LMFDB - Embedded newform 309.2.i.b.100.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [309,2,Mod(13,309)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(309, base_ring=CyclotomicField(34))

chi = DirichletCharacter(H, H._module([0, 24]))

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

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

chi := DirichletCharacter("309.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 309 = 3 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	309.i (of order $17$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.46737742246$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$10$ over $\Q(\zeta_{17})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{17}]$

Embedding invariants

Embedding label			100.6
Character	$\chi$	$=$	309.100
Dual form			309.2.i.b.34.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.264688 - 0.163888i) q^{2} +(-0.273663 - 0.961826i) q^{3} +(-0.848276 + 1.70357i) q^{4} +(-0.994818 + 0.385395i) q^{5} +(-0.230067 - 0.209734i) q^{6} +(0.417912 - 4.50998i) q^{7} +(0.112115 + 1.20992i) q^{8} +(-0.850217 + 0.526432i) q^{9} +O(q^{10})$	\(q+(0.264688 - 0.163888i) q^{2} +(-0.273663 - 0.961826i) q^{3} +(-0.848276 + 1.70357i) q^{4} +(-0.994818 + 0.385395i) q^{5} +(-0.230067 - 0.209734i) q^{6} +(0.417912 - 4.50998i) q^{7} +(0.112115 + 1.20992i) q^{8} +(-0.850217 + 0.526432i) q^{9} +(-0.200155 + 0.265049i) q^{10} +(4.48867 - 2.77927i) q^{11} +(1.87068 + 0.349690i) q^{12} +(0.414573 - 4.47396i) q^{13} +(-0.628517 - 1.26223i) q^{14} +(0.642928 + 0.851374i) q^{15} +(-2.06576 - 2.73551i) q^{16} +(5.95033 - 5.42444i) q^{17} +(-0.138767 + 0.278681i) q^{18} +(-2.15302 + 7.56708i) q^{19} +(0.187335 - 2.02166i) q^{20} +(-4.45218 + 0.832258i) q^{21} +(0.732610 - 1.47128i) q^{22} +(-1.19611 - 0.740598i) q^{23} +(1.13305 - 0.438945i) q^{24} +(-2.85391 + 2.60168i) q^{25} +(-0.623496 - 1.25215i) q^{26} +(0.739009 + 0.673696i) q^{27} +(7.32856 + 4.53765i) q^{28} +(0.0361267 - 0.0139956i) q^{29} +(0.309706 + 0.119981i) q^{30} +(0.548639 + 0.726516i) q^{31} +(-3.26120 - 1.26339i) q^{32} +(-3.90155 - 3.55673i) q^{33} +(0.685982 - 2.41097i) q^{34} +(1.32238 + 4.64768i) q^{35} +(-0.175594 - 1.89496i) q^{36} +(-4.98172 - 0.931244i) q^{37} +(0.670275 + 2.35577i) q^{38} +(-4.41662 + 0.825609i) q^{39} +(-0.577831 - 1.16044i) q^{40} +(2.48297 + 0.961906i) q^{41} +(-1.04204 + 0.949949i) q^{42} +(-1.49100 + 0.278716i) q^{43} +(0.927038 + 10.0043i) q^{44} +(0.642928 - 0.851374i) q^{45} -0.437971 q^{46} +1.62149 q^{47} +(-2.06576 + 2.73551i) q^{48} +(-13.2845 - 2.48330i) q^{49} +(-0.329012 + 1.15636i) q^{50} +(-6.84575 - 4.23871i) q^{51} +(7.27002 + 4.50140i) q^{52} +(2.55199 - 8.96932i) q^{53} +(0.306018 + 0.0572047i) q^{54} +(-3.39430 + 4.49478i) q^{55} +5.50357 q^{56} +7.86742 q^{57} +(0.00726862 - 0.00962521i) q^{58} +(1.00469 + 10.8423i) q^{59} +(-1.99575 + 0.373071i) q^{60} +(2.19237 - 1.99861i) q^{61} +(0.264286 + 0.102385i) q^{62} +(2.01888 + 4.05447i) q^{63} +(5.66877 - 1.05968i) q^{64} +(1.31181 + 4.61055i) q^{65} +(-1.61560 - 0.302008i) q^{66} +(-0.103862 - 1.12085i) q^{67} +(4.19338 + 14.7382i) q^{68} +(-0.384996 + 1.35312i) q^{69} +(1.11172 + 1.01346i) q^{70} +(11.3957 + 4.41470i) q^{71} +(-0.732262 - 0.969672i) q^{72} +(8.31133 + 3.21983i) q^{73} +(-1.47122 + 0.569955i) q^{74} +(3.28337 + 2.03298i) q^{75} +(-11.0647 - 10.0868i) q^{76} +(-10.6586 - 21.4053i) q^{77} +(-1.03372 + 0.942361i) q^{78} +(1.98193 - 0.767802i) q^{79} +(3.10930 + 1.92520i) q^{80} +(0.445738 - 0.895163i) q^{81} +(0.814858 - 0.152323i) q^{82} +(-0.571315 + 6.16548i) q^{83} +(2.35887 - 8.29058i) q^{84} +(-3.82895 + 7.68956i) q^{85} +(-0.348971 + 0.318130i) q^{86} +(-0.0233479 - 0.0309176i) q^{87} +(3.86593 + 5.11933i) q^{88} +(0.471373 + 0.946645i) q^{89} +(0.0306454 - 0.330717i) q^{90} +(-20.0042 - 3.73944i) q^{91} +(2.27629 - 1.40942i) q^{92} +(0.548639 - 0.726516i) q^{93} +(0.429189 - 0.265742i) q^{94} +(-0.774449 - 8.35764i) q^{95} +(-0.322696 + 3.48245i) q^{96} +(6.62042 + 6.03531i) q^{97} +(-3.92324 + 1.51987i) q^{98} +(-2.35325 + 4.72596i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - q^{2} - 10 q^{3} - 17 q^{4} - 4 q^{5} - q^{6} - 12 q^{7} + 36 q^{8} - 10 q^{9}+O(q^{10}) $ 160 * q - q^2 - 10 * q^3 - 17 * q^4 - 4 * q^5 - q^6 - 12 * q^7 + 36 * q^8 - 10 * q^9	\( 160 q - q^{2} - 10 q^{3} - 17 q^{4} - 4 q^{5} - q^{6} - 12 q^{7} + 36 q^{8} - 10 q^{9} + 12 q^{10} + q^{11} + 17 q^{12} - 18 q^{13} + 31 q^{14} - 4 q^{15} - 39 q^{16} - 14 q^{17} - q^{18} - 11 q^{19} + 31 q^{20} + 5 q^{21} + 3 q^{23} - 15 q^{24} - 8 q^{25} - 33 q^{26} - 10 q^{27} - 2 q^{28} - 28 q^{29} + 12 q^{30} - 20 q^{31} - 46 q^{32} + 18 q^{33} + 5 q^{34} - 3 q^{35} - 17 q^{36} - 34 q^{37} - 14 q^{38} - 18 q^{39} - 56 q^{40} + 40 q^{41} + 14 q^{42} - 42 q^{43} - 26 q^{44} - 4 q^{45} + 112 q^{46} - 40 q^{47} - 39 q^{48} + 30 q^{49} - 10 q^{50} + 3 q^{51} - 58 q^{52} - 48 q^{53} - q^{54} - 64 q^{55} + 86 q^{56} + 6 q^{57} - 36 q^{58} + 76 q^{59} - 20 q^{60} - 28 q^{61} - 66 q^{62} - 12 q^{63} + 88 q^{64} - 14 q^{65} - 34 q^{66} - 84 q^{67} - 107 q^{68} - 14 q^{69} + 8 q^{70} + 41 q^{71} - 15 q^{72} - 32 q^{73} + 3 q^{74} - 42 q^{75} - 68 q^{76} + 93 q^{77} + 18 q^{78} - 100 q^{79} - 168 q^{80} - 10 q^{81} + 99 q^{82} - 28 q^{83} + 151 q^{84} + 15 q^{85} + 64 q^{86} - 11 q^{87} - 25 q^{88} - 19 q^{89} - 5 q^{90} + 122 q^{91} - 78 q^{92} - 20 q^{93} + 138 q^{94} - 15 q^{95} + 56 q^{96} + 161 q^{97} + 65 q^{98} + q^{99}+O(q^{100}) \) 160 * q - q^2 - 10 * q^3 - 17 * q^4 - 4 * q^5 - q^6 - 12 * q^7 + 36 * q^8 - 10 * q^9 + 12 * q^10 + q^11 + 17 * q^12 - 18 * q^13 + 31 * q^14 - 4 * q^15 - 39 * q^16 - 14 * q^17 - q^18 - 11 * q^19 + 31 * q^20 + 5 * q^21 + 3 * q^23 - 15 * q^24 - 8 * q^25 - 33 * q^26 - 10 * q^27 - 2 * q^28 - 28 * q^29 + 12 * q^30 - 20 * q^31 - 46 * q^32 + 18 * q^33 + 5 * q^34 - 3 * q^35 - 17 * q^36 - 34 * q^37 - 14 * q^38 - 18 * q^39 - 56 * q^40 + 40 * q^41 + 14 * q^42 - 42 * q^43 - 26 * q^44 - 4 * q^45 + 112 * q^46 - 40 * q^47 - 39 * q^48 + 30 * q^49 - 10 * q^50 + 3 * q^51 - 58 * q^52 - 48 * q^53 - q^54 - 64 * q^55 + 86 * q^56 + 6 * q^57 - 36 * q^58 + 76 * q^59 - 20 * q^60 - 28 * q^61 - 66 * q^62 - 12 * q^63 + 88 * q^64 - 14 * q^65 - 34 * q^66 - 84 * q^67 - 107 * q^68 - 14 * q^69 + 8 * q^70 + 41 * q^71 - 15 * q^72 - 32 * q^73 + 3 * q^74 - 42 * q^75 - 68 * q^76 + 93 * q^77 + 18 * q^78 - 100 * q^79 - 168 * q^80 - 10 * q^81 + 99 * q^82 - 28 * q^83 + 151 * q^84 + 15 * q^85 + 64 * q^86 - 11 * q^87 - 25 * q^88 - 19 * q^89 - 5 * q^90 + 122 * q^91 - 78 * q^92 - 20 * q^93 + 138 * q^94 - 15 * q^95 + 56 * q^96 + 161 * q^97 + 65 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/309\mathbb{Z}\right)^\times$.

$n$	$104$	$211$
$\chi(n)$	$1$	$e\left(\frac{15}{17}\right)$

Coefficient data

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

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

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

$2$	0.264688	−	0.163888i	0.187163	−	0.115886i	−0.429652	−	0.902995i	$-0.641364\pi$
$2$	0.264688	−	0.163888i	0.187163	−	0.115886i	0.616815	+	0.787108i	$0.288423\pi$
$3$	−0.273663	−	0.961826i	−0.157999	−	0.555310i
$3$	−0.273663	−	0.961826i	−0.157999	−	0.555310i
$4$	−0.848276	+	1.70357i	−0.424138	+	0.851784i
$5$	−0.994818	+	0.385395i	−0.444896	+	0.172354i	−0.573260	−	0.819373i	$-0.694322\pi$
$5$	−0.994818	+	0.385395i	−0.444896	+	0.172354i	0.128364	+	0.991727i	$0.459027\pi$
$6$	−0.230067	−	0.209734i	−0.0939246	−	0.0856236i
$7$	0.417912	−	4.50998i	0.157956	−	1.70461i	−0.435862	−	0.900014i	$-0.643556\pi$
$7$	0.417912	−	4.50998i	0.157956	−	1.70461i	0.593817	−	0.804600i	$-0.297620\pi$
$8$	0.112115	+	1.20992i	0.0396388	+	0.427771i
$9$	−0.850217	+	0.526432i	−0.283406	+	0.175477i
$10$	−0.200155	+	0.265049i	−0.0632947	+	0.0838157i
$11$	4.48867	−	2.77927i	1.35338	−	0.837980i	0.357979	−	0.933730i	$-0.383466\pi$
$11$	4.48867	−	2.77927i	1.35338	−	0.837980i	0.995405	+	0.0957492i	$0.0305247\pi$
$12$	1.87068	+	0.349690i	0.540018	+	0.100947i
$13$	0.414573	−	4.47396i	0.114982	−	1.24085i	−0.721327	−	0.692594i	$-0.756468\pi$
$13$	0.414573	−	4.47396i	0.114982	−	1.24085i	0.836309	−	0.548258i	$-0.184709\pi$
$14$	−0.628517	−	1.26223i	−0.167978	−	0.337346i
$15$	0.642928	+	0.851374i	0.166003	+	0.219824i
$16$	−2.06576	−	2.73551i	−0.516439	−	0.683876i
$17$	5.95033	−	5.42444i	1.44317	−	1.31562i	0.576146	−	0.817346i	$-0.304556\pi$
$17$	5.95033	−	5.42444i	1.44317	−	1.31562i	0.867020	−	0.498274i	$-0.166032\pi$
$18$	−0.138767	+	0.278681i	−0.0327076	+	0.0656858i
$19$	−2.15302	+	7.56708i	−0.493937	+	1.73601i	0.167372	+	0.985894i	$0.446472\pi$
$19$	−2.15302	+	7.56708i	−0.493937	+	1.73601i	−0.661309	+	0.750114i	$0.729999\pi$
$20$	0.187335	−	2.02166i	0.0418893	−	0.452057i
$21$	−4.45218	+	0.832258i	−0.971546	+	0.181613i
$22$	0.732610	−	1.47128i	0.156193	−	0.313678i
$23$	−1.19611	−	0.740598i	−0.249406	−	0.154425i	0.396036	−	0.918235i	$-0.370385\pi$
$23$	−1.19611	−	0.740598i	−0.249406	−	0.154425i	−0.645442	+	0.763810i	$0.723327\pi$
$24$	1.13305	−	0.438945i	0.231283	−	0.0895994i
$25$	−2.85391	+	2.60168i	−0.570782	+	0.520337i
$26$	−0.623496	−	1.25215i	−0.122278	−	0.245566i
$27$	0.739009	+	0.673696i	0.142222	+	0.129653i
$28$	7.32856	+	4.53765i	1.38497	+	0.857536i
$29$	0.0361267	−	0.0139956i	0.00670857	−	0.00259891i	−0.357885	−	0.933766i	$-0.616502\pi$
$29$	0.0361267	−	0.0139956i	0.00670857	−	0.00259891i	0.364594	+	0.931167i	$0.381208\pi$
$30$	0.309706	+	0.119981i	0.0565442	+	0.0219054i
$31$	0.548639	+	0.726516i	0.0985385	+	0.130486i	0.844615	−	0.535374i	$-0.179829\pi$
$31$	0.548639	+	0.726516i	0.0985385	+	0.130486i	−0.746076	+	0.665860i	$0.768065\pi$
$32$	−3.26120	−	1.26339i	−0.576504	−	0.223339i
$33$	−3.90155	−	3.55673i	−0.679173	−	0.619148i
$34$	0.685982	−	2.41097i	0.117645	−	0.413479i
$35$	1.32238	+	4.64768i	0.223523	+	0.785601i
$36$	−0.175594	−	1.89496i	−0.0292657	−	0.315827i
$37$	−4.98172	−	0.931244i	−0.818989	−	0.153096i	−0.242449	−	0.970164i	$-0.577951\pi$
$37$	−4.98172	−	0.931244i	−0.818989	−	0.153096i	−0.576540	+	0.817069i	$0.695598\pi$
$38$	0.670275	+	2.35577i	0.108733	+	0.382157i
