LMFDB - Embedded newform 156.2.w.c.19.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,2,Mod(7,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 11]))

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

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

chi := DirichletCharacter("156.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	156.w (of order $12$, degree $4$, 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:	$1.24566627153$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.6
Character	$\chi$	$=$	156.19
Dual form			156.2.w.c.115.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.17059 + 0.793543i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.740580 + 1.85783i) q^{4} +(2.78626 - 2.78626i) q^{5} +(-0.616993 - 1.27253i) q^{6} +(-0.826736 - 0.221523i) q^{7} +(-0.607351 + 2.76245i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.17059 + 0.793543i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.740580 + 1.85783i) q^{4} +(2.78626 - 2.78626i) q^{5} +(-0.616993 - 1.27253i) q^{6} +(-0.826736 - 0.221523i) q^{7} +(-0.607351 + 2.76245i) q^{8} +(0.500000 + 0.866025i) q^{9} +(5.47259 - 1.05056i) q^{10} +(0.501266 + 1.87075i) q^{11} +(0.287555 - 1.97922i) q^{12} +(-3.13330 + 1.78393i) q^{13} +(-0.791983 - 0.915364i) q^{14} +(-3.80610 + 1.01984i) q^{15} +(-2.90308 + 2.75175i) q^{16} +(-2.65107 + 1.53060i) q^{17} +(-0.101931 + 1.41054i) q^{18} +(1.97847 - 7.38376i) q^{19} +(7.23984 + 3.11295i) q^{20} +(0.605212 + 0.605212i) q^{21} +(-0.897740 + 2.58766i) q^{22} +(-2.45250 + 4.24786i) q^{23} +(1.90721 - 2.08868i) q^{24} -10.5264i q^{25} +(-5.08345 - 0.398149i) q^{26} -1.00000i q^{27} +(-0.200711 - 1.69999i) q^{28} +(-0.186428 + 0.322902i) q^{29} +(-5.26468 - 1.82648i) q^{30} +(-4.47110 - 4.47110i) q^{31} +(-5.58196 + 0.917458i) q^{32} +(0.501266 - 1.87075i) q^{33} +(-4.31792 - 0.312031i) q^{34} +(-2.92072 + 1.68628i) q^{35} +(-1.23864 + 1.57028i) q^{36} +(-3.74614 + 1.00378i) q^{37} +(8.17531 - 7.07338i) q^{38} +(3.60549 + 0.0217206i) q^{39} +(6.00466 + 9.38913i) q^{40} +(1.09339 + 4.08059i) q^{41} +(0.228196 + 1.18872i) q^{42} +(5.31531 + 9.20638i) q^{43} +(-3.10431 + 2.31671i) q^{44} +(3.80610 + 1.01984i) q^{45} +(-6.24174 + 3.02635i) q^{46} +(3.26234 - 3.26234i) q^{47} +(3.89002 - 0.931542i) q^{48} +(-5.42776 - 3.13372i) q^{49} +(8.35318 - 12.3222i) q^{50} +3.06120 q^{51} +(-5.63471 - 4.50001i) q^{52} +6.37156 q^{53} +(0.793543 - 1.17059i) q^{54} +(6.60904 + 3.81573i) q^{55} +(1.11406 - 2.14927i) q^{56} +(-5.40528 + 5.40528i) q^{57} +(-0.474468 + 0.230049i) q^{58} +(4.25652 + 1.14053i) q^{59} +(-4.71341 - 6.31582i) q^{60} +(0.691124 + 1.19706i) q^{61} +(-1.68583 - 8.78184i) q^{62} +(-0.221523 - 0.826736i) q^{63} +(-7.26225 - 3.35555i) q^{64} +(-3.75969 + 13.7007i) q^{65} +(2.07130 - 1.79211i) q^{66} +(1.03810 - 0.278157i) q^{67} +(-4.80693 - 3.79172i) q^{68} +(4.24786 - 2.45250i) q^{69} +(-4.75711 - 0.343768i) q^{70} +(-0.390575 + 1.45765i) q^{71} +(-2.69603 + 0.855243i) q^{72} +(1.23523 + 1.23523i) q^{73} +(-5.18175 - 1.79771i) q^{74} +(-5.26322 + 9.11617i) q^{75} +(15.1830 - 1.79259i) q^{76} -1.65766i q^{77} +(4.20332 + 2.88653i) q^{78} -12.7475i q^{79} +(-0.421659 + 15.7558i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.95821 + 5.64437i) q^{82} +(4.18842 + 4.18842i) q^{83} +(-0.676175 + 1.57259i) q^{84} +(-3.12193 + 11.6512i) q^{85} +(-1.08359 + 14.9949i) q^{86} +(0.322902 - 0.186428i) q^{87} +(-5.47229 + 0.248520i) q^{88} +(10.8274 - 2.90119i) q^{89} +(3.64611 + 4.21412i) q^{90} +(2.98559 - 0.780741i) q^{91} +(-9.70808 - 1.41046i) q^{92} +(1.63653 + 6.10763i) q^{93} +(6.40769 - 1.23007i) q^{94} +(-15.0605 - 26.0856i) q^{95} +(5.29285 + 1.99644i) q^{96} +(6.63291 + 1.77728i) q^{97} +(-3.86696 - 7.97547i) q^{98} +(-1.36948 + 1.36948i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9}+O(q^{10}) $ 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9	\( 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9} + 12 q^{10} + 4 q^{11} - 4 q^{12} - 22 q^{14} - 4 q^{15} + 12 q^{16} - 2 q^{18} - 22 q^{19} - 4 q^{20} + 10 q^{21} - 34 q^{22} + 2 q^{24} - 4 q^{26} - 14 q^{28} + 8 q^{29} - 16 q^{30} - 2 q^{31} - 34 q^{32} + 4 q^{33} + 20 q^{34} + 24 q^{35} - 4 q^{36} - 12 q^{37} - 12 q^{38} - 6 q^{39} + 28 q^{40} - 36 q^{41} + 6 q^{42} + 10 q^{43} + 20 q^{44} + 4 q^{45} - 2 q^{46} + 20 q^{47} + 32 q^{48} - 54 q^{49} - 24 q^{50} + 36 q^{51} + 4 q^{52} - 36 q^{53} - 4 q^{54} - 24 q^{55} + 70 q^{56} - 32 q^{57} + 48 q^{58} - 36 q^{59} - 28 q^{60} - 2 q^{61} + 64 q^{62} + 8 q^{63} - 8 q^{64} + 16 q^{65} + 20 q^{66} - 16 q^{67} - 10 q^{68} + 12 q^{69} + 36 q^{71} - 2 q^{72} - 40 q^{73} - 30 q^{74} - 8 q^{75} + 58 q^{76} + 24 q^{78} - 48 q^{80} - 12 q^{81} - 30 q^{82} - 24 q^{83} - 26 q^{84} + 18 q^{85} + 30 q^{86} + 6 q^{87} - 78 q^{88} + 66 q^{89} + 12 q^{90} + 42 q^{91} + 36 q^{92} - 10 q^{93} + 6 q^{94} - 28 q^{95} + 8 q^{96} + 4 q^{97} + 44 q^{98} - 4 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9 + 12 * q^10 + 4 * q^11 - 4 * q^12 - 22 * q^14 - 4 * q^15 + 12 * q^16 - 2 * q^18 - 22 * q^19 - 4 * q^20 + 10 * q^21 - 34 * q^22 + 2 * q^24 - 4 * q^26 - 14 * q^28 + 8 * q^29 - 16 * q^30 - 2 * q^31 - 34 * q^32 + 4 * q^33 + 20 * q^34 + 24 * q^35 - 4 * q^36 - 12 * q^37 - 12 * q^38 - 6 * q^39 + 28 * q^40 - 36 * q^41 + 6 * q^42 + 10 * q^43 + 20 * q^44 + 4 * q^45 - 2 * q^46 + 20 * q^47 + 32 * q^48 - 54 * q^49 - 24 * q^50 + 36 * q^51 + 4 * q^52 - 36 * q^53 - 4 * q^54 - 24 * q^55 + 70 * q^56 - 32 * q^57 + 48 * q^58 - 36 * q^59 - 28 * q^60 - 2 * q^61 + 64 * q^62 + 8 * q^63 - 8 * q^64 + 16 * q^65 + 20 * q^66 - 16 * q^67 - 10 * q^68 + 12 * q^69 + 36 * q^71 - 2 * q^72 - 40 * q^73 - 30 * q^74 - 8 * q^75 + 58 * q^76 + 24 * q^78 - 48 * q^80 - 12 * q^81 - 30 * q^82 - 24 * q^83 - 26 * q^84 + 18 * q^85 + 30 * q^86 + 6 * q^87 - 78 * q^88 + 66 * q^89 + 12 * q^90 + 42 * q^91 + 36 * q^92 - 10 * q^93 + 6 * q^94 - 28 * q^95 + 8 * q^96 + 4 * q^97 + 44 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	1.17059	+	0.793543i	0.827735	+	0.561119i
$2$	1.17059	+	0.793543i	0.827735	+	0.561119i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	0.740580	+	1.85783i	0.370290	+	0.928916i
$5$	2.78626	−	2.78626i	1.24605	−	1.24605i	0.288603	−	0.957449i	$-0.406809\pi$
$5$	2.78626	−	2.78626i	1.24605	−	1.24605i	0.957449	−	0.288603i	$-0.0931906\pi$
$6$	−0.616993	−	1.27253i	−0.251886	−	0.519506i
$7$	−0.826736	−	0.221523i	−0.312477	−	0.0837279i	0.0991725	−	0.995070i	$-0.468380\pi$
$7$	−0.826736	−	0.221523i	−0.312477	−	0.0837279i	−0.411649	+	0.911342i	$0.635047\pi$
$8$	−0.607351	+	2.76245i	−0.214731	+	0.976673i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	5.47259	−	1.05056i	1.73058	−	0.332217i
$11$	0.501266	+	1.87075i	0.151137	+	0.564052i	0.999405	+	0.0344847i	$0.0109790\pi$
$11$	0.501266	+	1.87075i	0.151137	+	0.564052i	−0.848268	+	0.529567i	$0.822354\pi$
$12$	0.287555	−	1.97922i	0.0830100	−	0.571352i
$13$	−3.13330	+	1.78393i	−0.869022	+	0.494774i
$13$	−3.13330	+	1.78393i	−0.869022	+	0.494774i
$14$	−0.791983	−	0.915364i	−0.211666	−	0.244641i
$15$	−3.80610	+	1.01984i	−0.982730	+	0.263322i
$16$	−2.90308	+	2.75175i	−0.725771	+	0.687937i
$17$	−2.65107	+	1.53060i	−0.642980	+	0.371225i	−0.785761	−	0.618530i	$-0.787729\pi$
$17$	−2.65107	+	1.53060i	−0.642980	+	0.371225i	0.142782	+	0.989754i	$0.454395\pi$
$18$	−0.101931	+	1.41054i	−0.0240254	+	0.332466i
$19$	1.97847	−	7.38376i	0.453892	−	1.69395i	−0.237431	−	0.971404i	$-0.576305\pi$
$19$	1.97847	−	7.38376i	0.453892	−	1.69395i	0.691324	−	0.722545i	$-0.257028\pi$
$20$	7.23984	+	3.11295i	1.61888	+	0.696077i
$21$	0.605212	+	0.605212i	0.132068	+	0.132068i
$22$	−0.897740	+	2.58766i	−0.191399	+	0.551691i
$23$	−2.45250	+	4.24786i	−0.511382	+	0.885739i	0.488531	+	0.872546i	$0.337533\pi$
$23$	−2.45250	+	4.24786i	−0.511382	+	0.885739i	−0.999913	+	0.0131929i	$0.995800\pi$
$24$	1.90721	−	2.08868i	0.389307	−	0.426349i
$25$		−	10.5264i		−	2.10529i
$26$	−5.08345	−	0.398149i	−0.996947	−	0.0780835i
$27$		−	1.00000i		−	0.192450i
$28$	−0.200711	−	1.69999i	−0.0379308	−	0.321268i
$29$	−0.186428	+	0.322902i	−0.0346187	+	0.0599614i	−0.882816	−	0.469720i	$-0.844355\pi$
$29$	−0.186428	+	0.322902i	−0.0346187	+	0.0599614i	0.848197	+	0.529681i	$0.177688\pi$
$30$	−5.26468	−	1.82648i	−0.961195	−	0.333468i
$31$	−4.47110	−	4.47110i	−0.803033	−	0.803033i	0.180536	−	0.983568i	$-0.442217\pi$
$31$	−4.47110	−	4.47110i	−0.803033	−	0.803033i	−0.983568	+	0.180536i	$0.942217\pi$
$32$	−5.58196	+	0.917458i	−0.986760	+	0.162185i
$33$	0.501266	−	1.87075i	0.0872591	−	0.325656i
$34$	−4.31792	−	0.312031i	−0.740518	−	0.0535129i
$35$	−2.92072	+	1.68628i	−0.493691	+	0.285033i
$36$	−1.23864	+	1.57028i	−0.206440	+	0.261713i
$37$	−3.74614	+	1.00378i	−0.615862	+	0.165020i	−0.553246	−	0.833018i	$-0.686611\pi$
$37$	−3.74614	+	1.00378i	−0.615862	+	0.165020i	−0.0626161	+	0.998038i	$0.519944\pi$
$38$	8.17531	−	7.07338i	1.32621	−	1.14745i
$39$	3.60549	+	0.0217206i	0.577340	+	0.00347808i
$40$	6.00466	+	9.38913i	0.949419	+	1.48455i
$41$	1.09339	+	4.08059i	0.170759	+	0.637282i	0.997235	+	0.0743099i	$0.0236754\pi$
$41$	1.09339	+	4.08059i	0.170759	+	0.637282i	−0.826476	+	0.562972i	$0.809658\pi$
$42$	0.228196	+	1.18872i	0.0352114	+	0.183423i
$43$	5.31531	+	9.20638i	0.810577	+	1.40396i	0.912461	+	0.409164i	$0.134179\pi$
$43$	5.31531	+	9.20638i	0.810577	+	1.40396i	−0.101884	+	0.994796i	$0.532487\pi$
$44$	−3.10431	+	2.31671i	−0.467992	+	0.349257i
$45$	3.80610	+	1.01984i	0.567379	+	0.152029i
$46$	−6.24174	+	3.02635i	−0.920294	+	0.446211i
$47$	3.26234	−	3.26234i	0.475862	−	0.475862i	−0.427944	−	0.903805i	$-0.640762\pi$
$47$	3.26234	−	3.26234i	0.475862	−	0.475862i	0.903805	+	0.427944i	$0.140762\pi$
$48$	3.89002	−	0.931542i	0.561476	−	0.134456i
$49$	−5.42776	−	3.13372i	−0.775394	−	0.447674i
