LMFDB - Embedded newform 135.3.i.a.71.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,3,Mod(71,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("135.71");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	135.i (of order $6$, degree $2$, 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:	$3.67848356886$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 48x^{14} + 912x^{12} + 8704x^{10} + 43602x^{8} + 109032x^{6} + 117844x^{4} + 36000x^{2} + 81 $ x^16 + 48x^14 + 912x^12 + 8704x^10 + 43602x^8 + 109032x^6 + 117844x^4 + 36000*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			71.7
Root			$-3.27064i$ of defining polynomial
Character	$\chi$	$=$	135.71
Dual form			135.3.i.a.116.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.83245 - 1.63532i) q^{2} +(3.34853 - 5.79983i) q^{4} +(1.93649 + 1.11803i) q^{5} +(-3.16931 - 5.48940i) q^{7} -8.82112i q^{8} +O(q^{10})$	\(q+(2.83245 - 1.63532i) q^{2} +(3.34853 - 5.79983i) q^{4} +(1.93649 + 1.11803i) q^{5} +(-3.16931 - 5.48940i) q^{7} -8.82112i q^{8} +7.31337 q^{10} +(12.8821 - 7.43751i) q^{11} +(-7.73683 + 13.4006i) q^{13} +(-17.9538 - 10.3656i) q^{14} +(-1.03121 - 1.78610i) q^{16} +20.0994i q^{17} -25.1235 q^{19} +(12.9688 - 7.48755i) q^{20} +(24.3254 - 42.1328i) q^{22} +(-1.40763 - 0.812693i) q^{23} +(2.50000 + 4.33013i) q^{25} +50.6087i q^{26} -42.4501 q^{28} +(1.07318 - 0.619600i) q^{29} +(-6.69310 + 11.5928i) q^{31} +(24.7156 + 14.2695i) q^{32} +(32.8689 + 56.9306i) q^{34} -14.1736i q^{35} +3.89313 q^{37} +(-71.1610 + 41.0848i) q^{38} +(9.86231 - 17.0820i) q^{40} +(-50.3757 - 29.0844i) q^{41} +(13.6159 + 23.5834i) q^{43} -99.6189i q^{44} -5.31605 q^{46} +(54.2876 - 31.3429i) q^{47} +(4.41100 - 7.64007i) q^{49} +(14.1623 + 8.17659i) q^{50} +(51.8140 + 89.7446i) q^{52} +18.2849i q^{53} +33.2615 q^{55} +(-48.4226 + 27.9568i) q^{56} +(2.02649 - 3.50998i) q^{58} +(25.1430 + 14.5163i) q^{59} +(-55.5971 - 96.2970i) q^{61} +43.7814i q^{62} +101.591 q^{64} +(-29.9646 + 17.3001i) q^{65} +(8.56418 - 14.8336i) q^{67} +(116.573 + 67.3034i) q^{68} +(-23.1783 - 40.1460i) q^{70} -52.7477i q^{71} -71.0560 q^{73} +(11.0271 - 6.36651i) q^{74} +(-84.1267 + 145.712i) q^{76} +(-81.6549 - 47.1435i) q^{77} +(-30.2675 - 52.4248i) q^{79} -4.61169i q^{80} -190.249 q^{82} +(-70.2143 + 40.5382i) q^{83} +(-22.4718 + 38.9223i) q^{85} +(77.1327 + 44.5326i) q^{86} +(-65.6071 - 113.635i) q^{88} -6.34811i q^{89} +98.0815 q^{91} +(-9.42696 + 5.44266i) q^{92} +(102.511 - 177.555i) q^{94} +(-48.6514 - 28.0889i) q^{95} +(7.84018 + 13.5796i) q^{97} -28.8535i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4} + 2 q^{7}+O(q^{10}) $ 16 * q + 16 * q^4 + 2 * q^7	$ 16 q + 16 q^{4} + 2 q^{7} + 18 q^{11} - 10 q^{13} + 54 q^{14} - 32 q^{16} - 52 q^{19} - 24 q^{22} + 54 q^{23} + 40 q^{25} + 32 q^{28} + 54 q^{29} + 32 q^{31} - 216 q^{32} + 54 q^{34} + 44 q^{37} - 252 q^{38} - 30 q^{40} - 144 q^{41} - 124 q^{43} - 108 q^{46} + 216 q^{47} - 54 q^{49} + 62 q^{52} + 18 q^{56} + 90 q^{58} + 486 q^{59} + 62 q^{61} + 256 q^{64} + 90 q^{65} + 14 q^{67} + 288 q^{68} - 60 q^{70} - 268 q^{73} - 540 q^{74} - 106 q^{76} - 702 q^{77} - 40 q^{79} - 204 q^{82} - 522 q^{83} + 30 q^{85} - 54 q^{86} + 144 q^{88} + 136 q^{91} + 1332 q^{92} - 150 q^{94} - 180 q^{95} - 142 q^{97}+O(q^{100}) $ 16 * q + 16 * q^4 + 2 * q^7 + 18 * q^11 - 10 * q^13 + 54 * q^14 - 32 * q^16 - 52 * q^19 - 24 * q^22 + 54 * q^23 + 40 * q^25 + 32 * q^28 + 54 * q^29 + 32 * q^31 - 216 * q^32 + 54 * q^34 + 44 * q^37 - 252 * q^38 - 30 * q^40 - 144 * q^41 - 124 * q^43 - 108 * q^46 + 216 * q^47 - 54 * q^49 + 62 * q^52 + 18 * q^56 + 90 * q^58 + 486 * q^59 + 62 * q^61 + 256 * q^64 + 90 * q^65 + 14 * q^67 + 288 * q^68 - 60 * q^70 - 268 * q^73 - 540 * q^74 - 106 * q^76 - 702 * q^77 - 40 * q^79 - 204 * q^82 - 522 * q^83 + 30 * q^85 - 54 * q^86 + 144 * q^88 + 136 * q^91 + 1332 * q^92 - 150 * q^94 - 180 * q^95 - 142 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	2.83245	−	1.63532i	1.41623	−	0.817659i	0.420262	−	0.907403i	$-0.361938\pi$
$2$	2.83245	−	1.63532i	1.41623	−	0.817659i	0.995965	+	0.0897435i	$0.0286047\pi$
$3$		0			0
$3$		0			0
$4$	3.34853	−	5.79983i	0.837133	−	1.44996i
$5$	1.93649	+	1.11803i	0.387298	+	0.223607i
$5$	1.93649	+	1.11803i	0.387298	+	0.223607i
$6$		0			0
$7$	−3.16931	−	5.48940i	−0.452758	−	0.784200i	0.545798	−	0.837917i	$-0.316227\pi$
$7$	−3.16931	−	5.48940i	−0.452758	−	0.784200i	−0.998556	+	0.0537168i	$0.982893\pi$
$8$		−	8.82112i		−	1.10264i
$9$		0			0
$10$	7.31337			0.731337
$11$	12.8821	−	7.43751i	1.17110	−	0.676137i	0.217164	−	0.976135i	$-0.430319\pi$
$11$	12.8821	−	7.43751i	1.17110	−	0.676137i	0.953940	+	0.299998i	$0.0969860\pi$
$12$		0			0
$13$	−7.73683	+	13.4006i	−0.595141	+	1.03081i	0.398386	+	0.917218i	$0.369570\pi$
$13$	−7.73683	+	13.4006i	−0.595141	+	1.03081i	−0.993527	+	0.113596i	$0.963763\pi$
$14$	−17.9538	−	10.3656i	−1.28242	−	0.740403i
$15$		0			0
$16$	−1.03121	−	1.78610i	−0.0644503	−	0.111631i
$17$			20.0994i			1.18232i	0.806555	+	0.591159i	$0.201329\pi$
$17$			20.0994i			1.18232i	−0.806555	+	0.591159i	$0.798671\pi$
$18$		0			0
$19$	−25.1235			−1.32229			−0.661144	−	0.750259i	$-0.729929\pi$
$19$	−25.1235			−1.32229			−0.661144	+	0.750259i	$0.729929\pi$
$20$	12.9688	−	7.48755i	0.648440	−	0.374377i
$21$		0			0
$22$	24.3254	−	42.1328i	1.10570	−	1.91513i
$23$	−1.40763	−	0.812693i	−0.0612011	−	0.0353345i	0.469087	−	0.883152i	$-0.344583\pi$
$23$	−1.40763	−	0.812693i	−0.0612011	−	0.0353345i	−0.530288	+	0.847817i	$0.677916\pi$
$24$		0			0
$25$	2.50000	+	4.33013i	0.100000	+	0.173205i
$26$			50.6087i			1.94649i
$27$		0			0
$28$	−42.4501			−1.51607
$29$	1.07318	−	0.619600i	0.0370062	−	0.0213655i	−0.481383	−	0.876510i	$-0.659865\pi$
$29$	1.07318	−	0.619600i	0.0370062	−	0.0213655i	0.518389	+	0.855145i	$0.326532\pi$
$30$		0			0
$31$	−6.69310	+	11.5928i	−0.215907	+	0.373961i	−0.953553	−	0.301226i	$-0.902604\pi$
$31$	−6.69310	+	11.5928i	−0.215907	+	0.373961i	0.737646	+	0.675188i	$0.235937\pi$
$32$	24.7156	+	14.2695i	0.772361	+	0.445923i
$33$		0			0
$34$	32.8689	+	56.9306i	0.966732	+	1.67443i
$35$		−	14.1736i		−	0.404959i
$36$		0			0
$37$	3.89313			0.105220			0.0526099	−	0.998615i	$-0.483246\pi$
$37$	3.89313			0.105220			0.0526099	+	0.998615i	$0.483246\pi$
$38$	−71.1610	+	41.0848i	−1.87266	+	1.08118i
$39$		0			0
$40$	9.86231	−	17.0820i	0.246558	−	0.427050i
$41$	−50.3757	−	29.0844i	−1.22868	−	0.709376i	−0.261923	−	0.965089i	$-0.584357\pi$
$41$	−50.3757	−	29.0844i	−1.22868	−	0.709376i	−0.966753	+	0.255713i	$0.917690\pi$
$42$		0			0
$43$	13.6159	+	23.5834i	0.316648	+	0.548451i	0.979787	−	0.200046i	$-0.0641091\pi$
$43$	13.6159	+	23.5834i	0.316648	+	0.548451i	−0.663138	+	0.748497i	$0.730776\pi$
$44$		−	99.6189i		−	2.26407i
$45$		0			0
$46$	−5.31605			−0.115566
$47$	54.2876	−	31.3429i	1.15505	−	0.666871i	0.204941	−	0.978774i	$-0.434300\pi$
$47$	54.2876	−	31.3429i	1.15505	−	0.666871i	0.950114	+	0.311903i	$0.100966\pi$
$48$		0			0
$49$	4.41100	−	7.64007i	0.0900204	−	0.155920i
$50$	14.1623	+	8.17659i	0.283245	+	0.163532i
$51$		0			0
$52$	51.8140	+	89.7446i	0.996424	+	1.72586i
$53$			18.2849i			0.344999i	0.985010	+	0.172499i	$0.0551843\pi$
$53$			18.2849i			0.344999i	−0.985010	+	0.172499i	$0.944816\pi$
$54$		0			0
$55$	33.2615			0.604755
$56$	−48.4226	+	27.9568i	−0.864690	+	0.499229i
$57$		0			0
$58$	2.02649	−	3.50998i	0.0349394	−	0.0605169i
$59$	25.1430	+	14.5163i	0.426153	+	0.246039i	0.697706	−	0.716384i	$-0.254204\pi$