$39$	−4.41662	+	0.825609i	−0.707225	+	0.132203i
$40$	−0.577831	−	1.16044i	−0.0913631	−	0.183482i
$41$	2.48297	+	0.961906i	0.387774	+	0.150225i	0.547234	−	0.836980i	$-0.315681\pi$
$41$	2.48297	+	0.961906i	0.387774	+	0.150225i	−0.159459	+	0.987205i	$0.550975\pi$
$42$	−1.04204	+	0.949949i	−0.160791	+	0.146580i
$43$	−1.49100	+	0.278716i	−0.227375	+	0.0425037i	−0.296204	−	0.955125i	$-0.595721\pi$
$43$	−1.49100	+	0.278716i	−0.227375	+	0.0425037i	0.0688290	+	0.997628i	$0.478074\pi$
$44$	0.927038	+	10.0043i	0.139756	+	1.50821i
$45$	0.642928	−	0.851374i	0.0958420	−	0.126915i
$46$	−0.437971			−0.0645753
$47$	1.62149			0.236518			0.118259	−	0.992983i	$-0.462269\pi$
$47$	1.62149			0.236518			0.118259	+	0.992983i	$0.462269\pi$
$48$	−2.06576	+	2.73551i	−0.298166	+	0.394836i
$49$	−13.2845	−	2.48330i	−1.89778	−	0.354757i
$50$	−0.329012	+	1.15636i	−0.0465293	+	0.163534i
$51$	−6.84575	−	4.23871i	−0.958597	−	0.593538i
$52$	7.27002	+	4.50140i	1.00817	+	0.624232i
$53$	2.55199	−	8.96932i	0.350543	−	1.23203i	−0.563399	−	0.826185i	$-0.690507\pi$
$53$	2.55199	−	8.96932i	0.350543	−	1.23203i	0.913942	−	0.405845i	$-0.133023\pi$
$54$	0.306018	+	0.0572047i	0.0416438	+	0.00778457i
$55$	−3.39430	+	4.49478i	−0.457687	+	0.606075i
$56$	5.50357			0.735445
$57$	7.86742			1.04206
$58$	0.00726862	−	0.00962521i	0.000954417	−	0.00126385i
$59$	1.00469	+	10.8423i	0.130799	+	1.41155i	0.767804	+	0.640685i	$0.221350\pi$
$59$	1.00469	+	10.8423i	0.130799	+	1.41155i	−0.637005	+	0.770860i	$0.719827\pi$
$60$	−1.99575	+	0.373071i	−0.257651	+	0.0481632i
$61$	2.19237	−	1.99861i	0.280704	−	0.255895i	−0.521082	−	0.853506i	$-0.674472\pi$
$61$	2.19237	−	1.99861i	0.280704	−	0.255895i	0.801786	+	0.597611i	$0.203883\pi$
$62$	0.264286	+	0.102385i	0.0335643	+	0.0130029i
$63$	2.01888	+	4.05447i	0.254356	+	0.510815i
$64$	5.66877	−	1.05968i	0.708596	−	0.132460i
$65$	1.31181	+	4.61055i	0.162711	+	0.571868i
$66$	−1.61560	−	0.302008i	−0.198867	−	0.0371747i
$67$	−0.103862	−	1.12085i	−0.0126888	−	0.136934i	0.987033	−	0.160517i	$-0.0513161\pi$
$67$	−0.103862	−	1.12085i	−0.0126888	−	0.136934i	−0.999722	+	0.0235831i	$0.992493\pi$
$68$	4.19338	+	14.7382i	0.508522	+	1.78727i
$69$	−0.384996	+	1.35312i	−0.0463481	+	0.162897i
$70$	1.11172	+	1.01346i	0.132876	+	0.121132i
$71$	11.3957	+	4.41470i	1.35242	+	0.523929i	0.924945	−	0.380100i	$-0.124110\pi$
$71$	11.3957	+	4.41470i	1.35242	+	0.523929i	0.427471	+	0.904029i	$0.359404\pi$
$72$	−0.732262	−	0.969672i	−0.0862980	−	0.114277i
$73$	8.31133	+	3.21983i	0.972768	+	0.376852i	0.794590	−	0.607146i	$-0.207686\pi$
$73$	8.31133	+	3.21983i	0.972768	+	0.376852i	0.178178	+	0.983998i	$0.442980\pi$
$74$	−1.47122	+	0.569955i	−0.171026	+	0.0662559i
$75$	3.28337	+	2.03298i	0.379131	+	0.234748i
$76$	−11.0647	−	10.0868i	−1.26921	−	1.15703i
$77$	−10.6586	−	21.4053i	−1.21466	−	2.43936i
$78$	−1.03372	+	0.942361i	−0.117046	+	0.106701i
$79$	1.98193	−	0.767802i	0.222984	−	0.0863845i	−0.247158	−	0.968975i	$-0.579497\pi$
$79$	1.98193	−	0.767802i	0.222984	−	0.0863845i	0.470142	+	0.882591i	$0.344203\pi$
$80$	3.10930	+	1.92520i	0.347631	+	0.215244i
$81$	0.445738	−	0.895163i	0.0495265	−	0.0994626i
$82$	0.814858	−	0.152323i	0.0899860	−	0.0168213i
$83$	−0.571315	+	6.16548i	−0.0627100	+	0.676749i	0.905122	+	0.425152i	$0.139779\pi$
$83$	−0.571315	+	6.16548i	−0.0627100	+	0.676749i	−0.967832	+	0.251597i	$0.919044\pi$
$84$	2.35887	−	8.29058i	0.257374	−	0.904577i
$85$	−3.82895	+	7.68956i	−0.415307	+	0.834050i
$86$	−0.348971	+	0.318130i	−0.0376306	+	0.0343048i
$87$	−0.0233479	−	0.0309176i	−0.00250315	−	0.00331471i
$88$	3.86593	+	5.11933i	0.412110	+	0.545722i
$89$	0.471373	+	0.946645i	0.0499655	+	0.100344i	0.918739	−	0.394866i	$-0.129209\pi$
$89$	0.471373	+	0.946645i	0.0499655	+	0.100344i	−0.868773	+	0.495210i	$0.835091\pi$
$90$	0.0306454	−	0.330717i	0.00323031	−	0.0348606i
$91$	−20.0042	−	3.73944i	−2.09701	−	0.391999i
$92$	2.27629	−	1.40942i	0.237319	−	0.146942i
$93$	0.548639	−	0.726516i	0.0568912	−	0.0753362i
$94$	0.429189	−	0.265742i	0.0442675	−	0.0274092i
$95$	−0.774449	−	8.35764i	−0.0794568	−	0.857475i
$96$	−0.322696	+	3.48245i	−0.0329350	+	0.355426i
$97$	6.62042	+	6.03531i	0.672202	+	0.612793i	0.936090	−	0.351760i	$-0.114417\pi$
$97$	6.62042	+	6.03531i	0.672202	+	0.612793i	−0.263888	+	0.964553i	$0.585005\pi$
$98$	−3.92324	+	1.51987i	−0.396307	+	0.153530i
$99$	−2.35325	+	4.72596i	−0.236510	+	0.474977i
$100$	−2.01124	−	7.06877i	−0.201124	−	0.706877i
$101$	−12.9572	+	8.02274i	−1.28929	+	0.798292i	−0.987882	−	0.155204i	$-0.950396\pi$
$101$	−12.9572	+	8.02274i	−1.28929	+	0.798292i	−0.301404	+	0.953496i	$0.597455\pi$
$102$	−2.50667			−0.248197
$103$	−9.95287	−	1.98505i	−0.980685	−	0.195593i
$103$	−9.95287	−	1.98505i	−0.980685	−	0.195593i
$104$	5.45960			0.535358
$105$	4.10837	−	2.54379i	0.400936	−	0.248249i
$106$	−0.794482	−	2.79232i	−0.0771669	−	0.271214i
$107$	−2.39881	+	4.81745i	−0.231901	+	0.465721i	−0.980296	−	0.197533i	$-0.936707\pi$
$107$	−2.39881	+	4.81745i	−0.231901	+	0.465721i	0.748395	+	0.663253i	$0.230825\pi$
$108$	−1.77457	+	0.687472i	−0.170758	+	0.0661520i
$109$	3.68744	+	3.36155i	0.353193	+	0.321978i	0.830774	−	0.556610i	$-0.187898\pi$
$109$	3.68744	+	3.36155i	0.353193	+	0.321978i	−0.477581	+	0.878588i	$0.658486\pi$
$110$	−0.161791	+	1.74600i	−0.0154261	+	0.166475i
$111$	0.467617	+	5.04639i	0.0443842	+	0.478982i
$112$	−13.2004	+	8.17333i	−1.24732	+	0.772307i
$113$	−1.81306	+	2.40089i	−0.170559	+	0.225856i	−0.875266	−	0.483642i	$-0.839314\pi$
$113$	−1.81306	+	2.40089i	−0.170559	+	0.225856i	0.704707	+	0.709498i	$0.251078\pi$
$114$	2.08241	−	1.28938i	0.195036	−	0.120761i
$115$	1.47533	+	0.275787i	0.137575	+	0.0257173i
$116$	−0.00680304	+	0.0734165i	−0.000631646	+	0.00681655i
$117$	2.00276	+	4.02208i	0.185155	+	0.371841i
$118$	2.04285	+	2.70517i	0.188060	+	0.249031i
$119$	−21.9774	−	29.1028i	−2.01467	−	2.66785i
$120$	−0.958011	+	0.873342i	−0.0874540	+	0.0797249i
$121$	7.52071	−	15.1036i	0.683701	−	1.37306i
$122$	0.252746	−	0.888311i	0.0228826	−	0.0804239i
$123$	0.245690	−	2.65142i	0.0221531	−	0.239070i
$124$	−1.70307	+	0.318358i	−0.152940	+	0.0285894i
$125$	4.21415	−	8.46316i	0.376925	−	0.756968i
$126$	1.19885	+	0.742299i	0.106802	+	0.0661293i
$127$	−2.45612	+	0.951506i	−0.217945	+	0.0844325i	−0.467739	−	0.883867i	$-0.654931\pi$
$127$	−2.45612	+	0.951506i	−0.217945	+	0.0844325i	0.249794	+	0.968299i	$0.419637\pi$
$128$	6.49596	−	5.92185i	0.574167	−	0.523422i
$129$	0.676106	+	1.35780i	0.0595279	+	0.119548i
$130$	1.10284	+	1.00537i	0.0967251	+	0.0881766i
$131$	11.8621	+	7.34472i	1.03640	+	0.641711i	0.935551	−	0.353191i	$-0.114903\pi$
$131$	11.8621	+	7.34472i	1.03640	+	0.641711i	0.100848	+	0.994902i	$0.467845\pi$
$132$	9.36873	−	3.62947i	0.815444	−	0.315905i
$133$	33.2276	+	12.8725i	2.88120	+	1.11618i
$134$	−0.211185	−	0.279654i	−0.0182436	−	0.0241585i
$135$	−0.994818	−	0.385395i	−0.0856203	−	0.0331695i
$136$	7.23025	+	6.59125i	0.619989	+	0.565195i
$137$	3.18177	−	11.1828i	0.271837	−	0.955407i	−0.698892	−	0.715228i	$-0.746323\pi$
$137$	3.18177	−	11.1828i	0.271837	−	0.955407i	0.970728	−	0.240180i	$-0.0772063\pi$
$138$	0.119856	+	0.421252i	0.0102029	+	0.0358593i
$139$	−0.475855	−	5.13530i	−0.0403615	−	0.435570i	−0.991806	−	0.127751i	$-0.959224\pi$
$139$	−0.475855	−	5.13530i	−0.0403615	−	0.435570i	0.951445	−	0.307819i	$-0.0995993\pi$
$140$	−9.03937	−	1.68975i	−0.763966	−	0.142810i
$141$	−0.443741	−	1.55959i	−0.0373697	−	0.131341i
$142$	3.73982	−	0.699093i	0.313839	−	0.0586666i
$143$	−10.5734	−	21.2343i	−0.884195	−	1.77570i
$144$	3.19640	+	1.23829i	0.266367	+	0.103191i
$145$	−0.0305457	+	0.0278461i	−0.00253668	+	0.00231249i
$146$	2.72761	−	0.509878i	0.225738	−	0.0421978i
$147$	1.24697	+	13.4570i	0.102848	+	1.10991i
$148$	5.81231	−	7.69674i	0.477769	−	0.632668i
$149$	14.4885			1.18694			0.593472	−	0.804855i	$-0.297757\pi$
$149$	14.4885			1.18694			0.593472	+	0.804855i	$0.297757\pi$
$150$	1.20225			0.0981635
$151$	1.77161	−	2.34599i	0.144172	−	0.190914i	−0.720202	−	0.693765i	$-0.755951\pi$
$151$	1.77161	−	2.34599i	0.144172	−	0.190914i	0.864373	+	0.502851i	$0.167715\pi$
$152$	−9.39694	−	1.75659i	−0.762192	−	0.142478i
$153$	−2.20347	+	7.74440i	−0.178140	+	0.626097i
$154$	−6.32928	−	3.91892i	−0.510028	−	0.315796i
$155$	−0.825792	−	0.511309i	−0.0663292	−	0.0410693i
$156$	2.34003	−	8.22436i	0.187352	−	0.658475i
$157$	11.3941	+	2.12992i	0.909345	+	0.169986i	0.617584	−	0.786505i	$-0.288112\pi$
$157$	11.3941	+	2.12992i	0.909345	+	0.169986i	0.291761	+	0.956491i	$0.405759\pi$
$158$	0.398759	−	0.528042i	0.0317236	−	0.0420088i
$159$	−9.32530			−0.739545
$160$	3.73120			0.294978
$161$	−3.83995	+	5.08492i	−0.302631	+	0.400748i
$162$	−0.0287249	−	0.309991i	−0.00225684	−	0.0243552i
$163$	−15.2853	+	2.85733i	−1.19724	+	0.223803i	−0.744366	−	0.667771i	$-0.767248\pi$
$163$	−15.2853	+	2.85733i	−1.19724	+	0.223803i	−0.452874	+	0.891574i	$0.649601\pi$
$164$	−3.74491	+	3.41394i	−0.292429	+	0.266584i
$165$	5.25208	+	2.03467i	0.408874	+	0.158399i
$166$	0.859228	+	1.72556i	0.0666890	+	0.133930i
$167$	−14.4707	+	2.70505i	−1.11978	+	0.209323i	−0.710918	−	0.703274i	$-0.751720\pi$
$167$	−14.4707	+	2.70505i	−1.11978	+	0.209323i	−0.408860	+	0.912597i	$0.634073\pi$
$168$	−1.50612	−	5.29347i	−0.116200	−	0.408400i
$169$	−7.06576	−	1.32082i	−0.543520	−	0.101602i
$170$	0.246750	+	2.66286i	0.0189249	+	0.204232i
$171$	−2.15302	−	7.56708i	−0.164646	−	0.578669i
$172$	0.789966	−	2.77644i	0.0602343	−	0.211702i
$173$	9.53432	+	8.69168i	0.724881	+	0.660816i	0.949549	−	0.313619i	$-0.101542\pi$
$173$	9.53432	+	8.69168i	0.724881	+	0.660816i	−0.224668	+	0.974435i	$0.572130\pi$
$174$	−0.0112469	−	0.00435708i	−0.000852627	−	0.000330310i
$175$	10.5409	+	13.9584i	0.796814	+	1.05515i
$176$	−16.8752	−	6.53749i	−1.27202	−	0.492782i
$177$	10.1534	−	3.93346i	0.763179	−	0.295657i
$178$	0.279911	+	0.173314i	0.0209802	+	0.0129904i
$179$	0.627977	+	0.572477i	0.0469372	+	0.0427889i	0.696824	−	0.717242i	$-0.254596\pi$
$179$	0.627977	+	0.572477i	0.0469372	+	0.0427889i	−0.649887	+	0.760031i	$0.725184\pi$
$180$	0.904993	+	1.81747i	0.0674542	+	0.135466i
