LMFDB - Embedded newform 168.2.i.c.125.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,2,Mod(125,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("168.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.i (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			125.2
Root			$-1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	168.125
Dual form			168.2.i.c.125.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.41421i) q^{3} +(1.00000 - 1.73205i) q^{4} -1.41421i q^{5} +(-0.224745 + 2.43916i) q^{6} +(-2.00000 - 1.73205i) q^{7} +2.82843i q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})$	\(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.41421i) q^{3} +(1.00000 - 1.73205i) q^{4} -1.41421i q^{5} +(-0.224745 + 2.43916i) q^{6} +(-2.00000 - 1.73205i) q^{7} +2.82843i q^{8} +(-1.00000 - 2.82843i) q^{9} +(1.00000 + 1.73205i) q^{10} -2.44949 q^{11} +(-1.44949 - 3.14626i) q^{12} -2.00000 q^{13} +(3.67423 + 0.707107i) q^{14} +(-2.00000 - 1.41421i) q^{15} +(-2.00000 - 3.46410i) q^{16} +7.34847 q^{17} +(3.22474 + 2.75699i) q^{18} +4.00000 q^{19} +(-2.44949 - 1.41421i) q^{20} +(-4.44949 + 1.09638i) q^{21} +(3.00000 - 1.73205i) q^{22} +1.41421i q^{23} +(4.00000 + 2.82843i) q^{24} +3.00000 q^{25} +(2.44949 - 1.41421i) q^{26} +(-5.00000 - 1.41421i) q^{27} +(-5.00000 + 1.73205i) q^{28} +4.89898 q^{29} +(3.44949 + 0.317837i) q^{30} -6.92820i q^{31} +(4.89898 + 2.82843i) q^{32} +(-2.44949 + 3.46410i) q^{33} +(-9.00000 + 5.19615i) q^{34} +(-2.44949 + 2.82843i) q^{35} +(-5.89898 - 1.09638i) q^{36} +10.3923i q^{37} +(-4.89898 + 2.82843i) q^{38} +(-2.00000 + 2.82843i) q^{39} +4.00000 q^{40} -2.44949 q^{41} +(4.67423 - 4.48905i) q^{42} +3.46410i q^{43} +(-2.44949 + 4.24264i) q^{44} +(-4.00000 + 1.41421i) q^{45} +(-1.00000 - 1.73205i) q^{46} -4.89898 q^{47} +(-6.89898 - 0.635674i) q^{48} +(1.00000 + 6.92820i) q^{49} +(-3.67423 + 2.12132i) q^{50} +(7.34847 - 10.3923i) q^{51} +(-2.00000 + 3.46410i) q^{52} +(7.12372 - 1.80348i) q^{54} +3.46410i q^{55} +(4.89898 - 5.65685i) q^{56} +(4.00000 - 5.65685i) q^{57} +(-6.00000 + 3.46410i) q^{58} -5.65685i q^{59} +(-4.44949 + 2.04989i) q^{60} +10.0000 q^{61} +(4.89898 + 8.48528i) q^{62} +(-2.89898 + 7.38891i) q^{63} -8.00000 q^{64} +2.82843i q^{65} +(0.550510 - 5.97469i) q^{66} -3.46410i q^{67} +(7.34847 - 12.7279i) q^{68} +(2.00000 + 1.41421i) q^{69} +(1.00000 - 5.19615i) q^{70} +1.41421i q^{71} +(8.00000 - 2.82843i) q^{72} +(-7.34847 - 12.7279i) q^{74} +(3.00000 - 4.24264i) q^{75} +(4.00000 - 6.92820i) q^{76} +(4.89898 + 4.24264i) q^{77} +(0.449490 - 4.87832i) q^{78} +8.00000 q^{79} +(-4.89898 + 2.82843i) q^{80} +(-7.00000 + 5.65685i) q^{81} +(3.00000 - 1.73205i) q^{82} +11.3137i q^{83} +(-2.55051 + 8.80312i) q^{84} -10.3923i q^{85} +(-2.44949 - 4.24264i) q^{86} +(4.89898 - 6.92820i) q^{87} -6.92820i q^{88} -7.34847 q^{89} +(3.89898 - 4.56048i) q^{90} +(4.00000 + 3.46410i) q^{91} +(2.44949 + 1.41421i) q^{92} +(-9.79796 - 6.92820i) q^{93} +(6.00000 - 3.46410i) q^{94} -5.65685i q^{95} +(8.89898 - 4.09978i) q^{96} -13.8564i q^{97} +(-6.12372 - 7.77817i) q^{98} +(2.44949 + 6.92820i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} + 4 q^{4} + 4 q^{6} - 8 q^{7} - 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^3 + 4 * q^4 + 4 * q^6 - 8 * q^7 - 4 * q^9	$ 4 q + 4 q^{3} + 4 q^{4} + 4 q^{6} - 8 q^{7} - 4 q^{9} + 4 q^{10} + 4 q^{12} - 8 q^{13} - 8 q^{15} - 8 q^{16} + 8 q^{18} + 16 q^{19} - 8 q^{21} + 12 q^{22} + 16 q^{24} + 12 q^{25} - 20 q^{27} - 20 q^{28} + 4 q^{30} - 36 q^{34} - 4 q^{36} - 8 q^{39} + 16 q^{40} + 4 q^{42} - 16 q^{45} - 4 q^{46} - 8 q^{48} + 4 q^{49} - 8 q^{52} + 4 q^{54} + 16 q^{57} - 24 q^{58} - 8 q^{60} + 40 q^{61} + 8 q^{63} - 32 q^{64} + 12 q^{66} + 8 q^{69} + 4 q^{70} + 32 q^{72} + 12 q^{75} + 16 q^{76} - 8 q^{78} + 32 q^{79} - 28 q^{81} + 12 q^{82} - 20 q^{84} - 4 q^{90} + 16 q^{91} + 24 q^{94} + 16 q^{96}+O(q^{100}) $ 4 * q + 4 * q^3 + 4 * q^4 + 4 * q^6 - 8 * q^7 - 4 * q^9 + 4 * q^10 + 4 * q^12 - 8 * q^13 - 8 * q^15 - 8 * q^16 + 8 * q^18 + 16 * q^19 - 8 * q^21 + 12 * q^22 + 16 * q^24 + 12 * q^25 - 20 * q^27 - 20 * q^28 + 4 * q^30 - 36 * q^34 - 4 * q^36 - 8 * q^39 + 16 * q^40 + 4 * q^42 - 16 * q^45 - 4 * q^46 - 8 * q^48 + 4 * q^49 - 8 * q^52 + 4 * q^54 + 16 * q^57 - 24 * q^58 - 8 * q^60 + 40 * q^61 + 8 * q^63 - 32 * q^64 + 12 * q^66 + 8 * q^69 + 4 * q^70 + 32 * q^72 + 12 * q^75 + 16 * q^76 - 8 * q^78 + 32 * q^79 - 28 * q^81 + 12 * q^82 - 20 * q^84 - 4 * q^90 + 16 * q^91 + 24 * q^94 + 16 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	−1.22474	+	0.707107i	−0.866025	+	0.500000i
$2$	−1.22474	+	0.707107i	−0.866025	+	0.500000i
$3$	1.00000	−	1.41421i	0.577350	−	0.816497i
$3$	1.00000	−	1.41421i	0.577350	−	0.816497i
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$		−	1.41421i		−	0.632456i	−0.948683	−	0.316228i	$-0.897584\pi$
$5$		−	1.41421i		−	0.632456i	0.948683	−	0.316228i	$-0.102416\pi$
$6$	−0.224745	+	2.43916i	−0.0917517	+	0.995782i
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$8$			2.82843i			1.00000i
$9$	−1.00000	−	2.82843i	−0.333333	−	0.942809i
$10$	1.00000	+	1.73205i	0.316228	+	0.547723i
$11$	−2.44949			−0.738549			−0.369274	−	0.929320i	$-0.620394\pi$
$11$	−2.44949			−0.738549			−0.369274	+	0.929320i	$0.620394\pi$
$12$	−1.44949	−	3.14626i	−0.418432	−	0.908248i
$13$	−2.00000			−0.554700			−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000			−0.554700			−0.277350	+	0.960769i	$0.589456\pi$
$14$	3.67423	+	0.707107i	0.981981	+	0.188982i
$15$	−2.00000	−	1.41421i	−0.516398	−	0.365148i
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	7.34847			1.78227			0.891133	−	0.453743i	$-0.149911\pi$
$17$	7.34847			1.78227			0.891133	+	0.453743i	$0.149911\pi$
$18$	3.22474	+	2.75699i	0.760080	+	0.649830i
$19$	4.00000			0.917663			0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000			0.917663			0.458831	+	0.888523i	$0.348268\pi$
$20$	−2.44949	−	1.41421i	−0.547723	−	0.316228i
$21$	−4.44949	+	1.09638i	−0.970958	+	0.239249i
$22$	3.00000	−	1.73205i	0.639602	−	0.369274i
$23$			1.41421i			0.294884i	0.989071	+	0.147442i	$0.0471040\pi$
$23$			1.41421i			0.294884i	−0.989071	+	0.147442i	$0.952896\pi$
$24$	4.00000	+	2.82843i	0.816497	+	0.577350i
$25$	3.00000			0.600000
$26$	2.44949	−	1.41421i	0.480384	−	0.277350i
$27$	−5.00000	−	1.41421i	−0.962250	−	0.272166i
$28$	−5.00000	+	1.73205i	−0.944911	+	0.327327i
$29$	4.89898			0.909718			0.454859	−	0.890564i	$-0.349690\pi$
$29$	4.89898			0.909718			0.454859	+	0.890564i	$0.349690\pi$
$30$	3.44949	+	0.317837i	0.629788	+	0.0580289i
$31$		−	6.92820i		−	1.24434i	−0.782881	−	0.622171i	$-0.786251\pi$
$31$		−	6.92820i		−	1.24434i	0.782881	−	0.622171i	$-0.213749\pi$
$32$	4.89898	+	2.82843i	0.866025	+	0.500000i
$33$	−2.44949	+	3.46410i	−0.426401	+	0.603023i
$34$	−9.00000	+	5.19615i	−1.54349	+	0.891133i
$35$	−2.44949	+	2.82843i	−0.414039	+	0.478091i
$36$	−5.89898	−	1.09638i	−0.983163	−	0.182729i
$37$			10.3923i			1.70848i	0.519875	+	0.854242i	$0.325978\pi$
$37$			10.3923i			1.70848i	−0.519875	+	0.854242i	$0.674022\pi$
$38$	−4.89898	+	2.82843i	−0.794719	+	0.458831i
$39$	−2.00000	+	2.82843i	−0.320256	+	0.452911i
$40$	4.00000			0.632456
$41$	−2.44949			−0.382546			−0.191273	−	0.981537i	$-0.561262\pi$
$41$	−2.44949			−0.382546			−0.191273	+	0.981537i	$0.561262\pi$
$42$	4.67423	−	4.48905i	0.721250	−	0.692675i
$43$			3.46410i			0.528271i	0.964486	+	0.264135i	$0.0850865\pi$
$43$			3.46410i			0.528271i	−0.964486	+	0.264135i	$0.914913\pi$
$44$	−2.44949	+	4.24264i	−0.369274	+	0.639602i
$45$	−4.00000	+	1.41421i	−0.596285	+	0.210819i
$46$	−1.00000	−	1.73205i	−0.147442	−	0.255377i
$47$	−4.89898			−0.714590			−0.357295	−	0.933992i	$-0.616301\pi$
$47$	−4.89898			−0.714590			−0.357295	+	0.933992i	$0.616301\pi$
$48$	−6.89898	−	0.635674i	−0.995782	−	0.0917517i
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$	−3.67423	+	2.12132i	−0.519615	+	0.300000i
$51$	7.34847	−	10.3923i	1.02899	−	1.45521i
$52$	−2.00000	+	3.46410i	−0.277350	+	0.480384i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$	7.12372	−	1.80348i	0.969416	−	0.245423i
$55$			3.46410i			0.467099i
$56$	4.89898	−	5.65685i	0.654654	−	0.755929i
$57$	4.00000	−	5.65685i	0.529813	−	0.749269i
$58$	−6.00000	+	3.46410i	−0.787839	+	0.454859i
$59$		−	5.65685i		−	0.736460i	−0.929735	−	0.368230i	$-0.879964\pi$
