LMFDB - Embedded newform 576.3.t.a.223.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,3,Mod(31,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2]))

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

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

chi := DirichletCharacter("576.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	576.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.6948632272$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			223.4
Character	$\chi$	$=$	576.223
Dual form			576.3.t.a.31.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.70112 - 1.30536i) q^{3} +(4.53220 - 2.61667i) q^{5} +(-1.71711 - 0.991374i) q^{7} +(5.59208 + 7.05186i) q^{9} +O(q^{10})$	\(q+(-2.70112 - 1.30536i) q^{3} +(4.53220 - 2.61667i) q^{5} +(-1.71711 - 0.991374i) q^{7} +(5.59208 + 7.05186i) q^{9} +(0.183983 - 0.318668i) q^{11} +(10.4361 - 6.02529i) q^{13} +(-15.6577 + 1.15178i) q^{15} +5.50826 q^{17} +14.0784 q^{19} +(3.34402 + 4.91926i) q^{21} +(-0.357187 + 0.206222i) q^{23} +(1.19391 - 2.06792i) q^{25} +(-5.89965 - 26.3476i) q^{27} +(33.8161 + 19.5237i) q^{29} +(-26.7327 + 15.4341i) q^{31} +(-0.912936 + 0.620596i) q^{33} -10.3764 q^{35} -40.1971i q^{37} +(-36.0543 + 2.65215i) q^{39} +(-34.4198 - 59.6168i) q^{41} +(33.5082 - 58.0379i) q^{43} +(43.7968 + 17.3278i) q^{45} +(26.0961 + 15.0666i) q^{47} +(-22.5344 - 39.0307i) q^{49} +(-14.8785 - 7.19026i) q^{51} +15.9557i q^{53} -1.92569i q^{55} +(-38.0274 - 18.3773i) q^{57} +(-47.2149 - 81.7786i) q^{59} +(32.7986 + 18.9363i) q^{61} +(-2.61118 - 17.6526i) q^{63} +(31.5324 - 54.6157i) q^{65} +(-6.46484 - 11.1974i) q^{67} +(1.23400 - 0.0907728i) q^{69} -94.7164i q^{71} +138.807 q^{73} +(-5.92428 + 4.02721i) q^{75} +(-0.631838 + 0.364792i) q^{77} +(94.4089 + 54.5070i) q^{79} +(-18.4574 + 78.8690i) q^{81} +(28.9129 - 50.0785i) q^{83} +(24.9646 - 14.4133i) q^{85} +(-65.8557 - 96.8780i) q^{87} -98.5744 q^{89} -23.8932 q^{91} +(92.3552 - 6.79363i) q^{93} +(63.8061 - 36.8385i) q^{95} +(28.6381 - 49.6027i) q^{97} +(3.27605 - 0.484594i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 18 q^{5} + 18 q^{9}+O(q^{10}) $ 32 * q - 18 * q^5 + 18 * q^9	$ 32 q - 18 q^{5} + 18 q^{9} - 30 q^{13} - 36 q^{17} + 102 q^{21} + 86 q^{25} - 162 q^{29} + 12 q^{33} - 36 q^{41} + 186 q^{45} + 138 q^{49} - 162 q^{57} - 42 q^{61} - 198 q^{65} - 474 q^{69} - 196 q^{73} + 666 q^{77} + 462 q^{81} + 180 q^{85} + 792 q^{89} + 174 q^{93} + 64 q^{97}+O(q^{100}) $ 32 * q - 18 * q^5 + 18 * q^9 - 30 * q^13 - 36 * q^17 + 102 * q^21 + 86 * q^25 - 162 * q^29 + 12 * q^33 - 36 * q^41 + 186 * q^45 + 138 * q^49 - 162 * q^57 - 42 * q^61 - 198 * q^65 - 474 * q^69 - 196 * q^73 + 666 * q^77 + 462 * q^81 + 180 * q^85 + 792 * q^89 + 174 * q^93 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.70112	−	1.30536i	−0.900373	−	0.435120i
$3$	−2.70112	−	1.30536i	−0.900373	−	0.435120i
$4$		0			0
$5$	4.53220	−	2.61667i	0.906441	−	0.523334i	0.0271565	−	0.999631i	$-0.491355\pi$
$5$	4.53220	−	2.61667i	0.906441	−	0.523334i	0.879284	+	0.476297i	$0.158021\pi$
$6$		0			0
$7$	−1.71711	−	0.991374i	−0.245301	−	0.141625i	0.372310	−	0.928109i	$-0.378566\pi$
$7$	−1.71711	−	0.991374i	−0.245301	−	0.141625i	−0.617611	+	0.786484i	$0.711899\pi$
$8$		0			0
$9$	5.59208	+	7.05186i	0.621342	+	0.783540i
$10$		0			0
$11$	0.183983	−	0.318668i	0.0167257	−	0.0289698i	−0.857541	−	0.514415i	$-0.828009\pi$
$11$	0.183983	−	0.318668i	0.0167257	−	0.0289698i	0.874267	+	0.485445i	$0.161342\pi$
$12$		0			0
$13$	10.4361	−	6.02529i	0.802777	−	0.463484i	−0.0416642	−	0.999132i	$-0.513266\pi$
$13$	10.4361	−	6.02529i	0.802777	−	0.463484i	0.844441	+	0.535648i	$0.179933\pi$
$14$		0			0
$15$	−15.6577	+	1.15178i	−1.04385	+	0.0767852i
$16$		0			0
$17$	5.50826			0.324015			0.162008	−	0.986789i	$-0.448203\pi$
$17$	5.50826			0.324015			0.162008	+	0.986789i	$0.448203\pi$
$18$		0			0
$19$	14.0784			0.740968			0.370484	−	0.928839i	$-0.379192\pi$
$19$	14.0784			0.740968			0.370484	+	0.928839i	$0.379192\pi$
$20$		0			0
$21$	3.34402	+	4.91926i	0.159239	+	0.234251i
$22$		0			0
$23$	−0.357187	+	0.206222i	−0.0155299	+	0.00896618i	−0.507745	−	0.861508i	$-0.669521\pi$
$23$	−0.357187	+	0.206222i	−0.0155299	+	0.00896618i	0.492215	+	0.870474i	$0.336187\pi$
$24$		0			0
$25$	1.19391	−	2.06792i	0.0477566	−	0.0827168i
$26$		0			0
$27$	−5.89965	−	26.3476i	−0.218506	−	0.975836i
$28$		0			0
$29$	33.8161	+	19.5237i	1.16607	+	0.673231i	0.952751	−	0.303751i	$-0.0982391\pi$
$29$	33.8161	+	19.5237i	1.16607	+	0.673231i	0.213320	+	0.976982i	$0.431572\pi$
$30$		0			0
$31$	−26.7327	+	15.4341i	−0.862345	+	0.497875i	−0.864797	−	0.502122i	$-0.832553\pi$
$31$	−26.7327	+	15.4341i	−0.862345	+	0.497875i	0.00245215	+	0.999997i	$0.499219\pi$
$32$		0			0
$33$	−0.912936	+	0.620596i	−0.0276647	+	0.0188059i
$34$		0			0
$35$	−10.3764			−0.296468
$36$		0			0
$37$		−	40.1971i		−	1.08641i	−0.839601	−	0.543204i	$-0.817211\pi$
$37$		−	40.1971i		−	1.08641i	0.839601	−	0.543204i	$-0.182789\pi$
$38$		0			0
$39$	−36.0543	+	2.65215i	−0.924469	+	0.0680038i
$40$		0			0
$41$	−34.4198	−	59.6168i	−0.839507	−	1.45407i	−0.890307	−	0.455361i	$-0.849510\pi$
$41$	−34.4198	−	59.6168i	−0.839507	−	1.45407i	0.0507997	−	0.998709i	$-0.483823\pi$
$42$		0			0
$43$	33.5082	−	58.0379i	0.779261	−	1.34972i	−0.153107	−	0.988210i	$-0.548928\pi$
$43$	33.5082	−	58.0379i	0.779261	−	1.34972i	0.932368	−	0.361510i	$-0.117739\pi$
$44$		0			0
$45$	43.7968	+	17.3278i	0.973262	+	0.385063i
$46$		0			0
$47$	26.0961	+	15.0666i	0.555235	+	0.320565i	0.751231	−	0.660039i	$-0.229460\pi$
$47$	26.0961	+	15.0666i	0.555235	+	0.320565i	−0.195996	+	0.980605i	$0.562794\pi$
$48$		0			0
$49$	−22.5344	−	39.0307i	−0.459885	−	0.796544i
$50$		0			0
$51$	−14.8785	−	7.19026i	−0.291735	−	0.140985i
$52$		0			0
$53$			15.9557i			0.301052i	0.988606	+	0.150526i	$0.0480967\pi$
$53$			15.9557i			0.301052i	−0.988606	+	0.150526i	$0.951903\pi$
$54$		0			0
$55$		−	1.92569i		−	0.0350126i
$56$		0			0
$57$	−38.0274	−	18.3773i	−0.667147	−	0.322410i
$58$		0			0
$59$	−47.2149	−	81.7786i	−0.800252	−	1.38608i	−0.919450	−	0.393207i	$-0.871365\pi$
$59$	−47.2149	−	81.7786i	−0.800252	−	1.38608i	0.119197	−	0.992871i	$-0.461968\pi$
$60$		0			0
$61$	32.7986	+	18.9363i	0.537681	+	0.310430i	0.744139	−	0.668025i	$-0.232860\pi$
$61$	32.7986	+	18.9363i	0.537681	+	0.310430i	−0.206457	+	0.978456i	$0.566193\pi$
$62$		0			0
$63$	−2.61118	−	17.6526i	−0.0414473	−	0.280201i
$64$		0			0
$65$	31.5324	−	54.6157i	0.485113	−	0.840241i
$66$		0			0
$67$	−6.46484	−	11.1974i	−0.0964901	−	0.167126i	0.813739	−	0.581230i	$-0.197428\pi$
$67$	−6.46484	−	11.1974i	−0.0964901	−	0.167126i	−0.910230	+	0.414104i	$0.864095\pi$
$68$		0			0
$69$	1.23400	−	0.0907728i	0.0178840	−	0.00131555i
$70$		0			0
