LMFDB - Embedded newform 252.4.w.a.5.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(5,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 5]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("252.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.w (of order $6$, degree $2$, 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:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.14
Character	$\chi$	$=$	252.5
Dual form			252.4.w.a.101.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.973978 + 5.10405i) q^{3} +(-6.29153 - 10.8972i) q^{5} +(18.2954 + 2.87731i) q^{7} +(-25.1027 + 9.94247i) q^{9} +O(q^{10})$	\(q+(0.973978 + 5.10405i) q^{3} +(-6.29153 - 10.8972i) q^{5} +(18.2954 + 2.87731i) q^{7} +(-25.1027 + 9.94247i) q^{9} +(-59.5514 - 34.3820i) q^{11} +(34.1431 + 19.7125i) q^{13} +(49.4923 - 42.7260i) q^{15} +(-38.3848 - 66.4844i) q^{17} +(-69.3139 - 40.0184i) q^{19} +(3.13334 + 96.1831i) q^{21} +(-134.598 + 77.7101i) q^{23} +(-16.6667 + 28.8675i) q^{25} +(-75.1964 - 118.442i) q^{27} +(197.862 - 114.236i) q^{29} -145.493i q^{31} +(117.486 - 337.441i) q^{33} +(-83.7511 - 217.472i) q^{35} +(74.1910 - 128.503i) q^{37} +(-67.3591 + 193.468i) q^{39} +(27.9434 - 48.3994i) q^{41} +(-109.056 - 188.891i) q^{43} +(266.280 + 210.997i) q^{45} +109.953 q^{47} +(326.442 + 105.283i) q^{49} +(301.954 - 260.672i) q^{51} +(-257.488 + 148.661i) q^{53} +865.262i q^{55} +(136.746 - 392.759i) q^{57} -179.106 q^{59} -318.639i q^{61} +(-487.872 + 109.673i) q^{63} -496.087i q^{65} -653.822 q^{67} +(-527.732 - 611.307i) q^{69} -157.634i q^{71} +(-1055.68 + 609.495i) q^{73} +(-163.574 - 56.9513i) q^{75} +(-990.588 - 800.380i) q^{77} +818.802 q^{79} +(531.295 - 499.166i) q^{81} +(404.460 + 700.546i) q^{83} +(-482.998 + 836.577i) q^{85} +(775.779 + 898.636i) q^{87} +(20.9797 - 36.3379i) q^{89} +(567.941 + 458.888i) q^{91} +(742.606 - 141.707i) q^{93} +1007.11i q^{95} +(-161.296 + 93.1244i) q^{97} +(1836.74 + 270.994i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} + 12 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 + 12 * q^9	$ 48 q + 6 q^{7} + 12 q^{9} + 12 q^{11} - 36 q^{13} + 66 q^{15} - 72 q^{17} + 24 q^{21} + 30 q^{23} - 600 q^{25} - 396 q^{27} + 42 q^{29} + 390 q^{35} + 84 q^{37} - 840 q^{39} - 618 q^{41} - 42 q^{43} + 366 q^{45} + 396 q^{47} + 318 q^{49} - 738 q^{51} - 1620 q^{53} + 492 q^{57} + 1500 q^{59} + 672 q^{63} - 588 q^{67} - 924 q^{69} + 564 q^{75} - 2472 q^{77} + 1608 q^{79} + 2592 q^{81} - 360 q^{85} + 2640 q^{87} + 1722 q^{89} + 540 q^{91} + 660 q^{93} - 792 q^{97} - 54 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 + 12 * q^9 + 12 * q^11 - 36 * q^13 + 66 * q^15 - 72 * q^17 + 24 * q^21 + 30 * q^23 - 600 * q^25 - 396 * q^27 + 42 * q^29 + 390 * q^35 + 84 * q^37 - 840 * q^39 - 618 * q^41 - 42 * q^43 + 366 * q^45 + 396 * q^47 + 318 * q^49 - 738 * q^51 - 1620 * q^53 + 492 * q^57 + 1500 * q^59 + 672 * q^63 - 588 * q^67 - 924 * q^69 + 564 * q^75 - 2472 * q^77 + 1608 * q^79 + 2592 * q^81 - 360 * q^85 + 2640 * q^87 + 1722 * q^89 + 540 * q^91 + 660 * q^93 - 792 * q^97 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.973978	+	5.10405i	0.187442	+	0.982276i
$3$	0.973978	+	5.10405i	0.187442	+	0.982276i
$4$		0			0
$5$	−6.29153	−	10.8972i	−0.562731	−	0.974679i	−0.997257	−	0.0740198i	$-0.976417\pi$
$5$	−6.29153	−	10.8972i	−0.562731	−	0.974679i	0.434525	−	0.900660i	$-0.356916\pi$
$6$		0			0
$7$	18.2954	+	2.87731i	0.987858	+	0.155360i
$7$	18.2954	+	2.87731i	0.987858	+	0.155360i
$8$		0			0
$9$	−25.1027	+	9.94247i	−0.929731	+	0.368240i
$10$		0			0
$11$	−59.5514	−	34.3820i	−1.63231	−	0.942415i	−0.983378	−	0.181569i	$-0.941882\pi$
$11$	−59.5514	−	34.3820i	−1.63231	−	0.942415i	−0.648932	−	0.760846i	$-0.724784\pi$
$12$		0			0
$13$	34.1431	+	19.7125i	0.728429	+	0.420559i	0.817847	−	0.575435i	$-0.195167\pi$
$13$	34.1431	+	19.7125i	0.728429	+	0.420559i	−0.0894180	+	0.995994i	$0.528501\pi$
$14$		0			0
$15$	49.4923	−	42.7260i	0.851924	−	0.735453i
$16$		0			0
$17$	−38.3848	−	66.4844i	−0.547628	−	0.948520i	−0.998436	−	0.0558991i	$-0.982197\pi$
$17$	−38.3848	−	66.4844i	−0.547628	−	0.948520i	0.450808	−	0.892621i	$-0.351136\pi$
$18$		0			0
$19$	−69.3139	−	40.0184i	−0.836932	−	0.483203i	0.0192883	−	0.999814i	$-0.493860\pi$
$19$	−69.3139	−	40.0184i	−0.836932	−	0.483203i	−0.856220	+	0.516611i	$0.827193\pi$
$20$		0			0
$21$	3.13334	+	96.1831i	0.0325596	+	0.999470i
$22$		0			0
$23$	−134.598	+	77.7101i	−1.22024	+	0.704508i	−0.964970	−	0.262361i	$-0.915499\pi$
$23$	−134.598	+	77.7101i	−1.22024	+	0.704508i	−0.255273	+	0.966869i	$0.582165\pi$
$24$		0			0
$25$	−16.6667	+	28.8675i	−0.133333	+	0.230940i
$26$		0			0
$27$	−75.1964	−	118.442i	−0.535984	−	0.844228i
$28$		0			0
$29$	197.862	−	114.236i	1.26697	−	0.731484i	0.292555	−	0.956249i	$-0.405495\pi$
$29$	197.862	−	114.236i	1.26697	−	0.731484i	0.974413	+	0.224764i	$0.0721613\pi$
$30$		0			0
$31$		−	145.493i		−	0.842948i	−0.906841	−	0.421474i	$-0.861513\pi$
$31$		−	145.493i		−	0.842948i	0.906841	−	0.421474i	$-0.138487\pi$
$32$		0			0
$33$	117.486	−	337.441i	0.619748	−	1.78003i
$34$		0			0
$35$	−83.7511	−	217.472i	−0.404472	−	1.05027i
$36$		0			0
$37$	74.1910	−	128.503i	0.329647	−	0.570965i	−0.652795	−	0.757534i	$-0.726404\pi$
$37$	74.1910	−	128.503i	0.329647	−	0.570965i	0.982442	+	0.186570i	$0.0597371\pi$
$38$		0			0
$39$	−67.3591	+	193.468i	−0.276566	+	0.794349i
$40$		0			0
$41$	27.9434	−	48.3994i	0.106440	−	0.184359i	−0.807886	−	0.589339i	$-0.799388\pi$
$41$	27.9434	−	48.3994i	0.106440	−	0.184359i	0.914325	+	0.404980i	$0.132722\pi$
$42$		0			0
$43$	−109.056	−	188.891i	−0.386766	−	0.669898i	0.605246	−	0.796038i	$-0.293075\pi$
$43$	−109.056	−	188.891i	−0.386766	−	0.669898i	−0.992012	+	0.126140i	$0.959741\pi$
$44$		0			0
$45$	266.280	+	210.997i	0.882104	+	0.698970i
$46$		0			0
$47$	109.953			0.341241			0.170620	−	0.985337i	$-0.445423\pi$
$47$	109.953			0.341241			0.170620	+	0.985337i	$0.445423\pi$
$48$		0			0
$49$	326.442	+	105.283i	0.951726	+	0.306948i
$50$		0			0
$51$	301.954	−	260.672i	0.829059	−	0.715714i
$52$		0			0
$53$	−257.488	+	148.661i	−0.667335	+	0.385286i	−0.795066	−	0.606523i	$-0.792564\pi$
$53$	−257.488	+	148.661i	−0.667335	+	0.385286i	0.127731	+	0.991809i	$0.459231\pi$
$54$		0			0
$55$			865.262i			2.12131i
$56$		0			0
$57$	136.746	−	392.759i	0.317762	−	0.912670i
$58$		0			0
$59$	−179.106			−0.395214			−0.197607	−	0.980281i	$-0.563317\pi$
$59$	−179.106			−0.395214			−0.197607	+	0.980281i	$0.563317\pi$
$60$		0			0
$61$		−	318.639i		−	0.668813i	−0.942429	−	0.334406i	$-0.891464\pi$
$61$		−	318.639i		−	0.668813i	0.942429	−	0.334406i	$-0.108536\pi$
$62$		0			0
$63$	−487.872	+	109.673i	−0.975652	+	0.219325i
$64$		0			0
$65$		−	496.087i		−	0.946647i
$66$		0			0
