LMFDB - Embedded newform 507.2.q.a.55.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(16,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("507.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.q (of order $39$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$15$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			55.2
Character	$\chi$	$=$	507.55
Dual form			507.2.q.a.295.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.58863 + 1.94572i) q^{2} +(0.996757 + 0.0804666i) q^{3} +(-0.862027 - 4.22249i) q^{4} +(0.458750 + 3.77814i) q^{5} +(-1.74005 + 1.81158i) q^{6} +(2.22525 - 1.40716i) q^{7} +(5.13689 + 2.69605i) q^{8} +(0.987050 + 0.160411i) q^{9} +O(q^{10})$	\(q+(-1.58863 + 1.94572i) q^{2} +(0.996757 + 0.0804666i) q^{3} +(-0.862027 - 4.22249i) q^{4} +(0.458750 + 3.77814i) q^{5} +(-1.74005 + 1.81158i) q^{6} +(2.22525 - 1.40716i) q^{7} +(5.13689 + 2.69605i) q^{8} +(0.987050 + 0.160411i) q^{9} +(-8.07999 - 5.10948i) q^{10} +(3.29269 - 0.535115i) q^{11} +(-0.519462 - 4.27816i) q^{12} +(0.963352 + 3.47447i) q^{13} +(-0.797157 + 6.56518i) q^{14} +(0.153248 + 3.80280i) q^{15} +(-5.47693 + 2.33350i) q^{16} +(1.65576 - 1.04704i) q^{17} +(-1.88017 + 1.66569i) q^{18} +(2.60026 - 4.50378i) q^{19} +(15.5577 - 5.19392i) q^{20} +(2.33126 - 1.22354i) q^{21} +(-4.18970 + 7.25676i) q^{22} +(0.141247 + 0.244647i) q^{23} +(4.90329 + 3.10065i) q^{24} +(-9.20920 + 2.26986i) q^{25} +(-8.29076 - 3.64524i) q^{26} +(0.970942 + 0.239316i) q^{27} +(-7.85995 - 8.18307i) q^{28} +(-1.96967 + 2.41241i) q^{29} +(-7.64265 - 5.74308i) q^{30} +(5.08338 + 1.25294i) q^{31} +(0.932379 - 3.21895i) q^{32} +(3.32508 - 0.268428i) q^{33} +(-0.593148 + 4.88501i) q^{34} +(6.33729 + 7.76177i) q^{35} +(-0.173529 - 4.30608i) q^{36} +(-1.09500 - 3.78039i) q^{37} +(4.63225 + 12.2142i) q^{38} +(0.680650 + 3.54072i) q^{39} +(-7.82951 + 20.6447i) q^{40} +(-7.48388 - 0.604161i) q^{41} +(-1.32285 + 6.47974i) q^{42} +(-3.16497 + 10.9268i) q^{43} +(-5.09791 - 13.4421i) q^{44} +(-0.153248 + 3.80280i) q^{45} +(-0.700404 - 0.113827i) q^{46} +(-5.79045 - 5.12989i) q^{47} +(-5.64694 + 1.88523i) q^{48} +(-0.0292196 + 0.0615790i) q^{49} +(10.2135 - 21.5245i) q^{50} +(1.73464 - 0.910412i) q^{51} +(13.8405 - 7.06283i) q^{52} +(-8.33402 - 4.37403i) q^{53} +(-2.00811 + 1.50900i) q^{54} +(3.53226 + 12.1948i) q^{55} +(15.2246 - 1.22906i) q^{56} +(2.95423 - 4.27994i) q^{57} +(-1.56479 - 7.66485i) q^{58} +(4.46423 + 1.90203i) q^{59} +(15.9252 - 3.92521i) q^{60} +(0.613804 - 15.2314i) q^{61} +(-10.5135 + 7.90037i) q^{62} +(2.42216 - 1.03198i) q^{63} +(-1.98178 - 2.87110i) q^{64} +(-12.6851 + 5.23359i) q^{65} +(-4.76004 + 6.89610i) q^{66} +(0.888695 - 4.35312i) q^{67} +(-5.84842 - 6.08885i) q^{68} +(0.121103 + 0.255219i) q^{69} -25.1699 q^{70} +(-3.64505 - 7.68177i) q^{71} +(4.63789 + 3.48515i) q^{72} +(-4.90292 + 12.9279i) q^{73} +(9.09513 + 3.87507i) q^{74} +(-9.36198 + 1.52147i) q^{75} +(-21.2587 - 7.09718i) q^{76} +(6.57407 - 5.82412i) q^{77} +(-7.97056 - 4.30055i) q^{78} +(-11.3441 - 10.0500i) q^{79} +(-11.3288 - 19.6221i) q^{80} +(0.948536 + 0.316668i) q^{81} +(13.0647 - 13.6018i) q^{82} +(4.41554 + 6.39701i) q^{83} +(-7.17600 - 8.78900i) q^{84} +(4.71545 + 5.77537i) q^{85} +(-16.2324 - 23.5167i) q^{86} +(-2.15740 + 2.24609i) q^{87} +(18.3569 + 6.12843i) q^{88} +(7.97569 + 13.8143i) q^{89} +(-7.15574 - 6.33943i) q^{90} +(7.03284 + 6.37597i) q^{91} +(0.911260 - 0.807306i) q^{92} +(4.96607 + 1.65792i) q^{93} +(19.1802 - 3.11709i) q^{94} +(18.2088 + 7.75804i) q^{95} +(1.18837 - 3.13348i) q^{96} +(0.909825 + 0.683689i) q^{97} +(-0.0733963 - 0.154679i) q^{98} +3.33589 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q + q^{2} - 15 q^{3} + 15 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} + 15 q^{9}+O(q^{10}) $ 360 * q + q^2 - 15 * q^3 + 15 * q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 + 15 * q^9	\( 360 q + q^{2} - 15 q^{3} + 15 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} + 15 q^{9} - q^{10} - 2 q^{11} + 30 q^{12} - 19 q^{13} + q^{15} + 15 q^{16} - 7 q^{17} - 2 q^{18} - 6 q^{19} + q^{20} + 4 q^{21} + 22 q^{22} + 46 q^{23} + 3 q^{24} + 28 q^{25} + 34 q^{26} + 30 q^{27} - 2 q^{28} + 36 q^{29} + q^{30} - 34 q^{31} - 190 q^{32} + 15 q^{33} - 51 q^{34} - 80 q^{35} + 15 q^{36} + q^{37} - 53 q^{38} + 5 q^{39} - 45 q^{40} + 9 q^{41} + 130 q^{42} + 78 q^{43} + 35 q^{44} - q^{45} - 318 q^{46} - 12 q^{47} - 15 q^{48} - 71 q^{49} + 48 q^{50} - 14 q^{51} - 63 q^{52} - 26 q^{53} - q^{54} - 61 q^{55} - 4 q^{56} - 38 q^{57} - 27 q^{58} + 208 q^{59} - 180 q^{60} - 3 q^{61} - 61 q^{62} + 2 q^{63} + 140 q^{64} + 45 q^{65} - 60 q^{66} - 80 q^{67} - 140 q^{68} + 6 q^{69} - 100 q^{70} + 84 q^{71} - 3 q^{72} + 134 q^{73} - 151 q^{74} - 12 q^{75} + 32 q^{76} + 82 q^{77} - 63 q^{78} + 4 q^{79} - 155 q^{80} + 15 q^{81} - 56 q^{82} + 106 q^{83} + 2 q^{84} - 19 q^{85} + q^{86} - 49 q^{87} + 8 q^{88} - 14 q^{89} + 2 q^{90} - 368 q^{91} + 36 q^{92} - 4 q^{93} - 59 q^{94} + 104 q^{95} + 75 q^{96} - 28 q^{97} + 101 q^{98} + 30 q^{99}+O(q^{100}) \) 360 * q + q^2 - 15 * q^3 + 15 * q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 + 15 * q^9 - q^10 - 2 * q^11 + 30 * q^12 - 19 * q^13 + q^15 + 15 * q^16 - 7 * q^17 - 2 * q^18 - 6 * q^19 + q^20 + 4 * q^21 + 22 * q^22 + 46 * q^23 + 3 * q^24 + 28 * q^25 + 34 * q^26 + 30 * q^27 - 2 * q^28 + 36 * q^29 + q^30 - 34 * q^31 - 190 * q^32 + 15 * q^33 - 51 * q^34 - 80 * q^35 + 15 * q^36 + q^37 - 53 * q^38 + 5 * q^39 - 45 * q^40 + 9 * q^41 + 130 * q^42 + 78 * q^43 + 35 * q^44 - q^45 - 318 * q^46 - 12 * q^47 - 15 * q^48 - 71 * q^49 + 48 * q^50 - 14 * q^51 - 63 * q^52 - 26 * q^53 - q^54 - 61 * q^55 - 4 * q^56 - 38 * q^57 - 27 * q^58 + 208 * q^59 - 180 * q^60 - 3 * q^61 - 61 * q^62 + 2 * q^63 + 140 * q^64 + 45 * q^65 - 60 * q^66 - 80 * q^67 - 140 * q^68 + 6 * q^69 - 100 * q^70 + 84 * q^71 - 3 * q^72 + 134 * q^73 - 151 * q^74 - 12 * q^75 + 32 * q^76 + 82 * q^77 - 63 * q^78 + 4 * q^79 - 155 * q^80 + 15 * q^81 - 56 * q^82 + 106 * q^83 + 2 * q^84 - 19 * q^85 + q^86 - 49 * q^87 + 8 * q^88 - 14 * q^89 + 2 * q^90 - 368 * q^91 + 36 * q^92 - 4 * q^93 - 59 * q^94 + 104 * q^95 + 75 * q^96 - 28 * q^97 + 101 * q^98 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{28}{39}\right)$

Coefficient data

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

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

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

$2$	−1.58863	+	1.94572i	−1.12333	+	1.37583i	−0.205598	+	0.978636i	$0.565914\pi$
$2$	−1.58863	+	1.94572i	−1.12333	+	1.37583i	−0.917734	+	0.397196i	$0.869983\pi$
$3$	0.996757	+	0.0804666i	0.575478	+	0.0464574i
$3$	0.996757	+	0.0804666i	0.575478	+	0.0464574i
$4$	−0.862027	−	4.22249i	−0.431013	−	2.11124i
$5$	0.458750	+	3.77814i	0.205159	+	1.68964i	0.623879	+	0.781521i	$0.285556\pi$
$5$	0.458750	+	3.77814i	0.205159	+	1.68964i	−0.418720	+	0.908115i	$0.637521\pi$
$6$	−1.74005	+	1.81158i	−0.710371	+	0.739574i
$7$	2.22525	−	1.40716i	0.841065	−	0.531857i	−0.0430789	−	0.999072i	$-0.513717\pi$
$7$	2.22525	−	1.40716i	0.841065	−	0.531857i	0.884144	+	0.467214i	$0.154742\pi$
$8$	5.13689	+	2.69605i	1.81616	+	0.953197i
$9$	0.987050	+	0.160411i	0.329017	+	0.0534704i
$10$	−8.07999	−	5.10948i	−2.55512	−	1.61576i
$11$	3.29269	−	0.535115i	0.992785	−	0.161343i	0.357742	−	0.933820i	$-0.383547\pi$
$11$	3.29269	−	0.535115i	0.992785	−	0.161343i	0.635043	+	0.772477i	$0.280983\pi$
$12$	−0.519462	−	4.27816i	−0.149956	−	1.23500i
$13$	0.963352	+	3.47447i	0.267186	+	0.963645i
$13$	0.963352	+	3.47447i	0.267186	+	0.963645i
$14$	−0.797157	+	6.56518i	−0.213049	+	1.75462i
$15$	0.153248	+	3.80280i	0.0395684	+	0.981880i
$16$	−5.47693	+	2.33350i	−1.36923	+	0.583376i
$17$	1.65576	−	1.04704i	0.401581	−	0.253945i	−0.318374	−	0.947965i	$-0.603137\pi$
$17$	1.65576	−	1.04704i	0.401581	−	0.253945i	0.719955	+	0.694021i	$0.244162\pi$
$18$	−1.88017	+	1.66569i	−0.443161	+	0.392607i
$19$	2.60026	−	4.50378i	0.596541	−	1.03324i	−0.396787	−	0.917911i	$-0.629875\pi$
$19$	2.60026	−	4.50378i	0.596541	−	1.03324i	0.993327	−	0.115328i	$-0.0367918\pi$
$20$	15.5577	−	5.19392i	3.47881	−	1.16140i
$21$	2.33126	−	1.22354i	0.508723	−	0.266999i
$22$	−4.18970	+	7.25676i	−0.893246	+	1.54715i
$23$	0.141247	+	0.244647i	0.0294520	+	0.0510124i	0.880376	−	0.474277i	$-0.157290\pi$
$23$	0.141247	+	0.244647i	0.0294520	+	0.0510124i	−0.850924	+	0.525289i	$0.823957\pi$
$24$	4.90329	+	3.10065i	1.00088	+	0.632918i
$25$	−9.20920	+	2.26986i	−1.84184	+	0.453973i
$26$	−8.29076	−	3.64524i	−1.62595	−	0.714891i
$27$	0.970942	+	0.239316i	0.186858	+	0.0460563i
$28$	−7.85995	−	8.18307i	−1.48539	−	1.54646i
$29$	−1.96967	+	2.41241i	−0.365758	+	0.447973i	−0.924393	−	0.381441i	$-0.875428\pi$
$29$	−1.96967	+	2.41241i	−0.365758	+	0.447973i	0.558635	+	0.829414i	$0.311325\pi$
$30$	−7.64265	−	5.74308i	−1.39535	−	1.04854i
$31$	5.08338	+	1.25294i	0.913001	+	0.225035i	0.667716	−	0.744416i	$-0.267272\pi$
$31$	5.08338	+	1.25294i	0.913001	+	0.225035i	0.245285	+	0.969451i	$0.421118\pi$
$32$	0.932379	−	3.21895i	0.164823	−	0.569034i
$33$	3.32508	−	0.268428i	0.578821	−	0.0467273i
$34$	−0.593148	+	4.88501i	−0.101724	+	0.837773i
$35$	6.33729	+	7.76177i	1.07120	+	1.31198i
$36$	−0.173529	−	4.30608i	−0.0289215	−	0.717681i
$37$	−1.09500	−	3.78039i	−0.180017	−	0.621492i	−0.998872	−	0.0474905i	$-0.984878\pi$
$37$	−1.09500	−	3.78039i	−0.180017	−	0.621492i	0.818854	−	0.574001i	$-0.194610\pi$
$38$	4.63225	+	12.2142i	0.751450	+	1.98141i
$39$	0.680650	+	3.54072i	0.108991	+	0.566969i
$40$	−7.82951	+	20.6447i	−1.23795	+	3.26422i
$41$	−7.48388	−	0.604161i	−1.16879	−	0.0943542i	−0.519207	−	0.854648i	$-0.673773\pi$
$41$	−7.48388	−	0.604161i	−1.16879	−	0.0943542i	−0.649579	+	0.760294i	$0.725055\pi$
$42$	−1.32285	+	6.47974i	−0.204120	+	0.999846i
$43$	−3.16497	+	10.9268i	−0.482654	+	1.66631i	0.236631	+	0.971600i	$0.423957\pi$
$43$	−3.16497	+	10.9268i	−0.482654	+	1.66631i	−0.719285	+	0.694715i	$0.755530\pi$
$44$	−5.09791	−	13.4421i	−0.768538	−	2.02647i
