LMFDB - Embedded newform 1050.2.d.h.1049.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(1049,1050)]

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, 1, 1]))

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

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

chi := DirichletCharacter("1050.1049");

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.d (of order $2$, degree $1$, not 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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1049.1
Root			$-0.721683 + 1.57454i$ of defining polynomial
Character	$\chi$	$=$	1050.1049
Dual form			1050.2.d.h.1049.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.57454 - 0.721683i) q^{3} +1.00000 q^{4} +(-1.57454 - 0.721683i) q^{6} +(-2.29622 - 1.31429i) q^{7} +1.00000 q^{8} +(1.95835 + 2.27264i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.57454 - 0.721683i) q^{3} +1.00000 q^{4} +(-1.57454 - 0.721683i) q^{6} +(-2.29622 - 1.31429i) q^{7} +1.00000 q^{8} +(1.95835 + 2.27264i) q^{9} +3.91669i q^{11} +(-1.57454 - 0.721683i) q^{12} +4.99166 q^{13} +(-2.29622 - 1.31429i) q^{14} +1.00000 q^{16} -3.54830i q^{17} +(1.95835 + 2.27264i) q^{18} +3.14908i q^{19} +(2.66699 + 3.72655i) q^{21} +3.91669i q^{22} +7.54528 q^{23} +(-1.57454 - 0.721683i) q^{24} +4.99166 q^{26} +(-1.44337 - 4.99166i) q^{27} +(-2.29622 - 1.31429i) q^{28} -7.54528i q^{29} -4.19323i q^{31} +1.00000 q^{32} +(2.82661 - 6.16698i) q^{33} -3.54830i q^{34} +(1.95835 + 2.27264i) q^{36} -10.4620i q^{37} +3.14908i q^{38} +(-7.85957 - 3.60240i) q^{39} +9.32176 q^{41} +(2.66699 + 3.72655i) q^{42} +2.91669i q^{43} +3.91669i q^{44} +7.54528 q^{46} +8.00387i q^{47} +(-1.57454 - 0.721683i) q^{48} +(3.54528 + 6.03581i) q^{49} +(-2.56075 + 5.58693i) q^{51} +4.99166 q^{52} -0.288109 q^{53} +(-1.44337 - 4.99166i) q^{54} +(-2.29622 - 1.31429i) q^{56} +(2.27264 - 4.95835i) q^{57} -7.54528i q^{58} +5.89894 q^{59} -2.48752i q^{61} -4.19323i q^{62} +(-1.50989 - 7.79232i) q^{63} +1.00000 q^{64} +(2.82661 - 6.16698i) q^{66} +0.545275i q^{67} -3.54830i q^{68} +(-11.8803 - 5.44530i) q^{69} +5.37142i q^{71} +(1.95835 + 2.27264i) q^{72} -4.85479 q^{73} -10.4620i q^{74} +3.14908i q^{76} +(5.14768 - 8.99360i) q^{77} +(-7.85957 - 3.60240i) q^{78} -0.742834 q^{79} +(-1.32976 + 8.90122i) q^{81} +9.32176 q^{82} +4.45557i q^{83} +(2.66699 + 3.72655i) q^{84} +2.91669i q^{86} +(-5.44530 + 11.8803i) q^{87} +3.91669i q^{88} +12.3340 q^{89} +(-11.4620 - 6.56050i) q^{91} +7.54528 q^{92} +(-3.02618 + 6.60240i) q^{93} +8.00387i q^{94} +(-1.57454 - 0.721683i) q^{96} +0.524688 q^{97} +(3.54528 + 6.03581i) q^{98} +(-8.90122 + 7.67024i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 12 q^{4} + 12 q^{8}+O(q^{10}) $ 12 * q + 12 * q^2 + 12 * q^4 + 12 * q^8	$ 12 q + 12 q^{2} + 12 q^{4} + 12 q^{8} + 12 q^{16} + 14 q^{21} + 20 q^{23} + 12 q^{32} - 12 q^{39} + 14 q^{42} + 20 q^{46} - 28 q^{49} + 28 q^{51} + 20 q^{53} - 8 q^{57} + 30 q^{63} + 12 q^{64} - 44 q^{77} - 12 q^{78} - 56 q^{79} - 16 q^{81} + 14 q^{84} - 20 q^{91} + 20 q^{92} - 48 q^{93} - 28 q^{98} - 48 q^{99}+O(q^{100}) $ 12 * q + 12 * q^2 + 12 * q^4 + 12 * q^8 + 12 * q^16 + 14 * q^21 + 20 * q^23 + 12 * q^32 - 12 * q^39 + 14 * q^42 + 20 * q^46 - 28 * q^49 + 28 * q^51 + 20 * q^53 - 8 * q^57 + 30 * q^63 + 12 * q^64 - 44 * q^77 - 12 * q^78 - 56 * q^79 - 16 * q^81 + 14 * q^84 - 20 * q^91 + 20 * q^92 - 48 * q^93 - 28 * q^98 - 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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−1.57454	−	0.721683i	−0.909060	−	0.416664i
$3$	−1.57454	−	0.721683i	−0.909060	−	0.416664i
$4$	1.00000			0.500000
$5$		0			0
$5$		0			0
$6$	−1.57454	−	0.721683i	−0.642803	−	0.294626i
$7$	−2.29622	−	1.31429i	−0.867891	−	0.496756i
$7$	−2.29622	−	1.31429i	−0.867891	−	0.496756i
$8$	1.00000			0.353553
$9$	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	$0.798945\pi$
$12$	−1.57454	−	0.721683i	−0.454530	−	0.208332i
$13$	4.99166			1.38444			0.692219	−	0.721688i	$-0.256633\pi$
$13$	4.99166			1.38444			0.692219	+	0.721688i	$0.256633\pi$
$14$	−2.29622	−	1.31429i	−0.613691	−	0.351259i
$15$		0			0
$16$	1.00000			0.250000
$17$		−	3.54830i		−	0.860588i	−0.902689	−	0.430294i	$-0.858410\pi$
$17$		−	3.54830i		−	0.860588i	0.902689	−	0.430294i	$-0.141590\pi$
$18$	1.95835	+	2.27264i	0.461587	+	0.535666i
$19$			3.14908i			0.722448i	0.932479	+	0.361224i	$0.117641\pi$
$19$			3.14908i			0.722448i	−0.932479	+	0.361224i	$0.882359\pi$
$20$		0			0
$21$	2.66699	+	3.72655i	0.581985	+	0.813200i
$22$			3.91669i			0.835041i
$23$	7.54528			1.57330			0.786649	−	0.617400i	$-0.211814\pi$
$23$	7.54528			1.57330			0.786649	+	0.617400i	$0.211814\pi$
$24$	−1.57454	−	0.721683i	−0.321401	−	0.147313i
$25$		0			0
$26$	4.99166			0.978946
$27$	−1.44337	−	4.99166i	−0.277776	−	0.960646i
$28$	−2.29622	−	1.31429i	−0.433945	−	0.248378i
$29$		−	7.54528i		−	1.40112i	−0.713592	−	0.700561i	$-0.752933\pi$
$29$		−	7.54528i		−	1.40112i	0.713592	−	0.700561i	$-0.247067\pi$
$30$		0			0
$31$		−	4.19323i		−	0.753126i	−0.926391	−	0.376563i	$-0.877106\pi$
$31$		−	4.19323i		−	0.753126i	0.926391	−	0.376563i	$-0.122894\pi$
$32$	1.00000			0.176777
$33$	2.82661	−	6.16698i	0.492050	−	1.07353i
$34$		−	3.54830i		−	0.608528i
$35$		0			0
$36$	1.95835	+	2.27264i	0.326391	+	0.378773i
$37$		−	10.4620i		−	1.71994i	−0.510347	−	0.859968i	$-0.670483\pi$
$37$		−	10.4620i		−	1.71994i	0.510347	−	0.859968i	$-0.329517\pi$
$38$			3.14908i			0.510848i
$39$	−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	$0.240493\pi$
$42$	2.66699	+	3.72655i	0.411525	+	0.575019i
$43$			2.91669i			0.444791i	0.974956	+	0.222396i	$0.0713877\pi$
$43$			2.91669i			0.444791i	−0.974956	+	0.222396i	$0.928612\pi$
$44$			3.91669i			0.590464i
$45$		0			0
$46$	7.54528			1.11249
$47$			8.00387i			1.16748i	0.811939	+	0.583742i	$0.198412\pi$
$47$			8.00387i			1.16748i	−0.811939	+	0.583742i	$0.801588\pi$
$48$	−1.57454	−	0.721683i	−0.227265	−	0.104166i
$49$	3.54528	+	6.03581i	0.506468	+	0.862259i
$50$		0			0
$51$	−2.56075	+	5.58693i	−0.358576	+	0.782327i
$52$	4.99166			0.692219
$53$	−0.288109			−0.0395748			−0.0197874	−	0.999804i	$-0.506299\pi$
$53$	−0.288109			−0.0395748			−0.0197874	+	0.999804i	$0.506299\pi$
$54$	−1.44337	−	4.99166i	−0.196417	−	0.679279i
$55$		0			0
$56$	−2.29622	−	1.31429i	−0.306846	−	0.175630i
$57$	2.27264	−	4.95835i	0.301018	−	0.656749i
$58$		−	7.54528i		−	0.990743i
$59$	5.89894			0.767976			0.383988	−	0.923338i	$-0.374550\pi$
$59$	5.89894			0.767976			0.383988	+	0.923338i	$0.374550\pi$
$60$		0			0
$61$		−	2.48752i		−	0.318494i	−0.987239	−	0.159247i	$-0.949093\pi$