$67$	−653.822			−1.19219			−0.596097	−	0.802912i	$-0.703283\pi$
$67$	−653.822			−1.19219			−0.596097	+	0.802912i	$0.703283\pi$
$68$		0			0
$69$	−527.732	−	611.307i	−0.920746	−	1.06656i
$70$		0			0
$71$		−	157.634i		−	0.263490i	−0.991284	−	0.131745i	$-0.957942\pi$
$71$		−	157.634i		−	0.263490i	0.991284	−	0.131745i	$-0.0420579\pi$
$72$		0			0
$73$	−1055.68	+	609.495i	−1.69257	+	0.977205i	−0.740134	+	0.672459i	$0.765238\pi$
$73$	−1055.68	+	609.495i	−1.69257	+	0.977205i	−0.952434	+	0.304746i	$0.901429\pi$
$74$		0			0
$75$	−163.574	−	56.9513i	−0.251839	−	0.0876822i
$76$		0			0
$77$	−990.588	−	800.380i	−1.46608	−	1.18457i
$78$		0			0
$79$	818.802			1.16611			0.583053	−	0.812434i	$-0.301858\pi$
$79$	818.802			1.16611			0.583053	+	0.812434i	$0.301858\pi$
$80$		0			0
$81$	531.295	−	499.166i	0.728799	−	0.684728i
$82$		0			0
$83$	404.460	+	700.546i	0.534883	+	0.926444i	0.999169	+	0.0407592i	$0.0129776\pi$
$83$	404.460	+	700.546i	0.534883	+	0.926444i	−0.464286	+	0.885685i	$0.653689\pi$
$84$		0			0
$85$	−482.998	+	836.577i	−0.616335	+	1.06752i
$86$		0			0
$87$	775.779	+	898.636i	0.956002	+	1.10740i
$88$		0			0
$89$	20.9797	−	36.3379i	0.0249870	−	0.0432788i	−0.853261	−	0.521483i	$-0.825379\pi$
$89$	20.9797	−	36.3379i	0.0249870	−	0.0432788i	0.878249	+	0.478204i	$0.158712\pi$
$90$		0			0
$91$	567.941	+	458.888i	0.654246	+	0.528621i
$92$		0			0
$93$	742.606	−	141.707i	0.828007	−	0.158004i
$94$		0			0
$95$			1007.11i			1.08765i
$96$		0			0
$97$	−161.296	+	93.1244i	−0.168837	+	0.0974778i	−0.582037	−	0.813162i	$-0.697744\pi$
$97$	−161.296	+	93.1244i	−0.168837	+	0.0974778i	0.413201	+	0.910640i	$0.364411\pi$
$98$		0			0
$99$	1836.74	+	270.994i	1.86464	+	0.275111i
$100$		0			0
$101$	−438.603	+	759.683i	−0.432105	+	0.748428i	−0.997054	−	0.0766976i	$-0.975562\pi$
$101$	−438.603	+	759.683i	−0.432105	+	0.748428i	0.564949	+	0.825126i	$0.308896\pi$
$102$		0			0
$103$	−1306.14	+	754.100i	−1.24949	+	0.721395i	−0.971008	−	0.239046i	$-0.923165\pi$
$103$	−1306.14	+	754.100i	−1.24949	+	0.721395i	−0.278484	+	0.960441i	$0.589832\pi$
$104$		0			0
$105$	1028.42	−	639.283i	0.955840	−	0.594168i
$106$		0			0
$107$	−1401.91	−	809.390i	−1.26661	−	0.731278i	−0.292265	−	0.956337i	$-0.594409\pi$
$107$	−1401.91	−	809.390i	−1.26661	−	0.731278i	−0.974345	+	0.225060i	$0.927742\pi$
$108$		0			0
$109$	232.205	+	402.191i	0.204048	+	0.353421i	0.949829	−	0.312770i	$-0.101257\pi$
$109$	232.205	+	402.191i	0.204048	+	0.353421i	−0.745781	+	0.666191i	$0.767924\pi$
$110$		0			0
$111$	728.144	+	253.516i	0.622634	+	0.216781i
$112$		0			0
$113$	1075.98	+	621.220i	0.895754	+	0.517164i	0.875820	−	0.482638i	$-0.160321\pi$
$113$	1075.98	+	621.220i	0.895754	+	0.517164i	0.0199334	+	0.999801i	$0.493655\pi$
$114$		0			0
$115$	1693.65	+	977.831i	1.37334	+	0.792897i
$116$		0			0
$117$	−1053.08	−	155.371i	−0.832110	−	0.122770i
$118$		0			0
$119$	−510.968	−	1326.80i	−0.393617	−	1.02208i
$120$		0			0
$121$	1698.74	+	2942.31i	1.27629	+	2.21060i
$122$		0			0
$123$	274.249	+	95.4847i	0.201042	+	0.0699964i
$124$		0			0
$125$	−1153.45			−0.825339
$126$		0			0
$127$	1091.45			0.762604			0.381302	−	0.924450i	$-0.375476\pi$
$127$	1091.45			0.762604			0.381302	+	0.924450i	$0.375476\pi$
$128$		0			0
$129$	857.892	−	740.605i	0.585529	−	0.505478i
$130$		0			0
$131$	−449.557	−	778.656i	−0.299832	−	0.519324i	0.676265	−	0.736658i	$-0.263597\pi$
$131$	−449.557	−	778.656i	−0.299832	−	0.519324i	−0.976097	+	0.217334i	$0.930264\pi$
$132$		0			0
$133$	−1152.98	−	931.590i	−0.751699	−	0.607362i
$134$		0			0
$135$	−817.591	+	1564.62i	−0.521237	+	0.997486i
$136$		0			0
$137$	395.098	+	228.110i	0.246391	+	0.142254i	0.618110	−	0.786091i	$-0.287898\pi$
$137$	395.098	+	228.110i	0.246391	+	0.142254i	−0.371720	+	0.928345i	$0.621232\pi$
$138$		0			0
$139$	2341.95	+	1352.12i	1.42907	+	0.825076i	0.997048	−	0.0767853i	$-0.0244656\pi$
$139$	2341.95	+	1352.12i	1.42907	+	0.825076i	0.432026	+	0.901861i	$0.357799\pi$
$140$		0			0
$141$	107.092	+	561.207i	0.0639629	+	0.335192i
$142$		0			0
$143$	−1355.51	−	2347.81i	−0.792682	−	1.37297i
$144$		0			0
$145$	−2489.71	−	1437.43i	−1.42593	−	0.823258i
$146$		0			0
$147$	−219.423	+	1768.72i	−0.123114	+	0.992393i
$148$		0			0
$149$	2242.69	−	1294.82i	1.23307	−	0.711916i	0.265405	−	0.964137i	$-0.414494\pi$
$149$	2242.69	−	1294.82i	1.23307	−	0.711916i	0.967670	+	0.252221i	$0.0811610\pi$
$150$		0			0
$151$	476.831	−	825.896i	0.256980	−	0.445103i	−0.708451	−	0.705760i	$-0.750606\pi$
$151$	476.831	−	825.896i	0.256980	−	0.445103i	0.965431	+	0.260657i	$0.0839392\pi$
$152$		0			0
$153$	1624.58	+	1287.30i	0.858430	+	0.680210i
$154$		0			0
$155$	−1585.48	+	915.376i	−0.821604	+	0.474353i
$156$		0			0
$157$		−	2625.31i		−	1.33454i	−0.744816	−	0.667270i	$-0.767463\pi$
$157$		−	2625.31i		−	1.33454i	0.744816	−	0.667270i	$-0.232537\pi$
$158$		0			0
$159$	−1009.56	−	1169.44i	−0.503544	−	0.583288i
$160$		0			0
$161$	−2686.12	+	1034.46i	−1.31488	+	0.506376i
$162$		0			0
$163$	−986.513	+	1708.69i	−0.474047	+	0.821073i	−0.999558	−	0.0297132i	$-0.990541\pi$
$163$	−986.513	+	1708.69i	−0.474047	+	0.821073i	0.525512	+	0.850786i	$0.323874\pi$
$164$		0			0
$165$	−4416.34	+	842.746i	−2.08371	+	0.397622i
$166$		0			0
$167$	−784.607	+	1358.98i	−0.363561	+	0.629706i	−0.988544	−	0.150932i	$-0.951773\pi$
$167$	−784.607	+	1358.98i	−0.363561	+	0.629706i	0.624983	+	0.780638i	$0.285106\pi$
$168$		0			0
$169$	−321.334	−	556.568i	−0.146261	−	0.253331i
$170$		0			0
$171$	2137.85	+	315.420i	0.956056	+	0.141057i
$172$		0			0
$173$	1743.32			0.766142			0.383071	−	0.923719i	$-0.374867\pi$
$173$	1743.32			0.766142			0.383071	+	0.923719i	$0.374867\pi$
$174$		0			0
$175$	−387.984	+	480.187i	−0.167593	+	0.207421i
$176$		0			0
$177$	−174.445	−	914.166i	−0.0740797	−	0.388209i
$178$		0			0
$179$	1022.73	−	590.472i	0.427051	−	0.246558i	−0.271038	−	0.962569i	$-0.587367\pi$
$179$	1022.73	−	590.472i	0.427051	−	0.246558i	0.698090	+	0.716010i	$0.254034\pi$
$180$		0			0
$181$		−	2832.54i		−	1.16321i	−0.813471	−	0.581605i	$-0.802425\pi$
$181$		−	2832.54i		−	1.16321i	0.813471	−	0.581605i	$-0.197575\pi$
$182$		0			0
$183$	1626.35	−	310.348i	0.656958	−	0.125364i
$184$		0			0
$185$	−1867.10			−0.742010
$186$		0			0
$187$			5278.98i			2.06437i
$188$		0			0
$189$	−1034.95	−	2383.30i	−0.398316	−	0.917248i
$190$		0			0
$191$			1659.18i			0.628555i	0.949331	+	0.314277i	$0.101762\pi$
$191$			1659.18i			0.628555i	−0.949331	+	0.314277i	$0.898238\pi$
$192$		0			0
$193$	880.819			0.328512			0.164256	−	0.986418i	$-0.447478\pi$
$193$	880.819			0.328512			0.164256	+	0.986418i	$0.447478\pi$
$194$		0			0
$195$	2532.06	−	483.178i	0.929868	−	0.177441i
$196$		0			0
$197$		−	4941.78i		−	1.78724i	−0.448821	−	0.893622i	$-0.648156\pi$
$197$		−	4941.78i		−	1.78724i	0.448821	−	0.893622i	$-0.351844\pi$
$198$		0			0
