LMFDB - Embedded newform 1500.2.o.c.49.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1500,2,Mod(49,1500)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1500.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1500, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1500 = 2^{2} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1500.o (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,0,0,6,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.9775603032$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			49.1
Character	$\chi$	$=$	1500.49
Dual form			1500.2.o.c.949.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.951057 + 0.309017i) q^{3} -3.78808i q^{7} +(0.809017 - 0.587785i) q^{9} +(0.653426 + 0.474742i) q^{11} +(-2.79168 - 3.84242i) q^{13} +(1.09262 + 0.355012i) q^{17} +(-0.00463870 + 0.0142765i) q^{19} +(1.17058 + 3.60268i) q^{21} +(-3.68422 + 5.07089i) q^{23} +(-0.587785 + 0.809017i) q^{27} +(-1.14365 - 3.51978i) q^{29} +(-0.488893 + 1.50466i) q^{31} +(-0.768148 - 0.249586i) q^{33} +(-5.02074 - 6.91045i) q^{37} +(3.84242 + 2.79168i) q^{39} +(-9.30279 + 6.75887i) q^{41} +10.2458i q^{43} +(-0.500524 + 0.162630i) q^{47} -7.34957 q^{49} -1.14884 q^{51} +(2.80539 - 0.911527i) q^{53} -0.0150112i q^{57} +(9.25803 - 6.72635i) q^{59} +(-2.54203 - 1.84689i) q^{61} +(-2.22658 - 3.06462i) q^{63} +(-12.6312 - 4.10412i) q^{67} +(1.93691 - 5.96119i) q^{69} +(-1.51826 - 4.67271i) q^{71} +(-2.75001 + 3.78507i) q^{73} +(1.79836 - 2.47523i) q^{77} +(-2.86507 - 8.81777i) q^{79} +(0.309017 - 0.951057i) q^{81} +(1.35402 + 0.439947i) q^{83} +(2.17534 + 2.99410i) q^{87} +(-13.0306 - 9.46730i) q^{89} +(-14.5554 + 10.5751i) q^{91} -1.58209i q^{93} +(7.66744 - 2.49130i) q^{97} +0.807679 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{9} - 6 q^{11} - 10 q^{17} + 10 q^{19} - 4 q^{21} - 40 q^{23} + 4 q^{29} + 6 q^{31} - 10 q^{33} - 10 q^{41} + 40 q^{47} - 56 q^{49} + 16 q^{51} + 60 q^{53} - 36 q^{59} - 12 q^{61} + 10 q^{63}+ \cdots - 4 q^{99}+O(q^{100}) $ 24 * q + 6 * q^9 - 6 * q^11 - 10 * q^17 + 10 * q^19 - 4 * q^21 - 40 * q^23 + 4 * q^29 + 6 * q^31 - 10 * q^33 - 10 * q^41 + 40 * q^47 - 56 * q^49 + 16 * q^51 + 60 * q^53 - 36 * q^59 - 12 * q^61 + 10 * q^63 - 20 * q^67 + 4 * q^69 + 40 * q^71 - 60 * q^73 + 40 * q^77 + 8 * q^79 - 6 * q^81 + 50 * q^83 + 20 * q^87 - 30 * q^91 + 40 * q^97 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times$.

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	3.78808i		−	1.43176i	−0.698223	−	0.715880i	$-0.746026\pi$
$7$		−	3.78808i		−	1.43176i	0.698223	−	0.715880i	$-0.253974\pi$
$8$		0			0
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$		0			0
$11$	0.653426	+	0.474742i	0.197015	+	0.143140i	0.681919	−	0.731427i	$-0.261145\pi$
$11$	0.653426	+	0.474742i	0.197015	+	0.143140i	−0.484904	+	0.874567i	$0.661145\pi$
$12$		0			0
$13$	−2.79168	−	3.84242i	−0.774274	−	1.06570i	−0.995891	−	0.0905626i	$-0.971133\pi$
$13$	−2.79168	−	3.84242i	−0.774274	−	1.06570i	0.221617	−	0.975134i	$-0.428867\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.09262	+	0.355012i	0.264998	+	0.0861032i	0.438503	−	0.898730i	$-0.355509\pi$
$17$	1.09262	+	0.355012i	0.264998	+	0.0861032i	−0.173504	+	0.984833i	$0.555509\pi$
$18$		0			0
$19$	−0.00463870	+	0.0142765i	−0.00106419	+	0.00327524i	−0.951587	−	0.307379i	$-0.900548\pi$
$19$	−0.00463870	+	0.0142765i	−0.00106419	+	0.00327524i	0.950523	+	0.310654i	$0.100548\pi$
$20$		0			0
$21$	1.17058	+	3.60268i	0.255442	+	0.786169i
$22$		0			0
$23$	−3.68422	+	5.07089i	−0.768213	+	1.05735i	0.228274	+	0.973597i	$0.426692\pi$
$23$	−3.68422	+	5.07089i	−0.768213	+	1.05735i	−0.996486	+	0.0837569i	$0.973308\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.587785	+	0.809017i	−0.113119	+	0.155695i
$28$		0			0
$29$	−1.14365	−	3.51978i	−0.212370	−	0.653607i	−0.999330	−	0.0366030i	$-0.988346\pi$
$29$	−1.14365	−	3.51978i	−0.212370	−	0.653607i	0.786960	−	0.617004i	$-0.211654\pi$
$30$		0			0
$31$	−0.488893	+	1.50466i	−0.0878078	+	0.270245i	−0.985313	−	0.170760i	$-0.945378\pi$
$31$	−0.488893	+	1.50466i	−0.0878078	+	0.270245i	0.897505	+	0.441005i	$0.145378\pi$
$32$		0			0
$33$	−0.768148	−	0.249586i	−0.133717	−	0.0434474i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−5.02074	−	6.91045i	−0.825404	−	1.13607i	−0.988761	−	0.149504i	$-0.952232\pi$
$37$	−5.02074	−	6.91045i	−0.825404	−	1.13607i	0.163357	−	0.986567i	$-0.447768\pi$
$38$		0			0
$39$	3.84242	+	2.79168i	0.615280	+	0.447027i
$40$		0			0
$41$	−9.30279	+	6.75887i	−1.45285	+	1.05556i	−0.467697	+	0.883889i	$0.654916\pi$
$41$	−9.30279	+	6.75887i	−1.45285	+	1.05556i	−0.985155	+	0.171669i	$0.945084\pi$
$42$		0			0
$43$			10.2458i			1.56247i	0.624238	+	0.781234i	$0.285409\pi$
$43$			10.2458i			1.56247i	−0.624238	+	0.781234i	$0.714591\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.500524	+	0.162630i	−0.0730090	+	0.0237221i	−0.345294	−	0.938495i	$-0.612221\pi$
$47$	−0.500524	+	0.162630i	−0.0730090	+	0.0237221i	0.272285	+	0.962217i	$0.412221\pi$
$48$		0			0
$49$	−7.34957			−1.04994
$50$		0			0
$51$	−1.14884			−0.160870
$52$		0			0
$53$	2.80539	−	0.911527i	0.385350	−	0.125208i	−0.109934	−	0.993939i	$-0.535064\pi$
$53$	2.80539	−	0.911527i	0.385350	−	0.125208i	0.495284	+	0.868731i	$0.335064\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	0.0150112i		−	0.00198828i
$58$		0			0
$59$	9.25803	−	6.72635i	1.20529	−	0.875696i	0.210498	−	0.977594i	$-0.432492\pi$
$59$	9.25803	−	6.72635i	1.20529	−	0.875696i	0.994795	+	0.101898i	$0.0324916\pi$
$60$		0			0
$61$	−2.54203	−	1.84689i	−0.325473	−	0.236470i	0.413034	−	0.910716i	$-0.364469\pi$
$61$	−2.54203	−	1.84689i	−0.325473	−	0.236470i	−0.738507	+	0.674245i	$0.764469\pi$
$62$		0			0
$63$	−2.22658	−	3.06462i	−0.280523	−	0.386106i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−12.6312	−	4.10412i	−1.54314	−	0.501398i	−0.590901	−	0.806744i	$-0.701228\pi$
$67$	−12.6312	−	4.10412i	−1.54314	−	0.501398i	−0.952241	+	0.305346i	$0.901228\pi$
$68$		0			0
$69$	1.93691	−	5.96119i	0.233176	−	0.717643i
$70$		0			0
$71$	−1.51826	−	4.67271i	−0.180184	−	0.554549i	0.819648	−	0.572867i	$-0.194169\pi$
$71$	−1.51826	−	4.67271i	−0.180184	−	0.554549i	−0.999832	+	0.0183179i	$0.994169\pi$
$72$		0			0
$73$	−2.75001	+	3.78507i	−0.321865	+	0.443009i	−0.939035	−	0.343820i	$-0.888279\pi$
