LMFDB - Embedded newform 864.2.bi.a.95.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(95,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 17]))

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

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

chi := DirichletCharacter("864.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bi (of order $18$, degree $6$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			95.14
Character	$\chi$	$=$	864.95
Dual form			864.2.bi.a.191.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.633406 - 1.61208i) q^{3} +(-2.10172 + 2.50473i) q^{5} +(1.57289 - 4.32148i) q^{7} +(-2.19759 + 2.04220i) q^{9} +O(q^{10})$	\(q+(-0.633406 - 1.61208i) q^{3} +(-2.10172 + 2.50473i) q^{5} +(1.57289 - 4.32148i) q^{7} +(-2.19759 + 2.04220i) q^{9} +(-2.44813 + 2.05422i) q^{11} +(0.0980972 - 0.556337i) q^{13} +(5.36906 + 1.80162i) q^{15} +(1.00153 + 0.578233i) q^{17} +(1.01157 - 0.584028i) q^{19} +(-7.96284 + 0.201628i) q^{21} +(-7.28981 + 2.65327i) q^{23} +(-0.988210 - 5.60442i) q^{25} +(4.68415 + 2.24915i) q^{27} +(-4.89664 + 0.863410i) q^{29} +(2.64270 + 7.26075i) q^{31} +(4.86222 + 2.64541i) q^{33} +(7.51836 + 13.0222i) q^{35} +(-5.15812 + 8.93412i) q^{37} +(-0.958994 + 0.194247i) q^{39} +(7.04687 + 1.24255i) q^{41} +(4.67905 + 5.57628i) q^{43} +(-0.496434 - 9.79650i) q^{45} +(-7.50664 - 2.73219i) q^{47} +(-10.8389 - 9.09490i) q^{49} +(0.297783 - 1.98080i) q^{51} +9.28205i q^{53} -10.4493i q^{55} +(-1.58223 - 1.26080i) q^{57} +(-2.63531 - 2.21129i) q^{59} +(-3.37704 - 1.22914i) q^{61} +(5.36875 + 12.7090i) q^{63} +(1.18730 + 1.41497i) q^{65} +(-1.71598 - 0.302574i) q^{67} +(8.89469 + 10.0711i) q^{69} +(5.83837 - 10.1124i) q^{71} +(5.76835 + 9.99107i) q^{73} +(-8.40883 + 5.14294i) q^{75} +(5.02664 + 13.8106i) q^{77} +(-4.94240 + 0.871479i) q^{79} +(0.658843 - 8.97585i) q^{81} +(0.225399 + 1.27830i) q^{83} +(-3.55325 + 1.29328i) q^{85} +(4.49344 + 7.34688i) q^{87} +(-2.30786 + 1.33244i) q^{89} +(-2.24990 - 1.29898i) q^{91} +(10.0310 - 8.85924i) q^{93} +(-0.663194 + 3.76116i) q^{95} +(-13.4491 + 11.2851i) q^{97} +(1.18486 - 9.51390i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q+O(q^{10}) $ 216 * q	$ 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) $ 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{17}{18}\right)$	$-1$

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
$3$	−0.633406	−	1.61208i	−0.365697	−	0.930734i
$3$	−0.633406	−	1.61208i	−0.365697	−	0.930734i
$4$		0			0
$5$	−2.10172	+	2.50473i	−0.939916	+	1.12015i	0.0526707	+	0.998612i	$0.483227\pi$
$5$	−2.10172	+	2.50473i	−0.939916	+	1.12015i	−0.992587	+	0.121537i	$0.961218\pi$
$6$		0			0
$7$	1.57289	−	4.32148i	0.594496	−	1.63336i	−0.167566	−	0.985861i	$-0.553591\pi$
$7$	1.57289	−	4.32148i	0.594496	−	1.63336i	0.762062	−	0.647504i	$-0.224187\pi$
$8$		0			0
$9$	−2.19759	+	2.04220i	−0.732531	+	0.680733i
$10$		0			0
$11$	−2.44813	+	2.05422i	−0.738137	+	0.619371i	−0.932337	−	0.361591i	$-0.882234\pi$
$11$	−2.44813	+	2.05422i	−0.738137	+	0.619371i	0.194199	+	0.980962i	$0.437789\pi$
$12$		0			0
$13$	0.0980972	−	0.556337i	0.0272073	−	0.154300i	−0.968177	−	0.250265i	$-0.919482\pi$
$13$	0.0980972	−	0.556337i	0.0272073	−	0.154300i	0.995385	+	0.0959644i	$0.0305935\pi$
$14$		0			0
$15$	5.36906	+	1.80162i	1.38628	+	0.465177i
$16$		0			0
$17$	1.00153	+	0.578233i	0.242906	+	0.140242i	0.616512	−	0.787346i	$-0.288545\pi$
$17$	1.00153	+	0.578233i	0.242906	+	0.140242i	−0.373605	+	0.927588i	$0.621879\pi$
$18$		0			0
$19$	1.01157	−	0.584028i	0.232069	−	0.133985i	−0.379457	−	0.925209i	$-0.623889\pi$
$19$	1.01157	−	0.584028i	0.232069	−	0.133985i	0.611526	+	0.791224i	$0.290556\pi$
$20$		0			0
$21$	−7.96284	+	0.201628i	−1.73763	+	0.0439987i
$22$		0			0
$23$	−7.28981	+	2.65327i	−1.52003	+	0.553246i	−0.961156	−	0.276007i	$-0.910989\pi$
$23$	−7.28981	+	2.65327i	−1.52003	+	0.553246i	−0.558874	+	0.829252i	$0.688767\pi$
$24$		0			0
$25$	−0.988210	−	5.60442i	−0.197642	−	1.12088i
$26$		0			0
$27$	4.68415	+	2.24915i	0.901466	+	0.432850i
$28$		0			0
$29$	−4.89664	+	0.863410i	−0.909283	+	0.160331i	−0.608678	−	0.793417i	$-0.708300\pi$
$29$	−4.89664	+	0.863410i	−0.909283	+	0.160331i	−0.300605	+	0.953749i	$0.597189\pi$
$30$		0			0
$31$	2.64270	+	7.26075i	0.474643	+	1.30407i	0.913984	+	0.405750i	$0.132990\pi$
$31$	2.64270	+	7.26075i	0.474643	+	1.30407i	−0.439342	+	0.898320i	$0.644788\pi$
$32$		0			0
$33$	4.86222	+	2.64541i	0.846404	+	0.460508i
$34$		0			0
$35$	7.51836	+	13.0222i	1.27083	+	2.20115i
$36$		0			0
$37$	−5.15812	+	8.93412i	−0.847989	+	1.46876i	0.0350104	+	0.999387i	$0.488854\pi$
$37$	−5.15812	+	8.93412i	−0.847989	+	1.46876i	−0.883000	+	0.469374i	$0.844480\pi$
$38$		0			0
$39$	−0.958994	+	0.194247i	−0.153562	+	0.0311044i
$40$		0			0
$41$	7.04687	+	1.24255i	1.10054	+	0.194054i	0.694280	−	0.719705i	$-0.255723\pi$
$41$	7.04687	+	1.24255i	1.10054	+	0.194054i	0.406256	+	0.913759i	$0.366834\pi$
$42$		0			0
$43$	4.67905	+	5.57628i	0.713549	+	0.850374i	0.993987	−	0.109498i	$-0.0349243\pi$
$43$	4.67905	+	5.57628i	0.713549	+	0.850374i	−0.280438	+	0.959872i	$0.590480\pi$
$44$		0			0
$45$	−0.496434	−	9.79650i	−0.0740040	−	1.46038i
$46$		0			0
$47$	−7.50664	−	2.73219i	−1.09496	−	0.398531i	−0.269501	−	0.963000i	$-0.586859\pi$
$47$	−7.50664	−	2.73219i	−1.09496	−	0.398531i	−0.825454	+	0.564469i	$0.809081\pi$
$48$		0			0
$49$	−10.8389	−	9.09490i	−1.54841	−	1.29927i
$50$		0			0
$51$	0.297783	−	1.98080i	0.0416979	−	0.277367i
$52$		0			0
$53$			9.28205i			1.27499i	0.770456	+	0.637494i	$0.220029\pi$
$53$			9.28205i			1.27499i	−0.770456	+	0.637494i	$0.779971\pi$
$54$		0			0
$55$		−	10.4493i		−	1.40898i
$56$		0			0
$57$	−1.58223	−	1.26080i	−0.209572	−	0.166997i
$58$		0			0
$59$	−2.63531	−	2.21129i	−0.343089	−	0.287886i	0.454919	−	0.890533i	$-0.349668\pi$
$59$	−2.63531	−	2.21129i	−0.343089	−	0.287886i	−0.798008	+	0.602647i	$0.794113\pi$
$60$		0			0
$61$	−3.37704	−	1.22914i	−0.432385	−	0.157375i	0.116653	−	0.993173i	$-0.462784\pi$
$61$	−3.37704	−	1.22914i	−0.432385	−	0.157375i	−0.549038	+	0.835797i	$0.685006\pi$
$62$		0			0
$63$	5.36875	+	12.7090i	0.676398	+	1.60118i
$64$		0			0
$65$	1.18730	+	1.41497i	0.147267	+	0.175505i
$66$		0			0
$67$	−1.71598	−	0.302574i	−0.209641	−	0.0369653i	0.0678415	−	0.997696i	$-0.478389\pi$
$67$	−1.71598	−	0.302574i	−0.209641	−	0.0369653i	−0.277482	+	0.960731i	$0.589500\pi$
$68$		0			0
$69$	8.89469	+	10.0711i	1.07079	+	1.21242i
$70$		0			0
$71$	5.83837	−	10.1124i	0.692887	−	1.20012i	−0.278001	−	0.960581i	$-0.589672\pi$
$71$	5.83837	−	10.1124i	0.692887	−	1.20012i	0.970888	−	0.239535i	$-0.0769949\pi$
$72$		0			0
$73$	5.76835	+	9.99107i	0.675134	+	1.16937i	0.976430	+	0.215836i	$0.0692477\pi$
$73$	5.76835	+	9.99107i	0.675134	+	1.16937i	−0.301295	+	0.953531i	$0.597419\pi$
