LMFDB - Embedded newform 650.2.m.b.101.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(101,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("650.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.m (of order $6$, degree $2$, 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:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.3
Root			$-1.27597 - 0.609843i$ of defining polynomial
Character	$\chi$	$=$	650.101
Dual form			650.2.m.b.251.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.609843 - 1.05628i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.05628 - 0.609843i) q^{6} +(-3.07606 - 1.77597i) q^{7} -1.00000i q^{8} +(0.756182 - 1.30975i) q^{9} +(4.22982 - 2.44209i) q^{11} -1.21969 q^{12} +(-0.0197847 + 3.60550i) q^{13} -3.55193 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.57606 + 2.72982i) q^{17} -1.51236i q^{18} +(-6.90396 - 3.98601i) q^{19} +4.33225i q^{21} +(2.44209 - 4.22982i) q^{22} +(-2.45174 - 4.24653i) q^{23} +(-1.05628 + 0.609843i) q^{24} +(1.78561 + 3.13234i) q^{26} -5.50367 q^{27} +(-3.07606 + 1.77597i) q^{28} +(-2.02943 - 3.51508i) q^{29} +5.02473i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-5.15906 - 2.97859i) q^{33} +3.15213i q^{34} +(-0.756182 - 1.30975i) q^{36} +(1.82953 - 1.05628i) q^{37} -7.97201 q^{38} +(3.82048 - 2.17789i) q^{39} +(5.49674 - 3.17354i) q^{41} +(2.16612 + 3.75184i) q^{42} +(0.922305 - 1.59748i) q^{43} -4.88418i q^{44} +(-4.24653 - 2.45174i) q^{46} -6.08359i q^{47} +(-0.609843 + 1.05628i) q^{48} +(2.80812 + 4.86380i) q^{49} +3.84461 q^{51} +(3.11256 + 1.81988i) q^{52} +8.08903 q^{53} +(-4.76632 + 2.75184i) q^{54} +(-1.77597 + 3.07606i) q^{56} +9.72336i q^{57} +(-3.51508 - 2.02943i) q^{58} +(10.5964 + 6.11786i) q^{59} +(-2.09277 + 3.62479i) q^{61} +(2.51236 + 4.35154i) q^{62} +(-4.65213 + 2.68591i) q^{63} -1.00000 q^{64} -5.95717 q^{66} +(13.5630 - 7.83062i) q^{67} +(1.57606 + 2.72982i) q^{68} +(-2.99035 + 5.17944i) q^{69} +(6.33768 + 3.65906i) q^{71} +(-1.30975 - 0.756182i) q^{72} -5.54324i q^{73} +(1.05628 - 1.82953i) q^{74} +(-6.90396 + 3.98601i) q^{76} -17.3483 q^{77} +(2.21969 - 3.79635i) q^{78} -2.01506 q^{79} +(1.08783 + 1.88418i) q^{81} +(3.17354 - 5.49674i) q^{82} +6.23572i q^{83} +(3.75184 + 2.16612i) q^{84} -1.84461i q^{86} +(-2.47527 + 4.28730i) q^{87} +(-2.44209 - 4.22982i) q^{88} +(-5.30564 + 3.06321i) q^{89} +(6.46410 - 11.0556i) q^{91} -4.90348 q^{92} +(5.30752 - 3.06430i) q^{93} +(-3.04180 - 5.26855i) q^{94} +1.21969i q^{96} +(1.97163 + 1.13832i) q^{97} +(4.86380 + 2.80812i) q^{98} -7.38666i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 4 q^{4} - 6 q^{7} + 2 q^{9} + 12 q^{11} - 4 q^{12} + 10 q^{13} - 4 q^{16} + 6 q^{17} + 6 q^{19} - 6 q^{22} + 6 q^{26} + 4 q^{27} - 6 q^{28} - 12 q^{29} - 24 q^{33} - 2 q^{36} + 6 q^{37}+ \cdots + 24 q^{98}+O(q^{100}) $ 8 * q - 2 * q^3 + 4 * q^4 - 6 * q^7 + 2 * q^9 + 12 * q^11 - 4 * q^12 + 10 * q^13 - 4 * q^16 + 6 * q^17 + 6 * q^19 - 6 * q^22 + 6 * q^26 + 4 * q^27 - 6 * q^28 - 12 * q^29 - 24 * q^33 - 2 * q^36 + 6 * q^37 - 12 * q^38 - 10 * q^39 - 24 * q^41 + 6 * q^42 - 8 * q^43 - 24 * q^46 - 2 * q^48 - 10 * q^49 + 8 * q^52 + 12 * q^53 - 18 * q^54 - 6 * q^58 + 30 * q^59 - 10 * q^61 + 12 * q^62 - 8 * q^64 + 30 * q^67 - 6 * q^68 - 18 * q^69 - 12 * q^72 + 6 * q^76 - 60 * q^77 + 12 * q^78 - 4 * q^79 + 8 * q^81 + 12 * q^82 + 6 * q^84 - 36 * q^87 + 6 * q^88 - 6 * q^89 + 24 * q^91 + 36 * q^93 - 12 * q^94 - 18 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.609843	−	1.05628i	−0.352093	−	0.609843i	0.634523	−	0.772904i	$-0.281197\pi$
$3$	−0.609843	−	1.05628i	−0.352093	−	0.609843i	−0.986616	+	0.163061i	$0.947863\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.05628	−	0.609843i	−0.431224	−	0.248968i
$7$	−3.07606	−	1.77597i	−1.16264	−	0.671252i	−0.210707	−	0.977549i	$-0.567577\pi$
$7$	−3.07606	−	1.77597i	−1.16264	−	0.671252i	−0.951936	+	0.306297i	$0.900910\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.756182	−	1.30975i	0.252061	−	0.436582i
$10$		0			0
$11$	4.22982	−	2.44209i	1.27534	−	0.736318i	0.299352	−	0.954143i	$-0.403230\pi$
$11$	4.22982	−	2.44209i	1.27534	−	0.736318i	0.975988	+	0.217825i	$0.0698962\pi$
$12$	−1.21969			−0.352093
$13$	−0.0197847	+	3.60550i	−0.00548729	+	0.999985i
$13$	−0.0197847	+	3.60550i	−0.00548729	+	0.999985i
$14$	−3.55193			−0.949294
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.57606	+	2.72982i	−0.382252	+	0.662080i	−0.991384	−	0.130989i	$-0.958185\pi$
$17$	−1.57606	+	2.72982i	−0.382252	+	0.662080i	0.609132	+	0.793069i	$0.291518\pi$
$18$		−	1.51236i		−	0.356468i
$19$	−6.90396	−	3.98601i	−1.58388	−	0.914452i	−0.994286	−	0.106751i	$-0.965955\pi$
$19$	−6.90396	−	3.98601i	−1.58388	−	0.914452i	−0.589592	−	0.807701i	$-0.700712\pi$
$20$		0			0
$21$			4.33225i			0.945374i
$22$	2.44209	−	4.22982i	0.520655	−	0.901801i
$23$	−2.45174	−	4.24653i	−0.511223	−	0.885464i	−0.999915	−	0.0130076i	$-0.995859\pi$
$23$	−2.45174	−	4.24653i	−0.511223	−	0.885464i	0.488693	−	0.872456i	$-0.337474\pi$
$24$	−1.05628	+	0.609843i	−0.215612	+	0.124484i
$25$		0			0
$26$	1.78561	+	3.13234i	0.350188	+	0.614303i
$27$	−5.50367			−1.05918
$28$	−3.07606	+	1.77597i	−0.581322	+	0.335626i
$29$	−2.02943	−	3.51508i	−0.376856	−	0.652734i	0.613747	−	0.789503i	$-0.289662\pi$
$29$	−2.02943	−	3.51508i	−0.376856	−	0.652734i	−0.990603	+	0.136769i	$0.956328\pi$
$30$		0			0
$31$			5.02473i			0.902468i	0.892406	+	0.451234i	$0.149016\pi$
$31$			5.02473i			0.902468i	−0.892406	+	0.451234i	$0.850984\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−5.15906	−	2.97859i	−0.898077	−	0.518505i
$34$			3.15213i			0.540586i
$35$		0			0
$36$	−0.756182	−	1.30975i	−0.126030	−	0.218291i
$37$	1.82953	−	1.05628i	0.300773	−	0.173651i	−0.342017	−	0.939694i	$-0.611110\pi$
$37$	1.82953	−	1.05628i	0.300773	−	0.173651i	0.642790	+	0.766042i	$0.277777\pi$
$38$	−7.97201			−1.29323
$39$	3.82048	−	2.17789i	0.611766	−	0.348742i
$40$		0			0
$41$	5.49674	−	3.17354i	0.858446	−	0.495624i	−0.00504526	−	0.999987i	$-0.501606\pi$
$41$	5.49674	−	3.17354i	0.858446	−	0.495624i	0.863492	+	0.504363i	$0.168273\pi$
$42$	2.16612	+	3.75184i	0.334240	+	0.578921i
$43$	0.922305	−	1.59748i	0.140650	−	0.243613i	−0.787091	−	0.616836i	$-0.788414\pi$
$43$	0.922305	−	1.59748i	0.140650	−	0.243613i	0.927742	+	0.373223i	$0.121747\pi$
$44$		−	4.88418i		−	0.736318i
$45$		0			0
$46$	−4.24653	−	2.45174i	−0.626117	−	0.361489i
$47$		−	6.08359i		−	0.887383i	−0.896180	−	0.443692i	$-0.853669\pi$
$47$		−	6.08359i		−	0.887383i	0.896180	−	0.443692i	$-0.146331\pi$
$48$	−0.609843	+	1.05628i	−0.0880233	+	0.152461i
$49$	2.80812	+	4.86380i	0.401159	+	0.694828i
$50$		0			0
$51$	3.84461			0.538353
$52$	3.11256	+	1.81988i	0.431634	+	0.252372i
$53$	8.08903			1.11111			0.555557	−	0.831479i	$-0.312505\pi$
$53$	8.08903			1.11111			0.555557	+	0.831479i	$0.312505\pi$
$54$	−4.76632	+	2.75184i	−0.648614	+	0.374477i
$55$		0			0
$56$	−1.77597	+	3.07606i	−0.237324	+	0.411056i
$57$			9.72336i			1.28789i
$58$	−3.51508	−	2.02943i	−0.461553	−	0.266478i
$59$	10.5964	+	6.11786i	1.37954	+	0.796478i	0.992104	−	0.125419i	$-0.0400275\pi$
$59$	10.5964	+	6.11786i	1.37954	+	0.796478i	0.387436	+	0.921897i	$0.373361\pi$
$60$		0			0
$61$	−2.09277	+	3.62479i	−0.267952	+	0.464107i	−0.968333	−	0.249663i	$-0.919680\pi$
$61$	−2.09277	+	3.62479i	−0.267952	+	0.464107i	0.700381	+	0.713770i	$0.253014\pi$
$62$	2.51236	+	4.35154i	0.319071	+	0.552646i
$63$	−4.65213	+	2.68591i	−0.586113	+	0.338393i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−5.95717			−0.733277
$67$	13.5630	−	7.83062i	1.65699	−	0.956662i	0.682893	−	0.730518i	$-0.260721\pi$
$67$	13.5630	−	7.83062i	1.65699	−	0.956662i	0.974094	−	0.226144i	$-0.0726120\pi$
$68$	1.57606	+	2.72982i	0.191126	+	0.331040i
$69$	−2.99035	+	5.17944i	−0.359996	+	0.623532i
$70$		0			0
