LMFDB - Embedded newform 1260.2.n.a.71.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1260,2,Mod(71,1260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1260, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0, 0]))

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

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

chi := DirichletCharacter("1260.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1260.n (of order $2$, degree $1$, 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:	$10.0611506547$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.19
Character	$\chi$	$=$	1260.71
Dual form			1260.2.n.a.71.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.935018 - 1.06101i) q^{2} +(-0.251481 - 1.98413i) q^{4} -1.00000i q^{5} -1.00000i q^{7} +(-2.34032 - 1.58837i) q^{8} +(-1.06101 - 0.935018i) q^{10} -1.78504 q^{11} -6.14618 q^{13} +(-1.06101 - 0.935018i) q^{14} +(-3.87351 + 0.997940i) q^{16} +1.11477i q^{17} -2.67556i q^{19} +(-1.98413 + 0.251481i) q^{20} +(-1.66905 + 1.89395i) q^{22} +2.65580 q^{23} -1.00000 q^{25} +(-5.74679 + 6.52115i) q^{26} +(-1.98413 + 0.251481i) q^{28} -0.744661i q^{29} +8.66461i q^{31} +(-2.56298 + 5.04293i) q^{32} +(1.18278 + 1.04233i) q^{34} -1.00000 q^{35} -7.62886 q^{37} +(-2.83879 - 2.50170i) q^{38} +(-1.58837 + 2.34032i) q^{40} -10.5025i q^{41} -9.50600i q^{43} +(0.448904 + 3.54175i) q^{44} +(2.48322 - 2.81783i) q^{46} +5.00451 q^{47} -1.00000 q^{49} +(-0.935018 + 1.06101i) q^{50} +(1.54565 + 12.1948i) q^{52} -2.50082i q^{53} +1.78504i q^{55} +(-1.58837 + 2.34032i) q^{56} +(-0.790093 - 0.696272i) q^{58} +1.23850 q^{59} -6.41461 q^{61} +(9.19323 + 8.10157i) q^{62} +(2.95416 + 7.43458i) q^{64} +6.14618i q^{65} -3.77241i q^{67} +(2.21184 - 0.280343i) q^{68} +(-0.935018 + 1.06101i) q^{70} +15.5325 q^{71} -5.58799 q^{73} +(-7.13313 + 8.09430i) q^{74} +(-5.30865 + 0.672853i) q^{76} +1.78504i q^{77} -11.3475i q^{79} +(0.997940 + 3.87351i) q^{80} +(-11.1433 - 9.82007i) q^{82} -4.92476 q^{83} +1.11477 q^{85} +(-10.0860 - 8.88829i) q^{86} +(4.17756 + 2.83531i) q^{88} +11.2488i q^{89} +6.14618i q^{91} +(-0.667884 - 5.26945i) q^{92} +(4.67931 - 5.30984i) q^{94} -2.67556 q^{95} -17.2826 q^{97} +(-0.935018 + 1.06101i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{4} - 4 q^{10} - 4 q^{14} + 4 q^{20} - 4 q^{22} - 24 q^{25} - 40 q^{26} + 4 q^{28} + 40 q^{32} + 8 q^{34} - 24 q^{35} + 4 q^{40} + 48 q^{44} + 36 q^{46} + 16 q^{47} - 24 q^{49} + 32 q^{52} + 4 q^{56}+ \cdots + 12 q^{88}+O(q^{100}) $ 24 * q - 4 * q^4 - 4 * q^10 - 4 * q^14 + 4 * q^20 - 4 * q^22 - 24 * q^25 - 40 * q^26 + 4 * q^28 + 40 * q^32 + 8 * q^34 - 24 * q^35 + 4 * q^40 + 48 * q^44 + 36 * q^46 + 16 * q^47 - 24 * q^49 + 32 * q^52 + 4 * q^56 - 28 * q^58 - 16 * q^59 - 32 * q^61 - 56 * q^62 - 4 * q^64 + 64 * q^68 - 32 * q^74 - 72 * q^76 - 40 * q^82 - 80 * q^83 + 32 * q^85 - 80 * q^86 + 12 * q^88

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$757$	$1081$
$\chi(n)$	$-1$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	0.935018	−	1.06101i	0.661158	−	0.750247i
$2$	0.935018	−	1.06101i	0.661158	−	0.750247i
$3$		0			0
$3$		0			0
$4$	−0.251481	−	1.98413i	−0.125741	−	0.992063i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−2.34032	−	1.58837i	−0.827427	−	0.561574i
$9$		0			0
$10$	−1.06101	−	0.935018i	−0.335521	−	0.295679i
$11$	−1.78504			−0.538210			−0.269105	−	0.963111i	$-0.586728\pi$
$11$	−1.78504			−0.538210			−0.269105	+	0.963111i	$0.586728\pi$
$12$		0			0
$13$	−6.14618			−1.70464			−0.852321	−	0.523018i	$-0.824806\pi$
$13$	−6.14618			−1.70464			−0.852321	+	0.523018i	$0.824806\pi$
$14$	−1.06101	−	0.935018i	−0.283567	−	0.249894i
$15$		0			0
$16$	−3.87351	+	0.997940i	−0.968379	+	0.249485i
$17$			1.11477i			0.270371i	0.990820	+	0.135185i	$0.0431630\pi$
$17$			1.11477i			0.270371i	−0.990820	+	0.135185i	$0.956837\pi$
$18$		0			0
$19$		−	2.67556i		−	0.613816i	−0.951739	−	0.306908i	$-0.900706\pi$
$19$		−	2.67556i		−	0.613816i	0.951739	−	0.306908i	$-0.0992943\pi$
$20$	−1.98413	+	0.251481i	−0.443664	+	0.0562329i
$21$		0			0
$22$	−1.66905	+	1.89395i	−0.355842	+	0.403791i
$23$	2.65580			0.553773			0.276886	−	0.960903i	$-0.410697\pi$
$23$	2.65580			0.553773			0.276886	+	0.960903i	$0.410697\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−5.74679	+	6.52115i	−1.12704	+	1.27890i
$27$		0			0
$28$	−1.98413	+	0.251481i	−0.374965	+	0.0475255i
$29$		−	0.744661i		−	0.138280i	−0.997607	−	0.0691401i	$-0.977974\pi$
$29$		−	0.744661i		−	0.138280i	0.997607	−	0.0691401i	$-0.0220255\pi$
$30$		0			0
$31$			8.66461i			1.55621i	0.628135	+	0.778105i	$0.283819\pi$
$31$			8.66461i			1.55621i	−0.628135	+	0.778105i	$0.716181\pi$
$32$	−2.56298	+	5.04293i	−0.453076	+	0.891472i
$33$		0			0
$34$	1.18278	+	1.04233i	0.202845	+	0.178758i
$35$	−1.00000			−0.169031
$36$		0			0
$37$	−7.62886			−1.25418			−0.627089	−	0.778948i	$-0.715754\pi$
$37$	−7.62886			−1.25418			−0.627089	+	0.778948i	$0.715754\pi$
$38$	−2.83879	−	2.50170i	−0.460513	−	0.405829i
$39$		0			0
$40$	−1.58837	+	2.34032i	−0.251143	+	0.370036i
$41$		−	10.5025i		−	1.64022i	−0.572205	−	0.820111i	$-0.693912\pi$
$41$		−	10.5025i		−	1.64022i	0.572205	−	0.820111i	$-0.306088\pi$
$42$		0			0
$43$		−	9.50600i		−	1.44965i	−0.688932	−	0.724826i	$-0.741920\pi$
$43$		−	9.50600i		−	1.44965i	0.688932	−	0.724826i	$-0.258080\pi$
$44$	0.448904	+	3.54175i	0.0676749	+	0.533939i
$45$		0			0
$46$	2.48322	−	2.81783i	0.366131	−	0.415466i
$47$	5.00451			0.729984			0.364992	−	0.931011i	$-0.381072\pi$
$47$	5.00451			0.729984			0.364992	+	0.931011i	$0.381072\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	−0.935018	+	1.06101i	−0.132232	+	0.150049i
$51$		0			0
$52$	1.54565	+	12.1948i	0.214343	+	1.69111i
$53$		−	2.50082i		−	0.343513i	−0.985139	−	0.171757i	$-0.945056\pi$
$53$		−	2.50082i		−	0.343513i	0.985139	−	0.171757i	$-0.0549443\pi$
$54$		0			0
$55$			1.78504i			0.240695i
$56$	−1.58837	+	2.34032i	−0.212255	+	0.312738i
$57$		0			0
$58$	−0.790093	−	0.696272i	−0.103744	−	0.0914250i
$59$	1.23850			0.161238			0.0806192	−	0.996745i	$-0.474310\pi$
$59$	1.23850			0.161238			0.0806192	+	0.996745i	$0.474310\pi$
$60$		0			0
$61$	−6.41461			−0.821307			−0.410654	−	0.911791i	$-0.634699\pi$
$61$	−6.41461			−0.821307			−0.410654	+	0.911791i	$0.634699\pi$
$62$	9.19323	+	8.10157i	1.16754	+	1.02890i
$63$		0			0
$64$	2.95416	+	7.43458i	0.369269	+	0.929322i
$65$			6.14618i			0.762340i
$66$		0			0
$67$		−	3.77241i		−	0.460873i	−0.973087	−	0.230436i	$-0.925985\pi$
$67$		−	3.77241i		−	0.460873i	0.973087	−	0.230436i	$-0.0740154\pi$