$59$		−	5.65685i		−	0.736460i	0.929735	−	0.368230i	$-0.120036\pi$
$60$	−4.44949	+	2.04989i	−0.574427	+	0.264639i
$61$	10.0000			1.28037			0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000			1.28037			0.640184	+	0.768221i	$0.278858\pi$
$62$	4.89898	+	8.48528i	0.622171	+	1.07763i
$63$	−2.89898	+	7.38891i	−0.365237	+	0.930915i
$64$	−8.00000			−1.00000
$65$			2.82843i			0.350823i
$66$	0.550510	−	5.97469i	0.0677631	−	0.735434i
$67$		−	3.46410i		−	0.423207i	−0.977356	−	0.211604i	$-0.932131\pi$
$67$		−	3.46410i		−	0.423207i	0.977356	−	0.211604i	$-0.0678686\pi$
$68$	7.34847	−	12.7279i	0.891133	−	1.54349i
$69$	2.00000	+	1.41421i	0.240772	+	0.170251i
$70$	1.00000	−	5.19615i	0.119523	−	0.621059i
$71$			1.41421i			0.167836i	0.996473	+	0.0839181i	$0.0267434\pi$
$71$			1.41421i			0.167836i	−0.996473	+	0.0839181i	$0.973257\pi$
$72$	8.00000	−	2.82843i	0.942809	−	0.333333i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$	−7.34847	−	12.7279i	−0.854242	−	1.47959i
$75$	3.00000	−	4.24264i	0.346410	−	0.489898i
$76$	4.00000	−	6.92820i	0.458831	−	0.794719i
$77$	4.89898	+	4.24264i	0.558291	+	0.483494i
$78$	0.449490	−	4.87832i	0.0508947	−	0.552360i
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$	−4.89898	+	2.82843i	−0.547723	+	0.316228i
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$	3.00000	−	1.73205i	0.331295	−	0.191273i
$83$			11.3137i			1.24184i	0.783874	+	0.620920i	$0.213241\pi$
$83$			11.3137i			1.24184i	−0.783874	+	0.620920i	$0.786759\pi$
$84$	−2.55051	+	8.80312i	−0.278283	+	0.960499i
$85$		−	10.3923i		−	1.12720i
$86$	−2.44949	−	4.24264i	−0.264135	−	0.457496i
$87$	4.89898	−	6.92820i	0.525226	−	0.742781i
$88$		−	6.92820i		−	0.738549i
$89$	−7.34847			−0.778936			−0.389468	−	0.921040i	$-0.627341\pi$
$89$	−7.34847			−0.778936			−0.389468	+	0.921040i	$0.627341\pi$
$90$	3.89898	−	4.56048i	0.410989	−	0.480717i
$91$	4.00000	+	3.46410i	0.419314	+	0.363137i
$92$	2.44949	+	1.41421i	0.255377	+	0.147442i
$93$	−9.79796	−	6.92820i	−1.01600	−	0.718421i
$94$	6.00000	−	3.46410i	0.618853	−	0.357295i
$95$		−	5.65685i		−	0.580381i
$96$	8.89898	−	4.09978i	0.908248	−	0.418432i
$97$		−	13.8564i		−	1.40690i	−0.710742	−	0.703452i	$-0.751641\pi$
$97$		−	13.8564i		−	1.40690i	0.710742	−	0.703452i	$-0.248359\pi$
$98$	−6.12372	−	7.77817i	−0.618590	−	0.785714i
$99$	2.44949	+	6.92820i	0.246183	+	0.696311i
$100$	3.00000	−	5.19615i	0.300000	−	0.519615i
$101$		−	9.89949i		−	0.985037i	−0.870302	−	0.492518i	$-0.836076\pi$
$101$		−	9.89949i		−	0.985037i	0.870302	−	0.492518i	$-0.163924\pi$
$102$	−1.65153	+	17.9241i	−0.163526	+	1.77475i
$103$			13.8564i			1.36531i	0.730740	+	0.682656i	$0.239175\pi$
$103$			13.8564i			1.36531i	−0.730740	+	0.682656i	$0.760825\pi$
$104$		−	5.65685i		−	0.554700i
$105$	1.55051	+	6.29253i	0.151314	+	0.614088i
$106$		0			0
$107$	−7.34847			−0.710403			−0.355202	−	0.934790i	$-0.615588\pi$
$107$	−7.34847			−0.710403			−0.355202	+	0.934790i	$0.615588\pi$
$108$	−7.44949	+	7.24604i	−0.716827	+	0.697251i
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$	−2.44949	−	4.24264i	−0.233550	−	0.404520i
$111$	14.6969	+	10.3923i	1.39497	+	0.986394i
$112$	−2.00000	+	10.3923i	−0.188982	+	0.981981i
$113$			14.1421i			1.33038i	0.746674	+	0.665190i	$0.231650\pi$
$113$			14.1421i			1.33038i	−0.746674	+	0.665190i	$0.768350\pi$
$114$	−0.898979	+	9.75663i	−0.0841971	+	0.913792i
$115$	2.00000			0.186501
$116$	4.89898	−	8.48528i	0.454859	−	0.787839i
$117$	2.00000	+	5.65685i	0.184900	+	0.522976i
$118$	4.00000	+	6.92820i	0.368230	+	0.637793i
$119$	−14.6969	−	12.7279i	−1.34727	−	1.16677i
$120$	4.00000	−	5.65685i	0.365148	−	0.516398i
$121$	−5.00000			−0.454545
$122$	−12.2474	+	7.07107i	−1.10883	+	0.640184i
$123$	−2.44949	+	3.46410i	−0.220863	+	0.312348i
$124$	−12.0000	−	6.92820i	−1.07763	−	0.622171i
$125$		−	11.3137i		−	1.01193i
$126$	−1.67423	−	11.0994i	−0.149153	−	0.988814i
$127$	−4.00000			−0.354943			−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000			−0.354943			−0.177471	+	0.984126i	$0.556792\pi$
$128$	9.79796	−	5.65685i	0.866025	−	0.500000i
$129$	4.89898	+	3.46410i	0.431331	+	0.304997i
$130$	−2.00000	−	3.46410i	−0.175412	−	0.303822i
$131$			11.3137i			0.988483i	0.869325	+	0.494242i	$0.164554\pi$
$131$			11.3137i			0.988483i	−0.869325	+	0.494242i	$0.835446\pi$
$132$	3.55051	+	7.70674i	0.309032	+	0.670786i
$133$	−8.00000	−	6.92820i	−0.693688	−	0.600751i
$134$	2.44949	+	4.24264i	0.211604	+	0.366508i
$135$	−2.00000	+	7.07107i	−0.172133	+	0.608581i
$136$			20.7846i			1.78227i
$137$		−	11.3137i		−	0.966595i	−0.875456	−	0.483298i	$-0.839439\pi$
$137$		−	11.3137i		−	0.966595i	0.875456	−	0.483298i	$-0.160561\pi$
$138$	−3.44949	−	0.317837i	−0.293640	−	0.0270561i
$139$	−14.0000			−1.18746			−0.593732	−	0.804663i	$-0.702346\pi$
$139$	−14.0000			−1.18746			−0.593732	+	0.804663i	$0.702346\pi$
$140$	2.44949	+	7.07107i	0.207020	+	0.597614i
$141$	−4.89898	+	6.92820i	−0.412568	+	0.583460i
$142$	−1.00000	−	1.73205i	−0.0839181	−	0.145350i
$143$	4.89898			0.409673
$144$	−7.79796	+	9.12096i	−0.649830	+	0.760080i
$145$		−	6.92820i		−	0.575356i
$146$		0			0
$147$	10.7980	+	5.51399i	0.890601	+	0.454786i
$148$	18.0000	+	10.3923i	1.47959	+	0.854242i
$149$	9.79796			0.802680			0.401340	−	0.915929i	$-0.368545\pi$
$149$	9.79796			0.802680			0.401340	+	0.915929i	$0.368545\pi$
$150$	−0.674235	+	7.31747i	−0.0550510	+	0.597469i
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$			11.3137i			0.917663i
$153$	−7.34847	−	20.7846i	−0.594089	−	1.68034i
$154$	−9.00000	−	1.73205i	−0.725241	−	0.139573i
$155$	−9.79796			−0.786991
$156$	2.89898	+	6.29253i	0.232104	+	0.503806i
$157$	−14.0000			−1.11732			−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000			−1.11732			−0.558661	+	0.829396i	$0.688685\pi$
$158$	−9.79796	+	5.65685i	−0.779484	+	0.450035i
$159$		0			0
$160$	4.00000	−	6.92820i	0.316228	−	0.547723i
$161$	2.44949	−	2.82843i	0.193047	−	0.222911i
$162$	4.57321	−	11.8780i	0.359306	−	0.933220i
$163$			10.3923i			0.813988i	0.913431	+	0.406994i	$0.133423\pi$
$163$			10.3923i			0.813988i	−0.913431	+	0.406994i	$0.866577\pi$
$164$	−2.44949	+	4.24264i	−0.191273	+	0.331295i
$165$	4.89898	+	3.46410i	0.381385	+	0.269680i
$166$	−8.00000	−	13.8564i	−0.620920	−	1.07547i
$167$	19.5959			1.51638			0.758189	−	0.652035i	$-0.226085\pi$
$167$	19.5959			1.51638			0.758189	+	0.652035i	$0.226085\pi$
$168$	−3.10102	−	12.5851i	−0.239249	−	0.970958i
$169$	−9.00000			−0.692308
$170$	7.34847	+	12.7279i	0.563602	+	0.976187i
$171$	−4.00000	−	11.3137i	−0.305888	−	0.865181i
$172$	6.00000	+	3.46410i	0.457496	+	0.264135i
$173$		−	1.41421i		−	0.107521i	−0.998554	−	0.0537603i	$-0.982879\pi$
$173$		−	1.41421i		−	0.107521i	0.998554	−	0.0537603i	$-0.0171207\pi$
$174$	−1.10102	+	11.9494i	−0.0834681	+	0.905880i
$175$	−6.00000	−	5.19615i	−0.453557	−	0.392792i
$176$	4.89898	+	8.48528i	0.369274	+	0.639602i
$177$	−8.00000	−	5.65685i	−0.601317	−	0.425195i
$178$	9.00000	−	5.19615i	0.674579	−	0.389468i
$179$	22.0454			1.64775			0.823876	−	0.566771i	$-0.191807\pi$
$179$	22.0454			1.64775			0.823876	+	0.566771i	$0.191807\pi$
$180$	−1.55051	+	8.34242i	−0.115568	+	0.621807i
$181$	22.0000			1.63525			0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000			1.63525			0.817624	+	0.575753i	$0.195291\pi$
$182$	−7.34847	−	1.41421i	−0.544705	−	0.104828i
$183$	10.0000	−	14.1421i	0.739221	−	1.04542i
$184$	−4.00000			−0.294884
$185$	14.6969			1.08054
$186$	16.8990	+	1.55708i	1.23909	+	0.114171i
$187$	−18.0000			−1.31629
$188$	−4.89898	+	8.48528i	−0.357295	+	0.618853i
$189$	7.55051	+	11.4887i	0.549219	+	0.835679i
$190$	4.00000	+	6.92820i	0.290191	+	0.502625i
$191$		−	15.5563i		−	1.12562i	−0.826587	−	0.562809i	$-0.809721\pi$
$191$		−	15.5563i		−	1.12562i	0.826587	−	0.562809i	$-0.190279\pi$
$192$	−8.00000	+	11.3137i	−0.577350	+	0.816497i
$193$	−4.00000			−0.287926			−0.143963	−	0.989583i	$-0.545985\pi$
$193$	−4.00000			−0.287926			−0.143963	+	0.989583i	$0.545985\pi$
$194$	9.79796	+	16.9706i	0.703452	+	1.21842i
$195$	4.00000	+	2.82843i	0.286446	+	0.202548i
$196$	13.0000	+	5.19615i	0.928571	+	0.371154i
$197$	−14.6969			−1.04711			−0.523557	−	0.851991i	$-0.675395\pi$
$197$	−14.6969			−1.04711			−0.523557	+	0.851991i	$0.675395\pi$
$198$	−7.89898	−	6.75323i	−0.561356	−	0.479931i
$199$		−	10.3923i		−	0.736691i	−0.929689	−	0.368345i	$-0.879924\pi$
