LMFDB - Embedded newform 912.2.cc.h.401.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(257,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("912.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.cc (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			401.4
Character	$\chi$	$=$	912.401
Dual form			912.2.cc.h.257.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.602283 - 1.62396i) q^{3} +(1.11883 + 3.07396i) q^{5} +(-0.429476 - 0.743873i) q^{7} +(-2.27451 + 1.95617i) q^{9} +(0.0707492 + 0.0408471i) q^{11} +(-1.68439 - 2.00738i) q^{13} +(4.31815 - 3.66834i) q^{15} +(4.78209 + 0.843212i) q^{17} +(4.33435 + 0.461939i) q^{19} +(-0.949357 + 1.14547i) q^{21} +(-3.09543 + 8.50464i) q^{23} +(-4.36725 + 3.66456i) q^{25} +(4.54665 + 2.51555i) q^{27} +(0.482799 + 2.73809i) q^{29} +(2.12534 - 1.22707i) q^{31} +(0.0237231 - 0.139496i) q^{33} +(1.80613 - 2.15246i) q^{35} +6.54795i q^{37} +(-2.24543 + 3.94439i) q^{39} +(9.27084 + 7.77916i) q^{41} +(-3.08205 + 1.12177i) q^{43} +(-8.55799 - 4.80314i) q^{45} +(0.0616204 - 0.0108653i) q^{47} +(3.13110 - 5.42323i) q^{49} +(-1.51083 - 8.27379i) q^{51} +(-0.185336 - 0.0674568i) q^{53} +(-0.0464060 + 0.263181i) q^{55} +(-1.86033 - 7.31705i) q^{57} +(0.821982 - 4.66169i) q^{59} +(0.659376 + 0.239993i) q^{61} +(2.43199 + 0.851822i) q^{63} +(4.28605 - 7.42366i) q^{65} +(6.85018 - 1.20787i) q^{67} +(15.6755 - 0.0953242i) q^{69} +(0.998357 - 0.363372i) q^{71} +(4.95776 + 4.16006i) q^{73} +(8.58142 + 4.88515i) q^{75} -0.0701713i q^{77} +(-7.81462 + 9.31311i) q^{79} +(1.34680 - 8.89866i) q^{81} +(-7.40404 + 4.27472i) q^{83} +(2.75835 + 15.6434i) q^{85} +(4.15578 - 2.43315i) q^{87} +(1.87292 - 1.57156i) q^{89} +(-0.769830 + 2.11509i) q^{91} +(-3.27277 - 2.71244i) q^{93} +(3.42943 + 13.8405i) q^{95} +(17.2282 + 3.03779i) q^{97} +(-0.240824 + 0.0454903i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 3 q^{3} - 3 q^{9} + 3 q^{13} + 9 q^{15} + 6 q^{17} - 3 q^{19} + 6 q^{25} - 6 q^{27} - 6 q^{29} + 45 q^{33} + 24 q^{35} - 18 q^{39} - 3 q^{41} + 21 q^{43} - 45 q^{45} - 18 q^{47} - 30 q^{49} + 6 q^{51}+ \cdots + 3 q^{99}+O(q^{100}) $ 60 * q + 3 * q^3 - 3 * q^9 + 3 * q^13 + 9 * q^15 + 6 * q^17 - 3 * q^19 + 6 * q^25 - 6 * q^27 - 6 * q^29 + 45 * q^33 + 24 * q^35 - 18 * q^39 - 3 * q^41 + 21 * q^43 - 45 * q^45 - 18 * q^47 - 30 * q^49 + 6 * q^51 + 36 * q^53 - 18 * q^55 + 48 * q^57 - 21 * q^59 - 6 * q^61 - 78 * q^63 - 24 * q^65 + 48 * q^67 + 21 * q^69 + 36 * q^71 - 57 * q^73 + 36 * q^79 - 39 * q^81 - 36 * q^83 + 6 * q^85 + 90 * q^87 + 24 * q^89 + 18 * q^91 - 54 * q^93 + 30 * q^95 + 15 * q^97 + 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.602283	−	1.62396i	−0.347728	−	0.937595i
$3$	−0.602283	−	1.62396i	−0.347728	−	0.937595i
$4$		0			0
$5$	1.11883	+	3.07396i	0.500357	+	1.37472i	0.890927	+	0.454146i	$0.150055\pi$
$5$	1.11883	+	3.07396i	0.500357	+	1.37472i	−0.390571	+	0.920573i	$0.627722\pi$
$6$		0			0
$7$	−0.429476	−	0.743873i	−0.162326	−	0.281158i	0.773376	−	0.633947i	$-0.218566\pi$
$7$	−0.429476	−	0.743873i	−0.162326	−	0.281158i	−0.935703	+	0.352790i	$0.885233\pi$
$8$		0			0
$9$	−2.27451	+	1.95617i	−0.758170	+	0.652056i
$10$		0			0
$11$	0.0707492	+	0.0408471i	0.0213317	+	0.0123159i	0.510628	−	0.859802i	$-0.329413\pi$
$11$	0.0707492	+	0.0408471i	0.0213317	+	0.0123159i	−0.489296	+	0.872118i	$0.662746\pi$
$12$		0			0
$13$	−1.68439	−	2.00738i	−0.467165	−	0.556746i	0.480093	−	0.877218i	$-0.340603\pi$
$13$	−1.68439	−	2.00738i	−0.467165	−	0.556746i	−0.947258	+	0.320472i	$0.896159\pi$
$14$		0			0
$15$	4.31815	−	3.66834i	1.11494	−	0.947160i
$16$		0			0
$17$	4.78209	+	0.843212i	1.15983	+	0.204509i	0.720262	−	0.693702i	$-0.244021\pi$
$17$	4.78209	+	0.843212i	1.15983	+	0.204509i	0.439565	+	0.898211i	$0.355133\pi$
$18$		0			0
$19$	4.33435	+	0.461939i	0.994369	+	0.105976i
$19$	4.33435	+	0.461939i	0.994369	+	0.105976i
$20$		0			0
$21$	−0.949357	+	1.14547i	−0.207167	+	0.249963i
$22$		0			0
$23$	−3.09543	+	8.50464i	−0.645443	+	1.77334i	−0.0115312	+	0.999934i	$0.503671\pi$
$23$	−3.09543	+	8.50464i	−0.645443	+	1.77334i	−0.633911	+	0.773406i	$0.718552\pi$
$24$		0			0
$25$	−4.36725	+	3.66456i	−0.873450	+	0.732911i
$26$		0			0
$27$	4.54665	+	2.51555i	0.875002	+	0.484119i
$28$		0			0
$29$	0.482799	+	2.73809i	0.0896536	+	0.508451i	0.996255	+	0.0864628i	$0.0275564\pi$
$29$	0.482799	+	2.73809i	0.0896536	+	0.508451i	−0.906602	+	0.421988i	$0.861333\pi$
$30$		0			0
$31$	2.12534	−	1.22707i	0.381723	−	0.220388i	−0.296845	−	0.954926i	$-0.595934\pi$
$31$	2.12534	−	1.22707i	0.381723	−	0.220388i	0.678568	+	0.734538i	$0.262601\pi$
$32$		0			0
$33$	0.0237231	−	0.139496i	0.00412966	−	0.0242831i
$34$		0			0
$35$	1.80613	−	2.15246i	0.305292	−	0.363832i
$36$		0			0
$37$			6.54795i			1.07648i	0.842793	+	0.538238i	$0.180910\pi$
$37$			6.54795i			1.07648i	−0.842793	+	0.538238i	$0.819090\pi$
$38$		0			0
$39$	−2.24543	+	3.94439i	−0.359556	+	0.631608i
$40$		0			0
$41$	9.27084	+	7.77916i	1.44786	+	1.21490i	0.934122	+	0.356955i	$0.116185\pi$
$41$	9.27084	+	7.77916i	1.44786	+	1.21490i	0.513741	+	0.857945i	$0.328259\pi$
$42$		0			0
$43$	−3.08205	+	1.12177i	−0.470008	+	0.171069i	−0.566156	−	0.824298i	$-0.691570\pi$
$43$	−3.08205	+	1.12177i	−0.470008	+	0.171069i	0.0961482	+	0.995367i	$0.469348\pi$
$44$		0			0
$45$	−8.55799	−	4.80314i	−1.27575	−	0.716010i
$46$		0			0
$47$	0.0616204	−	0.0108653i	0.00898826	−	0.00158487i	−0.169152	−	0.985590i	$-0.554103\pi$
$47$	0.0616204	−	0.0108653i	0.00898826	−	0.00158487i	0.178140	+	0.984005i	$0.442992\pi$
$48$		0			0
$49$	3.13110	−	5.42323i	0.447300	−	0.774747i
$50$		0			0
$51$	−1.51083	−	8.27379i	−0.211558	−	1.15856i
$52$		0			0
$53$	−0.185336	−	0.0674568i	−0.0254579	−	0.00926591i	0.329260	−	0.944239i	$-0.393201\pi$
$53$	−0.185336	−	0.0674568i	−0.0254579	−	0.00926591i	−0.354718	+	0.934973i	$0.615423\pi$
$54$		0			0
$55$	−0.0464060	+	0.263181i	−0.00625738	+	0.0354874i
$56$		0			0
$57$	−1.86033	−	7.31705i	−0.246407	−	0.969166i
$58$		0			0
$59$	0.821982	−	4.66169i	0.107013	−	0.606900i	−0.883384	−	0.468649i	$-0.844741\pi$
$59$	0.821982	−	4.66169i	0.107013	−	0.606900i	0.990397	−	0.138251i	$-0.0441481\pi$
$60$		0			0
$61$	0.659376	+	0.239993i	0.0844245	+	0.0307280i	0.383887	−	0.923380i	$-0.374585\pi$
$61$	0.659376	+	0.239993i	0.0844245	+	0.0307280i	−0.299463	+	0.954108i	$0.596807\pi$
$62$		0			0
$63$	2.43199	+	0.851822i	0.306402	+	0.107319i
$64$		0			0
$65$	4.28605	−	7.42366i	0.531620	−	0.920792i
$66$		0			0
$67$	6.85018	−	1.20787i	0.836882	−	0.147565i	0.261248	−	0.965272i	$-0.415866\pi$
$67$	6.85018	−	1.20787i	0.836882	−	0.147565i	0.575635	+	0.817707i	$0.304755\pi$
$68$		0			0
$69$	15.6755	−	0.0953242i	1.88711	−	0.0114757i
$70$		0			0
$71$	0.998357	−	0.363372i	0.118483	−	0.0431243i	−0.282098	−	0.959386i	$-0.591030\pi$
$71$	0.998357	−	0.363372i	0.118483	−	0.0431243i	0.400581	+	0.916261i	$0.368808\pi$
$72$		0			0
$73$	4.95776	+	4.16006i	0.580262	+	0.486898i	0.885033	−	0.465528i	$-0.154136\pi$