$73$	−2.75001	+	3.78507i	−0.321865	+	0.443009i	0.617171	+	0.786829i	$0.288279\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.79836	−	2.47523i	0.204942	−	0.282079i
$78$		0			0
$79$	−2.86507	−	8.81777i	−0.322345	−	0.992076i	−0.972625	−	0.232381i	$-0.925348\pi$
$79$	−2.86507	−	8.81777i	−0.322345	−	0.992076i	0.650280	−	0.759695i	$-0.274652\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	1.35402	+	0.439947i	0.148623	+	0.0482904i	0.382384	−	0.924004i	$-0.375103\pi$
$83$	1.35402	+	0.439947i	0.148623	+	0.0482904i	−0.233761	+	0.972294i	$0.575103\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	2.17534	+	2.99410i	0.233221	+	0.321002i
$88$		0			0
$89$	−13.0306	−	9.46730i	−1.38124	−	1.00353i	−0.996763	−	0.0803985i	$-0.974381\pi$
$89$	−13.0306	−	9.46730i	−1.38124	−	1.00353i	−0.384480	−	0.923133i	$-0.625619\pi$
$90$		0			0
$91$	−14.5554	+	10.5751i	−1.52582	+	1.10857i
$92$		0			0
$93$		−	1.58209i		−	0.164055i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	7.66744	−	2.49130i	0.778511	−	0.252954i	0.107307	−	0.994226i	$-0.465777\pi$
$97$	7.66744	−	2.49130i	0.778511	−	0.252954i	0.671204	+	0.741272i	$0.265777\pi$
$98$		0			0
$99$	0.807679			0.0811748
$100$		0			0
$101$	11.6496			1.15918			0.579590	−	0.814908i	$-0.303213\pi$
$101$	11.6496			1.15918			0.579590	+	0.814908i	$0.303213\pi$
$102$		0			0
$103$	−17.9216	+	5.82307i	−1.76587	+	0.573764i	−0.997781	−	0.0665845i	$-0.978790\pi$
$103$	−17.9216	+	5.82307i	−1.76587	+	0.573764i	−0.768084	+	0.640349i	$0.778790\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			14.3957i			1.39168i	0.718195	+	0.695842i	$0.244969\pi$
$107$			14.3957i			1.39168i	−0.718195	+	0.695842i	$0.755031\pi$
$108$		0			0
$109$	−4.66144	+	3.38673i	−0.446485	+	0.324390i	−0.788206	−	0.615411i	$-0.788990\pi$
$109$	−4.66144	+	3.38673i	−0.446485	+	0.324390i	0.341722	+	0.939801i	$0.388990\pi$
$110$		0			0
$111$	6.91045	+	5.02074i	0.655911	+	0.476547i
$112$		0			0
$113$	−10.5368	−	14.5027i	−0.991223	−	1.36430i	−0.930559	−	0.366143i	$-0.880678\pi$
$113$	−10.5368	−	14.5027i	−0.991223	−	1.36430i	−0.0606641	−	0.998158i	$-0.519322\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−4.51704	−	1.46767i	−0.417600	−	0.135687i
$118$		0			0
$119$	1.34482	−	4.13892i	0.123279	−	0.379414i
$120$		0			0
$121$	−3.19760	−	9.84120i	−0.290691	−	0.894655i
$122$		0			0
$123$	6.75887	−	9.30279i	0.609427	−	0.838804i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	1.34592	−	1.85250i	0.119431	−	0.164382i	−0.745116	−	0.666935i	$-0.767606\pi$
$127$	1.34592	−	1.85250i	0.119431	−	0.164382i	0.864547	+	0.502553i	$0.167606\pi$
$128$		0			0
$129$	−3.16612	−	9.74432i	−0.278762	−	0.857940i
$130$		0			0
$131$	−2.17840	+	6.70444i	−0.190328	+	0.585769i	−0.999999	−	0.00111420i	$-0.999645\pi$
$131$	−2.17840	+	6.70444i	−0.190328	+	0.585769i	0.809671	+	0.586883i	$0.199645\pi$
$132$		0			0
$133$	0.0540804	+	0.0175718i	0.00468937	+	0.00152367i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−12.8918	−	17.7441i	−1.10142	−	1.51598i	−0.833484	−	0.552544i	$-0.813657\pi$
$137$	−12.8918	−	17.7441i	−1.10142	−	1.51598i	−0.267940	−	0.963436i	$-0.586343\pi$
$138$		0			0
$139$	7.86171	+	5.71187i	0.666822	+	0.484474i	0.868960	−	0.494883i	$-0.164789\pi$
$139$	7.86171	+	5.71187i	0.666822	+	0.484474i	−0.202138	+	0.979357i	$0.564789\pi$
$140$		0			0
$141$	0.425771	−	0.309341i	0.0358564	−	0.0260512i
$142$		0			0
$143$		−	3.83607i		−	0.320788i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	6.98985	−	2.27114i	0.576513	−	0.187321i
$148$		0			0
$149$	13.9712			1.14457			0.572284	−	0.820056i	$-0.306058\pi$
$149$	13.9712			1.14457			0.572284	+	0.820056i	$0.306058\pi$
$150$		0			0
$151$	−20.1871			−1.64280			−0.821400	−	0.570352i	$-0.806807\pi$
$151$	−20.1871			−1.64280			−0.821400	+	0.570352i	$0.806807\pi$
$152$		0			0
$153$	1.09262	−	0.355012i	0.0883328	−	0.0287011i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		−	7.76546i		−	0.619751i	−0.950777	−	0.309876i	$-0.899713\pi$
$157$		−	7.76546i		−	0.619751i	0.950777	−	0.309876i	$-0.100287\pi$
$158$		0			0
$159$	−2.38641	+	1.73383i	−0.189255	+	0.137502i
$160$		0			0
$161$	19.2090	+	13.9561i	1.51388	+	1.09990i
$162$		0			0
$163$	8.16480	+	11.2379i	0.639517	+	0.880219i	0.998590	−	0.0530901i	$-0.0169070\pi$
$163$	8.16480	+	11.2379i	0.639517	+	0.880219i	−0.359073	+	0.933310i	$0.616907\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.75604	+	0.895491i	0.213269	+	0.0692952i	0.413703	−	0.910412i	$-0.364235\pi$
$167$	2.75604	+	0.895491i	0.213269	+	0.0692952i	−0.200434	+	0.979707i	$0.564235\pi$
$168$		0			0
$169$	−2.95350	+	9.08992i	−0.227192	+	0.699225i
$170$		0			0
$171$	0.00463870	+	0.0142765i	0.000354730	+	0.00109175i
$172$		0			0
$173$	8.95423	−	12.3244i	0.680777	−	0.937009i	−0.319166	−	0.947699i	$-0.603403\pi$
$173$	8.95423	−	12.3244i	0.680777	−	0.937009i	0.999943	+	0.0106895i	$0.00340264\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−6.72635	+	9.25803i	−0.505583	+	0.695876i
$178$		0			0
$179$	7.20182	+	22.1649i	0.538290	+	1.65669i	0.736432	+	0.676512i	$0.236509\pi$
$179$	7.20182	+	22.1649i	0.538290	+	1.65669i	−0.198142	+	0.980173i	$0.563491\pi$
$180$		0			0
$181$	5.46913	−	16.8322i	0.406517	−	1.25113i	−0.513105	−	0.858326i	$-0.671505\pi$
$181$	5.46913	−	16.8322i	0.406517	−	1.25113i	0.919622	−	0.392805i	$-0.128495\pi$
$182$		0			0
$183$	2.98833	+	0.970968i	0.220904	+	0.0717760i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.545404	+	0.750685i	0.0398839	+	0.0548955i
$188$		0			0
$189$	3.06462	+	2.22658i	0.222919	+	0.161960i
$190$		0			0
$191$	−7.57575	+	5.50411i	−0.548162	+	0.398263i	−0.827107	−	0.562044i	$-0.810015\pi$
$191$	−7.57575	+	5.50411i	−0.548162	+	0.398263i	0.278945	+	0.960307i	$0.410015\pi$
$192$		0			0
$193$			18.9309i			1.36268i	0.731969	+	0.681338i	$0.238602\pi$
$193$			18.9309i			1.36268i	−0.731969	+	0.681338i	$0.761398\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−7.17436	+	2.33109i	−0.511152	+	0.166083i	−0.553226	−	0.833031i	$-0.686603\pi$
$197$	−7.17436	+	2.33109i	−0.511152	+	0.166083i	0.0420739	+	0.999114i	$0.486603\pi$
$198$		0			0
$199$	−3.58560			−0.254176			−0.127088	−	0.991891i	$-0.540563\pi$
$199$	−3.58560			−0.254176			−0.127088	+	0.991891i	$0.540563\pi$
$200$		0			0
$201$	13.2812			0.936783
$202$		0			0
$203$	−13.3332	+	4.33223i	−0.935808	+	0.304063i
$204$		0			0
$205$		0			0
$206$		0			0
$207$			6.26797i			0.435654i
$208$		0			0
