LMFDB - Embedded newform 1148.2.r.a.737.4

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			737.4
Character	$\chi$	$=$	1148.737
Dual form			1148.2.r.a.81.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.90271 + 1.09853i) q^{3} +(-1.32827 + 2.30063i) q^{5} +(-2.55338 + 0.693005i) q^{7} +(0.913540 - 1.58230i) q^{9} +O(q^{10})$	\(q+(-1.90271 + 1.09853i) q^{3} +(-1.32827 + 2.30063i) q^{5} +(-2.55338 + 0.693005i) q^{7} +(0.913540 - 1.58230i) q^{9} +(-4.86956 + 2.81144i) q^{11} +0.607650i q^{13} -5.83659i q^{15} +(1.42191 - 0.820938i) q^{17} +(-1.82996 - 1.05653i) q^{19} +(4.09706 - 4.12355i) q^{21} +(-3.27010 + 5.66398i) q^{23} +(-1.02861 - 1.78161i) q^{25} -2.57698i q^{27} +8.24339i q^{29} +(-0.755319 - 1.30825i) q^{31} +(6.17691 - 10.6987i) q^{33} +(1.79723 - 6.79489i) q^{35} +(1.09454 - 1.89581i) q^{37} +(-0.667522 - 1.15618i) q^{39} +(3.30952 - 5.48152i) q^{41} +9.42004 q^{43} +(2.42686 + 4.20344i) q^{45} +(3.70460 + 2.13885i) q^{47} +(6.03949 - 3.53901i) q^{49} +(-1.80365 + 3.12402i) q^{51} +(-4.13016 + 2.38455i) q^{53} -14.9374i q^{55} +4.64251 q^{57} +(-0.353734 - 0.612685i) q^{59} +(-3.16282 + 5.47817i) q^{61} +(-1.23607 + 4.67329i) q^{63} +(-1.39798 - 0.807124i) q^{65} +(-8.79728 + 5.07911i) q^{67} -14.3692i q^{69} -6.07874i q^{71} +(-5.47255 - 9.47873i) q^{73} +(3.91431 + 2.25993i) q^{75} +(10.4855 - 10.5533i) q^{77} +(4.65445 + 2.68725i) q^{79} +(5.57151 + 9.65014i) q^{81} +2.48606 q^{83} +4.36172i q^{85} +(-9.05562 - 15.6848i) q^{87} +(4.05879 + 2.34334i) q^{89} +(-0.421104 - 1.55156i) q^{91} +(2.87431 + 1.65948i) q^{93} +(4.86136 - 2.80671i) q^{95} -0.0178989i q^{97} +10.2734i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.90271	+	1.09853i	−1.09853	+	0.634237i	−0.935835	−	0.352439i	$-0.885352\pi$
$3$	−1.90271	+	1.09853i	−1.09853	+	0.634237i	−0.162696	+	0.986676i	$0.552019\pi$
$4$		0			0
$5$	−1.32827	+	2.30063i	−0.594021	+	1.02888i	0.399663	+	0.916662i	$0.369127\pi$
$5$	−1.32827	+	2.30063i	−0.594021	+	1.02888i	−0.993684	+	0.112213i	$0.964206\pi$
$6$		0			0
$7$	−2.55338	+	0.693005i	−0.965087	+	0.261931i
$7$	−2.55338	+	0.693005i	−0.965087	+	0.261931i
$8$		0			0
$9$	0.913540	−	1.58230i	0.304513	−	0.527433i
$10$		0			0
$11$	−4.86956	+	2.81144i	−1.46823	+	0.847681i	−0.999366	−	0.0355916i	$-0.988668\pi$
$11$	−4.86956	+	2.81144i	−1.46823	+	0.847681i	−0.468860	+	0.883272i	$0.655335\pi$
$12$		0			0
$13$			0.607650i			0.168532i	0.996443	+	0.0842659i	$0.0268545\pi$
$13$			0.607650i			0.168532i	−0.996443	+	0.0842659i	$0.973145\pi$
$14$		0			0
$15$		−	5.83659i		−	1.50700i
$16$		0			0
$17$	1.42191	−	0.820938i	0.344863	−	0.199107i	−0.317557	−	0.948239i	$-0.602863\pi$
$17$	1.42191	−	0.820938i	0.344863	−	0.199107i	0.662420	+	0.749132i	$0.269529\pi$
$18$		0			0
$19$	−1.82996	−	1.05653i	−0.419821	−	0.242384i	0.275180	−	0.961393i	$-0.411263\pi$
$19$	−1.82996	−	1.05653i	−0.419821	−	0.242384i	−0.695001	+	0.719009i	$0.744596\pi$
$20$		0			0
$21$	4.09706	−	4.12355i	0.894051	−	0.899833i
$22$		0			0
$23$	−3.27010	+	5.66398i	−0.681864	+	1.18102i	0.292548	+	0.956251i	$0.405497\pi$
$23$	−3.27010	+	5.66398i	−0.681864	+	1.18102i	−0.974412	+	0.224771i	$0.927836\pi$
$24$		0			0
$25$	−1.02861	−	1.78161i	−0.205723	−	0.356322i
$26$		0			0
$27$		−	2.57698i		−	0.495940i
$28$		0			0
$29$			8.24339i			1.53076i	0.643579	+	0.765380i	$0.277449\pi$
$29$			8.24339i			1.53076i	−0.643579	+	0.765380i	$0.722551\pi$
$30$		0			0
$31$	−0.755319	−	1.30825i	−0.135659	−	0.234969i	0.790190	−	0.612862i	$-0.209982\pi$
$31$	−0.755319	−	1.30825i	−0.135659	−	0.234969i	−0.925849	+	0.377893i	$0.876649\pi$
$32$		0			0
$33$	6.17691	−	10.6987i	1.07526	−	1.86241i
$34$		0			0
$35$	1.79723	−	6.79489i	0.303787	−	1.14855i
$36$		0			0
$37$	1.09454	−	1.89581i	0.179942	−	0.311669i	−0.761918	−	0.647673i	$-0.775742\pi$
$37$	1.09454	−	1.89581i	0.179942	−	0.311669i	0.941860	+	0.336004i	$0.109076\pi$
$38$		0			0
$39$	−0.667522	−	1.15618i	−0.106889	−	0.185137i
$40$		0			0
$41$	3.30952	−	5.48152i	0.516860	−	0.856070i
$41$	3.30952	−	5.48152i	0.516860	−	0.856070i
$42$		0			0
$43$	9.42004			1.43654			0.718271	−	0.695763i	$-0.244934\pi$
$43$	9.42004			1.43654			0.718271	+	0.695763i	$0.244934\pi$
$44$		0			0
$45$	2.42686	+	4.20344i	0.361775	+	0.626612i
$46$		0			0
$47$	3.70460	+	2.13885i	0.540372	+	0.311984i	0.745230	−	0.666808i	$-0.232340\pi$
$47$	3.70460	+	2.13885i	0.540372	+	0.311984i	−0.204858	+	0.978792i	$0.565673\pi$
$48$		0			0
$49$	6.03949	−	3.53901i	0.862784	−	0.505573i
$50$		0			0
$51$	−1.80365	+	3.12402i	−0.252562	+	0.437450i
$52$		0			0
$53$	−4.13016	+	2.38455i	−0.567320	+	0.327543i	−0.756078	−	0.654481i	$-0.772887\pi$
$53$	−4.13016	+	2.38455i	−0.567320	+	0.327543i	0.188758	+	0.982024i	$0.439554\pi$
$54$		0			0
$55$		−	14.9374i		−	2.01416i
$56$		0			0
$57$	4.64251			0.614915
$58$		0			0
$59$	−0.353734	−	0.612685i	−0.0460522	−	0.0797648i	0.842080	−	0.539352i	$-0.181331\pi$
$59$	−0.353734	−	0.612685i	−0.0460522	−	0.0797648i	−0.888133	+	0.459587i	$0.847997\pi$
$60$		0			0
$61$	−3.16282	+	5.47817i	−0.404958	+	0.701408i	−0.994317	−	0.106464i	$-0.966047\pi$
$61$	−3.16282	+	5.47817i	−0.404958	+	0.701408i	0.589359	+	0.807872i	$0.299381\pi$
$62$		0			0
$63$	−1.23607	+	4.67329i	−0.155731	+	0.588780i
$64$		0			0
$65$	−1.39798	−	0.807124i	−0.173398	−	0.100111i
$66$		0			0
$67$	−8.79728	+	5.07911i	−1.07476	+	0.620512i	−0.929478	−	0.368879i	$-0.879742\pi$
$67$	−8.79728	+	5.07911i	−1.07476	+	0.620512i	−0.145281	+	0.989390i	$0.546409\pi$
$68$		0			0
$69$		−	14.3692i		−	1.72985i
$70$		0			0
$71$		−	6.07874i		−	0.721413i	−0.932679	−	0.360707i	$-0.882536\pi$
$71$		−	6.07874i		−	0.721413i	0.932679	−	0.360707i	$-0.117464\pi$
$72$		0			0
$73$	−5.47255	−	9.47873i	−0.640513	−	1.10940i	−0.985318	−	0.170727i	$-0.945388\pi$
$73$	−5.47255	−	9.47873i	−0.640513	−	1.10940i	0.344805	−	0.938674i	$-0.387945\pi$
$74$		0			0
$75$	3.91431	+	2.25993i	0.451985	+	0.260954i
$76$		0			0
$77$	10.4855	−	10.5533i	1.19493	−	1.20266i
$78$		0			0
$79$	4.65445	+	2.68725i	0.523666	+	0.302339i	0.738433	−	0.674327i	$-0.235566\pi$
$79$	4.65445	+	2.68725i	0.523666	+	0.302339i	−0.214767	+	0.976665i	$0.568899\pi$
$80$		0			0
$81$	5.57151	+	9.65014i	0.619057	+	1.07224i
$82$		0			0
$83$	2.48606			0.272880			0.136440	−	0.990648i	$-0.456434\pi$
$83$	2.48606			0.272880			0.136440	+	0.990648i	$0.456434\pi$
