LMFDB - Embedded newform 1148.2.r.a.737.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(81,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 3]))

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

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

chi := DirichletCharacter("1148.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			737.19
Character	$\chi$	$=$	1148.737
Dual form			1148.2.r.a.81.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32068 - 0.762496i) q^{3} +(0.729632 - 1.26376i) q^{5} +(-0.676296 + 2.55786i) q^{7} +(-0.337200 + 0.584047i) q^{9} +O(q^{10})$	\(q+(1.32068 - 0.762496i) q^{3} +(0.729632 - 1.26376i) q^{5} +(-0.676296 + 2.55786i) q^{7} +(-0.337200 + 0.584047i) q^{9} +(3.72307 - 2.14952i) q^{11} +0.589521i q^{13} -2.22537i q^{15} +(6.82929 - 3.94290i) q^{17} +(-6.95046 - 4.01285i) q^{19} +(1.05718 + 3.89379i) q^{21} +(3.03094 - 5.24974i) q^{23} +(1.43527 + 2.48597i) q^{25} +5.60343i q^{27} -1.42277i q^{29} +(4.04502 + 7.00619i) q^{31} +(3.27799 - 5.67765i) q^{33} +(2.73907 + 2.72097i) q^{35} +(-1.05185 + 1.82185i) q^{37} +(0.449508 + 0.778570i) q^{39} +(5.10523 - 3.86479i) q^{41} +11.6330 q^{43} +(0.492063 + 0.852279i) q^{45} +(-1.69460 - 0.978379i) q^{47} +(-6.08525 - 3.45974i) q^{49} +(6.01288 - 10.4146i) q^{51} +(1.19703 - 0.691105i) q^{53} -6.27342i q^{55} -12.2391 q^{57} +(-1.36655 - 2.36694i) q^{59} +(-5.43617 + 9.41572i) q^{61} +(-1.26586 - 1.25750i) q^{63} +(0.745013 + 0.430133i) q^{65} +(1.45276 - 0.838749i) q^{67} -9.24432i q^{69} -8.55969i q^{71} +(1.00296 + 1.73718i) q^{73} +(3.79108 + 2.18878i) q^{75} +(2.98025 + 10.9768i) q^{77} +(-12.8327 - 7.40896i) q^{79} +(3.26099 + 5.64821i) q^{81} -6.67023 q^{83} -11.5074i q^{85} +(-1.08485 - 1.87902i) q^{87} +(-0.839938 - 0.484938i) q^{89} +(-1.50791 - 0.398691i) q^{91} +(10.6844 + 6.16863i) q^{93} +(-10.1425 + 5.85580i) q^{95} -2.46964i q^{97} +2.89926i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{5} + 32 q^{9}+O(q^{10}) $ 56 * q + 4 * q^5 + 32 * q^9	$ 56 q + 4 q^{5} + 32 q^{9} - 6 q^{21} + 2 q^{23} - 24 q^{25} - 4 q^{31} + 10 q^{33} + 10 q^{37} + 10 q^{39} + 20 q^{41} + 8 q^{43} - 22 q^{45} - 4 q^{49} + 18 q^{51} + 28 q^{57} - 16 q^{59} + 16 q^{61} + 2 q^{73} + 34 q^{77} - 28 q^{81} - 48 q^{83} - 2 q^{87} - 42 q^{91}+O(q^{100}) $ 56 * q + 4 * q^5 + 32 * q^9 - 6 * q^21 + 2 * q^23 - 24 * q^25 - 4 * q^31 + 10 * q^33 + 10 * q^37 + 10 * q^39 + 20 * q^41 + 8 * q^43 - 22 * q^45 - 4 * q^49 + 18 * q^51 + 28 * q^57 - 16 * q^59 + 16 * q^61 + 2 * q^73 + 34 * q^77 - 28 * q^81 - 48 * q^83 - 2 * q^87 - 42 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.32068	−	0.762496i	0.762496	−	0.440227i	−0.0676952	−	0.997706i	$-0.521565\pi$
$3$	1.32068	−	0.762496i	0.762496	−	0.440227i	0.830191	+	0.557479i	$0.188231\pi$
$4$		0			0
$5$	0.729632	−	1.26376i	0.326301	−	0.565170i	−0.655474	−	0.755218i	$-0.727531\pi$
$5$	0.729632	−	1.26376i	0.326301	−	0.565170i	0.981775	+	0.190048i	$0.0608643\pi$
$6$		0			0
$7$	−0.676296	+	2.55786i	−0.255616	+	0.966778i
$7$	−0.676296	+	2.55786i	−0.255616	+	0.966778i
$8$		0			0
$9$	−0.337200	+	0.584047i	−0.112400	+	0.194682i
$10$		0			0
$11$	3.72307	−	2.14952i	1.12255	−	0.648103i	0.180498	−	0.983575i	$-0.442229\pi$
$11$	3.72307	−	2.14952i	1.12255	−	0.648103i	0.942050	+	0.335472i	$0.108896\pi$
$12$		0			0
$13$			0.589521i			0.163504i	0.996653	+	0.0817519i	$0.0260515\pi$
$13$			0.589521i			0.163504i	−0.996653	+	0.0817519i	$0.973948\pi$
$14$		0			0
$15$		−	2.22537i		−	0.574587i
$16$		0			0
$17$	6.82929	−	3.94290i	1.65635	−	0.956293i	0.681968	−	0.731382i	$-0.261124\pi$
$17$	6.82929	−	3.94290i	1.65635	−	0.956293i	0.974379	−	0.224910i	$-0.0722089\pi$
$18$		0			0
$19$	−6.95046	−	4.01285i	−1.59454	−	0.920610i	−0.992513	−	0.122138i	$-0.961025\pi$
$19$	−6.95046	−	4.01285i	−1.59454	−	0.920610i	−0.602031	−	0.798473i	$-0.705642\pi$
$20$		0			0
$21$	1.05718	+	3.89379i	0.230696	+	0.849694i
$22$		0			0
$23$	3.03094	−	5.24974i	0.631995	−	1.09465i	−0.355149	−	0.934810i	$-0.615570\pi$
$23$	3.03094	−	5.24974i	0.631995	−	1.09465i	0.987143	−	0.159837i	$-0.0510969\pi$
$24$		0			0
$25$	1.43527	+	2.48597i	0.287055	+	0.497194i
$26$		0			0
$27$			5.60343i			1.07838i
$28$		0			0
$29$		−	1.42277i		−	0.264201i	−0.991236	−	0.132100i	$-0.957828\pi$
$29$		−	1.42277i		−	0.264201i	0.991236	−	0.132100i	$-0.0421722\pi$
$30$		0			0
$31$	4.04502	+	7.00619i	0.726508	+	1.25835i	0.958350	+	0.285595i	$0.0921912\pi$
$31$	4.04502	+	7.00619i	0.726508	+	1.25835i	−0.231843	+	0.972753i	$0.574475\pi$
$32$		0			0
$33$	3.27799	−	5.67765i	0.570625	−	0.988352i
$34$		0			0
$35$	2.73907	+	2.72097i	0.462987	+	0.459928i
$36$		0			0
$37$	−1.05185	+	1.82185i	−0.172923	+	0.299511i	−0.939440	−	0.342712i	$-0.888654\pi$
$37$	−1.05185	+	1.82185i	−0.172923	+	0.299511i	0.766518	+	0.642223i	$0.221988\pi$
$38$		0			0
$39$	0.449508	+	0.778570i	0.0719788	+	0.124671i
$40$		0			0
$41$	5.10523	−	3.86479i	0.797303	−	0.603579i
$41$	5.10523	−	3.86479i	0.797303	−	0.603579i
$42$		0			0
$43$	11.6330			1.77401			0.887006	−	0.461758i	$-0.152781\pi$
$43$	11.6330			1.77401			0.887006	+	0.461758i	$0.152781\pi$
$44$		0			0
$45$	0.492063	+	0.852279i	0.0733525	+	0.127050i
$46$		0			0
$47$	−1.69460	−	0.978379i	−0.247183	−	0.142711i	0.371291	−	0.928517i	$-0.378915\pi$
$47$	−1.69460	−	0.978379i	−0.247183	−	0.142711i	−0.618474	+	0.785805i	$0.712249\pi$
$48$		0			0
$49$	−6.08525	−	3.45974i	−0.869321	−	0.494248i
$50$		0			0
$51$	6.01288	−	10.4146i	0.841972	−	1.45834i
$52$		0			0
$53$	1.19703	−	0.691105i	0.164425	−	0.0949306i	−0.415530	−	0.909580i	$-0.636404\pi$
$53$	1.19703	−	0.691105i	0.164425	−	0.0949306i	0.579954	+	0.814649i	$0.303070\pi$
$54$		0			0
$55$		−	6.27342i		−	0.845908i
$56$		0			0
$57$	−12.2391			−1.62111
$58$		0			0
$59$	−1.36655	−	2.36694i	−0.177910	−	0.308149i	0.763254	−	0.646098i	$-0.223600\pi$
$59$	−1.36655	−	2.36694i	−0.177910	−	0.308149i	−0.941165	+	0.337949i	$0.890267\pi$
$60$		0			0
$61$	−5.43617	+	9.41572i	−0.696030	+	1.20556i	0.273802	+	0.961786i	$0.411719\pi$
$61$	−5.43617	+	9.41572i	−0.696030	+	1.20556i	−0.969832	+	0.243773i	$0.921615\pi$
$62$		0			0
$63$	−1.26586	−	1.25750i	−0.159484	−	0.158430i
$64$		0			0
$65$	0.745013	+	0.430133i	0.0924075	+	0.0533515i
$66$		0			0
$67$	1.45276	−	0.838749i	0.177482	−	0.102470i	−0.408627	−	0.912702i	$-0.633992\pi$
$67$	1.45276	−	0.838749i	0.177482	−	0.102470i	0.586109	+	0.810232i	$0.300659\pi$
$68$		0			0
$69$		−	9.24432i		−	1.11289i
$70$		0			0
$71$		−	8.55969i		−	1.01585i	−0.861402	−	0.507924i	$-0.830413\pi$
