LMFDB - Embedded newform 930.2.h.a.371.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(371,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("930.371");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.h (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			371.4
Root			$1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	930.371
Dual form			930.2.h.a.371.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(1.22474 - 1.22474i) q^{3} -1.00000 q^{4} -1.00000i q^{5} +(1.22474 + 1.22474i) q^{6} -4.00000 q^{7} -1.00000i q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(1.22474 - 1.22474i) q^{3} -1.00000 q^{4} -1.00000i q^{5} +(1.22474 + 1.22474i) q^{6} -4.00000 q^{7} -1.00000i q^{8} -3.00000i q^{9} +1.00000 q^{10} +4.89898 q^{11} +(-1.22474 + 1.22474i) q^{12} -2.44949i q^{13} -4.00000i q^{14} +(-1.22474 - 1.22474i) q^{15} +1.00000 q^{16} -7.34847 q^{17} +3.00000 q^{18} -2.00000 q^{19} +1.00000i q^{20} +(-4.89898 + 4.89898i) q^{21} +4.89898i q^{22} -7.34847 q^{23} +(-1.22474 - 1.22474i) q^{24} -1.00000 q^{25} +2.44949 q^{26} +(-3.67423 - 3.67423i) q^{27} +4.00000 q^{28} +(1.22474 - 1.22474i) q^{30} +(5.00000 - 2.44949i) q^{31} +1.00000i q^{32} +(6.00000 - 6.00000i) q^{33} -7.34847i q^{34} +4.00000i q^{35} +3.00000i q^{36} +2.44949i q^{37} -2.00000i q^{38} +(-3.00000 - 3.00000i) q^{39} -1.00000 q^{40} -12.0000i q^{41} +(-4.89898 - 4.89898i) q^{42} +2.44949i q^{43} -4.89898 q^{44} -3.00000 q^{45} -7.34847i q^{46} -12.0000i q^{47} +(1.22474 - 1.22474i) q^{48} +9.00000 q^{49} -1.00000i q^{50} +(-9.00000 + 9.00000i) q^{51} +2.44949i q^{52} -2.44949 q^{53} +(3.67423 - 3.67423i) q^{54} -4.89898i q^{55} +4.00000i q^{56} +(-2.44949 + 2.44949i) q^{57} +6.00000i q^{59} +(1.22474 + 1.22474i) q^{60} +(2.44949 + 5.00000i) q^{62} +12.0000i q^{63} -1.00000 q^{64} -2.44949 q^{65} +(6.00000 + 6.00000i) q^{66} +4.00000 q^{67} +7.34847 q^{68} +(-9.00000 + 9.00000i) q^{69} -4.00000 q^{70} -3.00000 q^{72} +2.44949i q^{73} -2.44949 q^{74} +(-1.22474 + 1.22474i) q^{75} +2.00000 q^{76} -19.5959 q^{77} +(3.00000 - 3.00000i) q^{78} -4.89898i q^{79} -1.00000i q^{80} -9.00000 q^{81} +12.0000 q^{82} +12.2474 q^{83} +(4.89898 - 4.89898i) q^{84} +7.34847i q^{85} -2.44949 q^{86} -4.89898i q^{88} -4.89898 q^{89} -3.00000i q^{90} +9.79796i q^{91} +7.34847 q^{92} +(3.12372 - 9.12372i) q^{93} +12.0000 q^{94} +2.00000i q^{95} +(1.22474 + 1.22474i) q^{96} +14.0000 q^{97} +9.00000i q^{98} -14.6969i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 16 q^{7}+O(q^{10}) $ 4 * q - 4 * q^4 - 16 * q^7	$ 4 q - 4 q^{4} - 16 q^{7} + 4 q^{10} + 4 q^{16} + 12 q^{18} - 8 q^{19} - 4 q^{25} + 16 q^{28} + 20 q^{31} + 24 q^{33} - 12 q^{39} - 4 q^{40} - 12 q^{45} + 36 q^{49} - 36 q^{51} - 4 q^{64} + 24 q^{66} + 16 q^{67} - 36 q^{69} - 16 q^{70} - 12 q^{72} + 8 q^{76} + 12 q^{78} - 36 q^{81} + 48 q^{82} - 12 q^{93} + 48 q^{94} + 56 q^{97}+O(q^{100}) $ 4 * q - 4 * q^4 - 16 * q^7 + 4 * q^10 + 4 * q^16 + 12 * q^18 - 8 * q^19 - 4 * q^25 + 16 * q^28 + 20 * q^31 + 24 * q^33 - 12 * q^39 - 4 * q^40 - 12 * q^45 + 36 * q^49 - 36 * q^51 - 4 * q^64 + 24 * q^66 + 16 * q^67 - 36 * q^69 - 16 * q^70 - 12 * q^72 + 8 * q^76 + 12 * q^78 - 36 * q^81 + 48 * q^82 - 12 * q^93 + 48 * q^94 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	1.22474	−	1.22474i	0.707107	−	0.707107i
$3$	1.22474	−	1.22474i	0.707107	−	0.707107i
$4$	−1.00000			−0.500000
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	1.22474	+	1.22474i	0.500000	+	0.500000i
$7$	−4.00000			−1.51186			−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−4.00000			−1.51186			−0.755929	+	0.654654i	$0.772814\pi$
$8$		−	1.00000i		−	0.353553i
$9$		−	3.00000i		−	1.00000i
$10$	1.00000			0.316228
$11$	4.89898			1.47710			0.738549	−	0.674200i	$-0.235511\pi$
$11$	4.89898			1.47710			0.738549	+	0.674200i	$0.235511\pi$
$12$	−1.22474	+	1.22474i	−0.353553	+	0.353553i
$13$		−	2.44949i		−	0.679366i	−0.940540	−	0.339683i	$-0.889680\pi$
$13$		−	2.44949i		−	0.679366i	0.940540	−	0.339683i	$-0.110320\pi$
$14$		−	4.00000i		−	1.06904i
$15$	−1.22474	−	1.22474i	−0.316228	−	0.316228i
$16$	1.00000			0.250000
$17$	−7.34847			−1.78227			−0.891133	−	0.453743i	$-0.850089\pi$
$17$	−7.34847			−1.78227			−0.891133	+	0.453743i	$0.850089\pi$
$18$	3.00000			0.707107
$19$	−2.00000			−0.458831			−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000			−0.458831			−0.229416	+	0.973329i	$0.573682\pi$
$20$			1.00000i			0.223607i
$21$	−4.89898	+	4.89898i	−1.06904	+	1.06904i
$22$			4.89898i			1.04447i
$23$	−7.34847			−1.53226			−0.766131	−	0.642685i	$-0.777821\pi$
$23$	−7.34847			−1.53226			−0.766131	+	0.642685i	$0.777821\pi$
$24$	−1.22474	−	1.22474i	−0.250000	−	0.250000i
$25$	−1.00000			−0.200000
$26$	2.44949			0.480384
$27$	−3.67423	−	3.67423i	−0.707107	−	0.707107i
$28$	4.00000			0.755929
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$	1.22474	−	1.22474i	0.223607	−	0.223607i
$31$	5.00000	−	2.44949i	0.898027	−	0.439941i
$31$	5.00000	−	2.44949i	0.898027	−	0.439941i
$32$			1.00000i			0.176777i
$33$	6.00000	−	6.00000i	1.04447	−	1.04447i
$34$		−	7.34847i		−	1.26025i
$35$			4.00000i			0.676123i
$36$			3.00000i			0.500000i
$37$			2.44949i			0.402694i	0.979520	+	0.201347i	$0.0645318\pi$
$37$			2.44949i			0.402694i	−0.979520	+	0.201347i	$0.935468\pi$
$38$		−	2.00000i		−	0.324443i
$39$	−3.00000	−	3.00000i	−0.480384	−	0.480384i
$40$	−1.00000			−0.158114
$41$		−	12.0000i		−	1.87409i	−0.349215	−	0.937043i	$-0.613552\pi$
$41$		−	12.0000i		−	1.87409i	0.349215	−	0.937043i	$-0.386448\pi$
$42$	−4.89898	−	4.89898i	−0.755929	−	0.755929i
$43$			2.44949i			0.373544i	0.982403	+	0.186772i	$0.0598025\pi$
$43$			2.44949i			0.373544i	−0.982403	+	0.186772i	$0.940197\pi$
$44$	−4.89898			−0.738549
$45$	−3.00000			−0.447214
$46$		−	7.34847i		−	1.08347i
$47$		−	12.0000i		−	1.75038i	−0.483779	−	0.875190i	$-0.660736\pi$
$47$		−	12.0000i		−	1.75038i	0.483779	−	0.875190i	$-0.339264\pi$
$48$	1.22474	−	1.22474i	0.176777	−	0.176777i
$49$	9.00000			1.28571
$50$		−	1.00000i		−	0.141421i
$51$	−9.00000	+	9.00000i	−1.26025	+	1.26025i
$52$			2.44949i			0.339683i
$53$	−2.44949			−0.336463			−0.168232	−	0.985747i	$-0.553806\pi$
$53$	−2.44949			−0.336463			−0.168232	+	0.985747i	$0.553806\pi$
$54$	3.67423	−	3.67423i	0.500000	−	0.500000i
$55$		−	4.89898i		−	0.660578i
$56$			4.00000i			0.534522i
$57$	−2.44949	+	2.44949i	−0.324443	+	0.324443i
$58$		0			0
$59$			6.00000i			0.781133i	0.920575	+	0.390567i	$0.127721\pi$
$59$			6.00000i			0.781133i	−0.920575	+	0.390567i	$0.872279\pi$
$60$	1.22474	+	1.22474i	0.158114	+	0.158114i
$61$		0			0		1.00000			$0$
$61$		0			0		−1.00000			$\pi$
$62$	2.44949	+	5.00000i	0.311086	+	0.635001i
$63$			12.0000i			1.51186i
$64$	−1.00000			−0.125000
$65$	−2.44949			−0.303822
$66$	6.00000	+	6.00000i	0.738549	+	0.738549i
$67$	4.00000			0.488678			0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000			0.488678			0.244339	+	0.969690i	$0.421429\pi$