$68$	2.21184	−	0.280343i	0.268225	−	0.0339966i
$69$		0			0
$70$	−0.935018	+	1.06101i	−0.111756	+	0.126815i
$71$	15.5325			1.84337			0.921683	−	0.387944i	$-0.126815\pi$
$71$	15.5325			1.84337			0.921683	+	0.387944i	$0.126815\pi$
$72$		0			0
$73$	−5.58799			−0.654024			−0.327012	−	0.945020i	$-0.606042\pi$
$73$	−5.58799			−0.654024			−0.327012	+	0.945020i	$0.606042\pi$
$74$	−7.13313	+	8.09430i	−0.829209	+	0.940943i
$75$		0			0
$76$	−5.30865	+	0.672853i	−0.608944	+	0.0771815i
$77$			1.78504i			0.203424i
$78$		0			0
$79$		−	11.3475i		−	1.27669i	−0.769750	−	0.638345i	$-0.779619\pi$
$79$		−	11.3475i		−	1.27669i	0.769750	−	0.638345i	$-0.220381\pi$
$80$	0.997940	+	3.87351i	0.111573	+	0.433072i
$81$		0			0
$82$	−11.1433	−	9.82007i	−1.23057	−	1.08445i
$83$	−4.92476			−0.540563			−0.270281	−	0.962781i	$-0.587117\pi$
$83$	−4.92476			−0.540563			−0.270281	+	0.962781i	$0.587117\pi$
$84$		0			0
$85$	1.11477			0.120913
$86$	−10.0860	−	8.88829i	−1.08760	−	0.958449i
$87$		0			0
$88$	4.17756	+	2.83531i	0.445330	+	0.302245i
$89$			11.2488i			1.19237i	0.802849	+	0.596183i	$0.203317\pi$
$89$			11.2488i			1.19237i	−0.802849	+	0.596183i	$0.796683\pi$
$90$		0			0
$91$			6.14618i			0.644294i
$92$	−0.667884	−	5.26945i	−0.0696317	−	0.549378i
$93$		0			0
$94$	4.67931	−	5.30984i	0.482634	−	0.547668i
$95$	−2.67556			−0.274507
$96$		0			0
$97$	−17.2826			−1.75478			−0.877392	−	0.479775i	$-0.840718\pi$
$97$	−17.2826			−1.75478			−0.877392	+	0.479775i	$0.840718\pi$
$98$	−0.935018	+	1.06101i	−0.0944511	+	0.107178i
$99$		0			0
$100$	0.251481	+	1.98413i	0.0251481	+	0.198413i
$101$		−	4.08304i		−	0.406278i	−0.979150	−	0.203139i	$-0.934886\pi$
$101$		−	4.08304i		−	0.406278i	0.979150	−	0.203139i	$-0.0651143\pi$
$102$		0			0
$103$		−	2.57171i		−	0.253398i	−0.991941	−	0.126699i	$-0.959562\pi$
$103$		−	2.57171i		−	0.253398i	0.991941	−	0.126699i	$-0.0404383\pi$
$104$	14.3840	+	9.76241i	1.41047	+	0.957283i
$105$		0			0
$106$	−2.65339	−	2.33831i	−0.257720	−	0.227117i
$107$	8.41742			0.813743			0.406871	−	0.913485i	$-0.366620\pi$
$107$	8.41742			0.813743			0.406871	+	0.913485i	$0.366620\pi$
$108$		0			0
$109$	10.9162			1.04558			0.522790	−	0.852462i	$-0.324891\pi$
$109$	10.9162			1.04558			0.522790	+	0.852462i	$0.324891\pi$
$110$	1.89395	+	1.66905i	0.180581	+	0.159137i
$111$		0			0
$112$	0.997940	+	3.87351i	0.0942965	+	0.366013i
$113$		−	1.78215i		−	0.167650i	−0.996480	−	0.0838251i	$-0.973286\pi$
$113$		−	1.78215i		−	0.167650i	0.996480	−	0.0838251i	$-0.0267137\pi$
$114$		0			0
$115$		−	2.65580i		−	0.247655i
$116$	−1.47750	+	0.187268i	−0.137183	+	0.0173874i
$117$		0			0
$118$	1.15802	−	1.31406i	0.106604	−	0.120969i
$119$	1.11477			0.102191
$120$		0			0
$121$	−7.81362			−0.710329
$122$	−5.99778	+	6.80597i	−0.543014	+	0.616183i
$123$		0			0
$124$	17.1917	−	2.17898i	1.54386	−	0.195679i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$			9.25356i			0.821121i	0.911833	+	0.410561i	$0.134667\pi$
$127$			9.25356i			0.821121i	−0.911833	+	0.410561i	$0.865333\pi$
$128$	10.6503	+	3.81708i	0.941367	+	0.337386i
$129$		0			0
$130$	6.52115	+	5.74679i	0.571943	+	0.504027i
$131$	−14.6313			−1.27834			−0.639172	−	0.769064i	$-0.720723\pi$
$131$	−14.6313			−1.27834			−0.639172	+	0.769064i	$0.720723\pi$
$132$		0			0
$133$	−2.67556			−0.232001
$134$	−4.00256	−	3.52727i	−0.345768	−	0.304710i
$135$		0			0
$136$	1.77066	−	2.60891i	0.151833	−	0.223712i
$137$			0.366817i			0.0313393i	0.999877	+	0.0156696i	$0.00498800\pi$
$137$			0.366817i			0.0313393i	−0.999877	+	0.0156696i	$0.995012\pi$
$138$		0			0
$139$		−	2.39442i		−	0.203092i	−0.994831	−	0.101546i	$-0.967621\pi$
$139$		−	2.39442i		−	0.203092i	0.994831	−	0.101546i	$-0.0323789\pi$
$140$	0.251481	+	1.98413i	0.0212540	+	0.167689i
$141$		0			0
$142$	14.5232	−	16.4801i	1.21876	−	1.38298i
$143$	10.9712			0.917457
$144$		0			0
$145$	−0.744661			−0.0618408
$146$	−5.22487	+	5.92891i	−0.432413	+	0.490680i
$147$		0			0
$148$	1.91852	+	15.1366i	0.157701	+	1.24422i
$149$		−	17.4267i		−	1.42765i	−0.700326	−	0.713824i	$-0.746962\pi$
$149$		−	17.4267i		−	1.42765i	0.700326	−	0.713824i	$-0.253038\pi$
$150$		0			0
$151$		−	20.8266i		−	1.69484i	−0.530920	−	0.847422i	$-0.678154\pi$
$151$		−	20.8266i		−	1.69484i	0.530920	−	0.847422i	$-0.321846\pi$
$152$	−4.24978	+	6.26166i	−0.344703	+	0.507887i
$153$		0			0
$154$	1.89395	+	1.66905i	0.152619	+	0.134496i
$155$	8.66461			0.695958
$156$		0			0
$157$	6.48357			0.517445			0.258723	−	0.965952i	$-0.416698\pi$
$157$	6.48357			0.517445			0.258723	+	0.965952i	$0.416698\pi$
$158$	−12.0398	−	10.6101i	−0.957832	−	0.844094i
$159$		0			0
$160$	5.04293	+	2.56298i	0.398678	+	0.202622i
$161$		−	2.65580i		−	0.209307i
$162$		0			0
$163$		−	20.9447i		−	1.64051i	−0.571995	−	0.820257i	$-0.693830\pi$
$163$		−	20.9447i		−	1.64051i	0.571995	−	0.820257i	$-0.306170\pi$
$164$	−20.8384	+	2.64119i	−1.62720	+	0.206242i
$165$		0			0
$166$	−4.60474	+	5.22522i	−0.357397	+	0.405555i
$167$	22.7297			1.75888			0.879438	−	0.476014i	$-0.157919\pi$
$167$	22.7297			1.75888			0.879438	+	0.476014i	$0.157919\pi$
$168$		0			0
$169$	24.7755			1.90581
$170$	1.04233	−	1.18278i	0.0799429	−	0.0907150i
$171$		0			0
$172$	−18.8611	+	2.39058i	−1.43815	+	0.182280i
$173$		−	4.89112i		−	0.371865i	−0.982563	−	0.185933i	$-0.940469\pi$
$173$		−	4.89112i		−	0.371865i	0.982563	−	0.185933i	$-0.0595306\pi$
$174$		0			0
$175$			1.00000i			0.0755929i
$176$	6.91439	−	1.78137i	0.521192	−	0.134276i
$177$		0			0
$178$	11.9350	+	10.5178i	0.894569	+	0.788342i
$179$	−0.638667			−0.0477362			−0.0238681	−	0.999715i	$-0.507598\pi$
$179$	−0.638667			−0.0477362			−0.0238681	+	0.999715i	$0.507598\pi$
$180$		0			0
$181$	14.0537			1.04461			0.522303	−	0.852760i	$-0.325073\pi$
$181$	14.0537			1.04461			0.522303	+	0.852760i	$0.325073\pi$
$182$	6.52115	+	5.74679i	0.483380	+	0.425980i
$183$		0			0
$184$	−6.21542	−	4.21840i	−0.458206	−	0.310984i
$185$			7.62886i			0.560885i
$186$		0			0
$187$		−	1.98991i		−	0.145516i
$188$	−1.25854	−	9.92959i	−0.0917885	−	0.724190i
$189$		0			0
$190$	−2.50170	+	2.83879i	−0.181492	+	0.205948i
$191$	4.42730			0.320348			0.160174	−	0.987089i	$-0.448794\pi$
$191$	4.42730			0.320348			0.160174	+	0.987089i	$0.448794\pi$
$192$		0			0
$193$	−16.8507			−1.21294			−0.606469	−	0.795107i	$-0.707415\pi$
$193$	−16.8507			−1.21294			−0.606469	+	0.795107i	$0.707415\pi$
$194$	−16.1596	+	18.3370i	−1.16019	+	1.31652i
$195$		0			0
$196$	0.251481	+	1.98413i	0.0179629	+	0.141723i
$197$			2.87374i			0.204746i	0.994746	+	0.102373i	$0.0326435\pi$
$197$			2.87374i			0.204746i	−0.994746	+	0.102373i	$0.967357\pi$
$198$		0			0