$199$		−	10.3923i		−	0.736691i	0.929689	−	0.368345i	$-0.120076\pi$
$200$			8.48528i			0.600000i
$201$	−4.89898	−	3.46410i	−0.345547	−	0.244339i
$202$	7.00000	+	12.1244i	0.492518	+	0.853067i
$203$	−9.79796	−	8.48528i	−0.687682	−	0.595550i
$204$	−10.6515	−	23.1202i	−0.745756	−	1.61874i
$205$			3.46410i			0.241943i
$206$	−9.79796	−	16.9706i	−0.682656	−	1.18240i
$207$	4.00000	−	1.41421i	0.278019	−	0.0982946i
$208$	4.00000	+	6.92820i	0.277350	+	0.480384i
$209$	−9.79796			−0.677739
$210$	−6.34847	−	6.61037i	−0.438086	−	0.456159i
$211$		−	24.2487i		−	1.66935i	−0.550743	−	0.834675i	$-0.685655\pi$
$211$		−	24.2487i		−	1.66935i	0.550743	−	0.834675i	$-0.314345\pi$
$212$		0			0
$213$	2.00000	+	1.41421i	0.137038	+	0.0969003i
$214$	9.00000	−	5.19615i	0.615227	−	0.355202i
$215$	4.89898			0.334108
$216$	4.00000	−	14.1421i	0.272166	−	0.962250i
$217$	−12.0000	+	13.8564i	−0.814613	+	0.940634i
$218$		0			0
$219$		0			0
$220$	6.00000	+	3.46410i	0.404520	+	0.233550i
$221$	−14.6969			−0.988623
$222$	−25.3485	−	2.33562i	−1.70128	−	0.156756i
$223$			17.3205i			1.15987i	0.814664	+	0.579934i	$0.196921\pi$
$223$			17.3205i			1.15987i	−0.814664	+	0.579934i	$0.803079\pi$
$224$	−4.89898	−	14.1421i	−0.327327	−	0.944911i
$225$	−3.00000	−	8.48528i	−0.200000	−	0.565685i
$226$	−10.0000	−	17.3205i	−0.665190	−	1.15214i
$227$			2.82843i			0.187729i	0.995585	+	0.0938647i	$0.0299221\pi$
$227$			2.82843i			0.187729i	−0.995585	+	0.0938647i	$0.970078\pi$
$228$	−5.79796	−	12.5851i	−0.383979	−	0.833466i
$229$	−14.0000			−0.925146			−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000			−0.925146			−0.462573	+	0.886581i	$0.653074\pi$
$230$	−2.44949	+	1.41421i	−0.161515	+	0.0932505i
$231$	10.8990	−	2.68556i	0.717100	−	0.176697i
$232$			13.8564i			0.909718i
$233$			14.1421i			0.926482i	0.886232	+	0.463241i	$0.153314\pi$
$233$			14.1421i			0.926482i	−0.886232	+	0.463241i	$0.846686\pi$
$234$	−6.44949	−	5.51399i	−0.421616	−	0.360461i
$235$			6.92820i			0.451946i
$236$	−9.79796	−	5.65685i	−0.637793	−	0.368230i
$237$	8.00000	−	11.3137i	0.519656	−	0.734904i
$238$	27.0000	+	5.19615i	1.75015	+	0.336817i
$239$			26.8701i			1.73808i	0.494742	+	0.869040i	$0.335262\pi$
$239$			26.8701i			1.73808i	−0.494742	+	0.869040i	$0.664738\pi$
$240$	−0.898979	+	9.75663i	−0.0580289	+	0.629788i
$241$			6.92820i			0.446285i	0.974786	+	0.223142i	$0.0716315\pi$
$241$			6.92820i			0.446285i	−0.974786	+	0.223142i	$0.928369\pi$
$242$	6.12372	−	3.53553i	0.393648	−	0.227273i
$243$	1.00000	+	15.5563i	0.0641500	+	0.997940i
$244$	10.0000	−	17.3205i	0.640184	−	1.10883i
$245$	9.79796	−	1.41421i	0.625969	−	0.0903508i
$246$	0.550510	−	5.97469i	0.0350993	−	0.380932i
$247$	−8.00000			−0.509028
$248$	19.5959			1.24434
$249$	16.0000	+	11.3137i	1.01396	+	0.716977i
$250$	8.00000	+	13.8564i	0.505964	+	0.876356i
$251$		−	14.1421i		−	0.892644i	−0.894873	−	0.446322i	$-0.852734\pi$
$251$		−	14.1421i		−	0.892644i	0.894873	−	0.446322i	$-0.147266\pi$
$252$	9.89898	+	12.4101i	0.623577	+	0.781762i
$253$		−	3.46410i		−	0.217786i
$254$	4.89898	−	2.82843i	0.307389	−	0.177471i
$255$	−14.6969	−	10.3923i	−0.920358	−	0.650791i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−2.44949			−0.152795			−0.0763975	−	0.997077i	$-0.524342\pi$
$257$	−2.44949			−0.152795			−0.0763975	+	0.997077i	$0.524342\pi$
$258$	−8.44949	−	0.778539i	−0.526042	−	0.0484697i
$259$	18.0000	−	20.7846i	1.11847	−	1.29149i
$260$	4.89898	+	2.82843i	0.303822	+	0.175412i
$261$	−4.89898	−	13.8564i	−0.303239	−	0.857690i
$262$	−8.00000	−	13.8564i	−0.494242	−	0.856052i
$263$			9.89949i			0.610429i	0.952284	+	0.305215i	$0.0987282\pi$
$263$			9.89949i			0.610429i	−0.952284	+	0.305215i	$0.901272\pi$
$264$	−9.79796	−	6.92820i	−0.603023	−	0.426401i
$265$		0			0
$266$	14.6969	+	2.82843i	0.901127	+	0.173422i
$267$	−7.34847	+	10.3923i	−0.449719	+	0.635999i
$268$	−6.00000	−	3.46410i	−0.366508	−	0.211604i
$269$			24.0416i			1.46584i	0.680313	+	0.732922i	$0.261844\pi$
$269$			24.0416i			1.46584i	−0.680313	+	0.732922i	$0.738156\pi$
$270$	−2.55051	−	10.0745i	−0.155219	−	0.613113i
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$	−14.6969	−	25.4558i	−0.891133	−	1.54349i
$273$	8.89898	−	2.19275i	0.538591	−	0.132711i
$274$	8.00000	+	13.8564i	0.483298	+	0.837096i
$275$	−7.34847			−0.443129
$276$	4.44949	−	2.04989i	0.267828	−	0.123389i
$277$			3.46410i			0.208138i	0.994570	+	0.104069i	$0.0331862\pi$
$277$			3.46410i			0.208138i	−0.994570	+	0.104069i	$0.966814\pi$
$278$	17.1464	−	9.89949i	1.02837	−	0.593732i
$279$	−19.5959	+	6.92820i	−1.17318	+	0.414781i
$280$	−8.00000	−	6.92820i	−0.478091	−	0.414039i
$281$		−	2.82843i		−	0.168730i	−0.996435	−	0.0843649i	$-0.973114\pi$
$281$		−	2.82843i		−	0.168730i	0.996435	−	0.0843649i	$-0.0268861\pi$
$282$	1.10102	−	11.9494i	0.0655648	−	0.711575i
$283$	4.00000			0.237775			0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000			0.237775			0.118888	+	0.992908i	$0.462067\pi$
$284$	2.44949	+	1.41421i	0.145350	+	0.0839181i
$285$	−8.00000	−	5.65685i	−0.473879	−	0.335083i
$286$	−6.00000	+	3.46410i	−0.354787	+	0.204837i
$287$	4.89898	+	4.24264i	0.289178	+	0.250435i
$288$	3.10102	−	16.6848i	0.182729	−	0.983163i
$289$	37.0000			2.17647
$290$	4.89898	+	8.48528i	0.287678	+	0.498273i
$291$	−19.5959	−	13.8564i	−1.14873	−	0.812277i
$292$		0			0
$293$		−	1.41421i		−	0.0826192i	−0.999146	−	0.0413096i	$-0.986847\pi$
$293$		−	1.41421i		−	0.0826192i	0.999146	−	0.0413096i	$-0.0131530\pi$
$294$	−17.1237	+	0.882079i	−0.998676	+	0.0514439i
$295$	−8.00000			−0.465778
$296$	−29.3939			−1.70848
$297$	12.2474	+	3.46410i	0.710669	+	0.201008i
$298$	−12.0000	+	6.92820i	−0.695141	+	0.401340i
$299$		−	2.82843i		−	0.163572i
$300$	−4.34847	−	9.43879i	−0.251059	−	0.544949i
$301$	6.00000	−	6.92820i	0.345834	−	0.399335i
$302$	−9.79796	+	5.65685i	−0.563809	+	0.325515i
$303$	−14.0000	−	9.89949i	−0.804279	−	0.568711i
$304$	−8.00000	−	13.8564i	−0.458831	−	0.794719i
$305$		−	14.1421i		−	0.809776i
$306$	23.6969	+	20.2597i	1.35466	+	1.15817i
$307$	4.00000			0.228292			0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000			0.228292			0.114146	+	0.993464i	$0.463587\pi$
$308$	12.2474	−	4.24264i	0.697863	−	0.241747i
$309$	19.5959	+	13.8564i	1.11477	+	0.788263i
$310$	12.0000	−	6.92820i	0.681554	−	0.393496i
$311$	−24.4949			−1.38898			−0.694489	−	0.719503i	$-0.744370\pi$
$311$	−24.4949			−1.38898			−0.694489	+	0.719503i	$0.744370\pi$
$312$	−8.00000	−	5.65685i	−0.452911	−	0.320256i
$313$			6.92820i			0.391605i	0.980643	+	0.195803i	$0.0627312\pi$
$313$			6.92820i			0.391605i	−0.980643	+	0.195803i	$0.937269\pi$
$314$	17.1464	−	9.89949i	0.967629	−	0.558661i
$315$	10.4495	+	4.09978i	0.588762	+	0.230996i
$316$	8.00000	−	13.8564i	0.450035	−	0.779484i
$317$	19.5959			1.10062			0.550308	−	0.834962i	$-0.314510\pi$
$317$	19.5959			1.10062			0.550308	+	0.834962i	$0.314510\pi$
$318$		0			0
$319$	−12.0000			−0.671871
$320$			11.3137i			0.632456i
$321$	−7.34847	+	10.3923i	−0.410152	+	0.580042i
$322$	−1.00000	+	5.19615i	−0.0557278	+	0.289570i
$323$	29.3939			1.63552
$324$	2.79796	+	17.7812i	0.155442	+	0.987845i
$325$	−6.00000			−0.332820
$326$	−7.34847	−	12.7279i	−0.406994	−	0.704934i
$327$		0			0
$328$		−	6.92820i		−	0.382546i
$329$	9.79796	+	8.48528i	0.540179	+	0.467809i
$330$	−8.44949	−	0.778539i	−0.465129	−	0.0428572i
$331$			24.2487i			1.33283i	0.745581	+	0.666415i	$0.232172\pi$
$331$			24.2487i			1.33283i	−0.745581	+	0.666415i	$0.767828\pi$
$332$	19.5959	+	11.3137i	1.07547	+	0.620920i
$333$	29.3939	−	10.3923i	1.61077	−	0.569495i
$334$	−24.0000	+	13.8564i	−1.31322	+	0.758189i
$335$	−4.89898			−0.267660
$336$	12.6969	+	13.2207i	0.692675	+	0.721250i
$337$	2.00000			0.108947			0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000			0.108947			0.0544735	+	0.998515i	$0.482652\pi$
$338$	11.0227	−	6.36396i	0.599556	−	0.346154i
$339$	20.0000	+	14.1421i	1.08625	+	0.768095i
$340$	−18.0000	−	10.3923i	−0.976187	−	0.563602i
$341$			16.9706i			0.919007i
$342$	12.8990	+	11.0280i	0.697497	+	0.596325i
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−9.79796			−0.528271
$345$	2.00000	−	2.82843i	0.107676	−	0.152277i
$346$	1.00000	+	1.73205i	0.0537603	+	0.0931156i
$347$	2.44949			0.131495			0.0657477	−	0.997836i	$-0.479057\pi$
$347$	2.44949			0.131495			0.0657477	+	0.997836i	$0.479057\pi$
$348$	−7.10102	−	15.4135i	−0.380655	−	0.826250i