$61$		−	2.48752i		−	0.318494i	0.987239	−	0.159247i	$-0.0509066\pi$
$62$		−	4.19323i		−	0.532540i
$63$	−1.50989	−	7.79232i	−0.190228	−	0.981740i
$64$	1.00000			0.125000
$65$		0			0
$66$	2.82661	−	6.16698i	0.347932	−	0.759103i
$67$			0.545275i			0.0666160i	0.999445	+	0.0333080i	$0.0106042\pi$
$67$			0.545275i			0.0666160i	−0.999445	+	0.0333080i	$0.989396\pi$
$68$		−	3.54830i		−	0.430294i
$69$	−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	$0.896742\pi$
$72$	1.95835	+	2.27264i	0.230793	+	0.267833i
$73$	−4.85479			−0.568210			−0.284105	−	0.958793i	$-0.591696\pi$
$73$	−4.85479			−0.568210			−0.284105	+	0.958793i	$0.591696\pi$
$74$		−	10.4620i		−	1.21618i
$75$		0			0
$76$			3.14908i			0.361224i
$77$	5.14768	−	8.99360i	0.586632	−	1.02492i
$78$	−7.85957	−	3.60240i	−0.889921	−	0.407891i
$79$	−0.742834			−0.0835753			−0.0417876	−	0.999127i	$-0.513305\pi$
$79$	−0.742834			−0.0835753			−0.0417876	+	0.999127i	$0.513305\pi$
$80$		0			0
$81$	−1.32976	+	8.90122i	−0.147751	+	0.989025i
$82$	9.32176			1.02942
$83$			4.45557i			0.489063i	0.969641	+	0.244531i	$0.0786341\pi$
$83$			4.45557i			0.489063i	−0.969641	+	0.244531i	$0.921366\pi$
$84$	2.66699	+	3.72655i	0.290992	+	0.406600i
$85$		0			0
$86$			2.91669i			0.314515i
$87$	−5.44530	+	11.8803i	−0.583797	+	1.27371i
$88$			3.91669i			0.417521i
$89$	12.3340			1.30740			0.653699	−	0.756755i	$-0.273216\pi$
$89$	12.3340			1.30740			0.653699	+	0.756755i	$0.273216\pi$
$90$		0			0
$91$	−11.4620	−	6.56050i	−1.20154	−	0.687727i
$92$	7.54528			0.786649
$93$	−3.02618	+	6.60240i	−0.313801	+	0.684637i
$94$			8.00387i			0.825536i
$95$		0			0
$96$	−1.57454	−	0.721683i	−0.160701	−	0.0736565i
$97$	0.524688			0.0532740			0.0266370	−	0.999645i	$-0.491520\pi$
$97$	0.524688			0.0532740			0.0266370	+	0.999645i	$0.491520\pi$
$98$	3.54528	+	6.03581i	0.358127	+	0.609709i
$99$	−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	$0.369632\pi$
$102$	−2.56075	+	5.58693i	−0.253552	+	0.553188i
$103$	−6.17269			−0.608213			−0.304106	−	0.952638i	$-0.598358\pi$
$103$	−6.17269			−0.608213			−0.304106	+	0.952638i	$0.598358\pi$
$104$	4.99166			0.489473
$105$		0			0
$106$	−0.288109			−0.0279836
$107$	2.65953			0.257106			0.128553	−	0.991703i	$-0.458967\pi$
$107$	2.65953			0.257106			0.128553	+	0.991703i	$0.458967\pi$
$108$	−1.44337	−	4.99166i	−0.138888	−	0.480323i
$109$	−14.9239			−1.42945			−0.714727	−	0.699404i	$-0.753449\pi$
$109$	−14.9239			−1.42945			−0.714727	+	0.699404i	$0.753449\pi$
$110$		0			0
$111$	−7.55023	+	16.4728i	−0.716636	+	1.56353i
$112$	−2.29622	−	1.31429i	−0.216973	−	0.124189i
$113$	11.8024			1.11028			0.555140	−	0.831757i	$-0.312665\pi$
$113$	11.8024			1.11028			0.555140	+	0.831757i	$0.312665\pi$
$114$	2.27264	−	4.95835i	0.212852	−	0.464392i
$115$		0			0
$116$		−	7.54528i		−	0.700561i
$117$	9.77540	+	11.3442i	0.903736	+	1.04878i
$118$	5.89894			0.543041
$119$	−4.66349	+	8.14768i	−0.427502	+	0.746896i
$120$		0			0
$121$	−4.34047			−0.394589
$122$		−	2.48752i		−	0.225209i
$123$	−14.6775	−	6.72736i	−1.32342	−	0.606586i
$124$		−	4.19323i		−	0.376563i
$125$		0			0
$126$	−1.50989	−	7.79232i	−0.134512	−	0.694195i
$127$			2.00000i			0.177471i	0.996055	+	0.0887357i	$0.0282826\pi$
$127$			2.00000i			0.177471i	−0.996055	+	0.0887357i	$0.971717\pi$
$128$	1.00000			0.0883883
$129$	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	$0.278312\pi$
$132$	2.82661	−	6.16698i	0.246025	−	0.536767i
$133$	4.13881	−	7.23098i	0.358880	−	0.627006i
$134$			0.545275i			0.0471046i
$135$		0			0
$136$		−	3.54830i		−	0.304264i
$137$	−18.3787			−1.57019			−0.785097	−	0.619372i	$-0.787387\pi$
$137$	−18.3787			−1.57019			−0.785097	+	0.619372i	$0.787387\pi$
$138$	−11.8803	−	5.44530i	−1.01132	−	0.463535i
$139$			12.6077i			1.06937i	0.845051	+	0.534686i	$0.179570\pi$
$139$			12.6077i			1.06937i	−0.845051	+	0.534686i	$0.820430\pi$
$140$		0			0
$141$	5.77626	−	12.6024i	0.486449	−	1.06131i
$142$			5.37142i			0.450759i
$143$			19.5508i			1.63492i
$144$	1.95835	+	2.27264i	0.163195	+	0.189386i
$145$		0			0
$146$	−4.85479			−0.401785
$147$	−1.22623	−	12.0622i	−0.101138	−	0.994872i
$148$		−	10.4620i		−	0.859968i
$149$			5.65953i			0.463646i	0.972758	+	0.231823i	$0.0744691\pi$
$149$			5.65953i			0.463646i	−0.972758	+	0.231823i	$0.925531\pi$
$150$		0			0
$151$	−2.62858			−0.213911			−0.106956	−	0.994264i	$-0.534110\pi$
$151$	−2.62858			−0.213911			−0.106956	+	0.994264i	$0.534110\pi$
$152$			3.14908i			0.255424i
$153$	8.06399	−	6.94879i	0.651935	−	0.561776i
$154$	5.14768	−	8.99360i	0.414811	−	0.724725i
$155$		0			0
$156$	−7.85957	−	3.60240i	−0.629269	−	0.288423i
$157$	−24.2853			−1.93818			−0.969091	−	0.246704i	$-0.920652\pi$
$157$	−24.2853			−1.93818			−0.969091	+	0.246704i	$0.920652\pi$
$158$	−0.742834			−0.0590967
$159$	0.453638	+	0.207923i	0.0359758	+	0.0164894i
$160$		0			0
$161$	−17.3256	−	9.91669i	−1.36545	−	0.781545i
$162$	−1.32976	+	8.90122i	−0.104476	+	0.699346i
$163$		−	13.4620i		−	1.05442i	−0.849734	−	0.527211i	$-0.823238\pi$
$163$		−	13.4620i		−	1.05442i	0.849734	−	0.527211i	$-0.176762\pi$
$164$	9.32176			0.727907
$165$		0			0
$166$			4.45557i			0.345819i
$167$		−	21.7812i		−	1.68548i	−0.538321	−	0.842740i	$-0.680941\pi$
$167$		−	21.7812i		−	1.68548i	0.538321	−	0.842740i	$-0.319059\pi$
$168$	2.66699	+	3.72655i	0.205763	+	0.287510i
$169$	11.9167			0.916669
$170$		0			0
$171$	−7.15671	+	6.16698i	−0.547287	+	0.471601i
$172$			2.91669i			0.222396i
$173$		−	0.907276i		−	0.0689789i	−0.999405	−	0.0344895i	$-0.989019\pi$
$173$		−	0.907276i		−	0.0689789i	0.999405	−	0.0344895i	$-0.0109805\pi$
$174$	−5.44530	+	11.8803i	−0.412807	+	0.900645i
$175$		0			0
$176$			3.91669i			0.295232i
$177$	−9.28811	−	4.25717i	−0.698137	−	0.319988i
$178$	12.3340			0.924470
$179$			2.08331i			0.155714i	0.996965	+	0.0778569i	$0.0248077\pi$
$179$			2.08331i			0.155714i	−0.996965	+	0.0778569i	$0.975192\pi$
$180$		0			0
$181$			24.6679i			1.83355i	0.399400	+	0.916777i	$0.369218\pi$
$181$			24.6679i			1.83355i	−0.399400	+	0.916777i	$0.630782\pi$
$182$	−11.4620	−	6.56050i	−0.849618	−	0.486297i
$183$	−1.79520	+	3.91669i	−0.132705	+	0.289530i
$184$	7.54528			0.556245
$185$		0			0
$186$	−3.02618	+	6.60240i	−0.221891	+	0.484111i
$187$	13.8976			1.01629
$188$			8.00387i			0.583742i
$189$	−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	$-0.196604\pi$
$192$	−1.57454	−	0.721683i	−0.113633	−	0.0520830i
$193$			26.4310i			1.90255i	0.308349	+	0.951273i	$0.400224\pi$
$193$			26.4310i			1.90255i	−0.308349	+	0.951273i	$0.599776\pi$
$194$	0.524688			0.0376704
$195$		0			0
$196$	3.54528	+	6.03581i	0.253234	+	0.431129i
