LMFDB - Embedded newform 354.2.e.a.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(7,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.e (of order $29$, degree $28$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$2$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			49.2
Character	$\chi$	$=$	354.49
Dual form			354.2.e.a.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.370138 + 0.928977i) q^{2} +(-0.994138 - 0.108119i) q^{3} +(-0.725995 - 0.687699i) q^{4} +(0.386052 - 0.454496i) q^{5} +(0.468408 - 0.883512i) q^{6} +(-0.965403 - 0.580863i) q^{7} +(0.907575 - 0.419889i) q^{8} +(0.976621 + 0.214970i) q^{9} +O(q^{10})$	\(q+(-0.370138 + 0.928977i) q^{2} +(-0.994138 - 0.108119i) q^{3} +(-0.725995 - 0.687699i) q^{4} +(0.386052 - 0.454496i) q^{5} +(0.468408 - 0.883512i) q^{6} +(-0.965403 - 0.580863i) q^{7} +(0.907575 - 0.419889i) q^{8} +(0.976621 + 0.214970i) q^{9} +(0.279324 + 0.526860i) q^{10} +(-0.122936 + 2.26742i) q^{11} +(0.647386 + 0.762162i) q^{12} +(4.07510 - 0.896998i) q^{13} +(0.896941 - 0.681837i) q^{14} +(-0.432929 + 0.410092i) q^{15} +(0.0541389 + 0.998533i) q^{16} +(5.71670 - 3.43962i) q^{17} +(-0.561187 + 0.827689i) q^{18} +(2.13760 - 7.69894i) q^{19} +(-0.592829 + 0.0644740i) q^{20} +(0.896941 + 0.681837i) q^{21} +(-2.06088 - 0.953462i) q^{22} +(2.81244 + 4.14804i) q^{23} +(-0.947653 + 0.319302i) q^{24} +(0.751380 + 4.58321i) q^{25} +(-0.675061 + 4.11769i) q^{26} +(-0.947653 - 0.319302i) q^{27} +(0.301418 + 1.08561i) q^{28} +(3.25034 + 8.15774i) q^{29} +(-0.220723 - 0.553972i) q^{30} +(-0.329268 - 1.18592i) q^{31} +(-0.947653 - 0.319302i) q^{32} +(0.367366 - 2.24083i) q^{33} +(1.07936 + 6.58382i) q^{34} +(-0.636696 + 0.214528i) q^{35} +(-0.561187 - 0.827689i) q^{36} +(-5.36817 - 2.48358i) q^{37} +(6.36093 + 4.83545i) q^{38} +(-4.14820 + 0.451144i) q^{39} +(0.159534 - 0.574589i) q^{40} +(4.88237 - 7.20096i) q^{41} +(-0.965403 + 0.580863i) q^{42} +(-0.0625351 - 1.15339i) q^{43} +(1.64855 - 1.56159i) q^{44} +(0.474730 - 0.360880i) q^{45} +(-4.89443 + 1.07735i) q^{46} +(1.55402 + 1.82954i) q^{47} +(0.0541389 - 0.998533i) q^{48} +(-2.68426 - 5.06305i) q^{49} +(-4.53581 - 0.998408i) q^{50} +(-6.05508 + 2.80138i) q^{51} +(-3.57537 - 2.15123i) q^{52} +(-0.784434 + 1.47960i) q^{53} +(0.647386 - 0.762162i) q^{54} +(0.983073 + 0.931216i) q^{55} +(-1.12007 - 0.121815i) q^{56} +(-2.95747 + 7.42269i) q^{57} -8.78142 q^{58} +(3.86141 + 6.64000i) q^{59} +0.596325 q^{60} +(5.03588 - 12.6391i) q^{61} +(1.22356 + 0.133070i) q^{62} +(-0.817963 - 0.774816i) q^{63} +(0.647386 - 0.762162i) q^{64} +(1.16552 - 2.19841i) q^{65} +(1.94571 + 1.17069i) q^{66} +(-5.55672 + 2.57081i) q^{67} +(-6.51573 - 1.43422i) q^{68} +(-2.34747 - 4.42781i) q^{69} +(0.0363741 - 0.670881i) q^{70} +(-8.37126 - 9.85541i) q^{71} +(0.976621 - 0.214970i) q^{72} +(-6.23187 + 4.73734i) q^{73} +(4.29415 - 4.06763i) q^{74} +(-0.251443 - 4.63759i) q^{75} +(-6.84645 + 4.11937i) q^{76} +(1.43574 - 2.11756i) q^{77} +(1.11630 - 4.02056i) q^{78} +(9.40326 - 1.02267i) q^{79} +(0.474730 + 0.360880i) q^{80} +(0.907575 + 0.419889i) q^{81} +(4.88237 + 7.20096i) q^{82} +(-15.2631 + 5.14275i) q^{83} +(-0.182276 - 1.11184i) q^{84} +(0.643650 - 3.92609i) q^{85} +(1.09462 + 0.368821i) q^{86} +(-2.34928 - 8.46134i) q^{87} +(0.840490 + 2.10947i) q^{88} +(2.45819 + 6.16959i) q^{89} +(0.159534 + 0.574589i) q^{90} +(-4.45515 - 1.50111i) q^{91} +(0.810786 - 4.94558i) q^{92} +(0.199118 + 1.21456i) q^{93} +(-2.27480 + 0.766471i) q^{94} +(-2.67391 - 3.94373i) q^{95} +(0.907575 + 0.419889i) q^{96} +(1.03773 + 0.788865i) q^{97} +(5.69700 - 0.619586i) q^{98} +(-0.607489 + 2.18798i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9	\( 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} - 18 q^{11} - 2 q^{12} + 13 q^{13} - 20 q^{14} + 4 q^{15} - 2 q^{16} + 21 q^{17} - 2 q^{18} + 20 q^{19} + 4 q^{20} - 20 q^{21} + 11 q^{22} + 34 q^{23} - 2 q^{24} - 28 q^{25} - 16 q^{26} - 2 q^{27} + 9 q^{28} + 38 q^{29} + 4 q^{30} + 34 q^{31} - 2 q^{32} + 11 q^{33} - 8 q^{34} - 19 q^{35} - 2 q^{36} - 29 q^{37} + 20 q^{38} + 13 q^{39} + 4 q^{40} + 43 q^{41} + 9 q^{42} - 65 q^{43} + 11 q^{44} + 4 q^{45} + 5 q^{46} - 60 q^{47} - 2 q^{48} - 13 q^{49} - 86 q^{50} + 21 q^{51} - 16 q^{52} - 15 q^{53} - 2 q^{54} - 15 q^{55} + 9 q^{56} + 20 q^{57} - 78 q^{58} - 2 q^{59} - 54 q^{60} + 4 q^{61} + 5 q^{62} + 9 q^{63} - 2 q^{64} - 57 q^{65} + 11 q^{66} - 56 q^{67} - 8 q^{68} - 53 q^{69} + 10 q^{70} + 23 q^{71} - 2 q^{72} - 21 q^{73} + 30 q^{75} - 9 q^{76} - 57 q^{77} + 13 q^{78} + 99 q^{79} + 4 q^{80} - 2 q^{81} + 43 q^{82} + 33 q^{83} + 9 q^{84} - 45 q^{85} - 7 q^{86} + 9 q^{87} - 18 q^{88} + 32 q^{89} + 4 q^{90} - 75 q^{91} + 34 q^{92} + 5 q^{93} + 27 q^{94} + 82 q^{95} - 2 q^{96} + 70 q^{97} + 45 q^{98} + 11 q^{99}+O(q^{100}) \) 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 - 18 * q^11 - 2 * q^12 + 13 * q^13 - 20 * q^14 + 4 * q^15 - 2 * q^16 + 21 * q^17 - 2 * q^18 + 20 * q^19 + 4 * q^20 - 20 * q^21 + 11 * q^22 + 34 * q^23 - 2 * q^24 - 28 * q^25 - 16 * q^26 - 2 * q^27 + 9 * q^28 + 38 * q^29 + 4 * q^30 + 34 * q^31 - 2 * q^32 + 11 * q^33 - 8 * q^34 - 19 * q^35 - 2 * q^36 - 29 * q^37 + 20 * q^38 + 13 * q^39 + 4 * q^40 + 43 * q^41 + 9 * q^42 - 65 * q^43 + 11 * q^44 + 4 * q^45 + 5 * q^46 - 60 * q^47 - 2 * q^48 - 13 * q^49 - 86 * q^50 + 21 * q^51 - 16 * q^52 - 15 * q^53 - 2 * q^54 - 15 * q^55 + 9 * q^56 + 20 * q^57 - 78 * q^58 - 2 * q^59 - 54 * q^60 + 4 * q^61 + 5 * q^62 + 9 * q^63 - 2 * q^64 - 57 * q^65 + 11 * q^66 - 56 * q^67 - 8 * q^68 - 53 * q^69 + 10 * q^70 + 23 * q^71 - 2 * q^72 - 21 * q^73 + 30 * q^75 - 9 * q^76 - 57 * q^77 + 13 * q^78 + 99 * q^79 + 4 * q^80 - 2 * q^81 + 43 * q^82 + 33 * q^83 + 9 * q^84 - 45 * q^85 - 7 * q^86 + 9 * q^87 - 18 * q^88 + 32 * q^89 + 4 * q^90 - 75 * q^91 + 34 * q^92 + 5 * q^93 + 27 * q^94 + 82 * q^95 - 2 * q^96 + 70 * q^97 + 45 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{18}{29}\right)$	$1$

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 $

$2$	−0.370138	+	0.928977i	−0.261727	+	0.656886i
$2$	−0.370138	+	0.928977i	−0.261727	+	0.656886i
$3$	−0.994138	−	0.108119i	−0.573966	−	0.0624225i
$3$	−0.994138	−	0.108119i	−0.573966	−	0.0624225i
$4$	−0.725995	−	0.687699i	−0.362998	−	0.343850i
$5$	0.386052	−	0.454496i	0.172648	−	0.203257i	−0.669032	−	0.743234i	$-0.733291\pi$
$5$	0.386052	−	0.454496i	0.172648	−	0.203257i	0.841680	+	0.539977i	$0.181567\pi$
$6$	0.468408	−	0.883512i	0.191227	−	0.360692i
$7$	−0.965403	−	0.580863i	−0.364888	−	0.219546i	0.321288	−	0.946982i	$-0.395884\pi$
$7$	−0.965403	−	0.580863i	−0.364888	−	0.219546i	−0.686176	+	0.727436i	$0.740712\pi$
$8$	0.907575	−	0.419889i	0.320876	−	0.148453i
$9$	0.976621	+	0.214970i	0.325540	+	0.0716568i
$10$	0.279324	+	0.526860i	0.0883299	+	0.166608i
$11$	−0.122936	+	2.26742i	−0.0370665	+	0.683652i	0.919669	+	0.392694i	$0.128457\pi$
$11$	−0.122936	+	2.26742i	−0.0370665	+	0.683652i	−0.956736	+	0.290958i	$0.906026\pi$
$12$	0.647386	+	0.762162i	0.186884	+	0.220017i
$13$	4.07510	−	0.896998i	1.13023	−	0.248782i	0.389789	−	0.920904i	$-0.372548\pi$
$13$	4.07510	−	0.896998i	1.13023	−	0.248782i	0.740441	+	0.672122i	$0.234617\pi$
$14$	0.896941	−	0.681837i	0.239718	−	0.182229i
$15$	−0.432929	+	0.410092i	−0.111782	+	0.105885i
$16$	0.0541389	+	0.998533i	0.0135347	+	0.249633i
$17$	5.71670	−	3.43962i	1.38650	−	0.834231i	0.390250	−	0.920709i	$-0.372389\pi$
$17$	5.71670	−	3.43962i	1.38650	−	0.834231i	0.996254	+	0.0864778i	$0.0275612\pi$
$18$	−0.561187	+	0.827689i	−0.132273	+	0.195088i
$19$	2.13760	−	7.69894i	0.490399	−	1.76626i	−0.140173	−	0.990127i	$-0.544766\pi$
$19$	2.13760	−	7.69894i	0.490399	−	1.76626i	0.630572	−	0.776131i	$-0.282820\pi$
$20$	−0.592829	+	0.0644740i	−0.132561	+	0.0144168i
$21$	0.896941	+	0.681837i	0.195729	+	0.148789i
$22$	−2.06088	−	0.953462i	−0.439380	−	0.203279i
$23$	2.81244	+	4.14804i	0.586435	+	0.864927i	0.998940	−	0.0460282i	$-0.0146564\pi$
$23$	2.81244	+	4.14804i	0.586435	+	0.864927i	−0.412505	+	0.910955i	$0.635346\pi$
$24$	−0.947653	+	0.319302i	−0.193439	+	0.0651772i
$25$	0.751380	+	4.58321i	0.150276	+	0.916643i
$26$	−0.675061	+	4.11769i	−0.132390	+	0.807545i
$27$	−0.947653	−	0.319302i	−0.182376	−	0.0614496i
$28$	0.301418	+	1.08561i	0.0569627	+	0.205161i
$29$	3.25034	+	8.15774i	0.603573	+	1.51485i	0.839655	+	0.543121i	$0.182757\pi$
$29$	3.25034	+	8.15774i	0.603573	+	1.51485i	−0.236082	+	0.971733i	$0.575863\pi$
$30$	−0.220723	−	0.553972i	−0.0402982	−	0.101141i
$31$	−0.329268	−	1.18592i	−0.0591382	−	0.212997i	0.928077	−	0.372388i	$-0.121461\pi$
$31$	−0.329268	−	1.18592i	−0.0591382	−	0.212997i	−0.987216	+	0.159391i	$0.949047\pi$
$32$	−0.947653	−	0.319302i	−0.167523	−	0.0564451i
$33$	0.367366	−	2.24083i	0.0639502	−	0.390079i
$34$	1.07936	+	6.58382i	0.185109	+	1.12912i
$35$	−0.636696	+	0.214528i	−0.107621	+	0.0362618i
$36$	−0.561187	−	0.827689i	−0.0935312	−	0.137948i
$37$	−5.36817	−	2.48358i	−0.882521	−	0.408298i	−0.0743407	−	0.997233i	$-0.523685\pi$
$37$	−5.36817	−	2.48358i	−0.882521	−	0.408298i	−0.808180	+	0.588935i	$0.799547\pi$
$38$	6.36093	+	4.83545i	1.03188	+	0.784414i
$39$	−4.14820	+	0.451144i	−0.664243	+	0.0722408i
$40$	0.159534	−	0.574589i	0.0252245	−	0.0908505i
$41$	4.88237	−	7.20096i	0.762499	−	1.12460i	−0.226111	−	0.974101i	$-0.572601\pi$
$41$	4.88237	−	7.20096i	0.762499	−	1.12460i	0.988610	−	0.150500i	$-0.0480883\pi$
$42$	−0.965403	+	0.580863i	−0.148965	+	0.0896292i
$43$	−0.0625351	−	1.15339i	−0.00953652	−	0.175891i	−0.999421	−	0.0340168i	$-0.989170\pi$
$43$	−0.0625351	−	1.15339i	−0.00953652	−	0.175891i	0.989885	−	0.141874i	$-0.0453127\pi$
$44$	1.64855	−	1.56159i	0.248529	−	0.235419i
$45$	0.474730	−	0.360880i	0.0707686	−	0.0537969i
$46$	−4.89443	+	1.07735i	−0.721644	+	0.158846i
$47$	1.55402	+	1.82954i	0.226678	+	0.266866i	0.863730	−	0.503955i	$-0.168122\pi$
$47$	1.55402	+	1.82954i	0.226678	+	0.266866i	−0.637052	+	0.770821i	$0.719846\pi$
$48$	0.0541389	−	0.998533i	0.00781428	−	0.144126i
$49$	−2.68426	−	5.06305i	−0.383466	−	0.723293i