$50$	8.35318	−	12.3222i	1.18132	−	1.74262i
$51$	3.06120			0.428653
$52$	−5.63471	−	4.50001i	−0.781393	−	0.624039i
$53$	6.37156			0.875201			0.437600	−	0.899170i	$-0.355829\pi$
$53$	6.37156			0.875201			0.437600	+	0.899170i	$0.355829\pi$
$54$	0.793543	−	1.17059i	0.107987	−	0.159298i
$55$	6.60904	+	3.81573i	0.891163	+	0.514513i
$56$	1.11406	−	2.14927i	0.148873	−	0.287209i
$57$	−5.40528	+	5.40528i	−0.715947	+	0.715947i
$58$	−0.474468	+	0.230049i	−0.0623006	+	0.0302069i
$59$	4.25652	+	1.14053i	0.554152	+	0.148485i	0.525018	−	0.851091i	$-0.324058\pi$
$59$	4.25652	+	1.14053i	0.554152	+	0.148485i	0.0291337	+	0.999576i	$0.490725\pi$
$60$	−4.71341	−	6.31582i	−0.608499	−	0.815368i
$61$	0.691124	+	1.19706i	0.0884893	+	0.153268i	0.906873	−	0.421405i	$-0.138463\pi$
$61$	0.691124	+	1.19706i	0.0884893	+	0.153268i	−0.818383	+	0.574673i	$0.805129\pi$
$62$	−1.68583	−	8.78184i	−0.214101	−	1.11530i
$63$	−0.221523	−	0.826736i	−0.0279093	−	0.104159i
$64$	−7.26225	−	3.35555i	−0.907781	−	0.419444i
$65$	−3.75969	+	13.7007i	−0.466332	+	1.69936i
$66$	2.07130	−	1.79211i	0.254959	−	0.220594i
$67$	1.03810	−	0.278157i	0.126824	−	0.0339823i	−0.194849	−	0.980833i	$-0.562422\pi$
$67$	1.03810	−	0.278157i	0.126824	−	0.0339823i	0.321673	+	0.946851i	$0.395755\pi$
$68$	−4.80693	−	3.79172i	−0.582925	−	0.459814i
$69$	4.24786	−	2.45250i	0.511382	−	0.295246i
$70$	−4.75711	−	0.343768i	−0.568583	−	0.0410882i
$71$	−0.390575	+	1.45765i	−0.0463527	+	0.172991i	−0.985222	−	0.171284i	$-0.945208\pi$
$71$	−0.390575	+	1.45765i	−0.0463527	+	0.172991i	0.938869	+	0.344275i	$0.111875\pi$
$72$	−2.69603	+	0.855243i	−0.317730	+	0.100791i
$73$	1.23523	+	1.23523i	0.144572	+	0.144572i	0.775688	−	0.631116i	$-0.217403\pi$
$73$	1.23523	+	1.23523i	0.144572	+	0.144572i	−0.631116	+	0.775688i	$0.717403\pi$
$74$	−5.18175	−	1.79771i	−0.602366	−	0.208980i
$75$	−5.26322	+	9.11617i	−0.607745	+	1.05264i
$76$	15.1830	−	1.79259i	1.74161	−	0.205625i
$77$		−	1.65766i		−	0.188907i
$78$	4.20332	+	2.88653i	0.475933	+	0.326835i
$79$		−	12.7475i		−	1.43421i	−0.696966	−	0.717104i	$-0.745467\pi$
$79$		−	12.7475i		−	1.43421i	0.696966	−	0.717104i	$-0.254533\pi$
$80$	−0.421659	+	15.7558i	−0.0471429	+	1.76155i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.95821	+	5.64437i	−0.216248	+	0.623317i
$83$	4.18842	+	4.18842i	0.459739	+	0.459739i	0.898570	−	0.438831i	$-0.144607\pi$
$83$	4.18842	+	4.18842i	0.459739	+	0.459739i	−0.438831	+	0.898570i	$0.644607\pi$
$84$	−0.676175	+	1.57259i	−0.0737767	+	0.171584i
$85$	−3.12193	+	11.6512i	−0.338621	+	1.26375i
$86$	−1.08359	+	14.9949i	−0.116847	+	1.61694i
$87$	0.322902	−	0.186428i	0.0346187	−	0.0199871i
$88$	−5.47229	+	0.248520i	−0.583348	+	0.0264923i
$89$	10.8274	−	2.90119i	1.14770	−	0.307526i	0.365658	−	0.930749i	$-0.380844\pi$
$89$	10.8274	−	2.90119i	1.14770	−	0.307526i	0.782044	+	0.623223i	$0.214177\pi$
$90$	3.64611	+	4.21412i	0.384333	+	0.444207i
$91$	2.98559	−	0.780741i	0.312975	−	0.0818439i
$92$	−9.70808	−	1.41046i	−1.01214	−	0.147050i
$93$	1.63653	+	6.10763i	0.169701	+	0.633332i
$94$	6.40769	−	1.23007i	0.660903	−	0.126872i
$95$	−15.0605	−	26.0856i	−1.54518	−	2.67632i
$96$	5.29285	+	1.99644i	0.540199	+	0.203761i
$97$	6.63291	+	1.77728i	0.673470	+	0.180456i	0.579317	−	0.815102i	$-0.303319\pi$
$97$	6.63291	+	1.77728i	0.673470	+	0.180456i	0.0941524	+	0.995558i	$0.469986\pi$
$98$	−3.86696	−	7.97547i	−0.390622	−	0.805644i
$99$	−1.36948	+	1.36948i	−0.137638	+	0.137638i
$100$	19.5564	−	7.79567i	1.95564	−	0.779567i
$101$	−4.03206	−	2.32791i	−0.401205	−	0.231636i	0.285799	−	0.958290i	$-0.407741\pi$
$101$	−4.03206	−	2.32791i	−0.401205	−	0.231636i	−0.687004	+	0.726654i	$0.741074\pi$
$102$	3.58342	+	2.42919i	0.354811	+	0.240526i
$103$	−3.22962			−0.318224			−0.159112	−	0.987261i	$-0.550863\pi$
$103$	−3.22962			−0.318224			−0.159112	+	0.987261i	$0.550863\pi$
$104$	−3.02501	−	9.73906i	−0.296626	−	0.954994i
$105$	3.37255			0.329128
$106$	7.45850	+	5.05610i	0.724434	+	0.491092i
$107$	10.5067	+	6.06607i	1.01573	+	0.586430i	0.912863	−	0.408266i	$-0.133866\pi$
$107$	10.5067	+	6.06607i	1.01573	+	0.586430i	0.102863	+	0.994696i	$0.467200\pi$
$108$	1.85783	−	0.740580i	0.178770	−	0.0712623i
$109$	3.20074	−	3.20074i	0.306575	−	0.306575i	−0.537004	−	0.843580i	$-0.680444\pi$
$109$	3.20074	−	3.20074i	0.306575	−	0.306575i	0.843580	+	0.537004i	$0.180444\pi$
$110$	4.70856	+	9.71122i	0.448943	+	0.925929i
$111$	3.74614	+	1.00378i	0.355568	+	0.0952742i
$112$	3.00966	−	1.63187i	0.284386	−	0.154197i
$113$	−8.21779	−	14.2336i	−0.773064	−	1.33899i	−0.935876	−	0.352329i	$-0.885390\pi$
$113$	−8.21779	−	14.2336i	−0.773064	−	1.33899i	0.162812	−	0.986657i	$-0.447944\pi$
$114$	−10.6167	+	2.03807i	−0.994347	+	0.190883i
$115$	5.00232	+	18.6689i	0.466469	+	1.74089i
$116$	−0.737962	−	0.107216i	−0.0685181	−	0.00995479i
$117$	−3.11158	−	1.82155i	−0.287666	−	0.168403i
$118$	4.07760	+	4.71283i	0.375373	+	0.433851i
$119$	2.53080	−	0.678126i	0.231998	−	0.0621637i
$120$	−0.505621	−	11.1335i	−0.0461567	−	1.01635i
$121$	6.27785	−	3.62452i	0.570713	−	0.329501i
$122$	−0.140894	+	1.94971i	−0.0127560	+	0.176518i
$123$	1.09339	−	4.08059i	0.0985878	−	0.367935i
$124$	4.99534	−	11.6178i	0.448595	−	1.04330i
$125$	−15.3981	−	15.3981i	−1.37725	−	1.37725i
$126$	0.396736	−	1.14356i	0.0353441	−	0.101876i
$127$	4.24127	−	7.34610i	0.376352	−	0.651861i	−0.614176	−	0.789169i	$-0.710512\pi$
$127$	4.24127	−	7.34610i	0.376352	−	0.651861i	0.990528	+	0.137308i	$0.0438450\pi$
$128$	−5.83837	−	9.69089i	−0.516044	−	0.856562i
$129$		−	10.6306i		−	0.935973i
$130$	−15.2731	+	13.0545i	−1.33954	+	1.14495i
$131$			10.4711i			0.914861i	0.889245	+	0.457431i	$0.151230\pi$
$131$			10.4711i			0.914861i	−0.889245	+	0.457431i	$0.848770\pi$
$132$	3.84676	−	0.454172i	0.334818	−	0.0395306i
$133$	−3.27134	+	5.66614i	−0.283662	+	0.491316i
$134$	1.43592	+	0.498165i	0.124045	+	0.0430349i
$135$	−2.78626	−	2.78626i	−0.239803	−	0.239803i
$136$	−2.61807	−	8.25307i	−0.224497	−	0.707694i
$137$	−3.85976	+	14.4048i	−0.329761	+	1.23069i	0.579676	+	0.814847i	$0.303179\pi$
$137$	−3.85976	+	14.4048i	−0.329761	+	1.23069i	−0.909438	+	0.415840i	$0.863488\pi$
$138$	6.91868	+	0.499973i	0.588957	+	0.0425605i
$139$	−14.8229	+	8.55802i	−1.25726	+	0.725881i	−0.972542	−	0.232729i	$-0.925235\pi$
$139$	−14.8229	+	8.55802i	−1.25726	+	0.725881i	−0.284722	+	0.958610i	$0.591901\pi$
$140$	−5.29584	−	4.17738i	−0.447581	−	0.353053i
$141$	−4.45644	+	1.19410i	−0.375300	+	0.100561i
$142$	−1.61391	+	1.39637i	−0.135436	+	0.117181i
$143$	−4.90791	−	4.96740i	−0.410420	−	0.415395i
$144$	−3.83462	−	1.13827i	−0.319552	−	0.0948558i
$145$	0.380253	+	1.41912i	0.0315783	+	0.117852i
$146$	0.465744	+	2.42615i	0.0385452	+	0.200790i
$147$	3.13372	+	5.42776i	0.258465	+	0.447674i
$148$	−4.63917	−	6.21633i	−0.381337	−	0.510979i
$149$	11.6792	+	3.12945i	0.956801	+	0.256374i	0.703246	−	0.710947i	$-0.251733\pi$
$149$	11.6792	+	3.12945i	0.956801	+	0.256374i	0.253555	+	0.967321i	$0.418400\pi$
$150$	−13.3952	+	6.49474i	−1.09371	+	0.530293i
$151$	−2.53404	+	2.53404i	−0.206217	+	0.206217i	−0.802657	−	0.596440i	$-0.796581\pi$
$151$	−2.53404	+	2.53404i	−0.206217	+	0.206217i	0.596440	+	0.802657i	$0.296581\pi$
$152$	19.1956	+	9.94996i	1.55697	+	0.807048i
$153$	−2.65107	−	1.53060i	−0.214327	−	0.123742i
$154$	1.31542	−	1.94044i	0.106000	−	0.156365i
$155$	−24.9152			−2.00124
$156$	2.62980	+	6.71447i	0.210552	+	0.537588i
$157$	−4.99846			−0.398921			−0.199460	−	0.979906i	$-0.563919\pi$
$157$	−4.99846			−0.398921			−0.199460	+	0.979906i	$0.563919\pi$
$158$	10.1157	−	14.9222i	0.804762	−	1.18714i
$159$	−5.51793	−	3.18578i	−0.437600	−	0.252649i
$160$	−12.9965	+	18.1090i	−1.02746	+	1.43165i
$161$	2.96857	−	2.96857i	0.233956	−	0.233956i
$162$	−1.27253	+	0.616993i	−0.0999790	+	0.0484755i
$163$	−2.32148	−	0.622040i	−0.181833	−	0.0487219i	0.166754	−	0.985999i	$-0.446672\pi$
$163$	−2.32148	−	0.622040i	−0.181833	−	0.0487219i	−0.348586	+	0.937277i	$0.613338\pi$
$164$	−6.77132	+	5.05335i	−0.528751	+	0.394600i
$165$	−3.81573	−	6.60904i	−0.297054	−	0.514513i
$166$	1.57925	+	8.22663i	0.122573	+	0.638510i
$167$	−1.30125	−	4.85633i	−0.100694	−	0.375794i	0.897127	−	0.441772i	$-0.145650\pi$
$167$	−1.30125	−	4.85633i	−0.100694	−	0.375794i	−0.997821	+	0.0659779i	$0.978983\pi$
$168$	−2.03944	+	1.30429i	−0.157347	+	0.100628i
$169$	6.63517	−	11.1792i	0.510398	−	0.859938i
$170$	−12.9002	+	11.1614i	−0.989404	+	0.856044i
$171$	7.38376	−	1.97847i	0.564650	−	0.151297i
$172$	−13.1675	+	16.6930i	−1.00401	+	1.27283i
$173$	4.43136	−	2.55844i	0.336910	−	0.194515i	−0.321995	−	0.946741i	$-0.604353\pi$
$173$	4.43136	−	2.55844i	0.336910	−	0.194515i	0.658905	+	0.752226i	$0.271020\pi$
$174$	0.525925	+	0.0380056i	0.0398703	+	0.00288119i
$175$	−2.33185	+	8.70259i	−0.176271	+	0.657854i
$176$	−6.60304	−	4.05158i	−0.497723	−	0.305399i
$177$	−3.11599	−	3.11599i	−0.234212	−	0.234212i
$178$	14.9767	+	5.19589i	1.12255	+	0.389448i
$179$	11.3505	−	19.6597i	0.848378	−	1.46943i	−0.0342774	−	0.999412i	$-0.510913\pi$
$179$	11.3505	−	19.6597i	0.848378	−	1.46943i	0.882655	−	0.470021i	$-0.155754\pi$
$180$	0.924026	+	7.82636i	0.0688729	+	0.583343i
$181$		−	15.5351i		−	1.15472i	−0.816491	−	0.577359i	$-0.804083\pi$
$181$		−	15.5351i		−	1.15472i	0.816491	−	0.577359i	$-0.195917\pi$
$182$	4.11447	+	1.45527i	0.304985	+	0.107871i
$183$		−	1.38225i		−	0.102179i
$184$	−10.2450	−	9.35485i	−0.755268	−	0.689649i
$185$	−7.64094	+	13.2345i	−0.561773	+	0.973019i
$186$	−2.93095	+	8.44822i	−0.214908	+	0.619453i
$187$	−4.19226	−	4.19226i	−0.306568	−	0.306568i
$188$	8.47691	+	3.64486i	0.618242	+	0.265829i
$189$	−0.221523	+	0.826736i	−0.0161134	+	0.0601362i
$190$	3.07027	−	42.4868i	0.222741	−	3.08231i
$191$	−20.3302	+	11.7376i	−1.47104	+	0.849307i	−0.999471	−	0.0325216i	$-0.989646\pi$
$191$	−20.3302	+	11.7376i	−1.47104	+	0.849307i	−0.471571	+	0.881828i	$0.656313\pi$