$68$	7.34847			0.891133
$69$	−9.00000	+	9.00000i	−1.08347	+	1.08347i
$70$	−4.00000			−0.478091
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	−3.00000			−0.353553
$73$			2.44949i			0.286691i	0.989673	+	0.143346i	$0.0457860\pi$
$73$			2.44949i			0.286691i	−0.989673	+	0.143346i	$0.954214\pi$
$74$	−2.44949			−0.284747
$75$	−1.22474	+	1.22474i	−0.141421	+	0.141421i
$76$	2.00000			0.229416
$77$	−19.5959			−2.23316
$78$	3.00000	−	3.00000i	0.339683	−	0.339683i
$79$		−	4.89898i		−	0.551178i	−0.961276	−	0.275589i	$-0.911127\pi$
$79$		−	4.89898i		−	0.551178i	0.961276	−	0.275589i	$-0.0888729\pi$
$80$		−	1.00000i		−	0.111803i
$81$	−9.00000			−1.00000
$82$	12.0000			1.32518
$83$	12.2474			1.34433			0.672166	−	0.740400i	$-0.265364\pi$
$83$	12.2474			1.34433			0.672166	+	0.740400i	$0.265364\pi$
$84$	4.89898	−	4.89898i	0.534522	−	0.534522i
$85$			7.34847i			0.797053i
$86$	−2.44949			−0.264135
$87$		0			0
$88$		−	4.89898i		−	0.522233i
$89$	−4.89898			−0.519291			−0.259645	−	0.965704i	$-0.583606\pi$
$89$	−4.89898			−0.519291			−0.259645	+	0.965704i	$0.583606\pi$
$90$		−	3.00000i		−	0.316228i
$91$			9.79796i			1.02711i
$92$	7.34847			0.766131
$93$	3.12372	−	9.12372i	0.323915	−	0.946086i
$94$	12.0000			1.23771
$95$			2.00000i			0.205196i
$96$	1.22474	+	1.22474i	0.125000	+	0.125000i
$97$	14.0000			1.42148			0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000			1.42148			0.710742	+	0.703452i	$0.248359\pi$
$98$			9.00000i			0.909137i
$99$		−	14.6969i		−	1.47710i
$100$	1.00000			0.100000
$101$		−	6.00000i		−	0.597022i	−0.954406	−	0.298511i	$-0.903510\pi$
$101$		−	6.00000i		−	0.597022i	0.954406	−	0.298511i	$-0.0964900\pi$
$102$	−9.00000	−	9.00000i	−0.891133	−	0.891133i
$103$	4.00000			0.394132			0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000			0.394132			0.197066	+	0.980390i	$0.436859\pi$
$104$	−2.44949			−0.240192
$105$	4.89898	+	4.89898i	0.478091	+	0.478091i
$106$		−	2.44949i		−	0.237915i
$107$		−	12.0000i		−	1.16008i	−0.814587	−	0.580042i	$-0.803036\pi$
$107$		−	12.0000i		−	1.16008i	0.814587	−	0.580042i	$-0.196964\pi$
$108$	3.67423	+	3.67423i	0.353553	+	0.353553i
$109$	−16.0000			−1.53252			−0.766261	−	0.642529i	$-0.777885\pi$
$109$	−16.0000			−1.53252			−0.766261	+	0.642529i	$0.777885\pi$
$110$	4.89898			0.467099
$111$	3.00000	+	3.00000i	0.284747	+	0.284747i
$112$	−4.00000			−0.377964
$113$			18.0000i			1.69330i	0.532152	+	0.846649i	$0.321383\pi$
$113$			18.0000i			1.69330i	−0.532152	+	0.846649i	$0.678617\pi$
$114$	−2.44949	−	2.44949i	−0.229416	−	0.229416i
$115$			7.34847i			0.685248i
$116$		0			0
$117$	−7.34847			−0.679366
$118$	−6.00000			−0.552345
$119$	29.3939			2.69453
$120$	−1.22474	+	1.22474i	−0.111803	+	0.111803i
$121$	13.0000			1.18182
$122$		0			0
$123$	−14.6969	−	14.6969i	−1.32518	−	1.32518i
$124$	−5.00000	+	2.44949i	−0.449013	+	0.219971i
$125$			1.00000i			0.0894427i
$126$	−12.0000			−1.06904
$127$			7.34847i			0.652071i	0.945357	+	0.326036i	$0.105713\pi$
$127$			7.34847i			0.652071i	−0.945357	+	0.326036i	$0.894287\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	3.00000	+	3.00000i	0.264135	+	0.264135i
$130$		−	2.44949i		−	0.214834i
$131$		−	12.0000i		−	1.04844i	−0.851581	−	0.524222i	$-0.824356\pi$
$131$		−	12.0000i		−	1.04844i	0.851581	−	0.524222i	$-0.175644\pi$
$132$	−6.00000	+	6.00000i	−0.522233	+	0.522233i
$133$	8.00000			0.693688
$134$			4.00000i			0.345547i
$135$	−3.67423	+	3.67423i	−0.316228	+	0.316228i
$136$			7.34847i			0.630126i
$137$	12.2474			1.04637			0.523185	−	0.852219i	$-0.324744\pi$
$137$	12.2474			1.04637			0.523185	+	0.852219i	$0.324744\pi$
$138$	−9.00000	−	9.00000i	−0.766131	−	0.766131i
$139$			4.89898i			0.415526i	0.978179	+	0.207763i	$0.0666183\pi$
$139$			4.89898i			0.415526i	−0.978179	+	0.207763i	$0.933382\pi$
$140$		−	4.00000i		−	0.338062i
$141$	−14.6969	−	14.6969i	−1.23771	−	1.23771i
$142$		0			0
$143$		−	12.0000i		−	1.00349i
$144$		−	3.00000i		−	0.250000i
$145$		0			0
$146$	−2.44949			−0.202721
$147$	11.0227	−	11.0227i	0.909137	−	0.909137i
$148$		−	2.44949i		−	0.201347i
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$	−1.22474	−	1.22474i	−0.100000	−	0.100000i
$151$			14.6969i			1.19602i	0.801489	+	0.598010i	$0.204042\pi$
$151$			14.6969i			1.19602i	−0.801489	+	0.598010i	$0.795958\pi$
$152$			2.00000i			0.162221i
$153$			22.0454i			1.78227i
$154$		−	19.5959i		−	1.57908i
$155$	−2.44949	−	5.00000i	−0.196748	−	0.401610i
$156$	3.00000	+	3.00000i	0.240192	+	0.240192i
$157$	10.0000			0.798087			0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000			0.798087			0.399043	+	0.916932i	$0.369342\pi$
$158$	4.89898			0.389742
$159$	−3.00000	+	3.00000i	−0.237915	+	0.237915i
$160$	1.00000			0.0790569
$161$	29.3939			2.31656
$162$		−	9.00000i		−	0.707107i
$163$	20.0000			1.56652			0.783260	−	0.621694i	$-0.213555\pi$
$163$	20.0000			1.56652			0.783260	+	0.621694i	$0.213555\pi$
$164$			12.0000i			0.937043i
$165$	−6.00000	−	6.00000i	−0.467099	−	0.467099i
$166$			12.2474i			0.950586i
$167$	−7.34847			−0.568642			−0.284321	−	0.958729i	$-0.591768\pi$
$167$	−7.34847			−0.568642			−0.284321	+	0.958729i	$0.591768\pi$
$168$	4.89898	+	4.89898i	0.377964	+	0.377964i
$169$	7.00000			0.538462
$170$	−7.34847			−0.563602
$171$			6.00000i			0.458831i
$172$		−	2.44949i		−	0.186772i
$173$			6.00000i			0.456172i	0.973641	+	0.228086i	$0.0732467\pi$
$173$			6.00000i			0.456172i	−0.973641	+	0.228086i	$0.926753\pi$
$174$		0			0
$175$	4.00000			0.302372
$176$	4.89898			0.369274
$177$	7.34847	+	7.34847i	0.552345	+	0.552345i
$178$		−	4.89898i		−	0.367194i
$179$	14.6969			1.09850			0.549250	−	0.835658i	$-0.314913\pi$
$179$	14.6969			1.09850			0.549250	+	0.835658i	$0.314913\pi$
$180$	3.00000			0.223607
$181$			24.4949i			1.82069i	0.413849	+	0.910346i	$0.364184\pi$
$181$			24.4949i			1.82069i	−0.413849	+	0.910346i	$0.635816\pi$
$182$	−9.79796			−0.726273
$183$		0			0
$184$			7.34847i			0.541736i
$185$	2.44949			0.180090
$186$	9.12372	+	3.12372i	0.668984	+	0.229043i
$187$	−36.0000			−2.63258
$188$			12.0000i			0.875190i
$189$	14.6969	+	14.6969i	1.06904	+	1.06904i
$190$	−2.00000			−0.145095
$191$		−	18.0000i		−	1.30243i	−0.758891	−	0.651217i	$-0.774259\pi$
$191$		−	18.0000i		−	1.30243i	0.758891	−	0.651217i	$-0.225741\pi$
$192$	−1.22474	+	1.22474i	−0.0883883	+	0.0883883i
$193$	−2.00000			−0.143963			−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000			−0.143963			−0.0719816	+	0.997406i	$0.522932\pi$
$194$			14.0000i			1.00514i
$195$	−3.00000	+	3.00000i	−0.214834	+	0.214834i
$196$	−9.00000			−0.642857
$197$	−22.0454			−1.57067			−0.785335	−	0.619071i	$-0.787509\pi$
$197$	−22.0454			−1.57067			−0.785335	+	0.619071i	$0.787509\pi$
$198$	14.6969			1.04447
$199$		−	9.79796i		−	0.694559i	−0.937762	−	0.347279i	$-0.887106\pi$
$199$		−	9.79796i		−	0.694559i	0.937762	−	0.347279i	$-0.112894\pi$
