LMFDB - Embedded newform 1575.2.bk.i.1151.3

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			1151.3
Character	$\chi$	$=$	1575.1151
Dual form			1575.2.bk.i.26.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Character values

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

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

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	−0.954046	−	0.299659i	$-0.903127\pi$
$2$	−1.65683	+	0.956572i	−1.17156	+	0.676399i	−0.217511	+	0.976058i	$0.569794\pi$
$3$		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	$-0.171589\pi$
$11$	2.79501	+	1.61370i	0.842728	+	0.486549i	−0.0154625	+	0.999880i	$0.504922\pi$
$12$		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	−0.906844	−	0.421466i	$-0.861516\pi$
$17$	−0.364571	+	0.631456i	−0.0884215	+	0.153150i	0.818423	+	0.574617i	$0.194849\pi$
$18$		0			0
$19$	6.81691	−	3.93574i	1.56391	−	0.902922i	0.567051	−	0.823683i	$-0.308084\pi$
$19$	6.81691	−	3.93574i	1.56391	−	0.902922i	0.996856	−	0.0792390i	$-0.0252490\pi$
$20$		0			0
$21$		0			0
$22$	−6.17449			−1.31641
$23$	−4.21599	+	2.43410i	−0.879094	+	0.507545i	−0.870360	−	0.492417i	$-0.836114\pi$
$23$	−4.21599	+	2.43410i	−0.879094	+	0.507545i	−0.00873433	+	0.999962i	$0.502780\pi$
$24$		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	0.384734	−	0.923027i	$-0.374293\pi$
$31$	−1.23751	−	0.714478i	−0.222264	−	0.128324i	−0.606998	+	0.794703i	$0.707626\pi$
$32$	−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	$-0.0828806\pi$
$37$	1.58269	+	2.74130i	0.260193	+	0.450667i	−0.706100	+	0.708112i	$0.749547\pi$
$38$	−7.52965	+	13.0417i	−1.22147	+	2.11565i
$39$		0			0
$40$		0			0
$41$	1.40264			0.219056			0.109528	−	0.993984i	$-0.465066\pi$
$41$	1.40264			0.219056			0.109528	+	0.993984i	$0.465066\pi$
$42$		0			0
$43$	6.42489			0.979787			0.489893	−	0.871782i	$-0.337036\pi$
$43$	6.42489			0.979787			0.489893	+	0.871782i	$0.337036\pi$
$44$	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	0.987155	−	0.159765i	$-0.0510737\pi$
$47$	2.43524	+	4.21797i	0.355217	+	0.615254i	−0.631938	+	0.775019i	$0.717740\pi$
$48$		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	0.406768	−	0.913532i	$-0.366656\pi$
$53$	−1.31763	−	0.760733i	−0.180990	−	0.104495i	−0.587758	+	0.809037i	$0.699989\pi$
$54$		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	$-0.698792\pi$
$59$	3.15081	−	5.45737i	0.410201	−	0.710489i	0.994911	+	0.100753i	$0.0321253\pi$
$60$		0			0
$61$	−2.05442	+	1.18612i	−0.263042	+	0.151867i	−0.625721	−	0.780047i	$-0.715195\pi$
$61$	−2.05442	+	1.18612i	−0.263042	+	0.151867i	0.362680	+	0.931914i	$0.381862\pi$
$62$	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	−0.295472	−	0.955351i	$-0.595477\pi$
$67$	5.56295	−	9.63531i	0.679622	−	1.17714i	0.975095	−	0.221789i	$-0.0711896\pi$
$68$	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	$-0.633314\pi$
$73$	−11.9718	−	6.91195i	−1.40120	−	0.808982i	−0.994516	+	0.104587i	$0.966648\pi$
$74$	−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	0.955993	−	0.293390i	$-0.0947834\pi$
$79$	1.99018	+	3.44710i	0.223913	+	0.387829i	−0.732080	+	0.681219i	$0.761450\pi$
$80$		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	0.993190	+	0.116505i	$0.0371691\pi$
