LMFDB - Embedded newform 138.2.f.a.65.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,2,Mod(5,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 1]))

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

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

chi := DirichletCharacter("138.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	138.f (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:	$1.10193554789$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			65.4
Character	$\chi$	$=$	138.65
Dual form			138.2.f.a.17.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.909632 + 0.415415i) q^{2} +(1.47913 - 0.901205i) q^{3} +(0.654861 - 0.755750i) q^{4} +(1.71394 + 1.10148i) q^{5} +(-0.971091 + 1.43422i) q^{6} +(-1.65113 + 0.237396i) q^{7} +(-0.281733 + 0.959493i) q^{8} +(1.37566 - 2.66600i) q^{9} +O(q^{10})$	\(q+(-0.909632 + 0.415415i) q^{2} +(1.47913 - 0.901205i) q^{3} +(0.654861 - 0.755750i) q^{4} +(1.71394 + 1.10148i) q^{5} +(-0.971091 + 1.43422i) q^{6} +(-1.65113 + 0.237396i) q^{7} +(-0.281733 + 0.959493i) q^{8} +(1.37566 - 2.66600i) q^{9} +(-2.01663 - 0.289948i) q^{10} +(1.59577 - 3.49424i) q^{11} +(0.287540 - 1.70802i) q^{12} +(-0.593583 + 4.12846i) q^{13} +(1.40330 - 0.901847i) q^{14} +(3.52781 + 0.0846264i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(0.576959 + 0.665847i) q^{17} +(-0.143848 + 2.99655i) q^{18} +(0.333530 + 0.289005i) q^{19} +(1.95484 - 0.573993i) q^{20} +(-2.22829 + 1.83915i) q^{21} +3.84138i q^{22} +(-3.17170 + 3.59726i) q^{23} +(0.447980 + 1.67311i) q^{24} +(-0.352744 - 0.772401i) q^{25} +(-1.17508 - 4.00196i) q^{26} +(-0.367831 - 5.18312i) q^{27} +(-0.901847 + 1.40330i) q^{28} +(-1.29303 + 1.12042i) q^{29} +(-3.24416 + 1.38853i) q^{30} +(-9.25241 - 2.71675i) q^{31} +(0.540641 + 0.841254i) q^{32} +(-0.788678 - 6.60656i) q^{33} +(-0.801424 - 0.365998i) q^{34} +(-3.09143 - 1.41181i) q^{35} +(-1.11396 - 2.78551i) q^{36} +(-1.72474 - 2.68374i) q^{37} +(-0.423447 - 0.124335i) q^{38} +(2.84260 + 6.64147i) q^{39} +(-1.53974 + 1.33419i) q^{40} +(-3.75293 + 5.83967i) q^{41} +(1.26292 - 2.59861i) q^{42} +(2.21377 + 7.53939i) q^{43} +(-1.59577 - 3.49424i) q^{44} +(5.29436 - 3.05410i) q^{45} +(1.39073 - 4.58976i) q^{46} -10.0192i q^{47} +(-1.10253 - 1.33582i) q^{48} +(-4.04658 + 1.18818i) q^{49} +(0.641734 + 0.556065i) q^{50} +(1.45346 + 0.464916i) q^{51} +(2.73137 + 3.15217i) q^{52} +(1.97228 + 13.7175i) q^{53} +(2.48774 + 4.56193i) q^{54} +(6.58390 - 4.23122i) q^{55} +(0.237396 - 1.65113i) q^{56} +(0.753787 + 0.126898i) q^{57} +(0.710743 - 1.55631i) q^{58} +(-9.07876 - 1.30533i) q^{59} +(2.37418 - 2.61072i) q^{60} +(0.253015 - 0.861690i) q^{61} +(9.54487 - 1.37234i) q^{62} +(-1.63849 + 4.72849i) q^{63} +(-0.841254 - 0.540641i) q^{64} +(-5.56480 + 6.42212i) q^{65} +(3.46187 + 5.68191i) q^{66} +(11.4487 - 5.22846i) q^{67} +0.881042 q^{68} +(-1.44950 + 8.17918i) q^{69} +3.39855 q^{70} +(10.8767 - 4.96722i) q^{71} +(2.17044 + 2.07104i) q^{72} +(5.44903 - 6.28852i) q^{73} +(2.68374 + 1.72474i) q^{74} +(-1.21785 - 0.824588i) q^{75} +(0.436831 - 0.0628068i) q^{76} +(-1.80530 + 6.14827i) q^{77} +(-5.34469 - 4.86044i) q^{78} +(9.67669 + 1.39130i) q^{79} +(0.846353 - 1.85325i) q^{80} +(-5.21512 - 7.33502i) q^{81} +(0.987897 - 6.87098i) q^{82} +(7.04095 - 4.52494i) q^{83} +(-0.0692884 + 2.88842i) q^{84} +(0.255456 + 1.77673i) q^{85} +(-5.14569 - 5.93844i) q^{86} +(-0.902836 + 2.82253i) q^{87} +(2.90312 + 2.51557i) q^{88} +(4.94463 - 1.45187i) q^{89} +(-3.54720 + 4.97747i) q^{90} -6.95753i q^{91} +(0.641606 + 4.75272i) q^{92} +(-16.1339 + 4.31988i) q^{93} +(4.16211 + 9.11374i) q^{94} +(0.253316 + 0.862716i) q^{95} +(1.55782 + 0.757097i) q^{96} +(-5.81077 + 9.04174i) q^{97} +(3.18731 - 2.76182i) q^{98} +(-7.12042 - 9.06120i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6}+O(q^{10}) $ 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6	$ 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6} - 4 q^{12} + 8 q^{13} - 22 q^{15} - 8 q^{16} - 28 q^{18} - 66 q^{21} - 4 q^{24} - 48 q^{25} - 38 q^{27} - 44 q^{30} - 16 q^{31} - 22 q^{33} - 44 q^{37} - 24 q^{39} - 44 q^{43} - 16 q^{46} + 4 q^{48} - 76 q^{49} - 8 q^{52} - 6 q^{54} + 64 q^{55} + 66 q^{57} + 36 q^{58} + 22 q^{60} + 88 q^{61} + 110 q^{63} + 8 q^{64} + 88 q^{66} + 44 q^{67} + 82 q^{69} + 112 q^{70} + 28 q^{72} + 52 q^{73} + 136 q^{75} + 82 q^{78} + 88 q^{79} + 36 q^{81} + 44 q^{82} + 22 q^{84} + 20 q^{85} - 10 q^{87} + 8 q^{93} - 56 q^{94} + 4 q^{96} - 132 q^{97} - 66 q^{99}+O(q^{100}) $ 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6 - 4 * q^12 + 8 * q^13 - 22 * q^15 - 8 * q^16 - 28 * q^18 - 66 * q^21 - 4 * q^24 - 48 * q^25 - 38 * q^27 - 44 * q^30 - 16 * q^31 - 22 * q^33 - 44 * q^37 - 24 * q^39 - 44 * q^43 - 16 * q^46 + 4 * q^48 - 76 * q^49 - 8 * q^52 - 6 * q^54 + 64 * q^55 + 66 * q^57 + 36 * q^58 + 22 * q^60 + 88 * q^61 + 110 * q^63 + 8 * q^64 + 88 * q^66 + 44 * q^67 + 82 * q^69 + 112 * q^70 + 28 * q^72 + 52 * q^73 + 136 * q^75 + 82 * q^78 + 88 * q^79 + 36 * q^81 + 44 * q^82 + 22 * q^84 + 20 * q^85 - 10 * q^87 + 8 * q^93 - 56 * q^94 + 4 * q^96 - 132 * q^97 - 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$-1$	$e\left(\frac{15}{22}\right)$

Coefficient data

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

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

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

$2$	−0.909632	+	0.415415i	−0.643207	+	0.293743i
$2$	−0.909632	+	0.415415i	−0.643207	+	0.293743i
$3$	1.47913	−	0.901205i	0.853977	−	0.520311i
$3$	1.47913	−	0.901205i	0.853977	−	0.520311i
$4$	0.654861	−	0.755750i	0.327430	−	0.377875i
$5$	1.71394	+	1.10148i	0.766498	+	0.492599i	0.864528	−	0.502585i	$-0.167618\pi$
$5$	1.71394	+	1.10148i	0.766498	+	0.492599i	−0.0980295	+	0.995184i	$0.531254\pi$
$6$	−0.971091	+	1.43422i	−0.396446	+	0.585517i
$7$	−1.65113	+	0.237396i	−0.624068	+	0.0897274i	−0.447092	−	0.894488i	$-0.647540\pi$
$7$	−1.65113	+	0.237396i	−0.624068	+	0.0897274i	−0.176976	+	0.984215i	$0.556631\pi$
$8$	−0.281733	+	0.959493i	−0.0996075	+	0.339232i
$9$	1.37566	−	2.66600i	0.458553	−	0.888667i
$10$	−2.01663	−	0.289948i	−0.637714	−	0.0916895i
$11$	1.59577	−	3.49424i	0.481142	−	1.05355i	−0.501006	−	0.865444i	$-0.667037\pi$
$11$	1.59577	−	3.49424i	0.481142	−	1.05355i	0.982148	−	0.188110i	$-0.0602361\pi$
$12$	0.287540	−	1.70802i	0.0830057	−	0.493062i
$13$	−0.593583	+	4.12846i	−0.164630	+	1.14503i	0.725134	+	0.688608i	$0.241778\pi$
$13$	−0.593583	+	4.12846i	−0.164630	+	1.14503i	−0.889764	+	0.456421i	$0.849131\pi$
$14$	1.40330	−	0.901847i	0.375048	−	0.241029i
$15$	3.52781	+	0.0846264i	0.910876	+	0.0218505i
$16$	−0.142315	−	0.989821i	−0.0355787	−	0.247455i
$17$	0.576959	+	0.665847i	0.139933	+	0.161492i	0.821390	−	0.570367i	$-0.193199\pi$
$17$	0.576959	+	0.665847i	0.139933	+	0.161492i	−0.681457	+	0.731858i	$0.738653\pi$
$18$	−0.143848	+	2.99655i	−0.0339052	+	0.706293i
$19$	0.333530	+	0.289005i	0.0765170	+	0.0663024i	0.692280	−	0.721629i	$-0.256607\pi$
$19$	0.333530	+	0.289005i	0.0765170	+	0.0663024i	−0.615763	+	0.787932i	$0.711152\pi$
$20$	1.95484	−	0.573993i	0.437115	−	0.128349i
$21$	−2.22829	+	1.83915i	−0.486253	+	0.401334i
$22$			3.84138i			0.818985i
$23$	−3.17170	+	3.59726i	−0.661346	+	0.750081i
$23$	−3.17170	+	3.59726i	−0.661346	+	0.750081i
$24$	0.447980	+	1.67311i	0.0914436	+	0.341523i
$25$	−0.352744	−	0.772401i	−0.0705487	−	0.154480i
$26$	−1.17508	−	4.00196i	−0.230453	−	0.784849i
$27$	−0.367831	−	5.18312i	−0.0707890	−	0.997491i
$28$	−0.901847	+	1.40330i	−0.170433	+	0.265199i
$29$	−1.29303	+	1.12042i	−0.240110	+	0.208056i	−0.766600	−	0.642125i	$-0.778053\pi$
$29$	−1.29303	+	1.12042i	−0.240110	+	0.208056i	0.526490	+	0.850181i	$0.323508\pi$
$30$	−3.24416	+	1.38853i	−0.592300	+	0.253509i
$31$	−9.25241	−	2.71675i	−1.66178	−	0.487943i	−0.689997	−	0.723812i	$-0.742388\pi$
$31$	−9.25241	−	2.71675i	−1.66178	−	0.487943i	−0.971785	+	0.235869i	$0.924206\pi$
$32$	0.540641	+	0.841254i	0.0955727	+	0.148714i
$33$	−0.788678	−	6.60656i	−0.137291	−	1.15005i
$34$	−0.801424	−	0.365998i	−0.137443	−	0.0627681i
$35$	−3.09143	−	1.41181i	−0.522547	−	0.238639i
$36$	−1.11396	−	2.78551i	−0.185661	−	0.464252i
$37$	−1.72474	−	2.68374i	−0.283545	−	0.441205i	0.670042	−	0.742324i	$-0.266276\pi$
$37$	−1.72474	−	2.68374i	−0.283545	−	0.441205i	−0.953587	+	0.301119i	$0.902640\pi$
$38$	−0.423447	−	0.124335i	−0.0686921	−	0.0201698i
$39$	2.84260	+	6.64147i	0.455180	+	1.06349i
$40$	−1.53974	+	1.33419i	−0.243454	+	0.210954i
$41$	−3.75293	+	5.83967i	−0.586109	+	0.912004i	0.413890	+	0.910327i	$0.364170\pi$
$41$	−3.75293	+	5.83967i	−0.586109	+	0.912004i	−0.999999	+	0.00167639i	$0.999466\pi$
$42$	1.26292	−	2.59861i	0.194873	−	0.400975i
$43$	2.21377	+	7.53939i	0.337596	+	1.14975i	0.937009	+	0.349306i	$0.113583\pi$
$43$	2.21377	+	7.53939i	0.337596	+	1.14975i	−0.599413	+	0.800440i	$0.704599\pi$
$44$	−1.59577	−	3.49424i	−0.240571	−	0.526777i
$45$	5.29436	−	3.05410i	0.789236	−	0.455279i
$46$	1.39073	−	4.58976i	0.205051	−	0.676723i
$47$		−	10.0192i		−	1.46144i	−0.682675	−	0.730722i	$-0.739184\pi$
$47$		−	10.0192i		−	1.46144i	0.682675	−	0.730722i	$-0.260816\pi$
$48$	−1.10253	−	1.33582i	−0.159137	−	0.192809i
$49$	−4.04658	+	1.18818i	−0.578083	+	0.169741i
$50$	0.641734	+	0.556065i	0.0907548	+	0.0786395i
$51$	1.45346	+	0.464916i	0.203526	+	0.0651013i
$52$	2.73137	+	3.15217i	0.378772	+	0.437127i
$53$	1.97228	+	13.7175i	0.270914	+	1.88425i	0.439016	+	0.898479i	$0.355327\pi$
$53$	1.97228	+	13.7175i	0.270914	+	1.88425i	−0.168102	+	0.985770i	$0.553764\pi$
$54$	2.48774	+	4.56193i	0.338538	+	0.620800i
$55$	6.58390	−	4.23122i	0.887773	−	0.570537i
$56$	0.237396	−	1.65113i	0.0317234	−	0.220641i