$74$		0			0
$75$	−8.40883	+	5.14294i	−0.970968	+	0.593856i
$76$		0			0
$77$	5.02664	+	13.8106i	0.572839	+	1.57386i
$78$		0			0
$79$	−4.94240	+	0.871479i	−0.556064	+	0.0980490i	−0.444616	−	0.895721i	$-0.646660\pi$
$79$	−4.94240	+	0.871479i	−0.556064	+	0.0980490i	−0.111448	+	0.993770i	$0.535549\pi$
$80$		0			0
$81$	0.658843	−	8.97585i	0.0732048	−	0.997317i
$82$		0			0
$83$	0.225399	+	1.27830i	0.0247407	+	0.140312i	0.994676	−	0.103051i	$-0.0328605\pi$
$83$	0.225399	+	1.27830i	0.0247407	+	0.140312i	−0.969935	+	0.243363i	$0.921749\pi$
$84$		0			0
$85$	−3.55325	+	1.29328i	−0.385404	+	0.140275i
$86$		0			0
$87$	4.49344	+	7.34688i	0.481748	+	0.787668i
$88$		0			0
$89$	−2.30786	+	1.33244i	−0.244632	+	0.141238i	−0.617304	−	0.786725i	$-0.711775\pi$
$89$	−2.30786	+	1.33244i	−0.244632	+	0.141238i	0.372672	+	0.927963i	$0.378442\pi$
$90$		0			0
$91$	−2.24990	−	1.29898i	−0.235854	−	0.136170i
$92$		0			0
$93$	10.0310	−	8.85924i	1.04017	−	0.918660i
$94$		0			0
$95$	−0.663194	+	3.76116i	−0.0680423	+	0.385887i
$96$		0			0
$97$	−13.4491	+	11.2851i	−1.36555	+	1.14583i	−0.391325	+	0.920253i	$0.627983\pi$
$97$	−13.4491	+	11.2851i	−1.36555	+	1.14583i	−0.974225	+	0.225580i	$0.927572\pi$
$98$		0			0
$99$	1.18486	−	9.51390i	0.119083	−	0.956183i
$100$		0			0
$101$	4.39645	−	12.0791i	0.437463	−	1.20192i	−0.503674	−	0.863894i	$-0.668019\pi$
$101$	4.39645	−	12.0791i	0.437463	−	1.20192i	0.941137	−	0.338026i	$-0.109759\pi$
$102$		0			0
$103$	−7.79944	+	9.29501i	−0.768502	+	0.915865i	−0.998354	−	0.0573608i	$-0.981731\pi$
$103$	−7.79944	+	9.29501i	−0.768502	+	0.915865i	0.229852	+	0.973226i	$0.426176\pi$
$104$		0			0
$105$	16.2306	−	20.3685i	1.58394	−	1.98776i
$106$		0			0
$107$	2.49466			0.241168			0.120584	−	0.992703i	$-0.461523\pi$
$107$	2.49466			0.241168			0.120584	+	0.992703i	$0.461523\pi$
$108$		0			0
$109$	−9.85639			−0.944071			−0.472035	−	0.881580i	$-0.656481\pi$
$109$	−9.85639			−0.944071			−0.472035	+	0.881580i	$0.656481\pi$
$110$		0			0
$111$	17.6697	+	2.65637i	1.67713	+	0.252131i
$112$		0			0
$113$	5.05795	−	6.02783i	0.475812	−	0.567050i	−0.473738	−	0.880666i	$-0.657096\pi$
$113$	5.05795	−	6.02783i	0.475812	−	0.567050i	0.949550	+	0.313615i	$0.101540\pi$
$114$		0			0
$115$	8.67538	−	23.8354i	0.808984	−	2.22266i
$116$		0			0
$117$	0.920573	+	1.42294i	0.0851070	+	0.131551i
$118$		0			0
$119$	4.07411	−	3.41859i	0.373473	−	0.313381i
$120$		0			0
$121$	−0.136637	+	0.774906i	−0.0124215	+	0.0704460i
$122$		0			0
$123$	−2.46043	−	12.1471i	−0.221850	−	1.09527i
$124$		0			0
$125$	1.95631	+	1.12948i	0.174978	+	0.101024i
$126$		0			0
$127$	9.55197	−	5.51483i	0.847600	−	0.489362i	−0.0122404	−	0.999925i	$-0.503896\pi$
$127$	9.55197	−	5.51483i	0.847600	−	0.489362i	0.859840	+	0.510563i	$0.170563\pi$
$128$		0			0
$129$	6.02566	−	11.0750i	0.530530	−	0.975103i
$130$		0			0
$131$	−1.86341	+	0.678226i	−0.162807	+	0.0592568i	−0.422138	−	0.906532i	$-0.638720\pi$
$131$	−1.86341	+	0.678226i	−0.162807	+	0.0592568i	0.259331	+	0.965789i	$0.416498\pi$
$132$		0			0
$133$	−0.932783	−	5.29008i	−0.0808825	−	0.458708i
$134$		0			0
$135$	−15.4783	+	7.00545i	−1.33216	+	0.602933i
$136$		0			0
$137$	2.79916	−	0.493567i	0.239148	−	0.0421683i	−0.0527893	−	0.998606i	$-0.516811\pi$
$137$	2.79916	−	0.493567i	0.239148	−	0.0421683i	0.291938	+	0.956437i	$0.405700\pi$
$138$		0			0
$139$	−3.94861	−	10.8487i	−0.334916	−	0.920175i	−0.986813	−	0.161867i	$-0.948248\pi$
$139$	−3.94861	−	10.8487i	−0.334916	−	0.920175i	0.651896	−	0.758308i	$-0.273974\pi$
$140$		0			0
$141$	0.350238	+	13.8319i	0.0294954	+	1.16485i
$142$		0			0
$143$	0.902685	+	1.56350i	0.0754863	+	0.130746i
$144$		0			0
$145$	8.12874	−	14.0794i	0.675056	−	1.16923i
$146$		0			0
$147$	−7.79628	+	23.2339i	−0.643026	+	1.91630i
$148$		0			0
$149$	−21.7819	−	3.84074i	−1.78445	−	0.314646i	−0.818717	−	0.574198i	$-0.805314\pi$
$149$	−21.7819	−	3.84074i	−1.78445	−	0.314646i	−0.965729	+	0.259552i	$0.916425\pi$
$150$		0			0
$151$	−6.36031	−	7.57992i	−0.517595	−	0.616845i	0.442415	−	0.896810i	$-0.354122\pi$
$151$	−6.36031	−	7.57992i	−0.517595	−	0.616845i	−0.960010	+	0.279965i	$0.909677\pi$
$152$		0			0
$153$	−3.38182	+	0.774600i	−0.273404	+	0.0626227i
$154$		0			0
$155$	−23.7404	−	8.64081i	−1.90688	−	0.694046i
$156$		0			0
$157$	−2.56268	−	2.15034i	−0.204524	−	0.171616i	0.534772	−	0.844996i	$-0.320397\pi$
$157$	−2.56268	−	2.15034i	−0.204524	−	0.171616i	−0.739296	+	0.673380i	$0.764842\pi$
$158$		0			0
$159$	14.9634	−	5.87930i	1.18667	−	0.466259i
$160$		0			0
$161$			35.6760i			2.81167i
$162$		0			0
$163$		−	15.3266i		−	1.20047i	−0.799824	−	0.600234i	$-0.795074\pi$
$163$		−	15.3266i		−	1.20047i	0.799824	−	0.600234i	$-0.204926\pi$
$164$		0			0
$165$	−16.8451	+	6.61863i	−1.31139	+	0.515260i
$166$		0			0
$167$	−4.16997	−	3.49902i	−0.322682	−	0.270762i	0.467028	−	0.884242i	$-0.345325\pi$
$167$	−4.16997	−	3.49902i	−0.322682	−	0.270762i	−0.789710	+	0.613480i	$0.789769\pi$
$168$		0			0
$169$	11.9161	+	4.33711i	0.916624	+	0.333624i
$170$		0			0
$171$	−1.03031	+	3.34928i	−0.0787899	+	0.256126i
$172$		0			0
$173$	2.70929	+	3.22881i	0.205984	+	0.245482i	0.859139	−	0.511742i	$-0.171000\pi$
$173$	2.70929	+	3.22881i	0.205984	+	0.245482i	−0.653156	+	0.757224i	$0.726555\pi$
$174$		0			0
$175$	−25.7737	−	4.54460i	−1.94831	−	0.343540i
$176$		0			0
$177$	−1.89555	+	5.64898i	−0.142478	+	0.424603i
$178$		0			0
$179$	−3.91858	+	6.78719i	−0.292889	+	0.507298i	−0.974492	−	0.224424i	$-0.927950\pi$
$179$	−3.91858	+	6.78719i	−0.292889	+	0.507298i	0.681603	+	0.731722i	$0.261283\pi$
$180$		0			0
$181$	−4.03056	−	6.98113i	−0.299589	−	0.518903i	0.676453	−	0.736486i	$-0.263516\pi$
$181$	−4.03056	−	6.98113i	−0.299589	−	0.518903i	−0.976042	+	0.217583i	$0.930183\pi$
$182$		0			0
$183$	0.157563	+	6.22259i	0.0116474	+	0.459987i
$184$		0			0
$185$	−11.5366	−	31.6967i	−0.848191	−	2.33039i
$186$		0			0
$187$	−3.63969	+	0.641775i	−0.266160	+	0.0469312i
$188$		0			0
$189$	17.0873	−	16.7048i	1.24292	−	1.21510i
$190$		0			0
$191$	−1.91535	−	10.8625i	−0.138590	−	0.785982i	−0.972292	−	0.233768i	$-0.924894\pi$
$191$	−1.91535	−	10.8625i	−0.138590	−	0.785982i	0.833703	−	0.552214i	$-0.186217\pi$
$192$		0			0
$193$	−5.29692	+	1.92792i	−0.381280	+	0.138775i	−0.525548	−	0.850764i	$-0.676140\pi$
$193$	−5.29692	+	1.92792i	−0.381280	+	0.138775i	0.144267	+	0.989539i	$0.453917\pi$
$194$		0			0
$195$	1.52900	−	2.81027i	0.109494	−	0.201248i
$196$		0			0
$197$	15.9901	−	9.23187i	1.13925	−	0.657744i	0.193002	−	0.981198i	$-0.438178\pi$
$197$	15.9901	−	9.23187i	1.13925	−	0.657744i	0.946244	+	0.323455i	$0.104844\pi$
$198$		0			0
$199$	−6.97385	−	4.02635i	−0.494363	−	0.285420i	0.232020	−	0.972711i	$-0.425467\pi$
$199$	−6.97385	−	4.02635i	−0.494363	−	0.285420i	−0.726383	+	0.687291i	$0.758800\pi$
$200$		0			0