$84$		0			0
$85$			4.36172i			0.473095i
$86$		0			0
$87$	−9.05562	−	15.6848i	−0.970864	−	1.68159i
$88$		0			0
$89$	4.05879	+	2.34334i	0.430231	+	0.248394i	0.699445	−	0.714686i	$-0.253431\pi$
$89$	4.05879	+	2.34334i	0.430231	+	0.248394i	−0.269214	+	0.963080i	$0.586764\pi$
$90$		0			0
$91$	−0.421104	−	1.55156i	−0.0441437	−	0.162648i
$92$		0			0
$93$	2.87431	+	1.65948i	0.298052	+	0.172080i
$94$		0			0
$95$	4.86136	−	2.80671i	0.498765	−	0.287962i
$96$		0			0
$97$		−	0.0178989i		−	0.00181736i	−1.00000		0.000908679i	$-0.999711\pi$
$97$		−	0.0178989i		−	0.00181736i	1.00000		0.000908679i	$-0.000289242\pi$
$98$		0			0
$99$			10.2734i			1.03252i
$100$		0			0
$101$	8.94699	−	5.16555i	0.890259	−	0.513991i	0.0162315	−	0.999868i	$-0.494833\pi$
$101$	8.94699	−	5.16555i	0.890259	−	0.513991i	0.874027	+	0.485877i	$0.161500\pi$
$102$		0			0
$103$	5.75167	−	9.96218i	0.566729	−	0.981603i	−0.430158	−	0.902754i	$-0.641542\pi$
$103$	5.75167	−	9.96218i	0.566729	−	0.981603i	0.996887	−	0.0788492i	$-0.0251246\pi$
$104$		0			0
$105$	4.04479	+	14.9030i	0.394731	+	1.45439i
$106$		0			0
$107$	1.34757	−	2.33406i	0.130275	−	0.225642i	−0.793508	−	0.608560i	$-0.791747\pi$
$107$	1.34757	−	2.33406i	0.130275	−	0.225642i	0.923782	+	0.382918i	$0.125081\pi$
$108$		0			0
$109$	10.9593	−	6.32734i	1.04971	−	0.606049i	0.127141	−	0.991885i	$-0.459420\pi$
$109$	10.9593	−	6.32734i	1.04971	−	0.606049i	0.922568	+	0.385835i	$0.126087\pi$
$110$		0			0
$111$			4.80956i			0.456503i
$112$		0			0
$113$	−17.0972			−1.60837			−0.804184	−	0.594381i	$-0.797397\pi$
$113$	−17.0972			−1.60837			−0.804184	+	0.594381i	$0.797397\pi$
$114$		0			0
$115$	−8.68717	−	15.0466i	−0.810083	−	1.40310i
$116$		0			0
$117$	0.961483	+	0.555112i	0.0888891	+	0.0513202i
$118$		0			0
$119$	−3.06175	+	3.08156i	−0.280670	+	0.282486i
$120$		0			0
$121$	10.3084	−	17.8546i	0.937126	−	1.62315i
$122$		0			0
$123$	−0.275430	+	14.0654i	−0.0248347	+	1.26823i
$124$		0			0
$125$	−7.81761			−0.699228
$126$		0			0
$127$	−20.0005			−1.77476			−0.887378	−	0.461043i	$-0.847476\pi$
$127$	−20.0005			−1.77476			−0.887378	+	0.461043i	$0.847476\pi$
$128$		0			0
$129$	−17.9236	+	10.3482i	−1.57809	+	0.911108i
$130$		0			0
$131$	−7.73245	+	13.3930i	−0.675587	+	1.17015i	0.300710	+	0.953716i	$0.402776\pi$
$131$	−7.73245	+	13.3930i	−0.675587	+	1.17015i	−0.976297	+	0.216436i	$0.930557\pi$
$132$		0			0
$133$	5.40475	+	1.42954i	0.468651	+	0.123957i
$134$		0			0
$135$	5.92868	+	3.42293i	0.510260	+	0.294599i
$136$		0			0
$137$	5.65407	−	3.26438i	0.483060	−	0.278895i	−0.238631	−	0.971110i	$-0.576699\pi$
$137$	5.65407	−	3.26438i	0.483060	−	0.278895i	0.721691	+	0.692216i	$0.243365\pi$
$138$		0			0
$139$	−4.22895			−0.358695			−0.179347	−	0.983786i	$-0.557399\pi$
$139$	−4.22895			−0.358695			−0.179347	+	0.983786i	$0.557399\pi$
$140$		0			0
$141$	−9.39839			−0.791487
$142$		0			0
$143$	−1.70837	−	2.95898i	−0.142861	−	0.247443i
$144$		0			0
$145$	−18.9650	−	10.9495i	−1.57496	−	0.909304i
$146$		0			0
$147$	−7.60369	+	13.3683i	−0.627142	+	1.10260i
$148$		0			0
$149$	17.3693	+	10.0282i	1.42295	+	0.821540i	0.996550	−	0.0829946i	$-0.0264484\pi$
$149$	17.3693	+	10.0282i	1.42295	+	0.821540i	0.426400	+	0.904535i	$0.359782\pi$
$150$		0			0
$151$	1.50353	−	0.868061i	0.122355	−	0.0706418i	−0.437573	−	0.899183i	$-0.644162\pi$
$151$	1.50353	−	0.868061i	0.122355	−	0.0706418i	0.559928	+	0.828541i	$0.310829\pi$
$152$		0			0
$153$		−	2.99984i		−	0.242523i
$154$		0			0
$155$	4.01308			0.322338
$156$		0			0
$157$	−13.1157	+	7.57235i	−1.04675	+	0.604339i	−0.921737	−	0.387817i	$-0.873229\pi$
$157$	−13.1157	+	7.57235i	−1.04675	+	0.604339i	−0.125009	+	0.992156i	$0.539896\pi$
$158$		0			0
$159$	5.23900	−	9.07421i	0.415479	−	0.719631i
$160$		0			0
$161$	4.42464	−	16.7285i	0.348711	−	1.31839i
$162$		0			0
$163$	−7.43488	+	12.8776i	−0.582345	+	1.00865i	0.412856	+	0.910796i	$0.364531\pi$
$163$	−7.43488	+	12.8776i	−0.582345	+	1.00865i	−0.995201	+	0.0978545i	$0.968802\pi$
$164$		0			0
$165$	16.4092	+	28.4216i	1.27746	+	2.21262i
$166$		0			0
$167$		−	1.18327i		−	0.0915638i	−0.998951	−	0.0457819i	$-0.985422\pi$
$167$		−	1.18327i		−	0.0915638i	0.998951	−	0.0457819i	$-0.0145779\pi$
$168$		0			0
$169$	12.6308			0.971597
$170$		0			0
$171$	−3.34348	+	1.93036i	−0.255682	+	0.147618i
$172$		0			0
$173$	−9.63807	+	16.6936i	−0.732769	+	1.26919i	0.222927	+	0.974835i	$0.428439\pi$
$173$	−9.63807	+	16.6936i	−0.732769	+	1.26919i	−0.955695	+	0.294357i	$0.904894\pi$
$174$		0			0
$175$	3.86110	+	3.83629i	0.291872	+	0.289996i
$176$		0			0
$177$	1.34611	+	0.777175i	0.101180	+	0.0584160i
$178$		0			0
$179$	−8.51655	+	4.91703i	−0.636557	+	0.367516i	−0.783287	−	0.621660i	$-0.786458\pi$
$179$	−8.51655	+	4.91703i	−0.636557	+	0.367516i	0.146730	+	0.989177i	$0.453125\pi$
$180$		0			0
$181$		−	10.4232i		−	0.774747i	−0.921923	−	0.387374i	$-0.873382\pi$
$181$		−	10.4232i		−	0.774747i	0.921923	−	0.387374i	$-0.126618\pi$
$182$		0			0
$183$		−	13.8978i		−	1.02736i
$184$		0			0
$185$	2.90770	+	5.03629i	0.213779	+	0.370276i
$186$		0			0
$187$	−4.61604	+	7.99521i	−0.337558	+	0.584668i
$188$		0			0
$189$	1.78586	+	6.58000i	0.129902	+	0.478625i
$190$		0			0
$191$	−16.5420	−	9.55050i	−1.19693	−	0.691050i	−0.237063	−	0.971494i	$-0.576185\pi$
$191$	−16.5420	−	9.55050i	−1.19693	−	0.691050i	−0.959870	+	0.280444i	$0.909518\pi$
$192$		0			0
$193$	−6.17354	+	3.56430i	−0.444381	+	0.256564i	−0.705454	−	0.708755i	$-0.749257\pi$
$193$	−6.17354	+	3.56430i	−0.444381	+	0.256564i	0.261073	+	0.965319i	$0.415924\pi$
$194$		0			0
$195$	3.54660			0.253978
$196$		0			0
$197$	−15.9761			−1.13825			−0.569126	−	0.822250i	$-0.692718\pi$
$197$	−15.9761			−1.13825			−0.569126	+	0.822250i	$0.692718\pi$
$198$		0			0
$199$	−2.36528	+	1.36559i	−0.167670	+	0.0968044i	−0.581487	−	0.813556i	$-0.697529\pi$
$199$	−2.36528	+	1.36559i	−0.167670	+	0.0968044i	0.413817	+	0.910360i	$0.364195\pi$
$200$		0			0
$201$	11.1591	−	19.3282i	0.787103	−	1.36330i
$202$		0			0
$203$	−5.71271	−	21.0485i	−0.400954	−	1.47732i
$204$		0			0
$205$	8.21505	+	14.8949i	0.573764	+	1.04031i
$206$		0			0
$207$	5.97474	+	10.3486i	0.415273	+	0.719274i
$208$		0			0
$209$	11.8814			0.821856
$210$		0			0
$211$			7.36113i			0.506761i	0.967367	+	0.253381i	$0.0815425\pi$
$211$			7.36113i			0.506761i	−0.967367	+	0.253381i	$0.918458\pi$
$212$		0			0