$57$	0.753787	+	0.126898i	0.0998416	+	0.0168081i
$58$	0.710743	−	1.55631i	0.0933251	−	0.204354i
$59$	−9.07876	−	1.30533i	−1.18195	−	0.169939i	−0.476812	−	0.879005i	$-0.658208\pi$
$59$	−9.07876	−	1.30533i	−1.18195	−	0.169939i	−0.705142	+	0.709066i	$0.749117\pi$
$60$	2.37418	−	2.61072i	0.306505	−	0.337043i
$61$	0.253015	−	0.861690i	0.0323953	−	0.110328i	−0.941708	−	0.336431i	$-0.890780\pi$
$61$	0.253015	−	0.861690i	0.0323953	−	0.110328i	0.974104	+	0.226102i	$0.0725984\pi$
$62$	9.54487	−	1.37234i	1.21220	−	0.174288i
$63$	−1.63849	+	4.72849i	−0.206431	+	0.595733i
$64$	−0.841254	−	0.540641i	−0.105157	−	0.0675801i
$65$	−5.56480	+	6.42212i	−0.690228	+	0.796566i
$66$	3.46187	+	5.68191i	0.426127	+	0.699394i
$67$	11.4487	−	5.22846i	1.39868	−	0.638758i	0.433698	−	0.901058i	$-0.357208\pi$
$67$	11.4487	−	5.22846i	1.39868	−	0.638758i	0.964986	+	0.262300i	$0.0844811\pi$
$68$	0.881042			0.106842
$69$	−1.44950	+	8.17918i	−0.174499	+	0.984657i
$70$	3.39855			0.406204
$71$	10.8767	−	4.96722i	1.29083	−	0.589501i	0.352682	−	0.935743i	$-0.385270\pi$
$71$	10.8767	−	4.96722i	1.29083	−	0.589501i	0.938145	+	0.346242i	$0.112542\pi$
$72$	2.17044	+	2.07104i	0.255789	+	0.244074i
$73$	5.44903	−	6.28852i	0.637761	−	0.736016i	−0.341216	−	0.939985i	$-0.610839\pi$
$73$	5.44903	−	6.28852i	0.637761	−	0.736016i	0.978977	+	0.203969i	$0.0653843\pi$
$74$	2.68374	+	1.72474i	0.311979	+	0.200497i
$75$	−1.21785	−	0.824588i	−0.140625	−	0.0952152i
$76$	0.436831	−	0.0628068i	0.0501080	−	0.00720444i
$77$	−1.80530	+	6.14827i	−0.205732	+	0.700661i
$78$	−5.34469	−	4.86044i	−0.605167	−	0.550336i
$79$	9.67669	+	1.39130i	1.08871	+	0.156533i	0.663217	−	0.748427i	$-0.269191\pi$
$79$	9.67669	+	1.39130i	1.08871	+	0.156533i	0.425495	+	0.904961i	$0.360100\pi$
$80$	0.846353	−	1.85325i	0.0946251	−	0.207200i
$81$	−5.21512	−	7.33502i	−0.579458	−	0.815002i
$82$	0.987897	−	6.87098i	0.109095	−	0.758772i
$83$	7.04095	−	4.52494i	0.772845	−	0.496677i	−0.0938073	−	0.995590i	$-0.529904\pi$
$83$	7.04095	−	4.52494i	0.772845	−	0.496677i	0.866652	+	0.498913i	$0.166267\pi$
$84$	−0.0692884	+	2.88842i	−0.00755999	+	0.315152i
$85$	0.255456	+	1.77673i	0.0277081	+	0.192714i
$86$	−5.14569	−	5.93844i	−0.554874	−	0.640359i
$87$	−0.902836	+	2.82253i	−0.0967942	+	0.302607i
$88$	2.90312	+	2.51557i	0.309474	+	0.268161i
$89$	4.94463	−	1.45187i	0.524130	−	0.153898i	−0.00895542	−	0.999960i	$-0.502851\pi$
$89$	4.94463	−	1.45187i	0.524130	−	0.153898i	0.533085	+	0.846061i	$0.321032\pi$
$90$	−3.54720	+	4.97747i	−0.373907	+	0.524671i
$91$		−	6.95753i		−	0.729347i
$92$	0.641606	+	4.75272i	0.0668920	+	0.495505i
$93$	−16.1339	+	4.31988i	−1.67301	+	0.447951i
$94$	4.16211	+	9.11374i	0.429289	+	0.940011i
$95$	0.253316	+	0.862716i	0.0259897	+	0.0885128i
$96$	1.55782	+	0.757097i	0.158994	+	0.0772708i
$97$	−5.81077	+	9.04174i	−0.589994	+	0.918049i	0.409988	+	0.912091i	$0.365533\pi$
$97$	−5.81077	+	9.04174i	−0.589994	+	0.918049i	−0.999982	+	0.00595827i	$0.998103\pi$
$98$	3.18731	−	2.76182i	0.321967	−	0.278986i
$99$	−7.12042	−	9.06120i	−0.715629	−	0.910685i
$100$	−0.814739	−	0.239229i	−0.0814739	−	0.0239229i
$101$	−0.957445	−	1.48981i	−0.0952693	−	0.148242i	0.790347	−	0.612659i	$-0.209900\pi$
$101$	−0.957445	−	1.48981i	−0.0952693	−	0.148242i	−0.885617	+	0.464417i	$0.846264\pi$
$102$	−1.51525	+	0.180888i	−0.150032	+	0.0179106i
$103$	−0.391193	−	0.178652i	−0.0385454	−	0.0176031i	0.396049	−	0.918229i	$-0.370381\pi$
$103$	−0.391193	−	0.178652i	−0.0385454	−	0.0176031i	−0.434594	+	0.900626i	$0.643108\pi$
$104$	−3.79400	−	1.73266i	−0.372032	−	0.169901i
$105$	−5.84495	+	0.697760i	−0.570409	+	0.0680944i
$106$	−7.49252	−	11.6586i	−0.727738	−	1.13238i
$107$	−17.5447	−	5.15160i	−1.69611	−	0.498024i	−0.716276	−	0.697817i	$-0.754155\pi$
$107$	−17.5447	−	5.15160i	−1.69611	−	0.498024i	−0.979838	+	0.199793i	$0.935973\pi$
$108$	−4.15802	−	3.11623i	−0.400105	−	0.299860i
$109$	7.69835	−	6.67066i	0.737368	−	0.638933i	−0.202966	−	0.979186i	$-0.565058\pi$
$109$	7.69835	−	6.67066i	0.737368	−	0.638933i	0.940334	+	0.340252i	$0.110513\pi$
$110$	−4.23122	+	6.58390i	−0.403431	+	0.627750i
$111$	−4.96971	−	2.41527i	−0.471704	−	0.229247i
$112$	0.469960	+	1.60054i	0.0444071	+	0.151237i
$113$	1.39156	+	3.04709i	0.130907	+	0.286646i	0.963723	−	0.266903i	$-0.0860003\pi$
$113$	1.39156	+	3.04709i	0.130907	+	0.286646i	−0.832816	+	0.553549i	$0.813273\pi$
$114$	−0.738385	+	0.197704i	−0.0691560	+	0.0185167i
$115$	−9.39844	+	2.67192i	−0.876409	+	0.249158i
$116$			1.71092i			0.158855i
$117$	10.1899	+	7.26185i	0.942057	+	0.671358i
$118$	8.80058	−	2.58408i	0.810159	−	0.237884i
$119$	−1.11070	−	0.962430i	−0.101818	−	0.0882258i
$120$	−1.07510	+	3.36107i	−0.0981425	+	0.306822i
$121$	−2.45979	−	2.83874i	−0.223617	−	0.258068i
$122$	0.127808	+	0.888927i	0.0115712	+	0.0804797i
$123$	−0.288336	+	12.0198i	−0.0259983	+	1.08379i
$124$	−8.11223	+	5.21341i	−0.728499	+	0.468178i
$125$	1.69594	−	11.7955i	0.151690	−	1.05503i
$126$	−0.473859	−	4.98184i	−0.0422147	−	0.443817i
$127$	−3.66827	+	8.03239i	−0.325506	+	0.712759i	−0.999666	−	0.0258261i	$-0.991778\pi$
$127$	−3.66827	+	8.03239i	−0.325506	+	0.712759i	0.674160	+	0.738585i	$0.264506\pi$
$128$	0.989821	+	0.142315i	0.0874887	+	0.0125790i
$129$	10.0690	+	9.15670i	0.886525	+	0.806202i
$130$	2.39407	−	8.15346i	0.209974	−	0.715106i
$131$	14.6796	−	2.11061i	1.28256	−	0.184404i	0.532873	−	0.846195i	$-0.321112\pi$
$131$	14.6796	−	2.11061i	1.28256	−	0.184404i	0.749689	+	0.661791i	$0.230203\pi$
$132$	−5.50938	−	3.73033i	−0.479530	−	0.324684i
$133$	−0.619309	−	0.398006i	−0.0537009	−	0.0345115i
$134$	−8.24215	+	9.51195i	−0.712013	+	0.821707i
$135$	5.07868	−	9.28872i	0.437103	−	0.799446i
$136$	−0.801424	+	0.365998i	−0.0687215	+	0.0313841i
$137$	18.3814			1.57043			0.785213	−	0.619225i	$-0.212553\pi$
$137$	18.3814			1.57043			0.785213	+	0.619225i	$0.212553\pi$
$138$	−2.07925	−	8.04218i	−0.176997	−	0.684596i
$139$	−7.58116			−0.643026			−0.321513	−	0.946905i	$-0.604191\pi$
$139$	−7.58116			−0.643026			−0.321513	+	0.946905i	$0.604191\pi$
$140$	−3.09143	+	1.41181i	−0.261273	+	0.119320i
$141$	−9.02931	−	14.8196i	−0.760405	−	1.24804i
$142$	−7.83034	+	9.03669i	−0.657107	+	0.758342i
$143$	13.4786	+	8.66218i	1.12714	+	0.724368i
$144$	−2.83464	−	0.982246i	−0.236220	−	0.0818539i
$145$	−3.45030	+	0.496078i	−0.286532	+	0.0411970i
$146$	−2.34427	+	7.98385i	−0.194013	+	0.660748i
$147$	−4.91463	+	5.40428i	−0.405352	+	0.445737i
$148$	−3.15770	−	0.454009i	−0.259561	−	0.0373193i
$149$	2.89272	−	6.33417i	0.236981	−	0.518915i	−0.753354	−	0.657616i	$-0.771565\pi$
$149$	2.89272	−	6.33417i	0.236981	−	0.518915i	0.990334	+	0.138700i	$0.0442924\pi$
$150$	1.45034	+	0.244160i	0.118420	+	0.0199356i
$151$	−0.741264	+	5.15560i	−0.0603232	+	0.419557i	0.937175	+	0.348861i	$0.113431\pi$
$151$	−0.741264	+	5.15560i	−0.0603232	+	0.419557i	−0.997498	+	0.0706966i	$0.977478\pi$
$152$	−0.371265	+	0.238597i	−0.0301135	+	0.0193528i
$153$	2.56885	−	0.622196i	0.207679	−	0.0503015i
$154$	−0.911930	−	6.34261i	−0.0734854	−	0.511102i
$155$	−12.8656	−	14.8477i	−1.03339	−	1.19260i
$156$	6.88080	+	2.20095i	0.550905	+	0.176217i
$157$	11.0542	+	9.57850i	0.882220	+	0.764448i	0.972850	−	0.231437i	$-0.0743427\pi$
$157$	11.0542	+	9.57850i	0.882220	+	0.764448i	−0.0906303	+	0.995885i	$0.528888\pi$
$158$	−9.38019	+	2.75427i	−0.746248	+	0.219118i
$159$	15.2796	+	18.5126i	1.21175	+	1.46815i
$160$			2.03737i			0.161068i
$161$	4.38291	−	6.69249i	0.345422	−	0.527442i
$162$	7.79092	+	4.50573i	0.612112	+	0.354004i
$163$	−1.34972	−	2.95548i	−0.105718	−	0.231491i	0.849379	−	0.527784i	$-0.176977\pi$
$163$	−1.34972	−	2.95548i	−0.105718	−	0.231491i	−0.955097	+	0.296293i	$0.904250\pi$
$164$	1.95568	+	6.66045i	0.152713	+	0.520093i
$165$	5.92526	−	12.1920i	0.461281	−	0.949144i
$166$	−4.52494	+	7.04095i	−0.351204	+	0.546484i
$167$	−8.25427	+	7.15237i	−0.638735	+	0.553467i	−0.912883	−	0.408220i	$-0.866149\pi$
$167$	−8.25427	+	7.15237i	−0.638735	+	0.553467i	0.274149	+	0.961687i	$0.411604\pi$
$168$	−1.13686	−	2.65618i	−0.0877110	−	0.204929i
$169$	−4.21842	−	1.23864i	−0.324494	−	0.0952800i
$170$	−0.970453	−	1.51005i	−0.0744303	−	0.115816i
$171$	1.22931	−	0.491618i	0.0940078	−	0.0375950i
$172$	7.14760	+	3.26420i	0.544999	+	0.248893i
$173$	4.16317	+	1.90126i	0.316520	+	0.144550i	0.567339	−	0.823484i	$-0.307973\pi$
$173$	4.16317	+	1.90126i	0.316520	+	0.144550i	−0.250819	+	0.968034i	$0.580700\pi$
$174$	−0.351272	−	2.94251i	−0.0266298	−	0.223071i
$175$	0.765790	+	1.19159i	0.0578883	+	0.0900759i
$176$	−3.68578	−	1.08224i	−0.277826	−	0.0815770i
$177$	−14.6050	+	6.25107i	−1.09778	+	0.469859i
$178$	−3.89466	+	3.37475i	−0.291917	+	0.252948i
$179$	3.25606	−	5.06653i	0.243370	−	0.378690i	−0.697983	−	0.716114i	$-0.745919\pi$
$179$	3.25606	−	5.06653i	0.243370	−	0.378690i	0.941353	+	0.337424i	$0.109555\pi$
$180$	1.15893	−	6.00122i	0.0863815	−	0.447305i
$181$	−5.38170	−	18.3284i	−0.400019	−	1.36234i	−0.875757	−	0.482752i	$-0.839637\pi$
$181$	−5.38170	−	18.3284i	−0.400019	−	1.36234i	0.475738	−	0.879587i	$-0.342181\pi$
$182$	2.89026	+	6.32879i	0.214241	+	0.469121i
$183$	−0.402317	−	1.50257i	−0.0297401	−	0.111073i
$184$	−2.55798	−	4.05669i	−0.188576	−	0.299063i
$185$		−	6.49955i		−	0.477856i
$186$	12.8814	−	10.6318i	0.944507	−	0.779558i
$187$	3.24732	−	0.953500i	0.237468	−	0.0697268i
$188$	−7.57197	−	6.56115i	−0.552243	−	0.478521i
$189$	1.83779	+	8.47067i	0.133679	+	0.616151i
$190$	−0.588810	−	0.679523i	−0.0427168	−	0.0492978i
$191$	0.166833	+	1.16035i	0.0120716	+	0.0839601i	0.994967	−	0.100207i	$-0.0319504\pi$
$191$	0.166833	+	1.16035i	0.0120716	+	0.0839601i	−0.982895	+	0.184167i	$0.941041\pi$
$192$	−1.73155	−	0.0415372i	−0.124964	−	0.00299769i
$193$	8.67054	−	5.57222i	0.624119	−	0.401097i	−0.190009	−	0.981782i	$-0.560852\pi$
