LMFDB - Embedded newform 135.3.g.a.82.1

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			82.1
Root			$-2.52312 - 2.52312i$ of defining polynomial
Character	$\chi$	$=$	135.82
Dual form			135.3.g.a.28.1

$q$-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 $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

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

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	−0.950336	−	0.311225i	$-0.899261\pi$
$2$	−2.52312	−	2.52312i	−1.26156	−	1.26156i	−0.311225	−	0.950336i	$-0.600739\pi$
$3$		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	0.320061	−	0.947397i	$-0.396297\pi$
$7$	−4.39136	−	4.39136i	−0.627337	−	0.627337i	−0.947397	+	0.320061i	$0.896297\pi$
$8$	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	$-0.888357\pi$
$11$	−20.6606			−1.87824			−0.939120	+	0.343589i	$0.888357\pi$
$12$		0			0
$13$	4.07650	−	4.07650i	0.313577	−	0.313577i	−0.532717	−	0.846294i	$-0.678829\pi$
$13$	4.07650	−	4.07650i	0.313577	−	0.313577i	0.846294	+	0.532717i	$0.178829\pi$
$14$			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	$-0.301254\pi$
$17$	−3.85449	−	3.85449i	−0.226735	−	0.226735i	−0.811327	+	0.584592i	$0.801254\pi$
$18$		0			0
$19$			18.4907i			0.973193i	0.873627	+	0.486597i	$0.161762\pi$
$19$			18.4907i			0.973193i	−0.873627	+	0.486597i	$0.838238\pi$
$20$	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	$-0.893549\pi$
$23$	−14.1766	+	14.1766i	−0.616373	+	0.616373i	0.328226	+	0.944599i	$0.393549\pi$
$24$		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	0.0318634	−	0.999492i	$-0.489856\pi$
$37$	−35.8023	−	35.8023i	−0.967629	−	0.967629i	−0.999492	+	0.0318634i	$0.989856\pi$
$38$	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	$-0.453021\pi$
$41$	12.0583			0.294106			0.147053	+	0.989129i	$0.453021\pi$
$42$		0			0
$43$	35.5972	−	35.5972i	0.827842	−	0.827842i	−0.159376	−	0.987218i	$-0.550948\pi$
$43$	35.5972	−	35.5972i	0.827842	−	0.827842i	0.987218	+	0.159376i	$0.0509483\pi$
$44$		−	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	$-0.247052\pi$
$47$	0.615624	+	0.615624i	0.0130984	+	0.0130984i	−0.700527	+	0.713626i	$0.747052\pi$
$48$		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	$-0.799791\pi$
$53$	−11.6767	+	11.6767i	−0.220315	+	0.220315i	0.588316	+	0.808631i	$0.299791\pi$
$54$		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	0.359261	−	0.933237i	$-0.383029\pi$
$67$	−38.4564	−	38.4564i	−0.573976	−	0.573976i	−0.933237	+	0.359261i	$0.883029\pi$
$68$	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	$-0.228343\pi$
$71$	107.003			1.50709			0.753543	+	0.657399i	$0.228343\pi$
$72$		0			0
$73$	8.17407	−	8.17407i	0.111974	−	0.111974i	−0.648900	−	0.760874i	$-0.724771\pi$
$73$	8.17407	−	8.17407i	0.111974	−	0.111974i	0.760874	+	0.648900i	$0.224771\pi$
$74$			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	$-0.846898\pi$
$79$		−	73.0992i		−	0.925306i	0.886539	−	0.462653i	$-0.153102\pi$
$80$	−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	$-0.738638\pi$
$83$	4.18896	−	4.18896i	0.0504694	−	0.0504694i	0.731891	+	0.681422i	$0.238638\pi$
$84$		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	0.364677	−	0.931134i	$-0.381180\pi$