$201$	0.599140	+	2.95795i	0.0422601	+	0.208638i
$202$		0			0
$203$	−3.97067	+	22.5188i	−0.278686	+	1.58051i
$204$		0			0
$205$	−17.9228	+	15.0390i	−1.25178	+	1.05037i
$206$		0			0
$207$	10.6015	−	20.7181i	0.736857	−	1.44000i
$208$		0			0
$209$	−1.27672	+	3.50776i	−0.0883125	+	0.242637i
$210$		0			0
$211$	15.5687	−	18.5541i	1.07180	−	1.27732i	0.112885	−	0.993608i	$-0.463991\pi$
$211$	15.5687	−	18.5541i	1.07180	−	1.27732i	0.958911	−	0.283708i	$-0.0915647\pi$
$212$		0			0
$213$	−20.0000	−	3.00669i	−1.37037	−	0.206015i
$214$		0			0
$215$	−23.8011			−1.62322
$216$		0			0
$217$	35.5339			2.41219
$218$		0			0
$219$	12.4527	−	15.6274i	0.841475	−	1.05600i
$220$		0			0
$221$	0.419940	−	0.500464i	0.0282482	−	0.0336649i
$222$		0			0
$223$	−8.96996	+	24.6448i	−0.600673	+	1.65034i	0.149242	+	0.988801i	$0.452317\pi$
$223$	−8.96996	+	24.6448i	−0.600673	+	1.65034i	−0.749915	+	0.661535i	$0.769905\pi$
$224$		0			0
$225$	13.6170	+	10.2981i	0.907802	+	0.686541i
$226$		0			0
$227$	−10.1018	+	8.47640i	−0.670479	+	0.562599i	−0.913207	−	0.407496i	$-0.866402\pi$
$227$	−10.1018	+	8.47640i	−0.670479	+	0.562599i	0.242728	+	0.970094i	$0.421958\pi$
$228$		0			0
$229$	2.20839	−	12.5244i	0.145934	−	0.827635i	−0.820678	−	0.571391i	$-0.806404\pi$
$229$	2.20839	−	12.5244i	0.145934	−	0.827635i	0.966612	−	0.256244i	$-0.0824850\pi$
$230$		0			0
$231$	19.0798	−	16.8510i	1.25536	−	1.10872i
$232$		0			0
$233$	−8.11418	−	4.68472i	−0.531578	−	0.306906i	0.210081	−	0.977684i	$-0.432627\pi$
$233$	−8.11418	−	4.68472i	−0.531578	−	0.306906i	−0.741659	+	0.670777i	$0.765961\pi$
$234$		0			0
$235$	22.6202	−	13.0598i	1.47558	−	0.851927i
$236$		0			0
$237$	4.53544	+	7.41554i	0.294608	+	0.481691i
$238$		0			0
$239$	0.430661	−	0.156748i	0.0278572	−	0.0101392i	−0.328054	−	0.944659i	$-0.606393\pi$
$239$	0.430661	−	0.156748i	0.0278572	−	0.0101392i	0.355911	+	0.934520i	$0.384171\pi$
$240$		0			0
$241$	−0.219014	−	1.24209i	−0.0141079	−	0.0800099i	0.976941	−	0.213510i	$-0.0684895\pi$
$241$	−0.219014	−	1.24209i	−0.0141079	−	0.0800099i	−0.991049	+	0.133500i	$0.957378\pi$
$242$		0			0
$243$	−14.8871	+	4.62325i	−0.955008	+	0.296582i
$244$		0			0
$245$	45.5605	−	8.03354i	2.91075	−	0.513244i
$246$		0			0
$247$	−0.225685	−	0.620064i	−0.0143600	−	0.0394537i
$248$		0			0
$249$	1.91795	−	1.17304i	0.121545	−	0.0743386i
$250$		0			0
$251$	−5.93959	−	10.2877i	−0.374904	−	0.649352i	0.615409	−	0.788208i	$-0.288991\pi$
$251$	−5.93959	−	10.2877i	−0.374904	−	0.649352i	−0.990313	+	0.138856i	$0.955658\pi$
$252$		0			0
$253$	12.3960	−	21.4704i	0.779327	−	1.34983i
$254$		0			0
$255$	4.33551	+	4.90894i	0.271500	+	0.307410i
$256$		0			0
$257$	8.93535	+	1.57554i	0.557372	+	0.0982797i	0.445236	−	0.895413i	$-0.353120\pi$
$257$	8.93535	+	1.57554i	0.557372	+	0.0982797i	0.112136	+	0.993693i	$0.464231\pi$
$258$		0			0
$259$	30.4955	+	36.3431i	1.89490	+	2.25825i
$260$		0			0
$261$	8.99758	−	11.8973i	0.556936	−	0.736427i
$262$		0			0
$263$	5.38096	+	1.95851i	0.331804	+	0.120767i	0.502550	−	0.864548i	$-0.332395\pi$
$263$	5.38096	+	1.95851i	0.331804	+	0.120767i	−0.170745	+	0.985315i	$0.554618\pi$
$264$		0			0
$265$	−23.2490	−	19.5082i	−1.42817	−	1.19838i
$266$		0			0
$267$	3.60981	+	2.87647i	0.220917	+	0.176037i
$268$		0			0
$269$			20.1350i			1.22765i	0.789442	+	0.613825i	$0.210370\pi$
$269$			20.1350i			1.22765i	−0.789442	+	0.613825i	$0.789630\pi$
$270$		0			0
$271$			9.45448i			0.574319i	0.957883	+	0.287159i	$0.0927110\pi$
$271$			9.45448i			0.574319i	−0.957883	+	0.287159i	$0.907289\pi$
$272$		0			0
$273$	−0.668959	+	4.44980i	−0.0404873	+	0.269314i
$274$		0			0
$275$	13.9320	+	11.6903i	0.840130	+	0.704953i
$276$		0			0
$277$	25.4133	+	9.24970i	1.52694	+	0.555761i	0.962870	−	0.269966i	$-0.0870126\pi$
$277$	25.4133	+	9.24970i	1.52694	+	0.555761i	0.564070	+	0.825727i	$0.309235\pi$
$278$		0			0
$279$	−20.6355	−	10.5593i	−1.23541	−	0.632167i
$280$		0			0
$281$	13.2458	+	15.7857i	0.790178	+	0.941698i	0.999345	−	0.0361822i	$-0.0115197\pi$
$281$	13.2458	+	15.7857i	0.790178	+	0.941698i	−0.209167	+	0.977880i	$0.567075\pi$
$282$		0			0
$283$	−18.3919	−	3.24298i	−1.09328	−	0.192775i	−0.402200	−	0.915552i	$-0.631754\pi$
$283$	−18.3919	−	3.24298i	−1.09328	−	0.192775i	−0.691082	+	0.722777i	$0.742866\pi$
$284$		0			0
$285$	6.48336	−	1.31322i	0.384041	−	0.0777885i
$286$		0			0
$287$	16.4536	−	28.4985i	0.971225	−	1.68221i
$288$		0			0
$289$	−7.83129	−	13.5642i	−0.460664	−	0.797894i
$290$		0			0
$291$	26.7113	+	14.5329i	1.56584	+	0.851936i
$292$		0			0
$293$	3.64482	+	10.0140i	0.212932	+	0.585027i	0.999471	−	0.0325138i	$-0.0103513\pi$
$293$	3.64482	+	10.0140i	0.212932	+	0.585027i	−0.786539	+	0.617541i	$0.788129\pi$
$294$		0			0
$295$	11.0774	−	1.95324i	0.644949	−	0.113722i
$296$		0			0
$297$	−16.0877	+	4.11608i	−0.933500	+	0.238839i
$298$		0			0
$299$	0.761004	+	4.31587i	0.0440100	+	0.249593i
$300$		0			0
$301$	31.4574	−	11.4495i	1.81317	−	0.659941i
$302$		0			0
$303$	−22.2573	+	0.563578i	−1.27865	+	0.0323767i
$304$		0			0
$305$	10.1762	−	5.87525i	0.582689	−	0.336416i
$306$		0			0
$307$	−0.399434	−	0.230613i	−0.0227969	−	0.0131618i	0.488558	−	0.872531i	$-0.337523\pi$
$307$	−0.399434	−	0.230613i	−0.0227969	−	0.0131618i	−0.511355	+	0.859369i	$0.670856\pi$
$308$		0			0
$309$	19.9245	+	6.68580i	1.13347	+	0.380342i
$310$		0			0
$311$	−0.0341064	+	0.193427i	−0.00193400	+	0.0109683i	−0.985759	−	0.168161i	$-0.946217\pi$
$311$	−0.0341064	+	0.193427i	−0.00193400	+	0.0109683i	0.983825	+	0.179130i	$0.0573281\pi$
$312$		0			0
$313$	−10.7615	+	9.02994i	−0.608274	+	0.510402i	−0.894093	−	0.447881i	$-0.852179\pi$
$313$	−10.7615	+	9.02994i	−0.608274	+	0.510402i	0.285819	+	0.958283i	$0.407734\pi$
$314$		0			0
$315$	−43.1162	−	13.2635i	−2.42932	−	0.747313i
$316$		0			0
$317$	1.81401	−	4.98396i	0.101885	−	0.279927i	−0.878268	−	0.478169i	$-0.841301\pi$
$317$	1.81401	−	4.98396i	0.101885	−	0.279927i	0.980153	+	0.198241i	$0.0635230\pi$
$318$		0			0
$319$	10.2140	−	12.1725i	0.571872	−	0.681530i
$320$		0			0
$321$	−1.58013	−	4.02160i	−0.0881945	−	0.224464i
$322$		0			0
$323$	1.35082			0.0751615
$324$		0			0
$325$	−3.21489			−0.178330
$326$		0			0
$327$	6.24309	+	15.8893i	0.345244	+	0.878679i
$328$		0			0
$329$	−23.6142	+	28.1423i	−1.30189	+	1.55154i
$330$		0			0
$331$	1.66136	−	4.56455i	0.0913166	−	0.250890i	−0.885623	−	0.464404i	$-0.846269\pi$
$331$	1.66136	−	4.56455i	0.0913166	−	0.250890i	0.976940	+	0.213514i	$0.0684908\pi$
$332$		0			0
$333$	−6.90981	−	30.1675i	−0.378655	−	1.65317i
$334$		0			0
$335$	4.36437	−	3.66214i	0.238451	−	0.200084i
$336$		0			0
$337$	−4.87384	+	27.6409i	−0.265495	+	1.50570i	0.502127	+	0.864794i	$0.332551\pi$
$337$	−4.87384	+	27.6409i	−0.265495	+	1.50570i	−0.767622	+	0.640903i	$0.778560\pi$
$338$		0			0
$339$	−12.9211	−	4.33575i	−0.701776	−	0.235486i
$340$		0			0