$71$	6.33768	+	3.65906i	0.752144	+	0.434251i	0.826468	−	0.562984i	$-0.190347\pi$
$71$	6.33768	+	3.65906i	0.752144	+	0.434251i	−0.0743240	+	0.997234i	$0.523680\pi$
$72$	−1.30975	−	0.756182i	−0.154355	−	0.0891169i
$73$		−	5.54324i		−	0.648787i	−0.945922	−	0.324394i	$-0.894840\pi$
$73$		−	5.54324i		−	0.648787i	0.945922	−	0.324394i	$-0.105160\pi$
$74$	1.05628	−	1.82953i	0.122790	−	0.212679i
$75$		0			0
$76$	−6.90396	+	3.98601i	−0.791939	+	0.457226i
$77$	−17.3483			−1.97702
$78$	2.21969	−	3.79635i	0.251330	−	0.429852i
$79$	−2.01506			−0.226712			−0.113356	−	0.993554i	$-0.536160\pi$
$79$	−2.01506			−0.226712			−0.113356	+	0.993554i	$0.536160\pi$
$80$		0			0
$81$	1.08783	+	1.88418i	0.120870	+	0.209353i
$82$	3.17354	−	5.49674i	0.350459	−	0.607013i
$83$			6.23572i			0.684459i	0.939616	+	0.342230i	$0.111182\pi$
$83$			6.23572i			0.684459i	−0.939616	+	0.342230i	$0.888818\pi$
$84$	3.75184	+	2.16612i	0.409359	+	0.236343i
$85$		0			0
$86$		−	1.84461i		−	0.198909i
$87$	−2.47527	+	4.28730i	−0.265377	+	0.459646i
$88$	−2.44209	−	4.22982i	−0.260328	−	0.450901i
$89$	−5.30564	+	3.06321i	−0.562396	+	0.324700i	−0.754107	−	0.656752i	$-0.771930\pi$
$89$	−5.30564	+	3.06321i	−0.562396	+	0.324700i	0.191710	+	0.981452i	$0.438597\pi$
$90$		0			0
$91$	6.46410	−	11.0556i	0.677622	−	1.15894i
$92$	−4.90348			−0.511223
$93$	5.30752	−	3.06430i	0.550364	−	0.317753i
$94$	−3.04180	−	5.26855i	−0.313737	−	0.543409i
$95$		0			0
$96$			1.21969i			0.124484i
$97$	1.97163	+	1.13832i	0.200189	+	0.115579i	0.596743	−	0.802432i	$-0.296461\pi$
$97$	1.97163	+	1.13832i	0.200189	+	0.115579i	−0.396555	+	0.918011i	$0.629794\pi$
$98$	4.86380	+	2.80812i	0.491318	+	0.283662i
$99$		−	7.38666i		−	0.742387i
$100$		0			0
$101$	−4.30377	−	7.45435i	−0.428241	−	0.741735i	0.568476	−	0.822700i	$-0.307533\pi$
$101$	−4.30377	−	7.45435i	−0.428241	−	0.741735i	−0.996717	+	0.0809647i	$0.974200\pi$
$102$	3.32953	−	1.92231i	0.329673	−	0.190337i
$103$	8.39726			0.827407			0.413703	−	0.910412i	$-0.364235\pi$
$103$	8.39726			0.827407			0.413703	+	0.910412i	$0.364235\pi$
$104$	3.60550	+	0.0197847i	0.353548	+	0.00194005i
$105$		0			0
$106$	7.00530	−	4.04451i	0.680415	−	0.392838i
$107$	−0.951738	−	1.64846i	−0.0920080	−	0.159362i	0.816348	−	0.577560i	$-0.195995\pi$
$107$	−0.951738	−	1.64846i	−0.0920080	−	0.159362i	−0.908356	+	0.418198i	$0.862662\pi$
$108$	−2.75184	+	4.76632i	−0.264795	+	0.458639i
$109$			19.9720i			1.91297i	0.291779	+	0.956486i	$0.405753\pi$
$109$			19.9720i			1.91297i	−0.291779	+	0.956486i	$0.594247\pi$
$110$		0			0
$111$	−2.23145	−	1.28833i	−0.211800	−	0.122283i
$112$			3.55193i			0.335626i
$113$	5.16933	−	8.95354i	0.486290	−	0.842278i	−0.513586	−	0.858038i	$-0.671683\pi$
$113$	5.16933	−	8.95354i	0.486290	−	0.842278i	0.999876	+	0.0157598i	$0.00501670\pi$
$114$	4.86168	+	8.42067i	0.455338	+	0.788668i
$115$		0			0
$116$	−4.05886			−0.376856
$117$	4.70732	+	2.75232i	0.435192	+	0.254453i
$118$	12.2357			1.12639
$119$	9.69615	−	5.59808i	0.888845	−	0.513175i
$120$		0			0
$121$	6.42761	−	11.1329i	0.584328	−	1.01209i
$122$			4.18555i			0.378942i
$123$	−6.70430	−	3.87073i	−0.604506	−	0.349012i
$124$	4.35154	+	2.51236i	0.390780	+	0.225617i
$125$		0			0
$126$	−2.68591	+	4.65213i	−0.239280	+	0.414445i
$127$	2.50753	+	4.34317i	0.222507	+	0.385394i	0.955569	−	0.294769i	$-0.0952426\pi$
$127$	2.50753	+	4.34317i	0.222507	+	0.385394i	−0.733061	+	0.680162i	$0.761909\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−2.24985			−0.198088
$130$		0			0
$131$	−9.40715			−0.821906			−0.410953	−	0.911656i	$-0.634804\pi$
$131$	−9.40715			−0.821906			−0.410953	+	0.911656i	$0.634804\pi$
$132$	−5.15906	+	2.97859i	−0.449039	+	0.259253i
$133$	14.1580	+	24.5224i	1.22766	+	2.12636i
$134$	7.83062	−	13.5630i	0.676462	−	1.17167i
$135$		0			0
$136$	2.72982	+	1.57606i	0.234080	+	0.135146i
$137$	−1.34420	−	0.776074i	−0.114843	−	0.0663045i	0.441478	−	0.897272i	$-0.354454\pi$
$137$	−1.34420	−	0.776074i	−0.114843	−	0.0663045i	−0.556321	+	0.830967i	$0.687788\pi$
$138$			5.98070i			0.509111i
$139$	10.9572	−	18.9784i	0.929375	−	1.60972i	0.145006	−	0.989431i	$-0.453680\pi$
$139$	10.9572	−	18.9784i	0.929375	−	1.60972i	0.784369	−	0.620294i	$-0.212987\pi$
$140$		0			0
$141$	−6.42598	+	3.71004i	−0.541165	+	0.312442i
$142$	7.31812			0.614123
$143$	8.72126	+	15.2989i	0.729309	+	1.27936i
$144$	−1.51236			−0.126030
$145$		0			0
$146$	−2.77162	−	4.80059i	−0.229381	−	0.397299i
$147$	3.42502	−	5.93231i	0.282491	−	0.489289i
$148$		−	2.11256i		−	0.173651i
$149$	18.3405	+	10.5889i	1.50252	+	0.867478i	0.999996	+	0.00291242i	$0.000927052\pi$
$149$	18.3405	+	10.5889i	1.50252	+	0.867478i	0.502520	+	0.864566i	$0.332406\pi$
$150$		0			0
$151$		−	11.8693i		−	0.965913i	−0.875644	−	0.482957i	$-0.839563\pi$
$151$		−	11.8693i		−	0.965913i	0.875644	−	0.482957i	$-0.160437\pi$
$152$	−3.98601	+	6.90396i	−0.323308	+	0.559985i
$153$	2.38358	+	4.12849i	0.192701	+	0.333768i
$154$	−15.0241	+	8.67414i	−1.21067	+	0.698982i
$155$		0			0
$156$	0.0241312	−	4.39758i	0.00193204	−	0.352088i
$157$	15.4552			1.23346			0.616729	−	0.787175i	$-0.288457\pi$
$157$	15.4552			1.23346			0.616729	+	0.787175i	$0.288457\pi$
$158$	−1.74509	+	1.00753i	−0.138832	+	0.0801546i
$159$	−4.93304	−	8.54427i	−0.391215	−	0.677605i
$160$		0			0
$161$			17.4168i			1.37264i
$162$	1.88418	+	1.08783i	0.148035	+	0.0854681i
$163$	−3.41863	−	1.97375i	−0.267768	−	0.154596i	0.360105	−	0.932912i	$-0.382741\pi$
$163$	−3.41863	−	1.97375i	−0.267768	−	0.154596i	−0.627873	+	0.778316i	$0.716074\pi$
$164$		−	6.34709i		−	0.495624i
$165$		0			0
$166$	3.11786	+	5.40029i	0.241993	+	0.419144i
$167$	1.64479	−	0.949618i	0.127277	−	0.0734837i	−0.435009	−	0.900426i	$-0.643255\pi$
$167$	1.64479	−	0.949618i	0.127277	−	0.0734837i	0.562287	+	0.826942i	$0.309922\pi$
$168$	4.33225			0.334240
$169$	−12.9992	−	0.142667i	−0.999940	−	0.0109744i
$170$		0			0
$171$	−10.4413	+	6.02829i	−0.798467	+	0.460995i
$172$	−0.922305	−	1.59748i	−0.0703251	−	0.121807i
$173$	3.47799	−	6.02405i	0.264427	−	0.458000i	−0.702987	−	0.711203i	$-0.748151\pi$
$173$	3.47799	−	6.02405i	0.264427	−	0.458000i	0.967413	+	0.253203i	$0.0814840\pi$
$174$			4.95054i			0.375300i
$175$		0			0
$176$	−4.22982	−	2.44209i	−0.318835	−	0.184079i
$177$		−	14.9237i		−	1.12174i
$178$	−3.06321	+	5.30564i	−0.229597	+	0.397674i
$179$	−4.50791	−	7.80793i	−0.336937	−	0.583592i	0.646918	−	0.762560i	$-0.276058\pi$
$179$	−4.50791	−	7.80793i	−0.336937	−	0.583592i	−0.983855	+	0.178968i	$0.942724\pi$
$180$		0			0
$181$	−8.60563			−0.639651			−0.319826	−	0.947476i	$-0.603624\pi$
$181$	−8.60563			−0.639651			−0.319826	+	0.947476i	$0.603624\pi$
$182$	0.0702740	−	12.8065i	0.00520906	−	0.949280i
$183$	5.10506			0.377377
$184$	−4.24653	+	2.45174i	−0.313059	+	0.180744i
$185$		0			0
$186$	3.06430	−	5.30752i	0.224685	−	0.389166i
$187$			15.3956i			1.12584i
$188$	−5.26855	−	3.04180i	−0.384248	−	0.221846i
$189$	16.9296	+	9.77434i	1.23145	+	0.710978i
$190$		0			0
$191$	−7.10020	+	12.2979i	−0.513752	+	0.889845i	0.486121	+	0.873892i	$0.338412\pi$
$191$	−7.10020	+	12.2979i	−0.513752	+	0.889845i	−0.999873	+	0.0159531i	$0.994922\pi$
$192$	0.609843	+	1.05628i	0.0440117	+	0.0762304i
$193$	16.3979	−	9.46731i	1.18034	−	0.681472i	0.224250	−	0.974532i	$-0.428007\pi$
$193$	16.3979	−	9.46731i	1.18034	−	0.681472i	0.956094	+	0.293060i	$0.0946736\pi$
$194$	2.27664			0.163453
$195$		0			0
$196$	5.61623			0.401159
$197$	−21.2827	+	12.2875i	−1.51633	+	0.875452i	−0.516510	+	0.856281i	$0.672769\pi$
$197$	−21.2827	+	12.2875i	−1.51633	+	0.875452i	−0.999816	+	0.0191706i	$0.993897\pi$
$198$	−3.69333	−	6.39703i	−0.262473	−	0.454617i
$199$	4.92067	−	8.52286i	0.348817	−	0.604169i	−0.637222	−	0.770680i	$-0.719917\pi$
$199$	4.92067	−	8.52286i	0.348817	−	0.604169i	0.986040	+	0.166511i	$0.0532500\pi$
$200$		0			0
$201$	−16.5426	−	9.55090i	−1.16683	−	0.673669i
$202$	−7.45435	−	4.30377i	−0.524486	−	0.302812i