$50$	−4.53581	−	0.998408i	−0.641461	−	0.141196i
$51$	−6.05508	+	2.80138i	−0.847880	+	0.392271i
$52$	−3.57537	−	2.15123i	−0.495815	−	0.298322i
$53$	−0.784434	+	1.47960i	−0.107750	+	0.203239i	−0.931524	−	0.363681i	$-0.881520\pi$
$53$	−0.784434	+	1.47960i	−0.107750	+	0.203239i	0.823773	+	0.566919i	$0.191865\pi$
$54$	0.647386	−	0.762162i	0.0880981	−	0.103717i
$55$	0.983073	+	0.931216i	0.132558	+	0.125565i
$56$	−1.12007	−	0.121815i	−0.149676	−	0.0162783i
$57$	−2.95747	+	7.42269i	−0.391727	+	0.983160i
$58$	−8.78142			−1.15306
$59$	3.86141	+	6.64000i	0.502712	+	0.864454i
$59$	3.86141	+	6.64000i	0.502712	+	0.864454i
$60$	0.596325			0.0769852
$61$	5.03588	−	12.6391i	0.644778	−	1.61827i	−0.134008	−	0.990980i	$-0.542785\pi$
$61$	5.03588	−	12.6391i	0.644778	−	1.61827i	0.778786	−	0.627290i	$-0.215836\pi$
$62$	1.22356	+	0.133070i	0.155393	+	0.0169000i
$63$	−0.817963	−	0.774816i	−0.103054	−	0.0976177i
$64$	0.647386	−	0.762162i	0.0809233	−	0.0952703i
$65$	1.16552	−	2.19841i	0.144565	−	0.272679i
$66$	1.94571	+	1.17069i	0.239500	+	0.144102i
$67$	−5.55672	+	2.57081i	−0.678861	+	0.314075i	−0.728848	−	0.684675i	$-0.759944\pi$
$67$	−5.55672	+	2.57081i	−0.678861	+	0.314075i	0.0499871	+	0.998750i	$0.484082\pi$
$68$	−6.51573	−	1.43422i	−0.790148	−	0.173925i
$69$	−2.34747	−	4.42781i	−0.282603	−	0.533045i
$70$	0.0363741	−	0.670881i	0.00434754	−	0.0801856i
$71$	−8.37126	−	9.85541i	−0.993486	−	1.16962i	−0.985504	−	0.169654i	$-0.945735\pi$
$71$	−8.37126	−	9.85541i	−0.993486	−	1.16962i	−0.00798228	−	0.999968i	$-0.502541\pi$
$72$	0.976621	−	0.214970i	0.115096	−	0.0253345i
$73$	−6.23187	+	4.73734i	−0.729385	+	0.554464i	−0.902631	−	0.430415i	$-0.858367\pi$
$73$	−6.23187	+	4.73734i	−0.729385	+	0.554464i	0.173247	+	0.984878i	$0.444574\pi$
$74$	4.29415	−	4.06763i	0.499185	−	0.472853i
$75$	−0.251443	−	4.63759i	−0.0290341	−	0.535502i
$76$	−6.84645	+	4.11937i	−0.785341	+	0.472524i
$77$	1.43574	−	2.11756i	0.163618	−	0.241319i
$78$	1.11630	−	4.02056i	0.126397	−	0.455239i
$79$	9.40326	−	1.02267i	1.05795	−	0.115059i	0.437432	−	0.899252i	$-0.355888\pi$
$79$	9.40326	−	1.02267i	1.05795	−	0.115059i	0.620518	+	0.784193i	$0.286923\pi$
$80$	0.474730	+	0.360880i	0.0530764	+	0.0403477i
$81$	0.907575	+	0.419889i	0.100842	+	0.0466543i
$82$	4.88237	+	7.20096i	0.539168	+	0.795213i
$83$	−15.2631	+	5.14275i	−1.67535	+	0.564490i	−0.986976	−	0.160867i	$-0.948571\pi$
$83$	−15.2631	+	5.14275i	−1.67535	+	0.564490i	−0.688372	+	0.725358i	$0.741674\pi$
$84$	−0.182276	−	1.11184i	−0.0198880	−	0.121311i
$85$	0.643650	−	3.92609i	0.0698137	−	0.425845i
$86$	1.09462	+	0.368821i	0.118036	+	0.0397710i
$87$	−2.34928	−	8.46134i	−0.251869	−	0.907151i
$88$	0.840490	+	2.10947i	0.0895966	+	0.224870i
$89$	2.45819	+	6.16959i	0.260568	+	0.653976i	0.999811	−	0.0194633i	$-0.00619574\pi$
$89$	2.45819	+	6.16959i	0.260568	+	0.653976i	−0.739243	+	0.673439i	$0.764816\pi$
$90$	0.159534	+	0.574589i	0.0168163	+	0.0605670i
$91$	−4.45515	−	1.50111i	−0.467026	−	0.157359i
$92$	0.810786	−	4.94558i	0.0845303	−	0.515612i
$93$	0.199118	+	1.21456i	0.0206475	+	0.125944i
$94$	−2.27480	+	0.766471i	−0.234628	+	0.0790554i
$95$	−2.67391	−	3.94373i	−0.274338	−	0.404618i
$96$	0.907575	+	0.419889i	0.0926290	+	0.0428548i
$97$	1.03773	+	0.788865i	0.105366	+	0.0800971i	0.656531	−	0.754299i	$-0.272023\pi$
$97$	1.03773	+	0.788865i	0.105366	+	0.0800971i	−0.551165	+	0.834396i	$0.685816\pi$
$98$	5.69700	−	0.619586i	0.575484	−	0.0625877i
$99$	−0.607489	+	2.18798i	−0.0610550	+	0.219900i
$100$	2.60638	−	3.84412i	0.260638	−	0.384412i
$101$	3.97202	−	2.38989i	0.395231	−	0.237803i	−0.304040	−	0.952659i	$-0.598336\pi$
$101$	3.97202	−	2.38989i	0.395231	−	0.237803i	0.699271	+	0.714857i	$0.253508\pi$
$102$	−0.361199	−	6.66192i	−0.0357640	−	0.659629i
$103$	−8.64154	+	8.18570i	−0.851476	+	0.806561i	−0.982780	−	0.184781i	$-0.940842\pi$
$103$	−8.64154	+	8.18570i	−0.851476	+	0.806561i	0.131303	+	0.991342i	$0.458084\pi$
$104$	3.32182	−	2.52518i	0.325732	−	0.247615i
$105$	0.656158	−	0.144431i	0.0640345	−	0.0140951i
$106$	−1.08416	−	1.27638i	−0.105303	−	0.123973i
$107$	0.682125	−	12.5811i	0.0659435	−	1.21626i	−0.759019	−	0.651069i	$-0.774321\pi$
$107$	0.682125	−	12.5811i	0.0659435	−	1.21626i	0.824962	−	0.565188i	$-0.191196\pi$
$108$	0.468408	+	0.883512i	0.0450726	+	0.0850160i
$109$	6.82277	+	1.50181i	0.653503	+	0.143847i	0.529333	−	0.848414i	$-0.322442\pi$
$109$	6.82277	+	1.50181i	0.653503	+	0.143847i	0.124170	+	0.992261i	$0.460373\pi$
$110$	−1.22895	+	0.568573i	−0.117176	+	0.0542113i
$111$	5.06817	+	3.04942i	0.481050	+	0.289438i
$112$	0.527746	−	0.995434i	0.0498673	−	0.0940597i
$113$	−4.42489	+	5.20939i	−0.416259	+	0.490058i	−0.929830	−	0.367989i	$-0.880046\pi$
$113$	−4.42489	+	5.20939i	−0.416259	+	0.490058i	0.513571	+	0.858047i	$0.328322\pi$
$114$	−5.80084	−	5.49484i	−0.543298	−	0.514639i
$115$	2.97102	+	0.323118i	0.277049	+	0.0301309i
$116$	3.25034	−	8.15774i	0.301787	−	0.757427i
$117$	4.17266			0.385762
$118$	−7.59766	+	1.12944i	−0.699421	+	0.103973i
$119$	−7.51687			−0.689070
$120$	−0.220723	+	0.553972i	−0.0201491	+	0.0505705i
$121$	5.80945	+	0.631816i	0.528132	+	0.0574378i
$122$	9.87746	+	9.35642i	0.894263	+	0.847091i
$123$	−5.63231	+	6.63087i	−0.507849	+	0.597886i
$124$	−0.576506	+	1.08741i	−0.0517718	+	0.0976520i
$125$	4.92795	+	2.96505i	0.440769	+	0.265202i
$126$	1.02255	−	0.473080i	0.0910956	−	0.0421453i
$127$	6.64643	+	1.46299i	0.589775	+	0.129819i	0.499824	−	0.866127i	$-0.333398\pi$
$127$	6.64643	+	1.46299i	0.589775	+	0.129819i	0.0899510	+	0.995946i	$0.471329\pi$
$128$	0.468408	+	0.883512i	0.0414018	+	0.0780922i
$129$	−0.0625351	+	1.15339i	−0.00550591	+	0.101551i
$130$	1.61086	+	1.89646i	0.141282	+	0.166330i
$131$	−6.23465	+	1.37235i	−0.544724	+	0.119903i	−0.478804	−	0.877922i	$-0.658929\pi$
$131$	−6.23465	+	1.37235i	−0.544724	+	0.119903i	−0.0659206	+	0.997825i	$0.520998\pi$
$132$	−1.80773	+	1.37420i	−0.157342	+	0.119609i
$133$	−6.53568	+	6.19092i	−0.566715	+	0.536821i
$134$	−0.331471	−	6.11362i	−0.0286347	−	0.528136i
$135$	−0.510965	+	0.307438i	−0.0439769	+	0.0264600i
$136$	3.74408	−	5.52210i	0.321052	−	0.473516i
$137$	−3.86157	+	13.9081i	−0.329916	+	1.18825i	0.593622	+	0.804744i	$0.297698\pi$
$137$	−3.86157	+	13.9081i	−0.329916	+	1.18825i	−0.923538	+	0.383507i	$0.874716\pi$
$138$	4.98222	−	0.541849i	0.424115	−	0.0461253i
$139$	−8.69994	−	6.61352i	−0.737919	−	0.560951i	0.167295	−	0.985907i	$-0.446497\pi$
$139$	−8.69994	−	6.61352i	−0.737919	−	0.560951i	−0.905214	+	0.424955i	$0.860290\pi$
$140$	0.609769	+	0.282109i	0.0515349	+	0.0238426i
$141$	−1.34711	−	1.98683i	−0.113447	−	0.167322i
$142$	12.2540	−	4.12884i	1.02833	−	0.346485i
$143$	1.53289	+	9.35023i	0.128187	+	0.781906i
$144$	−0.161782	+	0.986827i	−0.0134818	+	0.0822355i
$145$	4.96246	+	1.67205i	0.412110	+	0.138856i
$146$	−2.09423	−	7.54273i	−0.173320	−	0.624241i
$147$	2.12111	+	5.32359i	0.174946	+	0.439082i
$148$	2.18931	+	5.49475i	0.179960	+	0.451666i
$149$	−0.542190	−	1.95279i	−0.0444179	−	0.159979i	0.938015	−	0.346594i	$-0.112662\pi$
$149$	−0.542190	−	1.95279i	−0.0444179	−	0.159979i	−0.982433	+	0.186615i	$0.940248\pi$
$150$	4.40128	+	1.48296i	0.359363	+	0.121083i
$151$	−2.88221	+	17.5807i	−0.234551	+	1.43070i	0.562505	+	0.826794i	$0.309838\pi$
$151$	−2.88221	+	17.5807i	−0.234551	+	1.43070i	−0.797056	+	0.603905i	$0.793611\pi$
$152$	−1.29267	−	7.88492i	−0.104849	−	0.639552i
$153$	6.32246	−	2.13029i	0.511141	−	0.172223i
$154$	1.43574	+	2.11756i	0.115695	+	0.170638i
$155$	−0.666108	−	0.308175i	−0.0535031	−	0.0247532i
$156$	3.32182	+	2.52518i	0.265959	+	0.202177i
$157$	−9.66411	+	1.05104i	−0.771280	+	0.0838818i	−0.485293	−	0.874352i	$-0.661287\pi$
$157$	−9.66411	+	1.05104i	−0.771280	+	0.0838818i	−0.285987	+	0.958233i	$0.592321\pi$
$158$	−2.53047	+	9.11394i	−0.201314	+	0.725066i
$159$	0.939809	−	1.38611i	0.0745317	−	0.109926i
$160$	−0.510965	+	0.307438i	−0.0403953	+	0.0243051i
$161$	−0.305693	−	5.63818i	−0.0240920	−	0.444351i
$162$	−0.725995	+	0.687699i	−0.0570396	+	0.0540308i
$163$	6.46062	−	4.91123i	0.506035	−	0.384678i	−0.320778	−	0.947154i	$-0.603945\pi$
$163$	6.46062	−	4.91123i	0.506035	−	0.384678i	0.826813	+	0.562477i	$0.190151\pi$
$164$	−8.49668	+	1.87026i	−0.663479	+	0.146043i
$165$	−0.876628	−	1.03205i	−0.0682454	−	0.0803447i
$166$	0.871975	−	16.0826i	0.0676784	−	1.24825i
$167$	2.25024	+	4.24440i	0.174129	+	0.328442i	0.955180	−	0.296025i	$-0.0956611\pi$
$167$	2.25024	+	4.24440i	0.174129	+	0.328442i	−0.781051	+	0.624467i	$0.785316\pi$
$168$	1.10034	+	0.242203i	0.0848929	+	0.0186863i
$169$	4.00337	−	1.85216i	0.307952	−	0.142474i
$170$	3.40901	+	2.05113i	0.261459	+	0.157315i
$171$	3.74267	−	7.05942i	0.286209	−	0.539848i
$172$	−0.747787	+	0.880363i	−0.0570182	+	0.0671271i
$173$	−3.66404	−	3.47076i	−0.278572	−	0.263877i	0.535638	−	0.844447i	$-0.320071\pi$
$173$	−3.66404	−	3.47076i	−0.278572	−	0.263877i	−0.814210	+	0.580570i	$0.802830\pi$
$174$	8.72995	+	0.949439i	0.661816	+	0.0719768i
$175$	1.93684	−	4.86110i	0.146411	−	0.367464i
$176$	−2.27075			−0.171164
$177$	−3.12086	−	7.01856i	−0.234578	−	0.527548i
$178$	−6.64128			−0.497785
$179$	−3.14245	+	7.88696i	−0.234878	+	0.589499i	−0.998416	−	0.0562636i	$-0.982081\pi$
$179$	−3.14245	+	7.88696i	−0.234878	+	0.589499i	0.763538	+	0.645763i	$0.223461\pi$
$180$	−0.592829	−	0.0644740i	−0.0441869	−	0.00480561i
$181$	15.9618	+	15.1198i	1.18643	+	1.12384i	0.989666	+	0.143393i	$0.0458013\pi$
$181$	15.9618	+	15.1198i	1.18643	+	1.12384i	0.196762	+	0.980451i	$0.436957\pi$
$182$	3.04352	−	3.58311i	0.225601	−	0.265598i
$183$	−6.37288	+	12.0205i	−0.471097	+	0.888583i
$184$	4.29422	+	2.58375i	0.316574	+	0.190476i
$185$	−3.20117	+	1.48102i	−0.235355	+	0.108887i
$186$	−1.20200	−	0.264581i	−0.0881351	−	0.0194000i
$187$	7.09628	+	13.3850i	0.518931	+	0.978808i
$188$	0.129958	−	2.39694i	0.00947818	−	0.174815i
$189$	0.729396	+	0.858712i	0.0530558	+	0.0624621i
$190$	4.65335	−	1.02428i	0.337589	−	0.0743090i
$191$	4.31460	−	3.27987i	0.312193	−	0.237323i	−0.437330	−	0.899301i	$-0.644076\pi$
