LMFDB - Embedded newform 243.3.f.c.215.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,3,Mod(26,243)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(18))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("243.26");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	243.f (of order $18$, degree $6$, not 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:	$6.62127042396$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			215.2
Character	$\chi$	$=$	243.215
Dual form			243.3.f.c.26.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28330 + 0.226280i) q^{2} +(-2.16313 + 0.787313i) q^{4} +(0.280917 - 0.334784i) q^{5} +(5.71727 + 2.08092i) q^{7} +(7.11182 - 4.10601i) q^{8} +O(q^{10})$	\(q+(-1.28330 + 0.226280i) q^{2} +(-2.16313 + 0.787313i) q^{4} +(0.280917 - 0.334784i) q^{5} +(5.71727 + 2.08092i) q^{7} +(7.11182 - 4.10601i) q^{8} +(-0.284745 + 0.493192i) q^{10} +(-9.75958 - 11.6310i) q^{11} +(-1.65807 + 9.40337i) q^{13} +(-7.80781 - 1.37673i) q^{14} +(-1.14388 + 0.959828i) q^{16} +(4.20474 + 2.42761i) q^{17} +(17.7795 + 30.7949i) q^{19} +(-0.344079 + 0.945348i) q^{20} +(15.1563 + 12.7176i) q^{22} +(9.28414 + 25.5080i) q^{23} +(4.30804 + 24.4321i) q^{25} -12.4425i q^{26} -14.0055 q^{28} +(21.0632 - 3.71401i) q^{29} +(15.5752 - 5.66890i) q^{31} +(-19.8636 + 23.6725i) q^{32} +(-5.94524 - 2.16389i) q^{34} +(2.30273 - 1.32948i) q^{35} +(5.31270 - 9.20187i) q^{37} +(-29.7846 - 35.4959i) q^{38} +(0.623204 - 3.53437i) q^{40} +(21.7250 + 3.83071i) q^{41} +(-4.26098 + 3.57539i) q^{43} +(30.2685 + 17.4755i) q^{44} +(-17.6862 - 30.6334i) q^{46} +(-29.5345 + 81.1452i) q^{47} +(-9.17924 - 7.70230i) q^{49} +(-11.0570 - 30.3788i) q^{50} +(-3.81679 - 21.6461i) q^{52} +31.9927i q^{53} -6.63550 q^{55} +(49.2044 - 8.67607i) q^{56} +(-26.1899 + 9.53235i) q^{58} +(34.9066 - 41.6001i) q^{59} +(30.7427 + 11.1894i) q^{61} +(-18.7048 + 10.7992i) q^{62} +(23.1207 - 40.0463i) q^{64} +(2.68231 + 3.19666i) q^{65} +(0.489287 - 2.77488i) q^{67} +(-11.0067 - 1.94077i) q^{68} +(-2.65425 + 2.22718i) q^{70} +(-100.126 - 57.8080i) q^{71} +(1.01468 + 1.75747i) q^{73} +(-4.73557 + 13.0109i) q^{74} +(-62.7045 - 52.6153i) q^{76} +(-31.5950 - 86.8065i) q^{77} +(-12.8431 - 72.8366i) q^{79} +0.652583i q^{80} -28.7465 q^{82} +(121.842 - 21.4840i) q^{83} +(1.99390 - 0.725722i) q^{85} +(4.65906 - 5.55245i) q^{86} +(-117.166 - 42.6448i) q^{88} +(-31.0149 + 17.9065i) q^{89} +(-29.0472 + 50.3113i) q^{91} +(-40.1655 - 47.8674i) q^{92} +(19.5399 - 110.816i) q^{94} +(15.3042 + 2.69854i) q^{95} +(61.5608 - 51.6556i) q^{97} +(13.5226 + 7.80725i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} + 3 q^{4} - 6 q^{5} + 3 q^{7} - 9 q^{8}+O(q^{10}) $ 30 * q + 3 * q^2 + 3 * q^4 - 6 * q^5 + 3 * q^7 - 9 * q^8	$ 30 q + 3 q^{2} + 3 q^{4} - 6 q^{5} + 3 q^{7} - 9 q^{8} - 3 q^{10} - 51 q^{11} + 3 q^{13} + 129 q^{14} - 9 q^{16} - 9 q^{17} - 3 q^{19} - 30 q^{20} - 33 q^{22} - 168 q^{23} - 6 q^{25} - 12 q^{28} + 246 q^{29} + 48 q^{31} + 117 q^{32} + 99 q^{34} - 252 q^{35} - 3 q^{37} - 237 q^{38} + 201 q^{40} + 129 q^{41} + 183 q^{43} + 639 q^{44} - 3 q^{46} - 348 q^{47} + 147 q^{49} - 471 q^{50} + 45 q^{52} - 12 q^{55} + 570 q^{56} - 267 q^{58} + 426 q^{59} - 285 q^{61} - 900 q^{62} - 51 q^{64} - 213 q^{65} - 366 q^{67} + 378 q^{68} - 483 q^{70} + 315 q^{71} - 66 q^{73} + 159 q^{74} - 201 q^{76} - 654 q^{77} - 15 q^{79} - 12 q^{82} + 624 q^{83} + 18 q^{85} - 411 q^{86} + 51 q^{88} + 72 q^{89} + 96 q^{91} - 561 q^{92} - 96 q^{94} - 75 q^{95} - 114 q^{97} + 882 q^{98}+O(q^{100}) $ 30 * q + 3 * q^2 + 3 * q^4 - 6 * q^5 + 3 * q^7 - 9 * q^8 - 3 * q^10 - 51 * q^11 + 3 * q^13 + 129 * q^14 - 9 * q^16 - 9 * q^17 - 3 * q^19 - 30 * q^20 - 33 * q^22 - 168 * q^23 - 6 * q^25 - 12 * q^28 + 246 * q^29 + 48 * q^31 + 117 * q^32 + 99 * q^34 - 252 * q^35 - 3 * q^37 - 237 * q^38 + 201 * q^40 + 129 * q^41 + 183 * q^43 + 639 * q^44 - 3 * q^46 - 348 * q^47 + 147 * q^49 - 471 * q^50 + 45 * q^52 - 12 * q^55 + 570 * q^56 - 267 * q^58 + 426 * q^59 - 285 * q^61 - 900 * q^62 - 51 * q^64 - 213 * q^65 - 366 * q^67 + 378 * q^68 - 483 * q^70 + 315 * q^71 - 66 * q^73 + 159 * q^74 - 201 * q^76 - 654 * q^77 - 15 * q^79 - 12 * q^82 + 624 * q^83 + 18 * q^85 - 411 * q^86 + 51 * q^88 + 72 * q^89 + 96 * q^91 - 561 * q^92 - 96 * q^94 - 75 * q^95 - 114 * q^97 + 882 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{18}\right)$

Coefficient data

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

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

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

$2$	−1.28330	+	0.226280i	−0.641648	+	0.113140i	−0.484999	−	0.874515i	$-0.661180\pi$
$2$	−1.28330	+	0.226280i	−0.641648	+	0.113140i	−0.156649	+	0.987654i	$0.550069\pi$
$3$		0			0
$3$		0			0
$4$	−2.16313	+	0.787313i	−0.540781	+	0.196828i
$5$	0.280917	−	0.334784i	0.0561833	−	0.0669567i	−0.737221	−	0.675652i	$-0.763862\pi$
$5$	0.280917	−	0.334784i	0.0561833	−	0.0669567i	0.793404	+	0.608695i	$0.208307\pi$
$6$		0			0
$7$	5.71727	+	2.08092i	0.816752	+	0.297274i	0.716410	−	0.697679i	$-0.245784\pi$
$7$	5.71727	+	2.08092i	0.816752	+	0.297274i	0.100342	+	0.994953i	$0.468006\pi$
$8$	7.11182	−	4.10601i	0.888978	−	0.513251i
$9$		0			0
$10$	−0.284745	+	0.493192i	−0.0284745	+	0.0493192i
$11$	−9.75958	−	11.6310i	−0.887235	−	1.05737i	−0.997981	−	0.0635167i	$-0.979768\pi$
$11$	−9.75958	−	11.6310i	−0.887235	−	1.05737i	0.110746	−	0.993849i	$-0.464676\pi$
$12$		0			0
$13$	−1.65807	+	9.40337i	−0.127544	+	0.723336i	0.852221	+	0.523182i	$0.175255\pi$
$13$	−1.65807	+	9.40337i	−0.127544	+	0.723336i	−0.979765	+	0.200154i	$0.935856\pi$
$14$	−7.80781	−	1.37673i	−0.557701	−	0.0983377i
$15$		0			0
$16$	−1.14388	+	0.959828i	−0.0714924	+	0.0599892i
$17$	4.20474	+	2.42761i	0.247338	+	0.142800i	0.618545	−	0.785750i	$-0.287723\pi$
$17$	4.20474	+	2.42761i	0.247338	+	0.142800i	−0.371207	+	0.928550i	$0.621056\pi$
$18$		0			0
$19$	17.7795	+	30.7949i	0.935761	+	1.62079i	0.773271	+	0.634075i	$0.218619\pi$
$19$	17.7795	+	30.7949i	0.935761	+	1.62079i	0.162490	+	0.986710i	$0.448048\pi$
$20$	−0.344079	+	0.945348i	−0.0172039	+	0.0472674i
$21$		0			0
$22$	15.1563	+	12.7176i	0.688923	+	0.578075i
$23$	9.28414	+	25.5080i	0.403658	+	1.10904i	0.960465	+	0.278400i	$0.0898041\pi$
$23$	9.28414	+	25.5080i	0.403658	+	1.10904i	−0.556807	+	0.830642i	$0.687974\pi$
$24$		0			0
$25$	4.30804	+	24.4321i	0.172322	+	0.977284i
$26$		−	12.4425i		−	0.478557i
$27$		0			0
$28$	−14.0055			−0.500196
$29$	21.0632	−	3.71401i	0.726318	−	0.128069i	0.201749	−	0.979437i	$-0.435338\pi$
$29$	21.0632	−	3.71401i	0.726318	−	0.128069i	0.524569	+	0.851368i	$0.324226\pi$
$30$		0			0
$31$	15.5752	−	5.66890i	0.502425	−	0.182868i	−0.0783594	−	0.996925i	$-0.524968\pi$
$31$	15.5752	−	5.66890i	0.502425	−	0.182868i	0.580784	+	0.814057i	$0.302746\pi$
$32$	−19.8636	+	23.6725i	−0.620738	+	0.739766i
$33$		0			0
$34$	−5.94524	−	2.16389i	−0.174860	−	0.0636438i
$35$	2.30273	−	1.32948i	0.0657924	−	0.0379852i
$36$		0			0
$37$	5.31270	−	9.20187i	0.143587	−	0.248699i	−0.785258	−	0.619168i	$-0.787470\pi$
$37$	5.31270	−	9.20187i	0.143587	−	0.248699i	0.928845	+	0.370469i	$0.120803\pi$
$38$	−29.7846	−	35.4959i	−0.783804	−	0.934102i
$39$		0			0
$40$	0.623204	−	3.53437i	0.0155801	−	0.0883592i
$41$	21.7250	+	3.83071i	0.529879	+	0.0934320i	0.432186	−	0.901785i	$-0.357742\pi$
$41$	21.7250	+	3.83071i	0.529879	+	0.0934320i	0.0976933	+	0.995217i	$0.468854\pi$
$42$		0			0
$43$	−4.26098	+	3.57539i	−0.0990926	+	0.0831485i	−0.690988	−	0.722866i	$-0.742824\pi$
$43$	−4.26098	+	3.57539i	−0.0990926	+	0.0831485i	0.591895	+	0.806015i	$0.298380\pi$
$44$	30.2685	+	17.4755i	0.687920	+	0.397171i
$45$		0			0
$46$	−17.6862	−	30.6334i	−0.384483	−	0.665945i
$47$	−29.5345	+	81.1452i	−0.628393	+	1.72649i	0.0570536	+	0.998371i	$0.481829\pi$
$47$	−29.5345	+	81.1452i	−0.628393	+	1.72649i	−0.685446	+	0.728123i	$0.740393\pi$
$48$		0			0
$49$	−9.17924	−	7.70230i	−0.187331	−	0.157190i
$50$	−11.0570	−	30.3788i	−0.221139	−	0.607576i
$51$		0			0
$52$	−3.81679	−	21.6461i	−0.0733998	−	0.416271i
$53$			31.9927i			0.603635i	0.953366	+	0.301818i	$0.0975934\pi$