$199$			5.54254i			0.392900i	0.980514	+	0.196450i	$0.0629414\pi$
$199$			5.54254i			0.392900i	−0.980514	+	0.196450i	$0.937059\pi$
$200$	2.34032	+	1.58837i	0.165485	+	0.112315i
$201$		0			0
$202$	−4.33214	−	3.81772i	−0.304809	−	0.268614i
$203$	−0.744661			−0.0522650
$204$		0			0
$205$	−10.5025			−0.733529
$206$	−2.72861	−	2.40460i	−0.190111	−	0.167536i
$207$		0			0
$208$	23.8073	−	6.13352i	1.65074	−	0.425283i
$209$			4.77599i			0.330362i
$210$		0			0
$211$		−	10.9485i		−	0.753728i	−0.926269	−	0.376864i	$-0.877002\pi$
$211$		−	10.9485i		−	0.753728i	0.926269	−	0.376864i	$-0.122998\pi$
$212$	−4.96193	+	0.628908i	−0.340787	+	0.0431936i
$213$		0			0
$214$	7.87044	−	8.93096i	0.538012	−	0.610508i
$215$	−9.50600			−0.648304
$216$		0			0
$217$	8.66461			0.588192
$218$	10.2068	−	11.5822i	0.691293	−	0.784443i
$219$		0			0
$220$	3.54175	−	0.448904i	0.238785	−	0.0302651i
$221$		−	6.85156i		−	0.460886i
$222$		0			0
$223$			4.19996i			0.281250i	0.990063	+	0.140625i	$0.0449112\pi$
$223$			4.19996i			0.281250i	−0.990063	+	0.140625i	$0.955089\pi$
$224$	5.04293	+	2.56298i	0.336945	+	0.171247i
$225$		0			0
$226$	−1.89087	−	1.66634i	−0.125779	−	0.110843i
$227$	1.64703			0.109317			0.0546587	−	0.998505i	$-0.482593\pi$
$227$	1.64703			0.109317			0.0546587	+	0.998505i	$0.482593\pi$
$228$		0			0
$229$	0.841682			0.0556199			0.0278100	−	0.999613i	$-0.491147\pi$
$229$	0.841682			0.0556199			0.0278100	+	0.999613i	$0.491147\pi$
$230$	−2.81783	−	2.48322i	−0.185802	−	0.163739i
$231$		0			0
$232$	−1.18280	+	1.74274i	−0.0776545	+	0.114417i
$233$		−	27.1058i		−	1.77576i	−0.460073	−	0.887881i	$-0.652177\pi$
$233$		−	27.1058i		−	1.77576i	0.460073	−	0.887881i	$-0.347823\pi$
$234$		0			0
$235$		−	5.00451i		−	0.326459i
$236$	−0.311458	−	2.45733i	−0.0202742	−	0.159959i
$237$		0			0
$238$	1.04233	−	1.18278i	0.0675641	−	0.0766681i
$239$	11.9107			0.770441			0.385221	−	0.922825i	$-0.374125\pi$
$239$	11.9107			0.770441			0.385221	+	0.922825i	$0.374125\pi$
$240$		0			0
$241$	15.0360			0.968555			0.484277	−	0.874914i	$-0.339083\pi$
$241$	15.0360			0.968555			0.484277	+	0.874914i	$0.339083\pi$
$242$	−7.30588	+	8.29033i	−0.469640	+	0.532922i
$243$		0			0
$244$	1.61315	+	12.7274i	0.103272	+	0.814789i
$245$			1.00000i			0.0638877i
$246$		0			0
$247$			16.4445i			1.04634i
$248$	13.7626	−	20.2779i	0.873927	−	1.28765i
$249$		0			0
$250$	1.06101	+	0.935018i	0.0671041	+	0.0591358i
$251$	13.0078			0.821046			0.410523	−	0.911850i	$-0.365346\pi$
$251$	13.0078			0.821046			0.410523	+	0.911850i	$0.365346\pi$
$252$		0			0
$253$	−4.74072			−0.298046
$254$	9.81812	+	8.65225i	0.616043	+	0.542891i
$255$		0			0
$256$	14.0082	−	7.73107i	0.875514	−	0.483192i
$257$		−	31.6675i		−	1.97536i	−0.156474	−	0.987682i	$-0.550013\pi$
$257$		−	31.6675i		−	1.97536i	0.156474	−	0.987682i	$-0.449987\pi$
$258$		0			0
$259$			7.62886i			0.474035i
$260$	12.1948	−	1.54565i	0.756289	−	0.0958570i
$261$		0			0
$262$	−13.6805	+	15.5240i	−0.845187	+	0.959073i
$263$	−31.5615			−1.94616			−0.973082	−	0.230460i	$-0.925977\pi$
$263$	−31.5615			−1.94616			−0.973082	+	0.230460i	$0.925977\pi$
$264$		0			0
$265$	−2.50082			−0.153624
$266$	−2.50170	+	2.83879i	−0.153389	+	0.174058i
$267$		0			0
$268$	−7.48493	+	0.948689i	−0.457215	+	0.0579504i
$269$			23.3005i			1.42066i	0.703870	+	0.710328i	$0.251454\pi$
$269$			23.3005i			1.42066i	−0.703870	+	0.710328i	$0.748546\pi$
$270$		0			0
$271$			17.7738i			1.07968i	0.841768	+	0.539839i	$0.181515\pi$
$271$			17.7738i			1.07968i	−0.841768	+	0.539839i	$0.818485\pi$
$272$	−1.11247	−	4.31807i	−0.0674535	−	0.261821i
$273$		0			0
$274$	0.389196	+	0.342980i	0.0235122	+	0.0207202i
$275$	1.78504			0.107642
$276$		0			0
$277$	28.3983			1.70629			0.853145	−	0.521674i	$-0.174692\pi$
$277$	28.3983			1.70629			0.853145	+	0.521674i	$0.174692\pi$
$278$	−2.54050	−	2.23882i	−0.152369	−	0.134276i
$279$		0			0
$280$	2.34032	+	1.58837i	0.139861	+	0.0949233i
$281$			1.77885i			0.106117i	0.998591	+	0.0530586i	$0.0168970\pi$
$281$			1.77885i			0.106117i	−0.998591	+	0.0530586i	$0.983103\pi$
$282$		0			0
$283$			11.2173i			0.666798i	0.942786	+	0.333399i	$0.108196\pi$
$283$			11.2173i			0.666798i	−0.942786	+	0.333399i	$0.891804\pi$
$284$	−3.90612	−	30.8184i	−0.231786	−	1.82874i
$285$		0			0
$286$	10.2583	−	11.6405i	0.606584	−	0.688319i
$287$	−10.5025			−0.619945
$288$		0			0
$289$	15.7573			0.926900
$290$	−0.696272	+	0.790093i	−0.0408865	+	0.0463958i
$291$		0			0
$292$	1.40527	+	11.0873i	0.0822374	+	0.648833i
$293$		−	14.3304i		−	0.837193i	−0.908172	−	0.418596i	$-0.862522\pi$
$293$		−	14.3304i		−	0.837193i	0.908172	−	0.418596i	$-0.137478\pi$
$294$		0			0
$295$		−	1.23850i		−	0.0721080i
$296$	17.8540	+	12.1175i	1.03774	+	0.704313i
$297$		0			0
$298$	−18.4898	−	16.2942i	−1.07109	−	0.943900i
$299$	−16.3230			−0.943985
$300$		0			0
$301$	−9.50600			−0.547917
$302$	−22.0972	−	19.4732i	−1.27155	−	1.12056i
$303$		0			0
$304$	2.67005	+	10.3638i	0.153138	+	0.594406i
$305$			6.41461i			0.367300i
$306$		0			0
$307$			20.0746i			1.14572i	0.819653	+	0.572860i	$0.194166\pi$
$307$			20.0746i			1.14572i	−0.819653	+	0.572860i	$0.805834\pi$
$308$	3.54175	−	0.448904i	0.201810	−	0.0255787i
$309$		0			0
$310$	8.10157	−	9.19323i	0.460138	−	0.522140i
$311$	24.4717			1.38766			0.693831	−	0.720138i	$-0.255921\pi$
$311$	24.4717			1.38766			0.693831	+	0.720138i	$0.255921\pi$
$312$		0			0
$313$	−8.66395			−0.489715			−0.244858	−	0.969559i	$-0.578741\pi$
$313$	−8.66395			−0.489715			−0.244858	+	0.969559i	$0.578741\pi$
$314$	6.06226	−	6.87913i	0.342113	−	0.388212i
$315$		0			0
$316$	−22.5148	+	2.85367i	−1.26656	+	0.160532i
$317$			3.75557i			0.210934i	0.994423	+	0.105467i	$0.0336337\pi$
$317$			3.75557i			0.210934i	−0.994423	+	0.105467i	$0.966366\pi$
$318$		0			0
$319$			1.32925i			0.0744238i
$320$	7.43458	−	2.95416i	0.415606	−	0.165142i
$321$		0			0
$322$	−2.81783	−	2.48322i	−0.157032	−	0.138385i
$323$	2.98263			0.165958
$324$		0			0
$325$	6.14618			0.340929
$326$	−22.2225	−	19.5837i	−1.23079	−	1.08464i
$327$		0			0
$328$	−16.6819	+	24.5793i	−0.921105	+	1.35716i
$329$		−	5.00451i		−	0.275908i
$330$		0			0
$331$			26.5167i			1.45749i	0.684784	+	0.728746i	$0.259896\pi$
$331$			26.5167i			1.45749i	−0.684784	+	0.728746i	$0.740104\pi$
$332$	1.23848	+	9.77135i	0.0679707	+	0.536272i
$333$		0			0
$334$	21.2527	−	24.1164i	1.16289	−	1.31959i
$335$	−3.77241			−0.206109
$336$		0			0
$337$	−5.97601			−0.325534			−0.162767	−	0.986665i	$-0.552042\pi$
$337$	−5.97601			−0.325534			−0.162767	+	0.986665i	$0.552042\pi$
$338$	23.1655	−	26.2870i	1.26004	−	1.42983i
$339$		0			0
$340$	−0.280343	−	2.21184i	−0.0152037	−	0.119954i
