LMFDB - Embedded newform 770.2.bv.a.3.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(3,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([45, 10, 48]))

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

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

chi := DirichletCharacter("770.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bv (of order $60$, degree $16$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$768$
Relative dimension:	$48$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			3.9
Character	$\chi$	$=$	770.3
Dual form			770.2.bv.a.257.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.933580 + 0.358368i) q^{2} +(-0.971197 + 0.630703i) q^{3} +(0.743145 - 0.669131i) q^{4} +(-2.11038 - 0.739133i) q^{5} +(0.680667 - 0.936858i) q^{6} +(-0.542344 - 2.58957i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-0.674772 + 1.51556i) q^{9} +O(q^{10})$	\(q+(-0.933580 + 0.358368i) q^{2} +(-0.971197 + 0.630703i) q^{3} +(0.743145 - 0.669131i) q^{4} +(-2.11038 - 0.739133i) q^{5} +(0.680667 - 0.936858i) q^{6} +(-0.542344 - 2.58957i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-0.674772 + 1.51556i) q^{9} +(2.23509 - 0.0662510i) q^{10} +(-2.78935 - 1.79431i) q^{11} +(-0.299718 + 1.11856i) q^{12} +(-0.629780 + 3.97627i) q^{13} +(1.43434 + 2.22321i) q^{14} +(2.51576 - 0.613176i) q^{15} +(0.104528 - 0.994522i) q^{16} +(-0.729290 - 0.279948i) q^{17} +(0.0868248 - 1.65672i) q^{18} +(2.18575 - 2.42752i) q^{19} +(-2.06289 + 0.862834i) q^{20} +(2.15997 + 2.17292i) q^{21} +(3.24710 + 0.675516i) q^{22} +(-0.355251 + 1.32581i) q^{23} +(-0.121046 - 1.15168i) q^{24} +(3.90737 + 3.11969i) q^{25} +(-0.837019 - 3.93787i) q^{26} +(-0.843996 - 5.32878i) q^{27} +(-2.13580 - 1.56153i) q^{28} +(3.47187 + 1.12808i) q^{29} +(-2.12892 + 1.47402i) q^{30} +(9.65038 - 1.01430i) q^{31} +(0.258819 + 0.965926i) q^{32} +(3.84068 - 0.0166249i) q^{33} +0.781175 q^{34} +(-0.769486 + 5.86582i) q^{35} +(0.512656 + 1.57779i) q^{36} +(-0.464783 + 0.715704i) q^{37} +(-1.17063 + 3.04959i) q^{38} +(-1.89621 - 4.25895i) q^{39} +(1.61666 - 1.54480i) q^{40} +(8.53662 - 2.77372i) q^{41} +(-2.79521 - 1.25453i) q^{42} +(6.76915 + 6.76915i) q^{43} +(-3.27352 + 0.533009i) q^{44} +(2.54422 - 2.69966i) q^{45} +(-0.143474 - 1.36506i) q^{46} +(-8.14083 + 0.426643i) q^{47} +(0.525730 + 1.03180i) q^{48} +(-6.41173 + 2.80887i) q^{49} +(-4.76584 - 1.51221i) q^{50} +(0.884848 - 0.188080i) q^{51} +(2.19263 + 3.37635i) q^{52} +(-3.03651 + 3.74978i) q^{53} +(2.69760 + 4.67238i) q^{54} +(4.56034 + 5.84836i) q^{55} +(2.55354 + 0.692408i) q^{56} +(-0.591751 + 3.73617i) q^{57} +(-3.64554 + 0.191055i) q^{58} +(2.78690 + 3.09516i) q^{59} +(1.45928 - 2.13905i) q^{60} +(0.954796 + 0.100353i) q^{61} +(-8.64592 + 4.40531i) q^{62} +(4.29061 + 0.925412i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(4.26807 - 7.92594i) q^{65} +(-3.57963 + 1.39190i) q^{66} +(2.85975 + 10.6727i) q^{67} +(-0.729290 + 0.279948i) q^{68} +(-0.491176 - 1.51168i) q^{69} +(-1.38375 - 5.75198i) q^{70} +(12.2778 + 8.92033i) q^{71} +(-1.04404 - 1.28928i) q^{72} +(-7.28599 - 0.381842i) q^{73} +(0.177427 - 0.834730i) q^{74} +(-5.76242 - 0.565452i) q^{75} -3.26656i q^{76} +(-3.13369 + 8.19634i) q^{77} +(3.29653 + 3.29653i) q^{78} +(2.20765 - 4.95846i) q^{79} +(-0.955678 + 2.02155i) q^{80} +(0.850319 + 0.944374i) q^{81} +(-6.97561 + 5.64874i) q^{82} +(1.87056 - 0.296268i) q^{83} +(3.05914 + 0.169494i) q^{84} +(1.33216 + 1.12984i) q^{85} +(-8.74539 - 3.89370i) q^{86} +(-4.08336 + 1.09413i) q^{87} +(2.86508 - 1.67073i) q^{88} +(-4.75709 - 8.23953i) q^{89} +(-1.40777 + 3.43212i) q^{90} +(10.6384 - 0.525649i) q^{91} +(0.623140 + 1.22298i) q^{92} +(-8.73270 + 7.07160i) q^{93} +(7.44722 - 3.31572i) q^{94} +(-6.40702 + 3.50743i) q^{95} +(-0.860576 - 0.774866i) q^{96} +(7.72170 + 1.22300i) q^{97} +(4.97925 - 4.92007i) q^{98} +(4.60156 - 3.01669i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) $ 768 * q + 24 * q^5 + 4 * q^7	$ 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) $ 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.933580	+	0.358368i	−0.660141	+	0.253404i
$2$	−0.933580	+	0.358368i	−0.660141	+	0.253404i
$3$	−0.971197	+	0.630703i	−0.560721	+	0.364136i	−0.793666	−	0.608353i	$-0.791830\pi$
$3$	−0.971197	+	0.630703i	−0.560721	+	0.364136i	0.232945	+	0.972490i	$0.425164\pi$
$4$	0.743145	−	0.669131i	0.371572	−	0.334565i
$5$	−2.11038	−	0.739133i	−0.943788	−	0.330550i
$5$	−2.11038	−	0.739133i	−0.943788	−	0.330550i
$6$	0.680667	−	0.936858i	0.277881	−	0.382471i
$7$	−0.542344	−	2.58957i	−0.204987	−	0.978765i
$7$	−0.542344	−	2.58957i	−0.204987	−	0.978765i
$8$	−0.453990	+	0.891007i	−0.160510	+	0.315018i
$9$	−0.674772	+	1.51556i	−0.224924	+	0.505188i
$10$	2.23509	−	0.0662510i	0.706796	−	0.0209504i
$11$	−2.78935	−	1.79431i	−0.841020	−	0.541004i
$11$	−2.78935	−	1.79431i	−0.841020	−	0.541004i
$12$	−0.299718	+	1.11856i	−0.0865210	+	0.322901i
$13$	−0.629780	+	3.97627i	−0.174670	+	1.10282i	0.732101	+	0.681196i	$0.238540\pi$
$13$	−0.629780	+	3.97627i	−0.174670	+	1.10282i	−0.906771	+	0.421624i	$0.861460\pi$
$14$	1.43434	+	2.22321i	0.383343	+	0.594178i
$15$	2.51576	−	0.613176i	0.649567	−	0.158321i
$16$	0.104528	−	0.994522i	0.0261321	−	0.248630i
$17$	−0.729290	−	0.279948i	−0.176879	−	0.0678974i	0.268317	−	0.963331i	$-0.413533\pi$
$17$	−0.729290	−	0.279948i	−0.176879	−	0.0678974i	−0.445196	+	0.895433i	$0.646866\pi$
$18$	0.0868248	−	1.65672i	0.0204648	−	0.390492i
$19$	2.18575	−	2.42752i	0.501446	−	0.556912i	−0.438281	−	0.898838i	$-0.644412\pi$
$19$	2.18575	−	2.42752i	0.501446	−	0.556912i	0.939727	+	0.341926i	$0.111079\pi$
$20$	−2.06289	+	0.862834i	−0.461276	+	0.192936i
$21$	2.15997	+	2.17292i	0.471344	+	0.474171i
$22$	3.24710	+	0.675516i	0.692285	+	0.144020i
$23$	−0.355251	+	1.32581i	−0.0740749	+	0.276451i	−0.993022	−	0.117930i	$-0.962374\pi$
$23$	−0.355251	+	1.32581i	−0.0740749	+	0.276451i	0.918947	+	0.394381i	$0.129041\pi$
$24$	−0.121046	−	1.15168i	−0.0247084	−	0.235085i
$25$	3.90737	+	3.11969i	0.781473	+	0.623939i
$26$	−0.837019	−	3.93787i	−0.164153	−	0.772279i
$27$	−0.843996	−	5.32878i	−0.162427	−	1.02552i
$28$	−2.13580	−	1.56153i	−0.403628	−	0.295101i
$29$	3.47187	+	1.12808i	0.644711	+	0.209479i	0.613081	−	0.790020i	$-0.289930\pi$
$29$	3.47187	+	1.12808i	0.644711	+	0.209479i	0.0316302	+	0.999500i	$0.489930\pi$
$30$	−2.12892	+	1.47402i	−0.388687	+	0.269118i
$31$	9.65038	−	1.01430i	1.73326	−	0.182173i	0.815352	−	0.578966i	$-0.196544\pi$
$31$	9.65038	−	1.01430i	1.73326	−	0.182173i	0.917908	+	0.396793i	$0.129877\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	3.84068	−	0.0166249i	0.668577	−	0.00289402i
$34$	0.781175			0.133970
$35$	−0.769486	+	5.86582i	−0.130067	+	0.991505i
$36$	0.512656	+	1.57779i	0.0854427	+	0.262966i
$37$	−0.464783	+	0.715704i	−0.0764099	+	0.117661i	−0.874810	−	0.484467i	$-0.839014\pi$
$37$	−0.464783	+	0.715704i	−0.0764099	+	0.117661i	0.798400	+	0.602128i	$0.205680\pi$
$38$	−1.17063	+	3.04959i	−0.189901	+	0.494709i
$39$	−1.89621	−	4.25895i	−0.303636	−	0.681978i
$40$	1.61666	−	1.54480i	0.255617	−	0.244254i
$41$	8.53662	−	2.77372i	1.33320	−	0.433182i	0.446190	−	0.894938i	$-0.352781\pi$
$41$	8.53662	−	2.77372i	1.33320	−	0.433182i	0.887007	+	0.461757i	$0.152781\pi$
$42$	−2.79521	−	1.25453i	−0.431311	−	0.193579i
$43$	6.76915	+	6.76915i	1.03229	+	1.03229i	0.999461	+	0.0328248i	$0.0104503\pi$
$43$	6.76915	+	6.76915i	1.03229	+	1.03229i	0.0328248	+	0.999461i	$0.489550\pi$
$44$	−3.27352	+	0.533009i	−0.493501	+	0.0803541i
$45$	2.54422	−	2.69966i	0.379271	−	0.402442i
$46$	−0.143474	−	1.36506i	−0.0211541	−	0.201268i
$47$	−8.14083	+	0.426643i	−1.18746	+	0.0622322i	−0.635812	−	0.771844i	$-0.719335\pi$
$47$	−8.14083	+	0.426643i	−1.18746	+	0.0622322i	−0.551649	+	0.834076i	$0.686001\pi$
$48$	0.525730	+	1.03180i	0.0758826	+	0.148928i
$49$	−6.41173	+	2.80887i	−0.915961	+	0.401267i
$50$	−4.76584	−	1.51221i	−0.673991	−	0.213859i
$51$	0.884848	−	0.188080i	0.123904	−	0.0263365i
$52$	2.19263	+	3.37635i	0.304063	+	0.468216i
$53$	−3.03651	+	3.74978i	−0.417097	+	0.515072i	−0.941782	−	0.336225i	$-0.890850\pi$
$53$	−3.03651	+	3.74978i	−0.417097	+	0.515072i	0.524685	+	0.851296i	$0.324183\pi$
$54$	2.69760	+	4.67238i	0.367097	+	0.635831i
$55$	4.56034	+	5.84836i	0.614916	+	0.788592i
$56$	2.55354	+	0.692408i	0.341231	+	0.0925268i
$57$	−0.591751	+	3.73617i	−0.0783793	+	0.494867i
$58$	−3.64554	+	0.191055i	−0.478683	+	0.0250867i
$59$	2.78690	+	3.09516i	0.362823	+	0.402956i	0.896723	−	0.442592i	$-0.145941\pi$
$59$	2.78690	+	3.09516i	0.362823	+	0.402956i	−0.533900	+	0.845547i	$0.679274\pi$
$60$	1.45928	−	2.13905i	0.188392	−	0.276151i
$61$	0.954796	+	0.100353i	0.122249	+	0.0128489i	0.165455	−	0.986217i	$-0.447091\pi$
$61$	0.954796	+	0.100353i	0.122249	+	0.0128489i	−0.0432063	+	0.999066i	$0.513757\pi$
$62$	−8.64592	+	4.40531i	−1.09803	+	0.559475i
$63$	4.29061	+	0.925412i	0.540566	+	0.116591i
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$	4.26807	−	7.92594i	0.529389	−	0.983092i
$66$	−3.57963	+	1.39190i	−0.440622	+	0.171331i
$67$	2.85975	+	10.6727i	0.349374	+	1.30388i	0.887419	+	0.460964i	$0.152496\pi$
$67$	2.85975	+	10.6727i	0.349374	+	1.30388i	−0.538045	+	0.842916i	$0.680837\pi$
$68$	−0.729290	+	0.279948i	−0.0884394	+	0.0339487i
$69$	−0.491176	−	1.51168i	−0.0591307	−	0.181985i
$70$	−1.38375	−	5.75198i	−0.165389	−	0.687493i
$71$	12.2778	+	8.92033i	1.45710	+	1.05865i	0.984106	+	0.177585i	$0.0568283\pi$
$71$	12.2778	+	8.92033i	1.45710	+	1.05865i	0.472998	+	0.881063i	$0.343172\pi$
$72$	−1.04404	−	1.28928i	−0.123041	−	0.151943i
