LMFDB - Embedded newform 546.2.o.c.307.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(265,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("546.265");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.836829184.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 14x^{6} + 61x^{4} + 84x^{2} + 4 $ x^8 + 14x^6 + 61x^4 + 84*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.3
Root			$-0.222191i$ of defining polynomial
Character	$\chi$	$=$	546.307
Dual form			546.2.o.c.265.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} -1.00000i q^{3} +1.00000i q^{4} +(-0.864220 + 0.864220i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-1.70711 + 2.02133i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} -1.00000i q^{3} +1.00000i q^{4} +(-0.864220 + 0.864220i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-1.70711 + 2.02133i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} -1.22219 q^{10} +(-3.50062 + 3.50062i) q^{11} +1.00000 q^{12} +(-3.37930 - 1.25710i) q^{13} +(-2.63640 + 0.222191i) q^{14} +(0.864220 + 0.864220i) q^{15} -1.00000 q^{16} +0.322179 q^{17} +(-0.707107 - 0.707107i) q^{18} +(1.77219 - 1.77219i) q^{19} +(-0.864220 - 0.864220i) q^{20} +(2.02133 + 1.70711i) q^{21} -4.95063 q^{22} +2.70799i q^{23} +(0.707107 + 0.707107i) q^{24} +3.50625i q^{25} +(-1.50062 - 3.27843i) q^{26} +1.00000i q^{27} +(-2.02133 - 1.70711i) q^{28} +4.82047 q^{29} +1.22219i q^{30} +(-1.72844 + 1.72844i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(3.50062 + 3.50062i) q^{33} +(0.227815 + 0.227815i) q^{34} +(-0.271560 - 3.22219i) q^{35} -1.00000i q^{36} +(2.27843 - 2.27843i) q^{37} +2.50625 q^{38} +(-1.25710 + 3.37930i) q^{39} -1.22219i q^{40} +(-6.46483 + 6.46483i) q^{41} +(0.222191 + 2.63640i) q^{42} -0.393764i q^{43} +(-3.50062 - 3.50062i) q^{44} +(0.864220 - 0.864220i) q^{45} +(-1.91484 + 1.91484i) q^{46} +(1.41421 + 1.41421i) q^{47} +1.00000i q^{48} +(-1.17157 - 6.90126i) q^{49} +(-2.47929 + 2.47929i) q^{50} -0.322179i q^{51} +(1.25710 - 3.37930i) q^{52} -2.03142 q^{53} +(-0.707107 + 0.707107i) q^{54} -6.05062i q^{55} +(-0.222191 - 2.63640i) q^{56} +(-1.77219 - 1.77219i) q^{57} +(3.40859 + 3.40859i) q^{58} +(10.7599 + 10.7599i) q^{59} +(-0.864220 + 0.864220i) q^{60} -10.6389i q^{61} -2.44438 q^{62} +(1.70711 - 2.02133i) q^{63} -1.00000i q^{64} +(4.00687 - 1.83405i) q^{65} +4.95063i q^{66} +(5.38404 + 5.38404i) q^{67} +0.322179i q^{68} +2.70799 q^{69} +(2.08641 - 2.47046i) q^{70} +(-0.647652 - 0.647652i) q^{71} +(0.707107 - 0.707107i) q^{72} +(-6.85297 - 6.85297i) q^{73} +3.22219 q^{74} +3.50625 q^{75} +(1.77219 + 1.77219i) q^{76} +(-1.09999 - 13.0519i) q^{77} +(-3.27843 + 1.50062i) q^{78} +8.81718 q^{79} +(0.864220 - 0.864220i) q^{80} +1.00000 q^{81} -9.14265 q^{82} +(-6.09203 + 6.09203i) q^{83} +(-1.70711 + 2.02133i) q^{84} +(-0.278433 + 0.278433i) q^{85} +(0.278433 - 0.278433i) q^{86} -4.82047i q^{87} -4.95063i q^{88} +(3.68702 + 3.68702i) q^{89} +1.22219 q^{90} +(8.30985 - 4.68469i) q^{91} -2.70799 q^{92} +(1.72844 + 1.72844i) q^{93} +2.00000i q^{94} +3.06311i q^{95} +(-0.707107 + 0.707107i) q^{96} +(5.20299 - 5.20299i) q^{97} +(4.05150 - 5.70836i) q^{98} +(3.50062 - 3.50062i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{5} - 8 q^{7} - 8 q^{9}+O(q^{10}) $ 8 * q + 4 * q^5 - 8 * q^7 - 8 * q^9	$ 8 q + 4 q^{5} - 8 q^{7} - 8 q^{9} - 4 q^{10} + 8 q^{12} - 16 q^{13} - 4 q^{14} - 4 q^{15} - 8 q^{16} - 4 q^{17} + 8 q^{19} + 4 q^{20} - 12 q^{22} + 16 q^{26} + 12 q^{29} + 8 q^{31} + 8 q^{34} - 24 q^{35} - 4 q^{37} + 4 q^{38} - 4 q^{39} - 12 q^{41} - 4 q^{42} - 4 q^{45} + 24 q^{46} - 32 q^{49} - 8 q^{50} + 4 q^{52} + 40 q^{53} + 4 q^{56} - 8 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} - 8 q^{62} + 8 q^{63} - 12 q^{65} + 32 q^{67} + 28 q^{69} - 12 q^{71} - 20 q^{73} + 20 q^{74} + 12 q^{75} + 8 q^{76} - 8 q^{77} - 4 q^{78} + 24 q^{79} - 4 q^{80} + 8 q^{81} - 40 q^{82} - 44 q^{83} - 8 q^{84} + 20 q^{85} - 20 q^{86} - 16 q^{89} + 4 q^{90} - 12 q^{91} - 28 q^{92} - 8 q^{93} + 8 q^{97} + 16 q^{98}+O(q^{100}) $ 8 * q + 4 * q^5 - 8 * q^7 - 8 * q^9 - 4 * q^10 + 8 * q^12 - 16 * q^13 - 4 * q^14 - 4 * q^15 - 8 * q^16 - 4 * q^17 + 8 * q^19 + 4 * q^20 - 12 * q^22 + 16 * q^26 + 12 * q^29 + 8 * q^31 + 8 * q^34 - 24 * q^35 - 4 * q^37 + 4 * q^38 - 4 * q^39 - 12 * q^41 - 4 * q^42 - 4 * q^45 + 24 * q^46 - 32 * q^49 - 8 * q^50 + 4 * q^52 + 40 * q^53 + 4 * q^56 - 8 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 - 8 * q^62 + 8 * q^63 - 12 * q^65 + 32 * q^67 + 28 * q^69 - 12 * q^71 - 20 * q^73 + 20 * q^74 + 12 * q^75 + 8 * q^76 - 8 * q^77 - 4 * q^78 + 24 * q^79 - 4 * q^80 + 8 * q^81 - 40 * q^82 - 44 * q^83 - 8 * q^84 + 20 * q^85 - 20 * q^86 - 16 * q^89 + 4 * q^90 - 12 * q^91 - 28 * q^92 - 8 * q^93 + 8 * q^97 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$			1.00000i			0.500000i
$5$	−0.864220	+	0.864220i	−0.386491	+	0.386491i	−0.873434	−	0.486943i	$-0.838112\pi$
$5$	−0.864220	+	0.864220i	−0.386491	+	0.386491i	0.486943	+	0.873434i	$0.338112\pi$
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	−1.70711	+	2.02133i	−0.645226	+	0.763992i
$7$	−1.70711	+	2.02133i	−0.645226	+	0.763992i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.00000			−0.333333
$10$	−1.22219			−0.386491
$11$	−3.50062	+	3.50062i	−1.05548	+	1.05548i	−0.0571102	+	0.998368i	$0.518189\pi$
$11$	−3.50062	+	3.50062i	−1.05548	+	1.05548i	−0.998368	+	0.0571102i	$0.981811\pi$
$12$	1.00000			0.288675
$13$	−3.37930	−	1.25710i	−0.937250	−	0.348657i
$13$	−3.37930	−	1.25710i	−0.937250	−	0.348657i
$14$	−2.63640	+	0.222191i	−0.704609	+	0.0593831i
$15$	0.864220	+	0.864220i	0.223141	+	0.223141i
$16$	−1.00000			−0.250000
$17$	0.322179			0.0781399			0.0390699	−	0.999236i	$-0.487560\pi$
$17$	0.322179			0.0781399			0.0390699	+	0.999236i	$0.487560\pi$
$18$	−0.707107	−	0.707107i	−0.166667	−	0.166667i
$19$	1.77219	−	1.77219i	0.406567	−	0.406567i	−0.473972	−	0.880540i	$-0.657180\pi$
$19$	1.77219	−	1.77219i	0.406567	−	0.406567i	0.880540	+	0.473972i	$0.157180\pi$
$20$	−0.864220	−	0.864220i	−0.193245	−	0.193245i
$21$	2.02133	+	1.70711i	0.441091	+	0.372521i
$22$	−4.95063			−1.05548
$23$			2.70799i			0.564655i	0.959318	+	0.282328i	$0.0911065\pi$
$23$			2.70799i			0.564655i	−0.959318	+	0.282328i	$0.908894\pi$
$24$	0.707107	+	0.707107i	0.144338	+	0.144338i
$25$			3.50625i			0.701250i
$26$	−1.50062	−	3.27843i	−0.294297	−	0.642954i
$27$			1.00000i			0.192450i
$28$	−2.02133	−	1.70711i	−0.381996	−	0.322613i
$29$	4.82047			0.895140			0.447570	−	0.894249i	$-0.352290\pi$
$29$	4.82047			0.895140			0.447570	+	0.894249i	$0.352290\pi$
$30$			1.22219i			0.223141i
$31$	−1.72844	+	1.72844i	−0.310437	+	0.310437i	−0.845079	−	0.534642i	$-0.820447\pi$
$31$	−1.72844	+	1.72844i	−0.310437	+	0.310437i	0.534642	+	0.845079i	$0.320447\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	3.50062	+	3.50062i	0.609381	+	0.609381i
$34$	0.227815	+	0.227815i	0.0390699	+	0.0390699i
$35$	−0.271560	−	3.22219i	−0.0459021	−	0.544650i
$36$		−	1.00000i		−	0.166667i
$37$	2.27843	−	2.27843i	0.374572	−	0.374572i	−0.494567	−	0.869139i	$-0.664673\pi$
$37$	2.27843	−	2.27843i	0.374572	−	0.374572i	0.869139	+	0.494567i	$0.164673\pi$
$38$	2.50625			0.406567
$39$	−1.25710	+	3.37930i	−0.201297	+	0.541122i
$40$		−	1.22219i		−	0.193245i
$41$	−6.46483	+	6.46483i	−1.00964	+	1.00964i	−0.00968403	+	0.999953i	$0.503083\pi$
$41$	−6.46483	+	6.46483i	−1.00964	+	1.00964i	−0.999953	+	0.00968403i	$0.996917\pi$
$42$	0.222191	+	2.63640i	0.0342849	+	0.406806i
$43$		−	0.393764i		−	0.0600485i	−0.999549	−	0.0300242i	$-0.990442\pi$
$43$		−	0.393764i		−	0.0600485i	0.999549	−	0.0300242i	$-0.00955845\pi$
$44$	−3.50062	−	3.50062i	−0.527739	−	0.527739i
$45$	0.864220	−	0.864220i	0.128830	−	0.128830i
$46$	−1.91484	+	1.91484i	−0.282328	+	0.282328i
$47$	1.41421	+	1.41421i	0.206284	+	0.206284i	0.802686	−	0.596402i	$-0.203403\pi$
$47$	1.41421	+	1.41421i	0.206284	+	0.206284i	−0.596402	+	0.802686i	$0.703403\pi$
$48$			1.00000i			0.144338i
$49$	−1.17157	−	6.90126i	−0.167368	−	0.985895i
$50$	−2.47929	+	2.47929i	−0.350625	+	0.350625i
$51$		−	0.322179i		−	0.0451141i
$52$	1.25710	−	3.37930i	0.174328	−	0.468625i
$53$	−2.03142			−0.279037			−0.139518	−	0.990219i	$-0.544555\pi$
$53$	−2.03142			−0.279037			−0.139518	+	0.990219i	$0.544555\pi$
$54$	−0.707107	+	0.707107i	−0.0962250	+	0.0962250i
$55$		−	6.05062i		−	0.815865i
$56$	−0.222191	−	2.63640i	−0.0296916	−	0.352304i
$57$	−1.77219	−	1.77219i	−0.234732	−	0.234732i
$58$	3.40859	+	3.40859i	0.447570	+	0.447570i
$59$	10.7599	+	10.7599i	1.40081	+	1.40081i	0.797515	+	0.603300i	$0.206148\pi$
