LMFDB - Embedded newform 600.2.w.j.293.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(293,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))

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

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

chi := DirichletCharacter("600.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.w (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			293.8
Character	$\chi$	$=$	600.293
Dual form			600.2.w.j.557.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0941764 - 1.41107i) q^{2} +(-1.68122 - 0.416519i) q^{3} +(-1.98226 + 0.265780i) q^{4} +(-0.429408 + 2.41156i) q^{6} +(0.361989 - 0.361989i) q^{7} +(0.561717 + 2.77209i) q^{8} +(2.65302 + 1.40052i) q^{9} +O(q^{10})$	\(q+(-0.0941764 - 1.41107i) q^{2} +(-1.68122 - 0.416519i) q^{3} +(-1.98226 + 0.265780i) q^{4} +(-0.429408 + 2.41156i) q^{6} +(0.361989 - 0.361989i) q^{7} +(0.561717 + 2.77209i) q^{8} +(2.65302 + 1.40052i) q^{9} +2.63380 q^{11} +(3.44333 + 0.378815i) q^{12} +(-3.49376 + 3.49376i) q^{13} +(-0.544885 - 0.476703i) q^{14} +(3.85872 - 1.05369i) q^{16} +(3.61339 + 3.61339i) q^{17} +(1.72639 - 3.87551i) q^{18} -0.672266 q^{19} +(-0.759360 + 0.457809i) q^{21} +(-0.248041 - 3.71648i) q^{22} +(4.31851 - 4.31851i) q^{23} +(0.210256 - 4.89447i) q^{24} +(5.25899 + 4.60093i) q^{26} +(-3.87698 - 3.45963i) q^{27} +(-0.621348 + 0.813767i) q^{28} -4.76080i q^{29} +3.73793 q^{31} +(-1.85024 - 5.34571i) q^{32} +(-4.42800 - 1.09703i) q^{33} +(4.75847 - 5.43906i) q^{34} +(-5.63122 - 2.07108i) q^{36} +(2.82150 + 2.82150i) q^{37} +(0.0633116 + 0.948617i) q^{38} +(7.32901 - 4.41857i) q^{39} -4.10027i q^{41} +(0.717517 + 1.02840i) q^{42} +(7.57996 - 7.57996i) q^{43} +(-5.22087 + 0.700010i) q^{44} +(-6.50044 - 5.68704i) q^{46} +(0.987537 + 0.987537i) q^{47} +(-6.92626 + 0.164257i) q^{48} +6.73793i q^{49} +(-4.56987 - 7.57996i) q^{51} +(5.99698 - 7.85412i) q^{52} +(-0.646149 - 0.646149i) q^{53} +(-4.51667 + 5.79652i) q^{54} +(1.20680 + 0.800131i) q^{56} +(1.13023 + 0.280012i) q^{57} +(-6.71784 + 0.448355i) q^{58} +4.92247i q^{59} +6.07190i q^{61} +(-0.352025 - 5.27449i) q^{62} +(1.46734 - 0.453392i) q^{63} +(-7.36895 + 3.11426i) q^{64} +(-1.13097 + 6.35155i) q^{66} +(0.349085 + 0.349085i) q^{67} +(-8.12305 - 6.20232i) q^{68} +(-9.05912 + 5.46164i) q^{69} -8.63702i q^{71} +(-2.39213 + 8.14111i) q^{72} +(11.3261 + 11.3261i) q^{73} +(3.71562 - 4.24706i) q^{74} +(1.33261 - 0.178675i) q^{76} +(0.953406 - 0.953406i) q^{77} +(-6.92516 - 9.92565i) q^{78} +4.07707i q^{79} +(5.07707 + 7.43124i) q^{81} +(-5.78579 + 0.386149i) q^{82} +(8.53893 + 8.53893i) q^{83} +(1.38357 - 1.10932i) q^{84} +(-11.4097 - 9.98203i) q^{86} +(-1.98296 + 8.00397i) q^{87} +(1.47945 + 7.30111i) q^{88} +6.58584 q^{89} +2.52941i q^{91} +(-7.41264 + 9.70819i) q^{92} +(-6.28429 - 1.55692i) q^{93} +(1.30049 - 1.48649i) q^{94} +(0.884069 + 9.75799i) q^{96} +(0.660859 - 0.660859i) q^{97} +(9.50772 - 0.634554i) q^{98} +(6.98752 + 3.68869i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{6}+O(q^{10}) $ 32 * q - 4 * q^6	$ 32 q - 4 q^{6} + 8 q^{12} + 28 q^{16} + 20 q^{18} + 52 q^{22} - 12 q^{28} - 32 q^{31} - 8 q^{33} - 20 q^{36} - 16 q^{42} + 24 q^{46} - 44 q^{48} - 8 q^{52} + 16 q^{57} - 28 q^{58} - 48 q^{63} + 16 q^{66} - 32 q^{72} + 64 q^{73} - 88 q^{76} - 64 q^{78} + 48 q^{81} - 64 q^{82} + 8 q^{87} + 52 q^{88} - 52 q^{96} - 16 q^{97}+O(q^{100}) $ 32 * q - 4 * q^6 + 8 * q^12 + 28 * q^16 + 20 * q^18 + 52 * q^22 - 12 * q^28 - 32 * q^31 - 8 * q^33 - 20 * q^36 - 16 * q^42 + 24 * q^46 - 44 * q^48 - 8 * q^52 + 16 * q^57 - 28 * q^58 - 48 * q^63 + 16 * q^66 - 32 * q^72 + 64 * q^73 - 88 * q^76 - 64 * q^78 + 48 * q^81 - 64 * q^82 + 8 * q^87 + 52 * q^88 - 52 * q^96 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.0941764	−	1.41107i	−0.0665928	−	0.997780i
$2$	−0.0941764	−	1.41107i	−0.0665928	−	0.997780i
$3$	−1.68122	−	0.416519i	−0.970655	−	0.240477i
$3$	−1.68122	−	0.416519i	−0.970655	−	0.240477i
$4$	−1.98226	+	0.265780i	−0.991131	+	0.132890i
$5$		0			0
$5$		0			0
$6$	−0.429408	+	2.41156i	−0.175305	+	0.984514i
$7$	0.361989	−	0.361989i	0.136819	−	0.136819i	−0.635380	−	0.772199i	$-0.719157\pi$
$7$	0.361989	−	0.361989i	0.136819	−	0.136819i	0.772199	+	0.635380i	$0.219157\pi$
$8$	0.561717	+	2.77209i	0.198597	+	0.980081i
$9$	2.65302	+	1.40052i	0.884341	+	0.466841i
$10$		0			0
$11$	2.63380			0.794119			0.397060	−	0.917793i	$-0.370031\pi$
$11$	2.63380			0.794119			0.397060	+	0.917793i	$0.370031\pi$
$12$	3.44333	+	0.378815i	0.994003	+	0.109354i
$13$	−3.49376	+	3.49376i	−0.968995	+	0.968995i	−0.999534	−	0.0305386i	$-0.990278\pi$
$13$	−3.49376	+	3.49376i	−0.968995	+	0.968995i	0.0305386	+	0.999534i	$0.490278\pi$
$14$	−0.544885	−	0.476703i	−0.145627	−	0.127404i
$15$		0			0
$16$	3.85872	−	1.05369i	0.964681	−	0.263423i
$17$	3.61339	+	3.61339i	0.876376	+	0.876376i	0.993158	−	0.116782i	$-0.0372578\pi$
$17$	3.61339	+	3.61339i	0.876376	+	0.876376i	−0.116782	+	0.993158i	$0.537258\pi$
$18$	1.72639	−	3.87551i	0.406914	−	0.913466i
$19$	−0.672266			−0.154228			−0.0771142	−	0.997022i	$-0.524571\pi$
$19$	−0.672266			−0.154228			−0.0771142	+	0.997022i	$0.524571\pi$
$20$		0			0
$21$	−0.759360	+	0.457809i	−0.165706	+	0.0999022i
$22$	−0.248041	−	3.71648i	−0.0528826	−	0.792357i
$23$	4.31851	−	4.31851i	0.900472	−	0.900472i	−0.0950052	−	0.995477i	$-0.530287\pi$
$23$	4.31851	−	4.31851i	0.900472	−	0.900472i	0.995477	+	0.0950052i	$0.0302868\pi$
$24$	0.210256	−	4.89447i	0.0429182	−	0.999079i
$25$		0			0
$26$	5.25899	+	4.60093i	1.03137	+	0.902316i
$27$	−3.87698	−	3.45963i	−0.746125	−	0.665806i
$28$	−0.621348	+	0.813767i	−0.117424	+	0.153787i
$29$		−	4.76080i		−	0.884058i	−0.897001	−	0.442029i	$-0.854259\pi$
$29$		−	4.76080i		−	0.884058i	0.897001	−	0.442029i	$-0.145741\pi$
$30$		0			0
$31$	3.73793			0.671352			0.335676	−	0.941978i	$-0.391035\pi$
$31$	3.73793			0.671352			0.335676	+	0.941978i	$0.391035\pi$
$32$	−1.85024	−	5.34571i	−0.327079	−	0.944997i
$33$	−4.42800	−	1.09703i	−0.770816	−	0.190968i
$34$	4.75847	−	5.43906i	0.816070	−	0.932791i
$35$		0			0
$36$	−5.63122	−	2.07108i	−0.938536	−	0.345181i
$37$	2.82150	+	2.82150i	0.463851	+	0.463851i	0.899915	−	0.436064i	$-0.143628\pi$
$37$	2.82150	+	2.82150i	0.463851	+	0.463851i	−0.436064	+	0.899915i	$0.643628\pi$
$38$	0.0633116	+	0.948617i	0.0102705	+	0.153886i
$39$	7.32901	−	4.41857i	1.17358	−	0.707538i
$40$		0			0
$41$		−	4.10027i		−	0.640355i	−0.947358	−	0.320177i	$-0.896257\pi$
$41$		−	4.10027i		−	0.640355i	0.947358	−	0.320177i	$-0.103743\pi$
$42$	0.717517	+	1.02840i	0.110715	+	0.158685i
$43$	7.57996	−	7.57996i	1.15593	−	1.15593i	0.170591	−	0.985342i	$-0.445432\pi$
$43$	7.57996	−	7.57996i	1.15593	−	1.15593i	0.985342	−	0.170591i	$-0.0545678\pi$
$44$	−5.22087	+	0.700010i	−0.787076	+	0.105530i
$45$		0			0
$46$	−6.50044	−	5.68704i	−0.958438	−	0.838508i
$47$	0.987537	+	0.987537i	0.144047	+	0.144047i	0.775453	−	0.631406i	$-0.217522\pi$
$47$	0.987537	+	0.987537i	0.144047	+	0.144047i	−0.631406	+	0.775453i	$0.717522\pi$
$48$	−6.92626	+	0.164257i	−0.999719	+	0.0237085i
$49$			6.73793i			0.962561i
$50$		0			0
$51$	−4.56987	−	7.57996i	−0.639910	−	1.06141i
$52$	5.99698	−	7.85412i	0.831631	−	1.08917i
$53$	−0.646149	−	0.646149i	−0.0887554	−	0.0887554i	0.661335	−	0.750091i	$-0.269990\pi$
$53$	−0.646149	−	0.646149i	−0.0887554	−	0.0887554i	−0.750091	+	0.661335i	$0.769990\pi$
$54$	−4.51667	+	5.79652i	−0.614641	+	0.788807i
$55$		0			0
$56$	1.20680	+	0.800131i	0.161266	+	0.106922i
$57$	1.13023	+	0.280012i	0.149702	+	0.0370884i
$58$	−6.71784	+	0.448355i	−0.882096	+	0.0588719i
$59$			4.92247i			0.640851i	0.947274	+	0.320425i	$0.103826\pi$
$59$			4.92247i			0.640851i	−0.947274	+	0.320425i	$0.896174\pi$
$60$		0			0
$61$			6.07190i			0.777428i	0.921359	+	0.388714i	$0.127081\pi$
$61$			6.07190i			0.777428i	−0.921359	+	0.388714i	$0.872919\pi$
$62$	−0.352025	−	5.27449i	−0.0447072	−	0.669861i
$63$	1.46734	−	0.453392i	0.184868	−	0.0571220i
$64$	−7.36895	+	3.11426i	−0.921118	+	0.389283i
$65$		0			0
$66$	−1.13097	+	6.35155i	−0.139213	+	0.781822i
$67$	0.349085	+	0.349085i	0.0426476	+	0.0426476i	0.728109	−	0.685461i	$-0.240399\pi$
$67$	0.349085	+	0.349085i	0.0426476	+	0.0426476i	−0.685461	+	0.728109i	$0.740399\pi$
$68$	−8.12305	−	6.20232i	−0.985064	−	0.752141i