$341$	−21.3848	−	12.3465i	−1.15805	−	0.668603i
$342$		0			0
$343$	−28.4729	+	16.4388i	−1.53739	+	0.887613i
$344$		0			0
$345$	−43.9196	+	1.11209i	−2.36455	+	0.0598730i
$346$		0			0
$347$	−23.8394	+	8.67682i	−1.27976	+	0.465796i	−0.890354	−	0.455269i	$-0.849543\pi$
$347$	−23.8394	+	8.67682i	−1.27976	+	0.465796i	−0.389410	+	0.921065i	$0.627321\pi$
$348$		0			0
$349$	5.59767	+	31.7460i	0.299637	+	1.69932i	0.647735	+	0.761865i	$0.275716\pi$
$349$	5.59767	+	31.7460i	0.299637	+	1.69932i	−0.348099	+	0.937458i	$0.613173\pi$
$350$		0			0
$351$	1.71079	−	2.38533i	0.0913152	−	0.127320i
$352$		0			0
$353$	0.359268	−	0.0633486i	0.0191219	−	0.00337171i	−0.164079	−	0.986447i	$-0.552465\pi$
$353$	0.359268	−	0.0633486i	0.0191219	−	0.00337171i	0.183201	+	0.983075i	$0.441354\pi$
$354$		0			0
$355$	13.0581	+	35.8768i	0.693052	+	1.90414i
$356$		0			0
$357$	−8.09160	−	4.40244i	−0.428253	−	0.233002i
$358$		0			0
$359$	11.6108	+	20.1106i	0.612797	+	1.06139i	0.990767	+	0.135577i	$0.0432889\pi$
$359$	11.6108	+	20.1106i	0.612797	+	1.06139i	−0.377970	+	0.925818i	$0.623378\pi$
$360$		0			0
$361$	−8.81782	+	15.2729i	−0.464096	+	0.803838i
$362$		0			0
$363$	1.33576	−	0.270561i	0.0701090	−	0.0142007i
$364$		0			0
$365$	−37.1484	−	6.55026i	−1.94443	−	0.342856i
$366$		0			0
$367$	19.8404	+	23.6449i	1.03566	+	1.23425i	0.971680	+	0.236300i	$0.0759349\pi$
$367$	19.8404	+	23.6449i	1.03566	+	1.23425i	0.0639798	+	0.997951i	$0.479621\pi$
$368$		0			0
$369$	−18.0237	+	11.6605i	−0.938276	+	0.607020i
$370$		0			0
$371$	40.1121	+	14.5996i	2.08252	+	0.757975i
$372$		0			0
$373$	−15.1578	−	12.7189i	−0.784840	−	0.658559i	0.159622	−	0.987178i	$-0.448972\pi$
$373$	−15.1578	−	12.7189i	−0.784840	−	0.658559i	−0.944463	+	0.328619i	$0.893417\pi$
$374$		0			0
$375$	0.581667	−	3.86915i	0.0300372	−	0.199802i
$376$		0			0
$377$			2.80888i			0.144665i
$378$		0			0
$379$		−	15.8421i		−	0.813754i	−0.913483	−	0.406877i	$-0.866618\pi$
$379$		−	15.8421i		−	0.813754i	0.913483	−	0.406877i	$-0.133382\pi$
$380$		0			0
$381$	−14.9406	−	11.9054i	−0.765431	−	0.609932i
$382$		0			0
$383$	8.11893	+	6.81259i	0.414858	+	0.348107i	0.826203	−	0.563372i	$-0.190496\pi$
$383$	8.11893	+	6.81259i	0.414858	+	0.348107i	−0.411345	+	0.911480i	$0.634941\pi$
$384$		0			0
$385$	−45.1563	−	16.4356i	−2.30138	−	0.837633i
$386$		0			0
$387$	−21.6705	−	2.69884i	−1.10157	−	0.137190i
$388$		0			0
$389$	4.47165	+	5.32910i	0.226721	+	0.270196i	0.867398	−	0.497615i	$-0.165791\pi$
$389$	4.47165	+	5.32910i	0.226721	+	0.270196i	−0.640677	+	0.767811i	$0.721346\pi$
$390$		0			0
$391$	−8.83516	−	1.55788i	−0.446813	−	0.0787852i
$392$		0			0
$393$	2.27365	+	2.57437i	0.114690	+	0.129860i
$394$		0			0
$395$	8.20471	−	14.2110i	0.412824	−	0.715032i
$396$		0			0
$397$	5.96830	+	10.3374i	0.299540	+	0.518819i	0.976031	−	0.217632i	$-0.0698334\pi$
$397$	5.96830	+	10.3374i	0.299540	+	0.518819i	−0.676491	+	0.736451i	$0.736500\pi$
$398$		0			0
$399$	−7.93719	+	4.85448i	−0.397356	+	0.243028i
$400$		0			0
$401$	−12.3357	−	33.8921i	−0.616016	−	1.69249i	−0.716532	−	0.697554i	$-0.754272\pi$
$401$	−12.3357	−	33.8921i	−0.616016	−	1.69249i	0.100516	−	0.994935i	$-0.467950\pi$
$402$		0			0
$403$	4.29867	−	0.757971i	0.214132	−	0.0377572i
$404$		0			0
$405$	21.0974	+	20.5149i	1.04834	+	1.01939i
$406$		0			0
$407$	−5.72494	−	32.4678i	−0.283775	−	1.60937i
$408$		0			0
$409$	7.41377	−	2.69839i	0.366587	−	0.133427i	−0.152157	−	0.988356i	$-0.548622\pi$
$409$	7.41377	−	2.69839i	0.366587	−	0.133427i	0.518744	+	0.854930i	$0.326400\pi$
$410$		0			0
$411$	−2.56867	−	4.19984i	−0.126703	−	0.207163i
$412$		0			0
$413$	−13.7011	+	7.91033i	−0.674187	+	0.389242i
$414$		0			0
$415$	−3.67552	−	2.12206i	−0.180424	−	0.104168i
$416$		0			0
$417$	−14.9879	+	13.2371i	−0.733960	+	0.648223i
$418$		0			0
$419$	−0.978660	+	5.55026i	−0.0478107	+	0.271148i	−0.999337	−	0.0364210i	$-0.988404\pi$
$419$	−0.978660	+	5.55026i	−0.0478107	+	0.271148i	0.951526	+	0.307569i	$0.0995154\pi$
$420$		0			0
$421$	−6.74812	+	5.66235i	−0.328883	+	0.275966i	−0.792245	−	0.610204i	$-0.791088\pi$
$421$	−6.74812	+	5.66235i	−0.328883	+	0.275966i	0.463361	+	0.886169i	$0.346643\pi$
$422$		0			0
$423$	22.0762	−	9.32580i	1.07338	−	0.453436i
$424$		0			0
$425$	2.25094	−	6.18440i	0.109187	−	0.299988i
$426$		0			0
$427$	−10.6234	+	12.6605i	−0.514103	+	0.612684i
$428$		0			0
$429$	1.94871	−	2.44553i	0.0940847	−	0.118071i
$430$		0			0
$431$	26.6279			1.28262			0.641311	−	0.767281i	$-0.278391\pi$
$431$	26.6279			1.28262			0.641311	+	0.767281i	$0.278391\pi$
$432$		0			0
$433$	3.97664			0.191105			0.0955525	−	0.995424i	$-0.469538\pi$
$433$	3.97664			0.191105			0.0955525	+	0.995424i	$0.469538\pi$
$434$		0			0
$435$	−27.8459	−	4.18620i	−1.33511	−	0.200713i
$436$		0			0
$437$	−5.82454	+	6.94142i	−0.278626	+	0.332053i
$438$		0			0
$439$	−11.5242	+	31.6625i	−0.550020	+	1.51117i	0.283663	+	0.958924i	$0.408450\pi$
$439$	−11.5242	+	31.6625i	−0.550020	+	1.51117i	−0.833683	+	0.552243i	$0.813772\pi$
$440$		0			0
$441$	42.3930	−	2.14825i	2.01872	−	0.102298i
$442$		0			0
$443$	19.6953	−	16.5263i	0.935753	−	0.785190i	−0.0410880	−	0.999156i	$-0.513082\pi$
$443$	19.6953	−	16.5263i	0.935753	−	0.785190i	0.976841	+	0.213965i	$0.0686380\pi$
$444$		0			0
$445$	1.51306	−	8.58097i	0.0717257	−	0.406777i
$446$		0			0
$447$	7.60522	+	37.5469i	0.359715	+	1.77591i
$448$		0			0
$449$	35.5320	+	20.5144i	1.67686	+	0.968134i	0.963645	+	0.267185i	$0.0860936\pi$
$449$	35.5320	+	20.5144i	1.67686	+	0.968134i	0.713212	+	0.700948i	$0.247240\pi$
$450$		0			0
$451$	−19.8041	+	11.4339i	−0.932538	+	0.538401i
$452$		0			0
$453$	−8.19078	+	15.0545i	−0.384836	+	0.707322i
$454$		0			0
$455$	7.98225	−	2.90530i	0.374214	−	0.136203i
$456$		0			0
$457$	3.25767	+	18.4752i	0.152388	+	0.864232i	0.961135	+	0.276077i	$0.0890345\pi$
$457$	3.25767	+	18.4752i	0.152388	+	0.864232i	−0.808748	+	0.588155i	$0.799854\pi$
$458$		0			0
$459$	3.39078	+	4.96112i	0.158268	+	0.231565i
$460$		0			0
$461$	0.428328	−	0.0755258i	0.0199492	−	0.00351759i	−0.163665	−	0.986516i	$-0.552332\pi$
$461$	0.428328	−	0.0755258i	0.0199492	−	0.00351759i	0.183614	+	0.982998i	$0.441220\pi$
$462$		0			0
$463$	−2.95496	−	8.11869i	−0.137329	−	0.377307i	0.851896	−	0.523710i	$-0.175453\pi$
$463$	−2.95496	−	8.11869i	−0.137329	−	0.377307i	−0.989225	+	0.146403i	$0.953230\pi$
$464$		0			0
$465$	1.10766	+	43.7446i	0.0513664	+	2.02861i
$466$		0			0
$467$	1.96853	+	3.40960i	0.0910927	+	0.157777i	0.907971	−	0.419033i	$-0.137631\pi$
$467$	1.96853	+	3.40960i	0.0910927	+	0.157777i	−0.816878	+	0.576810i	$0.804297\pi$
$468$		0			0
$469$	−4.00661	+	6.93966i	−0.185008	+	0.320444i
$470$		0			0
$471$	−1.84331	+	5.49328i	−0.0849350	+	0.253117i
$472$		0			0
$473$	−22.9098	−	4.03962i	−1.05339	−	0.185742i
$474$		0			0
$475$	−4.27278	−	5.09210i	−0.196049	−	0.233642i