$193$	8.67054	−	5.57222i	0.624119	−	0.401097i	0.814128	+	0.580685i	$0.197215\pi$
$194$	1.52959	−	10.6385i	0.109818	−	0.763802i
$195$	−2.44342	+	14.5142i	−0.174977	+	1.03938i
$196$	−1.75198	+	3.83630i	−0.125141	+	0.274021i
$197$	−22.8286	−	3.28226i	−1.62647	−	0.233851i	−0.732106	−	0.681191i	$-0.761462\pi$
$197$	−22.8286	−	3.28226i	−1.62647	−	0.233851i	−0.894364	+	0.447339i	$0.852372\pi$
$198$	10.2411	+	5.28443i	0.727805	+	0.375548i
$199$	−0.330283	+	1.12484i	−0.0234131	+	0.0797378i	−0.970371	−	0.241620i	$-0.922321\pi$
$199$	−0.330283	+	1.12484i	−0.0234131	+	0.0797378i	0.946958	+	0.321358i	$0.104139\pi$
$200$	0.840492	−	0.120845i	0.0594318	−	0.00854500i
$201$	12.2223	−	18.0512i	0.862092	−	1.27324i
$202$	1.48981	+	0.957445i	0.104823	+	0.0673656i
$203$	1.86897	−	2.15691i	0.131176	−	0.151386i
$204$	1.30318	−	0.793999i	0.0912406	−	0.0555910i
$205$	−12.8646	+	5.87507i	−0.898503	+	0.410333i
$206$	0.430056			0.0299634
$207$	5.22712	+	13.4044i	0.363310	+	0.931668i
$208$	4.17091			0.289201
$209$	1.54209	−	0.704249i	0.106669	−	0.0487139i
$210$	5.02690	−	3.06279i	0.346889	−	0.211352i
$211$	−5.53127	+	6.38342i	−0.380788	+	0.439453i	−0.913497	−	0.406846i	$-0.866629\pi$
$211$	−5.53127	+	6.38342i	−0.380788	+	0.439453i	0.532709	+	0.846299i	$0.321174\pi$
$212$	11.6586	+	7.49252i	0.800716	+	0.514589i
$213$	11.6116	−	17.1493i	0.795613	−	1.17505i
$214$	18.0993	−	2.60229i	1.23724	−	0.177889i
$215$	−4.51025	+	15.3605i	−0.307597	+	1.04758i
$216$	5.07679	+	1.10732i	0.345432	+	0.0753437i
$217$	15.9219	+	2.28922i	1.08085	+	0.155402i
$218$	−4.23158	+	9.26586i	−0.286598	+	0.627563i
$219$	2.39259	−	14.2122i	0.161676	−	0.960374i
$220$	1.11380	−	7.74664i	0.0750923	−	0.522278i
$221$	−3.09139	+	1.98672i	−0.207950	+	0.133641i
$222$	5.52395	+	0.132511i	0.370743	+	0.00889353i
$223$	2.52620	+	17.5701i	0.169167	+	1.17658i	0.880612	+	0.473838i	$0.157132\pi$
$223$	2.52620	+	17.5701i	0.169167	+	1.17658i	−0.711445	+	0.702742i	$0.751959\pi$
$224$	−1.09238	−	1.26067i	−0.0729876	−	0.0842322i
$225$	−2.54448	−	0.122146i	−0.169632	−	0.00814307i
$226$	−2.53162	−	2.19366i	−0.168401	−	0.145920i
$227$	−12.2667	+	3.60182i	−0.814167	+	0.239061i	−0.662203	−	0.749325i	$-0.730378\pi$
$227$	−12.2667	+	3.60182i	−0.814167	+	0.239061i	−0.151965	+	0.988386i	$0.548560\pi$
$228$	0.589529	−	0.486574i	0.0390425	−	0.0322241i
$229$			7.54315i			0.498465i	0.968444	+	0.249233i	$0.0801784\pi$
$229$			7.54315i			0.498465i	−0.968444	+	0.249233i	$0.919822\pi$
$230$	7.43917	−	6.33472i	0.490524	−	0.417699i
$231$	2.87058	+	10.7210i	0.188870	+	0.705393i
$232$	−0.710743	−	1.55631i	−0.0466626	−	0.102177i
$233$	0.546301	+	1.86053i	0.0357894	+	0.121887i	0.975450	−	0.220220i	$-0.0706775\pi$
$233$	0.546301	+	1.86053i	0.0357894	+	0.121887i	−0.939661	+	0.342107i	$0.888859\pi$
$234$	−12.2857	−	2.37257i	−0.803144	−	0.155100i
$235$	11.0359	−	17.1723i	0.719905	−	1.12019i
$236$	−6.93182	+	6.00646i	−0.451223	+	0.390987i
$237$	15.5669	−	6.66276i	1.01118	−	0.432793i
$238$	1.41014	+	0.414054i	0.0914058	+	0.0268392i
$239$	7.38528	+	11.4917i	0.477714	+	0.743338i	0.993556	−	0.113346i	$-0.0361570\pi$
$239$	7.38528	+	11.4917i	0.477714	+	0.743338i	−0.515841	+	0.856684i	$0.672521\pi$
$240$	−0.418294	−	3.50394i	−0.0270008	−	0.226179i
$241$	−25.4368	−	11.6166i	−1.63853	−	0.748291i	−0.638753	−	0.769412i	$-0.720549\pi$
$241$	−25.4368	−	11.6166i	−1.63853	−	0.748291i	−0.999777	+	0.0211206i	$0.993277\pi$
$242$	3.41676	+	1.56038i	0.219637	+	0.100305i
$243$	−14.3242	−	6.14957i	−0.918898	−	0.394495i
$244$	−0.485532	−	0.755503i	−0.0310830	−	0.0483661i
$245$	−8.24437	−	2.42077i	−0.526714	−	0.154657i
$246$	−4.73093	−	11.0534i	−0.301633	−	0.704737i
$247$	−1.39112	+	1.20542i	−0.0885151	+	0.0766988i
$248$	5.21341	−	8.11223i	0.331052	−	0.515127i
$249$	6.33659	−	13.0383i	0.401565	−	0.826270i
$250$	3.35736	+	11.4341i	0.212338	+	0.723157i
$251$	2.92637	+	6.40786i	0.184711	+	0.404461i	0.979223	−	0.202788i	$-0.0650003\pi$
$251$	2.92637	+	6.40786i	0.184711	+	0.404461i	−0.794512	+	0.607249i	$0.792273\pi$
$252$	2.50057	+	4.33479i	0.157521	+	0.273066i
$253$	7.50841	+	16.8231i	0.472049	+	1.05766i
$254$		−	8.83037i		−	0.554067i
$255$	1.97905	+	2.39781i	0.123933	+	0.150156i
$256$	−0.959493	+	0.281733i	−0.0599683	+	0.0176083i
$257$	6.19953	+	5.37193i	0.386716	+	0.335092i	0.826423	−	0.563050i	$-0.190372\pi$
$257$	6.19953	+	5.37193i	0.386716	+	0.335092i	−0.439707	+	0.898141i	$0.644918\pi$
$258$	−12.9629	−	4.14642i	−0.807035	−	0.258145i
$259$	3.48487	+	4.02176i	0.216539	+	0.249900i
$260$	1.20935	+	8.41119i	0.0750005	+	0.521640i
$261$	1.20826	+	4.98853i	0.0747895	+	0.308782i
$262$	−12.4762	+	8.01799i	−0.770785	+	0.495353i
$263$	0.481045	−	3.34574i	0.0296625	−	0.206307i	−0.969600	−	0.244694i	$-0.921313\pi$
$263$	0.481045	−	3.34574i	0.0296625	−	0.206307i	0.999263	+	0.0383862i	$0.0122217\pi$
$264$	6.56114	+	1.10455i	0.403810	+	0.0679804i
$265$	−11.7293	+	25.6835i	−0.720523	+	1.57773i
$266$	0.728681	+	0.104769i	0.0446783	+	0.00642377i
$267$	6.00532	−	6.60364i	0.367520	−	0.404136i
$268$	3.54592	−	12.0763i	0.216601	−	0.737676i
$269$	10.7339	−	1.54330i	0.654458	−	0.0940969i	0.192916	−	0.981215i	$-0.438205\pi$
$269$	10.7339	−	1.54330i	0.654458	−	0.0940969i	0.461542	+	0.887118i	$0.347296\pi$
$270$	−0.761054	+	10.5591i	−0.0463163	+	0.642605i
$271$	−16.0400	−	10.3083i	−0.974361	−	0.626184i	−0.0464247	−	0.998922i	$-0.514783\pi$
$271$	−16.0400	−	10.3083i	−0.974361	−	0.626184i	−0.927937	+	0.372738i	$0.878419\pi$
$272$	0.576959	−	0.665847i	0.0349833	−	0.0403729i
$273$	−6.27016	−	10.2911i	−0.379487	−	0.622846i
$274$	−16.7203	+	7.63590i	−1.01011	+	0.461301i
$275$	−3.26185			−0.196697
$276$	5.23219	+	6.45168i	0.314941	+	0.388345i
$277$	14.5666			0.875221			0.437610	−	0.899165i	$-0.355825\pi$
$277$	14.5666			0.875221			0.437610	+	0.899165i	$0.355825\pi$
$278$	6.89607	−	3.14933i	0.413599	−	0.188884i
$279$	−19.9710	+	20.9296i	−1.19563	+	1.25302i
$280$	2.22558	−	2.56845i	0.133004	−	0.153494i
$281$	16.3467	+	10.5054i	0.975164	+	0.626700i	0.928155	−	0.372195i	$-0.121395\pi$
$281$	16.3467	+	10.5054i	0.975164	+	0.626700i	0.0470093	+	0.998894i	$0.485031\pi$
$282$	14.3697	+	9.72952i	0.855700	+	0.579384i
$283$	−16.5357	+	2.37748i	−0.982946	+	0.141326i	−0.615005	−	0.788523i	$-0.710846\pi$
$283$	−16.5357	+	2.37748i	−0.982946	+	0.141326i	−0.367941	+	0.929849i	$0.619937\pi$
$284$	3.36875	−	11.4729i	0.199898	−	0.680792i
$285$	1.15217	+	1.04778i	0.0682488	+	0.0620652i
$286$	−15.8590	−	2.28018i	−0.937761	−	0.134830i
$287$	4.81025	−	10.5330i	0.283940	−	0.621742i
$288$	2.98652	−	0.284070i	0.175982	−	0.0167390i
$289$	2.30888	−	16.0586i	0.135817	−	0.944625i
$290$	2.93242	−	1.88455i	0.172198	−	0.110665i
$291$	−0.446439	+	18.6106i	−0.0261707	+	1.09097i
$292$	−1.18419	−	8.23621i	−0.0692994	−	0.481988i
$293$	−18.4243	−	21.2628i	−1.07636	−	1.24218i	−0.968762	−	0.247990i	$-0.920230\pi$
$293$	−18.4243	−	21.2628i	−1.07636	−	1.24218i	−0.107597	−	0.994195i	$-0.534316\pi$
$294$	2.22549	−	6.95752i	0.129793	−	0.405771i
$295$	−14.1227	−	12.2374i	−0.822254	−	0.712487i
$296$	3.06095	−	0.898775i	0.177914	−	0.0522402i
$297$	−18.6980	−	6.98576i	−1.08497	−	0.405355i
$298$			6.96344i			0.403381i
$299$	−12.9685	−	15.2295i	−0.749987	−	0.880746i
$300$	−1.42070	+	0.380396i	−0.0820242	+	0.0219622i
$301$	−5.44504	−	11.9230i	−0.313847	−	0.687228i
$302$	−1.46744	−	4.99764i	−0.0844416	−	0.287582i
$303$	−2.75881	−	1.34078i	−0.158490	−	0.0770256i
$304$	0.238597	−	0.371265i	0.0136845	−	0.0212935i
$305$	1.38279	−	1.19820i	0.0791784	−	0.0686085i
$306$	−2.07824	+	1.63311i	−0.118805	+	0.0933585i
$307$	−17.7513	−	5.21225i	−1.01312	−	0.297479i	−0.267290	−	0.963616i	$-0.586128\pi$
$307$	−17.7513	−	5.21225i	−1.01312	−	0.297479i	−0.745829	+	0.666138i	$0.767946\pi$
$308$	3.46434	+	5.39061i	0.197399	+	0.307159i
$309$	−0.739628	+	0.0882954i	−0.0420760	+	0.00502295i
$310$	17.8710	+	8.16140i	1.01500	+	0.463536i
$311$	12.7233	+	5.81054i	0.721473	+	0.329486i	0.742088	−	0.670302i	$-0.233835\pi$
$311$	12.7233	+	5.81054i	0.721473	+	0.329486i	−0.0206158	+	0.999787i	$0.506563\pi$
$312$	−7.17330	+	0.856335i	−0.406108	+	0.0484804i
$313$	13.2283	+	20.5836i	0.747707	+	1.16346i	0.981555	+	0.191182i	$0.0612321\pi$
$313$	13.2283	+	20.5836i	0.747707	+	1.16346i	−0.233847	+	0.972273i	$0.575132\pi$
$314$	−14.0343	−	4.12084i	−0.792001	−	0.232552i
$315$	−8.01663	+	6.29958i	−0.451686	+	0.354941i
$316$	7.38835	−	6.40205i	0.415627	−	0.360143i
$317$	2.45801	−	3.82475i	0.138056	−	0.214819i	−0.765341	−	0.643626i	$-0.777429\pi$
$317$	2.45801	−	3.82475i	0.138056	−	0.214819i	0.903396	+	0.428806i	$0.141066\pi$
$318$	−21.5892	−	10.4923i	−1.21066	−	0.588379i
$319$	1.85163	+	6.30608i	0.103671	+	0.353073i
$320$	−0.846353	−	1.85325i	−0.0473126	−	0.103600i
$321$	−30.5936	+	8.19151i	−1.70757	+	0.457205i
$322$	−1.20668	+	7.90843i	−0.0672454	+	0.440720i
$323$			0.388824i			0.0216348i
$324$	−8.95862	−	0.862093i	−0.497701	−	0.0478940i
$325$	3.39821	−	0.997804i	0.188499	−	0.0553482i
$326$	2.45550	+	2.12770i	0.135998	+	0.117843i
$327$	5.37525	−	16.8046i	0.297252	−	0.929295i
$328$	−4.54580	−	5.24613i	−0.251000	−	0.289669i
$329$	2.37851	+	16.5429i	0.131132	+	0.912040i
$330$	−0.325082	+	13.5517i	−0.0178952	+	0.745994i
$331$	8.10093	−	5.20615i	0.445268	−	0.286156i	−0.298731	−	0.954337i	$-0.596563\pi$
$331$	8.10093	−	5.20615i	0.445268	−	0.286156i	0.743999	+	0.668181i	$0.232927\pi$
$332$	1.19112	−	8.28440i	0.0653710	−	0.454666i
$333$	−9.52751	+	0.906232i	−0.522104	+	0.0496612i
$334$	4.53715	−	9.93497i	0.248262	−	0.543617i
$335$	25.3815	+	3.64931i	1.38674	+	0.199383i
$336$	2.13754	+	1.94387i	0.116613	+	0.106047i
$337$	−0.506976	+	1.72660i	−0.0276167	+	0.0940539i	−0.972148	−	0.234367i	$-0.924698\pi$