$213$	6.67768	+	11.5661i	0.457547	+	0.792495i
$214$		0			0
$215$	−12.5124	+	21.6721i	−0.853337	+	1.47802i
$216$		0			0
$217$	2.83524	+	2.81702i	0.192469	+	0.191232i
$218$		0			0
$219$	20.8254	+	12.0235i	1.40725	+	0.812474i
$220$		0			0
$221$	0.498843	+	0.864021i	0.0335558	+	0.0581204i
$222$		0			0
$223$	1.82392			0.122139			0.0610694	−	0.998134i	$-0.480549\pi$
$223$	1.82392			0.122139			0.0610694	+	0.998134i	$0.480549\pi$
$224$		0			0
$225$	−3.75872			−0.250581
$226$		0			0
$227$	21.7317	−	12.5468i	1.44238	−	0.832761i	0.444376	−	0.895840i	$-0.353425\pi$
$227$	21.7317	−	12.5468i	1.44238	−	0.832761i	0.998009	+	0.0630793i	$0.0200921\pi$
$228$		0			0
$229$	12.1107	+	6.99212i	0.800298	+	0.462052i	0.843575	−	0.537011i	$-0.180447\pi$
$229$	12.1107	+	6.99212i	0.800298	+	0.462052i	−0.0432774	+	0.999063i	$0.513780\pi$
$230$		0			0
$231$	−8.35772	+	31.5985i	−0.549897	+	2.07903i
$232$		0			0
$233$	12.1910	+	7.03849i	0.798660	+	0.461107i	0.843002	−	0.537910i	$-0.180786\pi$
$233$	12.1910	+	7.03849i	0.798660	+	0.461107i	−0.0443423	+	0.999016i	$0.514119\pi$
$234$		0			0
$235$	−9.84144	+	5.68196i	−0.641985	+	0.370650i
$236$		0			0
$237$	−11.8081			−0.767018
$238$		0			0
$239$			12.7562i			0.825128i	0.910929	+	0.412564i	$0.135367\pi$
$239$			12.7562i			0.825128i	−0.910929	+	0.412564i	$0.864633\pi$
$240$		0			0
$241$	−0.116696	−	0.202124i	−0.00751706	−	0.0130199i	0.862242	−	0.506496i	$-0.169059\pi$
$241$	−0.116696	−	0.202124i	−0.00751706	−	0.0130199i	−0.869759	+	0.493476i	$0.835726\pi$
$242$		0			0
$243$	−14.5068	−	8.37548i	−0.930609	−	0.537287i
$244$		0			0
$245$	0.119886	+	18.5954i	0.00765923	+	1.18802i
$246$		0			0
$247$	0.641998	−	1.11197i	0.0408493	−	0.0707531i
$248$		0			0
$249$	−4.73025	+	2.73101i	−0.299767	+	0.173071i
$250$		0			0
$251$	−3.43814			−0.217013			−0.108507	−	0.994096i	$-0.534607\pi$
$251$	−3.43814			−0.217013			−0.108507	+	0.994096i	$0.534607\pi$
$252$		0			0
$253$		−	36.7748i		−	2.31201i
$254$		0			0
$255$	−4.79148	−	8.29909i	−0.300054	−	0.519709i
$256$		0			0
$257$	−20.5921	−	11.8889i	−1.28450	−	0.741607i	−0.306833	−	0.951763i	$-0.599269\pi$
$257$	−20.5921	−	11.8889i	−1.28450	−	0.741607i	−0.977668	+	0.210156i	$0.932603\pi$
$258$		0			0
$259$	−1.48098	+	5.59924i	−0.0920238	+	0.347920i
$260$		0			0
$261$	13.0435	+	7.53067i	0.807372	+	0.466137i
$262$		0			0
$263$	−8.99254	+	5.19185i	−0.554504	+	0.320143i	−0.750937	−	0.660374i	$-0.770398\pi$
$263$	−8.99254	+	5.19185i	−0.554504	+	0.320143i	0.196433	+	0.980517i	$0.437064\pi$
$264$		0			0
$265$		−	12.6693i		−	0.778269i
$266$		0			0
$267$	−10.2969			−0.630163
$268$		0			0
$269$	15.6306	+	27.0730i	0.953016	+	1.65067i	0.738844	+	0.673877i	$0.235372\pi$
$269$	15.6306	+	27.0730i	0.953016	+	1.65067i	0.214173	+	0.976796i	$0.431294\pi$
$270$		0			0
$271$	3.45413	−	5.98272i	0.209823	−	0.363425i	−0.741835	−	0.670582i	$-0.766044\pi$
$271$	3.45413	−	5.98272i	0.209823	−	0.363425i	0.951659	+	0.307157i	$0.0993778\pi$
$272$		0			0
$273$	2.50568	+	2.48957i	0.151650	+	0.150676i
$274$		0			0
$275$	10.0178	+	5.78377i	0.604095	+	0.348774i
$276$		0			0
$277$	−1.75366	−	3.03743i	−0.105367	−	0.182501i	0.808521	−	0.588467i	$-0.200268\pi$
$277$	−1.75366	−	3.03743i	−0.105367	−	0.182501i	−0.913888	+	0.405966i	$0.866935\pi$
$278$		0			0
$279$	−2.76006			−0.165240
$280$		0			0
$281$			4.36494i			0.260391i	0.991488	+	0.130195i	$0.0415604\pi$
$281$			4.36494i			0.260391i	−0.991488	+	0.130195i	$0.958440\pi$
$282$		0			0
$283$	−16.3571	−	28.3313i	−0.972326	−	1.68412i	−0.688490	−	0.725245i	$-0.741726\pi$
$283$	−16.3571	−	28.3313i	−0.972326	−	1.68412i	−0.283836	−	0.958873i	$-0.591607\pi$
$284$		0			0
$285$	−6.16651	+	10.6807i	−0.365273	+	0.632671i
$286$		0			0
$287$	−4.65172	+	16.2899i	−0.274583	+	0.961564i
$288$		0			0
$289$	−7.15212	+	12.3878i	−0.420713	+	0.728696i
$290$		0			0
$291$	0.0196625	+	0.0340564i	0.00115264	+	0.00199642i
$292$		0			0
$293$			6.15761i			0.359731i	0.983691	+	0.179866i	$0.0575663\pi$
$293$			6.15761i			0.359731i	−0.983691	+	0.179866i	$0.942434\pi$
$294$		0			0
$295$	1.87942			0.109424
$296$		0			0
$297$	7.24502	+	12.5487i	0.420399	+	0.728152i
$298$		0			0
$299$	−3.44172	−	1.98708i	−0.199040	−	0.114916i
$300$		0			0
$301$	−24.0529	+	6.52814i	−1.38639	+	0.376275i
$302$		0			0
$303$	−11.3490	+	19.6571i	−0.651984	+	1.12927i
$304$		0			0
$305$	−8.40218	−	14.5530i	−0.481107	−	0.833302i
$306$		0			0
$307$	−6.76955			−0.386359			−0.193179	−	0.981163i	$-0.561880\pi$
$307$	−6.76955			−0.386359			−0.193179	+	0.981163i	$0.561880\pi$
$308$		0			0
$309$			25.2735i			1.43776i
$310$		0			0
$311$	15.7802	−	9.11070i	0.894813	−	0.516620i	0.0192990	−	0.999814i	$-0.493857\pi$
$311$	15.7802	−	9.11070i	0.894813	−	0.516620i	0.875514	+	0.483193i	$0.160523\pi$
$312$		0			0
$313$	7.50103	+	4.33072i	0.423983	+	0.244787i	0.696780	−	0.717285i	$-0.254615\pi$
$313$	7.50103	+	4.33072i	0.423983	+	0.244787i	−0.272797	+	0.962072i	$0.587949\pi$
$314$		0			0
$315$	−9.10970	−	9.05116i	−0.513273	−	0.509975i
$316$		0			0
$317$	−2.75487	−	1.59053i	−0.154729	−	0.0893328i	0.420636	−	0.907229i	$-0.361807\pi$
$317$	−2.75487	−	1.59053i	−0.154729	−	0.0893328i	−0.575365	+	0.817896i	$0.695140\pi$
$318$		0			0
$319$	−23.1758	−	40.1417i	−1.29760	−	2.24750i
$320$		0			0
$321$			5.92140i			0.330500i
$322$		0			0
$323$	−3.46937			−0.193041
$324$		0			0
$325$	1.08259	−	0.625036i	0.0600516	−	0.0346708i
$326$		0			0
$327$	−13.9016	+	24.0782i	−0.768758	+	1.33153i
$328$		0			0
$329$	−10.9415	−	2.89399i	−0.603224	−	0.159551i
$330$		0			0
$331$	10.3410	+	5.97038i	0.568392	+	0.328162i	0.756507	−	0.653986i	$-0.226904\pi$
$331$	10.3410	+	5.97038i	0.568392	+	0.328162i	−0.188115	+	0.982147i	$0.560238\pi$
$332$		0			0
$333$	−1.99982	−	3.46379i	−0.109589	−	0.189814i
$334$		0			0
$335$		−	26.9858i		−	1.47439i
$336$		0			0
$337$	2.18719			0.119144			0.0595718	−	0.998224i	$-0.481026\pi$
$337$	2.18719			0.119144			0.0595718	+	0.998224i	$0.481026\pi$
$338$		0			0
$339$	32.5310	−	18.7818i	1.76684	−	1.02009i
$340$		0			0
$341$	7.35614	+	4.24707i	0.398357	+	0.229992i
$342$		0			0
$343$	−12.9685	+	13.2218i	−0.700236	+	0.713912i
$344$		0			0
$345$	33.0584	+	19.0863i	1.77980	+	1.02757i
$346$		0			0
$347$	15.6550	−	9.03843i	0.840405	−	0.485208i	−0.0169968	−	0.999856i	$-0.505411\pi$
$347$	15.6550	−	9.03843i	0.840405	−	0.485208i	0.857402	+	0.514647i	$0.172077\pi$
