LMFDB - Embedded newform 572.2.bc.a.197.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(197,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 1]))

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

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

chi := DirichletCharacter("572.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bc (of order $12$, degree $4$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			197.14
Character	$\chi$	$=$	572.197
Dual form			572.2.bc.a.241.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.46539 + 2.53814i) q^{3} +(2.04642 - 2.04642i) q^{5} +(1.22814 + 4.58348i) q^{7} +(-2.79476 + 4.84067i) q^{9} +O(q^{10})$	\(q+(1.46539 + 2.53814i) q^{3} +(2.04642 - 2.04642i) q^{5} +(1.22814 + 4.58348i) q^{7} +(-2.79476 + 4.84067i) q^{9} +(-3.20551 + 0.851295i) q^{11} +(-2.66280 - 2.43095i) q^{13} +(8.19292 + 2.19529i) q^{15} +(0.318123 - 0.551006i) q^{17} +(0.404054 - 0.108266i) q^{19} +(-9.83380 + 9.83380i) q^{21} +(3.94017 - 2.27486i) q^{23} -3.37570i q^{25} -7.58934 q^{27} +(5.03712 - 2.90818i) q^{29} +(4.09233 - 4.09233i) q^{31} +(-6.85804 - 6.88854i) q^{33} +(11.8930 + 6.86645i) q^{35} +(-0.491740 + 1.83520i) q^{37} +(2.26804 - 10.3208i) q^{39} +(2.11565 - 7.89572i) q^{41} +(-4.17054 + 7.22359i) q^{43} +(4.18679 + 15.6253i) q^{45} +(-0.241697 - 0.241697i) q^{47} +(-13.4378 + 7.75832i) q^{49} +1.86470 q^{51} -10.6811 q^{53} +(-4.81772 + 8.30194i) q^{55} +(0.866892 + 0.866892i) q^{57} +(6.12387 - 1.64089i) q^{59} +(10.7060 + 6.18113i) q^{61} +(-25.6195 - 6.86472i) q^{63} +(-10.4240 + 0.474453i) q^{65} +(-15.5135 - 4.15682i) q^{67} +(11.5478 + 6.66713i) q^{69} +(0.693560 + 2.58840i) q^{71} +(9.28992 - 9.28992i) q^{73} +(8.56798 - 4.94673i) q^{75} +(-7.83871 - 13.6469i) q^{77} -2.79612i q^{79} +(-2.73709 - 4.74078i) q^{81} +(6.50913 + 6.50913i) q^{83} +(-0.476576 - 1.77861i) q^{85} +(14.7627 + 8.52326i) q^{87} +(4.58118 - 17.0972i) q^{89} +(7.87193 - 15.1904i) q^{91} +(16.3838 + 4.39002i) q^{93} +(0.605308 - 1.04842i) q^{95} +(-0.508515 - 1.89780i) q^{97} +(4.83780 - 17.8960i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 28 q^{9}+O(q^{10}) $ 56 * q - 28 * q^9	$ 56 q - 28 q^{9} + 4 q^{11} + 8 q^{15} - 12 q^{23} - 24 q^{27} - 4 q^{31} - 10 q^{33} - 12 q^{37} - 64 q^{45} - 8 q^{47} + 40 q^{53} + 22 q^{55} + 48 q^{59} - 36 q^{67} - 48 q^{71} + 120 q^{75} + 28 q^{81} + 28 q^{89} + 36 q^{91} + 20 q^{93} - 68 q^{97} - 44 q^{99}+O(q^{100}) $ 56 * q - 28 * q^9 + 4 * q^11 + 8 * q^15 - 12 * q^23 - 24 * q^27 - 4 * q^31 - 10 * q^33 - 12 * q^37 - 64 * q^45 - 8 * q^47 + 40 * q^53 + 22 * q^55 + 48 * q^59 - 36 * q^67 - 48 * q^71 + 120 * q^75 + 28 * q^81 + 28 * q^89 + 36 * q^91 + 20 * q^93 - 68 * q^97 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$-1$

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
$3$	1.46539	+	2.53814i	0.846046	+	1.46539i	0.884710	+	0.466142i	$0.154356\pi$
$3$	1.46539	+	2.53814i	0.846046	+	1.46539i	−0.0386642	+	0.999252i	$0.512310\pi$
$4$		0			0
$5$	2.04642	−	2.04642i	0.915188	−	0.915188i	−0.0814861	−	0.996674i	$-0.525967\pi$
$5$	2.04642	−	2.04642i	0.915188	−	0.915188i	0.996674	+	0.0814861i	$0.0259666\pi$
$6$		0			0
$7$	1.22814	+	4.58348i	0.464193	+	1.73239i	0.659550	+	0.751661i	$0.270747\pi$
$7$	1.22814	+	4.58348i	0.464193	+	1.73239i	−0.195356	+	0.980732i	$0.562586\pi$
$8$		0			0
$9$	−2.79476	+	4.84067i	−0.931587	+	1.61356i
$10$		0			0
$11$	−3.20551	+	0.851295i	−0.966498	+	0.256675i
$11$	−3.20551	+	0.851295i	−0.966498	+	0.256675i
$12$		0			0
$13$	−2.66280	−	2.43095i	−0.738527	−	0.674224i
$13$	−2.66280	−	2.43095i	−0.738527	−	0.674224i
$14$		0			0
$15$	8.19292	+	2.19529i	2.11540	+	0.566821i
$16$		0			0
$17$	0.318123	−	0.551006i	0.0771562	−	0.133639i	−0.824866	−	0.565329i	$-0.808749\pi$
$17$	0.318123	−	0.551006i	0.0771562	−	0.133639i	0.902022	+	0.431690i	$0.142083\pi$
$18$		0			0
$19$	0.404054	−	0.108266i	0.0926964	−	0.0248379i	−0.212173	−	0.977232i	$-0.568054\pi$
$19$	0.404054	−	0.108266i	0.0926964	−	0.0248379i	0.304869	+	0.952394i	$0.401387\pi$
$20$		0			0
$21$	−9.83380	+	9.83380i	−2.14591	+	2.14591i
$22$		0			0
$23$	3.94017	−	2.27486i	0.821583	−	0.474341i	−0.0293793	−	0.999568i	$-0.509353\pi$
$23$	3.94017	−	2.27486i	0.821583	−	0.474341i	0.850962	+	0.525227i	$0.176020\pi$
$24$		0			0
$25$		−	3.37570i		−	0.675140i
$26$		0			0
$27$	−7.58934			−1.46057
$28$		0			0
$29$	5.03712	−	2.90818i	0.935369	−	0.540036i	0.0468635	−	0.998901i	$-0.485077\pi$
$29$	5.03712	−	2.90818i	0.935369	−	0.540036i	0.888506	+	0.458866i	$0.151744\pi$
$30$		0			0
$31$	4.09233	−	4.09233i	0.735004	−	0.735004i	−0.236602	−	0.971607i	$-0.576034\pi$
$31$	4.09233	−	4.09233i	0.735004	−	0.735004i	0.971607	+	0.236602i	$0.0760339\pi$
$32$		0			0
$33$	−6.85804	−	6.88854i	−1.19383	−	1.19914i
$34$		0			0
$35$	11.8930	+	6.86645i	2.01029	+	1.16064i
$36$		0			0
$37$	−0.491740	+	1.83520i	−0.0808416	+	0.301705i	−0.994494	−	0.104791i	$-0.966583\pi$
$37$	−0.491740	+	1.83520i	−0.0808416	+	0.301705i	0.913653	+	0.406496i	$0.133249\pi$
$38$		0			0
$39$	2.26804	−	10.3208i	0.363177	−	1.65266i
$40$		0			0
$41$	2.11565	−	7.89572i	0.330409	−	1.23310i	−0.578352	−	0.815787i	$-0.696304\pi$
$41$	2.11565	−	7.89572i	0.330409	−	1.23310i	0.908761	−	0.417317i	$-0.137029\pi$
$42$		0			0
$43$	−4.17054	+	7.22359i	−0.636002	+	1.10159i	0.350300	+	0.936637i	$0.386080\pi$
$43$	−4.17054	+	7.22359i	−0.636002	+	1.10159i	−0.986302	+	0.164950i	$0.947254\pi$
$44$		0			0
$45$	4.18679	+	15.6253i	0.624130	+	2.32928i
$46$		0			0
$47$	−0.241697	−	0.241697i	−0.0352551	−	0.0352551i	0.689259	−	0.724515i	$-0.257936\pi$
$47$	−0.241697	−	0.241697i	−0.0352551	−	0.0352551i	−0.724515	+	0.689259i	$0.757936\pi$
$48$		0			0
$49$	−13.4378	+	7.75832i	−1.91969	+	1.10833i
$50$		0			0
$51$	1.86470			0.261111
$52$		0			0
$53$	−10.6811			−1.46717			−0.733584	−	0.679598i	$-0.762154\pi$
$53$	−10.6811			−1.46717			−0.733584	+	0.679598i	$0.762154\pi$
$54$		0			0
$55$	−4.81772	+	8.30194i	−0.649621	+	1.11943i
$56$		0			0
$57$	0.866892	+	0.866892i	0.114823	+	0.114823i
$58$		0			0
$59$	6.12387	−	1.64089i	0.797259	−	0.213625i	0.162879	−	0.986646i	$-0.447922\pi$
$59$	6.12387	−	1.64089i	0.797259	−	0.213625i	0.634380	+	0.773021i	$0.281255\pi$
$60$		0			0
$61$	10.7060	+	6.18113i	1.37077	+	0.791413i	0.991025	−	0.133680i	$-0.0426794\pi$
$61$	10.7060	+	6.18113i	1.37077	+	0.791413i	0.379742	+	0.925092i	$0.376013\pi$
$62$		0			0
$63$	−25.6195	−	6.86472i	−3.22775	−	0.864873i
$64$		0			0
$65$	−10.4240	+	0.474453i	−1.29293	+	0.0588487i
$66$		0			0
$67$	−15.5135	−	4.15682i	−1.89527	−	0.507836i	−0.997764	−	0.0668331i	$-0.978710\pi$
$67$	−15.5135	−	4.15682i	−1.89527	−	0.507836i	−0.897506	−	0.441003i	$-0.854623\pi$
$68$		0			0
$69$	11.5478	+	6.66713i	1.39019	+	0.802628i
$70$		0			0