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$	11.0227	+	2.12132i	0.589188	+	0.113389i
$351$	10.0000	+	2.82843i	0.533761	+	0.150970i
$352$	−12.0000	−	6.92820i	−0.639602	−	0.369274i
$353$	−12.2474			−0.651866			−0.325933	−	0.945393i	$-0.605678\pi$
$353$	−12.2474			−0.651866			−0.325933	+	0.945393i	$0.605678\pi$
$354$	13.7980	+	1.27135i	0.733353	+	0.0675714i
$355$	2.00000			0.106149
$356$	−7.34847	+	12.7279i	−0.389468	+	0.674579i
$357$	−32.6969	+	8.05669i	−1.73051	+	0.426405i
$358$	−27.0000	+	15.5885i	−1.42699	+	0.823876i
$359$			26.8701i			1.41815i	0.705134	+	0.709074i	$0.250887\pi$
$359$			26.8701i			1.41815i	−0.705134	+	0.709074i	$0.749113\pi$
$360$	−4.00000	−	11.3137i	−0.210819	−	0.596285i
$361$	−3.00000			−0.157895
$362$	−26.9444	+	15.5563i	−1.41617	+	0.817624i
$363$	−5.00000	+	7.07107i	−0.262432	+	0.371135i
$364$	10.0000	−	3.46410i	0.524142	−	0.181568i
$365$		0			0
$366$	−2.24745	+	24.3916i	−0.117476	+	1.27497i
$367$		−	3.46410i		−	0.180825i	−0.995904	−	0.0904123i	$-0.971182\pi$
$367$		−	3.46410i		−	0.180825i	0.995904	−	0.0904123i	$-0.0288185\pi$
$368$	4.89898	−	2.82843i	0.255377	−	0.147442i
$369$	2.44949	+	6.92820i	0.127515	+	0.360668i
$370$	−18.0000	+	10.3923i	−0.935775	+	0.540270i
$371$		0			0
$372$	−21.7980	+	10.0424i	−1.13017	+	0.520672i
$373$		−	13.8564i		−	0.717458i	−0.933442	−	0.358729i	$-0.883210\pi$
$373$		−	13.8564i		−	0.717458i	0.933442	−	0.358729i	$-0.116790\pi$
$374$	22.0454	−	12.7279i	1.13994	−	0.658145i
$375$	−16.0000	−	11.3137i	−0.826236	−	0.584237i
$376$		−	13.8564i		−	0.714590i
$377$	−9.79796			−0.504621
$378$	−17.3712	−	8.73169i	−0.893477	−	0.449109i
$379$		−	10.3923i		−	0.533817i	−0.963722	−	0.266908i	$-0.913998\pi$
$379$		−	10.3923i		−	0.533817i	0.963722	−	0.266908i	$-0.0860021\pi$
$380$	−9.79796	−	5.65685i	−0.502625	−	0.290191i
$381$	−4.00000	+	5.65685i	−0.204926	+	0.289809i
$382$	11.0000	+	19.0526i	0.562809	+	0.974814i
$383$	4.89898			0.250326			0.125163	−	0.992136i	$-0.460055\pi$
$383$	4.89898			0.250326			0.125163	+	0.992136i	$0.460055\pi$
$384$	1.79796	−	19.5133i	0.0917517	−	0.995782i
$385$	6.00000	−	6.92820i	0.305788	−	0.353094i
$386$	4.89898	−	2.82843i	0.249351	−	0.143963i
$387$	9.79796	−	3.46410i	0.498058	−	0.176090i
$388$	−24.0000	−	13.8564i	−1.21842	−	0.703452i
$389$	−24.4949			−1.24194			−0.620970	−	0.783834i	$-0.713261\pi$
$389$	−24.4949			−1.24194			−0.620970	+	0.783834i	$0.713261\pi$
$390$	−6.89898	−	0.635674i	−0.349343	−	0.0321886i
$391$			10.3923i			0.525561i
$392$	−19.5959	+	2.82843i	−0.989743	+	0.142857i
$393$	16.0000	+	11.3137i	0.807093	+	0.570701i
$394$	18.0000	−	10.3923i	0.906827	−	0.523557i
$395$		−	11.3137i		−	0.569254i
$396$	14.4495	+	2.68556i	0.726114	+	0.134955i
$397$	−2.00000			−0.100377			−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000			−0.100377			−0.0501886	+	0.998740i	$0.515982\pi$
$398$	7.34847	+	12.7279i	0.368345	+	0.637993i
$399$	−17.7980	+	4.38551i	−0.891012	+	0.219550i
$400$	−6.00000	−	10.3923i	−0.300000	−	0.519615i
$401$		−	11.3137i		−	0.564980i	−0.959270	−	0.282490i	$-0.908840\pi$
$401$		−	11.3137i		−	0.564980i	0.959270	−	0.282490i	$-0.0911603\pi$
$402$	8.44949	+	0.778539i	0.421422	+	0.0388300i
$403$			13.8564i			0.690237i
$404$	−17.1464	−	9.89949i	−0.853067	−	0.492518i
$405$	8.00000	+	9.89949i	0.397523	+	0.491910i
$406$	18.0000	+	3.46410i	0.893325	+	0.171920i
$407$		−	25.4558i		−	1.26180i
$408$	29.3939	+	20.7846i	1.45521	+	1.02899i
$409$			34.6410i			1.71289i	0.516240	+	0.856444i	$0.327331\pi$
$409$			34.6410i			1.71289i	−0.516240	+	0.856444i	$0.672669\pi$
$410$	−2.44949	−	4.24264i	−0.120972	−	0.209529i
$411$	−16.0000	−	11.3137i	−0.789222	−	0.558064i
$412$	24.0000	+	13.8564i	1.18240	+	0.682656i
$413$	−9.79796	+	11.3137i	−0.482126	+	0.556711i
$414$	−3.89898	+	4.56048i	−0.191624	+	0.224135i
$415$	16.0000			0.785409
$416$	−9.79796	−	5.65685i	−0.480384	−	0.277350i
$417$	−14.0000	+	19.7990i	−0.685583	+	0.969561i
$418$	12.0000	−	6.92820i	0.586939	−	0.338869i
$419$			11.3137i			0.552711i	0.961056	+	0.276355i	$0.0891267\pi$
$419$			11.3137i			0.552711i	−0.961056	+	0.276355i	$0.910873\pi$
$420$	12.4495	+	3.60697i	0.607473	+	0.176002i
$421$			24.2487i			1.18181i	0.806741	+	0.590905i	$0.201229\pi$
$421$			24.2487i			1.18181i	−0.806741	+	0.590905i	$0.798771\pi$
$422$	17.1464	+	29.6985i	0.834675	+	1.44570i
$423$	4.89898	+	13.8564i	0.238197	+	0.673722i
$424$		0			0
$425$	22.0454			1.06936
$426$	−3.44949	−	0.317837i	−0.167128	−	0.0153993i
$427$	−20.0000	−	17.3205i	−0.967868	−	0.838198i
$428$	−7.34847	+	12.7279i	−0.355202	+	0.615227i
$429$	4.89898	−	6.92820i	0.236525	−	0.334497i
$430$	−6.00000	+	3.46410i	−0.289346	+	0.167054i
$431$			18.3848i			0.885564i	0.896629	+	0.442782i	$0.146008\pi$
$431$			18.3848i			0.885564i	−0.896629	+	0.442782i	$0.853992\pi$
$432$	5.10102	+	20.1489i	0.245423	+	0.969416i
$433$		−	20.7846i		−	0.998845i	−0.866359	−	0.499422i	$-0.833546\pi$
$433$		−	20.7846i		−	0.998845i	0.866359	−	0.499422i	$-0.166454\pi$
$434$	4.89898	−	25.4558i	0.235159	−	1.22192i
$435$	−9.79796	−	6.92820i	−0.469776	−	0.332182i
$436$		0			0
$437$			5.65685i			0.270604i
$438$		0			0
$439$		−	24.2487i		−	1.15733i	−0.815566	−	0.578664i	$-0.803574\pi$
$439$		−	24.2487i		−	1.15733i	0.815566	−	0.578664i	$-0.196426\pi$
$440$	−9.79796			−0.467099
$441$	18.5959	−	9.75663i	0.885520	−	0.464601i
$442$	18.0000	−	10.3923i	0.856173	−	0.494312i
$443$	−17.1464			−0.814651			−0.407326	−	0.913283i	$-0.633539\pi$
$443$	−17.1464			−0.814651			−0.407326	+	0.913283i	$0.633539\pi$
$444$	32.6969	−	15.0635i	1.55173	−	0.714884i
$445$			10.3923i			0.492642i
$446$	−12.2474	−	21.2132i	−0.579934	−	1.00447i
$447$	9.79796	−	13.8564i	0.463428	−	0.655386i
$448$	16.0000	+	13.8564i	0.755929	+	0.654654i
$449$		−	36.7696i		−	1.73526i	−0.497208	−	0.867631i	$-0.665642\pi$
$449$		−	36.7696i		−	1.73526i	0.497208	−	0.867631i	$-0.334358\pi$
$450$	9.67423	+	8.27098i	0.456048	+	0.389898i
$451$	6.00000			0.282529
$452$	24.4949	+	14.1421i	1.15214	+	0.665190i
$453$	8.00000	−	11.3137i	0.375873	−	0.531564i
$454$	−2.00000	−	3.46410i	−0.0938647	−	0.162578i
$455$	4.89898	−	5.65685i	0.229668	−	0.265197i
$456$	16.0000	+	11.3137i	0.749269	+	0.529813i
$457$	−10.0000			−0.467780			−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000			−0.467780			−0.233890	+	0.972263i	$0.575146\pi$
$458$	17.1464	−	9.89949i	0.801200	−	0.462573i
$459$	−36.7423	−	10.3923i	−1.71499	−	0.485071i
$460$	2.00000	−	3.46410i	0.0932505	−	0.161515i
$461$		−	9.89949i		−	0.461065i	−0.973065	−	0.230533i	$-0.925953\pi$
$461$		−	9.89949i		−	0.461065i	0.973065	−	0.230533i	$-0.0740469\pi$
$462$	−11.4495	+	10.9959i	−0.532678	+	0.511574i
$463$	−4.00000			−0.185896			−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000			−0.185896			−0.0929479	+	0.995671i	$0.529629\pi$
$464$	−9.79796	−	16.9706i	−0.454859	−	0.787839i
$465$	−9.79796	+	13.8564i	−0.454369	+	0.642575i
$466$	−10.0000	−	17.3205i	−0.463241	−	0.802357i
$467$		−	31.1127i		−	1.43972i	−0.694117	−	0.719862i	$-0.744205\pi$
$467$		−	31.1127i		−	1.43972i	0.694117	−	0.719862i	$-0.255795\pi$
$468$	11.7980	+	2.19275i	0.545361	+	0.101360i
$469$	−6.00000	+	6.92820i	−0.277054	+	0.319915i
$470$	−4.89898	−	8.48528i	−0.225973	−	0.391397i
$471$	−14.0000	+	19.7990i	−0.645086	+	0.912289i
$472$	16.0000			0.736460
$473$		−	8.48528i		−	0.390154i
$474$	−1.79796	+	19.5133i	−0.0825830	+	0.896274i
$475$	12.0000			0.550598
$476$	−36.7423	+	12.7279i	−1.68408	+	0.583383i
$477$		0			0
$478$	−19.0000	−	32.9090i	−0.869040	−	1.50522i
$479$	−4.89898			−0.223840			−0.111920	−	0.993717i	$-0.535700\pi$
$479$	−4.89898			−0.223840			−0.111920	+	0.993717i	$0.535700\pi$
$480$	−5.79796	−	12.5851i	−0.264639	−	0.574427i
$481$		−	20.7846i		−	0.947697i
$482$	−4.89898	−	8.48528i	−0.223142	−	0.386494i
$483$	−1.55051	−	6.29253i	−0.0705507	−	0.286320i
$484$	−5.00000	+	8.66025i	−0.227273	+	0.393648i
$485$	−19.5959			−0.889805
$486$	−12.2247	−	18.3455i	−0.554526	−	0.832167i
$487$	−4.00000			−0.181257			−0.0906287	−	0.995885i	$-0.528888\pi$
$487$	−4.00000			−0.181257			−0.0906287	+	0.995885i	$0.528888\pi$
$488$			28.2843i			1.28037i
$489$	14.6969	+	10.3923i	0.664619	+	0.469956i
$490$	−11.0000	+	8.66025i	−0.496929	+	0.391230i
$491$	17.1464			0.773807			0.386904	−	0.922120i	$-0.373545\pi$
$491$	17.1464			0.773807			0.386904	+	0.922120i	$0.373545\pi$
$492$	3.55051	+	7.70674i	0.160069	+	0.347447i
