LMFDB - Embedded newform 138.2.f.a.17.4

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			17.4
Character	$\chi$	$=$	138.17
Dual form			138.2.f.a.65.4

$q$-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 $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$-1$	$e\left(\frac{7}{22}\right)$

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	−0.0980295	−	0.995184i	$-0.531254\pi$
$5$	1.71394	−	1.10148i	0.766498	−	0.492599i	0.864528	+	0.502585i	$0.167618\pi$
$6$	−0.971091	−	1.43422i	−0.396446	−	0.585517i
$7$	−1.65113	−	0.237396i	−0.624068	−	0.0897274i	−0.176976	−	0.984215i	$-0.556631\pi$
$7$	−1.65113	−	0.237396i	−0.624068	−	0.0897274i	−0.447092	+	0.894488i	$0.647540\pi$
$8$	−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	0.982148	+	0.188110i	$0.0602361\pi$
$11$	1.59577	+	3.49424i	0.481142	+	1.05355i	−0.501006	+	0.865444i	$0.667037\pi$
$12$	0.287540	+	1.70802i	0.0830057	+	0.493062i
$13$	−0.593583	−	4.12846i	−0.164630	−	1.14503i	−0.889764	−	0.456421i	$-0.849131\pi$
$13$	−0.593583	−	4.12846i	−0.164630	−	1.14503i	0.725134	−	0.688608i	$-0.241778\pi$
$14$	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	−0.681457	−	0.731858i	$-0.738653\pi$
$17$	0.576959	−	0.665847i	0.139933	−	0.161492i	0.821390	+	0.570367i	$0.193199\pi$
$18$	−0.143848	−	2.99655i	−0.0339052	−	0.706293i
$19$	0.333530	−	0.289005i	0.0765170	−	0.0663024i	−0.615763	−	0.787932i	$-0.711152\pi$
$19$	0.333530	−	0.289005i	0.0765170	−	0.0663024i	0.692280	+	0.721629i	$0.256607\pi$
$20$	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	0.526490	−	0.850181i	$-0.323508\pi$
$29$	−1.29303	−	1.12042i	−0.240110	−	0.208056i	−0.766600	+	0.642125i	$0.778053\pi$
$30$	−3.24416	−	1.38853i	−0.592300	−	0.253509i
$31$	−9.25241	+	2.71675i	−1.66178	+	0.487943i	−0.971785	−	0.235869i	$-0.924206\pi$
$31$	−9.25241	+	2.71675i	−1.66178	+	0.487943i	−0.689997	+	0.723812i	$0.742388\pi$
$32$	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	−0.953587	−	0.301119i	$-0.902640\pi$
$37$	−1.72474	+	2.68374i	−0.283545	+	0.441205i	0.670042	+	0.742324i	$0.266276\pi$
$38$	−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	−0.999999	−	0.00167639i	$-0.999466\pi$
$41$	−3.75293	−	5.83967i	−0.586109	−	0.912004i	0.413890	−	0.910327i	$-0.364170\pi$
$42$	1.26292	+	2.59861i	0.194873	+	0.400975i
$43$	2.21377	−	7.53939i	0.337596	−	1.14975i	−0.599413	−	0.800440i	$-0.704599\pi$
$43$	2.21377	−	7.53939i	0.337596	−	1.14975i	0.937009	−	0.349306i	$-0.113583\pi$
$44$	−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	$0.260816\pi$
$47$			10.0192i			1.46144i	−0.682675	+	0.730722i	$0.739184\pi$
$48$	−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	−0.168102	−	0.985770i	$-0.553764\pi$
$53$	1.97228	−	13.7175i	0.270914	−	1.88425i	0.439016	−	0.898479i	$-0.355327\pi$
$54$	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	−0.705142	−	0.709066i	$-0.749117\pi$
$59$	−9.07876	+	1.30533i	−1.18195	+	0.169939i	−0.476812	+	0.879005i	$0.658208\pi$
$60$	2.37418	+	2.61072i	0.306505	+	0.337043i
$61$	0.253015	+	0.861690i	0.0323953	+	0.110328i	0.974104	−	0.226102i	$-0.0725984\pi$
$61$	0.253015	+	0.861690i	0.0323953	+	0.110328i	−0.941708	+	0.336431i	$0.890780\pi$
$62$	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	0.964986	−	0.262300i	$-0.0844811\pi$
$67$	11.4487	+	5.22846i	1.39868	+	0.638758i	0.433698	+	0.901058i	$0.357208\pi$
$68$	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	0.938145	−	0.346242i	$-0.112542\pi$
$71$	10.8767	+	4.96722i	1.29083	+	0.589501i	0.352682	+	0.935743i	$0.385270\pi$
$72$	2.17044	−	2.07104i	0.255789	−	0.244074i
$73$	5.44903	+	6.28852i	0.637761	+	0.736016i	0.978977	−	0.203969i	$-0.0653843\pi$
$73$	5.44903	+	6.28852i	0.637761	+	0.736016i	−0.341216	+	0.939985i	$0.610839\pi$
$74$	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	0.425495	−	0.904961i	$-0.360100\pi$
