LMFDB - Embedded newform 135.2.q.a.23.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(2,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("135.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.q (of order $36$, degree $12$, 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:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			23.1
Character	$\chi$	$=$	135.23
Dual form			135.2.q.a.47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15365 - 2.47401i) q^{2} +(-1.57848 - 0.713012i) q^{3} +(-3.50423 + 4.17618i) q^{4} +(-1.08960 - 1.95263i) q^{5} +(0.0570200 + 4.72775i) q^{6} +(-0.00587402 + 0.0671403i) q^{7} +(9.10104 + 2.43862i) q^{8} +(1.98323 + 2.25096i) q^{9} +O(q^{10})$	\(q+(-1.15365 - 2.47401i) q^{2} +(-1.57848 - 0.713012i) q^{3} +(-3.50423 + 4.17618i) q^{4} +(-1.08960 - 1.95263i) q^{5} +(0.0570200 + 4.72775i) q^{6} +(-0.00587402 + 0.0671403i) q^{7} +(9.10104 + 2.43862i) q^{8} +(1.98323 + 2.25096i) q^{9} +(-3.57380 + 4.94833i) q^{10} +(-2.84658 + 0.501928i) q^{11} +(8.50904 - 4.09348i) q^{12} +(-1.43375 - 0.668569i) q^{13} +(0.172882 - 0.0629240i) q^{14} +(0.327671 + 3.85910i) q^{15} +(-2.57292 - 14.5918i) q^{16} +(-0.265033 + 0.0710153i) q^{17} +(3.28093 - 7.50333i) q^{18} +(-1.42429 + 0.822315i) q^{19} +(11.9727 + 2.29209i) q^{20} +(0.0571439 - 0.101792i) q^{21} +(4.52572 + 6.46340i) q^{22} +(-7.26851 + 0.635912i) q^{23} +(-12.6271 - 10.3385i) q^{24} +(-2.62553 + 4.25518i) q^{25} +4.31840i q^{26} +(-1.52554 - 4.96717i) q^{27} +(-0.259806 - 0.259806i) q^{28} +(-0.282115 - 0.102681i) q^{29} +(9.16941 - 5.26270i) q^{30} +(-0.140950 - 0.118271i) q^{31} +(-17.6956 + 12.3906i) q^{32} +(4.85116 + 1.23736i) q^{33} +(0.481447 + 0.573766i) q^{34} +(0.137501 - 0.0616864i) q^{35} +(-16.3501 + 0.394444i) q^{36} +(-2.46210 - 9.18868i) q^{37} +(3.67754 + 2.57504i) q^{38} +(1.78646 + 2.07761i) q^{39} +(-5.15479 - 20.4281i) q^{40} +(-1.74933 - 4.80625i) q^{41} +(-0.317757 - 0.0239425i) q^{42} +(-3.11177 + 4.44406i) q^{43} +(7.87892 - 13.6467i) q^{44} +(2.23436 - 6.32516i) q^{45} +(9.95855 + 17.2487i) q^{46} +(-1.87998 - 0.164477i) q^{47} +(-6.34278 + 24.8674i) q^{48} +(6.88918 + 1.21475i) q^{49} +(13.5563 + 1.58661i) q^{50} +(0.468985 + 0.0768749i) q^{51} +(7.81625 - 3.64478i) q^{52} +(1.58658 - 1.58658i) q^{53} +(-10.5289 + 9.50455i) q^{54} +(4.08172 + 5.01141i) q^{55} +(-0.217189 + 0.596722i) q^{56} +(2.83454 - 0.282475i) q^{57} +(0.0714269 + 0.816413i) q^{58} +(2.10453 - 11.9354i) q^{59} +(-17.2645 - 12.1547i) q^{60} +(3.42343 - 2.87260i) q^{61} +(-0.129996 + 0.485153i) q^{62} +(-0.162779 + 0.119932i) q^{63} +(25.4054 + 14.6678i) q^{64} +(0.256749 + 3.52806i) q^{65} +(-2.53530 - 13.4293i) q^{66} +(1.04879 - 2.24913i) q^{67} +(0.632163 - 1.35568i) q^{68} +(11.9266 + 4.17875i) q^{69} +(-0.311240 - 0.269013i) q^{70} +(-4.91000 - 2.83479i) q^{71} +(12.5602 + 25.3224i) q^{72} +(2.33705 - 8.72199i) q^{73} +(-19.8925 + 16.6918i) q^{74} +(7.17836 - 4.84470i) q^{75} +(1.55691 - 8.82967i) q^{76} +(-0.0169788 - 0.194068i) q^{77} +(3.07907 - 6.81653i) q^{78} +(-2.57857 + 7.08457i) q^{79} +(-25.6889 + 20.9232i) q^{80} +(-1.13361 + 8.92832i) q^{81} +(-9.87258 + 9.87258i) q^{82} +(-11.1580 + 5.20307i) q^{83} +(0.224855 + 0.595345i) q^{84} +(0.427447 + 0.440133i) q^{85} +(14.5845 + 2.57164i) q^{86} +(0.372101 + 0.363233i) q^{87} +(-27.1308 - 2.37364i) q^{88} +(6.33320 + 10.9694i) q^{89} +(-18.2262 + 1.76919i) q^{90} +(0.0533098 - 0.0923353i) q^{91} +(22.8148 - 32.5830i) q^{92} +(0.138158 + 0.287188i) q^{93} +(1.76192 + 4.84082i) q^{94} +(3.15759 + 1.88512i) q^{95} +(36.7669 - 6.94119i) q^{96} +(-1.59804 - 1.11896i) q^{97} +(-4.94240 - 18.4453i) q^{98} +(-6.77523 - 5.41208i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.15365	−	2.47401i	−0.815752	−	1.74939i	−0.645163	−	0.764045i	$-0.723211\pi$
$2$	−1.15365	−	2.47401i	−0.815752	−	1.74939i	−0.170589	−	0.985342i	$-0.554567\pi$
$3$	−1.57848	−	0.713012i	−0.911339	−	0.411658i
$3$	−1.57848	−	0.713012i	−0.911339	−	0.411658i
$4$	−3.50423	+	4.17618i	−1.75211	+	2.08809i
$5$	−1.08960	−	1.95263i	−0.487285	−	0.873243i
$5$	−1.08960	−	1.95263i	−0.487285	−	0.873243i
$6$	0.0570200	+	4.72775i	0.0232783	+	1.93009i
$7$	−0.00587402	+	0.0671403i	−0.00222017	+	0.0253767i	−0.997224	−	0.0744603i	$-0.976277\pi$
$7$	−0.00587402	+	0.0671403i	−0.00222017	+	0.0253767i	0.995004	+	0.0998370i	$0.0318321\pi$
$8$	9.10104	+	2.43862i	3.21770	+	0.862181i
$9$	1.98323	+	2.25096i	0.661076	+	0.750319i
$10$	−3.57380	+	4.94833i	−1.13014	+	1.56480i
$11$	−2.84658	+	0.501928i	−0.858275	+	0.151337i	−0.585432	−	0.810721i	$-0.699075\pi$
$11$	−2.84658	+	0.501928i	−0.858275	+	0.151337i	−0.272843	+	0.962059i	$0.587964\pi$
$12$	8.50904	−	4.09348i	2.45635	−	1.18168i
$13$	−1.43375	−	0.668569i	−0.397651	−	0.185428i	0.213498	−	0.976944i	$-0.431514\pi$
$13$	−1.43375	−	0.668569i	−0.397651	−	0.185428i	−0.611149	+	0.791516i	$0.709292\pi$
$14$	0.172882	−	0.0629240i	0.0462047	−	0.0168171i
$15$	0.327671	+	3.85910i	0.0846043	+	0.996415i
$16$	−2.57292	−	14.5918i	−0.643230	−	3.64794i
$17$	−0.265033	+	0.0710153i	−0.0642799	+	0.0172237i	−0.290816	−	0.956779i	$-0.593927\pi$
$17$	−0.265033	+	0.0710153i	−0.0642799	+	0.0172237i	0.226536	+	0.974003i	$0.427260\pi$
$18$	3.28093	−	7.50333i	0.773324	−	1.76855i
$19$	−1.42429	+	0.822315i	−0.326755	+	0.188652i	−0.654399	−	0.756149i	$-0.727078\pi$
$19$	−1.42429	+	0.822315i	−0.326755	+	0.188652i	0.327645	+	0.944801i	$0.393745\pi$
$20$	11.9727	+	2.29209i	2.67719	+	0.512528i
$21$	0.0571439	−	0.101792i	0.0124698	−	0.0222128i
$22$	4.52572	+	6.46340i	0.964887	+	1.37800i
$23$	−7.26851	+	0.635912i	−1.51559	+	0.132597i	−0.814368	−	0.580348i	$-0.802916\pi$
$23$	−7.26851	+	0.635912i	−1.51559	+	0.132597i	−0.701220	+	0.712945i	$0.747361\pi$
$24$	−12.6271	−	10.3385i	−2.57749	−	2.11033i
$25$	−2.62553	+	4.25518i	−0.525107	+	0.851036i
$26$			4.31840i			0.846908i
$27$	−1.52554	−	4.96717i	−0.293590	−	0.955932i
$28$	−0.259806	−	0.259806i	−0.0490987	−	0.0490987i
$29$	−0.282115	−	0.102681i	−0.0523874	−	0.0190675i	0.315694	−	0.948861i	$-0.397763\pi$
$29$	−0.282115	−	0.102681i	−0.0523874	−	0.0190675i	−0.368081	+	0.929794i	$0.619985\pi$
$30$	9.16941	−	5.26270i	1.67410	−	0.960833i
$31$	−0.140950	−	0.118271i	−0.0253153	−	0.0212421i	0.630042	−	0.776561i	$-0.283038\pi$
$31$	−0.140950	−	0.118271i	−0.0253153	−	0.0212421i	−0.655358	+	0.755319i	$0.727482\pi$
$32$	−17.6956	+	12.3906i	−3.12817	+	2.19037i
$33$	4.85116	+	1.23736i	0.844478	+	0.215396i
$34$	0.481447	+	0.573766i	0.0825675	+	0.0984001i
$35$	0.137501	−	0.0616864i	0.0232418	−	0.0104269i
$36$	−16.3501	+	0.394444i	−2.72501	+	0.0657407i
$37$	−2.46210	−	9.18868i	−0.404767	−	1.51061i	−0.804485	−	0.593972i	$-0.797559\pi$
$37$	−2.46210	−	9.18868i	−0.404767	−	1.51061i	0.399719	−	0.916638i	$-0.369108\pi$
$38$	3.67754	+	2.57504i	0.596576	+	0.417727i
$39$	1.78646	+	2.07761i	0.286062	+	0.332683i
$40$	−5.15479	−	20.4281i	−0.815045	−	3.22997i
$41$	−1.74933	−	4.80625i	−0.273200	−	0.750610i	−0.998092	−	0.0617475i	$-0.980333\pi$
$41$	−1.74933	−	4.80625i	−0.273200	−	0.750610i	0.724892	−	0.688862i	$-0.241890\pi$
$42$	−0.317757	−	0.0239425i	−0.0490310	−	0.00369441i
$43$	−3.11177	+	4.44406i	−0.474540	+	0.677713i	−0.983049	−	0.183344i	$-0.941308\pi$
$43$	−3.11177	+	4.44406i	−0.474540	+	0.677713i	0.508509	+	0.861057i	$0.330197\pi$
$44$	7.87892	−	13.6467i	1.18779	−	2.05731i
$45$	2.23436	−	6.32516i	0.333078	−	0.942899i
$46$	9.95855	+	17.2487i	1.46831	+	2.54318i
$47$	−1.87998	−	0.164477i	−0.274223	−	0.0239914i	−0.0507851	−	0.998710i	$-0.516172\pi$
$47$	−1.87998	−	0.164477i	−0.274223	−	0.0239914i	−0.223438	+	0.974718i	$0.571728\pi$
$48$	−6.34278	+	24.8674i	−0.915502	+	3.58930i
$49$	6.88918	+	1.21475i	0.984169	+	0.173535i
$50$	13.5563	+	1.58661i	1.91715	+	0.224380i
$51$	0.468985	+	0.0768749i	0.0656710	+	0.0107646i
$52$	7.81625	−	3.64478i	1.08392	−	0.505440i
$53$	1.58658	−	1.58658i	0.217933	−	0.217933i	−0.589694	−	0.807627i	$-0.700752\pi$
$53$	1.58658	−	1.58658i	0.217933	−	0.217933i	0.807627	+	0.589694i	$0.200752\pi$
$54$	−10.5289	+	9.50455i	−1.43280	+	1.29341i
$55$	4.08172	+	5.01141i	0.550379	+	0.675739i
$56$	−0.217189	+	0.596722i	−0.0290231	+	0.0797404i
$57$	2.83454	−	0.282475i	0.375444	−	0.0374147i
$58$	0.0714269	+	0.816413i	0.00937881	+	0.107200i
$59$	2.10453	−	11.9354i	0.273987	−	1.55386i	−0.468175	−	0.883636i	$-0.655088\pi$
$59$	2.10453	−	11.9354i	0.273987	−	1.55386i	0.742162	−	0.670221i	$-0.233801\pi$
$60$	−17.2645	−	12.1547i	−2.22884	−	1.56917i
$61$	3.42343	−	2.87260i	0.438325	−	0.367799i	−0.396757	−	0.917924i	$-0.629864\pi$
$61$	3.42343	−	2.87260i	0.438325	−	0.367799i	0.835082	+	0.550125i	$0.185420\pi$
$62$	−0.129996	+	0.485153i	−0.0165096	+	0.0616146i
$63$	−0.162779	+	0.119932i	−0.0205083	+	0.0151101i
$64$	25.4054	+	14.6678i	3.17567	+	1.83348i
$65$	0.256749	+	3.52806i	0.0318458	+	0.437602i
$66$	−2.53530	−	13.4293i	−0.312074	−	1.65303i
$67$	1.04879	−	2.24913i	0.128130	−	0.274775i	−0.831769	−	0.555122i	$-0.812672\pi$
$67$	1.04879	−	2.24913i	0.128130	−	0.274775i	0.959899	+	0.280347i	$0.0904495\pi$
$68$	0.632163	−	1.35568i	0.0766610	−	0.164400i
$69$	11.9266	+	4.17875i	1.43580	+	0.503063i
$70$	−0.311240	−	0.269013i	−0.0372003	−	0.0321532i
$71$	−4.91000	−	2.83479i	−0.582710	−	0.336427i	0.179500	−	0.983758i	$-0.442552\pi$
$71$	−4.91000	−	2.83479i	−0.582710	−	0.336427i	−0.762209	+	0.647330i	$0.775885\pi$
$72$	12.5602	+	25.3224i	1.48024	+	2.98427i
$73$	2.33705	−	8.72199i	0.273531	−	1.02083i	−0.683288	−	0.730149i	$-0.739451\pi$
