LMFDB - Embedded newform 288.2.bf.a.59.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(11,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 15, 4]))

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

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

chi := DirichletCharacter("288.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bf (of order $24$, degree $8$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			59.3
Character	$\chi$	$=$	288.59
Dual form			288.2.bf.a.83.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36716 - 0.361752i) q^{2} +(-1.45571 - 0.938565i) q^{3} +(1.73827 + 0.989147i) q^{4} +(-0.644713 - 0.840206i) q^{5} +(1.65067 + 1.80978i) q^{6} +(3.32016 + 0.889635i) q^{7} +(-2.01868 - 1.98115i) q^{8} +(1.23819 + 2.73256i) q^{9} +O(q^{10})$	\(q+(-1.36716 - 0.361752i) q^{2} +(-1.45571 - 0.938565i) q^{3} +(1.73827 + 0.989147i) q^{4} +(-0.644713 - 0.840206i) q^{5} +(1.65067 + 1.80978i) q^{6} +(3.32016 + 0.889635i) q^{7} +(-2.01868 - 1.98115i) q^{8} +(1.23819 + 2.73256i) q^{9} +(0.577482 + 1.38193i) q^{10} +(-0.793379 + 0.104450i) q^{11} +(-1.60204 - 3.07139i) q^{12} +(0.0380530 - 0.289041i) q^{13} +(-4.21738 - 2.41735i) q^{14} +(0.149927 + 1.82820i) q^{15} +(2.04318 + 3.43881i) q^{16} +7.22314 q^{17} +(-0.704301 - 4.18377i) q^{18} +(-2.42399 - 5.85203i) q^{19} +(-0.289598 - 2.09822i) q^{20} +(-3.99822 - 4.41124i) q^{21} +(1.12246 + 0.144206i) q^{22} +(-1.46506 - 5.46767i) q^{23} +(1.07917 + 4.77864i) q^{24} +(1.00380 - 3.74625i) q^{25} +(-0.156586 + 0.381401i) q^{26} +(0.762238 - 5.13994i) q^{27} +(4.89137 + 4.83056i) q^{28} +(1.49960 + 1.15069i) q^{29} +(0.456380 - 2.55369i) q^{30} +(-5.11628 - 2.95388i) q^{31} +(-1.54936 - 5.44054i) q^{32} +(1.25296 + 0.592589i) q^{33} +(-9.87521 - 2.61298i) q^{34} +(-1.39308 - 3.36318i) q^{35} +(-0.550593 + 5.97468i) q^{36} +(10.4592 + 4.33233i) q^{37} +(1.19701 + 8.87756i) q^{38} +(-0.326678 + 0.385045i) q^{39} +(-0.363107 + 2.97338i) q^{40} +(-3.64338 + 0.976242i) q^{41} +(3.87045 + 7.47725i) q^{42} +(0.0508411 + 0.386176i) q^{43} +(-1.48243 - 0.603206i) q^{44} +(1.49764 - 2.80205i) q^{45} +(0.0250348 + 8.00518i) q^{46} +(6.09046 - 3.51633i) q^{47} +(0.253276 - 6.92357i) q^{48} +(4.16987 + 2.40747i) q^{49} +(-2.72757 + 4.75860i) q^{50} +(-10.5148 - 6.77939i) q^{51} +(0.352051 - 0.464792i) q^{52} +(-1.60078 - 0.663065i) q^{53} +(-2.90149 + 6.75140i) q^{54} +(0.599262 + 0.599262i) q^{55} +(-4.93984 - 8.37362i) q^{56} +(-1.96388 + 10.7939i) q^{57} +(-1.63394 - 2.11566i) q^{58} +(-2.49022 + 1.91082i) q^{59} +(-1.54775 + 3.32621i) q^{60} +(4.52830 - 5.90139i) q^{61} +(5.92622 + 5.88927i) q^{62} +(1.68001 + 10.1741i) q^{63} +(0.150102 + 7.99859i) q^{64} +(-0.267388 + 0.154376i) q^{65} +(-1.49864 - 1.26343i) q^{66} +(-1.18845 + 9.02718i) q^{67} +(12.5558 + 7.14475i) q^{68} +(-2.99906 + 9.33439i) q^{69} +(0.687926 + 5.10197i) q^{70} +(11.2269 + 11.2269i) q^{71} +(2.91410 - 7.96919i) q^{72} +(-1.93726 + 1.93726i) q^{73} +(-12.7322 - 9.70663i) q^{74} +(-4.97734 + 4.51132i) q^{75} +(1.57496 - 12.5701i) q^{76} +(-2.72707 - 0.359026i) q^{77} +(0.585913 - 0.408244i) q^{78} +(-2.05062 - 3.55178i) q^{79} +(1.57205 - 3.93374i) q^{80} +(-5.93377 + 6.76686i) q^{81} +(5.33426 - 0.0166820i) q^{82} +(4.03862 + 3.09894i) q^{83} +(-2.58662 - 11.6228i) q^{84} +(-4.65685 - 6.06893i) q^{85} +(0.0701918 - 0.546358i) q^{86} +(-1.10300 - 3.08254i) q^{87} +(1.80851 + 1.36095i) q^{88} +(-6.64871 + 6.64871i) q^{89} +(-3.06116 + 3.28909i) q^{90} +(0.383484 - 0.925811i) q^{91} +(2.86166 - 10.9534i) q^{92} +(4.67541 + 9.10196i) q^{93} +(-9.59869 + 2.60416i) q^{94} +(-3.35413 + 5.80953i) q^{95} +(-2.85088 + 9.37403i) q^{96} +(-5.82283 - 10.0854i) q^{97} +(-4.82998 - 4.79986i) q^{98} +(-1.26777 - 2.03863i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.36716	−	0.361752i	−0.966731	−	0.255797i
$2$	−1.36716	−	0.361752i	−0.966731	−	0.255797i
$3$	−1.45571	−	0.938565i	−0.840455	−	0.541881i
$3$	−1.45571	−	0.938565i	−0.840455	−	0.541881i
$4$	1.73827	+	0.989147i	0.869136	+	0.494574i
$5$	−0.644713	−	0.840206i	−0.288324	−	0.375752i	0.626625	−	0.779321i	$-0.284436\pi$
$5$	−0.644713	−	0.840206i	−0.288324	−	0.375752i	−0.914949	+	0.403570i	$0.867769\pi$
$6$	1.65067	+	1.80978i	0.673882	+	0.738839i
$7$	3.32016	+	0.889635i	1.25490	+	0.336251i	0.824229	−	0.566256i	$-0.191609\pi$
$7$	3.32016	+	0.889635i	1.25490	+	0.336251i	0.430675	+	0.902507i	$0.358275\pi$
$8$	−2.01868	−	1.98115i	−0.713710	−	0.700442i
$9$	1.23819	+	2.73256i	0.412730	+	0.910853i
$10$	0.577482	+	1.38193i	0.182616	+	0.437003i
$11$	−0.793379	+	0.104450i	−0.239213	+	0.0314930i	−0.249179	−	0.968457i	$-0.580161\pi$
$11$	−0.793379	+	0.104450i	−0.239213	+	0.0314930i	0.00996645	+	0.999950i	$0.496828\pi$
$12$	−1.60204	−	3.07139i	−0.462470	−	0.886635i
$13$	0.0380530	−	0.289041i	0.0105540	−	0.0801656i	−0.985357	−	0.170502i	$-0.945461\pi$
$13$	0.0380530	−	0.289041i	0.0105540	−	0.0801656i	0.995911	+	0.0903367i	$0.0287943\pi$
$14$	−4.21738	−	2.41735i	−1.12714	−	0.646065i
$15$	0.149927	+	1.82820i	0.0387111	+	0.472040i
$16$	2.04318	+	3.43881i	0.510794	+	0.859703i
$17$	7.22314			1.75187			0.875934	−	0.482431i	$-0.160246\pi$
$17$	7.22314			1.75187			0.875934	+	0.482431i	$0.160246\pi$
$18$	−0.704301	−	4.18377i	−0.166005	−	0.986125i
$19$	−2.42399	−	5.85203i	−0.556101	−	1.34255i	−0.912830	−	0.408339i	$-0.866108\pi$
$19$	−2.42399	−	5.85203i	−0.556101	−	1.34255i	0.356729	−	0.934208i	$-0.383892\pi$
$20$	−0.289598	−	2.09822i	−0.0647562	−	0.469177i
$21$	−3.99822	−	4.41124i	−0.872483	−	0.962612i
$22$	1.12246	+	0.144206i	0.239310	+	0.0307447i
$23$	−1.46506	−	5.46767i	−0.305485	−	1.14009i	−0.932527	−	0.361101i	$-0.882401\pi$
$23$	−1.46506	−	5.46767i	−0.305485	−	1.14009i	0.627041	−	0.778986i	$-0.284266\pi$
$24$	1.07917	+	4.77864i	0.220285	+	0.975436i
$25$	1.00380	−	3.74625i	0.200761	−	0.749249i
$26$	−0.156586	+	0.381401i	−0.0307090	+	0.0747989i
$27$	0.762238	−	5.13994i	0.146693	−	0.989182i
$28$	4.89137	+	4.83056i	0.924382	+	0.912890i
$29$	1.49960	+	1.15069i	0.278469	+	0.213677i	0.738548	−	0.674201i	$-0.235512\pi$
$29$	1.49960	+	1.15069i	0.278469	+	0.213677i	−0.460078	+	0.887878i	$0.652179\pi$
$30$	0.456380	−	2.55369i	0.0833232	−	0.466238i
$31$	−5.11628	−	2.95388i	−0.918911	−	0.530533i	−0.0356234	−	0.999365i	$-0.511342\pi$
$31$	−5.11628	−	2.95388i	−0.918911	−	0.530533i	−0.883287	+	0.468832i	$0.844675\pi$
$32$	−1.54936	−	5.44054i	−0.273891	−	0.961761i
$33$	1.25296	+	0.592589i	0.218113	+	0.103156i
$34$	−9.87521	−	2.61298i	−1.69358	−	0.448123i
$35$	−1.39308	−	3.36318i	−0.235473	−	0.568482i
$36$	−0.550593	+	5.97468i	−0.0917655	+	0.995781i
$37$	10.4592	+	4.33233i	1.71948	+	0.712231i	0.999840	+	0.0178804i	$0.00569182\pi$
$37$	10.4592	+	4.33233i	1.71948	+	0.712231i	0.719637	+	0.694350i	$0.244308\pi$
$38$	1.19701	+	8.87756i	0.194180	+	1.44013i
$39$	−0.326678	+	0.385045i	−0.0523104	+	0.0616566i
$40$	−0.363107	+	2.97338i	−0.0574123	+	0.470132i
$41$	−3.64338	+	0.976242i	−0.569001	+	0.152463i	−0.531838	−	0.846846i	$-0.678499\pi$
$41$	−3.64338	+	0.976242i	−0.569001	+	0.152463i	−0.0371627	+	0.999309i	$0.511832\pi$
$42$	3.87045	+	7.47725i	0.597223	+	1.15377i
$43$	0.0508411	+	0.386176i	0.00775319	+	0.0588913i	0.994884	−	0.101023i	$-0.0322116\pi$
$43$	0.0508411	+	0.386176i	0.00775319	+	0.0588913i	−0.987131	+	0.159914i	$0.948878\pi$
$44$	−1.48243	−	0.603206i	−0.223484	−	0.0909367i
$45$	1.49764	−	2.80205i	0.223254	−	0.417705i
$46$	0.0250348	+	8.00518i	0.00369118	+	1.18030i
$47$	6.09046	−	3.51633i	0.888385	−	0.512909i	0.0149710	−	0.999888i	$-0.495234\pi$
$47$	6.09046	−	3.51633i	0.888385	−	0.512909i	0.873414	+	0.486979i	$0.161901\pi$
$48$	0.253276	−	6.92357i	0.0365573	−	0.999332i
$49$	4.16987	+	2.40747i	0.595695	+	0.343925i
$50$	−2.72757	+	4.75860i	−0.385737	+	0.672968i
$51$	−10.5148	−	6.77939i	−1.47237	−	0.949304i
$52$	0.352051	−	0.464792i	0.0488207	−	0.0644551i
$53$	−1.60078	−	0.663065i	−0.219884	−	0.0910790i	0.270022	−	0.962854i	$-0.412969\pi$
$53$	−1.60078	−	0.663065i	−0.219884	−	0.0910790i	−0.489906	+	0.871775i	$0.662969\pi$
$54$	−2.90149	+	6.75140i	−0.394842	+	0.918749i
$55$	0.599262	+	0.599262i	0.0808044	+	0.0808044i
$56$	−4.93984	−	8.37362i	−0.660113	−	1.11897i
$57$	−1.96388	+	10.7939i	−0.260122	+	1.42969i
$58$	−1.63394	−	2.11566i	−0.214547	−	0.277800i
$59$	−2.49022	+	1.91082i	−0.324200	+	0.248767i	−0.758019	−	0.652233i	$-0.773832\pi$
$59$	−2.49022	+	1.91082i	−0.324200	+	0.248767i	0.433819	+	0.901000i	$0.357166\pi$
$60$	−1.54775	+	3.32621i	−0.199813	+	0.429412i
$61$	4.52830	−	5.90139i	0.579789	−	0.755595i	−0.407729	−	0.913103i	$-0.633679\pi$
$61$	4.52830	−	5.90139i	0.579789	−	0.755595i	0.987518	+	0.157508i	$0.0503459\pi$
$62$	5.92622	+	5.88927i	0.752630	+	0.747937i
$63$	1.68001	+	10.1741i	0.211662	+	1.28181i
$64$	0.150102	+	7.99859i	0.0187628	+	0.999824i
$65$	−0.267388	+	0.154376i	−0.0331653	+	0.0191480i
$66$	−1.49864	−	1.26343i	−0.184470	−	0.155517i
$67$	−1.18845	+	9.02718i	−0.145192	+	1.10285i	0.751355	+	0.659898i	$0.229400\pi$
$67$	−1.18845	+	9.02718i	−0.145192	+	1.10285i	−0.896548	+	0.442947i	$0.853933\pi$
$68$	12.5558	+	7.14475i	1.52261	+	0.866428i
$69$	−2.99906	+	9.33439i	−0.361045	+	1.12373i
$70$	0.687926	+	5.10197i	0.0822228	+	0.609802i
$71$	11.2269	+	11.2269i	1.33238	+	1.33238i	0.903234	+	0.429149i	$0.141187\pi$
$71$	11.2269	+	11.2269i	1.33238	+	1.33238i	0.429149	+	0.903234i	$0.358813\pi$
$72$	2.91410	−	7.96919i	0.343430	−	0.939178i