$181$	−7.00204	+	6.38320i	−0.520457	+	0.474460i	−0.890774	−	0.454446i	$-0.849837\pi$
$181$	−7.00204	+	6.38320i	−0.520457	+	0.474460i	0.370317	+	0.928905i	$0.379249\pi$
$182$	−5.90773	+	2.28867i	−0.437910	+	0.169647i
$183$	−2.52228	−	1.56173i	−0.186452	−	0.115446i
$184$	0.761961	−	1.53022i	0.0561725	−	0.112810i
$185$	5.31480	−	0.993508i	0.390752	−	0.0730442i
$186$	0.0261511	−	0.282216i	0.00191749	−	0.0206931i
$187$	11.6331	−	40.8861i	0.850696	−	2.98989i
$188$	−1.37547	+	2.76231i	−0.100316	+	0.201462i
$189$	3.34720	−	3.05137i	0.243473	−	0.221955i
$190$	−1.57471	−	2.08525i	−0.114241	−	0.151280i
$191$	10.8376	+	14.3514i	0.784185	+	1.03843i	0.998102	+	0.0615766i	$0.0196128\pi$
$191$	10.8376	+	14.3514i	0.784185	+	1.03843i	−0.213918	+	0.976852i	$0.568622\pi$
$192$	−2.57056	−	5.16237i	−0.185514	−	0.372562i
$193$	1.18901	−	12.8314i	0.0855867	−	0.923627i	−0.839371	−	0.543558i	$-0.817077\pi$
$193$	1.18901	−	12.8314i	0.0855867	−	0.923627i	0.924958	−	0.380069i	$-0.124100\pi$
$194$	2.74146	+	0.512469i	0.196826	+	0.0367931i
$195$	4.07555	−	2.52347i	0.291856	−	0.180710i
$196$	15.4994	−	20.5245i	1.10710	−	1.46604i
$197$	−12.5061	+	7.74343i	−0.891021	+	0.551697i	−0.893884	−	0.448299i	$-0.852030\pi$
$197$	−12.5061	+	7.74343i	−0.891021	+	0.551697i	0.00286260	+	0.999996i	$0.499089\pi$
$198$	0.151651	+	1.63658i	0.0107774	+	0.116306i
$199$	0.964769	−	10.4115i	0.0683907	−	0.738053i	−0.890632	−	0.454724i	$-0.849738\pi$
$199$	0.964769	−	10.4115i	0.0683907	−	0.738053i	0.959023	−	0.283329i	$-0.0914387\pi$
$200$	−3.46779	−	3.16131i	−0.245210	−	0.223538i
$201$	−1.04964	+	0.406633i	−0.0740359	+	0.0286817i
$202$	−2.11478	+	4.24705i	−0.148795	+	0.298822i
$203$	−0.0480220	−	0.168780i	−0.00337049	−	0.0118460i
$204$	13.0280	−	8.06661i	0.912143	−	0.564775i
$205$	−2.84081			−0.198411
$206$	−2.95974	+	1.10574i	−0.206215	+	0.0770404i
$207$	1.40683			0.0977811
$208$	−13.0949	+	8.10804i	−0.907971	+	0.562192i
$209$	11.3667	+	39.9499i	0.786254	+	2.76340i
$210$	0.670540	−	1.34663i	0.0462717	−	0.0929260i
$211$	−20.5999	+	7.98044i	−1.41815	+	0.549396i	−0.943676	−	0.330871i	$-0.892657\pi$
$211$	−20.5999	+	7.98044i	−1.41815	+	0.549396i	−0.474478	+	0.880267i	$0.657363\pi$
$212$	13.1150	+	11.9559i	0.900745	+	0.821138i
$213$	1.12760	−	12.1688i	0.0772622	−	0.833791i
$214$	0.154587	+	1.66826i	0.0105674	+	0.114040i
$215$	1.37586	−	0.851894i	0.0938326	−	0.0580987i
$216$	−0.732262	+	0.969672i	−0.0498242	+	0.0659778i
$217$	3.50586	−	2.17073i	0.237993	−	0.147359i
$218$	1.52694	+	0.285435i	0.103417	+	0.0193321i
$219$	0.822408	−	8.87520i	0.0555732	−	0.599730i
$220$	−4.77785	−	9.59523i	−0.322123	−	0.646910i
$221$	−21.8019	−	28.8703i	−1.46655	−	1.94203i
$222$	0.950816	+	1.25908i	0.0638146	+	0.0845042i
$223$	−2.94304	+	2.68293i	−0.197080	+	0.179662i	−0.766220	−	0.642579i	$-0.777865\pi$
$223$	−2.94304	+	2.68293i	−0.197080	+	0.179662i	0.569140	+	0.822241i	$0.307276\pi$
$224$	−7.06078	+	14.1800i	−0.471768	+	0.947438i
$225$	1.05683	−	3.71439i	0.0704556	−	0.247626i
$226$	−0.0864206	+	0.932627i	−0.00574861	+	0.0620374i
$227$	13.5491	−	2.53276i	0.899284	−	0.168105i	0.286243	−	0.958157i	$-0.407593\pi$
$227$	13.5491	−	2.53276i	0.899284	−	0.168105i	0.613040	+	0.790052i	$0.289946\pi$
$228$	−6.67374	+	13.4027i	−0.441979	+	0.887614i
$229$	24.2636	+	15.0234i	1.60338	+	0.992773i	0.976995	+	0.213262i	$0.0684089\pi$
$229$	24.2636	+	15.0234i	1.60338	+	0.992773i	0.626389	+	0.779511i	$0.284532\pi$
$230$	0.435702	−	0.168792i	0.0287293	−	0.0111298i
$231$	−17.6713	+	16.1095i	−1.16269	+	1.05993i
$232$	0.0209839	+	0.0421413i	0.00137766	+	0.00276671i
$233$	−12.0804	−	11.0128i	−0.791416	−	0.721471i	0.173270	−	0.984874i	$-0.444567\pi$
$233$	−12.0804	−	11.0128i	−0.791416	−	0.721471i	−0.964686	+	0.263403i	$0.915155\pi$
$234$	1.18928	+	0.736370i	0.0777455	+	0.0481380i
$235$	−1.61309	+	0.624912i	−0.105226	+	0.0407648i
$236$	−19.3228	−	7.48570i	−1.25781	−	0.487278i
$237$	−1.28087	−	1.69615i	−0.0832015	−	0.110177i
$238$	−10.5868	−	4.10134i	−0.686239	−	0.265850i
$239$	0.966450	+	0.881036i	0.0625145	+	0.0569895i	0.704350	−	0.709853i	$-0.251239\pi$
$239$	0.966450	+	0.881036i	0.0625145	+	0.0569895i	−0.641836	+	0.766842i	$0.721827\pi$
$240$	1.00080	−	3.51746i	0.0646017	−	0.227051i
$241$	2.37547	+	8.34890i	0.153017	+	0.537800i	0.999981	+	0.00614944i	$0.00195744\pi$
$241$	2.37547	+	8.34890i	0.153017	+	0.537800i	−0.846964	+	0.531651i	$0.821572\pi$
$242$	−0.484660	−	5.23031i	−0.0311551	−	0.336217i
$243$	−0.982973	−	0.183750i	−0.0630578	−	0.0117875i
$244$	1.54503	+	5.43022i	0.0989104	+	0.347634i
$245$	14.1727	−	2.64934i	0.905461	−	0.169260i
$246$	−0.369505	−	0.742066i	−0.0235588	−	0.0473124i
$247$	32.9622	+	12.7696i	2.09734	+	0.812512i
$248$	−0.817514	+	0.745262i	−0.0519122	+	0.0473242i
$249$	6.08646	−	1.13776i	0.385714	−	0.0721024i
$250$	−0.271574	−	2.93075i	−0.0171758	−	0.185357i
$251$	4.22212	−	5.59099i	0.266498	−	0.352900i	−0.645016	−	0.764169i	$-0.723149\pi$
$251$	4.22212	−	5.59099i	0.266498	−	0.352900i	0.911514	+	0.411269i	$0.134914\pi$
$252$	−8.61963			−0.542986
$253$	−7.42725			−0.466947
$254$	−0.494166	+	0.654382i	−0.0310067	+	0.0410596i
$255$	8.44385	+	1.57843i	0.528775	+	0.0988451i
$256$	−2.40752	+	8.46156i	−0.150470	+	0.528848i
$257$	−5.62550	−	3.48317i	−0.350909	−	0.217274i	0.339646	−	0.940553i	$-0.389693\pi$
$257$	−5.62550	−	3.48317i	−0.350909	−	0.217274i	−0.690555	+	0.723279i	$0.742634\pi$
$258$	0.401486	+	0.248589i	0.0249954	+	0.0154765i
$259$	−6.28181	+	22.0783i	−0.390333	+	1.37188i
$260$	−8.96716	−	1.67625i	−0.556120	−	0.103957i
$261$	−0.0233479	+	0.0309176i	−0.00144520	+	0.00191375i
$262$	4.34348			0.268341
$263$	−7.09495			−0.437493			−0.218747	−	0.975782i	$-0.570197\pi$
$263$	−7.09495			−0.437493			−0.218747	+	0.975782i	$0.570197\pi$
$264$	3.86593	−	5.11933i	0.237932	−	0.315073i
$265$	0.917960	+	9.90637i	0.0563898	+	0.608543i
$266$	10.9046	−	2.03843i	0.668605	−	0.124984i
$267$	0.781510	−	0.712441i	0.0478276	−	0.0436007i
$268$	1.99755	+	0.773855i	0.122020	+	0.0472707i
$269$	−2.85749	−	5.73861i	−0.174224	−	0.349889i	0.790790	−	0.612088i	$-0.209670\pi$
$269$	−2.85749	−	5.73861i	−0.174224	−	0.349889i	−0.965014	+	0.262199i	$0.915552\pi$
$270$	−0.326479	+	0.0610294i	−0.0198689	+	0.00371413i
$271$	3.09826	+	10.8892i	0.188206	+	0.661474i	0.997276	+	0.0737624i	$0.0235006\pi$
$271$	3.09826	+	10.8892i	0.188206	+	0.661474i	−0.809070	+	0.587712i	$0.800029\pi$
$272$	−27.1305	−	5.07157i	−1.64503	−	0.307509i
$273$	1.87773	+	20.2639i	0.113645	+	1.22643i
$274$	−0.990544	−	3.48140i	−0.0598409	−	0.210319i
$275$	−5.57949	+	19.6099i	−0.336456	+	1.18252i
$276$	−1.97855	−	1.80369i	−0.119095	−	0.108569i
$277$	0.589876	+	0.228519i	0.0354422	+	0.0137304i	0.378898	−	0.925439i	$-0.376303\pi$
$277$	0.589876	+	0.228519i	0.0354422	+	0.0137304i	−0.343455	+	0.939169i	$0.611597\pi$
$278$	−0.967568	−	1.28127i	−0.0580308	−	0.0768453i
$279$	−0.848924	−	0.328875i	−0.0508237	−	0.0196892i
$280$	−5.47505	+	2.12105i	−0.327197	+	0.126757i
$281$	−16.5474	−	10.2457i	−0.987137	−	0.611209i	−0.0649233	−	0.997890i	$-0.520680\pi$
$281$	−16.5474	−	10.2457i	−0.987137	−	0.611209i	−0.922214	+	0.386681i	$0.873621\pi$
$282$	−0.373051	−	0.340081i	−0.0222149	−	0.0202515i
$283$	11.0669	+	22.2252i	0.657856	+	1.32115i	0.933044	+	0.359763i	$0.117142\pi$
$283$	11.0669	+	22.2252i	0.657856	+	1.32115i	−0.275188	+	0.961391i	$0.588740\pi$
$284$	−17.1874	+	15.6684i	−1.01989	+	0.929749i
$285$	−7.82665	+	3.03206i	−0.463611	+	0.179604i
$286$	−6.27872	−	3.88762i	−0.371268	−	0.229880i
$287$	5.37584	−	10.7961i	0.317326	−	0.637276i
$288$	3.43782	−	0.642639i	0.202575	−	0.0378679i
$289$	4.41328	−	47.6269i	0.259605	−	2.80158i
$290$	−0.00352145	+	0.0123766i	−0.000206787	+	0.000726781i
$291$	3.99315	−	8.01933i	0.234083	−	0.470101i
$292$	−12.5355	+	11.4276i	−0.733585	+	0.668751i
$293$	7.08849	+	9.38668i	0.414114	+	0.548376i	0.956492	−	0.291759i	$-0.0942405\pi$
$293$	7.08849	+	9.38668i	0.414114	+	0.548376i	−0.542378	+	0.840135i	$0.682476\pi$
$294$	2.53549	+	3.35754i	0.147873	+	0.195815i
$295$	−5.17804	−	10.3989i	−0.301477	−	0.605448i
$296$	0.568202	−	6.13188i	0.0330261	−	0.356408i
$297$	5.18955	+	0.970094i	0.301128	+	0.0562906i
$298$	3.83494	−	2.37449i	0.222152	−	0.137551i
$299$	−3.80928	+	5.04430i	−0.220296	+	0.291719i
$300$	−6.24853	+	3.86892i	−0.360759	+	0.223372i
$301$	0.633898	+	6.84085i	0.0365373	+	0.394300i
$302$	0.0844447	−	0.911303i	0.00485925	−	0.0524396i
$303$	11.2624	+	10.2670i	0.647007	+	0.589824i
$304$	25.1474	−	9.74216i	1.44230	−	0.558751i
$305$	−1.41075	+	2.83318i	−0.0807796	+	0.162227i
$306$	0.685982	+	2.41097i	0.0392150	+	0.137826i
$307$	−25.6536	+	15.8841i	−1.46413	+	0.906551i	−0.464348	+	0.885653i	$0.653711\pi$
$307$	−25.6536	+	15.8841i	−1.46413	+	0.906551i	−0.999782	+	0.0208983i	$0.993347\pi$
$308$	45.5068			2.59299
$309$	0.814459	+	10.1162i	0.0463329	+	0.575488i
$310$	−0.302375			−0.0171737
$311$	24.4755	−	15.1546i	1.38788	−	0.859338i	0.389776	−	0.920910i	$-0.372553\pi$
$311$	24.4755	−	15.1546i	1.38788	−	0.859338i	0.998103	+	0.0615720i	$0.0196114\pi$
$312$	−1.49409	−	5.25119i	−0.0845862	−	0.297290i
$313$	−11.5669	+	23.2294i	−0.653799	+	1.31301i	0.281641	+	0.959520i	$0.409121\pi$
$313$	−11.5669	+	23.2294i	−0.653799	+	1.31301i	−0.935440	+	0.353486i	$0.884996\pi$
$314$	3.36495	−	1.30359i	0.189895	−	0.0735657i
$315$	−3.57099	−	3.25539i	−0.201203	−	0.183421i
$316$	−0.373217	+	4.02765i	−0.0209951	+	0.226573i
$317$	−0.964385	−	10.4074i	−0.0541653	−	0.584536i	−0.978958	−	0.204064i	$-0.934585\pi$
$317$	−0.964385	−	10.4074i	−0.0541653	−	0.584536i	0.924792	−	0.380472i	$-0.124239\pi$
$318$	−2.46830	+	1.52831i	−0.138415	+	0.0857032i
$319$	0.123264	−	0.163227i	0.00690143	−	0.00913898i
$320$	−5.23100	+	3.23890i	−0.292422	+	0.181060i
$321$	5.29001	+	0.988875i	0.295260	+	0.0551936i
$322$	−0.183033	+	1.97524i	−0.0102000	+	0.110076i
$323$	28.2360	+	56.7056i	1.57109	+	3.15518i
$324$	1.14686	+	1.51869i	0.0637146	+	0.0843717i
$325$	10.4567	+	13.8469i	0.580031	+	0.768085i
$326$	−3.57757	+	3.26139i	−0.198143	+	0.180632i
$327$	2.22411	−	4.46661i	0.122993	−	0.247004i
$328$	−0.885449	+	3.11203i	−0.0488908	+	0.171833i
$329$	0.677638	−	7.31288i	0.0373594	−	0.403172i