$73$	2.33705	−	8.72199i	0.273531	−	1.02083i	0.956819	−	0.290683i	$-0.0938825\pi$
$74$	−19.8925	+	16.6918i	−2.31245	+	1.94038i
$75$	7.17836	−	4.84470i	0.828886	−	0.559418i
$76$	1.55691	−	8.82967i	0.178590	−	1.01283i
$77$	−0.0169788	−	0.194068i	−0.00193491	−	0.0221161i
$78$	3.07907	−	6.81653i	0.348636	−	0.771820i
$79$	−2.57857	+	7.08457i	−0.290112	+	0.797076i	0.705937	+	0.708274i	$0.250526\pi$
$79$	−2.57857	+	7.08457i	−0.290112	+	0.797076i	−0.996049	+	0.0888020i	$0.971696\pi$
$80$	−25.6889	+	20.9232i	−2.87210	+	2.33928i
$81$	−1.13361	+	8.92832i	−0.125957	+	0.992036i
$82$	−9.87258	+	9.87258i	−1.09024	+	1.09024i
$83$	−11.1580	+	5.20307i	−1.22475	+	0.571111i	−0.923927	−	0.382568i	$-0.875040\pi$
$83$	−11.1580	+	5.20307i	−1.22475	+	0.571111i	−0.300825	+	0.953679i	$0.597262\pi$
$84$	0.224855	+	0.595345i	0.0245337	+	0.0649574i
$85$	0.427447	+	0.440133i	0.0463631	+	0.0477391i
$86$	14.5845	+	2.57164i	1.57269	+	0.277308i
$87$	0.372101	+	0.363233i	0.0398934	+	0.0389426i
$88$	−27.1308	−	2.37364i	−2.89216	−	0.253031i
$89$	6.33320	+	10.9694i	0.671318	+	1.16276i	0.977530	+	0.210794i	$0.0676050\pi$
$89$	6.33320	+	10.9694i	0.671318	+	1.16276i	−0.306212	+	0.951963i	$0.599062\pi$
$90$	−18.2262	+	1.76919i	−1.92120	+	0.186489i
$91$	0.0533098	−	0.0923353i	0.00558839	−	0.00967937i
$92$	22.8148	−	32.5830i	2.37861	−	3.39701i
$93$	0.138158	+	0.287188i	0.0143264	+	0.0297800i
$94$	1.76192	+	4.84082i	0.181728	+	0.499293i
$95$	3.15759	+	1.88512i	0.323962	+	0.193409i
$96$	36.7669	−	6.94119i	3.75251	−	0.708432i
$97$	−1.59804	−	1.11896i	−0.162256	−	0.113613i	0.489628	−	0.871931i	$-0.337132\pi$
$97$	−1.59804	−	1.11896i	−0.162256	−	0.113613i	−0.651885	+	0.758318i	$0.726021\pi$
$98$	−4.94240	−	18.4453i	−0.499257	−	1.86325i
$99$	−6.77523	−	5.41208i	−0.680936	−	0.543935i
$100$	−8.56992	−	25.8758i	−0.856992	−	2.58758i
$101$	−7.95401	−	9.47922i	−0.791454	−	0.943218i	0.207936	−	0.978142i	$-0.433325\pi$
$101$	−7.95401	−	9.47922i	−0.791454	−	0.943218i	−0.999390	+	0.0349247i	$0.988881\pi$
$102$	−0.350855	−	1.24896i	−0.0347398	−	0.123665i
$103$	−2.71909	+	1.90393i	−0.267920	+	0.187600i	−0.699815	−	0.714324i	$-0.746734\pi$
$103$	−2.71909	+	1.90393i	−0.267920	+	0.187600i	0.431895	+	0.901924i	$0.357845\pi$
$104$	−11.4182	−	9.58104i	−1.11965	−	0.939498i
$105$	−0.261026		0.000668456i	−0.0254735		6.52346e-5i
$106$	−5.75556	−	2.09485i	−0.559029	−	0.203470i
$107$	6.13426	+	6.13426i	0.593021	+	0.593021i	0.938446	−	0.345425i	$-0.112265\pi$
$107$	6.13426	+	6.13426i	0.593021	+	0.593021i	−0.345425	+	0.938446i	$0.612265\pi$
$108$	26.0896	+	11.0352i	2.51047	+	1.06186i
$109$		−	14.6291i		−	1.40122i	−0.713547	−	0.700608i	$-0.752912\pi$
$109$		−	14.6291i		−	1.40122i	0.713547	−	0.700608i	$-0.247088\pi$
$110$	7.68940	−	15.8796i	0.733156	−	1.51406i
$111$	−2.66525	+	16.2597i	−0.252975	+	1.54330i
$112$	0.994809	−	0.0870345i	0.0940006	−	0.00822398i
$113$	4.27558	+	6.10616i	0.402212	+	0.574419i	0.968257	−	0.249956i	$-0.0804160\pi$
$113$	4.27558	+	6.10616i	0.402212	+	0.574419i	−0.566045	+	0.824374i	$0.691527\pi$
$114$	−3.96891	−	6.68680i	−0.371722	−	0.626276i
$115$	9.16148	+	13.4998i	0.854312	+	1.25886i
$116$	1.41741	−	0.818343i	0.131603	−	0.0759813i
$117$	−1.33853	−	4.55324i	−0.123748	−	0.420947i
$118$	−31.9562	+	8.56263i	−2.94180	+	0.788254i
$119$	−0.00321118	−	0.0182115i	−0.000294369	−	0.00166945i
$120$	−6.42871	+	35.9209i	−0.586858	+	3.27911i
$121$	−2.48555	+	0.904666i	−0.225959	+	0.0822424i
$122$	−11.0563	−	5.15562i	−1.00099	−	0.466768i
$123$	−0.665620	+	8.83388i	−0.0600169	+	0.796525i
$124$	0.987840	−	0.174183i	0.0887107	−	0.0156421i
$125$	11.1696	+	0.490246i	0.999038	+	0.0438489i
$126$	0.484504	+	0.264358i	0.0431630	+	0.0235509i
$127$	−5.74740	−	1.54001i	−0.509999	−	0.136654i	−0.00536222	−	0.999986i	$-0.501707\pi$
$127$	−5.74740	−	1.54001i	−0.509999	−	0.136654i	−0.504637	+	0.863332i	$0.668374\pi$
$128$	3.21383	−	36.7343i	0.284065	−	3.24688i
$129$	8.08054	−	4.79616i	0.711452	−	0.422278i
$130$	8.43225	−	4.70534i	0.739557	−	0.412686i
$131$	−2.94865	+	3.51407i	−0.257625	+	0.307025i	−0.879318	−	0.476236i	$-0.842001\pi$
$131$	−2.94865	+	3.51407i	−0.257625	+	0.307025i	0.621693	+	0.783261i	$0.286445\pi$
$132$	−22.1670	+	15.9233i	−1.92939	+	1.38595i
$133$	−0.0468442	−	0.100458i	−0.00406190	−	0.00871078i
$134$	−6.77429			−0.585209
$135$	−8.03681	+	8.39104i	−0.691699	+	0.722186i
$136$	−2.58525			−0.221684
$137$	3.76963	+	8.08399i	0.322061	+	0.690662i	0.998969	−	0.0454058i	$-0.0144581\pi$
$137$	3.76963	+	8.08399i	0.322061	+	0.690662i	−0.676908	+	0.736068i	$0.736680\pi$
$138$	−3.42088	−	34.3274i	−0.291205	−	2.92214i
$139$	9.70032	−	11.5604i	0.822771	−	0.980540i	−0.177223	−	0.984171i	$-0.556711\pi$
$139$	9.70032	−	11.5604i	0.822771	−	0.980540i	0.999993	+	0.00363092i	$0.00115576\pi$
$140$	−0.224220	+	0.790390i	−0.0189501	+	0.0668002i
$141$	2.85024	+	1.60007i	0.240034	+	0.134750i
$142$	−1.34888	+	15.4177i	−0.113195	+	1.29383i
$143$	4.41686	+	1.18349i	0.369356	+	0.0989686i
$144$	27.7427	−	34.7303i	2.31189	−	2.89419i
$145$	0.106894	+	0.662749i	0.00887707	+	0.0550383i
$146$	−24.2744	+	4.28023i	−2.00896	+	0.354234i
$147$	−10.0083	−	6.82953i	−0.825474	−	0.563290i
$148$	47.0013	+	21.9171i	3.86349	+	1.80157i
$149$	−13.5292	+	4.92423i	−1.10836	+	0.403409i	−0.830390	−	0.557182i	$-0.811882\pi$
$149$	−13.5292	+	4.92423i	−1.10836	+	0.403409i	−0.277966	+	0.960591i	$0.589660\pi$
$150$	−20.2671	−	12.1702i	−1.65480	−	0.993695i
$151$	−0.377952	−	2.14347i	−0.0307573	−	0.174433i	0.965559	−	0.260182i	$-0.0837827\pi$
$151$	−0.377952	−	2.14347i	−0.0307573	−	0.174433i	−0.996317	+	0.0857493i	$0.972672\pi$
$152$	−14.9678	+	4.01062i	−1.21405	+	0.325304i
$153$	−0.685473	−	0.455738i	−0.0554172	−	0.0368442i
$154$	−0.460539	+	0.265892i	−0.0371113	+	0.0214262i
$155$	−0.0773602	+	0.404091i	−0.00621372	+	0.0324574i
$156$	−14.9366	+	0.180146i	−1.19589	+	0.0144232i
$157$	3.48717	+	4.98020i	0.278307	+	0.397463i	0.933833	−	0.357709i	$-0.116442\pi$
$157$	3.48717	+	4.98020i	0.278307	+	0.397463i	−0.655526	+	0.755172i	$0.727553\pi$
$158$	20.5020	−	1.79370i	1.63105	−	0.142699i
$159$	−3.63564	+	1.37314i	−0.288325	+	0.108897i
$160$	43.4754	+	21.0522i	3.43704	+	1.66432i
$161$		−	0.491745i		−	0.0387549i
$162$	23.3965	−	7.49558i	1.83820	−	0.588908i
$163$	−8.83178	−	8.83178i	−0.691758	−	0.691758i	0.270860	−	0.962619i	$-0.412692\pi$
$163$	−8.83178	−	8.83178i	−0.691758	−	0.691758i	−0.962619	+	0.270860i	$0.912692\pi$
$164$	26.2018	+	9.53668i	2.04602	+	0.744689i
$165$	−2.86973	−	10.8207i	−0.223408	−	0.842394i
$166$	25.7449	+	21.6025i	1.99819	+	1.67668i
$167$	18.2595	−	12.7854i	1.41296	−	0.989367i	0.416174	−	0.909285i	$-0.363371\pi$
$167$	18.2595	−	12.7854i	1.41296	−	0.989367i	0.996788	−	0.0800820i	$-0.0255182\pi$
$168$	0.768300	−	0.787059i	0.0592756	−	0.0607229i
$169$	−6.74758	−	8.04146i	−0.519045	−	0.618573i
$170$	0.595768	−	1.56526i	0.0456933	−	0.120050i
$171$	−4.67569	−	1.57518i	−0.357559	−	0.120457i
$172$	−7.65485	−	28.5683i	−0.583677	−	2.17831i
$173$	10.1501	+	7.10715i	0.771695	+	0.540347i	0.891808	−	0.452413i	$-0.149437\pi$
$173$	10.1501	+	7.10715i	0.771695	+	0.540347i	−0.120113	+	0.992760i	$0.538326\pi$
$174$	0.469366	−	1.33962i	0.0355825	−	0.101557i
$175$	−0.270272	−	0.201274i	−0.0204306	−	0.0152149i
$176$	14.6480	+	40.2451i	1.10414	+	3.03359i
$177$	−11.8321	+	17.3393i	−0.889352	+	1.30330i
$178$	19.8322	−	28.3233i	1.48648	−	2.12292i
$179$	−7.35758	+	12.7437i	−0.549932	+	0.952510i	0.448347	+	0.893860i	$0.352013\pi$
$179$	−7.35758	+	12.7437i	−0.549932	+	0.952510i	−0.998279	+	0.0586499i	$0.981320\pi$
$180$	18.5853	+	31.4959i	1.38527	+	2.34756i
$181$	1.50284	+	2.60299i	0.111705	+	0.193479i	0.916458	−	0.400131i	$-0.131035\pi$
$181$	1.50284	+	2.60299i	0.111705	+	0.193479i	−0.804753	+	0.593610i	$0.797702\pi$
$182$	−0.289939	−	0.0253664i	−0.0214917	−	0.00188028i
$183$	−7.45203	+	2.09341i	−0.550870	+	0.154749i
$184$	−67.7017	−	11.9376i	−4.99104	−	0.880054i
$185$	−15.2594	+	14.8196i	−1.12189	+	1.08956i
$186$	0.551118	−	0.673118i	0.0404099	−	0.0493554i
$187$	0.718791	−	0.335178i	0.0525632	−	0.0245106i
$188$	7.27475	−	7.27475i	0.530566	−	0.530566i
$189$	0.342458	−	0.0732478i	0.0249102	−	0.00532799i
$190$	1.02105	−	9.98666i	0.0740748	−	0.724508i
$191$	7.98174	−	21.9296i	0.577538	−	1.58677i	−0.214778	−	0.976663i	$-0.568903\pi$
$191$	7.98174	−	21.9296i	0.577538	−	1.58677i	0.792316	−	0.610110i	$-0.208875\pi$
$192$	−29.6437	−	41.2672i	−2.13935	−	2.97821i
$193$	−1.69115	−	19.3299i	−0.121731	−	1.39140i	−0.773893	−	0.633316i	$-0.781693\pi$
$193$	−1.69115	−	19.3299i	−0.121731	−	1.39140i	0.652162	−	0.758079i	$-0.273862\pi$
$194$	−0.924736	+	5.24444i	−0.0663922	+	0.376529i
$195$	2.11027	−	5.75205i	0.151120	−	0.411913i
$196$	−29.2143	+	24.5137i	−2.08673	+	1.75098i
$197$	−4.17203	+	15.5702i	−0.297245	+	1.10933i	0.642173	+	0.766560i	$0.278033\pi$
$197$	−4.17203	+	15.5702i	−0.297245	+	1.10933i	−0.939418	+	0.342774i	$0.888634\pi$
$198$	−5.57330	+	23.0056i	−0.396077	+	1.63494i
$199$	10.7021	+	6.17889i	0.758655	+	0.438010i	0.828813	−	0.559526i	$-0.189017\pi$
$199$	10.7021	+	6.17889i	0.758655	+	0.438010i	−0.0701576	+	0.997536i	$0.522350\pi$
$200$	−34.2719	+	32.3239i	−2.42339	+	2.28565i
$201$	−3.25915	+	2.80242i	−0.229882	+	0.197667i
$202$	−14.2755	+	30.6140i	−1.00442	+	2.15399i
$203$	0.00855122	−	0.0183381i	0.000600178	−	0.00128709i
$204$	−1.96447	+	1.68918i	−0.137541	+	0.118266i
$205$	−7.47875	+	8.65270i	−0.522339	+	0.604331i
$206$	7.84721	+	4.53059i	0.546741	+	0.315661i
$207$	−15.8465	−	15.0999i	−1.10141	−	1.04952i
$208$	−6.06667	+	22.6411i	−0.420648	+	1.56988i
