LMFDB - Embedded newform 135.3.g.a.28.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,3,Mod(28,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("135.28");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	135.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.67848356886$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 217x^{12} + 9264x^{8} + 59497x^{4} + 28561 $ x^16 + 217x^12 + 9264x^8 + 59497*x^4 + 28561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			28.8
Root			$2.52312 - 2.52312i$ of defining polynomial
Character	$\chi$	$=$	135.28
Dual form			135.3.g.a.82.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.52312 - 2.52312i) q^{2} -8.73230i q^{4} +(-2.81400 - 4.13296i) q^{5} +(-4.39136 + 4.39136i) q^{7} +(-11.9402 - 11.9402i) q^{8} +O(q^{10})$	\(q+(2.52312 - 2.52312i) q^{2} -8.73230i q^{4} +(-2.81400 - 4.13296i) q^{5} +(-4.39136 + 4.39136i) q^{7} +(-11.9402 - 11.9402i) q^{8} +(-17.5280 - 3.32790i) q^{10} +20.6606 q^{11} +(4.07650 + 4.07650i) q^{13} +22.1599i q^{14} -25.3238 q^{16} +(3.85449 - 3.85449i) q^{17} -18.4907i q^{19} +(-36.0903 + 24.5727i) q^{20} +(52.1293 - 52.1293i) q^{22} +(14.1766 + 14.1766i) q^{23} +(-9.16277 + 23.2603i) q^{25} +20.5710 q^{26} +(38.3466 + 38.3466i) q^{28} +10.6404i q^{29} -33.1465 q^{31} +(-16.1344 + 16.1344i) q^{32} -19.4507i q^{34} +(30.5066 + 5.79202i) q^{35} +(-35.8023 + 35.8023i) q^{37} +(-46.6542 - 46.6542i) q^{38} +(-15.7486 + 82.9479i) q^{40} -12.0583 q^{41} +(35.5972 + 35.5972i) q^{43} -180.415i q^{44} +71.5385 q^{46} +(-0.615624 + 0.615624i) q^{47} +10.4320i q^{49} +(35.5699 + 81.8075i) q^{50} +(35.5972 - 35.5972i) q^{52} +(11.6767 + 11.6767i) q^{53} +(-58.1391 - 85.3897i) q^{55} +104.867 q^{56} +(26.8470 + 26.8470i) q^{58} -84.1251i q^{59} +69.7745 q^{61} +(-83.6326 + 83.6326i) q^{62} -19.8770i q^{64} +(5.37674 - 28.3193i) q^{65} +(-38.4564 + 38.4564i) q^{67} +(-33.6586 - 33.6586i) q^{68} +(91.5859 - 62.3579i) q^{70} -107.003 q^{71} +(8.17407 + 8.17407i) q^{73} +180.667i q^{74} -161.466 q^{76} +(-90.7282 + 90.7282i) q^{77} +73.0992i q^{79} +(71.2613 + 104.662i) q^{80} +(-30.4246 + 30.4246i) q^{82} +(-4.18896 - 4.18896i) q^{83} +(-26.7770 - 5.08392i) q^{85} +179.632 q^{86} +(-246.691 - 246.691i) q^{88} -6.20731i q^{89} -35.8027 q^{91} +(123.794 - 123.794i) q^{92} +3.10659i q^{94} +(-76.4213 + 52.0328i) q^{95} +(-54.9464 + 54.9464i) q^{97} +(26.3212 + 26.3212i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} - 32 q^{10} + 28 q^{13} - 20 q^{16} + 176 q^{22} + 64 q^{25} + 80 q^{28} - 208 q^{31} - 176 q^{37} - 252 q^{40} - 188 q^{43} + 188 q^{46} - 188 q^{52} - 136 q^{55} + 504 q^{58} + 296 q^{61} + 304 q^{67} + 684 q^{70} - 56 q^{73} - 732 q^{76} - 76 q^{82} - 788 q^{85} - 1128 q^{88} + 200 q^{91} - 284 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 - 32 * q^10 + 28 * q^13 - 20 * q^16 + 176 * q^22 + 64 * q^25 + 80 * q^28 - 208 * q^31 - 176 * q^37 - 252 * q^40 - 188 * q^43 + 188 * q^46 - 188 * q^52 - 136 * q^55 + 504 * q^58 + 296 * q^61 + 304 * q^67 + 684 * q^70 - 56 * q^73 - 732 * q^76 - 76 * q^82 - 788 * q^85 - 1128 * q^88 + 200 * q^91 - 284 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$56$	$82$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	2.52312	−	2.52312i	1.26156	−	1.26156i	0.311225	−	0.950336i	$-0.399261\pi$
$2$	2.52312	−	2.52312i	1.26156	−	1.26156i	0.950336	−	0.311225i	$-0.100739\pi$
$3$		0			0
$3$		0			0
$4$		−	8.73230i		−	2.18307i
$5$	−2.81400	−	4.13296i	−0.562801	−	0.826593i
$5$	−2.81400	−	4.13296i	−0.562801	−	0.826593i
$6$		0			0
$7$	−4.39136	+	4.39136i	−0.627337	+	0.627337i	−0.947397	−	0.320061i	$-0.896297\pi$
$7$	−4.39136	+	4.39136i	−0.627337	+	0.627337i	0.320061	+	0.947397i	$0.396297\pi$
$8$	−11.9402	−	11.9402i	−1.49252	−	1.49252i
$9$		0			0
$10$	−17.5280	−	3.32790i	−1.75280	−	0.332790i
$11$	20.6606			1.87824			0.939120	−	0.343589i	$-0.111643\pi$
$11$	20.6606			1.87824			0.939120	+	0.343589i	$0.111643\pi$
$12$		0			0
$13$	4.07650	+	4.07650i	0.313577	+	0.313577i	0.846294	−	0.532717i	$-0.178829\pi$
$13$	4.07650	+	4.07650i	0.313577	+	0.313577i	−0.532717	+	0.846294i	$0.678829\pi$
$14$			22.1599i			1.58285i
$15$		0			0
$16$	−25.3238			−1.58274
$17$	3.85449	−	3.85449i	0.226735	−	0.226735i	−0.584592	−	0.811327i	$-0.698746\pi$
$17$	3.85449	−	3.85449i	0.226735	−	0.226735i	0.811327	+	0.584592i	$0.198746\pi$
$18$		0			0
$19$		−	18.4907i		−	0.973193i	−0.873627	−	0.486597i	$-0.838238\pi$
$19$		−	18.4907i		−	0.973193i	0.873627	−	0.486597i	$-0.161762\pi$
$20$	−36.0903	+	24.5727i	−1.80451	+	1.22864i
$21$		0			0
$22$	52.1293	−	52.1293i	2.36952	−	2.36952i
$23$	14.1766	+	14.1766i	0.616373	+	0.616373i	0.944599	−	0.328226i	$-0.106451\pi$
$23$	14.1766	+	14.1766i	0.616373	+	0.616373i	−0.328226	+	0.944599i	$0.606451\pi$
$24$		0			0
$25$	−9.16277	+	23.2603i	−0.366511	+	0.930414i
$26$	20.5710			0.791193
$27$		0			0
$28$	38.3466	+	38.3466i	1.36952	+	1.36952i
$29$			10.6404i			0.366910i	0.983028	+	0.183455i	$0.0587281\pi$
$29$			10.6404i			0.366910i	−0.983028	+	0.183455i	$0.941272\pi$
$30$		0			0
$31$	−33.1465			−1.06924			−0.534620	−	0.845092i	$-0.679545\pi$
$31$	−33.1465			−1.06924			−0.534620	+	0.845092i	$0.679545\pi$
$32$	−16.1344	+	16.1344i	−0.504200	+	0.504200i
$33$		0			0
$34$		−	19.4507i		−	0.572080i
$35$	30.5066	+	5.79202i	0.871617	+	0.165486i
$36$		0			0
$37$	−35.8023	+	35.8023i	−0.967629	+	0.967629i	−0.999492	−	0.0318634i	$-0.989856\pi$
$37$	−35.8023	+	35.8023i	−0.967629	+	0.967629i	0.0318634	+	0.999492i	$0.489856\pi$
$38$	−46.6542	−	46.6542i	−1.22774	−	1.22774i
$39$		0			0
$40$	−15.7486	+	82.9479i	−0.393715	+	2.07370i
$41$	−12.0583			−0.294106			−0.147053	−	0.989129i	$-0.546979\pi$
$41$	−12.0583			−0.294106			−0.147053	+	0.989129i	$0.546979\pi$
$42$		0			0
$43$	35.5972	+	35.5972i	0.827842	+	0.827842i	0.987218	−	0.159376i	$-0.0509483\pi$
$43$	35.5972	+	35.5972i	0.827842	+	0.827842i	−0.159376	+	0.987218i	$0.550948\pi$
$44$		−	180.415i		−	4.10034i
$45$		0			0
$46$	71.5385			1.55518
$47$	−0.615624	+	0.615624i	−0.0130984	+	0.0130984i	−0.713626	−	0.700527i	$-0.752948\pi$
$47$	−0.615624	+	0.615624i	−0.0130984	+	0.0130984i	0.700527	+	0.713626i	$0.252948\pi$
$48$		0			0
$49$			10.4320i			0.212898i
$50$	35.5699	+	81.8075i	0.711398	+	1.63615i
$51$		0			0
$52$	35.5972	−	35.5972i	0.684561	−	0.684561i
$53$	11.6767	+	11.6767i	0.220315	+	0.220315i	0.808631	−	0.588316i	$-0.200209\pi$
$53$	11.6767	+	11.6767i	0.220315	+	0.220315i	−0.588316	+	0.808631i	$0.700209\pi$
$54$		0			0
$55$	−58.1391	−	85.3897i	−1.05707	−	1.55254i
$56$	104.867			1.87263
$57$		0			0
$58$	26.8470	+	26.8470i	0.462879	+	0.462879i
$59$		−	84.1251i		−	1.42585i	−0.701241	−	0.712924i	$-0.747370\pi$
$59$		−	84.1251i		−	1.42585i	0.701241	−	0.712924i	$-0.252630\pi$
$60$		0			0
$61$	69.7745			1.14384			0.571922	−	0.820308i	$-0.306198\pi$
$61$	69.7745			1.14384			0.571922	+	0.820308i	$0.306198\pi$
$62$	−83.6326	+	83.6326i	−1.34891	+	1.34891i
$63$		0			0
$64$		−	19.8770i		−	0.310578i
$65$	5.37674	−	28.3193i	0.0827191	−	0.435681i
$66$		0			0
$67$	−38.4564	+	38.4564i	−0.573976	+	0.573976i	−0.933237	−	0.359261i	$-0.883029\pi$