$71$	0.693560	+	2.58840i	0.0823104	+	0.307187i	0.994791	−	0.101933i	$-0.0325026\pi$
$71$	0.693560	+	2.58840i	0.0823104	+	0.307187i	−0.912481	+	0.409119i	$0.865836\pi$
$72$		0			0
$73$	9.28992	−	9.28992i	1.08730	−	1.08730i	0.0914976	−	0.995805i	$-0.470835\pi$
$73$	9.28992	−	9.28992i	1.08730	−	1.08730i	0.995805	−	0.0914976i	$-0.0291654\pi$
$74$		0			0
$75$	8.56798	−	4.94673i	0.989346	−	0.571199i
$76$		0			0
$77$	−7.83871	−	13.6469i	−0.893304	−	1.55521i
$78$		0			0
$79$		−	2.79612i		−	0.314588i	−0.987552	−	0.157294i	$-0.949723\pi$
$79$		−	2.79612i		−	0.314588i	0.987552	−	0.157294i	$-0.0502770\pi$
$80$		0			0
$81$	−2.73709	−	4.74078i	−0.304121	−	0.526753i
$82$		0			0
$83$	6.50913	+	6.50913i	0.714470	+	0.714470i	0.967467	−	0.252997i	$-0.0814163\pi$
$83$	6.50913	+	6.50913i	0.714470	+	0.714470i	−0.252997	+	0.967467i	$0.581416\pi$
$84$		0			0
$85$	−0.476576	−	1.77861i	−0.0516919	−	0.192917i
$86$		0			0
$87$	14.7627	+	8.52326i	1.58273	+	0.913790i
$88$		0			0
$89$	4.58118	−	17.0972i	0.485604	−	1.81230i	−0.0917236	−	0.995785i	$-0.529238\pi$
$89$	4.58118	−	17.0972i	0.485604	−	1.81230i	0.577327	−	0.816513i	$-0.304096\pi$
$90$		0			0
$91$	7.87193	−	15.1904i	0.825203	−	1.59239i
$92$		0			0
$93$	16.3838	+	4.39002i	1.69892	+	0.455224i
$94$		0			0
$95$	0.605308	−	1.04842i	0.0621033	−	0.107566i
$96$		0			0
$97$	−0.508515	−	1.89780i	−0.0516318	−	0.192693i	0.935293	−	0.353875i	$-0.115136\pi$
$97$	−0.508515	−	1.89780i	−0.0516318	−	0.192693i	−0.986925	+	0.161182i	$0.948469\pi$
$98$		0			0
$99$	4.83780	−	17.8960i	0.486217	−	1.79861i
$100$		0			0
$101$	5.99581	+	10.3851i	0.596606	+	1.03335i	0.993318	+	0.115409i	$0.0368177\pi$
$101$	5.99581	+	10.3851i	0.596606	+	1.03335i	−0.396712	+	0.917943i	$0.629849\pi$
$102$		0			0
$103$			2.44246i			0.240662i	0.992734	+	0.120331i	$0.0383956\pi$
$103$			2.44246i			0.240662i	−0.992734	+	0.120331i	$0.961604\pi$
$104$		0			0
$105$			40.2482i			3.92782i
$106$		0			0
$107$	−0.0988519	+	0.0570722i	−0.00955637	+	0.00551737i	−0.504771	−	0.863254i	$-0.668423\pi$
$107$	−0.0988519	+	0.0570722i	−0.00955637	+	0.00551737i	0.495214	+	0.868771i	$0.335090\pi$
$108$		0			0
$109$	−6.16295	−	6.16295i	−0.590303	−	0.590303i	0.347410	−	0.937713i	$-0.387061\pi$
$109$	−6.16295	−	6.16295i	−0.590303	−	0.590303i	−0.937713	+	0.347410i	$0.887061\pi$
$110$		0			0
$111$	−5.37858	+	1.44119i	−0.510512	+	0.136791i
$112$		0			0
$113$	−2.97106	+	5.14602i	−0.279494	+	0.484097i	−0.971259	−	0.238025i	$-0.923500\pi$
$113$	−2.97106	+	5.14602i	−0.279494	+	0.484097i	0.691765	+	0.722122i	$0.256833\pi$
$114$		0			0
$115$	3.40793	−	12.7186i	0.317792	−	1.18601i
$116$		0			0
$117$	19.2093	−	6.09578i	1.77590	−	0.563555i
$118$		0			0
$119$	2.91623	+	0.781400i	0.267330	+	0.0716308i
$120$		0			0
$121$	9.55059	−	5.45767i	0.868236	−	0.496152i
$122$		0			0
$123$	23.1407	−	6.20053i	2.08652	−	0.559083i
$124$		0			0
$125$	3.32401	+	3.32401i	0.297308	+	0.297308i
$126$		0			0
$127$	−1.89865	−	3.28855i	−0.168478	−	0.291812i	0.769407	−	0.638759i	$-0.220552\pi$
$127$	−1.89865	−	3.28855i	−0.168478	−	0.291812i	−0.937885	+	0.346947i	$0.887218\pi$
$128$		0			0
$129$	−24.4459			−2.15235
$130$		0			0
$131$		−	11.8162i		−	1.03239i	−0.856471	−	0.516195i	$-0.827348\pi$
$131$		−	11.8162i		−	1.03239i	0.856471	−	0.516195i	$-0.172652\pi$
$132$		0			0
$133$	0.992470	+	1.71901i	0.0860581	+	0.149057i
$134$		0			0
$135$	−15.5310	+	15.5310i	−1.33670	+	1.33670i
$136$		0			0
$137$	11.9124	−	3.19192i	1.01775	−	0.272704i	0.288883	−	0.957364i	$-0.406716\pi$
$137$	11.9124	−	3.19192i	1.01775	−	0.272704i	0.728863	+	0.684660i	$0.240049\pi$
$138$		0			0
$139$	−7.92183	−	4.57367i	−0.671920	−	0.387933i	0.124883	−	0.992171i	$-0.460144\pi$
$139$	−7.92183	−	4.57367i	−0.671920	−	0.387933i	−0.796804	+	0.604238i	$0.793478\pi$
$140$		0			0
$141$	0.259279	−	0.967642i	0.0218352	−	0.0814901i
$142$		0			0
$143$	10.6051	+	5.52561i	0.886841	+	0.462075i
$144$		0			0
$145$	4.35671	−	16.2594i	0.361805	−	1.35027i
$146$		0			0
$147$	−39.3834	−	22.7380i	−3.24828	−	1.87540i
$148$		0			0
$149$	−8.97960	+	2.40608i	−0.735637	+	0.197113i	−0.607138	−	0.794596i	$-0.707683\pi$
$149$	−8.97960	+	2.40608i	−0.735637	+	0.197113i	−0.128499	+	0.991710i	$0.541016\pi$
$150$		0			0
$151$	5.00540	−	5.00540i	0.407334	−	0.407334i	−0.473474	−	0.880808i	$-0.657000\pi$
$151$	5.00540	−	5.00540i	0.407334	−	0.407334i	0.880808	+	0.473474i	$0.157000\pi$
$152$		0			0
$153$	1.77816	+	3.07986i	0.143755	+	0.248992i
$154$		0			0
$155$		−	16.7493i		−	1.34533i
$156$		0			0
$157$	−13.6573			−1.08997			−0.544987	−	0.838445i	$-0.683465\pi$
$157$	−13.6573			−1.08997			−0.544987	+	0.838445i	$0.683465\pi$
$158$		0			0
$159$	−15.6521	−	27.1102i	−1.24129	−	2.14998i
$160$		0			0
$161$	15.2659	+	15.2659i	1.20312	+	1.20312i
$162$		0			0
$163$	−5.72239	+	1.53331i	−0.448212	+	0.120098i	−0.475863	−	0.879520i	$-0.657864\pi$
$163$	−5.72239	+	1.53331i	−0.448212	+	0.120098i	0.0276505	+	0.999618i	$0.491197\pi$
$164$		0			0
$165$	−28.1313	−	0.0624223i	−2.19002	−	0.00485957i
$166$		0			0
$167$	−14.6221	−	3.91797i	−1.13149	−	0.303182i	−0.355965	−	0.934499i	$-0.615848\pi$
$167$	−14.6221	−	3.91797i	−1.13149	−	0.303182i	−0.775524	+	0.631318i	$0.782514\pi$
$168$		0			0
$169$	1.18096	+	12.9462i	0.0908431	+	0.995865i
$170$		0			0
$171$	−0.605155	+	2.25847i	−0.0462773	+	0.172709i
$172$		0			0
$173$	−5.37645	+	9.31228i	−0.408764	+	0.707999i	−0.994751	−	0.102320i	$-0.967373\pi$
$173$	−5.37645	+	9.31228i	−0.408764	+	0.707999i	0.585988	+	0.810320i	$0.300707\pi$
$174$		0			0
$175$	15.4725	−	4.14583i	1.16961	−	0.313395i
$176$		0			0
$177$	13.1387	+	13.1387i	0.987563	+	0.987563i
$178$		0			0
$179$	−5.41903	+	3.12868i	−0.405037	+	0.233848i	−0.688655	−	0.725089i	$-0.741799\pi$
$179$	−5.41903	+	3.12868i	−0.405037	+	0.233848i	0.283618	+	0.958937i	$0.408465\pi$
$180$		0			0
$181$			0.732814i			0.0544696i	0.999629	+	0.0272348i	$0.00867018\pi$
$181$			0.732814i			0.0544696i	−0.999629	+	0.0272348i	$0.991330\pi$
$182$		0			0
$183$			36.2312i			2.67828i
$184$		0			0
$185$	2.74929	+	4.76190i	0.202131	+	0.350102i
$186$		0			0
$187$	−0.550679	+	2.03707i	−0.0402697	+	0.148965i
$188$		0			0
$189$	−9.32077	−	34.7856i	−0.677986	−	2.53028i
$190$		0			0
$191$	1.12609	−	1.95045i	0.0814811	−	0.141129i	−0.822405	−	0.568902i	$-0.807368\pi$
$191$	1.12609	−	1.95045i	0.0814811	−	0.141129i	0.903886	+	0.427773i	$0.140702\pi$
$192$		0			0
$193$	−4.35290	−	1.16636i	−0.313329	−	0.0839561i	0.0987278	−	0.995114i	$-0.468523\pi$
$193$	−4.35290	−	1.16636i	−0.313329	−	0.0839561i	−0.412056	+	0.911158i	$0.635189\pi$
$194$		0			0
$195$	−16.4794	−	25.7622i	−1.18012	−	1.84487i
$196$		0			0
$197$	−4.35608	+	16.2571i	−0.310358	+	1.15827i	0.617876	+	0.786275i	$0.287993\pi$
$197$	−4.35608	+	16.2571i	−0.310358	+	1.15827i	−0.928234	+	0.371996i	$0.878673\pi$
$198$		0			0