$337$	−0.506976	+	1.72660i	−0.0276167	+	0.0940539i	0.944531	+	0.328421i	$0.106516\pi$
$338$	4.35176	−	0.625689i	0.236705	−	0.0340330i
$339$	4.80436	+	3.25297i	0.260937	+	0.176677i
$340$	1.51005	+	0.970453i	0.0818942	+	0.0526302i
$341$	−24.2577	+	27.9949i	−1.31363	+	1.51601i
$342$	−0.913996	+	0.957866i	−0.0494232	+	0.0517955i
$343$	17.0209	−	7.77319i	0.919042	−	0.419713i
$344$	−7.85768			−0.423658
$345$	−11.4936	+	12.4220i	−0.618794	+	0.668780i
$346$	−4.57676			−0.246048
$347$	−20.8305	+	9.51296i	−1.11824	+	0.510683i	−0.886794	−	0.462165i	$-0.847073\pi$
$347$	−20.8305	+	9.51296i	−1.11824	+	0.510683i	−0.231445	+	0.972848i	$0.574345\pi$
$348$	1.54189	+	2.53068i	0.0826541	+	0.135659i
$349$	−6.13437	+	7.07944i	−0.328365	+	0.378954i	−0.895795	−	0.444468i	$-0.853393\pi$
$349$	−6.13437	+	7.07944i	−0.328365	+	0.378954i	0.567429	+	0.823422i	$0.307938\pi$
$350$	−1.19159	−	0.765790i	−0.0636933	−	0.0409332i
$351$	21.6166	+	1.55804i	1.15381	+	0.0831618i
$352$	3.80228	−	0.546685i	0.202662	−	0.0291384i
$353$	4.81975	−	16.4146i	0.256529	−	0.873659i	−0.726023	−	0.687671i	$-0.758633\pi$
$353$	4.81975	−	16.4146i	0.256529	−	0.873659i	0.982552	−	0.185988i	$-0.0595486\pi$
$354$	10.6884	−	11.7533i	0.568084	−	0.624682i
$355$	24.1134	+	3.46698i	1.27980	+	0.184008i
$356$	2.14079	−	4.68768i	0.113462	−	0.248447i
$357$	−2.51022	−	0.422589i	−0.132855	−	0.0223658i
$358$	−0.857105	+	5.96130i	−0.0452994	+	0.315064i
$359$	−3.84333	+	2.46996i	−0.202843	+	0.130359i	−0.638119	−	0.769938i	$-0.720287\pi$
$359$	−3.84333	+	2.46996i	−0.202843	+	0.130359i	0.435276	+	0.900297i	$0.356651\pi$
$360$	1.43880	+	5.94034i	0.0758313	+	0.313083i
$361$	−2.67626	−	18.6138i	−0.140856	−	0.979675i
$362$	12.5093	+	14.4365i	0.657472	+	0.758763i
$363$	−6.19664	−	1.98211i	−0.325239	−	0.104034i
$364$	−5.25815	−	4.55621i	−0.275602	−	0.238810i
$365$	16.2660	−	4.77614i	0.851403	−	0.249994i
$366$	0.990151	+	1.19966i	0.0517560	+	0.0627072i
$367$			10.2975i			0.537527i	0.963206	+	0.268763i	$0.0866150\pi$
$367$			10.2975i			0.537527i	−0.963206	+	0.268763i	$0.913385\pi$
$368$	4.01203	+	2.62748i	0.209141	+	0.136967i
$369$	10.4058	+	18.0387i	0.541705	+	0.939058i
$370$	2.70001	+	5.91220i	0.140367	+	0.307361i
$371$	−6.51299	−	22.1812i	−0.338138	−	1.15159i
$372$	−7.30070	+	15.0221i	−0.378524	+	0.778859i
$373$	17.5298	−	27.2770i	0.907660	−	1.41235i	−0.00336401	−	0.999994i	$-0.501071\pi$
$373$	17.5298	−	27.2770i	0.907660	−	1.41235i	0.911024	−	0.412353i	$-0.135293\pi$
$374$	−2.55777	+	2.21632i	−0.132259	+	0.114603i
$375$	−8.12167	−	18.9755i	−0.419401	−	0.979893i
$376$	9.61331	+	2.82272i	0.495769	+	0.145571i
$377$	−3.85807	−	6.00328i	−0.198701	−	0.309185i
$378$	−5.19056	−	6.94175i	−0.266973	−	0.357045i
$379$	3.56578	+	1.62844i	0.183162	+	0.0836472i	0.504885	−	0.863186i	$-0.331535\pi$
$379$	3.56578	+	1.62844i	0.183162	+	0.0836472i	−0.321723	+	0.946834i	$0.604262\pi$
$380$	0.817884	+	0.373515i	0.0419566	+	0.0191609i
$381$	1.81297	+	15.1868i	0.0928815	+	0.778044i
$382$	−0.633784	−	0.986188i	−0.0324272	−	0.0504578i
$383$	−4.80812	−	1.41179i	−0.245684	−	0.0721392i	0.156572	−	0.987667i	$-0.449956\pi$
$383$	−4.80812	−	1.41179i	−0.245684	−	0.0721392i	−0.402256	+	0.915527i	$0.631774\pi$
$384$	1.59233	−	0.681529i	0.0812583	−	0.0347792i
$385$	−9.86639	+	8.54928i	−0.502838	+	0.435712i
$386$	−5.57222	+	8.67054i	−0.283618	+	0.441319i
$387$	23.1454	+	4.46974i	1.17655	+	0.227210i
$388$	3.02804	+	10.3126i	0.153726	+	0.523541i
$389$	−9.73330	−	21.3130i	−0.493498	−	1.08061i	−0.978528	−	0.206113i	$-0.933919\pi$
$389$	−9.73330	−	21.3130i	−0.493498	−	1.08061i	0.485030	−	0.874497i	$-0.338809\pi$
$390$	−3.80679	−	14.2176i	−0.192764	−	0.719936i
$391$	−4.22517	−	0.0363936i	−0.213676	−	0.00184050i
$392$		−	4.21742i		−	0.213012i
$393$	19.8109	−	16.3512i	0.999330	−	0.824808i
$394$	22.1291	−	6.49770i	1.11485	−	0.327349i
$395$	15.0528	+	13.0433i	0.757388	+	0.656280i
$396$	−11.5109	−	0.552573i	−0.578444	−	0.0277678i
$397$	−10.6167	−	12.2523i	−0.532835	−	0.614925i	0.423962	−	0.905680i	$-0.360639\pi$
$397$	−10.6167	−	12.2523i	−0.532835	−	0.614925i	−0.956797	+	0.290755i	$0.906093\pi$
$398$	−0.166840	−	1.16040i	−0.00836292	−	0.0581654i
$399$	−1.27473	−	0.0305786i	−0.0638161	−	0.00153084i
$400$	−0.714338	+	0.459077i	−0.0357169	+	0.0229539i
$401$	−4.94794	+	34.4137i	−0.247088	+	1.71854i	0.367786	+	0.929911i	$0.380116\pi$
$401$	−4.94794	+	34.4137i	−0.247088	+	1.71854i	−0.614874	+	0.788626i	$0.710793\pi$
$402$	−3.61901	+	21.4973i	−0.180500	+	1.07219i
$403$	16.7081	−	36.5856i	0.832288	−	1.82246i
$404$	−1.75292	−	0.252032i	−0.0872110	−	0.0125390i
$405$	−0.859007	−	18.3162i	−0.0426844	−	0.910138i
$406$	−0.804066	+	2.73840i	−0.0399051	+	0.135904i
$407$	−12.1299	+	1.74402i	−0.601258	+	0.0864478i
$408$	−0.855572	+	1.26361i	−0.0423571	+	0.0625578i
$409$	17.5509	+	11.2793i	0.867837	+	0.557725i	0.897090	−	0.441847i	$-0.145677\pi$
$409$	17.5509	+	11.2793i	0.867837	+	0.557725i	−0.0292535	+	0.999572i	$0.509313\pi$
$410$	9.26147	−	10.6883i	0.457391	−	0.527858i
$411$	27.1885	−	16.5654i	1.34111	−	0.817110i
$412$	−0.391193	+	0.178652i	−0.0192727	+	0.00880154i
$413$	15.3001			0.752868
$414$	−10.3231	−	10.0216i	−0.507354	−	0.492536i
$415$	17.0519			0.837046
$416$	−3.79400	+	1.73266i	−0.186016	+	0.0849506i
$417$	−11.2135	+	6.83218i	−0.549129	+	0.334573i
$418$	−1.11018	+	1.28121i	−0.0543006	+	0.0626663i
$419$	10.5508	+	6.78060i	0.515441	+	0.331254i	0.772366	−	0.635177i	$-0.219073\pi$
$419$	10.5508	+	6.78060i	0.515441	+	0.331254i	−0.256925	+	0.966431i	$0.582709\pi$
$420$	−3.30030	+	4.87426i	−0.161038	+	0.237839i
$421$	15.0207	−	2.15964i	0.732062	−	0.105255i	0.233804	−	0.972284i	$-0.424882\pi$
$421$	15.0207	−	2.15964i	0.732062	−	0.105255i	0.498258	+	0.867029i	$0.333973\pi$
$422$	2.37965	−	8.10434i	0.115839	−	0.394513i
$423$	−26.7111	−	13.7830i	−1.29874	−	0.670150i
$424$	−13.7175	−	1.97228i	−0.666182	−	0.0957826i
$425$	0.310782	−	0.680517i	0.0150751	−	0.0330099i
$426$	−3.43819	+	20.4232i	−0.166581	+	0.989507i
$427$	−0.213198	+	1.48283i	−0.0103174	+	0.0717590i
$428$	−15.3827	+	9.88585i	−0.743550	+	0.477850i
$429$	27.7430	+	0.665511i	1.33945	+	0.0321312i
$430$	−2.27832	−	15.8460i	−0.109870	−	0.764164i
$431$	11.3203	+	13.0644i	0.545282	+	0.629289i	0.959777	−	0.280763i	$-0.0905874\pi$
$431$	11.3203	+	13.0644i	0.545282	+	0.629289i	−0.414495	+	0.910051i	$0.636042\pi$
$432$	−5.07801	+	1.10172i	−0.244316	+	0.0530066i
$433$	22.9390	+	19.8767i	1.10238	+	0.955215i	0.999222	−	0.0394497i	$-0.0125605\pi$
$433$	22.9390	+	19.8767i	1.10238	+	0.955215i	0.103156	+	0.994665i	$0.467106\pi$
$434$	−15.4340	+	4.53184i	−0.740856	+	0.217535i
$435$	−4.65638	+	3.84319i	−0.223256	+	0.184267i
$436$		−	10.1864i		−	0.487839i
$437$	−2.09749	+	0.283155i	−0.100336	+	0.0135452i
$438$	3.72760	+	13.9218i	0.178112	+	0.665211i
$439$	−2.52149	−	5.52130i	−0.120344	−	0.263517i	0.839867	−	0.542793i	$-0.182633\pi$
$439$	−2.52149	−	5.52130i	−0.120344	−	0.263517i	−0.960211	+	0.279275i	$0.909906\pi$
$440$	2.20492	+	7.50928i	0.105116	+	0.357991i
$441$	−2.39902	+	12.4227i	−0.114239	+	0.591559i
$442$	1.98672	−	3.09139i	0.0944986	−	0.147043i
$443$	−19.8198	+	17.1740i	−0.941668	+	0.815960i	−0.983079	−	0.183183i	$-0.941360\pi$
$443$	−19.8198	+	17.1740i	−0.941668	+	0.815960i	0.0414113	+	0.999142i	$0.486815\pi$
$444$	−5.07981	+	2.17420i	−0.241077	+	0.103183i
$445$	10.0740	+	2.95800i	0.477555	+	0.140223i
$446$	−9.59679	−	14.9329i	−0.454421	−	0.707093i
$447$	−1.42967	−	11.9760i	−0.0676212	−	0.566446i
$448$	1.51736	+	0.692957i	0.0716887	+	0.0327391i
$449$	−4.21621	−	1.92548i	−0.198975	−	0.0908689i	0.313435	−	0.949610i	$-0.398520\pi$
$449$	−4.21621	−	1.92548i	−0.198975	−	0.0908689i	−0.512411	+	0.858741i	$0.671247\pi$
$450$	2.36528	−	0.945906i	0.111500	−	0.0445904i
$451$	14.4164	+	22.4324i	0.678843	+	1.05630i
$452$	3.21412	+	0.943750i	0.151179	+	0.0443903i
$453$	3.54983	+	8.29385i	0.166785	+	0.389679i
$454$	9.66190	−	8.37209i	0.453456	−	0.392922i
$455$	7.66361	−	11.9248i	0.359275	−	0.559043i
$456$	−0.334124	+	0.687502i	−0.0156468	+	0.0321952i
$457$	−3.96660	−	13.5090i	−0.185550	−	0.631925i	−0.998752	−	0.0499434i	$-0.984096\pi$
$457$	−3.96660	−	13.5090i	−0.185550	−	0.631925i	0.813202	−	0.581981i	$-0.197722\pi$
$458$	−3.13354	−	6.86149i	−0.146421	−	0.320616i
$459$	3.23894	−	3.23537i	0.151181	−	0.151014i
$460$	−4.13537	+	8.85260i	−0.192813	+	0.412755i
$461$		−	16.2737i		−	0.757941i	−0.925409	−	0.378971i	$-0.876278\pi$
$461$		−	16.2737i		−	0.757941i	0.925409	−	0.378971i	$-0.123722\pi$
$462$	−7.06486	−	8.55972i	−0.328687	−	0.398234i
$463$	−11.1875	+	3.28494i	−0.519926	+	0.152664i	−0.531158	−	0.847273i	$-0.678243\pi$
$463$	−11.1875	+	3.28494i	−0.519926	+	0.152664i	0.0112318	+	0.999937i	$0.496425\pi$
$464$	1.29303	+	1.12042i	0.0600274	+	0.0520140i
$465$	−32.4108	−	10.3672i	−1.50302	−	0.480767i
$466$	−1.26982	−	1.46546i	−0.0588235	−	0.0678859i
$467$	1.43982	+	10.0142i	0.0666271	+	0.463402i	0.995634	+	0.0933399i	$0.0297543\pi$
$467$	1.43982	+	10.0142i	0.0666271	+	0.463402i	−0.929007	+	0.370062i	$0.879337\pi$
$468$	12.1611	−	2.94552i	0.562147	−	0.136157i
$469$	−17.6621	+	11.3507i	−0.815560	+	0.524129i
$470$	−2.90503	+	20.2049i	−0.133999	+	0.931984i
$471$	24.9828	+	4.20578i	1.15115	+	0.193792i
$472$	3.81024	−	8.34325i	0.175380	−	0.384029i
$473$	29.8771	+	4.29568i	1.37375	+	0.197516i
$474$	−11.3924	+	12.5274i	−0.523269	+	0.575403i
$475$	0.105577	−	0.359563i	0.00484422	−	0.0164979i
$476$	−1.45471	+	0.209156i	−0.0666766	+	0.00958665i
$477$	39.2842	+	13.6126i	1.79870	+	0.623276i
$478$	−11.4917	−	7.38528i	−0.525619	−	0.337795i
$479$	3.34991	−	3.86601i	0.153062	−	0.176642i	−0.674040	−	0.738695i	$-0.735443\pi$
$479$	3.34991	−	3.86601i	0.153062	−	0.176642i	0.827102	+	0.562052i	$0.189988\pi$
$480$	1.83608	+	3.01353i	0.0838054	+	0.137548i