$59$	25.1430	+	14.5163i	0.426153	+	0.246039i	−0.271553	+	0.962423i	$0.587537\pi$
$60$		0			0
$61$	−55.5971	−	96.2970i	−0.911428	−	1.57864i	−0.812048	−	0.583590i	$-0.801647\pi$
$61$	−55.5971	−	96.2970i	−0.911428	−	1.57864i	−0.0993799	−	0.995050i	$-0.531686\pi$
$62$			43.7814i			0.706152i
$63$		0			0
$64$	101.591			1.58735
$65$	−29.9646	+	17.3001i	−0.460994	+	0.266155i
$66$		0			0
$67$	8.56418	−	14.8336i	0.127824	−	0.221397i	−0.795010	−	0.606597i	$-0.792534\pi$
$67$	8.56418	−	14.8336i	0.127824	−	0.221397i	0.922833	+	0.385200i	$0.125868\pi$
$68$	116.573	+	67.3034i	1.71431	+	0.989757i
$69$		0			0
$70$	−23.1783	−	40.1460i	−0.331118	−	0.573514i
$71$		−	52.7477i		−	0.742925i	−0.928448	−	0.371463i	$-0.878856\pi$
$71$		−	52.7477i		−	0.742925i	0.928448	−	0.371463i	$-0.121144\pi$
$72$		0			0
$73$	−71.0560			−0.973370			−0.486685	−	0.873577i	$-0.661794\pi$
$73$	−71.0560			−0.973370			−0.486685	+	0.873577i	$0.661794\pi$
$74$	11.0271	−	6.36651i	0.149015	−	0.0860339i
$75$		0			0
$76$	−84.1267	+	145.712i	−1.10693	+	1.91726i
$77$	−81.6549	−	47.1435i	−1.06045	−	0.612253i
$78$		0			0
$79$	−30.2675	−	52.4248i	−0.383133	−	0.663606i	0.608375	−	0.793649i	$-0.291822\pi$
$79$	−30.2675	−	52.4248i	−0.383133	−	0.663606i	−0.991508	+	0.130044i	$0.958488\pi$
$80$		−	4.61169i		−	0.0576461i
$81$		0			0
$82$	−190.249			−2.32011
$83$	−70.2143	+	40.5382i	−0.845955	+	0.488412i	−0.859284	−	0.511499i	$-0.829090\pi$
$83$	−70.2143	+	40.5382i	−0.845955	+	0.488412i	0.0133289	+	0.999911i	$0.495757\pi$
$84$		0			0
$85$	−22.4718	+	38.9223i	−0.264374	+	0.457909i
$86$	77.1327	+	44.5326i	0.896892	+	0.517821i
$87$		0			0
$88$	−65.6071	−	113.635i	−0.745535	−	1.29131i
$89$		−	6.34811i		−	0.0713271i	−0.999364	−	0.0356635i	$-0.988646\pi$
$89$		−	6.34811i		−	0.0713271i	0.999364	−	0.0356635i	$-0.0113545\pi$
$90$		0			0
$91$	98.0815			1.07782
$92$	−9.42696	+	5.44266i	−0.102467	+	0.0591593i
$93$		0			0
$94$	102.511	−	177.555i	1.09055	−	1.88888i
$95$	−48.6514	−	28.0889i	−0.512120	−	0.295672i
$96$		0			0
$97$	7.84018	+	13.5796i	0.0808266	+	0.139996i	0.903605	−	0.428366i	$-0.140911\pi$
$97$	7.84018	+	13.5796i	0.0808266	+	0.139996i	−0.822779	+	0.568362i	$0.807577\pi$
$98$		−	28.8535i		−	0.294424i
$99$		0			0
$100$	33.4853			0.334853
$101$	99.2919	−	57.3262i	0.983088	−	0.567586i	0.0798873	−	0.996804i	$-0.474544\pi$
$101$	99.2919	−	57.3262i	0.983088	−	0.567586i	0.903201	+	0.429218i	$0.141211\pi$
$102$		0			0
$103$	16.8128	−	29.1206i	0.163231	−	0.282724i	−0.772795	−	0.634656i	$-0.781142\pi$
$103$	16.8128	−	29.1206i	0.163231	−	0.282724i	0.936026	+	0.351932i	$0.114475\pi$
$104$	118.208	+	68.2475i	1.13662	+	0.656226i
$105$		0			0
$106$	29.9017	+	51.7913i	0.282092	+	0.488597i
$107$		−	21.9347i		−	0.204997i	−0.994733	−	0.102499i	$-0.967316\pi$
$107$		−	21.9347i		−	0.204997i	0.994733	−	0.102499i	$-0.0326837\pi$
$108$		0			0
$109$	76.0756			0.697941			0.348971	−	0.937134i	$-0.386531\pi$
$109$	76.0756			0.697941			0.348971	+	0.937134i	$0.386531\pi$
$110$	94.2118	−	54.3932i	0.856471	−	0.494484i
$111$		0			0
$112$	−6.53641	+	11.3214i	−0.0583608	+	0.101084i
$113$	−40.1717	−	23.1931i	−0.355502	−	0.205249i	0.311604	−	0.950212i	$-0.399134\pi$
$113$	−40.1717	−	23.1931i	−0.355502	−	0.205249i	−0.667106	+	0.744963i	$0.732467\pi$
$114$		0			0
$115$	−1.81724	−	3.14755i	−0.0158021	−	0.0273700i
$116$		−	8.29901i		−	0.0715432i
$117$		0			0
$118$	94.9553			0.804706
$119$	110.334	−	63.7011i	0.927173	−	0.535303i
$120$		0			0
$121$	50.1330	−	86.8330i	0.414323	−	0.717628i
$122$	−314.953	−	181.838i	−2.58158	−	1.49048i
$123$		0			0
$124$	44.8241	+	77.6377i	0.361485	+	0.626110i
$125$			11.1803i			0.0894427i
$126$		0			0
$127$	−34.5397			−0.271966			−0.135983	−	0.990711i	$-0.543419\pi$
$127$	−34.5397			−0.271966			−0.135983	+	0.990711i	$0.543419\pi$
$128$	188.888	−	109.055i	1.47569	−	0.851990i
$129$		0			0
$130$	−56.5823	+	98.0034i	−0.435248	+	0.753872i
$131$	97.0100	+	56.0088i	0.740535	+	0.427548i	0.822264	−	0.569107i	$-0.192711\pi$
$131$	97.0100	+	56.0088i	0.740535	+	0.427548i	−0.0817290	+	0.996655i	$0.526044\pi$
$132$		0			0
$133$	79.6239	+	137.913i	0.598676	+	1.03694i
$134$		−	56.0206i		−	0.418064i
$135$		0			0
$136$	177.299			1.30367
$137$	−66.9262	+	38.6399i	−0.488513	+	0.282043i	−0.723957	−	0.689845i	$-0.757679\pi$
$137$	−66.9262	+	38.6399i	−0.488513	+	0.282043i	0.235445	+	0.971888i	$0.424345\pi$
$138$		0			0
$139$	−69.2700	+	119.979i	−0.498345	+	0.863159i	−0.999998	−	0.00190987i	$-0.999392\pi$
$139$	−69.2700	+	119.979i	−0.498345	+	0.863159i	0.501653	+	0.865069i	$0.332725\pi$
$140$	−82.2042	−	47.4606i	−0.587173	−	0.339005i
$141$		0			0
$142$	−86.2593	−	149.405i	−0.607460	−	1.05215i
$143$			230.171i			1.60959i
$144$		0			0
$145$	2.77094			0.0191099
$146$	−201.263	+	116.199i	−1.37851	+	0.795885i
$147$		0			0
$148$	13.0363	−	22.5795i	0.0880830	−	0.152564i
$149$	36.1097	+	20.8479i	0.242347	+	0.139919i	0.616255	−	0.787547i	$-0.288649\pi$
$149$	36.1097	+	20.8479i	0.242347	+	0.139919i	−0.373908	+	0.927466i	$0.621982\pi$
$150$		0			0
$151$	−123.239	−	213.457i	−0.816156	−	1.41362i	−0.908495	−	0.417895i	$-0.862768\pi$
$151$	−123.239	−	213.457i	−0.816156	−	1.41362i	0.0923396	−	0.995728i	$-0.470565\pi$
$152$			221.617i			1.45801i
$153$		0			0
$154$	−308.378			−2.00246
$155$	−25.9223	+	14.9662i	−0.167240	+	0.0965563i
$156$		0			0
$157$	−108.853	+	188.539i	−0.693333	+	1.20089i	0.277407	+	0.960753i	$0.410525\pi$
$157$	−108.853	+	188.539i	−0.693333	+	1.20089i	−0.970740	+	0.240135i	$0.922808\pi$
$158$	−171.463	−	98.9940i	−1.08521	−	0.626544i
$159$		0			0
$160$	31.9077	+	55.2657i	0.199423	+	0.345410i
$161$			10.3027i			0.0639919i
$162$		0			0
$163$	134.018			0.822195			0.411098	−	0.911591i	$-0.365145\pi$
$163$	134.018			0.822195			0.411098	+	0.911591i	$0.365145\pi$
$164$	−337.369	+	194.780i	−2.05713	+	1.18768i
$165$		0			0
$166$	−132.586	+	229.645i	−0.798710	+	1.38341i
$167$	215.039	+	124.153i	1.28766	+	0.743431i	0.978236	−	0.207494i	$-0.0665306\pi$
$167$	215.039	+	124.153i	1.28766	+	0.743431i	0.309423	+	0.950924i	$0.399864\pi$
$168$		0			0
$169$	−35.2171	−	60.9978i	−0.208385	−	0.360934i
$170$			146.994i			0.864672i
$171$		0			0
$172$	182.373			1.06031
$173$	1.60349	−	0.925775i	0.00926873	−	0.00535130i	−0.495358	−	0.868689i	$-0.664963\pi$
$173$	1.60349	−	0.925775i	0.00926873	−	0.00535130i	0.504627	+	0.863337i	$0.331630\pi$
$174$		0			0
$175$	15.8465	−	27.4470i	0.0905516	−	0.156840i
$176$	−26.5683	−	15.3392i	−0.150956	−	0.0871545i
$177$		0			0
$178$	−10.3812	−	17.9807i	−0.0583213	−	0.101015i
$179$			142.825i			0.797907i	0.916971	+	0.398954i	$0.130627\pi$
$179$			142.825i			0.797907i	−0.916971	+	0.398954i	$0.869373\pi$
$180$		0			0
$181$	−16.4944			−0.0911291			−0.0455646	−	0.998961i	$-0.514509\pi$
$181$	−16.4944			−0.0911291			−0.0455646	+	0.998961i	$0.514509\pi$
$182$	277.811	−	160.395i	1.52644	−	0.881289i
$183$		0			0
$184$	−7.16886	+	12.4168i	−0.0389612	+	0.0674828i
$185$	7.53902	+	4.35265i	0.0407515	+	0.0235279i
$186$		0			0
$187$	149.489	+	258.923i	0.799408	+	1.38462i
$188$		−	419.811i		−	2.23304i
$189$		0			0
$190$	−183.737			−0.967037
$191$	−9.69871	+	5.59955i	−0.0507786	+	0.0293170i	−0.525174	−	0.850995i	$-0.676000\pi$
$191$	−9.69871	+	5.59955i	−0.0507786	+	0.0293170i	0.474396	+	0.880312i	$0.342667\pi$
$192$		0			0
$193$	−163.824	+	283.751i	−0.848826	+	1.47021i	0.0334298	+	0.999441i	$0.489357\pi$
$193$	−163.824	+	283.751i	−0.848826	+	1.47021i	−0.882256	+	0.470769i	$0.843976\pi$
$194$	44.4139	+	25.6424i	0.228938	+	0.132177i