$89$	5.63672	+	9.76309i	0.597491	+	1.03489i	−0.395699	+	0.918380i	$0.629498\pi$
$90$		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	−0.413017	−	0.910723i	$-0.635525\pi$
$101$	5.85104	−	10.1343i	0.582201	−	1.00840i	0.995218	−	0.0976779i	$-0.0311415\pi$
$102$		0			0
$103$	0.506851	−	0.292630i	0.0499415	−	0.0288337i	−0.474821	−	0.880082i	$-0.657487\pi$
$103$	0.506851	−	0.292630i	0.0499415	−	0.0288337i	0.524763	+	0.851248i	$0.324154\pi$
$104$	3.16109			0.309970
$105$		0			0
$106$	2.91079			0.282721
$107$	−1.46544	+	0.846073i	−0.141670	+	0.0817929i	−0.569159	−	0.822227i	$-0.692731\pi$
$107$	−1.46544	+	0.846073i	−0.141670	+	0.0817929i	0.427490	+	0.904020i	$0.359398\pi$
$108$		0			0
$109$	−6.70139	+	11.6072i	−0.641877	+	1.11176i	0.343136	+	0.939286i	$0.388511\pi$
$109$	−6.70139	+	11.6072i	−0.641877	+	1.11176i	−0.985013	+	0.172478i	$0.944823\pi$
$110$		0			0
$111$		0			0
$112$	1.04928	+	12.0302i	0.0991479	+	1.13674i
$113$			14.2129i			1.33704i	0.743694	+	0.668520i	$0.233072\pi$
$113$			14.2129i			1.33704i	−0.743694	+	0.668520i	$0.766928\pi$
$114$		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	$-0.470448\pi$
$127$	2.08954			0.185417			0.0927084	+	0.995693i	$0.470448\pi$
$128$	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	$-0.00385167\pi$
$131$	5.60241	+	9.70365i	0.489484	+	0.847812i	−0.510442	+	0.859912i	$0.670518\pi$
$132$		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	0.216415	−	0.976301i	$-0.430564\pi$
$137$	−6.09673	−	3.51995i	−0.520879	−	0.300730i	−0.737294	+	0.675572i	$0.763897\pi$
$138$		0			0
$139$		−	6.45903i		−	0.547848i	−0.961751	−	0.273924i	$-0.911678\pi$
$139$		−	6.45903i		−	0.547848i	0.961751	−	0.273924i	$-0.0883216\pi$
$140$		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	−0.703802	+	0.710396i	$0.748516\pi$
$149$	−20.3962	+	11.7758i	−1.67092	+	0.964709i	−0.967122	+	0.254312i	$0.918151\pi$
$150$		0			0
$151$	−9.05442	+	15.6827i	−0.736838	+	1.27624i	0.217074	+	0.976155i	$0.430349\pi$
$151$	−9.05442	+	15.6827i	−0.736838	+	1.27624i	−0.953912	+	0.300086i	$0.902985\pi$
$152$	−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	$-0.364944\pi$
$157$	−2.15168	−	1.24227i	−0.171723	−	0.0991441i	−0.583398	+	0.812187i	$0.698277\pi$
$158$	−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	$-0.117383\pi$
$163$	1.96885	+	3.41015i	0.154212	+	0.267104i	−0.778560	+	0.627571i	$0.784049\pi$
$164$	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	0.972219	−	0.234072i	$-0.0752053\pi$
$173$	3.72751	+	6.45623i	0.283397	+	0.490858i	−0.688822	+	0.724930i	$0.741872\pi$
$174$		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	$-0.167656\pi$
$179$	11.5242	+	6.65349i	0.861358	+	0.497305i	−0.00310866	+	0.999995i	$0.500990\pi$
$180$		0			0
$181$			9.95814i			0.740183i	0.928995	+	0.370091i	$0.120674\pi$
$181$			9.95814i			0.740183i	−0.928995	+	0.370091i	$0.879326\pi$
$182$	−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	0.543527	−	0.839392i	$-0.317089\pi$
$191$	21.3140	−	12.3056i	1.54223	−	0.890404i	0.998698	−	0.0510125i	$-0.0162448\pi$
$192$		0			0
$193$	6.25714	−	10.8377i	0.450399	−	0.780113i	−0.548012	−	0.836470i	$-0.684615\pi$
$193$	6.25714	−	10.8377i	0.450399	−	0.780113i	0.998411	+	0.0563571i	$0.0179485\pi$
$194$	−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	$0.188883\pi$