$199$	−4332.54	+	2501.39i	−1.54334	+	0.891050i	−0.544720	+	0.838618i	$0.683364\pi$
$199$	−4332.54	+	2501.39i	−1.54334	+	0.891050i	−0.998624	+	0.0524320i	$0.983303\pi$
$200$		0			0
$201$	−636.808	−	3337.14i	−0.223467	−	1.17106i
$202$		0			0
$203$	3948.66	−	1520.68i	1.36523	−	0.525766i
$204$		0			0
$205$	−703.227			−0.239588
$206$		0			0
$207$	2606.14	−	3288.97i	0.875070	−	1.10434i
$208$		0			0
$209$	2751.83	+	4766.30i	0.910755	+	1.57747i
$210$		0			0
$211$	2278.03	−	3945.66i	0.743251	−	1.28735i	−0.207756	−	0.978181i	$-0.566616\pi$
$211$	2278.03	−	3945.66i	0.743251	−	1.28735i	0.951007	−	0.309168i	$-0.100051\pi$
$212$		0			0
$213$	804.574	−	153.532i	0.258819	−	0.0493890i
$214$		0			0
$215$	−1372.26	+	2376.83i	−0.435291	+	0.753946i
$216$		0			0
$217$	418.630	−	2661.86i	0.130961	−	0.832713i
$218$		0			0
$219$	−4139.10	−	4794.59i	−1.27714	−	1.47940i
$220$		0			0
$221$		−	3026.64i		−	0.921240i
$222$		0			0
$223$	−5426.77	+	3133.14i	−1.62961	+	0.940856i	−0.645402	+	0.763843i	$0.723310\pi$
$223$	−5426.77	+	3133.14i	−1.62961	+	0.940856i	−0.984209	+	0.177013i	$0.943357\pi$
$224$		0			0
$225$	131.365	−	890.362i	0.0389228	−	0.263811i
$226$		0			0
$227$	−645.067	+	1117.29i	−0.188611	+	0.326683i	−0.944787	−	0.327684i	$-0.893732\pi$
$227$	−645.067	+	1117.29i	−0.188611	+	0.326683i	0.756177	+	0.654368i	$0.227065\pi$
$228$		0			0
$229$	−485.951	+	280.564i	−0.140230	+	0.0809616i	−0.568473	−	0.822702i	$-0.692466\pi$
$229$	−485.951	+	280.564i	−0.140230	+	0.0809616i	0.428244	+	0.903663i	$0.359132\pi$
$230$		0			0
$231$	3120.37	−	5835.56i	0.888768	−	1.66213i
$232$		0			0
$233$	−26.6649	−	15.3950i	−0.00749731	−	0.00432857i	0.496247	−	0.868182i	$-0.334711\pi$
$233$	−26.6649	−	15.3950i	−0.00749731	−	0.00432857i	−0.503744	+	0.863853i	$0.668044\pi$
$234$		0			0
$235$	−691.773	−	1198.19i	−0.192027	−	0.332600i
$236$		0			0
$237$	797.495	+	4179.21i	0.218577	+	1.14544i
$238$		0			0
$239$	−3204.80	−	1850.29i	−0.867369	−	0.500775i	−0.000895650	−	1.00000i	$-0.500285\pi$
$239$	−3204.80	−	1850.29i	−0.867369	−	0.500775i	−0.866473	+	0.499224i	$0.833618\pi$
$240$		0			0
$241$	−3896.08	−	2249.40i	−1.04136	−	0.601231i	−0.121143	−	0.992635i	$-0.538656\pi$
$241$	−3896.08	−	2249.40i	−1.04136	−	0.601231i	−0.920219	+	0.391404i	$0.871989\pi$
$242$		0			0
$243$	3065.24	+	2225.58i	0.809199	+	0.587535i
$244$		0			0
$245$	−906.524	−	4219.71i	−0.236391	−	1.10036i
$246$		0			0
$247$	−1577.73	−	2732.70i	−0.406430	−	0.703958i
$248$		0			0
$249$	−3181.69	+	2746.70i	−0.809764	+	0.699057i
$250$		0			0
$251$	−751.424			−0.188962			−0.0944810	−	0.995527i	$-0.530119\pi$
$251$	−751.424			−0.188962			−0.0944810	+	0.995527i	$0.530119\pi$
$252$		0			0
$253$	10687.3			2.65575
$254$		0			0
$255$	−4740.36	−	1650.44i	−1.16413	−	0.405312i
$256$		0			0
$257$	−49.2235	−	85.2577i	−0.0119474	−	0.0206935i	0.859990	−	0.510311i	$-0.170470\pi$
$257$	−49.2235	−	85.2577i	−0.0119474	−	0.0206935i	−0.871937	+	0.489618i	$0.837136\pi$
$258$		0			0
$259$	1727.09	−	2137.53i	0.414349	−	0.512818i
$260$		0			0
$261$	−3831.09	+	4834.87i	−0.908578	+	1.14663i
$262$		0			0
$263$	3253.75	+	1878.55i	0.762870	+	0.440443i	0.830325	−	0.557279i	$-0.188155\pi$
$263$	3253.75	+	1878.55i	0.762870	+	0.440443i	−0.0674551	+	0.997722i	$0.521488\pi$
$264$		0			0
$265$	3239.99	+	1870.61i	0.751061	+	0.433625i
$266$		0			0
$267$	205.905	+	71.6893i	0.0471953	+	0.0164319i
$268$		0			0
$269$	2234.67	+	3870.56i	0.506506	+	0.877295i	0.999972	+	0.00752932i	$0.00239668\pi$
$269$	2234.67	+	3870.56i	0.506506	+	0.877295i	−0.493465	+	0.869766i	$0.664270\pi$
$270$		0			0
$271$	1482.64	+	856.005i	0.332340	+	0.191877i	0.656880	−	0.753995i	$-0.271876\pi$
$271$	1482.64	+	856.005i	0.332340	+	0.191877i	−0.324539	+	0.945872i	$0.605209\pi$
$272$		0			0
$273$	−1789.03	+	3345.75i	−0.396619	+	0.741736i
$274$		0			0
$275$	1985.05	−	1146.07i	0.435283	−	0.251311i
$276$		0			0
$277$	3964.06	−	6865.95i	0.859845	−	1.48930i	−0.0122314	−	0.999925i	$-0.503893\pi$
$277$	3964.06	−	6865.95i	0.859845	−	1.48930i	0.872076	−	0.489370i	$-0.162773\pi$
$278$		0			0
$279$	1446.56	+	3652.28i	0.310407	+	0.783715i
$280$		0			0
$281$	4663.84	−	2692.67i	0.990112	−	0.571642i	0.0848043	−	0.996398i	$-0.472973\pi$
$281$	4663.84	−	2692.67i	0.990112	−	0.571642i	0.905308	+	0.424756i	$0.139640\pi$
$282$		0			0
$283$			2109.52i			0.443103i	0.975149	+	0.221552i	$0.0711121\pi$
$283$			2109.52i			0.443103i	−0.975149	+	0.221552i	$0.928888\pi$
$284$		0			0
$285$	−5140.33	+	980.901i	−1.06838	+	0.203872i
$286$		0			0
$287$	650.495	−	805.083i	0.133789	−	0.165584i
$288$		0			0
$289$	−490.285	+	849.198i	−0.0997934	+	0.172847i
$290$		0			0
$291$	−632.411	−	732.563i	−0.127397	−	0.147573i
$292$		0			0
$293$	1440.95	−	2495.80i	0.287308	−	0.497633i	−0.685858	−	0.727735i	$-0.740573\pi$
$293$	1440.95	−	2495.80i	0.287308	−	0.497633i	0.973166	+	0.230103i	$0.0739062\pi$
$294$		0			0
$295$	1126.85	+	1951.76i	0.222399	+	0.385207i
$296$		0			0
$297$	405.778	+	9638.79i	0.0792782	+	1.88316i
$298$		0			0
$299$	−6127.44			−1.18515
$300$		0			0
$301$	−1451.73	−	3769.63i	−0.277994	−	0.721852i
$302$		0			0
$303$	−4304.65	−	1498.74i	−0.816157	−	0.284159i
$304$		0			0
$305$	−3472.29	+	2004.73i	−0.651878	+	0.376362i
$306$		0			0
$307$		−	8035.89i		−	1.49392i	−0.664871	−	0.746959i	$-0.731513\pi$
$307$		−	8035.89i		−	1.49392i	0.664871	−	0.746959i	$-0.268487\pi$
$308$		0			0
$309$	−5121.12	−	5932.13i	−0.942816	−	1.09213i
$310$		0			0
$311$	9574.93			1.74580			0.872901	−	0.487897i	$-0.162236\pi$
$311$	9574.93			1.74580			0.872901	+	0.487897i	$0.162236\pi$
$312$		0			0
$313$		−	5196.75i		−	0.938460i	−0.883076	−	0.469230i	$-0.844532\pi$
$313$		−	5196.75i		−	0.938460i	0.883076	−	0.469230i	$-0.155468\pi$
$314$		0			0
$315$	4264.59	+	4626.45i	0.762802	+	0.827527i
$316$		0			0
$317$			8266.66i			1.46467i	0.680942	+	0.732337i	$0.261571\pi$
$317$			8266.66i			1.46467i	−0.680942	+	0.732337i	$0.738429\pi$
$318$		0			0
$319$	−15710.6			−2.75745
$320$		0			0
$321$	2765.75	−	7943.73i	0.480900	−	1.38123i
$322$		0			0
$323$			6144.39i			1.05846i
$324$		0			0
$325$	−1138.10	+	657.084i	−0.194248	+	0.112149i
$326$		0			0
$327$	−1826.64	+	1576.91i	−0.308910	+	0.266677i
$328$		0			0
$329$	2011.63	+	316.369i	0.337097	+	0.0530152i
$330$		0			0
$331$	4780.73			0.793875			0.396938	−	0.917846i	$-0.370073\pi$
$331$	4780.73			0.793875			0.396938	+	0.917846i	$0.370073\pi$
$332$		0			0
$333$	−584.764	+	3963.41i	−0.0962308	+	0.652232i
$334$		0			0
$335$	4113.54	+	7124.86i	0.670885	+	1.16201i
$336$		0			0
$337$	2466.28	−	4271.73i	0.398656	−	0.690492i	−0.594905	−	0.803796i	$-0.702810\pi$
$337$	2466.28	−	4271.73i	0.398656	−	0.690492i	0.993560	+	0.113305i	$0.0361436\pi$
$338$		0			0
$339$	−2122.76	+	6096.94i	−0.340095	+	0.976815i
$340$		0			0
