LMFDB - Embedded newform 144.4.k.a.37.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,4,Mod(37,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("144.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	144.k (of order $4$, 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:	$8.49627504083$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - x^{8} + 6x^{7} + 14x^{6} - 80x^{5} + 56x^{4} + 96x^{3} - 64x^{2} - 512x + 1024 $ x^10 - 2x^9 - x^8 + 6x^7 + 14x^6 - 80x^5 + 56x^4 + 96x^3 - 64x^2 - 512x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.5
Root			$1.28199 - 1.53509i$ of defining polynomial
Character	$\chi$	$=$	144.37
Dual form			144.4.k.a.109.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.81708 + 0.253099i) q^{2} +(7.87188 + 1.42600i) q^{4} +(4.66372 + 4.66372i) q^{5} +24.8965i q^{7} +(21.8148 + 6.00953i) q^{8} +O(q^{10})$	\(q+(2.81708 + 0.253099i) q^{2} +(7.87188 + 1.42600i) q^{4} +(4.66372 + 4.66372i) q^{5} +24.8965i q^{7} +(21.8148 + 6.00953i) q^{8} +(11.9577 + 14.3185i) q^{10} +(-22.3431 - 22.3431i) q^{11} +(-11.2714 + 11.2714i) q^{13} +(-6.30129 + 70.1355i) q^{14} +(59.9330 + 22.4506i) q^{16} +88.4846 q^{17} +(37.8187 - 37.8187i) q^{19} +(30.0618 + 43.3627i) q^{20} +(-57.2873 - 68.5974i) q^{22} +48.1224i q^{23} -81.4994i q^{25} +(-34.6053 + 28.8997i) q^{26} +(-35.5025 + 195.982i) q^{28} +(-10.4432 + 10.4432i) q^{29} -96.9578 q^{31} +(163.154 + 78.4142i) q^{32} +(249.268 + 22.3954i) q^{34} +(-116.110 + 116.110i) q^{35} +(-163.279 - 163.279i) q^{37} +(116.110 - 96.9665i) q^{38} +(73.7114 + 129.765i) q^{40} -360.519i q^{41} +(-100.249 - 100.249i) q^{43} +(-144.021 - 207.744i) q^{44} +(-12.1797 + 135.565i) q^{46} -220.669 q^{47} -276.837 q^{49} +(20.6274 - 229.590i) q^{50} +(-104.800 + 72.6542i) q^{52} +(175.752 + 175.752i) q^{53} -208.404i q^{55} +(-149.616 + 543.113i) q^{56} +(-32.0624 + 26.7761i) q^{58} +(-405.008 - 405.008i) q^{59} +(664.576 - 664.576i) q^{61} +(-273.138 - 24.5399i) q^{62} +(439.771 + 262.193i) q^{64} -105.133 q^{65} +(-107.377 + 107.377i) q^{67} +(696.540 + 126.179i) q^{68} +(-356.480 + 297.705i) q^{70} +215.050i q^{71} +668.587i q^{73} +(-418.644 - 501.296i) q^{74} +(351.634 - 243.775i) q^{76} +(556.266 - 556.266i) q^{77} -822.956 q^{79} +(174.808 + 384.215i) q^{80} +(91.2471 - 1015.61i) q^{82} +(-326.873 + 326.873i) q^{83} +(412.668 + 412.668i) q^{85} +(-257.037 - 307.783i) q^{86} +(-353.139 - 621.682i) q^{88} -262.733i q^{89} +(-280.619 - 280.619i) q^{91} +(-68.6226 + 378.814i) q^{92} +(-621.643 - 55.8512i) q^{94} +352.752 q^{95} -150.801 q^{97} +(-779.871 - 70.0671i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 8 q^{4} + 2 q^{5} + 44 q^{8}+O(q^{10}) $ 10 * q + 2 * q^2 + 8 * q^4 + 2 * q^5 + 44 * q^8	$ 10 q + 2 q^{2} + 8 q^{4} + 2 q^{5} + 44 q^{8} - 68 q^{10} - 18 q^{11} - 2 q^{13} - 188 q^{14} + 280 q^{16} + 4 q^{17} - 26 q^{19} + 196 q^{20} - 588 q^{22} + 264 q^{26} + 280 q^{28} + 202 q^{29} + 368 q^{31} - 968 q^{32} + 436 q^{34} - 476 q^{35} - 10 q^{37} + 1232 q^{38} - 1336 q^{40} - 838 q^{43} - 868 q^{44} + 1132 q^{46} + 944 q^{47} + 94 q^{49} - 726 q^{50} - 236 q^{52} + 378 q^{53} + 488 q^{56} + 8 q^{58} - 1706 q^{59} + 910 q^{61} + 80 q^{62} + 512 q^{64} + 492 q^{65} + 1942 q^{67} + 880 q^{68} + 160 q^{70} + 452 q^{74} - 1228 q^{76} + 268 q^{77} - 4416 q^{79} + 2648 q^{80} - 704 q^{82} + 2562 q^{83} - 12 q^{85} - 3764 q^{86} + 1528 q^{88} + 3332 q^{91} - 632 q^{92} - 3248 q^{94} - 6900 q^{95} - 4 q^{97} - 314 q^{98}+O(q^{100}) $ 10 * q + 2 * q^2 + 8 * q^4 + 2 * q^5 + 44 * q^8 - 68 * q^10 - 18 * q^11 - 2 * q^13 - 188 * q^14 + 280 * q^16 + 4 * q^17 - 26 * q^19 + 196 * q^20 - 588 * q^22 + 264 * q^26 + 280 * q^28 + 202 * q^29 + 368 * q^31 - 968 * q^32 + 436 * q^34 - 476 * q^35 - 10 * q^37 + 1232 * q^38 - 1336 * q^40 - 838 * q^43 - 868 * q^44 + 1132 * q^46 + 944 * q^47 + 94 * q^49 - 726 * q^50 - 236 * q^52 + 378 * q^53 + 488 * q^56 + 8 * q^58 - 1706 * q^59 + 910 * q^61 + 80 * q^62 + 512 * q^64 + 492 * q^65 + 1942 * q^67 + 880 * q^68 + 160 * q^70 + 452 * q^74 - 1228 * q^76 + 268 * q^77 - 4416 * q^79 + 2648 * q^80 - 704 * q^82 + 2562 * q^83 - 12 * q^85 - 3764 * q^86 + 1528 * q^88 + 3332 * q^91 - 632 * q^92 - 3248 * q^94 - 6900 * q^95 - 4 * q^97 - 314 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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 $

$2$	2.81708	+	0.253099i	0.995988	+	0.0894841i
$2$	2.81708	+	0.253099i	0.995988	+	0.0894841i
$3$		0			0
$3$		0			0
$4$	7.87188	+	1.42600i	0.983985	+	0.178250i
$5$	4.66372	+	4.66372i	0.417136	+	0.417136i	0.884215	−	0.467079i	$-0.154694\pi$
$5$	4.66372	+	4.66372i	0.417136	+	0.417136i	−0.467079	+	0.884215i	$0.654694\pi$
$6$		0			0
$7$			24.8965i			1.34429i	0.740422	+	0.672143i	$0.234626\pi$
$7$			24.8965i			1.34429i	−0.740422	+	0.672143i	$0.765374\pi$
$8$	21.8148	+	6.00953i	0.964087	+	0.265586i
$9$		0			0
$10$	11.9577	+	14.3185i	0.378136	+	0.452790i
$11$	−22.3431	−	22.3431i	−0.612427	−	0.612427i	0.331151	−	0.943578i	$-0.392563\pi$
$11$	−22.3431	−	22.3431i	−0.612427	−	0.612427i	−0.943578	+	0.331151i	$0.892563\pi$
$12$		0			0
$13$	−11.2714	+	11.2714i	−0.240471	+	0.240471i	−0.817045	−	0.576574i	$-0.804389\pi$
$13$	−11.2714	+	11.2714i	−0.240471	+	0.240471i	0.576574	+	0.817045i	$0.304389\pi$
$14$	−6.30129	+	70.1355i	−0.120292	+	1.33889i
$15$		0			0
$16$	59.9330	+	22.4506i	0.936454	+	0.350791i
$17$	88.4846			1.26239			0.631196	−	0.775623i	$-0.282564\pi$
$17$	88.4846			1.26239			0.631196	+	0.775623i	$0.282564\pi$
$18$		0			0
$19$	37.8187	−	37.8187i	0.456643	−	0.456643i	−0.440909	−	0.897552i	$-0.645344\pi$
$19$	37.8187	−	37.8187i	0.456643	−	0.456643i	0.897552	+	0.440909i	$0.145344\pi$
$20$	30.0618	+	43.3627i	0.336101	+	0.484810i
$21$		0			0
$22$	−57.2873	−	68.5974i	−0.555168	−	0.664773i
$23$			48.1224i			0.436270i	0.975919	+	0.218135i	$0.0699973\pi$
$23$			48.1224i			0.436270i	−0.975919	+	0.218135i	$0.930003\pi$
$24$		0			0
$25$		−	81.4994i		−	0.651995i
$26$	−34.6053	+	28.8997i	−0.261025	+	0.217988i
$27$		0			0
$28$	−35.5025	+	195.982i	−0.239619	+	1.32276i
$29$	−10.4432	+	10.4432i	−0.0668705	+	0.0668705i	−0.739751	−	0.672881i	$-0.765057\pi$
$29$	−10.4432	+	10.4432i	−0.0668705	+	0.0668705i	0.672881	+	0.739751i	$0.265057\pi$
$30$		0			0
$31$	−96.9578			−0.561746			−0.280873	−	0.959745i	$-0.590624\pi$
$31$	−96.9578			−0.561746			−0.280873	+	0.959745i	$0.590624\pi$
$32$	163.154	+	78.4142i	0.901307	+	0.433181i
$33$		0			0
$34$	249.268	+	22.3954i	1.25733	+	0.112964i
$35$	−116.110	+	116.110i	−0.560750	+	0.560750i
$36$		0			0
$37$	−163.279	−	163.279i	−0.725484	−	0.725484i	0.244233	−	0.969717i	$-0.421464\pi$
$37$	−163.279	−	163.279i	−0.725484	−	0.725484i	−0.969717	+	0.244233i	$0.921464\pi$
$38$	116.110	−	96.9665i	0.495673	−	0.413949i
$39$		0			0
$40$	73.7114	+	129.765i	0.291370	+	0.512941i
$41$		−	360.519i		−	1.37326i	−0.727008	−	0.686629i	$-0.759090\pi$
$41$		−	360.519i		−	1.37326i	0.727008	−	0.686629i	$-0.240910\pi$
$42$		0			0
$43$	−100.249	−	100.249i	−0.355531	−	0.355531i	0.506632	−	0.862163i	$-0.330890\pi$
$43$	−100.249	−	100.249i	−0.355531	−	0.355531i	−0.862163	+	0.506632i	$0.830890\pi$
$44$	−144.021	−	207.744i	−0.493454	−	0.711785i
$45$		0			0
$46$	−12.1797	+	135.565i	−0.0390392	+	0.434520i
$47$	−220.669			−0.684849			−0.342425	−	0.939545i	$-0.611248\pi$
$47$	−220.669			−0.684849			−0.342425	+	0.939545i	$0.611248\pi$
$48$		0			0
$49$	−276.837			−0.807104
$50$	20.6274	−	229.590i	0.0583432	−	0.649379i
$51$		0			0
$52$	−104.800	+	72.6542i	−0.279484	+	0.193756i
$53$	175.752	+	175.752i	0.455498	+	0.455498i	0.897174	−	0.441676i	$-0.145616\pi$
$53$	175.752	+	175.752i	0.455498	+	0.455498i	−0.441676	+	0.897174i	$0.645616\pi$
