LMFDB - Embedded newform 936.2.q.d.625.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [936,2,Mod(313,936)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(936, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))

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

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

chi := DirichletCharacter("936.313");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 29 x^{10} - 90 x^{9} + 217 x^{8} - 394 x^{7} + 555 x^{6} - 598 x^{5} + 483 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 29x^10 - 90x^9 + 217x^8 - 394x^7 + 555x^6 - 598x^5 + 483x^4 - 282x^3 + 112x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			625.4
Root			$0.500000 + 0.272034i$ of defining polynomial
Character	$\chi$	$=$	936.625
Dual form			936.2.q.d.313.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0876778 - 1.72983i) q^{3} +(-0.391618 + 0.678302i) q^{5} +(-0.823587 - 1.42649i) q^{7} +(-2.98463 - 0.303335i) q^{9} +(-0.453596 - 0.785652i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(1.13901 + 0.736904i) q^{15} -6.56503 q^{17} -1.23934 q^{19} +(-2.53980 + 1.29959i) q^{21} +(0.0313504 - 0.0543004i) q^{23} +(2.19327 + 3.79886i) q^{25} +(-0.786404 + 5.13630i) q^{27} +(-2.57767 - 4.46466i) q^{29} +(0.786907 - 1.36296i) q^{31} +(-1.39881 + 0.715760i) q^{33} +1.29012 q^{35} -9.04427 q^{37} +(1.45424 + 0.940846i) q^{39} +(-2.50583 + 4.34023i) q^{41} +(0.205281 + 0.355557i) q^{43} +(1.37458 - 1.90568i) q^{45} +(-1.33708 - 2.31588i) q^{47} +(2.14341 - 3.71249i) q^{49} +(-0.575607 + 11.3564i) q^{51} -5.61642 q^{53} +0.710545 q^{55} +(-0.108663 + 2.14385i) q^{57} +(-3.14465 + 5.44669i) q^{59} +(0.786600 + 1.36243i) q^{61} +(2.02539 + 4.50738i) q^{63} +(-0.391618 - 0.678302i) q^{65} +(6.75497 - 11.7000i) q^{67} +(-0.0911818 - 0.0589918i) q^{69} -8.83191 q^{71} +2.43859 q^{73} +(6.76368 - 3.46091i) q^{75} +(-0.747152 + 1.29411i) q^{77} +(2.20211 + 3.81417i) q^{79} +(8.81598 + 1.81069i) q^{81} +(5.96236 + 10.3271i) q^{83} +(2.57098 - 4.45307i) q^{85} +(-7.94911 + 4.06749i) q^{87} -11.6219 q^{89} +1.64717 q^{91} +(-2.28870 - 1.48072i) q^{93} +(0.485347 - 0.840646i) q^{95} +(-1.23743 - 2.14329i) q^{97} +(1.11550 + 2.48247i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{3} - q^{5} + 2 q^{7} + 2 q^{9} - q^{11} - 6 q^{13} - 2 q^{15} + 12 q^{17} - 14 q^{19} - 24 q^{21} + 19 q^{23} + 5 q^{25} - 7 q^{27} - 2 q^{29} + 8 q^{31} - 9 q^{33} + 2 q^{35} - 34 q^{37}+ \cdots - 39 q^{99}+O(q^{100}) $ 12 * q - 4 * q^3 - q^5 + 2 * q^7 + 2 * q^9 - q^11 - 6 * q^13 - 2 * q^15 + 12 * q^17 - 14 * q^19 - 24 * q^21 + 19 * q^23 + 5 * q^25 - 7 * q^27 - 2 * q^29 + 8 * q^31 - 9 * q^33 + 2 * q^35 - 34 * q^37 - q^39 - 2 * q^41 + 15 * q^43 + 10 * q^45 - 9 * q^47 + 12 * q^49 + 4 * q^51 + 32 * q^53 - 10 * q^55 - 14 * q^57 + 5 * q^59 + 6 * q^61 + 18 * q^63 - q^65 + 8 * q^67 + 15 * q^69 - 42 * q^71 - 2 * q^73 + 10 * q^75 + 3 * q^77 + 34 * q^79 + 62 * q^81 + 44 * q^83 + 7 * q^85 - 21 * q^87 + 22 * q^89 - 4 * q^91 - 18 * q^93 + 6 * q^95 + 12 * q^97 - 39 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	0.0876778	−	1.72983i	0.0506208	−	0.998718i
$3$	0.0876778	−	1.72983i	0.0506208	−	0.998718i
$4$		0			0
$5$	−0.391618	+	0.678302i	−0.175137	+	0.303346i	−0.940209	−	0.340599i	$-0.889370\pi$
$5$	−0.391618	+	0.678302i	−0.175137	+	0.303346i	0.765072	+	0.643945i	$0.222703\pi$
$6$		0			0
$7$	−0.823587	−	1.42649i	−0.311287	−	0.539164i	0.667355	−	0.744740i	$-0.267427\pi$
$7$	−0.823587	−	1.42649i	−0.311287	−	0.539164i	−0.978641	+	0.205576i	$0.934093\pi$
$8$		0			0
$9$	−2.98463	−	0.303335i	−0.994875	−	0.101112i
$10$		0			0
$11$	−0.453596	−	0.785652i	−0.136764	−	0.236883i	0.789506	−	0.613743i	$-0.210337\pi$
$11$	−0.453596	−	0.785652i	−0.136764	−	0.236883i	−0.926270	+	0.376860i	$0.877004\pi$
$12$		0			0
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$		0			0
$15$	1.13901	+	0.736904i	0.294091	+	0.190268i
$16$		0			0
$17$	−6.56503			−1.59225			−0.796126	−	0.605130i	$-0.793121\pi$
$17$	−6.56503			−1.59225			−0.796126	+	0.605130i	$0.793121\pi$
$18$		0			0
$19$	−1.23934			−0.284324			−0.142162	−	0.989843i	$-0.545405\pi$
$19$	−1.23934			−0.284324			−0.142162	+	0.989843i	$0.545405\pi$
$20$		0			0
$21$	−2.53980	+	1.29959i	−0.554231	+	0.283595i
$22$		0			0
$23$	0.0313504	−	0.0543004i	0.00653701	−	0.0113224i	−0.862738	−	0.505651i	$-0.831253\pi$
$23$	0.0313504	−	0.0543004i	0.00653701	−	0.0113224i	0.869275	+	0.494328i	$0.164586\pi$
$24$		0			0
$25$	2.19327	+	3.79886i	0.438654	+	0.759771i
$26$		0			0
$27$	−0.786404	+	5.13630i	−0.151344	+	0.988481i
$28$		0			0
$29$	−2.57767	−	4.46466i	−0.478662	−	0.829067i	0.521039	−	0.853533i	$-0.325545\pi$
$29$	−2.57767	−	4.46466i	−0.478662	−	0.829067i	−0.999701	+	0.0244662i	$0.992211\pi$
$30$		0			0
$31$	0.786907	−	1.36296i	0.141333	−	0.244795i	−0.786666	−	0.617379i	$-0.788195\pi$
$31$	0.786907	−	1.36296i	0.141333	−	0.244795i	0.927999	+	0.372583i	$0.121528\pi$
$32$		0			0
$33$	−1.39881	+	0.715760i	−0.243502	+	0.124598i
$34$		0			0
$35$	1.29012			0.218071
$36$		0			0
$37$	−9.04427			−1.48687			−0.743434	−	0.668809i	$-0.766804\pi$
$37$	−9.04427			−1.48687			−0.743434	+	0.668809i	$0.766804\pi$
$38$		0			0
$39$	1.45424	+	0.940846i	0.232864	+	0.150656i
$40$		0			0
$41$	−2.50583	+	4.34023i	−0.391345	+	0.677830i	−0.992627	−	0.121207i	$-0.961324\pi$
$41$	−2.50583	+	4.34023i	−0.391345	+	0.677830i	0.601282	+	0.799037i	$0.294657\pi$
$42$		0			0
$43$	0.205281	+	0.355557i	0.0313051	+	0.0542220i	0.881253	−	0.472644i	$-0.156700\pi$
$43$	0.205281	+	0.355557i	0.0313051	+	0.0542220i	−0.849948	+	0.526866i	$0.823367\pi$
$44$		0			0
$45$	1.37458	−	1.90568i	0.204911	−	0.284083i
$46$		0			0
$47$	−1.33708	−	2.31588i	−0.195033	−	0.337806i	0.751879	−	0.659302i	$-0.229148\pi$
$47$	−1.33708	−	2.31588i	−0.195033	−	0.337806i	−0.946911	+	0.321495i	$0.895815\pi$
$48$		0			0
$49$	2.14341	−	3.71249i	0.306201	−	0.530356i
$50$		0			0
$51$	−0.575607	+	11.3564i	−0.0806011	+	1.59021i
$52$		0			0
$53$	−5.61642			−0.771475			−0.385738	−	0.922609i	$-0.626053\pi$
$53$	−5.61642			−0.771475			−0.385738	+	0.922609i	$0.626053\pi$
$54$		0			0
$55$	0.710545			0.0958099
$56$		0			0
$57$	−0.108663	+	2.14385i	−0.0143927	+	0.283960i
$58$		0			0
$59$	−3.14465	+	5.44669i	−0.409398	+	0.709098i	−0.994822	−	0.101629i	$-0.967595\pi$
$59$	−3.14465	+	5.44669i	−0.409398	+	0.709098i	0.585424	+	0.810727i	$0.300928\pi$
$60$		0			0
$61$	0.786600	+	1.36243i	0.100714	+	0.174441i	0.911979	−	0.410237i	$-0.134554\pi$
$61$	0.786600	+	1.36243i	0.100714	+	0.174441i	−0.811265	+	0.584678i	$0.801221\pi$
$62$		0			0
$63$	2.02539	+	4.50738i	0.255175	+	0.567876i
$64$		0			0
$65$	−0.391618	−	0.678302i	−0.0485742	−	0.0841330i