$330$	1.72362	−	0.322201i	0.0948824	−	0.0177366i
$331$	9.66505	−	19.4100i	0.531239	−	1.06687i	−0.453243	−	0.891387i	$-0.649733\pi$
$331$	9.66505	−	19.4100i	0.531239	−	1.06687i	0.984482	−	0.175485i	$-0.0561494\pi$
$332$	−10.0187	−	6.20330i	−0.549846	−	0.340450i
$333$	4.72578	−	1.83078i	0.258971	−	0.100326i
$334$	−3.38691	+	3.08757i	−0.185323	+	0.168945i
$335$	0.535294	+	1.07502i	0.0292462	+	0.0587344i
$336$	11.4738	+	10.4597i	0.625946	+	0.570625i
$337$	12.7317	+	7.88313i	0.693540	+	0.429421i	0.827426	−	0.561575i	$-0.189804\pi$
$337$	12.7317	+	7.88313i	0.693540	+	0.429421i	−0.133886	+	0.990997i	$0.542746\pi$
$338$	−2.08669	+	0.808389i	−0.113501	+	0.0439706i
$339$	2.80540	+	1.08682i	0.152369	+	0.0590279i
$340$	−9.85168	−	13.0457i	−0.534283	−	0.707504i
$341$	4.48184	+	1.73627i	0.242705	+	0.0940245i
$342$	−1.81003	−	1.65006i	−0.0978755	−	0.0892253i
$343$	−8.07487	+	28.3802i	−0.436002	+	1.53239i
$344$	−0.504387	−	1.77274i	−0.0271947	−	0.0955795i
$345$	−0.138484	−	1.49449i	−0.00745575	−	0.0804604i
$346$	3.94809	+	0.738025i	0.212250	+	0.0396765i
$347$	6.12996	+	21.5446i	0.329073	+	1.15657i	0.933102	+	0.359611i	$0.117091\pi$
$347$	6.12996	+	21.5446i	0.329073	+	1.15657i	−0.604029	+	0.796962i	$0.706439\pi$
$348$	0.0724756	−	0.0135480i	0.00388510	−	0.000726251i
$349$	−7.88694	−	15.8391i	−0.422178	−	0.847848i	−0.999509	−	0.0313374i	$-0.990023\pi$
$349$	−7.88694	−	15.8391i	−0.422178	−	0.847848i	0.577331	−	0.816510i	$-0.304094\pi$
$350$	5.07766	+	1.96709i	0.271412	+	0.105146i
$351$	3.32046	−	3.02700i	0.177233	−	0.161569i
$352$	−18.1497	+	3.39277i	−0.967385	+	0.180836i
$353$	−2.20009	−	23.7427i	−0.117099	−	1.26370i	−0.828129	−	0.560537i	$-0.810595\pi$
$353$	−2.20009	−	23.7427i	−0.117099	−	1.26370i	0.711030	−	0.703162i	$-0.248229\pi$
$354$	2.04285	−	2.70517i	0.108576	−	0.143778i
$355$	−13.0380			−0.691986
$356$	−2.01253			−0.106664
$357$	−21.9774	+	29.1028i	−1.16317	+	1.54028i
$358$	0.260040	+	0.0486100i	0.0137436	+	0.00256912i
$359$	1.62485	−	5.71074i	0.0857561	−	0.301401i	−0.907068	−	0.420984i	$-0.861685\pi$
$359$	1.62485	−	5.71074i	0.0857561	−	0.301401i	0.992824	+	0.119582i	$0.0381556\pi$
$360$	1.10217	+	0.682438i	0.0580897	+	0.0359676i
$361$	−36.4711	−	22.5820i	−1.91953	−	1.18852i
$362$	−0.807228	+	2.83711i	−0.0424269	+	0.149115i
$363$	−16.5852	−	3.10031i	−0.870497	−	0.162724i
$364$	23.3395	−	30.9065i	1.22332	−	1.61994i
$365$	−9.50917			−0.497733
$366$	−0.923568			−0.0482757
$367$	6.68249	−	8.84905i	0.348823	−	0.461917i	−0.589453	−	0.807802i	$-0.700657\pi$
$367$	6.68249	−	8.84905i	0.348823	−	0.461917i	0.938277	+	0.345886i	$0.112422\pi$
$368$	0.444957	+	4.80185i	0.0231950	+	0.250314i
$369$	−2.61744	+	0.489284i	−0.136258	+	0.0254711i
$370$	1.24394	−	1.13400i	0.0646695	−	0.0589540i
$371$	−39.3850	−	15.2578i	−2.04477	−	0.792146i
$372$	0.772271	+	1.55093i	0.0400404	+	0.0804120i
$373$	−6.75018	+	1.26183i	−0.349511	+	0.0653349i	−0.355578	−	0.934647i	$-0.615716\pi$
$373$	−6.75018	+	1.26183i	−0.349511	+	0.0653349i	0.00606684	+	0.999982i	$0.498069\pi$
$374$	−3.62160	−	12.7286i	−0.187268	−	0.658180i
$375$	−9.29334	−	1.73723i	−0.479906	−	0.0897100i
$376$	0.181794	+	1.96187i	0.00937530	+	0.101176i
$377$	−0.0476384	−	0.167432i	−0.00245350	−	0.00862317i
$378$	0.385880	−	1.35623i	0.0198475	−	0.0697569i
$379$	5.64153	+	5.14293i	0.289786	+	0.264175i	0.805513	−	0.592578i	$-0.201890\pi$
$379$	5.64153	+	5.14293i	0.289786	+	0.264175i	−0.515727	+	0.856753i	$0.672478\pi$
$380$	14.8947	+	5.77026i	0.764084	+	0.296008i
$381$	1.58733	+	2.10197i	0.0813215	+	0.107687i
$382$	5.22062	+	2.02248i	0.267110	+	0.103479i
$383$	−29.7007	+	11.5061i	−1.51764	+	0.587935i	−0.968767	−	0.247973i	$-0.920236\pi$
$383$	−29.7007	+	11.5061i	−1.51764	+	0.587935i	−0.548869	+	0.835908i	$0.684941\pi$
$384$	−7.47349	−	4.62739i	−0.381380	−	0.236140i
$385$	18.8528	+	17.1866i	0.960830	+	0.875912i
$386$	−1.78820	−	3.59120i	−0.0910172	−	0.182787i
$387$	1.12095	−	1.02188i	0.0569809	−	0.0519450i
$388$	−15.8975	+	6.15873i	−0.807073	+	0.312662i
$389$	16.5802	+	10.2660i	0.840647	+	0.520507i	0.877925	−	0.478798i	$-0.158927\pi$
$389$	16.5802	+	10.2660i	0.840647	+	0.520507i	−0.0372776	+	0.999305i	$0.511869\pi$
$390$	0.665183	−	1.33587i	0.0336829	−	0.0676443i
$391$	−11.1346	+	2.08141i	−0.563099	+	0.105261i
$392$	1.51520	−	16.3516i	0.0765289	−	0.825879i
$393$	3.81811	−	13.4193i	0.192598	−	0.676913i
$394$	−2.04116	+	4.09920i	−0.102832	+	0.206514i
$395$	−1.67575	+	1.52765i	−0.0843161	+	0.0768643i
$396$	−6.05479	−	8.01784i	−0.304265	−	0.402911i
$397$	−12.0210	−	15.9184i	−0.603319	−	0.798924i	0.389182	−	0.921161i	$-0.372758\pi$
$397$	−12.0210	−	15.9184i	−0.603319	−	0.798924i	−0.992501	+	0.122237i	$0.960993\pi$
$398$	−1.45096	−	2.91392i	−0.0727301	−	0.146062i
$399$	3.28788	−	35.4819i	0.164600	−	1.77632i
$400$	13.0124	+	2.43244i	0.650620	+	0.121622i
$401$	31.2789	−	19.3671i	1.56200	−	0.967146i	0.572940	−	0.819597i	$-0.305803\pi$
$401$	31.2789	−	19.3671i	1.56200	−	0.967146i	0.989055	−	0.147549i	$-0.0471385\pi$
$402$	−0.211185	+	0.279654i	−0.0105330	+	0.0139479i
$403$	3.47785	−	2.15339i	0.173244	−	0.107268i
$404$	−2.67603	−	28.8789i	−0.133137	−	1.43678i
$405$	−0.0984375	+	1.06231i	−0.00489140	+	0.0527866i
$406$	−0.0403719	−	0.0368039i	−0.00200362	−	0.00182654i
$407$	−24.9494	+	9.66547i	−1.23670	+	0.479099i
$408$	4.36098	−	8.75802i	0.215901	−	0.433587i
$409$	0.977232	+	3.43462i	0.0483210	+	0.169831i	0.982230	−	0.187679i	$-0.0600965\pi$
$409$	0.977232	+	3.43462i	0.0483210	+	0.169831i	−0.933909	+	0.357510i	$0.883626\pi$
$410$	−0.751931	+	0.465576i	−0.0371352	+	0.0229932i
$411$	−11.6266			−0.573497
$412$	11.8244	−	15.2715i	0.582549	−	0.752374i
$413$	49.3184			2.42680
$414$	0.372370	−	0.230562i	0.0183010	−	0.0113315i
$415$	−1.80779	−	6.35371i	−0.0887408	−	0.311891i
$416$	−7.00437	+	14.0667i	−0.343418	+	0.689676i
$417$	−4.80904	+	1.86303i	−0.235499	+	0.0912330i
$418$	9.55597	+	8.71142i	0.467398	+	0.426089i
$419$	−1.72596	+	18.6260i	−0.0843185	+	0.909942i	0.843554	+	0.537044i	$0.180459\pi$
$419$	−1.72596	+	18.6260i	−0.0843185	+	0.909942i	−0.927873	+	0.372898i	$0.878364\pi$
$420$	0.848495	+	9.15672i	0.0414023	+	0.446802i
$421$	6.10494	−	3.78002i	0.297537	−	0.184227i	−0.369542	−	0.929214i	$-0.620486\pi$
$421$	6.10494	−	3.78002i	0.297537	−	0.184227i	0.667079	+	0.744987i	$0.267544\pi$
$422$	−4.14465	+	5.48841i	−0.201758	+	0.267171i
$423$	−1.37862	+	0.853603i	−0.0670306	+	0.0415036i
$424$	11.1383	+	2.08210i	0.540922	+	0.101116i
$425$	−2.86903	+	30.9617i	−0.139168	+	1.50186i
$426$	−1.69586	−	3.40574i	−0.0821645	−	0.165009i
$427$	−8.09747	−	10.7228i	−0.391864	−	0.518912i
$428$	−6.17201	−	8.17306i	−0.298335	−	0.395060i
$429$	−17.5302	+	15.9808i	−0.846364	+	0.771563i
$430$	0.224558	−	0.450973i	0.0108291	−	0.0217478i
$431$	5.62717	−	19.7775i	0.271051	−	0.952647i	−0.700073	−	0.714072i	$-0.746849\pi$
$431$	5.62717	−	19.7775i	0.271051	−	0.952647i	0.971124	−	0.238575i	$-0.0766804\pi$
$432$	0.316285	−	3.41325i	0.0152173	−	0.164220i
$433$	13.8674	−	2.59227i	0.666425	−	0.124576i	0.160342	−	0.987061i	$-0.448740\pi$
$433$	13.8674	−	2.59227i	0.666425	−	0.124576i	0.506082	+	0.862485i	$0.331093\pi$
$434$	0.572202	−	1.14914i	0.0274666	−	0.0551603i
$435$	0.0351423	+	0.0217592i	0.00168495	+	0.00104327i
$436$	−8.85459	+	3.43029i	−0.424058	+	0.164281i
$437$	8.17941	−	7.45652i	0.391274	−	0.356694i
$438$	−1.23686	−	2.48395i	−0.0590994	−	0.118688i
$439$	3.05030	+	2.78072i	0.145583	+	0.132716i	0.743211	−	0.669057i	$-0.233302\pi$
$439$	3.05030	+	2.78072i	0.145583	+	0.132716i	−0.597628	+	0.801773i	$0.703890\pi$
$440$	−5.81886	−	3.60289i	−0.277403	−	0.171761i
$441$	12.6020	−	4.88204i	0.600095	−	0.232478i
$442$	−10.5022	−	4.06858i	−0.499539	−	0.193522i
$443$	3.88776	+	5.14823i	0.184713	+	0.244600i	0.880947	−	0.473216i	$-0.156907\pi$
$443$	3.88776	+	5.14823i	0.184713	+	0.244600i	−0.696234	+	0.717815i	$0.745142\pi$
$444$	−8.99353	−	3.48411i	−0.426814	−	0.165349i
$445$	−0.833763	−	0.760075i	−0.0395242	−	0.0360310i
$446$	−0.339287	+	1.19247i	−0.0160657	+	0.0564651i
$447$	−3.96497	−	13.9354i	−0.187536	−	0.659122i
$448$	−2.41008	−	26.0089i	−0.113866	−	1.22880i
$449$	7.80812	+	1.45959i	0.368488	+	0.0688823i	0.364737	−	0.931111i	$-0.381159\pi$
$449$	7.80812	+	1.45959i	0.368488	+	0.0688823i	0.00375107	+	0.999993i	$0.498806\pi$
$450$	−0.329012	−	1.15636i	−0.0155098	−	0.0545112i
$451$	13.8186	−	2.58315i	0.650693	−	0.121636i
$452$	−2.55209	−	5.12529i	−0.120040	−	0.241073i
$453$	−2.74126	−	1.06197i	−0.128796	−	0.0498957i
$454$	3.17119	−	2.89092i	0.148831	−	0.135678i
$455$	21.3417	−	3.98946i	1.00052	−	0.187029i
$456$	0.882059	+	9.51893i	0.0413062	+	0.445765i
$457$	−8.58096	+	11.3630i	−0.401400	+	0.531540i	−0.953161	−	0.302462i	$-0.902191\pi$
$457$	−8.58096	+	11.3630i	−0.401400	+	0.531540i	0.551761	+	0.834002i	$0.313956\pi$
$458$	8.88445			0.415143
$459$	8.05177			0.375824
$460$	−1.72131	+	2.27938i	−0.0802566	+	0.106277i
$461$	21.9845	+	4.10961i	1.02392	+	0.191404i	0.668820	−	0.743425i	$-0.266800\pi$
$461$	21.9845	+	4.10961i	1.02392	+	0.191404i	0.355100	+	0.934828i	$0.384447\pi$
$462$	−2.03723	+	7.16013i	−0.0947806	+	0.333119i
$463$	0.135241	+	0.0837376i	0.00628518	+	0.00389162i	0.529571	−	0.848266i	$-0.322353\pi$
$463$	0.135241	+	0.0837376i	0.00628518	+	0.00389162i	−0.523286	+	0.852157i	$0.675294\pi$
$464$	−0.112914	−	0.0699134i	−0.00524190	−	0.00324565i
$465$	−0.265801	+	0.934194i	−0.0123262	+	0.0433222i
$466$	−5.00242	−	0.935114i	−0.231732	−	0.0433183i
$467$	−3.20607	+	4.24553i	−0.148359	+	0.196460i	−0.866128	−	0.499822i	$-0.833399\pi$
$467$	−3.20607	+	4.24553i	−0.148359	+	0.196460i	0.717769	+	0.696282i	$0.245163\pi$
$468$	−8.55078			−0.395260
$469$	−5.09842			−0.235423
$470$	−0.324549	+	0.429773i	−0.0149703	+	0.0198239i
$471$	−1.06952	−	11.5420i	−0.0492810	−	0.531826i
$472$	−13.0056	+	2.43118i	−0.598633	+	0.111904i
$473$	−5.91797	+	5.39494i	−0.272108	+	0.248060i
$474$	−0.617010	−	0.239031i	−0.0283402	−	0.0109791i
$475$	−13.5426	−	27.1972i	−0.621378	−	1.24790i
$476$	68.2215	−	12.7528i	3.12693	−	0.584524i
$477$	2.55199	+	8.96932i	0.116848	+	0.410677i
$478$	0.400200	+	0.0748103i	0.0183047	+	0.00342174i
