007	+	0.447329i
$16$	0.170580	+	1.18641i	0.0426451	+	0.296603i
$17$	−4.83440	+	4.18903i	−1.17251	+	1.01599i	−0.172997	+	0.984922i	$0.555345\pi$
$17$	−4.83440	+	4.18903i	−1.17251	+	1.01599i	−0.999517	+	0.0310666i	$0.990110\pi$
$18$	−0.554067	+	0.862145i	−0.130595	+	0.203210i
$19$	−1.16097	+	1.33983i	−0.266344	+	0.307377i	−0.873130	−	0.487488i	$-0.837913\pi$
$19$	−1.16097	+	1.33983i	−0.266344	+	0.307377i	0.606786	+	0.794865i	$0.292459\pi$
$20$	0.658327	−	2.01901i	0.147206	−	0.451464i
$21$	1.28446	+	2.81258i	0.280292	+	0.613754i
$22$		−	1.33620i		−	0.284879i
$23$	−2.16546	−	4.27911i	−0.451530	−	0.892256i
$23$	−2.16546	−	4.27911i	−0.451530	−	0.892256i
$24$	3.02297			0.617061
$25$	3.49210	−	3.57844i	0.698420	−	0.715688i
$26$	−0.769520	+	0.225952i	−0.150915	+	0.0443128i
$27$	0.755750	+	0.654861i	0.145444	+	0.126028i
$28$	1.58760	−	2.47035i	0.300028	−	0.466852i
$29$	3.28101	+	3.78648i	0.609267	+	0.703132i	0.973632	−	0.228124i	$-0.0732592\pi$
$29$	3.28101	+	3.78648i	0.609267	+	0.703132i	−0.364365	+	0.931256i	$0.618714\pi$
$30$	2.05543	+	1.01323i	0.375268	+	0.184990i
$31$	8.23549	+	2.41816i	1.47914	+	0.434314i	0.919057	−	0.394125i	$-0.128952\pi$
$31$	8.23549	+	2.41816i	1.47914	+	0.434314i	0.560080	+	0.828438i	$0.310770\pi$
$32$	−2.60457	−	4.05279i	−0.460427	−	0.716438i
$33$	−1.29055	−	0.185553i	−0.224656	−	0.0323006i
$34$	−2.72333	+	5.96326i	−0.467047	+	1.02269i
$35$	5.92441	−	3.56419i	1.00141	−	0.602459i
$36$	0.135158	−	0.940048i	0.0225264	−	0.156675i
$37$	0.824607	+	1.28311i	0.135565	+	0.210943i	0.902398	−	0.430904i	$-0.141805\pi$
$37$	0.824607	+	1.28311i	0.135565	+	0.210943i	−0.766833	+	0.641846i	$0.778169\pi$
$38$	−0.511872	+	1.74328i	−0.0830366	+	0.282797i
$39$	0.111372	+	0.774607i	0.0178337	+	0.124036i
$40$	−0.763582	−	6.71630i	−0.120733	−	1.06194i
$41$	−9.67353	−	6.21680i	−1.51075	−	0.970901i	−0.993347	−	0.115161i	$-0.963262\pi$
$41$	−9.67353	−	6.21680i	−1.51075	−	0.970901i	−0.517405	−	0.855741i	$-0.673102\pi$
$42$	2.39480	+	2.07511i	0.369526	+	0.320196i
$43$	−1.60487	−	5.46567i	−0.244740	−	0.833507i	−0.986629	−	0.162984i	$-0.947888\pi$
$43$	−1.60487	−	5.46567i	−0.244740	−	0.833507i	0.741889	−	0.670523i	$-0.233930\pi$
$44$	0.514391	+	1.12636i	0.0775473	+	0.169805i
$45$	1.26404	−	1.84450i	0.188432	−	0.274962i
$46$	−3.84044	−	3.06717i	−0.566242	−	0.452230i
$47$			9.88097i			1.44129i	0.693305	+	0.720644i	$0.256154\pi$
$47$			9.88097i			1.44129i	−0.693305	+	0.720644i	$0.743846\pi$
$48$	1.09030	−	0.497922i	0.157371	−	0.0718688i
$49$	2.45671	−	0.721354i	0.350958	−	0.103051i
$50$	1.73196	−	4.82260i	0.244936	−	0.682018i
$51$	5.38135	+	3.45839i	0.753540	+	0.484271i
$52$	0.561689	−	0.486706i	0.0778922	−	0.0674940i
$53$	−5.21723	+	0.750125i	−0.716642	+	0.103038i	−0.490983	−	0.871169i	$-0.663362\pi$
$53$	−5.21723	+	0.750125i	−0.716642	+	0.103038i	−0.225658	+	0.974206i	$0.572453\pi$
$54$	0.983321	+	0.288729i	0.133813	+	0.0392911i
$55$	−0.0862692	+	2.91415i	−0.0116325	+	0.392944i
$56$	1.33022	−	9.25186i	0.177758	−	1.23633i
$57$	1.61264	+	0.736466i	0.213599	+	0.0975473i
$58$	4.67065	+	2.13301i	0.613287	+	0.280079i
$59$	−0.387020	+	2.69178i	−0.0503857	+	0.350440i	0.948996	+	0.315287i	$0.102101\pi$
$59$	−0.387020	+	2.69178i	−0.0503857	+	0.350440i	−0.999382	+	0.0351528i	$0.988808\pi$
$60$	−2.12270	−	0.0628393i	−0.274039	−	0.00811252i
$61$	5.85465	+	1.71908i	0.749611	+	0.220106i	0.634154	−	0.773207i	$-0.281348\pi$
$61$	5.85465	+	1.71908i	0.749611	+	0.220106i	0.115457	+	0.993312i	$0.463167\pi$
$62$	8.70679	−	1.25185i	1.10576	−	0.158985i
$63$	2.33677	−	2.02482i	0.294406	−	0.255104i
$64$	−6.17011	−	3.96529i	−0.771264	−	0.495661i
$65$	1.69286	−	0.443101i	0.209973	−	0.0549600i
$66$	−1.28207	+	0.376451i	−0.157812	+	0.0463379i
$67$	−5.80137	+	2.64940i	−0.708750	+	0.323675i	−0.736969	−	0.675927i	$-0.763744\pi$
$67$	−5.80137	+	2.64940i	−0.708750	+	0.323675i	0.0282192	+	0.999602i	$0.491016\pi$
$68$		−	6.07516i		−	0.736721i
$69$	−3.49569	+	3.28331i	−0.420832	+	0.395264i
$70$	4.00548	−	5.84483i	0.478746	−	0.698591i
$71$	−4.09711	−	8.97141i	−0.486237	−	1.06471i	−0.980701	−	0.195513i	$-0.937363\pi$
$71$	−4.09711	−	8.97141i	−0.486237	−	1.06471i	0.494464	−	0.869198i	$-0.335364\pi$
$72$	−0.851669	−	2.90052i	−0.100370	−	0.341829i
$73$	6.68650	+	5.79389i	0.782596	+	0.678123i	0.951548	−	0.307501i	$-0.0994928\pi$
$73$	6.68650	+	5.79389i	0.782596	+	0.678123i	−0.168952	+	0.985624i	$0.554038\pi$
$74$	1.31498	+	0.845085i	0.152863	+	0.0982392i
$75$	−4.41733	−	2.34248i	−0.510069	−	0.270487i
$76$	−0.239615	−	1.66656i	−0.0274857	−	0.191167i
$77$	−1.13578	+	3.86810i	−0.129434	+	0.440811i
$78$	0.433598	+	0.674692i	0.0490953	+	0.0763938i
$79$	−0.946564	+	6.58349i	−0.106497	+	0.740701i	0.864677	+	0.502328i	$0.167523\pi$
$79$	−0.946564	+	6.58349i	−0.106497	+	0.740701i	−0.971174	+	0.238373i	$0.923386\pi$
$80$	−1.38166	−	2.29660i	−0.154475	−	0.256768i
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	−11.6646	−	1.67711i	−1.28814	−	0.185206i
$83$	1.64055	+	2.55274i	0.180073	+	0.280199i	0.919542	−	0.392991i	$-0.128560\pi$
$83$	1.64055	+	2.55274i	0.180073	+	0.280199i	−0.739469	+	0.673191i	$0.764923\pi$
$84$	−2.81756	−	0.827311i	−0.307421	−	0.0902670i
$85$	6.32439	−	12.8296i	0.685977	−	1.39157i
$86$	−3.82300	−	4.41198i	−0.412245	−	0.475756i
$87$	2.70874	−	4.21488i	0.290407	−	0.451882i
$88$	2.97872	+	2.58107i	0.317532	+	0.275143i
$89$	−14.0339	+	4.12073i	−1.48759	+	0.436797i	−0.921772	−	0.387732i	$-0.873259\pi$
$89$	−14.0339	+	4.12073i	−1.48759	+	0.436797i	−0.565820	+	0.824528i	$0.691440\pi$
$90$	0.393105	−	2.25763i	0.0414369	−	0.237975i
$91$	2.41971			0.253654
$92$	4.41808	+	1.10706i	0.460617	+	0.115419i
$93$		−	8.58316i		−	0.890033i
$94$	4.20664	+	9.21126i	0.433882	+	0.950069i
$95$	1.22891	−	3.76891i	0.126083	−	0.386682i
$96$	−3.15483	+	3.64087i	−0.321988	+	0.371594i
$97$	−1.61434	+	2.51196i	−0.163911	+	0.255051i	−0.913487	−	0.406868i	$-0.866621\pi$
$97$	−1.61434	+	2.51196i	−0.163911	+	0.255051i	0.749576	+	0.661918i	$0.230257\pi$
$98$	1.98309	−	1.71836i	0.200323	−	0.173581i
$99$	0.185553	+	1.29055i	0.0186488	+	0.129705i
$100$	0.396565	+	4.73199i	0.0396565	+	0.473199i
$101$	−6.52509	+	4.19342i	−0.649270	+	0.417261i	−0.823400	−	0.567462i	$-0.807925\pi$
$101$	−6.52509	+	4.19342i	−0.649270	+	0.417261i	0.174129	+	0.984723i	$0.444289\pi$
$102$	6.48896	+	0.932972i	0.642503	+	0.0923779i
$103$	15.0694	+	6.88195i	1.48483	+	0.678098i	0.982446	−	0.186548i	$-0.0597298\pi$
$103$	15.0694	+	6.88195i	1.48483	+	0.678098i	0.502382	+	0.864646i	$0.332457\pi$
$104$	0.982744	−	2.15191i	0.0963660	−	0.211012i
$105$	−5.08892	−	4.68028i	−0.496628	−	0.456749i
$106$	−4.54427	+	2.92042i	−0.441378	+	0.283657i
$107$	2.03804	−	6.94094i	0.197025	−	0.671006i	−0.800412	−	0.599451i	$-0.795386\pi$
$107$	2.03804	−	6.94094i	0.197025	−	0.671006i	0.997437	−	0.0715549i	$-0.0227961\pi$
$108$	−0.940048	+	0.135158i	−0.0904562	+	0.0130056i
$109$	−1.15409	−	1.33189i	−0.110542	−	0.127572i	0.697782	−	0.716310i	$-0.254170\pi$
$109$	−1.15409	−	1.33189i	−0.110542	−	0.127572i	−0.808324	+	0.588738i	$0.799625\pi$
$110$	1.16023	+	2.75337i	0.110623	+	0.262523i
$111$	0.998820	−	1.15270i	0.0948038	−	0.109409i
$112$	−1.04413	−	3.55598i	−0.0986610	−	0.336008i
$113$	−2.17288	+	0.992321i	−0.204407	+	0.0933497i	−0.514988	−	0.857197i	$-0.672204\pi$
$113$	−2.17288	+	0.992321i	−0.204407	+	0.0933497i	0.310581	+	0.950547i	$0.399476\pi$
$114$	1.81687			0.170166
$115$	8.17770	+	6.93723i	0.762574	+	0.646900i
$116$	−4.75829			−0.441796
$117$	0.711853	−	0.325092i	0.0658109	−	0.0300548i
$118$	0.785188	+	2.67411i	0.0722824	+	0.246171i
$119$	12.9525	−	14.9479i	1.18735	−	1.37027i
$120$	−6.22911	+	2.62485i	−0.568638	+	0.239615i
$121$	6.09024	+	7.02851i	0.553658	+	0.638956i
$122$	6.18970	−	0.889945i	0.560389	−	0.0805718i
$123$	−3.23963	+	11.0332i	−0.292107	+	0.994827i
$124$	−6.85753	+	4.40706i	−0.615824	+	0.395766i
$125$	−4.08864	+	10.4059i	−0.365699	+	0.930733i
$126$	1.31636	−	2.88242i	0.117271	−	0.256787i
$127$	5.43523	+	2.48219i	0.482299	+	0.220259i	0.641701	−	0.766955i	$-0.278229\pi$
$127$	5.43523	+	2.48219i	0.482299	+	0.220259i	−0.159402	+	0.987214i	$0.550956\pi$
$128$	2.09698	+	0.301501i	0.185349	+	0.0266491i
$129$	−4.79213	+	3.07971i	−0.421923	+	0.271154i
$130$	1.38948	−	1.13377i	0.121865	−	0.0994383i
$131$	2.20776	+	15.3553i	0.192892	+	1.34160i	0.824303	+	0.566148i	$0.191567\pi$
$131$	2.20776	+	15.3553i	0.192892	+	1.34160i	−0.631411	+	0.775448i	$0.717524\pi$
$132$	0.935812	−	0.810886i	0.0814520	−	0.0705786i
$133$	2.96359	−	4.61143i	0.256976	−	0.399862i
$134$	−4.28023	+	4.93965i	−0.369756	+	0.426721i
$135$	−2.12591	−	0.693184i	−0.182969	−	0.0596597i
$136$	−8.03305	−	17.5899i	−0.688828	−	1.50832i
$137$		−	11.3388i		−	0.968741i	−0.874863	−	0.484371i	$-0.839049\pi$
$137$		−	11.3388i		−	0.968741i	0.874863	−	0.484371i	$-0.160951\pi$
$138$	−1.86095	+	4.54900i	−0.158415	+	0.387237i