$79$	9.67669	−	1.39130i	1.08871	−	0.156533i	0.663217	+	0.748427i	$0.269191\pi$
$80$	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	0.866652	−	0.498913i	$-0.166267\pi$
$83$	7.04095	+	4.52494i	0.772845	+	0.496677i	−0.0938073	+	0.995590i	$0.529904\pi$
$84$	−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	0.533085	−	0.846061i	$-0.321032\pi$
$89$	4.94463	+	1.45187i	0.524130	+	0.153898i	−0.00895542	+	0.999960i	$0.502851\pi$
$90$	−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	−0.999982	−	0.00595827i	$-0.998103\pi$
$97$	−5.81077	−	9.04174i	−0.589994	−	0.918049i	0.409988	−	0.912091i	$-0.365533\pi$
$98$	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	−0.885617	−	0.464417i	$-0.846264\pi$
$101$	−0.957445	+	1.48981i	−0.0952693	+	0.148242i	0.790347	+	0.612659i	$0.209900\pi$
$102$	−1.51525	−	0.180888i	−0.150032	−	0.0179106i
$103$	−0.391193	+	0.178652i	−0.0385454	+	0.0176031i	−0.434594	−	0.900626i	$-0.643108\pi$
$103$	−0.391193	+	0.178652i	−0.0385454	+	0.0176031i	0.396049	+	0.918229i	$0.370381\pi$
$104$	−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	−0.979838	−	0.199793i	$-0.935973\pi$
$107$	−17.5447	+	5.15160i	−1.69611	+	0.498024i	−0.716276	+	0.697817i	$0.754155\pi$
$108$	−4.15802	+	3.11623i	−0.400105	+	0.299860i
$109$	7.69835	+	6.67066i	0.737368	+	0.638933i	0.940334	−	0.340252i	$-0.110513\pi$
$109$	7.69835	+	6.67066i	0.737368	+	0.638933i	−0.202966	+	0.979186i	$0.565058\pi$
$110$	−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	−0.832816	−	0.553549i	$-0.813273\pi$
$113$	1.39156	−	3.04709i	0.130907	−	0.286646i	0.963723	+	0.266903i	$0.0860003\pi$
$114$	−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	0.674160	−	0.738585i	$-0.264506\pi$
$127$	−3.66827	−	8.03239i	−0.325506	−	0.712759i	−0.999666	+	0.0258261i	$0.991778\pi$
$128$	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	0.749689	−	0.661791i	$-0.230203\pi$
$131$	14.6796	+	2.11061i	1.28256	+	0.184404i	0.532873	+	0.846195i	$0.321112\pi$
$132$	−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	0.990334	−	0.138700i	$-0.0442924\pi$
$149$	2.89272	+	6.33417i	0.236981	+	0.518915i	−0.753354	+	0.657616i	$0.771565\pi$
$150$	1.45034	−	0.244160i	0.118420	−	0.0199356i
$151$	−0.741264	−	5.15560i	−0.0603232	−	0.419557i	−0.997498	−	0.0706966i	$-0.977478\pi$
$151$	−0.741264	−	5.15560i	−0.0603232	−	0.419557i	0.937175	−	0.348861i	$-0.113431\pi$
$152$	−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	−0.0906303	−	0.995885i	$-0.528888\pi$
$157$	11.0542	−	9.57850i	0.882220	−	0.764448i	0.972850	+	0.231437i	$0.0743427\pi$
$158$	−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	−0.955097	−	0.296293i	$-0.904250\pi$
$163$	−1.34972	+	2.95548i	−0.105718	+	0.231491i	0.849379	+	0.527784i	$0.176977\pi$
$164$	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	0.274149	−	0.961687i	$-0.411604\pi$
$167$	−8.25427	−	7.15237i	−0.638735	−	0.553467i	−0.912883	+	0.408220i	$0.866149\pi$
$168$	−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	−0.250819	−	0.968034i	$-0.580700\pi$
$173$	4.16317	−	1.90126i	0.316520	−	0.144550i	0.567339	+	0.823484i	$0.307973\pi$
$174$	−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	0.941353	−	0.337424i	$-0.109555\pi$
$179$	3.25606	+	5.06653i	0.243370	+	0.378690i	−0.697983	+	0.716114i	$0.745919\pi$
$180$	1.15893	+	6.00122i	0.0863815	+	0.447305i
$181$	−5.38170	+	18.3284i	−0.400019	+	1.36234i	0.475738	+	0.879587i	$0.342181\pi$
$181$	−5.38170	+	18.3284i	−0.400019	+	1.36234i	−0.875757	+	0.482752i	$0.839637\pi$
$182$	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	−0.982895	−	0.184167i	$-0.941041\pi$
$191$	0.166833	−	1.16035i	0.0120716	−	0.0839601i	0.994967	+	0.100207i	$0.0319504\pi$
$192$	−1.73155	+	0.0415372i	−0.124964	+	0.00299769i