$348$		0			0
$349$	−16.4932			−0.882858			−0.441429	−	0.897296i	$-0.645528\pi$
$349$	−16.4932			−0.882858			−0.441429	+	0.897296i	$0.645528\pi$
$350$		0			0
$351$	1.56590			0.0835816
$352$		0			0
$353$	−8.58606	−	14.8715i	−0.456990	−	0.791530i	0.541810	−	0.840501i	$-0.317739\pi$
$353$	−8.58606	−	14.8715i	−0.456990	−	0.791530i	−0.998800	+	0.0489710i	$0.984406\pi$
$354$		0			0
$355$	13.9849	+	8.07421i	0.742244	+	0.428535i
$356$		0			0
$357$	2.44045	−	9.22674i	0.129162	−	0.488331i
$358$		0			0
$359$	15.4432	−	26.7485i	0.815063	−	1.41173i	−0.0942195	−	0.995551i	$-0.530036\pi$
$359$	15.4432	−	26.7485i	0.815063	−	1.41173i	0.909283	−	0.416179i	$-0.136631\pi$
$360$		0			0
$361$	−7.26751	−	12.5877i	−0.382500	−	0.662510i
$362$		0			0
$363$			45.2963i			2.37744i
$364$		0			0
$365$	29.0761			1.52191
$366$		0			0
$367$	2.53022	+	4.38247i	0.132076	+	0.228763i	0.924477	−	0.381238i	$-0.124502\pi$
$367$	2.53022	+	4.38247i	0.132076	+	0.228763i	−0.792400	+	0.610001i	$0.791169\pi$
$368$		0			0
$369$	−5.65003	−	10.2442i	−0.294129	−	0.533293i
$370$		0			0
$371$	8.89335	−	8.95087i	0.461720	−	0.464706i
$372$		0			0
$373$	15.3204	−	26.5357i	0.793260	−	1.37397i	−0.130679	−	0.991425i	$-0.541716\pi$
$373$	15.3204	−	26.5357i	0.793260	−	1.37397i	0.923938	−	0.382541i	$-0.124951\pi$
$374$		0			0
$375$	14.8747	−	8.58788i	0.768124	−	0.443476i
$376$		0			0
$377$	−5.00909			−0.257982
$378$		0			0
$379$	−24.9646			−1.28235			−0.641173	−	0.767397i	$-0.721552\pi$
$379$	−24.9646			−1.28235			−0.641173	+	0.767397i	$0.721552\pi$
$380$		0			0
$381$	38.0551	−	21.9711i	1.94962	−	1.12562i
$382$		0			0
$383$	26.5408	+	15.3233i	1.35617	+	0.782985i	0.989105	−	0.147211i	$-0.0470297\pi$
$383$	26.5408	+	15.3233i	1.35617	+	0.782985i	0.367064	+	0.930196i	$0.380363\pi$
$384$		0			0
$385$	10.3517	+	38.1409i	0.527572	+	1.94384i
$386$		0			0
$387$	8.60558	−	14.9053i	0.437446	−	0.757679i
$388$		0			0
$389$	−6.56134	−	11.3646i	−0.332673	−	0.576207i	0.650362	−	0.759625i	$-0.274617\pi$
$389$	−6.56134	−	11.3646i	−0.332673	−	0.576207i	−0.983035	+	0.183418i	$0.941284\pi$
$390$		0			0
$391$			10.7382i			0.543055i
$392$		0			0
$393$		−	33.9773i		−	1.71393i
$394$		0			0
$395$	−12.3647	+	7.13879i	−0.622138	+	0.359191i
$396$		0			0
$397$	−34.1612	−	19.7230i	−1.71450	−	0.989867i	−0.928249	−	0.371960i	$-0.878686\pi$
$397$	−34.1612	−	19.7230i	−1.71450	−	0.989867i	−0.786251	−	0.617907i	$-0.787981\pi$
$398$		0			0
$399$	−11.8541	+	3.21728i	−0.593446	+	0.161065i
$400$		0			0
$401$	5.07071	−	8.78274i	0.253219	−	0.438589i	−0.711191	−	0.702999i	$-0.751844\pi$
$401$	5.07071	−	8.78274i	0.253219	−	0.438589i	0.964410	+	0.264410i	$0.0851772\pi$
$402$		0			0
$403$	0.794958	−	0.458969i	0.0395997	−	0.0228629i
$404$		0			0
$405$	−29.6019			−1.47093
$406$		0			0
$407$			12.3090i			0.610133i
$408$		0			0
$409$	−11.9369	−	20.6753i	−0.590242	−	1.02233i	−0.994200	−	0.107551i	$-0.965699\pi$
$409$	−11.9369	−	20.6753i	−0.590242	−	1.02233i	0.403958	−	0.914778i	$-0.367634\pi$
$410$		0			0
$411$	−7.17204	+	12.4223i	−0.353771	+	0.612749i
$412$		0			0
$413$	1.32781	+	1.31928i	0.0653373	+	0.0649174i
$414$		0			0
$415$	−3.30216	+	5.71951i	−0.162097	+	0.280760i
$416$		0			0
$417$	8.04647	−	4.64563i	0.394037	−	0.227498i
$418$		0			0
$419$	22.8353			1.11558			0.557788	−	0.829984i	$-0.311650\pi$
$419$	22.8353			1.11558			0.557788	+	0.829984i	$0.311650\pi$
$420$		0			0
$421$		−	33.4896i		−	1.63218i	−0.577921	−	0.816092i	$-0.696136\pi$
$421$		−	33.4896i		−	1.63218i	0.577921	−	0.816092i	$-0.303864\pi$
$422$		0			0
$423$	6.76861	−	3.90786i	0.329101	−	0.190007i
$424$		0			0
$425$	−2.92518	−	1.68886i	−0.141892	−	0.0819215i
$426$		0			0
$427$	4.27948	−	16.1797i	0.207099	−	0.782990i
$428$		0			0
$429$	6.50107	+	3.75340i	0.313875	+	0.181216i
$430$		0			0
$431$	18.5254	+	32.0869i	0.892336	+	1.54557i	0.837067	+	0.547100i	$0.184268\pi$
$431$	18.5254	+	32.0869i	0.892336	+	1.54557i	0.0552687	+	0.998472i	$0.482398\pi$
$432$		0			0
$433$	0.347038			0.0166776			0.00833879	−	0.999965i	$-0.497346\pi$
$433$	0.347038			0.0166776			0.00833879	+	0.999965i	$0.497346\pi$
$434$		0			0
$435$	48.1133			2.30686
$436$		0			0
$437$	11.9683	−	6.90990i	0.572521	−	0.330545i
$438$		0			0
$439$	16.9779	+	9.80222i	0.810313	+	0.467835i	0.847065	−	0.531490i	$-0.178368\pi$
$439$	16.9779	+	9.80222i	0.810313	+	0.467835i	−0.0367514	+	0.999324i	$0.511701\pi$
$440$		0			0
$441$	−0.0824534	−	12.7893i	−0.00392635	−	0.609014i
$442$		0			0
$443$	16.2545	−	28.1536i	0.772273	−	1.33762i	−0.164042	−	0.986453i	$-0.552453\pi$
$443$	16.2545	−	28.1536i	0.772273	−	1.33762i	0.936315	−	0.351162i	$-0.114213\pi$
$444$		0			0
$445$	−10.7824	+	6.22520i	−0.511133	+	0.295103i
$446$		0			0
$447$	−44.0650			−2.08421
$448$		0			0
$449$	−21.8451			−1.03094			−0.515468	−	0.856909i	$-0.672382\pi$
$449$	−21.8451			−1.03094			−0.515468	+	0.856909i	$0.672382\pi$
$450$		0			0
$451$	−0.704901	+	35.9971i	−0.0331925	+	1.69504i
$452$		0			0
$453$	−1.90718	+	3.30334i	−0.0896073	+	0.155204i
$454$		0			0
$455$	4.12891	+	1.09209i	0.193566	+	0.0511978i
$456$		0			0
$457$	−29.4741	−	17.0169i	−1.37874	−	0.796017i	−0.386734	−	0.922191i	$-0.626397\pi$
$457$	−29.4741	−	17.0169i	−1.37874	−	0.796017i	−0.992008	+	0.126175i	$0.959730\pi$
$458$		0			0
$459$	−2.11554	−	3.66422i	−0.0987449	−	0.171031i
$460$		0			0
$461$	31.3417			1.45973			0.729865	−	0.683592i	$-0.239583\pi$
$461$	31.3417			1.45973			0.729865	+	0.683592i	$0.239583\pi$
$462$		0			0
$463$			10.0493i			0.467029i	0.972353	+	0.233515i	$0.0750227\pi$
$463$			10.0493i			0.467029i	−0.972353	+	0.233515i	$0.924977\pi$
$464$		0			0
$465$	−7.63572	+	4.40849i	−0.354098	+	0.204439i
$466$		0			0
$467$	−3.40402	+	5.89594i	−0.157519	+	0.272832i	−0.933974	−	0.357342i	$-0.883683\pi$
$467$	−3.40402	+	5.89594i	−0.157519	+	0.272832i	0.776454	+	0.630174i	$0.217016\pi$
$468$		0			0
$469$	18.9429	−	19.0654i	0.874703	−	0.880361i
$470$		0			0
$471$	16.6369	−	28.8160i	0.766588	−	1.32777i
$472$		0			0
$473$	−45.8714	+	26.4839i	−2.10917	+	1.21773i
$474$		0			0
$475$			4.34703i			0.199455i
$476$		0			0
$477$			8.71351i			0.398964i
$478$		0			0
$479$	8.57271	−	4.94946i	0.391697	−	0.226147i	−0.291198	−	0.956663i	$-0.594054\pi$
$479$	8.57271	−	4.94946i	0.391697	−	0.226147i	0.682895	+	0.730516i	$0.260721\pi$
$480$		0			0
$481$	1.15199	+	0.665099i	0.0525260	+	0.0303259i