$139$	18.8418			1.59814			0.799070	−	0.601238i	$-0.205326\pi$
$139$	18.8418			1.59814			0.799070	+	0.601238i	$0.205326\pi$
$140$	−1.12638	+	6.46891i	−0.0951969	+	0.546722i
$141$	9.48072	−	2.78379i	0.798421	−	0.234438i
$142$	−7.63883	−	6.61908i	−0.641036	−	0.555461i
$143$	−0.551634	+	0.858360i	−0.0461300	+	0.0717796i
$144$	−0.784925	−	0.905851i	−0.0654104	−	0.0754876i
$145$	−10.0486	−	4.95350i	−0.834494	−	0.411366i
$146$	8.69994	+	2.55453i	0.720012	+	0.211415i
$147$	−1.38427	−	2.15396i	−0.114173	−	0.177656i
$148$	−1.43380	−	0.206149i	−0.117858	−	0.0169454i
$149$	−7.63665	+	16.7219i	−0.625619	+	1.36991i	0.285742	+	0.958307i	$0.407760\pi$
$149$	−7.63665	+	16.7219i	−0.625619	+	1.36991i	−0.911361	+	0.411608i	$0.864967\pi$
$150$	−5.11520	−	0.303121i	−0.417654	−	0.0247498i
$151$	1.72350	−	11.9872i	0.140256	−	0.975502i	−0.791176	−	0.611588i	$-0.790531\pi$
$151$	1.72350	−	11.9872i	0.140256	−	0.975502i	0.931432	−	0.363914i	$-0.118560\pi$
$152$	−2.89743	−	4.50849i	−0.235013	−	0.365687i
$153$	1.80219	−	6.13771i	0.145699	−	0.496204i
$154$	0.587977	+	4.08947i	0.0473805	+	0.329539i
$155$	−19.0697	+	2.16805i	−1.53171	+	0.174142i
$156$	−0.625237	−	0.401815i	−0.0500590	−	0.0321710i
$157$	−12.8593	−	11.1426i	−1.02628	−	0.889280i	−0.0323735	−	0.999476i	$-0.510307\pi$
$157$	−12.8593	−	11.1426i	−1.02628	−	0.889280i	−0.993910	+	0.110196i	$0.964852\pi$
$158$	1.92039	+	6.54026i	0.152778	+	0.520315i
$159$	2.18960	+	4.79456i	0.173647	+	0.380234i
$160$	8.88601	+	6.08960i	0.702500	+	0.481425i
$161$	8.51041	+	12.1434i	0.670714	+	0.957036i
$162$		−	1.02483i		−	0.0805186i
$163$	−20.2585	+	9.25173i	−1.58676	+	0.724651i	−0.996581	−	0.0826177i	$-0.973672\pi$
$163$	−20.2585	+	9.25173i	−1.58676	+	0.724651i	−0.590184	+	0.807269i	$0.700945\pi$
$164$	10.4784	−	3.07672i	0.818222	−	0.240252i
$165$	2.82042	−	0.738237i	0.219569	−	0.0574717i
$166$	2.61613	+	1.68129i	0.203051	+	0.130493i
$167$	3.76785	−	3.26486i	0.291565	−	0.252643i	−0.496779	−	0.867877i	$-0.665484\pi$
$167$	3.76785	−	3.26486i	0.291565	−	0.252643i	0.788344	+	0.615234i	$0.210939\pi$
$168$	−9.25186	+	1.33022i	−0.713796	+	0.102628i
$169$	−11.8858	−	3.48998i	−0.914292	−	0.268460i
$170$	0.433767	−	14.6525i	0.0332684	−	1.12380i
$171$	0.252302	−	1.75480i	0.0192940	−	0.134193i
$172$	4.92108	+	2.24738i	0.375229	+	0.171361i
$173$	10.1137	+	4.61879i	0.768933	+	0.351160i	0.760952	−	0.648808i	$-0.224732\pi$
$173$	10.1137	+	4.61879i	0.768933	+	0.351160i	0.00798095	+	0.999968i	$0.497460\pi$
$174$	0.730738	−	5.08240i	0.0553971	−	0.385295i
$175$	−9.11301	+	12.4885i	−0.688879	+	0.944045i
$176$	1.49947	+	0.440285i	0.113027	+	0.0331877i
$177$	2.69178	−	0.387020i	0.202327	−	0.0290902i
$178$	−11.3284	+	9.81612i	−0.849100	+	0.735749i
$179$	−6.89281	−	4.42974i	−0.515193	−	0.331094i	0.257075	−	0.966391i	$-0.417241\pi$
$179$	−6.89281	−	4.42974i	−0.515193	−	0.331094i	−0.772268	+	0.635297i	$0.780878\pi$
$180$	0.537739	+	2.05442i	0.0400807	+	0.153127i
$181$	−8.70535	+	2.55612i	−0.647064	+	0.189995i	−0.588765	−	0.808304i	$-0.700386\pi$
$181$	−8.70535	+	2.55612i	−0.647064	+	0.189995i	−0.0582985	+	0.998299i	$0.518568\pi$
$182$	2.25571	−	1.03015i	0.167204	−	0.0763596i
$183$		−	6.10182i		−	0.451059i
$184$	14.2559	−	2.63658i	1.05096	−	0.194371i
$185$	−2.81331	−	1.92797i	−0.206839	−	0.141747i
$186$	−3.65412	−	8.00142i	−0.267933	−	0.586692i
$187$	2.34974	+	8.00247i	0.171830	+	0.585199i
$188$	−7.09203	−	6.14528i	−0.517240	−	0.448191i
$189$	−2.60115	−	1.67166i	−0.189206	−	0.121595i
$190$	−0.458930	−	4.03664i	−0.0332942	−	0.292849i
$191$	0.840903	+	5.84861i	0.0608456	+	0.423190i	0.997363	+	0.0725701i	$0.0231201\pi$
$191$	0.840903	+	5.84861i	0.0608456	+	0.423190i	−0.936518	+	0.350620i	$0.885971\pi$
$192$	−2.06635	+	7.03733i	−0.149126	+	0.507875i
$193$	−9.14611	−	14.2316i	−0.658351	−	1.02441i	−0.996522	−	0.0833297i	$-0.973445\pi$
$193$	−9.14611	−	14.2316i	−0.658351	−	1.02441i	0.338171	−	0.941085i	$-0.390192\pi$
$194$	−0.435501	+	3.02898i	−0.0312671	+	0.217468i
$195$	−0.902085	−	1.49945i	−0.0645997	−	0.107378i
$196$	−1.01015	+	2.21192i	−0.0721537	+	0.157995i
$197$	10.6125	+	1.52584i	0.756107	+	0.108712i	0.509579	−	0.860424i	$-0.329801\pi$
$197$	10.6125	+	1.52584i	0.756107	+	0.108712i	0.246528	+	0.969136i	$0.420710\pi$
$198$	0.722404	+	1.12408i	0.0513390	+	0.0798851i
$199$	−2.03869	−	0.598612i	−0.144519	−	0.0424345i	0.208673	−	0.977985i	$-0.433086\pi$
$199$	−2.03869	−	0.598612i	−0.144519	−	0.0424345i	−0.353192	+	0.935551i	$0.614904\pi$
$200$	7.40521	+	13.1765i	0.523627	+	0.931723i
$201$	4.17651	+	4.81995i	0.294588	+	0.339973i
$202$	−4.29756	+	6.68713i	−0.302375	+	0.470505i
$203$	−11.7078	−	10.1448i	−0.821725	−	0.712029i
$204$	−5.82907	+	1.71157i	−0.408117	+	0.119834i
$205$	25.3313	+	4.41076i	1.76921	+	0.308061i
$206$	16.9779			1.18290
$207$	4.13516	+	2.42908i	0.287414	+	0.168833i
$208$		−	0.938002i		−	0.0650387i
$209$	0.960219	+	2.10259i	0.0664198	+	0.145439i
$210$	−6.73654	−	2.19655i	−0.464866	−	0.151576i
$211$	−15.3730	+	17.7414i	−1.05832	+	1.22137i	−0.0839397	+	0.996471i	$0.526750\pi$
$211$	−15.3730	+	17.7414i	−1.05832	+	1.22137i	−0.974382	+	0.224898i	$0.927795\pi$
$212$	2.70636	−	4.21117i	0.185873	−	0.289225i
$213$	−7.45372	+	6.45868i	−0.510720	+	0.442542i
$214$	−1.05507	−	7.33815i	−0.0721229	−	0.501626i
$215$	8.05283	+	9.86902i	0.549198	+	0.673062i
$216$	−2.54308	+	1.63434i	−0.173035	+	0.111203i
$217$	−26.2690	−	3.77691i	−1.78325	−	0.256393i
$218$	−1.64290	−	0.750286i	−0.111271	−	0.0508158i
$219$	3.67539	−	8.04798i	0.248360	−	0.543832i
$220$	−2.03797	−	1.87432i	−0.137400	−	0.126367i
$221$	4.21130	−	2.70644i	0.283283	−	0.182055i
$222$	0.440381	−	1.49980i	0.0295565	−	0.100660i
$223$	22.6951	−	3.26306i	1.51978	−	0.218511i	0.668692	−	0.743540i	$-0.266855\pi$
$223$	22.6951	−	3.26306i	1.51978	−	0.218511i	0.851084	+	0.525029i	$0.175946\pi$
$224$	9.75471	+	11.2575i	0.651764	+	0.752176i
$225$	−1.00309	+	4.89835i	−0.0668729	+	0.326556i
$226$	−1.60314	+	1.85013i	−0.106640	+	0.123069i
$227$	4.65001	+	15.8365i	0.308632	+	1.05110i	0.957075	+	0.289841i	$0.0936023\pi$
$227$	4.65001	+	15.8365i	0.308632	+	1.05110i	−0.648443	+	0.761263i	$0.724580\pi$
$228$	−1.53154	+	0.699433i	−0.101429	+	0.0463211i
$229$	−14.8584			−0.981873			−0.490937	−	0.871195i	$-0.663345\pi$
$229$	−14.8584			−0.981873			−0.490937	+	0.871195i	$0.663345\pi$
$230$	10.5768	+	2.98554i	0.697416	+	0.196861i
$231$	4.03140			0.265247
$232$	−13.7771	+	6.29179i	−0.904510	+	0.413076i
$233$	0.776187	+	2.64345i	0.0508497	+	0.173178i	0.981003	−	0.193994i	$-0.0621442\pi$
$233$	0.776187	+	2.64345i	0.0508497	+	0.173178i	−0.930153	+	0.367172i	$0.880326\pi$
$234$	0.525203	−	0.606117i	0.0343336	−	0.0396231i
$235$	−8.57967	−	20.3607i	−0.559676	−	1.32818i
$236$	−1.69132	−	1.95188i	−0.110095	−	0.127057i
$237$	6.58349	−	0.946564i	0.427644	−	0.0614859i
$238$	5.71076	−	19.4491i	0.370173	−	1.26070i
$239$	5.62636	−	3.61584i	0.363939	−	0.233889i	−0.345872	−	0.938282i	$-0.612417\pi$
$239$	5.62636	−	3.61584i	0.363939	−	0.233889i	0.709811	+	0.704392i	$0.248780\pi$
$240$	−1.81431	+	1.97272i	−0.117113	+	0.127339i
$241$	1.08422	−	2.37412i	0.0698410	−	0.152930i	−0.871492	−	0.490410i	$-0.836847\pi$
$241$	1.08422	−	2.37412i	0.0698410	−	0.152930i	0.941333	+	0.337479i	$0.109574\pi$
$242$	8.66971	+	3.95933i	0.557310	+	0.254515i
$243$	−0.989821	−	0.142315i	−0.0634971	−	0.00912950i
$244$	−4.87505	+	3.13301i	−0.312093	+	0.200570i
$245$	−4.43592	+	3.61958i	−0.283401	+	0.231247i
$246$	1.67711	+	11.6646i	0.106929	+	0.743706i
$247$	1.04851	−	0.908540i	0.0667152	−	0.0578090i
$248$	−14.0278	+	21.8277i	−0.890767	+	1.38606i
$249$	1.98714	−	2.29328i	0.125930	−	0.145331i
$250$	0.618603	+	11.4413i	0.0391239	+	0.723610i
$251$	−7.46001	−	16.3351i	−0.470871	−	1.03106i	−0.984873	−	0.173276i	$-0.944565\pi$
$251$	−7.46001	−	16.3351i	−0.470871	−	1.03106i	0.514002	−	0.857789i	$-0.328162\pi$
$252$			2.93651i			0.184983i
$253$	−6.24788	+	0.250552i	−0.392801	+	0.0157521i
$254$	6.12359			0.384228
$255$	−14.0917	−	2.45369i	−0.882457	−	0.153656i
$256$	16.1579	−	4.74438i	1.00987	−	0.296524i
$257$	−10.7678	−	9.33034i	−0.671676	−	0.582011i	0.250812	−	0.968036i	$-0.419302\pi$
$257$	−10.7678	−	9.33034i	−0.671676	−	0.582011i	−0.922488	+	0.386025i	$0.873848\pi$
$258$	−3.15620	+	4.91114i	−0.196496	+	0.305754i
$259$	−3.08834	−	3.56414i	−0.191900	−	0.221465i
$260$	−0.734805	+	1.49062i	−0.0455707	+	0.0924443i
$261$	−4.80728	−	1.41155i	−0.297563	−	0.0873725i
$262$	8.59534	+	13.3746i	0.531022	+	0.826287i
$263$	17.6664	+	2.54005i	1.08936	+	0.156626i	0.663510	−	0.748168i	$-0.269066\pi$
$263$	17.6664	+	2.54005i	1.08936	+	0.156626i	0.425850	+	0.904794i	$0.359975\pi$
$264$	1.63732	−	3.58523i	0.100770	−	0.220656i
$265$	10.0993	−	6.07584i	0.620393	−	0.373236i
$266$	0.799490	−	5.56057i	0.0490199	−	0.340941i
$267$	7.90763	+	12.3045i	0.483939	+	0.753023i
$268$	1.70645	−	5.81165i	0.104238	−	0.355003i