$73$	−1.93726	+	1.93726i	−0.226739	+	0.226739i	−0.811329	−	0.584590i	$-0.801255\pi$
$73$	−1.93726	+	1.93726i	−0.226739	+	0.226739i	0.584590	+	0.811329i	$0.301255\pi$
$74$	−12.7322	−	9.70663i	−1.48008	−	1.12837i
$75$	−4.97734	+	4.51132i	−0.574734	+	0.520922i
$76$	1.57496	−	12.5701i	0.180661	−	1.44189i
$77$	−2.72707	−	0.359026i	−0.310779	−	0.0409148i
$78$	0.585913	−	0.408244i	0.0663416	−	0.0462245i
$79$	−2.05062	−	3.55178i	−0.230713	−	0.399607i	0.727305	−	0.686314i	$-0.240773\pi$
$79$	−2.05062	−	3.55178i	−0.230713	−	0.399607i	−0.958018	+	0.286707i	$0.907439\pi$
$80$	1.57205	−	3.93374i	0.175761	−	0.439805i
$81$	−5.93377	+	6.76686i	−0.659308	+	0.751873i
$82$	5.33426	−	0.0166820i	0.589070	−	0.00184222i
$83$	4.03862	+	3.09894i	0.443296	+	0.340153i	0.806169	−	0.591686i	$-0.201537\pi$
$83$	4.03862	+	3.09894i	0.443296	+	0.340153i	−0.362873	+	0.931839i	$0.618204\pi$
$84$	−2.58662	−	11.6228i	−0.282224	−	1.26815i
$85$	−4.65685	−	6.06893i	−0.505106	−	0.658267i
$86$	0.0701918	−	0.546358i	0.00756898	−	0.0589153i
$87$	−1.10300	−	3.08254i	−0.118253	−	0.330483i
$88$	1.80851	+	1.36095i	0.192788	+	0.145078i
$89$	−6.64871	+	6.64871i	−0.704762	+	0.704762i	−0.965429	−	0.260667i	$-0.916058\pi$
$89$	−6.64871	+	6.64871i	−0.704762	+	0.704762i	0.260667	+	0.965429i	$0.416058\pi$
$90$	−3.06116	+	3.28909i	−0.322675	+	0.346701i
$91$	0.383484	−	0.925811i	0.0402000	−	0.0970514i
$92$	2.86166	−	10.9534i	0.298349	−	1.14198i
$93$	4.67541	+	9.10196i	0.484817	+	0.943830i
$94$	−9.59869	+	2.60416i	−0.990029	+	0.268599i
$95$	−3.35413	+	5.80953i	−0.344127	+	0.596045i
$96$	−2.85088	+	9.37403i	−0.290967	+	0.956733i
$97$	−5.82283	−	10.0854i	−0.591219	−	1.02402i	−0.994069	−	0.108755i	$-0.965313\pi$
$97$	−5.82283	−	10.0854i	−0.591219	−	1.02402i	0.402849	−	0.915266i	$-0.368020\pi$
$98$	−4.82998	−	4.79986i	−0.487902	−	0.484860i
$99$	−1.26777	−	2.03863i	−0.127416	−	0.204890i
$100$	5.45047	−	5.51908i	0.545047	−	0.551908i
$101$	0.967359	−	0.127355i	0.0962559	−	0.0126723i	−0.0822444	−	0.996612i	$-0.526209\pi$
$101$	0.967359	−	0.127355i	0.0962559	−	0.0126723i	0.178500	+	0.983940i	$0.442875\pi$
$102$	11.9230	+	13.0723i	1.18055	+	1.29435i
$103$	0.209223	+	0.780830i	0.0206153	+	0.0769375i	0.975467	−	0.220145i	$-0.0706530\pi$
$103$	0.209223	+	0.780830i	0.0206153	+	0.0769375i	−0.954852	+	0.297082i	$0.903986\pi$
$104$	−0.649450	+	0.508092i	−0.0636838	+	0.0498225i
$105$	−1.12865	+	6.20332i	−0.110145	+	0.605382i
$106$	1.94866	+	1.48560i	0.189271	+	0.144295i
$107$	2.40160	−	5.79798i	0.232172	−	0.560512i	−0.764261	−	0.644907i	$-0.776896\pi$
$107$	2.40160	−	5.79798i	0.232172	−	0.560512i	0.996432	+	0.0843955i	$0.0268959\pi$
$108$	6.40914	−	8.18065i	0.616719	−	0.787183i
$109$	7.60001	−	3.14803i	0.727948	−	0.301526i	0.0122398	−	0.999925i	$-0.496104\pi$
$109$	7.60001	−	3.14803i	0.727948	−	0.301526i	0.715709	+	0.698399i	$0.246104\pi$
$110$	−0.602505	−	1.03607i	−0.0574466	−	0.0987857i
$111$	−11.1594	−	16.1232i	−1.05920	−	1.53035i
$112$	3.72439	+	13.2351i	0.351922	+	1.25060i
$113$	4.54970	−	7.88031i	0.428000	−	0.741317i	−0.568695	−	0.822548i	$-0.692552\pi$
$113$	4.54970	−	7.88031i	0.428000	−	0.741317i	0.996695	+	0.0812307i	$0.0258850\pi$
$114$	6.58967	−	14.0466i	0.617179	−	1.31559i
$115$	−3.64943	+	4.75602i	−0.340311	+	0.443502i
$116$	1.46852	+	3.48353i	0.136349	+	0.323438i
$117$	0.836940	−	0.253906i	0.0773751	−	0.0234736i
$118$	4.09578	−	1.71156i	0.377048	−	0.157561i
$119$	23.9820	+	6.42596i	2.19843	+	0.589067i
$120$	3.31929	−	3.98758i	0.303008	−	0.364014i
$121$	−10.0066	+	2.68127i	−0.909695	+	0.243752i
$122$	−8.32576	+	6.43005i	−0.753779	+	0.582149i
$123$	6.21998	+	1.99843i	0.560837	+	0.180192i
$124$	−5.97165	−	10.1954i	−0.536270	−	0.915575i
$125$	−8.68699	+	3.59827i	−0.776988	+	0.321839i
$126$	1.38364	−	14.5174i	0.123264	−	1.29331i
$127$		−	15.0604i		−	1.33639i	−0.743986	−	0.668195i	$-0.767067\pi$
$127$		−	15.0604i		−	1.33639i	0.743986	−	0.668195i	$-0.232933\pi$
$128$	2.68829	−	10.9897i	0.237613	−	0.971360i
$129$	0.288442	−	0.609879i	0.0253959	−	0.0536968i
$130$	0.421408	−	0.114330i	0.0369600	−	0.0100274i
$131$	5.37138	+	0.707156i	0.469300	+	0.0617845i	0.361468	−	0.932385i	$-0.382276\pi$
$131$	5.37138	+	0.707156i	0.469300	+	0.0617845i	0.107832	+	0.994169i	$0.465609\pi$
$132$	1.59184	+	2.26945i	0.138551	+	0.197530i
$133$	−2.84187	−	21.5862i	−0.246422	−	1.87176i
$134$	4.89040	−	11.9117i	0.422466	−	1.02901i
$135$	−4.81004	+	2.67335i	−0.413982	+	0.230085i
$136$	−14.5812	−	14.3101i	−1.25033	−	1.22708i
$137$	−5.10207	+	19.0412i	−0.435900	+	1.62680i	0.303005	+	0.952989i	$0.402010\pi$
$137$	−5.10207	+	19.0412i	−0.435900	+	1.62680i	−0.738904	+	0.673810i	$0.764656\pi$
$138$	7.47694	−	11.6767i	0.636479	−	0.993989i
$139$	−4.63766	+	3.55860i	−0.393362	+	0.301837i	−0.786438	−	0.617669i	$-0.788077\pi$
$139$	−4.63766	+	3.55860i	−0.393362	+	0.301837i	0.393077	+	0.919506i	$0.371411\pi$
$140$	0.905138	−	7.22408i	0.0764982	−	0.610546i
$141$	−12.1663	−	0.597535i	−1.02458	−	0.0503215i
$142$	−11.2876	−	19.4103i	−0.947236	−	1.62887i
$143$			0.233294i			0.0195090i
$144$	−6.86692	+	9.84101i	−0.572243	+	0.820084i
$145$		−	2.00184i		−	0.166244i
$146$	3.34935	−	1.94774i	0.277194	−	0.161196i
$147$	−3.81055	−	7.41828i	−0.314289	−	0.611849i
$148$	13.8956	+	17.8764i	1.14221	+	1.46943i
$149$	5.54916	−	4.25802i	0.454605	−	0.348830i	−0.355938	−	0.934509i	$-0.615839\pi$
$149$	5.54916	−	4.25802i	0.454605	−	0.348830i	0.810543	+	0.585679i	$0.199172\pi$
$150$	8.43682	−	4.36714i	0.688863	−	0.356576i
$151$	−4.11501	+	15.3574i	−0.334875	+	1.24977i	0.569131	+	0.822247i	$0.307280\pi$
$151$	−4.11501	+	15.3574i	−0.334875	+	1.24977i	−0.904005	+	0.427522i	$0.859387\pi$
$152$	−6.70049	+	16.6156i	−0.543481	+	1.34771i
$153$	8.94362	+	19.7377i	0.723049	+	1.59570i
$154$	3.59848	+	1.47737i	0.289973	+	0.119050i
$155$	0.816658	+	6.20314i	0.0655956	+	0.498248i
$156$	−0.948722	+	0.346181i	−0.0759586	+	0.0277166i
$157$	15.3282	+	2.01799i	1.22332	+	0.161053i	0.714386	−	0.699752i	$-0.246706\pi$
$157$	15.3282	+	2.01799i	1.22332	+	0.161053i	0.508935	+	0.860805i	$0.330040\pi$
$158$	1.51867	+	5.59769i	0.120819	+	0.445328i
$159$	1.70795	+	2.46767i	0.135449	+	0.195699i
$160$	−3.57228	+	4.80937i	−0.282414	+	0.380214i
$161$		−	19.4569i		−	1.53342i
$162$	10.5604	−	7.10485i	0.829700	−	0.558210i
$163$	−9.87294	+	4.08951i	−0.773309	+	0.320315i	−0.734212	−	0.678921i	$-0.762448\pi$
$163$	−9.87294	+	4.08951i	−0.773309	+	0.320315i	−0.0390968	+	0.999235i	$0.512448\pi$
$164$	−7.29884	−	1.90687i	−0.569944	−	0.148902i
$165$	−0.309906	−	1.43480i	−0.0241261	−	0.111699i
$166$	−4.40041	−	5.69774i	−0.341538	−	0.442230i
$167$	1.92836	−	0.516702i	0.149221	−	0.0399836i	−0.183435	−	0.983032i	$-0.558722\pi$
$167$	1.92836	−	0.516702i	0.149221	−	0.0399836i	0.332656	+	0.943048i	$0.392055\pi$
$168$	−0.668219	+	16.8259i	−0.0515542	+	1.29815i
$169$	12.4749	+	3.34265i	0.959611	+	0.257127i
$170$	4.17123	+	9.98184i	0.319919	+	0.765572i
$171$	12.9897	−	13.8696i	0.993344	−	1.06064i
$172$	−0.293610	+	0.721568i	−0.0223875	+	0.0550191i
$173$	2.59989	−	3.38824i	0.197666	−	0.257603i	−0.683995	−	0.729487i	$-0.739759\pi$
$173$	2.59989	−	3.38824i	0.197666	−	0.257603i	0.881661	+	0.471883i	$0.156426\pi$
$174$	0.392860	+	4.61335i	0.0297827	+	0.349737i
$175$	6.66559	−	11.5451i	0.503871	−	0.872730i
$176$	−1.98020	−	2.51487i	−0.149263	−	0.189566i
$177$	5.41847	−	0.444359i	0.407277	−	0.0334000i
$178$	11.4951	−	6.68469i	0.861591	−	0.501039i
$179$	−23.6871	+	9.81153i	−1.77046	+	0.733348i	−0.775701	+	0.631101i	$0.782603\pi$
$179$	−23.6871	+	9.81153i	−1.77046	+	0.733348i	−0.994759	+	0.102247i	$0.967397\pi$
$180$	5.37494	−	3.38934i	0.400624	−	0.252627i
$181$	−1.28076	+	3.09203i	−0.0951983	+	0.229829i	−0.964304	−	0.264797i	$-0.914695\pi$
$181$	−1.28076	+	3.09203i	−0.0951983	+	0.229829i	0.869106	+	0.494626i	$0.164695\pi$
$182$	−0.859199	+	1.12701i	−0.0636880	+	0.0835395i
$183$	−12.1307	+	4.34062i	−0.896729	+	0.320868i
$184$	−7.87478	+	13.9399i	−0.580537	+	1.02767i
$185$	−3.10311	−	11.5810i	−0.228145	−	0.851450i
$186$	−3.09940	−	14.1352i	−0.227259	−	1.03644i
$187$	−5.73069	+	0.754459i	−0.419069	+	0.0551715i
$188$	14.0650	−	0.0879728i	1.02580	−	0.00641608i
$189$	7.10343	−	16.3873i	0.516699	−	1.19200i
$190$	6.68725	−	6.72921i	0.485144	−	0.488188i
$191$	1.27910	+	2.21547i	0.0925528	+	0.160306i	0.908585	−	0.417701i	$-0.137164\pi$
$191$	1.27910	+	2.21547i	0.0925528	+	0.160306i	−0.816032	+	0.578007i	$0.803831\pi$
$192$	7.28869	−	11.7845i	0.526016	−	0.850475i
$193$	−10.9751	+	19.0095i	−0.790008	+	1.36833i	0.135952	+	0.990715i	$0.456591\pi$
$193$	−10.9751	+	19.0095i	−0.790008	+	1.36833i	−0.925961	+	0.377619i	$0.876743\pi$
$194$	4.31234	+	15.8949i	0.309608	+	1.14119i
$195$	0.534131	+	0.0262334i	0.0382499	+	0.00187861i
$196$	4.86701	+	8.30945i	0.347644	+	0.593532i
$197$	−8.14431	+	19.6621i	−0.580258	+	1.40087i	0.312322	+	0.949976i	$0.398893\pi$
$197$	−8.14431	+	19.6621i	−0.580258	+	1.40087i	−0.892579	+	0.450890i	$0.851107\pi$
$198$	0.995774	+	3.24576i	0.0707666	+	0.230666i
$199$	−6.72491	+	6.72491i	−0.476716	+	0.476716i	−0.904080	−	0.427364i	$-0.859442\pi$
$199$	−6.72491	+	6.72491i	−0.476716	+	0.476716i	0.427364	+	0.904080i	$0.359442\pi$
$200$	−9.44822	+	5.57377i	−0.668090	+	0.394125i
$201$	10.2026	−	12.0255i	0.719638	−	0.848215i
$202$	−1.36861	−	0.175828i	−0.0962950	−	0.0123712i
$203$	3.95524	+	5.15457i	0.277603	+	0.361780i
$204$	−11.5718	−	22.1851i	−0.810186	−	1.55327i
$205$	3.16918	+	2.43180i	0.221345	+	0.169844i