$73$	4.95776	+	4.16006i	0.580262	+	0.486898i	−0.304771	+	0.952426i	$0.598580\pi$
$74$		0			0
$75$	8.58142	+	4.88515i	0.990898	+	0.564089i
$76$		0			0
$77$		−	0.0701713i		−	0.00799676i
$78$		0			0
$79$	−7.81462	+	9.31311i	−0.879214	+	1.04781i	0.119275	+	0.992861i	$0.461943\pi$
$79$	−7.81462	+	9.31311i	−0.879214	+	1.04781i	−0.998489	+	0.0549452i	$0.982502\pi$
$80$		0			0
$81$	1.34680	−	8.89866i	0.149645	−	0.988740i
$82$		0			0
$83$	−7.40404	+	4.27472i	−0.812699	+	0.469212i	−0.847892	−	0.530169i	$-0.822129\pi$
$83$	−7.40404	+	4.27472i	−0.812699	+	0.469212i	0.0351935	+	0.999381i	$0.488795\pi$
$84$		0			0
$85$	2.75835	+	15.6434i	0.299185	+	1.69676i
$86$		0			0
$87$	4.15578	−	2.43315i	0.445546	−	0.260861i
$88$		0			0
$89$	1.87292	−	1.57156i	0.198529	−	0.166585i	−0.538104	−	0.842879i	$-0.680859\pi$
$89$	1.87292	−	1.57156i	0.198529	−	0.166585i	0.736633	+	0.676293i	$0.236415\pi$
$90$		0			0
$91$	−0.769830	+	2.11509i	−0.0807001	+	0.221722i
$92$		0			0
$93$	−3.27277	−	2.71244i	−0.339370	−	0.281267i
$94$		0			0
$95$	3.42943	+	13.8405i	0.351852	+	1.42000i
$96$		0			0
$97$	17.2282	+	3.03779i	1.74926	+	0.308441i	0.954439	−	0.298406i	$-0.0964549\pi$
$97$	17.2282	+	3.03779i	1.74926	+	0.308441i	0.794819	+	0.606847i	$0.207566\pi$
$98$		0			0
$99$	−0.240824	+	0.0454903i	−0.0242037	+	0.00457195i
$100$		0			0
$101$	−10.3508	−	12.3356i	−1.02995	−	1.22744i	−0.973417	−	0.229042i	$-0.926441\pi$
$101$	−10.3508	−	12.3356i	−1.02995	−	1.22744i	−0.0565300	−	0.998401i	$-0.518004\pi$
$102$		0			0
$103$	14.6928	+	8.48289i	1.44772	+	0.835844i	0.998346	−	0.0574976i	$-0.0183122\pi$
$103$	14.6928	+	8.48289i	1.44772	+	0.835844i	0.449378	+	0.893341i	$0.351645\pi$
$104$		0			0
$105$	−4.58332	−	1.63670i	−0.447286	−	0.159725i
$106$		0			0
$107$	−8.79441	−	15.2324i	−0.850188	−	1.47257i	−0.881039	−	0.473044i	$-0.843155\pi$
$107$	−8.79441	−	15.2324i	−0.850188	−	1.47257i	0.0308510	−	0.999524i	$-0.490178\pi$
$108$		0			0
$109$	−5.48720	−	15.0760i	−0.525579	−	1.44402i	−0.864227	−	0.503102i	$-0.832192\pi$
$109$	−5.48720	−	15.0760i	−0.525579	−	1.44402i	0.338648	−	0.940913i	$-0.390030\pi$
$110$		0			0
$111$	10.6336	−	3.94371i	1.00930	−	0.374321i
$112$		0			0
$113$	−7.51726			−0.707164			−0.353582	−	0.935403i	$-0.615036\pi$
$113$	−7.51726			−0.707164			−0.353582	+	0.935403i	$0.615036\pi$
$114$		0			0
$115$	−29.6062			−2.76079
$116$		0			0
$117$	7.75793	+	1.27085i	0.717221	+	0.117490i
$118$		0			0
$119$	−1.42655	−	3.91941i	−0.130771	−	0.359292i
$120$		0			0
$121$	−5.49666	−	9.52050i	−0.499697	−	0.865500i
$122$		0			0
$123$	7.04940	−	19.7408i	0.635623	−	1.77996i
$124$		0			0
$125$	−1.98603	−	1.14664i	−0.177636	−	0.102558i
$126$		0			0
$127$	6.88492	+	8.20512i	0.610938	+	0.728087i	0.979484	−	0.201522i	$-0.0645889\pi$
$127$	6.88492	+	8.20512i	0.610938	+	0.728087i	−0.368546	+	0.929609i	$0.620144\pi$
$128$		0			0
$129$	3.67798	+	4.32950i	0.323828	+	0.381192i
$130$		0			0
$131$	−10.3723	−	1.82892i	−0.906232	−	0.159793i	−0.298940	−	0.954272i	$-0.596633\pi$
$131$	−10.3723	−	1.82892i	−0.906232	−	0.159793i	−0.607292	+	0.794479i	$0.707744\pi$
$132$		0			0
$133$	−1.51787	−	3.42260i	−0.131616	−	0.296777i
$134$		0			0
$135$	−2.64580	+	16.7907i	−0.227714	+	1.44511i
$136$		0			0
$137$	−2.81895	+	7.74500i	−0.240839	+	0.661700i	0.759103	+	0.650970i	$0.225638\pi$
$137$	−2.81895	+	7.74500i	−0.240839	+	0.661700i	−0.999942	+	0.0107298i	$0.996585\pi$
$138$		0			0
$139$	−10.9726	+	9.20715i	−0.930688	+	0.780940i	−0.975941	−	0.218036i	$-0.930035\pi$
$139$	−10.9726	+	9.20715i	−0.930688	+	0.780940i	0.0452529	+	0.998976i	$0.485591\pi$
$140$		0			0
$141$	−0.0547578	−	0.0935252i	−0.00461144	−	0.00787625i
$142$		0			0
$143$	−0.0371737	−	0.210823i	−0.00310862	−	0.0176299i
$144$		0			0
$145$	−7.87662	+	4.54757i	−0.654118	+	0.377655i
$146$		0			0
$147$	−10.6929	−	1.81848i	−0.881938	−	0.149985i
$148$		0			0
$149$	4.58786	−	5.46760i	0.375852	−	0.447923i	−0.544648	−	0.838665i	$-0.683337\pi$
$149$	4.58786	−	5.46760i	0.375852	−	0.447923i	0.920501	+	0.390741i	$0.127781\pi$
$150$		0			0
$151$		−	12.9655i		−	1.05511i	−0.849520	−	0.527557i	$-0.823108\pi$
$151$		−	12.9655i		−	1.05511i	0.849520	−	0.527557i	$-0.176892\pi$
$152$		0			0
$153$	−12.5264	+	7.43669i	−1.01270	+	0.601220i
$154$		0			0
$155$	6.14986	+	5.16035i	0.493969	+	0.414489i
$156$		0			0
$157$	−9.95071	+	3.62176i	−0.794153	+	0.289048i	−0.707061	−	0.707152i	$-0.749980\pi$
$157$	−9.95071	+	3.62176i	−0.794153	+	0.289048i	−0.0870919	+	0.996200i	$0.527757\pi$
$158$		0			0
$159$	0.00207734	+	0.341607i	0.000164744	+	0.0270912i
$160$		0			0
$161$	7.65579	−	1.34992i	0.603360	−	0.106389i
$162$		0			0
$163$	−6.94030	+	12.0210i	−0.543607	+	0.941554i	0.455087	+	0.890447i	$0.349608\pi$
$163$	−6.94030	+	12.0210i	−0.543607	+	0.941554i	−0.998693	+	0.0511070i	$0.983725\pi$
$164$		0			0
$165$	0.455346	−	0.0831480i	0.0354487	−	0.00647306i
$166$		0			0
$167$	−2.52985	−	0.920790i	−0.195766	−	0.0712529i	0.242277	−	0.970207i	$-0.422106\pi$
$167$	−2.52985	−	0.920790i	−0.195766	−	0.0712529i	−0.438042	+	0.898954i	$0.644328\pi$
$168$		0			0
$169$	1.06503	−	6.04010i	0.0819256	−	0.464623i
$170$		0			0
$171$	−10.7622	+	7.42804i	−0.823003	+	0.568037i
$172$		0			0
$173$	2.01145	−	11.4075i	0.152928	−	0.867296i	−0.807728	−	0.589555i	$-0.799303\pi$
$173$	2.01145	−	11.4075i	0.152928	−	0.867296i	0.960656	−	0.277741i	$-0.0895858\pi$
$174$		0			0
$175$	4.60159	+	1.67484i	0.347848	+	0.126606i
$176$		0			0
$177$	−8.06548	+	1.47279i	−0.606238	+	0.110701i
$178$		0			0
$179$	7.22214	−	12.5091i	0.539808	−	0.934975i	−0.459106	−	0.888382i	$-0.651830\pi$
$179$	7.22214	−	12.5091i	0.539808	−	0.934975i	0.998914	−	0.0465934i	$-0.0148365\pi$
$180$		0			0
$181$	−8.37233	+	1.47627i	−0.622310	+	0.109730i	−0.475908	−	0.879495i	$-0.657881\pi$
$181$	−8.37233	+	1.47627i	−0.622310	+	0.109730i	−0.146402	+	0.989225i	$0.546769\pi$
$182$		0			0
$183$	−0.00739062	−	1.21535i	−0.000546330	−	0.0898410i
$184$		0			0
$185$	−20.1282	+	7.32605i	−1.47985	+	0.538622i
$186$		0			0
$187$	0.303886	+	0.254991i	0.0222224	+	0.0186468i
$188$		0			0
$189$	−0.0814184	−	4.46250i	−0.00592232	−	0.324599i
$190$		0			0
$191$			8.40418i			0.608105i	0.952655	+	0.304052i	$0.0983398\pi$
$191$			8.40418i			0.608105i	−0.952655	+	0.304052i	$0.901660\pi$
$192$		0			0
$193$	−11.6984	+	13.9416i	−0.842067	+	1.00354i	0.157804	+	0.987470i	$0.449558\pi$
$193$	−11.6984	+	13.9416i	−0.842067	+	1.00354i	−0.999871	+	0.0160655i	$0.994886\pi$
$194$		0			0
$195$	−14.6372	−	2.48925i	−1.04819	−	0.178259i
$196$		0			0
$197$	−13.1130	+	7.57082i	−0.934266	+	0.539399i	−0.888158	−	0.459538i	$-0.848015\pi$
$197$	−13.1130	+	7.57082i	−0.934266	+	0.539399i	−0.0461077	+	0.998936i	$0.514682\pi$
$198$		0			0
$199$	−2.17168	−	12.3162i	−0.153946	−	0.873072i	−0.959743	−	0.280880i	$-0.909374\pi$
$199$	−2.17168	−	12.3162i	−0.153946	−	0.873072i	0.805797	−	0.592192i	$-0.201737\pi$
$200$		0			0
$201$	−6.08728	−	10.3970i	−0.429364	−	0.733345i
$202$		0			0
