LMFDB - Embedded newform 546.2.bx.a.223.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(97,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 5]))

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

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

chi := DirichletCharacter("546.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bx (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			223.8
Character	$\chi$	$=$	546.223
Dual form			546.2.bx.a.475.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.10131 + 1.10131i) q^{5} +(0.965926 - 0.258819i) q^{6} +(-0.930231 + 2.47683i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(0.778741 + 1.34882i) q^{10} +(1.09562 - 4.08891i) q^{11} +1.00000 q^{12} +(2.26571 + 2.80474i) q^{13} +(-1.53958 + 2.15167i) q^{14} +(1.50441 + 0.403106i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.530824 + 0.919414i) q^{17} +(0.707107 - 0.707107i) q^{18} +(-2.52532 + 0.676658i) q^{19} +(0.403106 + 1.50441i) q^{20} +(0.432809 + 2.61011i) q^{21} +(2.11658 - 3.66602i) q^{22} +(-0.925495 + 0.534335i) q^{23} +(0.965926 + 0.258819i) q^{24} -2.57425i q^{25} +(1.46259 + 3.29558i) q^{26} -1.00000i q^{27} +(-2.04402 + 1.67988i) q^{28} +(2.14751 + 3.71959i) q^{29} +(1.34882 + 0.778741i) q^{30} +(0.172393 + 0.172393i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-1.09562 - 4.08891i) q^{33} +(-0.750699 + 0.750699i) q^{34} +(-3.75222 + 1.70328i) q^{35} +(0.866025 - 0.500000i) q^{36} +(1.83037 - 6.83102i) q^{37} -2.61441 q^{38} +(3.36453 + 1.29611i) q^{39} +1.55748i q^{40} +(-0.640215 + 2.38932i) q^{41} +(-0.257485 + 2.63319i) q^{42} +(-9.94138 - 5.73966i) q^{43} +(2.99329 - 2.99329i) q^{44} +(1.50441 - 0.403106i) q^{45} +(-1.03226 + 0.276592i) q^{46} +(6.64147 - 6.64147i) q^{47} +(0.866025 + 0.500000i) q^{48} +(-5.26934 - 4.60804i) q^{49} +(0.666264 - 2.48653i) q^{50} +1.06165i q^{51} +(0.559799 + 3.56183i) q^{52} +3.29120 q^{53} +(0.258819 - 0.965926i) q^{54} +(5.70976 - 3.29653i) q^{55} +(-2.40915 + 1.09361i) q^{56} +(-1.84866 + 1.84866i) q^{57} +(1.11163 + 4.14867i) q^{58} +(-1.79705 - 6.70667i) q^{59} +(1.10131 + 1.10131i) q^{60} +(-3.62769 - 2.09445i) q^{61} +(0.121900 + 0.211137i) q^{62} +(1.67988 + 2.04402i) q^{63} +1.00000i q^{64} +(-0.593627 + 5.58412i) q^{65} -4.23315i q^{66} +(5.87776 + 1.57494i) q^{67} +(-0.919414 + 0.530824i) q^{68} +(-0.534335 + 0.925495i) q^{69} +(-4.06520 + 0.674093i) q^{70} +(0.0551920 + 0.205979i) q^{71} +(0.965926 - 0.258819i) q^{72} +(-11.8203 + 11.8203i) q^{73} +(3.53600 - 6.12453i) q^{74} +(-1.28712 - 2.22936i) q^{75} +(-2.52532 - 0.676658i) q^{76} +(9.10834 + 6.51729i) q^{77} +(2.91443 + 2.12276i) q^{78} -15.8416 q^{79} +(-0.403106 + 1.50441i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.23680 + 2.14220i) q^{82} +(3.21397 + 3.21397i) q^{83} +(-0.930231 + 2.47683i) q^{84} +(-1.59716 + 0.427957i) q^{85} +(-8.11710 - 8.11710i) q^{86} +(3.71959 + 2.14751i) q^{87} +(3.66602 - 2.11658i) q^{88} +(-5.32335 - 1.42639i) q^{89} +1.55748 q^{90} +(-9.05448 + 3.00273i) q^{91} -1.06867 q^{92} +(0.235493 + 0.0631001i) q^{93} +(8.13411 - 4.69623i) q^{94} +(-3.52636 - 2.03595i) q^{95} +(0.707107 + 0.707107i) q^{96} +(3.13122 - 0.839007i) q^{97} +(-3.89714 - 5.81483i) q^{98} +(-2.99329 - 2.99329i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{7} + 20 q^{9} + 8 q^{11} + 40 q^{12} - 8 q^{14} + 20 q^{16} + 16 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 32 q^{26} + 8 q^{28} - 8 q^{33} + 16 q^{34} - 32 q^{35} + 40 q^{37} - 16 q^{38} - 16 q^{39}+ \cdots - 8 q^{99}+O(q^{100}) $ 40 * q - 8 * q^7 + 20 * q^9 + 8 * q^11 + 40 * q^12 - 8 * q^14 + 20 * q^16 + 16 * q^17 + 16 * q^19 + 4 * q^21 + 8 * q^22 + 32 * q^26 + 8 * q^28 - 8 * q^33 + 16 * q^34 - 32 * q^35 + 40 * q^37 - 16 * q^38 - 16 * q^39 - 4 * q^41 + 12 * q^42 + 24 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 - 4 * q^49 - 16 * q^50 - 8 * q^52 + 32 * q^53 - 72 * q^55 + 12 * q^56 + 8 * q^57 - 36 * q^58 + 84 * q^59 - 48 * q^61 - 4 * q^62 - 4 * q^63 - 16 * q^65 + 12 * q^68 - 8 * q^69 + 36 * q^70 - 40 * q^71 - 48 * q^73 + 8 * q^74 + 36 * q^75 + 16 * q^76 - 24 * q^77 - 8 * q^78 - 48 * q^79 - 20 * q^81 + 36 * q^83 - 8 * q^84 + 8 * q^85 - 8 * q^86 + 12 * q^89 - 48 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 + 8 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{12}\right)$

Coefficient data

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

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

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

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	1.10131	+	1.10131i	0.492519	+	0.492519i	0.909099	−	0.416580i	$-0.136771\pi$
$5$	1.10131	+	1.10131i	0.492519	+	0.492519i	−0.416580	+	0.909099i	$0.636771\pi$
$6$	0.965926	−	0.258819i	0.394338	−	0.105662i
$7$	−0.930231	+	2.47683i	−0.351594	+	0.936152i
$7$	−0.930231	+	2.47683i	−0.351594	+	0.936152i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	0.778741	+	1.34882i	0.246260	+	0.426534i
$11$	1.09562	−	4.08891i	0.330342	−	1.23285i	−0.578490	−	0.815690i	$-0.696358\pi$
$11$	1.09562	−	4.08891i	0.330342	−	1.23285i	0.908832	−	0.417163i	$-0.136976\pi$
$12$	1.00000			0.288675
$13$	2.26571	+	2.80474i	0.628396	+	0.777894i
$13$	2.26571	+	2.80474i	0.628396	+	0.777894i
$14$	−1.53958	+	2.15167i	−0.411471	+	0.575058i
$15$	1.50441	+	0.403106i	0.388438	+	0.104082i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.530824	+	0.919414i	−0.128744	+	0.222991i	−0.923190	−	0.384344i	$-0.874428\pi$
$17$	−0.530824	+	0.919414i	−0.128744	+	0.222991i	0.794446	+	0.607334i	$0.207761\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	−2.52532	+	0.676658i	−0.579349	+	0.155236i	−0.536581	−	0.843849i	$-0.680284\pi$
$19$	−2.52532	+	0.676658i	−0.579349	+	0.155236i	−0.0427680	+	0.999085i	$0.513618\pi$
$20$	0.403106	+	1.50441i	0.0901373	+	0.336397i
$21$	0.432809	+	2.61011i	0.0944467	+	0.569573i
$22$	2.11658	−	3.66602i	0.451255	−	0.781597i
$23$	−0.925495	+	0.534335i	−0.192979	+	0.111417i	−0.593376	−	0.804925i	$-0.702205\pi$
$23$	−0.925495	+	0.534335i	−0.192979	+	0.111417i	0.400397	+	0.916342i	$0.368872\pi$
$24$	0.965926	+	0.258819i	0.197169	+	0.0528312i
$25$		−	2.57425i		−	0.514849i
$26$	1.46259	+	3.29558i	0.286838	+	0.646316i
$27$		−	1.00000i		−	0.192450i
$28$	−2.04402	+	1.67988i	−0.386283	+	0.317467i
$29$	2.14751	+	3.71959i	0.398782	+	0.690711i	0.993576	−	0.113167i	$-0.0360996\pi$
$29$	2.14751	+	3.71959i	0.398782	+	0.690711i	−0.594794	+	0.803878i	$0.702766\pi$
$30$	1.34882	+	0.778741i	0.246260	+	0.142178i
$31$	0.172393	+	0.172393i	0.0309626	+	0.0309626i	0.722419	−	0.691456i	$-0.243030\pi$
$31$	0.172393	+	0.172393i	0.0309626	+	0.0309626i	−0.691456	+	0.722419i	$0.743030\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	−1.09562	−	4.08891i	−0.190723	−	0.711788i
$34$	−0.750699	+	0.750699i	−0.128744	+	0.128744i
$35$	−3.75222	+	1.70328i	−0.634240	+	0.287906i
$36$	0.866025	−	0.500000i	0.144338	−	0.0833333i
$37$	1.83037	−	6.83102i	0.300910	−	1.12301i	−0.635499	−	0.772102i	$-0.719205\pi$
$37$	1.83037	−	6.83102i	0.300910	−	1.12301i	0.936409	−	0.350911i	$-0.114128\pi$
$38$	−2.61441			−0.424113
$39$	3.36453	+	1.29611i	0.538757	+	0.207544i
$40$			1.55748i			0.246260i
$41$	−0.640215	+	2.38932i	−0.0999849	+	0.373149i	−0.997728	−	0.0673707i	$-0.978539\pi$
$41$	−0.640215	+	2.38932i	−0.0999849	+	0.373149i	0.897743	+	0.440519i	$0.145206\pi$
$42$	−0.257485	+	2.63319i	−0.0397307	+	0.406310i
$43$	−9.94138	−	5.73966i	−1.51605	−	0.875290i	−0.999823	−	0.0188360i	$-0.994004\pi$
$43$	−9.94138	−	5.73966i	−1.51605	−	0.875290i	−0.516224	−	0.856454i	$-0.672663\pi$
$44$	2.99329	−	2.99329i	0.451255	−	0.451255i
$45$	1.50441	−	0.403106i	0.224265	−	0.0600915i
$46$	−1.03226	+	0.276592i	−0.152198	+	0.0407813i
$47$	6.64147	−	6.64147i	0.968759	−	0.968759i	−0.0307679	−	0.999527i	$-0.509795\pi$
$47$	6.64147	−	6.64147i	0.968759	−	0.968759i	0.999527	+	0.0307679i	$0.00979527\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	−5.26934	−	4.60804i	−0.752763	−	0.658292i
$50$	0.666264	−	2.48653i	0.0942240	−	0.351649i
$51$			1.06165i			0.148660i
$52$	0.559799	+	3.56183i	0.0776301	+	0.493937i
$53$	3.29120			0.452080			0.226040	−	0.974118i	$-0.427422\pi$
$53$	3.29120			0.452080			0.226040	+	0.974118i	$0.427422\pi$
$54$	0.258819	−	0.965926i	0.0352208	−	0.131446i
$55$	5.70976	−	3.29653i	0.769904	−	0.444504i
$56$	−2.40915	+	1.09361i	−0.321937	+	0.146140i
$57$	−1.84866	+	1.84866i	−0.244862	+	0.244862i
$58$	1.11163	+	4.14867i	0.145964	+	0.544747i
$59$	−1.79705	−	6.70667i	−0.233955	−	0.873133i	−0.978617	−	0.205691i	$-0.934056\pi$
$59$	−1.79705	−	6.70667i	−0.233955	−	0.873133i	0.744662	−	0.667442i	$-0.232611\pi$
$60$	1.10131	+	1.10131i	0.142178	+	0.142178i
$61$	−3.62769	−	2.09445i	−0.464478	−	0.268166i	0.249447	−	0.968388i	$-0.419751\pi$
$61$	−3.62769	−	2.09445i	−0.464478	−	0.268166i	−0.713925	+	0.700222i	$0.753084\pi$
$62$	0.121900	+	0.211137i	0.0154813	+	0.0268144i
$63$	1.67988	+	2.04402i	0.211645	+	0.257522i
$64$			1.00000i			0.125000i
$65$	−0.593627	+	5.58412i	−0.0736304	+	0.692625i
$66$		−	4.23315i		−	0.521065i
$67$	5.87776	+	1.57494i	0.718083	+	0.192410i	0.599316	−	0.800513i	$-0.295439\pi$
$67$	5.87776	+	1.57494i	0.718083	+	0.192410i	0.118767	+	0.992922i	$0.462106\pi$