$71$		−	94.7164i		−	1.33403i	−0.745043	−	0.667017i	$-0.767571\pi$
$71$		−	94.7164i		−	1.33403i	0.745043	−	0.667017i	$-0.232429\pi$
$72$		0			0
$73$	138.807			1.90146			0.950731	−	0.310016i	$-0.100334\pi$
$73$	138.807			1.90146			0.950731	+	0.310016i	$0.100334\pi$
$74$		0			0
$75$	−5.92428	+	4.02721i	−0.0789905	+	0.0536961i
$76$		0			0
$77$	−0.631838	+	0.364792i	−0.00820569	+	0.00473756i
$78$		0			0
$79$	94.4089	+	54.5070i	1.19505	+	0.689962i	0.959447	−	0.281888i	$-0.0909606\pi$
$79$	94.4089	+	54.5070i	1.19505	+	0.689962i	0.235602	+	0.971850i	$0.424294\pi$
$80$		0			0
$81$	−18.4574	+	78.8690i	−0.227869	+	0.973692i
$82$		0			0
$83$	28.9129	−	50.0785i	0.348348	−	0.603356i	−0.637608	−	0.770361i	$-0.720076\pi$
$83$	28.9129	−	50.0785i	0.348348	−	0.603356i	0.985956	+	0.167005i	$0.0534095\pi$
$84$		0			0
$85$	24.9646	−	14.4133i	0.293701	−	0.169568i
$86$		0			0
$87$	−65.8557	−	96.8780i	−0.756962	−	1.11354i
$88$		0			0
$89$	−98.5744			−1.10758			−0.553789	−	0.832657i	$-0.686818\pi$
$89$	−98.5744			−1.10758			−0.553789	+	0.832657i	$0.686818\pi$
$90$		0			0
$91$	−23.8932			−0.262563
$92$		0			0
$93$	92.3552	−	6.79363i	0.993067	−	0.0730498i
$94$		0			0
$95$	63.8061	−	36.8385i	0.671643	−	0.387773i
$96$		0			0
$97$	28.6381	−	49.6027i	0.295238	−	0.511368i	−0.679802	−	0.733396i	$-0.737934\pi$
$97$	28.6381	−	49.6027i	0.295238	−	0.511368i	0.975040	+	0.222028i	$0.0712676\pi$
$98$		0			0
$99$	3.27605	−	0.484594i	0.0330914	−	0.00489488i
$100$		0			0
$101$	−140.697	−	81.2312i	−1.39304	−	0.804269i	−0.399385	−	0.916783i	$-0.630776\pi$
$101$	−140.697	−	81.2312i	−1.39304	−	0.804269i	−0.993650	+	0.112514i	$0.964110\pi$
$102$		0			0
$103$	−108.157	+	62.4447i	−1.05007	+	0.606259i	−0.922669	−	0.385592i	$-0.873997\pi$
$103$	−108.157	+	62.4447i	−1.05007	+	0.606259i	−0.127402	+	0.991851i	$0.540664\pi$
$104$		0			0
$105$	28.0278	+	13.5449i	0.266932	+	0.128999i
$106$		0			0
$107$	44.0778			0.411942			0.205971	−	0.978558i	$-0.433965\pi$
$107$	44.0778			0.411942			0.205971	+	0.978558i	$0.433965\pi$
$108$		0			0
$109$		−	40.9714i		−	0.375885i	−0.982180	−	0.187942i	$-0.939818\pi$
$109$		−	40.9714i		−	0.375885i	0.982180	−	0.187942i	$-0.0601818\pi$
$110$		0			0
$111$	−52.4717	+	108.577i	−0.472718	+	0.978172i
$112$		0			0
$113$	−35.5414	−	61.5595i	−0.314526	−	0.544774i	0.664811	−	0.747012i	$-0.268512\pi$
$113$	−35.5414	−	61.5595i	−0.314526	−	0.544774i	−0.979337	+	0.202237i	$0.935179\pi$
$114$		0			0
$115$	−1.07923	+	1.86928i	−0.00938461	+	0.0162546i
$116$		0			0
$117$	100.849	+	39.9000i	0.861957	+	0.341026i
$118$		0			0
$119$	−9.45829	−	5.46075i	−0.0794814	−	0.0458886i
$120$		0			0
$121$	60.4323	+	104.672i	0.499440	+	0.865056i
$122$		0			0
$123$	15.1506	+	205.962i	0.123175	+	1.67449i
$124$		0			0
$125$			118.337i			0.946697i
$126$		0			0
$127$			239.547i			1.88620i	0.332512	+	0.943099i	$0.392104\pi$
$127$			239.547i			1.88620i	−0.332512	+	0.943099i	$0.607896\pi$
$128$		0			0
$129$	−166.270	+	113.027i	−1.28891	+	0.876179i
$130$		0			0
$131$	−59.4540	−	102.977i	−0.453847	−	0.786086i	0.544774	−	0.838583i	$-0.316615\pi$
$131$	−59.4540	−	102.977i	−0.453847	−	0.786086i	−0.998621	+	0.0524965i	$0.983282\pi$
$132$		0			0
$133$	−24.1741	−	13.9569i	−0.181760	−	0.104939i
$134$		0			0
$135$	−95.6813	−	103.975i	−0.708750	−	0.770186i
$136$		0			0
$137$	−35.9168	+	62.2097i	−0.262166	+	0.454086i	−0.966817	−	0.255469i	$-0.917770\pi$
$137$	−35.9168	+	62.2097i	−0.262166	+	0.454086i	0.704651	+	0.709554i	$0.251104\pi$
$138$		0			0
$139$	81.6956	+	141.501i	0.587738	+	1.01799i	0.994528	+	0.104471i	$0.0333148\pi$
$139$	81.6956	+	141.501i	0.587738	+	1.01799i	−0.406790	+	0.913522i	$0.633352\pi$
$140$		0			0
$141$	−50.8213	−	74.7613i	−0.360434	−	0.530222i
$142$		0			0
$143$		−	4.43420i		−	0.0310084i
$144$		0			0
$145$	204.348			1.40930
$146$		0			0
$147$	9.91894	+	134.842i	0.0674758	+	0.917291i
$148$		0			0
$149$	−119.884	+	69.2150i	−0.804590	+	0.464530i	−0.845074	−	0.534650i	$-0.820444\pi$
$149$	−119.884	+	69.2150i	−0.804590	+	0.464530i	0.0404835	+	0.999180i	$0.487110\pi$
$150$		0			0
$151$	82.4534	+	47.6045i	0.546049	+	0.315262i	0.747527	−	0.664231i	$-0.231241\pi$
$151$	82.4534	+	47.6045i	0.546049	+	0.315262i	−0.201478	+	0.979493i	$0.564574\pi$
$152$		0			0
$153$	30.8026	+	38.8435i	0.201324	+	0.253879i
$154$		0			0
$155$	−80.7720	+	139.901i	−0.521110	+	0.902588i
$156$		0			0
$157$	−144.078	+	83.1837i	−0.917697	+	0.529833i	−0.882900	−	0.469562i	$-0.844412\pi$
$157$	−144.078	+	83.1837i	−0.917697	+	0.529833i	−0.0347974	+	0.999394i	$0.511079\pi$
$158$		0			0
$159$	20.8280	−	43.0983i	0.130994	−	0.271059i
$160$		0			0
$161$	0.817773			0.00507934
$162$		0			0
$163$	137.434			0.843151			0.421575	−	0.906793i	$-0.361477\pi$
$163$	137.434			0.843151			0.421575	+	0.906793i	$0.361477\pi$
$164$		0			0
$165$	−2.51372	+	5.20152i	−0.0152347	+	0.0315244i
$166$		0			0
$167$	184.371	−	106.447i	1.10402	−	0.637406i	0.166746	−	0.986000i	$-0.446674\pi$
$167$	184.371	−	106.447i	1.10402	−	0.637406i	0.937274	+	0.348594i	$0.113341\pi$
$168$		0			0
$169$	−11.8918	+	20.5973i	−0.0703660	+	0.121877i
$170$		0			0
$171$	78.7274	+	99.2788i	0.460394	+	0.580577i
$172$		0			0
$173$	−120.191	−	69.3924i	−0.694747	−	0.401112i	0.110641	−	0.993860i	$-0.464710\pi$
$173$	−120.191	−	69.3924i	−0.694747	−	0.401112i	−0.805388	+	0.592748i	$0.798043\pi$
$174$		0			0
$175$	−4.10016	+	2.36723i	−0.0234295	+	0.0135270i
$176$		0			0
$177$	20.7826	+	282.526i	0.117416	+	1.59619i
$178$		0			0
$179$	17.9994			0.100556			0.0502778	−	0.998735i	$-0.483989\pi$
$179$	17.9994			0.100556			0.0502778	+	0.998735i	$0.483989\pi$
$180$		0			0
$181$		−	167.214i		−	0.923832i	−0.886924	−	0.461916i	$-0.847162\pi$
$181$		−	167.214i		−	0.923832i	0.886924	−	0.461916i	$-0.152838\pi$
$182$		0			0
$183$	−63.8742	−	93.9630i	−0.349039	−	0.513459i
$184$		0			0
$185$	−105.183	−	182.181i	−0.568554	−	0.984765i
$186$		0			0
$187$	1.01343	−	1.75531i	0.00541940	−	0.00938667i
$188$		0			0
$189$	−15.9899	+	51.0904i	−0.0846028	+	0.270320i
$190$		0			0
$191$	301.084	+	173.831i	1.57636	+	0.910109i	0.995362	+	0.0962015i	$0.0306693\pi$
$191$	301.084	+	173.831i	1.57636	+	0.910109i	0.580994	+	0.813908i	$0.302664\pi$
$192$		0			0
$193$	1.33894	+	2.31911i	0.00693751	+	0.0120161i	0.869473	−	0.493980i	$-0.164458\pi$
$193$	1.33894	+	2.31911i	0.00693751	+	0.0120161i	−0.862536	+	0.505996i	$0.831125\pi$
$194$		0			0
$195$	−156.466	+	106.362i	−0.802388	+	0.545448i
$196$		0			0
$197$			155.022i			0.786911i	0.919344	+	0.393456i	$0.128721\pi$
$197$			155.022i			0.786911i	−0.919344	+	0.393456i	$0.871279\pi$
$198$		0			0
$199$		−	66.2901i		−	0.333116i	−0.986032	−	0.166558i	$-0.946735\pi$
$199$		−	66.2901i		−	0.333116i	0.986032	−	0.166558i	$-0.0532653\pi$
$200$		0			0
$201$	2.84563	+	38.6845i	0.0141573	+	0.192460i
