LMFDB - Embedded newform 1050.2.b.e.251.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(251,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1050.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.b (of order $2$, degree $1$, 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:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 4x^{8} - 30x^{6} + 36x^{4} + 729 $ x^12 + 4x^8 - 30x^6 + 36*x^4 + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.9
Root			$-0.721683 - 1.57454i$ of defining polynomial
Character	$\chi$	$=$	1050.251
Dual form			1050.2.b.e.251.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.721683 + 1.57454i) q^{3} -1.00000 q^{4} +(-1.57454 - 0.721683i) q^{6} +(1.31429 - 2.29622i) q^{7} -1.00000i q^{8} +(-1.95835 - 2.27264i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.721683 + 1.57454i) q^{3} -1.00000 q^{4} +(-1.57454 - 0.721683i) q^{6} +(1.31429 - 2.29622i) q^{7} -1.00000i q^{8} +(-1.95835 - 2.27264i) q^{9} +3.91669i q^{11} +(0.721683 - 1.57454i) q^{12} -4.99166i q^{13} +(2.29622 + 1.31429i) q^{14} +1.00000 q^{16} +3.54830 q^{17} +(2.27264 - 1.95835i) q^{18} -3.14908i q^{19} +(2.66699 + 3.72655i) q^{21} -3.91669 q^{22} -7.54528i q^{23} +(1.57454 + 0.721683i) q^{24} +4.99166 q^{26} +(4.99166 - 1.44337i) q^{27} +(-1.31429 + 2.29622i) q^{28} +7.54528i q^{29} -4.19323i q^{31} +1.00000i q^{32} +(-6.16698 - 2.82661i) q^{33} +3.54830i q^{34} +(1.95835 + 2.27264i) q^{36} +10.4620 q^{37} +3.14908 q^{38} +(7.85957 + 3.60240i) q^{39} +9.32176 q^{41} +(-3.72655 + 2.66699i) q^{42} +2.91669 q^{43} -3.91669i q^{44} +7.54528 q^{46} -8.00387 q^{47} +(-0.721683 + 1.57454i) q^{48} +(-3.54528 - 6.03581i) q^{49} +(-2.56075 + 5.58693i) q^{51} +4.99166i q^{52} +0.288109i q^{53} +(1.44337 + 4.99166i) q^{54} +(-2.29622 - 1.31429i) q^{56} +(4.95835 + 2.27264i) q^{57} -7.54528 q^{58} -5.89894 q^{59} -2.48752i q^{61} +4.19323 q^{62} +(-7.79232 + 1.50989i) q^{63} -1.00000 q^{64} +(2.82661 - 6.16698i) q^{66} -0.545275 q^{67} -3.54830 q^{68} +(11.8803 + 5.44530i) q^{69} +5.37142i q^{71} +(-2.27264 + 1.95835i) q^{72} +4.85479i q^{73} +10.4620i q^{74} +3.14908i q^{76} +(8.99360 + 5.14768i) q^{77} +(-3.60240 + 7.85957i) q^{78} +0.742834 q^{79} +(-1.32976 + 8.90122i) q^{81} +9.32176i q^{82} +4.45557 q^{83} +(-2.66699 - 3.72655i) q^{84} +2.91669i q^{86} +(-11.8803 - 5.44530i) q^{87} +3.91669 q^{88} -12.3340 q^{89} +(-11.4620 - 6.56050i) q^{91} +7.54528i q^{92} +(6.60240 + 3.02618i) q^{93} -8.00387i q^{94} +(-1.57454 - 0.721683i) q^{96} +0.524688i q^{97} +(6.03581 - 3.54528i) q^{98} +(8.90122 - 7.67024i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4} + 4 q^{7}+O(q^{10}) $ 12 * q - 12 * q^4 + 4 * q^7	$ 12 q - 12 q^{4} + 4 q^{7} + 12 q^{16} - 8 q^{18} + 14 q^{21} - 4 q^{28} + 8 q^{37} + 12 q^{39} - 14 q^{42} - 12 q^{43} + 20 q^{46} + 28 q^{49} + 28 q^{51} + 36 q^{57} - 20 q^{58} + 22 q^{63} - 12 q^{64} + 64 q^{67} + 8 q^{72} - 8 q^{78} + 56 q^{79} - 16 q^{81} - 14 q^{84} - 20 q^{91} + 44 q^{93} + 48 q^{99}+O(q^{100}) $ 12 * q - 12 * q^4 + 4 * q^7 + 12 * q^16 - 8 * q^18 + 14 * q^21 - 4 * q^28 + 8 * q^37 + 12 * q^39 - 14 * q^42 - 12 * q^43 + 20 * q^46 + 28 * q^49 + 28 * q^51 + 36 * q^57 - 20 * q^58 + 22 * q^63 - 12 * q^64 + 64 * q^67 + 8 * q^72 - 8 * q^78 + 56 * q^79 - 16 * q^81 - 14 * q^84 - 20 * q^91 + 44 * q^93 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.721683	+	1.57454i	−0.416664	+	0.909060i
$3$	−0.721683	+	1.57454i	−0.416664	+	0.909060i
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	−1.57454	−	0.721683i	−0.642803	−	0.294626i
$7$	1.31429	−	2.29622i	0.496756	−	0.867891i
$7$	1.31429	−	2.29622i	0.496756	−	0.867891i
$8$		−	1.00000i		−	0.353553i
$9$	−1.95835	−	2.27264i	−0.652782	−	0.757546i
$10$		0			0
$11$			3.91669i			1.18093i	0.807064	+	0.590464i	$0.201055\pi$
$11$			3.91669i			1.18093i	−0.807064	+	0.590464i	$0.798945\pi$
$12$	0.721683	−	1.57454i	0.208332	−	0.454530i
$13$		−	4.99166i		−	1.38444i	−0.721688	−	0.692219i	$-0.756633\pi$
$13$		−	4.99166i		−	1.38444i	0.721688	−	0.692219i	$-0.243367\pi$
$14$	2.29622	+	1.31429i	0.613691	+	0.351259i
$15$		0			0
$16$	1.00000			0.250000
$17$	3.54830			0.860588			0.430294	−	0.902689i	$-0.358410\pi$
$17$	3.54830			0.860588			0.430294	+	0.902689i	$0.358410\pi$
$18$	2.27264	−	1.95835i	0.535666	−	0.461587i
$19$		−	3.14908i		−	0.722448i	−0.932479	−	0.361224i	$-0.882359\pi$
$19$		−	3.14908i		−	0.722448i	0.932479	−	0.361224i	$-0.117641\pi$
$20$		0			0
$21$	2.66699	+	3.72655i	0.581985	+	0.813200i
$22$	−3.91669			−0.835041
$23$		−	7.54528i		−	1.57330i	−0.617400	−	0.786649i	$-0.711814\pi$
$23$		−	7.54528i		−	1.57330i	0.617400	−	0.786649i	$-0.288186\pi$
$24$	1.57454	+	0.721683i	0.321401	+	0.147313i
$25$		0			0
$26$	4.99166			0.978946
$27$	4.99166	−	1.44337i	0.960646	−	0.277776i
$28$	−1.31429	+	2.29622i	−0.248378	+	0.433945i
$29$			7.54528i			1.40112i	0.713592	+	0.700561i	$0.247067\pi$
$29$			7.54528i			1.40112i	−0.713592	+	0.700561i	$0.752933\pi$
$30$		0			0
$31$		−	4.19323i		−	0.753126i	−0.926391	−	0.376563i	$-0.877106\pi$
$31$		−	4.19323i		−	0.753126i	0.926391	−	0.376563i	$-0.122894\pi$
$32$			1.00000i			0.176777i
$33$	−6.16698	−	2.82661i	−1.07353	−	0.492050i
$34$			3.54830i			0.608528i
$35$		0			0
$36$	1.95835	+	2.27264i	0.326391	+	0.378773i
$37$	10.4620			1.71994			0.859968	−	0.510347i	$-0.170483\pi$
$37$	10.4620			1.71994			0.859968	+	0.510347i	$0.170483\pi$
$38$	3.14908			0.510848
$39$	7.85957	+	3.60240i	1.25854	+	0.576846i
$40$		0			0
$41$	9.32176			1.45581			0.727907	−	0.685675i	$-0.240493\pi$
$41$	9.32176			1.45581			0.727907	+	0.685675i	$0.240493\pi$
$42$	−3.72655	+	2.66699i	−0.575019	+	0.411525i
$43$	2.91669			0.444791			0.222396	−	0.974956i	$-0.428612\pi$
$43$	2.91669			0.444791			0.222396	+	0.974956i	$0.428612\pi$
$44$		−	3.91669i		−	0.590464i
$45$		0			0
$46$	7.54528			1.11249
$47$	−8.00387			−1.16748			−0.583742	−	0.811939i	$-0.698412\pi$
$47$	−8.00387			−1.16748			−0.583742	+	0.811939i	$0.698412\pi$
$48$	−0.721683	+	1.57454i	−0.104166	+	0.227265i
$49$	−3.54528	−	6.03581i	−0.506468	−	0.862259i
$50$		0			0
$51$	−2.56075	+	5.58693i	−0.358576	+	0.782327i
$52$			4.99166i			0.692219i
$53$			0.288109i			0.0395748i	0.999804	+	0.0197874i	$0.00629893\pi$
$53$			0.288109i			0.0395748i	−0.999804	+	0.0197874i	$0.993701\pi$
$54$	1.44337	+	4.99166i	0.196417	+	0.679279i
$55$		0			0
$56$	−2.29622	−	1.31429i	−0.306846	−	0.175630i
$57$	4.95835	+	2.27264i	0.656749	+	0.301018i
$58$	−7.54528			−0.990743
$59$	−5.89894			−0.767976			−0.383988	−	0.923338i	$-0.625450\pi$
$59$	−5.89894			−0.767976			−0.383988	+	0.923338i	$0.625450\pi$
$60$		0			0
$61$		−	2.48752i		−	0.318494i	−0.987239	−	0.159247i	$-0.949093\pi$
$61$		−	2.48752i		−	0.318494i	0.987239	−	0.159247i	$-0.0509066\pi$
$62$	4.19323			0.532540
$63$	−7.79232	+	1.50989i	−0.981740	+	0.190228i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	2.82661	−	6.16698i	0.347932	−	0.759103i
$67$	−0.545275			−0.0666160			−0.0333080	−	0.999445i	$-0.510604\pi$
$67$	−0.545275			−0.0666160			−0.0333080	+	0.999445i	$0.510604\pi$
$68$	−3.54830			−0.430294