$67$	−38.4564	+	38.4564i	−0.573976	+	0.573976i	0.359261	+	0.933237i	$0.383029\pi$
$68$	−33.6586	−	33.6586i	−0.494979	−	0.494979i
$69$		0			0
$70$	91.5859	−	62.3579i	1.30837	−	0.890827i
$71$	−107.003			−1.50709			−0.753543	−	0.657399i	$-0.771657\pi$
$71$	−107.003			−1.50709			−0.753543	+	0.657399i	$0.771657\pi$
$72$		0			0
$73$	8.17407	+	8.17407i	0.111974	+	0.111974i	0.760874	−	0.648900i	$-0.224771\pi$
$73$	8.17407	+	8.17407i	0.111974	+	0.111974i	−0.648900	+	0.760874i	$0.724771\pi$
$74$			180.667i			2.44145i
$75$		0			0
$76$	−161.466			−2.12455
$77$	−90.7282	+	90.7282i	−1.17829	+	1.17829i
$78$		0			0
$79$			73.0992i			0.925306i	0.886539	+	0.462653i	$0.153102\pi$
$79$			73.0992i			0.925306i	−0.886539	+	0.462653i	$0.846898\pi$
$80$	71.2613	+	104.662i	0.890766	+	1.30828i
$81$		0			0
$82$	−30.4246	+	30.4246i	−0.371032	+	0.371032i
$83$	−4.18896	−	4.18896i	−0.0504694	−	0.0504694i	0.681422	−	0.731891i	$-0.261362\pi$
$83$	−4.18896	−	4.18896i	−0.0504694	−	0.0504694i	−0.731891	+	0.681422i	$0.761362\pi$
$84$		0			0
$85$	−26.7770	−	5.08392i	−0.315024	−	0.0598109i
$86$	179.632			2.08875
$87$		0			0
$88$	−246.691	−	246.691i	−2.80331	−	2.80331i
$89$		−	6.20731i		−	0.0697451i	−0.999392	−	0.0348725i	$-0.988897\pi$
$89$		−	6.20731i		−	0.0697451i	0.999392	−	0.0348725i	$-0.0111025\pi$
$90$		0			0
$91$	−35.8027			−0.393436
$92$	123.794	−	123.794i	1.34559	−	1.34559i
$93$		0			0
$94$			3.10659i			0.0330488i
$95$	−76.4213	+	52.0328i	−0.804434	+	0.547714i
$96$		0			0
$97$	−54.9464	+	54.9464i	−0.566458	+	0.566458i	−0.931134	−	0.364677i	$-0.881180\pi$
$97$	−54.9464	+	54.9464i	−0.566458	+	0.566458i	0.364677	+	0.931134i	$0.381180\pi$
$98$	26.3212	+	26.3212i	0.268583	+	0.268583i
$99$		0			0
$100$	203.116	+	80.0120i	2.03116	+	0.800120i
$101$	28.8331			0.285476			0.142738	−	0.989760i	$-0.454409\pi$
$101$	28.8331			0.285476			0.142738	+	0.989760i	$0.454409\pi$
$102$		0			0
$103$	−53.8436	−	53.8436i	−0.522754	−	0.522754i	0.395648	−	0.918402i	$-0.370520\pi$
$103$	−53.8436	−	53.8436i	−0.522754	−	0.522754i	−0.918402	+	0.395648i	$0.870520\pi$
$104$		−	97.3481i		−	0.936039i
$105$		0			0
$106$	58.9235			0.555882
$107$	14.0751	−	14.0751i	0.131543	−	0.131543i	−0.638270	−	0.769813i	$-0.720350\pi$
$107$	14.0751	−	14.0751i	0.131543	−	0.131543i	0.769813	+	0.638270i	$0.220350\pi$
$108$		0			0
$109$		−	18.6923i		−	0.171489i	−0.996317	−	0.0857447i	$-0.972673\pi$
$109$		−	18.6923i		−	0.171489i	0.996317	−	0.0857447i	$-0.0273269\pi$
$110$	−362.141	−	68.7565i	−3.29219	−	0.625059i
$111$		0			0
$112$	111.206	−	111.206i	0.992909	−	0.992909i
$113$	−104.114	−	104.114i	−0.921362	−	0.921362i	0.0757641	−	0.997126i	$-0.475860\pi$
$113$	−104.114	−	104.114i	−0.921362	−	0.921362i	−0.997126	+	0.0757641i	$0.975860\pi$
$114$		0			0
$115$	18.6983	−	98.4842i	0.162594	−	0.856385i
$116$	92.9150			0.800991
$117$		0			0
$118$	−212.258	−	212.258i	−1.79880	−	1.79880i
$119$			33.8529i			0.284478i
$120$		0			0
$121$	305.862			2.52779
$122$	176.050	−	176.050i	1.44303	−	1.44303i
$123$		0			0
$124$			289.445i			2.33423i
$125$	121.918	−	27.5853i	0.975346	−	0.220682i
$126$		0			0
$127$	−37.9268	+	37.9268i	−0.298637	+	0.298637i	−0.840480	−	0.541843i	$-0.817727\pi$
$127$	−37.9268	+	37.9268i	−0.298637	+	0.298637i	0.541843	+	0.840480i	$0.317727\pi$
$128$	−114.690	−	114.690i	−0.896014	−	0.896014i
$129$		0			0
$130$	−57.8869	−	85.0192i	−0.445284	−	0.653994i
$131$	−65.4186			−0.499378			−0.249689	−	0.968326i	$-0.580328\pi$
$131$	−65.4186			−0.499378			−0.249689	+	0.968326i	$0.580328\pi$
$132$		0			0
$133$	81.1991	+	81.1991i	0.610520	+	0.610520i
$134$			194.060i			1.44821i
$135$		0			0
$136$	−92.0465			−0.676813
$137$	90.3791	−	90.3791i	0.659701	−	0.659701i	−0.295608	−	0.955309i	$-0.595522\pi$
$137$	90.3791	−	90.3791i	0.659701	−	0.659701i	0.955309	+	0.295608i	$0.0955222\pi$
$138$		0			0
$139$		−	247.432i		−	1.78008i	−0.455879	−	0.890042i	$-0.650675\pi$
$139$		−	247.432i		−	1.78008i	0.455879	−	0.890042i	$-0.349325\pi$
$140$	50.5777	−	266.393i	0.361269	−	1.90280i
$141$		0			0
$142$	−269.982	+	269.982i	−1.90128	+	1.90128i
$143$	84.2231	+	84.2231i	0.588972	+	0.588972i
$144$		0			0
$145$	43.9763	−	29.9421i	0.303285	−	0.206497i
$146$	41.2484			0.282523
$147$		0			0
$148$	312.636	+	312.636i	2.11241	+	2.11241i
$149$			22.9399i			0.153959i	0.997033	+	0.0769795i	$0.0245276\pi$
$149$			22.9399i			0.153959i	−0.997033	+	0.0769795i	$0.975472\pi$
$150$		0			0
$151$	−4.48158			−0.0296793			−0.0148397	−	0.999890i	$-0.504724\pi$
$151$	−4.48158			−0.0296793			−0.0148397	+	0.999890i	$0.504724\pi$
$152$	−220.782	+	220.782i	−1.45251	+	1.45251i
$153$		0			0
$154$			457.837i			2.97297i
$155$	93.2743	+	136.993i	0.601769	+	0.883827i
$156$		0			0
$157$	−130.611	+	130.611i	−0.831918	+	0.831918i	−0.987779	−	0.155861i	$-0.950185\pi$
$157$	−130.611	+	130.611i	−0.831918	+	0.831918i	0.155861	+	0.987779i	$0.450185\pi$
$158$	184.438	+	184.438i	1.16733	+	1.16733i
$159$		0			0
$160$	112.085	+	21.2806i	0.700533	+	0.133004i
$161$	−124.509			−0.773347
$162$		0			0
$163$	33.3255	+	33.3255i	0.204451	+	0.204451i	0.801904	−	0.597453i	$-0.203820\pi$
$163$	33.3255	+	33.3255i	0.204451	+	0.204451i	−0.597453	+	0.801904i	$0.703820\pi$
$164$			105.297i			0.642054i
$165$		0			0
$166$	−21.1385			−0.127341
$167$	−32.9436	+	32.9436i	−0.197267	+	0.197267i	−0.798827	−	0.601560i	$-0.794546\pi$
$167$	−32.9436	+	32.9436i	−0.197267	+	0.197267i	0.601560	+	0.798827i	$0.294546\pi$
$168$		0			0
$169$		−	135.764i		−	0.803339i
$170$	−80.3891	+	54.7344i	−0.472877	+	0.321967i
$171$		0			0
$172$	310.845	−	310.845i	1.80724	−	1.80724i
$173$	143.990	+	143.990i	0.832311	+	0.832311i	0.987832	−	0.155522i	$-0.0497059\pi$
$173$	143.990	+	143.990i	0.832311	+	0.832311i	−0.155522	+	0.987832i	$0.549706\pi$
$174$		0			0
$175$	−61.9075	−	142.381i	−0.353757	−	0.813608i
$176$	−523.206			−2.97276
$177$		0			0
$178$	−15.6618	−	15.6618i	−0.0879877	−	0.0879877i
$179$		−	151.248i		−	0.844962i	−0.906372	−	0.422481i	$-0.861159\pi$
$179$		−	151.248i		−	0.844962i	0.906372	−	0.422481i	$-0.138841\pi$
$180$		0			0
$181$	76.1404			0.420665			0.210333	−	0.977630i	$-0.432545\pi$
$181$	76.1404			0.420665			0.210333	+	0.977630i	$0.432545\pi$
$182$	−90.3346	+	90.3346i	−0.496344	+	0.496344i
$183$		0			0
$184$		−	338.541i		−	1.83990i
$185$	248.717	+	47.2218i	1.34442	+	0.255253i
$186$		0			0
$187$	79.6363	−	79.6363i	0.425863	−	0.425863i
$188$	5.37581	+	5.37581i	0.0285947	+	0.0285947i
$189$		0			0
$190$	−61.5351	+	324.105i	−0.323869	+	1.70582i
$191$	204.368			1.06999			0.534994	−	0.844856i	$-0.320314\pi$
$191$	204.368			1.06999			0.534994	+	0.844856i	$0.320314\pi$
$192$		0			0
$193$	206.929	+	206.929i	1.07217	+	1.07217i	0.997185	+	0.0749840i	$0.0238906\pi$
$193$	206.929	+	206.929i	1.07217	+	1.07217i	0.0749840	+	0.997185i	$0.476109\pi$
$194$			277.273i			1.42924i
$195$		0			0
$196$	91.0952			0.464771
$197$	−52.7467	+	52.7467i	−0.267750	+	0.267750i	−0.828193	−	0.560443i	$-0.810631\pi$
$197$	−52.7467	+	52.7467i	−0.267750	+	0.267750i	0.560443	+	0.828193i	$0.310631\pi$
$198$		0			0
