LMFDB - Embedded newform 1000.2.q.d.449.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1000,2,Mod(49,1000)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1000, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("1000.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.q (of order $10$, degree $4$, 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:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			449.2
Character	$\chi$	$=$	1000.449
Dual form			1000.2.q.d.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.37758 - 0.772523i) q^{3} -1.96923i q^{7} +(2.62905 + 1.91012i) q^{9} +O(q^{10})$	\(q+(-2.37758 - 0.772523i) q^{3} -1.96923i q^{7} +(2.62905 + 1.91012i) q^{9} +(-2.80465 + 2.03770i) q^{11} +(3.14385 - 4.32714i) q^{13} +(0.630686 - 0.204922i) q^{17} +(0.163997 + 0.504731i) q^{19} +(-1.52128 + 4.68201i) q^{21} +(-5.23253 - 7.20196i) q^{23} +(-0.366899 - 0.504994i) q^{27} +(0.939405 - 2.89119i) q^{29} +(0.921788 + 2.83697i) q^{31} +(8.24246 - 2.67814i) q^{33} +(-6.87504 + 9.46267i) q^{37} +(-10.8176 + 7.85944i) q^{39} +(-0.662310 - 0.481196i) q^{41} +9.68524i q^{43} +(-7.75769 - 2.52063i) q^{47} +3.12212 q^{49} -1.65782 q^{51} +(-8.88842 - 2.88802i) q^{53} -1.32673i q^{57} +(-2.82290 - 2.05096i) q^{59} +(-9.24453 + 6.71654i) q^{61} +(3.76147 - 5.17722i) q^{63} +(-8.95703 + 2.91032i) q^{67} +(6.87709 + 21.1655i) q^{69} +(1.27411 - 3.92130i) q^{71} +(6.20264 + 8.53720i) q^{73} +(4.01270 + 5.52301i) q^{77} +(2.31326 - 7.11949i) q^{79} +(-2.53041 - 7.78781i) q^{81} +(-3.60543 + 1.17148i) q^{83} +(-4.46702 + 6.14833i) q^{87} +(-11.3462 + 8.24351i) q^{89} +(-8.52115 - 6.19098i) q^{91} -7.45723i q^{93} +(0.910252 + 0.295759i) q^{97} -11.2658 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 22 q^{9}+O(q^{10}) $ 32 * q + 22 * q^9	$ 32 q + 22 q^{9} - 20 q^{11} - 6 q^{21} - 10 q^{29} - 18 q^{31} - 28 q^{39} - 4 q^{41} - 36 q^{49} + 200 q^{51} + 106 q^{59} + 8 q^{61} + 14 q^{69} - 12 q^{71} + 44 q^{79} - 12 q^{81} - 40 q^{89} - 54 q^{91} - 244 q^{99}+O(q^{100}) $ 32 * q + 22 * q^9 - 20 * q^11 - 6 * q^21 - 10 * q^29 - 18 * q^31 - 28 * q^39 - 4 * q^41 - 36 * q^49 + 200 * q^51 + 106 * q^59 + 8 * q^61 + 14 * q^69 - 12 * q^71 + 44 * q^79 - 12 * q^81 - 40 * q^89 - 54 * q^91 - 244 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.37758	−	0.772523i	−1.37270	−	0.446017i	−0.472436	−	0.881365i	$-0.656625\pi$
$3$	−2.37758	−	0.772523i	−1.37270	−	0.446017i	−0.900262	+	0.435349i	$0.856625\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	1.96923i		−	0.744300i	−0.928173	−	0.372150i	$-0.878621\pi$
$7$		−	1.96923i		−	0.744300i	0.928173	−	0.372150i	$-0.121379\pi$
$8$		0			0
$9$	2.62905	+	1.91012i	0.876351	+	0.636706i
$10$		0			0
$11$	−2.80465	+	2.03770i	−0.845635	+	0.614389i	−0.923939	−	0.382540i	$-0.875049\pi$
$11$	−2.80465	+	2.03770i	−0.845635	+	0.614389i	0.0783043	+	0.996930i	$0.475049\pi$
$12$		0			0
$13$	3.14385	−	4.32714i	0.871948	−	1.20013i	−0.106638	−	0.994298i	$-0.534009\pi$
$13$	3.14385	−	4.32714i	0.871948	−	1.20013i	0.978586	−	0.205836i	$-0.0659914\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.630686	−	0.204922i	0.152964	−	0.0497010i	−0.231534	−	0.972827i	$-0.574375\pi$
$17$	0.630686	−	0.204922i	0.152964	−	0.0497010i	0.384498	+	0.923126i	$0.374375\pi$
$18$		0			0
$19$	0.163997	+	0.504731i	0.0376235	+	0.115793i	0.968104	−	0.250547i	$-0.0806106\pi$
$19$	0.163997	+	0.504731i	0.0376235	+	0.115793i	−0.930481	+	0.366340i	$0.880611\pi$
$20$		0			0
$21$	−1.52128	+	4.68201i	−0.331970	+	1.02170i
$22$		0			0
$23$	−5.23253	−	7.20196i	−1.09106	−	1.50171i	−0.846733	−	0.532019i	$-0.821434\pi$
$23$	−5.23253	−	7.20196i	−1.09106	−	1.50171i	−0.244325	−	0.969693i	$-0.578566\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.366899	−	0.504994i	−0.0706098	−	0.0971861i
$28$		0			0
$29$	0.939405	−	2.89119i	0.174443	−	0.536881i	−0.825165	−	0.564892i	$-0.808918\pi$
$29$	0.939405	−	2.89119i	0.174443	−	0.536881i	0.999608	+	0.0280119i	$0.00891764\pi$
$30$		0			0
$31$	0.921788	+	2.83697i	0.165558	+	0.509535i	0.999077	−	0.0429557i	$-0.0136774\pi$
$31$	0.921788	+	2.83697i	0.165558	+	0.509535i	−0.833519	+	0.552491i	$0.813677\pi$
$32$		0			0
$33$	8.24246	−	2.67814i	1.43483	−	0.466204i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−6.87504	+	9.46267i	−1.13025	+	1.55565i	−0.342653	+	0.939462i	$0.611326\pi$
$37$	−6.87504	+	9.46267i	−1.13025	+	1.55565i	−0.787596	+	0.616192i	$0.788674\pi$
$38$		0			0
$39$	−10.8176	+	7.85944i	−1.73220	+	1.25852i
$40$		0			0
$41$	−0.662310	−	0.481196i	−0.103435	−	0.0751502i	0.534865	−	0.844937i	$-0.320362\pi$
$41$	−0.662310	−	0.481196i	−0.103435	−	0.0751502i	−0.638301	+	0.769787i	$0.720362\pi$
$42$		0			0
$43$			9.68524i			1.47699i	0.674261	+	0.738493i	$0.264462\pi$
$43$			9.68524i			1.47699i	−0.674261	+	0.738493i	$0.735538\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−7.75769	−	2.52063i	−1.13158	−	0.367671i	−0.317401	−	0.948291i	$-0.602810\pi$
$47$	−7.75769	−	2.52063i	−1.13158	−	0.367671i	−0.814174	+	0.580620i	$0.802810\pi$
$48$		0			0
$49$	3.12212			0.446018
$50$		0			0
$51$	−1.65782			−0.232141
$52$		0			0
$53$	−8.88842	−	2.88802i	−1.22092	−	0.396700i	−0.373502	−	0.927630i	$-0.621843\pi$
$53$	−8.88842	−	2.88802i	−1.22092	−	0.396700i	−0.847416	+	0.530929i	$0.821843\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	1.32673i		−	0.175730i
$58$		0			0
$59$	−2.82290	−	2.05096i	−0.367511	−	0.267012i	0.388667	−	0.921378i	$-0.372936\pi$
$59$	−2.82290	−	2.05096i	−0.367511	−	0.267012i	−0.756178	+	0.654366i	$0.772936\pi$
$60$		0			0
$61$	−9.24453	+	6.71654i	−1.18364	+	0.859965i	−0.992578	−	0.121613i	$-0.961193\pi$
$61$	−9.24453	+	6.71654i	−1.18364	+	0.859965i	−0.191063	+	0.981578i	$0.561193\pi$
$62$		0			0
$63$	3.76147	−	5.17722i	0.473900	−	0.652268i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−8.95703	+	2.91032i	−1.09428	+	0.355552i	−0.799897	−	0.600137i	$-0.795113\pi$
$67$	−8.95703	+	2.91032i	−1.09428	+	0.355552i	−0.294379	+	0.955689i	$0.595113\pi$
$68$		0			0
$69$	6.87709	+	21.1655i	0.827904	+	2.54803i
$70$		0			0
$71$	1.27411	−	3.92130i	0.151209	−	0.465373i	−0.846548	−	0.532312i	$-0.821323\pi$
$71$	1.27411	−	3.92130i	0.151209	−	0.465373i	0.997757	+	0.0669389i	$0.0213233\pi$
$72$		0			0
$73$	6.20264	+	8.53720i	0.725964	+	0.999203i	0.999305	+	0.0372862i	$0.0118713\pi$