$202$		0			0
$203$	−38.7106	−	67.0487i	−0.190693	−	0.330289i
$204$		0			0
$205$	−311.995	−	180.130i	−1.52193	−	0.878685i
$206$		0			0
$207$	−3.45167	−	1.36562i	−0.0166747	−	0.00659722i
$208$		0			0
$209$	2.59019	−	4.48633i	0.0123932	−	0.0214657i
$210$		0			0
$211$	33.5736	+	58.1511i	0.159116	+	0.275598i	0.934550	−	0.355831i	$-0.115802\pi$
$211$	33.5736	+	58.1511i	0.159116	+	0.275598i	−0.775434	+	0.631429i	$0.782469\pi$
$212$		0			0
$213$	−123.639	+	255.840i	−0.580464	+	1.20113i
$214$		0			0
$215$		−	350.720i		−	1.63125i
$216$		0			0
$217$	61.2039			0.282046
$218$		0			0
$219$	−374.934	−	181.193i	−1.71203	−	0.827364i
$220$		0			0
$221$	57.4848	−	33.1889i	0.260112	−	0.150176i
$222$		0			0
$223$	225.616	+	130.260i	1.01173	+	0.584124i	0.911699	−	0.410860i	$-0.134771\pi$
$223$	225.616	+	130.260i	1.01173	+	0.584124i	0.100034	+	0.994984i	$0.468105\pi$
$224$		0			0
$225$	21.2591	−	3.14465i	0.0944851	−	0.0139762i
$226$		0			0
$227$	−128.921	+	223.297i	−0.567933	+	0.983689i	0.428837	+	0.903382i	$0.358923\pi$
$227$	−128.921	+	223.297i	−0.567933	+	0.983689i	−0.996770	+	0.0803070i	$0.974410\pi$
$228$		0			0
$229$	198.873	−	114.820i	0.868443	−	0.501396i	0.00161217	−	0.999999i	$-0.499487\pi$
$229$	198.873	−	114.820i	0.868443	−	0.501396i	0.866830	+	0.498603i	$0.166153\pi$
$230$		0			0
$231$	2.18285	−	0.160570i	0.00944959	−	0.000695110i
$232$		0			0
$233$	24.7589			0.106261			0.0531307	−	0.998588i	$-0.483080\pi$
$233$	24.7589			0.106261			0.0531307	+	0.998588i	$0.483080\pi$
$234$		0			0
$235$	157.697			0.671051
$236$		0			0
$237$	−183.858	−	270.467i	−0.775773	−	1.14121i
$238$		0			0
$239$	176.640	−	101.983i	0.739079	−	0.426707i	−0.0826557	−	0.996578i	$-0.526340\pi$
$239$	176.640	−	101.983i	0.739079	−	0.426707i	0.821734	+	0.569871i	$0.193007\pi$
$240$		0			0
$241$	46.5967	−	80.7079i	0.193347	−	0.334888i	−0.753010	−	0.658009i	$-0.771399\pi$
$241$	46.5967	−	80.7079i	0.193347	−	0.334888i	0.946358	+	0.323121i	$0.104732\pi$
$242$		0			0
$243$	152.808	−	188.941i	0.628839	−	0.777535i
$244$		0			0
$245$	−204.261	−	117.930i	−0.833717	−	0.481347i
$246$		0			0
$247$	146.923	−	84.8263i	0.594832	−	0.343426i
$248$		0			0
$249$	−143.467	+	97.5264i	−0.576175	+	0.391672i
$250$		0			0
$251$	47.6106			0.189684			0.0948418	−	0.995492i	$-0.469765\pi$
$251$	47.6106			0.189684			0.0948418	+	0.995492i	$0.469765\pi$
$252$		0			0
$253$			0.151766i			0.000599864i
$254$		0			0
$255$	−86.2468	+	6.34430i	−0.338223	+	0.0248796i
$256$		0			0
$257$	−166.540	−	288.456i	−0.648017	−	1.12240i	−0.983596	−	0.180386i	$-0.942265\pi$
$257$	−166.540	−	288.456i	−0.648017	−	1.12240i	0.335579	−	0.942012i	$-0.391068\pi$
$258$		0			0
$259$	−39.8504	+	69.0228i	−0.153862	+	0.266497i
$260$		0			0
$261$	51.4236	+	347.644i	0.197025	+	1.33197i
$262$		0			0
$263$	90.2392	+	52.0997i	0.343115	+	0.198098i	0.661649	−	0.749814i	$-0.269857\pi$
$263$	90.2392	+	52.0997i	0.343115	+	0.198098i	−0.318534	+	0.947912i	$0.603190\pi$
$264$		0			0
$265$	41.7509	+	72.3147i	0.157551	+	0.272886i
$266$		0			0
$267$	266.261	+	128.675i	0.997232	+	0.481929i
$268$		0			0
$269$			308.100i			1.14535i	0.819781	+	0.572677i	$0.194095\pi$
$269$			308.100i			1.14535i	−0.819781	+	0.572677i	$0.805905\pi$
$270$		0			0
$271$			228.400i			0.842805i	0.906874	+	0.421402i	$0.138462\pi$
$271$			228.400i			0.842805i	−0.906874	+	0.421402i	$0.861538\pi$
$272$		0			0
$273$	64.5385	+	31.1893i	0.236405	+	0.114246i
$274$		0			0
$275$	−0.439320	−	0.760925i	−0.00159753	−	0.00276700i
$276$		0			0
$277$	95.3349	+	55.0416i	0.344169	+	0.198706i	0.662114	−	0.749403i	$-0.269659\pi$
$277$	95.3349	+	55.0416i	0.344169	+	0.198706i	−0.317945	+	0.948109i	$0.602993\pi$
$278$		0			0
$279$	−258.330	−	102.206i	−0.925915	−	0.366331i
$280$		0			0
$281$	−26.0128	+	45.0554i	−0.0925721	+	0.160340i	−0.908593	−	0.417683i	$-0.862842\pi$
$281$	−26.0128	+	45.0554i	−0.0925721	+	0.160340i	0.816021	+	0.578023i	$0.196176\pi$
$282$		0			0
$283$	−2.81699	−	4.87918i	−0.00995404	−	0.0172409i	0.861005	−	0.508596i	$-0.169835\pi$
$283$	−2.81699	−	4.87918i	−0.00995404	−	0.0172409i	−0.870960	+	0.491355i	$0.836502\pi$
$284$		0			0
$285$	−220.435	+	16.2152i	−0.773457	+	0.0568954i
$286$		0			0
$287$			136.492i			0.475580i
$288$		0			0
$289$	−258.659			−0.895014
$290$		0			0
$291$	−142.104	+	96.5996i	−0.488331	+	0.331958i
$292$		0			0
$293$	178.265	−	102.921i	0.608414	−	0.351268i	−0.163931	−	0.986472i	$-0.552417\pi$
$293$	178.265	−	102.921i	0.608414	−	0.351268i	0.772344	+	0.635204i	$0.219084\pi$
$294$		0			0
$295$	−427.975	−	247.092i	−1.45076	−	0.837598i
$296$		0			0
$297$	−9.48157	−	2.96748i	−0.0319245	−	0.00999150i
$298$		0			0
$299$	−2.48510	+	4.30431i	−0.00831136	+	0.0143957i
$300$		0			0
$301$	−115.075	+	66.4383i	−0.382307	+	0.220725i
$302$		0			0
$303$	274.002	+	403.075i	0.904298	+	1.33028i
$304$		0			0
$305$	198.200			0.649835
$306$		0			0
$307$	219.958			0.716475			0.358238	−	0.933630i	$-0.383378\pi$
$307$	219.958			0.716475			0.358238	+	0.933630i	$0.383378\pi$
$308$		0			0
$309$	373.659	−	27.4863i	1.20925	−	0.0889523i
$310$		0			0
$311$	−515.154	+	297.425i	−1.65645	+	0.956349i	−0.682109	+	0.731251i	$0.738937\pi$
$311$	−515.154	+	297.425i	−1.65645	+	0.956349i	−0.974336	+	0.225098i	$0.927730\pi$
$312$		0			0
$313$	122.865	−	212.809i	0.392541	−	0.679901i	−0.600243	−	0.799818i	$-0.704929\pi$
$313$	122.865	−	212.809i	0.392541	−	0.679901i	0.992784	+	0.119917i	$0.0382628\pi$
$314$		0			0
$315$	−58.0255	−	73.1728i	−0.184208	−	0.232295i
$316$		0			0
$317$	130.984	+	75.6236i	0.413198	+	0.238560i	0.692163	−	0.721741i	$-0.256658\pi$
$317$	130.984	+	75.6236i	0.413198	+	0.238560i	−0.278965	+	0.960301i	$0.589991\pi$
$318$		0			0
$319$	12.4432	−	7.18407i	0.0390068	−	0.0225206i
$320$		0			0
$321$	−119.059	−	57.5374i	−0.370901	−	0.179244i
$322$		0			0
$323$	77.5474			0.240085
$324$		0			0
$325$		−	28.7747i		−	0.0885376i
$326$		0			0
$327$	−53.4824	+	110.669i	−0.163555	+	0.338436i
$328$		0			0
$329$	−29.8732	−	51.7419i	−0.0908000	−	0.157270i
$330$		0			0
$331$	121.703	−	210.795i	0.367681	−	0.636843i	−0.621521	−	0.783397i	$-0.713485\pi$
$331$	121.703	−	210.795i	0.367681	−	0.636843i	0.989203	+	0.146555i	$0.0468184\pi$
$332$		0			0
$333$	283.464	−	224.785i	0.851244	−	0.675031i
$334$		0			0
$335$	−58.5999	−	33.8327i	−0.174925	−	0.100993i
$336$		0			0
$337$	200.050	+	346.496i	0.593620	+	1.02818i	0.993740	+	0.111717i	$0.0356349\pi$
$337$	200.050	+	346.496i	0.593620	+	1.02818i	−0.400121	+	0.916463i	$0.631032\pi$
$338$		0			0
$339$	15.6442	+	212.674i	0.0461482	+	0.627356i
$340$		0			0
$341$			11.3585i			0.0333093i
$342$		0			0
$343$			186.514i			0.543774i
$344$		0			0
$345$	5.35521	−	3.64037i	0.0155224	−	0.0105518i
$346$		0			0
$347$	−191.287	−	331.318i	−0.551259	−	0.954808i	−0.998184	−	0.0602368i	$-0.980814\pi$