$73$	−7.28599	−	0.381842i	−0.852760	−	0.0446913i	−0.379054	−	0.925374i	$-0.623751\pi$
$73$	−7.28599	−	0.381842i	−0.852760	−	0.0446913i	−0.473706	+	0.880683i	$0.657084\pi$
$74$	0.177427	−	0.834730i	0.0206255	−	0.0970354i
$75$	−5.76242	−	0.565452i	−0.665387	−	0.0652927i
$76$		−	3.26656i		−	0.374700i
$77$	−3.13369	+	8.19634i	−0.357117	+	0.934060i
$78$	3.29653	+	3.29653i	0.373259	+	0.373259i
$79$	2.20765	−	4.95846i	0.248380	−	0.557871i	−0.745730	−	0.666249i	$-0.767899\pi$
$79$	2.20765	−	4.95846i	0.248380	−	0.557871i	0.994110	+	0.108378i	$0.0345656\pi$
$80$	−0.955678	+	2.02155i	−0.106848	+	0.226017i
$81$	0.850319	+	0.944374i	0.0944798	+	0.104930i
$82$	−6.97561	+	5.64874i	−0.770327	+	0.623799i
$83$	1.87056	−	0.296268i	0.205321	−	0.0325196i	−0.0529267	−	0.998598i	$-0.516855\pi$
$83$	1.87056	−	0.296268i	0.205321	−	0.0325196i	0.258248	+	0.966079i	$0.416855\pi$
$84$	3.05914	+	0.169494i	0.333780	+	0.0184934i
$85$	1.33216	+	1.12984i	0.144493	+	0.122548i
$86$	−8.74539	−	3.89370i	−0.943040	−	0.419869i
$87$	−4.08336	+	1.09413i	−0.437782	+	0.117303i
$88$	2.86508	−	1.67073i	0.305418	−	0.178100i
$89$	−4.75709	−	8.23953i	−0.504251	−	0.873388i	−0.999988	−	0.00491555i	$-0.998435\pi$
$89$	−4.75709	−	8.23953i	−0.504251	−	0.873388i	0.495737	−	0.868473i	$-0.334898\pi$
$90$	−1.40777	+	3.43212i	−0.148392	+	0.361777i
$91$	10.6384	−	0.525649i	1.11521	−	0.0551030i
$92$	0.623140	+	1.22298i	0.0649668	+	0.127505i
$93$	−8.73270	+	7.07160i	−0.905539	+	0.733291i
$94$	7.44722	−	3.31572i	0.768122	−	0.341990i
$95$	−6.40702	+	3.50743i	−0.657347	+	0.359854i
$96$	−0.860576	−	0.774866i	−0.0878322	−	0.0790845i
$97$	7.72170	+	1.22300i	0.784020	+	0.124177i	0.535595	−	0.844475i	$-0.320087\pi$
$97$	7.72170	+	1.22300i	0.784020	+	0.124177i	0.248425	+	0.968651i	$0.420087\pi$
$98$	4.97925	−	4.92007i	0.502980	−	0.497002i
$99$	4.60156	−	3.01669i	0.462474	−	0.303188i
$100$	4.99122	−	0.296153i	0.499122	−	0.0296153i
$101$	−10.6370	+	1.11800i	−1.05843	+	0.111245i	−0.617713	−	0.786404i	$-0.711941\pi$
$101$	−10.6370	+	1.11800i	−1.05843	+	0.111245i	−0.440712	+	0.897649i	$0.645274\pi$
$102$	−0.758675	+	0.492689i	−0.0751200	+	0.0487835i
$103$	10.4092	−	16.0287i	1.02564	−	1.57935i	0.230371	−	0.973103i	$-0.426006\pi$
$103$	10.4092	−	16.0287i	1.02564	−	1.57935i	0.795274	−	0.606251i	$-0.207327\pi$
$104$	−3.25697	−	2.36633i	−0.319372	−	0.232038i
$105$	−2.95227	−	6.18219i	−0.288112	−	0.603320i
$106$	1.49103	−	4.58891i	0.144821	−	0.445714i
$107$	0.336676	+	6.42417i	0.0325477	+	0.621048i	0.965398	+	0.260782i	$0.0839805\pi$
$107$	0.336676	+	6.42417i	0.0325477	+	0.621048i	−0.932850	+	0.360265i	$0.882686\pi$
$108$	−4.19286	−	3.39531i	−0.403458	−	0.326714i
$109$	13.4077	+	7.74094i	1.28422	+	0.741447i	0.977618	−	0.210389i	$-0.0674730\pi$
$109$	13.4077	+	7.74094i	1.28422	+	0.741447i	0.306607	+	0.951836i	$0.400806\pi$
$110$	−6.35331	−	3.82563i	−0.605764	−	0.364760i
$111$		−	0.988230i		−	0.0937986i
$112$	−2.63207	+	0.268689i	−0.248707	+	0.0253887i
$113$	2.86262	−	5.61821i	0.269293	−	0.528516i	−0.716271	−	0.697822i	$-0.754153\pi$
$113$	2.86262	−	5.61821i	0.269293	−	0.528516i	0.985564	+	0.169306i	$0.0541526\pi$
$114$	−0.786475	−	3.70008i	−0.0736602	−	0.346544i
$115$	1.72967	−	2.53539i	0.161292	−	0.236426i
$116$	3.33494	−	1.48481i	0.309641	−	0.137861i
$117$	−5.60134	−	3.63755i	−0.517844	−	0.336292i
$118$	−3.71100	−	1.89085i	−0.341625	−	0.174067i
$119$	−0.329419	+	2.04037i	−0.0301978	+	0.187041i
$120$	−0.595789	+	2.51994i	−0.0543878	+	0.230038i
$121$	4.56093	+	10.0099i	0.414630	+	0.909990i
$122$	−0.927342	+	0.248480i	−0.0839576	+	0.0224964i
$123$	−6.54135	+	8.07790i	−0.589814	+	0.728359i
$124$	6.49293	−	7.21113i	0.583083	−	0.647579i
$125$	−5.94014	−	9.47179i	−0.531302	−	0.847182i
$126$	−4.33727	+	0.673671i	−0.386395	+	0.0600154i
$127$	−1.80942	+	0.286584i	−0.160560	+	0.0254302i	−0.236197	−	0.971705i	$-0.575901\pi$
$127$	−1.80942	+	0.286584i	−0.160560	+	0.0254302i	0.0756369	+	0.997135i	$0.475901\pi$
$128$	0.838671	+	0.544639i	0.0741287	+	0.0481397i
$129$	−10.8435	−	2.30486i	−0.954717	−	0.202931i
$130$	−1.14418	+	8.92904i	−0.100351	+	0.783129i
$131$	4.76784	−	2.75271i	0.416568	−	0.240505i	−0.277040	−	0.960858i	$-0.589353\pi$
$131$	4.76784	−	2.75271i	0.416568	−	0.240505i	0.693608	+	0.720353i	$0.256020\pi$
$132$	2.84306	−	2.58227i	0.247456	−	0.224758i
$133$	−7.47167	−	4.34360i	−0.647876	−	0.376638i
$134$	−6.49457	−	8.93900i	−0.561045	−	0.772212i
$135$	−2.15753	+	11.8695i	−0.185690	+	1.02157i
$136$	0.580526	−	0.522708i	0.0497797	−	0.0448219i
$137$	−1.59142	+	4.14579i	−0.135964	+	0.354198i	−0.984611	−	0.174762i	$-0.944085\pi$
$137$	−1.59142	+	4.14579i	−0.135964	+	0.354198i	0.848647	+	0.528960i	$0.177418\pi$
$138$	1.00029	+	1.23526i	0.0851505	+	0.105152i
$139$	−5.32343	+	16.3838i	−0.451528	+	1.38966i	0.423636	+	0.905833i	$0.360754\pi$
$139$	−5.32343	+	16.3838i	−0.451528	+	1.38966i	−0.875164	+	0.483827i	$0.839246\pi$
$140$	3.35316	+	4.87404i	0.283394	+	0.411932i
$141$	7.63726	−	5.54880i	0.643173	−	0.467293i
$142$	−14.6590	−	3.92788i	−1.23016	−	0.329620i
$143$	8.89133	−	9.96120i	0.743530	−	0.832997i
$144$	1.43673	+	0.829495i	0.119727	+	0.0691246i
$145$	−6.49315	−	4.94685i	−0.539227	−	0.410813i
$146$	6.93889	−	2.25458i	0.574267	−	0.186591i
$147$	4.45549	−	6.77186i	0.367482	−	0.558534i
$148$	0.133498	+	0.842872i	0.0109735	+	0.0692837i
$149$	−0.910366	−	0.0956833i	−0.0745801	−	0.00783868i	0.0671649	−	0.997742i	$-0.478605\pi$
$149$	−0.910366	−	0.0956833i	−0.0745801	−	0.00783868i	−0.141745	+	0.989903i	$0.545271\pi$
$150$	5.58232	−	1.53717i	0.455795	−	0.125510i
$151$	12.3166	+	2.61798i	1.00231	+	0.213049i	0.679707	−	0.733484i	$-0.262107\pi$
$151$	12.3166	+	2.61798i	1.00231	+	0.213049i	0.322608	+	0.946533i	$0.395440\pi$
$152$	1.17063	+	3.04959i	0.0949506	+	0.247355i
$153$	0.916383	−	0.916383i	0.0740852	−	0.0740852i
$154$	−0.0117513	−	8.77496i	−0.000946947	−	0.707106i
$155$	−21.1156	−	4.99237i	−1.69605	−	0.400997i
$156$	−4.25895	−	1.89621i	−0.340989	−	0.151818i
$157$	−8.24077	−	12.6897i	−0.657685	−	1.01275i	−0.997389	−	0.0722136i	$-0.976994\pi$
$157$	−8.24077	−	12.6897i	−0.657685	−	1.01275i	0.339704	−	0.940532i	$-0.389673\pi$
$158$	−0.284065	+	5.42028i	−0.0225990	+	0.431214i
$159$	0.584055	−	5.55691i	0.0463186	−	0.440692i
$160$	0.167742	−	2.22977i	0.0132612	−	0.176279i
$161$	3.62595	+	0.200899i	0.285765	+	0.0158331i
$162$	−1.13227	−	0.576923i	−0.0889599	−	0.0453273i
$163$	−5.79637	−	15.1001i	−0.454007	−	1.18273i	−0.949403	−	0.314060i	$-0.898311\pi$
$163$	−5.79637	−	15.1001i	−0.454007	−	1.18273i	0.495396	−	0.868667i	$-0.335023\pi$
$164$	4.48797	−	7.77339i	0.350451	−	0.607000i
$165$	−8.11757	−	2.80369i	−0.631952	−	0.218267i
$166$	−1.64015	+	0.946939i	−0.127300	+	0.0734968i
$167$	8.95598	+	1.41849i	0.693034	+	0.109766i	0.493008	−	0.870025i	$-0.335897\pi$
$167$	8.95598	+	1.41849i	0.693034	+	0.109766i	0.200026	+	0.979791i	$0.435897\pi$
$168$	−2.91670	+	0.938061i	−0.225028	+	0.0723730i
$169$	−3.05040	−	0.991136i	−0.234646	−	0.0762412i
$170$	−1.64857	−	0.577392i	−0.126440	−	0.0442839i
$171$	2.20418	+	4.95067i	0.168558	+	0.378587i
$172$	9.55991	+	0.501013i	0.728936	+	0.0382019i
$173$	0.473818	+	9.04098i	0.0360237	+	0.687373i	0.955637	+	0.294548i	$0.0951689\pi$
$173$	0.473818	+	9.04098i	0.0360237	+	0.687373i	−0.919613	+	0.392825i	$0.871498\pi$
$174$	3.42004	−	2.48480i	0.259273	−	0.188373i
$175$	5.95953	−	11.8103i	0.450498	−	0.892778i
$176$	−2.07604	+	2.58651i	−0.156488	+	0.194966i
$177$	−4.65875	−	1.24831i	−0.350173	−	0.0938286i
$178$	7.39391	+	5.98747i	0.554197	+	0.448780i
$179$	3.84783	−	18.1026i	0.287600	−	1.35305i	−0.562659	−	0.826689i	$-0.690222\pi$
$179$	3.84783	−	18.1026i	0.287600	−	1.35305i	0.850259	−	0.526364i	$-0.176445\pi$
$180$	0.0843019	−	3.70866i	0.00628349	−	0.276427i
$181$	5.42898	−	7.47234i	0.403533	−	0.555415i	−0.558094	−	0.829778i	$-0.688467\pi$
$181$	5.42898	−	7.47234i	0.403533	−	0.555415i	0.961626	+	0.274363i	$0.0884670\pi$
$182$	−9.74342	+	4.30319i	−0.722230	+	0.318974i
$183$	−0.990588	+	0.504730i	−0.0732263	+	0.0373107i
$184$	−1.02003	−	0.918438i	−0.0751975	−	0.0677081i
$185$	1.50987	−	1.16687i	0.111008	−	0.0857897i
$186$	5.61844	−	9.73143i	0.411964	−	0.713543i
$187$	1.53193	+	2.08944i	0.112026	+	0.152795i
$188$	−5.76433	+	5.76433i	−0.420407	+	0.420407i
$189$	−13.3415	+	5.07561i	−0.970451	+	0.369197i
$190$	4.72452	−	5.57054i	0.342753	−	0.404129i
$191$	−25.7369	+	5.47054i	−1.86225	+	0.395834i	−0.994814	−	0.101708i	$-0.967569\pi$
$191$	−25.7369	+	5.47054i	−1.86225	+	0.395834i	−0.867440	+	0.497542i	$0.834236\pi$
$192$	1.08110	+	0.414997i	0.0780220	+	0.0299498i
$193$	11.4323	+	4.38845i	0.822914	+	0.315887i	0.733142	−	0.680075i	$-0.238053\pi$
$193$	11.4323	+	4.38845i	0.822914	+	0.315887i	0.0897720	+	0.995962i	$0.471386\pi$
$194$	−7.64711	+	1.62544i	−0.549031	+	0.116700i
$195$	0.853778	+	10.3895i	0.0611403	+	0.744010i
$196$	−2.88534	+	6.37768i	−0.206096	+	0.455549i
$197$	1.29721	−	1.29721i	0.0924221	−	0.0924221i	−0.659384	−	0.751806i	$-0.729183\pi$
$197$	1.29721	−	1.29721i	0.0924221	−	0.0924221i	0.751806	+	0.659384i	$0.229183\pi$
$198$	−3.21484	+	4.46537i	−0.228469	+	0.317340i
$199$	8.42779	−	14.5974i	0.597430	−	1.03478i	−0.395769	−	0.918350i	$-0.629522\pi$
$199$	8.42779	−	14.5974i	0.597430	−	1.03478i	0.993199	−	0.116429i	$-0.0371448\pi$
$200$	−4.55357	+	2.06518i	−0.321986	+	0.146030i
$201$	−9.50869	−	8.56167i	−0.670692	−	0.603893i
$202$	9.52988	−	4.85572i	0.670520	−	0.341647i
$203$	1.03829	−	9.60246i	0.0728738	−	0.673961i
$204$	0.531720	−	0.731850i	0.0372279	−	0.0512397i
