LMFDB - Embedded newform 1575.2.bk.i.26.2

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			26.2
Character	$\chi$	$=$	1575.26
Dual form			1575.2.bk.i.1151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.22514 - 1.28469i) q^{2} +(2.30084 + 3.98517i) q^{4} +(-0.151755 - 2.64140i) q^{7} -6.68468i q^{8} +(-4.88189 + 2.81856i) q^{11} +3.53537i q^{13} +(-3.05569 + 6.07244i) q^{14} +(-3.98605 + 6.90403i) q^{16} +(-2.67142 - 4.62703i) q^{17} +(1.24942 + 0.721351i) q^{19} +14.4839 q^{22} +(2.59686 + 1.49930i) q^{23} +(4.54184 - 7.86670i) q^{26} +(10.1772 - 6.68220i) q^{28} -2.19404i q^{29} +(1.31899 - 0.761520i) q^{31} +(6.16083 - 3.55696i) q^{32} +13.7277i q^{34} +(-0.546572 + 0.946690i) q^{37} +(-1.85342 - 3.21022i) q^{38} +6.52058 q^{41} +0.486125 q^{43} +(-22.4649 - 12.9701i) q^{44} +(-3.85226 - 6.67231i) q^{46} +(2.12816 - 3.68608i) q^{47} +(-6.95394 + 0.801688i) q^{49} +(-14.0891 + 8.13432i) q^{52} +(-3.48318 + 2.01102i) q^{53} +(-17.6569 + 1.01443i) q^{56} +(-2.81866 + 4.88206i) q^{58} +(5.70978 + 9.88963i) q^{59} +(6.06957 + 3.50427i) q^{61} -3.91326 q^{62} -2.33411 q^{64} +(-1.24490 - 2.15623i) q^{67} +(12.2930 - 21.2921i) q^{68} +8.13849i q^{71} +(-2.71761 + 1.56901i) q^{73} +(2.43240 - 1.40435i) q^{74} +6.63886i q^{76} +(8.18578 + 12.4673i) q^{77} +(6.40252 - 11.0895i) q^{79} +(-14.5092 - 8.37690i) q^{82} +6.77241 q^{83} +(-1.08170 - 0.624518i) q^{86} +(18.8412 + 32.6339i) q^{88} +(5.16513 - 8.94627i) q^{89} +(9.33831 - 0.536509i) q^{91} +13.7986i q^{92} +(-9.47093 + 5.46804i) q^{94} +14.7321i q^{97} +(16.5034 + 7.14976i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1575\mathbb{Z}\right)^\times$.

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

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 $

$2$	−2.22514	−	1.28469i	−1.57341	−	0.908411i	−0.995746	−	0.0921382i	$-0.970630\pi$
$2$	−2.22514	−	1.28469i	−1.57341	−	0.908411i	−0.577667	−	0.816272i	$-0.696037\pi$
$3$		0			0
$3$		0			0
$4$	2.30084	+	3.98517i	1.15042	+	1.99259i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.151755	−	2.64140i	−0.0573579	−	0.998354i
$7$	−0.151755	−	2.64140i	−0.0573579	−	0.998354i
$8$		−	6.68468i		−	2.36339i
$9$		0			0
$10$		0			0
$11$	−4.88189	+	2.81856i	−1.47195	+	0.849828i	−0.999503	−	0.0315336i	$-0.989961\pi$
$11$	−4.88189	+	2.81856i	−1.47195	+	0.849828i	−0.472442	+	0.881362i	$0.656628\pi$
$12$		0			0
$13$			3.53537i			0.980535i	0.871572	+	0.490267i	$0.163101\pi$
$13$			3.53537i			0.980535i	−0.871572	+	0.490267i	$0.836899\pi$
$14$	−3.05569	+	6.07244i	−0.816667	+	1.62293i
$15$		0			0
$16$	−3.98605	+	6.90403i	−0.996512	+	1.72601i
$17$	−2.67142	−	4.62703i	−0.647914	−	1.12222i	−0.983620	−	0.180253i	$-0.942308\pi$
$17$	−2.67142	−	4.62703i	−0.647914	−	1.12222i	0.335707	−	0.941967i	$-0.391025\pi$
$18$		0			0
$19$	1.24942	+	0.721351i	0.286636	+	0.165489i	0.636424	−	0.771340i	$-0.280413\pi$
$19$	1.24942	+	0.721351i	0.286636	+	0.165489i	−0.349788	+	0.936829i	$0.613746\pi$
$20$		0			0
$21$		0			0
$22$	14.4839			3.08797
$23$	2.59686	+	1.49930i	0.541484	+	0.312626i	0.745680	−	0.666304i	$-0.232125\pi$
$23$	2.59686	+	1.49930i	0.541484	+	0.312626i	−0.204196	+	0.978930i	$0.565458\pi$
$24$		0			0
$25$		0			0
$26$	4.54184	−	7.86670i	0.890728	−	1.54279i
$27$		0			0
$28$	10.1772	−	6.68220i	1.92332	−	1.26282i
$29$		−	2.19404i		−	0.407423i	−0.979031	−	0.203712i	$-0.934699\pi$
$29$		−	2.19404i		−	0.407423i	0.979031	−	0.203712i	$-0.0653005\pi$
$30$		0			0
$31$	1.31899	−	0.761520i	0.236898	−	0.136773i	−0.376852	−	0.926273i	$-0.622994\pi$
$31$	1.31899	−	0.761520i	0.236898	−	0.136773i	0.613750	+	0.789500i	$0.289660\pi$
$32$	6.16083	−	3.55696i	1.08909	−	0.628787i
$33$		0			0
$34$			13.7277i			2.35429i
$35$		0			0
$36$		0			0
$37$	−0.546572	+	0.946690i	−0.0898558	+	0.155635i	−0.907450	−	0.420160i	$-0.861974\pi$
$37$	−0.546572	+	0.946690i	−0.0898558	+	0.155635i	0.817594	+	0.575795i	$0.195307\pi$
$38$	−1.85342	−	3.21022i	−0.300665	−	0.520766i
$39$		0			0
$40$		0			0
$41$	6.52058			1.01834			0.509172	−	0.860665i	$-0.329952\pi$
$41$	6.52058			1.01834			0.509172	+	0.860665i	$0.329952\pi$
$42$		0			0
$43$	0.486125			0.0741333			0.0370667	−	0.999313i	$-0.488199\pi$
$43$	0.486125			0.0741333			0.0370667	+	0.999313i	$0.488199\pi$
$44$	−22.4649	−	12.9701i	−3.38671	−	1.95532i
$45$		0			0
$46$	−3.85226	−	6.67231i	−0.567985	−	0.983779i
$47$	2.12816	−	3.68608i	0.310424	−	0.537671i	−0.668030	−	0.744134i	$-0.732862\pi$
$47$	2.12816	−	3.68608i	0.310424	−	0.537671i	0.978454	+	0.206464i	$0.0661955\pi$
$48$		0			0
$49$	−6.95394	+	0.801688i	−0.993420	+	0.114527i
$50$		0			0
$51$		0			0
$52$	−14.0891	+	8.13432i	−1.95380	+	1.12803i
$53$	−3.48318	+	2.01102i	−0.478452	+	0.276235i	−0.719771	−	0.694211i	$-0.755753\pi$
$53$	−3.48318	+	2.01102i	−0.478452	+	0.276235i	0.241319	+	0.970446i	$0.422420\pi$
$54$		0			0
$55$		0			0
$56$	−17.6569	+	1.01443i	−2.35950	+	0.135559i
$57$		0			0
$58$	−2.81866	+	4.88206i	−0.370108	+	0.641046i
$59$	5.70978	+	9.88963i	0.743350	+	1.28752i	0.950962	+	0.309309i	$0.100098\pi$
$59$	5.70978	+	9.88963i	0.743350	+	1.28752i	−0.207612	+	0.978211i	$0.566569\pi$
$60$		0			0
$61$	6.06957	+	3.50427i	0.777129	+	0.448676i	0.835412	−	0.549624i	$-0.185229\pi$
$61$	6.06957	+	3.50427i	0.777129	+	0.448676i	−0.0582826	+	0.998300i	$0.518562\pi$
$62$	−3.91326			−0.496984
$63$		0			0
$64$	−2.33411			−0.291764
$65$		0			0
$66$		0			0
$67$	−1.24490	−	2.15623i	−0.152089	−	0.263425i	0.779907	−	0.625896i	$-0.215267\pi$
$67$	−1.24490	−	2.15623i	−0.152089	−	0.263425i	−0.931995	+	0.362471i	$0.881933\pi$
$68$	12.2930	−	21.2921i	1.49075	−	2.58205i
$69$		0			0
$70$		0			0
$71$			8.13849i			0.965861i	0.875659	+	0.482930i	$0.160428\pi$
$71$			8.13849i			0.965861i	−0.875659	+	0.482930i	$0.839572\pi$
$72$		0			0
$73$	−2.71761	+	1.56901i	−0.318072	+	0.183639i	−0.650533	−	0.759478i	$-0.725454\pi$
$73$	−2.71761	+	1.56901i	−0.318072	+	0.183639i	0.332461	+	0.943117i	$0.392121\pi$
$74$	2.43240	−	1.40435i	0.282761	−	0.163252i
$75$		0			0
$76$			6.63886i			0.761529i
$77$	8.18578	+	12.4673i	0.932856	+	1.42078i
$78$		0			0
$79$	6.40252	−	11.0895i	0.720340	−	1.24766i	−0.240524	−	0.970643i	$-0.577319\pi$
$79$	6.40252	−	11.0895i	0.720340	−	1.24766i	0.960864	−	0.277022i	$-0.0893474\pi$
$80$		0			0
$81$		0			0
$82$	−14.5092	−	8.37690i	−1.60228	−	0.925074i
$83$	6.77241			0.743368			0.371684	−	0.928359i	$-0.378780\pi$
$83$	6.77241			0.743368			0.371684	+	0.928359i	$0.378780\pi$
$84$		0			0
$85$		0			0
$86$	−1.08170	−	0.624518i	−0.116642	−	0.0673435i
$87$		0			0
$88$	18.8412	+	32.6339i	2.00848	+	3.47878i
$89$	5.16513	−	8.94627i	0.547503	−	0.948303i	−0.450942	−	0.892553i	$-0.648912\pi$