$203$			14.4168i			1.01186i
$204$	1.92231	−	3.32953i	0.134588	−	0.233114i
$205$		0			0
$206$	7.27224	−	4.19863i	0.506681	−	0.292532i
$207$	−7.41584			−0.515436
$208$	3.13234	−	1.78561i	0.217189	−	0.123810i
$209$	−38.9367			−2.69331
$210$		0			0
$211$	−8.77754	−	15.2031i	−0.604271	−	1.04663i	−0.992166	−	0.124924i	$-0.960131\pi$
$211$	−8.77754	−	15.2031i	−0.604271	−	1.04663i	0.387895	−	0.921703i	$-0.373202\pi$
$212$	4.04451	−	7.00530i	0.277778	−	0.481126i
$213$		−	8.92582i		−	0.611587i
$214$	−1.64846	−	0.951738i	−0.112686	−	0.0650594i
$215$		0			0
$216$			5.50367i			0.374477i
$217$	8.92375	−	15.4564i	0.605784	−	1.04925i
$218$	9.98601	+	17.2963i	0.676338	+	1.17145i
$219$	−5.85521	+	3.38051i	−0.395659	+	0.228434i
$220$		0			0
$221$	−9.81119	−	5.73650i	−0.659972	−	0.385879i
$222$	−2.57666			−0.172934
$223$	−16.9972	+	9.81331i	−1.13821	+	0.657148i	−0.945988	−	0.324203i	$-0.894904\pi$
$223$	−16.9972	+	9.81331i	−1.13821	+	0.657148i	−0.192226	+	0.981351i	$0.561571\pi$
$224$	1.77597	+	3.07606i	0.118662	+	0.205528i
$225$		0			0
$226$		−	10.3387i		−	0.687717i
$227$	9.05935	+	5.23042i	0.601290	+	0.347155i	0.769549	−	0.638588i	$-0.220481\pi$
$227$	9.05935	+	5.23042i	0.601290	+	0.347155i	−0.168259	+	0.985743i	$0.553814\pi$
$228$	8.42067	+	4.86168i	0.557673	+	0.321973i
$229$		−	5.14381i		−	0.339912i	−0.985452	−	0.169956i	$-0.945637\pi$
$229$		−	5.14381i		−	0.339912i	0.985452	−	0.169956i	$-0.0543626\pi$
$230$		0			0
$231$	10.5797	+	18.3246i	0.696095	+	1.20567i
$232$	−3.51508	+	2.02943i	−0.230776	+	0.133239i
$233$	−19.1197			−1.25257			−0.626286	−	0.779593i	$-0.715426\pi$
$233$	−19.1197			−1.25257			−0.626286	+	0.779593i	$0.715426\pi$
$234$	5.45282	+	0.0299217i	0.356462	+	0.00195604i
$235$		0			0
$236$	10.5964	−	6.11786i	0.689770	−	0.398239i
$237$	1.22887	+	2.12846i	0.0798236	+	0.138259i
$238$	5.59808	−	9.69615i	0.362869	−	0.628508i
$239$			23.9572i			1.54966i	0.632169	+	0.774830i	$0.282165\pi$
$239$			23.9572i			1.54966i	−0.632169	+	0.774830i	$0.717835\pi$
$240$		0			0
$241$	14.1664	+	8.17898i	0.912538	+	0.526854i	0.881247	−	0.472656i	$-0.156705\pi$
$241$	14.1664	+	8.17898i	0.912538	+	0.526854i	0.0312913	+	0.999510i	$0.490038\pi$
$242$		−	12.8552i		−	0.826364i
$243$	−6.92869	+	12.0008i	−0.444476	+	0.769855i
$244$	2.09277	+	3.62479i	0.133976	+	0.232054i
$245$		0			0
$246$	−7.74146			−0.493577
$247$	14.5081	−	24.8134i	0.923130	−	1.57884i
$248$	5.02473			0.319071
$249$	6.58667	−	3.80281i	0.417413	−	0.240994i
$250$		0			0
$251$	−1.32260	+	2.29081i	−0.0834817	+	0.144595i	−0.904743	−	0.425957i	$-0.859937\pi$
$251$	−1.32260	+	2.29081i	−0.0834817	+	0.144595i	0.821262	+	0.570552i	$0.193271\pi$
$252$			5.37182i			0.338393i
$253$	−20.7408	−	11.9747i	−1.30397	−	0.752845i
$254$	4.34317	+	2.50753i	0.272514	+	0.157336i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	15.6006	+	27.0210i	0.973139	+	1.68553i	0.685944	+	0.727654i	$0.259389\pi$
$257$	15.6006	+	27.0210i	0.973139	+	1.68553i	0.287195	+	0.957872i	$0.407277\pi$
$258$	−1.94842	+	1.12492i	−0.121304	+	0.0700347i
$259$	−7.50367			−0.466255
$260$		0			0
$261$	−6.13848			−0.379962
$262$	−8.14683	+	4.70357i	−0.503313	+	0.290588i
$263$	−1.57606	−	2.72982i	−0.0971843	−	0.168328i	0.813334	−	0.581797i	$-0.197650\pi$
$263$	−1.57606	−	2.72982i	−0.0971843	−	0.168328i	−0.910518	+	0.413469i	$0.864317\pi$
$264$	−2.97859	+	5.15906i	−0.183319	+	0.317518i
$265$		0			0
$266$	24.5224	+	14.1580i	1.50357	+	0.868084i
$267$	6.47122	+	3.73616i	0.396032	+	0.228649i
$268$		−	15.6612i		−	0.956662i
$269$	6.85472	−	11.8727i	0.417940	−	0.723893i	−0.577792	−	0.816184i	$-0.696086\pi$
$269$	6.85472	−	11.8727i	0.417940	−	0.723893i	0.995732	+	0.0922908i	$0.0294189\pi$
$270$		0			0
$271$	6.92256	−	3.99674i	0.420515	−	0.242785i	−0.274782	−	0.961506i	$-0.588606\pi$
$271$	6.92256	−	3.99674i	0.420515	−	0.242785i	0.695298	+	0.718722i	$0.255272\pi$
$272$	3.15213			0.191126
$273$	−15.6199	−	0.0857123i	−0.945359	−	0.00518754i
$274$	−1.55215			−0.0937687
$275$		0			0
$276$	2.99035	+	5.17944i	0.179998	+	0.311766i
$277$	0.829530	−	1.43679i	0.0498416	−	0.0863283i	−0.840028	−	0.542543i	$-0.817462\pi$
$277$	0.829530	−	1.43679i	0.0498416	−	0.0863283i	0.889870	+	0.456214i	$0.150795\pi$
$278$		−	21.9143i		−	1.31433i
$279$	6.58112	+	3.79961i	0.394001	+	0.227477i
$280$		0			0
$281$		−	6.04076i		−	0.360362i	−0.983633	−	0.180181i	$-0.942332\pi$
$281$		−	6.04076i		−	0.360362i	0.983633	−	0.180181i	$-0.0576683\pi$
$282$	−3.71004	+	6.42598i	−0.220930	+	0.382661i
$283$	−15.3134	−	26.5236i	−0.910288	−	1.57667i	−0.813657	−	0.581345i	$-0.802527\pi$
$283$	−15.3134	−	26.5236i	−0.910288	−	1.57667i	−0.0966310	−	0.995320i	$-0.530807\pi$
$284$	6.33768	−	3.65906i	0.376072	−	0.217125i
$285$		0			0
$286$	15.2023	+	8.88863i	0.898931	+	0.525596i
$287$	−22.5444			−1.33076
$288$	−1.30975	+	0.756182i	−0.0771775	+	0.0445584i
$289$	3.53204	+	6.11767i	0.207767	+	0.359863i
$290$		0			0
$291$		−	2.77679i		−	0.162778i
$292$	−4.80059	−	2.77162i	−0.280933	−	0.162197i
$293$	−22.8183	−	13.1741i	−1.33306	−	0.769642i	−0.347291	−	0.937757i	$-0.612898\pi$
$293$	−22.8183	−	13.1741i	−1.33306	−	0.769642i	−0.985767	+	0.168116i	$0.946232\pi$
$294$		−	6.85004i		−	0.399503i
$295$		0			0
$296$	−1.05628	−	1.82953i	−0.0613950	−	0.106339i
$297$	−23.2796	+	13.4405i	−1.35082	+	0.779895i
$298$	21.1778			1.22680
$299$	15.3594	−	8.75572i	0.888255	−	0.506356i
$300$		0			0
$301$	−5.67414	+	3.27597i	−0.327052	+	0.188824i
$302$	−5.93467	−	10.2791i	−0.341502	−	0.591499i
$303$	−5.24925	+	9.09197i	−0.301562	+	0.522320i
$304$			7.97201i			0.457226i
$305$		0			0
$306$	4.12849	+	2.38358i	0.236010	+	0.136260i
$307$		−	16.3537i		−	0.933356i	−0.884427	−	0.466678i	$-0.845451\pi$
$307$		−	16.3537i		−	0.933356i	0.884427	−	0.466678i	$-0.154549\pi$
$308$	−8.67414	+	15.0241i	−0.494255	+	0.856075i
$309$	−5.12101	−	8.86986i	−0.291324	−	0.504588i
$310$		0			0
$311$	23.2857			1.32041			0.660205	−	0.751086i	$-0.270469\pi$
$311$	23.2857			1.32041			0.660205	+	0.751086i	$0.270469\pi$
$312$	−2.17789	−	3.82048i	−0.123299	−	0.216292i
$313$	3.62514			0.204905			0.102452	−	0.994738i	$-0.467331\pi$
$313$	3.62514			0.204905			0.102452	+	0.994738i	$0.467331\pi$
$314$	13.3846	−	7.72760i	0.755336	−	0.436094i
$315$		0			0
$316$	−1.00753	+	1.74509i	−0.0566779	+	0.0981690i
$317$			9.98609i			0.560875i	0.959872	+	0.280437i	$0.0904795\pi$
$317$			9.98609i			0.560875i	−0.959872	+	0.280437i	$0.909521\pi$
$318$	−8.54427	−	4.93304i	−0.479139	−	0.276631i
$319$	−17.1683	−	9.91211i	−0.961239	−	0.554972i
$320$		0			0
$321$	−1.16082	+	2.01060i	−0.0647908	+	0.112221i
$322$	8.70841	+	15.0834i	0.485301	+	0.840565i
$323$	21.7622	−	12.5644i	1.21088	−	0.699102i
$324$	2.17566			0.120870
$325$		0			0
$326$	−3.94750			−0.218632
$327$	21.0960	−	12.1798i	1.16661	−	0.673544i
$328$	−3.17354	−	5.49674i	−0.175230	−	0.303507i
$329$	−10.8043	+	18.7135i	−0.595658	+	1.03171i
$330$		0			0
$331$	−4.50815	−	2.60278i	−0.247790	−	0.143062i	0.370962	−	0.928648i	$-0.379028\pi$
$331$	−4.50815	−	2.60278i	−0.247790	−	0.143062i	−0.618752	+	0.785586i	$0.712361\pi$
$332$	5.40029	+	3.11786i	0.296380	+	0.171115i
$333$		−	3.19496i		−	0.175083i
$334$	0.949618	−	1.64479i	0.0519608	−	0.0899987i
$335$		0			0
$336$	3.75184	−	2.16612i	0.204679	−	0.118172i
$337$	7.08153			0.385755			0.192878	−	0.981223i	$-0.438218\pi$
$337$	7.08153			0.385755			0.192878	+	0.981223i	$0.438218\pi$
$338$	−11.3290	+	6.37605i	−0.616216	+	0.346812i
$339$	−12.6099			−0.684877
$340$		0			0
$341$	12.2708	+	21.2537i	0.664503	+	1.15095i
$342$	−6.02829	+	10.4413i	−0.325973	+	0.564601i
$343$			4.91506i			0.265388i
$344$	−1.59748	−	0.922305i	−0.0861303	−	0.0497274i
$345$		0			0
$346$		−	6.95598i		−	0.373956i
$347$	−10.9671	+	18.9955i	−0.588743	+	1.01973i	0.405654	+	0.914027i	$0.367044\pi$
$347$	−10.9671	+	18.9955i	−0.588743	+	1.01973i	−0.994397	+	0.105706i	$0.966290\pi$