$54$		0			0
$55$		−	208.404i		−	0.510931i
$56$	−149.616	+	543.113i	−0.357024	+	1.29601i
$57$		0			0
$58$	−32.0624	+	26.7761i	−0.0725861	+	0.0606184i
$59$	−405.008	−	405.008i	−0.893687	−	0.893687i	0.101181	−	0.994868i	$-0.467738\pi$
$59$	−405.008	−	405.008i	−0.893687	−	0.893687i	−0.994868	+	0.101181i	$0.967738\pi$
$60$		0			0
$61$	664.576	−	664.576i	1.39492	−	1.39492i	0.581061	−	0.813860i	$-0.302638\pi$
$61$	664.576	−	664.576i	1.39492	−	1.39492i	0.813860	−	0.581061i	$-0.197362\pi$
$62$	−273.138	−	24.5399i	−0.559493	−	0.0502674i
$63$		0			0
$64$	439.771	+	262.193i	0.858928	+	0.512096i
$65$	−105.133			−0.200619
$66$		0			0
$67$	−107.377	+	107.377i	−0.195794	+	0.195794i	−0.798194	−	0.602400i	$-0.794211\pi$
$67$	−107.377	+	107.377i	−0.195794	+	0.195794i	0.602400	+	0.798194i	$0.294211\pi$
$68$	696.540	+	126.179i	1.24218	+	0.225022i
$69$		0			0
$70$	−356.480	+	297.705i	−0.608679	+	0.508322i
$71$			215.050i			0.359461i	0.983716	+	0.179731i	$0.0575226\pi$
$71$			215.050i			0.359461i	−0.983716	+	0.179731i	$0.942477\pi$
$72$		0			0
$73$			668.587i			1.07195i	0.844235	+	0.535974i	$0.180055\pi$
$73$			668.587i			1.07195i	−0.844235	+	0.535974i	$0.819945\pi$
$74$	−418.644	−	501.296i	−0.657654	−	0.787492i
$75$		0			0
$76$	351.634	−	243.775i	0.530726	−	0.367933i
$77$	556.266	−	556.266i	0.823277	−	0.823277i
$78$		0			0
$79$	−822.956			−1.17202			−0.586012	−	0.810303i	$-0.699303\pi$
$79$	−822.956			−1.17202			−0.586012	+	0.810303i	$0.699303\pi$
$80$	174.808	+	384.215i	0.244301	+	0.536956i
$81$		0			0
$82$	91.2471	−	1015.61i	0.122885	−	1.36775i
$83$	−326.873	+	326.873i	−0.432277	+	0.432277i	−0.889402	−	0.457125i	$-0.848879\pi$
$83$	−326.873	+	326.873i	−0.432277	+	0.432277i	0.457125	+	0.889402i	$0.348879\pi$
$84$		0			0
$85$	412.668	+	412.668i	0.526589	+	0.526589i
$86$	−257.037	−	307.783i	−0.322290	−	0.385919i
$87$		0			0
$88$	−353.139	−	621.682i	−0.427781	−	0.753086i
$89$		−	262.733i		−	0.312918i	−0.987684	−	0.156459i	$-0.949992\pi$
$89$		−	262.733i		−	0.312918i	0.987684	−	0.156459i	$-0.0500079\pi$
$90$		0			0
$91$	−280.619	−	280.619i	−0.323262	−	0.323262i
$92$	−68.6226	+	378.814i	−0.0777652	+	0.429283i
$93$		0			0
$94$	−621.643	−	55.8512i	−0.682102	−	0.0612831i
$95$	352.752			0.380964
$96$		0			0
$97$	−150.801			−0.157850			−0.0789251	−	0.996881i	$-0.525149\pi$
$97$	−150.801			−0.157850			−0.0789251	+	0.996881i	$0.525149\pi$
$98$	−779.871	−	70.0671i	−0.803866	−	0.0722229i
$99$		0			0
$100$	116.218	−	641.553i	0.116218	−	0.641553i
$101$	−487.985	−	487.985i	−0.480755	−	0.480755i	0.424617	−	0.905373i	$-0.360409\pi$
$101$	−487.985	−	487.985i	−0.480755	−	0.480755i	−0.905373	+	0.424617i	$0.860409\pi$
$102$		0			0
$103$			1840.58i			1.76075i	0.474275	+	0.880377i	$0.342710\pi$
$103$			1840.58i			1.76075i	−0.474275	+	0.880377i	$0.657290\pi$
$104$	−313.620	+	178.148i	−0.295701	+	0.167970i
$105$		0			0
$106$	450.625	+	539.590i	0.412911	+	0.494431i
$107$	79.4098	+	79.4098i	0.0717461	+	0.0717461i	0.742069	−	0.670323i	$-0.233845\pi$
$107$	79.4098	+	79.4098i	0.0717461	+	0.0717461i	−0.670323	+	0.742069i	$0.733845\pi$
$108$		0			0
$109$	952.979	−	952.979i	0.837421	−	0.837421i	−0.151098	−	0.988519i	$-0.548281\pi$
$109$	952.979	−	952.979i	0.837421	−	0.837421i	0.988519	+	0.151098i	$0.0482809\pi$
$110$	52.7469	−	587.091i	0.0457202	−	0.508881i
$111$		0			0
$112$	−558.942	+	1492.12i	−0.471563	+	1.25886i
$113$	720.469			0.599788			0.299894	−	0.953973i	$-0.403049\pi$
$113$	720.469			0.599788			0.299894	+	0.953973i	$0.403049\pi$
$114$		0			0
$115$	−224.430	+	224.430i	−0.181984	+	0.181984i
$116$	−97.0993	+	67.3153i	−0.0777193	+	0.0538799i
$117$		0			0
$118$	−1038.43	−	1243.45i	−0.810131	−	0.970072i
$119$			2202.96i			1.69702i
$120$		0			0
$121$		−	332.571i		−	0.249865i
$122$	2040.37	−	1703.96i	1.51415	−	1.26450i
$123$		0			0
$124$	−763.240	−	138.262i	−0.552750	−	0.100131i
$125$	963.056	−	963.056i	0.689107	−	0.689107i
$126$		0			0
$127$	2622.35			1.83225			0.916124	−	0.400895i	$-0.131301\pi$
$127$	2622.35			1.83225			0.916124	+	0.400895i	$0.131301\pi$
$128$	1172.51	+	849.925i	0.809658	+	0.586902i
$129$		0			0
$130$	−296.169	−	26.6092i	−0.199814	−	0.0179522i
$131$	−657.574	+	657.574i	−0.438569	+	0.438569i	−0.891530	−	0.452961i	$-0.850368\pi$
$131$	−657.574	+	657.574i	−0.438569	+	0.438569i	0.452961	+	0.891530i	$0.350368\pi$
$132$		0			0
$133$	941.555	+	941.555i	0.613858	+	0.613858i
$134$	−329.666	+	275.312i	−0.212529	+	0.177488i
$135$		0			0
$136$	1930.27	+	531.751i	1.21706	+	0.335274i
$137$			2511.52i			1.56623i	0.621874	+	0.783117i	$0.286371\pi$
$137$			2511.52i			1.56623i	−0.621874	+	0.783117i	$0.713629\pi$
$138$		0			0
$139$	−1086.02	−	1086.02i	−0.662697	−	0.662697i	0.293318	−	0.956015i	$-0.405241\pi$
$139$	−1086.02	−	1086.02i	−0.662697	−	0.662697i	−0.956015	+	0.293318i	$0.905241\pi$
$140$	−1079.58	+	748.434i	−0.651723	+	0.451816i
$141$		0			0
$142$	−54.4290	+	605.813i	−0.0321661	+	0.358019i
$143$	503.677			0.294543
$144$		0			0
$145$	−97.4080			−0.0557882
$146$	−169.219	+	1883.46i	−0.0959222	+	1.06765i
$147$		0			0
$148$	−1052.48	−	1518.15i	−0.584547	−	0.843183i
$149$	2284.63	+	2284.63i	1.25614	+	1.25614i	0.952922	+	0.303214i	$0.0980598\pi$
$149$	2284.63	+	2284.63i	1.25614	+	1.25614i	0.303214	+	0.952922i	$0.401940\pi$
$150$		0			0
$151$			2814.39i			1.51677i	0.651809	+	0.758383i	$0.274010\pi$
$151$			2814.39i			1.51677i	−0.651809	+	0.758383i	$0.725990\pi$
$152$	1052.28	−	597.735i	0.561521	−	0.318965i
$153$		0			0
$154$	1707.84	−	1426.25i	0.893645	−	0.746304i
$155$	−452.184	−	452.184i	−0.234325	−	0.234325i
$156$		0			0
$157$	−906.308	+	906.308i	−0.460709	+	0.460709i	−0.898888	−	0.438179i	$-0.855624\pi$
$157$	−906.308	+	906.308i	−0.460709	+	0.460709i	0.438179	+	0.898888i	$0.355624\pi$
$158$	−2318.33	−	208.290i	−1.16732	−	0.104877i
$159$		0			0
$160$	395.203	+	1126.61i	0.195272	+	0.556663i
$161$	−1198.08			−0.586472
$162$		0			0
$163$	1392.36	−	1392.36i	0.669067	−	0.669067i	−0.288433	−	0.957500i	$-0.593134\pi$
$163$	1392.36	−	1392.36i	0.669067	−	0.669067i	0.957500	+	0.288433i	$0.0931342\pi$
$164$	514.101	−	2837.96i	0.244784	−	1.35127i
$165$		0			0
$166$	−1003.56	+	838.097i	−0.469225	+	0.391861i
$167$		−	1221.66i		−	0.566075i	−0.959109	−	0.283038i	$-0.908658\pi$
$167$		−	1221.66i		−	0.566075i	0.959109	−	0.283038i	$-0.0913421\pi$
$168$		0			0
$169$			1942.91i			0.884347i
$170$	1058.07	+	1266.96i	0.477356	+	0.571598i
$171$		0			0
$172$	−646.193	−	932.104i	−0.286464	−	0.413211i
$173$	563.418	−	563.418i	0.247606	−	0.247606i	−0.572381	−	0.819988i	$-0.693980\pi$
$173$	563.418	−	563.418i	0.247606	−	0.247606i	0.819988	+	0.572381i	$0.193980\pi$
$174$		0			0
$175$	2029.05			0.876468
$176$	−837.474	−	1840.71i	−0.358676	−	0.788344i
$177$		0			0
$178$	66.4976	−	740.141i	0.0280012	−	0.311662i
$179$	2202.23	−	2202.23i	0.919565	−	0.919565i	−0.0774329	−	0.996998i	$-0.524672\pi$
$179$	2202.23	−	2202.23i	0.919565	−	0.919565i	0.996998	+	0.0774329i	$0.0246724\pi$
$180$		0			0
$181$	121.294	+	121.294i	0.0498104	+	0.0498104i	0.731573	−	0.681763i	$-0.238786\pi$
$181$	121.294	+	121.294i	0.0498104	+	0.0498104i	−0.681763	+	0.731573i	$0.738786\pi$
$182$	−719.502	−	861.551i	−0.293039	−	0.350892i
$183$		0			0
$184$	−289.193	+	1049.78i	−0.115867	+	0.420602i
$185$		−	1522.98i		−	0.605251i
$186$		0			0
$187$	−1977.02	−	1977.02i	−0.773124	−	0.773124i
$188$	−1737.08	−	314.675i	−0.673882	−	0.122074i
$189$		0			0
$190$	993.731	+	89.2813i	0.379436	+	0.0340902i
$191$	−3927.65			−1.48793			−0.743966	−	0.668218i	$-0.767058\pi$
$191$	−3927.65			−1.48793			−0.743966	+	0.668218i	$0.767058\pi$
$192$		0			0
