LMFDB - Embedded newform 600.2.m.e.299.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [600,2,Mod(299,600)] 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("600.299"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(600, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.m (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,-20,0,14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			299.1
Character	$\chi$	$=$	600.299
Dual form			600.2.m.e.299.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.13191 - 0.847808i) q^{2} +(-1.71500 - 0.242431i) q^{3} +(0.562443 + 1.91929i) q^{4} +(1.73569 + 1.72840i) q^{6} +3.08957 q^{7} +(0.990551 - 2.64930i) q^{8} +(2.88245 + 0.831539i) q^{9} +2.54654i q^{11} +(-0.499295 - 3.42793i) q^{12} -5.06696 q^{13} +(-3.49711 - 2.61936i) q^{14} +(-3.36732 + 2.15898i) q^{16} -0.214179 q^{17} +(-2.55770 - 3.38500i) q^{18} -2.60975 q^{19} +(-5.29861 - 0.749006i) q^{21} +(2.15898 - 2.88245i) q^{22} +4.47647i q^{23} +(-2.34107 + 4.30342i) q^{24} +(5.73534 + 4.29581i) q^{26} +(-4.74182 - 2.12489i) q^{27} +(1.73770 + 5.92976i) q^{28} +7.86770 q^{29} +4.58758i q^{31} +(5.64190 + 0.411070i) q^{32} +(0.617360 - 4.36732i) q^{33} +(0.242431 + 0.181582i) q^{34} +(0.0252553 + 5.99995i) q^{36} +7.67714 q^{37} +(2.95400 + 2.21257i) q^{38} +(8.68984 + 1.22839i) q^{39} -9.26946i q^{41} +(5.36253 + 5.34001i) q^{42} +11.4049i q^{43} +(-4.88754 + 1.43228i) q^{44} +(3.79518 - 5.06696i) q^{46} +10.5972i q^{47} +(6.29835 - 2.88630i) q^{48} +2.54541 q^{49} +(0.367316 + 0.0519235i) q^{51} +(-2.84987 - 9.72494i) q^{52} +9.51198i q^{53} +(3.56582 + 6.42533i) q^{54} +(3.06037 - 8.18520i) q^{56} +(4.47572 + 0.632684i) q^{57} +(-8.90553 - 6.67030i) q^{58} +0.428357i q^{59} +1.11217i q^{61} +(3.88939 - 5.19273i) q^{62} +(8.90553 + 2.56909i) q^{63} +(-6.03762 - 5.24854i) q^{64} +(-4.40144 + 4.42001i) q^{66} -2.35998i q^{67} +(-0.120463 - 0.411070i) q^{68} +(1.08523 - 7.67714i) q^{69} +6.12075 q^{71} +(5.05822 - 6.81281i) q^{72} -12.0147i q^{73} +(-8.68984 - 6.50874i) q^{74} +(-1.46783 - 5.00885i) q^{76} +7.86770i q^{77} +(-8.79468 - 8.75774i) q^{78} +11.6319i q^{79} +(7.61709 + 4.79374i) q^{81} +(-7.85873 + 10.4922i) q^{82} +2.29913 q^{83} +(-1.54261 - 10.5908i) q^{84} +(9.66919 - 12.9094i) q^{86} +(-13.4931 - 1.90737i) q^{87} +(6.74655 + 2.52248i) q^{88} +12.4853i q^{89} -15.6547 q^{91} +(-8.59162 + 2.51776i) q^{92} +(1.11217 - 7.86770i) q^{93} +(8.98440 - 11.9951i) q^{94} +(-9.57620 - 2.07276i) q^{96} +8.04496i q^{97} +(-2.88118 - 2.15802i) q^{98} +(-2.11755 + 7.34028i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{4} + 14 q^{6} + 4 q^{9} - 12 q^{16} + 8 q^{19} - 10 q^{24} + 4 q^{34} + 38 q^{36} - 32 q^{46} + 72 q^{49} - 60 q^{51} + 60 q^{54} - 20 q^{64} + 14 q^{66} - 76 q^{76} - 20 q^{81} + 68 q^{84}+ \cdots - 116 q^{99}+O(q^{100}) $ 24 * q - 20 * q^4 + 14 * q^6 + 4 * q^9 - 12 * q^16 + 8 * q^19 - 10 * q^24 + 4 * q^34 + 38 * q^36 - 32 * q^46 + 72 * q^49 - 60 * q^51 + 60 * q^54 - 20 * q^64 + 14 * q^66 - 76 * q^76 - 20 * q^81 + 68 * q^84 - 48 * q^91 - 56 * q^94 - 62 * q^96 - 116 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	−1.13191	−	0.847808i	−0.800382	−	0.599491i
$2$	−1.13191	−	0.847808i	−0.800382	−	0.599491i
$3$	−1.71500	−	0.242431i	−0.990156	−	0.139968i
$3$	−1.71500	−	0.242431i	−0.990156	−	0.139968i
$4$	0.562443	+	1.91929i	0.281221	+	0.959643i
$5$		0			0
$5$		0			0
$6$	1.73569	+	1.72840i	0.708593	+	0.705617i
$7$	3.08957			1.16775			0.583873	−	0.811845i	$-0.301537\pi$
$7$	3.08957			1.16775			0.583873	+	0.811845i	$0.301537\pi$
$8$	0.990551	−	2.64930i	0.350213	−	0.936670i
$9$	2.88245	+	0.831539i	0.960818	+	0.277180i
$10$		0			0
$11$			2.54654i			0.767810i	0.923373	+	0.383905i	$0.125421\pi$
$11$			2.54654i			0.767810i	−0.923373	+	0.383905i	$0.874579\pi$
$12$	−0.499295	−	3.42793i	−0.144134	−	0.989558i
$13$	−5.06696			−1.40532			−0.702661	−	0.711525i	$-0.748005\pi$
$13$	−5.06696			−1.40532			−0.702661	+	0.711525i	$0.748005\pi$
$14$	−3.49711	−	2.61936i	−0.934642	−	0.700053i
$15$		0			0
$16$	−3.36732	+	2.15898i	−0.841829	+	0.539744i
$17$	−0.214179			−0.0519459			−0.0259730	−	0.999663i	$-0.508268\pi$
$17$	−0.214179			−0.0519459			−0.0259730	+	0.999663i	$0.508268\pi$
$18$	−2.55770	−	3.38500i	−0.602855	−	0.797851i
$19$	−2.60975			−0.598717			−0.299359	−	0.954141i	$-0.596773\pi$
$19$	−2.60975			−0.598717			−0.299359	+	0.954141i	$0.596773\pi$
$20$		0			0
$21$	−5.29861	−	0.749006i	−1.15625	−	0.163447i
$22$	2.15898	−	2.88245i	0.460295	−	0.614541i
$23$			4.47647i			0.933408i	0.884414	+	0.466704i	$0.154559\pi$
$23$			4.47647i			0.933408i	−0.884414	+	0.466704i	$0.845441\pi$
$24$	−2.34107	+	4.30342i	−0.477869	+	0.878431i
$25$		0			0
$26$	5.73534	+	4.29581i	1.12479	+	0.842478i
$27$	−4.74182	−	2.12489i	−0.912564	−	0.408934i
$28$	1.73770	+	5.92976i	0.328395	+	1.12062i
$29$	7.86770			1.46100			0.730498	−	0.682915i	$-0.239288\pi$
$29$	7.86770			1.46100			0.730498	+	0.682915i	$0.239288\pi$
$30$		0			0
$31$			4.58758i			0.823953i	0.911194	+	0.411977i	$0.135161\pi$
$31$			4.58758i			0.823953i	−0.911194	+	0.411977i	$0.864839\pi$
$32$	5.64190	+	0.411070i	0.997356	+	0.0726676i
$33$	0.617360	−	4.36732i	0.107469	−	0.760252i
$34$	0.242431	+	0.181582i	0.0415766	+	0.0311411i
$35$		0			0
$36$	0.0252553	+	5.99995i	0.00420921	+	0.999991i
$37$	7.67714			1.26211			0.631057	−	0.775736i	$-0.282621\pi$
$37$	7.67714			1.26211			0.631057	+	0.775736i	$0.282621\pi$
$38$	2.95400	+	2.21257i	0.479202	+	0.358925i
$39$	8.68984	+	1.22839i	1.39149	+	0.196700i
$40$		0			0
$41$		−	9.26946i		−	1.44765i	−0.689985	−	0.723823i	$-0.742383\pi$
$41$		−	9.26946i		−	1.44765i	0.689985	−	0.723823i	$-0.257617\pi$
$42$	5.36253	+	5.34001i	0.827457	+	0.823981i
$43$			11.4049i			1.73924i	0.493725	+	0.869618i	$0.335635\pi$
$43$			11.4049i			1.73924i	−0.493725	+	0.869618i	$0.664365\pi$
$44$	−4.88754	+	1.43228i	−0.736824	+	0.215925i
$45$		0			0
$46$	3.79518	−	5.06696i	0.559569	−	0.747082i
$47$			10.5972i			1.54576i	0.634551	+	0.772881i	$0.281185\pi$
$47$			10.5972i			1.54576i	−0.634551	+	0.772881i	$0.718815\pi$
$48$	6.29835	−	2.88630i	0.909089	−	0.416602i
$49$	2.54541			0.363631
$50$		0			0
$51$	0.367316	+	0.0519235i	0.0514346	+	0.00727075i
$52$	−2.84987	−	9.72494i	−0.395206	−	1.34861i
$53$			9.51198i			1.30657i	0.757112	+	0.653285i	$0.226610\pi$
$53$			9.51198i			1.30657i	−0.757112	+	0.653285i	$0.773390\pi$
$54$	3.56582	+	6.42533i	0.485247	+	0.874377i
$55$		0			0
$56$	3.06037	−	8.18520i	0.408960	−	1.09379i
$57$	4.47572	+	0.632684i	0.592823	+	0.0838010i
$58$	−8.90553	−	6.67030i	−1.16935	−	0.875853i
$59$			0.428357i			0.0557674i	0.999611	+	0.0278837i	$0.00887680\pi$
$59$			0.428357i			0.0557674i	−0.999611	+	0.0278837i	$0.991123\pi$
$60$		0			0
$61$			1.11217i			0.142399i	0.997462	+	0.0711995i	$0.0226827\pi$
$61$			1.11217i			0.142399i	−0.997462	+	0.0711995i	$0.977317\pi$
$62$	3.88939	−	5.19273i	0.493953	−	0.659477i
$63$	8.90553	+	2.56909i	1.12199	+	0.323675i
$64$	−6.03762	−	5.24854i	−0.754702	−	0.656068i
$65$		0			0
$66$	−4.40144	+	4.42001i	−0.541780	+	0.544065i
$67$		−	2.35998i		−	0.288317i	−0.989555	−	0.144159i	$-0.953952\pi$
$67$		−	2.35998i		−	0.288317i	0.989555	−	0.144159i	$-0.0460475\pi$
$68$	−0.120463	−	0.411070i	−0.0146083	−	0.0498495i
$69$	1.08523	−	7.67714i	0.130647	−	0.924219i
$70$		0			0
$71$	6.12075			0.726399			0.363199	−	0.931711i	$-0.381684\pi$
$71$	6.12075			0.726399			0.363199	+	0.931711i	$0.381684\pi$
$72$	5.05822	−	6.81281i	0.596117	−	0.802898i
$73$		−	12.0147i		−	1.40621i	−0.711085	−	0.703106i	$-0.751796\pi$
$73$		−	12.0147i		−	1.40621i	0.711085	−	0.703106i	$-0.248204\pi$
