LMFDB - Embedded newform 287.2.u.a.8.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(8,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 19]))

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

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

chi := DirichletCharacter("287.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.u (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			8.19
Character	$\chi$	$=$	287.8
Dual form			287.2.u.a.36.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41470 - 1.94717i) q^{2} +(0.651505 + 0.651505i) q^{3} +(-1.17206 - 3.60722i) q^{4} +(0.379466 - 0.123296i) q^{5} +(2.19028 - 0.346906i) q^{6} +(0.987688 + 0.156434i) q^{7} +(-4.10391 - 1.33344i) q^{8} -2.15108i q^{9} +O(q^{10})$	\(q+(1.41470 - 1.94717i) q^{2} +(0.651505 + 0.651505i) q^{3} +(-1.17206 - 3.60722i) q^{4} +(0.379466 - 0.123296i) q^{5} +(2.19028 - 0.346906i) q^{6} +(0.987688 + 0.156434i) q^{7} +(-4.10391 - 1.33344i) q^{8} -2.15108i q^{9} +(0.296753 - 0.913312i) q^{10} +(-2.42487 + 1.23553i) q^{11} +(1.58652 - 3.11372i) q^{12} +(0.0367267 + 0.231883i) q^{13} +(1.70189 - 1.70189i) q^{14} +(0.327552 + 0.166896i) q^{15} +(-2.26527 + 1.64582i) q^{16} +(2.24408 + 4.40426i) q^{17} +(-4.18852 - 3.04314i) q^{18} +(0.00955857 - 0.0603504i) q^{19} +(-0.889511 - 1.22431i) q^{20} +(0.541566 + 0.745402i) q^{21} +(-1.02468 + 6.46955i) q^{22} +(-1.99106 - 1.44659i) q^{23} +(-1.80497 - 3.54246i) q^{24} +(-3.91629 + 2.84535i) q^{25} +(0.503473 + 0.256533i) q^{26} +(3.35596 - 3.35596i) q^{27} +(-0.593333 - 3.74616i) q^{28} +(-2.69948 + 5.29803i) q^{29} +(0.788364 - 0.401692i) q^{30} +(-0.426055 + 1.31126i) q^{31} -1.89099i q^{32} +(-2.38477 - 0.774860i) q^{33} +(11.7506 + 1.86111i) q^{34} +(0.394082 - 0.0624165i) q^{35} +(-7.75942 + 2.52119i) q^{36} +(2.08563 + 6.41890i) q^{37} +(-0.103990 - 0.103990i) q^{38} +(-0.127145 + 0.175001i) q^{39} -1.72170 q^{40} +(0.0982975 + 6.40237i) q^{41} +2.21758 q^{42} +(1.77558 - 2.44388i) q^{43} +(7.29893 + 7.29893i) q^{44} +(-0.265220 - 0.816263i) q^{45} +(-5.63352 + 1.83044i) q^{46} +(4.79117 - 0.758847i) q^{47} +(-2.54810 - 0.403579i) q^{48} +(0.951057 + 0.309017i) q^{49} +11.6510i q^{50} +(-1.40737 + 4.33143i) q^{51} +(0.793408 - 0.404261i) q^{52} +(0.691095 - 1.35635i) q^{53} +(-1.78694 - 11.2823i) q^{54} +(-0.767821 + 0.767821i) q^{55} +(-3.84478 - 1.95902i) q^{56} +(0.0455461 - 0.0330912i) q^{57} +(6.49720 + 12.7515i) q^{58} +(2.59538 + 1.88566i) q^{59} +(0.218121 - 1.37716i) q^{60} +(-5.37806 - 7.40227i) q^{61} +(1.95051 + 2.68465i) q^{62} +(0.336503 - 2.12460i) q^{63} +(-8.21263 - 5.96682i) q^{64} +(0.0425268 + 0.0834636i) q^{65} +(-4.88253 + 3.54737i) q^{66} +(-8.71015 - 4.43804i) q^{67} +(13.2569 - 13.2569i) q^{68} +(-0.354726 - 2.23965i) q^{69} +(0.435973 - 0.855645i) q^{70} +(2.09749 - 1.06873i) q^{71} +(-2.86834 + 8.82784i) q^{72} -13.2249i q^{73} +(15.4492 + 5.01976i) q^{74} +(-4.40525 - 0.697723i) q^{75} +(-0.228900 + 0.0362542i) q^{76} +(-2.58830 + 0.840989i) q^{77} +(0.160883 + 0.495148i) q^{78} +(-1.91331 - 1.91331i) q^{79} +(-0.656672 + 0.903831i) q^{80} -2.08040 q^{81} +(12.6056 + 8.86604i) q^{82} -7.93897 q^{83} +(2.05408 - 2.82720i) q^{84} +(1.39458 + 1.39458i) q^{85} +(-2.24673 - 6.91473i) q^{86} +(-5.21042 + 1.69297i) q^{87} +(11.5990 - 1.83710i) q^{88} +(9.85104 + 1.56025i) q^{89} +(-1.96461 - 0.638340i) q^{90} +0.234774i q^{91} +(-2.88454 + 8.87769i) q^{92} +(-1.13187 + 0.576718i) q^{93} +(5.30047 - 10.4028i) q^{94} +(-0.00381381 - 0.0240795i) q^{95} +(1.23199 - 1.23199i) q^{96} +(-2.05084 - 1.04496i) q^{97} +(1.94717 - 1.41470i) q^{98} +(2.65774 + 5.21610i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 4 q^{3} + 36 q^{4} - 28 q^{6}+O(q^{10}) $ 160 * q - 4 * q^3 + 36 * q^4 - 28 * q^6	$ 160 q - 4 q^{3} + 36 q^{4} - 28 q^{6} - 48 q^{10} + 8 q^{11} - 16 q^{12} - 16 q^{13} - 32 q^{15} - 28 q^{16} - 20 q^{17} + 12 q^{18} - 40 q^{19} - 4 q^{22} - 36 q^{23} - 108 q^{24} + 40 q^{25} + 20 q^{26} + 20 q^{27} + 12 q^{29} - 4 q^{30} + 20 q^{31} - 32 q^{34} - 4 q^{35} + 140 q^{36} - 44 q^{38} + 80 q^{39} - 64 q^{40} + 4 q^{41} - 72 q^{42} - 8 q^{44} + 8 q^{45} + 40 q^{46} - 56 q^{47} + 120 q^{48} + 24 q^{51} + 16 q^{52} + 12 q^{53} - 52 q^{54} - 72 q^{55} + 48 q^{57} + 36 q^{58} - 48 q^{59} - 52 q^{60} + 8 q^{63} - 96 q^{64} - 96 q^{65} + 24 q^{66} + 20 q^{67} - 80 q^{68} - 68 q^{69} + 8 q^{70} + 60 q^{71} + 100 q^{72} - 40 q^{74} - 120 q^{75} + 4 q^{76} - 12 q^{78} + 12 q^{79} + 200 q^{80} - 56 q^{81} - 68 q^{82} - 40 q^{83} + 132 q^{85} + 80 q^{86} - 16 q^{88} + 8 q^{89} + 140 q^{92} + 64 q^{93} + 128 q^{94} - 68 q^{96} + 4 q^{98} + 96 q^{99}+O(q^{100}) $ 160 * q - 4 * q^3 + 36 * q^4 - 28 * q^6 - 48 * q^10 + 8 * q^11 - 16 * q^12 - 16 * q^13 - 32 * q^15 - 28 * q^16 - 20 * q^17 + 12 * q^18 - 40 * q^19 - 4 * q^22 - 36 * q^23 - 108 * q^24 + 40 * q^25 + 20 * q^26 + 20 * q^27 + 12 * q^29 - 4 * q^30 + 20 * q^31 - 32 * q^34 - 4 * q^35 + 140 * q^36 - 44 * q^38 + 80 * q^39 - 64 * q^40 + 4 * q^41 - 72 * q^42 - 8 * q^44 + 8 * q^45 + 40 * q^46 - 56 * q^47 + 120 * q^48 + 24 * q^51 + 16 * q^52 + 12 * q^53 - 52 * q^54 - 72 * q^55 + 48 * q^57 + 36 * q^58 - 48 * q^59 - 52 * q^60 + 8 * q^63 - 96 * q^64 - 96 * q^65 + 24 * q^66 + 20 * q^67 - 80 * q^68 - 68 * q^69 + 8 * q^70 + 60 * q^71 + 100 * q^72 - 40 * q^74 - 120 * q^75 + 4 * q^76 - 12 * q^78 + 12 * q^79 + 200 * q^80 - 56 * q^81 - 68 * q^82 - 40 * q^83 + 132 * q^85 + 80 * q^86 - 16 * q^88 + 8 * q^89 + 140 * q^92 + 64 * q^93 + 128 * q^94 - 68 * q^96 + 4 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$e\left(\frac{19}{20}\right)$

Coefficient data

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

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

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

$2$	1.41470	−	1.94717i	1.00035	−	1.37686i	0.0752321	−	0.997166i	$-0.476030\pi$
$2$	1.41470	−	1.94717i	1.00035	−	1.37686i	0.925113	−	0.379691i	$-0.123970\pi$
$3$	0.651505	+	0.651505i	0.376147	+	0.376147i	0.869710	−	0.493563i	$-0.164306\pi$
$3$	0.651505	+	0.651505i	0.376147	+	0.376147i	−0.493563	+	0.869710i	$0.664306\pi$
$4$	−1.17206	−	3.60722i	−0.586028	−	1.80361i
$5$	0.379466	−	0.123296i	0.169702	−	0.0551397i	−0.222933	−	0.974834i	$-0.571563\pi$
$5$	0.379466	−	0.123296i	0.169702	−	0.0551397i	0.392636	+	0.919694i	$0.371563\pi$
$6$	2.19028	−	0.346906i	0.894177	−	0.141624i
$7$	0.987688	+	0.156434i	0.373311	+	0.0591267i
$7$	0.987688	+	0.156434i	0.373311	+	0.0591267i
$8$	−4.10391	−	1.33344i	−1.45095	−	0.471442i
$9$		−	2.15108i		−	0.717027i
$10$	0.296753	−	0.913312i	0.0938416	−	0.288815i
$11$	−2.42487	+	1.23553i	−0.731127	+	0.372528i	−0.779584	−	0.626298i	$-0.784570\pi$
$11$	−2.42487	+	1.23553i	−0.731127	+	0.372528i	0.0484573	+	0.998825i	$0.484570\pi$
$12$	1.58652	−	3.11372i	0.457989	−	0.898854i
$13$	0.0367267	+	0.231883i	0.0101862	+	0.0643128i	0.992258	−	0.124195i	$-0.0396349\pi$
$13$	0.0367267	+	0.231883i	0.0101862	+	0.0643128i	−0.982072	+	0.188508i	$0.939635\pi$
$14$	1.70189	−	1.70189i	0.454849	−	0.454849i
$15$	0.327552	+	0.166896i	0.0845736	+	0.0430924i
$16$	−2.26527	+	1.64582i	−0.566318	+	0.411454i
$17$	2.24408	+	4.40426i	0.544270	+	1.06819i	0.985322	+	0.170709i	$0.0546057\pi$
$17$	2.24408	+	4.40426i	0.544270	+	1.06819i	−0.441051	+	0.897482i	$0.645394\pi$
$18$	−4.18852	−	3.04314i	−0.987244	−	0.717275i
$19$	0.00955857	−	0.0603504i	0.00219289	−	0.0138453i	−0.986568	−	0.163353i	$-0.947769\pi$
$19$	0.00955857	−	0.0603504i	0.00219289	−	0.0138453i	0.988761	+	0.149508i	$0.0477690\pi$
$20$	−0.889511	−	1.22431i	−0.198901	−	0.273763i
$21$	0.541566	+	0.745402i	0.118179	+	0.162660i
$22$	−1.02468	+	6.46955i	−0.218462	+	1.37931i
$23$	−1.99106	−	1.44659i	−0.415165	−	0.301635i	0.360524	−	0.932750i	$-0.382598\pi$
$23$	−1.99106	−	1.44659i	−0.415165	−	0.301635i	−0.775690	+	0.631114i	$0.782598\pi$
$24$	−1.80497	−	3.54246i	−0.368439	−	0.723102i
$25$	−3.91629	+	2.84535i	−0.783258	+	0.569071i
$26$	0.503473	+	0.256533i	0.0987393	+	0.0503102i
$27$	3.35596	−	3.35596i	0.645854	−	0.645854i
$28$	−0.593333	−	3.74616i	−0.112129	−	0.707957i
$29$	−2.69948	+	5.29803i	−0.501281	+	0.983819i	0.492271	+	0.870442i	$0.336167\pi$
$29$	−2.69948	+	5.29803i	−0.501281	+	0.983819i	−0.993552	+	0.113377i	$0.963833\pi$
$30$	0.788364	−	0.401692i	0.143935	−	0.0733385i
$31$	−0.426055	+	1.31126i	−0.0765218	+	0.235510i	−0.981999	−	0.188884i	$-0.939513\pi$
$31$	−0.426055	+	1.31126i	−0.0765218	+	0.235510i	0.905478	+	0.424394i	$0.139513\pi$
$32$		−	1.89099i		−	0.334283i
$33$	−2.38477	−	0.774860i	−0.415136	−	0.134886i
$34$	11.7506	+	1.86111i	2.01520	+	0.319177i
$35$	0.394082	−	0.0624165i	0.0666120	−	0.0105503i
$36$	−7.75942	+	2.52119i	−1.29324	+	0.420198i
$37$	2.08563	+	6.41890i	0.342875	+	1.05526i	0.962712	+	0.270530i	$0.0871989\pi$
$37$	2.08563	+	6.41890i	0.342875	+	1.05526i	−0.619837	+	0.784731i	$0.712801\pi$
$38$	−0.103990	−	0.103990i	−0.0168694	−	0.0168694i
$39$	−0.127145	+	0.175001i	−0.0203596	+	0.0280225i
$40$	−1.72170			−0.272225
$41$	0.0982975	+	6.40237i	0.0153515	+	0.999882i
$41$	0.0982975	+	6.40237i	0.0153515	+	0.999882i
$42$	2.21758			0.342180
$43$	1.77558	−	2.44388i	0.270774	−	0.372688i	−0.651877	−	0.758325i	$-0.726018\pi$
$43$	1.77558	−	2.44388i	0.270774	−	0.372688i	0.922651	+	0.385636i	$0.126018\pi$
$44$	7.29893	+	7.29893i	1.10036	+	1.10036i
$45$	−0.265220	−	0.816263i	−0.0395366	−	0.121681i
$46$	−5.63352	+	1.83044i	−0.830618	+	0.269884i
$47$	4.79117	−	0.758847i	0.698864	−	0.110689i	0.203115	−	0.979155i	$-0.434894\pi$
$47$	4.79117	−	0.758847i	0.698864	−	0.110689i	0.495749	+	0.868466i	$0.334894\pi$
$48$	−2.54810	−	0.403579i	−0.367786	−	0.0582516i
$49$	0.951057	+	0.309017i	0.135865	+	0.0441453i
$50$			11.6510i			1.64770i
$51$	−1.40737	+	4.33143i	−0.197071	+	0.606522i