$203$	1.82944	−	1.53508i	0.128402	−	0.107742i
$204$		0			0
$205$	−13.5403	+	37.2018i	−0.945699	+	2.59829i
$206$		0			0
$207$	−9.59591	−	25.3991i	−0.666962	−	1.76536i
$208$		0			0
$209$	0.287783	+	0.209727i	0.0199064	+	0.0145071i
$210$		0			0
$211$	3.97468	+	0.700843i	0.273628	+	0.0482480i	0.308778	−	0.951134i	$-0.400080\pi$
$211$	3.97468	+	0.700843i	0.273628	+	0.0482480i	−0.0351503	+	0.999382i	$0.511191\pi$
$212$		0			0
$213$	−1.19140	−	1.40244i	−0.0816331	−	0.0960937i
$214$		0			0
$215$	−6.89658	−	8.21902i	−0.470343	−	0.560533i
$216$		0			0
$217$	−1.82557	−	1.05399i	−0.123927	−	0.0715495i
$218$		0			0
$219$	3.76980	−	10.5567i	0.254740	−	0.713359i
$220$		0			0
$221$	−6.36226	−	11.0197i	−0.427972	−	0.741269i
$222$		0			0
$223$	4.91472	+	13.5031i	0.329114	+	0.904234i	0.988337	+	0.152286i	$0.0486634\pi$
$223$	4.91472	+	13.5031i	0.329114	+	0.904234i	−0.659222	+	0.751948i	$0.729114\pi$
$224$		0			0
$225$	2.76486	−	16.8782i	0.184324	−	1.12521i
$226$		0			0
$227$	−5.32884			−0.353688			−0.176844	−	0.984239i	$-0.556589\pi$
$227$	−5.32884			−0.353688			−0.176844	+	0.984239i	$0.556589\pi$
$228$		0			0
$229$	26.6471			1.76089			0.880445	−	0.474148i	$-0.157244\pi$
$229$	26.6471			1.76089			0.880445	+	0.474148i	$0.157244\pi$
$230$		0			0
$231$	−0.113956	+	0.0422629i	−0.00749772	+	0.00278070i
$232$		0			0
$233$	5.75863	+	15.8217i	0.377260	+	1.03651i	0.972487	+	0.232956i	$0.0748400\pi$
$233$	5.75863	+	15.8217i	0.377260	+	1.03651i	−0.595227	+	0.803558i	$0.702938\pi$
$234$		0			0
$235$	0.102342	+	0.177262i	0.00667609	+	0.0115633i
$236$		0			0
$237$	19.8308	+	7.08154i	1.28815	+	0.459995i
$238$		0			0
$239$	7.64559	+	4.41418i	0.494552	+	0.285530i	0.726461	−	0.687208i	$-0.241164\pi$
$239$	7.64559	+	4.41418i	0.494552	+	0.285530i	−0.231909	+	0.972737i	$0.574497\pi$
$240$		0			0
$241$	−5.37046	−	6.40027i	−0.345942	−	0.412277i	0.564817	−	0.825216i	$-0.308947\pi$
$241$	−5.37046	−	6.40027i	−0.345942	−	0.412277i	−0.910759	+	0.412939i	$0.864502\pi$
$242$		0			0
$243$	−15.2622	+	3.17235i	−0.979074	+	0.203506i
$244$		0			0
$245$	20.1740	+	3.55722i	1.28887	+	0.227262i
$246$		0			0
$247$	−6.37345	−	9.47876i	−0.405533	−	0.603119i
$248$		0			0
$249$	11.4013	+	9.44929i	0.722529	+	0.598824i
$250$		0			0
$251$	6.85409	−	18.8315i	0.432626	−	1.18863i	−0.511568	−	0.859243i	$-0.670935\pi$
$251$	6.85409	−	18.8315i	0.432626	−	1.18863i	0.944194	−	0.329389i	$-0.106843\pi$
$252$		0			0
$253$	−0.566389	+	0.475257i	−0.0356086	+	0.0298791i
$254$		0			0
$255$	23.7430	−	13.9012i	1.48684	−	0.870527i
$256$		0			0
$257$	−3.45168	−	19.5754i	−0.215310	−	1.22108i	−0.880368	−	0.474291i	$-0.842704\pi$
$257$	−3.45168	−	19.5754i	−0.215310	−	1.22108i	0.665058	−	0.746792i	$-0.268407\pi$
$258$		0			0
$259$	4.87084	−	2.81218i	0.302659	−	0.174741i
$260$		0			0
$261$	−6.45430	−	5.28338i	−0.399511	−	0.327033i
$262$		0			0
$263$	10.0603	−	11.9894i	0.620342	−	0.739295i	−0.360787	−	0.932648i	$-0.617492\pi$
$263$	10.0603	−	11.9894i	0.620342	−	0.739295i	0.981129	+	0.193353i	$0.0619363\pi$
$264$		0			0
$265$		−	0.645190i		−	0.0396337i
$266$		0			0
$267$	−3.68018	−	2.09502i	−0.225224	−	0.128213i
$268$		0			0
$269$	−0.365830	−	0.306968i	−0.0223051	−	0.0187162i	0.631567	−	0.775321i	$-0.282412\pi$
$269$	−0.365830	−	0.306968i	−0.0223051	−	0.0187162i	−0.653872	+	0.756605i	$0.726857\pi$
$270$		0			0
$271$	4.67021	−	1.69982i	0.283695	−	0.103257i	−0.196253	−	0.980553i	$-0.562878\pi$
$271$	4.67021	−	1.69982i	0.283695	−	0.103257i	0.479949	+	0.877297i	$0.340655\pi$
$272$		0			0
$273$	3.89848	−	0.0237070i	0.235947	−	0.00143481i
$274$		0			0
$275$	−0.458666	+	0.0808752i	−0.0276586	+	0.00487696i
$276$		0			0
$277$	−11.1334	+	19.2835i	−0.668939	+	1.15864i	0.309263	+	0.950977i	$0.399918\pi$
$277$	−11.1334	+	19.2835i	−0.668939	+	1.15864i	−0.978201	+	0.207659i	$0.933416\pi$
$278$		0			0
$279$	−2.43376	+	6.94851i	−0.145706	+	0.415996i
$280$		0			0
$281$	−8.78035	−	3.19578i	−0.523792	−	0.190645i	0.0665726	−	0.997782i	$-0.478794\pi$
$281$	−8.78035	−	3.19578i	−0.523792	−	0.190645i	−0.590364	+	0.807137i	$0.701016\pi$
$282$		0			0
$283$	2.03478	−	11.5398i	0.120955	−	0.685972i	−0.862673	−	0.505762i	$-0.831211\pi$
$283$	2.03478	−	11.5398i	0.120955	−	0.685972i	0.983628	−	0.180210i	$-0.0576776\pi$
$284$		0			0
$285$	20.4109	−	13.9051i	1.20904	−	0.823669i
$286$		0			0
$287$	1.80511	−	10.2373i	0.106552	−	0.604288i
$288$		0			0
$289$	6.18261	+	2.25029i	0.363683	+	0.132370i
$290$		0			0
$291$	−5.44297	−	29.8076i	−0.319073	−	1.74735i
$292$		0			0
$293$	−8.25942	+	14.3057i	−0.482520	+	0.835750i	−0.999799	−	0.0200674i	$-0.993612\pi$
$293$	−8.25942	+	14.3057i	−0.482520	+	0.835750i	0.517278	+	0.855817i	$0.326945\pi$
$294$		0			0
$295$	15.2495	−	2.68890i	0.887862	−	0.156554i
$296$		0			0
$297$	0.218918	+	0.363691i	0.0127029	+	0.0211035i
$298$		0			0
$299$	22.2859	−	8.11141i	1.28883	−	0.469095i
$300$		0			0
$301$	2.15812	+	1.81088i	0.124392	+	0.104377i
$302$		0			0
$303$	−13.7985	+	24.2389i	−0.792703	+	1.39249i
$304$		0			0
$305$			2.29541i			0.131435i
$306$		0			0
$307$	18.1070	−	21.5791i	1.03342	−	1.23158i	0.0610528	−	0.998135i	$-0.480554\pi$
$307$	18.1070	−	21.5791i	1.03342	−	1.23158i	0.972369	−	0.233449i	$-0.0750013\pi$
$308$		0			0
$309$	4.92668	−	28.9697i	0.280269	−	1.64803i
$310$		0			0
$311$	−26.8208	+	15.4850i	−1.52087	+	0.878074i	−0.521172	+	0.853451i	$0.674505\pi$
$311$	−26.8208	+	15.4850i	−1.52087	+	0.878074i	−0.999697	+	0.0246229i	$0.992162\pi$
$312$		0			0
$313$	−3.40251	−	19.2966i	−0.192321	−	1.09071i	−0.916182	−	0.400762i	$-0.868745\pi$
$313$	−3.40251	−	19.2966i	−0.192321	−	1.09071i	0.723861	−	0.689946i	$-0.242366\pi$
$314$		0			0
$315$	0.102517	+	8.42889i	0.00577620	+	0.474914i
$316$		0			0
$317$	20.3094	−	17.0416i	1.14069	−	0.957153i	0.141230	−	0.989977i	$-0.454894\pi$
$317$	20.3094	−	17.0416i	1.14069	−	0.957153i	0.999461	+	0.0328235i	$0.0104499\pi$
$318$		0			0
$319$	−0.0776853	+	0.213439i	−0.00434954	+	0.0119503i
$320$		0			0
$321$	−19.4401	+	23.4560i	−1.08504	+	1.30919i
$322$		0			0
$323$	20.3378	+	5.86381i	1.13162	+	0.326271i
$324$		0			0
$325$	14.7123	+	2.59417i	0.816091	+	0.143899i
$326$		0			0
$327$	−21.1780	+	17.9910i	−1.17114	+	0.994905i
$328$		0			0
$329$	−0.0345469	−	0.0411714i	−0.00190463	−	0.00226985i
$330$		0			0
$331$	7.69674	+	4.44371i	0.423051	+	0.244249i	0.696382	−	0.717672i	$-0.254792\pi$
$331$	7.69674	+	4.44371i	0.423051	+	0.244249i	−0.273331	+	0.961920i	$0.588125\pi$
$332$		0			0
$333$	−12.8089	−	14.8934i	−0.701923	−	0.816152i
$334$		0			0
$335$	11.3771	+	19.7058i	0.621600	+	1.07664i
$336$		0			0
$337$	−6.53898	−	17.9657i	−0.356201	−	0.978653i	−0.980336	−	0.197337i	$-0.936771\pi$
$337$	−6.53898	−	17.9657i	−0.356201	−	0.978653i	0.624135	−	0.781316i	$-0.285451\pi$
$338$		0			0
$339$	4.52751	+	12.2077i	0.245901	+	0.663034i
$340$		0			0
$341$	0.200488			0.0108571
$342$		0			0
$343$	−11.3916			−0.615088
$344$		0			0
$345$	17.8313	+	48.0794i	0.960005	+	2.58851i
$346$		0			0