$89$	5.16513	−	8.94627i	0.547503	−	0.948303i	0.998445	−	0.0557494i	$-0.0177548\pi$
$90$		0			0
$91$	9.33831	−	0.536509i	0.978921	−	0.0562414i
$92$			13.7986i			1.43860i
$93$		0			0
$94$	−9.47093	+	5.46804i	−0.976852	+	0.563985i
$95$		0			0
$96$		0			0
$97$			14.7321i			1.49582i	0.663802	+	0.747908i	$0.268942\pi$
$97$			14.7321i			1.49582i	−0.663802	+	0.747908i	$0.731058\pi$
$98$	16.5034	+	7.14976i	1.66710	+	0.722235i
$99$		0			0
$100$		0			0
$101$	7.46683	+	12.9329i	0.742977	+	1.28687i	0.951134	+	0.308779i	$0.0999202\pi$
$101$	7.46683	+	12.9329i	0.742977	+	1.28687i	−0.208157	+	0.978095i	$0.566746\pi$
$102$		0			0
$103$	−3.39058	−	1.95755i	−0.334084	−	0.192883i	0.323569	−	0.946205i	$-0.395117\pi$
$103$	−3.39058	−	1.95755i	−0.334084	−	0.192883i	−0.657653	+	0.753321i	$0.728451\pi$
$104$	23.6328			2.31739
$105$		0			0
$106$	10.3341			1.00374
$107$	12.8363	+	7.41102i	1.24093	+	0.716450i	0.969283	−	0.245948i	$-0.0790991\pi$
$107$	12.8363	+	7.41102i	1.24093	+	0.716450i	0.271645	+	0.962398i	$0.412432\pi$
$108$		0			0
$109$	5.51932	+	9.55974i	0.528655	+	0.915657i	0.999442	+	0.0334099i	$0.0106367\pi$
$109$	5.51932	+	9.55974i	0.528655	+	0.915657i	−0.470787	+	0.882247i	$0.656030\pi$
$110$		0			0
$111$		0			0
$112$	18.8412	+	9.48101i	1.78032	+	0.895871i
$113$			7.54314i			0.709599i	0.934942	+	0.354799i	$0.115451\pi$
$113$			7.54314i			0.709599i	−0.934942	+	0.354799i	$0.884549\pi$
$114$		0			0
$115$		0			0
$116$	8.74363	−	5.04814i	0.811826	−	0.468708i
$117$		0			0
$118$		−	29.3411i		−	2.70107i
$119$	−11.8164	+	7.75844i	−1.08321	+	0.711215i
$120$		0			0
$121$	10.3886	−	17.9935i	0.944415	−	1.63577i
$122$	−9.00378	−	15.5950i	−0.815164	−	1.41191i
$123$		0			0
$124$	6.06957	+	3.50427i	0.545064	+	0.314693i
$125$		0			0
$126$		0			0
$127$	−3.93715			−0.349366			−0.174683	−	0.984625i	$-0.555890\pi$
$127$	−3.93715			−0.349366			−0.174683	+	0.984625i	$0.555890\pi$
$128$	−7.12793	−	4.11531i	−0.630026	−	0.363746i
$129$		0			0
$130$		0			0
$131$	−1.97399	+	3.41906i	−0.172469	+	0.298724i	−0.939282	−	0.343145i	$-0.888508\pi$
$131$	−1.97399	+	3.41906i	−0.172469	+	0.298724i	0.766814	+	0.641870i	$0.221841\pi$
$132$		0			0
$133$	1.71577	−	3.40967i	0.148776	−	0.295656i
$134$			6.39722i			0.552635i
$135$		0			0
$136$	−30.9302	+	17.8576i	−2.65225	+	1.53127i
$137$	4.90279	−	2.83062i	0.418873	−	0.241837i	−0.275722	−	0.961237i	$-0.588917\pi$
$137$	4.90279	−	2.83062i	0.418873	−	0.241837i	0.694595	+	0.719401i	$0.255584\pi$
$138$		0			0
$139$		−	23.3015i		−	1.97640i	−0.153158	−	0.988202i	$-0.548944\pi$
$139$		−	23.3015i		−	1.97640i	0.153158	−	0.988202i	$-0.451056\pi$
$140$		0			0
$141$		0			0
$142$	10.4554	−	18.1093i	0.877398	−	1.51970i
$143$	−9.96465	−	17.2593i	−0.833286	−	1.44329i
$144$		0			0
$145$		0			0
$146$	8.06275			0.667278
$147$		0			0
$148$	−5.03030			−0.413488
$149$	4.04926	+	2.33784i	0.331728	+	0.191523i	0.656608	−	0.754232i	$-0.271991\pi$
$149$	4.04926	+	2.33784i	0.331728	+	0.191523i	−0.324880	+	0.945755i	$0.605324\pi$
$150$		0			0
$151$	−0.930426	−	1.61155i	−0.0757170	−	0.131146i	0.825681	−	0.564138i	$-0.190791\pi$
$151$	−0.930426	−	1.61155i	−0.0757170	−	0.131146i	−0.901398	+	0.432992i	$0.857458\pi$
$152$	4.82201	−	8.35196i	0.391116	−	0.677433i
$153$		0			0
$154$	−2.19799	−	38.2576i	−0.177119	−	3.08289i
$155$		0			0
$156$		0			0
$157$	−5.68802	+	3.28398i	−0.453953	+	0.262090i	−0.709498	−	0.704707i	$-0.751078\pi$
$157$	−5.68802	+	3.28398i	−0.453953	+	0.262090i	0.255545	+	0.966797i	$0.417745\pi$
$158$	−28.4930	+	16.4505i	−2.26678	+	1.30873i
$159$		0			0
$160$		0			0
$161$	3.56616	−	7.08687i	0.281053	−	0.558524i
$162$		0			0
$163$	9.38762	−	16.2598i	0.735295	−	1.27357i	−0.219299	−	0.975658i	$-0.570377\pi$
$163$	9.38762	−	16.2598i	0.735295	−	1.27357i	0.954594	−	0.297910i	$-0.0962896\pi$
$164$	15.0028	+	25.9856i	1.17152	+	2.02914i
$165$		0			0
$166$	−15.0696	−	8.70042i	−1.16963	−	0.675284i
$167$	4.80581			0.371884			0.185942	−	0.982561i	$-0.440466\pi$
$167$	4.80581			0.371884			0.185942	+	0.982561i	$0.440466\pi$
$168$		0			0
$169$	0.501166			0.0385512
$170$		0			0
$171$		0			0
$172$	1.11849	+	1.93729i	0.0852844	+	0.147717i
$173$	1.68189	−	2.91312i	0.127872	−	0.221480i	−0.794980	−	0.606635i	$-0.792519\pi$
$173$	1.68189	−	2.91312i	0.127872	−	0.221480i	0.922852	+	0.385155i	$0.125852\pi$
$174$		0			0
$175$		0			0
$176$		−	44.9396i		−	3.38745i
$177$		0			0
$178$	−22.9863	+	13.2712i	−1.72290	+	0.994715i
$179$	9.63782	−	5.56440i	0.720365	−	0.415903i	−0.0945223	−	0.995523i	$-0.530132\pi$
$179$	9.63782	−	5.56440i	0.720365	−	0.415903i	0.814887	+	0.579620i	$0.196799\pi$
$180$		0			0
$181$		−	2.19549i		−	0.163190i	−0.996666	−	0.0815949i	$-0.973999\pi$
$181$		−	2.19549i		−	0.163190i	0.996666	−	0.0815949i	$-0.0260014\pi$
$182$	−21.4683	−	10.8030i	−1.59134	−	0.800771i
$183$		0			0
$184$	10.0223	−	17.3592i	0.738857	−	1.27974i
$185$		0			0
$186$		0			0
$187$	26.0831	+	15.0591i	1.90739	+	1.10123i
$188$	19.5862			1.42847
$189$		0			0
$190$		0			0
$191$	−8.62053	−	4.97707i	−0.623760	−	0.360128i	0.154572	−	0.987982i	$-0.450600\pi$
$191$	−8.62053	−	4.97707i	−0.623760	−	0.360128i	−0.778331	+	0.627854i	$0.783934\pi$
$192$		0			0
$193$	12.4747	+	21.6068i	0.897948	+	1.55529i	0.830114	+	0.557594i	$0.188275\pi$
$193$	12.4747	+	21.6068i	0.897948	+	1.55529i	0.0678339	+	0.997697i	$0.478391\pi$
$194$	18.9261	−	32.7810i	1.35882	−	2.35354i
$195$		0			0
$196$	−19.1948	−	25.8681i	−1.37105	−	1.84772i
$197$		−	19.1023i		−	1.36098i	−0.732755	−	0.680492i	$-0.761766\pi$
$197$		−	19.1023i		−	1.36098i	0.732755	−	0.680492i	$-0.238234\pi$
$198$		0			0
$199$	−1.59632	+	0.921633i	−0.113160	+	0.0653329i	−0.555512	−	0.831509i	$-0.687478\pi$
$199$	−1.59632	+	0.921633i	−0.113160	+	0.0653329i	0.442352	+	0.896842i	$0.354144\pi$
$200$		0			0
$201$		0			0
$202$		−	38.3701i		−	2.69971i
$203$	−5.79533	+	0.332956i	−0.406753	+	0.0233689i
$204$		0			0
$205$		0			0
$206$	5.02968	+	8.71167i	0.350435	+	0.606971i
$207$		0			0
$208$	−24.4083	−	14.0921i	−1.69241	−	0.977114i
$209$	−8.13269			−0.562550
$210$		0			0
$211$	−9.77713			−0.673085			−0.336543	−	0.941668i	$-0.609258\pi$
$211$	−9.77713			−0.673085			−0.336543	+	0.941668i	$0.609258\pi$
$212$	−16.0285	−	9.25406i	−1.10084	−	0.635571i
$213$		0			0
$214$	−19.0417	−	32.9811i	−1.30166	−	2.25454i
$215$		0			0
$216$		0			0
$217$	−2.21164	−	3.36841i	−0.150136	−	0.228663i
$218$		−	28.3624i		−	1.92094i
$219$		0			0
$220$		0			0
$221$	16.3583	−	9.44444i	1.10038	−	0.635302i
$222$		0			0
$223$			7.84782i			0.525529i	0.964860	+	0.262765i	$0.0846342\pi$
$223$			7.84782i			0.525529i	−0.964860	+	0.262765i	$0.915366\pi$