$206$	−0.00357519	−	1.14321i	−0.000249095	−	0.0796512i
$207$	13.1267	−	10.7734i	0.912369	−	0.748801i
$208$	1.07171	−	0.459705i	0.0743096	−	0.0318748i
$209$	2.53439	+	4.38969i	0.175307	+	0.303641i
$210$	3.78711	−	8.07265i	0.261335	−	0.557066i
$211$	−17.7881	−	2.34185i	−1.22458	−	0.161220i	−0.509632	−	0.860393i	$-0.670218\pi$
$211$	−17.7881	−	2.34185i	−1.22458	−	0.161220i	−0.714953	+	0.699173i	$0.753552\pi$
$212$	−2.12672	−	2.73600i	−0.146064	−	0.187909i
$213$	−5.80592	−	26.8802i	−0.397815	−	1.84180i
$214$	−5.38081	+	7.05800i	−0.367825	+	0.482475i
$215$	0.291690	−	0.291690i	0.0198931	−	0.0198931i
$216$	−11.7217	+	8.86577i	−0.797560	+	0.603239i
$217$	−14.3590	−	14.3590i	−0.974753	−	0.974753i
$218$	−11.5293	+	1.55455i	−0.780859	+	0.105287i
$219$	4.63833	−	1.00184i	0.313429	−	0.0676983i
$220$	0.448922	+	1.63444i	0.0302663	+	0.110194i
$221$	0.274862	−	2.08778i	0.0184892	−	0.140440i
$222$	9.42406	+	26.0800i	0.632501	+	1.75038i
$223$	1.41945	−	0.819522i	0.0950537	−	0.0548793i	−0.451720	−	0.892160i	$-0.649189\pi$
$223$	1.41945	−	0.819522i	0.0950537	−	0.0548793i	0.546773	+	0.837281i	$0.315856\pi$
$224$	−0.304029	−	19.4419i	−0.0203138	−	1.29901i
$225$	11.4797	−	1.89561i	0.765316	−	0.126374i
$226$	−9.07090	+	9.12781i	−0.603387	+	0.607173i
$227$	4.75274	−	6.19389i	0.315450	−	0.411103i	−0.608537	−	0.793525i	$-0.708243\pi$
$227$	4.75274	−	6.19389i	0.315450	−	0.411103i	0.923988	+	0.382423i	$0.124910\pi$
$228$	−14.0905	+	16.8202i	−0.933169	+	1.11395i
$229$	8.90978	−	6.83671i	0.588775	−	0.451783i	−0.270912	−	0.962604i	$-0.587325\pi$
$229$	8.90978	−	6.83671i	0.588775	−	0.451783i	0.859687	+	0.510821i	$0.170659\pi$
$230$	6.70986	−	5.18208i	0.442435	−	0.341696i
$231$	3.63286	+	3.08217i	0.239025	+	0.202792i
$232$	−0.747533	−	5.29380i	−0.0490779	−	0.347555i
$233$	−1.79721	−	1.79721i	−0.117739	−	0.117739i	0.645782	−	0.763522i	$-0.276531\pi$
$233$	−1.79721	−	1.79721i	−0.117739	−	0.117739i	−0.763522	+	0.645782i	$0.776531\pi$
$234$	−1.23608	+	0.0443668i	−0.0808053	+	0.00290035i
$235$	−6.88104	−	2.85022i	−0.448870	−	0.185928i
$236$	−6.21877	+	0.858319i	−0.404807	+	0.0558718i
$237$	−0.348466	+	7.09502i	−0.0226353	+	0.460871i
$238$	−30.4627	−	17.4609i	−1.97460	−	1.13182i
$239$	11.0440	+	6.37627i	0.714378	+	0.412446i	0.812680	−	0.582710i	$-0.198008\pi$
$239$	11.0440	+	6.37627i	0.714378	+	0.412446i	−0.0983019	+	0.995157i	$0.531341\pi$
$240$	−5.98052	+	4.25091i	−0.386041	+	0.274395i
$241$	−16.6374	+	9.60560i	−1.07171	+	0.618751i	−0.928648	−	0.370963i	$-0.879028\pi$
$241$	−16.6374	+	9.60560i	−1.07171	+	0.618751i	−0.143061	+	0.989714i	$0.545694\pi$
$242$	14.6507	−	0.0458174i	0.941781	−	0.00294526i
$243$	14.9890	−	4.28136i	0.961544	−	0.274650i
$244$	13.7087	−	5.77907i	0.877613	−	0.369967i
$245$	−0.665592	−	5.05568i	−0.0425231	−	0.322995i
$246$	−7.78080	−	4.98227i	−0.496086	−	0.317658i
$247$	−1.78372	+	0.477946i	−0.113495	+	0.0304110i
$248$	4.47602	+	16.0990i	0.284228	+	1.02229i
$249$	−2.97051	−	8.30167i	−0.188248	−	0.526097i
$250$	13.1782	−	1.77689i	0.833463	−	0.112380i
$251$	−2.96907	−	1.22983i	−0.187406	−	0.0776262i	0.287007	−	0.957929i	$-0.407340\pi$
$251$	−2.96907	−	1.22983i	−0.187406	−	0.0776262i	−0.474413	+	0.880302i	$0.657340\pi$
$252$	−7.14335	+	19.3471i	−0.449989	+	1.21875i
$253$	1.73345	+	4.18491i	0.108981	+	0.263103i
$254$	−5.44811	+	20.5900i	−0.341845	+	1.29193i
$255$	1.08295	+	13.2054i	0.0678167	+	0.826952i
$256$	−7.65087	+	14.0522i	−0.478179	+	0.878262i
$257$	−20.1839	−	11.6532i	−1.25904	−	0.726906i	−0.286151	−	0.958185i	$-0.592376\pi$
$257$	−20.1839	−	11.6532i	−1.25904	−	0.726906i	−0.972888	+	0.231279i	$0.925709\pi$
$258$	−0.614971	+	0.729460i	−0.0382865	+	0.0454142i
$259$	30.8720	+	23.6889i	1.91829	+	1.47196i
$260$	−0.617493	+	0.00386224i	−0.0382953	+	0.000239526i
$261$	−1.28752	+	5.52252i	−0.0796958	+	0.341836i
$262$	−7.08774	−	2.90990i	−0.437882	−	0.179774i
$263$	−3.08101	+	11.4985i	−0.189983	+	0.709026i	0.803526	+	0.595270i	$0.202955\pi$
$263$	−3.08101	+	11.4985i	−0.189983	+	0.709026i	−0.993509	+	0.113756i	$0.963712\pi$
$264$	−1.35532	−	3.67855i	−0.0834144	−	0.226399i
$265$	0.474933	+	1.77247i	0.0291749	+	0.108882i
$266$	−3.92353	+	30.5399i	−0.240567	+	1.87252i
$267$	15.9188	−	3.43835i	0.974218	−	0.210424i
$268$	−10.9951	+	14.5161i	−0.671630	+	0.886714i
$269$	4.79391	+	11.5735i	0.292290	+	0.705651i	1.00000		0.000852873i	$-0.000271478\pi$
$269$	4.79391	+	11.5735i	0.292290	+	0.705651i	−0.707710	+	0.706503i	$0.750271\pi$
$270$	7.54319	−	1.91487i	0.459064	−	0.116535i
$271$	7.51244			0.456348			0.228174	−	0.973620i	$-0.426724\pi$
$271$	7.51244			0.456348			0.228174	+	0.973620i	$0.426724\pi$
$272$	14.7581	+	24.8390i	0.894844	+	1.50609i
$273$	−1.42718	+	0.987790i	−0.0863766	+	0.0597837i
$274$	13.8636	−	24.1867i	0.837528	−	1.46117i
$275$	−0.405100	+	3.07704i	−0.0244285	+	0.185553i
$276$	−14.4463	+	13.2592i	−0.869563	+	0.798110i
$277$	−25.1197	+	3.30708i	−1.50930	+	0.198703i	−0.839304	−	0.543663i	$-0.817037\pi$
$277$	−25.1197	+	3.30708i	−1.50930	+	0.198703i	−0.669995	+	0.742366i	$0.733704\pi$
$278$	7.62778	−	3.18751i	0.457484	−	0.191174i
$279$	1.73674	−	17.6380i	0.103976	−	1.05596i
$280$	−3.85080	+	9.54906i	−0.230129	+	0.570666i
$281$	−24.4236	−	6.54427i	−1.45699	−	0.390399i	−0.558539	−	0.829478i	$-0.688638\pi$
$281$	−24.4236	−	6.54427i	−1.45699	−	0.390399i	−0.898448	+	0.439079i	$0.855305\pi$
$282$	16.4171	+	5.21809i	0.977624	+	0.310733i
$283$	18.1396	+	23.6399i	1.07829	+	1.40525i	0.907556	+	0.419931i	$0.137946\pi$
$283$	18.1396	+	23.6399i	1.07829	+	1.40525i	0.170730	+	0.985318i	$0.445388\pi$
$284$	8.41031	+	30.6203i	0.499060	+	1.81698i
$285$	10.3353	−	5.30892i	0.612209	−	0.314473i
$286$	0.0843945	−	0.318951i	0.00499035	−	0.0188600i
$287$	−12.9651			−0.765308
$288$	12.9482	−	10.9701i	0.762980	−	0.646422i
$289$	35.1737			2.06904
$290$	−0.724168	+	2.73684i	−0.0425246	+	0.160713i
$291$	−0.989483	+	20.1466i	−0.0580045	+	1.18101i
$292$	−5.28371	+	1.45125i	−0.309206	+	0.0849277i
$293$	2.21378	+	2.88505i	0.129330	+	0.168547i	0.853530	−	0.521044i	$-0.174457\pi$
$293$	2.21378	+	2.88505i	0.129330	+	0.168547i	−0.724200	+	0.689591i	$0.757791\pi$
$294$	2.52607	+	11.5205i	0.147323	+	0.671887i
$295$	3.21096	+	0.860374i	0.186949	+	0.0500929i
$296$	−12.5307	−	29.4667i	−0.728331	−	1.71272i
$297$	−0.0678754	+	4.15754i	−0.00393853	+	0.241245i
$298$	−9.12695	+	3.81399i	−0.528710	+	0.220938i
$299$	−1.63613	+	0.215401i	−0.0946199	+	0.0124569i
$300$	−13.1143	+	2.91857i	−0.757156	+	0.168504i
$301$	−0.174755	+	1.32740i	−0.0100727	+	0.0765100i
$302$	11.1815	−	19.5075i	0.643421	−	1.12253i
$303$	−1.52773	−	0.722537i	−0.0877656	−	0.0415087i
$304$	15.1714	−	20.2924i	0.870139	−	1.16385i
$305$	−7.87783			−0.451083
$306$	−5.08726	−	30.2200i	−0.290819	−	1.72756i
$307$	10.7846	+	26.0362i	0.615508	+	1.48597i	0.856870	+	0.515532i	$0.172406\pi$
$307$	10.7846	+	26.0362i	0.615508	+	1.48597i	−0.241363	+	0.970435i	$0.577594\pi$
$308$	−4.38526	−	3.32156i	−0.249874	−	0.189264i
$309$	0.428292	−	1.33303i	0.0243647	−	0.0758336i
$310$	1.12749	−	8.77613i	0.0640371	−	0.498451i
$311$	−1.58220	−	5.90485i	−0.0897183	−	0.334833i	0.906448	−	0.422318i	$-0.138784\pi$
$311$	−1.58220	−	5.90485i	−0.0897183	−	0.334833i	−0.996166	+	0.0874853i	$0.972117\pi$
$312$	1.42229	−	0.130084i	0.0805213	−	0.00736453i
$313$	3.00403	−	11.2112i	0.169798	−	0.633694i	−0.827582	−	0.561346i	$-0.810284\pi$
$313$	3.00403	−	11.2112i	0.169798	−	0.633694i	0.997379	−	0.0723488i	$-0.0230495\pi$
$314$	−20.2261	−	8.30391i	−1.14142	−	0.468617i
$315$	7.46521	−	7.97092i	0.420617	−	0.449111i
$316$	−0.0513033	−	8.20233i	−0.00288603	−	0.461417i
$317$	−15.3862	−	11.8063i	−0.864177	−	0.663107i	0.0784629	−	0.996917i	$-0.474999\pi$
$317$	−15.3862	−	11.8063i	−0.864177	−	0.663107i	−0.942640	+	0.333810i	$0.891665\pi$
$318$	−1.44236	−	3.99156i	−0.0808834	−	0.223836i
$319$	−1.30994	−	0.756296i	−0.0733428	−	0.0423445i
$320$	6.62369	−	5.28291i	0.370276	−	0.295324i
$321$	−8.93782	+	6.18612i	−0.498861	+	0.345276i
$322$	−7.03857	+	26.6008i	−0.392244	+	1.48240i
$323$	−17.5088	−	42.2700i	−0.974216	−	2.35197i
$324$	−17.0079	+	5.89327i	−0.944885	+	0.327404i
$325$	−1.04462	−	0.432697i	−0.0579452	−	0.0240017i
$326$	14.9773	−	2.01947i	0.829517	−	0.111848i
$327$	−14.0180	−	2.55049i	−0.775199	−	0.141042i
$328$	9.28889	+	5.24737i	0.512893	+	0.289738i
$329$	23.3496	−	6.25650i	1.28730	−	0.344932i
$330$	−0.0953488	+	2.07371i	−0.00524878	+	0.114154i
$331$	−2.91001	−	22.1037i	−0.159949	−	1.21493i	−0.863523	−	0.504309i	$-0.831747\pi$
$331$	−2.91001	−	22.1037i	−0.159949	−	1.21493i	0.703574	−	0.710622i	$-0.251586\pi$
$332$	3.95491	+	9.38159i	0.217054	+	0.514882i
$333$	1.11209	+	33.9446i	0.0609423	+	1.86015i
$334$	−2.82330	+	0.00882938i	−0.154484	+	0.000483122i
$335$	8.35090	−	4.82139i	0.456258	−	0.263421i
$336$	7.00037	−	22.7621i	0.381902	−	1.24177i
$337$	−6.03129	−	3.48216i	−0.328545	−	0.189686i	0.326650	−	0.945145i	$-0.394080\pi$
$337$	−6.03129	−	3.48216i	−0.328545	−	0.189686i	−0.655195	+	0.755460i	$0.727414\pi$
$338$	−15.8461	−	9.08278i	−0.861913	−	0.494038i
$339$	−14.0192	+	7.20127i	−0.761421	+	0.391119i
$340$	−2.09181	−	15.1558i	−0.113444	−	0.821936i
$341$	4.36768	+	1.80915i	0.236523	+	0.0979712i
$342$	−22.7763	+	14.2630i	−1.23160	+	0.771255i
$343$	−5.31084	−	5.31084i	−0.286758	−	0.286758i
$344$	0.662441	−	0.880288i	0.0357164	−	0.0474620i
$345$	9.77635	−	3.49817i	0.526341	−	0.188335i
$346$	−4.78018	+	3.69177i	−0.256984	+	0.198471i
$347$	5.88530	−	4.51595i	0.315940	−	0.242429i	−0.438602	−	0.898682i	$-0.644526\pi$