$348$	2.47527	+	4.28730i	0.132689	+	0.229823i
$349$	−26.4773	+	15.2867i	−1.41730	+	0.818278i	−0.996061	−	0.0886715i	$-0.971738\pi$
$349$	−26.4773	+	15.2867i	−1.41730	+	0.818278i	−0.421239	+	0.906950i	$0.638405\pi$
$350$		0			0
$351$	0.108889	−	19.8435i	0.00581204	−	1.05917i
$352$	−4.88418			−0.260328
$353$	8.45042	−	4.87885i	0.449771	−	0.259675i	−0.257963	−	0.966155i	$-0.583051\pi$
$353$	8.45042	−	4.87885i	0.449771	−	0.259675i	0.707733	+	0.706480i	$0.249718\pi$
$354$	−7.46187	−	12.9243i	−0.396594	−	0.686921i
$355$		0			0
$356$			6.12642i			0.324700i
$357$	−11.8263	−	6.82790i	−0.625913	−	0.361371i
$358$	−7.80793	−	4.50791i	−0.412662	−	0.238250i
$359$			11.2129i			0.591794i	0.955220	+	0.295897i	$0.0956186\pi$
$359$			11.2129i			0.591794i	−0.955220	+	0.295897i	$0.904381\pi$
$360$		0			0
$361$	22.2765	+	38.5840i	1.17245	+	2.03074i
$362$	−7.45269	+	4.30281i	−0.391705	+	0.226151i
$363$	−15.6793			−0.822952
$364$	−6.34238	−	11.1259i	−0.332431	−	0.583154i
$365$		0			0
$366$	4.42111	−	2.55253i	0.231095	−	0.133423i
$367$	−2.68922	−	4.65787i	−0.140376	−	0.243139i	0.787262	−	0.616618i	$-0.211498\pi$
$367$	−2.68922	−	4.65787i	−0.140376	−	0.243139i	−0.927638	+	0.373480i	$0.878165\pi$
$368$	−2.45174	+	4.24653i	−0.127806	+	0.221366i
$369$		−	9.59911i		−	0.499710i
$370$		0			0
$371$	−24.8824	−	14.3658i	−1.29183	−	0.745837i
$372$		−	6.12859i		−	0.317753i
$373$	2.19941	−	3.80949i	0.113881	−	0.197248i	−0.803451	−	0.595371i	$-0.797005\pi$
$373$	2.19941	−	3.80949i	0.113881	−	0.197248i	0.917332	+	0.398123i	$0.130338\pi$
$374$	7.69778	+	13.3330i	0.398043	+	0.689430i
$375$		0			0
$376$	−6.08359			−0.313737
$377$	12.7138	−	7.24757i	0.654792	−	0.373269i
$378$	19.5487			1.00548
$379$	6.70731	−	3.87247i	0.344531	−	0.198915i	−0.317743	−	0.948177i	$-0.602925\pi$
$379$	6.70731	−	3.87247i	0.344531	−	0.198915i	0.662274	+	0.749262i	$0.269591\pi$
$380$		0			0
$381$	3.05840	−	5.29730i	0.156687	−	0.271389i
$382$			14.2004i			0.726555i
$383$	12.0979	+	6.98473i	0.618175	+	0.356903i	0.776158	−	0.630539i	$-0.217166\pi$
$383$	12.0979	+	6.98473i	0.618175	+	0.356903i	−0.157983	+	0.987442i	$0.550499\pi$
$384$	1.05628	+	0.609843i	0.0539031	+	0.0311209i
$385$		0			0
$386$	9.46731	−	16.3979i	0.481873	−	0.834629i
$387$	−1.39486	−	2.41597i	−0.0709048	−	0.122811i
$388$	1.97163	−	1.13832i	0.100094	−	0.0577895i
$389$	−14.2746			−0.723750			−0.361875	−	0.932227i	$-0.617863\pi$
$389$	−14.2746			−0.723750			−0.361875	+	0.932227i	$0.617863\pi$
$390$		0			0
$391$	15.4564			0.781663
$392$	4.86380	−	2.80812i	0.245659	−	0.141831i
$393$	5.73689	+	9.93658i	0.289388	+	0.501234i
$394$	−12.2875	+	21.2827i	−0.619038	+	1.07220i
$395$		0			0
$396$	−6.39703	−	3.69333i	−0.321463	−	0.185597i
$397$	−3.94186	−	2.27584i	−0.197836	−	0.114221i	0.397809	−	0.917468i	$-0.369771\pi$
$397$	−3.94186	−	2.27584i	−0.197836	−	0.114221i	−0.595646	+	0.803247i	$0.703104\pi$
$398$		−	9.84135i		−	0.493302i
$399$	17.2684	−	29.9097i	0.864499	−	1.49736i
$400$		0			0
$401$	−21.7923	+	12.5818i	−1.08825	+	0.628304i	−0.933111	−	0.359588i	$-0.882917\pi$
$401$	−21.7923	+	12.5818i	−1.08825	+	0.628304i	−0.155143	+	0.987892i	$0.549584\pi$
$402$	−19.1018			−0.952711
$403$	−18.1166	−	0.0994128i	−0.902454	−	0.00495211i
$404$	−8.60754			−0.428241
$405$		0			0
$406$	7.20841	+	12.4853i	0.357747	+	0.619637i
$407$	5.15906	−	8.93576i	0.255725	−	0.442929i
$408$		−	3.84461i		−	0.190337i
$409$	9.68881	+	5.59384i	0.479081	+	0.276597i	0.720033	−	0.693939i	$-0.244126\pi$
$409$	9.68881	+	5.59384i	0.479081	+	0.276597i	−0.240953	+	0.970537i	$0.577460\pi$
$410$		0			0
$411$			1.89313i			0.0933815i
$412$	4.19863	−	7.27224i	0.206852	−	0.358278i
$413$	−21.7302	−	37.6379i	−1.06927	−	1.85204i
$414$	−6.42231	+	3.70792i	−0.315639	+	0.182234i
$415$		0			0
$416$	1.81988	−	3.11256i	0.0892271	−	0.152606i
$417$	−26.7286			−1.30891
$418$	−33.7202	+	19.4684i	−1.64931	+	0.952229i
$419$	−7.25901	−	12.5730i	−0.354626	−	0.614230i	0.632428	−	0.774619i	$-0.282058\pi$
$419$	−7.25901	−	12.5730i	−0.354626	−	0.614230i	−0.987054	+	0.160389i	$0.948725\pi$
$420$		0			0
$421$		−	6.96332i		−	0.339371i	−0.985498	−	0.169686i	$-0.945725\pi$
$421$		−	6.96332i		−	0.339371i	0.985498	−	0.169686i	$-0.0542753\pi$
$422$	−15.2031	−	8.77754i	−0.740078	−	0.427284i
$423$	−7.96796	−	4.60030i	−0.387415	−	0.223674i
$424$		−	8.08903i		−	0.392838i
$425$		0			0
$426$	−4.46291	−	7.72998i	−0.216229	−	0.374519i
$427$	12.8750	−	7.43340i	0.623066	−	0.359727i
$428$	−1.90348			−0.0920080
$429$	10.8413	−	18.5420i	0.523425	−	0.895218i
$430$		0			0
$431$	−19.2718	+	11.1266i	−0.928290	+	0.535949i	−0.886270	−	0.463168i	$-0.846713\pi$
$431$	−19.2718	+	11.1266i	−0.928290	+	0.535949i	−0.0420198	+	0.999117i	$0.513379\pi$
$432$	2.75184	+	4.76632i	0.132398	+	0.229320i
$433$	0.311190	−	0.538996i	0.0149548	−	0.0259025i	−0.858451	−	0.512895i	$-0.828573\pi$
$433$	0.311190	−	0.538996i	0.0149548	−	0.0259025i	0.873406	+	0.486993i	$0.161906\pi$
$434$		−	17.8475i		−	0.856707i
$435$		0			0
$436$	17.2963	+	9.98601i	0.828341	+	0.478243i
$437$			39.0906i			1.86996i
$438$	−3.38051	+	5.85521i	−0.161527	+	0.279773i
$439$	16.5840	+	28.7243i	0.791511	+	1.37094i	0.925031	+	0.379892i	$0.124039\pi$
$439$	16.5840	+	28.7243i	0.791511	+	1.37094i	−0.133520	+	0.991046i	$0.542628\pi$
$440$		0			0
$441$	8.49378			0.404466
$442$	−11.3650	−	0.0623640i	−0.540578	−	0.00296635i
$443$	2.05137			0.0974633			0.0487317	−	0.998812i	$-0.484482\pi$
$443$	2.05137			0.0974633			0.0487317	+	0.998812i	$0.484482\pi$
$444$	−2.23145	+	1.28833i	−0.105900	+	0.0611415i
$445$		0			0
$446$	−9.81331	+	16.9972i	−0.464674	+	0.804838i
$447$		−	25.8303i		−	1.22173i
$448$	3.07606	+	1.77597i	0.145330	+	0.0839065i
$449$	−0.892538	−	0.515307i	−0.0421215	−	0.0243188i	0.478791	−	0.877929i	$-0.341075\pi$
$449$	−0.892538	−	0.515307i	−0.0421215	−	0.0243188i	−0.520913	+	0.853610i	$0.674408\pi$
$450$		0			0
$451$	15.5002	−	26.8471i	0.729874	−	1.26418i
$452$	−5.16933	−	8.95354i	−0.243145	−	0.421139i
$453$	−12.5373	+	7.23844i	−0.589056	+	0.340091i
$454$	10.4608			0.490952
$455$		0			0
$456$	9.72336			0.455338
$457$	36.3342	−	20.9776i	1.69964	−	0.981288i	0.753549	−	0.657392i	$-0.228340\pi$
$457$	36.3342	−	20.9776i	1.69964	−	0.981288i	0.946092	−	0.323897i	$-0.104993\pi$
$458$	−2.57190	−	4.45467i	−0.120177	−	0.208153i
$459$	8.67414	−	15.0241i	0.404874	−	0.701263i
$460$		0			0
$461$	3.54322	+	2.04568i	0.165024	+	0.0952767i	0.580237	−	0.814447i	$-0.302960\pi$
$461$	3.54322	+	2.04568i	0.165024	+	0.0952767i	−0.415213	+	0.909724i	$0.636293\pi$
$462$	18.3246	+	10.5797i	0.852539	+	0.492214i
$463$			31.7060i			1.47350i	0.676164	+	0.736751i	$0.263641\pi$
$463$			31.7060i			1.47350i	−0.676164	+	0.736751i	$0.736359\pi$
$464$	−2.02943	+	3.51508i	−0.0942140	+	0.163183i
$465$		0			0
$466$	−16.5581	+	9.55984i	−0.767041	+	0.442851i
$467$	5.72786			0.265054			0.132527	−	0.991179i	$-0.457691\pi$
$467$	5.72786			0.265054			0.132527	+	0.991179i	$0.457691\pi$
$468$	4.73724	−	2.70050i	0.218979	−	0.124831i
$469$	−55.6277			−2.56865
$470$		0			0
$471$	−9.42525	−	16.3250i	−0.434293	−	0.752217i
$472$	6.11786	−	10.5964i	0.281597	−	0.487741i
$473$		−	9.00941i		−	0.414253i
$474$	2.12846	+	1.22887i	0.0977636	+	0.0564438i
$475$		0			0
$476$		−	11.1962i		−	0.513175i
$477$	6.11677	−	10.5946i	0.280068	−	0.485092i
$478$	11.9786	+	20.7475i	0.547888	+	0.948969i
$479$	2.23145	−	1.28833i	0.101958	−	0.0588653i	−0.448154	−	0.893956i	$-0.647918\pi$
$479$	2.23145	−	1.28833i	0.101958	−	0.0588653i	0.550112	+	0.835091i	$0.314585\pi$
$480$		0			0
$481$	3.77222	+	6.61726i	0.171998	+	0.301721i
$482$	16.3580			0.745084
$483$	18.3970	−	10.6215i	0.837094	−	0.483296i
$484$	−6.42761	−	11.1329i	−0.292164	−	0.506043i
$485$		0			0
$486$			13.8574i			0.628584i
$487$	20.2759	+	11.7063i	0.918788	+	0.530463i	0.883248	−	0.468906i	$-0.155352\pi$
