LMFDB - Embedded newform 576.3.t.a.31.4

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			31.4
Character	$\chi$	$=$	576.31
Dual form			576.3.t.a.223.4

$q$-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 $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

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

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	0.879284	−	0.476297i	$-0.158021\pi$
$5$	4.53220	+	2.61667i	0.906441	+	0.523334i	0.0271565	+	0.999631i	$0.491355\pi$
$6$		0			0
$7$	−1.71711	+	0.991374i	−0.245301	+	0.141625i	−0.617611	−	0.786484i	$-0.711899\pi$
$7$	−1.71711	+	0.991374i	−0.245301	+	0.141625i	0.372310	+	0.928109i	$0.378566\pi$
$8$		0			0
$9$	5.59208	−	7.05186i	0.621342	−	0.783540i
$10$		0			0
$11$	0.183983	+	0.318668i	0.0167257	+	0.0289698i	0.874267	−	0.485445i	$-0.161342\pi$
$11$	0.183983	+	0.318668i	0.0167257	+	0.0289698i	−0.857541	+	0.514415i	$0.828009\pi$
$12$		0			0
$13$	10.4361	+	6.02529i	0.802777	+	0.463484i	0.844441	−	0.535648i	$-0.179933\pi$
$13$	10.4361	+	6.02529i	0.802777	+	0.463484i	−0.0416642	+	0.999132i	$0.513266\pi$
$14$		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	0.492215	−	0.870474i	$-0.336187\pi$
$23$	−0.357187	−	0.206222i	−0.0155299	−	0.00896618i	−0.507745	+	0.861508i	$0.669521\pi$
$24$		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	0.213320	−	0.976982i	$-0.431572\pi$
$29$	33.8161	−	19.5237i	1.16607	−	0.673231i	0.952751	+	0.303751i	$0.0982391\pi$
$30$		0			0
$31$	−26.7327	−	15.4341i	−0.862345	−	0.497875i	0.00245215	−	0.999997i	$-0.499219\pi$
$31$	−26.7327	−	15.4341i	−0.862345	−	0.497875i	−0.864797	+	0.502122i	$0.832553\pi$
$32$		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	$0.182789\pi$
$37$			40.1971i			1.08641i	−0.839601	+	0.543204i	$0.817211\pi$
$38$		0			0
$39$	−36.0543	−	2.65215i	−0.924469	−	0.0680038i
$40$		0			0
$41$	−34.4198	+	59.6168i	−0.839507	+	1.45407i	0.0507997	+	0.998709i	$0.483823\pi$
$41$	−34.4198	+	59.6168i	−0.839507	+	1.45407i	−0.890307	+	0.455361i	$0.849510\pi$
$42$		0			0
$43$	33.5082	+	58.0379i	0.779261	+	1.34972i	0.932368	+	0.361510i	$0.117739\pi$
$43$	33.5082	+	58.0379i	0.779261	+	1.34972i	−0.153107	+	0.988210i	$0.548928\pi$
$44$		0			0
$45$	43.7968	−	17.3278i	0.973262	−	0.385063i
$46$		0			0
$47$	26.0961	−	15.0666i	0.555235	−	0.320565i	−0.195996	−	0.980605i	$-0.562794\pi$
$47$	26.0961	−	15.0666i	0.555235	−	0.320565i	0.751231	+	0.660039i	$0.229460\pi$
$48$		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	$-0.951903\pi$
$53$		−	15.9557i		−	0.301052i	0.988606	−	0.150526i	$-0.0480967\pi$
$54$		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	0.119197	+	0.992871i	$0.461968\pi$
$59$	−47.2149	+	81.7786i	−0.800252	+	1.38608i	−0.919450	+	0.393207i	$0.871365\pi$
$60$		0			0
$61$	32.7986	−	18.9363i	0.537681	−	0.310430i	−0.206457	−	0.978456i	$-0.566193\pi$
$61$	32.7986	−	18.9363i	0.537681	−	0.310430i	0.744139	+	0.668025i	$0.232860\pi$
$62$		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	−0.910230	−	0.414104i	$-0.864095\pi$
$67$	−6.46484	+	11.1974i	−0.0964901	+	0.167126i	0.813739	+	0.581230i	$0.197428\pi$
$68$		0			0
$69$	1.23400	+	0.0907728i	0.0178840	+	0.00131555i
$70$		0			0
$71$			94.7164i			1.33403i	0.745043	+	0.667017i	$0.232429\pi$
$71$			94.7164i			1.33403i	−0.745043	+	0.667017i	$0.767571\pi$
$72$		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	0.235602	−	0.971850i	$-0.424294\pi$