$200$			1.00000i			0.0707107i
$201$	4.89898	−	4.89898i	0.345547	−	0.345547i
$202$	6.00000			0.422159
$203$		0			0
$204$	9.00000	−	9.00000i	0.630126	−	0.630126i
$205$	−12.0000			−0.838116
$206$			4.00000i			0.278693i
$207$			22.0454i			1.53226i
$208$		−	2.44949i		−	0.169842i
$209$	−9.79796			−0.677739
$210$	−4.89898	+	4.89898i	−0.338062	+	0.338062i
$211$	14.0000			0.963800			0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000			0.963800			0.481900	+	0.876226i	$0.339947\pi$
$212$	2.44949			0.168232
$213$		0			0
$214$	12.0000			0.820303
$215$	2.44949			0.167054
$216$	−3.67423	+	3.67423i	−0.250000	+	0.250000i
$217$	−20.0000	+	9.79796i	−1.35769	+	0.665129i
$218$		−	16.0000i		−	1.08366i
$219$	3.00000	+	3.00000i	0.202721	+	0.202721i
$220$			4.89898i			0.330289i
$221$			18.0000i			1.21081i
$222$	−3.00000	+	3.00000i	−0.201347	+	0.201347i
$223$		−	26.9444i		−	1.80433i	−0.431392	−	0.902165i	$-0.641977\pi$
$223$		−	26.9444i		−	1.80433i	0.431392	−	0.902165i	$-0.358023\pi$
$224$		−	4.00000i		−	0.267261i
$225$			3.00000i			0.200000i
$226$	−18.0000			−1.19734
$227$		0			0		1.00000			$0$
$227$		0			0		−1.00000			$\pi$
$228$	2.44949	−	2.44949i	0.162221	−	0.162221i
$229$			9.79796i			0.647467i	0.946148	+	0.323734i	$0.104938\pi$
$229$			9.79796i			0.647467i	−0.946148	+	0.323734i	$0.895062\pi$
$230$	−7.34847			−0.484544
$231$	−24.0000	+	24.0000i	−1.57908	+	1.57908i
$232$		0			0
$233$		−	6.00000i		−	0.393073i	−0.980497	−	0.196537i	$-0.937031\pi$
$233$		−	6.00000i		−	0.393073i	0.980497	−	0.196537i	$-0.0629694\pi$
$234$		−	7.34847i		−	0.480384i
$235$	−12.0000			−0.782794
$236$		−	6.00000i		−	0.390567i
$237$	−6.00000	−	6.00000i	−0.389742	−	0.389742i
$238$			29.3939i			1.90532i
$239$	14.6969			0.950666			0.475333	−	0.879806i	$-0.342328\pi$
$239$	14.6969			0.950666			0.475333	+	0.879806i	$0.342328\pi$
$240$	−1.22474	−	1.22474i	−0.0790569	−	0.0790569i
$241$		−	4.89898i		−	0.315571i	−0.987473	−	0.157786i	$-0.949565\pi$
$241$		−	4.89898i		−	0.315571i	0.987473	−	0.157786i	$-0.0504355\pi$
$242$			13.0000i			0.835672i
$243$	−11.0227	+	11.0227i	−0.707107	+	0.707107i
$244$		0			0
$245$		−	9.00000i		−	0.574989i
$246$	14.6969	−	14.6969i	0.937043	−	0.937043i
$247$			4.89898i			0.311715i
$248$	−2.44949	−	5.00000i	−0.155543	−	0.317500i
$249$	15.0000	−	15.0000i	0.950586	−	0.950586i
$250$	−1.00000			−0.0632456
$251$	−9.79796			−0.618442			−0.309221	−	0.950990i	$-0.600068\pi$
$251$	−9.79796			−0.618442			−0.309221	+	0.950990i	$0.600068\pi$
$252$		−	12.0000i		−	0.755929i
$253$	−36.0000			−2.26330
$254$	−7.34847			−0.461084
$255$	9.00000	+	9.00000i	0.563602	+	0.563602i
$256$	1.00000			0.0625000
$257$		−	18.0000i		−	1.12281i	−0.827541	−	0.561405i	$-0.810261\pi$
$257$		−	18.0000i		−	1.12281i	0.827541	−	0.561405i	$-0.189739\pi$
$258$	−3.00000	+	3.00000i	−0.186772	+	0.186772i
$259$		−	9.79796i		−	0.608816i
$260$	2.44949			0.151911
$261$		0			0
$262$	12.0000			0.741362
$263$	−31.8434			−1.96355			−0.981773	−	0.190057i	$-0.939133\pi$
$263$	−31.8434			−1.96355			−0.981773	+	0.190057i	$0.939133\pi$
$264$	−6.00000	−	6.00000i	−0.369274	−	0.369274i
$265$			2.44949i			0.150471i
$266$			8.00000i			0.490511i
$267$	−6.00000	+	6.00000i	−0.367194	+	0.367194i
$268$	−4.00000			−0.244339
$269$	−4.89898			−0.298696			−0.149348	−	0.988785i	$-0.547717\pi$
$269$	−4.89898			−0.298696			−0.149348	+	0.988785i	$0.547717\pi$
$270$	−3.67423	−	3.67423i	−0.223607	−	0.223607i
$271$		−	9.79796i		−	0.595184i	−0.954693	−	0.297592i	$-0.903817\pi$
$271$		−	9.79796i		−	0.595184i	0.954693	−	0.297592i	$-0.0961834\pi$
$272$	−7.34847			−0.445566
$273$	12.0000	+	12.0000i	0.726273	+	0.726273i
$274$			12.2474i			0.739895i
$275$	−4.89898			−0.295420
$276$	9.00000	−	9.00000i	0.541736	−	0.541736i
$277$			17.1464i			1.03023i	0.857121	+	0.515115i	$0.172251\pi$
$277$			17.1464i			1.03023i	−0.857121	+	0.515115i	$0.827749\pi$
$278$	−4.89898			−0.293821
$279$	−7.34847	−	15.0000i	−0.439941	−	0.898027i
$280$	4.00000			0.239046
$281$			6.00000i			0.357930i	0.983855	+	0.178965i	$0.0572749\pi$
$281$			6.00000i			0.357930i	−0.983855	+	0.178965i	$0.942725\pi$
$282$	14.6969	−	14.6969i	0.875190	−	0.875190i
$283$	−4.00000			−0.237775			−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000			−0.237775			−0.118888	+	0.992908i	$0.537933\pi$
$284$		0			0
$285$	2.44949	+	2.44949i	0.145095	+	0.145095i
$286$	12.0000			0.709575
$287$			48.0000i			2.83335i
$288$	3.00000			0.176777
$289$	37.0000			2.17647
$290$		0			0
$291$	17.1464	−	17.1464i	1.00514	−	1.00514i
$292$		−	2.44949i		−	0.143346i
$293$			6.00000i			0.350524i	0.984522	+	0.175262i	$0.0560772\pi$
$293$			6.00000i			0.350524i	−0.984522	+	0.175262i	$0.943923\pi$
$294$	11.0227	+	11.0227i	0.642857	+	0.642857i
$295$	6.00000			0.349334
$296$	2.44949			0.142374
$297$	−18.0000	−	18.0000i	−1.04447	−	1.04447i
$298$		0			0
$299$			18.0000i			1.04097i
$300$	1.22474	−	1.22474i	0.0707107	−	0.0707107i
$301$		−	9.79796i		−	0.564745i
$302$	−14.6969			−0.845714
$303$	−7.34847	−	7.34847i	−0.422159	−	0.422159i
$304$	−2.00000			−0.114708
$305$		0			0
$306$	−22.0454			−1.26025
$307$	16.0000			0.913168			0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000			0.913168			0.456584	+	0.889680i	$0.349073\pi$
$308$	19.5959			1.11658
$309$	4.89898	−	4.89898i	0.278693	−	0.278693i
$310$	5.00000	−	2.44949i	0.283981	−	0.139122i
$311$		−	6.00000i		−	0.340229i	−0.985424	−	0.170114i	$-0.945586\pi$
$311$		−	6.00000i		−	0.340229i	0.985424	−	0.170114i	$-0.0544137\pi$
$312$	−3.00000	+	3.00000i	−0.169842	+	0.169842i
$313$		−	17.1464i		−	0.969173i	−0.874743	−	0.484587i	$-0.838970\pi$
$313$		−	17.1464i		−	0.969173i	0.874743	−	0.484587i	$-0.161030\pi$
$314$			10.0000i			0.564333i
$315$	12.0000			0.676123
$316$			4.89898i			0.275589i
$317$		−	6.00000i		−	0.336994i	−0.985702	−	0.168497i	$-0.946109\pi$
$317$		−	6.00000i		−	0.336994i	0.985702	−	0.168497i	$-0.0538913\pi$
$318$	−3.00000	−	3.00000i	−0.168232	−	0.168232i
$319$		0			0
$320$			1.00000i			0.0559017i
$321$	−14.6969	−	14.6969i	−0.820303	−	0.820303i
$322$			29.3939i			1.63806i
$323$	14.6969			0.817760
$324$	9.00000			0.500000
$325$			2.44949i			0.135873i
$326$			20.0000i			1.10770i
$327$	−19.5959	+	19.5959i	−1.08366	+	1.08366i
$328$	−12.0000			−0.662589
$329$			48.0000i			2.64633i
$330$	6.00000	−	6.00000i	0.330289	−	0.330289i
$331$		−	24.4949i		−	1.34636i	−0.739478	−	0.673181i	$-0.764928\pi$
$331$		−	24.4949i		−	1.34636i	0.739478	−	0.673181i	$-0.235072\pi$
$332$	−12.2474			−0.672166
$333$	7.34847			0.402694
$334$		−	7.34847i		−	0.402090i
$335$		−	4.00000i		−	0.218543i
$336$	−4.89898	+	4.89898i	−0.267261	+	0.267261i
$337$		−	26.9444i		−	1.46775i	−0.679282	−	0.733877i	$-0.737709\pi$
$337$		−	26.9444i		−	1.46775i	0.679282	−	0.733877i	$-0.262291\pi$
$338$			7.00000i			0.380750i
$339$	22.0454	+	22.0454i	1.19734	+	1.19734i
$340$		−	7.34847i		−	0.398527i