$224$	−10.3303	−	15.7334i	−0.690220	−	1.05123i
$225$		0			0
$226$	9.69057	−	16.7846i	0.644607	−	1.11649i
$227$	0.274741	+	0.475865i	0.0182352	+	0.0315843i	0.874999	−	0.484125i	$-0.160862\pi$
$227$	0.274741	+	0.475865i	0.0182352	+	0.0315843i	−0.856764	+	0.515709i	$0.827529\pi$
$228$		0			0
$229$	18.5833	+	10.7291i	1.22802	+	0.708998i	0.966616	−	0.256231i	$-0.0824807\pi$
$229$	18.5833	+	10.7291i	1.22802	+	0.708998i	0.261406	+	0.965229i	$0.415814\pi$
$230$		0			0
$231$		0			0
$232$	−14.6665			−0.962902
$233$	16.2522	+	9.38319i	1.06471	+	0.614713i	0.926733	−	0.375722i	$-0.122605\pi$
$233$	16.2522	+	9.38319i	1.06471	+	0.614713i	0.137982	+	0.990435i	$0.455939\pi$
$234$		0			0
$235$		0			0
$236$	−26.2746	+	45.5089i	−1.71033	+	2.96238i
$237$		0			0
$238$	36.2604	−	2.08325i	2.35041	−	0.135037i
$239$		−	7.35866i		−	0.475992i	−0.971266	−	0.237996i	$-0.923509\pi$
$239$		−	7.35866i		−	0.475992i	0.971266	−	0.237996i	$-0.0764905\pi$
$240$		0			0
$241$	23.8467	−	13.7679i	1.53610	−	0.886868i	0.537040	−	0.843557i	$-0.319543\pi$
$241$	23.8467	−	13.7679i	1.53610	−	0.886868i	0.999062	−	0.0433114i	$-0.0137908\pi$
$242$	−46.2321	+	26.6921i	−2.97191	+	1.71583i
$243$		0			0
$244$			32.2511i			2.06466i
$245$		0			0
$246$		0			0
$247$	−2.55024	+	4.41715i	−0.162268	+	0.281057i
$248$	−5.09052	−	8.81704i	−0.323248	−	0.559883i
$249$		0			0
$250$		0			0
$251$	22.4204			1.41516			0.707582	−	0.706631i	$-0.249786\pi$
$251$	22.4204			1.41516			0.707582	+	0.706631i	$0.249786\pi$
$252$		0			0
$253$	−16.9035			−1.06271
$254$	8.76072	+	5.05801i	0.549697	+	0.317368i
$255$		0			0
$256$	12.9079	+	22.3571i	0.806743	+	1.39732i
$257$	−8.56373	+	14.8328i	−0.534191	+	0.925246i	0.465011	+	0.885305i	$0.346050\pi$
$257$	−8.56373	+	14.8328i	−0.534191	+	0.925246i	−0.999202	+	0.0399409i	$0.987283\pi$
$258$		0			0
$259$	2.58353	+	1.30005i	0.160533	+	0.0807810i
$260$		0			0
$261$		0			0
$262$	8.78483	−	5.07193i	0.542729	−	0.313345i
$263$	−1.40092	+	0.808821i	−0.0863844	+	0.0498741i	−0.542570	−	0.840011i	$-0.682549\pi$
$263$	−1.40092	+	0.808821i	−0.0863844	+	0.0498741i	0.456186	+	0.889885i	$0.349215\pi$
$264$		0			0
$265$		0			0
$266$	−8.19819	+	5.38278i	−0.502664	+	0.330040i
$267$		0			0
$268$	5.72862	−	9.92226i	0.349931	−	0.606099i
$269$	5.84048	+	10.1160i	0.356101	+	0.616784i	0.987306	−	0.158832i	$-0.0507727\pi$
$269$	5.84048	+	10.1160i	0.356101	+	0.616784i	−0.631205	+	0.775616i	$0.717439\pi$
$270$		0			0
$271$	5.05562	+	2.91886i	0.307107	+	0.177308i	0.645631	−	0.763649i	$-0.276594\pi$
$271$	5.05562	+	2.91886i	0.307107	+	0.177308i	−0.338524	+	0.940958i	$0.609928\pi$
$272$	42.5936			2.58261
$273$		0			0
$274$	−14.5459			−0.878748
$275$		0			0
$276$		0			0
$277$	8.29998	+	14.3760i	0.498698	+	0.863770i	0.999999	−	0.00150328i	$-0.000478509\pi$
$277$	8.29998	+	14.3760i	0.498698	+	0.863770i	−0.501301	+	0.865273i	$0.667145\pi$
$278$	−29.9351	+	51.8491i	−1.79539	+	3.10970i
$279$		0			0
$280$		0			0
$281$			20.4255i			1.21848i	0.792984	+	0.609242i	$0.208526\pi$
$281$			20.4255i			1.21848i	−0.792984	+	0.609242i	$0.791474\pi$
$282$		0			0
$283$	−5.74423	+	3.31643i	−0.341459	+	0.197141i	−0.660917	−	0.750459i	$-0.729832\pi$
$283$	−5.74423	+	3.31643i	−0.341459	+	0.197141i	0.319458	+	0.947600i	$0.396499\pi$
$284$	−32.4333	+	18.7254i	−1.92456	+	1.11115i
$285$		0			0
$286$			51.2058i			3.02786i
$287$	−0.989529	−	17.2234i	−0.0584100	−	1.01667i
$288$		0			0
$289$	−5.77293	+	9.99901i	−0.339584	+	0.588177i
$290$		0			0
$291$		0			0
$292$	−12.5055	−	7.22008i	−0.731832	−	0.422523i
$293$	16.3716			0.956437			0.478219	−	0.878241i	$-0.341283\pi$
$293$	16.3716			0.956437			0.478219	+	0.878241i	$0.341283\pi$
$294$		0			0
$295$		0			0
$296$	6.32832	+	3.65366i	0.367826	+	0.212365i
$297$		0			0
$298$	−6.00678	−	10.4040i	−0.347963	−	0.602690i
$299$	−5.30058	+	9.18087i	−0.306540	+	0.530944i
$300$		0			0
$301$	−0.0737717	−	1.28405i	−0.00425213	−	0.0740113i
$302$			4.78122i			0.275129i
$303$		0			0
$304$	−9.96047	+	5.75068i	−0.571272	+	0.329824i
$305$		0			0
$306$		0			0
$307$		−	25.5071i		−	1.45576i	−0.685702	−	0.727882i	$-0.740505\pi$
$307$		−	25.5071i		−	1.45576i	0.685702	−	0.727882i	$-0.259495\pi$
$308$	−30.8500	+	61.3069i	−1.75784	+	3.49329i
$309$		0			0
$310$		0			0
$311$	−15.5180	−	26.8780i	−0.879946	−	1.52411i	−0.851399	−	0.524519i	$-0.824245\pi$
$311$	−15.5180	−	26.8780i	−0.879946	−	1.52411i	−0.0285476	−	0.999592i	$-0.509088\pi$
$312$		0			0
$313$	−13.0310	−	7.52345i	−0.736556	−	0.425251i	0.0842599	−	0.996444i	$-0.473147\pi$
$313$	−13.0310	−	7.52345i	−0.736556	−	0.425251i	−0.820816	+	0.571193i	$0.806481\pi$
$314$	16.8755			0.952341
$315$		0			0
$316$	58.9247			3.31477
$317$	13.4937	+	7.79061i	0.757884	+	0.437564i	0.828535	−	0.559937i	$-0.189175\pi$
$317$	13.4937	+	7.79061i	0.757884	+	0.437564i	−0.0706518	+	0.997501i	$0.522508\pi$
$318$		0			0
$319$	6.18404	+	10.7111i	0.346240	+	0.599705i
$320$		0			0
$321$		0			0
$322$	−17.0396	+	11.1879i	−0.949581	+	0.623477i
$323$		−	7.70812i		−	0.428891i
$324$		0			0
$325$		0			0
$326$	−41.7776	+	24.1203i	−2.31385	+	1.33590i
$327$		0			0
$328$		−	43.5880i		−	2.40675i
$329$	−10.0594	−	5.06194i	−0.554591	−	0.279074i
$330$		0			0
$331$	−6.83411	+	11.8370i	−0.375637	+	0.650622i	−0.990422	−	0.138073i	$-0.955909\pi$
$331$	−6.83411	+	11.8370i	−0.375637	+	0.650622i	0.614785	+	0.788694i	$0.289243\pi$
$332$	15.5822	+	26.9892i	0.855186	+	1.48123i
$333$		0			0
$334$	−10.6936	−	6.17395i	−0.585128	−	0.337824i
$335$		0			0
$336$		0			0
$337$	−22.8443			−1.24441			−0.622204	−	0.782855i	$-0.713763\pi$
$337$	−22.8443			−1.24441			−0.622204	+	0.782855i	$0.713763\pi$
$338$	−1.11516	−	0.643841i	−0.0606570	−	0.0350203i
$339$		0			0
$340$		0			0
$341$	−4.29278	+	7.43531i	−0.232467	+	0.402645i
$342$		0			0
$343$	3.17287	+	18.2464i	0.171319	+	0.985216i
$344$		−	3.24959i		−	0.175206i
$345$		0			0
$346$	−7.48488	+	4.32140i	−0.402390	+	0.232320i
$347$	16.9956	−	9.81241i	0.912372	−	0.526758i	0.0311781	−	0.999514i	$-0.490074\pi$
$347$	16.9956	−	9.81241i	0.912372	−	0.526758i	0.881193	+	0.472756i	$0.156741\pi$
$348$		0			0
$349$			6.14050i			0.328693i	0.986403	+	0.164347i	$0.0525516\pi$
$349$			6.14050i			0.328693i	−0.986403	+	0.164347i	$0.947448\pi$
$350$		0			0
$351$		0			0
$352$	−20.0510	+	34.7293i	−1.06872	+	1.85108i
$353$	12.0021	+	20.7882i	0.638805	+	1.10644i	0.985695	+	0.168537i	$0.0539043\pi$
$353$	12.0021	+	20.7882i	0.638805	+	1.10644i	−0.346890	+	0.937906i	$0.612762\pi$
$354$		0			0
$355$		0			0
$356$	47.5366			2.51943
$357$		0			0
$358$	−28.5940			−1.51124
$359$	14.6798	+	8.47541i	0.774773	+	0.447315i	0.834575	−	0.550895i	$-0.185714\pi$