$59$	10.7599	+	10.7599i	1.40081	+	1.40081i	0.603300	+	0.797515i	$0.293852\pi$
$60$	−0.864220	+	0.864220i	−0.111570	+	0.111570i
$61$		−	10.6389i		−	1.36217i	−0.732203	−	0.681086i	$-0.761508\pi$
$61$		−	10.6389i		−	1.36217i	0.732203	−	0.681086i	$-0.238492\pi$
$62$	−2.44438			−0.310437
$63$	1.70711	−	2.02133i	0.215075	−	0.254664i
$64$		−	1.00000i		−	0.125000i
$65$	4.00687	−	1.83405i	0.496991	−	0.227486i
$66$			4.95063i			0.609381i
$67$	5.38404	+	5.38404i	0.657766	+	0.657766i	0.954851	−	0.297085i	$-0.0960146\pi$
$67$	5.38404	+	5.38404i	0.657766	+	0.657766i	−0.297085	+	0.954851i	$0.596015\pi$
$68$			0.322179i			0.0390699i
$69$	2.70799			0.326004
$70$	2.08641	−	2.47046i	0.249374	−	0.295276i
$71$	−0.647652	−	0.647652i	−0.0768621	−	0.0768621i	0.667631	−	0.744493i	$-0.267309\pi$
$71$	−0.647652	−	0.647652i	−0.0768621	−	0.0768621i	−0.744493	+	0.667631i	$0.767309\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	−6.85297	−	6.85297i	−0.802080	−	0.802080i	0.181341	−	0.983420i	$-0.441956\pi$
$73$	−6.85297	−	6.85297i	−0.802080	−	0.802080i	−0.983420	+	0.181341i	$0.941956\pi$
$74$	3.22219			0.374572
$75$	3.50625			0.404867
$76$	1.77219	+	1.77219i	0.203284	+	0.203284i
$77$	−1.09999	−	13.0519i	−0.125355	−	1.48740i
$78$	−3.27843	+	1.50062i	−0.371209	+	0.169912i
$79$	8.81718			0.992010			0.496005	−	0.868320i	$-0.334800\pi$
$79$	8.81718			0.992010			0.496005	+	0.868320i	$0.334800\pi$
$80$	0.864220	−	0.864220i	0.0966227	−	0.0966227i
$81$	1.00000			0.111111
$82$	−9.14265			−1.00964
$83$	−6.09203	+	6.09203i	−0.668688	+	0.668688i	−0.957412	−	0.288725i	$-0.906769\pi$
$83$	−6.09203	+	6.09203i	−0.668688	+	0.668688i	0.288725	+	0.957412i	$0.406769\pi$
$84$	−1.70711	+	2.02133i	−0.186261	+	0.220545i
$85$	−0.278433	+	0.278433i	−0.0302003	+	0.0302003i
$86$	0.278433	−	0.278433i	0.0300242	−	0.0300242i
$87$		−	4.82047i		−	0.516809i
$88$		−	4.95063i		−	0.527739i
$89$	3.68702	+	3.68702i	0.390824	+	0.390824i	0.874981	−	0.484157i	$-0.160874\pi$
$89$	3.68702	+	3.68702i	0.390824	+	0.390824i	−0.484157	+	0.874981i	$0.660874\pi$
$90$	1.22219			0.128830
$91$	8.30985	−	4.68469i	0.871109	−	0.491089i
$92$	−2.70799			−0.282328
$93$	1.72844	+	1.72844i	0.179231	+	0.179231i
$94$			2.00000i			0.206284i
$95$			3.06311i			0.314269i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$	5.20299	−	5.20299i	0.528284	−	0.528284i	−0.391777	−	0.920060i	$-0.628139\pi$
$97$	5.20299	−	5.20299i	0.528284	−	0.528284i	0.920060	+	0.391777i	$0.128139\pi$
$98$	4.05150	−	5.70836i	0.409264	−	0.576631i
$99$	3.50062	−	3.50062i	0.351826	−	0.351826i
$100$	−3.50625			−0.350625
$101$	−7.82968			−0.779082			−0.389541	−	0.921009i	$-0.627366\pi$
$101$	−7.82968			−0.779082			−0.389541	+	0.921009i	$0.627366\pi$
$102$	0.227815	−	0.227815i	0.0225570	−	0.0225570i
$103$	−14.8501			−1.46323			−0.731613	−	0.681720i	$-0.761232\pi$
$103$	−14.8501			−1.46323			−0.731613	+	0.681720i	$0.761232\pi$
$104$	3.27843	−	1.50062i	0.321477	−	0.147148i
$105$	−3.22219	+	0.271560i	−0.314454	+	0.0265016i
$106$	−1.43643	−	1.43643i	−0.139518	−	0.139518i
$107$	13.8184			1.33588			0.667939	−	0.744216i	$-0.267177\pi$
$107$	13.8184			1.33588			0.667939	+	0.744216i	$0.267177\pi$
$108$	−1.00000			−0.0962250
$109$	5.19435	+	5.19435i	0.497529	+	0.497529i	0.910668	−	0.413139i	$-0.135568\pi$
$109$	5.19435	+	5.19435i	0.497529	+	0.497529i	−0.413139	+	0.910668i	$0.635568\pi$
$110$	4.27843	−	4.27843i	0.407933	−	0.407933i
$111$	−2.27843	−	2.27843i	−0.216259	−	0.216259i
$112$	1.70711	−	2.02133i	0.161306	−	0.190998i
$113$	3.41598			0.321348			0.160674	−	0.987007i	$-0.448633\pi$
$113$	3.41598			0.321348			0.160674	+	0.987007i	$0.448633\pi$
$114$		−	2.50625i		−	0.234732i
$115$	−2.34030	−	2.34030i	−0.218234	−	0.218234i
$116$			4.82047i			0.447570i
$117$	3.37930	+	1.25710i	0.312417	+	0.116219i
$118$			15.2167i			1.40081i
$119$	−0.549994	+	0.651231i	−0.0504178	+	0.0596982i
$120$	−1.22219			−0.111570
$121$		−	13.5087i		−	1.22807i
$122$	7.52284	−	7.52284i	0.681086	−	0.681086i
$123$	6.46483	+	6.46483i	0.582914	+	0.582914i
$124$	−1.72844	−	1.72844i	−0.155218	−	0.155218i
$125$	−7.35127	−	7.35127i	−0.657517	−	0.657517i
$126$	2.63640	−	0.222191i	0.234870	−	0.0197944i
$127$		−	9.70595i		−	0.861263i	−0.902528	−	0.430632i	$-0.858291\pi$
$127$		−	9.70595i		−	0.861263i	0.902528	−	0.430632i	$-0.141709\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−0.393764			−0.0346690
$130$	4.13016	+	1.53642i	0.362239	+	0.134753i
$131$			18.3963i			1.60729i	0.595110	+	0.803644i	$0.297109\pi$
$131$			18.3963i			1.60729i	−0.595110	+	0.803644i	$0.702891\pi$
$132$	−3.50062	+	3.50062i	−0.304690	+	0.304690i
$133$	0.556867	+	6.60749i	0.0482865	+	0.572942i
$134$			7.61419i			0.657766i
$135$	−0.864220	−	0.864220i	−0.0743802	−	0.0743802i
$136$	−0.227815	+	0.227815i	−0.0195350	+	0.0195350i
$137$	−1.93705	+	1.93705i	−0.165494	+	0.165494i	−0.784995	−	0.619502i	$-0.787335\pi$
$137$	−1.93705	+	1.93705i	−0.165494	+	0.165494i	0.619502	+	0.784995i	$0.287335\pi$
$138$	1.91484	+	1.91484i	0.163002	+	0.163002i
$139$		−	15.4569i		−	1.31104i	−0.755180	−	0.655518i	$-0.772450\pi$
$139$		−	15.4569i		−	1.31104i	0.755180	−	0.655518i	$-0.227550\pi$
$140$	3.22219	−	0.271560i	0.272325	−	0.0229510i
$141$	1.41421	−	1.41421i	0.119098	−	0.119098i
$142$		−	0.915918i		−	0.0768621i
$143$	16.2303	−	7.42904i	1.35725	−	0.621247i
$144$	1.00000			0.0833333
$145$	−4.16595	+	4.16595i	−0.345963	+	0.345963i
$146$		−	9.69157i		−	0.802080i
$147$	−6.90126	+	1.17157i	−0.569206	+	0.0966297i
$148$	2.27843	+	2.27843i	0.187286	+	0.187286i
$149$	−3.16185	−	3.16185i	−0.259029	−	0.259029i	0.565630	−	0.824659i	$-0.308633\pi$
$149$	−3.16185	−	3.16185i	−0.259029	−	0.259029i	−0.824659	+	0.565630i	$0.808633\pi$
$150$	2.47929	+	2.47929i	0.202433	+	0.202433i
$151$	−15.8872	+	15.8872i	−1.29288	+	1.29288i	−0.359881	+	0.932998i	$0.617183\pi$
$151$	−15.8872	+	15.8872i	−1.29288	+	1.29288i	−0.932998	+	0.359881i	$0.882817\pi$
$152$			2.50625i			0.203284i
$153$	−0.322179			−0.0260466
$154$	8.45126	−	10.0069i	0.681022	−	0.806377i
$155$		−	2.98750i		−	0.239962i
$156$	−3.37930	−	1.25710i	−0.270561	−	0.100649i
$157$			10.9376i			0.872917i	0.899724	+	0.436458i	$0.143767\pi$
$157$			10.9376i			0.872917i	−0.899724	+	0.436458i	$0.856233\pi$
$158$	6.23469	+	6.23469i	0.496005	+	0.496005i
$159$			2.03142i			0.161102i
$160$	1.22219			0.0966227
$161$	−5.47375	−	4.62283i	−0.431392	−	0.364330i
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	−0.687541	+	0.687541i	−0.0538524	+	0.0538524i	−0.733520	−	0.679668i	$-0.762124\pi$
$163$	−0.687541	+	0.687541i	−0.0538524	+	0.0538524i	0.679668	+	0.733520i	$0.262124\pi$
$164$	−6.46483	−	6.46483i	−0.504819	−	0.504819i
$165$	−6.05062			−0.471040
$166$	−8.61544			−0.668688
$167$	11.5592	+	11.5592i	0.894477	+	0.894477i	0.994941	−	0.100463i	$-0.0320325\pi$
$167$	11.5592	+	11.5592i	0.894477	+	0.894477i	−0.100463	+	0.994941i	$0.532033\pi$
$168$	−2.63640	+	0.222191i	−0.203403	+	0.0171424i
$169$	9.83940	+	8.49625i	0.756877	+	0.653558i
$170$	−0.393764			−0.0302003
$171$	−1.77219	+	1.77219i	−0.135522	+	0.135522i
$172$	0.393764			0.0300242
$173$	10.4694			0.795972			0.397986	−	0.917392i	$-0.369709\pi$
$173$	10.4694			0.795972			0.397986	+	0.917392i	$0.369709\pi$
$174$	3.40859	−	3.40859i	0.258405	−	0.258405i
$175$	−7.08729	−	5.98554i	−0.535749	−	0.452464i
$176$	3.50062	−	3.50062i	0.263870	−	0.263870i
$177$	10.7599	−	10.7599i	0.808760	−	0.808760i
$178$			5.21424i			0.390824i
$179$			22.4990i			1.68166i	0.541302	+	0.840828i	$0.317932\pi$
$179$			22.4990i			1.68166i	−0.541302	+	0.840828i	$0.682068\pi$
$180$	0.864220	+	0.864220i	0.0644151	+	0.0644151i
$181$	24.5008			1.82113			0.910565	−	0.413366i	$-0.135647\pi$
$181$	24.5008			1.82113			0.910565	+	0.413366i	$0.135647\pi$
$182$	9.18853	+	2.56337i	0.681099	+	0.190010i
$183$	−10.6389			−0.786450
$184$	−1.91484	−	1.91484i	−0.141164	−	0.141164i
$185$			3.93813i			0.289537i
$186$			2.44438i			0.179231i
$187$	−1.12783	+	1.12783i	−0.0824749	+	0.0824749i
$188$	−1.41421	+	1.41421i	−0.103142	+	0.103142i
$189$	−2.02133	−	1.70711i	−0.147030	−	0.124174i
$190$	−2.16595	+	2.16595i	−0.157134	+	0.157134i
$191$	0.869566			0.0629196			0.0314598	−	0.999505i	$-0.489984\pi$
$191$	0.869566			0.0629196			0.0314598	+	0.999505i	$0.489984\pi$
$192$	−1.00000			−0.0721688
$193$	−6.38377	+	6.38377i	−0.459514	+	0.459514i	−0.898496	−	0.438982i	$-0.855339\pi$
$193$	−6.38377	+	6.38377i	−0.459514	+	0.459514i	0.438982	+	0.898496i	$0.355339\pi$
$194$	7.35814			0.528284
$195$	−1.83405	−	4.00687i	−0.131339	−	0.286938i
$196$	6.90126	−	1.17157i	0.492947	−	0.0836838i
$197$	−10.5087	−	10.5087i	−0.748717	−	0.748717i	0.225521	−	0.974238i	$-0.427592\pi$