$347$	5.88530	−	4.51595i	0.315940	−	0.242429i	0.754541	+	0.656253i	$0.227859\pi$
$348$	1.13178	−	6.44932i	0.0606699	−	0.345720i
$349$	13.0077	−	16.9519i	0.696285	−	0.907416i	−0.302671	−	0.953095i	$-0.597878\pi$
$349$	13.0077	−	16.9519i	0.696285	−	0.907416i	0.998956	+	0.0456789i	$0.0145451\pi$
$350$	−13.2894	+	13.3728i	−0.710349	+	0.714806i
$351$	−1.45665	−	0.415909i	−0.0777502	−	0.0221996i
$352$	1.79750	+	4.15458i	0.0958069	+	0.221440i
$353$	24.8199	−	14.3298i	1.32103	−	0.762697i	0.337137	−	0.941456i	$-0.390541\pi$
$353$	24.8199	−	14.3298i	1.32103	−	0.762697i	0.983893	+	0.178759i	$0.0572081\pi$
$354$	−7.56869	−	1.35263i	−0.402271	−	0.0718915i
$355$	2.19478	−	16.6710i	0.116487	−	0.884804i
$356$	−18.1338	+	4.98071i	−0.961090	+	0.263977i
$357$	−28.8797	−	31.8630i	−1.52848	−	1.68637i
$358$	35.9335	−	4.84511i	1.89915	−	0.256072i
$359$	21.1381	+	21.1381i	1.11563	+	1.11563i	0.992375	+	0.123252i	$0.0393323\pi$
$359$	21.1381	+	21.1381i	1.11563	+	1.11563i	0.123252	+	0.992375i	$0.460668\pi$
$360$	−8.57452	+	2.68939i	−0.451917	+	0.141743i
$361$	−14.9355	+	14.9355i	−0.786077	+	0.786077i
$362$	2.86956	−	3.76400i	0.150821	−	0.197831i
$363$	17.0833	+	5.48873i	0.896642	+	0.288084i
$364$	1.58236	−	1.22999i	0.0829383	−	0.0644690i
$365$	2.87667	+	0.378721i	0.150572	+	0.0198231i
$366$	18.1549	−	1.54602i	0.948973	−	0.0808119i
$367$	−1.04257	−	1.80579i	−0.0544218	−	0.0942613i	0.837531	−	0.546390i	$-0.183998\pi$
$367$	−1.04257	−	1.80579i	−0.0544218	−	0.0942613i	−0.891953	+	0.452128i	$0.850665\pi$
$368$	15.8089	−	16.2095i	0.824096	−	0.844976i
$369$	−7.17884	−	8.74699i	−0.373716	−	0.455350i
$370$	0.0530258	+	16.9556i	0.00275668	+	0.881482i
$371$	−4.72497	−	3.62560i	−0.245308	−	0.188232i
$372$	−0.876050	+	20.4464i	−0.0454211	+	1.06009i
$373$	−2.26245	−	2.94848i	−0.117145	−	0.152667i	0.731100	−	0.682270i	$-0.239007\pi$
$373$	−2.26245	−	2.94848i	−0.117145	−	0.152667i	−0.848245	+	0.529604i	$0.822341\pi$
$374$	8.10771	+	1.04162i	0.419240	+	0.0538607i
$375$	16.0230	+	2.91527i	0.827422	+	0.150544i
$376$	−19.2610	−	4.96778i	−0.993312	−	0.256194i
$377$	0.389660	−	0.389660i	0.0200685	−	0.0200685i
$378$	−15.6397	+	19.8345i	−0.804419	+	1.02018i
$379$	−9.66778	+	23.3401i	−0.496600	+	1.19890i	0.454703	+	0.890643i	$0.349745\pi$
$379$	−9.66778	+	23.3401i	−0.496600	+	1.19890i	−0.951303	+	0.308256i	$0.900255\pi$
$380$	−11.5769	+	6.78081i	−0.593881	+	0.347848i
$381$	−14.1351	+	21.9235i	−0.724164	+	1.12318i
$382$	−0.947294	−	3.49163i	−0.0484678	−	0.178648i
$383$	18.9097	−	32.7526i	0.966241	−	1.67358i	0.259996	−	0.965610i	$-0.416279\pi$
$383$	18.9097	−	32.7526i	0.966241	−	1.67358i	0.706244	−	0.707968i	$-0.250388\pi$
$384$	−14.2279	+	13.4747i	−0.726065	+	0.687626i
$385$	1.45652	+	2.52277i	0.0742313	+	0.128572i
$386$	21.8815	−	22.0188i	1.11374	−	1.12073i
$387$	−0.992299	+	0.617086i	−0.0504414	+	0.0313682i
$388$	−0.145678	−	23.2909i	−0.00739567	−	1.18242i
$389$	−22.3214	+	2.93866i	−1.13174	+	0.148996i	−0.673047	−	0.739600i	$-0.735015\pi$
$389$	−22.3214	+	2.93866i	−1.13174	+	0.148996i	−0.458691	+	0.888596i	$0.651681\pi$
$390$	−0.720755	−	0.229088i	−0.0364968	−	0.0116003i
$391$	−10.5823	−	39.4937i	−0.535170	−	1.99728i
$392$	−3.64804	−	13.1210i	−0.184254	−	0.662712i
$393$	−7.15547	−	6.07081i	−0.360946	−	0.306232i
$394$	18.2474	−	23.9351i	0.919291	−	1.20583i
$395$	−1.66217	+	4.01283i	−0.0836327	+	0.201907i
$396$	−0.187229	−	4.79770i	−0.00940861	−	0.241094i
$397$	19.1135	−	7.91709i	0.959281	−	0.397347i	0.152569	−	0.988293i	$-0.451245\pi$
$397$	19.1135	−	7.91709i	0.959281	−	0.397347i	0.806711	+	0.590946i	$0.201245\pi$
$398$	11.6268	−	6.76130i	0.582799	−	0.338914i
$399$	−16.1231	+	34.0905i	−0.807163	+	1.70666i
$400$	14.9336	−	4.20235i	0.746679	−	0.210117i
$401$	12.3007	−	21.3055i	0.614269	−	1.06394i	−0.376244	−	0.926521i	$-0.622784\pi$
$401$	12.3007	−	21.3055i	0.614269	−	1.06394i	0.990512	−	0.137424i	$-0.0438822\pi$
$402$	−18.2989	+	12.7500i	−0.912667	+	0.635914i
$403$	−1.04848	+	1.36641i	−0.0522287	+	0.0680658i
$404$	1.80751	+	0.735483i	0.0899268	+	0.0365916i
$405$	9.51113	+	0.622908i	0.472612	+	0.0309526i
$406$	−3.54278	−	8.47795i	−0.175825	−	0.420754i
$407$	−8.75060	−	2.34472i	−0.433751	−	0.116223i
$408$	7.79501	+	34.5168i	0.385910	+	1.70883i
$409$	5.12269	−	1.37262i	0.253301	−	0.0678718i	−0.129934	−	0.991523i	$-0.541477\pi$
$409$	5.12269	−	1.37262i	0.253301	−	0.0678718i	0.383235	+	0.923651i	$0.374810\pi$
$410$	−3.45308	−	4.47112i	−0.170536	−	0.220813i
$411$	25.2986	−	22.9299i	1.24789	−	1.13105i
$412$	−0.408670	+	1.56425i	−0.0201337	+	0.0770649i
$413$	−9.96789	+	4.12883i	−0.490488	+	0.203167i
$414$	−21.8436	+	9.98034i	−1.07356	+	0.490507i
$415$		−	5.39120i		−	0.264644i
$416$	−1.63150	+	0.240800i	−0.0799908	+	0.0118062i
$417$	10.0911	−	0.827550i	0.494162	−	0.0405253i
$418$	−1.87695	−	6.91824i	−0.0918044	−	0.338382i
$419$	−21.2891	−	2.80276i	−1.04004	−	0.136924i	−0.408889	−	0.912584i	$-0.634084\pi$
$419$	−21.2891	−	2.80276i	−1.04004	−	0.136924i	−0.631150	+	0.775660i	$0.717417\pi$
$420$	−8.09789	+	9.66665i	−0.395137	+	0.471684i
$421$	2.30974	+	17.5442i	0.112570	+	0.855053i	0.950815	+	0.309759i	$0.100248\pi$
$421$	2.30974	+	17.5442i	0.112570	+	0.855053i	−0.838245	+	0.545293i	$0.816418\pi$
$422$	23.4721	+	9.63657i	1.14260	+	0.469101i
$423$	17.1497	+	12.2887i	0.833848	+	0.597495i
$424$	1.91783	+	4.50990i	0.0931379	+	0.219020i
$425$	7.25061	−	27.0596i	0.351706	−	1.31259i
$426$	−1.78631	+	38.8499i	−0.0865470	+	1.88229i
$427$	20.2848	−	15.5651i	0.981649	−	0.753246i
$428$	9.90969	−	7.70293i	0.479003	−	0.372335i
$429$	0.218962	−	0.339609i	0.0105716	−	0.0163965i
$430$	−0.504307	+	0.293268i	−0.0243198	+	0.0141427i
$431$			21.8633i			1.05312i	0.850138	+	0.526560i	$0.176519\pi$
$431$			21.8633i			1.05312i	−0.850138	+	0.526560i	$0.823481\pi$
$432$	19.2327	−	7.88061i	0.925333	−	0.379156i
$433$		−	7.49630i		−	0.360249i	−0.983644	−	0.180125i	$-0.942350\pi$
$433$		−	7.49630i		−	0.360249i	0.983644	−	0.180125i	$-0.0576501\pi$
$434$	14.4367	+	24.8255i	0.692984	+	1.19166i
$435$	−1.87886	+	2.91410i	−0.0900842	+	0.139720i
$436$	16.3247	+	2.04540i	0.781813	+	0.0979569i
$437$	−28.4456	+	21.8271i	−1.36074	+	1.04413i
$438$	−6.70377	−	0.308238i	−0.320318	−	0.0147282i
$439$	−8.50673	+	31.7475i	−0.406004	+	1.51523i	0.396193	+	0.918167i	$0.370331\pi$
$439$	−8.50673	+	31.7475i	−0.406004	+	1.51523i	−0.802197	+	0.597060i	$0.796335\pi$
$440$	−0.0224886	−	2.39694i	−0.00107210	−	0.114270i
$441$	−1.41548	+	14.3753i	−0.0674037	+	0.684539i
$442$	−1.13104	+	2.75491i	−0.0537981	+	0.131038i
$443$	0.785824	+	5.96893i	0.0373356	+	0.283592i	0.999920	+	0.0126118i	$0.00401456\pi$
$443$	0.785824	+	5.96893i	0.0373356	+	0.283592i	−0.962585	+	0.270981i	$0.912652\pi$
$444$	−3.44974	−	39.0648i	−0.163717	−	1.85393i
$445$	9.87279	+	1.29978i	0.468015	+	0.0616154i
$446$	−2.23709	+	0.606931i	−0.105929	+	0.0287390i
$447$	−12.0744	+	0.990198i	−0.571099	+	0.0468348i
$448$	−6.61747	+	26.6902i	−0.312646	+	1.26099i
$449$		−	14.9356i		−	0.704857i	−0.935839	−	0.352428i	$-0.885356\pi$
$449$		−	14.9356i		−	0.704857i	0.935839	−	0.352428i	$-0.114644\pi$
$450$	−16.3804	−	1.56120i	−0.772180	−	0.0735958i
$451$	2.78862	−	1.15508i	0.131311	−	0.0543907i
$452$	15.7034	−	9.19780i	0.738626	−	0.432628i
$453$	20.4042	−	18.4938i	0.958673	−	0.868913i
$454$	−8.73841	+	6.74874i	−0.410114	+	0.316734i
$455$	−1.02511	+	0.274677i	−0.0480579	+	0.0128771i
$456$	25.3488	−	17.8987i	1.18707	−	0.838184i
$457$	−11.9724	−	3.20801i	−0.560047	−	0.150064i	−0.0323193	−	0.999478i	$-0.510289\pi$
$457$	−11.9724	−	3.20801i	−0.560047	−	0.150064i	−0.527728	+	0.849413i	$0.676956\pi$
$458$	−14.6543	+	6.12378i	−0.684751	+	0.286145i
$459$	5.50575	−	37.1265i	0.256987	−	1.73292i
$460$	−11.0481	+	4.65744i	−0.515120	+	0.217154i
$461$	0.00264069	−	0.00344141i	0.000122989	−	0.000160283i	−0.793292	−	0.608842i	$-0.791635\pi$
$461$	0.00264069	−	0.00344141i	0.000122989	−	0.000160283i	0.793415	+	0.608681i	$0.208301\pi$
$462$	−3.85173	−	5.52803i	−0.179199	−	0.257187i
$463$	−6.43556	+	11.1467i	−0.299086	+	0.518032i	−0.975927	−	0.218097i	$-0.930015\pi$
$463$	−6.43556	+	11.1467i	−0.299086	+	0.518032i	0.676841	+	0.736129i	$0.263348\pi$
$464$	−0.893041	+	7.50791i	−0.0414584	+	0.348546i
$465$	4.63323	−	9.79646i	0.214861	−	0.454300i
$466$	1.80694	+	3.10723i	0.0837048	+	0.143939i
$467$	29.1347	−	12.0680i	1.34819	−	0.558440i	0.412405	−	0.911001i	$-0.364689\pi$
$467$	29.1347	−	12.0680i	1.34819	−	0.558440i	0.935789	+	0.352560i	$0.114689\pi$
$468$	1.70598	+	0.386499i	0.0788589	+	0.0178659i
$469$	−11.9767	+	28.9144i	−0.553035	+	1.33514i
$470$	8.37643	+	6.38594i	0.386376	+	0.294562i
$471$	−20.4194	−	17.3241i	−0.940874	−	0.798252i
$472$	8.81257	+	1.07619i	0.405631	+	0.0495355i
$473$	−0.0806725	−	0.301074i	−0.00370933	−	0.0138434i
$474$	3.04304	−	9.57399i	0.139772	−	0.439748i
$475$	−24.3563	+	3.20657i	−1.11755	+	0.147128i
$476$	35.3310	+	34.8918i	1.61939	+	1.59926i
$477$	−0.170206	−	5.19523i	−0.00779321	−	0.237873i
$478$	−12.7924	−	12.7126i	−0.585109	−	0.581460i
$479$	−12.8812	−	22.3108i	−0.588555	−	1.01941i	−0.994422	−	0.105475i	$-0.966364\pi$
$479$	−12.8812	−	22.3108i	−0.588555	−	1.01941i	0.405867	−	0.913932i	$-0.366970\pi$
$480$	9.71412	−	3.64823i	0.443387	−	0.166518i
$481$	1.65023	−	2.85827i	0.0752438	−	0.130326i
$482$	26.2209	−	7.11382i	1.19433	−	0.324026i
$483$	−18.2616	+	28.3237i	−0.830931	+	1.28877i
$484$	−20.0464	−	5.23726i	−0.911202	−	0.238057i