$482$		0			0
$483$	9.95795	+	36.6901i	0.453103	+	1.66946i
$484$		0			0
$485$	0.0411788	+	0.0237746i	0.00186983	+	0.00107955i
$486$		0			0
$487$	−3.21788	−	5.57354i	−0.145816	−	0.252561i	0.783861	−	0.620936i	$-0.213247\pi$
$487$	−3.21788	−	5.57354i	−0.145816	−	0.252561i	−0.929677	+	0.368375i	$0.879914\pi$
$488$		0			0
$489$		−	32.6698i		−	1.47738i
$490$		0			0
$491$	22.3254			1.00753			0.503766	−	0.863840i	$-0.331947\pi$
$491$	22.3254			1.00753			0.503766	+	0.863840i	$0.331947\pi$
$492$		0			0
$493$	6.76732	+	11.7213i	0.304785	+	0.527902i
$494$		0			0
$495$	−23.6355	−	13.6459i	−1.06233	−	0.613339i
$496$		0			0
$497$	4.21260	+	15.5213i	0.188961	+	0.696226i
$498$		0			0
$499$	−15.4547	−	8.92278i	−0.691848	−	0.399439i	0.112456	−	0.993657i	$-0.464128\pi$
$499$	−15.4547	−	8.92278i	−0.691848	−	0.399439i	−0.804304	+	0.594218i	$0.797462\pi$
$500$		0			0
$501$	1.29985	+	2.25141i	0.0580732	+	0.100586i
$502$		0			0
$503$		−	33.7775i		−	1.50606i	−0.657985	−	0.753031i	$-0.728591\pi$
$503$		−	33.7775i		−	1.50606i	0.657985	−	0.753031i	$-0.271409\pi$
$504$		0			0
$505$			27.4450i			1.22129i
$506$		0			0
$507$	−24.0327	+	13.8753i	−1.06733	+	0.616223i
$508$		0			0
$509$	−32.6050	−	18.8245i	−1.44519	−	0.834382i	−0.447003	−	0.894533i	$-0.647509\pi$
$509$	−32.6050	−	18.8245i	−1.44519	−	0.834382i	−0.998189	+	0.0601506i	$0.980842\pi$
$510$		0			0
$511$	20.5423	+	20.4103i	0.908738	+	0.902898i
$512$		0			0
$513$	−2.72264	+	4.71576i	−0.120208	+	0.208206i
$514$		0			0
$515$	15.2796	+	26.4650i	0.673298	+	1.16619i
$516$		0			0
$517$	−24.0530			−1.05785
$518$		0			0
$519$		−	42.3509i		−	1.85900i
$520$		0			0
$521$	−23.9952	+	13.8536i	−1.05125	+	0.606939i	−0.922999	−	0.384803i	$-0.874270\pi$
$521$	−23.9952	+	13.8536i	−1.05125	+	0.606939i	−0.128251	+	0.991742i	$0.540936\pi$
$522$		0			0
$523$	−15.6807	+	27.1598i	−0.685670	+	1.18761i	0.287556	+	0.957764i	$0.407157\pi$
$523$	−15.6807	+	27.1598i	−0.685670	+	1.18761i	−0.973226	+	0.229851i	$0.926176\pi$
$524$		0			0
$525$	−11.5608	−	3.05781i	−0.504557	−	0.133454i
$526$		0			0
$527$	−2.14799	−	1.24014i	−0.0935677	−	0.0540214i
$528$		0			0
$529$	−9.88714	−	17.1250i	−0.429876	−	0.744567i
$530$		0			0
$531$	−1.29260			−0.0560940
$532$		0			0
$533$	3.33085	+	2.01103i	0.144275	+	0.0871072i
$534$		0			0
$535$	3.57988	+	6.20054i	0.154772	+	0.268073i
$536$		0			0
$537$	10.8030	−	18.7114i	0.466185	−	0.807456i
$538$		0			0
$539$	−19.4599	+	34.2131i	−0.838198	+	1.47366i
$540$		0			0
$541$	12.6521	−	21.9140i	0.543955	−	0.942157i	−0.454717	−	0.890636i	$-0.650260\pi$
$541$	12.6521	−	21.9140i	0.543955	−	0.942157i	0.998672	−	0.0515215i	$-0.0164071\pi$
$542$		0			0
$543$	11.4502	+	19.8323i	0.491374	+	0.851084i
$544$		0			0
$545$			33.6177i			1.44002i
$546$		0			0
$547$		−	21.1198i		−	0.903018i	−0.892266	−	0.451509i	$-0.850886\pi$
$547$		−	21.1198i		−	0.903018i	0.892266	−	0.451509i	$-0.149114\pi$
$548$		0			0
$549$	5.77873	+	10.0091i	0.246630	+	0.427176i
$550$		0			0
$551$	8.70936	−	15.0850i	0.371031	−	0.642645i
$552$		0			0
$553$	−13.7468	−	3.63600i	−0.584575	−	0.154618i
$554$		0			0
$555$	−11.0650	−	6.38841i	−0.469685	−	0.271173i
$556$		0			0
$557$	−31.6441	+	18.2697i	−1.34080	+	0.774113i	−0.986925	−	0.161179i	$-0.948470\pi$
$557$	−31.6441	+	18.2697i	−1.34080	+	0.774113i	−0.353878	+	0.935292i	$0.615137\pi$
$558$		0			0
$559$			5.72408i			0.242103i
$560$		0			0
$561$		−	20.2834i		−	0.856367i
$562$		0			0
$563$	23.8930	−	13.7946i	1.00697	−	0.581373i	0.0966657	−	0.995317i	$-0.469182\pi$
$563$	23.8930	−	13.7946i	1.00697	−	0.581373i	0.910303	+	0.413943i	$0.135849\pi$
$564$		0			0
$565$	22.7097	−	39.3344i	0.955405	−	1.65481i
$566$		0			0
$567$	−20.9138	−	20.7794i	−0.878296	−	0.872652i
$568$		0			0
$569$	0.799121	−	1.38412i	0.0335009	−	0.0580252i	−0.848789	−	0.528732i	$-0.822668\pi$
$569$	0.799121	−	1.38412i	0.0335009	−	0.0580252i	0.882290	+	0.470707i	$0.156001\pi$
$570$		0			0
$571$	−2.13072	+	1.23017i	−0.0891677	+	0.0514810i	−0.543921	−	0.839137i	$-0.683061\pi$
$571$	−2.13072	+	1.23017i	−0.0891677	+	0.0514810i	0.454753	+	0.890618i	$0.349727\pi$
$572$		0			0
$573$	41.9661			1.75316
$574$		0			0
$575$	13.4547			0.561099
$576$		0			0
$577$	10.0278	−	5.78956i	0.417463	−	0.241022i	−0.276528	−	0.961006i	$-0.589184\pi$
$577$	10.0278	−	5.78956i	0.417463	−	0.241022i	0.693991	+	0.719983i	$0.255851\pi$
$578$		0			0
$579$	7.83098	−	13.5637i	0.325444	−	0.563686i
$580$		0			0
$581$	−6.34785	+	1.72285i	−0.263353	+	0.0714759i
$582$		0			0
$583$	13.4080	−	23.2234i	0.555303	−	0.961813i
$584$		0			0
$585$	−2.55422	+	1.47468i	−0.105604	+	0.0609705i
$586$		0			0
$587$			1.57949i			0.0651923i	0.999469	+	0.0325962i	$0.0103775\pi$
$587$			1.57949i			0.0651923i	−0.999469	+	0.0325962i	$0.989622\pi$
$588$		0			0
$589$			3.19206i			0.131526i
$590$		0			0
$591$	30.3979	−	17.5503i	1.25040	−	0.721921i
$592$		0			0
$593$	−16.3656	−	9.44871i	−0.672057	−	0.388012i	0.124799	−	0.992182i	$-0.460171\pi$
$593$	−16.3656	−	9.44871i	−0.672057	−	0.388012i	−0.796855	+	0.604170i	$0.793505\pi$
$594$		0			0
$595$	−3.02269	−	11.1371i	−0.123918	−	0.456577i
$596$		0			0
$597$	3.00030	−	5.19667i	0.122794	−	0.212685i
$598$		0			0
$599$	18.8203	+	32.5977i	0.768976	+	1.33191i	0.938119	+	0.346314i	$0.112567\pi$
$599$	18.8203	+	32.5977i	0.768976	+	1.33191i	−0.169143	+	0.985592i	$0.554100\pi$
$600$		0			0
$601$		−	16.6115i		−	0.677597i	−0.940859	−	0.338799i	$-0.889979\pi$
$601$		−	16.6115i		−	0.677597i	0.940859	−	0.338799i	$-0.110021\pi$
$602$		0			0
$603$			18.5599i			0.755817i
$604$		0			0
$605$	27.3847	+	47.4317i	1.11335	+	1.92837i
$606$		0			0
$607$	−4.06622	+	7.04290i	−0.165043	+	0.285863i	−0.936671	−	0.350212i	$-0.886110\pi$
$607$	−4.06622	+	7.04290i	−0.165043	+	0.285863i	0.771628	+	0.636075i	$0.219443\pi$
$608$		0			0
$609$	33.9921	+	33.7736i	1.37743	+	1.36858i
$610$		0			0
$611$	−1.29967	+	2.25110i	−0.0525792	+	0.0910698i
$612$		0			0
$613$	7.90537	+	13.6925i	0.319295	+	0.553035i	0.980341	−	0.197310i	$-0.0632207\pi$
$613$	7.90537	+	13.6925i	0.319295	+	0.553035i	−0.661046	+	0.750345i	$0.729887\pi$
$614$		0			0
$615$	−31.9934	−	19.3163i	−1.29010	−	0.778908i
$616$		0			0
$617$	−14.1424			−0.569352			−0.284676	−	0.958624i	$-0.591886\pi$
$617$	−14.1424			−0.569352			−0.284676	+	0.958624i	$0.591886\pi$
$618$		0			0
$619$	−8.83099	−	15.2957i	−0.354947	−	0.614787i	0.632162	−	0.774837i	$-0.282168\pi$