$45$	−0.153248	+	3.80280i	−0.0228448	+	0.566889i
$46$	−0.700404	−	0.113827i	−0.103269	−	0.0167828i
$47$	−5.79045	−	5.12989i	−0.844623	−	0.748271i	0.125186	−	0.992133i	$-0.460047\pi$
$47$	−5.79045	−	5.12989i	−0.844623	−	0.748271i	−0.969810	+	0.243862i	$0.921586\pi$
$48$	−5.64694	+	1.88523i	−0.815066	+	0.272109i
$49$	−0.0292196	+	0.0615790i	−0.00417423	+	0.00879699i
$50$	10.2135	−	21.5245i	1.44441	−	3.04402i
$51$	1.73464	−	0.910412i	0.242899	−	0.127483i
$52$	13.8405	−	7.06283i	1.91933	−	0.979438i
$53$	−8.33402	−	4.37403i	−1.14477	−	0.600819i	−0.217810	−	0.975991i	$-0.569891\pi$
$53$	−8.33402	−	4.37403i	−1.14477	−	0.600819i	−0.926955	+	0.375172i	$0.877584\pi$
$54$	−2.00811	+	1.50900i	−0.273269	+	0.205348i
$55$	3.53226	+	12.1948i	0.476290	+	1.64434i
$56$	15.2246	−	1.22906i	2.03448	−	0.164240i
$57$	2.95423	−	4.27994i	0.391298	−	0.566892i
$58$	−1.56479	−	7.66485i	−0.205467	−	1.00644i
$59$	4.46423	+	1.90203i	0.581193	+	0.247623i	0.662495	−	0.749066i	$-0.269498\pi$
$59$	4.46423	+	1.90203i	0.581193	+	0.247623i	−0.0813018	+	0.996690i	$0.525908\pi$
$60$	15.9252	−	3.92521i	2.05593	−	0.506742i
$61$	0.613804	−	15.2314i	0.0785895	−	1.95018i	−0.178831	−	0.983880i	$-0.557232\pi$
$61$	0.613804	−	15.2314i	0.0785895	−	1.95018i	0.257421	−	0.966299i	$-0.417127\pi$
$62$	−10.5135	+	7.90037i	−1.33521	+	1.00335i
$63$	2.42216	−	1.03198i	0.305163	−	0.130018i
$64$	−1.98178	−	2.87110i	−0.247723	−	0.358888i
$65$	−12.6851	+	5.23359i	−1.57339	+	0.649148i
$66$	−4.76004	+	6.89610i	−0.585920	+	0.848852i
$67$	0.888695	−	4.35312i	0.108571	−	0.531818i	−0.888732	−	0.458427i	$-0.848413\pi$
$67$	0.888695	−	4.35312i	0.108571	−	0.531818i	0.997303	−	0.0733904i	$-0.0233819\pi$
$68$	−5.84842	−	6.08885i	−0.709226	−	0.738382i
$69$	0.121103	+	0.255219i	0.0145791	+	0.0307248i
$70$	−25.1699			−3.00837
$71$	−3.64505	−	7.68177i	−0.432587	−	0.911659i	−0.996321	−	0.0857018i	$-0.972687\pi$
$71$	−3.64505	−	7.68177i	−0.432587	−	0.911659i	0.563733	−	0.825957i	$-0.309365\pi$
$72$	4.63789	+	3.48515i	0.546581	+	0.410729i
$73$	−4.90292	+	12.9279i	−0.573844	+	1.51310i	0.262520	+	0.964927i	$0.415447\pi$
$73$	−4.90292	+	12.9279i	−0.573844	+	1.51310i	−0.836364	+	0.548175i	$0.815323\pi$
$74$	9.09513	+	3.87507i	1.05729	+	0.450468i
$75$	−9.36198	+	1.52147i	−1.08103	+	0.175684i
$76$	−21.2587	−	7.09718i	−2.43853	−	0.814102i
$77$	6.57407	−	5.82412i	0.749185	−	0.663720i
$78$	−7.97056	−	4.30055i	−0.902488	−	0.486941i
$79$	−11.3441	−	10.0500i	−1.27631	−	1.13071i	−0.984716	−	0.174170i	$-0.944276\pi$
$79$	−11.3441	−	10.0500i	−1.27631	−	1.13071i	−0.291594	−	0.956542i	$-0.594186\pi$
$80$	−11.3288	−	19.6221i	−1.26660	−	2.19382i
$81$	0.948536	+	0.316668i	0.105393	+	0.0351853i
$82$	13.0647	−	13.6018i	1.44275	−	1.50206i
$83$	4.41554	+	6.39701i	0.484668	+	0.702163i	0.986676	−	0.162700i	$-0.0520204\pi$
$83$	4.41554	+	6.39701i	0.484668	+	0.702163i	−0.502007	+	0.864863i	$0.667405\pi$
$84$	−7.17600	−	8.78900i	−0.782965	−	0.958959i
$85$	4.71545	+	5.77537i	0.511462	+	0.626427i
$86$	−16.2324	−	23.5167i	−1.75039	−	2.53588i
$87$	−2.15740	+	2.24609i	−0.231298	+	0.240806i
$88$	18.3569	+	6.12843i	1.95685	+	0.653293i
$89$	7.97569	+	13.8143i	0.845421	+	1.46431i	0.885255	+	0.465106i	$0.153984\pi$
$89$	7.97569	+	13.8143i	0.845421	+	1.46431i	−0.0398341	+	0.999206i	$0.512683\pi$
$90$	−7.15574	−	6.33943i	−0.754281	−	0.668235i
$91$	7.03284	+	6.37597i	0.737242	+	0.668383i
$92$	0.911260	−	0.807306i	0.0950054	−	0.0841675i
$93$	4.96607	+	1.65792i	0.514958	+	0.171918i
$94$	19.1802	−	3.11709i	1.97829	−	0.321503i
$95$	18.2088	+	7.75804i	1.86818	+	0.795959i
$96$	1.18837	−	3.13348i	0.121288	−	0.319810i
$97$	0.909825	+	0.683689i	0.0923787	+	0.0694181i	0.645928	−	0.763398i	$-0.276471\pi$
$97$	0.909825	+	0.683689i	0.0923787	+	0.0694181i	−0.553549	+	0.832816i	$0.686727\pi$
$98$	−0.0733963	−	0.154679i	−0.00741415	−	0.0156250i
$99$	3.33589			0.335270
$100$	17.5230	+	36.9290i	1.75230	+	3.69290i
$101$	−4.90734	−	5.10908i	−0.488299	−	0.508373i	0.430775	−	0.902460i	$-0.358240\pi$
$101$	−4.90734	−	5.10908i	−0.488299	−	0.508373i	−0.919073	+	0.394087i	$0.871061\pi$
$102$	−0.984304	+	4.82144i	−0.0974607	+	0.477394i
$103$	1.05655	−	1.53067i	0.104105	−	0.150821i	−0.767469	−	0.641086i	$-0.778484\pi$
$103$	1.05655	−	1.53067i	0.104105	−	0.150821i	0.871574	+	0.490264i	$0.163100\pi$
$104$	−4.41871	+	20.4452i	−0.433290	+	2.00482i
$105$	5.69218	+	8.24654i	0.555500	+	0.804780i
$106$	21.7503	−	9.26695i	2.11258	−	0.900086i
$107$	−0.940435	+	0.706691i	−0.0909152	+	0.0683184i	−0.645228	−	0.763990i	$-0.723238\pi$
$107$	−0.940435	+	0.706691i	−0.0909152	+	0.0683184i	0.554313	+	0.832309i	$0.312981\pi$
$108$	0.173529	−	4.30608i	0.0166979	−	0.414353i
$109$	11.2635	−	2.77620i	1.07884	−	0.265911i	0.340438	−	0.940267i	$-0.389425\pi$
$109$	11.2635	−	2.77620i	1.07884	−	0.265911i	0.738407	+	0.674356i	$0.235579\pi$
$110$	−29.3391	−	12.5002i	−2.79737	−	1.19185i
$111$	−0.787257	−	3.85624i	−0.0747231	−	0.366018i
$112$	−8.90392	+	12.8996i	−0.841341	+	1.21889i
$113$	16.7139	−	1.34928i	1.57231	−	0.126930i	0.736686	−	0.676235i	$-0.236390\pi$
$113$	16.7139	−	1.34928i	1.57231	−	0.126930i	0.835622	+	0.549305i	$0.185108\pi$
$114$	3.63439	+	12.5474i	0.340392	+	1.17517i
$115$	−0.859514	+	0.645883i	−0.0801501	+	0.0602289i
$116$	11.8843	+	6.23734i	1.10343	+	0.579123i
$117$	0.393533	+	3.58401i	0.0363821	+	0.331342i
$118$	−10.7928	+	5.66452i	−0.993562	+	0.521461i
$119$	2.21113	−	4.65985i	0.202694	−	0.427168i
$120$	−9.46533	+	19.9478i	−0.864062	+	1.82097i
$121$	0.121589	−	0.0405924i	0.0110535	−	0.00369022i
$122$	28.6609	+	25.3914i	2.59484	+	2.29883i
$123$	−7.41100	−	1.20440i	−0.668227	−	0.108597i
$124$	0.908514	−	22.5446i	0.0815870	−	2.02456i
$125$	−6.05265	−	15.9595i	−0.541365	−	1.42746i
$126$	−1.83996	+	6.35229i	−0.163917	+	0.565907i
$127$	−1.80898	+	8.86099i	−0.160521	+	0.786286i	0.817196	+	0.576360i	$0.195527\pi$
$127$	−1.80898	+	8.86099i	−0.160521	+	0.786286i	−0.977717	+	0.209926i	$0.932678\pi$
$128$	15.4155	+	1.24447i	1.36255	+	0.109996i
$129$	−4.03395	+	10.6367i	−0.355169	+	0.936505i
$130$	9.96886	−	32.9959i	0.874327	−	2.89394i
$131$	−0.950810	−	2.50708i	−0.0830726	−	0.219045i	0.887043	−	0.461686i	$-0.152755\pi$
$131$	−0.950810	−	2.50708i	−0.0830726	−	0.219045i	−0.970116	+	0.242642i	$0.921986\pi$
$132$	−3.99974	−	13.8087i	−0.348132	−	1.20189i
$133$	−0.551327	−	13.6810i	−0.0478061	−	1.18630i
$134$	7.05814	+	8.64465i	0.609730	+	0.746784i
$135$	−0.458750	+	3.77814i	−0.0394829	+	0.325171i
$136$	11.3283	−	0.914518i	0.971397	−	0.0784193i
$137$	1.16824	−	4.03323i	0.0998095	−	0.344582i	−0.895035	−	0.445996i	$-0.852849\pi$
$137$	1.16824	−	4.03323i	0.0998095	−	0.344582i	0.994844	+	0.101414i	$0.0323367\pi$
$138$	−0.688974	−	0.169817i	−0.0586494	−	0.0144558i
$139$	6.79701	+	5.10763i	0.576515	+	0.433223i	0.848589	−	0.529053i	$-0.177453\pi$
$139$	6.79701	+	5.10763i	0.576515	+	0.433223i	−0.272073	+	0.962277i	$0.587709\pi$
$140$	27.3111	−	33.4500i	2.30821	−	2.82704i
$141$	−5.35889	−	5.57919i	−0.451300	−	0.469853i
$142$	20.7372	+	5.11126i	1.74023	+	0.428928i
$143$	5.03127	+	10.9249i	0.420736	+	0.913583i
$144$	−5.78033	+	1.42472i	−0.481694	+	0.118727i
$145$	−10.0180	−	6.33500i	−0.831950	−	0.526093i
$146$	−17.3652	−	30.0775i	−1.43716	−	2.48923i
$147$	−0.0340799	+	0.0590281i	−0.00281086	+	0.00486855i
$148$	−15.0187	+	7.88243i	−1.23453	+	0.647932i
$149$	−12.3594	+	4.12618i	−1.01252	+	0.338030i	−0.774054	−	0.633120i	$-0.781774\pi$
$149$	−12.3594	+	4.12618i	−1.01252	+	0.338030i	−0.238470	+	0.971150i	$0.576646\pi$
$150$	11.9124	−	20.6329i	0.972643	−	1.68467i
$151$	16.0452	−	14.2148i	1.30574	−	1.15678i	0.328528	−	0.944494i	$-0.393447\pi$
$151$	16.0452	−	14.2148i	1.30574	−	1.15678i	0.977207	−	0.212287i	$-0.0680911\pi$
$152$	25.4997	−	16.1250i	2.06830	−	1.30791i
$153$	1.80228	−	0.767879i	0.145705	−	0.0620793i
$154$	0.888330	+	22.0437i	0.0715837	+	1.77633i
$155$	−2.40179	+	19.7805i	−0.192916	+	1.58881i
$156$	14.3639	−	5.92623i	1.15003	−	0.474478i
$157$	1.27285	+	10.4828i	0.101584	+	0.836622i	0.951063	+	0.308998i	$0.0999938\pi$
$157$	1.27285	+	10.4828i	0.101584	+	0.836622i	−0.849478	+	0.527624i	$0.823083\pi$
$158$	37.5760	−	6.10670i	2.98939	−	0.485823i
$159$	−7.95503	−	5.03046i	−0.630875	−	0.398941i
$160$	12.5894	+	2.04597i	0.995276	+	0.161748i
$161$	0.658568	+	0.345643i	0.0519024	+	0.0272405i
$162$	−2.12302	+	1.34252i	−0.166800	+	0.105478i
$163$	5.59153	−	5.82140i	0.437962	−	0.455967i	−0.465238	−	0.885185i	$-0.654031\pi$
$163$	5.59153	−	5.82140i	0.437962	−	0.455967i	0.903201	+	0.429218i	$0.141211\pi$
$164$	3.90024	+	32.1214i	0.304558	+	2.50826i
$165$	2.53954	+	12.4395i	0.197703	+	0.968411i
$166$	−19.4615	−	1.57109i	−1.51050	−	0.121940i
$167$	9.69082	−	11.8691i	0.749898	−	0.918459i	−0.248847	−	0.968543i	$-0.580052\pi$
$167$	9.69082	−	11.8691i	0.749898	−	0.918459i	0.998745	+	0.0500841i	$0.0159489\pi$
$168$	15.2742			1.17843
$169$	−11.1439	+	6.69428i	−0.857223	+	0.514945i
$170$	−18.7284			−1.43640
$171$	3.28904	−	4.02835i	0.251520	−	0.308056i
$172$	48.8664	+	3.94490i	3.72603	+	0.300796i
$173$	0.0348390	+	0.170653i	0.00264876	+	0.0129745i	0.981094	−	0.193534i	$-0.0619950\pi$
$173$	0.0348390	+	0.170653i	0.00264876	+	0.0129745i	−0.978445	+	0.206509i	$0.933790\pi$
$174$	−0.942952	−	7.76591i	−0.0714850	−	0.588732i
$175$	−17.2987	+	18.0099i	−1.30766	+	1.36142i
$176$	−16.7852	+	10.6143i	−1.26523	+	0.800083i
$177$	4.29671	+	2.25508i	0.322960	+	0.169503i
$178$	−39.5492	−	6.42737i	−2.96434	−	0.481752i
$179$	−12.9125	−	8.16538i	−0.965127	−	0.610309i	−0.0437758	−	0.999041i	$-0.513939\pi$
$179$	−12.9125	−	8.16538i	−0.965127	−	0.610309i	−0.921351	+	0.388732i	$0.872913\pi$
$180$	16.1894	−	2.63103i	1.20669	−	0.196106i
$181$	−1.24768	−	10.2756i	−0.0927394	−	0.763778i	−0.962684	−	0.270628i	$-0.912769\pi$
$181$	−1.24768	−	10.2756i	−0.0927394	−	0.763778i	0.869945	−	0.493149i	$-0.164154\pi$
$182$	−23.5785	+	3.55488i	−1.74775	+	0.263505i
$183$	1.83743	−	15.1326i	0.135827	−	1.11863i
$184$	0.0659904	+	1.63753i	0.00486487	+	0.120721i
$185$	13.7805	−	5.87133i	1.01316	−	0.431668i