$195$		0			0
$196$	−29.5407	−	51.1661i	−0.150718	−	0.261051i
$197$			63.0893i			0.320250i	0.987097	+	0.160125i	$0.0511898\pi$
$197$			63.0893i			0.320250i	−0.987097	+	0.160125i	$0.948810\pi$
$198$		0			0
$199$	227.527			1.14335			0.571677	−	0.820479i	$-0.306293\pi$
$199$	227.527			1.14335			0.571677	+	0.820479i	$0.306293\pi$
$200$	38.1966	−	22.0528i	0.190983	−	0.110264i
$201$		0			0
$202$	187.493	−	324.748i	0.928184	−	1.60766i
$203$	−6.80247	−	3.92741i	−0.0335097	−	0.0193468i
$204$		0			0
$205$	−65.0348	−	112.643i	−0.317243	−	0.549480i
$206$		−	109.977i		−	0.533869i
$207$		0			0
$208$	31.9130			0.153428
$209$	−323.644	+	186.856i	−1.54854	+	0.894047i
$210$		0			0
$211$	149.700	−	259.289i	0.709480	−	1.22886i	−0.255570	−	0.966791i	$-0.582263\pi$
$211$	149.700	−	259.289i	0.709480	−	1.22886i	0.965050	−	0.262065i	$-0.0844036\pi$
$212$	106.050	+	61.2277i	0.500234	+	0.288810i
$213$		0			0
$214$	−35.8702	−	62.1291i	−0.167618	−	0.290323i
$215$			60.8921i			0.283219i
$216$		0			0
$217$	84.8500			0.391014
$218$	215.481	−	124.408i	0.988443	−	0.570678i
$219$		0			0
$220$	111.377	−	192.911i	0.506261	−	0.876869i
$221$	−269.344	−	155.506i	−1.21875	−	0.703645i
$222$		0			0
$223$	20.8434	+	36.1018i	0.0934681	+	0.161891i	0.908968	−	0.416865i	$-0.136871\pi$
$223$	20.8434	+	36.1018i	0.0934681	+	0.161891i	−0.815500	+	0.578757i	$0.803538\pi$
$224$		−	180.898i		−	0.807581i
$225$		0			0
$226$	−151.713			−0.671295
$227$	175.818	−	101.508i	0.774527	−	0.447173i	−0.0599604	−	0.998201i	$-0.519097\pi$
$227$	175.818	−	101.508i	0.774527	−	0.447173i	0.834487	+	0.551028i	$0.185764\pi$
$228$		0			0
$229$	−188.616	+	326.693i	−0.823652	+	1.42661i	0.0792923	+	0.996851i	$0.474734\pi$
$229$	−188.616	+	326.693i	−0.823652	+	1.42661i	−0.902945	+	0.429757i	$0.858599\pi$
$230$	−10.2945	−	5.94352i	−0.0447586	−	0.0258414i
$231$		0			0
$232$	−5.46557	−	9.46664i	−0.0235585	−	0.0408045i
$233$		−	279.281i		−	1.19863i	−0.800513	−	0.599316i	$-0.795439\pi$
$233$		−	279.281i		−	1.19863i	0.800513	−	0.599316i	$-0.204561\pi$
$234$		0			0
$235$	140.170			0.596468
$236$	168.384	−	97.2168i	0.713493	−	0.411936i
$237$		0			0
$238$	208.343	−	360.861i	0.875392	−	1.51622i
$239$	217.621	+	125.643i	0.910547	+	0.525705i	0.880607	−	0.473847i	$-0.157135\pi$
$239$	217.621	+	125.643i	0.910547	+	0.525705i	0.0299401	+	0.999552i	$0.490468\pi$
$240$		0			0
$241$	161.874	+	280.373i	0.671675	+	1.16337i	0.977429	+	0.211264i	$0.0677581\pi$
$241$	161.874	+	280.373i	0.671675	+	1.16337i	−0.305754	+	0.952110i	$0.598909\pi$
$242$		−	327.934i		−	1.35510i
$243$		0			0
$244$	−744.675			−3.05195
$245$	17.0837	−	9.86329i	0.0697295	−	0.0402583i
$246$		0			0
$247$	194.376	−	336.669i	0.786947	−	1.36303i
$248$	102.261	+	59.0406i	0.412344	+	0.238067i
$249$		0			0
$250$	18.2834	+	31.6678i	0.0731337	+	0.126671i
$251$		−	290.467i		−	1.15724i	−0.815597	−	0.578620i	$-0.803592\pi$
$251$		−	290.467i		−	1.15724i	0.815597	−	0.578620i	$-0.196408\pi$
$252$		0			0
$253$	−24.1776			−0.0955638
$254$	−97.8321	+	56.4834i	−0.385166	+	0.222376i
$255$		0			0
$256$	153.497	−	265.865i	0.599599	−	1.03854i
$257$	293.855	+	169.657i	1.14340	+	0.660144i	0.947271	−	0.320433i	$-0.103828\pi$
$257$	293.855	+	169.657i	1.14340	+	0.660144i	0.196132	+	0.980577i	$0.437162\pi$
$258$		0			0
$259$	−12.3385	−	21.3710i	−0.0476391	−	0.0825134i
$260$			231.719i			0.891229i
$261$		0			0
$262$	366.369			1.39835
$263$	−268.275	+	154.889i	−1.02006	+	0.588930i	−0.914120	−	0.405443i	$-0.867117\pi$
$263$	−268.275	+	154.889i	−1.02006	+	0.588930i	−0.105937	+	0.994373i	$0.533784\pi$
$264$		0			0
$265$	−20.4432	+	35.4086i	−0.0771441	+	0.133617i
$266$	451.062	+	260.421i	1.69572	+	0.979026i
$267$		0			0
$268$	−57.3548	−	99.3415i	−0.214011	−	0.370677i
$269$		−	323.623i		−	1.20306i	−0.798850	−	0.601530i	$-0.794558\pi$
$269$		−	323.623i		−	1.20306i	0.798850	−	0.601530i	$-0.205442\pi$
$270$		0			0
$271$	−239.021			−0.881995			−0.440997	−	0.897508i	$-0.645375\pi$
$271$	−239.021			−0.881995			−0.440997	+	0.897508i	$0.645375\pi$
$272$	35.8995	−	20.7266i	0.131984	−	0.0762007i
$273$		0			0
$274$	−126.377	+	218.891i	−0.461230	+	0.798874i
$275$	64.4107	+	37.1875i	0.234221	+	0.135227i
$276$		0			0
$277$	−262.012	−	453.818i	−0.945892	−	1.63833i	−0.753955	−	0.656926i	$-0.771856\pi$
$277$	−262.012	−	453.818i	−0.945892	−	1.63833i	−0.191937	−	0.981407i	$-0.561477\pi$
$278$			453.114i			1.62991i
$279$		0			0
$280$	−125.027			−0.446524
$281$	−114.124	+	65.8895i	−0.406135	+	0.234482i	−0.689128	−	0.724640i	$-0.742006\pi$
$281$	−114.124	+	65.8895i	−0.406135	+	0.234482i	0.282993	+	0.959122i	$0.408673\pi$
$282$		0			0
$283$	222.049	−	384.600i	0.784624	−	1.35901i	−0.144599	−	0.989490i	$-0.546189\pi$
$283$	222.049	−	384.600i	0.784624	−	1.35901i	0.929223	−	0.369519i	$-0.120477\pi$
$284$	−305.927	−	176.627i	−1.07721	−	0.621927i
$285$		0			0
$286$	376.403	+	651.949i	1.31609	+	2.27954i
$287$			368.710i			1.28470i
$288$		0			0
$289$	−114.985			−0.397874
$290$	7.84855	−	4.53136i	0.0270640	−	0.0156254i
$291$		0			0
$292$	−237.933	+	412.113i	−0.814840	+	1.41134i
$293$	311.602	+	179.904i	1.06349	+	0.614005i	0.926395	−	0.376553i	$-0.122891\pi$
$293$	311.602	+	179.904i	1.06349	+	0.614005i	0.137093	+	0.990558i	$0.456224\pi$
$294$		0			0
$295$	32.4595	+	56.2215i	0.110032	+	0.190581i
$296$		−	34.3418i		−	0.116020i
$297$		0			0
$298$	136.372			0.457624
$299$	21.7811	−	12.5753i	0.0728465	−	0.0420580i
$300$		0			0
$301$	86.3058	−	149.486i	0.286730	−	0.496631i
$302$	−698.140	−	403.072i	−2.31172	−	1.33467i
$303$		0			0
$304$	25.9074	+	44.8730i	0.0852218	+	0.147609i
$305$		−	248.638i		−	0.815206i
$306$		0			0
$307$	−439.477			−1.43152			−0.715761	−	0.698345i	$-0.753920\pi$
$307$	−439.477			−1.43152			−0.715761	+	0.698345i	$0.753920\pi$
$308$	−546.848	+	315.723i	−1.77548	+	1.02507i
$309$		0			0
$310$	−48.9491	+	84.7823i	−0.157900	+	0.273491i
$311$	−237.295	−	137.002i	−0.763006	−	0.440522i	0.0673678	−	0.997728i	$-0.478540\pi$
$311$	−237.295	−	137.002i	−0.763006	−	0.440522i	−0.830374	+	0.557206i	$0.811873\pi$
$312$		0			0
$313$	20.4377	+	35.3992i	0.0652962	+	0.113096i	0.896825	−	0.442385i	$-0.145867\pi$
$313$	20.4377	+	35.3992i	0.0652962	+	0.113096i	−0.831529	+	0.555481i	$0.812534\pi$
$314$			712.039i			2.26764i
$315$		0			0
$316$	−405.407			−1.28293
$317$	−26.5772	+	15.3443i	−0.0838397	+	0.0484049i	−0.541334	−	0.840808i	$-0.682080\pi$
$317$	−26.5772	+	15.3443i	−0.0838397	+	0.0484049i	0.457494	+	0.889213i	$0.348747\pi$
$318$		0			0
$319$	9.21657	−	15.9636i	0.0288921	−	0.0500425i
$320$	196.729	+	113.582i	0.614779	+	0.354943i
$321$		0			0
$322$	16.8482	+	29.1819i	0.0523235	+	0.0906270i
$323$		−	504.966i		−	1.56336i
$324$		0			0
$325$	−77.3683			−0.238056
$326$	379.599	−	219.162i	1.16442	−	0.672276i
$327$		0			0
$328$	−256.557	+	444.370i	−0.782186	+	1.35479i
$329$	−344.108	−	198.671i	−1.04592	−	0.603863i
$330$		0			0
$331$	164.925	+	285.659i	0.498263	+	0.863017i	0.999998	−	0.00200416i	$-0.000637945\pi$
$331$	164.925	+	285.659i	0.498263	+	0.863017i	−0.501735	+	0.865022i	$0.667305\pi$
$332$			542.974i			1.63546i
$333$		0			0
$334$	812.118			2.43149
$335$	33.1689	−	19.1501i	0.0990117	−	0.0571644i
$336$		0			0
$337$	−328.585	+	569.127i	−0.975031	+	1.68880i	−0.295198	+	0.955436i	$0.595386\pi$
$337$	−328.585	+	569.127i	−0.975031	+	1.68880i	−0.679833	+	0.733367i	$0.737948\pi$
$338$	−199.502	−	115.182i	−0.590241	−	0.340776i
$339$		0			0
$340$	150.495	+	260.665i	0.442633	+	0.766662i
$341$			199.120i			0.583930i