$197$	−17.2644			−1.23004			−0.615019	−	0.788512i	$-0.710852\pi$
$197$	−17.2644			−1.23004			−0.615019	+	0.788512i	$0.710852\pi$
$198$	−8.90122	+	7.67024i	−0.632582	+	0.545100i
$199$		−	10.8906i		−	0.772014i	−0.922496	−	0.386007i	$-0.873854\pi$
$199$		−	10.8906i		−	0.772014i	0.922496	−	0.386007i	$-0.126146\pi$
$200$		0			0
$201$	0.393516	−	0.858557i	0.0277565	−	0.0605579i
$202$	8.00387			0.563150
$203$	−9.91669	+	17.3256i	−0.696015	+	1.21602i
$204$	−2.56075	+	5.58693i	−0.179288	+	0.391163i
$205$		0			0
$206$	−6.17269			−0.430071
$207$	14.7763	+	17.1477i	1.02702	+	1.19185i
$208$	4.99166			0.346110
$209$	−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	$0.576170\pi$
$212$	−0.288109			−0.0197874
$213$	3.87646	−	8.45750i	0.265611	−	0.579499i
$214$	2.65953			0.181801
$215$		0			0
$216$	−1.44337	−	4.99166i	−0.0982087	−	0.339640i
$217$	−5.51112	+	9.62858i	−0.374119	+	0.653631i
$218$	−14.9239			−1.01078
$219$	7.64405	+	3.50362i	0.516537	+	0.236753i
$220$		0			0
$221$		−	17.7119i		−	1.19143i
$222$	−7.55023	+	16.4728i	−0.506738	+	1.10558i
$223$	−2.90336			−0.194424			−0.0972118	−	0.995264i	$-0.530992\pi$
$223$	−2.90336			−0.194424			−0.0972118	+	0.995264i	$0.530992\pi$
$224$	−2.29622	−	1.31429i	−0.153423	−	0.0878148i
$225$		0			0
$226$	11.8024			0.785087
$227$			21.6557i			1.43734i	0.695351	+	0.718671i	$0.255249\pi$
$227$			21.6557i			1.43734i	−0.695351	+	0.718671i	$0.744751\pi$
$228$	2.27264	−	4.95835i	0.150509	−	0.328374i
$229$		−	16.9378i		−	1.11928i	−0.828735	−	0.559641i	$-0.810939\pi$
$229$		−	16.9378i		−	1.11928i	0.828735	−	0.559641i	$-0.189061\pi$
$230$		0			0
$231$	−14.5957	+	10.4458i	−0.960329	+	0.687282i
$232$		−	7.54528i		−	0.495372i
$233$	5.42378			0.355324			0.177662	−	0.984092i	$-0.443147\pi$
$233$	5.42378			0.355324			0.177662	+	0.984092i	$0.443147\pi$
$234$	9.77540	+	11.3442i	0.639038	+	0.741596i
$235$		0			0
$236$	5.89894			0.383988
$237$	1.16962	+	0.536091i	0.0759750	+	0.0348228i
$238$	−4.66349	+	8.14768i	−0.302289	+	0.528135i
$239$		−	13.2572i		−	0.857535i	−0.903415	−	0.428767i	$-0.858948\pi$
$239$		−	13.2572i		−	0.857535i	0.903415	−	0.428767i	$-0.141052\pi$
$240$		0			0
$241$		−	18.5233i		−	1.19319i	−0.802543	−	0.596595i	$-0.796520\pi$
$241$		−	18.5233i		−	1.19319i	0.802543	−	0.596595i	$-0.203480\pi$
$242$	−4.34047			−0.279016
$243$	8.51763	−	13.0557i	0.546406	−	0.837520i
$244$		−	2.48752i		−	0.159247i
$245$		0			0
$246$	−14.6775	−	6.72736i	−0.935802	−	0.428921i
$247$			15.7191i			1.00018i
$248$		−	4.19323i		−	0.266270i
$249$	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	$0.737870\pi$
$252$	−1.50989	−	7.79232i	−0.0951141	−	0.490870i
$253$			29.5525i			1.85795i
$254$			2.00000i			0.125491i
$255$		0			0
$256$	1.00000			0.0625000
$257$			31.8900i			1.98924i	0.103575	+	0.994622i	$0.466972\pi$
$257$			31.8900i			1.98924i	−0.103575	+	0.994622i	$0.533028\pi$
$258$	2.10493	−	4.59244i	0.131047	−	0.285913i
$259$	−13.7501	+	24.0230i	−0.854388	+	1.49272i
$260$		0			0
$261$	17.1477	−	14.7763i	1.06141	−	0.914627i
$262$	14.6846			0.907218
$263$	−14.1739			−0.873998			−0.436999	−	0.899462i	$-0.643959\pi$
$263$	−14.1739			−0.873998			−0.436999	+	0.899462i	$0.643959\pi$
$264$	2.82661	−	6.16698i	0.173966	−	0.379552i
$265$		0			0
$266$	4.13881	−	7.23098i	0.253767	−	0.443360i
$267$	−19.4203	−	8.90122i	−1.18850	−	0.544746i
$268$			0.545275i			0.0333080i
$269$	−6.68074			−0.407332			−0.203666	−	0.979040i	$-0.565286\pi$
$269$	−6.68074			−0.407332			−0.203666	+	0.979040i	$0.565286\pi$
$270$		0			0
$271$		−	9.45864i		−	0.574571i	−0.957845	−	0.287286i	$-0.907247\pi$
$271$		−	9.45864i		−	0.574571i	0.957845	−	0.287286i	$-0.0927529\pi$
$272$		−	3.54830i		−	0.215147i
$273$	13.3127	+	18.6017i	0.805722	+	1.12582i
$274$	−18.3787			−1.11030
$275$		0			0
$276$	−11.8803	−	5.44530i	−0.715112	−	0.327769i
$277$		−	11.2048i		−	0.673231i	−0.941642	−	0.336616i	$-0.890718\pi$
$277$		−	11.2048i		−	0.673231i	0.941642	−	0.336616i	$-0.109282\pi$
$278$			12.6077i			0.756160i
$279$	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	$0.972342\pi$
$282$	5.77626	−	12.6024i	0.343971	−	0.750462i
$283$	−24.4056			−1.45076			−0.725381	−	0.688348i	$-0.758336\pi$
$283$	−24.4056			−1.45076			−0.725381	+	0.688348i	$0.758336\pi$
$284$			5.37142i			0.318735i
$285$		0			0
$286$			19.5508i			1.15606i
$287$	−21.4048	−	12.2515i	−1.26349	−	0.723184i
$288$	1.95835	+	2.27264i	0.115397	+	0.133916i
$289$	4.40960			0.259388
$290$		0			0
$291$	−0.826142	−	0.378659i	−0.0484293	−	0.0221974i
$292$	−4.85479			−0.284105
$293$			17.0799i			0.997819i	0.866654	+	0.498910i	$0.166266\pi$
$293$			17.0799i			0.997819i	−0.866654	+	0.498910i	$0.833734\pi$
$294$	−1.22623	−	12.0622i	−0.0715151	−	0.703481i
$295$		0			0
$296$		−	10.4620i		−	0.608089i
$297$	19.5508	−	5.65322i	1.13445	−	0.328033i
$298$			5.65953i			0.327847i
$299$	37.6635			2.17813
$300$		0			0
$301$	3.83338	−	6.69737i	0.220953	−	0.386030i
$302$	−2.62858			−0.151258
$303$	−12.6024	−	5.77626i	−0.723989	−	0.331837i
$304$			3.14908i			0.180612i
$305$		0			0
$306$	8.06399	−	6.94879i	0.460988	−	0.397236i
$307$	−11.8093			−0.673991			−0.336996	−	0.941506i	$-0.609411\pi$
$307$	−11.8093			−0.673991			−0.336996	+	0.941506i	$0.609411\pi$
$308$	5.14768	−	8.99360i	0.293316	−	0.512458i
$309$	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	$0.473918\pi$
$312$	−7.85957	−	3.60240i	−0.444960	−	0.203946i
$313$	4.20986			0.237955			0.118978	−	0.992897i	$-0.462038\pi$
$313$	4.20986			0.237955			0.118978	+	0.992897i	$0.462038\pi$
$314$	−24.2853			−1.37050
$315$		0			0
$316$	−0.742834			−0.0417876
$317$	23.2644			1.30666			0.653330	−	0.757074i	$-0.273372\pi$
$317$	23.2644			1.30666			0.653330	+	0.757074i	$0.273372\pi$
$318$	0.453638	+	0.207923i	0.0254388	+	0.0116598i
$319$	29.5525			1.65462
$320$		0			0
$321$	−4.18753	−	1.91934i	−0.233725	−	0.107127i
$322$	−17.3256	−	9.91669i	−0.965520	−	0.552636i
$323$	11.1739			0.621730
$324$	−1.32976	+	8.90122i	−0.0738757	+	0.494512i
$325$		0			0
$326$		−	13.4620i		−	0.745589i
$327$	23.4983	+	10.7704i	1.29946	+	0.595602i
$328$	9.32176			0.514708
$329$	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	$0.746709\pi$
$332$			4.45557i			0.244531i
$333$	23.7763	−	20.4881i	1.30293	−	1.12274i
$334$		−	21.7812i		−	1.19181i
$335$		0			0
$336$	2.66699	+	3.72655i	0.145496	+	0.203300i
$337$			7.68095i			0.418408i	0.977872	+	0.209204i	$0.0670873\pi$
$337$			7.68095i			0.418408i	−0.977872	+	0.209204i	$0.932913\pi$
$338$	11.9167			0.648183
$339$	−18.5834	−	8.51763i	−1.00931	−	0.462614i
$340$		0			0
$341$	16.4236			0.889387
$342$	−7.15671	+	6.16698i	−0.386991	+	0.333472i