$193$	−3249.02			−1.21176			−0.605880	−	0.795556i	$-0.707179\pi$
$193$	−3249.02			−1.21176			−0.605880	+	0.795556i	$0.707179\pi$
$194$	−424.817	−	38.1675i	−0.157217	−	0.0141251i
$195$		0			0
$196$	−2179.23	−	394.769i	−0.794178	−	0.143866i
$197$	−2420.90	−	2420.90i	−0.875545	−	0.875545i	0.117525	−	0.993070i	$-0.462504\pi$
$197$	−2420.90	−	2420.90i	−0.875545	−	0.875545i	−0.993070	+	0.117525i	$0.962504\pi$
$198$		0			0
$199$		−	1371.30i		−	0.488488i	−0.969714	−	0.244244i	$-0.921460\pi$
$199$		−	1371.30i		−	0.488488i	0.969714	−	0.244244i	$-0.0785397\pi$
$200$	489.773	−	1777.89i	0.173161	−	0.628580i
$201$		0			0
$202$	−1251.18	−	1498.20i	−0.435807	−	0.521847i
$203$	−259.998	−	259.998i	−0.0898931	−	0.0898931i
$204$		0			0
$205$	1681.36	−	1681.36i	0.572836	−	0.572836i
$206$	−465.849	+	5185.06i	−0.157559	+	1.75369i
$207$		0			0
$208$	−928.580	+	422.480i	−0.309546	+	0.140835i
$209$	−1689.98			−0.559321
$210$		0			0
$211$	−1620.50	+	1620.50i	−0.528719	+	0.528719i	−0.920190	−	0.391471i	$-0.871966\pi$
$211$	−1620.50	+	1620.50i	−0.528719	+	0.528719i	0.391471	+	0.920190i	$0.371966\pi$
$212$	1132.88	+	1634.12i	0.367011	+	0.529396i
$213$		0			0
$214$	203.605	+	243.802i	0.0650382	+	0.0778784i
$215$		−	935.068i		−	0.296610i
$216$		0			0
$217$		−	2413.91i		−	0.755148i
$218$	2925.82	−	2443.42i	0.908997	−	0.759125i
$219$		0			0
$220$	297.185	−	1640.53i	0.0910736	−	0.502749i
$221$	−997.347	+	997.347i	−0.303569	+	0.303569i
$222$		0			0
$223$	−419.617			−0.126007			−0.0630036	−	0.998013i	$-0.520068\pi$
$223$	−419.617			−0.126007			−0.0630036	+	0.998013i	$0.520068\pi$
$224$	−1952.24	+	4061.97i	−0.582320	+	1.21161i
$225$		0			0
$226$	2029.62	+	182.350i	0.597381	+	0.0536714i
$227$	2133.64	−	2133.64i	0.623853	−	0.623853i	−0.322661	−	0.946515i	$-0.604577\pi$
$227$	2133.64	−	2133.64i	0.623853	−	0.623853i	0.946515	+	0.322661i	$0.104577\pi$
$228$		0			0
$229$	−1574.42	−	1574.42i	−0.454325	−	0.454325i	0.442462	−	0.896787i	$-0.354105\pi$
$229$	−1574.42	−	1574.42i	−0.454325	−	0.454325i	−0.896787	+	0.442462i	$0.854105\pi$
$230$	−689.039	+	575.433i	−0.197539	+	0.164969i
$231$		0			0
$232$	−290.574	+	165.057i	−0.0822289	+	0.0467091i
$233$			1194.86i			0.335957i	0.985791	+	0.167978i	$0.0537239\pi$
$233$			1194.86i			0.335957i	−0.985791	+	0.167978i	$0.946276\pi$
$234$		0			0
$235$	−1029.14	−	1029.14i	−0.285675	−	0.285675i
$236$	−2610.63	−	3765.71i	−0.720075	−	1.03867i
$237$		0			0
$238$	−557.567	+	6205.91i	−0.151856	+	1.69021i
$239$	4241.03			1.14782			0.573911	−	0.818917i	$-0.305425\pi$
$239$	4241.03			1.14782			0.573911	+	0.818917i	$0.305425\pi$
$240$		0			0
$241$	−5571.19			−1.48910			−0.744548	−	0.667569i	$-0.767335\pi$
$241$	−5571.19			−1.48910			−0.744548	+	0.667569i	$0.767335\pi$
$242$	84.1734	−	936.878i	0.0223590	−	0.248863i
$243$		0			0
$244$	6179.15	−	4283.77i	1.62123	−	1.12394i
$245$	−1291.09	−	1291.09i	−0.336672	−	0.336672i
$246$		0			0
$247$			852.541i			0.219619i
$248$	−2115.12	−	582.671i	−0.541572	−	0.149192i
$249$		0			0
$250$	2956.75	−	2469.26i	0.748006	−	0.624678i
$251$	482.728	+	482.728i	0.121393	+	0.121393i	0.765193	−	0.643801i	$-0.222643\pi$
$251$	482.728	+	482.728i	0.121393	+	0.121393i	−0.643801	+	0.765193i	$0.722643\pi$
$252$		0			0
$253$	1075.20	−	1075.20i	0.267184	−	0.267184i
$254$	7387.36	+	663.713i	1.82490	+	0.163957i
$255$		0			0
$256$	3087.94	+	2691.07i	0.753891	+	0.656999i
$257$	−8093.12			−1.96434			−0.982169	−	0.188002i	$-0.939799\pi$
$257$	−8093.12			−1.96434			−0.982169	+	0.188002i	$0.939799\pi$
$258$		0			0
$259$	4065.08	−	4065.08i	0.975257	−	0.975257i
$260$	−827.598	−	149.921i	−0.197406	−	0.0357603i
$261$		0			0
$262$	−2018.87	+	1686.01i	−0.476054	+	0.397564i
$263$		−	410.300i		−	0.0961984i	−0.998843	−	0.0480992i	$-0.984684\pi$
$263$		−	410.300i		−	0.0961984i	0.998843	−	0.0480992i	$-0.0153164\pi$
$264$		0			0
$265$			1639.32i			0.380009i
$266$	2414.13	+	2890.74i	0.556465	+	0.666326i
$267$		0			0
$268$	−998.378	+	692.139i	−0.227558	+	0.157758i
$269$	4.77962	−	4.77962i	0.00108334	−	0.00108334i	−0.706565	−	0.707648i	$-0.749756\pi$
$269$	4.77962	−	4.77962i	0.00108334	−	0.00108334i	0.707648	+	0.706565i	$0.249756\pi$
$270$		0			0
$271$	−2833.98			−0.635247			−0.317623	−	0.948217i	$-0.602885\pi$
$271$	−2833.98			−0.635247			−0.317623	+	0.948217i	$0.602885\pi$
$272$	5303.15	+	1986.54i	1.18217	+	0.442836i
$273$		0			0
$274$	−635.665	+	7075.17i	−0.140153	+	1.55995i
$275$	−1820.95	+	1820.95i	−0.399300	+	0.399300i
$276$		0			0
$277$	1525.80	+	1525.80i	0.330962	+	0.330962i	0.852952	−	0.521989i	$-0.174810\pi$
$277$	1525.80	+	1525.80i	0.330962	+	0.330962i	−0.521989	+	0.852952i	$0.674810\pi$
$278$	−2784.53	−	3334.27i	−0.600738	−	0.719339i
$279$		0			0
$280$	−3230.70	+	1835.16i	−0.689539	+	0.391684i
$281$			4750.23i			1.00845i	0.863572	+	0.504226i	$0.168222\pi$
$281$			4750.23i			1.00845i	−0.863572	+	0.504226i	$0.831778\pi$
$282$		0			0
$283$	644.104	+	644.104i	0.135293	+	0.135293i	0.771510	−	0.636217i	$-0.219502\pi$
$283$	644.104	+	644.104i	0.135293	+	0.135293i	−0.636217	+	0.771510i	$0.719502\pi$
$284$	−306.662	+	1692.85i	−0.0640740	+	0.353705i
$285$		0			0
$286$	1418.90	+	127.480i	0.293361	+	0.0263569i
$287$	8975.67			1.84605
$288$		0			0
$289$	2916.53			0.593635
$290$	−274.406	−	24.6539i	−0.0555644	−	0.00499216i
$291$		0			0
$292$	−953.405	+	5263.03i	−0.191075	+	1.05478i
$293$	1433.16	+	1433.16i	0.285755	+	0.285755i	0.835399	−	0.549644i	$-0.185237\pi$
$293$	1433.16	+	1433.16i	0.285755	+	0.285755i	−0.549644	+	0.835399i	$0.685237\pi$
$294$		0			0
$295$		−	3777.69i		−	0.745578i
$296$	−2580.67	−	4543.13i	−0.506751	−	0.892108i
$297$		0			0
$298$	5857.75	+	7014.23i	1.13869	+	1.36350i
$299$	−542.407	−	542.407i	−0.104910	−	0.104910i
$300$		0			0
$301$	2495.85	−	2495.85i	0.477935	−	0.477935i
$302$	−712.319	+	7928.36i	−0.135726	+	1.51068i
$303$		0			0
$304$	3115.65	−	1417.54i	0.587811	−	0.267439i
$305$	6198.79			1.16374
$306$		0			0
$307$	−231.211	+	231.211i	−0.0429834	+	0.0429834i	−0.728272	−	0.685288i	$-0.759676\pi$
$307$	−231.211	+	231.211i	−0.0429834	+	0.0429834i	0.685288	+	0.728272i	$0.259676\pi$
$308$	5172.09	−	3585.62i	0.956842	−	0.663343i
$309$		0			0
$310$	−1159.39	−	1388.29i	−0.212416	−	0.254353i
$311$			871.410i			0.158885i	0.996839	+	0.0794423i	$0.0253140\pi$
$311$			871.410i			0.158885i	−0.996839	+	0.0794423i	$0.974686\pi$
$312$		0			0
$313$			3515.02i			0.634762i	0.948298	+	0.317381i	$0.102803\pi$
$313$			3515.02i			0.634762i	−0.948298	+	0.317381i	$0.897197\pi$
$314$	−2782.53	+	2323.76i	−0.500087	+	0.417634i
$315$		0			0
$316$	−6478.22	−	1173.54i	−1.15325	−	0.208913i
$317$	−4723.77	+	4723.77i	−0.836951	+	0.836951i	−0.988456	−	0.151506i	$-0.951588\pi$
$317$	−4723.77	+	4723.77i	−0.836951	+	0.836951i	0.151506	+	0.988456i	$0.451588\pi$
$318$		0			0
$319$	466.665			0.0819067
$320$	828.174	+	3273.77i	0.144676	+	0.571904i
$321$		0			0
$322$	−3375.09	−	303.233i	−0.584119	−	0.0524799i
$323$	3346.38	−	3346.38i	0.576462	−	0.576462i
$324$		0			0
$325$	918.613	+	918.613i	0.156786	+	0.156786i
$326$	4274.79	−	3569.98i	0.726254	−	0.606512i
$327$		0			0
$328$	2166.55	−	7864.65i	0.364718	−	1.32394i
$329$		−	5493.90i		−	0.920633i
$330$		0			0
$331$	−1820.26	−	1820.26i	−0.302268	−	0.302268i	0.539633	−	0.841901i	$-0.318563\pi$
$331$	−1820.26	−	1820.26i	−0.302268	−	0.302268i	−0.841901	+	0.539633i	$0.818563\pi$
$332$	−3039.23	+	2106.99i	−0.502408	+	0.348301i
$333$		0			0
$334$	309.200	−	3441.50i	0.0506547	−	0.563804i
$335$	−1001.55			−0.163345
$336$		0			0
$337$	74.0970			0.0119772			0.00598861	−	0.999982i	$-0.498094\pi$
$337$	74.0970			0.0119772			0.00598861	+	0.999982i	$0.498094\pi$
$338$	−491.749	+	5473.33i	−0.0791350	+	0.880799i
$339$		0			0