$69$	−9.05912	+	5.46164i	−1.09059	+	0.657504i
$70$		0			0
$71$		−	8.63702i		−	1.02503i	−0.858680	−	0.512513i	$-0.828715\pi$
$71$		−	8.63702i		−	1.02503i	0.858680	−	0.512513i	$-0.171285\pi$
$72$	−2.39213	+	8.14111i	−0.281915	+	0.959439i
$73$	11.3261	+	11.3261i	1.32562	+	1.32562i	0.909152	+	0.416465i	$0.136731\pi$
$73$	11.3261	+	11.3261i	1.32562	+	1.32562i	0.416465	+	0.909152i	$0.363269\pi$
$74$	3.71562	−	4.24706i	0.431932	−	0.493711i
$75$		0			0
$76$	1.33261	−	0.178675i	0.152860	−	0.0204954i
$77$	0.953406	−	0.953406i	0.108651	−	0.108651i
$78$	−6.92516	−	9.92565i	−0.784120	−	1.12386i
$79$			4.07707i			0.458706i	0.973343	+	0.229353i	$0.0736610\pi$
$79$			4.07707i			0.458706i	−0.973343	+	0.229353i	$0.926339\pi$
$80$		0			0
$81$	5.07707	+	7.43124i	0.564119	+	0.825694i
$82$	−5.78579	+	0.386149i	−0.638933	+	0.0426430i
$83$	8.53893	+	8.53893i	0.937270	+	0.937270i	0.998145	−	0.0608758i	$-0.0193894\pi$
$83$	8.53893	+	8.53893i	0.937270	+	0.937270i	−0.0608758	+	0.998145i	$0.519389\pi$
$84$	1.38357	−	1.10932i	0.150960	−	0.121037i
$85$		0			0
$86$	−11.4097	−	9.98203i	−1.23034	−	1.07639i
$87$	−1.98296	+	8.00397i	−0.212596	+	0.858115i
$88$	1.47945	+	7.30111i	0.157710	+	0.778301i
$89$	6.58584			0.698097			0.349049	−	0.937105i	$-0.386505\pi$
$89$	6.58584			0.698097			0.349049	+	0.937105i	$0.386505\pi$
$90$		0			0
$91$			2.52941i			0.265154i
$92$	−7.41264	+	9.70819i	−0.772822	+	1.01215i
$93$	−6.28429	−	1.55692i	−0.651651	−	0.161445i
$94$	1.30049	−	1.48649i	0.134135	−	0.153320i
$95$		0			0
$96$	0.884069	+	9.75799i	0.0902299	+	0.995921i
$97$	0.660859	−	0.660859i	0.0671001	−	0.0671001i	−0.672760	−	0.739860i	$-0.734892\pi$
$97$	0.660859	−	0.660859i	0.0671001	−	0.0671001i	0.739860	+	0.672760i	$0.234892\pi$
$98$	9.50772	−	0.634554i	0.960424	−	0.0640996i
$99$	6.98752	+	3.68869i	0.702272	+	0.370728i
$100$		0			0
$101$	3.46850			0.345129			0.172564	−	0.984998i	$-0.444795\pi$
$101$	3.46850			0.345129			0.172564	+	0.984998i	$0.444795\pi$
$102$	−10.2655	+	7.16228i	−1.01644	+	0.709171i
$103$	−8.68806	−	8.68806i	−0.856060	−	0.856060i	0.134811	−	0.990871i	$-0.456957\pi$
$103$	−8.68806	−	8.68806i	−0.856060	−	0.856060i	−0.990871	+	0.134811i	$0.956957\pi$
$104$	−11.6475	−	7.72251i	−1.14213	−	0.757254i
$105$		0			0
$106$	−0.850913	+	0.972617i	−0.0826480	+	0.0944689i
$107$	3.10967	−	3.10967i	0.300623	−	0.300623i	−0.540634	−	0.841258i	$-0.681816\pi$
$107$	3.10967	−	3.10967i	0.300623	−	0.300623i	0.841258	+	0.540634i	$0.181816\pi$
$108$	8.60469	+	5.82746i	0.827987	+	0.560748i
$109$	4.14320			0.396846			0.198423	−	0.980116i	$-0.436418\pi$
$109$	4.14320			0.396846			0.198423	+	0.980116i	$0.436418\pi$
$110$		0			0
$111$	−3.56836	−	5.91877i	−0.338693	−	0.561785i
$112$	1.01539	−	1.77824i	0.0959455	−	0.168028i
$113$	4.38269	−	4.38269i	0.412289	−	0.412289i	−0.470247	−	0.882535i	$-0.655835\pi$
$113$	4.38269	−	4.38269i	0.412289	−	0.412289i	0.882535	+	0.470247i	$0.155835\pi$
$114$	0.288676	−	1.62121i	0.0270370	−	0.151840i
$115$		0			0
$116$	1.26532	+	9.43715i	0.117482	+	0.876217i
$117$	−14.1621	+	4.37594i	−1.30929	+	0.404555i
$118$	6.94597	−	0.463580i	0.639428	−	0.0426760i
$119$	2.61602			0.239810
$120$		0			0
$121$	−4.06312			−0.369374
$122$	8.56791	−	0.571830i	0.775702	−	0.0517711i
$123$	−1.70784	+	6.89347i	−0.153991	+	0.621563i
$124$	−7.40955	+	0.993466i	−0.665397	+	0.0892159i
$125$		0			0
$126$	−0.777958	−	2.02783i	−0.0693060	−	0.180653i
$127$	−9.88701	+	9.88701i	−0.877331	+	0.877331i	−0.993258	−	0.115927i	$-0.963016\pi$
$127$	−9.88701	+	9.88701i	−0.877331	+	0.877331i	0.115927	+	0.993258i	$0.463016\pi$
$128$	5.08843	+	10.1048i	0.449758	+	0.893150i
$129$	−15.9008	+	9.58641i	−1.39999	+	0.844036i
$130$		0			0
$131$	8.79462			0.768389			0.384195	−	0.923252i	$-0.374479\pi$
$131$	8.79462			0.768389			0.384195	+	0.923252i	$0.374479\pi$
$132$	9.06902	+	0.997721i	0.789357	+	0.0868404i
$133$	−0.243353	+	0.243353i	−0.0211014	+	0.0211014i
$134$	0.459710	−	0.525461i	0.0397129	−	0.0453929i
$135$		0			0
$136$	−7.98693	+	12.0463i	−0.684874	+	1.03297i
$137$	−1.48819	−	1.48819i	−0.127145	−	0.127145i	0.640671	−	0.767816i	$-0.278656\pi$
$137$	−1.48819	−	1.48819i	−0.127145	−	0.127145i	−0.767816	+	0.640671i	$0.778656\pi$
$138$	8.55993	+	12.2687i	0.728670	+	1.04438i
$139$	13.3028			1.12833			0.564164	−	0.825663i	$-0.309199\pi$
$139$	13.3028			1.12833			0.564164	+	0.825663i	$0.309199\pi$
$140$		0			0
$141$	−1.24894	−	2.07160i	−0.105180	−	0.174460i
$142$	−12.1875	+	0.813404i	−1.02275	+	0.0682593i
$143$	−9.20185	+	9.20185i	−0.769498	+	0.769498i
$144$	11.7130	+	2.60877i	0.976083	+	0.217397i
$145$		0			0
$146$	14.9153	−	17.0486i	1.23440	−	1.41095i
$147$	2.80648	−	11.3280i	0.231474	−	0.934314i
$148$	−6.34284	−	4.84305i	−0.521378	−	0.398096i
$149$		−	5.22462i		−	0.428018i	−0.976832	−	0.214009i	$-0.931348\pi$
$149$		−	5.22462i		−	0.428018i	0.976832	−	0.214009i	$-0.0686522\pi$
$150$		0			0
$151$	−11.8511			−0.964429			−0.482214	−	0.876053i	$-0.660167\pi$
$151$	−11.8511			−0.964429			−0.482214	+	0.876053i	$0.660167\pi$
$152$	−0.377623	−	1.86358i	−0.0306293	−	0.151156i
$153$	4.52577	+	14.6470i	0.365887	+	1.18414i
$154$	−1.43511	−	1.25554i	−0.115645	−	0.101174i
$155$		0			0
$156$	−13.3536	+	10.7067i	−1.06915	+	0.857220i
$157$	13.9522	+	13.9522i	1.11351	+	1.11351i	0.992673	+	0.120836i	$0.0385574\pi$
$157$	13.9522	+	13.9522i	1.11351	+	1.11351i	0.120836	+	0.992673i	$0.461443\pi$
$158$	5.75305	−	0.383964i	0.457688	−	0.0305465i
$159$	0.817188	+	1.35546i	0.0648072	+	0.107495i
$160$		0			0
$161$		−	3.12651i		−	0.246403i
$162$	10.0079	−	7.86397i	0.786295	−	0.617852i
$163$	6.66434	−	6.66434i	0.521992	−	0.521992i	−0.396181	−	0.918172i	$-0.629665\pi$
$163$	6.66434	−	6.66434i	0.521992	−	0.521992i	0.918172	+	0.396181i	$0.129665\pi$
$164$	1.08977	+	8.12781i	0.0850967	+	0.634675i
$165$		0			0
$166$	11.2449	−	12.8532i	0.872774	−	0.997604i
$167$	−15.6456	−	15.6456i	−1.21069	−	1.21069i	−0.970800	−	0.239890i	$-0.922889\pi$
$167$	−15.6456	−	15.6456i	−1.21069	−	1.21069i	−0.239890	−	0.970800i	$-0.577111\pi$
$168$	−1.69563	−	1.84785i	−0.130821	−	0.142565i
$169$		−	11.4127i		−	0.877903i
$170$		0			0
$171$	−1.78354	−	0.941524i	−0.136390	−	0.0720001i
$172$	−13.0109	+	17.0401i	−0.992069	+	1.29929i
$173$	−6.40332	−	6.40332i	−0.486836	−	0.486836i	0.420471	−	0.907306i	$-0.361865\pi$
$173$	−6.40332	−	6.40332i	−0.486836	−	0.486836i	−0.907306	+	0.420471i	$0.861865\pi$
$174$	11.4809	+	2.04433i	0.870368	+	0.154980i
$175$		0			0
$176$	10.1631	−	2.77521i	0.766071	−	0.209189i
$177$	2.05030	−	8.27577i	0.154110	−	0.622045i
$178$	−0.620231	−	9.29311i	−0.0464882	−	0.696548i
$179$			0.582525i			0.0435399i	0.999763	+	0.0217700i	$0.00693014\pi$
$179$			0.582525i			0.0435399i	−0.999763	+	0.0217700i	$0.993070\pi$
$180$		0			0
$181$			3.71429i			0.276081i	0.990427	+	0.138040i	$0.0440804\pi$
$181$			3.71429i			0.276081i	−0.990427	+	0.138040i	$0.955920\pi$
$182$	3.56918	−	0.238211i	0.264565	−	0.0176573i
$183$	2.52906	−	10.2082i	0.186954	−	0.754614i
$184$	14.3971	+	9.54551i	1.06137	+	0.703704i
$185$		0			0
$186$	−1.60510	+	9.01423i	−0.117691	+	0.660955i
$187$	9.51693	+	9.51693i	0.695947	+	0.695947i
$188$	−2.22002	−	1.69509i	−0.161912	−	0.123627i
$189$	−2.65577	+	0.151077i	−0.193179	+	0.0109892i
$190$		0			0
$191$			22.4496i			1.62440i	0.583380	+	0.812199i	$0.301730\pi$
$191$			22.4496i			1.62440i	−0.583380	+	0.812199i	$0.698270\pi$
$192$	13.6860	−	2.16646i	0.987702	−	0.156351i
$193$	−8.01395	−	8.01395i	−0.576857	−	0.576857i	0.357179	−	0.934036i	$-0.383739\pi$
$193$	−8.01395	−	8.01395i	−0.576857	−	0.576857i	−0.934036	+	0.357179i	$0.883739\pi$
$194$	−0.994759	−	0.870284i	−0.0714195	−	0.0624828i
$195$		0			0
$196$	−1.79081	−	13.3563i	−0.127915	−	0.954024i
$197$	1.49806	−	1.49806i	0.106733	−	0.106733i	−0.651724	−	0.758456i	$-0.725954\pi$
$197$	1.49806	−	1.49806i	0.106733	−	0.106733i	0.758456	+	0.651724i	$0.225954\pi$
$198$	4.54696	−	10.2073i	0.323138	−	0.725401i
$199$		−	12.6160i		−	0.894328i	−0.894452	−	0.447164i	$-0.852434\pi$
$199$		−	12.6160i		−	0.894328i	0.894452	−	0.447164i	$-0.147566\pi$
$200$		0			0
$201$	−0.441490	−	0.732291i	−0.0311403	−	0.0516519i
$202$	−0.326651	−	4.89431i	−0.0229831	−	0.344363i
$203$	−1.72336	−	1.72336i	−0.120956	−	0.120956i
$204$	11.0733	+	13.8109i	0.775284	+	0.966955i
$205$		0			0