$193$	8.67054	+	5.57222i	0.624119	+	0.401097i	0.814128	−	0.580685i	$-0.197215\pi$
$193$	8.67054	+	5.57222i	0.624119	+	0.401097i	−0.190009	+	0.981782i	$0.560852\pi$
$194$	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	−0.894364	−	0.447339i	$-0.852372\pi$
$197$	−22.8286	+	3.28226i	−1.62647	+	0.233851i	−0.732106	+	0.681191i	$0.761462\pi$
$198$	10.2411	−	5.28443i	0.727805	−	0.375548i
$199$	−0.330283	−	1.12484i	−0.0234131	−	0.0797378i	0.946958	−	0.321358i	$-0.104139\pi$
$199$	−0.330283	−	1.12484i	−0.0234131	−	0.0797378i	−0.970371	+	0.241620i	$0.922321\pi$
$200$	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	0.532709	−	0.846299i	$-0.321174\pi$
$211$	−5.53127	−	6.38342i	−0.380788	−	0.439453i	−0.913497	+	0.406846i	$0.866629\pi$
$212$	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	−0.711445	−	0.702742i	$-0.751959\pi$
$223$	2.52620	−	17.5701i	0.169167	−	1.17658i	0.880612	−	0.473838i	$-0.157132\pi$
$224$	−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	−0.151965	−	0.988386i	$-0.548560\pi$
$227$	−12.2667	−	3.60182i	−0.814167	−	0.239061i	−0.662203	+	0.749325i	$0.730378\pi$
$228$	0.589529	+	0.486574i	0.0390425	+	0.0322241i
$229$		−	7.54315i		−	0.498465i	−0.968444	−	0.249233i	$-0.919822\pi$
$229$		−	7.54315i		−	0.498465i	0.968444	−	0.249233i	$-0.0801784\pi$
$230$	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	−0.939661	−	0.342107i	$-0.888859\pi$
$233$	0.546301	−	1.86053i	0.0357894	−	0.121887i	0.975450	+	0.220220i	$0.0706775\pi$
$234$	−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	−0.515841	−	0.856684i	$-0.672521\pi$
$239$	7.38528	−	11.4917i	0.477714	−	0.743338i	0.993556	+	0.113346i	$0.0361570\pi$
$240$	−0.418294	+	3.50394i	−0.0270008	+	0.226179i
$241$	−25.4368	+	11.6166i	−1.63853	+	0.748291i	−0.999777	−	0.0211206i	$-0.993277\pi$
$241$	−25.4368	+	11.6166i	−1.63853	+	0.748291i	−0.638753	+	0.769412i	$0.720549\pi$
$242$	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	−0.794512	−	0.607249i	$-0.792273\pi$
$251$	2.92637	−	6.40786i	0.184711	−	0.404461i	0.979223	+	0.202788i	$0.0650003\pi$
$252$	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	−0.439707	−	0.898141i	$-0.644918\pi$
$257$	6.19953	−	5.37193i	0.386716	−	0.335092i	0.826423	+	0.563050i	$0.190372\pi$
$258$	−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	0.999263	−	0.0383862i	$-0.0122217\pi$
$263$	0.481045	+	3.34574i	0.0296625	+	0.206307i	−0.969600	+	0.244694i	$0.921313\pi$
$264$	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	0.461542	−	0.887118i	$-0.347296\pi$
$269$	10.7339	+	1.54330i	0.654458	+	0.0940969i	0.192916	+	0.981215i	$0.438205\pi$
$270$	−0.761054	−	10.5591i	−0.0463163	−	0.642605i
$271$	−16.0400	+	10.3083i	−0.974361	+	0.626184i	−0.927937	−	0.372738i	$-0.878419\pi$
$271$	−16.0400	+	10.3083i	−0.974361	+	0.626184i	−0.0464247	+	0.998922i	$0.514783\pi$
$272$	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	0.0470093	−	0.998894i	$-0.485031\pi$
$281$	16.3467	−	10.5054i	0.975164	−	0.626700i	0.928155	+	0.372195i	$0.121395\pi$
$282$	14.3697	−	9.72952i	0.855700	−	0.579384i
$283$	−16.5357	−	2.37748i	−0.982946	−	0.141326i	−0.367941	−	0.929849i	$-0.619937\pi$
$283$	−16.5357	−	2.37748i	−0.982946	−	0.141326i	−0.615005	+	0.788523i	$0.710846\pi$
$284$	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	−0.107597	+	0.994195i	$0.534316\pi$
$293$	−18.4243	+	21.2628i	−1.07636	+	1.24218i	−0.968762	+	0.247990i	$0.920230\pi$
$294$	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	−0.745829	−	0.666138i	$-0.767946\pi$
$307$	−17.7513	+	5.21225i	−1.01312	+	0.297479i	−0.267290	+	0.963616i	$0.586128\pi$
$308$	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	−0.0206158	−	0.999787i	$-0.506563\pi$
$311$	12.7233	−	5.81054i	0.721473	−	0.329486i	0.742088	+	0.670302i	$0.233835\pi$
$312$	−7.17330	−	0.856335i	−0.406108	−	0.0484804i