$52$	0.793408	−	0.404261i	0.110026	−	0.0560610i
$53$	0.691095	−	1.35635i	0.0949292	−	0.186309i	−0.838659	−	0.544657i	$-0.816660\pi$
$53$	0.691095	−	1.35635i	0.0949292	−	0.186309i	0.933588	+	0.358348i	$0.116660\pi$
$54$	−1.78694	−	11.2823i	−0.243172	−	1.53533i
$55$	−0.767821	+	0.767821i	−0.103533	+	0.103533i
$56$	−3.84478	−	1.95902i	−0.513781	−	0.261784i
$57$	0.0455461	−	0.0330912i	0.00603272	−	0.00438303i
$58$	6.49720	+	12.7515i	0.853124	+	1.67435i
$59$	2.59538	+	1.88566i	0.337890	+	0.245491i	0.743771	−	0.668434i	$-0.233035\pi$
$59$	2.59538	+	1.88566i	0.337890	+	0.245491i	−0.405881	+	0.913926i	$0.633035\pi$
$60$	0.218121	−	1.37716i	0.0281593	−	0.177791i
$61$	−5.37806	−	7.40227i	−0.688591	−	0.947764i	0.311406	−	0.950277i	$-0.399200\pi$
$61$	−5.37806	−	7.40227i	−0.688591	−	0.947764i	−0.999997	+	0.00251331i	$0.999200\pi$
$62$	1.95051	+	2.68465i	0.247715	+	0.340951i
$63$	0.336503	−	2.12460i	0.0423954	−	0.267674i
$64$	−8.21263	−	5.96682i	−1.02658	−	0.745853i
$65$	0.0425268	+	0.0834636i	0.00527480	+	0.0103524i
$66$	−4.88253	+	3.54737i	−0.600998	+	0.436651i
$67$	−8.71015	−	4.43804i	−1.06411	−	0.542193i	−0.167895	−	0.985805i	$-0.553697\pi$
$67$	−8.71015	−	4.43804i	−1.06411	−	0.542193i	−0.896219	+	0.443612i	$0.853697\pi$
$68$	13.2569	−	13.2569i	1.60764	−	1.60764i
$69$	−0.354726	−	2.23965i	−0.0427040	−	0.269622i
$70$	0.435973	−	0.855645i	0.0521088	−	0.102269i
$71$	2.09749	−	1.06873i	0.248927	−	0.126834i	−0.325076	−	0.945688i	$-0.605390\pi$
$71$	2.09749	−	1.06873i	0.248927	−	0.126834i	0.574003	+	0.818853i	$0.305390\pi$
$72$	−2.86834	+	8.82784i	−0.338037	+	1.04037i
$73$		−	13.2249i		−	1.54786i	−0.633270	−	0.773931i	$-0.718288\pi$
$73$		−	13.2249i		−	1.54786i	0.633270	−	0.773931i	$-0.281712\pi$
$74$	15.4492	+	5.01976i	1.79594	+	0.583535i
$75$	−4.40525	−	0.697723i	−0.508674	−	0.0805661i
$76$	−0.228900	+	0.0362542i	−0.0262567	+	0.00415865i
$77$	−2.58830	+	0.840989i	−0.294964	+	0.0958396i
$78$	0.160883	+	0.495148i	0.0182164	+	0.0560645i
$79$	−1.91331	−	1.91331i	−0.215265	−	0.215265i	0.591235	−	0.806499i	$-0.298641\pi$
$79$	−1.91331	−	1.91331i	−0.215265	−	0.215265i	−0.806499	+	0.591235i	$0.798641\pi$
$80$	−0.656672	+	0.903831i	−0.0734181	+	0.101051i
$81$	−2.08040			−0.231155
$82$	12.6056	+	8.86604i	1.39205	+	0.979091i
$83$	−7.93897			−0.871415			−0.435708	−	0.900088i	$-0.643502\pi$
$83$	−7.93897			−0.871415			−0.435708	+	0.900088i	$0.643502\pi$
$84$	2.05408	−	2.82720i	0.224119	−	0.308473i
$85$	1.39458	+	1.39458i	0.151264	+	0.151264i
$86$	−2.24673	−	6.91473i	−0.242271	−	0.745634i
$87$	−5.21042	+	1.69297i	−0.558615	+	0.181505i
$88$	11.5990	−	1.83710i	1.23645	−	0.195835i
$89$	9.85104	+	1.56025i	1.04421	+	0.165386i	0.654895	−	0.755720i	$-0.272713\pi$
$89$	9.85104	+	1.56025i	1.04421	+	0.165386i	0.389312	+	0.921106i	$0.372713\pi$
$90$	−1.96461	−	0.638340i	−0.207088	−	0.0672870i
$91$			0.234774i			0.0246110i
$92$	−2.88454	+	8.87769i	−0.300734	+	0.925563i
$93$	−1.13187	+	0.576718i	−0.117370	+	0.0598028i
$94$	5.30047	−	10.4028i	0.546702	−	1.07296i
$95$	−0.00381381	−	0.0240795i	−0.000391289	−	0.00247050i
$96$	1.23199	−	1.23199i	0.125740	−	0.125740i
$97$	−2.05084	−	1.04496i	−0.208231	−	0.106099i	0.346765	−	0.937952i	$-0.387280\pi$
$97$	−2.05084	−	1.04496i	−0.208231	−	0.106099i	−0.554996	+	0.831853i	$0.687280\pi$
$98$	1.94717	−	1.41470i	0.196694	−	0.142906i
$99$	2.65774	+	5.21610i	0.267113	+	0.524238i
$100$	14.8539	+	10.7920i	1.48539	+	1.07920i
$101$	−1.93324	+	12.2060i	−0.192365	+	1.21455i	0.682758	+	0.730645i	$0.260780\pi$
$101$	−1.93324	+	12.2060i	−0.192365	+	1.21455i	−0.875123	+	0.483900i	$0.839220\pi$
$102$	6.44303	+	8.86807i	0.637955	+	0.878070i
$103$	0.0994953	+	0.136943i	0.00980356	+	0.0134934i	0.813891	−	0.581018i	$-0.197345\pi$
$103$	0.0994953	+	0.136943i	0.00980356	+	0.0134934i	−0.804087	+	0.594512i	$0.797345\pi$
$104$	0.158479	−	1.00060i	0.0155402	−	0.0981169i
$105$	0.297411	+	0.216082i	0.0290244	+	0.0210874i
$106$	−1.66335	−	3.26451i	−0.161559	−	0.317077i
$107$	9.60544	−	6.97876i	0.928593	−	0.674662i	−0.0170550	−	0.999855i	$-0.505429\pi$
$107$	9.60544	−	6.97876i	0.928593	−	0.674662i	0.945648	+	0.325192i	$0.105429\pi$
$108$	−16.0390	−	8.17230i	−1.54336	−	0.786380i
$109$	4.93040	−	4.93040i	0.472247	−	0.472247i	−0.430394	−	0.902641i	$-0.641625\pi$
$109$	4.93040	−	4.93040i	0.472247	−	0.472247i	0.902641	+	0.430394i	$0.141625\pi$
$110$	0.408840	+	2.58132i	0.0389814	+	0.246119i
$111$	−2.82315	+	5.54074i	−0.267962	+	0.525904i
$112$	−2.49485	+	1.27119i	−0.235741	+	0.120116i
$113$	0.569088	−	1.75147i	0.0535353	−	0.164765i	−0.920714	−	0.390238i	$-0.872393\pi$
$113$	0.569088	−	1.75147i	0.0535353	−	0.164765i	0.974249	+	0.225473i	$0.0723928\pi$
$114$		−	0.135500i		−	0.0126907i
$115$	−0.933900	−	0.303443i	−0.0870866	−	0.0282962i
$116$	22.2751	+	3.52803i	2.06819	+	0.327569i
$117$	0.498800	−	0.0790021i	0.0461141	−	0.00730375i
$118$	7.34338	−	2.38601i	0.676013	−	0.219650i
$119$	1.52748	+	4.70109i	0.140024	+	0.430948i
$120$	−1.12170	−	1.12170i	−0.102396	−	0.102396i
$121$	−2.11217	+	2.90716i	−0.192016	+	0.264287i
$122$	−22.0218			−1.99376
$123$	−4.10714	+	4.23522i	−0.370328	+	0.381877i
$124$	5.22937			0.469612
$125$	−2.30789	+	3.17654i	−0.206424	+	0.284119i
$126$	−3.66090	−	3.66090i	−0.326139	−	0.326139i
$127$	−4.24341	−	13.0599i	−0.376542	−	1.15888i	−0.942433	−	0.334396i	$-0.891468\pi$
$127$	−4.24341	−	13.0599i	−0.376542	−	1.15888i	0.565891	−	0.824480i	$-0.308532\pi$
$128$	−19.6400	+	6.38141i	−1.73594	+	0.564042i
$129$	2.74900	−	0.435399i	0.242036	−	0.0383348i
$130$	0.222681	+	0.0352691i	0.0195304	+	0.00309331i
$131$	−19.2753	−	6.26294i	−1.68409	−	0.547195i	−0.698395	−	0.715712i	$-0.746102\pi$
$131$	−19.2753	−	6.26294i	−1.68409	−	0.547195i	−0.985699	+	0.168517i	$0.946102\pi$
$132$			9.51058i			0.827790i
$133$	0.0188818	−	0.0581121i	0.00163726	−	0.00503896i
$134$	−20.9639	+	10.6816i	−1.81100	+	0.922753i
$135$	0.859696	−	1.68725i	0.0739908	−	0.145215i
$136$	−3.33669	−	21.0670i	−0.286119	−	1.80648i
$137$	−0.265393	+	0.265393i	−0.0226740	+	0.0226740i	−0.718353	−	0.695679i	$-0.755104\pi$
$137$	−0.265393	+	0.265393i	−0.0226740	+	0.0226740i	0.695679	+	0.718353i	$0.255104\pi$
$138$	−4.86281	−	2.47773i	−0.413950	−	0.210918i
$139$	−5.22398	+	3.79544i	−0.443092	+	0.321925i	−0.786862	−	0.617128i	$-0.788296\pi$
$139$	−5.22398	+	3.79544i	−0.443092	+	0.321925i	0.343770	+	0.939054i	$0.388296\pi$
$140$	−0.687036	−	1.34838i	−0.0580651	−	0.113959i
$141$	3.61586	+	2.62708i	0.304511	+	0.221240i
$142$	0.886336	−	5.59610i	0.0743796	−	0.469615i
$143$	−0.375557	−	0.516910i	−0.0314057	−	0.0432262i
$144$	3.54029	+	4.87279i	0.295024	+	0.406066i
$145$	−0.371135	+	2.34326i	−0.0308211	+	0.194597i
$146$	−25.7512	−	18.7093i	−2.13118	−	1.54840i
$147$	0.418292	+	0.820945i	0.0345002	+	0.0677104i
$148$	20.7099	−	15.0466i	1.70234	−	1.23682i
$149$	−17.1754	−	8.75131i	−1.40706	−	0.716935i	−0.424949	−	0.905217i	$-0.639708\pi$
$149$	−17.1754	−	8.75131i	−1.40706	−	0.716935i	−0.982115	+	0.188282i	$0.939708\pi$
$150$	−7.59070	+	7.59070i	−0.619778	+	0.619778i
$151$	−3.50868	−	22.1529i	−0.285532	−	1.80278i	−0.546529	−	0.837440i	$-0.684051\pi$
$151$	−3.50868	−	22.1529i	−0.285532	−	1.80278i	0.260997	−	0.965340i	$-0.415949\pi$
$152$	−0.119701	+	0.234927i	−0.00970904	+	0.0190551i
$153$	9.47393	−	4.82721i	0.765922	−	0.390257i
$154$	−2.02412	+	6.22961i	−0.163108	+	0.501996i
$155$			0.550111i			0.0441860i
$156$	0.780288	+	0.253531i	0.0624730	+	0.0202987i
$157$	10.3641	+	1.64152i	0.827149	+	0.131008i	0.555634	−	0.831427i	$-0.312475\pi$
$157$	10.3641	+	1.64152i	0.827149	+	0.131008i	0.271515	+	0.962434i	$0.412475\pi$
$158$	−6.43232	+	1.01878i	−0.511728	+	0.0810497i
$159$	1.33392	−	0.433417i	0.105787	−	0.0343722i
$160$	−0.233152	−	0.717567i	−0.0184323	−	0.0567287i
$161$	−1.74025	−	1.74025i	−0.137151	−	0.137151i
$162$	−2.94314	+	4.05089i	−0.231235	+	0.318268i
$163$	−14.4238			−1.12976			−0.564880	−	0.825173i	$-0.691077\pi$
$163$	−14.4238			−1.12976			−0.564880	+	0.825173i	$0.691077\pi$
$164$	22.9795	−	7.85852i	1.79440	−	0.613647i
$165$	−1.00048			−0.0778871
$166$	−11.2313	+	15.4585i	−0.871716	+	1.19981i
$167$	4.10719	+	4.10719i	0.317824	+	0.317824i	0.847931	−	0.530107i	$-0.177848\pi$
$167$	4.10719	+	4.10719i	0.317824	+	0.317824i	−0.530107	+	0.847931i	$0.677848\pi$
$168$	−1.22859	−	3.78121i	−0.0947877	−	0.291726i
$169$	12.3113	−	4.00019i	0.947024	−	0.307707i
$170$	4.68841	−	0.742571i	0.359584	−	0.0569526i
$171$	−0.129819	−	0.0205613i	−0.00992748	−	0.00157236i
$172$	−10.8967	−	3.54055i	−0.830865	−	0.269965i
$173$			25.5167i			1.94000i	0.243110	+	0.969999i	$0.421832\pi$
$173$			25.5167i			1.94000i	−0.243110	+	0.969999i	$0.578168\pi$
$174$	−4.07469	+	12.5406i	−0.308902	+	0.950701i
$175$	−4.31319	+	2.19768i	−0.326046	+	0.166129i
$176$	3.45954	−	6.78972i	0.260772	−	0.511795i
$177$	0.462391	+	2.91942i	0.0347554	+	0.219437i
$178$	16.9744	−	16.9744i	1.27228	−	1.27228i
$179$	−6.27954	−	3.19959i	−0.469355	−	0.239148i	0.203283	−	0.979120i	$-0.434839\pi$
$179$	−6.27954	−	3.19959i	−0.469355	−	0.239148i	−0.672638	+	0.739972i	$0.734839\pi$
$180$	−2.63358	+	1.91341i	−0.196296	+	0.142617i
$181$	3.13294	+	6.14873i	0.232869	+	0.457032i	0.977639	−	0.210290i	$-0.0674408\pi$
$181$	3.13294	+	6.14873i	0.232869	+	0.457032i	−0.744770	+	0.667321i	$0.767441\pi$
$182$	0.457144	+	0.332135i	0.0338858	+	0.0246195i
$183$	1.31878	−	8.32645i	0.0974871	−	0.615509i
$184$	6.24219	+	8.59164i	0.460181	+	0.633384i
$185$	1.58285	+	2.17861i	0.116373	+	0.160174i
$186$	−0.478294	+	3.01983i	−0.0350702	+	0.221425i
$187$	−10.8832	−	7.90714i	−0.795861	−	0.578227i
$188$	−8.35284	−	16.3934i	−0.609194	−	1.19561i
$189$	3.83963	−	2.78965i	0.279292	−	0.202917i
$190$	−0.0522822	−	0.0266391i	−0.00379295	−	0.00193261i