$199$	−6.87090	−	3.96692i	−0.487065	−	0.281207i	0.236291	−	0.971682i	$-0.424068\pi$
$199$	−6.87090	−	3.96692i	−0.487065	−	0.281207i	−0.723356	+	0.690475i	$0.757401\pi$
$200$		0			0
$201$	−12.1828	−	45.4666i	−0.859305	−	3.20697i
$202$		0			0
$203$	19.5159	+	19.5159i	1.36975	+	1.36975i
$204$		0			0
$205$	−11.8285	−	20.4875i	−0.826136	−	1.43091i
$206$		0			0
$207$			25.4307i			1.76756i
$208$		0			0
$209$	−1.20303	+	0.691017i	−0.0832155	+	0.0477986i
$210$		0			0
$211$	9.21149	−	5.31825i	0.634145	−	0.366124i	−0.148211	−	0.988956i	$-0.547351\pi$
$211$	9.21149	−	5.31825i	0.634145	−	0.366124i	0.782356	+	0.622832i	$0.214018\pi$
$212$		0			0
$213$	−5.55338	+	5.55338i	−0.380511	+	0.380511i
$214$		0			0
$215$	6.24783	+	23.3172i	0.426098	+	1.59022i
$216$		0			0
$217$	23.7831	+	13.7312i	1.61450	+	0.932132i
$218$		0			0
$219$	37.1925	+	9.96570i	2.51324	+	0.673419i
$220$		0			0
$221$	−2.18657	+	0.693874i	−0.147084	+	0.0466750i
$222$		0			0
$223$	−11.5912	−	3.10585i	−0.776204	−	0.207983i	−0.151093	−	0.988520i	$-0.548279\pi$
$223$	−11.5912	−	3.10585i	−0.776204	−	0.207983i	−0.625110	+	0.780536i	$0.714946\pi$
$224$		0			0
$225$	16.3406	+	9.43427i	1.08938	+	0.628951i
$226$		0			0
$227$	0.0179256	−	0.00480315i	0.00118976	−	0.000318796i	−0.258224	−	0.966085i	$-0.583137\pi$
$227$	0.0179256	−	0.00480315i	0.00118976	−	0.000318796i	0.259414	+	0.965766i	$0.416471\pi$
$228$		0			0
$229$	−18.1244	−	18.1244i	−1.19769	−	1.19769i	−0.974855	−	0.222839i	$-0.928467\pi$
$229$	−18.1244	−	18.1244i	−1.19769	−	1.19769i	−0.222839	−	0.974855i	$-0.571533\pi$
$230$		0			0
$231$	23.1509	−	39.8938i	1.52322	−	2.62482i
$232$		0			0
$233$	−11.2320			−0.735831			−0.367915	−	0.929859i	$-0.619928\pi$
$233$	−11.2320			−0.735831			−0.367915	+	0.929859i	$0.619928\pi$
$234$		0			0
$235$	−0.989229			−0.0645302
$236$		0			0
$237$	7.09692	−	4.09741i	0.460995	−	0.266155i
$238$		0			0
$239$	−0.223773	−	0.223773i	−0.0144747	−	0.0144747i	0.699832	−	0.714307i	$-0.253258\pi$
$239$	−0.223773	−	0.223773i	−0.0144747	−	0.0144747i	−0.714307	+	0.699832i	$0.753258\pi$
$240$		0			0
$241$	−4.97035	−	18.5496i	−0.320169	−	1.19489i	−0.919080	−	0.394071i	$-0.871067\pi$
$241$	−4.97035	−	18.5496i	−0.320169	−	1.19489i	0.598912	−	0.800815i	$-0.295600\pi$
$242$		0			0
$243$	−3.36218	+	5.82346i	−0.215684	+	0.373575i
$244$		0			0
$245$	−11.6226	+	43.3762i	−0.742542	+	2.77121i
$246$		0			0
$247$	−1.33910	−	0.693945i	−0.0852050	−	0.0441547i
$248$		0			0
$249$	−6.98262	+	26.0595i	−0.442506	+	1.65145i
$250$		0			0
$251$	1.54746	+	0.893425i	0.0976746	+	0.0563925i	0.548042	−	0.836451i	$-0.315374\pi$
$251$	1.54746	+	0.893425i	0.0976746	+	0.0563925i	−0.450367	+	0.892844i	$0.648707\pi$
$252$		0			0
$253$	−10.6937	+	10.6463i	−0.672306	+	0.669329i
$254$		0			0
$255$	3.81597	−	3.81597i	0.238966	−	0.238966i
$256$		0			0
$257$	18.3393	−	10.5882i	1.14397	−	0.660474i	0.196562	−	0.980491i	$-0.437022\pi$
$257$	18.3393	−	10.5882i	1.14397	−	0.660474i	0.947412	+	0.320018i	$0.103689\pi$
$258$		0			0
$259$	−9.01553			−0.560197
$260$		0			0
$261$			32.5107i			2.01236i
$262$		0			0
$263$	−12.3107	+	7.10761i	−0.759112	+	0.438274i	−0.828977	−	0.559283i	$-0.811077\pi$
$263$	−12.3107	+	7.10761i	−0.759112	+	0.438274i	0.0698646	+	0.997556i	$0.477743\pi$
$264$		0			0
$265$	−21.8582	+	21.8582i	−1.34274	+	1.34274i
$266$		0			0
$267$	50.1082	−	13.4265i	3.06657	−	0.821686i
$268$		0			0
$269$	−10.2366	+	17.7303i	−0.624135	+	1.08103i	0.364572	+	0.931175i	$0.381215\pi$
$269$	−10.2366	+	17.7303i	−0.624135	+	1.08103i	−0.988707	+	0.149859i	$0.952118\pi$
$270$		0			0
$271$	28.0021	+	7.50314i	1.70101	+	0.455783i	0.973193	−	0.229991i	$-0.0738698\pi$
$271$	28.0021	+	7.50314i	1.70101	+	0.455783i	0.727814	+	0.685775i	$0.240536\pi$
$272$		0			0
$273$	50.0909	−	2.27992i	3.03164	−	0.137987i
$274$		0			0
$275$	2.87371	+	10.8208i	0.173291	+	0.652521i
$276$		0			0
$277$	1.49460	−	2.58873i	0.0898020	−	0.155542i	−0.817625	−	0.575751i	$-0.804710\pi$
$277$	1.49460	−	2.58873i	0.0898020	−	0.155542i	0.907427	+	0.420209i	$0.138043\pi$
$278$		0			0
$279$	8.37252	+	31.2467i	0.501250	+	1.87069i
$280$		0			0
$281$	3.88790	−	3.88790i	0.231933	−	0.231933i	−0.581566	−	0.813499i	$-0.697560\pi$
$281$	3.88790	−	3.88790i	0.231933	−	0.231933i	0.813499	+	0.581566i	$0.197560\pi$
$282$		0			0
$283$	−7.20628	−	12.4816i	−0.428369	−	0.741957i	0.568359	−	0.822780i	$-0.307578\pi$
$283$	−7.20628	−	12.4816i	−0.428369	−	0.741957i	−0.996728	+	0.0808235i	$0.974245\pi$
$284$		0			0
$285$	3.54806			0.210169
$286$		0			0
$287$	38.7882			2.28959
$288$		0			0
$289$	8.29760	+	14.3719i	0.488094	+	0.845403i
$290$		0			0
$291$	4.07171	−	4.07171i	0.238688	−	0.238688i
$292$		0			0
$293$	−5.32060	−	19.8567i	−0.310833	−	1.16004i	−0.927807	−	0.373060i	$-0.878309\pi$
$293$	−5.32060	−	19.8567i	−0.310833	−	1.16004i	0.616975	−	0.786983i	$-0.288358\pi$
$294$		0			0
$295$	9.17408	−	15.8900i	0.534135	−	0.925150i
$296$		0			0
$297$	24.3277	−	6.46076i	1.41164	−	0.374891i
$298$		0			0
$299$	−16.0219	−	3.52088i	−0.926573	−	0.203618i
$300$		0			0
$301$	−38.2312	−	10.2440i	−2.20361	−	0.590456i
$302$		0			0
$303$	−17.5725	+	30.4364i	−1.00951	+	1.74853i
$304$		0			0
$305$	34.5583	−	9.25986i	1.97880	−	0.530218i
$306$		0			0
$307$	−20.2265	+	20.2265i	−1.15439	+	1.15439i	−0.168721	+	0.985664i	$0.553964\pi$
$307$	−20.2265	+	20.2265i	−1.15439	+	1.15439i	−0.985664	+	0.168721i	$0.946036\pi$
$308$		0			0
$309$	−6.19929	+	3.57916i	−0.352665	+	0.203611i
$310$		0			0
$311$			0.216223i			0.0122609i	0.999981	+	0.00613044i	$0.00195139\pi$
$311$			0.216223i			0.0122609i	−0.999981	+	0.00613044i	$0.998049\pi$
$312$		0			0
$313$	11.2756			0.637336			0.318668	−	0.947866i	$-0.396765\pi$
$313$	11.2756			0.637336			0.318668	+	0.947866i	$0.396765\pi$
$314$		0			0
$315$	−66.4764	+	38.3802i	−3.74552	+	2.16248i
$316$		0			0
$317$	15.2024	−	15.2024i	0.853850	−	0.853850i	−0.136755	−	0.990605i	$-0.543667\pi$
$317$	15.2024	−	15.2024i	0.853850	−	0.853850i	0.990605	+	0.136755i	$0.0436674\pi$
$318$		0			0
$319$	−13.6708	+	13.6103i	−0.765419	+	0.762029i
$320$		0			0
$321$	−0.289714	−	0.167266i	−0.0161703	−	0.00933590i
$322$		0			0
$323$	0.0688839	−	0.257078i	0.00383280	−	0.0143042i
$324$		0			0
$325$	−8.20615	+	8.98879i	−0.455196	+	0.498609i
$326$		0			0
$327$	6.61126	−	24.6736i	0.365603	−	1.36445i
$328$		0			0
$329$	0.810976	−	1.40465i	0.0447106	−	0.0774410i
$330$		0			0
$331$	3.00254	+	11.2056i	0.165035	+	0.615918i	0.998036	+	0.0626466i	$0.0199541\pi$
$331$	3.00254	+	11.2056i	0.165035	+	0.615918i	−0.833001	+	0.553271i	$0.813379\pi$
$332$		0			0
$333$	−7.50929	−	7.50929i	−0.411507	−	0.411507i
$334$		0			0
$335$	−40.2537	+	23.2405i	−2.19929	+	1.26976i
$336$		0			0
$337$	−32.4226			−1.76617			−0.883087	−	0.469210i	$-0.844539\pi$
$337$	−32.4226			−1.76617			−0.883087	+	0.469210i	$0.844539\pi$