$66$		0			0
$67$	6.75497	−	11.7000i	0.825251	−	1.42938i	−0.0764757	−	0.997071i	$-0.524367\pi$
$67$	6.75497	−	11.7000i	0.825251	−	1.42938i	0.901727	−	0.432306i	$-0.142300\pi$
$68$		0			0
$69$	−0.0911818	−	0.0589918i	−0.0109770	−	0.00710178i
$70$		0			0
$71$	−8.83191			−1.04815			−0.524077	−	0.851671i	$-0.675590\pi$
$71$	−8.83191			−1.04815			−0.524077	+	0.851671i	$0.675590\pi$
$72$		0			0
$73$	2.43859			0.285416			0.142708	−	0.989765i	$-0.454419\pi$
$73$	2.43859			0.285416			0.142708	+	0.989765i	$0.454419\pi$
$74$		0			0
$75$	6.76368	−	3.46091i	0.781002	−	0.399632i
$76$		0			0
$77$	−0.747152	+	1.29411i	−0.0851459	+	0.147477i
$78$		0			0
$79$	2.20211	+	3.81417i	0.247757	+	0.429128i	0.962903	−	0.269847i	$-0.0869732\pi$
$79$	2.20211	+	3.81417i	0.247757	+	0.429128i	−0.715146	+	0.698975i	$0.753640\pi$
$80$		0			0
$81$	8.81598	+	1.81069i	0.979553	+	0.201187i
$82$		0			0
$83$	5.96236	+	10.3271i	0.654454	+	1.13355i	0.982030	+	0.188722i	$0.0604347\pi$
$83$	5.96236	+	10.3271i	0.654454	+	1.13355i	−0.327577	+	0.944825i	$0.606232\pi$
$84$		0			0
$85$	2.57098	−	4.45307i	0.278862	−	0.483003i
$86$		0			0
$87$	−7.94911	+	4.06749i	−0.852234	+	0.436080i
$88$		0			0
$89$	−11.6219			−1.23192			−0.615961	−	0.787777i	$-0.711232\pi$
$89$	−11.6219			−1.23192			−0.615961	+	0.787777i	$0.711232\pi$
$90$		0			0
$91$	1.64717			0.172671
$92$		0			0
$93$	−2.28870	−	1.48072i	−0.237327	−	0.153543i
$94$		0			0
$95$	0.485347	−	0.840646i	0.0497956	−	0.0862485i
$96$		0			0
$97$	−1.23743	−	2.14329i	−0.125642	−	0.217618i	0.796342	−	0.604847i	$-0.206766\pi$
$97$	−1.23743	−	2.14329i	−0.125642	−	0.217618i	−0.921984	+	0.387229i	$0.873432\pi$
$98$		0			0
$99$	1.11550	+	2.48247i	0.112112	+	0.249497i
$100$		0			0
$101$	−3.08962	−	5.35138i	−0.307429	−	0.532482i	0.670370	−	0.742027i	$-0.266135\pi$
$101$	−3.08962	−	5.35138i	−0.307429	−	0.532482i	−0.977799	+	0.209544i	$0.932802\pi$
$102$		0			0
$103$	−2.99527	+	5.18796i	−0.295133	+	0.511185i	−0.975016	−	0.222136i	$-0.928697\pi$
$103$	−2.99527	+	5.18796i	−0.295133	+	0.511185i	0.679883	+	0.733321i	$0.262031\pi$
$104$		0			0
$105$	0.113115	−	2.23170i	0.0110389	−	0.217791i
$106$		0			0
$107$	0.0906932			0.00876764			0.00438382	−	0.999990i	$-0.498605\pi$
$107$	0.0906932			0.00876764			0.00438382	+	0.999990i	$0.498605\pi$
$108$		0			0
$109$	−0.344120			−0.0329607			−0.0164804	−	0.999864i	$-0.505246\pi$
$109$	−0.344120			−0.0329607			−0.0164804	+	0.999864i	$0.505246\pi$
$110$		0			0
$111$	−0.792982	+	15.6450i	−0.0752665	+	1.48496i
$112$		0			0
$113$	−3.40706	+	5.90120i	−0.320509	+	0.555138i	−0.980593	−	0.196054i	$-0.937187\pi$
$113$	−3.40706	+	5.90120i	−0.320509	+	0.555138i	0.660084	+	0.751192i	$0.270521\pi$
$114$		0			0
$115$	0.0245547	+	0.0425300i	0.00228974	+	0.00396595i
$116$		0			0
$117$	1.75501	−	2.43309i	0.162251	−	0.224940i
$118$		0			0
$119$	5.40687	+	9.36498i	0.495647	+	0.858486i
$120$		0			0
$121$	5.08850	−	8.81354i	0.462591	−	0.801231i
$122$		0			0
$123$	7.28815	+	4.71521i	0.657151	+	0.425156i
$124$		0			0
$125$	−7.35187			−0.657571
$126$		0			0
$127$	−2.71040			−0.240509			−0.120254	−	0.992743i	$-0.538371\pi$
$127$	−2.71040			−0.240509			−0.120254	+	0.992743i	$0.538371\pi$
$128$		0			0
$129$	0.633053	−	0.323927i	0.0557372	−	0.0285202i
$130$		0			0
$131$	9.92814	−	17.1960i	0.867425	−	1.50242i	0.00280673	−	0.999996i	$-0.499107\pi$
$131$	9.92814	−	17.1960i	0.867425	−	1.50242i	0.864619	−	0.502429i	$-0.167560\pi$
$132$		0			0
$133$	1.02070	+	1.76791i	0.0885063	+	0.153297i
$134$		0			0
$135$	−3.17599	−	2.54488i	−0.273346	−	0.219029i
$136$		0			0
$137$	−3.89365	−	6.74400i	−0.332657	−	0.576179i	0.650375	−	0.759613i	$-0.274612\pi$
$137$	−3.89365	−	6.74400i	−0.332657	−	0.576179i	−0.983032	+	0.183434i	$0.941279\pi$
$138$		0			0
$139$	11.3241	−	19.6139i	0.960496	−	1.66363i	0.239239	−	0.970961i	$-0.423102\pi$
$139$	11.3241	−	19.6139i	0.960496	−	1.66363i	0.721257	−	0.692667i	$-0.243564\pi$
$140$		0			0
$141$	−4.12332	+	2.10986i	−0.347246	+	0.177683i
$142$		0			0
$143$	0.907192			0.0758632
$144$		0			0
$145$	4.03785			0.335325
$146$		0			0
$147$	−6.23405	−	4.03324i	−0.514176	−	0.332656i
$148$		0			0
$149$	4.55163	−	7.88365i	0.372884	−	0.645854i	−0.617124	−	0.786866i	$-0.711702\pi$
$149$	4.55163	−	7.88365i	0.372884	−	0.645854i	0.990008	+	0.141012i	$0.0450357\pi$
$150$		0			0
$151$	−11.4156	−	19.7723i	−0.928985	−	1.60905i	−0.785023	−	0.619467i	$-0.787349\pi$
$151$	−11.4156	−	19.7723i	−0.928985	−	1.60905i	−0.143962	−	0.989583i	$-0.545984\pi$
$152$		0			0
$153$	19.5941	+	1.99141i	1.58409	+	0.160996i
$154$		0			0
$155$	0.616333	+	1.06752i	0.0495051	+	0.0857453i
$156$		0			0
$157$	6.16187	−	10.6727i	0.491770	−	0.851771i	−0.508185	−	0.861248i	$-0.669683\pi$
$157$	6.16187	−	10.6727i	0.491770	−	0.851771i	0.999955	+	0.00947673i	$0.00301658\pi$
$158$		0			0
$159$	−0.492436	+	9.71546i	−0.0390527	+	0.770486i
$160$		0			0
$161$	−0.103279			−0.00813953
$162$		0			0
$163$	3.95905			0.310097			0.155048	−	0.987907i	$-0.450447\pi$
$163$	3.95905			0.310097			0.155048	+	0.987907i	$0.450447\pi$
$164$		0			0
$165$	0.0622990	−	1.22912i	0.00484997	−	0.0956870i
$166$		0			0
$167$	−5.16495	+	8.94596i	−0.399676	+	0.692259i	−0.993686	−	0.112198i	$-0.964211\pi$
$167$	−5.16495	+	8.94596i	−0.399676	+	0.692259i	0.594010	+	0.804458i	$0.297544\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$		0			0
$171$	3.69897	+	0.375936i	0.282867	+	0.0287485i
$172$		0			0
$173$	−12.2845	−	21.2773i	−0.933971	−	1.61769i	−0.776458	−	0.630169i	$-0.782986\pi$
$173$	−12.2845	−	21.2773i	−0.933971	−	1.61769i	−0.157513	−	0.987517i	$-0.550348\pi$
$174$		0			0
$175$	3.61270	−	6.25738i	0.273094	−	0.473013i
$176$		0			0
$177$	9.14613	+	5.91726i	0.687465	+	0.444768i
$178$		0			0
$179$	11.3281			0.846698			0.423349	−	0.905967i	$-0.360854\pi$
$179$	11.3281			0.846698			0.423349	+	0.905967i	$0.360854\pi$
$180$		0			0
$181$	13.3886			0.995169			0.497584	−	0.867416i	$-0.334220\pi$
$181$	13.3886			0.995169			0.497584	+	0.867416i	$0.334220\pi$
$182$		0			0
$183$	2.42574	−	1.24123i	0.179316	−	0.0917543i
$184$		0			0
$185$	3.54189	−	6.13474i	0.260405	−	0.451035i
$186$		0			0
$187$	2.97787	+	5.15782i	0.217763	+	0.377177i
$188$		0			0
$189$	7.97458	−	3.10839i	0.580065	−	0.226102i
$190$		0			0
$191$	−3.99635	−	6.92189i	−0.289166	−	0.500850i	0.684445	−	0.729065i	$-0.260045\pi$
$191$	−3.99635	−	6.92189i	−0.289166	−	0.500850i	−0.973611	+	0.228214i	$0.926711\pi$
$192$		0			0
$193$	−7.50754	+	13.0034i	−0.540404	+	0.936008i	0.458476	+	0.888707i	$0.348395\pi$
$193$	−7.50754	+	13.0034i	−0.540404	+	0.936008i	−0.998881	+	0.0473010i	$0.984938\pi$
$194$		0			0
$195$	−1.20768	+	0.617960i	−0.0864840	+	0.0442530i
$196$		0			0