$69$	11.8803	+	5.44530i	1.43022	+	0.655537i
$70$		0			0
$71$			5.37142i			0.637470i	0.947844	+	0.318735i	$0.103258\pi$
$71$			5.37142i			0.637470i	−0.947844	+	0.318735i	$0.896742\pi$
$72$	−2.27264	+	1.95835i	−0.267833	+	0.230793i
$73$			4.85479i			0.568210i	0.958793	+	0.284105i	$0.0916964\pi$
$73$			4.85479i			0.568210i	−0.958793	+	0.284105i	$0.908304\pi$
$74$			10.4620i			1.21618i
$75$		0			0
$76$			3.14908i			0.361224i
$77$	8.99360	+	5.14768i	1.02492	+	0.586632i
$78$	−3.60240	+	7.85957i	−0.407891	+	0.889921i
$79$	0.742834			0.0835753			0.0417876	−	0.999127i	$-0.486695\pi$
$79$	0.742834			0.0835753			0.0417876	+	0.999127i	$0.486695\pi$
$80$		0			0
$81$	−1.32976	+	8.90122i	−0.147751	+	0.989025i
$82$			9.32176i			1.02942i
$83$	4.45557			0.489063			0.244531	−	0.969641i	$-0.421366\pi$
$83$	4.45557			0.489063			0.244531	+	0.969641i	$0.421366\pi$
$84$	−2.66699	−	3.72655i	−0.290992	−	0.406600i
$85$		0			0
$86$			2.91669i			0.314515i
$87$	−11.8803	−	5.44530i	−1.27371	−	0.583797i
$88$	3.91669			0.417521
$89$	−12.3340			−1.30740			−0.653699	−	0.756755i	$-0.726784\pi$
$89$	−12.3340			−1.30740			−0.653699	+	0.756755i	$0.726784\pi$
$90$		0			0
$91$	−11.4620	−	6.56050i	−1.20154	−	0.687727i
$92$			7.54528i			0.786649i
$93$	6.60240	+	3.02618i	0.684637	+	0.313801i
$94$		−	8.00387i		−	0.825536i
$95$		0			0
$96$	−1.57454	−	0.721683i	−0.160701	−	0.0736565i
$97$			0.524688i			0.0532740i	0.999645	+	0.0266370i	$0.00847982\pi$
$97$			0.524688i			0.0532740i	−0.999645	+	0.0266370i	$0.991520\pi$
$98$	6.03581	−	3.54528i	0.609709	−	0.358127i
$99$	8.90122	−	7.67024i	0.894606	−	0.770888i
$100$		0			0
$101$	8.00387			0.796415			0.398207	−	0.917295i	$-0.369632\pi$
$101$	8.00387			0.796415			0.398207	+	0.917295i	$0.369632\pi$
$102$	−5.58693	−	2.56075i	−0.553188	−	0.253552i
$103$			6.17269i			0.608213i	0.952638	+	0.304106i	$0.0983578\pi$
$103$			6.17269i			0.608213i	−0.952638	+	0.304106i	$0.901642\pi$
$104$	−4.99166			−0.489473
$105$		0			0
$106$	−0.288109			−0.0279836
$107$			2.65953i			0.257106i	0.991703	+	0.128553i	$0.0410332\pi$
$107$			2.65953i			0.257106i	−0.991703	+	0.128553i	$0.958967\pi$
$108$	−4.99166	+	1.44337i	−0.480323	+	0.138888i
$109$	14.9239			1.42945			0.714727	−	0.699404i	$-0.246551\pi$
$109$	14.9239			1.42945			0.714727	+	0.699404i	$0.246551\pi$
$110$		0			0
$111$	−7.55023	+	16.4728i	−0.716636	+	1.56353i
$112$	1.31429	−	2.29622i	0.124189	−	0.216973i
$113$		−	11.8024i		−	1.11028i	−0.831757	−	0.555140i	$-0.812665\pi$
$113$		−	11.8024i		−	1.11028i	0.831757	−	0.555140i	$-0.187335\pi$
$114$	−2.27264	+	4.95835i	−0.212852	+	0.464392i
$115$		0			0
$116$		−	7.54528i		−	0.700561i
$117$	−11.3442	+	9.77540i	−1.04878	+	0.903736i
$118$		−	5.89894i		−	0.543041i
$119$	4.66349	−	8.14768i	0.427502	−	0.746896i
$120$		0			0
$121$	−4.34047			−0.394589
$122$	2.48752			0.225209
$123$	−6.72736	+	14.6775i	−0.606586	+	1.32342i
$124$			4.19323i			0.376563i
$125$		0			0
$126$	−1.50989	−	7.79232i	−0.134512	−	0.694195i
$127$	−2.00000			−0.177471			−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000			−0.177471			−0.0887357	+	0.996055i	$0.528283\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−2.10493	+	4.59244i	−0.185329	+	0.404342i
$130$		0			0
$131$	14.6846			1.28300			0.641500	−	0.767123i	$-0.278312\pi$
$131$	14.6846			1.28300			0.641500	+	0.767123i	$0.278312\pi$
$132$	6.16698	+	2.82661i	0.536767	+	0.246025i
$133$	−7.23098	−	4.13881i	−0.627006	−	0.358880i
$134$		−	0.545275i		−	0.0471046i
$135$		0			0
$136$		−	3.54830i		−	0.304264i
$137$		−	18.3787i		−	1.57019i	−0.619372	−	0.785097i	$-0.712613\pi$
$137$		−	18.3787i		−	1.57019i	0.619372	−	0.785097i	$-0.287387\pi$
$138$	−5.44530	+	11.8803i	−0.463535	+	1.01132i
$139$		−	12.6077i		−	1.06937i	−0.845051	−	0.534686i	$-0.820430\pi$
$139$		−	12.6077i		−	1.06937i	0.845051	−	0.534686i	$-0.179570\pi$
$140$		0			0
$141$	5.77626	−	12.6024i	0.486449	−	1.06131i
$142$	−5.37142			−0.450759
$143$	19.5508			1.63492
$144$	−1.95835	−	2.27264i	−0.163195	−	0.189386i
$145$		0			0
$146$	−4.85479			−0.401785
$147$	12.0622	−	1.22623i	0.994872	−	0.101138i
$148$	−10.4620			−0.859968
$149$		−	5.65953i		−	0.463646i	−0.972758	−	0.231823i	$-0.925531\pi$
$149$		−	5.65953i		−	0.463646i	0.972758	−	0.231823i	$-0.0744691\pi$
$150$		0			0
$151$	−2.62858			−0.213911			−0.106956	−	0.994264i	$-0.534110\pi$
$151$	−2.62858			−0.213911			−0.106956	+	0.994264i	$0.534110\pi$
$152$	−3.14908			−0.255424
$153$	−6.94879	−	8.06399i	−0.561776	−	0.651935i
$154$	−5.14768	+	8.99360i	−0.414811	+	0.724725i
$155$		0			0
$156$	−7.85957	−	3.60240i	−0.629269	−	0.288423i
$157$		−	24.2853i		−	1.93818i	−0.246704	−	0.969091i	$-0.579348\pi$
$157$		−	24.2853i		−	1.93818i	0.246704	−	0.969091i	$-0.420652\pi$
$158$			0.742834i			0.0590967i
$159$	−0.453638	−	0.207923i	−0.0359758	−	0.0164894i
$160$		0			0
$161$	−17.3256	−	9.91669i	−1.36545	−	0.781545i
$162$	−8.90122	−	1.32976i	−0.699346	−	0.104476i
$163$	−13.4620			−1.05442			−0.527211	−	0.849734i	$-0.676762\pi$
$163$	−13.4620			−1.05442			−0.527211	+	0.849734i	$0.676762\pi$
$164$	−9.32176			−0.727907
$165$		0			0
$166$			4.45557i			0.345819i
$167$	21.7812			1.68548			0.842740	−	0.538321i	$-0.180941\pi$
$167$	21.7812			1.68548			0.842740	+	0.538321i	$0.180941\pi$
$168$	3.72655	−	2.66699i	0.287510	−	0.205763i
$169$	−11.9167			−0.916669
$170$		0			0
$171$	−7.15671	+	6.16698i	−0.547287	+	0.471601i
$172$	−2.91669			−0.222396
$173$	−0.907276			−0.0689789			−0.0344895	−	0.999405i	$-0.510981\pi$
$173$	−0.907276			−0.0689789			−0.0344895	+	0.999405i	$0.510981\pi$
$174$	5.44530	−	11.8803i	0.412807	−	0.900645i
$175$		0			0
$176$			3.91669i			0.295232i
$177$	4.25717	−	9.28811i	0.319988	−	0.698137i
$178$		−	12.3340i		−	0.924470i
$179$		−	2.08331i		−	0.155714i	−0.996965	−	0.0778569i	$-0.975192\pi$
$179$		−	2.08331i		−	0.155714i	0.996965	−	0.0778569i	$-0.0248077\pi$
$180$		0			0
$181$			24.6679i			1.83355i	0.399400	+	0.916777i	$0.369218\pi$
$181$			24.6679i			1.83355i	−0.399400	+	0.916777i	$0.630782\pi$
$182$	6.56050	−	11.4620i	0.486297	−	0.849618i
$183$	3.91669	+	1.79520i	0.289530	+	0.132705i
$184$	−7.54528			−0.556245
$185$		0			0
$186$	−3.02618	+	6.60240i	−0.221891	+	0.484111i
$187$			13.8976i			1.01629i
$188$	8.00387			0.583742
$189$	3.24621	−	13.3590i	0.236127	−	0.971722i
$190$		0			0
$191$		−	16.0072i		−	1.15824i	−0.815241	−	0.579122i	$-0.803396\pi$
$191$		−	16.0072i		−	1.15824i	0.815241	−	0.579122i	$-0.196604\pi$
$192$	0.721683	−	1.57454i	0.0520830	−	0.113633i
$193$	26.4310			1.90255			0.951273	−	0.308349i	$-0.0997764\pi$
$193$	26.4310			1.90255			0.951273	+	0.308349i	$0.0997764\pi$
$194$	−0.524688			−0.0376704
$195$		0			0
$196$	3.54528	+	6.03581i	0.253234	+	0.431129i
$197$		−	17.2644i		−	1.23004i	−0.788512	−	0.615019i	$-0.789148\pi$
$197$		−	17.2644i		−	1.23004i	0.788512	−	0.615019i	$-0.210852\pi$
$198$	7.67024	+	8.90122i	0.545100	+	0.632582i
$199$			10.8906i			0.772014i	0.922496	+	0.386007i	$0.126146\pi$
$199$			10.8906i			0.772014i	−0.922496	+	0.386007i	$0.873854\pi$
$200$		0			0
$201$	0.393516	−	0.858557i	0.0277565	−	0.0605579i