$209$	3.64161	−	3.05567i	0.251895	−	0.211365i
$210$	0.299478	+	0.646551i	0.0206660	+	0.0446162i
$211$	2.28006	−	12.9309i	0.156966	−	0.890199i	−0.800000	−	0.600000i	$-0.795167\pi$
$211$	2.28006	−	12.9309i	0.156966	−	0.890199i	0.956966	−	0.290199i	$-0.0937216\pi$
$212$	1.06610	+	12.1856i	0.0732199	+	0.836908i
$213$	5.72912	+	7.97556i	0.392553	+	0.546476i
$214$	8.09942	−	22.2530i	0.553665	−	1.52118i
$215$	12.0682	+	1.23387i	0.823044	+	0.0841493i
$216$	−1.77095	−	48.9266i	−0.120498	−	3.32903i
$217$	0.00876868	−	0.00876868i	0.000595257	−	0.000595257i
$218$	−36.1925	+	16.8769i	−2.45127	+	1.14304i
$219$	−9.90788	+	12.1012i	−0.669512	+	0.817722i
$220$	−35.2318	−	0.515161i	−2.37533	−	0.0347321i
$221$	0.427470	+	0.0753744i	0.0287547	+	0.00507023i
$222$	43.3014	−	12.1641i	2.90620	−	0.816403i
$223$	12.1492	+	1.06292i	0.813571	+	0.0711782i	0.486344	−	0.873768i	$-0.338330\pi$
$223$	12.1492	+	1.06292i	0.813571	+	0.0711782i	0.327227	+	0.944946i	$0.393886\pi$
$224$	−0.727964	−	1.26087i	−0.0486392	−	0.0842455i
$225$	−14.7853	+	2.52903i	−0.985684	+	0.168602i
$226$	10.1742	−	17.6222i	0.676775	−	1.17221i
$227$	−3.12551	+	4.46369i	−0.207447	+	0.296265i	−0.909370	−	0.415987i	$-0.863436\pi$
$227$	−3.12551	+	4.46369i	−0.207447	+	0.296265i	0.701923	+	0.712253i	$0.252325\pi$
$228$	−8.75322	+	12.8274i	−0.579696	+	0.849516i
$229$	−0.0613439	−	0.168541i	−0.00405372	−	0.0111375i	0.937649	−	0.347583i	$-0.112997\pi$
$229$	−0.0613439	−	0.168541i	−0.00405372	−	0.0111375i	−0.941703	+	0.336445i	$0.890775\pi$
$230$	22.8295	−	38.2396i	1.50533	−	2.52144i
$231$	−0.111572	+	0.318440i	−0.00734092	+	0.0209518i
$232$	−2.31714	−	1.62248i	−0.152128	−	0.106521i
$233$	2.08623	+	7.78593i	0.136674	+	0.510073i	0.999985	+	0.00540204i	$0.00171953\pi$
$233$	2.08623	+	7.78593i	0.136674	+	0.510073i	−0.863312	+	0.504671i	$0.831614\pi$
$234$	−9.72054	+	8.56438i	−0.635451	+	0.559871i
$235$	1.72726	+	3.85011i	0.112674	+	0.251154i
$236$	42.4696	+	50.6133i	2.76454	+	3.29464i
$237$	9.12162	−	9.34433i	0.592513	−	0.606980i
$238$	−0.0413509	+	0.0289542i	−0.00268038	+	0.00187682i
$239$	−2.31718	−	1.94434i	−0.149886	−	0.125769i	0.564761	−	0.825254i	$-0.308968\pi$
$239$	−2.31718	−	1.94434i	−0.149886	−	0.125769i	−0.714647	+	0.699485i	$0.753413\pi$
$240$	55.4679	−	14.7104i	3.58044	−	0.949555i
$241$	10.3835	+	3.77929i	0.668861	+	0.243446i	0.654057	−	0.756445i	$-0.273065\pi$
$241$	10.3835	+	3.77929i	0.668861	+	0.243446i	0.0148037	+	0.999890i	$0.495288\pi$
$242$	5.10560	+	5.10560i	0.328200	+	0.328200i
$243$	8.15539	−	13.2849i	0.523169	−	0.852229i
$244$			24.3631i			1.55969i
$245$	−5.13451	−	14.7756i	−0.328032	−	0.943980i
$246$	22.6230	−	8.54445i	1.44239	−	0.544774i
$247$	2.59185	−	0.226758i	0.164916	−	0.0144282i
$248$	−0.994372	−	1.42011i	−0.0631427	−	0.0901771i
$249$	21.3226	−	0.257166i	1.35127	−	0.0162972i
$250$	−11.6729	−	28.1992i	−0.738259	−	1.78347i
$251$	21.4342	−	12.3751i	1.35292	−	0.781107i	0.364259	−	0.931298i	$-0.381322\pi$
$251$	21.4342	−	12.3751i	1.35292	−	0.781107i	0.988657	+	0.150191i	$0.0479889\pi$
$252$	0.0695575	−	1.10007i	0.00438171	−	0.0692977i
$253$	20.3712	−	5.45844i	1.28073	−	0.343169i
$254$	2.82048	+	15.9957i	0.176973	+	1.00366i
$255$	−0.360899	−	0.999517i	−0.0226003	−	0.0625922i
$256$	−39.4556	+	14.3607i	−2.46597	+	0.897541i
$257$	−21.7573	−	10.1456i	−1.35718	−	0.632865i	−0.398454	−	0.917188i	$-0.630453\pi$
$257$	−21.7573	−	10.1456i	−1.35718	−	0.632865i	−0.958728	+	0.284324i	$0.908231\pi$
$258$	−21.1878	−	14.4582i	−1.31910	−	0.900130i
$259$	0.631394	−	0.111332i	0.0392329	−	0.00691782i
$260$	−15.6335	−	11.2909i	−0.969549	−	0.700232i
$261$	−0.328367	−	0.838670i	−0.0203254	−	0.0519123i
$262$	12.0955	+	3.24099i	0.747264	+	0.200229i
$263$	0.352894	−	4.03359i	0.0217604	−	0.248722i	−0.977522	−	0.210835i	$-0.932382\pi$
$263$	0.352894	−	4.03359i	0.0217604	−	0.248722i	0.999282	−	0.0378870i	$-0.0120627\pi$
$264$	41.1332	+	23.0914i	2.53157	+	1.42117i
$265$	−4.82674	−	1.36926i	−0.296504	−	0.0841131i
$266$	−0.194491	+	0.231786i	−0.0119250	+	0.0142117i
$267$	−2.17553	−	21.8307i	−0.133140	−	1.33602i
$268$	5.71757	+	12.2614i	0.349256	+	0.748983i
$269$	−17.0798			−1.04137			−0.520686	−	0.853748i	$-0.674324\pi$
$269$	−17.0798			−1.04137			−0.520686	+	0.853748i	$0.674324\pi$
$270$	30.0312	+	10.2028i	1.82764	+	0.620924i
$271$	8.56847			0.520497			0.260249	−	0.965542i	$-0.416195\pi$
$271$	8.56847			0.520497			0.260249	+	0.965542i	$0.416195\pi$
$272$	1.71815	+	3.68458i	0.104178	+	0.223410i
$273$	−0.149985	+	0.107739i	−0.00907750	+	0.00652068i
$274$	15.6510	−	18.6522i	0.945513	−	1.12682i
$275$	5.33799	−	13.4305i	0.321893	−	0.809892i
$276$	−59.2449	+	35.1645i	−3.56612	+	2.11665i
$277$	0.952498	−	10.8871i	0.0572300	−	0.654142i	−0.912357	−	0.409396i	$-0.865740\pi$
$277$	0.952498	−	10.8871i	0.0572300	−	0.654142i	0.969587	−	0.244747i	$-0.0787048\pi$
$278$	−39.7913	−	10.6620i	−2.38652	−	0.639466i
$279$	−0.0133128	−	0.551830i	−0.000797019	−	0.0330372i
$280$	1.40183	−	0.226100i	0.0837752	−	0.0135120i
$281$	13.8445	−	2.44116i	0.825893	−	0.145627i	0.255302	−	0.966861i	$-0.417825\pi$
$281$	13.8445	−	2.44116i	0.825893	−	0.145627i	0.570591	+	0.821234i	$0.306714\pi$
$282$	0.670408	−	8.89743i	0.0399222	−	0.529834i
$283$	−22.8211	−	10.6416i	−1.35657	−	0.632580i	−0.397989	−	0.917390i	$-0.630292\pi$
$283$	−22.8211	−	10.6416i	−1.35657	−	0.632580i	−0.958584	+	0.284810i	$0.908070\pi$
$284$	29.0443	−	10.5713i	1.72346	−	0.627290i
$285$	−3.64009	−	5.22703i	−0.215620	−	0.309622i
$286$	−2.16753	−	12.2927i	−0.128169	−	0.726880i
$287$	0.332969	−	0.0892187i	0.0196545	−	0.00526641i
$288$	−62.9851	−	15.2587i	−3.71143	−	0.899126i
$289$	−14.6572	+	8.46236i	−0.862190	+	0.497786i
$290$	1.51633	−	1.02904i	0.0890417	−	0.0604270i
$291$	1.72465	+	2.90568i	0.101101	+	0.170334i
$292$	28.2350	+	40.3238i	1.65233	+	2.35977i
$293$	22.1966	−	1.94195i	1.29674	−	0.113450i	0.582199	−	0.813046i	$-0.302193\pi$
$293$	22.1966	−	1.94195i	1.29674	−	0.113450i	0.714538	+	0.699597i	$0.246637\pi$
$294$	−5.35020	+	32.6396i	−0.312030	+	1.90358i
$295$	−25.5985	+	8.89546i	−1.49040	+	0.517914i
$296$		−	89.6307i		−	5.20968i
$297$	6.83572	+	13.3737i	0.396649	+	0.776021i
$298$	27.7905	+	27.7905i	1.60986	+	1.60986i
$299$	10.8464	+	3.94776i	0.627262	+	0.228305i
$300$	−4.92229	+	46.9551i	−0.284189	+	2.71095i
$301$	−0.280097	−	0.235029i	−0.0161445	−	0.0135469i
$302$	−4.86693	+	3.40786i	−0.280061	+	0.196101i
$303$	5.79649	+	20.6341i	0.332999	+	1.18540i
$304$	15.6636	+	18.6672i	0.898369	+	1.07063i
$305$	−9.33930	−	3.55470i	−0.534767	−	0.203542i
$306$	−0.336704	+	2.22163i	−0.0192481	+	0.127002i
$307$	6.90384	+	25.7655i	0.394023	+	1.47051i	0.823437	+	0.567407i	$0.192053\pi$
$307$	6.90384	+	25.7655i	0.394023	+	1.47051i	−0.429414	+	0.903108i	$0.641280\pi$
$308$	0.869962	+	0.609154i	0.0495707	+	0.0347098i
$309$	5.64957	−	1.06658i	0.321393	−	0.0606755i
$310$	1.08897	−	0.274789i	0.0618493	−	0.0156070i
$311$	−3.92967	−	10.7967i	−0.222831	−	0.612223i	0.777020	−	0.629476i	$-0.216730\pi$
$311$	−3.92967	−	10.7967i	−0.222831	−	0.612223i	−0.999851	+	0.0172526i	$0.994508\pi$
$312$	11.1921	+	23.2649i	0.633629	+	1.31711i
$313$	−11.6660	+	16.6608i	−0.659404	+	0.941726i	0.340595	+	0.940210i	$0.389372\pi$
$313$	−11.6660	+	16.6608i	−0.659404	+	0.941726i	−0.999999	+	0.00151626i	$0.999517\pi$
$314$	8.29807	−	14.3727i	0.468287	−	0.811097i
$315$	0.411549	+	0.187170i	0.0231881	+	0.0105458i
$316$	−20.5505	−	35.5945i	−1.15606	−	2.00235i
$317$	6.87221	+	0.601241i	0.385982	+	0.0337690i	0.278496	−	0.960438i	$-0.410164\pi$
$317$	6.87221	+	0.601241i	0.385982	+	0.0337690i	0.107486	+	0.994207i	$0.465720\pi$
$318$	7.59140	+	7.41047i	0.425705	+	0.415558i
$319$	0.854601	+	0.150689i	0.0478485	+	0.00843698i
$320$	0.959051	−	65.5894i	0.0536126	−	3.66656i
$321$	−5.30903	−	14.0566i	−0.296321	−	0.784565i
$322$	−1.21658	+	0.567301i	−0.0677974	+	0.0316144i
$323$	0.319087	−	0.319087i	0.0177545	−	0.0177545i
$324$	−33.3138	−	36.0211i	−1.85077	−	2.00117i
$325$	6.60924	−	4.34552i	0.366615	−	0.241046i
$326$	−11.6611	+	32.0386i	−0.645849	+	1.77446i
$327$	−10.4307	+	23.0918i	−0.576821	+	1.27698i
$328$	−4.20014	−	48.0078i	−0.231914	−	2.65079i
$329$	0.0220860	−	0.125256i	0.00121764	−	0.00690559i
$330$	−23.4599	+	19.5831i	−1.29143	+	1.07801i
$331$	−8.89164	+	7.46097i	−0.488729	+	0.410092i	−0.853570	−	0.520977i	$-0.825568\pi$
$331$	−8.89164	+	7.46097i	−0.488729	+	0.410092i	0.364842	+	0.931070i	$0.381123\pi$
$332$	17.3713	−	64.8306i	0.953375	−	3.55804i
$333$	15.8004	−	23.7653i	0.865858	−	1.30233i
$334$	−52.6963	−	30.4242i	−2.88341	−	1.66474i
$335$	−5.53447	+	0.402763i	−0.302381	+	0.0220053i
$336$	−1.63235	−	0.571928i	−0.0890518	−	0.0312012i
$337$	−4.09908	+	8.79051i	−0.223291	+	0.478849i	−0.985756	−	0.168180i	$-0.946211\pi$
$337$	−4.09908	+	8.79051i	−0.223291	+	0.478849i	0.762465	+	0.647029i	$0.223989\pi$
$338$	−12.1103	+	25.9706i	−0.658712	+	1.41261i
$339$	−2.39517	−	12.6870i	−0.130088	−	0.689064i
$340$	−3.33594	+	0.242768i	−0.180917	+	0.0131660i
$341$	0.460588	+	0.265920i	0.0249422	+	0.0144004i
$342$	1.49710	+	13.3849i	0.0809536	+	0.723772i
$343$	−0.244131	+	0.911108i	−0.0131818	+	0.0491952i
$344$	−39.1577	+	32.8572i	−2.11124	+	1.77154i
$345$	−4.83573	−	27.8415i	−0.260347	−	1.49894i
$346$	5.87354	−	33.3105i	0.315763	−	1.79078i
$347$	2.06390	+	23.5905i	0.110796	+	1.26640i	0.824462	+	0.565918i	$0.191478\pi$
$347$	2.06390	+	23.5905i	0.110796	+	1.26640i	−0.713666	+	0.700487i	$0.752966\pi$
$348$	−2.82085	+	0.281111i	−0.151214	+	0.0150691i