$53$			31.9927i			0.603635i	−0.953366	+	0.301818i	$0.902407\pi$
$54$		0			0
$55$	−6.63550			−0.120646
$56$	49.2044	−	8.67607i	0.878651	−	0.154930i
$57$		0			0
$58$	−26.1899	+	9.53235i	−0.451550	+	0.164351i
$59$	34.9066	−	41.6001i	0.591638	−	0.705087i	−0.384282	−	0.923216i	$-0.625551\pi$
$59$	34.9066	−	41.6001i	0.591638	−	0.705087i	0.975920	+	0.218129i	$0.0699954\pi$
$60$		0			0
$61$	30.7427	+	11.1894i	0.503979	+	0.183433i	0.581483	−	0.813559i	$-0.302473\pi$
$61$	30.7427	+	11.1894i	0.503979	+	0.183433i	−0.0775038	+	0.996992i	$0.524695\pi$
$62$	−18.7048	+	10.7992i	−0.301690	+	0.174181i
$63$		0			0
$64$	23.1207	−	40.0463i	0.361261	−	0.625723i
$65$	2.68231	+	3.19666i	0.0412664	+	0.0491793i
$66$		0			0
$67$	0.489287	−	2.77488i	0.00730279	−	0.0414162i	−0.980939	−	0.194318i	$-0.937751\pi$
$67$	0.489287	−	2.77488i	0.00730279	−	0.0414162i	0.988241	+	0.152902i	$0.0488618\pi$
$68$	−11.0067	−	1.94077i	−0.161863	−	0.0285408i
$69$		0			0
$70$	−2.65425	+	2.22718i	−0.0379179	+	0.0318169i
$71$	−100.126	−	57.8080i	−1.41023	−	0.814197i	−0.414822	−	0.909903i	$-0.636156\pi$
$71$	−100.126	−	57.8080i	−1.41023	−	0.814197i	−0.995410	+	0.0957053i	$0.969489\pi$
$72$		0			0
$73$	1.01468	+	1.75747i	0.0138997	+	0.0240750i	0.872892	−	0.487914i	$-0.162242\pi$
$73$	1.01468	+	1.75747i	0.0138997	+	0.0240750i	−0.858992	+	0.511989i	$0.828909\pi$
$74$	−4.73557	+	13.0109i	−0.0639942	+	0.175823i
$75$		0			0
$76$	−62.7045	−	52.6153i	−0.825059	−	0.692306i
$77$	−31.5950	−	86.8065i	−0.410325	−	1.12736i
$78$		0			0
$79$	−12.8431	−	72.8366i	−0.162570	−	0.921982i	−0.951534	−	0.307543i	$-0.900493\pi$
$79$	−12.8431	−	72.8366i	−0.162570	−	0.921982i	0.788964	−	0.614440i	$-0.210618\pi$
$80$			0.652583i			0.00815729i
$81$		0			0
$82$	−28.7465			−0.350567
$83$	121.842	−	21.4840i	1.46798	−	0.258844i	0.618214	−	0.786010i	$-0.287857\pi$
$83$	121.842	−	21.4840i	1.46798	−	0.258844i	0.849762	+	0.527166i	$0.176746\pi$
$84$		0			0
$85$	1.99390	−	0.725722i	0.0234577	−	0.00853790i
$86$	4.65906	−	5.55245i	0.0541751	−	0.0645634i
$87$		0			0
$88$	−117.166	−	42.6448i	−1.33143	−	0.484600i
$89$	−31.0149	+	17.9065i	−0.348482	+	0.201196i	−0.664017	−	0.747718i	$-0.731150\pi$
$89$	−31.0149	+	17.9065i	−0.348482	+	0.201196i	0.315534	+	0.948914i	$0.397816\pi$
$90$		0			0
$91$	−29.0472	+	50.3113i	−0.319200	+	0.552871i
$92$	−40.1655	−	47.8674i	−0.436582	−	0.520298i
$93$		0			0
$94$	19.5399	−	110.816i	0.207871	−	1.17890i
$95$	15.3042	+	2.69854i	0.161097	+	0.0284057i
$96$		0			0
$97$	61.5608	−	51.6556i	0.634647	−	0.532532i	−0.267722	−	0.963496i	$-0.586271\pi$
$97$	61.5608	−	51.6556i	0.634647	−	0.532532i	0.902369	+	0.430964i	$0.141826\pi$
$98$	13.5226	+	7.80725i	0.137985	+	0.0796658i
$99$		0			0
$100$	−28.5545	−	49.4579i	−0.285545	−	0.494579i
$101$	−29.0636	+	79.8515i	−0.287758	+	0.790609i	0.708621	+	0.705589i	$0.249317\pi$
$101$	−29.0636	+	79.8515i	−0.287758	+	0.790609i	−0.996379	+	0.0850195i	$0.972905\pi$
$102$		0			0
$103$	33.7446	+	28.3151i	0.327617	+	0.274904i	0.791728	−	0.610874i	$-0.209182\pi$
$103$	33.7446	+	28.3151i	0.327617	+	0.274904i	−0.464111	+	0.885777i	$0.653626\pi$
$104$	26.8185	+	73.6831i	0.257870	+	0.708491i
$105$		0			0
$106$	−7.23929	−	41.0561i	−0.0682952	−	0.387321i
$107$		−	55.1601i		−	0.515515i	−0.966210	−	0.257757i	$-0.917016\pi$
$107$		−	55.1601i		−	0.515515i	0.966210	−	0.257757i	$-0.0829835\pi$
$108$		0			0
$109$	107.480			0.986052			0.493026	−	0.870015i	$-0.335891\pi$
$109$	107.480			0.986052			0.493026	+	0.870015i	$0.335891\pi$
$110$	8.51531	−	1.50148i	0.0774119	−	0.0136498i
$111$		0			0
$112$	−8.53718	+	3.10728i	−0.0762248	+	0.0277436i
$113$	17.7162	−	21.1133i	0.156781	−	0.186844i	−0.681936	−	0.731412i	$-0.738862\pi$
$113$	17.7162	−	21.1133i	0.156781	−	0.186844i	0.838717	+	0.544568i	$0.183306\pi$
$114$		0			0
$115$	11.1477	+	4.05744i	0.0969367	+	0.0352821i
$116$	−42.6383	+	24.6172i	−0.367571	+	0.212217i
$117$		0			0
$118$	−35.3823	+	61.2839i	−0.299850	+	0.519355i
$119$	18.9880	+	22.6290i	0.159563	+	0.190160i
$120$		0			0
$121$	−19.0197	+	107.866i	−0.157188	+	0.891456i
$122$	−41.9839	−	7.40290i	−0.344131	−	0.0606795i
$123$		0			0
$124$	−29.2279	+	24.5251i	−0.235708	+	0.197783i
$125$	18.8516	+	10.8840i	0.150813	+	0.0870719i
$126$		0			0
$127$	−63.8772	−	110.639i	−0.502970	−	0.871170i	−0.999994	−	0.00343329i	$-0.998907\pi$
$127$	−63.8772	−	110.639i	−0.502970	−	0.871170i	0.497024	−	0.867737i	$-0.334426\pi$
$128$	21.6677	−	59.5316i	0.169279	−	0.465091i
$129$		0			0
$130$	−4.16554	−	3.49530i	−0.0320426	−	0.0268869i
$131$	16.4628	+	45.2311i	0.125670	+	0.345276i	0.986533	−	0.163561i	$-0.0522980\pi$
$131$	16.4628	+	45.2311i	0.125670	+	0.345276i	−0.860863	+	0.508837i	$0.830076\pi$
$132$		0			0
$133$	37.5683	+	213.060i	0.282468	+	1.60196i
$134$			3.67171i			0.0274008i
$135$		0			0
$136$	39.8711			0.293170
$137$	−135.508	+	23.8938i	−0.989112	+	0.174407i	−0.644720	−	0.764419i	$-0.723026\pi$
$137$	−135.508	+	23.8938i	−0.989112	+	0.174407i	−0.344392	+	0.938826i	$0.611915\pi$
$138$		0			0
$139$	85.8823	−	31.2586i	0.617858	−	0.224882i	−0.0140798	−	0.999901i	$-0.504482\pi$
$139$	85.8823	−	31.2586i	0.617858	−	0.224882i	0.631938	+	0.775019i	$0.282260\pi$
$140$	−3.93438	+	4.68881i	−0.0281027	+	0.0334915i
$141$		0			0
$142$	141.573	+	51.5282i	0.996990	+	0.362875i
$143$	125.553	−	72.4879i	0.877992	−	0.506909i
$144$		0			0
$145$	4.67362	−	8.09495i	0.0322319	−	0.0558272i
$146$	−1.69981	−	2.02576i	−0.0116425	−	0.0138750i
$147$		0			0
$148$	−4.24729	+	24.0876i	−0.0286979	+	0.162754i
$149$	−31.4010	−	5.53684i	−0.210745	−	0.0371600i	0.0672790	−	0.997734i	$-0.478568\pi$
$149$	−31.4010	−	5.53684i	−0.210745	−	0.0371600i	−0.278024	+	0.960574i	$0.589679\pi$
$150$		0			0
$151$	−109.463	+	91.8500i	−0.724917	+	0.608278i	−0.928741	−	0.370730i	$-0.879108\pi$
$151$	−109.463	+	91.8500i	−0.724917	+	0.608278i	0.203823	+	0.979008i	$0.434663\pi$
$152$	252.889	+	146.005i	1.66374	+	0.960561i
$153$		0			0
$154$	60.1883	+	104.249i	0.390833	+	0.676942i
$155$	2.47747	−	6.80680i	0.0159837	−	0.0439148i
$156$		0			0
$157$	73.9044	+	62.0131i	0.470729	+	0.394988i	0.847060	−	0.531497i	$-0.178370\pi$
$157$	73.9044	+	62.0131i	0.470729	+	0.394988i	−0.376332	+	0.926485i	$0.622815\pi$
$158$	32.9629	+	90.5648i	0.208626	+	0.573195i
$159$		0			0
$160$	2.34515	+	13.3000i	0.0146572	+	0.0831251i
$161$			165.155i			1.02581i
$162$		0			0
$163$	−39.2776			−0.240967			−0.120483	−	0.992715i	$-0.538444\pi$
$163$	−39.2776			−0.240967			−0.120483	+	0.992715i	$0.538444\pi$
$164$	−50.0100	+	8.81811i	−0.304939	+	0.0537689i
$165$		0			0
$166$	−151.498	+	55.1407i	−0.912638	+	0.332173i
$167$	−83.9802	+	100.084i	−0.502876	+	0.599304i	−0.956443	−	0.291918i	$-0.905707\pi$
$167$	−83.9802	+	100.084i	−0.502876	+	0.599304i	0.453568	+	0.891222i	$0.350151\pi$
$168$		0			0
$169$	73.1340	+	26.6186i	0.432745	+	0.157506i
$170$	−2.39455	+	1.38250i	−0.0140856	+	0.00813233i
$171$		0			0
$172$	6.40208	−	11.0887i	0.0372214	−	0.0644694i
$173$	−55.1467	−	65.7212i	−0.318767	−	0.379891i	0.582738	−	0.812660i	$-0.301981\pi$
$173$	−55.1467	−	65.7212i	−0.318767	−	0.379891i	−0.901505	+	0.432768i	$0.857537\pi$
$174$		0			0
$175$	−26.2109	+	148.650i	−0.149777	+	0.849426i
$176$	22.3276	+	3.93695i	0.126861	+	0.0223690i
$177$		0			0
$178$	35.7494	−	29.9973i	0.200839	−	0.168524i
$179$	−217.959	−	125.838i	−1.21765	−	0.703008i	−0.253232	−	0.967406i	$-0.581494\pi$
$179$	−217.959	−	125.838i	−1.21765	−	0.703008i	−0.964414	+	0.264397i	$0.914827\pi$
$180$		0			0
$181$	113.776	+	197.066i	0.628596	+	1.08876i	0.987834	+	0.155514i	$0.0497034\pi$
$181$	113.776	+	197.066i	0.628596	+	1.08876i	−0.359238	+	0.933246i	$0.616963\pi$
$182$	25.8918	−	71.1370i	0.142262	−	0.390863i
$183$		0			0
$184$	170.763	+	143.287i	0.928061	+	0.778735i
$185$	−1.58821	−	4.36356i	−0.00858491	−	0.0235868i
$186$		0			0
$187$	−12.8010	−	72.5978i	−0.0684543	−	0.388224i
$188$		−	198.780i		−	1.05734i
$189$		0			0
$190$	−20.2504			−0.106581
$191$	−178.120	+	31.4074i	−0.932565	+	0.164436i	−0.619233	−	0.785207i	$-0.712556\pi$
$191$	−178.120	+	31.4074i	−0.932565	+	0.164436i	−0.313332	+	0.949644i	$0.601445\pi$