$197$	−0.883876			−0.0629736			−0.0314868	−	0.999504i	$-0.510024\pi$
$197$	−0.883876			−0.0629736			−0.0314868	+	0.999504i	$0.510024\pi$
$198$		0			0
$199$	−5.65447			−0.400835			−0.200417	−	0.979711i	$-0.564230\pi$
$199$	−5.65447			−0.400835			−0.200417	+	0.979711i	$0.564230\pi$
$200$		0			0
$201$	−19.6467	−	12.7108i	−1.38577	−	0.896550i
$202$		0			0
$203$	−4.24588	+	7.35408i	−0.298002	+	0.516155i
$204$		0			0
$205$	−1.96266	−	3.39942i	−0.137078	−	0.237426i
$206$		0			0
$207$	−0.110040	+	0.152557i	−0.00764834	+	0.0106034i
$208$		0			0
$209$	0.562160	+	0.973690i	0.0388854	+	0.0673515i
$210$		0			0
$211$	7.28894	−	12.6248i	0.501791	−	0.869128i	−0.498207	−	0.867058i	$-0.666008\pi$
$211$	7.28894	−	12.6248i	0.501791	−	0.869128i	0.999998	−	0.00206963i	$-0.000658783\pi$
$212$		0			0
$213$	−0.774362	+	15.2777i	−0.0530584	+	1.04681i
$214$		0			0
$215$	−0.321567			−0.0219307
$216$		0			0
$217$	−2.59235			−0.175980
$218$		0			0
$219$	0.213810	−	4.21835i	0.0144480	−	0.285050i
$220$		0			0
$221$	3.28251	−	5.68548i	0.220806	−	0.382447i
$222$		0			0
$223$	8.84781	+	15.3249i	0.592493	+	1.02623i	0.993895	+	0.110327i	$0.0351897\pi$
$223$	8.84781	+	15.3249i	0.592493	+	1.02623i	−0.401402	+	0.915902i	$0.631477\pi$
$224$		0			0
$225$	−5.39376	−	12.0035i	−0.359584	−	0.800231i
$226$		0			0
$227$	−1.77180	−	3.06885i	−0.117599	−	0.203687i	0.801217	−	0.598374i	$-0.204186\pi$
$227$	−1.77180	−	3.06885i	−0.117599	−	0.203687i	−0.918816	+	0.394687i	$0.870853\pi$
$228$		0			0
$229$	1.06782	−	1.84951i	0.0705634	−	0.122219i	−0.828585	−	0.559863i	$-0.810854\pi$
$229$	1.06782	−	1.84951i	0.0705634	−	0.122219i	0.899148	+	0.437644i	$0.144187\pi$
$230$		0			0
$231$	2.17307	+	1.40591i	0.142978	+	0.0925021i
$232$		0			0
$233$	−1.87149			−0.122606			−0.0613028	−	0.998119i	$-0.519526\pi$
$233$	−1.87149			−0.122606			−0.0613028	+	0.998119i	$0.519526\pi$
$234$		0			0
$235$	2.09449			0.136630
$236$		0			0
$237$	6.79094	−	3.47486i	0.441119	−	0.225717i
$238$		0			0
$239$	7.88260	−	13.6531i	0.509883	−	0.883144i	−0.490051	−	0.871694i	$-0.663022\pi$
$239$	7.88260	−	13.6531i	0.509883	−	0.883144i	0.999934	−	0.0114499i	$-0.00364471\pi$
$240$		0			0
$241$	13.9202	+	24.1105i	0.896678	+	1.55309i	0.831715	+	0.555203i	$0.187360\pi$
$241$	13.9202	+	24.1105i	0.896678	+	1.55309i	0.0649628	+	0.997888i	$0.479307\pi$
$242$		0			0
$243$	3.90514	−	15.0914i	0.250515	−	0.968113i
$244$		0			0
$245$	1.67879	+	2.90775i	0.107254	+	0.185770i
$246$		0			0
$247$	0.619670	−	1.07330i	0.0394287	−	0.0682924i
$248$		0			0
$249$	18.3869	−	9.40841i	1.16522	−	0.596234i
$250$		0			0
$251$	6.37044			0.402099			0.201049	−	0.979581i	$-0.435565\pi$
$251$	6.37044			0.402099			0.201049	+	0.979581i	$0.435565\pi$
$252$		0			0
$253$	−0.0568816			−0.00357612
$254$		0			0
$255$	−7.47763	−	4.83779i	−0.468268	−	0.302954i
$256$		0			0
$257$	−13.5076	+	23.3958i	−0.842579	+	1.45939i	0.0451291	+	0.998981i	$0.485630\pi$
$257$	−13.5076	+	23.3958i	−0.842579	+	1.45939i	−0.887708	+	0.460408i	$0.847703\pi$
$258$		0			0
$259$	7.44874	+	12.9016i	0.462842	+	0.801666i
$260$		0			0
$261$	6.33910	+	14.1072i	0.392380	+	0.873216i
$262$		0			0
$263$	−4.53371	−	7.85262i	−0.279561	−	0.484213i	0.691715	−	0.722171i	$-0.256855\pi$
$263$	−4.53371	−	7.85262i	−0.279561	−	0.484213i	−0.971276	+	0.237957i	$0.923522\pi$
$264$		0			0
$265$	2.19949	−	3.80963i	0.135114	−	0.234024i
$266$		0			0
$267$	−1.01899	+	20.1040i	−0.0623609	+	1.23034i
$268$		0			0
$269$	13.3977			0.816871			0.408435	−	0.912787i	$-0.366075\pi$
$269$	13.3977			0.816871			0.408435	+	0.912787i	$0.366075\pi$
$270$		0			0
$271$	0.397183			0.0241271			0.0120636	−	0.999927i	$-0.496160\pi$
$271$	0.397183			0.0241271			0.0120636	+	0.999927i	$0.496160\pi$
$272$		0			0
$273$	0.144421	−	2.84933i	0.00874073	−	0.172449i
$274$		0			0
$275$	1.98972	−	3.44629i	0.119985	−	0.207819i
$276$		0			0
$277$	−3.60417	−	6.24260i	−0.216553	−	0.375081i	0.737199	−	0.675676i	$-0.236148\pi$
$277$	−3.60417	−	6.24260i	−0.216553	−	0.375081i	−0.953752	+	0.300595i	$0.902815\pi$
$278$		0			0
$279$	−2.76206	+	3.82924i	−0.165360	+	0.229250i
$280$		0			0
$281$	9.09016	+	15.7446i	0.542274	+	0.939245i	0.998773	+	0.0495217i	$0.0157697\pi$
$281$	9.09016	+	15.7446i	0.542274	+	0.939245i	−0.456499	+	0.889724i	$0.650897\pi$
$282$		0			0
$283$	11.4890	−	19.8995i	0.682950	−	1.18290i	−0.291126	−	0.956685i	$-0.594030\pi$
$283$	11.4890	−	19.8995i	0.682950	−	1.18290i	0.974076	−	0.226220i	$-0.0726367\pi$
$284$		0			0
$285$	−1.41162	−	0.913275i	−0.0836172	−	0.0540977i
$286$		0			0
$287$	8.25509			0.487282
$288$		0			0
$289$	26.0996			1.53527
$290$		0			0
$291$	−3.81602	+	1.95262i	−0.223699	+	0.114465i
$292$		0			0
$293$	−12.3080	+	21.3181i	−0.719041	+	1.24542i	0.242339	+	0.970192i	$0.422085\pi$
$293$	−12.3080	+	21.3181i	−0.719041	+	1.24542i	−0.961380	+	0.275224i	$0.911248\pi$
$294$		0			0
$295$	−2.46300	−	4.26604i	−0.143401	−	0.248378i
$296$		0			0
$297$	4.39205	−	1.71197i	0.254853	−	0.0993383i
$298$		0			0
$299$	0.0313504	+	0.0543004i	0.00181304	+	0.00314028i
$300$		0			0
$301$	0.338134	−	0.585665i	0.0194897	−	0.0337572i
$302$		0			0
$303$	−9.52787	+	4.87532i	−0.547362	+	0.280080i
$304$		0			0
$305$	−1.23219			−0.0705548
$306$		0			0
$307$	−18.2640			−1.04238			−0.521191	−	0.853440i	$-0.674512\pi$
$307$	−18.2640			−1.04238			−0.521191	+	0.853440i	$0.674512\pi$
$308$		0			0
$309$	8.71167	+	5.63618i	0.495590	+	0.320631i
$310$		0			0
$311$	−5.13363	+	8.89171i	−0.291102	+	0.504203i	−0.974070	−	0.226245i	$-0.927355\pi$
$311$	−5.13363	+	8.89171i	−0.291102	+	0.504203i	0.682969	+	0.730447i	$0.260688\pi$
$312$		0			0
$313$	10.6619	+	18.4669i	0.602646	+	1.04381i	0.992419	+	0.122902i	$0.0392201\pi$
$313$	10.6619	+	18.4669i	0.602646	+	1.04381i	−0.389773	+	0.920911i	$0.627447\pi$
$314$		0			0
$315$	−3.85054	−	0.391341i	−0.216953	−	0.0220495i
$316$		0			0
$317$	−11.7713	−	20.3886i	−0.661145	−	1.14514i	−0.980315	−	0.197439i	$-0.936738\pi$
$317$	−11.7713	−	20.3886i	−0.661145	−	1.14514i	0.319171	−	0.947697i	$-0.396596\pi$
$318$		0			0
$319$	−2.33845	+	4.05031i	−0.130928	+	0.226774i
$320$		0			0
$321$	0.00795178	−	0.156884i	0.000443825	−	0.00875640i
$322$		0			0
$323$	8.13630			0.452716
$324$		0			0
$325$	−4.38654			−0.243322
$326$		0			0
$327$	−0.0301717	+	0.595269i	−0.00166850	+	0.0329185i
$328$		0			0
$329$	−2.20240	+	3.81467i	−0.121422	+	0.210309i
$330$		0			0
$331$	−6.60197	−	11.4349i	−0.362877	−	0.628521i	0.625556	−	0.780179i	$-0.284872\pi$
$331$	−6.60197	−	11.4349i	−0.362877	−	0.628521i	−0.988433	+	0.151658i	$0.951539\pi$
$332$		0			0
$333$	26.9937	+	2.74345i	1.47925	+	0.150340i
$334$		0			0
$335$	5.29073	+	9.16382i	0.289064	+	0.500673i
$336$		0			0