$341$	24.4949	−	12.0000i	1.32647	−	0.649836i
$342$	−6.00000			−0.324443
$343$	−8.00000			−0.431959
$344$	2.44949			0.132068
$345$	9.00000	+	9.00000i	0.484544	+	0.484544i
$346$	−6.00000			−0.322562
$347$	17.1464			0.920468			0.460234	−	0.887798i	$-0.347765\pi$
$347$	17.1464			0.920468			0.460234	+	0.887798i	$0.347765\pi$
$348$		0			0
$349$	−2.00000			−0.107058			−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000			−0.107058			−0.0535288	+	0.998566i	$0.517047\pi$
$350$			4.00000i			0.213809i
$351$	−9.00000	+	9.00000i	−0.480384	+	0.480384i
$352$			4.89898i			0.261116i
$353$	2.44949			0.130373			0.0651866	−	0.997873i	$-0.479236\pi$
$353$	2.44949			0.130373			0.0651866	+	0.997873i	$0.479236\pi$
$354$	−7.34847	+	7.34847i	−0.390567	+	0.390567i
$355$		0			0
$356$	4.89898			0.259645
$357$	36.0000	−	36.0000i	1.90532	−	1.90532i
$358$			14.6969i			0.776757i
$359$		−	24.0000i		−	1.26667i	−0.773877	−	0.633336i	$-0.781685\pi$
$359$		−	24.0000i		−	1.26667i	0.773877	−	0.633336i	$-0.218315\pi$
$360$			3.00000i			0.158114i
$361$	−15.0000			−0.789474
$362$	−24.4949			−1.28742
$363$	15.9217	−	15.9217i	0.835672	−	0.835672i
$364$		−	9.79796i		−	0.513553i
$365$	2.44949			0.128212
$366$		0			0
$367$			26.9444i			1.40649i	0.710950	+	0.703243i	$0.248265\pi$
$367$			26.9444i			1.40649i	−0.710950	+	0.703243i	$0.751735\pi$
$368$	−7.34847			−0.383065
$369$	−36.0000			−1.87409
$370$			2.44949i			0.127343i
$371$	9.79796			0.508685
$372$	−3.12372	+	9.12372i	−0.161958	+	0.473043i
$373$	2.00000			0.103556			0.0517780	−	0.998659i	$-0.483511\pi$
$373$	2.00000			0.103556			0.0517780	+	0.998659i	$0.483511\pi$
$374$		−	36.0000i		−	1.86152i
$375$	1.22474	+	1.22474i	0.0632456	+	0.0632456i
$376$	−12.0000			−0.618853
$377$		0			0
$378$	−14.6969	+	14.6969i	−0.755929	+	0.755929i
$379$	20.0000			1.02733			0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000			1.02733			0.513665	+	0.857991i	$0.328287\pi$
$380$		−	2.00000i		−	0.102598i
$381$	9.00000	+	9.00000i	0.461084	+	0.461084i
$382$	18.0000			0.920960
$383$	26.9444			1.37679			0.688397	−	0.725334i	$-0.258315\pi$
$383$	26.9444			1.37679			0.688397	+	0.725334i	$0.258315\pi$
$384$	−1.22474	−	1.22474i	−0.0625000	−	0.0625000i
$385$			19.5959i			0.998700i
$386$		−	2.00000i		−	0.101797i
$387$	7.34847			0.373544
$388$	−14.0000			−0.710742
$389$	−4.89898			−0.248388			−0.124194	−	0.992258i	$-0.539635\pi$
$389$	−4.89898			−0.248388			−0.124194	+	0.992258i	$0.539635\pi$
$390$	−3.00000	−	3.00000i	−0.151911	−	0.151911i
$391$	54.0000			2.73090
$392$		−	9.00000i		−	0.454569i
$393$	−14.6969	−	14.6969i	−0.741362	−	0.741362i
$394$		−	22.0454i		−	1.11063i
$395$	−4.89898			−0.246494
$396$			14.6969i			0.738549i
$397$	−34.0000			−1.70641			−0.853206	−	0.521575i	$-0.825345\pi$
$397$	−34.0000			−1.70641			−0.853206	+	0.521575i	$0.825345\pi$
$398$	9.79796			0.491127
$399$	9.79796	−	9.79796i	0.490511	−	0.490511i
$400$	−1.00000			−0.0500000
$401$	−19.5959			−0.978573			−0.489287	−	0.872123i	$-0.662743\pi$
$401$	−19.5959			−0.978573			−0.489287	+	0.872123i	$0.662743\pi$
$402$	4.89898	+	4.89898i	0.244339	+	0.244339i
$403$	−6.00000	−	12.2474i	−0.298881	−	0.610089i
$404$			6.00000i			0.298511i
$405$			9.00000i			0.447214i
$406$		0			0
$407$			12.0000i			0.594818i
$408$	9.00000	+	9.00000i	0.445566	+	0.445566i
$409$			19.5959i			0.968956i	0.874804	+	0.484478i	$0.160990\pi$
$409$			19.5959i			0.968956i	−0.874804	+	0.484478i	$0.839010\pi$
$410$		−	12.0000i		−	0.592638i
$411$	15.0000	−	15.0000i	0.739895	−	0.739895i
$412$	−4.00000			−0.197066
$413$		−	24.0000i		−	1.18096i
$414$	−22.0454			−1.08347
$415$		−	12.2474i		−	0.601204i
$416$	2.44949			0.120096
$417$	6.00000	+	6.00000i	0.293821	+	0.293821i
$418$		−	9.79796i		−	0.479234i
$419$			30.0000i			1.46560i	0.680446	+	0.732798i	$0.261786\pi$
$419$			30.0000i			1.46560i	−0.680446	+	0.732798i	$0.738214\pi$
$420$	−4.89898	−	4.89898i	−0.239046	−	0.239046i
$421$	−26.0000			−1.26716			−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000			−1.26716			−0.633581	+	0.773676i	$0.718416\pi$
$422$			14.0000i			0.681509i
$423$	−36.0000			−1.75038
$424$			2.44949i			0.118958i
$425$	7.34847			0.356453
$426$		0			0
$427$		0			0
$428$			12.0000i			0.580042i
$429$	−14.6969	−	14.6969i	−0.709575	−	0.709575i
$430$			2.44949i			0.118125i
$431$		−	24.0000i		−	1.15604i	−0.816023	−	0.578020i	$-0.803826\pi$
$431$		−	24.0000i		−	1.15604i	0.816023	−	0.578020i	$-0.196174\pi$
$432$	−3.67423	−	3.67423i	−0.176777	−	0.176777i
$433$		−	17.1464i		−	0.824005i	−0.911183	−	0.412002i	$-0.864830\pi$
$433$		−	17.1464i		−	0.824005i	0.911183	−	0.412002i	$-0.135170\pi$
$434$	−9.79796	−	20.0000i	−0.470317	−	0.960031i
$435$		0			0
$436$	16.0000			0.766261
$437$	14.6969			0.703050
$438$	−3.00000	+	3.00000i	−0.143346	+	0.143346i
$439$	−8.00000			−0.381819			−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000			−0.381819			−0.190910	+	0.981608i	$0.561144\pi$
$440$	−4.89898			−0.233550
$441$		−	27.0000i		−	1.28571i
$442$	−18.0000			−0.856173
$443$		−	24.0000i		−	1.14027i	−0.821549	−	0.570137i	$-0.806890\pi$
$443$		−	24.0000i		−	1.14027i	0.821549	−	0.570137i	$-0.193110\pi$
$444$	−3.00000	−	3.00000i	−0.142374	−	0.142374i
$445$			4.89898i			0.232234i
$446$	26.9444			1.27585
$447$		0			0
$448$	4.00000			0.188982
$449$	−29.3939			−1.38718			−0.693591	−	0.720369i	$-0.743973\pi$
$449$	−29.3939			−1.38718			−0.693591	+	0.720369i	$0.743973\pi$
$450$	−3.00000			−0.141421
$451$		−	58.7878i		−	2.76821i
$452$		−	18.0000i		−	0.846649i
$453$	18.0000	+	18.0000i	0.845714	+	0.845714i
$454$		0			0
$455$	9.79796			0.459335
$456$	2.44949	+	2.44949i	0.114708	+	0.114708i
$457$			7.34847i			0.343747i	0.985119	+	0.171873i	$0.0549820\pi$
$457$			7.34847i			0.343747i	−0.985119	+	0.171873i	$0.945018\pi$
$458$	−9.79796			−0.457829
$459$	27.0000	+	27.0000i	1.26025	+	1.26025i
$460$		−	7.34847i		−	0.342624i
$461$	−14.6969			−0.684505			−0.342252	−	0.939608i	$-0.611190\pi$
$461$	−14.6969			−0.684505			−0.342252	+	0.939608i	$0.611190\pi$
$462$	−24.0000	−	24.0000i	−1.11658	−	1.11658i
$463$		−	2.44949i		−	0.113837i	−0.998379	−	0.0569187i	$-0.981872\pi$
$463$		−	2.44949i		−	0.113837i	0.998379	−	0.0569187i	$-0.0181276\pi$
$464$		0			0
$465$	−9.12372	−	3.12372i	−0.423103	−	0.144859i
$466$	6.00000			0.277945
$467$			36.0000i			1.66588i	0.553362	+	0.832941i	$0.313345\pi$
$467$			36.0000i			1.66588i	−0.553362	+	0.832941i	$0.686655\pi$
$468$	7.34847			0.339683
$469$	−16.0000			−0.738811
$470$		−	12.0000i		−	0.553519i
$471$	12.2474	−	12.2474i	0.564333	−	0.564333i
$472$	6.00000			0.276172
$473$			12.0000i			0.551761i
$474$	6.00000	−	6.00000i	0.275589	−	0.275589i
$475$	2.00000			0.0917663
$476$	−29.3939			−1.34727
$477$			7.34847i			0.336463i
$478$			14.6969i			0.672222i
$479$		−	30.0000i		−	1.37073i	−0.728197	−	0.685367i	$-0.759642\pi$
$479$		−	30.0000i		−	1.37073i	0.728197	−	0.685367i	$-0.240358\pi$