$73$	6.20264	+	8.53720i	0.725964	+	0.999203i	−0.273341	+	0.961917i	$0.588129\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.01270	+	5.52301i	0.457290	+	0.629406i
$78$		0			0
$79$	2.31326	−	7.11949i	0.260262	−	0.801005i	−0.732485	−	0.680783i	$-0.761640\pi$
$79$	2.31326	−	7.11949i	0.260262	−	0.801005i	0.992747	−	0.120222i	$-0.0383605\pi$
$80$		0			0
$81$	−2.53041	−	7.78781i	−0.281157	−	0.865312i
$82$		0			0
$83$	−3.60543	+	1.17148i	−0.395748	+	0.128586i	−0.500129	−	0.865951i	$-0.666714\pi$
$83$	−3.60543	+	1.17148i	−0.395748	+	0.128586i	0.104381	+	0.994537i	$0.466714\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−4.46702	+	6.14833i	−0.478915	+	0.659170i
$88$		0			0
$89$	−11.3462	+	8.24351i	−1.20270	+	0.873810i	−0.994547	−	0.104287i	$-0.966744\pi$
$89$	−11.3462	+	8.24351i	−1.20270	+	0.873810i	−0.208149	+	0.978097i	$0.566744\pi$
$90$		0			0
$91$	−8.52115	−	6.19098i	−0.893260	−	0.648991i
$92$		0			0
$93$		−	7.45723i		−	0.773279i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	0.910252	+	0.295759i	0.0924221	+	0.0300298i	0.354863	−	0.934918i	$-0.384527\pi$
$97$	0.910252	+	0.295759i	0.0924221	+	0.0300298i	−0.262441	+	0.964948i	$0.584527\pi$
$98$		0			0
$99$	−11.2658			−1.13226
$100$		0			0
$101$	−10.7470			−1.06937			−0.534685	−	0.845052i	$-0.679570\pi$
$101$	−10.7470			−1.06937			−0.534685	+	0.845052i	$0.679570\pi$
$102$		0			0
$103$	−8.33773	−	2.70909i	−0.821541	−	0.266935i	−0.132063	−	0.991241i	$-0.542160\pi$
$103$	−8.33773	−	2.70909i	−0.821541	−	0.266935i	−0.689478	+	0.724306i	$0.742160\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			4.50888i			0.435890i	0.975961	+	0.217945i	$0.0699354\pi$
$107$			4.50888i			0.435890i	−0.975961	+	0.217945i	$0.930065\pi$
$108$		0			0
$109$	3.94816	+	2.86851i	0.378165	+	0.274753i	0.760589	−	0.649234i	$-0.224910\pi$
$109$	3.94816	+	2.86851i	0.378165	+	0.274753i	−0.382423	+	0.923987i	$0.624910\pi$
$110$		0			0
$111$	23.6561	−	17.1872i	2.24534	−	1.63133i
$112$		0			0
$113$	−1.21739	+	1.67560i	−0.114523	+	0.157627i	−0.862430	−	0.506176i	$-0.831059\pi$
$113$	−1.21739	+	1.67560i	−0.114523	+	0.157627i	0.747907	+	0.663803i	$0.231059\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	16.5307	−	5.37116i	1.52827	−	0.496564i
$118$		0			0
$119$	−0.403540	−	1.24197i	−0.0369924	−	0.113851i
$120$		0			0
$121$	0.314671	−	0.968456i	0.0286064	−	0.0880415i
$122$		0			0
$123$	1.20296	+	1.65573i	0.108467	+	0.149292i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	1.59158	+	2.19062i	0.141230	+	0.194386i	0.873772	−	0.486335i	$-0.161667\pi$
$127$	1.59158	+	2.19062i	0.141230	+	0.194386i	−0.732543	+	0.680721i	$0.761667\pi$
$128$		0			0
$129$	7.48208	−	23.0275i	0.658760	−	2.02745i
$130$		0			0
$131$	4.90254	+	15.0885i	0.428337	+	1.31829i	0.899762	+	0.436381i	$0.143740\pi$
$131$	4.90254	+	15.0885i	0.428337	+	1.31829i	−0.471425	+	0.881906i	$0.656260\pi$
$132$		0			0
$133$	0.993932	−	0.322948i	0.0861849	−	0.0280032i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	12.8047	−	17.6241i	1.09398	−	1.50573i	0.250840	−	0.968029i	$-0.419293\pi$
$137$	12.8047	−	17.6241i	1.09398	−	1.50573i	0.843136	−	0.537700i	$-0.180707\pi$
$138$		0			0
$139$	10.1974	−	7.40882i	0.864930	−	0.628408i	−0.0642920	−	0.997931i	$-0.520479\pi$
$139$	10.1974	−	7.40882i	0.864930	−	0.628408i	0.929222	+	0.369523i	$0.120479\pi$
$140$		0			0
$141$	16.4973	+	11.9860i	1.38932	+	1.00940i
$142$		0			0
$143$			18.5424i			1.55059i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−7.42311	−	2.41191i	−0.612247	−	0.198931i
$148$		0			0
$149$	−4.71325			−0.386124			−0.193062	−	0.981187i	$-0.561842\pi$
$149$	−4.71325			−0.386124			−0.193062	+	0.981187i	$0.561842\pi$
$150$		0			0
$151$	1.09617			0.0892052			0.0446026	−	0.999005i	$-0.485798\pi$
$151$	1.09617			0.0892052			0.0446026	+	0.999005i	$0.485798\pi$
$152$		0			0
$153$	2.04953	+	0.665934i	0.165695	+	0.0538376i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		−	11.4429i		−	0.913245i	−0.889660	−	0.456623i	$-0.849059\pi$
$157$		−	11.4429i		−	0.913245i	0.889660	−	0.456623i	$-0.150941\pi$
$158$		0			0
$159$	18.9019	+	13.7330i	1.49902	+	1.08910i
$160$		0			0
$161$	−14.1823	+	10.3041i	−1.11772	+	0.812074i
$162$		0			0
$163$	−0.197314	+	0.271579i	−0.0154548	+	0.0212717i	−0.816674	−	0.577099i	$-0.804185\pi$
$163$	−0.197314	+	0.271579i	−0.0154548	+	0.0212717i	0.801220	+	0.598370i	$0.204185\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	14.2592	−	4.63310i	1.10341	−	0.358520i	0.299996	−	0.953940i	$-0.403015\pi$
$167$	14.2592	−	4.63310i	1.10341	−	0.358520i	0.803414	+	0.595421i	$0.203015\pi$
$168$		0			0
$169$	−4.82314	−	14.8441i	−0.371011	−	1.14185i
$170$		0			0
$171$	−0.532939	+	1.64022i	−0.0407549	+	0.125431i
$172$		0			0
$173$	−2.14066	−	2.94636i	−0.162751	−	0.224008i	0.719851	−	0.694129i	$-0.244210\pi$
$173$	−2.14066	−	2.94636i	−0.162751	−	0.224008i	−0.882602	+	0.470121i	$0.844210\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	5.12727	+	7.05708i	0.385389	+	0.530443i
$178$		0			0
$179$	5.71933	−	17.6023i	0.427482	−	1.31566i	−0.473115	−	0.881001i	$-0.656870\pi$
$179$	5.71933	−	17.6023i	0.427482	−	1.31566i	0.900597	−	0.434655i	$-0.143130\pi$
$180$		0			0
$181$	−0.0102245	−	0.0314676i	−0.000759978	−	0.00233897i	0.950676	−	0.310186i	$-0.100391\pi$
$181$	−0.0102245	−	0.0314676i	−0.000759978	−	0.00233897i	−0.951436	+	0.307847i	$0.900391\pi$
$182$		0			0
$183$	27.1683	−	8.82752i	2.00834	−	0.652549i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.35129	+	1.85989i	−0.0988158	+	0.136008i
$188$		0			0
$189$	−0.994450	+	0.722510i	−0.0723356	+	0.0525549i
$190$		0			0
$191$	3.69432	+	2.68408i	0.267311	+	0.194213i	0.713364	−	0.700794i	$-0.247171\pi$
$191$	3.69432	+	2.68408i	0.267311	+	0.194213i	−0.446053	+	0.895007i	$0.647171\pi$
$192$		0			0
$193$		−	9.48674i		−	0.682870i	−0.939905	−	0.341435i	$-0.889087\pi$
$193$		−	9.48674i		−	0.682870i	0.939905	−	0.341435i	$-0.110913\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−11.9723	−	3.89003i	−0.852989	−	0.277153i	−0.150292	−	0.988642i	$-0.548021\pi$
$197$	−11.9723	−	3.89003i	−0.852989	−	0.277153i	−0.702698	+	0.711489i	$0.748021\pi$
$198$		0			0
$199$	−1.43593			−0.101791			−0.0508954	−	0.998704i	$-0.516207\pi$
$199$	−1.43593			−0.101791			−0.0508954	+	0.998704i	$0.516207\pi$
$200$		0			0
$201$	23.5444			1.66069
$202$		0			0
$203$	−5.69342	−	1.84991i	−0.399600	−	0.129838i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	28.9291i		−	2.01071i