$337$	−9.78511	+	16.9483i	−0.533029	+	0.923233i	0.466227	+	0.884665i	$0.345613\pi$
$337$	−9.78511	+	16.9483i	−0.533029	+	0.923233i	−0.999256	+	0.0385678i	$0.987720\pi$
$338$		0			0
$339$	9.90934	+	6.41103i	0.538202	+	0.348200i
$340$		0			0
$341$	−1.42775			−0.0773171
$342$		0			0
$343$	−18.5914			−1.00384
$344$		0			0
$345$	0.0757226	−	0.0387466i	0.00407677	−	0.00208604i
$346$		0			0
$347$	11.4262	−	19.7908i	0.613392	−	1.06243i	−0.377272	−	0.926102i	$-0.623138\pi$
$347$	11.4262	−	19.7908i	0.613392	−	1.06243i	0.990664	−	0.136324i	$-0.0435288\pi$
$348$		0			0
$349$	3.12860	+	5.41890i	0.167470	+	0.290067i	0.937530	−	0.347905i	$-0.113107\pi$
$349$	3.12860	+	5.41890i	0.167470	+	0.290067i	−0.770059	+	0.637972i	$0.779773\pi$
$350$		0			0
$351$	−4.05496	−	3.24920i	−0.216438	−	0.173429i
$352$		0			0
$353$	4.99749	+	8.65590i	0.265989	+	0.460707i	0.967822	−	0.251634i	$-0.0809681\pi$
$353$	4.99749	+	8.65590i	0.265989	+	0.460707i	−0.701833	+	0.712342i	$0.747635\pi$
$354$		0			0
$355$	3.45873	−	5.99070i	0.183570	−	0.317953i
$356$		0			0
$357$	16.6739	−	8.53187i	0.882475	−	0.451554i
$358$		0			0
$359$	−20.8670			−1.10132			−0.550658	−	0.834731i	$-0.685623\pi$
$359$	−20.8670			−1.10132			−0.550658	+	0.834731i	$0.685623\pi$
$360$		0			0
$361$	−17.4640			−0.919160
$362$		0			0
$363$	−14.7998	−	9.57500i	−0.776787	−	0.502557i
$364$		0			0
$365$	−0.954996	+	1.65410i	−0.0499868	+	0.0865796i
$366$		0			0
$367$	−7.87705	−	13.6434i	−0.411179	−	0.712182i	0.583840	−	0.811869i	$-0.301549\pi$
$367$	−7.87705	−	13.6434i	−0.411179	−	0.712182i	−0.995019	+	0.0996863i	$0.968216\pi$
$368$		0			0
$369$	8.79552	−	12.1938i	0.457876	−	0.634786i
$370$		0			0
$371$	4.62562	+	8.01180i	0.240150	+	0.415952i
$372$		0			0
$373$	−14.9651	+	25.9204i	−0.774865	+	1.34211i	0.160006	+	0.987116i	$0.448849\pi$
$373$	−14.9651	+	25.9204i	−0.774865	+	1.34211i	−0.934871	+	0.354989i	$0.884485\pi$
$374$		0			0
$375$	−0.644596	+	12.7175i	−0.0332868	+	0.656728i
$376$		0			0
$377$	5.15535			0.265514
$378$		0			0
$379$	−19.3193			−0.992365			−0.496183	−	0.868218i	$-0.665265\pi$
$379$	−19.3193			−0.992365			−0.496183	+	0.868218i	$0.665265\pi$
$380$		0			0
$381$	−0.237642	+	4.68853i	−0.0121748	+	0.240201i
$382$		0			0
$383$	7.62165	−	13.2011i	0.389448	−	0.674544i	−0.602927	−	0.797796i	$-0.705999\pi$
$383$	7.62165	−	13.2011i	0.389448	−	0.674544i	0.992375	+	0.123252i	$0.0393325\pi$
$384$		0			0
$385$	−0.585196	−	1.01359i	−0.0298243	−	0.0516573i
$386$		0			0
$387$	−0.504834	−	1.12347i	−0.0256622	−	0.0571094i
$388$		0			0
$389$	9.49426	+	16.4445i	0.481378	+	0.833771i	0.999772	−	0.0213711i	$-0.00680316\pi$
$389$	9.49426	+	16.4445i	0.481378	+	0.833771i	−0.518394	+	0.855142i	$0.673470\pi$
$390$		0			0
$391$	−0.205816	+	0.356484i	−0.0104086	+	0.0180282i
$392$		0			0
$393$	−28.8757	−	18.6817i	−1.45659	−	0.942367i
$394$		0			0
$395$	−3.44954			−0.173565
$396$		0			0
$397$	−25.4889			−1.27925			−0.639626	−	0.768686i	$-0.720911\pi$
$397$	−25.4889			−1.27925			−0.639626	+	0.768686i	$0.720911\pi$
$398$		0			0
$399$	3.14768	−	1.61064i	0.157581	−	0.0806328i
$400$		0			0
$401$	−7.28076	+	12.6106i	−0.363584	+	0.629746i	−0.988548	−	0.150908i	$-0.951780\pi$
$401$	−7.28076	+	12.6106i	−0.363584	+	0.629746i	0.624964	+	0.780654i	$0.285114\pi$
$402$		0			0
$403$	0.786907	+	1.36296i	0.0391986	+	0.0678940i
$404$		0			0
$405$	−4.68068	+	5.27079i	−0.232585	+	0.261908i
$406$		0			0
$407$	4.10244	+	7.10564i	0.203351	+	0.352214i
$408$		0			0
$409$	13.3650	−	23.1489i	0.660857	−	1.14464i	−0.319533	−	0.947575i	$-0.603526\pi$
$409$	13.3650	−	23.1489i	0.660857	−	1.14464i	0.980391	−	0.197063i	$-0.0631405\pi$
$410$		0			0
$411$	−12.0074	+	6.14406i	−0.592280	+	0.303064i
$412$		0			0
$413$	10.3596			0.509761
$414$		0			0
$415$	−9.33986			−0.458476
$416$		0			0
$417$	−32.9358	−	21.3084i	−1.61287	−	1.04348i
$418$		0			0
$419$	14.6383	−	25.3544i	0.715130	−	1.23864i	−0.247779	−	0.968816i	$-0.579701\pi$
$419$	14.6383	−	25.3544i	0.715130	−	1.23864i	0.962909	−	0.269825i	$-0.0869658\pi$
$420$		0			0
$421$	16.8068	+	29.1102i	0.819111	+	1.41874i	0.906338	+	0.422554i	$0.138866\pi$
$421$	16.8068	+	29.1102i	0.819111	+	1.41874i	−0.0872266	+	0.996188i	$0.527800\pi$
$422$		0			0
$423$	3.28818	+	7.31763i	0.159877	+	0.355795i
$424$		0			0
$425$	−14.3989	−	24.9396i	−0.698448	−	1.20975i
$426$		0			0
$427$	1.29567	−	2.24416i	0.0627017	−	0.108603i
$428$		0			0
$429$	0.0795406	−	1.56929i	0.00384026	−	0.0757660i
$430$		0			0
$431$	−25.7404			−1.23987			−0.619935	−	0.784653i	$-0.712841\pi$
$431$	−25.7404			−1.23987			−0.619935	+	0.784653i	$0.712841\pi$
$432$		0			0
$433$	2.97400			0.142921			0.0714607	−	0.997443i	$-0.477234\pi$
$433$	2.97400			0.142921			0.0714607	+	0.997443i	$0.477234\pi$
$434$		0			0
$435$	0.354030	−	6.98480i	0.0169744	−	0.334895i
$436$		0			0
$437$	−0.0388538	+	0.0672967i	−0.00185863	+	0.00321924i
$438$		0			0
$439$	−3.78711	−	6.55947i	−0.180749	−	0.313066i	0.761387	−	0.648298i	$-0.224519\pi$
$439$	−3.78711	−	6.55947i	−0.180749	−	0.313066i	−0.942136	+	0.335231i	$0.891185\pi$
$440$		0			0
$441$	−7.52340	+	10.4302i	−0.358257	+	0.496677i
$442$		0			0
$443$	2.35659	+	4.08174i	0.111965	+	0.193929i	0.916562	−	0.399891i	$-0.130952\pi$
$443$	2.35659	+	4.08174i	0.111965	+	0.193929i	−0.804597	+	0.593821i	$0.797619\pi$
$444$		0			0
$445$	4.55135	−	7.88318i	0.215755	−	0.373698i
$446$		0			0
$447$	−13.2383	−	8.56476i	−0.626150	−	0.405099i
$448$		0			0
$449$	−5.95827			−0.281188			−0.140594	−	0.990067i	$-0.544901\pi$
$449$	−5.95827			−0.281188			−0.140594	+	0.990067i	$0.544901\pi$
$450$		0			0
$451$	4.54654			0.214088
$452$		0			0
$453$	−35.2037	+	18.0134i	−1.65401	+	0.846343i
$454$		0			0
$455$	−0.645062	+	1.11728i	−0.0302410	+	0.0523789i
$456$		0			0
$457$	−4.39215	−	7.60743i	−0.205456	−	0.355861i	0.744822	−	0.667263i	$-0.232534\pi$
$457$	−4.39215	−	7.60743i	−0.205456	−	0.355861i	−0.950278	+	0.311403i	$0.899201\pi$
$458$		0			0
$459$	5.16276	−	33.7199i	0.240977	−	1.57391i
$460$		0			0
$461$	−7.22057	−	12.5064i	−0.336295	−	0.582480i	0.647438	−	0.762119i	$-0.275841\pi$
$461$	−7.22057	−	12.5064i	−0.336295	−	0.582480i	−0.983733	+	0.179638i	$0.942507\pi$
$462$		0			0
$463$	−4.95993	+	8.59085i	−0.230507	+	0.399250i	−0.957958	−	0.286910i	$-0.907372\pi$
$463$	−4.95993	+	8.59085i	−0.230507	+	0.399250i	0.727450	+	0.686161i	$0.240705\pi$
$464$		0			0
$465$	1.90067	−	0.972554i	0.0881414	−	0.0451011i
$466$		0			0
$467$	2.50545			0.115938			0.0579692	−	0.998318i	$-0.481537\pi$
$467$	2.50545			0.115938			0.0579692	+	0.998318i	$0.481537\pi$
$468$		0			0
$469$	−22.2532			−1.02756
$470$		0			0
$471$	−17.9216	−	11.5947i	−0.825786	−	0.534257i
$472$		0			0
$473$	0.186230	−	0.322559i	0.00856284	−	0.0148313i
$474$		0			0