$209$	−0.00980868	+	0.00712642i	−0.000678480	+	0.000492945i
$210$		0			0
$211$	−1.68674	−	1.22549i	−0.116120	−	0.0843663i	0.528210	−	0.849114i	$-0.322864\pi$
$211$	−1.68674	−	1.22549i	−0.116120	−	0.0843663i	−0.644330	+	0.764748i	$0.722864\pi$
$212$		0			0
$213$	2.88790	+	3.97485i	0.197875	+	0.272352i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	5.69977	+	1.85197i	0.386926	+	0.125720i
$218$		0			0
$219$	1.44577	−	4.44962i	0.0976960	−	0.300677i
$220$		0			0
$221$	−1.68613	−	5.18938i	−0.113421	−	0.349075i
$222$		0			0
$223$	8.25091	−	11.3564i	0.552522	−	0.760481i	−0.437830	−	0.899058i	$-0.644253\pi$
$223$	8.25091	−	11.3564i	0.552522	−	0.760481i	0.990352	+	0.138577i	$0.0442527\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.48995	−	2.05074i	0.0988915	−	0.136112i	−0.756704	−	0.653758i	$-0.773191\pi$
$227$	1.48995	−	2.05074i	0.0988915	−	0.136112i	0.855595	+	0.517646i	$0.173191\pi$
$228$		0			0
$229$	5.10687	+	15.7173i	0.337472	+	1.03863i	0.965492	+	0.260434i	$0.0838656\pi$
$229$	5.10687	+	15.7173i	0.337472	+	1.03863i	−0.628020	+	0.778197i	$0.716134\pi$
$230$		0			0
$231$	−0.945454	+	2.90981i	−0.0622063	+	0.191451i
$232$		0			0
$233$	25.2228	+	8.19539i	1.65240	+	0.536898i	0.979259	−	0.202614i	$-0.0649437\pi$
$233$	25.2228	+	8.19539i	1.65240	+	0.536898i	0.673143	+	0.739512i	$0.264944\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	5.44968	+	7.50084i	0.353995	+	0.487232i
$238$		0			0
$239$	−6.03839	−	4.38714i	−0.390591	−	0.283781i	0.375107	−	0.926982i	$-0.377606\pi$
$239$	−6.03839	−	4.38714i	−0.390591	−	0.283781i	−0.765698	+	0.643201i	$0.777606\pi$
$240$		0			0
$241$	−8.33107	+	6.05288i	−0.536651	+	0.389900i	−0.822840	−	0.568273i	$-0.807612\pi$
$241$	−8.33107	+	6.05288i	−0.536651	+	0.389900i	0.286189	+	0.958173i	$0.407612\pi$
$242$		0			0
$243$			1.00000i			0.0641500i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.0678060	−	0.0220315i	0.00431439	−	0.00140183i
$248$		0			0
$249$	−1.42370			−0.0902231
$250$		0			0
$251$	19.5809			1.23593			0.617967	−	0.786204i	$-0.287956\pi$
$251$	19.5809			1.23593			0.617967	+	0.786204i	$0.287956\pi$
$252$		0			0
$253$	−4.81473	+	1.56440i	−0.302699	+	0.0983530i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			5.98030i			0.373041i	0.982451	+	0.186520i	$0.0597210\pi$
$257$			5.98030i			0.373041i	−0.982451	+	0.186520i	$0.940279\pi$
$258$		0			0
$259$	−26.1774	+	19.0190i	−1.62658	+	1.18178i
$260$		0			0
$261$	−2.99410	−	2.17534i	−0.185330	−	0.134650i
$262$		0			0
$263$	−3.56808	−	4.91104i	−0.220017	−	0.302827i	0.684713	−	0.728813i	$-0.259928\pi$
$263$	−3.56808	−	4.91104i	−0.220017	−	0.302827i	−0.904730	+	0.425985i	$0.859928\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	15.3184	+	4.97725i	0.937472	+	0.304603i
$268$		0			0
$269$	−2.97152	+	9.14540i	−0.181177	+	0.557605i	−0.999862	−	0.0166382i	$-0.994704\pi$
$269$	−2.97152	+	9.14540i	−0.181177	+	0.557605i	0.818685	+	0.574243i	$0.194704\pi$
$270$		0			0
$271$	−9.40263	−	28.9383i	−0.571169	−	1.75788i	−0.648868	−	0.760901i	$-0.724757\pi$
$271$	−9.40263	−	28.9383i	−0.571169	−	1.75788i	0.0776990	−	0.996977i	$-0.475243\pi$
$272$		0			0
$273$	10.5751	−	14.5554i	0.640036	−	0.880934i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	4.23436	−	5.82810i	0.254418	−	0.350176i	−0.662634	−	0.748943i	$-0.730562\pi$
$277$	4.23436	−	5.82810i	0.254418	−	0.350176i	0.917052	+	0.398767i	$0.130562\pi$
$278$		0			0
$279$	0.488893	+	1.50466i	0.0292693	+	0.0900815i
$280$		0			0
$281$	9.20758	−	28.3380i	0.549278	−	1.69050i	−0.161316	−	0.986903i	$-0.551574\pi$
$281$	9.20758	−	28.3380i	0.549278	−	1.69050i	0.710594	−	0.703602i	$-0.248426\pi$
$282$		0			0
$283$	8.39215	+	2.72677i	0.498861	+	0.162090i	0.547631	−	0.836720i	$-0.315530\pi$
$283$	8.39215	+	2.72677i	0.498861	+	0.162090i	−0.0487693	+	0.998810i	$0.515530\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	25.6032	+	35.2397i	1.51131	+	2.08014i
$288$		0			0
$289$	−12.6855	−	9.21656i	−0.746207	−	0.542151i
$290$		0			0
$291$	−6.52232	+	4.73874i	−0.382345	+	0.277790i
$292$		0			0
$293$		−	4.20743i		−	0.245800i	−0.992419	−	0.122900i	$-0.960780\pi$
$293$		−	4.20743i		−	0.245800i	0.992419	−	0.122900i	$-0.0392195\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−0.768148	+	0.249586i	−0.0445725	+	0.0144825i
$298$		0			0
$299$	29.7697			1.72163
$300$		0			0
$301$	38.8119			2.23708
$302$		0			0
$303$	−11.0794	+	3.59993i	−0.636497	+	0.206811i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	4.41109i		−	0.251754i	−0.992046	−	0.125877i	$-0.959825\pi$
$307$		−	4.41109i		−	0.251754i	0.992046	−	0.125877i	$-0.0401745\pi$
$308$		0			0
$309$	15.2450	−	11.0761i	0.867258	−	0.630100i
$310$		0			0
$311$	5.11346	+	3.71514i	0.289958	+	0.210667i	0.723249	−	0.690587i	$-0.242648\pi$
$311$	5.11346	+	3.71514i	0.289958	+	0.210667i	−0.433291	+	0.901254i	$0.642648\pi$
$312$		0			0
$313$	9.00753	+	12.3978i	0.509136	+	0.700765i	0.983773	−	0.179416i	$-0.0574208\pi$
$313$	9.00753	+	12.3978i	0.509136	+	0.700765i	−0.474638	+	0.880181i	$0.657421\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	20.2723	+	6.58686i	1.13860	+	0.369955i	0.816840	−	0.576864i	$-0.195724\pi$
$317$	20.2723	+	6.58686i	1.13860	+	0.369955i	0.321765	+	0.946820i	$0.395724\pi$
$318$		0			0
$319$	0.923699	−	2.84285i	0.0517172	−	0.159169i
$320$		0			0
$321$	−4.44851	−	13.6911i	−0.248292	−	0.764164i
$322$		0			0
$323$	−0.0101366	+	0.0139519i	−0.000564018	+	0.000776304i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	3.38673	−	4.66144i	0.187287	−	0.257778i
$328$		0			0
$329$	0.616057	+	1.89603i	0.0339643	+	0.104531i
$330$		0			0
$331$	6.12237	−	18.8427i	0.336516	−	1.03569i	−0.629454	−	0.777037i	$-0.716722\pi$
$331$	6.12237	−	18.8427i	0.336516	−	1.03569i	0.965970	−	0.258652i	$-0.0832785\pi$
$332$		0			0
$333$	−8.12372	−	2.63956i	−0.445177	−	0.144647i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−5.89780	−	8.11762i	−0.321274	−	0.442195i	0.617582	−	0.786507i	$-0.288112\pi$
$337$	−5.89780	−	8.11762i	−0.321274	−	0.442195i	−0.938856	+	0.344311i	$0.888112\pi$
$338$		0			0
$339$	14.5027	+	10.5368i	0.787680	+	0.572283i
$340$		0			0
$341$	−1.03378	+	0.751085i	−0.0559823	+	0.0406735i
$342$		0			0
$343$			1.32419i			0.0714997i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	13.1885	−	4.28519i	0.707994	−	0.230041i	0.0671837	−	0.997741i	$-0.478599\pi$
$347$	13.1885	−	4.28519i	0.707994	−	0.230041i	0.640810	+	0.767700i	$0.278599\pi$