$480$	1.22474	−	1.22474i	0.0559017	−	0.0559017i
$481$	6.00000			0.273576
$482$	4.89898			0.223142
$483$	36.0000	−	36.0000i	1.63806	−	1.63806i
$484$	−13.0000			−0.590909
$485$		−	14.0000i		−	0.635707i
$486$	−11.0227	−	11.0227i	−0.500000	−	0.500000i
$487$		−	31.8434i		−	1.44296i	−0.692435	−	0.721480i	$-0.743462\pi$
$487$		−	31.8434i		−	1.44296i	0.692435	−	0.721480i	$-0.256538\pi$
$488$		0			0
$489$	24.4949	−	24.4949i	1.10770	−	1.10770i
$490$	9.00000			0.406579
$491$	−19.5959			−0.884351			−0.442176	−	0.896928i	$-0.645793\pi$
$491$	−19.5959			−0.884351			−0.442176	+	0.896928i	$0.645793\pi$
$492$	14.6969	+	14.6969i	0.662589	+	0.662589i
$493$		0			0
$494$	−4.89898			−0.220416
$495$	−14.6969			−0.660578
$496$	5.00000	−	2.44949i	0.224507	−	0.109985i
$497$		0			0
$498$	15.0000	+	15.0000i	0.672166	+	0.672166i
$499$			9.79796i			0.438617i	0.975656	+	0.219308i	$0.0703801\pi$
$499$			9.79796i			0.438617i	−0.975656	+	0.219308i	$0.929620\pi$
$500$		−	1.00000i		−	0.0447214i
$501$	−9.00000	+	9.00000i	−0.402090	+	0.402090i
$502$		−	9.79796i		−	0.437304i
$503$		−	24.0000i		−	1.07011i	−0.844818	−	0.535054i	$-0.820291\pi$
$503$		−	24.0000i		−	1.07011i	0.844818	−	0.535054i	$-0.179709\pi$
$504$	12.0000			0.534522
$505$	−6.00000			−0.266996
$506$		−	36.0000i		−	1.60040i
$507$	8.57321	−	8.57321i	0.380750	−	0.380750i
$508$		−	7.34847i		−	0.326036i
$509$	39.1918			1.73715			0.868574	−	0.495560i	$-0.165037\pi$
$509$	39.1918			1.73715			0.868574	+	0.495560i	$0.165037\pi$
$510$	−9.00000	+	9.00000i	−0.398527	+	0.398527i
$511$		−	9.79796i		−	0.433436i
$512$			1.00000i			0.0441942i
$513$	7.34847	+	7.34847i	0.324443	+	0.324443i
$514$	18.0000			0.793946
$515$		−	4.00000i		−	0.176261i
$516$	−3.00000	−	3.00000i	−0.132068	−	0.132068i
$517$		−	58.7878i		−	2.58548i
$518$	9.79796			0.430498
$519$	7.34847	+	7.34847i	0.322562	+	0.322562i
$520$			2.44949i			0.107417i
$521$		−	18.0000i		−	0.788594i	−0.918983	−	0.394297i	$-0.870988\pi$
$521$		−	18.0000i		−	0.788594i	0.918983	−	0.394297i	$-0.129012\pi$
$522$		0			0
$523$		−	22.0454i		−	0.963978i	−0.876177	−	0.481989i	$-0.839914\pi$
$523$		−	22.0454i		−	0.963978i	0.876177	−	0.481989i	$-0.160086\pi$
$524$			12.0000i			0.524222i
$525$	4.89898	−	4.89898i	0.213809	−	0.213809i
$526$		−	31.8434i		−	1.38844i
$527$	−36.7423	+	18.0000i	−1.60052	+	0.784092i
$528$	6.00000	−	6.00000i	0.261116	−	0.261116i
$529$	31.0000			1.34783
$530$	−2.44949			−0.106399
$531$	18.0000			0.781133
$532$	−8.00000			−0.346844
$533$	−29.3939			−1.27319
$534$	−6.00000	−	6.00000i	−0.259645	−	0.259645i
$535$	−12.0000			−0.518805
$536$		−	4.00000i		−	0.172774i
$537$	18.0000	−	18.0000i	0.776757	−	0.776757i
$538$		−	4.89898i		−	0.211210i
$539$	44.0908			1.89913
$540$	3.67423	−	3.67423i	0.158114	−	0.158114i
$541$	−8.00000			−0.343947			−0.171973	−	0.985102i	$-0.555014\pi$
$541$	−8.00000			−0.343947			−0.171973	+	0.985102i	$0.555014\pi$
$542$	9.79796			0.420858
$543$	30.0000	+	30.0000i	1.28742	+	1.28742i
$544$		−	7.34847i		−	0.315063i
$545$			16.0000i			0.685365i
$546$	−12.0000	+	12.0000i	−0.513553	+	0.513553i
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$	−12.2474			−0.523185
$549$		0			0
$550$		−	4.89898i		−	0.208893i
$551$		0			0
$552$	9.00000	+	9.00000i	0.383065	+	0.383065i
$553$			19.5959i			0.833303i
$554$	−17.1464			−0.728482
$555$	3.00000	−	3.00000i	0.127343	−	0.127343i
$556$		−	4.89898i		−	0.207763i
$557$	−26.9444			−1.14167			−0.570835	−	0.821065i	$-0.693380\pi$
$557$	−26.9444			−1.14167			−0.570835	+	0.821065i	$0.693380\pi$
$558$	15.0000	−	7.34847i	0.635001	−	0.311086i
$559$	6.00000			0.253773
$560$			4.00000i			0.169031i
$561$	−44.0908	+	44.0908i	−1.86152	+	1.86152i
$562$	−6.00000			−0.253095
$563$		−	12.0000i		−	0.505740i	−0.967500	−	0.252870i	$-0.918626\pi$
$563$		−	12.0000i		−	0.505740i	0.967500	−	0.252870i	$-0.0813744\pi$
$564$	14.6969	+	14.6969i	0.618853	+	0.618853i
$565$	18.0000			0.757266
$566$		−	4.00000i		−	0.168133i
$567$	36.0000			1.51186
$568$		0			0
$569$	−19.5959			−0.821504			−0.410752	−	0.911747i	$-0.634734\pi$
$569$	−19.5959			−0.821504			−0.410752	+	0.911747i	$0.634734\pi$
$570$	−2.44949	+	2.44949i	−0.102598	+	0.102598i
$571$			44.0908i			1.84514i	0.385826	+	0.922572i	$0.373917\pi$
$571$			44.0908i			1.84514i	−0.385826	+	0.922572i	$0.626083\pi$
$572$			12.0000i			0.501745i
$573$	−22.0454	−	22.0454i	−0.920960	−	0.920960i
$574$	−48.0000			−2.00348
$575$	7.34847			0.306452
$576$			3.00000i			0.125000i
$577$	−26.0000			−1.08239			−0.541197	−	0.840896i	$-0.682029\pi$
$577$	−26.0000			−1.08239			−0.541197	+	0.840896i	$0.682029\pi$
$578$			37.0000i			1.53900i
$579$	−2.44949	+	2.44949i	−0.101797	+	0.101797i
$580$		0			0
$581$	−48.9898			−2.03244
$582$	17.1464	+	17.1464i	0.710742	+	0.710742i
$583$	−12.0000			−0.496989
$584$	2.44949			0.101361
$585$			7.34847i			0.303822i
$586$	−6.00000			−0.247858
$587$	12.2474			0.505506			0.252753	−	0.967531i	$-0.418664\pi$
$587$	12.2474			0.505506			0.252753	+	0.967531i	$0.418664\pi$
$588$	−11.0227	+	11.0227i	−0.454569	+	0.454569i
$589$	−10.0000	+	4.89898i	−0.412043	+	0.201859i
$590$			6.00000i			0.247016i
$591$	−27.0000	+	27.0000i	−1.11063	+	1.11063i
$592$			2.44949i			0.100673i
$593$		−	6.00000i		−	0.246390i	−0.992382	−	0.123195i	$-0.960686\pi$
$593$		−	6.00000i		−	0.246390i	0.992382	−	0.123195i	$-0.0393141\pi$
$594$	18.0000	−	18.0000i	0.738549	−	0.738549i
$595$		−	29.3939i		−	1.20503i
$596$		0			0
$597$	−12.0000	−	12.0000i	−0.491127	−	0.491127i
$598$	−18.0000			−0.736075
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$	1.22474	+	1.22474i	0.0500000	+	0.0500000i
$601$		−	4.89898i		−	0.199834i	−0.994996	−	0.0999168i	$-0.968142\pi$
$601$		−	4.89898i		−	0.199834i	0.994996	−	0.0999168i	$-0.0318577\pi$
$602$	9.79796			0.399335
$603$		−	12.0000i		−	0.488678i
$604$		−	14.6969i		−	0.598010i
$605$		−	13.0000i		−	0.528525i
$606$	7.34847	−	7.34847i	0.298511	−	0.298511i
$607$	4.00000			0.162355			0.0811775	−	0.996700i	$-0.474132\pi$
$607$	4.00000			0.162355			0.0811775	+	0.996700i	$0.474132\pi$
$608$		−	2.00000i		−	0.0811107i
$609$		0			0
$610$		0			0
$611$	−29.3939			−1.18915
$612$		−	22.0454i		−	0.891133i
$613$			41.6413i			1.68188i	0.541130	+	0.840939i	$0.317997\pi$
$613$			41.6413i			1.68188i	−0.541130	+	0.840939i	$0.682003\pi$
$614$			16.0000i			0.645707i
$615$	−14.6969	+	14.6969i	−0.592638	+	0.592638i
$616$			19.5959i			0.789542i
$617$			18.0000i			0.724653i	0.932051	+	0.362326i	$0.118017\pi$
$617$			18.0000i			0.724653i	−0.932051	+	0.362326i	$0.881983\pi$
$618$	4.89898	+	4.89898i	0.197066	+	0.197066i
$619$			29.3939i			1.18144i	0.806877	+	0.590720i	$0.201156\pi$
$619$			29.3939i			1.18144i	−0.806877	+	0.590720i	$0.798844\pi$
$620$	2.44949	+	5.00000i	0.0983739	+	0.200805i
$621$	27.0000	+	27.0000i	1.08347	+	1.08347i
$622$	6.00000			0.240578
$623$	19.5959			0.785094
$624$	−3.00000	−	3.00000i	−0.120096	−	0.120096i
