LMFDB - Embedded newform 600.2.m.e.299.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(299,600)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			299.3
Character	$\chi$	$=$	600.299
Dual form			600.2.m.e.299.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13191 + 0.847808i) q^{2} +(-1.71500 - 0.242431i) q^{3} +(0.562443 - 1.91929i) q^{4} +(2.14676 - 1.17958i) q^{6} -3.08957 q^{7} +(0.990551 + 2.64930i) q^{8} +(2.88245 + 0.831539i) q^{9} +O(q^{10})$	\(q+(-1.13191 + 0.847808i) q^{2} +(-1.71500 - 0.242431i) q^{3} +(0.562443 - 1.91929i) q^{4} +(2.14676 - 1.17958i) q^{6} -3.08957 q^{7} +(0.990551 + 2.64930i) q^{8} +(2.88245 + 0.831539i) q^{9} +2.54654i q^{11} +(-1.42988 + 3.15522i) q^{12} +5.06696 q^{13} +(3.49711 - 2.61936i) q^{14} +(-3.36732 - 2.15898i) q^{16} -0.214179 q^{17} +(-3.96767 + 1.50254i) q^{18} -2.60975 q^{19} +(5.29861 + 0.749006i) q^{21} +(-2.15898 - 2.88245i) q^{22} -4.47647i q^{23} +(-1.05652 - 4.78370i) 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} +(3.21718 - 5.06456i) q^{36} -7.67714 q^{37} +(2.95400 - 2.21257i) q^{38} +(-8.68984 - 1.22839i) q^{39} -9.26946i q^{41} +(-6.63256 + 3.64439i) q^{42} +11.4049i q^{43} +(4.88754 + 1.43228i) q^{44} +(3.79518 + 5.06696i) q^{46} -10.5972i q^{47} +(5.25155 + 4.51899i) q^{48} +2.54541 q^{49} +(0.367316 + 0.0519235i) q^{51} +(2.84987 - 9.72494i) q^{52} -9.51198i q^{53} +(7.16881 - 1.61497i) 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} +(3.00385 + 5.46681i) q^{66} -2.35998i q^{67} +(-0.120463 + 0.411070i) q^{68} +(-1.08523 + 7.67714i) q^{69} -6.12075 q^{71} +(0.652221 + 8.46018i) q^{72} -12.0147i q^{73} +(8.68984 - 6.50874i) q^{74} +(-1.46783 + 5.00885i) q^{76} -7.86770i q^{77} +(10.8776 - 5.97689i) q^{78} -11.6319i q^{79} +(7.61709 + 4.79374i) q^{81} +(7.85873 + 10.4922i) q^{82} +2.29913 q^{83} +(4.41772 - 9.74827i) 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} +(-9.77552 - 0.662786i) 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}+O(q^{10}) $ 24 * q - 20 * q^4 + 14 * q^6 + 4 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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
$6$	2.14676	−	1.17958i	0.876412	−	0.481562i
$7$	−3.08957			−1.16775			−0.583873	−	0.811845i	$-0.698463\pi$
$7$	−3.08957			−1.16775			−0.583873	+	0.811845i	$0.698463\pi$
$8$	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	$0.874579\pi$
$12$	−1.42988	+	3.15522i	−0.412772	+	0.910834i
$13$	5.06696			1.40532			0.702661	−	0.711525i	$-0.251995\pi$
$13$	5.06696			1.40532			0.702661	+	0.711525i	$0.251995\pi$
$14$	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	$0.508268\pi$
$18$	−3.96767	+	1.50254i	−0.935188	+	0.354152i
$19$	−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	$-0.845441\pi$
$23$		−	4.47647i		−	0.933408i	0.884414	−	0.466704i	$-0.154559\pi$
$24$	−1.05652	−	4.78370i	−0.215662	−	0.976468i
$25$		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	$-0.760712\pi$
$29$	−7.86770			−1.46100			−0.730498	+	0.682915i	$0.760712\pi$
$30$		0			0
$31$		−	4.58758i		−	0.823953i	−0.911194	−	0.411977i	$-0.864839\pi$
$31$		−	4.58758i		−	0.823953i	0.911194	−	0.411977i	$-0.135161\pi$
$32$	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
$36$	3.21718	−	5.06456i	0.536196	−	0.844094i
$37$	−7.67714			−1.26211			−0.631057	−	0.775736i	$-0.717379\pi$
$37$	−7.67714			−1.26211			−0.631057	+	0.775736i	$0.717379\pi$
$38$	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	$-0.257617\pi$
$42$	−6.63256	+	3.64439i	−1.02343	+	0.562342i
$43$			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	$-0.718815\pi$
$47$		−	10.5972i		−	1.54576i	0.634551	−	0.772881i	$-0.281185\pi$
$48$	5.25155	+	4.51899i	0.757996	+	0.652260i
$49$	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	$-0.773390\pi$