$186$	−11.1151	+	7.02877i	−0.814999	+	0.515374i
$187$	4.89163	−	4.33361i	0.357711	−	0.316905i
$188$	−16.6694	+	28.8722i	−1.21574	+	2.10572i
$189$	2.49734	−	0.833736i	0.181655	−	0.0606454i
$190$	−44.0221	+	23.1046i	−3.19370	+	1.67618i
$191$	−7.97956	+	13.8210i	−0.577381	+	1.00005i	0.418398	+	0.908264i	$0.362592\pi$
$191$	−7.97956	+	13.8210i	−0.577381	+	1.00005i	−0.995778	+	0.0917891i	$0.970741\pi$
$192$	−1.74433	−	3.02126i	−0.125886	−	0.218041i
$193$	−10.4139	−	6.58533i	−0.749606	−	0.474022i	0.104237	−	0.994552i	$-0.466760\pi$
$193$	−10.4139	−	6.58533i	−0.749606	−	0.474022i	−0.853843	+	0.520530i	$0.825734\pi$
$194$	−2.77565	+	0.684135i	−0.199280	+	0.0491180i
$195$	−13.0651	+	4.19590i	−0.935612	+	0.300474i
$196$	0.285204	+	0.0702966i	0.0203717	+	0.00502118i
$197$	−2.33089	−	2.42671i	−0.166069	−	0.172896i	0.632968	−	0.774178i	$-0.281836\pi$
$197$	−2.33089	−	2.42671i	−0.166069	−	0.172896i	−0.799037	+	0.601282i	$0.794657\pi$
$198$	−5.29951	+	6.49072i	−0.376620	+	0.461275i
$199$	−2.92966	−	2.20150i	−0.207678	−	0.156060i	0.491814	−	0.870700i	$-0.336334\pi$
$199$	−2.92966	−	2.20150i	−0.207678	−	0.156060i	−0.699492	+	0.714640i	$0.746590\pi$
$200$	−53.4263	−	13.1684i	−3.77781	−	0.931147i
$201$	1.23609	−	4.26749i	0.0871873	−	0.301005i
$202$	17.7368	−	1.43186i	1.24796	−	0.100746i
$203$	−0.988357	+	8.13985i	−0.0693690	+	0.571305i
$204$	−5.33951	−	6.53971i	−0.373840	−	0.457871i
$205$	−1.15062	−	28.5523i	−0.0803628	−	1.99418i
$206$	1.29980	+	4.48741i	0.0905610	+	0.312653i
$207$	0.100174	+	0.264137i	0.00696256	+	0.0183588i
$208$	−13.3839	−	16.7815i	−0.928007	−	1.16358i
$209$	6.15182	−	16.2210i	0.425530	−	1.12203i
$210$	−25.0882	−	2.02533i	−1.73125	−	0.139761i
$211$	2.33024	−	11.4143i	0.160420	−	0.785790i	−0.817355	−	0.576134i	$-0.804560\pi$
$211$	2.33024	−	11.4143i	0.160420	−	0.785790i	0.977775	−	0.209656i	$-0.0672344\pi$
$212$	−11.2851	+	38.9608i	−0.775066	+	2.67584i
$213$	−3.01510	−	7.95017i	−0.206591	−	0.544736i
$214$	0.118981	−	2.95249i	0.00813340	−	0.201828i
$215$	−42.7348	−	6.94508i	−2.91449	−	0.473650i
$216$	4.34241	+	3.84704i	0.295464	+	0.261758i
$217$	13.0749	−	4.36503i	0.887580	−	0.296318i
$218$	−12.4918	+	26.3259i	−0.846052	+	1.78302i
$219$	−5.92729	+	12.4915i	−0.400529	+	0.844098i
$220$	48.4474	−	25.4272i	3.26632	−	1.71430i
$221$	5.23299	+	4.74423i	0.352009	+	0.319131i
$222$	8.75383	+	4.59436i	0.587518	+	0.308353i
$223$	14.0636	−	10.5681i	0.941769	−	0.707694i	−0.0145878	−	0.999894i	$-0.504644\pi$
$223$	14.0636	−	10.5681i	0.941769	−	0.707694i	0.956357	+	0.292200i	$0.0943872\pi$
$224$	−2.45480	−	8.47496i	−0.164018	−	0.566257i
$225$	−9.45405	+	0.763210i	−0.630270	+	0.0508807i
$226$	−23.9268	+	34.6640i	−1.59159	+	2.30582i
$227$	−1.12377	−	5.50457i	−0.0745870	−	0.365351i	0.925317	−	0.379194i	$-0.123799\pi$
$227$	−1.12377	−	5.50457i	−0.0745870	−	0.365351i	−0.999904	+	0.0138428i	$0.995594\pi$
$228$	−20.6186	−	8.78478i	−1.36550	−	0.581786i
$229$	22.0796	−	5.44212i	1.45906	−	0.359625i	0.571607	−	0.820528i	$-0.306320\pi$
$229$	22.0796	−	5.44212i	1.45906	−	0.359625i	0.887451	+	0.460902i	$0.152474\pi$
$230$	0.108744	−	2.69845i	0.00717034	−	0.177930i
$231$	7.02140	−	5.27624i	0.461974	−	0.347151i
$232$	−16.6219	+	7.08194i	−1.09128	+	0.464952i
$233$	7.51047	+	10.8808i	0.492028	+	0.712825i	0.987817	−	0.155618i	$-0.0497367\pi$
$233$	7.51047	+	10.8808i	0.492028	+	0.712825i	−0.495790	+	0.868443i	$0.665121\pi$
$234$	−7.59866	−	4.92797i	−0.496740	−	0.322151i
$235$	16.7251	−	24.2305i	1.09102	−	1.58062i
$236$	4.18301	−	20.4898i	0.272291	−	1.33377i
$237$	−10.4986	−	10.9302i	−0.681958	−	0.709994i
$238$	5.55410	+	11.7050i	0.360019	+	0.758724i
$239$	−15.5755			−1.00750			−0.503749	−	0.863850i	$-0.668046\pi$
$239$	−15.5755			−1.00750			−0.503749	+	0.863850i	$0.668046\pi$
$240$	−9.71318	−	20.4701i	−0.626983	−	1.32134i
$241$	−6.82821	−	5.13106i	−0.439843	−	0.330521i	0.357642	−	0.933859i	$-0.383581\pi$
$241$	−6.82821	−	5.13106i	−0.439843	−	0.330521i	−0.797486	+	0.603338i	$0.793837\pi$
$242$	−0.114179	+	0.301065i	−0.00733969	+	0.0193532i
$243$	0.919979	+	0.391967i	0.0590167	+	0.0251447i
$244$	−64.8434	+	10.5381i	−4.15118	+	0.674632i
$245$	−0.246059	−	0.0821464i	−0.0157201	−	0.00524814i
$246$	14.1168	−	12.5064i	0.900053	−	0.797378i
$247$	18.1532	+	4.69580i	1.15506	+	0.298787i
$248$	22.7348	+	20.1412i	1.44366	+	1.27897i
$249$	3.88647	+	6.73157i	0.246295	+	0.426596i
$250$	40.6682	+	13.5770i	2.57208	+	0.858687i
$251$	5.15081	−	5.36256i	0.325116	−	0.338482i	−0.538506	−	0.842622i	$-0.681011\pi$
$251$	5.15081	−	5.36256i	0.325116	−	0.338482i	0.863622	+	0.504140i	$0.168190\pi$
$252$	−6.44551	−	9.33793i	−0.406029	−	0.588234i
$253$	0.595998	+	0.729965i	0.0374701	+	0.0458925i
$254$	−14.3672	−	17.5966i	−0.901479	−	1.10411i
$255$	4.23543	+	6.13608i	0.265233	+	0.384256i
$256$	−22.0775	+	22.9852i	−1.37985	+	1.43657i
$257$	6.04392	+	2.01776i	0.377009	+	0.125864i	0.498856	−	0.866685i	$-0.333754\pi$
$257$	6.04392	+	2.01776i	0.377009	+	0.125864i	−0.121847	+	0.992549i	$0.538882\pi$
$258$	−14.2875	−	24.7467i	−0.889500	−	1.54066i
$259$	−7.75627	−	6.87146i	−0.481951	−	0.426972i
$260$	33.0337	+	49.0512i	2.04866	+	3.04203i
$261$	−2.33114	+	2.06521i	−0.144294	+	0.127833i
$262$	6.38856	+	2.13282i	0.394687	+	0.131766i
$263$	−19.5435	+	3.17613i	−1.20511	+	0.195849i	−0.729607	−	0.683867i	$-0.760297\pi$
$263$	−19.5435	+	3.17613i	−1.20511	+	0.195849i	−0.475500	+	0.879716i	$0.657733\pi$
$264$	17.8042	+	7.58568i	1.09578	+	0.466866i
$265$	12.7025	−	33.4937i	0.780307	−	2.05750i
$266$	27.4953	+	20.6614i	1.68585	+	1.26683i
$267$	6.83823	+	14.4113i	0.418493	+	0.881956i
$268$	−19.1470			−1.16959
$269$	−6.23792	−	13.1461i	−0.380332	−	0.801534i	−0.999863	−	0.0165610i	$-0.994728\pi$
$269$	−6.23792	−	13.1461i	−0.380332	−	0.801534i	0.619530	−	0.784973i	$-0.287323\pi$
$270$	−6.62243	−	6.89468i	−0.403028	−	0.419597i
$271$	−1.64242	+	8.04512i	−0.0997701	+	0.488706i	0.898946	+	0.438059i	$0.144334\pi$
$271$	−1.64242	+	8.04512i	−0.0997701	+	0.488706i	−0.998717	+	0.0506479i	$0.983871\pi$
$272$	−6.62522	+	9.59829i	−0.401713	+	0.581982i
$273$	6.49699	+	6.92121i	0.393216	+	0.418890i
$274$	5.99164	+	8.68039i	0.361968	+	0.524401i
$275$	−29.1084	+	12.4019i	−1.75531	+	0.747866i
$276$	0.973266	−	0.731362i	0.0585837	−	0.0440228i
$277$	0.489061	−	12.1359i	0.0293848	−	0.729177i	−0.915605	−	0.402078i	$-0.868288\pi$
$277$	0.489061	−	12.1359i	0.0293848	−	0.729177i	0.944990	−	0.327099i	$-0.106071\pi$
$278$	−20.7360	+	5.11096i	−1.24366	+	0.306535i
$279$	4.81656	+	2.05215i	0.288360	+	0.122859i
$280$	11.6279	+	56.9570i	0.694897	+	3.40383i
$281$	−9.97269	+	14.4479i	−0.594921	+	0.861892i	−0.998594	−	0.0530114i	$-0.983118\pi$
$281$	−9.97269	+	14.4479i	−0.594921	+	0.861892i	0.403673	+	0.914903i	$0.367733\pi$
$282$	19.3688	−	1.56361i	1.15340	−	0.0931119i
$283$	−3.82050	−	13.1899i	−0.227105	−	0.784059i	−0.990427	−	0.138040i	$-0.955920\pi$
$283$	−3.82050	−	13.1899i	−0.227105	−	0.784059i	0.763321	−	0.646019i	$-0.223567\pi$
$284$	−29.2940	+	22.0130i	−1.73828	+	1.30623i
$285$	17.5255	+	9.19809i	1.03812	+	0.544848i
$286$	−29.2496	−	7.56615i	−1.72956	−	0.447396i
$287$	−17.5037	+	9.18663i	−1.03321	+	0.542269i
$288$	1.43666	−	3.02770i	0.0846560	−	0.178409i
$289$	−5.64252	+	11.8914i	−0.331913	+	0.699492i
$290$	28.2410	−	9.42825i	1.65837	−	0.553646i
$291$	0.851861	+	0.754683i	0.0499370	+	0.0442403i
$292$	58.8145	+	9.55829i	3.44186	+	0.559357i
$293$	0.746062	−	18.5133i	0.0435854	−	1.08156i	−0.818407	−	0.574640i	$-0.805142\pi$
$293$	0.746062	−	18.5133i	0.0435854	−	1.08156i	0.861992	−	0.506922i	$-0.169217\pi$
$294$	−0.0607118	−	0.160084i	−0.00354078	−	0.00933628i
$295$	−5.13818	+	17.7391i	−0.299156	+	1.03281i
$296$	4.56720	−	22.3716i	0.265463	−	1.30032i
$297$	3.32508	+	0.268428i	0.192940	+	0.0155758i
$298$	11.6062	−	30.6030i	0.672327	−	1.77278i
$299$	−0.713949	+	0.726440i	−0.0412887	+	0.0420111i
$300$	14.4947	+	38.2193i	0.836850	+	2.20659i
$301$	8.33287	+	28.7684i	0.480298	+	1.65818i
$302$	2.16812	+	53.8014i	0.124761	+	3.09592i
$303$	−4.48032	−	5.48739i	−0.257388	−	0.315242i
$304$	−3.73186	+	30.7346i	−0.214037	+	1.76275i
$305$	57.8279	−	4.66835i	3.31122	−	0.267309i
$306$	−1.36908	+	4.72660i	−0.0782650	+	0.270202i
$307$	6.20054	+	1.52829i	0.353883	+	0.0872244i	0.412250	−	0.911071i	$-0.364743\pi$
$307$	6.20054	+	1.52829i	0.353883	+	0.0872244i	−0.0583666	+	0.998295i	$0.518589\pi$
$308$	−30.2593	−	22.7384i	−1.72418	−	1.29564i
$309$	1.17629	−	1.44069i	0.0669166	−	0.0819580i
$310$	−34.6718	−	36.0971i	−1.96922	−	2.05018i
$311$	−5.51074	−	1.35827i	−0.312485	−	0.0770207i	0.0799542	−	0.996799i	$-0.474523\pi$
$311$	−5.51074	−	1.35827i	−0.312485	−	0.0770207i	−0.392439	+	0.919778i	$0.628369\pi$
$312$	−6.04953	+	20.0234i	−0.342487	+	1.13360i
$313$	−8.77461	+	2.16275i	−0.495970	+	0.122246i	−0.479364	−	0.877616i	$-0.659132\pi$
$313$	−8.77461	+	2.16275i	−0.495970	+	0.122246i	−0.0166067	+	0.999862i	$0.505286\pi$
$314$	−22.4188	−	14.1768i	−1.26516	−	0.800042i
$315$	5.01015	+	8.67783i	0.282290	+	0.488941i
$316$	−32.6570	+	56.5636i	−1.83710	+	3.18195i
$317$	28.1797	−	14.7898i	1.58273	−	0.830680i	0.582893	−	0.812549i	$-0.301921\pi$
$317$	28.1797	−	14.7898i	1.58273	−	0.830680i	0.999836	−	0.0181312i	$-0.00577166\pi$
$318$	22.4255	−	7.48673i	1.25756	−	0.419835i
$319$	−5.19460	+	8.99732i	−0.290842	+	0.503753i
$320$	9.93830	−	8.80457i	0.555568	−	0.492190i
$321$	−0.994250	+	0.628726i	−0.0554936	+	0.0350920i
$322$	−1.71875	+	0.732290i	−0.0957820	+	0.0408089i
$323$	−0.410231	−	10.1798i	−0.0228258	−	0.566417i
$324$	0.519462	−	4.27816i	0.0288590	−	0.237675i
$325$	−16.7583	−	29.8104i	−0.929582	−	1.65358i
$326$	2.44394	+	20.1276i	0.135357	+	1.11477i
$327$	11.4503	−	1.86086i	0.633205	−	0.102906i
$328$	−36.8150	−	23.2804i	−2.03277	−	1.28545i
$329$	−20.1038	−	3.26718i	−1.10836	−	0.180126i
$330$	−28.2381	−	14.8205i	−1.55446	−	0.815842i
$331$	−23.1009	+	14.6081i	−1.26974	+	0.802936i	−0.987684	−	0.156462i	$-0.949991\pi$
$331$	−23.1009	+	14.6081i	−1.26974	+	0.802936i	−0.282058	+	0.959397i	$0.591017\pi$