$475$	−2.71821	−	4.70808i	−0.124720	−	0.216021i
$476$		0			0
$477$	16.7629	+	1.70366i	0.767522	+	0.0780053i
$478$		0			0
$479$	16.8818	+	29.2402i	0.771350	+	1.33602i	0.936823	+	0.349803i	$0.113751\pi$
$479$	16.8818	+	29.2402i	0.771350	+	1.33602i	−0.165474	+	0.986214i	$0.552915\pi$
$480$		0			0
$481$	4.52213	−	7.83256i	0.206192	−	0.357134i
$482$		0			0
$483$	−0.00905528	+	0.178655i	−0.000412030	+	0.00812910i
$484$		0			0
$485$	1.93839			0.0880180
$486$		0			0
$487$	−19.1173			−0.866289			−0.433144	−	0.901325i	$-0.642596\pi$
$487$	−19.1173			−0.866289			−0.433144	+	0.901325i	$0.642596\pi$
$488$		0			0
$489$	0.347121	−	6.84848i	0.0156973	−	0.309699i
$490$		0			0
$491$	−17.0555	+	29.5410i	−0.769703	+	1.33317i	0.168021	+	0.985783i	$0.446262\pi$
$491$	−17.0555	+	29.5410i	−0.769703	+	1.33317i	−0.937724	+	0.347382i	$0.887071\pi$
$492$		0			0
$493$	16.9225	+	29.3106i	0.762151	+	1.32008i
$494$		0			0
$495$	−2.12071	−	0.215534i	−0.0953189	−	0.00968751i
$496$		0			0
$497$	7.27384	+	12.5987i	0.326276	+	0.565127i
$498$		0			0
$499$	−19.6950	+	34.1127i	−0.881669	+	1.52710i	−0.0321850	+	0.999482i	$0.510247\pi$
$499$	−19.6950	+	34.1127i	−0.881669	+	1.52710i	−0.849484	+	0.527614i	$0.823087\pi$
$500$		0			0
$501$	15.0221	+	9.71886i	0.671140	+	0.434207i
$502$		0			0
$503$	16.1236			0.718915			0.359458	−	0.933161i	$-0.382962\pi$
$503$	16.1236			0.718915			0.359458	+	0.933161i	$0.382962\pi$
$504$		0			0
$505$	4.83980			0.215368
$506$		0			0
$507$	−1.54192	+	0.788984i	−0.0684789	+	0.0350400i
$508$		0			0
$509$	1.21074	−	2.09706i	0.0536650	−	0.0929505i	−0.837945	−	0.545755i	$-0.816243\pi$
$509$	1.21074	−	2.09706i	0.0536650	−	0.0929505i	0.891610	+	0.452804i	$0.149576\pi$
$510$		0			0
$511$	−2.00839	−	3.47864i	−0.0888461	−	0.153886i
$512$		0			0
$513$	0.974622	−	6.36562i	0.0430306	−	0.281049i
$514$		0			0
$515$	−2.34600	−	4.06339i	−0.103377	−	0.179055i
$516$		0			0
$517$	−1.21299	+	2.10095i	−0.0533470	+	0.0923998i
$518$		0			0
$519$	−37.8832	+	19.3845i	−1.66289	+	0.850885i
$520$		0			0
$521$	−0.682475			−0.0298998			−0.0149499	−	0.999888i	$-0.504759\pi$
$521$	−0.682475			−0.0298998			−0.0149499	+	0.999888i	$0.504759\pi$
$522$		0			0
$523$	−14.6293			−0.639694			−0.319847	−	0.947469i	$-0.603632\pi$
$523$	−14.6293			−0.639694			−0.319847	+	0.947469i	$0.603632\pi$
$524$		0			0
$525$	−10.5075	−	6.79799i	−0.458583	−	0.296689i
$526$		0			0
$527$	−5.16606	+	8.94789i	−0.225037	+	0.389776i
$528$		0			0
$529$	11.4980	+	19.9152i	0.499915	+	0.865877i
$530$		0			0
$531$	11.0378	−	15.3024i	0.478998	−	0.664069i
$532$		0			0
$533$	−2.50583	−	4.34023i	−0.108540	−	0.187996i
$534$		0			0
$535$	−0.0355171	+	0.0615173i	−0.00153554	+	0.00265963i
$536$		0			0
$537$	0.993219	−	19.5956i	0.0428606	−	0.845613i
$538$		0			0
$539$	−3.88897			−0.167510
$540$		0			0
$541$	−2.04386			−0.0878726			−0.0439363	−	0.999034i	$-0.513990\pi$
$541$	−2.04386			−0.0878726			−0.0439363	+	0.999034i	$0.513990\pi$
$542$		0			0
$543$	1.17389	−	23.1600i	0.0503762	−	0.993893i
$544$		0			0
$545$	0.134763	−	0.233417i	0.00577263	−	0.00999849i
$546$		0			0
$547$	2.16424	+	3.74857i	0.0925360	+	0.160277i	0.908578	−	0.417716i	$-0.137169\pi$
$547$	2.16424	+	3.74857i	0.0925360	+	0.160277i	−0.816042	+	0.577993i	$0.803836\pi$
$548$		0			0
$549$	−1.93443	−	4.30495i	−0.0825596	−	0.183731i
$550$		0			0
$551$	3.19461	+	5.53323i	0.136095	+	0.235724i
$552$		0			0
$553$	3.62726	−	6.28260i	0.154247	−	0.267163i
$554$		0			0
$555$	−10.3015	−	6.66476i	−0.437275	−	0.282903i
$556$		0			0
$557$	22.3991			0.949080			0.474540	−	0.880234i	$-0.342615\pi$
$557$	22.3991			0.949080			0.474540	+	0.880234i	$0.342615\pi$
$558$		0			0
$559$	−0.410562			−0.0173649
$560$		0			0
$561$	9.18325	−	4.69898i	0.387717	−	0.198391i
$562$		0			0
$563$	9.57770	−	16.5891i	0.403652	−	0.699146i	−0.590511	−	0.807029i	$-0.701074\pi$
$563$	9.57770	−	16.5891i	0.403652	−	0.699146i	0.994164	+	0.107883i	$0.0344073\pi$
$564$		0			0
$565$	−2.66853	−	4.62203i	−0.112266	−	0.194450i
$566$		0			0
$567$	−4.67779	−	14.0672i	−0.196449	−	0.590767i
$568$		0			0
$569$	3.73147	+	6.46310i	0.156431	+	0.270947i	0.933579	−	0.358371i	$-0.116668\pi$
$569$	3.73147	+	6.46310i	0.156431	+	0.270947i	−0.777148	+	0.629318i	$0.783334\pi$
$570$		0			0
$571$	−5.63821	+	9.76566i	−0.235952	+	0.408680i	−0.959549	−	0.281542i	$-0.909154\pi$
$571$	−5.63821	+	9.76566i	−0.235952	+	0.408680i	0.723597	+	0.690223i	$0.242487\pi$
$572$		0			0
$573$	−12.3241	+	6.30612i	−0.514846	+	0.263442i
$574$		0			0
$575$	0.275040			0.0114699
$576$		0			0
$577$	−14.6801			−0.611139			−0.305569	−	0.952170i	$-0.598847\pi$
$577$	−14.6801			−0.611139			−0.305569	+	0.952170i	$0.598847\pi$
$578$		0			0
$579$	21.8355	+	14.1269i	0.907452	+	0.587093i
$580$		0			0
$581$	9.82104	−	17.0105i	0.407445	−	0.705716i
$582$		0			0
$583$	2.54759	+	4.41255i	0.105510	+	0.182749i
$584$		0			0
$585$	0.963079	+	2.14327i	0.0398184	+	0.0886132i
$586$		0			0
$587$	3.29463	+	5.70647i	0.135984	+	0.235531i	0.925973	−	0.377590i	$-0.123247\pi$
$587$	3.29463	+	5.70647i	0.135984	+	0.235531i	−0.789989	+	0.613121i	$0.789914\pi$
$588$		0			0
$589$	−0.975245	+	1.68917i	−0.0401843	+	0.0696012i
$590$		0			0
$591$	−0.0774963	+	1.52896i	−0.00318777	+	0.0628928i
$592$		0			0
$593$	16.7923			0.689577			0.344789	−	0.938680i	$-0.387951\pi$
$593$	16.7923			0.689577			0.344789	+	0.938680i	$0.387951\pi$
$594$		0			0
$595$	−8.46970			−0.347224
$596$		0			0
$597$	−0.495772	+	9.78128i	−0.0202906	+	0.400321i
$598$		0			0
$599$	18.2838	−	31.6684i	0.747054	−	1.29394i	−0.202175	−	0.979350i	$-0.564801\pi$
$599$	18.2838	−	31.6684i	0.747054	−	1.29394i	0.949229	−	0.314586i	$-0.101866\pi$
$600$		0			0
$601$	12.5056	+	21.6603i	0.510114	+	0.883543i	0.999931	+	0.0117182i	$0.00373010\pi$
$601$	12.5056	+	21.6603i	0.510114	+	0.883543i	−0.489817	+	0.871825i	$0.662937\pi$
$602$		0			0
$603$	−23.7101	+	32.8710i	−0.965549	+	1.33861i
$604$		0			0
$605$	3.98549	+	6.90308i	0.162033	+	0.280650i
$606$		0			0
$607$	−8.40051	+	14.5501i	−0.340966	+	0.590571i	−0.984612	−	0.174752i	$-0.944088\pi$
$607$	−8.40051	+	14.5501i	−0.340966	+	0.590571i	0.643646	+	0.765323i	$0.277421\pi$
$608$		0			0
$609$	12.3490	+	7.98944i	0.500408	+	0.323748i
$610$		0			0
$611$	2.67415			0.108185
$612$		0			0
$613$	−23.6467			−0.955080			−0.477540	−	0.878610i	$-0.658471\pi$
$613$	−23.6467			−0.955080			−0.477540	+	0.878610i	$0.658471\pi$
$614$		0			0
$615$	−6.05250	+	3.09701i	−0.244060	+	0.124883i
$616$		0			0
$617$	0.438019	−	0.758671i	0.0176340	−	0.0305429i	−0.857074	−	0.515194i	$-0.827720\pi$
$617$	0.438019	−	0.758671i	0.0176340	−	0.0305429i	0.874708	+	0.484651i	$0.161053\pi$
$618$		0			0
$619$	−4.52703	−	7.84105i	−0.181957	−	0.315158i	0.760590	−	0.649232i	$-0.224910\pi$
