LMFDB - Embedded newform 1575.2.bk.i.26.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1575,2,Mod(26,1575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1575, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("1575.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1575 = 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1575.bk (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:	$12.5764383184$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.4
Character	$\chi$	$=$	1575.26
Dual form			1575.2.bk.i.1151.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.65683 - 0.956572i) q^{2} +(0.830062 + 1.43771i) q^{4} +(-2.39757 + 1.11878i) q^{7} +0.650234i q^{8} +O(q^{10})$	\(q+(-1.65683 - 0.956572i) q^{2} +(0.830062 + 1.43771i) q^{4} +(-2.39757 + 1.11878i) q^{7} +0.650234i q^{8} +(-2.79501 + 1.61370i) q^{11} +4.86146i q^{13} +(5.04256 + 0.439817i) q^{14} +(2.28212 - 3.95275i) q^{16} +(-0.364571 - 0.631456i) q^{17} +(6.81691 + 3.93574i) q^{19} +6.17449 q^{22} +(-4.21599 - 2.43410i) q^{23} +(4.65034 - 8.05463i) q^{26} +(-3.59861 - 2.51835i) q^{28} -7.75958i q^{29} +(-1.23751 + 0.714478i) q^{31} +(-6.43594 + 3.71579i) q^{32} +1.39495i q^{34} +(-1.58269 + 2.74130i) q^{37} +(-7.52965 - 13.0417i) q^{38} -1.40264 q^{41} -6.42489 q^{43} +(-4.64007 - 2.67894i) q^{44} +(4.65679 + 8.06579i) q^{46} +(2.43524 - 4.21797i) q^{47} +(4.49666 - 5.36470i) q^{49} +(-6.98937 + 4.03531i) q^{52} +(-1.31763 + 0.760733i) q^{53} +(-0.727468 - 1.55898i) q^{56} +(-7.42260 + 12.8563i) q^{58} +(-3.15081 - 5.45737i) q^{59} +(-2.05442 - 1.18612i) q^{61} +2.73380 q^{62} +5.08921 q^{64} +(-5.56295 - 9.63531i) q^{67} +(0.605233 - 1.04829i) q^{68} +10.1351i q^{71} +(11.9718 - 6.91195i) q^{73} +(5.24450 - 3.02792i) q^{74} +13.0676i q^{76} +(4.89586 - 6.99596i) q^{77} +(1.99018 - 3.44710i) q^{79} +(2.32395 + 1.34173i) q^{82} +4.19208 q^{83} +(10.6450 + 6.14587i) q^{86} +(-1.04928 - 1.81741i) q^{88} +(-5.63672 + 9.76309i) q^{89} +(-5.43891 - 11.6557i) q^{91} -8.08181i q^{92} +(-8.06958 + 4.65898i) q^{94} +2.21388i q^{97} +(-12.5819 + 4.58702i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4}+O(q^{10}) $ 24 * q + 24 * q^4	$ 24 q + 24 q^{4} + 36 q^{19} - 60 q^{31} - 24 q^{46} - 36 q^{49} + 48 q^{61} - 48 q^{64} + 60 q^{79} + 60 q^{91} - 48 q^{94}+O(q^{100}) $ 24 * q + 24 * q^4 + 36 * q^19 - 60 * q^31 - 24 * q^46 - 36 * q^49 + 48 * q^61 - 48 * q^64 + 60 * q^79 + 60 * q^91 - 48 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1575\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$1226$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.65683	−	0.956572i	−1.17156	−	0.676399i	−0.217511	−	0.976058i	$-0.569794\pi$
$2$	−1.65683	−	0.956572i	−1.17156	−	0.676399i	−0.954046	+	0.299659i	$0.903127\pi$
$3$		0			0
$3$		0			0
$4$	0.830062	+	1.43771i	0.415031	+	0.718854i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.39757	+	1.11878i	−0.906196	+	0.422859i
$7$	−2.39757	+	1.11878i	−0.906196	+	0.422859i
$8$			0.650234i			0.229892i
$9$		0			0
$10$		0			0
$11$	−2.79501	+	1.61370i	−0.842728	+	0.486549i	−0.858191	−	0.513331i	$-0.828411\pi$
$11$	−2.79501	+	1.61370i	−0.842728	+	0.486549i	0.0154625	+	0.999880i	$0.495078\pi$
$12$		0			0
$13$			4.86146i			1.34833i	0.738582	+	0.674164i	$0.235496\pi$
$13$			4.86146i			1.34833i	−0.738582	+	0.674164i	$0.764504\pi$
$14$	5.04256	+	0.439817i	1.34768	+	0.117546i
$15$		0			0
$16$	2.28212	−	3.95275i	0.570530	−	0.988186i
$17$	−0.364571	−	0.631456i	−0.0884215	−	0.153150i	0.818423	−	0.574617i	$-0.194849\pi$
$17$	−0.364571	−	0.631456i	−0.0884215	−	0.153150i	−0.906844	+	0.421466i	$0.861516\pi$
$18$		0			0
$19$	6.81691	+	3.93574i	1.56391	+	0.902922i	0.996856	+	0.0792390i	$0.0252490\pi$
$19$	6.81691	+	3.93574i	1.56391	+	0.902922i	0.567051	+	0.823683i	$0.308084\pi$
$20$		0			0
$21$		0			0
$22$	6.17449			1.31641
$23$	−4.21599	−	2.43410i	−0.879094	−	0.507545i	−0.00873433	−	0.999962i	$-0.502780\pi$
$23$	−4.21599	−	2.43410i	−0.879094	−	0.507545i	−0.870360	+	0.492417i	$0.836114\pi$
$24$		0			0
$25$		0			0
$26$	4.65034	−	8.05463i	0.912007	−	1.57964i
$27$		0			0
$28$	−3.59861	−	2.51835i	−0.680073	−	0.475923i
$29$		−	7.75958i		−	1.44092i	−0.693498	−	0.720459i	$-0.743931\pi$
$29$		−	7.75958i		−	1.44092i	0.693498	−	0.720459i	$-0.256069\pi$
$30$		0			0
$31$	−1.23751	+	0.714478i	−0.222264	+	0.128324i	−0.606998	−	0.794703i	$-0.707626\pi$
$31$	−1.23751	+	0.714478i	−0.222264	+	0.128324i	0.384734	+	0.923027i	$0.374293\pi$
$32$	−6.43594	+	3.71579i	−1.13772	+	0.656865i
$33$		0			0
$34$			1.39495i			0.239233i
$35$		0			0
$36$		0			0
$37$	−1.58269	+	2.74130i	−0.260193	+	0.450667i	−0.966293	−	0.257445i	$-0.917119\pi$
$37$	−1.58269	+	2.74130i	−0.260193	+	0.450667i	0.706100	+	0.708112i	$0.250453\pi$
$38$	−7.52965	−	13.0417i	−1.22147	−	2.11565i
$39$		0			0
$40$		0			0
$41$	−1.40264			−0.219056			−0.109528	−	0.993984i	$-0.534934\pi$
$41$	−1.40264			−0.219056			−0.109528	+	0.993984i	$0.534934\pi$
$42$		0			0
$43$	−6.42489			−0.979787			−0.489893	−	0.871782i	$-0.662964\pi$
$43$	−6.42489			−0.979787			−0.489893	+	0.871782i	$0.662964\pi$
$44$	−4.64007	−	2.67894i	−0.699516	−	0.403866i
$45$		0			0
$46$	4.65679	+	8.06579i	0.686606	+	1.18924i
$47$	2.43524	−	4.21797i	0.355217	−	0.615254i	−0.631938	−	0.775019i	$-0.717740\pi$
$47$	2.43524	−	4.21797i	0.355217	−	0.615254i	0.987155	+	0.159765i	$0.0510737\pi$
$48$		0			0
$49$	4.49666	−	5.36470i	0.642381	−	0.766386i
$50$		0			0
$51$		0			0
$52$	−6.98937	+	4.03531i	−0.969251	+	0.559597i
$53$	−1.31763	+	0.760733i	−0.180990	+	0.104495i	−0.587758	−	0.809037i	$-0.699989\pi$
$53$	−1.31763	+	0.760733i	−0.180990	+	0.104495i	0.406768	+	0.913532i	$0.366656\pi$
$54$		0			0
$55$		0			0
$56$	−0.727468	−	1.55898i	−0.0972120	−	0.208327i
$57$		0			0
$58$	−7.42260	+	12.8563i	−0.974635	+	1.68812i
$59$	−3.15081	−	5.45737i	−0.410201	−	0.710489i	0.584711	−	0.811242i	$-0.301208\pi$
$59$	−3.15081	−	5.45737i	−0.410201	−	0.710489i	−0.994911	+	0.100753i	$0.967875\pi$
$60$		0			0
$61$	−2.05442	−	1.18612i	−0.263042	−	0.151867i	0.362680	−	0.931914i	$-0.381862\pi$
$61$	−2.05442	−	1.18612i	−0.263042	−	0.151867i	−0.625721	+	0.780047i	$0.715195\pi$
$62$	2.73380			0.347193
$63$		0			0
$64$	5.08921			0.636152
$65$		0			0
$66$		0			0
$67$	−5.56295	−	9.63531i	−0.679622	−	1.17714i	−0.975095	−	0.221789i	$-0.928810\pi$
$67$	−5.56295	−	9.63531i	−0.679622	−	1.17714i	0.295472	−	0.955351i	$-0.404523\pi$
$68$	0.605233	−	1.04829i	0.0733953	−	0.127124i
$69$		0			0
$70$		0			0
$71$			10.1351i			1.20282i	0.798942	+	0.601408i	$0.205393\pi$
$71$			10.1351i			1.20282i	−0.798942	+	0.601408i	$0.794607\pi$
$72$		0			0
$73$	11.9718	−	6.91195i	1.40120	−	0.808982i	0.406683	−	0.913570i	$-0.366686\pi$
$73$	11.9718	−	6.91195i	1.40120	−	0.808982i	0.994516	+	0.104587i	$0.0333522\pi$