$485$	−4.71980	+	11.3946i	−0.214315	+	0.517402i
$486$	−22.0412	+	0.431031i	−0.999809	+	0.0195519i
$487$	−13.9290	+	13.9290i	−0.631181	+	0.631181i	−0.948364	−	0.317183i	$-0.897263\pi$
$487$	−13.9290	+	13.9290i	−0.631181	+	0.631181i	0.317183	+	0.948364i	$0.397263\pi$
$488$	−20.8327	+	2.94177i	−0.943051	+	0.133167i
$489$	18.2104	+	3.31326i	0.823504	+	0.149831i
$490$	−0.918925	+	7.15271i	−0.0415128	+	0.323127i
$491$	4.75332	+	6.19465i	0.214515	+	0.279561i	0.888200	−	0.459458i	$-0.151956\pi$
$491$	4.75332	+	6.19465i	0.214515	+	0.279561i	−0.673685	+	0.739019i	$0.735290\pi$
$492$	8.83528	+	9.62629i	0.398325	+	0.433987i
$493$	10.8318	+	8.31156i	0.487842	+	0.374334i
$494$	2.61153	−	0.00816711i	0.117498	−	0.000367456i
$495$	−0.895519	+	2.37952i	−0.0402506	+	0.106951i
$496$	−0.295600	−	23.6292i	−0.0132728	−	1.06098i
$497$	27.2872	+	47.2628i	1.22400	+	2.12003i
$498$	1.05802	+	12.4243i	0.0474111	+	0.556748i
$499$	43.7470	+	5.75940i	1.95838	+	0.257826i	0.999649	−	0.0264792i	$-0.00842958\pi$
$499$	43.7470	+	5.75940i	1.95838	+	0.257826i	0.958734	+	0.284305i	$0.0917629\pi$
$500$	−18.6596	−	2.33794i	−0.834481	−	0.104556i
$501$	−3.29209	−	1.05772i	−0.147080	−	0.0472555i
$502$	3.61432	+	2.75545i	0.161315	+	0.122982i
$503$	−3.83723	+	3.83723i	−0.171094	+	0.171094i	−0.787460	−	0.616366i	$-0.788604\pi$
$503$	−3.83723	+	3.83723i	−0.171094	+	0.171094i	0.616366	+	0.787460i	$0.288604\pi$
$504$	16.7650	−	23.8665i	0.746771	−	1.06310i
$505$	−0.730674	−	0.730674i	−0.0325146	−	0.0325146i
$506$	−0.856006	−	6.34853i	−0.0380541	−	0.282227i
$507$	−15.0226	−	16.5745i	−0.667178	−	0.736098i
$508$	14.8969	−	26.1790i	0.660943	−	1.16150i
$509$	−2.44369	+	18.5617i	−0.108315	+	0.822731i	0.847919	+	0.530126i	$0.177855\pi$
$509$	−2.44369	+	18.5617i	−0.108315	+	0.822731i	−0.956233	+	0.292605i	$0.905478\pi$
$510$	3.29650	−	18.4456i	0.145971	−	0.816787i
$511$	−8.15546	+	4.70856i	−0.360776	+	0.208294i
$512$	15.5434	−	16.4439i	0.686927	−	0.726726i
$513$	−31.9267	+	7.99852i	−1.40960	+	0.353143i
$514$	23.3792	+	23.2334i	1.03121	+	1.02478i
$515$	0.521170	−	0.679202i	0.0229655	−	0.0299292i
$516$	1.10465	−	0.774823i	0.0486295	−	0.0341097i
$517$	−4.46476	+	3.42593i	−0.196360	+	0.150672i
$518$	−33.6375	−	43.5546i	−1.47795	−	1.91368i
$519$	−6.96478	+	2.49214i	−0.305720	+	0.109393i
$520$	0.845611	+	0.218099i	0.0370825	+	0.00956426i
$521$	−4.10556	−	4.10556i	−0.179868	−	0.179868i	0.611430	−	0.791298i	$-0.290594\pi$
$521$	−4.10556	−	4.10556i	−0.179868	−	0.179868i	−0.791298	+	0.611430i	$0.790594\pi$
$522$	3.75804	−	7.08443i	0.164485	−	0.310077i
$523$	−15.2438	−	6.31420i	−0.666566	−	0.276101i	0.0236324	−	0.999721i	$-0.492477\pi$
$523$	−15.2438	−	6.31420i	−0.666566	−	0.276101i	−0.690199	+	0.723620i	$0.742477\pi$
$524$	8.63744	+	6.54231i	0.377328	+	0.285802i
$525$	−20.5390	+	10.5503i	−0.896397	+	0.460453i
$526$	8.37183	−	14.6057i	0.365029	−	0.636840i
$527$	−36.9556	−	21.3363i	−1.60981	−	0.929425i
$528$	0.522226	+	5.51947i	0.0227269	+	0.240204i
$529$	−7.83039	+	4.52088i	−0.340452	+	0.196560i
$530$	−0.00811563	−	2.59507i	−0.000352520	−	0.112723i
$531$	−8.30479	−	4.43873i	−0.360397	−	0.192625i
$532$	16.4119	−	40.3336i	0.711548	−	1.74868i
$533$	0.143532	+	1.09024i	0.00621708	+	0.0472234i
$534$	−23.0075	−	1.05788i	−0.995632	−	0.0457789i
$535$	−6.41984	+	1.72019i	−0.277554	+	0.0743704i
$536$	20.2833	−	15.8684i	0.876104	−	0.685413i
$537$	43.6904	+	7.94916i	1.88538	+	0.343032i
$538$	−2.36732	−	17.5571i	−0.102062	−	0.756941i
$539$	−3.55975	−	1.47450i	−0.153329	−	0.0635110i
$540$	−11.0055	−	0.110827i	−0.473601	−	0.00476921i
$541$	14.9347	+	36.0555i	0.642092	+	1.55015i	0.823853	+	0.566804i	$0.191820\pi$
$541$	14.9347	+	36.0555i	0.642092	+	1.55015i	−0.181761	+	0.983343i	$0.558180\pi$
$542$	−10.2707	−	2.71764i	−0.441166	−	0.116732i
$543$	4.76649	−	3.29903i	0.204550	−	0.141575i
$544$	−11.1912	−	39.2978i	−0.479820	−	1.68488i
$545$	−7.54481	−	4.35600i	−0.323184	−	0.186591i
$546$	2.30852	−	0.834187i	0.0987954	−	0.0356999i
$547$	23.7493	+	18.2235i	1.01545	+	0.779180i	0.975495	−	0.220022i	$-0.0706129\pi$
$547$	23.7493	+	18.2235i	1.01545	+	0.779180i	0.0399517	+	0.999202i	$0.487280\pi$
$548$	−27.7033	+	28.0521i	−1.18343	+	1.19833i
$549$	21.7328	+	5.06680i	0.927533	+	0.216246i
$550$	1.66696	−	4.06027i	0.0710795	−	0.173131i
$551$	3.09882	−	11.5650i	0.132014	−	0.492684i
$552$	24.5469	−	12.9015i	1.04479	−	0.549125i
$553$	−3.64861	−	13.6168i	−0.155155	−	0.579046i
$554$	35.5391	+	4.56579i	1.50991	+	0.193982i
$555$	−6.35226	+	19.7710i	−0.269639	+	0.839233i
$556$	−11.5815	+	1.59849i	−0.491165	+	0.0677910i
$557$	−12.9739	−	31.3219i	−0.549723	−	1.32715i	−0.917685	−	0.397308i	$-0.869944\pi$
$557$	−12.9739	−	31.3219i	−0.549723	−	1.32715i	0.367962	−	0.929841i	$-0.380056\pi$
$558$	−8.75499	+	23.4858i	−0.370628	+	0.994232i
$559$	0.113556			0.00480289
$560$	8.71906	−	11.6621i	0.368447	−	0.492814i
$561$	9.05034	+	4.28035i	0.382106	+	0.180717i
$562$	31.0236	+	17.7824i	1.30865	+	0.750103i
$563$	−3.25632	+	24.7342i	−0.137238	+	1.04242i	0.774768	+	0.632246i	$0.217867\pi$
$563$	−3.25632	+	24.7342i	−0.137238	+	1.04242i	−0.912006	+	0.410178i	$0.865467\pi$
$564$	−20.5572	−	13.0729i	−0.865614	−	0.550468i
$565$	−9.55434	+	1.25785i	−0.401954	+	0.0529183i
$566$	−16.2480	−	38.8817i	−0.682953	−	1.63432i
$567$	−25.7211	+	17.1882i	−1.08019	+	0.721836i
$568$	−0.421313	−	44.9055i	−0.0176779	−	1.88419i
$569$	19.7341	+	5.28773i	0.827295	+	0.221673i	0.647533	−	0.762037i	$-0.275801\pi$
$569$	19.7341	+	5.28773i	0.827295	+	0.221673i	0.179762	+	0.983710i	$0.442467\pi$
$570$	−16.0505	+	3.51936i	−0.672282	+	0.147410i
$571$	4.08792	+	5.32749i	0.171074	+	0.222948i	0.871020	−	0.491248i	$-0.163459\pi$
$571$	4.08792	+	5.32749i	0.171074	+	0.222948i	−0.699946	+	0.714196i	$0.746792\pi$
$572$	−0.230762	+	0.405528i	−0.00964865	+	0.0169560i
$573$	0.217360	−	4.42561i	0.00908035	−	0.184883i
$574$	17.7255	+	4.69016i	0.739846	+	0.195763i
$575$	−21.9538			−0.915539
$576$	−21.6708	+	10.3139i	−0.902949	+	0.429748i
$577$	2.32967			0.0969854			0.0484927	−	0.998824i	$-0.484558\pi$
$577$	2.32967			0.0969854			0.0484927	+	0.998824i	$0.484558\pi$
$578$	−48.0882	−	12.7242i	−2.00021	−	0.529255i
$579$	33.8183	−	17.3715i	1.40544	−	0.721934i
$580$	1.98011	−	3.47974i	0.0822197	−	0.144488i
$581$	10.6520	+	13.8819i	0.441918	+	0.575918i
$582$	8.64085	−	27.1858i	0.358175	−	1.12689i
$583$	1.33928	+	0.358860i	0.0554675	+	0.0148625i
$584$	7.74868	−	0.0726999i	0.320643	−	0.00300834i
$585$	−0.752919	−	0.539505i	−0.0311294	−	0.0223058i
$586$	−1.98293	−	4.74518i	−0.0819139	−	0.196022i
$587$	−28.0925	+	3.69844i	−1.15950	+	0.152651i	−0.685634	−	0.727946i	$-0.740475\pi$
$587$	−28.0925	+	3.69844i	−1.15950	+	0.152651i	−0.473866	+	0.880597i	$0.657142\pi$
$588$	0.713997	−	16.6642i	0.0294448	−	0.687219i
$589$	−4.88441	+	37.1008i	−0.201259	+	1.52871i
$590$	−4.07867	−	2.33784i	−0.167916	−	0.0962474i
$591$	30.3099	−	20.9784i	1.24678	−	0.862935i
$592$	6.47185	+	44.8188i	0.265991	+	1.84204i
$593$	−24.5064			−1.00636			−0.503178	−	0.864183i	$-0.667836\pi$
$593$	−24.5064			−1.00636			−0.503178	+	0.864183i	$0.667836\pi$
$594$	1.59679	−	5.65948i	0.0655172	−	0.232211i
$595$	−10.0624	−	24.2927i	−0.412517	−	0.995905i
$596$	13.8577	−	1.91266i	0.567635	−	0.0783455i
$597$	16.1013	−	3.47776i	0.658982	−	0.142335i
$598$	2.31478	+	0.297385i	0.0946584	+	0.0121610i
$599$	−5.74382	−	21.4362i	−0.234686	−	0.875861i	−0.978290	−	0.207240i	$-0.933552\pi$
$599$	−5.74382	−	21.4362i	−0.234686	−	0.875861i	0.743604	−	0.668620i	$-0.233115\pi$
$600$	18.9852	+	0.753972i	0.775069	+	0.0307808i
$601$	−0.706695	+	2.63742i	−0.0288267	+	0.107583i	−0.978840	−	0.204626i	$-0.934402\pi$
$601$	−0.706695	+	2.63742i	−0.0288267	+	0.107583i	0.950014	+	0.312209i	$0.101069\pi$
$602$	0.719108	−	1.75155i	0.0293086	−	0.0713880i
$603$	−26.1388	+	7.92985i	−1.06446	+	0.322929i
$604$	−22.3437	+	22.6250i	−0.909154	+	0.920599i
$605$	8.70423	+	6.67899i	0.353877	+	0.271540i
$606$	1.82727	+	1.54048i	0.0742279	+	0.0625779i
$607$	23.6343	+	13.6453i	0.959286	+	0.553844i	0.895953	−	0.444149i	$-0.146494\pi$
$607$	23.6343	+	13.6453i	0.959286	+	0.553844i	0.0633327	+	0.997992i	$0.479827\pi$
$608$	−28.0826	+	22.2547i	−1.13890	+	0.902547i
$609$	−0.919787	−	11.2158i	−0.0372717	−	0.454488i
$610$	10.7703	+	2.84982i	0.436076	+	0.115386i
$611$	−0.784604	−	1.89420i	−0.0317417	−	0.0766312i
$612$	−3.97701	+	43.1560i	−0.160761	+	1.74448i
$613$	−9.92675	−	4.11180i	−0.400938	−	0.166074i	0.173097	−	0.984905i	$-0.444623\pi$
$613$	−9.92675	−	4.11180i	−0.400938	−	0.166074i	−0.574035	+	0.818831i	$0.694623\pi$
$614$	−5.32561	−	39.4971i	−0.214924	−	1.59397i
$615$	−2.33101	−	6.51448i	−0.0939955	−	0.262689i
$616$	4.79379	+	6.12749i	0.193147	+	0.246884i
$617$	0.216018	−	0.0578818i	0.00869655	−	0.00233023i	−0.254468	−	0.967081i	$-0.581900\pi$
$617$	0.216018	−	0.0578818i	0.00869655	−	0.00233023i	0.263165	+	0.964751i	$0.415234\pi$
$618$	−1.06777	+	1.66754i	−0.0429521	+	0.0670782i
$619$	−1.19029	−	9.04118i	−0.0478419	−	0.363396i	−0.998574	−	0.0533823i	$-0.983000\pi$
$619$	−1.19029	−	9.04118i	−0.0478419	−	0.363396i	0.950732	−	0.310013i	$-0.100334\pi$
$620$	−4.71624	+	11.5905i	−0.189409	+	0.465487i
$621$	−29.2202	+	3.36264i	−1.17257	+	0.134938i
$622$	0.0270365	+	8.64525i	0.00108407	+	0.346643i
$623$	−27.9897	+	16.1599i	−1.12139	+	0.647432i
$624$	−1.99156	−	0.336670i	−0.0797262	−	0.0134776i
$625$	−8.17006	−	4.71699i	−0.326802	−	0.188679i
$626$	−8.16267	+	14.2408i	−0.326246	+	0.569178i