$341$		−	15.4667i		−	0.837568i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−15.0991	+	22.2470i	−0.814087	+	1.19948i
$345$		0			0
$346$	−5.18952	−	4.57329i	−0.278991	−	0.245861i
$347$	−18.6211			−0.999635			−0.499818	−	0.866131i	$-0.666600\pi$
$347$	−18.6211			−0.999635			−0.499818	+	0.866131i	$0.666600\pi$
$348$		0			0
$349$	18.8450			1.00875			0.504374	−	0.863485i	$-0.331723\pi$
$349$	18.8450			1.00875			0.504374	+	0.863485i	$0.331723\pi$
$350$	1.06101	+	0.935018i	0.0567133	+	0.0499788i
$351$		0			0
$352$	4.57503	−	9.00184i	0.243850	−	0.479800i
$353$			12.7221i			0.677129i	0.940943	+	0.338565i	$0.109941\pi$
$353$			12.7221i			0.677129i	−0.940943	+	0.338565i	$0.890059\pi$
$354$		0			0
$355$		−	15.5325i		−	0.824378i
$356$	22.3190	−	2.82885i	1.18290	−	0.149929i
$357$		0			0
$358$	−0.597166	+	0.677632i	−0.0315612	+	0.0358140i
$359$	−19.6912			−1.03926			−0.519630	−	0.854391i	$-0.673930\pi$
$359$	−19.6912			−1.03926			−0.519630	+	0.854391i	$0.673930\pi$
$360$		0			0
$361$	11.8414			0.623230
$362$	13.1405	−	14.9111i	0.690649	−	0.783712i
$363$		0			0
$364$	12.1948	−	1.54565i	0.639181	−	0.0810139i
$365$			5.58799i			0.292489i
$366$		0			0
$367$			4.33850i			0.226468i	0.993568	+	0.113234i	$0.0361209\pi$
$367$			4.33850i			0.226468i	−0.993568	+	0.113234i	$0.963879\pi$
$368$	−10.2873	+	2.65033i	−0.536262	+	0.138158i
$369$		0			0
$370$	8.09430	+	7.13313i	0.420802	+	0.370834i
$371$	−2.50082			−0.129836
$372$		0			0
$373$	−22.3464			−1.15705			−0.578526	−	0.815664i	$-0.696372\pi$
$373$	−22.3464			−1.15705			−0.578526	+	0.815664i	$0.696372\pi$
$374$	−2.11131	−	1.86060i	−0.109173	−	0.0962093i
$375$		0			0
$376$	−11.7121	−	7.94903i	−0.604008	−	0.409940i
$377$			4.57682i			0.235718i
$378$		0			0
$379$			19.7583i			1.01492i	0.861676	+	0.507458i	$0.169415\pi$
$379$			19.7583i			1.01492i	−0.861676	+	0.507458i	$0.830585\pi$
$380$	0.672853	+	5.30865i	0.0345166	+	0.272328i
$381$		0			0
$382$	4.13961	−	4.69741i	0.211801	−	0.240340i
$383$	−16.9359			−0.865384			−0.432692	−	0.901542i	$-0.642436\pi$
$383$	−16.9359			−0.865384			−0.432692	+	0.901542i	$0.642436\pi$
$384$		0			0
$385$	1.78504			0.0909742
$386$	−15.7557	+	17.8787i	−0.801944	+	0.910003i
$387$		0			0
$388$	4.34625	+	34.2909i	0.220647	+	1.74086i
$389$			5.00795i			0.253913i	0.991908	+	0.126957i	$0.0405209\pi$
$389$			5.00795i			0.253913i	−0.991908	+	0.126957i	$0.959479\pi$
$390$		0			0
$391$			2.96060i			0.149724i
$392$	2.34032	+	1.58837i	0.118204	+	0.0802248i
$393$		0			0
$394$	3.04907	+	2.68700i	0.153610	+	0.135369i
$395$	−11.3475			−0.570953
$396$		0			0
$397$	−18.6811			−0.937579			−0.468789	−	0.883310i	$-0.655310\pi$
$397$	−18.6811			−0.937579			−0.468789	+	0.883310i	$0.655310\pi$
$398$	5.88068	+	5.18238i	0.294772	+	0.259769i
$399$		0			0
$400$	3.87351	−	0.997940i	0.193676	−	0.0498970i
$401$		−	27.6477i		−	1.38066i	−0.723495	−	0.690330i	$-0.757465\pi$
$401$		−	27.6477i		−	1.38066i	0.723495	−	0.690330i	$-0.242535\pi$
$402$		0			0
$403$		−	53.2542i		−	2.65278i
$404$	−8.10127	+	1.02681i	−0.403053	+	0.0510856i
$405$		0			0
$406$	−0.696272	+	0.790093i	−0.0345554	+	0.0392116i
$407$	13.6178			0.675012
$408$		0			0
$409$	−22.7082			−1.12285			−0.561425	−	0.827527i	$-0.689747\pi$
$409$	−22.7082			−1.12285			−0.561425	+	0.827527i	$0.689747\pi$
$410$	−9.82007	+	11.1433i	−0.484979	+	0.550328i
$411$		0			0
$412$	−5.10260	+	0.646737i	−0.251387	+	0.0318625i
$413$		−	1.23850i		−	0.0609424i
$414$		0			0
$415$			4.92476i			0.241747i
$416$	15.7526	−	30.9947i	0.772332	−	1.51964i
$417$		0			0
$418$	5.06737	+	4.46564i	0.247853	+	0.218421i
$419$	2.91843			0.142574			0.0712872	−	0.997456i	$-0.477289\pi$
$419$	2.91843			0.142574			0.0712872	+	0.997456i	$0.477289\pi$
$420$		0			0
$421$	4.58992			0.223699			0.111850	−	0.993725i	$-0.464323\pi$
$421$	4.58992			0.223699			0.111850	+	0.993725i	$0.464323\pi$
$422$	−11.6165	−	10.2371i	−0.565482	−	0.498333i
$423$		0			0
$424$	−3.97222	+	5.85270i	−0.192908	+	0.284232i
$425$		−	1.11477i		−	0.0540742i
$426$		0			0
$427$			6.41461i			0.310425i
$428$	−2.11682	−	16.7012i	−0.102320	−	0.807284i
$429$		0			0
$430$	−8.88829	+	10.0860i	−0.428631	+	0.486388i
$431$	30.8239			1.48473			0.742366	−	0.669994i	$-0.233703\pi$
$431$	30.8239			1.48473			0.742366	+	0.669994i	$0.233703\pi$
$432$		0			0
$433$	−7.39741			−0.355497			−0.177748	−	0.984076i	$-0.556881\pi$
$433$	−7.39741			−0.355497			−0.177748	+	0.984076i	$0.556881\pi$
$434$	8.10157	−	9.19323i	0.388888	−	0.441289i
$435$		0			0
$436$	−2.74521	−	21.6591i	−0.131472	−	1.03728i
$437$		−	7.10576i		−	0.339915i
$438$		0			0
$439$			23.5342i			1.12322i	0.827401	+	0.561612i	$0.189819\pi$
$439$			23.5342i			1.12322i	−0.827401	+	0.561612i	$0.810181\pi$
$440$	2.83531	−	4.17756i	0.135168	−	0.199157i
$441$		0			0
$442$	−7.26957	−	6.40633i	−0.345778	−	0.304718i
$443$	1.52531			0.0724695			0.0362348	−	0.999343i	$-0.488464\pi$
$443$	1.52531			0.0724695			0.0362348	+	0.999343i	$0.488464\pi$
$444$		0			0
$445$	11.2488			0.533242
$446$	4.45620	+	3.92704i	0.211007	+	0.185951i
$447$		0			0
$448$	7.43458	−	2.95416i	0.351251	−	0.139571i
$449$			36.8140i			1.73736i	0.495372	+	0.868681i	$0.335032\pi$
$449$			36.8140i			1.73736i	−0.495372	+	0.868681i	$0.664968\pi$
$450$		0			0
$451$			18.7475i			0.882784i
$452$	−3.53600	+	0.448176i	−0.166320	+	0.0210804i
$453$		0			0
$454$	1.54001	−	1.74752i	0.0722760	−	0.0820150i
$455$	6.14618			0.288137
$456$		0			0
$457$	17.5387			0.820427			0.410213	−	0.911990i	$-0.365454\pi$
$457$	17.5387			0.820427			0.410213	+	0.911990i	$0.365454\pi$
$458$	0.786988	−	0.893033i	0.0367736	−	0.0417287i
$459$		0			0
$460$	−5.26945	+	0.667884i	−0.245689	+	0.0311402i
$461$		−	20.6600i		−	0.962232i	−0.876657	−	0.481116i	$-0.840232\pi$
$461$		−	20.6600i		−	0.962232i	0.876657	−	0.481116i	$-0.159768\pi$
$462$		0			0
$463$		−	33.8911i		−	1.57505i	−0.616281	−	0.787526i	$-0.711361\pi$
$463$		−	33.8911i		−	1.57505i	0.616281	−	0.787526i	$-0.288639\pi$
$464$	0.743128	+	2.88446i	0.0344988	+	0.133908i
$465$		0			0
$466$	−28.7595	−	25.3444i	−1.33226	−	1.17406i
$467$	−41.1355			−1.90353			−0.951763	−	0.306835i	$-0.900730\pi$
$467$	−41.1355			−1.90353			−0.951763	+	0.306835i	$0.900730\pi$
$468$		0			0
$469$	−3.77241			−0.174194
$470$	−5.30984	−	4.67931i	−0.244924	−	0.215841i
$471$		0			0
$472$	−2.89847	−	1.96719i	−0.133413	−	0.0905473i
$473$			16.9686i			0.780218i
$474$		0			0
$475$			2.67556i			0.122763i
$476$	−0.280343	−	2.21184i	−0.0128495	−	0.101379i
$477$		0			0
$478$	11.1368	−	12.6374i	0.509383	−	0.578021i
$479$	3.83901			0.175409			0.0877043	−	0.996147i	$-0.472047\pi$