$347$	−191.287	−	331.318i	−0.551259	−	0.954808i	0.446925	−	0.894571i	$-0.352519\pi$
$348$		0			0
$349$	69.4135	+	40.0759i	0.198892	+	0.114831i	0.596139	−	0.802881i	$-0.296701\pi$
$349$	69.4135	+	40.0759i	0.198892	+	0.114831i	−0.397246	+	0.917712i	$0.630034\pi$
$350$		0			0
$351$	−220.321	−	239.419i	−0.627695	−	0.682105i
$352$		0			0
$353$	−157.270	+	272.400i	−0.445525	+	0.771672i	−0.998089	−	0.0617986i	$-0.980316\pi$
$353$	−157.270	+	272.400i	−0.445525	+	0.771672i	0.552563	+	0.833471i	$0.313650\pi$
$354$		0			0
$355$	−247.841	−	429.274i	−0.698145	−	1.20922i
$356$		0			0
$357$	18.4197	+	27.0966i	0.0515959	+	0.0759008i
$358$		0			0
$359$		−	319.419i		−	0.889746i	−0.895594	−	0.444873i	$-0.853249\pi$
$359$		−	319.419i		−	0.889746i	0.895594	−	0.444873i	$-0.146751\pi$
$360$		0			0
$361$	−162.799			−0.450967
$362$		0			0
$363$	−26.6005	−	361.617i	−0.0732795	−	0.996189i
$364$		0			0
$365$	629.101	−	363.211i	1.72356	−	0.995100i
$366$		0			0
$367$	−226.375	−	130.698i	−0.616826	−	0.356125i	0.158806	−	0.987310i	$-0.449235\pi$
$367$	−226.375	−	130.698i	−0.616826	−	0.356125i	−0.775632	+	0.631185i	$0.782569\pi$
$368$		0			0
$369$	227.931	−	576.105i	0.617700	−	1.56126i
$370$		0			0
$371$	15.8181	−	27.3977i	0.0426364	−	0.0738484i
$372$		0			0
$373$	548.881	−	316.897i	1.47153	−	0.849589i	0.472042	−	0.881576i	$-0.343517\pi$
$373$	548.881	−	316.897i	1.47153	−	0.849589i	0.999488	+	0.0319873i	$0.0101836\pi$
$374$		0			0
$375$	154.472	−	319.643i	0.411927	−	0.852380i
$376$		0			0
$377$	470.544			1.24813
$378$		0			0
$379$	−614.762			−1.62206			−0.811032	−	0.585002i	$-0.801094\pi$
$379$	−614.762			−1.62206			−0.811032	+	0.585002i	$0.801094\pi$
$380$		0			0
$381$	312.695	−	647.045i	0.820722	−	1.69828i
$382$		0			0
$383$	−464.077	+	267.935i	−1.21169	+	0.699570i	−0.963127	−	0.269046i	$-0.913292\pi$
$383$	−464.077	+	267.935i	−1.21169	+	0.699570i	−0.248563	+	0.968616i	$0.579958\pi$
$384$		0			0
$385$	−1.90908	+	3.30662i	−0.00495865	+	0.00858863i
$386$		0			0
$387$	596.656	−	88.2574i	1.54175	−	0.228055i
$388$		0			0
$389$	−494.706	−	285.619i	−1.27174	−	0.734239i	−0.296423	−	0.955057i	$-0.595794\pi$
$389$	−494.706	−	285.619i	−1.27174	−	0.734239i	−0.975315	+	0.220818i	$0.929127\pi$
$390$		0			0
$391$	−1.96748	+	1.13593i	−0.00503192	+	0.00290518i
$392$		0			0
$393$	26.1699	+	355.763i	0.0665900	+	0.905249i
$394$		0			0
$395$	570.507			1.44432
$396$		0			0
$397$			669.819i			1.68720i	0.536971	+	0.843600i	$0.319568\pi$
$397$			669.819i			1.68720i	−0.536971	+	0.843600i	$0.680432\pi$
$398$		0			0
$399$	47.0783	+	69.2552i	0.117991	+	0.173572i
$400$		0			0
$401$	238.753	+	413.532i	0.595394	+	1.03125i	0.993491	+	0.113909i	$0.0363372\pi$
$401$	238.753	+	413.532i	0.595394	+	1.03125i	−0.398098	+	0.917343i	$0.630329\pi$
$402$		0			0
$403$	−185.990	+	322.144i	−0.461514	+	0.799365i
$404$		0			0
$405$	122.722	+	405.747i	0.303016	+	1.00185i
$406$		0			0
$407$	−12.8095	−	7.39559i	−0.0314731	−	0.0181710i
$408$		0			0
$409$	−219.267	−	379.782i	−0.536106	−	0.928563i	−0.999109	−	0.0422060i	$-0.986561\pi$
$409$	−219.267	−	379.782i	−0.536106	−	0.928563i	0.463003	−	0.886357i	$-0.346772\pi$
$410$		0			0
$411$	178.222	−	121.151i	0.433629	−	0.294772i
$412$		0			0
$413$			187.230i			0.453342i
$414$		0			0
$415$		−	302.621i		−	0.729208i
$416$		0			0
$417$	−35.9599	−	488.853i	−0.0862349	−	1.17231i
$418$		0			0
$419$	−315.577	−	546.596i	−0.753168	−	1.30453i	−0.946280	−	0.323348i	$-0.895191\pi$
$419$	−315.577	−	546.596i	−0.753168	−	1.30453i	0.193112	−	0.981177i	$-0.438142\pi$
$420$		0			0
$421$	414.883	+	239.533i	0.985471	+	0.568962i	0.903917	−	0.427707i	$-0.140679\pi$
$421$	414.883	+	239.533i	0.985471	+	0.568962i	0.0815534	+	0.996669i	$0.474012\pi$
$422$		0			0
$423$	39.6839	+	268.279i	0.0938153	+	0.634230i
$424$		0			0
$425$	6.57640	−	11.3907i	0.0154739	−	0.0268015i
$426$		0			0
$427$	−37.5458	−	65.0313i	−0.0879293	−	0.152298i
$428$		0			0
$429$	−5.78823	+	11.9773i	−0.0134924	+	0.0279191i
$430$		0			0
$431$			27.0391i			0.0627357i	0.999508	+	0.0313679i	$0.00998634\pi$
$431$			27.0391i			0.0627357i	−0.999508	+	0.0313679i	$0.990014\pi$
$432$		0			0
$433$	2.38838			0.00551589			0.00275795	−	0.999996i	$-0.499122\pi$
$433$	2.38838			0.00551589			0.00275795	+	0.999996i	$0.499122\pi$
$434$		0			0
$435$	−551.969	−	266.748i	−1.26889	−	0.613214i
$436$		0			0
$437$	−5.02862	+	2.90328i	−0.0115071	+	0.00664365i
$438$		0			0
$439$	25.7809	+	14.8846i	0.0587263	+	0.0339057i	0.529076	−	0.848575i	$-0.322539\pi$
$439$	25.7809	+	14.8846i	0.0587263	+	0.0339057i	−0.470349	+	0.882480i	$0.655872\pi$
$440$		0			0
$441$	149.225	−	377.171i	0.338378	−	0.855264i
$442$		0			0
$443$	−36.9071	+	63.9249i	−0.0833117	+	0.144300i	−0.904671	−	0.426112i	$-0.859883\pi$
$443$	−36.9071	+	63.9249i	−0.0833117	+	0.144300i	0.821359	+	0.570412i	$0.193216\pi$
$444$		0			0
$445$	−446.759	+	257.937i	−1.00395	+	0.579633i
$446$		0			0
$447$	414.171	−	30.4664i	0.926557	−	0.0681574i
$448$		0			0
$449$	−581.210			−1.29445			−0.647227	−	0.762297i	$-0.724072\pi$
$449$	−581.210			−1.29445			−0.647227	+	0.762297i	$0.724072\pi$
$450$		0			0
$451$	−25.3307			−0.0561655
$452$		0			0
$453$	−160.575	−	236.217i	−0.354471	−	0.521450i
$454$		0			0
$455$	−108.289	+	62.5207i	−0.237998	+	0.137408i
$456$		0			0
$457$	42.5537	−	73.7051i	0.0931153	−	0.161280i	−0.815705	−	0.578468i	$-0.803651\pi$
$457$	42.5537	−	73.7051i	0.0931153	−	0.161280i	0.908820	+	0.417187i	$0.136984\pi$
$458$		0			0
$459$	−32.4968	−	145.129i	−0.0707992	−	0.316186i
$460$		0			0
$461$	381.095	+	220.025i	0.826670	+	0.477278i	0.852711	−	0.522382i	$-0.174957\pi$
$461$	381.095	+	220.025i	0.826670	+	0.477278i	−0.0260409	+	0.999661i	$0.508290\pi$
$462$		0			0
$463$	41.0587	−	23.7053i	0.0886798	−	0.0511993i	−0.455004	−	0.890489i	$-0.650362\pi$
$463$	41.0587	−	23.7053i	0.0886798	−	0.0511993i	0.543684	+	0.839290i	$0.317029\pi$
$464$		0			0
$465$	400.796	−	272.453i	0.861927	−	0.585921i
$466$		0			0
$467$	755.784			1.61838			0.809191	−	0.587546i	$-0.199906\pi$
$467$	755.784			1.61838			0.809191	+	0.587546i	$0.199906\pi$
$468$		0			0
$469$			25.6363i			0.0546616i
$470$		0			0
$471$	497.757	−	36.6150i	1.05681	−	0.0777388i
$472$		0			0
$473$	−12.3299	−	21.3560i	−0.0260674	−	0.0451501i
$474$		0			0
$475$	16.8084	−	29.1130i	0.0353861	−	0.0612905i
$476$		0			0
$477$	−112.518	+	89.2257i	−0.235886	+	0.187056i
$478$		0			0
$479$	−498.203	−	287.638i	−1.04009	−	0.600497i	−0.120232	−	0.992746i	$-0.538364\pi$
$479$	−498.203	−	287.638i	−1.04009	−	0.600497i	−0.919859	+	0.392249i	$0.871697\pi$
$480$		0			0
$481$	−242.199	−	419.501i	−0.503532	−	0.872144i
$482$		0			0
$483$	−2.20890	−	1.06749i	−0.00457329	−	0.00221012i
$484$		0			0
$485$		−	299.746i		−	0.618033i
$486$		0			0