$349$	0.840919	−	2.31040i	0.0450133	−	0.123673i	−0.915149	−	0.403115i	$-0.867927\pi$
$349$	0.840919	−	2.31040i	0.0450133	−	0.123673i	0.960163	+	0.279442i	$0.0901495\pi$
$350$	−0.186155	+	0.900854i	−0.00995042	+	0.0481527i
$351$	−1.13365	+	8.14160i	−0.0605100	+	0.434567i
$352$	44.1527	−	44.1527i	2.35335	−	2.35335i
$353$	0.400070	−	0.186556i	0.0212936	−	0.00992935i	−0.411942	−	0.911210i	$-0.635149\pi$
$353$	0.400070	−	0.186556i	0.0212936	−	0.00992935i	0.433236	+	0.901281i	$0.357372\pi$
$354$	56.5476	+	9.26914i	3.00547	+	0.492649i
$355$	−0.185352	+	12.6762i	−0.00983746	+	0.672783i
$356$	−68.0033	−	11.9908i	−3.60417	−	0.635512i
$357$	−0.00791623	+	0.0310362i	−0.000418971	+	0.00164261i
$358$	40.0161	+	3.50095i	2.11492	+	0.185031i
$359$	−10.2203	−	17.7022i	−0.539409	−	0.934284i	−0.998936	−	0.0461203i	$-0.985314\pi$
$359$	−10.2203	−	17.7022i	−0.539409	−	0.934284i	0.459527	−	0.888164i	$-0.348019\pi$
$360$	35.7596	−	52.1168i	1.88470	−	2.74680i
$361$	−8.14760	+	14.1121i	−0.428821	+	0.742740i
$362$	4.70607	−	6.72096i	0.247346	−	0.353246i
$363$	4.56844	+	0.344225i	0.239781	+	0.0180671i
$364$	0.198799	+	0.546195i	0.0104199	+	0.0286284i
$365$	−19.5773	+	4.94010i	−1.02472	+	0.258577i
$366$	13.7761	+	16.0213i	0.720089	+	0.837447i
$367$	9.17042	+	6.42120i	0.478692	+	0.335184i	0.787892	−	0.615813i	$-0.211172\pi$
$367$	9.17042	+	6.42120i	0.478692	+	0.335184i	−0.309200	+	0.950997i	$0.600061\pi$
$368$	27.9804	+	104.424i	1.45858	+	5.44348i
$369$	7.34933	−	13.4696i	0.382591	−	0.701197i
$370$	54.2677	+	20.6553i	2.82124	+	1.07382i
$371$	0.0972037	+	0.115843i	0.00504657	+	0.00601426i
$372$	−1.68349	−	0.429397i	−0.0872846	−	0.0222632i
$373$	−31.2287	+	21.8665i	−1.61696	+	1.13221i	−0.716192	+	0.697903i	$0.754116\pi$
$373$	−31.2287	+	21.8665i	−1.61696	+	1.13221i	−0.900767	+	0.434303i	$0.856995\pi$
$374$	−1.65847	−	1.39162i	−0.0857572	−	0.0719588i
$375$	−17.2815	−	8.73789i	−0.892411	−	0.451223i
$376$	−16.7086	−	6.08145i	−0.861683	−	0.313627i
$377$	0.335833	+	0.335833i	0.0172963	+	0.0172963i
$378$	−0.576292	−	0.762742i	−0.0296412	−	0.0392312i
$379$			4.11755i			0.211504i	0.994393	+	0.105752i	$0.0337250\pi$
$379$			4.11755i			0.211504i	−0.994393	+	0.105752i	$0.966275\pi$
$380$	−18.9375	+	6.58076i	−0.971473	+	0.337586i
$381$	7.97413	+	6.52884i	0.408527	+	0.334483i
$382$	−63.4622	+	5.55222i	−3.24701	+	0.284076i
$383$	4.87836	+	6.96702i	0.249273	+	0.355998i	0.924215	−	0.381872i	$-0.124721\pi$
$383$	4.87836	+	6.96702i	0.249273	+	0.355998i	−0.674943	+	0.737870i	$0.735832\pi$
$384$	−31.2650	+	55.6930i	−1.59548	+	2.84207i
$385$	−0.360444	+	0.244611i	−0.0183699	+	0.0124665i
$386$	−45.8713	+	26.4838i	−2.33479	+	1.34799i
$387$	−16.1747	+	1.80914i	−0.822208	+	0.0919637i
$388$	10.2729	−	2.75260i	0.521525	−	0.139742i
$389$	−5.58151	−	31.6543i	−0.282994	−	1.60494i	−0.712365	−	0.701809i	$-0.752376\pi$
$389$	−5.58151	−	31.6543i	−0.282994	−	1.60494i	0.429371	−	0.903128i	$-0.358735\pi$
$390$	−16.6651	+	1.41502i	−0.843872	+	0.0716521i
$391$	1.88123	−	0.684713i	0.0951380	−	0.0346274i
$392$	59.7364	+	27.8555i	3.01714	+	1.40692i
$393$	7.15997	−	3.44448i	0.361173	−	0.173751i
$394$	43.3339	−	7.64094i	2.18313	−	0.384945i
$395$	16.6432	−	2.68436i	0.837409	−	0.135065i
$396$	46.3438	−	9.32939i	2.32886	−	0.468819i
$397$	−26.7823	−	7.17628i	−1.34416	−	0.360167i	−0.486186	−	0.873855i	$-0.661612\pi$
$397$	−26.7823	−	7.17628i	−1.34416	−	0.360167i	−0.857977	+	0.513688i	$0.828279\pi$
$398$	2.94010	−	33.6054i	0.147374	−	1.68449i
$399$	0.00231531	+	0.191971i	0.000115910	+	0.00961058i
$400$	68.8459	+	27.3629i	3.44229	+	1.36815i
$401$	−21.1044	+	25.1513i	−1.05390	+	1.25599i	−0.0882682	+	0.996097i	$0.528133\pi$
$401$	−21.1044	+	25.1513i	−1.05390	+	1.25599i	−0.965636	+	0.259898i	$0.916311\pi$
$402$	10.6931	+	4.83015i	0.533324	+	0.240906i
$403$	0.123015	+	0.263806i	0.00612779	+	0.0131411i
$404$	67.4596			3.35624
$405$	18.6689	−	7.51479i	0.927665	−	0.373413i
$406$	−0.0552338			−0.00274121
$407$	11.6206	+	24.9205i	0.576013	+	1.23526i
$408$	4.08078	+	1.84332i	0.202029	+	0.0912577i
$409$	−17.7773	+	21.1861i	−0.879029	+	1.04759i	0.119472	+	0.992838i	$0.461880\pi$
$409$	−17.7773	+	21.1861i	−0.879029	+	1.04759i	−0.998500	+	0.0547479i	$0.982564\pi$
$410$	30.0347	+	8.52032i	1.48331	+	0.420789i
$411$	−0.186317	−	15.4483i	−0.00919033	−	0.762006i
$412$	1.57718	−	18.0272i	0.0777019	−	0.888137i
$413$	0.788985	+	0.211408i	0.0388234	+	0.0104027i
$414$	−19.0760	+	56.6244i	−0.937536	+	2.78294i
$415$	22.3175	+	16.1182i	1.09552	+	0.791212i
$416$	33.6551	−	5.93430i	1.65008	−	0.290953i
$417$	−23.5545	+	11.3315i	−1.15347	+	0.554904i
$418$	−11.7609	−	5.48420i	−0.575244	−	0.268241i
$419$	−6.15194	+	2.23912i	−0.300542	+	0.109388i	−0.487890	−	0.872905i	$-0.662233\pi$
$419$	−6.15194	+	2.23912i	−0.300542	+	0.109388i	0.187348	+	0.982294i	$0.440011\pi$
$420$	0.917486	−	1.08775i	0.0447687	−	0.0530766i
$421$	0.0842371	+	0.477733i	0.00410547	+	0.0232833i	0.986792	−	0.161994i	$-0.0517927\pi$
$421$	0.0842371	+	0.477733i	0.00410547	+	0.0232833i	−0.982686	+	0.185278i	$0.940682\pi$
$422$	−34.6215	+	9.27680i	−1.68535	+	0.451588i
$423$	−3.35819	−	4.55794i	−0.163281	−	0.221615i
$424$	18.3086	−	10.5705i	0.889142	−	0.513346i
$425$	0.393670	−	1.31422i	0.0190958	−	0.0637488i
$426$	13.1222	−	23.3749i	0.635772	−	1.13252i
$427$	0.172758	+	0.246724i	0.00836034	+	0.0119398i
$428$	−47.1136	+	4.12191i	−2.27732	+	0.199240i
$429$	−6.12809	−	5.01740i	−0.295867	−	0.242242i
$430$	−10.8699	−	31.2803i	−0.524191	−	1.50847i
$431$		−	16.2782i		−	0.784091i	−0.919946	−	0.392046i	$-0.871768\pi$
$431$		−	16.2782i		−	0.784091i	0.919946	−	0.392046i	$-0.128232\pi$
$432$	−68.5546	+	35.0404i	−3.29833	+	1.68588i
$433$	−18.2154	−	18.2154i	−0.875374	−	0.875374i	0.117677	−	0.993052i	$-0.462455\pi$
$433$	−18.2154	−	18.2154i	−0.875374	−	0.875374i	−0.993052	+	0.117677i	$0.962455\pi$
$434$	−0.0318098	−	0.0115778i	−0.00152692	−	0.000555752i
$435$	0.303817	−	1.12236i	0.0145669	−	0.0538128i
$436$	61.0938	+	51.2638i	2.92586	+	2.45509i
$437$	9.82955	−	6.88272i	0.470211	−	0.329245i
$438$	41.3686	+	10.5517i	1.97667	+	0.504177i
$439$	−17.5389	−	20.9020i	−0.837085	−	0.997599i	−0.999940	−	0.0109489i	$-0.996515\pi$
$439$	−17.5389	−	20.9020i	−0.837085	−	0.997599i	0.162855	−	0.986650i	$-0.447930\pi$
$440$	24.9270	+	55.5628i	1.18835	+	2.64885i
$441$	10.9285	+	17.9164i	0.520403	+	0.853161i
$442$	−0.306673	−	1.14452i	−0.0145869	−	0.0544392i
$443$	−20.5553	−	14.3930i	−0.976613	−	0.683832i	−0.0277815	−	0.999614i	$-0.508844\pi$
$443$	−20.5553	−	14.3930i	−0.976613	−	0.683832i	−0.948832	+	0.315782i	$0.897733\pi$
$444$	−58.5638	−	68.1083i	−2.77931	−	3.23228i
$445$	14.5186	−	24.3187i	0.688247	−	1.15282i
$446$	−11.3862	−	31.2834i	−0.539154	−	1.48131i
$447$	24.8667	+	1.87367i	1.17615	+	0.0886214i
$448$	−1.13403	+	1.61957i	−0.0535780	+	0.0765173i
$449$	−13.1545	+	22.7842i	−0.620798	+	1.07525i	0.368540	+	0.929612i	$0.379858\pi$
$449$	−13.1545	+	22.7842i	−0.620798	+	1.07525i	−0.989338	+	0.145641i	$0.953476\pi$
$450$	23.3138	+	33.6612i	1.09902	+	1.58681i
$451$	7.39200	+	12.8033i	0.348076	+	0.602885i
$452$	−40.4830	−	3.54180i	−1.90416	−	0.166592i
$453$	−0.931729	+	3.65292i	−0.0437764	+	0.171629i
$454$	14.6489	+	2.58300i	0.687508	+	0.121226i
$455$	−0.238383	−	0.00348565i	−0.0111756	−	0.000163410i
$456$	26.4861	+	4.34154i	1.24033	+	0.203311i
$457$	35.3751	−	16.4957i	1.65478	−	0.771635i	0.654903	−	0.755713i	$-0.272710\pi$
$457$	35.3751	−	16.4957i	1.65478	−	0.771635i	0.999873	−	0.0159216i	$-0.00506822\pi$
$458$	−0.346202	+	0.346202i	−0.0161770	+	0.0161770i
$459$	0.757062	+	1.20813i	0.0353366	+	0.0563905i
$460$	−88.4816	−	9.04649i	−4.12547	−	0.421795i
$461$	−1.05017	+	2.88532i	−0.0489113	+	0.134383i	−0.961743	−	0.273953i	$-0.911669\pi$
$461$	−1.05017	+	2.88532i	−0.0489113	+	0.134383i	0.912832	+	0.408336i	$0.133891\pi$
$462$	0.916538	−	0.0913372i	0.0426412	−	0.00424939i
$463$	3.53412	+	40.3952i	0.164244	+	1.87732i	0.415767	+	0.909471i	$0.363513\pi$
$463$	3.53412	+	40.3952i	0.164244	+	1.87732i	−0.251523	+	0.967851i	$0.580931\pi$
$464$	−0.772444	+	4.38075i	−0.0358598	+	0.203371i
$465$	0.410234	−	0.582693i	0.0190241	−	0.0270217i
$466$	16.8557	−	14.1436i	0.780823	−	0.655188i
$467$	−1.18098	+	4.40748i	−0.0546493	+	0.203954i	−0.987852	−	0.155396i	$-0.950335\pi$
$467$	−1.18098	+	4.40748i	−0.0546493	+	0.203954i	0.933203	+	0.359350i	$0.117001\pi$
$468$	23.7057	+	10.3656i	1.09579	+	0.479151i
$469$	0.144847	+	0.0836272i	0.00668839	+	0.00386155i
$470$	7.53255	−	8.71494i	0.347451	−	0.401990i
$471$	−1.95351	−	10.3476i	−0.0900129	−	0.476790i
$472$	48.2593	−	103.492i	2.22131	−	4.76362i
$473$	6.62728	−	14.2122i	0.304723	−	0.653480i
$474$	−33.6411	−	11.7869i	−1.54519	−	0.541389i
$475$	0.240427	−	8.21963i	0.0110315	−	0.377143i
$476$	0.0873073	+	0.0504069i	0.00400172	+	0.00231040i
$477$	6.71786	+	0.424772i	0.307590	+	0.0194490i
$478$	−2.13711	+	7.97581i	−0.0977492	+	0.364805i
$479$	19.9896	−	16.7733i	0.913349	−	0.766391i	−0.0594042	−	0.998234i	$-0.518920\pi$
$479$	19.9896	−	16.7733i	0.913349	−	0.766391i	0.972753	+	0.231843i	$0.0744756\pi$
$480$	−53.6149	−	64.2290i	−2.44717	−	2.93164i
$481$	−2.61323	+	14.8204i	−0.119153	+	0.675750i
$482$	−2.62893	−	30.0489i	−0.119745	−	1.36869i
$483$	−0.350620	+	0.776212i	−0.0159538	+	0.0353189i
$484$	4.93189	−	13.5503i	0.224177	−	0.615921i
$485$	−0.443687	+	4.33959i	−0.0201468	+	0.197051i
$486$	−42.2755	−	4.85034i	−1.91765	−	0.220016i
$487$	10.3340	−	10.3340i	0.468280	−	0.468280i	−0.433077	−	0.901357i	$-0.642572\pi$
$487$	10.3340	−	10.3340i	0.468280	−	0.468280i	0.901357	+	0.433077i	$0.142572\pi$