$479$	3.83901			0.175409			0.0877043	+	0.996147i	$0.472047\pi$
$480$		0			0
$481$	46.8884			2.13793
$482$	14.0590	−	15.9534i	0.640368	−	0.726655i
$483$		0			0
$484$	1.96498	+	15.5032i	0.0893172	+	0.704692i
$485$			17.2826i			0.784763i
$486$		0			0
$487$		−	23.8493i		−	1.08072i	−0.841435	−	0.540358i	$-0.818289\pi$
$487$		−	23.8493i		−	1.08072i	0.841435	−	0.540358i	$-0.181711\pi$
$488$	15.0122	+	10.1888i	0.679571	+	0.461225i
$489$		0			0
$490$	1.06101	+	0.935018i	0.0479315	+	0.0422398i
$491$	−7.57026			−0.341641			−0.170821	−	0.985302i	$-0.554642\pi$
$491$	−7.57026			−0.341641			−0.170821	+	0.985302i	$0.554642\pi$
$492$		0			0
$493$	0.830124			0.0373869
$494$	17.4477	+	15.3759i	0.785011	+	0.691794i
$495$		0			0
$496$	−8.64676	−	33.5625i	−0.388251	−	1.50700i
$497$		−	15.5325i		−	0.696727i
$498$		0			0
$499$		−	40.2092i		−	1.80001i	−0.435878	−	0.900006i	$-0.643562\pi$
$499$		−	40.2092i		−	1.80001i	0.435878	−	0.900006i	$-0.356438\pi$
$500$	1.98413	−	0.251481i	0.0887328	−	0.0112466i
$501$		0			0
$502$	12.1625	−	13.8014i	0.542841	−	0.615987i
$503$	−37.9674			−1.69288			−0.846441	−	0.532483i	$-0.821259\pi$
$503$	−37.9674			−1.69288			−0.846441	+	0.532483i	$0.821259\pi$
$504$		0			0
$505$	−4.08304			−0.181693
$506$	−4.43266	+	5.02995i	−0.197056	+	0.223608i
$507$		0			0
$508$	18.3602	−	2.32710i	0.814604	−	0.103248i
$509$			26.9404i			1.19411i	0.802200	+	0.597056i	$0.203663\pi$
$509$			26.9404i			1.19411i	−0.802200	+	0.597056i	$0.796337\pi$
$510$		0			0
$511$			5.58799i			0.247198i
$512$	4.89521	−	22.0916i	0.216340	−	0.976318i
$513$		0			0
$514$	−33.5995	−	29.6097i	−1.48201	−	1.30603i
$515$	−2.57171			−0.113323
$516$		0			0
$517$	−8.93327			−0.392885
$518$	8.09430	+	7.13313i	0.355643	+	0.313412i
$519$		0			0
$520$	9.76241	−	14.3840i	0.428110	−	0.630780i
$521$			30.0568i			1.31681i	0.752663	+	0.658406i	$0.228769\pi$
$521$			30.0568i			1.31681i	−0.752663	+	0.658406i	$0.771231\pi$
$522$		0			0
$523$			1.53868i			0.0672817i	0.999434	+	0.0336409i	$0.0107102\pi$
$523$			1.53868i			0.0672817i	−0.999434	+	0.0336409i	$0.989290\pi$
$524$	3.67950	+	29.0304i	0.160740	+	1.26820i
$525$		0			0
$526$	−29.5106	+	33.4870i	−1.28672	+	1.46010i
$527$	−9.65902			−0.420754
$528$		0			0
$529$	−15.9467			−0.693335
$530$	−2.33831	+	2.65339i	−0.101570	+	0.115256i
$531$		0			0
$532$	0.672853	+	5.30865i	0.0291719	+	0.230159i
$533$			64.5505i			2.79599i
$534$		0			0
$535$		−	8.41742i		−	0.363917i
$536$	−5.99198	+	8.82862i	−0.258814	+	0.381339i
$537$		0			0
$538$	24.7220	+	21.7864i	1.06584	+	0.939278i
$539$	1.78504			0.0768872
$540$		0			0
$541$	20.0807			0.863338			0.431669	−	0.902032i	$-0.357925\pi$
$541$	20.0807			0.863338			0.431669	+	0.902032i	$0.357925\pi$
$542$	18.8581	+	16.6188i	0.810025	+	0.713838i
$543$		0			0
$544$	−5.62169	−	2.85713i	−0.241028	−	0.122498i
$545$		−	10.9162i		−	0.467597i
$546$		0			0
$547$		−	7.42216i		−	0.317349i	−0.987331	−	0.158674i	$-0.949278\pi$
$547$		−	7.42216i		−	0.317349i	0.987331	−	0.158674i	$-0.0507220\pi$
$548$	0.727811	−	0.0922474i	0.0310905	−	0.00394062i
$549$		0			0
$550$	1.66905	−	1.89395i	0.0711684	−	0.0807581i
$551$	−1.99239			−0.0848785
$552$		0			0
$553$	−11.3475			−0.482543
$554$	26.5529	−	30.1309i	1.12813	−	1.28014i
$555$		0			0
$556$	−4.75083	+	0.602151i	−0.201480	+	0.0255369i
$557$			26.2422i			1.11192i	0.831209	+	0.555960i	$0.187649\pi$
$557$			26.2422i			1.11192i	−0.831209	+	0.555960i	$0.812351\pi$
$558$		0			0
$559$			58.4256i			2.47114i
$560$	3.87351	−	0.997940i	0.163686	−	0.0421707i
$561$		0			0
$562$	1.88737	+	1.66325i	0.0796140	+	0.0701602i
$563$	−14.6337			−0.616736			−0.308368	−	0.951267i	$-0.599783\pi$
$563$	−14.6337			−0.616736			−0.308368	+	0.951267i	$0.599783\pi$
$564$		0			0
$565$	−1.78215			−0.0749755
$566$	11.9016	+	10.4884i	0.500263	+	0.440858i
$567$		0			0
$568$	−36.3509	−	24.6713i	−1.52525	−	1.03519i
$569$			11.2621i			0.472132i	0.971737	+	0.236066i	$0.0758581\pi$
$569$			11.2621i			0.472132i	−0.971737	+	0.236066i	$0.924142\pi$
$570$		0			0
$571$			27.9392i			1.16922i	0.811315	+	0.584610i	$0.198752\pi$
$571$			27.9392i			1.16922i	−0.811315	+	0.584610i	$0.801248\pi$
$572$	−2.75905	−	21.7682i	−0.115362	−	0.910175i
$573$		0			0
$574$	−9.82007	+	11.1433i	−0.409882	+	0.465112i
$575$	−2.65580			−0.110755
$576$		0			0
$577$	31.7206			1.32055			0.660273	−	0.751026i	$-0.270441\pi$
$577$	31.7206			1.32055			0.660273	+	0.751026i	$0.270441\pi$
$578$	14.7334	−	16.7186i	0.612827	−	0.695403i
$579$		0			0
$580$	0.187268	+	1.47750i	0.00777589	+	0.0613499i
$581$			4.92476i			0.204314i
$582$		0			0
$583$			4.46406i			0.184883i
$584$	13.0777	+	8.87580i	0.541157	+	0.367283i
$585$		0			0
$586$	−15.2047	−	13.3992i	−0.628101	−	0.553517i
$587$	−11.1828			−0.461564			−0.230782	−	0.973005i	$-0.574128\pi$
$587$	−11.1828			−0.461564			−0.230782	+	0.973005i	$0.574128\pi$
$588$		0			0
$589$	23.1827			0.955226
$590$	−1.31406	−	1.15802i	−0.0540988	−	0.0476748i
$591$		0			0
$592$	29.5505	−	7.61315i	1.21452	−	0.312899i
$593$			6.96062i			0.285838i	0.989734	+	0.142919i	$0.0456489\pi$
$593$			6.96062i			0.285838i	−0.989734	+	0.142919i	$0.954351\pi$
$594$		0			0
$595$		−	1.11477i		−	0.0457010i
$596$	−34.5767	+	4.38247i	−1.41632	+	0.179513i
$597$		0			0
$598$	−15.2623	+	17.3189i	−0.624123	+	0.708222i
$599$	1.08694			0.0444111			0.0222055	−	0.999753i	$-0.492931\pi$
$599$	1.08694			0.0444111			0.0222055	+	0.999753i	$0.492931\pi$
$600$		0			0
$601$	−25.4366			−1.03758			−0.518789	−	0.854902i	$-0.673617\pi$
$601$	−25.4366			−1.03758			−0.518789	+	0.854902i	$0.673617\pi$
$602$	−8.88829	+	10.0860i	−0.362259	+	0.411073i
$603$		0			0
$604$	−41.3226	+	5.23749i	−1.68139	+	0.213111i
$605$			7.81362i			0.317669i
$606$		0			0
$607$			1.83622i			0.0745299i	0.999305	+	0.0372649i	$0.0118645\pi$
$607$			1.83622i			0.0745299i	−0.999305	+	0.0372649i	$0.988135\pi$
$608$	13.4927	+	6.85742i	0.547199	+	0.278105i
$609$		0			0
$610$	6.80597	+	5.99778i	0.275565	+	0.242843i
$611$	−30.7586			−1.24436
$612$		0			0
$613$	−18.5165			−0.747876			−0.373938	−	0.927454i	$-0.621993\pi$
$613$	−18.5165			−0.747876			−0.373938	+	0.927454i	$0.621993\pi$
$614$	21.2994	+	18.7702i	0.859573	+	0.757502i
$615$		0			0
$616$	2.83531	−	4.17756i	0.114238	−	0.168319i
$617$			23.2330i			0.935324i	0.883907	+	0.467662i	$0.154904\pi$
$617$			23.2330i			0.935324i	−0.883907	+	0.467662i	$0.845096\pi$
$618$		0			0
$619$		−	35.9146i		−	1.44353i	−0.692138	−	0.721766i	$-0.743331\pi$
$619$		−	35.9146i		−	1.44353i	0.692138	−	0.721766i	$-0.256669\pi$
$620$	−2.17898	−	17.1917i	−0.0875101	−	0.690434i
$621$		0			0