$206$	−11.4413	+	13.0777i	−0.797152	+	0.911167i
$207$	17.5053	−	5.40893i	1.21670	−	0.375947i
$208$	−9.80011	+	17.1628i	−0.679515	+	1.19003i
$209$	−1.77061			−0.122476
$210$		0			0
$211$			14.0010i			0.963865i	0.876208	+	0.481933i	$0.160065\pi$
$211$			14.0010i			0.963865i	−0.876208	+	0.481933i	$0.839935\pi$
$212$	1.45257	+	1.10910i	0.0997630	+	0.0761736i
$213$	−3.59748	+	14.5208i	−0.246496	+	0.994946i
$214$	−4.68083	−	4.09512i	−0.319975	−	0.279937i
$215$		0			0
$216$	7.41263	−	12.6907i	0.504365	−	0.863490i
$217$	1.35309	−	1.35309i	0.0918537	−	0.0918537i
$218$	−0.390192	−	5.84636i	−0.0264271	−	0.395965i
$219$	−14.3241	−	23.7592i	−0.967935	−	1.60550i
$220$		0			0
$221$	−25.2486			−1.69841
$222$	−8.01577	+	5.59263i	−0.537983	+	0.375352i
$223$	2.56530	+	2.56530i	0.171785	+	0.171785i	0.787763	−	0.615978i	$-0.211239\pi$
$223$	2.56530	+	2.56530i	0.171785	+	0.171785i	−0.615978	+	0.787763i	$0.711239\pi$
$224$	−2.60486	−	1.26532i	−0.174044	−	0.0845431i
$225$		0			0
$226$	−6.59704	−	5.77155i	−0.438829	−	0.383918i
$227$	−13.3645	+	13.3645i	−0.887032	+	0.887032i	−0.994237	−	0.107205i	$-0.965810\pi$
$227$	−13.3645	+	13.3645i	−0.887032	+	0.887032i	0.107205	+	0.994237i	$0.465810\pi$
$228$	−2.31483	−	0.254664i	−0.153303	−	0.0168655i
$229$	−15.7606			−1.04149			−0.520746	−	0.853712i	$-0.674346\pi$
$229$	−15.7606			−1.04149			−0.520746	+	0.853712i	$0.674346\pi$
$230$		0			0
$231$	−2.00000	+	1.20578i	−0.131590	+	0.0793343i
$232$	13.1974	−	2.67422i	0.866449	−	0.175571i
$233$	−13.0197	+	13.0197i	−0.852949	+	0.852949i	−0.990495	−	0.137546i	$-0.956079\pi$
$233$	−13.0197	+	13.0197i	−0.852949	+	0.852949i	0.137546	+	0.990495i	$0.456079\pi$
$234$	7.50851	+	19.5717i	0.490847	+	1.27944i
$235$		0			0
$236$	−1.30829	−	9.75762i	−0.0851626	−	0.635167i
$237$	1.69818	−	6.85446i	0.110308	−	0.445245i
$238$	−0.246367	−	3.69139i	−0.0159696	−	0.239278i
$239$	−24.8336			−1.60635			−0.803177	−	0.595740i	$-0.796859\pi$
$239$	−24.8336			−1.60635			−0.803177	+	0.595740i	$0.796859\pi$
$240$		0			0
$241$	17.2991			1.11433			0.557165	−	0.830402i	$-0.311889\pi$
$241$	17.2991			1.11433			0.557165	+	0.830402i	$0.311889\pi$
$242$	0.382650	+	5.73336i	0.0245977	+	0.368555i
$243$	−5.44043	−	14.6083i	−0.349004	−	0.937121i
$244$	−1.61379	−	12.0361i	−0.103312	−	0.770532i
$245$		0			0
$246$	9.88804	+	1.76069i	0.630438	+	0.112257i
$247$	2.34874	−	2.34874i	0.149446	−	0.149446i
$248$	2.09966	+	10.3619i	0.133328	+	0.657979i
$249$	−10.7992	−	17.9125i	−0.684373	−	1.13516i
$250$		0			0
$251$	1.05032			0.0662958			0.0331479	−	0.999450i	$-0.489447\pi$
$251$	1.05032			0.0662958			0.0331479	+	0.999450i	$0.489447\pi$
$252$	−2.78815	+	1.28873i	−0.175637	+	0.0811824i
$253$	11.3741	−	11.3741i	0.715082	−	0.715082i
$254$	14.8824	+	13.0202i	0.933807	+	0.816959i
$255$		0			0
$256$	13.7795	−	8.13180i	0.861217	−	0.508237i
$257$	2.20315	+	2.20315i	0.137429	+	0.137429i	0.772474	−	0.635046i	$-0.219019\pi$
$257$	2.20315	+	2.20315i	0.137429	+	0.137429i	−0.635046	+	0.772474i	$0.719019\pi$
$258$	15.0246	+	21.5344i	0.935392	+	1.34067i
$259$	2.04270			0.126927
$260$		0			0
$261$	6.66761	−	12.6305i	0.412715	−	0.781809i
$262$	−0.828245	−	12.4099i	−0.0511692	−	0.766683i
$263$	7.49936	−	7.49936i	0.462430	−	0.462430i	−0.437021	−	0.899451i	$-0.643966\pi$
$263$	7.49936	−	7.49936i	0.462430	−	0.462430i	0.899451	+	0.437021i	$0.143966\pi$
$264$	0.553770	−	12.8910i	0.0340822	−	0.793388i
$265$		0			0
$266$	0.366307	+	0.320471i	0.0224597	+	0.0196493i
$267$	−11.0723	−	2.74313i	−0.677611	−	0.167877i
$268$	−0.784759	−	0.599199i	−0.0479368	−	0.0366019i
$269$		−	21.1993i		−	1.29254i	−0.763108	−	0.646271i	$-0.776327\pi$
$269$		−	21.1993i		−	1.29254i	0.763108	−	0.646271i	$-0.223673\pi$
$270$		0			0
$271$	−14.6748			−0.891431			−0.445716	−	0.895175i	$-0.647051\pi$
$271$	−14.6748			−0.891431			−0.445716	+	0.895175i	$0.647051\pi$
$272$	17.7505	+	10.1357i	1.07628	+	0.614565i
$273$	1.05355	−	4.25250i	0.0637636	−	0.257373i
$274$	−1.95980	+	2.24010i	−0.118396	+	0.135330i
$275$		0			0
$276$	16.5060	−	13.2341i	0.993542	−	0.796601i
$277$	−8.79593	−	8.79593i	−0.528496	−	0.528496i	0.391628	−	0.920124i	$-0.371912\pi$
$277$	−8.79593	−	8.79593i	−0.528496	−	0.528496i	−0.920124	+	0.391628i	$0.871912\pi$
$278$	−1.25281	−	18.7712i	−0.0751384	−	1.12582i
$279$	9.91681	+	5.23506i	0.593704	+	0.313415i
$280$		0			0
$281$			0.490821i			0.0292799i	0.999893	+	0.0146399i	$0.00466021\pi$
$281$			0.490821i			0.0292799i	−0.999893	+	0.0146399i	$0.995340\pi$
$282$	−2.80556	+	1.95745i	−0.167069	+	0.116564i
$283$	−9.43710	+	9.43710i	−0.560978	+	0.560978i	−0.929585	−	0.368608i	$-0.879835\pi$
$283$	−9.43710	+	9.43710i	−0.560978	+	0.560978i	0.368608	+	0.929585i	$0.379835\pi$
$284$	2.29555	+	17.1208i	0.136216	+	1.01593i
$285$		0			0
$286$	13.8511	+	12.1179i	0.819033	+	0.716547i
$287$	−1.48425	−	1.48425i	−0.0876127	−	0.0876127i
$288$	2.57807	−	16.7736i	0.151914	−	0.988394i
$289$			9.11317i			0.536069i
$290$		0			0
$291$	−1.38631	+	0.835791i	−0.0812671	+	0.0489950i
$292$	−25.4615	−	19.4410i	−1.49002	−	1.13770i
$293$	−4.01316	−	4.01316i	−0.234451	−	0.234451i	0.580096	−	0.814548i	$-0.303015\pi$
$293$	−4.01316	−	4.01316i	−0.234451	−	0.234451i	−0.814548	+	0.580096i	$0.803015\pi$
$294$	−16.2489	−	2.89332i	−0.947655	−	0.168742i
$295$		0			0
$296$	−6.23655	+	9.40632i	−0.362492	+	0.546731i
$297$	−10.2112	−	9.11195i	−0.592512	−	0.528729i
$298$	−7.37233	+	0.492036i	−0.427068	+	0.0285029i
$299$			30.1757i			1.74510i
$300$		0			0
$301$		−	5.48773i		−	0.316307i
$302$	1.11609	+	16.7228i	0.0642240	+	0.962288i
$303$	−5.83132	−	1.44470i	−0.335001	−	0.0829957i
$304$	−2.59409	+	0.708360i	−0.148781	+	0.0406272i
$305$		0			0
$306$	20.2418	−	7.76561i	1.15715	−	0.443930i
$307$	−8.00887	−	8.00887i	−0.457091	−	0.457091i	0.440609	−	0.897699i	$-0.354763\pi$
$307$	−8.00887	−	8.00887i	−0.457091	−	0.457091i	−0.897699	+	0.440609i	$0.854763\pi$
$308$	−1.63650	+	2.14330i	−0.0932485	+	0.122126i
$309$	10.9878	+	18.2253i	0.625076	+	1.03680i
$310$		0			0
$311$			12.8874i			0.730778i	0.930855	+	0.365389i	$0.119064\pi$
$311$			12.8874i			0.730778i	−0.930855	+	0.365389i	$0.880936\pi$
$312$	16.3655	+	17.8347i	0.926515	+	1.00969i
$313$	−12.2991	−	12.2991i	−0.695184	−	0.695184i	0.268184	−	0.963368i	$-0.413576\pi$
$313$	−12.2991	−	12.2991i	−0.695184	−	0.695184i	−0.963368	+	0.268184i	$0.913576\pi$
$314$	18.3736	−	21.0016i	1.03688	−	1.18519i
$315$		0			0
$316$	−1.08360	−	8.08182i	−0.0609574	−	0.454638i
$317$	9.24176	−	9.24176i	0.519069	−	0.519069i	−0.398221	−	0.917290i	$-0.630372\pi$
$317$	9.24176	−	9.24176i	0.519069	−	0.519069i	0.917290	+	0.398221i	$0.130372\pi$
$318$	1.83569	−	1.28076i	0.102940	−	0.0718217i
$319$		−	12.5390i		−	0.702048i
$320$		0			0
$321$	−6.52329	+	3.93281i	−0.364094	+	0.219508i
$322$	−4.41174	+	0.294443i	−0.245856	+	0.0164087i
$323$	−2.42916	−	2.42916i	−0.135162	−	0.135162i
$324$	−12.0392	−	13.3813i	−0.668842	−	0.743405i
$325$		0			0
$326$	−10.0315	−	8.77626i	−0.555594	−	0.486072i
$327$	−6.96564	−	1.72572i	−0.385201	−	0.0954326i
$328$	11.3663	−	2.30319i	0.627600	−	0.127173i
$329$	0.714956			0.0394168
$330$		0			0
$331$		−	22.2355i		−	1.22218i	−0.791563	−	0.611088i	$-0.790732\pi$
$331$		−	22.2355i		−	1.22218i	0.791563	−	0.611088i	$-0.209268\pi$
$332$	−19.1959	−	14.6569i	−1.05351	−	0.804403i
$333$	3.53392	+	11.4371i	0.193658	+	0.626747i
$334$	−20.6036	+	23.5505i	−1.12738	+	1.28863i
$335$		0			0
$336$	−2.44777	+	2.56669i	−0.133537	+	0.140024i
$337$	8.98693	−	8.98693i	0.489549	−	0.489549i	−0.418615	−	0.908164i	$-0.637484\pi$
$337$	8.98693	−	8.98693i	0.489549	−	0.489549i	0.908164	+	0.418615i	$0.137484\pi$
$338$	−16.1042	+	1.07481i	−0.875954	+	0.0584620i
$339$	−9.19375	+	5.54280i	−0.499336	+	0.301044i
$340$		0			0
$341$	9.84494			0.533133
$342$	−1.16059	+	2.60537i	−0.0627577	+	0.140882i
$343$	4.97298	+	4.97298i	0.268516	+	0.268516i
$344$	25.2701	+	16.7545i	1.36247	+	0.903343i
$345$		0			0
$346$	−8.43252	+	9.63861i	−0.453335	+	0.518175i
$347$	9.25494	−	9.25494i	0.496831	−	0.496831i	−0.413619	−	0.910450i	$-0.635735\pi$
$347$	9.25494	−	9.25494i	0.496831	−	0.496831i	0.910450	+	0.413619i	$0.135735\pi$
$348$	1.80346	−	16.3930i	0.0966756	−	0.878756i
$349$	17.5919			0.941671			0.470835	−	0.882221i	$-0.343953\pi$
$349$	17.5919			0.941671			0.470835	+	0.882221i	$0.343953\pi$