$79$	94.4089	−	54.5070i	1.19505	−	0.689962i	0.959447	+	0.281888i	$0.0909606\pi$
$80$		0			0
$81$	−18.4574	−	78.8690i	−0.227869	−	0.973692i
$82$		0			0
$83$	28.9129	+	50.0785i	0.348348	+	0.603356i	0.985956	−	0.167005i	$-0.0534095\pi$
$83$	28.9129	+	50.0785i	0.348348	+	0.603356i	−0.637608	+	0.770361i	$0.720076\pi$
$84$		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	0.975040	−	0.222028i	$-0.0712676\pi$
$97$	28.6381	+	49.6027i	0.295238	+	0.511368i	−0.679802	+	0.733396i	$0.737934\pi$
$98$		0			0
$99$	3.27605	+	0.484594i	0.0330914	+	0.00489488i
$100$		0			0
$101$	−140.697	+	81.2312i	−1.39304	+	0.804269i	−0.993650	−	0.112514i	$-0.964110\pi$
$101$	−140.697	+	81.2312i	−1.39304	+	0.804269i	−0.399385	+	0.916783i	$0.630776\pi$
$102$		0			0
$103$	−108.157	−	62.4447i	−1.05007	−	0.606259i	−0.127402	−	0.991851i	$-0.540664\pi$
$103$	−108.157	−	62.4447i	−1.05007	−	0.606259i	−0.922669	+	0.385592i	$0.873997\pi$
$104$		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	$0.0601818\pi$
$109$			40.9714i			0.375885i	−0.982180	+	0.187942i	$0.939818\pi$
$110$		0			0
$111$	−52.4717	−	108.577i	−0.472718	−	0.978172i
$112$		0			0
$113$	−35.5414	+	61.5595i	−0.314526	+	0.544774i	−0.979337	−	0.202237i	$-0.935179\pi$
$113$	−35.5414	+	61.5595i	−0.314526	+	0.544774i	0.664811	+	0.747012i	$0.268512\pi$
$114$		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	$-0.607896\pi$
$127$		−	239.547i		−	1.88620i	0.332512	−	0.943099i	$-0.392104\pi$
$128$		0			0
$129$	−166.270	−	113.027i	−1.28891	−	0.876179i
$130$		0			0
$131$	−59.4540	+	102.977i	−0.453847	+	0.786086i	−0.998621	−	0.0524965i	$-0.983282\pi$
$131$	−59.4540	+	102.977i	−0.453847	+	0.786086i	0.544774	+	0.838583i	$0.316615\pi$
$132$		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	0.704651	−	0.709554i	$-0.251104\pi$
$137$	−35.9168	−	62.2097i	−0.262166	−	0.454086i	−0.966817	+	0.255469i	$0.917770\pi$
$138$		0			0
$139$	81.6956	−	141.501i	0.587738	−	1.01799i	−0.406790	−	0.913522i	$-0.633352\pi$
$139$	81.6956	−	141.501i	0.587738	−	1.01799i	0.994528	−	0.104471i	$-0.0333148\pi$
$140$		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	0.0404835	−	0.999180i	$-0.487110\pi$
$149$	−119.884	−	69.2150i	−0.804590	−	0.464530i	−0.845074	+	0.534650i	$0.820444\pi$
$150$		0			0
$151$	82.4534	−	47.6045i	0.546049	−	0.315262i	−0.201478	−	0.979493i	$-0.564574\pi$
$151$	82.4534	−	47.6045i	0.546049	−	0.315262i	0.747527	+	0.664231i	$0.231241\pi$
$152$		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	−0.0347974	−	0.999394i	$-0.511079\pi$
$157$	−144.078	−	83.1837i	−0.917697	−	0.529833i	−0.882900	+	0.469562i	$0.844412\pi$
$158$		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	0.937274	−	0.348594i	$-0.113341\pi$
$167$	184.371	+	106.447i	1.10402	+	0.637406i	0.166746	+	0.986000i	$0.446674\pi$
$168$		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	−0.805388	−	0.592748i	$-0.798043\pi$
$173$	−120.191	+	69.3924i	−0.694747	+	0.401112i	0.110641	+	0.993860i	$0.464710\pi$
$174$		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	$0.152838\pi$
$181$			167.214i			0.923832i	−0.886924	+	0.461916i	$0.847162\pi$
$182$		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	0.580994	−	0.813908i	$-0.302664\pi$
$191$	301.084	−	173.831i	1.57636	−	0.910109i	0.995362	−	0.0962015i	$-0.0306693\pi$
$192$		0			0
$193$	1.33894	−	2.31911i	0.00693751	−	0.0120161i	−0.862536	−	0.505996i	$-0.831125\pi$
$193$	1.33894	−	2.31911i	0.00693751	−	0.0120161i	0.869473	+	0.493980i	$0.164458\pi$