$208$		0			0
$209$	−1.48844	−	1.08142i	−0.102958	−	0.0748033i
$210$		0			0
$211$	13.6070	−	9.88603i	0.936741	−	0.680582i	−0.0108927	−	0.999941i	$-0.503467\pi$
$211$	13.6070	−	9.88603i	0.936741	−	0.680582i	0.947634	+	0.319358i	$0.103467\pi$
$212$		0			0
$213$	−6.05860	+	8.33894i	−0.415128	+	0.571375i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	5.58666	−	1.81521i	0.379247	−	0.123225i
$218$		0			0
$219$	−8.15210	−	25.0896i	−0.550868	−	1.69540i
$220$		0			0
$221$	1.09606	−	3.37332i	0.0737288	−	0.226914i
$222$		0			0
$223$	−7.18409	−	9.88804i	−0.481082	−	0.662152i	0.497630	−	0.867389i	$-0.334204\pi$
$223$	−7.18409	−	9.88804i	−0.481082	−	0.662152i	−0.978712	+	0.205237i	$0.934204\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	8.95955	+	12.3318i	0.594666	+	0.818488i	0.995207	−	0.0977912i	$-0.0311777\pi$
$227$	8.95955	+	12.3318i	0.594666	+	0.818488i	−0.400541	+	0.916279i	$0.631178\pi$
$228$		0			0
$229$	6.01667	−	18.5174i	0.397592	−	1.22366i	−0.529332	−	0.848415i	$-0.677557\pi$
$229$	6.01667	−	18.5174i	0.397592	−	1.22366i	0.926924	−	0.375249i	$-0.122443\pi$
$230$		0			0
$231$	−5.27388	−	16.2313i	−0.346996	−	1.06794i
$232$		0			0
$233$	−19.1861	+	6.23396i	−1.25693	+	0.408400i	−0.860398	−	0.509623i	$-0.829785\pi$
$233$	−19.1861	+	6.23396i	−1.25693	+	0.408400i	−0.396528	+	0.918023i	$0.629785\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−10.9999	+	15.1401i	−0.714523	+	0.983456i
$238$		0			0
$239$	−0.0247410	+	0.0179754i	−0.00160036	+	0.00116273i	−0.588585	−	0.808435i	$-0.700315\pi$
$239$	−0.0247410	+	0.0179754i	−0.00160036	+	0.00116273i	0.586985	+	0.809598i	$0.300315\pi$
$240$		0			0
$241$	−7.54591	−	5.48242i	−0.486075	−	0.353154i	0.317598	−	0.948225i	$-0.397124\pi$
$241$	−7.54591	−	5.48242i	−0.486075	−	0.353154i	−0.803673	+	0.595071i	$0.797124\pi$
$242$		0			0
$243$			22.3436i			1.43334i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2.69963	+	0.877162i	0.171773	+	0.0558125i
$248$		0			0
$249$	9.47721			0.600594
$250$		0			0
$251$	−9.20030			−0.580718			−0.290359	−	0.956918i	$-0.593775\pi$
$251$	−9.20030			−0.580718			−0.290359	+	0.956918i	$0.593775\pi$
$252$		0			0
$253$	29.3509	+	9.53667i	1.84527	+	0.599565i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	4.27125i		−	0.266433i	−0.991087	−	0.133217i	$-0.957469\pi$
$257$		−	4.27125i		−	0.266433i	0.991087	−	0.133217i	$-0.0425306\pi$
$258$		0			0
$259$	18.6342	+	13.5385i	1.15787	+	0.841244i
$260$		0			0
$261$	7.99226	−	5.80672i	0.494709	−	0.359427i
$262$		0			0
$263$	−5.24873	+	7.22425i	−0.323650	+	0.445467i	−0.939577	−	0.342337i	$-0.888782\pi$
$263$	−5.24873	+	7.22425i	−0.323650	+	0.445467i	0.615927	+	0.787803i	$0.288782\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	33.3449	−	10.8344i	2.04067	−	0.663054i
$268$		0			0
$269$	−0.957949	−	2.94826i	−0.0584072	−	0.179759i	0.917596	−	0.397513i	$-0.130127\pi$
$269$	−0.957949	−	2.94826i	−0.0584072	−	0.179759i	−0.976004	+	0.217755i	$0.930127\pi$
$270$		0			0
$271$	2.38753	−	7.34805i	0.145032	−	0.446362i	−0.851983	−	0.523569i	$-0.824600\pi$
$271$	2.38753	−	7.34805i	0.145032	−	0.446362i	0.997015	+	0.0772069i	$0.0246002\pi$
$272$		0			0
$273$	15.4771	+	21.3024i	0.936715	+	1.28928i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	9.52967	+	13.1165i	0.572582	+	0.788092i	0.992858	−	0.119305i	$-0.0380666\pi$
$277$	9.52967	+	13.1165i	0.572582	+	0.788092i	−0.420276	+	0.907397i	$0.638067\pi$
$278$		0			0
$279$	−2.99552	+	9.21927i	−0.179337	+	0.551943i
$280$		0			0
$281$	−6.60078	−	20.3151i	−0.393770	−	1.21190i	−0.929916	−	0.367773i	$-0.880120\pi$
$281$	−6.60078	−	20.3151i	−0.393770	−	1.21190i	0.536146	−	0.844125i	$-0.319880\pi$
$282$		0			0
$283$	−26.0006	+	8.44812i	−1.54558	+	0.502189i	−0.952909	−	0.303257i	$-0.901926\pi$
$283$	−26.0006	+	8.44812i	−1.54558	+	0.502189i	−0.592669	+	0.805446i	$0.701926\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.947587	+	1.30424i	−0.0559343	+	0.0769870i
$288$		0			0
$289$	−13.3975	+	9.73387i	−0.788089	+	0.572580i
$290$		0			0
$291$	−1.93572	−	1.40638i	−0.113474	−	0.0824436i
$292$		0			0
$293$		−	15.7064i		−	0.917578i	−0.888545	−	0.458789i	$-0.848283\pi$
$293$		−	15.7064i		−	0.917578i	0.888545	−	0.458789i	$-0.151717\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	2.05805	+	0.668701i	0.119420	+	0.0388020i
$298$		0			0
$299$	−47.6142			−2.75360
$300$		0			0
$301$	19.0725			1.09932
$302$		0			0
$303$	25.5520	+	8.30233i	1.46792	+	0.476957i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			19.2486i			1.09858i	0.835633	+	0.549288i	$0.185101\pi$
$307$			19.2486i			1.09858i	−0.835633	+	0.549288i	$0.814899\pi$
$308$		0			0
$309$	17.7308	+	12.8822i	1.00867	+	0.732842i
$310$		0			0
$311$	−16.8369	+	12.2327i	−0.954735	+	0.693656i	−0.951922	−	0.306341i	$-0.900895\pi$
$311$	−16.8369	+	12.2327i	−0.954735	+	0.693656i	−0.00281293	+	0.999996i	$0.500895\pi$
$312$		0			0
$313$	−7.87098	+	10.8335i	−0.444894	+	0.612344i	−0.971291	−	0.237895i	$-0.923543\pi$
$313$	−7.87098	+	10.8335i	−0.444894	+	0.612344i	0.526397	+	0.850239i	$0.323543\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−10.2156	+	3.31924i	−0.573764	+	0.186427i	−0.581505	−	0.813543i	$-0.697536\pi$
$317$	−10.2156	+	3.31924i	−0.573764	+	0.186427i	0.00774123	+	0.999970i	$0.497536\pi$
$318$		0			0
$319$	3.25667	+	10.0230i	0.182339	+	0.561181i
$320$		0			0
$321$	3.48322	−	10.7202i	0.194414	−	0.598346i
$322$		0			0
$323$	0.206861	+	0.284720i	0.0115101	+	0.0158423i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−7.17109	−	9.87016i	−0.396562	−	0.545821i
$328$		0			0
$329$	−4.96370	+	15.2767i	−0.273658	+	0.842231i
$330$		0			0
$331$	2.63127	+	8.09821i	0.144627	+	0.445118i	0.996963	−	0.0778779i	$-0.0248144\pi$
$331$	2.63127	+	8.09821i	0.144627	+	0.445118i	−0.852335	+	0.522996i	$0.824814\pi$
$332$		0			0
$333$	−36.1497	+	11.7457i	−1.98099	+	0.643663i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−3.62042	+	4.98308i	−0.197217	+	0.271446i	−0.896160	−	0.443732i	$-0.853654\pi$
$337$	−3.62042	+	4.98308i	−0.197217	+	0.271446i	0.698943	+	0.715178i	$0.253654\pi$
$338$		0			0
$339$	4.18889	−	3.04341i	0.227509	−	0.165295i
$340$		0			0
$341$	−8.36619	−	6.07839i	−0.453055	−	0.329163i
$342$		0			0
$343$		−	19.9328i		−	1.07627i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	8.66854	+	2.81658i	0.465351	+	0.151202i	0.532302	−	0.846554i	$-0.321327\pi$