$197$			15.6968i			1.11835i	−0.829049	+	0.559177i	$0.811117\pi$
$198$		0			0
$199$	−17.1436	−	9.89788i	−1.21528	−	0.701642i	−0.251375	−	0.967890i	$-0.580883\pi$
$199$	−17.1436	−	9.89788i	−1.21528	−	0.701642i	−0.963905	+	0.266247i	$0.914216\pi$
$200$		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	−0.984081	−	0.177723i	$-0.943127\pi$
$227$	−5.09441	+	8.82377i	−0.338128	+	0.585654i	0.645953	+	0.763377i	$0.276460\pi$
$228$		0			0
$229$	−22.7373	+	13.1274i	−1.50252	+	0.867483i	−0.502529	+	0.864561i	$0.667597\pi$
$229$	−22.7373	+	13.1274i	−1.50252	+	0.867483i	−0.999996	+	0.00292226i	$0.999070\pi$
$230$		0			0
$231$		0			0
$232$	−5.04554			−0.331256
$233$	15.9291	−	9.19667i	1.04355	−	0.602494i	0.122713	−	0.992442i	$-0.460840\pi$
$233$	15.9291	−	9.19667i	1.04355	−	0.602494i	0.920837	+	0.389948i	$0.127507\pi$
$234$		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	0.307287	−	0.951617i	$-0.400579\pi$
$241$	−5.63829	−	3.25527i	−0.363194	−	0.209690i	−0.670481	+	0.741927i	$0.733912\pi$
$242$	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	$-0.520357\pi$
$251$	−2.02506			−0.127820			−0.0639102	+	0.997956i	$0.520357\pi$
$252$		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	0.996828	+	0.0795849i	$0.0253595\pi$
$257$	9.09510	+	15.7532i	0.567337	+	0.982656i	−0.429491	+	0.903071i	$0.641307\pi$
$258$		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	−0.123444	−	0.992351i	$-0.539394\pi$
$263$	−16.9400	−	9.78034i	−1.04457	−	0.603082i	−0.921124	+	0.389270i	$0.872727\pi$
$264$		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	$-0.878276\pi$
$269$	−2.30801	+	3.99759i	−0.140722	+	0.243738i	0.787047	+	0.616893i	$0.211609\pi$
$270$		0			0
$271$	−9.33654	+	5.39045i	−0.567154	+	0.327447i	−0.756012	−	0.654558i	$-0.772855\pi$
$271$	−9.33654	+	5.39045i	−0.567154	+	0.327447i	0.188858	+	0.982004i	$0.439522\pi$
$272$	−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	−0.374130	−	0.927376i	$-0.622059\pi$
$277$	10.2534	−	17.7594i	0.616067	−	1.06706i	0.990196	−	0.139682i	$-0.0446081\pi$
$278$	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	$-0.646635\pi$
$283$	−24.2677	−	14.0110i	−1.44257	−	0.832866i	−0.998020	+	0.0628908i	$0.979968\pi$
$284$	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	$-0.740809\pi$
$311$	5.05422	−	8.75417i	0.286599	−	0.496404i	0.972996	+	0.230824i	$0.0741420\pi$
$312$		0			0
$313$	20.3300	−	11.7375i	1.14912	−	0.663445i	0.200447	−	0.979705i	$-0.435760\pi$
$313$	20.3300	−	11.7375i	1.14912	−	0.663445i	0.948673	+	0.316260i	$0.102427\pi$
$314$	4.75329			0.268244
$315$		0			0
$316$	6.60790			0.371724
$317$	27.2202	−	15.7156i	1.52884	−	0.882677i	0.529430	−	0.848353i	$-0.322406\pi$
$317$	27.2202	−	15.7156i	1.52884	−	0.882677i	0.999411	−	0.0343235i	$-0.0109277\pi$
$318$		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	0.881764	−	0.471691i	$-0.156356\pi$
$331$	0.589214	+	1.02055i	0.0323861	+	0.0560944i	−0.849378	+	0.527785i	$0.823023\pi$
$332$	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	$-0.465874\pi$
$337$	3.92868			0.214009			0.107004	+	0.994259i	$0.465874\pi$
$338$	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	0.608069	−	0.793884i	$-0.291944\pi$
$347$	4.18346	+	2.41532i	0.224580	+	0.129661i	−0.383489	+	0.923545i	$0.625278\pi$