$74$	5.24450	−	3.02792i	0.609661	−	0.351988i
$75$		0			0
$76$			13.0676i			1.49896i
$77$	4.89586	−	6.99596i	0.557935	−	0.797264i
$78$		0			0
$79$	1.99018	−	3.44710i	0.223913	−	0.387829i	−0.732080	−	0.681219i	$-0.761450\pi$
$79$	1.99018	−	3.44710i	0.223913	−	0.387829i	0.955993	+	0.293390i	$0.0947834\pi$
$80$		0			0
$81$		0			0
$82$	2.32395	+	1.34173i	0.256637	+	0.148169i
$83$	4.19208			0.460141			0.230070	−	0.973174i	$-0.426104\pi$
$83$	4.19208			0.460141			0.230070	+	0.973174i	$0.426104\pi$
$84$		0			0
$85$		0			0
$86$	10.6450	+	6.14587i	1.14788	+	0.662727i
$87$		0			0
$88$	−1.04928	−	1.81741i	−0.111854	−	0.193737i
$89$	−5.63672	+	9.76309i	−0.597491	+	1.03489i	0.395699	+	0.918380i	$0.370502\pi$
$89$	−5.63672	+	9.76309i	−0.597491	+	1.03489i	−0.993190	+	0.116505i	$0.962831\pi$
$90$		0			0
$91$	−5.43891	−	11.6557i	−0.570152	−	1.22185i
$92$		−	8.08181i		−	0.842587i
$93$		0			0
$94$	−8.06958	+	4.65898i	−0.832314	+	0.480537i
$95$		0			0
$96$		0			0
$97$			2.21388i			0.224785i	0.993664	+	0.112393i	$0.0358514\pi$
$97$			2.21388i			0.224785i	−0.993664	+	0.112393i	$0.964149\pi$
$98$	−12.5819	+	4.58702i	−1.27097	+	0.463359i
$99$		0			0
$100$		0			0
$101$	−5.85104	−	10.1343i	−0.582201	−	1.00840i	−0.995218	−	0.0976779i	$-0.968859\pi$
$101$	−5.85104	−	10.1343i	−0.582201	−	1.00840i	0.413017	−	0.910723i	$-0.364475\pi$
$102$		0			0
$103$	−0.506851	−	0.292630i	−0.0499415	−	0.0288337i	0.474821	−	0.880082i	$-0.342513\pi$
$103$	−0.506851	−	0.292630i	−0.0499415	−	0.0288337i	−0.524763	+	0.851248i	$0.675846\pi$
$104$	−3.16109			−0.309970
$105$		0			0
$106$	2.91079			0.282721
$107$	−1.46544	−	0.846073i	−0.141670	−	0.0817929i	0.427490	−	0.904020i	$-0.359398\pi$
$107$	−1.46544	−	0.846073i	−0.141670	−	0.0817929i	−0.569159	+	0.822227i	$0.692731\pi$
$108$		0			0
$109$	−6.70139	−	11.6072i	−0.641877	−	1.11176i	−0.985013	−	0.172478i	$-0.944823\pi$
$109$	−6.70139	−	11.6072i	−0.641877	−	1.11176i	0.343136	−	0.939286i	$-0.388511\pi$
$110$		0			0
$111$		0			0
$112$	−1.04928	+	12.0302i	−0.0991479	+	1.13674i
$113$		−	14.2129i		−	1.33704i	−0.743694	−	0.668520i	$-0.766928\pi$
$113$		−	14.2129i		−	1.33704i	0.743694	−	0.668520i	$-0.233072\pi$
$114$		0			0
$115$		0			0
$116$	11.1560	−	6.44093i	1.03581	−	0.598025i
$117$		0			0
$118$			12.0559i			1.10984i
$119$	1.58054	+	1.10608i	0.144888	+	0.101394i
$120$		0			0
$121$	−0.291934	+	0.505645i	−0.0265395	+	0.0459677i
$122$	2.26922	+	3.93041i	0.205446	+	0.355842i
$123$		0			0
$124$	−2.05442	−	1.18612i	−0.184493	−	0.106517i
$125$		0			0
$126$		0			0
$127$	−2.08954			−0.185417			−0.0927084	−	0.995693i	$-0.529552\pi$
$127$	−2.08954			−0.185417			−0.0927084	+	0.995693i	$0.529552\pi$
$128$	4.43990	+	2.56338i	0.392436	+	0.226573i
$129$		0			0
$130$		0			0
$131$	−5.60241	+	9.70365i	−0.489484	+	0.847812i	−0.999927	−	0.0121001i	$-0.996148\pi$
$131$	−5.60241	+	9.70365i	−0.489484	+	0.847812i	0.510442	+	0.859912i	$0.329482\pi$
$132$		0			0
$133$	−20.7472	−	1.80960i	−1.79901	−	0.156912i
$134$			21.2855i			1.83878i
$135$		0			0
$136$	0.410594	−	0.237056i	0.0352081	−	0.0203274i
$137$	−6.09673	+	3.51995i	−0.520879	+	0.300730i	−0.737294	−	0.675572i	$-0.763897\pi$
$137$	−6.09673	+	3.51995i	−0.520879	+	0.300730i	0.216415	+	0.976301i	$0.430564\pi$
$138$		0			0
$139$			6.45903i			0.547848i	0.961751	+	0.273924i	$0.0883216\pi$
$139$			6.45903i			0.547848i	−0.961751	+	0.273924i	$0.911678\pi$
$140$		0			0
$141$		0			0
$142$	9.69496	−	16.7922i	0.813583	−	1.40917i
$143$	−7.84495	−	13.5879i	−0.656028	−	1.13627i
$144$		0			0
$145$		0			0
$146$	−26.4471			−2.18878
$147$		0			0
$148$	−5.25492			−0.431952
$149$	20.3962	+	11.7758i	1.67092	+	0.964709i	0.967122	+	0.254312i	$0.0818491\pi$
$149$	20.3962	+	11.7758i	1.67092	+	0.964709i	0.703802	+	0.710396i	$0.251484\pi$
$150$		0			0
$151$	−9.05442	−	15.6827i	−0.736838	−	1.27624i	−0.953912	−	0.300086i	$-0.902985\pi$
$151$	−9.05442	−	15.6827i	−0.736838	−	1.27624i	0.217074	−	0.976155i	$-0.430349\pi$
$152$	−2.55915	+	4.43258i	−0.207575	+	0.359530i
$153$		0			0
$154$	−14.8038	+	6.90789i	−1.19292	+	0.556654i
$155$		0			0
$156$		0			0
$157$	2.15168	−	1.24227i	0.171723	−	0.0991441i	−0.411675	−	0.911331i	$-0.635056\pi$
$157$	2.15168	−	1.24227i	0.171723	−	0.0991441i	0.583398	+	0.812187i	$0.301723\pi$
$158$	−6.59480	+	3.80751i	−0.524654	+	0.302909i
$159$		0			0
$160$		0			0
$161$	12.8313	+	1.11916i	1.01125	+	0.0882023i
$162$		0			0
$163$	−1.96885	+	3.41015i	−0.154212	+	0.267104i	−0.932772	−	0.360467i	$-0.882617\pi$
$163$	−1.96885	+	3.41015i	−0.154212	+	0.267104i	0.778560	+	0.627571i	$0.215951\pi$
$164$	−1.16428	−	2.01659i	−0.0909151	−	0.157470i
$165$		0			0
$166$	−6.94558	−	4.01003i	−0.539081	−	0.311239i
$167$	−5.31832			−0.411544			−0.205772	−	0.978600i	$-0.565971\pi$
$167$	−5.31832			−0.411544			−0.205772	+	0.978600i	$0.565971\pi$
$168$		0			0
$169$	−10.6338			−0.817986
$170$		0			0
$171$		0			0
$172$	−5.33306	−	9.23712i	−0.406642	−	0.704324i
$173$	3.72751	−	6.45623i	0.283397	−	0.490858i	−0.688822	−	0.724930i	$-0.741872\pi$
$173$	3.72751	−	6.45623i	0.283397	−	0.490858i	0.972219	+	0.234072i	$0.0752053\pi$
$174$		0			0
$175$		0			0
$176$			14.7306i			1.11036i
$177$		0			0
$178$	18.6782	−	10.7839i	1.39999	−	0.808285i
$179$	−11.5242	+	6.65349i	−0.861358	+	0.497305i	−0.864467	−	0.502690i	$-0.832344\pi$
$179$	−11.5242	+	6.65349i	−0.861358	+	0.497305i	0.00310866	+	0.999995i	$0.499010\pi$
$180$		0			0
$181$		−	9.95814i		−	0.740183i	−0.928995	−	0.370091i	$-0.879326\pi$
$181$		−	9.95814i		−	0.740183i	0.928995	−	0.370091i	$-0.120674\pi$
$182$	−2.13816	+	24.5142i	−0.158491	+	1.81712i
$183$		0			0
$184$	1.58273	−	2.74138i	0.116681	−	0.202097i
$185$		0			0
$186$		0			0
$187$	2.03796	+	1.17662i	0.149031	+	0.0860428i
$188$	8.08561			0.589704
$189$		0			0
$190$		0			0
$191$	−21.3140	−	12.3056i	−1.54223	−	0.890404i	−0.998698	−	0.0510125i	$-0.983755\pi$
$191$	−21.3140	−	12.3056i	−1.54223	−	0.890404i	−0.543527	−	0.839392i	$-0.682911\pi$
$192$		0			0
$193$	−6.25714	−	10.8377i	−0.450399	−	0.780113i	0.548012	−	0.836470i	$-0.315385\pi$
$193$	−6.25714	−	10.8377i	−0.450399	−	0.780113i	−0.998411	+	0.0563571i	$0.982051\pi$
$194$	2.11773	−	3.66802i	0.152044	−	0.263349i
$195$		0			0
$196$	11.4454	+	2.01186i	0.817528	+	0.143704i
$197$		−	15.6968i		−	1.11835i	−0.829049	−	0.559177i	$-0.811117\pi$
$197$		−	15.6968i		−	1.11835i	0.829049	−	0.559177i	$-0.188883\pi$
$198$		0			0
$199$	−17.1436	+	9.89788i	−1.21528	+	0.701642i	−0.963905	−	0.266247i	$-0.914216\pi$
$199$	−17.1436	+	9.89788i	−1.21528	+	0.701642i	−0.251375	+	0.967890i	$0.580883\pi$
$200$		0			0
$201$		0			0
$202$			22.3878i			1.57520i
$203$	8.68126	+	18.6041i	0.609305	+	1.30575i
$204$		0			0
$205$		0			0
$206$	0.559844	+	0.969678i	0.0390062	+	0.0675607i
$207$		0			0
$208$	19.2161	+	11.0944i	1.33240	+	0.769261i
$209$	−25.4045			−1.75726
$210$		0			0