$191$	−6.25125	+	6.25125i	−0.452325	+	0.452325i	−0.896126	−	0.443801i	$-0.853630\pi$
$191$	−6.25125	+	6.25125i	−0.452325	+	0.452325i	0.443801	+	0.896126i	$0.353630\pi$
$192$	−1.46315	−	9.23799i	−0.105594	−	0.666694i
$193$	−1.58485	+	3.11044i	−0.114080	+	0.223894i	−0.940986	−	0.338446i	$-0.890099\pi$
$193$	−1.58485	+	3.11044i	−0.114080	+	0.223894i	0.826906	+	0.562340i	$0.190099\pi$
$194$	−4.93603	+	2.51503i	−0.354386	+	0.180569i
$195$	−0.0266705	+	0.0820834i	−0.00190991	+	0.00587811i
$196$		−	3.79285i		−	0.270918i
$197$	12.5543	+	4.07914i	0.894457	+	0.290627i	0.719947	−	0.694029i	$-0.244166\pi$
$197$	12.5543	+	4.07914i	0.894457	+	0.290627i	0.174510	+	0.984655i	$0.444166\pi$
$198$	13.9165	+	2.20416i	0.989005	+	0.156643i
$199$	19.3072	−	3.05796i	1.36865	−	0.216773i	0.571523	−	0.820586i	$-0.306353\pi$
$199$	19.3072	−	3.05796i	1.36865	−	0.216773i	0.797126	+	0.603813i	$0.206353\pi$
$200$	19.8662	−	6.45492i	1.40475	−	0.456432i
$201$	−2.78330	−	8.56612i	−0.196319	−	0.604207i
$202$	21.0322	+	21.0322i	1.47982	+	1.47982i
$203$	−3.49504	+	4.81051i	−0.245304	+	0.337631i
$204$	17.2739			1.20942
$205$	0.826687	+	2.41736i	0.0577383	+	0.168836i
$206$	0.407408			0.0283855
$207$	−3.11174	+	4.28294i	−0.216281	+	0.297685i
$208$	−0.464833	−	0.464833i	−0.0322304	−	0.0322304i
$209$	0.0513867	+	0.158152i	0.00355449	+	0.0109396i
$210$	0.841496	−	0.273419i	0.0580688	−	0.0188677i
$211$	25.9423	−	4.10886i	1.78594	−	0.282865i	0.826124	−	0.563488i	$-0.190541\pi$
$211$	25.9423	−	4.10886i	1.78594	−	0.282865i	0.959818	+	0.280623i	$0.0905410\pi$
$212$	−5.70265	−	0.903212i	−0.391660	−	0.0620328i
$213$	2.06281	+	0.670247i	0.141341	+	0.0459246i
$214$		−	28.5763i		−	1.95344i
$215$	0.372453	−	1.14629i	0.0254011	−	0.0781765i
$216$	−18.2475	+	9.29757i	−1.24159	+	0.632619i
$217$	−0.625936	+	1.22847i	−0.0424913	+	0.0833939i
$218$	−2.62528	−	16.5754i	−0.177807	−	1.12263i
$219$	8.61611	−	8.61611i	0.582223	−	0.582223i
$220$	3.66963	+	1.86977i	0.247406	+	0.126060i
$221$	−0.938857	+	0.682119i	−0.0631543	+	0.0458843i
$222$	6.79486	+	13.3357i	0.456041	+	0.895031i
$223$	12.3360	+	8.96263i	0.826079	+	0.600182i	0.918447	−	0.395543i	$-0.129444\pi$
$223$	12.3360	+	8.96263i	0.826079	+	0.600182i	−0.0923680	+	0.995725i	$0.529444\pi$
$224$	0.295816	−	1.86771i	0.0197651	−	0.124792i
$225$	6.12059	+	8.42427i	0.408039	+	0.561618i
$226$	−2.60533	−	3.58592i	−0.173304	−	0.238532i
$227$	1.06484	−	6.72316i	0.0706762	−	0.446232i	−0.926820	−	0.375507i	$-0.877469\pi$
$227$	1.06484	−	6.72316i	0.0706762	−	0.446232i	0.997496	−	0.0707251i	$-0.0225313\pi$
$228$	−0.172750	−	0.125510i	−0.0114406	−	0.00831210i
$229$	−9.16097	−	17.9794i	−0.605374	−	1.18811i	−0.966757	−	0.255696i	$-0.917695\pi$
$229$	−9.16097	−	17.9794i	−0.605374	−	1.18811i	0.361383	−	0.932417i	$-0.382305\pi$
$230$	−1.91204	+	1.38918i	−0.126077	+	0.0915999i
$231$	−2.23420	−	1.13838i	−0.147000	−	0.0749000i
$232$	18.1430	−	18.1430i	1.19115	−	1.19115i
$233$	1.85570	+	11.7164i	0.121571	+	0.767568i	0.970861	+	0.239642i	$0.0770301\pi$
$233$	1.85570	+	11.7164i	0.121571	+	0.767568i	−0.849291	+	0.527926i	$0.822970\pi$
$234$	0.551822	−	1.08301i	0.0360738	−	0.0707987i
$235$	1.72452	−	0.878689i	0.112496	−	0.0573193i
$236$	3.76004	−	11.5722i	0.244758	−	0.753286i
$237$		−	2.49307i		−	0.161942i
$238$	11.3148	+	3.67639i	0.733426	+	0.238305i
$239$	−6.84256	−	1.08376i	−0.442609	−	0.0701023i	−0.0688472	−	0.997627i	$-0.521932\pi$
$239$	−6.84256	−	1.08376i	−0.442609	−	0.0701023i	−0.373761	+	0.927525i	$0.621932\pi$
$240$	−1.01668	+	0.161026i	−0.0656261	+	0.0103942i
$241$	16.7010	−	5.42649i	1.07581	−	0.349551i	0.283061	−	0.959102i	$-0.408650\pi$
$241$	16.7010	−	5.42649i	1.07581	−	0.349551i	0.792747	+	0.609551i	$0.208650\pi$
$242$	2.67263	+	8.22552i	0.171803	+	0.528757i
$243$	−11.4233	−	11.4233i	−0.732803	−	0.732803i
$244$	−20.3982	+	28.0757i	−1.30586	+	1.79736i
$245$	0.398994			0.0254908
$246$	2.43632	+	13.9889i	0.155334	+	0.891898i
$247$	0.0143453			0.000912770
$248$	3.49698	−	4.81318i	0.222059	−	0.305637i
$249$	−5.17228	−	5.17228i	−0.327780	−	0.327780i
$250$	2.92029	+	8.98773i	0.184695	+	0.568434i
$251$	26.5144	−	8.61506i	1.67358	−	0.543778i	0.689928	−	0.723878i	$-0.257642\pi$
$251$	26.5144	−	8.61506i	1.67358	−	0.543778i	0.983648	+	0.180100i	$0.0576420\pi$
$252$	−8.05829	+	1.27631i	−0.507625	+	0.0803998i
$253$	6.61539	+	1.04778i	0.415906	+	0.0658731i
$254$	−31.4329	−	10.2132i	−1.97228	−	0.640832i
$255$			1.81715i			0.113795i
$256$	−9.08511	+	27.9611i	−0.567820	+	1.74757i
$257$	−4.35070	+	2.21679i	−0.271389	+	0.138280i	−0.584390	−	0.811473i	$-0.698666\pi$
$257$	−4.35070	+	2.21679i	−0.271389	+	0.138280i	0.313000	+	0.949753i	$0.398666\pi$
$258$	3.04122	−	5.96874i	0.189338	−	0.371597i
$259$	1.05581	+	6.66614i	0.0656050	+	0.414214i
$260$	0.251227	−	0.251227i	0.0155805	−	0.0155805i
$261$	11.3965	+	5.80680i	0.705425	+	0.359432i
$262$	−39.4639	+	28.6722i	−2.43809	+	1.77137i
$263$	−7.74417	−	15.1988i	−0.477526	−	0.937198i	−0.996594	−	0.0824649i	$-0.973721\pi$
$263$	−7.74417	−	15.1988i	−0.477526	−	0.937198i	0.519068	−	0.854733i	$-0.326279\pi$
$264$	8.75366	+	6.35991i	0.538751	+	0.391425i
$265$	0.0950145	−	0.599898i	0.00583670	−	0.0368515i
$266$	−0.0864421	−	0.118977i	−0.00530011	−	0.00729497i
$267$	5.40149	+	7.43451i	0.330566	+	0.454985i
$268$	−5.80021	+	36.6211i	−0.354304	+	2.23699i
$269$	10.4540	+	7.59525i	0.637390	+	0.463091i	0.858952	−	0.512055i	$-0.171116\pi$
$269$	10.4540	+	7.59525i	0.637390	+	0.463091i	−0.221563	+	0.975146i	$0.571116\pi$
$270$	−2.06915	−	4.06093i	−0.125924	−	0.247140i
$271$	−14.9020	+	10.8270i	−0.905233	+	0.657691i	−0.939805	−	0.341712i	$-0.888993\pi$
$271$	−14.9020	+	10.8270i	−0.905233	+	0.657691i	0.0345714	+	0.999402i	$0.488993\pi$
$272$	−12.3321	−	6.28351i	−0.747742	−	0.380994i
$273$	−0.152956	+	0.152956i	−0.00925733	+	0.00925733i
$274$	0.141313	+	0.892216i	0.00853704	+	0.0539008i
$275$	5.98098	−	11.7383i	0.360667	−	0.707848i
$276$	−7.66315	+	3.90457i	−0.461267	+	0.235028i
$277$	−2.13398	+	6.56770i	−0.128218	+	0.394615i	−0.994474	−	0.104986i	$-0.966520\pi$
$277$	−2.13398	+	6.56770i	−0.128218	+	0.394615i	0.866255	+	0.499601i	$0.166520\pi$
$278$			15.5414i			0.932111i
$279$	2.82063	+	0.916480i	0.168867	+	0.0548682i
$280$	−1.70050	−	0.269333i	−0.101625	−	0.0160958i
$281$	30.3746	−	4.81086i	1.81200	−	0.286992i	0.843703	−	0.536811i	$-0.180371\pi$
$281$	30.3746	−	4.81086i	1.81200	−	0.286992i	0.968293	+	0.249819i	$0.0803711\pi$
$282$	10.2307	−	3.32417i	0.609232	−	0.197951i
$283$	−1.69277	−	5.20979i	−0.100624	−	0.309690i	0.888054	−	0.459739i	$-0.152057\pi$
$283$	−1.69277	−	5.20979i	−0.100624	−	0.309690i	−0.988679	+	0.150049i	$0.952057\pi$
$284$	−6.31351	−	6.31351i	−0.374638	−	0.374638i
$285$	0.0132032	−	0.0181726i	0.000782089	−	0.00107645i
$286$	−1.53781			−0.0909328
$287$	−0.904464	+	6.33892i	−0.0533888	+	0.374175i
$288$	−4.06768			−0.239690
$289$	−4.36927	+	6.01378i	−0.257016	+	0.353752i
$290$	4.03767	+	4.03767i	0.237100	+	0.237100i
$291$	−0.655339	−	2.01693i	−0.0384167	−	0.118234i
$292$	−47.7052	+	15.5004i	−2.79174	+	0.907090i
$293$	−29.0904	+	4.60747i	−1.69948	+	0.269171i	−0.929480	−	0.368873i	$-0.879744\pi$
$293$	−29.0904	+	4.60747i	−1.69948	+	0.269171i	−0.770000	+	0.638044i	$0.779744\pi$
$294$	2.19028	+	0.346906i	0.127740	+	0.0202320i
$295$	1.21735	+	0.395542i	0.0708771	+	0.0230294i
$296$		−	29.1236i		−	1.69278i
$297$	−3.99137	+	12.2842i	−0.231603	+	0.712800i
$298$	−41.3384	+	21.0630i	−2.39467	+	1.22014i
$299$	0.262315	−	0.514823i	0.0151701	−	0.0297730i
$300$	2.64636	+	16.7085i	0.152788	+	0.964663i
$301$	2.13603	−	2.13603i	0.123119	−	0.123119i
$302$	−48.0992	−	24.5078i	−2.76780	−	1.41026i
$303$	−9.21181	+	6.69277i	−0.529205	+	0.384490i
$304$	0.0776730	+	0.152442i	0.00445485	+	0.00874314i
$305$	−2.95346	−	2.14582i	−0.169115	−	0.122869i
$306$	4.00339	−	25.2764i	0.228859	−	1.44496i
$307$	12.8408	+	17.6738i	0.732862	+	1.00870i	0.998998	+	0.0447624i	$0.0142531\pi$
$307$	12.8408	+	17.6738i	0.732862	+	1.00870i	−0.266136	+	0.963936i	$0.585747\pi$
$308$	6.06726	+	8.35087i	0.345714	+	0.475835i
$309$	−0.0243977	+	0.154041i	−0.00138794	+	0.00876309i
$310$	1.07116	+	0.778243i	0.0608378	+	0.0442012i
$311$	11.3414	+	22.2587i	0.643109	+	1.26217i	0.950540	+	0.310602i	$0.100531\pi$
$311$	11.3414	+	22.2587i	0.643109	+	1.26217i	−0.307431	+	0.951570i	$0.599469\pi$
$312$	0.755146	−	0.548646i	0.0427517	−	0.0310610i
$313$	15.2972	+	7.79433i	0.864651	+	0.440562i	0.829294	−	0.558813i	$-0.188743\pi$
$313$	15.2972	+	7.79433i	0.864651	+	0.440562i	0.0353574	+	0.999375i	$0.488743\pi$
$314$	17.8585	−	17.8585i	1.00781	−	1.00781i
$315$	−0.134263	−	0.847703i	−0.00756486	−	0.0477626i
$316$	−4.65923	+	9.14426i	−0.262102	+	0.514405i
$317$	0.243706	−	0.124174i	0.0136879	−	0.00697433i	−0.447133	−	0.894467i	$-0.647555\pi$
$317$	0.243706	−	0.124174i	0.0136879	−	0.00697433i	0.460821	+	0.887493i	$0.347555\pi$
$318$	1.04316	−	3.21053i	0.0584977	−	0.180037i
$319$		−	16.1823i		−	0.906037i
$320$	−3.85210	−	1.25162i	−0.215339	−	0.0699679i
$321$	10.8047	+	1.71130i	0.603059	+	0.0955152i
$322$	−5.85051	+	0.926630i	−0.326036	+	0.0516391i
$323$	0.287249	−	0.0933330i	0.0159830	−	0.00519319i
$324$	2.43834	+	7.50445i	0.135464	+	0.416914i
$325$	−0.803622	−	0.803622i	−0.0445769	−	0.0445769i
$326$	−20.4054	+	28.0856i	−1.13015	+	1.55552i
$327$	6.42437			0.355268
$328$	8.13377	−	26.4058i	0.449112	−	1.45802i
$329$	4.85089			0.267438
$330$	−1.41538	+	1.94810i	−0.0779140	+	0.107239i
$331$	−15.1159	−	15.1159i	−0.830844	−	0.830844i	0.156789	−	0.987632i	$-0.449886\pi$
$331$	−15.1159	−	15.1159i	−0.830844	−	0.830844i	−0.987632	+	0.156789i	$0.949886\pi$
$332$	9.30492	+	28.6376i	0.510674	+	1.57169i
$333$	13.8076	−	4.48635i	0.756651	−	0.245851i
$334$	13.8078	−	2.18695i	0.755532	−	0.119664i