$348$		0			0
$349$		−	16.0461i		−	0.858927i	−0.903084	−	0.429463i	$-0.858703\pi$
$349$		−	16.0461i		−	0.858927i	0.903084	−	0.429463i	$-0.141297\pi$
$350$		0			0
$351$		0			0
$352$	−11.9924	−	20.7714i	−0.639195	−	1.10712i
$353$	2.94047	−	5.09305i	0.156505	−	0.271075i	−0.777101	−	0.629376i	$-0.783310\pi$
$353$	2.94047	−	5.09305i	0.156505	−	0.271075i	0.933606	+	0.358301i	$0.116644\pi$
$354$		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	$-0.598216\pi$
$359$	7.00295	−	4.04315i	0.369601	−	0.213389i	0.673284	+	0.739384i	$0.264883\pi$
$360$		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	$-0.494392\pi$
$367$	−16.0818	−	9.28484i	−0.839464	−	0.484665i	−0.857082	+	0.515180i	$0.827725\pi$
$368$	−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	$-0.188468\pi$
$373$	−1.32173	−	2.28930i	−0.0684365	−	0.118536i	−0.898213	+	0.439560i	$0.855134\pi$
$374$	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	0.688384	−	0.725346i	$-0.258320\pi$
$383$	−5.55752	−	9.62590i	−0.283976	−	0.491861i	−0.972360	+	0.233485i	$0.924987\pi$
$384$		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	$-0.436663\pi$
$389$	−10.8957	−	6.29064i	−0.552434	−	0.318948i	−0.750103	+	0.661321i	$0.769996\pi$
$390$		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	$-0.411509\pi$
$397$	24.7951	−	14.3154i	1.24443	−	0.718471i	0.969993	+	0.243134i	$0.0781755\pi$
$398$	37.8722			1.89836
$399$		0			0
$400$		0			0
$401$	−10.2994	+	5.94639i	−0.514330	+	0.296948i	−0.734612	−	0.678488i	$-0.762636\pi$
$401$	−10.2994	+	5.94639i	−0.514330	+	0.296948i	0.220282	+	0.975436i	$0.429302\pi$
$402$		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	0.775844	−	0.630925i	$-0.217324\pi$
$409$	12.4855	+	7.20852i	0.617369	+	0.356438i	−0.158475	+	0.987363i	$0.550658\pi$
$410$		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	$-0.825504\pi$
$419$	−34.9400			−1.70693			−0.853466	+	0.521149i	$0.825504\pi$
$420$		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	$-0.270378\pi$
$431$	7.06551	+	4.07928i	0.340334	+	0.196492i	−0.320086	+	0.947389i	$0.603712\pi$
$432$		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	−0.483486	−	0.875352i	$-0.660630\pi$
$439$	0.688243	−	0.397357i	0.0328480	−	0.0189648i	0.516334	+	0.856387i	$0.327296\pi$
$440$		0			0
$441$		0			0
$442$	6.78152			0.322564
$443$	−19.6145	+	11.3244i	−0.931913	+	0.538040i	−0.887416	−	0.460970i	$-0.847502\pi$
$443$	−19.6145	+	11.3244i	−0.931913	+	0.538040i	−0.0444966	+	0.999010i	$0.514168\pi$
$444$		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	$-0.125806\pi$
$457$	2.73666	+	4.74004i	0.128016	+	0.221730i	−0.794892	+	0.606751i	$0.792473\pi$
$458$	25.1146	−	43.4998i	1.17353	−	2.03261i
$459$		0			0
$460$		0			0
$461$	10.1084			0.470797			0.235399	−	0.971899i	$-0.424360\pi$
$461$	10.1084			0.470797			0.235399	+	0.971899i	$0.424360\pi$
$462$		0			0
$463$	−12.0455			−0.559800			−0.279900	−	0.960029i	$-0.590301\pi$
$463$	−12.0455			−0.559800			−0.279900	+	0.960029i	$0.590301\pi$
$464$	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	0.537832	−	0.843052i	$-0.319243\pi$
$467$	−9.96636	−	17.2622i	−0.461188	−	0.798801i	−0.999020	+	0.0442505i	$0.985910\pi$
$468$		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	$-0.687290\pi$