$194$		0			0
$195$	−156.466	−	106.362i	−0.802388	−	0.545448i
$196$		0			0
$197$		−	155.022i		−	0.786911i	−0.919344	−	0.393456i	$-0.871279\pi$
$197$		−	155.022i		−	0.786911i	0.919344	−	0.393456i	$-0.128721\pi$
$198$		0			0
$199$			66.2901i			0.333116i	0.986032	+	0.166558i	$0.0532653\pi$
$199$			66.2901i			0.333116i	−0.986032	+	0.166558i	$0.946735\pi$
$200$		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	−0.775434	−	0.631429i	$-0.782469\pi$
$211$	33.5736	−	58.1511i	0.159116	−	0.275598i	0.934550	+	0.355831i	$0.115802\pi$
$212$		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	0.100034	−	0.994984i	$-0.468105\pi$
$223$	225.616	−	130.260i	1.01173	−	0.584124i	0.911699	+	0.410860i	$0.134771\pi$
$224$		0			0
$225$	21.2591	+	3.14465i	0.0944851	+	0.0139762i
$226$		0			0
$227$	−128.921	−	223.297i	−0.567933	−	0.983689i	−0.996770	−	0.0803070i	$-0.974410\pi$
$227$	−128.921	−	223.297i	−0.567933	−	0.983689i	0.428837	−	0.903382i	$-0.358923\pi$
$228$		0			0
$229$	198.873	+	114.820i	0.868443	+	0.501396i	0.866830	−	0.498603i	$-0.166153\pi$
$229$	198.873	+	114.820i	0.868443	+	0.501396i	0.00161217	+	0.999999i	$0.499487\pi$
$230$		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	0.821734	−	0.569871i	$-0.193007\pi$
$239$	176.640	+	101.983i	0.739079	+	0.426707i	−0.0826557	+	0.996578i	$0.526340\pi$
$240$		0			0
$241$	46.5967	+	80.7079i	0.193347	+	0.334888i	0.946358	−	0.323121i	$-0.104732\pi$
$241$	46.5967	+	80.7079i	0.193347	+	0.334888i	−0.753010	+	0.658009i	$0.771399\pi$
$242$		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	0.335579	+	0.942012i	$0.391068\pi$
$257$	−166.540	+	288.456i	−0.648017	+	1.12240i	−0.983596	+	0.180386i	$0.942265\pi$
$258$		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	−0.318534	−	0.947912i	$-0.603190\pi$
$263$	90.2392	−	52.0997i	0.343115	−	0.198098i	0.661649	+	0.749814i	$0.269857\pi$
$264$		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	$-0.805905\pi$
$269$		−	308.100i		−	1.14535i	0.819781	−	0.572677i	$-0.194095\pi$
$270$		0			0
$271$		−	228.400i		−	0.842805i	−0.906874	−	0.421402i	$-0.861538\pi$
$271$		−	228.400i		−	0.842805i	0.906874	−	0.421402i	$-0.138462\pi$
$272$		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	−0.317945	−	0.948109i	$-0.602993\pi$
$277$	95.3349	−	55.0416i	0.344169	−	0.198706i	0.662114	+	0.749403i	$0.269659\pi$
$278$		0			0
$279$	−258.330	+	102.206i	−0.925915	+	0.366331i
$280$		0			0
$281$	−26.0128	−	45.0554i	−0.0925721	−	0.160340i	0.816021	−	0.578023i	$-0.196176\pi$
$281$	−26.0128	−	45.0554i	−0.0925721	−	0.160340i	−0.908593	+	0.417683i	$0.862842\pi$
$282$		0			0
$283$	−2.81699	+	4.87918i	−0.00995404	+	0.0172409i	−0.870960	−	0.491355i	$-0.836502\pi$
$283$	−2.81699	+	4.87918i	−0.00995404	+	0.0172409i	0.861005	+	0.508596i	$0.169835\pi$
$284$		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	0.772344	−	0.635204i	$-0.219084\pi$
$293$	178.265	+	102.921i	0.608414	+	0.351268i	−0.163931	+	0.986472i	$0.552417\pi$
$294$		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	−0.974336	−	0.225098i	$-0.927730\pi$
$311$	−515.154	−	297.425i	−1.65645	−	0.956349i	−0.682109	−	0.731251i	$-0.738937\pi$
$312$		0			0
$313$	122.865	+	212.809i	0.392541	+	0.679901i	0.992784	−	0.119917i	$-0.0382628\pi$
$313$	122.865	+	212.809i	0.392541	+	0.679901i	−0.600243	+	0.799818i	$0.704929\pi$
$314$		0			0
$315$	−58.0255	+	73.1728i	−0.184208	+	0.232295i