$340$	2660.01	+	3836.94i	0.424292	+	0.612021i
$341$	2166.34	+	2166.34i	0.344029	+	0.344029i
$342$		0			0
$343$			1647.24i			0.259307i
$344$	−1584.46	−	2789.36i	−0.248339	−	0.437187i
$345$		0			0
$346$	1729.80	−	1444.59i	0.268770	−	0.224456i
$347$	−2102.73	−	2102.73i	−0.325305	−	0.325305i	0.525493	−	0.850798i	$-0.323881\pi$
$347$	−2102.73	−	2102.73i	−0.325305	−	0.325305i	−0.850798	+	0.525493i	$0.823881\pi$
$348$		0			0
$349$	−6612.85	+	6612.85i	−1.01426	+	1.01426i	−0.0143661	+	0.999897i	$0.504573\pi$
$349$	−6612.85	+	6612.85i	−1.01426	+	1.01426i	−0.999897	+	0.0143661i	$0.995427\pi$
$350$	5716.00	+	513.551i	0.872951	+	0.0784299i
$351$		0			0
$352$	−1893.35	−	5397.38i	−0.286693	−	0.817277i
$353$	−2216.90			−0.334259			−0.167130	−	0.985935i	$-0.553450\pi$
$353$	−2216.90			−0.334259			−0.167130	+	0.985935i	$0.553450\pi$
$354$		0			0
$355$	−1002.93	+	1002.93i	−0.149944	+	0.149944i
$356$	374.658	−	2068.21i	0.0557776	−	0.307906i
$357$		0			0
$358$	6761.23	−	5646.46i	0.998162	−	0.833589i
$359$		−	2082.23i		−	0.306117i	−0.988217	−	0.153059i	$-0.951088\pi$
$359$		−	2082.23i		−	0.306117i	0.988217	−	0.153059i	$-0.0489123\pi$
$360$		0			0
$361$			3998.49i			0.582955i
$362$	310.995	+	372.393i	0.0451533	+	0.0540678i
$363$		0			0
$364$	−1808.84	−	2609.16i	−0.260464	−	0.375707i
$365$	−3118.10	+	3118.10i	−0.447148	+	0.447148i
$366$		0			0
$367$	4509.22			0.641360			0.320680	−	0.947188i	$-0.396089\pi$
$367$	4509.22			0.641360			0.320680	+	0.947188i	$0.396089\pi$
$368$	−1080.38	+	2884.12i	−0.153040	+	0.408547i
$369$		0			0
$370$	385.464	−	4290.34i	0.0541603	−	0.602823i
$371$	−4375.61	+	4375.61i	−0.612320	+	0.612320i
$372$		0			0
$373$	−8661.56	−	8661.56i	−1.20236	−	1.20236i	−0.973448	−	0.228908i	$-0.926485\pi$
$373$	−8661.56	−	8661.56i	−1.20236	−	1.20236i	−0.228908	−	0.973448i	$-0.573515\pi$
$374$	−5069.05	−	6069.81i	−0.700840	−	0.839205i
$375$		0			0
$376$	−4813.86	−	1326.12i	−0.660254	−	0.181886i
$377$		−	235.418i		−	0.0321609i
$378$		0			0
$379$	3522.46	+	3522.46i	0.477405	+	0.477405i	0.904301	−	0.426896i	$-0.140393\pi$
$379$	3522.46	+	3522.46i	0.477405	+	0.477405i	−0.426896	+	0.904301i	$0.640393\pi$
$380$	2776.82	+	503.025i	0.374863	+	0.0679069i
$381$		0			0
$382$	−11064.5	−	994.086i	−1.48196	−	0.133146i
$383$	−3044.88			−0.406229			−0.203115	−	0.979155i	$-0.565106\pi$
$383$	−3044.88			−0.406229			−0.203115	+	0.979155i	$0.565106\pi$
$384$		0			0
$385$	5188.54			0.686837
$386$	−9152.75	−	822.325i	−1.20690	−	0.108433i
$387$		0			0
$388$	−1187.08	−	215.042i	−0.155322	−	0.0281368i
$389$	−1932.73	−	1932.73i	−0.251911	−	0.251911i	0.569843	−	0.821754i	$-0.307004\pi$
$389$	−1932.73	−	1932.73i	−0.251911	−	0.251911i	−0.821754	+	0.569843i	$0.807004\pi$
$390$		0			0
$391$			4258.09i			0.550744i
$392$	−6039.14	−	1663.66i	−0.778119	−	0.214356i
$393$		0			0
$394$	−6207.15	−	7432.61i	−0.793685	−	0.950379i
$395$	−3838.04	−	3838.04i	−0.488893	−	0.488893i
$396$		0			0
$397$	−672.457	+	672.457i	−0.0850117	+	0.0850117i	−0.748334	−	0.663322i	$-0.769146\pi$
$397$	−672.457	+	672.457i	−0.0850117	+	0.0850117i	0.663322	+	0.748334i	$0.269146\pi$
$398$	347.075	−	3863.07i	0.0437119	−	0.486528i
$399$		0			0
$400$	1829.71	−	4884.51i	0.228714	−	0.610563i
$401$	7606.74			0.947288			0.473644	−	0.880716i	$-0.342938\pi$
$401$	7606.74			0.947288			0.473644	+	0.880716i	$0.342938\pi$
$402$		0			0
$403$	1092.85	−	1092.85i	0.135084	−	0.135084i
$404$	−3145.49	−	4537.23i	−0.387361	−	0.558751i
$405$		0			0
$406$	−666.631	−	798.241i	−0.0814885	−	0.0975765i
$407$			7296.32i			0.888612i
$408$		0			0
$409$		−	4981.58i		−	0.602257i	−0.953584	−	0.301129i	$-0.902637\pi$
$409$		−	4981.58i		−	0.602257i	0.953584	−	0.301129i	$-0.0973634\pi$
$410$	5162.08	−	4310.98i	0.621797	−	0.519278i
$411$		0			0
$412$	−2624.67	+	14488.8i	−0.313855	+	1.73256i
$413$	10083.3	−	10083.3i	1.20137	−	1.20137i
$414$		0			0
$415$	−3048.89			−0.360637
$416$	−2722.81	+	955.136i	−0.320906	+	0.112571i
$417$		0			0
$418$	−4760.80	−	427.732i	−0.557077	−	0.0500503i
$419$	3433.38	−	3433.38i	0.400314	−	0.400314i	−0.478030	−	0.878344i	$-0.658649\pi$
$419$	3433.38	−	3433.38i	0.400314	−	0.400314i	0.878344	+	0.478030i	$0.158649\pi$
$420$		0			0
$421$	7973.72	+	7973.72i	0.923077	+	0.923077i	0.997246	−	0.0741686i	$-0.0236303\pi$
$421$	7973.72	+	7973.72i	0.923077	+	0.923077i	−0.0741686	+	0.997246i	$0.523630\pi$
$422$	−4975.22	+	4154.93i	−0.573910	+	0.479286i
$423$		0			0
$424$	2777.81	+	4890.18i	0.318166	+	0.560114i
$425$		−	7211.44i		−	0.823074i
$426$		0			0
$427$	16545.6	+	16545.6i	1.87517	+	1.87517i
$428$	511.866	+	738.343i	0.0578084	+	0.0833859i
$429$		0			0
$430$	236.665	−	2634.16i	0.0265418	−	0.295420i
$431$	−4800.16			−0.536463			−0.268232	−	0.963354i	$-0.586439\pi$
$431$	−4800.16			−0.536463			−0.268232	+	0.963354i	$0.586439\pi$
$432$		0			0
$433$	6242.32			0.692810			0.346405	−	0.938085i	$-0.387402\pi$
$433$	6242.32			0.692810			0.346405	+	0.938085i	$0.387402\pi$
$434$	610.959	−	6800.18i	0.0675737	−	0.752118i
$435$		0			0
$436$	8860.69	−	6142.79i	0.973280	−	0.674739i
$437$	1819.93	+	1819.93i	0.199220	+	0.199220i
$438$		0			0
$439$		−	4929.27i		−	0.535903i	−0.963432	−	0.267951i	$-0.913653\pi$
$439$		−	4929.27i		−	0.535903i	0.963432	−	0.267951i	$-0.0863466\pi$
$440$	1252.41	−	4546.30i	0.135696	−	0.492582i
$441$		0			0
$442$	−3062.03	+	2557.18i	−0.329516	+	0.275187i
$443$	7670.67	+	7670.67i	0.822674	+	0.822674i	0.986491	−	0.163817i	$-0.0523807\pi$
$443$	7670.67	+	7670.67i	0.822674	+	0.822674i	−0.163817	+	0.986491i	$0.552381\pi$
$444$		0			0
$445$	1225.32	−	1225.32i	0.130529	−	0.130529i
$446$	−1182.09	−	106.205i	−0.125502	−	0.0112756i
$447$		0			0
$448$	−6527.70	+	10948.8i	−0.688404	+	1.15464i
$449$	11515.2			1.21032			0.605162	−	0.796102i	$-0.293108\pi$
$449$	11515.2			1.21032			0.605162	+	0.796102i	$0.293108\pi$
$450$		0			0
$451$	−8055.12	+	8055.12i	−0.841021	+	0.841021i
$452$	5671.44	+	1027.39i	0.590182	+	0.106912i
$453$		0			0
$454$	6550.66	−	5470.61i	0.677176	−	0.565526i
$455$		−	2617.46i		−	0.269689i
$456$		0			0
$457$		−	4829.89i		−	0.494383i	−0.968967	−	0.247191i	$-0.920492\pi$
$457$		−	4829.89i		−	0.494383i	0.968967	−	0.247191i	$-0.0795076\pi$
$458$	−4036.78	−	4833.74i	−0.411848	−	0.493157i
$459$		0			0
$460$	−2086.72	+	1446.65i	−0.211508	+	0.146631i
$461$	−8265.79	+	8265.79i	−0.835090	+	0.835090i	−0.988208	−	0.153118i	$-0.951069\pi$
$461$	−8265.79	+	8265.79i	−0.835090	+	0.835090i	0.153118	+	0.988208i	$0.451069\pi$
$462$		0			0
$463$	−5043.86			−0.506281			−0.253141	−	0.967430i	$-0.581464\pi$
$463$	−5043.86			−0.506281			−0.253141	+	0.967430i	$0.581464\pi$
$464$	−860.346	+	391.435i	−0.0860788	+	0.0391636i
$465$		0			0
$466$	−302.418	+	3366.02i	−0.0300628	+	0.334609i
$467$	−12438.8	+	12438.8i	−1.23255	+	1.23255i	−0.269564	+	0.962982i	$0.586880\pi$
$467$	−12438.8	+	12438.8i	−1.23255	+	1.23255i	−0.962982	+	0.269564i	$0.913120\pi$
$468$		0			0
$469$	−2673.31	−	2673.31i	−0.263203	−	0.263203i
$470$	−2638.70	−	3159.64i	−0.258966	−	0.310093i
$471$		0			0
$472$	−6401.26	−	11269.1i	−0.624241	−	1.09894i
$473$			4479.75i			0.435474i
$474$		0			0
$475$	−3082.20	−	3082.20i	−0.297729	−	0.297729i
$476$	−3141.42	+	17341.4i	−0.302493	+	1.66984i
$477$		0			0
$478$	11947.3	+	1073.40i	1.14322	+	0.102712i
$479$	−13059.7			−1.24575			−0.622875	−	0.782321i	$-0.714036\pi$
$479$	−13059.7			−1.24575			−0.622875	+	0.782321i	$0.714036\pi$
$480$		0			0
$481$	3680.77			0.348916
$482$	−15694.5	−	1410.06i	−1.48312	−	0.133250i
$483$		0			0
$484$	474.246	−	2617.96i	0.0445385	−	0.245864i
$485$	−703.292	−	703.292i	−0.0658450	−	0.0658450i
$486$		0			0
$487$		−	15549.3i		−	1.44683i	−0.690414	−	0.723414i	$-0.742572\pi$