$71$		−	8.55969i		−	1.01585i	0.861402	−	0.507924i	$-0.169587\pi$
$72$		0			0
$73$	1.00296	+	1.73718i	0.117387	+	0.203321i	0.918732	−	0.394883i	$-0.129215\pi$
$73$	1.00296	+	1.73718i	0.117387	+	0.203321i	−0.801344	+	0.598204i	$0.795881\pi$
$74$		0			0
$75$	3.79108	+	2.18878i	0.437757	+	0.252739i
$76$		0			0
$77$	2.98025	+	10.9768i	0.339631	+	1.25092i
$78$		0			0
$79$	−12.8327	−	7.40896i	−1.44379	−	0.833573i	−0.445691	−	0.895187i	$-0.647042\pi$
$79$	−12.8327	−	7.40896i	−1.44379	−	0.833573i	−0.998100	+	0.0616135i	$0.980375\pi$
$80$		0			0
$81$	3.26099	+	5.64821i	0.362333	+	0.627578i
$82$		0			0
$83$	−6.67023			−0.732153			−0.366077	−	0.930585i	$-0.619299\pi$
$83$	−6.67023			−0.732153			−0.366077	+	0.930585i	$0.619299\pi$
$84$		0			0
$85$		−	11.5074i		−	1.24816i
$86$		0			0
$87$	−1.08485	−	1.87902i	−0.116308	−	0.201452i
$88$		0			0
$89$	−0.839938	−	0.484938i	−0.0890332	−	0.0514033i	0.454822	−	0.890582i	$-0.349703\pi$
$89$	−0.839938	−	0.484938i	−0.0890332	−	0.0514033i	−0.543856	+	0.839179i	$0.683036\pi$
$90$		0			0
$91$	−1.50791	−	0.398691i	−0.158072	−	0.0417942i
$92$		0			0
$93$	10.6844	+	6.16863i	1.10792	+	0.639657i
$94$		0			0
$95$	−10.1425	+	5.85580i	−1.04060	+	0.600793i
$96$		0			0
$97$		−	2.46964i		−	0.250754i	−0.992109	−	0.125377i	$-0.959986\pi$
$97$		−	2.46964i		−	0.250754i	0.992109	−	0.125377i	$-0.0400140\pi$
$98$		0			0
$99$			2.89926i			0.291387i
$100$		0			0
$101$	−2.26127	+	1.30554i	−0.225004	+	0.129906i	−0.608265	−	0.793734i	$-0.708134\pi$
$101$	−2.26127	+	1.30554i	−0.225004	+	0.129906i	0.383261	+	0.923640i	$0.374801\pi$
$102$		0			0
$103$	−7.32559	+	12.6883i	−0.721812	+	1.25021i	0.238461	+	0.971152i	$0.423357\pi$
$103$	−7.32559	+	12.6883i	−0.721812	+	1.25021i	−0.960273	+	0.279062i	$0.909976\pi$
$104$		0			0
$105$	5.69216	+	1.50501i	0.555498	+	0.146874i
$106$		0			0
$107$	3.23008	−	5.59467i	0.312264	−	0.540857i	−0.666588	−	0.745426i	$-0.732246\pi$
$107$	3.23008	−	5.59467i	0.312264	−	0.540857i	0.978852	+	0.204569i	$0.0655793\pi$
$108$		0			0
$109$	6.96915	−	4.02364i	0.667524	−	0.385395i	−0.127614	−	0.991824i	$-0.540732\pi$
$109$	6.96915	−	4.02364i	0.667524	−	0.385395i	0.795138	+	0.606429i	$0.207399\pi$
$110$		0			0
$111$			3.20812i			0.304501i
$112$		0			0
$113$	−8.56663			−0.805881			−0.402940	−	0.915226i	$-0.632012\pi$
$113$	−8.56663			−0.805881			−0.402940	+	0.915226i	$0.632012\pi$
$114$		0			0
$115$	−4.42294	−	7.66076i	−0.412441	−	0.714369i
$116$		0			0
$117$	−0.344308	−	0.198786i	−0.0318313	−	0.0183778i
$118$		0			0
$119$	5.46673	+	20.1349i	0.501134	+	1.84576i
$120$		0			0
$121$	3.74083	−	6.47931i	0.340075	−	0.589028i
$122$		0			0
$123$	3.79550	−	8.99688i	0.342229	−	0.811221i
$124$		0			0
$125$	11.4852			1.02727
$126$		0			0
$127$	−5.18561			−0.460149			−0.230074	−	0.973173i	$-0.573897\pi$
$127$	−5.18561			−0.460149			−0.230074	+	0.973173i	$0.573897\pi$
$128$		0			0
$129$	15.3635	−	8.87009i	1.35268	−	0.780968i
$130$		0			0
$131$	−2.89522	+	5.01467i	−0.252956	+	0.438133i	−0.964338	−	0.264672i	$-0.914736\pi$
$131$	−2.89522	+	5.01467i	−0.252956	+	0.438133i	0.711382	+	0.702806i	$0.248070\pi$
$132$		0			0
$133$	14.9649	−	15.0644i	1.29762	−	1.30625i
$134$		0			0
$135$	7.08139	+	4.08844i	0.609469	+	0.351877i
$136$		0			0
$137$	−15.0513	+	8.68987i	−1.28592	+	0.742426i	−0.977924	−	0.208962i	$-0.932991\pi$
$137$	−15.0513	+	8.68987i	−1.28592	+	0.742426i	−0.307995	+	0.951388i	$0.599658\pi$
$138$		0			0
$139$	−16.8440			−1.42869			−0.714344	−	0.699795i	$-0.753275\pi$
$139$	−16.8440			−1.42869			−0.714344	+	0.699795i	$0.753275\pi$
$140$		0			0
$141$	−2.98404			−0.251302
$142$		0			0
$143$	1.26718	+	2.19483i	0.105967	+	0.183541i
$144$		0			0
$145$	−1.79803	−	1.03810i	−0.149319	−	0.0862091i
$146$		0			0
$147$	−10.6747	+	0.0707660i	−0.880435	+	0.00583668i
$148$		0			0
$149$	11.6002	+	6.69740i	0.950328	+	0.548672i	0.893183	−	0.449694i	$-0.148467\pi$
$149$	11.6002	+	6.69740i	0.950328	+	0.548672i	0.0571453	+	0.998366i	$0.481800\pi$
$150$		0			0
$151$	−12.7333	+	7.35156i	−1.03622	+	0.598261i	−0.918760	−	0.394817i	$-0.870808\pi$
$151$	−12.7333	+	7.35156i	−1.03622	+	0.598261i	−0.117459	+	0.993078i	$0.537475\pi$
$152$		0			0
$153$			5.31817i			0.429949i
$154$		0			0
$155$	11.8055			0.948242
$156$		0			0
$157$	8.58001	−	4.95367i	0.684760	−	0.395346i	−0.116886	−	0.993145i	$-0.537291\pi$
$157$	8.58001	−	4.95367i	0.684760	−	0.395346i	0.801646	+	0.597799i	$0.203958\pi$
$158$		0			0
$159$	1.05393	−	1.82546i	0.0835821	−	0.144768i
$160$		0			0
$161$	11.3783	+	11.3031i	0.896733	+	0.890808i
$162$		0			0
$163$	3.55284	−	6.15370i	0.278280	−	0.481995i	−0.692677	−	0.721248i	$-0.743569\pi$
$163$	3.55284	−	6.15370i	0.278280	−	0.481995i	0.970957	+	0.239252i	$0.0769024\pi$
$164$		0			0
$165$	−4.78346	−	8.28519i	−0.372392	−	0.645001i
$166$		0			0
$167$			8.35423i			0.646469i	0.946319	+	0.323235i	$0.104770\pi$
$167$			8.35423i			0.646469i	−0.946319	+	0.323235i	$0.895230\pi$
$168$		0			0
$169$	12.6525			0.973267
$170$		0			0
$171$	4.68739	−	2.70626i	0.358453	−	0.206953i
$172$		0			0
$173$	−10.4424	+	18.0868i	−0.793921	+	1.37511i	0.129601	+	0.991566i	$0.458630\pi$
$173$	−10.4424	+	18.0868i	−0.793921	+	1.37511i	−0.923522	+	0.383545i	$0.874703\pi$
$174$		0			0
$175$	−7.32942	+	1.98997i	−0.554052	+	0.150428i
$176$		0			0
$177$	−3.60956	−	2.08398i	−0.271311	−	0.156642i
$178$		0			0
$179$	−8.00997	+	4.62456i	−0.598693	+	0.345656i	−0.768527	−	0.639817i	$-0.779010\pi$
$179$	−8.00997	+	4.62456i	−0.598693	+	0.345656i	0.169834	+	0.985473i	$0.445677\pi$
$180$		0			0
$181$			15.8108i			1.17521i	0.809149	+	0.587604i	$0.199929\pi$
$181$			15.8108i			1.17521i	−0.809149	+	0.587604i	$0.800071\pi$
$182$		0			0
$183$			16.5802i			1.22565i
$184$		0			0
$185$	1.53492	+	2.65856i	0.112850	+	0.195462i
$186$		0			0
$187$	16.9506	−	29.3593i	1.23955	−	2.14697i
$188$		0			0
$189$	−14.3328	−	3.78958i	−1.04256	−	0.275651i
$190$		0			0
$191$	−12.0591	−	6.96231i	−0.872564	−	0.503775i	−0.00436474	−	0.999990i	$-0.501389\pi$
$191$	−12.0591	−	6.96231i	−0.872564	−	0.503775i	−0.868200	+	0.496215i	$0.834723\pi$
$192$		0			0
$193$	3.74475	−	2.16203i	0.269553	−	0.155627i	−0.359131	−	0.933287i	$-0.616927\pi$
$193$	3.74475	−	2.16203i	0.269553	−	0.155627i	0.628685	+	0.777660i	$0.283594\pi$
$194$		0			0
$195$	1.31190			0.0939471
$196$		0			0
$197$	11.8678			0.845542			0.422771	−	0.906236i	$-0.361057\pi$
$197$	11.8678			0.845542			0.422771	+	0.906236i	$0.361057\pi$
$198$		0			0
$199$	−11.1256	+	6.42336i	−0.788672	+	0.455340i	−0.839495	−	0.543368i	$-0.817149\pi$