$269$	0.756302	+	5.26020i	0.0461126	+	0.320720i	0.999801	+	0.0199252i	$0.00634282\pi$
$269$	0.756302	+	5.26020i	0.0461126	+	0.320720i	−0.953689	+	0.300795i	$0.902748\pi$
$270$	−2.27693	+	0.258866i	−0.138570	+	0.0157541i
$271$	−13.7109	−	8.81145i	−0.832877	−	0.535258i	0.0533138	−	0.998578i	$-0.483022\pi$
$271$	−13.7109	−	8.81145i	−0.832877	−	0.535258i	−0.886191	+	0.463320i	$0.846658\pi$
$272$	−5.79457	−	5.02103i	−0.351348	−	0.304444i
$273$	−0.681711	−	2.32169i	−0.0412590	−	0.140515i
$274$	−4.82730	−	10.5703i	−0.291628	−	0.638576i
$275$	−2.35260	−	6.07980i	−0.141867	−	0.366626i
$276$	−0.182504	−	4.55101i	−0.0109855	−	0.273939i
$277$		−	22.8200i		−	1.37112i	−0.728015	−	0.685561i	$-0.759557\pi$
$277$		−	22.8200i		−	1.37112i	0.728015	−	0.685561i	$-0.240443\pi$
$278$	17.5647	−	8.02155i	1.05346	−	0.481100i
$279$	−8.23549	+	2.41816i	−0.493046	+	0.144771i
$280$	5.29237	+	20.2194i	0.316280	+	1.20834i
$281$	−9.63266	−	6.19053i	−0.574636	−	0.369296i	0.220813	−	0.975316i	$-0.429129\pi$
$281$	−9.63266	−	6.19053i	−0.574636	−	0.369296i	−0.795450	+	0.606020i	$0.792765\pi$
$282$	7.65299	−	6.63135i	0.455729	−	0.394891i
$283$	−14.4955	+	2.08414i	−0.861670	+	0.123889i	−0.558961	−	0.829194i	$-0.688800\pi$
$283$	−14.4955	+	2.08414i	−0.861670	+	0.123889i	−0.302709	+	0.953083i	$0.597891\pi$
$284$	8.98732	+	2.63891i	0.533299	+	0.156591i
$285$	−3.96246	−	0.117303i	−0.234716	−	0.00694842i
$286$	−0.148815	+	1.03503i	−0.00879961	+	0.0612026i
$287$	32.3417	+	14.7699i	1.90907	+	0.871842i
$288$	4.38220	+	2.00129i	0.258224	+	0.117927i
$289$	3.40408	−	23.6759i	0.200240	−	1.39270i
$290$	−11.4764	−	0.339742i	−0.673919	−	0.0199504i
$291$	2.86502	+	0.841244i	0.167950	+	0.0493146i
$292$	−8.31708	+	1.19582i	−0.486720	+	0.0699798i
$293$	−2.14889	+	1.86203i	−0.125540	+	0.108781i	−0.715368	−	0.698748i	$-0.753741\pi$
$293$	−2.14889	+	1.86203i	−0.125540	+	0.108781i	0.589828	+	0.807529i	$0.299195\pi$
$294$	−2.20746	−	1.41865i	−0.128741	−	0.0827371i
$295$	−1.53979	−	5.88272i	−0.0896500	−	0.342505i
$296$	−4.42398	+	1.29900i	−0.257139	+	0.0755028i
$297$	1.18600	−	0.541626i	0.0688185	−	0.0314284i
$298$			18.8397i			1.09136i
$299$	1.20081	+	3.55580i	0.0694447	+	0.205637i
$300$	4.42858	−	1.71366i	0.255684	−	0.0989380i
$301$	7.31682	+	16.0216i	0.421734	+	0.923469i
$302$	−3.49664	−	11.9085i	−0.201209	−	0.685255i
$303$	5.86188	+	5.07935i	0.336756	+	0.291801i
$304$	−1.78762	−	1.14884i	−0.102527	−	0.0658903i
$305$	−13.5567	+	1.54128i	−0.776257	+	0.0882533i
$306$	−0.932972	−	6.48896i	−0.0533344	−	0.370949i
$307$	−0.913247	+	3.11023i	−0.0521218	+	0.177510i	−0.981440	−	0.191769i	$-0.938577\pi$
$307$	−0.913247	+	3.11023i	−0.0521218	+	0.177510i	0.929318	+	0.369280i	$0.120396\pi$
$308$	−2.06994	−	3.22089i	−0.117946	−	0.183527i
$309$	2.35765	−	16.3978i	0.134122	−	0.932839i
$310$	−16.8542	+	10.1397i	−0.957253	+	0.575895i
$311$	−12.7677	+	27.9575i	−0.723993	+	1.58532i	0.0842307	+	0.996446i	$0.473157\pi$
$311$	−12.7677	+	27.9575i	−0.723993	+	1.58532i	−0.808223	+	0.588876i	$0.799571\pi$
$312$	−2.34161	−	0.336673i	−0.132568	−	0.0190604i
$313$	−1.25653	−	1.95520i	−0.0710234	−	0.110515i	0.803925	−	0.594731i	$-0.202741\pi$
$313$	−1.25653	−	1.95520i	−0.0710234	−	0.110515i	−0.874948	+	0.484216i	$0.839105\pi$
$314$	−16.7315	−	4.91281i	−0.944213	−	0.277246i
$315$	−3.05698	+	6.20137i	−0.172241	+	0.349408i
$316$	−4.13658	−	4.77387i	−0.232701	−	0.268551i
$317$	5.85673	−	9.11325i	0.328947	−	0.511851i	−0.636906	−	0.770941i	$-0.719786\pi$
$317$	5.85673	−	9.11325i	0.328947	−	0.511851i	0.965853	+	0.259090i	$0.0834226\pi$
$318$	4.08239	+	3.53741i	0.228929	+	0.198368i
$319$	6.26783	−	1.84040i	0.350931	−	0.103043i
$320$	16.1572	+	2.81333i	0.903213	+	0.157270i
$321$	−7.23396			−0.403760
$322$	13.1034	+	7.69722i	0.730225	+	0.428949i
$323$		−	11.3406i		−	0.631006i
$324$	0.394526	+	0.863891i	0.0219181	+	0.0479939i
$325$	−3.10354	+	2.38296i	−0.172154	+	0.132183i
$326$	−14.9466	+	17.2493i	−0.827817	+	0.955352i
$327$	−0.952796	+	1.48258i	−0.0526897	+	0.0819868i
$328$	26.2706	−	22.7636i	1.45055	−	1.25691i
$329$	−4.34799	−	30.2409i	−0.239712	−	1.66724i
$330$	2.31496	−	1.88894i	0.127434	−	0.103983i
$331$	22.1190	−	14.2150i	1.21577	−	0.781329i	0.234156	−	0.972199i	$-0.424767\pi$
$331$	22.1190	−	14.2150i	1.21577	−	0.781329i	0.981615	+	0.190870i	$0.0611309\pi$
$332$	−2.85252	−	0.410131i	−0.156553	−	0.0225089i
$333$	−1.38741	−	0.633608i	−0.0760294	−	0.0347215i
$334$	2.12252	−	4.64767i	0.116139	−	0.254309i
$335$	9.65379	−	10.4967i	0.527443	−	0.573494i
$336$	−3.11777	+	2.00367i	−0.170088	+	0.109309i
$337$	6.57029	−	22.3764i	0.357907	−	1.21892i	−0.562118	−	0.827057i	$-0.690013\pi$
$337$	6.57029	−	22.3764i	0.357907	−	1.21892i	0.920024	−	0.391861i	$-0.128169\pi$
$338$	−12.5660	+	1.80672i	−0.683500	+	0.0982725i
$339$	1.56430	+	1.80529i	0.0849609	+	0.0980501i
$340$	5.27507	+	12.5184i	0.286081	+	0.678908i
$341$	7.32848	−	8.45752i	0.396860	−	0.458000i
$342$	−0.511872	−	1.74328i	−0.0276789	−	0.0942655i
$343$	12.4867	−	5.70246i	0.674216	−	0.307904i
$344$	17.2201			0.928444
$345$	4.35230	−	9.80089i	0.234320	−	0.527662i
$346$	11.3946			0.612578
$347$	14.3626	−	6.55920i	0.771027	−	0.352116i	0.00925147	−	0.999957i	$-0.497055\pi$
$347$	14.3626	−	6.55920i	0.771027	−	0.352116i	0.761776	+	0.647841i	$0.224328\pi$
$348$	1.34057	+	4.56555i	0.0718619	+	0.244739i
$349$	15.8779	−	18.3240i	0.849923	−	0.980863i	−0.150047	−	0.988679i	$-0.547942\pi$
$349$	15.8779	−	18.3240i	0.849923	−	0.980863i	0.999969	+	0.00781600i	$0.00248793\pi$
$350$	−3.17858	+	15.5218i	−0.169902	+	0.829674i
$351$	−0.512476	−	0.591429i	−0.0273540	−	0.0315681i
$352$	−6.21730	+	0.893912i	−0.331383	+	0.0476457i
$353$	5.87103	−	19.9949i	0.312483	−	1.06422i	−0.642185	−	0.766549i	$-0.721972\pi$
$353$	5.87103	−	19.9949i	0.312483	−	1.06422i	0.954669	−	0.297671i	$-0.0962097\pi$
$354$	2.34457	−	1.50676i	0.124613	−	0.0800837i
$355$	16.2324	+	14.9289i	0.861525	+	0.792345i
$356$	5.77049	−	12.6356i	0.305835	−	0.669686i
$357$	−17.9916	−	8.21647i	−0.952214	−	0.434862i
$358$	−8.31151	−	1.19501i	−0.439277	−	0.0631585i
$359$	20.0465	−	12.8831i	1.05802	−	0.679946i	0.108638	−	0.994081i	$-0.465351\pi$
$359$	20.0465	−	12.8831i	1.05802	−	0.679946i	0.949378	+	0.314136i	$0.101715\pi$
$360$	4.27347	+	5.23729i	0.225232	+	0.276029i
$361$	2.25669	+	15.6956i	0.118773	+	0.826085i
$362$	−7.02710	+	6.08902i	−0.369336	+	0.320032i
$363$	5.02799	−	7.82370i	0.263901	−	0.410638i
$364$	−1.50489	+	1.73674i	−0.0788778	+	0.0910298i
$365$	−18.8090	−	6.13295i	−0.984509	−	0.321013i
$366$	−2.59774	−	5.68825i	−0.135786	−	0.297330i
$367$		−	11.7611i		−	0.613925i	−0.951722	−	0.306962i	$-0.900687\pi$
$367$		−	11.7611i		−	0.613925i	0.951722	−	0.306962i	$-0.0993126\pi$
$368$	4.70740	−	3.29906i	0.245390	−	0.171976i
$369$	11.4990			0.598611
$370$	−3.44343	−	0.599580i	−0.179015	−	0.0311707i
$371$	15.6374	−	4.59154i	0.811851	−	0.238381i
$372$	6.16054	+	5.33813i	0.319409	+	0.276769i
$373$	−7.79811	+	12.1341i	−0.403771	+	0.628280i	−0.982285	−	0.187393i	$-0.939996\pi$
$373$	−7.79811	+	12.1341i	−0.403771	+	0.628280i	0.578514	+	0.815672i	$0.303633\pi$
$374$	5.59738	+	6.45972i	0.289434	+	0.334024i
$375$	11.1363	+	0.991339i	0.575076	+	0.0511925i
$376$	−28.6599	−	8.41531i	−1.47802	−	0.433987i
$377$	−2.11978	−	3.29845i	−0.109174	−	0.169879i
$378$	−3.13653	−	0.450965i	−0.161326	−	0.0231951i
$379$	−5.50859	+	12.0621i	−0.282957	+	0.619590i	−0.996731	−	0.0807857i	$-0.974257\pi$
$379$	−5.50859	+	12.0621i	−0.282957	+	0.619590i	0.713774	+	0.700376i	$0.246984\pi$
$380$	1.94083	+	3.22604i	0.0995622	+	0.165493i
$381$	0.850360	−	5.91438i	0.0435652	−	0.303003i
$382$	3.27384	+	5.09420i	0.167504	+	0.260642i
$383$	−2.36867	+	8.06696i	−0.121033	+	0.412202i	−0.997613	−	0.0690552i	$-0.978002\pi$
$383$	−2.36867	+	8.06696i	−0.121033	+	0.412202i	0.876579	+	0.481257i	$0.159820\pi$
$384$	−0.301501	−	2.09698i	−0.0153859	−	0.107011i
$385$	−1.01831	−	8.95679i	−0.0518976	−	0.456480i
$386$	−14.5851	−	9.37324i	−0.742360	−	0.477086i
$387$	4.30506	+	3.73036i	0.218839	+	0.189625i
$388$	−0.798942	−	2.72095i	−0.0405601	−	0.138135i
$389$	−3.14846	−	6.89416i	−0.159633	−	0.349548i	0.812867	−	0.582449i	$-0.197905\pi$
$389$	−3.14846	−	6.89416i	−0.159633	−	0.349548i	−0.972500	+	0.232901i	$0.925178\pi$
$390$	−1.47931	−	1.01377i	−0.0749076	−	0.0513343i
$391$	28.3940	+	11.6157i	1.43595	+	0.587433i
$392$			7.74007i			0.390933i
$393$	14.1113	−	6.44441i	0.711820	−	0.325077i
$394$	10.5428	−	3.09564i	0.531138	−	0.155956i
$395$	−3.76598	−	14.3878i	−0.189487	−	0.723930i
$396$	−1.04169	−	0.669452i	−0.0523468	−	0.0336412i
$397$	−19.7414	+	17.1060i	−0.990792	+	0.858526i	−0.989942	−	0.141474i	$-0.954816\pi$
$397$	−19.7414	+	17.1060i	−0.990792	+	0.858526i	−0.000849607		1.00000i	$0.500270\pi$
$398$	−2.15536	+	0.309893i	−0.108038	+	0.0155336i
$399$	−5.25958	−	1.54435i	−0.263308	−	0.0773143i
$400$	4.84119	+	3.53266i	0.242059	+	0.176633i