$97$	−54.9464	−	54.9464i	−0.566458	−	0.566458i	−0.931134	+	0.364677i	$0.881180\pi$
$98$	−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	$-0.545591\pi$
$101$	−28.8331			−0.285476			−0.142738	+	0.989760i	$0.545591\pi$
$102$		0			0
$103$	−53.8436	+	53.8436i	−0.522754	+	0.522754i	−0.918402	−	0.395648i	$-0.870520\pi$
$103$	−53.8436	+	53.8436i	−0.522754	+	0.522754i	0.395648	+	0.918402i	$0.370520\pi$
$104$		−	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	$-0.279650\pi$
$107$	−14.0751	−	14.0751i	−0.131543	−	0.131543i	−0.769813	+	0.638270i	$0.779650\pi$
$108$		0			0
$109$			18.6923i			0.171489i	0.996317	+	0.0857447i	$0.0273269\pi$
$109$			18.6923i			0.171489i	−0.996317	+	0.0857447i	$0.972673\pi$
$110$	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	$-0.524140\pi$
$113$	104.114	−	104.114i	0.921362	−	0.921362i	0.997126	+	0.0757641i	$0.0241396\pi$
$114$		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	0.541843	−	0.840480i	$-0.317727\pi$
$127$	−37.9268	−	37.9268i	−0.298637	−	0.298637i	−0.840480	+	0.541843i	$0.817727\pi$
$128$	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	$-0.419672\pi$
$131$	65.4186			0.499378			0.249689	+	0.968326i	$0.419672\pi$
$132$		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	$-0.404478\pi$
$137$	−90.3791	−	90.3791i	−0.659701	−	0.659701i	−0.955309	+	0.295608i	$0.904478\pi$
$138$		0			0
$139$			247.432i			1.78008i	0.455879	+	0.890042i	$0.349325\pi$
$139$			247.432i			1.78008i	−0.455879	+	0.890042i	$0.650675\pi$
$140$	−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	0.155861	−	0.987779i	$-0.450185\pi$
$157$	−130.611	−	130.611i	−0.831918	−	0.831918i	−0.987779	+	0.155861i	$0.950185\pi$
$158$	−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	−0.597453	−	0.801904i	$-0.703820\pi$
$163$	33.3255	−	33.3255i	0.204451	−	0.204451i	0.801904	+	0.597453i	$0.203820\pi$
$164$			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	$-0.205454\pi$
$167$	32.9436	+	32.9436i	0.197267	+	0.197267i	−0.601560	+	0.798827i	$0.705454\pi$
$168$		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	$-0.950294\pi$
$173$	−143.990	+	143.990i	−0.832311	+	0.832311i	0.155522	+	0.987832i	$0.450294\pi$
$174$		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	$-0.679686\pi$
$191$	−204.368			−1.06999			−0.534994	+	0.844856i	$0.679686\pi$
$192$		0			0
$193$	206.929	−	206.929i	1.07217	−	1.07217i	0.0749840	−	0.997185i	$-0.476109\pi$
$193$	206.929	−	206.929i	1.07217	−	1.07217i	0.997185	−	0.0749840i	$-0.0238906\pi$
$194$			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	$-0.189369\pi$
$197$	52.7467	+	52.7467i	0.267750	+	0.267750i	−0.560443	+	0.828193i	$0.689369\pi$
$198$		0			0
$199$			102.233i			0.513734i	0.966447	+	0.256867i	$0.0826902\pi$
$199$			102.233i			0.513734i	−0.966447	+	0.256867i	$0.917310\pi$
$200$	−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	−0.126331	+	0.991988i	$0.540320\pi$
$223$	−249.385	+	249.385i	−1.11832	+	1.11832i	−0.991988	+	0.126331i	$0.959680\pi$
$224$		−	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	$-0.0603944\pi$
$227$	180.115	+	180.115i	0.793456	+	0.793456i	−0.188598	+	0.982054i	$0.560394\pi$
$228$		0			0
$229$		−	308.106i		−	1.34544i	−0.739897	−	0.672720i	$-0.765126\pi$