$68$	−0.919414	+	0.530824i	−0.111495	+	0.0643719i
$69$	−0.534335	+	0.925495i	−0.0643264	+	0.111417i
$70$	−4.06520	+	0.674093i	−0.485885	+	0.0805695i
$71$	0.0551920	+	0.205979i	0.00655008	+	0.0244452i	0.969124	−	0.246576i	$-0.0793054\pi$
$71$	0.0551920	+	0.205979i	0.00655008	+	0.0244452i	−0.962573	+	0.271021i	$0.912639\pi$
$72$	0.965926	−	0.258819i	0.113835	−	0.0305021i
$73$	−11.8203	+	11.8203i	−1.38347	+	1.38347i	−0.545085	+	0.838381i	$0.683503\pi$
$73$	−11.8203	+	11.8203i	−1.38347	+	1.38347i	−0.838381	+	0.545085i	$0.816497\pi$
$74$	3.53600	−	6.12453i	0.411051	−	0.711962i
$75$	−1.28712	−	2.22936i	−0.148624	−	0.257425i
$76$	−2.52532	−	0.676658i	−0.289674	−	0.0776180i
$77$	9.10834	+	6.51729i	1.03799	+	0.742715i
$78$	2.91443	+	2.12276i	0.329994	+	0.240355i
$79$	−15.8416			−1.78232			−0.891160	−	0.453689i	$-0.850108\pi$
$79$	−15.8416			−1.78232			−0.891160	+	0.453689i	$0.850108\pi$
$80$	−0.403106	+	1.50441i	−0.0450686	+	0.168198i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.23680	+	2.14220i	−0.136582	+	0.236567i
$83$	3.21397	+	3.21397i	0.352779	+	0.352779i	0.861143	−	0.508363i	$-0.169749\pi$
$83$	3.21397	+	3.21397i	0.352779	+	0.352779i	−0.508363	+	0.861143i	$0.669749\pi$
$84$	−0.930231	+	2.47683i	−0.101497	+	0.270244i
$85$	−1.59716	+	0.427957i	−0.173236	+	0.0464184i
$86$	−8.11710	−	8.11710i	−0.875290	−	0.875290i
$87$	3.71959	+	2.14751i	0.398782	+	0.230237i
$88$	3.66602	−	2.11658i	0.390799	−	0.225628i
$89$	−5.32335	−	1.42639i	−0.564274	−	0.151197i	−0.0346050	−	0.999401i	$-0.511017\pi$
$89$	−5.32335	−	1.42639i	−0.564274	−	0.151197i	−0.529669	+	0.848204i	$0.677684\pi$
$90$	1.55748			0.164173
$91$	−9.05448	+	3.00273i	−0.949167	+	0.314772i
$92$	−1.06867			−0.111417
$93$	0.235493	+	0.0631001i	0.0244194	+	0.00654317i
$94$	8.13411	−	4.69623i	0.838970	−	0.484379i
$95$	−3.52636	−	2.03595i	−0.361797	−	0.208884i
$96$	0.707107	+	0.707107i	0.0721688	+	0.0721688i
$97$	3.13122	−	0.839007i	0.317927	−	0.0851883i	−0.0963266	−	0.995350i	$-0.530709\pi$
$97$	3.13122	−	0.839007i	0.317927	−	0.0851883i	0.414254	+	0.910162i	$0.364043\pi$
$98$	−3.89714	−	5.81483i	−0.393671	−	0.587387i
$99$	−2.99329	−	2.99329i	−0.300837	−	0.300837i
$100$	1.28712	−	2.22936i	0.128712	−	0.222936i
$101$	−5.97105	−	10.3422i	−0.594141	−	1.02908i	−0.993667	−	0.112361i	$-0.964159\pi$
$101$	−5.97105	−	10.3422i	−0.594141	−	1.02908i	0.399526	−	0.916722i	$-0.369175\pi$
$102$	−0.274775	+	1.02547i	−0.0272068	+	0.101537i
$103$	−1.57708			−0.155394			−0.0776971	−	0.996977i	$-0.524757\pi$
$103$	−1.57708			−0.155394			−0.0776971	+	0.996977i	$0.524757\pi$
$104$	−0.381145	+	3.58535i	−0.0373744	+	0.351572i
$105$	−2.39788	+	3.35119i	−0.234009	+	0.327042i
$106$	3.17905	+	0.851824i	0.308777	+	0.0827365i
$107$	−0.331915	−	0.574894i	−0.0320875	−	0.0555771i	0.849536	−	0.527531i	$-0.176882\pi$
$107$	−0.331915	−	0.574894i	−0.0320875	−	0.0555771i	−0.881623	+	0.471954i	$0.843549\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	7.42310	−	7.42310i	0.711004	−	0.711004i	−0.255741	−	0.966745i	$-0.582319\pi$
$109$	7.42310	−	7.42310i	0.711004	−	0.711004i	0.966745	+	0.255741i	$0.0823194\pi$
$110$	6.36841	−	1.70641i	0.607204	−	0.162700i
$111$	−1.83037	−	6.83102i	−0.173731	−	0.648372i
$112$	−2.61011	+	0.432809i	−0.246632	+	0.0408966i
$113$	−6.99210	+	12.1107i	−0.657761	+	1.13928i	0.323433	+	0.946251i	$0.395163\pi$
$113$	−6.99210	+	12.1107i	−0.657761	+	1.13928i	−0.981194	+	0.193025i	$0.938170\pi$
$114$	−2.26414	+	1.30720i	−0.212056	+	0.122431i
$115$	−1.60772	−	0.430787i	−0.149921	−	0.0401711i
$116$			4.29502i			0.398782i
$117$	3.56183	−	0.559799i	0.329291	−	0.0517534i
$118$		−	6.94325i		−	0.639178i
$119$	−1.78344	−	2.17003i	−0.163488	−	0.198926i
$120$	0.778741	+	1.34882i	0.0710890	+	0.123130i
$121$	−5.99253	−	3.45979i	−0.544775	−	0.314526i
$122$	−2.96200	−	2.96200i	−0.268166	−	0.268166i
$123$	0.640215	+	2.38932i	0.0577263	+	0.215437i
$124$	0.0631001	+	0.235493i	0.00566655	+	0.0211479i
$125$	8.34157	−	8.34157i	0.746093	−	0.746093i
$126$	1.09361	+	2.40915i	0.0974263	+	0.214624i
$127$	−5.44995	+	3.14653i	−0.483605	+	0.279210i	−0.721918	−	0.691979i	$-0.756739\pi$
$127$	−5.44995	+	3.14653i	−0.483605	+	0.279210i	0.238313	+	0.971189i	$0.423406\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	−11.4793			−1.01070
$130$	−2.01868	+	5.24020i	−0.177050	+	0.459596i
$131$			4.19364i			0.366400i	0.983076	+	0.183200i	$0.0586456\pi$
$131$			4.19364i			0.366400i	−0.983076	+	0.183200i	$0.941354\pi$
$132$	1.09562	−	4.08891i	0.0953615	−	0.355894i
$133$	0.673169	−	6.88423i	0.0583712	−	0.596939i
$134$	5.26986	+	3.04255i	0.455246	+	0.262836i
$135$	1.10131	−	1.10131i	0.0947854	−	0.0947854i
$136$	−1.02547	+	0.274775i	−0.0879336	+	0.0235617i
$137$	19.9165	−	5.33662i	1.70158	−	0.455938i	0.728246	−	0.685316i	$-0.240336\pi$
$137$	19.9165	−	5.33662i	1.70158	−	0.455938i	0.973337	+	0.229378i	$0.0736691\pi$
$138$	−0.755664	+	0.755664i	−0.0643264	+	0.0643264i
$139$	−11.8751	−	6.85609i	−1.00723	−	0.581526i	−0.0968522	−	0.995299i	$-0.530877\pi$
$139$	−11.8751	−	6.85609i	−1.00723	−	0.581526i	−0.910380	+	0.413773i	$0.864211\pi$
$140$	−4.10115	−	0.401028i	−0.346611	−	0.0338930i
$141$	2.43095	−	9.07242i	0.204723	−	0.764036i
$142$			0.213245i			0.0178952i
$143$	13.9507	−	6.19138i	1.16661	−	0.517749i
$144$	1.00000			0.0833333
$145$	−1.73135	+	6.46148i	−0.143781	+	0.536597i
$146$	−14.4769	+	8.35824i	−1.19812	+	0.691733i
$147$	−6.86740	−	1.35601i	−0.566414	−	0.111842i
$148$	5.00065	−	5.00065i	0.411051	−	0.411051i
$149$	5.71276	+	21.3203i	0.468008	+	1.74663i	0.646720	+	0.762727i	$0.276140\pi$
$149$	5.71276	+	21.3203i	0.468008	+	1.74663i	−0.178713	+	0.983901i	$0.557193\pi$
$150$	−0.666264	−	2.48653i	−0.0544003	−	0.203024i
$151$	−4.19913	−	4.19913i	−0.341720	−	0.341720i	0.515294	−	0.857014i	$-0.327683\pi$
$151$	−4.19913	−	4.19913i	−0.341720	−	0.341720i	−0.857014	+	0.515294i	$0.827683\pi$
$152$	−2.26414	−	1.30720i	−0.183646	−	0.106028i
$153$	0.530824	+	0.919414i	0.0429146	+	0.0743302i
$154$	7.11118	+	8.65263i	0.573035	+	0.697249i
$155$			0.379714i			0.0304994i
$156$	2.26571	+	2.80474i	0.181402	+	0.224559i
$157$			10.1359i			0.808934i	0.914553	+	0.404467i	$0.132543\pi$
$157$			10.1359i			0.808934i	−0.914553	+	0.404467i	$0.867457\pi$
$158$	−15.3018	−	4.10011i	−1.21735	−	0.326187i
$159$	2.85026	−	1.64560i	0.226040	−	0.130504i
$160$	−0.778741	+	1.34882i	−0.0615649	+	0.106634i
$161$	−0.462530	−	2.78935i	−0.0364525	−	0.219831i
$162$	−0.258819	−	0.965926i	−0.0203347	−	0.0758903i
$163$	3.81267	−	1.02160i	0.298631	−	0.0800181i	−0.106392	−	0.994324i	$-0.533930\pi$
$163$	3.81267	−	1.02160i	0.298631	−	0.0800181i	0.405024	+	0.914306i	$0.367263\pi$
$164$	−1.74910	+	1.74910i	−0.136582	+	0.136582i
$165$	3.29653	−	5.70976i	0.256635	−	0.444504i
$166$	2.27262	+	3.93630i	0.176390	+	0.305516i
$167$	−8.57608	−	2.29795i	−0.663637	−	0.177821i	−0.0887500	−	0.996054i	$-0.528287\pi$
$167$	−8.57608	−	2.29795i	−0.663637	−	0.177821i	−0.574887	+	0.818233i	$0.694954\pi$
$168$	−1.53958	+	2.15167i	−0.118782	+	0.166005i
$169$	−2.73308	+	12.7095i	−0.210237	+	0.977651i
$170$	−1.65350			−0.126818
$171$	−0.676658	+	2.52532i	−0.0517453	+	0.193116i
$172$	−5.73966	−	9.94138i	−0.437645	−	0.758023i
$173$	−5.10529	+	8.84262i	−0.388148	+	0.672292i	−0.992200	−	0.124653i	$-0.960218\pi$
$173$	−5.10529	+	8.84262i	−0.388148	+	0.672292i	0.604053	+	0.796944i	$0.293552\pi$
$174$	3.03704	+	3.03704i	0.230237	+	0.230237i
$175$	6.37596	+	2.39465i	0.481978	+	0.181018i
$176$	4.08891	−	1.09562i	0.308213	−	0.0825855i
$177$	−4.90962	−	4.90962i	−0.369030	−	0.369030i
$178$	−4.77279	−	2.75557i	−0.357736	−	0.206539i
$179$	23.1484	−	13.3647i	1.73019	−	0.998927i	0.841939	−	0.539572i	$-0.181414\pi$
$179$	23.1484	−	13.3647i	1.73019	−	0.998927i	0.888253	−	0.459355i	$-0.151919\pi$
$180$	1.50441	+	0.403106i	0.112132	+	0.0300458i
$181$	5.81054			0.431894			0.215947	−	0.976405i	$-0.430716\pi$
$181$	5.81054			0.431894			0.215947	+	0.976405i	$0.430716\pi$
$182$	−9.52312	+	0.556942i	−0.705901	+	0.0412833i
$183$	−4.18889			−0.309652
$184$	−1.03226	−	0.276592i	−0.0760989	−	0.0203906i
$185$	9.53884	−	5.50725i	0.701310	−	0.404901i
$186$	0.211137	+	0.121900i	0.0154813	+	0.00893814i
$187$	3.17782	+	3.17782i	0.232385	+	0.232385i
$188$	9.07242	−	2.43095i	0.661674	−	0.177295i
$189$	2.47683	+	0.930231i	0.180163	+	0.0676644i
$190$	−2.87926	−	2.87926i	−0.208884	−	0.208884i
$191$	1.98254	−	3.43385i	0.143451	−	0.248465i	−0.785343	−	0.619061i	$-0.787513\pi$
$191$	1.98254	−	3.43385i	0.143451	−	0.248465i	0.928794	+	0.370596i	$0.120847\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	6.46517	−	24.1284i	0.465373	−	1.73680i	−0.190275	−	0.981731i	$-0.560938\pi$
$193$	6.46517	−	24.1284i	0.465373	−	1.73680i	0.655648	−	0.755066i	$-0.272395\pi$
$194$	3.24167			0.232739
$195$	2.27796	+	5.13280i	0.163128	+	0.367568i
$196$	−2.25936	−	6.62535i	−0.161383	−	0.473239i
$197$	15.0491	+	4.03238i	1.07220	+	0.287295i	0.751397	−	0.659850i	$-0.229380\pi$
$197$	15.0491	+	4.03238i	1.07220	+	0.287295i	0.320804	+	0.947146i	$0.396047\pi$
$198$	−2.11658	−	3.66602i	−0.150418	−	0.260532i
$199$	−5.52602	+	9.57135i	−0.391729	+	0.678495i	−0.992678	−	0.120793i	$-0.961456\pi$
$199$	−5.52602	+	9.57135i	−0.391729	+	0.678495i	0.600949	+	0.799288i	$0.294790\pi$
$200$	1.82027	−	1.82027i	0.128712	−	0.128712i