$487$	20.2759	+	11.7063i	0.918788	+	0.530463i	0.0355399	+	0.999368i	$0.488685\pi$
$488$	3.62479	+	2.09277i	0.164087	+	0.0947355i
$489$			4.81471i			0.217729i
$490$		0			0
$491$	−11.8117	−	20.4584i	−0.533054	−	0.923276i	−0.999255	−	0.0385972i	$-0.987711\pi$
$491$	−11.8117	−	20.4584i	−0.533054	−	0.923276i	0.466201	−	0.884679i	$-0.345622\pi$
$492$	−6.70430	+	3.87073i	−0.302253	+	0.174506i
$493$	12.7941			0.576216
$494$	0.157724	−	28.7431i	0.00709634	−	1.29321i
$495$		0			0
$496$	4.35154	−	2.51236i	0.195390	−	0.112808i
$497$	−12.9967	−	22.5110i	−0.582983	−	1.00976i
$498$	3.80281	−	6.58667i	0.170408	−	0.295156i
$499$			32.5385i			1.45663i	0.685245	+	0.728313i	$0.259695\pi$
$499$			32.5385i			1.45663i	−0.685245	+	0.728313i	$0.740305\pi$
$500$		0			0
$501$	−2.00613	−	1.15824i	−0.0896271	−	0.0517462i
$502$			2.64520i			0.118061i
$503$	−4.42996	+	7.67292i	−0.197522	+	0.342119i	−0.947724	−	0.319090i	$-0.896623\pi$
$503$	−4.42996	+	7.67292i	−0.197522	+	0.342119i	0.750202	+	0.661209i	$0.229956\pi$
$504$	2.68591	+	4.65213i	0.119640	+	0.207222i
$505$		0			0
$506$	−23.9495			−1.06468
$507$	7.77679	+	13.8178i	0.345379	+	0.613671i
$508$	5.01506			0.222507
$509$	12.9967	−	7.50367i	0.576070	−	0.332594i	−0.183500	−	0.983020i	$-0.558743\pi$
$509$	12.9967	−	7.50367i	0.576070	−	0.332594i	0.759570	+	0.650425i	$0.225409\pi$
$510$		0			0
$511$	−9.84461	+	17.0514i	−0.435500	+	0.754308i
$512$			1.00000i			0.0441942i
$513$	37.9972	+	21.9377i	1.67762	+	0.968572i
$514$	27.0210	+	15.6006i	1.19185	+	0.688113i
$515$		0			0
$516$	−1.12492	+	1.94842i	−0.0495220	+	0.0857746i
$517$	−14.8567	−	25.7325i	−0.653396	−	1.13172i
$518$	−6.49837	+	3.75184i	−0.285522	+	0.164846i
$519$	−8.48411			−0.372411
$520$		0			0
$521$	−34.1259			−1.49508			−0.747541	−	0.664215i	$-0.768766\pi$
$521$	−34.1259			−1.49508			−0.747541	+	0.664215i	$0.768766\pi$
$522$	−5.31608	+	3.06924i	−0.232679	+	0.134337i
$523$	3.94207	+	6.82786i	0.172375	+	0.298561i	0.939250	−	0.343235i	$-0.111523\pi$
$523$	3.94207	+	6.82786i	0.172375	+	0.298561i	−0.766875	+	0.641796i	$0.778189\pi$
$524$	−4.70357	+	8.14683i	−0.205477	+	0.355896i
$525$		0			0
$526$	−2.72982	−	1.57606i	−0.119026	−	0.0687197i
$527$	−13.7166	−	7.91930i	−0.597505	−	0.344970i
$528$			5.95717i			0.259253i
$529$	−0.522035	+	0.904192i	−0.0226972	+	0.0393127i
$530$		0			0
$531$	16.0257	−	9.25243i	0.695455	−	0.401521i
$532$	28.3161			1.22766
$533$	11.3335	+	19.8813i	0.490906	+	0.861153i
$534$	7.47232			0.323359
$535$		0			0
$536$	−7.83062	−	13.5630i	−0.338231	−	0.585833i
$537$	−5.49824	+	9.52323i	−0.237267	+	0.410958i
$538$		−	13.7094i		−	0.591056i
$539$	23.7557	+	13.7153i	1.02323	+	0.590762i
$540$		0			0
$541$		−	21.7768i		−	0.936259i	−0.883660	−	0.468130i	$-0.844928\pi$
$541$		−	21.7768i		−	0.936259i	0.883660	−	0.468130i	$-0.155072\pi$
$542$	3.99674	−	6.92256i	0.171675	−	0.297349i
$543$	5.24809	+	9.08995i	0.225217	+	0.390087i
$544$	2.72982	−	1.57606i	0.117040	−	0.0675732i
$545$		0			0
$546$	−13.5701	+	7.73572i	−0.580746	+	0.331058i
$547$	−34.2671			−1.46515			−0.732577	−	0.680684i	$-0.761683\pi$
$547$	−34.2671			−1.46515			−0.732577	+	0.680684i	$0.761683\pi$
$548$	−1.34420	+	0.776074i	−0.0574214	+	0.0331522i
$549$	3.16504	+	5.48201i	0.135081	+	0.233966i
$550$		0			0
$551$			32.3573i			1.37847i
$552$	5.17944	+	2.99035i	0.220452	+	0.127278i
$553$	6.19844	+	3.57867i	0.263585	+	0.152181i
$554$		−	1.65906i		−	0.0704867i
$555$		0			0
$556$	−10.9572	−	18.9784i	−0.464688	−	0.804862i
$557$	−16.0546	+	9.26914i	−0.680256	+	0.392746i	−0.799952	−	0.600064i	$-0.795142\pi$
$557$	−16.0546	+	9.26914i	−0.680256	+	0.392746i	0.119695	+	0.992811i	$0.461808\pi$
$558$	7.59922			0.321701
$559$	5.74146	+	3.35697i	0.242838	+	0.141985i
$560$		0			0
$561$	16.2620	−	9.38888i	0.686583	−	0.396399i
$562$	−3.02038	−	5.23145i	−0.127407	−	0.220676i
$563$	−17.3888	+	30.1183i	−0.732851	+	1.26933i	0.222809	+	0.974862i	$0.428477\pi$
$563$	−17.3888	+	30.1183i	−0.732851	+	1.26933i	−0.955660	+	0.294473i	$0.904856\pi$
$564$			7.42008i			0.312442i
$565$		0			0
$566$	−26.5236	−	15.3134i	−1.11487	−	0.643671i
$567$		−	7.72781i		−	0.324538i
$568$	3.65906	−	6.33768i	0.153531	−	0.265923i
$569$	10.1799	+	17.6322i	0.426765	+	0.739179i	0.996583	−	0.0825920i	$-0.0263198\pi$
$569$	10.1799	+	17.6322i	0.426765	+	0.739179i	−0.569819	+	0.821771i	$0.692987\pi$
$570$		0			0
$571$	−20.5139			−0.858480			−0.429240	−	0.903190i	$-0.641219\pi$
$571$	−20.5139			−0.858480			−0.429240	+	0.903190i	$0.641219\pi$
$572$	17.6099	+	0.0966321i	0.736307	+	0.00404039i
$573$	17.3200			0.723555
$574$	−19.5241	+	11.2722i	−0.814918	+	0.470493i
$575$		0			0
$576$	−0.756182	+	1.30975i	−0.0315076	+	0.0545727i
$577$			32.6919i			1.36098i	0.732757	+	0.680491i	$0.238233\pi$
$577$			32.6919i			1.36098i	−0.732757	+	0.680491i	$0.761767\pi$
$578$	6.11767	+	3.53204i	0.254462	+	0.146914i
$579$	−20.0003	−	11.5472i	−0.831182	−	0.479883i
$580$		0			0
$581$	11.0744	−	19.1815i	0.459445	−	0.795782i
$582$	−1.38840	−	2.40477i	−0.0575508	−	0.0996810i
$583$	34.2152	−	19.7541i	1.41705	−	0.818132i
$584$	−5.54324			−0.229381
$585$		0			0
$586$	−26.3483			−1.08844
$587$	−3.19003	+	1.84176i	−0.131667	+	0.0760177i	−0.564386	−	0.825511i	$-0.690887\pi$
$587$	−3.19003	+	1.84176i	−0.131667	+	0.0760177i	0.432720	+	0.901528i	$0.357554\pi$
$588$	−3.42502	−	5.93231i	−0.141246	−	0.244644i
$589$	20.0286	−	34.6905i	0.825264	−	1.42940i
$590$		0			0
$591$	25.9582	+	14.9870i	1.06778	+	0.616481i
$592$	−1.82953	−	1.05628i	−0.0751932	−	0.0434128i
$593$			10.6452i			0.437144i	0.975821	+	0.218572i	$0.0701398\pi$
$593$			10.6452i			0.437144i	−0.975821	+	0.218572i	$0.929860\pi$
$594$	−13.4405	+	23.2796i	−0.551469	+	0.955172i
$595$		0			0
$596$	18.3405	−	10.5889i	0.751258	−	0.433739i
$597$	−12.0034			−0.491265
$598$	8.92375	−	15.2624i	0.364919	−	0.624124i
$599$	−1.74024			−0.0711044			−0.0355522	−	0.999368i	$-0.511319\pi$
$599$	−1.74024			−0.0711044			−0.0355522	+	0.999368i	$0.511319\pi$
$600$		0			0
$601$	−10.8181	−	18.7375i	−0.441280	−	0.764320i	0.556504	−	0.830845i	$-0.312142\pi$
$601$	−10.8181	−	18.7375i	−0.441280	−	0.764320i	−0.997785	+	0.0665246i	$0.978809\pi$
$602$	−3.27597	+	5.67414i	−0.133518	+	0.231261i
$603$		−	23.6855i		−	0.964547i
$604$	−10.2791	−	5.93467i	−0.418253	−	0.241478i
$605$		0			0
$606$			10.4985i			0.426472i
$607$	−5.35521	+	9.27550i	−0.217361	+	0.376481i	−0.954000	−	0.299805i	$-0.903078\pi$
$607$	−5.35521	+	9.27550i	−0.217361	+	0.376481i	0.736639	+	0.676286i	$0.236412\pi$
$608$	3.98601	+	6.90396i	0.161654	+	0.279993i
$609$	15.2282	−	8.79200i	0.617078	−	0.356270i
$610$		0			0
$611$	21.9344	+	0.120362i	0.887370	+	0.00486933i
$612$	4.76717			0.192701
$613$	33.3243	−	19.2398i	1.34596	−	0.777088i	0.358282	−	0.933613i	$-0.383362\pi$
$613$	33.3243	−	19.2398i	1.34596	−	0.777088i	0.987674	+	0.156525i	$0.0500291\pi$
$614$	−8.17686	−	14.1627i	−0.329991	−	0.571561i
$615$		0			0
$616$			17.3483i			0.698982i
$617$	34.6089	+	19.9815i	1.39330	+	0.804424i	0.993679	−	0.112256i	$-0.0358075\pi$
$617$	34.6089	+	19.9815i	1.39330	+	0.804424i	0.399624	+	0.916679i	$0.369141\pi$
$618$	−8.86986	−	5.12101i	−0.356798	−	0.205997i
$619$		−	40.4574i		−	1.62612i	−0.582181	−	0.813059i	$-0.697800\pi$
$619$		−	40.4574i		−	1.62612i	0.582181	−	0.813059i	$-0.302200\pi$
$620$		0			0
$621$	13.4936	+	23.3715i	0.541478	+	0.937867i
$622$	20.1660	−	11.6428i	0.808583	−	0.466835i
$623$	21.7606			0.871822
$624$	−3.79635	−	2.21969i	−0.151976	−	0.0888586i
$625$		0			0
$626$	3.13946	−	1.81257i	0.125478	−	0.0724448i
$627$	23.7453	+	41.1281i	0.948297	+	1.64250i
$628$	7.72760	−	13.3846i	0.308365	−	0.534103i
$629$			6.65906i			0.265514i
$630$		0			0
$631$	33.4508	+	19.3128i	1.33166	+	0.768832i	0.985554	−	0.169364i	$-0.0541714\pi$
$631$	33.4508	+	19.3128i	1.33166	+	0.768832i	0.346103	+	0.938196i	$0.387505\pi$
$632$			2.01506i			0.0801546i