$350$		0			0
$351$	25.6324	−	1.45813i	1.36815	−	0.0778292i
$352$	−4.87314	−	14.0795i	−0.259739	−	0.750440i
$353$	12.9654	−	12.9654i	0.690077	−	0.690077i	−0.272172	−	0.962249i	$-0.587742\pi$
$353$	12.9654	−	12.9654i	0.690077	−	0.690077i	0.962249	+	0.272172i	$0.0877419\pi$
$354$	−11.8708	−	2.11375i	−0.630927	−	0.112344i
$355$		0			0
$356$	−13.0549	+	1.75038i	−0.691906	+	0.0927701i
$357$	−4.39811	−	1.08962i	−0.232773	−	0.0576689i
$358$	0.821985	−	0.0548601i	0.0434433	−	0.00289945i
$359$	−16.5244			−0.872125			−0.436063	−	0.899916i	$-0.643627\pi$
$359$	−16.5244			−0.872125			−0.436063	+	0.899916i	$0.643627\pi$
$360$		0			0
$361$	−18.5481			−0.976214
$362$	5.24113	−	0.349798i	0.275468	−	0.0183850i
$363$	6.83101	+	1.69237i	0.358535	+	0.0888262i
$364$	−0.672266	−	5.01395i	−0.0352363	−	0.262802i
$365$		0			0
$366$	−14.6427	−	2.60732i	−0.765389	−	0.136287i
$367$	24.4900	−	24.4900i	1.27837	−	1.27837i	0.336786	−	0.941581i	$-0.390660\pi$
$367$	24.4900	−	24.4900i	1.27837	−	1.27837i	0.941581	−	0.336786i	$-0.109340\pi$
$368$	12.1136	−	21.2143i	0.631463	−	1.10587i
$369$	5.74253	−	10.8781i	0.298944	−	0.566292i
$370$		0			0
$371$	−0.467798			−0.0242869
$372$	12.8709	+	1.41598i	0.667325	+	0.0734152i
$373$	−0.406084	+	0.406084i	−0.0210262	+	0.0210262i	−0.717542	−	0.696516i	$-0.754733\pi$
$373$	−0.406084	+	0.406084i	−0.0210262	+	0.0210262i	0.696516	+	0.717542i	$0.254733\pi$
$374$	12.5328	−	14.3254i	0.648057	−	0.740747i
$375$		0			0
$376$	−2.18282	+	3.29226i	−0.112571	+	0.169785i
$377$	16.6331	+	16.6331i	0.856648	+	0.856648i
$378$	0.463292	+	3.73327i	0.0238292	+	0.192018i
$379$	5.73108			0.294386			0.147193	−	0.989108i	$-0.452976\pi$
$379$	5.73108			0.294386			0.147193	+	0.989108i	$0.452976\pi$
$380$		0			0
$381$	20.7404	−	12.5041i	1.06256	−	0.640607i
$382$	31.6781	−	2.11423i	1.62079	−	0.108173i
$383$	−17.2603	+	17.2603i	−0.881958	+	0.881958i	−0.993734	−	0.111775i	$-0.964346\pi$
$383$	−17.2603	+	17.2603i	−0.881958	+	0.881958i	0.111775	+	0.993734i	$0.464346\pi$
$384$	−4.34593	−	19.1079i	−0.221777	−	0.975097i
$385$		0			0
$386$	−10.5536	+	12.0630i	−0.537162	+	0.613991i
$387$	30.7257	−	9.49390i	1.56188	−	0.482602i
$388$	−1.13435	+	1.48564i	−0.0575880	+	0.0754219i
$389$			27.9300i			1.41611i	0.706159	+	0.708053i	$0.250426\pi$
$389$			27.9300i			1.41611i	−0.706159	+	0.708053i	$0.749574\pi$
$390$		0			0
$391$	31.2089			1.57830
$392$	−18.6781	+	3.78481i	−0.943388	+	0.191162i
$393$	−14.7857	−	3.66313i	−0.745841	−	0.184780i
$394$	−2.25496	−	1.97280i	−0.113603	−	0.0993881i
$395$		0			0
$396$	−14.8315	−	5.45481i	−0.745310	−	0.274115i
$397$	−3.16232	−	3.16232i	−0.158712	−	0.158712i	0.623284	−	0.781996i	$-0.285798\pi$
$397$	−3.16232	−	3.16232i	−0.158712	−	0.158712i	−0.781996	+	0.623284i	$0.785798\pi$
$398$	−17.8022	+	1.18813i	−0.892342	+	0.0595558i
$399$	0.510492	−	0.307770i	0.0255566	−	0.0154077i
$400$		0			0
$401$			11.2530i			0.561950i	0.959715	+	0.280975i	$0.0906578\pi$
$401$			11.2530i			0.561950i	−0.959715	+	0.280975i	$0.909342\pi$
$402$	−0.991740	+	0.691940i	−0.0494635	+	0.0345108i
$403$	−13.0594	+	13.0594i	−0.650536	+	0.650536i
$404$	−6.87548	+	0.921858i	−0.342068	+	0.0458641i
$405$		0			0
$406$	−2.26949	+	2.59409i	−0.112633	+	0.128742i
$407$	7.43124	+	7.43124i	0.368353	+	0.368353i
$408$	18.4453	−	16.9259i	0.913181	−	0.837956i
$409$			5.05965i			0.250183i	0.992145	+	0.125092i	$0.0399225\pi$
$409$			5.05965i			0.250183i	−0.992145	+	0.125092i	$0.960077\pi$
$410$		0			0
$411$	1.88212	+	3.12185i	0.0928384	+	0.153989i
$412$	19.5311	+	14.9129i	0.962229	+	0.734706i
$413$	1.78188	+	1.78188i	0.0876806	+	0.0876806i
$414$	−9.28099	−	24.1919i	−0.456136	−	1.18897i
$415$		0			0
$416$	25.1409	+	12.2124i	1.23264	+	0.598760i
$417$	−22.3649	−	5.54086i	−1.09522	−	0.271337i
$418$	0.166750	+	2.49846i	0.00815600	+	0.122204i
$419$		−	25.1822i		−	1.23023i	−0.788436	−	0.615116i	$-0.789109\pi$
$419$		−	25.1822i		−	1.23023i	0.788436	−	0.615116i	$-0.210891\pi$
$420$		0			0
$421$			31.5091i			1.53566i	0.640654	+	0.767830i	$0.278664\pi$
$421$			31.5091i			1.53566i	−0.640654	+	0.767830i	$0.721336\pi$
$422$	19.7564	−	1.31856i	0.961726	−	0.0641865i
$423$	1.23689	+	4.00303i	0.0601397	+	0.194634i
$424$	1.42823	−	2.15414i	0.0693610	−	0.104614i
$425$		0			0
$426$	20.8287	+	3.70880i	1.00915	+	0.179692i
$427$	2.19796	+	2.19796i	0.106367	+	0.106367i
$428$	−5.33769	+	6.99067i	−0.258007	+	0.337907i
$429$	19.3031	−	11.6376i	0.931963	−	0.561870i
$430$		0			0
$431$		−	13.6082i		−	0.655482i	−0.944768	−	0.327741i	$-0.893713\pi$
$431$		−	13.6082i		−	0.655482i	0.944768	−	0.327741i	$-0.106287\pi$
$432$	−18.6056	−	9.26461i	−0.895161	−	0.445744i
$433$	−2.81500	−	2.81500i	−0.135280	−	0.135280i	0.636224	−	0.771504i	$-0.280495\pi$
$433$	−2.81500	−	2.81500i	−0.135280	−	0.135280i	−0.771504	+	0.636224i	$0.780495\pi$
$434$	−2.03674	−	1.78188i	−0.0977666	−	0.0855330i
$435$		0			0
$436$	−8.21290	+	1.10118i	−0.393327	+	0.0527369i
$437$	−2.90319	+	2.90319i	−0.138878	+	0.138878i
$438$	−32.1770	+	22.4500i	−1.53748	+	1.07270i
$439$			5.56599i			0.265650i	0.991139	+	0.132825i	$0.0424049\pi$
$439$			5.56599i			0.265650i	−0.991139	+	0.132825i	$0.957595\pi$
$440$		0			0
$441$	−9.43663	+	17.8759i	−0.449363	+	0.851232i
$442$	2.37783	+	35.6277i	0.113102	+	1.69464i
$443$	−3.53450	−	3.53450i	−0.167929	−	0.167929i	0.618139	−	0.786069i	$-0.287887\pi$
$443$	−3.53450	−	3.53450i	−0.167929	−	0.167929i	−0.786069	+	0.618139i	$0.787887\pi$
$444$	8.64651	+	10.7842i	0.410345	+	0.511793i
$445$		0			0
$446$	3.37823	−	3.86141i	0.159964	−	0.182843i
$447$	−2.17616	+	8.78376i	−0.102929	+	0.415458i
$448$	−1.54015	+	3.79481i	−0.0727653	+	0.179288i
$449$	21.1895			0.999995			0.499998	−	0.866027i	$-0.333334\pi$
$449$	21.1895			0.999995			0.499998	+	0.866027i	$0.333334\pi$
$450$		0			0
$451$		−	10.7993i		−	0.508518i
$452$	−7.52280	+	9.85246i	−0.353843	+	0.463421i
$453$	19.9243	+	4.93621i	0.936127	+	0.231923i
$454$	20.1169	+	17.5997i	0.944133	+	0.825993i
$455$		0			0
$456$	−0.141348	+	3.29038i	−0.00661921	+	0.154086i
$457$	−16.8790	+	16.8790i	−0.789566	+	0.789566i	−0.981423	−	0.191857i	$-0.938549\pi$
$457$	−16.8790	+	16.8790i	−0.789566	+	0.789566i	0.191857	+	0.981423i	$0.438549\pi$
$458$	1.48428	+	22.2394i	0.0693558	+	1.03918i
$459$	−1.50806	−	26.5100i	−0.0703901	−	1.23738i
$460$		0			0
$461$	−3.58886			−0.167150			−0.0835749	−	0.996502i	$-0.526634\pi$
$461$	−3.58886			−0.167150			−0.0835749	+	0.996502i	$0.526634\pi$
$462$	1.88979	+	2.70859i	0.0879211	+	0.126015i
$463$	26.4996	+	26.4996i	1.23154	+	1.23154i	0.963372	+	0.268168i	$0.0864182\pi$
$463$	26.4996	+	26.4996i	1.23154	+	1.23154i	0.268168	+	0.963372i	$0.413582\pi$
$464$	−5.01641	−	18.3706i	−0.232881	−	0.852834i
$465$		0			0
$466$	19.5979	+	17.1456i	0.907856	+	0.794256i
$467$	−21.1839	+	21.1839i	−0.980274	+	0.980274i	−0.999809	−	0.0195348i	$-0.993781\pi$
$467$	−21.1839	+	21.1839i	−0.980274	+	0.980274i	0.0195348	+	0.999809i	$0.493781\pi$
$468$	26.9100	−	12.4383i	1.24392	−	0.574959i
$469$	0.252730			0.0116700
$470$		0			0
$471$	−17.6454	−	29.2682i	−0.813058	−	1.34861i
$472$	−13.6455	+	2.76504i	−0.628086	+	0.127271i
$473$	19.9641	−	19.9641i	0.917949	−	0.917949i
$474$	−9.83208	−	1.75073i	−0.451603	−	0.0804135i
$475$		0			0
$476$	−5.18563	+	0.695284i	−0.237683	+	0.0318683i
$477$	−0.809302	−	2.61920i	−0.0370554	−	0.119925i
$478$	2.33874	+	35.0421i	0.106972	+	1.60279i
$479$	2.58847			0.118270			0.0591350	−	0.998250i	$-0.481166\pi$
$479$	2.58847			0.118270			0.0591350	+	0.998250i	$0.481166\pi$
$480$		0			0
$481$	−19.7153			−0.898939
$482$	−1.62916	−	24.4103i	−0.0742063	−	1.11186i
$483$	−1.30225	+	5.25636i	−0.0592545	+	0.239173i
$484$	8.05417	−	1.07990i	0.366098	−	0.0490861i
$485$		0			0
$486$	−20.1010	+	9.05261i	−0.911800	+	0.410635i
$487$	−8.29975	+	8.29975i	−0.376098	+	0.376098i	−0.869692	−	0.493595i	$-0.835683\pi$
$487$	−8.29975	+	8.29975i	−0.376098	+	0.376098i	0.493595	+	0.869692i	$0.335683\pi$
$488$	−16.8319	+	3.41069i	−0.761942	+	0.154395i
$489$	−13.9801	+	8.42842i	−0.632201	+	0.381146i
$490$		0			0
$491$	−25.3703			−1.14494			−0.572472	−	0.819924i	$-0.694015\pi$
$491$	−25.3703			−1.14494			−0.572472	+	0.819924i	$0.694015\pi$
$492$	1.55324	−	14.1186i	0.0700256	−	0.636514i
$493$	17.2026	−	17.2026i	0.774767	−	0.774767i