$347$	2.26084	+	6.21161i	0.121368	+	0.333457i	0.985467	−	0.169865i	$-0.0543332\pi$
$347$	2.26084	+	6.21161i	0.121368	+	0.333457i	−0.864099	+	0.503322i	$0.832111\pi$
$348$		0			0
$349$	−18.2170	−	31.5528i	−0.975135	−	1.68898i	−0.679489	−	0.733686i	$-0.737798\pi$
$349$	−18.2170	−	31.5528i	−0.975135	−	1.68898i	−0.295646	−	0.955297i	$-0.595535\pi$
$350$		0			0
$351$	−2.60865	−	13.3640i	−0.139240	−	0.713317i
$352$		0			0
$353$	−23.6954	−	13.6805i	−1.26118	−	0.728142i	−0.287876	−	0.957668i	$-0.592949\pi$
$353$	−23.6954	−	13.6805i	−1.26118	−	0.728142i	−0.973303	+	0.229526i	$0.926282\pi$
$354$		0			0
$355$	2.23399	+	2.66236i	0.118568	+	0.141303i
$356$		0			0
$357$	−5.50579	+	4.67725i	−0.291397	+	0.247546i
$358$		0			0
$359$	30.3472	+	5.35104i	1.60167	+	0.282417i	0.901897	−	0.431952i	$-0.142175\pi$
$359$	30.3472	+	5.35104i	1.60167	+	0.282417i	0.699769	+	0.714369i	$0.253286\pi$
$360$		0			0
$361$	18.5732	+	4.00441i	0.977538	+	0.210759i
$362$		0			0
$363$	−12.1504	+	14.6604i	−0.637730	+	0.769472i
$364$		0			0
$365$	−7.24096	+	19.8944i	−0.379009	+	1.04132i
$366$		0			0
$367$	−3.31956	+	2.78544i	−0.173280	+	0.145399i	−0.725303	−	0.688430i	$-0.758300\pi$
$367$	−3.31956	+	2.78544i	−0.173280	+	0.145399i	0.552023	+	0.833829i	$0.313856\pi$
$368$		0			0
$369$	−36.3040	+	0.441551i	−1.88991	+	0.0229862i
$370$		0			0
$371$	0.0294180	+	0.166838i	0.00152731	+	0.00866178i
$372$		0			0
$373$	−8.73704	+	5.04433i	−0.452387	+	0.261186i	−0.708838	−	0.705372i	$-0.750780\pi$
$373$	−8.73704	+	5.04433i	−0.452387	+	0.261186i	0.256451	+	0.966557i	$0.417447\pi$
$374$		0			0
$375$	−0.665942	+	3.91584i	−0.0343891	+	0.202213i
$376$		0			0
$377$	4.68316	−	5.58117i	0.241195	−	0.287445i
$378$		0			0
$379$			20.2254i			1.03891i	0.854498	+	0.519455i	$0.173865\pi$
$379$			20.2254i			1.03891i	−0.854498	+	0.519455i	$0.826135\pi$
$380$		0			0
$381$	9.17815	−	16.1227i	0.470211	−	0.825989i
$382$		0			0
$383$	20.9229	+	17.5564i	1.06911	+	0.897091i	0.994972	−	0.100156i	$-0.0319343\pi$
$383$	20.9229	+	17.5564i	1.06911	+	0.897091i	0.0741401	+	0.997248i	$0.476379\pi$
$384$		0			0
$385$	0.215704	−	0.0785098i	0.0109933	−	0.00400123i
$386$		0			0
$387$	4.81577	−	8.58049i	0.244799	−	0.436171i
$388$		0			0
$389$	17.2366	−	3.03928i	0.873931	−	0.154098i	0.281347	−	0.959606i	$-0.409219\pi$
$389$	17.2366	−	3.03928i	0.873931	−	0.154098i	0.592584	+	0.805509i	$0.298108\pi$
$390$		0			0
$391$	−21.9739	+	38.0598i	−1.11127	+	1.92477i
$392$		0			0
$393$	3.27696	+	17.9457i	0.165301	+	0.905243i
$394$		0			0
$395$	−37.3714	−	13.6021i	−1.88036	−	0.684395i
$396$		0			0
$397$	−1.42602	+	8.08738i	−0.0715701	+	0.405894i	0.927884	+	0.372868i	$0.121626\pi$
$397$	−1.42602	+	8.08738i	−0.0715701	+	0.405894i	−0.999454	+	0.0330262i	$0.989486\pi$
$398$		0			0
$399$	−4.64399	+	4.52634i	−0.232490	+	0.226601i
$400$		0			0
$401$	1.40363	−	7.96038i	0.0700939	−	0.397522i	−0.929495	−	0.368836i	$-0.879756\pi$
$401$	1.40363	−	7.96038i	0.0700939	−	0.397522i	0.999588	−	0.0286865i	$-0.00913246\pi$
$402$		0			0
$403$	−6.04309	−	2.19950i	−0.301028	−	0.109565i
$404$		0			0
$405$	28.8610	−	5.81608i	1.43411	−	0.289003i
$406$		0			0
$407$	−0.267464	+	0.463262i	−0.0132577	+	0.0229630i
$408$		0			0
$409$	32.7238	−	5.77009i	1.61809	−	0.285313i	0.710035	−	0.704167i	$-0.248679\pi$
$409$	32.7238	−	5.77009i	1.61809	−	0.285313i	0.908053	+	0.418854i	$0.137568\pi$
$410$		0			0
$411$	14.2754	−	0.0868098i	0.704153	−	0.00428201i
$412$		0			0
$413$	−3.82073	+	1.39063i	−0.188006	+	0.0684285i
$414$		0			0
$415$	−21.4242	−	17.9771i	−1.05167	−	0.882459i
$416$		0			0
$417$	21.5607	+	12.2739i	1.05583	+	0.601054i
$418$		0			0
$419$			37.8098i			1.84713i	0.383441	+	0.923565i	$0.374739\pi$
$419$			37.8098i			1.84713i	−0.383441	+	0.923565i	$0.625261\pi$
$420$		0			0
$421$	8.59508	−	10.2432i	0.418898	−	0.499224i	−0.514787	−	0.857318i	$-0.672129\pi$
$421$	8.59508	−	10.2432i	0.418898	−	0.499224i	0.933685	+	0.358095i	$0.116573\pi$
$422$		0			0
$423$	−0.118902	+	0.145253i	−0.00578121	+	0.00706246i
$424$		0			0
$425$	−23.9746	+	13.8417i	−1.16294	+	0.671423i
$426$		0			0
$427$	−0.104661	−	0.593564i	−0.00506492	−	0.0287246i
$428$		0			0
$429$	−0.319979	+	0.187343i	−0.0154487	+	0.00904503i
$430$		0			0
$431$	1.27220	−	1.06750i	0.0612798	−	0.0514198i	−0.611633	−	0.791141i	$-0.709487\pi$
$431$	1.27220	−	1.06750i	0.0612798	−	0.0514198i	0.672913	+	0.739722i	$0.265043\pi$
$432$		0			0
$433$	7.77139	−	21.3517i	0.373469	−	1.02610i	−0.600541	−	0.799594i	$-0.705048\pi$
$433$	7.77139	−	21.3517i	0.373469	−	1.02610i	0.974010	−	0.226504i	$-0.0727297\pi$
$434$		0			0
$435$	12.1290	+	10.0524i	0.581543	+	0.481977i
$436$		0			0
$437$	−17.3453	+	35.4322i	−0.829740	+	1.69495i
$438$		0			0
$439$	−16.0874	−	2.83664i	−0.767810	−	0.135386i	−0.223994	−	0.974590i	$-0.571910\pi$
$439$	−16.0874	−	2.83664i	−0.767810	−	0.135386i	−0.543815	+	0.839205i	$0.683021\pi$
$440$		0			0
$441$	3.48703	+	18.4602i	0.166049	+	0.879055i
$442$		0			0
$443$	−0.317196	−	0.378020i	−0.0150705	−	0.0179603i	0.758457	−	0.651724i	$-0.225954\pi$
$443$	−0.317196	−	0.378020i	−0.0150705	−	0.0179603i	−0.773527	+	0.633763i	$0.781509\pi$
$444$		0			0
$445$	6.92640	+	3.99896i	0.328343	+	0.189569i
$446$		0			0
$447$	−11.6424	−	4.15748i	−0.550665	−	0.196642i
$448$		0			0
$449$	8.55441	+	14.8167i	0.403707	+	0.699242i	0.994170	−	0.107823i	$-0.0343880\pi$
$449$	8.55441	+	14.8167i	0.403707	+	0.699242i	−0.590463	+	0.807065i	$0.701055\pi$
$450$		0			0
$451$	0.338149	+	0.929056i	0.0159228	+	0.0437475i
$452$		0			0
$453$	−21.0554	+	7.80887i	−0.989270	+	0.366893i
$454$		0			0
$455$	−7.36302			−0.345184
$456$		0			0
$457$	10.8366			0.506914			0.253457	−	0.967347i	$-0.418432\pi$
$457$	10.8366			0.506914			0.253457	+	0.967347i	$0.418432\pi$
$458$		0			0
$459$	19.6213	+	15.8634i	0.915845	+	0.740440i
$460$		0			0
$461$	−2.84415	−	7.81424i	−0.132465	−	0.363945i	0.855672	−	0.517519i	$-0.173144\pi$
$461$	−2.84415	−	7.81424i	−0.132465	−	0.363945i	−0.988137	+	0.153573i	$0.950922\pi$
$462$		0			0
$463$	−7.82836	−	13.5591i	−0.363815	−	0.630146i	0.624770	−	0.780809i	$-0.285193\pi$
$463$	−7.82836	−	13.5591i	−0.363815	−	0.630146i	−0.988585	+	0.150663i	$0.951859\pi$
$464$		0			0
$465$	4.67626	−	13.0951i	0.216856	−	0.607272i
$466$		0			0
$467$	−0.978735	−	0.565073i	−0.0452904	−	0.0261484i	0.477184	−	0.878804i	$-0.341658\pi$
$467$	−0.978735	−	0.565073i	−0.0452904	−	0.0261484i	−0.522474	+	0.852655i	$0.674991\pi$
$468$		0			0
$469$	−3.84049	−	4.57691i	−0.177337	−	0.211342i
$470$		0			0
$471$	11.8748	+	13.9783i	0.547160	+	0.644084i
$472$		0			0
$473$	−0.263873	−	0.0465280i	−0.0121329	−	0.00213936i
$474$		0			0
$475$	−20.6220	+	13.8661i	−0.946202	+	0.636219i
$476$		0			0
$477$	0.553506	−	0.209118i	0.0253433	−	0.00957484i
$478$		0			0
$479$	−0.641136	+	1.76151i	−0.0292943	+	0.0804853i	−0.953478	−	0.301464i	$-0.902525\pi$
$479$	−0.641136	+	1.76151i	−0.0292943	+	0.0804853i	0.924183	+	0.381949i	$0.124747\pi$
$480$		0			0
$481$	13.1442	−	11.0293i	0.599323	−	0.502892i