$199$		−	102.233i		−	0.513734i	−0.966447	−	0.256867i	$-0.917310\pi$
$199$		−	102.233i		−	0.513734i	0.966447	−	0.256867i	$-0.0826902\pi$
$200$	387.137	−	168.327i	1.93569	−	0.841636i
$201$		0			0
$202$	72.7494	−	72.7494i	0.360146	−	0.360146i
$203$	−46.7257	−	46.7257i	−0.230176	−	0.230176i
$204$		0			0
$205$	33.9322	+	49.8366i	0.165523	+	0.243105i
$206$	−271.708			−1.31897
$207$		0			0
$208$	−103.232	−	103.232i	−0.496310	−	0.496310i
$209$		−	382.029i		−	1.82789i
$210$		0			0
$211$	−140.544			−0.666085			−0.333042	−	0.942912i	$-0.608075\pi$
$211$	−140.544			−0.666085			−0.333042	+	0.942912i	$0.608075\pi$
$212$	101.964	−	101.964i	0.480964	−	0.480964i
$213$		0			0
$214$		−	71.0265i		−	0.331900i
$215$	46.9513	−	247.292i	0.218378	−	1.15020i
$216$		0			0
$217$	145.558	−	145.558i	0.670774	−	0.670774i
$218$	−47.1631	−	47.1631i	−0.216344	−	0.216344i
$219$		0			0
$220$	−745.648	+	507.688i	−3.38931	+	2.30767i
$221$	31.4257			0.142198
$222$		0			0
$223$	−249.385	−	249.385i	−1.11832	−	1.11832i	−0.991988	−	0.126331i	$-0.959680\pi$
$223$	−249.385	−	249.385i	−1.11832	−	1.11832i	−0.126331	−	0.991988i	$-0.540320\pi$
$224$		−	141.704i		−	0.632607i
$225$		0			0
$226$	−525.384			−2.32471
$227$	−180.115	+	180.115i	−0.793456	+	0.793456i	−0.982054	−	0.188598i	$-0.939606\pi$
$227$	−180.115	+	180.115i	−0.793456	+	0.793456i	0.188598	+	0.982054i	$0.439606\pi$
$228$		0			0
$229$			308.106i			1.34544i	0.739897	+	0.672720i	$0.234874\pi$
$229$			308.106i			1.34544i	−0.739897	+	0.672720i	$0.765126\pi$
$230$	−201.310	−	295.666i	−0.875259	−	1.28550i
$231$		0			0
$232$	127.048	−	127.048i	0.547620	−	0.547620i
$233$	278.738	+	278.738i	1.19630	+	1.19630i	0.975266	+	0.221033i	$0.0709429\pi$
$233$	278.738	+	278.738i	1.19630	+	1.19630i	0.221033	+	0.975266i	$0.429057\pi$
$234$		0			0
$235$	4.27672	+	0.811984i	0.0181988	+	0.00345525i
$236$	−734.605			−3.11273
$237$		0			0
$238$	85.4150	+	85.4150i	0.358887	+	0.358887i
$239$		−	392.788i		−	1.64346i	−0.569875	−	0.821732i	$-0.693008\pi$
$239$		−	392.788i		−	1.64346i	0.569875	−	0.821732i	$-0.306992\pi$
$240$		0			0
$241$	−124.433			−0.516321			−0.258160	−	0.966102i	$-0.583116\pi$
$241$	−124.433			−0.516321			−0.258160	+	0.966102i	$0.583116\pi$
$242$	771.728	−	771.728i	3.18896	−	3.18896i
$243$		0			0
$244$		−	609.292i		−	2.49710i
$245$	43.1150	−	29.3556i	0.175980	−	0.119819i
$246$		0			0
$247$	75.3772	−	75.3772i	0.305171	−	0.305171i
$248$	395.774	+	395.774i	1.59586	+	1.59586i
$249$		0			0
$250$	238.014	−	377.216i	0.952054	−	1.50886i
$251$	11.9714			0.0476946			0.0238473	−	0.999716i	$-0.492408\pi$
$251$	11.9714			0.0476946			0.0238473	+	0.999716i	$0.492408\pi$
$252$		0			0
$253$	292.897	+	292.897i	1.15770	+	1.15770i
$254$			191.388i			0.753497i
$255$		0			0
$256$	−499.245			−1.95017
$257$	−212.404	+	212.404i	−0.826473	+	0.826473i	−0.987027	−	0.160554i	$-0.948672\pi$
$257$	−212.404	+	212.404i	−0.826473	+	0.826473i	0.160554	+	0.987027i	$0.448672\pi$
$258$		0			0
$259$		−	314.441i		−	1.21406i
$260$	−247.292	−	46.9513i	−0.951125	−	0.180582i
$261$		0			0
$262$	−165.059	+	165.059i	−0.629997	+	0.629997i
$263$	−2.21097	−	2.21097i	−0.00840674	−	0.00840674i	0.702891	−	0.711298i	$-0.251892\pi$
$263$	−2.21097	−	2.21097i	−0.00840674	−	0.00840674i	−0.711298	+	0.702891i	$0.751892\pi$
$264$		0			0
$265$	15.4011	−	81.1177i	0.0581174	−	0.306104i
$266$	409.751			1.54042
$267$		0			0
$268$	335.813	+	335.813i	1.25303	+	1.25303i
$269$			441.324i			1.64061i	0.571927	+	0.820304i	$0.306196\pi$
$269$			441.324i			1.64061i	−0.571927	+	0.820304i	$0.693804\pi$
$270$		0			0
$271$	395.437			1.45918			0.729589	−	0.683886i	$-0.239711\pi$
$271$	395.437			1.45918			0.729589	+	0.683886i	$0.239711\pi$
$272$	−97.6104	+	97.6104i	−0.358862	+	0.358862i
$273$		0			0
$274$		−	456.075i		−	1.66451i
$275$	−189.309	+	480.574i	−0.688396	+	1.74754i
$276$		0			0
$277$	95.1449	−	95.1449i	0.343483	−	0.343483i	−0.514192	−	0.857675i	$-0.671908\pi$
$277$	95.1449	−	95.1449i	0.343483	−	0.343483i	0.857675	+	0.514192i	$0.171908\pi$
$278$	−624.300	−	624.300i	−2.24568	−	2.24568i
$279$		0			0
$280$	−295.096	−	433.411i	−1.05391	−	1.54790i
$281$	−387.164			−1.37781			−0.688904	−	0.724853i	$-0.741908\pi$
$281$	−387.164			−1.37781			−0.688904	+	0.724853i	$0.741908\pi$
$282$		0			0
$283$	−39.1743	−	39.1743i	−0.138425	−	0.138425i	0.634499	−	0.772924i	$-0.281207\pi$
$283$	−39.1743	−	39.1743i	−0.138425	−	0.138425i	−0.772924	+	0.634499i	$0.781207\pi$
$284$			934.382i			3.29008i
$285$		0			0
$286$	425.010			1.48605
$287$	52.9524	−	52.9524i	0.184503	−	0.184503i
$288$		0			0
$289$			259.286i			0.897183i
$290$	35.4101	−	186.505i	0.122104	−	0.643122i
$291$		0			0
$292$	71.3784	−	71.3784i	0.244447	−	0.244447i
$293$	−310.954	−	310.954i	−1.06128	−	1.06128i	−0.997996	−	0.0632822i	$-0.979843\pi$
$293$	−310.954	−	310.954i	−1.06128	−	1.06128i	−0.0632822	−	0.997996i	$-0.520157\pi$
$294$		0			0
$295$	−347.686	+	236.728i	−1.17860	+	0.802469i
$296$	854.970			2.88841
$297$		0			0
$298$	57.8802	+	57.8802i	0.194229	+	0.194229i
$299$			115.582i			0.386561i
$300$		0			0
$301$	−312.640			−1.03867
$302$	−11.3076	+	11.3076i	−0.0374423	+	0.0374423i
$303$		0			0
$304$			468.254i			1.54031i
$305$	−196.346	−	288.376i	−0.643756	−	0.945494i
$306$		0			0
$307$	−352.515	+	352.515i	−1.14826	+	1.14826i	−0.161361	+	0.986895i	$0.551588\pi$
$307$	−352.515	+	352.515i	−1.14826	+	1.14826i	−0.986895	+	0.161361i	$0.948412\pi$
$308$	792.266	+	792.266i	2.57229	+	2.57229i
$309$		0			0
$310$	580.993	+	110.308i	1.87417	+	0.355833i
$311$	191.198			0.614786			0.307393	−	0.951583i	$-0.400543\pi$
$311$	191.198			0.614786			0.307393	+	0.951583i	$0.400543\pi$
$312$		0			0
$313$	−152.885	−	152.885i	−0.488450	−	0.488450i	0.419367	−	0.907817i	$-0.362252\pi$
$313$	−152.885	−	152.885i	−0.488450	−	0.488450i	−0.907817	+	0.419367i	$0.862252\pi$
$314$			659.096i			2.09903i
$315$		0			0
$316$	638.324			2.02001
$317$	96.0449	−	96.0449i	0.302981	−	0.302981i	−0.539198	−	0.842179i	$-0.681273\pi$
$317$	96.0449	−	96.0449i	0.302981	−	0.302981i	0.842179	+	0.539198i	$0.181273\pi$
$318$		0			0
$319$			219.837i			0.689145i
$320$	−82.1510	+	55.9340i	−0.256722	+	0.174794i
$321$		0			0
$322$	−314.151	+	314.151i	−0.975624	+	0.975624i
$323$	−71.2722	−	71.2722i	−0.220657	−	0.220657i
$324$		0			0
$325$	−132.173	+	57.4687i	−0.406685	+	0.176827i
$326$	168.169			0.515855
$327$		0			0
$328$	143.978	+	143.978i	0.438958	+	0.438958i
$329$		−	5.40685i		−	0.0164342i
$330$		0			0
$331$	−371.750			−1.12311			−0.561556	−	0.827439i	$-0.689797\pi$
$331$	−371.750			−1.12311			−0.561556	+	0.827439i	$0.689797\pi$
$332$	−36.5792	+	36.5792i	−0.110178	+	0.110178i
$333$		0			0
$334$			166.242i			0.497729i
$335$	267.155	+	50.7225i	0.797478	+	0.151410i
$336$		0			0
$337$	362.115	−	362.115i	1.07452	−	1.07452i	0.0775344	−	0.996990i	$-0.475295\pi$
$337$	362.115	−	362.115i	1.07452	−	1.07452i	0.996990	−	0.0775344i	$-0.0247048\pi$
$338$	−342.550	−	342.550i	−1.01346	−	1.01346i
$339$		0			0
$340$	−44.3943	+	233.825i	−0.130572	+	0.687720i
$341$	−684.827			−2.00829
$342$		0			0
$343$	−260.987	−	260.987i	−0.760895	−	0.760895i