$205$	−20.0656	−	0.456114i	−1.40144	−	0.0318564i
$206$	−3.97361	+	18.6944i	−0.276855	+	1.30250i
$207$	−1.76964	−	1.43303i	−0.122999	−	0.0996023i
$208$	3.88866	+	1.04196i	0.269630	+	0.0722472i
$209$	−10.4526	+	2.84930i	−0.723018	+	0.197090i
$210$	4.97168	+	4.71357i	0.343078	+	0.325267i
$211$	−19.6605	+	14.2842i	−1.35348	+	0.983362i	−0.354652	+	0.934998i	$0.615401\pi$
$211$	−19.6605	+	14.2842i	−1.35348	+	0.983362i	−0.998830	+	0.0483639i	$0.984599\pi$
$212$	0.252524	+	4.81845i	0.0173434	+	0.330933i
$213$	−17.5502	−	0.919768i	−1.20252	−	0.0630214i
$214$	−2.61653	−	5.87682i	−0.178862	−	0.401731i
$215$	−9.28215	−	19.2887i	−0.633037	−	1.31548i
$216$	5.13114	+	1.66721i	0.349130	+	0.113439i
$217$	−7.86041	−	24.4402i	−0.533600	−	1.65911i
$218$	−15.2913	−	2.42190i	−1.03566	−	0.164032i
$219$	7.31696	−	4.22445i	0.494434	−	0.285462i
$220$	7.30231	+	1.29471i	0.492322	+	0.0872895i
$221$	1.57244	−	2.72355i	0.105774	−	0.183206i
$222$	0.354150	+	0.922592i	0.0237690	+	0.0619203i
$223$	−10.1342	−	5.16363i	−0.678636	−	0.345782i	0.0804628	−	0.996758i	$-0.474360\pi$
$223$	−10.1342	−	5.16363i	−0.678636	−	0.345782i	−0.759099	+	0.650975i	$0.774360\pi$
$224$	2.36096	−	1.19409i	0.157748	−	0.0797837i
$225$	−7.36467	+	3.81678i	−0.490978	+	0.254452i
$226$	−0.659100	+	6.27092i	−0.0438427	+	0.417135i
$227$	−0.490100	+	9.35166i	−0.0325290	+	0.620691i	0.932918	+	0.360090i	$0.117254\pi$
$227$	−0.490100	+	9.35166i	−0.0325290	+	0.620691i	−0.965447	+	0.260601i	$0.916079\pi$
$228$	2.06023	+	3.17247i	0.136442	+	0.210102i
$229$	−13.8504	−	6.16660i	−0.915261	−	0.407500i	−0.105607	−	0.994408i	$-0.533678\pi$
$229$	−13.8504	−	6.16660i	−0.915261	−	0.407500i	−0.809654	+	0.586908i	$0.800345\pi$
$230$	−0.706180	+	2.98685i	−0.0465641	+	0.196947i
$231$	−2.12602	−	9.93669i	−0.139882	−	0.653786i
$232$	−2.58132	+	2.58132i	−0.169472	+	0.169472i
$233$	2.24380	+	5.84529i	0.146996	+	0.382938i	0.987233	−	0.159281i	$-0.0509176\pi$
$233$	2.24380	+	5.84529i	0.146996	+	0.382938i	−0.840237	+	0.542219i	$0.817584\pi$
$234$	6.53288	+	1.38861i	0.427068	+	0.0907760i
$235$	17.4955	+	5.11677i	1.14128	+	0.333782i
$236$	4.14213	+	0.435356i	0.269630	+	0.0283392i
$237$	0.983253	+	6.20802i	0.0638692	+	0.403254i
$238$	−0.423665	−	2.02291i	−0.0274622	−	0.131126i
$239$	0.530715	−	0.172440i	0.0343291	−	0.0111542i	−0.291802	−	0.956479i	$-0.594255\pi$
$239$	0.530715	−	0.172440i	0.0343291	−	0.0111542i	0.326131	+	0.945325i	$0.394255\pi$
$240$	−0.346848	−	2.56608i	−0.0223889	−	0.165639i
$241$	0.318397	+	0.183827i	0.0205098	+	0.0118413i	0.510220	−	0.860044i	$-0.329564\pi$
$241$	0.318397	+	0.183827i	0.0205098	+	0.0118413i	−0.489710	+	0.871885i	$0.662897\pi$
$242$	−7.84522	−	7.71055i	−0.504310	−	0.495653i
$243$	14.2127	+	3.80827i	0.911742	+	0.244301i
$244$	0.776701	−	0.564306i	0.0497232	−	0.0361260i
$245$	15.6073	−	1.18866i	0.997112	−	0.0759405i
$246$	3.21202	−	9.88558i	0.204791	−	0.630281i
$247$	8.27596	+	10.2200i	0.526587	+	0.650281i
$248$	−3.47744	+	9.05903i	−0.220817	+	0.575249i
$249$	−1.62983	+	1.46750i	−0.103286	+	0.0929992i
$250$	8.93998	+	6.71392i	0.565414	+	0.424626i
$251$	3.69345	+	5.08360i	0.233129	+	0.320874i	0.909514	−	0.415674i	$-0.136454\pi$
$251$	3.69345	+	5.08360i	0.233129	+	0.320874i	−0.676385	+	0.736548i	$0.736454\pi$
$252$	3.80777	−	2.18326i	0.239867	−	0.137533i
$253$	3.36984	−	3.06073i	0.211860	−	0.192426i
$254$	1.58654	−	0.915987i	0.0995481	−	0.0574741i
$255$	−2.00638	−	0.257100i	−0.125644	−	0.0161002i
$256$	−0.978148	−	0.207912i	−0.0611342	−	0.0129945i
$257$	24.5951	+	15.9722i	1.53420	+	0.996319i	0.987255	+	0.159149i	$0.0508751\pi$
$257$	24.5951	+	15.9722i	1.53420	+	0.996319i	0.546943	+	0.837170i	$0.315792\pi$
$258$	10.9493	−	1.73419i	0.681672	−	0.107966i
$259$	2.10544	+	0.815431i	0.130825	+	0.0506684i
$260$	−2.13170	−	8.74602i	−0.132202	−	0.542405i
$261$	−4.05240	+	4.50065i	−0.250837	+	0.278583i
$262$	−3.46467	+	4.27852i	−0.214048	+	0.264328i
$263$	29.2847	−	7.84682i	1.80577	−	0.483856i	0.810919	−	0.585158i	$-0.198968\pi$
$263$	29.2847	−	7.84682i	1.80577	−	0.483856i	0.994856	+	0.101302i	$0.0323009\pi$
$264$	−1.72882	+	3.42962i	−0.106402	+	0.211078i
$265$	9.17976	−	5.66905i	0.563908	−	0.348247i
$266$	8.53201	+	1.37750i	0.523131	+	0.0844597i
$267$	9.81677	+	5.00189i	0.600777	+	0.306111i
$268$	9.26665	+	6.01783i	0.566051	+	0.367598i
$269$	−22.8100	+	10.1557i	−1.39075	+	0.619203i	−0.959159	−	0.282866i	$-0.908715\pi$
$269$	−22.8100	+	10.1557i	−1.39075	+	0.619203i	−0.431592	+	0.902069i	$0.642048\pi$
$270$	−2.23944	−	11.8544i	−0.136288	−	0.721434i
$271$	−0.357428	−	1.68156i	−0.0217122	−	0.102148i	0.965957	−	0.258702i	$-0.0832947\pi$
$271$	−0.357428	−	1.68156i	−0.0217122	−	0.102148i	−0.987669	+	0.156554i	$0.949961\pi$
$272$	−0.354646	+	0.696032i	−0.0215036	+	0.0422031i
$273$	−10.0004	+	7.22017i	−0.605255	+	0.436985i
$274$		−	4.44074i		−	0.268275i
$275$	−5.30132	−	15.7129i	−0.319682	−	0.947525i
$276$	−1.37653	−	0.794740i	−0.0828573	−	0.0478377i
$277$	−11.8265	−	9.57691i	−0.710585	−	0.575421i	0.204410	−	0.978885i	$-0.434472\pi$
$277$	−11.8265	−	9.57691i	−0.710585	−	0.575421i	−0.914995	+	0.403465i	$0.867806\pi$
$278$	−0.901591	−	17.2034i	−0.0540738	−	1.03179i
$279$	−4.97458	+	15.3102i	−0.297820	+	0.916596i
$280$	−4.87715	−	3.34865i	−0.291465	−	0.200120i
$281$	14.6363	+	10.6339i	0.873130	+	0.634366i	0.931425	−	0.363933i	$-0.118566\pi$
$281$	14.6363	+	10.6339i	0.873130	+	0.634366i	−0.0582952	+	0.998299i	$0.518566\pi$
$282$	−5.14149	+	7.91720i	−0.306171	+	0.471462i
$283$	1.91415	−	1.24307i	0.113785	−	0.0738926i	−0.486492	−	0.873685i	$-0.661724\pi$
$283$	1.91415	−	1.24307i	0.113785	−	0.0738926i	0.600277	+	0.799792i	$0.295057\pi$
$284$	15.0930	−	1.58634i	0.895606	−	0.0941320i
$285$	4.01034	−	7.44733i	0.237552	−	0.441142i
$286$	−4.73100	+	12.4859i	−0.279750	+	0.738310i
$287$	−11.8125	−	20.6019i	−0.697271	−	1.21609i
$288$	−1.63857	−	0.259523i	−0.0965534	−	0.0152926i
$289$	−12.1800	−	10.9669i	−0.716469	−	0.645111i
$290$	7.83467	+	2.29134i	0.460068	+	0.134552i
$291$	−8.27064	+	3.68233i	−0.484834	+	0.215862i
$292$	−5.67005	+	4.59151i	−0.331814	+	0.268698i
$293$	1.66076	+	3.25943i	0.0970227	+	0.190418i	0.934416	−	0.356182i	$-0.115922\pi$
$293$	1.66076	+	3.25943i	0.0970227	+	0.190418i	−0.837394	+	0.546600i	$0.815922\pi$
$294$	−1.73274	+	7.91878i	−0.101055	+	0.461833i
$295$	−3.59366	−	8.59183i	−0.209231	−	0.500236i
$296$	−0.426689	−	0.739048i	−0.0248008	−	0.0429563i
$297$	−7.20726	+	16.3782i	−0.418208	+	0.950360i
$298$	0.884189	−	0.236918i	0.0512197	−	0.0137243i
$299$	−5.04807	−	2.24755i	−0.291938	−	0.129979i
$300$	−4.66068	+	3.43560i	−0.269084	+	0.198355i
$301$	13.8580	−	21.2004i	0.798760	−	1.22197i
$302$	−12.4368	+	1.96979i	−0.715657	+	0.113349i
$303$	9.62554	−	7.79461i	0.552973	−	0.447788i
$304$	−2.18575	−	2.42752i	−0.125362	−	0.139228i
$305$	−1.94080	−	0.917503i	−0.111130	−	0.0525361i
$306$	−0.527115	+	1.18392i	−0.0301332	+	0.0676802i
$307$	20.0863	+	20.0863i	1.14639	+	1.14639i	0.987258	+	0.159127i	$0.0508679\pi$
$307$	20.0863	+	20.0863i	1.14639	+	1.14639i	0.159127	+	0.987258i	$0.449132\pi$
$308$	3.15563	+	8.18792i	0.179809	+	0.466550i
$309$			22.1321i			1.25905i
$310$	21.5022	−	2.90639i	1.22124	−	0.165072i
$311$	2.83541	−	13.3395i	0.160781	−	0.756416i	−0.821680	−	0.569949i	$-0.806963\pi$
$311$	2.83541	−	13.3395i	0.160781	−	0.756416i	0.982461	−	0.186467i	$-0.0597037\pi$
$312$	4.65561	+	0.243990i	0.263572	+	0.0138132i
$313$	12.3779	+	15.2855i	0.699641	+	0.863985i	0.995838	−	0.0911420i	$-0.0290517\pi$
$313$	12.3779	+	15.2855i	0.699641	+	0.863985i	−0.296197	+	0.955127i	$0.595718\pi$
$314$	12.2410	+	8.89360i	0.690799	+	0.501895i
$315$	−8.37080	−	5.12430i	−0.471641	−	0.288721i
$316$	−1.67726	−	5.16206i	−0.0943530	−	0.290389i
$317$	1.67929	−	0.644618i	0.0943182	−	0.0362053i	−0.310751	−	0.950491i	$-0.600581\pi$
$317$	1.67929	−	0.644618i	0.0943182	−	0.0362053i	0.405070	+	0.914286i	$0.367247\pi$
$318$	1.44616	+	5.39713i	0.0810964	+	0.302656i
$319$	−7.66014	−	9.37621i	−0.428886	−	0.524967i
$320$	0.642476	+	2.14178i	0.0359155	+	0.119729i
$321$	−4.37872	−	6.02679i	−0.244396	−	0.336383i
$322$	−3.45712	+	1.11187i	−0.192658	+	0.0619621i
$323$	−2.27363	+	1.15847i	−0.126508	+	0.0644591i
$324$	1.26382	+	0.132833i	0.0702122	+	0.00737960i
$325$	−14.8655	+	13.5720i	−0.824592	+	0.752841i
$326$	10.8227	+	12.0199i	0.599417	+	0.665720i
$327$	−17.9037	+	0.938296i	−0.990080	+	0.0518879i
$328$	−1.40415	+	8.86543i	−0.0775310	+	0.489511i
$329$	5.51995	+	20.8498i	0.304324	+	1.14949i
$330$	8.58315	−	0.291607i	0.472487	−	0.0160524i
$331$	17.1442	+	29.6946i	0.942330	+	1.63216i	0.761012	+	0.648738i	$0.224703\pi$
$331$	17.1442	+	29.6946i	0.942330	+	1.63216i	0.181318	+	0.983425i	$0.441964\pi$
$332$	1.19186	−	1.47182i	0.0654116	−	0.0807766i
$333$	−0.771071	−	1.18735i	−0.0422544	−	0.0650661i
$334$	−8.86947	+	1.88526i	−0.485316	+	0.103157i
$335$	1.85342	−	24.6372i	0.101263	−	1.34607i
$336$	2.38680	−	1.92101i	0.130211	−	0.104799i
$337$	7.94253	+	15.5881i	0.432657	+	0.849137i	0.999677	+	0.0254328i	$0.00809637\pi$
$337$	7.94253	+	15.5881i	0.432657	+	0.849137i	−0.567020	+	0.823704i	$0.691904\pi$
$338$	3.20299	−	0.167862i	0.174220	−	0.00913046i
$339$	0.763251	+	7.26185i	0.0414541	+	0.394409i
$340$	1.74599	−	0.0517536i	0.0946898	−	0.00280674i
$341$	−28.7382	−	14.4865i	−1.55626	−	0.784489i
$342$	−3.83194	−	3.83194i	−0.207208	−	0.207208i
$343$	10.7511	+	15.0802i	0.580506	+	0.814256i
$344$	−9.10449	+	2.95823i	−0.490881	+	0.159497i
$345$	−0.0807697	+	3.55327i	−0.00434849	+	0.191301i
$346$	−3.68234	−	8.27068i	−0.197964	−	0.444634i