$347$	8.66854	+	2.81658i	0.465351	+	0.151202i	−0.0669508	+	0.997756i	$0.521327\pi$
$348$		0			0
$349$	−28.6909			−1.53579			−0.767893	−	0.640578i	$-0.778695\pi$
$349$	−28.6909			−1.53579			−0.767893	+	0.640578i	$0.778695\pi$
$350$		0			0
$351$	−3.33866			−0.178204
$352$		0			0
$353$	7.98376	+	2.59408i	0.424933	+	0.138069i	0.513673	−	0.857986i	$-0.328284\pi$
$353$	7.98376	+	2.59408i	0.424933	+	0.138069i	−0.0887408	+	0.996055i	$0.528284\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$			3.26462i			0.172782i
$358$		0			0
$359$	12.2475	+	8.89836i	0.646401	+	0.469638i	0.862043	−	0.506835i	$-0.169185\pi$
$359$	12.2475	+	8.89836i	0.646401	+	0.469638i	−0.215643	+	0.976472i	$0.569185\pi$
$360$		0			0
$361$	15.1435	−	11.0024i	0.797024	−	0.579072i
$362$		0			0
$363$	−1.49631	+	2.05949i	−0.0785359	+	0.108095i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−16.8511	+	5.47524i	−0.879618	+	0.285805i	−0.713799	−	0.700351i	$-0.753027\pi$
$367$	−16.8511	+	5.47524i	−0.879618	+	0.285805i	−0.165820	+	0.986156i	$0.553027\pi$
$368$		0			0
$369$	−0.822106	−	2.53018i	−0.0427971	−	0.131716i
$370$		0			0
$371$	−5.68718	+	17.5034i	−0.295264	+	0.908729i
$372$		0			0
$373$	15.9132	+	21.9026i	0.823954	+	1.13408i	0.989018	+	0.147793i	$0.0472169\pi$
$373$	15.9132	+	21.9026i	0.823954	+	1.13408i	−0.165064	+	0.986283i	$0.552783\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−9.55725	−	13.1544i	−0.492223	−	0.677487i
$378$		0			0
$379$	−1.64450	+	5.06126i	−0.0844724	+	0.259979i	−0.984367	−	0.176127i	$-0.943643\pi$
$379$	−1.64450	+	5.06126i	−0.0844724	+	0.259979i	0.899895	+	0.436107i	$0.143643\pi$
$380$		0			0
$381$	−2.09180	−	6.43791i	−0.107166	−	0.329824i
$382$		0			0
$383$	5.76377	−	1.87276i	0.294515	−	0.0956937i	−0.158033	−	0.987434i	$-0.550515\pi$
$383$	5.76377	−	1.87276i	0.294515	−	0.0956937i	0.452548	+	0.891740i	$0.350515\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−18.5000	+	25.4630i	−0.940406	+	1.29436i
$388$		0			0
$389$	−1.55863	+	1.13241i	−0.0790259	+	0.0574156i	−0.626597	−	0.779344i	$-0.715553\pi$
$389$	−1.55863	+	1.13241i	−0.0790259	+	0.0574156i	0.547571	+	0.836759i	$0.315553\pi$
$390$		0			0
$391$	−4.77593	−	3.46991i	−0.241529	−	0.175481i
$392$		0			0
$393$		−	39.6614i		−	2.00065i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−12.6395	−	4.10681i	−0.634357	−	0.206115i	−0.0258526	−	0.999666i	$-0.508230\pi$
$397$	−12.6395	−	4.10681i	−0.634357	−	0.206115i	−0.608504	+	0.793551i	$0.708230\pi$
$398$		0			0
$399$	−2.61264			−0.130796
$400$		0			0
$401$	−7.73185			−0.386110			−0.193055	−	0.981188i	$-0.561840\pi$
$401$	−7.73185			−0.386110			−0.193055	+	0.981188i	$0.561840\pi$
$402$		0			0
$403$	15.1740	+	4.93032i	0.755868	+	0.245597i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	40.5488i		−	2.00993i
$408$		0			0
$409$	−3.26771	−	2.37413i	−0.161578	−	0.117393i	0.504058	−	0.863670i	$-0.331840\pi$
$409$	−3.26771	−	2.37413i	−0.161578	−	0.117393i	−0.665636	+	0.746277i	$0.731840\pi$
$410$		0			0
$411$	−44.0592	+	32.0109i	−2.17328	+	1.57898i
$412$		0			0
$413$	−4.03881	+	5.55895i	−0.198737	+	0.273538i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−29.9686	+	9.73738i	−1.46757	+	0.476841i
$418$		0			0
$419$	1.86222	+	5.73132i	0.0909754	+	0.279993i	0.986184	−	0.165654i	$-0.0529735\pi$
$419$	1.86222	+	5.73132i	0.0909754	+	0.279993i	−0.895209	+	0.445647i	$0.852973\pi$
$420$		0			0
$421$	7.28165	−	22.4106i	0.354886	−	1.09223i	−0.601190	−	0.799106i	$-0.705306\pi$
$421$	7.28165	−	22.4106i	0.354886	−	1.09223i	0.956076	−	0.293120i	$-0.0946936\pi$
$422$		0			0
$423$	−15.5807	−	21.4450i	−0.757559	−	1.04269i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	13.2264	+	18.2046i	0.640072	+	0.880983i
$428$		0			0
$429$	14.3244	−	44.0860i	0.691589	−	2.12849i
$430$		0			0
$431$	5.10679	+	15.7171i	0.245985	+	0.757065i	0.995473	+	0.0950464i	$0.0302999\pi$
$431$	5.10679	+	15.7171i	0.245985	+	0.757065i	−0.749488	+	0.662018i	$0.769700\pi$
$432$		0			0
$433$	−4.54293	+	1.47609i	−0.218319	+	0.0709362i	−0.416134	−	0.909303i	$-0.636615\pi$
$433$	−4.54293	+	1.47609i	−0.218319	+	0.0709362i	0.197815	+	0.980239i	$0.436615\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.77693	−	3.82212i	0.132839	−	0.182837i
$438$		0			0
$439$	20.7020	−	15.0409i	0.988054	−	0.717863i	0.0285597	−	0.999592i	$-0.490908\pi$
$439$	20.7020	−	15.0409i	0.988054	−	0.717863i	0.959494	+	0.281729i	$0.0909079\pi$
$440$		0			0
$441$	8.20823	+	5.96363i	0.390868	+	0.283982i
$442$		0			0
$443$		−	29.2397i		−	1.38922i	−0.719387	−	0.694609i	$-0.755577\pi$
$443$		−	29.2397i		−	1.38922i	0.719387	−	0.694609i	$-0.244423\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	11.2061	+	3.64109i	0.530032	+	0.172218i
$448$		0			0
$449$	26.6658			1.25844			0.629219	−	0.777228i	$-0.283375\pi$
$449$	26.6658			1.25844			0.629219	+	0.777228i	$0.283375\pi$
$450$		0			0
$451$	2.83808			0.133640
$452$		0			0
$453$	−2.60624	−	0.846819i	−0.122452	−	0.0397870i
$454$		0			0
$455$		0			0
$456$		0			0
$457$			14.8582i			0.695037i	0.937673	+	0.347519i	$0.112976\pi$
$457$			14.8582i			0.695037i	−0.937673	+	0.347519i	$0.887024\pi$
$458$		0			0
$459$	−0.334883	−	0.243307i	−0.0156310	−	0.0113566i
$460$		0			0
$461$	8.80835	−	6.39964i	0.410246	−	0.298061i	−0.363456	−	0.931612i	$-0.618403\pi$
$461$	8.80835	−	6.39964i	0.410246	−	0.298061i	0.773701	+	0.633551i	$0.218403\pi$
$462$		0			0
$463$	18.3786	−	25.2959i	0.854124	−	1.17560i	−0.128815	−	0.991669i	$-0.541117\pi$
$463$	18.3786	−	25.2959i	0.854124	−	1.17560i	0.982939	−	0.183932i	$-0.0588828\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	9.98625	−	3.24473i	0.462109	−	0.150148i	−0.0687046	−	0.997637i	$-0.521887\pi$
$467$	9.98625	−	3.24473i	0.462109	−	0.150148i	0.530813	+	0.847489i	$0.321887\pi$
$468$		0			0
$469$	5.73109	+	17.6385i	0.264637	+	0.814469i
$470$		0			0
$471$	−8.83993	+	27.2065i	−0.407323	+	1.25361i
$472$		0			0
$473$	−19.7356	−	27.1637i	−0.907445	−	1.24899i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−17.8517	−	24.5707i	−0.817371	−	1.12501i
$478$		0			0
$479$	−5.34884	+	16.4620i	−0.244395	+	0.752170i	0.751341	+	0.659915i	$0.229408\pi$
$479$	−5.34884	+	16.4620i	−0.244395	+	0.752170i	−0.995735	+	0.0922552i	$0.970592\pi$
$480$		0			0
$481$	19.3323	+	59.4985i	0.881475	+	2.71290i
$482$		0			0