$481$	12.1035	−	5.52748i	0.551872	−	0.252031i
$482$	27.9639			1.27372
$483$	0.451597	−	13.8490i	0.0205484	−	0.630150i
$484$	−3.75620			−0.170736
$485$	−19.9187	+	9.09654i	−0.904459	+	0.413053i
$486$	15.5844	−	0.356644i	0.706922	−	0.0161777i
$487$	4.05223	−	4.67652i	0.183624	−	0.211913i	−0.656473	−	0.754349i	$-0.727952\pi$
$487$	4.05223	−	4.67652i	0.183624	−	0.211913i	0.840097	+	0.542436i	$0.182498\pi$
$488$	0.755503	+	0.485532i	0.0342000	+	0.0219790i
$489$	−4.65991	−	3.15517i	−0.210728	−	0.142682i
$490$	8.50497	−	1.22283i	0.384215	−	0.0552418i
$491$	11.1713	−	38.0460i	0.504155	−	1.71699i	−0.176421	−	0.984315i	$-0.556452\pi$
$491$	11.1713	−	38.0460i	0.504155	−	1.71699i	0.680575	−	0.732678i	$-0.261730\pi$
$492$	8.89514	+	8.08920i	0.401024	+	0.364690i
$493$	−1.49205	−	0.214525i	−0.0671986	−	0.00966170i
$494$	0.764663	−	1.67438i	0.0344038	−	0.0753338i
$495$	−2.22322	−	23.3734i	−0.0999262	−	1.05056i
$496$	−1.37234	+	9.54487i	−0.0616201	+	0.428577i
$497$	−16.7796	+	10.7836i	−0.752669	+	0.483711i
$498$	−0.347649	+	14.4924i	−0.0155785	+	0.649420i
$499$	3.82362	+	26.5938i	0.171169	+	1.19050i	0.876420	+	0.481547i	$0.159925\pi$
$499$	3.82362	+	26.5938i	0.171169	+	1.19050i	−0.705252	+	0.708957i	$0.749166\pi$
$500$	−7.80387	−	9.00614i	−0.349000	−	0.402767i
$501$	−5.76341	+	18.0181i	−0.257490	+	0.804989i
$502$	−5.32385	−	4.61314i	−0.237615	−	0.205894i
$503$	−34.7185	+	10.1943i	−1.54802	+	0.454541i	−0.940509	−	0.339768i	$-0.889651\pi$
$503$	−34.7185	+	10.1943i	−1.54802	+	0.454541i	−0.607514	+	0.794309i	$0.707833\pi$
$504$	−4.07533	−	2.90429i	−0.181530	−	0.129367i
$505$		−	3.60806i		−	0.160557i
$506$	−13.8185	−	12.1837i	−0.614305	−	0.541632i
$507$	−7.35587	+	1.96955i	−0.326686	+	0.0874708i
$508$	3.66827	+	8.03239i	0.162753	+	0.356379i
$509$	1.79366	+	6.10863i	0.0795024	+	0.270760i	0.989645	−	0.143534i	$-0.0458466\pi$
$509$	1.79366	+	6.10863i	0.0795024	+	0.270760i	−0.910143	+	0.414294i	$0.864028\pi$
$510$	−2.79630	−	1.35899i	−0.123822	−	0.0601772i
$511$	−7.50418	+	11.6767i	−0.331965	+	0.516548i
$512$	0.755750	−	0.654861i	0.0333997	−	0.0289410i
$513$	1.37527	−	1.83503i	0.0607195	−	0.0810185i
$514$	−7.87087	−	2.31110i	−0.347169	−	0.101938i
$515$	−0.473700	−	0.737092i	−0.0208737	−	0.0324801i
$516$	13.5140	−	1.61327i	0.594919	−	0.0710203i
$517$	−35.0094	−	15.9882i	−1.53971	−	0.703162i
$518$	−4.84065	−	2.21065i	−0.212686	−	0.0971304i
$519$	7.87130	−	0.939661i	0.345512	−	0.0412465i
$520$	−4.59419	−	7.14870i	−0.201469	−	0.313491i
$521$	−8.35959	−	2.45460i	−0.366240	−	0.107538i	0.0934339	−	0.995625i	$-0.470216\pi$
$521$	−8.35959	−	2.45460i	−0.366240	−	0.107538i	−0.459674	+	0.888088i	$0.652034\pi$
$522$	−3.17138	−	4.03580i	−0.138808	−	0.176642i
$523$	−33.7641	+	29.2567i	−1.47640	+	1.27931i	−0.597894	+	0.801575i	$0.703996\pi$
$523$	−33.7641	+	29.2567i	−1.47640	+	1.27931i	−0.878506	+	0.477732i	$0.841459\pi$
$524$	8.01799	−	12.4762i	0.350268	−	0.545027i
$525$	2.20657	+	1.07239i	0.0963028	+	0.0468029i
$526$	0.952298	+	3.24323i	0.0415222	+	0.141412i
$527$	−3.52932	−	7.72814i	−0.153740	−	0.336643i
$528$	−6.42707	+	1.72086i	−0.279702	+	0.0748909i
$529$	−2.88060	−	22.8189i	−0.125243	−	0.992126i
$530$		−	28.2350i		−	1.22645i
$531$	−15.9693	+	22.4083i	−0.693008	+	0.972437i
$532$	−0.706354	+	0.207404i	−0.0306243	+	0.00899212i
$533$	−21.8812	−	18.9601i	−0.947779	−	0.821255i
$534$	−2.71938	+	8.50158i	−0.117679	+	0.367900i
$535$	−24.3963	−	28.1548i	−1.05474	−	1.21724i
$536$	1.79119	+	12.4580i	0.0773676	+	0.538104i
$537$	0.250162	−	10.4284i	0.0107953	−	0.450021i
$538$	−9.12280	+	5.86287i	−0.393312	+	0.252766i
$539$	−2.30560	+	16.0358i	−0.0993092	+	0.690711i
$540$	−3.69412	−	9.92103i	−0.158970	−	0.426933i
$541$	−17.2729	+	37.8224i	−0.742620	+	1.62611i	0.0365772	+	0.999331i	$0.488355\pi$
$541$	−17.2729	+	37.8224i	−0.742620	+	1.62611i	−0.779197	+	0.626779i	$0.784373\pi$
$542$	18.8727	+	2.71349i	0.810653	+	0.116554i
$543$	−24.4779	−	22.2601i	−1.05045	−	0.955272i
$544$	−0.248218	+	0.845353i	−0.0106423	+	0.0362442i
$545$	20.5422	−	2.95352i	0.879929	−	0.126515i
$546$	9.97862	+	6.75640i	0.427045	+	0.289147i
$547$	−16.5886	−	10.6608i	−0.709277	−	0.455825i	0.135615	−	0.990762i	$-0.456699\pi$
$547$	−16.5886	−	10.6608i	−0.709277	−	0.455825i	−0.844892	+	0.534937i	$0.820335\pi$
$548$	12.0372	−	13.8917i	0.514205	−	0.593425i
$549$	−1.94920	−	1.85993i	−0.0831900	−	0.0793799i
$550$	2.96708	−	1.35502i	0.126517	−	0.0577783i
$551$	−0.755070			−0.0321671
$552$	−7.43949	−	3.69512i	−0.316646	−	0.157275i
$553$	−16.3077			−0.693476
$554$	−13.2502	+	6.05117i	−0.562948	+	0.257090i
$555$	−5.85742	−	9.61369i	−0.248634	−	0.408078i
$556$	−4.96460	+	5.72946i	−0.210546	+	0.242983i
$557$	−31.4533	−	20.2138i	−1.33272	−	0.856486i	−0.336359	−	0.941734i	$-0.609196\pi$
$557$	−31.4533	−	20.2138i	−1.33272	−	0.856486i	−0.996360	+	0.0852475i	$0.972832\pi$
$558$	9.47182	−	27.3345i	0.400974	−	1.15716i
$559$	−32.4401	+	4.66419i	−1.37207	+	0.197274i
$560$	−0.957481	+	3.26088i	−0.0404610	+	0.137797i
$561$	3.94392	−	4.33685i	0.166512	−	0.183102i
$562$	−19.2336	−	2.76538i	−0.811321	−	0.116650i
$563$	−3.17326	+	6.94846i	−0.133737	+	0.292843i	−0.964639	−	0.263576i	$-0.915098\pi$
$563$	−3.17326	+	6.94846i	−0.133737	+	0.292843i	0.830902	+	0.556419i	$0.187825\pi$
$564$	−17.1129	−	2.88091i	−0.720582	−	0.121308i
$565$	−0.971269	+	6.75532i	−0.0408616	+	0.284199i
$566$	14.0538	−	9.03181i	0.590724	−	0.379635i
$567$	10.3521	+	10.8730i	0.434749	+	0.456624i
$568$	1.70169	+	11.8355i	0.0714015	+	0.496609i
$569$	27.0015	+	31.1614i	1.13196	+	1.30635i	0.946136	+	0.323771i	$0.104951\pi$
$569$	27.0015	+	31.1614i	1.13196	+	1.30635i	0.185826	+	0.982583i	$0.440504\pi$
$570$	−1.48332	−	0.474465i	−0.0621293	−	0.0198732i
$571$	1.54189	+	1.33605i	0.0645259	+	0.0559120i	0.686527	−	0.727105i	$-0.259134\pi$
$571$	1.54189	+	1.33605i	0.0645259	+	0.0559120i	−0.622001	+	0.783017i	$0.713680\pi$
$572$	15.3731	−	4.51394i	0.642780	−	0.188737i
$573$	1.29248	+	1.56596i	0.0539942	+	0.0654190i
$574$			11.5794i			0.483314i
$575$	3.89733	+	1.18091i	0.162530	+	0.0492475i
$576$	−2.59863	+	1.49904i	−0.108276	+	0.0624602i
$577$	−12.0530	−	26.3923i	−0.501772	−	1.09873i	−0.975889	−	0.218266i	$-0.929960\pi$
$577$	−12.0530	−	26.3923i	−0.501772	−	1.09873i	0.474117	−	0.880462i	$-0.342767\pi$
$578$	4.57076	+	15.5666i	0.190119	+	0.647485i
$579$	7.80316	−	16.0560i	0.324288	−	0.667263i
$580$	−1.88455	+	2.93242i	−0.0782518	+	0.121762i
$581$	−10.5513	+	9.14276i	−0.437742	+	0.379306i
$582$	−7.32503	−	17.1143i	−0.303632	−	0.709409i
$583$	51.0797	+	14.9984i	2.11550	+	0.621168i
$584$	4.49862	+	6.99999i	0.186154	+	0.289662i
$585$	9.46610	+	23.6704i	0.391375	+	0.978651i
$586$	25.5922	+	11.6876i	1.05720	+	0.482809i
$587$	15.3411	+	7.00603i	0.633194	+	0.289170i	0.706039	−	0.708173i	$-0.250480\pi$
$587$	15.3411	+	7.00603i	0.633194	+	0.289170i	−0.0728447	+	0.997343i	$0.523208\pi$
$588$	0.865883	+	7.25328i	0.0357084	+	0.299120i
$589$	−2.30080	−	3.58011i	−0.0948028	−	0.147516i
$590$	17.9300	+	5.26473i	0.738167	+	0.216745i
$591$	−36.7245	+	15.7184i	−1.51064	+	0.646567i
$592$	−2.41097	+	2.08912i	−0.0990903	+	0.0858622i
$593$	−9.30879	+	14.4848i	−0.382266	+	0.594818i	−0.978061	−	0.208319i	$-0.933201\pi$
$593$	−9.30879	+	14.4848i	−0.382266	+	0.594818i	0.595795	+	0.803137i	$0.296837\pi$
$594$	19.9103	−	1.41298i	0.816930	−	0.0579752i
$595$	−0.843581	−	2.87297i	−0.0345834	−	0.117780i
$596$	−2.89272	−	6.33417i	−0.118490	−	0.259458i
$597$	0.525180	+	1.96144i	0.0214942	+	0.0802764i
$598$	18.1231	+	8.46596i	0.741109	+	0.346199i
$599$		−	11.8946i		−	0.485999i	−0.970026	−	0.242999i	$-0.921869\pi$
$599$		−	11.8946i		−	0.485999i	0.970026	−	0.242999i	$-0.0781313\pi$
$600$	1.13429	−	0.936201i	0.0463073	−	0.0382202i
$601$	0.134686	−	0.0395473i	0.00549395	−	0.00161317i	−0.278984	−	0.960296i	$-0.589998\pi$
$601$	0.134686	−	0.0395473i	0.00549395	−	0.00161317i	0.284478	+	0.958682i	$0.408180\pi$
$602$	9.90596	+	8.58356i	0.403737	+	0.349840i
$603$	1.81048	−	37.7149i	0.0737285	−	1.53587i
$604$	3.41092	+	3.93641i	0.138788	+	0.160170i
$605$	−1.08910	−	7.57486i	−0.0442782	−	0.307962i
$606$	3.06648	+	0.0735600i	0.124567	+	0.00298817i
$607$	9.04478	−	5.81273i	0.367116	−	0.235931i	−0.344056	−	0.938949i	$-0.611801\pi$
$607$	9.04478	−	5.81273i	0.367116	−	0.235931i	0.711172	+	0.703018i	$0.248165\pi$
$608$	−0.0628068	+	0.436831i	−0.00254715	+	0.0177158i
$609$	0.820640	−	4.87469i	0.0332540	−	0.197532i
$610$	−0.760083	+	1.66435i	−0.0307749	+	0.0673875i
$611$	41.3637	+	5.94720i	1.67339	+	0.240598i
$612$	1.21201	−	2.34886i	0.0489927	−	0.0949469i
$613$	−11.0077	+	37.4887i	−0.444596	+	1.51415i	0.367160	+	0.930158i	$0.380330\pi$
$613$	−11.0077	+	37.4887i	−0.444596	+	1.51415i	−0.811756	+	0.583996i	$0.801488\pi$
$614$	18.3124	−	2.63292i	0.739027	−	0.106256i
$615$	−13.7338	+	20.2836i	−0.553800	+	0.817916i
$616$	−5.39061	−	3.46434i	−0.217194	−	0.139582i
$617$	17.9751	−	20.7444i	0.723651	−	0.835138i	−0.268090	−	0.963394i	$-0.586392\pi$
$617$	17.9751	−	20.7444i	0.723651	−	0.835138i	0.991741	+	0.128256i	$0.0409379\pi$
$618$	0.636110	−	0.387569i	0.0255881	−	0.0155903i
$619$	19.9479	−	9.10991i	0.801774	−	0.366158i	0.0279907	−	0.999608i	$-0.491089\pi$
$619$	19.9479	−	9.10991i	0.801774	−	0.366158i	0.773783	+	0.633450i	$0.218362\pi$
$620$	−19.6464			−0.789017
$621$	19.8117	+	15.1161i	0.795015	+	0.606589i
$622$	−13.9873			−0.560840
$623$	−7.81955	+	3.57107i	−0.313284	+	0.143072i
$624$	6.16933	−	3.75885i	0.246971	−	0.150474i
$625$	13.1190	−	15.1402i	0.524761	−	0.605606i
$626$	−20.5836	−	13.2283i	−0.822687	−	0.528709i
$627$	1.64628	−	2.43142i	0.0657461	−	0.0971014i
$628$	14.4779	−	2.08161i	0.577731	−	0.0830652i
$629$	0.791858	−	2.69682i	0.0315734	−	0.107529i