$494$	−3.53544	−	3.09305i	−0.159067	−	0.139163i
$495$		0			0
$496$	14.4236	−	3.93862i	0.647640	−	0.176849i
$497$	−3.12651	−	3.12651i	−0.140243	−	0.140243i
$498$	−24.2588	+	16.9254i	−1.08706	+	0.758447i
$499$	−28.6742			−1.28363			−0.641816	−	0.766859i	$-0.721819\pi$
$499$	−28.6742			−1.28363			−0.641816	+	0.766859i	$0.721819\pi$
$500$		0			0
$501$	19.7870	+	32.8204i	0.884018	+	1.46631i
$502$	−0.0989156	−	1.48208i	−0.00441482	−	0.0661486i
$503$	−5.46994	+	5.46994i	−0.243893	+	0.243893i	−0.818458	−	0.574566i	$-0.805171\pi$
$503$	−5.46994	+	5.46994i	−0.243893	+	0.243893i	0.574566	+	0.818458i	$0.305171\pi$
$504$	2.08107	+	3.81292i	0.0926983	+	0.169841i
$505$		0			0
$506$	−17.1208	−	14.9785i	−0.761114	−	0.665875i
$507$	−4.75362	+	19.1874i	−0.211116	+	0.852140i
$508$	16.9709	−	22.2264i	0.752961	−	0.986138i
$509$		−	21.6722i		−	0.960605i	−0.877103	−	0.480303i	$-0.840527\pi$
$509$		−	21.6722i		−	0.960605i	0.877103	−	0.480303i	$-0.159473\pi$
$510$		0			0
$511$	8.19983			0.362739
$512$	−12.7723	−	18.6780i	−0.564460	−	0.825460i
$513$	2.60636	+	2.32579i	0.115074	+	0.102686i
$514$	2.90132	−	3.31629i	0.127972	−	0.146275i
$515$		0			0
$516$	28.9717	−	23.2289i	1.27541	−	1.02259i
$517$	2.60097	+	2.60097i	0.114391	+	0.114391i
$518$	−0.192374	−	2.88240i	−0.00845244	−	0.126646i
$519$	8.09831	+	13.4325i	0.355476	+	0.589622i
$520$		0			0
$521$		−	13.0236i		−	0.570576i	−0.958442	−	0.285288i	$-0.907911\pi$
$521$		−	13.0236i		−	0.570576i	0.958442	−	0.285288i	$-0.0920893\pi$
$522$	−18.4505	−	8.21900i	−0.807558	−	0.359736i
$523$	−1.57962	+	1.57962i	−0.0690720	+	0.0690720i	−0.740799	−	0.671727i	$-0.765553\pi$
$523$	−1.57962	+	1.57962i	−0.0690720	+	0.0690720i	0.671727	+	0.740799i	$0.265553\pi$
$524$	−17.4332	+	2.33743i	−0.761574	+	0.102111i
$525$		0			0
$526$	−11.2884	−	9.87589i	−0.492198	−	0.430609i
$527$	13.5066	+	13.5066i	0.588356	+	0.588356i
$528$	−18.2423	+	0.432619i	−0.793896	+	0.0188273i
$529$		−	14.2991i		−	0.621698i
$530$		0			0
$531$	−6.89403	+	13.0594i	−0.299176	+	0.566731i
$532$	0.417711	−	0.547068i	0.0181101	−	0.0237184i
$533$	14.3254	+	14.3254i	0.620501	+	0.620501i
$534$	−2.82801	+	15.8821i	−0.122380	+	0.687287i
$535$		0			0
$536$	−0.771608	+	1.16378i	−0.0333284	+	0.0502678i
$537$	0.242633	−	0.979354i	0.0104704	−	0.0422622i
$538$	−29.9137	+	1.99647i	−1.28967	+	0.0860740i
$539$			17.7463i			0.764388i
$540$		0			0
$541$		−	38.6062i		−	1.65981i	−0.557903	−	0.829906i	$-0.688394\pi$
$541$		−	38.6062i		−	1.65981i	0.557903	−	0.829906i	$-0.311606\pi$
$542$	1.38202	+	20.7072i	0.0593629	+	0.889452i
$543$	1.54707	−	6.24454i	0.0663912	−	0.267979i
$544$	12.6305	−	26.0018i	0.541529	−	1.11482i
$545$		0			0
$546$	−6.09981	−	1.08615i	−0.261048	−	0.0464828i
$547$	16.8276	+	16.8276i	0.719498	+	0.719498i	0.968502	−	0.249005i	$-0.0801034\pi$
$547$	16.8276	+	16.8276i	0.719498	+	0.719498i	−0.249005	+	0.968502i	$0.580103\pi$
$548$	3.34552	+	2.55446i	0.142914	+	0.109121i
$549$	−8.50384	+	16.1089i	−0.362935	+	0.687511i
$550$		0			0
$551$			3.20052i			0.136347i
$552$	−20.2288	−	22.0448i	−0.860995	−	0.938288i
$553$	1.47586	+	1.47586i	0.0627597	+	0.0627597i
$554$	−11.5833	+	13.2401i	−0.492129	+	0.562517i
$555$		0			0
$556$	−26.3696	+	3.53561i	−1.11832	+	0.149943i
$557$	15.9467	−	15.9467i	0.675684	−	0.675684i	−0.283337	−	0.959020i	$-0.591441\pi$
$557$	15.9467	−	15.9467i	0.675684	−	0.675684i	0.959020	+	0.283337i	$0.0914414\pi$
$558$	6.45312	−	14.4864i	0.273182	−	0.613257i
$559$			52.9651i			2.24019i
$560$		0			0
$561$	−12.0361	−	19.9641i	−0.508165	−	0.842884i
$562$	0.692584	−	0.0462237i	0.0292149	−	0.00194983i
$563$	−2.27954	−	2.27954i	−0.0960712	−	0.0960712i	0.657438	−	0.753509i	$-0.271640\pi$
$563$	−2.27954	−	2.27954i	−0.0960712	−	0.0960712i	−0.753509	+	0.657438i	$0.771640\pi$
$564$	3.02632	+	3.77451i	0.127431	+	0.158935i
$565$		0			0
$566$	14.2052	+	12.4277i	0.597089	+	0.522375i
$567$	4.52787	+	0.852186i	0.190153	+	0.0357885i
$568$	23.9426	−	4.85156i	1.00461	−	0.203567i
$569$	38.0835			1.59654			0.798272	−	0.602297i	$-0.205748\pi$
$569$	38.0835			1.59654			0.798272	+	0.602297i	$0.205748\pi$
$570$		0			0
$571$			39.4382i			1.65044i	0.564815	+	0.825218i	$0.308948\pi$
$571$			39.4382i			1.65044i	−0.564815	+	0.825218i	$0.691052\pi$
$572$	15.7948	−	20.6861i	0.660414	−	0.864931i
$573$	9.35070	−	37.7429i	0.390631	−	1.57673i
$574$	−1.95461	+	2.23417i	−0.0815839	+	0.0932526i
$575$		0			0
$576$	−23.9116	−	2.05818i	−0.996316	−	0.0857574i
$577$	−15.6617	+	15.6617i	−0.652007	+	0.652007i	−0.953476	−	0.301469i	$-0.902523\pi$
$577$	−15.6617	+	15.6617i	−0.652007	+	0.652007i	0.301469	+	0.953476i	$0.402523\pi$
$578$	12.8594	−	0.858246i	0.534879	−	0.0356983i
$579$	10.1353	+	16.8112i	0.421208	+	0.698650i
$580$		0			0
$581$	6.18200			0.256473
$582$	1.30992	+	1.87748i	0.0542980	+	0.0778240i
$583$	−1.70183	−	1.70183i	−0.0704824	−	0.0704824i
$584$	−25.0348	+	37.7589i	−1.03595	+	1.56248i
$585$		0			0
$586$	−5.28492	+	6.04081i	−0.218318	+	0.249544i
$587$	−8.03380	+	8.03380i	−0.331590	+	0.331590i	−0.853190	−	0.521600i	$-0.825335\pi$
$587$	−8.03380	+	8.03380i	−0.331590	+	0.331590i	0.521600	+	0.853190i	$0.325335\pi$
$588$	−2.55243	+	23.2009i	−0.105260	+	0.956788i
$589$	−2.51288			−0.103541
$590$		0			0
$591$	−3.14255	+	1.89461i	−0.129267	+	0.0779338i
$592$	13.8604	+	7.91438i	0.569657	+	0.325279i
$593$	−15.7097	+	15.7097i	−0.645122	+	0.645122i	−0.951810	−	0.306688i	$-0.900779\pi$
$593$	−15.7097	+	15.7097i	−0.645122	+	0.645122i	0.306688	+	0.951810i	$0.400779\pi$
$594$	−11.8960	+	15.2669i	−0.488098	+	0.626407i
$595$		0			0
$596$	1.38860	+	10.3566i	0.0568793	+	0.424222i
$597$	−5.25482	+	21.2104i	−0.215066	+	0.868083i
$598$	42.5801	−	2.84184i	1.74123	−	0.116211i
$599$	16.2242			0.662902			0.331451	−	0.943473i	$-0.392462\pi$
$599$	16.2242			0.662902			0.331451	+	0.943473i	$0.392462\pi$
$600$		0			0
$601$	30.2446			1.23370			0.616852	−	0.787079i	$-0.288408\pi$
$601$	30.2446			1.23370			0.616852	+	0.787079i	$0.288408\pi$
$602$	−7.74359	+	0.516815i	−0.315605	+	0.0210638i
$603$	0.437230	+	1.41503i	0.0178054	+	0.0576247i
$604$	23.4920	−	3.14978i	0.955875	−	0.128163i
$605$		0			0
$606$	−1.48940	+	8.36449i	−0.0605028	+	0.339784i
$607$	−26.6799	+	26.6799i	−1.08290	+	1.08290i	−0.0866645	+	0.996238i	$0.527621\pi$
$607$	−26.6799	+	26.6799i	−1.08290	+	1.08290i	−0.996238	+	0.0866645i	$0.972379\pi$
$608$	1.24385	+	3.59374i	0.0504448	+	0.145745i
$609$	2.17954	+	3.61516i	0.0883194	+	0.146494i
$610$		0			0
$611$	−6.90044			−0.279162
$612$	−12.8642	−	27.8314i	−0.520003	−	1.12502i
$613$	−11.2416	+	11.2416i	−0.454046	+	0.454046i	−0.896695	−	0.442649i	$-0.854039\pi$
$613$	−11.2416	+	11.2416i	−0.454046	+	0.454046i	0.442649	+	0.896695i	$0.354039\pi$
$614$	−10.5469	+	12.0554i	−0.425637	+	0.486515i
$615$		0			0
$616$	3.17847	+	2.10738i	0.128064	+	0.0849088i
$617$	−15.8402	−	15.8402i	−0.637702	−	0.637702i	0.312286	−	0.949988i	$-0.398905\pi$
$617$	−15.8402	−	15.8402i	−0.637702	−	0.637702i	−0.949988	+	0.312286i	$0.898905\pi$
$618$	24.6825	−	17.2210i	0.992875	−	0.692732i
$619$	−39.2267			−1.57665			−0.788327	−	0.615256i	$-0.789052\pi$
$619$	−39.2267			−1.57665			−0.788327	+	0.615256i	$0.789052\pi$
$620$		0			0
$621$	−31.6832	+	1.80234i	−1.27140	+	0.0723254i
$622$	18.1851	−	1.21369i	0.729156	−	0.0486645i
$623$	2.38400	−	2.38400i	0.0955130	−	0.0955130i
$624$	23.6248	−	24.7726i	0.945749	−	0.991696i
$625$		0			0
$626$	−16.1966	+	18.5132i	−0.647346	+	0.739935i
$627$	2.97679	+	0.737493i	0.118882	+	0.0294526i
$628$	−31.3652	−	23.9487i	−1.25161	−	0.955658i
$629$			20.3903i			0.813016i
$630$		0			0
$631$	9.52029			0.378997			0.189498	−	0.981881i	$-0.439314\pi$
$631$	9.52029			0.378997			0.189498	+	0.981881i	$0.439314\pi$
$632$	−11.3020	+	2.29016i	−0.449569	+	0.0910977i
$633$	5.83166	−	23.5387i	0.231788	−	0.935580i
$634$	−13.9112	−	12.1705i	−0.552483	−	0.483350i
$635$		0			0
$636$	−1.98013	−	2.46967i	−0.0785174	−	0.0979290i
$637$	−23.5407	−	23.5407i	−0.932717	−	0.932717i
$638$	−17.6934	+	1.18088i	−0.700489	+	0.0467513i
$639$	12.0963	−	22.9142i	0.478524	−	0.906472i
$640$		0			0
$641$		−	42.2578i		−	1.66908i	−0.550945	−	0.834541i	$-0.685733\pi$
$641$		−	42.2578i		−	1.66908i	0.550945	−	0.834541i	$-0.314267\pi$
$642$	6.16383	+	8.83447i	0.243267	+	0.348669i
$643$	−15.1060	+	15.1060i	−0.595722	+	0.595722i	−0.939171	−	0.343449i	$-0.888405\pi$