$201$	5.87776	−	1.57494i	0.414585	−	0.111088i
$202$	−3.09084	−	11.5352i	−0.217471	−	0.811612i
$203$	−11.2105	+	1.85892i	−0.786821	+	0.130471i
$204$	−0.530824	+	0.919414i	−0.0371651	+	0.0643719i
$205$	−3.33644	+	1.92630i	−0.233027	+	0.134538i
$206$	−1.52334	−	0.408178i	−0.106136	−	0.0284391i
$207$			1.06867i			0.0742777i
$208$	−1.29611	+	3.36453i	−0.0898694	+	0.233288i
$209$			11.0672i			0.765533i
$210$	−3.18352	+	2.61638i	−0.219684	+	0.180548i
$211$	−1.04970	−	1.81814i	−0.0722646	−	0.125166i	0.827629	−	0.561276i	$-0.189689\pi$
$211$	−1.04970	−	1.81814i	−0.0722646	−	0.125166i	−0.899893	+	0.436110i	$0.856356\pi$
$212$	2.85026	+	1.64560i	0.195757	+	0.113020i
$213$	0.150787	+	0.150787i	0.0103318	+	0.0103318i
$214$	−0.171812	−	0.641211i	−0.0117448	−	0.0438323i
$215$	−4.62738	−	17.2696i	−0.315585	−	1.17778i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	−0.587351	+	0.266622i	−0.0398720	+	0.0180994i
$218$	9.09141	−	5.24893i	0.615748	−	0.355502i
$219$	−4.32654	+	16.1469i	−0.292361	+	1.09111i
$220$	6.59306			0.444504
$221$	−3.78141	+	0.594309i	−0.254365	+	0.0399776i
$222$		−	7.07199i		−	0.474641i
$223$	4.06198	−	15.1595i	0.272010	−	1.01516i	−0.685808	−	0.727782i	$-0.740551\pi$
$223$	4.06198	−	15.1595i	0.272010	−	1.01516i	0.957818	−	0.287374i	$-0.0927823\pi$
$224$	−2.63319	−	0.257485i	−0.175938	−	0.0172039i
$225$	−2.22936	−	1.28712i	−0.148624	−	0.0858082i
$226$	−9.88832	+	9.88832i	−0.657761	+	0.657761i
$227$	10.2337	−	2.74212i	0.679237	−	0.182001i	0.0973250	−	0.995253i	$-0.468971\pi$
$227$	10.2337	−	2.74212i	0.679237	−	0.182001i	0.581912	+	0.813252i	$0.302305\pi$
$228$	−2.52532	+	0.676658i	−0.167244	+	0.0448128i
$229$	−17.7327	+	17.7327i	−1.17181	+	1.17181i	−0.190034	+	0.981777i	$0.560860\pi$
$229$	−17.7327	+	17.7327i	−1.17181	+	1.17181i	−0.981777	+	0.190034i	$0.939140\pi$
$230$	−1.44144	−	0.832217i	−0.0950459	−	0.0548748i
$231$	11.1467	+	1.08997i	0.733399	+	0.0717148i
$232$	−1.11163	+	4.14867i	−0.0729822	+	0.272373i
$233$			8.08015i			0.529348i	0.964338	+	0.264674i	$0.0852644\pi$
$233$			8.08015i			0.529348i	−0.964338	+	0.264674i	$0.914736\pi$
$234$	3.58535	+	0.381145i	0.234382	+	0.0249162i
$235$	14.6286			0.954265
$236$	1.79705	−	6.70667i	0.116978	−	0.436567i
$237$	−13.7192	+	7.92080i	−0.891160	+	0.514511i
$238$	−1.16103	−	2.55767i	−0.0752582	−	0.165789i
$239$	−1.78086	+	1.78086i	−0.115194	+	0.115194i	−0.762354	−	0.647160i	$-0.775957\pi$
$239$	−1.78086	+	1.78086i	−0.115194	+	0.115194i	0.647160	+	0.762354i	$0.275957\pi$
$240$	0.403106	+	1.50441i	0.0260204	+	0.0971094i
$241$	5.92466	+	22.1111i	0.381641	+	1.42430i	0.843394	+	0.537295i	$0.180554\pi$
$241$	5.92466	+	22.1111i	0.381641	+	1.42430i	−0.461753	+	0.887008i	$0.652779\pi$
$242$	−4.89288	−	4.89288i	−0.314526	−	0.314526i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−2.09445	−	3.62769i	−0.134083	−	0.232239i
$245$	−0.728290	−	10.8780i	−0.0465287	−	0.694972i
$246$			2.47360i			0.157711i
$247$	−7.61951	−	5.54975i	−0.484818	−	0.353122i
$248$			0.243800i			0.0154813i
$249$	4.39037	+	1.17640i	0.278228	+	0.0745511i
$250$	10.2163	−	5.89838i	0.646135	−	0.373046i
$251$	−9.39483	+	16.2723i	−0.592996	+	1.02710i	0.400830	+	0.916152i	$0.368722\pi$
$251$	−9.39483	+	16.2723i	−0.592996	+	1.02710i	−0.993826	+	0.110947i	$0.964612\pi$
$252$	0.432809	+	2.61011i	0.0272644	+	0.164421i
$253$	1.17086	+	4.36970i	0.0736111	+	0.274720i
$254$	−6.07863	+	1.62876i	−0.381407	+	0.102198i
$255$	−1.16920	+	1.16920i	−0.0732182	+	0.0732182i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.83613	+	11.8405i	0.426426	+	0.738591i	0.996552	−	0.0829657i	$-0.0264392\pi$
$257$	6.83613	+	11.8405i	0.426426	+	0.738591i	−0.570127	+	0.821557i	$0.693106\pi$
$258$	−11.0882	−	2.97107i	−0.690319	−	0.184970i
$259$	15.2166	+	10.8879i	0.945513	+	0.676543i
$260$	−3.30616	+	4.53918i	−0.205039	+	0.281508i
$261$	4.29502			0.265855
$262$	−1.08539	+	4.05074i	−0.0670559	+	0.250256i
$263$	8.27724	+	14.3366i	0.510396	+	0.884032i	0.999927	+	0.0120466i	$0.00383465\pi$
$263$	8.27724	+	14.3366i	0.510396	+	0.884032i	−0.489531	+	0.871986i	$0.662832\pi$
$264$	2.11658	−	3.66602i	0.130266	−	0.225628i
$265$	3.62461	+	3.62461i	0.222658	+	0.222658i
$266$	2.43200	−	6.47543i	0.149116	−	0.397034i
$267$	−5.32335	+	1.42639i	−0.325784	+	0.0872936i
$268$	4.30282	+	4.30282i	0.262836	+	0.262836i
$269$	0.0117614	+	0.00679046i	0.000717106	+	0.000414021i	0.500359	−	0.865818i	$-0.333202\pi$
$269$	0.0117614	+	0.00679046i	0.000717106	+	0.000414021i	−0.499641	+	0.866232i	$0.666535\pi$
$270$	1.34882	−	0.778741i	0.0820865	−	0.0473927i
$271$	9.32240	+	2.49793i	0.566295	+	0.151738i	0.530597	−	0.847624i	$-0.321968\pi$
$271$	9.32240	+	2.49793i	0.566295	+	0.151738i	0.0356984	+	0.999363i	$0.488634\pi$
$272$	−1.06165			−0.0643719
$273$	−6.34005	+	7.12768i	−0.383717	+	0.431387i
$274$	20.6191			1.24565
$275$	−10.5259	−	2.82040i	−0.634734	−	0.170076i
$276$	−0.925495	+	0.534335i	−0.0557083	+	0.0321632i
$277$	10.9261	+	6.30817i	0.656484	+	0.379021i	0.790936	−	0.611899i	$-0.209594\pi$
$277$	10.9261	+	6.30817i	0.656484	+	0.379021i	−0.134452	+	0.990920i	$0.542927\pi$
$278$	−9.69597	−	9.69597i	−0.581526	−	0.581526i
$279$	0.235493	−	0.0631001i	0.0140986	−	0.00377770i
$280$	−3.85761	−	1.44882i	−0.230537	−	0.0865835i
$281$	−10.1653	−	10.1653i	−0.606409	−	0.606409i	0.335597	−	0.942006i	$-0.391062\pi$
$281$	−10.1653	−	10.1653i	−0.606409	−	0.606409i	−0.942006	+	0.335597i	$0.891062\pi$
$282$	4.69623	−	8.13411i	0.279657	−	0.484379i
$283$	−9.84255	−	17.0478i	−0.585079	−	1.01339i	−0.994866	−	0.101205i	$-0.967730\pi$
$283$	−9.84255	−	17.0478i	−0.585079	−	1.01339i	0.409787	−	0.912181i	$-0.365603\pi$
$284$	−0.0551920	+	0.205979i	−0.00327504	+	0.0122226i
$285$	−4.07189			−0.241198
$286$	15.0778	−	2.36971i	0.891567	−	0.140124i
$287$	−5.32237	−	3.80832i	−0.314170	−	0.224798i
$288$	0.965926	+	0.258819i	0.0569177	+	0.0152511i
$289$	7.93645	+	13.7463i	0.466850	+	0.808608i
$290$	−3.34471	+	5.79320i	−0.196408	+	0.340189i
$291$	2.29221	−	2.29221i	0.134372	−	0.134372i
$292$	−16.1469	+	4.32654i	−0.944925	+	0.253192i
$293$	6.18693	+	23.0899i	0.361444	+	1.34893i	0.872178	+	0.489189i	$0.162707\pi$
$293$	6.18693	+	23.0899i	0.361444	+	1.34893i	−0.510733	+	0.859739i	$0.670626\pi$
$294$	−6.28244	−	3.08722i	−0.366399	−	0.180050i
$295$	5.40700	−	9.36519i	0.314808	−	0.545263i
$296$	6.12453	−	3.53600i	0.355981	−	0.205526i
$297$	−4.08891	−	1.09562i	−0.237263	−	0.0635743i
$298$			22.0724i			1.27862i
$299$	−3.59558	−	1.38512i	−0.207938	−	0.0801035i
$300$		−	2.57425i		−	0.148624i
$301$	23.4639	−	19.2839i	1.35244	−	1.11150i
$302$	−2.96923	−	5.14286i	−0.170860	−	0.295938i
$303$	−10.3422	−	5.97105i	−0.594141	−	0.343028i
$304$	−1.84866	−	1.84866i	−0.106028	−	0.106028i
$305$	−1.68857	−	6.30183i	−0.0966872	−	0.360841i
$306$	0.274775	+	1.02547i	0.0157078	+	0.0586224i
$307$	11.2077	−	11.2077i	0.639659	−	0.639659i	−0.310812	−	0.950471i	$-0.600601\pi$
$307$	11.2077	−	11.2077i	0.639659	−	0.639659i	0.950471	+	0.310812i	$0.100601\pi$
$308$	4.62941	+	10.1983i	0.263785	+	0.581103i
$309$	−1.36579	+	0.788540i	−0.0776971	+	0.0448585i
$310$	−0.0982773	+	0.366776i	−0.00558177	+	0.0208315i
$311$	29.7748			1.68837			0.844187	−	0.536049i	$-0.180084\pi$
$311$	29.7748			1.68837			0.844187	+	0.536049i	$0.180084\pi$
$312$	1.46259	+	3.29558i	0.0828030	+	0.186575i
$313$			31.4913i			1.77999i	0.455969	+	0.889996i	$0.349293\pi$
$313$			31.4913i			1.77999i	−0.455969	+	0.889996i	$0.650707\pi$
$314$	−2.62337	+	9.79054i	−0.148045	+	0.552512i
$315$	−0.401028	+	4.10115i	−0.0225954	+	0.231074i
$316$	−13.7192	−	7.92080i	−0.771767	−	0.445580i
$317$	−8.23824	+	8.23824i	−0.462706	+	0.462706i	−0.899541	−	0.436836i	$-0.856099\pi$
$317$	−8.23824	+	8.23824i	−0.462706	+	0.462706i	0.436836	+	0.899541i	$0.356099\pi$
$318$	3.17905	−	0.851824i	0.178272	−	0.0477679i
$319$	17.5619	−	4.70571i	0.983280	−	0.263469i
$320$	−1.10131	+	1.10131i	−0.0615649	+	0.0615649i
$321$	−0.574894	−	0.331915i	−0.0320875	−	0.0185257i
$322$	0.275166	−	2.81401i	0.0153344	−	0.156819i
$323$	0.718373	−	2.68100i	0.0399713	−	0.149175i
$324$		−	1.00000i		−	0.0555556i
$325$	7.22008	−	5.83251i	0.400498	−	0.323529i
$326$	3.94717			0.218613
$327$	2.71704	−	10.1401i	0.150253	−	0.560751i
$328$	−2.14220	+	1.23680i	−0.118283	+	0.0682909i
$329$	10.2717	+	22.6279i	0.566296	+	1.24752i
$330$	4.66200	−	4.66200i	0.256635	−	0.256635i
$331$	5.30297	+	19.7909i	0.291477	+	1.08781i	0.943975	+	0.330018i	$0.107055\pi$
$331$	5.30297	+	19.7909i	0.291477	+	1.08781i	−0.652497	+	0.757791i	$0.726279\pi$
$332$	1.17640	+	4.39037i	0.0645631	+	0.240953i
$333$	−5.00065	−	5.00065i	−0.274034	−	0.274034i
$334$	−7.68910	−	4.43930i	−0.420729	−	0.242908i
$335$	4.73872	+	8.20771i	0.258904	+	0.448435i
$336$	−2.04402	+	1.67988i	−0.111510	+	0.0916449i
$337$		−	4.85068i		−	0.264233i	−0.991234	−	0.132117i	$-0.957823\pi$
$337$		−	4.85068i		−	0.264233i	0.991234	−	0.132117i	$-0.0421774\pi$
$338$	−5.92940	+	11.5690i	−0.322517	+	0.629272i
$339$			13.9842i			0.759517i
$340$	−1.59716	−	0.427957i	−0.0866180	−	0.0232092i
$341$	0.893775	−	0.516021i	0.0484006	−	0.0279441i
$342$	−1.30720	+	2.26414i	−0.0706854	+	0.122431i
$343$	16.3150	−	8.76469i	0.880929	−	0.473249i
$344$	−2.97107	−	11.0882i	−0.160189	−	0.597834i
$345$	−1.60772	+	0.430787i	−0.0865568	+	0.0231928i