$482$		0			0
$483$	−6.80317	−	11.6197i	−0.309555	−	0.528714i
$484$		0			0
$485$	9.93737	+	56.3576i	0.451233	+	2.55907i
$486$		0			0
$487$	18.2707	−	10.5486i	0.827925	−	0.478003i	−0.0252166	−	0.999682i	$-0.508028\pi$
$487$	18.2707	−	10.5486i	0.827925	−	0.478003i	0.853142	+	0.521679i	$0.174694\pi$
$488$		0			0
$489$	23.7016	+	4.03078i	1.07182	+	0.182278i
$490$		0			0
$491$	23.2228	−	27.6759i	1.04803	−	1.24900i	0.0803646	−	0.996766i	$-0.474392\pi$
$491$	23.2228	−	27.6759i	1.04803	−	1.24900i	0.967667	−	0.252230i	$-0.0811640\pi$
$492$		0			0
$493$			13.5009i			0.608050i
$494$		0			0
$495$	−0.409277	−	0.689387i	−0.0183956	−	0.0309856i
$496$		0			0
$497$	−0.699072	−	0.586591i	−0.0313577	−	0.0263122i
$498$		0			0
$499$	16.7104	−	6.08209i	0.748061	−	0.272272i	0.0602711	−	0.998182i	$-0.480803\pi$
$499$	16.7104	−	6.08209i	0.748061	−	0.272272i	0.687789	+	0.725910i	$0.258581\pi$
$500$		0			0
$501$	0.0283558	+	4.66296i	0.00126684	+	0.208326i
$502$		0			0
$503$	−31.2763	+	5.51485i	−1.39454	+	0.245895i	−0.819898	−	0.572510i	$-0.805970\pi$
$503$	−31.2763	+	5.51485i	−1.39454	+	0.245895i	−0.574642	+	0.818405i	$0.694859\pi$
$504$		0			0
$505$	26.3385	−	45.6196i	1.17205	−	2.03005i
$506$		0			0
$507$	−10.4503	+	1.90827i	−0.464116	+	0.0847494i
$508$		0			0
$509$	−10.8141	−	3.93599i	−0.479324	−	0.174460i	0.0910472	−	0.995847i	$-0.470979\pi$
$509$	−10.8141	−	3.93599i	−0.479324	−	0.174460i	−0.570372	+	0.821387i	$0.693201\pi$
$510$		0			0
$511$	0.965318	−	5.47459i	0.0427031	−	0.242182i
$512$		0			0
$513$	18.5447	+	13.0036i	0.818770	+	0.574122i
$514$		0			0
$515$	−9.63734	+	54.6560i	−0.424672	+	2.40843i
$516$		0			0
$517$	0.00480341	+	0.00174830i	0.000211254	+	7.68901e-5i
$518$		0			0
$519$	−19.7368	+	3.60402i	−0.866350	+	0.158199i
$520$		0			0
$521$	8.33163	−	14.4308i	0.365015	−	0.632225i	−0.623763	−	0.781613i	$-0.714397\pi$
$521$	8.33163	−	14.4308i	0.365015	−	0.632225i	0.988779	+	0.149388i	$0.0477304\pi$
$522$		0			0
$523$	15.2485	−	2.68873i	0.666771	−	0.117570i	0.169990	−	0.985446i	$-0.445626\pi$
$523$	15.2485	−	2.68873i	0.666771	−	0.117570i	0.496781	+	0.867876i	$0.334515\pi$
$524$		0			0
$525$	−0.0515769	−	8.48155i	−0.00225100	−	0.370165i
$526$		0			0
$527$	11.1983	−	4.07583i	0.487804	−	0.177546i
$528$		0			0
$529$	−45.1281	−	37.8670i	−1.96209	−	1.64639i
$530$		0			0
$531$	7.24945	+	12.2110i	0.314599	+	0.529912i
$532$		0			0
$533$		−	31.7132i		−	1.37365i
$534$		0			0
$535$	36.9843	−	44.0761i	1.59897	−	1.90558i
$536$		0			0
$537$	−24.6641	−	4.19446i	−1.06433	−	0.181005i
$538$		0			0
$539$	0.443046	−	0.255793i	0.0190833	−	0.0110178i
$540$		0			0
$541$	4.81061	+	27.2823i	0.206824	+	1.17296i	0.894543	+	0.446982i	$0.147501\pi$
$541$	4.81061	+	27.2823i	0.206824	+	1.17296i	−0.687719	+	0.725977i	$0.741388\pi$
$542$		0			0
$543$	7.43991	+	12.7072i	0.319277	+	0.545319i
$544$		0			0
$545$	40.2037	−	33.7349i	1.72214	−	1.44505i
$546$		0			0
$547$	9.83988	−	27.0348i	0.420723	−	1.15593i	−0.530571	−	0.847641i	$-0.678022\pi$
$547$	9.83988	−	27.0348i	0.420723	−	1.15593i	0.951294	−	0.308286i	$-0.0997553\pi$
$548$		0			0
$549$	−1.96923	+	0.743984i	−0.0840445	+	0.0317525i
$550$		0			0
$551$	0.827791	+	12.0909i	0.0352651	+	0.515088i
$552$		0			0
$553$	10.2840	+	1.81334i	0.437319	+	0.0771111i
$554$		0			0
$555$	24.0201	+	28.2750i	1.01959	+	1.20021i
$556$		0			0
$557$	−16.0015	−	19.0699i	−0.678007	−	0.808017i	0.311843	−	0.950134i	$-0.399054\pi$
$557$	−16.0015	−	19.0699i	−0.678007	−	0.808017i	−0.989850	+	0.142117i	$0.954609\pi$
$558$		0			0
$559$	7.44318	+	4.29732i	0.314813	+	0.181757i
$560$		0			0
$561$	0.231070	−	0.647077i	0.00975580	−	0.0273196i
$562$		0			0
$563$	−3.66324	−	6.34492i	−0.154387	−	0.267406i	0.778449	−	0.627708i	$-0.216007\pi$
$563$	−3.66324	−	6.34492i	−0.154387	−	0.267406i	−0.932836	+	0.360302i	$0.882674\pi$
$564$		0			0
$565$	−8.41055	−	23.1078i	−0.353834	−	0.972152i
$566$		0			0
$567$	−7.19789	+	2.81991i	−0.302283	+	0.118425i
$568$		0			0
$569$	−24.9445			−1.04573			−0.522865	−	0.852416i	$-0.675137\pi$
$569$	−24.9445			−1.04573			−0.522865	+	0.852416i	$0.675137\pi$
$570$		0			0
$571$	12.0359			0.503685			0.251843	−	0.967768i	$-0.418963\pi$
$571$	12.0359			0.503685			0.251843	+	0.967768i	$0.418963\pi$
$572$		0			0
$573$	13.6481	−	5.06169i	0.570156	−	0.211455i
$574$		0			0
$575$	−17.6472	−	48.4853i	−0.735939	−	2.02198i
$576$		0			0
$577$	20.1125	+	34.8358i	0.837294	+	1.45023i	0.892149	+	0.451741i	$0.149197\pi$
$577$	20.1125	+	34.8358i	0.837294	+	1.45023i	−0.0548557	+	0.998494i	$0.517470\pi$
$578$		0			0
$579$	29.6863	+	10.6009i	1.23372	+	0.440560i
$580$		0			0
$581$	6.35971	+	3.67178i	0.263845	+	0.152331i
$582$		0			0
$583$	−0.0103570	−	0.0123430i	−0.000428942	−	0.000511193i
$584$		0			0
$585$	4.77327	+	25.2695i	0.197350	+	1.04476i
$586$		0			0
$587$	2.10163	+	0.370574i	0.0867435	+	0.0152952i	0.216851	−	0.976205i	$-0.430421\pi$
$587$	2.10163	+	0.370574i	0.0867435	+	0.0152952i	−0.130108	+	0.991500i	$0.541532\pi$
$588$		0			0
$589$	9.77881	−	4.33676i	0.402929	−	0.178693i
$590$		0			0
$591$	20.1925	+	16.7353i	0.830608	+	0.688399i
$592$		0			0
$593$	−8.28415	+	22.7605i	−0.340189	+	0.934663i	0.645150	+	0.764056i	$0.276795\pi$
$593$	−8.28415	+	22.7605i	−0.340189	+	0.934663i	−0.985339	+	0.170607i	$0.945427\pi$
$594$		0			0
$595$	10.4521	−	8.77032i	0.428492	−	0.359548i
$596$		0			0
$597$	−18.6931	+	10.9446i	−0.765057	+	0.447931i
$598$		0			0
$599$	−1.57564	−	8.93591i	−0.0643790	−	0.365111i	−0.999929	−	0.0119171i	$-0.996207\pi$
$599$	−1.57564	−	8.93591i	−0.0643790	−	0.365111i	0.935550	−	0.353194i	$-0.114905\pi$
$600$		0			0
$601$	−29.5677	+	17.0709i	−1.20609	+	0.696338i	−0.961903	−	0.273390i	$-0.911855\pi$
$601$	−29.5677	+	17.0709i	−1.20609	+	0.696338i	−0.244189	+	0.969728i	$0.578522\pi$
$602$		0			0
$603$	−13.2180	+	16.1474i	−0.538279	+	0.657574i
$604$		0			0
$605$	23.1158	−	27.5484i	0.939792	−	1.12000i
$606$		0			0
$607$			10.7948i			0.438147i	0.975708	+	0.219073i	$0.0703034\pi$
$607$			10.7948i			0.438147i	−0.975708	+	0.219073i	$0.929697\pi$
$608$		0			0
$609$	−3.59476	−	2.04639i	−0.145667	−	0.0829240i
$610$		0			0
$611$	−0.125604	−	0.105394i	−0.00508137	−	0.00426378i
$612$		0			0
$613$	−1.18462	+	0.431167i	−0.0478465	+	0.0174147i	−0.365833	−	0.930681i	$-0.619216\pi$
$613$	−1.18462	+	0.431167i	−0.0478465	+	0.0174147i	0.317986	+	0.948095i	$0.396993\pi$
$614$		0			0
$615$	68.5695	−	0.416976i	2.76499	−	0.0168141i
$616$		0			0
$617$	33.9744	−	5.99060i	1.36776	−	0.241173i	0.558928	−	0.829216i	$-0.311213\pi$
$617$	33.9744	−	5.99060i	1.36776	−	0.241173i	0.808829	+	0.588043i	$0.200102\pi$
$618$		0			0
$619$	6.38231	−	11.0545i	0.256527	−	0.444317i	−0.708782	−	0.705427i	$-0.750755\pi$
$619$	6.38231	−	11.0545i	0.256527	−	0.444317i	0.965309	+	0.261110i	$0.0840885\pi$
$620$		0			0
$621$	−35.4677	+	30.8808i	−1.42327	+	1.23920i
$622$		0			0
$623$	−1.97341	−	0.718264i	−0.0790632	−	0.0287767i
$624$		0			0
$625$	−3.64719	+	20.6843i	−0.145888	+	0.827370i