$342$		0			0
$343$	−366.511			−1.06855
$344$	208.032	−	120.107i	0.604744	−	0.349149i
$345$		0			0
$346$	3.02787	−	5.24443i	0.00875108	−	0.0151573i
$347$	−365.024	−	210.746i	−1.05194	−	0.607338i	−0.128749	−	0.991677i	$-0.541096\pi$
$347$	−365.024	−	210.746i	−1.05194	−	0.607338i	−0.923192	+	0.384339i	$0.874429\pi$
$348$		0			0
$349$	−242.288	−	419.656i	−0.694236	−	1.20245i	−0.970438	−	0.241352i	$-0.922409\pi$
$349$	−242.288	−	419.656i	−0.694236	−	1.20245i	0.276201	−	0.961100i	$-0.410924\pi$
$350$		−	103.656i		−	0.296161i
$351$		0			0
$352$	424.519			1.20602
$353$	239.766	−	138.429i	0.679223	−	0.392150i	−0.120339	−	0.992733i	$-0.538398\pi$
$353$	239.766	−	138.429i	0.679223	−	0.392150i	0.799562	+	0.600583i	$0.205065\pi$
$354$		0			0
$355$	58.9737	−	102.145i	0.166123	−	0.287734i
$356$	−36.8180	−	21.2569i	−0.103421	−	0.0597103i
$357$		0			0
$358$	233.565	+	404.547i	0.652416	+	1.13002i
$359$			42.5551i			0.118538i	0.998242	+	0.0592689i	$0.0188769\pi$
$359$			42.5551i			0.118538i	−0.998242	+	0.0592689i	$0.981123\pi$
$360$		0			0
$361$	270.188			0.748443
$362$	−46.7195	+	26.9735i	−0.129060	+	0.0745125i
$363$		0			0
$364$	328.429	−	568.856i	0.902278	−	1.56279i
$365$	−137.599	−	79.4431i	−0.376985	−	0.217652i
$366$		0			0
$367$	−72.0299	−	124.759i	−0.196267	−	0.339944i	0.751048	−	0.660247i	$-0.229548\pi$
$367$	−72.0299	−	124.759i	−0.196267	−	0.339944i	−0.947315	+	0.320303i	$0.896215\pi$
$368$			3.35221i			0.00910927i
$369$		0			0
$370$	28.4719			0.0769511
$371$	100.373	−	57.9506i	0.270548	−	0.156201i
$372$		0			0
$373$	200.312	−	346.951i	0.537030	−	0.930163i	−0.462032	−	0.886863i	$-0.652880\pi$
$373$	200.312	−	346.951i	0.537030	−	0.930163i	0.999062	−	0.0432998i	$-0.0137871\pi$
$374$	846.844	+	488.925i	2.26429	+	1.30729i
$375$		0			0
$376$	−276.480	−	478.877i	−0.735319	−	1.27361i
$377$			19.1750i			0.0508620i
$378$		0			0
$379$	550.038			1.45129			0.725643	−	0.688071i	$-0.241542\pi$
$379$	550.038			1.45129			0.725643	+	0.688071i	$0.241542\pi$
$380$	−325.821	+	188.113i	−0.857424	+	0.495034i
$381$		0			0
$382$	−18.3141	+	31.7210i	−0.0479427	+	0.0830391i
$383$	293.599	+	169.509i	0.766577	+	0.442583i	0.831652	−	0.555297i	$-0.187395\pi$
$383$	293.599	+	169.509i	0.766577	+	0.442583i	−0.0650751	+	0.997880i	$0.520729\pi$
$384$		0			0
$385$	−105.416	−	182.586i	−0.273808	−	0.474249i
$386$			1071.61i			2.77620i
$387$		0			0
$388$	105.012			0.270650
$389$	344.885	−	199.119i	0.886593	−	0.511875i	0.0137666	−	0.999905i	$-0.495618\pi$
$389$	344.885	−	199.119i	0.886593	−	0.511875i	0.872827	+	0.488030i	$0.162284\pi$
$390$		0			0
$391$	16.3346	−	28.2924i	0.0417765	−	0.0723591i
$392$	−67.3940	−	38.9099i	−0.171923	−	0.0992600i
$393$		0			0
$394$	103.171	+	178.698i	0.261856	+	0.453547i
$395$		−	135.360i		−	0.342684i
$396$		0			0
$397$	336.176			0.846791			0.423395	−	0.905945i	$-0.360838\pi$
$397$	336.176			0.846791			0.423395	+	0.905945i	$0.360838\pi$
$398$	644.461	−	372.080i	1.61925	−	0.934874i
$399$		0			0
$400$	5.15603	−	8.93050i	0.0128901	−	0.0223262i
$401$	−464.993	−	268.464i	−1.15958	−	0.669486i	−0.208379	−	0.978048i	$-0.566819\pi$
$401$	−464.993	−	268.464i	−1.15958	−	0.669486i	−0.951204	+	0.308562i	$0.900152\pi$
$402$		0			0
$403$	−103.567	−	179.383i	−0.256990	−	0.445119i
$404$		−	767.835i		−	1.90058i
$405$		0			0
$406$	−25.6902			−0.0632765
$407$	50.1519	−	28.9552i	0.123223	−	0.0711430i
$408$		0			0
$409$	39.3743	−	68.1984i	0.0962698	−	0.166744i	−0.813868	−	0.581050i	$-0.802642\pi$
$409$	39.3743	−	68.1984i	0.0962698	−	0.166744i	0.910138	+	0.414306i	$0.135976\pi$
$410$	−368.416	−	212.705i	−0.898575	−	0.518793i
$411$		0			0
$412$	−112.596	−	195.022i	−0.273292	−	0.473355i
$413$		−	184.027i		−	0.445585i
$414$		0			0
$415$	−181.292			−0.436849
$416$	−382.440	+	220.802i	−0.919327	+	0.530774i
$417$		0			0
$418$	−611.138	+	1058.52i	−1.46205	+	2.53235i
$419$	−91.0148	−	52.5474i	−0.217219	−	0.125412i	0.387443	−	0.921894i	$-0.373358\pi$
$419$	−91.0148	−	52.5474i	−0.217219	−	0.125412i	−0.604662	+	0.796482i	$0.706692\pi$
$420$		0			0
$421$	−85.0815	−	147.365i	−0.202094	−	0.350037i	0.747109	−	0.664701i	$-0.231441\pi$
$421$	−85.0815	−	147.365i	−0.202094	−	0.350037i	−0.949203	+	0.314665i	$0.898108\pi$
$422$		−	979.231i		−	2.32045i
$423$		0			0
$424$	161.294			0.380409
$425$	−87.0329	+	50.2485i	−0.204783	+	0.118232i
$426$		0			0
$427$	−352.409	+	610.390i	−0.825313	+	1.42948i
$428$	−127.218	−	73.4491i	−0.297237	−	0.171610i
$429$		0			0
$430$	99.5779	+	172.474i	0.231577	+	0.401102i
$431$			7.19773i			0.0167001i	0.999965	+	0.00835003i	$0.00265793\pi$
$431$			7.19773i			0.0167001i	−0.999965	+	0.00835003i	$0.997342\pi$
$432$		0			0
$433$	−270.714			−0.625206			−0.312603	−	0.949884i	$-0.601201\pi$
$433$	−270.714			−0.625206			−0.312603	+	0.949884i	$0.601201\pi$
$434$	240.334	−	138.757i	0.553764	−	0.319716i
$435$		0			0
$436$	254.742	−	441.225i	0.584270	−	1.01198i
$437$	35.3644	+	20.4177i	0.0809254	+	0.0467223i
$438$		0			0
$439$	371.407	+	643.296i	0.846030	+	1.46537i	0.884723	+	0.466116i	$0.154347\pi$
$439$	371.407	+	643.296i	0.846030	+	1.46537i	−0.0386931	+	0.999251i	$0.512319\pi$
$440$		−	293.404i		−	0.666827i
$441$		0			0
$442$	−1017.20			−2.30137
$443$	−456.076	+	263.316i	−1.02952	+	0.594392i	−0.916846	−	0.399241i	$-0.869274\pi$
$443$	−456.076	+	263.316i	−1.02952	+	0.594392i	−0.112670	+	0.993632i	$0.535940\pi$
$444$		0			0
$445$	7.09740	−	12.2931i	0.0159492	−	0.0276249i
$446$	118.076	+	68.1711i	0.264744	+	0.152850i
$447$		0			0
$448$	−321.972	−	557.671i	−0.718687	−	1.24480i
$449$			785.085i			1.74852i	0.485459	+	0.874259i	$0.338652\pi$
$449$			785.085i			1.74852i	−0.485459	+	0.874259i	$0.661348\pi$
$450$		0			0
$451$	−865.263			−1.91854
$452$	−269.033	+	155.326i	−0.595205	+	0.343642i
$453$		0			0
$454$	331.997	−	575.035i	0.731270	−	1.26660i
$455$	189.934	+	109.658i	0.417438	+	0.241008i
$456$		0			0
$457$	385.876	+	668.356i	0.844367	+	1.46249i	0.886170	+	0.463360i	$0.153356\pi$
$457$	385.876	+	668.356i	0.844367	+	1.46249i	−0.0418030	+	0.999126i	$0.513310\pi$
$458$			1233.79i			2.69387i
$459$		0			0
$460$	−24.3403			−0.0529137
$461$	−222.720	+	128.587i	−0.483123	+	0.278931i	−0.721717	−	0.692188i	$-0.756647\pi$
$461$	−222.720	+	128.587i	−0.483123	+	0.278931i	0.238594	+	0.971119i	$0.423313\pi$
$462$		0			0
$463$	256.040	−	443.475i	0.553003	−	0.957829i	−0.445053	−	0.895504i	$-0.646815\pi$
$463$	256.040	−	443.475i	0.553003	−	0.957829i	0.998056	−	0.0623247i	$-0.0198514\pi$
$464$	−2.21334	−	1.27787i	−0.00477012	−	0.00275403i
$465$		0			0
$466$	−456.714	−	791.051i	−0.980072	−	1.69753i
$467$			137.080i			0.293532i	0.989171	+	0.146766i	$0.0468865\pi$
$467$			137.080i			0.293532i	−0.989171	+	0.146766i	$0.953114\pi$
$468$		0			0
$469$	−108.570			−0.231492
$470$	397.025	−	229.222i	0.844734	−	0.487707i
$471$		0			0
$472$	128.050	−	221.790i	0.271293	−	0.469893i
$473$	350.803	+	202.536i	0.741656	+	0.428196i
$474$		0			0
$475$	−62.8086	−	108.788i	−0.132229	−	0.229027i
$476$		−	853.221i		−	1.79248i
$477$		0			0
$478$	821.868			1.71939
$479$	538.892	−	311.129i	1.12504	−	0.649540i	0.182354	−	0.983233i	$-0.441628\pi$
$479$	538.892	−	311.129i	1.12504	−	0.649540i	0.942682	+	0.333693i	$0.108295\pi$
$480$		0			0
$481$	−30.1205	+	52.1703i	−0.0626206	+	0.108462i
$482$	916.999	+	529.430i	1.90249	+	1.09840i
$483$		0			0
$484$	−335.744	−	581.526i	−0.693686	−	1.20150i
$485$			35.0624i			0.0722935i
$486$		0			0
$487$	−54.1396			−0.111170			−0.0555848	−	0.998454i	$-0.517702\pi$