$359$	14.6798	+	8.47541i	0.774773	+	0.447315i	−0.0598018	+	0.998210i	$0.519047\pi$
$360$		0			0
$361$	−8.45930	−	14.6519i	−0.445227	−	0.771155i
$362$	−2.82052	+	4.88529i	−0.148243	+	0.256765i
$363$		0			0
$364$	23.6240	+	35.9803i	1.23824	+	1.88588i
$365$		0			0
$366$		0			0
$367$	−30.3140	+	17.5018i	−1.58238	+	0.913587i	−0.587869	+	0.808956i	$0.700033\pi$
$367$	−30.3140	+	17.5018i	−1.58238	+	0.913587i	−0.994511	+	0.104631i	$0.966634\pi$
$368$	−20.7024	+	11.9526i	−1.07919	+	0.623070i
$369$		0			0
$370$		0			0
$371$	5.84048	+	8.89529i	0.303223	+	0.461820i
$372$		0			0
$373$	2.99576	−	5.18881i	0.155115	−	0.268667i	−0.777986	−	0.628282i	$-0.783759\pi$
$373$	2.99576	−	5.18881i	0.155115	−	0.268667i	0.933101	+	0.359615i	$0.117092\pi$
$374$	−38.6924	−	67.0173i	−2.00074	−	3.46538i
$375$		0			0
$376$	−24.6403	−	14.2261i	−1.27073	−	0.733655i
$377$	7.75675			0.399493
$378$		0			0
$379$	3.12842			0.160696			0.0803481	−	0.996767i	$-0.474397\pi$
$379$	3.12842			0.160696			0.0803481	+	0.996767i	$0.474397\pi$
$380$		0			0
$381$		0			0
$382$	12.7879	+	22.1494i	0.654288	+	1.13326i
$383$	8.48295	−	14.6929i	0.433459	−	0.750772i	−0.563710	−	0.825973i	$-0.690626\pi$
$383$	8.48295	−	14.6929i	0.433459	−	0.750772i	0.997168	+	0.0752006i	$0.0239597\pi$
$384$		0			0
$385$		0			0
$386$		−	64.1043i		−	3.26282i
$387$		0			0
$388$	−58.7099	+	33.8961i	−2.98054	+	1.72082i
$389$	−0.389255	+	0.224737i	−0.0197360	+	0.0113946i	−0.509836	−	0.860272i	$-0.670294\pi$
$389$	−0.389255	+	0.224737i	−0.0197360	+	0.0113946i	0.490100	+	0.871666i	$0.336960\pi$
$390$		0			0
$391$		−	16.0210i		−	0.810218i
$392$	5.35903	+	46.4849i	0.270672	+	2.34784i
$393$		0			0
$394$	−24.5405	+	42.5054i	−1.23633	+	2.14139i
$395$		0			0
$396$		0			0
$397$	19.6870	+	11.3663i	0.988064	+	0.570459i	0.904695	−	0.426060i	$-0.140099\pi$
$397$	19.6870	+	11.3663i	0.988064	+	0.570459i	0.0833689	+	0.996519i	$0.473432\pi$
$398$	4.73604			0.237396
$399$		0			0
$400$		0			0
$401$	−8.41308	−	4.85729i	−0.420129	−	0.242562i	0.275004	−	0.961443i	$-0.411321\pi$
$401$	−8.41308	−	4.85729i	−0.420129	−	0.242562i	−0.695132	+	0.718882i	$0.744654\pi$
$402$		0			0
$403$	2.69225	+	4.66312i	0.134111	+	0.232287i
$404$	−34.3599	+	59.5132i	−1.70947	+	2.96089i
$405$		0			0
$406$	13.3232	+	6.70431i	0.661219	+	0.332729i
$407$		−	6.16218i		−	0.305448i
$408$		0			0
$409$	−3.51628	+	2.03013i	−0.173869	+	0.100383i	−0.584409	−	0.811459i	$-0.698674\pi$
$409$	−3.51628	+	2.03013i	−0.173869	+	0.100383i	0.410540	+	0.911843i	$0.365340\pi$
$410$		0			0
$411$		0			0
$412$		−	18.0161i		−	0.887587i
$413$	25.2559	−	16.5826i	1.24276	−	0.815976i
$414$		0			0
$415$		0			0
$416$	12.5752	+	21.7808i	0.616548	+	1.06789i
$417$		0			0
$418$	18.0964	+	10.4480i	0.885124	+	0.511026i
$419$	−20.9314			−1.02257			−0.511283	−	0.859412i	$-0.670830\pi$
$419$	−20.9314			−1.02257			−0.511283	+	0.859412i	$0.670830\pi$
$420$		0			0
$421$	−19.7795			−0.963992			−0.481996	−	0.876173i	$-0.660088\pi$
$421$	−19.7795			−0.963992			−0.481996	+	0.876173i	$0.660088\pi$
$422$	21.7555	+	12.5605i	1.05904	+	0.611438i
$423$		0			0
$424$	13.4430	+	23.2840i	0.652851	+	1.13077i
$425$		0			0
$426$		0			0
$427$	8.33508	−	16.5639i	0.403363	−	0.801585i
$428$			68.2062i			3.29687i
$429$		0			0
$430$		0			0
$431$	−9.23148	+	5.32980i	−0.444665	+	0.256727i	−0.705574	−	0.708636i	$-0.749311\pi$
$431$	−9.23148	+	5.32980i	−0.444665	+	0.256727i	0.260910	+	0.965363i	$0.415978\pi$
$432$		0			0
$433$		−	21.2351i		−	1.02050i	−0.860028	−	0.510248i	$-0.829554\pi$
$433$		−	21.2351i		−	1.02050i	0.860028	−	0.510248i	$-0.170446\pi$
$434$	0.593855	+	10.3365i	0.0285060	+	0.496166i
$435$		0			0
$436$	−25.3981	+	43.9908i	−1.21635	+	2.10678i
$437$	2.16304	+	3.74650i	0.103472	+	0.179220i
$438$		0			0
$439$	−18.5707	−	10.7218i	−0.886333	−	0.511725i	−0.0135918	−	0.999908i	$-0.504327\pi$
$439$	−18.5707	−	10.7218i	−0.886333	−	0.511725i	−0.872741	+	0.488183i	$0.837660\pi$
$440$		0			0
$441$		0			0
$442$	−48.5326			−2.30846
$443$	0.148064	+	0.0854851i	0.00703475	+	0.00406152i	0.503513	−	0.863988i	$-0.332041\pi$
$443$	0.148064	+	0.0854851i	0.00703475	+	0.00406152i	−0.496478	+	0.868049i	$0.665374\pi$
$444$		0			0
$445$		0			0
$446$	10.0820	−	17.4625i	0.477396	−	0.826874i
$447$		0			0
$448$	0.354212	+	6.16531i	0.0167350	+	0.291283i
$449$		−	9.38752i		−	0.443025i	−0.975158	−	0.221512i	$-0.928901\pi$
$449$		−	9.38752i		−	0.443025i	0.975158	−	0.221512i	$-0.0710993\pi$
$450$		0			0
$451$	−31.8328	+	18.3786i	−1.49895	+	0.865417i
$452$	−30.0607	+	17.3556i	−1.41394	+	0.816337i
$453$		0			0
$454$		−	1.41182i		−	0.0662602i
$455$		0			0
$456$		0			0
$457$	8.44623	−	14.6293i	0.395098	−	0.684330i	−0.598016	−	0.801484i	$-0.704044\pi$
$457$	8.44623	−	14.6293i	0.395098	−	0.684330i	0.993114	+	0.117155i	$0.0373774\pi$
$458$	−27.5670	−	47.7475i	−1.28812	−	2.23110i
$459$		0			0
$460$		0			0
$461$	−31.0360			−1.44549			−0.722746	−	0.691113i	$-0.757120\pi$
$461$	−31.0360			−1.44549			−0.722746	+	0.691113i	$0.757120\pi$
$462$		0			0
$463$	11.9434			0.555055			0.277528	−	0.960718i	$-0.410485\pi$
$463$	11.9434			0.555055			0.277528	+	0.960718i	$0.410485\pi$
$464$	15.1477	+	8.74555i	0.703216	+	0.406002i
$465$		0			0
$466$	−24.1089	−	41.7579i	−1.11682	−	1.93440i
$467$	−17.2803	+	29.9304i	−0.799638	+	1.38501i	0.120215	+	0.992748i	$0.461642\pi$
$467$	−17.2803	+	29.9304i	−0.799638	+	1.38501i	−0.919852	+	0.392265i	$0.871692\pi$
$468$		0			0
$469$	−5.50653	+	3.61549i	−0.254268	+	0.166948i
$470$		0			0
$471$		0			0
$472$	66.1090	−	38.1681i	3.04292	−	1.75683i
$473$	−2.37321	+	1.37017i	−0.109120	+	0.0630006i
$474$		0			0
$475$		0			0
$476$	−58.1064	−	29.2395i	−2.66330	−	1.34019i
$477$		0			0
$478$	−9.45357	+	16.3741i	−0.432396	+	0.748932i
$479$	−1.48615	−	2.57409i	−0.0679040	−	0.117613i	0.830074	−	0.557653i	$-0.188298\pi$
$479$	−1.48615	−	2.57409i	−0.0679040	−	0.117613i	−0.897978	+	0.440039i	$0.854964\pi$
$480$		0			0
$481$	−3.34690	−	1.93233i	−0.152605	−	0.0881068i
$482$	−70.7498			−3.22256
$483$		0			0
$484$	95.6097			4.34589
$485$		0			0
$486$		0			0
$487$	11.3562	+	19.6695i	0.514598	+	0.891310i	0.999857	+	0.0169394i	$0.00539222\pi$
$487$	11.3562	+	19.6695i	0.514598	+	0.891310i	−0.485258	+	0.874371i	$0.661274\pi$
$488$	23.4249	−	40.5732i	1.06040	−	1.83666i
$489$		0			0
$490$		0			0
$491$		−	13.0036i		−	0.586846i	−0.955983	−	0.293423i	$-0.905206\pi$
$491$		−	13.0036i		−	0.586846i	0.955983	−	0.293423i	$-0.0947944\pi$
$492$		0			0
$493$	−10.1519	+	5.86120i	−0.457219	+	0.263975i
$494$	11.3493	−	6.55253i	0.510630	−	0.294812i
$495$		0			0
$496$			12.1418i			0.545184i
$497$	21.4970	−	1.23505i	0.964271	−	0.0553997i
$498$		0			0