$229$		−	308.106i		−	1.34544i	0.739897	−	0.672720i	$-0.234874\pi$
$230$	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	−0.221033	+	0.975266i	$0.570943\pi$
$233$	−278.738	+	278.738i	−1.19630	+	1.19630i	−0.975266	+	0.221033i	$0.929057\pi$
$234$		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	$-0.507592\pi$
$251$	−11.9714			−0.0476946			−0.0238473	+	0.999716i	$0.507592\pi$
$252$		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	$-0.0513280\pi$
$257$	212.404	+	212.404i	0.826473	+	0.826473i	−0.160554	+	0.987027i	$0.551328\pi$
$258$		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	$-0.748108\pi$
$263$	2.21097	−	2.21097i	0.00840674	−	0.00840674i	0.711298	+	0.702891i	$0.248108\pi$
$264$		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	0.857675	−	0.514192i	$-0.171908\pi$
$277$	95.1449	+	95.1449i	0.343483	+	0.343483i	−0.514192	+	0.857675i	$0.671908\pi$
$278$	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	$-0.258092\pi$
$281$	387.164			1.37781			0.688904	+	0.724853i	$0.258092\pi$
$282$		0			0
$283$	−39.1743	+	39.1743i	−0.138425	+	0.138425i	−0.772924	−	0.634499i	$-0.781207\pi$
$283$	−39.1743	+	39.1743i	−0.138425	+	0.138425i	0.634499	+	0.772924i	$0.281207\pi$
$284$			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	0.0632822	−	0.997996i	$-0.479843\pi$
$293$	310.954	−	310.954i	1.06128	−	1.06128i	0.997996	−	0.0632822i	$-0.0201568\pi$
$294$		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	−0.986895	−	0.161361i	$-0.948412\pi$
$307$	−352.515	−	352.515i	−1.14826	−	1.14826i	−0.161361	−	0.986895i	$-0.551588\pi$
$308$	−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	$-0.599457\pi$
$311$	−191.198			−0.614786			−0.307393	+	0.951583i	$0.599457\pi$
$312$		0			0
$313$	−152.885	+	152.885i	−0.488450	+	0.488450i	−0.907817	−	0.419367i	$-0.862252\pi$
$313$	−152.885	+	152.885i	−0.488450	+	0.488450i	0.419367	+	0.907817i	$0.362252\pi$
$314$			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	$-0.318727\pi$
$317$	−96.0449	−	96.0449i	−0.302981	−	0.302981i	−0.842179	+	0.539198i	$0.818727\pi$
$318$		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	0.996990	+	0.0775344i	$0.0247048\pi$
$337$	362.115	+	362.115i	1.07452	+	1.07452i	0.0775344	+	0.996990i	$0.475295\pi$
$338$	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	$-0.263508\pi$
$347$	−20.8181	−	20.8181i	−0.0599945	−	0.0599945i	−0.736467	+	0.676473i	$0.763508\pi$
$348$		0			0
$349$		−	443.992i		−	1.27218i	−0.771613	−	0.636092i	$-0.780550\pi$
$349$		−	443.992i		−	1.27218i	0.771613	−	0.636092i	$-0.219450\pi$
$350$	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	$-0.663114\pi$
$353$	134.580	−	134.580i	0.381248	−	0.381248i	0.871552	+	0.490304i	$0.163114\pi$
$354$		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	0.955774	−	0.294102i	$-0.0950204\pi$
$367$	242.834	+	242.834i	0.661673	+	0.661673i	−0.294102	+	0.955774i	$0.595020\pi$
$368$	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	−0.121013	+	0.992651i	$0.538614\pi$
$373$	−415.397	+	415.397i	−1.11366	+	1.11366i	−0.992651	+	0.121013i	$0.961386\pi$
$374$		−	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	$0.0369613\pi$
$379$			87.8194i			0.231713i	−0.993266	+	0.115857i	$0.963039\pi$