$401$	−2.97337	+	20.6803i	−0.148483	+	1.03272i	0.770221	+	0.637777i	$0.220146\pi$
$401$	−2.97337	+	20.6803i	−0.148483	+	1.03272i	−0.918704	+	0.394946i	$0.870763\pi$
$402$	5.94544	+	2.71519i	0.296532	+	0.135421i
$403$	−6.10995	−	2.79032i	−0.304358	−	0.138996i
$404$	1.04834	−	7.29137i	0.0521569	−	0.362759i
$405$	−0.0661665	+	2.23509i	−0.00328784	+	0.111062i
$406$	−15.2332	−	4.47288i	−0.756013	−	0.221985i
$407$	1.96840	−	0.283013i	0.0975698	−	0.0140284i
$408$	−14.6142	+	12.6633i	−0.723512	+	0.626927i
$409$	−17.7972	−	11.4376i	−0.880014	−	0.565551i	0.0207863	−	0.999784i	$-0.493383\pi$
$409$	−17.7972	−	11.4376i	−0.880014	−	0.565551i	−0.900801	+	0.434233i	$0.857019\pi$
$410$	25.4922	−	6.67252i	1.25897	−	0.329532i
$411$	−10.8795	+	3.19452i	−0.536647	+	0.157574i
$412$	−14.3116	+	6.53588i	−0.705081	+	0.322000i
$413$		−	8.40856i		−	0.413758i
$414$	4.88903	+	0.503971i	0.240283	+	0.0247688i
$415$	−5.59705	−	3.83567i	−0.274748	−	0.188286i
$416$	1.56615	+	3.42939i	0.0767869	+	0.168140i
$417$	−5.30835	−	18.0786i	−0.259951	−	0.885311i
$418$	1.79028	+	1.55128i	0.0875652	+	0.0758757i
$419$	−11.7577	−	7.55623i	−0.574402	−	0.369146i	0.220958	−	0.975283i	$-0.429082\pi$
$419$	−11.7577	−	7.55623i	−0.574402	−	0.369146i	−0.795360	+	0.606137i	$0.792718\pi$
$420$	6.52421	−	0.741743i	0.318349	−	0.0361934i
$421$	1.90153	+	13.2254i	0.0926747	+	0.644567i	0.982222	+	0.187724i	$0.0601109\pi$
$421$	1.90153	+	13.2254i	0.0926747	+	0.644567i	−0.889547	+	0.456843i	$0.848980\pi$
$422$	−6.77799	+	23.0837i	−0.329947	+	1.12370i
$423$	−5.34206	−	8.31240i	−0.259740	−	0.404163i
$424$	2.26760	−	15.7715i	0.110125	−	0.765933i
$425$	−1.89203	+	31.9281i	−0.0917768	+	1.54874i
$426$	−4.19886	+	9.19421i	−0.203435	+	0.445461i
$427$	−18.6747	−	2.68502i	−0.903734	−	0.129937i
$428$	3.71431	+	5.77958i	0.179538	+	0.279367i
$429$	0.979003	+	0.287461i	0.0472667	+	0.0138788i
$430$	11.7086	+	5.77178i	0.564638	+	0.278340i
$431$	9.23356	+	10.6561i	0.444765	+	0.513286i	0.933221	−	0.359302i	$-0.116985\pi$
$431$	9.23356	+	10.6561i	0.444765	+	0.513286i	−0.488456	+	0.872588i	$0.662440\pi$
$432$	−0.648019	+	1.00834i	−0.0311778	+	0.0485137i
$433$	14.7357	+	12.7686i	0.708154	+	0.613619i	0.932619	−	0.360863i	$-0.117518\pi$
$433$	14.7357	+	12.7686i	0.708154	+	0.613619i	−0.224465	+	0.974482i	$0.572063\pi$
$434$	−26.0964	+	7.66261i	−1.25267	+	0.367817i
$435$	−1.92182	+	11.0372i	−0.0921443	+	0.529191i
$436$	1.67373			0.0801569
$437$	8.24729	+	2.06656i	0.394521	+	0.0988568i
$438$		−	9.06723i		−	0.433249i
$439$	0.917069	+	2.00810i	0.0437693	+	0.0958415i	0.930254	−	0.366917i	$-0.119587\pi$
$439$	0.917069	+	2.00810i	0.0437693	+	0.0958415i	−0.886484	+	0.462759i	$0.846860\pi$
$440$	−8.37908	−	2.73212i	−0.399457	−	0.130249i
$441$	−1.67672	+	1.93504i	−0.0798438	+	0.0921446i
$442$	2.77365	−	4.31588i	0.131929	−	0.205286i
$443$	−2.67965	+	2.32193i	−0.127314	+	0.110318i	−0.716191	−	0.697905i	$-0.754116\pi$
$443$	−2.67965	+	2.32193i	−0.127314	+	0.110318i	0.588877	+	0.808223i	$0.299570\pi$
$444$	0.206149	+	1.43380i	0.00978340	+	0.0680451i
$445$	25.3402	−	20.6768i	1.20124	−	0.980176i
$446$	19.7677	−	12.7039i	0.936027	−	0.601548i
$447$	18.1961	+	2.61620i	0.860645	+	0.123742i
$448$	20.6286	+	9.42078i	0.974611	+	0.445090i
$449$	0.248102	−	0.543268i	0.0117087	−	0.0256384i	−0.903687	−	0.428193i	$-0.859150\pi$
$449$	0.248102	−	0.543268i	0.0117087	−	0.0256384i	0.915396	+	0.402555i	$0.131878\pi$
$450$	1.15028	+	4.99340i	0.0542245	+	0.235391i
$451$	−12.6125	+	8.10559i	−0.593902	+	0.381677i
$452$	0.639146	−	2.17673i	0.0300629	−	0.102385i
$453$	−11.9872	+	1.72350i	−0.563207	+	0.0809769i
$454$	11.0769	+	12.7835i	0.519866	+	0.599957i
$455$	−4.98604	+	2.10104i	−0.233749	+	0.0984982i
$456$	−3.50956	+	4.05025i	−0.164350	+	0.189670i
$457$	7.93184	+	27.0134i	0.371036	+	1.26363i	0.907623	+	0.419787i	$0.137895\pi$
$457$	7.93184	+	27.0134i	0.371036	+	1.26363i	−0.536587	+	0.843845i	$0.680287\pi$
$458$	−13.8514	+	6.32571i	−0.647232	+	0.295581i
$459$	−6.39683			−0.298578
$460$	−10.0651	+	1.55504i	−0.469290	+	0.0725039i
$461$	−27.0547			−1.26006			−0.630032	−	0.776570i	$-0.716958\pi$
$461$	−27.0547			−1.26006			−0.630032	+	0.776570i	$0.716958\pi$
$462$	3.75816	−	1.71630i	0.174846	−	0.0798493i
$463$	2.17285	+	7.40004i	0.100981	+	0.343909i	0.994449	−	0.105217i	$-0.0335537\pi$
$463$	2.17285	+	7.40004i	0.100981	+	0.343909i	−0.893468	+	0.449126i	$0.851735\pi$
$464$	−3.93266	+	4.53853i	−0.182569	+	0.210696i
$465$	7.45278	+	17.6864i	0.345614	+	0.820188i
$466$	1.84898	+	2.13384i	0.0856523	+	0.0988480i
$467$	−40.2688	+	5.78978i	−1.86342	+	0.267919i	−0.979755	−	0.200202i	$-0.935840\pi$
$467$	−40.2688	+	5.78978i	−1.86342	+	0.267919i	−0.883664	+	0.468122i	$0.844931\pi$
$468$	−0.209389	+	0.713115i	−0.00967903	+	0.0329638i
$469$	16.5894	−	10.6613i	0.766026	−	0.492295i
$470$	−16.6663	−	15.3280i	−0.768761	−	0.707030i
$471$	−7.06840	+	15.4776i	−0.325695	+	0.713172i
$472$	−7.47795	−	3.41506i	−0.344200	−	0.157191i
$473$	−7.35150	−	1.05699i	−0.338022	−	0.0486003i
$474$	5.73430	−	3.68521i	0.263385	−	0.169267i
$475$	0.740273	+	8.83325i	0.0339661	+	0.405298i
$476$	2.67329	+	18.5932i	0.122530	+	0.852216i
$477$	3.98347	−	3.45169i	0.182390	−	0.158042i
$478$	3.70564	−	5.76609i	0.169492	−	0.263735i
$479$	27.6816	−	31.9463i	1.26481	−	1.45966i	0.436184	−	0.899858i	$-0.356330\pi$
$479$	27.6816	−	31.9463i	1.26481	−	1.45966i	0.828623	−	0.559807i	$-0.189125\pi$
$480$	3.33945	−	10.2417i	0.152424	−	0.467467i
$481$	−0.495844	−	1.08575i	−0.0226085	−	0.0495058i
$482$		−	2.67480i		−	0.121834i
$483$	9.25387	−	11.5869i	0.421066	−	0.527221i
$484$	−8.83240			−0.401473
$485$	1.14536	−	6.57786i	0.0520079	−	0.298685i
$486$	−0.983321	+	0.288729i	−0.0446044	+	0.0130970i
$487$	10.1057	+	8.75666i	0.457934	+	0.396802i	0.853050	−	0.521829i	$-0.174750\pi$
$487$	10.1057	+	8.75666i	0.457934	+	0.396802i	−0.395116	+	0.918631i	$0.629296\pi$
$488$	−9.97245	+	15.5174i	−0.451432	+	0.702441i
$489$	14.5844	+	16.8313i	0.659531	+	0.761139i
$490$	−2.59429	+	5.26277i	−0.117198	+	0.237748i
$491$	13.4697	+	3.95505i	0.607877	+	0.178489i	0.571163	−	0.820837i	$-0.306493\pi$
$491$	13.4697	+	3.95505i	0.607877	+	0.178489i	0.0367146	+	0.999326i	$0.488311\pi$
$492$	−5.90419	−	9.18710i	−0.266181	−	0.414186i
$493$	−31.7234	−	4.56113i	−1.42875	−	0.205423i
$494$	0.590651	−	1.29335i	0.0265747	−	0.0581904i
$495$	−1.50294	−	2.49818i	−0.0675520	−	0.112285i
$496$	−1.46412	+	10.1832i	−0.0657409	+	0.457238i
$497$	16.4870	+	25.6543i	0.739544	+	1.15075i
$498$	0.876133	−	2.98384i	0.0392605	−	0.133709i
$499$	0.0858660	+	0.597211i	0.00384389	+	0.0267348i	0.991653	−	0.128934i	$-0.0411557\pi$
$499$	0.0858660	+	0.597211i	0.00384389	+	0.0267348i	−0.987809	+	0.155669i	$0.950247\pi$
$500$	−4.92595	−	9.40637i	−0.220295	−	0.420665i
$501$	−4.19414	−	2.69541i	−0.187380	−	0.120422i
$502$	−13.9088	−	12.0520i	−0.620779	−	0.537908i
$503$	2.12181	+	7.22622i	0.0946068	+	0.322201i	0.993175	−	0.116632i	$-0.0372099\pi$
$503$	2.12181	+	7.22622i	0.0946068	+	0.322201i	−0.898568	+	0.438834i	$0.855392\pi$
$504$	3.88288	+	8.50233i	0.172957	+	0.378724i
$505$	9.80440	−	14.3067i	0.436290	−	0.636639i
$506$	−5.71774	+	2.89349i	−0.254185	+	0.128631i
$507$			12.3876i			0.550152i
$508$	−5.16192	+	2.35737i	−0.229023	+	0.104591i
$509$	−29.9706	+	8.80016i	−1.32842	+	0.390060i	−0.867525	−	0.497393i	$-0.834291\pi$
$509$	−29.9706	+	8.80016i	−1.32842	+	0.390060i	−0.460898	+	0.887453i	$0.652473\pi$
$510$	−14.1812	+	3.71190i	−0.627955	+	0.164366i
$511$	−23.0137	−	14.7900i	−1.01807	−	0.654271i
$512$	9.84071	−	8.52702i	0.434902	−	0.376845i
$513$	−1.75480	+	0.252302i	−0.0774763	+	0.0111394i
$514$	−14.0102	−	4.11376i	−0.617963	−	0.181450i
$515$	−37.0275	−	1.09614i	−1.63162	−	0.0483018i
$516$	0.769919	−	5.35490i	0.0338938	−	0.235736i
$517$	11.7188	+	5.35180i	0.515392	+	0.235372i
$518$	−4.39639	−	2.00776i	−0.193166	−	0.0882161i
$519$	1.58233	−	11.0053i	0.0694564	−	0.483080i
$520$	−0.156530	+	5.28753i	−0.00686428	+	0.231874i
$521$	40.5583	+	11.9090i	1.77689	+	0.521742i	0.994839	−	0.101469i	$-0.0323544\pi$
$521$	40.5583	+	11.9090i	1.77689	+	0.521742i	0.782053	+	0.623212i	$0.214173\pi$
$522$	−5.08240	+	0.730738i	−0.222450	+	0.0319835i
$523$	−2.43400	+	2.10907i	−0.106431	+	0.0922231i	−0.706451	−	0.707762i	$-0.749705\pi$
$523$	−2.43400	+	2.10907i	−0.106431	+	0.0922231i	0.600020	+	0.799985i	$0.295159\pi$
$524$	−12.3943	−	7.96531i	−0.541446	−	0.347966i
$525$	14.5501	+	5.22544i	0.635018	+	0.228057i
$526$	17.5504	−	5.15327i	0.765235	−	0.224693i
$527$	−49.9434	+	22.8084i	−2.17557	+	0.993548i
$528$		−	1.56278i		−	0.0680111i
$529$	−13.6215	+	18.5325i	−0.592241	+	0.805761i
$530$	6.82808	−	9.96360i	0.296593	−	0.432791i
$531$	−1.12971	−	2.47371i	−0.0490250	−	0.107350i
$532$	1.46669	+	4.99510i	0.0635892	+	0.216565i
$533$	6.80081	+	5.89294i	0.294576	+	0.255251i
$534$	12.6101	+	8.10401i	0.545691	+	0.350695i