$499$	−10.8039	+	18.7129i	−0.483648	+	0.837702i	−0.999824	−	0.0187802i	$-0.994022\pi$
$499$	−10.8039	+	18.7129i	−0.483648	+	0.837702i	0.516176	+	0.856483i	$0.327355\pi$
$500$		0			0
$501$		0			0
$502$	−49.8886	−	28.8032i	−2.22664	−	1.28555i
$503$	−32.4125			−1.44520			−0.722601	−	0.691265i	$-0.757054\pi$
$503$	−32.4125			−1.44520			−0.722601	+	0.691265i	$0.757054\pi$
$504$		0			0
$505$		0			0
$506$	37.6126	+	21.7157i	1.67209	+	0.965379i
$507$		0			0
$508$	−9.05875	−	15.6902i	−0.401917	−	0.696141i
$509$	−18.2802	+	31.6622i	−0.810255	+	1.40340i	0.102430	+	0.994740i	$0.467338\pi$
$509$	−18.2802	+	31.6622i	−0.810255	+	1.40340i	−0.912685	+	0.408663i	$0.865995\pi$
$510$		0			0
$511$	4.55679	+	6.94017i	0.201580	+	0.307015i
$512$		−	49.8691i		−	2.20392i
$513$		0			0
$514$	38.1110	−	22.0034i	1.68101	−	0.970529i
$515$		0			0
$516$		0			0
$517$			23.9934i			1.05523i
$518$	−4.07856	−	6.21181i	−0.179202	−	0.272931i
$519$		0			0
$520$		0			0
$521$	9.43608	+	16.3438i	0.413402	+	0.716033i	0.995259	−	0.0972577i	$-0.0310071\pi$
$521$	9.43608	+	16.3438i	0.413402	+	0.716033i	−0.581857	+	0.813291i	$0.697674\pi$
$522$		0			0
$523$	24.4434	+	14.1124i	1.06884	+	0.617092i	0.927863	−	0.372921i	$-0.121644\pi$
$523$	24.4434	+	14.1124i	1.06884	+	0.617092i	0.140972	+	0.990014i	$0.454977\pi$
$524$	−18.1674			−0.793645
$525$		0			0
$526$	4.15633			0.181225
$527$	−7.04715	−	4.06867i	−0.306979	−	0.177234i
$528$		0			0
$529$	−7.00420	−	12.1316i	−0.304530	−	0.527462i
$530$		0			0
$531$		0			0
$532$	17.5358	−	1.00748i	0.760275	−	0.0436797i
$533$			23.0527i			0.998521i
$534$		0			0
$535$		0			0
$536$	−14.4137	+	8.32175i	−0.622577	+	0.359445i
$537$		0			0
$538$		−	30.0128i		−	1.29394i
$539$	31.6888	−	23.5139i	1.36493	−	1.01281i
$540$		0			0
$541$	−14.2269	+	24.6417i	−0.611661	+	1.05943i	0.379299	+	0.925274i	$0.376165\pi$
$541$	−14.2269	+	24.6417i	−0.611661	+	1.05943i	−0.990960	+	0.134154i	$0.957168\pi$
$542$	−7.49965	−	12.9898i	−0.322138	−	0.557959i
$543$		0			0
$544$	−32.9163	−	19.0042i	−1.41127	−	0.814799i
$545$		0			0
$546$		0			0
$547$	21.9338			0.937820			0.468910	−	0.883246i	$-0.344647\pi$
$547$	21.9338			0.937820			0.468910	+	0.883246i	$0.344647\pi$
$548$	22.5610	+	13.0256i	0.963760	+	0.556427i
$549$		0			0
$550$		0			0
$551$	1.58268	−	2.74127i	0.0674242	−	0.116782i
$552$		0			0
$553$	−30.2633	−	15.2287i	−1.28693	−	0.647590i
$554$		−	42.6515i		−	1.81209i
$555$		0			0
$556$	92.8603	−	53.6129i	3.93815	−	2.27369i
$557$	21.1601	−	12.2168i	0.896583	−	0.517643i	0.0204933	−	0.999790i	$-0.493476\pi$
$557$	21.1601	−	12.2168i	0.896583	−	0.517643i	0.876090	+	0.482147i	$0.160143\pi$
$558$		0			0
$559$			1.71863i			0.0726903i
$560$		0			0
$561$		0			0
$562$	26.2404	−	45.4497i	1.10688	−	1.91718i
$563$	−10.6570	−	18.4585i	−0.449139	−	0.777932i	0.549191	−	0.835697i	$-0.314936\pi$
$563$	−10.6570	−	18.4585i	−0.449139	−	0.777932i	−0.998330	+	0.0577647i	$0.981603\pi$
$564$		0			0
$565$		0			0
$566$	17.0423			0.716341
$567$		0			0
$568$	54.4032			2.28271
$569$	−24.1707	−	13.9549i	−1.01329	−	0.585022i	−0.101135	−	0.994873i	$-0.532247\pi$
$569$	−24.1707	−	13.9549i	−1.01329	−	0.585022i	−0.912152	+	0.409851i	$0.865581\pi$
$570$		0			0
$571$	23.1936	+	40.1725i	0.970622	+	1.68117i	0.693685	+	0.720279i	$0.255986\pi$
$571$	23.1936	+	40.1725i	0.970622	+	1.68117i	0.276937	+	0.960888i	$0.410681\pi$
$572$	45.8541	−	79.4217i	1.91726	−	3.32079i
$573$		0			0
$574$	−19.9249	+	39.5958i	−0.831648	+	1.65270i
$575$		0			0
$576$		0			0
$577$	−28.0881	+	16.2167i	−1.16932	+	0.675108i	−0.953520	−	0.301329i	$-0.902570\pi$
$577$	−28.0881	+	16.2167i	−1.16932	+	0.675108i	−0.215801	+	0.976437i	$0.569236\pi$
$578$	25.6912	−	14.8328i	1.06861	−	0.616964i
$579$		0			0
$580$		0			0
$581$	−1.02774	−	17.8886i	−0.0426380	−	0.742145i
$582$		0			0
$583$	11.3363	−	19.6351i	0.469504	−	0.813204i
$584$	10.4883	+	18.1663i	0.434011	+	0.751728i
$585$		0			0
$586$	−36.4291	−	21.0323i	−1.50487	−	0.868838i
$587$	−0.790380			−0.0326225			−0.0163112	−	0.999867i	$-0.505192\pi$
$587$	−0.790380			−0.0326225			−0.0163112	+	0.999867i	$0.505192\pi$
$588$		0			0
$589$	2.19729			0.0905379
$590$		0			0
$591$		0			0
$592$	−4.35732	−	7.54710i	−0.179085	−	0.310184i
$593$	−10.1424	+	17.5672i	−0.416499	+	0.721397i	−0.995585	−	0.0938695i	$-0.970076\pi$
$593$	−10.1424	+	17.5672i	−0.416499	+	0.721397i	0.579086	+	0.815267i	$0.303410\pi$
$594$		0			0
$595$		0			0
$596$			21.5160i			0.881328i
$597$		0			0
$598$	23.5891	−	13.6192i	0.964630	−	0.556929i
$599$	8.77781	−	5.06787i	0.358652	−	0.207068i	−0.309837	−	0.950790i	$-0.600275\pi$
$599$	8.77781	−	5.06787i	0.358652	−	0.207068i	0.668489	+	0.743722i	$0.266941\pi$
$600$		0			0
$601$			35.6657i			1.45483i	0.686196	+	0.727417i	$0.259279\pi$
$601$			35.6657i			1.45483i	−0.686196	+	0.727417i	$0.740721\pi$
$602$	−1.48545	+	2.95196i	−0.0605423	+	0.120313i
$603$		0			0
$604$	4.28152	−	7.41581i	0.174213	−	0.301745i
$605$		0			0
$606$		0			0
$607$	22.7475	+	13.1333i	0.923292	+	0.533063i	0.884684	−	0.466192i	$-0.154374\pi$
$607$	22.7475	+	13.1333i	0.923292	+	0.533063i	0.0386080	+	0.999254i	$0.487708\pi$
$608$	10.2633			0.416230
$609$		0			0
$610$		0			0
$611$	13.0317	+	7.52384i	0.527205	+	0.304382i
$612$		0			0
$613$	12.9410	+	22.4144i	0.522681	+	0.905310i	0.999652	+	0.0263906i	$0.00840138\pi$
$613$	12.9410	+	22.4144i	0.522681	+	0.905310i	−0.476971	+	0.878919i	$0.658265\pi$
$614$	−32.7686	+	56.7568i	−1.32243	+	2.29052i
$615$		0			0
$616$	83.3398	−	54.7194i	3.35786	−	2.20471i
$617$			16.1754i			0.651198i	0.945508	+	0.325599i	$0.105566\pi$
$617$			16.1754i			0.651198i	−0.945508	+	0.325599i	$0.894434\pi$
$618$		0			0
$619$	−5.29108	+	3.05481i	−0.212667	+	0.122783i	−0.602550	−	0.798081i	$-0.705849\pi$
$619$	−5.29108	+	3.05481i	−0.212667	+	0.122783i	0.389883	+	0.920864i	$0.372515\pi$
$620$		0			0
$621$		0			0
$622$			79.7432i			3.19741i
$623$	−24.4145	−	12.2855i	−0.978145	−	0.492209i
$624$		0			0
$625$		0			0
$626$	19.3306	+	33.4815i	0.772605	+	1.33819i
$627$		0			0
$628$	−26.1744	−	15.1118i	−1.04447	−	0.603027i
$629$	5.84048			0.232875
$630$		0			0
$631$	1.89949			0.0756174			0.0378087	−	0.999285i	$-0.487962\pi$
$631$	1.89949			0.0756174			0.0378087	+	0.999285i	$0.487962\pi$
$632$	−74.1297	−	42.7988i	−2.94872	−	1.70245i
$633$		0			0
$634$	−20.0170	−	34.6704i	−0.794976	−	1.37694i
$635$		0			0
$636$		0			0
$637$	−2.83426	−	24.5847i	−0.112298	−	0.974083i
$638$		−	31.7782i		−	1.25811i
$639$		0			0
$640$		0			0
$641$	9.82533	−	5.67266i	0.388077	−	0.224057i	−0.293249	−	0.956036i	$-0.594737\pi$
$641$	9.82533	−	5.67266i	0.388077	−	0.224057i	0.681327	+	0.731979i	$0.261403\pi$
$642$		0			0