$199$	−11.1256	+	6.42336i	−0.788672	+	0.455340i	0.0508230	+	0.998708i	$0.483816\pi$
$200$		0			0
$201$	1.27909	−	2.21544i	0.0902198	−	0.156265i
$202$		0			0
$203$	3.63923	+	0.962211i	0.255424	+	0.0675340i
$204$		0			0
$205$	−1.15923	−	9.27166i	−0.0809638	−	0.647561i
$206$		0			0
$207$	2.04406	+	3.54042i	0.142072	+	0.246076i
$208$		0			0
$209$	−34.5027			−2.38660
$210$		0			0
$211$			9.64326i			0.663869i	0.943302	+	0.331935i	$0.107701\pi$
$211$			9.64326i			0.663869i	−0.943302	+	0.331935i	$0.892299\pi$
$212$		0			0
$213$	−6.52673	−	11.3046i	−0.447204	−	0.774580i
$214$		0			0
$215$	8.48779	−	14.7013i	0.578862	−	1.00262i
$216$		0			0
$217$	−20.6564	+	5.60833i	−1.40225	+	0.380718i
$218$		0			0
$219$	2.64918	+	1.52950i	0.179015	+	0.103354i
$220$		0			0
$221$	2.32442	+	4.02601i	0.156357	+	0.270819i
$222$		0			0
$223$	−20.0793			−1.34461			−0.672306	−	0.740274i	$-0.734696\pi$
$223$	−20.0793			−1.34461			−0.672306	+	0.740274i	$0.734696\pi$
$224$		0			0
$225$	−1.93590			−0.129060
$226$		0			0
$227$	13.7445	−	7.93539i	0.912254	−	0.526690i	0.0310984	−	0.999516i	$-0.490099\pi$
$227$	13.7445	−	7.93539i	0.912254	−	0.526690i	0.881156	+	0.472826i	$0.156766\pi$
$228$		0			0
$229$	17.9479	+	10.3622i	1.18603	+	0.684756i	0.957402	−	0.288758i	$-0.0932423\pi$
$229$	17.9479	+	10.3622i	1.18603	+	0.684756i	0.228629	+	0.973514i	$0.426576\pi$
$230$		0			0
$231$	12.3057	+	12.2244i	0.809657	+	0.804307i
$232$		0			0
$233$	12.8926	+	7.44356i	0.844624	+	0.487644i	0.858833	−	0.512255i	$-0.171190\pi$
$233$	12.8926	+	7.44356i	0.844624	+	0.487644i	−0.0142091	+	0.999899i	$0.504523\pi$
$234$		0			0
$235$	−2.47287	+	1.42771i	−0.161312	+	0.0931338i
$236$		0			0
$237$	−22.5972			−1.46785
$238$		0			0
$239$			2.92386i			0.189129i	0.995519	+	0.0945644i	$0.0301458\pi$
$239$			2.92386i			0.189129i	−0.995519	+	0.0945644i	$0.969854\pi$
$240$		0			0
$241$	7.41298	+	12.8397i	0.477512	+	0.827075i	0.999668	−	0.0257753i	$-0.00820544\pi$
$241$	7.41298	+	12.8397i	0.477512	+	0.827075i	−0.522156	+	0.852850i	$0.674872\pi$
$242$		0			0
$243$	−5.94467	−	3.43216i	−0.381351	−	0.220173i
$244$		0			0
$245$	−8.81226	+	5.16595i	−0.562995	+	0.330041i
$246$		0			0
$247$	2.36566	−	4.09744i	0.150523	−	0.260714i
$248$		0			0
$249$	−8.80925	+	5.08603i	−0.558264	+	0.322314i
$250$		0			0
$251$	−16.7769			−1.05895			−0.529475	−	0.848325i	$-0.677611\pi$
$251$	−16.7769			−1.05895			−0.529475	+	0.848325i	$0.677611\pi$
$252$		0			0
$253$		−	26.0602i		−	1.63839i
$254$		0			0
$255$	−8.77438	−	15.1977i	−0.549473	−	0.951715i
$256$		0			0
$257$	−18.7494	−	10.8250i	−1.16956	−	0.675244i	−0.215981	−	0.976398i	$-0.569295\pi$
$257$	−18.7494	−	10.8250i	−1.16956	−	0.675244i	−0.953575	+	0.301154i	$0.902628\pi$
$258$		0			0
$259$	−3.94868	−	3.92259i	−0.245359	−	0.243738i
$260$		0			0
$261$	0.830962	+	0.479756i	0.0514353	+	0.0296962i
$262$		0			0
$263$	−17.3390	+	10.0107i	−1.06917	+	0.617284i	−0.927954	−	0.372696i	$-0.878434\pi$
$263$	−17.3390	+	10.0107i	−1.06917	+	0.617284i	−0.141213	+	0.989979i	$0.545100\pi$
$264$		0			0
$265$		−	2.01701i		−	0.123904i
$266$		0			0
$267$	−1.47905			−0.0905166
$268$		0			0
$269$	−2.26943	−	3.93077i	−0.138370	−	0.239664i	0.788510	−	0.615022i	$-0.210853\pi$
$269$	−2.26943	−	3.93077i	−0.138370	−	0.239664i	−0.926880	+	0.375359i	$0.877520\pi$
$270$		0			0
$271$	−10.5572	+	18.2856i	−0.641304	+	1.11077i	0.343838	+	0.939029i	$0.388273\pi$
$271$	−10.5572	+	18.2856i	−0.641304	+	1.11077i	−0.985142	+	0.171742i	$0.945061\pi$
$272$		0			0
$273$	−2.29547	+	0.623231i	−0.138928	+	0.0377197i
$274$		0			0
$275$	10.6873	+	6.17029i	0.644466	+	0.372082i
$276$		0			0
$277$	8.52120	+	14.7592i	0.511989	+	0.886792i	0.999903	+	0.0138999i	$0.00442461\pi$
$277$	8.52120	+	14.7592i	0.511989	+	0.886792i	−0.487914	+	0.872892i	$0.662242\pi$
$278$		0			0
$279$	−5.45593			−0.326638
$280$		0			0
$281$		−	8.49755i		−	0.506921i	−0.967346	−	0.253461i	$-0.918431\pi$
$281$		−	8.49755i		−	0.506921i	0.967346	−	0.253461i	$-0.0815688\pi$
$282$		0			0
$283$	−5.72640	−	9.91842i	−0.340399	−	0.589589i	0.644108	−	0.764935i	$-0.277229\pi$
$283$	−5.72640	−	9.91842i	−0.340399	−	0.589589i	−0.984507	+	0.175346i	$0.943896\pi$
$284$		0			0
$285$	−8.93005	+	15.4673i	−0.528971	+	0.916204i
$286$		0			0
$287$	6.43292	+	15.6722i	0.379724	+	0.925100i
$288$		0			0
$289$	22.5928	−	39.1320i	1.32899	−	2.30188i
$290$		0			0
$291$	−1.88309	−	3.26160i	−0.110389	−	0.191199i
$292$		0			0
$293$		−	12.0286i		−	0.702715i	−0.936241	−	0.351358i	$-0.885720\pi$
$293$		−	12.0286i		−	0.702715i	0.936241	−	0.351358i	$-0.114280\pi$
$294$		0			0
$295$	−3.98832			−0.232209
$296$		0			0
$297$	12.0447	+	20.8620i	0.698902	+	1.21053i
$298$		0			0
$299$	3.09483	+	1.78680i	0.178979	+	0.103334i
$300$		0			0
$301$	−7.86734	+	29.7555i	−0.453466	+	1.71508i
$302$		0			0
$303$	−1.99094	+	3.44841i	−0.114377	+	0.198106i
$304$		0			0
$305$	7.93280	+	13.7400i	0.454231	+	0.786751i
$306$		0			0
$307$	8.72556			0.497994			0.248997	−	0.968504i	$-0.419899\pi$
$307$	8.72556			0.497994			0.248997	+	0.968504i	$0.419899\pi$
$308$		0			0
$309$			22.3429i			1.27104i
$310$		0			0
$311$	0.568476	−	0.328210i	0.0322353	−	0.0186111i	−0.483796	−	0.875181i	$-0.660742\pi$
$311$	0.568476	−	0.328210i	0.0322353	−	0.0186111i	0.516031	+	0.856570i	$0.327409\pi$
$312$		0			0
$313$	−14.7110	−	8.49342i	−0.831517	−	0.480076i	0.0228551	−	0.999739i	$-0.492724\pi$
$313$	−14.7110	−	8.49342i	−0.831517	−	0.480076i	−0.854372	+	0.519662i	$0.826058\pi$
$314$		0			0
$315$	−2.51279	+	0.682234i	−0.141579	+	0.0384395i
$316$		0			0
$317$	11.5112	+	6.64602i	0.646536	+	0.373278i	0.787128	−	0.616790i	$-0.211567\pi$
$317$	11.5112	+	6.64602i	0.646536	+	0.373278i	−0.140592	+	0.990068i	$0.544901\pi$
$318$		0			0
$319$	−3.05826	−	5.29706i	−0.171229	−	0.296578i
$320$		0			0
$321$		−	9.85170i		−	0.549868i
$322$		0			0
$323$	−63.2890			−3.52149
$324$		0			0
$325$	−1.46553	+	0.846125i	−0.0812931	+	0.0469346i
$326$		0			0
$327$	6.13602	−	10.6279i	0.339323	−	0.587724i
$328$		0			0
$329$	3.64861	−	3.67287i	0.201154	−	0.202492i
$330$		0			0
$331$	21.2236	+	12.2534i	1.16655	+	0.673509i	0.952866	−	0.303393i	$-0.0981195\pi$
$331$	21.2236	+	12.2534i	1.16655	+	0.673509i	0.213687	+	0.976902i	$0.431453\pi$
$332$		0			0
$333$	−0.709366	−	1.22866i	−0.0388730	−	0.0673300i
$334$		0			0
$335$		−	2.44791i		−	0.133744i
$336$		0			0
$337$	3.30662			0.180123			0.0900616	−	0.995936i	$-0.471294\pi$
$337$	3.30662			0.180123			0.0900616	+	0.995936i	$0.471294\pi$
$338$		0			0
$339$	−11.3138	+	6.53202i	−0.614481	+	0.354771i
$340$		0			0