$622$	22.8815	−	25.9647i	0.917464	−	1.04109i
$623$	11.2488			0.450672
$624$		0			0
$625$	1.00000			0.0400000
$626$	−8.10095	+	9.19253i	−0.323779	+	0.367407i
$627$		0			0
$628$	−1.63050	−	12.8642i	−0.0650639	−	0.513338i
$629$		−	8.50441i		−	0.339093i
$630$		0			0
$631$			29.9098i			1.19069i	0.803469	+	0.595346i	$0.202985\pi$
$631$			29.9098i			1.19069i	−0.803469	+	0.595346i	$0.797015\pi$
$632$	−18.0240	+	26.5567i	−0.716956	+	1.05637i
$633$		0			0
$634$	3.98469	+	3.51153i	0.158252	+	0.139460i
$635$	9.25356			0.367216
$636$		0			0
$637$	6.14618			0.243520
$638$	1.41035	+	1.24288i	0.0558362	+	0.0492059i
$639$		0			0
$640$	3.81708	−	10.6503i	0.150883	−	0.420992i
$641$			15.0812i			0.595672i	0.954617	+	0.297836i	$0.0962648\pi$
$641$			15.0812i			0.595672i	−0.954617	+	0.297836i	$0.903735\pi$
$642$		0			0
$643$			15.2532i			0.601529i	0.953699	+	0.300764i	$0.0972417\pi$
$643$			15.2532i			0.601529i	−0.953699	+	0.300764i	$0.902758\pi$
$644$	−5.26945	+	0.667884i	−0.207645	+	0.0263183i
$645$		0			0
$646$	2.78881	−	3.16460i	0.109724	−	0.124509i
$647$	27.3851			1.07662			0.538309	−	0.842748i	$-0.319063\pi$
$647$	27.3851			1.07662			0.538309	+	0.842748i	$0.319063\pi$
$648$		0			0
$649$	−2.21077			−0.0867802
$650$	5.74679	−	6.52115i	0.225408	−	0.255781i
$651$		0			0
$652$	−41.5569	+	5.26719i	−1.62749	+	0.206279i
$653$			25.2084i			0.986480i	0.869893	+	0.493240i	$0.164188\pi$
$653$			25.2084i			0.986480i	−0.869893	+	0.493240i	$0.835812\pi$
$654$		0			0
$655$			14.6313i			0.571693i
$656$	10.4809	+	40.6817i	0.409211	+	1.58836i
$657$		0			0
$658$	−5.30984	−	4.67931i	−0.206999	−	0.182419i
$659$	31.4030			1.22329			0.611644	−	0.791133i	$-0.290509\pi$
$659$	31.4030			1.22329			0.611644	+	0.791133i	$0.290509\pi$
$660$		0			0
$661$	2.05842			0.0800631			0.0400316	−	0.999198i	$-0.487254\pi$
$661$	2.05842			0.0800631			0.0400316	+	0.999198i	$0.487254\pi$
$662$	28.1345	+	24.7936i	1.09348	+	0.963632i
$663$		0			0
$664$	11.5255	+	7.82235i	0.447276	+	0.303566i
$665$			2.67556i			0.103754i
$666$		0			0
$667$		−	1.97767i		−	0.0765758i
$668$	−5.71609	−	45.0986i	−0.221162	−	1.74492i
$669$		0			0
$670$	−3.52727	+	4.00256i	−0.136270	+	0.154632i
$671$	11.4504			0.442036
$672$		0			0
$673$	−14.8449			−0.572231			−0.286115	−	0.958195i	$-0.592364\pi$
$673$	−14.8449			−0.572231			−0.286115	+	0.958195i	$0.592364\pi$
$674$	−5.58768	+	6.34060i	−0.215229	+	0.244231i
$675$		0			0
$676$	−6.23057	−	49.1577i	−0.239637	−	1.89068i
$677$		−	11.8667i		−	0.456073i	−0.973653	−	0.228036i	$-0.926770\pi$
$677$		−	11.8667i		−	0.456073i	0.973653	−	0.228036i	$-0.0732305\pi$
$678$		0			0
$679$			17.2826i			0.663246i
$680$	−2.60891	−	1.77066i	−0.100047	−	0.0679019i
$681$		0			0
$682$	−16.4103	−	14.4616i	−0.628383	−	0.553765i
$683$	−18.8529			−0.721387			−0.360694	−	0.932684i	$-0.617460\pi$
$683$	−18.8529			−0.721387			−0.360694	+	0.932684i	$0.617460\pi$
$684$		0			0
$685$	0.366817			0.0140153
$686$	1.06101	+	0.935018i	0.0405095	+	0.0356992i
$687$		0			0
$688$	9.48642	+	36.8216i	0.361666	+	1.40381i
$689$			15.3705i			0.585568i
$690$		0			0
$691$		−	29.5363i		−	1.12362i	−0.827268	−	0.561808i	$-0.810106\pi$
$691$		−	29.5363i		−	1.12362i	0.827268	−	0.561808i	$-0.189894\pi$
$692$	−9.70460	+	1.23002i	−0.368914	+	0.0467585i
$693$		0			0
$694$	−17.4111	+	19.7572i	−0.660917	+	0.749973i
$695$	−2.39442			−0.0908254
$696$		0			0
$697$	11.7079			0.443468
$698$	17.6204	−	19.9947i	0.666942	−	0.756810i
$699$		0			0
$700$	1.98413	−	0.251481i	0.0749929	−	0.00950509i
$701$			11.7575i			0.444074i	0.975038	+	0.222037i	$0.0712706\pi$
$701$			11.7575i			0.444074i	−0.975038	+	0.222037i	$0.928729\pi$
$702$		0			0
$703$			20.4115i			0.769834i
$704$	−5.27329	−	13.2710i	−0.198745	−	0.500171i
$705$		0			0
$706$	13.4983	+	11.8954i	0.508014	+	0.447689i
$707$	−4.08304			−0.153559
$708$		0			0
$709$	−30.8039			−1.15686			−0.578432	−	0.815731i	$-0.696335\pi$
$709$	−30.8039			−1.15686			−0.578432	+	0.815731i	$0.696335\pi$
$710$	−16.4801	−	14.5232i	−0.618487	−	0.545044i
$711$		0			0
$712$	17.8672	−	26.3256i	0.669602	−	0.986595i
$713$			23.0115i			0.861787i
$714$		0			0
$715$		−	10.9712i		−	0.410299i
$716$	0.160613	+	1.26720i	0.00600238	+	0.0473574i
$717$		0			0
$718$	−18.4116	+	20.8925i	−0.687115	+	0.779702i
$719$	−10.5183			−0.392266			−0.196133	−	0.980577i	$-0.562838\pi$
$719$	−10.5183			−0.392266			−0.196133	+	0.980577i	$0.562838\pi$
$720$		0			0
$721$	−2.57171			−0.0957756
$722$	11.0719	−	12.5638i	0.412054	−	0.467577i
$723$		0			0
$724$	−3.53425	−	27.8844i	−0.131349	−	1.03631i
$725$			0.744661i			0.0276560i
$726$		0			0
$727$			36.9943i			1.37204i	0.727582	+	0.686021i	$0.240644\pi$
$727$			36.9943i			1.37204i	−0.727582	+	0.686021i	$0.759356\pi$
$728$	9.76241	−	14.3840i	0.361819	−	0.533106i
$729$		0			0
$730$	5.92891	+	5.22487i	0.219439	+	0.193381i
$731$	10.5970			0.391943
$732$		0			0
$733$	−25.6451			−0.947222			−0.473611	−	0.880734i	$-0.657050\pi$
$733$	−25.6451			−0.947222			−0.473611	+	0.880734i	$0.657050\pi$
$734$	4.60319	+	4.05658i	0.169907	+	0.149731i
$735$		0			0
$736$	−6.80678	+	13.3930i	−0.250901	+	0.493673i
$737$			6.73391i			0.248047i
$738$		0			0
$739$		−	17.7468i		−	0.652825i	−0.945227	−	0.326413i	$-0.894160\pi$
$739$		−	17.7468i		−	0.652825i	0.945227	−	0.326413i	$-0.105840\pi$
$740$	15.1366	−	1.91852i	0.556434	−	0.0705260i
$741$		0			0
$742$	−2.33831	+	2.65339i	−0.0858420	+	0.0974089i
$743$	50.3247			1.84623			0.923117	−	0.384520i	$-0.125633\pi$
$743$	50.3247			1.84623			0.923117	+	0.384520i	$0.125633\pi$
$744$		0			0
$745$	−17.4267			−0.638463
$746$	−20.8943	+	23.7097i	−0.764994	+	0.868074i
$747$		0			0
$748$	−3.94823	+	0.500424i	−0.144361	+	0.0182973i
$749$		−	8.41742i		−	0.307566i
$750$		0			0
$751$			35.2002i			1.28447i	0.766506	+	0.642237i	$0.221993\pi$
$751$			35.2002i			1.28447i	−0.766506	+	0.642237i	$0.778007\pi$
$752$	−19.3851	+	4.99421i	−0.706900	+	0.182120i
$753$		0			0
$754$	4.85605	+	4.27941i	0.176847	+	0.155847i
$755$	−20.8266			−0.757957
$756$		0			0
$757$	26.4292			0.960587			0.480293	−	0.877108i	$-0.340530\pi$
$757$	26.4292			0.960587			0.480293	+	0.877108i	$0.340530\pi$
$758$	20.9638	+	18.4744i	0.761438	+	0.671020i
$759$		0			0
$760$	6.26166	+	4.24978i	0.227134	+	0.154156i
$761$		−	40.8769i		−	1.48179i	−0.671623	−	0.740893i	$-0.734403\pi$
$761$		−	40.8769i		−	1.48179i	0.671623	−	0.740893i	$-0.265597\pi$
$762$		0			0
$763$		−	10.9162i		−	0.395192i
$764$	−1.11338	−	8.78433i	−0.0402808	−	0.317806i
$765$		0			0
$766$	−15.8354	+	17.9691i	−0.572155	+	0.649251i
$767$	−7.61201			−0.274854
$768$		0			0