$335$	−3.85240	−	0.610160i	−0.210479	−	0.0333366i
$336$	−2.45359	−	0.797220i	−0.133854	−	0.0434919i
$337$		−	8.27927i		−	0.451000i	−0.974243	−	0.225500i	$-0.927598\pi$
$337$		−	8.27927i		−	0.451000i	0.974243	−	0.225500i	$-0.0724016\pi$
$338$	9.62779	−	29.6313i	0.523683	−	1.61173i
$339$	1.51186	−	0.770330i	0.0821128	−	0.0418386i
$340$	3.39603	−	6.66509i	0.184176	−	0.361465i
$341$	−0.586981	−	3.70605i	−0.0317868	−	0.200694i
$342$	−0.223691	+	0.223691i	−0.0120958	+	0.0120958i
$343$	0.891007	+	0.453990i	0.0481098	+	0.0245132i
$344$	−10.5456	+	7.66183i	−0.568581	+	0.413098i
$345$	−0.410746	−	0.806135i	−0.0221138	−	0.0434009i
$346$	49.6853	+	36.0985i	2.67110	+	1.94067i
$347$	0.628841	−	3.97035i	0.0337580	−	0.213139i	−0.965043	−	0.262091i	$-0.915588\pi$
$347$	0.628841	−	3.97035i	0.0337580	−	0.213139i	0.998801	+	0.0489515i	$0.0155880\pi$
$348$	12.2138	+	16.8109i	0.654729	+	0.901157i
$349$	−2.07701	−	2.85875i	−0.111180	−	0.153026i	0.749801	−	0.661663i	$-0.230149\pi$
$349$	−2.07701	−	2.85875i	−0.111180	−	0.153026i	−0.860981	+	0.508638i	$0.830149\pi$
$350$	−1.82262	+	11.5076i	−0.0974231	+	0.615106i
$351$	0.901443	+	0.654937i	0.0481155	+	0.0349579i
$352$	2.33639	+	4.58541i	0.124530	+	0.244403i
$353$	16.0466	−	11.6585i	0.854073	−	0.620521i	−0.0721928	−	0.997391i	$-0.523000\pi$
$353$	16.0466	−	11.6585i	0.854073	−	0.620521i	0.926266	+	0.376870i	$0.123000\pi$
$354$	6.33875	+	3.22976i	0.336901	+	0.171660i
$355$	0.664158	−	0.664158i	0.0352498	−	0.0352498i
$356$	−5.91780	−	37.3635i	−0.313643	−	1.98026i
$357$	−2.06763	+	4.05795i	−0.109430	+	0.214769i
$358$	−15.1138	+	7.70088i	−0.798790	+	0.407004i
$359$	−6.70749	+	20.6435i	−0.354008	+	1.08952i	0.602575	+	0.798063i	$0.294142\pi$
$359$	−6.70749	+	20.6435i	−0.354008	+	1.08952i	−0.956583	+	0.291462i	$0.905858\pi$
$360$			3.70352i			0.195193i
$361$	18.0665	+	5.87017i	0.950870	+	0.308956i
$362$	16.4048	+	2.59826i	0.862217	+	0.136562i
$363$	−3.27012	+	0.517936i	−0.171637	+	0.0271846i
$364$	0.846880	−	0.275168i	0.0443886	−	0.0144227i
$365$	−1.63058	−	5.01841i	−0.0853485	−	0.262676i
$366$	−14.3473	−	14.3473i	−0.749948	−	0.749948i
$367$	4.32503	−	5.95289i	0.225765	−	0.310738i	−0.681076	−	0.732213i	$-0.738487\pi$
$367$	4.32503	−	5.95289i	0.225765	−	0.310738i	0.906840	+	0.421475i	$0.138487\pi$
$368$	6.89113			0.359225
$369$	13.7720	−	0.211446i	0.716943	−	0.0110074i
$370$	6.48138			0.336951
$371$	0.894766	−	1.23154i	0.0464540	−	0.0639384i
$372$	3.40696	+	3.40696i	0.176643	+	0.176643i
$373$	3.41714	+	10.5169i	0.176933	+	0.544544i	0.999716	−	0.0238111i	$-0.00758003\pi$
$373$	3.41714	+	10.5169i	0.176933	+	0.544544i	−0.822783	+	0.568355i	$0.807580\pi$
$374$	−30.7931	+	10.0053i	−1.59227	+	0.517361i
$375$	−3.57314	+	0.565930i	−0.184516	+	0.0292245i
$376$	−20.6744	−	3.27450i	−1.06620	−	0.168869i
$377$	−1.32767	−	0.431385i	−0.0683783	−	0.0222175i
$378$		−	11.4229i		−	0.587532i
$379$	6.58309	−	20.2607i	0.338151	−	1.04072i	−0.626998	−	0.779021i	$-0.715717\pi$
$379$	6.58309	−	20.2607i	0.338151	−	1.04072i	0.965149	−	0.261701i	$-0.0842833\pi$
$380$	−0.0823899	+	0.0419798i	−0.00422651	+	0.00215352i
$381$	5.74397	−	11.2732i	0.294272	−	0.577542i
$382$	3.32859	+	21.0159i	0.170306	+	1.07527i
$383$	−9.12003	+	9.12003i	−0.466012	+	0.466012i	−0.900620	−	0.434608i	$-0.856887\pi$
$383$	−9.12003	+	9.12003i	−0.466012	+	0.466012i	0.434608	+	0.900620i	$0.356887\pi$
$384$	−16.9531	−	8.63802i	−0.865132	−	0.440807i
$385$	−0.878481	+	0.638254i	−0.0447715	+	0.0325284i
$386$	3.81446	+	7.48630i	0.194151	+	0.381043i
$387$	−5.25699	−	3.81943i	−0.267228	−	0.194152i
$388$	−1.36568	+	8.62257i	−0.0693320	+	0.437745i
$389$	13.1372	+	18.0818i	0.666084	+	0.916786i	0.999664	−	0.0259359i	$-0.00825656\pi$
$389$	13.1372	+	18.0818i	0.666084	+	0.916786i	−0.333580	+	0.942722i	$0.608257\pi$
$390$	0.122100	+	0.168056i	0.00618275	+	0.00850982i
$391$	1.90306	−	12.0154i	0.0962418	−	0.607647i
$392$	−3.49099	−	2.53635i	−0.176322	−	0.128105i
$393$	−8.47765	−	16.6383i	−0.427641	−	0.839292i
$394$	25.7034	−	18.6746i	1.29492	−	0.940813i
$395$	−0.961942	−	0.490134i	−0.0484006	−	0.0246613i
$396$	15.7006	−	15.7006i	0.788985	−	0.788985i
$397$	5.84217	+	36.8860i	0.293210	+	1.85126i	0.491192	+	0.871051i	$0.336561\pi$
$397$	5.84217	+	36.8860i	0.293210	+	1.85126i	−0.197982	+	0.980206i	$0.563439\pi$
$398$	21.3595	−	41.9205i	1.07066	−	2.10128i
$399$	0.0501619	−	0.0255588i	0.00251124	−	0.00127954i
$400$	4.18854	−	12.8910i	0.209427	−	0.644550i
$401$		−	32.1485i		−	1.60542i	−0.596369	−	0.802710i	$-0.703391\pi$
$401$		−	32.1485i		−	1.60542i	0.596369	−	0.802710i	$-0.296609\pi$
$402$	−20.6172	−	6.69894i	−1.02829	−	0.334113i
$403$	−0.319707	−	0.0506367i	−0.0159258	−	0.00252239i
$404$	46.2957	−	7.33251i	2.30330	−	0.364806i
$405$	−0.789441	+	0.256505i	−0.0392276	+	0.0127458i
$406$	4.42244	+	13.6109i	0.219482	+	0.675496i
$407$	−12.9882	−	12.9882i	−0.643799	−	0.643799i
$408$	11.5514	−	15.8992i	0.571880	−	0.787126i
$409$	−28.9572			−1.43184			−0.715921	−	0.698182i	$-0.753993\pi$
$409$	−28.9572			−1.43184			−0.715921	+	0.698182i	$0.753993\pi$
$410$	5.87653	+	1.81015i	0.290221	+	0.0893968i
$411$	−0.345809			−0.0170575
$412$	0.377371	−	0.519407i	0.0185917	−	0.0255893i
$413$	2.26845	+	2.26845i	0.111623	+	0.111623i
$414$	3.93743	+	12.1182i	0.193514	+	0.595576i
$415$	−3.01257	+	0.978843i	−0.147881	+	0.0480495i
$416$	0.438489	−	0.0694499i	0.0214987	−	0.00340506i
$417$	−5.87620	−	0.930699i	−0.287759	−	0.0455765i
$418$	0.380646	+	0.123679i	0.0186180	+	0.00604935i
$419$			21.8482i			1.06735i	0.845689	+	0.533676i	$0.179190\pi$
$419$			21.8482i			1.06735i	−0.845689	+	0.533676i	$0.820810\pi$
$420$	0.430872	−	1.32609i	0.0210244	−	0.0647064i
$421$	−10.8892	+	5.54832i	−0.530707	+	0.270409i	−0.698744	−	0.715372i	$-0.746257\pi$
$421$	−10.8892	+	5.54832i	−0.530707	+	0.270409i	0.168037	+	0.985781i	$0.446257\pi$
$422$	28.7000	−	56.3269i	1.39709	−	2.74195i
$423$	−1.63234	−	10.3062i	−0.0793671	−	0.501104i
$424$	−4.64480	+	4.64480i	−0.225571	+	0.225571i
$425$	−21.3202	−	10.8632i	−1.03418	−	0.526941i
$426$	4.22334	−	3.06844i	0.204622	−	0.148666i
$427$	−4.15388	−	8.15245i	−0.201020	−	0.394525i
$428$	−36.4320	−	26.4694i	−1.76101	−	1.27945i
$429$	0.0920922	−	0.581447i	0.00444625	−	0.0280725i
$430$	−1.70512	−	2.34689i	−0.0822280	−	0.113177i
$431$	8.06608	+	11.1020i	0.388529	+	0.534765i	0.957819	−	0.287372i	$-0.0927817\pi$
$431$	8.06608	+	11.1020i	0.388529	+	0.534765i	−0.569290	+	0.822137i	$0.692782\pi$
$432$	−2.07887	+	13.1255i	−0.100020	+	0.631499i
$433$	−20.5662	−	14.9422i	−0.988348	−	0.718077i	−0.0287896	−	0.999585i	$-0.509165\pi$
$433$	−20.5662	−	14.9422i	−0.988348	−	0.718077i	−0.959559	+	0.281508i	$0.909165\pi$
$434$	1.50653	+	2.95672i	0.0723155	+	0.141927i
$435$	−1.76844	+	1.28485i	−0.0847902	+	0.0616037i
$436$	−23.5637	−	12.0063i	−1.12850	−	0.574999i
$437$	−0.106334	+	0.106334i	−0.00508665	+	0.00508665i
$438$	−4.58781	−	28.9663i	−0.219214	−	1.38406i
$439$	5.59668	−	10.9841i	0.267115	−	0.524242i	−0.718021	−	0.696022i	$-0.754952\pi$
$439$	5.59668	−	10.9841i	0.267115	−	0.524242i	0.985135	+	0.171780i	$0.0549517\pi$
$440$	4.17491	−	2.12722i	0.199031	−	0.101411i
$441$	0.664721	−	2.04580i	0.0316534	−	0.0974191i
$442$			2.79311i			0.132855i
$443$	−26.5404	−	8.62351i	−1.26097	−	0.409715i	−0.399132	−	0.916893i	$-0.630689\pi$
$443$	−26.5404	−	8.62351i	−1.26097	−	0.409715i	−0.861841	+	0.507178i	$0.830689\pi$
$444$	23.2956	+	3.68966i	1.10556	+	0.175103i
$445$	3.93051	−	0.622531i	0.186324	−	0.0295108i
$446$	34.9035	−	11.3408i	1.65273	−	0.537004i
$447$	−5.48835	−	16.8914i	−0.259590	−	0.798935i
$448$	−7.17810	−	7.17810i	−0.339133	−	0.339133i
$449$	−13.2414	+	18.2253i	−0.624902	+	0.860104i	−0.997698	−	0.0678089i	$-0.978399\pi$
$449$	−13.2414	+	18.2253i	−0.624902	+	0.860104i	0.372796	+	0.927913i	$0.378399\pi$
$450$	25.0623			1.18145
$451$	−8.14871	−	15.4035i	−0.383708	−	0.725322i
$452$	−6.98495			−0.328544
$453$	12.1468	−	16.7187i	0.570708	−	0.785512i
$454$	−11.5847	−	11.5847i	−0.543697	−	0.543697i
$455$	0.0289467	+	0.0890886i	0.00135704	+	0.00417654i
$456$	−0.231042	+	0.0750701i	−0.0108195	+	0.00351548i
$457$	24.2981	−	3.84843i	1.13662	−	0.180022i	0.440363	−	0.897820i	$-0.354850\pi$
$457$	24.2981	−	3.84843i	1.13662	−	0.180022i	0.696252	+	0.717798i	$0.254850\pi$
$458$	−47.9690	−	7.59755i	−2.24145	−	0.355010i
$459$	22.3116	+	7.24947i	1.04141	+	0.338376i
$460$			3.72443i			0.173653i
$461$	1.50133	−	4.62061i	0.0699238	−	0.215203i	−0.909988	−	0.414635i	$-0.863909\pi$
$461$	1.50133	−	4.62061i	0.0699238	−	0.215203i	0.979912	+	0.199431i	$0.0639094\pi$
$462$	−5.37735	+	2.73990i	−0.250177	+	0.127472i
$463$	−17.2005	+	33.7578i	−0.799373	+	1.56886i	0.0228821	+	0.999738i	$0.492716\pi$
$463$	−17.2005	+	33.7578i	−0.799373	+	1.56886i	−0.822255	+	0.569119i	$0.807284\pi$
$464$	−2.60453	−	16.4443i	−0.120912	−	0.763409i
$465$	−0.358400	+	0.358400i	−0.0166204	+	0.0166204i
$466$	25.4391	+	12.9619i	1.17844	+	0.600447i
$467$	−22.4908	+	16.3405i	−1.04075	+	0.756149i	−0.970432	−	0.241376i	$-0.922401\pi$
$467$	−22.4908	+	16.3405i	−1.04075	+	0.756149i	−0.0703178	+	0.997525i	$0.522401\pi$
$468$	−0.869599	−	1.70668i	−0.0401972	−	0.0788915i
$469$	−7.90865	−	5.74597i	−0.365188	−	0.265324i
$470$	0.728731	−	4.60102i	0.0336138	−	0.212229i
$471$	5.68284	+	7.82175i	0.261851	+	0.360407i
$472$	−8.13680	−	11.1993i	−0.374526	−	0.515491i
$473$	−1.28607	+	8.11990i	−0.0591334	+	0.373353i
$474$	−4.85443	−	3.52695i	−0.222971	−	0.161998i
$475$	0.134284	+	0.263547i	0.00616138	+	0.0120924i
$476$	15.1676	−	11.0199i	0.695205	−	0.505096i
$477$	−2.91762	−	1.48660i	−0.133589	−	0.0680668i
$478$	−11.7904	+	11.7904i	−0.539282	+	0.539282i
$479$	4.44796	+	28.0833i	0.203233	+	1.28316i	0.852551	+	0.522644i	$0.175054\pi$
$479$	4.44796	+	28.0833i	0.203233	+	1.28316i	−0.649318	+	0.760517i	$0.724946\pi$