$643$	−15.1060	+	15.1060i	−0.595722	+	0.595722i	0.343449	+	0.939171i	$0.388405\pi$
$644$	0.830963	+	6.19756i	0.0327445	+	0.244218i
$645$		0			0
$646$	−3.19895	+	3.65649i	−0.125861	+	0.143863i
$647$	−11.1088	−	11.1088i	−0.436732	−	0.436732i	0.454178	−	0.890911i	$-0.349933\pi$
$647$	−11.1088	−	11.1088i	−0.436732	−	0.436732i	−0.890911	+	0.454178i	$0.849933\pi$
$648$	−17.7482	+	18.2483i	−0.697215	+	0.716863i
$649$			12.9648i			0.508912i
$650$		0			0
$651$	−2.83843	+	1.71126i	−0.111247	+	0.0670695i
$652$	−11.4392	+	14.9817i	−0.447995	+	0.586729i
$653$	−15.4673	−	15.4673i	−0.605283	−	0.605283i	0.336426	−	0.941710i	$-0.390782\pi$
$653$	−15.4673	−	15.4673i	−0.605283	−	0.605283i	−0.941710	+	0.336426i	$0.890782\pi$
$654$	−1.77912	+	9.99156i	−0.0695692	+	0.390701i
$655$		0			0
$656$	−4.32042	−	15.8218i	−0.168684	−	0.617738i
$657$	14.1859	+	45.9108i	0.553445	+	1.79115i
$658$	−0.0673320	−	1.00886i	−0.00262487	−	0.0393293i
$659$		−	5.93274i		−	0.231107i	−0.993301	−	0.115553i	$-0.963136\pi$
$659$		−	5.93274i		−	0.231107i	0.993301	−	0.115553i	$-0.0368641\pi$
$660$		0			0
$661$		−	28.1054i		−	1.09317i	−0.837403	−	0.546586i	$-0.815927\pi$
$661$		−	28.1054i		−	1.09317i	0.837403	−	0.546586i	$-0.184073\pi$
$662$	−31.3760	+	2.09406i	−1.21946	+	0.0813881i
$663$	42.4486	+	10.5165i	1.64857	+	0.408429i
$664$	−18.8742	+	28.4671i	−0.732461	+	1.10474i
$665$		0			0
$666$	15.8057	−	6.06373i	0.612460	−	0.234965i
$667$	−20.5596	−	20.5596i	−0.796069	−	0.796069i
$668$	35.1719	+	26.8553i	1.36084	+	1.03906i
$669$	−3.24434	−	5.38133i	−0.125433	−	0.208054i
$670$		0			0
$671$			15.9922i			0.617370i
$672$	3.85231	+	3.21227i	0.148606	+	0.123916i
$673$	15.2277	+	15.2277i	0.586986	+	0.586986i	0.936814	−	0.349828i	$-0.113760\pi$
$673$	15.2277	+	15.2277i	0.586986	+	0.586986i	−0.349828	+	0.936814i	$0.613760\pi$
$674$	−13.5276	−	11.8349i	−0.521063	−	0.455862i
$675$		0			0
$676$	3.03327	+	22.6230i	0.116664	+	0.870116i
$677$	−28.2327	+	28.2327i	−1.08507	+	1.08507i	−0.0890415	+	0.996028i	$0.528380\pi$
$677$	−28.2327	+	28.2327i	−1.08507	+	1.08507i	−0.996028	+	0.0890415i	$0.971620\pi$
$678$	8.68714	+	12.4511i	0.333628	+	0.478180i
$679$		−	0.478448i		−	0.0183611i
$680$		0			0
$681$	28.0352	−	16.9021i	1.07431	−	0.647691i
$682$	−0.927161	−	13.8919i	−0.0355028	−	0.531950i
$683$	−26.1080	−	26.1080i	−0.998996	−	0.998996i	0.00100333	−	0.999999i	$-0.499681\pi$
$683$	−26.1080	−	26.1080i	−0.998996	−	0.998996i	−0.999999	+	0.00100333i	$0.999681\pi$
$684$	3.78567	+	1.39232i	0.144749	+	0.0532366i
$685$		0			0
$686$	6.54891	−	7.48559i	0.250039	−	0.285801i
$687$	26.4971	+	6.56460i	1.01093	+	0.250455i
$688$	21.2620	−	37.2359i	0.810607	−	1.41961i
$689$	4.51498			0.172007
$690$		0			0
$691$		−	9.65683i		−	0.367363i	−0.982986	−	0.183682i	$-0.941198\pi$
$691$		−	9.65683i		−	0.367363i	0.982986	−	0.183682i	$-0.0588015\pi$
$692$	14.3949	+	10.9912i	0.547213	+	0.417822i
$693$	3.86468	−	1.19414i	0.146807	−	0.0453617i
$694$	−13.9310	−	12.1878i	−0.528814	−	0.462643i
$695$		0			0
$696$	−23.3016	−	1.00098i	−0.883244	−	0.0379422i
$697$	14.8159	−	14.8159i	0.561191	−	0.561191i
$698$	−1.65674	−	24.8234i	−0.0627085	−	0.939580i
$699$	27.3120	−	16.4661i	1.03303	−	0.622804i
$700$		0			0
$701$	−22.2509			−0.840403			−0.420202	−	0.907431i	$-0.638041\pi$
$701$	−22.2509			−0.840403			−0.420202	+	0.907431i	$0.638041\pi$
$702$	−4.47149	−	36.0318i	−0.168766	−	1.35993i
$703$	−1.89679	−	1.89679i	−0.0715390	−	0.0715390i
$704$	−19.4083	+	8.20233i	−0.731478	+	0.309137i
$705$		0			0
$706$	−19.5161	−	17.0741i	−0.734499	−	0.642591i
$707$	1.25556	−	1.25556i	0.0472202	−	0.0472202i
$708$	−1.86470	+	16.9497i	−0.0700799	+	0.637008i
$709$	22.1309			0.831144			0.415572	−	0.909560i	$-0.363581\pi$
$709$	22.1309			0.831144			0.415572	+	0.909560i	$0.363581\pi$
$710$		0			0
$711$	−5.71003	+	10.8166i	−0.214143	+	0.405653i
$712$	3.69938	+	18.2565i	0.138640	+	0.684192i
$713$	16.1423	−	16.1423i	0.604533	−	0.604533i
$714$	−1.12334	+	6.30867i	−0.0420399	+	0.236096i
$715$		0			0
$716$	−0.154823	−	1.15472i	−0.00578602	−	0.0431538i
$717$	41.7509	+	10.3437i	1.55922	+	0.386292i
$718$	1.55621	+	23.3172i	0.0580772	+	0.870189i
$719$	−4.65932			−0.173763			−0.0868817	−	0.996219i	$-0.527690\pi$
$719$	−4.65932			−0.173763			−0.0868817	+	0.996219i	$0.527690\pi$
$720$		0			0
$721$	−6.28997			−0.234251
$722$	1.74679	+	26.1727i	0.0650088	+	0.974047i
$723$	−29.0836	−	7.20539i	−1.08163	−	0.267971i
$724$	−0.987182	−	7.36268i	−0.0366883	−	0.273632i
$725$		0			0
$726$	1.74474	−	9.79845i	0.0647532	−	0.363654i
$727$	28.8504	−	28.8504i	1.07000	−	1.07000i	0.0726443	−	0.997358i	$-0.476856\pi$
$727$	28.8504	−	28.8504i	1.07000	−	1.07000i	0.997358	−	0.0726443i	$-0.0231438\pi$
$728$	−7.01174	+	1.42081i	−0.259872	+	0.0526588i
$729$	3.06195	+	26.8258i	0.113406	+	0.993549i
$730$		0			0
$731$	54.7787			2.02606
$732$	−2.30013	+	20.9075i	−0.0850151	+	0.772765i
$733$	−23.8359	+	23.8359i	−0.880398	+	0.880398i	−0.993575	−	0.113177i	$-0.963897\pi$
$733$	−23.8359	+	23.8359i	−0.880398	+	0.880398i	0.113177	+	0.993575i	$0.463897\pi$
$734$	−36.8636	−	32.2508i	−1.36066	−	1.19040i
$735$		0			0
$736$	−31.0758	−	15.0952i	−1.14547	−	0.556418i
$737$	0.919420	+	0.919420i	0.0338673	+	0.0338673i
$738$	−15.8906	−	7.07867i	−0.584943	−	0.260569i
$739$	29.6476			1.09060			0.545302	−	0.838240i	$-0.316415\pi$
$739$	29.6476			1.09060			0.545302	+	0.838240i	$0.316415\pi$
$740$		0			0
$741$	−4.92704	+	2.97046i	−0.180999	+	0.109122i
$742$	0.0440556	+	0.660098i	0.00161733	+	0.0242330i
$743$	−8.41878	+	8.41878i	−0.308855	+	0.308855i	−0.844465	−	0.535610i	$-0.820082\pi$
$743$	−8.41878	+	8.41878i	−0.308855	+	0.308855i	0.535610	+	0.844465i	$0.320082\pi$
$744$	0.785920	−	18.2952i	0.0288132	−	0.670733i
$745$		0			0
$746$	0.611258	+	0.534771i	0.0223797	+	0.0195793i
$747$	10.6950	+	34.6130i	0.391310	+	1.26642i
$748$	−21.3945	−	16.3356i	−0.782259	−	0.597290i
$749$		−	2.25134i		−	0.0822620i
$750$		0			0
$751$	−31.5577			−1.15156			−0.575778	−	0.817606i	$-0.695301\pi$
$751$	−31.5577			−1.15156			−0.575778	+	0.817606i	$0.695301\pi$
$752$	4.85119	+	2.77007i	0.176905	+	0.101014i
$753$	−1.76583	−	0.437480i	−0.0643503	−	0.0159426i
$754$	21.9041	−	25.0370i	0.797700	−	0.911793i
$755$		0			0
$756$	5.22428	−	1.00533i	0.190005	−	0.0365633i
$757$	−25.5118	−	25.5118i	−0.927244	−	0.927244i	0.0702832	−	0.997527i	$-0.477610\pi$
$757$	−25.5118	−	25.5118i	−0.927244	−	0.927244i	−0.997527	+	0.0702832i	$0.977610\pi$
$758$	−0.539733	−	8.08698i	−0.0196040	−	0.293732i
$759$	−23.8599	+	14.3848i	−0.866059	+	0.522137i
$760$		0			0
$761$		−	2.30287i		−	0.0834789i	−0.999129	−	0.0417394i	$-0.986710\pi$
$761$		−	2.30287i		−	0.0834789i	0.999129	−	0.0417394i	$-0.0132899\pi$
$762$	−19.5975	−	28.0887i	−0.709944	−	1.01754i
$763$	1.49979	−	1.49979i	0.0542962	−	0.0542962i
$764$	−5.96666	−	44.5011i	−0.215866	−	1.60999i
$765$		0			0
$766$	25.9810	+	22.7300i	0.938733	+	0.821269i
$767$	−17.1979	−	17.1979i	−0.620981	−	0.620981i
$768$	−26.5534	+	7.93195i	−0.958164	+	0.286220i
$769$		−	46.5571i		−	1.67889i	−0.543442	−	0.839447i	$-0.682879\pi$
$769$		−	46.5571i		−	1.67889i	0.543442	−	0.839447i	$-0.317121\pi$
$770$		0			0
$771$	−2.78633	−	4.62164i	−0.100347	−	0.166444i
$772$	18.0157	+	13.7558i	0.648399	+	0.495082i
$773$	19.2506	+	19.2506i	0.692397	+	0.692397i	0.962759	−	0.270362i	$-0.0871434\pi$
$773$	19.2506	+	19.2506i	0.692397	+	0.692397i	−0.270362	+	0.962759i	$0.587143\pi$
$774$	−16.2902	−	42.4622i	−0.585541	−	1.52627i
$775$		0			0
$776$	2.20318	+	1.46074i	0.0790894	+	0.0524377i
$777$	−3.43424	−	0.850825i	−0.123203	−	0.0305232i
$778$	39.4113	−	2.63035i	1.41296	−	0.0943024i
$779$			2.75647i			0.0987608i
$780$		0			0
$781$		−	22.7481i		−	0.813993i
$782$	−2.93914	−	44.0381i	−0.105104	−	1.57480i
$783$	−16.4706	+	18.4575i	−0.588611	+	0.659618i
$784$	7.09969	+	25.9998i	0.253560	+	0.928564i
$785$		0			0
$786$	−3.77648	+	21.2087i	−0.134702	+	0.756490i
$787$	−3.79411	−	3.79411i	−0.135246	−	0.135246i	0.636243	−	0.771489i	$-0.280488\pi$
$787$	−3.79411	−	3.79411i	−0.135246	−	0.135246i	−0.771489	+	0.636243i	$0.780488\pi$
$788$	−2.57140	+	3.36771i	−0.0916023	+	0.119970i
$789$	−15.7317	+	9.48447i	−0.560064	+	0.337656i
$790$		0			0
$791$		−	3.17297i		−	0.112818i
$792$	−6.30037	+	21.4420i	−0.223874	+	0.761909i