$332$	23.2050	−	24.1589i	1.27354	−	1.32589i
$333$	−0.474406	−	3.90708i	−0.0259973	−	0.214107i
$334$	7.69881	+	37.7113i	0.421260	+	2.06347i
$335$	16.8544	+	1.36063i	0.920853	+	0.0743389i
$336$	−9.91303	+	12.1413i	−0.540800	+	0.662360i
$337$	28.4690			1.55081			0.775404	−	0.631466i	$-0.217546\pi$
$337$	28.4690			1.55081			0.775404	+	0.631466i	$0.217546\pi$
$338$	4.67836	−	32.3177i	0.254469	−	1.75785i
$339$	16.7682			0.910725
$340$	20.3216	−	24.8894i	1.10209	−	1.34982i
$341$	17.4085	+	1.40536i	0.942722	+	0.0761043i
$342$	2.61296	+	12.7991i	0.141293	+	0.692097i
$343$	2.24311	+	18.4736i	0.121116	+	0.997483i
$344$	−45.7172	+	47.5966i	−2.46491	+	2.56624i
$345$	−0.908699	+	0.574627i	−0.0489227	+	0.0309369i
$346$	−0.387389	−	0.203317i	−0.0208261	−	0.0109304i
$347$	−32.8378	−	5.33667i	−1.76283	−	0.286487i	−0.809212	−	0.587517i	$-0.800106\pi$
$347$	−32.8378	−	5.33667i	−1.76283	−	0.286487i	−0.953615	+	0.301030i	$0.902670\pi$
$348$	11.3438	+	7.17340i	0.608093	+	0.384535i
$349$	−26.0464	+	4.23295i	−1.39423	+	0.226585i	−0.810680	−	0.585490i	$-0.800902\pi$
$349$	−26.0464	+	4.23295i	−1.39423	+	0.226585i	−0.583553	+	0.812075i	$0.698338\pi$
$350$	−7.56088	−	62.2695i	−0.404146	−	3.32844i
$351$	0.103864	+	3.60405i	0.00554383	+	0.192370i
$352$	1.34753	−	11.0979i	0.0718238	−	0.591522i
$353$	0.404768	+	10.0442i	0.0215436	+	0.534600i	0.973544	+	0.228502i	$0.0733826\pi$
$353$	0.404768	+	10.0442i	0.0215436	+	0.534600i	−0.952000	+	0.306098i	$0.900976\pi$
$354$	−11.2136	+	4.77769i	−0.595999	+	0.253931i
$355$	27.3507	−	17.2955i	1.45162	−	0.917950i
$356$	51.4554	−	45.5855i	2.72713	−	2.41603i
$357$	2.57892	−	4.46682i	0.136491	−	0.236409i
$358$	36.4008	−	12.1524i	1.92384	−	0.642272i
$359$	−2.76669	+	1.45207i	−0.146020	+	0.0766374i	−0.536151	−	0.844122i	$-0.680122\pi$
$359$	−2.76669	+	1.45207i	−0.146020	+	0.0766374i	0.390131	+	0.920760i	$0.372430\pi$
$360$	−11.0398	+	19.1214i	−0.581846	+	1.00779i
$361$	−4.02270	−	6.96753i	−0.211721	−	0.366712i
$362$	21.9755	+	13.8965i	1.15501	+	0.730382i
$363$	0.124461	−	0.0306769i	0.00653251	−	0.00161012i
$364$	20.8600	−	35.1923i	1.09336	−	1.84458i
$365$	−51.0928	−	12.5933i	−2.67432	−	0.659161i
$366$	26.5248	+	27.6153i	1.38647	+	1.44347i
$367$	−2.59082	+	3.17318i	−0.135240	+	0.165638i	−0.837785	−	0.546001i	$-0.816150\pi$
$367$	−2.59082	+	3.17318i	−0.135240	+	0.165638i	0.702545	+	0.711639i	$0.252047\pi$
$368$	−1.34448	−	1.01031i	−0.0700861	−	0.0526663i
$369$	−7.29005	−	1.79684i	−0.379505	−	0.0935396i
$370$	−10.4682	+	36.1404i	−0.544215	+	1.87885i
$371$	−24.7002	+	1.99401i	−1.28237	+	0.103524i
$372$	2.71965	−	22.3983i	0.141007	−	1.16130i
$373$	−0.313235	−	0.383644i	−0.0162187	−	0.0198643i	0.766432	−	0.642326i	$-0.222030\pi$
$373$	−0.313235	−	0.383644i	−0.0162187	−	0.0198643i	−0.782651	+	0.622461i	$0.786133\pi$
$374$	0.660988	+	16.4023i	0.0341789	+	0.848140i
$375$	−4.74881	−	16.3948i	−0.245228	−	0.846624i
$376$	−15.9145	−	41.9630i	−0.820726	−	2.16408i
$377$	−10.2793	−	4.51956i	−0.529412	−	0.232769i
$378$	−2.34514	+	6.18363i	−0.120621	+	0.318052i
$379$	−14.6831	−	1.18534i	−0.754220	−	0.0608869i	−0.302625	−	0.953110i	$-0.597863\pi$
$379$	−14.6831	−	1.18534i	−0.754220	−	0.0608869i	−0.451595	+	0.892223i	$0.649145\pi$
$380$	17.0618	−	83.5740i	0.875250	−	4.28726i
$381$	−2.51613	+	8.68670i	−0.128905	+	0.445033i
$382$	−14.2152	−	37.4825i	−0.727315	−	1.91777i
$383$	−0.00537607	+	0.133406i	−0.000274705	+	0.00681672i	−0.999321	−	0.0368573i	$-0.988265\pi$
$383$	−0.00537607	+	0.133406i	−0.000274705	+	0.00681672i	0.999046	+	0.0436741i	$0.0139063\pi$
$384$	15.2653	+	2.48086i	0.779006	+	0.126601i
$385$	25.0202	+	22.1660i	1.27515	+	1.12968i
$386$	29.3570	−	9.80081i	1.49423	−	0.498848i
$387$	−4.87676	+	10.2776i	−0.247900	+	0.522438i
$388$	2.10257	−	4.43108i	0.106742	−	0.224954i
$389$	9.46709	−	4.96871i	0.480001	−	0.251924i	−0.207326	−	0.978272i	$-0.566476\pi$
$389$	9.46709	−	4.96871i	0.480001	−	0.251924i	0.687327	+	0.726348i	$0.258784\pi$
$390$	12.5916	−	32.0868i	0.637600	−	1.62478i
$391$	0.490027	+	0.257186i	0.0247817	+	0.0130065i
$392$	−0.316118	+	0.237547i	−0.0159663	+	0.0119979i
$393$	−0.745991	−	2.57546i	−0.0376302	−	0.129915i
$394$	8.42462	−	0.680106i	0.424426	−	0.0342632i
$395$	32.7662	−	47.4700i	1.64865	−	2.38848i
$396$	−2.87563	−	14.0858i	−0.144506	−	0.707836i
$397$	−13.7101	−	5.84133i	−0.688090	−	0.293168i	0.0194807	−	0.999810i	$-0.493799\pi$
$397$	−13.7101	−	5.84133i	−0.688090	−	0.293168i	−0.707571	+	0.706642i	$0.750209\pi$
$398$	8.93766	−	2.20293i	0.448004	−	0.110423i
$399$	0.551327	−	13.6810i	0.0276008	−	0.684908i
$400$	45.1414	−	33.9216i	2.25707	−	1.69608i
$401$	9.36521	−	3.99014i	0.467676	−	0.199258i	−0.145255	−	0.989394i	$-0.546400\pi$
$401$	9.36521	−	3.99014i	0.467676	−	0.199258i	0.612932	+	0.790136i	$0.289990\pi$
$402$	6.33965	+	9.18456i	0.316193	+	0.458084i
$403$	0.543779	+	18.8691i	0.0270876	+	0.939935i
$404$	−17.3428	+	25.1253i	−0.862835	+	1.25003i
$405$	−0.761276	+	3.72898i	−0.0378281	+	0.185294i
$406$	−14.2677	−	14.8543i	−0.708096	−	0.737206i
$407$	−5.62845	−	11.8617i	−0.278992	−	0.587963i
$408$	11.3652			0.562661
$409$	10.3004	+	21.7075i	0.509320	+	1.07337i	0.981429	+	0.191828i	$0.0614417\pi$
$409$	10.3004	+	21.7075i	0.509320	+	1.07337i	−0.472109	+	0.881540i	$0.656507\pi$
$410$	57.3828	+	43.1204i	2.83393	+	2.12956i
$411$	1.48899	−	3.92615i	0.0734466	−	0.193663i
$412$	−7.37400	−	3.14177i	−0.363291	−	0.154784i
$413$	12.6105	−	2.04940i	0.620522	−	0.100845i
$414$	−0.673075	−	0.224706i	−0.0330798	−	0.0110437i
$415$	−22.1432	+	19.6171i	−1.08697	+	0.962968i
$416$	12.0823	+	0.138545i	0.592386	+	0.00679274i
$417$	6.36398	+	5.63800i	0.311645	+	0.276094i
$418$	21.7886	+	37.7389i	1.06571	+	1.84587i
$419$	−3.58189	−	1.19581i	−0.174987	−	0.0584192i	0.227824	−	0.973702i	$-0.426839\pi$
$419$	−3.58189	−	1.19581i	−0.174987	−	0.0584192i	−0.402811	+	0.915283i	$0.631967\pi$
$420$	29.9141	−	31.1439i	1.45966	−	1.51967i
$421$	15.7597	+	22.8319i	0.768082	+	1.11276i	0.990460	+	0.137798i	$0.0440024\pi$
$421$	15.7597	+	22.8319i	0.768082	+	1.11276i	−0.222379	+	0.974960i	$0.571382\pi$
$422$	18.5071	+	22.6671i	0.900911	+	1.10342i
$423$	−4.89257	−	5.99231i	−0.237885	−	0.291356i
$424$	−31.0183	−	44.9378i	−1.50638	−	2.18237i
$425$	−12.8716	+	13.4008i	−0.624364	+	0.650032i
$426$	20.2587	+	6.76334i	0.981537	+	0.327685i
$427$	−20.0672	−	34.7574i	−0.971118	−	1.68203i
$428$	3.79467	+	3.36179i	0.183422	+	0.162498i
$429$	4.13587	+	11.2943i	0.199681	+	0.545294i
$430$	81.4030	−	72.1168i	3.92560	−	3.47778i
$431$	−9.25177	−	3.08869i	−0.445642	−	0.148777i	0.0849857	−	0.996382i	$-0.472916\pi$
$431$	−9.25177	−	3.08869i	−0.445642	−	0.148777i	−0.530628	+	0.847605i	$0.678044\pi$
$432$	−5.87623	+	0.954980i	−0.282720	+	0.0459465i
$433$	10.9666	+	4.67245i	0.527023	+	0.224543i	0.639055	−	0.769161i	$-0.279326\pi$
$433$	10.9666	+	4.67245i	0.527023	+	0.224543i	−0.112032	+	0.993705i	$0.535736\pi$
$434$	−12.2780	+	32.3745i	−0.589364	+	1.55402i
$435$	−9.47576	−	7.12057i	−0.454328	−	0.341405i
$436$	−21.4319	−	45.1667i	−1.02640	−	2.16309i
$437$	1.46912			0.0702774
$438$	−14.8887	−	31.3773i	−0.711409	−	1.49926i
$439$	−13.6598	−	14.2213i	−0.651945	−	0.678746i	0.310391	−	0.950609i	$-0.399540\pi$
$439$	−13.6598	−	14.2213i	−0.651945	−	0.678746i	−0.962336	+	0.271863i	$0.912360\pi$
$440$	−14.7329	+	72.1664i	−0.702362	+	3.44040i
$441$	−0.0387192	+	0.0560944i	−0.00184377	+	0.00267116i
$442$	−17.5442	+	2.64511i	−0.834495	+	0.125815i
$443$	13.8550	+	20.0725i	0.658272	+	0.953671i	0.999904	+	0.0138377i	$0.00440482\pi$
$443$	13.8550	+	20.0725i	0.658272	+	0.953671i	−0.341632	+	0.939834i	$0.610980\pi$
$444$	−15.6043	+	6.64836i	−0.740546	+	0.315517i
$445$	−48.5335	+	36.4706i	−2.30071	+	1.72887i
$446$	−1.77929	+	44.1527i	−0.0842520	+	2.09069i
$447$	−12.6514	+	3.11828i	−0.598389	+	0.147490i
$448$	−8.45007	−	3.60024i	−0.399228	−	0.170095i
$449$	−5.95432	−	29.1662i	−0.281002	−	1.37644i	−0.837885	−	0.545847i	$-0.816208\pi$
$449$	−5.95432	−	29.1662i	−0.281002	−	1.37644i	0.556883	−	0.830591i	$-0.311997\pi$
$450$	13.5340	−	19.6074i	0.638000	−	0.924302i
$451$	−24.9654	+	2.01542i	−1.17558	+	0.0949023i
$452$	−20.1051	−	69.4109i	−0.945665	−	3.26482i
$453$	17.1369	−	12.8776i	0.805163	−	0.605041i
$454$	12.4956	+	6.55820i	0.586448	+	0.307792i
$455$	−20.8630	+	29.4961i	−0.978073	+	1.38280i
$456$	26.7145	−	14.0208i	1.25102	−	0.656586i
$457$	−11.0032	+	23.1888i	−0.514709	+	1.08473i	0.465186	+	0.885213i	$0.345988\pi$
$457$	−11.0032	+	23.1888i	−0.514709	+	1.08473i	−0.979895	+	0.199514i	$0.936064\pi$
$458$	−24.4874	+	51.6062i	−1.14422	+	2.41140i
$459$	1.85822	−	0.620365i	0.0867344	−	0.0289562i
$460$	3.46816	+	3.07252i	0.161704	+	0.143257i
$461$	−22.7135	−	3.69130i	−1.05787	−	0.171921i	−0.393502	−	0.919324i	$-0.628737\pi$
$461$	−22.7135	−	3.69130i	−1.05787	−	0.171921i	−0.664371	+	0.747403i	$0.731301\pi$
$462$	−0.888330	+	22.0437i	−0.0413289	+	1.02557i
$463$	14.9563	+	39.4364i	0.695077	+	1.83277i	0.533271	+	0.845944i	$0.320963\pi$
$463$	14.9563	+	39.4364i	0.695077	+	1.83277i	0.161806	+	0.986823i	$0.448268\pi$
$464$	5.15838	−	17.8088i	0.239472	−	0.826753i
$465$	−3.98567	+	19.5231i	−0.184831	+	0.905362i
$466$	−33.1024	−	2.67230i	−1.53344	−	0.123792i
$467$	5.17516	−	13.6458i	0.239478	−	0.631451i	−0.760359	−	0.649503i	$-0.774977\pi$
$467$	5.17516	−	13.6458i	0.239478	−	0.631451i	0.999837	+	0.0180518i	$0.00574639\pi$
$468$	14.7942	−	4.75120i	0.683862	−	0.219624i
$469$	−4.14797	−	10.9373i	−0.191536	−	0.505038i
$470$	20.5757	+	71.0356i	0.949087	+	3.27663i
$471$	0.425202	+	10.5513i	0.0195923	+	0.486177i
$472$	17.8043	+	21.8063i	0.819509	+	1.00372i
$473$	−4.57422	+	37.6721i	−0.210323	+	1.73216i
$474$	37.9456	−	3.06328i	1.74290	−	0.140701i
$475$	−13.7233	+	47.3785i	−0.629670	+	2.17387i
$476$	−21.5822	−	5.31954i	−0.989219	−	0.243821i
$477$	−7.52445	−	5.65426i	−0.344521	−	0.258891i
$478$	24.7438	−	30.3056i	1.13175	−	1.38615i
$479$	25.5609	+	26.6117i	1.16791	+	1.21592i	0.971920	+	0.235313i	$0.0756115\pi$
$479$	25.5609	+	26.6117i	1.16791	+	1.21592i	0.195987	+	0.980607i	$0.437209\pi$