$619$	−8.83099	−	15.2957i	−0.354947	−	0.614787i	−0.987109	+	0.160050i	$0.948835\pi$
$620$		0			0
$621$	14.5960	+	8.42698i	0.585716	+	0.338163i
$622$		0			0
$623$	−11.9876	−	3.17068i	−0.480272	−	0.127031i
$624$		0			0
$625$	15.5270	−	26.8935i	0.621079	−	1.07574i
$626$		0			0
$627$	−22.6069	+	13.0521i	−0.902834	+	0.521252i
$628$		0			0
$629$		−	3.59421i		−	0.143311i
$630$		0			0
$631$	42.8327			1.70514			0.852572	−	0.522610i	$-0.175041\pi$
$631$	42.8327			1.70514			0.852572	+	0.522610i	$0.175041\pi$
$632$		0			0
$633$	−8.08643	−	14.0061i	−0.321407	−	0.556693i
$634$		0			0
$635$	26.5661	−	46.0138i	1.05424	−	1.82600i
$636$		0			0
$637$	2.15048	+	3.66989i	0.0852051	+	0.145406i
$638$		0			0
$639$	−9.61837	−	5.55317i	−0.380497	−	0.219680i
$640$		0			0
$641$	14.3596	−	8.29053i	0.567171	−	0.327456i	−0.188848	−	0.982006i	$-0.560475\pi$
$641$	14.3596	−	8.29053i	0.567171	−	0.327456i	0.756019	+	0.654550i	$0.227142\pi$
$642$		0			0
$643$		−	21.6210i		−	0.852651i	−0.904570	−	0.426325i	$-0.859808\pi$
$643$		−	21.6210i		−	0.852651i	0.904570	−	0.426325i	$-0.140192\pi$
$644$		0			0
$645$		−	54.9809i		−	2.16487i
$646$		0			0
$647$	−22.3834	−	38.7692i	−0.879982	−	1.52417i	−0.851359	−	0.524584i	$-0.824221\pi$
$647$	−22.3834	−	38.7692i	−0.879982	−	1.52417i	−0.0286236	−	0.999590i	$-0.509112\pi$
$648$		0			0
$649$	3.44505	+	1.98900i	0.135230	+	0.0780751i
$650$		0			0
$651$	−8.48923	−	2.24538i	−0.332719	−	0.0880033i
$652$		0			0
$653$	30.9645	+	17.8774i	1.21173	+	0.699595i	0.963137	−	0.269011i	$-0.0866969\pi$
$653$	30.9645	+	17.8774i	1.21173	+	0.699595i	0.248598	+	0.968607i	$0.420030\pi$
$654$		0			0
$655$	−20.5416	−	35.5791i	−0.802626	−	1.39019i
$656$		0			0
$657$	−19.9976			−0.780179
$658$		0			0
$659$			38.3505i			1.49392i	0.664867	+	0.746962i	$0.268488\pi$
$659$			38.3505i			1.49392i	−0.664867	+	0.746962i	$0.731512\pi$
$660$		0			0
$661$	18.7880	+	32.5418i	0.730769	+	1.26573i	0.956555	+	0.291552i	$0.0941718\pi$
$661$	18.7880	+	32.5418i	0.730769	+	1.26573i	−0.225786	+	0.974177i	$0.572495\pi$
$662$		0			0
$663$	−1.89831	−	1.09599i	−0.0737242	−	0.0425647i
$664$		0			0
$665$	−10.4678	+	10.5355i	−0.405925	+	0.408551i
$666$		0			0
$667$	−46.6904	−	26.9567i	−1.80786	−	1.04377i
$668$		0			0
$669$	−3.47039	+	2.00363i	−0.134173	+	0.0774649i
$670$		0			0
$671$		−	35.5683i		−	1.37310i
$672$		0			0
$673$			37.1558i			1.43225i	0.697971	+	0.716126i	$0.254087\pi$
$673$			37.1558i			1.43225i	−0.697971	+	0.716126i	$0.745913\pi$
$674$		0			0
$675$	−4.59117	+	2.65071i	−0.176714	+	0.102026i
$676$		0			0
$677$	−16.8264	+	29.1441i	−0.646690	+	1.12010i	0.337219	+	0.941426i	$0.390514\pi$
$677$	−16.8264	+	29.1441i	−0.646690	+	1.12010i	−0.983909	+	0.178673i	$0.942820\pi$
$678$		0			0
$679$	0.0124040	+	0.0457027i	0.000476023	+	0.00175391i
$680$		0			0
$681$	−27.5661	+	47.7459i	−1.05634	+	1.82963i
$682$		0			0
$683$	20.7124	−	11.9583i	0.792537	−	0.457571i	−0.0483180	−	0.998832i	$-0.515386\pi$
$683$	20.7124	−	11.9583i	0.792537	−	0.457571i	0.840855	+	0.541261i	$0.182053\pi$
$684$		0			0
$685$			17.3439i			0.662677i
$686$		0			0
$687$	−30.7242			−1.17220
$688$		0			0
$689$	−1.44897	−	2.50969i	−0.0552013	−	0.0956115i
$690$		0			0
$691$	−25.1427	−	14.5161i	−0.956472	−	0.552219i	−0.0613863	−	0.998114i	$-0.519552\pi$
$691$	−25.1427	−	14.5161i	−0.956472	−	0.552219i	−0.895085	+	0.445895i	$0.852885\pi$
$692$		0			0
$693$	−7.11955	−	26.2320i	−0.270449	−	0.996472i
$694$		0			0
$695$	5.61719	−	9.72927i	0.213072	−	0.369052i
$696$		0			0
$697$	0.205831	−	10.5111i	0.00779639	−	0.398137i
$698$		0			0
$699$	−30.9280			−1.16980
$700$		0			0
$701$	−28.3135			−1.06939			−0.534693	−	0.845047i	$-0.679573\pi$
$701$	−28.3135			−1.06939			−0.534693	+	0.845047i	$0.679573\pi$
$702$		0			0
$703$	−4.00594	+	2.31283i	−0.151087	+	0.0872300i
$704$		0			0
$705$	12.4836	−	21.6223i	0.470160	−	0.814341i
$706$		0			0
$707$	−19.2653	+	19.3899i	−0.724546	+	0.729232i
$708$		0			0
$709$	0.283526	+	0.163694i	0.0106480	+	0.00614764i	0.505315	−	0.862935i	$-0.331376\pi$
$709$	0.283526	+	0.163694i	0.0106480	+	0.00614764i	−0.494667	+	0.869083i	$0.664710\pi$
$710$		0			0
$711$	8.50404	−	4.90981i	0.318927	−	0.184132i
$712$		0			0
$713$	9.87988			0.370004
$714$		0			0
$715$	9.07672			0.339450
$716$		0			0
$717$	−14.0130	−	24.2713i	−0.523327	−	0.906428i
$718$		0			0
$719$	−25.4533	−	14.6954i	−0.949246	−	0.548048i	−0.0563995	−	0.998408i	$-0.517962\pi$
$719$	−25.4533	−	14.6954i	−0.949246	−	0.548048i	−0.892847	+	0.450361i	$0.851295\pi$
$720$		0			0
$721$	−7.78234	+	29.4232i	−0.289830	+	1.09578i
$722$		0			0
$723$	0.444078	+	0.256389i	0.0165154	+	0.00953519i
$724$		0			0
$725$	14.6865	−	8.47926i	0.545443	−	0.314912i
$726$		0			0
$727$			16.3409i			0.606050i	0.952983	+	0.303025i	$0.0979966\pi$
$727$			16.3409i			0.606050i	−0.952983	+	0.303025i	$0.902003\pi$
$728$		0			0
$729$	3.37385			0.124957
$730$		0			0
$731$	13.3944	−	7.73327i	0.495410	−	0.286025i
$732$		0			0
$733$	22.7375	−	39.3826i	0.839830	−	1.45463i	−0.0502067	−	0.998739i	$-0.515988\pi$
$733$	22.7375	−	39.3826i	0.839830	−	1.45463i	0.890037	−	0.455889i	$-0.150679\pi$
$734$		0			0
$735$	−20.6558	−	35.2500i	−0.761899	−	1.30022i
$736$		0			0
$737$	28.5592	−	49.4660i	1.05199	−	1.82210i
$738$		0			0
$739$	−16.0435	−	27.7881i	−0.590169	−	1.02220i	−0.994209	−	0.107461i	$-0.965728\pi$
$739$	−16.0435	−	27.7881i	−0.590169	−	1.02220i	0.404041	−	0.914741i	$-0.367605\pi$
$740$		0			0
$741$			2.82102i			0.103633i
$742$		0			0
$743$	1.71995			0.0630987			0.0315493	−	0.999502i	$-0.489956\pi$
$743$	1.71995			0.0630987			0.0315493	+	0.999502i	$0.489956\pi$
$744$		0			0
$745$	−46.1423	+	26.6403i	−1.69052	+	0.976025i
$746$		0			0
$747$	2.27111	−	3.93368i	0.0830957	−	0.143926i
$748$		0			0
$749$	−1.82334	+	6.89362i	−0.0666235	+	0.251887i
$750$		0			0
$751$	33.5940	+	19.3955i	1.22586	+	0.707752i	0.966162	−	0.257937i	$-0.0830427\pi$
$751$	33.5940	+	19.3955i	1.22586	+	0.707752i	0.259701	+	0.965689i	$0.416376\pi$
$752$		0			0
$753$	6.54179	−	3.77690i	0.238396	−	0.137638i
$754$		0			0
$755$			4.61208i			0.167851i
$756$		0			0
$757$			33.9280i			1.23313i	0.787302	+	0.616567i	$0.211477\pi$
$757$			33.9280i			1.23313i	−0.787302	+	0.616567i	$0.788523\pi$
$758$		0			0
$759$	40.3982	+	69.9718i	1.46636	+	2.53982i
$760$		0			0