$627$	0.430673	−	8.76881i	0.0171994	−	0.350193i
$628$	24.6484	+	18.6696i	0.983579	+	0.744999i
$629$	75.5480	+	31.2930i	3.01230	+	1.24773i
$630$	−13.0897	+	8.19701i	−0.521504	+	0.326577i
$631$	5.31271	+	5.31271i	0.211496	+	0.211496i	0.804903	−	0.593407i	$-0.202218\pi$
$631$	5.31271	+	5.31271i	0.211496	+	0.211496i	−0.593407	+	0.804903i	$0.702218\pi$
$632$	−2.89707	+	11.2325i	−0.115239	+	0.446804i
$633$	23.6964	+	20.1044i	0.941847	+	0.799077i
$634$	16.7646	+	21.7071i	0.665806	+	0.862099i
$635$	−12.6538	+	9.70960i	−0.502151	+	0.385314i
$636$	0.527984	+	5.97889i	0.0209359	+	0.237078i
$637$	0.854535	−	1.11365i	0.0338579	−	0.0441245i
$638$	1.51732	+	1.50786i	0.0600711	+	0.0596966i
$639$	−16.7771	+	44.5791i	−0.663691	+	1.76352i
$640$	−10.9668	+	4.82647i	−0.433500	+	0.190783i
$641$	28.3759	−	16.3828i	1.12078	−	0.647082i	0.179179	−	0.983816i	$-0.442656\pi$
$641$	28.3759	−	16.3828i	1.12078	−	0.647082i	0.941600	+	0.336734i	$0.109322\pi$
$642$	14.4573	−	5.22417i	0.570584	−	0.206182i
$643$	0.626621	−	4.75966i	0.0247115	−	0.187703i	−0.974637	−	0.223791i	$-0.928157\pi$
$643$	0.626621	−	4.75966i	0.0247115	−	0.187703i	0.999349	+	0.0360887i	$0.0114899\pi$
$644$	19.2458	−	33.8214i	0.758389	−	1.33275i
$645$	−0.698386	+	0.150846i	−0.0274989	+	0.00593956i
$646$	8.64616	+	64.1238i	0.340179	+	2.52292i
$647$	−11.9442	−	11.9442i	−0.469574	−	0.469574i	0.432202	−	0.901777i	$-0.357737\pi$
$647$	−11.9442	−	11.9442i	−0.469574	−	0.469574i	−0.901777	+	0.432202i	$0.857737\pi$
$648$	25.3845	−	1.90442i	0.997198	−	0.0748126i
$649$	1.77611	−	1.77611i	0.0697183	−	0.0697183i
$650$	1.27164	+	0.969461i	0.0498778	+	0.0380254i
$651$	7.42570	+	34.3794i	0.291036	+	1.34744i
$652$	−21.2070	−	2.65712i	−0.830529	−	0.104061i
$653$	−14.2210	−	1.87223i	−0.556512	−	0.0732662i	−0.152976	−	0.988230i	$-0.548886\pi$
$653$	−14.2210	−	1.87223i	−0.556512	−	0.0732662i	−0.403536	+	0.914964i	$0.632219\pi$
$654$	18.2423	+	8.55798i	0.713331	+	0.334643i
$655$	−2.86884	−	4.96898i	−0.112095	−	0.194154i
$656$	−10.8012	−	10.5343i	−0.421716	−	0.411295i
$657$	−7.69236	−	2.89498i	−0.300108	−	0.112944i
$658$	−34.1860	+	0.106911i	−1.33271	+	0.00416782i
$659$	−19.6589	−	15.0848i	−0.765803	−	0.587621i	0.150264	−	0.988646i	$-0.451988\pi$
$659$	−19.6589	−	15.0848i	−0.765803	−	0.587621i	−0.916067	+	0.401025i	$0.868654\pi$
$660$	0.880526	−	2.80061i	0.0342744	−	0.109014i
$661$	18.5899	+	24.2269i	0.723064	+	0.942316i	0.999827	−	0.0186226i	$-0.00592811\pi$
$661$	18.5899	+	24.2269i	0.723064	+	0.942316i	−0.276762	+	0.960938i	$0.589261\pi$
$662$	−4.01760	+	31.2721i	−0.156148	+	1.21543i
$663$	−2.35964	+	2.78124i	−0.0916409	+	0.108014i
$664$	−2.01320	−	14.2569i	−0.0781273	−	0.553274i
$665$	−16.3046	+	16.3046i	−0.632267	+	0.632267i
$666$	10.7591	−	46.8101i	0.416906	−	1.81385i
$667$	4.09456	−	9.88515i	0.158542	−	0.382754i
$668$	3.86311	+	1.00926i	0.149468	+	0.0390495i
$669$	−2.83549	−	0.139263i	−0.109626	−	0.00538421i
$670$	−13.1612	+	3.57068i	−0.508461	+	0.137947i
$671$	−2.97625	+	5.15502i	−0.114897	+	0.199007i
$672$	−17.8049	+	28.5871i	−0.686838	+	1.10277i
$673$	13.0846	+	22.6632i	0.504373	+	0.873600i	0.999987	+	0.00505738i	$0.00160982\pi$
$673$	13.0846	+	22.6632i	0.504373	+	0.873600i	−0.495614	+	0.868543i	$0.665057\pi$
$674$	6.98607	+	6.94252i	0.269094	+	0.267416i
$675$	−18.4903	−	8.01502i	−0.711694	−	0.308498i
$676$	18.3785	+	18.1500i	0.706864	+	0.698076i
$677$	22.4214	−	2.95183i	0.861724	−	0.113448i	0.313306	−	0.949652i	$-0.398564\pi$
$677$	22.4214	−	2.95183i	0.861724	−	0.113448i	0.548418	+	0.836204i	$0.315230\pi$
$678$	21.7717	−	4.77383i	0.836136	−	0.183338i
$679$	−10.3604	−	38.6655i	−0.397596	−	1.48385i
$680$	−2.62277	+	21.4771i	−0.100579	+	0.823609i
$681$	−12.7320	+	4.55576i	−0.487890	+	0.174577i
$682$	−5.31687	−	4.05343i	−0.203594	−	0.155214i
$683$	−11.2960	+	27.2710i	−0.432230	+	1.04349i	0.546337	+	0.837565i	$0.316022\pi$
$683$	−11.2960	+	27.2710i	−0.432230	+	1.04349i	−0.978567	+	0.205929i	$0.933978\pi$
$684$	36.2986	−	11.2605i	1.38791	−	0.430555i
$685$	19.2879	−	7.98931i	0.736953	−	0.305256i
$686$	5.33958	+	9.18199i	0.203866	+	0.350570i
$687$	−19.3868	+	1.58987i	−0.739651	+	0.0606574i
$688$	−1.22411	+	0.963859i	−0.0466688	+	0.0367468i
$689$	−0.252568	+	0.437460i	−0.00962207	+	0.0166659i
$690$	−14.6313	+	1.24596i	−0.557005	+	0.0474331i
$691$	−12.0459	+	15.6985i	−0.458247	+	0.597199i	−0.964139	−	0.265397i	$-0.914497\pi$
$691$	−12.0459	+	15.6985i	−0.458247	+	0.597199i	0.505892	+	0.862597i	$0.331163\pi$
$692$	7.87079	−	3.31801i	0.299202	−	0.126132i
$693$	−2.39558	−	7.89643i	−0.0910004	−	0.299961i
$694$	−9.67983	+	4.04503i	−0.367441	+	0.153547i
$695$	5.97992	+	1.60232i	0.226831	+	0.0607793i
$696$	−3.88038	+	8.40785i	−0.147086	+	0.318699i
$697$	−26.3167	+	7.05153i	−0.996815	+	0.267096i
$698$	−23.9160	+	18.4705i	−0.905234	+	0.699119i
$699$	0.929421	+	4.30302i	0.0351539	+	0.162755i
$700$	23.0064	−	13.4753i	0.869561	−	0.509320i
$701$	12.5238	−	5.18755i	0.473019	−	0.195931i	−0.133422	−	0.991059i	$-0.542597\pi$
$701$	12.5238	−	5.18755i	0.473019	−	0.195931i	0.606441	+	0.795128i	$0.292597\pi$
$702$	1.84102	+	1.09556i	0.0694849	+	0.0413493i
$703$		−	71.7089i		−	2.70455i
$704$	−0.954544	−	6.33024i	−0.0359757	−	0.238580i
$705$	7.34169	+	10.6074i	0.276504	+	0.399498i
$706$	−39.1167	+	10.6125i	−1.47218	+	0.399407i
$707$	3.32509	+	0.437757i	0.125053	+	0.0164635i
$708$	9.85832	+	4.58725i	0.370498	+	0.172399i
$709$	0.447983	+	3.40277i	0.0168244	+	0.127794i	0.997796	−	0.0663580i	$-0.0211379\pi$
$709$	0.447983	+	3.40277i	0.0168244	+	0.127794i	−0.980972	+	0.194152i	$0.937805\pi$
$710$	−9.03137	+	21.9980i	−0.338941	+	0.825570i
$711$	7.16640	−	10.0012i	0.268761	−	0.375076i
$712$	26.5937	−	0.249508i	0.996640	−	0.00935070i
$713$	−8.65522	+	32.3017i	−0.324140	+	1.20971i
$714$	27.9568	+	54.0092i	1.04626	+	2.02124i
$715$	0.196015	−	0.150408i	0.00733055	−	0.00562493i
$716$	−50.8797	−	6.37496i	−1.90146	−	0.238243i
$717$	−10.0924	−	19.6475i	−0.376906	−	0.733751i
$718$	−21.2525	−	36.5460i	−0.793137	−	1.36388i
$719$			21.3433i			0.795969i	0.917392	+	0.397985i	$0.130290\pi$
$719$			21.3433i			0.795969i	−0.917392	+	0.397985i	$0.869710\pi$
$720$	12.6957	−	0.574993i	0.473140	−	0.0214287i
$721$			2.77862i			0.103481i
$722$	25.8222	−	15.0163i	0.961001	−	0.558849i
$723$	33.2347	+	1.63229i	1.23601	+	0.0607057i
$724$	−5.28479	+	4.10793i	−0.196408	+	0.152670i
$725$	5.81606	−	4.46282i	0.216003	−	0.165745i
$726$	−21.3701	−	13.6839i	−0.793121	−	0.507858i
$727$	7.61014	−	28.4014i	0.282244	−	1.05335i	−0.668585	−	0.743636i	$-0.733100\pi$
$727$	7.61014	−	28.4014i	0.282244	−	1.05335i	0.950829	−	0.309715i	$-0.100234\pi$
$728$	−2.60830	+	1.10917i	−0.0966700	+	0.0411088i
$729$	−25.8380	−	7.83572i	−0.956962	−	0.290212i
$730$	−3.79587	−	1.55841i	−0.140492	−	0.0576794i
$731$	0.367232	+	2.78940i	0.0135826	+	0.103170i
$732$	−25.3800	−	4.45390i	−0.938072	−	0.164621i
$733$	−48.0106	−	6.32072i	−1.77331	−	0.233461i	−0.828252	−	0.560356i	$-0.810664\pi$
$733$	−48.0106	−	6.32072i	−1.77331	−	0.233461i	−0.945061	+	0.326895i	$0.893998\pi$
$734$	0.772119	+	2.84596i	0.0284994	+	0.105046i
$735$	−3.77617	+	7.98431i	−0.139286	+	0.294506i
$736$	−27.4772	+	16.4421i	−1.01282	+	0.606063i
$737$		−	7.28611i		−	0.268387i
$738$	6.65041	+	14.5555i	0.244805	+	0.535796i
$739$	−9.44035	+	3.91032i	−0.347269	+	0.143844i	−0.549499	−	0.835495i	$-0.685181\pi$
$739$	−9.44035	+	3.91032i	−0.347269	+	0.143844i	0.202230	+	0.979338i	$0.435181\pi$
$740$	6.06123	−	23.2003i	0.222815	−	0.852860i
$741$	3.04516	+	0.978384i	0.111867	+	0.0359418i
$742$	5.14824	+	6.66605i	0.188998	+	0.244718i
$743$	27.9249	−	7.48244i	1.02446	−	0.274504i	0.292803	−	0.956173i	$-0.405412\pi$
$743$	27.9249	−	7.48244i	1.02446	−	0.274504i	0.731661	+	0.681669i	$0.238745\pi$
$744$	8.59421	−	27.6366i	0.315079	−	1.01321i
$745$	−7.15523	−	1.91724i	−0.262147	−	0.0702421i
$746$	2.02652	+	4.84951i	0.0741962	+	0.177553i
$747$	−3.46747	+	14.8729i	−0.126868	+	0.544169i
$748$	−10.7078	−	4.35704i	−0.391515	−	0.159309i
$749$	13.1318	−	17.1137i	0.479826	−	0.625321i
$750$	−20.8514	−	9.78198i	−0.761385	−	0.357187i
$751$	16.3782	−	28.3679i	0.597649	−	1.03516i	−0.395518	−	0.918458i	$-0.629435\pi$
$751$	16.3782	−	28.3679i	0.597649	−	1.03516i	0.993167	−	0.116700i	$-0.0372316\pi$
$752$	24.5359	+	13.7595i	0.894731	+	0.501756i
$753$	3.16784	+	4.57695i	0.115442	+	0.166793i
$754$	−0.673689	+	0.391769i	−0.0245343	+	0.0142674i
$755$	15.5564	−	6.44367i	0.566155	−	0.234509i
$756$	28.5572	−	21.4593i	1.03861	−	0.780467i
$757$	12.1779	−	29.4001i	0.442614	−	1.06856i	−0.532414	−	0.846484i	$-0.678715\pi$
$757$	12.1779	−	29.4001i	0.442614	−	1.06856i	0.975028	−	0.222081i	$-0.0712848\pi$
$758$	21.6607	−	28.4124i	0.786754	−	1.03198i
$759$	1.40441	−	7.71897i	0.0509770	−	0.280181i
$760$	18.2804	−	5.08252i	0.663101	−	0.184362i
$761$	6.11751	+	22.8308i	0.221759	+	0.827618i	0.983677	+	0.179944i	$0.0575915\pi$
$761$	6.11751	+	22.8308i	0.221759	+	0.827618i	−0.761917	+	0.647674i	$0.775742\pi$
$762$	27.2559	−	24.8596i	0.987377	−	0.900570i
$763$	28.0339	−	3.69073i	1.01489	−	0.133613i
$764$	0.0320011	+	5.11632i	0.00115776	+	0.185102i
$765$	10.8176	−	20.2396i	0.391112	−	0.731765i
$766$	−37.7009	+	37.9375i	−1.36219	+	1.37074i
$767$	0.457544	+	0.792490i	0.0165210	+	0.0286152i
$768$	24.3264	−	13.2751i	0.877802	−	0.479024i
$769$	−21.2050	+	36.7282i	−0.764674	+	1.32445i	0.175745	+	0.984436i	$0.443766\pi$
$769$	−21.2050	+	36.7282i	−0.764674	+	1.32445i	−0.940419	+	0.340018i	$0.889567\pi$