$480$	12.3839	+	3.05236i	0.565245	+	0.139320i
$481$	12.0800	−	7.44640i	0.550799	−	0.339527i
$482$	20.8311	−	5.13441i	0.948832	−	0.233866i
$483$	0.628620	+	0.397515i	0.0286032	+	0.0180876i
$484$	−0.276214	−	0.478416i	−0.0125552	−	0.0217462i
$485$	−2.16569	+	3.75109i	−0.0983391	+	0.170328i
$486$	−2.22417	+	1.16733i	−0.100890	+	0.0529513i
$487$	33.7471	−	11.2665i	1.52923	−	0.510532i	0.577217	−	0.816591i	$-0.304139\pi$
$487$	33.7471	−	11.2665i	1.52923	−	0.510532i	0.952012	+	0.306059i	$0.0990106\pi$
$488$	44.2176	−	76.5871i	2.00164	−	3.46694i
$489$	6.04183	−	5.35259i	0.273221	−	0.242053i
$490$	0.550730	−	0.348261i	0.0248795	−	0.0157328i
$491$	18.0773	−	7.70202i	0.815818	−	0.347587i	0.0565776	−	0.998398i	$-0.481981\pi$
$491$	18.0773	−	7.70202i	0.815818	−	0.347587i	0.759240	+	0.650811i	$0.225571\pi$
$492$	1.30290	+	32.3311i	0.0587392	+	1.45760i
$493$	−0.735416	+	6.05669i	−0.0331215	+	0.272780i
$494$	−37.9755	+	27.8612i	−1.70860	+	1.25354i
$495$	1.53034	+	12.6035i	0.0687837	+	0.566484i
$496$	−30.7650	+	4.99981i	−1.38139	+	0.224498i
$497$	−18.9206	−	11.9647i	−0.848706	−	0.536689i
$498$	−19.2719	−	3.13199i	−0.863596	−	0.140348i
$499$	30.4579	+	15.9855i	1.36348	+	0.715611i	0.978293	−	0.207226i	$-0.0664436\pi$
$499$	30.4579	+	15.9855i	1.36348	+	0.715611i	0.385190	+	0.922837i	$0.374136\pi$
$500$	−62.1713	+	39.3147i	−2.78038	+	1.75821i
$501$	10.6145	−	11.0508i	0.474219	−	0.493715i
$502$	2.25131	+	18.5412i	0.100481	+	0.827533i
$503$	2.71435	+	13.2957i	0.121027	+	0.592828i	0.994392	+	0.105761i	$0.0337280\pi$
$503$	2.71435	+	13.2957i	0.121027	+	0.592828i	−0.873365	+	0.487067i	$0.838067\pi$
$504$	15.2246	+	1.22906i	0.678159	+	0.0547467i
$505$	17.0516	−	20.8844i	0.758786	−	0.929345i
$506$	−2.36713			−0.105232
$507$	−11.6464	+	5.77586i	−0.517236	+	0.256515i
$508$	38.9748			1.72923
$509$	10.0893	−	12.3571i	0.447200	−	0.547720i	−0.500978	−	0.865460i	$-0.667026\pi$
$509$	10.0893	−	12.3571i	0.447200	−	0.547720i	0.948178	+	0.317740i	$0.102924\pi$
$510$	−18.6676	−	1.50701i	−0.826617	−	0.0667314i
$511$	7.28149	+	35.6671i	0.322114	+	1.57782i
$512$	−5.92126	−	48.7660i	−0.261685	−	2.15517i
$513$	3.60253	−	3.75063i	0.159055	−	0.165594i
$514$	−13.5276	+	8.55430i	−0.596675	+	0.377314i
$515$	6.26778	+	3.28958i	0.276191	+	0.144956i
$516$	48.3905	+	7.86422i	2.13027	+	0.346203i
$517$	−21.8113	−	13.7926i	−0.959258	−	0.606598i
$518$	25.6918	−	4.17532i	1.12883	−	0.183453i
$519$	0.0209942	+	0.172903i	0.000921542	+	0.00758958i
$520$	−79.2720	−	7.31526i	−3.47631	−	0.320796i
$521$	3.63717	−	29.9548i	0.159347	−	1.31234i	−0.665249	−	0.746622i	$-0.731674\pi$
$521$	3.63717	−	29.9548i	0.159347	−	1.31234i	0.824596	−	0.565722i	$-0.191402\pi$
$522$	−0.314998	−	7.81660i	−0.0137871	−	0.342123i
$523$	−24.3389	+	10.3698i	−1.06427	+	0.453441i	−0.851876	−	0.523744i	$-0.824535\pi$
$523$	−24.3389	+	10.3698i	−1.06427	+	0.453441i	−0.212390	+	0.977185i	$0.568125\pi$
$524$	−9.76649	+	6.17595i	−0.426651	+	0.269798i
$525$	−18.6918	+	16.5595i	−0.815777	+	0.722715i
$526$	24.8676	−	43.0720i	1.08428	−	1.87803i
$527$	9.72874	−	3.24793i	0.423790	−	0.141482i
$528$	−17.5848	+	9.22924i	−0.765282	+	0.401651i
$529$	11.4601	−	19.8495i	0.498265	−	0.863021i
$530$	44.9898	+	77.9246i	1.95423	+	3.38483i
$531$	4.10131	+	2.59351i	0.177982	+	0.112549i
$532$	−57.2927	+	14.1214i	−2.48395	+	0.612239i
$533$	−5.11047	−	26.5846i	−0.221359	−	1.15150i
$534$	−38.9038	−	9.58891i	−1.68353	−	0.414953i
$535$	−3.10140	−	3.22890i	−0.134085	−	0.139598i
$536$	16.3013	−	19.9655i	0.704110	−	0.862379i
$537$	−12.2136	−	9.17793i	−0.527056	−	0.396057i
$538$	35.4884	+	8.74712i	1.53002	+	0.377115i
$539$	−0.0632593	+	0.218397i	−0.00272477	+	0.00940701i
$540$	16.3486	−	1.31980i	0.703532	−	0.0567950i
$541$	4.46769	−	36.7947i	0.192081	−	1.58193i	−0.503832	−	0.863802i	$-0.668077\pi$
$541$	4.46769	−	36.7947i	0.192081	−	1.58193i	0.695913	−	0.718126i	$-0.255000\pi$
$542$	−13.0444	−	15.9764i	−0.560303	−	0.686247i
$543$	−0.416795	−	10.3427i	−0.0178864	−	0.443846i
$544$	−1.82657	−	6.30604i	−0.0783135	−	0.270369i
$545$	15.6560	+	41.2814i	0.670628	+	1.76830i
$546$	−23.7881	+	1.64607i	−1.01803	+	0.0704455i
$547$	7.59064	−	20.0149i	0.324552	−	0.855775i	−0.669089	−	0.743182i	$-0.733315\pi$
$547$	7.59064	−	20.0149i	0.324552	−	0.855775i	0.993641	−	0.112592i	$-0.0359153\pi$
$548$	−18.0373	−	1.45612i	−0.770516	−	0.0622025i
$549$	3.04914	−	14.9357i	0.130134	−	0.637439i
$550$	22.1119	−	76.3390i	0.942853	−	3.25511i
$551$	5.74330	+	15.1438i	0.244673	+	0.645149i
$552$	−0.0659904	+	1.63753i	−0.00280874	+	0.0696981i
$553$	−39.3854	−	6.40075i	−1.67484	−	0.272188i
$554$	22.8362	+	20.2311i	0.970216	+	0.859536i
$555$	14.2083	−	4.74342i	0.603107	−	0.201347i
$556$	15.7077	−	33.1032i	0.666154	−	1.40389i
$557$	9.53905	−	20.1031i	0.404182	−	0.851796i	−0.594673	−	0.803968i	$-0.702719\pi$
$557$	9.53905	−	20.1031i	0.404182	−	0.851796i	0.998856	−	0.0478287i	$-0.0152302\pi$
$558$	−11.6446	+	6.11158i	−0.492957	+	0.258724i
$559$	−41.0137	−	0.470294i	−1.73469	−	0.0198913i
$560$	−52.8210	−	27.7226i	−2.23210	−	1.17149i
$561$	5.22448	−	3.92594i	0.220578	−	0.165753i
$562$	−12.2687	−	42.3565i	−0.517525	−	1.78670i
$563$	4.30705	−	0.347701i	0.181520	−	0.0146538i	0.0106279	−	0.999944i	$-0.496617\pi$
$563$	4.30705	−	0.347701i	0.181520	−	0.0146538i	0.170892	+	0.985290i	$0.445335\pi$
$564$	−18.9386	+	27.4372i	−0.797457	+	1.15532i
$565$	12.7653	+	62.5284i	0.537038	+	2.63059i
$566$	31.7333	+	13.5203i	1.33385	+	0.568300i
$567$	2.55633	−	0.630080i	0.107356	−	0.0264609i
$568$	1.98622	−	49.2876i	0.0833401	−	2.06806i
$569$	−4.07358	+	3.06110i	−0.170773	+	0.128328i	−0.682693	−	0.730706i	$-0.739191\pi$
$569$	−4.07358	+	3.06110i	−0.170773	+	0.128328i	0.511919	+	0.859034i	$0.328935\pi$
$570$	−45.7385	+	19.4873i	−1.91577	+	0.816235i
$571$	11.2912	+	16.3581i	0.472522	+	0.684566i	0.984689	−	0.174320i	$-0.0557726\pi$
$571$	11.2912	+	16.3581i	0.472522	+	0.684566i	−0.512167	+	0.858886i	$0.671157\pi$
$572$	41.7930	−	30.6620i	1.74745	−	1.28204i
$573$	−9.06582	+	13.1341i	−0.378730	+	0.548685i
$574$	9.93225	−	48.6514i	0.414564	−	2.03067i
$575$	−1.85609	−	1.93239i	−0.0774042	−	0.0805863i
$576$	−1.49556	−	3.15182i	−0.0623150	−	0.131326i
$577$	−15.6964			−0.653450			−0.326725	−	0.945119i	$-0.605945\pi$
$577$	−15.6964			−0.653450			−0.326725	+	0.945119i	$0.605945\pi$
$578$	−14.1734	−	29.8698i	−0.589535	−	1.24242i
$579$	−9.85020	−	7.40194i	−0.409360	−	0.307614i
$580$	−18.1137	+	47.7618i	−0.752129	+	1.98320i
$581$	18.8273	+	8.02156i	0.781088	+	0.332790i
$582$	−2.82169	+	0.458570i	−0.116963	+	0.0190083i
$583$	−29.7820	−	9.94269i	−1.23344	−	0.411784i
$584$	−60.0401	+	53.1909i	−2.48448	+	2.20106i
$585$	−13.3604	+	3.13099i	−0.552383	+	0.129450i
$586$	34.8366	+	30.8625i	1.43909	+	1.27492i
$587$	−0.864194	−	1.49683i	−0.0356691	−	0.0617807i	0.847640	−	0.530572i	$-0.178023\pi$
$587$	−0.864194	−	1.49683i	−0.0356691	−	0.0617807i	−0.883309	+	0.468791i	$0.844690\pi$
$588$	0.278623	+	0.0930180i	0.0114902	+	0.00383600i
$589$	18.8611	−	19.6364i	0.777157	−	0.809106i
$590$	−26.3526	−	38.1783i	−1.08492	−	1.57178i
$591$	−2.12806	−	2.60640i	−0.0875366	−	0.107213i
$592$	14.8188	+	18.1497i	0.609049	+	0.745949i
$593$	−21.0640	−	30.5164i	−0.864993	−	1.25316i	−0.966070	−	0.258280i	$-0.916844\pi$
$593$	−21.0640	−	30.5164i	−0.864993	−	1.25316i	0.101077	−	0.994879i	$-0.467771\pi$
$594$	−5.80461	+	6.04324i	−0.238166	+	0.247957i
$595$	18.6199	+	6.21625i	0.763343	+	0.254841i
$596$	28.0769	+	48.6306i	1.15007	+	1.99199i
$597$	−2.74302	−	2.43010i	−0.112264	−	0.0994574i
$598$	−0.279248	−	2.54319i	−0.0114193	−	0.103999i
$599$	5.45745	−	4.83488i	0.222985	−	0.197548i	−0.544232	−	0.838934i	$-0.683179\pi$
$599$	5.45745	−	4.83488i	0.222985	−	0.197548i	0.767218	+	0.641387i	$0.221641\pi$
$600$	−52.1934	−	17.4247i	−2.13079	−	0.711362i
$601$	−19.0523	+	3.09630i	−0.777161	+	0.126301i	−0.536038	−	0.844194i	$-0.680080\pi$
$601$	−19.0523	+	3.09630i	−0.777161	+	0.126301i	−0.241122	+	0.970495i	$0.577516\pi$
$602$	−69.2131	−	29.4889i	−2.82092	−	1.20188i
$603$	1.57548	−	4.15419i	0.0641583	−	0.169172i
$604$	−73.8530	−	55.4969i	−3.00504	−	2.25814i
$605$	0.209143	+	0.440759i	0.00850286	+	0.0179194i
$606$	17.7945			0.722853
$607$	−0.903065	−	1.90317i	−0.0366543	−	0.0772473i	0.884297	−	0.466924i	$-0.154638\pi$
$607$	−0.903065	−	1.90317i	−0.0366543	−	0.0772473i	−0.920952	+	0.389677i	$0.872587\pi$
$608$	−12.0730	−	12.5693i	−0.489625	−	0.509753i
$609$	−1.64014	+	8.03392i	−0.0664617	+	0.325551i
$610$	−82.7840	+	119.933i	−3.35182	+	4.85596i
$611$	12.2454	−	25.0606i	0.495396	−	1.01384i
$612$	−4.79597	−	6.94816i	−0.193865	−	0.280863i
$613$	33.1839	−	14.1383i	1.34028	−	0.571042i	0.401598	−	0.915816i	$-0.368455\pi$
$613$	33.1839	−	14.1383i	1.34028	−	0.571042i	0.938686	+	0.344774i	$0.112045\pi$
$614$	−12.8240	+	9.63661i	−0.517535	+	0.388902i
$615$	1.15062	−	28.5523i	0.0463975	−	1.15134i
$616$	49.4724	−	12.1938i	1.99330	−	0.491304i
$617$	28.9275	+	12.3249i	1.16458	+	0.496180i	0.885751	−	0.464161i	$-0.153644\pi$
$617$	28.9275	+	12.3249i	1.16458	+	0.496180i	0.278827	+	0.960341i	$0.410054\pi$
$618$	0.934494	+	4.57745i	0.0375908	+	0.184132i
$619$	14.1035	−	20.4325i	0.566868	−	0.821251i	−0.429790	−	0.902929i	$-0.641413\pi$
$619$	14.1035	−	20.4325i	0.566868	−	0.821251i	0.996659	+	0.0816780i	$0.0260279\pi$
$620$	85.5933	−	6.90981i	3.43751	−	0.277504i
$621$	0.0785948	+	0.271341i	0.00315390	+	0.0108885i
$622$	11.3974	−	8.56456i	0.456992	−	0.343407i
$623$	37.1868	+	19.5172i	1.48986	+	0.781939i
$624$	−11.9902	−	17.8040i	−0.479990	−	0.712730i
$625$	15.5288	−	8.15012i	0.621150	−	0.326005i
$626$	9.73152	−	20.5088i	0.388950	−	0.819695i
$627$	7.43712	−	15.6734i	0.297010	−	0.625935i
$628$	43.1664	−	14.4111i	1.72253	−	0.575064i
$629$	−5.77128	−	5.11291i	−0.230116	−	0.203865i
$630$	−24.8439	−	4.03753i	−0.989806	−	0.160859i
$631$	−0.868598	+	21.5540i	−0.0345783	+	0.858053i	0.885105	+	0.465392i	$0.154086\pi$
$631$	−0.868598	+	21.5540i	−0.0345783	+	0.858053i	−0.919683	+	0.392661i	$0.871555\pi$