$341$	−5002.35	+	8664.33i	−0.794407	+	1.37595i
$342$		0			0
$343$	5669.45	+	2865.47i	0.892483	+	0.451081i
$344$		0			0
$345$	−3341.32	+	9596.88i	−0.521422	+	1.49762i
$346$		0			0
$347$		−	6855.92i		−	1.06065i	−0.847795	−	0.530324i	$-0.822070\pi$
$347$		−	6855.92i		−	1.06065i	0.847795	−	0.530324i	$-0.177930\pi$
$348$		0			0
$349$	−240.494	+	138.849i	−0.0368864	+	0.0212964i	−0.518330	−	0.855181i	$-0.673446\pi$
$349$	−240.494	+	138.849i	−0.0368864	+	0.0212964i	0.481443	+	0.876477i	$0.340113\pi$
$350$		0			0
$351$	−232.648	−	5526.28i	−0.0353784	−	0.840373i
$352$		0			0
$353$	−1412.48	+	2446.49i	−0.212971	+	0.368877i	−0.952643	−	0.304091i	$-0.901647\pi$
$353$	−1412.48	+	2446.49i	−0.212971	+	0.368877i	0.739672	+	0.672968i	$0.234981\pi$
$354$		0			0
$355$	−1717.78	+	991.761i	−0.256818	+	0.148274i
$356$		0			0
$357$	6274.40	−	3900.29i	0.930186	−	0.578221i
$358$		0			0
$359$	200.509	+	115.764i	0.0294776	+	0.0170189i	0.514666	−	0.857391i	$-0.327916\pi$
$359$	200.509	+	115.764i	0.0294776	+	0.0170189i	−0.485189	+	0.874409i	$0.661249\pi$
$360$		0			0
$361$	−226.553	−	392.401i	−0.0330300	−	0.0572096i
$362$		0			0
$363$	−13363.2	+	11536.2i	−1.93219	+	1.66803i
$364$		0			0
$365$	13283.6	+	7669.30i	1.90492	+	1.09981i
$366$		0			0
$367$	3916.38	+	2261.12i	0.557039	+	0.321607i	0.751956	−	0.659213i	$-0.229110\pi$
$367$	3916.38	+	2261.12i	0.557039	+	0.321607i	−0.194917	+	0.980820i	$0.562444\pi$
$368$		0			0
$369$	−220.246	+	1492.78i	−0.0310720	+	0.210599i
$370$		0			0
$371$	−5138.59	+	1978.93i	−0.719090	+	0.276930i
$372$		0			0
$373$	−4570.77	−	7916.80i	−0.634492	−	1.09897i	−0.986623	−	0.163021i	$-0.947876\pi$
$373$	−4570.77	−	7916.80i	−0.634492	−	1.09897i	0.352131	−	0.935951i	$-0.385457\pi$
$374$		0			0
$375$	−1123.43	−	5887.25i	−0.154703	−	0.810711i
$376$		0			0
$377$	9007.49			1.23053
$378$		0			0
$379$	−1499.84			−0.203276			−0.101638	−	0.994821i	$-0.532408\pi$
$379$	−1499.84			−0.203276			−0.101638	+	0.994821i	$0.532408\pi$
$380$		0			0
$381$	1063.05	+	5570.83i	0.142944	+	0.749088i
$382$		0			0
$383$	−4065.00	−	7040.79i	−0.542328	−	0.939340i	−0.998770	−	0.0495869i	$-0.984210\pi$
$383$	−4065.00	−	7040.79i	−0.542328	−	0.939340i	0.456441	−	0.889753i	$-0.349124\pi$
$384$		0			0
$385$	−2489.63	+	15830.3i	−0.329567	+	2.09555i
$386$		0			0
$387$	4615.66	+	3657.39i	0.606271	+	0.480403i
$388$		0			0
$389$	4142.51	+	2391.68i	0.539932	+	0.311730i	0.745052	−	0.667007i	$-0.232425\pi$
$389$	4142.51	+	2391.68i	0.539932	+	0.311730i	−0.205119	+	0.978737i	$0.565758\pi$
$390$		0			0
$391$	10333.0	+	5965.77i	1.33648	+	0.771617i
$392$		0			0
$393$	3536.44	−	3052.96i	0.453919	−	0.391861i
$394$		0			0
$395$	−5151.51	−	8922.68i	−0.656205	−	1.13658i
$396$		0			0
$397$	1258.45	+	726.567i	0.159093	+	0.0918522i	0.577433	−	0.816438i	$-0.304055\pi$
$397$	1258.45	+	726.567i	0.159093	+	0.0918522i	−0.418340	+	0.908291i	$0.637388\pi$
$398$		0			0
$399$	3631.91	−	6792.22i	0.455697	−	0.852221i
$400$		0			0
$401$	277.398	−	160.156i	0.0345452	−	0.0199447i	−0.482628	−	0.875825i	$-0.660318\pi$
$401$	277.398	−	160.156i	0.0345452	−	0.0199447i	0.517173	+	0.855881i	$0.326984\pi$
$402$		0			0
$403$	2868.04	−	4967.59i	0.354509	−	0.614028i
$404$		0			0
$405$	−8782.20	−	2649.13i	−1.07751	−	0.325028i
$406$		0			0
$407$	−8836.35	+	5101.67i	−1.07617	+	0.621328i
$408$		0			0
$409$		−	6395.85i		−	0.773238i	−0.922239	−	0.386619i	$-0.873643\pi$
$409$		−	6395.85i		−	0.773238i	0.922239	−	0.386619i	$-0.126357\pi$
$410$		0			0
$411$	−779.469	+	2238.78i	−0.0935483	+	0.268688i
$412$		0			0
$413$	−3276.81	−	515.344i	−0.390415	−	0.0614005i
$414$		0			0
$415$	5089.35	−	8815.01i	0.601991	−	1.04268i
$416$		0			0
$417$	−4620.30	+	13270.4i	−0.542583	+	1.55840i
$418$		0			0
$419$	4472.71	−	7746.96i	0.521495	−	0.903255i	−0.478193	−	0.878255i	$-0.658708\pi$
$419$	4472.71	−	7746.96i	0.521495	−	0.903255i	0.999687	−	0.0250003i	$-0.00795867\pi$
$420$		0			0
$421$	−29.3000	−	50.7491i	−0.00339191	−	0.00587496i	0.864324	−	0.502935i	$-0.167746\pi$
$421$	−29.3000	−	50.7491i	−0.00339191	−	0.00587496i	−0.867716	+	0.497060i	$0.834413\pi$
$422$		0			0
$423$	−2760.12	+	1093.21i	−0.317262	+	0.125658i
$424$		0			0
$425$	2558.99			0.292068
$426$		0			0
$427$	916.825	−	5829.63i	0.103907	−	0.660692i
$428$		0			0
$429$	10663.1	−	9205.32i	1.20005	−	1.03598i
$430$		0			0
$431$	7923.61	−	4574.70i	0.885538	−	0.511266i	0.0130578	−	0.999915i	$-0.495843\pi$
$431$	7923.61	−	4574.70i	0.885538	−	0.511266i	0.872480	+	0.488649i	$0.162510\pi$
$432$		0			0
$433$			13367.0i			1.48355i	0.670651	+	0.741773i	$0.266015\pi$
$433$			13367.0i			1.48355i	−0.670651	+	0.741773i	$0.733985\pi$
$434$		0			0
$435$	4911.82	−	14107.6i	0.541388	−	1.55497i
$436$		0			0
$437$	12439.3			1.36168
$438$		0			0
$439$		−	331.588i		−	0.0360498i	−0.999838	−	0.0180249i	$-0.994262\pi$
$439$		−	331.588i		−	0.0360498i	0.999838	−	0.0180249i	$-0.00573781\pi$
$440$		0			0
$441$	−9241.36	+	602.748i	−0.997880	+	0.0650846i
$442$		0			0
$443$			13869.3i			1.48748i	0.668471	+	0.743738i	$0.266949\pi$
$443$			13869.3i			1.48748i	−0.668471	+	0.743738i	$0.733051\pi$
$444$		0			0
$445$	−527.978			−0.0562439
$446$		0			0
$447$	8793.14	+	10185.7i	0.930428	+	1.07778i
$448$		0			0
$449$			14773.0i			1.55275i	0.630274	+	0.776373i	$0.282943\pi$
$449$			14773.0i			1.55275i	−0.630274	+	0.776373i	$0.717057\pi$
$450$		0			0
$451$	−3328.14	+	1921.50i	−0.347485	+	0.200621i
$452$		0			0
$453$	4679.84	+	1629.37i	0.485382	+	0.168994i
$454$		0			0
$455$	1427.40	−	9076.10i	0.147071	−	0.935152i
$456$		0			0
$457$	1283.58			0.131386			0.0656930	−	0.997840i	$-0.479074\pi$
$457$	1283.58			0.131386			0.0656930	+	0.997840i	$0.479074\pi$
$458$		0			0
$459$	−4988.15	+	9545.76i	−0.507248	+	0.970714i
$460$		0			0
$461$	980.109	+	1697.60i	0.0990200	+	0.171508i	0.911279	−	0.411789i	$-0.135096\pi$
$461$	980.109	+	1697.60i	0.0990200	+	0.171508i	−0.812259	+	0.583297i	$0.801763\pi$
$462$		0			0
$463$	−5890.28	+	10202.3i	−0.591241	+	1.02406i	0.402824	+	0.915277i	$0.368029\pi$
$463$	−5890.28	+	10202.3i	−0.591241	+	1.02406i	−0.994066	+	0.108783i	$0.965305\pi$
$464$		0			0
$465$	−6216.35	−	7200.81i	−0.619949	−	0.718128i
$466$		0			0
$467$	3117.96	−	5400.47i	0.308955	−	0.535126i	−0.669179	−	0.743101i	$-0.733354\pi$
$467$	3117.96	−	5400.47i	0.308955	−	0.535126i	0.978134	+	0.207975i	$0.0666874\pi$
$468$		0			0
$469$	−11961.9	−	1881.25i	−1.17772	−	0.185220i
$470$		0			0
$471$	13399.7	−	2557.00i	1.31089	−	0.250149i
$472$		0			0
$473$			14998.3i			1.45798i
$474$		0			0
$475$	2310.47	−	1333.95i	0.223182	−	0.128854i
$476$		0			0
$477$	4985.60	−	6291.87i	0.478564	−	0.603951i
$478$		0			0
$479$	4434.31	−	7680.45i	0.422983	−	0.732627i	−0.573247	−	0.819383i	$-0.694316\pi$
$479$	4434.31	−	7680.45i	0.422983	−	0.732627i	0.996230	+	0.0867552i	$0.0276498\pi$