$202$			8.00387i			0.563150i
$203$	17.3256	+	9.91669i	1.21602	+	0.696015i
$204$	2.56075	−	5.58693i	0.179288	−	0.391163i
$205$		0			0
$206$	−6.17269			−0.430071
$207$	−17.1477	+	14.7763i	−1.19185	+	1.02702i
$208$		−	4.99166i		−	0.346110i
$209$	12.3340			0.853158
$210$		0			0
$211$	−6.88575			−0.474035			−0.237017	−	0.971505i	$-0.576170\pi$
$211$	−6.88575			−0.474035			−0.237017	+	0.971505i	$0.576170\pi$
$212$		−	0.288109i		−	0.0197874i
$213$	−8.45750	−	3.87646i	−0.579499	−	0.265611i
$214$	−2.65953			−0.181801
$215$		0			0
$216$	−1.44337	−	4.99166i	−0.0982087	−	0.339640i
$217$	−9.62858	−	5.51112i	−0.653631	−	0.374119i
$218$			14.9239i			1.01078i
$219$	−7.64405	−	3.50362i	−0.516537	−	0.236753i
$220$		0			0
$221$		−	17.7119i		−	1.19143i
$222$	−16.4728	−	7.55023i	−1.10558	−	0.506738i
$223$			2.90336i			0.194424i	0.995264	+	0.0972118i	$0.0309924\pi$
$223$			2.90336i			0.194424i	−0.995264	+	0.0972118i	$0.969008\pi$
$224$	2.29622	+	1.31429i	0.153423	+	0.0878148i
$225$		0			0
$226$	11.8024			0.785087
$227$	−21.6557			−1.43734			−0.718671	−	0.695351i	$-0.755249\pi$
$227$	−21.6557			−1.43734			−0.718671	+	0.695351i	$0.755249\pi$
$228$	−4.95835	−	2.27264i	−0.328374	−	0.150509i
$229$			16.9378i			1.11928i	0.828735	+	0.559641i	$0.189061\pi$
$229$			16.9378i			1.11928i	−0.828735	+	0.559641i	$0.810939\pi$
$230$		0			0
$231$	−14.5957	+	10.4458i	−0.960329	+	0.687282i
$232$	7.54528			0.495372
$233$		−	5.42378i		−	0.355324i	−0.984092	−	0.177662i	$-0.943147\pi$
$233$		−	5.42378i		−	0.355324i	0.984092	−	0.177662i	$-0.0568533\pi$
$234$	−9.77540	−	11.3442i	−0.639038	−	0.741596i
$235$		0			0
$236$	5.89894			0.383988
$237$	−0.536091	+	1.16962i	−0.0348228	+	0.0759750i
$238$	8.14768	+	4.66349i	0.528135	+	0.302289i
$239$			13.2572i			0.857535i	0.903415	+	0.428767i	$0.141052\pi$
$239$			13.2572i			0.857535i	−0.903415	+	0.428767i	$0.858948\pi$
$240$		0			0
$241$		−	18.5233i		−	1.19319i	−0.802543	−	0.596595i	$-0.796520\pi$
$241$		−	18.5233i		−	1.19319i	0.802543	−	0.596595i	$-0.203480\pi$
$242$		−	4.34047i		−	0.279016i
$243$	−13.0557	−	8.51763i	−0.837520	−	0.546406i
$244$			2.48752i			0.159247i
$245$		0			0
$246$	−14.6775	−	6.72736i	−0.935802	−	0.428921i
$247$	−15.7191			−1.00018
$248$	−4.19323			−0.266270
$249$	−3.21551	+	7.01547i	−0.203775	+	0.444587i
$250$		0			0
$251$	−21.5355			−1.35931			−0.679654	−	0.733533i	$-0.737870\pi$
$251$	−21.5355			−1.35931			−0.679654	+	0.733533i	$0.737870\pi$
$252$	7.79232	−	1.50989i	0.490870	−	0.0951141i
$253$	29.5525			1.85795
$254$		−	2.00000i		−	0.125491i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−31.8900			−1.98924			−0.994622	−	0.103575i	$-0.966972\pi$
$257$	−31.8900			−1.98924			−0.994622	+	0.103575i	$0.966972\pi$
$258$	−4.59244	−	2.10493i	−0.285913	−	0.131047i
$259$	13.7501	−	24.0230i	0.854388	−	1.49272i
$260$		0			0
$261$	17.1477	−	14.7763i	1.06141	−	0.914627i
$262$			14.6846i			0.907218i
$263$			14.1739i			0.873998i	0.899462	+	0.436999i	$0.143959\pi$
$263$			14.1739i			0.873998i	−0.899462	+	0.436999i	$0.856041\pi$
$264$	−2.82661	+	6.16698i	−0.173966	+	0.379552i
$265$		0			0
$266$	4.13881	−	7.23098i	0.253767	−	0.443360i
$267$	8.90122	−	19.4203i	0.544746	−	1.18850i
$268$	0.545275			0.0333080
$269$	6.68074			0.407332			0.203666	−	0.979040i	$-0.434714\pi$
$269$	6.68074			0.407332			0.203666	+	0.979040i	$0.434714\pi$
$270$		0			0
$271$		−	9.45864i		−	0.574571i	−0.957845	−	0.287286i	$-0.907247\pi$
$271$		−	9.45864i		−	0.574571i	0.957845	−	0.287286i	$-0.0927529\pi$
$272$	3.54830			0.215147
$273$	18.6017	−	13.3127i	1.12582	−	0.805722i
$274$	18.3787			1.11030
$275$		0			0
$276$	−11.8803	−	5.44530i	−0.715112	−	0.327769i
$277$	11.2048			0.673231			0.336616	−	0.941642i	$-0.390718\pi$
$277$	11.2048			0.673231			0.336616	+	0.941642i	$0.390718\pi$
$278$	12.6077			0.756160
$279$	−9.52969	+	8.21179i	−0.570527	+	0.491627i
$280$		0			0
$281$			2.90945i			0.173563i	0.996227	+	0.0867816i	$0.0276582\pi$
$281$			2.90945i			0.173563i	−0.996227	+	0.0867816i	$0.972342\pi$
$282$	12.6024	+	5.77626i	0.750462	+	0.343971i
$283$			24.4056i			1.45076i	0.688348	+	0.725381i	$0.258336\pi$
$283$			24.4056i			1.45076i	−0.688348	+	0.725381i	$0.741664\pi$
$284$		−	5.37142i		−	0.318735i
$285$		0			0
$286$			19.5508i			1.15606i
$287$	12.2515	−	21.4048i	0.723184	−	1.26349i
$288$	2.27264	−	1.95835i	0.133916	−	0.115397i
$289$	−4.40960			−0.259388
$290$		0			0
$291$	−0.826142	−	0.378659i	−0.0484293	−	0.0221974i
$292$		−	4.85479i		−	0.284105i
$293$	17.0799			0.997819			0.498910	−	0.866654i	$-0.333734\pi$
$293$	17.0799			0.997819			0.498910	+	0.866654i	$0.333734\pi$
$294$	1.22623	+	12.0622i	0.0715151	+	0.703481i
$295$		0			0
$296$		−	10.4620i		−	0.608089i
$297$	5.65322	+	19.5508i	0.328033	+	1.13445i
$298$	5.65953			0.327847
$299$	−37.6635			−2.17813
$300$		0			0
$301$	3.83338	−	6.69737i	0.220953	−	0.386030i
$302$		−	2.62858i		−	0.151258i
$303$	−5.77626	+	12.6024i	−0.331837	+	0.723989i
$304$		−	3.14908i		−	0.180612i
$305$		0			0
$306$	8.06399	−	6.94879i	0.460988	−	0.397236i
$307$		−	11.8093i		−	0.673991i	−0.941506	−	0.336996i	$-0.890589\pi$
$307$		−	11.8093i		−	0.673991i	0.941506	−	0.336996i	$-0.109411\pi$
$308$	−8.99360	−	5.14768i	−0.512458	−	0.293316i
$309$	−9.71913	−	4.45472i	−0.552902	−	0.253420i
$310$		0			0
$311$	2.88673			0.163692			0.0818458	−	0.996645i	$-0.473918\pi$
$311$	2.88673			0.163692			0.0818458	+	0.996645i	$0.473918\pi$
$312$	3.60240	−	7.85957i	0.203946	−	0.444960i
$313$		−	4.20986i		−	0.237955i	−0.992897	−	0.118978i	$-0.962038\pi$
$313$		−	4.20986i		−	0.237955i	0.992897	−	0.118978i	$-0.0379617\pi$
$314$	24.2853			1.37050
$315$		0			0
$316$	−0.742834			−0.0417876
$317$			23.2644i			1.30666i	0.757074	+	0.653330i	$0.226628\pi$
$317$			23.2644i			1.30666i	−0.757074	+	0.653330i	$0.773372\pi$
$318$	0.207923	−	0.453638i	0.0116598	−	0.0254388i
$319$	−29.5525			−1.65462
$320$		0			0
$321$	−4.18753	−	1.91934i	−0.233725	−	0.107127i
$322$	9.91669	−	17.3256i	0.552636	−	0.965520i
$323$		−	11.1739i		−	0.621730i
$324$	1.32976	−	8.90122i	0.0738757	−	0.494512i
$325$		0			0
$326$		−	13.4620i		−	0.745589i
$327$	−10.7704	+	23.4983i	−0.595602	+	1.29946i
$328$		−	9.32176i		−	0.514708i
$329$	−10.5194	+	18.3787i	−0.579954	+	1.01325i
$330$		0			0
$331$	−25.4620			−1.39952			−0.699758	−	0.714380i	$-0.746709\pi$
$331$	−25.4620			−1.39952			−0.699758	+	0.714380i	$0.746709\pi$
$332$	−4.45557			−0.244531
$333$	−20.4881	−	23.7763i	−1.12274	−	1.30293i
$334$			21.7812i			1.19181i
$335$		0			0
$336$	2.66699	+	3.72655i	0.145496	+	0.203300i
$337$	−7.68095			−0.418408			−0.209204	−	0.977872i	$-0.567087\pi$
$337$	−7.68095			−0.418408			−0.209204	+	0.977872i	$0.567087\pi$
$338$		−	11.9167i		−	0.648183i
$339$	18.5834	+	8.51763i	1.00931	+	0.462614i
$340$		0			0
$341$	16.4236			0.889387
$342$	−6.16698	−	7.15671i	−0.333472	−	0.386991i
$343$	−18.5191	+	0.207923i	−0.999937	+	0.0112268i
$344$		−	2.91669i		−	0.157257i
$345$		0			0
$346$		−	0.907276i		−	0.0487755i
$347$			8.26441i			0.443657i	0.975086	+	0.221828i	$0.0712025\pi$
$347$			8.26441i			0.443657i	−0.975086	+	0.221828i	$0.928798\pi$