$632$	−31.1781	−	82.2099i	−1.24020	−	3.27013i
$633$	3.24115	−	11.1897i	0.128824	−	0.444752i
$634$	−15.9902	+	78.3254i	−0.635054	+	3.11070i
$635$	−34.3080	−	2.76963i	−1.36147	−	0.109909i
$636$	−14.3836	+	37.9264i	−0.570346	+	1.50388i
$637$	−0.242103	−	0.0422004i	−0.00959247	−	0.00167204i
$638$	−9.25395	−	24.4007i	−0.366368	−	0.966032i
$639$	−2.36560	−	8.16700i	−0.0935817	−	0.323082i
$640$	2.37007	+	58.8127i	0.0936853	+	2.32478i
$641$	1.30457	+	1.59781i	0.0515274	+	0.0631097i	0.799726	−	0.600366i	$-0.204978\pi$
$641$	1.30457	+	1.59781i	0.0515274	+	0.0631097i	−0.748198	+	0.663475i	$0.769081\pi$
$642$	0.356173	−	2.93335i	0.0140570	−	0.115770i
$643$	14.7001	−	1.18672i	0.579716	−	0.0467995i	0.212869	−	0.977081i	$-0.431719\pi$
$643$	14.7001	−	1.18672i	0.579716	−	0.0467995i	0.366847	+	0.930281i	$0.380437\pi$
$644$	0.891770	−	3.07875i	0.0351407	−	0.121320i
$645$	−42.0374	−	10.3613i	−1.65522	−	0.407975i
$646$	20.4587	+	15.3737i	0.804936	+	0.604870i
$647$	−17.5422	+	21.4852i	−0.689653	+	0.844672i	−0.994169	−	0.107835i	$-0.965608\pi$
$647$	−17.5422	+	21.4852i	−0.689653	+	0.844672i	0.304515	+	0.952507i	$0.401506\pi$
$648$	4.01877	+	4.18399i	0.157872	+	0.164363i
$649$	15.7172	+	3.87393i	0.616952	+	0.152065i
$650$	84.6255	+	14.7508i	3.31928	+	0.578576i
$651$	13.3837	−	3.29879i	0.524549	−	0.129290i
$652$	−29.4008	−	18.5920i	−1.15143	−	0.728117i
$653$	13.9051	+	24.0844i	0.544151	+	0.942496i	0.998660	+	0.0517544i	$0.0164813\pi$
$653$	13.9051	+	24.0844i	0.544151	+	0.942496i	−0.454509	+	0.890742i	$0.650185\pi$
$654$	−14.5697	+	25.2354i	−0.569719	+	0.986781i
$655$	9.03592	−	4.74242i	0.353063	−	0.185302i
$656$	42.3985	−	14.1547i	1.65538	−	0.552648i
$657$	−6.91322	+	11.9740i	−0.269710	+	0.467152i
$658$	38.2945	−	33.9260i	1.49288	−	1.32257i
$659$	−33.7905	+	21.3678i	−1.31629	+	0.832373i	−0.993471	−	0.114087i	$-0.963606\pi$
$659$	−33.7905	+	21.3678i	−1.31629	+	0.832373i	−0.322821	+	0.946460i	$0.604631\pi$
$660$	50.3363	−	21.4463i	1.95934	−	0.834797i
$661$	1.45091	+	36.0039i	0.0564338	+	1.40039i	0.741032	+	0.671470i	$0.234337\pi$
$661$	1.45091	+	36.0039i	0.0564338	+	1.40039i	−0.684598	+	0.728921i	$0.740022\pi$
$662$	8.27550	−	68.1549i	0.321637	−	2.64892i
$663$	4.83427	+	5.14993i	0.187748	+	0.200007i
$664$	5.43548	+	44.7652i	0.210938	+	1.73723i
$665$	51.4359	−	8.35915i	1.99460	−	0.324154i
$666$	8.35575	+	5.28385i	0.323779	+	0.204745i
$667$	−0.868398	−	0.141128i	−0.0336245	−	0.00546451i
$668$	−58.4709	−	30.6879i	−2.26231	−	1.18735i
$669$	14.8684	−	9.40220i	0.574845	−	0.363510i
$670$	−29.4228	+	30.6324i	−1.13670	+	1.18343i
$671$	−6.12947	−	50.4808i	−0.236626	−	1.94879i
$672$	−1.76489	−	8.64501i	−0.0680822	−	0.333489i
$673$	−15.3221	−	1.23693i	−0.590623	−	0.0476800i	−0.218458	−	0.975846i	$-0.570103\pi$
$673$	−15.3221	−	1.23693i	−0.590623	−	0.0476800i	−0.372165	+	0.928166i	$0.621385\pi$
$674$	−45.2268	+	55.3928i	−1.74207	+	2.13365i
$675$	−9.48481			−0.365071
$676$	37.8729	+	41.2843i	1.45665	+	1.58786i
$677$	−22.4688			−0.863547			−0.431773	−	0.901982i	$-0.642112\pi$
$677$	−22.4688			−0.863547			−0.431773	+	0.901982i	$0.642112\pi$
$678$	−26.6386	+	32.6263i	−1.02305	+	1.25301i
$679$	2.98665	+	0.241107i	0.114617	+	0.00925285i
$680$	8.65205	+	42.3805i	0.331791	+	1.62522i
$681$	−0.677188	−	5.57715i	−0.0259499	−	0.213717i
$682$	−30.3901	+	31.6394i	−1.16370	+	1.21154i
$683$	−35.2548	+	22.2938i	−1.34899	+	0.853049i	−0.996567	−	0.0827920i	$-0.973616\pi$
$683$	−35.2548	+	22.2938i	−1.34899	+	0.853049i	−0.352422	+	0.935841i	$0.614642\pi$
$684$	−19.8449	−	10.4154i	−0.758788	−	0.398243i
$685$	15.7741	+	2.56353i	0.602696	+	0.0979476i
$686$	−39.5080	−	24.9834i	−1.50842	−	0.953869i
$687$	22.4459	−	3.64781i	0.856363	−	0.139173i
$688$	−8.16327	−	67.2306i	−0.311222	−	2.56314i
$689$	7.16885	−	33.1701i	0.273111	−	1.26368i
$690$	0.325526	−	2.68095i	0.0123926	−	0.102062i
$691$	−0.504143	−	12.5102i	−0.0191785	−	0.475909i	−0.980031	−	0.198847i	$-0.936280\pi$
$691$	−0.504143	−	12.5102i	−0.0191785	−	0.475909i	0.960852	−	0.277062i	$-0.0893608\pi$
$692$	0.690546	−	0.294214i	0.0262506	−	0.0111843i
$693$	7.42319	−	4.69414i	0.281984	−	0.178316i
$694$	62.5509	−	55.4152i	2.37440	−	2.10353i
$695$	−16.1792	+	28.0232i	−0.613712	+	1.06298i
$696$	−17.1379	+	5.72147i	−0.649610	+	0.216872i
$697$	−13.0241	+	6.83558i	−0.493323	+	0.258916i
$698$	33.1420	−	57.4037i	1.25444	−	2.17276i
$699$	6.61058	+	11.4499i	0.250035	+	0.433074i
$700$	90.9583	+	57.5185i	3.43790	+	2.17400i
$701$	−4.56090	+	1.12416i	−0.172263	+	0.0424590i	−0.324504	−	0.945884i	$-0.605197\pi$
$701$	−4.56090	+	1.12416i	−0.172263	+	0.0424590i	0.152241	+	0.988343i	$0.451351\pi$
$702$	−7.17749	−	5.52343i	−0.270897	−	0.208468i
$703$	−19.8733	−	4.89834i	−0.749537	−	0.184744i
$704$	−8.06177	−	8.39319i	−0.303839	−	0.316330i
$705$	18.6206	−	22.8061i	0.701292	−	0.858927i
$706$	−20.1863	−	15.1690i	−0.759720	−	0.570893i
$707$	−18.1094	−	4.46356i	−0.681073	−	0.167869i
$708$	5.81819	−	20.0867i	0.218661	−	0.754905i
$709$	10.3507	−	0.835598i	0.388730	−	0.0313816i	0.115443	−	0.993314i	$-0.463171\pi$
$709$	10.3507	−	0.835598i	0.388730	−	0.0313816i	0.273287	+	0.961933i	$0.411889\pi$
$710$	−9.79790	+	80.6929i	−0.367709	+	3.02835i
$711$	−9.58506	−	11.7396i	−0.359468	−	0.440268i
$712$	3.72623	+	92.4653i	0.139646	+	3.46528i
$713$	0.411484	+	1.42061i	0.0154102	+	0.0532021i
$714$	4.59423	+	12.1140i	0.171935	+	0.453355i
$715$	−38.9676	+	24.0206i	−1.45731	+	0.898320i
$716$	−23.3473	+	61.5617i	−0.872528	+	2.30067i
$717$	−15.5250	−	1.25331i	−0.579793	−	0.0468057i
$718$	1.56993	−	7.69001i	0.0585891	−	0.286989i
$719$	11.0754	−	38.2367i	0.413042	−	1.42599i	−0.437090	−	0.899418i	$-0.643991\pi$
$719$	11.0754	−	38.2367i	0.413042	−	1.42599i	0.850132	−	0.526569i	$-0.176522\pi$
$720$	−8.03453	−	21.1853i	−0.299429	−	0.789530i
$721$	0.197175	−	4.89285i	0.00734319	−	0.182219i
$722$	19.9475	+	3.24178i	0.742368	+	0.120646i
$723$	−6.39318	−	5.66387i	−0.237765	−	0.210641i
$724$	−42.3129	+	14.1261i	−1.57255	+	0.524994i
$725$	12.6632	−	26.6872i	0.470301	−	0.991138i
$726$	−0.138034	+	0.290901i	−0.00512293	+	0.0107963i
$727$	5.38528	−	2.82641i	0.199729	−	0.104826i	−0.361894	−	0.932219i	$-0.617870\pi$
$727$	5.38528	−	2.82641i	0.199729	−	0.104826i	0.561623	+	0.827394i	$0.310177\pi$
$728$	18.9370	+	51.7135i	0.701853	+	1.91663i
$729$	0.885456	+	0.464723i	0.0327947	+	0.0172120i
$730$	105.671	−	79.4064i	3.91105	−	2.93896i
$731$	6.20031	+	21.4060i	0.229327	+	0.791728i
$732$	−65.4811	+	5.28618i	−2.42025	+	0.195383i
$733$	−29.3078	+	42.4597i	−1.08251	+	1.56829i	−0.291411	+	0.956598i	$0.594125\pi$
$733$	−29.3078	+	42.4597i	−1.08251	+	1.56829i	−0.791099	+	0.611688i	$0.790491\pi$
$734$	−2.05826	−	10.0820i	−0.0759717	−	0.372134i
$735$	−0.238651	−	0.101680i	−0.00880276	−	0.00375051i
$736$	0.919201	−	0.226563i	0.0338822	−	0.00835121i
$737$	0.596784	−	14.8090i	0.0219828	−	0.545498i
$738$	15.0774	−	11.3299i	0.555005	−	0.417059i
$739$	28.0703	−	11.9596i	1.03258	−	0.439942i	0.191867	−	0.981421i	$-0.438546\pi$
$739$	28.0703	−	11.9596i	1.03258	−	0.439942i	0.840714	+	0.541479i	$0.182135\pi$
$740$	−36.6708	−	53.1268i	−1.34804	−	1.95298i
$741$	17.7165	+	6.14130i	0.650832	+	0.225606i
$742$	35.3598	−	51.2275i	1.29810	−	1.88062i
$743$	−1.48314	+	7.26488i	−0.0544110	+	0.266523i	−0.997891	−	0.0649057i	$-0.979325\pi$
$743$	−1.48314	+	7.26488i	−0.0544110	+	0.266523i	0.943480	+	0.331428i	$0.107530\pi$
$744$	21.0403	+	21.9053i	0.771376	+	0.803088i
$745$	−21.2592	−	44.8028i	−0.778876	−	1.64145i
$746$	1.24408			0.0455490
$747$	3.33220	+	7.02247i	0.121919	+	0.256939i
$748$	−22.5153	−	16.9192i	−0.823241	−	0.618626i
$749$	−1.09827	+	2.89591i	−0.0401300	+	0.105814i
$750$	39.4438	+	16.8054i	1.44028	+	0.613648i
$751$	5.67059	−	0.921561i	0.206923	−	0.0336282i	−0.0560662	−	0.998427i	$-0.517856\pi$
$751$	5.67059	−	0.921561i	0.206923	−	0.0336282i	0.262989	+	0.964799i	$0.415292\pi$
$752$	43.6845	+	14.5840i	1.59301	+	0.531825i
$753$	5.56562	−	4.93071i	0.202822	−	0.179685i
$754$	25.1239	−	12.8208i	0.914957	−	0.466905i
$755$	61.0661	+	54.0998i	2.22242	+	1.96890i
$756$	−5.67321	−	9.82630i	−0.206333	−	0.357379i
$757$	4.68676	+	1.56467i	0.170343	+	0.0568689i	0.400560	−	0.916270i	$-0.368815\pi$
$757$	4.68676	+	1.56467i	0.170343	+	0.0568689i	−0.230217	+	0.973139i	$0.573944\pi$
$758$	25.6324	−	26.6861i	0.931010	−	0.969284i
$759$	0.535327	+	0.775556i	0.0194312	+	0.0281509i
$760$	72.6205	+	88.9440i	2.63422	+	3.22634i
$761$	−15.3215	−	18.7654i	−0.555404	−	0.680246i	0.418236	−	0.908339i	$-0.362649\pi$
$761$	−15.3215	−	18.7654i	−0.555404	−	0.680246i	−0.973639	+	0.228092i	$0.926751\pi$
$762$	−12.9047	−	18.6957i	−0.467487	−	0.677272i
$763$	21.1575	−	22.0273i	0.765952	−	0.797440i
$764$	65.2376	+	21.7795i	2.36021	+	0.787955i
$765$	3.72795	+	6.45700i	0.134784	+	0.233453i
$766$	−0.251030	−	0.222393i	−0.00907008	−	0.00803539i
$767$	−2.30793	+	17.3432i	−0.0833343	+	0.626226i
$768$	−23.8555	+	21.1341i	−0.860811	+	0.762612i
$769$	−18.9834	−	6.33761i	−0.684561	−	0.228540i	−0.0469483	−	0.998897i	$-0.514950\pi$
$769$	−18.9834	−	6.33761i	−0.684561	−	0.228540i	−0.637612	+	0.770357i	$0.720078\pi$
$770$	−82.8767	+	13.4688i	−2.98667	+	0.485381i
$771$	5.86196	+	2.49755i	0.211113	+	0.0899470i
$772$	−18.8294	+	49.6491i	−0.677686	+	1.78691i
$773$	11.2677	+	8.46715i	0.405272	+	0.304542i	0.783760	−	0.621064i	$-0.213299\pi$
$773$	11.2677	+	8.46715i	0.405272	+	0.304542i	−0.378488	+	0.925606i	$0.623556\pi$
$774$	−12.2499	−	25.8161i	−0.440313	−	0.927940i
$775$	−49.6578			−1.78376
$776$	2.83041	+	5.96497i	0.101606	+	0.214130i
$777$	−7.17820	−	7.47330i	−0.257516	−	0.268103i
$778$	−5.37200	+	26.3138i	−0.192595	+	0.943395i
$779$	−22.1810	+	32.1348i	−0.794719	+	1.15135i
$780$	28.9796	+	51.5503i	1.03764	+	1.84580i
$781$	−16.1127	−	23.3432i	−0.576556	−	0.835286i
$782$	−1.27888	+	0.544882i	−0.0457328	+	0.0194849i
$783$	−2.48976	+	1.87093i	−0.0889768	+	0.0668617i
$784$	0.0163390	−	0.405448i	0.000583535	−	0.0144803i
$785$	−39.0218	+	9.61800i	−1.39275	+	0.343281i
$786$	6.19623	+	2.63997i	0.221012	+	0.0941645i