$480$		0			0
$481$	5066.21	−	2924.98i	0.480248	−	0.277272i
$482$		0			0
$483$	−7896.14	−	12702.5i	−0.743865	−	1.19666i
$484$		0			0
$485$	2029.60	+	1171.79i	0.190019	+	0.109708i
$486$		0			0
$487$	−2778.74	−	4812.92i	−0.258556	−	0.447832i	0.707299	−	0.706914i	$-0.249913\pi$
$487$	−2778.74	−	4812.92i	−0.258556	−	0.447832i	−0.965855	+	0.259082i	$0.916580\pi$
$488$		0			0
$489$	−9682.09	−	3370.99i	−0.895377	−	0.311741i
$490$		0			0
$491$	−10412.2	−	6011.50i	−0.957020	−	0.552536i	−0.0617653	−	0.998091i	$-0.519673\pi$
$491$	−10412.2	−	6011.50i	−0.957020	−	0.552536i	−0.895255	+	0.445555i	$0.853006\pi$
$492$		0			0
$493$	−15189.8	−	8769.83i	−1.38765	−	0.801163i
$494$		0			0
$495$	−8602.84	−	21720.4i	−0.781149	−	1.97224i
$496$		0			0
$497$	453.563	−	2883.98i	0.0409358	−	0.260290i
$498$		0			0
$499$	−9584.30	−	16600.5i	−0.859824	−	1.48926i	−0.872097	−	0.489334i	$-0.837240\pi$
$499$	−9584.30	−	16600.5i	−0.859824	−	1.48926i	0.0122729	−	0.999925i	$-0.496093\pi$
$500$		0			0
$501$	−7700.49	−	2681.06i	−0.686692	−	0.239084i
$502$		0			0
$503$	−13168.5			−1.16731			−0.583654	−	0.812002i	$-0.698378\pi$
$503$	−13168.5			−1.16731			−0.583654	+	0.812002i	$0.698378\pi$
$504$		0			0
$505$	11037.9			0.972637
$506$		0			0
$507$	2527.78	−	2182.19i	0.221425	−	0.191153i
$508$		0			0
$509$	−1777.96	−	3079.52i	−0.154827	−	0.268168i	0.778169	−	0.628055i	$-0.216149\pi$
$509$	−1777.96	−	3079.52i	−0.154827	−	0.268168i	−0.932996	+	0.359887i	$0.882815\pi$
$510$		0			0
$511$	−21067.7	+	8113.43i	−1.82384	+	0.702381i
$512$		0			0
$513$	472.299	+	11218.9i	0.0406482	+	0.965550i
$514$		0			0
$515$	16435.2	+	9488.88i	1.40626	+	0.811903i
$516$		0			0
$517$	−6547.86	−	3780.41i	−0.557011	−	0.321590i
$518$		0			0
$519$	1697.96	+	8898.02i	0.143607	+	0.752562i
$520$		0			0
$521$	−11705.2	−	20273.9i	−0.984285	−	1.70483i	−0.645072	−	0.764122i	$-0.723173\pi$
$521$	−11705.2	−	20273.9i	−0.984285	−	1.70483i	−0.339213	−	0.940710i	$-0.610161\pi$
$522$		0			0
$523$	6433.74	+	3714.52i	0.537911	+	0.310563i	0.744232	−	0.667921i	$-0.232816\pi$
$523$	6433.74	+	3714.52i	0.537911	+	0.310563i	−0.206321	+	0.978484i	$0.566149\pi$
$524$		0			0
$525$	−2828.79	−	1512.60i	−0.235159	−	0.125743i
$526$		0			0
$527$	−9673.04	+	5584.73i	−0.799553	+	0.461622i
$528$		0			0
$529$	5994.22	−	10382.3i	0.492662	−	0.853316i
$530$		0			0
$531$	4496.05	−	1780.76i	0.367442	−	0.145533i
$532$		0			0
$533$	1908.15	−	1101.67i	0.155067	−	0.0895283i
$534$		0			0
$535$			20369.2i			1.64605i
$536$		0			0
$537$	4009.91	+	4644.95i	0.322236	+	0.373267i
$538$		0			0
$539$	−15820.2	−	17493.5i	−1.26424	−	1.39796i
$540$		0			0
$541$	2767.89	−	4794.13i	0.219965	−	0.380990i	−0.734832	−	0.678249i	$-0.762739\pi$
$541$	2767.89	−	4794.13i	0.219965	−	0.380990i	0.954797	+	0.297259i	$0.0960724\pi$
$542$		0			0
$543$	14457.4	−	2758.83i	1.14259	−	0.218035i
$544$		0			0
$545$	2921.85	−	5060.79i	0.229648	−	0.397762i
$546$		0			0
$547$	728.680	+	1262.11i	0.0569581	+	0.0986544i	0.893099	−	0.449861i	$-0.148527\pi$
$547$	728.680	+	1262.11i	0.0569581	+	0.0986544i	−0.836140	+	0.548515i	$0.815193\pi$
$548$		0			0
$549$	3168.06	+	7998.72i	0.246283	+	0.621816i
$550$		0			0
$551$	−18286.1			−1.41382
$552$		0			0
$553$	14980.3	+	2355.95i	1.15195	+	0.181167i
$554$		0			0
$555$	−1818.51	−	9529.77i	−0.139084	−	0.728858i
$556$		0			0
$557$	−10451.5	+	6034.16i	−0.795051	+	0.459023i	−0.841738	−	0.539887i	$-0.818467\pi$
$557$	−10451.5	+	6034.16i	−0.795051	+	0.459023i	0.0466868	+	0.998910i	$0.485134\pi$
$558$		0			0
$559$		−	8599.10i		−	0.650631i
$560$		0			0
$561$	−26944.2	+	5141.61i	−2.02778	+	0.386950i
$562$		0			0
$563$	2238.24			0.167550			0.0837751	−	0.996485i	$-0.473302\pi$
$563$	2238.24			0.167550			0.0837751	+	0.996485i	$0.473302\pi$
$564$		0			0
$565$		−	15633.7i		−	1.16410i
$566$		0			0
$567$	11156.5	−	7603.74i	0.826329	−	0.563187i
$568$		0			0
$569$			356.878i			0.0262937i	0.999914	+	0.0131469i	$0.00418489\pi$
$569$			356.878i			0.0262937i	−0.999914	+	0.0131469i	$0.995815\pi$
$570$		0			0
$571$	26265.5			1.92501			0.962503	−	0.271270i	$-0.0874437\pi$
$571$	26265.5			1.92501			0.962503	+	0.271270i	$0.0874437\pi$
$572$		0			0
$573$	−8468.54	+	1616.00i	−0.617414	+	0.117818i
$574$		0			0
$575$		−	5180.67i		−	0.375738i
$576$		0			0
$577$	−15580.8	+	8995.60i	−1.12416	+	0.649032i	−0.942459	−	0.334322i	$-0.891493\pi$
$577$	−15580.8	+	8995.60i	−1.12416	+	0.649032i	−0.181698	+	0.983354i	$0.558159\pi$
$578$		0			0
$579$	857.898	+	4495.75i	0.0615769	+	0.322689i
$580$		0			0
$581$	5384.07	+	13980.5i	0.384456	+	0.998295i
$582$		0			0
$583$	20445.0			1.45240
$584$		0			0
$585$	4932.33	+	12453.1i	0.348593	+	0.880127i
$586$		0			0
$587$	−8123.48	−	14070.3i	−0.571196	−	0.989340i	−0.996444	−	0.0842634i	$-0.973146\pi$
$587$	−8123.48	−	14070.3i	−0.571196	−	0.989340i	0.425248	−	0.905077i	$-0.360187\pi$
$588$		0			0
$589$	−5822.41	+	10084.7i	−0.407315	+	0.705490i
$590$		0			0
$591$	25223.1	−	4813.18i	1.75557	−	0.335005i
$592$		0			0
$593$	2220.81	−	3846.55i	0.153790	−	0.266373i	−0.778828	−	0.627238i	$-0.784185\pi$
$593$	2220.81	−	3846.55i	0.153790	−	0.266373i	0.932618	+	0.360865i	$0.117519\pi$
$594$		0			0
$595$	−11243.7	+	13915.8i	−0.774702	+	0.958808i
$596$		0			0
$597$	−16987.0	−	19677.2i	−1.16454	−	1.34897i
$598$		0			0
$599$		−	10303.7i		−	0.702834i	−0.936219	−	0.351417i	$-0.885700\pi$
$599$		−	10303.7i		−	0.702834i	0.936219	−	0.351417i	$-0.114300\pi$
$600$		0			0
$601$	6090.03	−	3516.08i	0.413340	−	0.238642i	−0.278884	−	0.960325i	$-0.589964\pi$
$601$	6090.03	−	3516.08i	0.413340	−	0.238642i	0.692224	+	0.721683i	$0.256631\pi$
$602$		0			0
$603$	16412.7	−	6500.60i	1.10842	−	0.439013i
$604$		0			0
$605$	21375.4	−	37023.3i	1.43642	−	2.48795i
$606$		0			0
$607$	136.172	−	78.6191i	0.00910554	−	0.00525708i	−0.495440	−	0.868642i	$-0.664993\pi$
$607$	136.172	−	78.6191i	0.00910554	−	0.00525708i	0.504546	+	0.863385i	$0.331660\pi$
$608$		0			0
$609$	11607.5	+	18673.0i	0.772348	+	1.24248i
$610$		0			0
$611$	3754.13	+	2167.45i	0.248570	+	0.143512i
$612$		0			0
$613$	−8959.16	−	15517.7i	−0.590305	−	1.02244i	−0.994191	−	0.107629i	$-0.965674\pi$
$613$	−8959.16	−	15517.7i	−0.590305	−	1.02244i	0.403886	−	0.914809i	$-0.367659\pi$
$614$		0			0
$615$	−684.927	−	3589.31i	−0.0449088	−	0.235341i
$616$		0			0
$617$	−12365.0	−	7138.91i	−0.806798	−	0.465805i	0.0390445	−	0.999237i	$-0.487569\pi$
$617$	−12365.0	−	7138.91i	−0.806798	−	0.465805i	−0.845843	+	0.533432i	$0.820902\pi$
$618$		0			0
$619$	1438.84	+	830.716i	0.0934280	+	0.0539407i	0.545986	−	0.837794i	$-0.316155\pi$
$619$	1438.84	+	830.716i	0.0934280	+	0.0539407i	−0.452558	+	0.891735i	$0.649488\pi$
$620$		0			0
$621$	19325.4	+	10098.5i	1.24880	+	0.652559i
$622$		0			0
$623$	488.388	−	604.451i	0.0314074	−	0.0388713i
$624$		0			0