$197$	−10.5087	−	10.5087i	−0.748717	−	0.748717i	−0.974238	+	0.225521i	$0.927592\pi$
$198$	4.95063			0.351826
$199$	−16.9105			−1.19875			−0.599376	−	0.800468i	$-0.704584\pi$
$199$	−16.9105			−1.19875			−0.599376	+	0.800468i	$0.704584\pi$
$200$	−2.47929	−	2.47929i	−0.175312	−	0.175312i
$201$	5.38404	−	5.38404i	0.379761	−	0.379761i
$202$	−5.53642	−	5.53642i	−0.389541	−	0.389541i
$203$	−8.22906	+	9.74378i	−0.577567	+	0.683879i
$204$	0.322179			0.0225570
$205$		−	11.1741i		−	0.780431i
$206$	−10.5006	−	10.5006i	−0.731613	−	0.731613i
$207$		−	2.70799i		−	0.188218i
$208$	3.37930	+	1.25710i	0.234313	+	0.0871642i
$209$			12.4075i			0.858245i
$210$	−2.47046	−	2.08641i	−0.170478	−	0.143976i
$211$	4.96188			0.341590			0.170795	−	0.985307i	$-0.445366\pi$
$211$	4.96188			0.341590			0.170795	+	0.985307i	$0.445366\pi$
$212$		−	2.03142i		−	0.139518i
$213$	−0.647652	+	0.647652i	−0.0443764	+	0.0443764i
$214$	9.77111	+	9.77111i	0.667939	+	0.667939i
$215$	0.340299	+	0.340299i	0.0232082	+	0.0232082i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	−0.543121	−	6.44438i	−0.0368694	−	0.437473i
$218$			7.34592i			0.497529i
$219$	−6.85297	+	6.85297i	−0.463081	+	0.463081i
$220$	6.05062			0.407933
$221$	−1.08874	−	0.405011i	−0.0732366	−	0.0272440i
$222$		−	3.22219i		−	0.216259i
$223$	−5.69799	+	5.69799i	−0.381566	+	0.381566i	−0.871666	−	0.490100i	$-0.836960\pi$
$223$	−5.69799	+	5.69799i	−0.381566	+	0.381566i	0.490100	+	0.871666i	$0.336960\pi$
$224$	2.63640	−	0.222191i	0.176152	−	0.0148458i
$225$		−	3.50625i		−	0.233750i
$226$	2.41546	+	2.41546i	0.160674	+	0.160674i
$227$	0.501705	−	0.501705i	0.0332993	−	0.0332993i	−0.690261	−	0.723560i	$-0.742504\pi$
$227$	0.501705	−	0.501705i	0.0332993	−	0.0332993i	0.723560	+	0.690261i	$0.242504\pi$
$228$	1.77219	−	1.77219i	0.117366	−	0.117366i
$229$	−12.5167	−	12.5167i	−0.827127	−	0.827127i	0.159992	−	0.987118i	$-0.448853\pi$
$229$	−12.5167	−	12.5167i	−0.827127	−	0.827127i	−0.987118	+	0.159992i	$0.948853\pi$
$230$		−	3.30968i		−	0.218234i
$231$	−13.0519	+	1.09999i	−0.858750	+	0.0723739i
$232$	−3.40859	+	3.40859i	−0.223785	+	0.223785i
$233$		−	5.52846i		−	0.362182i	−0.983466	−	0.181091i	$-0.942037\pi$
$233$		−	5.52846i		−	0.362182i	0.983466	−	0.181091i	$-0.0579628\pi$
$234$	1.50062	+	3.27843i	0.0980989	+	0.214318i
$235$	−2.44438			−0.159454
$236$	−10.7599	+	10.7599i	−0.700407	+	0.700407i
$237$		−	8.81718i		−	0.572737i
$238$	−0.849394	+	0.0715854i	−0.0550580	+	0.00464019i
$239$	10.2332	+	10.2332i	0.661928	+	0.661928i	0.955834	−	0.293906i	$-0.0949553\pi$
$239$	10.2332	+	10.2332i	0.661928	+	0.661928i	−0.293906	+	0.955834i	$0.594955\pi$
$240$	−0.864220	−	0.864220i	−0.0557851	−	0.0557851i
$241$	16.8108	+	16.8108i	1.08288	+	1.08288i	0.996240	+	0.0866358i	$0.0276117\pi$
$241$	16.8108	+	16.8108i	1.08288	+	1.08288i	0.0866358	+	0.996240i	$0.472388\pi$
$242$	9.55213	−	9.55213i	0.614034	−	0.614034i
$243$		−	1.00000i		−	0.0641500i
$244$	10.6389			0.681086
$245$	6.97670	+	4.95171i	0.445725	+	0.316353i
$246$			9.14265i			0.582914i
$247$	−8.21657	+	3.76094i	−0.522808	+	0.239303i
$248$		−	2.44438i		−	0.155218i
$249$	6.09203	+	6.09203i	0.386067	+	0.386067i
$250$		−	10.3963i		−	0.657517i
$251$	−13.3838			−0.844776			−0.422388	−	0.906415i	$-0.638808\pi$
$251$	−13.3838			−0.844776			−0.422388	+	0.906415i	$0.638808\pi$
$252$	2.02133	+	1.70711i	0.127332	+	0.107538i
$253$	−9.47966	−	9.47966i	−0.595981	−	0.595981i
$254$	6.86314	−	6.86314i	0.430632	−	0.430632i
$255$	0.278433	+	0.278433i	0.0174362	+	0.0174362i
$256$	1.00000			0.0625000
$257$	−11.3581			−0.708501			−0.354251	−	0.935150i	$-0.615264\pi$
$257$	−11.3581			−0.708501			−0.354251	+	0.935150i	$0.615264\pi$
$258$	−0.278433	−	0.278433i	−0.0173345	−	0.0173345i
$259$	0.715943	+	8.49500i	0.0444865	+	0.527854i
$260$	1.83405	+	4.00687i	0.113743	+	0.248496i
$261$	−4.82047			−0.298380
$262$	−13.0081	+	13.0081i	−0.803644	+	0.803644i
$263$	−28.4021			−1.75135			−0.875673	−	0.482905i	$-0.839582\pi$
$263$	−28.4021			−1.75135			−0.875673	+	0.482905i	$0.839582\pi$
$264$	−4.95063			−0.304690
$265$	1.75559	−	1.75559i	0.107845	−	0.107845i
$266$	−4.27843	+	5.06596i	−0.262328	+	0.310614i
$267$	3.68702	−	3.68702i	0.225642	−	0.225642i
$268$	−5.38404	+	5.38404i	−0.328883	+	0.328883i
$269$		−	22.3912i		−	1.36522i	−0.730785	−	0.682608i	$-0.760846\pi$
$269$		−	22.3912i		−	1.36522i	0.730785	−	0.682608i	$-0.239154\pi$
$270$		−	1.22219i		−	0.0743802i
$271$	1.82388	+	1.82388i	0.110793	+	0.110793i	0.760330	−	0.649537i	$-0.225037\pi$
$271$	1.82388	+	1.82388i	0.110793	+	0.110793i	−0.649537	+	0.760330i	$0.725037\pi$
$272$	−0.322179			−0.0195350
$273$	−4.68469	−	8.30985i	−0.283531	−	0.502935i
$274$	−2.73941			−0.165494
$275$	−12.2741	−	12.2741i	−0.740154	−	0.740154i
$276$			2.70799i			0.163002i
$277$		−	16.7343i		−	1.00547i	−0.864441	−	0.502735i	$-0.832327\pi$
$277$		−	16.7343i		−	1.00547i	0.864441	−	0.502735i	$-0.167673\pi$
$278$	10.9297	−	10.9297i	0.655518	−	0.655518i
$279$	1.72844	−	1.72844i	0.103479	−	0.103479i
$280$	2.47046	+	2.08641i	0.147638	+	0.124687i
$281$	−5.38706	+	5.38706i	−0.321365	+	0.321365i	−0.849291	−	0.527926i	$-0.822970\pi$
$281$	−5.38706	+	5.38706i	−0.321365	+	0.321365i	0.527926	+	0.849291i	$0.322970\pi$
$282$	2.00000			0.119098
$283$	−17.0421			−1.01305			−0.506525	−	0.862225i	$-0.669070\pi$
$283$	−17.0421			−1.01305			−0.506525	+	0.862225i	$0.669070\pi$
$284$	0.647652	−	0.647652i	0.0384311	−	0.0384311i
$285$	3.06311			0.181443
$286$	16.7297	+	6.22344i	0.989247	+	0.368000i
$287$	−2.03142	−	24.1037i	−0.119911	−	1.42280i
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$	−16.8962			−0.993894
$290$	−5.89154			−0.345963
$291$	−5.20299	−	5.20299i	−0.305005	−	0.305005i
$292$	6.85297	−	6.85297i	0.401040	−	0.401040i
$293$	−4.20174	−	4.20174i	−0.245468	−	0.245468i	0.573639	−	0.819108i	$-0.305531\pi$
$293$	−4.20174	−	4.20174i	−0.245468	−	0.245468i	−0.819108	+	0.573639i	$0.805531\pi$
$294$	−5.70836	−	4.05150i	−0.332918	−	0.236288i
$295$	−18.5978			−1.08280
$296$			3.22219i			0.187286i
$297$	−3.50062	−	3.50062i	−0.203127	−	0.203127i
$298$		−	4.47154i		−	0.259029i
$299$	3.40422	−	9.15112i	0.196871	−	0.529223i
$300$			3.50625i			0.202433i
$301$	0.795929	+	0.672198i	0.0458766	+	0.0387448i
$302$	−22.4678			−1.29288
$303$			7.82968i			0.449803i
$304$	−1.77219	+	1.77219i	−0.101642	+	0.101642i
$305$	9.19435	+	9.19435i	0.526467	+	0.526467i
$306$	−0.227815	−	0.227815i	−0.0130233	−	0.0130233i
$307$	17.0150	+	17.0150i	0.971097	+	0.971097i	0.999594	−	0.0284968i	$-0.00907204\pi$
$307$	17.0150	+	17.0150i	0.971097	+	0.971097i	−0.0284968	+	0.999594i	$0.509072\pi$
$308$	13.0519	−	1.09999i	0.743699	−	0.0626776i
$309$			14.8501i			0.844794i
$310$	2.11248	−	2.11248i	0.119981	−	0.119981i
$311$	13.7090			0.777366			0.388683	−	0.921372i	$-0.372930\pi$
$311$	13.7090			0.777366			0.388683	+	0.921372i	$0.372930\pi$
$312$	−1.50062	−	3.27843i	−0.0849561	−	0.185605i
$313$			17.4456i			0.986085i	0.870005	+	0.493043i	$0.164115\pi$
$313$			17.4456i			0.986085i	−0.870005	+	0.493043i	$0.835885\pi$
$314$	−7.73406	+	7.73406i	−0.436458	+	0.436458i
$315$	0.271560	+	3.22219i	0.0153007	+	0.181550i
$316$			8.81718i			0.496005i
$317$	−21.4771	−	21.4771i	−1.20627	−	1.20627i	−0.972226	−	0.234046i	$-0.924803\pi$
$317$	−21.4771	−	21.4771i	−1.20627	−	1.20627i	−0.234046	−	0.972226i	$-0.575197\pi$
$318$	−1.43643	+	1.43643i	−0.0805510	+	0.0805510i
$319$	−16.8747	+	16.8747i	−0.944800	+	0.944800i
$320$	0.864220	+	0.864220i	0.0483114	+	0.0483114i
$321$		−	13.8184i		−	0.771270i
$322$	−0.601692	−	7.13936i	−0.0335310	−	0.397861i
$323$	0.570961	−	0.570961i	0.0317691	−	0.0317691i
$324$			1.00000i			0.0555556i
$325$	4.40771	−	11.8487i	0.244496	−	0.657247i
$326$	−0.972330			−0.0538524
$327$	5.19435	−	5.19435i	0.287248	−	0.287248i
$328$		−	9.14265i		−	0.504819i
$329$	−5.27281	+	0.444383i	−0.290699	+	0.0244996i
$330$	−4.27843	−	4.27843i	−0.235520	−	0.235520i
$331$	−5.19998	−	5.19998i	−0.285816	−	0.285816i	0.549607	−	0.835423i	$-0.314778\pi$
$331$	−5.19998	−	5.19998i	−0.285816	−	0.285816i	−0.835423	+	0.549607i	$0.814778\pi$
$332$	−6.09203	−	6.09203i	−0.334344	−	0.334344i
$333$	−2.27843	+	2.27843i	−0.124857	+	0.124857i
$334$			16.3472i			0.894477i
$335$	−9.30600			−0.508441
$336$	−2.02133	−	1.70711i	−0.110273	−	0.0931303i
$337$		−	1.35058i		−	0.0735708i	−0.999323	−	0.0367854i	$-0.988288\pi$
$337$		−	1.35058i		−	0.0735708i	0.999323	−	0.0367854i	$-0.0117118\pi$
$338$	0.949747	+	12.9653i	0.0516595	+	0.705217i
$339$		−	3.41598i		−	0.185531i
$340$	−0.278433	−	0.278433i	−0.0151002	−	0.0151002i
$341$		−	12.1012i		−	0.655319i
$342$	−2.50625			−0.135522