$626$		0			0
$627$	0.167263	−	0.593664i	0.00667983	−	0.0237087i
$628$		0			0
$629$	−5.52130	+	31.3129i	−0.220149	+	1.24853i
$630$		0			0
$631$	30.5499	+	11.1192i	1.21617	+	0.442650i	0.868840	−	0.495092i	$-0.164866\pi$
$631$	30.5499	+	11.1192i	1.21617	+	0.442650i	0.347331	+	0.937743i	$0.387088\pi$
$632$		0			0
$633$	−1.25574	−	6.87683i	−0.0499110	−	0.273329i
$634$		0			0
$635$	−17.5192	+	30.3441i	−0.695228	+	1.20417i
$636$		0			0
$637$	−16.1604	+	2.84952i	−0.640300	+	0.112902i
$638$		0			0
$639$	−1.55996	+	2.77945i	−0.0617109	+	0.109953i
$640$		0			0
$641$	3.47965	−	1.26649i	0.137438	−	0.0500233i	−0.272385	−	0.962188i	$-0.587813\pi$
$641$	3.47965	−	1.26649i	0.137438	−	0.0500233i	0.409823	+	0.912165i	$0.365590\pi$
$642$		0			0
$643$	−17.6425	−	14.8038i	−0.695752	−	0.583806i	0.224809	−	0.974403i	$-0.427824\pi$
$643$	−17.6425	−	14.8038i	−0.695752	−	0.583806i	−0.920562	+	0.390597i	$0.872269\pi$
$644$		0			0
$645$	−9.19370	+	16.1500i	−0.362002	+	0.635904i
$646$		0			0
$647$		−	40.9917i		−	1.61155i	−0.592221	−	0.805775i	$-0.701749\pi$
$647$		−	40.9917i		−	1.61155i	0.592221	−	0.805775i	$-0.298251\pi$
$648$		0			0
$649$	0.248571	−	0.296235i	0.00975726	−	0.0116283i
$650$		0			0
$651$	−0.612135	+	3.59945i	−0.0239915	+	0.141074i
$652$		0			0
$653$	20.9218	−	12.0792i	0.818733	−	0.472696i	−0.0312461	−	0.999512i	$-0.509948\pi$
$653$	20.9218	−	12.0792i	0.818733	−	0.472696i	0.849979	+	0.526816i	$0.176614\pi$
$654$		0			0
$655$	−5.98283	−	33.9303i	−0.233769	−	1.32577i
$656$		0			0
$657$	−19.4143	+	0.236128i	−0.757422	+	0.00921223i
$658$		0			0
$659$	1.56775	−	1.31550i	0.0610709	−	0.0512446i	−0.611741	−	0.791058i	$-0.709531\pi$
$659$	1.56775	−	1.31550i	0.0610709	−	0.0512446i	0.672812	+	0.739813i	$0.265086\pi$
$660$		0			0
$661$	6.54920	−	17.9938i	0.254734	−	0.699877i	−0.744737	−	0.667358i	$-0.767425\pi$
$661$	6.54920	−	17.9938i	0.254734	−	0.699877i	0.999471	−	0.0325185i	$-0.0103528\pi$
$662$		0			0
$663$	−14.0638	+	16.9691i	−0.546192	+	0.659024i
$664$		0			0
$665$	8.82271	−	8.49520i	0.342130	−	0.329430i
$666$		0			0
$667$	−24.7809	−	4.36955i	−0.959522	−	0.169190i
$668$		0			0
$669$	18.9685	−	16.1140i	0.733363	−	0.623003i
$670$		0			0
$671$	0.0368473	+	0.0439129i	0.00142247	+	0.00169524i
$672$		0			0
$673$	−34.8990	−	20.1490i	−1.34526	−	0.776686i	−0.357685	−	0.933842i	$-0.616434\pi$
$673$	−34.8990	−	20.1490i	−1.34526	−	0.776686i	−0.987574	+	0.157157i	$0.949767\pi$
$674$		0			0
$675$	−29.0747	+	5.67539i	−1.11909	+	0.218446i
$676$		0			0
$677$	15.7186	+	27.2254i	0.604115	+	1.04636i	0.992191	+	0.124730i	$0.0398066\pi$
$677$	15.7186	+	27.2254i	0.604115	+	1.04636i	−0.388076	+	0.921628i	$0.626860\pi$
$678$		0			0
$679$	−5.13935	−	14.1203i	−0.197230	−	0.541885i
$680$		0			0
$681$	3.20947	+	8.65384i	0.122987	+	0.331616i
$682$		0			0
$683$	−28.6574			−1.09655			−0.548273	−	0.836299i	$-0.684715\pi$
$683$	−28.6574			−1.09655			−0.548273	+	0.836299i	$0.684715\pi$
$684$		0			0
$685$	−26.9618			−1.03016
$686$		0			0
$687$	−16.0491	−	43.2739i	−0.612311	−	1.65100i
$688$		0			0
$689$	0.176767	+	0.485663i	0.00673428	+	0.0185023i
$690$		0			0
$691$	8.48032	+	14.6884i	0.322607	+	0.558771i	0.981025	−	0.193881i	$-0.0621075\pi$
$691$	8.48032	+	14.6884i	0.322607	+	0.558771i	−0.658418	+	0.752652i	$0.728774\pi$
$692$		0			0
$693$	0.137267	+	0.159605i	0.00521434	+	0.00606290i
$694$		0			0
$695$	−40.5790	−	23.4283i	−1.53925	−	0.888686i
$696$		0			0
$697$	37.7745	+	45.0179i	1.43081	+	1.70518i
$698$		0			0
$699$	22.2255	−	18.8809i	0.840647	−	0.714143i
$700$		0			0
$701$	33.0754	+	5.83208i	1.24924	+	0.220275i	0.758872	−	0.651240i	$-0.225751\pi$
$701$	33.0754	+	5.83208i	1.24924	+	0.220275i	0.490369	+	0.871515i	$0.336862\pi$
$702$		0			0
$703$	−3.02475	+	28.3811i	−0.114081	+	1.07041i
$704$		0			0
$705$	0.226228	−	0.272963i	0.00852026	−	0.0102804i
$706$		0			0
$707$	−4.73073	+	12.9976i	−0.177917	+	0.488824i
$708$		0			0
$709$	−25.4629	+	21.3659i	−0.956281	+	0.802415i	−0.980344	−	0.197296i	$-0.936784\pi$
$709$	−25.4629	+	21.3659i	−0.956281	+	0.802415i	0.0240635	+	0.999710i	$0.492340\pi$
$710$		0			0
$711$	−0.443564	−	36.4695i	−0.0166350	−	1.36771i
$712$		0			0
$713$	3.85690	+	21.8736i	0.144442	+	0.819172i
$714$		0			0
$715$	0.606470	−	0.350146i	0.0226807	−	0.0130947i
$716$		0			0
$717$	2.56366	−	15.0747i	0.0957418	−	0.562976i
$718$		0			0
$719$	8.99449	−	10.7192i	0.335438	−	0.399759i	−0.571789	−	0.820401i	$-0.693750\pi$
$719$	8.99449	−	10.7192i	0.335438	−	0.399759i	0.907227	+	0.420641i	$0.138195\pi$
$720$		0			0
$721$		−	14.5728i		−	0.542718i
$722$		0			0
$723$	−7.15926	+	12.5762i	−0.266256	+	0.467714i
$724$		0			0
$725$	−12.1424	−	10.1887i	−0.450957	−	0.378398i
$726$		0			0
$727$	−0.510067	+	0.185649i	−0.0189173	+	0.00688535i	−0.351461	−	0.936202i	$-0.614315\pi$
$727$	−0.510067	+	0.185649i	−0.0189173	+	0.00688535i	0.332544	+	0.943088i	$0.392093\pi$
$728$		0			0
$729$	14.3440	+	22.8747i	0.531258	+	0.847210i
$730$		0			0
$731$	−15.6845	+	2.76560i	−0.580113	+	0.102290i
$732$		0			0
$733$	5.12199	−	8.87154i	0.189185	−	0.327678i	−0.755794	−	0.654810i	$-0.772749\pi$
$733$	5.12199	−	8.87154i	0.189185	−	0.327678i	0.944979	+	0.327132i	$0.106082\pi$
$734$		0			0
$735$	−6.37365	−	34.9042i	−0.235096	−	1.28746i
$736$		0			0
$737$	0.533983	+	0.194354i	0.0196695	+	0.00715911i
$738$		0			0
$739$	3.59976	−	20.4152i	0.132419	−	0.750986i	−0.844203	−	0.536023i	$-0.819926\pi$
$739$	3.59976	−	20.4152i	0.132419	−	0.750986i	0.976622	−	0.214963i	$-0.0689630\pi$
$740$		0			0
$741$	−11.5545	+	16.0591i	−0.424467	+	0.589947i
$742$		0			0
$743$	8.26038	−	46.8469i	0.303044	−	1.71865i	−0.329528	−	0.944146i	$-0.606889\pi$
$743$	8.26038	−	46.8469i	0.303044	−	1.71865i	0.632572	−	0.774502i	$-0.281999\pi$
$744$		0			0
$745$	21.9403	+	7.98560i	0.803829	+	0.292570i
$746$		0			0
$747$	8.47848	−	24.2065i	0.310211	−	0.885668i
$748$		0			0
$749$	−7.55397	+	13.0839i	−0.276016	+	0.478074i
$750$		0			0
$751$	−17.2179	+	3.03598i	−0.628291	+	0.110785i	−0.478722	−	0.877967i	$-0.658900\pi$
$751$	−17.2179	+	3.03598i	−0.628291	+	0.110785i	−0.149569	+	0.988751i	$0.547789\pi$
$752$		0			0
$753$	−34.7097	+	0.211072i	−1.26489	+	0.00769190i
$754$		0			0
$755$	39.8553	−	14.5062i	1.45048	−	0.527933i
$756$		0			0
$757$	−20.3564	−	17.0811i	−0.739867	−	0.620822i	0.192935	−	0.981212i	$-0.438199\pi$
$757$	−20.3564	−	17.0811i	−0.739867	−	0.620822i	−0.932802	+	0.360389i	$0.882644\pi$
$758$		0			0
$759$	1.11293	+	0.633556i	0.0403966	+	0.0229966i
$760$		0			0
$761$		−	6.30880i		−	0.228694i	−0.993441	−	0.114347i	$-0.963522\pi$
$761$		−	6.30880i		−	0.228694i	0.993441	−	0.114347i	$-0.0364776\pi$
$762$		0			0
$763$	−8.85799	+	10.5565i	−0.320681	+	0.382172i
$764$		0			0
$765$	−36.8750	−	30.1853i	−1.33322	−	1.09135i
$766$		0			0
$767$	−10.7423	+	6.20207i	−0.387882	+	0.223944i
$768$		0			0
$769$	−7.34927	−	41.6798i	−0.265022	−	1.50301i	−0.768974	−	0.639280i	$-0.779232\pi$