$74$	−8.68984	−	6.50874i	−1.01017	−	0.756626i
$75$		0			0
$76$	−1.46783	−	5.00885i	−0.168372	−	0.574555i
$77$			7.86770i			0.896608i
$78$	−8.79468	−	8.75774i	−0.995802	−	0.991619i
$79$			11.6319i			1.30869i	0.756194	+	0.654347i	$0.227057\pi$
$79$			11.6319i			1.30869i	−0.756194	+	0.654347i	$0.772943\pi$
$80$		0			0
$81$	7.61709	+	4.79374i	0.846343	+	0.532638i
$82$	−7.85873	+	10.4922i	−0.867851	+	1.15867i
$83$	2.29913			0.252362			0.126181	−	0.992007i	$-0.459728\pi$
$83$	2.29913			0.252362			0.126181	+	0.992007i	$0.459728\pi$
$84$	−1.54261	−	10.5908i	−0.168312	−	1.15555i
$85$		0			0
$86$	9.66919	−	12.9094i	1.04266	−	1.39205i
$87$	−13.4931	−	1.90737i	−1.44661	−	0.204492i
$88$	6.74655	+	2.52248i	0.719185	+	0.268897i
$89$			12.4853i			1.32344i	0.749752	+	0.661719i	$0.230173\pi$
$89$			12.4853i			1.32344i	−0.749752	+	0.661719i	$0.769827\pi$
$90$		0			0
$91$	−15.6547			−1.64106
$92$	−8.59162	+	2.51776i	−0.895738	+	0.262494i
$93$	1.11217	−	7.86770i	0.115327	−	0.815842i
$94$	8.98440	−	11.9951i	0.926670	−	1.23720i
$95$		0			0
$96$	−9.57620	−	2.07276i	−0.977367	−	0.211550i
$97$			8.04496i			0.816842i	0.912794	+	0.408421i	$0.133920\pi$
$97$			8.04496i			0.816842i	−0.912794	+	0.408421i	$0.866080\pi$
$98$	−2.88118	−	2.15802i	−0.291043	−	0.217993i
$99$	−2.11755	+	7.34028i	−0.212821	+	0.737726i
$100$		0			0
$101$	1.08523			0.107985			0.0539924	−	0.998541i	$-0.482805\pi$
$101$	1.08523			0.107985			0.0539924	+	0.998541i	$0.482805\pi$
$102$	−0.371748	−	0.370187i	−0.0368085	−	0.0366539i
$103$	11.6319			1.14613			0.573064	−	0.819511i	$-0.305755\pi$
$103$	11.6319			1.14613			0.573064	+	0.819511i	$0.305755\pi$
$104$	−5.01908	+	13.4239i	−0.492162	+	1.31632i
$105$		0			0
$106$	8.06433	−	10.7667i	0.783277	−	1.04576i
$107$	6.50874			0.629224			0.314612	−	0.949220i	$-0.398126\pi$
$107$	6.50874			0.629224			0.314612	+	0.949220i	$0.398126\pi$
$108$	1.41126	−	10.2960i	0.135799	−	0.990736i
$109$		−	5.06696i		−	0.485327i	−0.970111	−	0.242663i	$-0.921979\pi$
$109$		−	5.06696i		−	0.485327i	0.970111	−	0.242663i	$-0.0780210\pi$
$110$		0			0
$111$	−13.1663	−	1.86118i	−1.24969	−	0.176655i
$112$	−10.4035	+	6.67030i	−0.983043	+	0.630284i
$113$	−6.05364			−0.569479			−0.284739	−	0.958605i	$-0.591907\pi$
$113$	−6.05364			−0.569479			−0.284739	+	0.958605i	$0.591907\pi$
$114$	−4.52972	−	4.51069i	−0.424247	−	0.422465i
$115$		0			0
$116$	4.42513	+	15.1004i	0.410863	+	1.40203i
$117$	−14.6053	−	4.21337i	−1.35026	−	0.389526i
$118$	0.363165	−	0.484862i	0.0334320	−	0.0446352i
$119$	−0.661719			−0.0606597
$120$		0			0
$121$	4.51514			0.410467
$122$	0.942908	−	1.25888i	0.0853668	−	0.113973i
$123$	−2.24720	+	15.8971i	−0.202624	+	1.43340i
$124$	−8.80487	+	2.58025i	−0.790701	+	0.231713i
$125$		0			0
$126$	−7.90217	−	10.4582i	−0.703981	−	0.931687i
$127$	−0.958763			−0.0850765			−0.0425382	−	0.999095i	$-0.513544\pi$
$127$	−0.958763			−0.0850765			−0.0425382	+	0.999095i	$0.513544\pi$
$128$	2.38428	+	11.0596i	0.210743	+	0.977542i
$129$	2.76491	−	19.5595i	0.243437	−	1.72211i
$130$		0			0
$131$		−	3.78126i		−	0.330370i	−0.986263	−	0.165185i	$-0.947178\pi$
$131$		−	3.78126i		−	0.330370i	0.986263	−	0.165185i	$-0.0528221\pi$
$132$	8.72936	−	1.27147i	0.759793	−	0.110668i
$133$	−8.06299			−0.699149
$134$	−2.00081	+	2.67128i	−0.172843	+	0.230764i
$135$		0			0
$136$	−0.212155	+	0.567424i	−0.0181921	+	0.0486562i
$137$	−13.1878			−1.12671			−0.563355	−	0.826215i	$-0.690490\pi$
$137$	−13.1878			−1.12671			−0.563355	+	0.826215i	$0.690490\pi$
$138$	−7.73713	+	7.76977i	−0.658628	+	0.661407i
$139$	−17.2947			−1.46692			−0.733460	−	0.679733i	$-0.762096\pi$
$139$	−17.2947			−1.46692			−0.733460	+	0.679733i	$0.762096\pi$
$140$		0			0
$141$	2.56909	−	18.1742i	0.216357	−	1.53055i
$142$	−6.92814	−	5.18922i	−0.581396	−	0.435470i
$143$		−	12.9032i		−	1.07902i
$144$	−11.5014	+	3.42310i	−0.958451	+	0.285258i
$145$		0			0
$146$	−10.1861	+	13.5995i	−0.843011	+	1.12551i
$147$	−4.36539	−	0.617087i	−0.360051	−	0.0508965i
$148$	4.31795	+	14.7346i	0.354934	+	1.21118i
$149$	−3.81475			−0.312516			−0.156258	−	0.987716i	$-0.549943\pi$
$149$	−3.81475			−0.312516			−0.156258	+	0.987716i	$0.549943\pi$
$150$		0			0
$151$			13.2235i			1.07611i	0.842909	+	0.538056i	$0.180841\pi$
$151$			13.2235i			1.07611i	−0.842909	+	0.538056i	$0.819159\pi$
$152$	−2.58509	+	6.91401i	−0.209678	+	0.560800i
$153$	−0.617360	−	0.178098i	−0.0499106	−	0.0143983i
$154$	6.67030	−	8.90553i	0.537508	−	0.717628i
$155$		0			0
$156$	2.52991	+	17.3692i	0.202555	+	1.39065i
$157$	6.56497			0.523942			0.261971	−	0.965076i	$-0.415628\pi$
$157$	6.56497			0.523942			0.261971	+	0.965076i	$0.415628\pi$
$158$	9.86165	−	13.1663i	0.784550	−	1.04746i
$159$	2.30600	−	16.3131i	0.182878	−	1.29371i
$160$		0			0
$161$			13.8303i			1.08998i
$162$	−4.55769	−	11.8839i	−0.358086	−	0.933689i
$163$		−	8.13957i		−	0.637540i	−0.947832	−	0.318770i	$-0.896730\pi$
$163$		−	8.13957i		−	0.637540i	0.947832	−	0.318770i	$-0.103270\pi$
$164$	17.7907	−	5.21354i	1.38922	−	0.407109i
$165$		0			0
$166$	−2.60241	−	1.94922i	−0.201986	−	0.151289i
$167$		−	21.8561i		−	1.69128i	−0.533754	−	0.845640i	$-0.679219\pi$
$167$		−	21.8561i		−	1.69128i	0.533754	−	0.845640i	$-0.320781\pi$
$168$	−7.23289	+	13.2957i	−0.558029	+	1.02578i
$169$	12.6741			0.974929
$170$		0			0
$171$	−7.52248	−	2.17011i	−0.575258	−	0.165952i
$172$	−21.8893	+	6.41462i	−1.66905	+	0.489110i
$173$			9.51198i			0.723182i	0.932337	+	0.361591i	$0.117766\pi$
$173$			9.51198i			0.723182i	−0.932337	+	0.361591i	$0.882234\pi$
$174$	13.6559	+	13.5985i	1.03525	+	1.03090i
$175$		0			0
$176$	−5.49792	−	8.57500i	−0.414421	−	0.646365i
$177$	0.103847	−	0.734633i	0.00780562	−	0.0552184i
$178$	10.5851	−	14.1322i	0.793389	−	1.05926i
$179$		−	16.2398i		−	1.21382i	−0.794771	−	0.606910i	$-0.792409\pi$
$179$		−	16.2398i		−	1.21382i	0.794771	−	0.606910i	$-0.207591\pi$
$180$		0			0
$181$		−	9.74808i		−	0.724569i	−0.932068	−	0.362284i	$-0.881997\pi$
$181$		−	9.74808i		−	0.724569i	0.932068	−	0.362284i	$-0.118003\pi$
$182$	17.7197	+	13.2722i	1.31347	+	0.983800i
$183$	0.269625	−	1.90737i	0.0199312	−	0.140997i
$184$	11.8595	+	4.43417i	0.874295	+	0.326891i
$185$		0			0
$186$	−7.92918	+	7.96262i	−0.581396	+	0.583848i
$187$		−	0.545414i		−	0.0398846i
$188$	−20.3391	+	5.96033i	−1.48338	+	0.434701i
$189$	−14.6502	−	6.56497i	−1.06564	−	0.477531i
$190$		0			0
$191$	2.30600			0.166856			0.0834281	−	0.996514i	$-0.473413\pi$
$191$	2.30600			0.166856			0.0834281	+	0.996514i	$0.473413\pi$
$192$	9.08211	+	10.4650i	0.655445	+	0.755243i
$193$		−	11.2498i		−	0.809776i	−0.914366	−	0.404888i	$-0.867310\pi$
$193$		−	11.2498i		−	0.809776i	0.914366	−	0.404888i	$-0.132690\pi$
$194$	6.82058	−	9.10617i	0.489689	−	0.653785i
$195$		0			0
$196$	1.43165	+	4.88538i	0.102261	+	0.348956i
$197$			6.78247i			0.483231i	0.970372	+	0.241615i	$0.0776772\pi$
$197$			6.78247i			0.483231i	−0.970372	+	0.241615i	$0.922323\pi$
$198$	8.62002	−	6.51327i	0.612598	−	0.462878i
$199$			0.632789i			0.0448573i	0.999748	+	0.0224286i	$0.00713985\pi$
$199$			0.632789i			0.0448573i	−0.999748	+	0.0224286i	$0.992860\pi$
$200$		0			0
$201$	−0.572131	+	4.04736i	−0.0403550	+	0.285479i
$202$	−1.22839	−	0.920070i	−0.0864291	−	0.0647359i
$203$	24.3078			1.70607
$204$	0.106938	+	0.734189i	0.00748718	+	0.0514035i
$205$		0			0
$206$	−13.1663	−	9.86165i	−0.917340	−	0.687093i
$207$	−3.72235	+	12.9032i	−0.258722	+	0.896835i
$208$	17.0621	−	10.9394i	1.18304	−	0.758514i
$209$		−	6.64582i		−	0.459701i
$210$		0			0
$211$	11.6400			0.801332			0.400666	−	0.916224i	$-0.368779\pi$
$211$	11.6400			0.801332			0.400666	+	0.916224i	$0.368779\pi$
$212$	−18.2562	+	5.34994i	−1.25384	+	0.367436i