$487$	−54.1396			−0.111170			−0.0555848	+	0.998454i	$0.517702\pi$
$488$	−849.447	+	490.429i	−1.74067	+	1.00498i
$489$		0			0
$490$	32.2592	−	55.8747i	0.0658352	−	0.114030i
$491$	532.410	+	307.387i	1.08434	+	0.626043i	0.932063	−	0.362296i	$-0.118007\pi$
$491$	532.410	+	307.387i	1.08434	+	0.626043i	0.152274	+	0.988338i	$0.451340\pi$
$492$		0			0
$493$	12.4536	+	21.5702i	0.0252608	+	0.0437530i
$494$		−	1271.47i		−	2.57382i
$495$		0			0
$496$	27.6079			0.0556610
$497$	−289.553	+	167.174i	−0.582602	+	0.336365i
$498$		0			0
$499$	−303.483	+	525.647i	−0.608181	+	1.05340i	0.383359	+	0.923600i	$0.374767\pi$
$499$	−303.483	+	525.647i	−0.608181	+	1.05340i	−0.991540	+	0.129802i	$0.958566\pi$
$500$	64.8440	+	37.4377i	0.129688	+	0.0748755i
$501$		0			0
$502$	−475.006	−	822.735i	−0.946227	−	1.63891i
$503$		−	408.360i		−	0.811850i	−0.913906	−	0.405925i	$-0.866949\pi$
$503$		−	408.360i		−	0.811850i	0.913906	−	0.405925i	$-0.133051\pi$
$504$		0			0
$505$	256.371			0.507665
$506$	−68.4821	+	39.5381i	−0.135340	+	0.0781386i
$507$		0			0
$508$	−115.657	+	200.324i	−0.227672	+	0.394339i
$509$	89.5809	+	51.7195i	0.175994	+	0.101610i	0.585409	−	0.810738i	$-0.300934\pi$
$509$	89.5809	+	51.7195i	0.175994	+	0.101610i	−0.409415	+	0.912348i	$0.634267\pi$
$510$		0			0
$511$	225.198	+	390.055i	0.440701	+	0.763317i
$512$		−	131.630i		−	0.257091i
$513$		0			0
$514$	1109.77			2.15909
$515$	65.1156	−	37.5945i	0.126438	−	0.0729990i
$516$		0			0
$517$	466.227	−	807.529i	0.901793	−	1.56195i
$518$	−69.8966	−	40.3548i	−0.134936	−	0.0779051i
$519$		0			0
$520$	152.606	+	264.321i	0.293473	+	0.508310i
$521$			581.188i			1.11552i	0.830001	+	0.557762i	$0.188340\pi$
$521$			581.188i			1.11552i	−0.830001	+	0.557762i	$0.811660\pi$
$522$		0			0
$523$	−462.515			−0.884350			−0.442175	−	0.896929i	$-0.645793\pi$
$523$	−462.515			−0.884350			−0.442175	+	0.896929i	$0.645793\pi$
$524$	649.683	−	375.094i	1.23985	−	0.715829i
$525$		0			0
$526$	−506.585	+	877.430i	−0.963088	+	1.66812i
$527$	−233.008	−	134.527i	−0.442141	−	0.255270i
$528$		0			0
$529$	−263.179	−	455.840i	−0.497503	−	0.861700i
$530$			133.724i			0.252310i
$531$		0			0
$532$	1066.49			2.00469
$533$	779.497	−	450.043i	1.46247	−	0.844357i
$534$		0			0
$535$	24.5238	−	42.4764i	0.0458388	−	0.0793951i
$536$	−130.849	−	75.5456i	−0.244121	−	0.140943i
$537$		0			0
$538$	−529.227	−	916.648i	−0.983693	−	1.70381i
$539$		−	131.227i		−	0.243464i
$540$		0			0
$541$	798.872			1.47666			0.738329	−	0.674440i	$-0.235615\pi$
$541$	798.872			1.47666			0.738329	+	0.674440i	$0.235615\pi$
$542$	−677.015	+	390.875i	−1.24910	+	0.721171i
$543$		0			0
$544$	−286.809	+	496.768i	−0.527222	+	0.913176i
$545$	147.320	+	85.0551i	0.270311	+	0.156064i
$546$		0			0
$547$	208.248	+	360.696i	0.380709	+	0.659408i	0.991164	−	0.132644i	$-0.0423466\pi$
$547$	208.248	+	360.696i	0.380709	+	0.659408i	−0.610455	+	0.792051i	$0.709013\pi$
$548$			517.547i			0.944430i
$549$		0			0
$550$	243.254			0.442280
$551$	−26.9620	+	15.5665i	−0.0489328	+	0.0282514i
$552$		0			0
$553$	−191.854	+	332.301i	−0.346933	+	0.600905i
$554$	−1484.27	−	856.947i	−2.67920	−	1.54683i
$555$		0			0
$556$	463.905	+	803.508i	0.834362	+	1.44516i
$557$		−	431.477i		−	0.774644i	−0.921945	−	0.387322i	$-0.873400\pi$
$557$		−	431.477i		−	0.774644i	0.921945	−	0.387322i	$-0.126600\pi$
$558$		0			0
$559$	−421.375			−0.753802
$560$	−25.3154	+	14.6159i	−0.0452061	+	0.0260997i
$561$		0			0
$562$	−215.500	+	373.258i	−0.383453	+	0.664160i
$563$	−819.969	−	473.409i	−1.45643	−	0.840869i	−0.457594	−	0.889161i	$-0.651289\pi$
$563$	−819.969	−	473.409i	−1.45643	−	0.840869i	−0.998833	+	0.0482920i	$0.984622\pi$
$564$		0			0
$565$	−51.8615	−	89.8267i	−0.0917902	−	0.158985i
$566$		−	1452.48i		−	2.56622i
$567$		0			0
$568$	−465.293			−0.819179
$569$	−900.651	+	519.991i	−1.58287	+	0.913868i	−0.588427	+	0.808550i	$0.700253\pi$
$569$	−900.651	+	519.991i	−1.58287	+	0.913868i	−0.994439	+	0.105317i	$0.966414\pi$
$570$		0			0
$571$	−185.680	+	321.607i	−0.325184	+	0.563234i	−0.981549	−	0.191208i	$-0.938759\pi$
$571$	−185.680	+	321.607i	−0.325184	+	0.563234i	0.656366	+	0.754443i	$0.272093\pi$
$572$	1334.95	+	770.735i	2.33383	+	1.34744i
$573$		0			0
$574$	602.958	+	1044.35i	1.05045	+	1.81943i
$575$		−	8.12693i		−	0.0141338i
$576$		0			0
$577$	111.372			0.193020			0.0965099	−	0.995332i	$-0.469232\pi$
$577$	111.372			0.193020			0.0965099	+	0.995332i	$0.469232\pi$
$578$	−325.691	+	188.038i	−0.563479	+	0.325325i
$579$		0			0
$580$	9.27857	−	16.0710i	0.0159975	−	0.0277085i
$581$	445.061	+	256.956i	0.766026	+	0.442265i
$582$		0			0
$583$	135.994	+	235.549i	0.233267	+	0.404030i
$584$			626.793i			1.07328i
$585$		0			0
$586$	1176.80			2.00819
$587$	124.634	−	71.9575i	0.212324	−	0.122585i	−0.390067	−	0.920786i	$-0.627548\pi$
$587$	124.634	−	71.9575i	0.212324	−	0.122585i	0.602391	+	0.798201i	$0.294215\pi$
$588$		0			0
$589$	168.154	−	291.251i	0.285490	−	0.494484i
$590$	183.880	+	106.163i	0.311661	+	0.179938i
$591$		0			0
$592$	−4.01462	−	6.95352i	−0.00678145	−	0.0117458i
$593$			589.394i			0.993920i	0.867774	+	0.496960i	$0.165550\pi$
$593$			589.394i			0.993920i	−0.867774	+	0.496960i	$0.834450\pi$
$594$		0			0
$595$	284.880			0.478790
$596$	241.829	−	139.620i	0.405753	−	0.234262i
$597$		0			0
$598$	41.1293	−	71.2381i	0.0687782	−	0.119127i
$599$	−175.988	−	101.607i	−0.293804	−	0.169628i	0.345852	−	0.938289i	$-0.387590\pi$
$599$	−175.988	−	101.607i	−0.293804	−	0.169628i	−0.639656	+	0.768661i	$0.720923\pi$
$600$		0			0
$601$	147.392	+	255.290i	0.245244	+	0.424776i	0.962200	−	0.272343i	$-0.0877984\pi$
$601$	147.392	+	255.290i	0.245244	+	0.424776i	−0.716956	+	0.697119i	$0.754465\pi$
$602$		−	564.550i		−	0.937790i
$603$		0			0
$604$	−1650.69			−2.73292
$605$	194.164	−	112.101i	0.320933	−	0.185291i
$606$		0			0
$607$	192.470	−	333.367i	0.317083	−	0.549204i	−0.662795	−	0.748801i	$-0.730630\pi$
$607$	192.470	−	333.367i	0.317083	−	0.549204i	0.979878	+	0.199597i	$0.0639632\pi$
$608$	−620.940	−	358.500i	−1.02128	−	0.589638i
$609$		0			0
$610$	−406.602	−	704.255i	−0.666561	−	1.15452i
$611$			969.980i			1.58753i
$612$		0			0
$613$	−102.262			−0.166822			−0.0834108	−	0.996515i	$-0.526581\pi$
$613$	−102.262			−0.166822			−0.0834108	+	0.996515i	$0.526581\pi$
$614$	−1244.80	+	718.685i	−2.02736	+	1.17050i
$615$		0			0
$616$	−415.858	+	720.287i	−0.675094	+	1.16930i
$617$	−165.318	−	95.4464i	−0.267939	−	0.154694i	0.360012	−	0.932948i	$-0.382773\pi$
$617$	−165.318	−	95.4464i	−0.267939	−	0.154694i	−0.627950	+	0.778253i	$0.716106\pi$
$618$		0			0
$619$	−141.201	−	244.567i	−0.228111	−	0.395100i	0.729137	−	0.684368i	$-0.239922\pi$
$619$	−141.201	−	244.567i	−0.228111	−	0.395100i	−0.957248	+	0.289268i	$0.906588\pi$
$620$			200.460i			0.323322i
$621$		0			0
$622$	−896.170			−1.44079
$623$	−34.8473	+	20.1191i	−0.0559347	+	0.0322939i
$624$		0			0
$625$	−12.5000	+	21.6506i	−0.0200000	+	0.0346410i
$626$	115.778	+	66.8444i	0.184949	+	0.106780i
$627$		0			0
$628$	728.997	+	1262.66i	1.16082	+	2.01061i
$629$			78.2496i			0.124403i
$630$		0			0
$631$	−300.716			−0.476571			−0.238285	−	0.971195i	$-0.576585\pi$
$631$	−300.716			−0.476571			−0.238285	+	0.971195i	$0.576585\pi$
$632$	−462.446	+	266.993i	−0.731718	+	0.422457i
$633$		0			0
$634$	−50.1858	+	86.9243i	−0.0791574	+	0.137105i
$635$	−66.8858	−	38.6166i	−0.105332	−	0.0608135i
$636$		0			0
$637$	68.2543	+	118.220i	0.107150	+	0.185589i
$638$		−	60.2881i		−	0.0944954i
$639$		0			0
$640$	487.708			0.762043