$487$		−	15549.3i		−	1.44683i	0.690414	−	0.723414i	$-0.257428\pi$
$488$	18491.4	−	10503.8i	1.71530	−	0.974354i
$489$		0			0
$490$	−3310.33	−	3963.88i	−0.305195	−	0.365448i
$491$	8628.34	+	8628.34i	0.793058	+	0.793058i	0.981990	−	0.188932i	$-0.0605027\pi$
$491$	8628.34	+	8628.34i	0.793058	+	0.793058i	−0.188932	+	0.981990i	$0.560503\pi$
$492$		0			0
$493$	−924.059	+	924.059i	−0.0844169	+	0.0844169i
$494$	−215.777	+	2401.68i	−0.0196524	+	0.218738i
$495$		0			0
$496$	−5810.98	−	2176.76i	−0.526049	−	0.197056i
$497$	−5354.00			−0.483219
$498$		0			0
$499$	1732.42	−	1732.42i	0.155418	−	0.155418i	−0.625115	−	0.780533i	$-0.714948\pi$
$499$	1732.42	−	1732.42i	0.155418	−	0.155418i	0.780533	+	0.625115i	$0.214948\pi$
$500$	8954.38	−	6207.74i	0.800904	−	0.555237i
$501$		0			0
$502$	1237.71	+	1482.06i	0.110043	+	0.131768i
$503$		−	16579.6i		−	1.46968i	−0.678241	−	0.734839i	$-0.737258\pi$
$503$		−	16579.6i		−	1.46968i	0.678241	−	0.734839i	$-0.262742\pi$
$504$		0			0
$505$		−	4551.65i		−	0.401081i
$506$	3301.07	−	2756.80i	0.290021	−	0.242203i
$507$		0			0
$508$	20642.8	+	3739.47i	1.80291	+	0.326599i
$509$	7830.92	−	7830.92i	0.681924	−	0.681924i	−0.278509	−	0.960434i	$-0.589840\pi$
$509$	7830.92	−	7830.92i	0.681924	−	0.681924i	0.960434	+	0.278509i	$0.0898403\pi$
$510$		0			0
$511$	−16645.5			−1.44100
$512$	8017.86	+	8362.51i	0.692076	+	0.721825i
$513$		0			0
$514$	−22799.0	−	2048.36i	−1.95646	−	0.175777i
$515$	−8583.95	+	8583.95i	−0.734474	+	0.734474i
$516$		0			0
$517$	4930.44	+	4930.44i	0.419420	+	0.419420i
$518$	12480.5	−	10422.8i	1.05861	−	0.884075i
$519$		0			0
$520$	−2293.47	−	631.803i	−0.193414	−	0.0532815i
$521$		−	3400.02i		−	0.285907i	−0.989729	−	0.142953i	$-0.954340\pi$
$521$		−	3400.02i		−	0.285907i	0.989729	−	0.142953i	$-0.0456599\pi$
$522$		0			0
$523$	−2019.50	−	2019.50i	−0.168847	−	0.168847i	0.617626	−	0.786472i	$-0.288095\pi$
$523$	−2019.50	−	2019.50i	−0.168847	−	0.168847i	−0.786472	+	0.617626i	$0.788095\pi$
$524$	−6114.05	+	4238.64i	−0.509720	+	0.353370i
$525$		0			0
$526$	103.847	−	1155.85i	0.00860822	−	0.0958124i
$527$	−8579.28			−0.709144
$528$		0			0
$529$	9851.23			0.809668
$530$	−414.910	+	4618.09i	−0.0340048	+	0.378485i
$531$		0			0
$532$	6069.15	+	8754.47i	0.494607	+	0.713448i
$533$	4063.56	+	4063.56i	0.330229	+	0.330229i
$534$		0			0
$535$			740.691i			0.0598558i
$536$	−2987.69	+	1697.12i	−0.240762	+	0.136762i
$537$		0			0
$538$	14.6743	−	12.2548i	0.00117594	−	0.000982052i
$539$	6185.39	+	6185.39i	0.494293	+	0.494293i
$540$		0			0
$541$	−13432.6	+	13432.6i	−1.06749	+	1.06749i	−0.0699388	+	0.997551i	$0.522280\pi$
$541$	−13432.6	+	13432.6i	−1.06749	+	1.06749i	−0.997551	+	0.0699388i	$0.977720\pi$
$542$	−7983.54	−	717.278i	−0.632699	−	0.0568445i
$543$		0			0
$544$	14436.6	+	6938.45i	1.13780	+	0.546845i
$545$	8888.86			0.698637
$546$		0			0
$547$	−5376.46	+	5376.46i	−0.420257	+	0.420257i	−0.885292	−	0.465035i	$-0.846042\pi$
$547$	−5376.46	+	5376.46i	−0.420257	+	0.420257i	0.465035	+	0.885292i	$0.346042\pi$
$548$	−3581.44	+	19770.4i	−0.279181	+	1.54115i
$549$		0			0
$550$	−5590.64	+	4668.88i	−0.433429	+	0.361967i
$551$			789.894i			0.0610719i
$552$		0			0
$553$		−	20488.7i		−	1.57553i
$554$	3912.13	+	4684.49i	0.300019	+	0.359251i
$555$		0			0
$556$	−7000.34	−	10097.7i	−0.533958	−	0.770210i
$557$	2076.28	−	2076.28i	0.157944	−	0.157944i	−0.623711	−	0.781655i	$-0.714376\pi$
$557$	2076.28	−	2076.28i	0.157944	−	0.157944i	0.781655	+	0.623711i	$0.214376\pi$
$558$		0			0
$559$	2259.90			0.170990
$560$	−9565.61	+	4352.10i	−0.721823	+	0.328410i
$561$		0			0
$562$	−1202.28	+	13381.8i	−0.0902405	+	1.00441i
$563$	16643.1	−	16643.1i	1.24587	−	1.24587i	0.288339	−	0.957528i	$-0.406897\pi$
$563$	16643.1	−	16643.1i	1.24587	−	1.24587i	0.957528	−	0.288339i	$-0.0931031\pi$
$564$		0			0
$565$	3360.07	+	3360.07i	0.250193	+	0.250193i
$566$	1651.47	+	1977.51i	0.122644	+	0.146857i
$567$		0			0
$568$	−1292.35	+	4691.28i	−0.0954679	+	0.346552i
$569$			5659.60i			0.416982i	0.978024	+	0.208491i	$0.0668551\pi$
$569$			5659.60i			0.416982i	−0.978024	+	0.208491i	$0.933145\pi$
$570$		0			0
$571$	4872.67	+	4872.67i	0.357119	+	0.357119i	0.862750	−	0.505631i	$-0.168740\pi$
$571$	4872.67	+	4872.67i	0.357119	+	0.357119i	−0.505631	+	0.862750i	$0.668740\pi$
$572$	3964.89	+	718.244i	0.289825	+	0.0525023i
$573$		0			0
$574$	25285.2	+	2271.73i	1.83865	+	0.165192i
$575$	3921.95			0.284446
$576$		0			0
$577$	10652.2			0.768556			0.384278	−	0.923217i	$-0.374450\pi$
$577$	10652.2			0.768556			0.384278	+	0.923217i	$0.374450\pi$
$578$	8216.10	+	738.171i	0.591254	+	0.0531209i
$579$		0			0
$580$	−766.784	−	138.904i	−0.0548948	−	0.00994426i
$581$	−8138.01	−	8138.01i	−0.581104	−	0.581104i
$582$		0			0
$583$		−	7853.69i		−	0.557919i
$584$	−4017.89	+	14585.1i	−0.284694	+	1.03345i
$585$		0			0
$586$	3674.61	+	4400.07i	0.259039	+	0.310180i
$587$	−9903.95	−	9903.95i	−0.696388	−	0.696388i	0.267242	−	0.963630i	$-0.413888\pi$
$587$	−9903.95	−	9903.95i	−0.696388	−	0.696388i	−0.963630	+	0.267242i	$0.913888\pi$
$588$		0			0
$589$	−3666.82	+	3666.82i	−0.256517	+	0.256517i
$590$	956.129	−	10642.0i	0.0667173	−	0.742587i
$591$		0			0
$592$	−6120.09	−	13451.5i	−0.424889	−	0.933875i
$593$	3528.04			0.244316			0.122158	−	0.992511i	$-0.461019\pi$
$593$	3528.04			0.244316			0.122158	+	0.992511i	$0.461019\pi$
$594$		0			0
$595$	−10274.0	+	10274.0i	−0.707887	+	0.707887i
$596$	14726.5	+	21242.2i	1.01211	+	1.45993i
$597$		0			0
$598$	−1390.72	−	1665.29i	−0.0951018	−	0.113877i
$599$			19024.9i			1.29772i	0.760907	+	0.648861i	$0.224754\pi$
$599$			19024.9i			1.29772i	−0.760907	+	0.648861i	$0.775246\pi$
$600$		0			0
$601$		−	1065.92i		−	0.0723460i	−0.999346	−	0.0361730i	$-0.988483\pi$
$601$		−	1065.92i		−	0.0723460i	0.999346	−	0.0361730i	$-0.0115167\pi$
$602$	7662.72	−	6399.32i	0.518786	−	0.433250i
$603$		0			0
$604$	−4013.32	+	22154.5i	−0.270364	+	1.49248i
$605$	1551.02	−	1551.02i	0.104228	−	0.104228i
$606$		0			0
$607$	12909.7			0.863242			0.431621	−	0.902055i	$-0.357942\pi$
$607$	12909.7			0.863242			0.431621	+	0.902055i	$0.357942\pi$
$608$	9135.80	−	3204.75i	0.609384	−	0.213766i
$609$		0			0
$610$	17462.5	+	1568.91i	1.15908	+	0.104137i
$611$	2487.25	−	2487.25i	0.164687	−	0.164687i
$612$		0			0
$613$	−8763.41	−	8763.41i	−0.577408	−	0.577408i	0.356781	−	0.934188i	$-0.383874\pi$
$613$	−8763.41	−	8763.41i	−0.577408	−	0.577408i	−0.934188	+	0.356781i	$0.883874\pi$
$614$	−709.859	+	592.820i	−0.0466573	+	0.0389646i
$615$		0			0
$616$	15477.7	−	8791.93i	1.01236	−	0.575060i
$617$		−	18921.2i		−	1.23459i	−0.786733	−	0.617293i	$-0.788229\pi$
$617$		−	18921.2i		−	1.23459i	0.786733	−	0.617293i	$-0.211771\pi$
$618$		0			0
$619$	−15116.6	−	15116.6i	−0.981565	−	0.981565i	0.0182677	−	0.999833i	$-0.494185\pi$
$619$	−15116.6	−	15116.6i	−0.981565	−	0.981565i	−0.999833	+	0.0182677i	$0.994185\pi$
$620$	−2914.73	−	4204.36i	−0.188804	−	0.272340i
$621$		0			0
$622$	−220.553	+	2454.83i	−0.0142176	+	0.158247i
$623$	6541.15			0.420651
$624$		0			0
$625$	−1204.57			−0.0770926
$626$	−889.648	+	9902.09i	−0.0568011	+	0.632216i
$627$		0			0
$628$	−8426.75	+	5841.95i	−0.535452	+	0.371209i
$629$	−14447.7	−	14447.7i	−0.915845	−	0.915845i
$630$		0			0
$631$			9602.80i			0.605834i	0.953017	+	0.302917i	$0.0979605\pi$
$631$			9602.80i			0.605834i	−0.953017	+	0.302917i	$0.902039\pi$
$632$	−17952.6	−	4945.58i	−1.12993	−	0.311273i
$633$		0			0
$634$	−14502.8	+	12111.7i	−0.908487	+	0.758699i
$635$	12229.9	+	12229.9i	0.764297	+	0.764297i
$636$		0			0
$637$	3120.34	−	3120.34i	0.194085	−	0.194085i
$638$	1314.63	+	118.113i	0.0815781	+	0.00732935i
$639$		0			0
$640$	1504.44	+	9432.08i	0.0929194	+	0.582556i