$191$	4.31460	−	3.27987i	0.312193	−	0.237323i	0.749523	+	0.661978i	$0.230283\pi$
$192$	−0.725995	+	0.687699i	−0.0523942	+	0.0496304i
$193$	0.520778	+	9.60518i	0.0374864	+	0.691396i	0.955526	+	0.294907i	$0.0952887\pi$
$193$	0.520778	+	9.60518i	0.0374864	+	0.691396i	−0.918040	+	0.396489i	$0.870229\pi$
$194$	−1.11694	+	0.672041i	−0.0801917	+	0.0482498i
$195$	−1.39638	+	2.05950i	−0.0999967	+	0.147484i
$196$	−1.53310	+	5.52172i	−0.109507	+	0.394408i
$197$	−12.7141	+	1.38274i	−0.905842	+	0.0985163i	−0.549167	−	0.835712i	$-0.685055\pi$
$197$	−12.7141	+	1.38274i	−0.905842	+	0.0985163i	−0.356675	+	0.934229i	$0.616090\pi$
$198$	−1.80773	−	1.37420i	−0.128470	−	0.0976600i
$199$	24.1505	+	11.1732i	1.71198	+	0.792048i	0.995534	+	0.0944086i	$0.0300960\pi$
$199$	24.1505	+	11.1732i	1.71198	+	0.792048i	0.716449	+	0.697639i	$0.245766\pi$
$200$	2.60638	+	3.84412i	0.184299	+	0.271820i
$201$	5.80210	−	1.95495i	0.409248	−	0.137892i
$202$	0.749952	+	4.57451i	0.0527665	+	0.321861i
$203$	1.60065	−	9.76351i	0.112343	−	0.685264i
$204$	6.32246	+	2.13029i	0.442661	+	0.149150i
$205$	−1.38796	−	4.99897i	−0.0969391	−	0.349143i
$206$	−4.40576	−	11.0576i	−0.306964	−	0.770422i
$207$	1.85498	+	4.65566i	0.128930	+	0.323591i
$208$	1.11630	+	4.02056i	0.0774017	+	0.278776i
$209$	17.1939	+	5.79331i	1.18933	+	0.400732i
$210$	−0.108696	+	0.663015i	−0.00750073	+	0.0457524i
$211$	−2.75338	−	16.7949i	−0.189551	−	1.15621i	−0.894539	−	0.446989i	$-0.852496\pi$
$211$	−2.75338	−	16.7949i	−0.189551	−	1.15621i	0.704989	−	0.709218i	$-0.250952\pi$
$212$	1.58702	−	0.534728i	0.108997	−	0.0367253i
$213$	7.25663	+	10.7027i	0.497216	+	0.733339i
$214$	11.4350	+	5.29041i	0.781682	+	0.361645i
$215$	−0.548354	−	0.416848i	−0.0373974	−	0.0284288i
$216$	−0.994138	+	0.108119i	−0.0676425	+	0.00735657i
$217$	−0.370979	+	1.33615i	−0.0251837	+	0.0907034i
$218$	−3.92051	+	5.78232i	−0.265531	+	0.391628i
$219$	6.70753	−	4.03579i	0.453253	−	0.272713i
$220$	−0.0733097	−	1.35212i	−0.00494254	−	0.0911597i
$221$	20.2108	−	19.1447i	1.35953	−	1.28781i
$222$	−4.70876	+	3.57951i	−0.316032	+	0.240241i
$223$	1.56778	−	0.345095i	0.104986	−	0.0231093i	−0.162166	−	0.986763i	$-0.551848\pi$
$223$	1.56778	−	0.345095i	0.104986	−	0.0231093i	0.267153	+	0.963654i	$0.413917\pi$
$224$	0.729396	+	0.858712i	0.0487348	+	0.0573751i
$225$	−0.251443	+	4.63759i	−0.0167628	+	0.309172i
$226$	−3.20158	−	6.03882i	−0.212966	−	0.401696i
$227$	−20.1402	−	4.43320i	−1.33675	−	0.294242i	−0.511636	−	0.859203i	$-0.670960\pi$
$227$	−20.1402	−	4.43320i	−1.33675	−	0.294242i	−0.825118	+	0.564961i	$0.808891\pi$
$228$	7.25169	−	3.35499i	0.480255	−	0.222190i
$229$	−23.3736	−	14.0634i	−1.54457	−	0.929339i	−0.995621	−	0.0934855i	$-0.970199\pi$
$229$	−23.3736	−	14.0634i	−1.54457	−	0.929339i	−0.548953	−	0.835853i	$-0.684973\pi$
$230$	−1.39986	+	2.64041i	−0.0923039	+	0.174104i
$231$	−1.65627	+	1.94992i	−0.108975	+	0.128295i
$232$	6.37527	+	6.03898i	0.418557	+	0.396479i
$233$	−0.574776	−	0.0625107i	−0.0376548	−	0.00409521i	0.0892722	−	0.996007i	$-0.471546\pi$
$233$	−0.574776	−	0.0625107i	−0.0376548	−	0.00409521i	−0.126927	+	0.991912i	$0.540511\pi$
$234$	−1.54446	+	3.87630i	−0.100964	+	0.253402i
$235$	1.43145			0.0933777
$236$	1.76296	−	7.47609i	0.114759	−	0.486652i
$237$	−9.45871			−0.614409
$238$	2.78228	−	6.98300i	0.180348	−	0.452640i
$239$	2.69339	+	0.292923i	0.174221	+	0.0189476i	0.194814	−	0.980840i	$-0.437590\pi$
$239$	2.69339	+	0.292923i	0.174221	+	0.0189476i	−0.0205928	+	0.999788i	$0.506555\pi$
$240$	−0.432929	−	0.410092i	−0.0279455	−	0.0264713i
$241$	9.24234	−	10.8809i	0.595352	−	0.700902i	−0.379137	−	0.925341i	$-0.623779\pi$
$241$	9.24234	−	10.8809i	0.595352	−	0.700902i	0.974488	+	0.224439i	$0.0720548\pi$
$242$	−2.73724	+	5.16298i	−0.175956	+	0.331889i
$243$	−0.856857	−	0.515554i	−0.0549674	−	0.0330728i
$244$	−12.3479	+	5.71276i	−0.790495	+	0.365722i
$245$	−3.33740	−	0.734618i	−0.213219	−	0.0469330i
$246$	−4.07519	−	7.68663i	−0.259825	−	0.490081i
$247$	1.80501	−	33.2914i	0.114850	−	2.11828i
$248$	−0.796788	−	0.938052i	−0.0505961	−	0.0595663i
$249$	15.7297	−	3.46237i	0.996829	−	0.219419i
$250$	−4.57848	+	3.48047i	−0.289569	+	0.220124i
$251$	−15.5410	+	14.7212i	−0.980937	+	0.929193i	−0.997500	−	0.0706698i	$-0.977486\pi$
$251$	−15.5410	+	14.7212i	−0.980937	+	0.929193i	0.0165626	+	0.999863i	$0.494728\pi$
$252$	0.0609971	+	1.12503i	0.00384246	+	0.0708700i
$253$	−9.75110	+	5.86704i	−0.613046	+	0.368858i
$254$	−3.81918	+	5.63287i	−0.239637	+	0.353438i
$255$	−1.06436	+	3.83349i	−0.0666530	+	0.240062i
$256$	−0.994138	+	0.108119i	−0.0621336	+	0.00675744i
$257$	−16.1647	−	12.2881i	−1.00833	−	0.766510i	−0.0358137	−	0.999358i	$-0.511402\pi$
$257$	−16.1647	−	12.2881i	−1.00833	−	0.766510i	−0.972513	+	0.232848i	$0.925195\pi$
$258$	−1.04833	−	0.485008i	−0.0652661	−	0.0301953i
$259$	3.73982	+	5.51582i	0.232381	+	0.342737i
$260$	−2.35801	+	0.794505i	−0.146237	+	0.0492731i
$261$	1.42068	+	8.66574i	0.0879377	+	0.536396i
$262$	1.03280	−	6.29981i	0.0638067	−	0.389203i
$263$	15.1446	+	5.10280i	0.933855	+	0.314652i	0.744780	−	0.667310i	$-0.232554\pi$
$263$	15.1446	+	5.10280i	0.933855	+	0.314652i	0.189075	+	0.981963i	$0.439451\pi$
$264$	−0.607489	−	2.18798i	−0.0373884	−	0.134661i
$265$	0.369640	+	0.927725i	0.0227068	+	0.0569897i
$266$	−3.33212	−	8.36299i	−0.204305	−	0.512768i
$267$	−1.77673	−	6.39920i	−0.108734	−	0.391625i
$268$	5.80210	+	1.95495i	0.354420	+	0.119418i
$269$	−1.25169	+	7.63498i	−0.0763170	+	0.465513i	0.920826	+	0.389974i	$0.127516\pi$
$269$	−1.25169	+	7.63498i	−0.0763170	+	0.465513i	−0.997143	+	0.0755389i	$0.975932\pi$
$270$	−0.0964746	−	0.588469i	−0.00587126	−	0.0358131i
$271$	−0.391546	+	0.131927i	−0.0237847	+	0.00801401i	−0.331169	−	0.943572i	$-0.607443\pi$
$271$	−0.391546	+	0.131927i	−0.0237847	+	0.00801401i	0.307384	+	0.951586i	$0.400546\pi$
$272$	3.74408	+	5.52210i	0.227018	+	0.334826i
$273$	4.26673	+	1.97400i	0.258234	+	0.119472i
$274$	−11.4910	−	8.73524i	−0.694197	−	0.527715i
$275$	−10.4844	+	1.14025i	−0.632235	+	0.0687597i
$276$	−1.34074	+	4.82893i	−0.0807033	+	0.290667i
$277$	1.94834	−	2.87359i	0.117065	−	0.172657i	−0.764642	−	0.644455i	$-0.777084\pi$
$277$	1.94834	−	2.87359i	0.117065	−	0.172657i	0.881707	+	0.471798i	$0.156395\pi$
$278$	9.36399	−	5.63412i	0.561615	−	0.337912i
$279$	−0.0666329	−	1.22897i	−0.00398921	−	0.0735766i
$280$	−0.487772	+	0.462042i	−0.0291499	+	0.0276123i
$281$	7.48856	−	5.69266i	0.446730	−	0.339596i	−0.357500	−	0.933913i	$-0.616371\pi$
$281$	7.48856	−	5.69266i	0.446730	−	0.339596i	0.804230	+	0.594318i	$0.202578\pi$
$282$	2.34434	−	0.516028i	0.139603	−	0.0307290i
$283$	2.04316	+	2.40540i	0.121453	+	0.142986i	0.819528	−	0.573039i	$-0.194236\pi$
$283$	2.04316	+	2.40540i	0.121453	+	0.142986i	−0.698075	+	0.716025i	$0.745960\pi$
$284$	−0.700063	+	12.9119i	−0.0415411	+	0.766180i
$285$	2.23185	+	4.20971i	0.132203	+	0.249362i
$286$	−9.25353	−	2.03686i	−0.547173	−	0.120442i
$287$	−8.89623	+	4.11583i	−0.525128	+	0.242950i
$288$	−0.856857	−	0.515554i	−0.0504908	−	0.0303793i
$289$	12.8867	−	24.3069i	0.758041	−	1.42982i
$290$	−3.39009	+	3.99112i	−0.199073	+	0.234367i
$291$	−0.946359	−	0.896439i	−0.0554765	−	0.0525502i
$292$	7.78217	+	0.846362i	0.455417	+	0.0495296i
$293$	−0.338073	+	0.848500i	−0.0197504	+	0.0495699i	−0.938521	−	0.345221i	$-0.887804\pi$
$293$	−0.338073	+	0.848500i	−0.0197504	+	0.0495699i	0.918771	+	0.394791i	$0.129183\pi$
$294$	−5.73060			−0.334215
$295$	4.50856	+	0.808393i	0.262498	+	0.0470664i
$296$	−5.91484			−0.343793
$297$	0.840490	−	2.10947i	0.0487702	−	0.122404i
$298$	2.01478	+	0.219121i	0.116713	+	0.0126933i
$299$	15.1818	+	14.3809i	0.877985	+	0.831672i
$300$	−3.00672	+	3.53978i	−0.173593	+	0.204369i
$301$	−0.609592	+	1.14981i	−0.0351363	+	0.0662741i
$302$	−15.2653	−	9.18480i	−0.878417	−	0.528526i
$303$	−4.20713	+	1.94643i	−0.241693	+	0.111819i
$304$	7.80338	+	1.71765i	0.447554	+	0.0985142i
$305$	−3.80031	−	7.16814i	−0.217605	−	0.410446i
$306$	−0.361199	+	6.66192i	−0.0206484	+	0.380837i
$307$	−7.43221	−	8.74987i	−0.424178	−	0.499381i	0.508012	−	0.861350i	$-0.330381\pi$
$307$	−7.43221	−	8.74987i	−0.424178	−	0.499381i	−0.932190	+	0.361969i	$0.882105\pi$
$308$	−2.49859	+	0.549981i	−0.142370	+	0.0313381i
$309$	9.47591	−	7.20340i	0.539066	−	0.409787i
$310$	0.532839	−	0.504732i	0.0302632	−	0.0286669i
$311$	−0.481271	−	8.87652i	−0.0272904	−	0.503341i	−0.979943	−	0.199280i	$-0.936140\pi$
$311$	−0.481271	−	8.87652i	−0.0272904	−	0.503341i	0.952652	−	0.304062i	$-0.0983429\pi$
$312$	−3.57537	+	2.15123i	−0.202416	+	0.121789i
$313$	−10.8642	+	16.0235i	−0.614081	+	0.905702i	−0.999857	−	0.0168904i	$-0.994623\pi$
$313$	−10.8642	+	16.0235i	−0.614081	+	0.905702i	0.385776	+	0.922592i	$0.373934\pi$
$314$	2.60067	−	9.36676i	0.146764	−	0.528597i
$315$	−0.667928	+	0.0726415i	−0.0376335	+	0.00409289i
$316$	−7.53001	−	5.72417i	−0.423596	−	0.322009i
$317$	−25.3569	−	11.7314i	−1.42419	−	0.658898i	−0.451766	−	0.892136i	$-0.649206\pi$
$317$	−25.3569	−	11.7314i	−1.42419	−	0.658898i	−0.972420	+	0.233238i	$0.925068\pi$
$318$	0.939809	+	1.38611i	0.0527019	+	0.0777294i
$319$	−18.8966	+	6.36700i	−1.05801	+	0.356484i
$320$	−0.0964746	−	0.588469i	−0.00539309	−	0.0328964i
$321$	−2.03838	+	12.4336i	−0.113771	+	0.693973i
$322$	5.35089	+	1.80292i	0.298193	+	0.100473i
$323$	−14.2614	−	51.3651i	−0.793528	−	2.85803i
$324$	−0.370138	−	0.928977i	−0.0205632	−	0.0516098i
$325$	7.17308	+	18.0031i	0.397891	+	0.998631i
$326$	2.17110	+	7.81960i	0.120246	+	0.433088i
$327$	−6.62040	−	2.23067i	−0.366109	−	0.123357i
$328$	1.40752	−	8.58547i	0.0777171	−	0.474053i
$329$	−0.437547	−	2.66892i	−0.0241227	−	0.147142i
$330$	1.28322	−	0.432367i	0.0706389	−	0.0238010i
$331$	−3.75755	−	5.54197i	−0.206533	−	0.304614i	0.710288	−	0.703911i	$-0.248565\pi$
$331$	−3.75755	−	5.54197i	−0.206533	−	0.304614i	−0.916822	+	0.399297i	$0.869254\pi$
$332$	14.6176	+	6.76284i	0.802247	+	0.371159i
$333$	−4.70876	−	3.57951i	−0.258039	−	0.196156i
$334$	−4.77585	+	0.519405i	−0.261323	+	0.0284206i
$335$	−0.976761	+	3.51798i	−0.0533662	+	0.192208i