$483$	41.6798	−	13.5426i	1.89650	−	0.616209i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	18.5319	−	25.5070i	0.839762	−	1.15583i	−0.146264	−	0.989246i	$-0.546725\pi$
$487$	18.5319	−	25.5070i	0.839762	−	1.15583i	0.986027	−	0.166588i	$-0.0532750\pi$
$488$		0			0
$489$	0.678930	−	0.493272i	0.0307023	−	0.0223065i
$490$		0			0
$491$	6.25902	+	4.54744i	0.282465	+	0.205223i	0.719992	−	0.693982i	$-0.244145\pi$
$491$	6.25902	+	4.54744i	0.282465	+	0.205223i	−0.437527	+	0.899205i	$0.644145\pi$
$492$		0			0
$493$		−	2.01594i		−	0.0907933i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−7.72196	−	2.50902i	−0.346377	−	0.112545i
$498$		0			0
$499$	21.6134			0.967551			0.483775	−	0.875192i	$-0.339265\pi$
$499$	21.6134			0.967551			0.483775	+	0.875192i	$0.339265\pi$
$500$		0			0
$501$	−37.4816			−1.67455
$502$		0			0
$503$	−20.0507	−	6.51486i	−0.894015	−	0.290483i	−0.174250	−	0.984701i	$-0.555750\pi$
$503$	−20.0507	−	6.51486i	−0.894015	−	0.290483i	−0.719764	+	0.694218i	$0.755750\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$			39.0190i			1.73290i
$508$		0			0
$509$	−26.9208	−	19.5591i	−1.19324	−	0.866942i	−0.199639	−	0.979869i	$-0.563977\pi$
$509$	−26.9208	−	19.5591i	−1.19324	−	0.866942i	−0.993603	+	0.112928i	$0.963977\pi$
$510$		0			0
$511$	16.8117	−	12.2144i	0.743707	−	0.540335i
$512$		0			0
$513$	0.194715	−	0.268003i	0.00859690	−	0.0118326i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	26.8939	−	8.73836i	1.18279	−	0.384313i
$518$		0			0
$519$	2.81345	+	8.65892i	0.123497	+	0.380084i
$520$		0			0
$521$	−12.9310	+	39.7975i	−0.566517	+	1.74356i	0.0968854	+	0.995296i	$0.469112\pi$
$521$	−12.9310	+	39.7975i	−0.566517	+	1.74356i	−0.663402	+	0.748263i	$0.730888\pi$
$522$		0			0
$523$	−7.94897	−	10.9408i	−0.347584	−	0.478408i	0.599053	−	0.800709i	$-0.295544\pi$
$523$	−7.94897	−	10.9408i	−0.347584	−	0.478408i	−0.946637	+	0.322301i	$0.895544\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.16272	+	1.60034i	0.0506488	+	0.0697121i
$528$		0			0
$529$	−17.3815	+	53.4946i	−0.755715	+	2.32585i
$530$		0			0
$531$	−3.50399	−	10.7842i	−0.152060	−	0.467993i
$532$		0			0
$533$	−4.16441	+	1.35310i	−0.180381	+	0.0586092i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−27.1963	+	37.4325i	−1.17361	+	1.61533i
$538$		0			0
$539$	−8.75647	+	6.36195i	−0.377168	+	0.274029i
$540$		0			0
$541$	−12.5679	−	9.13114i	−0.540338	−	0.392578i	0.283873	−	0.958862i	$-0.408381\pi$
$541$	−12.5679	−	9.13114i	−0.540338	−	0.392578i	−0.824210	+	0.566284i	$0.808381\pi$
$542$		0			0
$543$			0.0827155i			0.00354966i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−43.2969	−	14.0680i	−1.85124	−	0.601505i	−0.996610	−	0.0822677i	$-0.973784\pi$
$547$	−43.2969	−	14.0680i	−1.85124	−	0.601505i	−0.854630	−	0.519237i	$-0.826216\pi$
$548$		0			0
$549$	−37.1337			−1.58483
$550$		0			0
$551$	1.61333			0.0687303
$552$		0			0
$553$	−14.0199	−	4.55535i	−0.596188	−	0.193713i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	42.5997i		−	1.80501i	−0.430681	−	0.902504i	$-0.641726\pi$
$557$		−	42.5997i		−	1.80501i	0.430681	−	0.902504i	$-0.358274\pi$
$558$		0			0
$559$	41.9094	+	30.4490i	1.77258	+	1.28786i
$560$		0			0
$561$	4.64960	−	3.37813i	0.196306	−	0.142625i
$562$		0			0
$563$	−22.3929	+	30.8212i	−0.943749	+	1.29896i	0.0104990	+	0.999945i	$0.496658\pi$
$563$	−22.3929	+	30.8212i	−0.943749	+	1.29896i	−0.954248	+	0.299015i	$0.903342\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−15.3360	+	4.98297i	−0.644052	+	0.209265i
$568$		0			0
$569$	−7.50437	−	23.0961i	−0.314600	−	0.968238i	−0.975919	−	0.218133i	$-0.930003\pi$
$569$	−7.50437	−	23.0961i	−0.314600	−	0.968238i	0.661319	−	0.750104i	$-0.269997\pi$
$570$		0			0
$571$	6.78385	−	20.8786i	0.283895	−	0.873740i	−0.702832	−	0.711356i	$-0.748082\pi$
$571$	6.78385	−	20.8786i	0.283895	−	0.873740i	0.986728	−	0.162384i	$-0.0519185\pi$
$572$		0			0
$573$	−6.71003	−	9.23556i	−0.280315	−	0.385821i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−0.560344	−	0.771248i	−0.0233274	−	0.0321075i	0.797194	−	0.603723i	$-0.206317\pi$
$577$	−0.560344	−	0.771248i	−0.0233274	−	0.0321075i	−0.820521	+	0.571616i	$0.806317\pi$
$578$		0			0
$579$	−7.32873	+	22.5555i	−0.304572	+	0.937375i
$580$		0			0
$581$	2.30691	+	7.09994i	0.0957067	+	0.294555i
$582$		0			0
$583$	30.8138	−	10.0120i	1.27618	−	0.414656i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	20.3036	−	27.9455i	0.838018	−	1.15343i	−0.148359	−	0.988934i	$-0.547399\pi$
$587$	20.3036	−	27.9455i	0.838018	−	1.15343i	0.986377	−	0.164499i	$-0.0526008\pi$
$588$		0			0
$589$	−1.28074	+	0.930510i	−0.0527718	+	0.0383410i
$590$		0			0
$591$	25.4599	+	18.4977i	1.04728	+	0.760895i
$592$		0			0
$593$		−	6.57624i		−	0.270054i	−0.990842	−	0.135027i	$-0.956888\pi$
$593$		−	6.57624i		−	0.270054i	0.990842	−	0.135027i	$-0.0431121\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	3.41405	+	1.10929i	0.139728	+	0.0454003i
$598$		0			0
$599$	−12.2044			−0.498656			−0.249328	−	0.968419i	$-0.580210\pi$
$599$	−12.2044			−0.498656			−0.249328	+	0.968419i	$0.580210\pi$
$600$		0			0
$601$	−13.4214			−0.547470			−0.273735	−	0.961805i	$-0.588259\pi$
$601$	−13.4214			−0.547470			−0.273735	+	0.961805i	$0.588259\pi$
$602$		0			0
$603$	−29.1076	−	9.45762i	−1.18535	−	0.385144i
$604$		0			0
$605$		0			0
$606$		0			0
$607$			9.33640i			0.378953i	0.981885	+	0.189476i	$0.0606791\pi$
$607$			9.33640i			0.378953i	−0.981885	+	0.189476i	$0.939321\pi$
$608$		0			0
$609$	12.1075	+	8.79661i	0.490620	+	0.356456i
$610$		0			0
$611$	−35.2962	+	25.6442i	−1.42793	+	1.03745i
$612$		0			0
$613$	24.6243	−	33.8925i	0.994567	−	1.36890i	0.0659665	−	0.997822i	$-0.478987\pi$
$613$	24.6243	−	33.8925i	0.994567	−	1.36890i	0.928600	−	0.371082i	$-0.121013\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−10.5220	+	3.41880i	−0.423599	+	0.137636i	−0.513056	−	0.858355i	$-0.671487\pi$
$617$	−10.5220	+	3.41880i	−0.423599	+	0.137636i	0.0894573	+	0.995991i	$0.471487\pi$
$618$		0			0
$619$	−8.91155	−	27.4269i	−0.358185	−	1.10238i	−0.954139	−	0.299363i	$-0.903226\pi$
$619$	−8.91155	−	27.4269i	−0.358185	−	1.10238i	0.595954	−	0.803019i	$-0.296774\pi$
$620$		0			0
$621$	−1.71713	+	5.28479i	−0.0689061	+	0.212071i
$622$		0			0
$623$	16.2334	+	22.3433i	0.650377	+	0.895167i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	2.70348	+	3.72102i	0.107967	+	0.148603i
$628$		0			0
$629$	−2.39688	+	7.37683i	−0.0955697	+	0.294133i
$630$		0			0