$348$	11.8803	+	5.44530i	0.636853	+	0.291899i
$349$			24.6846i			1.32133i	0.750679	+	0.660667i	$0.229727\pi$
$349$			24.6846i			1.32133i	−0.750679	+	0.660667i	$0.770273\pi$
$350$		0			0
$351$	−7.20480	−	24.9167i	−0.384564	−	1.32995i
$352$	−3.91669			−0.208760
$353$	−18.8945			−1.00565			−0.502826	−	0.864388i	$-0.667706\pi$
$353$	−18.8945			−1.00565			−0.502826	+	0.864388i	$0.667706\pi$
$354$	9.28811	+	4.25717i	0.493657	+	0.226266i
$355$		0			0
$356$	12.3340			0.653699
$357$	9.46326	+	13.2229i	0.500849	+	0.699830i
$358$	2.08331			0.110106
$359$			1.49291i			0.0787927i	0.999224	+	0.0393964i	$0.0125435\pi$
$359$			1.49291i			0.0787927i	−0.999224	+	0.0393964i	$0.987457\pi$
$360$		0			0
$361$	9.08331			0.478069
$362$	−24.6679			−1.29652
$363$	3.13245	−	6.83425i	0.164411	−	0.358705i
$364$	11.4620	+	6.56050i	0.600770	+	0.343864i
$365$		0			0
$366$	−1.79520	+	3.91669i	−0.0938366	+	0.204729i
$367$			16.9544i			0.885015i	0.896765	+	0.442507i	$0.145911\pi$
$367$			16.9544i			0.885015i	−0.896765	+	0.442507i	$0.854089\pi$
$368$		−	7.54528i		−	0.393325i
$369$	−18.2552	−	21.1850i	−0.950330	−	1.10285i
$370$		0			0
$371$	0.661561	+	0.378659i	0.0343466	+	0.0196590i
$372$	−6.60240	−	3.02618i	−0.342319	−	0.156900i
$373$	22.8097			1.18104			0.590520	−	0.807023i	$-0.298923\pi$
$373$	22.8097			1.18104			0.590520	+	0.807023i	$0.298923\pi$
$374$	−13.8976			−0.718627
$375$		0			0
$376$			8.00387i			0.412768i
$377$	37.6635			1.93977
$378$	13.3590	+	3.24621i	0.687111	+	0.166967i
$379$	0.371417			0.0190784			0.00953920	−	0.999955i	$-0.496964\pi$
$379$	0.371417			0.0190784			0.00953920	+	0.999955i	$0.496964\pi$
$380$		0			0
$381$	1.44337	−	3.14908i	0.0739459	−	0.161332i
$382$	16.0072			0.819002
$383$	−32.8367			−1.67788			−0.838939	−	0.544226i	$-0.816823\pi$
$383$	−32.8367			−1.67788			−0.838939	+	0.544226i	$0.816823\pi$
$384$	1.57454	+	0.721683i	0.0803504	+	0.0368283i
$385$		0			0
$386$			26.4310i			1.34530i
$387$	−5.71189	−	6.62858i	−0.290352	−	0.336950i
$388$		−	0.524688i		−	0.0266370i
$389$		−	24.1287i		−	1.22338i	−0.791099	−	0.611688i	$-0.790491\pi$
$389$		−	24.1287i		−	1.22338i	0.791099	−	0.611688i	$-0.209509\pi$
$390$		0			0
$391$		−	26.7729i		−	1.35396i
$392$	−6.03581	+	3.54528i	−0.304855	+	0.179063i
$393$	−10.5976	+	23.1215i	−0.534580	+	1.16632i
$394$	17.2644			0.869768
$395$		0			0
$396$	−8.90122	+	7.67024i	−0.447303	+	0.385444i
$397$			7.35371i			0.369072i	0.982826	+	0.184536i	$0.0590782\pi$
$397$			7.35371i			0.369072i	−0.982826	+	0.184536i	$0.940922\pi$
$398$	−10.8906			−0.545896
$399$	11.7352	−	8.39856i	0.587495	−	0.420454i
$400$		0			0
$401$			17.1215i			0.855007i	0.904014	+	0.427503i	$0.140607\pi$
$401$			17.1215i			0.855007i	−0.904014	+	0.427503i	$0.859393\pi$
$402$	0.858557	+	0.393516i	0.0428209	+	0.0196268i
$403$	−20.9312			−1.04266
$404$	−8.00387			−0.398207
$405$		0			0
$406$	−9.91669	+	17.3256i	−0.492157	+	0.859857i
$407$			40.9763i			2.03112i
$408$	5.58693	+	2.56075i	0.276594	+	0.126776i
$409$			23.2246i			1.14838i	0.818722	+	0.574191i	$0.194683\pi$
$409$			23.2246i			1.14838i	−0.818722	+	0.574191i	$0.805317\pi$
$410$		0			0
$411$	28.9379	+	13.2636i	1.42740	+	0.654244i
$412$		−	6.17269i		−	0.304106i
$413$	−7.75293	+	13.5453i	−0.381497	+	0.666519i
$414$	−14.7763	−	17.1477i	−0.726213	−	0.842762i
$415$		0			0
$416$	4.99166			0.244736
$417$	19.8513	+	9.09878i	0.972124	+	0.445569i
$418$			12.3340i			0.603274i
$419$	11.5522			0.564360			0.282180	−	0.959361i	$-0.408942\pi$
$419$	11.5522			0.564360			0.282180	+	0.959361i	$0.408942\pi$
$420$		0			0
$421$	36.9239			1.79956			0.899781	−	0.436341i	$-0.143726\pi$
$421$	36.9239			1.79956			0.899781	+	0.436341i	$0.143726\pi$
$422$		−	6.88575i		−	0.335193i
$423$	15.6743	+	18.1899i	0.762112	+	0.884423i
$424$	0.288109			0.0139918
$425$		0			0
$426$	3.87646	−	8.45750i	0.187815	−	0.409767i
$427$	−5.71189	−	3.26932i	−0.276418	−	0.158214i
$428$		−	2.65953i		−	0.128553i
$429$	−14.1095	+	30.7835i	−0.681213	+	1.48624i
$430$		0			0
$431$		−	5.03094i		−	0.242332i	−0.992632	−	0.121166i	$-0.961337\pi$
$431$		−	5.03094i		−	0.242332i	0.992632	−	0.121166i	$-0.0386633\pi$
$432$	4.99166	−	1.44337i	0.240161	−	0.0694440i
$433$		−	3.04024i		−	0.146104i	−0.997328	−	0.0730522i	$-0.976726\pi$
$433$		−	3.04024i		−	0.146104i	0.997328	−	0.0730522i	$-0.0232740\pi$
$434$	5.51112	−	9.62858i	0.264542	−	0.462187i
$435$		0			0
$436$	−14.9239			−0.714727
$437$	−23.7607			−1.13663
$438$	3.50362	−	7.64405i	0.167409	−	0.365247i
$439$		−	19.8184i		−	0.945879i	−0.881095	−	0.472940i	$-0.843193\pi$
$439$		−	19.8184i		−	0.945879i	0.881095	−	0.472940i	$-0.156807\pi$
$440$		0			0
$441$	−6.77434	+	19.8773i	−0.322588	+	0.946540i
$442$	17.7119			0.842469
$443$			10.5976i			0.503509i	0.967791	+	0.251755i	$0.0810076\pi$
$443$			10.5976i			0.503509i	−0.967791	+	0.251755i	$0.918992\pi$
$444$	7.55023	−	16.4728i	0.358318	−	0.781763i
$445$		0			0
$446$	−2.90336			−0.137478
$447$	8.91114	+	4.08439i	0.421483	+	0.193185i
$448$	−1.31429	+	2.29622i	−0.0620944	+	0.108486i
$449$			6.19756i			0.292481i	0.989249	+	0.146240i	$0.0467173\pi$
$449$			6.19756i			0.292481i	−0.989249	+	0.146240i	$0.953283\pi$
$450$		0			0
$451$			36.5105i			1.71921i
$452$			11.8024i			0.555140i
$453$	1.89701	−	4.13881i	0.0891291	−	0.194458i
$454$		−	21.6557i		−	1.01635i
$455$		0			0
$456$	2.27264	−	4.95835i	0.106426	−	0.232196i
$457$	−19.7573			−0.924208			−0.462104	−	0.886826i	$-0.652905\pi$
$457$	−19.7573			−0.924208			−0.462104	+	0.886826i	$0.652905\pi$
$458$	−16.9378			−0.791452
$459$	17.7119	−	5.12149i	0.826720	−	0.239051i
$460$		0			0
$461$	−26.8983			−1.25278			−0.626390	−	0.779510i	$-0.715468\pi$
$461$	−26.8983			−1.25278			−0.626390	+	0.779510i	$0.715468\pi$
$462$	−10.4458	−	14.5957i	−0.485981	−	0.679055i
$463$	−38.7573			−1.80121			−0.900603	−	0.434643i	$-0.856874\pi$
$463$	−38.7573			−1.80121			−0.900603	+	0.434643i	$0.856874\pi$
$464$			7.54528i			0.350281i
$465$		0			0
$466$	5.42378			0.251252
$467$	18.5181			0.856913			0.428457	−	0.903562i	$-0.359057\pi$
$467$	18.5181			0.856913			0.428457	+	0.903562i	$0.359057\pi$
$468$	11.3442	−	9.77540i	0.524388	−	0.451868i
$469$	−0.716650	+	1.25207i	−0.0330918	+	0.0578154i
$470$		0			0
$471$	38.2382	+	17.5263i	1.76192	+	0.807571i
$472$			5.89894i			0.271521i
$473$			11.4238i			0.525266i
$474$	−1.16962	−	0.536091i	−0.0537224	−	0.0246235i
$475$		0			0
$476$	−4.66349	+	8.14768i	−0.213751	+	0.373448i
$477$	0.654766	−	0.564216i	0.0299797	−	0.0258337i
$478$	−13.2572			−0.606369
$479$	14.4337			0.659491			0.329746	−	0.944070i	$-0.393037\pi$
$479$	14.4337			0.659491			0.329746	+	0.944070i	$0.393037\pi$
$480$		0			0
$481$		−	52.2226i		−	2.38115i
$482$	18.5233			0.843712
$483$	28.1178	−	20.1232i	1.27941	−	0.915636i
$484$	4.34047			0.197294
$485$		0			0
$486$	8.51763	−	13.0557i	0.386367	−	0.592216i
$487$	−26.2430			−1.18918			−0.594592	−	0.804028i	$-0.702686\pi$
$487$	−26.2430			−1.18918			−0.594592	+	0.804028i	$0.702686\pi$
$488$	−2.48752			−0.112605
$489$	9.71528	−	21.1964i	0.439340	−	0.958534i
$490$		0			0
$491$			30.0000i			1.35388i	0.736038	+	0.676941i	$0.236695\pi$