$344$		−	850.072i		−	2.47114i
$345$		0			0
$346$	726.608			2.10002
$347$	20.8181	−	20.8181i	0.0599945	−	0.0599945i	−0.676473	−	0.736467i	$-0.736492\pi$
$347$	20.8181	−	20.8181i	0.0599945	−	0.0599945i	0.736467	+	0.676473i	$0.236492\pi$
$348$		0			0
$349$			443.992i			1.27218i	0.771613	+	0.636092i	$0.219450\pi$
$349$			443.992i			1.27218i	−0.771613	+	0.636092i	$0.780550\pi$
$350$	−515.446	−	203.046i	−1.47270	−	0.580131i
$351$		0			0
$352$	−333.347	+	333.347i	−0.947009	+	0.947009i
$353$	−134.580	−	134.580i	−0.381248	−	0.381248i	0.490304	−	0.871552i	$-0.336886\pi$
$353$	−134.580	−	134.580i	−0.381248	−	0.381248i	−0.871552	+	0.490304i	$0.836886\pi$
$354$		0			0
$355$	301.107	+	442.240i	0.848189	+	1.24575i
$356$	−54.2041			−0.152259
$357$		0			0
$358$	−381.618	−	381.618i	−1.06597	−	1.06597i
$359$		−	216.292i		−	0.602484i	−0.953548	−	0.301242i	$-0.902599\pi$
$359$		−	216.292i		−	0.602484i	0.953548	−	0.301242i	$-0.0974011\pi$
$360$		0			0
$361$	19.0951			0.0528949
$362$	192.112	−	192.112i	0.530695	−	0.530695i
$363$		0			0
$364$			312.640i			0.858901i
$365$	10.7813	−	56.7850i	0.0295377	−	0.155575i
$366$		0			0
$367$	242.834	−	242.834i	0.661673	−	0.661673i	−0.294102	−	0.955774i	$-0.595020\pi$
$367$	242.834	−	242.834i	0.661673	−	0.661673i	0.955774	+	0.294102i	$0.0950204\pi$
$368$	−359.005	−	359.005i	−0.975557	−	0.975557i
$369$		0			0
$370$	746.690	−	508.398i	2.01808	−	1.37405i
$371$	−102.553			−0.276423
$372$		0			0
$373$	−415.397	−	415.397i	−1.11366	−	1.11366i	−0.992651	−	0.121013i	$-0.961386\pi$
$373$	−415.397	−	415.397i	−1.11366	−	1.11366i	−0.121013	−	0.992651i	$-0.538614\pi$
$374$		−	401.864i		−	1.07450i
$375$		0			0
$376$	14.7013			0.0390992
$377$	−43.3755	+	43.3755i	−0.115054	+	0.115054i
$378$		0			0
$379$		−	87.8194i		−	0.231713i	−0.993266	−	0.115857i	$-0.963039\pi$
$379$		−	87.8194i		−	0.231713i	0.993266	−	0.115857i	$-0.0369613\pi$
$380$	454.366	+	667.333i	1.19570	+	1.75614i
$381$		0			0
$382$	515.645	−	515.645i	1.34986	−	1.34986i
$383$	157.427	+	157.427i	0.411038	+	0.411038i	0.882100	−	0.471062i	$-0.156129\pi$
$383$	157.427	+	157.427i	0.411038	+	0.411038i	−0.471062	+	0.882100i	$0.656129\pi$
$384$		0			0
$385$	630.286	+	119.667i	1.63711	+	0.310823i
$386$	1044.21			2.70521
$387$		0			0
$388$	479.808	+	479.808i	1.23662	+	1.23662i
$389$		−	506.212i		−	1.30132i	−0.759370	−	0.650659i	$-0.774493\pi$
$389$		−	506.212i		−	1.30132i	0.759370	−	0.650659i	$-0.225507\pi$
$390$		0			0
$391$	109.287			0.279507
$392$	124.560	−	124.560i	0.317754	−	0.317754i
$393$		0			0
$394$			266.173i			0.675566i
$395$	302.116	−	205.701i	0.764851	−	0.520763i
$396$		0			0
$397$	−434.470	+	434.470i	−1.09438	+	1.09438i	−0.0993269	+	0.995055i	$0.531669\pi$
$397$	−434.470	+	434.470i	−1.09438	+	1.09438i	−0.995055	+	0.0993269i	$0.968331\pi$
$398$	−257.946	−	257.946i	−0.648107	−	0.648107i
$399$		0			0
$400$	232.036	−	589.040i	0.580091	−	1.47260i
$401$	378.912			0.944918			0.472459	−	0.881353i	$-0.343367\pi$
$401$	378.912			0.944918			0.472459	+	0.881353i	$0.343367\pi$
$402$		0			0
$403$	−135.122	−	135.122i	−0.335289	−	0.335289i
$404$		−	251.779i		−	0.623216i
$405$		0			0
$406$	−235.790			−0.580762
$407$	−739.698	+	739.698i	−1.81744	+	1.81744i
$408$		0			0
$409$		−	136.322i		−	0.333305i	−0.986016	−	0.166652i	$-0.946704\pi$
$409$		−	136.322i		−	0.333305i	0.986016	−	0.166652i	$-0.0532958\pi$
$410$	211.359	+	40.1289i	0.515510	+	0.0978753i
$411$		0			0
$412$	−470.179	+	470.179i	−1.14121	+	1.14121i
$413$	369.423	+	369.423i	0.894487	+	0.894487i
$414$		0			0
$415$	−5.52507	+	29.1006i	−0.0133134	+	0.0701219i
$416$	−131.544			−0.316211
$417$		0			0
$418$	−963.906	−	963.906i	−2.30600	−	2.30600i
$419$		−	396.260i		−	0.945728i	−0.881136	−	0.472864i	$-0.843220\pi$
$419$		−	396.260i		−	0.945728i	0.881136	−	0.472864i	$-0.156780\pi$
$420$		0			0
$421$	−606.586			−1.44082			−0.720410	−	0.693548i	$-0.756046\pi$
$421$	−606.586			−1.44082			−0.720410	+	0.693548i	$0.756046\pi$
$422$	−354.609	+	354.609i	−0.840307	+	0.840307i
$423$		0			0
$424$		−	278.843i		−	0.657650i
$425$	54.3390	+	124.975i	0.127856	+	0.294058i
$426$		0			0
$427$	−306.405	+	306.405i	−0.717576	+	0.717576i
$428$	−122.908	−	122.908i	−0.287168	−	0.287168i
$429$		0			0
$430$	−505.485	−	742.413i	−1.17555	−	1.72654i
$431$	−137.454			−0.318920			−0.159460	−	0.987204i	$-0.550975\pi$
$431$	−137.454			−0.318920			−0.159460	+	0.987204i	$0.550975\pi$
$432$		0			0
$433$	101.718	+	101.718i	0.234915	+	0.234915i	0.814740	−	0.579826i	$-0.196879\pi$
$433$	101.718	+	101.718i	0.234915	+	0.234915i	−0.579826	+	0.814740i	$0.696879\pi$
$434$		−	734.521i		−	1.69244i
$435$		0			0
$436$	−163.227			−0.374374
$437$	262.134	−	262.134i	0.599850	−	0.599850i
$438$		0			0
$439$			818.214i			1.86381i	0.362700	+	0.931906i	$0.381855\pi$
$439$			818.214i			1.86381i	−0.362700	+	0.931906i	$0.618145\pi$
$440$	−325.376	+	1713.76i	−0.739491	+	3.89490i
$441$		0			0
$442$	79.2908	−	79.2908i	0.179391	−	0.179391i
$443$	−131.035	−	131.035i	−0.295789	−	0.295789i	0.543573	−	0.839362i	$-0.317071\pi$
$443$	−131.035	−	131.035i	−0.295789	−	0.295789i	−0.839362	+	0.543573i	$0.817071\pi$
$444$		0			0
$445$	−25.6546	+	17.4674i	−0.0576508	+	0.0392526i
$446$	−1258.46			−2.82166
$447$		0			0
$448$	87.2871	+	87.2871i	0.194837	+	0.194837i
$449$			548.270i			1.22109i	0.791981	+	0.610546i	$0.209050\pi$
$449$			548.270i			1.22109i	−0.791981	+	0.610546i	$0.790950\pi$
$450$		0			0
$451$	−249.133			−0.552401
$452$	−909.153	+	909.153i	−2.01140	+	2.01140i
$453$		0			0
$454$			908.902i			2.00199i
$455$	100.749	+	147.971i	0.221426	+	0.325212i
$456$		0			0
$457$	248.434	−	248.434i	0.543620	−	0.543620i	−0.380968	−	0.924588i	$-0.624409\pi$
$457$	248.434	−	248.434i	0.543620	−	0.543620i	0.924588	+	0.380968i	$0.124409\pi$
$458$	777.389	+	777.389i	1.69736	+	1.69736i
$459$		0			0
$460$	−859.993	−	163.279i	−1.86955	−	0.354955i
$461$	149.391			0.324060			0.162030	−	0.986786i	$-0.448196\pi$
$461$	149.391			0.324060			0.162030	+	0.986786i	$0.448196\pi$
$462$		0			0
$463$	352.014	+	352.014i	0.760289	+	0.760289i	0.976374	−	0.216085i	$-0.0693289\pi$
$463$	352.014	+	352.014i	0.760289	+	0.760289i	−0.216085	+	0.976374i	$0.569329\pi$
$464$		−	269.455i		−	0.580722i
$465$		0			0
$466$	1406.58			3.01841
$467$	439.025	−	439.025i	0.940095	−	0.940095i	−0.0582090	−	0.998304i	$-0.518539\pi$
$467$	439.025	−	439.025i	0.940095	−	0.940095i	0.998304	+	0.0582090i	$0.0185390\pi$
$468$		0			0
$469$		−	337.751i		−	0.720152i
$470$	12.8394	−	8.74196i	0.0273179	−	0.0185999i
$471$		0			0
$472$	−1004.47	+	1004.47i	−2.12811	+	2.12811i
$473$	735.461	+	735.461i	1.55489	+	1.55489i
$474$		0			0
$475$	430.099	+	169.426i	0.905472	+	0.356686i
$476$	295.614			0.621037
$477$		0			0
$478$	−991.051	−	991.051i	−2.07333	−	2.07333i
$479$			292.967i			0.611622i	0.952092	+	0.305811i	$0.0989275\pi$
$479$			292.967i			0.611622i	−0.952092	+	0.305811i	$0.901073\pi$
$480$		0			0
$481$	−291.896			−0.606852
$482$	−313.961	+	313.961i	−0.651370	+	0.651370i
$483$		0			0
$484$		−	2670.88i		−	5.51834i
$485$	381.711	+	72.4721i	0.787033	+	0.149427i
$486$		0			0