$479$	−2.41115	−	26.0204i	−0.110168	−	1.18890i	−0.853904	−	0.520430i	$-0.825772\pi$
$479$	−2.41115	−	26.0204i	−0.110168	−	1.18890i	0.743736	−	0.668473i	$-0.233052\pi$
$480$	−1.02109	−	3.58877i	−0.0466063	−	0.163804i
$481$	−6.23163	+	21.9019i	−0.284138	+	0.998641i
$482$	1.99704	+	1.82055i	0.0909629	+	0.0829236i
$483$	5.94166	+	2.30181i	0.270355	+	0.104736i
$484$	19.3504	+	25.6241i	0.879564	+	1.16473i
$485$	−8.91209	−	3.45256i	−0.404677	−	0.156773i
$486$	−0.290296	+	0.112461i	−0.0131681	+	0.00510135i
$487$	−21.4733	−	13.2957i	−0.973050	−	0.602487i	−0.0548040	−	0.998497i	$-0.517453\pi$
$487$	−21.4733	−	13.2957i	−0.973050	−	0.602487i	−0.918246	+	0.396010i	$0.870395\pi$
$488$	2.66395	+	2.42851i	0.120591	+	0.109933i
$489$	6.93128	+	13.9199i	0.313443	+	0.629479i
$490$	3.31716	−	3.02399i	0.149854	−	0.136610i
$491$	17.9437	−	6.95144i	0.809790	−	0.313714i	0.0794852	−	0.996836i	$-0.474672\pi$
$491$	17.9437	−	6.95144i	0.809790	−	0.313714i	0.730304	+	0.683122i	$0.239378\pi$
$492$	4.30846	+	2.66768i	0.194240	+	0.120269i
$493$	0.139048	−	0.279246i	0.00626240	−	0.0125766i
$494$	10.8175	−	2.02214i	0.486703	−	0.0909805i
$495$	0.519695	−	5.60840i	0.0233586	−	0.252079i
$496$	0.854032	−	3.00161i	0.0383472	−	0.134776i
$497$	24.6726	−	49.5493i	1.10672	−	2.22259i
$498$	1.42455	−	1.29865i	0.0638357	−	0.0581939i
$499$	−5.08721	−	6.73656i	−0.227735	−	0.301570i	0.669775	−	0.742564i	$-0.266391\pi$
$499$	−5.08721	−	6.73656i	−0.227735	−	0.301570i	−0.897510	+	0.440994i	$0.854626\pi$
$500$	10.8428	+	14.3582i	0.484905	+	0.642118i
$501$	6.56188	+	13.1780i	0.293163	+	0.588751i
$502$	0.201249	−	2.17183i	0.00898219	−	0.0969333i
$503$	33.9003	+	6.33707i	1.51154	+	0.282556i	0.873263	−	0.487250i	$-0.162000\pi$
$503$	33.9003	+	6.33707i	1.51154	+	0.282556i	0.638278	+	0.769806i	$0.279647\pi$
$504$	−4.67923	+	2.89725i	−0.208429	+	0.129054i
$505$	9.79811	−	12.9748i	0.436010	−	0.577371i
$506$	−1.96591	+	1.21724i	−0.0873952	+	0.0541128i
$507$	0.663239	+	7.15749i	0.0294555	+	0.317875i
$508$	0.462513	−	4.99131i	0.0205207	−	0.221453i
$509$	−18.8429	−	17.1775i	−0.835195	−	0.761381i	0.138227	−	0.990401i	$-0.455860\pi$
$509$	−18.8429	−	17.1775i	−0.835195	−	0.761381i	−0.973422	+	0.229020i	$0.926448\pi$
$510$	2.49368	−	0.966056i	0.110422	−	0.0427777i
$511$	17.9948	−	36.1384i	0.796042	−	1.59867i
$512$	5.56055	+	19.5433i	0.245744	+	0.863701i
$513$	−6.68901	+	4.14166i	−0.295327	+	0.182859i
$514$	−2.05986			−0.0908563
$515$	10.6663	−	1.86102i	0.470014	−	0.0820062i
$516$	−2.88664			−0.127077
$517$	7.27832	−	4.50654i	0.320100	−	0.198198i
$518$	1.95565	+	6.87338i	0.0859261	+	0.301999i
$519$	5.75069	−	11.5489i	0.252427	−	0.506942i
$520$	−5.43131	+	2.10410i	−0.238179	+	0.0922710i
$521$	−21.2260	−	19.3500i	−0.929928	−	0.847741i	0.0586769	−	0.998277i	$-0.481312\pi$
$521$	−21.2260	−	19.3500i	−0.929928	−	0.847741i	−0.988605	+	0.150536i	$0.951900\pi$
$522$	−0.00111289	+	0.0120100i	−4.87097e−5	+	0.000525662i
$523$	1.75672	+	18.9580i	0.0768160	+	0.828977i	0.943773	+	0.330594i	$0.107249\pi$
$523$	1.75672	+	18.9580i	0.0768160	+	0.828977i	−0.866957	+	0.498383i	$0.833927\pi$
$524$	−22.5746	+	13.9776i	−0.986175	+	0.610614i
$525$	10.5409	−	13.9584i	0.460041	−	0.609193i
$526$	−1.87795	+	1.16278i	−0.0818825	+	0.0506995i
$527$	7.20552	+	1.34695i	0.313878	+	0.0586739i
$528$	−1.66981	+	18.0201i	−0.0726690	+	0.784223i
$529$	−9.36980	−	18.8171i	−0.407382	−	0.818134i
$530$	1.86651	+	2.47166i	0.0810760	+	0.107362i
$531$	−6.56193	−	8.68940i	−0.284763	−	0.377088i
$532$	−50.1153	+	45.6862i	−2.17277	+	1.98075i
$533$	5.33290	−	10.7099i	0.230993	−	0.463897i
$534$	0.0900961	−	0.316655i	0.00389884	−	0.0137030i
$535$	0.529756	−	5.71698i	0.0229034	−	0.247167i
$536$	1.34449	−	0.251329i	0.0580733	−	0.0108558i
$537$	0.378769	−	0.760670i	0.0163451	−	0.0328253i
$538$	−1.69683	−	1.05064i	−0.0731557	−	0.0452961i
$539$	−66.5314	+	25.7744i	−2.86571	+	1.11018i
$540$	1.50043	−	1.36782i	0.0645681	−	0.0588616i
$541$	−6.23294	−	12.5174i	−0.267975	−	0.538166i	0.719776	−	0.694207i	$-0.244245\pi$
$541$	−6.23294	−	12.5174i	−0.267975	−	0.538166i	−0.987751	+	0.156041i	$0.950127\pi$
$542$	2.60469	+	2.37449i	0.111881	+	0.101993i
$543$	8.05573	+	4.98789i	0.345704	+	0.214051i
$544$	−26.2584	+	10.1726i	−1.12582	+	0.436145i
$545$	−4.96386	−	1.92301i	−0.212628	−	0.0823726i
$546$	3.81803	+	5.05589i	0.163397	+	0.216372i
$547$	9.92898	+	3.84651i	0.424533	+	0.164465i	0.564024	−	0.825758i	$-0.309253\pi$
$547$	9.92898	+	3.84651i	0.424533	+	0.164465i	−0.139491	+	0.990223i	$0.544547\pi$
$548$	16.3516	+	14.9064i	0.698504	+	0.636771i
$549$	−0.811857	+	2.85338i	−0.0346492	+	0.121779i
$550$	1.73700	+	6.10492i	0.0740659	+	0.260315i
$551$	0.0281240	+	0.303507i	0.00119812	+	0.0129298i
$552$	−1.68033	−	0.314108i	−0.0715196	−	0.0133693i
$553$	−2.63450	−	9.25932i	−0.112031	−	0.393746i
$554$	0.193585	−	0.0361873i	0.00822464	−	0.00153745i
$555$	−2.41005	−	4.84002i	−0.102301	−	0.205448i
$556$	9.15198	+	3.54550i	0.388130	+	0.150363i
$557$	−12.8470	+	11.7116i	−0.544345	+	0.496236i	−0.898514	−	0.438946i	$-0.855352\pi$
$557$	−12.8470	+	11.7116i	−0.544345	+	0.496236i	0.354169	+	0.935182i	$0.384764\pi$
$558$	−0.278599	+	0.0520792i	−0.0117940	+	0.00220469i
$559$	0.628834	+	6.78620i	0.0265969	+	0.287026i
$560$	9.98203	−	13.2183i	0.421818	−	0.558577i
$561$	−42.5088			−1.79472
$562$	−6.05907			−0.255586
$563$	−2.38456	+	3.15767i	−0.100497	+	0.133080i	−0.845487	−	0.533996i	$-0.820690\pi$
$563$	−2.38456	+	3.15767i	−0.100497	+	0.133080i	0.744990	+	0.667076i	$0.232454\pi$
$564$	3.03328	+	0.567018i	0.127724	+	0.0238758i
$565$	0.878382	−	3.08719i	0.0369538	−	0.129879i
$566$	6.57172	+	4.06904i	0.276230	+	0.171034i
$567$	−3.85089	−	2.38437i	−0.161722	−	0.100134i
$568$	−4.06380	+	14.2828i	−0.170513	+	0.599292i
$569$	−40.3631	−	7.54518i	−1.69211	−	0.316310i	−0.752509	−	0.658582i	$-0.771157\pi$
$569$	−40.3631	−	7.54518i	−1.69211	−	0.316310i	−0.939601	+	0.342272i	$0.888804\pi$
$570$	−1.57471	+	2.08525i	−0.0659571	+	0.0873414i
$571$	−13.6704			−0.572090			−0.286045	−	0.958216i	$-0.592341\pi$
$571$	−13.6704			−0.572090			−0.286045	+	0.958216i	$0.592341\pi$
$572$	45.1433			1.88754
$573$	10.8376	−	14.3514i	0.452749	−	0.599537i
$574$	−0.346437	−	3.73865i	−0.0144600	−	0.156048i
$575$	5.34038	−	0.998291i	0.222709	−	0.0416316i
$576$	−4.26183	+	3.88518i	−0.177576	+	0.161882i
$577$	−9.15994	−	3.54858i	−0.381333	−	0.147729i	0.162943	−	0.986636i	$-0.447901\pi$
$577$	−9.15994	−	3.54858i	−0.381333	−	0.147729i	−0.544276	+	0.838906i	$0.683196\pi$
$578$	−6.63734	−	13.3296i	−0.276077	−	0.554437i
$579$	−12.6670	+	2.36787i	−0.526422	+	0.0984054i
$580$	−0.0215265	−	0.0756579i	−0.000893841	−	0.00314152i
$581$	27.5674	+	5.15325i	1.14369	+	0.213793i
$582$	−0.257332	−	2.77705i	−0.0106668	−	0.115113i
$583$	−13.4731	−	47.3530i	−0.557998	−	1.96116i
$584$	−2.96390	+	10.4170i	−0.122647	+	0.431060i
$585$	−3.54247	−	3.22939i	−0.146463	−	0.133519i
$586$	3.41461	+	1.32283i	0.141056	+	0.0546454i
$587$	10.0584	+	13.3194i	0.415154	+	0.549752i	0.956759	−	0.290880i	$-0.0939482\pi$
$587$	10.0584	+	13.3194i	0.415154	+	0.549752i	−0.541606	+	0.840633i	$0.682183\pi$
$588$	−23.9826	−	9.29091i	−0.989026	−	0.383151i
$589$	−6.67884	+	2.58739i	−0.275197	+	0.106612i
$590$	−3.07482	−	1.90385i	−0.126589	−	0.0783803i
$591$	10.8703	+	9.90957i	0.447144	+	0.407625i
$592$	7.74359	+	15.5512i	0.318260	+	0.639152i
$593$	12.4203	−	11.3226i	0.510040	−	0.464963i	−0.377292	−	0.926094i	$-0.623145\pi$
$593$	12.4203	−	11.3226i	0.510040	−	0.464963i	0.887332	+	0.461132i	$0.152556\pi$
$594$	1.53260	−	0.593732i	0.0628833	−	0.0243611i
$595$	33.0796	+	20.4820i	1.35613	+	0.839682i
$596$	−12.2902	+	24.6821i	−0.503428	+	1.01102i
$597$	−10.2781	+	1.92131i	−0.420654	+	0.0786339i
$598$	−0.181571	+	1.95946i	−0.00742499	+	0.0801284i
$599$	−9.46372	+	33.2615i	−0.386677	+	1.35903i	0.487373	+	0.873194i	$0.337955\pi$
$599$	−9.46372	+	33.2615i	−0.386677	+	1.35903i	−0.874050	+	0.485835i	$0.838516\pi$
$600$	−2.09162	+	4.20054i	−0.0853901	+	0.171486i
$601$	4.29582	−	3.91616i	0.175230	−	0.159743i	−0.581329	−	0.813669i	$-0.697467\pi$
$601$	4.29582	−	3.91616i	0.175230	−	0.159743i	0.756559	+	0.653925i	$0.226879\pi$
$602$	1.28892	+	1.70681i	0.0525324	+	0.0695642i
$603$	0.678357	+	0.898290i	0.0276248	+	0.0365812i
$604$	2.49374	+	5.00811i	0.101469	+	0.203777i
$605$	−1.66088	+	17.9238i	−0.0675246	+	0.728706i
$606$	4.66366	+	0.871790i	0.189448	+	0.0354140i
$607$	14.5796	−	9.02732i	0.591769	−	0.366408i	−0.197641	−	0.980274i	$-0.563328\pi$
$607$	14.5796	−	9.02732i	0.591769	−	0.366408i	0.789410	+	0.613867i	$0.210387\pi$
$608$	16.5816	−	21.9576i	0.672474	−	0.890499i
$609$	−0.149195	+	0.0923776i	−0.00604569	+	0.00374333i
$610$	0.0909137	+	0.981115i	0.00368099	+	0.0397242i
$611$	0.672225	−	7.25446i	0.0271953	−	0.293484i
$612$	−11.3240	−	10.3231i	−0.457744	−	0.417288i
$613$	22.5045	−	8.71831i	0.908950	−	0.352129i	0.139044	−	0.990286i	$-0.455597\pi$
$613$	22.5045	−	8.71831i	0.908950	−	0.352129i	0.769906	+	0.638157i	$0.220303\pi$
$614$	−4.18701	+	8.40865i	−0.168974	+	0.339346i
$615$	0.777426	+	2.73237i	0.0313488	+	0.110180i
$616$	24.7037	−	15.2959i	0.995340	−	0.616289i
$617$	−36.0747			−1.45231			−0.726157	−	0.687529i	$-0.758695\pi$
$617$	−36.0747			−1.45231			−0.726157	+	0.687529i	$0.758695\pi$
$618$	1.87350	+	2.54415i	0.0753631	+	0.102341i
$619$	−2.03996			−0.0819929			−0.0409964	−	0.999159i	$-0.513053\pi$
$619$	−2.03996			−0.0819929			−0.0409964	+	0.999159i	$0.513053\pi$
$620$	1.57155	−	0.973062i	0.0631149	−	0.0390791i
$621$	−0.384996	−	1.35312i	−0.0154494	−	0.0542989i
$622$	3.99472	−	8.02249i	0.160174	−	0.321673i
$623$	4.46635	−	1.73027i	0.178940	−	0.0693219i
$624$	11.3821	+	10.3762i	0.455650	+	0.415379i
$625$	0.850953	−	9.18325i	0.0340381	−	0.367330i
$626$	0.745409	+	8.04424i	0.0297925	+	0.321512i
$627$	35.3142	−	21.8656i	1.41031	−	0.873230i
$628$	−13.2938	+	17.6038i	−0.530479	+	0.702468i
$629$	−34.6943	+	21.4818i	−1.38335	+	0.856536i
$630$	−1.47872	−	0.276421i	−0.0589137	−	0.0110129i
$631$	−1.72674	+	18.6345i	−0.0687406	+	0.741829i	0.889702	+	0.456542i	$0.150912\pi$
$631$	−1.72674	+	18.6345i	−0.0687406	+	0.741829i	−0.958442	+	0.285287i	$0.907911\pi$