$341$	30.1198	+	17.3897i	1.63108	+	0.941704i
$342$		0			0
$343$	12.9649	−	13.2254i	0.700041	−	0.714103i
$344$		0			0
$345$	−11.6826	−	6.74495i	−0.628970	−	0.363136i
$346$		0			0
$347$	−10.0006	+	5.77387i	−0.536863	+	0.309958i	−0.743806	−	0.668395i	$-0.766982\pi$
$347$	−10.0006	+	5.77387i	−0.536863	+	0.309958i	0.206944	+	0.978353i	$0.433648\pi$
$348$		0			0
$349$	25.9427			1.38868			0.694340	−	0.719648i	$-0.255697\pi$
$349$	25.9427			1.38868			0.694340	+	0.719648i	$0.255697\pi$
$350$		0			0
$351$	−3.30334			−0.176319
$352$		0			0
$353$	−8.68835	−	15.0487i	−0.462434	−	0.800959i	0.536648	−	0.843806i	$-0.319690\pi$
$353$	−8.68835	−	15.0487i	−0.462434	−	0.800959i	−0.999082	+	0.0428473i	$0.986357\pi$
$354$		0			0
$355$	−10.8174	−	6.24542i	−0.574127	−	0.331473i
$356$		0			0
$357$	22.5726	+	22.4235i	1.19467	+	1.18677i
$358$		0			0
$359$	11.2073	−	19.4116i	0.591497	−	1.02450i	−0.402534	−	0.915405i	$-0.631870\pi$
$359$	11.2073	−	19.4116i	0.591497	−	1.02450i	0.994031	−	0.109098i	$-0.0347963\pi$
$360$		0			0
$361$	22.7059	+	39.3278i	1.19505	+	2.06988i
$362$		0			0
$363$		−	11.4095i		−	0.598842i
$364$		0			0
$365$	2.92716			0.153215
$366$		0			0
$367$	1.82507	+	3.16111i	0.0952678	+	0.165009i	0.909720	−	0.415221i	$-0.136296\pi$
$367$	1.82507	+	3.16111i	0.0952678	+	0.165009i	−0.814453	+	0.580230i	$0.802963\pi$
$368$		0			0
$369$	0.535737	+	4.28490i	0.0278893	+	0.223063i
$370$		0			0
$371$	0.958201	+	3.52922i	0.0497473	+	0.183228i
$372$		0			0
$373$	−8.22386	+	14.2441i	−0.425815	+	0.737534i	−0.996496	−	0.0836381i	$-0.973346\pi$
$373$	−8.22386	+	14.2441i	−0.425815	+	0.737534i	0.570681	+	0.821172i	$0.306679\pi$
$374$		0			0
$375$	15.1683	−	8.75742i	0.783288	−	0.452231i
$376$		0			0
$377$	0.838751			0.0431979
$378$		0			0
$379$	2.04676			0.105135			0.0525676	−	0.998617i	$-0.483260\pi$
$379$	2.04676			0.105135			0.0525676	+	0.998617i	$0.483260\pi$
$380$		0			0
$381$	−6.84854	+	3.95401i	−0.350861	+	0.202570i
$382$		0			0
$383$	−11.9471	−	6.89766i	−0.610468	−	0.352454i	0.162681	−	0.986679i	$-0.447986\pi$
$383$	−11.9471	−	6.89766i	−0.610468	−	0.352454i	−0.773149	+	0.634225i	$0.781319\pi$
$384$		0			0
$385$	16.0465	+	4.24269i	0.817805	+	0.216227i
$386$		0			0
$387$	−3.92264	+	6.79420i	−0.199399	+	0.345369i
$388$		0			0
$389$	3.52297	+	6.10196i	0.178622	+	0.309382i	0.941409	−	0.337268i	$-0.109503\pi$
$389$	3.52297	+	6.10196i	0.178622	+	0.309382i	−0.762787	+	0.646650i	$0.776170\pi$
$390$		0			0
$391$		−	47.8027i		−	2.41749i
$392$		0			0
$393$			8.83037i			0.445433i
$394$		0			0
$395$	−18.7263	+	10.8116i	−0.942222	+	0.543992i
$396$		0			0
$397$	−15.5934	−	9.00284i	−0.782609	−	0.451840i	0.0547449	−	0.998500i	$-0.482565\pi$
$397$	−15.5934	−	9.00284i	−0.782609	−	0.451840i	−0.837354	+	0.546661i	$0.815899\pi$
$398$		0			0
$399$	8.27727	−	31.3059i	0.414382	−	1.56726i
$400$		0			0
$401$	−12.1360	+	21.0202i	−0.606045	+	1.04970i	0.385841	+	0.922565i	$0.373911\pi$
$401$	−12.1360	+	21.0202i	−0.606045	+	1.04970i	−0.991885	+	0.127135i	$0.959422\pi$
$402$		0			0
$403$	−4.13030	+	2.38463i	−0.205745	+	0.118787i
$404$		0			0
$405$	9.51730			0.472918
$406$		0			0
$407$			9.04385i			0.448287i
$408$		0			0
$409$	−17.2408	−	29.8620i	−0.852503	−	1.47658i	−0.878942	−	0.476929i	$-0.841750\pi$
$409$	−17.2408	−	29.8620i	−0.852503	−	1.47658i	0.0264386	−	0.999650i	$-0.491583\pi$
$410$		0			0
$411$	−13.2520	+	22.9531i	−0.653672	+	1.13219i
$412$		0			0
$413$	6.97848	−	1.89469i	0.343389	−	0.0932317i
$414$		0			0
$415$	−4.86681	+	8.42957i	−0.238902	+	0.413791i
$416$		0			0
$417$	−22.2455	+	12.8435i	−1.08937	+	0.628947i
$418$		0			0
$419$	−28.9701			−1.41528			−0.707642	−	0.706571i	$-0.750241\pi$
$419$	−28.9701			−1.41528			−0.707642	+	0.706571i	$0.750241\pi$
$420$		0			0
$421$		−	15.2542i		−	0.743446i	−0.928344	−	0.371723i	$-0.878767\pi$
$421$		−	15.2542i		−	0.743446i	0.928344	−	0.371723i	$-0.121233\pi$
$422$		0			0
$423$	1.14284	−	0.659819i	0.0555668	−	0.0320815i
$424$		0			0
$425$	19.6038	+	11.3183i	0.950925	+	0.549017i
$426$		0			0
$427$	−20.4076	−	20.2727i	−0.987592	−	0.981067i
$428$		0			0
$429$	3.34710	+	1.93245i	0.161599	+	0.0932994i
$430$		0			0
$431$	−16.8058	−	29.1085i	−0.809507	−	1.40211i	−0.913206	−	0.407498i	$-0.866401\pi$
$431$	−16.8058	−	29.1085i	−0.809507	−	1.40211i	0.103699	−	0.994609i	$-0.466932\pi$
$432$		0			0
$433$	−1.68550			−0.0810002			−0.0405001	−	0.999180i	$-0.512895\pi$
$433$	−1.68550			−0.0810002			−0.0405001	+	0.999180i	$0.512895\pi$
$434$		0			0
$435$	−3.16617			−0.151806
$436$		0			0
$437$	−42.1328	+	24.3254i	−2.01549	+	1.16364i
$438$		0			0
$439$	−28.4078	−	16.4012i	−1.35583	−	0.782789i	−0.366771	−	0.930311i	$-0.619537\pi$
$439$	−28.4078	−	16.4012i	−1.35583	−	0.782789i	−0.989059	+	0.147523i	$0.952870\pi$
$440$		0			0
$441$	4.07259	−	2.38745i	0.193933	−	0.113688i
$442$		0			0
$443$	−8.81775	+	15.2728i	−0.418944	+	0.725632i	−0.995834	−	0.0911901i	$-0.970933\pi$
$443$	−8.81775	+	15.2728i	−0.418944	+	0.725632i	0.576890	+	0.816822i	$0.304266\pi$
$444$		0			0
$445$	−1.22569	+	0.707653i	−0.0581033	+	0.0335460i
$446$		0			0
$447$	20.4270			0.966162
$448$		0			0
$449$	−22.8929			−1.08039			−0.540193	−	0.841541i	$-0.681649\pi$
$449$	−22.8929			−1.08039			−0.540193	+	0.841541i	$0.681649\pi$
$450$		0			0
$451$	10.6997	−	25.3627i	0.503830	−	1.19428i
$452$		0			0
$453$	−11.2111	+	19.4181i	−0.526742	+	0.912343i
$454$		0			0
$455$	−1.60407	+	1.61474i	−0.0751999	+	0.0757001i
$456$		0			0
$457$	1.45218	+	0.838416i	0.0679301	+	0.0392195i	0.533580	−	0.845749i	$-0.320846\pi$
$457$	1.45218	+	0.838416i	0.0679301	+	0.0392195i	−0.465650	+	0.884969i	$0.654180\pi$
$458$		0			0
$459$	22.0937	+	38.2675i	1.03125	+	1.78617i
$460$		0			0
$461$	−1.98850			−0.0926138			−0.0463069	−	0.998927i	$-0.514745\pi$
$461$	−1.98850			−0.0926138			−0.0463069	+	0.998927i	$0.514745\pi$
$462$		0			0
$463$			30.4782i			1.41644i	0.705991	+	0.708221i	$0.250502\pi$
$463$			30.4782i			1.41644i	−0.705991	+	0.708221i	$0.749498\pi$
$464$		0			0
$465$	15.5913	−	9.00166i	0.723030	−	0.417442i
$466$		0			0
$467$	19.9590	−	34.5700i	0.923592	−	1.59971i	0.129783	−	0.991542i	$-0.458572\pi$
$467$	19.9590	−	34.5700i	0.923592	−	1.59971i	0.793809	−	0.608167i	$-0.208095\pi$
$468$		0			0
$469$	1.16291	+	4.28318i	0.0536980	+	0.197779i
$470$		0			0
$471$	7.55431	−	13.0845i	0.348084	−	0.602900i
$472$		0			0
$473$	43.3104	−	25.0052i	1.99141	−	1.14974i
$474$		0			0
$475$		−	23.0382i		−	1.05706i
$476$		0			0
$477$			0.932162i			0.0426808i
$478$		0			0
$479$	19.3139	−	11.1509i	0.882475	−	0.509497i	0.0110011	−	0.999939i	$-0.496498\pi$