$347$	−6.62194	+	17.2507i	−0.355484	+	0.926068i	0.632919	+	0.774218i	$0.281856\pi$
$347$	−6.62194	+	17.2507i	−0.355484	+	0.926068i	−0.988404	+	0.151850i	$0.951477\pi$
$348$	−2.30241	+	3.54540i	−0.123422	+	0.190053i
$349$	0.259125	+	0.797503i	0.0138706	+	0.0426894i	0.957752	−	0.287594i	$-0.0928555\pi$
$349$	0.259125	+	0.797503i	0.0138706	+	0.0426894i	−0.943882	+	0.330284i	$0.892856\pi$
$350$	−1.33125	+	13.1616i	−0.0711583	+	0.703517i
$351$	21.7202			1.15934
$352$	1.01123	−	3.15870i	0.0538987	−	0.168360i
$353$	7.10656	+	26.5221i	0.378244	+	1.41163i	0.848546	+	0.529121i	$0.177478\pi$
$353$	7.10656	+	26.5221i	0.378244	+	1.41163i	−0.470302	+	0.882505i	$0.655855\pi$
$354$	4.79667	−	0.504151i	0.254940	−	0.0267953i
$355$	−19.3174	−	27.9001i	−1.02526	−	1.48079i
$356$	−9.04853	−	2.94005i	−0.479571	−	0.155822i
$357$	−0.966939	−	2.18937i	−0.0511758	−	0.115874i
$358$	2.89514	+	18.2792i	0.153013	+	0.966085i
$359$	0.958074	+	4.50738i	0.0505652	+	0.237891i	0.996171	−	0.0874234i	$-0.0278633\pi$
$359$	0.958074	+	4.50738i	0.0505652	+	0.237891i	−0.945606	+	0.325314i	$0.894530\pi$
$360$	1.25036	+	3.49254i	0.0658998	+	0.184073i
$361$	0.870681	+	8.28398i	0.0458253	+	0.435999i
$362$	−2.39054	+	8.92161i	−0.125644	+	0.468909i
$363$	−10.7428	−	6.84499i	−0.563852	−	0.359269i
$364$	7.55414	−	7.50911i	0.395944	−	0.393584i
$365$	15.0939	+	6.19114i	0.790052	+	0.324059i
$366$	0.743914	−	0.826201i	0.0388850	−	0.0431862i
$367$	0.878768	−	16.7679i	0.0458713	−	0.875277i	−0.874691	−	0.484681i	$-0.838936\pi$
$367$	0.878768	−	16.7679i	0.0458713	−	0.875277i	0.920562	−	0.390596i	$-0.127731\pi$
$368$	1.28142	+	0.491890i	0.0667985	+	0.0256415i
$369$	−1.55653	+	14.8094i	−0.0810298	+	0.770947i
$370$	−0.991415	+	1.63045i	−0.0515412	+	0.0847632i
$371$	11.3571	+	5.82958i	0.589633	+	0.302657i
$372$	−1.75784	+	11.0985i	−0.0911396	+	0.575433i
$373$	−1.16317	+	4.34101i	−0.0602267	+	0.224769i	−0.989479	−	0.144677i	$-0.953786\pi$
$373$	−1.16317	+	4.34101i	−0.0602267	+	0.224769i	0.929252	+	0.369446i	$0.120452\pi$
$374$	−2.17897	−	1.40167i	−0.112672	−	0.0724785i
$375$	11.7429	+	5.45251i	0.606402	+	0.281566i
$376$	3.31572	−	7.44722i	0.170995	−	0.384061i
$377$	−6.67207	+	13.0947i	−0.343629	+	0.674410i
$378$	10.6364	−	9.51966i	0.547079	−	0.489638i
$379$	17.9416	−	24.6946i	0.921601	−	1.26847i	−0.0414464	−	0.999141i	$-0.513197\pi$
$379$	17.9416	−	24.6946i	0.921601	−	1.26847i	0.963047	−	0.269334i	$-0.0868034\pi$
$380$	−2.41442	+	6.89366i	−0.123857	+	0.353637i
$381$	1.57655	−	1.41954i	0.0807693	−	0.0727250i
$382$	22.0670	−	14.3305i	1.12904	−	0.733210i
$383$	25.9361	−	9.95595i	1.32527	−	0.508725i	0.410195	−	0.911998i	$-0.365461\pi$
$383$	25.9361	−	9.95595i	1.32527	−	0.508725i	0.915080	+	0.403273i	$0.132127\pi$
$384$	−1.15802			−0.0590950
$385$	12.6714	−	14.9811i	0.645797	−	0.763509i
$386$	−12.2456			−0.623287
$387$	−14.8267	+	5.69144i	−0.753684	+	0.289312i
$388$	6.55669	−	4.25796i	0.332865	−	0.216165i
$389$	−7.92521	+	7.13589i	−0.401824	+	0.361804i	−0.845125	−	0.534569i	$-0.820474\pi$
$389$	−7.92521	+	7.13589i	−0.401824	+	0.361804i	0.443301	+	0.896373i	$0.353807\pi$
$390$	−4.52035	−	9.39350i	−0.228897	−	0.475658i
$391$	0.630240	−	0.867451i	0.0318726	−	0.0438689i
$392$	0.408139	−	6.98809i	0.0206142	−	0.352952i
$393$	−2.89437	+	5.68051i	−0.146001	+	0.286544i
$394$	−0.746169	+	1.67592i	−0.0375915	+	0.0844318i
$395$	−8.32393	+	8.83247i	−0.418823	+	0.444410i
$396$	1.40107	−	5.32088i	0.0704063	−	0.267384i
$397$	−1.93655	+	7.22731i	−0.0971928	+	0.362728i	−0.997343	−	0.0728516i	$-0.976790\pi$
$397$	−1.93655	+	7.22731i	−0.0971928	+	0.362728i	0.900150	+	0.435580i	$0.143457\pi$
$398$	−2.63679	+	16.6481i	−0.132171	+	0.834492i
$399$	9.99599	−	0.493908i	0.500425	−	0.0247263i
$400$	3.51104	−	3.55986i	0.175552	−	0.177993i
$401$	−2.19472	+	20.8813i	−0.109599	+	1.04276i	0.792098	+	0.610394i	$0.208989\pi$
$401$	−2.19472	+	20.8813i	−0.109599	+	1.04276i	−0.901697	+	0.432369i	$0.857678\pi$
$402$	11.9454	+	4.58539i	0.595780	+	0.228699i
$403$	−2.04450	+	39.0113i	−0.101844	+	1.94329i
$404$	−7.15677	+	7.94840i	−0.356063	+	0.395448i
$405$	−1.09647	−	2.62148i	−0.0544842	−	0.130263i
$406$	2.47189	+	9.33676i	0.122678	+	0.463376i
$407$	2.58063	−	1.16238i	0.127917	−	0.0576172i
$408$	−0.234132	+	0.873792i	−0.0115913	+	0.0432592i
$409$	1.53483	+	14.6029i	0.0758925	+	0.722068i	0.964622	+	0.263637i	$0.0849220\pi$
$409$	1.53483	+	14.6029i	0.0758925	+	0.722068i	−0.888730	+	0.458432i	$0.848411\pi$
$410$	18.8963	−	6.76506i	0.933223	−	0.334102i
$411$	−1.06918	−	5.03009i	−0.0527387	−	0.248116i
$412$	−2.98978	−	18.8767i	−0.147296	−	0.929989i
$413$	6.50367	−	8.89550i	0.320025	−	0.437719i
$414$	2.16565	+	0.703664i	0.106436	+	0.0345832i
$415$	−4.16657	−	0.757357i	−0.204529	−	0.0371772i
$416$	−4.00379	+	0.420815i	−0.196302	+	0.0206321i
$417$	−5.16323	−	19.2694i	−0.252845	−	0.943629i
$418$	8.73720	−	6.40591i	0.427350	−	0.313323i
$419$	2.10939			0.103051			0.0515253	−	0.998672i	$-0.483592\pi$
$419$	2.10939			0.103051			0.0515253	+	0.998672i	$0.483592\pi$
$420$	−6.33066	−	2.61881i	−0.308904	−	0.127785i
$421$	−0.149358	−	0.459677i	−0.00727928	−	0.0224033i	0.947351	−	0.320197i	$-0.103749\pi$
$421$	−0.149358	−	0.459677i	−0.00727928	−	0.0224033i	−0.954630	+	0.297794i	$0.903749\pi$
$422$	13.2356	−	20.3811i	0.644301	−	0.992136i
$423$	4.84660	−	12.6258i	0.235650	−	0.613888i
$424$	−1.96253	−	4.40791i	−0.0953089	−	0.214067i
$425$	−1.97625	−	3.36902i	−0.0958622	−	0.163422i
$426$	16.7142	−	5.43076i	0.809803	−	0.263121i
$427$	−0.257956	−	2.52693i	−0.0124834	−	0.122287i
$428$	4.54881	+	4.54881i	0.219875	+	0.219875i
$429$	−2.35268	+	15.2821i	−0.113588	+	0.737825i
$430$	15.5781	+	14.6812i	0.751243	+	0.707989i
$431$	−2.41087	−	22.9379i	−0.116128	−	1.10488i	−0.885037	−	0.465521i	$-0.845867\pi$
$431$	−2.41087	−	22.9379i	−0.116128	−	1.10488i	0.768909	−	0.639358i	$-0.220800\pi$
$432$	−5.38781	+	0.282363i	−0.259221	+	0.0135852i
$433$	−17.3698	−	34.0901i	−0.834739	−	1.63827i	−0.767959	−	0.640499i	$-0.778727\pi$
$433$	−17.3698	−	34.0901i	−0.834739	−	1.63827i	−0.0667801	−	0.997768i	$-0.521273\pi$
$434$	16.0969	+	20.0000i	0.772677	+	0.960030i
$435$	9.42612	+	0.709113i	0.451948	+	0.0339994i
$436$	15.1436	−	3.21886i	0.725245	−	0.154156i
$437$	2.44196	+	3.76028i	0.116815	+	0.179879i
$438$	−5.31706	+	6.56602i	−0.254059	+	0.313737i
$439$	17.0087	+	29.4599i	0.811781	+	1.40605i	0.911616	+	0.411042i	$0.134835\pi$
$439$	17.0087	+	29.4599i	0.811781	+	1.40605i	−0.0998351	+	0.995004i	$0.531832\pi$
$440$	−7.28128	+	1.40820i	−0.347121	+	0.0671331i
$441$	0.0694314	−	11.6127i	0.00330626	−	0.552987i
$442$	−0.491968	+	3.10617i	−0.0234006	+	0.147745i
$443$	−6.14808	+	0.322207i	−0.292104	+	0.0153085i	−0.197825	−	0.980237i	$-0.563388\pi$
$443$	−6.14808	+	0.322207i	−0.292104	+	0.0153085i	−0.0942788	+	0.995546i	$0.530055\pi$
$444$	−0.661255	−	0.734398i	−0.0313818	−	0.0348530i
$445$	3.94915	+	20.9046i	0.187208	+	0.990974i
$446$	11.3116	+	1.18889i	0.535618	+	0.0562958i
$447$	0.944492	−	0.481243i	0.0446729	−	0.0227620i
$448$	−1.77622	+	1.96088i	−0.0839186	+	0.0926426i
$449$	−13.5585	−	18.6616i	−0.639863	−	0.880696i	0.358745	−	0.933436i	$-0.383205\pi$
$449$	−13.5585	−	18.6616i	−0.639863	−	0.880696i	−0.998608	+	0.0527395i	$0.983205\pi$
$450$	5.50771	−	6.20253i	0.259636	−	0.292390i
$451$	−28.7885	−	7.58045i	−1.35560	−	0.356949i
$452$	−1.63197	−	6.09061i	−0.0767616	−	0.286478i
$453$	−13.6131	+	5.22557i	−0.639598	+	0.245519i
$454$	−2.89379	−	8.90616i	−0.135812	−	0.417987i
$455$	−22.8395	−	6.75387i	−1.07073	−	0.316626i
$456$	−3.06030	−	2.22344i	−0.143312	−	0.104122i
$457$	−14.2015	−	17.5374i	−0.664319	−	0.820366i	0.327921	−	0.944705i	$-0.393652\pi$
$457$	−14.2015	−	17.5374i	−0.664319	−	0.820366i	−0.992240	+	0.124340i	$0.960319\pi$
$458$	15.1404	+	0.793474i	0.707464	+	0.0370766i
$459$	−0.876264	+	4.12250i	−0.0409005	+	0.192422i
$460$	−0.411114	−	3.04153i	−0.0191683	−	0.141812i
$461$			11.1029i			0.517113i	0.965996	+	0.258557i	$0.0832469\pi$
$461$			11.1029i			0.517113i	−0.965996	+	0.258557i	$0.916753\pi$
$462$	5.54580	+	8.51480i	0.258014	+	0.396144i
$463$	−13.0893	−	13.0893i	−0.608314	−	0.608314i	0.334192	−	0.942505i	$-0.391537\pi$
$463$	−13.0893	−	13.0893i	−0.608314	−	0.608314i	−0.942505	+	0.334192i	$0.891537\pi$
$464$	1.48481	−	3.33494i	0.0689306	−	0.154821i
$465$	23.6561	−	8.46911i	1.09703	−	0.392746i
$466$	−4.18953	−	4.65295i	−0.194076	−	0.215544i
$467$	23.2013	−	18.7880i	1.07363	−	0.869406i	0.0817560	−	0.996652i	$-0.473947\pi$
$467$	23.2013	−	18.7880i	1.07363	−	0.869406i	0.991871	+	0.127246i	$0.0406138\pi$
$468$	−6.59660	+	1.04480i	−0.304928	+	0.0482958i
$469$	26.0868	−	13.1938i	1.20458	−	0.609233i
$470$	−18.1672	+	1.49292i	−0.837990	+	0.0688633i
$471$	16.0068	+	7.12670i	0.737555	+	0.328381i
$472$	−4.02303	+	1.07797i	−0.185175	+	0.0496175i
$473$	−6.73559	−	31.0275i	−0.309703	−	1.42664i
$474$	−3.14270	−	5.44332i	−0.144349	−	0.250020i
$475$	16.1137	−	2.66635i	0.739346	−	0.122340i
$476$	1.12047	+	1.73672i	0.0513567	+	0.0796023i
$477$	−3.63407	−	7.13227i	−0.166393	−	0.326564i
$478$	−0.433668	+	0.351178i	−0.0198355	+	0.0160625i
$479$	5.76706	−	2.56766i	0.263504	−	0.117319i	−0.270733	−	0.962655i	$-0.587266\pi$
$479$	5.76706	−	2.56766i	0.263504	−	0.117319i	0.534236	+	0.845335i	$0.320599\pi$
$480$	1.24341	+	2.27134i	0.0567536	+	0.103672i
$481$	−2.55312	−	2.29884i	−0.116412	−	0.104818i
$482$	−0.363127	−	0.0575137i	−0.0165400	−	0.00261968i
$483$	−3.64822	+	2.09179i	−0.166000	+	0.0951796i
$484$	10.0874	+	4.38694i	0.458516	+	0.199406i
$485$	−15.3917	−	8.28834i	−0.698902	−	0.376354i
$486$	−14.6334	+	1.53803i	−0.663785	+	0.0697666i