$619$	−4.52703	−	7.84105i	−0.181957	−	0.315158i	−0.942547	+	0.334074i	$0.891576\pi$
$620$		0			0
$621$	0.254249	+	0.203727i	0.0102027	+	0.00817528i
$622$		0			0
$623$	9.57167	+	16.5786i	0.383481	+	0.664209i
$624$		0			0
$625$	−8.08723	+	14.0075i	−0.323489	+	0.560300i
$626$		0			0
$627$	1.73361	−	0.887070i	0.0692336	−	0.0354262i
$628$		0			0
$629$	59.3758			2.36747
$630$		0			0
$631$	−32.2900			−1.28544			−0.642722	−	0.766100i	$-0.722195\pi$
$631$	−32.2900			−1.28544			−0.642722	+	0.766100i	$0.722195\pi$
$632$		0			0
$633$	−21.1997	−	13.7155i	−0.842613	−	0.545144i
$634$		0			0
$635$	1.06144	−	1.83847i	0.0421220	−	0.0729574i
$636$		0			0
$637$	2.14341	+	3.71249i	0.0849249	+	0.147094i
$638$		0			0
$639$	26.3599	+	2.67903i	1.04278	+	0.105981i
$640$		0			0
$641$	−12.6305	−	21.8767i	−0.498876	−	0.864078i	0.501123	−	0.865376i	$-0.332920\pi$
$641$	−12.6305	−	21.8767i	−0.498876	−	0.864078i	−0.999999	+	0.00129777i	$0.999587\pi$
$642$		0			0
$643$	−5.26799	+	9.12443i	−0.207749	+	0.359833i	−0.951005	−	0.309175i	$-0.899947\pi$
$643$	−5.26799	+	9.12443i	−0.207749	+	0.359833i	0.743256	+	0.669007i	$0.233281\pi$
$644$		0			0
$645$	−0.0281943	+	0.556256i	−0.00111015	+	0.0219026i
$646$		0			0
$647$	−40.2888			−1.58392			−0.791958	−	0.610576i	$-0.790938\pi$
$647$	−40.2888			−1.58392			−0.791958	+	0.610576i	$0.790938\pi$
$648$		0			0
$649$	5.70560			0.223964
$650$		0			0
$651$	−0.227291	+	4.48432i	−0.00890825	+	0.175754i
$652$		0			0
$653$	−17.9808	+	31.1437i	−0.703643	+	1.21875i	0.263536	+	0.964650i	$0.415111\pi$
$653$	−17.9808	+	31.1437i	−0.703643	+	1.21875i	−0.967179	+	0.254096i	$0.918222\pi$
$654$		0			0
$655$	7.77607	+	13.4685i	0.303836	+	0.526260i
$656$		0			0
$657$	−7.27828	−	0.739711i	−0.283953	−	0.0288589i
$658$		0			0
$659$	−6.04085	−	10.4631i	−0.235318	−	0.407583i	0.724047	−	0.689751i	$-0.242280\pi$
$659$	−6.04085	−	10.4631i	−0.235318	−	0.407583i	−0.959365	+	0.282168i	$0.908946\pi$
$660$		0			0
$661$	−14.3989	+	24.9397i	−0.560054	+	0.970042i	0.437437	+	0.899249i	$0.355886\pi$
$661$	−14.3989	+	24.9397i	−0.560054	+	0.970042i	−0.997491	+	0.0707927i	$0.977447\pi$
$662$		0			0
$663$	−9.54711	−	6.17668i	−0.370779	−	0.239882i
$664$		0			0
$665$	−1.59890			−0.0620028
$666$		0			0
$667$	−0.323244			−0.0125161
$668$		0			0
$669$	27.2852	−	13.9616i	1.05491	−	0.539785i
$670$		0			0
$671$	0.713598	−	1.23599i	0.0275481	−	0.0477148i
$672$		0			0
$673$	−17.0876	−	29.5966i	−0.658680	−	1.14087i	−0.980958	−	0.194222i	$-0.937782\pi$
$673$	−17.0876	−	29.5966i	−0.658680	−	1.14087i	0.322278	−	0.946645i	$-0.395551\pi$
$674$		0			0
$675$	−21.2369	+	8.27786i	−0.817407	+	0.318615i
$676$		0			0
$677$	2.57282	+	4.45626i	0.0988815	+	0.171268i	0.911222	−	0.411916i	$-0.135140\pi$
$677$	2.57282	+	4.45626i	0.0988815	+	0.171268i	−0.812340	+	0.583184i	$0.801807\pi$
$678$		0			0
$679$	−2.03826	+	3.53037i	−0.0782212	+	0.135483i
$680$		0			0
$681$	−5.46394	+	2.79584i	−0.209378	+	0.107137i
$682$		0			0
$683$	18.3466			0.702013			0.351007	−	0.936373i	$-0.385839\pi$
$683$	18.3466			0.702013			0.351007	+	0.936373i	$0.385839\pi$
$684$		0			0
$685$	6.09929			0.233042
$686$		0			0
$687$	−3.10572	−	2.00930i	−0.118491	−	0.0766598i
$688$		0			0
$689$	2.80821	−	4.86397i	0.106984	−	0.185302i
$690$		0			0
$691$	15.0012	+	25.9828i	0.570671	+	0.988431i	0.996497	+	0.0836261i	$0.0266501\pi$
$691$	15.0012	+	25.9828i	0.570671	+	0.988431i	−0.425826	+	0.904805i	$0.640017\pi$
$692$		0			0
$693$	2.62252	−	3.63578i	0.0996212	−	0.138112i
$694$		0			0
$695$	8.86942	+	15.3623i	0.336436	+	0.582725i
$696$		0			0
$697$	16.4509	−	28.4937i	0.623121	−	1.07928i
$698$		0			0
$699$	−0.164089	+	3.23737i	−0.00620640	+	0.122448i
$700$		0			0
$701$	39.4795			1.49112			0.745559	−	0.666439i	$-0.232182\pi$
$701$	39.4795			1.49112			0.745559	+	0.666439i	$0.232182\pi$
$702$		0			0
$703$	11.2089			0.422753
$704$		0			0
$705$	0.183640	−	3.62311i	0.00691630	−	0.136454i
$706$		0			0
$707$	−5.08915	+	8.81466i	−0.191397	+	0.331509i
$708$		0			0
$709$	−9.70645	−	16.8121i	−0.364533	−	0.631390i	0.624168	−	0.781290i	$-0.285438\pi$
$709$	−9.70645	−	16.8121i	−0.364533	−	0.631390i	−0.988701	+	0.149900i	$0.952105\pi$
$710$		0			0
$711$	−5.41551	−	12.0518i	−0.203097	−	0.451980i
$712$		0			0
$713$	−0.0493397	−	0.0854588i	−0.00184779	−	0.00320046i
$714$		0			0
$715$	−0.355273	+	0.615350i	−0.0132864	+	0.0230128i
$716$		0			0
$717$	−22.9264	−	14.8326i	−0.856201	−	0.553935i
$718$		0			0
$719$	9.22733			0.344121			0.172061	−	0.985086i	$-0.444957\pi$
$719$	9.22733			0.344121			0.172061	+	0.985086i	$0.444957\pi$
$720$		0			0
$721$	9.86747			0.367484
$722$		0			0
$723$	42.9275	−	21.9656i	1.59649	−	0.816909i
$724$		0			0
$725$	11.3071	−	19.5844i	0.419934	−	0.727347i
$726$		0			0
$727$	23.8975	+	41.3916i	0.886308	+	1.53513i	0.844207	+	0.536017i	$0.180072\pi$
$727$	23.8975	+	41.3916i	0.886308	+	1.53513i	0.0421009	+	0.999113i	$0.486595\pi$
$728$		0			0
$729$	−25.7631	−	8.07842i	−0.954190	−	0.299201i
$730$		0			0
$731$	−1.34768	−	2.33424i	−0.0498456	−	0.0863351i
$732$		0			0
$733$	−12.8761	+	22.3021i	−0.475591	+	0.823748i	−0.999609	−	0.0279595i	$-0.991099\pi$
$733$	−12.8761	+	22.3021i	−0.475591	+	0.823748i	0.524018	+	0.851707i	$0.324432\pi$
$734$		0			0
$735$	5.17712	−	2.64908i	0.190961	−	0.0977128i
$736$		0			0
$737$	−12.2561			−0.451460
$738$		0			0
$739$	40.6762			1.49630			0.748148	−	0.663532i	$-0.230943\pi$
$739$	40.6762			1.49630			0.748148	+	0.663532i	$0.230943\pi$
$740$		0			0
$741$	−1.80230	−	1.16603i	−0.0662090	−	0.0428351i
$742$		0			0
$743$	−2.95037	+	5.11019i	−0.108239	+	0.187475i	−0.915057	−	0.403325i	$-0.867854\pi$
$743$	−2.95037	+	5.11019i	−0.108239	+	0.187475i	0.806818	+	0.590800i	$0.201188\pi$
$744$		0			0
$745$	3.56499	+	6.17475i	0.130611	+	0.226225i
$746$		0			0
$747$	−14.6628	−	32.6311i	−0.536485	−	1.19391i
$748$		0			0
$749$	−0.0746938	−	0.129373i	−0.00272925	−	0.00472720i
$750$		0			0
$751$	21.2182	−	36.7511i	0.774264	−	1.34107i	−0.160943	−	0.986964i	$-0.551453\pi$
$751$	21.2182	−	36.7511i	0.774264	−	1.34107i	0.935207	−	0.354101i	$-0.115213\pi$
$752$		0			0
$753$	0.558547	−	11.0198i	0.0203546	−	0.401583i
$754$		0			0
$755$	17.8821			0.650798
$756$		0			0
$757$	−40.5212			−1.47277			−0.736384	−	0.676564i	$-0.763468\pi$
$757$	−40.5212			−1.47277			−0.736384	+	0.676564i	$0.763468\pi$
$758$		0			0
$759$	−0.00498726	+	0.0983956i	−0.000181026	+	0.00357153i
$760$		0			0
$761$	−12.3039	+	21.3110i	−0.446017	+	0.772524i	−0.998122	−	0.0612501i	$-0.980491\pi$
$761$	−12.3039	+	21.3110i	−0.446017	+	0.772524i	0.552105	+	0.833774i	$0.313825\pi$
$762$		0			0
$763$	0.283413	+	0.490885i	0.0102602	+	0.0177712i
$764$		0			0