$761$	−4.61568	+	7.99459i	−0.167318	+	0.289804i	−0.937476	−	0.348050i	$-0.886844\pi$
$761$	−4.61568	+	7.99459i	−0.167318	+	0.289804i	0.770158	+	0.637853i	$0.220177\pi$
$762$		0			0
$763$	−23.5983	+	23.7509i	−0.854316	+	0.859842i
$764$		0			0
$765$	6.90154	+	3.98460i	0.249526	+	0.144064i
$766$		0			0
$767$	0.372298	−	0.214946i	0.0134429	−	0.00776126i
$768$		0			0
$769$	42.9861			1.55012			0.775058	−	0.631890i	$-0.217720\pi$
$769$	42.9861			1.55012			0.775058	+	0.631890i	$0.217720\pi$
$770$		0			0
$771$	52.2411			1.88142
$772$		0			0
$773$	36.8306	−	21.2641i	1.32470	−	0.764818i	0.340228	−	0.940343i	$-0.389496\pi$
$773$	36.8306	−	21.2641i	1.32470	−	0.764818i	0.984475	+	0.175525i	$0.0561624\pi$
$774$		0			0
$775$	−1.55386	+	2.69137i	−0.0558164	+	0.0966768i
$776$		0			0
$777$	−3.33305	−	12.2806i	−0.119573	−	0.440565i
$778$		0			0
$779$	−11.8476	+	6.53436i	−0.424486	+	0.234118i
$780$		0			0
$781$	17.0900	+	29.6007i	0.611528	+	1.05920i
$782$		0			0
$783$	21.2430			0.759164
$784$		0			0
$785$		−	40.2325i		−	1.43596i
$786$		0			0
$787$	−3.12937	−	5.42022i	−0.111550	−	0.193210i	0.804845	−	0.593484i	$-0.202248\pi$
$787$	−3.12937	−	5.42022i	−0.111550	−	0.193210i	−0.916395	+	0.400274i	$0.868915\pi$
$788$		0			0
$789$	11.4068	−	19.7572i	0.406093	−	0.703374i
$790$		0			0
$791$	43.6556	−	11.8484i	1.55221	−	0.421282i
$792$		0			0
$793$	−3.32881	−	1.92189i	−0.118209	−	0.0682483i
$794$		0			0
$795$	13.9176	+	24.1060i	0.493607	+	0.854953i
$796$		0			0
$797$	−41.8954			−1.48401			−0.742005	−	0.670394i	$-0.766125\pi$
$797$	−41.8954			−1.48401			−0.742005	+	0.670394i	$0.766125\pi$
$798$		0			0
$799$	7.02347			0.248472
$800$		0			0
$801$	7.41573	−	4.28148i	0.262022	−	0.151279i
$802$		0			0
$803$	53.2977	+	30.7715i	1.88084	+	1.08590i
$804$		0			0
$805$	32.6090	+	32.3995i	1.14932	+	1.14193i
$806$		0			0
$807$	−59.4812	−	34.3415i	−2.09384	−	1.20888i
$808$		0			0
$809$	−34.7096	+	20.0396i	−1.22032	+	0.704554i	−0.964987	−	0.262298i	$-0.915520\pi$
$809$	−34.7096	+	20.0396i	−1.22032	+	0.704554i	−0.255336	+	0.966852i	$0.582186\pi$
$810$		0			0
$811$	40.0216			1.40535			0.702675	−	0.711511i	$-0.251989\pi$
$811$	40.0216			1.40535			0.702675	+	0.711511i	$0.251989\pi$
$812$		0			0
$813$			15.1779i			0.532311i
$814$		0			0
$815$	−19.7511	−	34.2099i	−0.691850	−	1.19832i
$816$		0			0
$817$	−17.2383	−	9.95251i	−0.603090	−	0.348194i
$818$		0			0
$819$	−2.83973	−	0.751100i	−0.0992280	−	0.0262455i
$820$		0			0
$821$	−5.30560	+	9.18957i	−0.185167	+	0.320718i	−0.943633	−	0.330994i	$-0.892616\pi$
$821$	−5.30560	+	9.18957i	−0.185167	+	0.320718i	0.758466	+	0.651713i	$0.225949\pi$
$822$		0			0
$823$	−18.6964	+	10.7943i	−0.651714	+	0.376267i	−0.789113	−	0.614249i	$-0.789459\pi$
$823$	−18.6964	+	10.7943i	−0.651714	+	0.376267i	0.137399	+	0.990516i	$0.456126\pi$
$824$		0			0
$825$	−25.4146			−0.884822
$826$		0			0
$827$			3.96041i			0.137717i	0.997626	+	0.0688585i	$0.0219357\pi$
$827$			3.96041i			0.137717i	−0.997626	+	0.0688585i	$0.978064\pi$
$828$		0			0
$829$	14.0022	+	24.2524i	0.486315	+	0.842322i	0.999876	−	0.0157306i	$-0.00500740\pi$
$829$	14.0022	+	24.2524i	0.486315	+	0.842322i	−0.513561	+	0.858053i	$0.671674\pi$
$830$		0			0
$831$	6.67341	+	3.85290i	0.231498	+	0.133656i
$832$		0			0
$833$	5.68228	−	9.99019i	0.196879	−	0.346140i
$834$		0			0
$835$	2.72226	+	1.57170i	0.0942077	+	0.0543909i
$836$		0			0
$837$	−3.37133	+	1.94644i	−0.116530	+	0.0672788i
$838$		0			0
$839$			4.70558i			0.162455i	0.996696	+	0.0812273i	$0.0258840\pi$
$839$			4.70558i			0.162455i	−0.996696	+	0.0812273i	$0.974116\pi$
$840$		0			0
$841$	−38.9535			−1.34322
$842$		0			0
$843$	−4.79502	−	8.30522i	−0.165149	−	0.286047i
$844$		0			0
$845$	−16.7771	+	29.0588i	−0.577149	+	0.999652i
$846$		0			0
$847$	−13.9478	+	52.7334i	−0.479254	+	1.81194i
$848$		0			0
$849$	62.2455	+	35.9375i	2.13626	+	1.23337i
$850$		0			0
$851$	7.15854	+	12.3990i	0.245392	+	0.425031i
$852$		0			0
$853$	−14.7972			−0.506645			−0.253322	−	0.967382i	$-0.581523\pi$
$853$	−14.7972			−0.506645			−0.253322	+	0.967382i	$0.581523\pi$
$854$		0			0
$855$		−	10.2562i		−	0.350753i
$856$		0			0
$857$	−0.836211	−	1.44836i	−0.0285644	−	0.0494750i	0.851390	−	0.524533i	$-0.175760\pi$
$857$	−0.836211	−	1.44836i	−0.0285644	−	0.0494750i	−0.879954	+	0.475058i	$0.842427\pi$
$858$		0			0
$859$	−3.95318	+	6.84711i	−0.134881	+	0.233620i	−0.925552	−	0.378621i	$-0.876398\pi$
$859$	−3.95318	+	6.84711i	−0.134881	+	0.233620i	0.790671	+	0.612241i	$0.209732\pi$
$860$		0			0
$861$	−9.04409	−	36.1051i	−0.308222	−	1.23046i
$862$		0			0
$863$	−7.91580	+	13.7106i	−0.269457	+	0.466713i	−0.968722	−	0.248150i	$-0.920178\pi$
$863$	−7.91580	+	13.7106i	−0.269457	+	0.466713i	0.699265	+	0.714863i	$0.253511\pi$
$864$		0			0
$865$	−25.6039	−	44.3473i	−0.870560	−	1.50785i
$866$		0			0
$867$		−	31.4273i		−	1.06733i
$868$		0			0
$869$	−30.2201			−1.02515
$870$		0			0
$871$	−3.08632	−	5.34566i	−0.104576	−	0.181131i
$872$		0			0
$873$	−0.0283214	−	0.0163514i	−0.000958534	−	0.000553410i
$874$		0			0
$875$	19.9613	−	5.41764i	0.674816	−	0.183150i
$876$		0			0
$877$	−1.90045	+	3.29168i	−0.0641738	+	0.111152i	−0.896327	−	0.443393i	$-0.853775\pi$
$877$	−1.90045	+	3.29168i	−0.0641738	+	0.111152i	0.832153	+	0.554545i	$0.187108\pi$
$878$		0			0
$879$	−6.76432	−	11.7161i	−0.228155	−	0.395176i
$880$		0			0
$881$	−0.545622			−0.0183825			−0.00919123	−	0.999958i	$-0.502926\pi$
$881$	−0.545622			−0.0183825			−0.00919123	+	0.999958i	$0.502926\pi$
$882$		0			0
$883$		−	5.49234i		−	0.184832i	−0.995720	−	0.0924159i	$-0.970541\pi$
$883$		−	5.49234i		−	0.184832i	0.995720	−	0.0924159i	$-0.0294589\pi$
$884$		0			0
$885$	−3.57599	+	2.06460i	−0.120206	+	0.0694007i
$886$		0			0
$887$	9.48763	+	5.47769i	0.318564	+	0.183923i	0.650752	−	0.759290i	$-0.274454\pi$
$887$	9.48763	+	5.47769i	0.318564	+	0.183923i	−0.332189	+	0.943213i	$0.607787\pi$
$888$		0			0
$889$	51.0688	−	13.8604i	1.71279	−	0.464864i
$890$		0			0
$891$	−54.2616	−	31.3279i	−1.81783	−	1.04952i
$892$		0			0
$893$	−4.51951	−	7.82802i	−0.151240	−	0.261955i
$894$		0			0
$895$		−	26.1246i		−	0.873250i
$896$		0			0
$897$	8.73146			0.291535
$898$		0			0
$899$	10.7844	−	6.22639i	0.359681	−	0.207662i
$900$		0			0
$901$	−3.91513	+	6.78121i	−0.130432	+	0.225915i
$902$		0			0
$903$	38.5944	−	38.8440i	1.28434	−	1.29265i
$904$		0			0