$769$	−7.34927	−	41.6798i	−0.265022	−	1.50301i	0.503952	−	0.863732i	$-0.331879\pi$
$770$		0			0
$771$	−29.7109	+	17.3954i	−1.07001	+	0.626478i
$772$		0			0
$773$	−28.9328	+	24.2775i	−1.04064	+	0.873200i	−0.992078	−	0.125620i	$-0.959908\pi$
$773$	−28.9328	+	24.2775i	−1.04064	+	0.873200i	−0.0485610	+	0.998820i	$0.515464\pi$
$774$		0			0
$775$	−4.78524	+	13.1473i	−0.171891	+	0.472267i
$776$		0			0
$777$	−7.50050	−	6.21634i	−0.269079	−	0.223010i
$778$		0			0
$779$	36.5896	+	38.0002i	1.31096	+	1.36150i
$780$		0			0
$781$	0.0854756	+	0.0150717i	0.00305856	+	0.000539306i
$782$		0			0
$783$	−4.69270	+	13.6636i	−0.167703	+	0.488298i
$784$		0			0
$785$	−22.2663	−	26.5360i	−0.794720	−	0.947110i
$786$		0			0
$787$	18.5458	+	10.7074i	0.661085	+	0.381677i	0.792690	−	0.609625i	$-0.208680\pi$
$787$	18.5458	+	10.7074i	0.661085	+	0.381677i	−0.131605	+	0.991302i	$0.542013\pi$
$788$		0			0
$789$	−25.5294	−	9.11651i	−0.908870	−	0.324556i
$790$		0			0
$791$	3.22848	+	5.59189i	0.114791	+	0.198825i
$792$		0			0
$793$	−0.628889	−	1.72786i	−0.0223325	−	0.0613580i
$794$		0			0
$795$	−1.04776	+	0.388586i	−0.0371604	+	0.0137817i
$796$		0			0
$797$	−0.749255			−0.0265400			−0.0132700	−	0.999912i	$-0.504224\pi$
$797$	−0.749255			−0.0265400			−0.0132700	+	0.999912i	$0.504224\pi$
$798$		0			0
$799$	0.303836			0.0107489
$800$		0			0
$801$	−1.18572	+	7.23828i	−0.0418955	+	0.255752i
$802$		0			0
$803$	0.180832	+	0.496830i	0.00638141	+	0.0175328i
$804$		0			0
$805$	12.7151	+	22.0233i	0.448150	+	0.776218i
$806$		0			0
$807$	−0.278172	+	0.778976i	−0.00979210	+	0.0274213i
$808$		0			0
$809$	13.1046	+	7.56593i	0.460732	+	0.266004i	0.712352	−	0.701822i	$-0.247630\pi$
$809$	13.1046	+	7.56593i	0.460732	+	0.266004i	−0.251620	+	0.967826i	$0.580963\pi$
$810$		0			0
$811$	−31.7015	−	37.7804i	−1.11319	−	1.32665i	−0.939772	−	0.341802i	$-0.888963\pi$
$811$	−31.7015	−	37.7804i	−1.11319	−	1.32665i	−0.173419	−	0.984848i	$-0.555482\pi$
$812$		0			0
$813$	−5.57323	−	6.56048i	−0.195462	−	0.230086i
$814$		0			0
$815$	−44.7170	−	7.88482i	−1.56637	−	0.276193i
$816$		0			0
$817$	−13.8769	+	3.43844i	−0.485490	+	0.120296i
$818$		0			0
$819$	−2.38649	−	6.31672i	−0.0833907	−	0.220724i
$820$		0			0
$821$	10.0630	−	27.6480i	0.351203	−	0.964922i	−0.630782	−	0.775960i	$-0.717266\pi$
$821$	10.0630	−	27.6480i	0.351203	−	0.964922i	0.981984	−	0.188961i	$-0.0605121\pi$
$822$		0			0
$823$	−15.4552	+	12.9684i	−0.538733	+	0.452051i	−0.871104	−	0.491098i	$-0.836596\pi$
$823$	−15.4552	+	12.9684i	−0.538733	+	0.452051i	0.332371	+	0.943149i	$0.392151\pi$
$824$		0			0
$825$	0.407585	+	0.696147i	0.0141903	+	0.0242367i
$826$		0			0
$827$	2.52531	+	14.3217i	0.0878135	+	0.498015i	0.996714	+	0.0810020i	$0.0258120\pi$
$827$	2.52531	+	14.3217i	0.0878135	+	0.498015i	−0.908900	+	0.417013i	$0.863077\pi$
$828$		0			0
$829$	−1.52475	+	0.880317i	−0.0529569	+	0.0305747i	−0.526245	−	0.850333i	$-0.676400\pi$
$829$	−1.52475	+	0.880317i	−0.0529569	+	0.0305747i	0.473288	+	0.880908i	$0.343067\pi$
$830$		0			0
$831$	38.0212	+	6.46602i	1.31894	+	0.224304i
$832$		0			0
$833$	19.5461	−	23.2942i	0.677234	−	0.807096i
$834$		0			0
$835$		−	8.80688i		−	0.304775i
$836$		0			0
$837$	12.7499	−	0.232623i	0.440702	−	0.00804062i
$838$		0			0
$839$	28.4230	+	23.8498i	0.981272	+	0.823385i	0.984281	−	0.176610i	$-0.0565132\pi$
$839$	28.4230	+	23.8498i	0.981272	+	0.823385i	−0.00300848	+	0.999995i	$0.500958\pi$
$840$		0			0
$841$	19.9870	−	7.27469i	0.689208	−	0.250851i
$842$		0			0
$843$	0.0984145	+	16.1837i	0.00338957	+	0.557397i
$844$		0			0
$845$	19.7586	−	3.48398i	0.679718	−	0.119853i
$846$		0			0
$847$	−4.72136	+	8.17764i	−0.162228	+	0.280987i
$848$		0			0
$849$	−19.9658	+	3.64583i	−0.685224	+	0.125124i
$850$		0			0
$851$	−55.6879	−	20.2687i	−1.90896	−	0.694803i
$852$		0			0
$853$	−2.78182	+	15.7765i	−0.0952477	+	0.540177i	0.899423	+	0.437078i	$0.143987\pi$
$853$	−2.78182	+	15.7765i	−0.0952477	+	0.540177i	−0.994671	+	0.103098i	$0.967124\pi$
$854$		0			0
$855$	−34.8746	−	24.7718i	−1.19269	−	0.847177i
$856$		0			0
$857$	−4.48905	+	25.4587i	−0.153343	+	0.869652i	0.806942	+	0.590631i	$0.201121\pi$
$857$	−4.48905	+	25.4587i	−0.153343	+	0.869652i	−0.960285	+	0.279021i	$0.909990\pi$
$858$		0			0
$859$	37.4616	+	13.6349i	1.27817	+	0.465217i	0.889828	−	0.456297i	$-0.150824\pi$
$859$	37.4616	+	13.6349i	1.27817	+	0.465217i	0.388346	+	0.921514i	$0.373047\pi$
$860$		0			0
$861$	−17.7122	+	3.23431i	−0.603629	+	0.110225i
$862$		0			0
$863$	−12.4764	+	21.6098i	−0.424703	+	0.735607i	−0.996393	−	0.0848630i	$-0.972955\pi$
$863$	−12.4764	+	21.6098i	−0.424703	+	0.735607i	0.571690	+	0.820470i	$0.306288\pi$
$864$		0			0
$865$	37.3167	−	6.57994i	1.26881	−	0.223725i
$866$		0			0
$867$	−0.0692978	−	11.3956i	−0.00235348	−	0.387016i
$868$		0			0
$869$	−0.933291	+	0.339690i	−0.0316597	+	0.0115232i
$870$		0			0
$871$	−13.9630	−	11.7164i	−0.473119	−	0.396994i
$872$		0			0
$873$	−45.1282	+	26.7918i	−1.52736	+	0.906764i
$874$		0			0
$875$			1.96981i			0.0665916i
$876$		0			0
$877$	20.4636	−	24.3876i	0.691007	−	0.823510i	−0.300470	−	0.953791i	$-0.597144\pi$
$877$	20.4636	−	24.3876i	0.691007	−	0.823510i	0.991477	+	0.130281i	$0.0415880\pi$
$878$		0			0
$879$	28.2065	+	4.79690i	0.951381	+	0.161795i
$880$		0			0
$881$	3.24440	−	1.87316i	0.109307	−	0.0631082i	−0.444350	−	0.895853i	$-0.646565\pi$
$881$	3.24440	−	1.87316i	0.109307	−	0.0631082i	0.553657	+	0.832745i	$0.313232\pi$
$882$		0			0
$883$	8.73510	+	49.5392i	0.293960	+	1.66713i	0.671401	+	0.741094i	$0.265693\pi$
$883$	8.73510	+	49.5392i	0.293960	+	1.66713i	−0.377441	+	0.926034i	$0.623196\pi$
$884$		0			0
$885$	−13.5512	−	23.1452i	−0.455519	−	0.778017i
$886$		0			0
$887$	40.3551	−	33.8620i	1.35499	−	1.13697i	0.377498	−	0.926010i	$-0.376784\pi$
$887$	40.3551	−	33.8620i	1.35499	−	1.13697i	0.977494	−	0.210963i	$-0.0676600\pi$
$888$		0			0
$889$	3.14667	−	8.64541i	0.105536	−	0.289958i
$890$		0			0
$891$	0.458769	−	0.574560i	0.0153693	−	0.0192485i
$892$		0			0
$893$	0.272104	−	0.0186293i	0.00910560	−	0.000623407i
$894$		0			0
$895$	46.5329	+	8.20501i	1.55542	+	0.274263i
$896$		0			0
$897$	−26.5950	−	31.3061i	−0.887983	−	1.04528i
$898$		0			0
$899$	4.38593	+	5.22695i	0.146279	+	0.174329i
$900$		0			0
$901$	−0.829414	−	0.478862i	−0.0276318	−	0.0159532i
$902$		0			0
$903$	1.64100	−	4.59537i	0.0546091	−	0.152924i
$904$		0			0
$905$	−13.9052	−	24.0845i	−0.462225	−	0.800597i
$906$		0			0
$907$	−6.50666	−	17.8769i	−0.216050	−	0.593593i	0.783566	−	0.621309i	$-0.213399\pi$
$907$	−6.50666	−	17.8769i	−0.216050	−	0.593593i	−0.999616	+	0.0277161i	$0.991177\pi$
$908$		0			0
$909$	47.6737	+	7.80958i	1.58124	+	0.259027i
$910$		0			0
$911$	−24.6803			−0.817694			−0.408847	−	0.912603i	$-0.634069\pi$
$911$	−24.6803			−0.817694			−0.408847	+	0.912603i	$0.634069\pi$
$912$		0			0
$913$	−0.698440			−0.0231150
$914$		0			0
$915$	3.72766	−	1.38249i	0.123233	−	0.0457036i
$916$		0			0
$917$	3.09417	+	8.50115i	0.102178	+	0.280733i
$918$		0			0