$192$	4.61152	+	6.53712i	0.332808	+	0.471776i
$193$	−4.77983	+	1.28075i	−0.344059	+	0.0921905i	−0.426711	−	0.904388i	$-0.640328\pi$
$193$	−4.77983	+	1.28075i	−0.344059	+	0.0921905i	0.0826515	+	0.996579i	$0.473661\pi$
$194$	6.35409	+	7.34397i	0.456197	+	0.527266i
$195$	10.1063	−	9.98529i	0.723729	−	0.715061i
$196$	1.80223	−	12.4046i	0.128731	−	0.886045i
$197$	−3.43979	−	12.8375i	−0.245075	−	0.914631i	−0.973346	−	0.229342i	$-0.926343\pi$
$197$	−3.43979	−	12.8375i	−0.245075	−	0.914631i	0.728271	−	0.685289i	$-0.240324\pi$
$198$	−2.68985	+	0.516365i	−0.191159	+	0.0366965i
$199$	−10.1532	−	17.5859i	−0.719743	−	1.24663i	−0.961102	−	0.276195i	$-0.910926\pi$
$199$	−10.1532	−	17.5859i	−0.719743	−	1.24663i	0.241359	−	0.970436i	$-0.422407\pi$
$200$	29.0788	+	6.39325i	2.05618	+	0.452071i
$201$	−1.03810	−	0.278157i	−0.0732217	−	0.0196197i
$202$	−2.87261	−	5.92465i	−0.202116	−	0.416857i
$203$	0.225657	−	0.225657i	0.0158380	−	0.0158380i
$204$	2.26706	+	5.68719i	0.158726	+	0.398183i
$205$	14.4161	+	8.32311i	1.00686	+	0.581311i
$206$	−3.78058	−	2.56284i	−0.263405	−	0.178562i
$207$	−4.90500			−0.340921
$208$	4.18731	−	13.8010i	0.290337	−	0.956924i
$209$	14.8049			1.02408
$210$	3.94789	+	2.67627i	0.272430	+	0.184680i
$211$	6.81491	+	3.93459i	0.469157	+	0.270868i	0.715887	−	0.698216i	$-0.246023\pi$
$211$	6.81491	+	3.93459i	0.469157	+	0.270868i	−0.246729	+	0.969084i	$0.579356\pi$
$212$	4.71865	+	11.8373i	0.324078	+	0.812988i
$213$	1.06707	−	1.06707i	0.0731145	−	0.0731145i
$214$	7.48545	+	15.4385i	0.511695	+	1.05535i
$215$	40.4611	+	10.8415i	2.75943	+	0.739386i
$216$	2.76245	+	0.607351i	0.187961	+	0.0413250i
$217$	2.70596	+	4.68686i	0.183693	+	0.318165i
$218$	6.28669	−	1.20684i	0.425789	−	0.0817377i
$219$	−0.452124	−	1.68735i	−0.0305517	−	0.114021i
$220$	−2.19447	+	15.1043i	−0.147951	+	1.01833i
$221$	5.57613	−	9.52516i	0.375091	−	0.640732i
$222$	3.58867	+	4.14774i	0.240856	+	0.278378i
$223$	−27.0259	+	7.24158i	−1.80979	+	0.484932i	−0.995436	−	0.0954346i	$-0.969576\pi$
$223$	−27.0259	+	7.24158i	−1.80979	+	0.484932i	−0.814355	+	0.580367i	$0.802909\pi$
$224$	4.81804	+	0.478038i	0.321919	+	0.0319402i
$225$	9.11617	−	5.26322i	0.607745	−	0.350882i
$226$	1.67530	−	23.1830i	0.111439	−	1.54211i
$227$	0.115737	−	0.431938i	0.00768176	−	0.0286687i	−0.961979	−	0.273125i	$-0.911943\pi$
$227$	0.115737	−	0.431938i	0.00768176	−	0.0286687i	0.969660	+	0.244456i	$0.0786094\pi$
$228$	−14.0452	−	6.03907i	−0.930163	−	0.399947i
$229$	17.2765	+	17.2765i	1.14166	+	1.14166i	0.988146	+	0.153516i	$0.0490595\pi$
$229$	17.2765	+	17.2765i	1.14166	+	1.14166i	0.153516	+	0.988146i	$0.450940\pi$
$230$	−8.95889	+	25.8233i	−0.590732	+	1.70274i
$231$	−0.828828	+	1.43557i	−0.0545329	+	0.0944537i
$232$	−0.778773	−	0.711112i	−0.0511290	−	0.0466868i
$233$			10.7566i			0.704685i	0.935871	+	0.352343i	$0.114615\pi$
$233$			10.7566i			0.704685i	−0.935871	+	0.352343i	$0.885385\pi$
$234$	−2.19692	−	4.60147i	−0.143617	−	0.300808i
$235$		−	18.1794i		−	1.18590i
$236$	1.03338	+	8.75256i	0.0672672	+	0.569743i
$237$	−6.37376	+	11.0397i	−0.414020	+	0.717104i
$238$	3.50066	+	1.21449i	0.226914	+	0.0787235i
$239$	18.3091	+	18.3091i	1.18432	+	1.18432i	0.978614	+	0.205703i	$0.0659481\pi$
$239$	18.3091	+	18.3091i	1.18432	+	1.18432i	0.205703	+	0.978614i	$0.434052\pi$
$240$	8.24307	−	13.4341i	0.532088	−	0.867167i
$241$	−7.60677	+	28.3888i	−0.489995	+	1.82869i	0.0664332	+	0.997791i	$0.478838\pi$
$241$	−7.60677	+	28.3888i	−0.489995	+	1.82869i	−0.556428	+	0.830896i	$0.687829\pi$
$242$	10.2250	+	0.738903i	0.657289	+	0.0474985i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−1.71211	+	2.17051i	−0.109606	+	0.138953i
$245$	−23.8545	+	6.39178i	−1.52401	+	0.408356i
$246$	4.51804	−	3.90907i	0.288060	−	0.249233i
$247$	6.97297	+	26.6650i	0.443680	+	1.69665i
$248$	15.0667	−	9.63565i	0.956736	−	0.611864i
$249$	−1.53307	−	5.72149i	−0.0971542	−	0.362584i
$250$	−5.80587	−	30.2440i	−0.367195	−	1.91280i
$251$	6.38971	+	11.0673i	0.403315	+	0.698562i	0.994124	−	0.108250i	$-0.0345245\pi$
$251$	6.38971	+	11.0673i	0.403315	+	0.698562i	−0.590809	+	0.806812i	$0.701191\pi$
$252$	1.37188	−	1.02382i	0.0864203	−	0.0644944i
$253$	−9.17603	−	2.45871i	−0.576892	−	0.154578i
$254$	10.7942	−	5.23367i	0.677291	−	0.328389i
$255$	8.52928	−	8.52928i	0.534124	−	0.534124i
$256$	0.855776	−	15.9771i	0.0534860	−	0.998569i
$257$	−0.872546	−	0.503765i	−0.0544279	−	0.0314240i	0.472539	−	0.881310i	$-0.343338\pi$
$257$	−0.872546	−	0.503765i	−0.0544279	−	0.0314240i	−0.526967	+	0.849886i	$0.676671\pi$
$258$	8.43584	−	12.4441i	0.525193	−	0.774738i
$259$	3.31943			0.206259
$260$	−28.2379	+	3.16157i	−1.75124	+	0.196072i
$261$	−0.372855			−0.0230792
$262$	−8.30924	+	12.2574i	−0.513346	+	0.757262i
$263$	−11.5823	−	6.68703i	−0.714194	−	0.412340i	0.0984180	−	0.995145i	$-0.468622\pi$
$263$	−11.5823	−	6.68703i	−0.714194	−	0.412340i	−0.812612	+	0.582805i	$0.801955\pi$
$264$	4.86340	+	2.52092i	0.299322	+	0.155152i
$265$	17.7528	−	17.7528i	1.09055	−	1.09055i
$266$	−8.32574	+	4.03679i	−0.510484	+	0.247512i
$267$	−10.8274	−	2.90119i	−0.662626	−	0.177550i
$268$	1.28556	+	1.72261i	0.0785283	+	0.105225i
$269$	−4.75660	−	8.23868i	−0.290015	−	0.502321i	0.683798	−	0.729672i	$-0.260327\pi$
$269$	−4.75660	−	8.23868i	−0.290015	−	0.502321i	−0.973813	+	0.227351i	$0.926994\pi$
$270$	−1.05056	−	5.47259i	−0.0639351	−	0.333051i
$271$	0.813794	+	3.03712i	0.0494344	+	0.184492i	0.986228	−	0.165390i	$-0.0528883\pi$
$271$	0.813794	+	3.03712i	0.0494344	+	0.184492i	−0.936794	+	0.349882i	$0.886222\pi$
$272$	3.48447	−	11.7385i	0.211277	−	0.711753i
$273$	−2.97597	−	0.816656i	−0.180114	−	0.0494262i
$274$	−15.9490	+	13.7993i	−0.963517	+	0.833647i
$275$	19.6923	−	5.27654i	1.18749	−	0.318188i
$276$	7.70221	+	6.07553i	0.463619	+	0.365704i
$277$	1.11008	−	0.640907i	0.0666984	−	0.0385084i	−0.466280	−	0.884637i	$-0.654406\pi$
$277$	1.11008	−	0.640907i	0.0666984	−	0.0385084i	0.532978	+	0.846129i	$0.321073\pi$
$278$	−24.1428	−	1.74466i	−1.44799	−	0.104638i
$279$	1.63653	−	6.10763i	0.0979768	−	0.365654i
$280$	−2.88435	−	9.09249i	−0.172373	−	0.543380i
$281$	6.45993	+	6.45993i	0.385367	+	0.385367i	0.873031	−	0.487664i	$-0.162151\pi$
$281$	6.45993	+	6.45993i	0.385367	+	0.385367i	−0.487664	+	0.873031i	$0.662151\pi$
$282$	−6.16426	−	2.13857i	−0.367076	−	0.127350i
$283$	−6.03896	+	10.4598i	−0.358979	+	0.621770i	−0.987791	−	0.155788i	$-0.950208\pi$
$283$	−6.03896	+	10.4598i	−0.358979	+	0.621770i	0.628812	+	0.777558i	$0.283542\pi$
$284$	−2.99731	+	0.353880i	−0.177858	+	0.0209989i
$285$			30.1210i			1.78421i
$286$	−1.80332	−	9.70944i	−0.106633	−	0.574131i
$287$		−	3.61578i		−	0.213433i
$288$	−3.58552	−	4.37539i	−0.211279	−	0.257822i
$289$	−3.81454	+	6.60698i	−0.224385	+	0.388646i
$290$	−0.681013	+	1.96296i	−0.0399905	+	0.115269i
$291$	−4.85563	−	4.85563i	−0.284642	−	0.284642i
$292$	−1.38006	+	3.20963i	−0.0807619	+	0.187829i
$293$	5.25925	−	19.6278i	0.307249	−	1.14667i	−0.623743	−	0.781629i	$-0.714389\pi$
$293$	5.25925	−	19.6278i	0.307249	−	1.14667i	0.930992	−	0.365039i	$-0.118944\pi$
$294$	−0.638847	+	8.84044i	−0.0372583	+	0.515585i
$295$	15.0376	−	8.68195i	0.875521	−	0.505482i
$296$	−0.497657	−	10.9582i	−0.0289257	−	0.636931i
$297$	1.87075	−	0.501266i	0.108552	−	0.0290864i
$298$	11.1883	+	12.9313i	0.648121	+	0.749090i
$299$	0.106539	−	17.6849i	0.00616134	−	1.02275i
$300$	−20.8342	−	3.02693i	−1.20286	−	0.174760i
$301$	−2.35493	−	8.78870i	−0.135736	−	0.506573i
$302$	−4.97720	+	0.955462i	−0.286406	+	0.0549807i
$303$	2.32791	+	4.03206i	0.133735	+	0.231636i
$304$	14.5746	+	26.8799i	0.835908	+	1.54167i
$305$	5.26097	+	1.40967i	0.301242	+	0.0807176i
$306$	−1.88874	−	3.89545i	−0.107972	−	0.222688i
$307$	−3.75237	+	3.75237i	−0.214159	+	0.214159i	−0.806032	−	0.591872i	$-0.798389\pi$
$307$	−3.75237	+	3.75237i	−0.214159	+	0.214159i	0.591872	+	0.806032i	$0.298389\pi$
$308$	3.07965	−	1.22763i	0.175479	−	0.0699505i
$309$	2.79694	+	1.61481i	0.159112	+	0.0918634i
$310$	−29.1656	−	19.7713i	−1.65650	−	1.12293i
$311$	7.65807			0.434250			0.217125	−	0.976144i	$-0.430332\pi$
$311$	7.65807			0.434250			0.217125	+	0.976144i	$0.430332\pi$
$312$	−2.24980	+	9.94678i	−0.127370	+	0.563125i
$313$	−24.3412			−1.37584			−0.687922	−	0.725784i	$-0.741477\pi$
$313$	−24.3412			−1.37584			−0.687922	+	0.725784i	$0.741477\pi$
$314$	−5.85117	−	3.96649i	−0.330201	−	0.223842i
$315$	−2.92072	−	1.68628i	−0.164564	−	0.0950109i
$316$	23.6828	−	9.44056i	1.33226	−	0.531073i
$317$	−13.5151	+	13.5151i	−0.759083	+	0.759083i	−0.976156	−	0.217072i	$-0.930349\pi$
$317$	−13.5151	+	13.5151i	−0.759083	+	0.759083i	0.217072	+	0.976156i	$0.430349\pi$
$318$	−3.93120	−	8.10796i	−0.220451	−	0.454672i
$319$	−0.697518	−	0.186899i	−0.0390535	−	0.0104644i
$320$	−29.5839	+	10.8851i	−1.65379	+	0.608493i
$321$	−6.06607	−	10.5067i	−0.338575	−	0.586430i
$322$	5.83067	−	1.11930i	0.324931	−	0.0623763i
$323$	6.05649	+	22.6031i	0.336992	+	1.25767i
$324$	−1.97922	−	0.287555i	−0.109957	−	0.0159753i
$325$	18.7785	+	32.9825i	1.04164	+	1.82954i
$326$	−2.22390	−	2.57035i	−0.123170	−	0.142359i
$327$	−4.37229	+	1.17155i	−0.241788	+	0.0647870i
$328$	−11.9365	+	0.542087i	−0.659083	+	0.0299317i
$329$	−3.41978	+	1.97441i	−0.188539	+	0.108853i
$330$	0.777884	−	10.7644i	0.0428211	−	0.592563i
$331$	7.76761	−	28.9891i	0.426946	−	1.59339i	−0.332689	−	0.943037i	$-0.607956\pi$
$331$	7.76761	−	28.9891i	0.426946	−	1.59339i	0.759635	−	0.650349i	$-0.225377\pi$
$332$	−4.67952	+	10.8832i	−0.256822	+	0.597295i
$333$	−2.74237	−	2.74237i	−0.150281	−	0.150281i
$334$	2.33047	−	6.71739i	0.127518	−	0.367559i
$335$	2.11739	−	3.66742i	0.115685	−	0.200373i
$336$	−3.42237	−	0.0915901i	−0.186706	−	0.00499665i
$337$			11.5413i			0.628693i	0.949308	+	0.314347i	$0.101785\pi$
$337$			11.5413i			0.628693i	−0.949308	+	0.314347i	$0.898215\pi$