$479$	9.69290	−	16.7886i	0.442880	−	0.767091i	0.997902	+	0.0647451i	$0.0206234\pi$
$480$		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	$-0.820000\pi$
$487$	0.924082	−	1.60056i	0.0418742	−	0.0725282i	0.886203	+	0.463297i	$0.153334\pi$
$488$	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	−0.994614	−	0.103652i	$-0.966947\pi$
$499$	−13.1142	−	22.7144i	−0.587072	−	1.01684i	0.407542	−	0.913187i	$-0.366386\pi$
$500$		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	$-0.305943\pi$
$509$	−9.55960	−	16.5577i	−0.423722	−	0.733907i	−0.996300	+	0.0859425i	$0.972610\pi$
$510$		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	$-0.999904\pi$
$521$	−11.4068	+	19.7571i	−0.499739	+	0.865573i	0.500261	+	0.865875i	$0.333237\pi$
$522$		0			0
$523$	2.71011	−	1.56468i	0.118505	−	0.0684188i	−0.439576	−	0.898205i	$-0.644871\pi$
$523$	2.71011	−	1.56468i	0.118505	−	0.0684188i	0.558081	+	0.829787i	$0.311538\pi$
$524$	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	0.999806	−	0.0196894i	$-0.00626775\pi$
$541$	11.2308	+	19.4524i	0.482852	+	0.836323i	−0.516955	+	0.856013i	$0.672934\pi$
$542$	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	$-0.428236\pi$
$547$	10.4567			0.447097			0.223549	+	0.974693i	$0.428236\pi$
$548$	−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	−0.198564	−	0.980088i	$-0.563628\pi$
$557$	−27.0614	−	15.6239i	−1.14663	−	0.662006i	−0.948063	+	0.318082i	$0.896961\pi$
$558$		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	0.358210	+	0.933641i	$0.383387\pi$
$563$	−14.9354	+	25.8689i	−0.629452	+	1.09024i	−0.987662	+	0.156601i	$0.949946\pi$
$564$		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	$-0.459591\pi$
$569$	25.0218	−	14.4464i	1.04897	−	0.605623i	0.922361	+	0.386330i	$0.126257\pi$
$570$		0			0
$571$	3.68844	−	6.38856i	0.154356	−	0.267353i	−0.778468	−	0.627684i	$-0.784003\pi$
$571$	3.68844	−	6.38856i	0.154356	−	0.267353i	0.932824	+	0.360331i	$0.117336\pi$
$572$	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	$-0.456120\pi$
$577$	−15.6540	−	9.03785i	−0.651686	−	0.376251i	−0.789102	+	0.614263i	$0.789454\pi$
$578$	−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	0.784425	−	0.620224i	$-0.212958\pi$
$593$	−3.52896	−	6.11233i	−0.144917	−	0.251003i	−0.929342	+	0.369220i	$0.879625\pi$
$594$		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	$-0.301503\pi$
$599$	4.23198	+	2.44333i	0.172914	+	0.0998318i	−0.411045	+	0.911615i	$0.634836\pi$
$600$		0			0
$601$		−	36.1905i		−	1.47624i	−0.674669	−	0.738121i	$-0.735714\pi$
$601$		−	36.1905i		−	1.47624i	0.674669	−	0.738121i	$-0.264286\pi$
$602$	−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	$-0.778276\pi$
$607$	−14.6579	+	8.46272i	−0.594944	+	0.343491i	0.172106	+	0.985078i	$0.444943\pi$
$608$	−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	$-0.710724\pi$
$613$	9.30275	−	16.1128i	0.375735	−	0.650792i	0.990437	+	0.137968i	$0.0440571\pi$
$614$	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	$-0.645158\pi$
$617$		−	44.6022i		−	1.79562i	0.440384	−	0.897809i	$-0.354842\pi$
$618$		0			0
$619$	9.80175	+	5.65904i	0.393966	+	0.227456i	0.683877	−	0.729597i	$-0.260293\pi$
$619$	9.80175	+	5.65904i	0.393966	+	0.227456i	−0.289911	+	0.957053i	$0.593626\pi$