$641$	680.974	−	393.160i	1.06236	−	0.613355i	0.136277	−	0.990671i	$-0.456486\pi$
$641$	680.974	−	393.160i	1.06236	−	0.613355i	0.926084	+	0.377316i	$0.123153\pi$
$642$		0			0
$643$	445.975	−	772.451i	0.693584	−	1.20132i	−0.277071	−	0.960849i	$-0.589364\pi$
$643$	445.975	−	772.451i	0.693584	−	1.20132i	0.970656	−	0.240474i	$-0.0773029\pi$
$644$	59.7538	+	34.4989i	0.0927854	+	0.0535697i
$645$		0			0
$646$	−825.780	−	1430.29i	−1.27830	−	2.21408i
$647$			360.702i			0.557499i	0.960364	+	0.278750i	$0.0899199\pi$
$647$			360.702i			0.557499i	−0.960364	+	0.278750i	$0.910080\pi$
$648$		0			0
$649$	431.861			0.665426
$650$	−219.142	+	126.522i	−0.337142	+	0.194649i
$651$		0			0
$652$	448.763	−	777.280i	0.688287	−	1.19215i
$653$	519.457	+	299.909i	0.795494	+	0.459279i	0.841893	−	0.539644i	$-0.181441\pi$
$653$	519.457	+	299.909i	0.795494	+	0.459279i	−0.0463993	+	0.998923i	$0.514775\pi$
$654$		0			0
$655$	125.239	+	216.921i	0.191205	+	0.331177i
$656$			119.968i			0.182878i
$657$		0			0
$658$	−1299.56			−1.97501
$659$	534.142	−	308.387i	0.810534	−	0.467962i	−0.0366073	−	0.999330i	$-0.511655\pi$
$659$	534.142	−	308.387i	0.810534	−	0.467962i	0.847141	+	0.531368i	$0.178322\pi$
$660$		0			0
$661$	−168.485	+	291.825i	−0.254894	+	0.441490i	−0.964867	−	0.262740i	$-0.915374\pi$
$661$	−168.485	+	291.825i	−0.254894	+	0.441490i	0.709973	+	0.704229i	$0.248707\pi$
$662$	934.286	+	539.410i	1.41131	+	0.814819i
$663$		0			0
$664$	357.592	+	619.368i	0.538543	+	0.932784i
$665$			356.089i			0.535472i
$666$		0			0
$667$	−2.01418			−0.00301976
$668$	1440.13	−	831.460i	2.15589	−	1.24470i
$669$		0			0
$670$	62.6329	−	108.483i	0.0934820	−	0.161916i
$671$	−1432.42	−	827.008i	−2.13475	−	1.23250i
$672$		0			0
$673$	400.482	+	693.656i	0.595070	+	1.03069i	0.993537	+	0.113509i	$0.0362091\pi$
$673$	400.482	+	693.656i	0.595070	+	1.03069i	−0.398467	+	0.917183i	$0.630458\pi$
$674$			2149.37i			3.18897i
$675$		0			0
$676$	−471.702			−0.697784
$677$	478.834	−	276.455i	0.707288	−	0.408353i	−0.102768	−	0.994705i	$-0.532770\pi$
$677$	478.834	−	276.455i	0.707288	−	0.408353i	0.810056	+	0.586352i	$0.199437\pi$
$678$		0			0
$679$	49.6959	−	86.0758i	0.0731898	−	0.126768i
$680$	343.338	+	198.226i	0.504909	+	0.291509i
$681$		0			0
$682$	325.625	+	563.998i	0.477455	+	0.826977i
$683$			945.597i			1.38448i	0.721669	+	0.692238i	$0.243375\pi$
$683$			945.597i			1.38448i	−0.721669	+	0.692238i	$0.756625\pi$
$684$		0			0
$685$	−172.803			−0.252267
$686$	−1038.13	+	599.362i	−1.51330	+	0.873706i
$687$		0			0
$688$	28.0815	−	48.6387i	0.0408162	−	0.0706957i
$689$	−245.029	−	141.467i	−0.355630	−	0.205323i
$690$		0			0
$691$	−175.387	−	303.779i	−0.253816	−	0.439622i	0.710757	−	0.703437i	$-0.248352\pi$
$691$	−175.387	−	303.779i	−0.253816	−	0.439622i	−0.964573	+	0.263815i	$0.915019\pi$
$692$		−	12.4000i		−	0.0179190i
$693$		0			0
$694$	−1378.55			−1.98638
$695$	−268.281	+	154.892i	−0.386016	+	0.222867i
$696$		0			0
$697$	584.579	−	1012.52i	0.838708	−	1.45268i
$698$	−1372.54	−	792.437i	−1.96639	−	1.13530i
$699$		0			0
$700$	−106.125	−	183.814i	−0.151607	−	0.262592i
$701$		−	290.038i		−	0.413749i	−0.978367	−	0.206874i	$-0.933671\pi$
$701$		−	290.038i		−	0.413749i	0.978367	−	0.206874i	$-0.0663292\pi$
$702$		0			0
$703$	−97.8089			−0.139131
$704$	1308.70	−	755.581i	1.85895	−	1.07327i
$705$		0			0
$706$	452.750	−	784.187i	0.641290	−	1.11075i
$707$	−629.373	−	363.369i	−0.890202	−	0.513959i
$708$		0			0
$709$	−351.376	−	608.600i	−0.495593	−	0.858392i	0.504394	−	0.863474i	$-0.331716\pi$
$709$	−351.376	−	608.600i	−0.495593	−	0.858392i	−0.999987	+	0.00508117i	$0.998383\pi$
$710$		−	385.763i		−	0.543328i
$711$		0			0
$712$	−55.9974			−0.0786481
$713$	18.8428	−	10.8789i	0.0264274	−	0.0152579i
$714$		0			0
$715$	−257.339	+	445.724i	−0.359915	+	0.623390i
$716$	828.363	+	478.256i	1.15693	+	0.667955i
$717$		0			0
$718$	69.5911	+	120.535i	0.0969235	+	0.167876i
$719$		−	1059.10i		−	1.47302i	−0.676427	−	0.736509i	$-0.736473\pi$
$719$		−	1059.10i		−	1.47302i	0.676427	−	0.736509i	$-0.263527\pi$
$720$		0			0
$721$	−213.139			−0.295616
$722$	765.295	−	441.843i	1.05997	−	0.611971i
$723$		0			0
$724$	−55.2319	+	95.6645i	−0.0762872	+	0.132133i
$725$	5.36590	+	3.09800i	0.00740124	+	0.00427311i
$726$		0			0
$727$	53.8874	+	93.3358i	0.0741230	+	0.128385i	0.900705	−	0.434432i	$-0.143051\pi$
$727$	53.8874	+	93.3358i	0.0741230	+	0.128385i	−0.826582	+	0.562817i	$0.809718\pi$
$728$		−	865.189i		−	1.18845i
$729$		0			0
$730$	−519.659			−0.711861
$731$	−474.012	+	273.671i	−0.648443	+	0.374379i
$732$		0			0
$733$	120.318	−	208.397i	0.164144	−	0.284306i	−0.772207	−	0.635371i	$-0.780847\pi$
$733$	120.318	−	208.397i	0.164144	−	0.284306i	0.936351	+	0.351065i	$0.114180\pi$
$734$	−408.043	−	235.584i	−0.555916	−	0.320958i
$735$		0			0
$736$	−23.1935	−	40.1723i	−0.0315129	−	0.0545820i
$737$		−	254.784i		−	0.345705i
$738$		0			0
$739$	84.9155			0.114906			0.0574530	−	0.998348i	$-0.481702\pi$
$739$	84.9155			0.114906			0.0574530	+	0.998348i	$0.481702\pi$
$740$	50.4893	−	29.1500i	0.0682288	−	0.0393919i
$741$		0			0
$742$	189.535	−	328.285i	0.255438	−	0.442432i
$743$	72.6340	+	41.9353i	0.0977578	+	0.0564405i	0.548082	−	0.836425i	$-0.315358\pi$
$743$	72.6340	+	41.9353i	0.0977578	+	0.0564405i	−0.450324	+	0.892865i	$0.648692\pi$
$744$		0			0
$745$	46.6174	+	80.7437i	0.0625737	+	0.108381i
$746$		−	1310.30i		−	1.75643i
$747$		0			0
$748$	2002.28			2.67684
$749$	−120.408	+	69.5178i	−0.160759	+	0.0928142i
$750$		0			0
$751$	185.335	−	321.009i	0.246784	−	0.427442i	−0.715848	−	0.698256i	$-0.753960\pi$
$751$	185.335	−	321.009i	0.246784	−	0.427442i	0.962632	+	0.270814i	$0.0872929\pi$
$752$	−111.963	−	64.6420i	−0.148887	−	0.0859601i
$753$		0			0
$754$	31.3572	+	54.3122i	0.0415878	+	0.0720321i
$755$		−	551.144i		−	0.729992i
$756$		0			0
$757$	45.1582			0.0596541			0.0298271	−	0.999555i	$-0.490504\pi$
$757$	45.1582			0.0596541			0.0298271	+	0.999555i	$0.490504\pi$
$758$	1557.96	−	899.487i	2.05535	−	1.18666i
$759$		0			0
$760$	−247.775	+	429.159i	−0.326020	+	0.564683i
$761$	660.624	+	381.411i	0.868099	+	0.501197i	0.866716	−	0.498802i	$-0.166226\pi$
$761$	660.624	+	381.411i	0.868099	+	0.501197i	0.00138318	+	0.999999i	$0.499560\pi$
$762$		0			0
$763$	−241.107	−	417.609i	−0.315998	−	0.547325i
$764$			75.0011i			0.0981690i
$765$		0			0
$766$	1108.81			1.44753
$767$	−389.055	+	224.621i	−0.507242	+	0.292856i
$768$		0			0
$769$	−69.5451	+	120.456i	−0.0904357	+	0.156639i	−0.907695	−	0.419632i	$-0.862159\pi$
$769$	−69.5451	+	120.456i	−0.0904357	+	0.156639i	0.817259	+	0.576271i	$0.195493\pi$
$770$	−597.172	−	344.777i	−0.775548	−	0.447763i
$771$		0			0
$772$	1097.14	+	1900.30i	1.42116	+	2.46152i
$773$		−	1302.81i		−	1.68539i	−0.538391	−	0.842695i	$-0.680968\pi$
$773$		−	1302.81i		−	1.68539i	0.538391	−	0.842695i	$-0.319032\pi$
$774$		0			0
$775$	−66.9310			−0.0863626
$776$	119.787	−	69.1591i	0.154365	−	0.0891226i
$777$		0			0
$778$	651.247	−	1127.99i	0.837078	−	1.44986i
$779$	1265.61	+	730.701i	1.62466	+	0.937999i
$780$		0			0
$781$	−392.311	−	679.503i	−0.502319	−	0.870042i
$782$		−	106.849i		−	0.136636i
$783$		0			0
$784$	−18.1946			−0.0232074
$785$	−421.587	+	243.403i	−0.537053	+	0.310068i
$786$		0			0
$787$	−46.9251	+	81.2766i	−0.0596253	+	0.103274i	−0.894297	−	0.447473i	$-0.852324\pi$
$787$	−46.9251	+	81.2766i	−0.0596253	+	0.103274i	0.834672	+	0.550747i	$0.185657\pi$
$788$	365.907	+	211.257i	0.464349	+	0.268092i
$789$		0			0
$790$	−221.357	−	383.402i	−0.280199	−	0.485319i