$641$	−4450.84			−0.274256			−0.137128	−	0.990553i	$-0.543787\pi$
$641$	−4450.84			−0.274256			−0.137128	+	0.990553i	$0.543787\pi$
$642$		0			0
$643$	6491.27	−	6491.27i	0.398119	−	0.398119i	−0.479450	−	0.877569i	$-0.659164\pi$
$643$	6491.27	−	6491.27i	0.398119	−	0.398119i	0.877569	+	0.479450i	$0.159164\pi$
$644$	−9431.15	−	1708.46i	−0.577080	−	0.104539i
$645$		0			0
$646$	10274.0	−	8580.05i	0.625734	−	0.522566i
$647$		−	5546.17i		−	0.337005i	−0.985701	−	0.168503i	$-0.946107\pi$
$647$		−	5546.17i		−	0.337005i	0.985701	−	0.168503i	$-0.0538932\pi$
$648$		0			0
$649$			18098.3i			1.09464i
$650$	2355.31	+	2820.31i	0.142127	+	0.170187i
$651$		0			0
$652$	12946.0	−	8974.98i	0.777613	−	0.539091i
$653$	−6327.58	+	6327.58i	−0.379200	+	0.379200i	−0.870813	−	0.491614i	$-0.836407\pi$
$653$	−6327.58	+	6327.58i	−0.379200	+	0.379200i	0.491614	+	0.870813i	$0.336407\pi$
$654$		0			0
$655$	−6133.49			−0.365886
$656$	8093.88	−	21607.0i	0.481727	−	1.28599i
$657$		0			0
$658$	1390.50	−	15476.7i	0.0823820	−	0.916940i
$659$	−15135.2	+	15135.2i	−0.894663	+	0.894663i	−0.994958	−	0.100294i	$-0.968022\pi$
$659$	−15135.2	+	15135.2i	−0.894663	+	0.894663i	0.100294	+	0.994958i	$0.468022\pi$
$660$		0			0
$661$	−23460.1	−	23460.1i	−1.38047	−	1.38047i	−0.843777	−	0.536694i	$-0.819673\pi$
$661$	−23460.1	−	23460.1i	−1.38047	−	1.38047i	−0.536694	−	0.843777i	$-0.680327\pi$
$662$	−4667.12	−	5588.53i	−0.274007	−	0.328103i
$663$		0			0
$664$	−9095.03	+	5166.32i	−0.531560	+	0.301946i
$665$			8782.30i			0.512125i
$666$		0			0
$667$	−502.550	−	502.550i	−0.0291736	−	0.0291736i
$668$	1742.08	−	9616.73i	0.100903	−	0.557009i
$669$		0			0
$670$	−2821.45	−	253.492i	−0.162690	−	0.0146168i
$671$	−29697.4			−1.70858
$672$		0			0
$673$	30638.5			1.75487			0.877436	−	0.479694i	$-0.159252\pi$
$673$	30638.5			1.75487			0.877436	+	0.479694i	$0.159252\pi$
$674$	208.737	+	18.7539i	0.0119292	+	0.00107177i
$675$		0			0
$676$	−2770.59	+	15294.4i	−0.157635	+	0.870184i
$677$	12468.9	+	12468.9i	0.707855	+	0.707855i	0.966084	−	0.258229i	$-0.0831388\pi$
$677$	12468.9	+	12468.9i	0.707855	+	0.707855i	−0.258229	+	0.966084i	$0.583139\pi$
$678$		0			0
$679$		−	3754.41i		−	0.212196i
$680$	6522.33	+	11482.2i	0.367823	+	0.647533i
$681$		0			0
$682$	5554.45	+	6651.05i	0.311864	+	0.373434i
$683$	−13838.5	−	13838.5i	−0.775280	−	0.775280i	0.203744	−	0.979024i	$-0.434689\pi$
$683$	−13838.5	−	13838.5i	−0.775280	−	0.775280i	−0.979024	+	0.203744i	$0.934689\pi$
$684$		0			0
$685$	−11713.1	+	11713.1i	−0.653333	+	0.653333i
$686$	−416.914	+	4640.40i	−0.0232039	+	0.258267i
$687$		0			0
$688$	−3757.58	−	8258.89i	−0.208221	−	0.457656i
$689$	−3961.95			−0.219068
$690$		0			0
$691$	−106.012	+	106.012i	−0.00583628	+	0.00583628i	−0.710019	−	0.704183i	$-0.751314\pi$
$691$	−106.012	+	106.012i	−0.00583628	+	0.00583628i	0.704183	+	0.710019i	$0.251314\pi$
$692$	5238.60	−	3631.73i	0.287777	−	0.199505i
$693$		0			0
$694$	−5391.37	−	6455.77i	−0.294890	−	0.353109i
$695$		−	10129.8i		−	0.552870i
$696$		0			0
$697$		−	31900.4i		−	1.73359i
$698$	−20302.6	+	16955.2i	−1.10095	+	0.919434i
$699$		0			0
$700$	15972.4	+	2893.43i	0.862431	+	0.156231i
$701$	−7839.35	+	7839.35i	−0.422380	+	0.422380i	−0.886022	−	0.463643i	$-0.846542\pi$
$701$	−7839.35	+	7839.35i	−0.422380	+	0.422380i	0.463643	+	0.886022i	$0.346542\pi$
$702$		0			0
$703$	−12350.0			−0.662574
$704$	−3967.64	−	15684.1i	−0.212409	−	0.839653i
$705$		0			0
$706$	−6245.17	−	561.095i	−0.332918	−	0.0299109i
$707$	12149.1	−	12149.1i	0.646273	−	0.646273i
$708$		0			0
$709$	2728.30	+	2728.30i	0.144518	+	0.144518i	0.775664	−	0.631146i	$-0.217415\pi$
$709$	2728.30	+	2728.30i	0.144518	+	0.144518i	−0.631146	+	0.775664i	$0.717415\pi$
$710$	−3079.19	+	2571.50i	−0.162760	+	0.135925i
$711$		0			0
$712$	1578.90	−	5731.48i	0.0831066	−	0.301680i
$713$		−	4665.84i		−	0.245073i
$714$		0			0
$715$	2349.01	+	2349.01i	0.122864	+	0.122864i
$716$	20476.0	−	14195.3i	1.06875	−	0.740925i
$717$		0			0
$718$	527.011	−	5865.82i	0.0273926	−	0.304889i
$719$	32717.8			1.69704			0.848519	−	0.529166i	$-0.177495\pi$
$719$	32717.8			1.69704			0.848519	+	0.529166i	$0.177495\pi$
$720$		0			0
$721$	−45824.0			−2.36696
$722$	−1012.01	+	11264.1i	−0.0521652	+	0.580616i
$723$		0			0
$724$	781.844	+	1127.77i	0.0401340	+	0.0578914i
$725$	851.111	+	851.111i	0.0435993	+	0.0435993i
$726$		0			0
$727$		−	25847.2i		−	1.31859i	−0.751883	−	0.659297i	$-0.770854\pi$
$727$		−	25847.2i		−	1.31859i	0.751883	−	0.659297i	$-0.229146\pi$
$728$	−4435.26	−	7808.03i	−0.225799	−	0.397507i
$729$		0			0
$730$	−9573.13	+	7994.75i	−0.485366	+	0.405341i
$731$	−8870.50	−	8870.50i	−0.448820	−	0.448820i
$732$		0			0
$733$	10131.9	−	10131.9i	0.510547	−	0.510547i	−0.404147	−	0.914694i	$-0.632432\pi$
$733$	10131.9	−	10131.9i	0.510547	−	0.510547i	0.914694	+	0.404147i	$0.132432\pi$
$734$	12702.8	+	1141.28i	0.638787	+	0.0573915i
$735$		0			0
$736$	−3773.48	+	7851.36i	−0.188984	+	0.393213i
$737$	4798.27			0.239819
$738$		0			0
$739$	19163.7	−	19163.7i	0.953921	−	0.953921i	−0.0450633	−	0.998984i	$-0.514349\pi$
$739$	19163.7	−	19163.7i	0.953921	−	0.953921i	0.998984	+	0.0450633i	$0.0143490\pi$
$740$	2171.76	−	11988.7i	0.107886	−	0.595558i
$741$		0			0
$742$	−13433.9	+	11219.0i	−0.664656	+	0.555070i
$743$		−	23322.1i		−	1.15155i	−0.817607	−	0.575777i	$-0.804699\pi$
$743$		−	23322.1i		−	1.15155i	0.817607	−	0.575777i	$-0.195301\pi$
$744$		0			0
$745$			21309.8i			1.04796i
$746$	−22208.1	−	26592.5i	−1.08994	−	1.30512i
$747$		0			0
$748$	−12743.6	−	18382.1i	−0.622933	−	0.898552i
$749$	−1977.03	+	1977.03i	−0.0964473	+	0.0964473i
$750$		0			0
$751$	25994.0			1.26303			0.631515	−	0.775364i	$-0.282434\pi$
$751$	25994.0			1.26303			0.631515	+	0.775364i	$0.282434\pi$
$752$	−13225.4	−	4954.16i	−0.641330	−	0.240239i
$753$		0			0
$754$	59.5842	−	663.192i	0.00287789	−	0.0320319i
$755$	−13125.5	+	13125.5i	−0.632698	+	0.632698i
$756$		0			0
$757$	22145.0	+	22145.0i	1.06324	+	1.06324i	0.997860	+	0.0653808i	$0.0208262\pi$
$757$	22145.0	+	22145.0i	1.06324	+	1.06324i	0.0653808	+	0.997860i	$0.479174\pi$
$758$	9031.52	+	10814.6i	0.432770	+	0.518210i
$759$		0			0
$760$	7695.22	+	2119.87i	0.367283	+	0.101179i
$761$			16497.5i			0.785853i	0.919570	+	0.392926i	$0.128537\pi$
$761$			16497.5i			0.785853i	−0.919570	+	0.392926i	$0.871463\pi$
$762$		0			0
$763$	23725.9	+	23725.9i	1.12573	+	1.12573i
$764$	−30918.0	−	5600.84i	−1.46410	−	0.265224i
$765$		0			0
$766$	−8577.66	−	770.656i	−0.404600	−	0.0363511i
$767$	9130.02			0.429812
$768$		0			0
$769$	−24867.3			−1.16611			−0.583055	−	0.812433i	$-0.698143\pi$
$769$	−24867.3			−1.16611			−0.583055	+	0.812433i	$0.698143\pi$
$770$	14616.5	+	1313.21i	0.684082	+	0.0614610i
$771$		0			0
$772$	−25575.9	−	4633.11i	−1.19235	−	0.215996i
$773$	−1881.72	−	1881.72i	−0.0875559	−	0.0875559i	0.661972	−	0.749528i	$-0.269720\pi$
$773$	−1881.72	−	1881.72i	−0.0875559	−	0.0875559i	−0.749528	+	0.661972i	$0.769720\pi$
$774$		0			0
$775$			7902.00i			0.366256i
$776$	−3289.68	−	906.240i	−0.152181	−	0.0419228i
$777$		0			0
$778$	−4955.49	−	5933.84i	−0.228359	−	0.273443i
$779$	−13634.4	−	13634.4i	−0.627089	−	0.627089i
$780$		0			0
$781$	4804.89	−	4804.89i	0.220144	−	0.220144i
$782$	−1077.72	+	11995.4i	−0.0492828	+	0.548535i
$783$		0			0
$784$	−16591.7	−	6215.16i	−0.755815	−	0.283125i
$785$	−8453.54			−0.384356
$786$		0			0
$787$	−7790.94	+	7790.94i	−0.352881	+	0.352881i	−0.861180	−	0.508300i	$-0.830274\pi$
$787$	−7790.94	+	7790.94i	−0.352881	+	0.352881i	0.508300	+	0.861180i	$0.330274\pi$
$788$	−15604.9	−	22509.3i	−0.705457	−	1.01759i
$789$		0			0
$790$	−9840.66	−	11783.5i	−0.443184	−	0.530680i
$791$			17937.2i			0.806286i