$348$		0			0
$349$	−27.2533			−1.45883			−0.729417	−	0.684069i	$-0.760209\pi$
$349$	−27.2533			−1.45883			−0.729417	+	0.684069i	$0.760209\pi$
$350$		0			0
$351$	4.74950			0.253509
$352$		0			0
$353$	11.8063	−	3.83609i	0.628384	−	0.204174i	0.0225248	−	0.999746i	$-0.492830\pi$
$353$	11.8063	−	3.83609i	0.628384	−	0.204174i	0.605859	+	0.795572i	$0.292830\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$			4.35192i			0.230328i
$358$		0			0
$359$	−15.3910	+	11.1823i	−0.812308	+	0.590177i	−0.914499	−	0.404588i	$-0.867415\pi$
$359$	−15.3910	+	11.1823i	−0.812308	+	0.590177i	0.102191	+	0.994765i	$0.467415\pi$
$360$		0			0
$361$	15.3711	+	11.1678i	0.809007	+	0.587778i
$362$		0			0
$363$	6.08220	+	8.37143i	0.319233	+	0.439386i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−0.927465	−	0.301352i	−0.0484133	−	0.0157304i	0.284710	−	0.958614i	$-0.408103\pi$
$367$	−0.927465	−	0.301352i	−0.0484133	−	0.0157304i	−0.333124	+	0.942883i	$0.608103\pi$
$368$		0			0
$369$	−3.55335	+	10.9361i	−0.184980	+	0.569310i
$370$		0			0
$371$	−3.45294	−	10.6271i	−0.179268	−	0.551729i
$372$		0			0
$373$	11.0341	−	15.1871i	0.571324	−	0.786360i	−0.421387	−	0.906881i	$-0.638457\pi$
$373$	11.0341	−	15.1871i	0.571324	−	0.786360i	0.992711	+	0.120521i	$0.0384566\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−10.3318	+	14.2205i	−0.532114	+	0.732392i
$378$		0			0
$379$	1.06536	+	3.27883i	0.0547236	+	0.168422i	0.974683	−	0.223592i	$-0.0717784\pi$
$379$	1.06536	+	3.27883i	0.0547236	+	0.168422i	−0.919959	+	0.392014i	$0.871778\pi$
$380$		0			0
$381$	−0.707591	+	2.17774i	−0.0362510	+	0.111569i
$382$		0			0
$383$	25.9681	+	8.43755i	1.32691	+	0.431139i	0.884862	−	0.465854i	$-0.154253\pi$
$383$	25.9681	+	8.43755i	1.32691	+	0.431139i	0.442046	+	0.896992i	$0.354253\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	6.02232	+	8.28902i	0.306132	+	0.421354i
$388$		0			0
$389$	7.94232	+	5.77044i	0.402692	+	0.292573i	0.770637	−	0.637275i	$-0.219938\pi$
$389$	7.94232	+	5.77044i	0.402692	+	0.292573i	−0.367945	+	0.929848i	$0.619938\pi$
$390$		0			0
$391$	−5.82567	+	4.23259i	−0.294617	+	0.214051i
$392$		0			0
$393$		−	7.04946i		−	0.355598i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−11.0447	+	3.58865i	−0.554319	+	0.180109i	−0.572763	−	0.819721i	$-0.694129\pi$
$397$	−11.0447	+	3.58865i	−0.554319	+	0.180109i	0.0184443	+	0.999830i	$0.494129\pi$
$398$		0			0
$399$	−0.0568635			−0.00284674
$400$		0			0
$401$	−25.4145			−1.26914			−0.634570	−	0.772865i	$-0.718823\pi$
$401$	−25.4145			−1.26914			−0.634570	+	0.772865i	$0.718823\pi$
$402$		0			0
$403$	7.14637	−	2.32200i	0.355986	−	0.115667i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	6.89902i		−	0.341972i
$408$		0			0
$409$	13.9568	−	10.1402i	0.690117	−	0.501399i	−0.186582	−	0.982439i	$-0.559741\pi$
$409$	13.9568	−	10.1402i	0.690117	−	0.501399i	0.876699	+	0.481040i	$0.159741\pi$
$410$		0			0
$411$	17.7441	+	12.8918i	0.875251	+	0.635907i
$412$		0			0
$413$	−25.4800	−	35.0702i	−1.25379	−	1.72569i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−9.24200	−	3.00291i	−0.452583	−	0.147053i
$418$		0			0
$419$	6.31956	−	19.4496i	0.308731	−	0.950176i	−0.669528	−	0.742787i	$-0.733503\pi$
$419$	6.31956	−	19.4496i	0.308731	−	0.950176i	0.978259	−	0.207389i	$-0.0664965\pi$
$420$		0			0
$421$	−6.46100	−	19.8849i	−0.314890	−	0.969132i	−0.975800	−	0.218666i	$-0.929829\pi$
$421$	−6.46100	−	19.8849i	−0.314890	−	0.969132i	0.660910	−	0.750466i	$-0.270171\pi$
$422$		0			0
$423$	−0.309341	+	0.425771i	−0.0150407	+	0.0207017i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−6.99618	+	9.62941i	−0.338569	+	0.466000i
$428$		0			0
$429$	1.18541	+	3.64832i	0.0572321	+	0.176142i
$430$		0			0
$431$	−2.85900	+	8.79908i	−0.137713	+	0.423837i	−0.996002	−	0.0893294i	$-0.971528\pi$
$431$	−2.85900	+	8.79908i	−0.137713	+	0.423837i	0.858289	+	0.513166i	$0.171528\pi$
$432$		0			0
$433$	−0.223727	−	0.0726932i	−0.0107516	−	0.00349341i	0.303636	−	0.952788i	$-0.401799\pi$
$433$	−0.223727	−	0.0726932i	−0.0107516	−	0.00349341i	−0.314388	+	0.949295i	$0.601799\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.0553044	−	0.0761199i	−0.00264557	−	0.00364131i
$438$		0			0
$439$	25.2424	+	18.3396i	1.20475	+	0.875304i	0.994744	−	0.102396i	$-0.0326509\pi$
$439$	25.2424	+	18.3396i	1.20475	+	0.875304i	0.210008	+	0.977700i	$0.432651\pi$
$440$		0			0
$441$	−5.94593	+	4.31997i	−0.283139	+	0.205713i
$442$		0			0
$443$			24.3862i			1.15862i	0.815106	+	0.579311i	$0.196678\pi$
$443$			24.3862i			1.15862i	−0.815106	+	0.579311i	$0.803322\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−13.2874	+	4.31735i	−0.628474	+	0.204203i
$448$		0			0
$449$	−23.9483			−1.13019			−0.565096	−	0.825025i	$-0.691161\pi$
$449$	−23.9483			−1.13019			−0.565096	+	0.825025i	$0.691161\pi$
$450$		0			0
$451$	−9.28740			−0.437327
$452$		0			0
$453$	19.1990	−	6.23815i	0.902050	−	0.293094i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	3.91244i		−	0.183016i	−0.995804	−	0.0915082i	$-0.970831\pi$
$457$		−	3.91244i		−	0.183016i	0.995804	−	0.0915082i	$-0.0291688\pi$
$458$		0			0
$459$	−0.929435	+	0.675274i	−0.0433823	+	0.0315191i
$460$		0			0
$461$	2.09170	+	1.51971i	0.0974202	+	0.0707799i	0.635429	−	0.772159i	$-0.280823\pi$
$461$	2.09170	+	1.51971i	0.0974202	+	0.0707799i	−0.538009	+	0.842939i	$0.680823\pi$
$462$		0			0
$463$	−12.8777	−	17.7247i	−0.598478	−	0.823734i	0.397090	−	0.917780i	$-0.370020\pi$
$463$	−12.8777	−	17.7247i	−0.598478	−	0.823734i	−0.995568	+	0.0940453i	$0.970020\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−7.79561	−	2.53295i	−0.360738	−	0.117211i	0.123040	−	0.992402i	$-0.460736\pi$
$467$	−7.79561	−	2.53295i	−0.360738	−	0.117211i	−0.483778	+	0.875191i	$0.660736\pi$
$468$		0			0
$469$	−15.5467	+	47.8479i	−0.717881	+	2.20941i
$470$		0			0
$471$	2.39966	+	7.38539i	0.110570	+	0.340301i
$472$		0			0
$473$	−4.86410	+	6.69486i	−0.223652	+	0.307830i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	1.73383	−	2.38641i	0.0793865	−	0.109266i
$478$		0			0
$479$	1.90100	+	5.85067i	0.0868588	+	0.267324i	0.985047	−	0.172288i	$-0.0551160\pi$
$479$	1.90100	+	5.85067i	0.0868588	+	0.267324i	−0.898188	+	0.439612i	$0.855116\pi$
$480$		0			0
$481$	−12.5366	+	38.5836i	−0.571618	+	1.75926i
$482$		0			0