$336$	−0.632277	+	0.932539i	−0.0344936	+	0.0508742i
$337$	10.1888	−	6.13039i	0.555018	−	0.333943i	−0.210257	−	0.977646i	$-0.567430\pi$
$337$	10.1888	−	6.13039i	0.555018	−	0.333943i	0.765276	+	0.643703i	$0.222603\pi$
$338$	0.238810	+	4.40459i	0.0129896	+	0.239578i
$339$	4.96219	−	4.70043i	0.269509	−	0.255293i
$340$	−3.16726	+	2.40769i	−0.171769	+	0.130575i
$341$	2.72944	−	0.600796i	0.147808	−	0.0325349i
$342$	5.17273	+	6.08981i	0.279709	+	0.329299i
$343$	−0.776530	+	14.3223i	−0.0419287	+	0.773329i
$344$	−0.541052	−	1.02053i	−0.0291716	−	0.0550234i
$345$	−2.91867	−	0.642448i	−0.157136	−	0.0345882i
$346$	4.58046	−	2.11914i	0.246247	−	0.113926i
$347$	−11.4148	−	6.86808i	−0.612781	−	0.368698i	0.175077	−	0.984555i	$-0.443982\pi$
$347$	−11.4148	−	6.86808i	−0.612781	−	0.368698i	−0.787858	+	0.615857i	$0.788810\pi$
$348$	−4.11329	+	7.75849i	−0.220496	+	0.415899i
$349$	−22.1803	+	26.1127i	−1.18729	+	1.39778i	−0.289597	+	0.957149i	$0.593521\pi$
$349$	−22.1803	+	26.1127i	−1.18729	+	1.39778i	−0.897688	+	0.440631i	$0.854755\pi$
$350$	3.79895	+	3.59855i	0.203062	+	0.192351i
$351$	−4.14820	−	0.451144i	−0.221414	−	0.0240803i
$352$	0.840490	−	2.10947i	0.0447983	−	0.112435i
$353$	0.848429			0.0451573			0.0225787	−	0.999745i	$-0.492812\pi$
$353$	0.848429			0.0451573			0.0225787	+	0.999745i	$0.492812\pi$
$354$	7.67523	−	0.301369i	0.407934	−	0.0160176i
$355$	−7.71099			−0.409257
$356$	2.45819	−	6.16959i	0.130284	−	0.326988i
$357$	7.47280	+	0.812716i	0.395503	+	0.0430135i
$358$	−6.16366	−	5.83853i	−0.325760	−	0.308576i
$359$	8.70576	−	10.2492i	0.459473	−	0.540933i	−0.482822	−	0.875719i	$-0.660388\pi$
$359$	8.70576	−	10.2492i	0.459473	−	0.540933i	0.942294	+	0.334786i	$0.108664\pi$
$360$	0.279324	−	0.526860i	0.0147216	−	0.0277680i
$361$	−38.4241	−	23.1190i	−2.02232	−	1.21679i
$362$	−19.9540	+	9.23169i	−1.04876	+	0.485207i
$363$	−5.70708	−	1.25622i	−0.299544	−	0.0659346i
$364$	2.20210	+	4.15360i	0.115421	+	0.217708i
$365$	−0.252724	+	4.66122i	−0.0132282	+	0.243979i
$366$	−8.80795	−	10.3695i	−0.460399	−	0.542023i
$367$	35.7451	−	7.86810i	1.86588	−	0.410711i	0.869369	−	0.494164i	$-0.164526\pi$
$367$	35.7451	−	7.86810i	1.86588	−	0.410711i	0.996512	+	0.0834527i	$0.0265948\pi$
$368$	−3.98970	+	3.03289i	−0.207977	+	0.158100i
$369$	6.31622	−	5.98304i	0.328809	−	0.311465i
$370$	−0.190957	−	3.52199i	−0.00992738	−	0.183100i
$371$	1.61674	−	0.972760i	0.0839370	−	0.0505032i
$372$	0.690696	−	1.01870i	0.0358109	−	0.0528172i
$373$	−5.08088	+	18.2997i	−0.263078	+	0.947520i	0.707496	+	0.706717i	$0.249825\pi$
$373$	−5.08088	+	18.2997i	−0.263078	+	0.947520i	−0.970574	+	0.240803i	$0.922589\pi$
$374$	−15.0610	+	1.63798i	−0.778783	+	0.0846978i
$375$	−4.57848	−	3.48047i	−0.236432	−	0.179731i
$376$	2.17860	+	1.00793i	0.112353	+	0.0519799i
$377$	20.5629	+	30.3281i	1.05905	+	1.56198i
$378$	−1.06770	+	0.359750i	−0.0549166	+	0.0185036i
$379$	1.12630	+	6.87012i	0.0578541	+	0.352894i	0.999851	+	0.0172723i	$0.00549821\pi$
$379$	1.12630	+	6.87012i	0.0578541	+	0.352894i	−0.941997	+	0.335622i	$0.891054\pi$
$380$	−0.770850	+	4.70198i	−0.0395438	+	0.241206i
$381$	−6.44929	−	2.17302i	−0.330407	−	0.111327i
$382$	1.44993	+	5.22217i	0.0741847	+	0.267189i
$383$	10.9102	+	27.3826i	0.557487	+	1.39919i	0.889944	+	0.456069i	$0.150743\pi$
$383$	10.9102	+	27.3826i	0.557487	+	1.39919i	−0.332457	+	0.943118i	$0.607878\pi$
$384$	−0.370138	−	0.928977i	−0.0188885	−	0.0474066i
$385$	−0.408152	−	1.47003i	−0.0208013	−	0.0749196i
$386$	−9.11574	−	3.07145i	−0.463979	−	0.156333i
$387$	0.186872	−	1.13987i	0.00949925	−	0.0579428i
$388$	−0.210888	−	1.28636i	−0.0107062	−	0.0653051i
$389$	−18.0856	+	6.09374i	−0.916976	+	0.308965i	−0.737931	−	0.674876i	$-0.764197\pi$
$389$	−18.0856	+	6.09374i	−0.916976	+	0.308965i	−0.179044	+	0.983841i	$0.557301\pi$
$390$	−1.39638	−	2.05950i	−0.0707084	−	0.104287i
$391$	30.3456	+	14.0394i	1.53464	+	0.710002i
$392$	−4.56209	−	3.46801i	−0.230420	−	0.175161i
$393$	6.34648	−	0.690222i	0.320138	−	0.0348171i
$394$	3.42144	−	12.3229i	0.172370	−	0.620819i
$395$	3.16535	−	4.66855i	0.159266	−	0.234900i
$396$	1.94571	−	1.17069i	0.0977754	−	0.0588295i
$397$	−1.72574	−	31.8295i	−0.0866126	−	1.59747i	−0.642545	−	0.766248i	$-0.722122\pi$
$397$	−1.72574	−	31.8295i	−0.0866126	−	1.59747i	0.555933	−	0.831227i	$-0.312361\pi$
$398$	−19.3187	+	18.2996i	−0.968357	+	0.917277i
$399$	7.16672	−	5.44800i	0.358785	−	0.272741i
$400$	−4.53581	+	0.998408i	−0.226791	+	0.0499204i
$401$	9.58339	+	11.2824i	0.478571	+	0.563418i	0.947474	−	0.319832i	$-0.103626\pi$
$401$	9.58339	+	11.2824i	0.478571	+	0.563418i	−0.468903	+	0.883250i	$0.655351\pi$
$402$	−0.331471	+	6.11362i	−0.0165323	+	0.304920i
$403$	−2.40556	−	4.53737i	−0.119830	−	0.226023i
$404$	−4.52720	−	0.996511i	−0.225236	−	0.0495783i
$405$	0.541210	−	0.250390i	0.0268929	−	0.0124420i
$406$	8.47761	+	5.10081i	0.420737	+	0.253149i
$407$	6.29125	−	11.8666i	0.311846	−	0.588203i
$408$	−4.31917	+	5.08492i	−0.213831	+	0.251741i
$409$	−26.1387	−	24.7599i	−1.29248	−	1.22430i	−0.959613	−	0.281324i	$-0.909227\pi$
$409$	−26.1387	−	24.7599i	−1.29248	−	1.22430i	−0.332863	−	0.942975i	$-0.608015\pi$
$410$	5.15766	+	0.560929i	0.254719	+	0.0277023i
$411$	5.34267	−	13.4091i	0.263534	−	0.661421i
$412$	11.9030			0.586420
$413$	0.129119	−	8.65322i	0.00635354	−	0.425797i
$414$	−5.01160			−0.246307
$415$	−3.55501	+	8.92241i	−0.174509	+	0.437984i
$416$	−4.14820	−	0.451144i	−0.203382	−	0.0221191i
$417$	7.93389	+	7.51538i	0.388524	+	0.368030i
$418$	−11.7460	+	13.8284i	−0.574514	+	0.676371i
$419$	13.8798	−	26.1800i	0.678071	−	1.27898i	−0.270593	−	0.962694i	$-0.587220\pi$
$419$	13.8798	−	26.1800i	0.678071	−	1.27898i	0.948664	−	0.316284i	$-0.102435\pi$
$420$	−0.575693	−	0.346383i	−0.0280910	−	0.0169018i
$421$	−11.7633	+	5.44228i	−0.573308	+	0.265240i	−0.685049	−	0.728497i	$-0.740219\pi$
$421$	−11.7633	+	5.44228i	−0.573308	+	0.265240i	0.111741	+	0.993737i	$0.464357\pi$
$422$	16.6212	+	3.65860i	0.809107	+	0.178098i
$423$	1.12440	+	2.12084i	0.0546700	+	0.103119i
$424$	−0.0906653	+	1.67222i	−0.00440310	+	0.0812104i
$425$	20.0599	+	23.6164i	0.973050	+	1.14556i
$426$	−12.6285	+	2.77975i	−0.611855	+	0.134679i
$427$	−12.2032	+	9.27666i	−0.590556	+	0.448929i
$428$	−9.14720	+	8.66469i	−0.442147	+	0.418824i
$429$	−0.512969	−	9.46116i	−0.0247664	−	0.456789i
$430$	0.590209	−	0.355117i	0.0284624	−	0.0171253i
$431$	−16.0559	+	23.6807i	−0.773386	+	1.14066i	0.213135	+	0.977023i	$0.431632\pi$
$431$	−16.0559	+	23.6807i	−0.773386	+	1.14066i	−0.986521	+	0.163636i	$0.947678\pi$
$432$	0.267528	−	0.963550i	0.0128715	−	0.0463588i
$433$	−29.3840	+	3.19571i	−1.41211	+	0.153576i	−0.782167	−	0.623069i	$-0.785886\pi$
$433$	−29.3840	+	3.19571i	−1.41211	+	0.153576i	−0.629939	+	0.776644i	$0.716920\pi$
$434$	−1.10393	−	0.839189i	−0.0529905	−	0.0402824i
$435$	−4.75259	−	2.19878i	−0.227869	−	0.105424i
$436$	−3.92051	−	5.78232i	−0.187758	−	0.276923i
$437$	37.9474	−	12.7860i	1.81527	−	0.611636i
$438$	1.26644	+	7.72494i	0.0605128	+	0.369112i
$439$	−1.38014	+	8.41851i	−0.0658707	+	0.401794i	0.933226	+	0.359291i	$0.116981\pi$
$439$	−1.38014	+	8.41851i	−0.0658707	+	0.401794i	−0.999096	+	0.0425027i	$0.986467\pi$
$440$	1.28322	+	0.432367i	0.0611751	+	0.0206123i
$441$	−1.53310	−	5.52172i	−0.0730046	−	0.262939i
$442$	10.3042	+	25.8615i	0.490120	+	1.23011i
$443$	−0.778059	−	1.95278i	−0.0369667	−	0.0927794i	0.909334	−	0.416066i	$-0.136592\pi$
$443$	−0.778059	−	1.95278i	−0.0369667	−	0.0927794i	−0.946301	+	0.323287i	$0.895212\pi$
$444$	−1.58239	−	5.69925i	−0.0750968	−	0.270474i
$445$	3.75305	+	1.26455i	0.177911	+	0.0599454i
$446$	−0.259711	+	1.58417i	−0.0122977	+	0.0750124i
$447$	0.327878	+	1.99997i	0.0155081	+	0.0945951i
$448$	−1.06770	+	0.359750i	−0.0504441	+	0.0169966i
$449$	2.65776	+	3.91990i	0.125427	+	0.184992i	0.885218	−	0.465176i	$-0.154009\pi$
$449$	2.65776	+	3.91990i	0.125427	+	0.184992i	−0.759791	+	0.650168i	$0.774699\pi$
$450$	−4.21514	−	1.95013i	−0.198704	−	0.0919301i
$451$	15.7274	+	11.9556i	0.740573	+	0.562969i
$452$	6.79495	−	0.738995i	0.319607	−	0.0347594i
$453$	4.76613	−	17.1660i	0.223932	−	0.806531i
$454$	11.5730	−	17.0689i	0.543148	−	0.801083i
$455$	−2.40217	+	1.44534i	−0.112616	+	0.0677585i
$456$	0.432580	+	7.97846i	0.0202574	+	0.373626i
$457$	1.79970	−	1.70476i	0.0841863	−	0.0797455i	−0.644449	−	0.764647i	$-0.722913\pi$
$457$	1.79970	−	1.70476i	0.0841863	−	0.0797455i	0.728636	+	0.684901i	$0.240155\pi$
$458$	21.7161	−	16.5081i	1.01473	−	0.771375i
$459$	−6.51573	+	1.43422i	−0.304128	+	0.0669436i
$460$	−1.93474	−	2.27775i	−0.0902077	−	0.106201i
$461$	1.02236	−	18.8563i	0.0476161	−	0.878227i	−0.872991	−	0.487736i	$-0.837823\pi$
$461$	1.02236	−	18.8563i	0.0476161	−	0.878227i	0.920607	−	0.390490i	$-0.127695\pi$
$462$	−1.19838	−	2.26038i	−0.0557536	−	0.105162i
$463$	26.9406	+	5.93007i	1.25204	+	0.275594i	0.791015	−	0.611796i	$-0.209553\pi$
$463$	26.9406	+	5.93007i	1.25204	+	0.275594i	0.461020	+	0.887390i	$0.347484\pi$
$464$	−7.96980	+	3.68722i	−0.369989	+	0.171175i
$465$	0.628884	+	0.378387i	0.0291638	+	0.0175473i
$466$	0.270817	−	0.510816i	0.0125454	−	0.0236631i
$467$	6.91780	−	8.14426i	0.320117	−	0.376871i	−0.578442	−	0.815724i	$-0.696339\pi$
$467$	6.91780	−	8.14426i	0.320117	−	0.376871i	0.898559	+	0.438852i	$0.144615\pi$
$468$	−3.02933	−	2.86953i	−0.140031	−	0.132644i
$469$	6.85776	+	0.745826i	0.316662	+	0.0344391i
$470$	−0.529836	+	1.32979i	−0.0244395	+	0.0613385i
$471$	9.72110			0.447925
$472$	6.29258	+	4.40493i	0.289639	+	0.202754i
$473$	2.62291			0.120602
$474$	3.50103	−	8.78692i	0.160808	−	0.403597i
$475$	36.8920	+	4.01225i	1.69272	+	0.184095i
$476$	5.45721	+	5.16935i	0.250131	+	0.236937i
$477$	−1.08416	+	1.27638i	−0.0496405	+	0.0584413i
$478$	−1.26904	+	2.39367i	−0.0580447	+	0.109484i
$479$	−14.7007	−	8.84511i	−0.671691	−	0.404143i	0.138457	−	0.990368i	$-0.455786\pi$
$479$	−14.7007	−	8.84511i	−0.671691	−	0.404143i	−0.810148	+	0.586225i	$0.800613\pi$
$480$	0.541210	−	0.250390i	0.0247027	−	0.0114287i
$481$	−24.1036	−	5.30560i	−1.09903	−	0.241915i