$380$	−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	$-0.843871\pi$
$383$	−157.427	+	157.427i	−0.411038	+	0.411038i	0.471062	+	0.882100i	$0.343871\pi$
$384$		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	−0.995055	−	0.0993269i	$-0.968331\pi$
$397$	−434.470	−	434.470i	−1.09438	−	1.09438i	−0.0993269	−	0.995055i	$-0.531669\pi$
$398$	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	$-0.656633\pi$
$401$	−378.912			−0.944918			−0.472459	+	0.881353i	$0.656633\pi$
$402$		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	$0.0532958\pi$
$409$			136.322i			0.333305i	−0.986016	+	0.166652i	$0.946704\pi$
$410$	−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	$-0.449025\pi$
$431$	137.454			0.318920			0.159460	+	0.987204i	$0.449025\pi$
$432$		0			0
$433$	101.718	−	101.718i	0.234915	−	0.234915i	−0.579826	−	0.814740i	$-0.696879\pi$
$433$	101.718	−	101.718i	0.234915	−	0.234915i	0.814740	+	0.579826i	$0.196879\pi$
$434$		−	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	$-0.618145\pi$
$439$		−	818.214i		−	1.86381i	0.362700	−	0.931906i	$-0.381855\pi$
$440$	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	$-0.682929\pi$
$443$	131.035	−	131.035i	0.295789	−	0.295789i	0.839362	+	0.543573i	$0.182929\pi$
$444$		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	0.924588	−	0.380968i	$-0.124409\pi$
$457$	248.434	+	248.434i	0.543620	+	0.543620i	−0.380968	+	0.924588i	$0.624409\pi$
$458$	−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	$-0.551804\pi$
$461$	−149.391			−0.324060			−0.162030	+	0.986786i	$0.551804\pi$
$462$		0			0
$463$	352.014	−	352.014i	0.760289	−	0.760289i	−0.216085	−	0.976374i	$-0.569329\pi$
$463$	352.014	−	352.014i	0.760289	−	0.760289i	0.976374	+	0.216085i	$0.0693289\pi$
$464$		−	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	$-0.481461\pi$
$467$	−439.025	−	439.025i	−0.940095	−	0.940095i	−0.998304	+	0.0582090i	$0.981461\pi$
$468$		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	0.992674	+	0.120824i	$0.0385538\pi$
$487$	542.274	+	542.274i	1.11350	+	1.11350i	0.120824	+	0.992674i	$0.461446\pi$
$488$	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	$-0.744701\pi$
$491$	−682.723			−1.39048			−0.695238	+	0.718780i	$0.744701\pi$
$492$		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	$0.134823\pi$
$499$			410.186i			0.822016i	−0.911632	+	0.411008i	$0.865177\pi$
$500$	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	0.0848064	−	0.996397i	$-0.472973\pi$
$503$	543.846	−	543.846i	1.08120	−	1.08120i	0.996397	−	0.0848064i	$-0.0270272\pi$
$504$		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	$-0.374302\pi$
$521$	400.865			0.769414			0.384707	+	0.923039i	$0.374302\pi$
$522$		0			0
$523$	−212.510	+	212.510i	−0.406330	+	0.406330i	−0.880457	−	0.474127i	$-0.842764\pi$
$523$	−212.510	+	212.510i	−0.406330	+	0.406330i	0.474127	+	0.880457i	$0.342764\pi$
$524$			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	0.999990	+	0.00444067i	$0.00141351\pi$
$547$	549.424	+	549.424i	1.00443	+	1.00443i	0.00444067	+	0.999990i	$0.498586\pi$
$548$	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	$-0.462963\pi$
$557$	−488.571	−	488.571i	−0.877147	−	0.877147i	−0.993239	+	0.116091i	$0.962963\pi$