$535$	1.82725	+	16.0721i	0.0789989	+	0.694857i
$536$	−2.74377	−	19.0834i	−0.118513	−	0.824276i
$537$	−2.30838	+	7.86161i	−0.0996138	+	0.339253i
$538$	2.94447	+	4.58169i	0.126945	+	0.197531i
$539$	0.475094	−	3.30435i	0.0204637	−	0.142328i
$540$	1.81970	−	1.09475i	0.0783074	−	0.0471107i
$541$	−6.12243	+	13.4063i	−0.263224	+	0.576380i	−0.994385	−	0.105825i	$-0.966252\pi$
$541$	−6.12243	+	13.4063i	−0.263224	+	0.576380i	0.731161	+	0.682205i	$0.238979\pi$
$542$	−16.5329	−	2.37707i	−0.710149	−	0.102104i
$543$	4.90516	+	7.63258i	0.210501	+	0.327545i
$544$	29.5688	+	8.68217i	1.26775	+	0.372245i
$545$	3.53460	+	1.74239i	0.151406	+	0.0746358i
$546$	−1.62392	−	1.87411i	−0.0694976	−	0.0802045i
$547$	7.29656	−	11.3537i	0.311978	−	0.485448i	−0.649487	−	0.760372i	$-0.725017\pi$
$547$	7.29656	−	11.3537i	0.311978	−	0.485448i	0.961466	+	0.274925i	$0.0886529\pi$
$548$	8.13840	+	7.05197i	0.347655	+	0.301245i
$549$	−5.85465	+	1.71908i	−0.249870	+	0.0733686i
$550$	−4.78151	−	4.66615i	−0.203884	−	0.198965i
$551$	−8.88236			−0.378401
$552$	−6.54612	−	12.9356i	−0.278622	−	0.550576i
$553$		−	20.5654i		−	0.874532i
$554$	−9.71521	−	21.2733i	−0.412760	−	0.903817i
$555$	−1.05727	+	3.24252i	−0.0448787	+	0.137637i
$556$	−11.7183	+	13.5236i	−0.496966	+	0.573530i
$557$	7.61676	−	11.8519i	0.322733	−	0.502182i	−0.641541	−	0.767088i	$-0.721705\pi$
$557$	7.61676	−	11.8519i	0.322733	−	0.502182i	0.964274	+	0.264907i	$0.0853411\pi$
$558$	−6.64782	+	5.76037i	−0.281425	+	0.243856i
$559$	0.634419	+	4.41248i	0.0268331	+	0.186628i
$560$	5.23919	+	6.42081i	0.221396	+	0.271329i
$561$	7.01632	−	4.50911i	0.296229	−	0.190375i
$562$	−11.6153	−	1.67003i	−0.489961	−	0.0704458i
$563$	−26.0288	−	11.8870i	−1.09698	−	0.500976i	−0.217093	−	0.976151i	$-0.569657\pi$
$563$	−26.0288	−	11.8870i	−1.09698	−	0.500976i	−0.879891	+	0.475175i	$0.842385\pi$
$564$	−3.89830	+	8.53608i	−0.164148	+	0.359434i
$565$	3.61579	−	3.93149i	0.152117	−	0.165399i
$566$	−12.6258	+	8.11409i	−0.530701	+	0.341061i
$567$	−0.871115	+	2.96675i	−0.0365834	+	0.124592i
$568$	29.5111	−	4.24306i	1.23826	−	0.178035i
$569$	−18.4203	−	21.2581i	−0.772217	−	0.891186i	0.224304	−	0.974519i	$-0.427989\pi$
$569$	−18.4203	−	21.2581i	−0.772217	−	0.891186i	−0.996522	+	0.0833328i	$0.973444\pi$
$570$	−3.74384	+	1.57759i	−0.156812	+	0.0660781i
$571$	5.98992	−	6.91273i	0.250670	−	0.289289i	−0.616443	−	0.787399i	$-0.711427\pi$
$571$	5.98992	−	6.91273i	0.250670	−	0.289289i	0.867114	+	0.498110i	$0.165973\pi$
$572$	−0.273006	−	0.929774i	−0.0114150	−	0.0388758i
$573$	5.37479	−	2.45458i	0.224535	−	0.102542i
$574$	36.4377			1.52088
$575$	−22.8745	−	7.19411i	−0.953934	−	0.300015i
$576$	7.33442			0.305601
$577$	−25.4231	+	11.6103i	−1.05838	+	0.483344i	−0.867070	−	0.498186i	$-0.834000\pi$
$577$	−25.4231	+	11.6103i	−1.05838	+	0.483344i	−0.191306	+	0.981530i	$0.561272\pi$
$578$	−6.90622	−	23.5204i	−0.287261	−	0.978321i
$579$	−11.0784	+	12.7851i	−0.460402	+	0.531332i
$580$	9.80491	−	4.13164i	0.407127	−	0.171557i
$581$	−6.14422	−	7.09081i	−0.254905	−	0.294176i
$582$	3.02898	−	0.435501i	0.125555	−	0.0180521i
$583$	−1.93615	+	6.59391i	−0.0801869	+	0.273092i
$584$	−22.4999	+	14.4598i	−0.931055	+	0.598352i
$585$	−1.18456	+	1.28799i	−0.0489756	+	0.0532517i
$586$	−1.21052	+	2.65067i	−0.0500062	+	0.109498i
$587$	−37.5341	−	17.1412i	−1.54920	−	0.707495i	−0.556809	−	0.830641i	$-0.687974\pi$
$587$	−37.5341	−	17.1412i	−1.54920	−	0.707495i	−0.992389	+	0.123146i	$0.960702\pi$
$588$	2.40692	+	0.346063i	0.0992596	+	0.0142714i
$589$	−12.8010	+	8.22672i	−0.527457	+	0.338976i
$590$	−3.93989	−	4.82847i	−0.162203	−	0.198785i
$591$	−1.52584	−	10.6125i	−0.0627648	−	0.436539i
$592$	−1.38164	+	1.19720i	−0.0567851	+	0.0492045i
$593$	−18.2703	+	28.4292i	−0.750272	+	1.16745i	0.230649	+	0.973037i	$0.425915\pi$
$593$	−18.2703	+	28.4292i	−0.750272	+	1.16745i	−0.980921	+	0.194409i	$0.937721\pi$
$594$	0.875025	−	1.00983i	0.0359027	−	0.0414339i
$595$	−13.7104	+	42.0483i	−0.562073	+	1.72381i
$596$	−7.25264	−	15.8811i	−0.297080	−	0.650514i
$597$			2.12475i			0.0869604i
$598$	2.63324	+	2.80357i	0.107681	+	0.114647i
$599$	38.1369			1.55823			0.779116	−	0.626880i	$-0.215668\pi$
$599$	38.1369			1.55823			0.779116	+	0.626880i	$0.215668\pi$
$600$	10.5565	−	10.8175i	0.430968	−	0.441623i
$601$	34.9261	−	10.2552i	1.42467	−	0.418320i	0.523586	−	0.851973i	$-0.324594\pi$
$601$	34.9261	−	10.2552i	1.42467	−	0.418320i	0.901080	+	0.433653i	$0.142776\pi$
$602$	13.6418	+	11.8207i	0.555998	+	0.481775i
$603$	3.44805	−	5.36527i	0.140415	−	0.218491i
$604$	7.53186	+	8.69222i	0.306467	+	0.353682i
$605$	−18.6524	−	9.19474i	−0.758327	−	0.373820i
$606$	7.62702	+	2.23949i	0.309826	+	0.0909733i
$607$	15.6896	+	24.4135i	0.636821	+	0.990913i	0.998286	+	0.0585272i	$0.0186404\pi$
$607$	15.6896	+	24.4135i	0.636821	+	0.990913i	−0.361465	+	0.932386i	$0.617723\pi$
$608$	8.45385	+	1.21548i	0.342849	+	0.0492942i
$609$	−6.43545	+	14.0917i	−0.260777	+	0.571023i
$610$	−11.9817	+	7.20835i	−0.485126	+	0.291858i
$611$	1.10046	−	7.65387i	0.0445199	−	0.309643i
$612$	3.28448	+	5.11075i	0.132767	+	0.206590i
$613$	−7.20723	+	24.5456i	−0.291097	+	0.991386i	0.675984	+	0.736917i	$0.263719\pi$
$613$	−7.20723	+	24.5456i	−0.291097	+	0.991386i	−0.967081	+	0.254469i	$0.918099\pi$
$614$	0.472776	+	3.28823i	0.0190797	+	0.132702i
$615$	−2.90456	−	25.5479i	−0.117123	−	1.03019i
$616$	−10.2522	−	6.58868i	−0.413073	−	0.265466i
$617$	2.50449	+	2.17015i	0.100827	+	0.0873670i	0.703816	−	0.710383i	$-0.251478\pi$
$617$	2.50449	+	2.17015i	0.100827	+	0.0873670i	−0.602989	+	0.797750i	$0.706024\pi$
$618$	−4.78321	−	16.2901i	−0.192409	−	0.655285i
$619$	17.6191	+	38.5805i	0.708173	+	1.55068i	0.829772	+	0.558102i	$0.188470\pi$
$619$	17.6191	+	38.5805i	0.708173	+	1.55068i	−0.121600	+	0.992579i	$0.538802\pi$
$620$	10.3039	−	15.0356i	0.413815	−	0.603843i
$621$	1.16567	−	4.65201i	0.0467769	−	0.186679i
$622$			31.4982i			1.26296i
$623$	41.1378	−	18.7870i	1.64815	−	0.752686i
$624$	−0.900006	+	0.264266i	−0.0360291	+	0.0105791i
$625$	−0.610444	−	24.9925i	−0.0244177	−	0.999702i
$626$	−2.00376	−	1.28774i	−0.0800863	−	0.0514683i
$627$	1.74689	−	1.51369i	0.0697642	−	0.0604510i
$628$	15.9952	−	2.29976i	0.638277	−	0.0917704i
$629$	−9.36148	−	2.74878i	−0.373267	−	0.109601i
$630$	−0.209667	+	7.08251i	−0.00835334	+	0.282174i
$631$	−0.0860791	+	0.598693i	−0.00342676	+	0.0238336i	−0.991463	−	0.130388i	$-0.958378\pi$
$631$	−0.0860791	+	0.598693i	−0.00342676	+	0.0238336i	0.988036	+	0.154221i	$0.0492869\pi$
$632$	−18.2894	−	8.35248i	−0.727512	−	0.332244i
$633$	21.3538	+	9.75197i	0.848739	+	0.387606i
$634$	1.57998	−	10.9890i	0.0627488	−	0.436428i
$635$	−13.3551	−	0.395358i	−0.529981	−	0.0156893i
$636$	−4.80306	−	1.41031i	−0.190454	−	0.0559223i
$637$	−1.98332	+	0.285159i	−0.0785820	+	0.0112984i
$638$	5.05950	−	4.38408i	0.200307	−	0.173567i
$639$	8.29702	+	5.33217i	0.328225	+	0.210937i
$640$	−4.58282	+	1.19954i	−0.181152	+	0.0474161i
$641$	20.0969	−	5.90097i	0.793779	−	0.233074i	0.140389	−	0.990096i	$-0.455165\pi$
$641$	20.0969	−	5.90097i	0.793779	−	0.233074i	0.653389	+	0.757022i	$0.273346\pi$
$642$	−6.74366	+	3.07973i	−0.266151	+	0.121547i
$643$			25.2292i			0.994941i	0.867481	+	0.497471i	$0.165738\pi$
$643$			25.2292i			0.994941i	−0.867481	+	0.497471i	$0.834262\pi$
$644$	−14.0088	−	1.44405i	−0.552023	−	0.0569037i
$645$	7.20051	−	10.5071i	0.283520	−	0.413715i
$646$	−4.82804	−	10.5719i	−0.189957	−	0.415947i
$647$	−3.41448	−	11.6287i	−0.134237	−	0.457170i	0.864748	−	0.502206i	$-0.167478\pi$
$647$	−3.41448	−	11.6287i	−0.134237	−	0.457170i	−0.998985	+	0.0450358i	$0.985660\pi$
$648$	2.28461	+	1.97962i	0.0897479	+	0.0777670i
$649$	2.98282	+	1.91694i	0.117086	+	0.0752467i
$650$	−1.87869	+	3.54273i	−0.0736883	+	0.138957i
$651$	3.77691	+	26.2690i	0.148029	+	1.02956i
$652$	5.95896	−	20.2944i	0.233371	−	0.794789i
$653$	23.9294	+	37.2348i	0.936428	+	1.45711i	0.888826	+	0.458245i	$0.151522\pi$
$653$	23.9294	+	37.2348i	0.936428	+	1.45711i	0.0476022	+	0.998866i	$0.484842\pi$
$654$	−0.257037	+	1.78773i	−0.0100509	+	0.0699057i
$655$	−17.8823	−	29.7240i	−0.698720	−	1.16141i
$656$	5.72558	−	12.5373i	0.223546	−	0.489498i
$657$	−8.75745	−	1.25913i	−0.341661	−	0.0491234i
$658$	−16.9278	−	26.3402i	−0.659915	−	1.02685i
$659$	12.0174	+	3.52863i	0.468132	+	0.137456i	0.507287	−	0.861777i	$-0.330648\pi$
$659$	12.0174	+	3.52863i	0.468132	+	0.137456i	−0.0391551	+	0.999233i	$0.512467\pi$
$660$	−1.22424	+	2.48348i	−0.0476533	+	0.0966691i
$661$	9.38523	+	10.8311i	0.365043	+	0.421282i	0.908323	−	0.418269i	$-0.137363\pi$
$661$	9.38523	+	10.8311i	0.365043	+	0.421282i	−0.543280	+	0.839552i	$0.682818\pi$
$662$	14.5681	−	22.6683i	0.566204	−	0.881030i
$663$	−3.78327	−	3.27822i	−0.146930	−	0.127316i
$664$	−8.80146	+	2.58434i	−0.341563	+	0.100292i
$665$	−2.10264	+	12.0756i	−0.0815367	+	0.468271i
$666$	−1.56312			−0.0605696
$667$	9.09788	−	22.2393i	0.352271	−	0.861108i