$53$		−	9.51198i		−	1.30657i	0.757112	−	0.653285i	$-0.226610\pi$
$54$	7.16881	−	1.61497i	0.975552	−	0.219770i
$55$		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	$-0.977317\pi$
$61$		−	1.11217i		−	0.142399i	0.997462	−	0.0711995i	$-0.0226827\pi$
$62$	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
$66$	3.00385	+	5.46681i	0.369748	+	0.672918i
$67$		−	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	$-0.618316\pi$
$71$	−6.12075			−0.726399			−0.363199	+	0.931711i	$0.618316\pi$
$72$	0.652221	+	8.46018i	0.0768650	+	0.997042i
$73$		−	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
$78$	10.8776	−	5.97689i	1.23164	−	0.676750i
$79$		−	11.6319i		−	1.30869i	−0.756194	−	0.654347i	$-0.772943\pi$
$79$		−	11.6319i		−	1.30869i	0.756194	−	0.654347i	$-0.227057\pi$
$80$		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	$0.459728\pi$
$84$	4.41772	−	9.74827i	0.482013	−	1.06362i
$85$		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
$96$	−9.77552	−	0.662786i	−0.997709	−	0.0676453i
$97$			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	$-0.517195\pi$
$101$	−1.08523			−0.107985			−0.0539924	+	0.998541i	$0.517195\pi$
$102$	−0.459790	+	0.252641i	−0.0455260	+	0.0250152i
$103$	−11.6319			−1.14613			−0.573064	−	0.819511i	$-0.694245\pi$
$103$	−11.6319			−1.14613			−0.573064	+	0.819511i	$0.694245\pi$
$104$	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	$0.398126\pi$
$108$	−6.74526	+	7.90578i	−0.649063	+	0.760734i
$109$			5.06696i			0.485327i	0.970111	+	0.242663i	$0.0780210\pi$
$109$			5.06696i			0.485327i	−0.970111	+	0.242663i	$0.921979\pi$
$110$		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	$0.591907\pi$
$114$	−5.60251	+	3.07841i	−0.524723	+	0.288319i
$115$		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
$126$	12.2584	−	4.64220i	1.09206	−	0.413560i
$127$	0.958763			0.0850765			0.0425382	−	0.999095i	$-0.486456\pi$
$127$	0.958763			0.0850765			0.0425382	+	0.999095i	$0.486456\pi$
$128$	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	$-0.0528221\pi$
$132$	−8.03490	−	3.64126i	−0.699348	−	0.316931i
$133$	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	$0.690490\pi$
$138$	−5.28036	−	9.60991i	−0.449494	−	0.818050i
$139$	−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
$144$	−7.91086	−	9.02321i	−0.659239	−	0.751934i
$145$		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	$-0.450057\pi$
$149$	3.81475			0.312516			0.156258	+	0.987716i	$0.450057\pi$
$150$		0			0
$151$		−	13.2235i		−	1.07611i	−0.842909	−	0.538056i	$-0.819159\pi$
$151$		−	13.2235i		−	1.07611i	0.842909	−	0.538056i	$-0.180841\pi$
$152$	−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
$156$	−7.24516	+	15.9874i	−0.580077	+	1.28002i
$157$	−6.56497			−0.523942			−0.261971	−	0.965076i	$-0.584372\pi$
$157$	−6.56497			−0.523942			−0.261971	+	0.965076i	$0.584372\pi$
$158$	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
$162$	−12.6860	+	1.03174i	−0.996709	+	0.0810611i
$163$		−	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	$0.320781\pi$
$167$			21.8561i			1.69128i	−0.533754	+	0.845640i	$0.679219\pi$
$168$	3.26420	+	14.7795i	0.251838	+	1.14027i
$169$	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	$-0.882234\pi$
$173$		−	9.51198i		−	0.723182i	0.932337	−	0.361591i	$-0.117766\pi$
$174$	−16.8901	+	9.28059i	−1.28043	+	0.703560i
$175$		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	$0.118003\pi$
$181$			9.74808i			0.724569i	−0.932068	+	0.362284i	$0.881997\pi$
$182$	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
$186$	−5.41142	−	9.84844i	−0.396785	−	0.722123i
$187$		−	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	$-0.526587\pi$
$191$	−2.30600			−0.166856			−0.0834281	+	0.996514i	$0.526587\pi$
$192$	11.6269	−	7.53755i	0.839101	−	0.543976i