$338$	16.6383	−	7.82101i	0.905002	−	0.425407i
$339$			16.4356i			0.892658i
$340$	−23.9580	+	2.82863i	−1.29931	+	0.153404i
$341$	6.12309	−	10.6055i	0.331584	−	0.574320i
$342$	10.2134	+	3.54334i	0.552276	+	0.191602i
$343$	8.02962	+	8.02962i	0.433559	+	0.433559i
$344$	−28.6604	+	9.09176i	−1.54527	+	0.490195i
$345$	5.00232	−	18.6689i	0.269316	−	1.00510i
$346$	7.21755	+	0.521571i	0.388018	+	0.0280398i
$347$	−4.46629	+	2.57861i	−0.239763	+	0.138427i	−0.615068	−	0.788474i	$-0.710871\pi$
$347$	−4.46629	+	2.57861i	−0.239763	+	0.138427i	0.375305	+	0.926901i	$0.377538\pi$
$348$	0.585486	+	0.461833i	0.0313853	+	0.0247569i
$349$	4.36312	−	1.16909i	0.233553	−	0.0625802i	−0.140144	−	0.990131i	$-0.544757\pi$
$349$	4.36312	−	1.16909i	0.233553	−	0.0625802i	0.373697	+	0.927551i	$0.378090\pi$
$350$	−9.63552	+	8.33677i	−0.515040	+	0.445619i
$351$	1.78393	+	3.13330i	0.0952193	+	0.167243i
$352$	−4.51438	−	9.98255i	−0.240617	−	0.532072i
$353$	1.20065	+	4.48090i	0.0639044	+	0.238494i	0.990489	−	0.137592i	$-0.0439363\pi$
$353$	1.20065	+	4.48090i	0.0639044	+	0.238494i	−0.926585	+	0.376086i	$0.877270\pi$
$354$	−1.17489	−	6.12023i	−0.0624446	−	0.325287i
$355$	2.97313	+	5.14961i	0.157797	+	0.273313i
$356$	13.4085	+	17.9669i	0.710649	+	0.952246i
$357$	−2.53080	−	0.678126i	−0.133944	−	0.0358902i
$358$	28.8876	−	14.0064i	1.52676	−	0.740260i
$359$	−12.8587	+	12.8587i	−0.678658	+	0.678658i	−0.959697	−	0.281038i	$-0.909321\pi$
$359$	−12.8587	+	12.8587i	−0.678658	+	0.678658i	0.281038	+	0.959697i	$0.409321\pi$
$360$	−5.12889	+	9.89475i	−0.270316	+	0.521499i
$361$	−34.1510	−	19.7171i	−1.79742	−	1.03774i
$362$	12.3278	−	18.1853i	0.647935	−	0.955800i
$363$	−7.24903			−0.380476
$364$	3.66156	+	4.96853i	0.191918	+	0.260422i
$365$	6.88332			0.360289
$366$	1.09687	−	1.61805i	0.0573344	−	0.0845768i
$367$	1.94694	+	1.12406i	0.101629	+	0.0586757i	0.549953	−	0.835195i	$-0.314646\pi$
$367$	1.94694	+	1.12406i	0.101629	+	0.0586757i	−0.448324	+	0.893871i	$0.647979\pi$
$368$	−4.56921	−	19.0805i	−0.238187	−	0.994642i
$369$	−2.98720	+	2.98720i	−0.155508	+	0.155508i
$370$	−19.4466	+	9.42880i	−1.01098	+	0.490180i
$371$	−5.26759	−	1.41145i	−0.273480	−	0.0732787i
$372$	−10.1350	+	7.56360i	−0.525474	+	0.392154i
$373$	−10.3801	−	17.9789i	−0.537463	−	0.930913i	−0.999040	−	0.0438127i	$-0.986050\pi$
$373$	−10.3801	−	17.9789i	−0.537463	−	0.930913i	0.461577	−	0.887100i	$-0.347284\pi$
$374$	−1.58069	−	8.23416i	−0.0817358	−	0.425778i
$375$	5.63609	+	21.0342i	0.291047	+	1.08620i
$376$	7.03067	+	10.9934i	0.362579	+	0.566944i
$377$	0.00809863	−	1.34432i	0.000417101	−	0.0692362i
$378$	−0.915364	+	0.791983i	−0.0470812	+	0.0407352i
$379$	12.5946	−	3.37473i	0.646943	−	0.173348i	0.0795969	−	0.996827i	$-0.474637\pi$
$379$	12.5946	−	3.37473i	0.646943	−	0.173348i	0.567347	+	0.823479i	$0.307970\pi$
$380$	37.3091	−	47.2983i	1.91392	−	2.42635i
$381$	−7.34610	+	4.24127i	−0.376352	+	0.217287i
$382$	−33.1127	−	2.39287i	−1.69420	−	0.122430i
$383$	−4.16021	+	15.5261i	−0.212577	+	0.793347i	0.774429	+	0.632661i	$0.218037\pi$
$383$	−4.16021	+	15.5261i	−0.212577	+	0.793347i	−0.987006	+	0.160686i	$0.948629\pi$
$384$	0.210731	+	11.3117i	0.0107538	+	0.577250i
$385$	−4.61865	−	4.61865i	−0.235388	−	0.235388i
$386$	−6.61157	−	2.29376i	−0.336520	−	0.116749i
$387$	−5.31531	+	9.20638i	−0.270192	+	0.467987i
$388$	1.61031	+	13.6391i	0.0817509	+	0.692418i
$389$			4.07117i			0.206416i	0.994660	+	0.103208i	$0.0329108\pi$
$389$			4.07117i			0.206416i	−0.994660	+	0.103208i	$0.967089\pi$
$390$	19.7542	−	3.66892i	1.00029	−	0.185783i
$391$		−	15.0152i		−	0.759350i
$392$	11.9533	−	13.0906i	0.603732	−	0.661177i
$393$	5.23553	−	9.06821i	0.264098	−	0.457431i
$394$	6.16048	−	17.7571i	0.310360	−	0.894588i
$395$	−35.5179	−	35.5179i	−1.78710	−	1.78710i
$396$	−3.55848	−	1.53006i	−0.178820	−	0.0768883i
$397$	5.05897	−	18.8803i	0.253903	−	0.947577i	−0.714795	−	0.699334i	$-0.753480\pi$
$397$	5.05897	−	18.8803i	0.253903	−	0.947577i	0.968698	−	0.248243i	$-0.0798533\pi$
$398$	2.06986	−	28.6430i	0.103753	−	1.43574i
$399$	5.66614	−	3.27134i	0.283662	−	0.163772i
$400$	28.9661	+	30.5591i	1.44831	+	1.52796i
$401$	−22.8257	+	6.11612i	−1.13986	+	0.305424i	−0.778894	−	0.627155i	$-0.784219\pi$
$401$	−22.8257	+	6.11612i	−1.13986	+	0.305424i	−0.360965	+	0.932579i	$0.617553\pi$
$402$	−0.994460	−	1.14938i	−0.0495992	−	0.0573260i
$403$	21.9854	+	6.03316i	1.09517	+	0.300533i
$404$	1.33881	−	9.21490i	0.0666081	−	0.458458i
$405$	1.01984	+	3.80610i	0.0506763	+	0.189126i
$406$	0.443220	−	0.0850841i	0.0219967	−	0.00422265i
$407$	−3.75563	−	6.50493i	−0.186159	−	0.322438i
$408$	−1.85922	+	8.45640i	−0.0920451	+	0.418654i
$409$	15.7270	+	4.21405i	0.777652	+	0.208371i	0.625749	−	0.780024i	$-0.284793\pi$
$409$	15.7270	+	4.21405i	0.777652	+	0.208371i	0.151903	+	0.988395i	$0.451460\pi$
$410$	10.2706	+	21.1827i	0.507229	+	1.04614i
$411$	10.5451	−	10.5451i	0.520149	−	0.520149i
$412$	−2.39179	−	6.00010i	−0.117835	−	0.295604i
$413$	−3.26636	−	1.88584i	−0.160727	−	0.0927959i
$414$	−5.74177	−	3.89233i	−0.282192	−	0.191298i
$415$	23.3400			1.14572
$416$	15.8533	−	12.8325i	0.777271	−	0.629166i
$417$	17.1160			0.838176
$418$	17.3305	+	11.7483i	0.847663	+	0.574629i
$419$	−16.5549	−	9.55798i	−0.808760	−	0.466938i	0.0377650	−	0.999287i	$-0.487976\pi$
$419$	−16.5549	−	9.55798i	−0.808760	−	0.466938i	−0.846525	+	0.532349i	$0.821310\pi$
$420$	2.49765	+	6.26564i	0.121873	+	0.305732i
$421$	−11.7263	+	11.7263i	−0.571503	+	0.571503i	−0.932548	−	0.361045i	$-0.882420\pi$
$421$	−11.7263	+	11.7263i	−0.571503	+	0.571503i	0.361045	+	0.932548i	$0.382420\pi$
$422$	4.85522	+	10.0137i	0.236349	+	0.487460i
$423$	4.45644	+	1.19410i	0.216680	+	0.0580592i
$424$	−3.86977	+	17.6011i	−0.187933	+	0.854785i
$425$	16.1118	+	27.9064i	0.781535	+	1.35366i
$426$	2.09587	−	0.402340i	0.101545	−	0.0194934i
$427$	−0.306200	−	1.14275i	−0.0148180	−	0.0553017i
$428$	−3.48866	+	24.0122i	−0.168631	+	1.16067i
$429$	1.76667	+	6.75585i	0.0852957	+	0.326175i
$430$	38.7603	+	44.7987i	1.86919	+	2.16038i
$431$	−35.7093	+	9.56828i	−1.72006	+	0.460888i	−0.977854	−	0.209287i	$-0.932886\pi$
$431$	−35.7093	+	9.56828i	−1.72006	+	0.460888i	−0.742203	+	0.670175i	$0.766219\pi$
$432$	2.75175	+	2.90308i	0.132393	+	0.139675i
$433$	−3.67694	+	2.12288i	−0.176702	+	0.102019i	−0.585742	−	0.810497i	$-0.699197\pi$
$433$	−3.67694	+	2.12288i	−0.176702	+	0.102019i	0.409040	+	0.912516i	$0.365864\pi$
$434$	−0.551644	+	7.63371i	−0.0264798	+	0.366430i
$435$	0.380253	−	1.41912i	0.0182317	−	0.0680417i
$436$	8.31685	+	3.57604i	0.398305	+	0.171261i
$437$	26.5129	+	26.5129i	1.26829	+	1.26829i
$438$	0.809731	−	2.33398i	0.0386905	−	0.111522i
$439$	−1.01395	+	1.75621i	−0.0483932	+	0.0838195i	−0.889207	−	0.457504i	$-0.848743\pi$
$439$	−1.01395	+	1.75621i	−0.0483932	+	0.0838195i	0.840814	+	0.541324i	$0.182077\pi$
$440$	−14.5548	+	15.9396i	−0.693871	+	0.759893i
$441$		−	6.26744i		−	0.298449i
$442$	14.0860	−	6.72520i	0.670003	−	0.319885i
$443$		−	4.66303i		−	0.221547i	−0.993846	−	0.110774i	$-0.964667\pi$
$443$		−	4.66303i		−	0.221547i	0.993846	−	0.110774i	$-0.0353329\pi$
$444$	0.909471	+	7.70308i	0.0431616	+	0.365572i
$445$	22.0844	−	38.2514i	1.04690	−	1.81329i
$446$	−37.3829	−	12.9693i	−1.77013	−	0.614114i
$447$	−8.54980	−	8.54980i	−0.404392	−	0.404392i
$448$	5.26063	+	4.38291i	0.248541	+	0.207073i
$449$	8.02976	−	29.9675i	0.378948	−	1.41425i	−0.468542	−	0.883441i	$-0.655221\pi$
$449$	8.02976	−	29.9675i	0.378948	−	1.41425i	0.847490	−	0.530811i	$-0.178113\pi$
$450$	14.8479	+	1.07297i	0.699938	+	0.0505804i
$451$	−7.08569	+	4.09092i	−0.333652	+	0.192634i
$452$	20.3578	−	25.8084i	0.957548	−	1.21393i
$453$	3.46156	−	0.927523i	0.162638	−	0.0435788i
$454$	0.478243	−	0.413781i	0.0224450	−	0.0194197i
$455$	6.14329	−	10.4940i	0.288002	−	0.491965i
$456$	−11.6489	−	18.2147i	−0.545511	−	0.852983i
$457$	−6.13280	−	22.8879i	−0.286880	−	1.07065i	−0.947454	−	0.319891i	$-0.896354\pi$
$457$	−6.13280	−	22.8879i	−0.286880	−	1.07065i	0.660574	−	0.750761i	$-0.270313\pi$
$458$	6.51412	+	33.9334i	0.304385	+	1.58560i
$459$	1.53060	+	2.65107i	0.0714422	+	0.123742i
$460$	−30.9791	+	23.1193i	−1.44441	+	1.07794i
$461$	−6.52593	−	1.74862i	−0.303943	−	0.0814413i	0.103624	−	0.994617i	$-0.466956\pi$
$461$	−6.52593	−	1.74862i	−0.303943	−	0.0814413i	−0.407567	+	0.913175i	$0.633623\pi$
$462$	−2.10941	+	1.02276i	−0.0981386	+	0.0475832i
$463$	−0.922819	+	0.922819i	−0.0428871	+	0.0428871i	−0.728225	−	0.685338i	$-0.759654\pi$
$463$	−0.922819	+	0.922819i	−0.0428871	+	0.0428871i	0.685338	+	0.728225i	$0.259654\pi$
$464$	−0.347330	−	1.45041i	−0.0161244	−	0.0673337i
$465$	21.5772	+	12.4576i	1.00062	+	0.577708i
$466$	−8.53579	+	12.5916i	−0.395413	+	0.583293i
$467$	12.3693			0.572383			0.286191	−	0.958172i	$-0.407611\pi$
$467$	12.3693			0.572383			0.286191	+	0.958172i	$0.407611\pi$
$468$	1.07977	−	7.12980i	0.0499122	−	0.329575i
$469$	−0.919850			−0.0424747
$470$	14.4262	−	21.2808i	0.665430	−	0.981608i
$471$	4.32880	+	2.49923i	0.199460	+	0.115159i
$472$	−5.73586	+	11.0657i	−0.264014	+	0.509341i
$473$	−14.5584	+	14.5584i	−0.669398	+	0.669398i
$474$	−16.2215	+	7.86513i	−0.745080	+	0.361257i
$475$	−77.7247	−	20.8263i	−3.56625	−	0.955575i
$476$	3.13410	+	4.19959i	0.143651	+	0.192488i
$477$	3.18578	+	5.51793i	0.145867	+	0.252649i
$478$	6.90347	+	35.9616i	0.315757	+	1.64484i
$479$	−8.60632	−	32.1192i	−0.393233	−	1.46756i	−0.824770	−	0.565469i	$-0.808695\pi$
$479$	−8.60632	−	32.1192i	−0.393233	−	1.46756i	0.431537	−	0.902095i	$-0.357971\pi$
$480$	20.3098	−	9.18464i	0.927012	−	0.419220i
$481$	9.94713	−	9.82800i	0.453550	−	0.448118i
$482$	−31.4322	+	27.1955i	−1.43170	+	1.23872i
$483$	−4.05514	+	1.08657i	−0.184515	+	0.0494407i
$484$	11.3830	+	8.97894i	0.517409	+	0.408134i
$485$	23.4329	−	13.5290i	1.06404	−	0.614321i
$486$	1.41054	+	0.101931i	0.0639832	+	0.00462369i