$558$		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	0.344490	−	0.938790i	$-0.388052\pi$
$563$	722.486	−	722.486i	1.28328	−	1.28328i	0.938790	−	0.344490i	$-0.111948\pi$
$564$		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	0.977730	−	0.209868i	$-0.0673034\pi$
$577$	443.056	+	443.056i	0.767862	+	0.767862i	−0.209868	+	0.977730i	$0.567303\pi$
$578$	−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	$-0.320684\pi$
$587$	−182.831	−	182.831i	−0.311468	−	0.311468i	−0.845478	+	0.534010i	$0.820684\pi$
$588$		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	$-0.975478\pi$
$593$	−545.602	+	545.602i	−0.920071	+	0.920071i	0.0769628	+	0.997034i	$0.475478\pi$
$594$		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	0.920084	−	0.391721i	$-0.128120\pi$
$607$	320.716	+	320.716i	0.528362	+	0.528362i	−0.391721	+	0.920084i	$0.628120\pi$
$608$	−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	−0.987442	−	0.157983i	$-0.949501\pi$
$613$	−508.458	+	508.458i	−0.829459	+	0.829459i	0.157983	+	0.987442i	$0.449501\pi$
$614$			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	$-0.156008\pi$
$617$	253.929	+	253.929i	0.411555	+	0.411555i	−0.470725	+	0.882280i	$0.656008\pi$
$618$		0			0
$619$		−	430.073i		−	0.694787i	−0.937719	−	0.347393i	$-0.887067\pi$
$619$		−	430.073i		−	0.694787i	0.937719	−	0.347393i	$-0.112933\pi$
$620$	−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	$-0.266392\pi$
$641$	858.647			1.33954			0.669772	+	0.742567i	$0.266392\pi$
$642$		0			0
$643$	712.636	−	712.636i	1.10830	−	1.10830i	0.114925	−	0.993374i	$-0.463337\pi$
$643$	712.636	−	712.636i	1.10830	−	1.10830i	0.993374	−	0.114925i	$-0.0366627\pi$
$644$			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	$-0.0618585\pi$
$647$	509.877	+	509.877i	0.788063	+	0.788063i	−0.193113	+	0.981176i	$0.561859\pi$
$648$		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	$-0.737090\pi$
$653$	37.4444	−	37.4444i	0.0573422	−	0.0573422i	0.735196	+	0.677854i	$0.237090\pi$
$654$		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	−0.923897	−	0.382642i	$-0.875014\pi$
$673$	−364.264	+	364.264i	−0.541254	+	0.541254i	0.382642	+	0.923897i	$0.375014\pi$
$674$		−	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	$-0.120453\pi$
$677$	378.986	+	378.986i	0.559802	+	0.559802i	−0.369449	+	0.929251i	$0.620453\pi$
$678$		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	$-0.713216\pi$
$683$	111.371	−	111.371i	0.163061	−	0.163061i	0.783921	+	0.620860i	$0.213216\pi$
$684$		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	$-0.327693\pi$
$701$	722.405			1.03053			0.515267	+	0.857030i	$0.327693\pi$
$702$		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	$0.134957\pi$
$709$			583.352i			0.822782i	−0.911459	+	0.411391i	$0.865043\pi$
$710$	−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	0.472092	−	0.881549i	$-0.343499\pi$
$727$	−297.676	−	297.676i	−0.409458	−	0.409458i	−0.881549	+	0.472092i	$0.843499\pi$
$728$	−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	−0.866907	−	0.498470i	$-0.833895\pi$
$733$	−270.064	+	270.064i	−0.368437	+	0.368437i	0.498470	+	0.866907i	$0.333895\pi$
$734$		−	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	$-0.599719\pi$
$739$		−	1406.06i		−	1.90266i	0.308177	−	0.951329i	$-0.400281\pi$