$632$	1.15118	+	2.31189i	0.0457916	+	0.0919619i
$633$	13.3132	+	17.6295i	0.529153	+	0.700711i
$634$	−1.96091	−	2.59666i	−0.0778775	−	0.103127i
$635$	2.07669	−	1.89315i	0.0824109	−	0.0751274i
$636$	7.91043	−	15.8863i	0.313669	−	0.629932i
$637$	−16.6176	+	58.4047i	−0.658412	+	2.31408i
$638$	0.00587542	−	0.0634058i	0.000232610	−	0.00251026i
$639$	−12.0128	+	2.24559i	−0.475220	+	0.0888341i
$640$	−4.18005	+	8.39467i	−0.165231	+	0.331829i
$641$	27.2376	+	16.8648i	1.07582	+	0.666120i	0.945589	−	0.325364i	$-0.105487\pi$
$641$	27.2376	+	16.8648i	1.07582	+	0.666120i	0.130231	+	0.991484i	$0.458428\pi$
$642$	1.56227	−	0.605227i	0.0616579	−	0.0238864i
$643$	−14.9729	+	13.6496i	−0.590472	+	0.538286i	−0.912834	−	0.408330i	$-0.866111\pi$
$643$	−14.9729	+	13.6496i	−0.590472	+	0.538286i	0.322362	+	0.946616i	$0.395523\pi$
$644$	−5.40517	−	10.8550i	−0.212993	−	0.427748i
$645$	−1.19589	−	1.09020i	−0.0470883	−	0.0429266i
$646$	16.7671	+	10.3818i	0.659693	+	0.408465i
$647$	−19.6390	+	7.60819i	−0.772089	+	0.299109i	−0.714874	−	0.699253i	$-0.753516\pi$
$647$	−19.6390	+	7.60819i	−0.772089	+	0.299109i	−0.0572145	+	0.998362i	$0.518222\pi$
$648$	1.13305	+	0.438945i	0.0445104	+	0.0172434i
$649$	34.6433	+	45.8751i	1.35987	+	1.80076i
$650$	5.03709	+	1.95138i	0.197571	+	0.0765394i
$651$	−3.04729	−	2.77797i	−0.119433	−	0.108877i
$652$	8.09854	−	28.4634i	0.317163	−	1.11471i
$653$	−5.07428	−	17.8342i	−0.198572	−	0.697907i	−0.995578	−	0.0939366i	$-0.970055\pi$
$653$	−5.07428	−	17.8342i	−0.198572	−	0.697907i	0.797006	−	0.603971i	$-0.206416\pi$
$654$	−0.143329	−	1.54676i	−0.00560460	−	0.0604832i
$655$	−14.6313	−	2.73506i	−0.571691	−	0.106868i
$656$	−2.49791	−	8.77923i	−0.0975269	−	0.342771i
$657$	−8.76146	+	1.63780i	−0.341817	+	0.0638967i
$658$	−1.01913	−	2.04669i	−0.0397299	−	0.0797883i
$659$	−2.05854	−	0.797483i	−0.0801894	−	0.0310655i	0.320813	−	0.947143i	$-0.396044\pi$
$659$	−2.05854	−	0.797483i	−0.0801894	−	0.0310655i	−0.401002	+	0.916077i	$0.631338\pi$
$660$	−7.92141	+	7.22132i	−0.308341	+	0.281090i
$661$	−45.1460	+	8.43924i	−1.75597	+	0.328248i	−0.960613	−	0.277888i	$-0.910366\pi$
$661$	−45.1460	+	8.43924i	−1.75597	+	0.328248i	−0.795361	+	0.606137i	$0.792719\pi$
$662$	−0.622848	−	6.72160i	−0.0242077	−	0.261242i
$663$	−21.8019	+	28.8703i	−0.846714	+	1.12123i
$664$	−7.52378			−0.291979
$665$	−38.0165			−1.47421
$666$	0.950816	−	1.25908i	0.0368434	−	0.0487885i
$667$	−0.0535765	−	0.0100152i	−0.00207449	−	0.000387790i
$668$	7.66694	−	26.9465i	0.296643	−	1.04259i
$669$	3.38591	+	2.09647i	0.130907	+	0.0810541i
$670$	0.317868	+	0.196816i	0.0122803	+	0.00760366i
$671$	4.28615	−	15.0643i	0.165465	−	0.581549i
$672$	15.5709	+	2.91071i	0.600661	+	0.112283i
$673$	−17.5086	+	23.1852i	−0.674908	+	0.893722i	−0.998625	−	0.0524316i	$-0.983303\pi$
$673$	−17.5086	+	23.1852i	−0.674908	+	0.893722i	0.323717	+	0.946154i	$0.395068\pi$
$674$	4.66188			0.179569
$675$	−3.86181			−0.148641
$676$	8.24382	−	10.9166i	0.317070	−	0.419869i
$677$	0.631696	+	6.81709i	0.0242781	+	0.262002i	0.999218	+	0.0395347i	$0.0125876\pi$
$677$	0.631696	+	6.81709i	0.0242781	+	0.262002i	−0.974940	+	0.222467i	$0.928589\pi$
$678$	0.920674	−	0.172104i	0.0353583	−	0.00660961i
$679$	29.9859	−	27.3358i	1.15075	−	1.04905i
$680$	−9.73302	−	3.77059i	−0.373244	−	0.144596i
$681$	−6.14395	−	12.3387i	−0.235437	−	0.472821i
$682$	1.47085	−	0.274949i	0.0563216	−	0.0105283i
$683$	−2.24857	−	7.90289i	−0.0860390	−	0.302396i	0.906848	−	0.421458i	$-0.138482\pi$
$683$	−2.24857	−	7.90289i	−0.0860390	−	0.302396i	−0.992887	+	0.119063i	$0.962011\pi$
$684$	14.7174	+	2.75116i	0.562734	+	0.105193i
$685$	1.14449	+	12.3510i	0.0437288	+	0.471909i
$686$	2.51386	+	8.83529i	0.0959795	+	0.337333i
$687$	7.80983	−	27.4487i	0.297963	−	1.04723i
$688$	3.84247	+	3.50287i	0.146493	+	0.133546i
$689$	−39.0703	−	15.1359i	−1.48846	−	0.576633i
$690$	−0.281584	−	0.372877i	−0.0107197	−	0.0141952i
$691$	−2.17563	−	0.842845i	−0.0827650	−	0.0320633i	0.319503	−	0.947585i	$-0.396484\pi$
$691$	−2.17563	−	0.842845i	−0.0827650	−	0.0320633i	−0.402268	+	0.915522i	$0.631778\pi$
$692$	−22.8946	+	8.86941i	−0.870322	+	0.337165i
$693$	20.3306	+	12.5881i	0.772294	+	0.478184i
$694$	5.15343	+	4.69797i	0.195622	+	0.178333i
$695$	2.45251	+	4.92530i	0.0930288	+	0.186827i
$696$	0.0347901	−	0.0317153i	0.00131871	−	0.00120217i
$697$	19.9923	−	7.74504i	0.757261	−	0.293364i
$698$	−4.68342	−	2.89985i	−0.177270	−	0.109761i
$699$	−7.28640	+	14.6331i	−0.275597	+	0.553473i
$700$	−32.7206	+	6.11654i	−1.23672	+	0.231183i
$701$	−0.123824	+	1.33628i	−0.00467678	+	0.0504705i	−0.997753	−	0.0670035i	$-0.978656\pi$
$701$	−0.123824	+	1.33628i	−0.00467678	+	0.0504705i	0.993076	+	0.117474i	$0.0374797\pi$
$702$	0.382798	−	1.34540i	0.0144478	−	0.0507787i
$703$	17.7725	−	35.6921i	0.670304	−	1.34615i
$704$	22.5001	−	20.5115i	0.848004	−	0.773058i
$705$	1.04250	+	1.38049i	0.0392628	+	0.0519923i
$706$	−4.47349	−	5.92386i	−0.168362	−	0.222948i
$707$	30.7675	+	61.7894i	1.15713	+	2.32383i
$708$	−1.91200	+	20.6337i	−0.0718573	+	0.775464i
$709$	19.2094	+	3.59086i	0.721424	+	0.134857i	0.531642	−	0.846969i	$-0.321575\pi$
$709$	19.2094	+	3.59086i	0.721424	+	0.134857i	0.189781	+	0.981826i	$0.439222\pi$
$710$	−3.45101	+	2.13678i	−0.129514	+	0.0801918i
$711$	−1.28087	+	1.69615i	−0.0480364	+	0.0636105i
$712$	−1.09252	+	0.676457i	−0.0409437	+	0.0253513i
$713$	−0.118175	−	1.27531i	−0.00442569	−	0.0477608i
$714$	−1.04756	+	11.3050i	−0.0392041	+	0.423080i
$715$	18.7022	+	17.0493i	0.699424	+	0.637609i
$716$	−1.50795	+	0.584183i	−0.0563548	+	0.0218320i
$717$	0.582921	−	1.17066i	0.0217696	−	0.0437192i
$718$	−0.505845	−	1.77786i	−0.0188780	−	0.0663491i
$719$	−7.88711	+	4.88349i	−0.294139	+	0.182123i	−0.665566	−	0.746339i	$-0.731810\pi$
$719$	−7.88711	+	4.88349i	−0.294139	+	0.182123i	0.371427	+	0.928462i	$0.378869\pi$
$720$	−3.65707			−0.136291
$721$	−13.1120	+	44.0577i	−0.488315	+	1.64079i
$722$	−13.3544			−0.496999
$723$	7.38011	−	4.56957i	0.274469	−	0.169944i
$724$	−4.93456	−	17.3432i	−0.183391	−	0.644554i
$725$	−0.0666904	+	0.133932i	−0.00247682	+	0.00497413i
$726$	−4.89801	+	1.89750i	−0.181782	+	0.0704228i
$727$	−12.8399	−	11.7052i	−0.476207	−	0.434120i	0.399667	−	0.916661i	$-0.369126\pi$
$727$	−12.8399	−	11.7052i	−0.476207	−	0.434120i	−0.875874	+	0.482541i	$0.839714\pi$
$728$	2.28163	−	24.6227i	0.0845629	−	0.912579i
$729$	0.0922684	+	0.995734i	0.00341735	+	0.0368790i
$730$	−2.51697	+	1.55844i	−0.0931572	+	0.0576805i
$731$	−7.36004	+	9.74627i	−0.272221	+	0.360479i
$732$	4.80010	−	2.97210i	0.177417	−	0.109852i
$733$	−41.8038	−	7.81448i	−1.54406	−	0.288634i	−0.658290	−	0.752764i	$-0.728720\pi$
$733$	−41.8038	−	7.81448i	−1.54406	−	0.288634i	−0.885767	+	0.464130i	$0.846367\pi$
$734$	0.318524	−	3.43742i	0.0117569	−	0.126878i
$735$	−6.42675	−	12.9066i	−0.237054	−	0.476069i
$736$	2.96507	+	3.92639i	0.109294	+	0.144729i
$737$	−3.58135	−	4.74247i	−0.131921	−	0.174691i
$738$	−0.612618	+	0.558475i	−0.0225508	+	0.0205578i
$739$	11.4716	−	23.0381i	0.421989	−	0.847469i	−0.577527	−	0.816371i	$-0.695982\pi$
$739$	11.4716	−	23.0381i	0.421989	−	0.847469i	0.999516	−	0.0310971i	$-0.00990012\pi$
$740$	−2.81591	+	9.89689i	−0.103515	+	0.363817i
$741$	3.26162	−	35.1985i	0.119819	−	1.29305i
$742$	−12.9253	+	2.41616i	−0.474503	+	0.0887001i
$743$	1.59118	−	3.19553i	0.0583749	−	0.117233i	−0.864055	−	0.503398i	$-0.832083\pi$
$743$	1.59118	−	3.19553i	0.0583749	−	0.117233i	0.922430	+	0.386165i	$0.126201\pi$
$744$	0.940536	+	0.582355i	0.0344817	+	0.0213502i
$745$	−14.4134	+	5.58379i	−0.528067	+	0.204574i
$746$	−1.57990	+	1.44027i	−0.0578441	+	0.0527319i
$747$	−2.75996	−	5.54275i	−0.100982	−	0.202799i
$748$	59.7841	+	54.5004i	2.18592	+	1.99273i
$749$	20.7241	+	12.8318i	0.757244	+	0.468866i
$750$	−2.74455	+	1.06324i	−0.100217	+	0.0388242i
$751$	12.6353	+	4.89496i	0.461070	+	0.178620i	0.580563	−	0.814215i	$-0.302833\pi$
$751$	12.6353	+	4.89496i	0.461070	+	0.178620i	−0.119492	+	0.992835i	$0.538127\pi$
$752$	−3.34960	−	4.43559i	−0.122147	−	0.161749i
$753$	−6.53299	−	2.53090i	−0.238076	−	0.0922310i
$754$	−0.0400494	−	0.0365099i	−0.00145851	−	0.00132961i
$755$	−0.858298	+	3.01661i	−0.0312367	+	0.109786i
$756$	2.35887	+	8.29058i	0.0857914	+	0.301526i
$757$	−2.03864	−	22.0004i	−0.0740956	−	0.799619i	−0.948990	−	0.315306i	$-0.897893\pi$
$757$	−2.03864	−	22.0004i	−0.0740956	−	0.799619i	0.874895	−	0.484313i	$-0.160931\pi$
$758$	2.33611	+	0.436695i	0.0848514	+	0.0158615i
$759$	2.03256	+	7.14372i	0.0737774	+	0.259301i
$760$	10.0252	−	1.87404i	0.363653	−	0.0679786i
$761$	−0.552009	−	1.10858i	−0.0200103	−	0.0401861i	0.884933	−	0.465719i	$-0.154204\pi$
$761$	−0.552009	−	1.10858i	−0.0200103	−	0.0401861i	−0.904943	+	0.425533i	$0.860087\pi$
$762$	0.764636	+	0.296222i	0.0276998	+	0.0107310i
$763$	16.7015	−	15.2255i	0.604636	−	0.551199i
$764$	−33.6418	+	6.28875i	−1.21712	+	0.227519i
$765$	−0.792596	−	8.55347i	−0.0286564	−	0.309252i
$766$	−5.97572	+	7.91313i	−0.215912	+	0.285913i
$767$	48.9244			1.76656
$768$	8.79740			0.317449
$769$	2.51760	−	3.33384i	0.0907869	−	0.120221i	−0.750357	−	0.661033i	$-0.770118\pi$
$769$	2.51760	−	3.33384i	0.0907869	−	0.120221i	0.841144	+	0.540812i	$0.181883\pi$
$770$	7.80682	+	1.45935i	0.281338	+	0.0525912i
$771$	−1.81071	+	6.36397i	−0.0652110	+	0.229193i
$772$	20.8506	+	12.9102i	0.750430	+	0.464647i
$773$	−28.8673	−	17.8739i	−1.03829	−	0.642879i	−0.102241	−	0.994760i	$-0.532601\pi$
$773$	−28.8673	−	17.8739i	−1.03829	−	0.642879i	−0.936045	+	0.351881i	$0.885542\pi$
$774$	0.129228	−	0.454189i	0.00464500	−	0.0163255i
$775$	−3.45593	−	0.646025i	−0.124141	−	0.0232059i
$776$	−6.55998	+	8.68682i	−0.235490	+	0.311839i
$777$	22.9546			0.823490
$778$	6.07105			0.217658
$779$	−12.6247	+	16.7178i	−0.452327	+	0.598978i
$780$	0.841717	+	9.08358i	0.0301383	+	0.325244i
$781$	63.4210	−	11.8554i	2.26938	−	0.424221i
$782$	−2.60607	+	2.37575i	−0.0931929	+	0.0849566i
$783$	0.0361267	+	0.0139956i	0.00129106	+	0.000500161i
$784$	20.6495	+	41.4697i	0.737481	+	1.48106i
$785$	−12.1559	+	2.27233i	−0.433862	+	0.0811029i
$786$	−1.18865	−	4.17767i	−0.0423977	−	0.149013i
$787$	−45.5094	−	8.50718i	−1.62223	−	0.303248i	−0.707319	−	0.706894i	$-0.750096\pi$