$476$		0			0
$477$	−18.9558	−	20.3982i	−0.867926	−	0.933968i
$478$		0			0
$479$	−36.6136	−	13.3263i	−1.67292	−	0.608893i	−0.680607	−	0.732649i	$-0.738284\pi$
$479$	−36.6136	−	13.3263i	−1.67292	−	0.608893i	−0.992313	+	0.123756i	$0.960506\pi$
$480$		0			0
$481$	4.46439	+	3.74606i	0.203558	+	0.170806i
$482$		0			0
$483$	57.5126	−	22.5974i	2.61691	−	1.02822i
$484$		0			0
$485$		−	57.4045i		−	2.60661i
$486$		0			0
$487$		−	9.69848i		−	0.439480i	−0.975558	−	0.219740i	$-0.929479\pi$
$487$		−	9.69848i		−	0.439480i	0.975558	−	0.219740i	$-0.0705209\pi$
$488$		0			0
$489$	−24.7076	+	9.70793i	−1.11732	+	0.439008i
$490$		0			0
$491$	24.3449	+	20.4278i	1.09867	+	0.921895i	0.997335	−	0.0729567i	$-0.0232435\pi$
$491$	24.3449	+	20.4278i	1.09867	+	0.921895i	0.101337	+	0.994852i	$0.467688\pi$
$492$		0			0
$493$	−5.40338	−	1.96667i	−0.243356	−	0.0885743i
$494$		0			0
$495$	21.3395	+	22.9633i	0.959140	+	1.03212i
$496$		0			0
$497$	−34.5172	−	41.1360i	−1.54831	−	1.84520i
$498$		0			0
$499$	−15.6275	−	2.75555i	−0.699582	−	0.123355i	−0.187466	−	0.982271i	$-0.560027\pi$
$499$	−15.6275	−	2.75555i	−0.699582	−	0.123355i	−0.512117	+	0.858916i	$0.671138\pi$
$500$		0			0
$501$	−2.99941	+	8.93862i	−0.134004	+	0.399348i
$502$		0			0
$503$	2.37837	−	4.11946i	0.106046	−	0.183678i	−0.808119	−	0.589019i	$-0.799514\pi$
$503$	2.37837	−	4.11946i	0.106046	−	0.183678i	0.914165	+	0.405342i	$0.132847\pi$
$504$		0			0
$505$	21.0149	+	36.3988i	0.935150	+	1.61973i
$506$		0			0
$507$	−0.555971	−	21.9569i	−0.0246916	−	0.975139i
$508$		0			0
$509$	−4.69911	−	12.9107i	−0.208284	−	0.572256i	0.790929	−	0.611908i	$-0.209598\pi$
$509$	−4.69911	−	12.9107i	−0.208284	−	0.572256i	−0.999214	+	0.0396512i	$0.987375\pi$
$510$		0			0
$511$	52.2492	−	9.21294i	2.31137	−	0.407556i
$512$		0			0
$513$	6.05191	−	0.460510i	0.267198	−	0.0203320i
$514$		0			0
$515$	−6.88927	−	39.0710i	−0.303577	−	1.72167i
$516$		0			0
$517$	23.9897	−	8.73154i	1.05507	−	0.384013i
$518$		0			0
$519$	3.48901	−	6.41273i	0.153151	−	0.281488i
$520$		0			0
$521$	−8.13386	+	4.69608i	−0.356351	+	0.205739i	−0.667479	−	0.744629i	$-0.732627\pi$
$521$	−8.13386	+	4.69608i	−0.356351	+	0.205739i	0.311128	+	0.950368i	$0.399293\pi$
$522$		0			0
$523$	−3.41236	−	1.97012i	−0.149212	−	0.0861475i	0.423535	−	0.905880i	$-0.360789\pi$
$523$	−3.41236	−	1.97012i	−0.149212	−	0.0861475i	−0.572747	+	0.819732i	$0.694122\pi$
$524$		0			0
$525$	8.99896	+	44.4278i	0.392747	+	1.93899i
$526$		0			0
$527$	−1.55167	+	8.79995i	−0.0675917	+	0.383332i
$528$		0			0
$529$	28.4824	−	23.8996i	1.23837	−	1.03911i
$530$		0			0
$531$	10.3072	−	0.522316i	0.447297	−	0.0226666i
$532$		0			0
$533$	1.38256	−	3.79854i	0.0598852	−	0.164533i
$534$		0			0
$535$	−5.24308	+	6.24846i	−0.226678	+	0.270144i
$536$		0			0
$537$	13.4235	+	2.01802i	0.579268	+	0.0870841i
$538$		0			0
$539$	45.2178			1.94767
$540$		0			0
$541$	24.4880			1.05282			0.526410	−	0.850231i	$-0.323538\pi$
$541$	24.4880			1.05282			0.526410	+	0.850231i	$0.323538\pi$
$542$		0			0
$543$	−8.70115	+	10.9195i	−0.373402	+	0.468599i
$544$		0			0
$545$	20.7153	−	24.6876i	0.887347	−	1.05750i
$546$		0			0
$547$	1.19550	−	3.28461i	0.0511159	−	0.140440i	−0.911507	−	0.411284i	$-0.865081\pi$
$547$	1.19550	−	3.28461i	0.0511159	−	0.140440i	0.962623	+	0.270844i	$0.0873028\pi$
$548$		0			0
$549$	9.93150	−	4.19543i	0.423866	−	0.179056i
$550$		0			0
$551$	−4.44902	+	3.73317i	−0.189535	+	0.159039i
$552$		0			0
$553$	−4.00777	+	22.7292i	−0.170428	+	0.966544i
$554$		0			0
$555$	−43.7902	+	38.6748i	−1.85879	+	1.64166i
$556$		0			0
$557$	−17.3226	−	10.0012i	−0.733982	−	0.423765i	0.0858951	−	0.996304i	$-0.472625\pi$
$557$	−17.3226	−	10.0012i	−0.733982	−	0.423765i	−0.819877	+	0.572539i	$0.805958\pi$
$558$		0			0
$559$	3.56129	−	2.05611i	0.150627	−	0.0869643i
$560$		0			0
$561$	3.33999	+	5.46095i	0.141014	+	0.230562i
$562$		0			0
$563$	2.89990	−	1.05548i	0.122216	−	0.0444831i	−0.280188	−	0.959945i	$-0.590397\pi$
$563$	2.89990	−	1.05548i	0.122216	−	0.0444831i	0.402404	+	0.915462i	$0.368175\pi$
$564$		0			0
$565$	4.46770	+	25.3376i	0.187957	+	1.06596i
$566$		0			0
$567$	−37.7527	−	16.9652i	−1.58546	−	0.712471i
$568$		0			0
$569$	−40.2366	+	7.09480i	−1.68681	+	0.297429i	−0.933056	−	0.359732i	$-0.882868\pi$
$569$	−40.2366	+	7.09480i	−1.68681	+	0.297429i	−0.753750	+	0.657161i	$0.771757\pi$
$570$		0			0
$571$	10.6194	+	29.1766i	0.444409	+	1.22100i	0.936564	+	0.350497i	$0.113987\pi$
$571$	10.6194	+	29.1766i	0.444409	+	1.22100i	−0.492155	+	0.870508i	$0.663791\pi$
$572$		0			0
$573$	−16.2980	+	9.96806i	−0.680858	+	0.416421i
$574$		0			0
$575$	22.0739	+	38.2332i	0.920546	+	1.59443i
$576$		0			0
$577$	9.89960	−	17.1466i	0.412126	−	0.713823i	−0.582996	−	0.812475i	$-0.698120\pi$
$577$	9.89960	−	17.1466i	0.412126	−	0.713823i	0.995122	+	0.0986520i	$0.0314531\pi$
$578$		0			0
$579$	6.46306	+	7.31789i	0.268595	+	0.304121i
$580$		0			0
$581$	5.87868	+	1.03657i	0.243889	+	0.0430041i
$582$		0			0
$583$	−19.0674	−	22.7236i	−0.789690	−	0.941116i
$584$		0			0
$585$	−5.49886	−	0.684825i	−0.227350	−	0.0283140i
$586$		0			0
$587$	1.64162	+	0.597503i	0.0677571	+	0.0246616i	0.375676	−	0.926751i	$-0.377410\pi$
$587$	1.64162	+	0.597503i	0.0677571	+	0.0246616i	−0.307919	+	0.951412i	$0.599633\pi$
$588$		0			0
$589$	6.91375	+	5.80133i	0.284876	+	0.239040i
$590$		0			0
$591$	−25.0107	−	19.9297i	−1.02880	−	0.819799i
$592$		0			0
$593$			2.88275i			0.118380i	0.998247	+	0.0591902i	$0.0188518\pi$
$593$			2.88275i			0.118380i	−0.998247	+	0.0591902i	$0.981148\pi$
$594$		0			0
$595$			17.3894i			0.712898i
$596$		0			0
$597$	−2.07352	+	13.7927i	−0.0848636	+	0.564498i
$598$		0			0
$599$	−25.3507	−	21.2718i	−1.03580	−	0.869142i	−0.0442729	−	0.999019i	$-0.514097\pi$
$599$	−25.3507	−	21.2718i	−1.03580	−	0.869142i	−0.991530	+	0.129878i	$0.958542\pi$
$600$		0			0
$601$	−9.17226	−	3.33843i	−0.374144	−	0.136177i	0.148102	−	0.988972i	$-0.452684\pi$
$601$	−9.17226	−	3.33843i	−0.374144	−	0.136177i	−0.522246	+	0.852795i	$0.674906\pi$
$602$		0			0
$603$	4.38895	−	2.83944i	0.178732	−	0.115631i
$604$		0			0
$605$	−1.65376	−	1.97087i	−0.0672348	−	0.0801273i
$606$		0			0
$607$	−16.5091	−	2.91100i	−0.670083	−	0.118154i	−0.171751	−	0.985140i	$-0.554943\pi$
$607$	−16.5091	−	2.91100i	−0.670083	−	0.118154i	−0.498331	+	0.866987i	$0.666054\pi$
$608$		0			0
$609$	38.8171	−	7.86249i	1.57295	−	0.318604i
$610$		0			0
$611$	−2.25640	+	3.90820i	−0.0912842	+	0.158109i
$612$		0			0
$613$	−13.2907	−	23.0201i	−0.536804	−	0.929773i	−0.999074	−	0.0430329i	$-0.986298\pi$
$613$	−13.2907	−	23.0201i	−0.536804	−	0.929773i	0.462269	−	0.886740i	$-0.347035\pi$
$614$		0			0
$615$	35.5964	+	19.3671i	1.43539	+	0.780958i
$616$		0			0
$617$	10.1134	+	27.7864i	0.407151	+	1.11864i	0.958681	+	0.284482i	$0.0918217\pi$