$487$		−	356.028i		−	0.731064i	−0.930799	−	0.365532i	$-0.880887\pi$
$487$		−	356.028i		−	0.731064i	0.930799	−	0.365532i	$-0.119113\pi$
$488$		0			0
$489$	−371.224	−	179.400i	−0.759150	−	0.366872i
$490$		0			0
$491$	−31.2238	−	54.0813i	−0.0635923	−	0.110145i	0.832476	−	0.554061i	$-0.186922\pi$
$491$	−31.2238	−	54.0813i	−0.0635923	−	0.110145i	−0.896069	+	0.443915i	$0.853589\pi$
$492$		0			0
$493$	186.268	+	107.542i	0.377825	+	0.218137i
$494$		0			0
$495$	13.5797	−	10.7686i	0.0274337	−	0.0217548i
$496$		0			0
$497$	−93.8993	+	162.638i	−0.188932	+	0.327240i
$498$		0			0
$499$	−221.129	−	383.007i	−0.443144	−	0.767548i	0.554777	−	0.831999i	$-0.312804\pi$
$499$	−221.129	−	383.007i	−0.443144	−	0.767548i	−0.997921	+	0.0644510i	$0.979470\pi$
$500$		0			0
$501$	−636.960	+	46.8547i	−1.27138	+	0.0935223i
$502$		0			0
$503$			643.704i			1.27973i	0.768487	+	0.639865i	$0.221010\pi$
$503$			643.704i			1.27973i	−0.768487	+	0.639865i	$0.778990\pi$
$504$		0			0
$505$	−850.221			−1.68361
$506$		0			0
$507$	59.0081	−	40.1126i	0.116387	−	0.0791175i
$508$		0			0
$509$	821.978	−	474.569i	1.61489	−	0.932356i	0.626673	−	0.779282i	$-0.284416\pi$
$509$	821.978	−	474.569i	1.61489	−	0.932356i	0.988215	−	0.153073i	$-0.0489171\pi$
$510$		0			0
$511$	−238.346	−	137.609i	−0.466431	−	0.269294i
$512$		0			0
$513$	−83.0576	−	370.931i	−0.161906	−	0.723063i
$514$		0			0
$515$	−326.794	+	566.024i	−0.634552	+	1.09908i
$516$		0			0
$517$	9.60247	−	5.54399i	0.0185734	−	0.0107234i
$518$		0			0
$519$	234.069	+	344.330i	0.450999	+	0.663448i
$520$		0			0
$521$	822.920			1.57950			0.789751	−	0.613428i	$-0.210210\pi$
$521$	822.920			1.57950			0.789751	+	0.613428i	$0.210210\pi$
$522$		0			0
$523$	−211.875			−0.405115			−0.202558	−	0.979270i	$-0.564925\pi$
$523$	−211.875			−0.405115			−0.202558	+	0.979270i	$0.564925\pi$
$524$		0			0
$525$	14.1651	−	1.04198i	0.0269812	−	0.00198473i
$526$		0			0
$527$	−147.251	+	85.0152i	−0.279413	+	0.161319i
$528$		0			0
$529$	−264.415	+	457.980i	−0.499839	+	0.865747i
$530$		0			0
$531$	312.662	−	790.265i	0.588817	−	1.48826i
$532$		0			0
$533$	−718.417	−	414.778i	−1.34787	−	0.778196i
$534$		0			0
$535$	199.770	−	115.337i	0.373401	−	0.215583i
$536$		0			0
$537$	−48.6186	−	23.4957i	−0.0905375	−	0.0437537i
$538$		0			0
$539$	−16.5838			−0.0307677
$540$		0			0
$541$			385.378i			0.712343i	0.934421	+	0.356172i	$0.115918\pi$
$541$			385.378i			0.712343i	−0.934421	+	0.356172i	$0.884082\pi$
$542$		0			0
$543$	−218.274	+	451.664i	−0.401977	+	0.831793i
$544$		0			0
$545$	−107.209	−	185.691i	−0.196713	−	0.340717i
$546$		0			0
$547$	15.1023	−	26.1580i	0.0276094	−	0.0478209i	−0.851891	−	0.523720i	$-0.824544\pi$
$547$	15.1023	−	26.1580i	0.0276094	−	0.0478209i	0.879500	+	0.475899i	$0.157877\pi$
$548$		0			0
$549$	49.8763	+	337.184i	0.0908493	+	0.614178i
$550$		0			0
$551$	476.076	+	274.862i	0.864021	+	0.498843i
$552$		0			0
$553$	−108.074	−	187.189i	−0.195431	−	0.338497i
$554$		0			0
$555$	46.2982	+	629.395i	0.0834201	+	1.13404i
$556$		0			0
$557$			940.743i			1.68895i	0.535598	+	0.844473i	$0.320086\pi$
$557$			940.743i			1.68895i	−0.535598	+	0.844473i	$0.679914\pi$
$558$		0			0
$559$		−	807.586i		−	1.44470i
$560$		0			0
$561$	−5.02869	+	3.41841i	−0.00896380	+	0.00609342i
$562$		0			0
$563$	27.9801	+	48.4629i	0.0496982	+	0.0860797i	0.889804	−	0.456342i	$-0.150841\pi$
$563$	27.9801	+	48.4629i	0.0496982	+	0.0860797i	−0.840106	+	0.542422i	$0.817507\pi$
$564$		0			0
$565$	−322.162	−	186.000i	−0.570198	−	0.329204i
$566$		0			0
$567$	109.882	−	117.129i	0.193795	−	0.206576i
$568$		0			0
$569$	−282.872	+	489.949i	−0.497139	+	0.861069i	−0.999995	−	0.00330083i	$-0.998949\pi$
$569$	−282.872	+	489.949i	−0.497139	+	0.861069i	0.502856	+	0.864370i	$0.332283\pi$
$570$		0			0
$571$	348.221	+	603.137i	0.609845	+	1.05628i	0.991266	+	0.131880i	$0.0421015\pi$
$571$	348.221	+	603.137i	0.609845	+	1.05628i	−0.381421	+	0.924401i	$0.624565\pi$
$572$		0			0
$573$	−586.352	−	862.560i	−1.02330	−	1.50534i
$574$		0			0
$575$			0.984847i			0.00171278i
$576$		0			0
$577$	−256.336			−0.444256			−0.222128	−	0.975018i	$-0.571300\pi$
$577$	−256.336			−0.444256			−0.222128	+	0.975018i	$0.571300\pi$
$578$		0			0
$579$	−0.589361	−	8.01199i	−0.00101789	−	0.0138376i
$580$		0			0
$581$	−99.2931	+	57.3269i	−0.170900	+	0.0986693i
$582$		0			0
$583$	5.08459	+	2.93559i	0.00872142	+	0.00503531i
$584$		0			0
$585$	561.473	−	83.0532i	0.959783	−	0.141971i
$586$		0			0
$587$	−476.928	+	826.064i	−0.812484	+	1.40726i	0.0986361	+	0.995124i	$0.468552\pi$
$587$	−476.928	+	826.064i	−0.812484	+	1.40726i	−0.911120	+	0.412140i	$0.864781\pi$
$588$		0			0
$589$	−376.353	+	217.287i	−0.638969	+	0.368909i
$590$		0			0
$591$	202.359	−	418.731i	0.342401	−	0.708513i
$592$		0			0
$593$	1028.79			1.73489			0.867443	−	0.497536i	$-0.165762\pi$
$593$	1028.79			1.73489			0.867443	+	0.497536i	$0.165762\pi$
$594$		0			0
$595$	−57.1559			−0.0960603
$596$		0			0
$597$	−86.5324	+	179.057i	−0.144945	+	0.299929i
$598$		0			0
$599$	−953.699	+	550.618i	−1.59215	+	0.919229i	−0.599214	+	0.800589i	$0.704520\pi$
$599$	−953.699	+	550.618i	−1.59215	+	0.919229i	−0.992937	+	0.118640i	$0.962146\pi$
$600$		0			0
$601$	−342.934	+	593.980i	−0.570606	+	0.988319i	0.425898	+	0.904771i	$0.359958\pi$
$601$	−342.934	+	593.980i	−0.570606	+	0.988319i	−0.996504	+	0.0835474i	$0.973375\pi$
$602$		0			0
$603$	42.8108	−	108.206i	0.0709963	−	0.179446i
$604$		0			0
$605$	547.783	+	316.263i	0.905426	+	0.522748i
$606$		0			0
$607$	370.226	−	213.750i	0.609927	−	0.352142i	−0.163010	−	0.986624i	$-0.552120\pi$
$607$	370.226	−	213.750i	0.609927	−	0.352142i	0.772937	+	0.634483i	$0.218787\pi$
$608$		0			0
$609$	17.0392	+	231.638i	0.0279790	+	0.380357i
$610$		0			0
$611$	363.122			0.594307
$612$		0			0
$613$		−	851.523i		−	1.38911i	−0.719440	−	0.694554i	$-0.755602\pi$
$613$		−	851.523i		−	1.38911i	0.719440	−	0.694554i	$-0.244398\pi$
$614$		0			0
$615$	607.601	+	893.819i	0.987969	+	1.45336i
$616$		0			0
$617$	585.852	+	1014.73i	0.949517	+	1.64461i	0.746444	+	0.665448i	$0.231760\pi$
$617$	585.852	+	1014.73i	0.949517	+	1.64461i	0.203073	+	0.979164i	$0.434907\pi$
$618$		0			0
$619$	−5.72669	+	9.91891i	−0.00925151	+	0.0160241i	−0.870614	−	0.491967i	$-0.836278\pi$
$619$	−5.72669	+	9.91891i	−0.00925151	+	0.0160241i	0.861363	+	0.507991i	$0.169612\pi$
$620$		0			0
$621$	7.54073	+	8.19438i	0.0121429	+	0.0131955i
$622$		0			0
$623$	169.263	+	97.7240i	0.271690	+	0.156860i
$624$		0			0
$625$	339.497	+	588.026i	0.543195	+	0.940842i
$626$		0			0
$627$	−12.8527	+	8.73699i	−0.0204987	+	0.0139346i
$628$		0			0
$629$		−	221.416i		−	0.352013i
$630$		0			0
$631$		−	449.462i		−	0.712301i	−0.934429	−	0.356151i	$-0.884089\pi$
$631$		−	449.462i		−	0.712301i	0.934429	−	0.356151i	$-0.115911\pi$
$632$		0			0