$625$	1.00000			0.0400000
$626$	17.1464			0.685309
$627$	−12.0000	+	12.0000i	−0.479234	+	0.479234i
$628$	−10.0000			−0.399043
$629$		−	18.0000i		−	0.717707i
$630$			12.0000i			0.478091i
$631$			9.79796i			0.390051i	0.980798	+	0.195025i	$0.0624789\pi$
$631$			9.79796i			0.390051i	−0.980798	+	0.195025i	$0.937521\pi$
$632$	−4.89898			−0.194871
$633$	17.1464	−	17.1464i	0.681509	−	0.681509i
$634$	6.00000			0.238290
$635$	7.34847			0.291615
$636$	3.00000	−	3.00000i	0.118958	−	0.118958i
$637$		−	22.0454i		−	0.873471i
$638$		0			0
$639$		0			0
$640$	−1.00000			−0.0395285
$641$	−4.89898			−0.193498			−0.0967490	−	0.995309i	$-0.530844\pi$
$641$	−4.89898			−0.193498			−0.0967490	+	0.995309i	$0.530844\pi$
$642$	14.6969	−	14.6969i	0.580042	−	0.580042i
$643$		−	22.0454i		−	0.869386i	−0.900579	−	0.434693i	$-0.856857\pi$
$643$		−	22.0454i		−	0.869386i	0.900579	−	0.434693i	$-0.143143\pi$
$644$	−29.3939			−1.15828
$645$	3.00000	−	3.00000i	0.118125	−	0.118125i
$646$			14.6969i			0.578243i
$647$	36.7423			1.44449			0.722245	−	0.691637i	$-0.243110\pi$
$647$	36.7423			1.44449			0.722245	+	0.691637i	$0.243110\pi$
$648$			9.00000i			0.353553i
$649$			29.3939i			1.15381i
$650$	−2.44949			−0.0960769
$651$	−12.4949	+	36.4949i	−0.489714	+	1.43035i
$652$	−20.0000			−0.783260
$653$		−	42.0000i		−	1.64359i	−0.569785	−	0.821794i	$-0.692974\pi$
$653$		−	42.0000i		−	1.64359i	0.569785	−	0.821794i	$-0.307026\pi$
$654$	−19.5959	−	19.5959i	−0.766261	−	0.766261i
$655$	−12.0000			−0.468879
$656$		−	12.0000i		−	0.468521i
$657$	7.34847			0.286691
$658$	−48.0000			−1.87123
$659$		−	36.0000i		−	1.40236i	−0.712984	−	0.701180i	$-0.752657\pi$
$659$		−	36.0000i		−	1.40236i	0.712984	−	0.701180i	$-0.247343\pi$
$660$	6.00000	+	6.00000i	0.233550	+	0.233550i
$661$	−4.00000			−0.155582			−0.0777910	−	0.996970i	$-0.524787\pi$
$661$	−4.00000			−0.155582			−0.0777910	+	0.996970i	$0.524787\pi$
$662$	24.4949			0.952021
$663$	22.0454	+	22.0454i	0.856173	+	0.856173i
$664$		−	12.2474i		−	0.475293i
$665$		−	8.00000i		−	0.310227i
$666$			7.34847i			0.284747i
$667$		0			0
$668$	7.34847			0.284321
$669$	−33.0000	−	33.0000i	−1.27585	−	1.27585i
$670$	4.00000			0.154533
$671$		0			0
$672$	−4.89898	−	4.89898i	−0.188982	−	0.188982i
$673$		−	26.9444i		−	1.03863i	−0.854583	−	0.519315i	$-0.826187\pi$
$673$		−	26.9444i		−	1.03863i	0.854583	−	0.519315i	$-0.173813\pi$
$674$	26.9444			1.03786
$675$	3.67423	+	3.67423i	0.141421	+	0.141421i
$676$	−7.00000			−0.269231
$677$	31.8434			1.22384			0.611920	−	0.790920i	$-0.290397\pi$
$677$	31.8434			1.22384			0.611920	+	0.790920i	$0.290397\pi$
$678$	−22.0454	+	22.0454i	−0.846649	+	0.846649i
$679$	−56.0000			−2.14908
$680$	7.34847			0.281801
$681$		0			0
$682$	12.0000	+	24.4949i	0.459504	+	0.937958i
$683$			48.0000i			1.83667i	0.395805	+	0.918334i	$0.370466\pi$
$683$			48.0000i			1.83667i	−0.395805	+	0.918334i	$0.629534\pi$
$684$		−	6.00000i		−	0.229416i
$685$		−	12.2474i		−	0.467951i
$686$		−	8.00000i		−	0.305441i
$687$	12.0000	+	12.0000i	0.457829	+	0.457829i
$688$			2.44949i			0.0933859i
$689$			6.00000i			0.228582i
$690$	−9.00000	+	9.00000i	−0.342624	+	0.342624i
$691$	−4.00000			−0.152167			−0.0760836	−	0.997101i	$-0.524242\pi$
$691$	−4.00000			−0.152167			−0.0760836	+	0.997101i	$0.524242\pi$
$692$		−	6.00000i		−	0.228086i
$693$			58.7878i			2.23316i
$694$			17.1464i			0.650870i
$695$	4.89898			0.185829
$696$		0			0
$697$			88.1816i			3.34012i
$698$		−	2.00000i		−	0.0757011i
$699$	−7.34847	−	7.34847i	−0.277945	−	0.277945i
$700$	−4.00000			−0.151186
$701$			36.0000i			1.35970i	0.733351	+	0.679851i	$0.237955\pi$
$701$			36.0000i			1.35970i	−0.733351	+	0.679851i	$0.762045\pi$
$702$	−9.00000	−	9.00000i	−0.339683	−	0.339683i
$703$		−	4.89898i		−	0.184769i
$704$	−4.89898			−0.184637
$705$	−14.6969	+	14.6969i	−0.553519	+	0.553519i
$706$			2.44949i			0.0921878i
$707$			24.0000i			0.902613i
$708$	−7.34847	−	7.34847i	−0.276172	−	0.276172i
$709$		0			0		1.00000			$0$
$709$		0			0		−1.00000			$\pi$
$710$		0			0
$711$	−14.6969			−0.551178
$712$			4.89898i			0.183597i
$713$	−36.7423	+	18.0000i	−1.37601	+	0.674105i
$714$	36.0000	+	36.0000i	1.34727	+	1.34727i
$715$	−12.0000			−0.448775
$716$	−14.6969			−0.549250
$717$	18.0000	−	18.0000i	0.672222	−	0.672222i
$718$	24.0000			0.895672
$719$	−4.89898			−0.182701			−0.0913506	−	0.995819i	$-0.529118\pi$
$719$	−4.89898			−0.182701			−0.0913506	+	0.995819i	$0.529118\pi$
$720$	−3.00000			−0.111803
$721$	−16.0000			−0.595871
$722$		−	15.0000i		−	0.558242i
$723$	−6.00000	−	6.00000i	−0.223142	−	0.223142i
$724$		−	24.4949i		−	0.910346i
$725$		0			0
$726$	15.9217	+	15.9217i	0.590909	+	0.590909i
$727$	8.00000			0.296704			0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000			0.296704			0.148352	+	0.988935i	$0.452603\pi$
$728$	9.79796			0.363137
$729$			27.0000i			1.00000i
$730$			2.44949i			0.0906597i
$731$		−	18.0000i		−	0.665754i
$732$		0			0
$733$	22.0000			0.812589			0.406294	−	0.913742i	$-0.366821\pi$
$733$	22.0000			0.812589			0.406294	+	0.913742i	$0.366821\pi$
$734$	−26.9444			−0.994535
$735$	−11.0227	−	11.0227i	−0.406579	−	0.406579i
$736$		−	7.34847i		−	0.270868i
$737$	19.5959			0.721825
$738$		−	36.0000i		−	1.32518i
$739$		−	14.6969i		−	0.540636i	−0.962771	−	0.270318i	$-0.912871\pi$
$739$		−	14.6969i		−	0.540636i	0.962771	−	0.270318i	$-0.0871288\pi$
$740$	−2.44949			−0.0900450
$741$	6.00000	+	6.00000i	0.220416	+	0.220416i
$742$			9.79796i			0.359694i
$743$	2.44949			0.0898631			0.0449315	−	0.998990i	$-0.485693\pi$
$743$	2.44949			0.0898631			0.0449315	+	0.998990i	$0.485693\pi$
$744$	−9.12372	−	3.12372i	−0.334492	−	0.114521i
$745$		0			0
$746$			2.00000i			0.0732252i
$747$		−	36.7423i		−	1.34433i
$748$	36.0000			1.31629
$749$			48.0000i			1.75388i
$750$	−1.22474	+	1.22474i	−0.0447214	+	0.0447214i
$751$	10.0000			0.364905			0.182453	−	0.983215i	$-0.441596\pi$
$751$	10.0000			0.364905			0.182453	+	0.983215i	$0.441596\pi$
$752$		−	12.0000i		−	0.437595i
$753$	−12.0000	+	12.0000i	−0.437304	+	0.437304i
$754$		0			0
$755$	14.6969			0.534876
$756$	−14.6969	−	14.6969i	−0.534522	−	0.534522i
$757$		−	51.4393i		−	1.86959i	−0.355184	−	0.934796i	$-0.615582\pi$
$757$		−	51.4393i		−	1.86959i	0.355184	−	0.934796i	$-0.384418\pi$
$758$			20.0000i			0.726433i
$759$	−44.0908	+	44.0908i	−1.60040	+	1.60040i
$760$	2.00000			0.0725476
$761$	29.3939			1.06553			0.532764	−	0.846264i	$-0.321153\pi$
$761$	29.3939			1.06553			0.532764	+	0.846264i	$0.321153\pi$
$762$	−9.00000	+	9.00000i	−0.326036	+	0.326036i
$763$	64.0000			2.31696
$764$			18.0000i			0.651217i
$765$	22.0454			0.797053
$766$			26.9444i			0.973540i
$767$	14.6969			0.530676
$768$	1.22474	−	1.22474i	0.0441942	−	0.0441942i
$769$	−50.0000			−1.80305			−0.901523	−	0.432731i	$-0.857550\pi$
$769$	−50.0000			−1.80305			−0.901523	+	0.432731i	$0.857550\pi$
$770$	−19.5959			−0.706188
$771$	−22.0454	−	22.0454i	−0.793946	−	0.793946i