$213$	−10.4971	−	1.48386i	−0.719248	−	0.101672i
$214$	−7.36732	−	5.51817i	−0.503619	−	0.377214i
$215$		0			0
$216$	−10.3265	+	10.4577i	−0.702628	+	0.711557i
$217$			14.1736i			0.962168i
$218$	−4.29581	+	5.73534i	−0.290949	+	0.388447i
$219$	−2.91273	+	20.6052i	−0.196824	+	1.39237i
$220$		0			0
$221$	1.08523			0.0730008
$222$	13.3252	+	13.2692i	0.894326	+	0.890570i
$223$	−10.7667			−0.720992			−0.360496	−	0.932761i	$-0.617393\pi$
$223$	−10.7667			−0.720992			−0.360496	+	0.932761i	$0.617393\pi$
$224$	17.4310	+	1.27003i	1.16466	+	0.0848573i
$225$		0			0
$226$	6.85218	+	5.13233i	0.455800	+	0.341397i
$227$	12.8365			0.851991			0.425996	−	0.904725i	$-0.359924\pi$
$227$	12.8365			0.851991			0.425996	+	0.904725i	$0.359924\pi$
$228$	1.30303	+	8.94603i	0.0862956	+	0.592465i
$229$			14.9684i			0.989143i	0.869137	+	0.494571i	$0.164675\pi$
$229$			14.9684i			0.989143i	−0.869137	+	0.494571i	$0.835325\pi$
$230$		0			0
$231$	1.90737	−	13.4931i	0.125496	−	0.887781i
$232$	7.79336	−	20.8439i	0.511659	−	1.36847i
$233$	−20.8980			−1.36908			−0.684538	−	0.728977i	$-0.739996\pi$
$233$	−20.8980			−1.36908			−0.684538	+	0.728977i	$0.739996\pi$
$234$	12.9597	+	17.1516i	0.847205	+	1.12124i
$235$		0			0
$236$	−0.822140	+	0.240926i	−0.0535167	+	0.0156830i
$237$	2.81994	−	19.9488i	0.183175	−	1.29581i
$238$	0.749006	+	0.561011i	0.0485509	+	0.0363649i
$239$	−28.6386			−1.85248			−0.926239	−	0.376937i	$-0.876977\pi$
$239$	−28.6386			−1.85248			−0.926239	+	0.376937i	$0.876977\pi$
$240$		0			0
$241$	9.24977			0.595830			0.297915	−	0.954592i	$-0.403709\pi$
$241$	9.24977			0.595830			0.297915	+	0.954592i	$0.403709\pi$
$242$	−5.11073	−	3.82797i	−0.328530	−	0.246071i
$243$	−11.9012	−	10.0679i	−0.763460	−	0.645856i
$244$	−2.13457	+	0.625532i	−0.136652	+	0.0400456i
$245$		0			0
$246$	16.0214	−	16.0889i	1.02148	−	1.02579i
$247$	13.2235			0.841390
$248$	12.1539	+	4.54423i	0.771773	+	0.288559i
$249$	−3.94301	−	0.557380i	−0.249878	−	0.0353225i
$250$		0			0
$251$			1.23472i			0.0779348i	0.999240	+	0.0389674i	$0.0124069\pi$
$251$			1.23472i			0.0779348i	−0.999240	+	0.0389674i	$0.987593\pi$
$252$	0.0780279	+	18.5372i	0.00491529	+	1.16774i
$253$	−11.3995			−0.716680
$254$	1.08523	+	0.812847i	0.0680937	+	0.0510026i
$255$		0			0
$256$	6.67764	−	14.5399i	0.417352	−	0.908745i
$257$	18.6054			1.16057			0.580286	−	0.814413i	$-0.302941\pi$
$257$	18.6054			1.16057			0.580286	+	0.814413i	$0.302941\pi$
$258$	−19.7123	+	19.7955i	−1.22723	+	1.23241i
$259$	23.7190			1.47383
$260$		0			0
$261$	22.6783	+	6.54230i	1.40375	+	0.404958i
$262$	−3.20578	+	4.28005i	−0.198054	+	0.264422i
$263$		−	11.2589i		−	0.694255i	−0.937818	−	0.347128i	$-0.887157\pi$
$263$		−	11.2589i		−	0.694255i	0.937818	−	0.347128i	$-0.112843\pi$
$264$	−10.9588	−	5.96163i	−0.674469	−	0.366913i
$265$		0			0
$266$	9.12658	+	6.83586i	0.559586	+	0.419134i
$267$	3.02682	−	21.4123i	0.185238	−	1.31041i
$268$	4.52947	−	1.32735i	0.276681	−	0.0810809i
$269$	−11.6824			−0.712291			−0.356146	−	0.934430i	$-0.615909\pi$
$269$	−11.6824			−0.712291			−0.356146	+	0.934430i	$0.615909\pi$
$270$		0			0
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$	0.721207	−	0.462407i	0.0437296	−	0.0280375i
$273$	26.8478	+	3.79518i	1.62490	+	0.229695i
$274$	14.9274	+	11.1807i	0.901798	+	0.675452i
$275$		0			0
$276$	15.3450	−	2.23508i	0.923661	−	0.134536i
$277$	17.4252			1.04698			0.523490	−	0.852032i	$-0.324630\pi$
$277$	17.4252			1.04698			0.523490	+	0.852032i	$0.324630\pi$
$278$	19.5761	+	14.6626i	1.17410	+	0.879405i
$279$	−3.81475	+	13.2235i	−0.228383	+	0.791669i
$280$		0			0
$281$		−	12.9736i		−	0.773941i	−0.922092	−	0.386971i	$-0.873521\pi$
$281$		−	12.9736i		−	0.773941i	0.922092	−	0.386971i	$-0.126479\pi$
$282$	−18.3162	+	18.3935i	−1.09072	+	1.09532i
$283$			12.3893i			0.736470i	0.929733	+	0.368235i	$0.120038\pi$
$283$			12.3893i			0.736470i	−0.929733	+	0.368235i	$0.879962\pi$
$284$	3.44257	+	11.7475i	0.204279	+	0.697084i
$285$		0			0
$286$	−10.9394	+	14.6053i	−0.646863	+	0.863628i
$287$		−	28.6386i		−	1.69048i
$288$	15.9207	+	5.87635i	0.938136	+	0.346267i
$289$	−16.9541			−0.997302
$290$		0			0
$291$	1.95035	−	13.7971i	0.114331	−	0.808801i
$292$	23.0596	−	6.75757i	1.34946	−	0.395457i
$293$		−	31.7916i		−	1.85729i	−0.370973	−	0.928644i	$-0.620976\pi$
$293$		−	31.7916i		−	1.85729i	0.370973	−	0.928644i	$-0.379024\pi$
$294$	4.41806	+	4.39950i	0.257666	+	0.256584i
$295$		0			0
$296$	7.60460	−	20.3391i	0.442009	−	1.18219i
$297$	5.41110	−	12.0752i	0.313984	−	0.700676i
$298$	4.31795	+	3.23417i	0.250132	+	0.187351i
$299$		−	22.6821i		−	1.31174i
$300$		0			0
$301$			35.2363i			2.03099i
$302$	11.2110	−	14.9678i	0.645119	−	0.861300i
$303$	−1.86118	−	0.263094i	−0.106922	−	0.0151144i
$304$	8.78785	−	5.63438i	0.504017	−	0.323154i
$305$		0			0
$306$	0.547804	+	0.724994i	0.0313158	+	0.0414451i
$307$			10.3288i			0.589495i	0.955575	+	0.294747i	$0.0952355\pi$
$307$			10.3288i			0.589495i	−0.955575	+	0.294747i	$0.904764\pi$
$308$	−15.1004	+	4.42513i	−0.860423	+	0.252145i
$309$	−19.9488	−	2.81994i	−1.13485	−	0.160421i
$310$		0			0
$311$	5.13819			0.291360			0.145680	−	0.989332i	$-0.453463\pi$
$311$	5.13819			0.291360			0.145680	+	0.989332i	$0.453463\pi$
$312$	11.8621	−	21.8052i	0.671559	−	1.23448i
$313$			15.6741i			0.885951i	0.896534	+	0.442976i	$0.146077\pi$
$313$			15.6741i			0.885951i	−0.896534	+	0.442976i	$0.853923\pi$
$314$	−7.43096	−	5.56584i	−0.419353	−	0.314098i
$315$		0			0
$316$	−22.3250	+	6.54230i	−1.25588	+	0.368033i
$317$		−	8.95293i		−	0.502847i	−0.967877	−	0.251423i	$-0.919101\pi$
$317$		−	8.95293i		−	0.502847i	0.967877	−	0.251423i	$-0.0808987\pi$
$318$	−16.4405	+	16.5099i	−0.921939	+	0.925827i
$319$			20.0354i			1.12177i
$320$		0			0
$321$	−11.1625	−	1.57792i	−0.623030	−	0.0880710i
$322$	11.7255	−	15.6547i	0.653435	−	0.872403i
$323$	0.558952			0.0311009
$324$	−4.91639	+	17.3156i	−0.273133	+	0.961976i
$325$		0			0
$326$	−6.90079	+	9.21326i	−0.382199	+	0.510275i
$327$	−1.22839	+	8.68984i	−0.0679300	+	0.480549i
$328$	−24.5576	−	9.18188i	−1.35597	−	0.506984i
$329$			32.7408i			1.80506i
$330$		0			0
$331$	−4.48486			−0.246510			−0.123255	−	0.992375i	$-0.539333\pi$
$331$	−4.48486			−0.246510			−0.123255	+	0.992375i	$0.539333\pi$
$332$	1.29313	+	4.41268i	0.0709696	+	0.242178i
$333$	22.1290	+	6.38384i	1.21266	+	0.349832i
$334$	−18.5298	+	24.7392i	−1.01391	+	1.35367i
$335$		0			0
$336$	19.4592	−	8.91743i	1.06158	−	0.486486i
$337$		−	25.9991i		−	1.41626i	−0.706082	−	0.708130i	$-0.749539\pi$
$337$		−	25.9991i		−	1.41626i	0.706082	−	0.708130i	$-0.250461\pi$
$338$	−14.3459	−	10.7452i	−0.780315	−	0.584461i
$339$	10.3820	+	1.46759i	0.563873	+	0.0797085i
$340$		0			0
$341$	−11.6824			−0.632640
$342$	6.67494	+	8.83398i	0.360939	+	0.477687i
$343$	−13.7627			−0.743118
$344$	30.2151	+	11.2972i	1.62909	+	0.609103i
$345$		0			0
$346$	8.06433	−	10.7667i	0.433541	−	0.578822i
$347$	−10.7184			−0.575392			−0.287696	−	0.957722i	$-0.592889\pi$
$347$	−10.7184			−0.575392			−0.287696	+	0.957722i	$0.592889\pi$
$348$	−3.92831	−	26.9699i	−0.210579	−	1.44574i
$349$			11.6319i			0.622643i	0.950305	+	0.311322i	$0.100772\pi$
$349$			11.6319i			0.622643i	−0.950305	+	0.311322i	$0.899228\pi$
$350$		0			0
$351$	24.0266	+	10.7667i	1.28245	+	0.574684i
$352$	−1.04681	+	14.3673i	−0.0557949	+	0.765781i
$353$	21.7547			1.15789			0.578944	−	0.815367i	$-0.303465\pi$
$353$	21.7547			1.15789			0.578944	+	0.815367i	$0.303465\pi$
$354$	−0.740373	+	0.743496i	−0.0393504	+	0.0395164i
$355$		0			0
$356$	−23.9628	+	7.02226i	−1.27003	+	0.372179i
$357$	1.13485	+	0.160421i	0.0600625	+	0.00849039i
$358$	−13.7682	+	18.3820i	−0.727674	+	0.971519i