$483$	−22.5815	−	7.33717i	−1.02749	−	0.333853i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	3.69230	+	5.08201i	0.167314	+	0.230288i	0.884438	−	0.466658i	$-0.154542\pi$
$487$	3.69230	+	5.08201i	0.167314	+	0.230288i	−0.717124	+	0.696945i	$0.754542\pi$
$488$		0			0
$489$	−11.2379	−	8.16480i	−0.508195	−	0.369225i
$490$		0			0
$491$	2.22591	−	1.61722i	0.100454	−	0.0729840i	−0.536424	−	0.843948i	$-0.680225\pi$
$491$	2.22591	−	1.61722i	0.100454	−	0.0729840i	0.636878	+	0.770964i	$0.280225\pi$
$492$		0			0
$493$		−	4.25178i		−	0.191490i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−17.7006	+	5.75128i	−0.793982	+	0.257980i
$498$		0			0
$499$	16.4263			0.735341			0.367670	−	0.929956i	$-0.380156\pi$
$499$	16.4263			0.735341			0.367670	+	0.929956i	$0.380156\pi$
$500$		0			0
$501$	−2.89787			−0.129467
$502$		0			0
$503$	11.6860	−	3.79701i	0.521053	−	0.169300i	−0.0366701	−	0.999327i	$-0.511675\pi$
$503$	11.6860	−	3.79701i	0.521053	−	0.169300i	0.557723	+	0.830027i	$0.311675\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		−	9.55771i		−	0.424473i
$508$		0			0
$509$	−8.50277	+	6.17763i	−0.376879	+	0.273818i	−0.760058	−	0.649856i	$-0.774829\pi$
$509$	−8.50277	+	6.17763i	−0.376879	+	0.273818i	0.383179	+	0.923674i	$0.374829\pi$
$510$		0			0
$511$	14.3382	+	10.4173i	0.634283	+	0.460833i
$512$		0			0
$513$	−0.00882334	−	0.0121443i	−0.000389560	−	0.000536183i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−0.404263	−	0.131353i	−0.0177795	−	0.00577690i
$518$		0			0
$519$	−4.70752	+	14.4882i	−0.206637	+	0.635963i
$520$		0			0
$521$	−2.41778	−	7.44115i	−0.105925	−	0.326003i	0.884022	−	0.467446i	$-0.154826\pi$
$521$	−2.41778	−	7.44115i	−0.105925	−	0.326003i	−0.989946	+	0.141443i	$0.954826\pi$
$522$		0			0
$523$	12.9592	−	17.8368i	0.566665	−	0.779947i	−0.425490	−	0.904963i	$-0.639898\pi$
$523$	12.9592	−	17.8368i	0.566665	−	0.779947i	0.992155	+	0.125016i	$0.0398982\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.06834	+	1.47045i	−0.0465378	+	0.0640538i
$528$		0			0
$529$	−5.03308	−	15.4902i	−0.218830	−	0.673489i
$530$		0			0
$531$	3.53625	−	10.8835i	0.153460	−	0.472302i
$532$		0			0
$533$	51.9409	+	16.8766i	2.24981	+	0.731007i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−13.6987	−	18.8546i	−0.591142	−	0.813637i
$538$		0			0
$539$	−4.80240	−	3.48915i	−0.206854	−	0.150288i
$540$		0			0
$541$	−10.0860	+	7.32791i	−0.433631	+	0.315052i	−0.783099	−	0.621897i	$-0.786362\pi$
$541$	−10.0860	+	7.32791i	−0.433631	+	0.315052i	0.349468	+	0.936948i	$0.386362\pi$
$542$		0			0
$543$			17.6985i			0.759514i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	2.39292	−	0.777505i	0.102314	−	0.0332437i	−0.257413	−	0.966302i	$-0.582870\pi$
$547$	2.39292	−	0.777505i	0.102314	−	0.0332437i	0.359726	+	0.933058i	$0.382870\pi$
$548$		0			0
$549$	−3.14212			−0.134102
$550$		0			0
$551$	0.0555550			0.00236672
$552$		0			0
$553$	−33.4024	+	10.8531i	−1.42042	+	0.461521i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			0.262544i			0.0111244i	0.999985	+	0.00556218i	$0.00177051\pi$
$557$			0.262544i			0.0111244i	−0.999985	+	0.00556218i	$0.998229\pi$
$558$		0			0
$559$	39.3687	−	28.6030i	1.66512	−	1.20978i
$560$		0			0
$561$	−0.750685	−	0.545404i	−0.0316939	−	0.0230270i
$562$		0			0
$563$	−19.0928	−	26.2790i	−0.804666	−	1.10753i	−0.992125	−	0.125255i	$-0.960025\pi$
$563$	−19.0928	−	26.2790i	−0.804666	−	1.10753i	0.187459	−	0.982272i	$-0.439975\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−3.60268	−	1.17058i	−0.151298	−	0.0491598i
$568$		0			0
$569$	11.9892	−	36.8991i	0.502615	−	1.54689i	−0.302128	−	0.953267i	$-0.597697\pi$
$569$	11.9892	−	36.8991i	0.502615	−	1.54689i	0.804743	−	0.593623i	$-0.202303\pi$
$570$		0			0
$571$	−11.0258	−	33.9338i	−0.461414	−	1.42009i	−0.863437	−	0.504456i	$-0.831693\pi$
$571$	−11.0258	−	33.9338i	−0.461414	−	1.42009i	0.402023	−	0.915629i	$-0.368307\pi$
$572$		0			0
$573$	5.50411	−	7.57575i	0.229937	−	0.316482i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	14.8962	−	20.5029i	0.620139	−	0.853548i	−0.377224	−	0.926122i	$-0.623121\pi$
$577$	14.8962	−	20.5029i	0.620139	−	0.853548i	0.997363	+	0.0725741i	$0.0231214\pi$
$578$		0			0
$579$	−5.84997	−	18.0044i	−0.243116	−	0.748236i
$580$		0			0
$581$	1.66655	−	5.12913i	0.0691403	−	0.212792i
$582$		0			0
$583$	2.26586	+	0.736221i	0.0938422	+	0.0304912i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.303103	+	0.417186i	0.0125104	+	0.0172191i	0.815226	−	0.579142i	$-0.196612\pi$
$587$	0.303103	+	0.417186i	0.0125104	+	0.0172191i	−0.802716	+	0.596362i	$0.796612\pi$
$588$		0			0
$589$	−0.0192134	−	0.0139593i	−0.000791673	−	0.000575184i
$590$		0			0
$591$	6.10288	−	4.43400i	0.251039	−	0.182390i
$592$		0			0
$593$			7.14389i			0.293364i	0.989184	+	0.146682i	$0.0468595\pi$
$593$			7.14389i			0.293364i	−0.989184	+	0.146682i	$0.953141\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	3.41011	−	1.10801i	0.139566	−	0.0453479i
$598$		0			0
$599$	−23.6627			−0.966833			−0.483417	−	0.875390i	$-0.660604\pi$
$599$	−23.6627			−0.966833			−0.483417	+	0.875390i	$0.660604\pi$
$600$		0			0
$601$	−7.98023			−0.325520			−0.162760	−	0.986666i	$-0.552040\pi$
$601$	−7.98023			−0.325520			−0.162760	+	0.986666i	$0.552040\pi$
$602$		0			0
$603$	−12.6312	+	4.10412i	−0.514381	+	0.167133i
$604$		0			0
$605$		0			0
$606$		0			0
$607$			17.2004i			0.698144i	0.937096	+	0.349072i	$0.113503\pi$
$607$			17.2004i			0.698144i	−0.937096	+	0.349072i	$0.886497\pi$
$608$		0			0
$609$	11.3419	−	8.24038i	0.459597	−	0.333917i
$610$		0			0
$611$	2.02220	+	1.46921i	0.0818094	+	0.0594380i
$612$		0			0
$613$	−8.67810	−	11.9444i	−0.350505	−	0.482429i	0.596968	−	0.802265i	$-0.296372\pi$
$613$	−8.67810	−	11.9444i	−0.350505	−	0.482429i	−0.947473	+	0.319836i	$0.896372\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−14.7142	−	4.78092i	−0.592370	−	0.192473i	−0.00253529	−	0.999997i	$-0.500807\pi$
$617$	−14.7142	−	4.78092i	−0.592370	−	0.192473i	−0.589834	+	0.807524i	$0.700807\pi$
$618$		0			0
$619$	11.5792	−	35.6370i	0.465406	−	1.43237i	−0.393066	−	0.919510i	$-0.628586\pi$
$619$	11.5792	−	35.6370i	0.465406	−	1.43237i	0.858471	−	0.512861i	$-0.171414\pi$
$620$		0			0
$621$	−1.93691	−	5.96119i	−0.0777254	−	0.239214i
$622$		0			0
$623$	−35.8629	+	49.3611i	−1.43682	+	1.97761i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	0.00712642	−	0.00980868i	0.000284602	−	0.000391721i
$628$		0			0
$629$	−3.03244	−	9.33290i	−0.120911	−	0.372127i