$630$	4.67525	−	9.06053i	0.186266	−	0.360980i
$631$	−4.22246	−	0.607099i	−0.168094	−	0.0241682i	0.0577540	−	0.998331i	$-0.481606\pi$
$631$	−4.22246	−	0.607099i	−0.168094	−	0.0241682i	−0.225848	+	0.974163i	$0.572515\pi$
$632$	−4.06118	+	8.89274i	−0.161545	+	0.353734i
$633$	−2.42870	+	14.4267i	−0.0965322	+	0.573411i
$634$	−0.647032	+	4.50021i	−0.0256969	+	0.178726i
$635$	−15.1347	+	9.72651i	−0.600604	+	0.385985i
$636$	23.9969	+	0.575647i	0.951539	+	0.0228259i
$637$	−2.50339	−	17.4114i	−0.0991878	−	0.689866i
$638$	−4.30394	−	4.96702i	−0.170395	−	0.196646i
$639$	1.72002	−	35.8305i	0.0680430	−	1.41743i
$640$	1.53974	+	1.33419i	0.0608635	+	0.0527386i
$641$	3.37742	−	0.991701i	0.133400	−	0.0391698i	−0.214351	−	0.976757i	$-0.568764\pi$
$641$	3.37742	−	0.991701i	0.133400	−	0.0391698i	0.347751	+	0.937587i	$0.386945\pi$
$642$	24.4261	−	20.1603i	0.964020	−	0.795664i
$643$		−	13.6466i		−	0.538169i	−0.963117	−	0.269084i	$-0.913279\pi$
$643$		−	13.6466i		−	0.538169i	0.963117	−	0.269084i	$-0.0867210\pi$
$644$	−2.18765	−	7.69504i	−0.0862056	−	0.303227i
$645$	7.17171	+	26.7849i	0.282386	+	1.05465i
$646$	−0.161523	−	0.353687i	−0.00635505	−	0.0139156i
$647$	−0.117428	−	0.399925i	−0.00461659	−	0.0157227i	0.957152	−	0.289584i	$-0.0935171\pi$
$647$	−0.117428	−	0.399925i	−0.00461659	−	0.0157227i	−0.961769	+	0.273862i	$0.911699\pi$
$648$	8.50717	−	2.93736i	0.334193	−	0.115390i
$649$	−19.0487	+	29.6404i	−0.747727	+	1.16349i
$650$	−2.67662	+	2.31930i	−0.104985	+	0.0909704i
$651$	25.6136	−	10.9628i	1.00388	−	0.429666i
$652$	−3.11748	−	0.915375i	−0.122090	−	0.0358489i
$653$	15.5441	+	24.1872i	0.608289	+	0.946516i	0.999655	+	0.0262811i	$0.00836650\pi$
$653$	15.5441	+	24.1872i	0.608289	+	0.946516i	−0.391365	+	0.920235i	$0.627997\pi$
$654$	2.09138	+	17.5189i	0.0817794	+	0.685045i
$655$	27.4848	+	12.5519i	1.07392	+	0.490442i
$656$	6.31433	+	2.88366i	0.246533	+	0.112588i
$657$	−9.26918	−	23.1780i	−0.361625	−	0.904260i
$658$	−9.03575	−	14.0599i	−0.352250	−	0.548112i
$659$	3.19255	+	0.937416i	0.124364	+	0.0365166i	0.343322	−	0.939218i	$-0.388448\pi$
$659$	3.19255	+	0.937416i	0.124364	+	0.0365166i	−0.218958	+	0.975734i	$0.570266\pi$
$660$	−5.33385	−	12.4621i	−0.207620	−	0.485085i
$661$	3.28355	−	2.84521i	0.127715	−	0.110666i	−0.588661	−	0.808380i	$-0.700345\pi$
$661$	3.28355	−	2.84521i	0.127715	−	0.110666i	0.716377	+	0.697714i	$0.245799\pi$
$662$	−5.20615	+	8.10093i	−0.202343	+	0.314852i
$663$	−2.78214	+	5.72460i	−0.108049	+	0.222325i
$664$	2.35799	+	8.03057i	0.0915076	+	0.311646i
$665$	−0.623063	−	1.36432i	−0.0241614	−	0.0529060i
$666$	8.29007	−	4.78221i	0.321234	−	0.185307i
$667$	0.0706739	−	8.20499i	0.00273651	−	0.317699i
$668$			10.9220i			0.422584i
$669$	19.5708	+	23.7118i	0.756652	+	0.916753i
$670$	−24.6038	+	7.22433i	−0.950529	+	0.279100i
$671$	−2.60720	−	2.25915i	−0.100650	−	0.0872136i
$672$	−2.75189	−	0.880243i	−0.106157	−	0.0339561i
$673$	19.0548	+	21.9904i	0.734507	+	0.847666i	0.992971	−	0.118355i	$-0.0377620\pi$
$673$	19.0548	+	21.9904i	0.734507	+	0.847666i	−0.258465	+	0.966021i	$0.583217\pi$
$674$	−0.256094	−	1.78118i	−0.00986439	−	0.0686083i
$675$	−3.87369	+	2.11242i	−0.149099	+	0.0813072i
$676$	−3.69858	+	2.37693i	−0.142253	+	0.0914205i
$677$	−3.75205	+	26.0961i	−0.144203	+	1.00295i	0.781284	+	0.624175i	$0.214565\pi$
$677$	−3.75205	+	26.0961i	−0.144203	+	1.00295i	−0.925487	+	0.378778i	$0.876344\pi$
$678$	−5.72153	−	0.963204i	−0.219734	−	0.0369916i
$679$	7.44785	−	16.3085i	0.285822	−	0.625864i
$680$	−1.77673	−	0.255456i	−0.0681347	−	0.00979628i
$681$	−14.8980	+	16.3823i	−0.570894	+	0.627773i
$682$	10.4361	−	35.5420i	0.399618	−	1.36097i
$683$	21.9463	−	3.15541i	0.839753	−	0.120738i	0.291000	−	0.956723i	$-0.406012\pi$
$683$	21.9463	−	3.15541i	0.839753	−	0.120738i	0.548753	+	0.835985i	$0.315103\pi$
$684$	0.433488	−	1.25099i	0.0165748	−	0.0478329i
$685$	31.5046	+	20.2468i	1.20373	+	0.773590i
$686$	−12.2537	+	14.1415i	−0.467847	+	0.539924i
$687$	6.79792	+	11.1573i	0.259357	+	0.425678i
$688$	7.14760	−	3.26420i	0.272500	−	0.124446i
$689$	−57.8030			−2.20212
$690$	5.29463	−	16.0741i	0.201563	−	0.611930i
$691$	−16.1928			−0.616002			−0.308001	−	0.951386i	$-0.599660\pi$
$691$	−16.1928			−0.616002			−0.308001	+	0.951386i	$0.599660\pi$
$692$	4.16317	−	1.90126i	0.158260	−	0.0722749i
$693$	13.9078	+	13.2708i	0.528315	+	0.504118i
$694$	14.9962	−	17.3066i	0.569250	−	0.656949i
$695$	−12.9937	−	8.35053i	−0.492878	−	0.316753i
$696$	−2.45384	−	1.66146i	−0.0930124	−	0.0629776i
$697$	−6.05361	+	0.870378i	−0.229297	+	0.0329679i
$698$	2.63911	−	8.98800i	0.0998919	−	0.340201i
$699$	2.48477	+	2.25964i	0.0939826	+	0.0854674i
$700$	1.40203	+	0.201582i	0.0529918	+	0.00761907i
$701$	12.9680	−	28.3960i	0.489796	−	1.07250i	−0.489856	−	0.871803i	$-0.662951\pi$
$701$	12.9680	−	28.3960i	0.489796	−	1.07250i	0.979653	−	0.200701i	$-0.0643219\pi$
$702$	−20.3104	+	7.56263i	−0.766567	+	0.285433i
$703$	0.200365	−	1.39357i	0.00755689	−	0.0525593i
$704$	−3.23157	+	2.07681i	−0.121795	+	0.0782726i
$705$	0.847885	−	35.3457i	0.0319332	−	1.33119i
$706$	2.43466	+	16.9334i	0.0916295	+	0.637297i
$707$	1.93454	+	2.23258i	0.0727559	+	0.0839648i
$708$	−4.84003	+	15.1313i	−0.181899	+	0.568670i
$709$	−20.2250	−	17.5251i	−0.759567	−	0.658168i	0.186385	−	0.982477i	$-0.440323\pi$
$709$	−20.2250	−	17.5251i	−0.759567	−	0.658168i	−0.945951	+	0.324308i	$0.894868\pi$
$710$	−23.3745	+	6.86338i	−0.877230	+	0.257578i
$711$	17.0210	−	23.8841i	0.638338	−	0.895724i
$712$			5.15338i			0.193131i
$713$	39.1188	−	24.6666i	1.46501	−	0.923772i
$714$	2.45893	−	0.658384i	0.0920231	−	0.0246394i
$715$	13.5603	+	29.6929i	0.507127	+	1.11045i
$716$	−1.69676	−	5.77864i	−0.0634110	−	0.215958i
$717$	21.2802	+	10.3421i	0.794723	+	0.386233i
$718$	2.46996	−	3.84333i	0.0921779	−	0.143432i
$719$	6.18311	−	5.35770i	0.230591	−	0.199808i	−0.531900	−	0.846807i	$-0.678522\pi$
$719$	6.18311	−	5.35770i	0.230591	−	0.199808i	0.762491	+	0.646999i	$0.223976\pi$
$720$	−3.77648	−	4.80583i	−0.140741	−	0.179103i
$721$	0.688321	+	0.202109i	0.0256344	+	0.00752694i
$722$	10.1669	+	15.8200i	0.378372	+	0.588758i
$723$	−48.0933	+	5.74130i	−1.78861	+	0.213521i
$724$	−17.3759	−	7.93533i	−0.645772	−	0.294914i
$725$	1.32152	+	0.603517i	0.0490799	+	0.0224141i
$726$	6.46005	−	0.771189i	0.239755	−	0.0286215i
$727$	−20.3825	−	31.7158i	−0.755945	−	1.17627i	−0.979473	−	0.201576i	$-0.935394\pi$
$727$	−20.3825	−	31.7158i	−0.755945	−	1.17627i	0.223527	−	0.974698i	$-0.428243\pi$
$728$	6.67570	+	1.96016i	0.247418	+	0.0726485i
$729$	−26.7294	+	3.81302i	−0.989978	+	0.141223i
$730$	−12.8120	+	11.1017i	−0.474194	+	0.410892i
$731$	−3.74283	+	5.82395i	−0.138433	+	0.215407i
$732$	−1.39903	−	0.679924i	−0.0517096	−	0.0251307i
$733$	−3.67525	−	12.5167i	−0.135748	−	0.462317i	0.863358	−	0.504593i	$-0.168357\pi$
$733$	−3.67525	−	12.5167i	−0.135748	−	0.462317i	−0.999106	+	0.0422760i	$0.986539\pi$
$734$	−4.27775	−	9.36697i	−0.157895	−	0.345741i
$735$	−14.3761	+	3.84924i	−0.530271	+	0.141981i
$736$	−4.74096	−	0.723380i	−0.174754	−	0.0266641i
$737$		−	48.3480i		−	1.78092i
$738$	−16.9590	−	12.0859i	−0.624270	−	0.444887i
$739$	1.05746	−	0.310498i	0.0388993	−	0.0114219i	−0.262225	−	0.965007i	$-0.584456\pi$
$739$	1.05746	−	0.310498i	0.0388993	−	0.0114219i	0.301124	+	0.953585i	$0.402638\pi$
$740$	−4.91203	−	4.25630i	−0.180570	−	0.156465i
$741$	−0.971329	+	3.03666i	−0.0356827	+	0.111554i
$742$	15.1388	+	17.4711i	0.555764	+	0.641386i
$743$	−1.58877	−	11.0501i	−0.0582862	−	0.405389i	−0.997988	−	0.0633956i	$-0.979807\pi$
$743$	−1.58877	−	11.0501i	−0.0582862	−	0.405389i	0.939702	−	0.341993i	$-0.111102\pi$
$744$	0.400544	−	16.6974i	0.0146846	−	0.612156i
$745$	11.9349	−	7.67012i	0.437262	−	0.281011i
$746$	−4.61444	+	32.0941i	−0.168947	+	1.17505i
$747$	−2.37755	−	24.9960i	−0.0869900	−	0.914554i
$748$	1.40594	−	3.07857i	0.0514061	−	0.112564i
$749$	30.1916	+	4.34090i	1.10318	+	0.158613i
$750$	15.2705	+	13.8869i	0.557598	+	0.507078i
$751$	0.416654	−	1.41899i	0.0152039	−	0.0517797i	−0.951542	−	0.307520i	$-0.900501\pi$
$751$	0.416654	−	1.41899i	0.0152039	−	0.0517797i	0.966746	+	0.255740i	$0.0823191\pi$
$752$	−9.91718	+	1.42587i	−0.361642	+	0.0519963i
$753$	10.1033	+	6.84081i	0.368184	+	0.249293i
$754$	6.00328	+	3.85807i	0.218626	+	0.140503i
$755$	−6.94930	+	8.01992i	−0.252911	+	0.291875i
$756$	7.60520	+	4.15820i	0.276598	+	0.151232i
$757$	−31.2048	+	14.2508i	−1.13416	+	0.517952i	−0.891888	−	0.452257i	$-0.850619\pi$
$757$	−31.2048	+	14.2508i	−1.13416	+	0.517952i	−0.242270	+	0.970209i	$0.577892\pi$
$758$	−3.92003			−0.142382
$759$	26.2670	+	18.1170i	0.953431	+	0.657604i
$760$	−0.899137			−0.0326151
$761$	−24.7421	+	11.2993i	−0.896901	+	0.409601i	−0.809873	−	0.586605i	$-0.800464\pi$
$761$	−24.7421	+	11.2993i	−0.896901	+	0.409601i	−0.0870278	+	0.996206i	$0.527737\pi$
$762$	−7.95797	−	13.0613i	−0.288287	−	0.473160i
$763$	−11.1274	+	12.8417i	−0.402838	+	0.464900i
$764$	0.986188	+	0.633784i	0.0356790	+	0.0229295i
$765$	5.08820	+	1.76314i	0.183964	+	0.0637463i
$766$	4.96010	−	0.713155i	0.179216	−	0.0257673i
$767$	10.7780	−	36.7065i	0.389171	−	1.32539i
$768$	−1.16532	+	1.28142i	−0.0420498	+	0.0462392i
$769$	5.83379	+	0.838772i	0.210372	+	0.0302469i	0.246695	−	0.969093i	$-0.420655\pi$
$769$	5.83379	+	0.838772i	0.210372	+	0.0302469i	−0.0363231	+	0.999340i	$0.511565\pi$
$770$	5.42329	−	11.8753i	0.195442	−	0.427958i
$771$	14.0111	+	2.35874i	0.504598	+	0.0849478i
$772$	1.46679	−	10.2018i	0.0527911	−	0.367170i
$773$	−8.81363	+	5.66417i	−0.317004	+	0.203726i	−0.689460	−	0.724324i	$-0.742152\pi$
$773$	−8.81363	+	5.66417i	−0.317004	+	0.203726i	0.372456	+	0.928050i	$0.378516\pi$
$774$	−22.9106	+	5.54913i	−0.823505	+	0.199459i
$775$	1.16531	+	8.10489i	0.0418590	+	0.291136i