$313$	13.2283	−	20.5836i	0.747707	−	1.16346i	−0.233847	−	0.972273i	$-0.575132\pi$
$313$	13.2283	−	20.5836i	0.747707	−	1.16346i	0.981555	−	0.191182i	$-0.0612321\pi$
$314$	−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	0.903396	−	0.428806i	$-0.141066\pi$
$317$	2.45801	+	3.82475i	0.138056	+	0.214819i	−0.765341	+	0.643626i	$0.777429\pi$
$318$	−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	0.743999	−	0.668181i	$-0.232927\pi$
$331$	8.10093	+	5.20615i	0.445268	+	0.286156i	−0.298731	+	0.954337i	$0.596563\pi$
$332$	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	0.944531	−	0.328421i	$-0.106516\pi$
$337$	−0.506976	−	1.72660i	−0.0276167	−	0.0940539i	−0.972148	+	0.234367i	$0.924698\pi$
$338$	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	−0.231445	−	0.972848i	$-0.574345\pi$
$347$	−20.8305	−	9.51296i	−1.11824	−	0.510683i	−0.886794	+	0.462165i	$0.847073\pi$
$348$	1.54189	−	2.53068i	0.0826541	−	0.135659i
$349$	−6.13437	−	7.07944i	−0.328365	−	0.378954i	0.567429	−	0.823422i	$-0.307938\pi$
$349$	−6.13437	−	7.07944i	−0.328365	−	0.378954i	−0.895795	+	0.444468i	$0.853393\pi$
$350$	−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	0.982552	+	0.185988i	$0.0595486\pi$
$353$	4.81975	+	16.4146i	0.256529	+	0.873659i	−0.726023	+	0.687671i	$0.758633\pi$
$354$	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	0.435276	−	0.900297i	$-0.356651\pi$
$359$	−3.84333	−	2.46996i	−0.202843	−	0.130359i	−0.638119	+	0.769938i	$0.720287\pi$
$360$	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	$-0.913385\pi$
$367$		−	10.2975i		−	0.537527i	0.963206	−	0.268763i	$-0.0866150\pi$
$368$	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	0.911024	+	0.412353i	$0.135293\pi$
$373$	17.5298	+	27.2770i	0.907660	+	1.41235i	−0.00336401	+	0.999994i	$0.501071\pi$
$374$	−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	−0.321723	−	0.946834i	$-0.604262\pi$
$379$	3.56578	−	1.62844i	0.183162	−	0.0836472i	0.504885	+	0.863186i	$0.331535\pi$
$380$	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	−0.402256	−	0.915527i	$-0.631774\pi$
$383$	−4.80812	+	1.41179i	−0.245684	+	0.0721392i	0.156572	+	0.987667i	$0.449956\pi$
$384$	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	0.485030	+	0.874497i	$0.338809\pi$
$389$	−9.73330	+	21.3130i	−0.493498	+	1.08061i	−0.978528	+	0.206113i	$0.933919\pi$
$390$	−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	−0.956797	−	0.290755i	$-0.906093\pi$
$397$	−10.6167	+	12.2523i	−0.532835	+	0.614925i	0.423962	+	0.905680i	$0.360639\pi$
$398$	−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	−0.614874	−	0.788626i	$-0.710793\pi$
$401$	−4.94794	−	34.4137i	−0.247088	−	1.71854i	0.367786	−	0.929911i	$-0.380116\pi$
$402$	−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	−0.0292535	−	0.999572i	$-0.509313\pi$
$409$	17.5509	−	11.2793i	0.867837	−	0.557725i	0.897090	+	0.441847i	$0.145677\pi$
$410$	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	−0.256925	−	0.966431i	$-0.582709\pi$
$419$	10.5508	−	6.78060i	0.515441	−	0.331254i	0.772366	+	0.635177i	$0.219073\pi$
$420$	−3.30030	−	4.87426i	−0.161038	−	0.237839i
$421$	15.0207	+	2.15964i	0.732062	+	0.105255i	0.498258	−	0.867029i	$-0.333973\pi$
$421$	15.0207	+	2.15964i	0.732062	+	0.105255i	0.233804	+	0.972284i	$0.424882\pi$
$422$	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	−0.414495	−	0.910051i	$-0.636042\pi$
$431$	11.3203	−	13.0644i	0.545282	−	0.629289i	0.959777	+	0.280763i	$0.0905874\pi$
$432$	−5.07801	−	1.10172i	−0.244316	−	0.0530066i
$433$	22.9390	−	19.8767i	1.10238	−	0.955215i	0.103156	−	0.994665i	$-0.467106\pi$
$433$	22.9390	−	19.8767i	1.10238	−	0.955215i	0.999222	+	0.0394497i	$0.0125605\pi$
$434$	−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	−0.960211	−	0.279275i	$-0.909906\pi$