$192$		0			0
$193$	182.786	−	66.5285i	0.947075	−	0.344707i	0.178119	−	0.984009i	$-0.442999\pi$
$193$	182.786	−	66.5285i	0.947075	−	0.344707i	0.768956	+	0.639302i	$0.220776\pi$
$194$	−67.3121	+	80.2194i	−0.346969	+	0.413502i
$195$		0			0
$196$	25.9200	+	9.43410i	0.132245	+	0.0481331i
$197$	224.675	−	129.716i	1.14048	−	0.658457i	0.193931	−	0.981015i	$-0.437876\pi$
$197$	224.675	−	129.716i	1.14048	−	0.658457i	0.946550	+	0.322558i	$0.104543\pi$
$198$		0			0
$199$	−52.3841	+	90.7319i	−0.263237	+	0.455939i	−0.967100	−	0.254396i	$-0.918123\pi$
$199$	−52.3841	+	90.7319i	−0.263237	+	0.455939i	0.703864	+	0.710335i	$0.251457\pi$
$200$	130.956	+	156.068i	0.654782	+	0.780339i
$201$		0			0
$202$	19.2284	−	109.050i	0.0951900	−	0.539849i
$203$	128.153	+	22.5968i	0.631294	+	0.111314i
$204$		0			0
$205$	7.38539	−	6.19708i	0.0360263	−	0.0302296i
$206$	−49.7114	−	28.7009i	−0.241318	−	0.139325i
$207$		0			0
$208$	−7.12899	−	12.3478i	−0.0342740	−	0.0593643i
$209$	184.656	−	507.339i	0.883523	−	2.42746i
$210$		0			0
$211$	−226.733	−	190.251i	−1.07456	−	0.901665i	−0.0791046	−	0.996866i	$-0.525206\pi$
$211$	−226.733	−	190.251i	−1.07456	−	0.901665i	−0.995458	+	0.0952012i	$0.969651\pi$
$212$	−25.1883	−	69.2042i	−0.118813	−	0.326435i
$213$		0			0
$214$	12.4816	+	70.7867i	0.0583252	+	0.330779i
$215$			2.43089i			0.0113065i
$216$		0			0
$217$	100.844			0.464719
$218$	−137.928	+	24.3205i	−0.632698	+	0.111562i
$219$		0			0
$220$	14.3534	−	5.22422i	0.0652429	−	0.0237465i
$221$	−29.7994	+	35.5136i	−0.134839	+	0.160695i
$222$		0			0
$223$	−286.754	−	104.370i	−1.28589	−	0.468027i	−0.393516	−	0.919318i	$-0.628741\pi$
$223$	−286.754	−	104.370i	−1.28589	−	0.468027i	−0.892377	+	0.451291i	$0.850964\pi$
$224$	−162.826	+	94.0077i	−0.726902	+	0.419677i
$225$		0			0
$226$	−17.9576	+	31.1035i	−0.0794584	+	0.137626i
$227$	61.0564	+	72.7642i	0.268971	+	0.320547i	0.883576	−	0.468288i	$-0.155129\pi$
$227$	61.0564	+	72.7642i	0.268971	+	0.320547i	−0.614605	+	0.788835i	$0.710685\pi$
$228$		0			0
$229$	19.9814	−	113.320i	0.0872551	−	0.494848i	−0.909592	−	0.415502i	$-0.863606\pi$
$229$	19.9814	−	113.320i	0.0872551	−	0.494848i	0.996847	−	0.0793458i	$-0.0252831\pi$
$230$	−15.2239	−	2.68439i	−0.0661910	−	0.0116713i
$231$		0			0
$232$	134.548	−	112.899i	0.579948	−	0.486635i
$233$	36.3210	+	20.9700i	0.155884	+	0.0899998i	0.575913	−	0.817511i	$-0.304647\pi$
$233$	36.3210	+	20.9700i	0.155884	+	0.0899998i	−0.420029	+	0.907511i	$0.637980\pi$
$234$		0			0
$235$	18.8694	+	32.6827i	0.0802952	+	0.139075i
$236$	−42.7551	+	117.469i	−0.181166	+	0.497749i
$237$		0			0
$238$	−29.4877	−	24.7431i	−0.123898	−	0.103963i
$239$	−11.0127	−	30.2571i	−0.0460782	−	0.126599i	0.914519	−	0.404543i	$-0.132569\pi$
$239$	−11.0127	−	30.2571i	−0.0460782	−	0.126599i	−0.960597	+	0.277944i	$0.910347\pi$
$240$		0			0
$241$	−24.8692	−	141.040i	−0.103192	−	0.585230i	−0.991927	−	0.126809i	$-0.959526\pi$
$241$	−24.8692	−	141.040i	−0.103192	−	0.585230i	0.888735	−	0.458421i	$-0.151585\pi$
$242$		−	142.728i		−	0.589785i
$243$		0			0
$244$	−75.3100			−0.308647
$245$	−5.15720	+	0.909354i	−0.0210498	+	0.00371165i
$246$		0			0
$247$	−319.056	+	116.127i	−1.29172	+	0.470149i
$248$	87.4913	−	104.268i	0.352787	−	0.420436i
$249$		0			0
$250$	−26.6550	−	9.70163i	−0.106620	−	0.0388065i
$251$	−192.508	+	111.145i	−0.766965	+	0.442808i	−0.831791	−	0.555089i	$-0.812684\pi$
$251$	−192.508	+	111.145i	−0.766965	+	0.442808i	0.0648257	+	0.997897i	$0.479351\pi$
$252$		0			0
$253$	206.074	−	356.931i	0.814523	−	1.41080i
$254$	107.009	+	127.528i	0.421294	+	0.502078i
$255$		0			0
$256$	−46.4543	+	263.455i	−0.181462	+	1.02912i
$257$	−218.505	−	38.5283i	−0.850214	−	0.149916i	−0.268471	−	0.963288i	$-0.586518\pi$
$257$	−218.505	−	38.5283i	−0.850214	−	0.149916i	−0.581744	+	0.813372i	$0.697629\pi$
$258$		0			0
$259$	49.5224	−	41.5543i	0.191206	−	0.160441i
$260$	−8.31895	−	4.80295i	−0.0319960	−	0.0184729i
$261$		0			0
$262$	−31.3615	−	54.3197i	−0.119700	−	0.207327i
$263$	−23.4096	+	64.3173i	−0.0890098	+	0.244552i	−0.976208	−	0.216836i	$-0.930426\pi$
$263$	−23.4096	+	64.3173i	−0.0890098	+	0.244552i	0.887198	+	0.461388i	$0.152649\pi$
$264$		0			0
$265$	10.7106	+	8.98728i	0.0404174	+	0.0339143i
$266$	−96.4225	−	264.919i	−0.362490	−	0.995934i
$267$		0			0
$268$	1.12631	+	6.38764i	0.00420266	+	0.0238345i
$269$			334.017i			1.24170i	0.783930	+	0.620850i	$0.213212\pi$
$269$			334.017i			1.24170i	−0.783930	+	0.620850i	$0.786788\pi$
$270$		0			0
$271$	−427.090			−1.57598			−0.787988	−	0.615690i	$-0.788877\pi$
$271$	−427.090			−1.57598			−0.787988	+	0.615690i	$0.788877\pi$
$272$	−7.13979	+	1.25894i	−0.0262492	+	0.00462845i
$273$		0			0
$274$	168.491	−	61.3256i	0.614929	−	0.223816i
$275$	242.126	−	288.554i	0.880457	−	1.04929i
$276$		0			0
$277$	261.939	+	95.3380i	0.945628	+	0.344181i	0.768386	−	0.639987i	$-0.221060\pi$
$277$	261.939	+	95.3380i	0.945628	+	0.344181i	0.177242	+	0.984167i	$0.443282\pi$
$278$	−103.139	+	59.5474i	−0.371004	+	0.214199i
$279$		0			0
$280$	10.9177	−	18.9101i	0.0389920	−	0.0675360i
$281$	271.263	+	323.279i	0.965349	+	1.15046i	0.988575	+	0.150728i	$0.0481618\pi$
$281$	271.263	+	323.279i	0.965349	+	1.15046i	−0.0232262	+	0.999730i	$0.507394\pi$
$282$		0			0
$283$	81.0447	−	459.627i	0.286377	−	1.62413i	−0.413948	−	0.910301i	$-0.635850\pi$
$283$	81.0447	−	459.627i	0.286377	−	1.62413i	0.700325	−	0.713824i	$-0.253039\pi$
$284$	262.099	+	46.2151i	0.922884	+	0.162729i
$285$		0			0
$286$	−144.719	+	121.433i	−0.506010	+	0.424593i
$287$	116.237	+	67.1092i	0.405005	+	0.233830i
$288$		0			0
$289$	−132.713	−	229.866i	−0.459216	−	0.795386i
$290$	−4.16591	+	11.4458i	−0.0143652	+	0.0394681i
$291$		0			0
$292$	−3.57855	−	3.00276i	−0.0122553	−	0.0102834i
$293$	3.75148	+	10.3071i	0.0128037	+	0.0351778i	0.945930	−	0.324371i	$-0.105153\pi$
$293$	3.75148	+	10.3071i	0.0128037	+	0.0351778i	−0.933126	+	0.359549i	$0.882931\pi$
$294$		0			0
$295$	−4.12117	−	23.3723i	−0.0139701	−	0.0792282i
$296$		−	87.2561i		−	0.294784i
$297$		0			0
$298$	41.5496			0.139428
$299$	−255.254	+	45.0082i	−0.853694	+	0.150529i
$300$		0			0
$301$	−31.8012	+	11.5747i	−0.105652	+	0.0384542i
$302$	119.689	−	142.640i	0.396321	−	0.472317i
$303$		0			0
$304$	−49.8954	−	18.1604i	−0.164129	−	0.0597383i
$305$	12.3822	−	7.14886i	0.0405973	−	0.0234389i
$306$		0			0
$307$	141.354	−	244.833i	0.460437	−	0.797500i	−0.538546	−	0.842596i	$-0.681026\pi$
$307$	141.354	−	244.833i	0.460437	−	0.797500i	0.998983	+	0.0450961i	$0.0143594\pi$
$308$	136.688	+	162.898i	0.443792	+	0.528890i
$309$		0			0
$310$	−1.63909	+	9.29574i	−0.00528739	+	0.0299863i
$311$	−72.0066	−	12.6967i	−0.231532	−	0.0408254i	0.0566781	−	0.998393i	$-0.481949\pi$
$311$	−72.0066	−	12.6967i	−0.231532	−	0.0408254i	−0.288210	+	0.957567i	$0.593060\pi$
$312$		0			0
$313$	−126.580	+	106.214i	−0.404410	+	0.339340i	−0.822195	−	0.569205i	$-0.807251\pi$
$313$	−126.580	+	106.214i	−0.404410	+	0.339340i	0.417785	+	0.908546i	$0.362806\pi$
$314$	−108.873	−	62.8581i	−0.346731	−	0.200185i
$315$		0			0
$316$	85.1264	+	147.443i	0.269387	+	0.466592i
$317$	53.7001	−	147.540i	0.169401	−	0.465426i	−0.825721	−	0.564079i	$-0.809231\pi$
$317$	53.7001	−	147.540i	0.169401	−	0.465426i	0.995122	+	0.0986535i	$0.0314535\pi$
$318$		0			0
$319$	−248.766	−	208.739i	−0.779831	−	0.654356i
$320$	−6.91183	−	18.9901i	−0.0215995	−	0.0593441i
$321$		0			0
$322$	−37.3713	−	211.943i	−0.116060	−	0.658209i
$323$			172.646i			0.534508i
$324$		0			0
$325$	−236.887			−0.728883
$326$	50.4047	−	8.88771i	0.154616	−	0.0272629i
$327$		0			0
$328$	170.234	−	61.9600i	0.519005	−	0.188902i
$329$	−337.713	+	402.470i	−1.02648	+	1.22331i
$330$		0			0
$331$	−457.275	−	166.434i	−1.38150	−	0.502823i	−0.458864	−	0.888506i	$-0.651744\pi$
$331$	−457.275	−	166.434i	−1.38150	−	0.502823i	−0.922631	+	0.385683i	$0.873966\pi$
$332$	−246.645	+	142.400i	−0.742906	+	0.428917i
$333$		0			0
$334$	85.1245	−	147.440i	0.254864	−	0.441437i
$335$	−0.791537	−	0.943317i	−0.00236280	−	0.00281587i
$336$		0			0
$337$	−10.3025	+	58.4283i	−0.0305712	+	0.173378i	−0.996270	−	0.0862853i	$-0.972500\pi$