$211$	11.5839			0.797466			0.398733	−	0.917067i	$-0.369450\pi$
$211$	11.5839			0.797466			0.398733	+	0.917067i	$0.369450\pi$
$212$	−2.18743	−	1.26291i	−0.150233	−	0.0867371i
$213$		0			0
$214$	1.61866	+	2.80360i	0.110649	+	0.191650i
$215$		0			0
$216$		0			0
$217$	2.16768	−	3.09751i	0.147151	−	0.210273i
$218$			25.6415i			1.73666i
$219$		0			0
$220$		0			0
$221$	3.06980	−	1.77235i	0.206497	−	0.119221i
$222$		0			0
$223$			24.1321i			1.61600i	0.589180	+	0.808002i	$0.299451\pi$
$223$			24.1321i			1.61600i	−0.589180	+	0.808002i	$0.700549\pi$
$224$	11.2734	−	16.1093i	0.753239	−	1.07634i
$225$		0			0
$226$	−13.5957	+	23.5484i	−0.904372	+	1.56642i
$227$	−5.09441	−	8.82377i	−0.338128	−	0.585654i	0.645953	−	0.763377i	$-0.276460\pi$
$227$	−5.09441	−	8.82377i	−0.338128	−	0.585654i	−0.984081	+	0.177723i	$0.943127\pi$
$228$		0			0
$229$	−22.7373	−	13.1274i	−1.50252	−	0.867483i	−0.999996	−	0.00292226i	$-0.999070\pi$
$229$	−22.7373	−	13.1274i	−1.50252	−	0.867483i	−0.502529	−	0.864561i	$-0.667597\pi$
$230$		0			0
$231$		0			0
$232$	5.04554			0.331256
$233$	15.9291	+	9.19667i	1.04355	+	0.602494i	0.920837	−	0.389948i	$-0.127507\pi$
$233$	15.9291	+	9.19667i	1.04355	+	0.602494i	0.122713	+	0.992442i	$0.460840\pi$
$234$		0			0
$235$		0			0
$236$	5.23074	−	9.05990i	0.340492	−	0.589749i
$237$		0			0
$238$	−1.56065	−	3.34450i	−0.101162	−	0.216792i
$239$		−	0.961317i		−	0.0621824i	−0.999517	−	0.0310912i	$-0.990102\pi$
$239$		−	0.961317i		−	0.0621824i	0.999517	−	0.0310912i	$-0.00989824\pi$
$240$		0			0
$241$	−5.63829	+	3.25527i	−0.363194	+	0.209690i	−0.670481	−	0.741927i	$-0.733912\pi$
$241$	−5.63829	+	3.25527i	−0.363194	+	0.209690i	0.307287	+	0.951617i	$0.400579\pi$
$242$	0.967371	−	0.558512i	0.0621850	−	0.0359025i
$243$		0			0
$244$		−	3.93821i		−	0.252118i
$245$		0			0
$246$		0			0
$247$	−19.1335	+	33.1402i	−1.21743	+	2.10866i
$248$	−0.464578	−	0.804672i	−0.0295007	−	0.0510967i
$249$		0			0
$250$		0			0
$251$	2.02506			0.127820			0.0639102	−	0.997956i	$-0.479643\pi$
$251$	2.02506			0.127820			0.0639102	+	0.997956i	$0.479643\pi$
$252$		0			0
$253$	15.7116			0.987783
$254$	3.46202	+	1.99880i	0.217226	+	0.125416i
$255$		0			0
$256$	−9.99333	−	17.3090i	−0.624583	−	1.08181i
$257$	9.09510	−	15.7532i	0.567337	−	0.982656i	−0.429491	−	0.903071i	$-0.641307\pi$
$257$	9.09510	−	15.7532i	0.567337	−	0.982656i	0.996828	−	0.0795849i	$-0.0253595\pi$
$258$		0			0
$259$	0.727697	−	8.34313i	0.0452169	−	0.518417i
$260$		0			0
$261$		0			0
$262$	18.5645	−	10.7182i	1.14692	−	0.662173i
$263$	−16.9400	+	9.78034i	−1.04457	+	0.603082i	−0.921124	−	0.389270i	$-0.872727\pi$
$263$	−16.9400	+	9.78034i	−1.04457	+	0.603082i	−0.123444	+	0.992351i	$0.539394\pi$
$264$		0			0
$265$		0			0
$266$	32.6437	+	22.8444i	2.00151	+	1.40068i
$267$		0			0
$268$	9.23518	−	15.9958i	0.564128	−	0.977099i
$269$	2.30801	+	3.99759i	0.140722	+	0.243738i	0.927769	−	0.373156i	$-0.121724\pi$
$269$	2.30801	+	3.99759i	0.140722	+	0.243738i	−0.787047	+	0.616893i	$0.788391\pi$
$270$		0			0
$271$	−9.33654	−	5.39045i	−0.567154	−	0.327447i	0.188858	−	0.982004i	$-0.439522\pi$
$271$	−9.33654	−	5.39045i	−0.567154	−	0.327447i	−0.756012	+	0.654558i	$0.772855\pi$
$272$	−3.32798			−0.201788
$273$		0			0
$274$	13.4684			0.813653
$275$		0			0
$276$		0			0
$277$	−10.2534	−	17.7594i	−0.616067	−	1.06706i	−0.990196	−	0.139682i	$-0.955392\pi$
$277$	−10.2534	−	17.7594i	−0.616067	−	1.06706i	0.374130	−	0.927376i	$-0.377941\pi$
$278$	6.17853	−	10.7015i	0.370564	−	0.641835i
$279$		0			0
$280$		0			0
$281$		−	0.714666i		−	0.0426334i	−0.999773	−	0.0213167i	$-0.993214\pi$
$281$		−	0.714666i		−	0.0426334i	0.999773	−	0.0213167i	$-0.00678583\pi$
$282$		0			0
$283$	24.2677	−	14.0110i	1.44257	−	0.832866i	0.444545	−	0.895756i	$-0.353365\pi$
$283$	24.2677	−	14.0110i	1.44257	−	0.832866i	0.998020	+	0.0628908i	$0.0200320\pi$
$284$	−14.5713	+	8.41276i	−0.864649	+	0.499206i
$285$		0			0
$286$			30.0171i			1.77495i
$287$	3.36293	−	1.56925i	0.198508	−	0.0926299i
$288$		0			0
$289$	8.23418	−	14.2620i	0.484363	−	0.838942i
$290$		0			0
$291$		0			0
$292$	19.8747	+	11.4747i	1.16308	+	0.671505i
$293$	9.79171			0.572038			0.286019	−	0.958224i	$-0.407668\pi$
$293$	9.79171			0.572038			0.286019	+	0.958224i	$0.407668\pi$
$294$		0			0
$295$		0			0
$296$	−1.78249	−	1.02912i	−0.103605	−	0.0598163i
$297$		0			0
$298$	−22.5287	−	39.0209i	−1.30506	−	2.26042i
$299$	11.8333	−	20.4959i	0.684337	−	1.18531i
$300$		0			0
$301$	15.4041	−	7.18804i	0.887878	−	0.414312i
$302$			34.6448i			1.99359i
$303$		0			0
$304$	31.1140	−	17.9637i	1.78451	−	1.03029i
$305$		0			0
$306$		0			0
$307$		−	25.4778i		−	1.45410i	−0.686586	−	0.727048i	$-0.740892\pi$
$307$		−	25.4778i		−	1.45410i	0.686586	−	0.727048i	$-0.259108\pi$
$308$	14.1220	+	1.23174i	0.804677	+	0.0701847i
$309$		0			0
$310$		0			0
$311$	−5.05422	−	8.75417i	−0.286599	−	0.496404i	0.686397	−	0.727227i	$-0.259191\pi$
$311$	−5.05422	−	8.75417i	−0.286599	−	0.496404i	−0.972996	+	0.230824i	$0.925858\pi$
$312$		0			0
$313$	−20.3300	−	11.7375i	−1.14912	−	0.663445i	−0.200447	−	0.979705i	$-0.564240\pi$
$313$	−20.3300	−	11.7375i	−1.14912	−	0.663445i	−0.948673	+	0.316260i	$0.897573\pi$
$314$	−4.75329			−0.268244
$315$		0			0
$316$	6.60790			0.371724
$317$	27.2202	+	15.7156i	1.52884	+	0.882677i	0.999411	+	0.0343235i	$0.0109277\pi$
$317$	27.2202	+	15.7156i	1.52884	+	0.882677i	0.529430	+	0.848353i	$0.322406\pi$
$318$		0			0
$319$	12.5216	+	21.6881i	0.701077	+	1.21430i
$320$		0			0
$321$		0			0
$322$	−20.1888	−	14.1284i	−1.12508	−	0.787343i
$323$		−	5.73943i		−	0.319351i
$324$		0			0
$325$		0			0
$326$	6.52412	−	3.76670i	0.361337	−	0.208618i
$327$		0			0
$328$		−	0.912047i		−	0.0503593i
$329$	−1.11969	+	12.8374i	−0.0617304	+	0.707747i
$330$		0			0
$331$	0.589214	−	1.02055i	0.0323861	−	0.0560944i	−0.849378	−	0.527785i	$-0.823023\pi$
$331$	0.589214	−	1.02055i	0.0323861	−	0.0560944i	0.881764	+	0.471691i	$0.156356\pi$
$332$	3.47969	+	6.02700i	0.190973	+	0.330774i
$333$		0			0
$334$	8.81156	+	5.08736i	0.482147	+	0.278368i
$335$		0			0
$336$		0			0
$337$	−3.92868			−0.214009			−0.107004	−	0.994259i	$-0.534126\pi$
$337$	−3.92868			−0.214009			−0.107004	+	0.994259i	$0.534126\pi$
$338$	17.6185	+	10.1720i	0.958318	+	0.553285i
$339$		0			0
$340$		0			0
$341$	2.30591	−	3.99395i	0.124872	−	0.216285i
$342$		0			0
$343$	−4.77914	+	17.8930i	−0.258049	+	0.966132i
$344$		−	4.17768i		−	0.225245i
$345$		0			0
$346$	−12.3517	+	7.13126i	−0.664032	+	0.383379i
$347$	4.18346	−	2.41532i	0.224580	−	0.129661i	−0.383489	−	0.923545i	$-0.625278\pi$
$347$	4.18346	−	2.41532i	0.224580	−	0.129661i	0.608069	+	0.793884i	$0.291944\pi$
$348$		0			0
$349$			16.0461i			0.858927i	0.903084	+	0.429463i	$0.141297\pi$
$349$			16.0461i			0.858927i	−0.903084	+	0.429463i	$0.858703\pi$
$350$		0			0
$351$		0			0