$769$	−19.6885			−0.709986			−0.354993	−	0.934869i	$-0.615517\pi$
$769$	−19.6885			−0.709986			−0.354993	+	0.934869i	$0.615517\pi$
$770$	1.66905	−	1.89395i	0.0601483	−	0.0682531i
$771$		0			0
$772$	4.23763	+	33.4339i	0.152516	+	1.20331i
$773$		−	38.9707i		−	1.40168i	−0.713319	−	0.700840i	$-0.752809\pi$
$773$		−	38.9707i		−	1.40168i	0.713319	−	0.700840i	$-0.247191\pi$
$774$		0			0
$775$		−	8.66461i		−	0.311242i
$776$	40.4468	+	27.4512i	1.45195	+	0.985441i
$777$		0			0
$778$	5.31348	+	4.68253i	0.190498	+	0.167877i
$779$	−28.1002			−1.00679
$780$		0			0
$781$	−27.7261			−0.992119
$782$	3.14123	+	2.76822i	0.112330	+	0.0989912i
$783$		0			0
$784$	3.87351	−	0.997940i	0.138340	−	0.0356407i
$785$		−	6.48357i		−	0.231409i
$786$		0			0
$787$		−	33.2816i		−	1.18636i	−0.805070	−	0.593180i	$-0.797872\pi$
$787$		−	33.2816i		−	1.18636i	0.805070	−	0.593180i	$-0.202128\pi$
$788$	5.70187	−	0.722692i	0.203121	−	0.0257448i
$789$		0			0
$790$	−10.6101	+	12.0398i	−0.377490	+	0.428356i
$791$	−1.78215			−0.0633659
$792$		0			0
$793$	39.4254			1.40004
$794$	−17.4672	+	19.8208i	−0.619888	+	0.703416i
$795$		0			0
$796$	10.9971	−	1.39384i	0.389782	−	0.0494035i
$797$		−	35.3250i		−	1.25128i	−0.780114	−	0.625638i	$-0.784839\pi$
$797$		−	35.3250i		−	1.25128i	0.780114	−	0.625638i	$-0.215161\pi$
$798$		0			0
$799$			5.57887i			0.197366i
$800$	2.56298	−	5.04293i	0.0906152	−	0.178294i
$801$		0			0
$802$	−29.3345	−	25.8511i	−1.03584	−	0.912834i
$803$	9.97479			0.352003
$804$		0			0
$805$	−2.65580			−0.0936047
$806$	−56.5032	−	49.7937i	−1.99024	−	1.75391i
$807$		0			0
$808$	−6.48539	+	9.55561i	−0.228155	+	0.336165i
$809$		−	25.3389i		−	0.890868i	−0.895315	−	0.445434i	$-0.853049\pi$
$809$		−	25.3389i		−	0.890868i	0.895315	−	0.445434i	$-0.146951\pi$
$810$		0			0
$811$		−	13.7848i		−	0.484048i	−0.970270	−	0.242024i	$-0.922189\pi$
$811$		−	13.7848i		−	0.484048i	0.970270	−	0.242024i	$-0.0778113\pi$
$812$	0.187268	+	1.47750i	0.00657183	+	0.0518502i
$813$		0			0
$814$	12.7329	−	14.4487i	0.446289	−	0.506425i
$815$	−20.9447			−0.733660
$816$		0			0
$817$	−25.4339			−0.889819
$818$	−21.2326	+	24.0937i	−0.742381	+	0.842415i
$819$		0			0
$820$	2.64119	+	20.8384i	0.0922344	+	0.727707i
$821$			29.9654i			1.04580i	0.852395	+	0.522899i	$0.175150\pi$
$821$			29.9654i			1.04580i	−0.852395	+	0.522899i	$0.824850\pi$
$822$		0			0
$823$			24.7094i			0.861315i	0.902516	+	0.430657i	$0.141718\pi$
$823$			24.7094i			0.861315i	−0.902516	+	0.430657i	$0.858282\pi$
$824$	−4.08484	+	6.01862i	−0.142302	+	0.209669i
$825$		0			0
$826$	−1.31406	−	1.15802i	−0.0457218	−	0.0402925i
$827$	51.5762			1.79348			0.896741	−	0.442556i	$-0.145928\pi$
$827$	51.5762			1.79348			0.896741	+	0.442556i	$0.145928\pi$
$828$		0			0
$829$	−7.45707			−0.258995			−0.129497	−	0.991580i	$-0.541336\pi$
$829$	−7.45707			−0.258995			−0.129497	+	0.991580i	$0.541336\pi$
$830$	5.22522	+	4.60474i	0.181370	+	0.159833i
$831$		0			0
$832$	−18.1568	−	45.6942i	−0.629473	−	1.58416i
$833$		−	1.11477i		−	0.0386244i
$834$		0			0
$835$		−	22.7297i		−	0.786593i
$836$	9.47616	−	1.20107i	0.327740	−	0.0415399i
$837$		0			0
$838$	2.72878	−	3.09648i	0.0942643	−	0.106966i
$839$	1.23046			0.0424803			0.0212401	−	0.999774i	$-0.493239\pi$
$839$	1.23046			0.0424803			0.0212401	+	0.999774i	$0.493239\pi$
$840$		0			0
$841$	28.4455			0.980879
$842$	4.29166	−	4.86995i	0.147900	−	0.167830i
$843$		0			0
$844$	−21.7233	+	2.75335i	−0.747746	+	0.0947742i
$845$		−	24.7755i		−	0.852303i
$846$		0			0
$847$			7.81362i			0.268479i
$848$	2.49566	+	9.68695i	0.0857015	+	0.332651i
$849$		0			0
$850$	−1.18278	−	1.04233i	−0.0405690	−	0.0357516i
$851$	−20.2608			−0.694530
$852$		0			0
$853$	−48.1173			−1.64750			−0.823752	−	0.566950i	$-0.808123\pi$
$853$	−48.1173			−1.64750			−0.823752	+	0.566950i	$0.808123\pi$
$854$	6.80597	+	5.99778i	0.232895	+	0.205240i
$855$		0			0
$856$	−19.6994	−	13.3700i	−0.673312	−	0.456977i
$857$		−	5.29995i		−	0.181043i	−0.995895	−	0.0905214i	$-0.971147\pi$
$857$		−	5.29995i		−	0.181043i	0.995895	−	0.0905214i	$-0.0288534\pi$
$858$		0			0
$859$			5.19530i			0.177261i	0.996065	+	0.0886306i	$0.0282491\pi$
$859$			5.19530i			0.177261i	−0.996065	+	0.0886306i	$0.971751\pi$
$860$	2.39058	+	18.8611i	0.0815181	+	0.643158i
$861$		0			0
$862$	28.8209	−	32.7044i	0.981643	−	1.11392i
$863$	−6.02897			−0.205228			−0.102614	−	0.994721i	$-0.532721\pi$
$863$	−6.02897			−0.205228			−0.102614	+	0.994721i	$0.532721\pi$
$864$		0			0
$865$	−4.89112			−0.166303
$866$	−6.91671	+	7.84872i	−0.235039	+	0.266710i
$867$		0			0
$868$	−2.17898	−	17.1917i	−0.0739596	−	0.583523i
$869$			20.2557i			0.687128i
$870$		0			0
$871$			23.1859i			0.785624i
$872$	−25.5473	−	17.3389i	−0.865140	−	0.587170i
$873$		0			0
$874$	−7.53927	−	6.64401i	−0.255020	−	0.224737i
$875$	1.00000			0.0338062
$876$		0			0
$877$	7.51155			0.253647			0.126823	−	0.991925i	$-0.459522\pi$
$877$	7.51155			0.253647			0.126823	+	0.991925i	$0.459522\pi$
$878$	24.9700	+	22.0049i	0.842695	+	0.742629i
$879$		0			0
$880$	−1.78137	−	6.91439i	−0.0600498	−	0.233084i
$881$			17.6401i			0.594311i	0.954829	+	0.297155i	$0.0960379\pi$
$881$			17.6401i			0.594311i	−0.954829	+	0.297155i	$0.903962\pi$
$882$		0			0
$883$		−	41.0668i		−	1.38201i	−0.722851	−	0.691004i	$-0.757169\pi$
$883$		−	41.0668i		−	1.38201i	0.722851	−	0.691004i	$-0.242831\pi$
$884$	−13.5944	+	1.72304i	−0.457228	+	0.0579520i
$885$		0			0
$886$	1.42619	−	1.61836i	0.0479138	−	0.0543700i
$887$	52.6103			1.76648			0.883241	−	0.468919i	$-0.155356\pi$
$887$	52.6103			1.76648			0.883241	+	0.468919i	$0.155356\pi$
$888$		0			0
$889$	9.25356			0.310355
$890$	10.5178	−	11.9350i	0.352557	−	0.400063i
$891$		0			0
$892$	8.33325	−	1.05621i	0.279018	−	0.0353645i
$893$		−	13.3899i		−	0.448075i
$894$		0			0
$895$			0.638667i			0.0213483i
$896$	3.81708	−	10.6503i	0.127520	−	0.355803i
$897$		0			0
$898$	39.0600	+	34.4218i	1.30345	+	1.14867i
$899$	6.45220			0.215193
$900$		0			0
$901$	2.78783			0.0928760
$902$	19.8912	+	17.5292i	0.662306	+	0.583660i
$903$		0			0
$904$	−2.83071	+	4.17079i	−0.0941480	+	0.138718i
$905$		−	14.0537i		−	0.467162i
$906$		0			0
$907$		−	40.0392i		−	1.32948i	−0.747075	−	0.664740i	$-0.768542\pi$
$907$		−	40.0392i		−	1.32948i	0.747075	−	0.664740i	$-0.231458\pi$
$908$	−0.414197	−	3.26792i	−0.0137456	−	0.108450i
$909$		0			0
$910$	5.74679	−	6.52115i	0.190504	−	0.216174i
$911$	−53.4697			−1.77153			−0.885765	−	0.464134i	$-0.846366\pi$
$911$	−53.4697			−1.77153			−0.885765	+	0.464134i	$0.846366\pi$
$912$		0			0
$913$	8.79091			0.290937
$914$	16.3990	−	18.6087i	0.542432	−	0.615523i
$915$		0			0