$793$	−21.2138	−	21.2138i	−0.753324	−	0.753324i
$794$	−4.16445	+	4.76008i	−0.147791	+	0.168929i
$795$		0			0
$796$	3.35309	+	25.0083i	0.118847	+	0.886396i
$797$	30.0747	−	30.0747i	1.06530	−	1.06530i	0.0675880	−	0.997713i	$-0.478470\pi$
$797$	30.0747	−	30.0747i	1.06530	−	1.06530i	0.997713	−	0.0675880i	$-0.0215303\pi$
$798$	−0.482362	−	0.691357i	−0.0170754	−	0.0244738i
$799$			7.13671i			0.252479i
$800$		0			0
$801$	17.4724	+	9.22362i	0.617356	+	0.325901i
$802$	15.8789	−	1.05977i	0.560702	−	0.0374218i
$803$	29.8306	+	29.8306i	1.05270	+	1.05270i
$804$	1.06978	+	1.33425i	0.0377281	+	0.0470555i
$805$		0			0
$806$	19.6577	+	17.1979i	0.692413	+	0.605771i
$807$	−8.82990	+	35.6407i	−0.310827	+	1.25461i
$808$	1.94832	+	9.61499i	0.0685416	+	0.338254i
$809$	−21.7890			−0.766061			−0.383031	−	0.923736i	$-0.625120\pi$
$809$	−21.7890			−0.766061			−0.383031	+	0.923736i	$0.625120\pi$
$810$		0			0
$811$			2.48698i			0.0873295i	0.999046	+	0.0436648i	$0.0139033\pi$
$811$			2.48698i			0.0873295i	−0.999046	+	0.0436648i	$0.986097\pi$
$812$	3.87418	+	2.95811i	0.135957	+	0.103809i
$813$	24.6716	+	6.11234i	0.865272	+	0.214369i
$814$	9.78619	−	11.1859i	0.343006	−	0.392065i
$815$		0			0
$816$	−25.6208	−	24.4337i	−0.896907	−	0.855352i
$817$	−5.09575	+	5.09575i	−0.178278	+	0.178278i
$818$	7.13954	−	0.476499i	0.249628	−	0.0166604i
$819$	−3.54250	+	6.71058i	−0.123785	+	0.234487i
$820$		0			0
$821$	7.50855			0.262050			0.131025	−	0.991379i	$-0.458173\pi$
$821$	7.50855			0.262050			0.131025	+	0.991379i	$0.458173\pi$
$822$	4.22791	−	2.94982i	0.147465	−	0.102887i
$823$	−33.8234	−	33.8234i	−1.17901	−	1.17901i	−0.979997	−	0.199012i	$-0.936227\pi$
$823$	−33.8234	−	33.8234i	−1.17901	−	1.17901i	−0.199012	−	0.979997i	$-0.563773\pi$
$824$	19.2038	−	28.9643i	0.668997	−	1.00902i
$825$		0			0
$826$	2.34656	−	2.68218i	0.0816471	−	0.0933249i
$827$	20.6186	−	20.6186i	0.716979	−	0.716979i	−0.251007	−	0.967985i	$-0.580762\pi$
$827$	20.6186	−	20.6186i	0.716979	−	0.716979i	0.967985	+	0.251007i	$0.0807616\pi$
$828$	−33.2625	+	15.3745i	−1.15595	+	0.534300i
$829$	16.9499			0.588694			0.294347	−	0.955699i	$-0.404898\pi$
$829$	16.9499			0.588694			0.294347	+	0.955699i	$0.404898\pi$
$830$		0			0
$831$	11.1243	+	18.4516i	0.385896	+	0.640079i
$832$	14.8649	−	36.6258i	0.515346	−	1.26977i
$833$	−24.3468	+	24.3468i	−0.843565	+	0.843565i
$834$	−5.71232	+	32.0804i	−0.197801	+	1.11085i
$835$		0			0
$836$	3.50981	−	0.470593i	0.121389	−	0.0162758i
$837$	−14.4919	−	12.9318i	−0.500912	−	0.446990i
$838$	−35.5340	+	2.37157i	−1.22750	+	0.0819246i
$839$	31.3869			1.08360			0.541798	−	0.840509i	$-0.317744\pi$
$839$	31.3869			1.08360			0.541798	+	0.840509i	$0.317744\pi$
$840$		0			0
$841$	6.33479			0.218441
$842$	44.4617	−	2.96742i	1.53225	−	0.102264i
$843$	0.204436	−	0.825179i	0.00704116	−	0.0284207i
$844$	−3.72117	−	27.7535i	−0.128088	−	0.955316i
$845$		0			0
$846$	5.53209	−	2.12234i	0.190197	−	0.0729674i
$847$	−1.47081	+	1.47081i	−0.0505375	+	0.0505375i
$848$	−3.17415	−	1.81247i	−0.109001	−	0.0622405i
$849$	19.7966	−	11.9351i	0.679418	−	0.409613i
$850$		0			0
$851$	24.3693			0.835369
$852$	3.27183	−	29.7401i	0.112091	−	1.01888i
$853$	4.93576	−	4.93576i	0.168997	−	0.168997i	−0.617541	−	0.786538i	$-0.711871\pi$
$853$	4.93576	−	4.93576i	0.168997	−	0.168997i	0.786538	+	0.617541i	$0.211871\pi$
$854$	2.89449	−	3.30849i	0.0990476	−	0.113214i
$855$		0			0
$856$	10.3670	+	6.87353i	0.354338	+	0.234932i
$857$	23.9182	+	23.9182i	0.817029	+	0.817029i	0.985676	−	0.168648i	$-0.0539400\pi$
$857$	23.9182	+	23.9182i	0.817029	+	0.817029i	−0.168648	+	0.985676i	$0.553940\pi$
$858$	−18.2394	−	26.1421i	−0.622685	−	0.892478i
$859$	−22.2708			−0.759871			−0.379935	−	0.925013i	$-0.624054\pi$
$859$	−22.2708			−0.759871			−0.379935	+	0.925013i	$0.624054\pi$
$860$		0			0
$861$	1.87714	+	3.11358i	0.0639728	+	0.106111i
$862$	−19.2021	+	1.28157i	−0.654027	+	0.0436503i
$863$	37.8907	−	37.8907i	1.28982	−	1.28982i	0.354918	−	0.934897i	$-0.384509\pi$
$863$	37.8907	−	37.8907i	1.28982	−	1.28982i	0.934897	−	0.354918i	$-0.115491\pi$
$864$	−11.3208	+	27.1263i	−0.385143	+	0.922857i
$865$		0			0
$866$	−3.70706	+	4.23727i	−0.125971	+	0.143988i
$867$	3.79581	−	15.3213i	0.128912	−	0.520338i
$868$	−2.32255	+	3.04180i	−0.0788326	+	0.103245i
$869$			10.7382i			0.364267i
$870$		0			0
$871$	−2.43924			−0.0826506
$872$	2.32731	+	11.4853i	0.0788125	+	0.388942i
$873$	2.67882	−	0.827726i	0.0906645	−	0.0280143i
$874$	4.37002	+	3.82320i	0.147818	+	0.129322i
$875$		0			0
$876$	34.7089	+	43.2899i	1.17270	+	1.46263i
$877$	19.4977	+	19.4977i	0.658392	+	0.658392i	0.954999	−	0.296608i	$-0.0958553\pi$
$877$	19.4977	+	19.4977i	0.658392	+	0.658392i	−0.296608	+	0.954999i	$0.595855\pi$
$878$	7.85403	−	0.524185i	0.265061	−	0.0176904i
$879$	5.07546	+	8.41857i	0.171191	+	0.283951i
$880$		0			0
$881$			36.8489i			1.24147i	0.784021	+	0.620735i	$0.213166\pi$
$881$			36.8489i			1.24147i	−0.784021	+	0.620735i	$0.786834\pi$
$882$	26.1129	+	11.6323i	0.879267	+	0.391680i
$883$	25.6982	−	25.6982i	0.864813	−	0.864813i	−0.127079	−	0.991893i	$-0.540560\pi$
$883$	25.6982	−	25.6982i	0.864813	−	0.864813i	0.991893	+	0.127079i	$0.0405602\pi$
$884$	50.0494	−	6.71058i	1.68334	−	0.225701i
$885$		0			0
$886$	−4.65458	+	5.32031i	−0.156374	+	0.178739i
$887$	19.3369	+	19.3369i	0.649270	+	0.649270i	0.952817	−	0.303547i	$-0.0981709\pi$
$887$	19.3369	+	19.3369i	0.649270	+	0.649270i	−0.303547	+	0.952817i	$0.598171\pi$
$888$	14.4029	−	13.2165i	0.483331	−	0.443516i
$889$			7.15799i			0.240071i
$890$		0			0
$891$	13.3720	+	19.5724i	0.447978	+	0.655699i
$892$	−5.76689	−	4.40328i	−0.193090	−	0.147433i
$893$	−0.663887	−	0.663887i	−0.0222161	−	0.0222161i
$894$	12.5995	+	2.24349i	0.421390	+	0.0750337i
$895$		0			0
$896$	5.49980	+	1.81589i	0.183736	+	0.0606645i
$897$	12.5688	−	50.7321i	0.419658	−	1.69389i
$898$	−1.99555	−	29.9000i	−0.0665925	−	0.997775i
$899$		−	17.7955i		−	0.593514i
$900$		0			0
$901$		−	4.66958i		−	0.155566i
$902$	−15.2386	+	1.01704i	−0.507389	+	0.0338636i
$903$	−2.28574	+	9.22610i	−0.0760648	+	0.307025i
$904$	14.6110	+	9.68737i	0.485956	+	0.322197i
$905$		0			0
$906$	5.08896	−	28.5796i	0.169069	−	0.949494i
$907$	−16.8535	−	16.8535i	−0.559613	−	0.559613i	0.369585	−	0.929197i	$-0.379500\pi$
$907$	−16.8535	−	16.8535i	−0.559613	−	0.559613i	−0.929197	+	0.369585i	$0.879500\pi$
$908$	22.9399	−	30.0439i	0.761287	−	0.997042i
$909$	9.20201	+	4.85772i	0.305212	+	0.161120i
$910$		0			0
$911$		−	31.3998i		−	1.04032i	−0.854068	−	0.520161i	$-0.825872\pi$
$911$		−	31.3998i		−	1.04032i	0.854068	−	0.520161i	$-0.174128\pi$
$912$	4.65628	−	0.110424i	0.154185	−	0.00365652i
$913$	22.4898	+	22.4898i	0.744304	+	0.744304i
$914$	25.4071	+	22.2279i	0.840393	+	0.735234i
$915$		0			0
$916$	31.2417	−	4.18886i	1.03225	−	0.138404i
$917$	3.18356	−	3.18356i	0.105130	−	0.105130i
$918$	−37.2656	+	4.62460i	−1.22995	+	0.152635i
$919$		−	26.0422i		−	0.859054i	−0.903054	−	0.429527i	$-0.858680\pi$
$919$		−	26.0422i		−	0.859054i	0.903054	−	0.429527i	$-0.141320\pi$
$920$		0			0
$921$	10.1289	+	16.8006i	0.333757	+	0.553597i
$922$	0.337986	+	5.06414i	0.0111310	+	0.166779i
$923$	30.1757	+	30.1757i	0.993245	+	0.993245i
$924$	3.64405	−	2.92172i	0.119881	−	0.0961177i
$925$		0			0
$926$	34.8972	−	39.8885i	1.14679	−	1.31082i
$927$	−10.8818	−	35.2175i	−0.357405	−	1.15669i
$928$	−25.4499	+	8.80860i	−0.835433	+	0.289157i
$929$	−16.2184			−0.532108			−0.266054	−	0.963958i	$-0.585720\pi$
$929$	−16.2184			−0.532108			−0.266054	+	0.963958i	$0.585720\pi$
$930$		0			0
$931$		−	4.52968i		−	0.148454i
$932$	22.3481	−	29.2688i	0.732036	−	0.958733i
$933$	5.36785	−	21.6666i	0.175736	−	0.709333i
$934$	31.8871	+	27.8970i	1.04338	+	0.912819i
$935$		0			0
$936$	−20.0856	−	36.8006i	−0.656518	−	1.20287i
$937$	14.3578	−	14.3578i	0.469050	−	0.469050i	−0.432557	−	0.901607i	$-0.642389\pi$
$937$	14.3578	−	14.3578i	0.469050	−	0.469050i	0.901607	+	0.432557i	$0.142389\pi$
$938$	−0.0238012	−	0.356621i	−0.000777138	−	0.0116441i
$939$	15.5547	+	25.8002i	0.507607	+	0.841959i
$940$		0			0
$941$	27.3264			0.890817			0.445408	−	0.895328i	$-0.353059\pi$
$941$	27.3264			0.890817			0.445408	+	0.895328i	$0.353059\pi$
$942$	−39.6378	+	27.6554i	−1.29147	+	0.901061i
$943$	−17.7071	−	17.7071i	−0.576621	−	0.576621i