$343$	15.9497	+	9.41305i	0.861205	+	0.508257i
$344$	0.278433	+	0.278433i	0.0150121	+	0.0150121i
$345$	−2.34030	+	2.34030i	−0.125997	+	0.125997i
$346$	7.40297	+	7.40297i	0.397986	+	0.397986i
$347$	21.6050			1.15982			0.579910	−	0.814681i	$-0.303088\pi$
$347$	21.6050			1.15982			0.579910	+	0.814681i	$0.303088\pi$
$348$	4.82047			0.258405
$349$	25.7255	+	25.7255i	1.37705	+	1.37705i	0.849557	+	0.527496i	$0.176869\pi$
$349$	25.7255	+	25.7255i	1.37705	+	1.37705i	0.527496	+	0.849557i	$0.323131\pi$
$350$	−0.779058	−	9.24389i	−0.0416424	−	0.494107i
$351$	1.25710	−	3.37930i	0.0670991	−	0.180374i
$352$	4.95063			0.263870
$353$	−9.77451	+	9.77451i	−0.520245	+	0.520245i	−0.917645	−	0.397400i	$-0.869912\pi$
$353$	−9.77451	+	9.77451i	−0.520245	+	0.520245i	0.397400	+	0.917645i	$0.369912\pi$
$354$	15.2167			0.808760
$355$	1.11943			0.0594130
$356$	−3.68702	+	3.68702i	−0.195412	+	0.195412i
$357$	0.651231	+	0.549994i	0.0344668	+	0.0291088i
$358$	−15.9092	+	15.9092i	−0.840828	+	0.840828i
$359$	−4.56016	+	4.56016i	−0.240676	+	0.240676i	−0.817130	−	0.576454i	$-0.804436\pi$
$359$	−4.56016	+	4.56016i	−0.240676	+	0.240676i	0.576454	+	0.817130i	$0.304436\pi$
$360$			1.22219i			0.0644151i
$361$			12.7187i			0.669406i
$362$	17.3247	+	17.3247i	0.910565	+	0.910565i
$363$	−13.5087			−0.709025
$364$	4.68469	+	8.30985i	0.245545	+	0.435555i
$365$	11.8449			0.619993
$366$	−7.52284	−	7.52284i	−0.393225	−	0.393225i
$367$			14.4983i			0.756805i	0.925641	+	0.378402i	$0.123526\pi$
$367$			14.4983i			0.756805i	−0.925641	+	0.378402i	$0.876474\pi$
$368$		−	2.70799i		−	0.141164i
$369$	6.46483	−	6.46483i	0.336546	−	0.336546i
$370$	−2.78468	+	2.78468i	−0.144769	+	0.144769i
$371$	3.46785	−	4.10617i	0.180042	−	0.213182i
$372$	−1.72844	+	1.72844i	−0.0896154	+	0.0896154i
$373$	21.2073			1.09807			0.549035	−	0.835799i	$-0.314995\pi$
$373$	21.2073			1.09807			0.549035	+	0.835799i	$0.314995\pi$
$374$	−1.59499			−0.0824749
$375$	−7.35127	+	7.35127i	−0.379618	+	0.379618i
$376$	−2.00000			−0.103142
$377$	−16.2899	−	6.05982i	−0.838970	−	0.312097i
$378$	−0.222191	−	2.63640i	−0.0114283	−	0.135602i
$379$	25.0372	+	25.0372i	1.28608	+	1.28608i	0.937151	+	0.348924i	$0.113453\pi$
$379$	25.0372	+	25.0372i	1.28608	+	1.28608i	0.348924	+	0.937151i	$0.386547\pi$
$380$	−3.06311			−0.157134
$381$	−9.70595			−0.497251
$382$	0.614876	+	0.614876i	0.0314598	+	0.0314598i
$383$	14.5420	−	14.5420i	0.743064	−	0.743064i	−0.230103	−	0.973166i	$-0.573906\pi$
$383$	14.5420	−	14.5420i	0.743064	−	0.743064i	0.973166	+	0.230103i	$0.0739062\pi$
$384$	−0.707107	−	0.707107i	−0.0360844	−	0.0360844i
$385$	12.2303	+	10.3291i	0.623315	+	0.526417i
$386$	−9.02801			−0.459514
$387$			0.393764i			0.0200162i
$388$	5.20299	+	5.20299i	0.264142	+	0.264142i
$389$			30.6758i			1.55532i	0.628683	+	0.777662i	$0.283594\pi$
$389$			30.6758i			1.55532i	−0.628683	+	0.777662i	$0.716406\pi$
$390$	1.53642	−	4.13016i	0.0777995	−	0.209139i
$391$			0.872457i			0.0441221i
$392$	5.70836	+	4.05150i	0.288316	+	0.204632i
$393$	18.3963			0.927969
$394$		−	14.8616i		−	0.748717i
$395$	−7.61998	+	7.61998i	−0.383403	+	0.383403i
$396$	3.50062	+	3.50062i	0.175913	+	0.175913i
$397$	−1.78156	−	1.78156i	−0.0894138	−	0.0894138i	0.660985	−	0.750399i	$-0.270139\pi$
$397$	−1.78156	−	1.78156i	−0.0894138	−	0.0894138i	−0.750399	+	0.660985i	$0.770139\pi$
$398$	−11.9575	−	11.9575i	−0.599376	−	0.599376i
$399$	6.60749	−	0.556867i	0.330788	−	0.0278782i
$400$		−	3.50625i		−	0.175312i
$401$	−2.02017	+	2.02017i	−0.100883	+	0.100883i	−0.755747	−	0.654864i	$-0.772726\pi$
$401$	−2.02017	+	2.02017i	−0.100883	+	0.100883i	0.654864	+	0.755747i	$0.272726\pi$
$402$	7.61419			0.379761
$403$	8.01375	−	3.66810i	0.399193	−	0.182721i
$404$		−	7.82968i		−	0.389541i
$405$	−0.864220	+	0.864220i	−0.0429434	+	0.0429434i
$406$	−12.7087	+	1.07107i	−0.630723	+	0.0531562i
$407$			15.9519i			0.790705i
$408$	0.227815	+	0.227815i	0.0112785	+	0.0112785i
$409$	11.7667	−	11.7667i	0.581827	−	0.581827i	−0.353578	−	0.935405i	$-0.615035\pi$
$409$	11.7667	−	11.7667i	0.581827	−	0.581827i	0.935405	+	0.353578i	$0.115035\pi$
$410$	7.90126	−	7.90126i	0.390216	−	0.390216i
$411$	1.93705	+	1.93705i	0.0955479	+	0.0955479i
$412$		−	14.8501i		−	0.731613i
$413$	−40.1175	+	3.38103i	−1.97405	+	0.166370i
$414$	1.91484	−	1.91484i	0.0941092	−	0.0941092i
$415$		−	10.5297i		−	0.516883i
$416$	1.50062	+	3.27843i	0.0735742	+	0.160738i
$417$	−15.4569			−0.756927
$418$	−8.77343	+	8.77343i	−0.429123	+	0.429123i
$419$			9.34287i			0.456429i	0.973611	+	0.228214i	$0.0732887\pi$
$419$			9.34287i			0.456429i	−0.973611	+	0.228214i	$0.926711\pi$
$420$	−0.271560	−	3.22219i	−0.0132508	−	0.157227i
$421$	7.32190	+	7.32190i	0.356848	+	0.356848i	0.862650	−	0.505802i	$-0.168803\pi$
$421$	7.32190	+	7.32190i	0.356848	+	0.356848i	−0.505802	+	0.862650i	$0.668803\pi$
$422$	3.50858	+	3.50858i	0.170795	+	0.170795i
$423$	−1.41421	−	1.41421i	−0.0687614	−	0.0687614i
$424$	1.43643	−	1.43643i	0.0697592	−	0.0697592i
$425$			1.12964i			0.0547955i
$426$	−0.915918			−0.0443764
$427$	21.5048	+	18.1617i	1.04069	+	0.878908i
$428$			13.8184i			0.667939i
$429$	−7.42904	−	16.2303i	−0.358677	−	0.783607i
$430$			0.481255i			0.0232082i
$431$	−26.9180	−	26.9180i	−1.29660	−	1.29660i	−0.930627	−	0.365968i	$-0.880738\pi$
$431$	−26.9180	−	26.9180i	−1.29660	−	1.29660i	−0.365968	−	0.930627i	$-0.619262\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	30.8370			1.48193			0.740965	−	0.671544i	$-0.234368\pi$
$433$	30.8370			1.48193			0.740965	+	0.671544i	$0.234368\pi$
$434$	4.17282	−	4.94091i	0.200302	−	0.237171i
$435$	4.16595	+	4.16595i	0.199742	+	0.199742i
$436$	−5.19435	+	5.19435i	−0.248764	+	0.248764i
$437$	4.79906	+	4.79906i	0.229570	+	0.229570i
$438$	−9.69157			−0.463081
$439$	−14.3229			−0.683595			−0.341798	−	0.939774i	$-0.611036\pi$
$439$	−14.3229			−0.683595			−0.341798	+	0.939774i	$0.611036\pi$
$440$	4.27843	+	4.27843i	0.203966	+	0.203966i
$441$	1.17157	+	6.90126i	0.0557892	+	0.328632i
$442$	−0.483470	−	1.05624i	−0.0229963	−	0.0502403i
$443$	21.5422			1.02350			0.511751	−	0.859134i	$-0.328997\pi$
$443$	21.5422			1.02350			0.511751	+	0.859134i	$0.328997\pi$
$444$	2.27843	−	2.27843i	0.108130	−	0.108130i
$445$	−6.37280			−0.302100
$446$	−8.05818			−0.381566
$447$	−3.16185	+	3.16185i	−0.149551	+	0.149551i
$448$	2.02133	+	1.70711i	0.0954990	+	0.0806532i
$449$	28.2383	−	28.2383i	1.33265	−	1.33265i	0.429651	−	0.902995i	$-0.358636\pi$
$449$	28.2383	−	28.2383i	1.33265	−	1.33265i	0.902995	−	0.429651i	$-0.141364\pi$
$450$	2.47929	−	2.47929i	0.116875	−	0.116875i
$451$		−	45.2619i		−	2.13130i
$452$			3.41598i			0.160674i
$453$	15.8872	+	15.8872i	0.746444	+	0.746444i
$454$	0.709517			0.0332993
$455$	−3.13293	+	11.2301i	−0.146874	+	0.526477i
$456$	2.50625			0.117366
$457$	−12.7653	−	12.7653i	−0.597136	−	0.597136i	0.342413	−	0.939549i	$-0.388756\pi$
$457$	−12.7653	−	12.7653i	−0.597136	−	0.597136i	−0.939549	+	0.342413i	$0.888756\pi$
$458$		−	17.7013i		−	0.827127i
$459$			0.322179i			0.0150380i
$460$	2.34030	−	2.34030i	0.109117	−	0.109117i
$461$	−13.3358	+	13.3358i	−0.621108	+	0.621108i	−0.945815	−	0.324707i	$-0.894734\pi$
$461$	−13.3358	+	13.3358i	−0.621108	+	0.621108i	0.324707	+	0.945815i	$0.394734\pi$
$462$	−10.0069	−	8.45126i	−0.465562	−	0.393188i
$463$	21.3712	−	21.3712i	0.993204	−	0.993204i	−0.00677317	−	0.999977i	$-0.502156\pi$
$463$	21.3712	−	21.3712i	0.993204	−	0.993204i	0.999977	+	0.00677317i	$0.00215598\pi$
$464$	−4.82047			−0.223785
$465$	−2.98750			−0.138542
$466$	3.90921	−	3.90921i	0.181091	−	0.181091i
$467$	−41.0053			−1.89750			−0.948749	−	0.316031i	$-0.897650\pi$
$467$	−41.0053			−1.89750			−0.948749	+	0.316031i	$0.897650\pi$
$468$	−1.25710	+	3.37930i	−0.0581095	+	0.156208i
$469$	−20.0741	+	1.69181i	−0.926935	+	0.0781204i
$470$	−1.72844	−	1.72844i	−0.0797270	−	0.0797270i
$471$	10.9376			0.503979
$472$	−15.2167			−0.700407
$473$	1.37842	+	1.37842i	0.0633799	+	0.0633799i
$474$	6.23469	−	6.23469i	0.286369	−	0.286369i
$475$	6.21372	+	6.21372i	0.285105	+	0.285105i
$476$	−0.651231	−	0.549994i	−0.0298491	−	0.0252089i
$477$	2.03142			0.0930123
$478$			14.4719i			0.661928i
$479$	6.94553	+	6.94553i	0.317349	+	0.317349i	0.847748	−	0.530399i	$-0.177958\pi$
$479$	6.94553	+	6.94553i	0.317349	+	0.317349i	−0.530399	+	0.847748i	$0.677958\pi$
$480$		−	1.22219i		−	0.0557851i
$481$	−10.5637	+	4.83530i	−0.481665	+	0.220471i
$482$			23.7740i			1.08288i
$483$	−4.62283	+	5.47375i	−0.210346	+	0.249064i
$484$	13.5087			0.614034
$485$			8.99306i			0.408354i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$	−23.1741	−	23.1741i	−1.05012	−	1.05012i	−0.998676	−	0.0514414i	$-0.983618\pi$