$617$	10.1134	+	27.7864i	0.407151	+	1.11864i	−0.551531	+	0.834155i	$0.685956\pi$
$618$		0			0
$619$	−31.5248	+	5.55867i	−1.26709	+	0.223422i	−0.766489	−	0.642257i	$-0.777998\pi$
$619$	−31.5248	+	5.55867i	−1.26709	+	0.223422i	−0.500599	+	0.865679i	$0.666887\pi$
$620$		0			0
$621$	−40.1142	−	3.96756i	−1.60973	−	0.159213i
$622$		0			0
$623$	2.12811	+	12.0691i	0.0852610	+	0.483539i
$624$		0			0
$625$	19.7977	−	7.20578i	0.791909	−	0.288231i
$626$		0			0
$627$	6.46346	−	0.163662i	0.258126	−	0.00653602i
$628$		0			0
$629$	−10.3320	+	5.96519i	−0.411964	+	0.237848i
$630$		0			0
$631$	−12.1912	−	7.03859i	−0.485324	−	0.280202i	0.237308	−	0.971434i	$-0.423735\pi$
$631$	−12.1912	−	7.03859i	−0.485324	−	0.280202i	−0.722633	+	0.691232i	$0.757068\pi$
$632$		0			0
$633$	−39.7720	−	13.3457i	−1.58079	−	0.530446i
$634$		0			0
$635$	−6.26237	+	35.5157i	−0.248515	+	1.40940i
$636$		0			0
$637$	−6.12309	+	5.13788i	−0.242606	+	0.203570i
$638$		0			0
$639$	7.82107	+	34.1460i	0.309397	+	1.35079i
$640$		0			0
$641$	4.04946	−	11.1258i	0.159944	−	0.439443i	−0.833672	−	0.552261i	$-0.813765\pi$
$641$	4.04946	−	11.1258i	0.159944	−	0.439443i	0.993616	+	0.112818i	$0.0359876\pi$
$642$		0			0
$643$	−16.5433	+	19.7155i	−0.652403	+	0.777503i	−0.986274	−	0.165115i	$-0.947200\pi$
$643$	−16.5433	+	19.7155i	−0.652403	+	0.777503i	0.333871	+	0.942619i	$0.391645\pi$
$644$		0			0
$645$	15.0758	+	38.3692i	0.593607	+	1.51079i
$646$		0			0
$647$	−12.9849			−0.510489			−0.255244	−	0.966877i	$-0.582156\pi$
$647$	−12.9849			−0.510489			−0.255244	+	0.966877i	$0.582156\pi$
$648$		0			0
$649$	10.9941			0.431555
$650$		0			0
$651$	−22.5073	−	57.2834i	−0.882132	−	2.24511i
$652$		0			0
$653$	9.24725	−	11.0204i	0.361873	−	0.431263i	−0.554133	−	0.832428i	$-0.686950\pi$
$653$	9.24725	−	11.0204i	0.361873	−	0.431263i	0.916006	+	0.401165i	$0.131395\pi$
$654$		0			0
$655$	2.21759	−	6.09277i	0.0866483	−	0.238064i
$656$		0			0
$657$	−33.0803	−	10.1762i	−1.29058	−	0.397012i
$658$		0			0
$659$	4.65277	−	3.90414i	0.181246	−	0.152084i	−0.547651	−	0.836707i	$-0.684478\pi$
$659$	4.65277	−	3.90414i	0.181246	−	0.152084i	0.728897	+	0.684623i	$0.240033\pi$
$660$		0			0
$661$	3.35960	−	19.0533i	0.130673	−	0.741086i	−0.847102	−	0.531430i	$-0.821655\pi$
$661$	3.35960	−	19.0533i	0.130673	−	0.741086i	0.977775	−	0.209655i	$-0.0672342\pi$
$662$		0			0
$663$	−1.07278	−	0.359978i	−0.0416633	−	0.0139804i
$664$		0			0
$665$	15.2106	+	8.78187i	0.589844	+	0.340546i
$666$		0			0
$667$	33.4047	−	19.2862i	1.29344	−	0.746765i
$668$		0			0
$669$	45.4109	−	1.14985i	1.75569	−	0.0444559i
$670$		0			0
$671$	10.7923	−	3.92809i	0.416633	−	0.151642i
$672$		0			0
$673$	−5.32198	−	30.1825i	−0.205147	−	1.16345i	−0.897208	−	0.441609i	$-0.854408\pi$
$673$	−5.32198	−	30.1825i	−0.205147	−	1.16345i	0.692060	−	0.721840i	$-0.256703\pi$
$674$		0			0
$675$	7.97627	−	28.4746i	0.307007	−	1.09599i
$676$		0			0
$677$	31.4858	−	5.55179i	1.21010	−	0.213373i	0.468038	−	0.883708i	$-0.344961\pi$
$677$	31.4858	−	5.55179i	1.21010	−	0.213373i	0.742058	+	0.670336i	$0.233850\pi$
$678$		0			0
$679$	27.6145	+	75.8703i	1.05975	+	2.91163i
$680$		0			0
$681$	20.0632	+	10.9159i	0.768822	+	0.418297i
$682$		0			0
$683$	−9.61320	−	16.6505i	−0.367839	−	0.637115i	0.621389	−	0.783502i	$-0.286569\pi$
$683$	−9.61320	−	16.6505i	−0.367839	−	0.637115i	−0.989227	+	0.146387i	$0.953235\pi$
$684$		0			0
$685$	−4.64679	+	8.04847i	−0.177545	+	0.307516i
$686$		0			0
$687$	−21.5891	+	4.37293i	−0.823676	+	0.166838i
$688$		0			0
$689$	5.16395	+	0.910543i	0.196731	+	0.0346889i
$690$		0			0
$691$	−13.6390	−	16.2543i	−0.518852	−	0.618344i	0.441457	−	0.897282i	$-0.354462\pi$
$691$	−13.6390	−	16.2543i	−0.518852	−	0.618344i	−0.960309	+	0.278939i	$0.910017\pi$
$692$		0			0
$693$	−39.2505	−	20.0846i	−1.49100	−	0.762953i
$694$		0			0
$695$	35.4719	+	12.9107i	1.34553	+	0.489731i
$696$		0			0
$697$	6.33915	+	5.31918i	0.240113	+	0.201478i
$698$		0			0
$699$	−2.41258	+	16.0480i	−0.0912520	+	0.606992i
$700$		0			0
$701$		−	0.844459i		−	0.0318948i	−0.999873	−	0.0159474i	$-0.994924\pi$
$701$		−	0.844459i		−	0.0318948i	0.999873	−	0.0159474i	$-0.00507643\pi$
$702$		0			0
$703$			12.0499i			0.454472i
$704$		0			0
$705$	−35.3812	−	28.1934i	−1.33253	−	1.06183i
$706$		0			0
$707$	−45.2846	−	37.9983i	−1.70310	−	1.42907i
$708$		0			0
$709$	−21.4125	−	7.79352i	−0.804164	−	0.292692i	−0.0929534	−	0.995670i	$-0.529631\pi$
$709$	−21.4125	−	7.79352i	−0.804164	−	0.292692i	−0.711211	+	0.702979i	$0.751853\pi$
$710$		0			0
$711$	9.08166	−	12.0085i	0.340589	−	0.450355i
$712$		0			0
$713$	−38.5295	−	45.9177i	−1.44294	−	1.71963i
$714$		0			0
$715$	−5.81332	−	1.02505i	−0.217406	−	0.0383345i
$716$		0			0
$717$	−0.525473	−	0.594975i	−0.0196242	−	0.0222197i
$718$		0			0
$719$	−3.72926	+	6.45927i	−0.139078	+	0.240890i	−0.927148	−	0.374696i	$-0.877747\pi$
$719$	−3.72926	+	6.45927i	−0.139078	+	0.240890i	0.788070	+	0.615586i	$0.211081\pi$
$720$		0			0
$721$	27.9005	+	48.3251i	1.03907	+	1.79972i
$722$		0			0
$723$	−1.86362	+	1.13981i	−0.0693087	+	0.0423901i
$724$		0			0
$725$	9.67782	+	26.5896i	0.359425	+	0.987513i
$726$		0			0
$727$	38.6980	−	6.82351i	1.43523	−	0.253070i	0.598693	−	0.800979i	$-0.295687\pi$
$727$	38.6980	−	6.82351i	1.43523	−	0.253070i	0.836538	+	0.547909i	$0.184576\pi$
$728$		0			0
$729$	16.8826	+	21.0708i	0.625282	+	0.780399i
$730$		0			0
$731$	1.46182	+	8.29038i	0.0540673	+	0.306631i
$732$		0			0
$733$	36.4677	−	13.2732i	1.34697	−	0.490256i	0.434967	−	0.900447i	$-0.356760\pi$
$733$	36.4677	−	13.2732i	1.34697	−	0.490256i	0.912000	+	0.410191i	$0.134538\pi$
$734$		0			0
$735$	−41.8090	−	68.3586i	−1.54215	−	2.52144i
$736$		0			0
$737$	4.82249	−	2.78427i	0.177639	−	0.102560i
$738$		0			0
$739$	6.04940	+	3.49262i	0.222531	+	0.128478i	0.607122	−	0.794609i	$-0.292324\pi$
$739$	6.04940	+	3.49262i	0.222531	+	0.128478i	−0.384591	+	0.923087i	$0.625657\pi$
$740$		0			0
$741$	−0.856641	+	0.756573i	−0.0314695	+	0.0277934i
$742$		0			0
$743$	1.66756	−	9.45719i	0.0611768	−	0.346951i	−0.938820	−	0.344408i	$-0.888080\pi$
$743$	1.66756	−	9.45719i	0.0611768	−	0.346951i	0.999997	−	0.00254251i	$-0.000809308\pi$
$744$		0			0
$745$	55.3995	−	46.4857i	2.02968	−	1.70310i
$746$		0			0
$747$	−3.10588	−	2.34888i	−0.113638	−	0.0859409i
$748$		0			0
$749$	3.92383	−	10.7806i	0.143374	−	0.393916i
$750$		0			0
$751$	7.93312	−	9.45432i	0.289483	−	0.344993i	−0.601629	−	0.798776i	$-0.705481\pi$
$751$	7.93312	−	9.45432i	0.289483	−	0.344993i	0.891112	+	0.453783i	$0.149926\pi$
$752$		0			0
$753$	−12.8224	+	16.0914i	−0.467273	+	0.586401i
$754$		0			0
$755$	32.3532			1.17745
$756$		0			0
$757$	14.2610			0.518326			0.259163	−	0.965834i	$-0.416553\pi$
$757$	14.2610			0.518326			0.259163	+	0.965834i	$0.416553\pi$
$758$		0			0
$759$	−42.4637	−	6.38376i	−1.54133	−	0.231716i
$760$		0			0