$493$	36.0000			1.62136
$494$	9.79796	−	5.65685i	0.440831	−	0.254514i
$495$	9.79796	−	3.46410i	0.440386	−	0.155700i
$496$	−24.0000	+	13.8564i	−1.07763	+	0.622171i
$497$	2.44949	−	2.82843i	0.109875	−	0.126872i
$498$	−27.5959	−	2.54270i	−1.23660	−	0.113941i
$499$		−	3.46410i		−	0.155074i	−0.996989	−	0.0775372i	$-0.975294\pi$
$499$		−	3.46410i		−	0.155074i	0.996989	−	0.0775372i	$-0.0247057\pi$
$500$	−19.5959	−	11.3137i	−0.876356	−	0.505964i
$501$	19.5959	−	27.7128i	0.875481	−	1.23812i
$502$	10.0000	+	17.3205i	0.446322	+	0.773052i
$503$	14.6969			0.655304			0.327652	−	0.944798i	$-0.393743\pi$
$503$	14.6969			0.655304			0.327652	+	0.944798i	$0.393743\pi$
$504$	−20.8990	−	8.19955i	−0.930915	−	0.365237i
$505$	−14.0000			−0.622992
$506$	2.44949	+	4.24264i	0.108893	+	0.188608i
$507$	−9.00000	+	12.7279i	−0.399704	+	0.565267i
$508$	−4.00000	+	6.92820i	−0.177471	+	0.307389i
$509$		−	18.3848i		−	0.814891i	−0.913230	−	0.407445i	$-0.866420\pi$
$509$		−	18.3848i		−	0.814891i	0.913230	−	0.407445i	$-0.133580\pi$
$510$	25.3485	+	2.33562i	1.12245	+	0.103423i
$511$		0			0
$512$		−	22.6274i		−	1.00000i
$513$	−20.0000	−	5.65685i	−0.883022	−	0.249756i
$514$	3.00000	−	1.73205i	0.132324	−	0.0763975i
$515$	19.5959			0.863499
$516$	10.8990	−	5.02118i	0.479801	−	0.221045i
$517$	12.0000			0.527759
$518$	−7.34847	+	38.1838i	−0.322873	+	1.67770i
$519$	−2.00000	−	1.41421i	−0.0877903	−	0.0620771i
$520$	−8.00000			−0.350823
$521$	−36.7423			−1.60971			−0.804856	−	0.593471i	$-0.797757\pi$
$521$	−36.7423			−1.60971			−0.804856	+	0.593471i	$0.797757\pi$
$522$	15.7980	+	13.5065i	0.691458	+	0.591162i
$523$	22.0000			0.961993			0.480996	−	0.876723i	$-0.340275\pi$
$523$	22.0000			0.961993			0.480996	+	0.876723i	$0.340275\pi$
$524$	19.5959	+	11.3137i	0.856052	+	0.494242i
$525$	−13.3485	+	3.28913i	−0.582575	+	0.143549i
$526$	−7.00000	−	12.1244i	−0.305215	−	0.528647i
$527$		−	50.9117i		−	2.21775i
$528$	16.8990	+	1.55708i	0.735434	+	0.0677631i
$529$	21.0000			0.913043
$530$		0			0
$531$	−16.0000	+	5.65685i	−0.694341	+	0.245487i
$532$	−20.0000	+	6.92820i	−0.867110	+	0.300376i
$533$	4.89898			0.212198
$534$	1.65153	−	17.9241i	0.0714687	−	0.775651i
$535$			10.3923i			0.449299i
$536$	9.79796			0.423207
$537$	22.0454	−	31.1769i	0.951330	−	1.34538i
$538$	−17.0000	−	29.4449i	−0.732922	−	1.26946i
$539$	−2.44949	−	16.9706i	−0.105507	−	0.730974i
$540$	10.2474	+	10.5352i	0.440980	+	0.453362i
$541$			31.1769i			1.34040i	0.742180	+	0.670200i	$0.233792\pi$
$541$			31.1769i			1.34040i	−0.742180	+	0.670200i	$0.766208\pi$
$542$		0			0
$543$	22.0000	−	31.1127i	0.944110	−	1.33517i
$544$	36.0000	+	20.7846i	1.54349	+	0.891133i
$545$		0			0
$546$	−9.34847	+	8.97809i	−0.400078	+	0.384227i
$547$			24.2487i			1.03680i	0.855138	+	0.518400i	$0.173472\pi$
$547$			24.2487i			1.03680i	−0.855138	+	0.518400i	$0.826528\pi$
$548$	−19.5959	−	11.3137i	−0.837096	−	0.483298i
$549$	−10.0000	−	28.2843i	−0.426790	−	1.20714i
$550$	9.00000	−	5.19615i	0.383761	−	0.221565i
$551$	19.5959			0.834814
$552$	−4.00000	+	5.65685i	−0.170251	+	0.240772i
$553$	−16.0000	−	13.8564i	−0.680389	−	0.589234i
$554$	−2.44949	−	4.24264i	−0.104069	−	0.180253i
$555$	14.6969	−	20.7846i	0.623850	−	0.882258i
$556$	−14.0000	+	24.2487i	−0.593732	+	1.02837i
$557$	−29.3939			−1.24546			−0.622729	−	0.782437i	$-0.713976\pi$
$557$	−29.3939			−1.24546			−0.622729	+	0.782437i	$0.713976\pi$
$558$	19.1010	−	22.3417i	0.808611	−	0.945799i
$559$		−	6.92820i		−	0.293032i
$560$	14.6969	+	2.82843i	0.621059	+	0.119523i
$561$	−18.0000	+	25.4558i	−0.759961	+	1.07475i
$562$	2.00000	+	3.46410i	0.0843649	+	0.146124i
$563$			11.3137i			0.476816i	0.971165	+	0.238408i	$0.0766255\pi$
$563$			11.3137i			0.476816i	−0.971165	+	0.238408i	$0.923374\pi$
$564$	7.10102	+	15.4135i	0.299007	+	0.649025i
$565$	20.0000			0.841406
$566$	−4.89898	+	2.82843i	−0.205919	+	0.118888i
$567$	23.7980	+	0.810647i	0.999420	+	0.0340440i
$568$	−4.00000			−0.167836
$569$			14.1421i			0.592869i	0.955053	+	0.296435i	$0.0957977\pi$
$569$			14.1421i			0.592869i	−0.955053	+	0.296435i	$0.904202\pi$
$570$	13.7980	+	1.27135i	0.577933	+	0.0532509i
$571$			17.3205i			0.724841i	0.932015	+	0.362420i	$0.118050\pi$
$571$			17.3205i			0.724841i	−0.932015	+	0.362420i	$0.881950\pi$
$572$	4.89898	−	8.48528i	0.204837	−	0.354787i
$573$	−22.0000	−	15.5563i	−0.919063	−	0.649876i
$574$	−9.00000	−	1.73205i	−0.375653	−	0.0722944i
$575$			4.24264i			0.176930i
$576$	8.00000	+	22.6274i	0.333333	+	0.942809i
$577$		−	20.7846i		−	0.865275i	−0.901568	−	0.432637i	$-0.857583\pi$
$577$		−	20.7846i		−	0.865275i	0.901568	−	0.432637i	$-0.142417\pi$
$578$	−45.3156	+	26.1630i	−1.88488	+	1.08824i
$579$	−4.00000	+	5.65685i	−0.166234	+	0.235091i
$580$	−12.0000	−	6.92820i	−0.498273	−	0.287678i
$581$	19.5959	−	22.6274i	0.812976	−	0.938743i
$582$	33.7980	+	3.11416i	1.40097	+	0.129086i
$583$		0			0
$584$		0			0
$585$	8.00000	−	2.82843i	0.330759	−	0.116941i
$586$	1.00000	+	1.73205i	0.0413096	+	0.0715504i
$587$			2.82843i			0.116742i	0.998295	+	0.0583708i	$0.0185906\pi$
$587$			2.82843i			0.116742i	−0.998295	+	0.0583708i	$0.981409\pi$
$588$	20.3485	−	13.1886i	0.839157	−	0.543890i
$589$		−	27.7128i		−	1.14189i
$590$	9.79796	−	5.65685i	0.403376	−	0.232889i
$591$	−14.6969	+	20.7846i	−0.604551	+	0.854965i
$592$	36.0000	−	20.7846i	1.47959	−	0.854242i
$593$	−7.34847			−0.301765			−0.150883	−	0.988552i	$-0.548212\pi$
$593$	−7.34847			−0.301765			−0.150883	+	0.988552i	$0.548212\pi$
$594$	−17.4495	+	4.41761i	−0.715961	+	0.181257i
$595$	−18.0000	+	20.7846i	−0.737928	+	0.852086i
$596$	9.79796	−	16.9706i	0.401340	−	0.695141i
$597$	−14.6969	−	10.3923i	−0.601506	−	0.425329i
$598$	2.00000	+	3.46410i	0.0817861	+	0.141658i
$599$			18.3848i			0.751182i	0.926786	+	0.375591i	$0.122560\pi$
$599$			18.3848i			0.751182i	−0.926786	+	0.375591i	$0.877440\pi$
$600$	12.0000	+	8.48528i	0.489898	+	0.346410i
$601$			6.92820i			0.282607i	0.989966	+	0.141304i	$0.0451294\pi$
$601$			6.92820i			0.282607i	−0.989966	+	0.141304i	$0.954871\pi$
$602$	−2.44949	+	12.7279i	−0.0998337	+	0.518751i
$603$	−9.79796	+	3.46410i	−0.399004	+	0.141069i
$604$	8.00000	−	13.8564i	0.325515	−	0.563809i
$605$			7.07107i			0.287480i
$606$	24.1464	+	2.22486i	0.980882	+	0.0903788i
$607$			3.46410i			0.140604i	0.997526	+	0.0703018i	$0.0223962\pi$
$607$			3.46410i			0.140604i	−0.997526	+	0.0703018i	$0.977604\pi$
$608$	19.5959	+	11.3137i	0.794719	+	0.458831i
$609$	−21.7980	+	5.37113i	−0.883298	+	0.217649i
$610$	10.0000	+	17.3205i	0.404888	+	0.701287i
$611$	9.79796			0.396383
$612$	−43.3485	−	8.05669i	−1.75226	−	0.325672i
$613$		0			0		1.00000			$0$
$613$		0			0		−1.00000			$\pi$
$614$	−4.89898	+	2.82843i	−0.197707	+	0.114146i
$615$	4.89898	+	3.46410i	0.197546	+	0.139686i
$616$	−12.0000	+	13.8564i	−0.483494	+	0.558291i
$617$			5.65685i			0.227736i	0.993496	+	0.113868i	$0.0363242\pi$
$617$			5.65685i			0.227736i	−0.993496	+	0.113868i	$0.963676\pi$
$618$	−33.7980	−	3.11416i	−1.35955	−	0.125270i
$619$	10.0000			0.401934			0.200967	−	0.979598i	$-0.435592\pi$
$619$	10.0000			0.401934			0.200967	+	0.979598i	$0.435592\pi$
$620$	−9.79796	+	16.9706i	−0.393496	+	0.681554i
$621$	2.00000	−	7.07107i	0.0802572	−	0.283752i
$622$	30.0000	−	17.3205i	1.20289	−	0.694489i
$623$	14.6969	+	12.7279i	0.588820	+	0.509933i
$624$	13.7980	+	1.27135i	0.552360	+	0.0508947i
$625$	−1.00000			−0.0400000
$626$	−4.89898	−	8.48528i	−0.195803	−	0.339140i
$627$	−9.79796	+	13.8564i	−0.391293	+	0.553372i
$628$	−14.0000	+	24.2487i	−0.558661	+	0.967629i
$629$			76.3675i			3.04497i
$630$	−15.6969	+	2.36773i	−0.625381	+	0.0943324i
$631$	32.0000			1.27390			0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000			1.27390			0.636950	+	0.770905i	$0.280196\pi$
$632$			22.6274i			0.900070i
$633$	−34.2929	−	24.2487i	−1.36302	−	0.963800i
$634$	−24.0000	+	13.8564i	−0.953162	+	0.550308i
$635$			5.65685i			0.224485i
$636$		0			0
$637$	−2.00000	−	13.8564i	−0.0792429	−	0.549011i
$638$	14.6969	−	8.48528i	0.581857	−	0.335936i
$639$	4.00000	−	1.41421i	0.158238	−	0.0559454i
$640$	−8.00000	−	13.8564i	−0.316228	−	0.547723i
$641$			22.6274i			0.893729i	0.894602	+	0.446865i	$0.147459\pi$
$641$			22.6274i			0.893729i	−0.894602	+	0.446865i	$0.852541\pi$
$642$	1.65153	−	17.9241i	0.0651807	−	0.707407i
$643$	−20.0000			−0.788723			−0.394362	−	0.918955i	$-0.629034\pi$
$643$	−20.0000			−0.788723			−0.394362	+	0.918955i	$0.629034\pi$