$740$	−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	$-0.708915\pi$
$743$	135.249	−	135.249i	0.182031	−	0.182031i	0.792240	+	0.610209i	$0.208915\pi$
$744$		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	0.0248625	−	0.999691i	$-0.492085\pi$
$757$	−737.945	−	737.945i	−0.974828	−	0.974828i	−0.999691	+	0.0248625i	$0.992085\pi$
$758$	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	$-0.268641\pi$
$761$	1011.38			1.32902			0.664509	+	0.747280i	$0.268641\pi$
$762$		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	$0.139708\pi$
$769$			653.574i			0.849901i	−0.905217	+	0.424950i	$0.860292\pi$
$770$	−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	$-0.750671\pi$
$773$	−2.30444	+	2.30444i	−0.00298116	+	0.00298116i	0.705615	+	0.708596i	$0.250671\pi$
$774$		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	0.683404	−	0.730040i	$-0.260499\pi$
$787$	−36.7027	−	36.7027i	−0.0466362	−	0.0466362i	−0.730040	+	0.683404i	$0.760499\pi$
$788$	−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	$-0.444257\pi$
$797$	−645.951	−	645.951i	−0.810479	−	0.810479i	−0.984706	+	0.174227i	$0.944257\pi$
$798$		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	$-0.700243\pi$
$821$	−966.156			−1.17680			−0.588402	+	0.808569i	$0.700243\pi$
$822$		0			0
$823$	−21.7648	+	21.7648i	−0.0264457	+	0.0264457i	−0.720206	−	0.693760i	$-0.755953\pi$
$823$	−21.7648	+	21.7648i	−0.0264457	+	0.0264457i	0.693760	+	0.720206i	$0.255953\pi$
$824$			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	$-0.371300\pi$
$827$	−434.978	−	434.978i	−0.525971	−	0.525971i	−0.919368	+	0.393398i	$0.871300\pi$
$828$		0			0
$829$		−	308.711i		−	0.372390i	−0.982513	−	0.186195i	$-0.940384\pi$
$829$		−	308.711i		−	0.372390i	0.982513	−	0.186195i	$-0.0596156\pi$
$830$	−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	−0.928722	−	0.370777i	$-0.879091\pi$
$853$	−475.927	+	475.927i	−0.557945	+	0.557945i	0.370777	+	0.928722i	$0.379091\pi$
$854$			1546.19i			1.81053i
$855$		0			0
$856$	−336.118			−0.392662
$857$	−1100.97	−	1100.97i	−1.28468	−	1.28468i	−0.937974	−	0.346705i	$-0.887301\pi$
$857$	−1100.97	−	1100.97i	−1.28468	−	1.28468i	−0.346705	−	0.937974i	$-0.612699\pi$
$858$		0			0
$859$		−	374.005i		−	0.435396i	−0.976016	−	0.217698i	$-0.930145\pi$
$859$		−	374.005i		−	0.435396i	0.976016	−	0.217698i	$-0.0698547\pi$
$860$	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	$-0.705740\pi$
$863$	169.154	−	169.154i	0.196007	−	0.196007i	0.798286	+	0.602279i	$0.205740\pi$
$864$		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	0.0126849	−	0.999920i	$-0.495962\pi$
$877$	−865.805	−	865.805i	−0.987235	−	0.987235i	−0.999920	+	0.0126849i	$0.995962\pi$
$878$	−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	$-0.751679\pi$
$881$	−1252.48			−1.42165			−0.710827	+	0.703366i	$0.751679\pi$
$882$		0			0
$883$	997.163	−	997.163i	1.12929	−	1.12929i	0.138998	−	0.990293i	$-0.455612\pi$
$883$	997.163	−	997.163i	1.12929	−	1.12929i	0.990293	−	0.138998i	$-0.0443880\pi$
$884$		−	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	$-0.375455\pi$
$887$	−481.697	−	481.697i	−0.543063	−	0.543063i	−0.924426	+	0.381362i	$0.875455\pi$
$888$		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	0.671860	−	0.740678i	$-0.265496\pi$