$338$		0			0
$339$	−17.4151			−0.945858
$340$		0			0
$341$	−9.63423	+	16.6018i	−0.521723	+	0.899037i
$342$		0			0
$343$	−28.5762	−	28.5762i	−1.54297	−	1.54297i
$344$		0			0
$345$	37.2755	−	9.98793i	2.00684	−	0.537732i
$346$		0			0
$347$	5.42512	+	3.13219i	0.291236	+	0.168145i	0.638499	−	0.769623i	$-0.279556\pi$
$347$	5.42512	+	3.13219i	0.291236	+	0.168145i	−0.347263	+	0.937768i	$0.612889\pi$
$348$		0			0
$349$	17.6923	+	4.74064i	0.947047	+	0.253760i	0.699109	−	0.715015i	$-0.253580\pi$
$349$	17.6923	+	4.74064i	0.947047	+	0.253760i	0.247938	+	0.968776i	$0.420247\pi$
$350$		0			0
$351$	20.2089	+	18.4493i	1.07867	+	0.984751i
$352$		0			0
$353$	1.41750	+	0.379817i	0.0754458	+	0.0202156i	0.296344	−	0.955081i	$-0.404232\pi$
$353$	1.41750	+	0.379817i	0.0754458	+	0.0202156i	−0.220899	+	0.975297i	$0.570899\pi$
$354$		0			0
$355$	6.71628	+	3.87765i	0.356463	+	0.205804i
$356$		0			0
$357$	2.29012	+	8.54684i	0.121206	+	0.452347i
$358$		0			0
$359$	0.917858	−	0.917858i	0.0484427	−	0.0484427i	−0.682470	−	0.730913i	$-0.739094\pi$
$359$	0.917858	−	0.917858i	0.0484427	−	0.0484427i	0.730913	+	0.682470i	$0.239094\pi$
$360$		0			0
$361$	−16.3029	+	9.41251i	−0.858050	+	0.495395i
$362$		0			0
$363$	27.8477	+	16.2431i	1.46163	+	0.852541i
$364$		0			0
$365$		−	38.0222i		−	1.99017i
$366$		0			0
$367$	8.78098	+	15.2091i	0.458363	+	0.793909i	0.998875	−	0.0474280i	$-0.0151025\pi$
$367$	8.78098	+	15.2091i	0.458363	+	0.793909i	−0.540511	+	0.841337i	$0.681769\pi$
$368$		0			0
$369$	32.3078	+	32.3078i	1.68188	+	1.68188i
$370$		0			0
$371$	−13.1179	−	48.9569i	−0.681050	−	2.54171i
$372$		0			0
$373$	8.13965	+	4.69943i	0.421455	+	0.243327i	0.695700	−	0.718333i	$-0.255094\pi$
$373$	8.13965	+	4.69943i	0.421455	+	0.243327i	−0.274245	+	0.961660i	$0.588428\pi$
$374$		0			0
$375$	−3.56581	+	13.3078i	−0.184138	+	0.687211i
$376$		0			0
$377$	−20.4825	−	4.50109i	−1.05490	−	0.231818i
$378$		0			0
$379$	−10.0760	−	2.69986i	−0.517570	−	0.138682i	−0.00942743	−	0.999956i	$-0.503001\pi$
$379$	−10.0760	−	2.69986i	−0.517570	−	0.138682i	−0.508142	+	0.861273i	$0.669668\pi$
$380$		0			0
$381$	5.56454	−	9.63806i	0.285080	−	0.493773i
$382$		0			0
$383$	2.55125	+	9.52139i	0.130363	+	0.486521i	0.999974	−	0.00721664i	$-0.00229715\pi$
$383$	2.55125	+	9.52139i	0.130363	+	0.486521i	−0.869611	+	0.493737i	$0.835630\pi$
$384$		0			0
$385$	−43.9686	−	11.8860i	−2.24085	−	0.605766i
$386$		0			0
$387$	−23.3113	−	40.3764i	−1.18498	−	2.05245i
$388$		0			0
$389$			28.1176i			1.42562i	0.701358	+	0.712809i	$0.252577\pi$
$389$			28.1176i			1.42562i	−0.701358	+	0.712809i	$0.747423\pi$
$390$		0			0
$391$		−	2.89474i		−	0.146393i
$392$		0			0
$393$	29.9912	−	17.3154i	1.51286	−	0.873449i
$394$		0			0
$395$	−5.72204	−	5.72204i	−0.287907	−	0.287907i
$396$		0			0
$397$	9.00354	−	2.41249i	0.451875	−	0.121079i	−0.0257018	−	0.999670i	$-0.508182\pi$
$397$	9.00354	−	2.41249i	0.451875	−	0.121079i	0.477576	+	0.878590i	$0.341515\pi$
$398$		0			0
$399$	−2.90872	+	5.03805i	−0.145618	+	0.252218i
$400$		0			0
$401$	9.03053	−	33.7024i	0.450963	−	1.68302i	−0.248729	−	0.968573i	$-0.580013\pi$
$401$	9.03053	−	33.7024i	0.450963	−	1.68302i	0.699692	−	0.714444i	$-0.253320\pi$
$402$		0			0
$403$	−20.8453	+	0.948787i	−1.03838	+	0.0472624i
$404$		0			0
$405$	−15.3029	−	4.10039i	−0.760406	−	0.203750i
$406$		0			0
$407$	0.0139825	−	6.30136i	0.000693086	−	0.312347i
$408$		0			0
$409$	−24.3075	+	6.51317i	−1.20193	+	0.322056i	−0.803590	−	0.595183i	$-0.797079\pi$
$409$	−24.3075	+	6.51317i	−1.20193	+	0.322056i	−0.398338	+	0.917239i	$0.630413\pi$
$410$		0			0
$411$	25.5579	+	25.5579i	1.26068	+	1.26068i
$412$		0			0
$413$	15.0419	+	26.0534i	0.740165	+	1.28200i
$414$		0			0
$415$	26.6409			1.30775
$416$		0			0
$417$		−	26.8089i		−	1.31284i
$418$		0			0
$419$	−5.26271	−	9.11528i	−0.257100	−	0.445311i	0.708364	−	0.705848i	$-0.249434\pi$
$419$	−5.26271	−	9.11528i	−0.257100	−	0.445311i	−0.965464	+	0.260537i	$0.916100\pi$
$420$		0			0
$421$	−1.49478	+	1.49478i	−0.0728511	+	0.0728511i	−0.742594	−	0.669742i	$-0.766405\pi$
$421$	−1.49478	+	1.49478i	−0.0728511	+	0.0728511i	0.669742	+	0.742594i	$0.266405\pi$
$422$		0			0
$423$	1.84546	−	0.494490i	0.0897293	−	0.0240429i
$424$		0			0
$425$	−1.86003	−	1.07389i	−0.0902247	−	0.0520912i
$426$		0			0
$427$	−15.1826	+	56.6622i	−0.734737	+	2.74208i
$428$		0			0
$429$	1.51585	+	35.0143i	0.0731860	+	1.69051i
$430$		0			0
$431$	−6.32720	+	23.6134i	−0.304770	+	1.13742i	0.628372	+	0.777913i	$0.283721\pi$
$431$	−6.32720	+	23.6134i	−0.304770	+	1.13742i	−0.933143	+	0.359506i	$0.882945\pi$
$432$		0			0
$433$	−21.4007	−	12.3557i	−1.02845	−	0.593778i	−0.111913	−	0.993718i	$-0.535698\pi$
$433$	−21.4007	−	12.3557i	−1.02845	−	0.593778i	−0.916541	+	0.399940i	$0.869031\pi$
$434$		0			0
$435$	47.6530	−	12.7686i	2.28479	−	0.612207i
$436$		0			0
$437$	1.34575	−	1.34575i	0.0643761	−	0.0643761i
$438$		0			0
$439$	16.5635	+	28.6888i	0.790532	+	1.36924i	0.925638	+	0.378410i	$0.123529\pi$
$439$	16.5635	+	28.6888i	0.790532	+	1.36924i	−0.135106	+	0.990831i	$0.543137\pi$
$440$		0			0
$441$		−	86.7306i		−	4.13003i
$442$		0			0
$443$	1.22993			0.0584357			0.0292178	−	0.999573i	$-0.490698\pi$
$443$	1.22993			0.0584357			0.0292178	+	0.999573i	$0.490698\pi$
$444$		0			0
$445$	−25.6130	−	44.3631i	−1.21417	−	2.10301i
$446$		0			0
$447$	−19.2656	−	19.2656i	−0.911231	−	0.911231i
$448$		0			0
$449$	−33.9714	+	9.10262i	−1.60321	+	0.429579i	−0.946010	−	0.324137i	$-0.894926\pi$
$449$	−33.9714	+	9.10262i	−1.60321	+	0.429579i	−0.657200	+	0.753716i	$0.728259\pi$
$450$		0			0
$451$	−0.0601579	+	27.1108i	−0.00283273	+	1.27660i
$452$		0			0
$453$	20.0393	+	5.36951i	0.941527	+	0.252281i
$454$		0			0
$455$	−14.9767	−	47.1953i	−0.702120	−	2.21255i
$456$		0			0
$457$	−2.49795	+	9.32246i	−0.116849	+	0.436087i	−0.999419	−	0.0340953i	$-0.989145\pi$
$457$	−2.49795	+	9.32246i	−0.116849	+	0.436087i	0.882570	+	0.470182i	$0.155812\pi$
$458$		0			0
$459$	−2.41435	+	4.18177i	−0.112692	+	0.195188i
$460$		0			0
$461$	6.37701	−	1.70871i	0.297007	−	0.0795828i	−0.107239	−	0.994233i	$-0.534201\pi$
$461$	6.37701	−	1.70871i	0.297007	−	0.0795828i	0.404245	+	0.914651i	$0.367534\pi$
$462$		0			0
$463$	6.73098	+	6.73098i	0.312815	+	0.312815i	0.845999	−	0.533184i	$-0.179005\pi$
$463$	6.73098	+	6.73098i	0.312815	+	0.312815i	−0.533184	+	0.845999i	$0.679005\pi$
$464$		0			0
$465$	42.5120	−	24.5443i	1.97145	−	1.13821i
$466$		0			0
$467$		−	11.1075i		−	0.513994i	−0.966412	−	0.256997i	$-0.917267\pi$
$467$		−	11.1075i		−	0.513994i	0.966412	−	0.256997i	$-0.0827331\pi$
$468$		0			0
$469$		−	76.2108i		−	3.51909i
$470$		0			0
$471$	−20.0134	−	34.6642i	−0.922168	−	1.59724i
$472$		0			0
$473$	7.21931	−	26.7057i	0.331944	−	1.22793i
$474$		0			0
$475$	−0.365473	−	1.36396i	−0.0167691	−	0.0625830i