$359$	−12.9032			−0.681005			−0.340503	−	0.940244i	$-0.610597\pi$
$359$	−12.9032			−0.681005			−0.340503	+	0.940244i	$0.610597\pi$
$360$		0			0
$361$	−12.1892			−0.641538
$362$	−8.26450	+	11.0340i	−0.434372	+	0.579932i
$363$	−7.74346	−	1.09461i	−0.406426	−	0.0574521i
$364$	−8.80487	−	30.0459i	−0.461501	−	1.57483i
$365$		0			0
$366$	−1.92228	+	1.93039i	−0.100479	+	0.100903i
$367$	11.7255			0.612065			0.306032	−	0.952021i	$-0.400998\pi$
$367$	11.7255			0.612065			0.306032	+	0.952021i	$0.400998\pi$
$368$	−9.66459	−	15.0737i	−0.503801	−	0.785770i
$369$	7.70792	−	26.7188i	0.401258	−	1.39093i
$370$		0			0
$371$			29.3879i			1.52574i
$372$	15.7259	−	2.29056i	0.815350	−	0.118760i
$373$	31.0944			1.61001			0.805004	−	0.593270i	$-0.202163\pi$
$373$	31.0944			1.61001			0.805004	+	0.593270i	$0.202163\pi$
$374$	−0.462407	+	0.617360i	−0.0239105	+	0.0319229i
$375$		0			0
$376$	28.0752	+	10.4971i	1.44787	+	0.541346i
$377$	−39.8653			−2.05317
$378$	11.0168	+	19.8515i	0.566645	+	1.02105i
$379$	−12.6097			−0.647719			−0.323860	−	0.946105i	$-0.604981\pi$
$379$	−12.6097			−0.647719			−0.323860	+	0.946105i	$0.604981\pi$
$380$		0			0
$381$	1.64428	+	0.232434i	0.0842390	+	0.0119080i
$382$	−2.61018	−	1.95504i	−0.133549	−	0.100029i
$383$			1.64428i			0.0840188i	0.999117	+	0.0420094i	$0.0133759\pi$
$383$			1.64428i			0.0840188i	−0.999117	+	0.0420094i	$0.986624\pi$
$384$	−1.40785	−	19.5453i	−0.0718443	−	0.997416i
$385$		0			0
$386$	−9.53765	+	12.7337i	−0.485453	+	0.648130i
$387$	−9.48364	+	32.8742i	−0.482081	+	1.67109i
$388$	−15.4406	+	4.52483i	−0.783876	+	0.229713i
$389$	37.4889			1.90076			0.950381	−	0.311090i	$-0.100694\pi$
$389$	37.4889			1.90076			0.950381	+	0.311090i	$0.100694\pi$
$390$		0			0
$391$		−	0.958763i		−	0.0484867i
$392$	2.52136	−	6.74357i	0.127348	−	0.340602i
$393$	−0.916694	+	6.48486i	−0.0462411	+	0.327118i
$394$	5.75023	−	7.67714i	0.289692	−	0.386769i
$395$		0			0
$396$	−15.2791	+	0.0643136i	−0.767804	+	0.00323188i
$397$	−19.8820			−0.997849			−0.498924	−	0.866646i	$-0.666271\pi$
$397$	−19.8820			−0.997849			−0.498924	+	0.866646i	$0.666271\pi$
$398$	0.536484	−	0.716261i	0.0268915	−	0.0359029i
$399$	13.8280	+	1.95472i	0.692267	+	0.0978583i
$400$		0			0
$401$		−	11.2570i		−	0.562150i	−0.959686	−	0.281075i	$-0.909309\pi$
$401$		−	11.2570i		−	0.562150i	0.959686	−	0.281075i	$-0.0906910\pi$
$402$	4.07899	−	4.09619i	0.203441	−	0.204300i
$403$		−	23.2451i		−	1.15792i
$404$	0.610382	+	2.08287i	0.0303676	+	0.103627i
$405$		0			0
$406$	−27.5142	−	20.6083i	−1.36551	−	1.02277i
$407$			19.5501i			0.969065i
$408$	0.501407	−	0.921700i	0.0248233	−	0.0456309i
$409$	−16.9007			−0.835685			−0.417843	−	0.908519i	$-0.637214\pi$
$409$	−16.9007			−0.835685			−0.417843	+	0.908519i	$0.637214\pi$
$410$		0			0
$411$	22.6171	+	3.19713i	1.11562	+	0.157703i
$412$	6.54230	+	22.3250i	0.322316	+	1.09987i
$413$			1.32344i			0.0651221i
$414$	15.1528	−	11.4494i	0.744720	−	0.562709i
$415$		0			0
$416$	−28.5873	−	2.08287i	−1.40161	−	0.102121i
$417$	29.6605	+	4.19278i	1.45248	+	0.205321i
$418$	−5.63438	+	7.52248i	−0.275587	+	0.367936i
$419$		−	7.21126i		−	0.352293i	−0.984364	−	0.176147i	$-0.943637\pi$
$419$		−	7.21126i		−	0.352293i	0.984364	−	0.176147i	$-0.0563633\pi$
$420$		0			0
$421$		−	11.3995i		−	0.555578i	−0.960642	−	0.277789i	$-0.910398\pi$
$421$		−	11.3995i		−	0.555578i	0.960642	−	0.277789i	$-0.0896015\pi$
$422$	−13.1755	−	9.86851i	−0.641372	−	0.480391i
$423$	−8.81199	+	30.5460i	−0.428454	+	1.48520i
$424$	25.2001	+	9.42210i	1.22383	+	0.457578i
$425$		0			0
$426$	10.6237	+	10.5791i	0.514722	+	0.512559i
$427$			3.43613i			0.166286i
$428$	3.66080	+	12.4921i	0.176951	+	0.603830i
$429$	−3.12814	+	22.1290i	−0.151028	+	1.06840i
$430$		0			0
$431$	−3.95028			−0.190278			−0.0951391	−	0.995464i	$-0.530330\pi$
$431$	−3.95028			−0.190278			−0.0951391	+	0.995464i	$0.530330\pi$
$432$	20.5548	−	3.08232i	0.988943	−	0.148298i
$433$			20.6509i			0.992420i	0.868203	+	0.496210i	$0.165275\pi$
$433$			20.6509i			0.992420i	−0.868203	+	0.496210i	$0.834725\pi$
$434$	12.0165	−	16.0433i	0.576811	−	0.770102i
$435$		0			0
$436$	9.72494	−	2.84987i	0.465740	−	0.136484i
$437$		−	11.6824i		−	0.558847i
$438$	20.7662	−	20.8538i	0.992247	−	0.996432i
$439$		−	28.5778i		−	1.36394i	−0.731379	−	0.681971i	$-0.761123\pi$
$439$		−	28.5778i		−	1.36394i	0.731379	−	0.681971i	$-0.238877\pi$
$440$		0			0
$441$	7.33704	+	2.11661i	0.349383	+	0.100791i
$442$	−1.22839	−	0.920070i	−0.0584285	−	0.0437633i
$443$	−21.9689			−1.04378			−0.521888	−	0.853014i	$-0.674772\pi$
$443$	−21.9689			−1.04378			−0.521888	+	0.853014i	$0.674772\pi$
$444$	−3.83316	−	26.3167i	−0.181914	−	1.24894i
$445$		0			0
$446$	12.1870	+	9.12810i	0.577069	+	0.432228i
$447$	6.54230	+	0.924813i	0.309440	+	0.0437422i
$448$	−18.6536	−	16.2157i	−0.881300	−	0.766120i
$449$		−	9.00493i		−	0.424969i	−0.977164	−	0.212485i	$-0.931844\pi$
$449$		−	9.00493i		−	0.424969i	0.977164	−	0.212485i	$-0.0681555\pi$
$450$		0			0
$451$	23.6050			1.11152
$452$	−3.40483	−	11.6187i	−0.160150	−	0.546496i
$453$	3.20578	−	22.6783i	0.150621	−	1.06552i
$454$	−14.5298	−	10.8829i	−0.681918	−	0.510761i
$455$		0			0
$456$	6.10960	−	11.2308i	0.286108	−	0.525932i
$457$		−	18.5748i		−	0.868891i	−0.900698	−	0.434446i	$-0.856944\pi$
$457$		−	18.5748i		−	0.868891i	0.900698	−	0.434446i	$-0.143056\pi$
$458$	12.6904	−	16.9429i	0.592982	−	0.791692i
$459$	1.01560	+	0.455105i	0.0474040	+	0.0212425i
$460$		0			0
$461$	−34.2003			−1.59287			−0.796434	−	0.604726i	$-0.793283\pi$
$461$	−34.2003			−1.59287			−0.796434	+	0.604726i	$0.793283\pi$
$462$	−13.5985	+	13.6559i	−0.632662	+	0.635330i
$463$	7.44471			0.345985			0.172992	−	0.984923i	$-0.444656\pi$
$463$	7.44471			0.345985			0.172992	+	0.984923i	$0.444656\pi$
$464$	−26.4930	+	16.9862i	−1.22991	+	0.788564i
$465$		0			0
$466$	23.6547	+	17.7175i	1.09578	+	0.820748i
$467$	7.26161			0.336027			0.168014	−	0.985785i	$-0.446265\pi$
$467$	7.26161			0.336027			0.168014	+	0.985785i	$0.446265\pi$
$468$	−0.127968	−	30.4015i	−0.00591530	−	1.40531i
$469$		−	7.29130i		−	0.336681i
$470$		0			0
$471$	−11.2589	−	1.59155i	−0.518784	−	0.0733349i
$472$	1.13485	+	0.424310i	0.0522356	+	0.0195304i
$473$	−29.0431			−1.33540
$474$	−20.1047	+	20.1895i	−0.923437	+	0.927332i
$475$		0			0
$476$	−0.372179	−	1.27003i	−0.0170588	−	0.0582116i
$477$	−7.90958	+	27.4178i	−0.362155	+	1.25538i
$478$	32.4163	+	24.2800i	1.48269	+	1.11054i
$479$	23.3649			1.06757			0.533785	−	0.845620i	$-0.320769\pi$
$479$	23.3649			1.06757			0.533785	+	0.845620i	$0.320769\pi$
$480$		0			0
$481$	−38.8998			−1.77368
$482$	−10.4699	−	7.84203i	−0.476891	−	0.357195i
$483$	3.35290	−	23.7190i	0.152562	−	1.07925i
$484$	2.53951	+	8.66584i	0.115432	+	0.393902i
$485$		0			0
$486$	4.93540	+	21.4859i	0.223874	+	0.974618i
$487$	−7.77068			−0.352123			−0.176062	−	0.984379i	$-0.556336\pi$
$487$	−7.77068			−0.352123			−0.176062	+	0.984379i	$0.556336\pi$
$488$	2.94648	+	1.10166i	0.133381	+	0.0498699i
$489$	−1.97328	+	13.9594i	−0.0892349	+	0.631264i
$490$		0			0
$491$			20.5265i			0.926349i	0.886267	+	0.463174i	$0.153290\pi$
$491$			20.5265i			0.926349i	−0.886267	+	0.463174i	$0.846710\pi$
$492$	−31.7751	+	4.62820i	−1.43253	+	0.208655i
$493$	−1.68509			−0.0758928
$494$	−14.9678	−	11.2110i	−0.673433	−	0.504406i
$495$		0			0
$496$	−9.90447	−	15.4478i	−0.444724	−	0.693628i
$497$	18.9104			0.848249
$498$	3.99058	+	3.97382i	0.178822	+	0.178071i
$499$	26.4958			1.18611			0.593057	−	0.805161i	$-0.297921\pi$
$499$	26.4958			1.18611			0.593057	+	0.805161i	$0.297921\pi$
$500$		0			0
$501$	−5.29861	+	37.4833i	−0.236724	+	1.67463i