$343$	−0.207923	−	18.5191i	−0.0112268	−	0.999937i
$344$			2.91669i			0.157257i
$345$		0			0
$346$		−	0.907276i		−	0.0487755i
$347$	8.26441			0.443657			0.221828	−	0.975086i	$-0.428798\pi$
$347$	8.26441			0.443657			0.221828	+	0.975086i	$0.428798\pi$
$348$	−5.44530	+	11.8803i	−0.291899	+	0.636853i
$349$		−	24.6846i		−	1.32133i	−0.750679	−	0.660667i	$-0.770273\pi$
$349$		−	24.6846i		−	1.32133i	0.750679	−	0.660667i	$-0.229727\pi$
$350$		0			0
$351$	−7.20480	−	24.9167i	−0.384564	−	1.32995i
$352$			3.91669i			0.208760i
$353$		−	18.8945i		−	1.00565i	−0.864388	−	0.502826i	$-0.832294\pi$
$353$		−	18.8945i		−	1.00565i	0.864388	−	0.502826i	$-0.167706\pi$
$354$	−9.28811	−	4.25717i	−0.493657	−	0.226266i
$355$		0			0
$356$	12.3340			0.653699
$357$	13.2229	−	9.46326i	0.699830	−	0.500849i
$358$			2.08331i			0.110106i
$359$		−	1.49291i		−	0.0787927i	−0.999224	−	0.0393964i	$-0.987457\pi$
$359$		−	1.49291i		−	0.0787927i	0.999224	−	0.0393964i	$-0.0125435\pi$
$360$		0			0
$361$	9.08331			0.478069
$362$			24.6679i			1.29652i
$363$	6.83425	+	3.13245i	0.358705	+	0.164411i
$364$	−11.4620	−	6.56050i	−0.600770	−	0.343864i
$365$		0			0
$366$	−1.79520	+	3.91669i	−0.0938366	+	0.204729i
$367$	16.9544			0.885015			0.442507	−	0.896765i	$-0.354089\pi$
$367$	16.9544			0.885015			0.442507	+	0.896765i	$0.354089\pi$
$368$	7.54528			0.393325
$369$	18.2552	+	21.1850i	0.950330	+	1.10285i
$370$		0			0
$371$	0.661561	+	0.378659i	0.0343466	+	0.0196590i
$372$	−3.02618	+	6.60240i	−0.156900	+	0.342319i
$373$			22.8097i			1.18104i	0.807023	+	0.590520i	$0.201077\pi$
$373$			22.8097i			1.18104i	−0.807023	+	0.590520i	$0.798923\pi$
$374$	13.8976			0.718627
$375$		0			0
$376$			8.00387i			0.412768i
$377$		−	37.6635i		−	1.93977i
$378$	−3.24621	+	13.3590i	−0.166967	+	0.687111i
$379$	−0.371417			−0.0190784			−0.00953920	−	0.999955i	$-0.503036\pi$
$379$	−0.371417			−0.0190784			−0.00953920	+	0.999955i	$0.503036\pi$
$380$		0			0
$381$	1.44337	−	3.14908i	0.0739459	−	0.161332i
$382$		−	16.0072i		−	0.819002i
$383$		−	32.8367i		−	1.67788i	−0.544226	−	0.838939i	$-0.683177\pi$
$383$		−	32.8367i		−	1.67788i	0.544226	−	0.838939i	$-0.316823\pi$
$384$	−1.57454	−	0.721683i	−0.0803504	−	0.0368283i
$385$		0			0
$386$			26.4310i			1.34530i
$387$	−6.62858	+	5.71189i	−0.336950	+	0.290352i
$388$	0.524688			0.0266370
$389$			24.1287i			1.22338i	0.791099	+	0.611688i	$0.209509\pi$
$389$			24.1287i			1.22338i	−0.791099	+	0.611688i	$0.790491\pi$
$390$		0			0
$391$		−	26.7729i		−	1.35396i
$392$	3.54528	+	6.03581i	0.179063	+	0.304855i
$393$	−23.1215	−	10.5976i	−1.16632	−	0.534580i
$394$	−17.2644			−0.869768
$395$		0			0
$396$	−8.90122	+	7.67024i	−0.447303	+	0.385444i
$397$	7.35371			0.369072			0.184536	−	0.982826i	$-0.440922\pi$
$397$	7.35371			0.369072			0.184536	+	0.982826i	$0.440922\pi$
$398$		−	10.8906i		−	0.545896i
$399$	−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	$0.859393\pi$
$402$	0.393516	−	0.858557i	0.0196268	−	0.0428209i
$403$		−	20.9312i		−	1.04266i
$404$	8.00387			0.398207
$405$		0			0
$406$	−9.91669	+	17.3256i	−0.492157	+	0.859857i
$407$	40.9763			2.03112
$408$	−2.56075	+	5.58693i	−0.126776	+	0.276594i
$409$		−	23.2246i		−	1.14838i	−0.818722	−	0.574191i	$-0.805317\pi$
$409$		−	23.2246i		−	1.14838i	0.818722	−	0.574191i	$-0.194683\pi$
$410$		0			0
$411$	28.9379	+	13.2636i	1.42740	+	0.654244i
$412$	−6.17269			−0.304106
$413$	−13.5453	−	7.75293i	−0.666519	−	0.381497i
$414$	14.7763	+	17.1477i	0.726213	+	0.842762i
$415$		0			0
$416$	4.99166			0.244736
$417$	9.09878	−	19.8513i	0.445569	−	0.972124i
$418$	−12.3340			−0.603274
$419$	−11.5522			−0.564360			−0.282180	−	0.959361i	$-0.591058\pi$
$419$	−11.5522			−0.564360			−0.282180	+	0.959361i	$0.591058\pi$
$420$		0			0
$421$	36.9239			1.79956			0.899781	−	0.436341i	$-0.143726\pi$
$421$	36.9239			1.79956			0.899781	+	0.436341i	$0.143726\pi$
$422$	−6.88575			−0.335193
$423$	−18.1899	+	15.6743i	−0.884423	+	0.762112i
$424$	−0.288109			−0.0139918
$425$		0			0
$426$	3.87646	−	8.45750i	0.187815	−	0.409767i
$427$	−3.26932	+	5.71189i	−0.158214	+	0.276418i
$428$	2.65953			0.128553
$429$	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	$-0.0386633\pi$
$432$	−1.44337	−	4.99166i	−0.0694440	−	0.240161i
$433$	3.04024			0.146104			0.0730522	−	0.997328i	$-0.476726\pi$
$433$	3.04024			0.146104			0.0730522	+	0.997328i	$0.476726\pi$
$434$	−5.51112	+	9.62858i	−0.264542	+	0.462187i
$435$		0			0
$436$	−14.9239			−0.714727
$437$			23.7607i			1.13663i
$438$	7.64405	+	3.50362i	0.365247	+	0.167409i
$439$			19.8184i			0.945879i	0.881095	+	0.472940i	$0.156807\pi$
$439$			19.8184i			0.945879i	−0.881095	+	0.472940i	$0.843193\pi$
$440$		0			0
$441$	−6.77434	+	19.8773i	−0.322588	+	0.946540i
$442$		−	17.7119i		−	0.842469i
$443$	−10.5976			−0.503509			−0.251755	−	0.967791i	$-0.581008\pi$
$443$	−10.5976			−0.503509			−0.251755	+	0.967791i	$0.581008\pi$
$444$	−7.55023	+	16.4728i	−0.358318	+	0.781763i
$445$		0			0
$446$	−2.90336			−0.137478
$447$	4.08439	−	8.91114i	0.193185	−	0.421483i
$448$	−2.29622	−	1.31429i	−0.108486	−	0.0620944i
$449$		−	6.19756i		−	0.292481i	−0.989249	−	0.146240i	$-0.953283\pi$
$449$		−	6.19756i		−	0.292481i	0.989249	−	0.146240i	$-0.0467173\pi$
$450$		0			0
$451$			36.5105i			1.71921i
$452$	11.8024			0.555140
$453$	4.13881	+	1.89701i	0.194458	+	0.0891291i
$454$			21.6557i			1.01635i
$455$		0			0
$456$	2.27264	−	4.95835i	0.106426	−	0.232196i
$457$			19.7573i			0.924208i	0.886826	+	0.462104i	$0.152905\pi$
$457$			19.7573i			0.924208i	−0.886826	+	0.462104i	$0.847095\pi$
$458$		−	16.9378i		−	0.791452i
$459$	−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	$0.715468\pi$
$462$	−14.5957	+	10.4458i	−0.679055	+	0.485981i
$463$		−	38.7573i		−	1.80121i	−0.434643	−	0.900603i	$-0.643126\pi$
$463$		−	38.7573i		−	1.80121i	0.434643	−	0.900603i	$-0.356874\pi$
$464$		−	7.54528i		−	0.350281i
$465$		0			0
$466$	5.42378			0.251252
$467$		−	18.5181i		−	0.856913i	−0.903562	−	0.428457i	$-0.859057\pi$
$467$		−	18.5181i		−	0.856913i	0.903562	−	0.428457i	$-0.140943\pi$
$468$	9.77540	+	11.3442i	0.451868	+	0.524388i
$469$	0.716650	−	1.25207i	0.0330918	−	0.0578154i
$470$		0			0
$471$	38.2382	+	17.5263i	1.76192	+	0.807571i
$472$	5.89894			0.271521
$473$	−11.4238			−0.525266
$474$	1.16962	+	0.536091i	0.0537224	+	0.0246235i
$475$		0			0
$476$	−4.66349	+	8.14768i	−0.213751	+	0.373448i
$477$	−0.564216	−	0.654766i	−0.0258337	−	0.0299797i
$478$		−	13.2572i		−	0.606369i
$479$	−14.4337			−0.659491			−0.329746	−	0.944070i	$-0.606963\pi$
$479$	−14.4337			−0.659491			−0.329746	+	0.944070i	$0.606963\pi$
$480$		0			0
$481$		−	52.2226i		−	2.38115i