$439$	−2.52149	+	5.52130i	−0.120344	+	0.263517i	0.839867	+	0.542793i	$0.182633\pi$
$440$	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	0.0414113	−	0.999142i	$-0.486815\pi$
$443$	−19.8198	−	17.1740i	−0.941668	−	0.815960i	−0.983079	+	0.183183i	$0.941360\pi$
$444$	−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	−0.512411	−	0.858741i	$-0.671247\pi$
$449$	−4.21621	+	1.92548i	−0.198975	+	0.0908689i	0.313435	+	0.949610i	$0.398520\pi$
$450$	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	0.813202	+	0.581981i	$0.197722\pi$
$457$	−3.96660	+	13.5090i	−0.185550	+	0.631925i	−0.998752	+	0.0499434i	$0.984096\pi$
$458$	−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	$0.123722\pi$
$461$			16.2737i			0.757941i	−0.925409	+	0.378971i	$0.876278\pi$
$462$	−7.06486	+	8.55972i	−0.328687	+	0.398234i
$463$	−11.1875	−	3.28494i	−0.519926	−	0.152664i	0.0112318	−	0.999937i	$-0.496425\pi$
$463$	−11.1875	−	3.28494i	−0.519926	−	0.152664i	−0.531158	+	0.847273i	$0.678243\pi$
$464$	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	−0.929007	−	0.370062i	$-0.879337\pi$
$467$	1.43982	−	10.0142i	0.0666271	−	0.463402i	0.995634	−	0.0933399i	$-0.0297543\pi$
$468$	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	0.827102	−	0.562052i	$-0.189988\pi$
$479$	3.34991	+	3.86601i	0.153062	+	0.176642i	−0.674040	+	0.738695i	$0.735443\pi$
$480$	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	0.840097	−	0.542436i	$-0.182498\pi$
$487$	4.05223	+	4.67652i	0.183624	+	0.211913i	−0.656473	+	0.754349i	$0.727952\pi$
$488$	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	0.680575	+	0.732678i	$0.261730\pi$
$491$	11.1713	+	38.0460i	0.504155	+	1.71699i	−0.176421	+	0.984315i	$0.556452\pi$
$492$	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	−0.705252	−	0.708957i	$-0.749166\pi$
$499$	3.82362	−	26.5938i	0.171169	−	1.19050i	0.876420	−	0.481547i	$-0.159925\pi$
$500$	−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	−0.607514	−	0.794309i	$-0.707833\pi$
$503$	−34.7185	−	10.1943i	−1.54802	−	0.454541i	−0.940509	+	0.339768i	$0.889651\pi$
$504$	−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	−0.910143	−	0.414294i	$-0.864028\pi$
$509$	1.79366	−	6.10863i	0.0795024	−	0.270760i	0.989645	+	0.143534i	$0.0458466\pi$
$510$	−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	−0.459674	−	0.888088i	$-0.652034\pi$
$521$	−8.35959	+	2.45460i	−0.366240	+	0.107538i	0.0934339	+	0.995625i	$0.470216\pi$
$522$	−3.17138	+	4.03580i	−0.138808	+	0.176642i
$523$	−33.7641	−	29.2567i	−1.47640	−	1.27931i	−0.878506	−	0.477732i	$-0.841459\pi$
$523$	−33.7641	−	29.2567i	−1.47640	−	1.27931i	−0.597894	−	0.801575i	$-0.703996\pi$
$524$	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	−0.779197	−	0.626779i	$-0.784373\pi$
$541$	−17.2729	−	37.8224i	−0.742620	−	1.62611i	0.0365772	−	0.999331i	$-0.488355\pi$
$542$	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	−0.844892	−	0.534937i	$-0.820335\pi$
$547$	−16.5886	+	10.6608i	−0.709277	+	0.455825i	0.135615	+	0.990762i	$0.456699\pi$
$548$	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	−0.996360	−	0.0852475i	$-0.972832\pi$
$557$	−31.4533	+	20.2138i	−1.33272	+	0.856486i	−0.336359	+	0.941734i	$0.609196\pi$
$558$	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	0.830902	−	0.556419i	$-0.187825\pi$
$563$	−3.17326	−	6.94846i	−0.133737	−	0.292843i	−0.964639	+	0.263576i	$0.915098\pi$
$564$	−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	0.185826	−	0.982583i	$-0.440504\pi$
$569$	27.0015	−	31.1614i	1.13196	−	1.30635i	0.946136	−	0.323771i	$-0.104951\pi$
$570$	−1.48332	+	0.474465i	−0.0621293	+	0.0198732i
$571$	1.54189	−	1.33605i	0.0645259	−	0.0559120i	−0.622001	−	0.783017i	$-0.713680\pi$
$571$	1.54189	−	1.33605i	0.0645259	−	0.0559120i	0.686527	+	0.727105i	$0.259134\pi$