$491$			30.0000i			1.35388i	−0.736038	+	0.676941i	$0.763305\pi$
$492$	6.72736	−	14.6775i	0.303293	−	0.661712i
$493$			26.7729i			1.20579i
$494$		−	15.7191i		−	0.707237i
$495$		0			0
$496$		−	4.19323i		−	0.188281i
$497$	12.3340	+	7.05961i	0.553254	+	0.316667i
$498$	−7.01547	−	3.21551i	−0.314371	−	0.144091i
$499$	41.6740			1.86558			0.932792	−	0.360414i	$-0.117365\pi$
$499$	41.6740			1.86558			0.932792	+	0.360414i	$0.117365\pi$
$500$		0			0
$501$	−15.7191	+	34.2954i	−0.702279	+	1.53220i
$502$		−	21.5355i		−	0.961176i
$503$	−0.415846			−0.0185417			−0.00927084	−	0.999957i	$-0.502951\pi$
$503$	−0.415846			−0.0185417			−0.00927084	+	0.999957i	$0.502951\pi$
$504$	1.50989	+	7.79232i	0.0672558	+	0.347097i
$505$		0			0
$506$			29.5525i			1.31377i
$507$	8.60008	−	18.7633i	0.381943	−	0.833307i
$508$	2.00000			0.0887357
$509$	11.3064			0.501149			0.250575	−	0.968097i	$-0.419380\pi$
$509$	11.3064			0.501149			0.250575	+	0.968097i	$0.419380\pi$
$510$		0			0
$511$	11.1477	+	6.38061i	0.493144	+	0.282261i
$512$			1.00000i			0.0441942i
$513$	−4.54528	−	15.7191i	−0.200679	−	0.694017i
$514$		−	31.8900i		−	1.40661i
$515$		0			0
$516$	2.10493	−	4.59244i	0.0926643	−	0.202171i
$517$		−	31.3487i		−	1.37871i
$518$	24.0230	+	13.7501i	1.05551	+	0.604144i
$519$	0.654766	−	1.42854i	0.0287411	−	0.0627060i
$520$		0			0
$521$	−2.47611			−0.108481			−0.0542403	−	0.998528i	$-0.517274\pi$
$521$	−2.47611			−0.108481			−0.0542403	+	0.998528i	$0.517274\pi$
$522$	14.7763	+	17.1477i	0.646739	+	0.750533i
$523$		−	12.0602i		−	0.527357i	−0.964611	−	0.263678i	$-0.915064\pi$
$523$		−	12.0602i		−	0.527357i	0.964611	−	0.263678i	$-0.0849357\pi$
$524$	−14.6846			−0.641500
$525$		0			0
$526$	−14.1739			−0.618010
$527$		−	14.8788i		−	0.648131i
$528$	−6.16698	−	2.82661i	−0.268384	−	0.123012i
$529$	−33.9312			−1.47527
$530$		0			0
$531$	11.5522	+	13.4061i	0.501321	+	0.581777i
$532$	7.23098	+	4.13881i	0.313503	+	0.179440i
$533$		−	46.5311i		−	2.01549i
$534$	19.4203	+	8.90122i	0.840399	+	0.385193i
$535$		0			0
$536$			0.545275i			0.0235523i
$537$	3.28025	+	1.50349i	0.141553	+	0.0648803i
$538$			6.68074i			0.288027i
$539$	23.6404	−	13.8857i	1.01826	−	0.598102i
$540$		0			0
$541$	5.14292			0.221111			0.110556	−	0.993870i	$-0.464737\pi$
$541$	5.14292			0.221111			0.110556	+	0.993870i	$0.464737\pi$
$542$	9.45864			0.406283
$543$	−38.8406	−	17.8024i	−1.66681	−	0.763976i
$544$			3.54830i			0.152132i
$545$		0			0
$546$	13.3127	+	18.6017i	0.569731	+	0.796078i
$547$	−3.11425			−0.133156			−0.0665779	−	0.997781i	$-0.521208\pi$
$547$	−3.11425			−0.133156			−0.0665779	+	0.997781i	$0.521208\pi$
$548$			18.3787i			0.785097i
$549$	−5.65322	+	4.87142i	−0.241274	+	0.207907i
$550$		0			0
$551$	23.7607			1.01224
$552$	5.44530	−	11.8803i	0.231767	−	0.505660i
$553$	0.976300	−	1.70571i	0.0415165	−	0.0725342i
$554$			11.2048i			0.476046i
$555$		0			0
$556$			12.6077i			0.534686i
$557$		−	1.93812i		−	0.0821206i	−0.999157	−	0.0410603i	$-0.986926\pi$
$557$		−	1.93812i		−	0.0821206i	0.999157	−	0.0410603i	$-0.0130736\pi$
$558$	−8.21179	−	9.52969i	−0.347633	−	0.403424i
$559$		−	14.5591i		−	0.615786i
$560$		0			0
$561$	−21.8823	−	10.0297i	−0.923871	−	0.423452i
$562$	−2.90945			−0.122728
$563$	−25.8656			−1.09010			−0.545052	−	0.838402i	$-0.683490\pi$
$563$	−25.8656			−1.09010			−0.545052	+	0.838402i	$0.683490\pi$
$564$	−5.77626	+	12.6024i	−0.243224	+	0.530657i
$565$		0			0
$566$	−24.4056			−1.02584
$567$	18.6915	+	14.7522i	0.784969	+	0.619535i
$568$	5.37142			0.225380
$569$			30.3787i			1.27354i	0.771054	+	0.636770i	$0.219730\pi$
$569$			30.3787i			1.27354i	−0.771054	+	0.636770i	$0.780270\pi$
$570$		0			0
$571$	4.56898			0.191206			0.0956028	−	0.995420i	$-0.469522\pi$
$571$	4.56898			0.191206			0.0956028	+	0.995420i	$0.469522\pi$
$572$	−19.5508			−0.817460
$573$	25.2040	+	11.5522i	1.05291	+	0.482598i
$574$	21.4048	+	12.2515i	0.893421	+	0.511368i
$575$		0			0
$576$	1.95835	+	2.27264i	0.0815977	+	0.0946932i
$577$		−	23.7493i		−	0.988694i	−0.869265	−	0.494347i	$-0.835407\pi$
$577$		−	23.7493i		−	0.988694i	0.869265	−	0.494347i	$-0.164593\pi$
$578$		−	4.40960i		−	0.183415i
$579$	−19.0748	+	41.6167i	−0.792723	+	1.72953i
$580$		0			0
$581$	5.85592	−	10.2310i	0.242945	−	0.424453i
$582$	0.378659	−	0.826142i	0.0156959	−	0.0342447i
$583$	−1.12843			−0.0467349
$584$	4.85479			0.200893
$585$		0			0
$586$			17.0799i			0.705565i
$587$	−28.8726			−1.19170			−0.595849	−	0.803096i	$-0.703184\pi$
$587$	−28.8726			−1.19170			−0.595849	+	0.803096i	$0.703184\pi$
$588$	−12.0622	+	1.22623i	−0.497436	+	0.0505688i
$589$	−13.2048			−0.544094
$590$		0			0
$591$	27.1835	+	12.4594i	1.11818	+	0.512513i
$592$	10.4620			0.429984
$593$	4.74595			0.194893			0.0974463	−	0.995241i	$-0.468933\pi$
$593$	4.74595			0.194893			0.0974463	+	0.995241i	$0.468933\pi$
$594$	−19.5508	+	5.65322i	−0.802179	+	0.231955i
$595$		0			0
$596$			5.65953i			0.231823i
$597$	−17.1477	−	7.85957i	−0.701808	−	0.321671i
$598$		−	37.6635i		−	1.54017i
$599$		−	3.19756i		−	0.130649i	−0.997864	−	0.0653243i	$-0.979192\pi$
$599$		−	3.19756i		−	0.130649i	0.997864	−	0.0653243i	$-0.0208082\pi$
$600$		0			0
$601$		−	1.16962i		−	0.0477098i	−0.999715	−	0.0238549i	$-0.992406\pi$
$601$		−	1.16962i		−	0.0477098i	0.999715	−	0.0238549i	$-0.00759397\pi$
$602$	6.69737	+	3.83338i	0.272965	+	0.156237i
$603$	1.06784	+	1.23921i	0.0434857	+	0.0504646i
$604$	2.62858			0.106956
$605$		0			0
$606$	−12.6024	−	5.77626i	−0.511938	−	0.234644i
$607$			42.5463i			1.72690i	0.504434	+	0.863450i	$0.331701\pi$
$607$			42.5463i			1.72690i	−0.504434	+	0.863450i	$0.668299\pi$
$608$	3.14908			0.127712
$609$	−28.1178	+	20.1232i	−1.13939	+	0.815432i
$610$		0			0
$611$			39.9526i			1.61631i
$612$	6.94879	+	8.06399i	0.280888	+	0.325967i
$613$	11.1524			0.450443			0.225221	−	0.974308i	$-0.427689\pi$
$613$	11.1524			0.450443			0.225221	+	0.974308i	$0.427689\pi$
$614$	11.8093			0.476584
$615$		0			0
$616$	5.14768	−	8.99360i	0.207406	−	0.362362i
$617$			42.1811i			1.69815i	0.528275	+	0.849074i	$0.322839\pi$
$617$			42.1811i			1.69815i	−0.528275	+	0.849074i	$0.677161\pi$
$618$	4.45472	−	9.71913i	0.179195	−	0.390961i
$619$			11.0327i			0.443442i	0.975110	+	0.221721i	$0.0711674\pi$
$619$			11.0327i			0.443442i	−0.975110	+	0.221721i	$0.928833\pi$
$620$		0			0
$621$	−10.8906	−	37.6635i	−0.437025	−	1.51138i
$622$			2.88673i			0.115747i
$623$	−16.2104	+	28.3215i	−0.649457	+	1.13468i
$624$	7.85957	+	3.60240i	0.314634	+	0.144211i
$625$		0			0
$626$	4.20986			0.168260
$627$	−8.90122	+	19.4203i	−0.355481	+	0.775573i
$628$			24.2853i			0.969091i
$629$	37.1221			1.48016
$630$		0			0
$631$	4.46197			0.177628			0.0888140	−	0.996048i	$-0.471692\pi$
$631$	4.46197			0.177628			0.0888140	+	0.996048i	$0.471692\pi$
$632$		−	0.742834i		−	0.0295483i
$633$	4.96933	−	10.8419i	0.197513	−	0.430926i
$634$	−23.2644			−0.923948
$635$		0			0
$636$	0.453638	+	0.207923i	0.0179879	+	0.00824469i
$637$	−30.1287	+	17.6968i	−1.19374	+	0.701173i
$638$		−	29.5525i		−	1.17000i
$639$	12.2073	−	10.5191i	0.482913	−	0.416129i
$640$		0			0