$487$	−2.56872	+	9.58660i	−0.116400	+	0.434410i	−0.999388	−	0.0349854i	$-0.988862\pi$
$487$	−2.56872	+	9.58660i	−0.116400	+	0.434410i	0.882988	+	0.469396i	$0.155528\pi$
$488$	−3.72658	+	1.18216i	−0.168694	+	0.0535138i
$489$	1.69944	+	1.69944i	0.0768515	+	0.0768515i
$490$	−32.9960	−	11.4474i	−1.49061	−	0.517139i
$491$	−10.6521	+	18.4500i	−0.480723	+	0.832637i	−0.999755	−	0.0221174i	$-0.992959\pi$
$491$	−10.6521	+	18.4500i	−0.480723	+	0.832637i	0.519032	+	0.854755i	$0.326293\pi$
$492$	8.39080	−	0.990668i	0.378287	−	0.0446627i
$493$		−	1.14138i		−	0.0514053i
$494$	−12.9973	+	36.7472i	−0.584776	+	1.65334i
$495$			7.63146i			0.343009i
$496$	25.2833	+	0.676635i	1.13525	+	0.0303818i
$497$	0.645804	−	1.11857i	0.0289683	−	0.0501745i
$498$	2.74564	−	7.91409i	0.123035	−	0.354639i
$499$	6.55108	+	6.55108i	0.293267	+	0.293267i	0.838369	−	0.545103i	$-0.183509\pi$
$499$	6.55108	+	6.55108i	0.293267	+	0.293267i	−0.545103	+	0.838369i	$0.683509\pi$
$500$	17.2036	−	40.0106i	0.769366	−	1.78933i
$501$	−1.30125	+	4.85633i	−0.0581356	+	0.216965i
$502$	−1.30262	+	18.0258i	−0.0581389	+	0.804532i
$503$	16.8800	−	9.74567i	0.752642	−	0.434538i	−0.0740059	−	0.997258i	$-0.523578\pi$
$503$	16.8800	−	9.74567i	0.752642	−	0.434538i	0.826648	+	0.562720i	$0.190245\pi$
$504$	2.41836	−	0.109828i	0.107722	−	0.00489212i
$505$	−17.7205	+	4.74820i	−0.788552	+	0.211292i
$506$	−8.79031	−	10.1597i	−0.390777	−	0.451655i
$507$	−11.3358	+	6.36389i	−0.503442	+	0.282630i
$508$	16.7888	+	2.43920i	0.744883	+	0.108222i
$509$	−2.01071	−	7.50408i	−0.0891233	−	0.332613i	0.906940	−	0.421260i	$-0.138412\pi$
$509$	−2.01071	−	7.50408i	−0.0891233	−	0.332613i	−0.996063	+	0.0886477i	$0.971745\pi$
$510$	16.7527	−	3.21597i	0.741820	−	0.142406i
$511$	−0.747575	−	1.29484i	−0.0330708	−	0.0572802i
$512$	13.6803	−	18.0236i	0.604588	−	0.796538i
$513$	−7.38376	−	1.97847i	−0.326001	−	0.0873516i
$514$	−0.621638	−	1.28211i	−0.0274193	−	0.0565513i
$515$	−8.99856	+	8.99856i	−0.396524	+	0.396524i
$516$	19.7499	−	7.87282i	0.869441	−	0.346582i
$517$	7.73833	+	4.46772i	0.340331	+	0.196490i
$518$	3.88570	+	2.63411i	0.170728	+	0.115736i
$519$	−5.11689			−0.224607
$520$	−35.5640	−	18.7071i	−1.55958	−	0.820359i
$521$	1.26485			0.0554142			0.0277071	−	0.999616i	$-0.491179\pi$
$521$	1.26485			0.0554142			0.0277071	+	0.999616i	$0.491179\pi$
$522$	−0.436462	−	0.295876i	−0.0191034	−	0.0129502i
$523$	4.92131	+	2.84132i	0.215194	+	0.124242i	0.603723	−	0.797194i	$-0.293683\pi$
$523$	4.92131	+	2.84132i	0.215194	+	0.124242i	−0.388529	+	0.921436i	$0.627017\pi$
$524$	−19.4535	+	7.75466i	−0.849829	+	0.338764i
$525$	6.37074	−	6.37074i	0.278042	−	0.278042i
$526$	−8.25170	−	17.0188i	−0.359791	−	0.742056i
$527$	18.6967	+	5.00975i	0.814439	+	0.218228i
$528$	3.69261	+	6.81029i	0.160700	+	0.296380i
$529$	−0.529526	−	0.917166i	−0.0230229	−	0.0398768i
$530$	34.8689	−	6.69371i	1.51461	−	0.290756i
$531$	1.14053	+	4.25652i	0.0494949	+	0.184717i
$532$	−12.9494	−	1.88138i	−0.561429	−	0.0815683i
$533$	−10.7054	−	10.8352i	−0.463704	−	0.469325i
$534$	−10.3723	−	11.9881i	−0.448852	−	0.518777i
$535$	46.1761	−	12.3729i	1.99637	−	0.534925i
$536$	0.137906	+	3.03663i	0.00595664	+	0.131162i
$537$	−19.6597	+	11.3505i	−0.848378	+	0.489811i
$538$	0.969692	−	13.4187i	0.0418064	−	0.578522i
$539$	3.14165	−	11.7248i	0.135320	−	0.505023i
$540$	3.11295	−	7.23984i	0.133960	−	0.311553i
$541$	15.6951	+	15.6951i	0.674785	+	0.674785i	0.958815	−	0.284030i	$-0.0916716\pi$
$541$	15.6951	+	15.6951i	0.674785	+	0.674785i	−0.284030	+	0.958815i	$0.591672\pi$
$542$	−1.45746	+	4.20101i	−0.0626034	+	0.180449i
$543$	−7.76757	+	13.4538i	−0.333338	+	0.577359i
$544$	13.3939	−	10.9760i	0.574260	−	0.470591i
$545$		−	17.8362i		−	0.764017i
$546$	−2.83560	−	3.31753i	−0.121353	−	0.141977i
$547$			8.11420i			0.346938i	0.984839	+	0.173469i	$0.0554977\pi$
$547$			8.11420i			0.346938i	−0.984839	+	0.173469i	$0.944502\pi$
$548$	−29.6202	+	3.49713i	−1.26531	+	0.149390i
$549$	−0.691124	+	1.19706i	−0.0294964	+	0.0510893i
$550$	27.2389	+	9.45002i	1.16147	+	0.402950i
$551$	2.01539	+	2.01539i	0.0858584	+	0.0858584i
$552$	4.19497	+	13.2240i	0.178550	+	0.562852i
$553$	−2.82387	+	10.5388i	−0.120083	+	0.448157i
$554$	1.80804	+	0.130657i	0.0768164	+	0.00555107i
$555$	13.2345	−	7.64094i	0.561773	−	0.324340i
$556$	−26.8769	−	21.2006i	−1.13984	−	0.899106i
$557$	−11.2012	+	3.00136i	−0.474611	+	0.127172i	−0.488192	−	0.872736i	$-0.662344\pi$
$557$	−11.2012	+	3.00136i	−0.474611	+	0.127172i	0.0135812	+	0.999908i	$0.495677\pi$
$558$	6.76238	−	5.85089i	0.286275	−	0.247688i
$559$	−33.0780	−	19.3642i	−1.39905	−	0.819020i
$560$	3.83888	−	12.9325i	0.162222	−	0.546497i
$561$	1.53447	+	5.72673i	0.0647855	+	0.241783i
$562$	2.43572	+	12.6882i	0.102745	+	0.535219i
$563$	10.6421	+	18.4327i	0.448511	+	0.776844i	0.998289	−	0.0584665i	$-0.0186211\pi$
$563$	10.6421	+	18.4327i	0.448511	+	0.776844i	−0.549778	+	0.835311i	$0.685288\pi$
$564$	−5.51879	−	7.39500i	−0.232383	−	0.311386i
$565$	−62.5554	−	16.7617i	−2.63172	−	0.705168i
$566$	−15.3695	+	7.45199i	−0.646027	+	0.313231i
$567$	0.605212	−	0.605212i	0.0254165	−	0.0254165i
$568$	−3.78946	−	1.96425i	−0.159002	−	0.0824179i
$569$	40.2521	+	23.2396i	1.68746	+	0.974254i	0.956455	+	0.291880i	$0.0942807\pi$
$569$	40.2521	+	23.2396i	1.68746	+	0.974254i	0.731003	+	0.682374i	$0.239053\pi$
$570$	−23.9023	+	35.2595i	−1.00116	+	1.47686i
$571$	1.03347			0.0432494			0.0216247	−	0.999766i	$-0.493116\pi$
$571$	1.03347			0.0432494			0.0216247	+	0.999766i	$0.493116\pi$
$572$	5.59390	−	12.7968i	0.233893	−	0.535062i
$573$	23.4753			0.980695
$574$	2.86928	−	4.23261i	0.119761	−	0.176666i
$575$	44.7148	+	25.8161i	1.86474	+	1.07661i
$576$	−0.725132	−	7.96707i	−0.0302138	−	0.331961i
$577$	21.0670	−	21.0670i	0.877031	−	0.877031i	−0.116196	−	0.993226i	$-0.537070\pi$
$577$	21.0670	−	21.0670i	0.877031	−	0.877031i	0.993226	+	0.116196i	$0.0370700\pi$
$578$	−9.70820	+	4.70709i	−0.403808	+	0.195789i
$579$	4.77983	+	1.28075i	0.198643	+	0.0532262i
$580$	−2.35488	+	1.75742i	−0.0977813	+	0.0729729i
$581$	−2.53488	−	4.39055i	−0.105165	−	0.182151i
$582$	−1.83082	−	9.53711i	−0.0758899	−	0.395326i
$583$	3.19384	+	11.9196i	0.132275	+	0.493659i
$584$	−4.16247	+	2.66204i	−0.172244	+	0.110156i
$585$	−13.7450	+	3.59435i	−0.568285	+	0.148608i
$586$	21.7319	−	18.8027i	0.897739	−	0.776734i
$587$	−22.4137	+	6.00573i	−0.925112	+	0.247883i	−0.689769	−	0.724030i	$-0.742288\pi$
$587$	−22.4137	+	6.00573i	−0.925112	+	0.247883i	−0.235343	+	0.971912i	$0.575621\pi$
$588$	−7.76310	+	9.84161i	−0.320145	+	0.405861i
$589$	−41.8594	+	24.1675i	−1.72479	+	0.995806i
$590$	24.4924	+	1.76992i	1.00834	+	0.0728665i
$591$	−3.43979	+	12.8375i	−0.141494	+	0.528062i
$592$	8.11322	−	13.2225i	0.333451	−	0.543441i
$593$	−2.08220	−	2.08220i	−0.0855058	−	0.0855058i	0.663060	−	0.748566i	$-0.269257\pi$
$593$	−2.08220	−	2.08220i	−0.0855058	−	0.0855058i	−0.748566	+	0.663060i	$0.769257\pi$
$594$	2.58766	+	0.897740i	0.106173	+	0.0368347i
$595$	5.16202	−	8.94089i	0.211622	−	0.366541i
$596$	2.83543	+	24.0157i	0.116144	+	0.983721i
$597$			20.3064i			0.831087i
$598$	14.1585	−	20.6173i	0.578982	−	0.843105i
$599$			24.1528i			0.986858i	0.869786	+	0.493429i	$0.164257\pi$
$599$			24.1528i			0.986858i	−0.869786	+	0.493429i	$0.835743\pi$
$600$	−21.9863	−	20.0761i	−0.897588	−	0.819603i
$601$	11.8395	−	20.5066i	0.482942	−	0.836480i	−0.516866	−	0.856066i	$-0.672901\pi$
$601$	11.8395	−	20.5066i	0.482942	−	0.836480i	0.999808	+	0.0195860i	$0.00623481\pi$
$602$	4.21755	−	12.1567i	0.171895	−	0.495472i
$603$	0.759940	+	0.759940i	0.0309471	+	0.0309471i
$604$	−6.58448	−	2.83116i	−0.267919	−	0.115198i
$605$	7.39286	−	27.5905i	0.300562	−	1.12171i
$606$	−0.474574	+	6.56720i	−0.0192782	+	0.266774i
$607$	−16.9632	+	9.79369i	−0.688514	+	0.397514i	−0.803055	−	0.595905i	$-0.796793\pi$
$607$	−16.9632	+	9.79369i	−0.688514	+	0.397514i	0.114541	+	0.993418i	$0.463460\pi$
$608$	−4.26946	+	43.0310i	−0.173149	+	1.74514i
$609$	−0.308253	+	0.0825960i	−0.0124910	+	0.00334696i
$610$	5.03982	+	5.82495i	0.204056	+	0.235846i
$611$	−4.40211	+	16.0417i	−0.178090	+	0.648978i
$612$	0.880262	−	6.05878i	0.0355825	−	0.244912i
$613$	−1.64537	−	6.14059i	−0.0664557	−	0.248016i	0.924705	−	0.380685i	$-0.124312\pi$
$613$	−1.64537	−	6.14059i	−0.0664557	−	0.248016i	−0.991160	+	0.132669i	$0.957645\pi$
$614$	−7.37017	+	1.41484i	−0.297436	+	0.0570982i
$615$	−8.32311	−	14.4161i	−0.335620	−	0.581311i
$616$	4.57919	+	1.00678i	0.184501	+	0.0405643i
$617$	−17.0972	−	4.58119i	−0.688309	−	0.184432i	−0.102321	−	0.994751i	$-0.532627\pi$
$617$	−17.0972	−	4.58119i	−0.688309	−	0.184432i	−0.585988	+	0.810320i	$0.699293\pi$
$618$	1.99265	+	4.10978i	0.0801563	+	0.165319i
$619$	23.0812	−	23.0812i	0.927711	−	0.927711i	−0.0698464	−	0.997558i	$-0.522251\pi$
$619$	23.0812	−	23.0812i	0.927711	−	0.927711i	0.997558	+	0.0698464i	$0.0222509\pi$
$620$	−18.4517	−	46.2883i	−0.741039	−	1.85898i
$621$	4.24786	+	2.45250i	0.170461	+	0.0984155i
$622$	8.96450	+	6.07701i	0.359444	+	0.243666i
$623$	−9.59408			−0.384379
$624$	−10.5268	+	9.85833i	−0.421409	+	0.394649i
$625$	−33.1738			−1.32695
$626$	−28.4936	−	19.3158i	−1.13883	−	0.772013i
$627$	−12.8214	−	7.40244i	−0.512038	−	0.295625i
$628$	−3.70176	−	9.28631i	−0.147716	−	0.370564i
$629$	8.39492	−	8.39492i	0.334727	−	0.334727i
$630$	−2.08084	−	4.29166i	−0.0829027	−	0.170984i
$631$	6.93451	+	1.85810i	0.276058	+	0.0739696i	0.394192	−	0.919028i	$-0.371024\pi$
$631$	6.93451	+	1.85810i	0.276058	+	0.0739696i	−0.118134	+	0.992998i	$0.537691\pi$
$632$	35.2144	+	7.74222i	1.40075	+	0.307969i
$633$	−3.93459	−	6.81491i	−0.156386	−	0.270868i
$634$	−26.5455	+	5.09588i	−1.05426	+	0.202383i
$635$	−8.65084	−	32.2854i	−0.343298	−	1.28121i
$636$	1.83217	−	12.6107i	0.0726504	−	0.500047i
$637$	22.5972	+	0.136132i	0.895332	+	0.00539376i