$944$	5.18676	+	18.9944i	0.168815	+	0.618216i
$945$		0			0
$946$	−30.0509	−	26.2906i	−0.977040	−	0.854783i
$947$	17.5336	−	17.5336i	0.569766	−	0.569766i	−0.362297	−	0.932063i	$-0.618007\pi$
$947$	17.5336	−	17.5336i	0.569766	−	0.569766i	0.932063	+	0.362297i	$0.118007\pi$
$948$	−1.54445	+	14.0387i	−0.0501615	+	0.455955i
$949$	−79.1412			−2.56903
$950$		0			0
$951$	−19.3868	+	11.6881i	−0.628661	+	0.379012i
$952$	1.46946	+	7.25183i	0.0476255	+	0.235033i
$953$	19.5859	−	19.5859i	0.634449	−	0.634449i	−0.314732	−	0.949181i	$-0.601915\pi$
$953$	19.5859	−	19.5859i	0.634449	−	0.634449i	0.949181	+	0.314732i	$0.101915\pi$
$954$	−3.61966	+	1.38865i	−0.117191	+	0.0449593i
$955$		0			0
$956$	49.2268	−	6.60028i	1.59211	−	0.213468i
$957$	−5.22272	+	21.0808i	−0.168827	+	0.681446i
$958$	−0.243772	−	3.65252i	−0.00787593	−	0.118008i
$959$	−1.07742			−0.0347917
$960$		0			0
$961$	−17.0279			−0.549287
$962$	1.85671	+	27.8197i	0.0598628	+	0.896943i
$963$	12.6052	−	3.89486i	0.406197	−	0.125510i
$964$	−34.2913	+	4.59774i	−1.10445	+	0.148083i
$965$		0			0
$966$	7.53975	+	1.34255i	0.242588	+	0.0431958i
$967$	16.0917	−	16.0917i	0.517475	−	0.517475i	−0.399332	−	0.916806i	$-0.630758\pi$
$967$	16.0917	−	16.0917i	0.517475	−	0.517475i	0.916806	+	0.399332i	$0.130758\pi$
$968$	−2.28232	−	11.2633i	−0.0733567	−	0.362017i
$969$	3.07217	+	5.09575i	0.0986922	+	0.163699i
$970$		0			0
$971$	−56.1374			−1.80154			−0.900768	−	0.434301i	$-0.856995\pi$
$971$	−56.1374			−1.80154			−0.900768	+	0.434301i	$0.856995\pi$
$972$	14.6669	+	27.5115i	0.470442	+	0.882431i
$973$	4.81546	−	4.81546i	0.154377	−	0.154377i
$974$	12.4932	+	10.9299i	0.400308	+	0.350217i
$975$		0			0
$976$	6.39791	+	23.4298i	0.204792	+	0.749969i
$977$	−1.50786	−	1.50786i	−0.0482409	−	0.0482409i	0.682575	−	0.730816i	$-0.260860\pi$
$977$	−1.50786	−	1.50786i	−0.0482409	−	0.0482409i	−0.730816	+	0.682575i	$0.760860\pi$
$978$	13.2097	+	18.9332i	0.422400	+	0.605416i
$979$	17.3458			0.554373
$980$		0			0
$981$	10.9920	+	5.80265i	0.350948	+	0.185264i
$982$	2.38928	+	35.7993i	0.0762450	+	1.14240i
$983$	−20.1605	+	20.1605i	−0.643021	+	0.643021i	−0.951297	−	0.308276i	$-0.900248\pi$
$983$	−20.1605	+	20.1605i	−0.643021	+	0.643021i	0.308276	+	0.951297i	$0.400248\pi$
$984$	−20.0686	−	0.862105i	−0.639765	−	0.0274829i
$985$		0			0
$986$	−25.8943	−	22.6541i	−0.824641	−	0.721454i
$987$	−1.20200	−	0.297793i	−0.0382601	−	0.00947885i
$988$	−4.03156	+	5.28006i	−0.128261	+	0.167981i
$989$		−	65.4683i		−	2.08177i
$990$		0			0
$991$	36.8471			1.17049			0.585244	−	0.810858i	$-0.300999\pi$
$991$	36.8471			1.17049			0.585244	+	0.810858i	$0.300999\pi$
$992$	−6.91605	−	19.9819i	−0.219585	−	0.634425i
$993$	−9.26153	+	37.3829i	−0.293906	+	1.18631i
$994$	−4.11729	+	4.70618i	−0.130593	+	0.149271i
$995$		0			0
$996$	26.1677	+	32.6370i	0.829154	+	1.03414i
$997$	−28.1250	−	28.1250i	−0.890726	−	0.890726i	0.103865	−	0.994591i	$-0.466879\pi$
$997$	−28.1250	−	28.1250i	−0.890726	−	0.890726i	−0.994591	+	0.103865i	$0.966879\pi$
$998$	2.70043	+	40.4614i	0.0854806	+	1.28078i
$999$	−1.17756	−	20.7002i	−0.0372563	−	0.654926i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.w.j.293.8		32
3.2	odd	2	inner	600.2.w.j.293.9		32
5.2	odd	4	inner	600.2.w.j.557.16		32
5.3	odd	4		120.2.w.c.77.1	yes	32
5.4	even	2		120.2.w.c.53.9	yes	32
8.5	even	2	inner	600.2.w.j.293.1		32
15.2	even	4	inner	600.2.w.j.557.1		32
15.8	even	4		120.2.w.c.77.16	yes	32
15.14	odd	2		120.2.w.c.53.8	yes	32
20.3	even	4		480.2.bi.c.17.7		32
20.19	odd	2		480.2.bi.c.113.2		32
24.5	odd	2	inner	600.2.w.j.293.16		32
40.3	even	4		480.2.bi.c.17.10		32
40.13	odd	4		120.2.w.c.77.8	yes	32
40.19	odd	2		480.2.bi.c.113.15		32
40.29	even	2		120.2.w.c.53.16	yes	32
40.37	odd	4	inner	600.2.w.j.557.9		32
60.23	odd	4		480.2.bi.c.17.15		32
60.59	even	2		480.2.bi.c.113.10		32
120.29	odd	2		120.2.w.c.53.1	✓	32
120.53	even	4		120.2.w.c.77.9	yes	32
120.59	even	2		480.2.bi.c.113.7		32
120.77	even	4	inner	600.2.w.j.557.8		32
120.83	odd	4		480.2.bi.c.17.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.w.c.53.1	✓	32	120.29	odd	2
120.2.w.c.53.8	yes	32	15.14	odd	2
120.2.w.c.53.9	yes	32	5.4	even	2
120.2.w.c.53.16	yes	32	40.29	even	2
120.2.w.c.77.1	yes	32	5.3	odd	4
120.2.w.c.77.8	yes	32	40.13	odd	4
120.2.w.c.77.9	yes	32	120.53	even	4
120.2.w.c.77.16	yes	32	15.8	even	4
480.2.bi.c.17.2		32	120.83	odd	4
480.2.bi.c.17.7		32	20.3	even	4
480.2.bi.c.17.10		32	40.3	even	4
480.2.bi.c.17.15		32	60.23	odd	4
480.2.bi.c.113.2		32	20.19	odd	2
480.2.bi.c.113.7		32	120.59	even	2
480.2.bi.c.113.10		32	60.59	even	2
480.2.bi.c.113.15		32	40.19	odd	2
600.2.w.j.293.1		32	8.5	even	2	inner
600.2.w.j.293.8		32	1.1	even	1	trivial
600.2.w.j.293.9		32	3.2	odd	2	inner
600.2.w.j.293.16		32	24.5	odd	2	inner
600.2.w.j.557.1		32	15.2	even	4	inner
600.2.w.j.557.8		32	120.77	even	4	inner
600.2.w.j.557.9		32	40.37	odd	4	inner
600.2.w.j.557.16		32	5.2	odd	4	inner

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.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0941764 - 1.41107i) q^{2} +(-1.68122 - 0.416519i) q^{3} +(-1.98226 + 0.265780i) q^{4} +(-0.429408 + 2.41156i) q^{6} +(0.361989 - 0.361989i) q^{7} +(0.561717 + 2.77209i) q^{8} +(2.65302 + 1.40052i) q^{9} +O(q^{10})\)	\(q+(-0.0941764 - 1.41107i) q^{2} +(-1.68122 - 0.416519i) q^{3} +(-1.98226 + 0.265780i) q^{4} +(-0.429408 + 2.41156i) q^{6} +(0.361989 - 0.361989i) q^{7} +(0.561717 + 2.77209i) q^{8} +(2.65302 + 1.40052i) q^{9} +2.63380 q^{11} +(3.44333 + 0.378815i) q^{12} +(-3.49376 + 3.49376i) q^{13} +(-0.544885 - 0.476703i) q^{14} +(3.85872 - 1.05369i) q^{16} +(3.61339 + 3.61339i) q^{17} +(1.72639 - 3.87551i) q^{18} -0.672266 q^{19} +(-0.759360 + 0.457809i) q^{21} +(-0.248041 - 3.71648i) q^{22} +(4.31851 - 4.31851i) q^{23} +(0.210256 - 4.89447i) q^{24} +(5.25899 + 4.60093i) q^{26} +(-3.87698 - 3.45963i) q^{27} +(-0.621348 + 0.813767i) q^{28} -4.76080i q^{29} +3.73793 q^{31} +(-1.85024 - 5.34571i) q^{32} +(-4.42800 - 1.09703i) q^{33} +(4.75847 - 5.43906i) q^{34} +(-5.63122 - 2.07108i) q^{36} +(2.82150 + 2.82150i) q^{37} +(0.0633116 + 0.948617i) q^{38} +(7.32901 - 4.41857i) q^{39} -4.10027i q^{41} +(0.717517 + 1.02840i) q^{42} +(7.57996 - 7.57996i) q^{43} +(-5.22087 + 0.700010i) q^{44} +(-6.50044 - 5.68704i) q^{46} +(0.987537 + 0.987537i) q^{47} +(-6.92626 + 0.164257i) q^{48} +6.73793i q^{49} +(-4.56987 - 7.57996i) q^{51} +(5.99698 - 7.85412i) q^{52} +(-0.646149 - 0.646149i) q^{53} +(-4.51667 + 5.79652i) q^{54} +(1.20680 + 0.800131i) q^{56} +(1.13023 + 0.280012i) q^{57} +(-6.71784 + 0.448355i) q^{58} +4.92247i q^{59} +6.07190i q^{61} +(-0.352025 - 5.27449i) q^{62} +(1.46734 - 0.453392i) q^{63} +(-7.36895 + 3.11426i) q^{64} +(-1.13097 + 6.35155i) q^{66} +(0.349085 + 0.349085i) q^{67} +(-8.12305 - 6.20232i) q^{68} +(-9.05912 + 5.46164i) q^{69} -8.63702i q^{71} +(-2.39213 + 8.14111i) q^{72} +(11.3261 + 11.3261i) q^{73} +(3.71562 - 4.24706i) q^{74} +(1.33261 - 0.178675i) q^{76} +(0.953406 - 0.953406i) q^{77} +(-6.92516 - 9.92565i) q^{78} +4.07707i q^{79} +(5.07707 + 7.43124i) q^{81} +(-5.78579 + 0.386149i) q^{82} +(8.53893 + 8.53893i) q^{83} +(1.38357 - 1.10932i) q^{84} +(-11.4097 - 9.98203i) q^{86} +(-1.98296 + 8.00397i) q^{87} +(1.47945 + 7.30111i) q^{88} +6.58584 q^{89} +2.52941i q^{91} +(-7.41264 + 9.70819i) q^{92} +(-6.28429 - 1.55692i) q^{93} +(1.30049 - 1.48649i) q^{94} +(0.884069 + 9.75799i) q^{96} +(0.660859 - 0.660859i) q^{97} +(9.50772 - 0.634554i) q^{98} +(6.98752 + 3.68869i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{6}+O(q^{10}) \) 32 * q - 4 * q^6	\( 32 q - 4 q^{6} + 8 q^{12} + 28 q^{16} + 20 q^{18} + 52 q^{22} - 12 q^{28} - 32 q^{31} - 8 q^{33} - 20 q^{36} - 16 q^{42} + 24 q^{46} - 44 q^{48} - 8 q^{52} + 16 q^{57} - 28 q^{58} - 48 q^{63} + 16 q^{66} - 32 q^{72} + 64 q^{73} - 88 q^{76} - 64 q^{78} + 48 q^{81} - 64 q^{82} + 8 q^{87} + 52 q^{88} - 52 q^{96} - 16 q^{97}+O(q^{100}) \) 32 * q - 4 * q^6 + 8 * q^12 + 28 * q^16 + 20 * q^18 + 52 * q^22 - 12 * q^28 - 32 * q^31 - 8 * q^33 - 20 * q^36 - 16 * q^42 + 24 * q^46 - 44 * q^48 - 8 * q^52 + 16 * q^57 - 28 * q^58 - 48 * q^63 + 16 * q^66 - 32 * q^72 + 64 * q^73 - 88 * q^76 - 64 * q^78 + 48 * q^81 - 64 * q^82 + 8 * q^87 + 52 * q^88 - 52 * q^96 - 16 * q^97

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