$476$		0			0
$477$	29.8513	−	51.7039i	1.36679	−	2.36736i
$478$		0			0
$479$	−23.9979	−	6.43022i	−1.09649	−	0.293804i	−0.335157	−	0.942162i	$-0.608789\pi$
$479$	−23.9979	−	6.43022i	−1.09649	−	0.293804i	−0.761336	+	0.648358i	$0.775456\pi$
$480$		0			0
$481$	5.77068	−	3.69136i	0.263120	−	0.168312i
$482$		0			0
$483$	−16.3763	+	61.1173i	−0.745149	+	2.78094i
$484$		0			0
$485$	−4.92434	−	2.84307i	−0.223603	−	0.129097i
$486$		0			0
$487$	3.69088	+	13.7746i	0.167250	+	0.624185i	0.997743	+	0.0671555i	$0.0213924\pi$
$487$	3.69088	+	13.7746i	0.167250	+	0.624185i	−0.830493	+	0.557030i	$0.811941\pi$
$488$		0			0
$489$	−12.2773	−	12.2773i	−0.555199	−	0.555199i
$490$		0			0
$491$	19.1842	+	33.2280i	0.865771	+	1.49956i	0.866280	+	0.499559i	$0.166505\pi$
$491$	19.1842	+	33.2280i	0.865771	+	1.49956i	−0.000508767		1.00000i	$0.500162\pi$
$492$		0			0
$493$		−	3.70064i		−	0.166668i
$494$		0			0
$495$	−26.7226	−	46.5229i	−1.20109	−	2.09105i
$496$		0			0
$497$	−11.0121	+	6.35784i	−0.493960	+	0.285188i
$498$		0			0
$499$	15.4344	−	15.4344i	0.690938	−	0.690938i	−0.271500	−	0.962438i	$-0.587520\pi$
$499$	15.4344	−	15.4344i	0.690938	−	0.690938i	0.962438	+	0.271500i	$0.0875198\pi$
$500$		0			0
$501$	−11.4827	−	42.8542i	−0.513011	−	1.91458i
$502$		0			0
$503$	13.7424	+	7.93416i	0.612742	+	0.353767i	0.774038	−	0.633140i	$-0.218234\pi$
$503$	13.7424	+	7.93416i	0.612742	+	0.353767i	−0.161296	+	0.986906i	$0.551567\pi$
$504$		0			0
$505$	33.5222	+	8.98224i	1.49172	+	0.399705i
$506$		0			0
$507$	−31.1288	+	21.9688i	−1.38248	+	0.975668i
$508$		0			0
$509$	38.7881	+	10.3932i	1.71925	+	0.460672i	0.977662	−	0.210183i	$-0.0674059\pi$
$509$	38.7881	+	10.3932i	1.71925	+	0.460672i	0.741589	+	0.670855i	$0.234073\pi$
$510$		0			0
$511$	53.9895	+	31.1709i	2.38836	+	1.37892i
$512$		0			0
$513$	−3.06650	+	0.821667i	−0.135389	+	0.0362775i
$514$		0			0
$515$	4.99830	+	4.99830i	0.220251	+	0.220251i
$516$		0			0
$517$	0.980518	+	0.569007i	0.0431231	+	0.0250249i
$518$		0			0
$519$	−31.5145			−1.38333
$520$		0			0
$521$	14.0373			0.614987			0.307493	−	0.951550i	$-0.400510\pi$
$521$	14.0373			0.614987			0.307493	+	0.951550i	$0.400510\pi$
$522$		0			0
$523$	−31.1544	+	17.9870i	−1.36229	+	0.786517i	−0.989928	−	0.141572i	$-0.954784\pi$
$523$	−31.1544	+	17.9870i	−1.36229	+	0.786517i	−0.372359	+	0.928089i	$0.621451\pi$
$524$		0			0
$525$	33.1959	+	33.1959i	1.44879	+	1.44879i
$526$		0			0
$527$	−0.953032	−	3.55676i	−0.0415147	−	0.154935i
$528$		0			0
$529$	−1.15003	+	1.99191i	−0.0500014	+	0.0866050i
$530$		0			0
$531$	−9.17176	+	34.2295i	−0.398020	+	1.48543i
$532$		0			0
$533$	−24.8276	+	15.8816i	−1.07540	+	0.687910i
$534$		0			0
$535$	−0.0854990	+	0.319087i	−0.00369644	+	0.0137953i
$536$		0			0
$537$	−15.8820	−	9.16949i	−0.685360	−	0.395693i
$538$		0			0
$539$	36.4704	−	36.3089i	1.57089	−	1.56394i
$540$		0			0
$541$	−17.6720	+	17.6720i	−0.759778	+	0.759778i	−0.976282	−	0.216504i	$-0.930535\pi$
$541$	−17.6720	+	17.6720i	−0.759778	+	0.759778i	0.216504	+	0.976282i	$0.430535\pi$
$542$		0			0
$543$	−1.85998	+	1.07386i	−0.0798195	+	0.0460838i
$544$		0			0
$545$	−25.2240			−1.08048
$546$		0			0
$547$			18.7197i			0.800398i	0.916428	+	0.400199i	$0.131059\pi$
$547$			18.7197i			0.800398i	−0.916428	+	0.400199i	$0.868941\pi$
$548$		0			0
$549$	−59.8416	+	34.5495i	−2.55398	+	1.47454i
$550$		0			0
$551$	1.72041	−	1.72041i	0.0732920	−	0.0732920i
$552$		0			0
$553$	12.8159	−	3.43402i	0.544989	−	0.146029i
$554$		0			0
$555$	−8.05757	+	13.9561i	−0.342025	+	0.592405i
$556$		0			0
$557$	−4.12236	−	1.10458i	−0.174670	−	0.0468027i	0.170424	−	0.985371i	$-0.445486\pi$
$557$	−4.12236	−	1.10458i	−0.174670	−	0.0468027i	−0.345094	+	0.938568i	$0.612153\pi$
$558$		0			0
$559$	28.6655	−	9.09656i	1.21242	−	0.384744i
$560$		0			0
$561$	−5.97733	+	1.58741i	−0.252363	+	0.0670206i
$562$		0			0
$563$	−6.30767	+	10.9252i	−0.265837	+	0.460442i	−0.967782	−	0.251788i	$-0.918981\pi$
$563$	−6.30767	+	10.9252i	−0.265837	+	0.460442i	0.701946	+	0.712230i	$0.252315\pi$
$564$		0			0
$565$	4.45090	+	16.6110i	0.187251	+	0.698829i
$566$		0			0
$567$	18.3677	−	18.3677i	0.771372	−	0.771372i
$568$		0			0
$569$	3.20931	+	5.55869i	0.134541	+	0.233032i	0.925422	−	0.378938i	$-0.123711\pi$
$569$	3.20931	+	5.55869i	0.134541	+	0.233032i	−0.790881	+	0.611970i	$0.790377\pi$
$570$		0			0
$571$	25.1851			1.05396			0.526981	−	0.849877i	$-0.323324\pi$
$571$	25.1851			1.05396			0.526981	+	0.849877i	$0.323324\pi$
$572$		0			0
$573$	6.60067			0.275747
$574$		0			0
$575$	−7.67924	−	13.3008i	−0.320246	−	0.554683i
$576$		0			0
$577$	−2.64094	+	2.64094i	−0.109944	+	0.109944i	−0.759939	−	0.649995i	$-0.774771\pi$
$577$	−2.64094	+	2.64094i	−0.109944	+	0.109944i	0.649995	+	0.759939i	$0.274771\pi$
$578$		0			0
$579$	−3.41834	−	12.7574i	−0.142061	−	0.530181i
$580$		0			0
$581$	−21.8404	+	37.8286i	−0.906091	+	1.56940i
$582$		0			0
$583$	34.2385	−	9.09281i	1.41802	−	0.376586i
$584$		0			0
$585$	26.8358	−	51.7849i	1.10952	−	2.14104i
$586$		0			0
$587$	4.31754	+	1.15688i	0.178204	+	0.0477496i	0.346818	−	0.937933i	$-0.387262\pi$
$587$	4.31754	+	1.15688i	0.178204	+	0.0477496i	−0.168613	+	0.985682i	$0.553929\pi$
$588$		0			0
$589$	1.21046	−	2.09658i	0.0498762	−	0.0863882i
$590$		0			0
$591$	−47.6462	+	12.7668i	−1.95990	+	0.525154i
$592$		0			0
$593$	15.9446	−	15.9446i	0.654765	−	0.654765i	−0.299372	−	0.954137i	$-0.596777\pi$
$593$	15.9446	−	15.9446i	0.654765	−	0.654765i	0.954137	+	0.299372i	$0.0967770\pi$
$594$		0			0
$595$	7.56691	−	4.36876i	0.310213	−	0.179102i
$596$		0			0
$597$		−	23.2524i		−	0.951656i
$598$		0			0
$599$	−21.7539			−0.888842			−0.444421	−	0.895818i	$-0.646591\pi$
$599$	−21.7539			−0.888842			−0.444421	+	0.895818i	$0.646591\pi$
$600$		0			0
$601$	25.1068	−	14.4954i	1.02413	−	0.591280i	0.108831	−	0.994060i	$-0.465289\pi$
$601$	25.1068	−	14.4954i	1.02413	−	0.591280i	0.915297	+	0.402780i	$0.131956\pi$
$602$		0			0
$603$	63.4781	−	63.4781i	2.58503	−	2.58503i
$604$		0			0
$605$	8.37586	−	30.7133i	0.340527	−	1.24867i
$606$		0			0
$607$	−31.0365	−	17.9189i	−1.25973	−	0.727306i	−0.286709	−	0.958018i	$-0.592561\pi$
$607$	−31.0365	−	17.9189i	−1.25973	−	0.727306i	−0.973022	+	0.230711i	$0.925895\pi$
$608$		0			0
$609$	−20.9355	+	78.1324i	−0.848350	+	3.16609i
$610$		0			0
$611$	0.0560363	+	1.23114i	0.00226699	+	0.0498067i
$612$		0			0
$613$	−5.19868	+	19.4017i	−0.209973	+	0.783628i	0.777904	+	0.628384i	$0.216283\pi$
$613$	−5.19868	+	19.4017i	−0.209973	+	0.783628i	−0.987876	+	0.155244i	$0.950383\pi$
$614$		0			0
$615$	34.6667	−	60.0445i	1.39790	−	2.42123i
$616$		0			0
$617$	6.72157	+	25.0853i	0.270600	+	1.00989i	0.958733	+	0.284309i	$0.0917642\pi$
$617$	6.72157	+	25.0853i	0.270600	+	1.00989i	−0.688132	+	0.725585i	$0.741569\pi$
$618$		0			0