$919$	−1.95798	−	3.39132i	−0.0645877	−	0.111869i	0.831923	−	0.554891i	$-0.187240\pi$
$919$	−1.95798	−	3.39132i	−0.0645877	−	0.111869i	−0.896511	+	0.443021i	$0.853907\pi$
$920$		0			0
$921$	−45.9492	−	16.4084i	−1.51408	−	0.540675i
$922$		0			0
$923$	−2.41104	−	1.39202i	−0.0793605	−	0.0458188i
$924$		0			0
$925$	−23.9953	−	28.5965i	−0.788961	−	0.940248i
$926$		0			0
$927$	−50.0129	+	9.44717i	−1.64264	+	0.310286i
$928$		0			0
$929$	29.7716	+	5.24954i	0.976775	+	0.172232i	0.639178	−	0.769059i	$-0.279275\pi$
$929$	29.7716	+	5.24954i	0.976775	+	0.172232i	0.337597	+	0.941291i	$0.390386\pi$
$930$		0			0
$931$	16.0765	−	22.0598i	0.526886	−	0.722981i
$932$		0			0
$933$	41.3008	+	34.2297i	1.35213	+	1.12063i
$934$		0			0
$935$	−0.443835	+	1.21943i	−0.0145150	+	0.0398795i
$936$		0			0
$937$	−17.2010	+	14.4334i	−0.561933	+	0.471518i	−0.878958	−	0.476900i	$-0.841761\pi$
$937$	−17.2010	+	14.4334i	−0.561933	+	0.471518i	0.317025	+	0.948417i	$0.397316\pi$
$938$		0			0
$939$	−29.2877	+	17.1476i	−0.955768	+	0.559590i
$940$		0			0
$941$	−3.28693	−	18.6411i	−0.107151	−	0.607683i	−0.990339	−	0.138665i	$-0.955719\pi$
$941$	−3.28693	−	18.6411i	−0.107151	−	0.607683i	0.883188	−	0.469018i	$-0.155392\pi$
$942$		0			0
$943$	−94.8562	+	54.7653i	−3.08894	+	1.78340i
$944$		0			0
$945$	13.6265	−	5.24306i	0.443269	−	0.170557i
$946$		0			0
$947$	2.81773	−	3.35804i	0.0915638	−	0.109122i	−0.718317	−	0.695716i	$-0.755087\pi$
$947$	2.81773	−	3.35804i	0.0915638	−	0.109122i	0.809881	+	0.586594i	$0.199532\pi$
$948$		0			0
$949$		−	16.9592i		−	0.550520i
$950$		0			0
$951$	−39.9070	−	22.7179i	−1.29407	−	0.736678i
$952$		0			0
$953$	16.8127	+	14.1075i	0.544617	+	0.456988i	0.873113	−	0.487517i	$-0.162097\pi$
$953$	16.8127	+	14.1075i	0.544617	+	0.456988i	−0.328496	+	0.944505i	$0.606542\pi$
$954$		0			0
$955$	−25.8341	+	9.40286i	−0.835973	+	0.304269i
$956$		0			0
$957$	0.393405	−	0.00239233i	0.0127170	−	7.73329e-5i
$958$		0			0
$959$	6.97197	−	1.22935i	0.225137	−	0.0396977i
$960$		0			0
$961$	−12.4886	+	21.6309i	−0.402858	+	0.697771i
$962$		0			0
$963$	49.8001	+	17.4428i	1.60478	+	0.562087i
$964$		0			0
$965$	−55.9444	−	20.3621i	−1.80091	−	0.655479i
$966$		0			0
$967$	−7.14586	+	40.5262i	−0.229795	+	1.30323i	0.623507	+	0.781818i	$0.285707\pi$
$967$	−7.14586	+	40.5262i	−0.229795	+	1.30323i	−0.853302	+	0.521416i	$0.825404\pi$
$968$		0			0
$969$	−2.72646	−	36.5594i	−0.0875867	−	1.17446i
$970$		0			0
$971$	−5.59380	+	31.7240i	−0.179513	+	1.01807i	0.753291	+	0.657688i	$0.228465\pi$
$971$	−5.59380	+	31.7240i	−0.179513	+	1.01807i	−0.932804	+	0.360384i	$0.882646\pi$
$972$		0			0
$973$	11.5614	+	4.20802i	0.370643	+	0.134903i
$974$		0			0
$975$	−4.64812	−	25.4546i	−0.148859	−	0.815201i
$976$		0			0
$977$	11.8264	−	20.4838i	0.378359	−	0.655336i	−0.612465	−	0.790498i	$-0.709822\pi$
$977$	11.8264	−	20.4838i	0.378359	−	0.655336i	0.990824	+	0.135161i	$0.0431553\pi$
$978$		0			0
$979$	0.196701	−	0.0346837i	0.00628659	−	0.00110850i
$980$		0			0
$981$	41.9718	+	23.5565i	1.34006	+	0.752103i
$982$		0			0
$983$	−2.60157	+	0.946893i	−0.0829771	+	0.0302012i	−0.383175	−	0.923676i	$-0.625169\pi$
$983$	−2.60157	+	0.946893i	−0.0829771	+	0.0302012i	0.300198	+	0.953877i	$0.402947\pi$
$984$		0			0
$985$	−37.9437	−	31.8386i	−1.20899	−	1.01446i
$986$		0			0
$987$	−0.0460538	+	0.0808997i	−0.00146591	+	0.00257506i
$988$		0			0
$989$		−	29.6841i		−	0.943898i
$990$		0			0
$991$	14.2221	−	16.9493i	0.451781	−	0.538412i	−0.491293	−	0.870994i	$-0.663476\pi$
$991$	14.2221	−	16.9493i	0.451781	−	0.538412i	0.943074	+	0.332583i	$0.107920\pi$
$992$		0			0
$993$	2.58081	−	15.1756i	0.0818997	−	0.481583i
$994$		0			0
$995$	35.4298	−	20.4554i	1.12320	−	0.648480i
$996$		0			0
$997$	8.17166	+	46.3438i	0.258799	+	1.46772i	0.786129	+	0.618062i	$0.212082\pi$
$997$	8.17166	+	46.3438i	0.258799	+	1.46772i	−0.527330	+	0.849661i	$0.676807\pi$
$998$		0			0
$999$	−16.4717	+	29.7712i	−0.521142	+	0.941919i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.cc.h.401.4		60
3.2	odd	2		912.2.cc.g.401.9		60
4.3	odd	2		456.2.bm.a.401.7	yes	60
12.11	even	2		456.2.bm.b.401.2	yes	60
19.10	odd	18		912.2.cc.g.257.9		60
57.29	even	18	inner	912.2.cc.h.257.4		60
76.67	even	18		456.2.bm.b.257.2	yes	60
228.143	odd	18		456.2.bm.a.257.7	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bm.a.257.7	✓	60	228.143	odd	18
456.2.bm.a.401.7	yes	60	4.3	odd	2
456.2.bm.b.257.2	yes	60	76.67	even	18
456.2.bm.b.401.2	yes	60	12.11	even	2
912.2.cc.g.257.9		60	19.10	odd	18
912.2.cc.g.401.9		60	3.2	odd	2
912.2.cc.h.257.4		60	57.29	even	18	inner
912.2.cc.h.401.4		60	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.cc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.602283 - 1.62396i) q^{3} +(1.11883 + 3.07396i) q^{5} +(-0.429476 - 0.743873i) q^{7} +(-2.27451 + 1.95617i) q^{9} +(0.0707492 + 0.0408471i) q^{11} +(-1.68439 - 2.00738i) q^{13} +(4.31815 - 3.66834i) q^{15} +(4.78209 + 0.843212i) q^{17} +(4.33435 + 0.461939i) q^{19} +(-0.949357 + 1.14547i) q^{21} +(-3.09543 + 8.50464i) q^{23} +(-4.36725 + 3.66456i) q^{25} +(4.54665 + 2.51555i) q^{27} +(0.482799 + 2.73809i) q^{29} +(2.12534 - 1.22707i) q^{31} +(0.0237231 - 0.139496i) q^{33} +(1.80613 - 2.15246i) q^{35} +6.54795i q^{37} +(-2.24543 + 3.94439i) q^{39} +(9.27084 + 7.77916i) q^{41} +(-3.08205 + 1.12177i) q^{43} +(-8.55799 - 4.80314i) q^{45} +(0.0616204 - 0.0108653i) q^{47} +(3.13110 - 5.42323i) q^{49} +(-1.51083 - 8.27379i) q^{51} +(-0.185336 - 0.0674568i) q^{53} +(-0.0464060 + 0.263181i) q^{55} +(-1.86033 - 7.31705i) q^{57} +(0.821982 - 4.66169i) q^{59} +(0.659376 + 0.239993i) q^{61} +(2.43199 + 0.851822i) q^{63} +(4.28605 - 7.42366i) q^{65} +(6.85018 - 1.20787i) q^{67} +(15.6755 - 0.0953242i) q^{69} +(0.998357 - 0.363372i) q^{71} +(4.95776 + 4.16006i) q^{73} +(8.58142 + 4.88515i) q^{75} -0.0701713i q^{77} +(-7.81462 + 9.31311i) q^{79} +(1.34680 - 8.89866i) q^{81} +(-7.40404 + 4.27472i) q^{83} +(2.75835 + 15.6434i) q^{85} +(4.15578 - 2.43315i) q^{87} +(1.87292 - 1.57156i) q^{89} +(-0.769830 + 2.11509i) q^{91} +(-3.27277 - 2.71244i) q^{93} +(3.42943 + 13.8405i) q^{95} +(17.2282 + 3.03779i) q^{97} +(-0.240824 + 0.0454903i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 3 q^{3} - 3 q^{9} + 3 q^{13} + 9 q^{15} + 6 q^{17} - 3 q^{19} + 6 q^{25} - 6 q^{27} - 6 q^{29} + 45 q^{33} + 24 q^{35} - 18 q^{39} - 3 q^{41} + 21 q^{43} - 45 q^{45} - 18 q^{47} - 30 q^{49} + 6 q^{51}+ \cdots + 3 q^{99}+O(q^{100}) \) 60 * q + 3 * q^3 - 3 * q^9 + 3 * q^13 + 9 * q^15 + 6 * q^17 - 3 * q^19 + 6 * q^25 - 6 * q^27 - 6 * q^29 + 45 * q^33 + 24 * q^35 - 18 * q^39 - 3 * q^41 + 21 * q^43 - 45 * q^45 - 18 * q^47 - 30 * q^49 + 6 * q^51 + 36 * q^53 - 18 * q^55 + 48 * q^57 - 21 * q^59 - 6 * q^61 - 78 * q^63 - 24 * q^65 + 48 * q^67 + 21 * q^69 + 36 * q^71 - 57 * q^73 + 36 * q^79 - 39 * q^81 - 36 * q^83 + 6 * q^85 + 90 * q^87 + 24 * q^89 + 18 * q^91 - 54 * q^93 + 30 * q^95 + 15 * q^97 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more