$487$	−23.1741	−	23.1741i	−1.05012	−	1.05012i	−0.0514414	−	0.998676i	$-0.516382\pi$
$488$	7.52284	+	7.52284i	0.340543	+	0.340543i
$489$	0.687541	+	0.687541i	0.0310917	+	0.0310917i
$490$	1.43189	+	8.43466i	0.0646860	+	0.381039i
$491$		−	15.6206i		−	0.704948i	−0.935822	−	0.352474i	$-0.885340\pi$
$491$		−	15.6206i		−	0.704948i	0.935822	−	0.352474i	$-0.114660\pi$
$492$	−6.46483	+	6.46483i	−0.291457	+	0.291457i
$493$	1.55306			0.0699461
$494$	−8.46938	−	3.15061i	−0.381055	−	0.141752i
$495$			6.05062i			0.271955i
$496$	1.72844	−	1.72844i	0.0776092	−	0.0776092i
$497$	2.41473	−	0.203509i	0.108315	−	0.00912863i
$498$			8.61544i			0.386067i
$499$	25.6581	+	25.6581i	1.14861	+	1.14861i	0.986825	+	0.161789i	$0.0517264\pi$
$499$	25.6581	+	25.6581i	1.14861	+	1.14861i	0.161789	+	0.986825i	$0.448274\pi$
$500$	7.35127	−	7.35127i	0.328759	−	0.328759i
$501$	11.5592	−	11.5592i	0.516427	−	0.516427i
$502$	−9.46375	−	9.46375i	−0.422388	−	0.422388i
$503$		−	31.3187i		−	1.39643i	−0.715887	−	0.698216i	$-0.753977\pi$
$503$		−	31.3187i		−	1.39643i	0.715887	−	0.698216i	$-0.246023\pi$
$504$	0.222191	+	2.63640i	0.00989719	+	0.117435i
$505$	6.76656	−	6.76656i	0.301108	−	0.301108i
$506$		−	13.4063i		−	0.595981i
$507$	8.49625	−	9.83940i	0.377332	−	0.436983i
$508$	9.70595			0.430632
$509$	20.3793	−	20.3793i	0.903296	−	0.903296i	−0.0924241	−	0.995720i	$-0.529462\pi$
$509$	20.3793	−	20.3793i	0.903296	−	0.903296i	0.995720	+	0.0924241i	$0.0294616\pi$
$510$			0.393764i			0.0174362i
$511$	25.5509	−	2.15338i	1.13031	−	0.0952600i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	1.77219	+	1.77219i	0.0782439	+	0.0782439i
$514$	−8.03142	−	8.03142i	−0.354251	−	0.354251i
$515$	12.8338	−	12.8338i	0.565524	−	0.565524i
$516$		−	0.393764i		−	0.0173345i
$517$	−9.90126			−0.435457
$518$	−5.50062	+	6.51312i	−0.241684	+	0.286170i
$519$		−	10.4694i		−	0.459555i
$520$	−1.53642	+	4.13016i	−0.0673764	+	0.181119i
$521$			33.7078i			1.47677i	0.674382	+	0.738383i	$0.264410\pi$
$521$			33.7078i			1.47677i	−0.674382	+	0.738383i	$0.735590\pi$
$522$	−3.40859	−	3.40859i	−0.149190	−	0.149190i
$523$			19.2350i			0.841086i	0.907273	+	0.420543i	$0.138160\pi$
$523$			19.2350i			0.841086i	−0.907273	+	0.420543i	$0.861840\pi$
$524$	−18.3963			−0.803644
$525$	−5.98554	+	7.08729i	−0.261230	+	0.309315i
$526$	−20.0833	−	20.0833i	−0.875673	−	0.875673i
$527$	−0.556867	+	0.556867i	−0.0242575	+	0.0242575i
$528$	−3.50062	−	3.50062i	−0.152345	−	0.152345i
$529$	15.6668			0.681165
$530$	2.48278			0.107845
$531$	−10.7599	−	10.7599i	−0.466938	−	0.466938i
$532$	−6.60749	+	0.556867i	−0.286471	+	0.0241432i
$533$	29.9736	−	13.7197i	1.29830	−	0.594266i
$534$	5.21424			0.225642
$535$	−11.9422	+	11.9422i	−0.516305	+	0.516305i
$536$	−7.61419			−0.328883
$537$	22.4990			0.970905
$538$	15.8330	−	15.8330i	0.682608	−	0.682608i
$539$	28.2600	+	20.0575i	1.21724	+	0.863937i
$540$	0.864220	−	0.864220i	0.0371901	−	0.0371901i
$541$	24.8685	−	24.8685i	1.06918	−	1.06918i	0.0717576	−	0.997422i	$-0.477139\pi$
$541$	24.8685	−	24.8685i	1.06918	−	1.06918i	0.997422	−	0.0717576i	$-0.0228608\pi$
$542$			2.57936i			0.110793i
$543$		−	24.5008i		−	1.05143i
$544$	−0.227815	−	0.227815i	−0.00976748	−	0.00976748i
$545$	−8.97812			−0.384581
$546$	2.56337	−	9.18853i	0.109702	−	0.393233i
$547$	31.2150			1.33466			0.667328	−	0.744764i	$-0.267438\pi$
$547$	31.2150			1.33466			0.667328	+	0.744764i	$0.267438\pi$
$548$	−1.93705	−	1.93705i	−0.0827469	−	0.0827469i
$549$			10.6389i			0.454057i
$550$		−	17.3581i		−	0.740154i
$551$	8.54277	−	8.54277i	0.363934	−	0.363934i
$552$	−1.91484	+	1.91484i	−0.0815009	+	0.0815009i
$553$	−15.0519	+	17.8225i	−0.640071	+	0.757888i
$554$	11.8330	−	11.8330i	0.502735	−	0.502735i
$555$	3.93813			0.167165
$556$	15.4569			0.655518
$557$	5.05010	−	5.05010i	0.213980	−	0.213980i	−0.591976	−	0.805956i	$-0.701652\pi$
$557$	5.05010	−	5.05010i	0.213980	−	0.213980i	0.805956	+	0.591976i	$0.201652\pi$
$558$	2.44438			0.103479
$559$	−0.495001	+	1.33065i	−0.0209363	+	0.0562805i
$560$	0.271560	+	3.22219i	0.0114755	+	0.136162i
$561$	1.12783	+	1.12783i	0.0476169	+	0.0476169i
$562$	−7.61845			−0.321365
$563$	33.9410			1.43044			0.715221	−	0.698899i	$-0.246326\pi$
$563$	33.9410			1.43044			0.715221	+	0.698899i	$0.246326\pi$
$564$	1.41421	+	1.41421i	0.0595491	+	0.0595491i
$565$	−2.95216	+	2.95216i	−0.124198	+	0.124198i
$566$	−12.0506	−	12.0506i	−0.506525	−	0.506525i
$567$	−1.70711	+	2.02133i	−0.0716917	+	0.0848880i
$568$	0.915918			0.0384311
$569$			1.28622i			0.0539210i	0.999636	+	0.0269605i	$0.00858283\pi$
$569$			1.28622i			0.0539210i	−0.999636	+	0.0269605i	$0.991417\pi$
$570$	2.16595	+	2.16595i	0.0907216	+	0.0907216i
$571$		−	36.5188i		−	1.52826i	−0.645060	−	0.764132i	$-0.723167\pi$
$571$		−	36.5188i		−	1.52826i	0.645060	−	0.764132i	$-0.276833\pi$
$572$	7.42904	+	16.2303i	0.310624	+	0.678624i
$573$		−	0.869566i		−	0.0363266i
$574$	15.6075	−	18.4803i	0.651444	−	0.771355i
$575$	−9.49489			−0.395964
$576$			1.00000i			0.0416667i
$577$	−9.37228	+	9.37228i	−0.390173	+	0.390173i	−0.874749	−	0.484576i	$-0.838974\pi$
$577$	−9.37228	+	9.37228i	−0.390173	+	0.390173i	0.484576	+	0.874749i	$0.338974\pi$
$578$	−11.9474	−	11.9474i	−0.496947	−	0.496947i
$579$	6.38377	+	6.38377i	0.265300	+	0.265300i
$580$	−4.16595	−	4.16595i	−0.172982	−	0.172982i
$581$	−1.91428	−	22.7138i	−0.0794176	−	0.942327i
$582$		−	7.35814i		−	0.305005i
$583$	7.11123	−	7.11123i	0.294517	−	0.294517i
$584$	9.69157			0.401040
$585$	−4.00687	+	1.83405i	−0.165664	+	0.0758287i
$586$		−	5.94216i		−	0.245468i
$587$	19.0646	−	19.0646i	0.786880	−	0.786880i	−0.194101	−	0.980982i	$-0.562179\pi$
$587$	19.0646	−	19.0646i	0.786880	−	0.786880i	0.980982	+	0.194101i	$0.0621790\pi$
$588$	−1.17157	−	6.90126i	−0.0483149	−	0.284603i
$589$			6.12623i			0.252427i
$590$	−13.1506	−	13.1506i	−0.541402	−	0.541402i
$591$	−10.5087	+	10.5087i	−0.432272	+	0.432272i
$592$	−2.27843	+	2.27843i	−0.0936430	+	0.0936430i
$593$	−25.5883	−	25.5883i	−1.05078	−	1.05078i	−0.998640	−	0.0521454i	$-0.983394\pi$
$593$	−25.5883	−	25.5883i	−1.05078	−	1.05078i	−0.0521454	−	0.998640i	$-0.516606\pi$
$594$		−	4.95063i		−	0.203127i
$595$	−0.0874910	−	1.03812i	−0.00358678	−	0.0425589i
$596$	3.16185	−	3.16185i	0.129515	−	0.129515i
$597$			16.9105i			0.692099i
$598$	8.87797	−	4.06368i	0.363047	−	0.166176i
$599$	4.67868			0.191166			0.0955828	−	0.995421i	$-0.469529\pi$
$599$	4.67868			0.191166			0.0955828	+	0.995421i	$0.469529\pi$
$600$	−2.47929	+	2.47929i	−0.101217	+	0.101217i
$601$		−	18.8059i		−	0.767110i	−0.923518	−	0.383555i	$-0.874700\pi$
$601$		−	18.8059i		−	0.767110i	0.923518	−	0.383555i	$-0.125300\pi$
$602$	0.0874910	+	1.03812i	0.00356587	+	0.0423107i
$603$	−5.38404	−	5.38404i	−0.219255	−	0.219255i
$604$	−15.8872	−	15.8872i	−0.646440	−	0.646440i
$605$	11.6745	+	11.6745i	0.474637	+	0.474637i
$606$	−5.53642	+	5.53642i	−0.224902	+	0.224902i
$607$			4.66106i			0.189187i	0.995516	+	0.0945933i	$0.0301551\pi$
$607$			4.66106i			0.189187i	−0.995516	+	0.0945933i	$0.969845\pi$
$608$	−2.50625			−0.101642
$609$	9.74378	+	8.22906i	0.394838	+	0.333459i
$610$			13.0028i			0.526467i
$611$	−3.00125	−	6.55687i	−0.121418	−	0.265262i
$612$		−	0.322179i		−	0.0130233i
$613$	31.7107	+	31.7107i	1.28078	+	1.28078i	0.940224	+	0.340558i	$0.110616\pi$
$613$	31.7107	+	31.7107i	1.28078	+	1.28078i	0.340558	+	0.940224i	$0.389384\pi$
$614$			24.0628i			0.971097i
$615$	−11.1741			−0.450582
$616$	10.0069	+	8.45126i	0.403188	+	0.340511i
$617$	−5.26417	−	5.26417i	−0.211927	−	0.211927i	0.593158	−	0.805086i	$-0.297881\pi$
$617$	−5.26417	−	5.26417i	−0.211927	−	0.211927i	−0.805086	+	0.593158i	$0.797881\pi$
$618$	−10.5006	+	10.5006i	−0.422397	+	0.422397i
$619$	−9.61527	−	9.61527i	−0.386470	−	0.386470i	0.486956	−	0.873426i	$-0.338107\pi$
$619$	−9.61527	−	9.61527i	−0.386470	−	0.386470i	−0.873426	+	0.486956i	$0.838107\pi$
$620$	2.98750			0.119981
$621$	−2.70799			−0.108668
$622$	9.69373	+	9.69373i	0.388683	+	0.388683i
$623$	−13.7468	+	1.15856i	−0.550756	+	0.0464167i
$624$	1.25710	−	3.37930i	0.0503243	−	0.135280i
$625$	−4.82502			−0.193001
$626$	−12.3359	+	12.3359i	−0.493043	+	0.493043i
$627$	12.4075			0.495508
$628$	−10.9376			−0.436458
$629$	0.734063	−	0.734063i	0.0292690	−	0.0292690i
$630$	−2.08641	+	2.47046i	−0.0831246	+	0.0984253i
$631$	−14.4462	+	14.4462i	−0.575094	+	0.575094i	−0.933548	−	0.358454i	$-0.883304\pi$
$631$	−14.4462	+	14.4462i	−0.575094	+	0.575094i	0.358454	+	0.933548i	$0.383304\pi$
$632$	−6.23469	+	6.23469i	−0.248003	+	0.248003i
$633$		−	4.96188i		−	0.197217i
$634$		−	30.3731i		−	1.20627i
$635$	8.38807	+	8.38807i	0.332870	+	0.332870i
$636$	−2.03142			−0.0805510