$620$		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	$-0.337043\pi$
$641$	−0.511044	−	0.295051i	−0.0201850	−	0.0116538i	−0.510059	+	0.860140i	$0.670376\pi$
$642$		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	−0.959121	−	0.282998i	$-0.908671\pi$
$647$	−5.96420	+	10.3303i	−0.234477	+	0.406126i	0.724644	+	0.689124i	$0.242004\pi$
$648$		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	−0.203887	−	0.978994i	$-0.565357\pi$
$653$	13.8503	−	7.99647i	0.542004	−	0.312926i	0.745891	+	0.666068i	$0.232024\pi$
$654$		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	−0.411030	−	0.911622i	$-0.634831\pi$
$661$	−36.1490	−	20.8706i	−1.40603	−	0.811773i	−0.995003	+	0.0998487i	$0.968164\pi$
$662$	−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	$-0.548777\pi$
$673$	−7.91950			−0.305274			−0.152637	+	0.988282i	$0.548777\pi$
$674$	−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	0.950129	−	0.311858i	$-0.100951\pi$
$677$	5.33360	+	9.23807i	0.204987	+	0.355048i	−0.745142	+	0.666906i	$0.767618\pi$
$678$		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	0.536158	−	0.844118i	$-0.319875\pi$
$683$	1.91327	+	1.10463i	0.0732093	+	0.0422674i	−0.462948	+	0.886385i	$0.653209\pi$
$684$		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	−0.644814	−	0.764339i	$-0.723065\pi$
$691$	−8.02498	+	4.63322i	−0.305284	+	0.176256i	0.339530	+	0.940595i	$0.389732\pi$
$692$	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	−0.994858	−	0.101279i	$-0.967707\pi$
$709$	−15.5805	−	26.9863i	−0.585139	−	1.01349i	0.409719	−	0.912212i	$-0.365627\pi$
$710$		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	$-0.220711\pi$
$719$	−4.53080	−	7.84758i	−0.168970	−	0.292665i	−0.938058	+	0.346478i	$0.887378\pi$
$720$		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	$-0.571394\pi$
$733$	13.8270	−	7.98301i	0.510711	−	0.294859i	0.733126	+	0.680093i	$0.238061\pi$
$734$	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	−0.964832	−	0.262866i	$-0.915332\pi$
$739$	−6.92575	+	11.9958i	−0.254768	+	0.441271i	0.710064	+	0.704137i	$0.248666\pi$
$740$		0			0
$741$		0			0
$742$	6.97881	+	3.25653i	0.256200	+	0.119551i
$743$		−	27.6801i		−	1.01548i	−0.861510	−	0.507741i	$-0.830481\pi$
$743$		−	27.6801i		−	1.01548i	0.861510	−	0.507741i	$-0.169519\pi$
$744$		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	−0.991541	−	0.129791i	$-0.958569\pi$
$751$	−16.6666	−	28.8674i	−0.608173	−	1.05339i	0.383368	−	0.923596i	$-0.374764\pi$
$752$	−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	$-0.440983\pi$
$757$	10.1442			0.368697			0.184348	+	0.982861i	$0.440983\pi$
$758$	−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	$-0.252520\pi$
$761$	−7.35057	−	12.7316i	−0.266458	−	0.461519i	−0.967945	+	0.251164i	$0.919187\pi$
$762$		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	$0.132962\pi$
$769$			22.4992i			0.811340i	−0.914020	+	0.405670i	$0.867038\pi$
$770$		0			0
$771$		0			0
$772$	−10.3876	−	17.9919i	−0.373859	−	0.647542i
$773$	−10.6266	+	18.4057i	−0.382211	+	0.662008i	−0.991378	−	0.131034i	$-0.958170\pi$
$773$	−10.6266	+	18.4057i	−0.382211	+	0.662008i	0.609167	+	0.793042i	$0.291504\pi$
$774$		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	$-0.242945\pi$