$316$		0			0
$317$	130.984	−	75.6236i	0.413198	−	0.238560i	−0.278965	−	0.960301i	$-0.589991\pi$
$317$	130.984	−	75.6236i	0.413198	−	0.238560i	0.692163	+	0.721741i	$0.256658\pi$
$318$		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	0.989203	−	0.146555i	$-0.0468184\pi$
$331$	121.703	+	210.795i	0.367681	+	0.636843i	−0.621521	+	0.783397i	$0.713485\pi$
$332$		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	−0.400121	−	0.916463i	$-0.631032\pi$
$337$	200.050	−	346.496i	0.593620	−	1.02818i	0.993740	−	0.111717i	$-0.0356349\pi$
$338$		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	0.446925	+	0.894571i	$0.352519\pi$
$347$	−191.287	+	331.318i	−0.551259	+	0.954808i	−0.998184	+	0.0602368i	$0.980814\pi$
$348$		0			0
$349$	69.4135	−	40.0759i	0.198892	−	0.114831i	−0.397246	−	0.917712i	$-0.630034\pi$
$349$	69.4135	−	40.0759i	0.198892	−	0.114831i	0.596139	+	0.802881i	$0.296701\pi$
$350$		0			0
$351$	−220.321	+	239.419i	−0.627695	+	0.682105i
$352$		0			0
$353$	−157.270	−	272.400i	−0.445525	−	0.771672i	0.552563	−	0.833471i	$-0.313650\pi$
$353$	−157.270	−	272.400i	−0.445525	−	0.771672i	−0.998089	+	0.0617986i	$0.980316\pi$
$354$		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	$0.146751\pi$
$359$			319.419i			0.889746i	−0.895594	+	0.444873i	$0.853249\pi$
$360$		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	−0.775632	−	0.631185i	$-0.782569\pi$
$367$	−226.375	+	130.698i	−0.616826	+	0.356125i	0.158806	+	0.987310i	$0.449235\pi$
$368$		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	0.999488	−	0.0319873i	$-0.0101836\pi$
$373$	548.881	+	316.897i	1.47153	+	0.849589i	0.472042	+	0.881576i	$0.343517\pi$
$374$		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	−0.248563	−	0.968616i	$-0.579958\pi$
$383$	−464.077	−	267.935i	−1.21169	−	0.699570i	−0.963127	+	0.269046i	$0.913292\pi$
$384$		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	−0.975315	−	0.220818i	$-0.929127\pi$
$389$	−494.706	+	285.619i	−1.27174	+	0.734239i	−0.296423	+	0.955057i	$0.595794\pi$
$390$		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	$-0.680432\pi$
$397$		−	669.819i		−	1.68720i	0.536971	−	0.843600i	$-0.319568\pi$
$398$		0			0
$399$	47.0783	−	69.2552i	0.117991	−	0.173572i
$400$		0			0
$401$	238.753	−	413.532i	0.595394	−	1.03125i	−0.398098	−	0.917343i	$-0.630329\pi$
$401$	238.753	−	413.532i	0.595394	−	1.03125i	0.993491	−	0.113909i	$-0.0363372\pi$
$402$		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	0.463003	+	0.886357i	$0.346772\pi$
$409$	−219.267	+	379.782i	−0.536106	+	0.928563i	−0.999109	+	0.0422060i	$0.986561\pi$
$410$		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	0.193112	+	0.981177i	$0.438142\pi$
$419$	−315.577	+	546.596i	−0.753168	+	1.30453i	−0.946280	+	0.323348i	$0.895191\pi$
$420$		0			0
$421$	414.883	−	239.533i	0.985471	−	0.568962i	0.0815534	−	0.996669i	$-0.474012\pi$
$421$	414.883	−	239.533i	0.985471	−	0.568962i	0.903917	+	0.427707i	$0.140679\pi$
$422$		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	$-0.990014\pi$
$431$		−	27.0391i		−	0.0627357i	0.999508	−	0.0313679i	$-0.00998634\pi$
$432$		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	−0.470349	−	0.882480i	$-0.655872\pi$
$439$	25.7809	−	14.8846i	0.0587263	−	0.0339057i	0.529076	+	0.848575i	$0.322539\pi$
$440$		0			0
$441$	149.225	+	377.171i	0.338378	+	0.855264i
$442$		0			0
$443$	−36.9071	−	63.9249i	−0.0833117	−	0.144300i	0.821359	−	0.570412i	$-0.193216\pi$