$487$	−11.9181	+	7.73971i	−0.540061	+	0.350720i	−0.785667	−	0.618650i	$-0.787680\pi$
$487$	−11.9181	+	7.73971i	−0.540061	+	0.350720i	0.245606	+	0.969370i	$0.421013\pi$
$488$	−0.522883	+	0.805170i	−0.0236698	+	0.0364483i
$489$	15.1531	+	11.0093i	0.685245	+	0.497860i
$490$	−14.1447	+	6.70286i	−0.638991	+	0.302804i
$491$	−5.79078	+	17.8222i	−0.261334	+	0.804304i	0.731181	+	0.682183i	$0.238969\pi$
$491$	−5.79078	+	17.8222i	−0.261334	+	0.804304i	−0.992515	+	0.122120i	$0.961031\pi$
$492$	0.543996	+	10.3801i	0.0245252	+	0.467969i
$493$	−2.21620	−	1.79464i	−0.0998125	−	0.0808266i
$494$	−11.3888	−	6.57532i	−0.512406	−	0.295837i
$495$	−11.9407	+	2.96518i	−0.536697	+	0.133275i
$496$		−	9.70354i		−	0.435702i
$497$	16.4410	−	36.6320i	0.737480	−	1.64317i
$498$	0.995669	−	1.95411i	0.0446170	−	0.0875658i
$499$	5.99711	+	28.2142i	0.268468	+	1.26304i	0.881198	+	0.472748i	$0.156738\pi$
$499$	5.99711	+	28.2142i	0.268468	+	1.26304i	−0.612730	+	0.790292i	$0.709929\pi$
$500$	−10.7522	−	3.06418i	−0.480855	−	0.137034i
$501$	−9.59266	+	4.27093i	−0.428569	+	0.190811i
$502$	−5.26993	−	3.42233i	−0.235209	−	0.152746i
$503$	−8.05513	−	4.10429i	−0.359160	−	0.183001i	0.265094	−	0.964223i	$-0.414597\pi$
$503$	−8.05513	−	4.10429i	−0.359160	−	0.183001i	−0.624254	+	0.781221i	$0.714597\pi$
$504$	−2.77245	+	3.40283i	−0.123495	+	0.151574i
$505$	23.2745	+	5.50279i	1.03570	+	0.244871i
$506$	−2.04914	+	4.06508i	−0.0910956	+	0.180715i
$507$	3.58766	−	0.961309i	0.159333	−	0.0426932i
$508$	−1.15290	+	1.42371i	−0.0511516	+	0.0631670i
$509$	2.34365	−	2.60288i	0.103880	−	0.115371i	−0.688962	−	0.724797i	$-0.741934\pi$
$509$	2.34365	−	2.60288i	0.103880	−	0.115371i	0.792843	+	0.609426i	$0.208600\pi$
$510$	1.96525	−	0.478998i	0.0870228	−	0.0212104i
$511$	2.96270	+	19.0746i	0.131062	+	0.843813i
$512$	0.987688	−	0.156434i	0.0436501	−	0.00691349i
$513$	−14.7805	−	9.59858i	−0.652575	−	0.423787i
$514$	−28.6854	−	6.09727i	−1.26526	−	0.268939i
$515$	−33.8145	+	26.1328i	−1.49005	+	1.15155i
$516$	−9.60054	+	5.54288i	−0.422640	+	0.244012i
$517$	23.4731	+	13.4171i	1.03235	+	0.590082i
$518$	−2.25782	−	0.00674958i	−0.0992028	−	0.000296560i
$519$	−6.16234	−	8.48173i	−0.270497	−	0.372307i
$520$	5.12440	+	7.40118i	0.224720	+	0.324563i
$521$	−12.5105	+	11.2645i	−0.548096	+	0.493508i	−0.896019	−	0.444015i	$-0.853554\pi$
$521$	−12.5105	+	11.2645i	−0.548096	+	0.493508i	0.347923	+	0.937523i	$0.386887\pi$
$522$	2.17035	−	5.65396i	0.0949938	−	0.247467i
$523$	−12.5297	−	15.4729i	−0.547884	−	0.676581i	0.425712	−	0.904859i	$-0.360024\pi$
$523$	−12.5297	−	15.4729i	−0.547884	−	0.676581i	−0.973596	+	0.228278i	$0.926690\pi$
$524$	1.70127	−	5.23597i	0.0743203	−	0.228734i
$525$	1.66094	+	15.2289i	0.0724893	+	0.664642i
$526$	−24.5276	+	17.8204i	−1.06945	+	0.777004i
$527$	−7.32187	−	1.96189i	−0.318946	−	0.0854613i
$528$	0.384927	−	3.82138i	0.0167518	−	0.166304i
$529$	18.2870	+	10.5580i	0.795087	+	0.459044i
$530$	−6.53844	+	8.58225i	−0.284012	+	0.372789i
$531$	−6.57143	+	2.13519i	−0.285176	+	0.0926592i
$532$	−8.45897	+	1.77160i	−0.366743	+	0.0768085i
$533$	5.65286	+	35.6908i	0.244853	+	1.54594i
$534$	−10.9573	−	1.15165i	−0.474167	−	0.0498370i
$535$	4.03780	−	13.8063i	0.174569	−	0.596896i
$536$	−10.8078	−	2.29726i	−0.466824	−	0.0992266i
$537$	7.68037	+	20.0080i	0.331432	+	0.863411i
$538$	17.6555	−	17.6555i	0.761184	−	0.761184i
$539$	22.9245	+	3.66968i	0.987429	+	0.158064i
$540$	6.33892	+	10.2645i	0.272784	+	0.441712i
$541$	9.93732	+	4.42438i	0.427239	+	0.190219i	0.609080	−	0.793109i	$-0.291539\pi$
$541$	9.93732	+	4.42438i	0.427239	+	0.190219i	−0.181841	+	0.983328i	$0.558206\pi$
$542$	0.936306	+	1.44178i	0.0402178	+	0.0619300i
$543$	−0.559777	+	10.6812i	−0.0240223	+	0.458374i
$544$	0.0816550	−	0.776896i	0.00350093	−	0.0333091i
$545$	−22.5737	−	26.2463i	−0.966951	−	1.12427i
$546$	6.74874	−	10.3245i	0.288820	−	0.441846i
$547$	−4.21940	−	2.14989i	−0.180409	−	0.0919227i	0.361454	−	0.932390i	$-0.382281\pi$
$547$	−4.21940	−	2.14989i	−0.180409	−	0.0919227i	−0.541862	+	0.840467i	$0.682281\pi$
$548$	1.59142	+	4.14579i	0.0679820	+	0.177099i
$549$	−0.796361	+	1.37934i	−0.0339879	+	0.0588687i
$550$	10.5802	+	12.7695i	0.451142	+	0.544491i
$551$	10.3271	−	5.96235i	0.439949	−	0.254005i
$552$	1.56991	+	0.248649i	0.0668198	+	0.0105832i
$553$	−14.0376	−	3.02767i	−0.596939	−	0.128750i
$554$	14.4730	+	4.70258i	0.614901	+	0.199793i
$555$	−0.730433	+	2.08553i	−0.0310051	+	0.0885260i
$556$	7.00685	+	15.7376i	0.297157	+	0.667425i
$557$	7.77866	+	0.407662i	0.329592	+	0.0172732i	0.216415	−	0.976302i	$-0.430564\pi$
$557$	7.77866	+	0.407662i	0.329592	+	0.0172732i	0.113178	+	0.993575i	$0.463897\pi$
$558$	−0.842508	−	16.0760i	−0.0356662	−	0.680552i
$559$	−31.1791	+	22.6529i	−1.31873	+	0.958117i
$560$	5.75326	+	1.37842i	0.243119	+	0.0582487i
$561$	−2.80562	−	1.06307i	−0.118454	−	0.0448827i
$562$	−17.4750	−	4.68242i	−0.737140	−	0.197516i
$563$	9.97235	+	8.07545i	0.420285	+	0.340340i	0.816019	−	0.578025i	$-0.196177\pi$
$563$	9.97235	+	8.07545i	0.420285	+	0.340340i	−0.395734	+	0.918365i	$0.629510\pi$
$564$	1.96272	−	9.23388i	0.0826455	−	0.388817i
$565$	−10.1938	+	9.74067i	−0.428856	+	0.409793i
$566$	−1.34154	+	1.84647i	−0.0563892	+	0.0776130i
$567$	1.98436	−	2.71413i	0.0833352	−	0.113983i
$568$	−13.5221	+	6.88983i	−0.567373	+	0.289091i
$569$	15.1319	+	13.6248i	0.634361	+	0.571182i	0.922304	−	0.386466i	$-0.126304\pi$
$569$	15.1319	+	13.6248i	0.634361	+	0.571182i	−0.287942	+	0.957648i	$0.592971\pi$
$570$	−1.07509	+	8.38986i	−0.0450305	+	0.351412i
$571$	−0.776748	+	1.34537i	−0.0325059	+	0.0563019i	−0.881821	−	0.471585i	$-0.843682\pi$
$571$	−0.776748	+	1.34537i	−0.0325059	+	0.0563019i	0.849315	+	0.527887i	$0.177015\pi$
$572$	−0.0577962	−	13.3521i	−0.00241658	−	0.558278i
$573$	21.5453	−	21.5453i	0.900067	−	0.900067i
$574$	18.4110	+	15.0003i	0.768459	+	0.626099i
$575$	−5.52423	+	4.07217i	−0.230376	+	0.169821i
$576$	1.62274	−	0.344923i	0.0676141	−	0.0143718i
$577$	13.2413	+	5.08284i	0.551241	+	0.211601i	0.618015	−	0.786167i	$-0.287937\pi$
$577$	13.2413	+	5.08284i	0.551241	+	0.211601i	−0.0667739	+	0.997768i	$0.521271\pi$
$578$	15.3012	+	5.87357i	0.636445	+	0.244308i
$579$	−13.8708	+	2.94833i	−0.576451	+	0.122529i
$580$	−8.13544	+	0.668544i	−0.337806	+	0.0277598i
$581$	−1.78169	−	4.68327i	−0.0739171	−	0.194295i
$582$	6.40168	−	6.40168i	0.265358	−	0.265358i
$583$	15.1981	−	5.01101i	0.629443	−	0.207535i
$584$	3.64799	−	6.31851i	0.150955	−	0.261462i
$585$	9.13229	+	11.8167i	0.377574	+	0.488562i
$586$	−2.71853	−	2.44777i	−0.112301	−	0.101117i
$587$	3.76148	−	1.91657i	0.155253	−	0.0791054i	−0.374638	−	0.927171i	$-0.622233\pi$
$587$	3.76148	−	1.91657i	0.155253	−	0.0791054i	0.529891	+	0.848066i	$0.322233\pi$
$588$	−1.22019	−	8.01378i	−0.0503197	−	0.330483i
$589$	18.6311	−	25.6435i	0.767682	−	1.05662i
$590$	6.43401	+	6.73332i	0.264884	+	0.277206i
$591$	−0.441691	+	2.07800i	−0.0181688	+	0.0854773i
$592$	0.663200	+	0.537049i	0.0272573	+	0.0220726i
$593$	−19.2141	−	5.14841i	−0.789030	−	0.211420i	−0.158268	−	0.987396i	$-0.550591\pi$
$593$	−19.2141	−	5.14841i	−0.789030	−	0.211420i	−0.630762	+	0.775976i	$0.717258\pi$
$594$	0.859135	−	17.8732i	0.0352507	−	0.733347i
$595$	2.20330	−	4.06247i	0.0903267	−	0.166545i
$596$	−0.740558	+	0.538047i	−0.0303344	+	0.0220393i
$597$	1.02155	+	19.4923i	0.0418093	+	0.797769i
$598$	5.51823	+	0.289198i	0.225657	+	0.0118262i
$599$	−8.90237	−	19.9951i	−0.363741	−	0.816976i	−0.999001	−	0.0446779i	$-0.985774\pi$
$599$	−8.90237	−	19.9951i	−0.363741	−	0.816976i	0.635260	−	0.772298i	$-0.280893\pi$
$600$	3.11991	−	4.87765i	0.127370	−	0.199129i
$601$	19.6359	+	6.38010i	0.800966	+	0.260250i	0.680767	−	0.732500i	$-0.261647\pi$
$601$	19.6359	+	6.38010i	0.800966	+	0.260250i	0.120199	+	0.992750i	$0.461647\pi$
$602$	−5.33999	+	24.7585i	−0.217642	+	1.00908i
$603$	−18.1049	−	2.86753i	−0.737287	−	0.116775i
$604$	10.9048	−	6.29591i	0.443711	−	0.256177i
$605$	−2.22664	−	24.4958i	−0.0905257	−	0.995894i
$606$	−6.19288	+	10.7264i	−0.251568	+	0.435729i
$607$	4.72329	+	12.3046i	0.191713	+	0.499428i	0.995420	−	0.0955961i	$-0.0304757\pi$
$607$	4.72329	+	12.3046i	0.191713	+	0.499428i	−0.803708	+	0.595024i	$0.797142\pi$
$608$	2.91052	+	1.48299i	0.118037	+	0.0601430i
$609$	5.04791	+	9.98073i	0.204552	+	0.404440i
$610$	2.14070	+	0.161042i	0.0866744	+	0.00652038i
$611$	3.43048	−	32.6389i	0.138782	−	1.32043i
$612$	0.0678254	−	1.29419i	0.00274168	−	0.0523144i
$613$	10.5070	+	16.1794i	0.424376	+	0.653481i	0.984592	−	0.174865i	$-0.0559489\pi$
$613$	10.5070	+	16.1794i	0.424376	+	0.653481i	−0.560217	+	0.828346i	$0.689282\pi$
$614$	−25.9505	−	11.5539i	−1.04727	−	0.466277i
$615$	19.7753	−	12.2125i	0.797419	−	0.492454i
$616$	−5.88032	−	6.51320i	−0.236925	−	0.262424i
$617$	23.8896	−	23.8896i	0.961760	−	0.961760i	−0.0375356	−	0.999295i	$-0.511951\pi$
$617$	23.8896	−	23.8896i	0.961760	−	0.961760i	0.999295	+	0.0375356i	$0.0119508\pi$
$618$	−7.93143	−	20.6621i	−0.319049	−	0.831151i
$619$	−35.6293	−	7.57323i	−1.43206	−	0.304394i	−0.574385	−	0.818585i	$-0.694759\pi$
$619$	−35.6293	−	7.57323i	−1.43206	−	0.304394i	−0.857676	+	0.514191i	$0.828092\pi$
$620$	−19.0325	+	10.4191i	−0.764364	+	0.418439i
$621$	7.36480	+	0.774072i	0.295539	+	0.0310624i
$622$	2.13338	+	13.4697i	0.0855409	+	0.540084i
$623$	−18.7568	+	16.7875i	−0.751477	+	0.672576i
$624$	−4.43383	+	1.44064i	−0.177495	+	0.0576717i
$625$	5.53502	+	24.3796i	0.221401	+	0.975183i
$626$	−17.0336	−	9.83435i	−0.680799	−	0.393060i
$627$	8.35442	−	9.35969i	0.333644	−	0.373790i
$628$	−14.6151	−	3.91611i	−0.583207	−	0.156270i