$637$	−4.71648	+	24.7942i	−0.186874	+	0.982384i
$638$	−23.8644			−0.944800
$639$	0.647652	+	0.647652i	0.0256207	+	0.0256207i
$640$			1.22219i			0.0483114i
$641$			4.88105i			0.192790i	0.995343	+	0.0963950i	$0.0307312\pi$
$641$			4.88105i			0.192790i	−0.995343	+	0.0963950i	$0.969269\pi$
$642$	9.77111	−	9.77111i	0.385635	−	0.385635i
$643$	−25.2403	+	25.2403i	−0.995381	+	0.995381i	−0.999989	−	0.00460867i	$-0.998533\pi$
$643$	−25.2403	+	25.2403i	−0.995381	+	0.995381i	0.00460867	+	0.999989i	$0.498533\pi$
$644$	4.62283	−	5.47375i	0.182165	−	0.215696i
$645$	0.340299	−	0.340299i	0.0133993	−	0.0133993i
$646$	0.807460			0.0317691
$647$	18.9818			0.746252			0.373126	−	0.927781i	$-0.378286\pi$
$647$	18.9818			0.746252			0.373126	+	0.927781i	$0.378286\pi$
$648$	−0.707107	+	0.707107i	−0.0277778	+	0.0277778i
$649$	−75.3325			−2.95706
$650$	11.4950	−	5.26156i	0.450871	−	0.206375i
$651$	−6.44438	+	0.543121i	−0.252575	+	0.0212866i
$652$	−0.687541	−	0.687541i	−0.0269262	−	0.0269262i
$653$	28.5652			1.11784			0.558921	−	0.829221i	$-0.311216\pi$
$653$	28.5652			1.11784			0.558921	+	0.829221i	$0.311216\pi$
$654$	7.34592			0.287248
$655$	−15.8984	−	15.8984i	−0.621202	−	0.621202i
$656$	6.46483	−	6.46483i	0.252409	−	0.252409i
$657$	6.85297	+	6.85297i	0.267360	+	0.267360i
$658$	−4.04267	−	3.41421i	−0.157600	−	0.133100i
$659$	11.6879			0.455295			0.227648	−	0.973744i	$-0.426897\pi$
$659$	11.6879			0.455295			0.227648	+	0.973744i	$0.426897\pi$
$660$		−	6.05062i		−	0.235520i
$661$	−16.7977	−	16.7977i	−0.653356	−	0.653356i	0.300443	−	0.953800i	$-0.402865\pi$
$661$	−16.7977	−	16.7977i	−0.653356	−	0.653356i	−0.953800	+	0.300443i	$0.902865\pi$
$662$		−	7.35388i		−	0.285816i
$663$	−0.405011	+	1.08874i	−0.0157293	+	0.0422832i
$664$		−	8.61544i		−	0.334344i
$665$	−6.19157	−	5.22906i	−0.240099	−	0.202774i
$666$	−3.22219			−0.124857
$667$			13.0538i			0.505445i
$668$	−11.5592	+	11.5592i	−0.447239	+	0.447239i
$669$	5.69799	+	5.69799i	0.220297	+	0.220297i
$670$	−6.58033	−	6.58033i	−0.254220	−	0.254220i
$671$	37.2428	+	37.2428i	1.43774	+	1.43774i
$672$	−0.222191	−	2.63640i	−0.00857122	−	0.101702i
$673$		−	35.7487i		−	1.37801i	−0.724756	−	0.689006i	$-0.758047\pi$
$673$		−	35.7487i		−	1.37801i	0.724756	−	0.689006i	$-0.241953\pi$
$674$	0.955005	−	0.955005i	0.0367854	−	0.0367854i
$675$	−3.50625			−0.134956
$676$	−8.49625	+	9.83940i	−0.326779	+	0.378438i
$677$		−	31.5694i		−	1.21331i	−0.794966	−	0.606655i	$-0.792511\pi$
$677$		−	31.5694i		−	1.21331i	0.794966	−	0.606655i	$-0.207489\pi$
$678$	2.41546	−	2.41546i	0.0927653	−	0.0927653i
$679$	1.63492	+	19.3990i	0.0627423	+	0.744467i
$680$		−	0.393764i		−	0.0151002i
$681$	−0.501705	−	0.501705i	−0.0192254	−	0.0192254i
$682$	8.55687	−	8.55687i	0.327659	−	0.327659i
$683$	23.7613	−	23.7613i	0.909200	−	0.909200i	−0.0870076	−	0.996208i	$-0.527730\pi$
$683$	23.7613	−	23.7613i	0.909200	−	0.909200i	0.996208	+	0.0870076i	$0.0277305\pi$
$684$	−1.77219	−	1.77219i	−0.0677612	−	0.0677612i
$685$		−	3.34808i		−	0.127924i
$686$	4.62214	+	17.9342i	0.176474	+	0.684731i
$687$	−12.5167	+	12.5167i	−0.477542	+	0.477542i
$688$			0.393764i			0.0150121i
$689$	6.86478	+	2.55370i	0.261527	+	0.0972881i
$690$	−3.30968			−0.125997
$691$	−2.90001	+	2.90001i	−0.110322	+	0.110322i	−0.760113	−	0.649791i	$-0.774856\pi$
$691$	−2.90001	+	2.90001i	−0.110322	+	0.110322i	0.649791	+	0.760113i	$0.274856\pi$
$692$			10.4694i			0.397986i
$693$	1.09999	+	13.0519i	0.0417851	+	0.495799i
$694$	15.2771	+	15.2771i	0.579910	+	0.579910i
$695$	13.3581	+	13.3581i	0.506703	+	0.506703i
$696$	3.40859	+	3.40859i	0.129202	+	0.129202i
$697$	−2.08283	+	2.08283i	−0.0788929	+	0.0788929i
$698$			36.3813i			1.37705i
$699$	−5.52846			−0.209106
$700$	5.98554	−	7.08729i	0.226232	−	0.267875i
$701$			25.6279i			0.967954i	0.875081	+	0.483977i	$0.160808\pi$
$701$			25.6279i			0.967954i	−0.875081	+	0.483977i	$0.839192\pi$
$702$	3.27843	−	1.50062i	0.123736	−	0.0566374i
$703$		−	8.07561i		−	0.304577i
$704$	3.50062	+	3.50062i	0.131935	+	0.131935i
$705$			2.44438i			0.0920608i
$706$	−13.8233			−0.520245
$707$	13.3661	−	15.8264i	0.502684	−	0.595212i
$708$	10.7599	+	10.7599i	0.404380	+	0.404380i
$709$	−31.7063	+	31.7063i	−1.19075	+	1.19075i	−0.213899	+	0.976856i	$0.568616\pi$
$709$	−31.7063	+	31.7063i	−1.19075	+	1.19075i	−0.976856	+	0.213899i	$0.931384\pi$
$710$	0.791555	+	0.791555i	0.0297065	+	0.0297065i
$711$	−8.81718			−0.330670
$712$	−5.21424			−0.195412
$713$	−4.68060	−	4.68060i	−0.175290	−	0.175290i
$714$	0.0715854	+	0.849394i	0.00267902	+	0.0317878i
$715$	−7.60624	+	20.4469i	−0.284457	+	0.764670i
$716$	−22.4990			−0.840828
$717$	10.2332	−	10.2332i	0.382164	−	0.382164i
$718$	−6.44904			−0.240676
$719$	−0.852526			−0.0317938			−0.0158969	−	0.999874i	$-0.505060\pi$
$719$	−0.852526			−0.0317938			−0.0158969	+	0.999874i	$0.505060\pi$
$720$	−0.864220	+	0.864220i	−0.0322076	+	0.0322076i
$721$	25.3508	−	30.0170i	0.944111	−	1.11789i
$722$	−8.99349	+	8.99349i	−0.334703	+	0.334703i
$723$	16.8108	−	16.8108i	0.625199	−	0.625199i
$724$			24.5008i			0.910565i
$725$			16.9018i			0.627716i
$726$	−9.55213	−	9.55213i	−0.354513	−	0.354513i
$727$	−8.14896			−0.302228			−0.151114	−	0.988516i	$-0.548286\pi$
$727$	−8.14896			−0.302228			−0.151114	+	0.988516i	$0.548286\pi$
$728$	−2.56337	+	9.18853i	−0.0950050	+	0.340550i
$729$	−1.00000			−0.0370370
$730$	8.37564	+	8.37564i	0.309997	+	0.309997i
$731$		−	0.126863i		−	0.00469218i
$732$		−	10.6389i		−	0.393225i
$733$	6.44262	−	6.44262i	0.237963	−	0.237963i	−0.578043	−	0.816006i	$-0.696183\pi$
$733$	6.44262	−	6.44262i	0.237963	−	0.237963i	0.816006	+	0.578043i	$0.196183\pi$
$734$	−10.2518	+	10.2518i	−0.378402	+	0.378402i
$735$	4.95171	−	6.97670i	0.182647	−	0.257340i
$736$	1.91484	−	1.91484i	0.0705819	−	0.0705819i
$737$	−37.6950			−1.38851
$738$	9.14265			0.336546
$739$	20.2641	−	20.2641i	0.745426	−	0.745426i	−0.228191	−	0.973616i	$-0.573281\pi$
$739$	20.2641	−	20.2641i	0.745426	−	0.745426i	0.973616	+	0.228191i	$0.0732810\pi$
$740$	−3.93813			−0.144769
$741$	3.76094	+	8.21657i	0.138162	+	0.301843i
$742$	5.35564	−	0.451364i	0.196612	−	0.0165701i
$743$	−32.6975	−	32.6975i	−1.19955	−	1.19955i	−0.974300	−	0.225254i	$-0.927679\pi$
$743$	−32.6975	−	32.6975i	−1.19955	−	1.19955i	−0.225254	−	0.974300i	$-0.572321\pi$
$744$	−2.44438			−0.0896154
$745$	5.46507			0.200225
$746$	14.9958	+	14.9958i	0.549035	+	0.549035i
$747$	6.09203	−	6.09203i	0.222896	−	0.222896i
$748$	−1.12783	−	1.12783i	−0.0412375	−	0.0412375i
$749$	−23.5895	+	27.9316i	−0.861943	+	1.02060i
$750$	−10.3963			−0.379618
$751$			39.6528i			1.44695i	0.690351	+	0.723475i	$0.257456\pi$
$751$			39.6528i			1.44695i	−0.690351	+	0.723475i	$0.742544\pi$
$752$	−1.41421	−	1.41421i	−0.0515711	−	0.0515711i
$753$			13.3838i			0.487732i
$754$	−7.23372	−	15.8036i	−0.263437	−	0.575533i
$755$		−	27.4600i		−	0.999372i
$756$	1.70711	−	2.02133i	0.0620869	−	0.0735152i
$757$	−32.1926			−1.17006			−0.585030	−	0.811012i	$-0.698917\pi$
$757$	−32.1926			−1.17006			−0.585030	+	0.811012i	$0.698917\pi$
$758$			35.4080i			1.28608i
$759$	−9.47966	+	9.47966i	−0.344090	+	0.344090i
$760$	−2.16595	−	2.16595i	−0.0785672	−	0.0785672i
$761$	22.8646	+	22.8646i	0.828842	+	0.828842i	0.987357	−	0.158514i	$-0.0506705\pi$
$761$	22.8646	+	22.8646i	0.828842	+	0.828842i	−0.158514	+	0.987357i	$0.550670\pi$
$762$	−6.86314	−	6.86314i	−0.248625	−	0.248625i
$763$	−19.3668	+	1.63220i	−0.701126	+	0.0590896i
$764$			0.869566i			0.0314598i
$765$	0.278433	−	0.278433i	0.0100668	−	0.0100668i
$766$	20.5656			0.743064
$767$	−22.8346	−	49.8871i	−0.824510	−	1.80132i
$768$		−	1.00000i		−	0.0360844i
$769$	13.5311	−	13.5311i	0.487943	−	0.487943i	−0.419714	−	0.907657i	$-0.637870\pi$
$769$	13.5311	−	13.5311i	0.487943	−	0.487943i	0.907657	+	0.419714i	$0.137870\pi$
$770$	1.34440	+	15.9519i	0.0484486	+	0.574866i
$771$			11.3581i			0.409053i
$772$	−6.38377	−	6.38377i	−0.229757	−	0.229757i
$773$	9.19917	−	9.19917i	0.330871	−	0.330871i	−0.522046	−	0.852917i	$-0.674831\pi$
$773$	9.19917	−	9.19917i	0.330871	−	0.330871i	0.852917	+	0.522046i	$0.174831\pi$
$774$	−0.278433	+	0.278433i	−0.0100081	+	0.0100081i
$775$	−6.06034	−	6.06034i	−0.217694	−	0.217694i
$776$			7.35814i			0.264142i
$777$	8.49500	−	0.715943i	0.304756	−	0.0256843i
$778$	−21.6910	+	21.6910i	−0.777662	+	0.777662i
$779$			22.9138i			0.820971i
$780$	4.00687	−	1.83405i	0.143469	−	0.0656695i
$781$	4.53437			0.162253
$782$	−0.616920	+	0.616920i	−0.0220610	+	0.0220610i
$783$			4.82047i			0.172270i
$784$	1.17157	+	6.90126i	0.0418419	+	0.246474i
$785$	−9.45251	−	9.45251i	−0.337374	−	0.337374i
$786$	13.0081	+	13.0081i	0.463984	+	0.463984i