$193$		−	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	$-0.922323\pi$
$197$		−	6.78247i		−	0.483231i	0.970372	−	0.241615i	$-0.0776772\pi$
$198$	−3.82628	−	10.1038i	−0.271922	−	0.718047i
$199$		−	0.632789i		−	0.0448573i	−0.999748	−	0.0224286i	$-0.992860\pi$
$199$		−	0.632789i		−	0.0448573i	0.999748	−	0.0224286i	$-0.00713985\pi$
$200$		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
$204$	0.306251	−	0.675781i	0.0214418	−	0.0473141i
$205$		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
$216$	0.932449	−	14.6673i	0.0634451	−	0.997985i
$217$			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
$222$	−16.4810	+	9.05582i	−1.10613	+	0.607787i
$223$	10.7667			0.720992			0.360496	−	0.932761i	$-0.382607\pi$
$223$	10.7667			0.720992			0.360496	+	0.932761i	$0.382607\pi$
$224$	−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	$0.359924\pi$
$228$	3.73164	−	8.23433i	0.247134	−	0.545332i
$229$		−	14.9684i		−	0.989143i	−0.869137	−	0.494571i	$-0.835325\pi$
$229$		−	14.9684i		−	0.989143i	0.869137	−	0.494571i	$-0.164675\pi$
$230$		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	$0.739996\pi$
$234$	−20.1040	+	7.61332i	−1.31424	+	0.497698i
$235$		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	$-0.123023\pi$
$239$	28.6386			1.85248			0.926239	+	0.376937i	$0.123023\pi$
$240$		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
$246$	−10.9341	−	19.8993i	−0.697132	−	1.26874i
$247$	−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	$0.987593\pi$
$252$	−9.93967	+	15.6473i	−0.626141	+	0.985687i
$253$	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	$0.302941\pi$
$258$	13.4530	+	24.4837i	0.837550	+	1.52429i
$259$	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	$0.112843\pi$
$263$			11.2589i			0.694255i	−0.937818	+	0.347128i	$0.887157\pi$
$264$	12.1819	−	2.69048i	0.749742	−	0.165587i
$265$		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	$-0.384091\pi$
$269$	11.6824			0.712291			0.356146	+	0.934430i	$0.384091\pi$
$270$		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
$276$	14.1243	+	6.40083i	0.850180	+	0.385285i
$277$	−17.4252			−1.04698			−0.523490	−	0.852032i	$-0.675370\pi$
$277$	−17.4252			−1.04698			−0.523490	+	0.852032i	$0.675370\pi$
$278$	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	$-0.126479\pi$
$282$	−12.5003	−	22.7497i	−0.744381	−	1.35472i
$283$			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
$288$	16.6043	+	3.50657i	0.978420	+	0.206626i
$289$	−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	$0.379024\pi$
$293$			31.7916i			1.85729i	−0.370973	+	0.928644i	$0.620976\pi$
$294$	5.46440	−	3.00252i	0.318690	−	0.175111i
$295$		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
$306$	0.849789	−	0.321812i	0.0485792	−	0.0183968i
$307$			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	$-0.546537\pi$
$311$	−5.13819			−0.291360			−0.145680	+	0.989332i	$0.546537\pi$
$312$	−5.35336	−	24.2388i	−0.303074	−	1.37225i
$313$			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	$0.0808987\pi$
$317$			8.95293i			0.502847i	−0.967877	+	0.251423i	$0.919101\pi$
$318$	−11.2202	−	20.4200i	−0.629195	−	1.14509i
$319$		−	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
$324$	13.4847	−	11.9232i	0.749152	−	0.662398i
$325$		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
$336$	−16.2250	−	13.9617i	−0.885146	−	0.761674i
$337$		−	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
$342$	10.3546	−	3.92125i	0.559913	−	0.212037i
$343$	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	$0.592889\pi$
$348$	11.2499	−	24.8243i	0.603058	−	1.33072i
$349$		−	11.6319i		−	0.622643i	−0.950305	−	0.311322i	$-0.899228\pi$
$349$		−	11.6319i		−	0.622643i	0.950305	−	0.311322i	$-0.100772\pi$
$350$		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	$0.303465\pi$