$787$	−45.5094	−	8.50718i	−1.62223	−	0.303248i	−0.914915	+	0.403646i	$0.867743\pi$
$788$	−2.58286	−	27.8735i	−0.0920107	−	0.992953i
$789$	1.94162	+	6.82410i	0.0691236	+	0.242944i
$790$	−0.193188	+	0.678986i	−0.00687333	+	0.0241572i
$791$	10.0703	+	9.18025i	0.358057	+	0.326412i
$792$	−5.98186	−	2.31739i	−0.212556	−	0.0823447i
$793$	−8.03278	−	10.6371i	−0.285252	−	0.377735i
$794$	−5.79068	−	2.24332i	−0.205503	−	0.0796125i
$795$	9.27699	−	3.59392i	0.329021	−	0.127463i
$796$	16.9183	+	10.4754i	0.599655	+	0.371290i
$797$	28.8755	+	26.3235i	1.02282	+	0.932426i	0.997736	−	0.0672592i	$-0.0214255\pi$
$797$	28.8755	+	26.3235i	1.02282	+	0.932426i	0.0250871	+	0.999685i	$0.492014\pi$
$798$	−4.94480	−	9.93050i	−0.175044	−	0.351536i
$799$	9.64838	−	8.79566i	0.341335	−	0.311168i
$800$	12.5941	−	4.87899i	0.445269	−	0.172498i
$801$	−0.899114	−	0.556708i	−0.0317686	−	0.0196703i
$802$	5.10513	−	10.2525i	0.180269	−	0.362028i
$803$	46.2556	−	8.64667i	1.63232	−	0.305134i
$804$	0.197658	−	2.13307i	0.00697086	−	0.0752276i
$805$	1.86035	−	6.53847i	0.0655689	−	0.230451i
$806$	0.567631	−	1.13996i	0.0199940	−	0.0401533i
$807$	−4.73755	+	4.31885i	−0.166770	+	0.152031i
$808$	−11.1596	−	14.7776i	−0.392592	−	0.519876i
$809$	−3.52509	−	4.66797i	−0.123936	−	0.164117i	0.731819	−	0.681499i	$-0.238672\pi$
$809$	−3.52509	−	4.66797i	−0.123936	−	0.164117i	−0.855755	+	0.517382i	$0.826907\pi$
$810$	0.148045	+	0.297314i	0.00520176	+	0.0104465i
$811$	−3.65150	+	39.4060i	−0.128222	+	1.38373i	0.651996	+	0.758223i	$0.273932\pi$
$811$	−3.65150	+	39.4060i	−0.128222	+	1.38373i	−0.780217	+	0.625509i	$0.784891\pi$
$812$	0.328264	+	0.0613632i	0.0115198	+	0.00215343i
$813$	9.62568	−	5.95997i	0.337587	−	0.209025i
$814$	−5.01978	+	6.64726i	−0.175943	+	0.232986i
$815$	14.1049	−	8.73341i	0.494075	−	0.305918i
$816$	2.54665	+	27.4827i	0.0891506	+	0.962088i
$817$	1.10108	−	11.8826i	0.0385220	−	0.415719i
$818$	0.821555	+	0.748946i	0.0287250	+	0.0261863i
$819$	18.9765	−	7.35153i	0.663092	−	0.256883i
$820$	2.40979	−	4.83952i	0.0841537	−	0.169003i
$821$	−7.57896	−	26.6373i	−0.264507	−	0.929647i	−0.974303	−	0.225240i	$-0.927683\pi$
$821$	−7.57896	−	26.6373i	−0.264507	−	0.929647i	0.709796	−	0.704407i	$-0.248787\pi$
$822$	−3.07742	+	1.90546i	−0.107338	+	0.0664606i
$823$	−21.5828			−0.752328			−0.376164	−	0.926553i	$-0.622757\pi$
$823$	−21.5828			−0.752328			−0.376164	+	0.926553i	$0.622757\pi$
$824$	1.28588	−	12.2647i	0.0447957	−	0.427262i
$825$	20.3882			0.709825
$826$	13.0540	−	8.08270i	0.454207	−	0.281233i
$827$	−13.4453	−	47.2553i	−0.467538	−	1.64323i	−0.733829	−	0.679334i	$-0.762269\pi$
$827$	−13.4453	−	47.2553i	−0.467538	−	1.64323i	0.266291	−	0.963893i	$-0.414202\pi$
$828$	−1.19338	+	2.39662i	−0.0414727	+	0.0832884i
$829$	1.56733	−	0.607186i	0.0544356	−	0.0210885i	−0.333870	−	0.942619i	$-0.608355\pi$
$829$	1.56733	−	0.607186i	0.0544356	−	0.0210885i	0.388306	+	0.921531i	$0.373061\pi$
$830$	−1.51980	−	1.38548i	−0.0527530	−	0.0480907i
$831$	0.0583684	−	0.629895i	0.00202478	−	0.0218508i
$832$	−2.39083	−	25.8011i	−0.0828870	−	0.894493i
$833$	−92.5176	+	57.2845i	−3.20554	+	1.98479i
$834$	−0.967568	+	1.28127i	−0.0335041	+	0.0443666i
$835$	13.3532	−	8.26797i	0.462108	−	0.286125i
$836$	−77.6996	−	14.5246i	−2.68730	−	0.502343i
$837$	−0.0840012	+	0.906517i	−0.00290351	+	0.0313338i
$838$	2.59575	+	5.21296i	0.0896686	+	0.180079i
$839$	−29.7134	−	39.3469i	−1.02582	−	1.35841i	−0.931855	−	0.362832i	$-0.881810\pi$
$839$	−29.7134	−	39.3469i	−1.02582	−	1.35841i	−0.0939667	−	0.995575i	$-0.529955\pi$
$840$	3.53839	+	4.68559i	0.122086	+	0.161668i
$841$	−21.4301	+	19.5362i	−0.738971	+	0.673661i
$842$	0.996408	−	2.00106i	0.0343385	−	0.0689609i
$843$	−5.32619	+	18.7196i	−0.183444	+	0.644738i
$844$	3.87917	−	41.8629i	0.133527	−	1.44098i
$845$	7.53819	−	1.40913i	0.259322	−	0.0484756i
$846$	−0.225008	+	0.451878i	−0.00773595	+	0.0155359i
$847$	−64.9741	−	40.2303i	−2.23254	−	1.38233i
$848$	−29.8074	+	11.5475i	−1.02359	+	0.396541i
$849$	18.3482	−	16.7266i	0.629709	−	0.574056i
$850$	4.31486	+	8.66541i	0.147999	+	0.297221i
$851$	5.26899	+	4.80332i	0.180619	+	0.164656i
$852$	19.7738	+	12.2434i	0.677440	+	0.419453i
$853$	44.8870	−	17.3893i	1.53690	−	0.595398i	0.563827	−	0.825893i	$-0.309329\pi$
$853$	44.8870	−	17.3893i	1.53690	−	0.595398i	0.973074	+	0.230495i	$0.0740344\pi$
$854$	−3.90064	−	1.51112i	−0.133477	−	0.0517094i
$855$	5.05818	+	6.69811i	0.172986	+	0.229071i
$856$	−6.09767	−	2.36225i	−0.208414	−	0.0807400i
$857$	−13.1438	−	11.9822i	−0.448985	−	0.409304i	0.417367	−	0.908738i	$-0.362953\pi$
$857$	−13.1438	−	11.9822i	−0.448985	−	0.409304i	−0.866352	+	0.499434i	$0.833541\pi$
$858$	−2.02096	+	7.10293i	−0.0689944	+	0.242490i
$859$	10.6849	+	37.5536i	0.364565	+	1.28131i	0.899686	+	0.436538i	$0.143795\pi$
$859$	10.6849	+	37.5536i	0.364565	+	1.28131i	−0.535121	+	0.844776i	$0.679734\pi$
$860$	0.284154	+	3.06650i	0.00968955	+	0.104567i
$861$	−11.8552	−	2.21612i	−0.404023	−	0.0755251i
$862$	−1.75184	−	6.15709i	−0.0596681	−	0.209711i
$863$	−24.5117	+	4.58204i	−0.834389	+	0.155974i	−0.583573	−	0.812060i	$-0.698346\pi$
$863$	−24.5117	+	4.58204i	−0.834389	+	0.155974i	−0.250816	+	0.968035i	$0.580699\pi$
$864$	−1.55891	−	3.13071i	−0.0530352	−	0.106509i
$865$	−12.8346	−	4.97217i	−0.436391	−	0.169059i
$866$	3.24570	−	2.95885i	0.110293	−	0.100546i
$867$	−47.0165	+	8.78891i	−1.59677	+	0.298487i
$868$	0.724060	+	7.81385i	0.0245762	+	0.265219i
$869$	6.76228	−	8.95471i	0.229395	−	0.303768i
$870$	0.0128678			0.000436261
$871$	−5.05770			−0.171373
$872$	−3.65378	+	4.83838i	−0.123733	+	0.163848i
$873$	−8.80598	−	1.64612i	−0.298037	−	0.0557128i
$874$	0.942961	−	3.31416i	0.0318961	−	0.112103i
$875$	−36.4076	−	22.5426i	−1.23080	−	0.762079i
$876$	14.4219	+	8.92965i	0.487270	+	0.301705i
$877$	−8.88807	+	31.2383i	−0.300129	+	1.05484i	0.654258	+	0.756271i	$0.272981\pi$
$877$	−8.88807	+	31.2383i	−0.300129	+	1.05484i	−0.954387	+	0.298572i	$0.903490\pi$
$878$	1.26311	+	0.236115i	0.0426278	+	0.00796851i
$879$	7.08849	−	9.38668i	0.239089	−	0.316605i
$880$	19.3073			0.650848
$881$	37.5699			1.26576			0.632882	−	0.774248i	$-0.281872\pi$
$881$	37.5699			1.26576			0.632882	+	0.774248i	$0.281872\pi$
$882$	2.53549	−	3.35754i	0.0853745	−	0.113054i
$883$	−0.506772	−	5.46894i	−0.0170542	−	0.184044i	−1.00000		0.000148680i	$-0.999953\pi$
$883$	−0.506772	−	5.46894i	−0.0170542	−	0.184044i	0.982946	−	0.183896i	$-0.0588709\pi$
$884$	67.6766	−	12.6509i	2.27621	−	0.425497i
$885$	−8.58490	+	7.82617i	−0.288578	+	0.263074i
$886$	1.87278	+	0.725518i	0.0629172	+	0.0243743i
$887$	10.5361	+	21.1593i	0.353768	+	0.710461i	0.998546	−	0.0539087i	$-0.0171680\pi$
$887$	10.5361	+	21.1593i	0.353768	+	0.710461i	−0.644778	+	0.764370i	$0.723050\pi$
$888$	−6.05329	+	1.13156i	−0.203135	+	0.0379725i
$889$	3.26484	+	11.4747i	0.109499	+	0.384849i
$890$	−0.345255	−	0.0645393i	−0.0115730	−	0.00216336i
$891$	−0.487125	−	5.25692i	−0.0163193	−	0.176113i
$892$	−2.07405	−	7.28953i	−0.0694443	−	0.244071i
$893$	−3.49109	+	12.2699i	−0.116825	+	0.410597i
$894$	−3.33333	−	3.03873i	−0.111483	−	0.101630i
$895$	−0.845353	−	0.327491i	−0.0282570	−	0.0109468i
$896$	−23.9927	−	31.7715i	−0.801540	−	1.06141i
$897$	5.89419	+	2.28342i	0.196801	+	0.0762413i
$898$	2.30593	−	0.893322i	0.0769498	−	0.0298105i
$899$	0.0299886	+	0.0185681i	0.00100017	+	0.000619282i
$900$	5.43122	+	4.95121i	0.181041	+	0.165040i
$901$	−33.4683	−	67.2135i	−1.11499	−	2.23921i
$902$	3.23428	−	2.94844i	0.107690	−	0.0981722i
$903$	6.40623	−	2.48179i	0.213186	−	0.0825887i
$904$	−3.10815	−	1.92448i	−0.103375	−	0.0640074i
$905$	4.50570	−	9.04867i	0.149775	−	0.300788i
$906$	−0.899624	+	0.168169i	−0.0298880	+	0.00558704i
$907$	−4.89786	+	52.8564i	−0.162631	+	1.75507i	0.389240	+	0.921137i	$0.372738\pi$
$907$	−4.89786	+	52.8564i	−0.162631	+	1.75507i	−0.551870	+	0.833930i	$0.686086\pi$
$908$	−7.17862	+	25.2302i	−0.238231	+	0.837295i
$909$	6.79298	−	13.6421i	0.225309	−	0.452481i
$910$	4.99508	−	4.55362i	0.165585	−	0.150951i
$911$	14.7342	+	19.5112i	0.488164	+	0.646434i	0.973714	−	0.227775i	$-0.0731451\pi$
$911$	14.7342	+	19.5112i	0.488164	+	0.646434i	−0.485549	+	0.874209i	$0.661380\pi$
$912$	−16.2522	−	21.5214i	−0.538163	−	0.712643i
$913$	14.5711	+	29.2626i	0.482231	+	0.968451i
$914$	−0.409015	+	4.41398i	−0.0135290	+	0.146001i
$915$	3.11109	+	0.581564i	0.102850	+	0.0192259i
$916$	−46.1756	+	28.5907i	−1.52568	+	0.944664i
$917$	38.0819	−	50.4286i	1.25757	−	1.66530i
$918$	2.13121	−	1.31959i	0.0703404	−	0.0435529i
$919$	0.0538087	+	0.580688i	0.00177498	+	0.0191551i	0.996576	−	0.0826865i	$-0.0263500\pi$
$919$	0.0538087	+	0.580688i	0.00177498	+	0.0191551i	−0.994801	+	0.101842i	$0.967526\pi$
$920$	−0.168273	+	1.81595i	−0.00554779	+	0.0598701i
$921$	22.2981	+	20.3274i	0.734749	+	0.669812i
$922$	6.49256	−	2.51523i	0.213821	−	0.0828347i
$923$	24.4755	−	49.1535i	0.805622	−	1.61791i
$924$	−12.4535	−	43.7696i	−0.409691	−	1.43992i
$925$	16.6402	−	10.3032i	0.547125	−	0.338766i
$926$	0.0495203			0.00162734
$927$	9.50709	−	3.55179i	0.312254	−	0.116656i
$928$	−0.135498			−0.00444795
$929$	−12.5371	+	7.76267i	−0.411330	+	0.254685i	−0.716463	−	0.697625i	$-0.754240\pi$
$929$	−12.5371	+	7.76267i	−0.411330	+	0.254685i	0.305133	+	0.952310i	$0.401299\pi$
$930$	0.0827488	+	0.290832i	0.00271344	+	0.00953676i
$931$	47.3931	−	95.1782i	1.55325	−	3.11934i
$932$	29.0086	−	11.2380i	0.950207	−	0.368112i
$933$	−21.2741	−	19.3939i	−0.696483	−	0.634928i
$934$	−0.152819	+	1.64918i	−0.00500039	+	0.0539628i
$935$	4.18446	+	45.1575i	0.136847	+	1.47681i
$936$	−4.64185	+	2.87411i	−0.151724	+	0.0939432i
$937$	20.4714	−	27.1085i	0.668771	−	0.885595i	−0.329514	−	0.944151i	$-0.606885\pi$
$937$	20.4714	−	27.1085i	0.668771	−	0.885595i	0.998284	+	0.0585554i	$0.0186494\pi$
$938$	−1.34949	+	0.835571i	−0.0440625	+	0.0272824i
$939$	25.5081	+	4.76829i	0.832425	+	0.155607i
$940$	0.303761	−	3.27810i	0.00990758	−	0.106920i
$941$	13.2443	+	26.5982i	0.431752	+	0.867075i	0.999051	+	0.0435629i	$0.0138709\pi$
$941$	13.2443	+	26.5982i	0.431752	+	0.867075i	−0.567299	+	0.823512i	$0.692011\pi$
$942$	−2.17468	−	2.87975i	−0.0708550	−	0.0938272i