$482$		−	18.5233i		−	0.843712i
$483$	20.1232	+	28.1178i	0.915636	+	1.27941i
$484$	−4.34047			−0.197294
$485$		0			0
$486$	8.51763	−	13.0557i	0.386367	−	0.592216i
$487$			26.2430i			1.18918i	0.804028	+	0.594592i	$0.202686\pi$
$487$			26.2430i			1.18918i	−0.804028	+	0.594592i	$0.797314\pi$
$488$		−	2.48752i		−	0.112605i
$489$	−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	$0.763305\pi$
$492$	−14.6775	−	6.72736i	−0.661712	−	0.303293i
$493$	−26.7729			−1.20579
$494$			15.7191i			0.707237i
$495$		0			0
$496$		−	4.19323i		−	0.188281i
$497$	7.05961	−	12.3340i	0.316667	−	0.553254i
$498$	3.21551	−	7.01547i	0.144091	−	0.314371i
$499$	−41.6740			−1.86558			−0.932792	−	0.360414i	$-0.882635\pi$
$499$	−41.6740			−1.86558			−0.932792	+	0.360414i	$0.882635\pi$
$500$		0			0
$501$	−15.7191	+	34.2954i	−0.702279	+	1.53220i
$502$	−21.5355			−0.961176
$503$		−	0.415846i		−	0.0185417i	−0.999957	−	0.00927084i	$-0.997049\pi$
$503$		−	0.415846i		−	0.0185417i	0.999957	−	0.00927084i	$-0.00295104\pi$
$504$	−1.50989	−	7.79232i	−0.0672558	−	0.347097i
$505$		0			0
$506$			29.5525i			1.31377i
$507$	−18.7633	−	8.60008i	−0.833307	−	0.381943i
$508$			2.00000i			0.0887357i
$509$	−11.3064			−0.501149			−0.250575	−	0.968097i	$-0.580620\pi$
$509$	−11.3064			−0.501149			−0.250575	+	0.968097i	$0.580620\pi$
$510$		0			0
$511$	11.1477	+	6.38061i	0.493144	+	0.282261i
$512$	1.00000			0.0441942
$513$	15.7191	−	4.54528i	0.694017	−	0.200679i
$514$			31.8900i			1.40661i
$515$		0			0
$516$	2.10493	−	4.59244i	0.0926643	−	0.202171i
$517$	−31.3487			−1.37871
$518$	−13.7501	+	24.0230i	−0.604144	+	1.05551i
$519$	−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	$0.517274\pi$
$522$	17.1477	−	14.7763i	0.750533	−	0.646739i
$523$	12.0602			0.527357			0.263678	−	0.964611i	$-0.415064\pi$
$523$	12.0602			0.527357			0.263678	+	0.964611i	$0.415064\pi$
$524$	14.6846			0.641500
$525$		0			0
$526$	−14.1739			−0.618010
$527$	−14.8788			−0.648131
$528$	2.82661	−	6.16698i	0.123012	−	0.268384i
$529$	33.9312			1.47527
$530$		0			0
$531$	11.5522	+	13.4061i	0.501321	+	0.581777i
$532$	4.13881	−	7.23098i	0.179440	−	0.313503i
$533$	46.5311			2.01549
$534$	−19.4203	−	8.90122i	−0.840399	−	0.385193i
$535$		0			0
$536$			0.545275i			0.0235523i
$537$	1.50349	−	3.28025i	0.0648803	−	0.141553i
$538$	−6.68074			−0.288027
$539$	−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	$0.464737\pi$
$542$		−	9.45864i		−	0.406283i
$543$	17.8024	−	38.8406i	0.763976	−	1.66681i
$544$		−	3.54830i		−	0.152132i
$545$		0			0
$546$	13.3127	+	18.6017i	0.569731	+	0.796078i
$547$			3.11425i			0.133156i	0.997781	+	0.0665779i	$0.0212081\pi$
$547$			3.11425i			0.133156i	−0.997781	+	0.0665779i	$0.978792\pi$
$548$	−18.3787			−0.785097
$549$	5.65322	−	4.87142i	0.241274	−	0.207907i
$550$		0			0
$551$	23.7607			1.01224
$552$	−11.8803	−	5.44530i	−0.505660	−	0.231767i
$553$	1.70571	+	0.976300i	0.0725342	+	0.0415165i
$554$		−	11.2048i		−	0.476046i
$555$		0			0
$556$			12.6077i			0.534686i
$557$	−1.93812			−0.0821206			−0.0410603	−	0.999157i	$-0.513074\pi$
$557$	−1.93812			−0.0821206			−0.0410603	+	0.999157i	$0.513074\pi$
$558$	9.52969	−	8.21179i	0.403424	−	0.347633i
$559$			14.5591i			0.615786i
$560$		0			0
$561$	−21.8823	−	10.0297i	−0.923871	−	0.423452i
$562$			2.90945i			0.122728i
$563$		−	25.8656i		−	1.09010i	−0.838402	−	0.545052i	$-0.816510\pi$
$563$		−	25.8656i		−	1.09010i	0.838402	−	0.545052i	$-0.183490\pi$
$564$	5.77626	−	12.6024i	0.243224	−	0.530657i
$565$		0			0
$566$	−24.4056			−1.02584
$567$	14.7522	−	18.6915i	0.619535	−	0.784969i
$568$			5.37142i			0.225380i
$569$		−	30.3787i		−	1.27354i	−0.771054	−	0.636770i	$-0.780270\pi$
$569$		−	30.3787i		−	1.27354i	0.771054	−	0.636770i	$-0.219730\pi$
$570$		0			0
$571$	4.56898			0.191206			0.0956028	−	0.995420i	$-0.469522\pi$
$571$	4.56898			0.191206			0.0956028	+	0.995420i	$0.469522\pi$
$572$			19.5508i			0.817460i
$573$	−11.5522	+	25.2040i	−0.482598	+	1.05291i
$574$	−21.4048	−	12.2515i	−0.893421	−	0.511368i
$575$		0			0
$576$	1.95835	+	2.27264i	0.0815977	+	0.0946932i
$577$	−23.7493			−0.988694			−0.494347	−	0.869265i	$-0.664593\pi$
$577$	−23.7493			−0.988694			−0.494347	+	0.869265i	$0.664593\pi$
$578$	4.40960			0.183415
$579$	19.0748	−	41.6167i	0.792723	−	1.72953i
$580$		0			0
$581$	5.85592	−	10.2310i	0.242945	−	0.424453i
$582$	−0.826142	−	0.378659i	−0.0342447	−	0.0156959i
$583$		−	1.12843i		−	0.0467349i
$584$	−4.85479			−0.200893
$585$		0			0
$586$			17.0799i			0.705565i
$587$			28.8726i			1.19170i	0.803096	+	0.595849i	$0.203184\pi$
$587$			28.8726i			1.19170i	−0.803096	+	0.595849i	$0.796816\pi$
$588$	−1.22623	−	12.0622i	−0.0505688	−	0.497436i
$589$	13.2048			0.544094
$590$		0			0
$591$	27.1835	+	12.4594i	1.11818	+	0.512513i
$592$		−	10.4620i		−	0.429984i
$593$			4.74595i			0.194893i	0.995241	+	0.0974463i	$0.0310674\pi$
$593$			4.74595i			0.194893i	−0.995241	+	0.0974463i	$0.968933\pi$
$594$	19.5508	−	5.65322i	0.802179	−	0.231955i
$595$		0			0
$596$			5.65953i			0.231823i
$597$	−7.85957	+	17.1477i	−0.321671	+	0.701808i
$598$	37.6635			1.54017
$599$			3.19756i			0.130649i	0.997864	+	0.0653243i	$0.0208082\pi$
$599$			3.19756i			0.130649i	−0.997864	+	0.0653243i	$0.979192\pi$
$600$		0			0
$601$		−	1.16962i		−	0.0477098i	−0.999715	−	0.0238549i	$-0.992406\pi$
$601$		−	1.16962i		−	0.0477098i	0.999715	−	0.0238549i	$-0.00759397\pi$
$602$	3.83338	−	6.69737i	0.156237	−	0.272965i
$603$	−1.23921	+	1.06784i	−0.0504646	+	0.0434857i
$604$	−2.62858			−0.106956
$605$		0			0
$606$	−12.6024	−	5.77626i	−0.511938	−	0.234644i
$607$	42.5463			1.72690			0.863450	−	0.504434i	$-0.168299\pi$
$607$	42.5463			1.72690			0.863450	+	0.504434i	$0.168299\pi$
$608$			3.14908i			0.127712i
$609$	28.1178	−	20.1232i	1.13939	−	0.815432i
$610$		0			0
$611$			39.9526i			1.61631i
$612$	8.06399	−	6.94879i	0.325967	−	0.280888i
$613$			11.1524i			0.450443i	0.974308	+	0.225221i	$0.0723105\pi$
$613$			11.1524i			0.450443i	−0.974308	+	0.225221i	$0.927689\pi$
$614$	−11.8093			−0.476584
$615$		0			0
$616$	5.14768	−	8.99360i	0.207406	−	0.362362i
$617$	42.1811			1.69815			0.849074	−	0.528275i	$-0.177161\pi$
$617$	42.1811			1.69815			0.849074	+	0.528275i	$0.177161\pi$
$618$	9.71913	+	4.45472i	0.390961	+	0.179195i
$619$		−	11.0327i		−	0.443442i	−0.975110	−	0.221721i	$-0.928833\pi$
$619$		−	11.0327i		−	0.443442i	0.975110	−	0.221721i	$-0.0711674\pi$
$620$		0			0
$621$	−10.8906	−	37.6635i	−0.437025	−	1.51138i
$622$	2.88673			0.115747
$623$	−28.3215	−	16.2104i	−1.13468	−	0.649457i
$624$	−7.85957	−	3.60240i	−0.314634	−	0.144211i
$625$		0			0
$626$	4.20986			0.168260
$627$	19.4203	+	8.90122i	0.775573	+	0.355481i