$770$	−1.07869	−	3.97594i	−0.0388732	−	0.143283i
$771$	18.4447	+	35.9076i	0.664269	+	1.29318i
$772$	−37.8810	+	22.1877i	−1.36337	+	0.798551i
$773$	12.2806	−	29.6480i	0.441703	−	1.06637i	−0.533648	−	0.845707i	$-0.679179\pi$
$773$	12.2806	−	29.6480i	0.441703	−	1.06637i	0.975351	−	0.220659i	$-0.0708208\pi$
$774$	1.57987	−	0.484692i	0.0567871	−	0.0174219i
$775$	−16.2017	+	16.2017i	−0.581983	+	0.581983i
$776$	−8.22635	+	31.8951i	−0.295309	+	1.14497i
$777$	−22.7071	−	63.4596i	−0.814613	−	2.27660i
$778$	31.5800	+	4.05716i	1.13220	+	0.145456i
$779$	14.5445	+	18.9548i	0.521111	+	0.679126i
$780$	0.902516	+	0.573935i	0.0323153	+	0.0205502i
$781$	−10.0798	−	7.73451i	−0.360684	−	0.276762i
$782$	0.180830	+	57.8225i	0.00646646	+	2.06773i
$783$	7.05751	−	6.83077i	0.252215	−	0.244112i
$784$	0.240919	+	19.2583i	0.00860427	+	0.687796i
$785$	−8.18673	−	14.1798i	−0.292197	−	0.506100i
$786$	7.58657	+	10.8883i	0.270604	+	0.388372i
$787$	20.3717	+	2.68199i	0.726174	+	0.0956027i	0.484545	−	0.874766i	$-0.338985\pi$
$787$	20.3717	+	2.68199i	0.726174	+	0.0956027i	0.241629	+	0.970369i	$0.422318\pi$
$788$	−33.6057	+	26.1221i	−1.19715	+	0.930563i
$789$	15.2771	−	13.8467i	0.543880	−	0.492957i
$790$	3.72410	−	4.88490i	0.132498	−	0.173797i
$791$	22.1164	−	22.1164i	0.786367	−	0.786367i
$792$	−1.47960	+	6.62697i	−0.0525754	+	0.235479i
$793$	−1.53343	−	1.53343i	−0.0544537	−	0.0544537i
$794$	−28.9953	+	3.90960i	−1.02901	+	0.138746i
$795$	0.972217	−	3.02596i	0.0344810	−	0.107320i
$796$	−18.3416	+	5.03779i	−0.650102	+	0.178560i
$797$	−5.16266	+	39.2143i	−0.182871	+	1.38904i	0.616098	+	0.787669i	$0.288712\pi$
$797$	−5.16266	+	39.2143i	−0.182871	+	1.38904i	−0.798969	+	0.601372i	$0.794621\pi$
$798$	34.3752	−	40.7747i	1.21687	−	1.44341i
$799$	43.9922	−	25.3989i	1.55633	−	0.898549i
$800$	−21.9369	+	0.343045i	−0.775585	+	0.0121285i
$801$	−26.4004	−	9.93563i	−0.932811	−	0.351058i
$802$	−24.5244	+	24.6783i	−0.865986	+	0.871419i
$803$	1.33463	−	1.73933i	0.0470981	−	0.0613795i
$804$	29.6300	−	10.8117i	1.04497	−	0.381300i
$805$	−16.3478	+	12.5441i	−0.576185	+	0.442122i
$806$	1.92775	−	1.48882i	0.0679021	−	0.0524413i
$807$	3.88396	−	21.3471i	0.136722	−	0.751454i
$808$	−2.20509	−	1.65939i	−0.0775750	−	0.0583773i
$809$	1.15824	+	1.15824i	0.0407215	+	0.0407215i	0.727174	−	0.686453i	$-0.240833\pi$
$809$	1.15824	+	1.15824i	0.0407215	+	0.0407215i	−0.686453	+	0.727174i	$0.740833\pi$
$810$	−12.7779	−	4.29229i	−0.448971	−	0.150816i
$811$	−13.8537	−	5.73839i	−0.486469	−	0.201502i	0.125948	−	0.992037i	$-0.459803\pi$
$811$	−13.8537	−	5.73839i	−0.486469	−	0.201502i	−0.612417	+	0.790535i	$0.709803\pi$
$812$	1.77665	+	12.8724i	0.0623483	+	0.451731i
$813$	−10.9359	−	7.05091i	−0.383540	−	0.247286i
$814$	11.1153	+	6.37116i	0.389591	+	0.223309i
$815$	9.80124	+	5.65875i	0.343323	+	0.198217i
$816$	1.82945	−	50.0099i	0.0640436	−	1.75070i
$817$	2.13668	−	1.23361i	0.0747528	−	0.0431586i
$818$	−7.50011	+	0.0234553i	−0.262235	+	0.000820095i
$819$	3.00466	−	0.0984387i	0.104991	−	0.00343973i
$820$	3.10349	+	7.36191i	0.108379	+	0.257089i
$821$	2.06432	+	15.6801i	0.0720454	+	0.547239i	0.988963	+	0.148163i	$0.0473359\pi$
$821$	2.06432	+	15.6801i	0.0720454	+	0.547239i	−0.916918	+	0.399077i	$0.869331\pi$
$822$	−42.8822	+	22.1971i	−1.49569	+	0.774212i
$823$	17.5326	−	4.69785i	0.611149	−	0.163757i	0.0600479	−	0.998195i	$-0.480875\pi$
$823$	17.5326	−	4.69785i	0.611149	−	0.163757i	0.551101	+	0.834439i	$0.314208\pi$
$824$	1.12459	−	1.99075i	0.0391769	−	0.0693509i
$825$	3.47771	−	4.09907i	0.121078	−	0.142711i
$826$	15.1213	−	2.03889i	0.526139	−	0.0709421i
$827$	36.8154	+	15.2494i	1.28020	+	0.530275i	0.916049	−	0.401066i	$-0.131360\pi$
$827$	36.8154	+	15.2494i	1.28020	+	0.530275i	0.364149	+	0.931341i	$0.381360\pi$
$828$	33.4742	−	5.74279i	1.16331	−	0.199576i
$829$	−17.1148	−	41.3189i	−0.594423	−	1.43506i	−0.879192	−	0.476468i	$-0.841917\pi$
$829$	−17.1148	−	41.3189i	−0.594423	−	1.43506i	0.284769	−	0.958596i	$-0.408083\pi$
$830$	−1.95028	+	7.37065i	−0.0676951	+	0.255839i
$831$	39.6710	+	18.7624i	1.37617	+	0.650859i
$832$	2.31764	+	0.260985i	0.0803495	+	0.00904802i
$833$	30.1195	+	17.3895i	1.04358	+	0.602511i
$834$	−14.0955	−	2.51907i	−0.488088	−	0.0872282i
$835$	−1.67738	−	1.28710i	−0.0580480	−	0.0445418i
$836$	0.0634063	+	10.1374i	0.00219295	+	0.350608i
$837$	−19.0826	+	24.0458i	−0.659592	+	0.831145i
$838$	28.0917	+	11.5332i	0.970413	+	0.398407i
$839$	−3.89691	+	14.5435i	−0.134536	+	0.502097i	0.865463	+	0.500973i	$0.167024\pi$
$839$	−3.89691	+	14.5435i	−0.134536	+	0.502097i	−0.999999	+	0.00112378i	$0.999642\pi$
$840$	14.5681	−	10.2865i	0.502646	−	0.354917i
$841$	−6.58102	−	24.5607i	−0.226932	−	0.846921i
$842$	3.18886	−	24.8214i	0.109895	−	0.855401i
$843$	29.4114	+	32.4497i	1.01298	+	1.11763i
$844$	−28.6041	−	21.6658i	−0.984595	−	0.745769i
$845$	−5.23424	−	12.6366i	−0.180063	−	0.434711i
$846$	−19.0010	−	23.0046i	−0.653269	−	0.790913i
$847$	−35.6091			−1.22354
$848$	−0.990520	−	6.85955i	−0.0340146	−	0.235558i
$849$	−4.21834	−	51.4381i	−0.144773	−	1.76535i
$850$	−19.7016	+	34.3720i	−0.675761	+	1.17895i
$851$	8.36446	−	63.5344i	0.286730	−	2.17793i
$852$	16.4962	−	52.4680i	0.565151	−	1.79752i
$853$	−11.9089	+	1.56783i	−0.407752	+	0.0536816i	−0.331613	−	0.943416i	$-0.607593\pi$
$853$	−11.9089	+	1.56783i	−0.407752	+	0.0536816i	−0.0761394	+	0.997097i	$0.524259\pi$
$854$	−33.3633	+	13.9419i	−1.14167	+	0.477083i
$855$	−20.0279	−	1.97207i	−0.684941	−	0.0674433i
$856$	−16.3347	+	6.94631i	−0.558309	+	0.237420i
$857$	19.6815	+	5.27364i	0.672308	+	0.180144i	0.578794	−	0.815474i	$-0.303524\pi$
$857$	19.6815	+	5.27364i	0.672308	+	0.180144i	0.0935135	+	0.995618i	$0.470190\pi$
$858$	−0.422210	+	0.385091i	−0.0144140	+	0.0131468i
$859$	−22.6944	−	29.5759i	−0.774323	−	1.00912i	−0.999395	−	0.0347757i	$-0.988928\pi$
$859$	−22.6944	−	29.5759i	−0.774323	−	1.00912i	0.225072	−	0.974342i	$-0.427738\pi$
$860$	0.795560	−	0.218512i	0.0271284	−	0.00745119i
$861$	18.8735	+	12.1686i	0.643207	+	0.414706i
$862$	7.90910	−	29.8908i	0.269385	−	1.01808i
$863$	−27.1686			−0.924828			−0.462414	−	0.886664i	$-0.653017\pi$
$863$	−27.1686			−0.924828			−0.462414	+	0.886664i	$0.653017\pi$
$864$	−29.1450	+	3.81662i	−0.991534	+	0.129844i
$865$	−4.52301			−0.153787
$866$	−2.71180	+	10.2487i	−0.0921506	+	0.348264i
$867$	−51.2028	−	33.0128i	−1.73894	−	1.12117i
$868$	−10.7567	−	39.1630i	−0.365106	−	1.32928i
$869$	1.99791	+	2.60372i	0.0677744	+	0.0883253i
$870$	3.62288	−	3.30437i	0.122827	−	0.112029i
$871$	2.56400	+	0.687022i	0.0868779	+	0.0232789i
$872$	−21.5786	−	8.70190i	−0.730745	−	0.294683i
$873$	20.3493	−	28.3989i	0.688720	−	0.961159i
$874$	46.7858	−	19.5510i	1.58255	−	0.661321i
$875$	−32.0434	+	4.21859i	−1.08326	+	0.142614i
$876$	9.05364	+	2.84651i	0.305894	+	0.0961747i
$877$	4.59734	−	34.9203i	0.155241	−	1.17917i	−0.719468	−	0.694525i	$-0.755614\pi$
$877$	4.59734	−	34.9203i	0.155241	−	1.17917i	0.874709	−	0.484648i	$-0.161052\pi$
$878$	23.1148	−	40.3267i	0.780087	−	1.36096i
$879$	−0.514813	−	6.27758i	−0.0173642	−	0.211738i
$880$	−0.836352	+	3.28515i	−0.0281934	+	0.110742i
$881$	41.6804			1.40425			0.702125	−	0.712054i	$-0.252235\pi$
$881$	41.6804			1.40425			0.702125	+	0.712054i	$0.252235\pi$
$882$	7.13548	−	19.1414i	0.240264	−	0.644523i
$883$	−4.61476	−	11.1410i	−0.155299	−	0.374925i	0.827011	−	0.562185i	$-0.190039\pi$
$883$	−4.61476	−	11.1410i	−0.155299	−	0.374925i	−0.982310	+	0.187260i	$0.940039\pi$
$884$	2.54291	−	3.35726i	0.0855274	−	0.112917i
$885$	−3.86671	−	4.26615i	−0.129978	−	0.143405i
$886$	1.08492	−	8.44477i	0.0364486	−	0.283708i
$887$	0.835816	+	3.11931i	0.0280640	+	0.104736i	0.978537	−	0.206070i	$-0.0660676\pi$
$887$	0.835816	+	3.11931i	0.0280640	+	0.104736i	−0.950473	+	0.310806i	$0.899401\pi$
$888$	−9.41540	+	54.6559i	−0.315960	+	1.83413i
$889$	13.3982	−	50.0028i	0.449362	−	1.67704i
$890$	−13.0275	−	5.34851i	−0.436684	−	0.179282i
$891$	4.00093	−	5.98847i	0.134036	−	0.200621i
$892$	3.27803	−	0.0205031i	0.109756	−	0.000686495i
$893$	−35.3409	−	27.1180i	−1.18264	−	0.907469i
$894$	16.8659	+	3.01417i	0.564079	+	0.100809i
$895$	23.5151	+	13.5765i	0.786024	+	0.453811i
$896$	18.7024	−	34.0960i	0.624802	−	1.13907i
$897$	2.58390	+	1.22205i	0.0862740	+	0.0408032i
$898$	−5.40299	+	20.4195i	−0.180300	+	0.681406i
$899$	−4.27339	−	10.3169i	−0.142526	−	0.344087i
$900$	21.8299	+	8.06006i	0.727665	+	0.268669i
$901$	−11.5627	−	4.78941i	−0.385208	−	0.159558i
$902$	−4.23035	+	0.570401i	−0.140855	+	0.0189923i
$903$	1.50024	−	1.76829i	0.0499250	−	0.0588450i
$904$	−24.7964	+	6.89416i	−0.824717	+	0.229296i
$905$	3.42367	−	0.917369i	0.113807	−	0.0304944i
$906$	−34.5860	+	17.9027i	−1.14904	+	0.594779i
$907$	−1.27876	−	9.71315i	−0.0424605	−	0.322520i	−0.999473	−	0.0324718i	$-0.989662\pi$
$907$	−1.27876	−	9.71315i	−0.0424605	−	0.322520i	0.957012	−	0.290048i	$-0.0936712\pi$
$908$	14.3882	−	6.06550i	0.477489	−	0.201291i
$909$	1.54578	+	2.48568i	0.0512703	+	0.0824447i
$910$	1.50086	−	0.00469367i	0.0497529	−	0.000155594i
$911$	19.6744	−	11.3590i	0.651843	−	0.376342i	−0.137319	−	0.990527i	$-0.543848\pi$
$911$	19.6744	−	11.3590i	0.651843	−	0.376342i	0.789162	+	0.614185i	$0.210515\pi$
$912$	−41.1309	+	15.3005i	−1.36198	+	0.506650i
$913$	−3.52784	−	2.03680i	−0.116755	−	0.0674083i
$914$	15.2078	+	8.71692i	0.503029	+	0.288330i
$915$	11.4679	+	7.39386i	0.379115	+	0.244434i
$916$	22.2501	−	3.07098i	0.735165	−	0.101468i
$917$	17.2048	+	7.12644i	0.568151	+	0.235336i