$502$	1.04681	−	1.39759i	0.0467212	−	0.0623776i
$503$		−	26.9943i		−	1.20362i	−0.798640	−	0.601809i	$-0.794447\pi$
$503$		−	26.9943i		−	1.20362i	0.798640	−	0.601809i	$-0.205553\pi$
$504$	15.6277	−	21.0486i	0.696113	−	0.937581i
$505$		0			0
$506$	12.9032	+	9.66459i	0.573618	+	0.429643i
$507$	−21.7361	−	3.07259i	−0.965332	−	0.136459i
$508$	−0.539249	−	1.84014i	−0.0239253	−	0.0816430i
$509$	25.8064			1.14385			0.571925	−	0.820306i	$-0.306197\pi$
$509$	25.8064			1.14385			0.571925	+	0.820306i	$0.306197\pi$
$510$		0			0
$511$		−	37.1201i		−	1.64210i
$512$	−19.8855	+	10.7965i	−0.878825	+	0.477144i
$513$	12.3750	+	5.54541i	0.546368	+	0.244836i
$514$	−21.0596	−	15.7738i	−0.928901	−	0.695753i
$515$		0			0
$516$	39.0953	−	5.69443i	1.72108	−	0.250683i
$517$	−26.9862			−1.18685
$518$	−26.8478	−	20.1092i	−1.17963	−	0.883547i
$519$	2.30600	−	16.3131i	0.101222	−	0.716063i
$520$		0			0
$521$			1.70694i			0.0747826i	0.999301	+	0.0373913i	$0.0119048\pi$
$521$			1.70694i			0.0747826i	−0.999301	+	0.0373913i	$0.988095\pi$
$522$	−20.1232	−	26.6321i	−0.880768	−	1.16566i
$523$		−	24.0790i		−	1.05290i	−0.850206	−	0.526451i	$-0.823522\pi$
$523$		−	24.0790i		−	1.05290i	0.850206	−	0.526451i	$-0.176478\pi$
$524$	7.25732	−	2.12674i	0.317037	−	0.0929071i
$525$		0			0
$526$	−9.54541	+	12.7441i	−0.416200	+	0.555669i
$527$		−	0.982561i		−	0.0428010i
$528$	7.35009	+	16.0390i	0.319872	+	0.698008i
$529$	2.96125			0.128750
$530$		0			0
$531$	−0.356195	+	1.23472i	−0.0154576	+	0.0535823i
$532$	−4.53497	−	15.4752i	−0.196616	−	0.670934i
$533$			46.9680i			2.03441i
$534$	−21.5796	+	21.6706i	−0.933840	+	0.937779i
$535$		0			0
$536$	−6.25229	−	2.33768i	−0.270058	−	0.100972i
$537$	−3.93703	+	27.8513i	−0.169895	+	1.20187i
$538$	13.2235	+	9.90447i	0.570105	+	0.427012i
$539$			6.48200i			0.279199i
$540$		0			0
$541$		−	16.6989i		−	0.717941i	−0.933349	−	0.358971i	$-0.883128\pi$
$541$		−	16.6989i		−	0.717941i	0.933349	−	0.358971i	$-0.116872\pi$
$542$		0			0
$543$	−2.36324	+	16.7180i	−0.101416	+	0.717436i
$544$	−1.20837	−	0.0880424i	−0.0518086	−	0.00377479i
$545$		0			0
$546$	−27.1717	−	27.0576i	−1.16284	−	1.15796i
$547$		−	15.5833i		−	0.666292i	−0.942875	−	0.333146i	$-0.891890\pi$
$547$		−	15.5833i		−	0.666292i	0.942875	−	0.333146i	$-0.108110\pi$
$548$	−7.41738	−	25.3112i	−0.316855	−	1.08124i
$549$	−0.924813	+	3.20578i	−0.0394701	+	0.136819i
$550$		0			0
$551$	−20.5327			−0.874723
$552$	−19.2641	−	10.4797i	−0.819935	−	0.446046i
$553$			35.9376i			1.52822i
$554$	−19.7238	−	14.7732i	−0.837984	−	0.627655i
$555$		0			0
$556$	−9.72729	−	33.1935i	−0.412529	−	1.40772i
$557$			2.96772i			0.125746i	0.998022	+	0.0628731i	$0.0200263\pi$
$557$			2.96772i			0.125746i	−0.998022	+	0.0628731i	$0.979974\pi$
$558$	15.5289	−	11.7336i	0.657392	−	0.496724i
$559$		−	57.7883i		−	2.44419i
$560$		0			0
$561$	−0.132225	+	0.935386i	−0.00558256	+	0.0394920i
$562$	−10.9991	+	14.6850i	−0.463971	+	0.619448i
$563$	−11.7057			−0.493335			−0.246668	−	0.969100i	$-0.579336\pi$
$563$	−11.7057			−0.493335			−0.246668	+	0.969100i	$0.579336\pi$
$564$	36.3265	−	5.29114i	1.52962	−	0.222797i
$565$		0			0
$566$	10.5038	−	14.0236i	0.441507	−	0.589457i
$567$	23.5335	+	14.8106i	0.988314	+	0.621986i
$568$	6.06291	−	16.2157i	0.254394	−	0.680396i
$569$			43.3618i			1.81782i	0.416992	+	0.908910i	$0.363084\pi$
$569$			43.3618i			1.81782i	−0.416992	+	0.908910i	$0.636916\pi$
$570$		0			0
$571$	−8.18544			−0.342550			−0.171275	−	0.985223i	$-0.554789\pi$
$571$	−8.18544			−0.342550			−0.171275	+	0.985223i	$0.554789\pi$
$572$	24.7650	−	7.25732i	1.03547	−	0.303444i
$573$	−3.95479	−	0.559045i	−0.165214	−	0.0233545i
$574$	−24.2800	+	32.4163i	−1.01343	+	1.35303i
$575$		0			0
$576$	−13.0388	−	20.1492i	−0.543283	−	0.839550i
$577$			18.9612i			0.789367i	0.918817	+	0.394683i	$0.129146\pi$
$577$			18.9612i			0.789367i	−0.918817	+	0.394683i	$0.870854\pi$
$578$	19.1906	+	14.3738i	0.798222	+	0.597873i
$579$	−2.72729	+	19.2934i	−0.113342	+	0.801805i
$580$		0			0
$581$	7.10331			0.294695
$582$	−13.9049	+	13.9636i	−0.576377	+	0.578808i
$583$	−24.2226			−1.00320
$584$	−31.8305	−	11.9012i	−1.31716	−	0.492473i
$585$		0			0
$586$	−26.9532	+	35.9853i	−1.11343	+	1.48654i
$587$	19.9546			0.823614			0.411807	−	0.911271i	$-0.364898\pi$
$587$	19.9546			0.823614			0.411807	+	0.911271i	$0.364898\pi$
$588$	−1.27091	−	8.72550i	−0.0524116	−	0.359834i
$589$		−	11.9724i		−	0.493315i
$590$		0			0
$591$	1.64428	−	11.6319i	0.0676366	−	0.478474i
$592$	−25.8514	+	16.5748i	−1.06248	+	0.681219i
$593$	27.4465			1.12709			0.563546	−	0.826085i	$-0.309437\pi$
$593$	27.4465			1.12709			0.563546	+	0.826085i	$0.309437\pi$
$594$	−16.3624	+	9.08050i	−0.671356	+	0.372578i
$595$		0			0
$596$	−2.14558	−	7.32159i	−0.0878863	−	0.299904i
$597$	0.153408	−	1.08523i	0.00627856	−	0.0444157i
$598$	−19.2300	+	25.6741i	−0.786375	+	1.04989i
$599$	−13.8858			−0.567357			−0.283679	−	0.958919i	$-0.591555\pi$
$599$	−13.8858			−0.567357			−0.283679	+	0.958919i	$0.591555\pi$
$600$		0			0
$601$	−10.7502			−0.438511			−0.219255	−	0.975667i	$-0.570363\pi$
$601$	−10.7502			−0.438511			−0.219255	+	0.975667i	$0.570363\pi$
$602$	29.8736	−	39.8843i	1.21756	−	1.62556i
$603$	1.96241	−	6.80252i	0.0799156	−	0.277020i
$604$	−25.3796	+	7.43745i	−1.03268	+	0.302626i
$605$		0			0
$606$	1.88363	+	1.87572i	0.0765173	+	0.0761959i
$607$	−30.7086			−1.24642			−0.623211	−	0.782054i	$-0.714172\pi$
$607$	−30.7086			−1.24642			−0.623211	+	0.782054i	$0.714172\pi$
$608$	−14.7239	−	1.07279i	−0.597134	−	0.0435073i
$609$	−41.6878	−	5.89296i	−1.68928	−	0.238795i
$610$		0			0
$611$		−	53.6957i		−	2.17229i
$612$	−0.00540914	−	1.28506i	−0.000218652	−	0.0519455i
$613$	13.3170			0.537870			0.268935	−	0.963158i	$-0.413328\pi$
$613$	13.3170			0.537870			0.268935	+	0.963158i	$0.413328\pi$
$614$	8.75683	−	11.6913i	0.353397	−	0.471821i
$615$		0			0
$616$	20.8439	+	7.79336i	0.839826	+	0.314003i
$617$	−38.3725			−1.54482			−0.772410	−	0.635124i	$-0.780949\pi$
$617$	−38.3725			−1.54482			−0.772410	+	0.635124i	$0.780949\pi$
$618$	20.1895	+	20.1047i	0.812139	+	0.808728i
$619$	−4.59507			−0.184691			−0.0923457	−	0.995727i	$-0.529436\pi$
$619$	−4.59507			−0.184691			−0.0923457	+	0.995727i	$0.529436\pi$
$620$		0			0
$621$	9.51198	−	21.2266i	0.381703	−	0.851794i
$622$	−5.81597	−	4.35620i	−0.233199	−	0.174668i
$623$			38.5741i			1.54544i
$624$	−31.9135	+	14.6248i	−1.27756	+	0.585460i
$625$		0			0
$626$	13.2886	−	17.7417i	0.531120	−	0.709099i
$627$	−1.61115	+	11.3976i	−0.0643433	+	0.455176i
$628$	3.69242	+	12.6001i	0.147344	+	0.502797i
$629$	−1.64428			−0.0655617
$630$		0			0
$631$		−	40.2097i		−	1.60072i	−0.599518	−	0.800362i	$-0.704641\pi$
$631$		−	40.2097i		−	1.60072i	0.599518	−	0.800362i	$-0.295359\pi$
$632$	30.8165	+	11.5220i	1.22582	+	0.458322i
$633$	−19.9626	−	2.82190i	−0.793444	−	0.112161i
$634$	−7.59037	+	10.1339i	−0.301452	+	0.402469i
$635$		0			0
$636$	32.6064	−	4.74929i	1.29293	−	0.188321i
$637$	−12.8975			−0.511018
$638$	16.9862	−	22.6783i	0.672489	−	0.897842i
$639$	17.6428	+	5.08964i	0.697937	+	0.201343i
$640$		0			0
$641$			7.56252i			0.298702i	0.988784	+	0.149351i	$0.0477184\pi$
$641$			7.56252i			0.298702i	−0.988784	+	0.149351i	$0.952282\pi$
$642$	11.2972	+	11.2497i	0.445864	+	0.443991i
$643$		−	2.47018i		−	0.0974145i	−0.998813	−	0.0487072i	$-0.984490\pi$
$643$		−	2.47018i		−	0.0974145i	0.998813	−	0.0487072i	$-0.0155101\pi$
$644$	−26.5444	+	7.77877i	−1.04599	+	0.306527i
$645$		0			0
$646$	−0.632684	−	0.473884i	−0.0248926	−	0.0186447i
$647$			30.1474i			1.18522i	0.805491	+	0.592608i	$0.201901\pi$
$647$			30.1474i			1.18522i	−0.805491	+	0.592608i	$0.798099\pi$