$482$	6.68719	+	12.6134i	0.304593	+	0.574523i
$483$	−0.305693	+	5.63818i	−0.0139095	+	0.256546i
$484$	−3.78313	−	4.45385i	−0.171961	−	0.202448i
$485$	0.759155	−	0.167103i	0.0344715	−	0.00758774i
$486$	0.796093	−	0.605174i	0.0361115	−	0.0274513i
$487$	3.63749	−	3.44561i	0.164830	−	0.156136i	−0.600839	−	0.799370i	$-0.705167\pi$
$487$	3.63749	−	3.44561i	0.164830	−	0.156136i	0.765669	+	0.643235i	$0.222408\pi$
$488$	−0.736581	−	13.5854i	−0.0333435	−	0.614984i
$489$	−6.95374	+	4.18393i	−0.314459	+	0.189204i
$490$	1.91774	−	2.82846i	0.0866348	−	0.127777i
$491$	−2.87678	+	10.3612i	−0.129827	+	0.467596i	−0.999669	−	0.0257356i	$-0.991807\pi$
$491$	−2.87678	+	10.3612i	−0.129827	+	0.467596i	0.869841	+	0.493331i	$0.164221\pi$
$492$	8.64908	−	0.940644i	0.389931	−	0.0424075i
$493$	46.6408	+	35.4554i	2.10059	+	1.59683i
$494$	30.2588	+	13.9992i	1.36141	+	0.629855i
$495$	0.759905	+	1.12078i	0.0341552	+	0.0503751i
$496$	1.16635	−	0.392989i	0.0523707	−	0.0176457i
$497$	2.35699	+	14.3770i	0.105725	+	0.644897i
$498$	−2.60570	+	15.8941i	−0.116764	+	0.712231i
$499$	−31.1313	−	10.4894i	−1.39363	−	0.469569i	−0.480413	−	0.877042i	$-0.659513\pi$
$499$	−31.1313	−	10.4894i	−1.39363	−	0.469569i	−0.913217	+	0.407474i	$0.866410\pi$
$500$	−1.53861	−	5.54156i	−0.0688086	−	0.247826i
$501$	−1.77815	−	4.46282i	−0.0794418	−	0.199384i
$502$	−7.92333	−	19.8861i	−0.353636	−	0.887559i
$503$	4.46662	+	16.0873i	0.199157	+	0.717298i	0.993894	+	0.110343i	$0.0351951\pi$
$503$	4.46662	+	16.0873i	0.199157	+	0.717298i	−0.794737	+	0.606954i	$0.792391\pi$
$504$	−1.06770	−	0.359750i	−0.0475592	−	0.0160245i
$505$	0.447215	−	2.72789i	0.0199008	−	0.121390i
$506$	−1.84109	−	11.2302i	−0.0818465	−	0.499242i
$507$	−4.18016	+	1.40846i	−0.185647	+	0.0625518i
$508$	−3.81918	−	5.63287i	−0.169449	−	0.249918i
$509$	9.74723	+	4.50955i	0.432038	+	0.199882i	0.623841	−	0.781551i	$-0.285571\pi$
$509$	9.74723	+	4.50955i	0.432038	+	0.199882i	−0.191803	+	0.981434i	$0.561433\pi$
$510$	−3.16726	−	2.40769i	−0.140249	−	0.106614i
$511$	8.76801	−	0.953578i	0.387874	−	0.0421838i
$512$	0.267528	−	0.963550i	0.0118232	−	0.0425833i
$513$	−4.48399	+	6.61339i	−0.197973	+	0.291988i
$514$	17.3985	−	10.4683i	0.767416	−	0.461739i
$515$	0.384282	+	7.08766i	0.0169335	+	0.312319i
$516$	0.838588	−	0.794352i	0.0369168	−	0.0349694i
$517$	−4.33938	+	3.29871i	−0.190846	+	0.145077i
$518$	−6.50832	+	1.43259i	−0.285959	+	0.0629444i
$519$	3.26730	+	3.84657i	0.143419	+	0.168846i
$520$	0.134712	−	2.48461i	0.00590749	−	0.108957i
$521$	−18.7282	−	35.3251i	−0.820498	−	1.54762i	−0.836640	−	0.547753i	$-0.815483\pi$
$521$	−18.7282	−	35.3251i	−0.820498	−	1.54762i	0.0161425	−	0.999870i	$-0.494861\pi$
$522$	−8.57612	−	1.88775i	−0.375367	−	0.0826244i
$523$	−15.3120	+	7.08408i	−0.669546	+	0.309765i	−0.725053	−	0.688693i	$-0.758185\pi$
$523$	−15.3120	+	7.08408i	−0.669546	+	0.309765i	0.0555065	+	0.998458i	$0.482323\pi$
$524$	5.47010	+	3.29125i	0.238962	+	0.143779i
$525$	−2.45106	+	4.62319i	−0.106973	+	0.201773i
$526$	−10.3460	+	12.1802i	−0.451106	+	0.531083i
$527$	−5.96143	−	5.64696i	−0.259684	−	0.245986i
$528$	2.25744	+	0.245511i	0.0982423	+	0.0106845i
$529$	−0.783255	+	1.96582i	−0.0340546	+	0.0854705i
$530$	−0.998653			−0.0433787
$531$	2.34373	+	7.31484i	0.101709	+	0.317437i
$532$	9.00237			0.390302
$533$	13.4369	−	33.7241i	0.582018	−	1.46075i
$534$	6.60235	+	0.718049i	0.285712	+	0.0310730i
$535$	−5.45470	−	5.16697i	−0.235827	−	0.223388i
$536$	−3.96369	+	4.66641i	−0.171205	+	0.201558i
$537$	3.97676	−	7.50097i	0.171610	−	0.323691i
$538$	−6.62942	−	3.98879i	−0.285815	−	0.171969i
$539$	11.8100	−	5.46391i	0.508694	−	0.235347i
$540$	0.582383	+	0.128192i	0.0250618	+	0.00551651i
$541$	−5.25992	−	9.92125i	−0.226141	−	0.426548i	0.744314	−	0.667830i	$-0.232777\pi$
$541$	−5.25992	−	9.92125i	−0.226141	−	0.426548i	−0.970455	+	0.241282i	$0.922432\pi$
$542$	0.0223688	−	0.412569i	0.000960823	−	0.0177213i
$543$	−14.2335	−	16.7569i	−0.610816	−	0.719108i
$544$	−6.51573	+	1.43422i	−0.279359	+	0.0614917i
$545$	3.31651	−	2.52115i	0.142064	−	0.107994i
$546$	−3.41308	+	3.23304i	−0.146066	+	0.138361i
$547$	−0.522545	−	9.63777i	−0.0223424	−	0.412081i	−0.988216	−	0.153067i	$-0.951085\pi$
$547$	−0.522545	−	9.63777i	−0.0223424	−	0.412081i	0.965873	−	0.259014i	$-0.0833977\pi$
$548$	12.3681	−	7.44163i	0.528339	−	0.317891i
$549$	7.63517	−	11.2610i	0.325861	−	0.480609i
$550$	2.82142	−	10.1618i	0.120306	−	0.433302i
$551$	69.7539	−	7.58619i	2.97161	−	0.323183i
$552$	−3.98970	−	3.03289i	−0.169813	−	0.129088i
$553$	−9.67196	−	4.47473i	−0.411294	−	0.190285i
$554$	1.94834	+	2.87359i	0.0827772	+	0.122087i
$555$	3.34253	−	1.12623i	0.141883	−	0.0478058i
$556$	1.76800	+	10.7843i	0.0749799	+	0.457357i
$557$	−1.91035	+	11.6526i	−0.0809440	+	0.493737i	0.914977	+	0.403506i	$0.132209\pi$
$557$	−1.91035	+	11.6526i	−0.0809440	+	0.493737i	−0.995921	+	0.0902304i	$0.971240\pi$
$558$	1.16635	+	0.392989i	0.0493755	+	0.0166366i
$559$	−1.28943	−	4.64410i	−0.0545370	−	0.196424i
$560$	−0.248683	−	0.624148i	−0.0105088	−	0.0263751i
$561$	−5.60751	−	14.0738i	−0.236749	−	0.594195i
$562$	2.51654	+	9.06377i	0.106154	+	0.382332i
$563$	38.7596	+	13.0596i	1.63352	+	0.550397i	0.978684	−	0.205372i	$-0.0658406\pi$
$563$	38.7596	+	13.0596i	1.63352	+	0.550397i	0.654837	+	0.755770i	$0.272737\pi$
$564$	−0.388351	+	2.36884i	−0.0163525	+	0.0997461i
$565$	0.659405	+	4.02219i	0.0277414	+	0.169215i
$566$	−2.99081	+	1.00772i	−0.125713	+	0.0423577i
$567$	−0.632277	−	0.932539i	−0.0265532	−	0.0391630i
$568$	−11.7357	−	5.42953i	−0.492420	−	0.227818i
$569$	23.4344	+	17.8144i	0.982422	+	0.746818i	0.967448	−	0.253070i	$-0.0814402\pi$
$569$	23.4344	+	17.8144i	0.982422	+	0.746818i	0.0149743	+	0.999888i	$0.495233\pi$
$570$	−4.73681	+	0.515159i	−0.198403	+	0.0215777i
$571$	−2.55305	+	9.19525i	−0.106842	+	0.384809i	−0.997565	−	0.0697358i	$-0.977784\pi$
$571$	−2.55305	+	9.19525i	−0.106842	+	0.384809i	0.890724	+	0.454545i	$0.150198\pi$
$572$	5.31728	−	7.84240i	0.222326	−	0.327907i
$573$	−4.64392	+	2.79416i	−0.194003	+	0.116728i
$574$	−0.530680	−	9.78782i	−0.0221502	−	0.408536i
$575$	−16.8982	+	16.0068i	−0.704702	+	0.667529i
$576$	0.796093	−	0.605174i	0.0331705	−	0.0252156i
$577$	−36.6148	+	8.05954i	−1.52430	+	0.335523i	−0.896567	−	0.442909i	$-0.853947\pi$
$577$	−36.6148	+	8.05954i	−1.52430	+	0.335523i	−0.627729	+	0.778432i	$0.716016\pi$
$578$	17.8107	+	20.9683i	0.740826	+	0.872168i
$579$	0.520778	−	9.60518i	0.0216428	−	0.399178i
$580$	−2.45286	−	4.62658i	−0.101849	−	0.192108i
$581$	17.7223	+	3.90098i	0.735246	+	0.161840i
$582$	1.18305	−	0.547339i	0.0490392	−	0.0226879i
$583$	−3.25844	−	1.96054i	−0.134951	−	0.0811971i
$584$	−3.66673	+	6.91619i	−0.151730	+	0.286194i
$585$	1.61086	−	1.89646i	0.0666010	−	0.0784088i
$586$	−0.663103	−	0.628124i	−0.0273925	−	0.0259476i
$587$	−20.6630	−	2.24724i	−0.852854	−	0.0927535i	−0.328760	−	0.944414i	$-0.606631\pi$
$587$	−20.6630	−	2.24724i	−0.852854	−	0.0927535i	−0.524095	+	0.851660i	$0.675596\pi$
$588$	2.12111	−	5.32359i	0.0874732	−	0.219541i
$589$	−9.83413			−0.405208
$590$	−2.41977	+	3.88913i	−0.0996202	+	0.160113i
$591$	12.7891			0.526072
$592$	2.18931	−	5.49475i	0.0899800	−	0.225833i
$593$	22.0856	+	2.40196i	0.906949	+	0.0986366i	0.549690	−	0.835369i	$-0.314746\pi$
$593$	22.0856	+	2.40196i	0.906949	+	0.0986366i	0.357259	+	0.934005i	$0.383711\pi$
$594$	1.64855	+	1.56159i	0.0676409	+	0.0640729i
$595$	−2.90191	+	3.41639i	−0.118967	+	0.140058i
$596$	−0.949306	+	1.79058i	−0.0388851	+	0.0733451i
$597$	−22.8009	−	13.7188i	−0.933178	−	0.561475i
$598$	−18.9789	+	8.78059i	−0.776106	+	0.359065i
$599$	−12.2798	−	2.70299i	−0.501738	−	0.110441i	−0.0431122	−	0.999070i	$-0.513727\pi$
$599$	−12.2798	−	2.70299i	−0.501738	−	0.110441i	−0.458626	+	0.888629i	$0.651658\pi$
$600$	−2.17547	−	4.10338i	−0.0888134	−	0.167520i
$601$	−2.26424	+	41.7615i	−0.0923604	+	1.70349i	0.474974	+	0.880000i	$0.342458\pi$
$601$	−2.26424	+	41.7615i	−0.0923604	+	1.70349i	−0.567334	+	0.823488i	$0.692025\pi$
$602$	−0.842516	−	0.991886i	−0.0343384	−	0.0404263i
$603$	−5.97945	+	1.31618i	−0.243502	+	0.0535989i
$604$	14.1827	−	10.7814i	0.577087	−	0.438690i
$605$	2.52991	−	2.39646i	0.102855	−	0.0974298i
$606$	−0.250965	−	4.62877i	−0.0101948	−	0.188031i
$607$	4.89442	−	2.94487i	0.198658	−	0.119529i	−0.412749	−	0.910845i	$-0.635431\pi$
$607$	4.89442	−	2.94487i	0.198658	−	0.119529i	0.611407	+	0.791316i	$0.290604\pi$
$608$	−4.48399	+	6.61339i	−0.181850	+	0.268208i
$609$	−2.64688	+	9.53321i	−0.107257	+	0.386305i
$610$	8.06567	−	0.877195i	0.326570	−	0.0355166i
$611$	7.97390	+	6.06160i	0.322590	+	0.245226i
$612$	−6.05508	−	2.80138i	−0.244762	−	0.113239i
$613$	26.2945	+	38.7814i	1.06202	+	1.56637i	0.798766	+	0.601642i	$0.205487\pi$
$613$	26.2945	+	38.7814i	1.06202	+	1.56637i	0.263258	+	0.964726i	$0.415203\pi$
$614$	10.8794	−	3.66569i	0.439056	−	0.147935i
$615$	0.839337	+	5.11973i	0.0338453	+	0.206447i
$616$	0.413904	−	2.52470i	0.0166766	−	0.101723i
$617$	29.9315	+	10.0851i	1.20500	+	0.406010i	0.848957	−	0.528461i	$-0.177231\pi$
$617$	29.9315	+	10.0851i	1.20500	+	0.406010i	0.356038	+	0.934472i	$0.384127\pi$
$618$	3.18440	+	11.4692i	0.128095	+	0.461357i
$619$	−4.30683	−	10.8093i	−0.173106	−	0.434464i	0.816668	−	0.577108i	$-0.195819\pi$
$619$	−4.30683	−	10.8093i	−0.173106	−	0.434464i	−0.989774	+	0.142644i	$0.954440\pi$
$620$	0.271660	+	0.681816i	0.0109101	+	0.0273824i
$621$	−1.34074	−	4.82893i	−0.0538022	−	0.193778i
$622$	8.42422	+	2.83845i	0.337780	+	0.113811i
$623$	1.21055	−	7.38402i	0.0484996	−	0.295834i
$624$	−0.675061	−	4.11769i	−0.0270241	−	0.164839i
$625$	−18.7563	+	6.31975i	−0.750253	+	0.252790i
$626$	−10.8642	−	16.0235i	−0.434221	−	0.640428i
$627$	−16.4668	−	7.61834i	−0.657619	−	0.304247i
$628$	7.73890	+	5.88296i	0.308816	+	0.234756i
$629$	−39.2308	+	4.26660i	−1.56423	+	0.170121i
$630$	0.179743	−	0.647377i	0.00716114	−	0.0257921i
$631$	12.7838	−	18.8547i	0.508916	−	0.750596i	−0.483255	−	0.875480i	$-0.660546\pi$
$631$	12.7838	−	18.8547i	0.508916	−	0.750596i	0.992171	+	0.124884i	$0.0398559\pi$