$918$	−20.9578	+	48.7663i	−0.691712	+	1.60953i
$919$	5.02805	+	5.02805i	0.165860	+	0.165860i	0.785157	−	0.619297i	$-0.212582\pi$
$919$	5.02805	+	5.02805i	0.165860	+	0.165860i	−0.619297	+	0.785157i	$0.712582\pi$
$920$	16.7894	−	2.37082i	0.553530	−	0.0781635i
$921$	8.73750	−	48.0233i	0.287910	−	1.58242i
$922$	−0.00485519	+	0.00374970i	−0.000159897	+	0.000123490i
$923$	3.67224	−	2.81781i	0.120873	−	0.0927493i
$924$	3.26618	+	8.95109i	0.107449	+	0.294469i
$925$	26.7289	−	34.8338i	0.878842	−	1.14533i
$926$	12.8308	−	12.9113i	0.421646	−	0.424292i
$927$	−1.87461	+	1.53853i	−0.0615702	+	0.0505320i
$928$	3.93693	−	9.94148i	0.129236	−	0.326345i
$929$	−43.7577	+	25.2635i	−1.43564	+	0.828870i	−0.997543	−	0.0700557i	$-0.977682\pi$
$929$	−43.7577	+	25.2635i	−1.43564	+	0.828870i	−0.438102	+	0.898926i	$0.644349\pi$
$930$	−9.87827	+	11.7173i	−0.323921	+	0.384225i
$931$	3.98089	−	30.2379i	0.130468	−	0.991006i
$932$	−1.34634	−	4.90175i	−0.0441007	−	0.160562i
$933$	−3.23886	+	10.0807i	−0.106035	+	0.330029i
$934$	−44.1975	+	5.95939i	−1.44619	+	0.194997i
$935$	4.32855	+	4.32855i	0.141559	+	0.141559i
$936$	−2.19253	−	1.14555i	−0.0716652	−	0.0374434i
$937$	−2.66619	+	2.66619i	−0.0871006	+	0.0871006i	−0.749315	−	0.662214i	$-0.769617\pi$
$937$	−2.66619	+	2.66619i	−0.0871006	+	0.0871006i	0.662214	+	0.749315i	$0.269617\pi$
$938$	26.8340	−	35.1981i	0.876162	−	1.14926i
$939$	−14.8954	+	13.5008i	−0.486094	+	0.440582i
$940$	−9.14183	−	11.7608i	−0.298174	−	0.383596i
$941$	28.5473	+	3.75832i	0.930615	+	0.122518i	0.580566	−	0.814213i	$-0.302831\pi$
$941$	28.5473	+	3.75832i	0.930615	+	0.122518i	0.350049	+	0.936731i	$0.386165\pi$
$942$	21.6496	+	31.0716i	0.705382	+	1.01237i
$943$	10.6755	+	18.4906i	0.347643	+	0.602135i
$944$	−11.6589	−	4.65928i	−0.379465	−	0.151647i
$945$	−18.3484	+	4.59678i	−0.596874	+	0.149533i
$946$	0.00137853	+	0.440801i	4.48198e−5	+	0.0143317i
$947$	20.8065	+	15.9654i	0.676119	+	0.518805i	0.888787	−	0.458320i	$-0.151549\pi$
$947$	20.8065	+	15.9654i	0.676119	+	0.518805i	−0.212668	+	0.977125i	$0.568215\pi$
$948$	−7.62374	+	11.9884i	−0.247608	+	0.389364i
$949$	0.486228	+	0.633665i	0.0157836	+	0.0205696i
$950$	34.4591	+	4.42704i	1.11800	+	0.143632i
$951$	11.3170	+	31.6275i	0.366978	+	1.02559i
$952$	−35.6811	−	60.4838i	−1.15643	−	1.96029i
$953$	−7.78668	+	7.78668i	−0.252235	+	0.252235i	−0.821887	−	0.569651i	$-0.807078\pi$
$953$	−7.78668	+	7.78668i	−0.252235	+	0.252235i	0.569651	+	0.821887i	$0.307078\pi$
$954$	−1.64668	+	7.16430i	−0.0533134	+	0.231953i
$955$	1.03680	−	2.50306i	0.0335501	−	0.0809970i
$956$	12.8904	+	22.0078i	0.416906	+	0.711784i
$957$	1.19707	+	2.33042i	0.0386957	+	0.0753317i
$958$	9.53968	+	35.1623i	0.308213	+	1.13604i
$959$	−33.8795	+	58.6809i	−1.09402	+	1.89491i
$960$	−14.6005	+	1.47363i	−0.471231	+	0.0475611i
$961$	1.95087	+	3.37901i	0.0629313	+	0.109000i
$962$	−3.29011	+	3.31076i	−0.106078	+	0.106743i
$963$	18.8170	−	0.616482i	0.606368	−	0.0198658i
$964$	−38.4216	+	0.240316i	−1.23748	+	0.00774007i
$965$	23.0477	−	3.03429i	0.741933	−	0.0976773i
$966$	35.2127	−	32.1169i	1.13295	−	1.03334i
$967$	13.4912	+	50.3499i	0.433848	+	1.61914i	0.743807	+	0.668394i	$0.233018\pi$
$967$	13.4912	+	50.3499i	0.433848	+	1.61914i	−0.309959	+	0.950750i	$0.600315\pi$
$968$	25.5122	+	14.4120i	0.819992	+	0.463220i
$969$	−14.1854	+	77.9661i	−0.455700	+	2.50463i
$970$	10.5747	−	13.8709i	0.339535	−	0.445367i
$971$	7.17414	−	17.3199i	0.230229	−	0.555822i	−0.765975	−	0.642870i	$-0.777743\pi$
$971$	7.17414	−	17.3199i	0.230229	−	0.555822i	0.996204	+	0.0870482i	$0.0277434\pi$
$972$	30.2898	+	7.38415i	0.971547	+	0.236847i
$973$	−18.5637	+	7.68932i	−0.595124	+	0.246508i
$974$	24.0820	−	14.0043i	0.771636	−	0.448728i
$975$	1.11455	+	1.61033i	0.0356943	+	0.0515717i
$976$	29.5459	+	3.51438i	0.945740	+	0.112493i
$977$	1.54188	−	2.67062i	0.0493292	−	0.0854407i	−0.840306	−	0.542112i	$-0.817625\pi$
$977$	1.54188	−	2.67062i	0.0493292	−	0.0854407i	0.889636	+	0.456671i	$0.150958\pi$
$978$	−23.6980	−	11.1174i	−0.757780	−	0.355496i
$979$	4.58049	−	5.96941i	0.146393	−	0.190783i
$980$	3.84383	−	9.44651i	0.122787	−	0.301758i
$981$	18.0124	+	16.8696i	0.575092	+	0.538605i
$982$	−4.25764	−	10.1886i	−0.135867	−	0.325132i
$983$	29.0104	+	7.77331i	0.925288	+	0.247930i	0.689844	−	0.723958i	$-0.257679\pi$
$983$	29.0104	+	7.77331i	0.925288	+	0.247930i	0.235443	+	0.971888i	$0.424346\pi$
$984$	−8.59694	−	16.3569i	−0.274061	−	0.521438i
$985$	21.7710	−	5.83351i	0.693680	−	0.185871i
$986$	−11.8022	−	15.2817i	−0.375858	−	0.486668i
$987$	−39.8624	−	12.8074i	−1.26883	−	0.407666i
$988$	−3.57334	−	0.933560i	−0.113683	−	0.0297005i
$989$	2.03700	−	0.843752i	0.0647727	−	0.0268297i
$990$	2.08512	−	2.92924i	0.0662693	−	0.0930972i
$991$			27.2803i			0.866588i	0.901253	+	0.433294i	$0.142649\pi$
$991$			27.2803i			0.866588i	−0.901253	+	0.433294i	$0.857351\pi$
$992$	−8.14378	+	32.4120i	−0.258565	+	1.02908i
$993$	−16.5097	+	34.9079i	−0.523918	+	1.10777i
$994$	−20.2087	−	74.4872i	−0.640980	−	2.36259i
$995$	9.98595	+	1.31467i	0.316576	+	0.0416780i
$996$	3.04803	−	17.3688i	0.0965806	−	0.550353i
$997$	2.25192	+	17.1050i	0.0713190	+	0.541721i	0.989388	+	0.145300i	$0.0464147\pi$
$997$	2.25192	+	17.1050i	0.0713190	+	0.541721i	−0.918069	+	0.396421i	$0.870252\pi$
$998$	−57.7258	−	23.6996i	−1.82728	−	0.750197i
$999$	30.2403	−	50.4573i	0.956761	−	1.59640i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.59.3	✓	368
3.2	odd	2		864.2.bn.a.827.44		368
9.2	odd	6	inner	288.2.bf.a.155.20	yes	368
9.7	even	3		864.2.bn.a.251.27		368
32.19	odd	8	inner	288.2.bf.a.275.20	yes	368
96.83	even	8		864.2.bn.a.179.27		368
288.83	even	24	inner	288.2.bf.a.83.3	yes	368
288.115	odd	24		864.2.bn.a.467.44		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.59.3	✓	368	1.1	even	1	trivial
288.2.bf.a.83.3	yes	368	288.83	even	24	inner
288.2.bf.a.155.20	yes	368	9.2	odd	6	inner
288.2.bf.a.275.20	yes	368	32.19	odd	8	inner
864.2.bn.a.179.27		368	96.83	even	8
864.2.bn.a.251.27		368	9.7	even	3
864.2.bn.a.467.44		368	288.115	odd	24
864.2.bn.a.827.44		368	3.2	odd	2

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bf (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36716 - 0.361752i) q^{2} +(-1.45571 - 0.938565i) q^{3} +(1.73827 + 0.989147i) q^{4} +(-0.644713 - 0.840206i) q^{5} +(1.65067 + 1.80978i) q^{6} +(3.32016 + 0.889635i) q^{7} +(-2.01868 - 1.98115i) q^{8} +(1.23819 + 2.73256i) q^{9} +O(q^{10})\)	\(q+(-1.36716 - 0.361752i) q^{2} +(-1.45571 - 0.938565i) q^{3} +(1.73827 + 0.989147i) q^{4} +(-0.644713 - 0.840206i) q^{5} +(1.65067 + 1.80978i) q^{6} +(3.32016 + 0.889635i) q^{7} +(-2.01868 - 1.98115i) q^{8} +(1.23819 + 2.73256i) q^{9} +(0.577482 + 1.38193i) q^{10} +(-0.793379 + 0.104450i) q^{11} +(-1.60204 - 3.07139i) q^{12} +(0.0380530 - 0.289041i) q^{13} +(-4.21738 - 2.41735i) q^{14} +(0.149927 + 1.82820i) q^{15} +(2.04318 + 3.43881i) q^{16} +7.22314 q^{17} +(-0.704301 - 4.18377i) q^{18} +(-2.42399 - 5.85203i) q^{19} +(-0.289598 - 2.09822i) q^{20} +(-3.99822 - 4.41124i) q^{21} +(1.12246 + 0.144206i) q^{22} +(-1.46506 - 5.46767i) q^{23} +(1.07917 + 4.77864i) q^{24} +(1.00380 - 3.74625i) q^{25} +(-0.156586 + 0.381401i) q^{26} +(0.762238 - 5.13994i) q^{27} +(4.89137 + 4.83056i) q^{28} +(1.49960 + 1.15069i) q^{29} +(0.456380 - 2.55369i) q^{30} +(-5.11628 - 2.95388i) q^{31} +(-1.54936 - 5.44054i) q^{32} +(1.25296 + 0.592589i) q^{33} +(-9.87521 - 2.61298i) q^{34} +(-1.39308 - 3.36318i) q^{35} +(-0.550593 + 5.97468i) q^{36} +(10.4592 + 4.33233i) q^{37} +(1.19701 + 8.87756i) q^{38} +(-0.326678 + 0.385045i) q^{39} +(-0.363107 + 2.97338i) q^{40} +(-3.64338 + 0.976242i) q^{41} +(3.87045 + 7.47725i) q^{42} +(0.0508411 + 0.386176i) q^{43} +(-1.48243 - 0.603206i) q^{44} +(1.49764 - 2.80205i) q^{45} +(0.0250348 + 8.00518i) q^{46} +(6.09046 - 3.51633i) q^{47} +(0.253276 - 6.92357i) q^{48} +(4.16987 + 2.40747i) q^{49} +(-2.72757 + 4.75860i) q^{50} +(-10.5148 - 6.77939i) q^{51} +(0.352051 - 0.464792i) q^{52} +(-1.60078 - 0.663065i) q^{53} +(-2.90149 + 6.75140i) q^{54} +(0.599262 + 0.599262i) q^{55} +(-4.93984 - 8.37362i) q^{56} +(-1.96388 + 10.7939i) q^{57} +(-1.63394 - 2.11566i) q^{58} +(-2.49022 + 1.91082i) q^{59} +(-1.54775 + 3.32621i) q^{60} +(4.52830 - 5.90139i) q^{61} +(5.92622 + 5.88927i) q^{62} +(1.68001 + 10.1741i) q^{63} +(0.150102 + 7.99859i) q^{64} +(-0.267388 + 0.154376i) q^{65} +(-1.49864 - 1.26343i) q^{66} +(-1.18845 + 9.02718i) q^{67} +(12.5558 + 7.14475i) q^{68} +(-2.99906 + 9.33439i) q^{69} +(0.687926 + 5.10197i) q^{70} +(11.2269 + 11.2269i) q^{71} +(2.91410 - 7.96919i) q^{72} +(-1.93726 + 1.93726i) q^{73} +(-12.7322 - 9.70663i) q^{74} +(-4.97734 + 4.51132i) q^{75} +(1.57496 - 12.5701i) q^{76} +(-2.72707 - 0.359026i) q^{77} +(0.585913 - 0.408244i) q^{78} +(-2.05062 - 3.55178i) q^{79} +(1.57205 - 3.93374i) q^{80} +(-5.93377 + 6.76686i) q^{81} +(5.33426 - 0.0166820i) q^{82} +(4.03862 + 3.09894i) q^{83} +(-2.58662 - 11.6228i) q^{84} +(-4.65685 - 6.06893i) q^{85} +(0.0701918 - 0.546358i) q^{86} +(-1.10300 - 3.08254i) q^{87} +(1.80851 + 1.36095i) q^{88} +(-6.64871 + 6.64871i) q^{89} +(-3.06116 + 3.28909i) q^{90} +(0.383484 - 0.925811i) q^{91} +(2.86166 - 10.9534i) q^{92} +(4.67541 + 9.10196i) q^{93} +(-9.59869 + 2.60416i) q^{94} +(-3.35413 + 5.80953i) q^{95} +(-2.85088 + 9.37403i) q^{96} +(-5.82283 - 10.0854i) q^{97} +(-4.82998 - 4.79986i) q^{98} +(-1.26777 - 2.03863i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more