$648$	20.2452	−	15.4315i	0.795306	−	0.606208i
$649$	−1.09083			−0.0428188
$650$		0			0
$651$	3.43613	−	24.3078i	0.134672	−	0.952697i
$652$	15.6222	−	4.57804i	0.611811	−	0.179290i
$653$		−	8.42674i		−	0.329764i	−0.986313	−	0.164882i	$-0.947276\pi$
$653$		−	8.42674i		−	0.329764i	0.986313	−	0.164882i	$-0.0527243\pi$
$654$	8.75774	−	8.79468i	0.342455	−	0.343899i
$655$		0			0
$656$	20.0126	+	31.2132i	0.781359	+	1.21867i
$657$	9.99067	−	34.6318i	0.389773	−	1.35111i
$658$	27.7579	−	37.0596i	1.08212	−	1.44474i
$659$		−	13.5764i		−	0.528863i	−0.964404	−	0.264432i	$-0.914816\pi$
$659$		−	13.5764i		−	0.528863i	0.964404	−	0.264432i	$-0.0851843\pi$
$660$		0			0
$661$		−	1.68509i		−	0.0655425i	−0.999463	−	0.0327713i	$-0.989567\pi$
$661$		−	1.68509i		−	0.0655425i	0.999463	−	0.0327713i	$-0.0104333\pi$
$662$	5.07646	+	3.80230i	0.197302	+	0.147781i
$663$	−1.86118	−	0.263094i	−0.0722821	−	0.0102177i
$664$	2.27740	−	6.09109i	0.0883804	−	0.236380i
$665$		0			0
$666$	−19.6358	−	25.9871i	−0.760872	−	1.00698i
$667$			35.2195i			1.36370i
$668$	41.9482	−	12.2928i	1.62302	−	0.475624i
$669$	18.4649	+	2.61018i	0.713895	+	0.100916i
$670$		0			0
$671$	−2.83219			−0.109335
$672$	−29.5863	−	6.40392i	−1.14132	−	0.247036i
$673$		−	7.03784i		−	0.271289i	−0.990758	−	0.135644i	$-0.956690\pi$
$673$		−	7.03784i		−	0.271289i	0.990758	−	0.135644i	$-0.0433105\pi$
$674$	−22.0422	+	29.4286i	−0.849035	+	1.13355i
$675$		0			0
$676$	7.12844	+	24.3252i	0.274171	+	0.935584i
$677$			41.8298i			1.60765i	0.594866	+	0.803825i	$0.297205\pi$
$677$			41.8298i			1.60765i	−0.594866	+	0.803825i	$0.702795\pi$
$678$	−10.5073	−	10.4631i	−0.403529	−	0.401834i
$679$			24.8554i			0.953863i
$680$		0			0
$681$	−22.0147	−	3.11198i	−0.843604	−	0.119251i
$682$	13.2235	+	9.90447i	0.506353	+	0.379262i
$683$	28.2464			1.08082			0.540409	−	0.841403i	$-0.318270\pi$
$683$	28.2464			1.08082			0.540409	+	0.841403i	$0.318270\pi$
$684$	−0.0659099	−	15.6583i	−0.00252013	−	0.598712i
$685$		0			0
$686$	15.5782	+	11.6682i	0.594778	+	0.445492i
$687$	3.62881	−	25.6709i	0.138448	−	0.979406i
$688$	−24.6230	−	38.4040i	−0.938742	−	1.46414i
$689$		−	48.1968i		−	1.83615i
$690$		0			0
$691$	24.8633			0.945844			0.472922	−	0.881104i	$-0.343199\pi$
$691$	24.8633			0.945844			0.472922	+	0.881104i	$0.343199\pi$
$692$	−18.2562	+	5.34994i	−0.693997	+	0.203374i
$693$	−6.54230	+	22.6783i	−0.248521	+	0.861477i
$694$	12.1322	+	9.08711i	0.460533	+	0.344942i
$695$		0			0
$696$	−18.4188	+	33.8580i	−0.698164	+	1.28338i
$697$			1.98532i			0.0751994i
$698$	9.86165	−	13.1663i	0.373269	−	0.498352i
$699$	35.8401	+	5.06633i	1.35560	+	0.191626i
$700$		0			0
$701$	42.6271			1.61000			0.805001	−	0.593274i	$-0.202165\pi$
$701$	42.6271			1.61000			0.805001	+	0.593274i	$0.202165\pi$
$702$	−18.0679	−	32.5569i	−0.681928	−	1.22878i
$703$	−20.0354			−0.755650
$704$	13.3656	−	15.3750i	0.503736	−	0.579468i
$705$		0			0
$706$	−24.6244	−	18.4439i	−0.926753	−	0.694144i
$707$	3.35290			0.126099
$708$	1.46838	−	0.213877i	0.0551850	−	0.00803798i
$709$		−	17.0057i		−	0.638663i	−0.947643	−	0.319331i	$-0.896542\pi$
$709$		−	17.0057i		−	0.638663i	0.947643	−	0.319331i	$-0.103458\pi$
$710$		0			0
$711$	−9.67240	+	33.5285i	−0.362743	+	1.25742i
$712$	33.0773	+	12.3673i	1.23962	+	0.463485i
$713$	−20.5361			−0.769085
$714$	−1.14854	−	1.14372i	−0.0429830	−	0.0428025i
$715$		0			0
$716$	31.1688	−	9.13396i	1.16483	−	0.341352i
$717$	49.1152	+	6.94289i	1.83424	+	0.259287i
$718$	14.6053	+	10.9394i	0.545064	+	0.408257i
$719$	28.6386			1.06804			0.534020	−	0.845472i	$-0.320681\pi$
$719$	28.6386			1.06804			0.534020	+	0.845472i	$0.320681\pi$
$720$		0			0
$721$	35.9376			1.33839
$722$	13.7971	+	10.3341i	0.513475	+	0.384596i
$723$	−15.8634	−	2.24243i	−0.589965	−	0.0833969i
$724$	18.7093	−	5.48274i	0.695327	−	0.203764i
$725$		0			0
$726$	7.83689	+	7.80397i	0.290854	+	0.289633i
$727$	−14.1822			−0.525990			−0.262995	−	0.964797i	$-0.584710\pi$
$727$	−14.1822			−0.525990			−0.262995	+	0.964797i	$0.584710\pi$
$728$	−15.5068	+	41.4741i	−0.574720	+	1.53713i
$729$	17.9697	+	20.1517i	0.665545	+	0.746357i
$730$		0			0
$731$		−	2.44269i		−	0.0903462i
$732$	3.81244	−	0.555302i	0.140912	−	0.0205245i
$733$	51.7027			1.90968			0.954842	−	0.297113i	$-0.0960240\pi$
$733$	51.7027			1.90968			0.954842	+	0.297113i	$0.0960240\pi$
$734$	−13.2722	−	9.94095i	−0.489885	−	0.366927i
$735$		0			0
$736$	−1.84014	+	25.2558i	−0.0678285	+	0.930940i
$737$	6.00977			0.221373
$738$	−31.3771	+	23.7085i	−1.15501	+	0.872720i
$739$	16.7493			0.616133			0.308067	−	0.951365i	$-0.400318\pi$
$739$	16.7493			0.616133			0.308067	+	0.951365i	$0.400318\pi$
$740$		0			0
$741$	−22.6783	−	3.20578i	−0.833108	−	0.117767i
$742$	24.9153	−	33.2645i	0.914669	−	1.22118i
$743$			13.5649i			0.497649i	0.968549	+	0.248825i	$0.0800442\pi$
$743$			13.5649i			0.497649i	−0.968549	+	0.248825i	$0.919956\pi$
$744$	−19.7423	−	10.7398i	−0.723786	−	0.393742i
$745$		0			0
$746$	−35.1961	−	26.3621i	−1.28862	−	0.965185i
$747$	6.62713	+	1.91181i	0.242474	+	0.0699496i
$748$	1.04681	−	0.306764i	0.0382750	−	0.0112164i
$749$	20.1092			0.734774
$750$		0			0
$751$			37.3072i			1.36136i	0.732581	+	0.680680i	$0.238316\pi$
$751$			37.3072i			1.36136i	−0.732581	+	0.680680i	$0.761684\pi$
$752$	−22.8791	−	35.6842i	−0.834316	−	1.30127i
$753$	0.299334	−	2.11755i	0.0109084	−	0.0771676i
$754$	45.1240	+	33.7981i	1.64332	+	1.23086i
$755$		0			0
$756$	4.36018	−	31.8103i	0.158578	−	1.15693i
$757$	−0.385842			−0.0140237			−0.00701183	−	0.999975i	$-0.502232\pi$
$757$	−0.385842			−0.0140237			−0.00701183	+	0.999975i	$0.502232\pi$
$758$	14.2731	+	10.6906i	0.518423	+	0.388302i
$759$	19.5501	+	2.76359i	0.709625	+	0.100312i
$760$		0			0
$761$		−	10.2235i		−	0.370603i	−0.982682	−	0.185302i	$-0.940674\pi$
$761$		−	10.2235i		−	0.370603i	0.982682	−	0.185302i	$-0.0593262\pi$
$762$	−1.66412	−	1.65713i	−0.0602846	−	0.0600314i
$763$		−	15.6547i		−	0.566738i
$764$	1.29699	+	4.42587i	0.0469235	+	0.160122i
$765$		0			0
$766$	1.39403	−	1.86118i	0.0503685	−	0.0672471i
$767$		−	2.17047i		−	0.0783711i
$768$	−14.9771	+	23.3171i	−0.540439	+	0.841383i
$769$	−4.34816			−0.156799			−0.0783994	−	0.996922i	$-0.524981\pi$
$769$	−4.34816			−0.156799			−0.0783994	+	0.996922i	$0.524981\pi$
$770$		0			0
$771$	−31.9083	−	4.51052i	−1.14915	−	0.162443i
$772$	21.5915	−	6.32735i	0.777096	−	0.227726i
$773$			21.4326i			0.770878i	0.922733	+	0.385439i	$0.125950\pi$
$773$			21.4326i			0.770878i	−0.922733	+	0.385439i	$0.874050\pi$
$774$	38.6056	−	29.1703i	1.38765	−	1.04851i
$775$		0			0
$776$	21.3135	+	7.96894i	0.765111	+	0.286068i
$777$	−40.6782	−	5.75023i	−1.45932	−	0.206288i
$778$	−42.4340	−	31.7834i	−1.52133	−	1.13949i
$779$			24.1910i			0.866731i
$780$		0			0
$781$			15.5867i			0.557737i
$782$	−0.812847	+	1.08523i	−0.0290674	+	0.0388079i
$783$	−37.3072	−	16.7180i	−1.33325	−	0.597451i
$784$	−8.57121	+	5.49549i	−0.306115	+	0.196267i
$785$		0			0
$786$	6.53553	−	6.56310i	0.233115	−	0.234098i
$787$		−	32.2753i		−	1.15049i	−0.817980	−	0.575246i	$-0.804906\pi$
$787$		−	32.2753i		−	1.15049i	0.817980	−	0.575246i	$-0.195094\pi$
$788$	−13.0175	+	3.81475i	−0.463729	+	0.135895i
$789$	−2.72951	+	19.3091i	−0.0971733	+	0.687421i
$790$		0			0
$791$	−18.7031			−0.665006
$792$	17.3491	+	12.8809i	0.616473	+	0.457705i
$793$		−	5.63533i		−	0.200116i
$794$	22.5046	+	16.8561i	0.798660	+	0.598201i
$795$		0			0
$796$	−1.21450	+	0.355908i	−0.0430469	+	0.0126148i
$797$			14.4120i			0.510498i	0.966875	+	0.255249i	$0.0821574\pi$
$797$			14.4120i			0.510498i	−0.966875	+	0.255249i	$0.917843\pi$
$798$	−13.9949	−	13.9361i	−0.495413	−	0.493332i
$799$		−	2.26970i		−	0.0802961i
$800$		0			0