$337$	−10.3025	+	58.4283i	−0.0305712	+	0.173378i	0.965699	+	0.259663i	$0.0836115\pi$
$338$	−99.8757	−	17.6108i	−0.295490	−	0.0521029i
$339$		0			0
$340$	−3.74169	+	3.13965i	−0.0110050	+	0.00923428i
$341$	−217.942	−	125.829i	−0.639127	−	0.369000i
$342$		0			0
$343$	−185.515	−	321.321i	−0.540860	−	0.936797i
$344$	−15.6227	+	42.9231i	−0.0454150	+	0.124777i
$345$		0			0
$346$	85.6408	+	71.8612i	0.247517	+	0.207691i
$347$	206.366	+	566.986i	0.594715	+	1.63397i	0.761643	+	0.647997i	$0.224393\pi$
$347$	206.366	+	566.986i	0.594715	+	1.63397i	−0.166927	+	0.985969i	$0.553385\pi$
$348$		0			0
$349$	−68.0222	−	385.773i	−0.194906	−	1.10537i	−0.912553	−	0.408959i	$-0.865892\pi$
$349$	−68.0222	−	385.773i	−0.194906	−	1.10537i	0.717647	−	0.696407i	$-0.245219\pi$
$350$		−	196.692i		−	0.561978i
$351$		0			0
$352$	469.196			1.33294
$353$	468.585	−	82.6242i	1.32744	−	0.234063i	0.535432	−	0.844579i	$-0.320149\pi$
$353$	468.585	−	82.6242i	1.32744	−	0.234063i	0.792004	+	0.610516i	$0.209038\pi$
$354$		0			0
$355$	−47.4804	+	17.2814i	−0.133748	+	0.0486801i
$356$	52.9911	−	63.1524i	0.148851	−	0.177394i
$357$		0			0
$358$	308.180	+	112.168i	0.860838	+	0.313319i
$359$	570.105	−	329.150i	1.58804	−	0.916853i	0.594405	−	0.804166i	$-0.297388\pi$
$359$	570.105	−	329.150i	1.58804	−	0.916853i	0.993631	−	0.112687i	$-0.0359457\pi$
$360$		0			0
$361$	−451.718	+	782.399i	−1.25130	+	2.16731i
$362$	−190.600	−	227.148i	−0.526519	−	0.627481i
$363$		0			0
$364$	23.2221	−	131.699i	0.0637969	−	0.361810i
$365$	0.873412	+	0.154006i	0.00239291	+	0.000421935i
$366$		0			0
$367$	293.068	−	245.913i	0.798550	−	0.670063i	−0.149296	−	0.988793i	$-0.547701\pi$
$367$	293.068	−	245.913i	0.798550	−	0.670063i	0.947846	+	0.318730i	$0.103256\pi$
$368$	−35.1032	−	20.2668i	−0.0953891	−	0.0550729i
$369$		0			0
$370$	3.02553	+	5.24036i	0.00817710	+	0.0141631i
$371$	−66.5740	+	182.911i	−0.179445	+	0.493021i
$372$		0			0
$373$	243.282	+	204.138i	0.652231	+	0.547287i	0.907747	−	0.419518i	$-0.137801\pi$
$373$	243.282	+	204.138i	0.652231	+	0.547287i	−0.255516	+	0.966805i	$0.582245\pi$
$374$	32.8548	+	90.2679i	0.0878471	+	0.241358i
$375$		0			0
$376$	123.140	+	698.359i	0.327499	+	1.85734i
$377$			204.223i			0.541706i
$378$		0			0
$379$	276.424			0.729350			0.364675	−	0.931135i	$-0.381180\pi$
$379$	276.424			0.729350			0.364675	+	0.931135i	$0.381180\pi$
$380$	−35.2295	+	6.21190i	−0.0927091	+	0.0163471i
$381$		0			0
$382$	221.474	−	80.6098i	0.579774	−	0.211021i
$383$	224.446	−	267.485i	0.586022	−	0.698393i	−0.388815	−	0.921316i	$-0.627115\pi$
$383$	224.446	−	267.485i	0.586022	−	0.698393i	0.974836	+	0.222923i	$0.0715598\pi$
$384$		0			0
$385$	−37.9370	−	13.8079i	−0.0985375	−	0.0358647i
$386$	−219.514	+	126.736i	−0.568689	+	0.328333i
$387$		0			0
$388$	−92.4945	+	160.205i	−0.238388	+	0.412900i
$389$	−271.814	−	323.935i	−0.698750	−	0.832738i	0.293634	−	0.955918i	$-0.405135\pi$
$389$	−271.814	−	323.935i	−0.698750	−	0.832738i	−0.992384	+	0.123180i	$0.960691\pi$
$390$		0			0
$391$	−22.8859	+	129.793i	−0.0585318	+	0.331950i
$392$	−96.9068	−	17.0873i	−0.247211	−	0.0435900i
$393$		0			0
$394$	−258.972	+	217.303i	−0.657289	+	0.551531i
$395$	−27.9923	−	16.1614i	−0.0708667	−	0.0409149i
$396$		0			0
$397$	238.751	+	413.529i	0.601389	+	1.04164i	0.992611	+	0.121340i	$0.0387190\pi$
$397$	238.751	+	413.529i	0.601389	+	1.04164i	−0.391222	+	0.920296i	$0.627948\pi$
$398$	46.6935	−	128.289i	0.117320	−	0.322335i
$399$		0			0
$400$	−28.3785	−	23.8124i	−0.0709462	−	0.0595309i
$401$	−218.809	−	601.173i	−0.545659	−	1.49918i	−0.839516	−	0.543335i	$-0.817161\pi$
$401$	−218.809	−	601.173i	−0.545659	−	1.49918i	0.293857	−	0.955849i	$-0.405061\pi$
$402$		0			0
$403$	27.4821	+	155.858i	0.0681937	+	0.386746i
$404$		−	195.611i		−	0.484185i
$405$		0			0
$406$	−169.571			−0.417662
$407$	−158.877	+	28.0143i	−0.390361	+	0.0688312i
$408$		0			0
$409$	−256.759	+	93.4526i	−0.627772	+	0.228490i	−0.636261	−	0.771474i	$-0.719520\pi$
$409$	−256.759	+	93.4526i	−0.627772	+	0.228490i	0.00848909	+	0.999964i	$0.497298\pi$
$410$	−8.07536	+	9.62384i	−0.0196960	+	0.0234728i
$411$		0			0
$412$	−95.2866	−	34.6815i	−0.231278	−	0.0841784i
$413$	286.137	−	165.201i	0.692825	−	0.400003i
$414$		0			0
$415$	27.0350	−	46.8259i	0.0651445	−	0.112834i
$416$	−189.666	−	226.035i	−0.455928	−	0.543354i
$417$		0			0
$418$	−122.168	+	692.850i	−0.292268	+	1.65754i
$419$	−132.565	−	23.3749i	−0.316385	−	0.0557873i	0.0132005	−	0.999913i	$-0.495798\pi$
$419$	−132.565	−	23.3749i	−0.316385	−	0.0557873i	−0.329586	+	0.944126i	$0.606909\pi$
$420$		0			0
$421$	260.118	−	218.265i	0.617857	−	0.518444i	−0.279272	−	0.960212i	$-0.590093\pi$
$421$	260.118	−	218.265i	0.617857	−	0.518444i	0.897129	+	0.441768i	$0.145649\pi$
$422$	334.015	+	192.844i	0.791505	+	0.456976i
$423$		0			0
$424$	131.362	+	227.526i	0.309817	+	0.536618i
$425$	−41.1974	+	113.189i	−0.0969350	+	0.266327i
$426$		0			0
$427$	152.480	+	127.946i	0.357096	+	0.299639i
$428$	43.4283	+	119.318i	0.101468	+	0.278781i
$429$		0			0
$430$	−0.550061	−	3.11955i	−0.00127921	−	0.00725477i
$431$		−	369.724i		−	0.857829i	−0.903345	−	0.428914i	$-0.858896\pi$
$431$		−	369.724i		−	0.857829i	0.903345	−	0.428914i	$-0.141104\pi$
$432$		0			0
$433$	553.428			1.27813			0.639063	−	0.769155i	$-0.279322\pi$
$433$	553.428			1.27813			0.639063	+	0.769155i	$0.279322\pi$
$434$	−129.413	+	22.8189i	−0.298186	+	0.0525782i
$435$		0			0
$436$	−232.492	+	84.6202i	−0.533239	+	0.194083i
$437$	−620.449	+	739.422i	−1.41979	+	1.69204i
$438$		0			0
$439$	634.460	+	230.924i	1.44524	+	0.526024i	0.941257	−	0.337691i	$-0.109646\pi$
$439$	634.460	+	230.924i	1.44524	+	0.526024i	0.503982	+	0.863714i	$0.331868\pi$
$440$	−47.1905	+	27.2455i	−0.107251	+	0.0619215i
$441$		0			0
$442$	30.2055	−	52.3174i	0.0683382	−	0.118365i
$443$	−356.645	−	425.033i	−0.805069	−	0.959444i	0.194702	−	0.980862i	$-0.437626\pi$
$443$	−356.645	−	425.033i	−0.805069	−	0.959444i	−0.999771	+	0.0214190i	$0.993182\pi$
$444$		0			0
$445$	−2.71782	+	15.4135i	−0.00610745	+	0.0346371i
$446$	391.607	+	69.0509i	0.878043	+	0.154823i
$447$		0			0
$448$	215.520	−	180.843i	0.481072	−	0.403667i
$449$	514.326	+	296.946i	1.14549	+	0.661351i	0.947785	−	0.318910i	$-0.103317\pi$
$449$	514.326	+	296.946i	1.14549	+	0.661351i	0.197708	+	0.980261i	$0.436650\pi$
$450$		0			0
$451$	−167.472	−	290.071i	−0.371336	−	0.643172i
$452$	−21.6995	+	59.6190i	−0.0480079	+	0.131900i
$453$		0			0
$454$	−94.8185	−	79.5622i	−0.208851	−	0.175247i
$455$	8.68353	+	23.8578i	0.0190847	+	0.0524347i
$456$		0			0
$457$	64.8516	+	367.791i	0.141907	+	0.804795i	0.969799	+	0.243907i	$0.0784292\pi$
$457$	64.8516	+	367.791i	0.141907	+	0.804795i	−0.827891	+	0.560888i	$0.810460\pi$
$458$			149.945i			0.327390i
$459$		0			0
$460$	−27.3084			−0.0593661
$461$	410.804	−	72.4358i	0.891114	−	0.157127i	0.290698	−	0.956815i	$-0.406113\pi$
$461$	410.804	−	72.4358i	0.891114	−	0.157127i	0.600416	+	0.799688i	$0.295002\pi$
$462$		0			0
$463$	−256.423	+	93.3305i	−0.553830	+	0.201578i	−0.603748	−	0.797176i	$-0.706326\pi$
$463$	−256.423	+	93.3305i	−0.553830	+	0.201578i	0.0499171	+	0.998753i	$0.484104\pi$
$464$	−20.5289	+	24.4654i	−0.0442434	+	0.0527272i
$465$		0			0
$466$	−51.3557	−	18.6919i	−0.110205	−	0.0401115i
$467$	86.4172	−	49.8930i	0.185047	−	0.106837i	−0.404615	−	0.914487i	$-0.632594\pi$
$467$	86.4172	−	49.8930i	0.185047	−	0.106837i	0.589662	+	0.807650i	$0.299261\pi$
$468$		0			0
$469$	8.57168	−	14.8466i	0.0182765	−	0.0316558i
$470$	−31.6104	−	37.6718i	−0.0672562	−	0.0801528i
$471$		0			0
$472$	77.4392	−	439.180i	0.164066	−	0.930465i
$473$	83.1708	+	14.6653i	0.175837	+	0.0310048i
$474$		0			0
$475$	−675.790	+	567.055i	−1.42272	+	1.19380i
$476$	−58.8895	−	33.9998i	−0.123717	−	0.0714282i
$477$		0			0
$478$	20.9791	+	36.3369i	0.0438894	+	0.0760186i
$479$	−164.163	+	451.034i	−0.342720	+	0.941616i	0.641881	+	0.766804i	$0.278154\pi$
$479$	−164.163	+	451.034i	−0.342720	+	0.941616i	−0.984602	+	0.174812i	$0.944068\pi$
$480$		0			0
$481$	77.7197	+	65.2146i	0.161579	+	0.135581i
$482$	63.8292	+	175.369i	0.132426	+	0.363837i
$483$		0			0