$354$	0.505282	+	0.919581i	0.0268554	+	0.0488752i
$355$		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	$-0.389403\pi$
$359$	12.9032			0.681005			0.340503	+	0.940244i	$0.389403\pi$
$360$		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
$366$	−1.31190	−	2.38757i	−0.0685739	−	0.124800i
$367$	−11.7255			−0.612065			−0.306032	−	0.952021i	$-0.599002\pi$
$367$	−11.7255			−0.612065			−0.306032	+	0.952021i	$0.599002\pi$
$368$	−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
$372$	14.4748	+	6.55970i	0.750485	+	0.340105i
$373$	−31.0944			−1.61001			−0.805004	−	0.593270i	$-0.797837\pi$
$373$	−31.0944			−1.61001			−0.805004	+	0.593270i	$0.797837\pi$
$374$	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
$378$	−22.1485	+	4.98957i	−1.13920	+	0.256636i
$379$	−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	$-0.986624\pi$
$383$		−	1.64428i		−	0.0840188i	0.999117	−	0.0420094i	$-0.0133759\pi$
$384$	−6.77024	+	18.3892i	−0.345493	+	0.938421i
$385$		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	$-0.899306\pi$
$389$	−37.4889			−1.90076			−0.950381	+	0.311090i	$0.899306\pi$
$390$		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
$396$	12.8971	+	8.19266i	0.648104	+	0.411697i
$397$	19.8820			0.997849			0.498924	−	0.866646i	$-0.333729\pi$
$397$	19.8820			0.997849			0.498924	+	0.866646i	$0.333729\pi$
$398$	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	$-0.0906910\pi$
$402$	−2.78378	−	5.06631i	−0.138843	−	0.252684i
$403$		−	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
$408$	0.226285	+	1.02457i	0.0112028	+	0.0507235i
$409$	−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
$414$	6.72608	+	17.7611i	0.330569	+	0.872912i
$415$		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	$0.0896015\pi$
$421$			11.3995i			0.555578i	−0.960642	+	0.277789i	$0.910398\pi$
$422$	−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
$426$	−13.1398	+	7.21992i	−0.636625	+	0.349806i
$427$			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	$-0.469670\pi$
$431$	3.95028			0.190278			0.0951391	+	0.995464i	$0.469670\pi$
$432$	11.3796	+	17.3926i	0.547503	+	0.836804i
$433$			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
$438$	−14.1723	−	25.7927i	−0.677178	−	1.23242i
$439$			28.5778i			1.36394i	0.731379	+	0.681971i	$0.238877\pi$
$439$			28.5778i			1.36394i	−0.731379	+	0.681971i	$0.761123\pi$
$440$		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	$0.674772\pi$
$444$	10.9774	−	24.2231i	0.520965	−	1.14958i
$445$		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
$456$	2.75726	+	12.4842i	0.129120	+	0.584628i
$457$		−	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	$-0.206717\pi$
$461$	34.2003			1.59287			0.796434	+	0.604726i	$0.206717\pi$
$462$	−9.28059	−	16.8901i	−0.431772	−	0.785798i
$463$	−7.44471			−0.345985			−0.172992	−	0.984923i	$-0.555344\pi$
$463$	−7.44471			−0.345985			−0.172992	+	0.984923i	$0.555344\pi$
$464$	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	$0.446265\pi$
$468$	16.3013	−	25.6619i	0.753528	−	1.18622i
$469$			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
$474$	−13.7208	−	24.9710i	−0.630218	−	1.14696i
$475$		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	$-0.679231\pi$
$479$	−23.3649			−1.06757			−0.533785	+	0.845620i	$0.679231\pi$
$480$		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
$486$	22.0067	+	1.30605i	0.998244	+	0.0592438i
$487$	7.77068			0.352123			0.176062	−	0.984379i	$-0.443664\pi$
$487$	7.77068			0.352123			0.176062	+	0.984379i	$0.443664\pi$
$488$	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	$0.846710\pi$
$492$	29.2472	+	13.2543i	1.31857	+	0.597548i
$493$	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
$498$	4.93568	−	2.71201i	0.221173	−	0.121528i