$641$		−	2.90945i		−	0.114916i	−0.998348	−	0.0574582i	$-0.981700\pi$
$641$		−	2.90945i		−	0.114916i	0.998348	−	0.0574582i	$-0.0182996\pi$
$642$	1.91934	−	4.18753i	0.0757501	−	0.165268i
$643$			31.7645i			1.25267i	0.779554	+	0.626335i	$0.215446\pi$
$643$			31.7645i			1.25267i	−0.779554	+	0.626335i	$0.784554\pi$
$644$	17.3256	+	9.91669i	0.682725	+	0.390772i
$645$		0			0
$646$	11.1739			0.439630
$647$	23.3448			0.917779			0.458890	−	0.888493i	$-0.348247\pi$
$647$	23.3448			0.917779			0.458890	+	0.888493i	$0.348247\pi$
$648$	8.90122	+	1.32976i	0.349673	+	0.0522380i
$649$		−	23.1043i		−	0.906924i
$650$		0			0
$651$	15.6263	−	11.1833i	0.612442	−	0.438308i
$652$	13.4620			0.527211
$653$		−	2.28087i		−	0.0892572i	−0.999004	−	0.0446286i	$-0.985790\pi$
$653$		−	2.28087i		−	0.0892572i	0.999004	−	0.0446286i	$-0.0142104\pi$
$654$	−23.4983	−	10.7704i	−0.918857	−	0.421154i
$655$		0			0
$656$	9.32176			0.363954
$657$	11.0332	−	9.50736i	0.430445	−	0.370917i
$658$	−18.3787	−	10.5194i	−0.716475	−	0.410089i
$659$		−	2.08331i		−	0.0811542i	−0.999176	−	0.0405771i	$-0.987080\pi$
$659$		−	2.08331i		−	0.0811542i	0.999176	−	0.0405771i	$-0.0129196\pi$
$660$		0			0
$661$		−	4.34150i		−	0.168865i	−0.996429	−	0.0844325i	$-0.973092\pi$
$661$		−	4.34150i		−	0.168865i	0.996429	−	0.0844325i	$-0.0269077\pi$
$662$		−	25.4620i		−	0.989607i
$663$	27.8881	+	12.7824i	1.08308	+	0.496426i
$664$		−	4.45557i		−	0.172910i
$665$		0			0
$666$	23.7763	−	20.4881i	0.921311	−	0.793900i
$667$	56.9312			2.20438
$668$	−21.7812			−0.842740
$669$	−4.57146	−	2.09531i	−0.176743	−	0.0810093i
$670$		0			0
$671$	9.74284			0.376118
$672$	−3.72655	+	2.66699i	−0.143755	+	0.102881i
$673$	−2.00724			−0.0773735			−0.0386867	−	0.999251i	$-0.512317\pi$
$673$	−2.00724			−0.0773735			−0.0386867	+	0.999251i	$0.512317\pi$
$674$		−	7.68095i		−	0.295859i
$675$		0			0
$676$	11.9167			0.458334
$677$	−27.5547			−1.05901			−0.529506	−	0.848306i	$-0.677623\pi$
$677$	−27.5547			−1.05901			−0.529506	+	0.848306i	$0.677623\pi$
$678$	−8.51763	+	18.5834i	−0.327117	+	0.713691i
$679$	1.20480	+	0.689593i	0.0462360	+	0.0264642i
$680$		0			0
$681$	15.6286	−	34.0978i	0.598889	−	1.30663i
$682$			16.4236i			0.628891i
$683$		−	5.75008i		−	0.220021i	−0.993930	−	0.110010i	$-0.964912\pi$
$683$		−	5.75008i		−	0.220021i	0.993930	−	0.110010i	$-0.0350884\pi$
$684$	7.15671	−	6.16698i	0.273644	−	0.235801i
$685$		0			0
$686$	−0.207923	−	18.5191i	−0.00793854	−	0.707062i
$687$	−26.6693	−	12.2237i	−1.01750	−	0.466365i
$688$	2.91669			0.111198
$689$	1.43814			0.0547888
$690$		0			0
$691$			23.6404i			0.899324i	0.893199	+	0.449662i	$0.148456\pi$
$691$			23.6404i			0.899324i	−0.893199	+	0.449662i	$0.851544\pi$
$692$	0.907276			0.0344895
$693$	−5.91377	−	30.5201i	−0.224646	−	1.15936i
$694$	−8.26441			−0.313713
$695$		0			0
$696$	−5.44530	+	11.8803i	−0.206404	+	0.450323i
$697$	33.0764			1.25286
$698$	−24.6846			−0.934325
$699$	8.53996	+	3.91425i	0.323011	+	0.148051i
$700$		0			0
$701$			46.6882i			1.76339i	0.471821	+	0.881694i	$0.343597\pi$
$701$			46.6882i			1.76339i	−0.471821	+	0.881694i	$0.656403\pi$
$702$	24.9167	−	7.20480i	0.940420	−	0.271928i
$703$		−	32.9455i		−	1.24256i
$704$		−	3.91669i		−	0.147616i
$705$		0			0
$706$		−	18.8945i		−	0.711103i
$707$	10.5194	−	18.3787i	0.395623	−	0.691201i
$708$	−4.25717	+	9.28811i	−0.159994	+	0.349068i
$709$	17.8334			0.669747			0.334873	−	0.942263i	$-0.391306\pi$
$709$	17.8334			0.669747			0.334873	+	0.942263i	$0.391306\pi$
$710$		0			0
$711$	−1.45472	−	1.68819i	−0.0545564	−	0.0633121i
$712$			12.3340i			0.462235i
$713$	−31.6391			−1.18489
$714$	−13.2229	+	9.46326i	−0.494854	+	0.354154i
$715$		0			0
$716$			2.08331i			0.0778569i
$717$	−20.8739	−	9.56748i	−0.779551	−	0.357304i
$718$	−1.49291			−0.0557149
$719$	18.4786			0.689136			0.344568	−	0.938761i	$-0.388025\pi$
$719$	18.4786			0.689136			0.344568	+	0.938761i	$0.388025\pi$
$720$		0			0
$721$	14.1739	+	8.11271i	0.527862	+	0.302133i
$722$			9.08331i			0.338046i
$723$	29.1656	+	13.3679i	1.08468	+	0.497159i
$724$		−	24.6679i		−	0.916777i
$725$		0			0
$726$	6.83425	+	3.13245i	0.253643	+	0.116256i
$727$		−	8.92777i		−	0.331113i	−0.986200	−	0.165556i	$-0.947058\pi$
$727$		−	8.92777i		−	0.331113i	0.986200	−	0.165556i	$-0.0529420\pi$
$728$	−6.56050	+	11.4620i	−0.243148	+	0.424809i
$729$	22.8334	−	14.4096i	0.845681	−	0.533689i
$730$		0			0
$731$	10.3493			0.382782
$732$	−3.91669	−	1.79520i	−0.144765	−	0.0663525i
$733$			24.7934i			0.915765i	0.889013	+	0.457883i	$0.151392\pi$
$733$			24.7934i			0.915765i	−0.889013	+	0.457883i	$0.848608\pi$
$734$	−16.9544			−0.625800
$735$		0			0
$736$	7.54528			0.278123
$737$		−	2.13567i		−	0.0786686i
$738$	21.1850	−	18.2552i	0.779830	−	0.671985i
$739$	5.32629			0.195931			0.0979654	−	0.995190i	$-0.468767\pi$
$739$	5.32629			0.195931			0.0979654	+	0.995190i	$0.468767\pi$
$740$		0			0
$741$	11.3442	−	24.7504i	0.416741	−	0.909228i
$742$	−0.378659	+	0.661561i	−0.0139010	+	0.0242867i
$743$			45.7409i			1.67807i	0.544078	+	0.839035i	$0.316880\pi$
$743$			45.7409i			1.67807i	−0.544078	+	0.839035i	$0.683120\pi$
$744$	3.02618	−	6.60240i	0.110945	−	0.242056i
$745$		0			0
$746$			22.8097i			0.835122i
$747$	−8.72555	−	10.1259i	−0.319251	−	0.370487i
$748$		−	13.8976i		−	0.508146i
$749$	6.10686	+	3.49539i	0.223140	+	0.127719i
$750$		0			0
$751$	−21.8857			−0.798622			−0.399311	−	0.916815i	$-0.630751\pi$
$751$	−21.8857			−0.798622			−0.399311	+	0.916815i	$0.630751\pi$
$752$	−8.00387			−0.291871
$753$	15.5418	−	33.9085i	0.566375	−	1.23569i
$754$			37.6635i			1.37162i
$755$		0			0
$756$	−3.24621	+	13.3590i	−0.118063	+	0.485861i
$757$	14.0524			0.510742			0.255371	−	0.966843i	$-0.417802\pi$
$757$	14.0524			0.510742			0.255371	+	0.966843i	$0.417802\pi$
$758$			0.371417i			0.0134905i
$759$	−21.3276	+	46.5316i	−0.774142	+	1.68899i
$760$		0			0
$761$	−49.6210			−1.79876			−0.899380	−	0.437167i	$-0.855982\pi$
$761$	−49.6210			−1.79876			−0.899380	+	0.437167i	$0.855982\pi$
$762$	3.14908	+	1.44337i	0.114079	+	0.0522877i
$763$	19.6144	−	34.2687i	0.710089	−	1.24061i
$764$			16.0072i			0.579122i
$765$		0			0
$766$		−	32.8367i		−	1.18644i
$767$			29.4455i			1.06322i
$768$	−0.721683	+	1.57454i	−0.0260415	+	0.0568163i
$769$			12.9903i			0.468442i	0.972183	+	0.234221i	$0.0752540\pi$
$769$			12.9903i			0.468442i	−0.972183	+	0.234221i	$0.924746\pi$
$770$		0			0
$771$	23.0145	−	50.2120i	0.828846	−	1.80834i
$772$	−26.4310			−0.951273
$773$	29.9500			1.07723			0.538613	−	0.842553i	$-0.318949\pi$
$773$	29.9500			1.07723			0.538613	+	0.842553i	$0.318949\pi$
$774$	6.62858	−	5.71189i	0.238260	−	0.205310i
$775$		0			0
$776$	0.524688			0.0188352
$777$	27.9020	+	38.9870i	1.00098	+	1.39865i
$778$	24.1287			0.865057
$779$		−	29.3550i		−	1.05175i
$780$		0			0
$781$	−21.0382			−0.752805
$782$	26.7729			0.957396
$783$	10.8906	+	37.6635i	0.389198	+	1.34598i
$784$	−3.54528	−	6.03581i	−0.126617	−	0.215565i
$785$		0			0
$786$	−23.1215	−	10.5976i	−0.824716	−	0.378005i
$787$			1.01612i			0.0362207i	0.999836	+	0.0181103i	$0.00576502\pi$
$787$			1.01612i			0.0362207i	−0.999836	+	0.0181103i	$0.994235\pi$