$484$	−43.7824	−	248.302i	−0.0904595	−	0.513021i
$485$		−	35.1205i		−	0.0724133i
$486$		0			0
$487$	−305.419			−0.627143			−0.313572	−	0.949565i	$-0.601526\pi$
$487$	−305.419			−0.627143			−0.313572	+	0.949565i	$0.601526\pi$
$488$	264.581	−	46.6527i	0.542174	−	0.0955998i
$489$		0			0
$490$	6.41245	−	2.33394i	0.0130866	−	0.00476314i
$491$	219.310	−	261.364i	0.446661	−	0.532309i	−0.494991	−	0.868898i	$-0.664829\pi$
$491$	219.310	−	261.364i	0.446661	−	0.532309i	0.941652	+	0.336589i	$0.109273\pi$
$492$		0			0
$493$	97.5815	+	35.5168i	0.197934	+	0.0720421i
$494$	383.165	−	221.221i	0.775639	−	0.447815i
$495$		0			0
$496$	−12.3749	+	21.4340i	−0.0249495	+	0.0432137i
$497$	−452.156	−	538.859i	−0.909771	−	1.08422i
$498$		0			0
$499$	−57.5325	+	326.283i	−0.115296	+	0.653873i	0.871308	+	0.490737i	$0.163272\pi$
$499$	−57.5325	+	326.283i	−0.115296	+	0.653873i	−0.986603	+	0.163137i	$0.947839\pi$
$500$	−49.3475	−	8.70130i	−0.0986950	−	0.0174026i
$501$		0			0
$502$	221.895	−	186.192i	0.442022	−	0.370901i
$503$	−189.269	−	109.275i	−0.376281	−	0.217246i	0.299918	−	0.953965i	$-0.403041\pi$
$503$	−189.269	−	109.275i	−0.376281	−	0.217246i	−0.676199	+	0.736719i	$0.736374\pi$
$504$		0			0
$505$	18.5685	+	32.1616i	0.0367693	+	0.0636864i
$506$	−183.688	+	504.679i	−0.363020	+	0.997389i
$507$		0			0
$508$	225.282	+	189.034i	0.443468	+	0.372114i
$509$	24.7841	+	68.0939i	0.0486918	+	0.133780i	0.961655	−	0.274263i	$-0.0884338\pi$
$509$	24.7841	+	68.0939i	0.0486918	+	0.133780i	−0.912963	+	0.408042i	$0.866212\pi$
$510$		0			0
$511$	2.14403	+	12.1594i	0.00419575	+	0.0237953i
$512$		−	95.1938i		−	0.185925i
$513$		0			0
$514$	289.125			0.562499
$515$	18.9588	−	3.34296i	0.0368133	−	0.00649118i
$516$		0			0
$517$	1232.05	−	448.428i	2.38307	−	0.867366i
$518$	−54.1491	+	64.5323i	−0.104535	+	0.124580i
$519$		0			0
$520$	32.2016	+	11.7204i	0.0619262	+	0.0225393i
$521$	−624.343	+	360.464i	−1.19835	+	0.691870i	−0.960188	−	0.279354i	$-0.909880\pi$
$521$	−624.343	+	360.464i	−1.19835	+	0.691870i	−0.238166	+	0.971224i	$0.576546\pi$
$522$		0			0
$523$	−128.115	+	221.903i	−0.244963	+	0.424288i	−0.962121	−	0.272622i	$-0.912109\pi$
$523$	−128.115	+	221.903i	−0.244963	+	0.424288i	0.717158	+	0.696910i	$0.245442\pi$
$524$	−71.2221	−	84.8792i	−0.135920	−	0.161983i
$525$		0			0
$526$	15.4877	−	87.8352i	0.0294443	−	0.166987i
$527$	79.2514	+	13.9742i	0.150382	+	0.0265164i
$528$		0			0
$529$	−159.224	+	133.604i	−0.300990	+	0.252560i
$530$	−15.7785	−	9.10974i	−0.0297708	−	0.0171882i
$531$		0			0
$532$	−249.010	−	431.298i	−0.468064	−	0.810711i
$533$	−72.0432	+	197.937i	−0.135165	+	0.371364i
$534$		0			0
$535$	−18.4667	−	15.4954i	−0.0345172	−	0.0289633i
$536$	−7.91399	−	21.7435i	−0.0147649	−	0.0405662i
$537$		0			0
$538$	−75.5813	−	428.643i	−0.140486	−	0.796734i
$539$			181.935i			0.337542i
$540$		0			0
$541$	226.157			0.418035			0.209017	−	0.977912i	$-0.432973\pi$
$541$	226.157			0.418035			0.209017	+	0.977912i	$0.432973\pi$
$542$	548.082	−	96.6417i	1.01122	−	0.178306i
$543$		0			0
$544$	−140.989	+	51.3157i	−0.259171	+	0.0943304i
$545$	30.1928	−	35.9824i	0.0553997	−	0.0660228i
$546$		0			0
$547$	−481.247	−	175.160i	−0.879794	−	0.320219i	−0.137667	−	0.990479i	$-0.543960\pi$
$547$	−481.247	−	175.160i	−0.879794	−	0.320219i	−0.742127	+	0.670260i	$0.766183\pi$
$548$	274.310	−	158.373i	0.500565	−	0.289001i
$549$		0			0
$550$	−245.425	+	425.088i	−0.446227	+	0.772888i
$551$	488.865	+	582.607i	0.887233	+	1.05736i
$552$		0			0
$553$	78.1396	−	443.152i	0.141301	−	0.801359i
$554$	−357.718	−	63.0754i	−0.645701	−	0.113854i
$555$		0			0
$556$	−161.164	+	135.233i	−0.289863	+	0.243224i
$557$	−385.269	−	222.435i	−0.691686	−	0.399345i	0.112557	−	0.993645i	$-0.464096\pi$
$557$	−385.269	−	222.435i	−0.691686	−	0.399345i	−0.804243	+	0.594300i	$0.797429\pi$
$558$		0			0
$559$	−26.5557	−	45.9958i	−0.0475057	−	0.0822823i
$560$	−1.35797	+	3.73099i	−0.00242495	+	0.00666249i
$561$		0			0
$562$	−421.262	−	353.481i	−0.749577	−	0.628970i
$563$	122.079	+	335.408i	0.216836	+	0.595751i	0.999649	−	0.0265058i	$-0.00843805\pi$
$563$	122.079	+	335.408i	0.216836	+	0.595751i	−0.782813	+	0.622257i	$0.786216\pi$
$564$		0			0
$565$	−2.09162	−	11.8622i	−0.00370199	−	0.0209950i
$566$			608.177i			1.07452i
$567$		0			0
$568$	−949.442			−1.67155
$569$	653.295	−	115.194i	1.14815	−	0.202449i	0.432980	−	0.901404i	$-0.357462\pi$
$569$	653.295	−	115.194i	1.14815	−	0.202449i	0.715166	+	0.698955i	$0.246351\pi$
$570$		0			0
$571$	−726.894	+	264.568i	−1.27302	+	0.463341i	−0.888118	−	0.459616i	$-0.847987\pi$
$571$	−726.894	+	264.568i	−1.27302	+	0.463341i	−0.384902	+	0.922957i	$0.625765\pi$
$572$	−214.516	+	255.650i	−0.375027	+	0.446940i
$573$		0			0
$574$	−164.351	−	59.8190i	−0.286326	−	0.104214i
$575$	−583.217	+	336.720i	−1.01429	+	0.585601i
$576$		0			0
$577$	432.933	−	749.861i	0.750316	−	1.29959i	−0.197353	−	0.980333i	$-0.563234\pi$
$577$	432.933	−	749.861i	0.750316	−	1.29959i	0.947669	−	0.319254i	$-0.103432\pi$
$578$	222.325	+	264.956i	0.384645	+	0.458402i
$579$		0			0
$580$	−3.73637	+	21.1900i	−0.00644201	+	0.0365345i
$581$	741.310	+	130.713i	1.27592	+	0.224979i
$582$		0			0
$583$	372.107	−	312.235i	0.638263	−	0.535566i
$584$	14.4324	+	8.33255i	0.0247130	+	0.0142681i
$585$		0			0
$586$	−7.14654	−	12.3782i	−0.0121955	−	0.0211232i
$587$	88.7289	−	243.781i	0.151156	−	0.415299i	−0.840884	−	0.541215i	$-0.817965\pi$
$587$	88.7289	−	243.781i	0.151156	−	0.415299i	0.992041	+	0.125916i	$0.0401869\pi$
$588$		0			0
$589$	451.492	+	378.846i	0.766539	+	0.643203i
$590$	10.5774	+	29.0611i	0.0179277	+	0.0492561i
$591$		0			0
$592$	2.75513	+	15.6251i	0.00465393	+	0.0263937i
$593$		−	32.9690i		−	0.0555969i	−0.999614	−	0.0277985i	$-0.991150\pi$
$593$		−	32.9690i		−	0.0555969i	0.999614	−	0.0277985i	$-0.00884967\pi$
$594$		0			0
$595$	12.9099			0.0216972
$596$	72.2834	−	12.7455i	0.121281	−	0.0213851i
$597$		0			0
$598$	317.382	−	115.518i	0.530740	−	0.193174i
$599$	581.105	−	692.534i	0.970125	−	1.15615i	−0.0175842	−	0.999845i	$-0.505597\pi$
$599$	581.105	−	692.534i	0.970125	−	1.15615i	0.987709	−	0.156304i	$-0.0499581\pi$
$600$		0			0
$601$	−280.993	−	102.273i	−0.467543	−	0.170172i	0.0974960	−	0.995236i	$-0.468917\pi$
$601$	−280.993	−	102.273i	−0.467543	−	0.170172i	−0.565039	+	0.825064i	$0.691139\pi$
$602$	38.1913	−	22.0497i	0.0634407	−	0.0366275i
$603$		0			0
$604$	164.466	−	284.864i	0.272295	−	0.471630i
$605$	30.7688	+	36.6689i	0.0508576	+	0.0606097i
$606$		0			0
$607$	112.629	−	638.749i	0.185550	−	1.05230i	−0.739697	−	0.672940i	$-0.765031\pi$
$607$	112.629	−	638.749i	0.185550	−	1.05230i	0.925247	−	0.379365i	$-0.123857\pi$
$608$	−1082.16	−	190.814i	−1.77986	−	0.313838i
$609$		0			0
$610$	−14.2724	+	11.9759i	−0.0233973	+	0.0196327i
$611$	−714.068	−	412.267i	−1.16869	−	0.674742i
$612$		0			0
$613$	137.890	+	238.832i	0.224942	+	0.389612i	0.956302	−	0.292380i	$-0.0944473\pi$
$613$	137.890	+	238.832i	0.224942	+	0.389612i	−0.731360	+	0.681992i	$0.761114\pi$
$614$	−125.999	+	346.178i	−0.205209	+	0.563808i
$615$		0			0
$616$	−581.127	−	487.623i	−0.943387	−	0.791596i
$617$	−291.954	−	802.136i	−0.473182	−	1.30006i	−0.915181	−	0.403042i	$-0.867953\pi$
$617$	−291.954	−	802.136i	−0.473182	−	1.30006i	0.441999	−	0.897016i	$-0.354269\pi$
$618$		0			0
$619$	1.13605	+	6.44284i	0.00183529	+	0.0104085i	0.985712	−	0.168442i	$-0.0538734\pi$
$619$	1.13605	+	6.44284i	0.00183529	+	0.0104085i	−0.983876	+	0.178850i	$0.942762\pi$
$620$			16.6745i			0.0268944i
$621$		0			0
$622$	95.2787			0.153181
$623$	−214.582	+	37.8367i	−0.344434	+	0.0607330i
$624$		0			0
$625$	−573.881	+	208.876i	−0.918210	+	0.334201i
$626$	138.406	−	164.946i	0.221096	−	0.263492i
$627$		0			0
$628$	−208.688	−	75.9563i	−0.332306	−	0.120950i
$629$	44.6770	−	25.7943i	0.0710287	−	0.0410084i
$630$		0			0
$631$	249.531	−	432.200i	0.395453	−	0.684945i	−0.597706	−	0.801716i	$-0.703921\pi$
$631$	249.531	−	432.200i	0.395453	−	0.684945i	0.993159	+	0.116770i	$0.0372542\pi$
$632$	−390.406	−	465.267i	−0.617730	−	0.736182i
$633$		0			0
$634$	−35.5279	+	201.489i	−0.0560376	+	0.317805i