$487$	542.274	−	542.274i	1.11350	−	1.11350i	0.120824	−	0.992674i	$-0.461446\pi$
$487$	542.274	−	542.274i	1.11350	−	1.11350i	0.992674	−	0.120824i	$-0.0385538\pi$
$488$	−833.119	−	833.119i	−1.70721	−	1.70721i
$489$		0			0
$490$	34.7166	−	182.852i	0.0708502	−	0.373168i
$491$	682.723			1.39048			0.695238	−	0.718780i	$-0.255299\pi$
$491$	682.723			1.39048			0.695238	+	0.718780i	$0.255299\pi$
$492$		0			0
$493$	41.0133	+	41.0133i	0.0831913	+	0.0831913i
$494$		−	380.372i		−	0.769983i
$495$		0			0
$496$	839.395			1.69233
$497$	469.889	−	469.889i	0.945450	−	0.945450i
$498$		0			0
$499$		−	410.186i		−	0.822016i	−0.911632	−	0.411008i	$-0.865177\pi$
$499$		−	410.186i		−	0.822016i	0.911632	−	0.411008i	$-0.134823\pi$
$500$	−240.883	−	1064.63i	−0.481765	−	2.12925i
$501$		0			0
$502$	30.2052	−	30.2052i	0.0601697	−	0.0601697i
$503$	−543.846	−	543.846i	−1.08120	−	1.08120i	−0.996397	−	0.0848064i	$-0.972973\pi$
$503$	−543.846	−	543.846i	−1.08120	−	1.08120i	−0.0848064	−	0.996397i	$-0.527027\pi$
$504$		0			0
$505$	−81.1364	−	119.166i	−0.160666	−	0.235973i
$506$	1478.03			2.92101
$507$		0			0
$508$	331.188	+	331.188i	0.651946	+	0.651946i
$509$			117.094i			0.230047i	0.993363	+	0.115024i	$0.0366944\pi$
$509$			117.094i			0.230047i	−0.993363	+	0.115024i	$0.963306\pi$
$510$		0			0
$511$	−71.7905			−0.140490
$512$	−800.897	+	800.897i	−1.56425	+	1.56425i
$513$		0			0
$514$			1071.84i			2.08529i
$515$	−71.0176	+	374.050i	−0.137898	+	0.726311i
$516$		0			0
$517$	−12.7192	+	12.7192i	−0.0246019	+	0.0246019i
$518$	−793.373	−	793.373i	−1.53161	−	1.53161i
$519$		0			0
$520$	−402.336	+	273.938i	−0.773723	+	0.526804i
$521$	−400.865			−0.769414			−0.384707	−	0.923039i	$-0.625698\pi$
$521$	−400.865			−0.769414			−0.384707	+	0.923039i	$0.625698\pi$
$522$		0			0
$523$	−212.510	−	212.510i	−0.406330	−	0.406330i	0.474127	−	0.880457i	$-0.342764\pi$
$523$	−212.510	−	212.510i	−0.406330	−	0.406330i	−0.880457	+	0.474127i	$0.842764\pi$
$524$			571.254i			1.09018i
$525$		0			0
$526$	−11.1571			−0.0212112
$527$	−127.763	+	127.763i	−0.242434	+	0.242434i
$528$		0			0
$529$		−	127.049i		−	0.240169i
$530$	−165.811	−	243.529i	−0.312851	−	0.459488i
$531$		0			0
$532$	709.055	−	709.055i	1.33281	−	1.33281i
$533$	−49.1557	−	49.1557i	−0.0922247	−	0.0922247i
$534$		0			0
$535$	−97.7794	−	18.5645i	−0.182765	−	0.0347000i
$536$	918.351			1.71334
$537$		0			0
$538$	1113.51	+	1113.51i	2.06973	+	2.06973i
$539$			215.531i			0.399873i
$540$		0			0
$541$	−253.010			−0.467671			−0.233836	−	0.972276i	$-0.575128\pi$
$541$	−253.010			−0.467671			−0.233836	+	0.972276i	$0.575128\pi$
$542$	997.737	−	997.737i	1.84084	−	1.84084i
$543$		0			0
$544$			124.380i			0.228640i
$545$	−77.2548	+	52.6003i	−0.141752	+	0.0965143i
$546$		0			0
$547$	549.424	−	549.424i	1.00443	−	1.00443i	0.00444067	−	0.999990i	$-0.498586\pi$
$547$	549.424	−	549.424i	1.00443	−	1.00443i	0.999990	−	0.00444067i	$-0.00141351\pi$
$548$	−789.217	−	789.217i	−1.44018	−	1.44018i
$549$		0			0
$550$	734.897	+	1690.20i	1.33618	+	3.07308i
$551$	196.748			0.357074
$552$		0			0
$553$	−321.004	−	321.004i	−0.580478	−	0.580478i
$554$		−	480.124i		−	0.866651i
$555$		0			0
$556$	−2160.65			−3.88605
$557$	488.571	−	488.571i	0.877147	−	0.877147i	−0.116091	−	0.993239i	$-0.537037\pi$
$557$	488.571	−	488.571i	0.877147	−	0.877147i	0.993239	+	0.116091i	$0.0370365\pi$
$558$		0			0
$559$			290.224i			0.519184i
$560$	−772.543	−	146.676i	−1.37954	−	0.261922i
$561$		0			0
$562$	−976.862	+	976.862i	−1.73819	+	1.73819i
$563$	−722.486	−	722.486i	−1.28328	−	1.28328i	−0.938790	−	0.344490i	$-0.888052\pi$
$563$	−722.486	−	722.486i	−1.28328	−	1.28328i	−0.344490	−	0.938790i	$-0.611948\pi$
$564$		0			0
$565$	−137.322	+	723.276i	−0.243048	+	1.28013i
$566$	−197.683			−0.349263
$567$		0			0
$568$	1277.63	+	1277.63i	2.24936	+	2.24936i
$569$		−	44.8358i		−	0.0787975i	−0.999224	−	0.0393987i	$-0.987456\pi$
$569$		−	44.8358i		−	0.0787975i	0.999224	−	0.0393987i	$-0.0125443\pi$
$570$		0			0
$571$	−117.428			−0.205653			−0.102826	−	0.994699i	$-0.532789\pi$
$571$	−117.428			−0.205653			−0.102826	+	0.994699i	$0.532789\pi$
$572$	735.461	−	735.461i	1.28577	−	1.28577i
$573$		0			0
$574$		−	267.211i		−	0.465524i
$575$	−459.649	+	199.855i	−0.799389	+	0.347574i
$576$		0			0
$577$	443.056	−	443.056i	0.767862	−	0.767862i	−0.209868	−	0.977730i	$-0.567303\pi$
$577$	443.056	−	443.056i	0.767862	−	0.767862i	0.977730	+	0.209868i	$0.0673034\pi$
$578$	654.210	+	654.210i	1.13185	+	1.13185i
$579$		0			0
$580$	−261.463	−	384.014i	−0.450799	−	0.662094i
$581$	36.7904			0.0633226
$582$		0			0
$583$	241.248	+	241.248i	0.413805	+	0.413805i
$584$		−	195.199i		−	0.334246i
$585$		0			0
$586$	−1569.15			−2.67773
$587$	182.831	−	182.831i	0.311468	−	0.311468i	−0.534010	−	0.845478i	$-0.679316\pi$
$587$	182.831	−	182.831i	0.311468	−	0.311468i	0.845478	+	0.534010i	$0.179316\pi$
$588$		0			0
$589$			612.900i			1.04058i
$590$	−279.960	+	1474.55i	−0.474508	+	2.49923i
$591$		0			0
$592$	906.649	−	906.649i	1.53150	−	1.53150i
$593$	545.602	+	545.602i	0.920071	+	0.920071i	0.997034	−	0.0769628i	$-0.0245223\pi$
$593$	545.602	+	545.602i	0.920071	+	0.920071i	−0.0769628	+	0.997034i	$0.524522\pi$
$594$		0			0
$595$	139.913	−	95.2622i	0.235148	−	0.160104i
$596$	200.318			0.336104
$597$		0			0
$598$	291.627	+	291.627i	0.487670	+	0.487670i
$599$		−	117.320i		−	0.195859i	−0.995193	−	0.0979296i	$-0.968778\pi$
$599$		−	117.320i		−	0.195859i	0.995193	−	0.0979296i	$-0.0312220\pi$
$600$		0			0
$601$	1000.71			1.66508			0.832540	−	0.553964i	$-0.186886\pi$
$601$	1000.71			1.66508			0.832540	+	0.553964i	$0.186886\pi$
$602$	−788.829	+	788.829i	−1.31035	+	1.31035i
$603$		0			0
$604$			39.1345i			0.0647922i
$605$	−860.697	−	1264.12i	−1.42264	−	2.08945i
$606$		0			0
$607$	320.716	−	320.716i	0.528362	−	0.528362i	−0.391721	−	0.920084i	$-0.628120\pi$
$607$	320.716	−	320.716i	0.528362	−	0.528362i	0.920084	+	0.391721i	$0.128120\pi$
$608$	298.336	+	298.336i	0.490684	+	0.490684i
$609$		0			0
$610$	−1223.01	−	232.203i	−2.00494	−	0.380660i
$611$	−5.01918			−0.00821470
$612$		0			0
$613$	−508.458	−	508.458i	−0.829459	−	0.829459i	0.157983	−	0.987442i	$-0.449501\pi$
$613$	−508.458	−	508.458i	−0.829459	−	0.829459i	−0.987442	+	0.157983i	$0.949501\pi$
$614$			1778.88i			2.89719i
$615$		0			0
$616$	2166.62			3.51724
$617$	−253.929	+	253.929i	−0.411555	+	0.411555i	−0.882280	−	0.470725i	$-0.843992\pi$
$617$	−253.929	+	253.929i	−0.411555	+	0.411555i	0.470725	+	0.882280i	$0.343992\pi$
$618$		0			0
$619$			430.073i			0.694787i	0.937719	+	0.347393i	$0.112933\pi$
$619$			430.073i			0.694787i	−0.937719	+	0.347393i	$0.887067\pi$
$620$	1196.26	−	814.498i	1.92946	−	1.31371i
$621$		0			0
$622$	482.417	−	482.417i	0.775590	−	0.775590i
$623$	27.2585	+	27.2585i	0.0437536	+	0.0437536i
$624$		0			0
$625$	−457.087	−	426.259i	−0.731339	−	0.682014i
$626$	−771.494			−1.23242
$627$		0			0
$628$	1140.53	+	1140.53i	1.81614	+	1.81614i
$629$			275.999i			0.438790i
$630$		0			0
$631$	−42.6090			−0.0675261			−0.0337631	−	0.999430i	$-0.510749\pi$
$631$	−42.6090			−0.0675261			−0.0337631	+	0.999430i	$0.510749\pi$