$346$	−7.21997	+	7.21997i	−0.388148	+	0.388148i
$347$	11.0803	−	19.1917i	0.594822	−	1.03026i	−0.398750	−	0.917060i	$-0.630556\pi$
$347$	11.0803	−	19.1917i	0.594822	−	1.03026i	0.993572	−	0.113202i	$-0.0361108\pi$
$348$	2.14751	+	3.71959i	0.115119	+	0.199391i
$349$	−18.6321	−	4.99246i	−0.997355	−	0.267240i	−0.277018	−	0.960865i	$-0.589346\pi$
$349$	−18.6321	−	4.99246i	−0.997355	−	0.267240i	−0.720337	+	0.693624i	$0.756013\pi$
$350$	5.53893	+	3.96327i	0.296068	+	0.211846i
$351$	2.80474	−	2.26571i	0.149706	−	0.120935i
$352$	4.23315			0.225628
$353$	1.97500	−	7.37081i	0.105119	−	0.392309i	−0.893240	−	0.449581i	$-0.851573\pi$
$353$	1.97500	−	7.37081i	0.105119	−	0.392309i	0.998359	+	0.0572718i	$0.0182402\pi$
$354$	−3.47163	−	6.01303i	−0.184515	−	0.319589i
$355$	−0.166063	+	0.287630i	−0.00881371	+	0.0152658i
$356$	−3.89697	−	3.89697i	−0.206539	−	0.206539i
$357$	−2.62952	−	0.987578i	−0.139169	−	0.0522682i
$358$	25.8187	−	6.91809i	1.36456	−	0.365633i
$359$	−16.0561	−	16.0561i	−0.847409	−	0.847409i	0.142400	−	0.989809i	$-0.454518\pi$
$359$	−16.0561	−	16.0561i	−0.847409	−	0.847409i	−0.989809	+	0.142400i	$0.954518\pi$
$360$	1.34882	+	0.778741i	0.0710890	+	0.0410433i
$361$	−10.5351	+	6.08244i	−0.554479	+	0.320128i
$362$	5.61255	+	1.50388i	0.294989	+	0.0790420i
$363$	−6.91957			−0.363183
$364$	−9.34277	−	1.92680i	−0.489694	−	0.100992i
$365$	−26.0356			−1.36277
$366$	−4.04616	−	1.08417i	−0.211496	−	0.0566702i
$367$	14.9043	−	8.60499i	0.777997	−	0.449177i	−0.0577227	−	0.998333i	$-0.518384\pi$
$367$	14.9043	−	8.60499i	0.777997	−	0.449177i	0.835720	+	0.549156i	$0.185051\pi$
$368$	−0.925495	−	0.534335i	−0.0482448	−	0.0278541i
$369$	1.74910	+	1.74910i	0.0910546	+	0.0910546i
$370$	10.6392	−	2.85076i	0.553105	−	0.148204i
$371$	−3.06157	+	8.15172i	−0.158949	+	0.423216i
$372$	0.172393	+	0.172393i	0.00893814	+	0.00893814i
$373$	2.24671	−	3.89142i	0.116330	−	0.201490i	−0.801980	−	0.597350i	$-0.796220\pi$
$373$	2.24671	−	3.89142i	0.116330	−	0.201490i	0.918311	+	0.395860i	$0.129554\pi$
$374$	2.24706	+	3.89202i	0.116193	+	0.201252i
$375$	3.05323	−	11.3948i	0.157668	−	0.588425i
$376$	9.39246			0.484379
$377$	−5.56683	+	14.4507i	−0.286707	+	0.744250i
$378$	2.15167	+	1.53958i	0.110670	+	0.0791877i
$379$	34.0830	+	9.13250i	1.75072	+	0.469105i	0.984780	−	0.173803i	$-0.0556056\pi$
$379$	34.0830	+	9.13250i	1.75072	+	0.469105i	0.765943	+	0.642908i	$0.222272\pi$
$380$	−2.03595	−	3.52636i	−0.104442	−	0.180899i
$381$	−3.14653	+	5.44995i	−0.161202	+	0.279210i
$382$	2.80373	−	2.80373i	0.143451	−	0.143451i
$383$	−7.50455	+	2.01084i	−0.383465	+	0.102749i	−0.445401	−	0.895331i	$-0.646939\pi$
$383$	−7.50455	+	2.01084i	−0.383465	+	0.102749i	0.0619367	+	0.998080i	$0.480272\pi$
$384$	0.258819	+	0.965926i	0.0132078	+	0.0492922i
$385$	2.85354	+	17.2086i	0.145430	+	0.877032i
$386$	12.4898	−	21.6329i	0.635712	−	1.10109i
$387$	−9.94138	+	5.73966i	−0.505349	+	0.291763i
$388$	3.13122	+	0.839007i	0.158963	+	0.0425941i
$389$			11.0265i			0.559067i	0.960136	+	0.279534i	$0.0901798\pi$
$389$			11.0265i			0.559067i	−0.960136	+	0.279534i	$0.909820\pi$
$390$	0.871877	+	5.54749i	0.0441492	+	0.280908i
$391$		−	1.13455i		−	0.0573767i
$392$	−0.467607	−	6.98436i	−0.0236177	−	0.352764i
$393$	2.09682	+	3.63180i	0.105771	+	0.183200i
$394$	13.4926	+	7.78997i	0.679748	+	0.392453i
$395$	−17.4465	−	17.4465i	−0.877827	−	0.877827i
$396$	−1.09562	−	4.08891i	−0.0550570	−	0.205475i
$397$	−6.33388	−	23.6384i	−0.317888	−	1.18638i	−0.921270	−	0.388923i	$-0.872847\pi$
$397$	−6.33388	−	23.6384i	−0.317888	−	1.18638i	0.603382	−	0.797453i	$-0.293820\pi$
$398$	−7.81497	+	7.81497i	−0.391729	+	0.391729i
$399$	−2.85914	−	6.29851i	−0.143136	−	0.315320i
$400$	2.22936	−	1.28712i	0.111468	−	0.0643562i
$401$	4.92974	−	18.3981i	0.246180	−	0.918755i	−0.726607	−	0.687053i	$-0.758904\pi$
$401$	4.92974	−	18.3981i	0.246180	−	0.918755i	0.972787	−	0.231702i	$-0.0744294\pi$
$402$	6.08510			0.303497
$403$	−0.0929232	+	0.874108i	−0.00462883	+	0.0435424i
$404$		−	11.9421i		−	0.594141i
$405$	0.403106	−	1.50441i	0.0200305	−	0.0747549i
$406$	−11.3096	−	1.10590i	−0.561286	−	0.0548849i
$407$	−25.9260	−	14.9684i	−1.28511	−	0.741956i
$408$	−0.750699	+	0.750699i	−0.0371651	+	0.0371651i
$409$	11.0614	−	2.96390i	0.546953	−	0.146555i	0.0252472	−	0.999681i	$-0.491963\pi$
$409$	11.0614	−	2.96390i	0.546953	−	0.146555i	0.521705	+	0.853126i	$0.325296\pi$
$410$	−3.72132	+	0.997125i	−0.183783	+	0.0492445i
$411$	14.5799	−	14.5799i	0.719174	−	0.719174i
$412$	−1.36579	−	0.788540i	−0.0672877	−	0.0388486i
$413$	18.2829	+	1.78778i	0.899643	+	0.0879709i
$414$	−0.276592	+	1.03226i	−0.0135938	+	0.0507326i
$415$			7.07914i			0.347501i
$416$	−2.12276	+	2.91443i	−0.104077	+	0.142892i
$417$	−13.7122			−0.671488
$418$	−2.86440	+	10.6901i	−0.140102	+	0.522869i
$419$	−26.9378	+	15.5525i	−1.31600	+	0.759791i	−0.983082	−	0.183166i	$-0.941365\pi$
$419$	−26.9378	+	15.5525i	−1.31600	+	0.759791i	−0.332914	+	0.942957i	$0.608032\pi$
$420$	−3.75222	+	1.70328i	−0.183089	+	0.0831113i
$421$	−18.4475	+	18.4475i	−0.899076	+	0.899076i	−0.995354	−	0.0962783i	$-0.969306\pi$
$421$	−18.4475	+	18.4475i	−0.899076	+	0.899076i	0.0962783	+	0.995354i	$0.469306\pi$
$422$	−0.543367	−	2.02787i	−0.0264507	−	0.0987153i
$423$	−2.43095	−	9.07242i	−0.118197	−	0.441116i
$424$	2.32723	+	2.32723i	0.113020	+	0.113020i
$425$	2.36680	+	1.36647i	0.114807	+	0.0662837i
$426$	0.106623	+	0.184676i	0.00516589	+	0.00894758i
$427$	8.56217	−	7.03683i	0.414352	−	0.340536i
$428$		−	0.663830i		−	0.0320875i
$429$	8.98595	−	12.3372i	0.433846	−	0.595647i
$430$		−	17.8788i		−	0.862194i
$431$	3.37983	+	0.905623i	0.162801	+	0.0436223i	0.339299	−	0.940679i	$-0.389810\pi$
$431$	3.37983	+	0.905623i	0.162801	+	0.0436223i	−0.176498	+	0.984301i	$0.556477\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	14.1431	−	24.4966i	0.679676	−	1.17723i	−0.295403	−	0.955373i	$-0.595454\pi$
$433$	14.1431	−	24.4966i	0.679676	−	1.17723i	0.975079	−	0.221860i	$-0.0712127\pi$
$434$	−0.636345	+	0.105519i	−0.0305455	+	0.00506507i
$435$	1.73135	+	6.46148i	0.0830118	+	0.309804i
$436$	10.1401	−	2.71704i	0.485625	−	0.130123i
$437$	1.97561	−	1.97561i	0.0945063	−	0.0945063i
$438$	−8.35824	+	14.4769i	−0.399372	+	0.691733i
$439$	3.23957	+	5.61110i	0.154616	+	0.267803i	0.932919	−	0.360086i	$-0.117253\pi$
$439$	3.23957	+	5.61110i	0.154616	+	0.267803i	−0.778303	+	0.627889i	$0.783919\pi$
$440$	6.36841	+	1.70641i	0.303602	+	0.0813499i
$441$	−6.62535	+	2.25936i	−0.315493	+	0.107589i
$442$	−3.80638	−	0.404642i	−0.181051	−	0.0192469i
$443$	−31.3996			−1.49184			−0.745919	−	0.666037i	$-0.767989\pi$
$443$	−31.3996			−1.49184			−0.745919	+	0.666037i	$0.767989\pi$
$444$	1.83037	−	6.83102i	0.0868653	−	0.324186i
$445$	−4.29175	−	7.43354i	−0.203449	−	0.352383i
$446$	7.84714	−	13.5917i	0.371573	−	0.643583i
$447$	15.6076	+	15.6076i	0.738212	+	0.738212i
$448$	−2.47683	−	0.930231i	−0.117019	−	0.0439493i
$449$	24.5989	−	6.59127i	1.16090	−	0.311061i	0.373572	−	0.927601i	$-0.378133\pi$
$449$	24.5989	−	6.59127i	1.16090	−	0.311061i	0.787324	+	0.616540i	$0.211466\pi$
$450$	−1.82027	−	1.82027i	−0.0858082	−	0.0858082i
$451$	9.06827	+	5.23557i	0.427008	+	0.246533i
$452$	−12.1107	+	6.99210i	−0.569638	+	0.328881i
$453$	−5.73611	−	1.53699i	−0.269506	−	0.0722140i
$454$	10.5947			0.497236
$455$	−13.2787	−	6.66483i	−0.622514	−	0.312452i
$456$	−2.61441			−0.122431
$457$	−0.339935	−	0.0910852i	−0.0159015	−	0.00426079i	0.250860	−	0.968023i	$-0.419287\pi$
$457$	−0.339935	−	0.0910852i	−0.0159015	−	0.00426079i	−0.266761	+	0.963763i	$0.585953\pi$
$458$	−21.7181	+	12.5389i	−1.01482	+	0.585906i
$459$	0.919414	+	0.530824i	0.0429146	+	0.0247767i
$460$	−1.17693	−	1.17693i	−0.0548748	−	0.0548748i
$461$	19.3407	−	5.18234i	0.900788	−	0.241366i	0.221434	−	0.975175i	$-0.428926\pi$
$461$	19.3407	−	5.18234i	0.900788	−	0.241366i	0.679355	+	0.733810i	$0.262260\pi$
$462$	10.4848	+	3.93781i	0.487796	+	0.183204i
$463$	2.80134	+	2.80134i	0.130189	+	0.130189i	0.769199	−	0.639010i	$-0.220656\pi$
$463$	2.80134	+	2.80134i	0.130189	+	0.130189i	−0.639010	+	0.769199i	$0.720656\pi$
$464$	−2.14751	+	3.71959i	−0.0996956	+	0.172678i
$465$	0.189857	+	0.328842i	0.00880441	+	0.0152497i
$466$	−2.09130	+	7.80482i	−0.0968774	+	0.361551i
$467$	4.26072			0.197163			0.0985814	−	0.995129i	$-0.468570\pi$
$467$	4.26072			0.197163			0.0985814	+	0.995129i	$0.468570\pi$
$468$	3.36453	+	1.29611i	0.155526	+	0.0599129i
$469$	−9.36853	+	13.0931i	−0.432599	+	0.604585i
$470$	14.1301	+	3.78616i	0.651775	+	0.174643i
$471$	5.06796	+	8.77796i	0.233519	+	0.404467i
$472$	3.47163	−	6.01303i	0.159795	−	0.276772i
$473$	−34.3609	+	34.3609i	−1.57992	+	1.57992i
$474$	−15.3018	+	4.10011i	−0.702836	+	0.188324i
$475$	1.74189	+	6.50081i	0.0799232	+	0.298277i
$476$	−0.459491	−	2.77102i	−0.0210607	−	0.127009i
$477$	1.64560	−	2.85026i	0.0753467	−	0.130504i
$478$	−2.18110	+	1.25926i	−0.0997611	+	0.0575971i
$479$	−37.1882	−	9.96454i	−1.69917	−	0.455292i	−0.726441	−	0.687229i	$-0.758827\pi$
$479$	−37.1882	−	9.96454i	−1.69917	−	0.455292i	−0.972731	+	0.231938i	$0.925493\pi$
$480$			1.55748i			0.0710890i
$481$	23.3063	−	10.3434i	1.06268	−	0.471621i
$482$			22.8911i			1.04266i
$483$	−1.79524	−	2.18438i	−0.0816861	−	0.0993927i
$484$	−3.45979	−	5.99253i	−0.157263	−	0.272388i