$488$	38.1619	−	17.7952i	1.72751	−	0.805551i
$489$	7.64366	+	20.2380i	0.345658	+	0.915194i
$490$	−30.6316	+	29.7487i	−1.38379	+	1.34391i
$491$	21.2487	+	3.74671i	0.958939	+	0.169087i	0.631147	−	0.775663i	$-0.282584\pi$
$491$	21.2487	+	3.74671i	0.958939	+	0.169087i	0.327792	+	0.944750i	$0.393696\pi$
$492$	−34.5594	−	33.7357i	−1.55806	−	1.52092i
$493$	0.0820617	+	0.00717947i	0.00369587	+	0.000323347i
$494$	−3.55109	−	6.15066i	−0.159771	−	0.276731i
$495$	−3.18550	+	19.1265i	−0.143177	+	0.859674i
$496$	−1.36313	+	2.36101i	−0.0612062	+	0.106012i
$497$	0.219170	−	0.313007i	0.00983112	−	0.0140403i
$498$	−25.2350	−	52.4556i	−1.13081	−	2.35059i
$499$	8.93292	+	24.5430i	0.399892	+	1.09870i	0.962337	+	0.271860i	$0.0876388\pi$
$499$	8.93292	+	24.5430i	0.399892	+	1.09870i	−0.562444	+	0.826835i	$0.690139\pi$
$500$	−41.1881	+	44.9282i	−1.84199	+	2.00925i
$501$	−37.9385	+	7.16238i	−1.69497	+	0.319992i
$502$	−55.3435	−	38.7520i	−2.47010	−	1.72958i
$503$	−6.91747	−	25.8163i	−0.308435	−	1.15109i	−0.929948	−	0.367690i	$-0.880149\pi$
$503$	−6.91747	−	25.8163i	−0.308435	−	1.15109i	0.621514	−	0.783403i	$-0.286518\pi$
$504$	−1.77393	+	0.694553i	−0.0790172	+	0.0309378i
$505$	−9.84271	+	25.8598i	−0.437995	+	1.15075i
$506$	−37.0054	−	44.1013i	−1.64509	−	1.96054i
$507$	4.91730	+	17.5044i	0.218385	+	0.777399i
$508$	26.5715	−	18.6056i	1.17892	−	0.825490i
$509$	12.1514	+	10.1962i	0.538601	+	0.451940i	0.871059	−	0.491178i	$-0.163434\pi$
$509$	12.1514	+	10.1962i	0.538601	+	0.451940i	−0.332458	+	0.943118i	$0.607878\pi$
$510$	−2.05646	+	2.04596i	−0.0910617	+	0.0905965i
$511$	0.571869	+	0.208143i	0.0252980	+	0.00920772i
$512$	28.8976	+	28.8976i	1.27711	+	1.27711i
$513$	6.25738	+	5.82022i	0.276270	+	0.256969i
$514$			65.5321i			2.89050i
$515$	6.68040	+	3.23486i	0.294373	+	0.142545i
$516$	−8.28647	+	50.5526i	−0.364791	+	2.22545i
$517$	5.43405	−	0.475418i	0.238989	−	0.0209089i
$518$	−1.00384	−	1.43363i	−0.0441063	−	0.0629903i
$519$	−10.9542	−	18.4556i	−0.480838	−	0.810113i
$520$	−6.26690	+	32.7351i	−0.274822	+	1.43553i
$521$	−4.16523	+	2.40480i	−0.182482	+	0.105356i	−0.588458	−	0.808528i	$-0.700265\pi$
$521$	−4.16523	+	2.40480i	−0.182482	+	0.105356i	0.405976	+	0.913884i	$0.366932\pi$
$522$	−1.69605	+	1.77991i	−0.0742343	+	0.0779046i
$523$	26.4967	−	7.09977i	1.15862	−	0.310451i	0.372206	−	0.928150i	$-0.378602\pi$
$523$	26.4967	−	7.09977i	1.15862	−	0.310451i	0.786415	+	0.617699i	$0.211935\pi$
$524$	−4.34261	−	24.6282i	−0.189708	−	1.07589i
$525$	0.283109	+	0.510415i	0.0123559	+	0.0222764i
$526$	−10.3862	+	3.78029i	−0.452862	+	0.164828i
$527$	0.0457553	+	0.0213361i	0.00199313	+	0.000929413i
$528$	5.57357	−	73.9706i	0.242558	−	3.21916i
$529$	29.7762	−	5.25035i	1.29462	−	0.228276i
$530$	2.18079	+	13.5210i	0.0947277	+	0.587316i
$531$	31.0398	−	18.9334i	1.34701	−	0.821640i
$532$	0.583682	+	0.156397i	0.0253058	+	0.00678067i
$533$	−0.705203	+	8.06051i	−0.0305457	+	0.349140i
$534$	−51.4996	+	30.5673i	−2.22860	+	1.32277i
$535$	5.29404	−	18.6618i	0.228881	−	0.806822i
$536$	15.0298	−	17.9118i	0.649188	−	0.773673i
$537$	20.7002	−	14.8697i	0.893282	−	0.641675i
$538$	19.7041	+	42.2555i	0.849502	+	1.82176i
$539$	−20.2203			−0.870950
$540$	−6.87965	−	62.9673i	−0.296053	−	2.70968i
$541$	6.59325			0.283466			0.141733	−	0.989905i	$-0.454733\pi$
$541$	6.59325			0.283466			0.141733	+	0.989905i	$0.454733\pi$
$542$	−9.88500	−	21.1984i	−0.424597	−	0.910551i
$543$	−0.516242	−	5.18032i	−0.0221541	−	0.222309i
$544$	3.80999	−	4.54057i	0.163352	−	0.194675i
$545$	−28.5653	+	15.9399i	−1.22360	+	0.682791i
$546$	0.439578	+	0.246770i	0.0188122	+	0.0105608i
$547$	−1.89295	+	21.6365i	−0.0809366	+	0.925110i	0.841828	+	0.539746i	$0.181480\pi$
$547$	−1.89295	+	21.6365i	−0.0809366	+	0.925110i	−0.922765	+	0.385364i	$0.874076\pi$
$548$	−46.9698	−	12.5855i	−2.00645	−	0.537627i
$549$	13.2555	+	2.00897i	0.565732	+	0.0857409i
$550$	−39.3854	+	2.28788i	−1.67940	+	0.0975557i
$551$	0.486250	−	0.0857391i	0.0207150	−	0.00365261i
$552$	98.3544	+	67.1155i	4.18624	+	2.85663i
$553$	−0.460514	−	0.214741i	−0.0195830	−	0.00913172i
$554$	−28.0336	+	10.2034i	−1.19103	+	0.433501i
$555$	34.6533	−	12.5124i	1.47095	−	0.531120i
$556$	14.2861	+	81.0205i	0.605866	+	3.43604i
$557$	15.7494	−	4.22003i	0.667323	−	0.178809i	0.0907742	−	0.995871i	$-0.471066\pi$
$557$	15.7494	−	4.22003i	0.667323	−	0.178809i	0.576549	+	0.817063i	$0.304399\pi$
$558$	−1.34987	+	0.669553i	−0.0571446	+	0.0283445i
$559$	7.43266	−	4.29125i	0.314368	−	0.181500i
$560$	−1.25389	−	1.84766i	−0.0529866	−	0.0780779i
$561$	−1.37359	+	0.0165664i	−0.0579929	+	0.000699435i
$562$	−22.0111	−	31.4351i	−0.928483	−	1.32601i
$563$	19.6276	−	1.71719i	0.827204	−	0.0723710i	0.334313	−	0.942462i	$-0.391496\pi$
$563$	19.6276	−	1.71719i	0.827204	−	0.0723710i	0.492891	+	0.870091i	$0.335940\pi$
$564$	−16.6701	+	6.29610i	−0.701937	+	0.265114i
$565$	7.26439	−	15.0019i	0.305615	−	0.631135i
$566$			68.7362i			2.88920i
$567$	−0.592791	−	0.128556i	−0.0248949	−	0.00539885i
$568$	−37.7731	−	37.7731i	−1.58493	−	1.58493i
$569$	4.06034	+	1.47784i	0.170218	+	0.0619544i	0.425724	−	0.904853i	$-0.360020\pi$
$569$	4.06034	+	1.47784i	0.170218	+	0.0619544i	−0.255505	+	0.966808i	$0.582242\pi$
$570$	−8.73232	+	15.0358i	−0.365757	+	0.629779i
$571$	−17.9249	−	15.0408i	−0.750135	−	0.629438i	0.185404	−	0.982662i	$-0.440641\pi$
$571$	−17.9249	−	15.0408i	−0.750135	−	0.629438i	−0.935539	+	0.353224i	$0.885085\pi$
$572$	−20.4202	+	14.2983i	−0.853809	+	0.597844i
$573$	−28.2351	+	28.9245i	−1.17954	+	1.20834i
$574$	−0.604856	−	0.720840i	−0.0252462	−	0.0300873i
$575$	16.3778	−	32.5984i	0.683001	−	1.35945i
$576$	17.3681	+	86.2760i	0.723670	+	3.59483i
$577$	−2.74624	−	10.2491i	−0.114328	−	0.426677i	0.884908	−	0.465766i	$-0.154221\pi$
$577$	−2.74624	−	10.2491i	−0.114328	−	0.426677i	−0.999236	+	0.0390891i	$0.987554\pi$
$578$	37.8452	+	26.4995i	1.57415	+	1.10223i
$579$	−11.1130	+	31.7177i	−0.461840	+	1.31814i
$580$	−3.14234	−	1.87601i	−0.130478	−	0.0778972i
$581$	−0.283793	−	0.779716i	−0.0117737	−	0.0323481i
$582$	5.19903	−	7.61892i	0.215507	−	0.315814i
$583$	−3.71997	+	5.31266i	−0.154065	+	0.220028i
$584$	42.5392	−	73.6800i	1.76028	−	3.04890i
$585$	−7.43232	+	7.57488i	−0.307289	+	0.313183i
$586$	−30.4114	−	52.6741i	−1.25628	−	2.17595i
$587$	19.2661	+	1.68557i	0.795197	+	0.0695708i	0.477512	−	0.878625i	$-0.341539\pi$
$587$	19.2661	+	1.68557i	0.795197	+	0.0695708i	0.317686	+	0.948196i	$0.397094\pi$
$588$	63.5928	−	17.8644i	2.62252	−	0.736714i
$589$	0.298009	+	0.0525471i	0.0122793	+	0.00216516i
$590$	51.5391	+	53.0687i	2.12183	+	2.18480i
$591$	17.6873	−	21.6027i	0.727556	−	0.888615i
$592$	−127.744	+	59.5681i	−5.25026	+	2.44823i
$593$	−0.516721	+	0.516721i	−0.0212192	+	0.0212192i	−0.717637	−	0.696418i	$-0.754776\pi$
$593$	−0.516721	+	0.516721i	−0.0212192	+	0.0212192i	0.696418	+	0.717637i	$0.254776\pi$
$594$	25.2006	−	32.3402i	1.03399	−	1.32693i
$595$	−0.0320615	+	0.0261136i	−0.00131439	+	0.00107055i
$596$	26.8450	−	73.7560i	1.09961	−	3.02116i
$597$	−12.4876	−	17.3840i	−0.511082	−	0.711481i
$598$	−2.74612	−	31.3883i	−0.112297	−	1.28356i
$599$	1.33236	−	7.55620i	0.0544389	−	0.308738i	−0.945414	−	0.325871i	$-0.894343\pi$
$599$	1.33236	−	7.55620i	0.0544389	−	0.308738i	0.999853	+	0.0171325i	$0.00545372\pi$
$600$	77.1449	−	26.5866i	3.14943	−	1.08539i
$601$	−13.5931	+	11.4060i	−0.554475	+	0.465260i	−0.876453	−	0.481488i	$-0.840097\pi$
$601$	−13.5931	+	11.4060i	−0.554475	+	0.465260i	0.321978	+	0.946747i	$0.395652\pi$
$602$	−0.258331	+	0.964103i	−0.0105288	+	0.0392939i
$603$	7.14267	−	2.09976i	0.290872	−	0.0855089i
$604$	10.2759	+	5.93282i	0.418122	+	0.241403i
$605$	4.47474	+	3.86764i	0.181924	+	0.157242i
$606$	44.3618	−	38.1450i	1.80208	−	1.54954i
$607$	11.2775	−	24.1847i	0.457740	−	0.981627i	−0.533033	−	0.846095i	$-0.678948\pi$
$607$	11.2775	−	24.1847i	0.457740	−	0.981627i	0.990773	−	0.135532i	$-0.0432744\pi$
$608$	15.0147	−	32.1992i	0.608927	−	1.30585i
$609$	−0.0265733	+	0.0228494i	−0.00107680	+	0.000925903i
$610$	1.97990	+	27.2064i	0.0801639	+	1.10155i
$611$	2.58545	+	1.49271i	0.104596	+	0.0603887i
$612$	4.30530	−	1.26565i	0.174031	−	0.0511607i
$613$	10.4926	−	39.1590i	0.423793	−	1.58162i	−0.342750	−	0.939427i	$-0.611358\pi$
$613$	10.4926	−	39.1590i	0.423793	−	1.58162i	0.766544	−	0.642192i	$-0.221975\pi$
$614$	55.7794	−	46.8045i	2.25107	−	1.88888i
$615$	17.9746	−	8.32571i	0.724805	−	0.335725i
$616$	0.318734	−	1.80763i	0.0128422	−	0.0728315i
$617$	−1.60510	−	18.3464i	−0.0646189	−	0.738597i	−0.957524	−	0.288353i	$-0.906892\pi$
$617$	−1.60510	−	18.3464i	−0.0646189	−	0.738597i	0.892905	−	0.450244i	$-0.148663\pi$
$618$	−9.15633	−	12.7466i	−0.368322	−	0.512744i
$619$	−3.93502	+	10.8114i	−0.158162	+	0.434546i	−0.993310	−	0.115479i	$-0.963160\pi$
$619$	−3.93502	+	10.8114i	−0.158162	+	0.434546i	0.835148	+	0.550025i	$0.185382\pi$
$620$	−1.41647	−	1.73910i	−0.0568867	−	0.0698438i
$621$	14.2470	+	35.1338i	0.571714	+	1.40987i
$622$	−22.1776	+	22.1776i	−0.889240	+	0.889240i
$623$	−0.773692	+	0.360779i	−0.0309973	+	0.0144543i
$624$	25.7195	−	31.4131i	1.02961	−	1.25753i
$625$	−11.2131	−	22.3443i	−0.448525	−	0.893770i
$626$	54.6775	+	9.64113i	2.18535	+	0.385337i
$627$	−7.92696	+	2.22682i	−0.316572	+	0.0889308i
$628$	−33.0180	−	2.88870i	−1.31756	−	0.115272i
$629$	1.30507	+	2.26045i	0.0520367	+	0.0901302i
$630$	−0.0117234	−	1.23410i	−0.000467071	−	0.0491678i
$631$	−8.72085	+	15.1050i	−0.347172	+	0.601319i	−0.985746	−	0.168241i	$-0.946191\pi$