$480$	0.315599	−	0.619398i	0.0144051	−	0.0282715i
$481$	−1.41184	+	0.719367i	−0.0643742	+	0.0328003i
$482$	13.0607	−	40.1966i	0.594897	−	1.83091i
$483$		−	2.26757i		−	0.103178i
$484$	12.9623	+	4.21172i	0.589197	+	0.191442i
$485$	−0.907063	−	0.143665i	−0.0411876	−	0.00652348i
$486$	−38.4035	+	6.08252i	−1.74202	+	0.275909i
$487$	2.84827	−	0.925458i	0.129067	−	0.0419365i	−0.243771	−	0.969833i	$-0.578385\pi$
$487$	2.84827	−	0.925458i	0.129067	−	0.0419365i	0.372838	+	0.927896i	$0.378385\pi$
$488$	12.2006	+	37.5495i	0.552295	+	1.69979i
$489$	−9.39718	−	9.39718i	−0.424955	−	0.424955i
$490$	0.564458	−	0.776910i	0.0254996	−	0.0350972i
$491$	24.1055			1.08786			0.543932	−	0.839129i	$-0.316935\pi$
$491$	24.1055			1.08786			0.543932	+	0.839129i	$0.316935\pi$
$492$	20.0912	+	9.85142i	0.905779	+	0.444136i
$493$	−29.3918			−1.32374
$494$	0.0202943	−	0.0279327i	0.000913085	−	0.00125675i
$495$	1.65165	+	1.65165i	0.0742359	+	0.0742359i
$496$	−1.19297	−	3.67158i	−0.0535658	−	0.164859i
$497$	2.23885	−	0.727448i	0.100426	−	0.0326305i
$498$	−17.3885	+	2.75407i	−0.779199	+	0.123413i
$499$	−5.59482	−	0.886133i	−0.250459	−	0.0396688i	0.0299426	−	0.999552i	$-0.490468\pi$
$499$	−5.59482	−	0.886133i	−0.250459	−	0.0396688i	−0.280401	+	0.959883i	$0.590468\pi$
$500$	14.1635	+	4.60199i	0.633410	+	0.205807i
$501$			5.35171i			0.239097i
$502$	20.7350	−	63.8159i	0.925450	−	2.84824i
$503$	−20.4994	+	10.4450i	−0.914023	+	0.465718i	−0.846734	−	0.532016i	$-0.821435\pi$
$503$	−20.4994	+	10.4450i	−0.914023	+	0.465718i	−0.0672882	+	0.997734i	$0.521435\pi$
$504$	−4.21400	+	8.27045i	−0.187707	+	0.368395i
$505$	0.771354	+	4.87013i	0.0343248	+	0.216718i
$506$	11.3990	−	11.3990i	0.506748	−	0.506748i
$507$	10.6270	+	5.41474i	0.471963	+	0.240477i
$508$	−42.1363	+	30.6138i	−1.86950	+	1.35827i
$509$	16.5882	+	32.5562i	0.735259	+	1.44303i	0.890421	+	0.455138i	$0.150410\pi$
$509$	16.5882	+	32.5562i	0.735259	+	1.44303i	−0.155162	+	0.987889i	$0.549590\pi$
$510$	3.53831	+	2.57073i	0.156679	+	0.113834i
$511$	2.06884	−	13.0621i	0.0915199	−	0.577834i
$512$	17.3160	+	23.8334i	0.765265	+	1.05330i
$513$	−0.170455	−	0.234612i	−0.00752578	−	0.0103584i
$514$	−1.83847	+	11.6077i	−0.0810916	+	0.511992i
$515$	0.0546397	+	0.0396980i	0.00240771	+	0.00174930i
$516$	−4.79257	−	9.40594i	−0.210981	−	0.414074i
$517$	−10.6804	+	7.75976i	−0.469723	+	0.341274i
$518$	14.4738	+	7.37475i	0.635941	+	0.324028i
$519$	−16.6243	+	16.6243i	−0.729724	+	0.729724i
$520$	−0.0632324	−	0.399234i	−0.00277292	−	0.0175076i
$521$	17.5082	−	34.3617i	0.767048	−	1.50542i	−0.0932610	−	0.995642i	$-0.529729\pi$
$521$	17.5082	−	34.3617i	0.767048	−	1.50542i	0.860308	−	0.509774i	$-0.170271\pi$
$522$	27.4295	−	13.9760i	1.20056	−	0.611713i
$523$	5.54067	−	17.0524i	0.242277	−	0.745650i	−0.753796	−	0.657109i	$-0.771779\pi$
$523$	5.54067	−	17.0524i	0.242277	−	0.745650i	0.996072	−	0.0885419i	$-0.0282207\pi$
$524$			76.8709i			3.35812i
$525$	−4.24186	−	1.37827i	−0.185130	−	0.0601524i
$526$	−40.5503	−	6.42254i	−1.76808	−	0.280036i
$527$	−6.73125	+	1.06613i	−0.293218	+	0.0464412i
$528$	6.67745	−	2.16963i	0.290599	−	0.0944212i
$529$	−5.23569	−	16.1138i	−0.227639	−	0.700599i
$530$	−1.03369	−	1.03369i	−0.0449005	−	0.0449005i
$531$	4.05620	−	5.58288i	0.176024	−	0.242276i
$532$	−0.231754			−0.0100478
$533$	−1.48099	+	0.257931i	−0.0641489	+	0.0111722i
$534$	22.1178			0.957129
$535$	2.78449	−	3.83252i	0.120384	−	0.165694i
$536$	29.8278	+	29.8278i	1.28836	+	1.28836i
$537$	−2.00661	−	6.17570i	−0.0865915	−	0.266501i
$538$	29.5785	−	9.61064i	1.27522	−	0.414344i
$539$	−2.68799	+	0.425736i	−0.115780	+	0.0183378i
$540$	−7.09388	−	1.12356i	−0.305272	−	0.0483504i
$541$	34.4314	+	11.1875i	1.48032	+	0.480986i	0.934210	−	0.356725i	$-0.116107\pi$
$541$	34.4314	+	11.1875i	1.48032	+	0.480986i	0.546114	+	0.837711i	$0.316107\pi$
$542$			44.3337i			1.90429i
$543$	−1.96481	+	6.04705i	−0.0843179	+	0.259504i
$544$	8.32842	−	4.24354i	0.357078	−	0.181940i
$545$	1.26302	−	2.47882i	0.0541019	−	0.106181i
$546$	0.0814444	+	0.514219i	0.00348550	+	0.0220066i
$547$	−20.3837	+	20.3837i	−0.871546	+	0.871546i	−0.992641	−	0.121095i	$-0.961359\pi$
$547$	−20.3837	+	20.3837i	−0.871546	+	0.871546i	0.121095	+	0.992641i	$0.461359\pi$
$548$	1.26838	+	0.646274i	0.0541827	+	0.0276075i
$549$	−15.9229	+	11.5687i	−0.679572	+	0.493738i
$550$	−14.3952	−	28.2522i	−0.613815	−	1.20468i
$551$	0.293935	+	0.213556i	0.0125221	+	0.00909780i
$552$	−1.53068	+	9.66432i	−0.0651500	+	0.411341i
$553$	−1.59045	−	2.18907i	−0.0676328	−	0.0930886i
$554$	9.76950	+	13.4466i	0.415066	+	0.571290i
$555$	−0.388138	+	2.45061i	−0.0164755	+	0.104023i
$556$	19.8138	+	14.3956i	0.840292	+	0.610508i
$557$	7.26874	+	14.2657i	0.307986	+	0.604457i	0.992176	−	0.124847i	$-0.0398440\pi$
$557$	7.26874	+	14.2657i	0.307986	+	0.604457i	−0.684190	+	0.729304i	$0.739844\pi$
$558$	5.77490	−	4.19571i	0.244471	−	0.177619i
$559$	0.631906	+	0.321972i	0.0267268	+	0.0136180i
$560$	−0.789977	+	0.789977i	−0.0333826	+	0.0333826i
$561$	−1.93895	−	12.2420i	−0.0818624	−	0.516859i
$562$	33.6034	−	65.9504i	1.41747	−	2.78195i
$563$	−12.3733	+	6.30451i	−0.521472	+	0.265703i	−0.694853	−	0.719151i	$-0.744531\pi$
$563$	−12.3733	+	6.30451i	−0.521472	+	0.265703i	0.173381	+	0.984855i	$0.444531\pi$
$564$	5.23845	−	16.1223i	0.220579	−	0.678871i
$565$		−	0.734791i		−	0.0309129i
$566$	−12.5391	−	4.07421i	−0.527058	−	0.171252i
$567$	−2.05479	−	0.325446i	−0.0862929	−	0.0136674i
$568$	−10.0330	+	1.58907i	−0.420975	+	0.0666759i
$569$	−39.8281	+	12.9409i	−1.66968	+	0.542512i	−0.982866	−	0.184320i	$-0.940992\pi$
$569$	−39.8281	+	12.9409i	−1.66968	+	0.542512i	−0.686815	+	0.726832i	$0.740992\pi$
$570$	−0.0167066	−	0.0514177i	−0.000699763	−	0.00215365i
$571$	−17.7793	−	17.7793i	−0.744039	−	0.744039i	0.229313	−	0.973353i	$-0.426352\pi$
$571$	−17.7793	−	17.7793i	−0.744039	−	0.744039i	−0.973353	+	0.229313i	$0.926352\pi$
$572$	−1.42443	+	1.96056i	−0.0595586	+	0.0819753i
$573$	−8.14545			−0.340281
$574$	11.0634	+	10.7288i	0.461778	+	0.447813i
$575$	11.9137			0.496834
$576$	−12.8351	+	17.6660i	−0.534797	+	0.736085i
$577$	−29.6417	−	29.6417i	−1.23400	−	1.23400i	−0.962414	−	0.271588i	$-0.912451\pi$
$577$	−29.6417	−	29.6417i	−1.23400	−	1.23400i	−0.271588	−	0.962414i	$-0.587549\pi$
$578$	5.52865	+	17.0154i	0.229961	+	0.707748i
$579$	−3.05900	+	0.993929i	−0.127128	+	0.0413063i
$580$	8.88763	−	1.40766i	0.369039	−	0.0584500i
$581$	−7.84123	−	1.24193i	−0.325309	−	0.0515239i
$582$	−4.85441	−	1.57729i	−0.201222	−	0.0653809i
$583$			4.14285i			0.171579i
$584$	−17.6347	+	54.2739i	−0.729727	+	2.24587i
$585$	0.179537	−	0.0914786i	0.00742294	−	0.00378218i
$586$	−32.1827	+	63.1621i	−1.32946	+	2.60920i
$587$	−1.60702	−	10.1463i	−0.0663289	−	0.418784i	−0.998402	−	0.0565134i	$-0.982002\pi$
$587$	−1.60702	−	10.1463i	−0.0663289	−	0.418784i	0.932073	−	0.362271i	$-0.117998\pi$
$588$	2.47106	−	2.47106i	0.101905	−	0.101905i
$589$	0.0750628	+	0.0382464i	0.00309291	+	0.00157592i
$590$	2.49238	−	1.81082i	0.102610	−	0.0745503i
$591$	5.52161	+	10.8368i	0.227129	+	0.445765i
$592$	−15.2889	−	11.1080i	−0.628368	−	0.456536i
$593$	−2.92231	+	18.4507i	−0.120005	+	0.757680i	0.852143	+	0.523310i	$0.175303\pi$
$593$	−2.92231	+	18.4507i	−0.120005	+	0.757680i	−0.972147	+	0.234371i	$0.924697\pi$
$594$	18.2728	+	25.1503i	0.749741	+	1.03193i
$595$	1.15925	+	1.59557i	0.0475247	+	0.0654121i
$596$	−11.4373	+	72.2125i	−0.468491	+	2.95794i
$597$	14.5710	+	10.5865i	0.596351	+	0.433275i
$598$	−0.631350	−	1.23909i	−0.0258178	−	0.0506703i
$599$	22.2977	−	16.2003i	0.911061	−	0.661925i	−0.0302220	−	0.999543i	$-0.509621\pi$
$599$	22.2977	−	16.2003i	0.911061	−	0.661925i	0.941283	+	0.337619i	$0.109621\pi$
$600$	17.1484	+	8.73752i	0.700079	+	0.356708i
$601$	−5.12248	+	5.12248i	−0.208950	+	0.208950i	−0.803821	−	0.594871i	$-0.797203\pi$
$601$	−5.12248	+	5.12248i	−0.208950	+	0.208950i	0.594871	+	0.803821i	$0.297203\pi$
$602$	−1.13737	−	7.18106i	−0.0463557	−	0.292678i
$603$	−9.54660	+	18.7362i	−0.388767	+	0.762999i
$604$	−75.7981	+	38.6210i	−3.08418	+	1.57147i
$605$	−0.443057	+	1.36359i	−0.0180128	+	0.0554378i
$606$			27.4052i			1.11326i
$607$	−25.6633	−	8.33853i	−1.04164	−	0.338450i	−0.262259	−	0.964997i	$-0.584468\pi$
$607$	−25.6633	−	8.33853i	−1.04164	−	0.338450i	−0.779384	+	0.626547i	$0.784468\pi$
$608$	−0.114122	−	0.0180752i	−0.00462826	−	0.000733045i
$609$	−5.41111	+	0.857035i	−0.219269	+	0.0347288i
$610$	−8.35654	+	2.71520i	−0.338346	+	0.109935i
$611$	0.351928	+	1.08312i	0.0142375	+	0.0438184i
$612$	−28.5168	−	28.5168i	−1.15272	−	1.15272i
$613$	−10.4017	+	14.3166i	−0.420119	+	0.578244i	−0.965650	−	0.259847i	$-0.916328\pi$
$613$	−10.4017	+	14.3166i	−0.420119	+	0.578244i	0.545531	+	0.838091i	$0.316328\pi$
$614$	52.5798			2.12195
$615$	−1.03633	+	2.11352i	−0.0417890	+	0.0852252i
$616$	11.7435			0.473161
$617$	21.0767	−	29.0096i	0.848515	−	1.16788i	−0.135673	−	0.990754i	$-0.543320\pi$
$617$	21.0767	−	29.0096i	0.848515	−	1.16788i	0.984188	−	0.177127i	$-0.0566804\pi$
$618$	0.265429	+	0.265429i	0.0106771	+	0.0106771i
$619$	−0.312770	−	0.962607i	−0.0125713	−	0.0386904i	0.944574	−	0.328298i	$-0.106475\pi$
$619$	−0.312770	−	0.962607i	−0.0125713	−	0.0386904i	−0.957145	+	0.289608i	$0.906475\pi$
$620$	1.98437	−	0.644761i	0.0796942	−	0.0258942i
$621$	−11.5366	+	1.82722i	−0.462949	+	0.0733239i
$622$	59.3860	+	9.40582i	2.38116	+	0.377139i
$623$	9.48568	+	3.08208i	0.380036	+	0.123481i
$624$		−	0.605683i		−	0.0242467i
$625$	6.99534	−	21.5294i	0.279814	−	0.861178i
$626$	36.8179	−	18.7597i	1.47154	−	0.749787i
$627$	−0.0695582	+	0.136516i	−0.00277789	+	0.00545191i
$628$	−6.22604	−	39.3097i	−0.248446	−	1.56863i
$629$	−23.5902	+	23.5902i	−0.940603	+	0.940603i
$630$	−1.84056	−	0.937814i	−0.0733298	−	0.0373634i