$499$	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	$0.205553\pi$
$503$			26.9943i			1.20362i	−0.798640	+	0.601809i	$0.794447\pi$
$504$	−2.01508	−	26.1383i	−0.0897588	−	1.16429i
$505$		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	$-0.693803\pi$
$509$	−25.8064			−1.14385			−0.571925	+	0.820306i	$0.693803\pi$
$510$		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
$516$	−35.9851	−	16.3077i	−1.58416	−	0.717908i
$517$	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	$0.988095\pi$
$522$	31.2164	−	11.8215i	1.36630	−	0.517415i
$523$		−	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
$528$	−11.5078	+	13.3733i	−0.500812	+	0.581997i
$529$	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
$534$	14.7274	+	26.8029i	0.637317	+	1.15988i
$535$		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	$0.116872\pi$
$541$			16.6989i			0.717941i	−0.933349	+	0.358971i	$0.883128\pi$
$542$		0			0
$543$	2.36324	−	16.7180i	0.101416	−	0.717436i
$544$	−1.20837	+	0.0880424i	−0.0518086	+	0.00377479i
$545$		0			0
$546$	−33.6069	+	18.4660i	−1.43824	+	0.790272i
$547$		−	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
$552$	−21.4141	+	4.72949i	−0.911443	+	0.201300i
$553$			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	$-0.979974\pi$
$557$		−	2.96772i		−	0.125746i	0.998022	−	0.0628731i	$-0.0200263\pi$
$558$	6.89302	+	18.2020i	0.291805	+	0.770551i
$559$			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	$0.579336\pi$
$564$	33.4366	+	15.1528i	1.40793	+	0.638047i
$565$		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
$576$	−21.7675	+	10.1082i	−0.906980	+	0.421174i
$577$			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
$582$	9.48968	+	17.2706i	0.393360	+	0.715890i
$583$	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	$0.364898\pi$
$588$	−3.63965	+	8.03135i	−0.150097	+	0.331207i
$589$			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	$0.309437\pi$
$594$	4.11259	+	18.2557i	0.168742	+	0.749039i
$595$		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	$-0.408445\pi$
$599$	13.8858			0.567357			0.283679	+	0.958919i	$0.408445\pi$
$600$		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
$606$	−2.32974	+	1.28012i	−0.0946392	+	0.0520014i
$607$	30.7086			1.24642			0.623211	−	0.782054i	$-0.285828\pi$
$607$	30.7086			1.24642			0.623211	+	0.782054i	$0.285828\pi$
$608$	−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
$612$	−0.689050	+	1.08472i	−0.0278532	+	0.0438472i
$613$	−13.3170			−0.537870			−0.268935	−	0.963158i	$-0.586672\pi$
$613$	−13.3170			−0.537870			−0.268935	+	0.963158i	$0.586672\pi$
$614$	−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	$0.780949\pi$
$618$	−24.9710	+	13.7208i	−1.00448	+	0.551932i
$619$	−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
$624$	26.6094	+	22.8975i	1.06523	+	0.916635i
$625$		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	$0.295359\pi$
$631$			40.2097i			1.60072i	−0.599518	+	0.800362i	$0.704641\pi$
$632$	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
$636$	30.0124	+	13.6010i	1.19007	+	0.539316i
$637$	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	$0.952282\pi$
$642$	13.9727	−	7.67759i	0.551460	−	0.303010i
$643$		−	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	$-0.798099\pi$
$647$		−	30.1474i		−	1.18522i	0.805491	−	0.592608i	$-0.201901\pi$
$648$	−5.15497	+	24.9284i	−0.202506	+	0.979281i
$649$	−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	$0.0527243\pi$
$653$			8.42674i			0.329764i	−0.986313	+	0.164882i	$0.947276\pi$
$654$	5.97689	+	10.8776i	0.233715	+	0.425346i
$655$		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	$0.0104333\pi$
$661$			1.68509i			0.0655425i	−0.999463	+	0.0327713i	$0.989567\pi$
$662$	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
$666$	30.4603	−	11.5352i	1.18031	−	0.446981i