$619$	−21.6140	−	21.6140i	−0.868741	−	0.868741i	0.123592	−	0.992333i	$-0.460559\pi$
$619$	−21.6140	−	21.6140i	−0.868741	−	0.868741i	−0.992333	+	0.123592i	$0.960559\pi$
$620$		0			0
$621$	−29.9033	+	17.2647i	−1.19998	+	0.692807i
$622$		0			0
$623$	83.9909			3.36503
$624$		0			0
$625$	30.4832			1.21933
$626$		0			0
$627$	−3.51681	−	2.04085i	−0.140448	−	0.0815037i
$628$		0			0
$629$	0.854771	+	0.854771i	0.0340820	+	0.0340820i
$630$		0			0
$631$	10.7181	−	2.87190i	0.426681	−	0.114329i	−0.0390870	−	0.999236i	$-0.512445\pi$
$631$	10.7181	−	2.87190i	0.426681	−	0.114329i	0.465768	+	0.884907i	$0.345778\pi$
$632$		0			0
$633$	26.9969	+	15.5867i	1.07303	+	0.619515i
$634$		0			0
$635$	−10.6152	−	2.84434i	−0.421252	−	0.112874i
$636$		0			0
$637$	54.6422	+	12.0078i	2.16500	+	0.475767i
$638$		0			0
$639$	−14.4679	−	3.87667i	−0.572342	−	0.153359i
$640$		0			0
$641$	−17.0918	−	9.86798i	−0.675087	−	0.389762i	0.122914	−	0.992417i	$-0.460776\pi$
$641$	−17.0918	−	9.86798i	−0.675087	−	0.389762i	−0.798001	+	0.602656i	$0.794109\pi$
$642$		0			0
$643$	4.94731	+	18.4636i	0.195103	+	0.728134i	0.992240	+	0.124336i	$0.0396800\pi$
$643$	4.94731	+	18.4636i	0.195103	+	0.728134i	−0.797137	+	0.603798i	$0.793653\pi$
$644$		0			0
$645$	−50.0268	+	50.0268i	−1.96980	+	1.96980i
$646$		0			0
$647$	22.3682	−	12.9143i	0.879386	−	0.507714i	0.00893024	−	0.999960i	$-0.497157\pi$
$647$	22.3682	−	12.9143i	0.879386	−	0.507714i	0.870456	+	0.492246i	$0.163824\pi$
$648$		0			0
$649$	−18.2332	+	10.4731i	−0.715717	+	0.411105i
$650$		0			0
$651$			80.4863i			3.15451i
$652$		0			0
$653$	−20.3137	−	35.1844i	−0.794937	−	1.37687i	−0.922879	−	0.385090i	$-0.874170\pi$
$653$	−20.3137	−	35.1844i	−0.794937	−	1.37687i	0.127942	−	0.991782i	$-0.459163\pi$
$654$		0			0
$655$	−24.1810	−	24.1810i	−0.944831	−	0.944831i
$656$		0			0
$657$	19.0063	+	70.9325i	0.741507	+	2.76734i
$658$		0			0
$659$	−27.3437	−	15.7869i	−1.06516	−	0.614969i	−0.138304	−	0.990390i	$-0.544165\pi$
$659$	−27.3437	−	15.7869i	−1.06516	−	0.614969i	−0.926855	+	0.375421i	$0.877498\pi$
$660$		0			0
$661$	−1.88644	+	7.04029i	−0.0733740	+	0.273835i	−0.992860	−	0.119288i	$-0.961939\pi$
$661$	−1.88644	+	7.04029i	−0.0733740	+	0.273835i	0.919486	+	0.393123i	$0.128605\pi$
$662$		0			0
$663$	−4.96533	−	4.53300i	−0.192837	−	0.176047i
$664$		0			0
$665$	5.54883	+	1.48681i	0.215175	+	0.0576558i
$666$		0			0
$667$	13.2314	−	22.9175i	0.512322	−	0.887368i
$668$		0			0
$669$	−9.10259	−	33.9713i	−0.351927	−	1.31341i
$670$		0			0
$671$	−39.5803	−	10.6997i	−1.52798	−	0.413057i
$672$		0			0
$673$	−17.5515	−	30.4001i	−0.676560	−	1.17184i	−0.976010	−	0.217725i	$-0.930137\pi$
$673$	−17.5515	−	30.4001i	−0.676560	−	1.17184i	0.299450	−	0.954112i	$-0.403197\pi$
$674$		0			0
$675$			25.6193i			0.986088i
$676$		0			0
$677$			7.77180i			0.298695i	0.988785	+	0.149347i	$0.0477172\pi$
$677$			7.77180i			0.298695i	−0.988785	+	0.149347i	$0.952283\pi$
$678$		0			0
$679$	8.07402	−	4.66154i	0.309852	−	0.178893i
$680$		0			0
$681$	0.0384591	+	0.0384591i	0.00147376	+	0.00147376i
$682$		0			0
$683$	8.01595	−	2.14787i	0.306722	−	0.0821859i	−0.102175	−	0.994766i	$-0.532580\pi$
$683$	8.01595	−	2.14787i	0.306722	−	0.0821859i	0.408897	+	0.912581i	$0.365914\pi$
$684$		0			0
$685$	17.8458	−	30.9099i	0.681854	−	1.18100i
$686$		0			0
$687$	19.4428	−	72.5616i	0.741790	−	2.76840i
$688$		0			0
$689$	28.4417	+	25.9653i	1.08354	+	0.989201i
$690$		0			0
$691$	−4.38939	−	1.17613i	−0.166980	−	0.0447423i	0.174360	−	0.984682i	$-0.444214\pi$
$691$	−4.38939	−	1.17613i	−0.166980	−	0.0447423i	−0.341341	+	0.939940i	$0.610881\pi$
$692$		0			0
$693$	87.9674	+	0.195196i	3.34160	+	0.00741489i
$694$		0			0
$695$	−25.5711	+	6.85175i	−0.969966	+	0.259902i
$696$		0			0
$697$	−3.67755	−	3.67755i	−0.139297	−	0.139297i
$698$		0			0
$699$	−16.4593	−	28.5083i	−0.622546	−	1.07828i
$700$		0			0
$701$	−42.2190			−1.59459			−0.797295	−	0.603590i	$-0.793737\pi$
$701$	−42.2190			−1.59459			−0.797295	+	0.603590i	$0.793737\pi$
$702$		0			0
$703$			0.794758i			0.0299749i
$704$		0			0
$705$	−1.44961	−	2.51080i	−0.0545955	−	0.0945622i
$706$		0			0
$707$	−40.2360	+	40.2360i	−1.51323	+	1.51323i
$708$		0			0
$709$	−11.7842	+	3.15756i	−0.442564	+	0.118585i	−0.473218	−	0.880945i	$-0.656908\pi$
$709$	−11.7842	+	3.15756i	−0.442564	+	0.118585i	0.0306540	+	0.999530i	$0.490241\pi$
$710$		0			0
$711$	13.5351	+	7.81447i	0.507605	+	0.293066i
$712$		0			0
$713$	6.81501	−	25.4340i	0.255224	−	0.952509i
$714$		0			0
$715$	33.0102	−	10.3947i	1.23451	−	0.388741i
$716$		0			0
$717$	0.240051	−	0.895884i	0.00896488	−	0.0334574i
$718$		0			0
$719$	−23.5977	−	13.6241i	−0.880045	−	0.508095i	−0.00937208	−	0.999956i	$-0.502983\pi$
$719$	−23.5977	−	13.6241i	−0.880045	−	0.508095i	−0.870673	+	0.491862i	$0.836317\pi$
$720$		0			0
$721$	−11.1950	+	2.99968i	−0.416922	+	0.111714i
$722$		0			0
$723$	39.7979	−	39.7979i	1.48010	−	1.48010i
$724$		0			0
$725$	−9.81714	−	17.0038i	−0.364599	−	0.631505i
$726$		0			0
$727$			42.0228i			1.55854i	0.626689	+	0.779269i	$0.284409\pi$
$727$			42.0228i			1.55854i	−0.626689	+	0.779269i	$0.715591\pi$
$728$		0			0
$729$	−36.1302			−1.33816
$730$		0			0
$731$	2.65349	+	4.59599i	0.0981430	+	0.169989i
$732$		0			0
$733$	−35.3983	−	35.3983i	−1.30747	−	1.30747i	−0.923239	−	0.384227i	$-0.874468\pi$
$733$	−35.3983	−	35.3983i	−1.30747	−	1.30747i	−0.384227	−	0.923239i	$-0.625532\pi$
$734$		0			0
$735$	−127.127	+	34.0635i	−4.68913	+	1.25645i
$736$		0			0
$737$	53.2672	+	0.118198i	1.96212	+	0.00435387i
$738$		0			0
$739$	7.07601	+	1.89601i	0.260295	+	0.0697459i	0.386607	−	0.922245i	$-0.373647\pi$
$739$	7.07601	+	1.89601i	0.260295	+	0.0697459i	−0.126311	+	0.991991i	$0.540314\pi$
$740$		0			0
$741$	−0.200985	−	4.41573i	−0.00738336	−	0.162216i
$742$		0			0
$743$	−2.24196	+	8.36711i	−0.0822495	+	0.306959i	−0.994779	−	0.102051i	$-0.967459\pi$
$743$	−2.24196	+	8.36711i	−0.0822495	+	0.306959i	0.912530	+	0.409011i	$0.134126\pi$
$744$		0			0
$745$	−13.4522	+	23.2999i	−0.492851	+	0.853642i
$746$		0			0
$747$	−49.7000	+	13.3171i	−1.81843	+	0.487246i
$748$		0			0
$749$	−0.382993	−	0.382993i	−0.0139943	−	0.0139943i
$750$		0			0
$751$	27.6569	−	15.9677i	1.00921	−	0.582670i	0.0982522	−	0.995162i	$-0.468675\pi$
$751$	27.6569	−	15.9677i	1.00921	−	0.582670i	0.910961	+	0.412492i	$0.135341\pi$
$752$		0			0
$753$			5.23688i			0.190842i
$754$		0			0
$755$		−	20.4863i		−	0.745574i
$756$		0			0
$757$	4.55094	+	7.88246i	0.165407	+	0.286493i	0.936800	−	0.349866i	$-0.113773\pi$
$757$	4.55094	+	7.88246i	0.165407	+	0.286493i	−0.771393	+	0.636359i	$0.780440\pi$
$758$		0			0
$759$	−42.6923	−	11.5410i	−1.54963	−	0.418911i
$760$		0			0
$761$	4.99686	+	18.6485i	0.181136	+	0.676009i	0.995425	+	0.0955488i	$0.0304606\pi$
$761$	4.99686	+	18.6485i	0.181136	+	0.676009i	−0.814289	+	0.580460i	$0.802873\pi$