$633$	−10.7059	+	18.5431i	−0.425519	+	0.737021i
$634$	4.99304	+	8.64821i	0.198299	+	0.343464i
$635$		0			0
$636$	−9.86608			−0.391215
$637$	−17.5920	+	10.0284i	−0.697019	+	0.397341i
$638$	−19.8242			−0.784849
$639$	9.58488	−	5.53383i	0.379172	−	0.218915i
$640$		0			0
$641$	14.4286	−	24.9910i	0.569895	−	0.987087i	−0.426681	−	0.904402i	$-0.640317\pi$
$641$	14.4286	−	24.9910i	0.569895	−	0.987087i	0.996576	−	0.0826846i	$-0.0263494\pi$
$642$			2.32164i			0.0916280i
$643$	17.5451	+	10.1297i	0.691910	+	0.399475i	0.804327	−	0.594186i	$-0.202526\pi$
$643$	17.5451	+	10.1297i	0.691910	+	0.399475i	−0.112417	+	0.993661i	$0.535859\pi$
$644$	15.0834	+	8.70841i	0.594369	+	0.343159i
$645$		0			0
$646$	12.5644	−	21.7622i	0.494340	−	0.856222i
$647$	−8.30197	−	14.3794i	−0.326384	−	0.565314i	0.655407	−	0.755275i	$-0.272497\pi$
$647$	−8.30197	−	14.3794i	−0.326384	−	0.565314i	−0.981791	+	0.189962i	$0.939164\pi$
$648$	1.88418	−	1.08783i	0.0740176	−	0.0427341i
$649$	59.7615			2.34584
$650$		0			0
$651$	−21.7684			−0.853169
$652$	−3.41863	+	1.97375i	−0.133884	+	0.0772980i
$653$	−6.54182	−	11.3308i	−0.256001	−	0.443407i	0.709166	−	0.705042i	$-0.249072\pi$
$653$	−6.54182	−	11.3308i	−0.256001	−	0.443407i	−0.965167	+	0.261635i	$0.915738\pi$
$654$	12.1798	−	21.0960i	0.476268	−	0.824920i
$655$		0			0
$656$	−5.49674	−	3.17354i	−0.214612	−	0.123906i
$657$	−7.26023	−	4.19170i	−0.283249	−	0.163534i
$658$			21.6085i			0.842388i
$659$	−23.7597	+	41.1530i	−0.925545	+	1.60309i	−0.134863	+	0.990864i	$0.543060\pi$
$659$	−23.7597	+	41.1530i	−0.925545	+	1.60309i	−0.790682	+	0.612227i	$0.790274\pi$
$660$		0			0
$661$	16.3500	−	9.43968i	0.635941	−	0.367161i	−0.147108	−	0.989120i	$-0.546997\pi$
$661$	16.3500	−	9.43968i	0.635941	−	0.367161i	0.783049	+	0.621960i	$0.213663\pi$
$662$	−5.20556			−0.202320
$663$	−0.0760645	+	13.8617i	−0.00295410	+	0.538345i
$664$	6.23572			0.241993
$665$		0			0
$666$	−1.59748	−	2.76692i	−0.0619011	−	0.107216i
$667$	−9.95127	+	17.2361i	−0.385315	+	0.667385i
$668$		−	1.89924i		−	0.0734837i
$669$	20.7312	+	11.9692i	0.801515	+	0.462755i
$670$		0			0
$671$			20.4430i			0.789192i
$672$	2.16612	−	3.75184i	0.0835600	−	0.144730i
$673$	−0.0774441	−	0.134137i	−0.00298525	−	0.00517061i	0.864529	−	0.502583i	$-0.167617\pi$
$673$	−0.0774441	−	0.134137i	−0.00298525	−	0.00517061i	−0.867514	+	0.497412i	$0.834284\pi$
$674$	6.13278	−	3.54076i	0.236226	−	0.136385i
$675$		0			0
$676$	−6.62316	+	11.1863i	−0.254737	+	0.430243i
$677$	5.90445			0.226927			0.113463	−	0.993542i	$-0.463806\pi$
$677$	5.90445			0.226927			0.113463	+	0.993542i	$0.463806\pi$
$678$	−10.9205	+	6.30496i	−0.419400	+	0.242141i
$679$	−4.04324	−	7.00310i	−0.155165	−	0.268754i
$680$		0			0
$681$		−	12.7590i		−	0.488924i
$682$	21.2537	+	12.2708i	0.813847	+	0.469875i
$683$	−8.39051	−	4.84426i	−0.321054	−	0.185361i	0.330808	−	0.943698i	$-0.392679\pi$
$683$	−8.39051	−	4.84426i	−0.321054	−	0.185361i	−0.651862	+	0.758337i	$0.726012\pi$
$684$			12.0566i			0.460995i
$685$		0			0
$686$	2.45753	+	4.25656i	0.0938289	+	0.162516i
$687$	−5.43330	+	3.13692i	−0.207293	+	0.119681i
$688$	−1.84461			−0.0703251
$689$	−0.160039	+	29.1650i	−0.00609700	+	1.11110i
$690$		0			0
$691$	−19.8748	+	11.4747i	−0.756072	+	0.436518i	−0.827884	−	0.560900i	$-0.810455\pi$
$691$	−19.8748	+	11.4747i	−0.756072	+	0.436518i	0.0718117	+	0.997418i	$0.477122\pi$
$692$	−3.47799	−	6.02405i	−0.132213	−	0.229000i
$693$	−13.1185	+	22.7218i	−0.498329	+	0.863131i
$694$			21.9341i			0.832608i
$695$		0			0
$696$	4.28730	+	2.47527i	0.162510	+	0.0938249i
$697$			20.0068i			0.757813i
$698$	−15.2867	+	26.4773i	−0.578610	+	1.00218i
$699$	11.6600	+	20.1957i	0.441022	+	0.763873i
$700$		0			0
$701$	−7.77875			−0.293799			−0.146900	−	0.989151i	$-0.546929\pi$
$701$	−7.77875			−0.293799			−0.146900	+	0.989151i	$0.546929\pi$
$702$	−9.82743	−	17.2394i	−0.370913	−	0.650659i
$703$	−16.8413			−0.635184
$704$	−4.22982	+	2.44209i	−0.159417	+	0.0920397i
$705$		0			0
$706$	4.87885	−	8.45042i	0.183618	−	0.318036i
$707$			30.5734i			1.14983i
$708$	−12.9243	−	7.46187i	−0.485727	−	0.280434i
$709$	24.2737	+	14.0144i	0.911618	+	0.526323i	0.880951	−	0.473207i	$-0.156904\pi$
$709$	24.2737	+	14.0144i	0.911618	+	0.526323i	0.0306666	+	0.999530i	$0.490237\pi$
$710$		0			0
$711$	−1.52375	+	2.63921i	−0.0571451	+	0.0989782i
$712$	3.06321	+	5.30564i	0.114799	+	0.198837i
$713$	21.3377	−	12.3193i	0.799102	−	0.461362i
$714$	−13.6558			−0.511055
$715$		0			0
$716$	−9.01582			−0.336937
$717$	25.3055	−	14.6101i	0.945050	−	0.545625i
$718$	5.60645	+	9.71066i	0.209231	+	0.362399i
$719$	4.64553	−	8.04630i	0.173249	−	0.300076i	−0.766305	−	0.642477i	$-0.777907\pi$
$719$	4.64553	−	8.04630i	0.173249	−	0.300076i	0.939554	+	0.342401i	$0.111240\pi$
$720$		0			0
$721$	−25.8305	−	14.9133i	−0.961979	−	0.555399i
$722$	38.5840	+	22.2765i	1.43595	+	0.829045i
$723$		−	19.9516i		−	0.742007i
$724$	−4.30281	+	7.45269i	−0.159913	+	0.276977i
$725$		0			0
$726$	−13.5787	+	7.83967i	−0.503953	+	0.290957i
$727$	−8.60852			−0.319272			−0.159636	−	0.987176i	$-0.551032\pi$
$727$	−8.60852			−0.319272			−0.159636	+	0.987176i	$0.551032\pi$
$728$	−11.0556	−	6.46410i	−0.409748	−	0.239576i
$729$	23.4287			0.867728
$730$		0			0
$731$	2.90723	+	5.03546i	0.107528	+	0.186243i
$732$	2.55253	−	4.42111i	0.0943442	−	0.163409i
$733$			36.4209i			1.34524i	0.739990	+	0.672618i	$0.234830\pi$
$733$			36.4209i			1.34524i	−0.739990	+	0.672618i	$0.765170\pi$
$734$	−4.65787	−	2.68922i	−0.171925	−	0.0992610i
$735$		0			0
$736$			4.90348i			0.180744i
$737$	38.2461	−	66.2443i	1.40881	−	2.44014i
$738$	−4.79955	−	8.31307i	−0.176674	−	0.306008i
$739$	14.0669	−	8.12156i	0.517461	−	0.298756i	−0.218434	−	0.975852i	$-0.570095\pi$
$739$	14.0669	−	8.12156i	0.517461	−	0.298756i	0.735895	+	0.677095i	$0.236762\pi$
$740$		0			0
$741$	−35.0575	−	0.192374i	−1.28787	−	0.00706703i
$742$	−28.7317			−1.05477
$743$	35.9902	−	20.7790i	1.32035	−	0.762306i	0.336568	−	0.941659i	$-0.390734\pi$
$743$	35.9902	−	20.7790i	1.32035	−	0.762306i	0.983785	+	0.179353i	$0.0574004\pi$
$744$	−3.06430	−	5.30752i	−0.112343	−	0.194583i
$745$		0			0
$746$		−	4.39883i		−	0.161052i
$747$	8.16721	+	4.71534i	0.298823	+	0.172525i
$748$	13.3330	+	7.69778i	0.487501	+	0.281459i
$749$			6.76102i			0.247042i
$750$		0			0
$751$	−1.19863	−	2.07609i	−0.0437386	−	0.0757575i	0.843327	−	0.537400i	$-0.180594\pi$
$751$	−1.19863	−	2.07609i	−0.0437386	−	0.0757575i	−0.887066	+	0.461643i	$0.847260\pi$
$752$	−5.26855	+	3.04180i	−0.192124	+	0.110923i
$753$	3.22631			0.117573
$754$	7.38666	−	12.6335i	0.269006	−	0.460083i
$755$		0			0
$756$	16.9296	−	9.77434i	0.615725	−	0.355489i
$757$	−21.6800	−	37.5509i	−0.787974	−	1.36481i	−0.927206	−	0.374552i	$-0.877797\pi$
$757$	−21.6800	−	37.5509i	−0.787974	−	1.36481i	0.139232	−	0.990260i	$-0.455537\pi$
$758$	3.87247	−	6.70731i	0.140654	−	0.243621i
$759$			29.2108i			1.06029i
$760$		0			0
$761$	42.7888	+	24.7041i	1.55109	+	0.895523i	0.998053	+	0.0623680i	$0.0198653\pi$
$761$	42.7888	+	24.7041i	1.55109	+	0.895523i	0.553039	+	0.833155i	$0.313468\pi$
$762$		−	6.11680i		−	0.221588i
$763$	35.4696	−	61.4352i	1.28409	−	2.22410i
$764$	7.10020	+	12.2979i	0.256876	+	0.444922i
$765$		0			0
$766$	13.9695			0.504737
$767$	−22.2676	+	38.0844i	−0.804036	+	1.37515i
$768$	1.21969			0.0440117
$769$	9.40452	−	5.42970i	0.339136	−	0.195800i	−0.320754	−	0.947163i	$-0.603936\pi$
$769$	9.40452	−	5.42970i	0.339136	−	0.195800i	0.659890	+	0.751362i	$0.270603\pi$
$770$		0			0
$771$	19.0279	−	32.9572i	0.685271	−	1.18692i
$772$		−	18.9346i		−	0.681472i
$773$	−17.1828	−	9.92049i	−0.618022	−	0.356815i	0.158076	−	0.987427i	$-0.449471\pi$
$773$	−17.1828	−	9.92049i	−0.618022	−	0.356815i	−0.776099	+	0.630612i	$0.782804\pi$
$774$	−2.41597	−	1.39486i	−0.0868403	−	0.0501372i
$775$		0			0
$776$	1.13832	−	1.97163i	0.0408633	−	0.0707774i