$631$	5.55516	−	4.03606i	0.221147	−	0.160673i	−0.471696	−	0.881761i	$-0.656358\pi$
$631$	5.55516	−	4.03606i	0.221147	−	0.160673i	0.692843	+	0.721088i	$0.256358\pi$
$632$	5.30077	+	10.4034i	0.210853	+	0.413823i
$633$	19.5785	+	14.2246i	0.778175	+	0.565377i
$634$	0.102983	−	0.650207i	0.00408996	−	0.0258230i
$635$	−3.22046	−	4.43258i	−0.127800	−	0.175902i
$636$	−3.12686	−	4.30376i	−0.123988	−	0.170655i
$637$	−0.0367267	+	0.231883i	−0.00145516	+	0.00918755i
$638$	−31.5098	−	22.8932i	−1.24748	−	0.906350i
$639$	−2.29892	−	4.51188i	−0.0909437	−	0.178487i
$640$	−6.66590	+	4.84306i	−0.263493	+	0.191439i
$641$	15.4840	+	7.88950i	0.611582	+	0.311617i	0.732208	−	0.681082i	$-0.238490\pi$
$641$	15.4840	+	7.88950i	0.611582	+	0.311617i	−0.120626	+	0.992698i	$0.538490\pi$
$642$	18.6176	−	18.6176i	0.734778	−	0.734778i
$643$	−6.97616	−	44.0458i	−0.275113	−	1.73700i	−0.607918	−	0.794000i	$-0.707995\pi$
$643$	−6.97616	−	44.0458i	−0.275113	−	1.73700i	0.332805	−	0.942996i	$-0.392005\pi$
$644$	−4.23780	+	8.31715i	−0.166993	+	0.327742i
$645$	0.989471	−	0.504161i	0.0389604	−	0.0198513i
$646$	0.224637	−	0.691362i	0.00883823	−	0.0272013i
$647$		−	18.8191i		−	0.739856i	−0.929060	−	0.369928i	$-0.879382\pi$
$647$		−	18.8191i		−	0.739856i	0.929060	−	0.369928i	$-0.120618\pi$
$648$	8.53776	+	2.77409i	0.335395	+	0.108976i
$649$	−8.62327	−	1.36579i	−0.338493	−	0.0536120i
$650$	−2.70167	+	0.427903i	−0.105968	+	0.0167837i
$651$	−1.20816	+	0.392553i	−0.0473513	+	0.0153854i
$652$	16.9055	+	52.0298i	0.662071	+	2.03764i
$653$	1.49227	+	1.49227i	0.0583971	+	0.0583971i	0.735702	−	0.677305i	$-0.236852\pi$
$653$	1.49227	+	1.49227i	0.0583971	+	0.0583971i	−0.677305	+	0.735702i	$0.736852\pi$
$654$	9.08856	−	12.5093i	0.355391	−	0.489154i
$655$	−8.08653			−0.315967
$656$	−10.7598	−	14.3413i	−0.420100	−	0.559935i
$657$	−28.4479			−1.10986
$658$	6.86257	−	9.44551i	0.267531	−	0.368224i
$659$	3.33746	+	3.33746i	0.130009	+	0.130009i	0.769117	−	0.639108i	$-0.220696\pi$
$659$	3.33746	+	3.33746i	0.130009	+	0.130009i	−0.639108	+	0.769117i	$0.720696\pi$
$660$	1.17262	+	3.60894i	0.0456441	+	0.140478i
$661$	−46.9032	+	15.2398i	−1.82432	+	0.592758i	−0.824692	+	0.565582i	$0.808652\pi$
$661$	−46.9032	+	15.2398i	−1.82432	+	0.592758i	−0.999631	+	0.0271763i	$0.991348\pi$
$662$	−50.8176	+	8.04872i	−1.97508	+	0.312822i
$663$	−1.05607	−	0.167266i	−0.0410145	−	0.00649606i
$664$	32.5808	+	10.5861i	1.26438	+	0.410822i
$665$		−	0.0243796i		−	0.000945401i
$666$	10.7979	−	33.2326i	0.418411	−	1.28774i
$667$	13.0389	−	6.64366i	0.504869	−	0.257244i
$668$	10.0017	−	19.6294i	0.386976	−	0.759484i
$669$	2.19777	+	13.8762i	0.0849706	+	0.536483i
$670$	−6.63808	+	6.63808i	−0.256452	+	0.256452i
$671$	22.1869	+	11.3048i	0.856515	+	0.436416i
$672$	1.40955	−	1.02410i	0.0543745	−	0.0395054i
$673$	−0.765505	−	1.50239i	−0.0295081	−	0.0579128i	0.875782	−	0.482707i	$-0.160346\pi$
$673$	−0.765505	−	1.50239i	−0.0295081	−	0.0579128i	−0.905290	+	0.424794i	$0.860346\pi$
$674$	−16.1211	−	11.7127i	−0.620963	−	0.451156i
$675$	−3.59403	+	22.6918i	−0.138334	+	0.873407i
$676$	−28.8591	−	39.7211i	−1.10997	−	1.52774i
$677$	13.3203	+	18.3339i	0.511942	+	0.704628i	0.984245	−	0.176808i	$-0.0565772\pi$
$677$	13.3203	+	18.3339i	0.511942	+	0.704628i	−0.472303	+	0.881436i	$0.656577\pi$
$678$	0.638864	−	4.03363i	0.0245354	−	0.154911i
$679$	−1.86212	−	1.35291i	−0.0714617	−	0.0519200i
$680$	−3.86364	−	7.58283i	−0.148164	−	0.290788i
$681$	5.07393	−	3.68642i	0.194433	−	0.141264i
$682$	−8.04672	−	4.10001i	−0.308125	−	0.156997i
$683$	−23.9709	+	23.9709i	−0.917222	+	0.917222i	−0.996826	−	0.0796049i	$-0.974634\pi$
$683$	−23.9709	+	23.9709i	−0.917222	+	0.917222i	0.0796049	+	0.996826i	$0.474634\pi$
$684$	0.0779859	+	0.492383i	0.00298186	+	0.0188267i
$685$	−0.0679857	+	0.133429i	−0.00259760	+	0.00509808i
$686$	2.14451	−	1.09268i	0.0818776	−	0.0417187i
$687$	5.74527	−	17.6821i	0.219196	−	0.674615i
$688$			8.45835i			0.322471i
$689$	0.339896	+	0.110439i	0.0129490	+	0.00420739i
$690$	−2.15077	−	0.340648i	−0.0818783	−	0.0129682i
$691$	31.9928	−	5.06715i	1.21706	−	0.192764i	0.485314	−	0.874340i	$-0.338705\pi$
$691$	31.9928	−	5.06715i	1.21706	−	0.192764i	0.731747	+	0.681576i	$0.238705\pi$
$692$	92.0442	−	29.9070i	3.49900	−	1.13689i
$693$	1.80904	+	5.56764i	0.0687196	+	0.211497i
$694$	−6.84132	−	6.84132i	−0.259693	−	0.259693i
$695$	−1.51436	+	2.08434i	−0.0574430	+	0.0790635i
$696$	23.6405			0.896092
$697$	−27.9771	+	14.8004i	−1.05971	+	0.560605i
$698$	−8.50482			−0.321912
$699$	−6.42431	+	8.84230i	−0.242990	+	0.334447i
$700$	12.9828	+	12.9828i	0.490704	+	0.490704i
$701$	−5.76795	−	17.7519i	−0.217852	−	0.670480i	−0.998939	−	0.0460576i	$-0.985334\pi$
$701$	−5.76795	−	17.7519i	−0.217852	−	0.670480i	0.781086	−	0.624423i	$-0.214666\pi$
$702$	2.55055	−	0.828723i	0.0962642	−	0.0312781i
$703$	0.407319	−	0.0645130i	0.0153623	−	0.00243315i
$704$	27.2868	+	4.32180i	1.02841	+	0.162884i
$705$	1.69601	+	0.551066i	0.0638753	+	0.0207543i
$706$		−	47.7388i		−	1.79667i
$707$	−3.81889	+	11.7533i	−0.143624	+	0.442029i
$708$	9.98904	−	5.08967i	0.375411	−	0.191281i
$709$	4.11404	−	8.07425i	0.154506	−	0.303235i	−0.800759	−	0.598987i	$-0.795570\pi$
$709$	4.11404	−	8.07425i	0.154506	−	0.303235i	0.955265	+	0.295752i	$0.0955702\pi$
$710$	−0.353643	−	2.23281i	−0.0132720	−	0.0837960i
$711$	−4.11570	+	4.11570i	−0.154351	+	0.154351i
$712$	−38.3472	−	19.5389i	−1.43712	−	0.732251i
$713$	2.74517	−	1.99448i	0.102807	−	0.0746939i
$714$	4.97643	+	9.76680i	0.186238	+	0.365513i
$715$	−0.206244	−	0.149845i	−0.00771310	−	0.00560389i
$716$	−4.18163	+	26.4018i	−0.156275	+	0.986681i
$717$	−3.75189	−	5.16404i	−0.140117	−	0.192855i
$718$	30.7074	+	42.2651i	1.14599	+	1.57732i
$719$	5.31684	−	33.5692i	0.198285	−	1.25192i	−0.664862	−	0.746966i	$-0.731510\pi$
$719$	5.31684	−	33.5692i	0.198285	−	1.25192i	0.863146	−	0.504954i	$-0.168490\pi$
$720$	1.94421	+	1.41255i	0.0724566	+	0.0526428i
$721$	0.0768476	+	0.150822i	0.00286196	+	0.00561690i
$722$	36.9890	−	26.8741i	1.37659	−	1.00015i
$723$	14.4162	+	7.34542i	0.536144	+	0.273179i
$724$	18.5078	−	18.5078i	0.687838	−	0.687838i
$725$	−4.50280	−	28.4296i	−0.167230	−	1.05585i
$726$	−3.61774	+	7.10021i	−0.134267	+	0.263513i
$727$	25.2087	−	12.8445i	0.934938	−	0.476375i	0.0809795	−	0.996716i	$-0.474195\pi$
$727$	25.2087	−	12.8445i	0.934938	−	0.476375i	0.853959	+	0.520341i	$0.174195\pi$
$728$	0.313057	−	0.963489i	0.0116026	−	0.0357093i
$729$		−	8.64343i		−	0.320127i
$730$	−12.0785	−	3.92454i	−0.447045	−	0.145254i
$731$	14.7481	+	2.33586i	0.545477	+	0.0863950i
$732$	−31.5810	+	5.00194i	−1.16727	+	0.184877i
$733$	−30.0370	+	9.75963i	−1.10944	+	0.360480i	−0.805730	−	0.592283i	$-0.798227\pi$
$733$	−30.0370	+	9.75963i	−1.10944	+	0.360480i	−0.303714	+	0.952763i	$0.598227\pi$
$734$	−5.47266	−	16.8431i	−0.202000	−	0.621691i
$735$	0.259947	+	0.259947i	0.00958828	+	0.00958828i
$736$	−2.73549	+	3.76508i	−0.100832	+	0.138783i
$737$	26.6044			0.979984
$738$	19.0716	−	27.1156i	0.702035	−	0.998139i
$739$	−3.16954			−0.116593			−0.0582966	−	0.998299i	$-0.518567\pi$
$739$	−3.16954			−0.116593			−0.0582966	+	0.998299i	$0.518567\pi$
$740$	6.00352	−	8.26313i	0.220694	−	0.303759i
$741$	0.00934604	+	0.00934604i	0.000343335	+	0.000343335i
$742$	−1.13219	−	3.48452i	−0.0415640	−	0.127921i
$743$	17.1075	−	5.55858i	0.627615	−	0.203924i	0.0220966	−	0.999756i	$-0.492966\pi$
$743$	17.1075	−	5.55858i	0.627615	−	0.203924i	0.605518	+	0.795831i	$0.292966\pi$
$744$	5.41412	−	0.857512i	0.198491	−	0.0314379i
$745$	−7.59649	−	1.20317i	−0.278314	−	0.0440806i
$746$	25.3124	+	8.22450i	0.926753	+	0.301120i
$747$			17.0774i			0.624828i
$748$	−15.7670	+	48.5258i	−0.576498	+	1.77428i
$749$	10.5789	−	5.39022i	0.386545	−	0.196954i
$750$	−3.95297	+	7.75813i	−0.144342	+	0.283287i
$751$	−3.18543	−	20.1120i	−0.116238	−	0.733898i	−0.975112	−	0.221711i	$-0.928836\pi$
$751$	−3.18543	−	20.1120i	−0.116238	−	0.733898i	0.858874	−	0.512186i	$-0.171164\pi$
$752$	−9.60438	+	9.60438i	−0.350236	+	0.350236i
$753$	22.8871	+	11.6615i	0.834051	+	0.424970i
$754$	−2.71823	+	1.97491i	−0.0989922	+	0.0719220i
$755$	−4.06279	−	7.97368i	−0.147860	−	0.290192i
$756$	−14.5631	−	10.5807i	−0.529656	−	0.384818i
$757$	−0.625951	+	3.95210i	−0.0227506	+	0.143642i	−0.996449	−	0.0841995i	$-0.973167\pi$
$757$	−0.625951	+	3.95210i	−0.0227506	+	0.143642i	0.973698	+	0.227841i	$0.0731667\pi$
$758$	−30.1379	−	41.4812i	−1.09466	−	1.50667i
$759$	3.62733	+	4.99259i	0.131664	+	0.181220i
$760$	−0.0164570	+	0.103905i	−0.000596958	+	0.00376904i
$761$	12.5791	+	9.13925i	0.455992	+	0.331298i	0.791957	−	0.610577i	$-0.209062\pi$
$761$	12.5791	+	9.13925i	0.455992	+	0.331298i	−0.335965	+	0.941874i	$0.609062\pi$
$762$	−13.8248	−	27.1327i	−0.500819	−	0.982913i
$763$	5.64099	−	4.09842i	0.204217	−	0.148373i
$764$	29.8765	+	15.2228i	1.08089	+	0.550742i
$765$	2.99986	−	2.99986i	0.108460	−	0.108460i
$766$	4.85613	+	30.6604i	0.175459	+	1.10780i
$767$	−0.341932	+	0.671079i	−0.0123465	+	0.0242313i
$768$	−24.1358	+	12.2978i	−0.870926	+	0.443759i
$769$	4.79675	−	14.7629i	0.172975	−	0.532363i	−0.826560	−	0.562849i	$-0.809705\pi$
$769$	4.79675	−	14.7629i	0.172975	−	0.532363i	0.999535	+	0.0304857i	$0.00970539\pi$
$770$			2.61349i			0.0941837i
$771$	−4.27876	−	1.39025i	−0.154096	−	0.0500687i
$772$	13.0775	+	2.07128i	0.470671	+	0.0745470i
$773$	−1.17120	+	0.185499i	−0.0421250	+	0.00667194i	−0.177461	−	0.984128i	$-0.556788\pi$
$773$	−1.17120	+	0.185499i	−0.0421250	+	0.00667194i	0.135336	+	0.990800i	$0.456788\pi$
$774$	−14.8741	+	4.83290i	−0.534640	+	0.173715i
$775$	−2.06245	−	6.34757i	−0.0740854	−	0.228011i
$776$	7.02307	+	7.02307i	0.252114	+	0.252114i
$777$	−3.65516	+	5.03089i	−0.131128	+	0.180482i
$778$	53.7937			1.92860