$479$	19.3139	−	11.1509i	0.882475	−	0.509497i	0.871474	+	0.490442i	$0.163165\pi$
$480$		0			0
$481$	−1.07402	−	0.620087i	−0.0489712	−	0.0282735i
$482$		0			0
$483$	23.6456	+	6.25190i	1.07591	+	0.284471i
$484$		0			0
$485$	−3.12103	−	1.80193i	−0.141718	−	0.0818212i
$486$		0			0
$487$	−12.9597	−	22.4469i	−0.587262	−	1.01717i	−0.994589	−	0.103885i	$-0.966873\pi$
$487$	−12.9597	−	22.4469i	−0.587262	−	1.01717i	0.407328	−	0.913282i	$-0.366461\pi$
$488$		0			0
$489$		−	10.8361i		−	0.490026i
$490$		0			0
$491$	42.4677			1.91654			0.958270	−	0.285864i	$-0.0922807\pi$
$491$	42.4677			1.91654			0.958270	+	0.285864i	$0.0922807\pi$
$492$		0			0
$493$	−5.60982	−	9.71649i	−0.252653	−	0.437609i
$494$		0			0
$495$	3.66397	+	2.11540i	0.164683	+	0.0950799i
$496$		0			0
$497$	21.8944	+	5.78889i	0.982100	+	0.259667i
$498$		0			0
$499$	2.06748	+	1.19366i	0.0925531	+	0.0534355i	0.545562	−	0.838070i	$-0.316316\pi$
$499$	2.06748	+	1.19366i	0.0925531	+	0.0534355i	−0.453009	+	0.891506i	$0.649649\pi$
$500$		0			0
$501$	6.37006	+	11.0333i	0.284593	+	0.492930i
$502$		0			0
$503$		−	43.4584i		−	1.93771i	−0.247621	−	0.968857i	$-0.579649\pi$
$503$		−	43.4584i		−	1.93771i	0.247621	−	0.968857i	$-0.420351\pi$
$504$		0			0
$505$			3.81026i			0.169554i
$506$		0			0
$507$	16.7099	−	9.64745i	0.742112	−	0.428458i
$508$		0			0
$509$	22.2168	+	12.8269i	0.984741	+	0.568540i	0.903698	−	0.428170i	$-0.140842\pi$
$509$	22.2168	+	12.8269i	0.984741	+	0.568540i	0.0810428	+	0.996711i	$0.474175\pi$
$510$		0			0
$511$	−5.12174	+	1.39058i	−0.226573	+	0.0615156i
$512$		0			0
$513$	22.4857	−	38.9464i	0.992768	−	1.71953i
$514$		0			0
$515$	10.6900	+	18.5156i	0.471056	+	0.815893i
$516$		0			0
$517$	−8.41216			−0.369967
$518$		0			0
$519$			31.8491i			1.39802i
$520$		0			0
$521$	−16.0074	+	9.24190i	−0.701299	+	0.404895i	−0.807831	−	0.589414i	$-0.799359\pi$
$521$	−16.0074	+	9.24190i	−0.701299	+	0.404895i	0.106532	+	0.994309i	$0.466025\pi$
$522$		0			0
$523$	22.3451	−	38.7028i	0.977081	−	1.69235i	0.304191	−	0.952611i	$-0.401614\pi$
$523$	22.3451	−	38.7028i	0.977081	−	1.69235i	0.672890	−	0.739743i	$-0.265053\pi$
$524$		0			0
$525$	−8.16248	+	8.21678i	−0.356240	+	0.358609i
$526$		0			0
$527$	55.2493	+	31.8982i	2.40670	+	1.38951i
$528$		0			0
$529$	−6.87320	−	11.9047i	−0.298835	−	0.517597i
$530$		0			0
$531$	1.84321			0.0799883
$532$		0			0
$533$	2.27838	+	3.00964i	0.0986874	+	0.130362i
$534$		0			0
$535$	−4.71354	−	8.16410i	−0.203784	−	0.352965i
$536$		0			0
$537$	−7.05241	+	12.2151i	−0.304334	+	0.527122i
$538$		0			0
$539$	−30.0925	+	0.199493i	−1.29618	+	0.00859276i
$540$		0			0
$541$	10.9765	−	19.0118i	0.471915	−	0.817381i	−0.527568	−	0.849513i	$-0.676896\pi$
$541$	10.9765	−	19.0118i	0.471915	−	0.817381i	0.999484	+	0.0321312i	$0.0102294\pi$
$542$		0			0
$543$	12.0557	+	20.8810i	0.517358	+	0.896091i
$544$		0			0
$545$		−	11.7431i		−	0.503019i
$546$		0			0
$547$			19.7339i			0.843759i	0.906652	+	0.421879i	$0.138629\pi$
$547$			19.7339i			0.843759i	−0.906652	+	0.421879i	$0.861371\pi$
$548$		0			0
$549$	−3.66615	−	6.34996i	−0.156467	−	0.271010i
$550$		0			0
$551$	−5.70934	+	9.88887i	−0.243226	+	0.421280i
$552$		0			0
$553$	27.6298	−	27.8135i	1.17494	−	1.18275i
$554$		0			0
$555$	4.05429	+	2.34075i	0.172095	+	0.0993591i
$556$		0			0
$557$	−4.83198	+	2.78974i	−0.204738	+	0.118205i	−0.598863	−	0.800851i	$-0.704381\pi$
$557$	−4.83198	+	2.78974i	−0.204738	+	0.118205i	0.394126	+	0.919056i	$0.371047\pi$
$558$		0			0
$559$			6.85788i			0.290058i
$560$		0			0
$561$		−	51.6991i		−	2.18274i
$562$		0			0
$563$	−21.8198	+	12.5977i	−0.919597	+	0.530929i	−0.883506	−	0.468419i	$-0.844824\pi$
$563$	−21.8198	+	12.5977i	−0.919597	+	0.530929i	−0.0360904	+	0.999349i	$0.511490\pi$
$564$		0			0
$565$	−6.25049	+	10.8262i	−0.262960	+	0.455460i
$566$		0			0
$567$	−16.6527	+	4.52129i	−0.699347	+	0.189876i
$568$		0			0
$569$	5.94197	−	10.2918i	0.249100	−	0.431454i	−0.714176	−	0.699966i	$-0.753198\pi$
$569$	5.94197	−	10.2918i	0.249100	−	0.431454i	0.963276	+	0.268512i	$0.0865318\pi$
$570$		0			0
$571$	29.1083	−	16.8057i	1.21814	−	0.703296i	0.253624	−	0.967303i	$-0.418377\pi$
$571$	29.1083	−	16.8057i	1.21814	−	0.703296i	0.964521	+	0.264007i	$0.0850441\pi$
$572$		0			0
$573$	−21.2349			−0.887102
$574$		0			0
$575$	17.4009			0.725669
$576$		0			0
$577$	−4.47004	+	2.58078i	−0.186090	+	0.107439i	−0.590151	−	0.807293i	$-0.700932\pi$
$577$	−4.47004	+	2.58078i	−0.186090	+	0.107439i	0.404061	+	0.914732i	$0.367598\pi$
$578$		0			0
$579$	3.29708	−	5.71072i	0.137022	−	0.237329i
$580$		0			0
$581$	4.51105	−	17.0615i	0.187150	−	0.707830i
$582$		0			0
$583$	2.97108	−	5.14607i	0.123050	−	0.213128i
$584$		0			0
$585$	−0.502436	+	0.290082i	−0.0207732	+	0.0119934i
$586$		0			0
$587$			37.1044i			1.53146i	0.643160	+	0.765732i	$0.277623\pi$
$587$			37.1044i			1.53146i	−0.643160	+	0.765732i	$0.722377\pi$
$588$		0			0
$589$		−	64.9283i		−	2.67532i
$590$		0			0
$591$	15.6735	−	9.04911i	0.644723	−	0.372231i
$592$		0			0
$593$	−9.82032	−	5.66977i	−0.403272	−	0.232829i	0.284623	−	0.958640i	$-0.408132\pi$
$593$	−9.82032	−	5.66977i	−0.403272	−	0.232829i	−0.687895	+	0.725810i	$0.741465\pi$
$594$		0			0
$595$	29.4344	+	7.78244i	1.20669	+	0.319049i
$596$		0			0
$597$	−9.79557	+	16.9664i	−0.400906	+	0.694390i
$598$		0			0
$599$	14.4679	+	25.0592i	0.591144	+	1.02389i	0.994079	+	0.108662i	$0.0346568\pi$
$599$	14.4679	+	25.0592i	0.591144	+	1.02389i	−0.402935	+	0.915229i	$0.632010\pi$
$600$		0			0
$601$		−	23.9854i		−	0.978387i	−0.872175	−	0.489193i	$-0.837291\pi$
$601$		−	23.9854i		−	0.978387i	0.872175	−	0.489193i	$-0.162709\pi$
$602$		0			0
$603$			1.13130i			0.0460703i
$604$		0			0
$605$	−5.45886	−	9.45502i	−0.221934	−	0.384401i
$606$		0			0
$607$	−12.9193	+	22.3769i	−0.524378	+	0.908249i	0.475219	+	0.879867i	$0.342369\pi$
$607$	−12.9193	+	22.3769i	−0.524378	+	0.908249i	−0.999597	+	0.0283817i	$0.990965\pi$
$608$		0			0
$609$	5.53994	−	1.50412i	0.224490	−	0.0609501i
$610$		0			0
$611$	0.576775	−	0.999004i	0.0233338	−	0.0404154i
$612$		0			0
$613$	4.16662	+	7.21680i	0.168288	+	0.291484i	0.937818	−	0.347127i	$-0.112843\pi$
$613$	4.16662	+	7.21680i	0.168288	+	0.291484i	−0.769530	+	0.638611i	$0.779509\pi$
$614$		0			0
$615$	−8.60057	−	11.3610i	−0.346808	−	0.458120i
$616$		0			0
$617$	−0.255718			−0.0102948			−0.00514742	−	0.999987i	$-0.501638\pi$
$617$	−0.255718			−0.0102948			−0.00514742	+	0.999987i	$0.501638\pi$
$618$		0			0
$619$	13.2054	+	22.8724i	0.530770	+	0.919320i	0.999355	+	0.0359018i	$0.0114304\pi$