$668$			4.73488i			0.183198i
$669$	−9.52483	−	20.8565i	−0.368251	−	0.806358i
$670$	4.53071	−	13.8952i	0.175037	−	0.536817i
$671$	5.20986	−	6.01250i	0.201124	−	0.232110i
$672$	8.05331	−	12.5312i	0.310663	−	0.483401i
$673$	0.269220	−	0.233281i	0.0103777	−	0.00899230i	−0.649656	−	0.760228i	$-0.725087\pi$
$673$	0.269220	−	0.233281i	0.0103777	−	0.00899230i	0.660034	+	0.751236i	$0.270542\pi$
$674$	−3.40135	−	23.6569i	−0.131015	−	0.911230i
$675$	4.98253	−	0.417563i	0.191778	−	0.0160720i
$676$	9.89707	−	6.36046i	0.380656	−	0.244633i
$677$	36.6583	+	5.27066i	1.40889	+	0.202568i	0.804421	−	0.594059i	$-0.202476\pi$
$677$	36.6583	+	5.27066i	1.40889	+	0.202568i	0.604471	+	0.796627i	$0.293385\pi$
$678$	2.22684	+	1.01696i	0.0855213	+	0.0390563i
$679$	3.83536	−	8.39826i	0.147188	−	0.322296i
$680$	31.8262	+	29.2706i	1.22048	+	1.12248i
$681$	13.8849	−	8.92330i	0.532072	−	0.341942i
$682$	3.23114	−	11.0043i	0.123727	−	0.421375i
$683$	0.590919	−	0.0849613i	0.0226109	−	0.00325095i	−0.131000	−	0.991382i	$-0.541819\pi$
$683$	0.590919	−	0.0849613i	0.0226109	−	0.00325095i	0.153611	+	0.988131i	$0.450910\pi$
$684$	1.10259	+	1.27245i	0.0421584	+	0.0486534i
$685$	9.84553	+	23.3647i	0.376178	+	0.892720i
$686$	9.21261	−	10.6319i	0.351739	−	0.405929i
$687$	4.18611	+	14.2566i	0.159710	+	0.543922i
$688$	6.21078	−	2.83637i	0.236784	−	0.108136i
$689$	4.12485			0.157144
$690$	−0.115235	−	10.9895i	−0.00438693	−	0.418364i
$691$	19.5454			0.743541			0.371770	−	0.928325i	$-0.378751\pi$
$691$	19.5454			0.743541			0.371770	+	0.928325i	$0.378751\pi$
$692$	−9.60516	+	4.38653i	−0.365133	+	0.166751i
$693$	−1.13578	−	3.86810i	−0.0431446	−	0.146937i
$694$	10.5967	−	12.2293i	0.402246	−	0.464216i
$695$	−38.8253	+	16.3604i	−1.47273	+	0.620584i
$696$	9.91838	+	11.4464i	0.375955	+	0.433875i
$697$	72.8081	−	10.4682i	2.75780	−	0.396512i
$698$	7.00058	−	23.8418i	0.264976	−	0.902424i
$699$	2.31770	−	1.48949i	0.0876633	−	0.0563378i
$700$	−3.29594	−	14.3078i	−0.124575	−	0.540785i
$701$	−3.78078	+	8.27876i	−0.142798	+	0.312685i	−0.967495	−	0.252891i	$-0.918619\pi$
$701$	−3.78078	+	8.27876i	−0.142798	+	0.312685i	0.824697	+	0.565575i	$0.191346\pi$
$702$	−0.729532	−	0.333166i	−0.0275344	−	0.0125745i
$703$	−2.67649	−	0.384821i	−0.100946	−	0.0145138i
$704$	−8.04471	+	5.17002i	−0.303197	+	0.194853i
$705$	−17.1188	+	13.9684i	−0.644730	+	0.526080i
$706$	−3.03935	−	21.1391i	−0.114387	−	0.795582i
$707$	18.1249	−	15.7053i	0.681657	−	0.590659i
$708$	−1.39632	+	2.17272i	−0.0524769	+	0.0816557i
$709$	−34.1889	+	39.4561i	−1.28399	+	1.48180i	−0.492927	+	0.870071i	$0.664073\pi$
$709$	−34.1889	+	39.4561i	−1.28399	+	1.48180i	−0.791064	+	0.611733i	$0.790472\pi$
$710$	21.4879	+	7.00643i	0.806426	+	0.262947i
$711$	−2.76301	−	6.05014i	−0.103621	−	0.226898i
$712$		−	44.2151i		−	1.65703i
$713$	−7.48608	−	40.4770i	−0.280356	−	1.51587i
$714$	−20.2701			−0.758591
$715$	0.391379	−	2.24772i	0.0146367	−	0.0840598i
$716$	7.46628	−	2.19230i	0.279028	−	0.0819300i
$717$	−5.05451	−	4.37975i	−0.188764	−	0.163565i
$718$	13.2031	−	20.5444i	0.492734	−	0.766709i
$719$	19.1878	+	22.1439i	0.715584	+	0.825828i	0.990769	−	0.135563i	$-0.0432844\pi$
$719$	19.1878	+	22.1439i	0.715584	+	0.825828i	−0.275184	+	0.961391i	$0.588739\pi$
$720$	2.40396	+	1.18504i	0.0895905	+	0.0441639i
$721$	−49.1484	−	14.4313i	−1.83038	−	0.537449i
$722$	8.78586	+	13.6711i	0.326976	+	0.508784i
$723$	−2.58341	−	0.371439i	−0.0960781	−	0.0138140i
$724$	3.57948	−	7.83797i	0.133030	−	0.291296i
$725$	25.0073	+	1.48191i	0.928748	+	0.0550366i
$726$	1.35640	−	9.43400i	0.0503409	−	0.350129i
$727$	−15.3275	−	23.8501i	−0.568466	−	0.884551i	0.431379	−	0.902171i	$-0.358027\pi$
$727$	−15.3275	−	23.8501i	−0.568466	−	0.884551i	−0.999845	+	0.0176204i	$0.994391\pi$
$728$	−2.06079	+	7.01841i	−0.0763780	+	0.260120i
$729$	0.142315	+	0.989821i	0.00527092	+	0.0366601i
$730$	−20.1452	+	2.29032i	−0.745606	+	0.0847686i
$731$	30.6544	+	19.7004i	1.13379	+	0.728645i
$732$	4.37956	+	3.79491i	0.161873	+	0.140264i
$733$	6.29904	+	21.4526i	0.232660	+	0.792369i	0.990209	+	0.139590i	$0.0445786\pi$
$733$	6.29904	+	21.4526i	0.232660	+	0.792369i	−0.757549	+	0.652778i	$0.773603\pi$
$734$	−5.00707	−	10.9640i	−0.184814	−	0.404687i
$735$	4.72271	+	3.23648i	0.174200	+	0.119379i
$736$	−11.7022	+	19.9214i	−0.431350	+	0.734312i
$737$			8.31538i			0.306301i
$738$	10.7196	−	4.89547i	0.394593	−	0.180205i
$739$	−9.41290	+	2.76388i	−0.346259	+	0.101671i	−0.450238	−	0.892909i	$-0.648661\pi$
$739$	−9.41290	+	2.76388i	−0.346259	+	0.101671i	0.103979	+	0.994580i	$0.466843\pi$
$740$	3.13348	−	0.820181i	0.115189	−	0.0301504i
$741$	−1.16714	−	0.750074i	−0.0428759	−	0.0275547i
$742$	12.6227	−	10.9377i	0.463395	−	0.401534i
$743$	−8.42819	+	1.21179i	−0.309200	+	0.0444563i	−0.295168	−	0.955445i	$-0.595376\pi$
$743$	−8.42819	+	1.21179i	−0.309200	+	0.0444563i	−0.0140319	+	0.999902i	$0.504467\pi$
$744$	24.8956	+	7.31001i	0.912718	+	0.267998i
$745$	1.21635	−	41.0881i	0.0445637	−	1.50535i
$746$	−2.10370	+	14.6316i	−0.0770220	+	0.535700i
$747$	−2.76023	−	1.26055i	−0.100992	−	0.0461213i
$748$	−7.20512	−	3.29047i	−0.263445	−	0.120311i
$749$	−3.18321	+	22.1397i	−0.116312	+	0.808967i
$750$	10.8036	−	3.81693i	0.394490	−	0.139375i
$751$	−44.3570	−	13.0244i	−1.61861	−	0.475267i	−0.657965	−	0.753048i	$-0.728583\pi$
$751$	−44.3570	−	13.0244i	−1.61861	−	0.475267i	−0.960644	+	0.277781i	$0.910401\pi$
$752$	−11.7229	+	1.68550i	−0.427491	+	0.0614639i
$753$	−13.5717	+	11.7600i	−0.494581	+	0.428557i
$754$	−3.38036	−	2.17243i	−0.123106	−	0.0791151i
$755$	6.85706	+	26.1972i	0.249554	+	0.953415i
$756$	2.81756	−	0.827311i	0.102474	−	0.0300890i
$757$	15.3167	−	6.99492i	0.556696	−	0.254235i	−0.117140	−	0.993115i	$-0.537373\pi$
$757$	15.3167	−	6.99492i	0.556696	−	0.254235i	0.673836	+	0.738881i	$0.264645\pi$
$758$			13.5898i			0.493603i
$759$	2.00063	+	5.92421i	0.0726184	+	0.215035i
$760$	9.88516	+	6.77433i	0.358573	+	0.245731i
$761$	1.78628	+	3.91142i	0.0647527	+	0.141789i	0.939241	−	0.343257i	$-0.111530\pi$
$761$	1.78628	+	3.91142i	0.0647527	+	0.141789i	−0.874489	+	0.485046i	$0.838803\pi$
$762$	−1.72521	−	5.87554i	−0.0624979	−	0.212848i
$763$	4.11820	+	3.56844i	0.149089	+	0.129186i
$764$	−4.72080	−	3.03387i	−0.170793	−	0.109762i
$765$	1.61580	+	14.2122i	0.0584192	+	0.513843i
$766$	1.22623	+	8.52861i	0.0443055	+	0.308151i
$767$	0.599577	−	2.04197i	0.0216495	−	0.0737313i
$768$	−9.10440	−	14.1667i	−0.328527	−	0.511197i
$769$	−7.18003	+	49.9382i	−0.258918	+	1.80082i	0.281650	+	0.959517i	$0.409118\pi$
$769$	−7.18003	+	49.9382i	−0.258918	+	1.80082i	−0.540568	+	0.841300i	$0.681791\pi$
$770$	−4.76248	−	7.91619i	−0.171628	−	0.285280i
$771$	−5.91876	+	12.9603i	−0.213159	+	0.466753i
$772$	15.9029	+	2.28650i	0.572359	+	0.0822929i
$773$	12.0823	+	18.8004i	0.434569	+	0.676203i	0.987606	−	0.156954i	$-0.0501675\pi$
$773$	12.0823	+	18.8004i	0.434569	+	0.676203i	−0.553037	+	0.833157i	$0.686531\pi$
$774$	5.60140	+	1.64472i	0.201338	+	0.0591183i
$775$	37.4124	−	21.0257i	1.34389	−	0.755267i
$776$	−5.91109	−	6.82177i	−0.212196	−	0.244887i
$777$	−2.54968	+	3.96738i	−0.0914692	+	0.142329i
$778$	−5.87013	−	5.08649i	−0.210454	−	0.182360i
$779$	19.5601	−	5.74336i	0.700812	−	0.205777i
$780$	1.63726	+	0.285084i	0.0586232	+	0.0102076i
$781$	−12.8592			−0.460137
$782$	31.4147	−	1.25979i	1.12339	−	0.0450500i
$783$			5.01023i			0.179051i
$784$	1.27489	+	2.79162i	0.0455318	+	0.0997007i
$785$	36.1730	+	11.7947i	1.29107	+	0.420971i
$786$	10.4113	−	12.0152i	0.371357	−	0.428569i
$787$	26.6818	−	41.5176i	0.951102	−	1.47994i	0.0753643	−	0.997156i	$-0.475988\pi$
$787$	26.6818	−	41.5176i	0.951102	−	1.47994i	0.875738	−	0.482787i	$-0.160376\pi$
$788$	−7.69539	+	6.66809i	−0.274137	+	0.237541i
$789$	−2.54005	−	17.6664i	−0.0904282	−	0.628942i
$790$	−9.63608	−	11.8093i	−0.342836	−	0.420158i
$791$	6.21348	−	3.99316i	0.220926	−	0.141981i
$792$	−3.90129	−	0.560921i	−0.138626	−	0.0199315i
$793$	−4.34360	−	1.98366i	−0.154246	−	0.0704417i
$794$	−11.1208	+	24.3511i	−0.394662	+	0.864189i
$795$	−8.67501	−	7.97841i	−0.307671	−	0.282965i
$796$	1.69757	−	1.09096i	0.0601689	−	0.0386682i
$797$	5.45614	−	18.5819i	0.193266	−	0.658205i	−0.804654	−	0.593744i	$-0.797649\pi$
$797$	5.45614	−	18.5819i	0.193266	−	0.658205i	0.997920	−	0.0644606i	$-0.0205327\pi$
$798$	−5.56057	+	0.799490i	−0.196842	+	0.0283016i
$799$	−41.3917	−	47.7686i	−1.46433	−	1.68993i
$800$	−23.5981	−	4.83246i	−0.834318	−	0.170853i
$801$	9.57825	−	11.0539i	0.338431	−	0.390570i
$802$	6.03240	+	20.5445i	0.213011	+	0.725450i
$803$	10.4931	−	4.79204i	0.370294	−	0.169108i
$804$	−6.05700			−0.213614
$805$	−28.0807	−	17.6331i	−0.989713	−	0.621484i
$806$	−6.88376			−0.242470
$807$	4.83405	−	2.20764i	0.170167	−	0.0777125i
$808$	−6.60587	−	22.4975i	−0.232394	−	0.791460i
$809$	7.72358	−	8.91349i	0.271547	−	0.313382i	−0.603554	−	0.797322i	$-0.706249\pi$