$638$	−0.668198	−	0.772294i	−0.0264542	−	0.0305754i
$639$	−1.45765	+	0.390575i	−0.0576636	+	0.0154509i
$640$	−43.2685	−	10.7341i	−1.71034	−	0.424303i
$641$	−15.6014	+	9.00745i	−0.616217	+	0.355773i	−0.775395	−	0.631477i	$-0.782449\pi$
$641$	−15.6014	+	9.00745i	−0.616217	+	0.355773i	0.159178	+	0.987250i	$0.449116\pi$
$642$	1.23664	−	17.1128i	0.0488065	−	0.675389i
$643$	10.0813	−	37.6241i	0.397569	−	1.48375i	−0.419790	−	0.907621i	$-0.637896\pi$
$643$	10.0813	−	37.6241i	0.397569	−	1.48375i	0.817360	−	0.576128i	$-0.195437\pi$
$644$	7.71357	+	3.31664i	0.303957	+	0.130694i
$645$	−29.6196	−	29.6196i	−1.16627	−	1.16627i
$646$	−10.8469	+	31.2652i	−0.426764	+	1.23011i
$647$	15.3696	−	26.6209i	0.604241	−	1.04658i	−0.387930	−	0.921689i	$-0.626810\pi$
$647$	15.3696	−	26.6209i	0.604241	−	1.04658i	0.992171	−	0.124887i	$-0.0398569\pi$
$648$	−2.08868	−	1.90721i	−0.0820509	−	0.0749221i
$649$			8.53459i			0.335012i
$650$	−4.19109	+	53.5107i	−0.164388	+	2.09886i
$651$		−	5.41193i		−	0.212110i
$652$	−0.563599	−	4.77360i	−0.0220722	−	0.186949i
$653$	−9.85277	+	17.0655i	−0.385569	+	0.667825i	−0.991848	−	0.127427i	$-0.959328\pi$
$653$	−9.85277	+	17.0655i	−0.385569	+	0.667825i	0.606279	+	0.795252i	$0.292661\pi$
$654$	−6.04786	−	2.09819i	−0.236490	−	0.0820457i
$655$	29.1751	+	29.1751i	1.13996	+	1.13996i
$656$	−14.4030	−	8.83756i	−0.562342	−	0.345049i
$657$	−0.452124	+	1.68735i	−0.0176391	+	0.0658299i
$658$	−5.56995	−	0.402508i	−0.217139	−	0.0156914i
$659$	26.8778	−	15.5179i	1.04701	−	0.604492i	0.125200	−	0.992132i	$-0.460043\pi$
$659$	26.8778	−	15.5179i	1.04701	−	0.604492i	0.921811	+	0.387639i	$0.126709\pi$
$660$	9.45263	−	11.9835i	0.367943	−	0.466457i
$661$	13.1031	−	3.51096i	0.509651	−	0.136561i	0.00517546	−	0.999987i	$-0.498353\pi$
$661$	13.1031	−	3.51096i	0.509651	−	0.136561i	0.504475	+	0.863426i	$0.331686\pi$
$662$	32.0968	−	27.7705i	1.24748	−	1.07933i
$663$	−9.59165	+	5.46097i	−0.372509	+	0.212086i
$664$	−14.1141	+	9.02645i	−0.547735	+	0.350294i
$665$	6.67250	+	24.9021i	0.258748	+	0.965662i
$666$	−1.03401	−	5.38638i	−0.0400672	−	0.208718i
$667$	−0.914428	−	1.58384i	−0.0354068	−	0.0613263i
$668$	8.05857	−	6.01401i	0.311795	−	0.232689i
$669$	27.0259	+	7.24158i	1.04488	+	0.279976i
$670$	5.38886	−	2.61282i	0.208190	−	0.100942i
$671$	−1.89296	+	1.89296i	−0.0730771	+	0.0730771i
$672$	−3.93353	−	2.82301i	−0.151739	−	0.108900i
$673$	17.3587	+	10.0220i	0.669128	+	0.386321i	0.795746	−	0.605630i	$-0.207079\pi$
$673$	17.3587	+	10.0220i	0.669128	+	0.386321i	−0.126618	+	0.991952i	$0.540412\pi$
$674$	−9.15849	+	13.5101i	−0.352772	+	0.520391i
$675$	−10.5264			−0.405163
$676$	25.6830	+	4.04794i	0.987806	+	0.155690i
$677$	−35.4848			−1.36379			−0.681895	−	0.731450i	$-0.738844\pi$
$677$	−35.4848			−1.36379			−0.681895	+	0.731450i	$0.738844\pi$
$678$	−13.0423	+	19.2394i	−0.500888	+	0.738884i
$679$	−5.08995	−	2.93868i	−0.195334	−	0.112776i
$680$	−30.2898	−	15.7005i	−1.16156	−	0.602089i
$681$	−0.316201	+	0.316201i	−0.0121168	+	0.0121168i
$682$	15.5836	−	7.55580i	0.596726	−	0.289327i
$683$	9.06636	+	2.42932i	0.346915	+	0.0929555i	0.428069	−	0.903746i	$-0.359194\pi$
$683$	9.06636	+	2.42932i	0.346915	+	0.0929555i	−0.0811543	+	0.996702i	$0.525861\pi$
$684$	9.14393	+	12.2526i	0.349627	+	0.468488i
$685$	29.3812	+	50.8898i	1.12260	+	1.94440i
$686$	3.02758	+	15.7713i	0.115593	+	0.602150i
$687$	−6.32363	−	23.6001i	−0.241262	−	0.900400i
$688$	−40.7644	−	12.1005i	−1.55413	−	0.461327i
$689$	−19.9640	+	11.3664i	−0.760568	+	0.433026i
$690$	20.6703	−	17.8842i	0.786904	−	0.680838i
$691$	11.7332	−	3.14389i	0.446351	−	0.119599i	−0.0286407	−	0.999590i	$-0.509118\pi$
$691$	11.7332	−	3.14389i	0.446351	−	0.119599i	0.474991	+	0.879990i	$0.342451\pi$
$692$	8.03494	+	6.33798i	0.305442	+	0.240934i
$693$	1.43557	−	0.828828i	0.0545329	−	0.0314846i
$694$	−7.27445	−	0.525682i	−0.276134	−	0.0199546i
$695$	−17.4556	+	65.1453i	−0.662129	+	2.47110i
$696$	0.318882	+	1.00523i	0.0120872	+	0.0381030i
$697$	−9.14441	−	9.14441i	−0.346369	−	0.346369i
$698$	6.03517	+	2.09379i	0.228435	+	0.0792510i
$699$	5.37828	−	9.31545i	0.203425	−	0.352343i
$700$	−17.8949	+	2.11277i	−0.676362	+	0.0798553i
$701$			20.6827i			0.781174i	0.920566	+	0.390587i	$0.127728\pi$
$701$			20.6827i			0.781174i	−0.920566	+	0.390587i	$0.872272\pi$
$702$	−0.398149	+	5.08345i	−0.0150272	+	0.191863i
$703$			29.6465i			1.11814i
$704$	2.63708	−	15.2679i	0.0993886	−	0.575429i
$705$	−9.08972	+	15.7439i	−0.342339	+	0.592948i
$706$	−2.15031	+	6.19808i	−0.0809279	+	0.233268i
$707$	2.81776	+	2.81776i	0.105973	+	0.105973i
$708$	3.48135	−	8.09663i	0.130837	−	0.304290i
$709$	−12.0392	+	44.9311i	−0.452143	+	1.68742i	0.244210	+	0.969722i	$0.421471\pi$
$709$	−12.0392	+	44.9311i	−0.452143	+	1.68742i	−0.696353	+	0.717699i	$0.745195\pi$
$710$	−0.606110	+	8.38741i	−0.0227469	+	0.314774i
$711$	11.0397	−	6.37376i	0.414020	−	0.239035i
$712$	1.43837	+	31.6722i	0.0539051	+	1.18697i
$713$	29.9579	−	8.02721i	1.12193	−	0.300621i
$714$	−2.42442	−	2.80211i	−0.0907315	−	0.104866i
$715$	−27.5151	−	0.165760i	−1.02901	−	0.00619906i
$716$	44.9304	+	6.52780i	1.67913	+	0.243955i
$717$	−6.70160	−	25.0107i	−0.250276	−	0.934042i
$718$	−25.2563	+	4.84840i	−0.942558	+	0.180941i
$719$	6.95181	+	12.0409i	0.259259	+	0.449049i	0.966044	−	0.258379i	$-0.0831884\pi$
$719$	6.95181	+	12.0409i	0.259259	+	0.449049i	−0.706785	+	0.707429i	$0.749855\pi$
$720$	−13.8558	+	7.51273i	−0.516374	+	0.279983i
$721$	2.67004	+	0.715436i	0.0994376	+	0.0266442i
$722$	−24.3306	−	50.1810i	−0.905491	−	1.86754i
$723$	20.7821	−	20.7821i	0.772894	−	0.772894i
$724$	28.8617	−	11.5050i	1.07264	−	0.427580i
$725$	3.39901	+	1.96242i	0.126236	+	0.0728824i
$726$	−8.48567	−	5.75242i	−0.314933	−	0.213492i
$727$	37.8077			1.40221			0.701105	−	0.713058i	$-0.252690\pi$
$727$	37.8077			1.40221			0.701105	+	0.713058i	$0.252690\pi$
$728$	0.343454	+	8.72174i	0.0127293	+	0.323249i
$729$	−1.00000			−0.0370370
$730$	8.05757	+	5.46221i	0.298224	+	0.202165i
$731$	−28.1825	−	16.2712i	−1.04237	−	0.601812i
$732$	2.56798	−	1.02366i	0.0949154	−	0.0378357i
$733$	−28.2991	+	28.2991i	−1.04525	+	1.04525i	−0.0463247	+	0.998926i	$0.514751\pi$
$733$	−28.2991	+	28.2991i	−1.04525	+	1.04525i	−0.998926	+	0.0463247i	$0.985249\pi$
$734$	1.38708	+	2.86080i	0.0511980	+	0.105594i
$735$	23.8545	+	6.39178i	0.879885	+	0.235765i
$736$	9.79253	−	25.9614i	0.360957	−	0.956951i
$737$	1.04072	+	1.80259i	0.0383356	+	0.0663992i
$738$	−5.86727	+	1.12633i	−0.215977	+	0.0414607i
$739$	−4.02275	−	15.0131i	−0.147979	−	0.552266i	−0.999605	−	0.0281152i	$-0.991049\pi$
$739$	−4.02275	−	15.0131i	−0.147979	−	0.552266i	0.851625	−	0.524151i	$-0.175617\pi$
$740$	−30.2462	−	4.39438i	−1.11187	−	0.161541i
$741$	7.29373	−	26.5791i	0.267942	−	0.976406i
$742$	−5.04617	−	5.83229i	−0.185251	−	0.214110i
$743$	18.9054	−	5.06569i	0.693572	−	0.185842i	0.105222	−	0.994449i	$-0.466445\pi$
$743$	18.9054	−	5.06569i	0.693572	−	0.185842i	0.588350	+	0.808607i	$0.299778\pi$
$744$	−17.8660	+	0.811369i	−0.654998	+	0.0297462i
$745$	41.2608	−	23.8219i	1.51168	−	0.872768i
$746$	2.11612	−	29.2831i	0.0774766	−	1.07213i
$747$	−1.53307	+	5.72149i	−0.0560920	+	0.209338i
$748$	4.68381	−	10.8932i	0.171257	−	0.398295i
$749$	−7.34253	−	7.34253i	−0.268290	−	0.268290i
$750$	−10.0939	+	29.0950i	−0.368579	+	1.06240i
$751$	8.07680	−	13.9894i	0.294726	−	0.510481i	−0.680195	−	0.733031i	$-0.738105\pi$
$751$	8.07680	−	13.9894i	0.294726	−	0.510481i	0.974921	+	0.222550i	$0.0714381\pi$
$752$	−0.493708	+	18.4480i	−0.0180037	+	0.672729i
$753$		−	12.7794i		−	0.465708i
$754$	1.07626	−	1.56723i	0.0391950	−	0.0570752i
$755$			14.1210i			0.513914i
$756$	−1.69999	+	0.200711i	−0.0618281	+	0.00729979i
$757$	12.5367	−	21.7142i	0.455655	−	0.789217i	−0.543071	−	0.839687i	$-0.682738\pi$
$757$	12.5367	−	21.7142i	0.455655	−	0.789217i	0.998726	+	0.0504695i	$0.0160718\pi$
$758$	17.4212	+	6.04396i	0.632767	+	0.219526i
$759$	6.71732	+	6.71732i	0.243823	+	0.243823i
$760$	81.2070	−	25.7608i	2.94569	−	0.934442i
$761$	−5.79316	+	21.6204i	−0.210002	+	0.783738i	0.777865	+	0.628432i	$0.216303\pi$
$761$	−5.79316	+	21.6204i	−0.210002	+	0.783738i	−0.987866	+	0.155306i	$0.950364\pi$
$762$	−11.9649	−	0.864636i	−0.433443	−	0.0313224i
$763$	−3.35520	+	1.93713i	−0.121467	+	0.0701287i
$764$	−36.8627	−	29.0774i	−1.33365	−	1.05199i
$765$	−11.6512	+	3.12193i	−0.421250	+	0.112874i
$766$	−17.1905	+	14.8735i	−0.621120	+	0.537400i
$767$	−15.3716	+	4.01972i	−0.555036	+	0.145144i
$768$	−8.72967	+	13.4087i	−0.315005	+	0.483844i
$769$	6.76554	+	25.2494i	0.243972	+	0.910515i	0.973897	+	0.226989i	$0.0728880\pi$
$769$	6.76554	+	25.2494i	0.243972	+	0.910515i	−0.729926	+	0.683527i	$0.760445\pi$
$770$	−1.74147	−	9.07167i	−0.0627582	−	0.326920i
$771$	0.503765	+	0.872546i	0.0181426	+	0.0314240i
$772$	−5.91926	−	7.93162i	−0.213039	−	0.285465i
$773$	6.78069	+	1.81688i	0.243884	+	0.0653486i	0.378690	−	0.925523i	$-0.376374\pi$
$773$	6.78069	+	1.81688i	0.243884	+	0.0653486i	−0.134806	+	0.990872i	$0.543041\pi$
$774$	−13.5277	+	6.55901i	−0.486244	+	0.235759i
$775$	−47.0647	+	47.0647i	−1.69062	+	1.69062i
$776$	−8.93815	+	17.2436i	−0.320861	+	0.619010i
$777$	−2.87471	−	1.65971i	−0.103130	−	0.0595419i
$778$	−3.23064	+	4.76568i	−0.115824	+	0.170858i
$779$	32.2934			1.15703
$780$	26.0355	+	11.3810i	0.932222	+	0.407504i
$781$	−2.92267			−0.104581
$782$	11.9152	−	17.5767i	0.426086	−	0.628540i
$783$	0.322902	+	0.186428i	0.0115396	+	0.00666238i
$784$	24.3804	−	5.83838i	0.870730	−	0.208513i
$785$	−13.9270	+	13.9270i	−0.497076	+	0.497076i
$786$	13.3247	−	6.46057i	0.475276	−	0.230441i
$787$	7.08082	+	1.89730i	0.252404	+	0.0676314i	0.382802	−	0.923830i	$-0.374959\pi$
$787$	7.08082	+	1.89730i	0.252404	+	0.0676314i	−0.130399	+	0.991462i	$0.541626\pi$
$788$	21.3024	−	15.8977i	0.758867	−	0.566332i
$789$	6.68703	+	11.5823i	0.238065	+	0.412340i