$787$	5.37421	+	26.3246i	0.191570	+	0.938372i	0.955933	+	0.293585i	$0.0948485\pi$
$787$	5.37421	+	26.3246i	0.191570	+	0.938372i	−0.764363	+	0.644786i	$0.776946\pi$
$788$	−8.23746	+	11.9340i	−0.293447	+	0.425132i
$789$	−19.7357	+	1.59323i	−0.702611	+	0.0567206i
$790$	40.3100	+	139.166i	1.43416	+	4.95131i
$791$	35.2938	−	26.5216i	1.25490	−	0.943000i
$792$	17.1361	+	8.99373i	0.608905	+	0.319578i
$793$	53.5123	−	12.5405i	1.90028	−	0.445328i
$794$	33.1459	−	17.3963i	1.17630	−	0.617372i
$795$	15.3564	−	32.3630i	0.544636	−	1.14780i
$796$	−6.77035	+	14.2682i	−0.239969	+	0.505723i
$797$	12.1165	−	4.04507i	0.429187	−	0.143284i	−0.0938641	−	0.995585i	$-0.529922\pi$
$797$	12.1165	−	4.04507i	0.429187	−	0.143284i	0.523051	+	0.852301i	$0.324794\pi$
$798$	25.7436	+	22.8068i	0.911314	+	0.807353i
$799$	−14.9588	−	2.43104i	−0.529204	−	0.0860041i
$800$	−1.27990	+	31.7603i	−0.0452511	+	1.12290i
$801$	5.65643	+	14.9148i	0.199860	+	0.526988i
$802$	−7.11416	+	24.5609i	−0.251210	+	0.867277i
$803$	−9.22589	+	45.1914i	−0.325575	+	1.59477i
$804$	−19.0850	−	1.54070i	−0.673075	−	0.0543362i
$805$	−1.00377	+	2.64673i	−0.0353783	+	0.0932849i
$806$	−37.5778	−	28.9180i	−1.32362	−	1.01859i
$807$	−5.15986	−	13.6054i	−0.181636	−	0.478934i
$808$	−11.4341	−	39.4752i	−0.402252	−	1.38873i
$809$	−1.40958	−	34.9783i	−0.0495581	−	1.22977i	−0.812366	−	0.583147i	$-0.801821\pi$
$809$	−1.40958	−	34.9783i	−0.0495581	−	1.22977i	0.762808	−	0.646625i	$-0.223820\pi$
$810$	−6.04616	−	7.40520i	−0.212440	−	0.260192i
$811$	1.70640	−	14.0535i	0.0599198	−	0.493484i	−0.931596	−	0.363496i	$-0.881583\pi$
$811$	1.70640	−	14.0535i	0.0599198	−	0.493484i	0.991516	−	0.129988i	$-0.0414938\pi$
$812$	35.2224	−	2.84345i	1.23606	−	0.0997854i
$813$	−2.28446	+	7.88688i	−0.0801196	+	0.276605i
$814$	32.0211	+	7.89249i	1.12234	+	0.276632i
$815$	24.5592	+	18.4550i	0.860271	+	0.646452i
$816$	−7.37608	+	9.03406i	−0.258214	+	0.316255i
$817$	40.9820	+	42.6668i	1.43378	+	1.49272i
$818$	−58.6003	−	14.4437i	−2.04891	−	0.505011i
$819$	5.91899	+	7.42155i	0.206826	+	0.259330i
$820$	−119.570	+	29.4713i	−4.17556	+	1.02918i
$821$	7.17824	+	4.53924i	0.250522	+	0.158421i	0.653825	−	0.756646i	$-0.273163\pi$
$821$	7.17824	+	4.53924i	0.250522	+	0.158421i	−0.403302	+	0.915067i	$0.632138\pi$
$822$	5.27373	+	9.13437i	0.183942	+	0.318598i
$823$	−6.92332	+	11.9915i	−0.241332	+	0.417999i	−0.961094	−	0.276222i	$-0.910918\pi$
$823$	−6.92332	+	11.9915i	−0.241332	+	0.417999i	0.719762	+	0.694221i	$0.244251\pi$
$824$	9.55412	−	5.01439i	0.332833	−	0.174684i
$825$	−30.0120	+	10.0195i	−1.04488	+	0.348833i
$826$	−16.0459	+	27.7922i	−0.558307	+	0.967016i
$827$	−26.0165	+	23.0486i	−0.904683	+	0.801479i	−0.980678	−	0.195629i	$-0.937325\pi$
$827$	−26.0165	+	23.0486i	−0.904683	+	0.801479i	0.0759950	+	0.997108i	$0.475787\pi$
$828$	1.02896	−	0.650675i	0.0357589	−	0.0226125i
$829$	−21.6257	+	9.21387i	−0.751093	+	0.320011i	−0.733368	−	0.679832i	$-0.762053\pi$
$829$	−21.6257	+	9.21387i	−0.751093	+	0.320011i	−0.0177252	+	0.999843i	$0.505642\pi$
$830$	−2.99213	−	74.2489i	−0.103858	−	2.57722i
$831$	1.46401	−	12.0572i	0.0507860	−	0.418260i
$832$	8.06642	−	9.65153i	0.279653	−	0.334606i
$833$	0.0160950	+	0.132554i	0.000557658	+	0.00459273i
$834$	−21.0800	+	3.42583i	−0.729940	+	0.118627i
$835$	49.2888	+	31.1684i	1.70571	+	1.07863i
$836$	−73.7961	−	11.9930i	−2.55229	−	0.414788i
$837$	4.63581	+	2.43306i	0.160237	+	0.0840990i
$838$	8.01703	−	5.06966i	0.276944	−	0.175129i
$839$	−1.33755	+	1.39253i	−0.0461773	+	0.0480756i	−0.743890	−	0.668302i	$-0.767022\pi$
$839$	−1.33755	+	1.39253i	−0.0461773	+	0.0480756i	0.697713	+	0.716377i	$0.254201\pi$
$840$	7.00702	+	57.7080i	0.241765	+	1.99111i
$841$	3.86064	+	18.9106i	0.133125	+	0.652091i
$842$	−69.4609	−	5.60746i	−2.39378	−	0.193246i
$843$	−11.1029	+	13.5986i	−0.382405	+	0.468361i
$844$	−50.2053			−1.72814
$845$	−30.4042	−	39.0323i	−1.04594	−	1.34275i
$846$	19.4319			0.668081
$847$	0.213446	−	0.261424i	0.00733408	−	0.00898262i
$848$	55.8517	+	4.50881i	1.91795	+	0.154833i
$849$	−2.74677	−	13.4546i	−0.0942688	−	0.461759i
$850$	−5.62589	−	46.3334i	−0.192967	−	1.58922i
$851$	0.770195	−	0.801858i	0.0264019	−	0.0274873i
$852$	−30.9704	+	19.5845i	−1.06103	+	0.670953i
$853$	−7.06805	−	3.70960i	−0.242006	−	0.127014i	0.339361	−	0.940656i	$-0.389789\pi$
$853$	−7.06805	−	3.70960i	−0.242006	−	0.127014i	−0.581366	+	0.813642i	$0.697482\pi$
$854$	99.5074	+	16.1715i	3.40507	+	0.553378i
$855$	16.7285	+	10.5785i	0.572103	+	0.361776i
$856$	−6.73618	+	1.09474i	−0.230238	+	0.0374173i
$857$	−5.16979	−	42.5771i	−0.176597	−	1.45441i	−0.764055	−	0.645151i	$-0.776795\pi$
$857$	−5.16979	−	42.5771i	−0.176597	−	1.45441i	0.587458	−	0.809254i	$-0.300129\pi$
$858$	−28.5459	−	9.89523i	−0.974541	−	0.337818i
$859$	0.710874	−	5.85457i	0.0242547	−	0.199755i	−0.975544	−	0.219803i	$-0.929459\pi$
$859$	0.710874	−	5.85457i	0.0242547	−	0.199755i	0.999799	+	0.0200473i	$0.00638169\pi$
$860$	7.51303	+	186.434i	0.256192	+	6.35734i
$861$	−18.1861	+	7.74838i	−0.619781	+	0.264064i
$862$	20.7074	−	13.0946i	0.705296	−	0.446002i
$863$	32.2314	−	28.5545i	1.09717	−	0.972008i	0.0974402	−	0.995241i	$-0.468935\pi$
$863$	32.2314	−	28.5545i	1.09717	−	0.972008i	0.999730	+	0.0232334i	$0.00739607\pi$
$864$	1.67563	−	2.90228i	0.0570061	−	0.0987374i
$865$	−0.628767	+	0.209913i	−0.0213787	+	0.00713727i
$866$	−26.5132	+	13.9152i	−0.900956	+	0.472858i
$867$	−6.58108	+	11.3988i	−0.223505	+	0.387122i
$868$	−29.7022	−	51.4457i	−1.00816	−	1.74618i
$869$	−42.7305	−	27.0211i	−1.44953	−	0.916630i
$870$	28.9081	−	7.12521i	0.980077	−	0.241567i
$871$	15.9809	−	1.10584i	0.541492	−	0.0374699i
$872$	65.3440	+	16.1058i	2.21283	+	0.545413i
$873$	0.788372	+	0.820782i	0.0266823	+	0.0277793i
$874$	−2.33388	+	2.85849i	−0.0789448	+	0.0966899i
$875$	−35.9263	−	26.9968i	−1.21453	−	0.912660i
$876$	57.8547	+	14.2599i	1.95473	+	0.481797i
$877$	−4.27765	+	14.7682i	−0.144446	+	0.498685i	−0.999813	−	0.0193371i	$-0.993844\pi$
$877$	−4.27765	+	14.7682i	−0.144446	+	0.498685i	0.855367	+	0.518022i	$0.173332\pi$
$878$	49.3710	−	3.98564i	1.66619	−	0.134509i
$879$	2.23335	−	18.3933i	0.0753290	−	0.620390i
$880$	−47.8025	−	58.5475i	−1.61142	−	1.97363i
$881$	−0.340668	−	8.45358i	−0.0114774	−	0.284808i	−0.994728	−	0.102549i	$-0.967300\pi$
$881$	−0.340668	−	8.45358i	−0.0114774	−	0.284808i	0.983251	−	0.182259i	$-0.0583410\pi$
$882$	−0.0476335	−	0.164450i	−0.00160390	−	0.00553732i
$883$	13.3655	+	35.2419i	0.449784	+	1.18598i	0.947814	+	0.318824i	$0.103288\pi$
$883$	13.3655	+	35.2419i	0.449784	+	1.18598i	−0.498030	+	0.867160i	$0.665943\pi$
$884$	15.5215	−	26.1859i	0.522043	−	0.880727i
$885$	−6.54892	+	17.2681i	−0.220140	+	0.580460i
$886$	−61.0659	−	4.92975i	−2.05155	−	0.165618i
$887$	2.18444	−	10.7001i	0.0733464	−	0.359274i	−0.926509	−	0.376272i	$-0.877206\pi$
$887$	2.18444	−	10.7001i	0.0733464	−	0.359274i	0.999856	+	0.0169979i	$0.00541085\pi$
$888$	6.35255	−	21.9316i	0.213178	−	0.735975i
$889$	8.44342	+	22.2635i	0.283183	+	0.746692i
$890$	6.14034	−	152.371i	0.205825	−	5.10749i
$891$	3.29269	+	0.535115i	0.110309	+	0.0179270i
$892$	−56.7470	−	50.2734i	−1.90003	−	1.68328i
$893$	−38.1606	+	12.7399i	−1.27699	+	0.426323i
$894$	14.0311	−	29.5698i	0.469269	−	0.988963i
$895$	24.9264	−	52.5312i	0.833196	−	1.75592i
$896$	36.0544	−	18.9228i	1.20449	−	0.632167i
$897$	−0.770088	+	0.666636i	−0.0257125	+	0.0222583i
$898$	66.2085	+	34.7489i	2.20941	+	1.15959i
$899$	−13.0352	+	9.79529i	−0.434747	+	0.326691i
$900$	11.3723	+	39.2617i	0.379076	+	1.30872i
$901$	−18.3789	+	1.48370i	−0.612291	+	0.0494293i
$902$	35.7394	−	51.7775i	1.18999	−	1.72400i
$903$	5.99095	+	29.3456i	0.199366	+	0.976561i
$904$	89.4950	+	38.1302i	2.97656	+	1.26819i
$905$	38.2502	−	9.42783i	1.27148	−	0.313392i
$906$	−2.16812	+	53.8014i	−0.0720310	+	1.78743i
$907$	27.1376	−	20.3926i	0.901089	−	0.677125i	−0.0457080	−	0.998955i	$-0.514554\pi$
$907$	27.1376	−	20.3926i	0.901089	−	0.677125i	0.946797	+	0.321830i	$0.104298\pi$
$908$	−22.2743	+	9.49018i	−0.739197	+	0.314943i
$909$	−4.02424	−	5.83011i	−0.133476	−	0.193373i
$910$	−24.2475	−	87.4520i	−0.803795	−	2.89900i
$911$	12.4602	−	18.0517i	0.412824	−	0.598078i	−0.560320	−	0.828276i	$-0.689322\pi$
$911$	12.4602	−	18.0517i	0.412824	−	0.598078i	0.973144	+	0.230198i	$0.0739373\pi$
$912$	−6.19287	+	30.3347i	−0.205066	+	1.00448i
$913$	17.9621	+	18.7006i	0.594460	+	0.618899i
$914$	−27.6389	−	58.2477i	−0.914213	−	1.92666i
$915$	58.0161			1.91795
$916$	−42.0124	−	88.5394i	−1.38813	−	2.92542i
$917$	−5.64366	−	4.24093i	−0.186370	−	0.140048i
$918$	−1.74497	+	4.60111i	−0.0575926	+	0.151859i
$919$	−23.6756	−	10.0872i	−0.780986	−	0.332747i	−0.0355880	−	0.999367i	$-0.511330\pi$
$919$	−23.6756	−	10.0872i	−0.780986	−	0.332747i	−0.745398	+	0.666619i	$0.767741\pi$
$920$	−6.15656	+	1.00054i	−0.202976	+	0.0329868i
$921$	6.05745	+	2.02228i	0.199600	+	0.0666362i
$922$	43.2656	−	38.3300i	1.42488	−	1.26233i
$923$	23.1786	−	20.0649i	0.762934	−	0.660443i
$924$	−28.3315	−	25.0995i	−0.932038	−	0.825713i
$925$	18.6651	+	32.3288i	0.613703	+	1.06297i
$926$	−100.492	−	33.5493i	−3.30238	−	1.10250i
$927$	1.28840	−	1.34137i	0.0423166	−	0.0440563i
$928$	5.92893	+	8.58953i	0.194627	+	0.281965i
$929$	−5.00043	−	6.12442i	−0.164059	−	0.200936i	0.686032	−	0.727571i	$-0.259351\pi$
$929$	−5.00043	−	6.12442i	−0.164059	−	0.200936i	−0.850091	+	0.526635i	$0.823453\pi$
$930$	−31.6547	−	38.7700i	−1.03800	−	1.27132i
$931$	0.201360	+	0.291720i	0.00659930	+	0.00956074i
$932$	39.4698	−	41.0924i	1.29288	−	1.34603i
$933$	−5.38357	−	1.79730i	−0.176250	−	0.0588410i
$934$	18.3294	+	31.7475i	0.599757	+	1.03881i
$935$	18.6170	+	16.4932i	0.608842	+	0.539387i
$936$	−7.64113	+	19.4716i	−0.249758	+	0.636451i
$937$	−34.4035	+	30.4788i	−1.12391	+	0.995700i	−0.123919	+	0.992292i	$0.539546\pi$
$937$	−34.4035	+	30.4788i	−1.12391	+	0.995700i	−0.999994	+	0.00340744i	$0.998915\pi$
$938$	27.8705	+	9.30455i	0.910005	+	0.303804i
$939$	−8.92019	+	1.44967i	−0.291099	+	0.0473082i
$940$	−116.730	−	49.7341i	−3.80732	−	1.62215i