$809$	7.72358	−	8.91349i	0.271547	−	0.313382i	0.875101	+	0.483940i	$0.160795\pi$
$810$	0.889866	+	2.11177i	0.0312667	+	0.0742000i
$811$	−36.6438	−	42.2892i	−1.28674	−	1.48497i	−0.784330	−	0.620344i	$-0.786993\pi$
$811$	−36.6438	−	42.2892i	−1.28674	−	1.48497i	−0.502408	−	0.864631i	$-0.667552\pi$
$812$	14.5629	−	2.09382i	0.511056	−	0.0734788i
$813$	−4.59172	+	15.6380i	−0.161039	+	0.548448i
$814$	1.71450	−	1.10184i	0.0600930	−	0.0386195i
$815$	33.7112	−	36.6545i	1.18085	−	1.28395i
$816$	−3.18512	+	6.97444i	−0.111501	+	0.244154i
$817$	9.18624	+	4.19521i	0.321386	+	0.146772i
$818$	−21.4603	−	3.08552i	−0.750340	−	0.107883i
$819$	−2.03559	+	1.30819i	−0.0711292	+	0.0457120i
$820$	−18.9201	+	15.4383i	−0.660719	+	0.539127i
$821$	3.50746	+	24.3949i	0.122411	+	0.851389i	0.954811	+	0.297213i	$0.0960573\pi$
$821$	3.50746	+	24.3949i	0.122411	+	0.851389i	−0.832400	+	0.554176i	$0.813034\pi$
$822$	−8.78213	+	7.60976i	−0.306312	+	0.265421i
$823$	−17.7800	+	27.6663i	−0.619773	+	0.964386i	0.379459	+	0.925209i	$0.376110\pi$
$823$	−17.7800	+	27.6663i	−0.619773	+	0.964386i	−0.999232	+	0.0391776i	$0.987526\pi$
$824$	−32.7953	+	37.8478i	−1.14248	+	1.31849i
$825$	−5.17072	+	3.97018i	−0.180021	+	0.138224i
$826$	−3.57979	−	7.83864i	−0.124557	−	0.272741i
$827$			0.872041i			0.0303238i	0.999885	+	0.0151619i	$0.00482637\pi$
$827$			0.872041i			0.0303238i	−0.999885	+	0.0151619i	$0.995174\pi$
$828$	−4.31525	+	1.45728i	−0.149965	+	0.0506440i
$829$	1.05945			0.0367962			0.0183981	−	0.999831i	$-0.494143\pi$
$829$	1.05945			0.0367962			0.0183981	+	0.999831i	$0.494143\pi$
$830$	−6.85066	−	1.19286i	−0.237790	−	0.0414047i
$831$	−21.8957	+	6.42914i	−0.759552	+	0.223025i
$832$	4.33779	+	3.75872i	0.150386	+	0.130310i
$833$	−8.85492	+	13.7785i	−0.306805	+	0.477398i
$834$	−12.6452	−	14.5933i	−0.437867	−	0.505325i
$835$	−4.92913	+	9.99919i	−0.170580	+	0.346036i
$836$	−2.10631	−	0.618470i	−0.0728484	−	0.0213902i
$837$	4.64041	+	7.22062i	0.160396	+	0.249581i
$838$	−14.1777	−	2.03845i	−0.489762	−	0.0704171i
$839$	−1.89214	+	4.14321i	−0.0653239	+	0.143039i	−0.939478	−	0.342609i	$-0.888689\pi$
$839$	−1.89214	+	4.14321i	−0.0653239	+	0.143039i	0.874154	+	0.485649i	$0.161417\pi$
$840$	17.9093	−	10.7744i	0.617930	−	0.371754i
$841$	0.554680	−	3.85788i	0.0191269	−	0.133030i
$842$	7.40312	+	11.5195i	0.255128	+	0.396987i
$843$	−3.22594	+	10.9865i	−0.111107	+	0.378397i
$844$	−3.17288	−	22.0679i	−0.109215	−	0.759607i
$845$	27.5222	−	3.12902i	0.946791	−	0.107642i
$846$	−8.51883	−	5.47472i	−0.292884	−	0.188225i
$847$	−21.7321	−	18.8310i	−0.746724	−	0.647040i
$848$	−1.77991	−	6.06183i	−0.0611225	−	0.208164i
$849$	6.08359	+	13.3212i	0.208788	+	0.457182i
$850$	11.8290	+	30.5696i	0.405732	+	1.04853i
$851$	3.70493	−	6.30712i	0.127003	−	0.216205i
$852$		−	9.36674i		−	0.320899i
$853$	−36.3929	+	16.6201i	−1.24607	+	0.569061i	−0.925710	−	0.378234i	$-0.876531\pi$
$853$	−36.3929	+	16.6201i	−1.24607	+	0.569061i	−0.320361	+	0.947296i	$0.603804\pi$
$854$	−18.5521	+	5.44739i	−0.634840	+	0.186406i
$855$	1.00380	+	3.83500i	0.0343294	+	0.131154i
$856$	18.3966	+	11.8228i	0.628782	+	0.404094i
$857$	−21.1415	+	18.3192i	−0.722180	+	0.625772i	−0.936368	−	0.351020i	$-0.885835\pi$
$857$	−21.1415	+	18.3192i	−0.722180	+	0.625772i	0.214188	+	0.976792i	$0.431289\pi$
$858$	1.03503	−	0.148815i	0.0353353	−	0.00508046i
$859$	−5.00540	−	1.46972i	−0.170782	−	0.0501461i	0.195224	−	0.980759i	$-0.437457\pi$
$859$	−5.00540	−	1.46972i	−0.170782	−	0.0501461i	−0.366006	+	0.930613i	$0.619275\pi$
$860$	−12.0918	−	0.357959i	−0.412325	−	0.0122063i
$861$	5.05996	−	35.1928i	0.172443	−	1.19937i
$862$	13.1444	+	6.00283i	0.447699	+	0.204457i
$863$	−33.0439	−	15.0906i	−1.12483	−	0.513691i	−0.235917	−	0.971773i	$-0.575809\pi$
$863$	−33.0439	−	15.0906i	−1.12483	−	0.513691i	−0.888910	+	0.458082i	$0.848537\pi$
$864$	0.685610	−	4.76852i	0.0233249	−	0.162228i
$865$	−24.8508	−	0.735671i	−0.844953	−	0.0250136i
$866$	19.1730	+	5.62969i	0.651524	+	0.191305i
$867$	−23.6759	+	3.40408i	−0.804076	+	0.115609i
$868$	19.0483	−	16.5055i	0.646543	−	0.560232i
$869$	7.29532	+	4.68842i	0.247477	+	0.159044i
$870$	2.90730	+	11.1073i	0.0985667	+	0.376571i
$871$	4.78885	−	1.40613i	0.162264	−	0.0476450i
$872$	4.84608	−	2.21313i	0.164109	−	0.0749460i
$873$		−	2.98597i		−	0.101060i
$874$	8.56810	−	1.58464i	0.289820	−	0.0536013i
$875$	7.93439	−	33.6467i	0.268231	−	1.13746i
$876$	3.49057	+	7.64328i	0.117935	+	0.258243i
$877$	14.0508	+	47.8526i	0.474462	+	1.61587i	0.754792	+	0.655964i	$0.227738\pi$
$877$	14.0508	+	47.8526i	0.474462	+	1.61587i	−0.280330	+	0.959904i	$0.590444\pi$
$878$	1.70982	+	1.48157i	0.0577038	+	0.0500006i
$879$	2.39202	+	1.53725i	0.0806807	+	0.0518503i
$880$	−3.47211	+	0.394747i	−0.117045	+	0.0133069i
$881$	−6.08587	−	42.3281i	−0.205038	−	1.42607i	−0.789052	−	0.614327i	$-0.789428\pi$
$881$	−6.08587	−	42.3281i	−0.205038	−	1.42607i	0.584014	−	0.811744i	$-0.301481\pi$
$882$	−0.739268	+	2.51772i	−0.0248925	+	0.0847759i
$883$	−0.944432	−	1.46957i	−0.0317827	−	0.0494548i	0.824999	−	0.565135i	$-0.191176\pi$
$883$	−0.944432	−	1.46957i	−0.0317827	−	0.0494548i	−0.856781	+	0.515680i	$0.827539\pi$
$884$	−0.676601	+	4.70586i	−0.0227566	+	0.158275i
$885$	−5.21062	+	3.13477i	−0.175153	+	0.105374i
$886$	−1.50951	+	3.30537i	−0.0507130	+	0.111046i
$887$	−2.06929	−	0.297519i	−0.0694799	−	0.00998971i	0.107487	−	0.994206i	$-0.465720\pi$
$887$	−2.06929	−	0.297519i	−0.0694799	−	0.00998971i	−0.176967	+	0.984217i	$0.556629\pi$
$888$	2.49276	+	3.87881i	0.0836516	+	0.130164i
$889$	−17.7269	−	5.20509i	−0.594541	−	0.174573i
$890$	14.8199	−	30.0635i	0.496764	−	1.00773i
$891$	−0.853821	−	0.985362i	−0.0286041	−	0.0330109i
$892$	−11.7727	+	18.3187i	−0.394180	+	0.613356i
$893$	−13.2388	−	11.4715i	−0.443019	−	0.383878i
$894$	18.0766	−	5.30776i	0.604571	−	0.177518i
$895$	18.0496	+	3.14286i	0.603333	+	0.105054i
$896$	−6.55053			−0.218838
$897$	3.07346	−	2.15395i	0.102620	−	0.0719184i
$898$		−	0.612071i		−	0.0204251i
$899$	17.8644	+	39.1175i	0.595810	+	1.30464i
$900$	−2.89192	−	3.76640i	−0.0963972	−	0.125547i
$901$	22.0799	−	25.4815i	0.735587	−	0.848913i
$902$	−8.30689	+	12.9258i	−0.276589	+	0.430381i
$903$	13.3112	−	11.5342i	0.442970	−	0.383835i
$904$	−1.02767	−	7.14760i	−0.0341798	−	0.237726i
$905$	15.7187	−	12.8260i	0.522508	−	0.426351i
$906$	−10.4410	+	6.71000i	−0.346878	+	0.222925i
$907$	−30.4473	−	4.37765i	−1.01098	−	0.145358i	−0.383135	−	0.923692i	$-0.625156\pi$
$907$	−30.4473	−	4.37765i	−1.01098	−	0.145358i	−0.627850	+	0.778335i	$0.716065\pi$
$908$	−14.2586	−	6.51166i	−0.473187	−	0.216097i
$909$	3.22212	−	7.05546i	0.106871	−	0.234015i
$910$	−3.75362	+	4.08135i	−0.124431	+	0.135295i
$911$	10.1380	−	6.51528i	0.335886	−	0.215861i	−0.361815	−	0.932250i	$-0.617843\pi$
$911$	10.1380	−	6.51528i	0.335886	−	0.215861i	0.697701	+	0.716389i	$0.254206\pi$
$912$	−0.598669	+	2.03888i	−0.0198239	+	0.0675140i
$913$	3.91610	−	0.563050i	0.129604	−	0.0186342i
$914$	18.8947	+	21.8056i	0.624981	+	0.721266i
$915$	5.29822	+	12.5734i	0.175154	+	0.415663i
$916$	9.24092	−	10.6646i	0.305329	−	0.352368i
$917$	−13.5138	−	46.0237i	−0.446264	−	1.51983i
$918$	−5.96326	+	2.72333i	−0.196817	+	0.0898833i
$919$	29.5738			0.975550			0.487775	−	0.872969i	$-0.337809\pi$
$919$	29.5738			0.975550			0.487775	+	0.872969i	$0.337809\pi$
$920$	−27.0863	+	17.8113i	−0.893008	+	0.587222i
$921$	3.24154			0.106812
$922$	−25.2210	+	11.5180i	−0.830609	+	0.379326i
$923$	2.17449	+	7.40562i	0.0715741	+	0.243759i
$924$	−2.50725	+	2.89353i	−0.0824826	+	0.0951900i
$925$	7.47115	+	1.52996i	0.245650	+	0.0503047i
$926$	5.17601	+	5.97343i	0.170094	+	0.196299i
$927$	−16.3978	+	2.35765i	−0.538575	+	0.0774354i
$928$	6.80021	−	23.1594i	0.223228	−	0.760244i
$929$	−14.0143	+	9.00642i	−0.459793	+	0.295491i	−0.749958	−	0.661486i	$-0.769926\pi$
$929$	−14.0143	+	9.00642i	−0.459793	+	0.295491i	0.290165	+	0.956977i	$0.406290\pi$
$930$	14.4773	+	13.3148i	0.474730	+	0.436609i
$931$	−1.88566	+	4.12903i	−0.0618001	+	0.135323i
$932$	−2.38006	−	1.08694i	−0.0779615	−	0.0356038i
$933$	30.4221	+	4.37404i	0.995974	+	0.143199i
$934$	−35.0746	+	22.5411i	−1.14768	+	0.737566i
$935$	−11.7904	−	14.4496i	−0.385588	−	0.472551i
$936$	0.336673	+	2.34161i	0.0110045	+	0.0765380i
$937$	18.1076	−	15.6903i	0.591548	−	0.512579i	−0.306852	−	0.951757i	$-0.599276\pi$
$937$	18.1076	−	15.6903i	0.591548	−	0.512579i	0.898400	+	0.439178i	$0.144730\pi$
$938$	10.9261	−	17.0014i	0.356750	−	0.555114i
$939$	−1.52200	+	1.75648i	−0.0496685	+	0.0573205i
$940$	19.9498	+	6.50491i	0.650690	+	0.212167i
$941$	15.9496	+	34.9247i	0.519941	+	1.13851i	0.969462	+	0.245243i	$0.0788676\pi$
$941$	15.9496	+	34.9247i	0.519941	+	1.13851i	−0.449520	+	0.893270i	$0.648405\pi$
$942$			17.4378i			0.568156i
$943$	−5.65471	+	54.8563i	−0.184143	+	1.78637i
$944$	−3.25958			−0.106090
$945$	6.81142	+	1.18602i	0.221576	+	0.0385814i
$946$	−7.30322	+	2.14442i	−0.237448	+	0.0697211i