$667$			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
$672$	30.2021	+	2.04772i	1.16507	+	0.0789925i
$673$		−	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	$-0.702795\pi$
$677$		−	41.8298i		−	1.60765i	0.594866	−	0.803825i	$-0.297205\pi$
$678$	−12.9957	+	7.14076i	−0.499098	+	0.274239i
$679$		−	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	$0.318270\pi$
$684$	−8.39602	+	13.2172i	−0.321030	+	0.505373i
$685$		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
$696$	8.31241	+	37.6367i	0.315081	+	1.42662i
$697$			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	$-0.797835\pi$
$701$	−42.6271			−1.61000			−0.805001	+	0.593274i	$0.797835\pi$
$702$	36.3241	−	8.18301i	1.37096	−	0.308848i
$703$	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
$708$	−1.35156	−	0.612501i	−0.0507948	−	0.0230192i
$709$			17.0057i			0.638663i	0.947643	+	0.319331i	$0.103458\pi$
$709$			17.0057i			0.638663i	−0.947643	+	0.319331i	$0.896542\pi$
$710$		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
$714$	1.42055	−	0.780551i	0.0531628	−	0.0292114i
$715$		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	$-0.679319\pi$
$719$	−28.6386			−1.06804			−0.534020	+	0.845472i	$0.679319\pi$
$720$		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
$726$	9.69293	−	5.32597i	0.359738	−	0.197665i
$727$	14.1822			0.525990			0.262995	−	0.964797i	$-0.415290\pi$
$727$	14.1822			0.525990			0.262995	+	0.964797i	$0.415290\pi$
$728$	−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
$732$	3.50915	+	1.59028i	0.129702	+	0.0587783i
$733$	−51.7027			−1.90968			−0.954842	−	0.297113i	$-0.903976\pi$
$733$	−51.7027			−1.90968			−0.954842	+	0.297113i	$0.903976\pi$
$734$	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
$738$	13.9277	+	36.7781i	0.512688	+	1.35382i
$739$	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	$-0.919956\pi$
$743$		−	13.5649i		−	0.497649i	0.968549	−	0.248825i	$-0.0800442\pi$
$744$	−21.9456	+	4.84688i	−0.804564	+	0.177695i
$745$		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	$-0.761684\pi$
$751$		−	37.3072i		−	1.36136i	0.732581	−	0.680680i	$-0.238316\pi$
$752$	−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
$756$	20.8399	−	24.4254i	0.757941	−	0.888344i
$757$	0.385842			0.0140237			0.00701183	−	0.999975i	$-0.497768\pi$
$757$	0.385842			0.0140237			0.00701183	+	0.999975i	$0.497768\pi$
$758$	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	$-0.0593262\pi$
$762$	2.05824	−	1.13094i	0.0745621	−	0.0409696i
$763$		−	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
$768$	−7.92723	−	26.5548i	−0.286049	−	0.958215i
$769$	−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	$-0.874050\pi$
$773$		−	21.4326i		−	0.770878i	0.922733	−	0.385439i	$-0.125950\pi$
$774$	−17.1364	−	45.2510i	−0.615954	−	1.62651i
$775$		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
$786$	−4.46030	−	8.11746i	−0.159094	−	0.289540i
$787$		−	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
$792$	−21.5442	+	1.66091i	−0.765539	+	0.0590178i
$793$		−	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	$-0.917843\pi$
$797$		−	14.4120i		−	0.510498i	0.966875	−	0.255249i	$-0.0821574\pi$
$798$	17.3093	−	9.51095i	0.612743	−	0.336684i
$799$			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
$804$	7.44625	+	3.37449i	0.262609	+	0.119009i
$805$		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
$816$	−1.12477	−	0.967870i	−0.0393748	−	0.0338822i
$817$		−	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	$-0.404982\pi$
$821$	16.8535			0.588191			0.294095	+	0.955776i	$0.404982\pi$
$822$	−28.3111	+	15.5561i	−0.987462	+	0.542581i
$823$	−47.6544			−1.66113			−0.830564	−	0.556923i	$-0.811982\pi$
$823$	−47.6544			−1.66113			−0.830564	+	0.556923i	$0.811982\pi$