$631$	−9.34671	−	28.7662i	−0.372087	−	1.14516i	−0.945423	−	0.325845i	$-0.894351\pi$
$631$	−9.34671	−	28.7662i	−0.372087	−	1.14516i	0.573337	−	0.819320i	$-0.305649\pi$
$632$		0			0
$633$	−39.9888	+	12.9932i	−1.58941	+	0.516432i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	9.81550	−	13.5099i	0.388904	−	0.535281i
$638$		0			0
$639$	10.8399	−	7.87562i	0.428818	−	0.311555i
$640$		0			0
$641$	−3.27077	−	2.37635i	−0.129188	−	0.0938603i	0.521315	−	0.853364i	$-0.325442\pi$
$641$	−3.27077	−	2.37635i	−0.129188	−	0.0938603i	−0.650503	+	0.759504i	$0.725442\pi$
$642$		0			0
$643$			31.8273i			1.25515i	0.778558	+	0.627573i	$0.215952\pi$
$643$			31.8273i			1.25515i	−0.778558	+	0.627573i	$0.784048\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	37.0574	+	12.0407i	1.45688	+	0.473369i	0.927115	−	0.374777i	$-0.122281\pi$
$647$	37.0574	+	12.0407i	1.45688	+	0.473369i	0.529764	+	0.848145i	$0.322281\pi$
$648$		0			0
$649$	12.0965			0.474829
$650$		0			0
$651$	−14.6850			−0.575552
$652$		0			0
$653$	−0.751655	−	0.244228i	−0.0294145	−	0.00955736i	0.294273	−	0.955721i	$-0.404923\pi$
$653$	−0.751655	−	0.244228i	−0.0294145	−	0.00955736i	−0.323687	+	0.946164i	$0.604923\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			34.2925i			1.33788i
$658$		0			0
$659$	1.76143	+	1.27975i	0.0686156	+	0.0498521i	0.621564	−	0.783363i	$-0.286497\pi$
$659$	1.76143	+	1.27975i	0.0686156	+	0.0498521i	−0.552949	+	0.833215i	$0.686497\pi$
$660$		0			0
$661$	11.5681	−	8.40468i	0.449945	−	0.326904i	−0.339629	−	0.940559i	$-0.610302\pi$
$661$	11.5681	−	8.40468i	0.449945	−	0.326904i	0.789574	+	0.613655i	$0.210302\pi$
$662$		0			0
$663$	−5.21193	+	7.17361i	−0.202415	+	0.278600i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−25.7377	+	8.36268i	−0.996567	+	0.323804i
$668$		0			0
$669$	9.44201	+	29.0595i	0.365049	+	1.12351i
$670$		0			0
$671$	12.2414	−	37.6751i	0.472574	−	1.45443i
$672$		0			0
$673$	−6.88964	−	9.48277i	−0.265576	−	0.365534i	0.655314	−	0.755357i	$-0.272536\pi$
$673$	−6.88964	−	9.48277i	−0.265576	−	0.365534i	−0.920890	+	0.389823i	$0.872536\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	20.5331	+	28.2613i	0.789149	+	1.08617i	0.994213	+	0.107422i	$0.0342597\pi$
$677$	20.5331	+	28.2613i	0.789149	+	1.08617i	−0.205064	+	0.978749i	$0.565740\pi$
$678$		0			0
$679$	0.582418	−	1.79250i	0.0223511	−	0.0687897i
$680$		0			0
$681$	−11.7755	−	36.2412i	−0.451238	−	1.38877i
$682$		0			0
$683$	37.4584	−	12.1710i	1.43330	−	0.465709i	0.513501	−	0.858089i	$-0.328348\pi$
$683$	37.4584	−	12.1710i	1.43330	−	0.465709i	0.919803	+	0.392380i	$0.128348\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−28.6102	+	39.3786i	−1.09155	+	1.50239i
$688$		0			0
$689$	−40.4408	+	29.3819i	−1.54067	+	1.11936i
$690$		0			0
$691$	−25.2175	−	18.3216i	−0.959318	−	0.696985i	−0.00632573	−	0.999980i	$-0.502014\pi$
$691$	−25.2175	−	18.3216i	−0.959318	−	0.696985i	−0.952992	+	0.302995i	$0.902014\pi$
$692$		0			0
$693$			22.1850i			0.842740i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−0.516317	−	0.167762i	−0.0195569	−	0.00635443i
$698$		0			0
$699$	50.4325			1.90753
$700$		0			0
$701$	29.1939			1.10264			0.551319	−	0.834295i	$-0.314125\pi$
$701$	29.1939			1.10264			0.551319	+	0.834295i	$0.314125\pi$
$702$		0			0
$703$	−5.90359	−	1.91819i	−0.222658	−	0.0723460i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			21.1634i			0.795932i
$708$		0			0
$709$	−38.5139	−	27.9820i	−1.44642	−	1.05089i	−0.986651	−	0.162847i	$-0.947932\pi$
$709$	−38.5139	−	27.9820i	−1.44642	−	1.05089i	−0.459769	−	0.888039i	$-0.652068\pi$
$710$		0			0
$711$	19.6808	−	14.2989i	0.738086	−	0.536251i
$712$		0			0
$713$	15.6085	−	21.4832i	0.584542	−	0.804553i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	0.0727102	−	0.0236250i	0.00271541	−	0.000882291i
$718$		0			0
$719$	6.88230	+	21.1816i	0.256667	+	0.789939i	0.993497	+	0.113861i	$0.0363218\pi$
$719$	6.88230	+	21.1816i	0.256667	+	0.789939i	−0.736830	+	0.676078i	$0.763678\pi$
$720$		0			0
$721$	−5.33483	+	16.4189i	−0.198680	+	0.611473i
$722$		0			0
$723$	13.7057	+	18.8643i	0.509721	+	0.701571i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	1.86512	+	2.56712i	0.0691735	+	0.0952091i	0.842202	−	0.539162i	$-0.181259\pi$
$727$	1.86512	+	2.56712i	0.0691735	+	0.0952091i	−0.773028	+	0.634371i	$0.781259\pi$
$728$		0			0
$729$	9.66970	−	29.7603i	0.358137	−	1.10223i
$730$		0			0
$731$	1.98472	+	6.10835i	0.0734076	+	0.225925i
$732$		0			0
$733$	−18.7721	+	6.09944i	−0.693365	+	0.225288i	−0.634437	−	0.772974i	$-0.718768\pi$
$733$	−18.7721	+	6.09944i	−0.693365	+	0.225288i	−0.0589275	+	0.998262i	$0.518768\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	19.1910	−	26.4142i	0.706910	−	0.972978i
$738$		0			0
$739$	−12.3197	+	8.95076i	−0.453186	+	0.329259i	−0.790852	−	0.612007i	$-0.790362\pi$
$739$	−12.3197	+	8.95076i	−0.453186	+	0.329259i	0.337666	+	0.941266i	$0.390362\pi$
$740$		0			0
$741$	−5.74096	−	4.17105i	−0.210899	−	0.153227i
$742$		0			0
$743$			2.56670i			0.0941631i	0.998891	+	0.0470816i	$0.0149921\pi$
$743$			2.56670i			0.0941631i	−0.998891	+	0.0470816i	$0.985008\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−11.7165	−	3.80693i	−0.428686	−	0.139288i
$748$		0			0
$749$	8.87904			0.324433
$750$		0			0
$751$	−2.25050			−0.0821220			−0.0410610	−	0.999157i	$-0.513074\pi$
$751$	−2.25050			−0.0821220			−0.0410610	+	0.999157i	$0.513074\pi$
$752$		0			0
$753$	21.8745	+	7.10744i	0.797150	+	0.259010i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			0.226086i			0.00821722i	0.999992	+	0.00410861i	$0.00130782\pi$
$757$			0.226086i			0.00821722i	−0.999992	+	0.00410861i	$0.998692\pi$
$758$		0			0
$759$	−62.4168	−	45.3484i	−2.26558	−	1.64604i
$760$		0			0
$761$	−1.72984	+	1.25680i	−0.0627065	+	0.0455589i	−0.618697	−	0.785630i	$-0.712339\pi$
$761$	−1.72984	+	1.25680i	−0.0627065	+	0.0455589i	0.555990	+	0.831189i	$0.312339\pi$
$762$		0			0
$763$	5.64876	−	7.77485i	0.204499	−	0.281468i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−17.7496	+	5.76719i	−0.640901	+	0.208241i
$768$		0			0
$769$	7.07289	+	21.7681i	0.255055	+	0.784979i	0.993819	+	0.111014i	$0.0354099\pi$
$769$	7.07289	+	21.7681i	0.255055	+	0.784979i	−0.738764	+	0.673964i	$0.764590\pi$
$770$		0			0
$771$	−3.29964	+	10.1552i	−0.118834	+	0.365732i
$772$		0			0
$773$	13.5676	+	18.6742i	0.487993	+	0.671665i	0.980016	−	0.198917i	$-0.0637425\pi$