$625$	9340.28	+	16177.8i	0.597778	+	1.03538i
$626$		0			0
$627$	−21647.3	+	18687.7i	−1.37880	+	1.19030i
$628$		0			0
$629$	−11391.2			−0.722095
$630$		0			0
$631$	23414.7			1.47722			0.738610	−	0.674133i	$-0.235482\pi$
$631$	23414.7			1.47722			0.738610	+	0.674133i	$0.235482\pi$
$632$		0			0
$633$	22357.6	+	7784.20i	1.40385	+	0.488774i
$634$		0			0
$635$	−6866.90	−	11893.8i	−0.429141	−	0.743295i
$636$		0			0
$637$	9070.34	+	10029.7i	0.564176	+	0.623847i
$638$		0			0
$639$	1567.28	+	3957.05i	0.0970273	+	0.244974i
$640$		0			0
$641$	24560.4	+	14179.9i	1.51338	+	0.873751i	0.999877	+	0.0156631i	$0.00498591\pi$
$641$	24560.4	+	14179.9i	1.51338	+	0.873751i	0.513503	+	0.858088i	$0.328347\pi$
$642$		0			0
$643$	−11821.1	−	6824.94i	−0.725008	−	0.418584i	0.0915851	−	0.995797i	$-0.470807\pi$
$643$	−11821.1	−	6824.94i	−0.725008	−	0.418584i	−0.816593	+	0.577214i	$0.804140\pi$
$644$		0			0
$645$	−13468.0	−	4689.12i	−0.822174	−	0.286254i
$646$		0			0
$647$	−2516.28	−	4358.33i	−0.152898	−	0.264828i	0.779393	−	0.626535i	$-0.215527\pi$
$647$	−2516.28	−	4358.33i	−0.152898	−	0.264828i	−0.932292	+	0.361707i	$0.882194\pi$
$648$		0			0
$649$	10666.0	+	6158.02i	0.645111	+	0.372455i
$650$		0			0
$651$	13994.0	−	455.880i	0.842501	−	0.0274460i
$652$		0			0
$653$	−12367.2	+	7140.21i	−0.741143	+	0.427899i	−0.822485	−	0.568787i	$-0.807413\pi$
$653$	−12367.2	+	7140.21i	−0.741143	+	0.427899i	0.0813421	+	0.996686i	$0.474079\pi$
$654$		0			0
$655$	−5656.80	+	9797.87i	−0.337450	+	0.584480i
$656$		0			0
$657$	20440.5	−	25796.0i	1.21379	−	1.53181i
$658$		0			0
$659$	−26681.2	+	15404.4i	−1.57716	+	0.910575i	−0.581910	+	0.813253i	$0.697694\pi$
$659$	−26681.2	+	15404.4i	−1.57716	+	0.910575i	−0.995253	+	0.0973220i	$0.968972\pi$
$660$		0			0
$661$			18078.7i			1.06381i	0.846804	+	0.531905i	$0.178524\pi$
$661$			18078.7i			1.06381i	−0.846804	+	0.531905i	$0.821476\pi$
$662$		0			0
$663$	15448.1	−	2947.88i	0.904911	−	0.172679i
$664$		0			0
$665$	−2897.76	+	18425.4i	−0.168978	+	1.07445i
$666$		0			0
$667$	−17754.5	+	30751.8i	−1.03067	+	1.78518i
$668$		0			0
$669$	−21277.3	−	24646.9i	−1.22964	−	1.42437i
$670$		0			0
$671$	−10955.5	+	18975.4i	−0.630299	+	1.09171i
$672$		0			0
$673$	5751.89	+	9962.57i	0.329449	+	0.570622i	0.982403	−	0.186776i	$-0.0598037\pi$
$673$	5751.89	+	9962.57i	0.329449	+	0.570622i	−0.652954	+	0.757398i	$0.726470\pi$
$674$		0			0
$675$	4672.40	−	196.701i	0.266431	−	0.0112163i
$676$		0			0
$677$	−11700.0			−0.664208			−0.332104	−	0.943243i	$-0.607759\pi$
$677$	−11700.0			−0.664208			−0.332104	+	0.943243i	$0.607759\pi$
$678$		0			0
$679$	−3218.92	+	1239.65i	−0.181931	+	0.0700638i
$680$		0			0
$681$	−6330.98	−	2204.24i	−0.356246	−	0.124033i
$682$		0			0
$683$	13060.7	−	7540.58i	0.731702	−	0.422448i	−0.0873425	−	0.996178i	$-0.527837\pi$
$683$	13060.7	−	7540.58i	0.731702	−	0.422448i	0.819044	+	0.573730i	$0.194504\pi$
$684$		0			0
$685$		−	5740.64i		−	0.320202i
$686$		0			0
$687$	−1905.32	−	2207.06i	−0.105812	−	0.122568i
$688$		0			0
$689$	−11721.9			−0.648142
$690$		0			0
$691$			23744.0i			1.30719i	0.756847	+	0.653593i	$0.226739\pi$
$691$			23744.0i			1.30719i	−0.756847	+	0.653593i	$0.773261\pi$
$692$		0			0
$693$	32824.2	+	10242.8i	1.79926	+	0.561462i
$694$		0			0
$695$		−	34027.7i		−	1.85718i
$696$		0			0
$697$	−4290.41			−0.233157
$698$		0			0
$699$	52.6057	−	151.093i	0.00284654	−	0.00817578i
$700$		0			0
$701$		−	25267.5i		−	1.36140i	−0.732563	−	0.680699i	$-0.761676\pi$
$701$		−	25267.5i		−	1.36140i	0.732563	−	0.680699i	$-0.238324\pi$
$702$		0			0
$703$	−10284.9	+	5938.01i	−0.551783	+	0.318572i
$704$		0			0
$705$	5441.83	−	4697.85i	0.290711	−	0.250967i
$706$		0			0
$707$	−10210.3	+	12636.7i	−0.543134	+	0.672209i
$708$		0			0
$709$	−5937.88			−0.314530			−0.157265	−	0.987556i	$-0.550268\pi$
$709$	−5937.88			−0.314530			−0.157265	+	0.987556i	$0.550268\pi$
$710$		0			0
$711$	−20554.2	+	8140.91i	−1.08416	+	0.429407i
$712$		0			0
$713$	11306.3	+	19583.1i	0.593863	+	1.02860i
$714$		0			0
$715$	−17056.5	+	29542.7i	−0.892134	+	1.54522i
$716$		0			0
$717$	6322.58	−	18159.6i	0.329318	−	0.945861i
$718$		0			0
$719$	−4987.87	+	8639.24i	−0.258715	+	0.448107i	−0.965898	−	0.258923i	$-0.916632\pi$
$719$	−4987.87	+	8639.24i	−0.258715	+	0.448107i	0.707183	+	0.707031i	$0.249966\pi$
$720$		0			0
$721$	−26066.1	+	10038.4i	−1.34640	+	0.518514i
$722$		0			0
$723$	7686.37	−	22076.6i	0.395379	−	1.13560i
$724$		0			0
$725$			7615.72i			0.390125i
$726$		0			0
$727$	−5220.07	+	3013.81i	−0.266302	+	0.153750i	−0.627206	−	0.778853i	$-0.715802\pi$
$727$	−5220.07	+	3013.81i	−0.266302	+	0.153750i	0.360904	+	0.932603i	$0.382468\pi$
$728$		0			0
$729$	−8374.00	+	17812.8i	−0.425443	+	0.904985i
$730$		0			0
$731$	−8372.21	+	14501.1i	−0.423608	+	0.733711i
$732$		0			0
$733$	15699.4	−	9064.07i	0.791094	−	0.456738i	−0.0492536	−	0.998786i	$-0.515684\pi$
$733$	15699.4	−	9064.07i	0.791094	−	0.456738i	0.840348	+	0.542048i	$0.182351\pi$
$734$		0			0
$735$	20654.7	−	8736.86i	1.03654	−	0.438454i
$736$		0			0
$737$	38936.0	+	22479.7i	1.94603	+	1.12354i
$738$		0			0
$739$	−14881.9	−	25776.2i	−0.740784	−	1.28308i	−0.952139	−	0.305667i	$-0.901121\pi$
$739$	−14881.9	−	25776.2i	−0.740784	−	1.28308i	0.211354	−	0.977410i	$-0.432213\pi$
$740$		0			0
$741$	12411.2	−	10714.4i	0.615299	−	0.531178i
$742$		0			0
$743$	1928.67	+	1113.52i	0.0952301	+	0.0549811i	0.546859	−	0.837225i	$-0.315823\pi$
$743$	1928.67	+	1113.52i	0.0952301	+	0.0549811i	−0.451629	+	0.892206i	$0.649157\pi$
$744$		0			0
$745$	−28219.9	−	16292.7i	−1.38778	−	0.801235i
$746$		0			0
$747$	−17118.2	−	13564.3i	−0.838451	−	0.664379i
$748$		0			0
$749$	−23319.5	−	18841.8i	−1.13762	−	0.919179i
$750$		0			0
$751$	7141.11	+	12368.8i	0.346981	+	0.600989i	0.985712	−	0.168442i	$-0.0538734\pi$
$751$	7141.11	+	12368.8i	0.346981	+	0.600989i	−0.638730	+	0.769431i	$0.720540\pi$
$752$		0			0
$753$	−731.870	−	3835.31i	−0.0354194	−	0.185613i
$754$		0			0
$755$	−12000.0			−0.578443
$756$		0			0
$757$	7484.80			0.359365			0.179683	−	0.983725i	$-0.442493\pi$
$757$	7484.80			0.359365			0.179683	+	0.983725i	$0.442493\pi$
$758$		0			0
$759$	10409.2	+	54548.6i	0.497800	+	2.60868i
$760$		0			0
$761$	9634.94	+	16688.2i	0.458957	+	0.794937i	0.998906	−	0.0467607i	$-0.0148898\pi$
$761$	9634.94	+	16688.2i	0.458957	+	0.794937i	−0.539949	+	0.841698i	$0.681556\pi$
$762$		0			0
$763$	3091.05	+	8026.36i	0.146662	+	0.380830i
$764$		0			0
$765$	3806.93	−	25802.6i	0.179921	−	1.21947i
$766$		0			0
$767$	−6115.22	−	3530.63i	−0.287885	−	0.166211i
$768$		0			0
$769$	3478.65	+	2008.40i	0.163125	+	0.0941805i	0.579340	−	0.815086i	$-0.303310\pi$
$769$	3478.65	+	2008.40i	0.163125	+	0.0941805i	−0.416215	+	0.909266i	$0.636644\pi$
$770$		0			0
$771$	387.217	−	334.279i	0.0180873	−	0.0156145i
$772$		0			0