$633$	−14.7781	−	200.899i	−0.0233461	−	0.317375i
$634$		0			0
$635$	626.816	+	1085.68i	0.987111	+	1.70973i
$636$		0			0
$637$	−470.342	−	271.552i	−0.738370	−	0.426298i
$638$		0			0
$639$	667.927	−	529.661i	1.04527	−	0.828891i
$640$		0			0
$641$	−105.068	+	181.983i	−0.163913	+	0.283905i	−0.936269	−	0.351285i	$-0.885745\pi$
$641$	−105.068	+	181.983i	−0.163913	+	0.283905i	0.772356	+	0.635190i	$0.219078\pi$
$642$		0			0
$643$	121.492	+	210.430i	0.188945	+	0.327263i	0.944899	−	0.327362i	$-0.106160\pi$
$643$	121.492	+	210.430i	0.188945	+	0.327263i	−0.755954	+	0.654625i	$0.772826\pi$
$644$		0			0
$645$	−457.815	+	947.335i	−0.709791	+	1.46874i
$646$		0			0
$647$		−	636.733i		−	0.984131i	−0.870558	−	0.492065i	$-0.836242\pi$
$647$		−	636.733i		−	0.984131i	0.870558	−	0.492065i	$-0.163758\pi$
$648$		0			0
$649$	−34.7470			−0.0535393
$650$		0			0
$651$	−165.319	−	79.8931i	−0.253946	−	0.122724i
$652$		0			0
$653$	515.185	−	297.442i	0.788951	−	0.455501i	−0.0506424	−	0.998717i	$-0.516127\pi$
$653$	515.185	−	297.442i	0.788951	−	0.455501i	0.839593	+	0.543216i	$0.182794\pi$
$654$		0			0
$655$	−538.915	−	311.143i	−0.822771	−	0.475027i
$656$		0			0
$657$	776.218	+	978.846i	1.18146	+	1.48987i
$658$		0			0
$659$	−380.457	+	658.972i	−0.577325	+	0.999957i	0.418459	+	0.908236i	$0.362570\pi$
$659$	−380.457	+	658.972i	−0.577325	+	0.999957i	−0.995785	+	0.0917213i	$0.970763\pi$
$660$		0			0
$661$	327.531	−	189.100i	0.495508	−	0.286082i	−0.231349	−	0.972871i	$-0.574314\pi$
$661$	327.531	−	189.100i	0.495508	−	0.286082i	0.726857	+	0.686789i	$0.240980\pi$
$662$		0			0
$663$	−198.597	+	14.6087i	−0.299542	+	0.0220343i
$664$		0			0
$665$	−146.083			−0.219673
$666$		0			0
$667$	−16.1049			−0.0241453
$668$		0			0
$669$	−439.381	−	646.357i	−0.656773	−	0.966154i
$670$		0			0
$671$	12.0688	−	6.96790i	0.0179862	−	0.0103844i
$672$		0			0
$673$	−311.989	+	540.381i	−0.463579	+	0.802943i	−0.999136	−	0.0415563i	$-0.986768\pi$
$673$	−311.989	+	540.381i	−0.463579	+	0.802943i	0.535557	+	0.844499i	$0.320102\pi$
$674$		0			0
$675$	−61.5284	−	19.2567i	−0.0911531	−	0.0285285i
$676$		0			0
$677$	−567.922	−	327.890i	−0.838881	−	0.484328i	0.0180028	−	0.999838i	$-0.494269\pi$
$677$	−567.922	−	327.890i	−0.838881	−	0.484328i	−0.856884	+	0.515510i	$0.827603\pi$
$678$		0			0
$679$	−98.3496	+	56.7821i	−0.144845	+	0.0836261i
$680$		0			0
$681$	639.713	−	434.865i	0.939374	−	0.638568i
$682$		0			0
$683$	−291.543			−0.426856			−0.213428	−	0.976959i	$-0.568463\pi$
$683$	−291.543			−0.426856			−0.213428	+	0.976959i	$0.568463\pi$
$684$		0			0
$685$			375.930i			0.548802i
$686$		0			0
$687$	−687.061	+	50.5401i	−1.00009	+	0.0735664i
$688$		0			0
$689$	96.1379	+	166.516i	0.139533	+	0.241677i
$690$		0			0
$691$	−422.090	+	731.082i	−0.610840	+	1.05801i	0.380259	+	0.924880i	$0.375835\pi$
$691$	−422.090	+	731.082i	−0.610840	+	1.05801i	−0.991099	+	0.133126i	$0.957499\pi$
$692$		0			0
$693$	−6.10575	−	2.41569i	−0.00881060	−	0.00348584i
$694$		0			0
$695$	740.522	+	427.541i	1.06550	+	0.615166i
$696$		0			0
$697$	−189.593	−	328.385i	−0.272013	−	0.471141i
$698$		0			0
$699$	−66.8767	−	32.3192i	−0.0956748	−	0.0462364i
$700$		0			0
$701$		−	399.101i		−	0.569332i	−0.958627	−	0.284666i	$-0.908117\pi$
$701$		−	399.101i		−	0.569332i	0.958627	−	0.284666i	$-0.0918826\pi$
$702$		0			0
$703$		−	565.910i		−	0.804993i
$704$		0			0
$705$	−425.958	−	205.851i	−0.604196	−	0.291987i
$706$		0			0
$707$	161.061	+	278.966i	0.227809	+	0.394577i
$708$		0			0
$709$	708.680	+	409.157i	0.999549	+	0.577090i	0.908115	−	0.418721i	$-0.137521\pi$
$709$	708.680	+	409.157i	0.999549	+	0.577090i	0.0914344	+	0.995811i	$0.470855\pi$
$710$		0			0
$711$	143.566	+	970.565i	0.201921	+	1.36507i
$712$		0			0
$713$	6.36572	−	11.0257i	0.00892808	−	0.0154639i
$714$		0			0
$715$	−11.6028	−	20.0967i	−0.0162278	−	0.0281073i
$716$		0			0
$717$	−610.249	+	44.8898i	−0.851115	+	0.0626079i
$718$		0			0
$719$			233.988i			0.325435i	0.986673	+	0.162718i	$0.0520259\pi$
$719$			233.988i			0.325435i	−0.986673	+	0.162718i	$0.947974\pi$
$720$		0			0
$721$	247.624			0.343445
$722$		0			0
$723$	−231.216	+	157.176i	−0.319801	+	0.217394i
$724$		0			0
$725$	80.7470	−	46.6193i	0.111375	−	0.0643025i
$726$		0			0
$727$	1184.66	+	683.963i	1.62952	+	0.940802i	0.984237	+	0.176857i	$0.0565931\pi$
$727$	1184.66	+	683.963i	1.62952	+	0.940802i	0.645281	+	0.763945i	$0.276740\pi$
$728$		0			0
$729$	−659.388	+	310.883i	−0.904511	+	0.426451i
$730$		0			0
$731$	184.572	−	319.688i	0.252493	−	0.437330i
$732$		0			0
$733$	−1035.52	+	597.860i	−1.41272	+	0.815635i	−0.995644	−	0.0932365i	$-0.970279\pi$
$733$	−1035.52	+	597.860i	−1.41272	+	0.815635i	−0.417077	+	0.908871i	$0.636945\pi$
$734$		0			0
$735$	397.791	+	585.176i	0.541212	+	0.796158i
$736$		0			0
$737$	−4.75768			−0.00645547
$738$		0			0
$739$	−79.0367			−0.106951			−0.0534754	−	0.998569i	$-0.517030\pi$
$739$	−79.0367			−0.106951			−0.0534754	+	0.998569i	$0.517030\pi$
$740$		0			0
$741$	−507.586	+	37.3380i	−0.685002	+	0.0503886i
$742$		0			0
$743$	−648.677	+	374.514i	−0.873051	+	0.504056i	−0.868361	−	0.495933i	$-0.834826\pi$
$743$	−648.677	+	374.514i	−0.873051	+	0.504056i	−0.00469039	+	0.999989i	$0.501493\pi$
$744$		0			0
$745$	−362.226	+	627.393i	−0.486209	+	0.842138i
$746$		0			0
$747$	514.830	−	76.1536i	0.689196	−	0.101946i
$748$		0			0
$749$	−75.6864	−	43.6976i	−0.101050	−	0.0583412i
$750$		0			0
$751$	−387.688	+	223.832i	−0.516230	+	0.298045i	−0.735391	−	0.677643i	$-0.763001\pi$
$751$	−387.688	+	223.832i	−0.516230	+	0.298045i	0.219161	+	0.975689i	$0.429668\pi$
$752$		0			0
$753$	−128.602	−	62.1489i	−0.170786	−	0.0825351i
$754$		0			0
$755$	498.261			0.659948
$756$		0			0
$757$			148.852i			0.196634i	0.995155	+	0.0983169i	$0.0313459\pi$
$757$			148.852i			0.196634i	−0.995155	+	0.0983169i	$0.968654\pi$
$758$		0			0
$759$	0.198109	−	0.409937i	0.000261013	−	0.000540101i
$760$		0			0
$761$	−216.335	−	374.704i	−0.284278	−	0.492384i	0.688156	−	0.725563i	$-0.258420\pi$
$761$	−216.335	−	374.704i	−0.284278	−	0.492384i	−0.972434	+	0.233179i	$0.925087\pi$
$762$		0			0
$763$	−40.6180	+	70.3524i	−0.0532346	+	0.0922050i
$764$		0			0
$765$	241.244	+	95.4463i	0.315352	+	0.124766i
$766$		0			0
$767$	−985.479	−	568.967i	−1.28485	−	0.741808i
$768$		0			0
$769$	−634.073	−	1098.25i	−0.824543	−	1.42815i	−0.902268	−	0.431175i	$-0.858099\pi$
$769$	−634.073	−	1098.25i	−0.824543	−	1.42815i	0.0777254	−	0.996975i	$-0.475234\pi$
$770$		0			0
$771$	73.3061	+	996.550i	0.0950792	+	1.29254i
$772$		0			0
$773$			446.238i			0.577281i	0.957438	+	0.288640i	$0.0932032\pi$
$773$			446.238i			0.577281i	−0.957438	+	0.288640i	$0.906797\pi$
$774$		0			0
$775$			73.7081i			0.0951072i
$776$		0			0
$777$	197.740	−	134.420i	0.254492	−	0.172998i
$778$		0			0