$629$	0.539322	−	0.391840i	0.0215042	−	0.0156237i
$630$	9.65120	+	1.78412i	0.384513	+	0.0710810i
$631$	−6.00510	+	18.4818i	−0.239059	+	0.735749i	0.757498	+	0.652838i	$0.226422\pi$
$631$	−6.00510	+	18.4818i	−0.239059	+	0.735749i	−0.996557	+	0.0829112i	$0.973578\pi$
$632$	3.41577	+	4.21813i	0.135872	+	0.167788i
$633$	10.0851	−	26.2726i	0.400848	−	1.04424i
$634$	−1.33674	+	1.20361i	−0.0530887	+	0.0478013i
$635$	4.03038	+	0.732602i	0.159941	+	0.0290724i
$636$	−3.28426	−	4.52040i	−0.130229	−	0.179245i
$637$	−7.13087	−	27.2638i	−0.282535	−	1.08023i
$638$	10.5115	+	6.00830i	0.416154	+	0.237871i
$639$	−21.8040	+	12.5886i	−0.862554	+	0.497996i
$640$	−1.36735	−	1.76928i	−0.0540492	−	0.0699370i
$641$	−18.9911	−	4.03668i	−0.750102	−	0.159439i	−0.183030	−	0.983107i	$-0.558591\pi$
$641$	−18.9911	−	4.03668i	−0.750102	−	0.159439i	−0.567072	+	0.823668i	$0.691924\pi$
$642$	6.24769	+	4.05730i	0.246577	+	0.160129i
$643$	−9.64241	+	1.52721i	−0.380259	+	0.0602272i	−0.343638	−	0.939102i	$-0.611659\pi$
$643$	−9.64241	+	1.52721i	−0.380259	+	0.0602272i	−0.0366210	+	0.999329i	$0.511659\pi$
$644$	2.82904	−	2.27694i	0.111480	−	0.0897240i
$645$	21.1803	+	12.8789i	0.833972	+	0.507106i
$646$	1.70746	−	1.89632i	0.0671790	−	0.0746098i
$647$	14.0490	−	17.3491i	0.552324	−	0.682063i	−0.422160	−	0.906521i	$-0.638728\pi$
$647$	14.0490	−	17.3491i	0.552324	−	0.682063i	0.974484	+	0.224458i	$0.0720612\pi$
$648$	−1.22748	+	0.328902i	−0.0482200	+	0.0129205i
$649$	−2.21996	−	13.6340i	−0.0871409	−	0.535182i
$650$	9.01440	−	17.9979i	0.353574	−	0.705937i
$651$	23.0485	+	18.7787i	0.903343	+	0.735995i
$652$	−14.4114	−	7.34300i	−0.564396	−	0.287574i
$653$	18.3090	+	11.8900i	0.716488	+	0.465293i	0.850694	−	0.525660i	$-0.176182\pi$
$653$	18.3090	+	11.8900i	0.716488	+	0.465293i	−0.134206	+	0.990953i	$0.542848\pi$
$654$	16.3783	−	7.29210i	0.640444	−	0.285144i
$655$	−12.0965	+	2.28519i	−0.472651	+	0.0892898i
$656$	−1.86620	−	8.77979i	−0.0728629	−	0.342793i
$657$	5.49509	−	10.7847i	0.214384	−	0.420752i
$658$	−12.6252	−	17.4868i	−0.492183	−	0.681707i
$659$			24.1807i			0.941945i	0.882148	+	0.470972i	$0.156097\pi$
$659$			24.1807i			0.941945i	−0.882148	+	0.470972i	$0.843903\pi$
$660$	−7.90856	+	3.34817i	−0.307840	+	0.130327i
$661$	−2.07302	−	1.19686i	−0.0806312	−	0.0465524i	0.459142	−	0.888363i	$-0.348157\pi$
$661$	−2.07302	−	1.19686i	−0.0806312	−	0.0465524i	−0.539774	+	0.841810i	$0.681490\pi$
$662$	−26.6471	−	21.5784i	−1.03567	−	0.838667i
$663$	0.190599	+	3.63685i	0.00740226	+	0.141244i
$664$	−0.585241	+	1.80119i	−0.0227117	+	0.0698996i
$665$	12.5575	+	14.6892i	0.486960	+	0.569622i
$666$	1.14536	+	0.832155i	0.0443819	+	0.0322454i
$667$	−2.72901	+	4.20231i	−0.105668	+	0.162714i
$668$	7.60474	−	4.93858i	0.294236	−	0.191079i
$669$	13.0990	−	1.37676i	0.506438	−	0.0532287i
$670$	7.09886	+	23.6650i	0.274253	+	0.914259i
$671$	−2.48319	−	1.99312i	−0.0958626	−	0.0769434i
$672$	−1.53984	+	2.64877i	−0.0594007	+	0.102178i
$673$	−47.5252	−	7.52726i	−1.83196	−	0.290154i	−0.857464	−	0.514545i	$-0.827961\pi$
$673$	−47.5252	−	7.52726i	−1.83196	−	0.290154i	−0.974499	+	0.224390i	$0.927961\pi$
$674$	−13.0013	−	11.7064i	−0.500790	−	0.450913i
$675$	13.3264	−	23.4545i	0.512932	−	0.902764i
$676$	−2.93009	+	1.30456i	−0.112696	+	0.0501754i
$677$	3.07264	−	2.48818i	0.118091	−	0.0956285i	−0.568456	−	0.822714i	$-0.692459\pi$
$677$	3.07264	−	2.48818i	0.118091	−	0.0956285i	0.686547	+	0.727085i	$0.259126\pi$
$678$	−3.31497	−	6.50599i	−0.127311	−	0.249861i
$679$	−1.02078	−	20.6592i	−0.0391740	−	0.792826i
$680$	−1.61148	+	0.674024i	−0.0617974	+	0.0258477i
$681$	−5.42213	−	9.39141i	−0.207777	−	0.359880i
$682$	32.0210	+	3.22546i	1.22615	+	0.123509i
$683$	−34.9910	+	9.37580i	−1.33889	+	0.358755i	−0.856023	−	0.516937i	$-0.827072\pi$
$683$	−34.9910	+	9.37580i	−1.33889	+	0.358755i	−0.482869	+	0.875693i	$0.660405\pi$
$684$	4.95067	+	2.20418i	0.189294	+	0.0842790i
$685$	6.42278	−	7.57290i	0.245402	−	0.289345i
$686$	−15.4413	−	10.2257i	−0.589552	−	0.390421i
$687$	17.3408	−	2.74651i	0.661592	−	0.104786i
$688$	7.43964	−	6.02450i	0.283634	−	0.229682i
$689$	−12.9978	−	14.4355i	−0.495177	−	0.549950i
$690$	−1.19797	−	3.34620i	−0.0456060	−	0.127388i
$691$	−3.60826	+	8.10429i	−0.137265	+	0.308302i	−0.969078	−	0.246753i	$-0.920636\pi$
$691$	−3.60826	+	8.10429i	−0.137265	+	0.308302i	0.831813	+	0.555055i	$0.187303\pi$
$692$	6.40171	+	6.40171i	0.243356	+	0.243356i
$693$	−10.3075	−	10.2800i	−0.391551	−	0.390504i
$694$		−	18.4780i		−	0.701417i
$695$	23.3443	−	30.6413i	0.885499	−	1.16229i
$696$	0.878926	−	4.13502i	0.0333156	−	0.156738i
$697$	−7.00217	−	0.366968i	−0.265226	−	0.0138999i
$698$	−0.527713	−	0.651671i	−0.0199742	−	0.0246661i
$699$	−5.86581	−	4.26176i	−0.221865	−	0.161195i
$700$	−3.47387	−	12.7645i	−0.131300	−	0.482452i
$701$	−12.9492	−	39.8536i	−0.489085	−	1.50525i	−0.825977	−	0.563705i	$-0.809376\pi$
$701$	−12.9492	−	39.8536i	−0.489085	−	1.50525i	0.336892	−	0.941543i	$-0.390624\pi$
$702$	−20.2776	+	7.78383i	−0.765328	+	0.293782i
$703$	0.721487	+	2.69262i	0.0272114	+	0.101554i
$704$	0.187914	+	3.31130i	0.00708227	+	0.124799i
$705$	−20.2188	+	6.06509i	−0.761483	+	0.228425i
$706$	−16.1392	−	22.2137i	−0.607407	−	0.836024i
$707$	8.66406	+	26.9390i	0.325846	+	1.01315i
$708$	−4.29741	+	2.18964i	−0.161506	+	0.0822917i
$709$	11.4316	+	1.20151i	0.429324	+	0.0451238i	0.316726	−	0.948517i	$-0.397416\pi$
$709$	11.4316	+	1.20151i	0.429324	+	0.0451238i	0.112597	+	0.993641i	$0.464083\pi$
$710$	28.0329	+	19.1243i	1.05205	+	0.717722i
$711$	6.02520	+	6.69167i	0.225963	+	0.250957i
$712$	9.50115	−	0.497934i	0.356071	−	0.0186609i
$713$	−2.08354	+	13.1549i	−0.0780291	+	0.492656i
$714$	1.68732	+	1.69743i	0.0631462	+	0.0635249i
$715$	−26.1267	+	14.4500i	−0.977083	+	0.540399i
$716$	−9.25352	−	16.0276i	−0.345820	−	0.598978i
$717$	−0.406671	+	0.502197i	−0.0151874	+	0.0187549i
$718$	−2.50974	−	3.86466i	−0.0936627	−	0.144228i
$719$	37.7008	−	8.01355i	1.40600	−	0.298855i	0.558437	−	0.829547i	$-0.311401\pi$
$719$	37.7008	−	8.01355i	1.40600	−	0.298855i	0.847565	+	0.530692i	$0.178068\pi$
$720$	−2.41893	−	2.81248i	−0.0901481	−	0.104815i
$721$	−47.1527	−	18.2621i	−1.75606	−	0.680118i
$722$	−3.78156	−	7.42173i	−0.140735	−	0.276208i
$723$	−0.425167	+	0.0222820i	−0.0158121	+	0.000828678i
$724$	−0.965459	−	9.18573i	−0.0358810	−	0.341385i
$725$	10.0466	+	15.2390i	0.373122	+	0.565962i
$726$	12.4823	+	2.54046i	0.463262	+	0.0942853i
$727$	−8.55595	−	8.55595i	−0.317323	−	0.317323i	0.530415	−	0.847738i	$-0.322036\pi$
$727$	−8.55595	−	8.55595i	−0.317323	−	0.317323i	−0.847738	+	0.530415i	$0.822036\pi$
$728$	−4.36137	+	9.71752i	−0.161643	+	0.360155i
$729$	−19.8309	+	6.44346i	−0.734479	+	0.238647i
$730$	−16.3101	−	0.370747i	−0.603664	−	0.0137219i
$731$	−3.04166	−	6.83168i	−0.112500	−	0.252679i
$732$	−0.398420	+	1.03792i	−0.0147260	+	0.0383626i
$733$	−14.3843	+	22.1498i	−0.531294	+	0.818122i	−0.997793	−	0.0664002i	$-0.978849\pi$
$733$	−14.3843	+	22.1498i	−0.531294	+	0.818122i	0.466499	+	0.884522i	$0.345515\pi$
$734$	5.18867	+	15.9691i	0.191517	+	0.589430i
$735$	−14.4081	+	10.9980i	−0.531449	+	0.405666i
$736$	−1.37258			−0.0505941
$737$	11.1733	−	34.9012i	0.411574	−	1.28560i
$738$	−3.85407	−	14.3836i	−0.141870	−	0.529467i
$739$	39.8699	−	4.19049i	1.46664	−	0.154150i	0.662709	−	0.748877i	$-0.269406\pi$
$739$	39.8699	−	4.19049i	1.46664	−	0.154150i	0.803928	+	0.594727i	$0.202740\pi$
$740$	0.341264	−	1.87745i	0.0125451	−	0.0690164i
$741$	−14.4833	−	4.70593i	−0.532059	−	0.172876i
$742$	−12.6919	−	1.37235i	−0.465936	−	0.0503805i
$743$	−3.51407	−	22.1870i	−0.128919	−	0.813961i	−0.964401	−	0.264444i	$-0.914812\pi$
$743$	−3.51407	−	22.1870i	−0.128919	−	0.813961i	0.835482	−	0.549517i	$-0.185188\pi$
$744$	−2.33628	−	10.9913i	−0.0856522	−	0.402962i
$745$	1.85049	+	0.874809i	0.0677967	+	0.0320505i
$746$	−0.469766	−	4.46953i	−0.0171994	−	0.163641i
$747$	−0.813190	+	3.03487i	−0.0297531	+	0.111040i
$748$	2.53656	+	0.527696i	0.0927457	+	0.0192945i
$749$	16.4532	−	4.35595i	0.601188	−	0.159163i
$750$	−12.9170	−	0.882067i	−0.471661	−	0.0322085i
$751$	−4.89516	+	5.43663i	−0.178627	+	0.198385i	−0.825809	−	0.563950i	$-0.809281\pi$
$751$	−4.89516	+	5.43663i	−0.178627	+	0.198385i	0.647182	+	0.762336i	$0.275948\pi$
$752$	−0.426643	+	8.14083i	−0.0155581	+	0.296865i
$753$	−6.79331	−	2.60771i	−0.247562	−	0.0950301i
$754$	1.53620	−	14.6160i	0.0559452	−	0.532283i
$755$	−24.0577	−	14.6286i	−0.875550	−	0.532388i
$756$	−6.51842	+	12.6991i	−0.237073	+	0.461863i
$757$	1.77526	−	11.2086i	0.0645230	−	0.407382i	−0.934195	−	0.356763i	$-0.883880\pi$
$757$	1.77526	−	11.2086i	0.0645230	−	0.407382i	0.998718	−	0.0506194i	$-0.0161195\pi$
$758$	−7.90023	+	29.4841i	−0.286949	+	1.07091i
$759$	−1.34236	+	5.09794i	−0.0487247	+	0.185043i
$760$	−0.216413	−	7.30104i	−0.00785011	−	0.264836i
$761$	−12.5221	+	28.1250i	−0.453924	+	1.01953i	0.531131	+	0.847290i	$0.321767\pi$
$761$	−12.5221	+	28.1250i	−0.453924	+	1.01953i	−0.985055	+	0.172241i	$0.944899\pi$
$762$	−0.963124	+	1.89024i	−0.0348903	+	0.0684761i
$763$	12.7741	−	38.9184i	0.462454	−	1.40894i
$764$	−15.4657	+	21.2867i	−0.559530	+	0.770127i
$765$	−2.61124	+	1.25658i	−0.0944096	+	0.0454319i
$766$	−20.6456	+	18.5894i	−0.745955	+	0.671661i
$767$	−14.0623	+	9.13219i	−0.507762	+	0.329744i
$768$	1.08110	−	0.414997i	0.0390110	−	0.0149749i
$769$	−30.4601			−1.09842			−0.549209	−	0.835685i	$-0.685071\pi$
$769$	−30.4601			−1.09842			−0.549209	+	0.835685i	$0.685071\pi$
$770$	−6.46106	+	18.5271i	−0.232840	+	0.667672i
$771$	−33.9604			−1.22305
$772$	11.4323	−	4.38845i	0.411457	−	0.157944i