$644$	−2.44949	−	7.07107i	−0.0965234	−	0.278639i
$645$	4.89898	−	6.92820i	0.192897	−	0.272798i
$646$	−36.0000	+	20.7846i	−1.41640	+	0.817760i
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$	−16.0000	−	19.7990i	−0.628539	−	0.777778i
$649$			13.8564i			0.543912i
$650$	7.34847	−	4.24264i	0.288231	−	0.166410i
$651$	7.59592	+	30.8270i	0.297707	+	1.20820i
$652$	18.0000	+	10.3923i	0.704934	+	0.406994i
$653$	9.79796			0.383424			0.191712	−	0.981451i	$-0.438596\pi$
$653$	9.79796			0.383424			0.191712	+	0.981451i	$0.438596\pi$
$654$		0			0
$655$	16.0000			0.625172
$656$	4.89898	+	8.48528i	0.191273	+	0.331295i
$657$		0			0
$658$	−18.0000	−	3.46410i	−0.701713	−	0.135045i
$659$	−31.8434			−1.24044			−0.620221	−	0.784427i	$-0.712957\pi$
$659$	−31.8434			−1.24044			−0.620221	+	0.784427i	$0.712957\pi$
$660$	10.8990	−	5.02118i	0.424242	−	0.195449i
$661$	−14.0000			−0.544537			−0.272268	−	0.962221i	$-0.587774\pi$
$661$	−14.0000			−0.544537			−0.272268	+	0.962221i	$0.587774\pi$
$662$	−17.1464	−	29.6985i	−0.666415	−	1.15426i
$663$	−14.6969	+	20.7846i	−0.570782	+	0.807207i
$664$	−32.0000			−1.24184
$665$	−9.79796	+	11.3137i	−0.379949	+	0.438727i
$666$	−28.6515	+	33.5125i	−1.11022	+	1.29858i
$667$			6.92820i			0.268261i
$668$	19.5959	−	33.9411i	0.758189	−	1.31322i
$669$	24.4949	+	17.3205i	0.947027	+	0.669650i
$670$	6.00000	−	3.46410i	0.231800	−	0.133830i
$671$	−24.4949			−0.945615
$672$	−24.8990	−	7.21393i	−0.960499	−	0.278283i
$673$	8.00000			0.308377			0.154189	−	0.988041i	$-0.450724\pi$
$673$	8.00000			0.308377			0.154189	+	0.988041i	$0.450724\pi$
$674$	−2.44949	+	1.41421i	−0.0943508	+	0.0544735i
$675$	−15.0000	−	4.24264i	−0.577350	−	0.163299i
$676$	−9.00000	+	15.5885i	−0.346154	+	0.599556i
$677$		−	26.8701i		−	1.03270i	−0.856378	−	0.516350i	$-0.827290\pi$
$677$		−	26.8701i		−	1.03270i	0.856378	−	0.516350i	$-0.172710\pi$
$678$	−34.4949	−	3.17837i	−1.32477	−	0.122065i
$679$	−24.0000	+	27.7128i	−0.921035	+	1.06352i
$680$	29.3939			1.12720
$681$	4.00000	+	2.82843i	0.153280	+	0.108386i
$682$	−12.0000	−	20.7846i	−0.459504	−	0.795884i
$683$	51.4393			1.96827			0.984135	−	0.177423i	$-0.0567759\pi$
$683$	51.4393			1.96827			0.984135	+	0.177423i	$0.0567759\pi$
$684$	−23.5959	−	4.38551i	−0.902212	−	0.167684i
$685$	−16.0000			−0.611329
$686$	−1.22474	+	26.1630i	−0.0467610	+	0.998906i
$687$	−14.0000	+	19.7990i	−0.534133	+	0.755379i
$688$	12.0000	−	6.92820i	0.457496	−	0.264135i
$689$		0			0
$690$	−0.449490	+	4.87832i	−0.0171118	+	0.185714i
$691$	10.0000			0.380418			0.190209	−	0.981744i	$-0.439083\pi$
$691$	10.0000			0.380418			0.190209	+	0.981744i	$0.439083\pi$
$692$	−2.44949	−	1.41421i	−0.0931156	−	0.0537603i
$693$	7.10102	−	18.0990i	0.269745	−	0.687526i
$694$	−3.00000	+	1.73205i	−0.113878	+	0.0657477i
$695$			19.7990i			0.751018i
$696$	19.5959	+	13.8564i	0.742781	+	0.525226i
$697$	−18.0000			−0.681799
$698$	17.1464	−	9.89949i	0.649002	−	0.374701i
$699$	20.0000	+	14.1421i	0.756469	+	0.534905i
$700$	−15.0000	+	5.19615i	−0.566947	+	0.196396i
$701$	−29.3939			−1.11019			−0.555096	−	0.831786i	$-0.687318\pi$
$701$	−29.3939			−1.11019			−0.555096	+	0.831786i	$0.687318\pi$
$702$	−14.2474	+	3.60697i	−0.537735	+	0.136136i
$703$			41.5692i			1.56781i
$704$	19.5959			0.738549
$705$	9.79796	+	6.92820i	0.369012	+	0.260931i
$706$	15.0000	−	8.66025i	0.564532	−	0.325933i
$707$	−17.1464	+	19.7990i	−0.644858	+	0.744618i
$708$	−17.7980	+	8.19955i	−0.668888	+	0.308158i
$709$			13.8564i			0.520388i	0.965556	+	0.260194i	$0.0837866\pi$
$709$			13.8564i			0.520388i	−0.965556	+	0.260194i	$0.916213\pi$
$710$	−2.44949	+	1.41421i	−0.0919277	+	0.0530745i
$711$	−8.00000	−	22.6274i	−0.300023	−	0.848594i
$712$		−	20.7846i		−	0.778936i
$713$	9.79796			0.366936
$714$	34.3485	−	32.9876i	1.28546	−	1.23453i
$715$		−	6.92820i		−	0.259100i
$716$	22.0454	−	38.1838i	0.823876	−	1.42699i
$717$	38.0000	+	26.8701i	1.41914	+	1.00348i
$718$	−19.0000	−	32.9090i	−0.709074	−	1.22815i
$719$	14.6969			0.548103			0.274052	−	0.961715i	$-0.411636\pi$
$719$	14.6969			0.548103			0.274052	+	0.961715i	$0.411636\pi$
$720$	12.8990	+	11.0280i	0.480717	+	0.410989i
$721$	24.0000	−	27.7128i	0.893807	−	1.03208i
$722$	3.67423	−	2.12132i	0.136741	−	0.0789474i
$723$	9.79796	+	6.92820i	0.364390	+	0.257663i
$724$	22.0000	−	38.1051i	0.817624	−	1.41617i
$725$	14.6969			0.545831
$726$	1.12372	−	12.1958i	0.0417053	−	0.452628i
$727$		−	13.8564i		−	0.513906i	−0.966424	−	0.256953i	$-0.917281\pi$
$727$		−	13.8564i		−	0.513906i	0.966424	−	0.256953i	$-0.0827185\pi$
$728$	−9.79796	+	11.3137i	−0.363137	+	0.419314i
$729$	23.0000	+	14.1421i	0.851852	+	0.523783i
$730$		0			0
$731$			25.4558i			0.941518i
$732$	−14.4949	−	31.4626i	−0.535747	−	1.16289i
$733$	−14.0000			−0.517102			−0.258551	−	0.965998i	$-0.583245\pi$
$733$	−14.0000			−0.517102			−0.258551	+	0.965998i	$0.583245\pi$
$734$	2.44949	+	4.24264i	0.0904123	+	0.156599i
$735$	7.79796	−	15.2706i	0.287632	−	0.563265i
$736$	−4.00000	+	6.92820i	−0.147442	+	0.255377i
$737$			8.48528i			0.312559i
$738$	−7.89898	−	6.75323i	−0.290765	−	0.248590i
$739$		−	31.1769i		−	1.14686i	−0.819254	−	0.573431i	$-0.805612\pi$
$739$		−	31.1769i		−	1.14686i	0.819254	−	0.573431i	$-0.194388\pi$
$740$	14.6969	−	25.4558i	0.540270	−	0.935775i
$741$	−8.00000	+	11.3137i	−0.293887	+	0.415619i
$742$		0			0
$743$		−	7.07107i		−	0.259412i	−0.991552	−	0.129706i	$-0.958597\pi$
$743$		−	7.07107i		−	0.259412i	0.991552	−	0.129706i	$-0.0414034\pi$
$744$	19.5959	−	27.7128i	0.718421	−	1.01600i
$745$		−	13.8564i		−	0.507659i
$746$	9.79796	+	16.9706i	0.358729	+	0.621336i
$747$	32.0000	−	11.3137i	1.17082	−	0.413947i
$748$	−18.0000	+	31.1769i	−0.658145	+	1.13994i
$749$	14.6969	+	12.7279i	0.537014	+	0.465068i
$750$	27.5959	+	2.54270i	1.00766	+	0.0928462i
$751$	32.0000			1.16770			0.583848	−	0.811863i	$-0.301546\pi$
$751$	32.0000			1.16770			0.583848	+	0.811863i	$0.301546\pi$
$752$	9.79796	+	16.9706i	0.357295	+	0.618853i
$753$	−20.0000	−	14.1421i	−0.728841	−	0.515368i
$754$	12.0000	−	6.92820i	0.437014	−	0.252310i
$755$		−	11.3137i		−	0.411748i
$756$	27.4495	−	1.58919i	0.998328	−	0.0577981i
$757$		−	41.5692i		−	1.51086i	−0.655230	−	0.755429i	$-0.727428\pi$
$757$		−	41.5692i		−	1.51086i	0.655230	−	0.755429i	$-0.272572\pi$
$758$	7.34847	+	12.7279i	0.266908	+	0.462299i
$759$	−4.89898	−	3.46410i	−0.177822	−	0.125739i
$760$	16.0000			0.580381
$761$	−17.1464			−0.621558			−0.310779	−	0.950482i	$-0.600590\pi$
$761$	−17.1464			−0.621558			−0.310779	+	0.950482i	$0.600590\pi$
$762$	0.898979	−	9.75663i	0.0325666	−	0.353445i
$763$		0			0
$764$	−26.9444	−	15.5563i	−0.974814	−	0.562809i
$765$	−29.3939	+	10.3923i	−1.06274	+	0.375735i
$766$	−6.00000	+	3.46410i	−0.216789	+	0.125163i
$767$			11.3137i			0.408514i
$768$	11.5959	+	25.1701i	0.418432	+	0.908248i
$769$			34.6410i			1.24919i	0.780950	+	0.624593i	$0.214735\pi$
$769$			34.6410i			1.24919i	−0.780950	+	0.624593i	$0.785265\pi$
$770$	−2.44949	+	12.7279i	−0.0882735	+	0.458682i
$771$	−2.44949	+	3.46410i	−0.0882162	+	0.124757i
$772$	−4.00000	+	6.92820i	−0.143963	+	0.249351i
$773$		−	26.8701i		−	0.966449i	−0.875497	−	0.483224i	$-0.839466\pi$
$773$		−	26.8701i		−	0.966449i	0.875497	−	0.483224i	$-0.160534\pi$
$774$	−9.55051	+	11.1708i	−0.343286	+	0.401528i
$775$		−	20.7846i		−	0.746605i
$776$	39.1918			1.40690
$777$	−11.3939	−	46.2405i	−0.408753	−	1.65887i
$778$	30.0000	−	17.3205i	1.07555	−	0.620970i
$779$	−9.79796			−0.351048
$780$	8.89898	−	4.09978i	0.318635	−	0.146796i
$781$		−	3.46410i		−	0.123955i
$782$	−7.34847	−	12.7279i	−0.262781	−	0.455150i
$783$	−24.4949	−	6.92820i	−0.875376	−	0.247594i
$784$	22.0000	−	17.3205i	0.785714	−	0.618590i
$785$			19.7990i			0.706656i
$786$	−27.5959	−	2.54270i	−0.984314	−	0.0906950i
$787$	−2.00000			−0.0712923			−0.0356462	−	0.999364i	$-0.511349\pi$
$787$	−2.00000			−0.0712923			−0.0356462	+	0.999364i	$0.511349\pi$
$788$	−14.6969	+	25.4558i	−0.523557	+	0.906827i
$789$	14.0000	+	9.89949i	0.498413	+	0.352431i
$790$	8.00000	+	13.8564i	0.284627	+	0.492989i
$791$	24.4949	−	28.2843i	0.870938	−	1.00567i
$792$	−19.5959	+	6.92820i	−0.696311	+	0.246183i
$793$	−20.0000			−0.710221
$794$	2.44949	−	1.41421i	0.0869291	−	0.0501886i
$795$		0			0
$796$	−18.0000	−	10.3923i	−0.637993	−	0.368345i
$797$		−	52.3259i		−	1.85348i	−0.375705	−	0.926739i	$-0.622599\pi$