$443$	−36.9071	−	63.9249i	−0.0833117	−	0.144300i	−0.904671	+	0.426112i	$0.859883\pi$
$444$		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	0.908820	−	0.417187i	$-0.136984\pi$
$457$	42.5537	+	73.7051i	0.0931153	+	0.161280i	−0.815705	+	0.578468i	$0.803651\pi$
$458$		0			0
$459$	−32.4968	+	145.129i	−0.0707992	+	0.316186i
$460$		0			0
$461$	381.095	−	220.025i	0.826670	−	0.477278i	−0.0260409	−	0.999661i	$-0.508290\pi$
$461$	381.095	−	220.025i	0.826670	−	0.477278i	0.852711	+	0.522382i	$0.174957\pi$
$462$		0			0
$463$	41.0587	+	23.7053i	0.0886798	+	0.0511993i	0.543684	−	0.839290i	$-0.317029\pi$
$463$	41.0587	+	23.7053i	0.0886798	+	0.0511993i	−0.455004	+	0.890489i	$0.650362\pi$
$464$		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	−0.919859	−	0.392249i	$-0.871697\pi$
$479$	−498.203	+	287.638i	−1.04009	+	0.600497i	−0.120232	+	0.992746i	$0.538364\pi$
$480$		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	$0.119113\pi$
$487$			356.028i			0.731064i	−0.930799	+	0.365532i	$0.880887\pi$
$488$		0			0
$489$	−371.224	+	179.400i	−0.759150	+	0.366872i
$490$		0			0
$491$	−31.2238	+	54.0813i	−0.0635923	+	0.110145i	−0.896069	−	0.443915i	$-0.853589\pi$
$491$	−31.2238	+	54.0813i	−0.0635923	+	0.110145i	0.832476	+	0.554061i	$0.186922\pi$
$492$		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	−0.997921	−	0.0644510i	$-0.979470\pi$
$499$	−221.129	+	383.007i	−0.443144	+	0.767548i	0.554777	+	0.831999i	$0.312804\pi$
$500$		0			0
$501$	−636.960	−	46.8547i	−1.27138	−	0.0935223i
$502$		0			0
$503$		−	643.704i		−	1.27973i	−0.768487	−	0.639865i	$-0.778990\pi$
$503$		−	643.704i		−	1.27973i	0.768487	−	0.639865i	$-0.221010\pi$
$504$		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	0.988215	+	0.153073i	$0.0489171\pi$
$509$	821.978	+	474.569i	1.61489	+	0.932356i	0.626673	+	0.779282i	$0.284416\pi$
$510$		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	$-0.884082\pi$
$541$		−	385.378i		−	0.712343i	0.934421	−	0.356172i	$-0.115918\pi$
$542$		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	0.879500	−	0.475899i	$-0.157877\pi$
$547$	15.1023	+	26.1580i	0.0276094	+	0.0478209i	−0.851891	+	0.523720i	$0.824544\pi$
$548$		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	$-0.679914\pi$
$557$		−	940.743i		−	1.68895i	0.535598	−	0.844473i	$-0.320086\pi$
$558$		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	−0.840106	−	0.542422i	$-0.817507\pi$
$563$	27.9801	−	48.4629i	0.0496982	−	0.0860797i	0.889804	+	0.456342i	$0.150841\pi$
$564$		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	0.502856	−	0.864370i	$-0.332283\pi$
$569$	−282.872	−	489.949i	−0.497139	−	0.861069i	−0.999995	+	0.00330083i	$0.998949\pi$
$570$		0			0
$571$	348.221	−	603.137i	0.609845	−	1.05628i	−0.381421	−	0.924401i	$-0.624565\pi$
$571$	348.221	−	603.137i	0.609845	−	1.05628i	0.991266	−	0.131880i	$-0.0421015\pi$
$572$		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	−0.911120	−	0.412140i	$-0.864781\pi$
$587$	−476.928	−	826.064i	−0.812484	−	1.40726i	0.0986361	−	0.995124i	$-0.468552\pi$
$588$		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	−0.992937	−	0.118640i	$-0.962146\pi$
$599$	−953.699	−	550.618i	−1.59215	−	0.919229i	−0.599214	−	0.800589i	$-0.704520\pi$
$600$		0			0
$601$	−342.934	−	593.980i	−0.570606	−	0.988319i	−0.996504	−	0.0835474i	$-0.973375\pi$
$601$	−342.934	−	593.980i	−0.570606	−	0.988319i	0.425898	−	0.904771i	$-0.359958\pi$