$635$	−54.9842	−	9.69519i	−0.0865892	−	0.0152680i
$636$		0			0
$637$	87.6473	−	73.5448i	0.137594	−	0.115455i
$638$	366.474	+	211.584i	0.574410	+	0.331636i
$639$		0			0
$640$	−13.8434	−	23.9774i	−0.0216303	−	0.0374648i
$641$	−219.721	+	603.679i	−0.342779	+	0.941776i	0.641806	+	0.766867i	$0.278185\pi$
$641$	−219.721	+	603.679i	−0.342779	+	0.941776i	−0.984585	+	0.174909i	$0.944037\pi$
$642$		0			0
$643$	−520.470	−	436.726i	−0.809440	−	0.679201i	0.141034	−	0.990005i	$-0.454957\pi$
$643$	−520.470	−	436.726i	−0.809440	−	0.679201i	−0.950474	+	0.310804i	$0.899402\pi$
$644$	−130.029	−	357.252i	−0.201908	−	0.554739i
$645$		0			0
$646$	−39.0663	−	221.556i	−0.0604742	−	0.342966i
$647$		−	232.654i		−	0.359589i	−0.983704	−	0.179794i	$-0.942457\pi$
$647$		−	232.654i		−	0.359589i	0.983704	−	0.179794i	$-0.0575432\pi$
$648$		0			0
$649$	−824.526			−1.27046
$650$	303.996	−	53.6027i	0.467686	−	0.0824657i
$651$		0			0
$652$	84.9623	−	30.9237i	0.130310	−	0.0474290i
$653$	616.972	−	735.279i	0.944827	−	1.12600i	−0.0470614	−	0.998892i	$-0.514986\pi$
$653$	616.972	−	735.279i	0.944827	−	1.12600i	0.991889	−	0.127109i	$-0.0405699\pi$
$654$		0			0
$655$	19.7673	+	7.19471i	0.0301791	+	0.0109843i
$656$	−28.5276	+	16.4704i	−0.0434872	+	0.0251074i
$657$		0			0
$658$	342.314	−	592.906i	0.520235	−	0.901073i
$659$	−69.1810	−	82.4467i	−0.104979	−	0.125109i	0.710997	−	0.703195i	$-0.248244\pi$
$659$	−69.1810	−	82.4467i	−0.104979	−	0.125109i	−0.815975	+	0.578087i	$0.803800\pi$
$660$		0			0
$661$	−80.5728	+	456.951i	−0.121895	+	0.691302i	0.861208	+	0.508252i	$0.169708\pi$
$661$	−80.5728	+	456.951i	−0.121895	+	0.691302i	−0.983104	+	0.183050i	$0.941403\pi$
$662$	624.480	+	110.113i	0.943323	+	0.166333i
$663$		0			0
$664$	778.305	−	653.075i	1.17215	−	0.983547i
$665$	81.8827	+	47.2750i	0.123132	+	0.0710902i
$666$		0			0
$667$	290.291	+	502.798i	0.435219	+	0.753821i
$668$	102.862	−	282.612i	0.153986	−	0.423072i
$669$		0			0
$670$	1.22923	+	1.03145i	0.00183467	+	0.00153947i
$671$	−169.892	−	466.773i	−0.253192	−	0.695639i
$672$		0			0
$673$	14.3386	+	81.3180i	0.0213054	+	0.120829i	0.993606	−	0.112907i	$-0.0360161\pi$
$673$	14.3386	+	81.3180i	0.0213054	+	0.120829i	−0.972300	+	0.233736i	$0.924905\pi$
$674$		−	77.3120i		−	0.114706i
$675$		0			0
$676$	−179.155			−0.265022
$677$	−569.867	+	100.483i	−0.841754	+	0.148424i	−0.577868	−	0.816130i	$-0.696115\pi$
$677$	−569.867	+	100.483i	−0.841754	+	0.148424i	−0.263886	+	0.964554i	$0.585004\pi$
$678$		0			0
$679$	459.450	−	167.226i	0.676657	−	0.246283i
$680$	11.2005	−	13.3482i	0.0164713	−	0.0196297i
$681$		0			0
$682$	308.157	+	112.160i	0.451843	+	0.164457i
$683$	−323.144	+	186.567i	−0.473124	+	0.273158i	−0.717547	−	0.696510i	$-0.754735\pi$
$683$	−323.144	+	186.567i	−0.473124	+	0.273158i	0.244422	+	0.969669i	$0.421402\pi$
$684$		0			0
$685$	−30.0673	+	52.0781i	−0.0438939	+	0.0760265i
$686$	310.779	+	370.372i	0.453031	+	0.539901i
$687$		0			0
$688$	1.44229	−	8.17961i	0.00209635	−	0.0118890i
$689$	−300.839	−	53.0460i	−0.436631	−	0.0769899i
$690$		0			0
$691$	−118.117	+	99.1122i	−0.170937	+	0.143433i	−0.724243	−	0.689545i	$-0.757811\pi$
$691$	−118.117	+	99.1122i	−0.170937	+	0.143433i	0.553306	+	0.832978i	$0.313366\pi$
$692$	171.032	+	98.7456i	0.247157	+	0.142696i
$693$		0			0
$694$	−393.126	−	680.915i	−0.566464	−	0.981145i
$695$	13.6609	−	37.5330i	0.0196560	−	0.0540044i
$696$		0			0
$697$	82.0487	+	68.8470i	0.117717	+	0.0987762i
$698$	174.585	+	479.669i	0.250122	+	0.687205i
$699$		0			0
$700$	−60.3362	−	342.184i	−0.0861946	−	0.488834i
$701$		−	781.764i		−	1.11521i	−0.830105	−	0.557606i	$-0.811720\pi$
$701$		−	781.764i		−	1.11521i	0.830105	−	0.557606i	$-0.188280\pi$
$702$		0			0
$703$	377.828			0.537451
$704$	−691.428	+	121.917i	−0.982141	+	0.173178i
$705$		0			0
$706$	−582.637	+	212.062i	−0.825264	+	0.300372i
$707$	−332.328	+	396.053i	−0.470054	+	0.560189i
$708$		0			0
$709$	640.559	+	233.145i	0.903469	+	0.328836i	0.751642	−	0.659571i	$-0.229262\pi$
$709$	640.559	+	233.145i	0.903469	+	0.328836i	0.151827	+	0.988407i	$0.451484\pi$
$710$	57.0209	−	32.9210i	0.0803111	−	0.0463677i
$711$		0			0
$712$	−147.048	+	254.695i	−0.206529	+	0.357718i
$713$	289.204	+	344.660i	0.405616	+	0.483394i
$714$		0			0
$715$	11.0021	−	62.3961i	0.0153876	−	0.0872672i
$716$	570.546	+	100.603i	0.796852	+	0.140507i
$717$		0			0
$718$	−657.133	+	551.400i	−0.915227	+	0.767967i
$719$	419.068	+	241.949i	0.582849	+	0.336508i	0.762265	−	0.647265i	$-0.224087\pi$
$719$	419.068	+	241.949i	0.582849	+	0.336508i	−0.179416	+	0.983773i	$0.557421\pi$
$720$		0			0
$721$	134.006	+	232.104i	0.185861	+	0.321920i
$722$	402.647	−	1106.26i	0.557683	−	1.53222i
$723$		0			0
$724$	−401.264	−	336.700i	−0.554232	−	0.465056i
$725$	181.482	+	498.619i	0.250320	+	0.687750i
$726$		0			0
$727$	−121.395	−	688.465i	−0.166981	−	0.946994i	−0.946999	−	0.321237i	$-0.895901\pi$
$727$	−121.395	−	688.465i	−0.166981	−	0.946994i	0.780018	−	0.625757i	$-0.215210\pi$
$728$			477.073i			0.655320i
$729$		0			0
$730$	−1.15569			−0.00158314
$731$	−26.5959	+	4.68958i	−0.0363830	+	0.00641530i
$732$		0			0
$733$	−322.370	+	117.333i	−0.439796	+	0.160073i	−0.552422	−	0.833565i	$-0.686296\pi$
$733$	−322.370	+	117.333i	−0.439796	+	0.160073i	0.112626	+	0.993637i	$0.464074\pi$
$734$	−320.447	+	381.894i	−0.436577	+	0.520292i
$735$		0			0
$736$	−788.254	−	286.901i	−1.07100	−	0.389811i
$737$	−37.0500	+	21.3908i	−0.0502713	+	0.0290242i
$738$		0			0
$739$	−246.292	+	426.590i	−0.333277	+	0.577253i	−0.983152	−	0.182788i	$-0.941488\pi$
$739$	−246.292	+	426.590i	−0.333277	+	0.577253i	0.649875	+	0.760041i	$0.274821\pi$
$740$	6.87098	+	8.18852i	0.00928511	+	0.0110656i
$741$		0			0
$742$	44.0452	−	249.793i	0.0593601	−	0.336648i
$743$	−1095.94	−	193.243i	−1.47502	−	0.260085i	−0.622432	−	0.782674i	$-0.713855\pi$
$743$	−1095.94	−	193.243i	−1.47502	−	0.260085i	−0.852585	+	0.522589i	$0.824966\pi$
$744$		0			0
$745$	−10.6747	+	8.95713i	−0.0143285	+	0.0120230i
$746$	−358.395	−	206.920i	−0.480422	−	0.277372i
$747$		0			0
$748$	84.8473	+	146.960i	0.113432	+	0.196470i
$749$	114.783	−	315.365i	0.153249	−	0.421048i
$750$		0			0
$751$	997.317	+	836.848i	1.32799	+	1.11431i	0.984544	+	0.175138i	$0.0560371\pi$
$751$	997.317	+	836.848i	1.32799	+	1.11431i	0.343441	+	0.939174i	$0.388407\pi$
$752$	−44.1016	−	121.168i	−0.0586458	−	0.161128i
$753$		0			0
$754$	−46.2116	−	262.079i	−0.0612885	−	0.347585i
$755$			62.4484i			0.0827132i
$756$		0			0
$757$	850.358			1.12333			0.561663	−	0.827366i	$-0.310162\pi$
$757$	850.358			1.12333			0.561663	+	0.827366i	$0.310162\pi$
$758$	−354.733	+	62.5491i	−0.467986	+	0.0825186i
$759$		0			0
$760$	119.921	−	43.6476i	0.157791	−	0.0574311i
$761$	−288.411	+	343.715i	−0.378990	+	0.451663i	−0.921495	−	0.388390i	$-0.873031\pi$
$761$	−288.411	+	343.715i	−0.378990	+	0.451663i	0.542505	+	0.840052i	$0.317476\pi$
$762$		0			0
$763$	614.490	+	223.656i	0.805361	+	0.293127i
$764$	360.568	−	208.174i	0.471948	−	0.272479i
$765$		0			0
$766$	−227.505	+	394.049i	−0.297003	+	0.514425i
$767$	333.303	+	397.216i	0.434555	+	0.517882i
$768$		0			0
$769$	−17.2057	+	97.5785i	−0.0223741	+	0.126890i	−0.993949	−	0.109842i	$-0.964965\pi$
$769$	−17.2057	+	97.5785i	−0.0223741	+	0.126890i	0.971575	+	0.236732i	$0.0760765\pi$
$770$	51.8088	+	9.13529i	0.0672841	+	0.0118640i
$771$		0			0
$772$	−343.009	+	287.819i	−0.444313	+	0.372822i
$773$	185.243	+	106.950i	0.239642	+	0.138357i	0.615012	−	0.788518i	$-0.289151\pi$
$773$	185.243	+	106.950i	0.239642	+	0.138357i	−0.375370	+	0.926875i	$0.622484\pi$
$774$		0			0
$775$	205.602	+	356.112i	0.265292	+	0.459500i
$776$	225.711	−	620.135i	0.290864	−	0.799143i
$777$		0			0
$778$	422.117	+	354.198i	0.542567	+	0.455268i
$779$	268.293	+	737.129i	0.344407	+	0.946251i
$780$		0			0
$781$	304.826	+	1728.75i	0.390302	+	2.21351i
$782$		−	171.741i		−	0.219617i
$783$		0			0
$784$	17.8928			0.0228225
$785$	41.5220	−	7.32144i	0.0528942	−	0.00932668i
$786$		0			0
$787$	1283.91	−	467.304i	1.63139	−	0.593779i	0.645890	−	0.763431i	$-0.276487\pi$
$787$	1283.91	−	467.304i	1.63139	−	0.593779i	0.985504	+	0.169652i	$0.0542643\pi$