$632$	872.816	−	872.816i	1.38104	−	1.38104i
$633$		0			0
$634$		−	484.666i		−	0.764457i
$635$	263.477	+	50.0240i	0.414924	+	0.0787780i
$636$		0			0
$637$	−42.5260	+	42.5260i	−0.0667597	+	0.0667597i
$638$	554.676	+	554.676i	0.869399	+	0.869399i
$639$		0			0
$640$	−151.271	+	796.746i	−0.236361	+	1.24492i
$641$	−858.647			−1.33954			−0.669772	−	0.742567i	$-0.733608\pi$
$641$	−858.647			−1.33954			−0.669772	+	0.742567i	$0.733608\pi$
$642$		0			0
$643$	712.636	+	712.636i	1.10830	+	1.10830i	0.993374	+	0.114925i	$0.0366627\pi$
$643$	712.636	+	712.636i	1.10830	+	1.10830i	0.114925	+	0.993374i	$0.463337\pi$
$644$			1087.25i			1.68827i
$645$		0			0
$646$	−359.657			−0.556744
$647$	−509.877	+	509.877i	−0.788063	+	0.788063i	−0.981176	−	0.193113i	$-0.938141\pi$
$647$	−509.877	+	509.877i	−0.788063	+	0.788063i	0.193113	+	0.981176i	$0.438141\pi$
$648$		0			0
$649$		−	1738.08i		−	2.67809i
$650$	−188.487	+	478.489i	−0.289981	+	0.736137i
$651$		0			0
$652$	291.009	−	291.009i	0.446332	−	0.446332i
$653$	−37.4444	−	37.4444i	−0.0573422	−	0.0573422i	0.677854	−	0.735196i	$-0.262910\pi$
$653$	−37.4444	−	37.4444i	−0.0573422	−	0.0573422i	−0.735196	+	0.677854i	$0.762910\pi$
$654$		0			0
$655$	184.088	+	270.373i	0.281050	+	0.412783i
$656$	305.363			0.465492
$657$		0			0
$658$	−13.6421	−	13.6421i	−0.0207327	−	0.0207327i
$659$			830.172i			1.25975i	0.776698	+	0.629873i	$0.216893\pi$
$659$			830.172i			1.25975i	−0.776698	+	0.629873i	$0.783107\pi$
$660$		0			0
$661$	701.677			1.06154			0.530770	−	0.847516i	$-0.321903\pi$
$661$	701.677			1.06154			0.530770	+	0.847516i	$0.321903\pi$
$662$	−937.971	+	937.971i	−1.41687	+	1.41687i
$663$		0			0
$664$			100.034i			0.150653i
$665$	107.098	−	564.088i	0.161050	−	0.848252i
$666$		0			0
$667$	−150.844	+	150.844i	−0.226153	+	0.226153i
$668$	287.673	+	287.673i	0.430649	+	0.430649i
$669$		0			0
$670$	802.045	−	546.087i	1.19708	−	0.815055i
$671$	1441.59			2.14841
$672$		0			0
$673$	−364.264	−	364.264i	−0.541254	−	0.541254i	0.382642	−	0.923897i	$-0.375014\pi$
$673$	−364.264	−	364.264i	−0.541254	−	0.541254i	−0.923897	+	0.382642i	$0.875014\pi$
$674$		−	1827.32i		−	2.71116i
$675$		0			0
$676$	−1185.53			−1.75375
$677$	−378.986	+	378.986i	−0.559802	+	0.559802i	−0.929251	−	0.369449i	$-0.879547\pi$
$677$	−378.986	+	378.986i	−0.559802	+	0.559802i	0.369449	+	0.929251i	$0.379547\pi$
$678$		0			0
$679$		−	482.578i		−	0.710719i
$680$	259.019	+	380.425i	0.380911	+	0.559448i
$681$		0			0
$682$	−1727.90	+	1727.90i	−2.53358	+	2.53358i
$683$	−111.371	−	111.371i	−0.163061	−	0.163061i	0.620860	−	0.783921i	$-0.286784\pi$
$683$	−111.371	−	111.371i	−0.163061	−	0.163061i	−0.783921	+	0.620860i	$0.786784\pi$
$684$		0			0
$685$	−627.861	−	119.206i	−0.916585	−	0.174024i
$686$	−1317.00			−1.91983
$687$		0			0
$688$	−901.456	−	901.456i	−1.31026	−	1.31026i
$689$			95.2001i			0.138171i
$690$		0			0
$691$	681.088			0.985656			0.492828	−	0.870127i	$-0.335963\pi$
$691$	681.088			0.985656			0.492828	+	0.870127i	$0.335963\pi$
$692$	1257.36	−	1257.36i	1.81700	−	1.81700i
$693$		0			0
$694$		−	105.053i		−	0.151373i
$695$	−1022.63	+	696.273i	−1.47140	+	1.00183i
$696$		0			0
$697$	−46.4787	+	46.4787i	−0.0666840	+	0.0666840i
$698$	1120.25	+	1120.25i	1.60494	+	1.60494i
$699$		0			0
$700$	−1243.32	+	540.594i	−1.77617	+	0.772277i
$701$	−722.405			−1.03053			−0.515267	−	0.857030i	$-0.672307\pi$
$701$	−722.405			−1.03053			−0.515267	+	0.857030i	$0.672307\pi$
$702$		0			0
$703$	662.008	+	662.008i	0.941690	+	0.941690i
$704$		−	410.672i		−	0.583341i
$705$		0			0
$706$	−679.126			−0.961935
$707$	−126.616	+	126.616i	−0.179090	+	0.179090i
$708$		0			0
$709$		−	583.352i		−	0.822782i	−0.911459	−	0.411391i	$-0.865043\pi$
$709$		−	583.352i		−	0.822782i	0.911459	−	0.411391i	$-0.134957\pi$
$710$	1875.55	+	356.095i	2.64163	+	0.501543i
$711$		0			0
$712$	−74.1163	+	74.1163i	−0.104096	+	0.104096i
$713$	−469.904	−	469.904i	−0.659051	−	0.659051i
$714$		0			0
$715$	111.087	−	585.095i	0.155366	−	0.818314i
$716$	−1320.74			−1.84462
$717$		0			0
$718$	−545.730	−	545.730i	−0.760070	−	0.760070i
$719$		−	1116.43i		−	1.55276i	−0.630266	−	0.776379i	$-0.717054\pi$
$719$		−	1116.43i		−	1.55276i	0.630266	−	0.776379i	$-0.282946\pi$
$720$		0			0
$721$	472.893			0.655885
$722$	48.1792	−	48.1792i	0.0667301	−	0.0667301i
$723$		0			0
$724$		−	664.880i		−	0.918343i
$725$	−247.499	−	97.4955i	−0.341378	−	0.134477i
$726$		0			0
$727$	−297.676	+	297.676i	−0.409458	+	0.409458i	−0.881549	−	0.472092i	$-0.843499\pi$
$727$	−297.676	+	297.676i	−0.409458	+	0.409458i	0.472092	+	0.881549i	$0.343499\pi$
$728$	427.490	+	427.490i	0.587212	+	0.587212i
$729$		0			0
$730$	−116.073	−	170.478i	−0.159004	−	0.233531i
$731$	274.418			0.375401
$732$		0			0
$733$	−270.064	−	270.064i	−0.368437	−	0.368437i	0.498470	−	0.866907i	$-0.333895\pi$
$733$	−270.064	−	270.064i	−0.368437	−	0.368437i	−0.866907	+	0.498470i	$0.833895\pi$
$734$		−	1225.40i		−	1.66948i
$735$		0			0
$736$	−457.461			−0.621551
$737$	−794.534	+	794.534i	−1.07806	+	1.07806i
$738$		0			0
$739$			1406.06i			1.90266i	0.308177	+	0.951329i	$0.400281\pi$
$739$			1406.06i			1.90266i	−0.308177	+	0.951329i	$0.599719\pi$
$740$	412.354	−	2171.87i	0.557236	−	2.93496i
$741$		0			0
$742$	−258.754	+	258.754i	−0.348725	+	0.348725i
$743$	−135.249	−	135.249i	−0.182031	−	0.182031i	0.610209	−	0.792240i	$-0.291085\pi$
$743$	−135.249	−	135.249i	−0.182031	−	0.182031i	−0.792240	+	0.610209i	$0.791085\pi$
$744$		0			0
$745$	94.8098	−	64.5529i	0.127261	−	0.0866483i
$746$	−2096.19			−2.80991
$747$		0			0
$748$	−695.408	−	695.408i	−0.929689	−	0.929689i
$749$			123.618i			0.165044i
$750$		0			0
$751$	−115.124			−0.153294			−0.0766472	−	0.997058i	$-0.524422\pi$
$751$	−115.124			−0.153294			−0.0766472	+	0.997058i	$0.524422\pi$
$752$	15.5899	−	15.5899i	0.0207313	−	0.0207313i
$753$		0			0
$754$			218.884i			0.290296i
$755$	12.6112	+	18.5222i	0.0167035	+	0.0245327i
$756$		0			0
$757$	−737.945	+	737.945i	−0.974828	+	0.974828i	−0.999691	−	0.0248625i	$-0.992085\pi$
$757$	−737.945	+	737.945i	−0.974828	+	0.974828i	0.0248625	+	0.999691i	$0.492085\pi$
$758$	−221.579	−	221.579i	−0.292321	−	0.292321i
$759$		0			0
$760$	1533.76	+	291.202i	2.01811	+	0.383161i
$761$	−1011.38			−1.32902			−0.664509	−	0.747280i	$-0.731359\pi$
$761$	−1011.38			−1.32902			−0.664509	+	0.747280i	$0.731359\pi$
$762$		0			0
$763$	82.0847	+	82.0847i	0.107582	+	0.107582i
$764$		−	1784.60i		−	2.33586i
$765$		0			0
$766$	794.418			1.03710
$767$	342.936	−	342.936i	0.447113	−	0.447113i
$768$		0			0
$769$		−	653.574i		−	0.849901i	−0.905217	−	0.424950i	$-0.860292\pi$
$769$		−	653.574i		−	0.849901i	0.905217	−	0.424950i	$-0.139708\pi$
$770$	1892.22	−	1288.35i	2.45743	−	1.67319i
$771$		0			0
$772$	1806.96	−	1806.96i	2.34062	−	2.34062i
$773$	2.30444	+	2.30444i	0.00298116	+	0.00298116i	0.708596	−	0.705615i	$-0.249329\pi$
$773$	2.30444	+	2.30444i	0.00298116	+	0.00298116i	−0.705615	+	0.708596i	$0.749329\pi$
$774$		0			0
$775$	303.714	−	770.998i	0.391888	−	0.994836i
$776$	1312.14			1.69090
$777$		0			0
$778$	−1277.24	−	1277.24i	−1.64169	−	1.64169i