$776$	−7.03840	−	8.12275i	−0.252664	−	0.291590i
$777$	8.77901	+	2.80812i	0.314945	+	0.100741i
$778$	17.7075	+	15.3436i	0.634843	+	0.550094i
$779$	−2.93941	+	0.863089i	−0.105315	+	0.0309234i
$780$	9.36898	+	11.3514i	0.335463	+	0.406445i
$781$		−	45.9324i		−	1.64359i
$782$	3.85847	−	1.72209i	0.137979	−	0.0615820i
$783$	6.28286	+	6.28980i	0.224531	+	0.224779i
$784$	1.75198	+	3.83630i	0.0625707	+	0.137011i
$785$	8.39566	+	28.5930i	0.299654	+	1.02053i
$786$	−11.2281	+	23.1033i	−0.400495	+	0.824068i
$787$	5.12854	−	7.98016i	0.182813	−	0.284462i	−0.737737	−	0.675089i	$-0.764105\pi$
$787$	5.12854	−	7.98016i	0.182813	−	0.284462i	0.920549	+	0.390627i	$0.127742\pi$
$788$	−17.4301	+	15.1033i	−0.620922	+	0.538032i
$789$	−2.30367	−	5.38232i	−0.0820129	−	0.191616i
$790$	−19.1109	−	5.61146i	−0.679935	−	0.199647i
$791$	−3.02102	−	4.70079i	−0.107415	−	0.167141i
$792$	10.7002	−	4.27916i	0.380216	−	0.152053i
$793$	3.40727	+	1.55605i	0.120996	+	0.0552568i
$794$	14.7470	+	6.73475i	0.523353	+	0.239007i
$795$	5.79697	+	48.5597i	0.205597	+	1.72224i
$796$	0.633808	+	0.986225i	0.0224647	+	0.0349558i
$797$	−3.82588	−	1.12338i	−0.135520	−	0.0397922i	0.213269	−	0.976993i	$-0.431589\pi$
$797$	−3.82588	−	1.12338i	−0.135520	−	0.0397922i	−0.348789	+	0.937201i	$0.613407\pi$
$798$	1.17223	−	0.501725i	0.0414966	−	0.0177609i
$799$	6.67122	−	5.78065i	0.236011	−	0.204505i
$800$	0.459077	−	0.714338i	0.0162308	−	0.0252557i
$801$	2.93143	−	15.1797i	0.103577	−	0.536348i
$802$	−9.79515	−	33.3592i	−0.345879	−	1.17795i
$803$	−13.2782	−	29.0753i	−0.468578	−	1.02604i
$804$	−5.63833	−	21.0580i	−0.198848	−	0.742659i
$805$	14.8837	−	6.64284i	0.524583	−	0.234129i
$806$			40.2202i			1.41670i
$807$	14.4860	−	11.9562i	0.509933	−	0.420878i
$808$	1.69921	−	0.498933i	0.0597780	−	0.0175524i
$809$	11.2648	+	9.76098i	0.396048	+	0.343178i	0.830005	−	0.557756i	$-0.188337\pi$
$809$	11.2648	+	9.76098i	0.396048	+	0.343178i	−0.433957	+	0.900934i	$0.642883\pi$
$810$	8.39019	+	16.3041i	0.294801	+	0.572869i
$811$	31.5368	+	36.3954i	1.10741	+	1.27802i	0.957221	+	0.289358i	$0.0934418\pi$
$811$	31.5368	+	36.3954i	1.10741	+	1.27802i	0.150186	+	0.988658i	$0.452013\pi$
$812$	−0.406167	−	2.82495i	−0.0142537	−	0.0991364i
$813$	−33.0152	−	0.791981i	−1.15789	−	0.0277760i
$814$	10.3093	−	6.62537i	0.361340	−	0.232219i
$815$	0.942067	−	6.55222i	0.0329992	−	0.229514i
$816$	0.253335	−	1.50483i	0.00886849	−	0.0526797i
$817$	−1.44057	+	3.15440i	−0.0503991	+	0.110359i
$818$	−20.6505	−	2.96909i	−0.722026	−	0.103812i
$819$	−18.5488	−	9.57120i	−0.648147	−	0.334445i
$820$	−3.98445	+	13.5698i	−0.139143	+	0.473877i
$821$	−21.7358	+	3.12513i	−0.758584	+	0.109068i	−0.510744	−	0.859733i	$-0.670630\pi$
$821$	−21.7358	+	3.12513i	−0.758584	+	0.109068i	−0.247840	+	0.968801i	$0.579721\pi$
$822$	−17.8500	+	26.3629i	−0.622590	+	0.919512i
$823$	−2.81510	−	1.80916i	−0.0981282	−	0.0630632i	0.490656	−	0.871353i	$-0.336757\pi$
$823$	−2.81510	−	1.80916i	−0.0981282	−	0.0630632i	−0.588785	+	0.808290i	$0.700393\pi$
$824$	0.281627	−	0.325015i	0.00981094	−	0.0113224i
$825$	−4.82471	+	2.93960i	−0.167975	+	0.102344i
$826$	−13.9174	+	6.35588i	−0.484250	+	0.221149i
$827$	25.5724			0.889240			0.444620	−	0.895719i	$-0.353339\pi$
$827$	25.5724			0.889240			0.444620	+	0.895719i	$0.353339\pi$
$828$	13.5534	+	4.82760i	0.471013	+	0.167771i
$829$	−15.2088			−0.528223			−0.264111	−	0.964492i	$-0.585079\pi$
$829$	−15.2088			−0.528223			−0.264111	+	0.964492i	$0.585079\pi$
$830$	−15.5110	+	7.08363i	−0.538394	+	0.245876i
$831$	21.5459	−	13.1275i	0.747418	−	0.455387i
$832$	2.73137	−	3.15217i	0.0946931	−	0.109282i
$833$	−3.12586	−	2.00887i	−0.108305	−	0.0696032i
$834$	7.36200	−	10.8730i	0.254925	−	0.376503i
$835$	−22.0256	+	3.16680i	−0.762226	+	0.109592i
$836$	0.477618	−	1.62662i	0.0165188	−	0.0562578i
$837$	−10.6779	+	48.9556i	−0.369083	+	1.69215i
$838$	−12.4141	−	1.78488i	−0.428839	−	0.0616577i
$839$	−16.0344	+	35.1104i	−0.553569	+	1.21215i	0.401526	+	0.915848i	$0.368480\pi$
$839$	−16.0344	+	35.1104i	−0.553569	+	1.21215i	−0.955095	+	0.296300i	$0.904247\pi$
$840$	0.977218	−	5.80477i	0.0337172	−	0.200284i
$841$	−3.71054	+	25.8074i	−0.127950	+	0.889909i
$842$	−12.7661	+	8.20429i	−0.439949	+	0.282738i
$843$	33.6465	+	0.807125i	1.15885	+	0.0277989i
$844$	1.20206	+	8.36050i	0.0413766	+	0.287780i
$845$	−5.86579	−	6.76948i	−0.201789	−	0.232877i
$846$	30.0229	+	1.44123i	1.03221	+	0.0495505i
$847$	4.73533	+	4.10319i	0.162708	+	0.140987i
$848$	13.2972	−	3.90442i	0.456629	−	0.134078i
$849$	−22.3159	+	18.4187i	−0.765879	+	0.632127i
$850$			0.748123i			0.0256604i
$851$	15.1245	+	2.30770i	0.518460	+	0.0791071i
$852$	−5.35661	−	20.0059i	−0.183515	−	0.685390i
$853$	−4.77807	−	10.4625i	−0.163598	−	0.358230i	0.810024	−	0.586397i	$-0.199454\pi$
$853$	−4.77807	−	10.4625i	−0.163598	−	0.358230i	−0.973622	+	0.228167i	$0.926727\pi$
$854$	−0.422056	−	1.43739i	−0.0144425	−	0.0491865i
$855$	2.64848	+	0.511462i	0.0905761	+	0.0174916i
$856$	9.88585	−	15.3827i	0.337891	−	0.525769i
$857$	19.1347	−	16.5803i	0.653630	−	0.566374i	−0.263649	−	0.964619i	$-0.584926\pi$
$857$	19.1347	−	16.5803i	0.653630	−	0.566374i	0.917279	+	0.398245i	$0.130381\pi$
$858$	−25.5124	+	10.9195i	−0.870980	+	0.372786i
$859$	−28.7048	−	8.42850i	−0.979397	−	0.287577i	−0.247421	−	0.968908i	$-0.579583\pi$
$859$	−28.7048	−	8.42850i	−0.979397	−	0.287577i	−0.731975	+	0.681331i	$0.761401\pi$
$860$	8.65511	+	13.4676i	0.295137	+	0.459242i
$861$	−2.37738	−	19.9147i	−0.0810208	−	0.678691i
$862$	−15.7245	−	7.18113i	−0.535578	−	0.244590i
$863$	23.4783	+	10.7222i	0.799210	+	0.364987i	0.772788	−	0.634664i	$-0.218862\pi$
$863$	23.4783	+	10.7222i	0.799210	+	0.364987i	0.0264215	+	0.999651i	$0.491589\pi$
$864$	4.16145	−	3.11164i	0.141575	−	0.105860i
$865$	5.04123	+	7.84431i	0.171407	+	0.266714i
$866$	−29.1231	−	8.55132i	−0.989644	−	0.290586i
$867$	−11.0570	−	25.8336i	−0.375515	−	0.877355i
$868$	12.1567	−	10.5338i	0.412625	−	0.357541i
$869$	20.3033	−	31.5925i	0.688741	−	1.07170i
$870$	2.63907	−	5.43022i	0.0894729	−	0.184102i
$871$	14.7897	+	50.3691i	0.501130	+	1.70669i
$872$	4.23158	+	9.26586i	0.143299	+	0.313782i
$873$	16.1116	+	27.9299i	0.545296	+	0.945283i
$874$	1.79031	−	1.12889i	0.0605582	−	0.0381854i
$875$			19.8786i			0.672018i
$876$	−9.17408	−	11.1152i	−0.309963	−	0.375549i
$877$	6.98626	−	2.05135i	0.235909	−	0.0692692i	−0.161641	−	0.986850i	$-0.551679\pi$
$877$	6.98626	−	2.05135i	0.235909	−	0.0692692i	0.397550	+	0.917580i	$0.369860\pi$
$878$	4.58726	+	3.97488i	0.154813	+	0.134146i
$879$	−46.4141	−	14.8464i	−1.56551	−	0.500756i
$880$	−5.12514	−	5.91472i	−0.172768	−	0.199385i
$881$	−5.34869	−	37.2010i	−0.180202	−	1.25333i	−0.856284	−	0.516506i	$-0.827232\pi$
$881$	−5.34869	−	37.2010i	−0.180202	−	1.25333i	0.676082	−	0.736827i	$-0.263677\pi$
$882$	−2.97836	−	12.2967i	−0.100287	−	0.414051i
$883$	30.1350	−	19.3666i	1.01412	−	0.651737i	0.0756656	−	0.997133i	$-0.475892\pi$
$883$	30.1350	−	19.3666i	1.01412	−	0.651737i	0.938457	+	0.345396i	$0.112255\pi$
$884$	−0.522971	+	3.63734i	−0.0175894	+	0.122337i
$885$	−31.9177	−	5.37325i	−1.07290	−	0.180620i
$886$	10.8944	−	23.8554i	0.366005	−	0.801439i
$887$	−44.8295	−	6.44550i	−1.50523	−	0.216419i	−0.660178	−	0.751109i	$-0.729519\pi$
$887$	−44.8295	−	6.44550i	−1.50523	−	0.216419i	−0.845048	+	0.534690i	$0.820428\pi$
$888$	3.71756	−	4.08795i	0.124753	−	0.137182i
$889$	4.14992	−	14.1333i	0.139184	−	0.474017i
$890$	−10.3925	+	1.49421i	−0.348356	+	0.0500860i
$891$	−33.9524	+	6.51791i	−1.13745	+	0.218358i
$892$	14.9329	+	9.59679i	0.499990	+	0.321324i
$893$	2.89559	−	3.34169i	0.0968972	−	0.111825i
$894$	6.27549	+	10.2998i	0.209884	+	0.344478i
$895$	11.1614	−	5.09724i	0.373085	−	0.170382i
$896$	−1.66811			−0.0557276
$897$	−32.9070	−	10.8392i	−1.09873	−	0.361910i
$898$	4.63507			0.154674
$899$	15.0075	−	6.85371i	0.500529	−	0.228584i
$900$	−1.75859	+	1.84300i	−0.0586196	+	0.0614333i
$901$	−7.99585	+	9.22770i	−0.266380	+	0.307419i
$902$	−22.4324	−	14.4164i	−0.746917	−	0.480014i
$903$	−18.7990	−	12.7285i	−0.625590	−	0.423579i
$904$	−3.31571	+	0.476728i	−0.110279	+	0.0158557i
$905$	10.9645	−	37.3417i	0.364472	−	1.24128i
$906$	−6.67443	−	6.06970i	−0.221743	−	0.201652i
$907$	−36.7563	−	5.28476i	−1.22047	−	0.175478i	−0.498186	−	0.867070i	$-0.666000\pi$
$907$	−36.7563	−	5.28476i	−1.22047	−	0.175478i	−0.722288	+	0.691593i	$0.756909\pi$
$908$	−5.31089	+	11.6292i	−0.176248	+	0.385929i
$909$	−5.28896	+	0.503072i	−0.175424	+	0.0166859i
$910$	−2.01732	+	14.0308i	−0.0668735	+	0.465115i
$911$	6.40957	−	4.11918i	0.212358	−	0.136474i	−0.430138	−	0.902763i	$-0.641535\pi$
$911$	6.40957	−	4.11918i	0.212358	−	0.136474i	0.642496	+	0.766289i	$0.277899\pi$
$912$	0.0183313	−	0.764174i	0.000607010	−	0.0253043i
$913$	−4.57553	−	31.8235i	−0.151428	−	1.05321i
$914$	9.21999	+	10.6404i	0.304970	+	0.351954i
$915$	0.965511	−	3.01847i	0.0319188	−	0.0997874i
$916$	5.70073	+	4.93971i	0.188357	+	0.163213i
$917$	−23.7368	+	6.96976i	−0.783859	+	0.230162i
$918$	−1.60222	+	4.28850i	−0.0528812	+	0.141541i
$919$			6.94467i			0.229084i	0.993418	+	0.114542i	$0.0365400\pi$
$919$			6.94467i			0.229084i	−0.993418	+	0.114542i	$0.963460\pi$
$920$	0.0841585	−	9.77051i	0.00277462	−	0.322124i
$921$	−30.9538	+	8.28794i	−1.01996	+	0.273097i
$922$	6.76033	+	14.8031i	0.222640	+	0.487513i
$923$	14.0508	+	47.8525i	0.462486	+	1.57508i
$924$	9.98225	+	4.85135i	0.328392	+	0.159598i
$925$	−1.46453	+	2.27886i	−0.0481536	+	0.0749285i
$926$	8.81187	−	7.63553i	0.289576	−	0.250919i
$927$	−1.01443	+	0.797157i	−0.0333184	+	0.0261821i
$928$	−1.64162	−	0.482023i	−0.0538888	−	0.0158232i
$929$	−4.20125	−	6.53728i	−0.137839	−	0.214481i	0.765471	−	0.643471i	$-0.222506\pi$
$929$	−4.20125	−	6.53728i	−0.137839	−	0.214481i	−0.903309	+	0.428989i	$0.858870\pi$