$572$	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	0.474117	+	0.880462i	$0.342767\pi$
$577$	−12.0530	+	26.3923i	−0.501772	+	1.09873i	−0.975889	+	0.218266i	$0.929960\pi$
$578$	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	−0.0728447	−	0.997343i	$-0.523208\pi$
$587$	15.3411	−	7.00603i	0.633194	−	0.289170i	0.706039	+	0.708173i	$0.250480\pi$
$588$	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	0.595795	−	0.803137i	$-0.296837\pi$
$593$	−9.30879	−	14.4848i	−0.382266	−	0.594818i	−0.978061	+	0.208319i	$0.933201\pi$
$594$	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	$0.0781313\pi$
$599$			11.8946i			0.485999i	−0.970026	+	0.242999i	$0.921869\pi$
$600$	1.13429	+	0.936201i	0.0463073	+	0.0382202i
$601$	0.134686	+	0.0395473i	0.00549395	+	0.00161317i	0.284478	−	0.958682i	$-0.408180\pi$
$601$	0.134686	+	0.0395473i	0.00549395	+	0.00161317i	−0.278984	+	0.960296i	$0.589998\pi$
$602$	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	0.711172	−	0.703018i	$-0.248165\pi$
$607$	9.04478	+	5.81273i	0.367116	+	0.235931i	−0.344056	+	0.938949i	$0.611801\pi$
$608$	−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	−0.811756	−	0.583996i	$-0.801488\pi$
$613$	−11.0077	−	37.4887i	−0.444596	−	1.51415i	0.367160	−	0.930158i	$-0.380330\pi$
$614$	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	0.991741	−	0.128256i	$-0.0409379\pi$
$617$	17.9751	+	20.7444i	0.723651	+	0.835138i	−0.268090	+	0.963394i	$0.586392\pi$
$618$	0.636110	+	0.387569i	0.0255881	+	0.0155903i
$619$	19.9479	+	9.10991i	0.801774	+	0.366158i	0.773783	−	0.633450i	$-0.218362\pi$
$619$	19.9479	+	9.10991i	0.801774	+	0.366158i	0.0279907	+	0.999608i	$0.491089\pi$
$620$	−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	−0.225848	−	0.974163i	$-0.572515\pi$
$631$	−4.22246	+	0.607099i	−0.168094	+	0.0241682i	0.0577540	+	0.998331i	$0.481606\pi$
$632$	−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	0.347751	−	0.937587i	$-0.386945\pi$
$641$	3.37742	+	0.991701i	0.133400	+	0.0391698i	−0.214351	+	0.976757i	$0.568764\pi$
$642$	24.4261	+	20.1603i	0.964020	+	0.795664i
$643$			13.6466i			0.538169i	0.963117	+	0.269084i	$0.0867210\pi$
$643$			13.6466i			0.538169i	−0.963117	+	0.269084i	$0.913279\pi$
$644$	−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	−0.961769	−	0.273862i	$-0.911699\pi$
$647$	−0.117428	+	0.399925i	−0.00461659	+	0.0157227i	0.957152	+	0.289584i	$0.0935171\pi$
$648$	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	−0.391365	−	0.920235i	$-0.627997\pi$
$653$	15.5441	−	24.1872i	0.608289	−	0.946516i	0.999655	−	0.0262811i	$-0.00836650\pi$
$654$	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	−0.218958	−	0.975734i	$-0.570266\pi$
$659$	3.19255	−	0.937416i	0.124364	−	0.0365166i	0.343322	+	0.939218i	$0.388448\pi$
$660$	−5.33385	+	12.4621i	−0.207620	+	0.485085i
$661$	3.28355	+	2.84521i	0.127715	+	0.110666i	0.716377	−	0.697714i	$-0.245799\pi$
$661$	3.28355	+	2.84521i	0.127715	+	0.110666i	−0.588661	+	0.808380i	$0.700345\pi$
$662$	−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	−0.258465	−	0.966021i	$-0.583217\pi$
$673$	19.0548	−	21.9904i	0.734507	−	0.847666i	0.992971	+	0.118355i	$0.0377620\pi$
$674$	−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	−0.925487	−	0.378778i	$-0.876344\pi$
$677$	−3.75205	−	26.0961i	−0.144203	−	1.00295i	0.781284	−	0.624175i	$-0.214565\pi$
$678$	−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	0.548753	−	0.835985i	$-0.315103\pi$
$683$	21.9463	+	3.15541i	0.839753	+	0.120738i	0.291000	+	0.956723i	$0.406012\pi$
$684$	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	0.979653	+	0.200701i	$0.0643219\pi$
$701$	12.9680	+	28.3960i	0.489796	+	1.07250i	−0.489856	+	0.871803i	$0.662951\pi$
$702$	−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	−0.945951	−	0.324308i	$-0.894868\pi$