$941$	6.50897	−	17.1627i	0.212186	−	0.559489i	−0.786094	−	0.618107i	$-0.787900\pi$
$941$	6.50897	−	17.1627i	0.212186	−	0.559489i	0.998281	+	0.0586173i	$0.0186692\pi$
$942$	−21.2053	−	15.9348i	−0.690907	−	0.519183i
$943$	−0.909270	−	1.91625i	−0.0296099	−	0.0624015i
$944$	−28.8887			−0.940247
$945$	4.29563	+	9.05284i	0.139737	+	0.294489i
$946$	−66.0326	−	68.7473i	−2.14691	−	2.23517i
$947$	−7.67522	+	37.5957i	−0.249411	+	1.22170i	0.641358	+	0.767241i	$0.278371\pi$
$947$	−7.67522	+	37.5957i	−0.249411	+	1.22170i	−0.890770	+	0.454455i	$0.849834\pi$
$948$	−37.1026	+	53.7524i	−1.20504	+	1.74580i
$949$	−49.6410	−	4.58090i	−1.61142	−	0.148702i
$950$	−70.3839	−	101.969i	−2.28356	−	3.30830i
$951$	29.2784	−	12.4744i	0.949417	−	0.404509i
$952$	23.9215	−	17.9758i	0.775300	−	0.582600i
$953$	−0.619201	+	15.3653i	−0.0200579	+	0.497731i	0.957672	+	0.287863i	$0.0929447\pi$
$953$	−0.619201	+	15.3653i	−0.0200579	+	0.497731i	−0.977730	+	0.209869i	$0.932696\pi$
$954$	22.9552	−	5.65795i	0.743202	−	0.183183i
$955$	−55.8784	−	23.8075i	−1.80818	−	0.770394i
$956$	13.4265	+	65.7674i	0.434245	+	2.12707i
$957$	−5.90174	+	8.55015i	−0.190776	+	0.276387i
$958$	−92.3858	+	7.45815i	−2.98485	+	0.240962i
$959$	−3.07579	−	10.6188i	−0.0993224	−	0.342901i
$960$	10.6145	−	7.97631i	0.342583	−	0.257434i
$961$	−3.17829	−	1.66809i	−0.102525	−	0.0538095i
$962$	−4.70202	+	35.3338i	−0.151599	+	1.13921i
$963$	−1.04162	+	0.546683i	−0.0335656	+	0.0176166i
$964$	−15.7797	+	33.2551i	−0.508231	+	1.07108i
$965$	20.1030	−	42.3661i	0.647137	−	1.36381i
$966$	−1.77210	+	0.591613i	−0.0570163	+	0.0190349i
$967$	−34.7689	−	30.8026i	−1.11809	−	0.990544i	−0.118096	−	0.993002i	$-0.537679\pi$
$967$	−34.7689	−	30.8026i	−1.11809	−	0.990544i	−0.999997	+	0.00245832i	$0.999217\pi$
$968$	0.734028	+	0.119291i	0.0235926	+	0.00383416i
$969$	0.410231	−	10.1798i	0.0131785	−	0.327021i
$970$	−3.85809	−	10.1729i	−0.123876	−	0.326633i
$971$	−8.41948	+	29.0674i	−0.270194	+	0.932818i	0.704580	+	0.709624i	$0.251135\pi$
$971$	−8.41948	+	29.0674i	−0.270194	+	0.932818i	−0.974774	+	0.223193i	$0.928352\pi$
$972$	0.862027	−	4.22249i	0.0276495	−	0.135436i
$973$	22.3123	+	1.80124i	0.715300	+	0.0577450i
$974$	−31.6904	+	83.5608i	−1.01543	+	2.67746i
$975$	−14.3052	−	31.0622i	−0.458133	−	0.994788i
$976$	32.1807	+	84.8536i	1.03008	+	2.71610i
$977$	3.54454	+	12.2372i	0.113400	+	0.391502i	0.997060	−	0.0766275i	$-0.0244152\pi$
$977$	3.54454	+	12.2372i	0.113400	+	0.391502i	−0.883660	+	0.468130i	$0.844928\pi$
$978$	0.816410	+	20.2590i	0.0261059	+	0.647812i
$979$	33.6537	+	41.2183i	1.07558	+	1.31734i
$980$	−0.134753	+	1.10979i	−0.00430453	+	0.0354510i
$981$	11.5629	−	0.933457i	0.369176	−	0.0298030i
$982$	−13.7322	+	47.4091i	−0.438212	+	1.51288i
$983$	33.9877	+	8.37722i	1.08404	+	0.267192i	0.740575	−	0.671974i	$-0.234553\pi$
$983$	33.9877	+	8.37722i	1.08404	+	0.267192i	0.343465	+	0.939166i	$0.388399\pi$
$984$	−34.8223	−	26.1673i	−1.11010	−	0.834183i
$985$	8.09916	−	9.91967i	0.258061	−	0.316067i
$986$	−10.6163	−	11.0528i	−0.338093	−	0.351992i
$987$	−19.7757	−	4.87427i	−0.629467	−	0.155150i
$988$	4.17938	−	80.6997i	0.132964	−	2.56740i
$989$	−3.12024	+	0.769071i	−0.0992179	+	0.0244550i
$990$	−26.9540	−	17.0447i	−0.856654	−	0.541715i
$991$	0.981739	+	1.70042i	0.0311860	+	0.0540157i	0.881197	−	0.472749i	$-0.156738\pi$
$991$	0.981739	+	1.70042i	0.0311860	+	0.0540157i	−0.850011	+	0.526765i	$0.823405\pi$
$992$	8.77278	−	15.1949i	0.278536	−	0.482438i
$993$	−24.2015	+	12.7019i	−0.768011	+	0.403083i
$994$	53.3379	−	17.8068i	1.69177	−	0.564797i
$995$	6.97359	−	12.0786i	0.221078	−	0.382918i
$996$	25.0737	−	22.2134i	0.794491	−	0.703857i
$997$	18.7838	−	11.8781i	0.594889	−	0.376185i	−0.202831	−	0.979214i	$-0.565014\pi$
$997$	18.7838	−	11.8781i	0.594889	−	0.376185i	0.797719	+	0.603029i	$0.206040\pi$
$998$	−79.4898	+	33.8674i	−2.51621	+	1.07206i
$999$	−0.158478	−	3.93259i	−0.00501402	−	0.124422i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.q.a.55.2	✓	360
169.126	even	39	inner	507.2.q.a.295.2	yes	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.q.a.55.2	✓	360	1.1	even	1	trivial
507.2.q.a.295.2	yes	360	169.126	even	39	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.58863 + 1.94572i) q^{2} +(0.996757 + 0.0804666i) q^{3} +(-0.862027 - 4.22249i) q^{4} +(0.458750 + 3.77814i) q^{5} +(-1.74005 + 1.81158i) q^{6} +(2.22525 - 1.40716i) q^{7} +(5.13689 + 2.69605i) q^{8} +(0.987050 + 0.160411i) q^{9} +O(q^{10})\)	\(q+(-1.58863 + 1.94572i) q^{2} +(0.996757 + 0.0804666i) q^{3} +(-0.862027 - 4.22249i) q^{4} +(0.458750 + 3.77814i) q^{5} +(-1.74005 + 1.81158i) q^{6} +(2.22525 - 1.40716i) q^{7} +(5.13689 + 2.69605i) q^{8} +(0.987050 + 0.160411i) q^{9} +(-8.07999 - 5.10948i) q^{10} +(3.29269 - 0.535115i) q^{11} +(-0.519462 - 4.27816i) q^{12} +(0.963352 + 3.47447i) q^{13} +(-0.797157 + 6.56518i) q^{14} +(0.153248 + 3.80280i) q^{15} +(-5.47693 + 2.33350i) q^{16} +(1.65576 - 1.04704i) q^{17} +(-1.88017 + 1.66569i) q^{18} +(2.60026 - 4.50378i) q^{19} +(15.5577 - 5.19392i) q^{20} +(2.33126 - 1.22354i) q^{21} +(-4.18970 + 7.25676i) q^{22} +(0.141247 + 0.244647i) q^{23} +(4.90329 + 3.10065i) q^{24} +(-9.20920 + 2.26986i) q^{25} +(-8.29076 - 3.64524i) q^{26} +(0.970942 + 0.239316i) q^{27} +(-7.85995 - 8.18307i) q^{28} +(-1.96967 + 2.41241i) q^{29} +(-7.64265 - 5.74308i) q^{30} +(5.08338 + 1.25294i) q^{31} +(0.932379 - 3.21895i) q^{32} +(3.32508 - 0.268428i) q^{33} +(-0.593148 + 4.88501i) q^{34} +(6.33729 + 7.76177i) q^{35} +(-0.173529 - 4.30608i) q^{36} +(-1.09500 - 3.78039i) q^{37} +(4.63225 + 12.2142i) q^{38} +(0.680650 + 3.54072i) q^{39} +(-7.82951 + 20.6447i) q^{40} +(-7.48388 - 0.604161i) q^{41} +(-1.32285 + 6.47974i) q^{42} +(-3.16497 + 10.9268i) q^{43} +(-5.09791 - 13.4421i) q^{44} +(-0.153248 + 3.80280i) q^{45} +(-0.700404 - 0.113827i) q^{46} +(-5.79045 - 5.12989i) q^{47} +(-5.64694 + 1.88523i) q^{48} +(-0.0292196 + 0.0615790i) q^{49} +(10.2135 - 21.5245i) q^{50} +(1.73464 - 0.910412i) q^{51} +(13.8405 - 7.06283i) q^{52} +(-8.33402 - 4.37403i) q^{53} +(-2.00811 + 1.50900i) q^{54} +(3.53226 + 12.1948i) q^{55} +(15.2246 - 1.22906i) q^{56} +(2.95423 - 4.27994i) q^{57} +(-1.56479 - 7.66485i) q^{58} +(4.46423 + 1.90203i) q^{59} +(15.9252 - 3.92521i) q^{60} +(0.613804 - 15.2314i) q^{61} +(-10.5135 + 7.90037i) q^{62} +(2.42216 - 1.03198i) q^{63} +(-1.98178 - 2.87110i) q^{64} +(-12.6851 + 5.23359i) q^{65} +(-4.76004 + 6.89610i) q^{66} +(0.888695 - 4.35312i) q^{67} +(-5.84842 - 6.08885i) q^{68} +(0.121103 + 0.255219i) q^{69} -25.1699 q^{70} +(-3.64505 - 7.68177i) q^{71} +(4.63789 + 3.48515i) q^{72} +(-4.90292 + 12.9279i) q^{73} +(9.09513 + 3.87507i) q^{74} +(-9.36198 + 1.52147i) q^{75} +(-21.2587 - 7.09718i) q^{76} +(6.57407 - 5.82412i) q^{77} +(-7.97056 - 4.30055i) q^{78} +(-11.3441 - 10.0500i) q^{79} +(-11.3288 - 19.6221i) q^{80} +(0.948536 + 0.316668i) q^{81} +(13.0647 - 13.6018i) q^{82} +(4.41554 + 6.39701i) q^{83} +(-7.17600 - 8.78900i) q^{84} +(4.71545 + 5.77537i) q^{85} +(-16.2324 - 23.5167i) q^{86} +(-2.15740 + 2.24609i) q^{87} +(18.3569 + 6.12843i) q^{88} +(7.97569 + 13.8143i) q^{89} +(-7.15574 - 6.33943i) q^{90} +(7.03284 + 6.37597i) q^{91} +(0.911260 - 0.807306i) q^{92} +(4.96607 + 1.65792i) q^{93} +(19.1802 - 3.11709i) q^{94} +(18.2088 + 7.75804i) q^{95} +(1.18837 - 3.13348i) q^{96} +(0.909825 + 0.683689i) q^{97} +(-0.0733963 - 0.154679i) q^{98} +3.33589 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q + q^{2} - 15 q^{3} + 15 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} + 15 q^{9}+O(q^{10}) \) 360 * q + q^2 - 15 * q^3 + 15 * q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 + 15 * q^9	\( 360 q + q^{2} - 15 q^{3} + 15 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} + 15 q^{9} - q^{10} - 2 q^{11} + 30 q^{12} - 19 q^{13} + q^{15} + 15 q^{16} - 7 q^{17} - 2 q^{18} - 6 q^{19} + q^{20} + 4 q^{21} + 22 q^{22} + 46 q^{23} + 3 q^{24} + 28 q^{25} + 34 q^{26} + 30 q^{27} - 2 q^{28} + 36 q^{29} + q^{30} - 34 q^{31} - 190 q^{32} + 15 q^{33} - 51 q^{34} - 80 q^{35} + 15 q^{36} + q^{37} - 53 q^{38} + 5 q^{39} - 45 q^{40} + 9 q^{41} + 130 q^{42} + 78 q^{43} + 35 q^{44} - q^{45} - 318 q^{46} - 12 q^{47} - 15 q^{48} - 71 q^{49} + 48 q^{50} - 14 q^{51} - 63 q^{52} - 26 q^{53} - q^{54} - 61 q^{55} - 4 q^{56} - 38 q^{57} - 27 q^{58} + 208 q^{59} - 180 q^{60} - 3 q^{61} - 61 q^{62} + 2 q^{63} + 140 q^{64} + 45 q^{65} - 60 q^{66} - 80 q^{67} - 140 q^{68} + 6 q^{69} - 100 q^{70} + 84 q^{71} - 3 q^{72} + 134 q^{73} - 151 q^{74} - 12 q^{75} + 32 q^{76} + 82 q^{77} - 63 q^{78} + 4 q^{79} - 155 q^{80} + 15 q^{81} - 56 q^{82} + 106 q^{83} + 2 q^{84} - 19 q^{85} + q^{86} - 49 q^{87} + 8 q^{88} - 14 q^{89} + 2 q^{90} - 368 q^{91} + 36 q^{92} - 4 q^{93} - 59 q^{94} + 104 q^{95} + 75 q^{96} - 28 q^{97} + 101 q^{98} + 30 q^{99}+O(q^{100}) \) 360 * q + q^2 - 15 * q^3 + 15 * q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 + 15 * q^9 - q^10 - 2 * q^11 + 30 * q^12 - 19 * q^13 + q^15 + 15 * q^16 - 7 * q^17 - 2 * q^18 - 6 * q^19 + q^20 + 4 * q^21 + 22 * q^22 + 46 * q^23 + 3 * q^24 + 28 * q^25 + 34 * q^26 + 30 * q^27 - 2 * q^28 + 36 * q^29 + q^30 - 34 * q^31 - 190 * q^32 + 15 * q^33 - 51 * q^34 - 80 * q^35 + 15 * q^36 + q^37 - 53 * q^38 + 5 * q^39 - 45 * q^40 + 9 * q^41 + 130 * q^42 + 78 * q^43 + 35 * q^44 - q^45 - 318 * q^46 - 12 * q^47 - 15 * q^48 - 71 * q^49 + 48 * q^50 - 14 * q^51 - 63 * q^52 - 26 * q^53 - q^54 - 61 * q^55 - 4 * q^56 - 38 * q^57 - 27 * q^58 + 208 * q^59 - 180 * q^60 - 3 * q^61 - 61 * q^62 + 2 * q^63 + 140 * q^64 + 45 * q^65 - 60 * q^66 - 80 * q^67 - 140 * q^68 + 6 * q^69 - 100 * q^70 + 84 * q^71 - 3 * q^72 + 134 * q^73 - 151 * q^74 - 12 * q^75 + 32 * q^76 + 82 * q^77 - 63 * q^78 + 4 * q^79 - 155 * q^80 + 15 * q^81 - 56 * q^82 + 106 * q^83 + 2 * q^84 - 19 * q^85 + q^86 - 49 * q^87 + 8 * q^88 - 14 * q^89 + 2 * q^90 - 368 * q^91 + 36 * q^92 - 4 * q^93 - 59 * q^94 + 104 * q^95 + 75 * q^96 - 28 * q^97 + 101 * q^98 + 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more