$762$		0			0
$763$	20.6788	−	35.8167i	0.748623	−	1.29665i
$764$		0			0
$765$	9.94156	+	2.66383i	0.359438	+	0.0963110i
$766$		0			0
$767$	−20.2955	−	10.5175i	−0.732829	−	0.379764i
$768$		0			0
$769$	4.89434	−	18.2659i	0.176494	−	0.658686i	−0.819798	−	0.572653i	$-0.805914\pi$
$769$	4.89434	−	18.2659i	0.176494	−	0.658686i	0.996292	−	0.0860328i	$-0.0274190\pi$
$770$		0			0
$771$	53.7486	+	31.0318i	1.93571	+	1.11758i
$772$		0			0
$773$	4.72875	+	17.6479i	0.170081	+	0.634753i	0.997337	+	0.0729272i	$0.0232341\pi$
$773$	4.72875	+	17.6479i	0.170081	+	0.634753i	−0.827256	+	0.561825i	$0.810099\pi$
$774$		0			0
$775$	−13.8145	−	13.8145i	−0.496230	−	0.496230i
$776$		0			0
$777$	−13.2113	−	22.8826i	−0.473953	−	0.820910i
$778$		0			0
$779$		−	3.41935i		−	0.122511i
$780$		0			0
$781$	−4.42671	−	7.70672i	−0.158400	−	0.275768i
$782$		0			0
$783$	−38.2284	+	22.0712i	−1.36617	+	0.788759i
$784$		0			0
$785$	−27.9487	+	27.9487i	−0.997531	+	0.997531i
$786$		0			0
$787$	−2.85862	−	10.6685i	−0.101899	−	0.380291i	0.896076	−	0.443900i	$-0.146406\pi$
$787$	−2.85862	−	10.6685i	−0.101899	−	0.380291i	−0.997975	+	0.0636090i	$0.979739\pi$
$788$		0			0
$789$	−36.0802	−	20.8309i	−1.28449	−	0.741599i
$790$		0			0
$791$	−27.2356	−	7.29775i	−0.968386	−	0.259478i
$792$		0			0
$793$	−13.4820	−	42.4849i	−0.478758	−	1.50868i
$794$		0			0
$795$	−87.5098	−	23.4482i	−3.10365	−	0.831621i
$796$		0			0
$797$	8.40326	+	4.85162i	0.297659	+	0.171853i	0.641391	−	0.767215i	$-0.278358\pi$
$797$	8.40326	+	4.85162i	0.297659	+	0.171853i	−0.343732	+	0.939068i	$0.611691\pi$
$798$		0			0
$799$	−0.210066	+	0.0562870i	−0.00743160	+	0.00199129i
$800$		0			0
$801$	69.9585	+	69.9585i	2.47186	+	2.47186i
$802$		0			0
$803$	−21.8705	+	37.6874i	−0.771792	+	1.32996i
$804$		0			0
$805$	62.4808			2.20216
$806$		0			0
$807$	−60.0025			−2.11219
$808$		0			0
$809$	22.7201	−	13.1175i	0.798797	−	0.461186i	−0.0442534	−	0.999020i	$-0.514091\pi$
$809$	22.7201	−	13.1175i	0.798797	−	0.461186i	0.843050	+	0.537835i	$0.180758\pi$
$810$		0			0
$811$	−5.44079	−	5.44079i	−0.191052	−	0.191052i	0.605098	−	0.796151i	$-0.293134\pi$
$811$	−5.44079	−	5.44079i	−0.191052	−	0.191052i	−0.796151	+	0.605098i	$0.793134\pi$
$812$		0			0
$813$	21.9901	+	82.0682i	0.771227	+	2.87826i
$814$		0			0
$815$	−8.57263	+	14.8482i	−0.300286	+	0.520111i
$816$		0			0
$817$	−0.903055	+	3.37025i	−0.0315939	+	0.117910i
$818$		0			0
$819$	51.5316	+	80.5590i	1.80066	+	2.81496i
$820$		0			0
$821$	7.35518	−	27.4499i	0.256697	−	0.958008i	−0.710441	−	0.703757i	$-0.751504\pi$
$821$	7.35518	−	27.4499i	0.256697	−	0.958008i	0.967138	−	0.254251i	$-0.0818289\pi$
$822$		0			0
$823$	5.96790	+	3.44557i	0.208028	+	0.120105i	0.600395	−	0.799704i	$-0.295010\pi$
$823$	5.96790	+	3.44557i	0.208028	+	0.120105i	−0.392367	+	0.919809i	$0.628344\pi$
$824$		0			0
$825$	−23.2536	+	23.1507i	−0.809588	+	0.806003i
$826$		0			0
$827$	1.20730	−	1.20730i	0.0419821	−	0.0419821i	−0.685804	−	0.727786i	$-0.740549\pi$
$827$	1.20730	−	1.20730i	0.0419821	−	0.0419821i	0.727786	+	0.685804i	$0.240549\pi$
$828$		0			0
$829$	−7.20634	+	4.16058i	−0.250287	+	0.144503i	−0.619895	−	0.784684i	$-0.712825\pi$
$829$	−7.20634	+	4.16058i	−0.250287	+	0.144503i	0.369609	+	0.929187i	$0.379492\pi$
$830$		0			0
$831$	8.76073			0.303906
$832$		0			0
$833$			9.87241i			0.342059i
$834$		0			0
$835$	−37.9407	+	21.9051i	−1.31299	+	0.758057i
$836$		0			0
$837$	−31.0581	+	31.0581i	−1.07352	+	1.07352i
$838$		0			0
$839$	26.3035	−	7.04800i	0.908097	−	0.243324i	0.225607	−	0.974218i	$-0.427564\pi$
$839$	26.3035	−	7.04800i	0.908097	−	0.243324i	0.682490	+	0.730894i	$0.260897\pi$
$840$		0			0
$841$	2.41503	−	4.18296i	0.0832770	−	0.144240i
$842$		0			0
$843$	15.5653	+	4.17072i	0.536098	+	0.143647i
$844$		0			0
$845$	28.9102	+	24.0768i	0.994543	+	0.828266i
$846$		0			0
$847$	36.7446	+	37.0722i	1.26256	+	1.27382i
$848$		0			0
$849$	21.1201	−	36.5811i	0.724839	−	1.25546i
$850$		0			0
$851$	2.23728	+	8.34964i	0.0766929	+	0.286222i
$852$		0			0
$853$	−26.6286	+	26.6286i	−0.911746	+	0.911746i	−0.996410	−	0.0846635i	$-0.973018\pi$
$853$	−26.6286	+	26.6286i	−0.911746	+	0.911746i	0.0846635	+	0.996410i	$0.473018\pi$
$854$		0			0
$855$	3.38338	+	5.86019i	0.115709	+	0.200414i
$856$		0			0
$857$	−35.7429			−1.22095			−0.610477	−	0.792034i	$-0.709022\pi$
$857$	−35.7429			−1.22095			−0.610477	+	0.792034i	$0.709022\pi$
$858$		0			0
$859$	15.4391			0.526776			0.263388	−	0.964690i	$-0.415160\pi$
$859$	15.4391			0.526776			0.263388	+	0.964690i	$0.415160\pi$
$860$		0			0
$861$	56.8400	+	98.4498i	1.93710	+	3.35516i
$862$		0			0
$863$	37.8394	−	37.8394i	1.28807	−	1.28807i	0.352110	−	0.935959i	$-0.385464\pi$
$863$	37.8394	−	37.8394i	1.28807	−	1.28807i	0.935959	−	0.352110i	$-0.114536\pi$
$864$		0			0
$865$	8.05438	+	30.0594i	0.273857	+	1.02205i
$866$		0			0
$867$	−24.3185	+	42.1209i	−0.825899	+	1.43050i
$868$		0			0
$869$	2.38032	+	8.96298i	0.0807468	+	0.304048i
$870$		0			0
$871$	31.2041	+	48.7812i	1.05731	+	1.65289i
$872$		0			0
$873$	10.6078	+	2.84235i	0.359020	+	0.0961991i
$874$		0			0
$875$	−11.1532	+	19.3179i	−0.377047	+	0.653064i
$876$		0			0
$877$	25.0291	−	6.70653i	0.845173	−	0.226463i	0.189851	−	0.981813i	$-0.439200\pi$
$877$	25.0291	−	6.70653i	0.845173	−	0.226463i	0.655322	+	0.755350i	$0.272533\pi$
$878$		0			0
$879$	42.6024	−	42.6024i	1.43694	−	1.43694i
$880$		0			0
$881$	7.30126	−	4.21538i	0.245986	−	0.142020i	−0.371939	−	0.928257i	$-0.621307\pi$
$881$	7.30126	−	4.21538i	0.245986	−	0.142020i	0.617925	+	0.786237i	$0.287974\pi$
$882$		0			0
$883$		−	3.38001i		−	0.113746i	−0.998381	−	0.0568731i	$-0.981887\pi$
$883$		−	3.38001i		−	0.113746i	0.998381	−	0.0568731i	$-0.0181131\pi$
$884$		0			0
$885$	53.7746			1.80761
$886$		0			0
$887$	41.3111	−	23.8510i	1.38709	−	0.800837i	0.394103	−	0.919066i	$-0.371055\pi$
$887$	41.3111	−	23.8510i	1.38709	−	0.800837i	0.992986	+	0.118230i	$0.0377219\pi$
$888$		0			0
$889$	12.7412	−	12.7412i	0.427327	−	0.427327i
$890$		0			0
$891$	12.8096	+	12.8665i	0.429137	+	0.431045i
$892$		0			0
$893$	−0.123826	−	0.0714911i	−0.00414369	−	0.00239236i
$894$		0			0
$895$	−4.68703	+	17.4922i	−0.156670	+	0.584701i
$896$		0			0
$897$	−14.5420	−	45.8254i	−0.485543	−	1.53006i
$898$		0			0
$899$	8.71231	−	32.5148i	0.290572	−	1.08443i
$900$		0			0
$901$	−3.39792	+	5.88538i	−0.113201	+	0.196070i
$902$		0			0
$903$	−30.0231	−	112.048i	−0.999105	−	3.72871i
$904$		0			0
$905$	1.49965	+	1.49965i	0.0498500	+	0.0498500i
$906$		0			0
$907$	9.62956	−	5.55963i	0.319744	−	0.184605i	−0.331534	−	0.943443i	$-0.607566\pi$
$907$	9.62956	−	5.55963i	0.319744	−	0.184605i	0.651279	+	0.758839i	$0.274233\pi$
$908$		0			0
$909$	−67.0274			−2.22316
$910$		0			0
$911$	34.9550			1.15811			0.579055	−	0.815289i	$-0.303422\pi$