$643$			18.2255i			0.718742i	0.933195	+	0.359371i	$0.117009\pi$
$643$			18.2255i			0.718742i	−0.933195	+	0.359371i	$0.882991\pi$
$644$	36.4476	−	2.09400i	1.43623	−	0.0825152i
$645$		0			0
$646$	−9.90252	+	17.1517i	−0.389609	+	0.674823i
$647$	−12.2706	−	21.2533i	−0.482406	−	0.835552i	0.517390	−	0.855750i	$-0.326904\pi$
$647$	−12.2706	−	21.2533i	−0.482406	−	0.835552i	−0.999796	+	0.0201980i	$0.993570\pi$
$648$		0			0
$649$	−55.7490	−	32.1867i	−2.18834	−	1.26344i
$650$		0			0
$651$		0			0
$652$	86.3976			3.38359
$653$	−7.58043	−	4.37656i	−0.296645	−	0.171268i	0.344290	−	0.938863i	$-0.388120\pi$
$653$	−7.58043	−	4.37656i	−0.296645	−	0.171268i	−0.640935	+	0.767595i	$0.721453\pi$
$654$		0			0
$655$		0			0
$656$	−25.9913	+	45.0183i	−1.01479	+	1.75767i
$657$		0			0
$658$	15.8805	+	24.1867i	0.619087	+	0.942894i
$659$			2.51324i			0.0979020i	0.998801	+	0.0489510i	$0.0155878\pi$
$659$			2.51324i			0.0979020i	−0.998801	+	0.0489510i	$0.984412\pi$
$660$		0			0
$661$	−34.5393	+	19.9413i	−1.34342	+	0.775626i	−0.987308	−	0.158815i	$-0.949233\pi$
$661$	−34.5393	+	19.9413i	−1.34342	+	0.775626i	−0.356116	+	0.934442i	$0.615899\pi$
$662$	30.4137	−	17.5594i	1.18206	−	0.682465i
$663$		0			0
$664$		−	45.2714i		−	1.75687i
$665$		0			0
$666$		0			0
$667$	3.28953	−	5.69763i	0.127371	−	0.220613i
$668$	11.0574	+	19.1520i	0.427823	+	0.741011i
$669$		0			0
$670$		0			0
$671$	−39.5080			−1.52519
$672$		0			0
$673$	36.0634			1.39014			0.695071	−	0.718941i	$-0.255373\pi$
$673$	36.0634			1.39014			0.695071	+	0.718941i	$0.255373\pi$
$674$	50.8318	+	29.3478i	1.95797	+	1.13043i
$675$		0			0
$676$	1.15310	+	1.99723i	0.0443501	+	0.0768166i
$677$	−3.95189	+	6.84487i	−0.151883	+	0.263070i	−0.931920	−	0.362664i	$-0.881867\pi$
$677$	−3.95189	+	6.84487i	−0.151883	+	0.263070i	0.780036	+	0.625734i	$0.215200\pi$
$678$		0			0
$679$	38.9132	−	2.23566i	1.49335	−	0.0857968i
$680$		0			0
$681$		0			0
$682$	19.1041	−	11.0298i	0.731534	−	0.422351i
$683$	−21.8984	+	12.6430i	−0.837918	+	0.483772i	−0.856556	−	0.516054i	$-0.827400\pi$
$683$	−21.8984	+	12.6430i	−0.837918	+	0.483772i	0.0186377	+	0.999826i	$0.494067\pi$
$684$		0			0
$685$		0			0
$686$	16.3809	−	44.6771i	0.625425	−	1.70578i
$687$		0			0
$688$	−1.93772	+	3.35622i	−0.0738747	+	0.127955i
$689$	−7.10969	−	12.3143i	−0.270858	−	0.469139i
$690$		0			0
$691$	−13.1380	−	7.58522i	−0.499792	−	0.288555i	0.228835	−	0.973465i	$-0.426508\pi$
$691$	−13.1380	−	7.58522i	−0.499792	−	0.288555i	−0.728628	+	0.684910i	$0.759842\pi$
$692$	15.4790			0.588424
$693$		0			0
$694$	−50.4235			−1.91405
$695$		0			0
$696$		0			0
$697$	−17.4192	−	30.1709i	−0.659799	−	1.14280i
$698$	7.88861	−	13.6635i	0.298588	−	0.517170i
$699$		0			0
$700$		0			0
$701$		−	34.6815i		−	1.30990i	−0.755671	−	0.654951i	$-0.772689\pi$
$701$		−	34.6815i		−	1.30990i	0.755671	−	0.654951i	$-0.227311\pi$
$702$		0			0
$703$	−1.36579	+	0.788541i	−0.0515118	+	0.0297404i
$704$	11.3949	−	6.57883i	0.429460	−	0.247949i
$705$		0			0
$706$		−	61.6755i		−	2.32119i
$707$	33.0278	−	21.6855i	1.24214	−	0.815566i
$708$		0			0
$709$	17.2311	−	29.8451i	0.647126	−	1.12086i	−0.336680	−	0.941619i	$-0.609304\pi$
$709$	17.2311	−	29.8451i	0.647126	−	1.12086i	0.983806	−	0.179237i	$-0.0573628\pi$
$710$		0			0
$711$		0			0
$712$	−59.8030	−	34.5273i	−2.24121	−	1.29396i
$713$	4.56699			0.171035
$714$		0			0
$715$		0			0
$716$	44.3502	+	25.6056i	1.65744	+	0.956925i
$717$		0			0
$718$	−21.7765	−	37.7180i	−0.812692	−	1.40762i
$719$	13.4825	−	23.3523i	0.502812	−	0.870895i	−0.497183	−	0.867646i	$-0.665632\pi$
$719$	13.4825	−	23.3523i	0.502812	−	0.870895i	0.999995	−	0.00324951i	$-0.00103435\pi$
$720$		0			0
$721$	−4.65613	+	9.25293i	−0.173403	+	0.344597i
$722$			43.4702i			1.61779i
$723$		0			0
$724$	8.74942	−	5.05148i	0.325170	−	0.187737i
$725$		0			0
$726$		0			0
$727$			10.4196i			0.386442i	0.981155	+	0.193221i	$0.0618935\pi$
$727$			10.4196i			0.386442i	−0.981155	+	0.193221i	$0.938106\pi$
$728$	−3.58639	−	62.4236i	−0.132921	−	2.31357i
$729$		0			0
$730$		0			0
$731$	−1.29864	−	2.24931i	−0.0480320	−	0.0831938i
$732$		0			0
$733$	−19.6659	−	11.3541i	−0.726377	−	0.419374i	0.0907181	−	0.995877i	$-0.471084\pi$
$733$	−19.6659	−	11.3541i	−0.726377	−	0.419374i	−0.817095	+	0.576503i	$0.804417\pi$
$734$	89.9374			3.31965
$735$		0			0
$736$	21.3318			0.786300
$737$	12.1549	+	7.01764i	0.447732	+	0.258498i
$738$		0			0
$739$	14.8897	+	25.7898i	0.547728	+	0.948692i	0.998430	+	0.0560176i	$0.0178403\pi$
$739$	14.8897	+	25.7898i	0.547728	+	0.948692i	−0.450702	+	0.892674i	$0.648826\pi$
$740$		0			0
$741$		0			0
$742$	−1.56825	−	27.2965i	−0.0575723	−	1.00209i
$743$		−	34.8044i		−	1.27685i	−0.769684	−	0.638424i	$-0.779586\pi$
$743$		−	34.8044i		−	1.27685i	0.769684	−	0.638424i	$-0.220414\pi$
$744$		0			0
$745$		0			0
$746$	−13.3320	+	7.69723i	−0.488119	+	0.281816i
$747$		0			0
$748$			138.594i			5.06751i
$749$	17.6275	−	35.0303i	0.644093	−	1.27998i
$750$		0			0
$751$	−3.74522	+	6.48691i	−0.136665	+	0.236711i	−0.926232	−	0.376953i	$-0.876972\pi$
$751$	−3.74522	+	6.48691i	−0.136665	+	0.236711i	0.789567	+	0.613664i	$0.210305\pi$
$752$	16.9659	+	29.3858i	0.618683	+	1.07159i
$753$		0			0
$754$	−17.2599	−	9.96499i	−0.628568	−	0.362904i
$755$		0			0
$756$		0			0
$757$	−2.66139			−0.0967300			−0.0483650	−	0.998830i	$-0.515401\pi$
$757$	−2.66139			−0.0967300			−0.0483650	+	0.998830i	$0.515401\pi$
$758$	−6.96118	−	4.01904i	−0.252842	−	0.145978i
$759$		0			0
$760$		0			0
$761$	2.78479	−	4.82340i	0.100949	−	0.174848i	−0.811127	−	0.584870i	$-0.801146\pi$
$761$	2.78479	−	4.82340i	0.100949	−	0.174848i	0.912076	+	0.410022i	$0.134479\pi$
$762$		0			0
$763$	24.4135	−	16.0294i	0.883827	−	0.580304i
$764$		−	45.8057i		−	1.65719i
$765$		0			0
$766$	−37.7516	+	21.7959i	−1.36402	+	0.787517i
$767$	−34.9635	+	20.1862i	−1.26246	+	0.728881i
$768$		0			0
$769$		−	11.5002i		−	0.414709i	−0.978266	−	0.207355i	$-0.933515\pi$
$769$		−	11.5002i		−	0.414709i	0.978266	−	0.207355i	$-0.0664854\pi$
$770$		0			0
$771$		0			0
$772$	−57.4045	+	99.4275i	−2.06603	+	3.57847i
$773$	12.6872	+	21.9748i	0.456325	+	0.790378i	0.998763	−	0.0497174i	$-0.0158321\pi$
$773$	12.6872	+	21.9748i	0.456325	+	0.790378i	−0.542438	+	0.840096i	$0.682499\pi$
$774$		0			0
$775$		0			0
$776$	98.4793			3.53520
$777$		0			0
$778$	1.15486			0.0414039
$779$	8.14692	+	4.70363i	0.291894	+	0.168525i
$780$		0			0
$781$	−22.9388	−	39.7312i	−0.820816	−	1.42169i
$782$	−20.5820	+	35.6491i	−0.736011	+	1.27481i
$783$		0			0
$784$	22.1838	−	51.2058i	0.792280	−	1.82878i
$785$		0			0
$786$		0			0
$787$	−20.7789	+	11.9967i	−0.740688	+	0.427636i	−0.822319	−	0.569026i	$-0.807320\pi$