$773$	−432.297	−	748.761i	−0.0201147	−	0.0348397i	0.855793	−	0.517319i	$-0.173070\pi$
$773$	−432.297	−	748.761i	−0.0201147	−	0.0348397i	−0.875908	+	0.482479i	$0.839736\pi$
$774$		0			0
$775$	4200.03	+	2424.89i	0.194671	+	0.112393i
$776$		0			0
$777$	12592.2	+	6733.27i	0.581395	+	0.310881i
$778$		0			0
$779$	−3873.73	+	2236.50i	−0.178165	+	0.102864i
$780$		0			0
$781$	−5419.79	+	9387.34i	−0.248316	+	0.430097i
$782$		0			0
$783$	−28408.8	−	14845.1i	−1.29661	−	0.677547i
$784$		0			0
$785$	−28608.7	+	16517.2i	−1.30075	+	0.750987i
$786$		0			0
$787$			6816.15i			0.308729i	0.988014	+	0.154364i	$0.0493330\pi$
$787$			6816.15i			0.308729i	−0.988014	+	0.154364i	$0.950667\pi$
$788$		0			0
$789$	−6419.16	+	18437.0i	−0.289643	+	0.831907i
$790$		0			0
$791$	17898.1	+	14461.4i	0.804530	+	0.650049i
$792$		0			0
$793$	6281.18	−	10879.3i	0.281275	−	0.487183i
$794$		0			0
$795$	−6392.01	+	18359.0i	−0.285159	+	0.819028i
$796$		0			0
$797$	5482.05	−	9495.19i	0.243644	−	0.422004i	−0.718105	−	0.695934i	$-0.754990\pi$
$797$	5482.05	−	9495.19i	0.243644	−	0.422004i	0.961750	+	0.273930i	$0.0883238\pi$
$798$		0			0
$799$	−4220.53	−	7310.17i	−0.186873	−	0.323673i
$800$		0			0
$801$	−165.359	+	1120.77i	−0.00729424	+	0.0494388i
$802$		0			0
$803$	83822.6			3.68373
$804$		0			0
$805$	28172.5	+	22763.0i	1.23348	+	0.996632i
$806$		0			0
$807$	−17579.0	+	15175.7i	−0.766805	+	0.661971i
$808$		0			0
$809$	17637.3	−	10182.9i	0.766497	−	0.442537i	−0.0651265	−	0.997877i	$-0.520745\pi$
$809$	17637.3	−	10182.9i	0.766497	−	0.442537i	0.831624	+	0.555340i	$0.187412\pi$
$810$		0			0
$811$		−	42250.7i		−	1.82937i	−0.404163	−	0.914687i	$-0.632437\pi$
$811$		−	42250.7i		−	1.82937i	0.404163	−	0.914687i	$-0.367563\pi$
$812$		0			0
$813$	−2925.03	+	8401.22i	−0.126181	+	0.362415i
$814$		0			0
$815$	24826.7			1.06704
$816$		0			0
$817$			17457.1i			0.747546i
$818$		0			0
$819$	−18819.4	−	5872.61i	−0.802932	−	0.250556i
$820$		0			0
$821$		−	15822.4i		−	0.672602i	−0.941755	−	0.336301i	$-0.890824\pi$
$821$		−	15822.4i		−	0.672602i	0.941755	−	0.336301i	$-0.109176\pi$
$822$		0			0
$823$	24247.9			1.02701			0.513505	−	0.858086i	$-0.328347\pi$
$823$	24247.9			1.02701			0.513505	+	0.858086i	$0.328347\pi$
$824$		0			0
$825$	7782.98	+	9015.54i	0.328447	+	0.380462i
$826$		0			0
$827$			37190.0i			1.56375i	0.623434	+	0.781876i	$0.285737\pi$
$827$			37190.0i			1.56375i	−0.623434	+	0.781876i	$0.714263\pi$
$828$		0			0
$829$	−15763.2	+	9100.86i	−0.660406	+	0.381286i	−0.792432	−	0.609961i	$-0.791185\pi$
$829$	−15763.2	+	9100.86i	−0.660406	+	0.381286i	0.132025	+	0.991246i	$0.457852\pi$
$830$		0			0
$831$	38905.1	+	13545.5i	1.62407	+	0.565448i
$832$		0			0
$833$	−5530.73	−	25744.6i	−0.230046	−	1.07082i
$834$		0			0
$835$	19745.5			0.818349
$836$		0			0
$837$	−17232.5	+	10940.6i	−0.711640	+	0.451806i
$838$		0			0
$839$	−14170.6	−	24544.3i	−0.583105	−	1.00997i	−0.995109	−	0.0987850i	$-0.968504\pi$
$839$	−14170.6	−	24544.3i	−0.583105	−	1.00997i	0.412004	−	0.911182i	$-0.364829\pi$
$840$		0			0
$841$	13905.1	−	24084.4i	0.570139	−	0.987509i
$842$		0			0
$843$	18286.0	+	21181.9i	0.747098	+	0.865413i
$844$		0			0
$845$	−4043.37	+	7003.32i	−0.164611	+	0.285114i
$846$		0			0
$847$	22613.2	+	58718.5i	0.917355	+	2.38205i
$848$		0			0
$849$	−10767.1	+	2054.63i	−0.435250	+	0.0830562i
$850$		0			0
$851$			23061.6i			0.928954i
$852$		0			0
$853$	19445.5	−	11226.8i	0.780540	−	0.450645i	−0.0560819	−	0.998426i	$-0.517861\pi$
$853$	19445.5	−	11226.8i	0.780540	−	0.450645i	0.836622	+	0.547781i	$0.184527\pi$
$854$		0			0
$855$	−10013.1	−	25281.2i	−0.400517	−	1.01123i
$856$		0			0
$857$	20802.9	−	36031.7i	0.829187	−	1.43619i	−0.0694905	−	0.997583i	$-0.522137\pi$
$857$	20802.9	−	36031.7i	0.829187	−	1.43619i	0.898677	−	0.438611i	$-0.144529\pi$
$858$		0			0
$859$	−10183.2	+	5879.26i	−0.404477	+	0.233525i	−0.688414	−	0.725318i	$-0.741693\pi$
$859$	−10183.2	+	5879.26i	−0.404477	+	0.233525i	0.283937	+	0.958843i	$0.408359\pi$
$860$		0			0
$861$	4742.76	+	2536.03i	0.187727	+	0.100381i
$862$		0			0
$863$	−40160.8	−	23186.8i	−1.58411	−	0.914587i	−0.994250	−	0.107083i	$-0.965849\pi$
$863$	−40160.8	−	23186.8i	−1.58411	−	0.914587i	−0.589861	−	0.807505i	$-0.700818\pi$
$864$		0			0
$865$	−10968.2	−	18997.4i	−0.431132	−	0.746743i
$866$		0			0
$867$	−4811.88	−	1675.34i	−0.188489	−	0.0656257i
$868$		0			0
$869$	−48760.8	−	28152.0i	−1.90345	−	1.09896i
$870$		0			0
$871$	−22323.5	−	12888.5i	−0.868429	−	0.501388i
$872$		0			0
$873$	3123.09	−	3941.36i	0.121077	−	0.152800i
$874$		0			0
$875$	−21102.8	−	3318.83i	−0.815318	−	0.128225i
$876$		0			0
$877$	−17458.2	−	30238.6i	−0.672204	−	1.16429i	−0.977278	−	0.211963i	$-0.932014\pi$
$877$	−17458.2	−	30238.6i	−0.672204	−	1.16429i	0.305074	−	0.952329i	$-0.401319\pi$
$878$		0			0
$879$	14142.2	+	4923.84i	0.542666	+	0.188939i
$880$		0			0
$881$	7604.81			0.290820			0.145410	−	0.989371i	$-0.453550\pi$
$881$	7604.81			0.290820			0.145410	+	0.989371i	$0.453550\pi$
$882$		0			0
$883$	−218.735			−0.00833636			−0.00416818	−	0.999991i	$-0.501327\pi$
$883$	−218.735			−0.00833636			−0.00416818	+	0.999991i	$0.501327\pi$
$884$		0			0
$885$	−8864.37	+	7652.47i	−0.336692	+	0.290661i
$886$		0			0
$887$	16647.2	+	28833.8i	0.630167	+	1.09148i	0.987517	+	0.157511i	$0.0503471\pi$
$887$	16647.2	+	28833.8i	0.630167	+	1.09148i	−0.357350	+	0.933971i	$0.616320\pi$
$888$		0			0
$889$	19968.5	+	3140.45i	0.753345	+	0.118478i
$890$		0			0
$891$	−48801.7	+	11459.1i	−1.83492	+	0.430857i
$892$		0			0
$893$	−7621.28	−	4400.15i	−0.285595	−	0.164888i
$894$		0			0
$895$	−12869.0	−	7429.94i	−0.480630	−	0.277492i
$896$		0			0
$897$	−5967.99	−	31274.8i	−0.222147	−	1.16414i
$898$		0			0
$899$	−16620.5	−	28787.6i	−0.616603	−	1.06799i
$900$		0			0
$901$	19767.3	+	11412.6i	0.730903	+	0.421987i
$902$		0			0
$903$	17826.4	−	11081.2i	0.656950	−	0.408373i
$904$		0			0
$905$	−30866.9	+	17821.0i	−1.13376	+	0.654575i
$906$		0			0
$907$	22269.5	−	38571.9i	0.815265	−	1.41208i	−0.0938721	−	0.995584i	$-0.529924\pi$
$907$	22269.5	−	38571.9i	0.815265	−	1.41208i	0.909137	−	0.416497i	$-0.136742\pi$
$908$		0			0
$909$	3457.01	−	23430.9i	0.126141	−	0.854955i
$910$		0			0
$911$	−31804.3	+	18362.2i	−1.15667	+	0.667802i	−0.950503	−	0.310715i	$-0.899432\pi$
$911$	−31804.3	+	18362.2i	−1.15667	+	0.667802i	−0.206165	+	0.978517i	$0.566098\pi$
$912$		0			0
$913$		−	55624.6i		−	2.01633i
$914$		0			0
$915$	−13614.2	−	15770.2i	−0.491881	−	0.569778i
$916$		0			0
$917$	−5984.39	−	15539.3i	−0.215509	−	0.559601i
$918$		0			0
$919$	2484.42	−	4303.15i	0.0891769	−	0.154459i	−0.817987	−	0.575237i	$-0.804910\pi$
$919$	2484.42	−	4303.15i	0.0891769	−	0.154459i	0.907163	+	0.420778i	$0.138243\pi$
$920$		0			0
$921$	41015.6	−	7826.78i	1.46744	−	0.280023i
$922$		0			0
$923$	3107.37	−	5382.12i	0.110813	−	0.191933i