$352$	11.9924	−	20.7714i	0.639195	−	1.10712i
$353$	2.94047	+	5.09305i	0.156505	+	0.271075i	0.933606	−	0.358301i	$-0.116644\pi$
$353$	2.94047	+	5.09305i	0.156505	+	0.271075i	−0.777101	+	0.629376i	$0.783310\pi$
$354$		0			0
$355$		0			0
$356$	−18.7153			−0.991909
$357$		0			0
$358$	25.4582			1.34551
$359$	−7.00295	−	4.04315i	−0.369601	−	0.213389i	0.303683	−	0.952773i	$-0.401784\pi$
$359$	−7.00295	−	4.04315i	−0.369601	−	0.213389i	−0.673284	+	0.739384i	$0.735117\pi$
$360$		0			0
$361$	21.4802	+	37.2048i	1.13054	+	1.95815i
$362$	−9.52569	+	16.4990i	−0.500659	+	0.867167i
$363$		0			0
$364$	12.2429	−	17.4945i	0.641700	−	0.916961i
$365$		0			0
$366$		0			0
$367$	16.0818	−	9.28484i	0.839464	−	0.484665i	−0.0176181	−	0.999845i	$-0.505608\pi$
$367$	16.0818	−	9.28484i	0.839464	−	0.484665i	0.857082	+	0.515180i	$0.172275\pi$
$368$	−19.2428	+	11.1098i	−1.00310	+	0.579139i
$369$		0			0
$370$		0			0
$371$	2.30801	−	3.29805i	0.119826	−	0.171226i
$372$		0			0
$373$	1.32173	−	2.28930i	0.0684365	−	0.118536i	−0.829777	−	0.558095i	$-0.811532\pi$
$373$	1.32173	−	2.28930i	0.0684365	−	0.118536i	0.898213	+	0.439560i	$0.144866\pi$
$374$	−2.25104	−	3.89892i	−0.116399	−	0.201608i
$375$		0			0
$376$	2.74266	+	1.58348i	0.141442	+	0.0816617i
$377$	37.7229			1.94283
$378$		0			0
$379$	23.8582			1.22551			0.612756	−	0.790272i	$-0.290061\pi$
$379$	23.8582			1.22551			0.612756	+	0.790272i	$0.290061\pi$
$380$		0			0
$381$		0			0
$382$	23.5425	+	40.7767i	1.20454	+	2.08632i
$383$	−5.55752	+	9.62590i	−0.283976	+	0.491861i	−0.972360	−	0.233485i	$-0.924987\pi$
$383$	−5.55752	+	9.62590i	−0.283976	+	0.491861i	0.688384	+	0.725346i	$0.258320\pi$
$384$		0			0
$385$		0			0
$386$			23.9416i			1.21860i
$387$		0			0
$388$	−3.18291	+	1.83765i	−0.161588	+	0.0932928i
$389$	10.8957	−	6.29064i	0.552434	−	0.318948i	−0.197669	−	0.980269i	$-0.563337\pi$
$389$	10.8957	−	6.29064i	0.552434	−	0.318948i	0.750103	+	0.661321i	$0.230004\pi$
$390$		0			0
$391$			3.54961i			0.179512i
$392$	3.48831	+	2.92388i	0.176186	+	0.147678i
$393$		0			0
$394$	−15.0152	+	26.0070i	−0.756453	+	1.31021i
$395$		0			0
$396$		0			0
$397$	−24.7951	−	14.3154i	−1.24443	−	0.718471i	−0.274436	−	0.961605i	$-0.588491\pi$
$397$	−24.7951	−	14.3154i	−1.24443	−	0.718471i	−0.969993	+	0.243134i	$0.921825\pi$
$398$	37.8722			1.89836
$399$		0			0
$400$		0			0
$401$	10.2994	+	5.94639i	0.514330	+	0.296948i	0.734612	−	0.678488i	$-0.237364\pi$
$401$	10.2994	+	5.94639i	0.514330	+	0.296948i	−0.220282	+	0.975436i	$0.570698\pi$
$402$		0			0
$403$	−3.47341	−	6.01612i	−0.173023	−	0.299684i
$404$	9.71345	−	16.8242i	0.483262	−	0.837035i
$405$		0			0
$406$	3.41280	−	39.1281i	0.169374	−	1.94190i
$407$		−	10.2160i		−	0.506386i
$408$		0			0
$409$	12.4855	−	7.20852i	0.617369	−	0.356438i	−0.158475	−	0.987363i	$-0.550658\pi$
$409$	12.4855	−	7.20852i	0.617369	−	0.356438i	0.775844	+	0.630925i	$0.217324\pi$
$410$		0			0
$411$		0			0
$412$		−	0.971605i		−	0.0478675i
$413$	13.6599	+	9.55934i	0.672159	+	0.470384i
$414$		0			0
$415$		0			0
$416$	−18.0642	−	31.2881i	−0.885669	−	1.53402i
$417$		0			0
$418$	42.0909	+	24.3012i	2.05874	+	1.18861i
$419$	34.9400			1.70693			0.853466	−	0.521149i	$-0.174496\pi$
$419$	34.9400			1.70693			0.853466	+	0.521149i	$0.174496\pi$
$420$		0			0
$421$	23.8515			1.16245			0.581226	−	0.813742i	$-0.302573\pi$
$421$	23.8515			1.16245			0.581226	+	0.813742i	$0.302573\pi$
$422$	−19.1925	−	11.0808i	−0.934277	−	0.539405i
$423$		0			0
$424$	−0.494655	−	0.856767i	−0.0240225	−	0.0416083i
$425$		0			0
$426$		0			0
$427$	6.25262	+	0.545360i	0.302586	+	0.0263918i
$428$		−	2.80917i		−	0.135786i
$429$		0			0
$430$		0			0
$431$	−7.06551	+	4.07928i	−0.340334	+	0.196492i	−0.660420	−	0.750897i	$-0.729622\pi$
$431$	−7.06551	+	4.07928i	−0.340334	+	0.196492i	0.320086	+	0.947389i	$0.396288\pi$
$432$		0			0
$433$		−	25.2667i		−	1.21424i	−0.794610	−	0.607121i	$-0.792324\pi$
$433$		−	25.2667i		−	1.21424i	0.794610	−	0.607121i	$-0.207676\pi$
$434$	−6.55447	+	3.05852i	−0.314625	+	0.146814i
$435$		0			0
$436$	11.1251	−	19.2693i	0.532798	−	0.922832i
$437$	−19.1600	−	33.1861i	−0.916547	−	1.58751i
$438$		0			0
$439$	0.688243	+	0.397357i	0.0328480	+	0.0189648i	0.516334	−	0.856387i	$-0.327296\pi$
$439$	0.688243	+	0.397357i	0.0328480	+	0.0189648i	−0.483486	+	0.875352i	$0.660630\pi$
$440$		0			0
$441$		0			0
$442$	−6.78152			−0.322564
$443$	−19.6145	−	11.3244i	−0.931913	−	0.538040i	−0.0444966	−	0.999010i	$-0.514168\pi$
$443$	−19.6145	−	11.3244i	−0.931913	−	0.538040i	−0.887416	+	0.460970i	$0.847502\pi$
$444$		0			0
$445$		0			0
$446$	23.0841	−	39.9828i	1.09306	−	1.89324i
$447$		0			0
$448$	−12.2017	+	5.69371i	−0.576478	+	0.269002i
$449$			2.15664i			0.101778i	0.998704	+	0.0508891i	$0.0162055\pi$
$449$			2.15664i			0.101778i	−0.998704	+	0.0508891i	$0.983794\pi$
$450$		0			0
$451$	3.92041	−	2.26345i	0.184605	−	0.106582i
$452$	20.4340	−	11.7976i	0.961137	−	0.554913i
$453$		0			0
$454$			19.4927i			0.914836i
$455$		0			0
$456$		0			0
$457$	−2.73666	+	4.74004i	−0.128016	+	0.221730i	−0.922908	−	0.385021i	$-0.874194\pi$
$457$	−2.73666	+	4.74004i	−0.128016	+	0.221730i	0.794892	+	0.606751i	$0.207527\pi$
$458$	25.1146	+	43.4998i	1.17353	+	2.03261i
$459$		0			0
$460$		0			0
$461$	−10.1084			−0.470797			−0.235399	−	0.971899i	$-0.575640\pi$
$461$	−10.1084			−0.470797			−0.235399	+	0.971899i	$0.575640\pi$
$462$		0			0
$463$	12.0455			0.559800			0.279900	−	0.960029i	$-0.409699\pi$
$463$	12.0455			0.559800			0.279900	+	0.960029i	$0.409699\pi$
$464$	−30.6716	−	17.7083i	−1.42389	−	0.822086i
$465$		0			0
$466$	−17.5946	−	30.4747i	−0.815052	−	1.41171i
$467$	−9.96636	+	17.2622i	−0.461188	+	0.798801i	−0.999020	−	0.0442505i	$-0.985910\pi$
$467$	−9.96636	+	17.2622i	−0.461188	+	0.798801i	0.537832	+	0.843052i	$0.319243\pi$
$468$		0			0
$469$	24.1173	+	16.8776i	1.11363	+	0.779335i
$470$		0			0
$471$		0			0
$472$	3.54856	−	2.04876i	0.163336	−	0.0943020i
$473$	17.9577	−	10.3679i	0.825694	−	0.476715i
$474$		0			0
$475$		0			0
$476$	−0.278277	+	3.19048i	−0.0127548	+	0.146235i
$477$		0			0
$478$	−0.919569	+	1.59274i	−0.0420601	+	0.0728503i
$479$	−9.69290	−	16.7886i	−0.442880	−	0.767091i	0.555022	−	0.831836i	$-0.312710\pi$
$479$	−9.69290	−	16.7886i	−0.442880	−	0.767091i	−0.997902	+	0.0647451i	$0.979377\pi$
$480$		0			0
$481$	−13.3267	−	7.69419i	−0.607646	−	0.350825i
$482$	12.4556			0.567337
$483$		0			0
$484$	−0.969293			−0.0440588
$485$		0			0
$486$		0			0
$487$	−0.924082	−	1.60056i	−0.0418742	−	0.0725282i	0.844329	−	0.535826i	$-0.180000\pi$
$487$	−0.924082	−	1.60056i	−0.0418742	−	0.0725282i	−0.886203	+	0.463297i	$0.846666\pi$
$488$	0.771256	−	1.33585i	0.0349131	−	0.0604713i
$489$		0			0
$490$		0			0
$491$			25.4836i			1.15006i	0.818133	+	0.575030i	$0.195009\pi$
$491$			25.4836i			1.15006i	−0.818133	+	0.575030i	$0.804991\pi$
$492$		0			0