$630$		0			0
$631$	−0.468691	+	1.44248i	−0.0186583	+	0.0574244i	−0.959952	−	0.280164i	$-0.909611\pi$
$631$	−0.468691	+	1.44248i	−0.0186583	+	0.0574244i	0.941294	+	0.337588i	$0.109611\pi$
$632$		0			0
$633$	1.98289	+	0.644279i	0.0788126	+	0.0256078i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	20.5177	+	28.2401i	0.812940	+	1.11892i
$638$		0			0
$639$	−3.97485	−	2.88790i	−0.157243	−	0.114243i
$640$		0			0
$641$	3.12903	−	2.27338i	0.123589	−	0.0897930i	−0.524273	−	0.851550i	$-0.675663\pi$
$641$	3.12903	−	2.27338i	0.123589	−	0.0897930i	0.647863	+	0.761757i	$0.275663\pi$
$642$		0			0
$643$			23.2212i			0.915756i	0.889015	+	0.457878i	$0.151390\pi$
$643$			23.2212i			0.915756i	−0.889015	+	0.457878i	$0.848610\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	24.8795	−	8.08384i	0.978114	−	0.317808i	0.224027	−	0.974583i	$-0.428080\pi$
$647$	24.8795	−	8.08384i	0.978114	−	0.317808i	0.754087	+	0.656775i	$0.228080\pi$
$648$		0			0
$649$	9.24271			0.362808
$650$		0			0
$651$	−5.99309			−0.234888
$652$		0			0
$653$	8.13602	−	2.64355i	0.318387	−	0.103450i	−0.145464	−	0.989364i	$-0.546467\pi$
$653$	8.13602	−	2.64355i	0.318387	−	0.103450i	0.463851	+	0.885913i	$0.346467\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			4.67860i			0.182530i
$658$		0			0
$659$	−33.9288	+	24.6507i	−1.32168	+	0.960255i	−0.321767	+	0.946819i	$0.604277\pi$
$659$	−33.9288	+	24.6507i	−1.32168	+	0.960255i	−0.999910	+	0.0134358i	$0.995723\pi$
$660$		0			0
$661$	14.1713	+	10.2961i	0.551201	+	0.400471i	0.828228	−	0.560391i	$-0.189349\pi$
$661$	14.1713	+	10.2961i	0.551201	+	0.400471i	−0.277027	+	0.960862i	$0.589349\pi$
$662$		0			0
$663$	3.20721	+	4.41435i	0.124558	+	0.171439i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	22.0619	+	7.16833i	0.854239	+	0.277559i
$668$		0			0
$669$	−4.33776	+	13.3503i	−0.167708	+	0.516151i
$670$		0			0
$671$	−0.784230	−	2.41361i	−0.0302749	−	0.0931765i
$672$		0			0
$673$	−17.1017	+	23.5385i	−0.659223	+	0.907343i	−0.999455	−	0.0329986i	$-0.989494\pi$
$673$	−17.1017	+	23.5385i	−0.659223	+	0.907343i	0.340232	+	0.940341i	$0.389494\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	17.5667	−	24.1785i	0.675143	−	0.929255i	−0.324720	−	0.945810i	$-0.605270\pi$
$677$	17.5667	−	24.1785i	0.675143	−	0.929255i	0.999863	+	0.0165555i	$0.00527003\pi$
$678$		0			0
$679$	−9.43726	−	29.0449i	−0.362169	−	1.11464i
$680$		0			0
$681$	−0.783313	+	2.41079i	−0.0300166	+	0.0923817i
$682$		0			0
$683$	−35.3984	−	11.5016i	−1.35448	−	0.440097i	−0.460284	−	0.887772i	$-0.652252\pi$
$683$	−35.3984	−	11.5016i	−1.35448	−	0.440097i	−0.894197	+	0.447674i	$0.852252\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−9.71385	−	13.3700i	−0.370607	−	0.510096i
$688$		0			0
$689$	−11.3342	−	8.23481i	−0.431800	−	0.313721i
$690$		0			0
$691$	−13.6397	+	9.90980i	−0.518877	+	0.376986i	−0.816181	−	0.577797i	$-0.803913\pi$
$691$	−13.6397	+	9.90980i	−0.518877	+	0.376986i	0.297303	+	0.954783i	$0.403913\pi$
$692$		0			0
$693$		−	3.05955i		−	0.116223i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−12.5639	+	4.08225i	−0.475890	+	0.154626i
$698$		0			0
$699$	−26.5208			−1.00311
$700$		0			0
$701$	−23.3495			−0.881898			−0.440949	−	0.897532i	$-0.645358\pi$
$701$	−23.3495			−0.881898			−0.440949	+	0.897532i	$0.645358\pi$
$702$		0			0
$703$	0.121947	−	0.0396228i	0.00459930	−	0.00149440i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	44.1297i		−	1.65967i
$708$		0			0
$709$	15.4019	−	11.1901i	0.578429	−	0.420253i	−0.259728	−	0.965682i	$-0.583633\pi$
$709$	15.4019	−	11.1901i	0.578429	−	0.420253i	0.838157	+	0.545428i	$0.183633\pi$
$710$		0			0
$711$	−7.50084	−	5.44968i	−0.281303	−	0.204379i
$712$		0			0
$713$	−5.82877	−	8.02261i	−0.218289	−	0.300449i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	7.09855	+	2.30646i	0.265100	+	0.0861363i
$718$		0			0
$719$	4.55488	−	14.0185i	0.169868	−	0.522801i	−0.829494	−	0.558516i	$-0.811371\pi$
$719$	4.55488	−	14.0185i	0.169868	−	0.522801i	0.999362	+	0.0357149i	$0.0113708\pi$
$720$		0			0
$721$	22.0583	+	67.8884i	0.821493	+	2.52830i
$722$		0			0
$723$	6.05288	−	8.33107i	0.225109	−	0.309836i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−17.6698	+	24.3204i	−0.655336	+	0.901993i	−0.999316	−	0.0369839i	$-0.988225\pi$
$727$	−17.6698	+	24.3204i	−0.655336	+	0.901993i	0.343979	+	0.938977i	$0.388225\pi$
$728$		0			0
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$		0			0
$731$	−3.63738	+	11.1947i	−0.134533	+	0.414051i
$732$		0			0
$733$	−21.5355	−	6.99732i	−0.795433	−	0.258452i	−0.117017	−	0.993130i	$-0.537333\pi$
$733$	−21.5355	−	6.99732i	−0.795433	−	0.258452i	−0.678416	+	0.734678i	$0.737333\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−6.30514	−	8.67828i	−0.232253	−	0.319668i
$738$		0			0
$739$	−20.7764	−	15.0949i	−0.764272	−	0.555276i	0.135946	−	0.990716i	$-0.456593\pi$
$739$	−20.7764	−	15.0949i	−0.764272	−	0.555276i	−0.900218	+	0.435440i	$0.856593\pi$
$740$		0			0
$741$	−0.0576792	+	0.0419064i	−0.00211890	+	0.00153947i
$742$		0			0
$743$		−	24.9796i		−	0.916411i	−0.888846	−	0.458205i	$-0.848492\pi$
$743$		−	24.9796i		−	0.916411i	0.888846	−	0.458205i	$-0.151508\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.35402	−	0.439947i	0.0495409	−	0.0160968i
$748$		0			0
$749$	54.5321			1.99256
$750$		0			0
$751$	17.9383			0.654580			0.327290	−	0.944924i	$-0.393865\pi$
$751$	17.9383			0.654580			0.327290	+	0.944924i	$0.393865\pi$
$752$		0			0
$753$	−18.6225	+	6.05083i	−0.678643	+	0.220504i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			9.91474i			0.360357i	0.983634	+	0.180179i	$0.0576676\pi$
$757$			9.91474i			0.360357i	−0.983634	+	0.180179i	$0.942332\pi$
$758$		0			0
$759$	4.09565	−	2.97566i	0.148663	−	0.108010i
$760$		0			0
$761$	25.6076	+	18.6050i	0.928273	+	0.674430i	0.945569	−	0.325420i	$-0.105506\pi$
$761$	25.6076	+	18.6050i	0.928273	+	0.674430i	−0.0172961	+	0.999850i	$0.505506\pi$
$762$		0			0
$763$	12.8292	+	17.6579i	0.464449	+	0.639259i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−51.6910	−	16.7954i	−1.86645	−	0.606447i
$768$		0			0
$769$	−6.91430	+	21.2800i	−0.249336	+	0.767377i	0.745557	+	0.666442i	$0.232184\pi$
$769$	−6.91430	+	21.2800i	−0.249336	+	0.767377i	−0.994893	+	0.100935i	$0.967816\pi$
$770$		0			0
$771$	−1.84801	−	5.68760i	−0.0665546	−	0.204834i
$772$		0			0
$773$	−28.1148	+	38.6967i	−1.01122	+	1.39182i	−0.0930367	+	0.995663i	$0.529657\pi$