$709$	−20.2250	+	17.5251i	−0.759567	+	0.658168i	0.186385	+	0.982477i	$0.440323\pi$
$710$	−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	0.762491	−	0.646999i	$-0.223976\pi$
$719$	6.18311	+	5.35770i	0.230591	+	0.199808i	−0.531900	+	0.846807i	$0.678522\pi$
$720$	−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	0.223527	+	0.974698i	$0.428243\pi$
$727$	−20.3825	+	31.7158i	−0.755945	+	1.17627i	−0.979473	+	0.201576i	$0.935394\pi$
$728$	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	−0.999106	−	0.0422760i	$-0.986539\pi$
$733$	−3.67525	+	12.5167i	−0.135748	+	0.462317i	0.863358	+	0.504593i	$0.168357\pi$
$734$	−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	0.301124	−	0.953585i	$-0.402638\pi$
$739$	1.05746	+	0.310498i	0.0388993	+	0.0114219i	−0.262225	+	0.965007i	$0.584456\pi$
$740$	−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	0.939702	+	0.341993i	$0.111102\pi$
$743$	−1.58877	+	11.0501i	−0.0582862	+	0.405389i	−0.997988	+	0.0633956i	$0.979807\pi$
$744$	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	0.966746	−	0.255740i	$-0.0823191\pi$
$751$	0.416654	+	1.41899i	0.0152039	+	0.0517797i	−0.951542	+	0.307520i	$0.900501\pi$
$752$	−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	−0.242270	−	0.970209i	$-0.577892\pi$
$757$	−31.2048	−	14.2508i	−1.13416	−	0.517952i	−0.891888	+	0.452257i	$0.850619\pi$
$758$	−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	−0.0870278	−	0.996206i	$-0.527737\pi$
$761$	−24.7421	−	11.2993i	−0.896901	−	0.409601i	−0.809873	+	0.586605i	$0.800464\pi$
$762$	−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	−0.0363231	−	0.999340i	$-0.511565\pi$
$769$	5.83379	−	0.838772i	0.210372	−	0.0302469i	0.246695	+	0.969093i	$0.420655\pi$
$770$	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	0.372456	−	0.928050i	$-0.378516\pi$
$773$	−8.81363	−	5.66417i	−0.317004	−	0.203726i	−0.689460	+	0.724324i	$0.742152\pi$
$774$	−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	0.920549	−	0.390627i	$-0.127742\pi$
$787$	5.12854	+	7.98016i	0.182813	+	0.284462i	−0.737737	+	0.675089i	$0.764105\pi$
$788$	−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	−0.348789	−	0.937201i	$-0.613407\pi$
$797$	−3.82588	+	1.12338i	−0.135520	+	0.0397922i	0.213269	+	0.976993i	$0.431589\pi$
$798$	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	−0.433957	−	0.900934i	$-0.642883\pi$
$809$	11.2648	−	9.76098i	0.396048	−	0.343178i	0.830005	+	0.557756i	$0.188337\pi$
$810$	8.39019	−	16.3041i	0.294801	−	0.572869i
$811$	31.5368	−	36.3954i	1.10741	−	1.27802i	0.150186	−	0.988658i	$-0.452013\pi$
$811$	31.5368	−	36.3954i	1.10741	−	1.27802i	0.957221	−	0.289358i	$-0.0934418\pi$
$812$	−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	−0.247840	−	0.968801i	$-0.579721\pi$
$821$	−21.7358	−	3.12513i	−0.758584	−	0.109068i	−0.510744	+	0.859733i	$0.670630\pi$
$822$	−17.8500	−	26.3629i	−0.622590	−	0.919512i
$823$	−2.81510	+	1.80916i	−0.0981282	+	0.0630632i	−0.588785	−	0.808290i	$-0.700393\pi$
$823$	−2.81510	+	1.80916i	−0.0981282	+	0.0630632i	0.490656	+	0.871353i	$0.336757\pi$
$824$	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	−0.955095	−	0.296300i	$-0.904247\pi$
$839$	−16.0344	−	35.1104i	−0.553569	−	1.21215i	0.401526	−	0.915848i	$-0.368480\pi$
$840$	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	−0.973622	−	0.228167i	$-0.926727\pi$
$853$	−4.77807	+	10.4625i	−0.163598	+	0.358230i	0.810024	+	0.586397i	$0.199454\pi$
$854$	−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	0.917279	−	0.398245i	$-0.130381\pi$
$857$	19.1347	+	16.5803i	0.653630	+	0.566374i	−0.263649	+	0.964619i	$0.584926\pi$
$858$	−25.5124	−	10.9195i	−0.870980	−	0.372786i
$859$	−28.7048	+	8.42850i	−0.979397	+	0.287577i	−0.731975	−	0.681331i	$-0.761401\pi$