$788$			17.2644i			0.615019i
$789$	−22.3173	−	10.2290i	−0.794517	−	0.364163i
$790$		0			0
$791$	−27.1010	−	15.5119i	−0.963602	−	0.551538i
$792$	−7.67024	−	8.90122i	−0.272550	−	0.316291i
$793$	−12.4168			−0.440935
$794$	−7.35371			−0.260973
$795$		0			0
$796$		−	10.8906i		−	0.386007i
$797$	−40.4247			−1.43192			−0.715959	−	0.698143i	$-0.754010\pi$
$797$	−40.4247			−1.43192			−0.715959	+	0.698143i	$0.754010\pi$
$798$	8.39856	+	11.7352i	0.297306	+	0.415421i
$799$	−28.4001			−1.00472
$800$		0			0
$801$	24.1542	+	28.0306i	0.853446	+	0.990414i
$802$	−17.1215			−0.604581
$803$	−19.0147			−0.671015
$804$	−0.393516	+	0.858557i	−0.0138782	+	0.0302790i
$805$		0			0
$806$		−	20.9312i		−	0.737269i
$807$	−4.82138	+	10.5191i	−0.169721	+	0.370290i
$808$		−	8.00387i		−	0.281575i
$809$		−	23.0287i		−	0.809645i	−0.914395	−	0.404822i	$-0.867333\pi$
$809$		−	23.0287i		−	0.809645i	0.914395	−	0.404822i	$-0.132667\pi$
$810$		0			0
$811$		−	29.9272i		−	1.05089i	−0.850829	−	0.525443i	$-0.823900\pi$
$811$		−	29.9272i		−	1.05089i	0.850829	−	0.525443i	$-0.176100\pi$
$812$	−17.3256	−	9.91669i	−0.608010	−	0.348008i
$813$	14.8930	+	6.82614i	0.522320	+	0.239403i
$814$	−40.9763			−1.43622
$815$		0			0
$816$	−2.56075	+	5.58693i	−0.0896440	+	0.195582i
$817$		−	9.18489i		−	0.321339i
$818$	−23.2246			−0.812028
$819$	7.53686	+	38.8966i	0.263359	+	1.35916i
$820$		0			0
$821$		−	10.9763i		−	0.383076i	−0.981485	−	0.191538i	$-0.938653\pi$
$821$		−	10.9763i		−	0.383076i	0.981485	−	0.191538i	$-0.0613474\pi$
$822$	−13.2636	+	28.9379i	−0.462620	+	1.00933i
$823$	28.6286			0.997930			0.498965	−	0.866622i	$-0.333714\pi$
$823$	28.6286			0.997930			0.498965	+	0.866622i	$0.333714\pi$
$824$	6.17269			0.215036
$825$		0			0
$826$	−13.5453	−	7.75293i	−0.471300	−	0.269759i
$827$			1.97858i			0.0688018i	0.999408	+	0.0344009i	$0.0109523\pi$
$827$			1.97858i			0.0688018i	−0.999408	+	0.0344009i	$0.989048\pi$
$828$	17.1477	−	14.7763i	0.595923	−	0.513510i
$829$			39.7518i			1.38064i	0.723506	+	0.690318i	$0.242529\pi$
$829$			39.7518i			1.38064i	−0.723506	+	0.690318i	$0.757471\pi$
$830$		0			0
$831$	−8.08632	+	17.6424i	−0.280511	+	0.612008i
$832$			4.99166i			0.173055i
$833$	−12.5797	−	21.4168i	−0.435860	−	0.742050i
$834$	−9.09878	+	19.8513i	−0.315065	+	0.687396i
$835$		0			0
$836$	−12.3340			−0.426579
$837$	−6.05237	−	20.9312i	−0.209200	−	0.723487i
$838$			11.5522i			0.399063i
$839$	−19.5508			−0.674969			−0.337484	−	0.941331i	$-0.609576\pi$
$839$	−19.5508			−0.674969			−0.337484	+	0.941331i	$0.609576\pi$
$840$		0			0
$841$	−27.9312			−0.963144
$842$			36.9239i			1.27248i
$843$	−4.58104	−	2.09970i	−0.157779	−	0.0723176i
$844$	6.88575			0.237017
$845$		0			0
$846$	−18.1899	+	15.6743i	−0.625381	+	0.538895i
$847$	−5.70465	+	9.96670i	−0.196014	+	0.342460i
$848$			0.288109i			0.00989369i
$849$	−38.4276	−	17.6131i	−1.31883	−	0.604480i
$850$		0			0
$851$		−	78.9384i		−	2.70597i
$852$	8.45750	+	3.87646i	0.289749	+	0.132805i
$853$		−	11.6724i		−	0.399656i	−0.979831	−	0.199828i	$-0.935962\pi$
$853$		−	11.6724i		−	0.399656i	0.979831	−	0.199828i	$-0.0640383\pi$
$854$	3.26932	−	5.71189i	0.111874	−	0.195457i
$855$		0			0
$856$	2.65953			0.0909007
$857$	−3.91425			−0.133708			−0.0668542	−	0.997763i	$-0.521296\pi$
$857$	−3.91425			−0.133708			−0.0668542	+	0.997763i	$0.521296\pi$
$858$	−30.7835	−	14.1095i	−1.05093	−	0.481690i
$859$		−	43.3229i		−	1.47816i	−0.673619	−	0.739079i	$-0.735261\pi$
$859$		−	43.3229i		−	1.47816i	0.673619	−	0.739079i	$-0.264739\pi$
$860$		0			0
$861$	24.8610	+	34.7380i	0.847262	+	1.18387i
$862$	5.03094			0.171355
$863$		−	33.8479i		−	1.15219i	−0.817381	−	0.576097i	$-0.804575\pi$
$863$		−	33.8479i		−	1.15219i	0.817381	−	0.576097i	$-0.195425\pi$
$864$	1.44337	+	4.99166i	0.0491043	+	0.169820i
$865$		0			0
$866$	3.04024			0.103311
$867$	3.18234	−	6.94309i	0.108078	−	0.235800i
$868$	9.62858	+	5.51112i	0.326815	+	0.187060i
$869$			2.90945i			0.0986963i
$870$		0			0
$871$			2.72183i			0.0922257i
$872$		−	14.9239i		−	0.505388i
$873$	1.19243	−	1.02752i	0.0403575	−	0.0347763i
$874$		−	23.7607i		−	0.803716i
$875$		0			0
$876$	7.64405	+	3.50362i	0.258269	+	0.118376i
$877$	−15.4383			−0.521313			−0.260657	−	0.965432i	$-0.583939\pi$
$877$	−15.4383			−0.521313			−0.260657	+	0.965432i	$0.583939\pi$
$878$	19.8184			0.668838
$879$	−12.3263	+	26.8930i	−0.415756	+	0.907078i
$880$		0			0
$881$	−5.64800			−0.190286			−0.0951429	−	0.995464i	$-0.530331\pi$
$881$	−5.64800			−0.190286			−0.0951429	+	0.995464i	$0.530331\pi$
$882$	−19.8773	−	6.77434i	−0.669305	−	0.228104i
$883$	−7.05237			−0.237331			−0.118666	−	0.992934i	$-0.537862\pi$
$883$	−7.05237			−0.237331			−0.118666	+	0.992934i	$0.537862\pi$
$884$			17.7119i			0.595715i
$885$		0			0
$886$	−10.5976			−0.356035
$887$	−21.9461			−0.736878			−0.368439	−	0.929652i	$-0.620108\pi$
$887$	−21.9461			−0.736878			−0.368439	+	0.929652i	$0.620108\pi$
$888$	16.4728	+	7.55023i	0.552790	+	0.253369i
$889$	−2.62858	+	4.59244i	−0.0881599	+	0.154026i
$890$		0			0
$891$	−34.8633	−	5.20827i	−1.16797	−	0.174484i
$892$		−	2.90336i		−	0.0972118i
$893$			25.2048i			0.843446i
$894$	−4.08439	+	8.91114i	−0.136602	+	0.298033i
$895$		0			0
$896$	−2.29622	−	1.31429i	−0.0767114	−	0.0439074i
$897$	27.1811	−	59.3026i	0.907551	−	1.98006i
$898$	−6.19756			−0.206815
$899$	31.6391			1.05522
$900$		0			0
$901$			1.02229i			0.0340576i
$902$	−36.5105			−1.21567
$903$	7.77879	+	10.8692i	0.258862	+	0.361704i
$904$	−11.8024			−0.392543
$905$		0			0
$906$	4.13881	+	1.89701i	0.137503	+	0.0630238i
$907$	51.7787			1.71928			0.859642	−	0.510896i	$-0.170686\pi$
$907$	51.7787			1.71928			0.859642	+	0.510896i	$0.170686\pi$
$908$	21.6557			0.718671
$909$	−15.6743	−	18.1899i	−0.519885	−	0.603321i
$910$		0			0
$911$			35.2644i			1.16836i	0.811623	+	0.584181i	$0.198584\pi$
$911$			35.2644i			1.16836i	−0.811623	+	0.584181i	$0.801416\pi$
$912$	4.95835	+	2.27264i	0.164187	+	0.0752545i
$913$			17.4511i			0.577547i
$914$		−	19.7573i		−	0.653514i
$915$		0			0
$916$		−	16.9378i		−	0.559641i
$917$	19.2999	−	33.7191i	0.637338	−	1.11350i
$918$	5.12149	+	17.7119i	0.169034	+	0.584580i
$919$	−22.0145			−0.726191			−0.363095	−	0.931752i	$-0.618280\pi$
$919$	−22.0145			−0.726191			−0.363095	+	0.931752i	$0.618280\pi$
$920$		0			0
$921$	18.5942	+	8.52256i	0.612699	+	0.280828i
$922$		−	26.8983i		−	0.885849i
$923$	26.8123			0.882538
$924$	14.5957	−	10.4458i	0.480165	−	0.343641i
$925$		0			0
$926$		−	38.7573i		−	1.27364i
$927$	14.0283	−	12.0883i	0.460749	−	0.397030i
$928$	−7.54528			−0.247686
$929$	−21.4048			−0.702268			−0.351134	−	0.936325i	$-0.614204\pi$
$929$	−21.4048			−0.702268			−0.351134	+	0.936325i	$0.614204\pi$
$930$		0			0
$931$	−19.0072	+	11.1643i	−0.622937	+	0.365897i
$932$			5.42378i			0.177662i
$933$	−2.08331	+	4.54528i	−0.0682044	+	0.148806i
$934$			18.5181i			0.605929i
$935$		0			0
$936$	9.77540	+	11.3442i	0.319519	+	0.370798i
$937$			37.3845i			1.22130i	0.791901	+	0.610649i	$0.209091\pi$
$937$			37.3845i			1.22130i	−0.791901	+	0.610649i	$0.790909\pi$
$938$	−1.25207	−	0.716650i	−0.0408816	−	0.0233995i