$911$	34.9550			1.15811			0.579055	+	0.815289i	$0.303422\pi$
$912$		0			0
$913$	−26.4063	−	15.3239i	−0.873920	−	0.507147i
$914$		0			0
$915$	74.1443	+	74.1443i	2.45114	+	2.45114i
$916$		0			0
$917$	54.1595	−	14.5120i	1.78850	−	0.479228i
$918$		0			0
$919$	19.3010	+	11.1435i	0.636682	+	0.367589i	0.783335	−	0.621599i	$-0.213517\pi$
$919$	19.3010	+	11.1435i	0.636682	+	0.367589i	−0.146653	+	0.989188i	$0.546850\pi$
$920$		0			0
$921$	−80.9773	−	21.6978i	−2.66829	−	0.714967i
$922$		0			0
$923$	4.44547	−	8.57839i	0.146324	−	0.282361i
$924$		0			0
$925$	6.19508	+	1.65997i	0.203693	+	0.0545793i
$926$		0			0
$927$	−11.8231	−	6.82608i	−0.388322	−	0.224198i
$928$		0			0
$929$	4.57756	+	17.0837i	0.150185	+	0.560498i	0.999470	+	0.0325628i	$0.0103669\pi$
$929$	4.57756	+	17.0837i	0.150185	+	0.560498i	−0.849285	+	0.527935i	$0.822966\pi$
$930$		0			0
$931$	−4.58964	+	4.58964i	−0.150419	+	0.150419i
$932$		0			0
$933$	−0.548804	+	0.316852i	−0.0179670	+	0.0103733i
$934$		0			0
$935$	3.04179	+	5.29563i	0.0994771	+	0.173186i
$936$		0			0
$937$			20.7669i			0.678426i	0.940710	+	0.339213i	$0.110161\pi$
$937$			20.7669i			0.678426i	−0.940710	+	0.339213i	$0.889839\pi$
$938$		0			0
$939$	16.5232	+	28.6191i	0.539215	+	0.933948i
$940$		0			0
$941$	4.57177	+	4.57177i	0.149035	+	0.149035i	0.777687	−	0.628652i	$-0.216393\pi$
$941$	4.57177	+	4.57177i	0.149035	+	0.149035i	−0.628652	+	0.777687i	$0.716393\pi$
$942$		0			0
$943$	−9.62562	−	35.9233i	−0.313453	−	1.16982i
$944$		0			0
$945$	−90.2603	−	52.1118i	−2.93617	−	1.69520i
$946$		0			0
$947$	2.91395	−	10.8750i	0.0946907	−	0.353391i	−0.902282	−	0.431147i	$-0.858109\pi$
$947$	2.91395	−	10.8750i	0.0946907	−	0.353391i	0.996972	+	0.0777565i	$0.0247757\pi$
$948$		0			0
$949$	−47.3205	+	2.15382i	−1.53609	+	0.0699160i
$950$		0			0
$951$	60.8631	+	16.3082i	1.97362	+	0.528831i
$952$		0			0
$953$	−7.47362	+	12.9447i	−0.242094	+	0.419319i	−0.961311	−	0.275467i	$-0.911168\pi$
$953$	−7.47362	+	12.9447i	−0.242094	+	0.419319i	0.719216	+	0.694786i	$0.244501\pi$
$954$		0			0
$955$	−1.68698	−	6.29590i	−0.0545894	−	0.203731i
$956$		0			0
$957$	−54.5779	−	14.7540i	−1.76425	−	0.476928i
$958$		0			0
$959$	29.2602	+	50.6802i	0.944862	+	1.63655i
$960$		0			0
$961$		−	2.49433i		−	0.0804622i
$962$		0			0
$963$		−	0.638012i		−	0.0205597i
$964$		0			0
$965$	−11.2947	+	6.52102i	−0.363590	+	0.209919i
$966$		0			0
$967$	21.9864	+	21.9864i	0.707034	+	0.707034i	0.965911	−	0.258876i	$-0.0833521\pi$
$967$	21.9864	+	21.9864i	0.707034	+	0.707034i	−0.258876	+	0.965911i	$0.583352\pi$
$968$		0			0
$969$	0.753441	−	0.201884i	0.0242040	−	0.00648545i
$970$		0			0
$971$	6.27244	−	10.8642i	0.201292	−	0.348648i	−0.747653	−	0.664090i	$-0.768819\pi$
$971$	6.27244	−	10.8642i	0.201292	−	0.348648i	0.948945	+	0.315442i	$0.102153\pi$
$972$		0			0
$973$	11.2342	−	41.9267i	0.360152	−	1.34411i
$974$		0			0
$975$	−34.8400	−	7.65622i	−1.11577	−	0.245195i
$976$		0			0
$977$	5.46118	+	1.46332i	0.174719	+	0.0468157i	0.345118	−	0.938559i	$-0.387839\pi$
$977$	5.46118	+	1.46332i	0.174719	+	0.0468157i	−0.170399	+	0.985375i	$0.554506\pi$
$978$		0			0
$979$	−0.130264	+	58.7051i	−0.00416327	+	1.87622i
$980$		0			0
$981$	47.0567	−	12.6088i	1.50241	−	0.402568i
$982$		0			0
$983$	14.7533	+	14.7533i	0.470559	+	0.470559i	0.902095	−	0.431537i	$-0.142028\pi$
$983$	14.7533	+	14.7533i	0.470559	+	0.470559i	−0.431537	+	0.902095i	$0.642028\pi$
$984$		0			0
$985$	24.3546	+	42.1833i	0.776001	+	1.34407i
$986$		0			0
$987$	4.75360			0.151309
$988$		0			0
$989$			37.9496i			1.20673i
$990$		0			0
$991$	−0.906536	−	1.57017i	−0.0287971	−	0.0498780i	0.851268	−	0.524732i	$-0.175834\pi$
$991$	−0.906536	−	1.57017i	−0.0287971	−	0.0498780i	−0.880065	+	0.474854i	$0.842501\pi$
$992$		0			0
$993$	−24.0416	+	24.0416i	−0.762936	+	0.762936i
$994$		0			0
$995$	−22.1788	+	5.94278i	−0.703114	+	0.188399i
$996$		0			0
$997$	39.4734	+	22.7900i	1.25014	+	0.721767i	0.971137	−	0.238524i	$-0.0766637\pi$
$997$	39.4734	+	22.7900i	1.25014	+	0.721767i	0.279000	+	0.960291i	$0.409997\pi$
$998$		0			0
$999$	3.73198	−	13.9279i	0.118075	−	0.440660i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bc.a.197.14	yes	56
11.10	odd	2	inner	572.2.bc.a.197.13	✓	56
13.7	odd	12	inner	572.2.bc.a.241.13	yes	56
143.98	even	12	inner	572.2.bc.a.241.14	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bc.a.197.13	✓	56	11.10	odd	2	inner
572.2.bc.a.197.14	yes	56	1.1	even	1	trivial
572.2.bc.a.241.13	yes	56	13.7	odd	12	inner
572.2.bc.a.241.14	yes	56	143.98	even	12	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.46539 + 2.53814i) q^{3} +(2.04642 - 2.04642i) q^{5} +(1.22814 + 4.58348i) q^{7} +(-2.79476 + 4.84067i) q^{9} +O(q^{10})\)	\(q+(1.46539 + 2.53814i) q^{3} +(2.04642 - 2.04642i) q^{5} +(1.22814 + 4.58348i) q^{7} +(-2.79476 + 4.84067i) q^{9} +(-3.20551 + 0.851295i) q^{11} +(-2.66280 - 2.43095i) q^{13} +(8.19292 + 2.19529i) q^{15} +(0.318123 - 0.551006i) q^{17} +(0.404054 - 0.108266i) q^{19} +(-9.83380 + 9.83380i) q^{21} +(3.94017 - 2.27486i) q^{23} -3.37570i q^{25} -7.58934 q^{27} +(5.03712 - 2.90818i) q^{29} +(4.09233 - 4.09233i) q^{31} +(-6.85804 - 6.88854i) q^{33} +(11.8930 + 6.86645i) q^{35} +(-0.491740 + 1.83520i) q^{37} +(2.26804 - 10.3208i) q^{39} +(2.11565 - 7.89572i) q^{41} +(-4.17054 + 7.22359i) q^{43} +(4.18679 + 15.6253i) q^{45} +(-0.241697 - 0.241697i) q^{47} +(-13.4378 + 7.75832i) q^{49} +1.86470 q^{51} -10.6811 q^{53} +(-4.81772 + 8.30194i) q^{55} +(0.866892 + 0.866892i) q^{57} +(6.12387 - 1.64089i) q^{59} +(10.7060 + 6.18113i) q^{61} +(-25.6195 - 6.86472i) q^{63} +(-10.4240 + 0.474453i) q^{65} +(-15.5135 - 4.15682i) q^{67} +(11.5478 + 6.66713i) q^{69} +(0.693560 + 2.58840i) q^{71} +(9.28992 - 9.28992i) q^{73} +(8.56798 - 4.94673i) q^{75} +(-7.83871 - 13.6469i) q^{77} -2.79612i q^{79} +(-2.73709 - 4.74078i) q^{81} +(6.50913 + 6.50913i) q^{83} +(-0.476576 - 1.77861i) q^{85} +(14.7627 + 8.52326i) q^{87} +(4.58118 - 17.0972i) q^{89} +(7.87193 - 15.1904i) q^{91} +(16.3838 + 4.39002i) q^{93} +(0.605308 - 1.04842i) q^{95} +(-0.508515 - 1.89780i) q^{97} +(4.83780 - 17.8960i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 28 q^{9}+O(q^{10}) \) 56 * q - 28 * q^9	\( 56 q - 28 q^{9} + 4 q^{11} + 8 q^{15} - 12 q^{23} - 24 q^{27} - 4 q^{31} - 10 q^{33} - 12 q^{37} - 64 q^{45} - 8 q^{47} + 40 q^{53} + 22 q^{55} + 48 q^{59} - 36 q^{67} - 48 q^{71} + 120 q^{75} + 28 q^{81} + 28 q^{89} + 36 q^{91} + 20 q^{93} - 68 q^{97} - 44 q^{99}+O(q^{100}) \) 56 * q - 28 * q^9 + 4 * q^11 + 8 * q^15 - 12 * q^23 - 24 * q^27 - 4 * q^31 - 10 * q^33 - 12 * q^37 - 64 * q^45 - 8 * q^47 + 40 * q^53 + 22 * q^55 + 48 * q^59 - 36 * q^67 - 48 * q^71 + 120 * q^75 + 28 * q^81 + 28 * q^89 + 36 * q^91 + 20 * q^93 - 68 * q^97 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more