$628$	−24.2853			−0.969091
$629$	−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	$0.471692\pi$
$632$	−0.742834			−0.0295483
$633$	10.8419	+	4.96933i	0.430926	+	0.197513i
$634$	23.2644			0.923948
$635$		0			0
$636$	0.453638	+	0.207923i	0.0179879	+	0.00824469i
$637$	17.6968	+	30.1287i	0.701173	+	1.19374i
$638$	29.5525			1.17000
$639$	−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	$-0.0182996\pi$
$642$	−4.18753	−	1.91934i	−0.165268	−	0.0757501i
$643$	−31.7645			−1.25267			−0.626335	−	0.779554i	$-0.715446\pi$
$643$	−31.7645			−1.25267			−0.626335	+	0.779554i	$0.715446\pi$
$644$	−17.3256	−	9.91669i	−0.682725	−	0.390772i
$645$		0			0
$646$	11.1739			0.439630
$647$		−	23.3448i		−	0.917779i	−0.888493	−	0.458890i	$-0.848247\pi$
$647$		−	23.3448i		−	0.917779i	0.888493	−	0.458890i	$-0.151753\pi$
$648$	−1.32976	+	8.90122i	−0.0522380	+	0.349673i
$649$			23.1043i			0.906924i
$650$		0			0
$651$	15.6263	−	11.1833i	0.612442	−	0.438308i
$652$		−	13.4620i		−	0.527211i
$653$	2.28087			0.0892572			0.0446286	−	0.999004i	$-0.485790\pi$
$653$	2.28087			0.0892572			0.0446286	+	0.999004i	$0.485790\pi$
$654$	23.4983	+	10.7704i	0.918857	+	0.421154i
$655$		0			0
$656$	9.32176			0.363954
$657$	−9.50736	−	11.0332i	−0.370917	−	0.430445i
$658$	10.5194	−	18.3787i	0.410089	−	0.716475i
$659$			2.08331i			0.0811542i	0.999176	+	0.0405771i	$0.0129196\pi$
$659$			2.08331i			0.0811542i	−0.999176	+	0.0405771i	$0.987080\pi$
$660$		0			0
$661$		−	4.34150i		−	0.168865i	−0.996429	−	0.0844325i	$-0.973092\pi$
$661$		−	4.34150i		−	0.168865i	0.996429	−	0.0844325i	$-0.0269077\pi$
$662$	−25.4620			−0.989607
$663$	−12.7824	+	27.8881i	−0.496426	+	1.08308i
$664$			4.45557i			0.172910i
$665$		0			0
$666$	23.7763	−	20.4881i	0.921311	−	0.793900i
$667$		−	56.9312i		−	2.20438i
$668$		−	21.7812i		−	0.842740i
$669$	4.57146	+	2.09531i	0.176743	+	0.0810093i
$670$		0			0
$671$	9.74284			0.376118
$672$	2.66699	+	3.72655i	0.102881	+	0.143755i
$673$		−	2.00724i		−	0.0773735i	−0.999251	−	0.0386867i	$-0.987683\pi$
$673$		−	2.00724i		−	0.0773735i	0.999251	−	0.0386867i	$-0.0123174\pi$
$674$			7.68095i			0.295859i
$675$		0			0
$676$	11.9167			0.458334
$677$			27.5547i			1.05901i	0.848306	+	0.529506i	$0.177623\pi$
$677$			27.5547i			1.05901i	−0.848306	+	0.529506i	$0.822377\pi$
$678$	−18.5834	−	8.51763i	−0.713691	−	0.327117i
$679$	−1.20480	−	0.689593i	−0.0462360	−	0.0264642i
$680$		0			0
$681$	15.6286	−	34.0978i	0.598889	−	1.30663i
$682$	16.4236			0.628891
$683$	5.75008			0.220021			0.110010	−	0.993930i	$-0.464912\pi$
$683$	5.75008			0.220021			0.110010	+	0.993930i	$0.464912\pi$
$684$	−7.15671	+	6.16698i	−0.273644	+	0.235801i
$685$		0			0
$686$	−0.207923	−	18.5191i	−0.00793854	−	0.707062i
$687$	−12.2237	+	26.6693i	−0.466365	+	1.01750i
$688$			2.91669i			0.111198i
$689$	−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	$0.851544\pi$
$692$		−	0.907276i		−	0.0344895i
$693$	30.5201	−	5.91377i	1.15936	−	0.224646i
$694$	8.26441			0.313713
$695$		0			0
$696$	−5.44530	+	11.8803i	−0.206404	+	0.450323i
$697$		−	33.0764i		−	1.25286i
$698$		−	24.6846i		−	0.934325i
$699$	−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	$0.656403\pi$
$702$	−7.20480	−	24.9167i	−0.271928	−	0.940420i
$703$	32.9455			1.24256
$704$			3.91669i			0.147616i
$705$		0			0
$706$		−	18.8945i		−	0.711103i
$707$	−18.3787	−	10.5194i	−0.691201	−	0.395623i
$708$	−9.28811	−	4.25717i	−0.349068	−	0.159994i
$709$	−17.8334			−0.669747			−0.334873	−	0.942263i	$-0.608694\pi$
$709$	−17.8334			−0.669747			−0.334873	+	0.942263i	$0.608694\pi$
$710$		0			0
$711$	−1.45472	−	1.68819i	−0.0545564	−	0.0633121i
$712$	12.3340			0.462235
$713$		−	31.6391i		−	1.18489i
$714$	13.2229	−	9.46326i	0.494854	−	0.354154i
$715$		0			0
$716$			2.08331i			0.0778569i
$717$	−9.56748	+	20.8739i	−0.357304	+	0.779551i
$718$		−	1.49291i		−	0.0557149i
$719$	−18.4786			−0.689136			−0.344568	−	0.938761i	$-0.611975\pi$
$719$	−18.4786			−0.689136			−0.344568	+	0.938761i	$0.611975\pi$
$720$		0			0
$721$	14.1739	+	8.11271i	0.527862	+	0.302133i
$722$	9.08331			0.338046
$723$	−13.3679	+	29.1656i	−0.497159	+	1.08468i
$724$			24.6679i			0.916777i
$725$		0			0
$726$	6.83425	+	3.13245i	0.253643	+	0.116256i
$727$	−8.92777			−0.331113			−0.165556	−	0.986200i	$-0.552942\pi$
$727$	−8.92777			−0.331113			−0.165556	+	0.986200i	$0.552942\pi$
$728$	−11.4620	−	6.56050i	−0.424809	−	0.243148i
$729$	−22.8334	+	14.4096i	−0.845681	+	0.533689i
$730$		0			0
$731$	10.3493			0.382782
$732$	−1.79520	+	3.91669i	−0.0663525	+	0.144765i
$733$	−24.7934			−0.915765			−0.457883	−	0.889013i	$-0.651392\pi$
$733$	−24.7934			−0.915765			−0.457883	+	0.889013i	$0.651392\pi$
$734$	16.9544			0.625800
$735$		0			0
$736$	7.54528			0.278123
$737$	−2.13567			−0.0786686
$738$	18.2552	+	21.1850i	0.671985	+	0.779830i
$739$	−5.32629			−0.195931			−0.0979654	−	0.995190i	$-0.531233\pi$
$739$	−5.32629			−0.195931			−0.0979654	+	0.995190i	$0.531233\pi$
$740$		0			0
$741$	11.3442	−	24.7504i	0.416741	−	0.909228i
$742$	0.661561	+	0.378659i	0.0242867	+	0.0139010i
$743$	−45.7409			−1.67807			−0.839035	−	0.544078i	$-0.816880\pi$
$743$	−45.7409			−1.67807			−0.839035	+	0.544078i	$0.816880\pi$
$744$	−3.02618	+	6.60240i	−0.110945	+	0.242056i
$745$		0			0
$746$			22.8097i			0.835122i
$747$	−10.1259	+	8.72555i	−0.370487	+	0.319251i
$748$	13.8976			0.508146
$749$	−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	$0.630751\pi$
$752$			8.00387i			0.291871i
$753$	33.9085	+	15.5418i	1.23569	+	0.566375i
$754$		−	37.6635i		−	1.37162i
$755$		0			0
$756$	−3.24621	+	13.3590i	−0.118063	+	0.485861i
$757$		−	14.0524i		−	0.510742i	−0.966843	−	0.255371i	$-0.917802\pi$
$757$		−	14.0524i		−	0.510742i	0.966843	−	0.255371i	$-0.0821976\pi$
$758$	−0.371417			−0.0134905
$759$	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	$0.855982\pi$
$762$	1.44337	−	3.14908i	0.0522877	−	0.114079i
$763$	34.2687	+	19.6144i	1.24061	+	0.710089i
$764$		−	16.0072i		−	0.579122i
$765$		0			0
$766$		−	32.8367i		−	1.18644i
$767$	29.4455			1.06322
$768$	−1.57454	−	0.721683i	−0.0568163	−	0.0260415i
$769$		−	12.9903i		−	0.468442i	−0.972183	−	0.234221i	$-0.924746\pi$
$769$		−	12.9903i		−	0.468442i	0.972183	−	0.234221i	$-0.0752540\pi$
$770$		0			0
$771$	23.0145	−	50.2120i	0.828846	−	1.80834i
$772$			26.4310i			0.951273i
$773$			29.9500i			1.07723i	0.842553	+	0.538613i	$0.181051\pi$
$773$			29.9500i			1.07723i	−0.842553	+	0.538613i	$0.818949\pi$
$774$	−6.62858	+	5.71189i	−0.238260	+	0.205310i
$775$		0			0
$776$	0.524688			0.0188352
$777$	38.9870	−	27.9020i	1.39865	−	1.00098i
$778$			24.1287i			0.865057i