$792$		0			0
$793$			14981.4i			0.670877i
$794$	−2064.56	+	1724.17i	−0.0922778	+	0.0770634i
$795$		0			0
$796$	1955.48	−	10794.7i	0.0870730	−	0.480665i
$797$	4209.84	−	4209.84i	0.187102	−	0.187102i	−0.607340	−	0.794442i	$-0.707763\pi$
$797$	4209.84	−	4209.84i	0.187102	−	0.187102i	0.794442	+	0.607340i	$0.207763\pi$
$798$		0			0
$799$	−19525.8			−0.864549
$800$	6390.71	−	13296.9i	0.282432	−	0.587648i
$801$		0			0
$802$	21428.8	+	1925.26i	0.943488	+	0.0847672i
$803$	14938.3	−	14938.3i	0.656490	−	0.656490i
$804$		0			0
$805$	−5587.51	−	5587.51i	−0.244639	−	0.244639i
$806$	3355.25	−	2802.05i	0.146630	−	0.122454i
$807$		0			0
$808$	−7712.73	−	13577.8i	−0.335808	−	0.591172i
$809$			27554.3i			1.19747i	0.800946	+	0.598737i	$0.204330\pi$
$809$			27554.3i			1.19747i	−0.800946	+	0.598737i	$0.795670\pi$
$810$		0			0
$811$	3406.54	+	3406.54i	0.147497	+	0.147497i	0.776999	−	0.629502i	$-0.216741\pi$
$811$	3406.54	+	3406.54i	0.147497	+	0.147497i	−0.629502	+	0.776999i	$0.716741\pi$
$812$	−1675.92	−	2417.43i	−0.0724300	−	0.104477i
$813$		0			0
$814$	−1846.69	+	20554.3i	−0.0795166	+	0.885047i
$815$	12987.1			0.558184
$816$		0			0
$817$	−7582.59			−0.324701
$818$	1260.83	−	14033.5i	0.0538924	−	0.599841i
$819$		0			0
$820$	15633.1	−	10837.8i	0.665770	−	0.461554i
$821$	9839.14	+	9839.14i	0.418256	+	0.418256i	0.884602	−	0.466346i	$-0.154430\pi$
$821$	9839.14	+	9839.14i	0.418256	+	0.418256i	−0.466346	+	0.884602i	$0.654430\pi$
$822$		0			0
$823$			36653.5i			1.55244i	0.630461	+	0.776221i	$0.282866\pi$
$823$			36653.5i			1.55244i	−0.630461	+	0.776221i	$0.717134\pi$
$824$	−11061.0	+	40151.9i	−0.467632	+	1.69752i
$825$		0			0
$826$	30957.5	−	25853.3i	1.30405	−	1.08905i
$827$	22223.2	+	22223.2i	0.934431	+	0.934431i	0.997979	−	0.0635475i	$-0.0202414\pi$
$827$	22223.2	+	22223.2i	0.934431	+	0.934431i	−0.0635475	+	0.997979i	$0.520241\pi$
$828$		0			0
$829$	14715.5	−	14715.5i	0.616516	−	0.616516i	−0.328120	−	0.944636i	$-0.606415\pi$
$829$	14715.5	−	14715.5i	0.616516	−	0.616516i	0.944636	+	0.328120i	$0.106415\pi$
$830$	−8588.98	−	771.672i	−0.359190	−	0.0322713i
$831$		0			0
$832$	−7912.13	+	2001.55i	−0.329692	+	0.0834031i
$833$	−24495.8			−1.01888
$834$		0			0
$835$	5697.46	−	5697.46i	0.236130	−	0.236130i
$836$	−13303.3	−	2409.91i	−0.550364	−	0.0996991i
$837$		0			0
$838$	10541.1	−	8803.12i	0.434530	−	0.362886i
$839$		−	11010.0i		−	0.453050i	−0.974005	−	0.226525i	$-0.927263\pi$
$839$		−	11010.0i		−	0.453050i	0.974005	−	0.226525i	$-0.0727365\pi$
$840$		0			0
$841$			24170.9i			0.991057i
$842$	20444.5	+	24480.8i	0.836773	+	1.00197i
$843$		0			0
$844$	−15067.2	+	10445.5i	−0.614496	+	0.426007i
$845$	−9061.20	+	9061.20i	−0.368893	+	0.368893i
$846$		0			0
$847$	8279.85			0.335890
$848$	6587.61	+	14479.1i	0.266768	+	0.586338i
$849$		0			0
$850$	1825.21	−	20315.2i	0.0736520	−	0.819772i
$851$	7857.37	−	7857.37i	0.316507	−	0.316507i
$852$		0			0
$853$	12809.9	+	12809.9i	0.514190	+	0.514190i	0.915808	−	0.401617i	$-0.131552\pi$
$853$	12809.9	+	12809.9i	0.514190	+	0.514190i	−0.401617	+	0.915808i	$0.631552\pi$
$854$	42422.7	+	50798.0i	1.69985	+	2.03545i
$855$		0			0
$856$	1255.09	+	2209.52i	0.0501147	+	0.0882243i
$857$		−	38510.8i		−	1.53501i	−0.641043	−	0.767505i	$-0.721498\pi$
$857$		−	38510.8i		−	1.53501i	0.641043	−	0.767505i	$-0.278502\pi$
$858$		0			0
$859$	23234.6	+	23234.6i	0.922882	+	0.922882i	0.997232	−	0.0743503i	$-0.0236883\pi$
$859$	23234.6	+	23234.6i	0.922882	+	0.922882i	−0.0743503	+	0.997232i	$0.523688\pi$
$860$	1333.41	−	7360.74i	0.0528707	−	0.291860i
$861$		0			0
$862$	−13522.4	−	1214.92i	−0.534311	−	0.0480049i
$863$	22079.5			0.870911			0.435456	−	0.900210i	$-0.356587\pi$
$863$	22079.5			0.870911			0.435456	+	0.900210i	$0.356587\pi$
$864$		0			0
$865$	5255.26			0.206571
$866$	17585.1	+	1579.93i	0.690031	+	0.0619955i
$867$		0			0
$868$	3442.24	−	19002.0i	0.134605	−	0.743054i
$869$	18387.4	+	18387.4i	0.717779	+	0.717779i
$870$		0			0
$871$		−	2420.58i		−	0.0941656i
$872$	26516.0	−	15062.1i	1.02975	−	0.584939i
$873$		0			0
$874$	4666.26	+	5587.51i	0.180593	+	0.216247i
$875$	23976.7	+	23976.7i	0.926356	+	0.926356i
$876$		0			0
$877$	4082.13	−	4082.13i	0.157176	−	0.157176i	−0.624138	−	0.781314i	$-0.714550\pi$
$877$	4082.13	−	4082.13i	0.157176	−	0.157176i	0.781314	+	0.624138i	$0.214550\pi$
$878$	1247.59	−	13886.2i	0.0479547	−	0.533753i
$879$		0			0
$880$	4678.80	−	12490.3i	0.179230	−	0.478463i
$881$	−7132.59			−0.272762			−0.136381	−	0.990656i	$-0.543547\pi$
$881$	−7132.59			−0.272762			−0.136381	+	0.990656i	$0.543547\pi$
$882$		0			0
$883$	19170.0	−	19170.0i	0.730601	−	0.730601i	−0.240138	−	0.970739i	$-0.577193\pi$
$883$	19170.0	−	19170.0i	0.730601	−	0.730601i	0.970739	+	0.240138i	$0.0771926\pi$
$884$	−9273.21	+	6428.78i	−0.352819	+	0.244596i
$885$		0			0
$886$	19667.4	+	23550.3i	0.745757	+	0.892989i
$887$			45045.7i			1.70517i	0.522589	+	0.852585i	$0.324966\pi$
$887$			45045.7i			1.70517i	−0.522589	+	0.852585i	$0.675034\pi$
$888$		0			0
$889$			65287.3i			2.46306i
$890$	3761.94	−	3141.69i	0.141686	−	0.118325i
$891$		0			0
$892$	−3303.17	−	598.374i	−0.123989	−	0.0224608i
$893$	−8345.43	+	8345.43i	−0.312731	+	0.312731i
$894$		0			0
$895$	20541.1			0.767167
$896$	−21160.2	+	29191.4i	−0.788964	+	1.08841i
$897$		0			0
$898$	32439.2	+	2914.49i	1.20547	+	0.108305i
$899$	1012.55	−	1012.55i	0.0375643	−	0.0375643i
$900$		0			0
$901$	15551.4	+	15551.4i	0.575017	+	0.575017i
$902$	−24730.6	+	20653.2i	−0.912905	+	0.762389i
$903$		0			0
$904$	15716.9	+	4329.68i	0.578247	+	0.159295i
$905$			1131.36i			0.0415554i
$906$		0			0
$907$	−33658.2	−	33658.2i	−1.23220	−	1.23220i	−0.963118	−	0.269079i	$-0.913281\pi$
$907$	−33658.2	−	33658.2i	−1.23220	−	1.23220i	−0.269079	−	0.963118i	$-0.586719\pi$
$908$	19838.3	−	13753.2i	0.725065	−	0.502661i
$909$		0			0
$910$	662.476	−	7373.59i	0.0241328	−	0.268607i
$911$	42503.8			1.54579			0.772895	−	0.634534i	$-0.218808\pi$
$911$	42503.8			1.54579			0.772895	+	0.634534i	$0.218808\pi$
$912$		0			0
$913$	14606.7			0.529477
$914$	1222.44	−	13606.2i	0.0442394	−	0.492399i
$915$		0			0
$916$	−10148.5	−	14638.7i	−0.366066	−	0.528033i
$917$	−16371.3	−	16371.3i	−0.589562	−	0.589562i
$918$		0			0
$919$		−	8819.41i		−	0.316568i	−0.987394	−	0.158284i	$-0.949404\pi$
$919$		−	8819.41i		−	0.316568i	0.987394	−	0.158284i	$-0.0505961\pi$
$920$	−6244.60	+	3547.17i	−0.223781	+	0.127116i
$921$		0			0
$922$	−25377.5	+	21193.3i	−0.906467	+	0.757012i
$923$	−2423.92	−	2423.92i	−0.0864402	−	0.0864402i
$924$		0			0
$925$	−13307.1	+	13307.1i	−0.473012	+	0.473012i
$926$	−14209.0	−	1276.60i	−0.504250	−	0.0453041i
$927$		0			0
$928$	−2522.73	+	884.950i	−0.0892380	+	0.0313038i
$929$	14155.6			0.499925			0.249963	−	0.968256i	$-0.419582\pi$
$929$	14155.6			0.499925			0.249963	+	0.968256i	$0.419582\pi$
$930$		0			0
$931$	−10469.6	+	10469.6i	−0.368558	+	0.368558i
$932$	−1703.87	+	9405.80i	−0.0598844	+	0.330577i
$933$		0			0
$934$	−38189.4	+	31892.9i	−1.33790	+	1.11731i
$935$		−	18440.6i		−	0.644996i
$936$		0			0
$937$		−	38518.7i		−	1.34296i	−0.741023	−	0.671479i	$-0.765659\pi$
$937$		−	38518.7i		−	1.34296i	0.741023	−	0.671479i	$-0.234341\pi$
$938$	−6854.32	−	8207.55i	−0.238594	−	0.285699i
$939$		0			0
$940$	−6633.71	−	9568.82i	−0.230179	−	0.332022i
$941$	−27998.2	+	27998.2i	−0.969942	+	0.969942i	−0.999561	−	0.0296196i	$-0.990570\pi$
$941$	−27998.2	+	27998.2i	−0.969942	+	0.969942i	0.0296196	+	0.999561i	$0.490570\pi$
$942$		0			0
$943$	17349.0			0.599112
$944$	−15180.7	−	33366.0i	−0.523399	−	1.15039i
$945$		0			0
$946$	−1133.82	+	12619.8i	−0.0389680	+	0.433727i
$947$	32839.5	−	32839.5i	1.12687	−	1.12687i	0.136181	−	0.990684i	$-0.456517\pi$