$602$		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	0.772937	−	0.634483i	$-0.218787\pi$
$607$	370.226	+	213.750i	0.609927	+	0.352142i	−0.163010	+	0.986624i	$0.552120\pi$
$608$		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	$0.244398\pi$
$613$			851.523i			1.38911i	−0.719440	+	0.694554i	$0.755602\pi$
$614$		0			0
$615$	607.601	−	893.819i	0.987969	−	1.45336i
$616$		0			0
$617$	585.852	−	1014.73i	0.949517	−	1.64461i	0.203073	−	0.979164i	$-0.434907\pi$
$617$	585.852	−	1014.73i	0.949517	−	1.64461i	0.746444	−	0.665448i	$-0.231760\pi$
$618$		0			0
$619$	−5.72669	−	9.91891i	−0.00925151	−	0.0160241i	0.861363	−	0.507991i	$-0.169612\pi$
$619$	−5.72669	−	9.91891i	−0.00925151	−	0.0160241i	−0.870614	+	0.491967i	$0.836278\pi$
$620$		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	$0.115911\pi$
$631$			449.462i			0.712301i	−0.934429	+	0.356151i	$0.884089\pi$
$632$		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	0.772356	−	0.635190i	$-0.219078\pi$
$641$	−105.068	−	181.983i	−0.163913	−	0.283905i	−0.936269	+	0.351285i	$0.885745\pi$
$642$		0			0
$643$	121.492	−	210.430i	0.188945	−	0.327263i	−0.755954	−	0.654625i	$-0.772826\pi$
$643$	121.492	−	210.430i	0.188945	−	0.327263i	0.944899	+	0.327362i	$0.106160\pi$
$644$		0			0
$645$	−457.815	−	947.335i	−0.709791	−	1.46874i
$646$		0			0
$647$			636.733i			0.984131i	0.870558	+	0.492065i	$0.163758\pi$
$647$			636.733i			0.984131i	−0.870558	+	0.492065i	$0.836242\pi$
$648$		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	0.839593	−	0.543216i	$-0.182794\pi$
$653$	515.185	+	297.442i	0.788951	+	0.455501i	−0.0506424	+	0.998717i	$0.516127\pi$
$654$		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	−0.995785	−	0.0917213i	$-0.970763\pi$
$659$	−380.457	−	658.972i	−0.577325	−	0.999957i	0.418459	−	0.908236i	$-0.362570\pi$
$660$		0			0
$661$	327.531	+	189.100i	0.495508	+	0.286082i	0.726857	−	0.686789i	$-0.240980\pi$
$661$	327.531	+	189.100i	0.495508	+	0.286082i	−0.231349	+	0.972871i	$0.574314\pi$
$662$		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	0.535557	−	0.844499i	$-0.320102\pi$
$673$	−311.989	−	540.381i	−0.463579	−	0.802943i	−0.999136	+	0.0415563i	$0.986768\pi$
$674$		0			0
$675$	−61.5284	+	19.2567i	−0.0911531	+	0.0285285i
$676$		0			0
$677$	−567.922	+	327.890i	−0.838881	+	0.484328i	−0.856884	−	0.515510i	$-0.827603\pi$
$677$	−567.922	+	327.890i	−0.838881	+	0.484328i	0.0180028	+	0.999838i	$0.494269\pi$
$678$		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	−0.991099	−	0.133126i	$-0.957499\pi$
$691$	−422.090	−	731.082i	−0.610840	−	1.05801i	0.380259	−	0.924880i	$-0.375835\pi$
$692$		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	$0.0918826\pi$
$701$			399.101i			0.569332i	−0.958627	+	0.284666i	$0.908117\pi$
$702$		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	0.0914344	−	0.995811i	$-0.470855\pi$
$709$	708.680	−	409.157i	0.999549	−	0.577090i	0.908115	+	0.418721i	$0.137521\pi$
$710$		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	$-0.947974\pi$
$719$		−	233.988i		−	0.325435i	0.986673	−	0.162718i	$-0.0520259\pi$
$720$		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	0.645281	−	0.763945i	$-0.276740\pi$
$727$	1184.66	−	683.963i	1.62952	−	0.940802i	0.984237	−	0.176857i	$-0.0565931\pi$
$728$		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	−0.417077	−	0.908871i	$-0.636945\pi$
$733$	−1035.52	−	597.860i	−1.41272	−	0.815635i	−0.995644	+	0.0932365i	$0.970279\pi$