$632$	8.10476	−	4.87647i	0.322390	−	0.193976i
$633$	0.921395	+	16.9941i	0.0366221	+	0.675456i
$634$	20.2837	−	19.2138i	0.805569	−	0.763076i
$635$	3.23079	−	2.45599i	0.128210	−	0.0974628i
$636$	−1.63553	+	0.360007i	−0.0648529	+	0.0142752i
$637$	−15.4802	−	18.2247i	−0.613347	−	0.722088i
$638$	1.07955	−	19.9112i	0.0427399	−	0.788290i
$639$	−6.05692	−	11.4246i	−0.239608	−	0.451949i
$640$	0.582383	+	0.128192i	0.0230207	+	0.00506724i
$641$	−42.2550	+	19.5492i	−1.66897	+	0.772148i	−0.669399	+	0.742903i	$0.733448\pi$
$641$	−42.2550	+	19.5492i	−1.66897	+	0.772148i	−0.999572	+	0.0292450i	$0.990690\pi$
$642$	−10.7960	−	6.49574i	−0.426084	−	0.256366i
$643$	8.46372	−	15.9643i	0.333776	−	0.629569i	−0.658644	−	0.752454i	$-0.728870\pi$
$643$	8.46372	−	15.9643i	0.333776	−	0.629569i	0.992421	+	0.122885i	$0.0392147\pi$
$644$	−3.65544	+	4.30352i	−0.144045	+	0.169582i
$645$	0.500070	+	0.473692i	0.0196903	+	0.0186516i
$646$	52.9957	+	5.76363i	2.08509	+	0.226767i
$647$	−2.94898	+	7.40139i	−0.115937	+	0.290979i	−0.975482	−	0.220081i	$-0.929368\pi$
$647$	−2.94898	+	7.40139i	−0.115937	+	0.290979i	0.859545	+	0.511060i	$0.170747\pi$
$648$	1.00000			0.0392837
$649$	−15.5303	+	7.93913i	−0.609620	+	0.311638i
$650$	−19.3795			−0.760125
$651$	0.513267	−	1.28820i	0.0201165	−	0.0504886i
$652$	−8.06783	−	0.877430i	−0.315961	−	0.0343628i
$653$	−14.0084	−	13.2695i	−0.548191	−	0.519274i	0.362709	−	0.931903i	$-0.381852\pi$
$653$	−14.0084	−	13.2695i	−0.548191	−	0.519274i	−0.910899	+	0.412629i	$0.864611\pi$
$654$	4.52271	−	5.32454i	0.176852	−	0.208206i
$655$	−1.78318	+	3.36343i	−0.0696744	+	0.131420i
$656$	7.45473	+	4.48536i	0.291058	+	0.175124i
$657$	−7.10456	+	3.28692i	−0.277175	+	0.128235i
$658$	2.64132	+	0.581398i	0.102969	+	0.0226652i
$659$	6.14381	+	11.5885i	0.239329	+	0.451422i	0.973859	−	0.227154i	$-0.0729421\pi$
$659$	6.14381	+	11.5885i	0.239329	+	0.451422i	−0.734530	+	0.678576i	$0.762597\pi$
$660$	−0.0733097	+	1.35212i	−0.00285357	+	0.0526311i
$661$	−0.239620	−	0.282103i	−0.00932015	−	0.0109725i	0.757482	−	0.652856i	$-0.226429\pi$
$661$	−0.239620	−	0.282103i	−0.00932015	−	0.0109725i	−0.766802	+	0.641883i	$0.778153\pi$
$662$	6.53917	−	1.43938i	0.254152	−	0.0559431i
$663$	−22.1622	+	16.8473i	−0.860710	+	0.654294i
$664$	−11.6931	+	11.0763i	−0.453779	+	0.429842i
$665$	0.290636	+	5.36046i	0.0112704	+	0.207870i
$666$	5.06817	−	3.04942i	0.196388	−	0.118163i
$667$	−24.6973	+	36.4257i	−0.956282	+	1.41041i
$668$	1.28521	−	4.62891i	0.0497263	−	0.179098i
$669$	−1.59590	+	0.173565i	−0.0617012	+	0.00671041i
$670$	−2.90658	−	2.20953i	−0.112291	−	0.0853614i
$671$	28.0390	+	12.9722i	1.08243	+	0.500787i
$672$	−0.632277	−	0.932539i	−0.0243906	−	0.0359735i
$673$	−42.2600	+	14.2391i	−1.62901	+	0.548876i	−0.977712	−	0.209950i	$-0.932670\pi$
$673$	−42.2600	+	14.2391i	−1.62901	+	0.548876i	−0.651293	+	0.758826i	$0.725773\pi$
$674$	1.92373	+	11.7342i	0.0740993	+	0.451986i
$675$	0.751380	−	4.58321i	0.0289206	−	0.176408i
$676$	−4.18016	−	1.40846i	−0.160775	−	0.0541715i
$677$	−10.0843	−	36.3205i	−0.387572	−	1.39591i	−0.858081	−	0.513514i	$-0.828343\pi$
$677$	−10.0843	−	36.3205i	−0.387572	−	1.39591i	0.470508	−	0.882395i	$-0.344071\pi$
$678$	2.52990	+	6.34957i	0.0971602	+	0.243854i
$679$	−0.543608	−	1.36435i	−0.0208618	−	0.0523591i
$680$	−1.06436	−	3.83349i	−0.0408164	−	0.147008i
$681$	19.5428	+	6.58475i	0.748883	+	0.252328i
$682$	−0.452146	+	2.75797i	−0.0173136	+	0.105608i
$683$	5.77115	+	35.2025i	0.220827	+	1.34699i	0.831686	+	0.555246i	$0.187376\pi$
$683$	5.77115	+	35.2025i	0.220827	+	1.34699i	−0.610859	+	0.791739i	$0.709176\pi$
$684$	−7.57192	+	2.55128i	−0.289520	+	0.0975505i
$685$	4.83042	+	7.12433i	0.184561	+	0.272207i
$686$	−13.0176	−	6.02259i	−0.497015	−	0.229944i
$687$	21.7161	+	16.5081i	0.828521	+	0.629825i
$688$	1.14832	−	0.124887i	0.0437791	−	0.00476126i
$689$	−1.86945	+	6.73316i	−0.0712204	+	0.256513i
$690$	1.67713	−	2.47358i	0.0638472	−	0.0941676i
$691$	22.1436	−	13.3233i	0.842381	−	0.506844i	−0.0277786	−	0.999614i	$-0.508843\pi$
$691$	22.1436	−	13.3233i	0.842381	−	0.506844i	0.870159	+	0.492770i	$0.164016\pi$
$692$	0.273234	+	5.03951i	0.0103868	+	0.191574i
$693$	1.85739	−	1.75941i	0.0705564	−	0.0668345i
$694$	10.6054	−	8.06198i	0.402574	−	0.306029i
$695$	−6.36445	+	1.40092i	−0.241417	+	0.0531400i
$696$	−5.68497	−	6.69287i	−0.215488	−	0.253693i
$697$	3.14246	−	57.9593i	0.119029	−	2.19536i
$698$	−16.0483	−	30.2703i	−0.607437	−	1.14575i
$699$	0.564648	+	0.124288i	0.0213569	+	0.00470102i
$700$	−4.74911	+	2.19717i	−0.179499	+	0.0830453i
$701$	−8.85475	−	5.32773i	−0.334439	−	0.201225i	0.338421	−	0.940995i	$-0.390107\pi$
$701$	−8.85475	−	5.32773i	−0.334439	−	0.201225i	−0.672861	+	0.739769i	$0.734935\pi$
$702$	1.95451	−	3.68659i	0.0737681	−	0.139141i
$703$	−30.5959	+	36.0203i	−1.15395	+	1.35853i
$704$	1.64855	+	1.56159i	0.0621322	+	0.0588547i
$705$	−1.42306	−	0.154767i	−0.0535956	−	0.00582888i
$706$	−0.314036	+	0.788171i	−0.0118189	+	0.0296632i
$707$	−5.22280			−0.196424
$708$	−2.56093	+	7.24166i	−0.0962457	+	0.272158i
$709$	−1.93994			−0.0728561			−0.0364280	−	0.999336i	$-0.511598\pi$
$709$	−1.93994			−0.0728561			−0.0364280	+	0.999336i	$0.511598\pi$
$710$	2.85413	−	7.16333i	0.107114	−	0.268835i
$711$	9.40326	+	1.02267i	0.352650	+	0.0383530i
$712$	4.82154	+	4.56720i	0.180695	+	0.171163i
$713$	3.99318	−	4.70114i	0.149546	−	0.176059i
$714$	−3.52096	+	6.64124i	−0.131769	+	0.248542i
$715$	4.84142	+	2.91299i	0.181059	+	0.108940i
$716$	7.70527	−	3.56484i	0.287959	−	0.133224i
$717$	−2.64593	−	0.582413i	−0.0988140	−	0.0217506i
$718$	6.29895	+	11.8811i	0.235075	+	0.443398i
$719$	−0.678813	+	12.5200i	−0.0253155	+	0.466916i	0.958201	+	0.286097i	$0.0923578\pi$
$719$	−0.678813	+	12.5200i	−0.0253155	+	0.466916i	−0.983516	+	0.180820i	$0.942125\pi$
$720$	0.386052	+	0.454496i	0.0143873	+	0.0169381i
$721$	13.0973	−	2.88294i	0.487770	−	0.107366i
$722$	35.6992	−	27.1378i	1.32859	−	1.00997i
$723$	−10.3646	+	9.81787i	−0.385464	+	0.365131i
$724$	−1.19030	−	21.9538i	−0.0442371	−	0.815906i
$725$	−34.9464	+	21.0266i	−1.29788	+	0.780907i
$726$	3.27941	−	4.83677i	0.121710	−	0.179509i
$727$	−2.07994	+	7.49126i	−0.0771406	+	0.277835i	−0.992054	−	0.125816i	$-0.959845\pi$
$727$	−2.07994	+	7.49126i	−0.0771406	+	0.277835i	0.914913	+	0.403651i	$0.132259\pi$
$728$	−4.67368	+	0.508294i	−0.173218	+	0.0188386i
$729$	0.796093	+	0.605174i	0.0294849	+	0.0224139i
$730$	−4.23662	−	1.96007i	−0.156804	−	0.0725455i
$731$	−4.32473	−	6.37850i	−0.159956	−	0.235917i
$732$	12.8932	−	4.34422i	0.476546	−	0.160567i
$733$	−0.765684	−	4.67046i	−0.0282812	−	0.172508i	0.968909	−	0.247417i	$-0.0795816\pi$
$733$	−0.765684	−	4.67046i	−0.0282812	−	0.172508i	−0.997190	+	0.0749091i	$0.976133\pi$
$734$	−5.92136	+	36.1187i	−0.218561	+	1.33316i
$735$	3.23841	+	1.09115i	0.119451	+	0.0402476i
$736$	−1.34074	−	4.82893i	−0.0494205	−	0.177997i
$737$	−5.14598	−	12.9154i	−0.189555	−	0.475747i
$738$	3.22023	+	8.08217i	0.118538	+	0.297509i
$739$	−7.40006	−	26.6526i	−0.272216	−	0.980432i	−0.965636	−	0.259899i	$-0.916311\pi$
$739$	−7.40006	−	26.6526i	−0.272216	−	0.980432i	0.693420	−	0.720533i	$-0.256103\pi$
$740$	3.34253	+	1.12623i	0.122874	+	0.0414010i
$741$	−5.39386	+	32.9011i	−0.198148	+	1.20865i
$742$	0.305254	+	1.86197i	0.0112062	+	0.0683551i
$743$	−14.8648	+	5.00854i	−0.545337	+	0.183745i	−0.578467	−	0.815706i	$-0.696349\pi$
$743$	−14.8648	+	5.00854i	−0.545337	+	0.183745i	0.0331302	+	0.999451i	$0.489452\pi$
$744$	0.690696	+	1.01870i	0.0253222	+	0.0373474i
$745$	−1.09685	−	0.507457i	−0.0401855	−	0.0185918i
$746$	−15.1193	−	11.4934i	−0.553558	−	0.420804i
$747$	−16.0118	+	1.74139i	−0.585843	+	0.0637142i
$748$	4.05299	−	14.5976i	0.148192	−	0.533739i
$749$	−7.96640	+	11.7496i	−0.291086	+	0.429320i
$750$	4.92795	−	2.96505i	0.179943	−	0.108268i
$751$	−1.54854	−	28.5611i	−0.0565070	−	1.04221i	−0.880027	−	0.474923i	$-0.842476\pi$
$751$	−1.54854	−	28.5611i	−0.0565070	−	1.04221i	0.823520	−	0.567287i	$-0.192007\pi$
$752$	−1.74272	+	1.65079i	−0.0635506	+	0.0601983i
$753$	17.0415	−	12.9546i	0.621027	−	0.472092i
$754$	−35.7852	+	7.87692i	−1.30322	+	0.286860i
$755$	6.87768	+	8.09703i	0.250304	+	0.294681i
$756$	0.0609971	−	1.12503i	0.00221844	−	0.0409168i
$757$	20.2574	+	38.2096i	0.736269	+	1.38875i	0.914428	+	0.404749i	$0.132641\pi$
$757$	20.2574	+	38.2096i	0.736269	+	1.38875i	−0.178159	+	0.984002i	$0.557014\pi$
$758$	−6.79907	−	1.49659i	−0.246953	−	0.0543585i
$759$	10.3283	−	4.77837i	0.374893	−	0.173444i
$760$	−4.08270	−	2.45648i	−0.148095	−	0.0891060i
$761$	9.21402	−	17.3795i	0.334008	−	0.630006i	−0.658446	−	0.752628i	$-0.728786\pi$
$761$	9.21402	−	17.3795i	0.334008	−	0.630006i	0.992453	+	0.122623i	$0.0391305\pi$
$762$	4.40581	−	5.18692i	0.159606	−	0.187902i
$763$	−5.71438	−	5.41295i	−0.206874	−	0.195962i
$764$	−5.38794	−	0.585974i	−0.194929	−	0.0211998i
$765$	1.47260	−	3.69594i	0.0532418	−	0.133627i
$766$	−29.4761			−1.06502
$767$	21.6917	+	23.5950i	0.783241	+	0.851966i
$768$	1.00000			0.0360844
$769$	3.87381	−	9.72253i	0.139693	−	0.350604i	−0.842440	−	0.538790i	$-0.818882\pi$
$769$	3.87381	−	9.72253i	0.139693	−	0.350604i	0.982133	+	0.188186i	$0.0602609\pi$
$770$	1.51670	+	0.164951i	0.0546579	+	0.00594441i
$771$	14.7414	+	13.9638i	0.530898	+	0.502893i
$772$	6.22739	−	7.33145i	0.224129	−	0.263865i
$773$	−15.0327	+	28.3546i	−0.540687	+	1.01984i	0.451164	+	0.892441i	$0.351009\pi$
$773$	−15.0327	+	28.3546i	−0.540687	+	1.01984i	−0.991851	+	0.127403i	$0.959336\pi$
$774$	0.989744	+	0.595509i	0.0355756	+	0.0214051i
$775$	5.18790	−	2.40018i	0.186355	−	0.0862169i
$776$	1.27306	+	0.280221i	0.0457001	+	0.0100593i
$777$	−3.12153	−	5.88783i	−0.111984	−	0.211225i
$778$	1.03322	−	19.0566i	0.0370427	−	0.683213i
$779$	−45.0032	−	52.9819i	−1.61241	−	1.89827i
$780$	2.43008	−	0.534902i	0.0870110	−	0.0191526i
$781$	23.3755	−	17.7696i	0.836440	−	0.635845i
$782$	−24.2743	+	22.9939i	−0.868048	+	0.822259i
$783$	−0.475417	−	8.76855i	−0.0169900	−	0.313362i
$784$	4.91030	−	2.95443i	0.175368	−	0.105515i