$485$	4.37243	+	2.52443i	0.198542	+	0.114628i
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$	2.74505	+	10.2447i	0.124390	+	0.464230i	0.999817	−	0.0191201i	$-0.00608648\pi$
$487$	2.74505	+	10.2447i	0.124390	+	0.464230i	−0.875427	+	0.483350i	$0.839420\pi$
$488$	−1.08417	−	4.04616i	−0.0490779	−	0.183161i
$489$	2.79107	−	2.79107i	0.126217	−	0.126217i
$490$	2.11197	−	10.6959i	0.0954089	−	0.483190i
$491$	−0.153678	+	0.0887260i	−0.00693539	+	0.00400415i	−0.503464	−	0.864016i	$-0.667941\pi$
$491$	−0.153678	+	0.0887260i	−0.00693539	+	0.00400415i	0.496528	+	0.868021i	$0.334608\pi$
$492$	−0.640215	+	2.38932i	−0.0288631	+	0.107719i
$493$	−4.55980			−0.205363
$494$	−5.92350	−	7.33272i	−0.266511	−	0.329915i
$495$		−	6.59306i		−	0.296336i
$496$	−0.0631001	+	0.235493i	−0.00283328	+	0.0105739i
$497$	−0.561516	−	0.0549074i	−0.0251874	−	0.00246293i
$498$	3.93630	+	2.27262i	0.176390	+	0.101839i
$499$	−17.2923	+	17.2923i	−0.774110	+	0.774110i	−0.978822	−	0.204712i	$-0.934374\pi$
$499$	−17.2923	+	17.2923i	−0.774110	+	0.774110i	0.204712	+	0.978822i	$0.434374\pi$
$500$	11.3948	−	3.05323i	0.509591	−	0.136544i
$501$	−8.57608	+	2.29795i	−0.383151	+	0.102665i
$502$	−13.2863	+	13.2863i	−0.592996	+	0.592996i
$503$	−23.3904	−	13.5045i	−1.04293	−	0.602134i	−0.122266	−	0.992497i	$-0.539016\pi$
$503$	−23.3904	−	13.5045i	−1.04293	−	0.602134i	−0.920661	+	0.390364i	$0.872349\pi$
$504$	−0.257485	+	2.63319i	−0.0114693	+	0.117292i
$505$	4.81393	−	17.9658i	0.214217	−	0.799469i
$506$			4.52384i			0.201109i
$507$	3.98781	+	12.3733i	0.177105	+	0.549515i
$508$	−6.29306			−0.279210
$509$	1.05976	−	3.95507i	0.0469730	−	0.175306i	−0.938454	−	0.345404i	$-0.887742\pi$
$509$	1.05976	−	3.95507i	0.0469730	−	0.175306i	0.985427	+	0.170098i	$0.0544086\pi$
$510$	−1.43197	+	0.826749i	−0.0634088	+	0.0366091i
$511$	−18.2813	−	40.2726i	−0.808716	−	1.78155i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	0.676658	+	2.52532i	0.0298752	+	0.111496i
$514$	3.53864	+	13.2064i	0.156083	+	0.582508i
$515$	−1.73685	−	1.73685i	−0.0765347	−	0.0765347i
$516$	−9.94138	−	5.73966i	−0.437645	−	0.252674i
$517$	−19.8799	−	34.4329i	−0.874315	−	1.51436i
$518$	11.8801	+	14.4553i	0.521981	+	0.635128i
$519$			10.2106i			0.448195i
$520$	−4.36833	+	3.52881i	−0.191564	+	0.154749i
$521$		−	41.7595i		−	1.82952i	−0.404000	−	0.914759i	$-0.632380\pi$
$521$		−	41.7595i		−	1.82952i	0.404000	−	0.914759i	$-0.367620\pi$
$522$	4.14867	+	1.11163i	0.181582	+	0.0486548i
$523$	−12.4904	+	7.21135i	−0.546168	+	0.315330i	−0.747575	−	0.664177i	$-0.768782\pi$
$523$	−12.4904	+	7.21135i	−0.546168	+	0.315330i	0.201407	+	0.979508i	$0.435449\pi$
$524$	−2.09682	+	3.63180i	−0.0916000	+	0.158656i
$525$	6.71907	−	1.11416i	0.293244	−	0.0486259i
$526$	4.28461	+	15.9904i	0.186818	+	0.697214i
$527$	−0.250010	+	0.0669901i	−0.0108906	+	0.00291813i
$528$	2.99329	−	2.99329i	0.130266	−	0.130266i
$529$	−10.9290	+	18.9295i	−0.475173	+	0.823023i
$530$	2.56299	+	4.43923i	0.111329	+	0.192828i
$531$	−6.70667	−	1.79705i	−0.291044	−	0.0779851i
$532$	4.02510	−	5.62534i	0.174510	−	0.243889i
$533$	−8.15195	+	3.61787i	−0.353100	+	0.156708i
$534$	−5.51114			−0.238490
$535$	0.267594	−	0.998675i	0.0115691	−	0.0431765i
$536$	3.04255	+	5.26986i	0.131418	+	0.227623i
$537$	13.3647	−	23.1484i	0.576731	−	0.998927i
$538$	0.00960316	+	0.00960316i	0.000414021	+	0.000414021i
$539$	−24.6151	+	16.4972i	−1.06025	+	0.710584i
$540$	1.50441	−	0.403106i	0.0647396	−	0.0173469i
$541$	6.74610	+	6.74610i	0.290038	+	0.290038i	0.837095	−	0.547058i	$-0.184252\pi$
$541$	6.74610	+	6.74610i	0.290038	+	0.290038i	−0.547058	+	0.837095i	$0.684252\pi$
$542$	8.35824	+	4.82563i	0.359017	+	0.207279i
$543$	5.03207	−	2.90527i	0.215947	−	0.124677i
$544$	−1.02547	−	0.274775i	−0.0439668	−	0.0117809i
$545$	16.3502			0.700367
$546$	−7.96879	+	5.24389i	−0.341033	+	0.224418i
$547$	−18.8470			−0.805841			−0.402921	−	0.915235i	$-0.632005\pi$
$547$	−18.8470			−0.805841			−0.402921	+	0.915235i	$0.632005\pi$
$548$	19.9165	+	5.33662i	0.850792	+	0.227969i
$549$	−3.62769	+	2.09445i	−0.154826	+	0.0893888i
$550$	−9.43723	−	5.44859i	−0.402405	−	0.232329i
$551$	−7.94005	−	7.94005i	−0.338257	−	0.338257i
$552$	−1.03226	+	0.276592i	−0.0439357	+	0.0117725i
$553$	14.7364	−	39.2369i	0.626654	−	1.66852i
$554$	8.92110	+	8.92110i	0.379021	+	0.379021i
$555$	5.50725	−	9.53884i	0.233770	−	0.404901i
$556$	−6.85609	−	11.8751i	−0.290763	−	0.503616i
$557$	−3.88409	+	14.4956i	−0.164574	+	0.614199i	0.833520	+	0.552489i	$0.186322\pi$
$557$	−3.88409	+	14.4956i	−0.164574	+	0.614199i	−0.998094	+	0.0617100i	$0.980345\pi$
$558$	0.243800			0.0103209
$559$	−6.42611	−	40.8874i	−0.271795	−	1.72935i
$560$	−3.35119	−	2.39788i	−0.141614	−	0.101329i
$561$	4.34098	+	1.16316i	0.183276	+	0.0491088i
$562$	−7.18793	−	12.4499i	−0.303204	−	0.525166i
$563$	−14.4040	+	24.9484i	−0.607056	+	1.05145i	0.384667	+	0.923055i	$0.374316\pi$
$563$	−14.4040	+	24.9484i	−0.607056	+	1.05145i	−0.991723	+	0.128396i	$0.959017\pi$
$564$	6.64147	−	6.64147i	0.279657	−	0.279657i
$565$	−21.0380	+	5.63712i	−0.885076	+	0.237155i
$566$	−5.09488	−	19.0143i	−0.214154	−	0.799232i
$567$	2.61011	−	0.432809i	0.109614	−	0.0181763i
$568$	−0.106623	+	0.184676i	−0.00447379	+	0.00774883i
$569$	−14.0069	+	8.08691i	−0.587202	+	0.339021i	−0.763990	−	0.645228i	$-0.776762\pi$
$569$	−14.0069	+	8.08691i	−0.587202	+	0.339021i	0.176789	+	0.984249i	$0.443429\pi$
$570$	−3.93315	−	1.05388i	−0.164741	−	0.0441423i
$571$			18.3342i			0.767261i	0.923487	+	0.383631i	$0.125326\pi$
$571$			18.3342i			0.767261i	−0.923487	+	0.383631i	$0.874674\pi$
$572$	15.1773	+	1.61345i	0.634596	+	0.0674615i
$573$		−	3.96507i		−	0.165643i
$574$	−4.15535	−	5.05609i	−0.173441	−	0.211037i
$575$	1.37551	+	2.38245i	0.0573627	+	0.0993552i
$576$	0.866025	+	0.500000i	0.0360844	+	0.0208333i
$577$	−12.7228	−	12.7228i	−0.529658	−	0.529658i	0.390812	−	0.920470i	$-0.372194\pi$
$577$	−12.7228	−	12.7228i	−0.529658	−	0.529658i	−0.920470	+	0.390812i	$0.872194\pi$
$578$	4.10821	+	15.3320i	0.170879	+	0.637729i
$579$	−6.46517	−	24.1284i	−0.268683	−	1.00274i
$580$	−4.73013	+	4.73013i	−0.196408	+	0.196408i
$581$	−10.9502	+	4.97072i	−0.454291	+	0.206220i
$582$	2.80737	−	1.62084i	0.116369	−	0.0671859i
$583$	3.60590	−	13.4574i	0.149341	−	0.557349i
$584$	−16.7165			−0.691733
$585$	4.53918	+	3.30616i	0.187672	+	0.136693i
$586$			23.9045i			0.987484i
$587$	9.81940	−	36.6465i	0.405290	−	1.51256i	−0.398230	−	0.917286i	$-0.630375\pi$
$587$	9.81940	−	36.6465i	0.405290	−	1.51256i	0.803520	−	0.595278i	$-0.202958\pi$
$588$	−5.26934	−	4.60804i	−0.217304	−	0.190032i
$589$	−0.551998	−	0.318696i	−0.0227447	−	0.0131316i
$590$	7.64665	−	7.64665i	0.314808	−	0.314808i
$591$	15.0491	−	4.03238i	0.619036	−	0.165870i
$592$	6.83102	−	1.83037i	0.280753	−	0.0752276i
$593$	22.4679	−	22.4679i	0.922645	−	0.922645i	−0.0745704	−	0.997216i	$-0.523759\pi$
$593$	22.4679	−	22.4679i	0.922645	−	0.922645i	0.997216	+	0.0745704i	$0.0237585\pi$
$594$	−3.66602	−	2.11658i	−0.150418	−	0.0868442i
$595$	0.425750	−	4.35398i	0.0174541	−	0.178496i
$596$	−5.71276	+	21.3203i	−0.234004	+	0.873314i
$597$			11.0520i			0.452330i
$598$	−3.11456	−	2.26853i	−0.127364	−	0.0927669i
$599$	−38.3389			−1.56648			−0.783242	−	0.621716i	$-0.786436\pi$
$599$	−38.3389			−1.56648			−0.783242	+	0.621716i	$0.786436\pi$
$600$	0.666264	−	2.48653i	0.0272001	−	0.101512i
$601$	18.4014	−	10.6241i	0.750609	−	0.433364i	−0.0753048	−	0.997161i	$-0.523993\pi$
$601$	18.4014	−	10.6241i	0.750609	−	0.433364i	0.825914	+	0.563796i	$0.190660\pi$
$602$	27.6554	−	12.5539i	1.12715	−	0.511658i
$603$	4.30282	−	4.30282i	0.175224	−	0.175224i
$604$	−1.53699	−	5.73611i	−0.0625391	−	0.233399i
$605$	−2.78932	−	10.4099i	−0.113402	−	0.423222i
$606$	−8.44434	−	8.44434i	−0.343028	−	0.343028i
$607$	28.1458	+	16.2500i	1.14240	+	0.659567i	0.947025	−	0.321160i	$-0.104073\pi$
$607$	28.1458	+	16.2500i	1.14240	+	0.659567i	0.195379	+	0.980728i	$0.437406\pi$
$608$	−1.30720	−	2.26414i	−0.0530141	−	0.0918231i
$609$	−8.77909	+	7.21511i	−0.355747	+	0.292371i
$610$		−	6.52413i		−	0.264154i
$611$	33.6753	+	3.57989i	1.36236	+	0.144827i
$612$			1.06165i			0.0429146i
$613$	−21.6309	−	5.79599i	−0.873665	−	0.234098i	−0.205993	−	0.978553i	$-0.566042\pi$
$613$	−21.6309	−	5.79599i	−0.873665	−	0.234098i	−0.667672	+	0.744456i	$0.732709\pi$
$614$	13.7266	−	7.92507i	0.553961	−	0.319830i
$615$	−1.92630	+	3.33644i	−0.0776758	+	0.134538i
$616$	1.83215	+	11.0490i	0.0738193	+	0.445177i
$617$	−9.83109	−	36.6901i	−0.395785	−	1.47709i	−0.820439	−	0.571734i	$-0.806271\pi$
$617$	−9.83109	−	36.6901i	−0.395785	−	1.47709i	0.424654	−	0.905356i	$-0.360396\pi$
$618$	−1.52334	+	0.408178i	−0.0612778	+	0.0164193i
$619$	−26.6827	+	26.6827i	−1.07247	+	1.07247i	−0.0753098	+	0.997160i	$0.523995\pi$
$619$	−26.6827	+	26.6827i	−1.07247	+	1.07247i	−0.997160	+	0.0753098i	$0.976005\pi$
$620$	−0.189857	+	0.328842i	−0.00762484	+	0.0132066i
$621$	0.534335	+	0.925495i	0.0214421	+	0.0371388i
$622$	28.7602	+	7.70629i	1.15318	+	0.308994i
$623$	8.48487	−	11.8582i	0.339939	−	0.475087i
$624$	0.559799	+	3.56183i	0.0224099	+	0.142587i
$625$	5.50201			0.220080
$626$	−8.15054	+	30.4182i	−0.325761	+	1.21576i
$627$	5.53359	+	9.58446i	0.220990	+	0.382766i
$628$	−5.06796	+	8.77796i	−0.202233	+	0.350279i