$797$		−	52.3259i		−	1.85348i	0.375705	−	0.926739i	$-0.377401\pi$
$798$	18.6969	−	17.9562i	0.661864	−	0.635642i
$799$	−36.0000			−1.27359
$800$	14.6969	+	8.48528i	0.519615	+	0.300000i
$801$	7.34847	+	20.7846i	0.259645	+	0.734388i
$802$	8.00000	+	13.8564i	0.282490	+	0.489287i
$803$		0			0
$804$	−10.8990	+	5.02118i	−0.384377	+	0.177083i
$805$	−4.00000	−	3.46410i	−0.140981	−	0.122094i
$806$	−9.79796	−	16.9706i	−0.345118	−	0.597763i
$807$	34.0000	+	24.0416i	1.19686	+	0.846305i
$808$	28.0000			0.985037
$809$		−	19.7990i		−	0.696095i	−0.937477	−	0.348048i	$-0.886845\pi$
$809$		−	19.7990i		−	0.696095i	0.937477	−	0.348048i	$-0.113155\pi$
$810$	−16.7980	−	6.46750i	−0.590220	−	0.227245i
$811$	−2.00000			−0.0702295			−0.0351147	−	0.999383i	$-0.511180\pi$
$811$	−2.00000			−0.0702295			−0.0351147	+	0.999383i	$0.511180\pi$
$812$	−24.4949	+	8.48528i	−0.859602	+	0.297775i
$813$		0			0
$814$	18.0000	+	31.1769i	0.630900	+	1.09275i
$815$	14.6969			0.514811
$816$	−50.6969	−	4.67123i	−1.77475	−	0.163526i
$817$			13.8564i			0.484774i
$818$	−24.4949	−	42.4264i	−0.856444	−	1.48340i
$819$	5.79796	−	14.7778i	0.202597	−	0.516378i
$820$	6.00000	+	3.46410i	0.209529	+	0.120972i
$821$	48.9898			1.70976			0.854878	−	0.518829i	$-0.173632\pi$
$821$	48.9898			1.70976			0.854878	+	0.518829i	$0.173632\pi$
$822$	27.5959	+	2.54270i	0.962518	+	0.0886868i
$823$	20.0000			0.697156			0.348578	−	0.937280i	$-0.386665\pi$
$823$	20.0000			0.697156			0.348578	+	0.937280i	$0.386665\pi$
$824$	−39.1918			−1.36531
$825$	−7.34847	+	10.3923i	−0.255841	+	0.361814i
$826$	4.00000	−	20.7846i	0.139178	−	0.723189i
$827$	7.34847			0.255531			0.127766	−	0.991804i	$-0.459219\pi$
$827$	7.34847			0.255531			0.127766	+	0.991804i	$0.459219\pi$
$828$	1.55051	−	8.34242i	0.0538840	−	0.289919i
$829$	34.0000			1.18087			0.590434	−	0.807086i	$-0.298956\pi$
$829$	34.0000			1.18087			0.590434	+	0.807086i	$0.298956\pi$
$830$	−19.5959	+	11.3137i	−0.680184	+	0.392705i
$831$	4.89898	+	3.46410i	0.169944	+	0.120168i
$832$	16.0000			0.554700
$833$	7.34847	+	50.9117i	0.254609	+	1.76399i
$834$	3.14643	−	34.1482i	0.108952	−	1.18246i
$835$		−	27.7128i		−	0.959041i
$836$	−9.79796	+	16.9706i	−0.338869	+	0.586939i
$837$	−9.79796	+	34.6410i	−0.338667	+	1.19737i
$838$	−8.00000	−	13.8564i	−0.276355	−	0.478662i
$839$	−48.9898			−1.69132			−0.845658	−	0.533726i	$-0.820792\pi$
$839$	−48.9898			−1.69132			−0.845658	+	0.533726i	$0.820792\pi$
$840$	−17.7980	+	4.38551i	−0.614088	+	0.151314i
$841$	−5.00000			−0.172414
$842$	−17.1464	−	29.6985i	−0.590905	−	1.02348i
$843$	−4.00000	−	2.82843i	−0.137767	−	0.0974162i
$844$	−42.0000	−	24.2487i	−1.44570	−	0.834675i
$845$			12.7279i			0.437854i
$846$	−15.7980	−	13.5065i	−0.543145	−	0.464362i
$847$	10.0000	+	8.66025i	0.343604	+	0.297570i
$848$		0			0
$849$	4.00000	−	5.65685i	0.137280	−	0.194143i
$850$	−27.0000	+	15.5885i	−0.926092	+	0.534680i
$851$	−14.6969			−0.503805
$852$	4.44949	−	2.04989i	0.152437	−	0.0702280i
$853$	10.0000			0.342393			0.171197	−	0.985237i	$-0.445237\pi$
$853$	10.0000			0.342393			0.171197	+	0.985237i	$0.445237\pi$
$854$	36.7423	+	7.07107i	1.25730	+	0.241967i
$855$	−16.0000	+	5.65685i	−0.547188	+	0.193460i
$856$		−	20.7846i		−	0.710403i
$857$	31.8434			1.08775			0.543874	−	0.839167i	$-0.316957\pi$
$857$	31.8434			1.08775			0.543874	+	0.839167i	$0.316957\pi$
$858$	−1.10102	+	11.9494i	−0.0375882	+	0.407945i
$859$	−20.0000			−0.682391			−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000			−0.682391			−0.341196	+	0.939992i	$0.610832\pi$
$860$	4.89898	−	8.48528i	0.167054	−	0.289346i
$861$	10.8990	−	2.68556i	0.371436	−	0.0915237i
$862$	−13.0000	−	22.5167i	−0.442782	−	0.766921i
$863$			1.41421i			0.0481404i	0.999710	+	0.0240702i	$0.00766252\pi$
$863$			1.41421i			0.0481404i	−0.999710	+	0.0240702i	$0.992337\pi$
$864$	−20.4949	−	21.0703i	−0.697251	−	0.716827i
$865$	−2.00000			−0.0680020
$866$	14.6969	+	25.4558i	0.499422	+	0.865025i
$867$	37.0000	−	52.3259i	1.25659	−	1.77708i
$868$	12.0000	+	34.6410i	0.407307	+	1.17579i
$869$	−19.5959			−0.664746
$870$	16.8990	+	1.55708i	0.572929	+	0.0527899i
$871$			6.92820i			0.234753i
$872$		0			0
$873$	−39.1918	+	13.8564i	−1.32644	+	0.468968i
$874$	−4.00000	−	6.92820i	−0.135302	−	0.234350i
$875$	−19.5959	+	22.6274i	−0.662463	+	0.764946i
$876$		0			0
$877$		−	13.8564i		−	0.467898i	−0.972249	−	0.233949i	$-0.924835\pi$
$877$		−	13.8564i		−	0.467898i	0.972249	−	0.233949i	$-0.0751648\pi$
$878$	17.1464	+	29.6985i	0.578664	+	1.00228i
$879$	−2.00000	−	1.41421i	−0.0674583	−	0.0477002i
$880$	12.0000	−	6.92820i	0.404520	−	0.233550i
$881$	22.0454			0.742729			0.371364	−	0.928487i	$-0.378890\pi$
$881$	22.0454			0.742729			0.371364	+	0.928487i	$0.378890\pi$
$882$	−15.8763	+	25.0987i	−0.534582	+	0.845117i
$883$			10.3923i			0.349729i	0.984593	+	0.174864i	$0.0559487\pi$
$883$			10.3923i			0.349729i	−0.984593	+	0.174864i	$0.944051\pi$
$884$	−14.6969	+	25.4558i	−0.494312	+	0.856173i
$885$	−8.00000	+	11.3137i	−0.268917	+	0.380306i
$886$	21.0000	−	12.1244i	0.705509	−	0.407326i
$887$	−39.1918			−1.31593			−0.657967	−	0.753047i	$-0.728583\pi$
$887$	−39.1918			−1.31593			−0.657967	+	0.753047i	$0.728583\pi$
$888$	−29.3939	+	41.5692i	−0.986394	+	1.39497i
$889$	8.00000	+	6.92820i	0.268311	+	0.232364i
$890$	−7.34847	−	12.7279i	−0.246321	−	0.426641i
$891$	17.1464	−	13.8564i	0.574427	−	0.464207i
$892$	30.0000	+	17.3205i	1.00447	+	0.579934i
$893$	−19.5959			−0.655752
$894$	−2.20204	+	23.8988i	−0.0736473	+	0.799294i
$895$		−	31.1769i		−	1.04213i
$896$	−29.3939	−	5.65685i	−0.981981	−	0.188982i
$897$	−4.00000	−	2.82843i	−0.133556	−	0.0944384i
$898$	26.0000	+	45.0333i	0.867631	+	1.50278i
$899$		−	33.9411i		−	1.13200i
$900$	−17.6969	−	3.28913i	−0.589898	−	0.109638i
$901$		0			0
$902$	−7.34847	+	4.24264i	−0.244677	+	0.141264i
$903$	−3.79796	−	15.4135i	−0.126388	−	0.512929i
$904$	−40.0000			−1.33038
$905$		−	31.1127i		−	1.03422i
$906$	−1.79796	+	19.5133i	−0.0597332	+	0.648285i
$907$		−	38.1051i		−	1.26526i	−0.774454	−	0.632630i	$-0.781975\pi$
$907$		−	38.1051i		−	1.26526i	0.774454	−	0.632630i	$-0.218025\pi$
$908$	4.89898	+	2.82843i	0.162578	+	0.0938647i
$909$	−28.0000	+	9.89949i	−0.928701	+	0.328346i
$910$	−2.00000	+	10.3923i	−0.0662994	+	0.344502i
$911$		−	15.5563i		−	0.515405i	−0.966224	−	0.257702i	$-0.917035\pi$
$911$		−	15.5563i		−	0.515405i	0.966224	−	0.257702i	$-0.0829654\pi$
$912$	−27.5959	−	2.54270i	−0.913792	−	0.0841971i
$913$		−	27.7128i		−	0.917160i
$914$	12.2474	−	7.07107i	0.405110	−	0.233890i
$915$	−20.0000	−	14.1421i	−0.661180	−	0.467525i
$916$	−14.0000	+	24.2487i	−0.462573	+	0.801200i
$917$	19.5959	−	22.6274i	0.647114	−	0.747223i
$918$	52.3485	−	13.2528i	1.72776	−	0.437409i
$919$	−40.0000			−1.31948			−0.659739	−	0.751495i	$-0.729333\pi$
$919$	−40.0000			−1.31948			−0.659739	+	0.751495i	$0.729333\pi$
$920$			5.65685i			0.186501i
$921$	4.00000	−	5.65685i	0.131804	−	0.186400i
$922$	7.00000	+	12.1244i	0.230533	+	0.399294i
$923$		−	2.82843i		−	0.0930988i
$924$	6.24745	−	21.5631i	0.205526	−	0.709376i
$925$			31.1769i			1.02509i
$926$	4.89898	−	2.82843i	0.160990	−	0.0929479i
$927$	39.1918	−	13.8564i	1.28723	−	0.455104i
$928$	24.0000	+	13.8564i	0.787839	+	0.454859i
$929$	31.8434			1.04475			0.522373	−	0.852717i	$-0.325047\pi$
$929$	31.8434			1.04475			0.522373	+	0.852717i	$0.325047\pi$
$930$	2.20204	−	23.8988i	0.0722078	−	0.783671i
$931$	4.00000	+	27.7128i	0.131095	+	0.908251i
$932$	24.4949	+	14.1421i	0.802357	+	0.463241i
$933$	−24.4949	+	34.6410i	−0.801927	+	1.13410i
$934$	22.0000	+	38.1051i	0.719862	+	1.24684i
$935$			25.4558i			0.832495i
$936$	−16.0000	+	5.65685i	−0.522976	+	0.184900i
$937$			41.5692i			1.35801i	0.734135	+	0.679004i	$0.237588\pi$
$937$			41.5692i			1.35801i	−0.734135	+	0.679004i	$0.762412\pi$
$938$	2.44949	−	12.7279i	0.0799787	−	0.415581i
$939$	9.79796	+	6.92820i	0.319744	+	0.226093i
$940$	12.0000	+	6.92820i	0.391397	+	0.225973i
$941$		−	1.41421i		−	0.0461020i	−0.999734	−	0.0230510i	$-0.992662\pi$
$941$		−	1.41421i		−	0.0461020i	0.999734	−	0.0230510i	$-0.00733802\pi$
$942$	3.14643	−	34.1482i	0.102516	−	1.11261i
$943$		−	3.46410i		−	0.112807i
$944$	−19.5959	+	11.3137i	−0.637793	+	0.368230i
$945$	16.2474	−	10.6780i	0.528530	−	0.347356i
$946$	6.00000	+	10.3923i	0.195077	+	0.337883i
$947$	−46.5403			−1.51236			−0.756178	−	0.654366i	$-0.772936\pi$
$947$	−46.5403			−1.51236			−0.756178	+	0.654366i	$0.772936\pi$