$787$	−20.7789	+	11.9967i	−0.740688	+	0.427636i	0.0816315	+	0.996663i	$0.473987\pi$
$788$	76.1260	−	43.9514i	2.71188	−	1.56570i
$789$		0			0
$790$		0			0
$791$	19.9244	−	1.14471i	0.708431	−	0.0407011i
$792$		0			0
$793$	−12.3889	+	21.4582i	−0.439942	+	0.762002i
$794$	−29.2043	−	50.5833i	−1.03642	−	1.79514i
$795$		0			0
$796$	−7.34573	−	4.24106i	−0.260363	−	0.150320i
$797$	−28.1188			−0.996020			−0.498010	−	0.867171i	$-0.665936\pi$
$797$	−28.1188			−0.996020			−0.498010	+	0.867171i	$0.665936\pi$
$798$		0			0
$799$	−22.7408			−0.804513
$800$		0			0
$801$		0			0
$802$	12.4802	+	21.6163i	0.440691	+	0.763299i
$803$	8.84470	−	15.3195i	0.312123	−	0.540612i
$804$		0			0
$805$		0			0
$806$		−	13.8348i		−	0.487310i
$807$		0			0
$808$	86.4525	−	49.9134i	3.04139	−	1.75595i
$809$	24.2977	−	14.0283i	0.854263	−	0.493209i	−0.00782425	−	0.999969i	$-0.502491\pi$
$809$	24.2977	−	14.0283i	0.854263	−	0.493209i	0.862087	+	0.506761i	$0.169157\pi$
$810$		0			0
$811$		−	43.4980i		−	1.52742i	−0.645559	−	0.763710i	$-0.723376\pi$
$811$		−	43.4980i		−	1.52742i	0.645559	−	0.763710i	$-0.276624\pi$
$812$	−14.6610	−	22.3293i	−0.514501	−	0.783605i
$813$		0			0
$814$	−7.91647	+	13.7117i	−0.277472	+	0.480596i
$815$		0			0
$816$		0			0
$817$	0.607373	+	0.350667i	0.0212493	+	0.0122683i
$818$	10.4323			0.364757
$819$		0			0
$820$		0			0
$821$	−31.5875	−	18.2371i	−1.10241	−	0.636477i	−0.165558	−	0.986200i	$-0.552942\pi$
$821$	−31.5875	−	18.2371i	−1.10241	−	0.636477i	−0.936853	+	0.349723i	$0.886276\pi$
$822$		0			0
$823$	−23.0523	−	39.9277i	−0.803551	−	1.39179i	−0.917265	−	0.398278i	$-0.869608\pi$
$823$	−23.0523	−	39.9277i	−0.803551	−	1.39179i	0.113713	−	0.993514i	$-0.463725\pi$
$824$	−13.0856	+	22.6650i	−0.455859	+	0.789571i
$825$		0			0
$826$	−77.5015	+	4.45265i	−2.69662	+	0.154928i
$827$			20.1533i			0.700800i	0.936600	+	0.350400i	$0.113954\pi$
$827$			20.1533i			0.700800i	−0.936600	+	0.350400i	$0.886046\pi$
$828$		0			0
$829$	−6.13818	+	3.54388i	−0.213188	+	0.123084i	−0.602792	−	0.797898i	$-0.705945\pi$
$829$	−6.13818	+	3.54388i	−0.213188	+	0.123084i	0.389604	+	0.920982i	$0.372612\pi$
$830$		0			0
$831$		0			0
$832$		−	8.25194i		−	0.286085i
$833$	22.2863	+	30.0344i	0.772175	+	1.04063i
$834$		0			0
$835$		0			0
$836$	−18.7120	−	32.4102i	−0.647169	−	1.12093i
$837$		0			0
$838$	46.5754	+	26.8903i	1.60892	+	0.928911i
$839$	−33.0805			−1.14206			−0.571032	−	0.820928i	$-0.693457\pi$
$839$	−33.0805			−1.14206			−0.571032	+	0.820928i	$0.693457\pi$
$840$		0			0
$841$	24.1862			0.834006
$842$	44.0121	+	25.4104i	1.51676	+	0.875701i
$843$		0			0
$844$	−22.4956	−	38.9635i	−0.774331	−	1.34118i
$845$		0			0
$846$		0			0
$847$	−49.1045	−	24.7097i	−1.68725	−	0.849036i
$848$		−	32.0640i		−	1.10108i
$849$		0			0
$850$		0			0
$851$	−2.83875	+	1.63895i	−0.0973109	+	0.0561825i
$852$		0			0
$853$			38.1187i			1.30516i	0.757719	+	0.652580i	$0.226314\pi$
$853$			38.1187i			1.30516i	−0.757719	+	0.652580i	$0.773686\pi$
$854$	−39.8262	+	26.1492i	−1.36282	+	0.894806i
$855$		0			0
$856$	49.5403	−	85.8063i	1.69325	−	2.93280i
$857$	−3.51807	−	6.09347i	−0.120175	−	0.208149i	0.799662	−	0.600451i	$-0.205012\pi$
$857$	−3.51807	−	6.09347i	−0.120175	−	0.208149i	−0.919837	+	0.392302i	$0.871679\pi$
$858$		0			0
$859$	−22.2343	−	12.8370i	−0.758624	−	0.437992i	0.0701772	−	0.997535i	$-0.477644\pi$
$859$	−22.2343	−	12.8370i	−0.758624	−	0.437992i	−0.828802	+	0.559543i	$0.810977\pi$
$860$		0			0
$861$		0			0
$862$	27.3885			0.932855
$863$	44.1550	+	25.4929i	1.50305	+	0.867788i	0.999994	+	0.00353683i	$0.00112581\pi$
$863$	44.1550	+	25.4929i	1.50305	+	0.867788i	0.503060	+	0.864252i	$0.332208\pi$
$864$		0			0
$865$		0			0
$866$	−27.2805	+	47.2512i	−0.927029	+	1.60566i
$867$		0			0
$868$	8.33508	−	16.5639i	0.282911	−	0.562217i
$869$			72.1835i			2.44866i
$870$		0			0
$871$	7.62306	−	4.40117i	0.258297	−	0.149128i
$872$	63.9038	−	36.8949i	2.16406	−	1.24942i
$873$		0			0
$874$		−	11.1153i		−	0.375982i
$875$		0			0
$876$		0			0
$877$	19.2766	−	33.3881i	0.650925	−	1.12743i	−0.331974	−	0.943289i	$-0.607715\pi$
$877$	19.2766	−	33.3881i	0.650925	−	1.12743i	0.982899	−	0.184146i	$-0.0589520\pi$
$878$	27.5484	+	47.7152i	0.929712	+	1.61031i
$879$		0			0
$880$		0			0
$881$	−34.4764			−1.16154			−0.580770	−	0.814068i	$-0.697248\pi$
$881$	−34.4764			−1.16154			−0.580770	+	0.814068i	$0.697248\pi$
$882$		0			0
$883$	−25.5869			−0.861068			−0.430534	−	0.902574i	$-0.641675\pi$
$883$	−25.5869			−0.861068			−0.430534	+	0.902574i	$0.641675\pi$
$884$	75.2754	+	43.4603i	2.53179	+	1.46173i
$885$		0			0
$886$	−0.219643	−	0.380433i	−0.00737905	−	0.0127809i
$887$	11.8978	−	20.6076i	0.399489	−	0.691936i	−0.594174	−	0.804337i	$-0.702521\pi$
$887$	11.8978	−	20.6076i	0.399489	−	0.691936i	0.993663	+	0.112401i	$0.0358541\pi$
$888$		0			0
$889$	0.597481	+	10.3996i	0.0200389	+	0.348791i
$890$		0			0
$891$		0			0
$892$	−31.2749	+	18.0566i	−1.04716	+	0.604579i
$893$	5.31792	−	3.07031i	0.177958	−	0.102744i
$894$		0			0
$895$		0			0
$896$	−9.78847	+	19.4522i	−0.327010	+	0.649852i
$897$		0			0
$898$	−12.0600	+	20.8886i	−0.402448	+	0.697061i
$899$	−1.67081	−	2.89392i	−0.0557245	−	0.0965177i
$900$		0			0
$901$	18.6101	+	10.7445i	0.619991	+	0.357952i
$902$	94.4432			3.14461
$903$		0			0
$904$	50.4235			1.67706
$905$		0			0
$906$		0			0
$907$	−19.3878	−	33.5806i	−0.643760	−	1.11503i	−0.984586	−	0.174899i	$-0.944040\pi$
$907$	−19.3878	−	33.5806i	−0.643760	−	1.11503i	0.340826	−	0.940126i	$-0.389293\pi$
$908$	−1.26427	+	2.18978i	−0.0419563	+	0.0726704i
$909$		0			0
$910$		0			0
$911$		−	31.4438i		−	1.04178i	−0.853624	−	0.520889i	$-0.825600\pi$
$911$		−	31.4438i		−	1.04178i	0.853624	−	0.520889i	$-0.174400\pi$
$912$		0			0
$913$	−33.0622	+	19.0884i	−1.09420	+	0.631735i
$914$	−37.5881	+	21.7015i	−1.24330	+	0.717822i
$915$		0			0
$916$			98.7437i			3.26258i
$917$	9.33064	+	4.69524i	0.308125	+	0.155050i
$918$		0			0
$919$	13.9872	−	24.2266i	0.461396	−	0.799161i	−0.537635	−	0.843178i	$-0.680682\pi$
$919$	13.9872	−	24.2266i	0.461396	−	0.799161i	0.999031	+	0.0440170i	$0.0140156\pi$
$920$		0			0
$921$		0			0
$922$	69.0596	+	39.8716i	2.27436	+	1.31310i
$923$	−28.7726			−0.947060
$924$		0			0
$925$		0			0
$926$	−26.5757	−	15.3435i	−0.873332	−	0.504218i
$927$		0			0
$928$	−7.80411	−	13.5171i	−0.256183	−	0.443721i
$929$	11.2452	−	19.4772i	0.368943	−	0.639027i	−0.620458	−	0.784240i	$-0.713053\pi$
$929$	11.2452	−	19.4772i	0.368943	−	0.639027i	0.989400	+	0.145212i	$0.0463866\pi$
$930$		0			0
$931$	−9.26667	−	4.01459i	−0.303703	−	0.131573i
$932$			86.3568i			2.82871i
$933$		0			0
$934$	76.9023	−	44.3996i	2.51632	−	1.45280i
$935$		0			0
$936$		0			0