$779$			222.967i			0.286222i
$780$		0			0
$781$	−2210.75			−2.83067
$782$	275.745	−	275.745i	0.352615	−	0.352615i
$783$		0			0
$784$		−	264.177i		−	0.336961i
$785$	907.351	+	172.271i	1.15586	+	0.219453i
$786$		0			0
$787$	−36.7027	+	36.7027i	−0.0466362	+	0.0466362i	−0.730040	−	0.683404i	$-0.760499\pi$
$787$	−36.7027	+	36.7027i	−0.0466362	+	0.0466362i	0.683404	+	0.730040i	$0.260499\pi$
$788$	460.600	+	460.600i	0.584518	+	0.584518i
$789$		0			0
$790$	243.267	−	1281.29i	0.307932	−	1.62188i
$791$	914.402			1.15601
$792$		0			0
$793$	284.436	+	284.436i	0.358683	+	0.358683i
$794$			2192.44i			2.76126i
$795$		0			0
$796$	−892.729			−1.12152
$797$	645.951	−	645.951i	0.810479	−	0.810479i	−0.174227	−	0.984706i	$-0.555743\pi$
$797$	645.951	−	645.951i	0.810479	−	0.810479i	0.984706	+	0.174227i	$0.0557426\pi$
$798$		0			0
$799$			4.74584i			0.00593972i
$800$	−227.456	−	523.128i	−0.284320	−	0.653910i
$801$		0			0
$802$	956.041	−	956.041i	1.19207	−	1.19207i
$803$	168.881	+	168.881i	0.210313	+	0.210313i
$804$		0			0
$805$	350.368	+	514.590i	0.435240	+	0.639243i
$806$	−681.856			−0.845976
$807$		0			0
$808$	−344.272	−	344.272i	−0.426079	−	0.426079i
$809$			467.239i			0.577552i	0.957397	+	0.288776i	$0.0932483\pi$
$809$			467.239i			0.577552i	−0.957397	+	0.288776i	$0.906752\pi$
$810$		0			0
$811$	984.857			1.21437			0.607187	−	0.794559i	$-0.292298\pi$
$811$	984.857			1.21437			0.607187	+	0.794559i	$0.292298\pi$
$812$	−408.023	+	408.023i	−0.502491	+	0.502491i
$813$		0			0
$814$			3732.70i			4.58562i
$815$	43.9551	−	231.511i	0.0539326	−	0.284063i
$816$		0			0
$817$	658.216	−	658.216i	0.805650	−	0.805650i
$818$	−343.956	−	343.956i	−0.420485	−	0.420485i
$819$		0			0
$820$	435.188	−	296.306i	0.530717	−	0.361348i
$821$	966.156			1.17680			0.588402	−	0.808569i	$-0.299757\pi$
$821$	966.156			1.17680			0.588402	+	0.808569i	$0.299757\pi$
$822$		0			0
$823$	−21.7648	−	21.7648i	−0.0264457	−	0.0264457i	0.693760	−	0.720206i	$-0.255953\pi$
$823$	−21.7648	−	21.7648i	−0.0264457	−	0.0264457i	−0.720206	+	0.693760i	$0.755953\pi$
$824$			1285.80i			1.56044i
$825$		0			0
$826$	1864.20			2.25690
$827$	434.978	−	434.978i	0.525971	−	0.525971i	−0.393398	−	0.919368i	$-0.628700\pi$
$827$	434.978	−	434.978i	0.525971	−	0.525971i	0.919368	+	0.393398i	$0.128700\pi$
$828$		0			0
$829$			308.711i			0.372390i	0.982513	+	0.186195i	$0.0596156\pi$
$829$			308.711i			0.372390i	−0.982513	+	0.186195i	$0.940384\pi$
$830$	59.4839	+	87.3647i	0.0716673	+	0.105259i
$831$		0			0
$832$	81.0286	−	81.0286i	0.0973902	−	0.0973902i
$833$	40.2100	+	40.2100i	0.0482713	+	0.0482713i
$834$		0			0
$835$	228.858	+	43.4513i	0.274082	+	0.0520375i
$836$	−3335.99			−3.99042
$837$		0			0
$838$	−999.812	−	999.812i	−1.19309	−	1.19309i
$839$		−	349.372i		−	0.416414i	−0.978085	−	0.208207i	$-0.933237\pi$
$839$		−	349.372i		−	0.416414i	0.978085	−	0.208207i	$-0.0667628\pi$
$840$		0			0
$841$	727.782			0.865377
$842$	−1530.49	+	1530.49i	−1.81768	+	1.81768i
$843$		0			0
$844$			1227.27i			1.45411i
$845$	−561.109	+	382.041i	−0.664034	+	0.452120i
$846$		0			0
$847$	−1343.15	+	1343.15i	−1.58577	+	1.58577i
$848$	−295.698	−	295.698i	−0.348701	−	0.348701i
$849$		0			0
$850$	452.430	+	178.223i	0.532271	+	0.209674i
$851$	−1015.11			−1.19284
$852$		0			0
$853$	−475.927	−	475.927i	−0.557945	−	0.557945i	0.370777	−	0.928722i	$-0.379091\pi$
$853$	−475.927	−	475.927i	−0.557945	−	0.557945i	−0.928722	+	0.370777i	$0.879091\pi$
$854$			1546.19i			1.81053i
$855$		0			0
$856$	−336.118			−0.392662
$857$	1100.97	−	1100.97i	1.28468	−	1.28468i	0.346705	−	0.937974i	$-0.387301\pi$
$857$	1100.97	−	1100.97i	1.28468	−	1.28468i	0.937974	−	0.346705i	$-0.112699\pi$
$858$		0			0
$859$			374.005i			0.435396i	0.976016	+	0.217698i	$0.0698547\pi$
$859$			374.005i			0.435396i	−0.976016	+	0.217698i	$0.930145\pi$
$860$	−2159.43	−	409.992i	−2.51097	−	0.476735i
$861$		0			0
$862$	−346.814	+	346.814i	−0.402337	+	0.402337i
$863$	−169.154	−	169.154i	−0.196007	−	0.196007i	0.602279	−	0.798286i	$-0.294260\pi$
$863$	−169.154	−	169.154i	−0.196007	−	0.196007i	−0.798286	+	0.602279i	$0.794260\pi$
$864$		0			0
$865$	189.917	−	1000.29i	0.219557	−	1.15641i
$866$	513.294			0.592718
$867$		0			0
$868$	−1271.06	−	1271.06i	−1.46435	−	1.46435i
$869$			1510.28i			1.73795i
$870$		0			0
$871$	−313.535			−0.359971
$872$	−223.190	+	223.190i	−0.255951	+	0.255951i
$873$		0			0
$874$		−	1322.79i		−	1.51350i
$875$	−414.250	+	656.523i	−0.473428	+	0.750312i
$876$		0			0
$877$	−865.805	+	865.805i	−0.987235	+	0.987235i	−0.999920	−	0.0126849i	$-0.995962\pi$
$877$	−865.805	+	865.805i	−0.987235	+	0.987235i	0.0126849	+	0.999920i	$0.495962\pi$
$878$	2064.45	+	2064.45i	2.35131	+	2.35131i
$879$		0			0
$880$	1472.30	+	2162.39i	1.67307	+	2.45726i
$881$	1252.48			1.42165			0.710827	−	0.703366i	$-0.248321\pi$
$881$	1252.48			1.42165			0.710827	+	0.703366i	$0.248321\pi$
$882$		0			0
$883$	997.163	+	997.163i	1.12929	+	1.12929i	0.990293	+	0.138998i	$0.0443880\pi$
$883$	997.163	+	997.163i	1.12929	+	1.12929i	0.138998	+	0.990293i	$0.455612\pi$
$884$		−	274.418i		−	0.310428i
$885$		0			0
$886$	−661.233			−0.746313
$887$	481.697	−	481.697i	0.543063	−	0.543063i	−0.381362	−	0.924426i	$-0.624545\pi$
$887$	481.697	−	481.697i	0.543063	−	0.543063i	0.924426	+	0.381362i	$0.124545\pi$
$888$		0			0
$889$		−	333.101i		−	0.374691i
$890$	−20.6573	+	108.802i	−0.0232104	+	0.122249i
$891$		0			0
$892$	−2177.70	+	2177.70i	−2.44137	+	2.44137i
$893$	11.3833	+	11.3833i	0.0127473	+	0.0127473i
$894$		0			0
$895$	−625.103	+	425.613i	−0.698440	+	0.475545i
$896$	1007.29			1.12420
$897$		0			0
$898$	1383.35	+	1383.35i	1.54048	+	1.54048i
$899$		−	352.691i		−	0.392315i
$900$		0			0
$901$	90.0155			0.0999062
$902$	−628.592	+	628.592i	−0.696887	+	0.696887i
$903$		0			0
$904$			2486.27i			2.75030i
$905$	−214.259	−	314.685i	−0.236751	−	0.347719i
$906$		0			0
$907$	−62.4184	+	62.4184i	−0.0688185	+	0.0688185i	−0.740678	−	0.671860i	$-0.765496\pi$
$907$	−62.4184	+	62.4184i	−0.0688185	+	0.0688185i	0.671860	+	0.740678i	$0.265496\pi$
$908$	1572.81	+	1572.81i	1.73217	+	1.73217i
$909$		0			0
$910$	627.552	+	119.148i	0.689617	+	0.130932i
$911$	1319.23			1.44812			0.724058	−	0.689739i	$-0.242275\pi$
$911$	1319.23			1.44812			0.724058	+	0.689739i	$0.242275\pi$
$912$		0			0
$913$	−86.5466	−	86.5466i	−0.0947937	−	0.0947937i
$914$		−	1253.66i		−	1.37162i
$915$		0			0
$916$	2690.47			2.93720
$917$	287.276	−	287.276i	0.313278	−	0.313278i
$918$		0			0
$919$		−	669.478i		−	0.728486i	−0.931304	−	0.364243i	$-0.881328\pi$
$919$		−	669.478i		−	0.728486i	0.931304	−	0.364243i	$-0.118672\pi$
$920$	−1399.18	+	952.656i	−1.52085	+	1.03550i
$921$		0			0
$922$	376.933	−	376.933i	0.408821	−	0.408821i
$923$	−436.198	−	436.198i	−0.472587	−	0.472587i
$924$		0			0
$925$	−504.725	−	1160.82i	−0.545649	−	1.25494i
$926$	1776.35			1.91830
$927$		0			0
$928$	−171.676	−	171.676i	−0.184996	−	0.184996i
$929$			1410.96i			1.51880i	0.650626	+	0.759398i	$0.274506\pi$
$929$			1410.96i			1.51880i	−0.650626	+	0.759398i	$0.725494\pi$
$930$		0			0
$931$	192.894			0.207191
$932$	2434.02	−	2434.02i	2.61161	−	2.61161i