$773$	−28.1148	+	38.6967i	−1.01122	+	1.39182i	−0.918182	+	0.396160i	$0.870343\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	19.0190	−	26.1774i	0.682302	−	0.939108i
$778$		0			0
$779$	−0.0533399	−	0.164163i	−0.00191110	−	0.00588176i
$780$		0			0
$781$	1.22626	−	3.77405i	0.0438792	−	0.135046i
$782$		0			0
$783$	3.51978	+	1.14365i	0.125787	+	0.0408706i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−16.2038	−	22.3026i	−0.577603	−	0.795002i	0.415827	−	0.909444i	$-0.363492\pi$
$787$	−16.2038	−	22.3026i	−0.577603	−	0.795002i	−0.993430	+	0.114442i	$0.963492\pi$
$788$		0			0
$789$	4.91104	+	3.56808i	0.174838	+	0.127027i
$790$		0			0
$791$	−54.9375	+	39.9144i	−1.95335	+	1.41919i
$792$		0			0
$793$			14.9235i			0.529948i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−21.9712	+	7.13887i	−0.778260	+	0.252872i	−0.671097	−	0.741370i	$-0.734177\pi$
$797$	−21.9712	+	7.13887i	−0.778260	+	0.252872i	−0.107163	+	0.994241i	$0.534177\pi$
$798$		0			0
$799$	−0.604617			−0.0213898
$800$		0			0
$801$	−16.1067			−0.569103
$802$		0			0
$803$	−3.59386	+	1.16772i	−0.126825	+	0.0412078i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		−	9.61605i		−	0.338501i
$808$		0			0
$809$	−1.36960	+	0.995071i	−0.0481525	+	0.0349848i	−0.611601	−	0.791166i	$-0.709474\pi$
$809$	−1.36960	+	0.995071i	−0.0481525	+	0.0349848i	0.563449	+	0.826151i	$0.309474\pi$
$810$		0			0
$811$	−16.6435	−	12.0922i	−0.584434	−	0.424616i	0.255886	−	0.966707i	$-0.417633\pi$
$811$	−16.6435	−	12.0922i	−0.584434	−	0.424616i	−0.840320	+	0.542091i	$0.817633\pi$
$812$		0			0
$813$	17.8849	+	24.6164i	0.627250	+	0.863335i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−0.146274	−	0.0475272i	−0.00511746	−	0.00166277i
$818$		0			0
$819$	−5.55967	+	17.1109i	−0.194271	+	0.597904i
$820$		0			0
$821$	−14.2235	−	43.7754i	−0.496403	−	1.52777i	−0.814759	−	0.579800i	$-0.803131\pi$
$821$	−14.2235	−	43.7754i	−0.496403	−	1.52777i	0.318356	−	0.947971i	$-0.396869\pi$
$822$		0			0
$823$	32.9082	−	45.2942i	1.14711	−	1.57886i	0.396605	−	0.917990i	$-0.370188\pi$
$823$	32.9082	−	45.2942i	1.14711	−	1.57886i	0.750502	−	0.660868i	$-0.229812\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−12.1319	+	16.6981i	−0.421866	+	0.580648i	−0.966062	−	0.258309i	$-0.916835\pi$
$827$	−12.1319	+	16.6981i	−0.421866	+	0.580648i	0.544196	+	0.838958i	$0.316835\pi$
$828$		0			0
$829$	0.599179	+	1.84408i	0.0208103	+	0.0640476i	0.960922	−	0.276818i	$-0.0892799\pi$
$829$	0.599179	+	1.84408i	0.0208103	+	0.0640476i	−0.940112	+	0.340866i	$0.889280\pi$
$830$		0			0
$831$	−2.22614	+	6.85134i	−0.0772238	+	0.237670i
$832$		0			0
$833$	−8.03026	−	2.60919i	−0.278232	−	0.0904030i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−0.929930	−	1.27994i	−0.0321431	−	0.0442412i
$838$		0			0
$839$	42.2783	+	30.7170i	1.45961	+	1.06047i	0.983464	+	0.181102i	$0.0579665\pi$
$839$	42.2783	+	30.7170i	1.45961	+	1.06047i	0.476146	+	0.879366i	$0.342034\pi$
$840$		0			0
$841$	12.3806	−	8.99501i	0.426916	−	0.310173i
$842$		0			0
$843$			29.7964i			1.02624i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−37.2793	+	12.1128i	−1.28093	+	0.416200i
$848$		0			0
$849$	−8.82402			−0.302840
$850$		0			0
$851$	53.5397			1.83532
$852$		0			0
$853$	16.7010	−	5.42649i	0.571832	−	0.185799i	−0.00880614	−	0.999961i	$-0.502803\pi$
$853$	16.7010	−	5.42649i	0.571832	−	0.185799i	0.580638	+	0.814162i	$0.302803\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	50.9890i		−	1.74175i	−0.491503	−	0.870876i	$-0.663552\pi$
$857$		−	50.9890i		−	1.74175i	0.491503	−	0.870876i	$-0.336448\pi$
$858$		0			0
$859$	15.0749	−	10.9525i	0.514349	−	0.373696i	−0.300122	−	0.953901i	$-0.597027\pi$
$859$	15.0749	−	10.9525i	0.514349	−	0.373696i	0.814471	+	0.580205i	$0.197027\pi$
$860$		0			0
$861$	−35.2397	−	25.6032i	−1.20097	−	0.872553i
$862$		0			0
$863$	−0.171716	−	0.236347i	−0.00584529	−	0.00804536i	0.806084	−	0.591801i	$-0.201583\pi$
$863$	−0.171716	−	0.236347i	−0.00584529	−	0.00804536i	−0.811930	+	0.583755i	$0.801583\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	14.9127	+	4.84543i	0.506462	+	0.164560i
$868$		0			0
$869$	2.31405	−	7.12192i	0.0784989	−	0.241595i
$870$		0			0
$871$	19.4925	+	59.9917i	0.660477	+	2.03274i
$872$		0			0
$873$	4.73874	−	6.52232i	0.160382	−	0.220747i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	22.3126	−	30.7106i	0.753442	−	1.03702i	−0.244289	−	0.969702i	$-0.578555\pi$
$877$	22.3126	−	30.7106i	0.753442	−	1.03702i	0.997731	−	0.0673215i	$-0.0214453\pi$
$878$		0			0
$879$	1.30017	+	4.00150i	0.0438535	+	0.134967i
$880$		0			0
$881$	−11.3378	+	34.8942i	−0.381981	+	1.17562i	0.556666	+	0.830736i	$0.312080\pi$
$881$	−11.3378	+	34.8942i	−0.381981	+	1.17562i	−0.938647	+	0.344879i	$0.887920\pi$
$882$		0			0
$883$	−21.5128	−	6.98993i	−0.723964	−	0.235230i	−0.0762228	−	0.997091i	$-0.524286\pi$
$883$	−21.5128	−	6.98993i	−0.723964	−	0.235230i	−0.647741	+	0.761861i	$0.724286\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−14.3643	−	19.7708i	−0.482306	−	0.663838i	0.496640	−	0.867957i	$-0.334567\pi$
$887$	−14.3643	−	19.7708i	−0.482306	−	0.663838i	−0.978946	+	0.204119i	$0.934567\pi$
$888$		0			0
$889$	−7.01741	−	5.09845i	−0.235356	−	0.170996i
$890$		0			0
$891$	0.653426	−	0.474742i	0.0218906	−	0.0159044i
$892$		0			0
$893$		−	0.00790011i		−	0.000264367i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−28.3126	+	9.19934i	−0.945332	+	0.307157i
$898$		0			0
$899$	5.85519			0.195281
$900$		0			0
$901$	3.38882			0.112898
$902$		0			0
$903$	−36.9123	+	11.9935i	−1.22836	+	0.399120i
$904$		0			0
$905$		0			0
$906$		0			0
$907$		−	32.7792i		−	1.08842i	−0.838950	−	0.544208i	$-0.816830\pi$
$907$		−	32.7792i		−	1.08842i	0.838950	−	0.544208i	$-0.183170\pi$
$908$		0			0
$909$	9.42474	−	6.84747i	0.312599	−	0.227116i
$910$		0			0
$911$	−22.0778	−	16.0405i	−0.731470	−	0.531444i	0.158558	−	0.987350i	$-0.449315\pi$
$911$	−22.0778	−	16.0405i	−0.731470	−	0.531444i	−0.890028	+	0.455906i	$0.849315\pi$
$912$		0			0
$913$	0.675888	+	0.930280i	0.0223686	+	0.0307878i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	25.3970	+	8.25197i	0.838681	+	0.272504i
$918$		0			0
$919$	12.8923	−	39.6783i	0.425277	−	1.30887i	−0.477453	−	0.878658i	$-0.658440\pi$
$919$	12.8923	−	39.6783i	0.425277	−	1.30887i	0.902729	−	0.430209i	$-0.141560\pi$
$920$		0			0