$779$	−484.575	−	839.309i	−0.622048	−	1.07742i
$780$		0			0
$781$	−30.1831	−	17.4262i	−0.0386467	−	0.0223127i
$782$		0			0
$783$	314.899	−	1006.15i	0.402170	−	1.28500i
$784$		0			0
$785$	−435.329	+	754.011i	−0.554559	+	0.960524i
$786$		0			0
$787$	620.167	+	1074.16i	0.788013	+	1.36488i	0.927182	+	0.374611i	$0.122224\pi$
$787$	620.167	+	1074.16i	0.788013	+	1.36488i	−0.139169	+	0.990269i	$0.544443\pi$
$788$		0			0
$789$	−175.738	−	258.522i	−0.222735	−	0.327658i
$790$		0			0
$791$			140.939i			0.178178i
$792$		0			0
$793$	456.386			0.575518
$794$		0			0
$795$	−18.3775	−	249.830i	−0.0231163	−	0.314252i
$796$		0			0
$797$	−766.722	+	442.667i	−0.962011	+	0.555417i	−0.896791	−	0.442454i	$-0.854108\pi$
$797$	−766.722	+	442.667i	−0.962011	+	0.555417i	−0.0652193	+	0.997871i	$0.520775\pi$
$798$		0			0
$799$	143.744	+	82.9906i	0.179905	+	0.103868i
$800$		0			0
$801$	−551.235	−	695.132i	−0.688184	−	0.867831i
$802$		0			0
$803$	25.5381	−	44.2333i	0.0318034	−	0.0550851i
$804$		0			0
$805$	3.70631	−	2.13984i	0.00460412	−	0.00265819i
$806$		0			0
$807$	402.181	−	832.215i	0.498366	−	1.03124i
$808$		0			0
$809$	−286.883			−0.354614			−0.177307	−	0.984156i	$-0.556739\pi$
$809$	−286.883			−0.354614			−0.177307	+	0.984156i	$0.556739\pi$
$810$		0			0
$811$	−616.502			−0.760175			−0.380088	−	0.924950i	$-0.624106\pi$
$811$	−616.502			−0.760175			−0.380088	+	0.924950i	$0.624106\pi$
$812$		0			0
$813$	298.144	−	616.936i	0.366721	−	0.758838i
$814$		0			0
$815$	622.877	−	359.618i	0.764266	−	0.441249i
$816$		0			0
$817$	471.742	−	817.080i	0.577407	−	1.00010i
$818$		0			0
$819$	−133.613	−	168.492i	−0.163141	−	0.205729i
$820$		0			0
$821$	−869.949	−	502.265i	−1.05962	−	0.611772i	−0.134293	−	0.990942i	$-0.542876\pi$
$821$	−869.949	−	502.265i	−1.05962	−	0.611772i	−0.925327	+	0.379169i	$0.876210\pi$
$822$		0			0
$823$	−137.084	+	79.1453i	−0.166566	+	0.0961669i	−0.580966	−	0.813928i	$-0.697325\pi$
$823$	−137.084	+	79.1453i	−0.166566	+	0.0961669i	0.414400	+	0.910095i	$0.363992\pi$
$824$		0			0
$825$	0.193376	+	2.62882i	0.000234395	+	0.00318645i
$826$		0			0
$827$	888.994			1.07496			0.537481	−	0.843276i	$-0.319376\pi$
$827$	888.994			1.07496			0.537481	+	0.843276i	$0.319376\pi$
$828$		0			0
$829$			18.5040i			0.0223209i	0.999938	+	0.0111604i	$0.00355255\pi$
$829$			18.5040i			0.0223209i	−0.999938	+	0.0111604i	$0.996447\pi$
$830$		0			0
$831$	−185.662	−	273.120i	−0.223420	−	0.328664i
$832$		0			0
$833$	−124.125	−	214.991i	−0.149010	−	0.258093i
$834$		0			0
$835$	557.072	−	964.877i	0.667152	−	1.15554i
$836$		0			0
$837$	564.365	+	613.285i	0.674271	+	0.732718i
$838$		0			0
$839$	1199.76	+	692.681i	1.42999	+	0.825603i	0.997119	−	0.0758538i	$-0.0241682\pi$
$839$	1199.76	+	692.681i	1.42999	+	0.825603i	0.432868	+	0.901457i	$0.357502\pi$
$840$		0			0
$841$	341.851	+	592.103i	0.406481	+	0.704046i
$842$		0			0
$843$	129.077	−	87.7440i	0.153116	−	0.104085i
$844$		0			0
$845$			124.468i			0.147300i
$846$		0			0
$847$		−	239.644i		−	0.282933i
$848$		0			0
$849$	1.23996	+	16.8564i	0.00146049	+	0.0198544i
$850$		0			0
$851$	8.28954	+	14.3579i	0.00974094	+	0.0168718i
$852$		0			0
$853$	91.3745	+	52.7551i	0.107121	+	0.0618466i	0.552604	−	0.833444i	$-0.313634\pi$
$853$	91.3745	+	52.7551i	0.107121	+	0.0618466i	−0.445482	+	0.895291i	$0.646968\pi$
$854$		0			0
$855$	616.588	+	243.948i	0.721156	+	0.285319i
$856$		0			0
$857$	−41.3561	+	71.6309i	−0.0482568	+	0.0835833i	−0.889145	−	0.457626i	$-0.848700\pi$
$857$	−41.3561	+	71.6309i	−0.0482568	+	0.0835833i	0.840888	+	0.541209i	$0.182033\pi$
$858$		0			0
$859$	−536.687	−	929.570i	−0.624782	−	1.08215i	−0.988583	−	0.150677i	$-0.951855\pi$
$859$	−536.687	−	929.570i	−0.624782	−	1.08215i	0.363801	−	0.931477i	$-0.381479\pi$
$860$		0			0
$861$	178.170	−	368.680i	0.206934	−	0.428199i
$862$		0			0
$863$		−	413.449i		−	0.479083i	−0.970886	−	0.239542i	$-0.923003\pi$
$863$		−	413.449i		−	0.479083i	0.970886	−	0.239542i	$-0.0769971\pi$
$864$		0			0
$865$	−726.308			−0.839662
$866$		0			0
$867$	698.669	+	337.643i	0.805846	+	0.389438i
$868$		0			0
$869$	34.7393	−	20.0567i	0.0399762	−	0.0230802i
$870$		0			0
$871$	−134.935	−	77.9050i	−0.154920	−	0.0894431i
$872$		0			0
$873$	509.937	−	75.4300i	0.584121	−	0.0864032i
$874$		0			0
$875$	117.316	−	203.198i	0.134076	−	0.232226i
$876$		0			0
$877$	−787.546	+	454.690i	−0.898000	+	0.518460i	−0.876551	−	0.481310i	$-0.840161\pi$
$877$	−787.546	+	454.690i	−0.898000	+	0.518460i	−0.0214489	+	0.999770i	$0.506828\pi$
$878$		0			0
$879$	−615.865	+	45.3029i	−0.700642	+	0.0515392i
$880$		0			0
$881$	849.052			0.963737			0.481868	−	0.876244i	$-0.339958\pi$
$881$	849.052			0.963737			0.481868	+	0.876244i	$0.339958\pi$
$882$		0			0
$883$	−1449.72			−1.64182			−0.820908	−	0.571061i	$-0.806532\pi$
$883$	−1449.72			−1.64182			−0.820908	+	0.571061i	$0.806532\pi$
$884$		0			0
$885$	833.468	+	1226.08i	0.941772	+	1.38541i
$886$		0			0
$887$	728.034	−	420.330i	0.820782	−	0.473879i	−0.0299041	−	0.999553i	$-0.509520\pi$
$887$	728.034	−	420.330i	0.820782	−	0.473879i	0.850686	+	0.525674i	$0.176187\pi$
$888$		0			0
$889$	237.481	−	411.329i	0.267132	−	0.462687i
$890$		0			0
$891$	21.7372	+	20.3924i	0.0243964	+	0.0228870i
$892$		0			0
$893$	367.390	+	212.113i	0.411411	+	0.237528i
$894$		0			0
$895$	81.5772	−	47.0986i	0.0911477	−	0.0526241i
$896$		0			0
$897$	12.3312	−	8.38251i	0.0137472	−	0.00934505i
$898$		0			0
$899$	−1205.33			−1.34074
$900$		0			0
$901$			87.8884i			0.0975454i
$902$		0			0
$903$	397.556	−	29.2441i	0.440261	−	0.0323855i
$904$		0			0
$905$	−437.543	−	757.846i	−0.483473	−	0.837399i
$906$		0			0
$907$	26.6190	−	46.1055i	0.0293484	−	0.0508330i	−0.850978	−	0.525201i	$-0.823990\pi$
$907$	26.6190	−	46.1055i	0.0293484	−	0.0508330i	0.880327	+	0.474368i	$0.157323\pi$
$908$		0			0
$909$	−213.955	−	1446.42i	−0.235374	−	1.59122i
$910$		0			0
$911$	−1154.18	−	666.365i	−1.26694	−	0.731465i	−0.292528	−	0.956257i	$-0.594497\pi$
$911$	−1154.18	−	666.365i	−1.26694	−	0.731465i	−0.974407	+	0.224791i	$0.927830\pi$
$912$		0			0
$913$	−10.6390	−	18.4272i	−0.0116527	−	0.0201831i
$914$		0			0
$915$	−535.361	−	258.722i	−0.585094	−	0.282756i
$916$		0			0
$917$			235.764i			0.257104i
$918$		0			0
$919$			1460.07i			1.58876i	0.607419	+	0.794381i	$0.292205\pi$
$919$			1460.07i			1.58876i	−0.607419	+	0.794381i	$0.707795\pi$
$920$		0			0
$921$	−594.132	−	287.124i	−0.645095	−	0.311752i
$922$		0			0
$923$	−570.693	−	988.470i	−0.618303	−	1.07093i
$924$		0			0
$925$	−83.1244	−	47.9919i	−0.0898643	−	0.0518832i
$926$		0			0
$927$	−1045.18	−	413.515i	−1.12748	−	0.446079i
$928$		0			0
$929$	435.813	−	754.851i	0.469121	−	0.812541i	−0.530256	−	0.847838i	$-0.677904\pi$
$929$	435.813	−	754.851i	0.469121	−	0.812541i	0.999377	+	0.0352963i	$0.0112375\pi$