$772$	2.00000			0.0719816
$773$	46.5403			1.67394			0.836969	−	0.547250i	$-0.184325\pi$
$773$	46.5403			1.67394			0.836969	+	0.547250i	$0.184325\pi$
$774$			7.34847i			0.264135i
$775$	−5.00000	+	2.44949i	−0.179605	+	0.0879883i
$776$		−	14.0000i		−	0.502571i
$777$	−12.0000	−	12.0000i	−0.430498	−	0.430498i
$778$		−	4.89898i		−	0.175637i
$779$			24.0000i			0.859889i
$780$	3.00000	−	3.00000i	0.107417	−	0.107417i
$781$		0			0
$782$			54.0000i			1.93104i
$783$		0			0
$784$	9.00000			0.321429
$785$		−	10.0000i		−	0.356915i
$786$	14.6969	−	14.6969i	0.524222	−	0.524222i
$787$			7.34847i			0.261945i	0.991386	+	0.130972i	$0.0418099\pi$
$787$			7.34847i			0.261945i	−0.991386	+	0.130972i	$0.958190\pi$
$788$	22.0454			0.785335
$789$	−39.0000	+	39.0000i	−1.38844	+	1.38844i
$790$		−	4.89898i		−	0.174298i
$791$		−	72.0000i		−	2.56003i
$792$	−14.6969			−0.522233
$793$		0			0
$794$		−	34.0000i		−	1.20661i
$795$	3.00000	+	3.00000i	0.106399	+	0.106399i
$796$			9.79796i			0.347279i
$797$	−12.2474			−0.433827			−0.216913	−	0.976191i	$-0.569599\pi$
$797$	−12.2474			−0.433827			−0.216913	+	0.976191i	$0.569599\pi$
$798$	9.79796	+	9.79796i	0.346844	+	0.346844i
$799$			88.1816i			3.11964i
$800$		−	1.00000i		−	0.0353553i
$801$			14.6969i			0.519291i
$802$		−	19.5959i		−	0.691956i
$803$			12.0000i			0.423471i
$804$	−4.89898	+	4.89898i	−0.172774	+	0.172774i
$805$		−	29.3939i		−	1.03600i
$806$	12.2474	−	6.00000i	0.431398	−	0.211341i
$807$	−6.00000	+	6.00000i	−0.211210	+	0.211210i
$808$	−6.00000			−0.211079
$809$	−24.4949			−0.861195			−0.430597	−	0.902544i	$-0.641697\pi$
$809$	−24.4949			−0.861195			−0.430597	+	0.902544i	$0.641697\pi$
$810$	−9.00000			−0.316228
$811$	−20.0000			−0.702295			−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000			−0.702295			−0.351147	+	0.936320i	$0.614208\pi$
$812$		0			0
$813$	−12.0000	−	12.0000i	−0.420858	−	0.420858i
$814$	−12.0000			−0.420600
$815$		−	20.0000i		−	0.700569i
$816$	−9.00000	+	9.00000i	−0.315063	+	0.315063i
$817$		−	4.89898i		−	0.171394i
$818$	−19.5959			−0.685155
$819$	29.3939			1.02711
$820$	12.0000			0.419058
$821$	48.9898			1.70976			0.854878	−	0.518829i	$-0.173632\pi$
$821$	48.9898			1.70976			0.854878	+	0.518829i	$0.173632\pi$
$822$	15.0000	+	15.0000i	0.523185	+	0.523185i
$823$			41.6413i			1.45153i	0.687945	+	0.725763i	$0.258513\pi$
$823$			41.6413i			1.45153i	−0.687945	+	0.725763i	$0.741487\pi$
$824$		−	4.00000i		−	0.139347i
$825$	−6.00000	+	6.00000i	−0.208893	+	0.208893i
$826$	24.0000			0.835067
$827$	−46.5403			−1.61836			−0.809182	−	0.587557i	$-0.800090\pi$
$827$	−46.5403			−1.61836			−0.809182	+	0.587557i	$0.800090\pi$
$828$		−	22.0454i		−	0.766131i
$829$		−	34.2929i		−	1.19104i	−0.803340	−	0.595520i	$-0.796946\pi$
$829$		−	34.2929i		−	1.19104i	0.803340	−	0.595520i	$-0.203054\pi$
$830$	12.2474			0.425115
$831$	21.0000	+	21.0000i	0.728482	+	0.728482i
$832$			2.44949i			0.0849208i
$833$	−66.1362			−2.29148
$834$	−6.00000	+	6.00000i	−0.207763	+	0.207763i
$835$			7.34847i			0.254304i
$836$	9.79796			0.338869
$837$	−27.3712	−	9.37117i	−0.946086	−	0.323915i
$838$	−30.0000			−1.03633
$839$		0			0		1.00000			$0$
$839$		0			0		−1.00000			$\pi$
$840$	4.89898	−	4.89898i	0.169031	−	0.169031i
$841$	−29.0000			−1.00000
$842$		−	26.0000i		−	0.896019i
$843$	7.34847	+	7.34847i	0.253095	+	0.253095i
$844$	−14.0000			−0.481900
$845$		−	7.00000i		−	0.240807i
$846$		−	36.0000i		−	1.23771i
$847$	−52.0000			−1.78674
$848$	−2.44949			−0.0841158
$849$	−4.89898	+	4.89898i	−0.168133	+	0.168133i
$850$			7.34847i			0.252050i
$851$		−	18.0000i		−	0.617032i
$852$		0			0
$853$	−26.0000			−0.890223			−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000			−0.890223			−0.445112	+	0.895475i	$0.646836\pi$
$854$		0			0
$855$	6.00000			0.205196
$856$	−12.0000			−0.410152
$857$		−	18.0000i		−	0.614868i	−0.951569	−	0.307434i	$-0.900530\pi$
$857$		−	18.0000i		−	0.614868i	0.951569	−	0.307434i	$-0.0994704\pi$
$858$	14.6969	−	14.6969i	0.501745	−	0.501745i
$859$		−	19.5959i		−	0.668604i	−0.942466	−	0.334302i	$-0.891499\pi$
$859$		−	19.5959i		−	0.668604i	0.942466	−	0.334302i	$-0.108501\pi$
$860$	−2.44949			−0.0835269
$861$	58.7878	+	58.7878i	2.00348	+	2.00348i
$862$	24.0000			0.817443
$863$	−2.44949			−0.0833816			−0.0416908	−	0.999131i	$-0.513274\pi$
$863$	−2.44949			−0.0833816			−0.0416908	+	0.999131i	$0.513274\pi$
$864$	3.67423	−	3.67423i	0.125000	−	0.125000i
$865$	6.00000			0.204006
$866$	17.1464			0.582659
$867$	45.3156	−	45.3156i	1.53900	−	1.53900i
$868$	20.0000	−	9.79796i	0.678844	−	0.332564i
$869$		−	24.0000i		−	0.814144i
$870$		0			0
$871$		−	9.79796i		−	0.331991i
$872$			16.0000i			0.541828i
$873$		−	42.0000i		−	1.42148i
$874$			14.6969i			0.497131i
$875$		−	4.00000i		−	0.135225i
$876$	−3.00000	−	3.00000i	−0.101361	−	0.101361i
$877$	22.0000			0.742887			0.371444	−	0.928456i	$-0.378863\pi$
$877$	22.0000			0.742887			0.371444	+	0.928456i	$0.378863\pi$
$878$		−	8.00000i		−	0.269987i
$879$	7.34847	+	7.34847i	0.247858	+	0.247858i
$880$		−	4.89898i		−	0.165145i
$881$	53.8888			1.81556			0.907779	−	0.419448i	$-0.137776\pi$
$881$	53.8888			1.81556			0.907779	+	0.419448i	$0.137776\pi$
$882$	27.0000			0.909137
$883$			36.7423i			1.23648i	0.785990	+	0.618239i	$0.212154\pi$
$883$			36.7423i			1.23648i	−0.785990	+	0.618239i	$0.787846\pi$
$884$		−	18.0000i		−	0.605406i
$885$	7.34847	−	7.34847i	0.247016	−	0.247016i
$886$	24.0000			0.806296
$887$		−	48.0000i		−	1.61168i	−0.592132	−	0.805841i	$-0.701714\pi$
$887$		−	48.0000i		−	1.61168i	0.592132	−	0.805841i	$-0.298286\pi$
$888$	3.00000	−	3.00000i	0.100673	−	0.100673i
$889$		−	29.3939i		−	0.985839i
$890$	−4.89898			−0.164214
$891$	−44.0908			−1.47710
$892$			26.9444i			0.902165i
$893$			24.0000i			0.803129i
$894$		0			0
$895$		−	14.6969i		−	0.491264i
$896$			4.00000i			0.133631i
$897$	22.0454	+	22.0454i	0.736075	+	0.736075i
$898$		−	29.3939i		−	0.980886i
$899$		0			0
$900$		−	3.00000i		−	0.100000i
$901$	18.0000			0.599667
$902$	58.7878			1.95742
$903$	−12.0000	−	12.0000i	−0.399335	−	0.399335i
$904$	18.0000			0.598671
$905$	24.4949			0.814238
$906$	−18.0000	+	18.0000i	−0.598010	+	0.598010i
$907$	16.0000			0.531271			0.265636	−	0.964073i	$-0.414418\pi$
$907$	16.0000			0.531271			0.265636	+	0.964073i	$0.414418\pi$
$908$		0			0
$909$	−18.0000			−0.597022
$910$			9.79796i			0.324799i
$911$	29.3939			0.973863			0.486931	−	0.873440i	$-0.338116\pi$
$911$	29.3939			0.973863			0.486931	+	0.873440i	$0.338116\pi$
$912$	−2.44949	+	2.44949i	−0.0811107	+	0.0811107i
$913$	60.0000			1.98571
$914$	−7.34847			−0.243066
$915$		0			0
$916$		−	9.79796i		−	0.323734i
$917$			48.0000i			1.58510i
$918$	−27.0000	+	27.0000i	−0.891133	+	0.891133i
$919$	−2.00000			−0.0659739			−0.0329870	−	0.999456i	$-0.510502\pi$
$919$	−2.00000			−0.0659739			−0.0329870	+	0.999456i	$0.510502\pi$
$920$	7.34847			0.242272
$921$	19.5959	−	19.5959i	0.645707	−	0.645707i