$787$	13.6131	+	7.85952i	0.485254	+	0.280162i	−0.237349	+	0.971424i	$0.576279\pi$
$788$	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	$-0.0518462\pi$
$809$	38.1053	+	22.0001i	1.33971	+	0.773483i	0.352947	+	0.935643i	$0.385180\pi$
$810$		0			0
$811$		−	44.9306i		−	1.57773i	−0.614567	−	0.788864i	$-0.710669\pi$
$811$		−	44.9306i		−	1.57773i	0.614567	−	0.788864i	$-0.289331\pi$
$812$	−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	$-0.751713\pi$
$821$	−13.1026	+	7.56481i	−0.457285	+	0.264014i	0.253617	+	0.967305i	$0.418380\pi$
$822$		0			0
$823$	−15.7898	+	27.3487i	−0.550397	+	0.953316i	0.447848	+	0.894109i	$0.352190\pi$
$823$	−15.7898	+	27.3487i	−0.550397	+	0.953316i	−0.998246	+	0.0592066i	$0.981143\pi$
$824$	−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	$0.320777\pi$
$827$			48.6368i			1.69127i	−0.533765	+	0.845633i	$0.679223\pi$
$828$		0			0
$829$	−40.4900	−	23.3769i	−1.40628	−	0.811914i	−0.411249	−	0.911523i	$-0.634907\pi$
$829$	−40.4900	−	23.3769i	−1.40628	−	0.811914i	−0.995027	+	0.0996095i	$0.968241\pi$
$830$		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	$-0.667563\pi$
$839$	−29.1067			−1.00488			−0.502438	+	0.864613i	$0.667563\pi$
$840$		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	−0.278290	−	0.960497i	$-0.589768\pi$
$857$	20.2776	−	35.1219i	0.692670	−	1.19974i	0.970960	−	0.239243i	$-0.0768991\pi$
$858$		0			0
$859$	−32.6686	+	18.8612i	−1.11464	+	0.643537i	−0.940027	−	0.341100i	$-0.889200\pi$
$859$	−32.6686	+	18.8612i	−1.11464	+	0.643537i	−0.174612	+	0.984637i	$0.555867\pi$
$860$		0			0
$861$		0			0
$862$	−15.6085			−0.531627
$863$	−22.2387	+	12.8395i	−0.757014	+	0.437062i	−0.828223	−	0.560399i	$-0.810648\pi$
$863$	−22.2387	+	12.8395i	−0.757014	+	0.437062i	0.0712087	+	0.997461i	$0.477314\pi$
$864$		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	$-0.270873\pi$
$877$	−9.52270	−	16.4938i	−0.321559	−	0.556956i	−0.980810	+	0.194967i	$0.937540\pi$
$878$	−0.760202	+	1.31671i	−0.0256556	+	0.0444367i
$879$		0			0
$880$		0			0
$881$	30.7115			1.03470			0.517349	−	0.855774i	$-0.326919\pi$
$881$	30.7115			1.03470			0.517349	+	0.855774i	$0.326919\pi$
$882$		0			0
$883$	36.8466			1.23999			0.619993	−	0.784607i	$-0.287135\pi$
$883$	36.8466			1.23999			0.619993	+	0.784607i	$0.287135\pi$
$884$	−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	−0.996691	−	0.0812870i	$-0.974097\pi$
$887$	−16.9386	−	29.3385i	−0.568742	−	0.985090i	0.427949	−	0.903803i	$-0.359236\pi$
$888$		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	$-0.827695\pi$
$907$	0.533407	−	0.923888i	0.0177115	−	0.0306772i	0.874745	+	0.484583i	$0.161029\pi$
$908$	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	0.804169	−	0.594401i	$-0.202611\pi$
$919$	−3.41594	−	5.91658i	−0.112681	−	0.195170i	−0.916851	+	0.399231i	$0.869277\pi$
$920$		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	−0.847063	−	0.531493i	$-0.821631\pi$
$929$	−26.9383	−	46.6585i	−0.883818	−	1.53082i	−0.0367547	−	0.999324i	$-0.511702\pi$
$930$		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	0.200389	−	0.979716i	$-0.435779\pi$
$941$	29.1006	−	50.4038i	0.948654	−	1.64312i	0.748265	−	0.663400i	$-0.230887\pi$
$942$		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	−0.183510	−	0.983018i	$-0.558746\pi$