$779$			29.3550i			1.05175i
$780$		0			0
$781$	−21.0382			−0.752805
$782$		−	26.7729i		−	0.957396i
$783$	−37.6635	+	10.8906i	−1.34598	+	0.389198i
$784$	3.54528	+	6.03581i	0.126617	+	0.215565i
$785$		0			0
$786$	−23.1215	−	10.5976i	−0.824716	−	0.378005i
$787$	1.01612			0.0362207			0.0181103	−	0.999836i	$-0.494235\pi$
$787$	1.01612			0.0362207			0.0181103	+	0.999836i	$0.494235\pi$
$788$	−17.2644			−0.615019
$789$	22.3173	+	10.2290i	0.794517	+	0.364163i
$790$		0			0
$791$	−27.1010	−	15.5119i	−0.963602	−	0.551538i
$792$	−8.90122	+	7.67024i	−0.316291	+	0.272550i
$793$		−	12.4168i		−	0.440935i
$794$	7.35371			0.260973
$795$		0			0
$796$		−	10.8906i		−	0.386007i
$797$			40.4247i			1.43192i	0.698143	+	0.715959i	$0.254010\pi$
$797$			40.4247i			1.43192i	−0.698143	+	0.715959i	$0.745990\pi$
$798$	−11.7352	+	8.39856i	−0.415421	+	0.297306i
$799$	28.4001			1.00472
$800$		0			0
$801$	24.1542	+	28.0306i	0.853446	+	0.990414i
$802$			17.1215i			0.604581i
$803$		−	19.0147i		−	0.671015i
$804$	0.393516	−	0.858557i	0.0138782	−	0.0302790i
$805$		0			0
$806$		−	20.9312i		−	0.737269i
$807$	10.5191	+	4.82138i	0.370290	+	0.169721i
$808$	8.00387			0.281575
$809$			23.0287i			0.809645i	0.914395	+	0.404822i	$0.132667\pi$
$809$			23.0287i			0.809645i	−0.914395	+	0.404822i	$0.867333\pi$
$810$		0			0
$811$		−	29.9272i		−	1.05089i	−0.850829	−	0.525443i	$-0.823900\pi$
$811$		−	29.9272i		−	1.05089i	0.850829	−	0.525443i	$-0.176100\pi$
$812$	−9.91669	+	17.3256i	−0.348008	+	0.608010i
$813$	−6.82614	+	14.8930i	−0.239403	+	0.522320i
$814$	40.9763			1.43622
$815$		0			0
$816$	−2.56075	+	5.58693i	−0.0896440	+	0.195582i
$817$	−9.18489			−0.321339
$818$		−	23.2246i		−	0.812028i
$819$	−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	$-0.0613474\pi$
$822$	28.9379	+	13.2636i	1.00933	+	0.462620i
$823$			28.6286i			0.997930i	0.866622	+	0.498965i	$0.166286\pi$
$823$			28.6286i			0.997930i	−0.866622	+	0.498965i	$0.833714\pi$
$824$	−6.17269			−0.215036
$825$		0			0
$826$	−13.5453	−	7.75293i	−0.471300	−	0.269759i
$827$	1.97858			0.0688018			0.0344009	−	0.999408i	$-0.489048\pi$
$827$	1.97858			0.0688018			0.0344009	+	0.999408i	$0.489048\pi$
$828$	14.7763	+	17.1477i	0.513510	+	0.595923i
$829$		−	39.7518i		−	1.38064i	−0.723506	−	0.690318i	$-0.757471\pi$
$829$		−	39.7518i		−	1.38064i	0.723506	−	0.690318i	$-0.242529\pi$
$830$		0			0
$831$	−8.08632	+	17.6424i	−0.280511	+	0.612008i
$832$	4.99166			0.173055
$833$	21.4168	−	12.5797i	0.742050	−	0.435860i
$834$	9.09878	−	19.8513i	0.315065	−	0.687396i
$835$		0			0
$836$	−12.3340			−0.426579
$837$	−20.9312	+	6.05237i	−0.723487	+	0.209200i
$838$	−11.5522			−0.399063
$839$	19.5508			0.674969			0.337484	−	0.941331i	$-0.390424\pi$
$839$	19.5508			0.674969			0.337484	+	0.941331i	$0.390424\pi$
$840$		0			0
$841$	−27.9312			−0.963144
$842$	36.9239			1.27248
$843$	2.09970	−	4.58104i	0.0723176	−	0.157779i
$844$	−6.88575			−0.237017
$845$		0			0
$846$	−18.1899	+	15.6743i	−0.625381	+	0.538895i
$847$	9.96670	+	5.70465i	0.342460	+	0.196014i
$848$	−0.288109			−0.00989369
$849$	38.4276	+	17.6131i	1.31883	+	0.604480i
$850$		0			0
$851$		−	78.9384i		−	2.70597i
$852$	3.87646	−	8.45750i	0.132805	−	0.289749i
$853$	11.6724			0.399656			0.199828	−	0.979831i	$-0.435962\pi$
$853$	11.6724			0.399656			0.199828	+	0.979831i	$0.435962\pi$
$854$	−3.26932	+	5.71189i	−0.111874	+	0.195457i
$855$		0			0
$856$	2.65953			0.0909007
$857$			3.91425i			0.133708i	0.997763	+	0.0668542i	$0.0212962\pi$
$857$			3.91425i			0.133708i	−0.997763	+	0.0668542i	$0.978704\pi$
$858$	14.1095	−	30.7835i	0.481690	−	1.05093i
$859$			43.3229i			1.47816i	0.673619	+	0.739079i	$0.264739\pi$
$859$			43.3229i			1.47816i	−0.673619	+	0.739079i	$0.735261\pi$
$860$		0			0
$861$	24.8610	+	34.7380i	0.847262	+	1.18387i
$862$		−	5.03094i		−	0.171355i
$863$	33.8479			1.15219			0.576097	−	0.817381i	$-0.304575\pi$
$863$	33.8479			1.15219			0.576097	+	0.817381i	$0.304575\pi$
$864$	−1.44337	−	4.99166i	−0.0491043	−	0.169820i
$865$		0			0
$866$	3.04024			0.103311
$867$	−6.94309	−	3.18234i	−0.235800	−	0.108078i
$868$	−5.51112	+	9.62858i	−0.187060	+	0.326815i
$869$		−	2.90945i		−	0.0986963i
$870$		0			0
$871$			2.72183i			0.0922257i
$872$	−14.9239			−0.505388
$873$	1.02752	+	1.19243i	0.0347763	+	0.0403575i
$874$			23.7607i			0.803716i
$875$		0			0
$876$	7.64405	+	3.50362i	0.258269	+	0.118376i
$877$			15.4383i			0.521313i	0.965432	+	0.260657i	$0.0839390\pi$
$877$			15.4383i			0.521313i	−0.965432	+	0.260657i	$0.916061\pi$
$878$			19.8184i			0.668838i
$879$	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	$0.530331\pi$
$882$	−6.77434	+	19.8773i	−0.228104	+	0.669305i
$883$		−	7.05237i		−	0.237331i	−0.992934	−	0.118666i	$-0.962138\pi$
$883$		−	7.05237i		−	0.237331i	0.992934	−	0.118666i	$-0.0378616\pi$
$884$		−	17.7119i		−	0.595715i
$885$		0			0
$886$	−10.5976			−0.356035
$887$			21.9461i			0.736878i	0.929652	+	0.368439i	$0.120108\pi$
$887$			21.9461i			0.736878i	−0.929652	+	0.368439i	$0.879892\pi$
$888$	−7.55023	+	16.4728i	−0.253369	+	0.552790i
$889$	2.62858	−	4.59244i	0.0881599	−	0.154026i
$890$		0			0
$891$	−34.8633	−	5.20827i	−1.16797	−	0.174484i
$892$	−2.90336			−0.0972118
$893$	−25.2048			−0.843446
$894$	4.08439	−	8.91114i	0.136602	−	0.298033i
$895$		0			0
$896$	−2.29622	−	1.31429i	−0.0767114	−	0.0439074i
$897$	−59.3026	−	27.1811i	−1.98006	−	0.907551i
$898$		−	6.19756i		−	0.206815i
$899$	−31.6391			−1.05522
$900$		0			0
$901$			1.02229i			0.0340576i
$902$			36.5105i			1.21567i
$903$	−10.8692	+	7.77879i	−0.361704	+	0.258862i
$904$	11.8024			0.392543
$905$		0			0
$906$	4.13881	+	1.89701i	0.137503	+	0.0630238i
$907$		−	51.7787i		−	1.71928i	−0.510896	−	0.859642i	$-0.670686\pi$
$907$		−	51.7787i		−	1.71928i	0.510896	−	0.859642i	$-0.329314\pi$
$908$			21.6557i			0.718671i
$909$	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	$0.801416\pi$
$912$	2.27264	−	4.95835i	0.0752545	−	0.164187i
$913$	−17.4511			−0.577547
$914$			19.7573i			0.653514i
$915$		0			0
$916$		−	16.9378i		−	0.559641i
$917$	−33.7191	−	19.2999i	−1.11350	−	0.637338i
$918$	−17.7119	+	5.12149i	−0.584580	+	0.169034i
$919$	22.0145			0.726191			0.363095	−	0.931752i	$-0.381720\pi$
$919$	22.0145			0.726191			0.363095	+	0.931752i	$0.381720\pi$
$920$		0			0
$921$	18.5942	+	8.52256i	0.612699	+	0.280828i
$922$	−26.8983			−0.885849
$923$			26.8123i			0.882538i
$924$	−14.5957	+	10.4458i	−0.480165	+	0.343641i
$925$		0			0
$926$		−	38.7573i		−	1.27364i
$927$	−12.0883	−	14.0283i	−0.397030	−	0.460749i
$928$		−	7.54528i		−	0.247686i
$929$	21.4048			0.702268			0.351134	−	0.936325i	$-0.385796\pi$