$922$		−	14.6969i		−	0.484018i
$923$		0			0
$924$	24.0000	−	24.0000i	0.789542	−	0.789542i
$925$		−	2.44949i		−	0.0805387i
$926$	2.44949			0.0804952
$927$		−	12.0000i		−	0.394132i
$928$		0			0
$929$		0			0			−	1.00000i	$-0.5\pi$
$929$		0			0				1.00000i	$0.5\pi$
$930$	3.12372	−	9.12372i	0.102431	−	0.299179i
$931$	−18.0000			−0.589926
$932$			6.00000i			0.196537i
$933$	−7.34847	−	7.34847i	−0.240578	−	0.240578i
$934$	−36.0000			−1.17796
$935$			36.0000i			1.17733i
$936$			7.34847i			0.240192i
$937$	10.0000			0.326686			0.163343	−	0.986569i	$-0.447772\pi$
$937$	10.0000			0.326686			0.163343	+	0.986569i	$0.447772\pi$
$938$		−	16.0000i		−	0.522419i
$939$	−21.0000	−	21.0000i	−0.685309	−	0.685309i
$940$	12.0000			0.391397
$941$	4.89898			0.159702			0.0798511	−	0.996807i	$-0.474556\pi$
$941$	4.89898			0.159702			0.0798511	+	0.996807i	$0.474556\pi$
$942$	12.2474	+	12.2474i	0.399043	+	0.399043i
$943$			88.1816i			2.87159i
$944$			6.00000i			0.195283i
$945$	14.6969	−	14.6969i	0.478091	−	0.478091i
$946$	−12.0000			−0.390154
$947$	−12.2474			−0.397989			−0.198994	−	0.980001i	$-0.563768\pi$
$947$	−12.2474			−0.397989			−0.198994	+	0.980001i	$0.563768\pi$
$948$	6.00000	+	6.00000i	0.194871	+	0.194871i
$949$	6.00000			0.194768
$950$			2.00000i			0.0648886i
$951$	−7.34847	−	7.34847i	−0.238290	−	0.238290i
$952$		−	29.3939i		−	0.952661i
$953$	−22.0454			−0.714121			−0.357060	−	0.934081i	$-0.616221\pi$
$953$	−22.0454			−0.714121			−0.357060	+	0.934081i	$0.616221\pi$
$954$	−7.34847			−0.237915
$955$	−18.0000			−0.582466
$956$	−14.6969			−0.475333
$957$		0			0
$958$	30.0000			0.969256
$959$	−48.9898			−1.58196
$960$	1.22474	+	1.22474i	0.0395285	+	0.0395285i
$961$	19.0000	−	24.4949i	0.612903	−	0.790158i
$962$			6.00000i			0.193448i
$963$	−36.0000			−1.16008
$964$			4.89898i			0.157786i
$965$			2.00000i			0.0643823i
$966$	36.0000	+	36.0000i	1.15828	+	1.15828i
$967$			46.5403i			1.49664i	0.663341	+	0.748318i	$0.269138\pi$
$967$			46.5403i			1.49664i	−0.663341	+	0.748318i	$0.730862\pi$
$968$		−	13.0000i		−	0.417836i
$969$	18.0000	−	18.0000i	0.578243	−	0.578243i
$970$	14.0000			0.449513
$971$			54.0000i			1.73294i	0.499227	+	0.866471i	$0.333617\pi$
$971$			54.0000i			1.73294i	−0.499227	+	0.866471i	$0.666383\pi$
$972$	11.0227	−	11.0227i	0.353553	−	0.353553i
$973$		−	19.5959i		−	0.628216i
$974$	31.8434			1.02033
$975$	3.00000	+	3.00000i	0.0960769	+	0.0960769i
$976$		0			0
$977$		−	30.0000i		−	0.959785i	−0.877327	−	0.479893i	$-0.840676\pi$
$977$		−	30.0000i		−	0.959785i	0.877327	−	0.479893i	$-0.159324\pi$
$978$	24.4949	+	24.4949i	0.783260	+	0.783260i
$979$	−24.0000			−0.767043
$980$			9.00000i			0.287494i
$981$			48.0000i			1.53252i
$982$		−	19.5959i		−	0.625331i
$983$	−22.0454			−0.703139			−0.351570	−	0.936162i	$-0.614352\pi$
$983$	−22.0454			−0.703139			−0.351570	+	0.936162i	$0.614352\pi$
$984$	−14.6969	+	14.6969i	−0.468521	+	0.468521i
$985$			22.0454i			0.702425i
$986$		0			0
$987$	58.7878	+	58.7878i	1.87123	+	1.87123i
$988$		−	4.89898i		−	0.155857i
$989$		−	18.0000i		−	0.572367i
$990$		−	14.6969i		−	0.467099i
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$	2.44949	+	5.00000i	0.0777714	+	0.158750i
$993$	−30.0000	−	30.0000i	−0.952021	−	0.952021i
$994$		0			0
$995$	−9.79796			−0.310616
$996$	−15.0000	+	15.0000i	−0.475293	+	0.475293i
$997$	−10.0000			−0.316703			−0.158352	−	0.987383i	$-0.550618\pi$
$997$	−10.0000			−0.316703			−0.158352	+	0.987383i	$0.550618\pi$
$998$	−9.79796			−0.310149
$999$	9.00000	−	9.00000i	0.284747	−	0.284747i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.h.a.371.4	yes	4
3.2	odd	2	inner	930.2.h.a.371.1	✓	4
31.30	odd	2	inner	930.2.h.a.371.3	yes	4
93.92	even	2	inner	930.2.h.a.371.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.h.a.371.1	✓	4	3.2	odd	2	inner
930.2.h.a.371.2	yes	4	93.92	even	2	inner
930.2.h.a.371.3	yes	4	31.30	odd	2	inner
930.2.h.a.371.4	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(1.22474 - 1.22474i) q^{3} -1.00000 q^{4} -1.00000i q^{5} +(1.22474 + 1.22474i) q^{6} -4.00000 q^{7} -1.00000i q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(1.22474 - 1.22474i) q^{3} -1.00000 q^{4} -1.00000i q^{5} +(1.22474 + 1.22474i) q^{6} -4.00000 q^{7} -1.00000i q^{8} -3.00000i q^{9} +1.00000 q^{10} +4.89898 q^{11} +(-1.22474 + 1.22474i) q^{12} -2.44949i q^{13} -4.00000i q^{14} +(-1.22474 - 1.22474i) q^{15} +1.00000 q^{16} -7.34847 q^{17} +3.00000 q^{18} -2.00000 q^{19} +1.00000i q^{20} +(-4.89898 + 4.89898i) q^{21} +4.89898i q^{22} -7.34847 q^{23} +(-1.22474 - 1.22474i) q^{24} -1.00000 q^{25} +2.44949 q^{26} +(-3.67423 - 3.67423i) q^{27} +4.00000 q^{28} +(1.22474 - 1.22474i) q^{30} +(5.00000 - 2.44949i) q^{31} +1.00000i q^{32} +(6.00000 - 6.00000i) q^{33} -7.34847i q^{34} +4.00000i q^{35} +3.00000i q^{36} +2.44949i q^{37} -2.00000i q^{38} +(-3.00000 - 3.00000i) q^{39} -1.00000 q^{40} -12.0000i q^{41} +(-4.89898 - 4.89898i) q^{42} +2.44949i q^{43} -4.89898 q^{44} -3.00000 q^{45} -7.34847i q^{46} -12.0000i q^{47} +(1.22474 - 1.22474i) q^{48} +9.00000 q^{49} -1.00000i q^{50} +(-9.00000 + 9.00000i) q^{51} +2.44949i q^{52} -2.44949 q^{53} +(3.67423 - 3.67423i) q^{54} -4.89898i q^{55} +4.00000i q^{56} +(-2.44949 + 2.44949i) q^{57} +6.00000i q^{59} +(1.22474 + 1.22474i) q^{60} +(2.44949 + 5.00000i) q^{62} +12.0000i q^{63} -1.00000 q^{64} -2.44949 q^{65} +(6.00000 + 6.00000i) q^{66} +4.00000 q^{67} +7.34847 q^{68} +(-9.00000 + 9.00000i) q^{69} -4.00000 q^{70} -3.00000 q^{72} +2.44949i q^{73} -2.44949 q^{74} +(-1.22474 + 1.22474i) q^{75} +2.00000 q^{76} -19.5959 q^{77} +(3.00000 - 3.00000i) q^{78} -4.89898i q^{79} -1.00000i q^{80} -9.00000 q^{81} +12.0000 q^{82} +12.2474 q^{83} +(4.89898 - 4.89898i) q^{84} +7.34847i q^{85} -2.44949 q^{86} -4.89898i q^{88} -4.89898 q^{89} -3.00000i q^{90} +9.79796i q^{91} +7.34847 q^{92} +(3.12372 - 9.12372i) q^{93} +12.0000 q^{94} +2.00000i q^{95} +(1.22474 + 1.22474i) q^{96} +14.0000 q^{97} +9.00000i q^{98} -14.6969i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 16 q^{7}+O(q^{10}) \) 4 * q - 4 * q^4 - 16 * q^7	\( 4 q - 4 q^{4} - 16 q^{7} + 4 q^{10} + 4 q^{16} + 12 q^{18} - 8 q^{19} - 4 q^{25} + 16 q^{28} + 20 q^{31} + 24 q^{33} - 12 q^{39} - 4 q^{40} - 12 q^{45} + 36 q^{49} - 36 q^{51} - 4 q^{64} + 24 q^{66} + 16 q^{67} - 36 q^{69} - 16 q^{70} - 12 q^{72} + 8 q^{76} + 12 q^{78} - 36 q^{81} + 48 q^{82} - 12 q^{93} + 48 q^{94} + 56 q^{97}+O(q^{100}) \) 4 * q - 4 * q^4 - 16 * q^7 + 4 * q^10 + 4 * q^16 + 12 * q^18 - 8 * q^19 - 4 * q^25 + 16 * q^28 + 20 * q^31 + 24 * q^33 - 12 * q^39 - 4 * q^40 - 12 * q^45 + 36 * q^49 - 36 * q^51 - 4 * q^64 + 24 * q^66 + 16 * q^67 - 36 * q^69 - 16 * q^70 - 12 * q^72 + 8 * q^76 + 12 * q^78 - 36 * q^81 + 48 * q^82 - 12 * q^93 + 48 * q^94 + 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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