$493$	−4.89983	+	2.82892i	−0.220677	+	0.127408i
$494$	63.4019	−	36.6051i	2.85259	−	1.64694i
$495$		0			0
$496$			6.52209i			0.292851i
$497$	−11.3390	−	24.2996i	−0.508621	−	1.08999i
$498$		0			0
$499$	−13.1142	+	22.7144i	−0.587072	+	1.01684i	0.407542	+	0.913187i	$0.366386\pi$
$499$	−13.1142	+	22.7144i	−0.587072	+	1.01684i	−0.994614	+	0.103652i	$0.966947\pi$
$500$		0			0
$501$		0			0
$502$	−3.35518	−	1.93711i	−0.149749	−	0.0864576i
$503$	4.25713			0.189816			0.0949081	−	0.995486i	$-0.469744\pi$
$503$	4.25713			0.189816			0.0949081	+	0.995486i	$0.469744\pi$
$504$		0			0
$505$		0			0
$506$	−26.0316	−	15.0293i	−1.15724	−	0.668135i
$507$		0			0
$508$	−1.73445	−	3.00415i	−0.0769537	−	0.133288i
$509$	9.55960	−	16.5577i	0.423722	−	0.733907i	−0.572578	−	0.819850i	$-0.694057\pi$
$509$	9.55960	−	16.5577i	0.423722	−	0.733907i	0.996300	+	0.0859425i	$0.0273901\pi$
$510$		0			0
$511$	−20.9704	+	29.9657i	−0.927674	+	1.32561i
$512$			27.9839i			1.23672i
$513$		0			0
$514$	−30.1381	+	17.4002i	−1.32933	+	0.767492i
$515$		0			0
$516$		0			0
$517$			15.7190i			0.691322i
$518$	−9.18648	+	13.1271i	−0.403631	+	0.576771i
$519$		0			0
$520$		0			0
$521$	11.4068	+	19.7571i	0.499739	+	0.865573i	1.00000		0.000301478i	$-9.59634e-5\pi$
$521$	11.4068	+	19.7571i	0.499739	+	0.865573i	−0.500261	+	0.865875i	$0.666763\pi$
$522$		0			0
$523$	−2.71011	−	1.56468i	−0.118505	−	0.0684188i	0.439576	−	0.898205i	$-0.355129\pi$
$523$	−2.71011	−	1.56468i	−0.118505	−	0.0684188i	−0.558081	+	0.829787i	$0.688462\pi$
$524$	−18.6014			−0.812604
$525$		0			0
$526$	37.4224			1.63169
$527$	0.902322	+	0.520956i	0.0393058	+	0.0226932i
$528$		0			0
$529$	0.349692	+	0.605685i	0.0152040	+	0.0263341i
$530$		0			0
$531$		0			0
$532$	−14.6198	−	31.3306i	−0.633849	−	1.35835i
$533$		−	6.81890i		−	0.295359i
$534$		0			0
$535$		0			0
$536$	6.26520	−	3.61722i	0.270616	−	0.156240i
$537$		0			0
$538$		−	8.83112i		−	0.380737i
$539$	−3.91121	+	22.2507i	−0.168468	+	0.958405i
$540$		0			0
$541$	11.2308	−	19.4524i	0.482852	−	0.836323i	−0.516955	−	0.856013i	$-0.672934\pi$
$541$	11.2308	−	19.4524i	0.482852	−	0.836323i	0.999806	+	0.0196894i	$0.00626775\pi$
$542$	10.3127	+	17.8622i	0.442969	+	0.767245i
$543$		0			0
$544$	4.69271	+	2.70934i	0.201198	+	0.116162i
$545$		0			0
$546$		0			0
$547$	−10.4567			−0.447097			−0.223549	−	0.974693i	$-0.571764\pi$
$547$	−10.4567			−0.447097			−0.223549	+	0.974693i	$0.571764\pi$
$548$	−10.1213	−	5.84355i	−0.432362	−	0.249624i
$549$		0			0
$550$		0			0
$551$	30.5397	−	52.8963i	1.30104	−	2.25346i
$552$		0			0
$553$	−0.915056	+	10.4912i	−0.0389122	+	0.446133i
$554$			39.2324i			1.66683i
$555$		0			0
$556$	−9.28620	+	5.36139i	−0.393823	+	0.227374i
$557$	−27.0614	+	15.6239i	−1.14663	+	0.662006i	−0.948063	−	0.318082i	$-0.896961\pi$
$557$	−27.0614	+	15.6239i	−1.14663	+	0.662006i	−0.198564	+	0.980088i	$0.563628\pi$
$558$		0			0
$559$		−	31.2344i		−	1.32107i
$560$		0			0
$561$		0			0
$562$	−0.683630	+	1.18408i	−0.0288372	+	0.0499475i
$563$	−14.9354	−	25.8689i	−0.629452	−	1.09024i	−0.987662	−	0.156601i	$-0.949946\pi$
$563$	−14.9354	−	25.8689i	−0.629452	−	1.09024i	0.358210	−	0.933641i	$-0.383387\pi$
$564$		0			0
$565$		0			0
$566$	−53.6100			−2.25340
$567$		0			0
$568$	−6.59019			−0.276518
$569$	−25.0218	−	14.4464i	−1.04897	−	0.605623i	−0.126608	−	0.991953i	$-0.540409\pi$
$569$	−25.0218	−	14.4464i	−1.04897	−	0.605623i	−0.922361	+	0.386330i	$0.873743\pi$
$570$		0			0
$571$	3.68844	+	6.38856i	0.154356	+	0.267353i	0.932824	−	0.360331i	$-0.117336\pi$
$571$	3.68844	+	6.38856i	0.154356	+	0.267353i	−0.778468	+	0.627684i	$0.784003\pi$
$572$	13.0236	−	22.5575i	0.544543	−	0.943177i
$573$		0			0
$574$	−7.07292	−	0.616907i	−0.295218	−	0.0257492i
$575$		0			0
$576$		0			0
$577$	15.6540	−	9.03785i	0.651686	−	0.376251i	−0.137416	−	0.990513i	$-0.543880\pi$
$577$	15.6540	−	9.03785i	0.651686	−	0.376251i	0.789102	+	0.614263i	$0.210546\pi$
$578$	−27.2853	+	15.7532i	−1.13492	+	0.655246i
$579$		0			0
$580$		0			0
$581$	−10.0508	+	4.69002i	−0.416978	+	0.194575i
$582$		0			0
$583$	2.45519	−	4.25252i	0.101684	−	0.176121i
$584$	4.49438	+	7.78450i	0.185979	+	0.322125i
$585$		0			0
$586$	−16.2232	−	9.36648i	−0.670175	−	0.386926i
$587$	−35.0876			−1.44822			−0.724111	−	0.689684i	$-0.757750\pi$
$587$	−35.0876			−1.44822			−0.724111	+	0.689684i	$0.757750\pi$
$588$		0			0
$589$	−11.2480			−0.463466
$590$		0			0
$591$		0			0
$592$	7.22377	+	12.5119i	0.296895	+	0.514238i
$593$	−3.52896	+	6.11233i	−0.144917	+	0.251003i	−0.929342	−	0.369220i	$-0.879625\pi$
$593$	−3.52896	+	6.11233i	−0.144917	+	0.251003i	0.784425	+	0.620224i	$0.212958\pi$
$594$		0			0
$595$		0			0
$596$			39.0984i			1.60153i
$597$		0			0
$598$	−39.2115	+	22.6388i	−1.60348	+	0.925769i
$599$	−4.23198	+	2.44333i	−0.172914	+	0.0998318i	−0.583959	−	0.811783i	$-0.698497\pi$
$599$	−4.23198	+	2.44333i	−0.172914	+	0.0998318i	0.411045	+	0.911615i	$0.365164\pi$
$600$		0			0
$601$			36.1905i			1.47624i	0.674669	+	0.738121i	$0.264286\pi$
$601$			36.1905i			1.47624i	−0.674669	+	0.738121i	$0.735714\pi$
$602$	−32.3979	−	2.82578i	−1.32044	−	0.115170i
$603$		0			0
$604$	15.0315	−	26.0352i	0.611621	−	1.05936i
$605$		0			0
$606$		0			0
$607$	14.6579	+	8.46272i	0.594944	+	0.343491i	0.767050	−	0.641587i	$-0.221724\pi$
$607$	14.6579	+	8.46272i	0.594944	+	0.343491i	−0.172106	+	0.985078i	$0.555057\pi$
$608$	−58.4976			−2.37239
$609$		0			0
$610$		0			0
$611$	20.5055	+	11.8389i	0.829563	+	0.478949i
$612$		0			0
$613$	−9.30275	−	16.1128i	−0.375735	−	0.650792i	0.614702	−	0.788759i	$-0.289276\pi$
$613$	−9.30275	−	16.1128i	−0.375735	−	0.650792i	−0.990437	+	0.137968i	$0.955943\pi$
$614$	−24.3714	+	42.2125i	−0.983549	+	1.70356i
$615$		0			0
$616$	4.54901	+	3.18345i	0.183285	+	0.128265i
$617$			44.6022i			1.79562i	0.440384	+	0.897809i	$0.354842\pi$
$617$			44.6022i			1.79562i	−0.440384	+	0.897809i	$0.645158\pi$
$618$		0			0
$619$	9.80175	−	5.65904i	0.393966	−	0.227456i	−0.289911	−	0.957053i	$-0.593626\pi$
$619$	9.80175	−	5.65904i	0.393966	−	0.227456i	0.683877	+	0.729597i	$0.260293\pi$
$620$		0			0
$621$		0			0
$622$			19.3389i			0.775420i
$623$	2.59168	−	29.7139i	0.103833	−	1.19046i
$624$		0			0
$625$		0			0
$626$	22.4556	+	38.8942i	0.897506	+	1.55453i
$627$		0			0
$628$	3.57205	+	2.06233i	0.142540	+	0.0822957i
$629$	2.30801			0.0920265
$630$		0			0
$631$	−6.29394			−0.250558			−0.125279	−	0.992122i	$-0.539983\pi$
$631$	−6.29394			−0.250558			−0.125279	+	0.992122i	$0.539983\pi$
$632$	2.24142	+	1.29409i	0.0891589	+	0.0514759i
$633$		0			0
$634$	−30.0662	−	52.0763i	−1.19408	−	2.06821i
$635$		0			0
$636$		0			0
$637$	26.0803	+	21.8604i	1.03334	+	0.866139i
$638$		−	47.9114i		−	1.89683i
$639$		0			0
$640$		0			0
$641$	0.511044	−	0.295051i	0.0201850	−	0.0116538i	−0.489874	−	0.871794i	$-0.662957\pi$