$788$	−383.872	+	457.481i	−0.487148	+	0.580560i
$789$		0			0
$790$	39.5794	+	14.4057i	0.0501005	+	0.0182351i
$791$	145.223	−	83.8447i	0.183595	−	0.105998i
$792$		0			0
$793$	−156.192	+	270.532i	−0.196963	+	0.341150i
$794$	−399.962	−	476.656i	−0.503730	−	0.600322i
$795$		0			0
$796$	41.8789	−	237.507i	0.0526117	−	0.298376i
$797$	1089.55	+	192.117i	1.36706	+	0.241050i	0.808541	−	0.588440i	$-0.200258\pi$
$797$	1089.55	+	192.117i	1.36706	+	0.241050i	0.558522	+	0.829490i	$0.311369\pi$
$798$		0			0
$799$	−321.173	+	269.496i	−0.401969	+	0.337292i
$800$	−663.943	−	383.327i	−0.829928	−	0.479159i
$801$		0			0
$802$	416.830	+	721.971i	0.519738	+	0.900213i
$803$	10.5384	−	28.9539i	0.0131237	−	0.0360572i
$804$		0			0
$805$	55.2913	+	46.3949i	0.0686848	+	0.0576334i
$806$	−70.5352	−	193.794i	−0.0875126	−	0.240439i
$807$		0			0
$808$	121.176	+	687.225i	0.149971	+	0.850526i
$809$		−	384.421i		−	0.475180i	−0.971365	−	0.237590i	$-0.923642\pi$
$809$		−	384.421i		−	0.475180i	0.971365	−	0.237590i	$-0.0763575\pi$
$810$		0			0
$811$	−575.544			−0.709672			−0.354836	−	0.934929i	$-0.615463\pi$
$811$	−575.544			−0.709672			−0.354836	+	0.934929i	$0.615463\pi$
$812$	−295.001	+	52.0166i	−0.363302	+	0.0640599i
$813$		0			0
$814$	197.547	−	71.9012i	0.242687	−	0.0883307i
$815$	−11.0337	+	13.1495i	−0.0135383	+	0.0161343i
$816$		0			0
$817$	−185.862	−	67.6481i	−0.227493	−	0.0828007i
$818$	308.351	−	178.027i	0.376957	−	0.217636i
$819$		0			0
$820$	−11.0965	+	19.2197i	−0.0135323	+	0.0234386i
$821$	544.254	+	648.617i	0.662916	+	0.790033i	0.987801	−	0.155721i	$-0.0497699\pi$
$821$	544.254	+	648.617i	0.662916	+	0.790033i	−0.324885	+	0.945754i	$0.605325\pi$
$822$		0			0
$823$	−215.314	+	1221.11i	−0.261621	+	1.48373i	0.516866	+	0.856066i	$0.327098\pi$
$823$	−215.314	+	1221.11i	−0.261621	+	1.48373i	−0.778487	+	0.627660i	$0.784013\pi$
$824$	356.248	+	62.8161i	0.432339	+	0.0762331i
$825$		0			0
$826$	−329.816	+	276.749i	−0.399294	+	0.335047i
$827$	989.439	+	571.253i	1.19642	+	0.690753i	0.959755	−	0.280839i	$-0.0906126\pi$
$827$	989.439	+	571.253i	1.19642	+	0.690753i	0.236664	+	0.971592i	$0.423946\pi$
$828$		0			0
$829$	−150.614	−	260.872i	−0.181682	−	0.314683i	0.760771	−	0.649020i	$-0.224821\pi$
$829$	−150.614	−	260.872i	−0.181682	−	0.314683i	−0.942453	+	0.334337i	$0.891487\pi$
$830$	−24.0981	+	66.2090i	−0.0290338	+	0.0797698i
$831$		0			0
$832$	338.234	+	283.812i	0.406531	+	0.341120i
$833$	−19.8982	−	54.6697i	−0.0238873	−	0.0656299i
$834$		0			0
$835$	9.91493	+	56.2304i	0.0118742	+	0.0673418i
$836$			1242.82i			1.48663i
$837$		0			0
$838$	175.410			0.209320
$839$	34.9187	−	6.15711i	0.0416194	−	0.00733863i	−0.152800	−	0.988257i	$-0.548829\pi$
$839$	34.9187	−	6.15711i	0.0416194	−	0.00733863i	0.194419	+	0.980919i	$0.437718\pi$
$840$		0			0
$841$	−360.416	+	131.181i	−0.428557	+	0.155982i
$842$	−284.419	+	338.958i	−0.337790	+	0.402562i
$843$		0			0
$844$	640.239	+	233.028i	0.758577	+	0.276099i
$845$	29.4560	−	17.0064i	0.0348592	−	0.0201260i
$846$		0			0
$847$	−333.201	+	577.121i	−0.393390	+	0.681371i
$848$	−30.7075	−	36.5957i	−0.0362116	−	0.0431553i
$849$		0			0
$850$	27.2561	−	154.577i	0.0320660	−	0.181855i
$851$	284.045	+	50.0848i	0.333778	+	0.0588540i
$852$		0			0
$853$	1101.67	−	924.412i	1.29153	−	1.08372i	0.299982	−	0.953945i	$-0.403019\pi$
$853$	1101.67	−	924.412i	1.29153	−	1.08372i	0.991544	−	0.129774i	$-0.0414252\pi$
$854$	−224.629	−	129.689i	−0.263031	−	0.151861i
$855$		0			0
$856$	−226.488	−	392.289i	−0.264589	−	0.458281i
$857$	135.657	−	372.715i	0.158293	−	0.434906i	−0.835040	−	0.550190i	$-0.814555\pi$
$857$	135.657	−	372.715i	0.158293	−	0.434906i	0.993333	+	0.115283i	$0.0367776\pi$
$858$		0			0
$859$	134.206	+	112.612i	0.156235	+	0.131097i	0.717554	−	0.696502i	$-0.245261\pi$
$859$	134.206	+	112.612i	0.156235	+	0.131097i	−0.561319	+	0.827600i	$0.689706\pi$
$860$	−1.91387	−	5.25832i	−0.00222543	−	0.00611433i
$861$		0			0
$862$	83.6610	+	474.465i	0.0970546	+	0.550424i
$863$		−	220.638i		−	0.255664i	−0.991796	−	0.127832i	$-0.959198\pi$
$863$		−	220.638i		−	0.255664i	0.991796	−	0.127832i	$-0.0408018\pi$
$864$		0			0
$865$	−37.4940			−0.0433457
$866$	−710.212	+	125.230i	−0.820107	+	0.144607i
$867$		0			0
$868$	−218.138	+	79.3958i	−0.251311	+	0.0914698i
$869$	−721.821	+	860.233i	−0.830634	+	0.989911i
$870$		0			0
$871$	25.2820	+	9.20189i	0.0290264	+	0.0105647i
$872$	764.376	−	441.313i	0.876578	−	0.506093i
$873$		0			0
$874$	628.903	−	1089.29i	0.719569	−	1.24633i
$875$	85.1311	+	101.455i	0.0972927	+	0.115949i
$876$		0			0
$877$	−116.145	+	658.692i	−0.132435	+	0.751074i	0.844177	+	0.536064i	$0.180089\pi$
$877$	−116.145	+	658.692i	−0.132435	+	0.751074i	−0.976612	+	0.215010i	$0.931022\pi$
$878$	−866.453	−	152.779i	−0.986849	−	0.174008i
$879$		0			0
$880$	7.59021	−	6.36894i	0.00862524	−	0.00723743i
$881$	750.509	+	433.306i	0.851883	+	0.491835i	0.861286	−	0.508121i	$-0.169660\pi$
$881$	750.509	+	433.306i	0.851883	+	0.491835i	−0.00940287	+	0.999956i	$0.502993\pi$
$882$		0			0
$883$	93.3464	+	161.681i	0.105715	+	0.183104i	0.914030	−	0.405646i	$-0.132954\pi$
$883$	93.3464	+	161.681i	0.105715	+	0.183104i	−0.808315	+	0.588750i	$0.799620\pi$
$884$	36.4996	−	100.282i	0.0412891	−	0.113441i
$885$		0			0
$886$	553.858	+	464.742i	0.625122	+	0.524539i
$887$	355.796	+	977.541i	0.401123	+	1.10208i	0.961731	+	0.273995i	$0.0883450\pi$
$887$	355.796	+	977.541i	0.401123	+	1.10208i	−0.560609	+	0.828081i	$0.689433\pi$
$888$		0			0
$889$	−134.974	−	765.474i	−0.151826	−	0.861050i
$890$		−	20.3951i		−	0.0229158i
$891$		0			0
$892$	702.457			0.787508
$893$	−3023.97	+	533.207i	−3.38630	+	0.597097i
$894$		0			0
$895$	−103.357	+	37.6188i	−0.115483	+	0.0420322i
$896$	247.761	−	295.270i	0.276519	−	0.329542i
$897$		0			0
$898$	−727.226	−	264.688i	−0.809828	−	0.294753i
$899$	307.009	−	177.252i	0.341500	−	0.197165i
$900$		0			0
$901$	−77.6657	+	134.521i	−0.0861994	+	0.149302i
$902$	280.554	+	334.351i	0.311035	+	0.370677i
$903$		0			0
$904$	39.3028	−	222.897i	0.0434766	−	0.246568i
$905$	97.9358	+	17.2687i	0.108216	+	0.0190815i
$906$		0			0
$907$	48.5015	−	40.6976i	0.0534746	−	0.0448705i	−0.615659	−	0.788013i	$-0.711110\pi$
$907$	48.5015	−	40.6976i	0.0534746	−	0.0448705i	0.669133	+	0.743142i	$0.266666\pi$
$908$	−189.361	−	109.328i	−0.208547	−	0.120405i
$909$		0			0
$910$	−16.5421	−	28.6517i	−0.0181781	−	0.0314854i
$911$	455.175	−	1250.58i	0.499644	−	1.37276i	−0.391977	−	0.919975i	$-0.628209\pi$
$911$	455.175	−	1250.58i	0.499644	−	1.37276i	0.891620	−	0.452784i	$-0.149569\pi$
$912$		0			0
$913$	−1439.01	−	1207.47i	−1.57613	−	1.32253i
$914$	−166.447	−	457.311i	−0.182109	−	0.500340i
$915$		0			0
$916$	45.9962	+	260.858i	0.0502142	+	0.284779i
$917$			292.856i			0.319363i
$918$		0			0
$919$	351.465			0.382443			0.191222	−	0.981547i	$-0.438755\pi$
$919$	351.465			0.382443			0.191222	+	0.981547i	$0.438755\pi$
$920$	95.9405	−	16.9169i	0.104283	−	0.0183879i
$921$		0			0
$922$	−510.792	+	185.913i	−0.554004	+	0.201641i
$923$	709.606	−	845.676i	0.768804	−	0.916225i
$924$		0			0
$925$	247.708	+	90.1585i	0.267793	+	0.0974686i
$926$	307.948	−	177.794i	0.332558	−	0.192002i
$927$		0			0
$928$	−330.471	+	572.393i	−0.356111	+	0.616803i
$929$	−47.7111	−	56.8599i	−0.0513575	−	0.0612055i	0.739754	−	0.672877i	$-0.234942\pi$
$929$	−47.7111	−	56.8599i	−0.0513575	−	0.0612055i	−0.791112	+	0.611672i	$0.790497\pi$
$930$		0			0
$931$	73.9897	−	419.617i	0.0794734	−	0.450716i
$932$	−95.0769	−	16.7646i	−0.102014	−	0.0179878i
$933$		0			0
$934$	−99.6090	+	83.5819i	−0.106648	+	0.0894881i
$935$	−27.9006	−	16.1084i	−0.0298402	−	0.0172282i
$936$		0			0
$937$	−808.594	−	1400.53i	−0.862961	−	1.49469i	−0.869058	−	0.494710i	$-0.835274\pi$
$937$	−808.594	−	1400.53i	−0.862961	−	1.49469i	0.00609719	−	0.999981i	$-0.498059\pi$
$938$	−7.64052	+	20.9922i	−0.00814555	+	0.0223797i
$939$		0			0
$940$	−66.5483	−	55.8407i	−0.0707961	−	0.0594050i
$941$	−415.315	−	1141.07i	−0.441355	−	1.21261i	−0.938602	−	0.345003i	$-0.887878\pi$
$941$	−415.315	−	1141.07i	−0.441355	−	1.21261i	0.497247	−	0.867609i	$-0.334344\pi$
$942$		0			0