$824$	−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	$0.436219\pi$
$828$	−22.6713	−	14.4016i	−0.787884	−	0.500490i
$829$			13.6692i			0.474751i	0.971418	+	0.237375i	$0.0762871\pi$
$829$			13.6692i			0.474751i	−0.971418	+	0.237375i	$0.923713\pi$
$830$		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
$834$	−37.1277	+	20.4005i	−1.28563	+	0.706413i
$835$		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	$-0.593184\pi$
$839$	−16.7180			−0.577168			−0.288584	+	0.957455i	$0.593184\pi$
$840$		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
$846$	15.9227	+	42.0462i	0.547435	+	1.44558i
$847$	−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
$852$	8.75196	−	19.3123i	0.299837	−	0.661629i
$853$	7.83055			0.268113			0.134056	−	0.990974i	$-0.457200\pi$
$853$	7.83055			0.268113			0.134056	+	0.990974i	$0.457200\pi$
$854$	−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	$0.355210\pi$
$858$	15.2204	+	27.7001i	0.519615	+	0.945667i
$859$	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	$0.134906\pi$
$863$			24.1621i			0.822489i	−0.911525	+	0.411244i	$0.865094\pi$
$864$	−27.6263	−	10.0392i	−0.939867	−	0.341539i
$865$		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
$876$	37.9090	+	17.1796i	1.28083	+	0.580445i
$877$	18.7362			0.632675			0.316337	−	0.948647i	$-0.397547\pi$
$877$	18.7362			0.632675			0.316337	+	0.948647i	$0.397547\pi$
$878$	−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	$0.723873\pi$
$882$	−10.0994	+	3.82459i	−0.340063	+	0.128781i
$883$			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	$0.136035\pi$
$887$			24.6883i			0.828953i	−0.910060	+	0.414477i	$0.863965\pi$
$888$	8.11108	+	36.7251i	0.272190	+	1.23241i
$889$	−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
$894$	8.18936	−	4.49981i	0.273893	−	0.150496i
$895$		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
$906$	−15.5982	−	28.3877i	−0.518215	−	0.943117i
$907$			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	$-0.815392\pi$
$911$	−50.4948			−1.67297			−0.836483	+	0.547993i	$0.815392\pi$
$912$	−13.7052	−	11.7934i	−0.453825	−	0.390519i
$913$			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
$918$	−1.53541	+	0.345893i	−0.0506759	+	0.0114162i
$919$		−	22.6311i		−	0.746530i	−0.927725	−	0.373265i	$-0.878238\pi$
$919$		−	22.6311i		−	0.746530i	0.927725	−	0.373265i	$-0.121762\pi$
$920$		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
$924$	24.8243	+	11.2499i	0.816661	+	0.370094i
$925$		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
$936$	3.30478	+	42.8674i	0.108020	+	1.40116i
$937$		−	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	$-0.653797\pi$
$941$	−28.5031			−0.929174			−0.464587	+	0.885528i	$0.653797\pi$
$942$	−14.0934	+	7.74392i	−0.459189	+	0.252311i
$943$	−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	$0.922654\pi$
$948$	36.7013	+	16.6323i	1.19200	+	0.540192i
$949$		−	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	$0.673437\pi$
$954$	14.2921	+	37.7404i	0.462725	+	1.22189i
$955$		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
$966$	16.3140	+	29.6904i	0.524895	+	0.955274i
$967$	30.7086			0.987521			0.493761	−	0.869598i	$-0.335622\pi$
$967$	30.7086			0.987521			0.493761	+	0.869598i	$0.335622\pi$
$968$	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	$-0.335964\pi$
$972$	−26.0169	+	17.1791i	−0.834492	+	0.551020i
$973$	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	$0.440787\pi$
$978$	−9.60128	−	17.4737i	−0.307015	−	0.558748i
$979$	−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	$-0.715705\pi$
$983$		−	48.8505i		−	1.55809i	0.626969	−	0.779044i	$-0.284295\pi$
$984$	−44.3423	+	9.79340i	−1.41358	+	0.312202i
$985$		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	$-0.955492\pi$