$641$	0.511044	−	0.295051i	0.0201850	−	0.0116538i	0.510059	+	0.860140i	$0.329624\pi$
$642$		0			0
$643$			28.7107i			1.13224i	0.824323	+	0.566119i	$0.191556\pi$
$643$			28.7107i			1.13224i	−0.824323	+	0.566119i	$0.808444\pi$
$644$	9.04177	+	19.3767i	0.356296	+	0.763549i
$645$		0			0
$646$	−5.49018	+	9.50928i	−0.216008	+	0.374138i
$647$	−5.96420	−	10.3303i	−0.234477	−	0.406126i	0.724644	−	0.689124i	$-0.242004\pi$
$647$	−5.96420	−	10.3303i	−0.234477	−	0.406126i	−0.959121	+	0.282998i	$0.908671\pi$
$648$		0			0
$649$	17.6131	+	10.1689i	0.691375	+	0.399166i
$650$		0			0
$651$		0			0
$652$	−6.53708			−0.256012
$653$	13.8503	+	7.99647i	0.542004	+	0.312926i	0.745891	−	0.666068i	$-0.232024\pi$
$653$	13.8503	+	7.99647i	0.542004	+	0.312926i	−0.203887	+	0.978994i	$0.565357\pi$
$654$		0			0
$655$		0			0
$656$	−3.20100	+	5.54430i	−0.124978	+	0.216468i
$657$		0			0
$658$	14.1350	−	20.1983i	0.551040	−	0.787412i
$659$			27.6958i			1.07887i	0.842026	+	0.539437i	$0.181363\pi$
$659$			27.6958i			1.07887i	−0.842026	+	0.539437i	$0.818637\pi$
$660$		0			0
$661$	−36.1490	+	20.8706i	−1.40603	+	0.811773i	−0.995003	−	0.0998487i	$-0.968164\pi$
$661$	−36.1490	+	20.8706i	−1.40603	+	0.811773i	−0.411030	+	0.911622i	$0.634831\pi$
$662$	−1.95246	+	1.12725i	−0.0758844	+	0.0438119i
$663$		0			0
$664$			2.72583i			0.105783i
$665$		0			0
$666$		0			0
$667$	−18.8876	+	32.7143i	−0.731330	+	1.26670i
$668$	−4.41453	−	7.64620i	−0.170803	−	0.295840i
$669$		0			0
$670$		0			0
$671$	7.65618			0.295564
$672$		0			0
$673$	7.91950			0.305274			0.152637	−	0.988282i	$-0.451223\pi$
$673$	7.91950			0.305274			0.152637	+	0.988282i	$0.451223\pi$
$674$	6.50916	+	3.75807i	0.250724	+	0.144755i
$675$		0			0
$676$	−8.82673	−	15.2883i	−0.339489	−	0.588013i
$677$	5.33360	−	9.23807i	0.204987	−	0.355048i	−0.745142	−	0.666906i	$-0.767618\pi$
$677$	5.33360	−	9.23807i	0.204987	−	0.355048i	0.950129	+	0.311858i	$0.100951\pi$
$678$		0			0
$679$	−2.47684	−	5.30792i	−0.0950524	−	0.203699i
$680$		0			0
$681$		0			0
$682$	−7.64100	+	4.41154i	−0.292589	+	0.168926i
$683$	1.91327	−	1.10463i	0.0732093	−	0.0422674i	−0.462948	−	0.886385i	$-0.653209\pi$
$683$	1.91327	−	1.10463i	0.0732093	−	0.0422674i	0.536158	+	0.844118i	$0.319875\pi$
$684$		0			0
$685$		0			0
$686$	25.0342	−	25.0741i	0.955810	−	0.957334i
$687$		0			0
$688$	−14.6624	+	25.3960i	−0.558997	+	0.968212i
$689$	−3.69828	−	6.40560i	−0.140893	−	0.244034i
$690$		0			0
$691$	−8.02498	−	4.63322i	−0.305284	−	0.176256i	0.339530	−	0.940595i	$-0.389732\pi$
$691$	−8.02498	−	4.63322i	−0.305284	−	0.176256i	−0.644814	+	0.764339i	$0.723065\pi$
$692$	12.3762			0.470474
$693$		0			0
$694$	−9.24172			−0.350811
$695$		0			0
$696$		0			0
$697$	0.511363	+	0.885707i	0.0193693	+	0.0335486i
$698$	15.3492	−	26.5857i	0.580977	−	1.00628i
$699$		0			0
$700$		0			0
$701$			6.99882i			0.264342i	0.991227	+	0.132171i	$0.0421948\pi$
$701$			6.99882i			0.264342i	−0.991227	+	0.132171i	$0.957805\pi$
$702$		0			0
$703$	−21.5781	+	12.4581i	−0.813834	+	0.469867i
$704$	−14.2244	+	8.21247i	−0.536103	+	0.309519i
$705$		0			0
$706$		−	11.2511i		−	0.423441i
$707$	25.3663	+	17.7517i	0.953999	+	0.667620i
$708$		0			0
$709$	−15.5805	+	26.9863i	−0.585139	+	1.01349i	0.409719	+	0.912212i	$0.365627\pi$
$709$	−15.5805	+	26.9863i	−0.585139	+	1.01349i	−0.994858	+	0.101279i	$0.967707\pi$
$710$		0			0
$711$		0			0
$712$	−6.34829	−	3.66519i	−0.237912	−	0.137359i
$713$	6.95644			0.260521
$714$		0			0
$715$		0			0
$716$	−19.1316	−	11.0456i	−0.714980	−	0.412794i
$717$		0			0
$718$	7.73514	+	13.3976i	0.288673	+	0.499996i
$719$	4.53080	−	7.84758i	0.168970	−	0.292665i	−0.769088	−	0.639143i	$-0.779289\pi$
$719$	4.53080	−	7.84758i	0.168970	−	0.292665i	0.938058	+	0.346478i	$0.112622\pi$
$720$		0			0
$721$	1.54260	+	0.134547i	0.0574493	+	0.00501079i
$722$		−	82.1894i		−	3.05877i
$723$		0			0
$724$	14.3169	−	8.26587i	0.532084	−	0.307199i
$725$		0			0
$726$		0			0
$727$		−	17.0567i		−	0.632599i	−0.948659	−	0.316300i	$-0.897559\pi$
$727$		−	17.0567i		−	0.632599i	0.948659	−	0.316300i	$-0.102441\pi$
$728$	7.57892	−	3.53656i	0.280893	−	0.131074i
$729$		0			0
$730$		0			0
$731$	2.34233	+	4.05703i	0.0866342	+	0.150055i
$732$		0			0
$733$	−13.8270	−	7.98301i	−0.510711	−	0.294859i	0.222415	−	0.974952i	$-0.428606\pi$
$733$	−13.8270	−	7.98301i	−0.510711	−	0.294859i	−0.733126	+	0.680093i	$0.761939\pi$
$734$	−35.5265			−1.31131
$735$		0			0
$736$	36.1784			1.33355
$737$	31.0970	+	17.9539i	1.14547	+	0.661340i
$738$		0			0
$739$	−6.92575	−	11.9958i	−0.254768	−	0.441271i	0.710064	−	0.704137i	$-0.248666\pi$
$739$	−6.92575	−	11.9958i	−0.254768	−	0.441271i	−0.964832	+	0.262866i	$0.915332\pi$
$740$		0			0
$741$		0			0
$742$	−6.97881	+	3.25653i	−0.256200	+	0.119551i
$743$			27.6801i			1.01548i	0.861510	+	0.507741i	$0.169519\pi$
$743$			27.6801i			1.01548i	−0.861510	+	0.507741i	$0.830481\pi$
$744$		0			0
$745$		0			0
$746$	−4.37976	+	2.52866i	−0.160355	+	0.0925807i
$747$		0			0
$748$			3.90666i			0.142842i
$749$	4.46006	+	0.389011i	0.162967	+	0.0142142i
$750$		0			0
$751$	−16.6666	+	28.8674i	−0.608173	+	1.05339i	0.383368	+	0.923596i	$0.374764\pi$
$751$	−16.6666	+	28.8674i	−0.608173	+	1.05339i	−0.991541	+	0.129791i	$0.958569\pi$
$752$	−11.1150	−	19.2518i	−0.405324	−	0.702041i
$753$		0			0
$754$	−62.5005	−	36.0847i	−2.27613	−	1.31413i
$755$		0			0
$756$		0			0
$757$	−10.1442			−0.368697			−0.184348	−	0.982861i	$-0.559017\pi$
$757$	−10.1442			−0.368697			−0.184348	+	0.982861i	$0.559017\pi$
$758$	−39.5290	−	22.8221i	−1.43576	−	0.828935i
$759$		0			0
$760$		0			0
$761$	7.35057	−	12.7316i	0.266458	−	0.461519i	−0.701487	−	0.712683i	$-0.747480\pi$
$761$	7.35057	−	12.7316i	0.266458	−	0.461519i	0.967945	+	0.251164i	$0.0808133\pi$
$762$		0			0
$763$	29.0529	+	20.3316i	1.05179	+	0.736052i
$764$		−	40.8577i		−	1.47818i
$765$		0			0
$766$	18.4157	−	10.6323i	0.665388	−	0.384162i
$767$	26.5308	−	15.3176i	0.957971	−	0.553085i
$768$		0			0
$769$		−	22.4992i		−	0.811340i	−0.914020	−	0.405670i	$-0.867038\pi$
$769$		−	22.4992i		−	0.811340i	0.914020	−	0.405670i	$-0.132962\pi$
$770$		0			0
$771$		0			0
$772$	10.3876	−	17.9919i	0.373859	−	0.647542i
$773$	−10.6266	−	18.4057i	−0.382211	−	0.662008i	0.609167	−	0.793042i	$-0.291504\pi$
$773$	−10.6266	−	18.4057i	−0.382211	−	0.662008i	−0.991378	+	0.131034i	$0.958170\pi$
$774$		0			0
$775$		0			0
$776$	−1.43954			−0.0516764
$777$		0			0
$778$	−24.0698			−0.862945
$779$	−9.56170	−	5.52045i	−0.342583	−	0.197791i
$780$		0			0
$781$	−16.3550	−	28.3278i	−0.585229	−	1.01365i
$782$	3.39546	−	5.88111i	0.121421	−	0.210308i
$783$		0			0
$784$	−10.9434	−	30.0171i	−0.390835	−	1.07204i
$785$		0			0
$786$		0			0
$787$	−13.6131	+	7.85952i	−0.485254	+	0.280162i	−0.722603	−	0.691263i	$-0.757055\pi$
$787$	−13.6131	+	7.85952i	−0.485254	+	0.280162i	0.237349	+	0.971424i	$0.423721\pi$