$777$	4.57606	+	7.92598i	0.164165	+	0.284343i
$778$	−12.3621	+	7.13729i	−0.443204	+	0.255884i
$779$	−50.5991			−1.81290
$780$		0			0
$781$	35.7430			1.27899
$782$	13.3856	−	7.72819i	0.478669	−	0.276360i
$783$	11.1693	+	19.3458i	0.399159	+	0.691364i
$784$	2.80812	−	4.86380i	0.100290	−	0.173707i
$785$		0			0
$786$	9.93658	+	5.73689i	0.354426	+	0.204628i
$787$	15.6836	+	9.05493i	0.559060	+	0.322773i	0.752768	−	0.658286i	$-0.228718\pi$
$787$	15.6836	+	9.05493i	0.559060	+	0.322773i	−0.193708	+	0.981059i	$0.562052\pi$
$788$			24.5751i			0.875452i
$789$	−1.92231	+	3.32953i	−0.0684359	+	0.118534i
$790$		0			0
$791$	−31.8024	+	18.3611i	−1.13076	+	0.652846i
$792$	−7.38666			−0.262473
$793$	−13.0278	−	7.61721i	−0.462630	−	0.270495i
$794$	−4.55167			−0.161533
$795$		0			0
$796$	−4.92067	−	8.52286i	−0.174409	−	0.302085i
$797$	10.8107	−	18.7247i	0.382935	−	0.663262i	−0.608546	−	0.793519i	$-0.708247\pi$
$797$	10.8107	−	18.7247i	0.382935	−	0.663262i	0.991480	+	0.130257i	$0.0415801\pi$
$798$		−	34.5367i		−	1.22259i
$799$	16.6071	+	9.58813i	0.587518	+	0.339204i
$800$		0			0
$801$			9.26538i			0.327376i
$802$	−12.5818	+	21.7923i	−0.444278	+	0.769512i
$803$	−13.5371	−	23.4469i	−0.477714	−	0.827424i
$804$	−16.5426	+	9.55090i	−0.583414	+	0.336834i
$805$		0			0
$806$	−15.7392	+	8.97223i	−0.554389	+	0.316033i
$807$	−16.7212			−0.588615
$808$	−7.45435	+	4.30377i	−0.262243	+	0.151406i
$809$	−19.5890	−	33.9291i	−0.688711	−	1.19288i	−0.972255	−	0.233923i	$-0.924844\pi$
$809$	−19.5890	−	33.9291i	−0.688711	−	1.19288i	0.283544	−	0.958959i	$-0.408490\pi$
$810$		0			0
$811$		−	19.6903i		−	0.691418i	−0.938342	−	0.345709i	$-0.887638\pi$
$811$		−	19.6903i		−	0.691418i	0.938342	−	0.345709i	$-0.112362\pi$
$812$	12.4853	+	7.20841i	0.438149	+	0.252966i
$813$	−8.44335	−	4.87477i	−0.296121	−	0.170966i
$814$		−	10.3181i		−	0.361650i
$815$		0			0
$816$	−1.92231	−	3.32953i	−0.0672941	−	0.116557i
$817$	−12.7351	+	7.35263i	−0.445546	+	0.257236i
$818$	11.1877			0.391168
$819$	−9.59199	−	16.8264i	−0.335171	−	0.587961i
$820$		0			0
$821$	−5.68009	+	3.27940i	−0.198236	+	0.114452i	−0.595833	−	0.803109i	$-0.703178\pi$
$821$	−5.68009	+	3.27940i	−0.198236	+	0.114452i	0.397596	+	0.917560i	$0.369844\pi$
$822$	0.946567	+	1.63950i	0.0330153	+	0.0571842i
$823$	−20.7672	+	35.9698i	−0.723898	+	1.25383i	0.235528	+	0.971868i	$0.424318\pi$
$823$	−20.7672	+	35.9698i	−0.723898	+	1.25383i	−0.959426	+	0.281960i	$0.909015\pi$
$824$		−	8.39726i		−	0.292532i
$825$		0			0
$826$	−37.6379	−	21.7302i	−1.30959	−	0.756092i
$827$		−	27.7512i		−	0.965005i	−0.875895	−	0.482503i	$-0.839728\pi$
$827$		−	27.7512i		−	0.965005i	0.875895	−	0.482503i	$-0.160272\pi$
$828$	−3.70792	+	6.42231i	−0.128859	+	0.223191i
$829$	−27.3651	−	47.3977i	−0.950428	−	1.64619i	−0.744501	−	0.667622i	$-0.767312\pi$
$829$	−27.3651	−	47.3977i	−0.950428	−	1.64619i	−0.205927	−	0.978567i	$-0.566021\pi$
$830$		0			0
$831$	−2.02353			−0.0701956
$832$	0.0197847	−	3.60550i	0.000685912	−	0.124998i
$833$	−17.7031			−0.613376
$834$	−23.1477	+	13.3643i	−0.801538	+	0.462768i
$835$		0			0
$836$	−19.4684	+	33.7202i	−0.673328	+	1.16624i
$837$		−	27.6544i		−	0.955878i
$838$	−12.5730	−	7.25901i	−0.434326	−	0.250758i
$839$	−19.0899	−	11.0216i	−0.659057	−	0.380507i	0.132860	−	0.991135i	$-0.457584\pi$
$839$	−19.0899	−	11.0216i	−0.659057	−	0.380507i	−0.791918	+	0.610628i	$0.790917\pi$
$840$		0			0
$841$	6.26281	−	10.8475i	0.215959	−	0.374052i
$842$	−3.48166	−	6.03041i	−0.119986	−	0.207822i
$843$	−6.38074	+	3.68392i	−0.219764	+	0.126881i
$844$	−17.5551			−0.604271
$845$		0			0
$846$	−9.20061			−0.316323
$847$	−39.5435	+	22.8304i	−1.35873	+	0.784463i
$848$	−4.04451	−	7.00530i	−0.138889	−	0.240563i
$849$	−18.6776	+	32.3505i	−0.641013	+	1.11027i
$850$		0			0
$851$	−8.97106	−	5.17944i	−0.307524	−	0.177549i
$852$	−7.72998	−	4.46291i	−0.264825	−	0.152897i
$853$			2.19144i			0.0750334i	0.999296	+	0.0375167i	$0.0119447\pi$
$853$			2.19144i			0.0750334i	−0.999296	+	0.0375167i	$0.988055\pi$
$854$	7.43340	−	12.8750i	0.254366	−	0.440574i
$855$		0			0
$856$	−1.64846	+	0.951738i	−0.0563431	+	0.0325297i
$857$	−1.17805			−0.0402414			−0.0201207	−	0.999798i	$-0.506405\pi$
$857$	−1.17805			−0.0402414			−0.0201207	+	0.999798i	$0.506405\pi$
$858$	0.117861	−	21.4786i	0.00402371	−	0.733266i
$859$	−5.66200			−0.193185			−0.0965924	−	0.995324i	$-0.530794\pi$
$859$	−5.66200			−0.193185			−0.0965924	+	0.995324i	$0.530794\pi$
$860$		0			0
$861$	13.7486	+	23.8132i	0.468550	+	0.811553i
$862$	−11.1266	+	19.2718i	−0.378973	+	0.656400i
$863$		−	23.8414i		−	0.811571i	−0.913968	−	0.405785i	$-0.866998\pi$
$863$		−	23.8414i		−	0.811571i	0.913968	−	0.405785i	$-0.133002\pi$
$864$	4.76632	+	2.75184i	0.162153	+	0.0936193i
$865$		0			0
$866$		−	0.622379i		−	0.0211493i
$867$	4.30798	−	7.46165i	0.146307	−	0.253411i
$868$	−8.92375	−	15.4564i	−0.302892	−	0.524624i
$869$	−8.52333	+	4.92095i	−0.289134	+	0.166932i
$870$		0			0
$871$	27.9649	+	49.0564i	0.947555	+	1.66221i
$872$	19.9720			0.676338
$873$	2.98182	−	1.72156i	0.100919	−	0.0582658i
$874$	19.5453	+	33.8534i	0.661129	+	1.14511i
$875$		0			0
$876$			6.76102i			0.228434i
$877$	−1.60755	−	0.928119i	−0.0542831	−	0.0313404i	0.472613	−	0.881270i	$-0.343311\pi$
$877$	−1.60755	−	0.928119i	−0.0542831	−	0.0313404i	−0.526896	+	0.849930i	$0.676644\pi$
$878$	28.7243	+	16.5840i	0.969399	+	0.559683i
$879$			32.1367i			1.08394i
$880$		0			0
$881$	−9.15449	−	15.8560i	−0.308423	−	0.534203i	0.669595	−	0.742726i	$-0.266468\pi$
$881$	−9.15449	−	15.8560i	−0.308423	−	0.534203i	−0.978017	+	0.208523i	$0.933134\pi$
$882$	7.35583	−	4.24689i	0.247684	−	0.143000i
$883$	−16.6599			−0.560650			−0.280325	−	0.959905i	$-0.590442\pi$
$883$	−16.6599			−0.560650			−0.280325	+	0.959905i	$0.590442\pi$
$884$	−9.87355	+	5.62849i	−0.332084	+	0.189307i
$885$		0			0
$886$	1.77653	−	1.02568i	0.0596838	−	0.0344585i
$887$	−10.8748	−	18.8357i	−0.365139	−	0.632439i	0.623659	−	0.781696i	$-0.285645\pi$
$887$	−10.8748	−	18.8357i	−0.365139	−	0.632439i	−0.988798	+	0.149257i	$0.952312\pi$
$888$	−1.28833	+	2.23145i	−0.0432335	+	0.0748827i
$889$		−	17.8131i		−	0.597434i
$890$		0			0
$891$	9.20267	+	5.31317i	0.308301	+	0.177998i
$892$			19.6266i			0.657148i
$893$	−24.2492	+	42.0009i	−0.811470	+	1.40551i
$894$	−12.9152	−	22.3697i	−0.431948	−	0.748155i
$895$		0			0
$896$	3.55193			0.118662
$897$	−18.6153	−	10.8842i	−0.621547	−	0.363412i
$898$	−1.03061			−0.0343920
$899$	17.6623	−	10.1973i	0.589071	−	0.340101i
$900$		0			0
$901$	−12.7488	+	22.0816i	−0.424725	+	0.735645i
$902$		−	31.0003i		−	1.03220i
$903$	6.92067	+	3.99565i	0.230306	+	0.132967i
$904$	−8.95354	−	5.16933i	−0.297790	−	0.171929i
$905$		0			0
$906$	−7.23844	+	12.5373i	−0.240481	+	0.416525i
$907$	−3.56340	−	6.17199i	−0.118321	−	0.204937i	0.800782	−	0.598956i	$-0.204418\pi$
$907$	−3.56340	−	6.17199i	−0.118321	−	0.204937i	−0.919102	+	0.394019i	$0.871084\pi$
$908$	9.05935	−	5.23042i	0.300645	−	0.173578i
$909$	−13.0177			−0.431771
$910$		0			0
$911$	42.6390			1.41269			0.706347	−	0.707866i	$-0.250342\pi$
$911$	42.6390			1.41269			0.706347	+	0.707866i	$0.250342\pi$
$912$	8.42067	−	4.86168i	0.278836	−	0.160986i
$913$	15.2282	+	26.3760i	0.503980	+	0.872918i
$914$	20.9776	−	36.3342i	0.693876	−	1.20183i
$915$		0			0
$916$	−4.45467	−	2.57190i	−0.147186	−	0.0849781i
$917$	28.9370	+	16.7068i	0.955584	+	0.551706i
$918$		−	17.3483i		−	0.572579i
$919$	−1.50248	+	2.60237i	−0.0495622	+	0.0858442i	−0.889742	−	0.456463i	$-0.849116\pi$
$919$	−1.50248	+	2.60237i	−0.0495622	+	0.0858442i	0.840180	+	0.542308i	$0.182449\pi$
$920$		0			0
$921$	−17.2741	+	9.97321i	−0.569201	+	0.328628i
$922$	4.09135			0.134742
$923$	−13.3181	+	22.7781i	−0.438371	+	0.749750i
$924$	21.1595			0.696095
$925$		0			0
$926$	15.8530	+	27.4582i	0.520961	+	0.902332i
$927$	6.34986	−	10.9983i	0.208557	−	0.361231i
$928$			4.05886i			0.133239i