$801$	−10.3820	+	35.9883i	−0.366830	+	1.27158i
$802$	−9.54382	+	12.7420i	−0.337004	+	0.449935i
$803$	30.5959			1.07970
$804$	−8.08983	+	1.17833i	−0.285306	+	0.0415563i
$805$		0			0
$806$	−19.7074	+	26.3113i	−0.694162	+	0.926777i
$807$	20.0354	+	2.83219i	0.705280	+	0.0996977i
$808$	1.07498	−	2.87511i	0.0378177	−	0.101146i
$809$			27.3297i			0.960860i	0.877033	+	0.480430i	$0.159519\pi$
$809$			27.3297i			0.960860i	−0.877033	+	0.480430i	$0.840481\pi$
$810$		0			0
$811$	1.18452			0.0415942			0.0207971	−	0.999784i	$-0.493380\pi$
$811$	1.18452			0.0415942			0.0207971	+	0.999784i	$0.493380\pi$
$812$	13.6717	+	46.6536i	0.479784	+	1.63722i
$813$		0			0
$814$	16.5748	−	22.1290i	0.580946	−	0.775622i
$815$		0			0
$816$	−1.34897	+	0.618185i	−0.0472235	+	0.0216408i
$817$		−	29.7640i		−	1.04131i
$818$	19.1301	+	14.3285i	0.668867	+	0.500986i
$819$	−45.1240	−	13.0175i	−1.57676	−	0.454868i
$820$		0			0
$821$	−16.8535			−0.588191			−0.294095	−	0.955776i	$-0.595018\pi$
$821$	−16.8535			−0.588191			−0.294095	+	0.955776i	$0.595018\pi$
$822$	−22.8900	−	22.7938i	−0.798379	−	0.795026i
$823$	47.6544			1.66113			0.830564	−	0.556923i	$-0.188018\pi$
$823$	47.6544			1.66113			0.830564	+	0.556923i	$0.188018\pi$
$824$	11.5220	−	30.8165i	0.401389	−	1.07354i
$825$		0			0
$826$	1.12202	−	1.49801i	0.0390401	−	0.0521225i
$827$	11.4476			0.398073			0.199036	−	0.979992i	$-0.436219\pi$
$827$	11.4476			0.398073			0.199036	+	0.979992i	$0.436219\pi$
$828$	−26.8586	+	0.113054i	−0.933400	+	0.00392891i
$829$		−	13.6692i		−	0.474751i	−0.971418	−	0.237375i	$-0.923713\pi$
$829$		−	13.6692i		−	0.474751i	0.971418	−	0.237375i	$-0.0762871\pi$
$830$		0			0
$831$	−29.8843	−	4.22441i	−1.03667	−	0.146543i
$832$	30.5924	+	26.5942i	1.06060	+	0.921986i
$833$	−0.545173			−0.0188891
$834$	−30.0183	−	29.8922i	−1.03945	−	1.03508i
$835$		0			0
$836$	12.7552	−	3.73790i	0.441149	−	0.129278i
$837$	9.74808	−	21.7535i	0.336943	−	0.751910i
$838$	−6.11377	+	8.16250i	−0.211197	+	0.281969i
$839$	16.7180			0.577168			0.288584	−	0.957455i	$-0.406816\pi$
$839$	16.7180			0.577168			0.288584	+	0.957455i	$0.406816\pi$
$840$		0			0
$841$	32.9007			1.13451
$842$	−9.66459	+	12.9032i	−0.333064	+	0.444674i
$843$	−3.14521	+	22.2498i	−0.108327	+	0.766323i
$844$	6.54685	+	22.3405i	0.225352	+	0.768993i
$845$		0			0
$846$	35.8715	−	27.1044i	1.23329	−	0.931870i
$847$	13.9498			0.479321
$848$	−20.5361	−	32.0298i	−0.705214	−	1.09991i
$849$	3.00356	−	21.2477i	0.103082	−	0.729220i
$850$		0			0
$851$			34.3665i			1.17807i
$852$	−3.05606	−	20.9815i	−0.104699	−	0.718814i
$853$	−7.83055			−0.268113			−0.134056	−	0.990974i	$-0.542800\pi$
$853$	−7.83055			−0.268113			−0.134056	+	0.990974i	$0.542800\pi$
$854$	2.91317	−	3.88939i	0.0996868	−	0.133092i
$855$		0			0
$856$	6.44725	−	17.2436i	0.220362	−	0.589375i
$857$	25.7234			0.878696			0.439348	−	0.898317i	$-0.355210\pi$
$857$	25.7234			0.878696			0.439348	+	0.898317i	$0.355210\pi$
$858$	22.3019	−	22.3960i	0.761375	−	0.764587i
$859$	12.5142			0.426980			0.213490	−	0.976945i	$-0.431517\pi$
$859$	12.5142			0.426980			0.213490	+	0.976945i	$0.431517\pi$
$860$		0			0
$861$	−6.94289	+	49.1152i	−0.236613	+	1.67384i
$862$	4.47136	+	3.34908i	0.152295	+	0.114070i
$863$		−	24.1621i		−	0.822489i	−0.911525	−	0.411244i	$-0.865094\pi$
$863$		−	24.1621i		−	0.822489i	0.911525	−	0.411244i	$-0.134906\pi$
$864$	−25.8794	−	13.9376i	−0.880435	−	0.474167i
$865$		0			0
$866$	17.5080	−	23.3750i	0.594947	−	0.794315i
$867$	29.0763	+	4.11021i	0.987484	+	0.139590i
$868$	−27.2032	+	7.97185i	−0.923338	+	0.270582i
$869$	−29.6212			−1.00483
$870$		0			0
$871$			11.9579i			0.405178i
$872$	−13.4239	−	5.01908i	−0.454591	−	0.169968i
$873$	−6.68969	+	23.1892i	−0.226412	+	0.784836i
$874$	−9.90447	+	13.2235i	−0.335024	+	0.447291i
$875$		0			0
$876$	−41.1855	+	5.99887i	−1.39153	+	0.202683i
$877$	−18.7362			−0.632675			−0.316337	−	0.948647i	$-0.602453\pi$
$877$	−18.7362			−0.632675			−0.316337	+	0.948647i	$0.602453\pi$
$878$	−24.2285	+	32.3475i	−0.817671	+	1.09167i
$879$	−7.70728	+	54.5227i	−0.259960	+	1.83900i
$880$		0			0
$881$			45.2764i			1.52540i	0.646752	+	0.762701i	$0.276127\pi$
$881$			45.2764i			1.52540i	−0.646752	+	0.762701i	$0.723873\pi$
$882$	−6.51039	−	8.61622i	−0.219216	−	0.290123i
$883$			32.6703i			1.09944i	0.835348	+	0.549722i	$0.185266\pi$
$883$			32.6703i			1.09944i	−0.835348	+	0.549722i	$0.814734\pi$
$884$	0.610382	+	2.08287i	0.0205294	+	0.0700547i
$885$		0			0
$886$	24.8669	+	18.6254i	0.835418	+	0.625734i
$887$		−	24.6883i		−	0.828953i	−0.910060	−	0.414477i	$-0.863965\pi$
$887$		−	24.6883i		−	0.828953i	0.910060	−	0.414477i	$-0.136035\pi$
$888$	−17.9727	+	33.0379i	−0.603125	+	1.10868i
$889$	−2.96216			−0.0993477
$890$		0			0
$891$	−12.2075	+	19.3972i	−0.408965	+	0.649831i
$892$	−6.05566	−	20.6644i	−0.202758	−	0.691895i
$893$		−	27.6560i		−	0.925474i
$894$	−6.62123	−	6.59342i	−0.221447	−	0.220517i
$895$		0			0
$896$	7.36640	+	34.1694i	0.246094	+	1.14152i
$897$	−5.49884	+	38.8998i	−0.183601	+	1.29883i
$898$	−7.63446	+	10.1928i	−0.254765	+	0.340137i
$899$			36.0937i			1.20379i
$900$		0			0
$901$		−	2.03726i		−	0.0678710i
$902$	−26.7188	−	20.0126i	−0.889639	−	0.666345i
$903$	8.54237	−	60.4302i	0.284272	−	2.01099i
$904$	−5.99644	+	16.0379i	−0.199439	+	0.533414i
$905$		0			0
$906$	−22.8555	+	22.9519i	−0.759323	+	0.762526i
$907$			15.7502i			0.522978i	0.965206	+	0.261489i	$0.0842135\pi$
$907$			15.7502i			0.522978i	−0.965206	+	0.261489i	$0.915787\pi$
$908$	7.21982	+	24.6370i	0.239598	+	0.817607i
$909$	3.12814	+	0.902414i	0.103754	+	0.0299312i
$910$		0			0
$911$	50.4948			1.67297			0.836483	−	0.547993i	$-0.184608\pi$
$911$	50.4948			1.67297			0.836483	+	0.547993i	$0.184608\pi$
$912$	−16.4371	+	7.53253i	−0.544287	+	0.249427i
$913$			5.85482i			0.193766i
$914$	−15.7478	+	21.0250i	−0.520892	+	0.695445i
$915$		0			0
$916$	−28.7287	+	8.41889i	−0.949224	+	0.278168i
$917$		−	11.6824i		−	0.385788i
$918$	−0.763723	−	1.37617i	−0.0252066	−	0.0454203i
$919$			22.6311i			0.746530i	0.927725	+	0.373265i	$0.121762\pi$
$919$			22.6311i			0.746530i	−0.927725	+	0.373265i	$0.878238\pi$
$920$		0			0
$921$	2.50402	−	17.7139i	0.0825102	−	0.583692i
$922$	38.7117	+	28.9953i	1.27490	+	0.954909i
$923$	−31.0136			−1.02082
$924$	26.9699	−	3.92831i	0.887245	−	0.129232i
$925$		0			0
$926$	−8.42674	−	6.31169i	−0.276920	−	0.207415i
$927$	33.5285	+	9.67240i	1.10122	+	0.317683i
$928$	44.3888	+	3.23417i	1.45713	+	0.106167i
$929$		−	45.8021i		−	1.50272i	−0.659893	−	0.751360i	$-0.729398\pi$
$929$		−	45.8021i		−	1.50272i	0.659893	−	0.751360i	$-0.270602\pi$
$930$		0			0
$931$	−6.64289			−0.217712
$932$	−11.7539	−	40.1093i	−0.385013	−	1.31382i
$933$	−8.81199	−	1.24566i	−0.288492	−	0.0407809i
$934$	−8.21949	−	6.15645i	−0.268950	−	0.201445i
$935$		0			0
$936$	−25.6298	+	34.5203i	−0.837736	+	1.12833i
$937$		−	4.77203i		−	0.155895i	−0.996957	−	0.0779477i	$-0.975163\pi$
$937$		−	4.77203i		−	0.155895i	0.996957	−	0.0779477i	$-0.0248367\pi$
$938$	−6.18162	+	8.25310i	−0.201837	+	0.269473i
$939$	3.79988	−	26.8811i	0.124004	−	0.877230i
$940$		0			0
$941$	28.5031			0.929174			0.464587	−	0.885528i	$-0.346203\pi$
$941$	28.5031			0.929174			0.464587	+	0.885528i	$0.346203\pi$
$942$	11.3948	+	11.3469i	0.371262	+	0.369702i
$943$	41.4944			1.35124
$944$	−0.924813	−	1.44241i	−0.0301001	−	0.0469466i
$945$		0			0
$946$	32.8742	+	24.6230i	1.06883	+	0.800562i
$947$	−59.7387			−1.94125			−0.970623	−	0.240606i	$-0.922654\pi$
$947$	−59.7387			−1.94125			−0.970623	+	0.240606i	$0.922654\pi$
$948$	39.8734	−	5.80777i	1.29503	−	0.188628i
$949$			60.8779i			1.97618i
$950$		0			0
$951$	−2.17047	+	15.3543i	−0.0703823	+	0.497897i