$785$	−3.25316	+	4.79806i	−0.116110	+	0.171250i
$786$	−1.70788	+	6.15121i	−0.0609179	+	0.219407i
$787$	0.665997	−	0.0724315i	0.0237402	−	0.00258190i	−0.0962412	−	0.995358i	$-0.530682\pi$
$787$	0.665997	−	0.0724315i	0.0237402	−	0.00258190i	0.119981	+	0.992776i	$0.461716\pi$
$788$	10.1813	+	7.73962i	0.362693	+	0.275712i
$789$	−14.5041	−	6.71031i	−0.516359	−	0.238893i
$790$	3.16535	+	4.66855i	0.112618	+	0.166099i
$791$	7.29775	−	2.45890i	0.259478	−	0.0874283i
$792$	0.367366	+	2.24083i	0.0130538	+	0.0796246i
$793$	9.18447	−	56.0228i	0.326150	−	1.98943i
$794$	30.2076	+	10.1781i	1.07203	+	0.361208i
$795$	−0.267168	−	0.962252i	−0.00947547	−	0.0341276i
$796$	−9.84934	−	24.7200i	−0.349101	−	0.876176i
$797$	9.72377	+	24.4048i	0.344434	+	0.864463i	0.994515	+	0.104598i	$0.0333556\pi$
$797$	9.72377	+	24.4048i	0.344434	+	0.864463i	−0.650081	+	0.759865i	$0.725265\pi$
$798$	2.40839	+	8.67423i	0.0852560	+	0.307064i
$799$	15.1768	+	5.11367i	0.536917	+	0.180909i
$800$	0.751380	−	4.58321i	0.0265653	−	0.162041i
$801$	1.07444	+	6.55379i	0.0379635	+	0.231567i
$802$	−14.0283	+	4.72668i	−0.495356	+	0.166905i
$803$	−9.97541	−	14.7126i	−0.352025	−	0.519197i
$804$	−5.55672	−	2.57081i	−0.195970	−	0.0906655i
$805$	−2.68054	−	2.03770i	−0.0944768	−	0.0718194i
$806$	5.10550	−	0.555257i	0.179834	−	0.0195581i
$807$	2.06984	−	7.45489i	0.0728618	−	0.262425i
$808$	2.60142	−	3.83681i	0.0915178	−	0.134979i
$809$	−46.7803	+	28.1468i	−1.64471	+	0.989587i	−0.677526	+	0.735499i	$0.736948\pi$
$809$	−46.7803	+	28.1468i	−1.64471	+	0.989587i	−0.967181	+	0.254089i	$0.918225\pi$
$810$	0.0322844	+	0.595450i	0.00113436	+	0.0209220i
$811$	10.8024	−	10.2325i	0.379322	−	0.359313i	−0.474157	−	0.880440i	$-0.657247\pi$
$811$	10.8024	−	10.2325i	0.379322	−	0.359313i	0.853479	+	0.521127i	$0.174488\pi$
$812$	−7.87642	+	5.98750i	−0.276408	+	0.210120i
$813$	0.403515	−	0.0888203i	0.0141519	−	0.00311507i
$814$	8.69512	+	10.2367i	0.304764	+	0.358796i
$815$	0.262001	−	4.83232i	0.00917749	−	0.169269i
$816$	−3.12508	−	5.89453i	−0.109400	−	0.206350i
$817$	−9.01357	−	1.98404i	−0.315345	−	0.0694127i
$818$	32.6763	−	15.1177i	1.14250	−	0.528577i
$819$	−4.02829	−	2.42374i	−0.140760	−	0.0846925i
$820$	−2.43014	+	4.58373i	−0.0848641	+	0.160071i
$821$	−25.2354	+	29.7095i	−0.880723	+	1.03687i	0.118313	+	0.992976i	$0.462251\pi$
$821$	−25.2354	+	29.7095i	−0.880723	+	1.03687i	−0.999036	+	0.0438908i	$0.986025\pi$
$822$	10.4792	+	9.92643i	0.365504	+	0.346224i
$823$	44.0928	+	4.79538i	1.53698	+	0.167156i	0.837077	−	0.547085i	$-0.184263\pi$
$823$	44.0928	+	4.79538i	1.53698	+	0.167156i	0.699900	+	0.714241i	$0.253228\pi$
$824$	−4.40576	+	11.0576i	−0.153482	+	0.385211i
$825$	10.5463			0.367173
$826$	7.99085	+	3.32283i	0.278037	+	0.115616i
$827$	−13.6695			−0.475335			−0.237668	−	0.971347i	$-0.576383\pi$
$827$	−13.6695			−0.475335			−0.237668	+	0.971347i	$0.576383\pi$
$828$	1.85498	−	4.65566i	0.0644651	−	0.161795i
$829$	−19.4540	−	2.11575i	−0.675664	−	0.0734829i	−0.236147	−	0.971717i	$-0.575885\pi$
$829$	−19.4540	−	2.11575i	−0.675664	−	0.0734829i	−0.439517	+	0.898234i	$0.644850\pi$
$830$	−6.97287	−	6.60505i	−0.242032	−	0.229265i
$831$	−2.24761	+	2.64609i	−0.0779688	+	0.0917920i
$832$	1.95451	−	3.68659i	0.0677604	−	0.127810i
$833$	−32.7601	−	19.7111i	−1.13507	−	0.682949i
$834$	−9.91825	+	4.58867i	−0.343441	+	0.158893i
$835$	2.79778	+	0.615837i	0.0968210	+	0.0213119i
$836$	−8.49866	−	16.0302i	−0.293932	−	0.554415i
$837$	−0.0666329	+	1.22897i	−0.00230317	+	0.0424795i
$838$	19.1832	+	22.5842i	0.662673	+	0.780159i
$839$	28.6641	−	6.30944i	0.989594	−	0.217826i	0.309459	−	0.950913i	$-0.399852\pi$
$839$	28.6641	−	6.30944i	0.989594	−	0.217826i	0.680135	+	0.733087i	$0.261921\pi$
$840$	0.534868	−	0.406596i	0.0184547	−	0.0140289i
$841$	−34.9301	+	33.0876i	−1.20449	+	1.14095i
$842$	−0.701707	−	12.9422i	−0.0241824	−	0.446018i
$843$	−8.06015	+	4.84963i	−0.277606	+	0.167030i
$844$	−9.55089	+	14.0865i	−0.328755	+	0.484878i
$845$	0.703713	−	2.53455i	0.0242085	−	0.0871910i
$846$	−2.38639	+	0.259535i	−0.0820457	+	0.00892301i
$847$	−5.24146	−	3.98445i	−0.180099	−	0.136907i
$848$	−1.51990	−	0.703180i	−0.0521935	−	0.0241473i
$849$	−1.77112	−	2.61220i	−0.0607845	−	0.0896505i
$850$	−29.3640	+	9.89389i	−1.00718	+	0.339358i
$851$	−4.79567	−	29.2523i	−0.164394	−	1.00276i
$852$	2.09198	−	12.7605i	0.0716701	−	0.437168i
$853$	2.54607	+	0.857870i	0.0871757	+	0.0293729i	0.362551	−	0.931964i	$-0.381906\pi$
$853$	2.54607	+	0.857870i	0.0871757	+	0.0293729i	−0.275376	+	0.961337i	$0.588802\pi$
$854$	−4.10092	−	14.7702i	−0.140330	−	0.505425i
$855$	−1.76361	−	4.42634i	−0.0603143	−	0.151377i
$856$	−4.66357	−	11.7047i	−0.159397	−	0.400057i
$857$	−5.69880	−	20.5252i	−0.194667	−	0.701128i	−0.994849	−	0.101370i	$-0.967677\pi$
$857$	−5.69880	−	20.5252i	−0.194667	−	0.701128i	0.800182	−	0.599758i	$-0.204736\pi$
$858$	8.97906	+	3.02540i	0.306540	+	0.103285i
$859$	3.09350	−	18.8695i	0.105549	−	0.643821i	−0.880071	−	0.474843i	$-0.842505\pi$
$859$	3.09350	−	18.8695i	0.105549	−	0.643821i	0.985620	−	0.168978i	$-0.0540467\pi$
$860$	0.111437	+	0.679733i	0.00379995	+	0.0231787i
$861$	9.28908	−	3.12986i	0.316571	−	0.106665i
$862$	−16.0559	−	23.6807i	−0.546866	−	0.806567i
$863$	−2.31702	−	1.07197i	−0.0788722	−	0.0364902i	0.380056	−	0.924963i	$-0.375905\pi$
$863$	−2.31702	−	1.07197i	−0.0788722	−	0.0364902i	−0.458929	+	0.888473i	$0.651767\pi$
$864$	0.796093	+	0.605174i	0.0270836	+	0.0205884i
$865$	−2.99196	+	0.325395i	−0.101730	+	0.0110638i
$866$	7.90742	−	28.4799i	0.268705	−	0.967788i
$867$	−15.4392	+	22.7711i	−0.524342	+	0.773347i
$868$	1.18820	−	0.714913i	0.0403300	−	0.0242657i
$869$	1.16281	+	21.4468i	0.0394458	+	0.727534i
$870$	3.80173	−	3.60119i	0.128891	−	0.122092i
$871$	−20.3382	+	15.4607i	−0.689133	+	0.523865i
$872$	6.82277	−	1.50181i	0.231048	−	0.0508576i
$873$	0.843889	+	0.993503i	0.0285613	+	0.0336250i
$874$	−2.16792	+	39.9849i	−0.0733308	+	1.35251i
$875$	−3.03517	−	5.72493i	−0.102607	−	0.193538i
$876$	−7.64505	−	1.68280i	−0.258302	−	0.0568566i
$877$	10.3188	−	4.77396i	0.348440	−	0.161205i	−0.237860	−	0.971299i	$-0.576446\pi$
$877$	10.3188	−	4.77396i	0.348440	−	0.161205i	0.586300	+	0.810094i	$0.300584\pi$
$878$	−7.30976	−	4.39813i	−0.246692	−	0.148430i
$879$	0.427830	−	0.806974i	0.0144304	−	0.0272185i
$880$	−0.876628	+	1.03205i	−0.0295511	+	0.0347903i
$881$	−16.7429	−	15.8597i	−0.564082	−	0.534327i	0.351642	−	0.936134i	$-0.385623\pi$
$881$	−16.7429	−	15.8597i	−0.564082	−	0.534327i	−0.915724	+	0.401808i	$0.868382\pi$
$882$	5.69700	+	0.619586i	0.191828	+	0.0208626i
$883$	17.9333	−	45.0091i	0.603503	−	1.51468i	−0.236241	−	0.971695i	$-0.575915\pi$
$883$	17.9333	−	45.0091i	0.603503	−	1.51468i	0.839743	−	0.542983i	$-0.182705\pi$
$884$	−27.8387			−0.936318
$885$	−4.39473	−	1.29111i	−0.147727	−	0.0434003i
$886$	2.10208			0.0706207
$887$	7.68015	−	19.2757i	0.257874	−	0.647215i	−0.741853	−	0.670562i	$-0.766053\pi$
$887$	7.68015	−	19.2757i	0.257874	−	0.647215i	0.999727	+	0.0233468i	$0.00743220\pi$
$888$	5.88017	+	0.639507i	0.197326	+	0.0214604i
$889$	−5.56668	−	5.27304i	−0.186701	−	0.176852i
$890$	−2.56388	+	3.01844i	−0.0859415	+	0.101178i
$891$	−1.06364	+	2.00623i	−0.0356332	+	0.0672113i
$892$	−1.37552	−	0.827625i	−0.0460559	−	0.0277109i
$893$	17.4074	−	8.05352i	0.582516	−	0.269501i
$894$	−1.97928	−	0.435673i	−0.0661971	−	0.0145711i
$895$	2.37144	+	4.47302i	0.0792686	+	0.149516i
$896$	0.0609971	−	1.12503i	0.00203777	−	0.0375845i
$897$	−13.5379	−	15.9381i	−0.452018	−	0.532157i
$898$	−4.62524	+	1.01809i	−0.154346	+	0.0339742i
$899$	8.60415	−	6.54071i	0.286965	−	0.218145i
$900$	3.37181	−	3.19395i	0.112394	−	0.106465i
$901$	0.604892	+	11.1566i	0.0201519	+	0.371680i
$902$	−16.9278	+	10.1851i	−0.563634	+	0.339128i
$903$	0.730335	−	1.07716i	0.0243040	−	0.0358458i
$904$	−1.82856	+	6.58588i	−0.0608170	+	0.219043i
$905$	13.0340	−	1.41753i	0.433263	−	0.0471202i
$906$	14.1827	+	10.7814i	0.471189	+	0.358189i
$907$	10.4748	+	4.84615i	0.347809	+	0.160914i	0.586013	−	0.810301i	$-0.300697\pi$
$907$	10.4748	+	4.84615i	0.347809	+	0.160914i	−0.238204	+	0.971215i	$0.576559\pi$
$908$	11.5730	+	17.0689i	0.384064	+	0.566451i
$909$	4.39292	−	1.48015i	0.145704	−	0.0490933i
$910$	−0.453550	−	2.76654i	−0.0150351	−	0.0917098i
$911$	1.87369	−	11.4290i	0.0620780	−	0.378659i	−0.937455	−	0.348106i	$-0.886825\pi$
$911$	1.87369	−	11.4290i	0.0620780	−	0.378659i	0.999533	−	0.0305529i	$-0.00972682\pi$
$912$	−7.57192	−	2.55128i	−0.250731	−	0.0844812i
$913$	−9.78438	−	35.2402i	−0.323816	−	1.16628i
$914$	0.917549	+	2.30287i	0.0303498	+	0.0761723i
$915$	3.00302	+	7.53700i	0.0992767	+	0.249166i
$916$	7.29773	+	26.2840i	0.241124	+	0.868449i
$917$	6.81610	+	2.29661i	0.225087	+	0.0758408i
$918$	1.07936	−	6.58382i	0.0356243	−	0.217298i
$919$	−5.08816	−	31.0364i	−0.167843	−	1.02380i	−0.927596	−	0.373585i	$-0.878128\pi$
$919$	−5.08816	−	31.0364i	−0.167843	−	1.02380i	0.759753	−	0.650212i	$-0.225320\pi$
$920$	2.83210	−	0.954245i	0.0933716	−	0.0314605i
$921$	6.44261	+	9.50214i	0.212291	+	0.313106i
$922$	17.1387	+	7.92920i	0.564432	+	0.261134i
$923$	−42.9540	−	32.6528i	−1.41385	−	1.07478i
$924$	2.54341	−	0.276612i	0.0836719	−	0.00909987i
$925$	7.34924	−	26.4696i	0.241641	−	0.870314i
$926$	−15.4806	+	22.8322i	−0.508725	+	0.750314i
$927$	−10.1992	+	6.13665i	−0.334985	+	0.201554i
$928$	−0.475417	−	8.76855i	−0.0156063	−	0.287842i
$929$	12.0985	−	11.4603i	0.396937	−	0.375999i	−0.463035	−	0.886340i	$-0.653239\pi$
$929$	12.0985	−	11.4603i	0.396937	−	0.375999i	0.859972	+	0.510341i	$0.170481\pi$
$930$	−0.584287	+	0.444163i	−0.0191595	+	0.0145647i
$931$	−44.7180	+	9.84318i	−1.46557	+	0.322597i
$932$	0.374296	+	0.440656i	0.0122605	+	0.0144342i
$933$	−0.481271	+	8.87652i	−0.0157561	+	0.290604i
$934$	5.00529	+	9.44097i	0.163778	+	0.308918i
$935$	8.82296	+	1.94208i	0.288542	+	0.0635129i
$936$	3.78700	−	1.75205i	0.123782	−	0.0572676i
$937$	27.8030	+	16.7285i	0.908284	+	0.546497i	0.891328	−	0.453360i	$-0.149775\pi$