$619$	13.2054	+	22.8724i	0.530770	+	0.919320i	−0.468586	+	0.883418i	$0.655236\pi$
$620$		0			0
$621$	29.4166	+	16.9837i	1.18045	+	0.681531i
$622$		0			0
$623$	1.80845	−	1.82048i	0.0724540	−	0.0729359i
$624$		0			0
$625$	1.20360	−	2.08469i	0.0481439	−	0.0833877i
$626$		0			0
$627$	−45.5671	+	26.3082i	−1.81977	+	1.05065i
$628$		0			0
$629$			16.5893i			0.661459i
$630$		0			0
$631$	32.5391			1.29536			0.647681	−	0.761911i	$-0.275739\pi$
$631$	32.5391			1.29536			0.647681	+	0.761911i	$0.275739\pi$
$632$		0			0
$633$	7.35295	+	12.7357i	0.292253	+	0.506198i
$634$		0			0
$635$	−3.78359	+	6.55336i	−0.150147	+	0.260062i
$636$		0			0
$637$	2.03959	−	3.58738i	0.0808114	−	0.142137i
$638$		0			0
$639$	4.99926	+	2.88633i	0.197768	+	0.114181i
$640$		0			0
$641$	15.2222	−	8.78852i	0.601239	−	0.347126i	−0.168290	−	0.985738i	$-0.553824\pi$
$641$	15.2222	−	8.78852i	0.601239	−	0.347126i	0.769529	+	0.638612i	$0.220491\pi$
$642$		0			0
$643$		−	7.48432i		−	0.295153i	−0.989051	−	0.147576i	$-0.952853\pi$
$643$		−	7.48432i		−	0.295153i	0.989051	−	0.147576i	$-0.0471472\pi$
$644$		0			0
$645$		−	25.8876i		−	1.01932i
$646$		0			0
$647$	11.0310	+	19.1062i	0.433673	+	0.751143i	0.997186	−	0.0749635i	$-0.0238840\pi$
$647$	11.0310	+	19.1062i	0.433673	+	0.751143i	−0.563513	+	0.826107i	$0.690551\pi$
$648$		0			0
$649$	−10.1755	−	5.87485i	−0.399425	−	0.230608i
$650$		0			0
$651$	−23.0043	+	23.1573i	−0.901608	+	0.907605i
$652$		0			0
$653$	0.198065	+	0.114353i	0.00775090	+	0.00447498i	0.503870	−	0.863779i	$-0.331909\pi$
$653$	0.198065	+	0.114353i	0.00775090	+	0.00447498i	−0.496120	+	0.868254i	$0.665242\pi$
$654$		0			0
$655$	4.22489	+	7.31772i	0.165080	+	0.285927i
$656$		0			0
$657$	−1.35279			−0.0527774
$658$		0			0
$659$		−	49.3304i		−	1.92164i	−0.277172	−	0.960820i	$-0.589397\pi$
$659$		−	49.3304i		−	1.92164i	0.277172	−	0.960820i	$-0.410603\pi$
$660$		0			0
$661$	8.72211	+	15.1071i	0.339251	+	0.587599i	0.984292	−	0.176548i	$-0.0564932\pi$
$661$	8.72211	+	15.1071i	0.339251	+	0.587599i	−0.645041	+	0.764148i	$0.723160\pi$
$662$		0			0
$663$	6.13964	+	3.54472i	0.238444	+	0.137666i
$664$		0			0
$665$	−8.11893	−	29.9034i	−0.314839	−	1.15961i
$666$		0			0
$667$	−7.46915	−	4.31232i	−0.289207	−	0.166974i
$668$		0			0
$669$	−26.5184	+	15.3104i	−1.02526	+	0.591935i
$670$		0			0
$671$			46.7405i			1.80440i
$672$		0			0
$673$			20.1822i			0.777966i	0.921245	+	0.388983i	$0.127174\pi$
$673$			20.1822i			0.777966i	−0.921245	+	0.388983i	$0.872826\pi$
$674$		0			0
$675$	−13.9300	+	8.04246i	−0.536164	+	0.309555i
$676$		0			0
$677$	13.1071	−	22.7021i	0.503745	−	0.872512i	−0.496245	−	0.868182i	$-0.665288\pi$
$677$	13.1071	−	22.7021i	0.503745	−	0.872512i	0.999991	−	0.00432992i	$-0.00137826\pi$
$678$		0			0
$679$	6.31697	+	1.67021i	0.242423	+	0.0640966i
$680$		0			0
$681$	12.1014	−	20.9602i	0.463727	−	0.803198i
$682$		0			0
$683$	37.7999	−	21.8238i	1.44637	−	0.835063i	0.448109	−	0.893979i	$-0.352098\pi$
$683$	37.7999	−	21.8238i	1.44637	−	0.835063i	0.998263	+	0.0589158i	$0.0187643\pi$
$684$		0			0
$685$			25.3616i			0.969018i
$686$		0			0
$687$	31.6046			1.20579
$688$		0			0
$689$	0.407421	+	0.705674i	0.0155215	+	0.0268840i
$690$		0			0
$691$	−2.90363	−	1.67641i	−0.110459	−	0.0637737i	0.443753	−	0.896149i	$-0.353647\pi$
$691$	−2.90363	−	1.67641i	−0.110459	−	0.0637737i	−0.554212	+	0.832376i	$0.686980\pi$
$692$		0			0
$693$	−7.41590	−	1.96076i	−0.281707	−	0.0744832i
$694$		0			0
$695$	−12.2899	+	21.2867i	−0.466182	+	0.807452i
$696$		0			0
$697$	19.6267	−	46.5232i	0.743413	−	1.76219i
$698$		0			0
$699$	22.7028			0.858697
$700$		0			0
$701$	−27.9595			−1.05601			−0.528007	−	0.849240i	$-0.677061\pi$
$701$	−27.9595			−1.05601			−0.528007	+	0.849240i	$0.677061\pi$
$702$		0			0
$703$	14.6216	−	8.44181i	0.551466	−	0.318389i
$704$		0			0
$705$	−2.17725	+	3.77111i	−0.0820000	+	0.142028i
$706$		0			0
$707$	−1.81010	−	6.66692i	−0.0680759	−	0.250736i
$708$		0			0
$709$	20.2288	+	11.6791i	0.759708	+	0.438618i	0.829191	−	0.558966i	$-0.188802\pi$
$709$	20.2288	+	11.6791i	0.759708	+	0.438618i	−0.0694829	+	0.997583i	$0.522135\pi$
$710$		0			0
$711$	8.65437	−	4.99660i	0.324564	−	0.187387i
$712$		0			0
$713$	49.0409			1.83660
$714$		0			0
$715$	3.69831			0.138309
$716$		0			0
$717$	2.22943	+	3.86149i	0.0832596	+	0.144210i
$718$		0			0
$719$	−3.96445	−	2.28888i	−0.147849	−	0.0853608i	0.424250	−	0.905545i	$-0.360538\pi$
$719$	−3.96445	−	2.28888i	−0.147849	−	0.0853608i	−0.572100	+	0.820184i	$0.693871\pi$
$720$		0			0
$721$	−27.5005	−	27.3188i	−1.02417	−	1.01741i
$722$		0			0
$723$	19.5804	+	11.3047i	0.728202	+	0.420427i
$724$		0			0
$725$	3.53695	−	2.04206i	0.131359	−	0.0758402i
$726$		0			0
$727$		−	22.5364i		−	0.835830i	−0.908486	−	0.417915i	$-0.862761\pi$
$727$		−	22.5364i		−	0.835830i	0.908486	−	0.417915i	$-0.137239\pi$
$728$		0			0
$729$	−30.0340			−1.11237
$730$		0			0
$731$	79.4450	−	45.8676i	2.93838	−	1.69647i
$732$		0			0
$733$	−10.2630	+	17.7760i	−0.379073	+	0.656573i	−0.990928	−	0.134397i	$-0.957090\pi$
$733$	−10.2630	+	17.7760i	−0.379073	+	0.656573i	0.611855	+	0.790970i	$0.290424\pi$
$734$		0			0
$735$	−7.69918	+	13.5419i	−0.283988	+	0.499500i
$736$		0			0
$737$	3.60581	−	6.24544i	0.132822	−	0.230054i
$738$		0			0
$739$	−10.7104	−	18.5509i	−0.393987	−	0.682406i	0.598984	−	0.800761i	$-0.295571\pi$
$739$	−10.7104	−	18.5509i	−0.393987	−	0.682406i	−0.992971	+	0.118355i	$0.962238\pi$
$740$		0			0
$741$		−	7.21522i		−	0.265058i
$742$		0			0
$743$	26.6899			0.979159			0.489579	−	0.871959i	$-0.337150\pi$
$743$	26.6899			0.979159			0.489579	+	0.871959i	$0.337150\pi$
$744$		0			0
$745$	16.9278	−	9.77327i	0.620187	−	0.358065i
$746$		0			0
$747$	2.24920	−	3.89573i	0.0822940	−	0.142537i
$748$		0			0
$749$	12.1259	+	12.0457i	0.443069	+	0.440142i
$750$		0			0
$751$	−20.3644	−	11.7574i	−0.743109	−	0.429034i	0.0800899	−	0.996788i	$-0.474479\pi$
$751$	−20.3644	−	11.7574i	−0.743109	−	0.429034i	−0.823198	+	0.567754i	$0.807813\pi$
$752$		0			0
$753$	−22.1570	+	12.7923i	−0.807446	+	0.466179i
$754$		0			0
$755$			21.4557i			0.780854i
$756$		0			0
$757$			27.6041i			1.00329i	0.865074	+	0.501644i	$0.167271\pi$
$757$			27.6041i			1.00329i	−0.865074	+	0.501644i	$0.832729\pi$
$758$		0			0
$759$	−19.8708	−	34.4172i	−0.721264	−	1.24927i
$760$		0			0
$761$	−0.775880	+	1.34386i	−0.0281256	+	0.0487150i	−0.879746	−	0.475445i	$-0.842287\pi$
$761$	−0.775880	+	1.34386i	−0.0281256	+	0.0487150i	0.851620	+	0.524160i	$0.175621\pi$
$762$		0			0
$763$	5.57868	+	20.5473i	0.201962	+	0.743861i
$764$		0			0