$734$		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	−0.00469039	−	0.999989i	$-0.501493\pi$
$743$	−648.677	−	374.514i	−0.873051	−	0.504056i	−0.868361	+	0.495933i	$0.834826\pi$
$744$		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	0.219161	−	0.975689i	$-0.429668\pi$
$751$	−387.688	−	223.832i	−0.516230	−	0.298045i	−0.735391	+	0.677643i	$0.763001\pi$
$752$		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	$-0.968654\pi$
$757$		−	148.852i		−	0.196634i	0.995155	−	0.0983169i	$-0.0313459\pi$
$758$		0			0
$759$	0.198109	+	0.409937i	0.000261013	+	0.000540101i
$760$		0			0
$761$	−216.335	+	374.704i	−0.284278	+	0.492384i	−0.972434	−	0.233179i	$-0.925087\pi$
$761$	−216.335	+	374.704i	−0.284278	+	0.492384i	0.688156	+	0.725563i	$0.258420\pi$
$762$		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	0.0777254	+	0.996975i	$0.475234\pi$
$769$	−634.073	+	1098.25i	−0.824543	+	1.42815i	−0.902268	+	0.431175i	$0.858099\pi$
$770$		0			0
$771$	73.3061	−	996.550i	0.0950792	−	1.29254i
$772$		0			0
$773$		−	446.238i		−	0.577281i	−0.957438	−	0.288640i	$-0.906797\pi$
$773$		−	446.238i		−	0.577281i	0.957438	−	0.288640i	$-0.0932032\pi$
$774$		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	−0.139169	−	0.990269i	$-0.544443\pi$
$787$	620.167	−	1074.16i	0.788013	−	1.36488i	0.927182	−	0.374611i	$-0.122224\pi$
$788$		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	−0.0652193	−	0.997871i	$-0.520775\pi$
$797$	−766.722	−	442.667i	−0.962011	−	0.555417i	−0.896791	+	0.442454i	$0.854108\pi$
$798$		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	−0.925327	−	0.379169i	$-0.876210\pi$
$821$	−869.949	+	502.265i	−1.05962	+	0.611772i	−0.134293	+	0.990942i	$0.542876\pi$
$822$		0			0
$823$	−137.084	−	79.1453i	−0.166566	−	0.0961669i	0.414400	−	0.910095i	$-0.363992\pi$
$823$	−137.084	−	79.1453i	−0.166566	−	0.0961669i	−0.580966	+	0.813928i	$0.697325\pi$
$824$		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	$-0.996447\pi$
$829$		−	18.5040i		−	0.0223209i	0.999938	−	0.0111604i	$-0.00355255\pi$
$830$		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	0.432868	−	0.901457i	$-0.357502\pi$
$839$	1199.76	−	692.681i	1.42999	−	0.825603i	0.997119	+	0.0758538i	$0.0241682\pi$
$840$		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	−0.445482	−	0.895291i	$-0.646968\pi$
$853$	91.3745	−	52.7551i	0.107121	−	0.0618466i	0.552604	+	0.833444i	$0.313634\pi$
$854$		0			0
$855$	616.588	−	243.948i	0.721156	−	0.285319i
$856$		0			0
$857$	−41.3561	−	71.6309i	−0.0482568	−	0.0835833i	0.840888	−	0.541209i	$-0.182033\pi$
$857$	−41.3561	−	71.6309i	−0.0482568	−	0.0835833i	−0.889145	+	0.457626i	$0.848700\pi$
$858$		0			0
$859$	−536.687	+	929.570i	−0.624782	+	1.08215i	0.363801	+	0.931477i	$0.381479\pi$
$859$	−536.687	+	929.570i	−0.624782	+	1.08215i	−0.988583	+	0.150677i	$0.951855\pi$
$860$		0			0
$861$	178.170	+	368.680i	0.206934	+	0.428199i
$862$		0			0
$863$			413.449i			0.479083i	0.970886	+	0.239542i	$0.0769971\pi$
$863$			413.449i			0.479083i	−0.970886	+	0.239542i	$0.923003\pi$
$864$		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	−0.0214489	−	0.999770i	$-0.506828\pi$
$877$	−787.546	−	454.690i	−0.898000	−	0.518460i	−0.876551	+	0.481310i	$0.840161\pi$
$878$		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	0.850686	−	0.525674i	$-0.176187\pi$
$887$	728.034	+	420.330i	0.820782	+	0.473879i	−0.0299041	+	0.999553i	$0.509520\pi$