$629$	5.30893	+	5.30893i	0.211681	+	0.211681i
$630$	−1.44882	+	3.85761i	−0.0577223	+	0.153691i
$631$	−27.8117	+	7.45212i	−1.10717	+	0.296664i	−0.765679	−	0.643222i	$-0.777597\pi$
$631$	−27.8117	+	7.45212i	−1.10717	+	0.296664i	−0.341487	+	0.939887i	$0.610930\pi$
$632$	−11.2017	−	11.2017i	−0.445580	−	0.445580i
$633$	−1.81814	−	1.04970i	−0.0722646	−	0.0417220i
$634$	−10.0897	+	5.82532i	−0.400715	+	0.231353i
$635$	−9.46737	−	2.53677i	−0.375701	−	0.100669i
$636$	3.29120			0.130504
$637$	0.985522	−	25.2196i	0.0390478	−	0.999237i
$638$	18.1815			0.719811
$639$	0.205979	+	0.0551920i	0.00814842	+	0.00218336i
$640$	−1.34882	+	0.778741i	−0.0533168	+	0.0307825i
$641$	−25.3663	−	14.6453i	−1.00191	−	0.578453i	−0.0930971	−	0.995657i	$-0.529677\pi$
$641$	−25.3663	−	14.6453i	−1.00191	−	0.578453i	−0.908813	+	0.417204i	$0.863010\pi$
$642$	−0.469399	−	0.469399i	−0.0185257	−	0.0185257i
$643$	−23.8800	+	6.39861i	−0.941733	+	0.252337i	−0.696851	−	0.717216i	$-0.745416\pi$
$643$	−23.8800	+	6.39861i	−0.941733	+	0.252337i	−0.244882	+	0.969553i	$0.578749\pi$
$644$	0.994110	−	2.64691i	0.0391734	−	0.104303i
$645$	−12.6422	−	12.6422i	−0.497788	−	0.497788i
$646$	1.38779	−	2.40372i	0.0546019	−	0.0945732i
$647$	13.8976	+	24.0713i	0.546370	+	0.946341i	0.998519	+	0.0543984i	$0.0173241\pi$
$647$	13.8976	+	24.0713i	0.546370	+	0.946341i	−0.452149	+	0.891942i	$0.649343\pi$
$648$	0.258819	−	0.965926i	0.0101674	−	0.0379452i
$649$	−29.3918			−1.15373
$650$	8.48363	−	3.76508i	0.332755	−	0.147678i
$651$	−0.375351	+	0.524577i	−0.0147111	+	0.0205598i
$652$	3.81267	+	1.02160i	0.149316	+	0.0400090i
$653$	4.30708	+	7.46008i	0.168549	+	0.291935i	0.937910	−	0.346879i	$-0.112759\pi$
$653$	4.30708	+	7.46008i	0.168549	+	0.291935i	−0.769361	+	0.638814i	$0.779425\pi$
$654$	5.24893	−	9.09141i	0.205249	−	0.355502i
$655$	−4.61848	+	4.61848i	−0.180459	+	0.180459i
$656$	−2.38932	+	0.640215i	−0.0932871	+	0.0249962i
$657$	4.32654	+	16.1469i	0.168795	+	0.629950i
$658$	4.06515	+	24.5154i	0.158476	+	0.955709i
$659$	−14.6270	+	25.3347i	−0.569787	+	0.986901i	0.426799	+	0.904346i	$0.359641\pi$
$659$	−14.6270	+	25.3347i	−0.569787	+	0.986901i	−0.996587	+	0.0825544i	$0.973692\pi$
$660$	5.70976	−	3.29653i	0.222252	−	0.128317i
$661$	−9.35466	−	2.50657i	−0.363854	−	0.0974944i	0.0722599	−	0.997386i	$-0.476979\pi$
$661$	−9.35466	−	2.50657i	−0.363854	−	0.0974944i	−0.436114	+	0.899891i	$0.643646\pi$
$662$			20.4891i			0.796331i
$663$	−2.97764	+	2.40539i	−0.115642	+	0.0934177i
$664$			4.54524i			0.176390i
$665$	8.32302	−	6.84029i	0.322753	−	0.265255i
$666$	−3.53600	−	6.12453i	−0.137017	−	0.237321i
$667$	−3.97502	−	2.29498i	−0.153913	−	0.0888619i
$668$	−6.27812	−	6.27812i	−0.242908	−	0.242908i
$669$	−4.06198	−	15.1595i	−0.157045	−	0.586101i
$670$	2.45294	+	9.15451i	0.0947655	+	0.353670i
$671$	−12.5386	+	12.5386i	−0.484046	+	0.484046i
$672$	−2.40915	+	1.09361i	−0.0929351	+	0.0421868i
$673$	−34.0157	+	19.6390i	−1.31121	+	0.757027i	−0.982296	−	0.187333i	$-0.940016\pi$
$673$	−34.0157	+	19.6390i	−1.31121	+	0.757027i	−0.328913	+	0.944360i	$0.606682\pi$
$674$	1.25545	−	4.68540i	0.0483581	−	0.180475i
$675$	−2.57425			−0.0990828
$676$	−8.72164	+	9.64017i	−0.335448	+	0.370776i
$677$			34.9699i			1.34400i	0.740550	+	0.672002i	$0.234565\pi$
$677$			34.9699i			1.34400i	−0.740550	+	0.672002i	$0.765435\pi$
$678$	−3.61938	+	13.5077i	−0.139001	+	0.518760i
$679$	−0.834681	+	8.53595i	−0.0320321	+	0.327580i
$680$	−1.43197	−	0.826749i	−0.0549136	−	0.0317044i
$681$	7.49162	−	7.49162i	0.287079	−	0.287079i
$682$	0.996876	−	0.267112i	0.0381724	−	0.0102283i
$683$	25.5592	−	6.84857i	0.977996	−	0.262053i	0.265795	−	0.964029i	$-0.414365\pi$
$683$	25.5592	−	6.84857i	0.977996	−	0.262053i	0.712200	+	0.701976i	$0.247699\pi$
$684$	−1.84866	+	1.84866i	−0.0706854	+	0.0706854i
$685$	27.8115	+	16.0569i	1.06262	+	0.613505i
$686$	18.0276	−	4.24340i	0.688296	−	0.162014i
$687$	−6.49063	+	24.2234i	−0.247633	+	0.924179i
$688$		−	11.4793i		−	0.437645i
$689$	7.45691	+	9.23093i	0.284086	+	0.351670i
$690$	−1.66443			−0.0633639
$691$	−10.9410	+	40.8325i	−0.416217	+	1.55334i	0.366168	+	0.930549i	$0.380669\pi$
$691$	−10.9410	+	40.8325i	−0.416217	+	1.55334i	−0.782385	+	0.622795i	$0.785997\pi$
$692$	−8.84262	+	5.10529i	−0.336146	+	0.194074i
$693$	10.1983	−	4.62941i	0.387402	−	0.175857i
$694$	15.6699	−	15.6699i	0.594822	−	0.594822i
$695$	−5.52746	−	20.6288i	−0.209669	−	0.782494i
$696$	1.11163	+	4.14867i	0.0421363	+	0.157255i
$697$	−1.85693	−	1.85693i	−0.0703362	−	0.0703362i
$698$	−16.7051	−	9.64470i	−0.632298	−	0.365057i
$699$	4.04007	+	6.99761i	0.152810	+	0.264674i
$700$	4.32442	+	5.26181i	0.163448	+	0.198878i
$701$		−	34.8972i		−	1.31805i	−0.752121	−	0.659025i	$-0.770969\pi$
$701$		−	34.8972i		−	1.31805i	0.752121	−	0.659025i	$-0.229031\pi$
$702$	3.29558	−	1.46259i	0.124384	−	0.0552020i
$703$			18.4891i			0.697328i
$704$	4.08891	+	1.09562i	0.154107	+	0.0412927i
$705$	12.6687	−	7.31430i	0.477132	−	0.275472i
$706$	3.81541	−	6.60849i	0.143595	−	0.248714i
$707$	31.1702	−	5.16865i	1.17228	−	0.194387i
$708$	−1.79705	−	6.70667i	−0.0675371	−	0.252052i
$709$	30.9173	−	8.28427i	1.16112	−	0.311122i	0.373709	−	0.927546i	$-0.378086\pi$
$709$	30.9173	−	8.28427i	1.16112	−	0.311122i	0.787415	+	0.616424i	$0.211419\pi$
$710$	−0.234849	+	0.234849i	−0.00881371	+	0.00881371i
$711$	−7.92080	+	13.7192i	−0.297053	+	0.514511i
$712$	−2.75557	−	4.77279i	−0.103269	−	0.178868i
$713$	−0.251664	−	0.0674331i	−0.00942489	−	0.00252539i
$714$	−2.28432	−	1.63450i	−0.0854884	−	0.0611695i
$715$	22.1826	+	8.54536i	0.829581	+	0.319578i
$716$	26.7295			0.998927
$717$	−0.651840	+	2.43270i	−0.0243434	+	0.0908508i
$718$	−11.3534	−	19.6646i	−0.423705	−	0.733878i
$719$	18.6516	−	32.3055i	0.695586	−	1.20479i	−0.274397	−	0.961617i	$-0.588478\pi$
$719$	18.6516	−	32.3055i	0.695586	−	1.20479i	0.969983	−	0.243174i	$-0.0781885\pi$
$720$	1.10131	+	1.10131i	0.0410433	+	0.0410433i
$721$	1.46705	−	3.90615i	0.0546358	−	0.145473i
$722$	−11.7504	+	3.14850i	−0.437304	+	0.117175i
$723$	16.1865	+	16.1865i	0.601981	+	0.601981i
$724$	5.03207	+	2.90527i	0.187015	+	0.107973i
$725$	9.57516	−	5.52822i	0.355612	−	0.205313i
$726$	−6.68379	−	1.79092i	−0.248059	−	0.0664672i
$727$	16.1793			0.600057			0.300029	−	0.953930i	$-0.403004\pi$
$727$	16.1793			0.600057			0.300029	+	0.953930i	$0.403004\pi$
$728$	−8.52573	−	4.27923i	−0.315985	−	0.158599i
$729$	−1.00000			−0.0370370
$730$	−25.1485	−	6.73852i	−0.930787	−	0.249404i
$731$	10.5542	−	6.09350i	0.390363	−	0.225376i
$732$	−3.62769	−	2.09445i	−0.134083	−	0.0774130i
$733$	−4.64763	−	4.64763i	−0.171664	−	0.171664i	0.616046	−	0.787710i	$-0.288734\pi$
$733$	−4.64763	−	4.64763i	−0.171664	−	0.171664i	−0.787710	+	0.616046i	$0.788734\pi$
$734$	16.6236	−	4.45427i	0.613587	−	0.164410i
$735$	−6.06973	−	9.05650i	−0.223885	−	0.334054i
$736$	−0.755664	−	0.755664i	−0.0278541	−	0.0278541i
$737$	12.8796	−	22.3081i	0.474426	−	0.821729i
$738$	1.23680	+	2.14220i	0.0455273	+	0.0788556i
$739$	1.25931	−	4.69980i	0.0463243	−	0.172885i	−0.938888	−	0.344223i	$-0.888142\pi$
$739$	1.25931	−	4.69980i	0.0463243	−	0.172885i	0.985212	+	0.171338i	$0.0548091\pi$
$740$	11.0145			0.404901
$741$	−9.37356	−	0.996468i	−0.344346	−	0.0366062i
$742$	−5.06707	+	7.08156i	−0.186018	+	0.259972i
$743$	8.50421	+	2.27870i	0.311989	+	0.0835972i	0.411416	−	0.911448i	$-0.365034\pi$
$743$	8.50421	+	2.27870i	0.311989	+	0.0835972i	−0.0994270	+	0.995045i	$0.531701\pi$
$744$	0.121900	+	0.211137i	0.00446907	+	0.00774065i
$745$	−17.1887	+	29.7717i	−0.629745	+	1.09075i
$746$	3.17733	−	3.17733i	0.116330	−	0.116330i
$747$	4.39037	−	1.17640i	0.160635	−	0.0430421i
$748$	1.16316	+	4.34098i	0.0425295	+	0.158722i
$749$	1.73267	−	0.287312i	0.0633104	−	0.0104982i
$750$	5.89838	−	10.2163i	0.215378	−	0.373046i
$751$	−3.69838	+	2.13526i	−0.134956	+	0.0779167i	−0.565958	−	0.824434i	$-0.691493\pi$
$751$	−3.69838	+	2.13526i	−0.134956	+	0.0779167i	0.431002	+	0.902351i	$0.358160\pi$
$752$	9.07242	+	2.43095i	0.330837	+	0.0886476i
$753$			18.7897i			0.684733i
$754$	−9.11727	+	12.5175i	−0.332032	+	0.455862i
$755$		−	9.24905i		−	0.336607i
$756$	1.67988	+	2.04402i	0.0610966	+	0.0743402i
$757$	−16.2993	−	28.2313i	−0.592410	−	1.02608i	−0.993907	−	0.110223i	$-0.964843\pi$
$757$	−16.2993	−	28.2313i	−0.592410	−	1.02608i	0.401497	−	0.915860i	$-0.368490\pi$
$758$	30.5579	+	17.6426i	1.10991	+	0.640809i
$759$	3.19884	+	3.19884i	0.116110	+	0.116110i
$760$	−1.05388	−	3.93315i	−0.0382284	−	0.142670i
$761$	−5.50285	−	20.5369i	−0.199478	−	0.744463i	−0.991062	−	0.133402i	$-0.957410\pi$
$761$	−5.50285	−	20.5369i	−0.199478	−	0.744463i	0.791584	−	0.611061i	$-0.209257\pi$
$762$	−4.44987	+	4.44987i	−0.161202	+	0.161202i
$763$	11.4805	+	25.2909i	0.415623	+	0.915594i
$764$	3.43385	−	1.98254i	0.124232	−	0.0717256i
$765$	−0.427957	+	1.59716i	−0.0154728	+	0.0577453i
$766$	−7.76928			−0.280716
$767$	14.7388	−	20.2356i	0.532188	−	0.730666i
$768$			1.00000i			0.0360844i
$769$	−3.66217	+	13.6674i	−0.132061	+	0.492859i	−0.999993	−	0.00382487i	$-0.998783\pi$
$769$	−3.66217	+	13.6674i	−0.132061	+	0.492859i	0.867932	+	0.496684i	$0.165449\pi$
$770$	−1.69761	+	17.3608i	−0.0611777	+	0.625640i
$771$	11.8405	+	6.83613i	0.426426	+	0.246197i
$772$	17.6632	−	17.6632i	0.635712	−	0.635712i
$773$	36.3219	−	9.73243i	1.30641	−	0.350051i	0.462539	−	0.886599i	$-0.346938\pi$