$930$	33.7886	−	4.03362i	1.10797	−	0.132268i
$931$	−1.69305	−	0.773189i	−0.0554874	−	0.0253402i
$932$	1.76385	+	0.805521i	0.0577767	+	0.0263857i
$933$	24.0559	−	2.87175i	0.787556	−	0.0940170i
$934$	−5.46975	−	8.51110i	−0.178976	−	0.278492i
$935$	6.61599	+	1.94263i	0.216366	+	0.0635308i
$936$	−9.83852	+	7.73124i	−0.321582	+	0.252704i
$937$	31.5494	−	27.3377i	1.03067	−	0.893085i	0.0363357	−	0.999340i	$-0.488431\pi$
$937$	31.5494	−	27.3377i	1.03067	−	0.893085i	0.994339	+	0.106255i	$0.0338860\pi$
$938$	11.3507	−	17.6621i	0.370615	−	0.576688i
$939$	38.1165	+	18.5245i	1.24388	+	0.604524i
$940$	−5.75092	−	19.5858i	−0.187574	−	0.638820i
$941$	2.84751	+	6.23518i	0.0928262	+	0.203261i	0.950350	−	0.311184i	$-0.100725\pi$
$941$	2.84751	+	6.23518i	0.0928262	+	0.203261i	−0.857524	+	0.514445i	$0.827998\pi$
$942$	−24.4723	+	6.55251i	−0.797350	+	0.213492i
$943$	−9.10365	−	32.0220i	−0.296456	−	1.04278i
$944$			9.17212i			0.298527i
$945$	−6.18044	+	16.5425i	−0.201050	+	0.538129i
$946$	−28.9617	+	8.50391i	−0.941625	+	0.276486i
$947$	18.9284	+	16.4016i	0.615091	+	0.532979i	0.905731	−	0.423853i	$-0.139323\pi$
$947$	18.9284	+	16.4016i	0.615091	+	0.532979i	−0.290640	+	0.956832i	$0.593868\pi$
$948$	5.15879	−	16.1279i	0.167550	−	0.523809i
$949$	22.7274	+	26.2289i	0.737764	+	0.851425i
$950$	0.0533315	+	0.370929i	0.00173030	+	0.0120345i
$951$	0.188848	−	7.87248i	0.00612382	−	0.255283i
$952$	1.23637	−	0.794565i	0.0400709	−	0.0257520i
$953$	4.83692	−	33.6415i	0.156683	−	1.08976i	−0.748009	−	0.663689i	$-0.768990\pi$
$953$	4.83692	−	33.6415i	0.156683	−	1.08976i	0.904692	−	0.426066i	$-0.140101\pi$
$954$	−41.3890	+	3.93681i	−1.34002	+	0.127459i
$955$	−0.992166	+	2.17254i	−0.0321057	+	0.0703017i
$956$	13.5212	+	1.94405i	0.437307	+	0.0628752i
$957$	8.42188	+	7.65882i	0.272241	+	0.247575i
$958$	−1.44119	+	4.90825i	−0.0465628	+	0.158578i
$959$	−30.3500	+	4.36367i	−0.980053	+	0.140910i
$960$	−2.92203	−	1.97847i	−0.0943081	−	0.0638548i
$961$	52.1475	+	33.5132i	1.68218	+	1.08107i
$962$	−8.71353	+	10.0559i	−0.280935	+	0.324217i
$963$	−37.8698	+	39.6874i	−1.22034	+	1.27891i
$964$	−25.4368	+	11.6166i	−0.819265	+	0.374146i
$965$	20.9985			0.675966
$966$	5.34229	+	12.7851i	0.171885	+	0.411353i
$967$	35.2691			1.13418			0.567089	−	0.823657i	$-0.308070\pi$
$967$	35.2691			1.13418			0.567089	+	0.823657i	$0.308070\pi$
$968$	3.41676	−	1.56038i	0.109819	−	0.0501525i
$969$	0.350410	+	0.575122i	0.0112568	+	0.0184756i
$970$	14.3398	−	16.5490i	0.460423	−	0.531357i
$971$	44.8361	+	28.8144i	1.43886	+	0.924699i	0.999654	+	0.0263125i	$0.00837650\pi$
$971$	44.8361	+	28.8144i	1.43886	+	0.924699i	0.439206	+	0.898386i	$0.355260\pi$
$972$	−14.0279	+	6.79840i	−0.449945	+	0.218059i
$973$	12.5175	−	1.79974i	0.401292	−	0.0576970i
$974$	−1.74334	+	5.93727i	−0.0558602	+	0.190242i
$975$	4.12717	−	4.53836i	0.132175	−	0.145344i
$976$	−0.888927	−	0.127808i	−0.0284539	−	0.00409105i
$977$	−8.57680	+	18.7806i	−0.274396	+	0.600844i	−0.995788	−	0.0916830i	$-0.970775\pi$
$977$	−8.57680	+	18.7806i	−0.274396	+	0.600844i	0.721392	+	0.692527i	$0.243503\pi$
$978$	5.54951	+	0.934244i	0.177454	+	0.0298738i
$979$	2.81728	−	19.5946i	0.0900406	−	0.626246i
$980$	−7.22841	+	4.64542i	−0.230903	+	0.148392i
$981$	−7.19367	−	29.7004i	−0.229676	−	0.948260i
$982$	5.64310	+	39.2486i	0.180079	+	1.25247i
$983$	−5.09708	−	5.88234i	−0.162571	−	0.187618i	0.668619	−	0.743605i	$-0.266886\pi$
$983$	−5.09708	−	5.88234i	−0.162571	−	0.187618i	−0.831191	+	0.555988i	$0.812340\pi$
$984$	−11.4517	−	3.66303i	−0.365066	−	0.116773i
$985$	−35.5115	−	30.7709i	−1.13149	−	0.980443i
$986$	1.44633	−	0.424682i	0.0460607	−	0.0135246i
$987$	18.4267	+	22.3256i	0.586528	+	0.710632i
$988$			1.84072i			0.0585611i
$989$	−34.1426	−	15.9492i	−1.08567	−	0.507156i
$990$	11.7320	+	20.3376i	0.372867	+	0.646373i
$991$	−12.6581	−	27.7173i	−0.402097	−	0.880470i	−0.997053	−	0.0767116i	$-0.975558\pi$
$991$	−12.6581	−	27.7173i	−0.402097	−	0.880470i	0.594956	−	0.803758i	$-0.297169\pi$
$992$	−2.71675	−	9.25241i	−0.0862570	−	0.293764i
$993$	7.29054	−	15.0012i	0.231358	−	0.476048i
$994$	10.7836	−	16.7796i	0.342035	−	0.532218i
$995$	−1.80508	+	1.56411i	−0.0572249	+	0.0495856i
$996$	−5.70412	−	13.3272i	−0.180742	−	0.422287i
$997$	46.7190	+	13.7179i	1.47961	+	0.434451i	0.919208	−	0.393772i	$-0.128830\pi$
$997$	46.7190	+	13.7179i	1.47961	+	0.434451i	0.560398	+	0.828224i	$0.310648\pi$
$998$	−14.5256	−	22.6022i	−0.459799	−	0.715461i
$999$	−13.2757	+	9.92667i	−0.420026	+	0.314066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.2.f.a.65.4	yes	80
3.2	odd	2	inner	138.2.f.a.65.8	yes	80
23.17	odd	22	inner	138.2.f.a.17.8	yes	80
69.17	even	22	inner	138.2.f.a.17.4	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.f.a.17.4	✓	80	69.17	even	22	inner
138.2.f.a.17.8	yes	80	23.17	odd	22	inner
138.2.f.a.65.4	yes	80	1.1	even	1	trivial
138.2.f.a.65.8	yes	80	3.2	odd	2	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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	138.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.909632 + 0.415415i) q^{2} +(1.47913 - 0.901205i) q^{3} +(0.654861 - 0.755750i) q^{4} +(1.71394 + 1.10148i) q^{5} +(-0.971091 + 1.43422i) q^{6} +(-1.65113 + 0.237396i) q^{7} +(-0.281733 + 0.959493i) q^{8} +(1.37566 - 2.66600i) q^{9} +O(q^{10})\)	\(q+(-0.909632 + 0.415415i) q^{2} +(1.47913 - 0.901205i) q^{3} +(0.654861 - 0.755750i) q^{4} +(1.71394 + 1.10148i) q^{5} +(-0.971091 + 1.43422i) q^{6} +(-1.65113 + 0.237396i) q^{7} +(-0.281733 + 0.959493i) q^{8} +(1.37566 - 2.66600i) q^{9} +(-2.01663 - 0.289948i) q^{10} +(1.59577 - 3.49424i) q^{11} +(0.287540 - 1.70802i) q^{12} +(-0.593583 + 4.12846i) q^{13} +(1.40330 - 0.901847i) q^{14} +(3.52781 + 0.0846264i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(0.576959 + 0.665847i) q^{17} +(-0.143848 + 2.99655i) q^{18} +(0.333530 + 0.289005i) q^{19} +(1.95484 - 0.573993i) q^{20} +(-2.22829 + 1.83915i) q^{21} +3.84138i q^{22} +(-3.17170 + 3.59726i) q^{23} +(0.447980 + 1.67311i) q^{24} +(-0.352744 - 0.772401i) q^{25} +(-1.17508 - 4.00196i) q^{26} +(-0.367831 - 5.18312i) q^{27} +(-0.901847 + 1.40330i) q^{28} +(-1.29303 + 1.12042i) q^{29} +(-3.24416 + 1.38853i) q^{30} +(-9.25241 - 2.71675i) q^{31} +(0.540641 + 0.841254i) q^{32} +(-0.788678 - 6.60656i) q^{33} +(-0.801424 - 0.365998i) q^{34} +(-3.09143 - 1.41181i) q^{35} +(-1.11396 - 2.78551i) q^{36} +(-1.72474 - 2.68374i) q^{37} +(-0.423447 - 0.124335i) q^{38} +(2.84260 + 6.64147i) q^{39} +(-1.53974 + 1.33419i) q^{40} +(-3.75293 + 5.83967i) q^{41} +(1.26292 - 2.59861i) q^{42} +(2.21377 + 7.53939i) q^{43} +(-1.59577 - 3.49424i) q^{44} +(5.29436 - 3.05410i) q^{45} +(1.39073 - 4.58976i) q^{46} -10.0192i q^{47} +(-1.10253 - 1.33582i) q^{48} +(-4.04658 + 1.18818i) q^{49} +(0.641734 + 0.556065i) q^{50} +(1.45346 + 0.464916i) q^{51} +(2.73137 + 3.15217i) q^{52} +(1.97228 + 13.7175i) q^{53} +(2.48774 + 4.56193i) q^{54} +(6.58390 - 4.23122i) q^{55} +(0.237396 - 1.65113i) q^{56} +(0.753787 + 0.126898i) q^{57} +(0.710743 - 1.55631i) q^{58} +(-9.07876 - 1.30533i) q^{59} +(2.37418 - 2.61072i) q^{60} +(0.253015 - 0.861690i) q^{61} +(9.54487 - 1.37234i) q^{62} +(-1.63849 + 4.72849i) q^{63} +(-0.841254 - 0.540641i) q^{64} +(-5.56480 + 6.42212i) q^{65} +(3.46187 + 5.68191i) q^{66} +(11.4487 - 5.22846i) q^{67} +0.881042 q^{68} +(-1.44950 + 8.17918i) q^{69} +3.39855 q^{70} +(10.8767 - 4.96722i) q^{71} +(2.17044 + 2.07104i) q^{72} +(5.44903 - 6.28852i) q^{73} +(2.68374 + 1.72474i) q^{74} +(-1.21785 - 0.824588i) q^{75} +(0.436831 - 0.0628068i) q^{76} +(-1.80530 + 6.14827i) q^{77} +(-5.34469 - 4.86044i) q^{78} +(9.67669 + 1.39130i) q^{79} +(0.846353 - 1.85325i) q^{80} +(-5.21512 - 7.33502i) q^{81} +(0.987897 - 6.87098i) q^{82} +(7.04095 - 4.52494i) q^{83} +(-0.0692884 + 2.88842i) q^{84} +(0.255456 + 1.77673i) q^{85} +(-5.14569 - 5.93844i) q^{86} +(-0.902836 + 2.82253i) q^{87} +(2.90312 + 2.51557i) q^{88} +(4.94463 - 1.45187i) q^{89} +(-3.54720 + 4.97747i) q^{90} -6.95753i q^{91} +(0.641606 + 4.75272i) q^{92} +(-16.1339 + 4.31988i) q^{93} +(4.16211 + 9.11374i) q^{94} +(0.253316 + 0.862716i) q^{95} +(1.55782 + 0.757097i) q^{96} +(-5.81077 + 9.04174i) q^{97} +(3.18731 - 2.76182i) q^{98} +(-7.12042 - 9.06120i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6}+O(q^{10}) \) 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6	\( 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6} - 4 q^{12} + 8 q^{13} - 22 q^{15} - 8 q^{16} - 28 q^{18} - 66 q^{21} - 4 q^{24} - 48 q^{25} - 38 q^{27} - 44 q^{30} - 16 q^{31} - 22 q^{33} - 44 q^{37} - 24 q^{39} - 44 q^{43} - 16 q^{46} + 4 q^{48} - 76 q^{49} - 8 q^{52} - 6 q^{54} + 64 q^{55} + 66 q^{57} + 36 q^{58} + 22 q^{60} + 88 q^{61} + 110 q^{63} + 8 q^{64} + 88 q^{66} + 44 q^{67} + 82 q^{69} + 112 q^{70} + 28 q^{72} + 52 q^{73} + 136 q^{75} + 82 q^{78} + 88 q^{79} + 36 q^{81} + 44 q^{82} + 22 q^{84} + 20 q^{85} - 10 q^{87} + 8 q^{93} - 56 q^{94} + 4 q^{96} - 132 q^{97} - 66 q^{99}+O(q^{100}) \) 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6 - 4 * q^12 + 8 * q^13 - 22 * q^15 - 8 * q^16 - 28 * q^18 - 66 * q^21 - 4 * q^24 - 48 * q^25 - 38 * q^27 - 44 * q^30 - 16 * q^31 - 22 * q^33 - 44 * q^37 - 24 * q^39 - 44 * q^43 - 16 * q^46 + 4 * q^48 - 76 * q^49 - 8 * q^52 - 6 * q^54 + 64 * q^55 + 66 * q^57 + 36 * q^58 + 22 * q^60 + 88 * q^61 + 110 * q^63 + 8 * q^64 + 88 * q^66 + 44 * q^67 + 82 * q^69 + 112 * q^70 + 28 * q^72 + 52 * q^73 + 136 * q^75 + 82 * q^78 + 88 * q^79 + 36 * q^81 + 44 * q^82 + 22 * q^84 + 20 * q^85 - 10 * q^87 + 8 * q^93 - 56 * q^94 + 4 * q^96 - 132 * q^97 - 66 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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