$765$	6.72089	+	3.88031i	0.242994	+	0.140293i
$766$		0			0
$767$	1.39536	−	0.805612i	0.0503836	−	0.0290890i
$768$		0			0
$769$	25.9895			0.937205			0.468602	−	0.883409i	$-0.344758\pi$
$769$	25.9895			0.937205			0.468602	+	0.883409i	$0.344758\pi$
$770$		0			0
$771$	−33.0160			−1.18904
$772$		0			0
$773$	−34.6558	+	20.0085i	−1.24648	+	0.719657i	−0.970406	−	0.241479i	$-0.922368\pi$
$773$	−34.6558	+	20.0085i	−1.24648	+	0.719657i	−0.276077	+	0.961136i	$0.589034\pi$
$774$		0			0
$775$	−11.6114	+	20.1116i	−0.417095	+	0.722430i
$776$		0			0
$777$	−8.20590	−	2.16964i	−0.294385	−	0.0778354i
$778$		0			0
$779$	−50.9925	+	6.37554i	−1.82700	+	0.228427i
$780$		0			0
$781$	−18.3992	−	31.8683i	−0.658374	−	1.14034i
$782$		0			0
$783$	7.97237			0.284909
$784$		0			0
$785$		−	14.4574i		−	0.516008i
$786$		0			0
$787$	5.65837	+	9.80058i	0.201699	+	0.349353i	0.949076	−	0.315047i	$-0.102020\pi$
$787$	5.65837	+	9.80058i	0.201699	+	0.349353i	−0.747377	+	0.664400i	$0.768687\pi$
$788$		0			0
$789$	−15.2662	+	26.4418i	−0.543490	+	0.941352i
$790$		0			0
$791$	5.79358	−	21.9122i	0.205996	−	0.779108i
$792$		0			0
$793$	−5.55077	−	3.20474i	−0.197113	−	0.113804i
$794$		0			0
$795$	−1.53796	−	2.66383i	−0.0545459	−	0.0944762i
$796$		0			0
$797$	0.164861			0.00583967			0.00291984	−	0.999996i	$-0.499071\pi$
$797$	0.164861			0.00583967			0.00291984	+	0.999996i	$0.499071\pi$
$798$		0			0
$799$	−15.4306			−0.545895
$800$		0			0
$801$	0.566454	−	0.327042i	0.0200147	−	0.0115555i
$802$		0			0
$803$	7.46817	+	4.31175i	0.263546	+	0.152158i
$804$		0			0
$805$	22.5863	−	6.13230i	0.796063	−	0.216135i
$806$		0			0
$807$	−5.99440	−	3.46087i	−0.211013	−	0.121828i
$808$		0			0
$809$	8.73074	−	5.04069i	0.306956	−	0.177221i	−0.338607	−	0.940928i	$-0.609956\pi$
$809$	8.73074	−	5.04069i	0.306956	−	0.177221i	0.645564	+	0.763706i	$0.276622\pi$
$810$		0			0
$811$	−31.5118			−1.10653			−0.553265	−	0.833006i	$-0.686618\pi$
$811$	−31.5118			−1.10653			−0.553265	+	0.833006i	$0.686618\pi$
$812$		0			0
$813$			32.1993i			1.12928i
$814$		0			0
$815$	−5.18453	−	8.97987i	−0.181606	−	0.314551i
$816$		0			0
$817$	−80.8545	−	46.6813i	−2.82874	−	1.63317i
$818$		0			0
$819$	0.741321	−	0.746252i	0.0259039	−	0.0260762i
$820$		0			0
$821$	−4.08990	+	7.08392i	−0.142739	+	0.247230i	−0.928527	−	0.371265i	$-0.878924\pi$
$821$	−4.08990	+	7.08392i	−0.142739	+	0.247230i	0.785788	+	0.618495i	$0.212257\pi$
$822$		0			0
$823$	−46.5279	+	26.8629i	−1.62186	+	0.936381i	−0.635437	+	0.772153i	$0.719180\pi$
$823$	−46.5279	+	26.8629i	−1.62186	+	0.936381i	−0.986422	+	0.164229i	$0.947487\pi$
$824$		0			0
$825$	18.8193			0.655203
$826$		0			0
$827$		−	50.1038i		−	1.74228i	−0.491035	−	0.871140i	$-0.663381\pi$
$827$		−	50.1038i		−	1.74228i	0.491035	−	0.871140i	$-0.336619\pi$
$828$		0			0
$829$	7.49830	+	12.9874i	0.260427	+	0.451072i	0.966355	−	0.257211i	$-0.0828034\pi$
$829$	7.49830	+	12.9874i	0.260427	+	0.451072i	−0.705929	+	0.708283i	$0.749470\pi$
$830$		0			0
$831$	22.5076	+	12.9948i	0.780780	+	0.450783i
$832$		0			0
$833$	−55.1993	+	0.365933i	−1.91254	+	0.0126788i
$834$		0			0
$835$	10.5577	+	6.09551i	0.365365	+	0.210944i
$836$		0			0
$837$	−39.2587	+	22.6660i	−1.35698	+	0.783452i
$838$		0			0
$839$			9.49202i			0.327701i	0.986485	+	0.163850i	$0.0523915\pi$
$839$			9.49202i			0.327701i	−0.986485	+	0.163850i	$0.947609\pi$
$840$		0			0
$841$	26.9757			0.930198
$842$		0			0
$843$	−6.47934	−	11.2226i	−0.223160	−	0.386525i
$844$		0			0
$845$	9.23164	−	15.9897i	0.317578	−	0.550061i
$846$		0			0
$847$	14.0432	+	13.9504i	0.482531	+	0.479343i
$848$		0			0
$849$	−15.1255	−	8.73272i	−0.519106	−	0.299706i
$850$		0			0
$851$	6.37618	+	11.0439i	0.218572	+	0.378579i
$852$		0			0
$853$	−16.3425			−0.559558			−0.279779	−	0.960064i	$-0.590261\pi$
$853$	−16.3425			−0.559558			−0.279779	+	0.960064i	$0.590261\pi$
$854$		0			0
$855$		−	7.89830i		−	0.270116i
$856$		0			0
$857$	−6.26897	−	10.8582i	−0.214144	−	0.370908i	0.738864	−	0.673855i	$-0.235363\pi$
$857$	−6.26897	−	10.8582i	−0.214144	−	0.370908i	−0.953007	+	0.302947i	$0.902029\pi$
$858$		0			0
$859$	−15.6879	+	27.1722i	−0.535264	+	0.927105i	0.463886	+	0.885895i	$0.346455\pi$
$859$	−15.6879	+	27.1722i	−0.535264	+	0.927105i	−0.999151	+	0.0412099i	$0.986879\pi$
$860$		0			0
$861$	20.4458	+	15.7929i	0.696792	+	0.538220i
$862$		0			0
$863$	−19.7705	+	34.2434i	−0.672994	+	1.16566i	0.304056	+	0.952654i	$0.401659\pi$
$863$	−19.7705	+	34.2434i	−0.672994	+	1.16566i	−0.977051	+	0.213006i	$0.931674\pi$
$864$		0			0
$865$	15.2382	+	26.3934i	0.518115	+	0.897401i
$866$		0			0
$867$		−	68.9078i		−	2.34023i
$868$		0			0
$869$	−63.7027			−2.16097
$870$		0			0
$871$	0.494461	+	0.856431i	0.0167542	+	0.0290190i
$872$		0			0
$873$	1.44238	+	0.832761i	0.0488173	+	0.0281847i
$874$		0			0
$875$	−7.76740	+	29.3775i	−0.262586	+	0.993141i
$876$		0			0
$877$	15.1295	−	26.2051i	0.510888	−	0.884884i	−0.489032	−	0.872266i	$-0.662650\pi$
$877$	15.1295	−	26.2051i	0.510888	−	0.884884i	0.999920	−	0.0126185i	$-0.00401671\pi$
$878$		0			0
$879$	−9.17172	−	15.8859i	−0.309354	−	0.535818i
$880$		0			0
$881$	−44.7586			−1.50796			−0.753978	−	0.656900i	$-0.771867\pi$
$881$	−44.7586			−1.50796			−0.753978	+	0.656900i	$0.771867\pi$
$882$		0			0
$883$			30.3401i			1.02102i	0.859870	+	0.510512i	$0.170544\pi$
$883$			30.3401i			1.02102i	−0.859870	+	0.510512i	$0.829456\pi$
$884$		0			0
$885$	−5.26731	+	3.04108i	−0.177059	+	0.102225i
$886$		0			0
$887$	10.9815	+	6.34015i	0.368721	+	0.212881i	0.672900	−	0.739734i	$-0.265049\pi$
$887$	10.9815	+	6.34015i	0.368721	+	0.212881i	−0.304178	+	0.952615i	$0.598382\pi$
$888$		0			0
$889$	3.50701	−	13.2640i	0.117621	−	0.444862i
$890$		0			0
$891$	24.2818	+	14.0191i	0.813471	+	0.469658i
$892$		0			0
$893$	7.85218	+	13.6004i	0.262763	+	0.455119i
$894$		0			0
$895$			13.4969i			0.451152i
$896$		0			0
$897$	5.44972			0.181961
$898$		0			0
$899$	9.96816	−	5.75512i	0.332457	−	0.191944i
$900$		0			0
$901$	5.44991	−	9.43952i	0.181563	−	0.314476i
$902$		0			0
$903$	12.2982	+	45.2963i	0.409257	+	1.50737i
$904$		0			0
$905$	19.9810	+	11.5361i	0.664192	+	0.383472i
$906$		0			0
$907$	−19.4607	−	33.7070i	−0.646183	−	1.11922i	−0.984027	−	0.178019i	$-0.943031\pi$
$907$	−19.4607	−	33.7070i	−0.646183	−	1.11922i	0.337844	−	0.941202i	$-0.390302\pi$
$908$		0			0
$909$		−	1.76091i		−	0.0584059i
$910$		0			0
$911$	−2.58844			−0.0857588			−0.0428794	−	0.999080i	$-0.513653\pi$
$911$	−2.58844			−0.0857588			−0.0428794	+	0.999080i	$0.513653\pi$
$912$		0			0
$913$	−24.8337	+	14.3378i	−0.821877	+	0.474511i