$930$		0			0
$931$	−317.247	−	549.488i	−0.340760	−	0.590213i
$932$		0			0
$933$	1779.74	−	130.917i	1.90754	−	0.140319i
$934$		0			0
$935$		−	10.6072i		−	0.0113446i
$936$		0			0
$937$	1406.04			1.50058			0.750290	−	0.661109i	$-0.229914\pi$
$937$	1406.04			1.50058			0.750290	+	0.661109i	$0.229914\pi$
$938$		0			0
$939$	−609.666	+	414.439i	−0.649271	+	0.441362i
$940$		0			0
$941$	514.910	−	297.283i	0.547194	−	0.315923i	−0.200795	−	0.979633i	$-0.564353\pi$
$941$	514.910	−	297.283i	0.547194	−	0.315923i	0.747989	+	0.663711i	$0.231019\pi$
$942$		0			0
$943$	24.5886	+	14.1963i	0.0260749	+	0.0150544i
$944$		0			0
$945$	61.2171	+	273.393i	0.0647800	+	0.289304i
$946$		0			0
$947$	844.920	−	1463.44i	0.892207	−	1.54535i	0.0549826	−	0.998487i	$-0.482490\pi$
$947$	844.920	−	1463.44i	0.892207	−	1.54535i	0.837224	−	0.546860i	$-0.184177\pi$
$948$		0			0
$949$	1448.60	−	836.351i	1.52645	−	0.881297i
$950$		0			0
$951$	−255.087	−	375.249i	−0.268230	−	0.394584i
$952$		0			0
$953$	−1165.49			−1.22297			−0.611485	−	0.791256i	$-0.709428\pi$
$953$	−1165.49			−1.22297			−0.611485	+	0.791256i	$0.709428\pi$
$954$		0			0
$955$	1819.43			1.90516
$956$		0			0
$957$	−42.9883	+	3.16221i	−0.0449198	+	0.00330429i
$958$		0			0
$959$	123.346	−	71.2139i	0.128620	−	0.0742585i
$960$		0			0
$961$	−4.07581	+	7.05951i	−0.00424122	+	0.00734600i
$962$		0			0
$963$	246.486	+	310.830i	0.255957	+	0.322773i
$964$		0			0
$965$	12.1367	+	7.00713i	0.0125769	+	0.00726127i
$966$		0			0
$967$	−224.372	+	129.541i	−0.232029	+	0.133962i	−0.611508	−	0.791239i	$-0.709437\pi$
$967$	−224.372	+	129.541i	−0.232029	+	0.133962i	0.379479	+	0.925200i	$0.376103\pi$
$968$		0			0
$969$	−209.465	−	101.227i	−0.216166	−	0.104466i
$970$		0			0
$971$	−814.330			−0.838650			−0.419325	−	0.907836i	$-0.637733\pi$
$971$	−814.330			−0.838650			−0.419325	+	0.907836i	$0.637733\pi$
$972$		0			0
$973$		−	323.963i		−	0.332953i
$974$		0			0
$975$	−37.5613	+	77.7239i	−0.0385244	+	0.0797168i
$976$		0			0
$977$	181.789	+	314.867i	0.186068	+	0.322280i	0.943936	−	0.330129i	$-0.107092\pi$
$977$	181.789	+	314.867i	0.186068	+	0.322280i	−0.757868	+	0.652408i	$0.773759\pi$
$978$		0			0
$979$	−18.1360	+	31.4125i	−0.0185251	+	0.0320863i
$980$		0			0
$981$	288.925	−	229.115i	0.294521	−	0.233553i
$982$		0			0
$983$	−531.421	−	306.816i	−0.540612	−	0.312122i	0.204715	−	0.978822i	$-0.434373\pi$
$983$	−531.421	−	306.816i	−0.540612	−	0.312122i	−0.745327	+	0.666699i	$0.767707\pi$
$984$		0			0
$985$	405.640	+	702.589i	0.411817	+	0.713289i
$986$		0			0
$987$	13.1493	+	178.756i	0.0133225	+	0.181111i
$988$		0			0
$989$			27.6406i			0.0279480i
$990$		0			0
$991$			331.121i			0.334128i	0.985946	+	0.167064i	$0.0534286\pi$
$991$			331.121i			0.334128i	−0.985946	+	0.167064i	$0.946571\pi$
$992$		0			0
$993$	−603.896	+	410.516i	−0.608153	+	0.413410i
$994$		0			0
$995$	−173.459	−	300.440i	−0.174331	−	0.301950i
$996$		0			0
$997$	704.962	+	407.010i	0.707083	+	0.408234i	0.809980	−	0.586458i	$-0.199478\pi$
$997$	704.962	+	407.010i	0.707083	+	0.408234i	−0.102897	+	0.994692i	$0.532811\pi$
$998$		0			0
$999$	−1059.10	+	237.149i	−1.06016	+	0.237386i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.3.t.a.223.4	yes	32
3.2	odd	2		1728.3.t.c.991.3		32
4.3	odd	2	inner	576.3.t.a.223.13	yes	32
8.3	odd	2		576.3.t.c.223.4	yes	32
8.5	even	2		576.3.t.c.223.13	yes	32
9.4	even	3		576.3.t.c.31.4	yes	32
9.5	odd	6		1728.3.t.a.415.13		32
12.11	even	2		1728.3.t.c.991.4		32
24.5	odd	2		1728.3.t.a.991.14		32
24.11	even	2		1728.3.t.a.991.13		32
36.23	even	6		1728.3.t.a.415.14		32
36.31	odd	6		576.3.t.c.31.13	yes	32
72.5	odd	6		1728.3.t.c.415.4		32
72.13	even	6	inner	576.3.t.a.31.13	yes	32
72.59	even	6		1728.3.t.c.415.3		32
72.67	odd	6	inner	576.3.t.a.31.4	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
576.3.t.a.31.4	✓	32	72.67	odd	6	inner
576.3.t.a.31.13	yes	32	72.13	even	6	inner
576.3.t.a.223.4	yes	32	1.1	even	1	trivial
576.3.t.a.223.13	yes	32	4.3	odd	2	inner
576.3.t.c.31.4	yes	32	9.4	even	3
576.3.t.c.31.13	yes	32	36.31	odd	6
576.3.t.c.223.4	yes	32	8.3	odd	2
576.3.t.c.223.13	yes	32	8.5	even	2
1728.3.t.a.415.13		32	9.5	odd	6
1728.3.t.a.415.14		32	36.23	even	6
1728.3.t.a.991.13		32	24.11	even	2
1728.3.t.a.991.14		32	24.5	odd	2
1728.3.t.c.415.3		32	72.59	even	6
1728.3.t.c.415.4		32	72.5	odd	6
1728.3.t.c.991.3		32	3.2	odd	2
1728.3.t.c.991.4		32	12.11	even	2

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	576.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.70112 - 1.30536i) q^{3} +(4.53220 - 2.61667i) q^{5} +(-1.71711 - 0.991374i) q^{7} +(5.59208 + 7.05186i) q^{9} +O(q^{10})\)	\(q+(-2.70112 - 1.30536i) q^{3} +(4.53220 - 2.61667i) q^{5} +(-1.71711 - 0.991374i) q^{7} +(5.59208 + 7.05186i) q^{9} +(0.183983 - 0.318668i) q^{11} +(10.4361 - 6.02529i) q^{13} +(-15.6577 + 1.15178i) q^{15} +5.50826 q^{17} +14.0784 q^{19} +(3.34402 + 4.91926i) q^{21} +(-0.357187 + 0.206222i) q^{23} +(1.19391 - 2.06792i) q^{25} +(-5.89965 - 26.3476i) q^{27} +(33.8161 + 19.5237i) q^{29} +(-26.7327 + 15.4341i) q^{31} +(-0.912936 + 0.620596i) q^{33} -10.3764 q^{35} -40.1971i q^{37} +(-36.0543 + 2.65215i) q^{39} +(-34.4198 - 59.6168i) q^{41} +(33.5082 - 58.0379i) q^{43} +(43.7968 + 17.3278i) q^{45} +(26.0961 + 15.0666i) q^{47} +(-22.5344 - 39.0307i) q^{49} +(-14.8785 - 7.19026i) q^{51} +15.9557i q^{53} -1.92569i q^{55} +(-38.0274 - 18.3773i) q^{57} +(-47.2149 - 81.7786i) q^{59} +(32.7986 + 18.9363i) q^{61} +(-2.61118 - 17.6526i) q^{63} +(31.5324 - 54.6157i) q^{65} +(-6.46484 - 11.1974i) q^{67} +(1.23400 - 0.0907728i) q^{69} -94.7164i q^{71} +138.807 q^{73} +(-5.92428 + 4.02721i) q^{75} +(-0.631838 + 0.364792i) q^{77} +(94.4089 + 54.5070i) q^{79} +(-18.4574 + 78.8690i) q^{81} +(28.9129 - 50.0785i) q^{83} +(24.9646 - 14.4133i) q^{85} +(-65.8557 - 96.8780i) q^{87} -98.5744 q^{89} -23.8932 q^{91} +(92.3552 - 6.79363i) q^{93} +(63.8061 - 36.8385i) q^{95} +(28.6381 - 49.6027i) q^{97} +(3.27605 - 0.484594i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 18 q^{5} + 18 q^{9}+O(q^{10}) \) 32 * q - 18 * q^5 + 18 * q^9	\( 32 q - 18 q^{5} + 18 q^{9} - 30 q^{13} - 36 q^{17} + 102 q^{21} + 86 q^{25} - 162 q^{29} + 12 q^{33} - 36 q^{41} + 186 q^{45} + 138 q^{49} - 162 q^{57} - 42 q^{61} - 198 q^{65} - 474 q^{69} - 196 q^{73} + 666 q^{77} + 462 q^{81} + 180 q^{85} + 792 q^{89} + 174 q^{93} + 64 q^{97}+O(q^{100}) \) 32 * q - 18 * q^5 + 18 * q^9 - 30 * q^13 - 36 * q^17 + 102 * q^21 + 86 * q^25 - 162 * q^29 + 12 * q^33 - 36 * q^41 + 186 * q^45 + 138 * q^49 - 162 * q^57 - 42 * q^61 - 198 * q^65 - 474 * q^69 - 196 * q^73 + 666 * q^77 + 462 * q^81 + 180 * q^85 + 792 * q^89 + 174 * q^93 + 64 * q^97

Introduction

L-functions

Modular forms

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