$791$			294.025i			0.371713i
$792$		0			0
$793$	1720.58			2.16971
$794$	952.203	−	549.755i	1.19925	−	0.692386i
$795$		0			0
$796$	761.883	−	1319.62i	0.957139	−	1.65781i
$797$	500.534	+	288.983i	0.628023	+	0.362589i	0.779986	−	0.625797i	$-0.215226\pi$
$797$	500.534	+	288.983i	0.628023	+	0.362589i	−0.151963	+	0.988386i	$0.548560\pi$
$798$		0			0
$799$	629.974	+	1091.15i	0.788453	+	1.36564i
$800$			142.695i			0.178369i
$801$		0			0
$802$	−1756.09			−2.18964
$803$	−915.354	+	528.480i	−1.13992	+	0.658132i
$804$		0			0
$805$	−11.5188	+	19.9511i	−0.0143090	+	0.0247839i
$806$	−586.697	−	338.729i	−0.727911	−	0.420260i
$807$		0			0
$808$	−505.681	−	875.866i	−0.625843	−	1.08399i
$809$			666.886i			0.824334i	0.911108	+	0.412167i	$0.135228\pi$
$809$			666.886i			0.824334i	−0.911108	+	0.412167i	$0.864772\pi$
$810$		0			0
$811$	918.647			1.13273			0.566367	−	0.824153i	$-0.308349\pi$
$811$	918.647			1.13273			0.566367	+	0.824153i	$0.308349\pi$
$812$	−45.5566	+	26.3021i	−0.0561041	+	0.0323917i
$813$		0			0
$814$	94.7020	−	164.029i	0.116341	−	0.201509i
$815$	259.524	+	149.837i	0.318435	+	0.183848i
$816$		0			0
$817$	−342.078	−	592.497i	−0.418700	−	0.725210i
$818$		−	257.558i		−	0.314863i
$819$		0			0
$820$	−871.084			−1.06230
$821$	1262.93	−	729.154i	1.53828	−	0.888129i	0.539345	−	0.842085i	$-0.318672\pi$
$821$	1262.93	−	729.154i	1.53828	−	0.888129i	0.998939	−	0.0460438i	$-0.0146614\pi$
$822$		0			0
$823$	−799.847	+	1385.37i	−0.971867	+	1.68332i	−0.281958	+	0.959427i	$0.590984\pi$
$823$	−799.847	+	1385.37i	−0.971867	+	1.68332i	−0.689909	+	0.723896i	$0.742349\pi$
$824$	−256.876	−	148.307i	−0.311743	−	0.179985i
$825$		0			0
$826$	−300.942	−	521.247i	−0.364337	−	0.631050i
$827$		−	144.531i		−	0.174766i	−0.996175	−	0.0873830i	$-0.972150\pi$
$827$		−	144.531i		−	0.174766i	0.996175	−	0.0873830i	$-0.0278504\pi$
$828$		0			0
$829$	−160.171			−0.193210			−0.0966050	−	0.995323i	$-0.530798\pi$
$829$	−160.171			−0.193210			−0.0966050	+	0.995323i	$0.530798\pi$
$830$	−513.503	+	296.471i	−0.618678	+	0.357194i
$831$		0			0
$832$	−785.989	+	1361.37i	−0.944698	+	1.63627i
$833$	153.561	+	88.6584i	0.184347	+	0.106433i
$834$		0			0
$835$	277.614	+	480.842i	0.332472	+	0.575859i
$836$			2502.77i			2.99375i
$837$		0			0
$838$	−343.727			−0.410176
$839$	−789.432	+	455.779i	−0.940920	+	0.543241i	−0.890249	−	0.455475i	$-0.849469\pi$
$839$	−789.432	+	455.779i	−0.940920	+	0.543241i	−0.0506715	+	0.998715i	$0.516136\pi$
$840$		0			0
$841$	−419.732	+	726.997i	−0.499087	+	0.864444i
$842$	−481.979	−	278.271i	−0.572421	−	0.330488i
$843$		0			0
$844$	−1002.55	−	1736.47i	−1.18786	−	2.05743i
$845$		−	157.496i		−	0.186385i
$846$		0			0
$847$	−635.548			−0.750352
$848$	32.6587	−	18.8555i	0.0385127	−	0.0222353i
$849$		0			0
$850$	−164.344	+	284.653i	−0.193346	+	0.334886i
$851$	−5.48007	−	3.16392i	−0.00643957	−	0.00371789i
$852$		0			0
$853$	−258.857	−	448.354i	−0.303467	−	0.525620i	0.673452	−	0.739231i	$-0.264811\pi$
$853$	−258.857	−	448.354i	−0.303467	−	0.525620i	−0.976919	+	0.213611i	$0.931478\pi$
$854$			2305.20i			2.69930i
$855$		0			0
$856$	−193.489			−0.226038
$857$	−855.578	+	493.968i	−0.998341	+	0.576392i	−0.907757	−	0.419497i	$-0.862207\pi$
$857$	−855.578	+	493.968i	−0.998341	+	0.576392i	−0.0905838	+	0.995889i	$0.528873\pi$
$858$		0			0
$859$	575.225	−	996.319i	0.669645	−	1.15986i	−0.308359	−	0.951270i	$-0.599780\pi$
$859$	575.225	−	996.319i	0.669645	−	1.15986i	0.978003	−	0.208589i	$-0.0668870\pi$
$860$	353.164	+	203.899i	0.410655	+	0.237092i
$861$		0			0
$862$	11.7706	+	20.3872i	0.0136550	+	0.0236511i
$863$		−	859.922i		−	0.996433i	−0.867053	−	0.498217i	$-0.833988\pi$
$863$		−	859.922i		−	0.996433i	0.867053	−	0.498217i	$-0.166012\pi$
$864$		0			0
$865$	4.14019			0.00478635
$866$	−766.785	+	442.704i	−0.885433	+	0.511205i
$867$		0			0
$868$	284.123	−	492.115i	0.327330	−	0.566953i
$869$	−779.820	−	450.229i	−0.897377	−	0.518101i
$870$		0			0
$871$	132.519	+	229.530i	0.152146	+	0.263525i
$872$		−	671.072i		−	0.769577i
$873$		0			0
$874$	133.557			0.152812
$875$	61.3733	−	35.4339i	0.0701410	−	0.0404959i
$876$		0			0
$877$	−305.818	+	529.693i	−0.348710	+	0.603983i	−0.986020	−	0.166624i	$-0.946713\pi$
$877$	−305.818	+	529.693i	−0.348710	+	0.603983i	0.637311	+	0.770607i	$0.280047\pi$
$878$	2103.99	+	1214.74i	2.39634	+	1.38353i
$879$		0			0
$880$	−34.2995	−	59.4084i	−0.0389767	−	0.0675096i
$881$			151.803i			0.172307i	0.996282	+	0.0861537i	$0.0274576\pi$
$881$			151.803i			0.172307i	−0.996282	+	0.0861537i	$0.972542\pi$
$882$		0			0
$883$	−823.520			−0.932639			−0.466320	−	0.884616i	$-0.654420\pi$
$883$	−823.520			−0.932639			−0.466320	+	0.884616i	$0.654420\pi$
$884$	−1803.81	+	1041.43i	−2.04051	+	1.17809i
$885$		0			0
$886$	−861.209	+	1491.66i	−0.972020	+	1.68359i
$887$	−598.324	−	345.443i	−0.674548	−	0.389450i	0.123250	−	0.992376i	$-0.460668\pi$
$887$	−598.324	−	345.443i	−0.674548	−	0.389450i	−0.797798	+	0.602925i	$0.794002\pi$
$888$		0			0
$889$	109.467	+	189.602i	0.123135	+	0.213276i
$890$		−	46.4261i		−	0.0521641i
$891$		0			0
$892$	279.179			0.312981
$893$	−1363.89	+	787.443i	−1.52731	+	0.881795i
$894$		0			0
$895$	−159.684	+	276.580i	−0.178418	+	0.309028i
$896$	−1197.29	−	691.256i	−1.33626	−	0.771491i
$897$		0			0
$898$	1283.86	+	2223.72i	1.42969	+	2.47630i
$899$			16.5882i			0.0184518i
$900$		0			0
$901$	−367.516			−0.407898
$902$	−2450.82	+	1414.98i	−2.71709	+	1.56871i
$903$		0			0
$904$	−204.589	+	354.359i	−0.226316	+	0.391990i
$905$	−31.9412	−	18.4413i	−0.0352941	−	0.0203771i
$906$		0			0
$907$	−488.566	−	846.220i	−0.538661	−	0.932988i	−0.998976	−	0.0452328i	$-0.985597\pi$
$907$	−488.566	−	846.220i	−0.538661	−	0.932988i	0.460315	−	0.887755i	$-0.347736\pi$
$908$		−	1359.62i		−	1.49737i
$909$		0			0
$910$	717.306			0.788249
$911$	895.587	−	517.068i	0.983082	−	0.567582i	0.0798826	−	0.996804i	$-0.474545\pi$
$911$	895.587	−	517.068i	0.983082	−	0.567582i	0.903199	+	0.429222i	$0.141212\pi$
$912$		0			0
$913$	−603.007	+	1044.44i	−0.660468	+	1.14396i
$914$	2185.95	+	1262.06i	2.39163	+	1.38081i
$915$		0			0
$916$	1263.18	+	2187.89i	1.37901	+	2.38852i
$917$		−	710.036i		−	0.774303i
$918$		0			0
$919$	−1219.02			−1.32646			−0.663230	−	0.748416i	$-0.730815\pi$
$919$	−1219.02			−1.32646			−0.663230	+	0.748416i	$0.730815\pi$
$920$	−27.7649	+	16.0301i	−0.0301792	+	0.0174240i
$921$		0			0
$922$	−420.562	+	728.435i	−0.456141	+	0.790060i
$923$	706.850	+	408.100i	0.765818	+	0.442145i
$924$		0			0
$925$	9.73283	+	16.8578i	0.0105220	+	0.0182246i
$926$		−	1674.83i		−	1.80867i
$927$		0			0
$928$	35.3656			0.0381095
$929$	1084.77	−	626.290i	1.16767	−	0.674155i	0.214541	−	0.976715i	$-0.431175\pi$
$929$	1084.77	−	626.290i	1.16767	−	0.674155i	0.953130	+	0.302560i	$0.0978413\pi$
$930$		0			0
$931$	−110.820	+	191.945i	−0.119033	+	0.206171i
$932$	−1619.78	−	935.182i	−1.73796	−	1.00341i
$933$		0			0
$934$	224.169	+	388.271i	0.240009	+	0.415708i
$935$			668.537i			0.715013i
$936$		0			0
$937$	−760.345			−0.811468			−0.405734	−	0.913991i	$-0.632984\pi$
$937$	−760.345			−0.811468			−0.405734	+	0.913991i	$0.632984\pi$
$938$	−307.519	+	177.546i	−0.327846	+	0.189282i
$939$		0			0
$940$	469.363	−	812.961i	0.499323	−	0.864852i
$941$	871.984	+	503.440i	0.926657	+	0.535006i	0.885753	−	0.464158i	$-0.153643\pi$
$941$	871.984	+	503.440i	0.926657	+	0.535006i	0.0409041	+	0.999163i	$0.486976\pi$
$942$		0			0
$943$	47.2734	+	81.8799i	0.0501309	+	0.0868292i
$944$		−	59.8773i		−	0.0634293i