$948$	−11.5959	−	25.1701i	−0.376618	−	0.817487i
$949$		0			0
$950$	−14.6969	+	8.48528i	−0.476832	+	0.275299i
$951$	19.5959	−	27.7128i	0.635441	−	0.898650i
$952$	36.0000	−	41.5692i	1.16677	−	1.34727i
$953$		−	45.2548i		−	1.46595i	−0.680257	−	0.732974i	$-0.738132\pi$
$953$		−	45.2548i		−	1.46595i	0.680257	−	0.732974i	$-0.261868\pi$
$954$		0			0
$955$	−22.0000			−0.711903
$956$	46.5403	+	26.8701i	1.50522	+	0.869040i
$957$	−12.0000	+	16.9706i	−0.387905	+	0.548580i
$958$	6.00000	−	3.46410i	0.193851	−	0.111920i
$959$	−19.5959	+	22.6274i	−0.632785	+	0.730677i
$960$	16.0000	+	11.3137i	0.516398	+	0.365148i
$961$	−17.0000			−0.548387
$962$	14.6969	+	25.4558i	0.473848	+	0.820729i
$963$	7.34847	+	20.7846i	0.236801	+	0.669775i
$964$	12.0000	+	6.92820i	0.386494	+	0.223142i
$965$			5.65685i			0.182101i
$966$	6.34847	+	6.61037i	0.204259	+	0.212685i
$967$	−4.00000			−0.128631			−0.0643157	−	0.997930i	$-0.520486\pi$
$967$	−4.00000			−0.128631			−0.0643157	+	0.997930i	$0.520486\pi$
$968$		−	14.1421i		−	0.454545i
$969$	29.3939	−	41.5692i	0.944267	−	1.33540i
$970$	24.0000	−	13.8564i	0.770594	−	0.444902i
$971$			36.7696i			1.17999i	0.807406	+	0.589996i	$0.200871\pi$
$971$			36.7696i			1.17999i	−0.807406	+	0.589996i	$0.799129\pi$
$972$	27.9444	+	13.8243i	0.896317	+	0.443415i
$973$	28.0000	+	24.2487i	0.897639	+	0.777378i
$974$	4.89898	−	2.82843i	0.156973	−	0.0906287i
$975$	−6.00000	+	8.48528i	−0.192154	+	0.271746i
$976$	−20.0000	−	34.6410i	−0.640184	−	1.10883i
$977$		−	19.7990i		−	0.633426i	−0.948521	−	0.316713i	$-0.897421\pi$
$977$		−	19.7990i		−	0.633426i	0.948521	−	0.316713i	$-0.102579\pi$
$978$	−25.3485	−	2.33562i	−0.810555	−	0.0746848i
$979$	18.0000			0.575282
$980$	7.34847	−	18.3848i	0.234738	−	0.587280i
$981$		0			0
$982$	−21.0000	+	12.1244i	−0.670137	+	0.386904i
$983$	39.1918			1.25003			0.625013	−	0.780615i	$-0.285094\pi$
$983$	39.1918			1.25003			0.625013	+	0.780615i	$0.285094\pi$
$984$	−9.79796	−	6.92820i	−0.312348	−	0.220863i
$985$			20.7846i			0.662253i
$986$	−44.0908	+	25.4558i	−1.40414	+	0.810679i
$987$	21.7980	−	5.37113i	0.693837	−	0.170965i
$988$	−8.00000	+	13.8564i	−0.254514	+	0.440831i
$989$	−4.89898			−0.155778
$990$	−9.55051	+	11.1708i	−0.303535	+	0.355033i
$991$	−52.0000			−1.65183			−0.825917	−	0.563791i	$-0.809342\pi$
$991$	−52.0000			−1.65183			−0.825917	+	0.563791i	$0.809342\pi$
$992$	19.5959	−	33.9411i	0.622171	−	1.07763i
$993$	34.2929	+	24.2487i	1.08825	+	0.769510i
$994$	−1.00000	+	5.19615i	−0.0317181	+	0.164812i
$995$	−14.6969			−0.465924
$996$	35.5959	−	16.3991i	1.12790	−	0.519626i
$997$	−62.0000			−1.96356			−0.981780	−	0.190022i	$-0.939144\pi$
$997$	−62.0000			−1.96356			−0.981780	+	0.190022i	$0.939144\pi$
$998$	2.44949	+	4.24264i	0.0775372	+	0.134298i
$999$	14.6969	−	51.9615i	0.464991	−	1.64399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.i.c.125.2	yes	4
3.2	odd	2	inner	168.2.i.c.125.3	yes	4
4.3	odd	2		672.2.i.a.209.4		4
7.6	odd	2		168.2.i.a.125.2	yes	4
8.3	odd	2		672.2.i.c.209.2		4
8.5	even	2		168.2.i.a.125.4	yes	4
12.11	even	2		672.2.i.a.209.2		4
21.20	even	2		168.2.i.a.125.3	yes	4
24.5	odd	2		168.2.i.a.125.1	✓	4
24.11	even	2		672.2.i.c.209.4		4
28.27	even	2		672.2.i.c.209.1		4
56.13	odd	2	inner	168.2.i.c.125.4	yes	4
56.27	even	2		672.2.i.a.209.3		4
84.83	odd	2		672.2.i.c.209.3		4
168.83	odd	2		672.2.i.a.209.1		4
168.125	even	2	inner	168.2.i.c.125.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.i.a.125.1	✓	4	24.5	odd	2
168.2.i.a.125.2	yes	4	7.6	odd	2
168.2.i.a.125.3	yes	4	21.20	even	2
168.2.i.a.125.4	yes	4	8.5	even	2
168.2.i.c.125.1	yes	4	168.125	even	2	inner
168.2.i.c.125.2	yes	4	1.1	even	1	trivial
168.2.i.c.125.3	yes	4	3.2	odd	2	inner
168.2.i.c.125.4	yes	4	56.13	odd	2	inner
672.2.i.a.209.1		4	168.83	odd	2
672.2.i.a.209.2		4	12.11	even	2
672.2.i.a.209.3		4	56.27	even	2
672.2.i.a.209.4		4	4.3	odd	2
672.2.i.c.209.1		4	28.27	even	2
672.2.i.c.209.2		4	8.3	odd	2
672.2.i.c.209.3		4	84.83	odd	2
672.2.i.c.209.4		4	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.i (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.41421i) q^{3} +(1.00000 - 1.73205i) q^{4} -1.41421i q^{5} +(-0.224745 + 2.43916i) q^{6} +(-2.00000 - 1.73205i) q^{7} +2.82843i q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\)	\(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.41421i) q^{3} +(1.00000 - 1.73205i) q^{4} -1.41421i q^{5} +(-0.224745 + 2.43916i) q^{6} +(-2.00000 - 1.73205i) q^{7} +2.82843i q^{8} +(-1.00000 - 2.82843i) q^{9} +(1.00000 + 1.73205i) q^{10} -2.44949 q^{11} +(-1.44949 - 3.14626i) q^{12} -2.00000 q^{13} +(3.67423 + 0.707107i) q^{14} +(-2.00000 - 1.41421i) q^{15} +(-2.00000 - 3.46410i) q^{16} +7.34847 q^{17} +(3.22474 + 2.75699i) q^{18} +4.00000 q^{19} +(-2.44949 - 1.41421i) q^{20} +(-4.44949 + 1.09638i) q^{21} +(3.00000 - 1.73205i) q^{22} +1.41421i q^{23} +(4.00000 + 2.82843i) q^{24} +3.00000 q^{25} +(2.44949 - 1.41421i) q^{26} +(-5.00000 - 1.41421i) q^{27} +(-5.00000 + 1.73205i) q^{28} +4.89898 q^{29} +(3.44949 + 0.317837i) q^{30} -6.92820i q^{31} +(4.89898 + 2.82843i) q^{32} +(-2.44949 + 3.46410i) q^{33} +(-9.00000 + 5.19615i) q^{34} +(-2.44949 + 2.82843i) q^{35} +(-5.89898 - 1.09638i) q^{36} +10.3923i q^{37} +(-4.89898 + 2.82843i) q^{38} +(-2.00000 + 2.82843i) q^{39} +4.00000 q^{40} -2.44949 q^{41} +(4.67423 - 4.48905i) q^{42} +3.46410i q^{43} +(-2.44949 + 4.24264i) q^{44} +(-4.00000 + 1.41421i) q^{45} +(-1.00000 - 1.73205i) q^{46} -4.89898 q^{47} +(-6.89898 - 0.635674i) q^{48} +(1.00000 + 6.92820i) q^{49} +(-3.67423 + 2.12132i) q^{50} +(7.34847 - 10.3923i) q^{51} +(-2.00000 + 3.46410i) q^{52} +(7.12372 - 1.80348i) q^{54} +3.46410i q^{55} +(4.89898 - 5.65685i) q^{56} +(4.00000 - 5.65685i) q^{57} +(-6.00000 + 3.46410i) q^{58} -5.65685i q^{59} +(-4.44949 + 2.04989i) q^{60} +10.0000 q^{61} +(4.89898 + 8.48528i) q^{62} +(-2.89898 + 7.38891i) q^{63} -8.00000 q^{64} +2.82843i q^{65} +(0.550510 - 5.97469i) q^{66} -3.46410i q^{67} +(7.34847 - 12.7279i) q^{68} +(2.00000 + 1.41421i) q^{69} +(1.00000 - 5.19615i) q^{70} +1.41421i q^{71} +(8.00000 - 2.82843i) q^{72} +(-7.34847 - 12.7279i) q^{74} +(3.00000 - 4.24264i) q^{75} +(4.00000 - 6.92820i) q^{76} +(4.89898 + 4.24264i) q^{77} +(0.449490 - 4.87832i) q^{78} +8.00000 q^{79} +(-4.89898 + 2.82843i) q^{80} +(-7.00000 + 5.65685i) q^{81} +(3.00000 - 1.73205i) q^{82} +11.3137i q^{83} +(-2.55051 + 8.80312i) q^{84} -10.3923i q^{85} +(-2.44949 - 4.24264i) q^{86} +(4.89898 - 6.92820i) q^{87} -6.92820i q^{88} -7.34847 q^{89} +(3.89898 - 4.56048i) q^{90} +(4.00000 + 3.46410i) q^{91} +(2.44949 + 1.41421i) q^{92} +(-9.79796 - 6.92820i) q^{93} +(6.00000 - 3.46410i) q^{94} -5.65685i q^{95} +(8.89898 - 4.09978i) q^{96} -13.8564i q^{97} +(-6.12372 - 7.77817i) q^{98} +(2.44949 + 6.92820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} + 4 q^{4} + 4 q^{6} - 8 q^{7} - 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^3 + 4 * q^4 + 4 * q^6 - 8 * q^7 - 4 * q^9	\( 4 q + 4 q^{3} + 4 q^{4} + 4 q^{6} - 8 q^{7} - 4 q^{9} + 4 q^{10} + 4 q^{12} - 8 q^{13} - 8 q^{15} - 8 q^{16} + 8 q^{18} + 16 q^{19} - 8 q^{21} + 12 q^{22} + 16 q^{24} + 12 q^{25} - 20 q^{27} - 20 q^{28} + 4 q^{30} - 36 q^{34} - 4 q^{36} - 8 q^{39} + 16 q^{40} + 4 q^{42} - 16 q^{45} - 4 q^{46} - 8 q^{48} + 4 q^{49} - 8 q^{52} + 4 q^{54} + 16 q^{57} - 24 q^{58} - 8 q^{60} + 40 q^{61} + 8 q^{63} - 32 q^{64} + 12 q^{66} + 8 q^{69} + 4 q^{70} + 32 q^{72} + 12 q^{75} + 16 q^{76} - 8 q^{78} + 32 q^{79} - 28 q^{81} + 12 q^{82} - 20 q^{84} - 4 q^{90} + 16 q^{91} + 24 q^{94} + 16 q^{96}+O(q^{100}) \) 4 * q + 4 * q^3 + 4 * q^4 + 4 * q^6 - 8 * q^7 - 4 * q^9 + 4 * q^10 + 4 * q^12 - 8 * q^13 - 8 * q^15 - 8 * q^16 + 8 * q^18 + 16 * q^19 - 8 * q^21 + 12 * q^22 + 16 * q^24 + 12 * q^25 - 20 * q^27 - 20 * q^28 + 4 * q^30 - 36 * q^34 - 4 * q^36 - 8 * q^39 + 16 * q^40 + 4 * q^42 - 16 * q^45 - 4 * q^46 - 8 * q^48 + 4 * q^49 - 8 * q^52 + 4 * q^54 + 16 * q^57 - 24 * q^58 - 8 * q^60 + 40 * q^61 + 8 * q^63 - 32 * q^64 + 12 * q^66 + 8 * q^69 + 4 * q^70 + 32 * q^72 + 12 * q^75 + 16 * q^76 - 8 * q^78 + 32 * q^79 - 28 * q^81 + 12 * q^82 - 20 * q^84 - 4 * q^90 + 16 * q^91 + 24 * q^94 + 16 * q^96

Introduction

L-functions

Modular forms

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Database

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