$631$	−8.72085	+	15.1050i	−0.347172	+	0.601319i	0.638574	+	0.769560i	$0.279525\pi$
$632$	−40.7442	+	58.1888i	−1.62072	+	2.31463i
$633$	−12.8189	+	18.7855i	−0.509506	+	0.746656i
$634$	−6.44064	−	17.6955i	−0.255791	−	0.702779i
$635$	3.25530	+	12.9005i	0.129183	+	0.511942i
$636$	7.00563	−	19.9949i	0.277791	−	0.792848i
$637$	−9.06523	−	6.34754i	−0.359177	−	0.251499i
$638$	−0.613103	−	2.28813i	−0.0242730	−	0.0905880i
$639$	−3.35666	−	16.6742i	−0.132787	−	0.659622i
$640$	−75.2303	+	33.7503i	−2.97374	+	1.33410i
$641$	13.6102	+	16.2200i	0.537569	+	0.640650i	0.964641	−	0.263568i	$-0.0848992\pi$
$641$	13.6102	+	16.2200i	0.537569	+	0.640650i	−0.427072	+	0.904218i	$0.640455\pi$
$642$	−28.6514	+	29.3510i	−1.13078	+	1.15839i
$643$	−4.30134	+	3.01183i	−0.169628	+	0.118775i	−0.655308	−	0.755362i	$-0.727461\pi$
$643$	−4.30134	+	3.01183i	−0.169628	+	0.118775i	0.485680	+	0.874137i	$0.338572\pi$
$644$	2.05362	+	1.72319i	0.0809238	+	0.0679031i
$645$	−18.1697	−	10.5524i	−0.715431	−	0.415501i
$646$	−1.15754	−	0.421309i	−0.0455427	−	0.0165762i
$647$	−25.4612	−	25.4612i	−1.00098	−	1.00098i	−1.00000		0.000982063i	$-0.999687\pi$
$647$	−25.4612	−	25.4612i	−1.00098	−	1.00098i	−0.000982063	−	1.00000i	$-0.500313\pi$
$648$	−32.0898	+	78.4926i	−1.26061	+	3.08348i
$649$			35.0314i			1.37510i
$650$	−18.3756	−	11.3381i	−0.720750	−	0.444717i
$651$	−0.0200934	+	0.00758906i	−0.000787523	+	0.000297439i
$652$	67.8317	−	5.93450i	2.65649	−	0.232413i
$653$	22.0800	+	31.5335i	0.864056	+	1.23400i	0.970843	+	0.239718i	$0.0770549\pi$
$653$	22.0800	+	31.5335i	0.864056	+	1.23400i	−0.106787	+	0.994282i	$0.534056\pi$
$654$	69.1628	−	0.834152i	2.70448	−	0.0326179i
$655$	10.0745	+	1.92869i	0.393644	+	0.0753603i
$656$	−65.6307	+	37.8919i	−2.56245	+	1.47943i
$657$	24.2677	−	12.0371i	0.946774	−	0.469612i
$658$	−0.335364	+	0.0898605i	−0.0130738	+	0.00350313i
$659$	4.48911	+	25.4590i	0.174871	+	0.991742i	0.938293	+	0.345842i	$0.112407\pi$
$659$	4.48911	+	25.4590i	0.174871	+	0.991742i	−0.763422	+	0.645900i	$0.776482\pi$
$660$	55.2456	+	25.9339i	2.15043	+	1.00947i
$661$	−30.7185	+	11.1806i	−1.19481	+	0.434875i	−0.861410	−	0.507910i	$-0.830418\pi$
$661$	−30.7185	+	11.1806i	−1.19481	+	0.434875i	−0.333400	+	0.942786i	$0.608196\pi$
$662$	28.7163	+	13.3906i	1.11609	+	0.520442i
$663$	−0.621011	−	0.423768i	−0.0241181	−	0.0164578i
$664$	−114.238	+	20.1432i	−4.43329	+	0.781709i
$665$	−0.145115	+	0.200928i	−0.00562733	+	0.00779166i
$666$	−77.0237	−	11.6735i	−2.98461	−	0.452339i
$667$	2.11585	+	0.566941i	0.0819261	+	0.0219520i
$668$	−10.5912	+	121.058i	−0.409786	+	4.68388i
$669$	−18.4195	−	10.3403i	−0.712137	−	0.399780i
$670$	7.38128	+	13.2277i	0.285164	+	0.511030i
$671$	−8.30322	+	9.89539i	−0.320542	+	0.382007i
$672$	0.250064	+	2.50931i	0.00964645	+	0.0967989i
$673$	−9.15859	−	19.6407i	−0.353038	−	0.757092i	0.646948	−	0.762534i	$-0.276045\pi$
$673$	−9.15859	−	19.6407i	−0.353038	−	0.757092i	−0.999985	+	0.00544291i	$0.998267\pi$
$674$	26.4767			1.01984
$675$	25.1415	+	6.55003i	0.967698	+	0.252111i
$676$	57.2276			2.20106
$677$	−5.19717	−	11.1454i	−0.199743	−	0.428351i	0.780766	−	0.624824i	$-0.214829\pi$
$677$	−5.19717	−	11.1454i	−0.199743	−	0.428351i	−0.980509	+	0.196473i	$0.937051\pi$
$678$	−28.6246	+	20.5620i	−1.09932	+	0.789679i
$679$	0.0845141	−	0.100720i	0.00324335	−	0.00386528i
$680$	2.81690	+	5.04804i	0.108023	+	0.193584i
$681$	8.11623	−	4.81734i	0.311015	−	0.184601i
$682$	0.126533	−	1.44628i	0.00484519	−	0.0553808i
$683$	−33.5011	−	8.97660i	−1.28188	−	0.343480i	−0.447312	−	0.894378i	$-0.647619\pi$
$683$	−33.5011	−	8.97660i	−1.28188	−	0.343480i	−0.834573	+	0.550898i	$0.814285\pi$
$684$	22.9629	−	14.0067i	0.878009	−	0.535560i
$685$	11.6777	−	16.1690i	0.446181	−	0.617787i
$686$	2.53573	−	0.447117i	0.0968146	−	0.0170710i
$687$	−0.0233413	+	0.309778i	−0.000890527	+	0.0118188i
$688$	72.8530	+	33.9719i	2.77749	+	1.29517i
$689$	−3.33549	+	1.21402i	−0.127072	+	0.0462505i
$690$	−63.3013	+	44.0829i	−2.40984	+	1.67821i
$691$	−8.06781	−	45.7548i	−0.306914	−	1.74060i	−0.614356	−	0.789029i	$-0.710584\pi$
$691$	−8.06781	−	45.7548i	−0.306914	−	1.74060i	0.307442	−	0.951567i	$-0.400527\pi$
$692$	−65.2489	+	17.4834i	−2.48039	+	0.664619i
$693$	0.403167	−	0.423100i	0.0153150	−	0.0160723i
$694$	55.9820	−	32.3212i	2.12505	−	1.22690i
$695$	−33.1427	−	6.34492i	−1.25717	−	0.240677i
$696$	2.50072	+	4.21321i	0.0947897	+	0.159701i
$697$	0.804947	+	1.14958i	0.0304896	+	0.0435436i
$698$	−6.68608	+	0.584956i	−0.253072	+	0.0221409i
$699$	2.25837	−	13.7775i	0.0854195	−	0.521112i
$700$	1.78765	−	0.423392i	0.0675669	−	0.0160027i
$701$			23.7132i			0.895637i	0.894125	+	0.447818i	$0.147799\pi$
$701$			23.7132i			0.895637i	−0.894125	+	0.447818i	$0.852201\pi$
$702$	21.4502	−	6.58788i	0.809586	−	0.248643i
$703$	11.0627	+	11.0627i	0.417239	+	0.417239i
$704$	−79.6806	−	29.0014i	−3.00307	−	1.09303i
$705$	0.0187172	−	7.30891i	0.000704932	−	0.275269i
$706$	−0.923079	−	0.774556i	−0.0347406	−	0.0291508i
$707$	0.683160	−	0.478354i	0.0256929	−	0.0179903i
$708$	−30.9497	−	110.174i	−1.16316	−	4.14058i
$709$	−17.8373	−	21.2576i	−0.669892	−	0.798346i	0.318877	−	0.947796i	$-0.396694\pi$
$709$	−17.8373	−	21.2576i	−0.669892	−	0.798346i	−0.988769	+	0.149450i	$0.952250\pi$
$710$	31.5748	−	14.1653i	1.18498	−	0.531615i
$711$	−21.0610	+	8.24606i	−0.789848	+	0.309252i
$712$	30.8885	+	115.277i	1.15760	+	4.32021i
$713$	1.09970	+	0.770021i	0.0411842	+	0.0288375i
$714$	0.0859164	−	0.0162201i	0.00321534	−	0.000607021i
$715$	−2.50169	−	9.91402i	−0.0935579	−	0.370764i
$716$	−27.4373	−	75.3835i	−1.02538	−	2.81721i
$717$	2.27129	+	4.72129i	0.0848229	+	0.176320i
$718$	−32.0046	+	45.7073i	−1.19440	+	1.70578i
$719$	−13.3000	+	23.0362i	−0.496005	+	0.859105i	−0.999989	−	0.00460740i	$-0.998533\pi$
$719$	−13.3000	+	23.0362i	−0.496005	+	0.859105i	0.503985	+	0.863713i	$0.331867\pi$
$720$	−98.0440	−	16.3291i	−3.65388	−	0.608549i
$721$	−0.111858	−	0.193744i	−0.00416582	−	0.00721542i
$722$	44.3128	+	3.87687i	1.64915	+	0.144282i
$723$	−13.6955	−	13.3691i	−0.509343	−	0.497203i
$724$	−16.1368	−	2.84536i	−0.599721	−	0.105747i
$725$	1.17763	−	0.930857i	0.0437361	−	0.0345712i
$726$	−4.41876	−	11.6995i	−0.163996	−	0.434208i
$727$	31.1801	−	14.5395i	1.15640	−	0.539240i	0.252762	−	0.967528i	$-0.418661\pi$
$727$	31.1801	−	14.5395i	1.15640	−	0.539240i	0.903642	+	0.428288i	$0.140883\pi$
$728$	0.710345	−	0.710345i	0.0263271	−	0.0263271i
$729$	−22.3455	+	15.1552i	−0.827610	+	0.561303i
$730$	34.8071	+	42.7352i	1.28827	+	1.58170i
$731$	0.509123	−	1.39880i	0.0188306	−	0.0517367i
$732$	17.3712	−	38.4568i	0.642057	−	1.42140i
$733$	−0.208175	−	2.37945i	−0.00768910	−	0.0878868i	0.991380	−	0.131014i	$-0.0418234\pi$
$733$	−0.208175	−	2.37945i	−0.00768910	−	0.0878868i	−0.999070	+	0.0431275i	$0.986268\pi$
$734$	5.30665	−	30.0955i	0.195872	−	1.11085i
$735$	−2.43045	+	26.9841i	−0.0896484	+	0.995322i
$736$	120.741	−	101.314i	4.45058	−	3.73448i
$737$	−1.85655	+	6.92873i	−0.0683868	+	0.255223i
$738$	−41.8023	−	2.64317i	−1.53876	−	0.0972965i
$739$	4.08269	+	2.35714i	0.150184	+	0.0867088i	0.573209	−	0.819409i	$-0.305698\pi$
$739$	4.08269	+	2.35714i	0.150184	+	0.0867088i	−0.423025	+	0.906118i	$0.639032\pi$
$740$	−8.41678	−	115.657i	−0.309407	−	4.25164i
$741$	−4.25288	−	1.49009i	−0.156233	−	0.0547397i
$742$	0.174457	−	0.374125i	0.00640452	−	0.0137345i
$743$	19.9613	−	42.8072i	0.732310	−	1.57044i	−0.0864151	−	0.996259i	$-0.527541\pi$
$743$	19.9613	−	42.8072i	0.732310	−	1.57044i	0.818725	−	0.574185i	$-0.194681\pi$
$744$	0.557045	+	2.95062i	0.0204223	+	0.108175i
$745$	24.3567	+	21.0521i	0.892359	+	0.771289i
$746$	90.1249	+	52.0336i	3.29971	+	1.90509i
$747$	−33.8408	−	14.7973i	−1.23817	−	0.541407i
$748$	−1.11905	+	4.17634i	−0.0409164	+	0.152702i
$749$	−0.447889	+	0.375823i	−0.0163655	+	0.0137323i
$750$	−1.68087	+	52.8349i	−0.0613767	+	1.92926i
$751$	8.23787	−	46.7193i	0.300604	−	1.70481i	−0.342904	−	0.939371i	$-0.611410\pi$
$751$	8.23787	−	46.7193i	0.300604	−	1.70481i	0.643508	−	0.765440i	$-0.277478\pi$
$752$	2.43703	+	27.8553i	0.0888692	+	1.01578i
$753$	−42.6572	+	4.25098i	−1.55451	+	0.154914i
$754$	0.443420	−	1.21829i	0.0161484	−	0.0443674i
$755$	−3.77359	+	3.07353i	−0.137335	+	0.111857i
$756$	−0.894156	+	1.68684i	−0.0325201	+	0.0613499i
$757$	4.48441	−	4.48441i	0.162989	−	0.162989i	−0.620901	−	0.783889i	$-0.713233\pi$
$757$	4.48441	−	4.48441i	0.162989	−	0.162989i	0.783889	+	0.620901i	$0.213233\pi$
$758$	10.1868	−	4.75020i	0.370003	−	0.172535i
$759$	−36.0475	−	5.90883i	−1.30844	−	0.214477i
$760$	24.1402	+	24.8567i	0.875659	+	0.901647i
$761$	−35.8871	−	6.32786i	−1.30091	−	0.229385i	−0.520071	−	0.854123i	$-0.674095\pi$
$761$	−35.8871	−	6.32786i	−1.30091	−	0.229385i	−0.780834	+	0.624738i	$0.785206\pi$
$762$	6.95306	−	27.2600i	0.251883	−	0.987527i
$763$	0.982204	+	0.0859317i	0.0355582	+	0.00311094i
$764$	63.6122	+	110.180i	2.30141	+	3.98616i
$765$	−0.142995	+	1.83505i	−0.00516999	+	0.0663463i
$766$	11.6085	−	20.1066i	0.419434	−	0.726480i
$767$	−10.9970	+	15.7054i	−0.397079	+	0.567088i
$768$	72.5193	+	5.46422i	2.61682	+	0.197173i
$769$	12.5047	+	34.3564i	0.450931	+	1.23892i	0.932070	+	0.362279i	$0.118001\pi$
$769$	12.5047	+	34.3564i	0.450931	+	1.23892i	−0.481139	+	0.876645i	$0.659777\pi$
$770$	1.02099	+	0.609546i	0.0367941	+	0.0219665i
$771$	27.1096	+	31.5279i	0.976329	+	1.13545i
$772$	86.6512	+	60.6738i	3.11864	+	2.18370i
$773$	−8.96378	−	33.4533i	−0.322405	−	1.20323i	−0.916895	−	0.399128i	$-0.869313\pi$
$773$	−8.96378	−	33.4533i	−0.322405	−	1.20323i	0.594491	−	0.804103i	$-0.297354\pi$