$921$	1.36310	+	4.19520i	0.0449158	+	0.138236i
$922$		0			0
$923$	−13.7161	+	18.8785i	−0.451469	+	0.621394i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−11.0761	+	15.2450i	−0.363788	+	0.500711i
$928$		0			0
$929$	10.4151	+	32.0542i	0.341707	+	1.05167i	0.963323	+	0.268344i	$0.0864763\pi$
$929$	10.4151	+	32.0542i	0.341707	+	1.05167i	−0.621616	+	0.783322i	$0.713524\pi$
$930$		0			0
$931$	0.0340925	−	0.104926i	0.00111734	−	0.00343880i
$932$		0			0
$933$	−6.01123	−	1.95317i	−0.196799	−	0.0639438i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−0.614857	−	0.846278i	−0.0200865	−	0.0276467i	0.798856	−	0.601523i	$-0.205439\pi$
$937$	−0.614857	−	0.846278i	−0.0200865	−	0.0276467i	−0.818942	+	0.573876i	$0.805439\pi$
$938$		0			0
$939$	−12.3978	−	9.00753i	−0.404587	−	0.293950i
$940$		0			0
$941$	−4.62928	+	3.36337i	−0.150910	+	0.109643i	−0.660678	−	0.750669i	$-0.729731\pi$
$941$	−4.62928	+	3.36337i	−0.150910	+	0.109643i	0.509768	+	0.860312i	$0.329731\pi$
$942$		0			0
$943$		−	72.0746i		−	2.34707i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	11.9783	−	3.89200i	0.389244	−	0.126473i	−0.107856	−	0.994167i	$-0.534398\pi$
$947$	11.9783	−	3.89200i	0.389244	−	0.126473i	0.497099	+	0.867694i	$0.334398\pi$
$948$		0			0
$949$	22.2210			0.721325
$950$		0			0
$951$	−21.3155			−0.691204
$952$		0			0
$953$	−54.5813	+	17.7346i	−1.76806	+	0.574479i	−0.997984	−	0.0634695i	$-0.979783\pi$
$953$	−54.5813	+	17.7346i	−1.76806	+	0.574479i	−0.770079	+	0.637948i	$0.779783\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			2.98915i			0.0966255i
$958$		0			0
$959$	−67.2161	+	48.8353i	−2.17052	+	1.57698i
$960$		0			0
$961$	23.0545	+	16.7501i	0.743695	+	0.540326i
$962$		0			0
$963$	8.46158	+	11.6464i	0.272671	+	0.375299i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−8.40935	−	2.73236i	−0.270427	−	0.0878669i	0.170665	−	0.985329i	$-0.445409\pi$
$967$	−8.40935	−	2.73236i	−0.270427	−	0.0878669i	−0.441091	+	0.897462i	$0.645409\pi$
$968$		0			0
$969$	0.00532915	−	0.0164014i	0.000171197	−	0.000526890i
$970$		0			0
$971$	16.0493	+	49.3945i	0.515045	+	1.58515i	0.783200	+	0.621770i	$0.213586\pi$
$971$	16.0493	+	49.3945i	0.515045	+	1.58515i	−0.268155	+	0.963376i	$0.586414\pi$
$972$		0			0
$973$	21.6370	−	29.7808i	0.693651	−	0.954729i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−21.8859	+	30.1234i	−0.700193	+	0.963732i	0.299760	+	0.954015i	$0.403093\pi$
$977$	−21.8859	+	30.1234i	−0.700193	+	0.963732i	−0.999953	+	0.00971780i	$0.996907\pi$
$978$		0			0
$979$	−4.02002	−	12.3724i	−0.128480	−	0.395422i
$980$		0			0
$981$	−1.78051	+	5.47985i	−0.0568473	+	0.174958i
$982$		0			0
$983$	34.0107	+	11.0507i	1.08477	+	0.352464i	0.796225	−	0.605001i	$-0.206827\pi$
$983$	34.0107	+	11.0507i	1.08477	+	0.352464i	0.288548	+	0.957465i	$0.406827\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−1.17181	−	1.61286i	−0.0372991	−	0.0513378i
$988$		0			0
$989$	−51.9553	−	37.7477i	−1.65208	−	1.20031i
$990$		0			0
$991$	35.4505	−	25.7563i	1.12612	−	0.818175i	0.140996	−	0.990010i	$-0.454970\pi$
$991$	35.4505	−	25.7563i	1.12612	−	0.818175i	0.985126	+	0.171835i	$0.0549697\pi$
$992$		0			0
$993$			19.8124i			0.628728i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	37.5746	−	12.2087i	1.19000	−	0.386654i	0.353927	−	0.935273i	$-0.384846\pi$
$997$	37.5746	−	12.2087i	1.19000	−	0.386654i	0.836072	+	0.548619i	$0.184846\pi$
$998$		0			0
$999$	8.54179			0.270250

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1500.2.o.c.49.1		24
5.2	odd	4		1500.2.m.c.1201.5		24
5.3	odd	4		1500.2.m.d.1201.2		24
5.4	even	2		300.2.o.a.109.5	✓	24
15.14	odd	2		900.2.w.c.109.4		24
25.2	odd	20		1500.2.m.c.301.5		24
25.6	even	5		7500.2.d.g.1249.16		24
25.8	odd	20		7500.2.a.m.1.4		12
25.11	even	5		300.2.o.a.289.5	yes	24
25.14	even	10	inner	1500.2.o.c.949.1		24
25.17	odd	20		7500.2.a.n.1.9		12
25.19	even	10		7500.2.d.g.1249.9		24
25.23	odd	20		1500.2.m.d.301.2		24
75.11	odd	10		900.2.w.c.289.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.109.5	✓	24	5.4	even	2
300.2.o.a.289.5	yes	24	25.11	even	5
900.2.w.c.109.4		24	15.14	odd	2
900.2.w.c.289.4		24	75.11	odd	10
1500.2.m.c.301.5		24	25.2	odd	20
1500.2.m.c.1201.5		24	5.2	odd	4
1500.2.m.d.301.2		24	25.23	odd	20
1500.2.m.d.1201.2		24	5.3	odd	4
1500.2.o.c.49.1		24	1.1	even	1	trivial
1500.2.o.c.949.1		24	25.14	even	10	inner
7500.2.a.m.1.4		12	25.8	odd	20
7500.2.a.n.1.9		12	25.17	odd	20
7500.2.d.g.1249.9		24	25.19	even	10
7500.2.d.g.1249.16		24	25.6	even	5

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1500.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{3} -3.78808i q^{7} +(0.809017 - 0.587785i) q^{9} +(0.653426 + 0.474742i) q^{11} +(-2.79168 - 3.84242i) q^{13} +(1.09262 + 0.355012i) q^{17} +(-0.00463870 + 0.0142765i) q^{19} +(1.17058 + 3.60268i) q^{21} +(-3.68422 + 5.07089i) q^{23} +(-0.587785 + 0.809017i) q^{27} +(-1.14365 - 3.51978i) q^{29} +(-0.488893 + 1.50466i) q^{31} +(-0.768148 - 0.249586i) q^{33} +(-5.02074 - 6.91045i) q^{37} +(3.84242 + 2.79168i) q^{39} +(-9.30279 + 6.75887i) q^{41} +10.2458i q^{43} +(-0.500524 + 0.162630i) q^{47} -7.34957 q^{49} -1.14884 q^{51} +(2.80539 - 0.911527i) q^{53} -0.0150112i q^{57} +(9.25803 - 6.72635i) q^{59} +(-2.54203 - 1.84689i) q^{61} +(-2.22658 - 3.06462i) q^{63} +(-12.6312 - 4.10412i) q^{67} +(1.93691 - 5.96119i) q^{69} +(-1.51826 - 4.67271i) q^{71} +(-2.75001 + 3.78507i) q^{73} +(1.79836 - 2.47523i) q^{77} +(-2.86507 - 8.81777i) q^{79} +(0.309017 - 0.951057i) q^{81} +(1.35402 + 0.439947i) q^{83} +(2.17534 + 2.99410i) q^{87} +(-13.0306 - 9.46730i) q^{89} +(-14.5554 + 10.5751i) q^{91} -1.58209i q^{93} +(7.66744 - 2.49130i) q^{97} +0.807679 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{9} - 6 q^{11} - 10 q^{17} + 10 q^{19} - 4 q^{21} - 40 q^{23} + 4 q^{29} + 6 q^{31} - 10 q^{33} - 10 q^{41} + 40 q^{47} - 56 q^{49} + 16 q^{51} + 60 q^{53} - 36 q^{59} - 12 q^{61} + 10 q^{63}+ \cdots - 4 q^{99}+O(q^{100}) \) 24 * q + 6 * q^9 - 6 * q^11 - 10 * q^17 + 10 * q^19 - 4 * q^21 - 40 * q^23 + 4 * q^29 + 6 * q^31 - 10 * q^33 - 10 * q^41 + 40 * q^47 - 56 * q^49 + 16 * q^51 + 60 * q^53 - 36 * q^59 - 12 * q^61 + 10 * q^63 - 20 * q^67 + 4 * q^69 + 40 * q^71 - 60 * q^73 + 40 * q^77 + 8 * q^79 - 6 * q^81 + 50 * q^83 + 20 * q^87 - 30 * q^91 + 40 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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