$773$	10.3437	−	6.71726i	0.372036	−	0.241603i	−0.345055	−	0.938582i	$-0.612140\pi$
$773$	10.3437	−	6.71726i	0.372036	−	0.241603i	0.717091	+	0.696979i	$0.245473\pi$
$774$	11.8023	−	10.6268i	0.424225	−	0.381974i
$775$	40.8719	+	26.1430i	1.46816	+	0.939085i
$776$	−4.59528	+	6.32486i	−0.164961	+	0.227049i
$777$	−2.55909	+	0.535960i	−0.0918068	+	0.0192275i
$778$	4.84155	−	9.50207i	0.173578	−	0.340666i
$779$	11.9257	−	26.7855i	0.427282	−	0.959691i
$780$	7.58643	+	7.14964i	0.271638	+	0.255998i
$781$	−18.2412	−	46.9120i	−0.652721	−	1.67864i
$782$	−0.277513	+	1.03569i	−0.00992385	+	0.0370363i
$783$	3.08104	−	19.4529i	0.110107	−	0.695191i
$784$	2.12328	+	6.67021i	0.0758313	+	0.238222i
$785$	8.01176	+	32.8710i	0.285952	+	1.17322i
$786$	0.666409	−	6.34046i	0.0237700	−	0.226157i
$787$	−38.2995	−	14.7018i	−1.36523	−	0.524062i	−0.438141	−	0.898906i	$-0.644363\pi$
$787$	−38.2995	−	14.7018i	−1.36523	−	0.524062i	−0.927088	+	0.374844i	$0.877696\pi$
$788$	0.0960117	−	1.83201i	0.00342028	−	0.0652628i
$789$	−23.4922	+	26.0908i	−0.836346	+	0.928857i
$790$	4.60579	−	11.2289i	0.163867	−	0.399505i
$791$	−16.1013	−	4.36595i	−0.572495	−	0.155235i
$792$	0.598823	+	5.46957i	0.0212782	+	0.194353i
$793$	−1.00034	+	3.73333i	−0.0355232	+	0.132574i
$794$	−0.782110	−	7.44128i	−0.0277560	−	0.264081i
$795$	−5.33987	+	11.2955i	−0.189386	+	0.400609i
$796$	−3.50447	−	16.4872i	−0.124213	−	0.584375i
$797$	1.46677	+	9.26079i	0.0519555	+	0.328034i	0.999952	+	0.00975458i	$0.00310503\pi$
$797$	1.46677	+	9.26079i	0.0519555	+	0.328034i	−0.947997	+	0.318279i	$0.896895\pi$
$798$	−9.15506	+	4.04334i	−0.324086	+	0.143133i
$799$	6.05646	+	1.96786i	0.214262	+	0.0696180i
$800$	−2.00209	+	4.58166i	−0.0707847	+	0.161986i
$801$	15.6975	−	1.64987i	0.554643	−	0.0582953i
$802$	−5.43425	−	20.2809i	−0.191890	−	0.716144i
$803$	19.6380	+	14.1384i	0.693010	+	0.498933i
$804$	−12.7952			−0.451252
$805$	−7.50363	−	3.10403i	−0.264468	−	0.109403i
$806$	−12.0717	−	37.1529i	−0.425208	−	1.30866i
$807$	15.7478	−	24.2495i	0.554349	−	0.853623i
$808$	3.83297	−	9.98523i	0.134843	−	0.351279i
$809$	15.5911	+	35.0181i	0.548153	+	1.23117i	0.949072	+	0.315059i	$0.102024\pi$
$809$	15.5911	+	35.0181i	0.548153	+	1.23117i	−0.400919	+	0.916113i	$0.631309\pi$
$810$	1.96310	+	2.05442i	0.0689763	+	0.0721851i
$811$	45.3958	−	14.7500i	1.59406	−	0.517942i	0.628431	−	0.777865i	$-0.283697\pi$
$811$	45.3958	−	14.7500i	1.59406	−	0.517942i	0.965629	+	0.259923i	$0.0836973\pi$
$812$	−5.65370	−	7.83077i	−0.198406	−	0.274806i
$813$	1.40770	+	1.40770i	0.0493702	+	0.0493702i
$814$	−1.99267	+	2.00999i	−0.0698430	+	0.0704503i
$815$	1.07157	+	36.1511i	0.0375353	+	1.26632i
$816$	−0.0945581	−	0.899661i	−0.00331020	−	0.0314944i
$817$	31.2280	−	1.63659i	1.09253	−	0.0572570i
$818$	−6.66611	−	13.0830i	−0.233075	−	0.457436i
$819$	−6.38184	+	16.4778i	−0.222999	+	0.575783i
$820$	−15.2169	+	13.0876i	−0.531396	+	0.457037i
$821$	50.5235	−	10.7391i	1.76328	−	0.374797i	0.791591	−	0.611051i	$-0.209253\pi$
$821$	50.5235	−	10.7391i	1.76328	−	0.374797i	0.971691	+	0.236254i	$0.0759196\pi$
$822$	2.80079	+	4.31283i	0.0976886	+	0.150427i
$823$	3.43733	−	4.24475i	0.119818	−	0.147963i	−0.713708	−	0.700444i	$-0.752985\pi$
$823$	3.43733	−	4.24475i	0.119818	−	0.147963i	0.833525	+	0.552481i	$0.186319\pi$
$824$	9.55601	+	16.5515i	0.332899	+	0.576599i
$825$	15.0588	+	11.9168i	0.524281	+	0.414889i
$826$	−2.88384	+	10.6354i	−0.100342	+	0.370052i
$827$	0.0295603	−	0.186636i	0.00102791	−	0.00648997i	−0.987169	−	0.159679i	$-0.948954\pi$
$827$	0.0295603	−	0.186636i	0.00102791	−	0.00648997i	0.988197	+	0.153189i	$0.0489542\pi$
$828$	−2.27398	+	0.119174i	−0.0790264	+	0.00414160i
$829$	−37.2967	−	41.4222i	−1.29537	−	1.43865i	−0.834322	−	0.551278i	$-0.814140\pi$
$829$	−37.2967	−	41.4222i	−1.29537	−	1.43865i	−0.461048	−	0.887375i	$-0.652526\pi$
$830$	4.16124	−	0.786111i	0.144439	−	0.0272863i
$831$	17.5260	+	1.84206i	0.607972	+	0.0639004i
$832$	3.58705	−	1.82769i	0.124359	−	0.0633639i
$833$	5.46235	−	0.253531i	0.189259	−	0.00878433i
$834$	11.7258	+	16.1392i	0.406033	+	0.558856i
$835$	−17.8520	−	9.61320i	−0.617795	−	0.332678i
$836$	−5.86120	+	9.11157i	−0.202714	+	0.315130i
$837$	−13.5498	−	50.5687i	−0.468351	−	1.74791i
$838$	−1.96929	+	0.755939i	−0.0680279	+	0.0261135i
$839$	5.82324	+	17.9221i	0.201041	+	0.618739i	0.999853	+	0.0171588i	$0.00546208\pi$
$839$	5.82324	+	17.9221i	0.201041	+	0.618739i	−0.798812	+	0.601580i	$0.794538\pi$
$840$	6.84867	+	0.176163i	0.236302	+	0.00607822i
$841$	−12.6802	−	9.21267i	−0.437247	−	0.317678i
$842$	0.304172	+	0.375621i	0.0104824	+	0.0129447i
$843$	−20.9216	−	1.09645i	−0.720578	−	0.0377639i
$844$	−5.05260	+	23.7706i	−0.173918	+	0.818218i
$845$	5.70491	+	4.34632i	0.196255	+	0.149518i
$846$			13.5241i			0.464968i
$847$	23.4477	−	17.2396i	0.805673	−	0.592361i
$848$	3.41183	+	3.41183i	0.117163	+	0.117163i
$849$	−1.07501	+	2.41452i	−0.0368944	+	0.0828662i
$850$	3.05234	+	2.43703i	0.104694	+	0.0835894i
$851$	−0.783775	−	0.870471i	−0.0268675	−	0.0298394i
$852$	−13.6578	+	11.0599i	−0.467908	+	0.378905i
$853$	28.5655	−	4.52433i	0.978064	−	0.154910i	0.353118	−	0.935579i	$-0.385121\pi$
$853$	28.5655	−	4.52433i	0.978064	−	0.154910i	0.624945	+	0.780669i	$0.285121\pi$
$854$	1.14640	+	2.26665i	0.0392288	+	0.0775633i
$855$	−0.992446	−	12.0770i	−0.0339409	−	0.413023i
$856$	−5.87682	−	2.61653i	−0.200866	−	0.0894312i
$857$	39.9291	−	10.6990i	1.36395	−	0.365470i	0.498686	−	0.866783i	$-0.333816\pi$
$857$	39.9291	−	10.6990i	1.36395	−	0.365470i	0.865266	+	0.501313i	$0.167149\pi$
$858$	−3.28019	−	15.1102i	−0.111984	−	0.515853i
$859$	−7.86215	−	13.6176i	−0.268253	−	0.464628i	0.700158	−	0.713988i	$-0.253113\pi$
$859$	−7.86215	−	13.6176i	−0.268253	−	0.464628i	−0.968411	+	0.249360i	$0.919780\pi$
$860$	−19.8047	−	8.12337i	−0.675334	−	0.277004i
$861$	24.4659	+	12.5583i	0.833796	+	0.427985i
$862$	10.4709	+	20.5504i	0.356642	+	0.699949i
$863$	21.4923	−	17.4041i	0.731605	−	0.592442i	−0.189442	−	0.981892i	$-0.560668\pi$
$863$	21.4923	−	17.4041i	0.731605	−	0.592442i	0.921048	+	0.389449i	$0.127335\pi$
$864$	4.92876	−	2.19443i	0.167680	−	0.0746559i
$865$	5.68255	−	19.4301i	0.193212	−	0.660642i
$866$	28.4329	+	25.6011i	0.966189	+	0.869961i
$867$	18.7460	+	2.96907i	0.636648	+	0.100835i
$868$	−22.1951	−	12.9030i	−0.753352	−	0.437956i
$869$	−15.0549	+	9.86968i	−0.510703	+	0.334806i
$870$	−9.05417	+	2.71601i	−0.306965	+	0.0920812i
$871$	−44.2387	+	4.64967i	−1.49897	+	0.157548i
$872$	−12.9842	+	8.43203i	−0.439700	+	0.285545i
$873$	−7.06392	+	10.8775i	−0.239077	+	0.368147i
$874$	−3.62733	−	2.63541i	−0.122696	−	0.0891440i
$875$	−21.3062	+	20.5194i	−0.720282	+	0.693681i
$876$	2.61085	−	8.03538i	0.0882125	−	0.271490i
$877$	1.96531	+	37.5004i	0.0663639	+	1.26630i	0.805441	+	0.592677i	$0.201929\pi$
$877$	1.96531	+	37.5004i	0.0663639	+	1.26630i	−0.739077	+	0.673621i	$0.764738\pi$
$878$	−26.4365	−	21.4078i	−0.892188	−	0.722480i
$879$	−3.66865	−	2.11810i	−0.123741	−	0.0714417i
$880$	6.29301	−	3.92404i	0.212137	−	0.132279i
$881$			10.8529i			0.365644i	0.983146	+	0.182822i	$0.0585232\pi$
$881$			10.8529i			0.365644i	−0.983146	+	0.182822i	$0.941477\pi$
$882$	4.09681	+	10.8663i	0.137947	+	0.365887i
$883$	12.6616	−	24.8499i	0.426098	−	0.836265i	−0.573753	−	0.819028i	$-0.694513\pi$
$883$	12.6616	−	24.8499i	0.426098	−	0.836265i	0.999851	−	0.0172368i	$-0.00548692\pi$
$884$	−0.653858	−	3.07616i	−0.0219916	−	0.103463i
$885$	8.90905	+	6.07783i	0.299474	+	0.204304i
$886$	5.62426	−	2.50408i	0.188951	−	0.0841262i
$887$	−12.9969	−	8.44027i	−0.436392	−	0.283396i	0.307687	−	0.951488i	$-0.400445\pi$
$887$	−12.9969	−	8.44027i	−0.436392	−	0.283396i	−0.744079	+	0.668091i	$0.767112\pi$
$888$	0.880519	+	0.448647i	0.0295483	+	0.0150556i
$889$	1.72346	+	4.53019i	0.0578029	+	0.151938i
$890$	−11.1784	−	18.1009i	−0.374701	−	0.606743i
$891$	−0.677338	−	4.15992i	−0.0226917	−	0.139363i
$892$	−10.9863	+	2.94378i	−0.367849	+	0.0985649i
$893$	−16.7582	+	20.6946i	−0.560790	+	0.692518i
$894$	−0.709297	+	0.787755i	−0.0237225	+	0.0263465i
$895$	−21.5006	+	35.3593i	−0.718686	+	1.18193i
$896$	0.955532	−	2.46718i	0.0319221	−	0.0824226i
$897$	6.32021	−	1.00102i	0.211026	−	0.0334232i
$898$	19.3456	+	12.5632i	0.645572	+	0.419239i
$899$	34.6491	+	7.36489i	1.15561	+	0.245633i
$900$	−2.91910	+	7.76435i	−0.0973033	+	0.258812i
$901$	3.26424	−	1.88461i	0.108748	−	0.0627854i
$902$	29.5930	−	3.23992i	0.985338	−	0.107877i
$903$	−0.0876799	+	29.3300i	−0.00291781	+	0.976042i
$904$	3.70626	+	5.10122i	0.123268	+	0.169664i
$905$	−16.9802	+	11.7567i	−0.564442	+	0.390806i
$906$	10.8362	−	9.75697i	0.360009	−	0.324154i
$907$	−13.1844	+	34.3465i	−0.437780	+	1.14046i	0.520307	+	0.853979i	$0.325817\pi$
$907$	−13.1844	+	34.3465i	−0.437780	+	1.14046i	−0.958087	+	0.286476i	$0.907516\pi$
$908$	5.89326	+	7.27758i	0.195575	+	0.241515i
$909$	5.48318	−	16.8755i	0.181866	−	0.559725i
$910$	23.7429	−	1.87968i	0.787069	−	0.0623107i
$911$	27.8476	−	20.2324i	0.922631	−	0.670331i	−0.0215462	−	0.999768i	$-0.506859\pi$
$911$	27.8476	−	20.2324i	0.922631	−	0.670331i	0.944178	+	0.329437i	$0.106859\pi$
$912$	3.65384	+	0.979045i	0.120991	+	0.0324194i
$913$	−5.74925	−	2.52997i	−0.190272	−	0.0837297i
$914$	19.5431	+	11.2832i	0.646428	+	0.373216i
$915$	2.46357	−	0.332993i	0.0814432	−	0.0110084i
$916$	−14.4191	+	4.68506i	−0.476421	+	0.154799i
$917$	−9.71414	−	10.8537i	−0.320789	−	0.358421i
$918$	−0.659308	−	4.16271i	−0.0217604	−	0.137390i
$919$	9.29270	+	0.976702i	0.306538	+	0.0322184i	0.256549	−	0.966531i	$-0.417415\pi$
$919$	9.29270	+	0.976702i	0.306538	+	0.0322184i	0.0499892	+	0.998750i	$0.484081\pi$