$905$	23.9799	+	13.8448i	0.797118	+	0.460216i
$906$		0			0
$907$	29.6926	+	51.4292i	0.985928	+	1.70768i	0.637739	+	0.770253i	$0.279870\pi$
$907$	29.6926	+	51.4292i	0.985928	+	1.70768i	0.348189	+	0.937424i	$0.386797\pi$
$908$		0			0
$909$		−	18.8757i		−	0.626068i
$910$		0			0
$911$	19.6473			0.650945			0.325472	−	0.945552i	$-0.394477\pi$
$911$	19.6473			0.650945			0.325472	+	0.945552i	$0.394477\pi$
$912$		0			0
$913$	−12.1060	+	6.98940i	−0.400650	+	0.231315i
$914$		0			0
$915$	31.9738	+	18.4601i	1.05702	+	0.610272i
$916$		0			0
$917$	10.4625	−	39.5560i	0.345501	−	1.30625i
$918$		0			0
$919$	24.1662	+	13.9524i	0.797170	+	0.460246i	0.842481	−	0.538727i	$-0.181094\pi$
$919$	24.1662	+	13.9524i	0.797170	+	0.460246i	−0.0453106	+	0.998973i	$0.514428\pi$
$920$		0			0
$921$	12.8805	−	7.43656i	0.424427	−	0.245043i
$922$		0			0
$923$	3.69374			0.121581
$924$		0			0
$925$	−4.50345			−0.148072
$926$		0			0
$927$	−10.5088	−	18.2017i	−0.345153	−	0.597822i
$928$		0			0
$929$	−19.8290	−	11.4483i	−0.650568	−	0.375606i	0.138106	−	0.990417i	$-0.455899\pi$
$929$	−19.8290	−	11.4483i	−0.650568	−	0.375606i	−0.788674	+	0.614812i	$0.789232\pi$
$930$		0			0
$931$	−14.7911	+	0.0953589i	−0.484757	+	0.00312526i
$932$		0			0
$933$	−20.0168	+	34.6701i	−0.655319	+	1.13505i
$934$		0			0
$935$	−12.2627	−	21.2396i	−0.401033	−	0.694610i
$936$		0			0
$937$		−	15.9121i		−	0.519825i	−0.965632	−	0.259913i	$-0.916306\pi$
$937$		−	15.9121i		−	0.519825i	0.965632	−	0.259913i	$-0.0836938\pi$
$938$		0			0
$939$	−19.0297			−0.621011
$940$		0			0
$941$	18.9183	+	32.7675i	0.616720	+	1.06819i	0.990080	+	0.140504i	$0.0448723\pi$
$941$	18.9183	+	32.7675i	0.616720	+	1.06819i	−0.373360	+	0.927687i	$0.621794\pi$
$942$		0			0
$943$	20.2248	+	36.6702i	0.658610	+	1.19415i
$944$		0			0
$945$	−17.5103	−	4.63142i	−0.569610	−	0.150660i
$946$		0			0
$947$	9.81543	−	17.0008i	0.318959	−	0.552452i	−0.661312	−	0.750111i	$-0.730000\pi$
$947$	9.81543	−	17.0008i	0.318959	−	0.552452i	0.980271	+	0.197658i	$0.0633336\pi$
$948$		0			0
$949$	5.75975	−	3.32539i	0.186969	−	0.107947i
$950$		0			0
$951$	6.98897			0.226633
$952$		0			0
$953$	33.4487			1.08351			0.541755	−	0.840536i	$-0.317760\pi$
$953$	33.4487			1.08351			0.541755	+	0.840536i	$0.317760\pi$
$954$		0			0
$955$	43.9444	−	25.3713i	1.42201	−	0.820997i
$956$		0			0
$957$	88.1937	+	50.9187i	2.85090	+	1.64597i
$958$		0			0
$959$	−12.1747	+	12.2535i	−0.393143	+	0.395686i
$960$		0			0
$961$	14.3590	−	24.8705i	0.463193	−	0.802274i
$962$		0			0
$963$	−2.46212	−	4.26452i	−0.0793407	−	0.137422i
$964$		0			0
$965$		−	18.9374i		−	0.609617i
$966$		0			0
$967$		−	5.00952i		−	0.161095i	−0.996751	−	0.0805477i	$-0.974333\pi$
$967$		−	5.00952i		−	0.161095i	0.996751	−	0.0805477i	$-0.0256669\pi$
$968$		0			0
$969$	6.60121	−	3.81121i	0.212061	−	0.122434i
$970$		0			0
$971$	−33.9822	−	19.6197i	−1.09054	−	0.629625i	−0.156821	−	0.987627i	$-0.550125\pi$
$971$	−33.9822	−	19.6197i	−1.09054	−	0.629625i	−0.933721	+	0.358002i	$0.883458\pi$
$972$		0			0
$973$	10.7981	−	2.93068i	0.346171	−	0.0939534i
$974$		0			0
$975$	−1.37324	+	2.37853i	−0.0439790	+	0.0761738i
$976$		0			0
$977$	−31.5565	+	18.2191i	−1.00958	+	0.582882i	−0.911069	−	0.412254i	$-0.864742\pi$
$977$	−31.5565	+	18.2191i	−1.00958	+	0.582882i	−0.0985125	+	0.995136i	$0.531408\pi$
$978$		0			0
$979$	−26.3527			−0.842235
$980$		0			0
$981$		−	23.1211i		−	0.738200i
$982$		0			0
$983$	9.83504	+	17.0348i	0.313689	+	0.543326i	0.979158	−	0.203100i	$-0.0651017\pi$
$983$	9.83504	+	17.0348i	0.313689	+	0.543326i	−0.665469	+	0.746426i	$0.731768\pi$
$984$		0			0
$985$	21.2206	−	36.7552i	0.676146	−	1.17112i
$986$		0			0
$987$	23.9976	−	6.51313i	0.763853	−	0.207315i
$988$		0			0
$989$	−30.8045	+	53.3549i	−0.979526	+	1.69659i
$990$		0			0
$991$	8.15427	−	4.70787i	0.259029	−	0.149550i	−0.364863	−	0.931061i	$-0.618884\pi$
$991$	8.15427	−	4.70787i	0.259029	−	0.149550i	0.623891	+	0.781511i	$0.285551\pi$
$992$		0			0
$993$	−26.2346			−0.832529
$994$		0			0
$995$		−	7.25553i		−	0.230016i
$996$		0			0
$997$	−27.6997	+	15.9924i	−0.877259	+	0.506486i	−0.869754	−	0.493486i	$-0.835722\pi$
$997$	−27.6997	+	15.9924i	−0.877259	+	0.506486i	−0.00750531	+	0.999972i	$0.502389\pi$
$998$		0			0
$999$	−4.88545	−	2.82062i	−0.154569	−	0.0892403i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.r.a.737.4	yes	56
7.4	even	3	inner	1148.2.r.a.81.25	yes	56
41.40	even	2	inner	1148.2.r.a.737.25	yes	56
287.81	even	6	inner	1148.2.r.a.81.4	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.r.a.81.4	✓	56	287.81	even	6	inner
1148.2.r.a.81.25	yes	56	7.4	even	3	inner
1148.2.r.a.737.4	yes	56	1.1	even	1	trivial
1148.2.r.a.737.25	yes	56	41.40	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.90271 + 1.09853i) q^{3} +(-1.32827 + 2.30063i) q^{5} +(-2.55338 + 0.693005i) q^{7} +(0.913540 - 1.58230i) q^{9} +O(q^{10})\)	\(q+(-1.90271 + 1.09853i) q^{3} +(-1.32827 + 2.30063i) q^{5} +(-2.55338 + 0.693005i) q^{7} +(0.913540 - 1.58230i) q^{9} +(-4.86956 + 2.81144i) q^{11} +0.607650i q^{13} -5.83659i q^{15} +(1.42191 - 0.820938i) q^{17} +(-1.82996 - 1.05653i) q^{19} +(4.09706 - 4.12355i) q^{21} +(-3.27010 + 5.66398i) q^{23} +(-1.02861 - 1.78161i) q^{25} -2.57698i q^{27} +8.24339i q^{29} +(-0.755319 - 1.30825i) q^{31} +(6.17691 - 10.6987i) q^{33} +(1.79723 - 6.79489i) q^{35} +(1.09454 - 1.89581i) q^{37} +(-0.667522 - 1.15618i) q^{39} +(3.30952 - 5.48152i) q^{41} +9.42004 q^{43} +(2.42686 + 4.20344i) q^{45} +(3.70460 + 2.13885i) q^{47} +(6.03949 - 3.53901i) q^{49} +(-1.80365 + 3.12402i) q^{51} +(-4.13016 + 2.38455i) q^{53} -14.9374i q^{55} +4.64251 q^{57} +(-0.353734 - 0.612685i) q^{59} +(-3.16282 + 5.47817i) q^{61} +(-1.23607 + 4.67329i) q^{63} +(-1.39798 - 0.807124i) q^{65} +(-8.79728 + 5.07911i) q^{67} -14.3692i q^{69} -6.07874i q^{71} +(-5.47255 - 9.47873i) q^{73} +(3.91431 + 2.25993i) q^{75} +(10.4855 - 10.5533i) q^{77} +(4.65445 + 2.68725i) q^{79} +(5.57151 + 9.65014i) q^{81} +2.48606 q^{83} +4.36172i q^{85} +(-9.05562 - 15.6848i) q^{87} +(4.05879 + 2.34334i) q^{89} +(-0.421104 - 1.55156i) q^{91} +(2.87431 + 1.65948i) q^{93} +(4.86136 - 2.80671i) q^{95} -0.0178989i q^{97} +10.2734i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{5} + 32 q^{9}+O(q^{10}) \) 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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