$943$	−2.25751	−	2.98942i	−0.0735146	−	0.0973490i
$944$	27.5837	−	25.1459i	0.897773	−	0.818428i
$945$	−2.15387	+	4.32555i	−0.0700654	+	0.140710i
$946$	−0.682251	+	2.39786i	−0.0221819	+	0.0779612i
$947$	−4.74657	+	51.2236i	−0.154243	+	1.66454i	0.469513	+	0.882926i	$0.344429\pi$
$947$	−4.74657	+	51.2236i	−0.154243	+	1.66454i	−0.623756	+	0.781619i	$0.714394\pi$
$948$	3.97603	−	0.743250i	0.129136	−	0.0241396i
$949$	17.8510	−	35.8497i	0.579469	−	1.16373i
$950$	−8.04188	−	4.97932i	−0.260913	−	0.161551i
$951$	−9.74616	+	3.77568i	−0.316041	+	0.122435i
$952$	32.7480	−	29.8538i	1.06137	−	0.967566i
$953$	−2.22728	−	4.47297i	−0.0721485	−	0.144894i	0.856153	−	0.516723i	$-0.172848\pi$
$953$	−2.22728	−	4.47297i	−0.0721485	−	0.144894i	−0.928301	+	0.371829i	$0.878731\pi$
$954$	2.14545	+	1.95583i	0.0694614	+	0.0633225i
$955$	−16.3124	−	10.1002i	−0.527858	−	0.326836i
$956$	−2.32072	+	0.899052i	−0.0750575	+	0.0290774i
$957$	−0.190729	−	0.0738888i	−0.00616539	−	0.00238848i
$958$	−4.90264	−	6.49215i	−0.158397	−	0.209752i
$959$	−49.1043	−	19.0231i	−1.58566	−	0.614289i
$960$	4.54679	+	4.14494i	0.146747	+	0.133777i
$961$	8.25673	−	29.0194i	0.266346	−	0.936110i
$962$	1.94002	+	6.81847i	0.0625488	+	0.219836i
$963$	−0.496556	−	5.35869i	−0.0160013	−	0.172681i
$964$	−16.2380	−	3.03540i	−0.522990	−	0.0977638i
$965$	3.76232	+	13.2232i	0.121113	+	0.425670i
$966$	1.94993	−	0.364505i	0.0627379	−	0.0117277i
$967$	5.39525	+	10.8351i	0.173500	+	0.348434i	0.964796	−	0.262998i	$-0.0847113\pi$
$967$	5.39525	+	10.8351i	0.173500	+	0.348434i	−0.791297	+	0.611432i	$0.790594\pi$
$968$	19.1173	+	7.40610i	0.614454	+	0.238041i
$969$	46.8137	−	42.6763i	1.50387	−	1.37096i
$970$	−2.92476	+	0.546733i	−0.0939085	+	0.0175545i
$971$	5.07645	+	54.7836i	0.162911	+	1.75809i	0.549181	+	0.835704i	$0.314940\pi$
$971$	5.07645	+	54.7836i	0.162911	+	1.75809i	−0.386270	+	0.922386i	$0.626237\pi$
$972$	1.14686	−	1.51869i	0.0367856	−	0.0487120i
$973$	−23.3590			−0.748854
$974$	−7.86276			−0.251939
$975$	10.4567	−	13.8469i	0.334881	−	0.443454i
$976$	−9.99610	−	1.86859i	−0.319967	−	0.0598122i
$977$	6.98937	−	24.5651i	0.223610	−	0.785906i	−0.766088	−	0.642735i	$-0.777799\pi$
$977$	6.98937	−	24.5651i	0.223610	−	0.785906i	0.989698	−	0.143171i	$-0.0457299\pi$
$978$	4.11594	+	2.54848i	0.131613	+	0.0814914i
$979$	4.74682	+	2.93911i	0.151709	+	0.0939342i
$980$	−7.50904	+	26.3915i	−0.239868	+	0.843047i
$981$	−4.90475	−	0.916857i	−0.156597	−	0.0292730i
$982$	3.61024	−	4.78073i	0.115207	−	0.152559i
$983$	−7.95916			−0.253858			−0.126929	−	0.991912i	$-0.540512\pi$
$983$	−7.95916			−0.253858			−0.126929	+	0.991912i	$0.540512\pi$
$984$	3.23555			0.103145
$985$	9.45700	−	12.5231i	0.301325	−	0.399019i
$986$	−0.00896070	−	0.0967014i	−0.000285367	−	0.00307960i
$987$	−7.21916	+	1.34949i	−0.229788	+	0.0429549i
$988$	−49.7150	+	45.3212i	−1.58164	+	1.44186i
$989$	1.98981	+	0.770856i	0.0632722	+	0.0245118i
$990$	−0.781593	−	1.56965i	−0.0248407	−	0.0498868i
$991$	−10.1773	+	1.90247i	−0.323293	+	0.0604340i	−0.342895	−	0.939374i	$-0.611407\pi$
$991$	−10.1773	+	1.90247i	−0.323293	+	0.0604340i	0.0196012	+	0.999808i	$0.493760\pi$
$992$	−0.871345	−	3.06246i	−0.0276652	−	0.0972331i
$993$	−21.3140	−	3.98428i	−0.676381	−	0.126437i
$994$	−1.58999	−	17.1587i	−0.0504313	−	0.544240i
$995$	3.05277	+	10.7294i	0.0967794	+	0.340144i
$996$	−3.22475	+	11.3338i	−0.102180	+	0.359126i
$997$	26.6664	+	24.3097i	0.844534	+	0.769894i	0.975152	−	0.221538i	$-0.0711078\pi$
$997$	26.6664	+	24.3097i	0.844534	+	0.769894i	−0.130618	+	0.991433i	$0.541696\pi$
$998$	−2.45057	−	0.949355i	−0.0775714	−	0.0300513i
$999$	−3.05416	−	4.04436i	−0.0966293	−	0.127958i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	309.2.i.b.100.6	yes	160
3.2	odd	2		927.2.u.c.100.5		160
103.34	even	17	inner	309.2.i.b.34.6	✓	160
309.137	odd	34		927.2.u.c.343.5		160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
309.2.i.b.34.6	✓	160	103.34	even	17	inner
309.2.i.b.100.6	yes	160	1.1	even	1	trivial
927.2.u.c.100.5		160	3.2	odd	2
927.2.u.c.343.5		160	309.137	odd	34

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:	\( N \)	\(=\)	\( 309 = 3 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	309.i (of order \(17\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.264688 - 0.163888i) q^{2} +(-0.273663 - 0.961826i) q^{3} +(-0.848276 + 1.70357i) q^{4} +(-0.994818 + 0.385395i) q^{5} +(-0.230067 - 0.209734i) q^{6} +(0.417912 - 4.50998i) q^{7} +(0.112115 + 1.20992i) q^{8} +(-0.850217 + 0.526432i) q^{9} +O(q^{10})\)	\(q+(0.264688 - 0.163888i) q^{2} +(-0.273663 - 0.961826i) q^{3} +(-0.848276 + 1.70357i) q^{4} +(-0.994818 + 0.385395i) q^{5} +(-0.230067 - 0.209734i) q^{6} +(0.417912 - 4.50998i) q^{7} +(0.112115 + 1.20992i) q^{8} +(-0.850217 + 0.526432i) q^{9} +(-0.200155 + 0.265049i) q^{10} +(4.48867 - 2.77927i) q^{11} +(1.87068 + 0.349690i) q^{12} +(0.414573 - 4.47396i) q^{13} +(-0.628517 - 1.26223i) q^{14} +(0.642928 + 0.851374i) q^{15} +(-2.06576 - 2.73551i) q^{16} +(5.95033 - 5.42444i) q^{17} +(-0.138767 + 0.278681i) q^{18} +(-2.15302 + 7.56708i) q^{19} +(0.187335 - 2.02166i) q^{20} +(-4.45218 + 0.832258i) q^{21} +(0.732610 - 1.47128i) q^{22} +(-1.19611 - 0.740598i) q^{23} +(1.13305 - 0.438945i) q^{24} +(-2.85391 + 2.60168i) q^{25} +(-0.623496 - 1.25215i) q^{26} +(0.739009 + 0.673696i) q^{27} +(7.32856 + 4.53765i) q^{28} +(0.0361267 - 0.0139956i) q^{29} +(0.309706 + 0.119981i) q^{30} +(0.548639 + 0.726516i) q^{31} +(-3.26120 - 1.26339i) q^{32} +(-3.90155 - 3.55673i) q^{33} +(0.685982 - 2.41097i) q^{34} +(1.32238 + 4.64768i) q^{35} +(-0.175594 - 1.89496i) q^{36} +(-4.98172 - 0.931244i) q^{37} +(0.670275 + 2.35577i) q^{38} +(-4.41662 + 0.825609i) q^{39} +(-0.577831 - 1.16044i) q^{40} +(2.48297 + 0.961906i) q^{41} +(-1.04204 + 0.949949i) q^{42} +(-1.49100 + 0.278716i) q^{43} +(0.927038 + 10.0043i) q^{44} +(0.642928 - 0.851374i) q^{45} -0.437971 q^{46} +1.62149 q^{47} +(-2.06576 + 2.73551i) q^{48} +(-13.2845 - 2.48330i) q^{49} +(-0.329012 + 1.15636i) q^{50} +(-6.84575 - 4.23871i) q^{51} +(7.27002 + 4.50140i) q^{52} +(2.55199 - 8.96932i) q^{53} +(0.306018 + 0.0572047i) q^{54} +(-3.39430 + 4.49478i) q^{55} +5.50357 q^{56} +7.86742 q^{57} +(0.00726862 - 0.00962521i) q^{58} +(1.00469 + 10.8423i) q^{59} +(-1.99575 + 0.373071i) q^{60} +(2.19237 - 1.99861i) q^{61} +(0.264286 + 0.102385i) q^{62} +(2.01888 + 4.05447i) q^{63} +(5.66877 - 1.05968i) q^{64} +(1.31181 + 4.61055i) q^{65} +(-1.61560 - 0.302008i) q^{66} +(-0.103862 - 1.12085i) q^{67} +(4.19338 + 14.7382i) q^{68} +(-0.384996 + 1.35312i) q^{69} +(1.11172 + 1.01346i) q^{70} +(11.3957 + 4.41470i) q^{71} +(-0.732262 - 0.969672i) q^{72} +(8.31133 + 3.21983i) q^{73} +(-1.47122 + 0.569955i) q^{74} +(3.28337 + 2.03298i) q^{75} +(-11.0647 - 10.0868i) q^{76} +(-10.6586 - 21.4053i) q^{77} +(-1.03372 + 0.942361i) q^{78} +(1.98193 - 0.767802i) q^{79} +(3.10930 + 1.92520i) q^{80} +(0.445738 - 0.895163i) q^{81} +(0.814858 - 0.152323i) q^{82} +(-0.571315 + 6.16548i) q^{83} +(2.35887 - 8.29058i) q^{84} +(-3.82895 + 7.68956i) q^{85} +(-0.348971 + 0.318130i) q^{86} +(-0.0233479 - 0.0309176i) q^{87} +(3.86593 + 5.11933i) q^{88} +(0.471373 + 0.946645i) q^{89} +(0.0306454 - 0.330717i) q^{90} +(-20.0042 - 3.73944i) q^{91} +(2.27629 - 1.40942i) q^{92} +(0.548639 - 0.726516i) q^{93} +(0.429189 - 0.265742i) q^{94} +(-0.774449 - 8.35764i) q^{95} +(-0.322696 + 3.48245i) q^{96} +(6.62042 + 6.03531i) q^{97} +(-3.92324 + 1.51987i) q^{98} +(-2.35325 + 4.72596i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - q^{2} - 10 q^{3} - 17 q^{4} - 4 q^{5} - q^{6} - 12 q^{7} + 36 q^{8} - 10 q^{9}+O(q^{10}) \) 160 * q - q^2 - 10 * q^3 - 17 * q^4 - 4 * q^5 - q^6 - 12 * q^7 + 36 * q^8 - 10 * q^9	\( 160 q - q^{2} - 10 q^{3} - 17 q^{4} - 4 q^{5} - q^{6} - 12 q^{7} + 36 q^{8} - 10 q^{9} + 12 q^{10} + q^{11} + 17 q^{12} - 18 q^{13} + 31 q^{14} - 4 q^{15} - 39 q^{16} - 14 q^{17} - q^{18} - 11 q^{19} + 31 q^{20} + 5 q^{21} + 3 q^{23} - 15 q^{24} - 8 q^{25} - 33 q^{26} - 10 q^{27} - 2 q^{28} - 28 q^{29} + 12 q^{30} - 20 q^{31} - 46 q^{32} + 18 q^{33} + 5 q^{34} - 3 q^{35} - 17 q^{36} - 34 q^{37} - 14 q^{38} - 18 q^{39} - 56 q^{40} + 40 q^{41} + 14 q^{42} - 42 q^{43} - 26 q^{44} - 4 q^{45} + 112 q^{46} - 40 q^{47} - 39 q^{48} + 30 q^{49} - 10 q^{50} + 3 q^{51} - 58 q^{52} - 48 q^{53} - q^{54} - 64 q^{55} + 86 q^{56} + 6 q^{57} - 36 q^{58} + 76 q^{59} - 20 q^{60} - 28 q^{61} - 66 q^{62} - 12 q^{63} + 88 q^{64} - 14 q^{65} - 34 q^{66} - 84 q^{67} - 107 q^{68} - 14 q^{69} + 8 q^{70} + 41 q^{71} - 15 q^{72} - 32 q^{73} + 3 q^{74} - 42 q^{75} - 68 q^{76} + 93 q^{77} + 18 q^{78} - 100 q^{79} - 168 q^{80} - 10 q^{81} + 99 q^{82} - 28 q^{83} + 151 q^{84} + 15 q^{85} + 64 q^{86} - 11 q^{87} - 25 q^{88} - 19 q^{89} - 5 q^{90} + 122 q^{91} - 78 q^{92} - 20 q^{93} + 138 q^{94} - 15 q^{95} + 56 q^{96} + 161 q^{97} + 65 q^{98} + q^{99}+O(q^{100}) \) 160 * q - q^2 - 10 * q^3 - 17 * q^4 - 4 * q^5 - q^6 - 12 * q^7 + 36 * q^8 - 10 * q^9 + 12 * q^10 + q^11 + 17 * q^12 - 18 * q^13 + 31 * q^14 - 4 * q^15 - 39 * q^16 - 14 * q^17 - q^18 - 11 * q^19 + 31 * q^20 + 5 * q^21 + 3 * q^23 - 15 * q^24 - 8 * q^25 - 33 * q^26 - 10 * q^27 - 2 * q^28 - 28 * q^29 + 12 * q^30 - 20 * q^31 - 46 * q^32 + 18 * q^33 + 5 * q^34 - 3 * q^35 - 17 * q^36 - 34 * q^37 - 14 * q^38 - 18 * q^39 - 56 * q^40 + 40 * q^41 + 14 * q^42 - 42 * q^43 - 26 * q^44 - 4 * q^45 + 112 * q^46 - 40 * q^47 - 39 * q^48 + 30 * q^49 - 10 * q^50 + 3 * q^51 - 58 * q^52 - 48 * q^53 - q^54 - 64 * q^55 + 86 * q^56 + 6 * q^57 - 36 * q^58 + 76 * q^59 - 20 * q^60 - 28 * q^61 - 66 * q^62 - 12 * q^63 + 88 * q^64 - 14 * q^65 - 34 * q^66 - 84 * q^67 - 107 * q^68 - 14 * q^69 + 8 * q^70 + 41 * q^71 - 15 * q^72 - 32 * q^73 + 3 * q^74 - 42 * q^75 - 68 * q^76 + 93 * q^77 + 18 * q^78 - 100 * q^79 - 168 * q^80 - 10 * q^81 + 99 * q^82 - 28 * q^83 + 151 * q^84 + 15 * q^85 + 64 * q^86 - 11 * q^87 - 25 * q^88 - 19 * q^89 - 5 * q^90 + 122 * q^91 - 78 * q^92 - 20 * q^93 + 138 * q^94 - 15 * q^95 + 56 * q^96 + 161 * q^97 + 65 * q^98 + q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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