$920$	1.47380	+	2.69218i	0.0485896	+	0.0887587i
$921$	−32.1762	−	6.83927i	−1.06024	−	0.225362i
$922$	−3.97892	−	10.3654i	−0.131039	−	0.341368i
$923$	−43.2020	+	43.2020i	−1.42201	+	1.42201i
$924$	−8.22888	−	5.96181i	−0.270710	−	0.196129i
$925$	−4.04886	+	1.34653i	−0.133126	+	0.0442738i
$926$	16.9108	+	7.52916i	0.555722	+	0.247423i
$927$	17.2687	+	26.5914i	0.567178	+	0.873377i
$928$	−0.191055	+	3.64554i	−0.00627168	+	0.119671i
$929$	2.07305	−	19.7238i	0.0680146	−	0.647116i	−0.906410	−	0.422400i	$-0.861188\pi$
$929$	2.07305	−	19.7238i	0.0680146	−	0.647116i	0.974424	−	0.224716i	$-0.0721454\pi$
$930$	−19.0498	+	16.3842i	−0.624669	+	0.537259i
$931$	−7.19584	+	21.7041i	−0.235834	+	0.711324i
$932$	5.57873	+	2.84251i	0.182737	+	0.0931094i
$933$	5.65955	+	14.7436i	0.185285	+	0.482685i
$934$	−14.9272	+	25.8547i	−0.488434	+	0.845993i
$935$	−1.68857	−	5.54181i	−0.0552223	−	0.181236i
$936$	5.78403	−	3.33941i	0.189057	−	0.109152i
$937$	−52.4636	−	8.30942i	−1.71391	−	0.271457i	−0.779178	−	0.626803i	$-0.784363\pi$
$937$	−52.4636	−	8.30942i	−1.71391	−	0.271457i	−0.934735	+	0.355346i	$0.884363\pi$
$938$	−19.6259	+	21.6661i	−0.640807	+	0.707424i
$939$	−21.6620	−	7.03840i	−0.706912	−	0.229690i
$940$	16.4255	−	7.90430i	0.535741	−	0.257810i
$941$	2.63139	+	5.91020i	0.0857809	+	0.192667i	0.951342	−	0.308135i	$-0.0997050\pi$
$941$	2.63139	+	5.91020i	0.0857809	+	0.192667i	−0.865562	+	0.500802i	$0.833038\pi$
$942$	−17.4976	−	0.917012i	−0.570104	−	0.0298779i
$943$	0.644791	+	12.3033i	0.0209973	+	0.400652i
$944$	3.36951	−	2.44810i	0.109668	−	0.0796787i
$945$	31.9071	−	0.850311i	1.03794	−	0.0276606i
$946$	17.4075	+	26.5528i	0.565965	+	0.863306i
$947$	−3.85469	−	1.03286i	−0.125260	−	0.0335634i	0.195644	−	0.980675i	$-0.437320\pi$
$947$	−3.85469	−	1.03286i	−0.125260	−	0.0335634i	−0.320905	+	0.947112i	$0.603987\pi$
$948$	4.88467	+	3.95553i	0.158647	+	0.128470i
$949$	6.10688	−	28.7306i	0.198238	−	0.932635i
$950$	−14.0879	+	8.26387i	−0.457071	+	0.268115i
$951$	−1.22436	+	1.68518i	−0.0397025	+	0.0546458i
$952$	−1.66843	−	1.21982i	−0.0540742	−	0.0395347i
$953$	30.5395	−	15.5606i	0.989271	−	0.504059i	0.117027	−	0.993129i	$-0.462664\pi$
$953$	30.5395	−	15.5606i	0.989271	−	0.504059i	0.872245	+	0.489070i	$0.162664\pi$
$954$	5.94868	+	5.35621i	0.192595	+	0.173414i
$955$	58.3579	+	7.47807i	1.88842	+	0.241985i
$956$	0.279013	−	0.483265i	0.00902394	−	0.0156299i
$957$	13.3531	+	4.27488i	0.431645	+	0.138187i
$958$	−4.46385	+	4.46385i	−0.144220	+	0.144220i
$959$	11.5989	+	1.87264i	0.374548	+	0.0604709i
$960$	−1.97480	−	1.67488i	−0.0637363	−	0.0540565i
$961$	61.7785	−	13.1314i	1.99285	−	0.423594i
$962$	3.20738	+	1.23120i	0.103410	+	0.0396954i
$963$	−9.96341	−	3.82459i	−0.321066	−	0.123246i
$964$	0.359619	−	0.0764395i	0.0115826	−	0.00246195i
$965$	−20.8828	−	17.7112i	−0.672241	−	0.570145i
$966$	2.65628	−	3.26026i	0.0854645	−	0.104897i
$967$	11.0049	−	11.0049i	0.353894	−	0.353894i	−0.507662	−	0.861556i	$-0.669490\pi$
$967$	11.0049	−	11.0049i	0.353894	−	0.353894i	0.861556	+	0.507662i	$0.169490\pi$
$968$	−10.9895	−	0.480576i	−0.353216	−	0.0154463i
$969$	1.47749	−	2.55909i	0.0474638	−	0.0822098i
$970$	17.3397	+	2.22193i	0.556744	+	0.0713420i
$971$	33.0626	+	29.7697i	1.06103	+	0.955354i	0.999087	−	0.0427256i	$-0.0136041\pi$
$971$	33.0626	+	29.7697i	1.06103	+	0.955354i	0.0619414	+	0.998080i	$0.480271\pi$
$972$	13.1103	−	6.68002i	0.420513	−	0.214262i
$973$	45.3142	+	4.89972i	1.45271	+	0.157078i
$974$	8.35284	−	11.4967i	0.267642	−	0.368378i
$975$	5.87745	−	22.5569i	0.188229	−	0.722398i
$976$	0.199607	−	0.939075i	0.00638925	−	0.0300591i
$977$	31.9340	+	25.8597i	1.02166	+	0.827324i	0.985096	−	0.172007i	$-0.0550252\pi$
$977$	31.9340	+	25.8597i	1.02166	+	0.827324i	0.0365646	+	0.999331i	$0.488359\pi$
$978$	−18.0920	−	4.84774i	−0.578518	−	0.155013i
$979$	−1.51504	+	31.5186i	−0.0484210	+	1.00734i
$980$	10.8031	−	11.3267i	0.345092	−	0.361817i
$981$	−20.7790	+	15.0968i	−0.663423	+	0.482005i
$982$	−0.980742	−	18.7137i	−0.0312967	−	0.597177i
$983$	17.1931	+	0.901050i	0.548373	+	0.0287390i	0.324511	−	0.945882i	$-0.394800\pi$
$983$	17.1931	+	0.901050i	0.548373	+	0.0287390i	0.223862	+	0.974621i	$0.428134\pi$
$984$	−4.22775	−	9.49568i	−0.134776	−	0.302711i
$985$	−3.69640	+	1.77878i	−0.117777	+	0.0566768i
$986$	2.71214	+	0.881228i	0.0863722	+	0.0280640i
$987$	−18.5110	−	16.7679i	−0.589212	−	0.533727i
$988$	12.9887	+	2.05721i	0.413226	+	0.0654486i
$989$	−11.3794	+	6.56989i	−0.361843	+	0.208910i
$990$	10.0850	−	7.04741i	0.320523	−	0.223981i
$991$	−14.4064	+	24.9525i	−0.457633	+	0.792644i	−0.998835	−	0.0482487i	$-0.984636\pi$
$991$	−14.4064	+	24.9525i	−0.457633	+	0.792644i	0.541202	+	0.840892i	$0.317969\pi$
$992$	3.47744	+	9.05903i	0.110409	+	0.287625i
$993$	−35.3788	−	18.0264i	−1.12271	−	0.572051i
$994$	−2.22127	+	40.0909i	−0.0704544	+	1.27161i
$995$	−28.5752	+	24.5766i	−0.905894	+	0.779132i
$996$	−0.229247	+	2.18114i	−0.00726395	+	0.0691119i
$997$	−2.76313	+	52.7237i	−0.0875093	+	1.66978i	0.504170	+	0.863604i	$0.331798\pi$
$997$	−2.76313	+	52.7237i	−0.0875093	+	1.66978i	−0.591680	+	0.806173i	$0.701535\pi$
$998$	−15.7098	−	24.1910i	−0.497286	−	0.765754i
$999$	4.20610	+	1.87268i	0.133075	+	0.0592489i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bv.a.3.9	✓	768
5.2	odd	4	inner	770.2.bv.a.157.16	yes	768
7.5	odd	6	inner	770.2.bv.a.663.40	yes	768
11.4	even	5	inner	770.2.bv.a.213.16	yes	768
35.12	even	12	inner	770.2.bv.a.47.16	yes	768
55.37	odd	20	inner	770.2.bv.a.367.40	yes	768
77.26	odd	30	inner	770.2.bv.a.103.16	yes	768
385.257	even	60	inner	770.2.bv.a.257.9	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bv.a.3.9	✓	768	1.1	even	1	trivial
770.2.bv.a.47.16	yes	768	35.12	even	12	inner
770.2.bv.a.103.16	yes	768	77.26	odd	30	inner
770.2.bv.a.157.16	yes	768	5.2	odd	4	inner
770.2.bv.a.213.16	yes	768	11.4	even	5	inner
770.2.bv.a.257.9	yes	768	385.257	even	60	inner
770.2.bv.a.367.40	yes	768	55.37	odd	20	inner
770.2.bv.a.663.40	yes	768	7.5	odd	6	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.933580 + 0.358368i) q^{2} +(-0.971197 + 0.630703i) q^{3} +(0.743145 - 0.669131i) q^{4} +(-2.11038 - 0.739133i) q^{5} +(0.680667 - 0.936858i) q^{6} +(-0.542344 - 2.58957i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-0.674772 + 1.51556i) q^{9} +O(q^{10})\)	\(q+(-0.933580 + 0.358368i) q^{2} +(-0.971197 + 0.630703i) q^{3} +(0.743145 - 0.669131i) q^{4} +(-2.11038 - 0.739133i) q^{5} +(0.680667 - 0.936858i) q^{6} +(-0.542344 - 2.58957i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-0.674772 + 1.51556i) q^{9} +(2.23509 - 0.0662510i) q^{10} +(-2.78935 - 1.79431i) q^{11} +(-0.299718 + 1.11856i) q^{12} +(-0.629780 + 3.97627i) q^{13} +(1.43434 + 2.22321i) q^{14} +(2.51576 - 0.613176i) q^{15} +(0.104528 - 0.994522i) q^{16} +(-0.729290 - 0.279948i) q^{17} +(0.0868248 - 1.65672i) q^{18} +(2.18575 - 2.42752i) q^{19} +(-2.06289 + 0.862834i) q^{20} +(2.15997 + 2.17292i) q^{21} +(3.24710 + 0.675516i) q^{22} +(-0.355251 + 1.32581i) q^{23} +(-0.121046 - 1.15168i) q^{24} +(3.90737 + 3.11969i) q^{25} +(-0.837019 - 3.93787i) q^{26} +(-0.843996 - 5.32878i) q^{27} +(-2.13580 - 1.56153i) q^{28} +(3.47187 + 1.12808i) q^{29} +(-2.12892 + 1.47402i) q^{30} +(9.65038 - 1.01430i) q^{31} +(0.258819 + 0.965926i) q^{32} +(3.84068 - 0.0166249i) q^{33} +0.781175 q^{34} +(-0.769486 + 5.86582i) q^{35} +(0.512656 + 1.57779i) q^{36} +(-0.464783 + 0.715704i) q^{37} +(-1.17063 + 3.04959i) q^{38} +(-1.89621 - 4.25895i) q^{39} +(1.61666 - 1.54480i) q^{40} +(8.53662 - 2.77372i) q^{41} +(-2.79521 - 1.25453i) q^{42} +(6.76915 + 6.76915i) q^{43} +(-3.27352 + 0.533009i) q^{44} +(2.54422 - 2.69966i) q^{45} +(-0.143474 - 1.36506i) q^{46} +(-8.14083 + 0.426643i) q^{47} +(0.525730 + 1.03180i) q^{48} +(-6.41173 + 2.80887i) q^{49} +(-4.76584 - 1.51221i) q^{50} +(0.884848 - 0.188080i) q^{51} +(2.19263 + 3.37635i) q^{52} +(-3.03651 + 3.74978i) q^{53} +(2.69760 + 4.67238i) q^{54} +(4.56034 + 5.84836i) q^{55} +(2.55354 + 0.692408i) q^{56} +(-0.591751 + 3.73617i) q^{57} +(-3.64554 + 0.191055i) q^{58} +(2.78690 + 3.09516i) q^{59} +(1.45928 - 2.13905i) q^{60} +(0.954796 + 0.100353i) q^{61} +(-8.64592 + 4.40531i) q^{62} +(4.29061 + 0.925412i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(4.26807 - 7.92594i) q^{65} +(-3.57963 + 1.39190i) q^{66} +(2.85975 + 10.6727i) q^{67} +(-0.729290 + 0.279948i) q^{68} +(-0.491176 - 1.51168i) q^{69} +(-1.38375 - 5.75198i) q^{70} +(12.2778 + 8.92033i) q^{71} +(-1.04404 - 1.28928i) q^{72} +(-7.28599 - 0.381842i) q^{73} +(0.177427 - 0.834730i) q^{74} +(-5.76242 - 0.565452i) q^{75} -3.26656i q^{76} +(-3.13369 + 8.19634i) q^{77} +(3.29653 + 3.29653i) q^{78} +(2.20765 - 4.95846i) q^{79} +(-0.955678 + 2.02155i) q^{80} +(0.850319 + 0.944374i) q^{81} +(-6.97561 + 5.64874i) q^{82} +(1.87056 - 0.296268i) q^{83} +(3.05914 + 0.169494i) q^{84} +(1.33216 + 1.12984i) q^{85} +(-8.74539 - 3.89370i) q^{86} +(-4.08336 + 1.09413i) q^{87} +(2.86508 - 1.67073i) q^{88} +(-4.75709 - 8.23953i) q^{89} +(-1.40777 + 3.43212i) q^{90} +(10.6384 - 0.525649i) q^{91} +(0.623140 + 1.22298i) q^{92} +(-8.73270 + 7.07160i) q^{93} +(7.44722 - 3.31572i) q^{94} +(-6.40702 + 3.50743i) q^{95} +(-0.860576 - 0.774866i) q^{96} +(7.72170 + 1.22300i) q^{97} +(4.97925 - 4.92007i) q^{98} +(4.60156 - 3.01669i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) \) 768 * q + 24 * q^5 + 4 * q^7	\( 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) \) 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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