$929$	21.4048			0.702268			0.351134	+	0.936325i	$0.385796\pi$
$930$		0			0
$931$	−19.0072	+	11.1643i	−0.622937	+	0.365897i
$932$	5.42378			0.177662
$933$	−4.54528	−	2.08331i	−0.148806	−	0.0682044i
$934$		−	18.5181i		−	0.605929i
$935$		0			0
$936$	9.77540	+	11.3442i	0.319519	+	0.370798i
$937$	37.3845			1.22130			0.610649	−	0.791901i	$-0.290909\pi$
$937$	37.3845			1.22130			0.610649	+	0.791901i	$0.290909\pi$
$938$	0.716650	−	1.25207i	0.0233995	−	0.0408816i
$939$	−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	$0.687967\pi$
$942$	38.2382	+	17.5263i	1.24587	+	0.571039i
$943$	70.3353			2.29043
$944$	5.89894			0.191994
$945$		0			0
$946$	−11.4238			−0.371419
$947$	−46.2430			−1.50270			−0.751348	−	0.659907i	$-0.770596\pi$
$947$	−46.2430			−1.50270			−0.751348	+	0.659907i	$0.770596\pi$
$948$	1.16962	+	0.536091i	0.0379875	+	0.0174114i
$949$	−24.2335			−0.786652
$950$		0			0
$951$	−36.6307	−	16.7895i	−1.18783	−	0.544438i
$952$	−4.66349	+	8.14768i	−0.151145	+	0.264068i
$953$	−25.1360			−0.814234			−0.407117	−	0.913376i	$-0.633466\pi$
$953$	−25.1360			−0.814234			−0.407117	+	0.913376i	$0.633466\pi$
$954$	−0.564216	−	0.654766i	−0.0182672	−	0.0211988i
$955$		0			0
$956$		−	13.2572i		−	0.428767i
$957$	−46.5316	−	21.3276i	−1.50415	−	0.689422i
$958$	−14.4337			−0.466331
$959$	42.2015	+	24.1549i	1.36276	+	0.780003i
$960$		0			0
$961$	13.4168			0.432801
$962$		−	52.2226i		−	1.68372i
$963$	5.20827	+	6.04414i	0.167834	+	0.194770i
$964$		−	18.5233i		−	0.596595i
$965$		0			0
$966$	20.1232	+	28.1178i	0.647452	+	0.904677i
$967$			50.1287i			1.61203i	0.591894	+	0.806016i	$0.298380\pi$
$967$			50.1287i			1.61203i	−0.591894	+	0.806016i	$0.701620\pi$
$968$	−4.34047			−0.139508
$969$	−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	$0.801040\pi$
$972$	8.51763	−	13.0557i	0.273203	−	0.418760i
$973$	16.5702	−	28.9501i	0.531217	−	0.928098i
$974$			26.2430i			0.840879i
$975$		0			0
$976$		−	2.48752i		−	0.0796235i
$977$	−61.1360			−1.95591			−0.977957	−	0.208808i	$-0.933042\pi$
$977$	−61.1360			−1.95591			−0.977957	+	0.208808i	$0.933042\pi$
$978$	−9.71528	+	21.1964i	−0.310660	+	0.677786i
$979$			48.3084i			1.54394i
$980$		0			0
$981$	−29.2262	−	33.9167i	−0.933122	−	1.08288i
$982$			30.0000i			0.957338i
$983$			9.32699i			0.297485i	0.988876	+	0.148742i	$0.0475225\pi$
$983$			9.32699i			0.297485i	−0.988876	+	0.148742i	$0.952477\pi$
$984$	−14.6775	−	6.72736i	−0.467901	−	0.214460i
$985$		0			0
$986$	−26.7729			−0.852622
$987$	−29.8268	+	21.3462i	−0.949398	+	0.679458i
$988$			15.7191i			0.500092i
$989$			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	$0.246166\pi$
$992$		−	4.19323i		−	0.133135i
$993$	40.0909	+	18.3755i	1.27224	+	0.583128i
$994$	7.05961	−	12.3340i	0.223917	−	0.391210i
$995$		0			0
$996$	3.21551	−	7.01547i	0.101887	−	0.222294i
$997$	14.0283			0.444280			0.222140	−	0.975015i	$-0.428696\pi$
$997$	14.0283			0.444280			0.222140	+	0.975015i	$0.428696\pi$
$998$	−41.6740			−1.31917
$999$	−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.d.h.1049.1		12
3.2	odd	2		1050.2.d.g.1049.2		12
5.2	odd	4		1050.2.b.e.251.9	yes	12
5.3	odd	4		1050.2.b.d.251.4	yes	12
5.4	even	2		1050.2.d.g.1049.12		12
7.6	odd	2	inner	1050.2.d.h.1049.12		12
15.2	even	4		1050.2.b.e.251.4	yes	12
15.8	even	4		1050.2.b.d.251.9	yes	12
15.14	odd	2	inner	1050.2.d.h.1049.11		12
21.20	even	2		1050.2.d.g.1049.11		12
35.13	even	4		1050.2.b.d.251.3	✓	12
35.27	even	4		1050.2.b.e.251.10	yes	12
35.34	odd	2		1050.2.d.g.1049.1		12
105.62	odd	4		1050.2.b.e.251.3	yes	12
105.83	odd	4		1050.2.b.d.251.10	yes	12
105.104	even	2	inner	1050.2.d.h.1049.2		12

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

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.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.57454 - 0.721683i) q^{3} +1.00000 q^{4} +(-1.57454 - 0.721683i) q^{6} +(-2.29622 - 1.31429i) q^{7} +1.00000 q^{8} +(1.95835 + 2.27264i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.57454 - 0.721683i) q^{3} +1.00000 q^{4} +(-1.57454 - 0.721683i) q^{6} +(-2.29622 - 1.31429i) q^{7} +1.00000 q^{8} +(1.95835 + 2.27264i) q^{9} +3.91669i q^{11} +(-1.57454 - 0.721683i) q^{12} +4.99166 q^{13} +(-2.29622 - 1.31429i) q^{14} +1.00000 q^{16} -3.54830i q^{17} +(1.95835 + 2.27264i) q^{18} +3.14908i q^{19} +(2.66699 + 3.72655i) q^{21} +3.91669i q^{22} +7.54528 q^{23} +(-1.57454 - 0.721683i) q^{24} +4.99166 q^{26} +(-1.44337 - 4.99166i) q^{27} +(-2.29622 - 1.31429i) q^{28} -7.54528i q^{29} -4.19323i q^{31} +1.00000 q^{32} +(2.82661 - 6.16698i) q^{33} -3.54830i q^{34} +(1.95835 + 2.27264i) q^{36} -10.4620i q^{37} +3.14908i q^{38} +(-7.85957 - 3.60240i) q^{39} +9.32176 q^{41} +(2.66699 + 3.72655i) q^{42} +2.91669i q^{43} +3.91669i q^{44} +7.54528 q^{46} +8.00387i q^{47} +(-1.57454 - 0.721683i) q^{48} +(3.54528 + 6.03581i) q^{49} +(-2.56075 + 5.58693i) q^{51} +4.99166 q^{52} -0.288109 q^{53} +(-1.44337 - 4.99166i) q^{54} +(-2.29622 - 1.31429i) q^{56} +(2.27264 - 4.95835i) q^{57} -7.54528i q^{58} +5.89894 q^{59} -2.48752i q^{61} -4.19323i q^{62} +(-1.50989 - 7.79232i) q^{63} +1.00000 q^{64} +(2.82661 - 6.16698i) q^{66} +0.545275i q^{67} -3.54830i q^{68} +(-11.8803 - 5.44530i) q^{69} +5.37142i q^{71} +(1.95835 + 2.27264i) q^{72} -4.85479 q^{73} -10.4620i q^{74} +3.14908i q^{76} +(5.14768 - 8.99360i) q^{77} +(-7.85957 - 3.60240i) q^{78} -0.742834 q^{79} +(-1.32976 + 8.90122i) q^{81} +9.32176 q^{82} +4.45557i q^{83} +(2.66699 + 3.72655i) q^{84} +2.91669i q^{86} +(-5.44530 + 11.8803i) q^{87} +3.91669i q^{88} +12.3340 q^{89} +(-11.4620 - 6.56050i) q^{91} +7.54528 q^{92} +(-3.02618 + 6.60240i) q^{93} +8.00387i q^{94} +(-1.57454 - 0.721683i) q^{96} +0.524688 q^{97} +(3.54528 + 6.03581i) q^{98} +(-8.90122 + 7.67024i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 12 q^{4} + 12 q^{8}+O(q^{10}) \) 12 * q + 12 * q^2 + 12 * q^4 + 12 * q^8	\( 12 q + 12 q^{2} + 12 q^{4} + 12 q^{8} + 12 q^{16} + 14 q^{21} + 20 q^{23} + 12 q^{32} - 12 q^{39} + 14 q^{42} + 20 q^{46} - 28 q^{49} + 28 q^{51} + 20 q^{53} - 8 q^{57} + 30 q^{63} + 12 q^{64} - 44 q^{77} - 12 q^{78} - 56 q^{79} - 16 q^{81} + 14 q^{84} - 20 q^{91} + 20 q^{92} - 48 q^{93} - 28 q^{98} - 48 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^4 + 12 * q^8 + 12 * q^16 + 14 * q^21 + 20 * q^23 + 12 * q^32 - 12 * q^39 + 14 * q^42 + 20 * q^46 - 28 * q^49 + 28 * q^51 + 20 * q^53 - 8 * q^57 + 30 * q^63 + 12 * q^64 - 44 * q^77 - 12 * q^78 - 56 * q^79 - 16 * q^81 + 14 * q^84 - 20 * q^91 + 20 * q^92 - 48 * q^93 - 28 * q^98 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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