$787$	−7.86571	−	7.86571i	−0.280382	−	0.280382i	0.552879	−	0.833261i	$-0.313529\pi$
$787$	−7.86571	−	7.86571i	−0.280382	−	0.280382i	−0.833261	+	0.552879i	$0.813529\pi$
$788$	10.5087	−	10.5087i	0.374359	−	0.374359i
$789$			28.4021i			1.01114i
$790$	−10.7763			−0.383403
$791$	−5.83144	+	6.90483i	−0.207342	+	0.245508i
$792$			4.95063i			0.175913i
$793$	−13.3742	+	35.9521i	−0.474931	+	1.27670i
$794$		−	2.51950i		−	0.0894138i
$795$	−1.75559	−	1.75559i	−0.0622644	−	0.0622644i
$796$		−	16.9105i		−	0.599376i
$797$	−15.6097			−0.552924			−0.276462	−	0.961025i	$-0.589162\pi$
$797$	−15.6097			−0.552924			−0.276462	+	0.961025i	$0.589162\pi$
$798$	5.06596	+	4.27843i	0.179333	+	0.151455i
$799$	0.455630	+	0.455630i	0.0161190	+	0.0161190i
$800$	2.47929	−	2.47929i	0.0876562	−	0.0876562i
$801$	−3.68702	−	3.68702i	−0.130275	−	0.130275i
$802$	−2.85695			−0.100883
$803$	47.9794			1.69316
$804$	5.38404	+	5.38404i	0.189881	+	0.189881i
$805$	8.72566	−	0.735383i	0.307539	−	0.0259188i
$806$	8.26031	+	3.07283i	0.290957	+	0.108236i
$807$	−22.3912			−0.788208
$808$	5.53642	−	5.53642i	0.194770	−	0.194770i
$809$	−0.500062			−0.0175813			−0.00879063	−	0.999961i	$-0.502798\pi$
$809$	−0.500062			−0.0175813			−0.00879063	+	0.999961i	$0.502798\pi$
$810$	−1.22219			−0.0429434
$811$	1.13249	−	1.13249i	0.0397670	−	0.0397670i	−0.686944	−	0.726711i	$-0.741048\pi$
$811$	1.13249	−	1.13249i	0.0397670	−	0.0397670i	0.726711	+	0.686944i	$0.241048\pi$
$812$	−9.74378	−	8.22906i	−0.341940	−	0.288784i
$813$	1.82388	−	1.82388i	0.0639664	−	0.0639664i
$814$	−11.2797	+	11.2797i	−0.395353	+	0.395353i
$815$		−	1.18837i		−	0.0416269i
$816$			0.322179i			0.0112785i
$817$	−0.697823	−	0.697823i	−0.0244137	−	0.0244137i
$818$	16.6407			0.581827
$819$	−8.30985	+	4.68469i	−0.290370	+	0.163696i
$820$	11.1741			0.390216
$821$	26.7861	+	26.7861i	0.934841	+	0.934841i	0.998003	−	0.0631619i	$-0.0201185\pi$
$821$	26.7861	+	26.7861i	0.934841	+	0.934841i	−0.0631619	+	0.998003i	$0.520118\pi$
$822$			2.73941i			0.0955479i
$823$		−	31.9038i		−	1.11210i	−0.831150	−	0.556048i	$-0.812317\pi$
$823$		−	31.9038i		−	1.11210i	0.831150	−	0.556048i	$-0.187683\pi$
$824$	10.5006	−	10.5006i	0.365807	−	0.365807i
$825$	−12.2741	+	12.2741i	−0.427328	+	0.427328i
$826$	−30.7581	−	25.9766i	−1.07021	−	0.903841i
$827$	−10.2391	+	10.2391i	−0.356047	+	0.356047i	−0.862354	−	0.506307i	$-0.831010\pi$
$827$	−10.2391	+	10.2391i	−0.356047	+	0.356047i	0.506307	+	0.862354i	$0.331010\pi$
$828$	2.70799			0.0941092
$829$	−29.3502			−1.01937			−0.509687	−	0.860360i	$-0.670239\pi$
$829$	−29.3502			−1.01937			−0.509687	+	0.860360i	$0.670239\pi$
$830$	7.44563	−	7.44563i	0.258442	−	0.258442i
$831$	−16.7343			−0.580508
$832$	−1.25710	+	3.37930i	−0.0435821	+	0.117156i
$833$	−0.377456	−	2.22344i	−0.0130781	−	0.0770377i
$834$	−10.9297	−	10.9297i	−0.378463	−	0.378463i
$835$	−19.9794			−0.691415
$836$	−12.4075			−0.429123
$837$	−1.72844	−	1.72844i	−0.0597436	−	0.0597436i
$838$	−6.60641	+	6.60641i	−0.228214	+	0.228214i
$839$	5.00302	+	5.00302i	0.172723	+	0.172723i	0.788175	−	0.615451i	$-0.211026\pi$
$839$	5.00302	+	5.00302i	0.172723	+	0.172723i	−0.615451	+	0.788175i	$0.711026\pi$
$840$	2.08641	−	2.47046i	0.0719880	−	0.0852388i
$841$	−5.76303			−0.198725
$842$			10.3547i			0.356848i
$843$	5.38706	+	5.38706i	0.185540	+	0.185540i
$844$			4.96188i			0.170795i
$845$	−15.8460	+	1.16077i	−0.545120	+	0.0399318i
$846$		−	2.00000i		−	0.0687614i
$847$	27.3057	+	23.0609i	0.938234	+	0.792381i
$848$	2.03142			0.0697592
$849$			17.0421i			0.584885i
$850$	−0.798775	+	0.798775i	−0.0273978	+	0.0273978i
$851$	6.16998	+	6.16998i	0.211504	+	0.211504i
$852$	−0.647652	−	0.647652i	−0.0221882	−	0.0221882i
$853$	−1.25690	−	1.25690i	−0.0430356	−	0.0430356i	0.685262	−	0.728297i	$-0.259688\pi$
$853$	−1.25690	−	1.25690i	−0.0430356	−	0.0430356i	−0.728297	+	0.685262i	$0.759688\pi$
$854$	2.36387	+	28.0485i	0.0808901	+	0.959799i
$855$		−	3.06311i		−	0.104756i
$856$	−9.77111	+	9.77111i	−0.333970	+	0.333970i
$857$	2.59639			0.0886910			0.0443455	−	0.999016i	$-0.485880\pi$
$857$	2.59639			0.0886910			0.0443455	+	0.999016i	$0.485880\pi$
$858$	6.22344	−	16.7297i	0.212465	−	0.571142i
$859$		−	15.8670i		−	0.541376i	−0.962667	−	0.270688i	$-0.912749\pi$
$859$		−	15.8670i		−	0.541376i	0.962667	−	0.270688i	$-0.0872512\pi$
$860$	−0.340299	+	0.340299i	−0.0116041	+	0.0116041i
$861$	−24.1037	+	2.03142i	−0.821453	+	0.0692306i
$862$		−	38.0678i		−	1.29660i
$863$	17.3932	+	17.3932i	0.592073	+	0.592073i	0.938191	−	0.346118i	$-0.112500\pi$
$863$	17.3932	+	17.3932i	0.592073	+	0.592073i	−0.346118	+	0.938191i	$0.612500\pi$
$864$	0.707107	−	0.707107i	0.0240563	−	0.0240563i
$865$	−9.04784	+	9.04784i	−0.307636	+	0.307636i
$866$	21.8050	+	21.8050i	0.740965	+	0.740965i
$867$			16.8962i			0.573825i
$868$	6.44438	−	0.543121i	0.218737	−	0.0184347i
$869$	−30.8656	+	30.8656i	−1.04705	+	1.04705i
$870$			5.89154i			0.199742i
$871$	−11.4260	−	24.9626i	−0.387157	−	0.845826i
$872$	−7.34592			−0.248764
$873$	−5.20299	+	5.20299i	−0.176095	+	0.176095i
$874$			6.78690i			0.229570i
$875$	27.4088	−	2.30996i	0.926585	−	0.0780909i
$876$	−6.85297	−	6.85297i	−0.231540	−	0.231540i
$877$	−4.65810	−	4.65810i	−0.157293	−	0.157293i	0.624073	−	0.781366i	$-0.285477\pi$
$877$	−4.65810	−	4.65810i	−0.157293	−	0.157293i	−0.781366	+	0.624073i	$0.785477\pi$
$878$	−10.1278	−	10.1278i	−0.341798	−	0.341798i
$879$	−4.20174	+	4.20174i	−0.141721	+	0.141721i
$880$			6.05062i			0.203966i
$881$	−15.3188			−0.516102			−0.258051	−	0.966131i	$-0.583080\pi$
$881$	−15.3188			−0.516102			−0.258051	+	0.966131i	$0.583080\pi$
$882$	−4.05150	+	5.70836i	−0.136421	+	0.192210i
$883$		−	41.5251i		−	1.39743i	−0.715399	−	0.698716i	$-0.753755\pi$
$883$		−	41.5251i		−	1.39743i	0.715399	−	0.698716i	$-0.246245\pi$
$884$	0.405011	−	1.08874i	0.0136220	−	0.0366183i
$885$			18.5978i			0.625157i
$886$	15.2326	+	15.2326i	0.511751	+	0.511751i
$887$			45.8470i			1.53939i	0.638410	+	0.769697i	$0.279592\pi$
$887$			45.8470i			1.53939i	−0.638410	+	0.769697i	$0.720408\pi$
$888$	3.22219			0.108130
$889$	19.6189	+	16.5691i	0.657998	+	0.555709i
$890$	−4.50625	−	4.50625i	−0.151050	−	0.151050i
$891$	−3.50062	+	3.50062i	−0.117275	+	0.117275i
$892$	−5.69799	−	5.69799i	−0.190783	−	0.190783i
$893$	5.01250			0.167737
$894$	−4.47154			−0.149551
$895$	−19.4441	−	19.4441i	−0.649945	−	0.649945i
$896$	0.222191	+	2.63640i	0.00742289	+	0.0880761i
$897$	−9.15112	−	3.40422i	−0.305547	−	0.113663i
$898$	39.9349			1.33265
$899$	−8.33190	+	8.33190i	−0.277884	+	0.277884i
$900$	3.50625			0.116875
$901$	−0.654480			−0.0218039
$902$	32.0050	−	32.0050i	1.06565	−	1.06565i
$903$	0.672198	−	0.795929i	0.0223693	−	0.0264868i
$904$	−2.41546	+	2.41546i	−0.0803371	+	0.0803371i
$905$	−21.1741	+	21.1741i	−0.703850	+	0.703850i
$906$			22.4678i			0.746444i
$907$		−	19.6544i		−	0.652612i	−0.945264	−	0.326306i	$-0.894196\pi$
$907$		−	19.6544i		−	0.652612i	0.945264	−	0.326306i	$-0.105804\pi$
$908$	0.501705	+	0.501705i	0.0166497	+	0.0166497i
$909$	7.82968			0.259694
$910$	−10.1562	+	5.72559i	−0.336676	+	0.189802i
$911$	−28.4979			−0.944177			−0.472089	−	0.881551i	$-0.656500\pi$
$911$	−28.4979			−0.944177			−0.472089	+	0.881551i	$0.656500\pi$
$912$	1.77219	+	1.77219i	0.0586829	+	0.0586829i
$913$		−	42.6519i		−	1.41157i
$914$		−	18.0529i		−	0.597136i
$915$	9.19435	−	9.19435i	0.303956	−	0.303956i
$916$	12.5167	−	12.5167i	0.413563	−	0.413563i
$917$	−37.1850	−	31.4044i	−1.22796	−	1.03706i
$918$	−0.227815	+	0.227815i	−0.00751901	+	0.00751901i
$919$	−6.44938			−0.212745			−0.106373	−	0.994326i	$-0.533924\pi$
$919$	−6.44938			−0.212745			−0.106373	+	0.994326i	$0.533924\pi$
$920$	3.30968			0.109117
$921$	17.0150	−	17.0150i	0.560663	−	0.560663i
$922$	−18.8596			−0.621108
$923$	1.37445	+	3.00278i	0.0452406	+	0.0988376i
$924$	−1.09999	−	13.0519i	−0.0361869	−	0.429375i
$925$	7.98875	+	7.98875i	0.262669	+	0.262669i
$926$	30.2234			0.993204
$927$	14.8501			0.487742
$928$	−3.40859	−	3.40859i	−0.111892	−	0.111892i
$929$	30.8995	−	30.8995i	1.01378	−	1.01378i	0.0138758	−	0.999904i	$-0.495583\pi$
$929$	30.8995	−	30.8995i	1.01378	−	1.01378i	0.999904	−	0.0138758i	$-0.00441695\pi$
$930$	−2.11248	−	2.11248i	−0.0692711	−	0.0692711i
$931$	−14.3066	−	10.1541i	−0.468878	−	0.332786i
$932$	5.52846			0.181091
$933$		−	13.7090i		−	0.448813i
$934$	−28.9951	−	28.9951i	−0.948749	−	0.948749i
$935$		−	1.94938i		−	0.0637516i
$936$	−3.27843	+	1.50062i	−0.107159	+	0.0490495i
$937$		−	50.5081i		−	1.65003i	−0.565112	−	0.825014i	$-0.691167\pi$
$937$		−	50.5081i		−	1.65003i	0.565112	−	0.825014i	$-0.308833\pi$
$938$	−15.3908	−	12.9982i	−0.502528	−	0.424407i