$761$	4.05193	−	4.82890i	0.146882	−	0.175047i	−0.687587	−	0.726102i	$-0.741330\pi$
$761$	4.05193	−	4.82890i	0.146882	−	0.175047i	0.834469	+	0.551055i	$0.185774\pi$
$762$		0			0
$763$	−15.5030	+	42.5942i	−0.561246	+	1.54201i
$764$		0			0
$765$	5.16747	−	10.0985i	0.186830	−	0.365113i
$766$		0			0
$767$	−1.48874	+	1.24920i	−0.0537553	+	0.0451060i
$768$		0			0
$769$	0.396417	−	2.24819i	0.0142951	−	0.0810718i	−0.976826	−	0.214037i	$-0.931339\pi$
$769$	0.396417	−	2.24819i	0.0142951	−	0.0810718i	0.991121	+	0.132965i	$0.0424498\pi$
$770$		0			0
$771$	−3.11980	−	15.4024i	−0.112357	−	0.554706i
$772$		0			0
$773$	24.6458	+	14.2292i	0.886446	+	0.511790i	0.872778	−	0.488117i	$-0.162316\pi$
$773$	24.6458	+	14.2292i	0.886446	+	0.511790i	0.0136679	+	0.999907i	$0.495649\pi$
$774$		0			0
$775$	38.0808	−	21.9859i	1.36790	−	0.789758i
$776$		0			0
$777$	39.2719	−	72.1810i	1.40887	−	2.58948i
$778$		0			0
$779$	7.85406	−	2.85865i	0.281401	−	0.102422i
$780$		0			0
$781$	6.47995	+	36.7496i	0.231871	+	1.31500i
$782$		0			0
$783$	−24.8786	−	6.96895i	−0.889087	−	0.249050i
$784$		0			0
$785$	10.7720	−	1.89940i	0.384471	−	0.0677926i
$786$		0			0
$787$	3.38301	+	9.29476i	0.120591	+	0.331322i	0.985271	−	0.171002i	$-0.0547005\pi$
$787$	3.38301	+	9.29476i	0.120591	+	0.331322i	−0.864679	+	0.502324i	$0.832478\pi$
$788$		0			0
$789$	−0.251060	−	9.91507i	−0.00893797	−	0.352986i
$790$		0			0
$791$	−18.0935	−	31.3389i	−0.643332	−	1.11428i
$792$		0			0
$793$	−1.01509	+	1.75819i	−0.0360470	+	0.0624353i
$794$		0			0
$795$	−16.7227	+	49.8358i	−0.593095	+	1.76750i
$796$		0			0
$797$	31.9924	+	5.64112i	1.13323	+	0.199819i	0.708642	−	0.705568i	$-0.249308\pi$
$797$	31.9924	+	5.64112i	1.13323	+	0.199819i	0.424587	+	0.905387i	$0.360419\pi$
$798$		0			0
$799$	−5.93827	−	7.07695i	−0.210081	−	0.250365i
$800$		0			0
$801$	2.35062	−	7.64127i	0.0830551	−	0.269991i
$802$		0			0
$803$	−34.6455	−	12.6099i	−1.22261	−	0.444995i
$804$		0			0
$805$	−89.3588	−	74.9809i	−3.14948	−	2.64273i
$806$		0			0
$807$	32.4592	−	12.7536i	1.14262	−	0.448948i
$808$		0			0
$809$			29.1121i			1.02353i	0.859126	+	0.511764i	$0.171008\pi$
$809$			29.1121i			1.02353i	−0.859126	+	0.511764i	$0.828992\pi$
$810$		0			0
$811$		−	5.00258i		−	0.175664i	−0.996135	−	0.0878322i	$-0.972006\pi$
$811$		−	5.00258i		−	0.175664i	0.996135	−	0.0878322i	$-0.0279939\pi$
$812$		0			0
$813$	15.2414	−	5.98852i	0.534538	−	0.210027i
$814$		0			0
$815$	38.3889	+	32.2121i	1.34470	+	1.12834i
$816$		0			0
$817$	7.98988	+	2.90808i	0.279530	+	0.101741i
$818$		0			0
$819$	7.59715	−	1.74011i	0.265466	−	0.0608045i
$820$		0			0
$821$	24.5976	+	29.3142i	0.858461	+	1.02307i	0.999453	+	0.0330628i	$0.0105261\pi$
$821$	24.5976	+	29.3142i	0.858461	+	1.02307i	−0.140993	+	0.990011i	$0.545029\pi$
$822$		0			0
$823$	−25.1659	−	4.43743i	−0.877229	−	0.154679i	−0.283140	−	0.959079i	$-0.591376\pi$
$823$	−25.1659	−	4.43743i	−0.877229	−	0.154679i	−0.594089	+	0.804399i	$0.702487\pi$
$824$		0			0
$825$	10.0211	−	29.8642i	0.348891	−	1.03974i
$826$		0			0
$827$	−10.1843	+	17.6397i	−0.354142	+	0.613391i	−0.986971	−	0.160900i	$-0.948560\pi$
$827$	−10.1843	+	17.6397i	−0.354142	+	0.613391i	0.632829	+	0.774292i	$0.281894\pi$
$828$		0			0
$829$	6.73571	+	11.6666i	0.233941	+	0.405198i	0.958964	−	0.283527i	$-0.0915044\pi$
$829$	6.73571	+	11.6666i	0.233941	+	0.405198i	−0.725023	+	0.688724i	$0.758171\pi$
$830$		0			0
$831$	−1.18571	−	46.8271i	−0.0411319	−	1.62441i
$832$		0			0
$833$	−5.59648	−	15.3762i	−0.193906	−	0.532753i
$834$		0			0
$835$	17.5282	−	3.09069i	0.606588	−	0.106958i
$836$		0			0
$837$	−3.95175	+	39.9543i	−0.136592	+	1.38102i
$838$		0			0
$839$	−2.23795	−	12.6921i	−0.0772627	−	0.438178i	−0.998760	−	0.0497926i	$-0.984144\pi$
$839$	−2.23795	−	12.6921i	−0.0772627	−	0.438178i	0.921497	−	0.388386i	$-0.126967\pi$
$840$		0			0
$841$	−4.01947	+	1.46297i	−0.138602	+	0.0504471i
$842$		0			0
$843$	17.0579	−	31.3520i	0.587504	−	1.07982i
$844$		0			0
$845$	−35.9076	+	20.7313i	−1.23526	+	0.713177i
$846$		0			0
$847$	3.13382	+	1.80931i	0.107679	+	0.0621688i
$848$		0			0
$849$	6.42157	+	31.7032i	0.220388	+	1.08805i
$850$		0			0
$851$	13.8970	−	78.8139i	0.476384	−	2.70171i
$852$		0			0
$853$	5.63368	−	4.72722i	0.192893	−	0.161857i	−0.541226	−	0.840877i	$-0.682040\pi$
$853$	5.63368	−	4.72722i	0.192893	−	0.161857i	0.734119	+	0.679020i	$0.237595\pi$
$854$		0			0
$855$	−6.22361	−	9.61989i	−0.212843	−	0.328993i
$856$		0			0
$857$	−8.52082	+	23.4108i	−0.291066	+	0.799696i	0.704846	+	0.709361i	$0.251016\pi$
$857$	−8.52082	+	23.4108i	−0.291066	+	0.799696i	−0.995911	+	0.0903355i	$0.971206\pi$
$858$		0			0
$859$	22.4999	−	26.8143i	0.767686	−	0.914892i	−0.230622	−	0.973043i	$-0.574076\pi$
$859$	22.4999	−	26.8143i	0.767686	−	0.914892i	0.998308	+	0.0581510i	$0.0185205\pi$
$860$		0			0
$861$	−56.3636	−	8.47340i	−1.92087	−	0.288773i
$862$		0			0
$863$	26.3037			0.895388			0.447694	−	0.894187i	$-0.352245\pi$
$863$	26.3037			0.895388			0.447694	+	0.894187i	$0.352245\pi$
$864$		0			0
$865$	−13.7814			−0.468583
$866$		0			0
$867$	−16.9062	+	21.2163i	−0.574164	+	0.720543i
$868$		0			0
$869$	10.3094	−	12.2863i	0.349723	−	0.416783i
$870$		0			0
$871$	−0.336666	+	0.924982i	−0.0114075	+	0.0313418i
$872$		0			0
$873$	6.50917	−	52.2659i	0.220302	−	1.76893i
$874$		0			0
$875$	7.95807	−	6.67762i	0.269032	−	0.225745i
$876$		0			0
$877$	−8.19047	+	46.4505i	−0.276573	+	1.56852i	0.457349	+	0.889287i	$0.348799\pi$
$877$	−8.19047	+	46.4505i	−0.276573	+	1.56852i	−0.733922	+	0.679234i	$0.762312\pi$
$878$		0			0
$879$	13.8348	−	12.2187i	0.466636	−	0.412126i
$880$		0			0
$881$	26.1305	+	15.0864i	0.880359	+	0.508275i	0.870777	−	0.491679i	$-0.163617\pi$
$881$	26.1305	+	15.0864i	0.880359	+	0.508275i	0.00958201	+	0.999954i	$0.496950\pi$
$882$		0			0
$883$	−38.0607	+	21.9744i	−1.28085	+	0.739497i	−0.977003	−	0.213225i	$-0.931603\pi$
$883$	−38.0607	+	21.9744i	−1.28085	+	0.739497i	−0.303843	+	0.952722i	$0.598270\pi$
$884$		0			0
$885$	−10.1652	−	16.6204i	−0.341701	−	0.558688i
$886$		0			0
$887$	−26.8874	+	9.78620i	−0.902790	+	0.328589i	−0.751370	−	0.659881i	$-0.770607\pi$
$887$	−26.8874	+	9.78620i	−0.902790	+	0.328589i	−0.151420	+	0.988470i	$0.548384\pi$
$888$		0			0
$889$	−8.80803	−	49.9528i	−0.295412	−	1.67536i
$890$		0			0
$891$	16.8255	+	23.3274i	0.563674	+	0.781498i
$892$		0			0
$893$	−9.18915	+	1.62029i	−0.307503	+	0.0542211i
$894$		0			0
$895$	−8.76430	−	24.0797i	−0.292958	−	0.804896i
$896$		0			0
$897$	6.47550	−	3.96049i	0.216210	−	0.132237i
$898$		0			0
$899$	−19.2094	−	33.2716i	−0.640668	−	1.10967i
$900$		0			0
$901$	−5.36718	+	9.29623i	−0.178807	+	0.309702i
$902$		0			0
$903$	−38.3829	−	43.4596i	−1.27730	−	1.44624i
$904$		0			0
$905$	25.9569	+	4.57691i	0.862837	+	0.152141i
$906$		0			0