$765$	−9.02419	+	12.5109i	−0.326270	+	0.452331i
$766$		0			0
$767$	−3.14465	−	5.44669i	−0.113547	−	0.196669i
$768$		0			0
$769$	5.66189	−	9.80667i	0.204173	−	0.353638i	−0.745696	−	0.666286i	$-0.767883\pi$
$769$	5.66189	−	9.80667i	0.204173	−	0.353638i	0.949869	+	0.312649i	$0.101216\pi$
$770$		0			0
$771$	39.2864	+	25.4171i	1.41487	+	0.915374i
$772$		0			0
$773$	44.3945			1.59676			0.798380	−	0.602154i	$-0.205690\pi$
$773$	44.3945			1.59676			0.798380	+	0.602154i	$0.205690\pi$
$774$		0			0
$775$	6.90360			0.247985
$776$		0			0
$777$	22.9707	−	11.7539i	0.824068	−	0.421668i
$778$		0			0
$779$	3.10558	−	5.37902i	0.111269	−	0.192723i
$780$		0			0
$781$	4.00612	+	6.93880i	0.143350	+	0.248290i
$782$		0			0
$783$	24.9589	−	9.72867i	0.891960	−	0.347674i
$784$		0			0
$785$	4.82619	+	8.35921i	0.172254	+	0.298353i
$786$		0			0
$787$	−6.04833	+	10.4760i	−0.215600	+	0.373429i	−0.953458	−	0.301526i	$-0.902504\pi$
$787$	−6.04833	+	10.4760i	−0.215600	+	0.373429i	0.737858	+	0.674956i	$0.235837\pi$
$788$		0			0
$789$	−13.9812	+	7.15405i	−0.497744	+	0.254691i
$790$		0			0
$791$	11.2240			0.399081
$792$		0			0
$793$	−1.57320			−0.0558660
$794$		0			0
$795$	−6.39717	−	4.13877i	−0.226884	−	0.146787i
$796$		0			0
$797$	9.30467	−	16.1162i	0.329588	−	0.570864i	−0.652842	−	0.757494i	$-0.726423\pi$
$797$	9.30467	−	16.1162i	0.329588	−	0.570864i	0.982430	+	0.186631i	$0.0597567\pi$
$798$		0			0
$799$	8.77794	+	15.2038i	0.310541	+	0.537873i
$800$		0			0
$801$	34.6871	+	3.52534i	1.22561	+	0.124562i
$802$		0			0
$803$	−1.10614	−	1.91588i	−0.0390347	−	0.0676101i
$804$		0			0
$805$	0.0404459	−	0.0700544i	0.00142553	−	0.00246909i
$806$		0			0
$807$	1.17468	−	23.1757i	0.0413506	−	0.815823i
$808$		0			0
$809$	−0.352346			−0.0123878			−0.00619392	−	0.999981i	$-0.501972\pi$
$809$	−0.352346			−0.0123878			−0.00619392	+	0.999981i	$0.501972\pi$
$810$		0			0
$811$	49.6357			1.74295			0.871473	−	0.490444i	$-0.163165\pi$
$811$	49.6357			1.74295			0.871473	+	0.490444i	$0.163165\pi$
$812$		0			0
$813$	0.0348241	−	0.687059i	0.00122133	−	0.0240962i
$814$		0			0
$815$	−1.55043	+	2.68543i	−0.0543093	+	0.0940665i
$816$		0			0
$817$	−0.254413	−	0.440657i	−0.00890079	−	0.0154166i
$818$		0			0
$819$	−4.91620	−	0.499646i	−0.171786	−	0.0174591i
$820$		0			0
$821$	−3.18105	−	5.50974i	−0.111019	−	0.192291i	0.805162	−	0.593055i	$-0.202078\pi$
$821$	−3.18105	−	5.50974i	−0.111019	−	0.192291i	−0.916182	+	0.400764i	$0.868745\pi$
$822$		0			0
$823$	18.2846	−	31.6698i	0.637361	−	1.10394i	−0.348649	−	0.937253i	$-0.613360\pi$
$823$	18.2846	−	31.6698i	0.637361	−	1.10394i	0.986010	−	0.166688i	$-0.0533072\pi$
$824$		0			0
$825$	−5.78705	−	3.74404i	−0.201479	−	0.130351i
$826$		0			0
$827$	−15.3316			−0.533131			−0.266566	−	0.963817i	$-0.585889\pi$
$827$	−15.3316			−0.533131			−0.266566	+	0.963817i	$0.585889\pi$
$828$		0			0
$829$	−51.8318			−1.80019			−0.900096	−	0.435692i	$-0.856504\pi$
$829$	−51.8318			−1.80019			−0.900096	+	0.435692i	$0.856504\pi$
$830$		0			0
$831$	−11.1146	+	5.68726i	−0.385563	+	0.197289i
$832$		0			0
$833$	−14.0715	+	24.3726i	−0.487550	+	0.844461i
$834$		0			0
$835$	−4.04537	−	7.00679i	−0.139996	−	0.242480i
$836$		0			0
$837$	6.38176	+	5.11363i	0.220586	+	0.176753i
$838$		0			0
$839$	25.7655	+	44.6271i	0.889522	+	1.54070i	0.840441	+	0.541903i	$0.182296\pi$
$839$	25.7655	+	44.6271i	0.889522	+	1.54070i	0.0490810	+	0.998795i	$0.484371\pi$
$840$		0			0
$841$	1.21120	−	2.09785i	0.0417654	−	0.0723397i
$842$		0			0
$843$	28.0325	−	14.3440i	0.965492	−	0.494033i
$844$		0			0
$845$	0.783235			0.0269441
$846$		0			0
$847$	−16.7633			−0.575994
$848$		0			0
$849$	−33.4155	−	21.6188i	−1.14682	−	0.741954i
$850$		0			0
$851$	−0.283541	+	0.491108i	−0.00971967	+	0.0168350i
$852$		0			0
$853$	−15.6483	−	27.1036i	−0.535787	−	0.928010i	−0.999125	−	0.0418283i	$-0.986682\pi$
$853$	−15.6483	−	27.1036i	−0.535787	−	0.928010i	0.463338	−	0.886182i	$-0.346652\pi$
$854$		0			0
$855$	−1.70358	+	2.36179i	−0.0582611	+	0.0807716i
$856$		0			0
$857$	−5.95728	−	10.3183i	−0.203497	−	0.352467i	0.746156	−	0.665771i	$-0.231897\pi$
$857$	−5.95728	−	10.3183i	−0.203497	−	0.352467i	−0.949653	+	0.313305i	$0.898564\pi$
$858$		0			0
$859$	−11.5781	+	20.0538i	−0.395038	+	0.684227i	−0.993106	−	0.117219i	$-0.962602\pi$
$859$	−11.5781	+	20.0538i	−0.395038	+	0.684227i	0.598068	+	0.801446i	$0.295935\pi$
$860$		0			0
$861$	0.723788	−	14.2799i	0.0246666	−	0.486658i
$862$		0			0
$863$	−33.0833			−1.12617			−0.563084	−	0.826400i	$-0.690385\pi$
$863$	−33.0833			−1.12617			−0.563084	+	0.826400i	$0.690385\pi$
$864$		0			0
$865$	19.2433			0.654291
$866$		0			0
$867$	2.28835	−	45.1478i	0.0777165	−	1.53330i
$868$		0			0
$869$	1.99774	−	3.46019i	0.0677687	−	0.117379i
$870$		0			0
$871$	6.75497	+	11.7000i	0.228884	+	0.396438i
$872$		0			0
$873$	3.04312	+	6.77227i	0.102994	+	0.229207i
$874$		0			0
$875$	6.05491	+	10.4874i	0.204693	+	0.354539i
$876$		0			0
$877$	12.3320	−	21.3596i	0.416421	−	0.721262i	−0.579156	−	0.815217i	$-0.696618\pi$
$877$	12.3320	−	21.3596i	0.416421	−	0.721262i	0.995576	+	0.0939551i	$0.0299510\pi$
$878$		0			0
$879$	35.7975	+	23.1599i	1.20742	+	0.781163i
$880$		0			0
$881$	−41.9696			−1.41399			−0.706996	−	0.707217i	$-0.749950\pi$
$881$	−41.9696			−1.41399			−0.706996	+	0.707217i	$0.749950\pi$
$882$		0			0
$883$	−17.7822			−0.598418			−0.299209	−	0.954188i	$-0.596723\pi$
$883$	−17.7822			−0.598418			−0.299209	+	0.954188i	$0.596723\pi$
$884$		0			0
$885$	−7.59547	+	3.88653i	−0.255319	+	0.130644i
$886$		0			0
$887$	13.1573	−	22.7890i	0.441777	−	0.765181i	−0.556044	−	0.831153i	$-0.687681\pi$
$887$	13.1573	−	22.7890i	0.441777	−	0.765181i	0.997821	+	0.0659721i	$0.0210148\pi$
$888$		0			0
$889$	2.23225	+	3.86637i	0.0748672	+	0.129674i
$890$		0			0
$891$	−2.57632	−	7.74760i	−0.0863101	−	0.259555i
$892$		0			0
$893$	1.65709	+	2.87017i	0.0554525	+	0.0960465i
$894$		0			0
$895$	−4.43627	+	7.68384i	−0.148288	+	0.256842i
$896$		0			0
$897$	0.0966793	−	0.0494699i	0.00322803	−	0.00165175i
$898$		0			0
$899$	−8.11356			−0.270602
$900$		0			0
$901$	36.8720			1.22838
$902$		0			0
$903$	−0.983454	−	0.636264i	−0.0327273	−	0.0211735i
$904$		0			0
$905$	−5.24322	+	9.08153i	−0.174291	+	0.301880i
$906$		0			0
$907$	−7.94116	−	13.7545i	−0.263682	−	0.456710i	0.703536	−	0.710660i	$-0.251604\pi$
$907$	−7.94116	−	13.7545i	−0.263682	−	0.456710i	−0.967217	+	0.253950i	$0.918270\pi$
$908$		0			0
$909$	7.59810	+	16.9091i	0.252013	+	0.560838i
$910$		0			0
$911$	−28.8078	−	49.8966i	−0.954445	−	1.65315i	−0.735633	−	0.677380i	$-0.763115\pi$
$911$	−28.8078	−	49.8966i	−0.954445	−	1.65315i	−0.218812	−	0.975767i	$-0.570218\pi$
$912$		0			0
$913$	5.40900	−	9.36867i	0.179012	−	0.310058i
$914$		0			0