$916$	−0.211667	−	1.67000i	−0.00699368	−	0.0551785i
$917$			14.6313i			0.483169i
$918$		0			0
$919$			59.5338i			1.96384i	0.189301	+	0.981919i	$0.439378\pi$
$919$			59.5338i			1.96384i	−0.189301	+	0.981919i	$0.560622\pi$
$920$	−4.21840	+	6.21542i	−0.139076	+	0.204916i
$921$		0			0
$922$	−21.9204	−	19.3175i	−0.721911	−	0.636187i
$923$	−95.4654			−3.14228
$924$		0			0
$925$	7.62886			0.250836
$926$	−35.9588	−	31.6888i	−1.18168	−	1.04136i
$927$		0			0
$928$	3.75527	+	1.90855i	0.123273	+	0.0626514i
$929$		−	22.8841i		−	0.750804i	−0.926862	−	0.375402i	$-0.877505\pi$
$929$		−	22.8841i		−	0.750804i	0.926862	−	0.375402i	$-0.122495\pi$
$930$		0			0
$931$			2.67556i			0.0876879i
$932$	−53.7814	+	6.81660i	−1.76167	+	0.223285i
$933$		0			0
$934$	−38.4625	+	43.6452i	−1.25853	+	1.42811i
$935$	−1.98991			−0.0650769
$936$		0			0
$937$	31.4871			1.02864			0.514319	−	0.857599i	$-0.328045\pi$
$937$	31.4871			1.02864			0.514319	+	0.857599i	$0.328045\pi$
$938$	−3.52727	+	4.00256i	−0.115169	+	0.130688i
$939$		0			0
$940$	−9.92959	+	1.25854i	−0.323868	+	0.0410491i
$941$		−	22.8467i		−	0.744780i	−0.928076	−	0.372390i	$-0.878538\pi$
$941$		−	22.8467i		−	0.744780i	0.928076	−	0.372390i	$-0.121462\pi$
$942$		0			0
$943$		−	27.8927i		−	0.908310i
$944$	−4.79733	+	1.23594i	−0.156140	+	0.0402266i
$945$		0			0
$946$	18.0039	+	15.8660i	0.585356	+	0.515847i
$947$	−60.4353			−1.96388			−0.981942	−	0.189180i	$-0.939417\pi$
$947$	−60.4353			−1.96388			−0.981942	+	0.189180i	$0.939417\pi$
$948$		0			0
$949$	34.3448			1.11488
$950$	2.83879	+	2.50170i	0.0921026	+	0.0811658i
$951$		0			0
$952$	−2.60891	−	1.77066i	−0.0845552	−	0.0573876i
$953$			24.3381i			0.788389i	0.919027	+	0.394195i	$0.128976\pi$
$953$			24.3381i			0.788389i	−0.919027	+	0.394195i	$0.871024\pi$
$954$		0			0
$955$		−	4.42730i		−	0.143264i
$956$	−2.99532	−	23.6324i	−0.0968757	−	0.764326i
$957$		0			0
$958$	3.58954	−	4.07322i	0.115973	−	0.131600i
$959$	0.366817			0.0118451
$960$		0			0
$961$	−44.0754			−1.42179
$962$	43.8415	−	49.7490i	1.41351	−	1.60397i
$963$		0			0
$964$	−3.78127	−	29.8334i	−0.121787	−	0.960868i
$965$			16.8507i			0.542443i
$966$		0			0
$967$			1.74714i			0.0561844i	0.999605	+	0.0280922i	$0.00894320\pi$
$967$			1.74714i			0.0561844i	−0.999605	+	0.0280922i	$0.991057\pi$
$968$	18.2863	+	12.4109i	0.587745	+	0.398903i
$969$		0			0
$970$	18.3370	+	16.1596i	0.588766	+	0.518852i
$971$	−30.5704			−0.981050			−0.490525	−	0.871427i	$-0.663195\pi$
$971$	−30.5704			−0.981050			−0.490525	+	0.871427i	$0.663195\pi$
$972$		0			0
$973$	−2.39442			−0.0767615
$974$	−25.3043	−	22.2995i	−0.810803	−	0.714523i
$975$		0			0
$976$	24.8471	−	6.40140i	0.795336	−	0.204904i
$977$		−	23.2429i		−	0.743605i	−0.928312	−	0.371803i	$-0.878740\pi$
$977$		−	23.2429i		−	0.743605i	0.928312	−	0.371803i	$-0.121260\pi$
$978$		0			0
$979$		−	20.0795i		−	0.641744i
$980$	1.98413	−	0.251481i	0.0633806	−	0.00803327i
$981$		0			0
$982$	−7.07834	+	8.03212i	−0.225879	+	0.256315i
$983$	49.4169			1.57615			0.788077	−	0.615577i	$-0.211077\pi$
$983$	49.4169			1.57615			0.788077	+	0.615577i	$0.211077\pi$
$984$		0			0
$985$	2.87374			0.0915650
$986$	0.776181	−	0.880769i	0.0247187	−	0.0280494i
$987$		0			0
$988$	32.6279	−	4.13547i	1.03803	−	0.131567i
$989$		−	25.2461i		−	0.802778i
$990$		0			0
$991$		−	9.52952i		−	0.302715i	−0.988479	−	0.151358i	$-0.951635\pi$
$991$		−	9.52952i		−	0.302715i	0.988479	−	0.151358i	$-0.0483645\pi$
$992$	−43.6950	−	22.2072i	−1.38732	−	0.705081i
$993$		0			0
$994$	−16.4801	−	14.5232i	−0.522717	−	0.460646i
$995$	5.54254			0.175710
$996$		0			0
$997$	45.9421			1.45500			0.727500	−	0.686108i	$-0.240682\pi$
$997$	45.9421			1.45500			0.727500	+	0.686108i	$0.240682\pi$
$998$	−42.6623	−	37.5964i	−1.35045	−	1.19009i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.n.a.71.19	✓	24
3.2	odd	2		1260.2.n.b.71.6	yes	24
4.3	odd	2		1260.2.n.b.71.5	yes	24
12.11	even	2	inner	1260.2.n.a.71.20	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1260.2.n.a.71.19	✓	24	1.1	even	1	trivial
1260.2.n.a.71.20	yes	24	12.11	even	2	inner
1260.2.n.b.71.5	yes	24	4.3	odd	2
1260.2.n.b.71.6	yes	24	3.2	odd	2

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:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.n (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.935018 - 1.06101i) q^{2} +(-0.251481 - 1.98413i) q^{4} -1.00000i q^{5} -1.00000i q^{7} +(-2.34032 - 1.58837i) q^{8} +(-1.06101 - 0.935018i) q^{10} -1.78504 q^{11} -6.14618 q^{13} +(-1.06101 - 0.935018i) q^{14} +(-3.87351 + 0.997940i) q^{16} +1.11477i q^{17} -2.67556i q^{19} +(-1.98413 + 0.251481i) q^{20} +(-1.66905 + 1.89395i) q^{22} +2.65580 q^{23} -1.00000 q^{25} +(-5.74679 + 6.52115i) q^{26} +(-1.98413 + 0.251481i) q^{28} -0.744661i q^{29} +8.66461i q^{31} +(-2.56298 + 5.04293i) q^{32} +(1.18278 + 1.04233i) q^{34} -1.00000 q^{35} -7.62886 q^{37} +(-2.83879 - 2.50170i) q^{38} +(-1.58837 + 2.34032i) q^{40} -10.5025i q^{41} -9.50600i q^{43} +(0.448904 + 3.54175i) q^{44} +(2.48322 - 2.81783i) q^{46} +5.00451 q^{47} -1.00000 q^{49} +(-0.935018 + 1.06101i) q^{50} +(1.54565 + 12.1948i) q^{52} -2.50082i q^{53} +1.78504i q^{55} +(-1.58837 + 2.34032i) q^{56} +(-0.790093 - 0.696272i) q^{58} +1.23850 q^{59} -6.41461 q^{61} +(9.19323 + 8.10157i) q^{62} +(2.95416 + 7.43458i) q^{64} +6.14618i q^{65} -3.77241i q^{67} +(2.21184 - 0.280343i) q^{68} +(-0.935018 + 1.06101i) q^{70} +15.5325 q^{71} -5.58799 q^{73} +(-7.13313 + 8.09430i) q^{74} +(-5.30865 + 0.672853i) q^{76} +1.78504i q^{77} -11.3475i q^{79} +(0.997940 + 3.87351i) q^{80} +(-11.1433 - 9.82007i) q^{82} -4.92476 q^{83} +1.11477 q^{85} +(-10.0860 - 8.88829i) q^{86} +(4.17756 + 2.83531i) q^{88} +11.2488i q^{89} +6.14618i q^{91} +(-0.667884 - 5.26945i) q^{92} +(4.67931 - 5.30984i) q^{94} -2.67556 q^{95} -17.2826 q^{97} +(-0.935018 + 1.06101i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{4} - 4 q^{10} - 4 q^{14} + 4 q^{20} - 4 q^{22} - 24 q^{25} - 40 q^{26} + 4 q^{28} + 40 q^{32} + 8 q^{34} - 24 q^{35} + 4 q^{40} + 48 q^{44} + 36 q^{46} + 16 q^{47} - 24 q^{49} + 32 q^{52} + 4 q^{56}+ \cdots + 12 q^{88}+O(q^{100}) \) 24 * q - 4 * q^4 - 4 * q^10 - 4 * q^14 + 4 * q^20 - 4 * q^22 - 24 * q^25 - 40 * q^26 + 4 * q^28 + 40 * q^32 + 8 * q^34 - 24 * q^35 + 4 * q^40 + 48 * q^44 + 36 * q^46 + 16 * q^47 - 24 * q^49 + 32 * q^52 + 4 * q^56 - 28 * q^58 - 16 * q^59 - 32 * q^61 - 56 * q^62 - 4 * q^64 + 64 * q^68 - 32 * q^74 - 72 * q^76 - 40 * q^82 - 80 * q^83 + 32 * q^85 - 80 * q^86 + 12 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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