$773$	13.5676	+	18.6742i	0.487993	+	0.671665i	−0.492023	+	0.870582i	$0.663742\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−33.8455	−	46.5844i	−1.21420	−	1.67120i
$778$		0			0
$779$	0.134258	−	0.413203i	0.00481028	−	0.0148045i
$780$		0			0
$781$	4.41701	+	13.5941i	0.158053	+	0.486437i
$782$		0			0
$783$	−1.80470	+	0.586382i	−0.0644947	+	0.0209556i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	10.3875	−	14.2972i	0.370275	−	0.509640i	−0.582700	−	0.812687i	$-0.698004\pi$
$787$	10.3875	−	14.2972i	0.370275	−	0.509640i	0.952976	+	0.303047i	$0.0980039\pi$
$788$		0			0
$789$	18.0602	−	13.1215i	0.642960	−	0.467138i
$790$		0			0
$791$	3.29964	+	2.39733i	0.117322	+	0.0852393i
$792$		0			0
$793$			61.1182i			2.17037i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−36.3480	−	11.8102i	−1.28751	−	0.418339i	−0.416293	−	0.909230i	$-0.636671\pi$
$797$	−36.3480	−	11.8102i	−1.28751	−	0.418339i	−0.871221	+	0.490892i	$0.836671\pi$
$798$		0			0
$799$	−5.40920			−0.191364
$800$		0			0
$801$	−45.5759			−1.61034
$802$		0			0
$803$	−34.7925	−	11.3048i	−1.22780	−	0.398936i
$804$		0			0
$805$		0			0
$806$		0			0
$807$			7.74977i			0.272805i
$808$		0			0
$809$	−9.35284	−	6.79523i	−0.328828	−	0.238908i	0.411105	−	0.911588i	$-0.365143\pi$
$809$	−9.35284	−	6.79523i	−0.328828	−	0.238908i	−0.739933	+	0.672680i	$0.765143\pi$
$810$		0			0
$811$	11.1233	−	8.08153i	0.390591	−	0.283781i	−0.375107	−	0.926982i	$-0.622394\pi$
$811$	11.1233	−	8.08153i	0.390591	−	0.283781i	0.765698	+	0.643201i	$0.222394\pi$
$812$		0			0
$813$	−11.3531	+	15.6262i	−0.398170	+	0.548034i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−4.88844	+	1.58835i	−0.171025	+	0.0555694i
$818$		0			0
$819$	−10.5771	−	32.5528i	−0.369592	−	1.13749i
$820$		0			0
$821$	3.66994	−	11.2949i	0.128082	−	0.394195i	−0.866368	−	0.499406i	$-0.833552\pi$
$821$	3.66994	−	11.2949i	0.128082	−	0.394195i	0.994450	+	0.105211i	$0.0335517\pi$
$822$		0			0
$823$	−0.479642	−	0.660171i	−0.0167193	−	0.0230121i	0.800576	−	0.599232i	$-0.204527\pi$
$823$	−0.479642	−	0.660171i	−0.0167193	−	0.0230121i	−0.817295	+	0.576220i	$0.804527\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−18.6431	−	25.6601i	−0.648285	−	0.892288i	0.350738	−	0.936474i	$-0.385931\pi$
$827$	−18.6431	−	25.6601i	−0.648285	−	0.892288i	−0.999023	+	0.0441855i	$0.985931\pi$
$828$		0			0
$829$	5.21242	−	16.0422i	0.181035	−	0.557168i	−0.818823	−	0.574046i	$-0.805373\pi$
$829$	5.21242	−	16.0422i	0.181035	−	0.557168i	0.999858	+	0.0168788i	$0.00537293\pi$
$830$		0			0
$831$	−12.5248	−	38.5473i	−0.434480	−	1.33719i
$832$		0			0
$833$	1.96908	−	0.639793i	0.0682246	−	0.0221675i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	1.09445	−	1.50638i	0.0378297	−	0.0520681i
$838$		0			0
$839$	−10.4252	+	7.57437i	−0.359919	+	0.261496i	−0.753018	−	0.658000i	$-0.771403\pi$
$839$	−10.4252	+	7.57437i	−0.359919	+	0.261496i	0.393099	+	0.919496i	$0.371403\pi$
$840$		0			0
$841$	15.9850	+	11.6138i	0.551207	+	0.400475i
$842$		0			0
$843$			53.4001i			1.83920i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−1.90712	−	0.619659i	−0.0655293	−	0.0212917i
$848$		0			0
$849$	68.3450			2.34560
$850$		0			0
$851$	104.124			3.56931
$852$		0			0
$853$	51.1109	+	16.6069i	1.75000	+	0.568610i	0.996088	−	0.0883619i	$-0.0281632\pi$
$853$	51.1109	+	16.6069i	1.75000	+	0.568610i	0.753915	+	0.656972i	$0.228163\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			26.0296i			0.889154i	0.895741	+	0.444577i	$0.146646\pi$
$857$			26.0296i			0.889154i	−0.895741	+	0.444577i	$0.853354\pi$
$858$		0			0
$859$	−29.6664	−	21.5539i	−1.01221	−	0.735410i	−0.0475348	−	0.998870i	$-0.515137\pi$
$859$	−29.6664	−	21.5539i	−1.01221	−	0.735410i	−0.964670	+	0.263459i	$0.915137\pi$
$860$		0			0
$861$	3.26052	−	2.36891i	0.111118	−	0.0807322i
$862$		0			0
$863$	5.81525	−	8.00400i	0.197953	−	0.272459i	−0.698488	−	0.715622i	$-0.746143\pi$
$863$	5.81525	−	8.00400i	0.197953	−	0.272459i	0.896441	+	0.443162i	$0.146143\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	39.3733	−	12.7932i	1.33719	−	0.434479i
$868$		0			0
$869$	8.01948	+	24.6814i	0.272042	+	0.837260i
$870$		0			0
$871$	−15.5663	+	47.9080i	−0.527442	+	1.62330i
$872$		0			0
$873$	1.82817	+	2.51626i	0.0618741	+	0.0851623i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	32.5796	+	44.8420i	1.10014	+	1.51421i	0.835203	+	0.549941i	$0.185350\pi$
$877$	32.5796	+	44.8420i	1.10014	+	1.51421i	0.264933	+	0.964267i	$0.414650\pi$
$878$		0			0
$879$	−12.1336	+	37.3433i	−0.409255	+	1.25956i
$880$		0			0
$881$	0.808559	+	2.48849i	0.0272410	+	0.0838393i	0.963753	−	0.266797i	$-0.0859653\pi$
$881$	0.808559	+	2.48849i	0.0272410	+	0.0838393i	−0.936512	+	0.350636i	$0.885965\pi$
$882$		0			0
$883$	4.78654	−	1.55524i	0.161080	−	0.0523380i	−0.227367	−	0.973809i	$-0.573012\pi$
$883$	4.78654	−	1.55524i	0.161080	−	0.0523380i	0.388447	+	0.921471i	$0.373012\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	14.3668	−	19.7742i	0.482391	−	0.663954i	−0.496571	−	0.867996i	$-0.665408\pi$
$887$	14.3668	−	19.7742i	0.482391	−	0.663954i	0.978962	+	0.204042i	$0.0654078\pi$
$888$		0			0
$889$	4.31384	−	3.13419i	0.144682	−	0.105117i
$890$		0			0
$891$	22.9661	+	16.6859i	0.769395	+	0.558998i
$892$		0			0
$893$		−	4.32892i		−	0.144862i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	113.207	+	36.7831i	3.77986	+	1.22815i
$898$		0			0
$899$	9.06816			0.302440
$900$		0			0
$901$	−6.19762			−0.206473
$902$		0			0
$903$	−45.3464	−	14.7339i	−1.50903	−	0.490315i
$904$		0			0
$905$		0			0
$906$		0			0
$907$		−	25.7407i		−	0.854705i	−0.904085	−	0.427353i	$-0.859446\pi$
$907$		−	25.7407i		−	0.854705i	0.904085	−	0.427353i	$-0.140554\pi$
$908$		0			0
$909$	−28.2545	−	20.5281i	−0.937143	−	0.680874i
$910$		0			0
$911$	−23.5524	+	17.1119i	−0.780327	+	0.566941i	−0.905077	−	0.425247i	$-0.860187\pi$
$911$	−23.5524	+	17.1119i	−0.780327	+	0.566941i	0.124750	+	0.992188i	$0.460187\pi$
$912$		0			0
$913$	7.72487	−	10.6324i	0.255656	−	0.351880i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	29.7127	−	9.65425i	0.981201	−	0.318811i
$918$		0			0
$919$	−3.40072	−	10.4664i	−0.112180	−	0.345253i	0.879169	−	0.476510i	$-0.158099\pi$
$919$	−3.40072	−	10.4664i	−0.112180	−	0.345253i	−0.991348	+	0.131257i	$0.958099\pi$
$920$		0			0
$921$	14.8700	−	45.7651i	0.489983	−	1.50801i
$922$		0			0