$915$	−0.108035	+	2.13147i	−0.00357154	+	0.0704643i
$916$		0			0
$917$	−32.7067			−1.08007
$918$		0			0
$919$	41.0937			1.35555			0.677777	−	0.735267i	$-0.262943\pi$
$919$	41.0937			1.35555			0.677777	+	0.735267i	$0.262943\pi$
$920$		0			0
$921$	−1.60135	+	31.5936i	−0.0527662	+	1.04105i
$922$		0			0
$923$	4.41595	−	7.64865i	0.145353	−	0.251759i
$924$		0			0
$925$	−19.8365	−	34.3579i	−0.652221	−	1.12968i
$926$		0			0
$927$	10.5135	−	14.5755i	0.345307	−	0.478724i
$928$		0			0
$929$	−12.9823	−	22.4860i	−0.425935	−	0.737740i	0.570573	−	0.821247i	$-0.306721\pi$
$929$	−12.9823	−	22.4860i	−0.425935	−	0.737740i	−0.996507	+	0.0835069i	$0.973388\pi$
$930$		0			0
$931$	−2.65641	+	4.60104i	−0.0870604	+	0.150793i
$932$		0			0
$933$	14.9310	+	9.65992i	0.488820	+	0.316252i
$934$		0			0
$935$	−4.66475			−0.152554
$936$		0			0
$937$	−2.82397			−0.0922549			−0.0461275	−	0.998936i	$-0.514688\pi$
$937$	−2.82397			−0.0922549			−0.0461275	+	0.998936i	$0.514688\pi$
$938$		0			0
$939$	32.8795	−	16.8241i	1.07298	−	0.549034i
$940$		0			0
$941$	29.9326	−	51.8447i	0.975774	−	1.69009i	0.298416	−	0.954436i	$-0.403542\pi$
$941$	29.9326	−	51.8447i	0.975774	−	1.69009i	0.677357	−	0.735654i	$-0.263125\pi$
$942$		0			0
$943$	0.157118	+	0.272136i	0.00511645	+	0.00886196i
$944$		0			0
$945$	−1.01456	+	6.62647i	−0.0330036	+	0.215559i
$946$		0			0
$947$	1.75316	+	3.03656i	0.0569700	+	0.0986749i	0.893104	−	0.449850i	$-0.148523\pi$
$947$	1.75316	+	3.03656i	0.0569700	+	0.0986749i	−0.836134	+	0.548525i	$0.815189\pi$
$948$		0			0
$949$	−1.21930	+	2.11188i	−0.0395800	+	0.0685546i
$950$		0			0
$951$	−36.3008	+	18.5748i	−1.17714	+	0.602329i
$952$		0			0
$953$	46.8431			1.51740			0.758699	−	0.651442i	$-0.225835\pi$
$953$	46.8431			1.51740			0.758699	+	0.651442i	$0.225835\pi$
$954$		0			0
$955$	6.26017			0.202574
$956$		0			0
$957$	6.80131	+	4.40024i	0.219855	+	0.142239i
$958$		0			0
$959$	−6.41352	+	11.1085i	−0.207103	+	0.358714i
$960$		0			0
$961$	14.2616	+	24.7017i	0.460050	+	0.796830i
$962$		0			0
$963$	−0.270685	−	0.0275105i	−0.00872271	−	0.000886512i
$964$		0			0
$965$	−5.88017	−	10.1847i	−0.189289	−	0.327859i
$966$		0			0
$967$	4.21858	−	7.30679i	0.135660	−	0.234971i	−0.790189	−	0.612863i	$-0.790018\pi$
$967$	4.21858	−	7.30679i	0.135660	−	0.234971i	0.925850	+	0.377892i	$0.123351\pi$
$968$		0			0
$969$	0.713373	−	14.0744i	0.0229168	−	0.452135i
$970$		0			0
$971$	44.0574			1.41387			0.706935	−	0.707279i	$-0.250078\pi$
$971$	44.0574			1.41387			0.706935	+	0.707279i	$0.250078\pi$
$972$		0			0
$973$	−37.3055			−1.19596
$974$		0			0
$975$	−0.384602	+	7.58797i	−0.0123171	+	0.243010i
$976$		0			0
$977$	−4.63827	+	8.03373i	−0.148392	+	0.257022i	−0.930633	−	0.365953i	$-0.880743\pi$
$977$	−4.63827	+	8.03373i	−0.148392	+	0.257022i	0.782242	+	0.622975i	$0.214076\pi$
$978$		0			0
$979$	5.27166	+	9.13079i	0.168483	+	0.291821i
$980$		0			0
$981$	1.02707	+	0.104384i	0.0327918	+	0.00333272i
$982$		0			0
$983$	22.6276	+	39.1921i	0.721708	+	1.25003i	0.960315	+	0.278919i	$0.0899760\pi$
$983$	22.6276	+	39.1921i	0.721708	+	1.25003i	−0.238607	+	0.971116i	$0.576691\pi$
$984$		0			0
$985$	0.346142	−	0.599535i	0.0110290	−	0.0191028i
$986$		0			0
$987$	6.40562	+	4.14424i	0.203893	+	0.131913i
$988$		0			0
$989$	0.0257426			0.000818566
$990$		0			0
$991$	−15.1227			−0.480389			−0.240194	−	0.970725i	$-0.577211\pi$
$991$	−15.1227			−0.480389			−0.240194	+	0.970725i	$0.577211\pi$
$992$		0			0
$993$	−20.3594	+	10.4177i	−0.646085	+	0.330595i
$994$		0			0
$995$	2.21439	−	3.83544i	0.0702009	−	0.121592i
$996$		0			0
$997$	−22.1783	−	38.4139i	−0.702393	−	1.21658i	−0.967624	−	0.252395i	$-0.918782\pi$
$997$	−22.1783	−	38.4139i	−0.702393	−	1.21658i	0.265231	−	0.964185i	$-0.414552\pi$
$998$		0			0
$999$	7.11245	−	46.4541i	0.225028	−	1.46974i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.q.d.625.4	yes	12
3.2	odd	2		2808.2.q.d.1873.4		12
9.2	odd	6		2808.2.q.d.937.4		12
9.4	even	3		8424.2.a.v.1.4		6
9.5	odd	6		8424.2.a.u.1.3		6
9.7	even	3	inner	936.2.q.d.313.4	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.q.d.313.4	✓	12	9.7	even	3	inner
936.2.q.d.625.4	yes	12	1.1	even	1	trivial
2808.2.q.d.937.4		12	9.2	odd	6
2808.2.q.d.1873.4		12	3.2	odd	2
8424.2.a.u.1.3		6	9.5	odd	6
8424.2.a.v.1.4		6	9.4	even	3

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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0876778 - 1.72983i) q^{3} +(-0.391618 + 0.678302i) q^{5} +(-0.823587 - 1.42649i) q^{7} +(-2.98463 - 0.303335i) q^{9} +(-0.453596 - 0.785652i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(1.13901 + 0.736904i) q^{15} -6.56503 q^{17} -1.23934 q^{19} +(-2.53980 + 1.29959i) q^{21} +(0.0313504 - 0.0543004i) q^{23} +(2.19327 + 3.79886i) q^{25} +(-0.786404 + 5.13630i) q^{27} +(-2.57767 - 4.46466i) q^{29} +(0.786907 - 1.36296i) q^{31} +(-1.39881 + 0.715760i) q^{33} +1.29012 q^{35} -9.04427 q^{37} +(1.45424 + 0.940846i) q^{39} +(-2.50583 + 4.34023i) q^{41} +(0.205281 + 0.355557i) q^{43} +(1.37458 - 1.90568i) q^{45} +(-1.33708 - 2.31588i) q^{47} +(2.14341 - 3.71249i) q^{49} +(-0.575607 + 11.3564i) q^{51} -5.61642 q^{53} +0.710545 q^{55} +(-0.108663 + 2.14385i) q^{57} +(-3.14465 + 5.44669i) q^{59} +(0.786600 + 1.36243i) q^{61} +(2.02539 + 4.50738i) q^{63} +(-0.391618 - 0.678302i) q^{65} +(6.75497 - 11.7000i) q^{67} +(-0.0911818 - 0.0589918i) q^{69} -8.83191 q^{71} +2.43859 q^{73} +(6.76368 - 3.46091i) q^{75} +(-0.747152 + 1.29411i) q^{77} +(2.20211 + 3.81417i) q^{79} +(8.81598 + 1.81069i) q^{81} +(5.96236 + 10.3271i) q^{83} +(2.57098 - 4.45307i) q^{85} +(-7.94911 + 4.06749i) q^{87} -11.6219 q^{89} +1.64717 q^{91} +(-2.28870 - 1.48072i) q^{93} +(0.485347 - 0.840646i) q^{95} +(-1.23743 - 2.14329i) q^{97} +(1.11550 + 2.48247i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{3} - q^{5} + 2 q^{7} + 2 q^{9} - q^{11} - 6 q^{13} - 2 q^{15} + 12 q^{17} - 14 q^{19} - 24 q^{21} + 19 q^{23} + 5 q^{25} - 7 q^{27} - 2 q^{29} + 8 q^{31} - 9 q^{33} + 2 q^{35} - 34 q^{37}+ \cdots - 39 q^{99}+O(q^{100}) \) 12 * q - 4 * q^3 - q^5 + 2 * q^7 + 2 * q^9 - q^11 - 6 * q^13 - 2 * q^15 + 12 * q^17 - 14 * q^19 - 24 * q^21 + 19 * q^23 + 5 * q^25 - 7 * q^27 - 2 * q^29 + 8 * q^31 - 9 * q^33 + 2 * q^35 - 34 * q^37 - q^39 - 2 * q^41 + 15 * q^43 + 10 * q^45 - 9 * q^47 + 12 * q^49 + 4 * q^51 + 32 * q^53 - 10 * q^55 - 14 * q^57 + 5 * q^59 + 6 * q^61 + 18 * q^63 - q^65 + 8 * q^67 + 15 * q^69 - 42 * q^71 - 2 * q^73 + 10 * q^75 + 3 * q^77 + 34 * q^79 + 62 * q^81 + 44 * q^83 + 7 * q^85 - 21 * q^87 + 22 * q^89 - 4 * q^91 - 18 * q^93 + 6 * q^95 + 12 * q^97 - 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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