$774$	23.1358	+	37.9293i	0.831598	+	1.36334i
$775$	0.873332	−	0.289242i	0.0313710	−	0.0103899i
$776$	−11.8151	−	14.0807i	−0.424137	−	0.505467i
$777$	−1.07603	−	0.274456i	−0.0386022	−	0.00984604i
$778$	−71.8739	+	50.3266i	−2.57680	+	1.80430i
$779$	6.44381	+	5.40700i	0.230873	+	0.193726i
$780$	16.6267	+	28.9694i	0.595332	+	1.03727i
$781$	15.3995	+	5.60498i	0.551039	+	0.200562i
$782$	−3.86426	−	3.86426i	−0.138186	−	0.138186i
$783$	−0.0796592	+	1.55796i	−0.00284679	+	0.0556768i
$784$		−	103.651i		−	3.70181i
$785$	5.92486	−	12.2356i	0.211467	−	0.436707i
$786$	−16.7817	−	13.7401i	−0.598585	−	0.490093i
$787$	11.0579	−	0.967441i	0.394172	−	0.0344855i	0.111653	−	0.993747i	$-0.464386\pi$
$787$	11.0579	−	0.967441i	0.394172	−	0.0344855i	0.282519	+	0.959262i	$0.408830\pi$
$788$	−50.4043	−	71.9848i	−1.79558	−	2.56435i
$789$	−3.43304	+	6.11535i	−0.122219	+	0.217712i
$790$	−25.8415	−	38.0785i	−0.919399	−	1.35477i
$791$	−0.435084	+	0.251196i	−0.0154698	+	0.00893150i
$792$	−48.4636	−	65.7778i	−1.72208	−	2.33731i
$793$	−6.82887	+	1.82979i	−0.242500	+	0.0649778i
$794$	13.1431	+	74.5384i	0.466432	+	2.64527i
$795$	6.64263	+	5.60288i	0.235590	+	0.198714i
$796$	−63.3069	+	23.0418i	−2.24385	+	0.816696i
$797$	−19.8376	−	9.25041i	−0.702683	−	0.327666i	0.0382286	−	0.999269i	$-0.487828\pi$
$797$	−19.8376	−	9.25041i	−0.702683	−	0.327666i	−0.740912	+	0.671603i	$0.765606\pi$
$798$	0.472267	−	0.227195i	0.0167181	−	0.00804263i
$799$	0.509936	−	0.0899154i	0.0180402	−	0.00318098i
$800$	−6.26381	−	107.830i	−0.221459	−	3.81237i
$801$	−12.1315	+	36.0107i	−0.428646	+	1.27237i
$802$	86.5715	+	23.1968i	3.05695	+	0.819106i
$803$	−2.27478	+	26.0008i	−0.0802752	+	0.917550i
$804$	−0.282595	−	23.4311i	−0.00996637	−	0.826351i
$805$	−0.960197	+	0.535807i	−0.0338425	+	0.0188847i
$806$	0.510741	−	0.608678i	0.0179901	−	0.0214398i
$807$	26.9602	+	12.1781i	0.949043	+	0.428689i
$808$	−49.2736	−	105.668i	−1.73344	−	3.71737i
$809$	27.2653			0.958598			0.479299	−	0.877652i	$-0.340891\pi$
$809$	27.2653			0.958598			0.479299	+	0.877652i	$0.340891\pi$
$810$	−40.1290	−	37.5176i	−1.40999	−	1.31823i
$811$	−36.1569			−1.26964			−0.634820	−	0.772660i	$-0.718926\pi$
$811$	−36.1569			−1.26964			−0.634820	+	0.772660i	$0.718926\pi$
$812$	0.0466179	+	0.0999725i	0.00163597	+	0.00350835i
$813$	−13.5252	−	6.10942i	−0.474349	−	0.214267i
$814$	48.2474	−	57.4990i	1.69107	−	2.01534i
$815$	−7.62208	+	26.8683i	−0.266990	+	0.941156i
$816$	−0.0849207	−	7.04111i	−0.00297282	−	0.246488i
$817$	0.777642	−	8.88849i	0.0272062	−	0.310969i
$818$	72.9233	+	19.5397i	2.54970	+	0.683191i
$819$	0.313568	−	0.0631239i	0.0109570	−	0.00220573i
$820$	−9.92793	−	61.5536i	−0.346698	−	2.14955i
$821$	−0.864071	+	0.152359i	−0.0301563	+	0.00531736i	−0.188706	−	0.982034i	$-0.560429\pi$
$821$	−0.864071	+	0.152359i	−0.0301563	+	0.00531736i	0.158550	+	0.987351i	$0.449318\pi$
$822$	−38.0041	+	18.2828i	−1.32555	+	0.637686i
$823$	21.5215	+	10.0357i	0.750194	+	0.349821i	0.759821	−	0.650132i	$-0.225287\pi$
$823$	21.5215	+	10.0357i	0.750194	+	0.349821i	−0.00962693	+	0.999954i	$0.503064\pi$
$824$	−29.3895	+	10.6969i	−1.02383	+	0.372644i
$825$	−18.0021	+	17.3938i	−0.626751	+	0.605576i
$826$	−0.387186	−	2.19584i	−0.0134719	−	0.0764032i
$827$	−33.6948	+	9.02850i	−1.17168	+	0.313952i	−0.791623	−	0.611010i	$-0.790764\pi$
$827$	−33.6948	+	9.02850i	−1.17168	+	0.313952i	−0.380061	+	0.924961i	$0.624097\pi$
$828$	118.590	−	13.2642i	4.12128	−	0.460964i
$829$	−30.9073	+	17.8443i	−1.07345	+	0.619759i	−0.929123	−	0.369771i	$-0.879436\pi$
$829$	−30.9073	+	17.8443i	−1.07345	+	0.619759i	−0.144330	+	0.989530i	$0.546103\pi$
$830$	14.1301	−	73.8083i	0.490462	−	2.56193i
$831$	−9.26613	+	16.5060i	−0.321439	+	0.572586i
$832$	−26.6185	−	38.0152i	−0.922832	−	1.31794i
$833$	−1.91212	+	0.167289i	−0.0662512	+	0.00579623i
$834$	55.2077	+	45.2015i	1.91169	+	1.56520i
$835$	−44.8608	−	21.7230i	−1.55247	−	0.751756i
$836$			25.9158i			0.896317i
$837$	−0.372447	+	0.880547i	−0.0128737	+	0.0304362i
$838$	12.6368	+	12.6368i	0.436530	+	0.436530i
$839$	9.08974	+	3.30839i	0.313813	+	0.114218i	0.494125	−	0.869391i	$-0.335489\pi$
$839$	9.08974	+	3.30839i	0.313813	+	0.114218i	−0.180312	+	0.983609i	$0.557711\pi$
$840$	−2.37398	−	0.642625i	−0.0819099	−	0.0221727i
$841$	−22.1462	−	18.5829i	−0.763664	−	0.640790i
$842$	1.08473	−	0.759539i	0.0373824	−	0.0261754i
$843$	−23.5939	−	6.01796i	−0.812617	−	0.207270i
$844$	46.0118	+	54.8347i	1.58379	+	1.88749i
$845$	−8.34981	+	21.9375i	−0.287242	+	0.754674i
$846$	−7.40220	+	13.5665i	−0.254493	+	0.466424i
$847$	−0.0461394	−	0.172195i	−0.00158537	−	0.00591668i
$848$	−27.2331	−	19.0688i	−0.935188	−	0.654826i
$849$	28.4351	+	33.0694i	0.975891	+	1.13494i
$850$	−3.70553	+	0.542201i	−0.127099	+	0.0185973i
$851$	23.7390	+	65.2223i	0.813762	+	2.23579i
$852$	−53.3835	−	4.02236i	−1.82889	−	0.137804i
$853$	16.0773	−	22.9607i	0.550476	−	0.786161i	−0.443440	−	0.896304i	$-0.646242\pi$
$853$	16.0773	−	22.9607i	0.550476	−	0.786161i	0.993916	+	0.110143i	$0.0351309\pi$
$854$	0.411095	−	0.712037i	0.0140674	−	0.0243654i
$855$	2.01890	+	10.8462i	0.0690448	+	0.370933i
$856$	40.8690	+	70.7872i	1.39687	+	2.41946i
$857$	9.91389	+	0.867353i	0.338652	+	0.0296282i	0.255214	−	0.966885i	$-0.417854\pi$
$857$	9.91389	+	0.867353i	0.338652	+	0.0296282i	0.0834385	+	0.996513i	$0.473410\pi$
$858$	−5.34341	+	20.9493i	−0.182421	+	0.715196i
$859$	−4.41290	−	0.778113i	−0.150566	−	0.0265489i	0.0978570	−	0.995200i	$-0.468801\pi$
$859$	−4.41290	−	0.778113i	−0.150566	−	0.0265489i	−0.248423	+	0.968652i	$0.579912\pi$
$860$	−47.4426	+	46.0752i	−1.61778	+	1.57115i
$861$	−0.589200	−	0.0965803i	−0.0200799	−	0.00329145i
$862$	−40.2723	+	18.7793i	−1.37168	+	0.639624i
$863$	−9.71940	+	9.71940i	−0.330852	+	0.330852i	−0.852910	−	0.522058i	$-0.825165\pi$
$863$	−9.71940	+	9.71940i	−0.330852	+	0.330852i	0.522058	+	0.852910i	$0.325165\pi$
$864$	88.5415	+	68.9947i	3.01224	+	2.34725i
$865$	2.81811	−	27.5633i	0.0958187	−	0.937180i
$866$	−24.0508	+	66.0790i	−0.817280	+	2.24546i
$867$	29.1700	−	2.90692i	0.990664	−	0.0987242i
$868$	0.00589210	+	0.0673471i	0.000199991	+	0.00228591i
$869$	3.78416	−	21.4610i	0.128369	−	0.728016i
$870$	−3.12721	+	0.543158i	−0.106022	+	0.0184148i
$871$	−3.00739	+	2.52350i	−0.101902	+	0.0855056i
$872$	35.6748	−	133.140i	1.20810	−	4.50870i
$873$	−0.650547	−	5.81626i	−0.0220177	−	0.196851i
$874$	−28.3677	−	16.3781i	−0.959553	−	0.553998i
$875$	−0.0985256	+	0.747050i	−0.00333077	+	0.0252549i
$876$	−15.8172	−	83.7824i	−0.534414	−	2.83074i
$877$	−4.69203	+	10.0621i	−0.158438	+	0.339772i	−0.969462	−	0.245241i	$-0.921133\pi$
$877$	−4.69203	+	10.0621i	−0.158438	+	0.339772i	0.811024	+	0.585013i	$0.198911\pi$
$878$	−31.4780	+	67.5049i	−1.06233	+	2.27818i
$879$	−36.4216	−	12.7611i	−1.22847	−	0.430420i
$880$	62.6234	−	72.4534i	2.11103	−	2.44240i
$881$	6.04019	+	3.48730i	0.203499	+	0.117490i	0.598287	−	0.801282i	$-0.295848\pi$
$881$	6.04019	+	3.48730i	0.203499	+	0.117490i	−0.394787	+	0.918772i	$0.629182\pi$
$882$	31.7176	−	47.7063i	1.06799	−	1.60635i
$883$	1.70073	−	6.34719i	0.0572340	−	0.213600i	−0.931386	−	0.364032i	$-0.881400\pi$
$883$	1.70073	−	6.34719i	0.0572340	−	0.213600i	0.988620	+	0.150432i	$0.0480665\pi$
$884$	−1.81273	+	1.52106i	−0.0609686	+	0.0511588i
$885$	46.7495	+	4.21071i	1.57147	+	0.141542i
$886$	−11.8947	+	67.4585i	−0.399612	+	2.26631i
$887$	0.889770	+	10.1701i	0.0298756	+	0.341479i	0.996392	+	0.0848735i	$0.0270486\pi$
$887$	0.889770	+	10.1701i	0.0298756	+	0.341479i	−0.966516	+	0.256606i	$0.917396\pi$
$888$	−63.9077	+	141.481i	−2.14460	+	4.74778i
$889$	0.137157	−	0.376836i	0.00460010	−	0.0126387i
$890$	−76.9140	−	7.86380i	−2.57816	−	0.263595i
$891$	−1.25446	−	25.9841i	−0.0420260	−	0.870502i
$892$	−47.0125	+	47.0125i	−1.57410	+	1.57410i
$893$	2.81288	−	1.31167i	0.0941296	−	0.0438934i
$894$	−24.0519	−	63.6819i	−0.804417	−	2.12984i
$895$	32.9006	+	0.481074i	1.09975	+	0.0160805i
$896$	2.44747	+	0.431556i	0.0817643	+	0.0144173i
$897$	−14.3060	−	13.9651i	−0.477665	−	0.466280i
$898$	71.5439	+	6.25928i	2.38745	+	0.208875i
$899$	0.0276198	+	0.0478389i	0.000921172	+	0.00159552i
$900$	41.2493	−	70.6082i	1.37498	−	2.35361i
$901$	−0.307824	+	0.533166i	−0.0102551	+	0.0177623i
$902$	23.1477	−	33.0584i	0.770735	−	1.10072i
$903$	0.274550	+	0.570703i	0.00913646	+	0.0189918i
$904$	24.0216	+	65.9989i	0.798947	+	2.19509i
$905$	3.44519	−	5.77071i	0.114522	−	0.191825i
$906$	10.1122	−	1.90908i	0.335956	−	0.0634249i
$907$	−17.4992	−	12.2531i	−0.581053	−	0.406858i	0.245763	−	0.969330i	$-0.420961\pi$
$907$	−17.4992	−	12.2531i	−0.581053	−	0.406858i	−0.826816	+	0.562472i	$0.809850\pi$
$908$	−7.68866	−	28.6945i	−0.255157	−	0.952259i
$909$	5.56270	−	36.7036i	0.184503	−	1.21738i
$910$	0.266387	+	0.593783i	0.00883064	+	0.0196837i
$911$	−1.27365	−	1.51788i	−0.0421979	−	0.0502895i	0.744533	−	0.667586i	$-0.232672\pi$
$911$	−1.27365	−	1.51788i	−0.0421979	−	0.0502895i	−0.786731	+	0.617296i	$0.788228\pi$
$912$	−11.4149	−	40.6342i	−0.377984	−	1.34553i
$913$	29.1506	−	20.4115i	0.964744	−	0.675521i
$914$	−81.6208	−	68.4880i	−2.69978	−	2.26538i
$915$	12.2074	+	12.2701i	0.403564	+	0.405636i
$916$	0.918820	+	0.334423i	0.0303587	+	0.0110497i
$917$	−0.218615	−	0.218615i	−0.00721930	−	0.00721930i
$918$	2.11553	−	3.26673i	0.0698228	−	0.107818i
$919$		−	49.9403i		−	1.64738i	−0.567042	−	0.823689i	$-0.691912\pi$
$919$		−	49.9403i		−	1.64738i	0.567042	−	0.823689i	$-0.308088\pi$
$920$	50.4581	+	145.204i	1.66355	+	4.78722i
$921$	7.47349	−	45.5930i	0.246260	−	1.50234i