$773$	36.3219	−	9.73243i	1.30641	−	0.350051i	0.843870	+	0.536548i	$0.180272\pi$
$774$	−11.0882	+	2.97107i	−0.398556	+	0.106793i
$775$	0.443781	−	0.443781i	0.0159411	−	0.0159411i
$776$	2.80737	+	1.62084i	0.100779	+	0.0581847i
$777$	18.6219	+	1.82093i	0.668058	+	0.0653255i
$778$	−2.85387	+	10.6508i	−0.102316	+	0.381850i
$779$		−	6.46700i		−	0.231704i
$780$	−0.593627	+	5.58412i	−0.0212553	+	0.199944i
$781$	0.902700			0.0323012
$782$	0.293643	−	1.09589i	0.0105007	−	0.0391890i
$783$	3.71959	−	2.14751i	0.132927	−	0.0767457i
$784$	1.35601	−	6.86740i	0.0484290	−	0.245264i
$785$	−11.1627	+	11.1627i	−0.398416	+	0.398416i
$786$	1.08539	+	4.05074i	0.0387147	+	0.144485i
$787$	0.0598510	+	0.223367i	0.00213346	+	0.00796217i	0.966984	−	0.254836i	$-0.0820214\pi$
$787$	0.0598510	+	0.223367i	0.00213346	+	0.00796217i	−0.964851	+	0.262798i	$0.915355\pi$
$788$	11.0167	+	11.0167i	0.392453	+	0.392453i
$789$	14.3366	+	8.27724i	0.510396	+	0.294677i
$790$	−12.3365	−	21.3675i	−0.438913	−	0.760220i
$791$	−23.4918	−	28.5839i	−0.835271	−	1.01633i
$792$		−	4.23315i		−	0.150418i
$793$	−2.34494	−	14.9201i	−0.0832712	−	0.529829i
$794$		−	24.4722i		−	0.868487i
$795$	4.95132	+	1.32670i	0.175605	+	0.0470532i
$796$	−9.57135	+	5.52602i	−0.339247	+	0.195865i
$797$	10.0690	−	17.4400i	0.356662	−	0.617757i	−0.630739	−	0.775995i	$-0.717248\pi$
$797$	10.0690	−	17.4400i	0.356662	−	0.617757i	0.987401	+	0.158238i	$0.0505815\pi$
$798$	−1.13154	−	6.82389i	−0.0400561	−	0.241563i
$799$	2.58081	+	9.63172i	0.0913026	+	0.340746i
$800$	2.48653	−	0.666264i	0.0879122	−	0.0235560i
$801$	−3.89697	+	3.89697i	−0.137693	+	0.137693i
$802$	9.52353	−	16.4952i	0.336288	−	0.582467i
$803$	35.3817	+	61.2829i	1.24859	+	2.16263i
$804$	5.87776	+	1.57494i	0.207293	+	0.0555439i
$805$	2.56254	−	3.58131i	0.0903176	−	0.126225i
$806$	−0.315993	+	0.820273i	−0.0111304	+	0.0288929i
$807$	0.0135809			0.000478071
$808$	3.09084	−	11.5352i	0.108735	−	0.405806i
$809$	12.8962	+	22.3368i	0.453405	+	0.785320i	0.998595	−	0.0529926i	$-0.0168760\pi$
$809$	12.8962	+	22.3368i	0.453405	+	0.785320i	−0.545190	+	0.838312i	$0.683543\pi$
$810$	0.778741	−	1.34882i	0.0273622	−	0.0473927i
$811$	9.23829	+	9.23829i	0.324400	+	0.324400i	0.850452	−	0.526052i	$-0.176328\pi$
$811$	9.23829	+	9.23829i	0.324400	+	0.324400i	−0.526052	+	0.850452i	$0.676328\pi$
$812$	−10.6380	−	3.99536i	−0.373321	−	0.140210i
$813$	9.32240	−	2.49793i	0.326951	−	0.0876062i
$814$	−21.1685	−	21.1685i	−0.741956	−	0.741956i
$815$	5.32402	+	3.07382i	0.186492	+	0.107671i
$816$	−0.919414	+	0.530824i	−0.0321859	+	0.0185826i
$817$	28.9890	+	7.76757i	1.01420	+	0.271753i
$818$	11.4516			0.400397
$819$	−1.92680	+	9.34277i	−0.0673279	+	0.326463i
$820$	−3.85259			−0.134538
$821$	44.0425	+	11.8012i	1.53709	+	0.411863i	0.925325	−	0.379174i	$-0.123792\pi$
$821$	44.0425	+	11.8012i	1.53709	+	0.411863i	0.611769	+	0.791037i	$0.290458\pi$
$822$	17.8567	−	10.3096i	0.622823	−	0.359587i
$823$	23.6104	+	13.6315i	0.823007	+	0.475163i	0.851452	−	0.524432i	$-0.175722\pi$
$823$	23.6104	+	13.6315i	0.823007	+	0.475163i	−0.0284454	+	0.999595i	$0.509056\pi$
$824$	−1.11516	−	1.11516i	−0.0388486	−	0.0388486i
$825$	−10.5259	+	2.82040i	−0.366464	+	0.0981936i
$826$	17.1972	+	6.45883i	0.598368	+	0.224731i
$827$	2.01680	+	2.01680i	0.0701309	+	0.0701309i	0.741302	−	0.671171i	$-0.234209\pi$
$827$	2.01680	+	2.01680i	0.0701309	+	0.0701309i	−0.671171	+	0.741302i	$0.734209\pi$
$828$	−0.534335	+	0.925495i	−0.0185694	+	0.0321632i
$829$	−11.5651	−	20.0313i	−0.401672	−	0.695716i	0.592256	−	0.805750i	$-0.298237\pi$
$829$	−11.5651	−	20.0313i	−0.401672	−	0.695716i	−0.993928	+	0.110034i	$0.964904\pi$
$830$	−1.83222	+	6.83792i	−0.0635972	+	0.237348i
$831$	12.6163			0.437656
$832$	−2.80474	+	2.26571i	−0.0972367	+	0.0785495i
$833$	7.03379	−	2.39865i	0.243706	−	0.0831081i
$834$	−13.2449	−	3.54897i	−0.458635	−	0.122891i
$835$	−6.91414	−	11.9756i	−0.239274	−	0.414434i
$836$	−5.53359	+	9.58446i	−0.191383	+	0.331485i
$837$	0.172393	−	0.172393i	0.00595876	−	0.00595876i
$838$	−30.0452	+	8.05058i	−1.03789	+	0.278103i
$839$	12.5075	+	46.6787i	0.431808	+	1.61153i	0.748592	+	0.663031i	$0.230730\pi$
$839$	12.5075	+	46.6787i	0.431808	+	1.61153i	−0.316785	+	0.948498i	$0.602603\pi$
$840$	−4.06520	+	0.674093i	−0.140263	+	0.0232584i
$841$	5.27641	−	9.13902i	0.181945	−	0.315139i
$842$	−22.5935	+	13.0444i	−0.778623	+	0.449538i
$843$	−13.8860	−	3.72075i	−0.478260	−	0.128149i
$844$		−	2.09941i		−	0.0722646i
$845$	−17.0070	+	10.9871i	−0.585057	+	0.377966i
$846$		−	9.39246i		−	0.322920i
$847$	14.1437	−	11.6240i	0.485984	−	0.399407i
$848$	1.64560	+	2.85026i	0.0565101	+	0.0978783i
$849$	−17.0478	−	9.84255i	−0.585079	−	0.337795i
$850$	1.93248	+	1.93248i	0.0662837	+	0.0662837i
$851$	1.95606	+	7.30011i	0.0670528	+	0.250244i
$852$	0.0551920	+	0.205979i	0.00189085	+	0.00705673i
$853$	−25.7777	+	25.7777i	−0.882612	+	0.882612i	−0.993799	−	0.111187i	$-0.964535\pi$
$853$	−25.7777	+	25.7777i	−0.882612	+	0.882612i	0.111187	+	0.993799i	$0.464535\pi$
$854$	10.0917	−	4.58101i	0.345330	−	0.156759i
$855$	−3.52636	+	2.03595i	−0.120599	+	0.0696279i
$856$	0.171812	−	0.641211i	0.00587241	−	0.0219161i
$857$	−35.1467			−1.20059			−0.600293	−	0.799780i	$-0.704950\pi$
$857$	−35.1467			−1.20059			−0.600293	+	0.799780i	$0.704950\pi$
$858$	11.8729	−	9.59111i	0.405333	−	0.327435i
$859$			49.9855i			1.70548i	0.522334	+	0.852741i	$0.325061\pi$
$859$			49.9855i			1.70548i	−0.522334	+	0.852741i	$0.674939\pi$
$860$	4.62738	−	17.2696i	0.157792	−	0.588890i
$861$	−6.51347	−	0.636915i	−0.221979	−	0.0217060i
$862$	3.03027	+	1.74953i	0.103212	+	0.0595892i
$863$	22.2466	−	22.2466i	0.757284	−	0.757284i	−0.218544	−	0.975827i	$-0.570131\pi$
$863$	22.2466	−	22.2466i	0.757284	−	0.757284i	0.975827	+	0.218544i	$0.0701306\pi$
$864$	0.965926	−	0.258819i	0.0328615	−	0.00880520i
$865$	−15.3609	+	4.11595i	−0.522287	+	0.139946i
$866$	20.0014	−	20.0014i	0.679676	−	0.679676i
$867$	13.7463	+	7.93645i	0.466850	+	0.269536i
$868$	−0.641972	−	0.0627747i	−0.0217900	−	0.00213071i
$869$	−17.3564	+	64.7749i	−0.588775	+	2.19734i
$870$			6.68941i			0.226792i
$871$	8.90003	+	20.0539i	0.301566	+	0.679501i
$872$	10.4979			0.355502
$873$	0.839007	−	3.13122i	0.0283961	−	0.105976i
$874$	2.41962	−	1.39697i	0.0818449	−	0.0472532i
$875$	12.9010	+	28.4202i	0.436134	+	0.960778i
$876$	−11.8203	+	11.8203i	−0.399372	+	0.399372i
$877$	−5.26102	−	19.6344i	−0.177652	−	0.663006i	−0.996085	−	0.0884036i	$-0.971823\pi$
$877$	−5.26102	−	19.6344i	−0.177652	−	0.663006i	0.818433	−	0.574602i	$-0.194843\pi$
$878$	1.67692	+	6.25837i	0.0565935	+	0.211210i
$879$	16.9030	+	16.9030i	0.570124	+	0.570124i
$880$	5.70976	+	3.29653i	0.192476	+	0.111126i
$881$	−15.5082	−	26.8609i	−0.522484	−	0.904968i	−0.999658	−	0.0261596i	$-0.991672\pi$
$881$	−15.5082	−	26.8609i	−0.522484	−	0.904968i	0.477174	−	0.878809i	$-0.341661\pi$
$882$	−6.98436	+	0.467607i	−0.235176	+	0.0157451i
$883$			15.7168i			0.528912i	0.964398	+	0.264456i	$0.0851924\pi$
$883$			15.7168i			0.528912i	−0.964398	+	0.264456i	$0.914808\pi$
$884$	−3.57195	−	1.37602i	−0.120138	−	0.0462805i
$885$		−	10.8140i		−	0.363508i
$886$	−30.3296	−	8.12680i	−1.01894	−	0.273025i
$887$	7.28089	−	4.20362i	0.244468	−	0.141144i	−0.372760	−	0.927928i	$-0.621589\pi$
$887$	7.28089	−	4.20362i	0.244468	−	0.141144i	0.617229	+	0.786784i	$0.288255\pi$
$888$	3.53600	−	6.12453i	0.118660	−	0.205526i
$889$	−2.72370	−	16.4256i	−0.0913499	−	0.550897i
$890$	−2.22158	−	8.29103i	−0.0744674	−	0.277916i
$891$	−4.08891	+	1.09562i	−0.136984	+	0.0367047i
$892$	11.0975	−	11.0975i	0.371573	−	0.371573i
$893$	−12.2779	+	21.2659i	−0.410863	+	0.711635i
$894$	11.0362	+	19.1153i	0.369106	+	0.639310i
$895$	40.2121	+	10.7748i	1.34414	+	0.360162i
$896$	−2.15167	−	1.53958i	−0.0718822	−	0.0514339i
$897$	−3.80642	+	0.598240i	−0.127093	+	0.0199747i
$898$	25.4667			0.849835
$899$	−0.271016	+	1.01144i	−0.00903888	+	0.0337336i
$900$	−1.28712	−	2.22936i	−0.0429041	−	0.0743121i
$901$	−1.74705	+	3.02597i	−0.0582025	+	0.100810i
$902$	7.40421	+	7.40421i	0.246533	+	0.246533i
$903$	10.6784	−	28.4323i	0.355356	−	0.946167i
$904$	−13.5077	+	3.61938i	−0.449259	+	0.120379i
$905$	6.39918	+	6.39918i	0.212716	+	0.212716i
$906$	−5.14286	−	2.96923i	−0.170860	−	0.0986461i
$907$	−19.9604	+	11.5241i	−0.662773	+	0.382652i	−0.793333	−	0.608788i	$-0.791656\pi$
$907$	−19.9604	+	11.5241i	−0.662773	+	0.382652i	0.130560	+	0.991440i	$0.458323\pi$
$908$	10.2337	+	2.74212i	0.339619	+	0.0910005i
$909$	−11.9421			−0.396094
$910$	−11.1012	−	9.87451i	−0.368002	−	0.327337i
$911$	41.6382			1.37954			0.689768	−	0.724031i	$-0.257713\pi$
$911$	41.6382			1.37954			0.689768	+	0.724031i	$0.257713\pi$
$912$	−2.52532	−	0.676658i	−0.0836218	−	0.0224064i
$913$	16.6629	−	9.62036i	0.551463	−	0.318387i
$914$	−0.304777	−	0.175963i	−0.0100811	−	0.00582034i
$915$	−4.61326	−	4.61326i	−0.152510	−	0.152510i
$916$	−24.2234	+	6.49063i	−0.800362	+	0.214456i
$917$	−10.3869	−	3.90105i	−0.343006	−	0.128824i
$918$	0.750699	+	0.750699i	0.0247767	+	0.0247767i
$919$	24.2181	−	41.9469i	0.798880	−	1.38370i	−0.121465	−	0.992596i	$-0.538759\pi$
$919$	24.2181	−	41.9469i	0.798880	−	1.38370i	0.920346	−	0.391106i	$-0.127907\pi$
$920$	−0.832217	−	1.44144i	−0.0274374	−	0.0475230i