$907$	−11.4910	−	13.6944i	−0.381553	−	0.454717i	0.540751	−	0.841183i	$-0.318140\pi$
$907$	−11.4910	−	13.6944i	−0.381553	−	0.454717i	−0.922304	+	0.386466i	$0.873696\pi$
$908$		0			0
$909$	15.0064	+	35.5235i	0.497731	+	1.17824i
$910$		0			0
$911$	−47.6644	−	17.3484i	−1.57919	−	0.574779i	−0.604163	−	0.796861i	$-0.706492\pi$
$911$	−47.6644	−	17.3484i	−1.57919	−	0.574779i	−0.975028	+	0.222082i	$0.928715\pi$
$912$		0			0
$913$	−3.17772	−	2.66642i	−0.105167	−	0.0882457i
$914$		0			0
$915$	−15.9171	−	12.6835i	−0.526201	−	0.419303i
$916$		0			0
$917$			9.11946i			0.301151i
$918$		0			0
$919$		−	8.38232i		−	0.276507i	−0.990397	−	0.138254i	$-0.955851\pi$
$919$		−	8.38232i		−	0.276507i	0.990397	−	0.138254i	$-0.0441489\pi$
$920$		0			0
$921$	−0.118763	+	0.789991i	−0.00391338	+	0.0260311i
$922$		0			0
$923$	−5.05315	−	4.24010i	−0.166326	−	0.139564i
$924$		0			0
$925$	55.1679	+	20.0795i	1.81391	+	0.660209i
$926$		0			0
$927$	−1.84226	−	36.3547i	−0.0605078	−	1.19404i
$928$		0			0
$929$	20.2331	+	24.1128i	0.663825	+	0.791116i	0.987929	−	0.154905i	$-0.0495072\pi$
$929$	20.2331	+	24.1128i	0.663825	+	0.791116i	−0.324104	+	0.946021i	$0.605063\pi$
$930$		0			0
$931$	−16.2759	−	2.86988i	−0.533422	−	0.0940567i
$932$		0			0
$933$	0.333423	−	0.0675356i	0.0109158	−	0.00221102i
$934$		0			0
$935$	6.04212	−	10.4653i	0.197598	−	0.342250i
$936$		0			0
$937$	−29.6346	−	51.3286i	−0.968119	−	1.67683i	−0.700990	−	0.713171i	$-0.747258\pi$
$937$	−29.6346	−	51.3286i	−0.968119	−	1.67683i	−0.267129	−	0.963661i	$-0.586075\pi$
$938$		0			0
$939$	21.3733	+	11.6287i	0.697492	+	0.379488i
$940$		0			0
$941$	−8.29508	−	22.7905i	−0.270412	−	0.742950i	−0.998356	−	0.0573141i	$-0.981746\pi$
$941$	−8.29508	−	22.7905i	−0.270412	−	0.742950i	0.727944	−	0.685636i	$-0.240476\pi$
$942$		0			0
$943$	−54.6671	+	9.63929i	−1.78021	+	0.313898i
$944$		0			0
$945$	5.92827	+	77.9079i	0.192847	+	2.53434i
$946$		0			0
$947$	5.29234	+	30.0144i	0.171978	+	0.975336i	0.941574	+	0.336805i	$0.109346\pi$
$947$	5.29234	+	30.0144i	0.171978	+	0.975336i	−0.769596	+	0.638531i	$0.779543\pi$
$948$		0			0
$949$	6.12426	−	2.22905i	0.198802	−	0.0723580i
$950$		0			0
$951$	−9.18354	+	0.232537i	−0.297797	+	0.00754053i
$952$		0			0
$953$	12.8821	−	7.43746i	0.417291	−	0.240923i	−0.276627	−	0.960977i	$-0.589217\pi$
$953$	12.8821	−	7.43746i	0.417291	−	0.240923i	0.693917	+	0.720055i	$0.255883\pi$
$954$		0			0
$955$	31.2331	+	18.0324i	1.01068	+	0.583516i
$956$		0			0
$957$	−26.0926	−	8.75556i	−0.843455	−	0.283027i
$958$		0			0
$959$	2.26983	−	12.8728i	0.0732965	−	0.415685i
$960$		0			0
$961$	−21.9873	+	18.4495i	−0.709268	+	0.595147i
$962$		0			0
$963$	−5.48226	+	5.09460i	−0.176663	+	0.164171i
$964$		0			0
$965$	6.30370	−	17.3193i	0.202923	−	0.557527i
$966$		0			0
$967$	22.4365	−	26.7388i	0.721511	−	0.859863i	−0.273266	−	0.961939i	$-0.588104\pi$
$967$	22.4365	−	26.7388i	0.721511	−	0.859863i	0.994777	+	0.102076i	$0.0325484\pi$
$968$		0			0
$969$	−0.855616	−	2.17762i	−0.0274863	−	0.0699554i
$970$		0			0
$971$	−6.91776			−0.222002			−0.111001	−	0.993820i	$-0.535406\pi$
$971$	−6.91776			−0.222002			−0.111001	+	0.993820i	$0.535406\pi$
$972$		0			0
$973$	−53.0931			−1.70209
$974$		0			0
$975$	2.03633	+	5.18265i	0.0652147	+	0.165978i
$976$		0			0
$977$	23.1527	−	27.5923i	0.740720	−	0.882755i	−0.255747	−	0.966744i	$-0.582321\pi$
$977$	23.1527	−	27.5923i	0.740720	−	0.882755i	0.996467	+	0.0839883i	$0.0267658\pi$
$978$		0			0
$979$	2.91279	−	8.00283i	0.0930932	−	0.255771i
$980$		0			0
$981$	21.6603	−	20.1287i	0.691561	−	0.642660i
$982$		0			0
$983$	−35.0158	+	29.3818i	−1.11683	+	0.937133i	−0.998440	−	0.0558338i	$-0.982218\pi$
$983$	−35.0158	+	29.3818i	−1.11683	+	0.937133i	−0.118392	+	0.992967i	$0.537774\pi$
$984$		0			0
$985$	−10.4833	+	59.4536i	−0.334025	+	1.89435i
$986$		0			0
$987$	60.3250	+	20.2425i	1.92017	+	0.644325i
$988$		0			0
$989$	−48.9048	−	28.2352i	−1.55508	−	0.897827i
$990$		0			0
$991$	−0.705174	+	0.407132i	−0.0224006	+	0.0129330i	−0.511158	−	0.859486i	$-0.670783\pi$
$991$	−0.705174	+	0.407132i	−0.0224006	+	0.0129330i	0.488758	+	0.872419i	$0.337450\pi$
$992$		0			0
$993$	−8.41072	+	0.212969i	−0.266906	+	0.00675835i
$994$		0			0
$995$	24.7420	−	9.00534i	0.784373	−	0.285488i
$996$		0			0
$997$	4.74921	+	26.9341i	0.150409	+	0.853012i	0.962864	+	0.269988i	$0.0870197\pi$
$997$	4.74921	+	26.9341i	0.150409	+	0.853012i	−0.812455	+	0.583024i	$0.801869\pi$
$998$		0			0
$999$	−44.2556	+	30.2474i	−1.40019	+	0.956986i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bi.a.95.14	✓	216
4.3	odd	2	inner	864.2.bi.a.95.23	yes	216
27.2	odd	18	inner	864.2.bi.a.191.23	yes	216
108.83	even	18	inner	864.2.bi.a.191.14	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.bi.a.95.14	✓	216	1.1	even	1	trivial
864.2.bi.a.95.23	yes	216	4.3	odd	2	inner
864.2.bi.a.191.14	yes	216	108.83	even	18	inner
864.2.bi.a.191.23	yes	216	27.2	odd	18	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bi (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.633406 - 1.61208i) q^{3} +(-2.10172 + 2.50473i) q^{5} +(1.57289 - 4.32148i) q^{7} +(-2.19759 + 2.04220i) q^{9} +O(q^{10})\)	\(q+(-0.633406 - 1.61208i) q^{3} +(-2.10172 + 2.50473i) q^{5} +(1.57289 - 4.32148i) q^{7} +(-2.19759 + 2.04220i) q^{9} +(-2.44813 + 2.05422i) q^{11} +(0.0980972 - 0.556337i) q^{13} +(5.36906 + 1.80162i) q^{15} +(1.00153 + 0.578233i) q^{17} +(1.01157 - 0.584028i) q^{19} +(-7.96284 + 0.201628i) q^{21} +(-7.28981 + 2.65327i) q^{23} +(-0.988210 - 5.60442i) q^{25} +(4.68415 + 2.24915i) q^{27} +(-4.89664 + 0.863410i) q^{29} +(2.64270 + 7.26075i) q^{31} +(4.86222 + 2.64541i) q^{33} +(7.51836 + 13.0222i) q^{35} +(-5.15812 + 8.93412i) q^{37} +(-0.958994 + 0.194247i) q^{39} +(7.04687 + 1.24255i) q^{41} +(4.67905 + 5.57628i) q^{43} +(-0.496434 - 9.79650i) q^{45} +(-7.50664 - 2.73219i) q^{47} +(-10.8389 - 9.09490i) q^{49} +(0.297783 - 1.98080i) q^{51} +9.28205i q^{53} -10.4493i q^{55} +(-1.58223 - 1.26080i) q^{57} +(-2.63531 - 2.21129i) q^{59} +(-3.37704 - 1.22914i) q^{61} +(5.36875 + 12.7090i) q^{63} +(1.18730 + 1.41497i) q^{65} +(-1.71598 - 0.302574i) q^{67} +(8.89469 + 10.0711i) q^{69} +(5.83837 - 10.1124i) q^{71} +(5.76835 + 9.99107i) q^{73} +(-8.40883 + 5.14294i) q^{75} +(5.02664 + 13.8106i) q^{77} +(-4.94240 + 0.871479i) q^{79} +(0.658843 - 8.97585i) q^{81} +(0.225399 + 1.27830i) q^{83} +(-3.55325 + 1.29328i) q^{85} +(4.49344 + 7.34688i) q^{87} +(-2.30786 + 1.33244i) q^{89} +(-2.24990 - 1.29898i) q^{91} +(10.0310 - 8.85924i) q^{93} +(-0.663194 + 3.76116i) q^{95} +(-13.4491 + 11.2851i) q^{97} +(1.18486 - 9.51390i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 216 * q	\( 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) \) 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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