$991$		−	8.77480i		−	0.278741i	0.990240	−	0.139370i	$-0.0445079\pi$
$992$	−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
$996$	−3.28749	+	7.25426i	−0.104168	+	0.229860i
$997$	−5.99205			−0.189770			−0.0948851	−	0.995488i	$-0.530248\pi$
$997$	−5.99205			−0.189770			−0.0948851	+	0.995488i	$0.530248\pi$
$998$	−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.299.3		24
3.2	odd	2	inner	600.2.m.e.299.21		24
4.3	odd	2		2400.2.m.e.1199.24		24
5.2	odd	4		600.2.b.g.251.5	✓	12
5.3	odd	4		600.2.b.h.251.8	yes	12
5.4	even	2	inner	600.2.m.e.299.22		24
8.3	odd	2	inner	600.2.m.e.299.1		24
8.5	even	2		2400.2.m.e.1199.23		24
12.11	even	2		2400.2.m.e.1199.4		24
15.2	even	4		600.2.b.g.251.8	yes	12
15.8	even	4		600.2.b.h.251.5	yes	12
15.14	odd	2	inner	600.2.m.e.299.4		24
20.3	even	4		2400.2.b.g.2351.7		12
20.7	even	4		2400.2.b.h.2351.6		12
20.19	odd	2		2400.2.m.e.1199.1		24
24.5	odd	2		2400.2.m.e.1199.3		24
24.11	even	2	inner	600.2.m.e.299.23		24
40.3	even	4		600.2.b.h.251.6	yes	12
40.13	odd	4		2400.2.b.g.2351.8		12
40.19	odd	2	inner	600.2.m.e.299.24		24
40.27	even	4		600.2.b.g.251.7	yes	12
40.29	even	2		2400.2.m.e.1199.2		24
40.37	odd	4		2400.2.b.h.2351.5		12
60.23	odd	4		2400.2.b.g.2351.5		12
60.47	odd	4		2400.2.b.h.2351.8		12
60.59	even	2		2400.2.m.e.1199.21		24
120.29	odd	2		2400.2.m.e.1199.22		24
120.53	even	4		2400.2.b.g.2351.6		12
120.59	even	2	inner	600.2.m.e.299.2		24
120.77	even	4		2400.2.b.h.2351.7		12
120.83	odd	4		600.2.b.h.251.7	yes	12
120.107	odd	4		600.2.b.g.251.6	yes	12

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.13191 + 0.847808i) q^{2} +(-1.71500 - 0.242431i) q^{3} +(0.562443 - 1.91929i) q^{4} +(2.14676 - 1.17958i) q^{6} -3.08957 q^{7} +(0.990551 + 2.64930i) q^{8} +(2.88245 + 0.831539i) q^{9} +O(q^{10})\)	\(q+(-1.13191 + 0.847808i) q^{2} +(-1.71500 - 0.242431i) q^{3} +(0.562443 - 1.91929i) q^{4} +(2.14676 - 1.17958i) q^{6} -3.08957 q^{7} +(0.990551 + 2.64930i) q^{8} +(2.88245 + 0.831539i) q^{9} +2.54654i q^{11} +(-1.42988 + 3.15522i) q^{12} +5.06696 q^{13} +(3.49711 - 2.61936i) q^{14} +(-3.36732 - 2.15898i) q^{16} -0.214179 q^{17} +(-3.96767 + 1.50254i) q^{18} -2.60975 q^{19} +(5.29861 + 0.749006i) q^{21} +(-2.15898 - 2.88245i) q^{22} -4.47647i q^{23} +(-1.05652 - 4.78370i) 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} +(3.21718 - 5.06456i) q^{36} -7.67714 q^{37} +(2.95400 - 2.21257i) q^{38} +(-8.68984 - 1.22839i) q^{39} -9.26946i q^{41} +(-6.63256 + 3.64439i) q^{42} +11.4049i q^{43} +(4.88754 + 1.43228i) q^{44} +(3.79518 + 5.06696i) q^{46} -10.5972i q^{47} +(5.25155 + 4.51899i) q^{48} +2.54541 q^{49} +(0.367316 + 0.0519235i) q^{51} +(2.84987 - 9.72494i) q^{52} -9.51198i q^{53} +(7.16881 - 1.61497i) 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} +(3.00385 + 5.46681i) q^{66} -2.35998i q^{67} +(-0.120463 + 0.411070i) q^{68} +(-1.08523 + 7.67714i) q^{69} -6.12075 q^{71} +(0.652221 + 8.46018i) q^{72} -12.0147i q^{73} +(8.68984 - 6.50874i) q^{74} +(-1.46783 + 5.00885i) q^{76} -7.86770i q^{77} +(10.8776 - 5.97689i) q^{78} -11.6319i q^{79} +(7.61709 + 4.79374i) q^{81} +(7.85873 + 10.4922i) q^{82} +2.29913 q^{83} +(4.41772 - 9.74827i) 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} +(-9.77552 - 0.662786i) q^{96} +8.04496i q^{97} +(-2.88118 + 2.15802i) q^{98} +(-2.11755 + 7.34028i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{4} + 14 q^{6} + 4 q^{9}+O(q^{10}) \) 24 * q - 20 * q^4 + 14 * q^6 + 4 * q^9	\( 24 q - 20 q^{4} + 14 q^{6} + 4 q^{9} - 12 q^{16} + 8 q^{19} - 10 q^{24} + 4 q^{34} + 38 q^{36} - 32 q^{46} + 72 q^{49} - 60 q^{51} + 60 q^{54} - 20 q^{64} + 14 q^{66} - 76 q^{76} - 20 q^{81} + 68 q^{84} - 48 q^{91} - 56 q^{94} - 62 q^{96} - 116 q^{99}+O(q^{100}) \) 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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