$907$	−62.4184	−	62.4184i	−0.0688185	−	0.0688185i	−0.740678	+	0.671860i	$0.765496\pi$
$908$	−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	$-0.757725\pi$
$911$	−1319.23			−1.44812			−0.724058	+	0.689739i	$0.757725\pi$
$912$		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	$0.118672\pi$
$919$			669.478i			0.728486i	−0.931304	+	0.364243i	$0.881328\pi$
$920$	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	0.400958	−	0.916097i	$-0.368677\pi$
$937$	−482.685	−	482.685i	−0.515139	−	0.515139i	−0.916097	+	0.400958i	$0.868677\pi$
$938$	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	$-0.372340\pi$
$941$	734.717			0.780784			0.390392	+	0.920649i	$0.372340\pi$
$942$		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	$-0.131576\pi$
$947$	486.842	+	486.842i	0.514088	+	0.514088i	−0.401688	+	0.915777i	$0.631576\pi$
$948$		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	$-0.738764\pi$
$953$	47.5647	−	47.5647i	0.0499105	−	0.0499105i	0.731622	+	0.681711i	$0.238764\pi$
$954$		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	0.183432	−	0.983032i	$-0.441279\pi$
$967$	−773.213	−	773.213i	−0.799600	−	0.799600i	−0.983032	+	0.183432i	$0.941279\pi$
$968$	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	$-0.806939\pi$
$971$	−1595.62			−1.64327			−0.821637	+	0.570011i	$0.806939\pi$
$972$		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	−0.999107	−	0.0422453i	$-0.986549\pi$
$977$	−1017.40	−	1017.40i	−1.04135	−	1.04135i	−0.0422453	−	0.999107i	$-0.513451\pi$
$978$		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	$-0.811950\pi$
$983$	−268.852	+	268.852i	−0.273501	+	0.273501i	0.557007	+	0.830508i	$0.311950\pi$
$984$		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	0.124860	−	0.992174i	$-0.460152\pi$
$997$	−864.713	−	864.713i	−0.867315	−	0.867315i	−0.992174	+	0.124860i	$0.960152\pi$
$998$	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.82.1	yes	16
3.2	odd	2	inner	135.3.g.a.82.8	yes	16
5.2	odd	4		675.3.g.k.568.8		16
5.3	odd	4	inner	135.3.g.a.28.1	✓	16
5.4	even	2		675.3.g.k.82.8		16
9.2	odd	6		405.3.l.o.352.8		32
9.4	even	3		405.3.l.o.217.8		32
9.5	odd	6		405.3.l.o.217.1		32
9.7	even	3		405.3.l.o.352.1		32
15.2	even	4		675.3.g.k.568.1		16
15.8	even	4	inner	135.3.g.a.28.8	yes	16
15.14	odd	2		675.3.g.k.82.1		16
45.13	odd	12		405.3.l.o.298.1		32
45.23	even	12		405.3.l.o.298.8		32
45.38	even	12		405.3.l.o.28.1		32
45.43	odd	12		405.3.l.o.28.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.g.a.28.1	✓	16	5.3	odd	4	inner
135.3.g.a.28.8	yes	16	15.8	even	4	inner
135.3.g.a.82.1	yes	16	1.1	even	1	trivial
135.3.g.a.82.8	yes	16	3.2	odd	2	inner
405.3.l.o.28.1		32	45.38	even	12
405.3.l.o.28.8		32	45.43	odd	12
405.3.l.o.217.1		32	9.5	odd	6
405.3.l.o.217.8		32	9.4	even	3
405.3.l.o.298.1		32	45.13	odd	12
405.3.l.o.298.8		32	45.23	even	12
405.3.l.o.352.1		32	9.7	even	3
405.3.l.o.352.8		32	9.2	odd	6
675.3.g.k.82.1		16	15.14	odd	2
675.3.g.k.82.8		16	5.4	even	2
675.3.g.k.568.1		16	15.2	even	4
675.3.g.k.568.8		16	5.2	odd	4

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

Fields

Representations

Groups

Database

Properties

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