$923$	−12.9624	−	17.8413i	−0.426664	−	0.587252i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−16.7456	−	23.0484i	−0.549999	−	0.757009i
$928$		0			0
$929$	6.10267	−	18.7821i	0.200222	−	0.616221i	−0.799654	−	0.600462i	$-0.794984\pi$
$929$	6.10267	−	18.7821i	0.200222	−	0.616221i	0.999876	−	0.0157591i	$-0.00501648\pi$
$930$		0			0
$931$	0.512019	+	1.57583i	0.0167807	+	0.0516458i
$932$		0			0
$933$	49.4813	−	16.0774i	1.61994	−	0.526352i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	31.2061	−	42.9514i	1.01946	−	1.40316i	0.106874	−	0.994273i	$-0.465916\pi$
$937$	31.2061	−	42.9514i	1.01946	−	1.40316i	0.912584	−	0.408890i	$-0.134084\pi$
$938$		0			0
$939$	27.0830	−	19.6770i	0.883820	−	0.642133i
$940$		0			0
$941$	−19.0947	−	13.8731i	−0.622469	−	0.452250i	0.231314	−	0.972879i	$-0.425698\pi$
$941$	−19.0947	−	13.8731i	−0.622469	−	0.452250i	−0.853783	+	0.520629i	$0.825698\pi$
$942$		0			0
$943$			7.28780i			0.237323i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	18.8492	+	6.12449i	0.612518	+	0.199019i	0.598816	−	0.800887i	$-0.295638\pi$
$947$	18.8492	+	6.12449i	0.612518	+	0.199019i	0.0137025	+	0.999906i	$0.495638\pi$
$948$		0			0
$949$	56.4419			1.83218
$950$		0			0
$951$	26.8525			0.870754
$952$		0			0
$953$	−18.1111	−	5.88467i	−0.586678	−	0.190623i	0.000612273	−	1.00000i	$-0.499805\pi$
$953$	−18.1111	−	5.88467i	−0.586678	−	0.190623i	−0.587290	+	0.809377i	$0.699805\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		−	26.3464i		−	0.851658i
$958$		0			0
$959$	−34.7060	−	25.2154i	−1.12071	−	0.814246i
$960$		0			0
$961$	17.8808	−	12.9912i	0.576800	−	0.419070i
$962$		0			0
$963$	−8.61251	+	11.8541i	−0.277534	+	0.381993i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−28.6648	+	9.31375i	−0.921798	+	0.299510i	−0.731204	−	0.682159i	$-0.761041\pi$
$967$	−28.6648	+	9.31375i	−0.921798	+	0.299510i	−0.190594	+	0.981669i	$0.561041\pi$
$968$		0			0
$969$	−0.271877	−	0.836751i	−0.00873394	−	0.0268803i
$970$		0			0
$971$	8.52605	−	26.2405i	0.273614	−	0.842097i	−0.715969	−	0.698132i	$-0.754015\pi$
$971$	8.52605	−	26.2405i	0.273614	−	0.842097i	0.989583	−	0.143965i	$-0.0459852\pi$
$972$		0			0
$973$	−14.5897	−	20.0810i	−0.467724	−	0.643767i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5.96395	+	8.20867i	0.190804	+	0.262619i	0.893691	−	0.448682i	$-0.148106\pi$
$977$	5.96395	+	8.20867i	0.190804	+	0.262619i	−0.702888	+	0.711301i	$0.748106\pi$
$978$		0			0
$979$	15.0244	−	46.2403i	0.480182	−	1.47785i
$980$		0			0
$981$	4.90074	+	15.0829i	0.156468	+	0.481560i
$982$		0			0
$983$	−23.2572	+	7.55672i	−0.741789	+	0.241022i	−0.655445	−	0.755243i	$-0.727519\pi$
$983$	−23.2572	+	7.55672i	−0.741789	+	0.241022i	−0.0863449	+	0.996265i	$0.527519\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	23.6032	−	32.4870i	0.751298	−	1.03407i
$988$		0			0
$989$	69.7527	−	50.6783i	2.21801	−	1.61148i
$990$		0			0
$991$	26.5943	+	19.3219i	0.844797	+	0.613781i	0.923706	−	0.383101i	$-0.125144\pi$
$991$	26.5943	+	19.3219i	0.844797	+	0.613781i	−0.0789097	+	0.996882i	$0.525144\pi$
$992$		0			0
$993$		−	21.2869i		−	0.675518i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	25.1350	+	8.16684i	0.796032	+	0.258647i	0.678671	−	0.734443i	$-0.262556\pi$
$997$	25.1350	+	8.16684i	0.796032	+	0.258647i	0.117362	+	0.993089i	$0.462556\pi$
$998$		0			0
$999$	7.30104			0.230995

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.q.d.449.2		32
5.2	odd	4		1000.2.m.c.801.1		16
5.3	odd	4		200.2.m.c.161.4	yes	16
5.4	even	2	inner	1000.2.q.d.449.7		32
20.3	even	4		400.2.u.g.161.1		16
25.3	odd	20		5000.2.a.l.1.8		8
25.9	even	10	inner	1000.2.q.d.49.2		32
25.12	odd	20		1000.2.m.c.201.1		16
25.13	odd	20		200.2.m.c.41.4	✓	16
25.16	even	5	inner	1000.2.q.d.49.7		32
25.22	odd	20		5000.2.a.m.1.1		8
100.3	even	20		10000.2.a.bk.1.1		8
100.47	even	20		10000.2.a.bh.1.8		8
100.63	even	20		400.2.u.g.241.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.m.c.41.4	✓	16	25.13	odd	20
200.2.m.c.161.4	yes	16	5.3	odd	4
400.2.u.g.161.1		16	20.3	even	4
400.2.u.g.241.1		16	100.63	even	20
1000.2.m.c.201.1		16	25.12	odd	20
1000.2.m.c.801.1		16	5.2	odd	4
1000.2.q.d.49.2		32	25.9	even	10	inner
1000.2.q.d.49.7		32	25.16	even	5	inner
1000.2.q.d.449.2		32	1.1	even	1	trivial
1000.2.q.d.449.7		32	5.4	even	2	inner
5000.2.a.l.1.8		8	25.3	odd	20
5000.2.a.m.1.1		8	25.22	odd	20
10000.2.a.bh.1.8		8	100.47	even	20
10000.2.a.bk.1.1		8	100.3	even	20

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:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.q (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.37758 - 0.772523i) q^{3} -1.96923i q^{7} +(2.62905 + 1.91012i) q^{9} +O(q^{10})\)	\(q+(-2.37758 - 0.772523i) q^{3} -1.96923i q^{7} +(2.62905 + 1.91012i) q^{9} +(-2.80465 + 2.03770i) q^{11} +(3.14385 - 4.32714i) q^{13} +(0.630686 - 0.204922i) q^{17} +(0.163997 + 0.504731i) q^{19} +(-1.52128 + 4.68201i) q^{21} +(-5.23253 - 7.20196i) q^{23} +(-0.366899 - 0.504994i) q^{27} +(0.939405 - 2.89119i) q^{29} +(0.921788 + 2.83697i) q^{31} +(8.24246 - 2.67814i) q^{33} +(-6.87504 + 9.46267i) q^{37} +(-10.8176 + 7.85944i) q^{39} +(-0.662310 - 0.481196i) q^{41} +9.68524i q^{43} +(-7.75769 - 2.52063i) q^{47} +3.12212 q^{49} -1.65782 q^{51} +(-8.88842 - 2.88802i) q^{53} -1.32673i q^{57} +(-2.82290 - 2.05096i) q^{59} +(-9.24453 + 6.71654i) q^{61} +(3.76147 - 5.17722i) q^{63} +(-8.95703 + 2.91032i) q^{67} +(6.87709 + 21.1655i) q^{69} +(1.27411 - 3.92130i) q^{71} +(6.20264 + 8.53720i) q^{73} +(4.01270 + 5.52301i) q^{77} +(2.31326 - 7.11949i) q^{79} +(-2.53041 - 7.78781i) q^{81} +(-3.60543 + 1.17148i) q^{83} +(-4.46702 + 6.14833i) q^{87} +(-11.3462 + 8.24351i) q^{89} +(-8.52115 - 6.19098i) q^{91} -7.45723i q^{93} +(0.910252 + 0.295759i) q^{97} -11.2658 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 22 q^{9}+O(q^{10}) \) 32 * q + 22 * q^9	\( 32 q + 22 q^{9} - 20 q^{11} - 6 q^{21} - 10 q^{29} - 18 q^{31} - 28 q^{39} - 4 q^{41} - 36 q^{49} + 200 q^{51} + 106 q^{59} + 8 q^{61} + 14 q^{69} - 12 q^{71} + 44 q^{79} - 12 q^{81} - 40 q^{89} - 54 q^{91} - 244 q^{99}+O(q^{100}) \) 32 * q + 22 * q^9 - 20 * q^11 - 6 * q^21 - 10 * q^29 - 18 * q^31 - 28 * q^39 - 4 * q^41 - 36 * q^49 + 200 * q^51 + 106 * q^59 + 8 * q^61 + 14 * q^69 - 12 * q^71 + 44 * q^79 - 12 * q^81 - 40 * q^89 - 54 * q^91 - 244 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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