$924$		0			0
$925$	2473.03	+	4283.42i	0.0879058	+	0.152257i
$926$		0			0
$927$	25290.0	−	31916.2i	0.896045	−	1.13082i
$928$		0			0
$929$	6608.44			0.233386			0.116693	−	0.993168i	$-0.462771\pi$
$929$	6608.44			0.233386			0.116693	+	0.993168i	$0.462771\pi$
$930$		0			0
$931$	−18413.7	−	20361.3i	−0.648212	−	0.716771i
$932$		0			0
$933$	9325.77	+	48871.0i	0.327237	+	1.71486i
$934$		0			0
$935$	57526.4	−	33212.9i	2.01210	−	1.16169i
$936$		0			0
$937$		−	3091.16i		−	0.107773i	−0.998547	−	0.0538867i	$-0.982839\pi$
$937$		−	3091.16i		−	0.107773i	0.998547	−	0.0538867i	$-0.0171610\pi$
$938$		0			0
$939$	26524.5	−	5061.52i	0.921826	−	0.175907i
$940$		0			0
$941$	−6953.45			−0.240888			−0.120444	−	0.992720i	$-0.538432\pi$
$941$	−6953.45			−0.240888			−0.120444	+	0.992720i	$0.538432\pi$
$942$		0			0
$943$			8685.94i			0.299950i
$944$		0			0
$945$	−19460.0	+	26272.8i	−0.669878	+	0.904395i
$946$		0			0
$947$			24604.6i			0.844289i	0.906529	+	0.422144i	$0.138722\pi$
$947$			24604.6i			0.844289i	−0.906529	+	0.422144i	$0.861278\pi$
$948$		0			0
$949$	−48058.7			−1.64389
$950$		0			0
$951$	−42193.5	+	8051.54i	−1.43871	+	0.274542i
$952$		0			0
$953$			31429.2i			1.06830i	0.845389	+	0.534151i	$0.179369\pi$
$953$			31429.2i			1.06830i	−0.845389	+	0.534151i	$0.820631\pi$
$954$		0			0
$955$	18080.5	−	10438.8i	0.612639	−	0.353707i
$956$		0			0
$957$	−15301.8	−	80187.8i	−0.516862	−	2.70857i
$958$		0			0
$959$	6572.13	+	5310.18i	0.221298	+	0.178806i
$960$		0			0
$961$	8622.68			0.289439
$962$		0			0
$963$	43239.0	+	6379.51i	1.44689	+	0.213475i
$964$		0			0
$965$	−5541.70	−	9598.50i	−0.184864	−	0.320194i
$966$		0			0
$967$	−1990.71	+	3448.01i	−0.0662016	+	0.114664i	−0.897226	−	0.441571i	$-0.854421\pi$
$967$	−1990.71	+	3448.01i	−0.0662016	+	0.114664i	0.831025	+	0.556235i	$0.187755\pi$
$968$		0			0
$969$	−31361.3	+	5984.50i	−1.03970	+	0.198400i
$970$		0			0
$971$	−3738.21	+	6474.76i	−0.123548	+	0.213991i	−0.921164	−	0.389174i	$-0.872761\pi$
$971$	−3738.21	+	6474.76i	−0.123548	+	0.213991i	0.797617	+	0.603165i	$0.206094\pi$
$972$		0			0
$973$	38956.3	+	31476.1i	1.28354	+	1.03708i
$974$		0			0
$975$	−4462.28	−	5168.95i	−0.146572	−	0.169783i
$976$		0			0
$977$			20777.2i			0.680372i	0.940358	+	0.340186i	$0.110490\pi$
$977$			20777.2i			0.680372i	−0.940358	+	0.340186i	$0.889510\pi$
$978$		0			0
$979$	−2498.74	+	1442.65i	−0.0815732	+	0.0470963i
$980$		0			0
$981$	−9827.75	−	7787.39i	−0.319853	−	0.253448i
$982$		0			0
$983$	1547.16	−	2679.75i	0.0502000	−	0.0869490i	−0.839833	−	0.542844i	$-0.817347\pi$
$983$	1547.16	−	2679.75i	0.0502000	−	0.0869490i	0.890034	+	0.455895i	$0.150681\pi$
$984$		0			0
$985$	−53851.8	+	31091.3i	−1.74199	+	1.00574i
$986$		0			0
$987$	344.520	+	10575.6i	0.0111106	+	0.341060i
$988$		0			0
$989$	29357.5	+	16949.6i	0.943897	+	0.544959i
$990$		0			0
$991$	−7775.65	−	13467.8i	−0.249245	−	0.431705i	0.714072	−	0.700073i	$-0.246849\pi$
$991$	−7775.65	−	13467.8i	−0.249245	−	0.431705i	−0.963317	+	0.268368i	$0.913516\pi$
$992$		0			0
$993$	4656.33	+	24401.1i	0.148806	+	0.779804i
$994$		0			0
$995$	54516.6	+	31475.2i	1.73698	+	1.00284i
$996$		0			0
$997$	4477.20	+	2584.91i	0.142221	+	0.0821114i	0.569422	−	0.822045i	$-0.307167\pi$
$997$	4477.20	+	2584.91i	0.142221	+	0.0821114i	−0.427201	+	0.904157i	$0.640500\pi$
$998$		0			0
$999$	−20799.0	+	875.606i	−0.658710	+	0.0277307i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.w.a.5.14	✓	48
3.2	odd	2		756.4.w.a.341.20		48
7.3	odd	6		252.4.bm.a.185.6	yes	48
9.2	odd	6		252.4.bm.a.173.6	yes	48
9.7	even	3		756.4.bm.a.89.20		48
21.17	even	6		756.4.bm.a.17.20		48
63.38	even	6	inner	252.4.w.a.101.14	yes	48
63.52	odd	6		756.4.w.a.521.20		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.w.a.5.14	✓	48	1.1	even	1	trivial
252.4.w.a.101.14	yes	48	63.38	even	6	inner
252.4.bm.a.173.6	yes	48	9.2	odd	6
252.4.bm.a.185.6	yes	48	7.3	odd	6
756.4.w.a.341.20		48	3.2	odd	2
756.4.w.a.521.20		48	63.52	odd	6
756.4.bm.a.17.20		48	21.17	even	6
756.4.bm.a.89.20		48	9.7	even	3

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.973978 + 5.10405i) q^{3} +(-6.29153 - 10.8972i) q^{5} +(18.2954 + 2.87731i) q^{7} +(-25.1027 + 9.94247i) q^{9} +O(q^{10})\)	\(q+(0.973978 + 5.10405i) q^{3} +(-6.29153 - 10.8972i) q^{5} +(18.2954 + 2.87731i) q^{7} +(-25.1027 + 9.94247i) q^{9} +(-59.5514 - 34.3820i) q^{11} +(34.1431 + 19.7125i) q^{13} +(49.4923 - 42.7260i) q^{15} +(-38.3848 - 66.4844i) q^{17} +(-69.3139 - 40.0184i) q^{19} +(3.13334 + 96.1831i) q^{21} +(-134.598 + 77.7101i) q^{23} +(-16.6667 + 28.8675i) q^{25} +(-75.1964 - 118.442i) q^{27} +(197.862 - 114.236i) q^{29} -145.493i q^{31} +(117.486 - 337.441i) q^{33} +(-83.7511 - 217.472i) q^{35} +(74.1910 - 128.503i) q^{37} +(-67.3591 + 193.468i) q^{39} +(27.9434 - 48.3994i) q^{41} +(-109.056 - 188.891i) q^{43} +(266.280 + 210.997i) q^{45} +109.953 q^{47} +(326.442 + 105.283i) q^{49} +(301.954 - 260.672i) q^{51} +(-257.488 + 148.661i) q^{53} +865.262i q^{55} +(136.746 - 392.759i) q^{57} -179.106 q^{59} -318.639i q^{61} +(-487.872 + 109.673i) q^{63} -496.087i q^{65} -653.822 q^{67} +(-527.732 - 611.307i) q^{69} -157.634i q^{71} +(-1055.68 + 609.495i) q^{73} +(-163.574 - 56.9513i) q^{75} +(-990.588 - 800.380i) q^{77} +818.802 q^{79} +(531.295 - 499.166i) q^{81} +(404.460 + 700.546i) q^{83} +(-482.998 + 836.577i) q^{85} +(775.779 + 898.636i) q^{87} +(20.9797 - 36.3379i) q^{89} +(567.941 + 458.888i) q^{91} +(742.606 - 141.707i) q^{93} +1007.11i q^{95} +(-161.296 + 93.1244i) q^{97} +(1836.74 + 270.994i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} + 12 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 + 12 * q^9	\( 48 q + 6 q^{7} + 12 q^{9} + 12 q^{11} - 36 q^{13} + 66 q^{15} - 72 q^{17} + 24 q^{21} + 30 q^{23} - 600 q^{25} - 396 q^{27} + 42 q^{29} + 390 q^{35} + 84 q^{37} - 840 q^{39} - 618 q^{41} - 42 q^{43} + 366 q^{45} + 396 q^{47} + 318 q^{49} - 738 q^{51} - 1620 q^{53} + 492 q^{57} + 1500 q^{59} + 672 q^{63} - 588 q^{67} - 924 q^{69} + 564 q^{75} - 2472 q^{77} + 1608 q^{79} + 2592 q^{81} - 360 q^{85} + 2640 q^{87} + 1722 q^{89} + 540 q^{91} + 660 q^{93} - 792 q^{97} - 54 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 + 12 * q^9 + 12 * q^11 - 36 * q^13 + 66 * q^15 - 72 * q^17 + 24 * q^21 + 30 * q^23 - 600 * q^25 - 396 * q^27 + 42 * q^29 + 390 * q^35 + 84 * q^37 - 840 * q^39 - 618 * q^41 - 42 * q^43 + 366 * q^45 + 396 * q^47 + 318 * q^49 - 738 * q^51 - 1620 * q^53 + 492 * q^57 + 1500 * q^59 + 672 * q^63 - 588 * q^67 - 924 * q^69 + 564 * q^75 - 2472 * q^77 + 1608 * q^79 + 2592 * q^81 - 360 * q^85 + 2640 * q^87 + 1722 * q^89 + 540 * q^91 + 660 * q^93 - 792 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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