$779$	0.387325	+	0.0552652i	0.0138774	+	0.00198008i
$780$	0.327352			0.0117211
$781$	−3.76571	+	5.18305i	−0.134748	+	0.185464i
$782$	−20.7039	−	20.7039i	−0.740368	−	0.740368i
$783$	8.72061	+	26.8393i	0.311649	+	0.959158i
$784$	−2.66299	+	0.865257i	−0.0951067	+	0.0309020i
$785$	4.13524	−	0.654957i	0.147593	−	0.0233764i
$786$	−44.3910	−	7.03084i	−1.58337	−	0.250782i
$787$	31.7859	+	10.3279i	1.13304	+	0.368148i	0.814732	−	0.579837i	$-0.196884\pi$
$787$	31.7859	+	10.3279i	1.13304	+	0.368148i	0.318312	+	0.947986i	$0.396884\pi$
$788$		−	50.0671i		−	1.78357i
$789$	4.85673	−	14.9475i	0.172904	−	0.532144i
$790$	−2.31524	+	1.17967i	−0.0823724	+	0.0419708i
$791$	0.836072	−	1.64088i	0.0297273	−	0.0583431i
$792$	−3.95174	−	24.9503i	−0.140419	−	0.886571i
$793$	1.51894	−	1.51894i	0.0539393	−	0.0539393i
$794$	80.0883	+	40.8070i	2.84223	+	1.44819i
$795$	0.452739	−	0.328934i	0.0160570	−	0.0116661i
$796$	−33.6598	−	66.0611i	−1.19304	−	2.34147i
$797$	−27.2251	−	19.7802i	−0.964363	−	0.700651i	−0.0102032	−	0.999948i	$-0.503248\pi$
$797$	−27.2251	−	19.7802i	−0.964363	−	0.700651i	−0.954160	+	0.299297i	$0.903248\pi$
$798$	0.0211969	−	0.133832i	0.000750362	−	0.00473760i
$799$	14.0939	+	19.3987i	0.498608	+	0.686275i
$800$	5.38054	+	7.40568i	0.190231	+	0.261830i
$801$	3.35623	−	21.1904i	0.118586	−	0.748725i
$802$	−62.5986	−	45.4806i	−2.21043	−	1.60598i
$803$	16.3399	+	32.0688i	0.576621	+	1.13168i
$804$	−27.6377	+	20.0799i	−0.974706	+	0.708165i
$805$	−0.874933	−	0.445801i	−0.0308374	−	0.0157124i
$806$	−0.550889	+	0.550889i	−0.0194042	+	0.0194042i
$807$	1.86247	+	11.7592i	0.0655620	+	0.413942i
$808$	24.2099	−	47.5145i	0.851700	−	1.67156i
$809$	28.8154	−	14.6822i	1.01309	−	0.516197i	0.133060	−	0.991108i	$-0.457520\pi$
$809$	28.8154	−	14.6822i	1.01309	−	0.516197i	0.880034	+	0.474911i	$0.157520\pi$
$810$	−0.617365	+	1.90005i	−0.0216920	+	0.0667611i
$811$			47.7529i			1.67683i	0.545030	+	0.838416i	$0.316518\pi$
$811$			47.7529i			1.67683i	−0.545030	+	0.838416i	$0.683482\pi$
$812$	21.4489	+	6.96918i	0.752710	+	0.244570i
$813$	−16.7626	−	2.65493i	−0.587889	−	0.0931124i
$814$	−43.6645	+	6.91578i	−1.53044	+	0.242398i
$815$	−5.47334	+	1.77840i	−0.191723	+	0.0622945i
$816$	−3.94067	−	12.1282i	−0.137951	−	0.424570i
$817$	−0.130517	−	0.130517i	−0.00456622	−	0.00456622i
$818$	−40.9658	+	56.3846i	−1.43234	+	1.97144i
$819$	0.505017			0.0176467
$820$	7.75103	−	5.81533i	0.270678	−	0.203080i
$821$	−23.1325			−0.807330			−0.403665	−	0.914907i	$-0.632264\pi$
$821$	−23.1325			−0.807330			−0.403665	+	0.914907i	$0.632264\pi$
$822$	−0.489217	+	0.673350i	−0.0170634	+	0.0234858i
$823$	13.4617	+	13.4617i	0.469245	+	0.469245i	0.901670	−	0.432425i	$-0.142342\pi$
$823$	13.4617	+	13.4617i	0.469245	+	0.469245i	−0.432425	+	0.901670i	$0.642342\pi$
$824$	−0.225713	−	0.694674i	−0.00786310	−	0.0242001i
$825$	11.5442	−	3.75095i	0.401918	−	0.130591i
$826$	7.62623	−	1.20788i	0.265350	−	0.0420274i
$827$	14.8604	+	2.35366i	0.516747	+	0.0818447i	0.409361	−	0.912373i	$-0.365752\pi$
$827$	14.8604	+	2.35366i	0.516747	+	0.0818447i	0.107387	+	0.994217i	$0.465752\pi$
$828$	19.0966	+	6.20487i	0.663654	+	0.215634i
$829$			9.26690i			0.321853i	0.986966	+	0.160926i	$0.0514481\pi$
$829$			9.26690i			0.321853i	−0.986966	+	0.160926i	$0.948552\pi$
$830$	−2.35591	+	7.25076i	−0.0817750	+	0.251677i
$831$	−5.66919	+	2.88860i	−0.196662	+	0.100204i
$832$	1.08198	−	2.12351i	0.0375110	−	0.0736195i
$833$	0.773259	+	4.88216i	0.0267918	+	0.169157i
$834$	−10.1253	+	10.1253i	−0.350611	+	0.350611i
$835$	2.06494	+	1.05214i	0.0714602	+	0.0364108i
$836$	0.510261	−	0.370726i	0.0176477	−	0.0128218i
$837$	2.97072	+	5.83037i	0.102683	+	0.201527i
$838$	42.5421	+	30.9086i	1.46959	+	1.06772i
$839$	−6.39704	+	40.3893i	−0.220850	+	1.39439i	0.589178	+	0.808004i	$0.299452\pi$
$839$	−6.39704	+	40.3893i	−0.220850	+	1.39439i	−0.810028	+	0.586391i	$0.800548\pi$
$840$	−0.932415	−	1.28336i	−0.0321714	−	0.0442801i
$841$	−3.73612	−	5.14233i	−0.128832	−	0.177322i
$842$	−4.60144	+	29.0523i	−0.158576	+	1.00121i
$843$	22.9235	+	16.6549i	0.789527	+	0.573625i
$844$	−45.2274	−	88.7638i	−1.55679	−	3.05537i
$845$	4.17852	−	3.03587i	0.143745	−	0.104437i
$846$	−22.3772	−	11.4018i	−0.769344	−	0.392000i
$847$	−2.54095	+	2.54095i	−0.0873081	+	0.0873081i
$848$	0.666786	+	4.20992i	0.0228975	+	0.144569i
$849$	2.29136	−	4.49705i	0.0786394	−	0.154338i
$850$	−51.3141	+	26.1459i	−1.76006	+	0.896795i
$851$	5.13292	−	15.7975i	0.175954	−	0.541531i
$852$		−	8.22657i		−	0.281837i
$853$	−6.47138	−	2.10268i	−0.221576	−	0.0719944i	0.196125	−	0.980579i	$-0.437164\pi$
$853$	−6.47138	−	2.10268i	−0.221576	−	0.0719944i	−0.417701	+	0.908584i	$0.637164\pi$
$854$	−21.7507	−	3.44497i	−0.744294	−	0.117885i
$855$	−0.0517969	+	0.00820383i	−0.00177142	+	0.000280565i
$856$	−48.7256	+	15.8319i	−1.66541	+	0.541123i
$857$	−15.5173	−	47.7573i	−0.530060	−	1.63136i	−0.754087	−	0.656775i	$-0.771920\pi$
$857$	−15.5173	−	47.7573i	−0.530060	−	1.63136i	0.224027	−	0.974583i	$-0.428080\pi$
$858$	−1.00189	−	1.00189i	−0.0342041	−	0.0342041i
$859$	1.52256	−	2.09562i	0.0519490	−	0.0715016i	−0.782252	−	0.622962i	$-0.785929\pi$
$859$	1.52256	−	2.09562i	0.0519490	−	0.0715016i	0.834201	+	0.551460i	$0.185929\pi$
$860$	−4.57146			−0.155886
$861$	−4.71910	+	3.54058i	−0.160827	+	0.120663i
$862$	33.0286			1.12496
$863$	6.12219	−	8.42647i	0.208402	−	0.286840i	−0.692002	−	0.721896i	$-0.743271\pi$
$863$	6.12219	−	8.42647i	0.208402	−	0.286840i	0.900404	+	0.435055i	$0.143271\pi$
$864$	−6.34609	−	6.34609i	−0.215898	−	0.215898i
$865$	3.14611	+	9.68272i	0.106971	+	0.329222i
$866$	−58.1901	+	18.9071i	−1.97738	+	0.642489i
$867$	−6.76461	+	1.07141i	−0.229738	+	0.0363870i
$868$	5.16499	+	0.818054i	0.175311	+	0.0277666i
$869$	7.00351	+	2.27558i	0.237578	+	0.0771937i
$870$			5.26113i			0.178369i
$871$	0.709213	−	2.18273i	0.0240308	−	0.0739591i
$872$	−26.8083	+	13.6595i	−0.907844	+	0.462570i
$873$	−2.24778	+	4.41152i	−0.0760760	+	0.149307i
$874$	0.0566196	+	0.357482i	0.00191519	+	0.0120920i
$875$	−2.77640	+	2.77640i	−0.0938595	+	0.0938595i
$876$	−41.1788	−	20.9816i	−1.39130	−	0.708904i
$877$	−33.1476	+	24.0831i	−1.11931	+	0.813229i	−0.984105	−	0.177588i	$-0.943170\pi$
$877$	−33.1476	+	24.0831i	−1.11931	+	0.813229i	−0.135208	+	0.990817i	$0.543170\pi$
$878$	−13.4703	−	26.4369i	−0.454600	−	0.892202i
$879$	−21.9543	−	15.9508i	−0.740501	−	0.538006i
$880$	0.475631	−	3.00302i	0.0160335	−	0.101232i
$881$	−18.8111	−	25.8913i	−0.633763	−	0.872300i	0.364500	−	0.931203i	$-0.381240\pi$
$881$	−18.8111	−	25.8913i	−0.633763	−	0.872300i	−0.998264	+	0.0589028i	$0.981240\pi$
$882$	−3.04314	−	4.18852i	−0.102468	−	0.141035i
$883$	0.230334	−	1.45427i	0.00775137	−	0.0489402i	−0.983509	−	0.180857i	$-0.942113\pi$
$883$	0.230334	−	1.45427i	0.00775137	−	0.0489402i	0.991261	+	0.131916i	$0.0421130\pi$
$884$	3.56095	+	2.58718i	0.119768	+	0.0870163i
$885$	0.535414	+	1.05081i	0.0179978	+	0.0353226i
$886$	−54.3382	+	39.4790i	−1.82553	+	1.32632i
$887$	16.6731	+	8.49538i	0.559829	+	0.285247i	0.710920	−	0.703273i	$-0.248279\pi$
$887$	16.6731	+	8.49538i	0.559829	+	0.285247i	−0.151091	+	0.988520i	$0.548279\pi$
$888$	18.9742	−	18.9742i	0.636732	−	0.636732i
$889$	−2.14815	−	13.5629i	−0.0720467	−	0.454885i
$890$	4.34832	−	8.53406i	0.145756	−	0.286062i
$891$	5.04470	−	2.57040i	0.169004	−	0.0861118i
$892$	17.8717	−	55.0033i	0.598388	−	1.84165i
$893$		−	0.296403i		−	0.00991873i
$894$	−40.6548	−	13.2095i	−1.35970	−	0.441793i
$895$	−2.77737	−	0.439892i	−0.0928372	−	0.0147040i
$896$	−20.3964	+	3.23048i	−0.681397	+	0.107923i
$897$	0.506310	−	0.164510i	0.0169052	−	0.00549283i
$898$	16.7550	+	51.5667i	0.559123	+	1.72080i
$899$	−5.79698	−	5.79698i	−0.193340	−	0.193340i
$900$	23.2145	−	31.9520i	0.773816	−	1.06507i
$901$	7.52460			0.250681
$902$	−41.5212	−	5.92442i	−1.38250	−	0.197262i
$903$	2.78327			0.0926214
$904$	−4.67097	+	6.42903i	−0.155354	+	0.213827i
$905$	1.94696	+	1.94696i	0.0647190	+	0.0647190i
$906$	−15.3700	−	47.3039i	−0.510633	−	1.57157i
$907$	43.0426	−	13.9854i	1.42921	−	0.464377i	0.510691	−	0.859764i	$-0.329389\pi$
$907$	43.0426	−	13.9854i	1.42921	−	0.464377i	0.918515	+	0.395387i	$0.129389\pi$
$908$	−25.5000	+	4.03880i	−0.846246	+	0.134032i
$909$	26.2562	+	4.15857i	0.870862	+	0.137931i
$910$	0.214422	+	0.0696698i	0.00710801	+	0.00230953i
$911$		−	35.6944i		−	1.18261i	−0.806448	−	0.591305i	$-0.798613\pi$
$911$		−	35.6944i		−	1.18261i	0.806448	−	0.591305i	$-0.201387\pi$
$912$	−0.0487123	+	0.149921i	−0.00161303	+	0.00496438i
$913$	19.2510	−	9.80887i	0.637115	−	0.324626i
$914$	26.8810	−	52.7568i	0.889143	−	1.74504i
$915$	−0.526186	−	3.32221i	−0.0173952	−	0.109829i
$916$	−54.1185	+	54.1185i	−1.78813	+	1.78813i
$917$	−18.0583	−	9.20116i	−0.596337	−	0.303849i
$918$	45.6802	−	33.1886i	1.50767	−	1.09539i
$919$	20.1336	+	39.5144i	0.664147	+	1.30346i	0.939642	+	0.342159i	$0.111158\pi$
$919$	20.1336	+	39.5144i	0.664147	+	1.30346i	−0.275496	+	0.961302i	$0.588842\pi$
$920$	3.42802	+	2.49060i	0.113018	+	0.0821126i
$921$	−3.14875	+	19.8804i	−0.103755	+	0.655082i
$922$	−6.87319	−	9.46013i	−0.226356	−	0.311553i
$923$	0.324854	+	0.447123i	0.0106927	+	0.0147172i
$924$	−1.48778	+	9.39349i	−0.0489445	+	0.309023i
$925$	−26.4320	−	19.2039i	−0.869078	−	0.631422i
$926$	41.3986	+	81.2494i	1.36044	+	2.67002i
$927$	0.294577	−	0.214022i	0.00967517	−	0.00702942i
$928$	10.0185	+	5.10469i	0.328874	+	0.167570i
$929$	−21.6346	+	21.6346i	−0.709807	+	0.709807i	−0.966495	−	0.256687i	$-0.917369\pi$
$929$	−21.6346	+	21.6346i	−0.709807	+	0.709807i	0.256687	+	0.966495i	$0.417369\pi$
$930$	0.190837	+	1.20490i	0.00625778	+	0.0395101i
$931$	0.0277400	−	0.0544429i	0.000909143	−	0.00178429i
$932$	40.0887	−	20.4262i	1.31315	−	0.669083i
$933$	−7.11268	+	21.8906i	−0.232859	+	0.716666i
$934$			66.9103i			2.18937i