$952$	−0.655466	+	1.75309i	−0.0212438	+	0.0568181i
$953$	−32.0009			−1.03661			−0.518305	−	0.855196i	$-0.673437\pi$
$953$	−32.0009			−1.03661			−0.518305	+	0.855196i	$0.673437\pi$
$954$	32.1980	−	24.3287i	1.04245	−	0.787672i
$955$		0			0
$956$	−16.1076	−	54.9657i	−0.520956	−	1.77772i
$957$	4.85720	−	34.3607i	0.157011	−	1.11072i
$958$	−26.4470	−	19.8089i	−0.854463	−	0.639998i
$959$	−40.7446			−1.31571
$960$		0			0
$961$	9.95413			0.321101
$962$	44.0311	+	32.9795i	1.41962	+	1.06330i
$963$	18.7612	+	5.41227i	0.604570	+	0.174408i
$964$	5.20247	+	17.7530i	0.167560	+	0.571784i
$965$		0			0
$966$	−23.9044	+	24.0052i	−0.769111	+	0.772355i
$967$	−30.7086			−0.987521			−0.493761	−	0.869598i	$-0.664378\pi$
$967$	−30.7086			−0.987521			−0.493761	+	0.869598i	$0.664378\pi$
$968$	4.47248	−	11.9620i	0.143751	−	0.384472i
$969$	−0.958603	−	0.135507i	−0.0307948	−	0.00435312i
$970$		0			0
$971$		−	54.2279i		−	1.74025i	−0.492827	−	0.870127i	$-0.664036\pi$
$971$		−	54.2279i		−	1.74025i	0.492827	−	0.870127i	$-0.335964\pi$
$972$	12.6294	−	28.5043i	0.405090	−	0.914277i
$973$	−53.4332			−1.71299
$974$	8.79572	+	6.58805i	0.281833	+	0.211095i
$975$		0			0
$976$	−2.40115	−	3.74503i	−0.0768590	−	0.119876i
$977$	11.5621			0.369905			0.184952	−	0.982748i	$-0.440787\pi$
$977$	11.5621			0.369905			0.184952	+	0.982748i	$0.440787\pi$
$978$	14.0684	−	14.1278i	0.449859	−	0.451757i
$979$	−31.7943			−1.01615
$980$		0			0
$981$	4.21337	−	14.6053i	0.134523	−	0.466311i
$982$	17.4025	−	23.2342i	0.555338	−	0.741432i
$983$			48.8505i			1.55809i	0.626969	+	0.779044i	$0.284295\pi$
$983$			48.8505i			1.55809i	−0.626969	+	0.779044i	$0.715705\pi$
$984$	39.8904	+	21.7005i	1.27166	+	0.691785i
$985$		0			0
$986$	1.90737	+	1.42864i	0.0607432	+	0.0454970i
$987$	7.93738	−	56.1505i	0.252650	−	1.78729i
$988$	7.43745	+	25.3796i	0.236617	+	0.807434i
$989$	−51.0538			−1.62342
$990$		0			0
$991$			8.77480i			0.278741i	0.990240	+	0.139370i	$0.0445079\pi$
$991$			8.77480i			0.278741i	−0.990240	+	0.139370i	$0.955492\pi$
$992$	−1.88582	+	25.8827i	−0.0598747	+	0.821775i
$993$	7.69154	+	1.08727i	0.244084	+	0.0345035i
$994$	−21.4049	−	16.0324i	−0.678923	−	0.508518i
$995$		0			0
$996$	−1.14794	−	7.88125i	−0.0363740	−	0.249727i
$997$	5.99205			0.189770			0.0948851	−	0.995488i	$-0.469752\pi$
$997$	5.99205			0.189770			0.0948851	+	0.995488i	$0.469752\pi$
$998$	−29.9908	−	22.4633i	−0.949343	−	0.711064i
$999$	−36.4036	−	16.3131i	−1.15176	−	0.516122i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.m.e.299.1		24
3.2	odd	2	inner	600.2.m.e.299.23		24
4.3	odd	2		2400.2.m.e.1199.23		24
5.2	odd	4		600.2.b.g.251.7	yes	12
5.3	odd	4		600.2.b.h.251.6	yes	12
5.4	even	2	inner	600.2.m.e.299.24		24
8.3	odd	2	inner	600.2.m.e.299.3		24
8.5	even	2		2400.2.m.e.1199.24		24
12.11	even	2		2400.2.m.e.1199.3		24
15.2	even	4		600.2.b.g.251.6	yes	12
15.8	even	4		600.2.b.h.251.7	yes	12
15.14	odd	2	inner	600.2.m.e.299.2		24
20.3	even	4		2400.2.b.g.2351.8		12
20.7	even	4		2400.2.b.h.2351.5		12
20.19	odd	2		2400.2.m.e.1199.2		24
24.5	odd	2		2400.2.m.e.1199.4		24
24.11	even	2	inner	600.2.m.e.299.21		24
40.3	even	4		600.2.b.h.251.8	yes	12
40.13	odd	4		2400.2.b.g.2351.7		12
40.19	odd	2	inner	600.2.m.e.299.22		24
40.27	even	4		600.2.b.g.251.5	✓	12
40.29	even	2		2400.2.m.e.1199.1		24
40.37	odd	4		2400.2.b.h.2351.6		12
60.23	odd	4		2400.2.b.g.2351.6		12
60.47	odd	4		2400.2.b.h.2351.7		12
60.59	even	2		2400.2.m.e.1199.22		24
120.29	odd	2		2400.2.m.e.1199.21		24
120.53	even	4		2400.2.b.g.2351.5		12
120.59	even	2	inner	600.2.m.e.299.4		24
120.77	even	4		2400.2.b.h.2351.8		12
120.83	odd	4		600.2.b.h.251.5	yes	12
120.107	odd	4		600.2.b.g.251.8	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.b.g.251.5	✓	12	40.27	even	4
600.2.b.g.251.6	yes	12	15.2	even	4
600.2.b.g.251.7	yes	12	5.2	odd	4
600.2.b.g.251.8	yes	12	120.107	odd	4
600.2.b.h.251.5	yes	12	120.83	odd	4
600.2.b.h.251.6	yes	12	5.3	odd	4
600.2.b.h.251.7	yes	12	15.8	even	4
600.2.b.h.251.8	yes	12	40.3	even	4
600.2.m.e.299.1		24	1.1	even	1	trivial
600.2.m.e.299.2		24	15.14	odd	2	inner
600.2.m.e.299.3		24	8.3	odd	2	inner
600.2.m.e.299.4		24	120.59	even	2	inner
600.2.m.e.299.21		24	24.11	even	2	inner
600.2.m.e.299.22		24	40.19	odd	2	inner
600.2.m.e.299.23		24	3.2	odd	2	inner
600.2.m.e.299.24		24	5.4	even	2	inner
2400.2.b.g.2351.5		12	120.53	even	4
2400.2.b.g.2351.6		12	60.23	odd	4
2400.2.b.g.2351.7		12	40.13	odd	4
2400.2.b.g.2351.8		12	20.3	even	4
2400.2.b.h.2351.5		12	20.7	even	4
2400.2.b.h.2351.6		12	40.37	odd	4
2400.2.b.h.2351.7		12	60.47	odd	4
2400.2.b.h.2351.8		12	120.77	even	4
2400.2.m.e.1199.1		24	40.29	even	2
2400.2.m.e.1199.2		24	20.19	odd	2
2400.2.m.e.1199.3		24	12.11	even	2
2400.2.m.e.1199.4		24	24.5	odd	2
2400.2.m.e.1199.21		24	120.29	odd	2
2400.2.m.e.1199.22		24	60.59	even	2
2400.2.m.e.1199.23		24	4.3	odd	2
2400.2.m.e.1199.24		24	8.5	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.m (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.13191 - 0.847808i) q^{2} +(-1.71500 - 0.242431i) q^{3} +(0.562443 + 1.91929i) q^{4} +(1.73569 + 1.72840i) q^{6} +3.08957 q^{7} +(0.990551 - 2.64930i) q^{8} +(2.88245 + 0.831539i) q^{9} +2.54654i q^{11} +(-0.499295 - 3.42793i) q^{12} -5.06696 q^{13} +(-3.49711 - 2.61936i) q^{14} +(-3.36732 + 2.15898i) q^{16} -0.214179 q^{17} +(-2.55770 - 3.38500i) q^{18} -2.60975 q^{19} +(-5.29861 - 0.749006i) q^{21} +(2.15898 - 2.88245i) q^{22} +4.47647i q^{23} +(-2.34107 + 4.30342i) q^{24} +(5.73534 + 4.29581i) q^{26} +(-4.74182 - 2.12489i) q^{27} +(1.73770 + 5.92976i) q^{28} +7.86770 q^{29} +4.58758i q^{31} +(5.64190 + 0.411070i) q^{32} +(0.617360 - 4.36732i) q^{33} +(0.242431 + 0.181582i) q^{34} +(0.0252553 + 5.99995i) q^{36} +7.67714 q^{37} +(2.95400 + 2.21257i) q^{38} +(8.68984 + 1.22839i) q^{39} -9.26946i q^{41} +(5.36253 + 5.34001i) q^{42} +11.4049i q^{43} +(-4.88754 + 1.43228i) q^{44} +(3.79518 - 5.06696i) q^{46} +10.5972i q^{47} +(6.29835 - 2.88630i) q^{48} +2.54541 q^{49} +(0.367316 + 0.0519235i) q^{51} +(-2.84987 - 9.72494i) q^{52} +9.51198i q^{53} +(3.56582 + 6.42533i) q^{54} +(3.06037 - 8.18520i) q^{56} +(4.47572 + 0.632684i) q^{57} +(-8.90553 - 6.67030i) q^{58} +0.428357i q^{59} +1.11217i q^{61} +(3.88939 - 5.19273i) q^{62} +(8.90553 + 2.56909i) q^{63} +(-6.03762 - 5.24854i) q^{64} +(-4.40144 + 4.42001i) q^{66} -2.35998i q^{67} +(-0.120463 - 0.411070i) q^{68} +(1.08523 - 7.67714i) q^{69} +6.12075 q^{71} +(5.05822 - 6.81281i) q^{72} -12.0147i q^{73} +(-8.68984 - 6.50874i) q^{74} +(-1.46783 - 5.00885i) q^{76} +7.86770i q^{77} +(-8.79468 - 8.75774i) q^{78} +11.6319i q^{79} +(7.61709 + 4.79374i) q^{81} +(-7.85873 + 10.4922i) q^{82} +2.29913 q^{83} +(-1.54261 - 10.5908i) q^{84} +(9.66919 - 12.9094i) q^{86} +(-13.4931 - 1.90737i) q^{87} +(6.74655 + 2.52248i) q^{88} +12.4853i q^{89} -15.6547 q^{91} +(-8.59162 + 2.51776i) q^{92} +(1.11217 - 7.86770i) q^{93} +(8.98440 - 11.9951i) q^{94} +(-9.57620 - 2.07276i) q^{96} +8.04496i q^{97} +(-2.88118 - 2.15802i) q^{98} +(-2.11755 + 7.34028i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{4} + 14 q^{6} + 4 q^{9} - 12 q^{16} + 8 q^{19} - 10 q^{24} + 4 q^{34} + 38 q^{36} - 32 q^{46} + 72 q^{49} - 60 q^{51} + 60 q^{54} - 20 q^{64} + 14 q^{66} - 76 q^{76} - 20 q^{81} + 68 q^{84}+ \cdots - 116 q^{99}+O(q^{100}) \) 24 * q - 20 * q^4 + 14 * q^6 + 4 * q^9 - 12 * q^16 + 8 * q^19 - 10 * q^24 + 4 * q^34 + 38 * q^36 - 32 * q^46 + 72 * q^49 - 60 * q^51 + 60 * q^54 - 20 * q^64 + 14 * q^66 - 76 * q^76 - 20 * q^81 + 68 * q^84 - 48 * q^91 - 56 * q^94 - 62 * q^96 - 116 * q^99

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