$937$	27.8030	+	16.7285i	0.908284	+	0.546497i	0.0169567	+	0.999856i	$0.494602\pi$
$938$	−3.23117	+	6.09464i	−0.105502	+	0.198997i
$939$	12.5330	−	14.7549i	0.408998	−	0.481509i
$940$	−1.03923	−	0.984410i	−0.0338959	−	0.0321079i
$941$	7.70032	+	0.837460i	0.251023	+	0.0273004i	0.232766	−	0.972533i	$-0.425223\pi$
$941$	7.70032	+	0.837460i	0.251023	+	0.0273004i	0.0182578	+	0.999833i	$0.494188\pi$
$942$	−3.59815	+	9.03067i	−0.117234	+	0.294235i
$943$	43.6013			1.41985
$944$	−6.42121	+	4.21523i	−0.208992	+	0.137194i
$945$	0.671866			0.0218558
$946$	−0.970839	+	2.43662i	−0.0315647	+	0.0792214i
$947$	−15.6246	−	1.69928i	−0.507732	−	0.0552191i	−0.149331	−	0.988787i	$-0.547712\pi$
$947$	−15.6246	−	1.69928i	−0.507732	−	0.0552191i	−0.358400	+	0.933568i	$0.616678\pi$
$948$	6.86698	+	6.50475i	0.223029	+	0.211264i
$949$	−21.1461	+	24.8951i	−0.686432	+	0.808130i
$950$	−17.3824	+	32.7868i	−0.563961	+	1.06374i
$951$	23.9399	+	14.4041i	0.776304	+	0.467087i
$952$	−6.82212	+	3.15625i	−0.221106	+	0.102295i
$953$	−24.2280	−	5.33298i	−0.784822	−	0.172752i	−0.195557	−	0.980692i	$-0.562651\pi$
$953$	−24.2280	−	5.33298i	−0.784822	−	0.172752i	−0.589265	+	0.807940i	$0.700582\pi$
$954$	−0.784434	−	1.47960i	−0.0253970	−	0.0479038i
$955$	0.174972	−	3.22717i	0.00566196	−	0.104429i
$956$	−1.75394	−	2.06490i	−0.0567266	−	0.0667837i
$957$	19.4742	−	4.28660i	0.629512	−	0.138566i
$958$	13.6582	−	10.3827i	0.441276	−	0.335449i
$959$	11.8067	−	11.1839i	0.381258	−	0.361147i
$960$	0.0322844	+	0.595450i	0.00104197	+	0.0192181i
$961$	25.2646	−	15.2012i	0.814987	−	0.490361i
$962$	13.8504	−	20.4279i	0.446556	−	0.658621i
$963$	3.37073	−	12.1403i	0.108620	−	0.391215i
$964$	−14.1927	+	1.54355i	−0.457116	+	0.0497144i
$965$	4.56656	+	3.47141i	0.147003	+	0.111749i
$966$	−5.12459	−	2.37089i	−0.164881	−	0.0762820i
$967$	23.0924	+	34.0588i	0.742603	+	1.09526i	0.991924	+	0.126836i	$0.0404822\pi$
$967$	23.0924	+	34.0588i	0.742603	+	1.09526i	−0.249321	+	0.968421i	$0.580207\pi$
$968$	5.53780	−	1.86590i	0.177992	−	0.0599724i
$969$	8.62430	+	52.6059i	0.277052	+	1.68994i
$970$	−0.125758	+	0.767089i	−0.00403784	+	0.0246297i
$971$	34.1720	+	11.5139i	1.09663	+	0.369498i	0.808741	−	0.588165i	$-0.200149\pi$
$971$	34.1720	+	11.5139i	1.09663	+	0.369498i	0.287891	+	0.957663i	$0.407046\pi$
$972$	0.267528	+	0.963550i	0.00858098	+	0.0309059i
$973$	4.55739	+	11.4382i	0.146103	+	0.366691i
$974$	1.85452	+	4.65450i	0.0594227	+	0.149140i
$975$	−5.18456	−	18.6731i	−0.166039	−	0.598017i
$976$	12.8932	+	4.34422i	0.412701	+	0.139055i
$977$	0.784606	−	4.78588i	0.0251018	−	0.153114i	−0.971302	−	0.237851i	$-0.923557\pi$
$977$	0.784606	−	4.78588i	0.0251018	−	0.153114i	0.996403	+	0.0847375i	$0.0270052\pi$
$978$	−1.31293	−	8.00850i	−0.0419828	−	0.256084i
$979$	−14.2912	+	4.81528i	−0.456750	+	0.153897i
$980$	1.91774	+	2.82846i	0.0612600	+	0.0903518i
$981$	6.34042	+	2.93339i	0.202434	+	0.0936559i
$982$	−8.56054	−	6.50755i	−0.273178	−	0.207664i
$983$	−43.4773	+	4.72844i	−1.38671	+	0.150814i	−0.770837	−	0.637033i	$-0.780162\pi$
$983$	−43.4773	+	4.72844i	−1.38671	+	0.150814i	−0.615872	+	0.787846i	$0.711196\pi$
$984$	−2.32752	+	8.38296i	−0.0741986	+	0.267239i
$985$	−4.27986	+	6.31232i	−0.136368	+	0.201127i
$986$	−50.2008	+	30.2048i	−1.59872	+	0.961917i
$987$	0.146421	+	2.70058i	0.00466064	+	0.0859604i
$988$	−24.2049	+	22.9281i	−0.770060	+	0.729440i
$989$	4.60845	−	3.50325i	0.146540	−	0.111397i
$990$	−1.32244	+	0.291092i	−0.0420301	+	0.00925152i
$991$	19.3697	+	22.8038i	0.615299	+	0.724386i	0.978252	−	0.207422i	$-0.0665073\pi$
$991$	19.3697	+	22.8038i	0.615299	+	0.724386i	−0.362953	+	0.931807i	$0.618231\pi$
$992$	−0.0666329	+	1.22897i	−0.00211560	+	0.0390199i
$993$	3.13633	+	5.91574i	0.0995284	+	0.187730i
$994$	−14.2283	−	3.13189i	−0.451295	−	0.0993374i
$995$	14.4015	−	6.66286i	0.456559	−	0.211227i
$996$	−13.8008	−	8.30364i	−0.437294	−	0.263111i
$997$	12.6801	−	23.9171i	0.401581	−	0.757463i	−0.597430	−	0.801921i	$-0.703811\pi$
$997$	12.6801	−	23.9171i	0.401581	−	0.757463i	0.999011	+	0.0444582i	$0.0141562\pi$
$998$	21.2673	−	25.0378i	0.673204	−	0.792557i
$999$	4.29415	+	4.06763i	0.135861	+	0.128694i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.a.49.2	✓	56
59.53	even	29	inner	354.2.e.a.289.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.a.49.2	✓	56	1.1	even	1	trivial
354.2.e.a.289.2	yes	56	59.53	even	29	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.370138 + 0.928977i) q^{2} +(-0.994138 - 0.108119i) q^{3} +(-0.725995 - 0.687699i) q^{4} +(0.386052 - 0.454496i) q^{5} +(0.468408 - 0.883512i) q^{6} +(-0.965403 - 0.580863i) q^{7} +(0.907575 - 0.419889i) q^{8} +(0.976621 + 0.214970i) q^{9} +O(q^{10})\)	\(q+(-0.370138 + 0.928977i) q^{2} +(-0.994138 - 0.108119i) q^{3} +(-0.725995 - 0.687699i) q^{4} +(0.386052 - 0.454496i) q^{5} +(0.468408 - 0.883512i) q^{6} +(-0.965403 - 0.580863i) q^{7} +(0.907575 - 0.419889i) q^{8} +(0.976621 + 0.214970i) q^{9} +(0.279324 + 0.526860i) q^{10} +(-0.122936 + 2.26742i) q^{11} +(0.647386 + 0.762162i) q^{12} +(4.07510 - 0.896998i) q^{13} +(0.896941 - 0.681837i) q^{14} +(-0.432929 + 0.410092i) q^{15} +(0.0541389 + 0.998533i) q^{16} +(5.71670 - 3.43962i) q^{17} +(-0.561187 + 0.827689i) q^{18} +(2.13760 - 7.69894i) q^{19} +(-0.592829 + 0.0644740i) q^{20} +(0.896941 + 0.681837i) q^{21} +(-2.06088 - 0.953462i) q^{22} +(2.81244 + 4.14804i) q^{23} +(-0.947653 + 0.319302i) q^{24} +(0.751380 + 4.58321i) q^{25} +(-0.675061 + 4.11769i) q^{26} +(-0.947653 - 0.319302i) q^{27} +(0.301418 + 1.08561i) q^{28} +(3.25034 + 8.15774i) q^{29} +(-0.220723 - 0.553972i) q^{30} +(-0.329268 - 1.18592i) q^{31} +(-0.947653 - 0.319302i) q^{32} +(0.367366 - 2.24083i) q^{33} +(1.07936 + 6.58382i) q^{34} +(-0.636696 + 0.214528i) q^{35} +(-0.561187 - 0.827689i) q^{36} +(-5.36817 - 2.48358i) q^{37} +(6.36093 + 4.83545i) q^{38} +(-4.14820 + 0.451144i) q^{39} +(0.159534 - 0.574589i) q^{40} +(4.88237 - 7.20096i) q^{41} +(-0.965403 + 0.580863i) q^{42} +(-0.0625351 - 1.15339i) q^{43} +(1.64855 - 1.56159i) q^{44} +(0.474730 - 0.360880i) q^{45} +(-4.89443 + 1.07735i) q^{46} +(1.55402 + 1.82954i) q^{47} +(0.0541389 - 0.998533i) q^{48} +(-2.68426 - 5.06305i) q^{49} +(-4.53581 - 0.998408i) q^{50} +(-6.05508 + 2.80138i) q^{51} +(-3.57537 - 2.15123i) q^{52} +(-0.784434 + 1.47960i) q^{53} +(0.647386 - 0.762162i) q^{54} +(0.983073 + 0.931216i) q^{55} +(-1.12007 - 0.121815i) q^{56} +(-2.95747 + 7.42269i) q^{57} -8.78142 q^{58} +(3.86141 + 6.64000i) q^{59} +0.596325 q^{60} +(5.03588 - 12.6391i) q^{61} +(1.22356 + 0.133070i) q^{62} +(-0.817963 - 0.774816i) q^{63} +(0.647386 - 0.762162i) q^{64} +(1.16552 - 2.19841i) q^{65} +(1.94571 + 1.17069i) q^{66} +(-5.55672 + 2.57081i) q^{67} +(-6.51573 - 1.43422i) q^{68} +(-2.34747 - 4.42781i) q^{69} +(0.0363741 - 0.670881i) q^{70} +(-8.37126 - 9.85541i) q^{71} +(0.976621 - 0.214970i) q^{72} +(-6.23187 + 4.73734i) q^{73} +(4.29415 - 4.06763i) q^{74} +(-0.251443 - 4.63759i) q^{75} +(-6.84645 + 4.11937i) q^{76} +(1.43574 - 2.11756i) q^{77} +(1.11630 - 4.02056i) q^{78} +(9.40326 - 1.02267i) q^{79} +(0.474730 + 0.360880i) q^{80} +(0.907575 + 0.419889i) q^{81} +(4.88237 + 7.20096i) q^{82} +(-15.2631 + 5.14275i) q^{83} +(-0.182276 - 1.11184i) q^{84} +(0.643650 - 3.92609i) q^{85} +(1.09462 + 0.368821i) q^{86} +(-2.34928 - 8.46134i) q^{87} +(0.840490 + 2.10947i) q^{88} +(2.45819 + 6.16959i) q^{89} +(0.159534 + 0.574589i) q^{90} +(-4.45515 - 1.50111i) q^{91} +(0.810786 - 4.94558i) q^{92} +(0.199118 + 1.21456i) q^{93} +(-2.27480 + 0.766471i) q^{94} +(-2.67391 - 3.94373i) q^{95} +(0.907575 + 0.419889i) q^{96} +(1.03773 + 0.788865i) q^{97} +(5.69700 - 0.619586i) q^{98} +(-0.607489 + 2.18798i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9	\( 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} - 18 q^{11} - 2 q^{12} + 13 q^{13} - 20 q^{14} + 4 q^{15} - 2 q^{16} + 21 q^{17} - 2 q^{18} + 20 q^{19} + 4 q^{20} - 20 q^{21} + 11 q^{22} + 34 q^{23} - 2 q^{24} - 28 q^{25} - 16 q^{26} - 2 q^{27} + 9 q^{28} + 38 q^{29} + 4 q^{30} + 34 q^{31} - 2 q^{32} + 11 q^{33} - 8 q^{34} - 19 q^{35} - 2 q^{36} - 29 q^{37} + 20 q^{38} + 13 q^{39} + 4 q^{40} + 43 q^{41} + 9 q^{42} - 65 q^{43} + 11 q^{44} + 4 q^{45} + 5 q^{46} - 60 q^{47} - 2 q^{48} - 13 q^{49} - 86 q^{50} + 21 q^{51} - 16 q^{52} - 15 q^{53} - 2 q^{54} - 15 q^{55} + 9 q^{56} + 20 q^{57} - 78 q^{58} - 2 q^{59} - 54 q^{60} + 4 q^{61} + 5 q^{62} + 9 q^{63} - 2 q^{64} - 57 q^{65} + 11 q^{66} - 56 q^{67} - 8 q^{68} - 53 q^{69} + 10 q^{70} + 23 q^{71} - 2 q^{72} - 21 q^{73} + 30 q^{75} - 9 q^{76} - 57 q^{77} + 13 q^{78} + 99 q^{79} + 4 q^{80} - 2 q^{81} + 43 q^{82} + 33 q^{83} + 9 q^{84} - 45 q^{85} - 7 q^{86} + 9 q^{87} - 18 q^{88} + 32 q^{89} + 4 q^{90} - 75 q^{91} + 34 q^{92} + 5 q^{93} + 27 q^{94} + 82 q^{95} - 2 q^{96} + 70 q^{97} + 45 q^{98} + 11 q^{99}+O(q^{100}) \) 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 - 18 * q^11 - 2 * q^12 + 13 * q^13 - 20 * q^14 + 4 * q^15 - 2 * q^16 + 21 * q^17 - 2 * q^18 + 20 * q^19 + 4 * q^20 - 20 * q^21 + 11 * q^22 + 34 * q^23 - 2 * q^24 - 28 * q^25 - 16 * q^26 - 2 * q^27 + 9 * q^28 + 38 * q^29 + 4 * q^30 + 34 * q^31 - 2 * q^32 + 11 * q^33 - 8 * q^34 - 19 * q^35 - 2 * q^36 - 29 * q^37 + 20 * q^38 + 13 * q^39 + 4 * q^40 + 43 * q^41 + 9 * q^42 - 65 * q^43 + 11 * q^44 + 4 * q^45 + 5 * q^46 - 60 * q^47 - 2 * q^48 - 13 * q^49 - 86 * q^50 + 21 * q^51 - 16 * q^52 - 15 * q^53 - 2 * q^54 - 15 * q^55 + 9 * q^56 + 20 * q^57 - 78 * q^58 - 2 * q^59 - 54 * q^60 + 4 * q^61 + 5 * q^62 + 9 * q^63 - 2 * q^64 - 57 * q^65 + 11 * q^66 - 56 * q^67 - 8 * q^68 - 53 * q^69 + 10 * q^70 + 23 * q^71 - 2 * q^72 - 21 * q^73 + 30 * q^75 - 9 * q^76 - 57 * q^77 + 13 * q^78 + 99 * q^79 + 4 * q^80 - 2 * q^81 + 43 * q^82 + 33 * q^83 + 9 * q^84 - 45 * q^85 - 7 * q^86 + 9 * q^87 - 18 * q^88 + 32 * q^89 + 4 * q^90 - 75 * q^91 + 34 * q^92 + 5 * q^93 + 27 * q^94 + 82 * q^95 - 2 * q^96 + 70 * q^97 + 45 * q^98 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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