$922$	8.34983	−	0.730515i	0.274987	−	0.0240582i
$923$	5.14446	+	7.34705i	0.169332	+	0.241831i
$924$	−0.938887	−	1.58183i	−0.0308871	−	0.0520385i
$925$	45.5638	+	13.6485i	1.49813	+	0.448761i
$926$	95.8608	−	55.3452i	3.15018	−	1.81876i
$927$	−9.67824	−	2.34463i	−0.317875	−	0.0770079i
$928$	6.26448	−	1.67856i	0.205642	−	0.0551015i
$929$	−4.34439	−	24.6383i	−0.142535	−	0.808355i	−0.969314	−	0.245828i	$-0.920940\pi$
$929$	−4.34439	−	24.6383i	−0.142535	−	0.808355i	0.826779	−	0.562527i	$-0.190171\pi$
$930$	−1.91485	−	0.342698i	−0.0627904	−	0.0112375i
$931$	−10.8111	+	3.93492i	−0.354320	+	0.128962i
$932$	−39.8261	−	18.5712i	−1.30455	−	0.608320i
$933$	−1.49524	+	19.8443i	−0.0489518	+	0.649673i
$934$	12.2666	−	2.16293i	0.401374	−	0.0707731i
$935$	−1.43768	−	1.03832i	−0.0470170	−	0.0339568i
$936$	−1.07846	−	44.7034i	−0.0352507	−	1.46117i
$937$	−30.1964	−	8.09111i	−0.986475	−	0.264325i	−0.270706	−	0.962662i	$-0.587257\pi$
$937$	−30.1964	−	8.09111i	−0.986475	−	0.264325i	−0.715769	+	0.698337i	$0.753924\pi$
$938$	0.0397923	−	0.454828i	0.00129926	−	0.0148507i
$939$	30.2941	−	17.9809i	0.988609	−	0.586783i
$940$	−22.1315	−	6.27832i	−0.721850	−	0.204776i
$941$	20.9973	−	25.0236i	0.684491	−	0.815745i	−0.306186	−	0.951972i	$-0.599053\pi$
$941$	20.9973	−	25.0236i	0.684491	−	0.815745i	0.990678	+	0.136227i	$0.0434975\pi$
$942$	−23.3463	+	16.7704i	−0.760663	+	0.546410i
$943$	15.7714	+	33.8218i	0.513587	+	1.10139i
$944$	−179.573			−5.84461
$945$	−0.516169	−	0.588883i	−0.0167910	−	0.0191564i
$946$	−42.8067			−1.39177
$947$	9.61412	+	20.6175i	0.312417	+	0.669980i	0.998334	−	0.0576996i	$-0.0183766\pi$
$947$	9.61412	+	20.6175i	0.312417	+	0.669980i	−0.685917	+	0.727680i	$0.740599\pi$
$948$	7.05935	+	70.8382i	0.229277	+	2.30072i
$949$	−9.18200	+	10.9427i	−0.298060	+	0.355214i
$950$	−20.6128	+	8.88775i	−0.668767	+	0.288357i
$951$	−10.4190	−	5.84902i	−0.337859	−	0.189667i
$952$	0.0151858	−	0.173575i	0.000492175	−	0.00562559i
$953$	30.6787	+	8.22034i	0.993781	+	0.266283i	0.718838	−	0.695178i	$-0.244674\pi$
$953$	30.6787	+	8.22034i	0.993781	+	0.266283i	0.274943	+	0.961461i	$0.411341\pi$
$954$	−6.69916	−	17.1101i	−0.216893	−	0.553959i
$955$	−51.5174	+	8.30920i	−1.66706	+	0.268879i
$956$	16.2399	−	2.86352i	0.525235	−	0.0926130i
$957$	−1.24153	−	0.847201i	−0.0401330	−	0.0273861i
$958$	−64.5582	−	30.1040i	−2.08578	−	0.972615i
$959$	−0.564905	+	0.205609i	−0.0182417	+	0.00663945i
$960$	−48.2799	+	102.848i	−1.55823	+	3.31941i
$961$	−5.37721	−	30.4957i	−0.173459	−	0.983732i
$962$	39.6804	−	10.6323i	1.27935	−	0.342800i
$963$	−1.64232	+	25.9736i	−0.0529229	+	0.836987i
$964$	−52.1692	+	30.1199i	−1.68026	+	0.970097i
$965$	−35.9014	+	24.3641i	−1.15571	+	0.784307i
$966$	2.32485	−	0.0280393i	0.0748007	−	0.000902149i
$967$	−6.54972	−	9.35397i	−0.210625	−	0.300803i	0.699914	−	0.714227i	$-0.253222\pi$
$967$	−6.54972	−	9.35397i	−0.210625	−	0.300803i	−0.910539	+	0.413424i	$0.864333\pi$
$968$	−24.8272	+	2.17210i	−0.797977	+	0.0698140i
$969$	−0.731186	+	0.276161i	−0.0234891	+	0.00887157i
$970$	11.2480	−	3.90868i	0.361153	−	0.125500i
$971$		−	1.87641i		−	0.0602168i	−0.999547	−	0.0301084i	$-0.990415\pi$
$971$		−	1.87641i		−	0.0602168i	0.999547	−	0.0301084i	$-0.00958525\pi$
$972$	26.9019	+	80.6118i	0.862879	+	2.58563i
$973$	0.719189	+	0.719189i	0.0230561	+	0.0230561i
$974$	−37.4883	−	13.6446i	−1.20120	−	0.437202i
$975$	−13.5310	+	2.14686i	−0.433339	+	0.0687547i
$976$	−50.7245	−	42.5629i	−1.62365	−	1.36240i
$977$	8.47065	−	5.93121i	0.271000	−	0.189756i	−0.430175	−	0.902746i	$-0.641548\pi$
$977$	8.47065	−	5.93121i	0.271000	−	0.189756i	0.701175	+	0.712989i	$0.252659\pi$
$978$	41.2508	−	42.2580i	1.31906	−	1.35126i
$979$	−23.5338	−	28.0465i	−0.752144	−	0.896371i
$980$	79.6981	+	30.3345i	2.54586	+	0.969001i
$981$	32.9295	−	29.0129i	1.05136	−	0.926310i
$982$	−15.2441	−	56.8917i	−0.486459	−	1.81549i
$983$	−31.7007	−	22.1970i	−1.01109	−	0.707976i	−0.0542350	−	0.998528i	$-0.517272\pi$
$983$	−31.7007	−	22.1970i	−1.01109	−	0.707976i	−0.956859	+	0.290552i	$0.906161\pi$
$984$	−27.6003	+	78.7743i	−0.879865	+	2.51123i
$985$	34.9488	−	8.81892i	1.11356	−	0.280994i
$986$	−0.0769083	−	0.211304i	−0.00244926	−	0.00672928i
$987$	−0.124172	+	0.181967i	−0.00395242	+	0.00579208i
$988$	−8.13546	+	11.6186i	−0.258824	+	0.369638i
$989$	19.7919	−	34.2805i	0.629344	−	1.09006i
$990$	50.9941	−	14.1844i	1.62070	−	0.450809i
$991$	22.3137	+	38.6485i	0.708818	+	1.22771i	0.965296	+	0.261159i	$0.0841048\pi$
$991$	22.3137	+	38.6485i	0.708818	+	1.22771i	−0.256477	+	0.966550i	$0.582562\pi$
$992$	3.95964	+	0.346423i	0.125719	+	0.0109990i
$993$	19.3551	−	5.43719i	0.614215	−	0.172544i
$994$	−1.02723	−	0.181128i	−0.0325817	−	0.00574503i
$995$	0.404005	−	27.6299i	0.0128078	−	0.875926i
$996$	−73.6454	+	89.9482i	−2.33354	+	2.85012i
$997$	−13.3064	+	6.20488i	−0.421418	+	0.196511i	−0.621747	−	0.783218i	$-0.713577\pi$
$997$	−13.3064	+	6.20488i	−0.421418	+	0.196511i	0.200329	+	0.979729i	$0.435799\pi$
$998$	50.4141	−	50.4141i	1.59583	−	1.59583i
$999$	−41.8857	+	26.2473i	−1.32520	+	0.830429i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.23.1	✓	192
3.2	odd	2		405.2.r.a.98.16		192
5.2	odd	4	inner	135.2.q.a.77.16	yes	192
5.3	odd	4		675.2.ba.b.482.1		192
5.4	even	2		675.2.ba.b.293.16		192
15.2	even	4		405.2.r.a.17.1		192
27.7	even	9		405.2.r.a.143.1		192
27.20	odd	18	inner	135.2.q.a.128.16	yes	192
135.7	odd	36		405.2.r.a.62.16		192
135.47	even	36	inner	135.2.q.a.47.1	yes	192
135.74	odd	18		675.2.ba.b.668.1		192
135.128	even	36		675.2.ba.b.182.16		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.23.1	✓	192	1.1	even	1	trivial
135.2.q.a.47.1	yes	192	135.47	even	36	inner
135.2.q.a.77.16	yes	192	5.2	odd	4	inner
135.2.q.a.128.16	yes	192	27.20	odd	18	inner
405.2.r.a.17.1		192	15.2	even	4
405.2.r.a.62.16		192	135.7	odd	36
405.2.r.a.98.16		192	3.2	odd	2
405.2.r.a.143.1		192	27.7	even	9
675.2.ba.b.182.16		192	135.128	even	36
675.2.ba.b.293.16		192	5.4	even	2
675.2.ba.b.482.1		192	5.3	odd	4
675.2.ba.b.668.1		192	135.74	odd	18

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15365 - 2.47401i) q^{2} +(-1.57848 - 0.713012i) q^{3} +(-3.50423 + 4.17618i) q^{4} +(-1.08960 - 1.95263i) q^{5} +(0.0570200 + 4.72775i) q^{6} +(-0.00587402 + 0.0671403i) q^{7} +(9.10104 + 2.43862i) q^{8} +(1.98323 + 2.25096i) q^{9} +O(q^{10})\)	\(q+(-1.15365 - 2.47401i) q^{2} +(-1.57848 - 0.713012i) q^{3} +(-3.50423 + 4.17618i) q^{4} +(-1.08960 - 1.95263i) q^{5} +(0.0570200 + 4.72775i) q^{6} +(-0.00587402 + 0.0671403i) q^{7} +(9.10104 + 2.43862i) q^{8} +(1.98323 + 2.25096i) q^{9} +(-3.57380 + 4.94833i) q^{10} +(-2.84658 + 0.501928i) q^{11} +(8.50904 - 4.09348i) q^{12} +(-1.43375 - 0.668569i) q^{13} +(0.172882 - 0.0629240i) q^{14} +(0.327671 + 3.85910i) q^{15} +(-2.57292 - 14.5918i) q^{16} +(-0.265033 + 0.0710153i) q^{17} +(3.28093 - 7.50333i) q^{18} +(-1.42429 + 0.822315i) q^{19} +(11.9727 + 2.29209i) q^{20} +(0.0571439 - 0.101792i) q^{21} +(4.52572 + 6.46340i) q^{22} +(-7.26851 + 0.635912i) q^{23} +(-12.6271 - 10.3385i) q^{24} +(-2.62553 + 4.25518i) q^{25} +4.31840i q^{26} +(-1.52554 - 4.96717i) q^{27} +(-0.259806 - 0.259806i) q^{28} +(-0.282115 - 0.102681i) q^{29} +(9.16941 - 5.26270i) q^{30} +(-0.140950 - 0.118271i) q^{31} +(-17.6956 + 12.3906i) q^{32} +(4.85116 + 1.23736i) q^{33} +(0.481447 + 0.573766i) q^{34} +(0.137501 - 0.0616864i) q^{35} +(-16.3501 + 0.394444i) q^{36} +(-2.46210 - 9.18868i) q^{37} +(3.67754 + 2.57504i) q^{38} +(1.78646 + 2.07761i) q^{39} +(-5.15479 - 20.4281i) q^{40} +(-1.74933 - 4.80625i) q^{41} +(-0.317757 - 0.0239425i) q^{42} +(-3.11177 + 4.44406i) q^{43} +(7.87892 - 13.6467i) q^{44} +(2.23436 - 6.32516i) q^{45} +(9.95855 + 17.2487i) q^{46} +(-1.87998 - 0.164477i) q^{47} +(-6.34278 + 24.8674i) q^{48} +(6.88918 + 1.21475i) q^{49} +(13.5563 + 1.58661i) q^{50} +(0.468985 + 0.0768749i) q^{51} +(7.81625 - 3.64478i) q^{52} +(1.58658 - 1.58658i) q^{53} +(-10.5289 + 9.50455i) q^{54} +(4.08172 + 5.01141i) q^{55} +(-0.217189 + 0.596722i) q^{56} +(2.83454 - 0.282475i) q^{57} +(0.0714269 + 0.816413i) q^{58} +(2.10453 - 11.9354i) q^{59} +(-17.2645 - 12.1547i) q^{60} +(3.42343 - 2.87260i) q^{61} +(-0.129996 + 0.485153i) q^{62} +(-0.162779 + 0.119932i) q^{63} +(25.4054 + 14.6678i) q^{64} +(0.256749 + 3.52806i) q^{65} +(-2.53530 - 13.4293i) q^{66} +(1.04879 - 2.24913i) q^{67} +(0.632163 - 1.35568i) q^{68} +(11.9266 + 4.17875i) q^{69} +(-0.311240 - 0.269013i) q^{70} +(-4.91000 - 2.83479i) q^{71} +(12.5602 + 25.3224i) q^{72} +(2.33705 - 8.72199i) q^{73} +(-19.8925 + 16.6918i) q^{74} +(7.17836 - 4.84470i) q^{75} +(1.55691 - 8.82967i) q^{76} +(-0.0169788 - 0.194068i) q^{77} +(3.07907 - 6.81653i) q^{78} +(-2.57857 + 7.08457i) q^{79} +(-25.6889 + 20.9232i) q^{80} +(-1.13361 + 8.92832i) q^{81} +(-9.87258 + 9.87258i) q^{82} +(-11.1580 + 5.20307i) q^{83} +(0.224855 + 0.595345i) q^{84} +(0.427447 + 0.440133i) q^{85} +(14.5845 + 2.57164i) q^{86} +(0.372101 + 0.363233i) q^{87} +(-27.1308 - 2.37364i) q^{88} +(6.33320 + 10.9694i) q^{89} +(-18.2262 + 1.76919i) q^{90} +(0.0533098 - 0.0923353i) q^{91} +(22.8148 - 32.5830i) q^{92} +(0.138158 + 0.287188i) q^{93} +(1.76192 + 4.84082i) q^{94} +(3.15759 + 1.88512i) q^{95} +(36.7669 - 6.94119i) q^{96} +(-1.59804 - 1.11896i) q^{97} +(-4.94240 - 18.4453i) q^{98} +(-6.77523 - 5.41208i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Introduction

L-functions

Modular forms

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Database

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