$859$	−28.7048	+	8.42850i	−0.979397	+	0.287577i	−0.247421	+	0.968908i	$0.579583\pi$
$860$	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	0.0264215	−	0.999651i	$-0.491589\pi$
$863$	23.4783	−	10.7222i	0.799210	−	0.364987i	0.772788	+	0.634664i	$0.218862\pi$
$864$	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	0.397550	−	0.917580i	$-0.369860\pi$
$877$	6.98626	+	2.05135i	0.235909	+	0.0692692i	−0.161641	+	0.986850i	$0.551679\pi$
$878$	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	0.676082	+	0.736827i	$0.263677\pi$
$881$	−5.34869	+	37.2010i	−0.180202	+	1.25333i	−0.856284	+	0.516506i	$0.827232\pi$
$882$	−2.97836	+	12.2967i	−0.100287	+	0.414051i
$883$	30.1350	+	19.3666i	1.01412	+	0.651737i	0.938457	−	0.345396i	$-0.112255\pi$
$883$	30.1350	+	19.3666i	1.01412	+	0.651737i	0.0756656	+	0.997133i	$0.475892\pi$
$884$	−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	−0.845048	−	0.534690i	$-0.820428\pi$
$887$	−44.8295	+	6.44550i	−1.50523	+	0.216419i	−0.660178	+	0.751109i	$0.729519\pi$
$888$	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	−0.722288	−	0.691593i	$-0.756909\pi$
$907$	−36.7563	+	5.28476i	−1.22047	+	0.175478i	−0.498186	+	0.867070i	$0.666000\pi$
$908$	−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	0.642496	−	0.766289i	$-0.277899\pi$
$911$	6.40957	+	4.11918i	0.212358	+	0.136474i	−0.430138	+	0.902763i	$0.641535\pi$
$912$	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	$-0.963460\pi$
$919$		−	6.94467i		−	0.229084i	0.993418	−	0.114542i	$-0.0365400\pi$
$920$	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	−0.903309	−	0.428989i	$-0.858870\pi$
$929$	−4.20125	+	6.53728i	−0.137839	+	0.214481i	0.765471	+	0.643471i	$0.222506\pi$
$930$	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	0.994339	−	0.106255i	$-0.0338860\pi$
$937$	31.5494	+	27.3377i	1.03067	+	0.893085i	0.0363357	+	0.999340i	$0.488431\pi$
$938$	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	−0.857524	−	0.514445i	$-0.827998\pi$
$941$	2.84751	−	6.23518i	0.0928262	−	0.203261i	0.950350	+	0.311184i	$0.100725\pi$
$942$	−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	−0.290640	−	0.956832i	$-0.593868\pi$
$947$	18.9284	−	16.4016i	0.615091	−	0.532979i	0.905731	+	0.423853i	$0.139323\pi$
$948$	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	0.904692	+	0.426066i	$0.140101\pi$
$953$	4.83692	+	33.6415i	0.156683	+	1.08976i	−0.748009	+	0.663689i	$0.768990\pi$
$954$	−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	0.439206	−	0.898386i	$-0.355260\pi$
$971$	44.8361	−	28.8144i	1.43886	−	0.924699i	0.999654	−	0.0263125i	$-0.00837650\pi$
$972$	−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	0.721392	−	0.692527i	$-0.243503\pi$
$977$	−8.57680	−	18.7806i	−0.274396	−	0.600844i	−0.995788	+	0.0916830i	$0.970775\pi$
$978$	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	−0.831191	−	0.555988i	$-0.812340\pi$
$983$	−5.09708	+	5.88234i	−0.162571	+	0.187618i	0.668619	+	0.743605i	$0.266886\pi$
$984$	−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	0.594956	+	0.803758i	$0.297169\pi$
$991$	−12.6581	+	27.7173i	−0.402097	+	0.880470i	−0.997053	+	0.0767116i	$0.975558\pi$
$992$	−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	0.560398	−	0.828224i	$-0.310648\pi$
$997$	46.7190	−	13.7179i	1.47961	−	0.434451i	0.919208	+	0.393772i	$0.128830\pi$
$998$	−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.17.4	✓	80
3.2	odd	2	inner	138.2.f.a.17.8	yes	80
23.19	odd	22	inner	138.2.f.a.65.8	yes	80
69.65	even	22	inner	138.2.f.a.65.4	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.f.a.17.4	✓	80	1.1	even	1	trivial
138.2.f.a.17.8	yes	80	3.2	odd	2	inner
138.2.f.a.65.4	yes	80	69.65	even	22	inner
138.2.f.a.65.8	yes	80	23.19	odd	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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more