$939$	6.62858	+	3.03818i	0.216316	+	0.0991474i
$940$		0			0
$941$	−34.1598			−1.11358			−0.556789	−	0.830654i	$-0.687967\pi$
$941$	−34.1598			−1.11358			−0.556789	+	0.830654i	$0.687967\pi$
$942$	−17.5263	+	38.2382i	−0.571039	+	1.24587i
$943$		−	70.3353i		−	2.29043i
$944$	−5.89894			−0.191994
$945$		0			0
$946$	−11.4238			−0.371419
$947$		−	46.2430i		−	1.50270i	−0.659907	−	0.751348i	$-0.729404\pi$
$947$		−	46.2430i		−	1.50270i	0.659907	−	0.751348i	$-0.270596\pi$
$948$	0.536091	−	1.16962i	0.0174114	−	0.0379875i
$949$	24.2335			0.786652
$950$		0			0
$951$	−36.6307	−	16.7895i	−1.18783	−	0.544438i
$952$	−8.14768	−	4.66349i	−0.264068	−	0.151145i
$953$			25.1360i			0.814234i	0.913376	+	0.407117i	$0.133466\pi$
$953$			25.1360i			0.814234i	−0.913376	+	0.407117i	$0.866534\pi$
$954$	0.564216	+	0.654766i	0.0182672	+	0.0211988i
$955$		0			0
$956$		−	13.2572i		−	0.428767i
$957$	21.3276	−	46.5316i	0.689422	−	1.50415i
$958$			14.4337i			0.466331i
$959$	−42.2015	−	24.1549i	−1.36276	−	0.780003i
$960$		0			0
$961$	13.4168			0.432801
$962$	52.2226			1.68372
$963$	6.04414	−	5.20827i	0.194770	−	0.167834i
$964$			18.5233i			0.596595i
$965$		0			0
$966$	20.1232	+	28.1178i	0.647452	+	0.904677i
$967$	−50.1287			−1.61203			−0.806016	−	0.591894i	$-0.798380\pi$
$967$	−50.1287			−1.61203			−0.806016	+	0.591894i	$0.798380\pi$
$968$			4.34047i			0.139508i
$969$	17.5937	+	8.06399i	0.565190	+	0.259053i
$970$		0			0
$971$	−50.5387			−1.62187			−0.810933	−	0.585139i	$-0.801040\pi$
$971$	−50.5387			−1.62187			−0.810933	+	0.585139i	$0.801040\pi$
$972$	13.0557	+	8.51763i	0.418760	+	0.273203i
$973$	−28.9501	−	16.5702i	−0.928098	−	0.531217i
$974$		−	26.2430i		−	0.840879i
$975$		0			0
$976$		−	2.48752i		−	0.0796235i
$977$		−	61.1360i		−	1.95591i	−0.208808	−	0.977957i	$-0.566958\pi$
$977$		−	61.1360i		−	1.95591i	0.208808	−	0.977957i	$-0.433042\pi$
$978$	21.1964	+	9.71528i	0.677786	+	0.310660i
$979$		−	48.3084i		−	1.54394i
$980$		0			0
$981$	−29.2262	−	33.9167i	−0.933122	−	1.08288i
$982$	−30.0000			−0.957338
$983$	9.32699			0.297485			0.148742	−	0.988876i	$-0.452477\pi$
$983$	9.32699			0.297485			0.148742	+	0.988876i	$0.452477\pi$
$984$	14.6775	+	6.72736i	0.467901	+	0.214460i
$985$		0			0
$986$	−26.7729			−0.852622
$987$	−21.3462	−	29.8268i	−0.679458	−	0.949398i
$988$	15.7191			0.500092
$989$		−	22.0072i		−	0.699790i
$990$		0			0
$991$	45.0527			1.43115			0.715573	−	0.698538i	$-0.246166\pi$
$991$	45.0527			1.43115			0.715573	+	0.698538i	$0.246166\pi$
$992$	4.19323			0.133135
$993$	18.3755	−	40.0909i	0.583128	−	1.27224i
$994$	−7.05961	+	12.3340i	−0.223917	+	0.391210i
$995$		0			0
$996$	3.21551	−	7.01547i	0.101887	−	0.222294i
$997$			14.0283i			0.444280i	0.975015	+	0.222140i	$0.0713042\pi$
$997$			14.0283i			0.444280i	−0.975015	+	0.222140i	$0.928696\pi$
$998$			41.6740i			1.31917i
$999$	52.2226	−	15.1005i	1.65225	−	0.477757i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.b.e.251.9	yes	12
3.2	odd	2	inner	1050.2.b.e.251.4	yes	12
5.2	odd	4		1050.2.d.g.1049.12		12
5.3	odd	4		1050.2.d.h.1049.1		12
5.4	even	2		1050.2.b.d.251.4	yes	12
7.6	odd	2	inner	1050.2.b.e.251.10	yes	12
15.2	even	4		1050.2.d.h.1049.11		12
15.8	even	4		1050.2.d.g.1049.2		12
15.14	odd	2		1050.2.b.d.251.9	yes	12
21.20	even	2	inner	1050.2.b.e.251.3	yes	12
35.13	even	4		1050.2.d.h.1049.12		12
35.27	even	4		1050.2.d.g.1049.1		12
35.34	odd	2		1050.2.b.d.251.3	✓	12
105.62	odd	4		1050.2.d.h.1049.2		12
105.83	odd	4		1050.2.d.g.1049.11		12
105.104	even	2		1050.2.b.d.251.10	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.b.d.251.3	✓	12	35.34	odd	2
1050.2.b.d.251.4	yes	12	5.4	even	2
1050.2.b.d.251.9	yes	12	15.14	odd	2
1050.2.b.d.251.10	yes	12	105.104	even	2
1050.2.b.e.251.3	yes	12	21.20	even	2	inner
1050.2.b.e.251.4	yes	12	3.2	odd	2	inner
1050.2.b.e.251.9	yes	12	1.1	even	1	trivial
1050.2.b.e.251.10	yes	12	7.6	odd	2	inner
1050.2.d.g.1049.1		12	35.27	even	4
1050.2.d.g.1049.2		12	15.8	even	4
1050.2.d.g.1049.11		12	105.83	odd	4
1050.2.d.g.1049.12		12	5.2	odd	4
1050.2.d.h.1049.1		12	5.3	odd	4
1050.2.d.h.1049.2		12	105.62	odd	4
1050.2.d.h.1049.11		12	15.2	even	4
1050.2.d.h.1049.12		12	35.13	even	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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.721683 + 1.57454i) q^{3} -1.00000 q^{4} +(-1.57454 - 0.721683i) q^{6} +(1.31429 - 2.29622i) q^{7} -1.00000i q^{8} +(-1.95835 - 2.27264i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.721683 + 1.57454i) q^{3} -1.00000 q^{4} +(-1.57454 - 0.721683i) q^{6} +(1.31429 - 2.29622i) q^{7} -1.00000i q^{8} +(-1.95835 - 2.27264i) q^{9} +3.91669i q^{11} +(0.721683 - 1.57454i) q^{12} -4.99166i q^{13} +(2.29622 + 1.31429i) q^{14} +1.00000 q^{16} +3.54830 q^{17} +(2.27264 - 1.95835i) q^{18} -3.14908i q^{19} +(2.66699 + 3.72655i) q^{21} -3.91669 q^{22} -7.54528i q^{23} +(1.57454 + 0.721683i) q^{24} +4.99166 q^{26} +(4.99166 - 1.44337i) q^{27} +(-1.31429 + 2.29622i) q^{28} +7.54528i q^{29} -4.19323i q^{31} +1.00000i q^{32} +(-6.16698 - 2.82661i) q^{33} +3.54830i q^{34} +(1.95835 + 2.27264i) q^{36} +10.4620 q^{37} +3.14908 q^{38} +(7.85957 + 3.60240i) q^{39} +9.32176 q^{41} +(-3.72655 + 2.66699i) q^{42} +2.91669 q^{43} -3.91669i q^{44} +7.54528 q^{46} -8.00387 q^{47} +(-0.721683 + 1.57454i) q^{48} +(-3.54528 - 6.03581i) q^{49} +(-2.56075 + 5.58693i) q^{51} +4.99166i q^{52} +0.288109i q^{53} +(1.44337 + 4.99166i) q^{54} +(-2.29622 - 1.31429i) q^{56} +(4.95835 + 2.27264i) q^{57} -7.54528 q^{58} -5.89894 q^{59} -2.48752i q^{61} +4.19323 q^{62} +(-7.79232 + 1.50989i) q^{63} -1.00000 q^{64} +(2.82661 - 6.16698i) q^{66} -0.545275 q^{67} -3.54830 q^{68} +(11.8803 + 5.44530i) q^{69} +5.37142i q^{71} +(-2.27264 + 1.95835i) q^{72} +4.85479i q^{73} +10.4620i q^{74} +3.14908i q^{76} +(8.99360 + 5.14768i) q^{77} +(-3.60240 + 7.85957i) q^{78} +0.742834 q^{79} +(-1.32976 + 8.90122i) q^{81} +9.32176i q^{82} +4.45557 q^{83} +(-2.66699 - 3.72655i) q^{84} +2.91669i q^{86} +(-11.8803 - 5.44530i) q^{87} +3.91669 q^{88} -12.3340 q^{89} +(-11.4620 - 6.56050i) q^{91} +7.54528i q^{92} +(6.60240 + 3.02618i) q^{93} -8.00387i q^{94} +(-1.57454 - 0.721683i) q^{96} +0.524688i q^{97} +(6.03581 - 3.54528i) q^{98} +(8.90122 - 7.67024i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4} + 4 q^{7}+O(q^{10}) \) 12 * q - 12 * q^4 + 4 * q^7	\( 12 q - 12 q^{4} + 4 q^{7} + 12 q^{16} - 8 q^{18} + 14 q^{21} - 4 q^{28} + 8 q^{37} + 12 q^{39} - 14 q^{42} - 12 q^{43} + 20 q^{46} + 28 q^{49} + 28 q^{51} + 36 q^{57} - 20 q^{58} + 22 q^{63} - 12 q^{64} + 64 q^{67} + 8 q^{72} - 8 q^{78} + 56 q^{79} - 16 q^{81} - 14 q^{84} - 20 q^{91} + 44 q^{93} + 48 q^{99}+O(q^{100}) \) 12 * q - 12 * q^4 + 4 * q^7 + 12 * q^16 - 8 * q^18 + 14 * q^21 - 4 * q^28 + 8 * q^37 + 12 * q^39 - 14 * q^42 - 12 * q^43 + 20 * q^46 + 28 * q^49 + 28 * q^51 + 36 * q^57 - 20 * q^58 + 22 * q^63 - 12 * q^64 + 64 * q^67 + 8 * q^72 - 8 * q^78 + 56 * q^79 - 16 * q^81 - 14 * q^84 - 20 * q^91 + 44 * q^93 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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