$790$	−13.3921	−	69.7620i	−0.476468	−	2.48202i
$791$	3.64086	+	13.5879i	0.129454	+	0.483129i
$792$	−2.95137	−	4.61488i	−0.104872	−	0.163983i
$793$	−4.30098	−	2.51784i	−0.152732	−	0.0894110i
$794$	20.9044	−	18.0867i	0.741868	−	0.641873i
$795$	−24.2508	+	6.49797i	−0.860086	+	0.230459i
$796$	25.1524	−	31.8867i	0.891502	−	1.13020i
$797$	43.6205	−	25.1843i	1.54512	−	0.892074i	0.546614	−	0.837385i	$-0.315916\pi$
$797$	43.6205	−	25.1843i	1.54512	−	0.892074i	0.998503	−	0.0546895i	$-0.0174169\pi$
$798$	9.22870	+	0.666904i	0.326692	+	0.0236082i
$799$	−3.65538	+	13.6420i	−0.129318	+	0.482621i
$800$	9.65758	+	58.7582i	0.341447	+	2.07742i
$801$	7.92621	+	7.92621i	0.280059	+	0.280059i
$802$	−31.5730	−	10.9536i	−1.11488	−	0.386787i
$803$	−1.69162	+	2.92998i	−0.0596961	+	0.103397i
$804$	−0.252024	−	2.13461i	−0.00888821	−	0.0752818i
$805$		−	16.5424i		−	0.583042i
$806$	20.9484	+	24.5088i	0.737877	+	0.863284i
$807$			9.51320i			0.334881i
$808$	8.87961	−	9.72450i	0.312384	−	0.342107i
$809$	4.33418	−	7.50702i	0.152382	−	0.263933i	−0.779721	−	0.626127i	$-0.784639\pi$
$809$	4.33418	−	7.50702i	0.152382	−	0.263933i	0.932103	+	0.362194i	$0.117972\pi$
$810$	−1.82648	+	5.26468i	−0.0641760	+	0.184982i
$811$	16.0529	+	16.0529i	0.563692	+	0.563692i	0.930354	−	0.366662i	$-0.119499\pi$
$811$	16.0529	+	16.0529i	0.563692	+	0.563692i	−0.366662	+	0.930354i	$0.619499\pi$
$812$	0.586349	+	0.252115i	0.0205768	+	0.00884751i
$813$	0.813794	−	3.03712i	0.0285410	−	0.106516i
$814$	0.765631	−	10.5949i	0.0268353	−	0.371350i
$815$	−8.20141	+	4.73509i	−0.287283	+	0.165863i
$816$	−8.88690	+	8.42364i	−0.311104	+	0.294886i
$817$	78.4938	−	21.0324i	2.74615	−	0.735829i
$818$	15.0660	+	17.4130i	0.526769	+	0.608832i
$819$	2.16894	+	2.19523i	0.0757889	+	0.0767076i
$820$	−4.78671	+	32.9465i	−0.167159	+	1.15054i
$821$	11.1758	+	41.7086i	0.390038	+	1.45564i	0.830070	+	0.557659i	$0.188300\pi$
$821$	11.1758	+	41.7086i	0.390038	+	1.45564i	−0.440033	+	0.897982i	$0.645033\pi$
$822$	20.7119	−	3.97603i	0.722412	−	0.138680i
$823$	−2.42318	−	4.19707i	−0.0844667	−	0.146301i	0.820697	−	0.571363i	$-0.193585\pi$
$823$	−2.42318	−	4.19707i	−0.0844667	−	0.146301i	−0.905164	+	0.425063i	$0.860252\pi$
$824$	1.96151	−	8.92167i	0.0683326	−	0.310801i
$825$	−19.6923	−	5.27654i	−0.685599	−	0.183706i
$826$	−2.32709	−	4.79955i	−0.0809700	−	0.166998i
$827$	30.1737	−	30.1737i	1.04924	−	1.04924i	0.0505203	−	0.998723i	$-0.483912\pi$
$827$	30.1737	−	30.1737i	1.04924	−	1.04924i	0.998723	−	0.0505203i	$-0.0160880\pi$
$828$	−3.63255	−	9.11267i	−0.126240	−	0.316687i
$829$	−19.4215	−	11.2130i	−0.674535	−	0.389443i	0.123258	−	0.992375i	$-0.460666\pi$
$829$	−19.4215	−	11.2130i	−0.674535	−	0.389443i	−0.797793	+	0.602932i	$0.793999\pi$
$830$	27.3217	+	18.5213i	0.948349	+	0.642884i
$831$	−1.28181			−0.0444656
$832$	28.7409	−	2.44140i	0.996412	−	0.0846404i
$833$	19.1858			0.664750
$834$	20.0359	+	13.5823i	0.693787	+	0.470317i
$835$	−17.1566	−	9.90537i	−0.593728	−	0.342789i
$836$	10.9642	+	27.5050i	0.379205	+	0.951280i
$837$	−4.47110	+	4.47110i	−0.154544	+	0.154544i
$838$	−11.7944	−	24.3255i	−0.407431	−	0.840312i
$839$	2.69035	+	0.720876i	0.0928811	+	0.0248874i	0.304960	−	0.952365i	$-0.401357\pi$
$839$	2.69035	+	0.720876i	0.0928811	+	0.0248874i	−0.212079	+	0.977252i	$0.568023\pi$
$840$	−2.04832	+	9.31651i	−0.0706739	+	0.321450i
$841$	14.4305	+	24.9943i	0.497603	+	0.861874i
$842$	−23.0320	+	4.42140i	−0.793735	+	0.152372i
$843$	−2.36450	−	8.82443i	−0.0814376	−	0.303929i
$844$	−2.26282	+	15.5748i	−0.0778895	+	0.536108i
$845$	−12.6608	−	49.6354i	−0.435546	−	1.70751i
$846$	4.26912	+	4.93419i	0.146775	+	0.169641i
$847$	−5.99303	+	1.60583i	−0.205923	+	0.0551769i
$848$	−18.4972	+	17.5329i	−0.635195	+	0.602083i
$849$	10.4598	−	6.03896i	0.358979	−	0.207257i
$850$	−3.28458	+	45.4524i	−0.112660	+	1.55900i
$851$	4.92352	−	18.3748i	0.168776	−	0.629881i
$852$	2.77269	+	1.19219i	0.0949908	+	0.0408437i
$853$	−21.1156	−	21.1156i	−0.722984	−	0.722984i	0.246228	−	0.969212i	$-0.420809\pi$
$853$	−21.1156	−	21.1156i	−0.722984	−	0.722984i	−0.969212	+	0.246228i	$0.920809\pi$
$854$	0.548388	−	1.58068i	0.0187654	−	0.0540898i
$855$	15.0605	−	26.0856i	0.515058	−	0.892107i
$856$	−23.1385	+	25.3401i	−0.790858	+	0.866108i
$857$		−	7.93370i		−	0.271010i	−0.990777	−	0.135505i	$-0.956734\pi$
$857$		−	7.93370i		−	0.271010i	0.990777	−	0.135505i	$-0.0432657\pi$
$858$	−3.29300	+	9.31028i	−0.112421	+	0.317848i
$859$		−	42.5438i		−	1.45157i	−0.687919	−	0.725787i	$-0.741476\pi$
$859$		−	42.5438i		−	1.45157i	0.687919	−	0.725787i	$-0.258524\pi$
$860$	9.82297	+	83.1990i	0.334960	+	2.83706i
$861$	−1.80789	+	3.13136i	−0.0616128	+	0.106716i
$862$	−49.3939	−	17.1363i	−1.68236	−	0.583664i
$863$	−18.1830	−	18.1830i	−0.618957	−	0.618957i	0.326307	−	0.945264i	$-0.394196\pi$
$863$	−18.1830	−	18.1830i	−0.618957	−	0.618957i	−0.945264	+	0.326307i	$0.894196\pi$
$864$	0.917458	+	5.58196i	0.0312126	+	0.189902i
$865$	5.21841	−	19.4754i	0.177431	−	0.662183i
$866$	−5.98880	−	0.432776i	−0.203508	−	0.0147063i
$867$	6.60698	−	3.81454i	0.224385	−	0.129549i
$868$	−6.70343	+	8.49822i	−0.227529	+	0.288449i
$869$	23.8474	−	6.38990i	0.808968	−	0.216762i
$870$	1.57126	−	1.35947i	0.0532706	−	0.0460903i
$871$	−2.75646	+	2.72345i	−0.0933990	+	0.0922804i
$872$	6.89791	+	10.7859i	0.233593	+	0.365255i
$873$	1.77728	+	6.63291i	0.0601519	+	0.224490i
$874$	9.99673	+	52.0750i	0.338145	+	1.76146i
$875$	9.31912	+	16.1412i	0.315044	+	0.545672i
$876$	2.79998	−	2.08959i	0.0946026	−	0.0706007i
$877$	15.3573	+	4.11497i	0.518579	+	0.138953i	0.508609	−	0.860997i	$-0.330160\pi$
$877$	15.3573	+	4.11497i	0.518579	+	0.138953i	0.00996975	+	0.999950i	$0.496826\pi$
$878$	−2.58056	+	1.25120i	−0.0870895	+	0.0422260i
$879$	−14.3685	+	14.3685i	−0.484639	+	0.484639i
$880$	−29.6865	+	7.10902i	−1.00073	+	0.239645i
$881$	−18.3164	−	10.5750i	−0.617096	−	0.356281i	0.158641	−	0.987336i	$-0.449289\pi$
$881$	−18.3164	−	10.5750i	−0.617096	−	0.356281i	−0.775738	+	0.631056i	$0.782622\pi$
$882$	4.97348	−	7.33662i	0.167466	−	0.247037i
$883$	−19.3164			−0.650047			−0.325023	−	0.945706i	$-0.605372\pi$
$883$	−19.3164			−0.650047			−0.325023	+	0.945706i	$0.605372\pi$
$884$	21.8257	+	3.30537i	0.734079	+	0.111172i
$885$	−17.3639			−0.583681
$886$	3.70031	−	5.45852i	0.124314	−	0.183382i
$887$	−31.3163	−	18.0805i	−1.05150	−	0.607082i	−0.128429	−	0.991719i	$-0.540994\pi$
$887$	−31.3163	−	18.0805i	−1.05150	−	0.607082i	−0.923068	+	0.384636i	$0.874327\pi$
$888$	−5.04810	+	9.73889i	−0.169403	+	0.326816i
$889$	−5.13374	+	5.13374i	−0.172180	+	0.172180i
$890$	56.2060	−	27.2519i	1.88403	−	0.913485i
$891$	−1.87075	−	0.501266i	−0.0626724	−	0.0167930i
$892$	−33.4685	−	44.8467i	−1.12061	−	1.50158i
$893$	−17.6339	−	30.5428i	−0.590096	−	1.02208i
$894$	−3.22371	−	16.7930i	−0.107817	−	0.561641i
$895$	−23.1514	−	86.4024i	−0.773867	−	2.88811i
$896$	2.68003	+	9.30514i	0.0895336	+	0.310863i
$897$	−8.93472	+	15.2623i	−0.298322	+	0.509594i
$898$	33.1801	−	28.7078i	1.10723	−	0.957991i
$899$	2.27726	−	0.610190i	0.0759509	−	0.0203510i
$900$	16.5294	+	13.0385i	0.550981	+	0.434616i
$901$	−16.8915	+	9.75229i	−0.562736	+	0.324896i
$902$	−11.5408	−	0.833985i	−0.384266	−	0.0277687i
$903$	−2.35493	+	8.78870i	−0.0783670	+	0.292470i
$904$	44.3107	−	14.0564i	1.47375	−	0.467509i
$905$	−43.2849	−	43.2849i	−1.43884	−	1.43884i
$906$	4.78811	+	1.66114i	0.159074	+	0.0551878i
$907$	−21.4405	+	37.1361i	−0.711921	+	1.23308i	0.252215	+	0.967671i	$0.418841\pi$
$907$	−21.4405	+	37.1361i	−0.711921	+	1.23308i	−0.964135	+	0.265411i	$0.914492\pi$
$908$	0.888181	−	0.104864i	0.0294753	−	0.00348003i
$909$		−	4.65582i		−	0.154424i
$910$	15.5187	−	7.40922i	0.514440	−	0.245613i
$911$		−	25.9636i		−	0.860213i	−0.902778	−	0.430107i	$-0.858476\pi$
$911$		−	25.9636i		−	0.860213i	0.902778	−	0.430107i	$-0.141524\pi$
$912$	0.818011	−	30.5660i	0.0270871	−	1.01214i
$913$	−5.73597	+	9.93499i	−0.189833	+	0.328800i
$914$	10.9835	−	31.6591i	0.363303	−	1.04719i
$915$	−3.85129	−	3.85129i	−0.127320	−	0.127320i
$916$	−19.3022	+	44.8914i	−0.637762	+	1.48325i
$917$	2.31958	−	8.65680i	0.0765994	−	0.285873i
$918$	−0.312031	+	4.31792i	−0.0102986	+	0.142513i
$919$	−35.4693	+	20.4782i	−1.17002	+	0.675514i	−0.953686	−	0.300804i	$-0.902745\pi$
$919$	−35.4693	+	20.4782i	−1.17002	+	0.675514i	−0.216339	+	0.976318i	$0.569412\pi$
$920$	−54.6101	+	2.48007i	−1.80044	+	0.0817656i
$921$	5.12584	−	1.37346i	0.168902	−	0.0452572i
$922$	−6.25161	−	7.22553i	−0.205886	−	0.237960i
$923$	−1.37655	−	5.26400i	−0.0453097	−	0.173267i
$924$	−3.28087	−	0.476668i	−0.107933	−	0.0156812i
$925$	10.5662	+	39.4336i	0.347414	+	1.29657i
$926$	−1.81254	+	0.347950i	−0.0595639	+	0.0114344i
$927$	−1.61481	−	2.79694i	−0.0530374	−	0.0918634i
$928$	0.744382	−	1.97347i	0.0244355	−	0.0647822i
$929$	−14.1790	−	3.79924i	−0.465197	−	0.124649i	0.0186047	−	0.999827i	$-0.494078\pi$
$929$	−14.1790	−	3.79924i	−0.465197	−	0.124649i	−0.483801	+	0.875178i	$0.660744\pi$
$930$	15.3725	+	31.7053i	0.504085	+	1.03966i
$931$	−33.8773	+	33.8773i	−1.11028	+	1.11028i
$932$	−19.9839	+	7.96609i	−0.654594	+	0.260938i
$933$	−6.63209	−	3.82904i	−0.217125	−	0.125357i
$934$	14.4794	+	9.81557i	0.473781	+	0.321175i
$935$	−23.3614			−0.763999
$936$	6.92177	−	7.48926i	0.226245	−	0.244794i
$937$	−28.5151			−0.931549			−0.465774	−	0.884904i	$-0.654224\pi$
$937$	−28.5151			−0.931549			−0.465774	+	0.884904i	$0.654224\pi$
$938$	−1.07677	−	0.729940i	−0.0351578	−	0.0238334i
$939$	21.0801	+	12.1706i	0.687922	+	0.397172i
$940$	33.7744	−	13.4633i	1.10160	−	0.439126i
$941$	35.8692	−	35.8692i	1.16930	−	1.16930i	0.186930	−	0.982373i	$-0.440146\pi$
$941$	35.8692	−	35.8692i	1.16930	−	1.16930i	0.982373	−	0.186930i	$-0.0598537\pi$
$942$	3.08402	+	6.36067i	0.100483	+	0.207242i
$943$	−20.0153	−	5.36309i	−0.651789	−	0.174646i
$944$	−15.4955	+	8.40181i	−0.504335	+	0.273456i