$788$	22.5675	−	13.0293i	0.803933	−	0.464151i
$789$		0			0
$790$		0			0
$791$	15.9011	+	34.0765i	0.565379	+	1.21162i
$792$		0			0
$793$	5.76628	−	9.98750i	0.204767	−	0.354666i
$794$	27.3875	+	47.4366i	0.971946	+	1.68346i
$795$		0			0
$796$	−28.4605	−	16.4317i	−1.00876	−	0.582406i
$797$	−39.5812			−1.40204			−0.701019	−	0.713143i	$-0.747271\pi$
$797$	−39.5812			−1.40204			−0.701019	+	0.713143i	$0.747271\pi$
$798$		0			0
$799$	−3.55128			−0.125635
$800$		0			0
$801$		0			0
$802$	−11.3763	−	19.7043i	−0.401711	−	0.695784i
$803$	−22.3076	+	38.6380i	−0.787220	+	1.36350i
$804$		0			0
$805$		0			0
$806$			13.2903i			0.468130i
$807$		0			0
$808$	6.58967	−	3.80455i	0.231824	−	0.133843i
$809$	−38.1053	+	22.0001i	−1.33971	+	0.773483i	−0.986764	−	0.162160i	$-0.948154\pi$
$809$	−38.1053	+	22.0001i	−1.33971	+	0.773483i	−0.352947	+	0.935643i	$0.614820\pi$
$810$		0			0
$811$			44.9306i			1.57773i	0.614567	+	0.788864i	$0.289331\pi$
$811$			44.9306i			1.57773i	−0.614567	+	0.788864i	$0.710669\pi$
$812$	−19.5413	+	27.9237i	−0.685766	+	0.979929i
$813$		0			0
$814$	−9.77230	+	16.9261i	−0.342519	+	0.593260i
$815$		0			0
$816$		0			0
$817$	−43.7979	−	25.2867i	−1.53229	−	0.884671i
$818$	−27.5819			−0.964378
$819$		0			0
$820$		0			0
$821$	13.1026	+	7.56481i	0.457285	+	0.264014i	0.710902	−	0.703291i	$-0.248287\pi$
$821$	13.1026	+	7.56481i	0.457285	+	0.264014i	−0.253617	+	0.967305i	$0.581620\pi$
$822$		0			0
$823$	15.7898	+	27.3487i	0.550397	+	0.953316i	0.998246	+	0.0592066i	$0.0188571\pi$
$823$	15.7898	+	27.3487i	0.550397	+	0.953316i	−0.447848	+	0.894109i	$0.647810\pi$
$824$	0.190278	−	0.329571i	0.00662865	−	0.0114812i
$825$		0			0
$826$	−13.4879	−	28.9049i	−0.469305	−	1.00573i
$827$		−	48.6368i		−	1.69127i	−0.533765	−	0.845633i	$-0.679223\pi$
$827$		−	48.6368i		−	1.69127i	0.533765	−	0.845633i	$-0.320777\pi$
$828$		0			0
$829$	−40.4900	+	23.3769i	−1.40628	+	0.811914i	−0.995027	−	0.0996095i	$-0.968241\pi$
$829$	−40.4900	+	23.3769i	−1.40628	+	0.811914i	−0.411249	+	0.911523i	$0.634907\pi$
$830$		0			0
$831$		0			0
$832$			24.7410i			0.857741i
$833$	−5.02692	−	0.883629i	−0.174173	−	0.0306159i
$834$		0			0
$835$		0			0
$836$	−21.0873	−	36.5242i	−0.729319	−	1.26322i
$837$		0			0
$838$	−57.8898	−	33.4227i	−1.99977	−	1.15457i
$839$	29.1067			1.00488			0.502438	−	0.864613i	$-0.332437\pi$
$839$	29.1067			1.00488			0.502438	+	0.864613i	$0.332437\pi$
$840$		0			0
$841$	−31.2110			−1.07624
$842$	−39.5179	−	22.8157i	−1.36188	−	0.786281i
$843$		0			0
$844$	9.61532	+	16.6542i	0.330973	+	0.573262i
$845$		0			0
$846$		0			0
$847$	0.134227	−	1.53893i	0.00461209	−	0.0528782i
$848$			6.94434i			0.238469i
$849$		0			0
$850$		0			0
$851$	13.3452	−	7.70485i	0.457467	−	0.264119i
$852$		0			0
$853$		−	28.4915i		−	0.975531i	−0.872975	−	0.487766i	$-0.837812\pi$
$853$		−	28.4915i		−	0.975531i	0.872975	−	0.487766i	$-0.162188\pi$
$854$	−9.83787	−	6.88466i	−0.336645	−	0.235588i
$855$		0			0
$856$	0.550145	−	0.952879i	0.0188036	−	0.0325687i
$857$	20.2776	+	35.1219i	0.692670	+	1.19974i	0.970960	+	0.239243i	$0.0768991\pi$
$857$	20.2776	+	35.1219i	0.692670	+	1.19974i	−0.278290	+	0.960497i	$0.589768\pi$
$858$		0			0
$859$	−32.6686	−	18.8612i	−1.11464	−	0.643537i	−0.174612	−	0.984637i	$-0.555867\pi$
$859$	−32.6686	−	18.8612i	−1.11464	−	0.643537i	−0.940027	+	0.341100i	$0.889200\pi$
$860$		0			0
$861$		0			0
$862$	15.6085			0.531627
$863$	−22.2387	−	12.8395i	−0.757014	−	0.437062i	0.0712087	−	0.997461i	$-0.477314\pi$
$863$	−22.2387	−	12.8395i	−0.757014	−	0.437062i	−0.828223	+	0.560399i	$0.810648\pi$
$864$		0			0
$865$		0			0
$866$	−24.1695	+	41.8627i	−0.821311	+	1.42255i
$867$		0			0
$868$	6.25262	+	0.545360i	0.212228	+	0.0185107i
$869$			12.8463i			0.435779i
$870$		0			0
$871$	46.8417	−	27.0441i	1.58717	−	0.916353i
$872$	7.54736	−	4.35747i	0.255586	−	0.147563i
$873$		0			0
$874$			73.3117i			2.47981i
$875$		0			0
$876$		0			0
$877$	9.52270	−	16.4938i	0.321559	−	0.556956i	−0.659251	−	0.751923i	$-0.729127\pi$
$877$	9.52270	−	16.4938i	0.321559	−	0.556956i	0.980810	+	0.194967i	$0.0624599\pi$
$878$	−0.760202	−	1.31671i	−0.0256556	−	0.0444367i
$879$		0			0
$880$		0			0
$881$	−30.7115			−1.03470			−0.517349	−	0.855774i	$-0.673081\pi$
$881$	−30.7115			−1.03470			−0.517349	+	0.855774i	$0.673081\pi$
$882$		0			0
$883$	−36.8466			−1.23999			−0.619993	−	0.784607i	$-0.712865\pi$
$883$	−36.8466			−1.23999			−0.619993	+	0.784607i	$0.712865\pi$
$884$	5.09624	+	2.94232i	0.171405	+	0.0989608i
$885$		0			0
$886$	21.6653	+	37.5254i	0.727859	+	1.26069i
$887$	−16.9386	+	29.3385i	−0.568742	+	0.985090i	0.427949	+	0.903803i	$0.359236\pi$
$887$	−16.9386	+	29.3385i	−0.568742	+	0.985090i	−0.996691	+	0.0812870i	$0.974097\pi$
$888$		0			0
$889$	5.00982	−	2.33774i	0.168024	−	0.0784051i
$890$		0			0
$891$		0			0
$892$	−34.6949	+	20.0311i	−1.16167	+	0.670691i
$893$	33.2017	−	19.1690i	1.11105	−	0.641466i
$894$		0			0
$895$		0			0
$896$	−13.5128	−	1.17860i	−0.451432	−	0.0393743i
$897$		0			0
$898$	2.06298	−	3.57319i	0.0688427	−	0.119239i
$899$	5.54404	+	9.60257i	0.184904	+	0.320264i
$900$		0			0
$901$	0.960739	+	0.554683i	0.0320068	+	0.0184792i
$902$	−8.66061			−0.288367
$903$		0			0
$904$	9.24172			0.307375
$905$		0			0
$906$		0			0
$907$	−0.533407	−	0.923888i	−0.0177115	−	0.0306772i	0.857034	−	0.515260i	$-0.172305\pi$
$907$	−0.533407	−	0.923888i	−0.0177115	−	0.0306772i	−0.874745	+	0.484583i	$0.838971\pi$
$908$	8.45734	−	14.6485i	0.280667	−	0.486129i
$909$		0			0
$910$		0			0
$911$		−	9.61157i		−	0.318445i	−0.987243	−	0.159223i	$-0.949101\pi$
$911$		−	9.61157i		−	0.318445i	0.987243	−	0.159223i	$-0.0508988\pi$
$912$		0			0
$913$	−11.7169	+	6.76477i	−0.387774	+	0.223881i
$914$	9.06839	−	5.23564i	0.299956	−	0.173179i
$915$		0			0
$916$		−	43.5862i		−	1.44013i
$917$	2.57590	−	29.5330i	0.0850637	−	0.975266i
$918$		0			0
$919$	−3.41594	+	5.91658i	−0.112681	+	0.195170i	−0.916851	−	0.399231i	$-0.869277\pi$
$919$	−3.41594	+	5.91658i	−0.112681	+	0.195170i	0.804169	+	0.594401i	$0.202611\pi$
$920$		0			0
$921$		0			0
$922$	16.7480	+	9.66946i	0.551566	+	0.318447i
$923$	−49.2714			−1.62179
$924$		0			0
$925$		0			0
$926$	−19.9573	−	11.5224i	−0.655838	−	0.378648i
$927$		0			0
$928$	28.8330	+	49.9401i	0.946488	+	1.63937i
$929$	26.9383	−	46.6585i	0.883818	−	1.53082i	0.0367547	−	0.999324i	$-0.488298\pi$
$929$	26.9383	−	46.6585i	0.883818	−	1.53082i	0.847063	−	0.531493i	$-0.178369\pi$
$930$		0			0
$931$	51.7674	−	18.8730i	1.69661	−	0.618536i
$932$			30.5352i			1.00021i
$933$		0			0
$934$	33.0252	−	19.0671i	1.08062	−	0.623894i
$935$		0			0
$936$		0			0
$937$		−	21.6036i		−	0.705759i	−0.935669	−	0.352880i	$-0.885203\pi$
$937$		−	21.6036i		−	0.705759i	0.935669	−	0.352880i	$-0.114797\pi$
$938$	−23.8137	−	51.0333i	−0.777546	−	1.66630i
$939$		0			0
$940$		0			0