$921$	4.10232	−	15.3101i	0.135176	−	0.504483i
$922$	20.0230			0.659423
$923$	−0.452668	+	0.621489i	−0.0148998	+	0.0204566i
$924$	9.10834	+	6.51729i	0.299642	+	0.214403i
$925$	−17.5847	−	4.71182i	−0.578183	−	0.154924i
$926$	1.98084	+	3.43092i	0.0650946	+	0.112747i
$927$	−0.788540	+	1.36579i	−0.0258990	+	0.0448585i
$928$	−3.03704	+	3.03704i	−0.0996956	+	0.0996956i
$929$	−42.4511	+	11.3747i	−1.39277	+	0.373193i	−0.875745	−	0.482775i	$-0.839629\pi$
$929$	−42.4511	+	11.3747i	−1.39277	+	0.373193i	−0.517030	+	0.855967i	$0.672962\pi$
$930$	0.0982773	+	0.366776i	0.00322264	+	0.0120270i
$931$	16.4249	+	8.07125i	0.538303	+	0.264525i
$932$	−4.04007	+	6.99761i	−0.132337	+	0.229214i
$933$	25.7857	−	14.8874i	0.844187	−	0.487392i
$934$	4.11554	+	1.10276i	0.134665	+	0.0360833i
$935$			6.99951i			0.228908i
$936$	2.91443	+	2.12276i	0.0952612	+	0.0693844i
$937$			7.41621i			0.242277i	0.992636	+	0.121139i	$0.0386545\pi$
$937$			7.41621i			0.242277i	−0.992636	+	0.121139i	$0.961345\pi$
$938$	−12.4381	+	10.2222i	−0.406117	+	0.333768i
$939$	15.7456	+	27.2722i	0.513839	+	0.889996i
$940$	12.6687	+	7.31430i	0.413209	+	0.238566i
$941$	41.6904	+	41.6904i	1.35907	+	1.35907i	0.875069	+	0.483999i	$0.160816\pi$
$941$	41.6904	+	41.6904i	1.35907	+	1.35907i	0.483999	+	0.875069i	$0.339184\pi$
$942$	2.62337	+	9.79054i	0.0854739	+	0.318993i
$943$	−0.684179	−	2.55339i	−0.0222799	−	0.0831498i
$944$	4.90962	−	4.90962i	0.159795	−	0.159795i
$945$	1.70328	+	3.75222i	0.0554076	+	0.122060i
$946$	−42.0834	+	24.2968i	−1.36825	+	0.789959i
$947$	−2.86872	+	10.7062i	−0.0932208	+	0.347905i	−0.996744	−	0.0806351i	$-0.974305\pi$
$947$	−2.86872	+	10.7062i	−0.0932208	+	0.347905i	0.903523	+	0.428540i	$0.140972\pi$
$948$	−15.8416			−0.514511
$949$	−59.9344	−	6.37141i	−1.94555	−	0.206825i
$950$			6.73013i			0.218354i
$951$	−3.01541	+	11.2536i	−0.0977812	+	0.364925i
$952$	0.273358	−	2.79552i	0.00885958	−	0.0906034i
$953$	10.0879	+	5.82426i	0.326779	+	0.188666i	0.654410	−	0.756140i	$-0.272917\pi$
$953$	10.0879	+	5.82426i	0.326779	+	0.188666i	−0.327631	+	0.944806i	$0.606250\pi$
$954$	2.32723	−	2.32723i	0.0753467	−	0.0753467i
$955$	5.96510	−	1.59834i	0.193026	−	0.0517212i
$956$	−2.43270	+	0.651840i	−0.0786791	+	0.0210820i
$957$	12.8562	−	12.8562i	0.415583	−	0.415583i
$958$	−33.3420	−	19.2500i	−1.07723	−	0.621940i
$959$	−5.30910	+	54.2941i	−0.171440	+	1.75325i
$960$	−0.403106	+	1.50441i	−0.0130102	+	0.0485547i
$961$		−	30.9406i		−	0.998083i
$962$	25.1892	−	3.95889i	0.812133	−	0.127640i
$963$	−0.663830			−0.0213916
$964$	−5.92466	+	22.1111i	−0.190820	+	0.712152i
$965$	33.6929	−	19.4526i	1.08461	−	0.626201i
$966$	−1.16871	−	2.57459i	−0.0376025	−	0.0828361i
$967$	17.9382	−	17.9382i	0.576853	−	0.576853i	−0.357182	−	0.934035i	$-0.616262\pi$
$967$	17.9382	−	17.9382i	0.576853	−	0.576853i	0.934035	+	0.357182i	$0.116262\pi$
$968$	−1.79092	−	6.68379i	−0.0575623	−	0.214825i
$969$	−0.718373	−	2.68100i	−0.0230775	−	0.0861263i
$970$	3.57008	+	3.57008i	0.114628	+	0.114628i
$971$	−41.0891	−	23.7228i	−1.31861	−	0.761300i	−0.335105	−	0.942181i	$-0.608772\pi$
$971$	−41.0891	−	23.7228i	−1.31861	−	0.761300i	−0.983505	+	0.180880i	$0.942105\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	28.0279	−	23.0348i	0.898534	−	0.738462i
$974$			10.6061i			0.339840i
$975$	3.33652	−	8.66114i	0.106854	−	0.277379i
$976$		−	4.18889i		−	0.134083i
$977$	−39.9150	−	10.6952i	−1.27699	−	0.342169i	−0.444287	−	0.895884i	$-0.646543\pi$
$977$	−39.9150	−	10.6952i	−1.27699	−	0.342169i	−0.832706	+	0.553715i	$0.813210\pi$
$978$	3.41835	−	1.97358i	0.109307	−	0.0631083i
$979$	−11.6647	+	20.2039i	−0.372807	+	0.645721i
$980$	4.80830	−	9.78479i	0.153595	−	0.312564i
$981$	−2.71704	−	10.1401i	−0.0867486	−	0.323750i
$982$	−0.171405	+	0.0459279i	−0.00546977	+	0.00146562i
$983$	36.9823	−	36.9823i	1.17955	−	1.17955i	0.199695	−	0.979858i	$-0.436005\pi$
$983$	36.9823	−	36.9823i	1.17955	−	1.17955i	0.979858	−	0.199695i	$-0.0639952\pi$
$984$	−1.23680	+	2.14220i	−0.0394278	+	0.0682909i
$985$	12.1327	+	21.0145i	0.386581	+	0.669578i
$986$	−4.40443	−	1.18016i	−0.140265	−	0.0375840i
$987$	20.2095	+	14.4605i	0.643275	+	0.460282i
$988$	−3.82381	−	8.61597i	−0.121652	−	0.274111i
$989$	12.2676			0.390087
$990$	1.70641	−	6.36841i	0.0542333	−	0.202401i
$991$	0.910397	+	1.57685i	0.0289197	+	0.0500904i	0.880123	−	0.474746i	$-0.157460\pi$
$991$	0.910397	+	1.57685i	0.0289197	+	0.0500904i	−0.851203	+	0.524836i	$0.824127\pi$
$992$	−0.121900	+	0.211137i	−0.00387033	+	0.00670360i
$993$	14.4880	+	14.4880i	0.459762	+	0.459762i
$994$	−0.528172	−	0.198368i	−0.0167526	−	0.00629184i
$995$	−16.6268	+	4.45515i	−0.527106	+	0.141238i
$996$	3.21397	+	3.21397i	0.101839	+	0.101839i
$997$	−17.7054	−	10.2222i	−0.560737	−	0.323741i	0.192704	−	0.981257i	$-0.438274\pi$
$997$	−17.7054	−	10.2222i	−0.560737	−	0.323741i	−0.753441	+	0.657515i	$0.771607\pi$
$998$	−21.1787	+	12.2275i	−0.670399	+	0.387055i
$999$	−6.83102	−	1.83037i	−0.216124	−	0.0579102i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bx.a.223.8	✓	40
7.6	odd	2		546.2.bx.b.223.8	yes	40
13.7	odd	12		546.2.bx.b.475.8	yes	40
91.20	even	12	inner	546.2.bx.a.475.8	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bx.a.223.8	✓	40	1.1	even	1	trivial
546.2.bx.a.475.8	yes	40	91.20	even	12	inner
546.2.bx.b.223.8	yes	40	7.6	odd	2
546.2.bx.b.475.8	yes	40	13.7	odd	12

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bx (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.10131 + 1.10131i) q^{5} +(0.965926 - 0.258819i) q^{6} +(-0.930231 + 2.47683i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(0.778741 + 1.34882i) q^{10} +(1.09562 - 4.08891i) q^{11} +1.00000 q^{12} +(2.26571 + 2.80474i) q^{13} +(-1.53958 + 2.15167i) q^{14} +(1.50441 + 0.403106i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.530824 + 0.919414i) q^{17} +(0.707107 - 0.707107i) q^{18} +(-2.52532 + 0.676658i) q^{19} +(0.403106 + 1.50441i) q^{20} +(0.432809 + 2.61011i) q^{21} +(2.11658 - 3.66602i) q^{22} +(-0.925495 + 0.534335i) q^{23} +(0.965926 + 0.258819i) q^{24} -2.57425i q^{25} +(1.46259 + 3.29558i) q^{26} -1.00000i q^{27} +(-2.04402 + 1.67988i) q^{28} +(2.14751 + 3.71959i) q^{29} +(1.34882 + 0.778741i) q^{30} +(0.172393 + 0.172393i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-1.09562 - 4.08891i) q^{33} +(-0.750699 + 0.750699i) q^{34} +(-3.75222 + 1.70328i) q^{35} +(0.866025 - 0.500000i) q^{36} +(1.83037 - 6.83102i) q^{37} -2.61441 q^{38} +(3.36453 + 1.29611i) q^{39} +1.55748i q^{40} +(-0.640215 + 2.38932i) q^{41} +(-0.257485 + 2.63319i) q^{42} +(-9.94138 - 5.73966i) q^{43} +(2.99329 - 2.99329i) q^{44} +(1.50441 - 0.403106i) q^{45} +(-1.03226 + 0.276592i) q^{46} +(6.64147 - 6.64147i) q^{47} +(0.866025 + 0.500000i) q^{48} +(-5.26934 - 4.60804i) q^{49} +(0.666264 - 2.48653i) q^{50} +1.06165i q^{51} +(0.559799 + 3.56183i) q^{52} +3.29120 q^{53} +(0.258819 - 0.965926i) q^{54} +(5.70976 - 3.29653i) q^{55} +(-2.40915 + 1.09361i) q^{56} +(-1.84866 + 1.84866i) q^{57} +(1.11163 + 4.14867i) q^{58} +(-1.79705 - 6.70667i) q^{59} +(1.10131 + 1.10131i) q^{60} +(-3.62769 - 2.09445i) q^{61} +(0.121900 + 0.211137i) q^{62} +(1.67988 + 2.04402i) q^{63} +1.00000i q^{64} +(-0.593627 + 5.58412i) q^{65} -4.23315i q^{66} +(5.87776 + 1.57494i) q^{67} +(-0.919414 + 0.530824i) q^{68} +(-0.534335 + 0.925495i) q^{69} +(-4.06520 + 0.674093i) q^{70} +(0.0551920 + 0.205979i) q^{71} +(0.965926 - 0.258819i) q^{72} +(-11.8203 + 11.8203i) q^{73} +(3.53600 - 6.12453i) q^{74} +(-1.28712 - 2.22936i) q^{75} +(-2.52532 - 0.676658i) q^{76} +(9.10834 + 6.51729i) q^{77} +(2.91443 + 2.12276i) q^{78} -15.8416 q^{79} +(-0.403106 + 1.50441i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.23680 + 2.14220i) q^{82} +(3.21397 + 3.21397i) q^{83} +(-0.930231 + 2.47683i) q^{84} +(-1.59716 + 0.427957i) q^{85} +(-8.11710 - 8.11710i) q^{86} +(3.71959 + 2.14751i) q^{87} +(3.66602 - 2.11658i) q^{88} +(-5.32335 - 1.42639i) q^{89} +1.55748 q^{90} +(-9.05448 + 3.00273i) q^{91} -1.06867 q^{92} +(0.235493 + 0.0631001i) q^{93} +(8.13411 - 4.69623i) q^{94} +(-3.52636 - 2.03595i) q^{95} +(0.707107 + 0.707107i) q^{96} +(3.13122 - 0.839007i) q^{97} +(-3.89714 - 5.81483i) q^{98} +(-2.99329 - 2.99329i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7} + 20 q^{9} + 8 q^{11} + 40 q^{12} - 8 q^{14} + 20 q^{16} + 16 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 32 q^{26} + 8 q^{28} - 8 q^{33} + 16 q^{34} - 32 q^{35} + 40 q^{37} - 16 q^{38} - 16 q^{39}+ \cdots - 8 q^{99}+O(q^{100}) \) 40 * q - 8 * q^7 + 20 * q^9 + 8 * q^11 + 40 * q^12 - 8 * q^14 + 20 * q^16 + 16 * q^17 + 16 * q^19 + 4 * q^21 + 8 * q^22 + 32 * q^26 + 8 * q^28 - 8 * q^33 + 16 * q^34 - 32 * q^35 + 40 * q^37 - 16 * q^38 - 16 * q^39 - 4 * q^41 + 12 * q^42 + 24 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 - 4 * q^49 - 16 * q^50 - 8 * q^52 + 32 * q^53 - 72 * q^55 + 12 * q^56 + 8 * q^57 - 36 * q^58 + 84 * q^59 - 48 * q^61 - 4 * q^62 - 4 * q^63 - 16 * q^65 + 12 * q^68 - 8 * q^69 + 36 * q^70 - 40 * q^71 - 48 * q^73 + 8 * q^74 + 36 * q^75 + 16 * q^76 - 24 * q^77 - 8 * q^78 - 48 * q^79 - 20 * q^81 + 36 * q^83 - 8 * q^84 + 8 * q^85 - 8 * q^86 + 12 * q^89 - 48 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 + 8 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more