$888$		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	0.880327	−	0.474368i	$-0.157323\pi$
$907$	26.6190	+	46.1055i	0.0293484	+	0.0508330i	−0.850978	+	0.525201i	$0.823990\pi$
$908$		0			0
$909$	−213.955	+	1446.42i	−0.235374	+	1.59122i
$910$		0			0
$911$	−1154.18	+	666.365i	−1.26694	+	0.731465i	−0.974407	−	0.224791i	$-0.927830\pi$
$911$	−1154.18	+	666.365i	−1.26694	+	0.731465i	−0.292528	+	0.956257i	$0.594497\pi$
$912$		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	$-0.707795\pi$
$919$		−	1460.07i		−	1.58876i	0.607419	−	0.794381i	$-0.292205\pi$
$920$		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	0.999377	−	0.0352963i	$-0.0112375\pi$
$929$	435.813	+	754.851i	0.469121	+	0.812541i	−0.530256	+	0.847838i	$0.677904\pi$
$930$		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	0.747989	−	0.663711i	$-0.231019\pi$
$941$	514.910	+	297.283i	0.547194	+	0.315923i	−0.200795	+	0.979633i	$0.564353\pi$
$942$		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	0.837224	+	0.546860i	$0.184177\pi$
$947$	844.920	+	1463.44i	0.892207	+	1.54535i	0.0549826	+	0.998487i	$0.482490\pi$
$948$		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	0.379479	−	0.925200i	$-0.376103\pi$
$967$	−224.372	−	129.541i	−0.232029	−	0.133962i	−0.611508	+	0.791239i	$0.709437\pi$
$968$		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	−0.757868	−	0.652408i	$-0.773759\pi$
$977$	181.789	−	314.867i	0.186068	−	0.322280i	0.943936	+	0.330129i	$0.107092\pi$
$978$		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	−0.745327	−	0.666699i	$-0.767707\pi$
$983$	−531.421	+	306.816i	−0.540612	+	0.312122i	0.204715	+	0.978822i	$0.434373\pi$
$984$		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	$-0.946571\pi$
$991$		−	331.121i		−	0.334128i	0.985946	−	0.167064i	$-0.0534286\pi$
$992$		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	−0.102897	−	0.994692i	$-0.532811\pi$
$997$	704.962	−	407.010i	0.707083	−	0.408234i	0.809980	+	0.586458i	$0.199478\pi$
$998$		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.31.4	✓	32
3.2	odd	2		1728.3.t.c.415.3		32
4.3	odd	2	inner	576.3.t.a.31.13	yes	32
8.3	odd	2		576.3.t.c.31.4	yes	32
8.5	even	2		576.3.t.c.31.13	yes	32
9.2	odd	6		1728.3.t.a.991.13		32
9.7	even	3		576.3.t.c.223.4	yes	32
12.11	even	2		1728.3.t.c.415.4		32
24.5	odd	2		1728.3.t.a.415.14		32
24.11	even	2		1728.3.t.a.415.13		32
36.7	odd	6		576.3.t.c.223.13	yes	32
36.11	even	6		1728.3.t.a.991.14		32
72.11	even	6		1728.3.t.c.991.3		32
72.29	odd	6		1728.3.t.c.991.4		32
72.43	odd	6	inner	576.3.t.a.223.4	yes	32
72.61	even	6	inner	576.3.t.a.223.13	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
576.3.t.a.31.4	✓	32	1.1	even	1	trivial
576.3.t.a.31.13	yes	32	4.3	odd	2	inner
576.3.t.a.223.4	yes	32	72.43	odd	6	inner
576.3.t.a.223.13	yes	32	72.61	even	6	inner
576.3.t.c.31.4	yes	32	8.3	odd	2
576.3.t.c.31.13	yes	32	8.5	even	2
576.3.t.c.223.4	yes	32	9.7	even	3
576.3.t.c.223.13	yes	32	36.7	odd	6
1728.3.t.a.415.13		32	24.11	even	2
1728.3.t.a.415.14		32	24.5	odd	2
1728.3.t.a.991.13		32	9.2	odd	6
1728.3.t.a.991.14		32	36.11	even	6
1728.3.t.c.415.3		32	3.2	odd	2
1728.3.t.c.415.4		32	12.11	even	2
1728.3.t.c.991.3		32	72.11	even	6
1728.3.t.c.991.4		32	72.29	odd	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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
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

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