$939$	17.4456			0.569317
$940$		−	2.44438i		−	0.0797270i
$941$	−13.7563	+	13.7563i	−0.448443	+	0.448443i	−0.894837	−	0.446393i	$-0.852708\pi$
$941$	−13.7563	+	13.7563i	−0.448443	+	0.448443i	0.446393	+	0.894837i	$0.352708\pi$
$942$	7.73406	+	7.73406i	0.251989	+	0.251989i
$943$	−17.5067	−	17.5067i	−0.570097	−	0.570097i
$944$	−10.7599	−	10.7599i	−0.350204	−	0.350204i
$945$	3.22219	−	0.271560i	0.104818	−	0.00883386i
$946$			1.94938i			0.0633799i
$947$	−16.6588	+	16.6588i	−0.541338	+	0.541338i	−0.923921	−	0.382583i	$-0.875035\pi$
$947$	−16.6588	+	16.6588i	−0.541338	+	0.541338i	0.382583	+	0.923921i	$0.375035\pi$
$948$	8.81718			0.286369
$949$	14.5434	+	31.7732i	0.472099	+	1.03140i
$950$			8.78753i			0.285105i
$951$	−21.4771	+	21.4771i	−0.696441	+	0.696441i
$952$	−0.0715854	−	0.849394i	−0.00232010	−	0.0275290i
$953$			17.6456i			0.571597i	0.958290	+	0.285799i	$0.0922589\pi$
$953$			17.6456i			0.571597i	−0.958290	+	0.285799i	$0.907741\pi$
$954$	1.43643	+	1.43643i	0.0465061	+	0.0465061i
$955$	−0.751496	+	0.751496i	−0.0243178	+	0.0243178i
$956$	−10.2332	+	10.2332i	−0.330964	+	0.330964i
$957$	16.8747	+	16.8747i	0.545481	+	0.545481i
$958$			9.82246i			0.317349i
$959$	−0.608673	−	7.22219i	−0.0196551	−	0.233217i
$960$	0.864220	−	0.864220i	0.0278926	−	0.0278926i
$961$			25.0250i			0.807258i
$962$	−10.8888	−	4.05062i	−0.351068	−	0.130597i
$963$	−13.8184			−0.445293
$964$	−16.8108	+	16.8108i	−0.541438	+	0.541438i
$965$		−	11.0340i		−	0.355196i
$966$	−7.13936	+	0.601692i	−0.229705	+	0.0193591i
$967$	−38.6204	−	38.6204i	−1.24195	−	1.24195i	−0.959192	−	0.282756i	$-0.908751\pi$
$967$	−38.6204	−	38.6204i	−1.24195	−	1.24195i	−0.282756	−	0.959192i	$-0.591249\pi$
$968$	9.55213	+	9.55213i	0.307017	+	0.307017i
$969$	−0.570961	−	0.570961i	−0.0183419	−	0.0183419i
$970$	−6.35905	+	6.35905i	−0.204177	+	0.204177i
$971$		−	1.62095i		−	0.0520189i	−0.999662	−	0.0260094i	$-0.991720\pi$
$971$		−	1.62095i		−	0.0520189i	0.999662	−	0.0260094i	$-0.00828000\pi$
$972$	1.00000			0.0320750
$973$	31.2435	+	26.3865i	1.00162	+	0.845914i
$974$		−	32.7731i		−	1.05012i
$975$	−11.8487	−	4.40771i	−0.379461	−	0.141160i
$976$			10.6389i			0.340543i
$977$	−35.9201	−	35.9201i	−1.14919	−	1.14919i	−0.986713	−	0.162473i	$-0.948053\pi$
$977$	−35.9201	−	35.9201i	−1.14919	−	1.14919i	−0.162473	−	0.986713i	$-0.551947\pi$
$978$			0.972330i			0.0310917i
$979$	−25.8138			−0.825012
$980$	−4.95171	+	6.97670i	−0.158177	+	0.222863i
$981$	−5.19435	−	5.19435i	−0.165843	−	0.165843i
$982$	11.0454	−	11.0454i	0.352474	−	0.352474i
$983$	−7.99017	−	7.99017i	−0.254847	−	0.254847i	0.568107	−	0.822954i	$-0.307676\pi$
$983$	−7.99017	−	7.99017i	−0.254847	−	0.254847i	−0.822954	+	0.568107i	$0.807676\pi$
$984$	−9.14265			−0.291457
$985$	18.1637			0.578745
$986$	1.09818	+	1.09818i	0.0349730	+	0.0349730i
$987$	0.444383	+	5.27281i	0.0141449	+	0.167835i
$988$	−3.76094	−	8.21657i	−0.119651	−	0.261404i
$989$	1.06631			0.0339067
$990$	−4.27843	+	4.27843i	−0.135978	+	0.135978i
$991$	−20.8202			−0.661377			−0.330688	−	0.943740i	$-0.607281\pi$
$991$	−20.8202			−0.661377			−0.330688	+	0.943740i	$0.607281\pi$
$992$	2.44438			0.0776092
$993$	−5.19998	+	5.19998i	−0.165016	+	0.165016i
$994$	1.85138	+	1.56357i	0.0587221	+	0.0495934i
$995$	14.6144	−	14.6144i	0.463306	−	0.463306i
$996$	−6.09203	+	6.09203i	−0.193034	+	0.193034i
$997$			32.4465i			1.02759i	0.857913	+	0.513795i	$0.171761\pi$
$997$			32.4465i			1.02759i	−0.857913	+	0.513795i	$0.828239\pi$
$998$			36.2860i			1.14861i
$999$	2.27843	+	2.27843i	0.0720864	+	0.0720864i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.o.c.307.3	yes	8
3.2	odd	2		1638.2.x.a.307.2		8
7.6	odd	2		546.2.o.b.307.4	yes	8
13.5	odd	4		546.2.o.b.265.4	✓	8
21.20	even	2		1638.2.x.c.307.1		8
39.5	even	4		1638.2.x.c.811.1		8
91.83	even	4	inner	546.2.o.c.265.3	yes	8
273.83	odd	4		1638.2.x.a.811.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.o.b.265.4	✓	8	13.5	odd	4
546.2.o.b.307.4	yes	8	7.6	odd	2
546.2.o.c.265.3	yes	8	91.83	even	4	inner
546.2.o.c.307.3	yes	8	1.1	even	1	trivial
1638.2.x.a.307.2		8	3.2	odd	2
1638.2.x.a.811.2		8	273.83	odd	4
1638.2.x.c.307.1		8	21.20	even	2
1638.2.x.c.811.1		8	39.5	even	4

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

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} -1.00000i q^{3} +1.00000i q^{4} +(-0.864220 + 0.864220i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-1.70711 + 2.02133i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} -1.00000i q^{3} +1.00000i q^{4} +(-0.864220 + 0.864220i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-1.70711 + 2.02133i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} -1.22219 q^{10} +(-3.50062 + 3.50062i) q^{11} +1.00000 q^{12} +(-3.37930 - 1.25710i) q^{13} +(-2.63640 + 0.222191i) q^{14} +(0.864220 + 0.864220i) q^{15} -1.00000 q^{16} +0.322179 q^{17} +(-0.707107 - 0.707107i) q^{18} +(1.77219 - 1.77219i) q^{19} +(-0.864220 - 0.864220i) q^{20} +(2.02133 + 1.70711i) q^{21} -4.95063 q^{22} +2.70799i q^{23} +(0.707107 + 0.707107i) q^{24} +3.50625i q^{25} +(-1.50062 - 3.27843i) q^{26} +1.00000i q^{27} +(-2.02133 - 1.70711i) q^{28} +4.82047 q^{29} +1.22219i q^{30} +(-1.72844 + 1.72844i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(3.50062 + 3.50062i) q^{33} +(0.227815 + 0.227815i) q^{34} +(-0.271560 - 3.22219i) q^{35} -1.00000i q^{36} +(2.27843 - 2.27843i) q^{37} +2.50625 q^{38} +(-1.25710 + 3.37930i) q^{39} -1.22219i q^{40} +(-6.46483 + 6.46483i) q^{41} +(0.222191 + 2.63640i) q^{42} -0.393764i q^{43} +(-3.50062 - 3.50062i) q^{44} +(0.864220 - 0.864220i) q^{45} +(-1.91484 + 1.91484i) q^{46} +(1.41421 + 1.41421i) q^{47} +1.00000i q^{48} +(-1.17157 - 6.90126i) q^{49} +(-2.47929 + 2.47929i) q^{50} -0.322179i q^{51} +(1.25710 - 3.37930i) q^{52} -2.03142 q^{53} +(-0.707107 + 0.707107i) q^{54} -6.05062i q^{55} +(-0.222191 - 2.63640i) q^{56} +(-1.77219 - 1.77219i) q^{57} +(3.40859 + 3.40859i) q^{58} +(10.7599 + 10.7599i) q^{59} +(-0.864220 + 0.864220i) q^{60} -10.6389i q^{61} -2.44438 q^{62} +(1.70711 - 2.02133i) q^{63} -1.00000i q^{64} +(4.00687 - 1.83405i) q^{65} +4.95063i q^{66} +(5.38404 + 5.38404i) q^{67} +0.322179i q^{68} +2.70799 q^{69} +(2.08641 - 2.47046i) q^{70} +(-0.647652 - 0.647652i) q^{71} +(0.707107 - 0.707107i) q^{72} +(-6.85297 - 6.85297i) q^{73} +3.22219 q^{74} +3.50625 q^{75} +(1.77219 + 1.77219i) q^{76} +(-1.09999 - 13.0519i) q^{77} +(-3.27843 + 1.50062i) q^{78} +8.81718 q^{79} +(0.864220 - 0.864220i) q^{80} +1.00000 q^{81} -9.14265 q^{82} +(-6.09203 + 6.09203i) q^{83} +(-1.70711 + 2.02133i) q^{84} +(-0.278433 + 0.278433i) q^{85} +(0.278433 - 0.278433i) q^{86} -4.82047i q^{87} -4.95063i q^{88} +(3.68702 + 3.68702i) q^{89} +1.22219 q^{90} +(8.30985 - 4.68469i) q^{91} -2.70799 q^{92} +(1.72844 + 1.72844i) q^{93} +2.00000i q^{94} +3.06311i q^{95} +(-0.707107 + 0.707107i) q^{96} +(5.20299 - 5.20299i) q^{97} +(4.05150 - 5.70836i) q^{98} +(3.50062 - 3.50062i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{5} - 8 q^{7} - 8 q^{9}+O(q^{10}) \) 8 * q + 4 * q^5 - 8 * q^7 - 8 * q^9	\( 8 q + 4 q^{5} - 8 q^{7} - 8 q^{9} - 4 q^{10} + 8 q^{12} - 16 q^{13} - 4 q^{14} - 4 q^{15} - 8 q^{16} - 4 q^{17} + 8 q^{19} + 4 q^{20} - 12 q^{22} + 16 q^{26} + 12 q^{29} + 8 q^{31} + 8 q^{34} - 24 q^{35} - 4 q^{37} + 4 q^{38} - 4 q^{39} - 12 q^{41} - 4 q^{42} - 4 q^{45} + 24 q^{46} - 32 q^{49} - 8 q^{50} + 4 q^{52} + 40 q^{53} + 4 q^{56} - 8 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} - 8 q^{62} + 8 q^{63} - 12 q^{65} + 32 q^{67} + 28 q^{69} - 12 q^{71} - 20 q^{73} + 20 q^{74} + 12 q^{75} + 8 q^{76} - 8 q^{77} - 4 q^{78} + 24 q^{79} - 4 q^{80} + 8 q^{81} - 40 q^{82} - 44 q^{83} - 8 q^{84} + 20 q^{85} - 20 q^{86} - 16 q^{89} + 4 q^{90} - 12 q^{91} - 28 q^{92} - 8 q^{93} + 8 q^{97} + 16 q^{98}+O(q^{100}) \) 8 * q + 4 * q^5 - 8 * q^7 - 8 * q^9 - 4 * q^10 + 8 * q^12 - 16 * q^13 - 4 * q^14 - 4 * q^15 - 8 * q^16 - 4 * q^17 + 8 * q^19 + 4 * q^20 - 12 * q^22 + 16 * q^26 + 12 * q^29 + 8 * q^31 + 8 * q^34 - 24 * q^35 - 4 * q^37 + 4 * q^38 - 4 * q^39 - 12 * q^41 - 4 * q^42 - 4 * q^45 + 24 * q^46 - 32 * q^49 - 8 * q^50 + 4 * q^52 + 40 * q^53 + 4 * q^56 - 8 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 - 8 * q^62 + 8 * q^63 - 12 * q^65 + 32 * q^67 + 28 * q^69 - 12 * q^71 - 20 * q^73 + 20 * q^74 + 12 * q^75 + 8 * q^76 - 8 * q^77 - 4 * q^78 + 24 * q^79 - 4 * q^80 + 8 * q^81 - 40 * q^82 - 44 * q^83 - 8 * q^84 + 20 * q^85 - 20 * q^86 - 16 * q^89 + 4 * q^90 - 12 * q^91 - 28 * q^92 - 8 * q^93 + 8 * q^97 + 16 * q^98

Introduction

L-functions

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