$947$	−11.8696	−	10.2851i	−0.385711	−	0.334221i	0.440324	−	0.897839i	$-0.354864\pi$
$947$	−11.8696	−	10.2851i	−0.385711	−	0.334221i	−0.826035	+	0.563618i	$0.809409\pi$
$948$	−3.41509	+	5.31398i	−0.110917	+	0.172590i
$949$	−4.53414	−	5.23267i	−0.147184	−	0.169860i
$950$	4.45069	+	7.91940i	0.144400	+	0.256939i
$951$	−10.3941	−	3.05199i	−0.337053	−	0.0989676i
$952$	32.3255	+	50.2995i	1.04768	+	1.63022i
$953$	49.4797	+	7.11411i	1.60281	+	0.230449i	0.884931	−	0.465723i	$-0.154206\pi$
$953$	49.4797	+	7.11411i	1.60281	+	0.230449i	0.717875	+	0.696172i	$0.245115\pi$
$954$	2.24398	−	4.91363i	0.0726515	−	0.159085i
$955$	−6.81112	−	11.3214i	−0.220403	−	0.366353i
$956$	−0.903949	+	6.28711i	−0.0292358	+	0.203340i
$957$	−3.53171	−	5.49544i	−0.114164	−	0.177642i
$958$	12.2049	−	41.5660i	0.394322	−	1.34294i
$959$	4.98950	+	34.7027i	0.161119	+	1.12061i
$960$	−1.85263	−	16.2953i	−0.0597933	−	0.525928i
$961$	35.8969	+	23.0695i	1.15796	+	0.744178i
$962$	−0.924473	−	0.801061i	−0.0298062	−	0.0258272i
$963$	2.03804	+	6.94094i	0.0656750	+	0.223669i
$964$	1.02970	+	2.25474i	0.0331645	+	0.0726202i
$965$	31.2038	+	21.3840i	1.00448	+	0.688376i
$966$	3.69376	−	14.7412i	0.118845	−	0.474290i
$967$		−	10.0368i		−	0.322762i	−0.986892	−	0.161381i	$-0.948405\pi$
$967$		−	10.0368i		−	0.322762i	0.986892	−	0.161381i	$-0.0515947\pi$
$968$	−25.5732	+	11.6789i	−0.821953	+	0.375373i
$969$	−10.8812	+	3.19501i	−0.349555	+	0.102638i
$970$	−1.73268	−	6.61964i	−0.0556328	−	0.212544i
$971$	−0.00931618	−	0.00598714i	−0.000298970	−	0.000192137i	0.540491	−	0.841350i	$-0.318238\pi$
$971$	−0.00931618	−	0.00598714i	−0.000298970	−	0.000192137i	−0.540790	+	0.841157i	$0.681875\pi$
$972$	0.717746	−	0.621931i	0.0230217	−	0.0199484i
$973$	−57.6657	+	8.29108i	−1.84868	+	0.265800i
$974$	13.1488	+	3.86083i	0.421314	+	0.123709i
$975$	3.16081	+	2.30647i	0.101227	+	0.0738662i
$976$	−1.04085	+	7.23928i	−0.0333168	+	0.231724i
$977$	43.4795	+	19.8564i	1.39103	+	0.635264i	0.963247	−	0.268617i	$-0.0865665\pi$
$977$	43.4795	+	19.8564i	1.39103	+	0.635264i	0.427786	+	0.903880i	$0.359294\pi$
$978$	20.7616	+	9.48149i	0.663882	+	0.303185i
$979$	−2.71397	+	18.8761i	−0.0867389	+	0.603282i
$980$	0.160895	−	5.43500i	0.00513960	−	0.173615i
$981$	1.69096	+	0.496510i	0.0539881	+	0.0158523i
$982$	14.2405	−	2.04748i	0.454433	−	0.0653376i
$983$	32.8339	−	28.4508i	1.04724	−	0.907439i	0.0514110	−	0.998678i	$-0.483628\pi$
$983$	32.8339	−	28.4508i	1.04724	−	0.907439i	0.995829	+	0.0912390i	$0.0290827\pi$
$984$	−29.2428	−	18.7932i	−0.932226	−	0.599105i
$985$	−23.1929	+	6.07069i	−0.738987	+	0.193428i
$986$	−31.5151	+	9.25365i	−1.00364	+	0.294696i
$987$	−27.7910	+	12.6917i	−0.884597	+	0.403982i
$988$			1.31761i			0.0419189i
$989$	−19.9129	+	18.7031i	−0.633194	+	0.594724i
$990$	−2.46463	−	1.68901i	−0.0783309	−	0.0536804i
$991$	4.69113	+	10.2721i	0.149019	+	0.326305i	0.969390	−	0.245526i	$-0.0789605\pi$
$991$	4.69113	+	10.2721i	0.149019	+	0.326305i	−0.820371	+	0.571831i	$0.806233\pi$
$992$	−11.6496	−	39.6749i	−0.369876	−	1.25968i
$993$	−19.8709	−	17.2182i	−0.630583	−	0.546403i
$994$	26.2914	+	16.8965i	0.833914	+	0.535924i
$995$	4.72068	−	0.536698i	0.149656	−	0.0170145i
$996$	0.410131	+	2.85252i	0.0129955	+	0.0903857i
$997$	−6.45376	+	21.9795i	−0.204392	+	0.696097i	0.791945	+	0.610592i	$0.209068\pi$
$997$	−6.45376	+	21.9795i	−0.204392	+	0.696097i	−0.996338	+	0.0855048i	$0.972750\pi$
$998$	0.334298	+	0.520178i	0.0105820	+	0.0164659i
$999$	−0.217064	+	1.50972i	−0.00686761	+	0.0477653i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	345.2.t.a.4.16	yes	240
5.4	even	2	inner	345.2.t.a.4.9	✓	240
23.6	even	11	inner	345.2.t.a.259.9	yes	240
115.29	even	22	inner	345.2.t.a.259.16	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.t.a.4.9	✓	240	5.4	even	2	inner
345.2.t.a.4.16	yes	240	1.1	even	1	trivial
345.2.t.a.259.9	yes	240	23.6	even	11	inner
345.2.t.a.259.16	yes	240	115.29	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	345.t (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.932222 - 0.425732i) q^{2} +(-0.281733 - 0.959493i) q^{3} +(-0.621931 + 0.717746i) q^{4} +(-2.06059 + 0.868302i) q^{5} +(-0.671124 - 0.774518i) q^{6} +(-3.06052 + 0.440036i) q^{7} +(-0.851669 + 2.90052i) q^{8} +(-0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(0.932222 - 0.425732i) q^{2} +(-0.281733 - 0.959493i) q^{3} +(-0.621931 + 0.717746i) q^{4} +(-2.06059 + 0.868302i) q^{5} +(-0.671124 - 0.774518i) q^{6} +(-3.06052 + 0.440036i) q^{7} +(-0.851669 + 2.90052i) q^{8} +(-0.841254 + 0.540641i) q^{9} +(-1.55127 + 1.68671i) q^{10} +(0.541626 - 1.18600i) q^{11} +(0.863891 + 0.394526i) q^{12} +(-0.774607 - 0.111372i) q^{13} +(-2.66575 + 1.71317i) q^{14} +(1.41367 + 1.73250i) q^{15} +(0.170580 + 1.18641i) q^{16} +(-4.83440 + 4.18903i) q^{17} +(-0.554067 + 0.862145i) q^{18} +(-1.16097 + 1.33983i) q^{19} +(0.658327 - 2.01901i) q^{20} +(1.28446 + 2.81258i) q^{21} -1.33620i q^{22} +(-2.16546 - 4.27911i) q^{23} +3.02297 q^{24} +(3.49210 - 3.57844i) q^{25} +(-0.769520 + 0.225952i) q^{26} +(0.755750 + 0.654861i) q^{27} +(1.58760 - 2.47035i) q^{28} +(3.28101 + 3.78648i) q^{29} +(2.05543 + 1.01323i) q^{30} +(8.23549 + 2.41816i) q^{31} +(-2.60457 - 4.05279i) q^{32} +(-1.29055 - 0.185553i) q^{33} +(-2.72333 + 5.96326i) q^{34} +(5.92441 - 3.56419i) q^{35} +(0.135158 - 0.940048i) q^{36} +(0.824607 + 1.28311i) q^{37} +(-0.511872 + 1.74328i) q^{38} +(0.111372 + 0.774607i) q^{39} +(-0.763582 - 6.71630i) q^{40} +(-9.67353 - 6.21680i) q^{41} +(2.39480 + 2.07511i) q^{42} +(-1.60487 - 5.46567i) q^{43} +(0.514391 + 1.12636i) q^{44} +(1.26404 - 1.84450i) q^{45} +(-3.84044 - 3.06717i) q^{46} +9.88097i q^{47} +(1.09030 - 0.497922i) q^{48} +(2.45671 - 0.721354i) q^{49} +(1.73196 - 4.82260i) q^{50} +(5.38135 + 3.45839i) q^{51} +(0.561689 - 0.486706i) q^{52} +(-5.21723 + 0.750125i) q^{53} +(0.983321 + 0.288729i) q^{54} +(-0.0862692 + 2.91415i) q^{55} +(1.33022 - 9.25186i) q^{56} +(1.61264 + 0.736466i) q^{57} +(4.67065 + 2.13301i) q^{58} +(-0.387020 + 2.69178i) q^{59} +(-2.12270 - 0.0628393i) q^{60} +(5.85465 + 1.71908i) q^{61} +(8.70679 - 1.25185i) q^{62} +(2.33677 - 2.02482i) q^{63} +(-6.17011 - 3.96529i) q^{64} +(1.69286 - 0.443101i) q^{65} +(-1.28207 + 0.376451i) q^{66} +(-5.80137 + 2.64940i) q^{67} -6.07516i q^{68} +(-3.49569 + 3.28331i) q^{69} +(4.00548 - 5.84483i) q^{70} +(-4.09711 - 8.97141i) q^{71} +(-0.851669 - 2.90052i) q^{72} +(6.68650 + 5.79389i) q^{73} +(1.31498 + 0.845085i) q^{74} +(-4.41733 - 2.34248i) q^{75} +(-0.239615 - 1.66656i) q^{76} +(-1.13578 + 3.86810i) q^{77} +(0.433598 + 0.674692i) q^{78} +(-0.946564 + 6.58349i) q^{79} +(-1.38166 - 2.29660i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-11.6646 - 1.67711i) q^{82} +(1.64055 + 2.55274i) q^{83} +(-2.81756 - 0.827311i) q^{84} +(6.32439 - 12.8296i) q^{85} +(-3.82300 - 4.41198i) q^{86} +(2.70874 - 4.21488i) q^{87} +(2.97872 + 2.58107i) q^{88} +(-14.0339 + 4.12073i) q^{89} +(0.393105 - 2.25763i) q^{90} +2.41971 q^{91} +(4.41808 + 1.10706i) q^{92} -8.58316i q^{93} +(4.20664 + 9.21126i) q^{94} +(1.22891 - 3.76891i) q^{95} +(-3.15483 + 3.64087i) q^{96} +(-1.61434 + 2.51196i) q^{97} +(1.98309 - 1.71836i) q^{98} +(0.185553 + 1.29055i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 28 q^{4} - 4 q^{5} - 4 q^{6} + 24 q^{9}+O(q^{10}) \) 240 * q + 28 * q^4 - 4 * q^5 - 4 * q^6 + 24 * q^9	\( 240 q + 28 q^{4} - 4 q^{5} - 4 q^{6} + 24 q^{9} + 8 q^{14} + 4 q^{15} - 36 q^{16} - 8 q^{19} - 92 q^{20} + 8 q^{21} + 12 q^{24} - 44 q^{25} + 32 q^{26} - 12 q^{29} + 8 q^{30} - 20 q^{31} - 54 q^{34} + 36 q^{35} - 28 q^{36} - 36 q^{39} - 24 q^{40} - 28 q^{41} - 224 q^{44} + 4 q^{45} - 8 q^{46} + 52 q^{49} - 48 q^{50} - 18 q^{54} - 22 q^{55} - 56 q^{59} - 36 q^{60} + 44 q^{61} + 12 q^{64} - 16 q^{65} + 8 q^{66} + 8 q^{69} - 152 q^{70} + 4 q^{71} + 88 q^{74} - 8 q^{75} - 100 q^{76} - 84 q^{79} + 122 q^{80} - 24 q^{81} - 56 q^{84} + 186 q^{85} - 392 q^{86} + 48 q^{89} - 304 q^{91} + 80 q^{94} + 190 q^{95} + 16 q^{96} + 44 q^{99}+O(q^{100}) \) 240 * q + 28 * q^4 - 4 * q^5 - 4 * q^6 + 24 * q^9 + 8 * q^14 + 4 * q^15 - 36 * q^16 - 8 * q^19 - 92 * q^20 + 8 * q^21 + 12 * q^24 - 44 * q^25 + 32 * q^26 - 12 * q^29 + 8 * q^30 - 20 * q^31 - 54 * q^34 + 36 * q^35 - 28 * q^36 - 36 * q^39 - 24 * q^40 - 28 * q^41 - 224 * q^44 + 4 * q^45 - 8 * q^46 + 52 * q^49 - 48 * q^50 - 18 * q^54 - 22 * q^55 - 56 * q^59 - 36 * q^60 + 44 * q^61 + 12 * q^64 - 16 * q^65 + 8 * q^66 + 8 * q^69 - 152 * q^70 + 4 * q^71 + 88 * q^74 - 8 * q^75 - 100 * q^76 - 84 * q^79 + 122 * q^80 - 24 * q^81 - 56 * q^84 + 186 * q^85 - 392 * q^86 + 48 * q^89 - 304 * q^91 + 80 * q^94 + 190 * q^95 + 16 * q^96 + 44 * q^99

Introduction

L-functions

Modular forms

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Database

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