$929$	−40.6460	−	23.4670i	−1.33355	−	0.769927i	−0.347710	−	0.937602i	$-0.613041\pi$
$929$	−40.6460	−	23.4670i	−1.33355	−	0.769927i	−0.985842	+	0.167675i	$0.946374\pi$
$930$		0			0
$931$		−	44.7727i		−	1.46736i
$932$	−9.55984	+	16.5581i	−0.313143	+	0.542380i
$933$	−14.2006	−	24.5962i	−0.464907	−	0.805243i
$934$	4.96047	−	2.86393i	0.162312	−	0.0937106i
$935$		0			0
$936$	2.75232	−	4.70732i	0.0899625	−	0.153864i
$937$	−4.72153			−0.154246			−0.0771228	−	0.997022i	$-0.524573\pi$
$937$	−4.72153			−0.154246			−0.0771228	+	0.997022i	$0.524573\pi$
$938$	−48.1750	+	27.8138i	−1.57297	+	0.908154i
$939$	−2.21077	−	3.82916i	−0.0721457	−	0.124960i
$940$		0			0
$941$		−	54.2684i		−	1.76910i	−0.466446	−	0.884550i	$-0.654466\pi$
$941$		−	54.2684i		−	1.76910i	0.466446	−	0.884550i	$-0.345534\pi$
$942$	−16.3250	−	9.42525i	−0.531898	−	0.307091i
$943$	−26.9531	−	15.5614i	−0.877715	−	0.506749i
$944$		−	12.2357i		−	0.398239i
$945$		0			0
$946$	−4.50470	−	7.80238i	−0.146461	−	0.253677i
$947$	23.0803	−	13.3254i	0.750009	−	0.433018i	−0.0756880	−	0.997132i	$-0.524115\pi$
$947$	23.0803	−	13.3254i	0.750009	−	0.433018i	0.825697	+	0.564114i	$0.190782\pi$
$948$	2.45774			0.0798236
$949$	19.9861	+	0.109671i	0.648777	+	0.00356009i
$950$		0			0
$951$	10.5481	−	6.08995i	0.342046	−	0.197480i
$952$	−5.59808	−	9.69615i	−0.181435	−	0.314254i
$953$	18.3992	−	31.8684i	0.596010	−	1.03232i	−0.397394	−	0.917648i	$-0.630085\pi$
$953$	18.3992	−	31.8684i	0.596010	−	1.03232i	0.993404	−	0.114671i	$-0.0365814\pi$
$954$		−	12.2335i		−	0.396076i
$955$		0			0
$956$	20.7475	+	11.9786i	0.671023	+	0.387415i
$957$			24.1793i			0.781607i
$958$	1.28833	−	2.23145i	0.0416241	−	0.0720950i
$959$	2.75656	+	4.77451i	0.0890141	+	0.154177i
$960$		0			0
$961$	5.75211			0.185552
$962$	6.57547	+	3.84461i	0.212002	+	0.123955i
$963$	−2.87875			−0.0927663
$964$	14.1664	−	8.17898i	0.456269	−	0.263427i
$965$		0			0
$966$	10.6215	−	18.3970i	0.341742	−	0.591915i
$967$		−	17.9486i		−	0.577188i	−0.957452	−	0.288594i	$-0.906812\pi$
$967$		−	17.9486i		−	0.577188i	0.957452	−	0.288594i	$-0.0931877\pi$
$968$	−11.1329	−	6.42761i	−0.357826	−	0.206591i
$969$	−26.5431	−	15.3246i	−0.852686	−	0.492298i
$970$		0			0
$971$	−19.9994	+	34.6399i	−0.641810	+	1.11165i	0.343219	+	0.939256i	$0.388483\pi$
$971$	−19.9994	+	34.6399i	−0.641810	+	1.11165i	−0.985028	+	0.172392i	$0.944851\pi$
$972$	6.92869	+	12.0008i	0.222238	+	0.384927i
$973$	−67.4099	+	38.9191i	−2.16106	+	1.24769i
$974$	23.4126			0.750187
$975$		0			0
$976$	4.18555			0.133976
$977$	−5.95019	+	3.43534i	−0.190363	+	0.109906i	−0.592153	−	0.805826i	$-0.701722\pi$
$977$	−5.95019	+	3.43534i	−0.190363	+	0.109906i	0.401789	+	0.915732i	$0.368388\pi$
$978$	2.40736	+	4.16966i	0.0769788	+	0.133331i
$979$	−14.9613	+	25.9137i	−0.478164	+	0.828205i
$980$		0			0
$981$	26.1583	+	15.1025i	0.835169	+	0.482185i
$982$	−20.4584	−	11.8117i	−0.652855	−	0.376926i
$983$		−	17.3627i		−	0.553784i	−0.960901	−	0.276892i	$-0.910696\pi$
$983$		−	17.3627i		−	0.553784i	0.960901	−	0.276892i	$-0.0893044\pi$
$984$	−3.87073	+	6.70430i	−0.123394	+	0.213725i
$985$		0			0
$986$	11.0800	−	6.39703i	0.352859	−	0.203723i
$987$	26.3556			0.838909
$988$	−14.2349	−	24.9711i	−0.452874	−	0.794436i
$989$	−9.04500			−0.287614
$990$		0			0
$991$	13.2814	+	23.0041i	0.421899	+	0.730750i	0.996125	−	0.0879463i	$-0.0280304\pi$
$991$	13.2814	+	23.0041i	0.421899	+	0.730750i	−0.574226	+	0.818697i	$0.694697\pi$
$992$	2.51236	−	4.35154i	0.0797676	−	0.138162i
$993$			6.34916i			0.201484i
$994$	−22.5110	−	12.9967i	−0.714006	−	0.412232i
$995$		0			0
$996$		−	7.60563i		−	0.240994i
$997$	−9.18396	+	15.9071i	−0.290859	+	0.503782i	−0.974013	−	0.226492i	$-0.927274\pi$
$997$	−9.18396	+	15.9071i	−0.290859	+	0.503782i	0.683154	+	0.730274i	$0.260608\pi$
$998$	16.2693	+	28.1792i	0.514995	+	0.891997i
$999$	−10.0691	+	5.81342i	−0.318573	+	0.183928i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.m.b.101.3	✓	8
5.2	odd	4		650.2.n.f.49.2		8
5.3	odd	4		650.2.n.c.49.3		8
5.4	even	2		650.2.m.d.101.2	yes	8
13.2	odd	12		8450.2.a.co.1.3		4
13.4	even	6	inner	650.2.m.b.251.3	yes	8
13.11	odd	12		8450.2.a.ck.1.3		4
65.4	even	6		650.2.m.d.251.2	yes	8
65.17	odd	12		650.2.n.c.199.3		8
65.24	odd	12		8450.2.a.cl.1.2		4
65.43	odd	12		650.2.n.f.199.2		8
65.54	odd	12		8450.2.a.ch.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.m.b.101.3	✓	8	1.1	even	1	trivial
650.2.m.b.251.3	yes	8	13.4	even	6	inner
650.2.m.d.101.2	yes	8	5.4	even	2
650.2.m.d.251.2	yes	8	65.4	even	6
650.2.n.c.49.3		8	5.3	odd	4
650.2.n.c.199.3		8	65.17	odd	12
650.2.n.f.49.2		8	5.2	odd	4
650.2.n.f.199.2		8	65.43	odd	12
8450.2.a.ch.1.2		4	65.54	odd	12
8450.2.a.ck.1.3		4	13.11	odd	12
8450.2.a.cl.1.2		4	65.24	odd	12
8450.2.a.co.1.3		4	13.2	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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.609843 - 1.05628i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.05628 - 0.609843i) q^{6} +(-3.07606 - 1.77597i) q^{7} -1.00000i q^{8} +(0.756182 - 1.30975i) q^{9} +(4.22982 - 2.44209i) q^{11} -1.21969 q^{12} +(-0.0197847 + 3.60550i) q^{13} -3.55193 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.57606 + 2.72982i) q^{17} -1.51236i q^{18} +(-6.90396 - 3.98601i) q^{19} +4.33225i q^{21} +(2.44209 - 4.22982i) q^{22} +(-2.45174 - 4.24653i) q^{23} +(-1.05628 + 0.609843i) q^{24} +(1.78561 + 3.13234i) q^{26} -5.50367 q^{27} +(-3.07606 + 1.77597i) q^{28} +(-2.02943 - 3.51508i) q^{29} +5.02473i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-5.15906 - 2.97859i) q^{33} +3.15213i q^{34} +(-0.756182 - 1.30975i) q^{36} +(1.82953 - 1.05628i) q^{37} -7.97201 q^{38} +(3.82048 - 2.17789i) q^{39} +(5.49674 - 3.17354i) q^{41} +(2.16612 + 3.75184i) q^{42} +(0.922305 - 1.59748i) q^{43} -4.88418i q^{44} +(-4.24653 - 2.45174i) q^{46} -6.08359i q^{47} +(-0.609843 + 1.05628i) q^{48} +(2.80812 + 4.86380i) q^{49} +3.84461 q^{51} +(3.11256 + 1.81988i) q^{52} +8.08903 q^{53} +(-4.76632 + 2.75184i) q^{54} +(-1.77597 + 3.07606i) q^{56} +9.72336i q^{57} +(-3.51508 - 2.02943i) q^{58} +(10.5964 + 6.11786i) q^{59} +(-2.09277 + 3.62479i) q^{61} +(2.51236 + 4.35154i) q^{62} +(-4.65213 + 2.68591i) q^{63} -1.00000 q^{64} -5.95717 q^{66} +(13.5630 - 7.83062i) q^{67} +(1.57606 + 2.72982i) q^{68} +(-2.99035 + 5.17944i) q^{69} +(6.33768 + 3.65906i) q^{71} +(-1.30975 - 0.756182i) q^{72} -5.54324i q^{73} +(1.05628 - 1.82953i) q^{74} +(-6.90396 + 3.98601i) q^{76} -17.3483 q^{77} +(2.21969 - 3.79635i) q^{78} -2.01506 q^{79} +(1.08783 + 1.88418i) q^{81} +(3.17354 - 5.49674i) q^{82} +6.23572i q^{83} +(3.75184 + 2.16612i) q^{84} -1.84461i q^{86} +(-2.47527 + 4.28730i) q^{87} +(-2.44209 - 4.22982i) q^{88} +(-5.30564 + 3.06321i) q^{89} +(6.46410 - 11.0556i) q^{91} -4.90348 q^{92} +(5.30752 - 3.06430i) q^{93} +(-3.04180 - 5.26855i) q^{94} +1.21969i q^{96} +(1.97163 + 1.13832i) q^{97} +(4.86380 + 2.80812i) q^{98} -7.38666i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 4 q^{4} - 6 q^{7} + 2 q^{9} + 12 q^{11} - 4 q^{12} + 10 q^{13} - 4 q^{16} + 6 q^{17} + 6 q^{19} - 6 q^{22} + 6 q^{26} + 4 q^{27} - 6 q^{28} - 12 q^{29} - 24 q^{33} - 2 q^{36} + 6 q^{37}+ \cdots + 24 q^{98}+O(q^{100}) \) 8 * q - 2 * q^3 + 4 * q^4 - 6 * q^7 + 2 * q^9 + 12 * q^11 - 4 * q^12 + 10 * q^13 - 4 * q^16 + 6 * q^17 + 6 * q^19 - 6 * q^22 + 6 * q^26 + 4 * q^27 - 6 * q^28 - 12 * q^29 - 24 * q^33 - 2 * q^36 + 6 * q^37 - 12 * q^38 - 10 * q^39 - 24 * q^41 + 6 * q^42 - 8 * q^43 - 24 * q^46 - 2 * q^48 - 10 * q^49 + 8 * q^52 + 12 * q^53 - 18 * q^54 - 6 * q^58 + 30 * q^59 - 10 * q^61 + 12 * q^62 - 8 * q^64 + 30 * q^67 - 6 * q^68 - 18 * q^69 - 12 * q^72 + 6 * q^76 - 60 * q^77 + 12 * q^78 - 4 * q^79 + 8 * q^81 + 12 * q^82 + 6 * q^84 - 36 * q^87 + 6 * q^88 - 6 * q^89 + 24 * q^91 + 36 * q^93 - 12 * q^94 - 18 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more