$937$			32.0994i			1.04864i	0.851521	+	0.524321i	$0.175681\pi$
$937$			32.0994i			1.04864i	−0.851521	+	0.524321i	$0.824319\pi$
$938$	16.8976	−	0.970808i	0.551725	−	0.0316980i
$939$		0			0
$940$		0			0
$941$	−5.10912	−	8.84925i	−0.166552	−	0.288477i	0.770653	−	0.637255i	$-0.219930\pi$
$941$	−5.10912	−	8.84925i	−0.166552	−	0.288477i	−0.937206	+	0.348778i	$0.886597\pi$
$942$		0			0
$943$	16.9331	+	9.77631i	0.551416	+	0.318360i
$944$	−91.0378			−2.96303
$945$		0			0
$946$	7.04097			0.228922
$947$	−8.91925	−	5.14953i	−0.289837	−	0.167337i	0.348031	−	0.937483i	$-0.386850\pi$
$947$	−8.91925	−	5.14953i	−0.289837	−	0.167337i	−0.637868	+	0.770146i	$0.720184\pi$
$948$		0			0
$949$	−5.54703	−	9.60774i	−0.180064	−	0.311880i
$950$		0			0
$951$		0			0
$952$	51.8627	+	78.9890i	1.68088	+	2.56005i
$953$		−	0.930159i		−	0.0301308i	−0.999887	−	0.0150654i	$-0.995204\pi$
$953$		−	0.930159i		−	0.0301308i	0.999887	−	0.0150654i	$-0.00479565\pi$
$954$		0			0
$955$		0			0
$956$	29.3255	−	16.9311i	0.948455	−	0.547591i
$957$		0			0
$958$			7.63696i			0.246739i
$959$	−8.22082	−	12.5206i	−0.265464	−	0.404312i
$960$		0			0
$961$	−14.3402	+	24.8379i	−0.462586	+	0.801223i
$962$	4.96488	+	8.59943i	0.160074	+	0.277257i
$963$		0			0
$964$	109.735	+	63.3555i	3.53432	+	2.04054i
$965$		0			0
$966$		0			0
$967$	−4.22117			−0.135744			−0.0678719	−	0.997694i	$-0.521621\pi$
$967$	−4.22117			−0.135744			−0.0678719	+	0.997694i	$0.521621\pi$
$968$	−120.281	−	69.4443i	−3.86598	−	2.23202i
$969$		0			0
$970$		0			0
$971$	2.28935	−	3.96527i	0.0734688	−	0.127252i	−0.826951	−	0.562275i	$-0.809926\pi$
$971$	2.28935	−	3.96527i	0.0734688	−	0.127252i	0.900419	+	0.435023i	$0.143260\pi$
$972$		0			0
$973$	−61.5483	+	3.53610i	−1.97315	+	0.113362i
$974$		−	58.3566i		−	1.86987i
$975$		0			0
$976$	−48.3872	+	27.9364i	−1.54884	+	0.894221i
$977$	−39.4138	+	22.7556i	−1.26096	+	0.728015i	−0.973260	−	0.229707i	$-0.926223\pi$
$977$	−39.4138	+	22.7556i	−1.26096	+	0.728015i	−0.287698	+	0.957721i	$0.592890\pi$
$978$		0			0
$979$			58.2329i			1.86113i
$980$		0			0
$981$		0			0
$982$	−16.7056	+	28.9350i	−0.533097	+	0.923351i
$983$	−5.25831	−	9.10765i	−0.167714	−	0.290489i	0.769902	−	0.638162i	$-0.220305\pi$
$983$	−5.25831	−	9.10765i	−0.167714	−	0.290489i	−0.937616	+	0.347673i	$0.886972\pi$
$984$		0			0
$985$		0			0
$986$	30.1192			0.959192
$987$		0			0
$988$	−23.4708			−0.746706
$989$	1.26240	+	0.728847i	0.0401420	+	0.0231760i
$990$		0			0
$991$	13.9539	+	24.1689i	0.443262	+	0.767752i	0.997929	−	0.0643204i	$-0.0204880\pi$
$991$	13.9539	+	24.1689i	0.443262	+	0.767752i	−0.554668	+	0.832072i	$0.687155\pi$
$992$	5.41739	−	9.38319i	0.172002	−	0.297916i
$993$		0			0
$994$	−49.4205	−	24.8687i	−1.56752	−	0.788787i
$995$		0			0
$996$		0			0
$997$	33.7000	−	19.4567i	1.06729	−	0.616201i	0.139851	−	0.990173i	$-0.455338\pi$
$997$	33.7000	−	19.4567i	1.06729	−	0.616201i	0.927440	+	0.373972i	$0.122004\pi$
$998$	48.0803	−	27.7592i	1.52196	−	0.878701i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1575.2.bk.i.26.2		24
3.2	odd	2	inner	1575.2.bk.i.26.11		24
5.2	odd	4		315.2.bb.b.89.12	yes	24
5.3	odd	4		315.2.bb.b.89.2	yes	24
5.4	even	2	inner	1575.2.bk.i.26.12		24
7.3	odd	6	inner	1575.2.bk.i.1151.11		24
15.2	even	4		315.2.bb.b.89.1	✓	24
15.8	even	4		315.2.bb.b.89.11	yes	24
15.14	odd	2	inner	1575.2.bk.i.26.1		24
21.17	even	6	inner	1575.2.bk.i.1151.2		24
35.2	odd	12		2205.2.g.b.2204.4		24
35.3	even	12		315.2.bb.b.269.1	yes	24
35.12	even	12		2205.2.g.b.2204.3		24
35.17	even	12		315.2.bb.b.269.11	yes	24
35.23	odd	12		2205.2.g.b.2204.24		24
35.24	odd	6	inner	1575.2.bk.i.1151.1		24
35.33	even	12		2205.2.g.b.2204.23		24
105.2	even	12		2205.2.g.b.2204.22		24
105.17	odd	12		315.2.bb.b.269.2	yes	24
105.23	even	12		2205.2.g.b.2204.2		24
105.38	odd	12		315.2.bb.b.269.12	yes	24
105.47	odd	12		2205.2.g.b.2204.21		24
105.59	even	6	inner	1575.2.bk.i.1151.12		24
105.68	odd	12		2205.2.g.b.2204.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bb.b.89.1	✓	24	15.2	even	4
315.2.bb.b.89.2	yes	24	5.3	odd	4
315.2.bb.b.89.11	yes	24	15.8	even	4
315.2.bb.b.89.12	yes	24	5.2	odd	4
315.2.bb.b.269.1	yes	24	35.3	even	12
315.2.bb.b.269.2	yes	24	105.17	odd	12
315.2.bb.b.269.11	yes	24	35.17	even	12
315.2.bb.b.269.12	yes	24	105.38	odd	12
1575.2.bk.i.26.1		24	15.14	odd	2	inner
1575.2.bk.i.26.2		24	1.1	even	1	trivial
1575.2.bk.i.26.11		24	3.2	odd	2	inner
1575.2.bk.i.26.12		24	5.4	even	2	inner
1575.2.bk.i.1151.1		24	35.24	odd	6	inner
1575.2.bk.i.1151.2		24	21.17	even	6	inner
1575.2.bk.i.1151.11		24	7.3	odd	6	inner
1575.2.bk.i.1151.12		24	105.59	even	6	inner
2205.2.g.b.2204.1		24	105.68	odd	12
2205.2.g.b.2204.2		24	105.23	even	12
2205.2.g.b.2204.3		24	35.12	even	12
2205.2.g.b.2204.4		24	35.2	odd	12
2205.2.g.b.2204.21		24	105.47	odd	12
2205.2.g.b.2204.22		24	105.2	even	12
2205.2.g.b.2204.23		24	35.33	even	12
2205.2.g.b.2204.24		24	35.23	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)

\(f(q)\)	\(=\)	\(q+(-2.22514 - 1.28469i) q^{2} +(2.30084 + 3.98517i) q^{4} +(-0.151755 - 2.64140i) q^{7} -6.68468i q^{8} +(-4.88189 + 2.81856i) q^{11} +3.53537i q^{13} +(-3.05569 + 6.07244i) q^{14} +(-3.98605 + 6.90403i) q^{16} +(-2.67142 - 4.62703i) q^{17} +(1.24942 + 0.721351i) q^{19} +14.4839 q^{22} +(2.59686 + 1.49930i) q^{23} +(4.54184 - 7.86670i) q^{26} +(10.1772 - 6.68220i) q^{28} -2.19404i q^{29} +(1.31899 - 0.761520i) q^{31} +(6.16083 - 3.55696i) q^{32} +13.7277i q^{34} +(-0.546572 + 0.946690i) q^{37} +(-1.85342 - 3.21022i) q^{38} +6.52058 q^{41} +0.486125 q^{43} +(-22.4649 - 12.9701i) q^{44} +(-3.85226 - 6.67231i) q^{46} +(2.12816 - 3.68608i) q^{47} +(-6.95394 + 0.801688i) q^{49} +(-14.0891 + 8.13432i) q^{52} +(-3.48318 + 2.01102i) q^{53} +(-17.6569 + 1.01443i) q^{56} +(-2.81866 + 4.88206i) q^{58} +(5.70978 + 9.88963i) q^{59} +(6.06957 + 3.50427i) q^{61} -3.91326 q^{62} -2.33411 q^{64} +(-1.24490 - 2.15623i) q^{67} +(12.2930 - 21.2921i) q^{68} +8.13849i q^{71} +(-2.71761 + 1.56901i) q^{73} +(2.43240 - 1.40435i) q^{74} +6.63886i q^{76} +(8.18578 + 12.4673i) q^{77} +(6.40252 - 11.0895i) q^{79} +(-14.5092 - 8.37690i) q^{82} +6.77241 q^{83} +(-1.08170 - 0.624518i) q^{86} +(18.8412 + 32.6339i) q^{88} +(5.16513 - 8.94627i) q^{89} +(9.33831 - 0.536509i) q^{91} +13.7986i q^{92} +(-9.47093 + 5.46804i) q^{94} +14.7321i q^{97} +(16.5034 + 7.14976i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} + 36 q^{19} - 60 q^{31} - 24 q^{46} - 36 q^{49} + 48 q^{61} - 48 q^{64} + 60 q^{79} + 60 q^{91} - 48 q^{94}+O(q^{100}) \) 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

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