$935$	−5.10474	−	1.65863i	−0.166943	−	0.0542430i
$936$	−2.15237	−	0.340902i	−0.0703525	−	0.0111427i
$937$	31.1770	−	4.93796i	1.01851	−	0.161316i	0.375217	−	0.926937i	$-0.377568\pi$
$937$	31.1770	−	4.93796i	1.01851	−	0.161316i	0.643292	+	0.765621i	$0.277568\pi$
$938$	−22.3768	+	7.27065i	−0.730627	+	0.237395i
$939$	4.88818	+	15.0443i	0.159520	+	0.490952i
$940$	−5.19086	−	5.19086i	−0.169307	−	0.169307i
$941$	12.7655	−	17.5702i	0.416144	−	0.572773i	−0.548559	−	0.836112i	$-0.684824\pi$
$941$	12.7655	−	17.5702i	0.416144	−	0.572773i	0.964704	+	0.263338i	$0.0848235\pi$
$942$	23.2698			0.758171
$943$	9.06590	−	12.8897i	0.295226	−	0.419747i
$944$	−8.98269			−0.292362
$945$	1.11306	−	1.53199i	0.0362077	−	0.0498356i
$946$	13.9914	+	13.9914i	0.454900	+	0.454900i
$947$	−5.70131	−	17.5468i	−0.185268	−	0.570195i	0.814685	−	0.579903i	$-0.196910\pi$
$947$	−5.70131	−	17.5468i	−0.185268	−	0.570195i	−0.999953	+	0.00970836i	$0.996910\pi$
$948$	−8.99304	+	2.92202i	−0.292080	+	0.0949027i
$949$	3.06664	−	0.485708i	0.0995473	−	0.0157667i
$950$	0.703144	+	0.111367i	0.0228130	+	0.00361322i
$951$	0.239676	+	0.0778755i	0.00777203	+	0.00252529i
$952$		−	21.3296i		−	0.691298i
$953$	10.1437	−	31.2190i	0.328586	−	1.01128i	−0.641210	−	0.767366i	$-0.721567\pi$
$953$	10.1437	−	31.2190i	0.328586	−	1.01128i	0.969796	−	0.243918i	$-0.0784329\pi$
$954$	−7.02223	+	3.57800i	−0.227353	+	0.115842i
$955$	−1.60138	+	3.14289i	−0.0518196	+	0.101702i
$956$	4.11053	+	25.9528i	0.132944	+	0.839375i
$957$	10.5429	−	10.5429i	0.340803	−	0.340803i
$958$	60.9756	+	31.0686i	1.97003	+	1.00378i
$959$	−0.303642	+	0.220609i	−0.00980511	+	0.00712383i
$960$	−1.69422	−	3.32510i	−0.0546809	−	0.107317i
$961$	23.5416	+	17.1040i	0.759408	+	0.551742i
$962$	−0.596599	+	3.76678i	−0.0192351	+	0.121446i
$963$	−15.0119	−	20.6621i	−0.483751	−	0.665826i
$964$	−39.1491	−	53.8841i	−1.26091	−	1.73549i
$965$	−0.217891	+	1.37571i	−0.00701416	+	0.0442857i
$966$	−4.41534	−	3.20793i	−0.142061	−	0.103214i
$967$	22.2591	+	43.6859i	0.715804	+	1.40484i	0.906077	+	0.423114i	$0.139063\pi$
$967$	22.2591	+	43.6859i	0.715804	+	1.40484i	−0.190272	+	0.981731i	$0.560937\pi$
$968$	12.5447	−	9.11425i	0.403201	−	0.292943i
$969$	0.247951	+	0.126338i	0.00796535	+	0.00405855i
$970$	−1.56296	+	1.56296i	−0.0501837	+	0.0501837i
$971$	3.36189	+	21.2261i	0.107888	+	0.681179i	0.981051	+	0.193750i	$0.0620651\pi$
$971$	3.36189	+	21.2261i	0.107888	+	0.681179i	−0.873163	+	0.487429i	$0.837935\pi$
$972$	−27.8175	+	54.5949i	−0.892246	+	1.75113i
$973$	−5.75340	+	2.93151i	−0.184446	+	0.0939797i
$974$	2.22743	−	6.85531i	0.0713713	−	0.219658i
$975$		−	1.04713i		−	0.0335349i
$976$	24.3656	+	7.91685i	0.779923	+	0.253412i
$977$	48.7491	+	7.72110i	1.55962	+	0.247020i	0.875816	−	0.482645i	$-0.160324\pi$
$977$	48.7491	+	7.72110i	1.55962	+	0.247020i	0.683805	+	0.729665i	$0.260324\pi$
$978$	−31.5921	+	5.00370i	−1.01020	+	0.160001i
$979$	−25.8153	+	8.38788i	−0.825059	+	0.268078i
$980$	−0.467644	−	1.43926i	−0.0149383	−	0.0459755i
$981$	−10.6057	−	10.6057i	−0.338614	−	0.338614i
$982$	34.1021	−	46.9375i	1.08824	−	1.49783i
$983$	−15.9249			−0.507927			−0.253963	−	0.967214i	$-0.581734\pi$
$983$	−15.9249			−0.507927			−0.253963	+	0.967214i	$0.581734\pi$
$984$	22.5027	−	11.9043i	0.717360	−	0.379496i
$985$	5.26688			0.167817
$986$	−41.5806	+	57.2308i	−1.32420	+	1.82260i
$987$	3.16038	+	3.16038i	0.100596	+	0.100596i
$988$	−0.0168135	−	0.0517466i	−0.000534909	−	0.00164628i
$989$	−7.07060	+	2.29738i	−0.224832	+	0.0730524i
$990$	5.55262	−	0.879449i	0.176474	−	0.0279507i
$991$	28.5780	+	4.52630i	0.907809	+	0.143783i	0.592841	−	0.805320i	$-0.298006\pi$
$991$	28.5780	+	4.52630i	0.907809	+	0.143783i	0.314968	+	0.949102i	$0.398006\pi$
$992$	2.47959	+	0.805667i	0.0787270	+	0.0255799i
$993$		−	19.6961i		−	0.625038i
$994$	1.75085	−	5.38855i	0.0555335	−	0.170915i
$995$	6.94938	−	3.54089i	0.220310	−	0.112254i
$996$	−12.5953	+	24.7197i	−0.399099	+	0.783275i
$997$	0.0100098	+	0.0631992i	0.000317013	+	0.00200154i	0.987846	−	0.155434i	$-0.0496775\pi$
$997$	0.0100098	+	0.0631992i	0.000317013	+	0.00200154i	−0.987529	+	0.157435i	$0.949677\pi$
$998$	−9.64046	+	9.64046i	−0.305163	+	0.305163i
$999$	28.5408	+	14.5423i	0.902992	+	0.460097i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.u.a.8.19	✓	160
41.36	even	20	inner	287.2.u.a.36.19	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.u.a.8.19	✓	160	1.1	even	1	trivial
287.2.u.a.36.19	yes	160	41.36	even	20	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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.u (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41470 - 1.94717i) q^{2} +(0.651505 + 0.651505i) q^{3} +(-1.17206 - 3.60722i) q^{4} +(0.379466 - 0.123296i) q^{5} +(2.19028 - 0.346906i) q^{6} +(0.987688 + 0.156434i) q^{7} +(-4.10391 - 1.33344i) q^{8} -2.15108i q^{9} +O(q^{10})\)	\(q+(1.41470 - 1.94717i) q^{2} +(0.651505 + 0.651505i) q^{3} +(-1.17206 - 3.60722i) q^{4} +(0.379466 - 0.123296i) q^{5} +(2.19028 - 0.346906i) q^{6} +(0.987688 + 0.156434i) q^{7} +(-4.10391 - 1.33344i) q^{8} -2.15108i q^{9} +(0.296753 - 0.913312i) q^{10} +(-2.42487 + 1.23553i) q^{11} +(1.58652 - 3.11372i) q^{12} +(0.0367267 + 0.231883i) q^{13} +(1.70189 - 1.70189i) q^{14} +(0.327552 + 0.166896i) q^{15} +(-2.26527 + 1.64582i) q^{16} +(2.24408 + 4.40426i) q^{17} +(-4.18852 - 3.04314i) q^{18} +(0.00955857 - 0.0603504i) q^{19} +(-0.889511 - 1.22431i) q^{20} +(0.541566 + 0.745402i) q^{21} +(-1.02468 + 6.46955i) q^{22} +(-1.99106 - 1.44659i) q^{23} +(-1.80497 - 3.54246i) q^{24} +(-3.91629 + 2.84535i) q^{25} +(0.503473 + 0.256533i) q^{26} +(3.35596 - 3.35596i) q^{27} +(-0.593333 - 3.74616i) q^{28} +(-2.69948 + 5.29803i) q^{29} +(0.788364 - 0.401692i) q^{30} +(-0.426055 + 1.31126i) q^{31} -1.89099i q^{32} +(-2.38477 - 0.774860i) q^{33} +(11.7506 + 1.86111i) q^{34} +(0.394082 - 0.0624165i) q^{35} +(-7.75942 + 2.52119i) q^{36} +(2.08563 + 6.41890i) q^{37} +(-0.103990 - 0.103990i) q^{38} +(-0.127145 + 0.175001i) q^{39} -1.72170 q^{40} +(0.0982975 + 6.40237i) q^{41} +2.21758 q^{42} +(1.77558 - 2.44388i) q^{43} +(7.29893 + 7.29893i) q^{44} +(-0.265220 - 0.816263i) q^{45} +(-5.63352 + 1.83044i) q^{46} +(4.79117 - 0.758847i) q^{47} +(-2.54810 - 0.403579i) q^{48} +(0.951057 + 0.309017i) q^{49} +11.6510i q^{50} +(-1.40737 + 4.33143i) q^{51} +(0.793408 - 0.404261i) q^{52} +(0.691095 - 1.35635i) q^{53} +(-1.78694 - 11.2823i) q^{54} +(-0.767821 + 0.767821i) q^{55} +(-3.84478 - 1.95902i) q^{56} +(0.0455461 - 0.0330912i) q^{57} +(6.49720 + 12.7515i) q^{58} +(2.59538 + 1.88566i) q^{59} +(0.218121 - 1.37716i) q^{60} +(-5.37806 - 7.40227i) q^{61} +(1.95051 + 2.68465i) q^{62} +(0.336503 - 2.12460i) q^{63} +(-8.21263 - 5.96682i) q^{64} +(0.0425268 + 0.0834636i) q^{65} +(-4.88253 + 3.54737i) q^{66} +(-8.71015 - 4.43804i) q^{67} +(13.2569 - 13.2569i) q^{68} +(-0.354726 - 2.23965i) q^{69} +(0.435973 - 0.855645i) q^{70} +(2.09749 - 1.06873i) q^{71} +(-2.86834 + 8.82784i) q^{72} -13.2249i q^{73} +(15.4492 + 5.01976i) q^{74} +(-4.40525 - 0.697723i) q^{75} +(-0.228900 + 0.0362542i) q^{76} +(-2.58830 + 0.840989i) q^{77} +(0.160883 + 0.495148i) q^{78} +(-1.91331 - 1.91331i) q^{79} +(-0.656672 + 0.903831i) q^{80} -2.08040 q^{81} +(12.6056 + 8.86604i) q^{82} -7.93897 q^{83} +(2.05408 - 2.82720i) q^{84} +(1.39458 + 1.39458i) q^{85} +(-2.24673 - 6.91473i) q^{86} +(-5.21042 + 1.69297i) q^{87} +(11.5990 - 1.83710i) q^{88} +(9.85104 + 1.56025i) q^{89} +(-1.96461 - 0.638340i) q^{90} +0.234774i q^{91} +(-2.88454 + 8.87769i) q^{92} +(-1.13187 + 0.576718i) q^{93} +(5.30047 - 10.4028i) q^{94} +(-0.00381381 - 0.0240795i) q^{95} +(1.23199 - 1.23199i) q^{96} +(-2.05084 - 1.04496i) q^{97} +(1.94717 - 1.41470i) q^{98} +(2.65774 + 5.21610i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 4 q^{3} + 36 q^{4} - 28 q^{6}+O(q^{10}) \) 160 * q - 4 * q^3 + 36 * q^4 - 28 * q^6	\( 160 q - 4 q^{3} + 36 q^{4} - 28 q^{6} - 48 q^{10} + 8 q^{11} - 16 q^{12} - 16 q^{13} - 32 q^{15} - 28 q^{16} - 20 q^{17} + 12 q^{18} - 40 q^{19} - 4 q^{22} - 36 q^{23} - 108 q^{24} + 40 q^{25} + 20 q^{26} + 20 q^{27} + 12 q^{29} - 4 q^{30} + 20 q^{31} - 32 q^{34} - 4 q^{35} + 140 q^{36} - 44 q^{38} + 80 q^{39} - 64 q^{40} + 4 q^{41} - 72 q^{42} - 8 q^{44} + 8 q^{45} + 40 q^{46} - 56 q^{47} + 120 q^{48} + 24 q^{51} + 16 q^{52} + 12 q^{53} - 52 q^{54} - 72 q^{55} + 48 q^{57} + 36 q^{58} - 48 q^{59} - 52 q^{60} + 8 q^{63} - 96 q^{64} - 96 q^{65} + 24 q^{66} + 20 q^{67} - 80 q^{68} - 68 q^{69} + 8 q^{70} + 60 q^{71} + 100 q^{72} - 40 q^{74} - 120 q^{75} + 4 q^{76} - 12 q^{78} + 12 q^{79} + 200 q^{80} - 56 q^{81} - 68 q^{82} - 40 q^{83} + 132 q^{85} + 80 q^{86} - 16 q^{88} + 8 q^{89} + 140 q^{92} + 64 q^{93} + 128 q^{94} - 68 q^{96} + 4 q^{98} + 96 q^{99}+O(q^{100}) \) 160 * q - 4 * q^3 + 36 * q^4 - 28 * q^6 - 48 * q^10 + 8 * q^11 - 16 * q^12 - 16 * q^13 - 32 * q^15 - 28 * q^16 - 20 * q^17 + 12 * q^18 - 40 * q^19 - 4 * q^22 - 36 * q^23 - 108 * q^24 + 40 * q^25 + 20 * q^26 + 20 * q^27 + 12 * q^29 - 4 * q^30 + 20 * q^31 - 32 * q^34 - 4 * q^35 + 140 * q^36 - 44 * q^38 + 80 * q^39 - 64 * q^40 + 4 * q^41 - 72 * q^42 - 8 * q^44 + 8 * q^45 + 40 * q^46 - 56 * q^47 + 120 * q^48 + 24 * q^51 + 16 * q^52 + 12 * q^53 - 52 * q^54 - 72 * q^55 + 48 * q^57 + 36 * q^58 - 48 * q^59 - 52 * q^60 + 8 * q^63 - 96 * q^64 - 96 * q^65 + 24 * q^66 + 20 * q^67 - 80 * q^68 - 68 * q^69 + 8 * q^70 + 60 * q^71 + 100 * q^72 - 40 * q^74 - 120 * q^75 + 4 * q^76 - 12 * q^78 + 12 * q^79 + 200 * q^80 - 56 * q^81 - 68 * q^82 - 40 * q^83 + 132 * q^85 + 80 * q^86 - 16 * q^88 + 8 * q^89 + 140 * q^92 + 64 * q^93 + 128 * q^94 - 68 * q^96 + 4 * q^98 + 96 * q^99

Introduction

L-functions

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