$947$	32839.5	−	32839.5i	1.12687	−	1.12687i	0.990684	−	0.136181i	$-0.0434829\pi$
$948$		0			0
$949$	−7535.92	−	7535.92i	−0.257773	−	0.257773i
$950$	−7902.71	−	9462.92i	−0.269892	−	0.323176i
$951$		0			0
$952$	−13238.7	+	48057.1i	−0.450704	+	1.63607i
$953$			20600.1i			0.700211i	0.936710	+	0.350106i	$0.113854\pi$
$953$			20600.1i			0.700211i	−0.936710	+	0.350106i	$0.886146\pi$
$954$		0			0
$955$	−18317.5	−	18317.5i	−0.620670	−	0.620670i
$956$	33384.9	+	6047.72i	1.12944	+	0.204600i
$957$		0			0
$958$	−36790.3	−	3305.41i	−1.24075	−	0.111475i
$959$	−62528.2			−2.10547
$960$		0			0
$961$	−20390.2			−0.684441
$962$	10369.0	+	931.599i	0.347516	+	0.0312224i
$963$		0			0
$964$	−43855.8	−	7944.53i	−1.46525	−	0.265432i
$965$	−15152.5	−	15152.5i	−0.505469	−	0.505469i
$966$		0			0
$967$			38210.9i			1.27071i	0.772219	+	0.635356i	$0.219147\pi$
$967$			38210.9i			1.27071i	−0.772219	+	0.635356i	$0.780853\pi$
$968$	1998.59	−	7254.96i	0.0663607	−	0.240892i
$969$		0			0
$970$	−1803.23	−	2159.23i	−0.0596888	−	0.0714730i
$971$	−37224.9	−	37224.9i	−1.23028	−	1.23028i	−0.963855	−	0.266427i	$-0.914157\pi$
$971$	−37224.9	−	37224.9i	−1.23028	−	1.23028i	−0.266427	−	0.963855i	$-0.585843\pi$
$972$		0			0
$973$	27038.1	−	27038.1i	0.890854	−	0.890854i
$974$	3935.51	−	43803.6i	0.129468	−	1.44102i
$975$		0			0
$976$	54750.2	−	24909.9i	1.79560	−	0.816953i
$977$	−7985.95			−0.261508			−0.130754	−	0.991415i	$-0.541740\pi$
$977$	−7985.95			−0.261508			−0.130754	+	0.991415i	$0.541740\pi$
$978$		0			0
$979$	−5870.28	+	5870.28i	−0.191639	+	0.191639i
$980$	−8322.21	−	12004.4i	−0.271269	−	0.391292i
$981$		0			0
$982$	22122.9	+	26490.5i	0.718910	+	0.860842i
$983$			10703.1i			0.347279i	0.984809	+	0.173639i	$0.0555527\pi$
$983$			10703.1i			0.347279i	−0.984809	+	0.173639i	$0.944447\pi$
$984$		0			0
$985$		−	22580.9i		−	0.730442i
$986$	−2837.03	+	2369.27i	−0.0916322	+	0.0765243i
$987$		0			0
$988$	−1215.72	+	6711.10i	−0.0391471	+	0.216102i
$989$	4824.23	−	4824.23i	0.155108	−	0.155108i
$990$		0			0
$991$	−23945.4			−0.767558			−0.383779	−	0.923425i	$-0.625377\pi$
$991$	−23945.4			−0.767558			−0.383779	+	0.923425i	$0.625377\pi$
$992$	−15819.0	−	7602.87i	−0.506306	−	0.243338i
$993$		0			0
$994$	−15082.6	−	1355.09i	−0.481280	−	0.0432404i
$995$	6395.37	−	6395.37i	0.203766	−	0.203766i
$996$		0			0
$997$	−14292.5	−	14292.5i	−0.454010	−	0.454010i	0.442673	−	0.896683i	$-0.354030\pi$
$997$	−14292.5	−	14292.5i	−0.454010	−	0.454010i	−0.896683	+	0.442673i	$0.854030\pi$
$998$	5318.83	−	4441.88i	0.168702	−	0.140887i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.4.k.a.37.5		10
3.2	odd	2		16.4.e.a.5.1	✓	10
4.3	odd	2		576.4.k.a.433.4		10
12.11	even	2		64.4.e.a.49.1		10
16.3	odd	4		576.4.k.a.145.4		10
16.13	even	4	inner	144.4.k.a.109.5		10
24.5	odd	2		128.4.e.b.97.1		10
24.11	even	2		128.4.e.a.97.5		10
48.5	odd	4		128.4.e.b.33.1		10
48.11	even	4		128.4.e.a.33.5		10
48.29	odd	4		16.4.e.a.13.1	yes	10
48.35	even	4		64.4.e.a.17.1		10
96.5	odd	8		1024.4.b.j.513.9		10
96.11	even	8		1024.4.b.k.513.9		10
96.29	odd	8		1024.4.a.n.1.9		10
96.35	even	8		1024.4.a.m.1.2		10
96.53	odd	8		1024.4.b.j.513.2		10
96.59	even	8		1024.4.b.k.513.2		10
96.77	odd	8		1024.4.a.n.1.2		10
96.83	even	8		1024.4.a.m.1.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.4.e.a.5.1	✓	10	3.2	odd	2
16.4.e.a.13.1	yes	10	48.29	odd	4
64.4.e.a.17.1		10	48.35	even	4
64.4.e.a.49.1		10	12.11	even	2
128.4.e.a.33.5		10	48.11	even	4
128.4.e.a.97.5		10	24.11	even	2
128.4.e.b.33.1		10	48.5	odd	4
128.4.e.b.97.1		10	24.5	odd	2
144.4.k.a.37.5		10	1.1	even	1	trivial
144.4.k.a.109.5		10	16.13	even	4	inner
576.4.k.a.145.4		10	16.3	odd	4
576.4.k.a.433.4		10	4.3	odd	2
1024.4.a.m.1.2		10	96.35	even	8
1024.4.a.m.1.9		10	96.83	even	8
1024.4.a.n.1.2		10	96.77	odd	8
1024.4.a.n.1.9		10	96.29	odd	8
1024.4.b.j.513.2		10	96.53	odd	8
1024.4.b.j.513.9		10	96.5	odd	8
1024.4.b.k.513.2		10	96.59	even	8
1024.4.b.k.513.9		10	96.11	even	8

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	144.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.81708 + 0.253099i) q^{2} +(7.87188 + 1.42600i) q^{4} +(4.66372 + 4.66372i) q^{5} +24.8965i q^{7} +(21.8148 + 6.00953i) q^{8} +O(q^{10})\)	\(q+(2.81708 + 0.253099i) q^{2} +(7.87188 + 1.42600i) q^{4} +(4.66372 + 4.66372i) q^{5} +24.8965i q^{7} +(21.8148 + 6.00953i) q^{8} +(11.9577 + 14.3185i) q^{10} +(-22.3431 - 22.3431i) q^{11} +(-11.2714 + 11.2714i) q^{13} +(-6.30129 + 70.1355i) q^{14} +(59.9330 + 22.4506i) q^{16} +88.4846 q^{17} +(37.8187 - 37.8187i) q^{19} +(30.0618 + 43.3627i) q^{20} +(-57.2873 - 68.5974i) q^{22} +48.1224i q^{23} -81.4994i q^{25} +(-34.6053 + 28.8997i) q^{26} +(-35.5025 + 195.982i) q^{28} +(-10.4432 + 10.4432i) q^{29} -96.9578 q^{31} +(163.154 + 78.4142i) q^{32} +(249.268 + 22.3954i) q^{34} +(-116.110 + 116.110i) q^{35} +(-163.279 - 163.279i) q^{37} +(116.110 - 96.9665i) q^{38} +(73.7114 + 129.765i) q^{40} -360.519i q^{41} +(-100.249 - 100.249i) q^{43} +(-144.021 - 207.744i) q^{44} +(-12.1797 + 135.565i) q^{46} -220.669 q^{47} -276.837 q^{49} +(20.6274 - 229.590i) q^{50} +(-104.800 + 72.6542i) q^{52} +(175.752 + 175.752i) q^{53} -208.404i q^{55} +(-149.616 + 543.113i) q^{56} +(-32.0624 + 26.7761i) q^{58} +(-405.008 - 405.008i) q^{59} +(664.576 - 664.576i) q^{61} +(-273.138 - 24.5399i) q^{62} +(439.771 + 262.193i) q^{64} -105.133 q^{65} +(-107.377 + 107.377i) q^{67} +(696.540 + 126.179i) q^{68} +(-356.480 + 297.705i) q^{70} +215.050i q^{71} +668.587i q^{73} +(-418.644 - 501.296i) q^{74} +(351.634 - 243.775i) q^{76} +(556.266 - 556.266i) q^{77} -822.956 q^{79} +(174.808 + 384.215i) q^{80} +(91.2471 - 1015.61i) q^{82} +(-326.873 + 326.873i) q^{83} +(412.668 + 412.668i) q^{85} +(-257.037 - 307.783i) q^{86} +(-353.139 - 621.682i) q^{88} -262.733i q^{89} +(-280.619 - 280.619i) q^{91} +(-68.6226 + 378.814i) q^{92} +(-621.643 - 55.8512i) q^{94} +352.752 q^{95} -150.801 q^{97} +(-779.871 - 70.0671i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 8 q^{4} + 2 q^{5} + 44 q^{8}+O(q^{10}) \) 10 * q + 2 * q^2 + 8 * q^4 + 2 * q^5 + 44 * q^8	\( 10 q + 2 q^{2} + 8 q^{4} + 2 q^{5} + 44 q^{8} - 68 q^{10} - 18 q^{11} - 2 q^{13} - 188 q^{14} + 280 q^{16} + 4 q^{17} - 26 q^{19} + 196 q^{20} - 588 q^{22} + 264 q^{26} + 280 q^{28} + 202 q^{29} + 368 q^{31} - 968 q^{32} + 436 q^{34} - 476 q^{35} - 10 q^{37} + 1232 q^{38} - 1336 q^{40} - 838 q^{43} - 868 q^{44} + 1132 q^{46} + 944 q^{47} + 94 q^{49} - 726 q^{50} - 236 q^{52} + 378 q^{53} + 488 q^{56} + 8 q^{58} - 1706 q^{59} + 910 q^{61} + 80 q^{62} + 512 q^{64} + 492 q^{65} + 1942 q^{67} + 880 q^{68} + 160 q^{70} + 452 q^{74} - 1228 q^{76} + 268 q^{77} - 4416 q^{79} + 2648 q^{80} - 704 q^{82} + 2562 q^{83} - 12 q^{85} - 3764 q^{86} + 1528 q^{88} + 3332 q^{91} - 632 q^{92} - 3248 q^{94} - 6900 q^{95} - 4 q^{97} - 314 q^{98}+O(q^{100}) \) 10 * q + 2 * q^2 + 8 * q^4 + 2 * q^5 + 44 * q^8 - 68 * q^10 - 18 * q^11 - 2 * q^13 - 188 * q^14 + 280 * q^16 + 4 * q^17 - 26 * q^19 + 196 * q^20 - 588 * q^22 + 264 * q^26 + 280 * q^28 + 202 * q^29 + 368 * q^31 - 968 * q^32 + 436 * q^34 - 476 * q^35 - 10 * q^37 + 1232 * q^38 - 1336 * q^40 - 838 * q^43 - 868 * q^44 + 1132 * q^46 + 944 * q^47 + 94 * q^49 - 726 * q^50 - 236 * q^52 + 378 * q^53 + 488 * q^56 + 8 * q^58 - 1706 * q^59 + 910 * q^61 + 80 * q^62 + 512 * q^64 + 492 * q^65 + 1942 * q^67 + 880 * q^68 + 160 * q^70 + 452 * q^74 - 1228 * q^76 + 268 * q^77 - 4416 * q^79 + 2648 * q^80 - 704 * q^82 + 2562 * q^83 - 12 * q^85 - 3764 * q^86 + 1528 * q^88 + 3332 * q^91 - 632 * q^92 - 3248 * q^94 - 6900 * q^95 - 4 * q^97 - 314 * q^98

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