$947$	17.7271	−	10.2347i	0.576053	−	0.332584i	0.759563	+	0.650434i	$0.225413\pi$
$948$		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	$0.0542642\pi$
$953$			10.4745i			0.339303i	−0.985504	+	0.169651i	$0.945736\pi$
$954$		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	$-0.743884\pi$
$967$	−43.1242			−1.38678			−0.693391	+	0.720562i	$0.743884\pi$
$968$	−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	$-0.123883\pi$
$971$	4.17572	+	7.23256i	0.134005	+	0.232104i	−0.791212	+	0.611542i	$0.790549\pi$
$972$		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	0.823080	−	0.567926i	$-0.192254\pi$
$977$	23.2171	+	13.4044i	0.742781	+	0.428845i	−0.0802983	+	0.996771i	$0.525587\pi$
$978$		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	−0.529630	−	0.848229i	$-0.677669\pi$
$983$	14.7287	−	25.5109i	0.469773	−	0.813671i	0.999403	+	0.0345581i	$0.0110024\pi$
$984$		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	−0.823522	−	0.567284i	$-0.807994\pi$
$991$	2.50334	−	4.33591i	0.0795211	−	0.137735i	0.903043	+	0.429549i	$0.141328\pi$
$992$	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	$-0.378238\pi$
$997$	−7.68960	−	4.43960i	−0.243532	−	0.140603i	−0.616799	+	0.787121i	$0.711571\pi$
$998$	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.1151.3		24
3.2	odd	2	inner	1575.2.bk.i.1151.10		24
5.2	odd	4		315.2.bb.b.269.3	yes	24
5.3	odd	4		315.2.bb.b.269.9	yes	24
5.4	even	2	inner	1575.2.bk.i.1151.9		24
7.5	odd	6	inner	1575.2.bk.i.26.10		24
15.2	even	4		315.2.bb.b.269.10	yes	24
15.8	even	4		315.2.bb.b.269.4	yes	24
15.14	odd	2	inner	1575.2.bk.i.1151.4		24
21.5	even	6	inner	1575.2.bk.i.26.3		24
35.3	even	12		2205.2.g.b.2204.5		24
35.12	even	12		315.2.bb.b.89.4	yes	24
35.17	even	12		2205.2.g.b.2204.17		24
35.18	odd	12		2205.2.g.b.2204.6		24
35.19	odd	6	inner	1575.2.bk.i.26.4		24
35.32	odd	12		2205.2.g.b.2204.18		24
35.33	even	12		315.2.bb.b.89.10	yes	24
105.17	odd	12		2205.2.g.b.2204.7		24
105.32	even	12		2205.2.g.b.2204.8		24
105.38	odd	12		2205.2.g.b.2204.19		24
105.47	odd	12		315.2.bb.b.89.9	yes	24
105.53	even	12		2205.2.g.b.2204.20		24
105.68	odd	12		315.2.bb.b.89.3	✓	24
105.89	even	6	inner	1575.2.bk.i.26.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bb.b.89.3	✓	24	105.68	odd	12
315.2.bb.b.89.4	yes	24	35.12	even	12
315.2.bb.b.89.9	yes	24	105.47	odd	12
315.2.bb.b.89.10	yes	24	35.33	even	12
315.2.bb.b.269.3	yes	24	5.2	odd	4
315.2.bb.b.269.4	yes	24	15.8	even	4
315.2.bb.b.269.9	yes	24	5.3	odd	4
315.2.bb.b.269.10	yes	24	15.2	even	4
1575.2.bk.i.26.3		24	21.5	even	6	inner
1575.2.bk.i.26.4		24	35.19	odd	6	inner
1575.2.bk.i.26.9		24	105.89	even	6	inner
1575.2.bk.i.26.10		24	7.5	odd	6	inner
1575.2.bk.i.1151.3		24	1.1	even	1	trivial
1575.2.bk.i.1151.4		24	15.14	odd	2	inner
1575.2.bk.i.1151.9		24	5.4	even	2	inner
1575.2.bk.i.1151.10		24	3.2	odd	2	inner
2205.2.g.b.2204.5		24	35.3	even	12
2205.2.g.b.2204.6		24	35.18	odd	12
2205.2.g.b.2204.7		24	105.17	odd	12
2205.2.g.b.2204.8		24	105.32	even	12
2205.2.g.b.2204.17		24	35.17	even	12
2205.2.g.b.2204.18		24	35.32	odd	12
2205.2.g.b.2204.19		24	105.38	odd	12
2205.2.g.b.2204.20		24	105.53	even	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)

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

Properties

Related objects

Downloads

Learn more