$941$	−29.1006	−	50.4038i	−0.948654	−	1.64312i	−0.748265	−	0.663400i	$-0.769113\pi$
$941$	−29.1006	−	50.4038i	−0.948654	−	1.64312i	−0.200389	−	0.979716i	$-0.564221\pi$
$942$		0			0
$943$	5.91353	+	3.41418i	0.192571	+	0.111181i
$944$	−28.7621			−0.936127
$945$		0			0
$946$	−39.6704			−1.28980
$947$	17.7271	+	10.2347i	0.576053	+	0.332584i	0.759563	−	0.650434i	$-0.225413\pi$
$947$	17.7271	+	10.2347i	0.576053	+	0.332584i	−0.183510	+	0.983018i	$0.558746\pi$
$948$		0			0
$949$	33.6022	+	58.2007i	1.09077	+	1.88927i
$950$		0			0
$951$		0			0
$952$	−0.719212	+	1.02772i	−0.0233098	+	0.0333087i
$953$		−	10.4745i		−	0.339303i	−0.985504	−	0.169651i	$-0.945736\pi$
$953$		−	10.4745i		−	0.339303i	0.985504	−	0.169651i	$-0.0542642\pi$
$954$		0			0
$955$		0			0
$956$	1.38209	−	0.797952i	0.0447001	−	0.0258076i
$957$		0			0
$958$			37.0879i			1.19825i
$959$	10.6793	−	15.2602i	0.344852	−	0.492778i
$960$		0			0
$961$	−14.4790	+	25.0784i	−0.467066	+	0.808982i
$962$	14.7201	+	25.4960i	0.474595	+	0.822023i
$963$		0			0
$964$	−9.36026	−	5.40415i	−0.301474	−	0.174056i
$965$		0			0
$966$		0			0
$967$	43.1242			1.38678			0.693391	−	0.720562i	$-0.256116\pi$
$967$	43.1242			1.38678			0.693391	+	0.720562i	$0.256116\pi$
$968$	−0.328787	−	0.189825i	−0.0105676	−	0.00610122i
$969$		0			0
$970$		0			0
$971$	−4.17572	+	7.23256i	−0.134005	+	0.232104i	−0.925217	−	0.379438i	$-0.876117\pi$
$971$	−4.17572	+	7.23256i	−0.134005	+	0.232104i	0.791212	+	0.611542i	$0.209451\pi$
$972$		0			0
$973$	−7.22623	−	15.4860i	−0.231662	−	0.496457i
$974$			3.53581i			0.113295i
$975$		0			0
$976$	−9.37687	+	5.41374i	−0.300146	+	0.173290i
$977$	23.2171	−	13.4044i	0.742781	−	0.428845i	−0.0802983	−	0.996771i	$-0.525587\pi$
$977$	23.2171	−	13.4044i	0.742781	−	0.428845i	0.823080	+	0.567926i	$0.192254\pi$
$978$		0			0
$979$		−	36.3840i		−	1.16284i
$980$		0			0
$981$		0			0
$982$	24.3769	−	42.2221i	0.777899	−	1.34736i
$983$	14.7287	+	25.5109i	0.469773	+	0.813671i	0.999403	−	0.0345581i	$-0.0110024\pi$
$983$	14.7287	+	25.5109i	0.469773	+	0.813671i	−0.529630	+	0.848229i	$0.677669\pi$
$984$		0			0
$985$		0			0
$986$	10.8243			0.344714
$987$		0			0
$988$	−63.5279			−2.02109
$989$	27.0873	+	15.6388i	0.861325	+	0.497286i
$990$		0			0
$991$	2.50334	+	4.33591i	0.0795211	+	0.137735i	0.903043	−	0.429549i	$-0.141328\pi$
$991$	2.50334	+	4.33591i	0.0795211	+	0.137735i	−0.823522	+	0.567284i	$0.807994\pi$
$992$	5.30970	−	9.19667i	0.168583	−	0.291995i
$993$		0			0
$994$	−4.45760	+	51.1069i	−0.141386	+	1.62101i
$995$		0			0
$996$		0			0
$997$	7.68960	−	4.43960i	0.243532	−	0.140603i	−0.373267	−	0.927724i	$-0.621762\pi$
$997$	7.68960	−	4.43960i	0.243532	−	0.140603i	0.616799	+	0.787121i	$0.288429\pi$
$998$	43.4560	−	25.0893i	1.37558	−	0.794189i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1575.2.bk.i.26.4		24
3.2	odd	2	inner	1575.2.bk.i.26.9		24
5.2	odd	4		315.2.bb.b.89.10	yes	24
5.3	odd	4		315.2.bb.b.89.4	yes	24
5.4	even	2	inner	1575.2.bk.i.26.10		24
7.3	odd	6	inner	1575.2.bk.i.1151.9		24
15.2	even	4		315.2.bb.b.89.3	✓	24
15.8	even	4		315.2.bb.b.89.9	yes	24
15.14	odd	2	inner	1575.2.bk.i.26.3		24
21.17	even	6	inner	1575.2.bk.i.1151.4		24
35.2	odd	12		2205.2.g.b.2204.5		24
35.3	even	12		315.2.bb.b.269.3	yes	24
35.12	even	12		2205.2.g.b.2204.6		24
35.17	even	12		315.2.bb.b.269.9	yes	24
35.23	odd	12		2205.2.g.b.2204.17		24
35.24	odd	6	inner	1575.2.bk.i.1151.3		24
35.33	even	12		2205.2.g.b.2204.18		24
105.2	even	12		2205.2.g.b.2204.19		24
105.17	odd	12		315.2.bb.b.269.4	yes	24
105.23	even	12		2205.2.g.b.2204.7		24
105.38	odd	12		315.2.bb.b.269.10	yes	24
105.47	odd	12		2205.2.g.b.2204.20		24
105.59	even	6	inner	1575.2.bk.i.1151.10		24
105.68	odd	12		2205.2.g.b.2204.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bb.b.89.3	✓	24	15.2	even	4
315.2.bb.b.89.4	yes	24	5.3	odd	4
315.2.bb.b.89.9	yes	24	15.8	even	4
315.2.bb.b.89.10	yes	24	5.2	odd	4
315.2.bb.b.269.3	yes	24	35.3	even	12
315.2.bb.b.269.4	yes	24	105.17	odd	12
315.2.bb.b.269.9	yes	24	35.17	even	12
315.2.bb.b.269.10	yes	24	105.38	odd	12
1575.2.bk.i.26.3		24	15.14	odd	2	inner
1575.2.bk.i.26.4		24	1.1	even	1	trivial
1575.2.bk.i.26.9		24	3.2	odd	2	inner
1575.2.bk.i.26.10		24	5.4	even	2	inner
1575.2.bk.i.1151.3		24	35.24	odd	6	inner
1575.2.bk.i.1151.4		24	21.17	even	6	inner
1575.2.bk.i.1151.9		24	7.3	odd	6	inner
1575.2.bk.i.1151.10		24	105.59	even	6	inner
2205.2.g.b.2204.5		24	35.2	odd	12
2205.2.g.b.2204.6		24	35.12	even	12
2205.2.g.b.2204.7		24	105.23	even	12
2205.2.g.b.2204.8		24	105.68	odd	12
2205.2.g.b.2204.17		24	35.23	odd	12
2205.2.g.b.2204.18		24	35.33	even	12
2205.2.g.b.2204.19		24	105.2	even	12
2205.2.g.b.2204.20		24	105.47	odd	12

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:	\( N \)	\(=\)	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1575.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.65683 - 0.956572i) q^{2} +(0.830062 + 1.43771i) q^{4} +(-2.39757 + 1.11878i) q^{7} +0.650234i q^{8} +O(q^{10})\)	\(q+(-1.65683 - 0.956572i) q^{2} +(0.830062 + 1.43771i) q^{4} +(-2.39757 + 1.11878i) q^{7} +0.650234i q^{8} +(-2.79501 + 1.61370i) q^{11} +4.86146i q^{13} +(5.04256 + 0.439817i) q^{14} +(2.28212 - 3.95275i) q^{16} +(-0.364571 - 0.631456i) q^{17} +(6.81691 + 3.93574i) q^{19} +6.17449 q^{22} +(-4.21599 - 2.43410i) q^{23} +(4.65034 - 8.05463i) q^{26} +(-3.59861 - 2.51835i) q^{28} -7.75958i q^{29} +(-1.23751 + 0.714478i) q^{31} +(-6.43594 + 3.71579i) q^{32} +1.39495i q^{34} +(-1.58269 + 2.74130i) q^{37} +(-7.52965 - 13.0417i) q^{38} -1.40264 q^{41} -6.42489 q^{43} +(-4.64007 - 2.67894i) q^{44} +(4.65679 + 8.06579i) q^{46} +(2.43524 - 4.21797i) q^{47} +(4.49666 - 5.36470i) q^{49} +(-6.98937 + 4.03531i) q^{52} +(-1.31763 + 0.760733i) q^{53} +(-0.727468 - 1.55898i) q^{56} +(-7.42260 + 12.8563i) q^{58} +(-3.15081 - 5.45737i) q^{59} +(-2.05442 - 1.18612i) q^{61} +2.73380 q^{62} +5.08921 q^{64} +(-5.56295 - 9.63531i) q^{67} +(0.605233 - 1.04829i) q^{68} +10.1351i q^{71} +(11.9718 - 6.91195i) q^{73} +(5.24450 - 3.02792i) q^{74} +13.0676i q^{76} +(4.89586 - 6.99596i) q^{77} +(1.99018 - 3.44710i) q^{79} +(2.32395 + 1.34173i) q^{82} +4.19208 q^{83} +(10.6450 + 6.14587i) q^{86} +(-1.04928 - 1.81741i) q^{88} +(-5.63672 + 9.76309i) q^{89} +(-5.43891 - 11.6557i) q^{91} -8.08181i q^{92} +(-8.06958 + 4.65898i) q^{94} +2.21388i q^{97} +(-12.5819 + 4.58702i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4}+O(q^{10}) \) 24 * q + 24 * q^4	\( 24 q + 24 q^{4} + 36 q^{19} - 60 q^{31} - 24 q^{46} - 36 q^{49} + 48 q^{61} - 48 q^{64} + 60 q^{79} + 60 q^{91} - 48 q^{94}+O(q^{100}) \) 24 * q + 24 * q^4 + 36 * q^19 - 60 * q^31 - 24 * q^46 - 36 * q^49 + 48 * q^61 - 48 * q^64 + 60 * q^79 + 60 * q^91 - 48 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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