$945$		0			0
$946$	1324.85			1.40047
$947$	782.197	−	451.602i	0.825974	−	0.476876i	−0.0264982	−	0.999649i	$-0.508436\pi$
$947$	782.197	−	451.602i	0.825974	−	0.476876i	0.852472	+	0.522773i	$0.175102\pi$
$948$		0			0
$949$	549.748	−	952.192i	0.579292	−	1.00336i
$950$	−355.805	−	205.424i	−0.374532	−	0.216236i
$951$		0			0
$952$	−561.915	−	973.265i	−0.590247	−	1.02234i
$953$			401.690i			0.421500i	0.977540	+	0.210750i	$0.0675907\pi$
$953$			401.690i			0.421500i	−0.977540	+	0.210750i	$0.932409\pi$
$954$		0			0
$955$	−25.0420			−0.0262219
$956$	1457.42	−	841.442i	1.52450	−	0.880170i
$957$		0			0
$958$	1017.59	−	1762.52i	1.06220	−	1.83979i
$959$	424.219	+	244.923i	0.442356	+	0.255394i
$960$		0			0
$961$	390.905	+	677.067i	0.406769	+	0.704544i
$962$			197.026i			0.204809i
$963$		0			0
$964$	2168.16			2.24912
$965$	−634.486	+	366.320i	−0.657498	+	0.379607i
$966$		0			0
$967$	666.123	−	1153.76i	0.688855	−	1.19313i	−0.283353	−	0.959016i	$-0.591447\pi$
$967$	666.123	−	1153.76i	0.688855	−	1.19313i	0.972209	−	0.234117i	$-0.0752198\pi$
$968$	−765.964	−	442.229i	−0.791285	−	0.456849i
$969$		0			0
$970$	57.3381	+	99.3125i	0.0591115	+	0.102384i
$971$		−	982.430i		−	1.01177i	−0.862601	−	0.505886i	$-0.831166\pi$
$971$		−	982.430i		−	1.01177i	0.862601	−	0.505886i	$-0.168834\pi$
$972$		0			0
$973$	878.151			0.902519
$974$	−153.348	+	88.5355i	−0.157441	+	0.0908989i
$975$		0			0
$976$	−114.664	+	198.604i	−0.117484	+	0.203488i
$977$	56.9052	+	32.8542i	0.0582448	+	0.0336277i	0.528840	−	0.848722i	$-0.322627\pi$
$977$	56.9052	+	32.8542i	0.0582448	+	0.0336277i	−0.470595	+	0.882349i	$0.655961\pi$
$978$		0			0
$979$	−47.2141	−	81.7773i	−0.0482269	−	0.0835314i
$980$		−	132.110i		−	0.134806i
$981$		0			0
$982$	2010.70			2.04756
$983$	−1178.39	+	680.344i	−1.19877	+	0.692110i	−0.960281	−	0.279035i	$-0.909985\pi$
$983$	−1178.39	+	680.344i	−1.19877	+	0.692110i	−0.238489	+	0.971145i	$0.576652\pi$
$984$		0			0
$985$	−70.5360	+	122.172i	−0.0716102	+	0.124032i
$986$	70.5484	+	40.7312i	0.0715501	+	0.0413095i
$987$		0			0
$988$	−1301.75	−	2254.69i	−1.31756	−	2.28208i
$989$		−	44.2621i		−	0.0447544i
$990$		0			0
$991$	−667.221			−0.673281			−0.336640	−	0.941633i	$-0.609291\pi$
$991$	−667.221			−0.673281			−0.336640	+	0.941633i	$0.609291\pi$
$992$	−330.848	+	191.015i	−0.333516	+	0.192555i
$993$		0			0
$994$	−546.764	+	947.023i	−0.550064	+	0.952739i
$995$	440.605	+	254.383i	0.442819	+	0.255662i
$996$		0			0
$997$	−87.0845	−	150.835i	−0.0873465	−	0.151289i	0.819042	−	0.573733i	$-0.194505\pi$
$997$	−87.0845	−	150.835i	−0.0873465	−	0.151289i	−0.906389	+	0.422445i	$0.861172\pi$
$998$			1985.16i			1.98914i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.3.i.a.71.7		16
3.2	odd	2		45.3.i.a.41.2	yes	16
4.3	odd	2		2160.3.bs.c.881.7		16
5.2	odd	4		675.3.i.c.449.15		32
5.3	odd	4		675.3.i.c.449.2		32
5.4	even	2		675.3.j.b.476.2		16
9.2	odd	6	inner	135.3.i.a.116.7		16
9.4	even	3		405.3.c.a.161.15		16
9.5	odd	6		405.3.c.a.161.2		16
9.7	even	3		45.3.i.a.11.2	✓	16
12.11	even	2		720.3.bs.c.401.7		16
15.2	even	4		225.3.i.b.149.2		32
15.8	even	4		225.3.i.b.149.15		32
15.14	odd	2		225.3.j.b.176.7		16
36.7	odd	6		720.3.bs.c.641.7		16
36.11	even	6		2160.3.bs.c.1601.7		16
45.2	even	12		675.3.i.c.224.2		32
45.7	odd	12		225.3.i.b.74.15		32
45.29	odd	6		675.3.j.b.251.2		16
45.34	even	6		225.3.j.b.101.7		16
45.38	even	12		675.3.i.c.224.15		32
45.43	odd	12		225.3.i.b.74.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.i.a.11.2	✓	16	9.7	even	3
45.3.i.a.41.2	yes	16	3.2	odd	2
135.3.i.a.71.7		16	1.1	even	1	trivial
135.3.i.a.116.7		16	9.2	odd	6	inner
225.3.i.b.74.2		32	45.43	odd	12
225.3.i.b.74.15		32	45.7	odd	12
225.3.i.b.149.2		32	15.2	even	4
225.3.i.b.149.15		32	15.8	even	4
225.3.j.b.101.7		16	45.34	even	6
225.3.j.b.176.7		16	15.14	odd	2
405.3.c.a.161.2		16	9.5	odd	6
405.3.c.a.161.15		16	9.4	even	3
675.3.i.c.224.2		32	45.2	even	12
675.3.i.c.224.15		32	45.38	even	12
675.3.i.c.449.2		32	5.3	odd	4
675.3.i.c.449.15		32	5.2	odd	4
675.3.j.b.251.2		16	45.29	odd	6
675.3.j.b.476.2		16	5.4	even	2
720.3.bs.c.401.7		16	12.11	even	2
720.3.bs.c.641.7		16	36.7	odd	6
2160.3.bs.c.881.7		16	4.3	odd	2
2160.3.bs.c.1601.7		16	36.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.83245 - 1.63532i) q^{2} +(3.34853 - 5.79983i) q^{4} +(1.93649 + 1.11803i) q^{5} +(-3.16931 - 5.48940i) q^{7} -8.82112i q^{8} +O(q^{10})\)	\(q+(2.83245 - 1.63532i) q^{2} +(3.34853 - 5.79983i) q^{4} +(1.93649 + 1.11803i) q^{5} +(-3.16931 - 5.48940i) q^{7} -8.82112i q^{8} +7.31337 q^{10} +(12.8821 - 7.43751i) q^{11} +(-7.73683 + 13.4006i) q^{13} +(-17.9538 - 10.3656i) q^{14} +(-1.03121 - 1.78610i) q^{16} +20.0994i q^{17} -25.1235 q^{19} +(12.9688 - 7.48755i) q^{20} +(24.3254 - 42.1328i) q^{22} +(-1.40763 - 0.812693i) q^{23} +(2.50000 + 4.33013i) q^{25} +50.6087i q^{26} -42.4501 q^{28} +(1.07318 - 0.619600i) q^{29} +(-6.69310 + 11.5928i) q^{31} +(24.7156 + 14.2695i) q^{32} +(32.8689 + 56.9306i) q^{34} -14.1736i q^{35} +3.89313 q^{37} +(-71.1610 + 41.0848i) q^{38} +(9.86231 - 17.0820i) q^{40} +(-50.3757 - 29.0844i) q^{41} +(13.6159 + 23.5834i) q^{43} -99.6189i q^{44} -5.31605 q^{46} +(54.2876 - 31.3429i) q^{47} +(4.41100 - 7.64007i) q^{49} +(14.1623 + 8.17659i) q^{50} +(51.8140 + 89.7446i) q^{52} +18.2849i q^{53} +33.2615 q^{55} +(-48.4226 + 27.9568i) q^{56} +(2.02649 - 3.50998i) q^{58} +(25.1430 + 14.5163i) q^{59} +(-55.5971 - 96.2970i) q^{61} +43.7814i q^{62} +101.591 q^{64} +(-29.9646 + 17.3001i) q^{65} +(8.56418 - 14.8336i) q^{67} +(116.573 + 67.3034i) q^{68} +(-23.1783 - 40.1460i) q^{70} -52.7477i q^{71} -71.0560 q^{73} +(11.0271 - 6.36651i) q^{74} +(-84.1267 + 145.712i) q^{76} +(-81.6549 - 47.1435i) q^{77} +(-30.2675 - 52.4248i) q^{79} -4.61169i q^{80} -190.249 q^{82} +(-70.2143 + 40.5382i) q^{83} +(-22.4718 + 38.9223i) q^{85} +(77.1327 + 44.5326i) q^{86} +(-65.6071 - 113.635i) q^{88} -6.34811i q^{89} +98.0815 q^{91} +(-9.42696 + 5.44266i) q^{92} +(102.511 - 177.555i) q^{94} +(-48.6514 - 28.0889i) q^{95} +(7.84018 + 13.5796i) q^{97} -28.8535i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4} + 2 q^{7}+O(q^{10}) \) 16 * q + 16 * q^4 + 2 * q^7	\( 16 q + 16 q^{4} + 2 q^{7} + 18 q^{11} - 10 q^{13} + 54 q^{14} - 32 q^{16} - 52 q^{19} - 24 q^{22} + 54 q^{23} + 40 q^{25} + 32 q^{28} + 54 q^{29} + 32 q^{31} - 216 q^{32} + 54 q^{34} + 44 q^{37} - 252 q^{38} - 30 q^{40} - 144 q^{41} - 124 q^{43} - 108 q^{46} + 216 q^{47} - 54 q^{49} + 62 q^{52} + 18 q^{56} + 90 q^{58} + 486 q^{59} + 62 q^{61} + 256 q^{64} + 90 q^{65} + 14 q^{67} + 288 q^{68} - 60 q^{70} - 268 q^{73} - 540 q^{74} - 106 q^{76} - 702 q^{77} - 40 q^{79} - 204 q^{82} - 522 q^{83} + 30 q^{85} - 54 q^{86} + 144 q^{88} + 136 q^{91} + 1332 q^{92} - 150 q^{94} - 180 q^{95} - 142 q^{97}+O(q^{100}) \) 16 * q + 16 * q^4 + 2 * q^7 + 18 * q^11 - 10 * q^13 + 54 * q^14 - 32 * q^16 - 52 * q^19 - 24 * q^22 + 54 * q^23 + 40 * q^25 + 32 * q^28 + 54 * q^29 + 32 * q^31 - 216 * q^32 + 54 * q^34 + 44 * q^37 - 252 * q^38 - 30 * q^40 - 144 * q^41 - 124 * q^43 - 108 * q^46 + 216 * q^47 - 54 * q^49 + 62 * q^52 + 18 * q^56 + 90 * q^58 + 486 * q^59 + 62 * q^61 + 256 * q^64 + 90 * q^65 + 14 * q^67 + 288 * q^68 - 60 * q^70 - 268 * q^73 - 540 * q^74 - 106 * q^76 - 702 * q^77 - 40 * q^79 - 204 * q^82 - 522 * q^83 + 30 * q^85 - 54 * q^86 + 144 * q^88 + 136 * q^91 + 1332 * q^92 - 150 * q^94 - 180 * q^95 - 142 * q^97

Introduction

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