$933$		0			0
$934$		−	2215.43i		−	2.37198i
$935$	−553.231	−	105.037i	−0.591691	−	0.112339i
$936$		0			0
$937$	−482.685	+	482.685i	−0.515139	+	0.515139i	−0.916097	−	0.400958i	$-0.868677\pi$
$937$	−482.685	+	482.685i	−0.515139	+	0.515139i	0.400958	+	0.916097i	$0.368677\pi$
$938$	−852.188	−	852.188i	−0.908516	−	0.908516i
$939$		0			0
$940$	7.09048	−	37.3456i	0.00754307	−	0.0397293i
$941$	−734.717			−0.780784			−0.390392	−	0.920649i	$-0.627660\pi$
$941$	−734.717			−0.780784			−0.390392	+	0.920649i	$0.627660\pi$
$942$		0			0
$943$	−170.946	−	170.946i	−0.181279	−	0.181279i
$944$			2130.37i			2.25674i
$945$		0			0
$946$	3711.31			3.92317
$947$	−486.842	+	486.842i	−0.514088	+	0.514088i	−0.915777	−	0.401688i	$-0.868424\pi$
$947$	−486.842	+	486.842i	−0.514088	+	0.514088i	0.401688	+	0.915777i	$0.368424\pi$
$948$		0			0
$949$			66.6431i			0.0702246i
$950$	1512.68	−	657.711i	1.59229	−	0.692328i
$951$		0			0
$952$	404.209	−	404.209i	0.424589	−	0.424589i
$953$	−47.5647	−	47.5647i	−0.0499105	−	0.0499105i	0.681711	−	0.731622i	$-0.261236\pi$
$953$	−47.5647	−	47.5647i	−0.0499105	−	0.0499105i	−0.731622	+	0.681711i	$0.761236\pi$
$954$		0			0
$955$	−575.092	−	844.645i	−0.602190	−	0.884445i
$956$	−3429.94			−3.58780
$957$		0			0
$958$	739.191	+	739.191i	0.771598	+	0.771598i
$959$			793.774i			0.827710i
$960$		0			0
$961$	137.688			0.143276
$962$	−736.489	+	736.489i	−0.765581	+	0.765581i
$963$		0			0
$964$			1086.59i			1.12717i
$965$	272.931	−	1437.53i	0.282830	−	1.48966i
$966$		0			0
$967$	−773.213	+	773.213i	−0.799600	+	0.799600i	−0.983032	−	0.183432i	$-0.941279\pi$
$967$	−773.213	+	773.213i	−0.799600	+	0.799600i	0.183432	+	0.983032i	$0.441279\pi$
$968$	−3652.04	−	3652.04i	−3.77277	−	3.77277i
$969$		0			0
$970$	1145.96	−	780.247i	1.18140	−	0.804378i
$971$	1595.62			1.64327			0.821637	−	0.570011i	$-0.193061\pi$
$971$	1595.62			1.64327			0.821637	+	0.570011i	$0.193061\pi$
$972$		0			0
$973$	1086.56	+	1086.56i	1.11671	+	1.11671i
$974$		−	2736.45i		−	2.80949i
$975$		0			0
$976$	−1766.96			−1.81041
$977$	1017.40	−	1017.40i	1.04135	−	1.04135i	0.0422453	−	0.999107i	$-0.486549\pi$
$977$	1017.40	−	1017.40i	1.04135	−	1.04135i	0.999107	−	0.0422453i	$-0.0134511\pi$
$978$		0			0
$979$		−	128.247i		−	0.130998i
$980$	−256.342	−	376.493i	−0.261574	−	0.384176i
$981$		0			0
$982$	1722.60	−	1722.60i	1.75417	−	1.75417i
$983$	268.852	+	268.852i	0.273501	+	0.273501i	0.830508	−	0.557007i	$-0.188050\pi$
$983$	268.852	+	268.852i	0.273501	+	0.273501i	−0.557007	+	0.830508i	$0.688050\pi$
$984$		0			0
$985$	366.430	+	69.5708i	0.372010	+	0.0706303i
$986$	206.963			0.209902
$987$		0			0
$988$	−658.216	−	658.216i	−0.666210	−	0.666210i
$989$			1009.29i			1.02052i
$990$		0			0
$991$	563.583			0.568701			0.284350	−	0.958720i	$-0.408222\pi$
$991$	563.583			0.568701			0.284350	+	0.958720i	$0.408222\pi$
$992$	534.799	−	534.799i	0.539112	−	0.539112i
$993$		0			0
$994$		−	2371.17i		−	2.38549i
$995$	−422.525	+	287.684i	−0.424649	+	0.289130i
$996$		0			0
$997$	−864.713	+	864.713i	−0.867315	+	0.867315i	−0.992174	−	0.124860i	$-0.960152\pi$
$997$	−864.713	+	864.713i	−0.867315	+	0.867315i	0.124860	+	0.992174i	$0.460152\pi$
$998$	−1034.95	−	1034.95i	−1.03702	−	1.03702i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.3.g.a.28.8	yes	16
3.2	odd	2	inner	135.3.g.a.28.1	✓	16
5.2	odd	4	inner	135.3.g.a.82.8	yes	16
5.3	odd	4		675.3.g.k.82.1		16
5.4	even	2		675.3.g.k.568.1		16
9.2	odd	6		405.3.l.o.28.8		32
9.4	even	3		405.3.l.o.298.8		32
9.5	odd	6		405.3.l.o.298.1		32
9.7	even	3		405.3.l.o.28.1		32
15.2	even	4	inner	135.3.g.a.82.1	yes	16
15.8	even	4		675.3.g.k.82.8		16
15.14	odd	2		675.3.g.k.568.8		16
45.2	even	12		405.3.l.o.352.1		32
45.7	odd	12		405.3.l.o.352.8		32
45.22	odd	12		405.3.l.o.217.1		32
45.32	even	12		405.3.l.o.217.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.g.a.28.1	✓	16	3.2	odd	2	inner
135.3.g.a.28.8	yes	16	1.1	even	1	trivial
135.3.g.a.82.1	yes	16	15.2	even	4	inner
135.3.g.a.82.8	yes	16	5.2	odd	4	inner
405.3.l.o.28.1		32	9.7	even	3
405.3.l.o.28.8		32	9.2	odd	6
405.3.l.o.217.1		32	45.22	odd	12
405.3.l.o.217.8		32	45.32	even	12
405.3.l.o.298.1		32	9.5	odd	6
405.3.l.o.298.8		32	9.4	even	3
405.3.l.o.352.1		32	45.2	even	12
405.3.l.o.352.8		32	45.7	odd	12
675.3.g.k.82.1		16	5.3	odd	4
675.3.g.k.82.8		16	15.8	even	4
675.3.g.k.568.1		16	5.4	even	2
675.3.g.k.568.8		16	15.14	odd	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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.52312 - 2.52312i) q^{2} -8.73230i q^{4} +(-2.81400 - 4.13296i) q^{5} +(-4.39136 + 4.39136i) q^{7} +(-11.9402 - 11.9402i) q^{8} +O(q^{10})\)	\(q+(2.52312 - 2.52312i) q^{2} -8.73230i q^{4} +(-2.81400 - 4.13296i) q^{5} +(-4.39136 + 4.39136i) q^{7} +(-11.9402 - 11.9402i) q^{8} +(-17.5280 - 3.32790i) q^{10} +20.6606 q^{11} +(4.07650 + 4.07650i) q^{13} +22.1599i q^{14} -25.3238 q^{16} +(3.85449 - 3.85449i) q^{17} -18.4907i q^{19} +(-36.0903 + 24.5727i) q^{20} +(52.1293 - 52.1293i) q^{22} +(14.1766 + 14.1766i) q^{23} +(-9.16277 + 23.2603i) q^{25} +20.5710 q^{26} +(38.3466 + 38.3466i) q^{28} +10.6404i q^{29} -33.1465 q^{31} +(-16.1344 + 16.1344i) q^{32} -19.4507i q^{34} +(30.5066 + 5.79202i) q^{35} +(-35.8023 + 35.8023i) q^{37} +(-46.6542 - 46.6542i) q^{38} +(-15.7486 + 82.9479i) q^{40} -12.0583 q^{41} +(35.5972 + 35.5972i) q^{43} -180.415i q^{44} +71.5385 q^{46} +(-0.615624 + 0.615624i) q^{47} +10.4320i q^{49} +(35.5699 + 81.8075i) q^{50} +(35.5972 - 35.5972i) q^{52} +(11.6767 + 11.6767i) q^{53} +(-58.1391 - 85.3897i) q^{55} +104.867 q^{56} +(26.8470 + 26.8470i) q^{58} -84.1251i q^{59} +69.7745 q^{61} +(-83.6326 + 83.6326i) q^{62} -19.8770i q^{64} +(5.37674 - 28.3193i) q^{65} +(-38.4564 + 38.4564i) q^{67} +(-33.6586 - 33.6586i) q^{68} +(91.5859 - 62.3579i) q^{70} -107.003 q^{71} +(8.17407 + 8.17407i) q^{73} +180.667i q^{74} -161.466 q^{76} +(-90.7282 + 90.7282i) q^{77} +73.0992i q^{79} +(71.2613 + 104.662i) q^{80} +(-30.4246 + 30.4246i) q^{82} +(-4.18896 - 4.18896i) q^{83} +(-26.7770 - 5.08392i) q^{85} +179.632 q^{86} +(-246.691 - 246.691i) q^{88} -6.20731i q^{89} -35.8027 q^{91} +(123.794 - 123.794i) q^{92} +3.10659i q^{94} +(-76.4213 + 52.0328i) q^{95} +(-54.9464 + 54.9464i) q^{97} +(26.3212 + 26.3212i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} - 32 q^{10} + 28 q^{13} - 20 q^{16} + 176 q^{22} + 64 q^{25} + 80 q^{28} - 208 q^{31} - 176 q^{37} - 252 q^{40} - 188 q^{43} + 188 q^{46} - 188 q^{52} - 136 q^{55} + 504 q^{58} + 296 q^{61} + 304 q^{67} + 684 q^{70} - 56 q^{73} - 732 q^{76} - 76 q^{82} - 788 q^{85} - 1128 q^{88} + 200 q^{91} - 284 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 - 32 * q^10 + 28 * q^13 - 20 * q^16 + 176 * q^22 + 64 * q^25 + 80 * q^28 - 208 * q^31 - 176 * q^37 - 252 * q^40 - 188 * q^43 + 188 * q^46 - 188 * q^52 - 136 * q^55 + 504 * q^58 + 296 * q^61 + 304 * q^67 + 684 * q^70 - 56 * q^73 - 732 * q^76 - 76 * q^82 - 788 * q^85 - 1128 * q^88 + 200 * q^91 - 284 * q^97

Introduction

L-functions

Modular forms

Varieties

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