$943$	103.985	+	589.727i	0.110270	+	0.625373i
$944$			81.0898i			0.0859002i
$945$		0			0
$946$	−110.051			−0.116333
$947$	992.049	−	174.925i	1.04757	−	0.184715i	0.376735	−	0.926321i	$-0.377047\pi$
$947$	992.049	−	174.925i	1.04757	−	0.184715i	0.670835	+	0.741606i	$0.265936\pi$
$948$		0			0
$949$	−18.2086	+	6.62737i	−0.0191871	+	0.00698353i
$950$	738.926	−	880.617i	0.777816	−	0.926965i
$951$		0			0
$952$	227.954	+	82.9684i	0.239447	+	0.0871517i
$953$	−1029.21	+	594.215i	−1.07997	+	0.623521i	−0.930888	−	0.365304i	$-0.880965\pi$
$953$	−1029.21	+	594.215i	−1.07997	+	0.623521i	−0.149082	+	0.988825i	$0.547632\pi$
$954$		0			0
$955$	−39.5222	+	68.4545i	−0.0413845	+	0.0716801i
$956$	47.6437	+	56.7795i	0.0498365	+	0.0593928i
$957$		0			0
$958$	108.610	−	615.957i	0.113371	−	0.642961i
$959$	−824.458	−	145.374i	−0.859706	−	0.151589i
$960$		0			0
$961$	−525.719	+	441.131i	−0.547054	+	0.459033i
$962$	−114.494	−	66.1032i	−0.119017	−	0.0687144i
$963$		0			0
$964$	164.838	+	285.508i	0.170994	+	0.296171i
$965$	29.0749	−	79.8826i	0.0301294	−	0.0827799i
$966$		0			0
$967$	−194.236	−	162.983i	−0.200864	−	0.168545i	0.536807	−	0.843705i	$-0.319630\pi$
$967$	−194.236	−	162.983i	−0.200864	−	0.168545i	−0.737672	+	0.675160i	$0.764075\pi$
$968$	307.635	+	845.220i	0.317805	+	0.873161i
$969$		0			0
$970$	7.94705	+	45.0699i	0.00819283	+	0.0464638i
$971$		−	1630.38i		−	1.67907i	−0.543302	−	0.839537i	$-0.682826\pi$
$971$		−	1630.38i		−	1.67907i	0.543302	−	0.839537i	$-0.317174\pi$
$972$		0			0
$973$	556.059			0.571489
$974$	391.942	−	69.1100i	0.402405	−	0.0709549i
$975$		0			0
$976$	−45.9059	+	16.7084i	−0.0470347	+	0.0171192i
$977$	52.8082	−	62.9344i	0.0540514	−	0.0644160i	−0.738341	−	0.674427i	$-0.764391\pi$
$977$	52.8082	−	62.9344i	0.0540514	−	0.0644160i	0.792393	+	0.610011i	$0.208835\pi$
$978$		0			0
$979$	510.963	+	185.975i	0.521923	+	0.189965i
$980$	10.4397	−	6.02738i	0.0106528	−	0.00615039i
$981$		0			0
$982$	−222.299	+	385.033i	−0.226373	+	0.392090i
$983$	332.927	+	396.767i	0.338685	+	0.403629i	0.908325	−	0.418266i	$-0.137362\pi$
$983$	332.927	+	396.767i	0.338685	+	0.403629i	−0.569640	+	0.821894i	$0.692917\pi$
$984$		0			0
$985$	19.6881	−	111.657i	0.0199879	−	0.113357i
$986$	−133.263	−	23.4978i	−0.135155	−	0.0238314i
$987$		0			0
$988$	598.729	−	502.393i	0.606001	−	0.508495i
$989$	−130.760	−	75.4945i	−0.132215	−	0.0763342i
$990$		0			0
$991$	−35.3222	−	61.1798i	−0.0356430	−	0.0617354i	0.847654	−	0.530550i	$-0.178015\pi$
$991$	−35.3222	−	61.1798i	−0.0356430	−	0.0617354i	−0.883297	+	0.468815i	$0.844681\pi$
$992$	−175.182	+	481.308i	−0.176595	+	0.485190i
$993$		0			0
$994$	702.182	+	589.201i	0.706421	+	0.592758i
$995$	15.6600	+	43.0254i	0.0157387	+	0.0432416i
$996$		0			0
$997$	−269.483	−	1528.32i	−0.270294	−	1.53292i	−0.753523	−	0.657421i	$-0.771647\pi$
$997$	−269.483	−	1528.32i	−0.270294	−	1.53292i	0.483229	−	0.875494i	$-0.339464\pi$
$998$		−	431.736i		−	0.432601i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.3.f.c.215.2		30
3.2	odd	2		243.3.f.b.215.4		30
9.2	odd	6		81.3.f.a.44.2		30
9.4	even	3		243.3.f.d.53.4		30
9.5	odd	6		243.3.f.a.53.2		30
9.7	even	3		27.3.f.a.5.4	✓	30
27.2	odd	18	inner	243.3.f.c.26.2		30
27.5	odd	18		729.3.b.a.728.11		30
27.7	even	9		81.3.f.a.35.2		30
27.11	odd	18		243.3.f.d.188.4		30
27.16	even	9		243.3.f.a.188.2		30
27.20	odd	18		27.3.f.a.11.4	yes	30
27.22	even	9		729.3.b.a.728.20		30
27.25	even	9		243.3.f.b.26.4		30
36.7	odd	6		432.3.bc.a.113.3		30
108.47	even	18		432.3.bc.a.65.3		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.5.4	✓	30	9.7	even	3
27.3.f.a.11.4	yes	30	27.20	odd	18
81.3.f.a.35.2		30	27.7	even	9
81.3.f.a.44.2		30	9.2	odd	6
243.3.f.a.53.2		30	9.5	odd	6
243.3.f.a.188.2		30	27.16	even	9
243.3.f.b.26.4		30	27.25	even	9
243.3.f.b.215.4		30	3.2	odd	2
243.3.f.c.26.2		30	27.2	odd	18	inner
243.3.f.c.215.2		30	1.1	even	1	trivial
243.3.f.d.53.4		30	9.4	even	3
243.3.f.d.188.4		30	27.11	odd	18
432.3.bc.a.65.3		30	108.47	even	18
432.3.bc.a.113.3		30	36.7	odd	6
729.3.b.a.728.11		30	27.5	odd	18
729.3.b.a.728.20		30	27.22	even	9

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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	243.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.28330 + 0.226280i) q^{2} +(-2.16313 + 0.787313i) q^{4} +(0.280917 - 0.334784i) q^{5} +(5.71727 + 2.08092i) q^{7} +(7.11182 - 4.10601i) q^{8} +O(q^{10})\)	\(q+(-1.28330 + 0.226280i) q^{2} +(-2.16313 + 0.787313i) q^{4} +(0.280917 - 0.334784i) q^{5} +(5.71727 + 2.08092i) q^{7} +(7.11182 - 4.10601i) q^{8} +(-0.284745 + 0.493192i) q^{10} +(-9.75958 - 11.6310i) q^{11} +(-1.65807 + 9.40337i) q^{13} +(-7.80781 - 1.37673i) q^{14} +(-1.14388 + 0.959828i) q^{16} +(4.20474 + 2.42761i) q^{17} +(17.7795 + 30.7949i) q^{19} +(-0.344079 + 0.945348i) q^{20} +(15.1563 + 12.7176i) q^{22} +(9.28414 + 25.5080i) q^{23} +(4.30804 + 24.4321i) q^{25} -12.4425i q^{26} -14.0055 q^{28} +(21.0632 - 3.71401i) q^{29} +(15.5752 - 5.66890i) q^{31} +(-19.8636 + 23.6725i) q^{32} +(-5.94524 - 2.16389i) q^{34} +(2.30273 - 1.32948i) q^{35} +(5.31270 - 9.20187i) q^{37} +(-29.7846 - 35.4959i) q^{38} +(0.623204 - 3.53437i) q^{40} +(21.7250 + 3.83071i) q^{41} +(-4.26098 + 3.57539i) q^{43} +(30.2685 + 17.4755i) q^{44} +(-17.6862 - 30.6334i) q^{46} +(-29.5345 + 81.1452i) q^{47} +(-9.17924 - 7.70230i) q^{49} +(-11.0570 - 30.3788i) q^{50} +(-3.81679 - 21.6461i) q^{52} +31.9927i q^{53} -6.63550 q^{55} +(49.2044 - 8.67607i) q^{56} +(-26.1899 + 9.53235i) q^{58} +(34.9066 - 41.6001i) q^{59} +(30.7427 + 11.1894i) q^{61} +(-18.7048 + 10.7992i) q^{62} +(23.1207 - 40.0463i) q^{64} +(2.68231 + 3.19666i) q^{65} +(0.489287 - 2.77488i) q^{67} +(-11.0067 - 1.94077i) q^{68} +(-2.65425 + 2.22718i) q^{70} +(-100.126 - 57.8080i) q^{71} +(1.01468 + 1.75747i) q^{73} +(-4.73557 + 13.0109i) q^{74} +(-62.7045 - 52.6153i) q^{76} +(-31.5950 - 86.8065i) q^{77} +(-12.8431 - 72.8366i) q^{79} +0.652583i q^{80} -28.7465 q^{82} +(121.842 - 21.4840i) q^{83} +(1.99390 - 0.725722i) q^{85} +(4.65906 - 5.55245i) q^{86} +(-117.166 - 42.6448i) q^{88} +(-31.0149 + 17.9065i) q^{89} +(-29.0472 + 50.3113i) q^{91} +(-40.1655 - 47.8674i) q^{92} +(19.5399 - 110.816i) q^{94} +(15.3042 + 2.69854i) q^{95} +(61.5608 - 51.6556i) q^{97} +(13.5226 + 7.80725i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} + 3 q^{4} - 6 q^{5} + 3 q^{7} - 9 q^{8}+O(q^{10}) \) 30 * q + 3 * q^2 + 3 * q^4 - 6 * q^5 + 3 * q^7 - 9 * q^8	\( 30 q + 3 q^{2} + 3 q^{4} - 6 q^{5} + 3 q^{7} - 9 q^{8} - 3 q^{10} - 51 q^{11} + 3 q^{13} + 129 q^{14} - 9 q^{16} - 9 q^{17} - 3 q^{19} - 30 q^{20} - 33 q^{22} - 168 q^{23} - 6 q^{25} - 12 q^{28} + 246 q^{29} + 48 q^{31} + 117 q^{32} + 99 q^{34} - 252 q^{35} - 3 q^{37} - 237 q^{38} + 201 q^{40} + 129 q^{41} + 183 q^{43} + 639 q^{44} - 3 q^{46} - 348 q^{47} + 147 q^{49} - 471 q^{50} + 45 q^{52} - 12 q^{55} + 570 q^{56} - 267 q^{58} + 426 q^{59} - 285 q^{61} - 900 q^{62} - 51 q^{64} - 213 q^{65} - 366 q^{67} + 378 q^{68} - 483 q^{70} + 315 q^{71} - 66 q^{73} + 159 q^{74} - 201 q^{76} - 654 q^{77} - 15 q^{79} - 12 q^{82} + 624 q^{83} + 18 q^{85} - 411 q^{86} + 51 q^{88} + 72 q^{89} + 96 q^{91} - 561 q^{92} - 96 q^{94} - 75 q^{95} - 114 q^{97} + 882 q^{98}+O(q^{100}) \) 30 * q + 3 * q^2 + 3 * q^4 - 6 * q^5 + 3 * q^7 - 9 * q^8 - 3 * q^10 - 51 * q^11 + 3 * q^13 + 129 * q^14 - 9 * q^16 - 9 * q^17 - 3 * q^19 - 30 * q^20 - 33 * q^22 - 168 * q^23 - 6 * q^25 - 12 * q^28 + 246 * q^29 + 48 * q^31 + 117 * q^32 + 99 * q^34 - 252 * q^35 - 3 * q^37 - 237 * q^38 + 201 * q^40 + 129 * q^41 + 183 * q^43 + 639 * q^44 - 3 * q^46 - 348 * q^47 + 147 * q^49 - 471 * q^50 + 45 * q^52 - 12 * q^55 + 570 * q^56 - 267 * q^58 + 426 * q^59 - 285 * q^61 - 900 * q^62 - 51 * q^64 - 213 * q^65 - 366 * q^67 + 378 * q^68 - 483 * q^70 + 315 * q^71 - 66 * q^73 + 159 * q^74 - 201 * q^76 - 654 * q^77 - 15 * q^79 - 12 * q^82 + 624 * q^83 + 18 * q^85 - 411 * q^86 + 51 * q^88 + 72 * q^89 + 96 * q^91 - 561 * q^92 - 96 * q^94 - 75 * q^95 - 114 * q^97 + 882 * q^98

Introduction

L-functions

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