$945$	1.68628	+	2.92072i	0.0548546	+	0.0950109i
$946$	−28.5948	+	5.48928i	−0.929696	+	0.178472i
$947$	−1.61990	−	6.04555i	−0.0526397	−	0.196454i	0.934599	−	0.355704i	$-0.115759\pi$
$947$	−1.61990	−	6.04555i	−0.0526397	−	0.196454i	−0.987238	+	0.159250i	$0.949092\pi$
$948$	−25.2302	−	3.66562i	−0.819438	−	0.119054i
$949$	−6.07390	−	1.66678i	−0.197167	−	0.0541059i
$950$	−74.4575	−	86.0570i	−2.41572	−	2.79206i
$951$	18.4620	−	4.94687i	0.598670	−	0.160413i
$952$	0.336204	+	7.40306i	0.0108964	+	0.239935i
$953$	−43.1790	+	24.9294i	−1.39871	+	0.807544i	−0.994257	−	0.107017i	$-0.965870\pi$
$953$	−43.1790	+	24.9294i	−1.39871	+	0.807544i	−0.404449	+	0.914560i	$0.632537\pi$
$954$	−0.649460	+	8.98731i	−0.0210271	+	0.290975i
$955$	−23.9411	+	89.3493i	−0.774715	+	2.89127i
$956$	−20.4559	+	47.5746i	−0.661591	+	1.53867i
$957$	0.510619	+	0.510619i	0.0165060	+	0.0165060i
$958$	15.4135	−	44.4280i	0.497986	−	1.43540i
$959$	6.38200	−	11.0539i	0.206085	−	0.356951i
$960$	31.0630	+	5.36522i	1.00255	+	0.173162i
$961$			8.98140i			0.289723i
$962$	19.4430	−	3.61112i	0.626867	−	0.116427i
$963$			12.1321i			0.390953i
$964$	−58.3751	+	6.89211i	−1.88014	+	0.221980i
$965$	−9.74932	+	16.8863i	−0.313842	+	0.543590i
$966$	−5.60916	−	1.94599i	−0.180472	−	0.0626113i
$967$	18.5575	+	18.5575i	0.596769	+	0.596769i	0.939451	−	0.342682i	$-0.111335\pi$
$967$	18.5575	+	18.5575i	0.596769	+	0.596769i	−0.342682	+	0.939451i	$0.611335\pi$
$968$	6.19969	+	19.5436i	0.199265	+	0.628155i
$969$	6.05649	−	22.6031i	0.194562	−	0.726117i
$970$	38.1663	+	2.75806i	1.22545	+	0.0885559i
$971$	24.3285	−	14.0461i	0.780739	−	0.450760i	−0.0559530	−	0.998433i	$-0.517820\pi$
$971$	24.3285	−	14.0461i	0.780739	−	0.450760i	0.836692	+	0.547673i	$0.184486\pi$
$972$	1.57028	+	1.23864i	0.0503667	+	0.0397294i
$973$	14.1504	−	3.79160i	0.453642	−	0.121553i
$974$	−10.6143	+	9.18362i	−0.340104	+	0.294262i
$975$	0.228640	−	37.9529i	0.00732235	−	1.21547i
$976$	−5.30040	−	1.57337i	−0.169662	−	0.0503623i
$977$	−8.79297	−	32.8158i	−0.281312	−	1.04987i	−0.951492	−	0.307672i	$-0.900450\pi$
$977$	−8.79297	−	32.8158i	−0.281312	−	1.04987i	0.670181	−	0.742198i	$-0.266217\pi$
$978$	0.640777	+	3.33794i	0.0204898	+	0.106736i
$979$	10.8548	+	18.8011i	0.346921	+	0.600885i
$980$	−29.5410	−	39.5840i	−0.943653	−	1.26446i
$981$	4.37229	+	1.17155i	0.139597	+	0.0374048i
$982$	−27.1102	+	13.1446i	−0.865121	+	0.419460i
$983$	16.6056	−	16.6056i	0.529636	−	0.529636i	−0.390828	−	0.920464i	$-0.627811\pi$
$983$	16.6056	−	16.6056i	0.529636	−	0.529636i	0.920464	+	0.390828i	$0.127811\pi$
$984$	10.6084	+	5.49879i	0.338182	+	0.175295i
$985$	−45.3526	−	26.1843i	−1.44505	−	0.834302i
$986$	0.905736	−	1.33610i	0.0288445	−	0.0425499i
$987$	3.94882			0.125692
$988$	−44.3751	+	32.7022i	−1.41176	+	1.04039i
$989$	−52.1432			−1.65806
$990$	−6.05589	+	8.93334i	−0.192469	+	0.283920i
$991$	14.9519	+	8.63247i	0.474962	+	0.274219i	0.718314	−	0.695719i	$-0.244914\pi$
$991$	14.9519	+	8.63247i	0.474962	+	0.274219i	−0.243353	+	0.969938i	$0.578247\pi$
$992$	29.0595	+	20.8554i	0.922641	+	0.662161i
$993$	−21.2215	+	21.2215i	−0.673444	+	0.673444i
$994$	1.64360	−	0.796913i	0.0521320	−	0.0252765i
$995$	−77.2883	−	20.7093i	−2.45020	−	0.656530i
$996$	9.49420	−	7.08540i	0.300835	−	0.224510i
$997$	−10.1337	−	17.5521i	−0.320937	−	0.555879i	0.659744	−	0.751490i	$-0.270665\pi$
$997$	−10.1337	−	17.5521i	−0.320937	−	0.555879i	−0.980682	+	0.195610i	$0.937331\pi$
$998$	2.47009	+	12.8672i	0.0781894	+	0.407305i
$999$	1.00378	+	3.74614i	0.0317581	+	0.118523i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.2.w.c.19.6	✓	24
3.2	odd	2		468.2.cb.h.19.1		24
4.3	odd	2		156.2.w.d.19.3	yes	24
12.11	even	2		468.2.cb.g.19.4		24
13.11	odd	12		156.2.w.d.115.3	yes	24
39.11	even	12		468.2.cb.g.271.4		24
52.11	even	12	inner	156.2.w.c.115.6	yes	24
156.11	odd	12		468.2.cb.h.271.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.2.w.c.19.6	✓	24	1.1	even	1	trivial
156.2.w.c.115.6	yes	24	52.11	even	12	inner
156.2.w.d.19.3	yes	24	4.3	odd	2
156.2.w.d.115.3	yes	24	13.11	odd	12
468.2.cb.g.19.4		24	12.11	even	2
468.2.cb.g.271.4		24	39.11	even	12
468.2.cb.h.19.1		24	3.2	odd	2
468.2.cb.h.271.1		24	156.11	odd	12

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:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	156.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.17059 + 0.793543i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.740580 + 1.85783i) q^{4} +(2.78626 - 2.78626i) q^{5} +(-0.616993 - 1.27253i) q^{6} +(-0.826736 - 0.221523i) q^{7} +(-0.607351 + 2.76245i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.17059 + 0.793543i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.740580 + 1.85783i) q^{4} +(2.78626 - 2.78626i) q^{5} +(-0.616993 - 1.27253i) q^{6} +(-0.826736 - 0.221523i) q^{7} +(-0.607351 + 2.76245i) q^{8} +(0.500000 + 0.866025i) q^{9} +(5.47259 - 1.05056i) q^{10} +(0.501266 + 1.87075i) q^{11} +(0.287555 - 1.97922i) q^{12} +(-3.13330 + 1.78393i) q^{13} +(-0.791983 - 0.915364i) q^{14} +(-3.80610 + 1.01984i) q^{15} +(-2.90308 + 2.75175i) q^{16} +(-2.65107 + 1.53060i) q^{17} +(-0.101931 + 1.41054i) q^{18} +(1.97847 - 7.38376i) q^{19} +(7.23984 + 3.11295i) q^{20} +(0.605212 + 0.605212i) q^{21} +(-0.897740 + 2.58766i) q^{22} +(-2.45250 + 4.24786i) q^{23} +(1.90721 - 2.08868i) q^{24} -10.5264i q^{25} +(-5.08345 - 0.398149i) q^{26} -1.00000i q^{27} +(-0.200711 - 1.69999i) q^{28} +(-0.186428 + 0.322902i) q^{29} +(-5.26468 - 1.82648i) q^{30} +(-4.47110 - 4.47110i) q^{31} +(-5.58196 + 0.917458i) q^{32} +(0.501266 - 1.87075i) q^{33} +(-4.31792 - 0.312031i) q^{34} +(-2.92072 + 1.68628i) q^{35} +(-1.23864 + 1.57028i) q^{36} +(-3.74614 + 1.00378i) q^{37} +(8.17531 - 7.07338i) q^{38} +(3.60549 + 0.0217206i) q^{39} +(6.00466 + 9.38913i) q^{40} +(1.09339 + 4.08059i) q^{41} +(0.228196 + 1.18872i) q^{42} +(5.31531 + 9.20638i) q^{43} +(-3.10431 + 2.31671i) q^{44} +(3.80610 + 1.01984i) q^{45} +(-6.24174 + 3.02635i) q^{46} +(3.26234 - 3.26234i) q^{47} +(3.89002 - 0.931542i) q^{48} +(-5.42776 - 3.13372i) q^{49} +(8.35318 - 12.3222i) q^{50} +3.06120 q^{51} +(-5.63471 - 4.50001i) q^{52} +6.37156 q^{53} +(0.793543 - 1.17059i) q^{54} +(6.60904 + 3.81573i) q^{55} +(1.11406 - 2.14927i) q^{56} +(-5.40528 + 5.40528i) q^{57} +(-0.474468 + 0.230049i) q^{58} +(4.25652 + 1.14053i) q^{59} +(-4.71341 - 6.31582i) q^{60} +(0.691124 + 1.19706i) q^{61} +(-1.68583 - 8.78184i) q^{62} +(-0.221523 - 0.826736i) q^{63} +(-7.26225 - 3.35555i) q^{64} +(-3.75969 + 13.7007i) q^{65} +(2.07130 - 1.79211i) q^{66} +(1.03810 - 0.278157i) q^{67} +(-4.80693 - 3.79172i) q^{68} +(4.24786 - 2.45250i) q^{69} +(-4.75711 - 0.343768i) q^{70} +(-0.390575 + 1.45765i) q^{71} +(-2.69603 + 0.855243i) q^{72} +(1.23523 + 1.23523i) q^{73} +(-5.18175 - 1.79771i) q^{74} +(-5.26322 + 9.11617i) q^{75} +(15.1830 - 1.79259i) q^{76} -1.65766i q^{77} +(4.20332 + 2.88653i) q^{78} -12.7475i q^{79} +(-0.421659 + 15.7558i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.95821 + 5.64437i) q^{82} +(4.18842 + 4.18842i) q^{83} +(-0.676175 + 1.57259i) q^{84} +(-3.12193 + 11.6512i) q^{85} +(-1.08359 + 14.9949i) q^{86} +(0.322902 - 0.186428i) q^{87} +(-5.47229 + 0.248520i) q^{88} +(10.8274 - 2.90119i) q^{89} +(3.64611 + 4.21412i) q^{90} +(2.98559 - 0.780741i) q^{91} +(-9.70808 - 1.41046i) q^{92} +(1.63653 + 6.10763i) q^{93} +(6.40769 - 1.23007i) q^{94} +(-15.0605 - 26.0856i) q^{95} +(5.29285 + 1.99644i) q^{96} +(6.63291 + 1.77728i) q^{97} +(-3.86696 - 7.97547i) q^{98} +(-1.36948 + 1.36948i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9}+O(q^{10}) \) 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9	\( 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9} + 12 q^{10} + 4 q^{11} - 4 q^{12} - 22 q^{14} - 4 q^{15} + 12 q^{16} - 2 q^{18} - 22 q^{19} - 4 q^{20} + 10 q^{21} - 34 q^{22} + 2 q^{24} - 4 q^{26} - 14 q^{28} + 8 q^{29} - 16 q^{30} - 2 q^{31} - 34 q^{32} + 4 q^{33} + 20 q^{34} + 24 q^{35} - 4 q^{36} - 12 q^{37} - 12 q^{38} - 6 q^{39} + 28 q^{40} - 36 q^{41} + 6 q^{42} + 10 q^{43} + 20 q^{44} + 4 q^{45} - 2 q^{46} + 20 q^{47} + 32 q^{48} - 54 q^{49} - 24 q^{50} + 36 q^{51} + 4 q^{52} - 36 q^{53} - 4 q^{54} - 24 q^{55} + 70 q^{56} - 32 q^{57} + 48 q^{58} - 36 q^{59} - 28 q^{60} - 2 q^{61} + 64 q^{62} + 8 q^{63} - 8 q^{64} + 16 q^{65} + 20 q^{66} - 16 q^{67} - 10 q^{68} + 12 q^{69} + 36 q^{71} - 2 q^{72} - 40 q^{73} - 30 q^{74} - 8 q^{75} + 58 q^{76} + 24 q^{78} - 48 q^{80} - 12 q^{81} - 30 q^{82} - 24 q^{83} - 26 q^{84} + 18 q^{85} + 30 q^{86} + 6 q^{87} - 78 q^{88} + 66 q^{89} + 12 q^{90} + 42 q^{91} + 36 q^{92} - 10 q^{93} + 6 q^{94} - 28 q^{95} + 8 q^{96} + 4 q^{97} + 44 q^{98} - 4 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9 + 12 * q^10 + 4 * q^11 - 4 * q^12 - 22 * q^14 - 4 * q^15 + 12 * q^16 - 2 * q^18 - 22 * q^19 - 4 * q^20 + 10 * q^21 - 34 * q^22 + 2 * q^24 - 4 * q^26 - 14 * q^28 + 8 * q^29 - 16 * q^30 - 2 * q^31 - 34 * q^32 + 4 * q^33 + 20 * q^34 + 24 * q^35 - 4 * q^36 - 12 * q^37 - 12 * q^38 - 6 * q^39 + 28 * q^40 - 36 * q^41 + 6 * q^42 + 10 * q^43 + 20 * q^44 + 4 * q^45 - 2 * q^46 + 20 * q^47 + 32 * q^48 - 54 * q^49 - 24 * q^50 + 36 * q^51 + 4 * q^52 - 36 * q^53 - 4 * q^54 - 24 * q^55 + 70 * q^56 - 32 * q^57 + 48 * q^58 - 36 * q^59 - 28 * q^60 - 2 * q^61 + 64 * q^62 + 8 * q^63 - 8 * q^64 + 16 * q^65 + 20 * q^66 - 16 * q^67 - 10 * q^68 + 12 * q^69 + 36 * q^71 - 2 * q^72 - 40 * q^73 - 30 * q^74 - 8 * q^75 + 58 * q^76 + 24 * q^78 - 48 * q^80 - 12 * q^81 - 30 * q^82 - 24 * q^83 - 26 * q^84 + 18 * q^85 + 30 * q^86 + 6 * q^87 - 78 * q^88 + 66 * q^89 + 12 * q^90 + 42 * q^91 + 36 * q^92 - 10 * q^93 + 6 * q^94 - 28 * q^95 + 8 * q^96 + 4 * q^97 + 44 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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