$914$		0			0
$915$	20.9534	+	12.0975i	0.692698	+	0.399930i
$916$		0			0
$917$	−10.8688	−	10.7970i	−0.358918	−	0.356547i
$918$		0			0
$919$	7.79897	+	4.50274i	0.257264	+	0.148532i	0.623086	−	0.782153i	$-0.285879\pi$
$919$	7.79897	+	4.50274i	0.257264	+	0.148532i	−0.365822	+	0.930685i	$0.619212\pi$
$920$		0			0
$921$	11.5237	−	6.65321i	0.379719	−	0.219231i
$922$		0			0
$923$	5.04612			0.166095
$924$		0			0
$925$	−6.03876			−0.198553
$926$		0			0
$927$	−4.94037	−	8.55698i	−0.162263	−	0.281048i
$928$		0			0
$929$	4.05996	+	2.34402i	0.133203	+	0.0769048i	0.565121	−	0.825008i	$-0.308830\pi$
$929$	4.05996	+	2.34402i	0.133203	+	0.0769048i	−0.431918	+	0.901913i	$0.642163\pi$
$930$		0			0
$931$	28.4118	+	48.4659i	0.931161	+	1.58841i
$932$		0			0
$933$	0.500517	−	0.866922i	0.0163862	−	0.0283817i
$934$		0			0
$935$	−24.7354	−	42.8430i	−0.808935	−	1.40112i
$936$		0			0
$937$		−	1.10111i		−	0.0359718i	−0.999838	−	0.0179859i	$-0.994275\pi$
$937$		−	1.10111i		−	0.0359718i	0.999838	−	0.0179859i	$-0.00572539\pi$
$938$		0			0
$939$	−25.9048			−0.845371
$940$		0			0
$941$	−25.9549	−	44.9552i	−0.846105	−	1.46550i	−0.884658	−	0.466241i	$-0.845608\pi$
$941$	−25.9549	−	44.9552i	−0.846105	−	1.46550i	0.0385527	−	0.999257i	$-0.487725\pi$
$942$		0			0
$943$	−4.81550	−	38.5151i	−0.156814	−	1.25422i
$944$		0			0
$945$	−15.2468	+	15.3482i	−0.495977	+	0.499276i
$946$		0			0
$947$	3.39395	−	5.87850i	0.110289	−	0.191026i	−0.805598	−	0.592463i	$-0.798156\pi$
$947$	3.39395	−	5.87850i	0.110289	−	0.191026i	0.915887	+	0.401437i	$0.131489\pi$
$948$		0			0
$949$	−1.02410	+	0.591266i	−0.0332438	+	0.0191933i
$950$		0			0
$951$	20.2703			0.657308
$952$		0			0
$953$	−7.62816			−0.247100			−0.123550	−	0.992338i	$-0.539428\pi$
$953$	−7.62816			−0.247100			−0.123550	+	0.992338i	$0.539428\pi$
$954$		0			0
$955$	−17.5974	+	10.1598i	−0.569438	+	0.328765i
$956$		0			0
$957$	−8.07797	−	4.66382i	−0.261124	−	0.150760i
$958$		0			0
$959$	−12.0483	−	44.3760i	−0.389060	−	1.43297i
$960$		0			0
$961$	−17.2244	+	29.8336i	−0.555627	+	0.962374i
$962$		0			0
$963$	2.17837	+	3.77304i	0.0701969	+	0.121585i
$964$		0			0
$965$		−	6.30995i		−	0.203125i
$966$		0			0
$967$			51.3057i			1.64988i	0.565221	+	0.824939i	$0.308791\pi$
$967$			51.3057i			1.64988i	−0.565221	+	0.824939i	$0.691209\pi$
$968$		0			0
$969$	−83.5846	+	48.2576i	−2.68512	+	1.55026i
$970$		0			0
$971$	9.87117	+	5.69912i	0.316781	+	0.182893i	0.649957	−	0.759971i	$-0.274787\pi$
$971$	9.87117	+	5.69912i	0.316781	+	0.182893i	−0.333176	+	0.942865i	$0.608120\pi$
$972$		0			0
$973$	11.3915	−	43.0844i	0.365195	−	1.38122i
$974$		0			0
$975$	−1.29033	+	2.23492i	−0.0413238	+	0.0715748i
$976$		0			0
$977$	−15.1986	+	8.77490i	−0.486245	+	0.280734i	−0.723016	−	0.690832i	$-0.757245\pi$
$977$	−15.1986	+	8.77490i	−0.486245	+	0.280734i	0.236770	+	0.971566i	$0.423911\pi$
$978$		0			0
$979$	−4.16953			−0.133259
$980$		0			0
$981$			5.42708i			0.173273i
$982$		0			0
$983$	25.9238	+	44.9013i	0.826839	+	1.43213i	0.900505	+	0.434845i	$0.143197\pi$
$983$	25.9238	+	44.9013i	0.826839	+	1.43213i	−0.0736660	+	0.997283i	$0.523470\pi$
$984$		0			0
$985$	8.65909	−	14.9980i	0.275902	−	0.477876i
$986$		0			0
$987$	2.01810	−	7.63275i	0.0642367	−	0.242953i
$988$		0			0
$989$	35.2588	−	61.0701i	1.12117	−	1.94192i
$990$		0			0
$991$	24.3044	−	14.0321i	0.772054	−	0.445745i	−0.0615531	−	0.998104i	$-0.519605\pi$
$991$	24.3044	−	14.0321i	0.772054	−	0.445745i	0.833607	+	0.552358i	$0.186272\pi$
$992$		0			0
$993$	37.3728			1.18599
$994$		0			0
$995$			18.7467i			0.594312i
$996$		0			0
$997$	12.3672	−	7.14021i	0.391674	−	0.226133i	−0.291211	−	0.956659i	$-0.594058\pi$
$997$	12.3672	−	7.14021i	0.391674	−	0.226133i	0.682885	+	0.730526i	$0.260725\pi$
$998$		0			0
$999$	−10.2086	−	5.89395i	−0.322987	−	0.186476i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.r.a.737.19	yes	56
7.4	even	3	inner	1148.2.r.a.81.10	✓	56
41.40	even	2	inner	1148.2.r.a.737.10	yes	56
287.81	even	6	inner	1148.2.r.a.81.19	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.r.a.81.10	✓	56	7.4	even	3	inner
1148.2.r.a.81.19	yes	56	287.81	even	6	inner
1148.2.r.a.737.10	yes	56	41.40	even	2	inner
1148.2.r.a.737.19	yes	56	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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.32068 - 0.762496i) q^{3} +(0.729632 - 1.26376i) q^{5} +(-0.676296 + 2.55786i) q^{7} +(-0.337200 + 0.584047i) q^{9} +O(q^{10})\)	\(q+(1.32068 - 0.762496i) q^{3} +(0.729632 - 1.26376i) q^{5} +(-0.676296 + 2.55786i) q^{7} +(-0.337200 + 0.584047i) q^{9} +(3.72307 - 2.14952i) q^{11} +0.589521i q^{13} -2.22537i q^{15} +(6.82929 - 3.94290i) q^{17} +(-6.95046 - 4.01285i) q^{19} +(1.05718 + 3.89379i) q^{21} +(3.03094 - 5.24974i) q^{23} +(1.43527 + 2.48597i) q^{25} +5.60343i q^{27} -1.42277i q^{29} +(4.04502 + 7.00619i) q^{31} +(3.27799 - 5.67765i) q^{33} +(2.73907 + 2.72097i) q^{35} +(-1.05185 + 1.82185i) q^{37} +(0.449508 + 0.778570i) q^{39} +(5.10523 - 3.86479i) q^{41} +11.6330 q^{43} +(0.492063 + 0.852279i) q^{45} +(-1.69460 - 0.978379i) q^{47} +(-6.08525 - 3.45974i) q^{49} +(6.01288 - 10.4146i) q^{51} +(1.19703 - 0.691105i) q^{53} -6.27342i q^{55} -12.2391 q^{57} +(-1.36655 - 2.36694i) q^{59} +(-5.43617 + 9.41572i) q^{61} +(-1.26586 - 1.25750i) q^{63} +(0.745013 + 0.430133i) q^{65} +(1.45276 - 0.838749i) q^{67} -9.24432i q^{69} -8.55969i q^{71} +(1.00296 + 1.73718i) q^{73} +(3.79108 + 2.18878i) q^{75} +(2.98025 + 10.9768i) q^{77} +(-12.8327 - 7.40896i) q^{79} +(3.26099 + 5.64821i) q^{81} -6.67023 q^{83} -11.5074i q^{85} +(-1.08485 - 1.87902i) q^{87} +(-0.839938 - 0.484938i) q^{89} +(-1.50791 - 0.398691i) q^{91} +(10.6844 + 6.16863i) q^{93} +(-10.1425 + 5.85580i) q^{95} -2.46964i q^{97} +2.89926i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{5} + 32 q^{9}+O(q^{10}) \) 56 * q + 4 * q^5 + 32 * q^9	\( 56 q + 4 q^{5} + 32 q^{9} - 6 q^{21} + 2 q^{23} - 24 q^{25} - 4 q^{31} + 10 q^{33} + 10 q^{37} + 10 q^{39} + 20 q^{41} + 8 q^{43} - 22 q^{45} - 4 q^{49} + 18 q^{51} + 28 q^{57} - 16 q^{59} + 16 q^{61} + 2 q^{73} + 34 q^{77} - 28 q^{81} - 48 q^{83} - 2 q^{87} - 42 q^{91}+O(q^{100}) \) 56 * q + 4 * q^5 + 32 * q^9 - 6 * q^21 + 2 * q^23 - 24 * q^25 - 4 * q^31 + 10 * q^33 + 10 * q^37 + 10 * q^39 + 20 * q^41 + 8 * q^43 - 22 * q^45 - 4 * q^49 + 18 * q^51 + 28 * q^57 - 16 * q^59 + 16 * q^61 + 2 * q^73 + 34 * q^77 - 28 * q^81 - 48 * q^83 - 2 * q^87 - 42 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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