LMFDB - Embedded newform 546.2.cg.b.241.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(145,546)]

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, 10, 1]))

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

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

chi := DirichletCharacter("546.145");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.cg (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			241.6
Character	$\chi$	$=$	546.241
Dual form			546.2.cg.b.145.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(-2.31481 - 0.620250i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(-2.57277 - 0.617120i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(-2.31481 - 0.620250i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(-2.57277 - 0.617120i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.19823 - 2.07540i) q^{10} +(3.24561 + 0.869658i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(2.14551 - 2.89772i) q^{13} +(-1.38286 - 2.25560i) q^{14} +(2.31481 - 0.620250i) q^{15} -1.00000 q^{16} -6.37060 q^{17} +(0.965926 - 0.258819i) q^{18} +(-1.65086 - 6.16110i) q^{19} +(0.620250 - 2.31481i) q^{20} +(2.53665 - 0.751945i) q^{21} +(1.68005 + 2.90993i) q^{22} -6.51073i q^{23} +(0.258819 - 0.965926i) q^{24} +(0.643487 + 0.371517i) q^{25} +(3.56610 - 0.531892i) q^{26} +1.00000i q^{27} +(0.617120 - 2.57277i) q^{28} +(1.87496 - 3.24753i) q^{29} +(2.07540 + 1.19823i) q^{30} +(-1.56651 - 5.84629i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.24561 + 0.869658i) q^{33} +(-4.50469 - 4.50469i) q^{34} +(5.57270 + 3.02428i) q^{35} +(0.866025 + 0.500000i) q^{36} +(-2.23541 + 2.23541i) q^{37} +(3.18922 - 5.52389i) q^{38} +(-0.409207 + 3.58225i) q^{39} +(2.07540 - 1.19823i) q^{40} +(2.36414 + 8.82310i) q^{41} +(2.32539 + 1.26197i) q^{42} +(-7.35081 + 4.24399i) q^{43} +(-0.869658 + 3.24561i) q^{44} +(-1.69456 + 1.69456i) q^{45} +(4.60378 - 4.60378i) q^{46} +(-2.14578 + 8.00816i) q^{47} +(0.866025 - 0.500000i) q^{48} +(6.23833 + 3.17542i) q^{49} +(0.192312 + 0.717716i) q^{50} +(5.51710 - 3.18530i) q^{51} +(2.89772 + 2.14551i) q^{52} +(-4.65896 + 8.06956i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(-6.97354 - 4.02618i) q^{55} +(2.25560 - 1.38286i) q^{56} +(4.51024 + 4.51024i) q^{57} +(3.62215 - 0.970553i) q^{58} +(-1.73579 - 1.73579i) q^{59} +(0.620250 + 2.31481i) q^{60} +(-6.53195 - 3.77122i) q^{61} +(3.02626 - 5.24164i) q^{62} +(-1.82083 + 1.91953i) q^{63} -1.00000i q^{64} +(-6.76375 + 5.37690i) q^{65} +(-2.90993 - 1.68005i) q^{66} +(1.93283 - 7.21342i) q^{67} -6.37060i q^{68} +(3.25536 + 5.63845i) q^{69} +(1.80201 + 6.07898i) q^{70} +(0.165170 - 0.616423i) q^{71} +(0.258819 + 0.965926i) q^{72} +(10.6978 - 2.86646i) q^{73} -3.16135 q^{74} -0.743035 q^{75} +(6.16110 - 1.65086i) q^{76} +(-7.81353 - 4.24036i) q^{77} +(-2.82239 + 2.24368i) q^{78} +(-2.75688 - 4.77505i) q^{79} +(2.31481 + 0.620250i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.56717 + 7.91058i) q^{82} +(0.287435 - 0.287435i) q^{83} +(0.751945 + 2.53665i) q^{84} +(14.7467 + 3.95136i) q^{85} +(-8.19877 - 2.19685i) q^{86} +3.74993i q^{87} +(-2.90993 + 1.68005i) q^{88} +(-1.95367 - 1.95367i) q^{89} -2.39646 q^{90} +(-7.30815 + 6.13114i) q^{91} +6.51073 q^{92} +(4.27978 + 4.27978i) q^{93} +(-7.17992 + 4.14533i) q^{94} +15.2857i q^{95} +(0.965926 + 0.258819i) q^{96} +(-3.55971 - 0.953822i) q^{97} +(2.16580 + 6.65652i) q^{98} +(2.37595 - 2.37595i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q + 4 * q^7 + 20 * q^9	$ 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q + 4 * q^7 + 20 * q^9 + 8 * q^11 - 20 * q^12 + 4 * q^14 - 40 * q^16 + 16 * q^17 + 4 * q^19 + 4 * q^21 - 4 * q^22 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 8 * q^33 - 8 * q^34 - 32 * q^35 + 40 * q^37 + 8 * q^38 + 20 * q^39 + 20 * q^41 + 12 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 + 4 * q^47 + 32 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^52 - 4 * q^53 + 24 * q^55 + 12 * q^56 + 8 * q^57 + 12 * q^58 + 24 * q^59 + 60 * q^61 + 32 * q^62 - 4 * q^63 + 44 * q^65 - 12 * q^67 - 8 * q^69 - 24 * q^70 - 28 * q^71 + 60 * q^73 - 40 * q^74 - 72 * q^75 + 4 * q^76 - 12 * q^77 + 4 * q^78 - 20 * q^81 - 24 * q^82 + 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 - 16 * q^92 - 24 * q^93 - 48 * q^97 - 88 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$			1.00000i			0.500000i
$5$	−2.31481	−	0.620250i	−1.03521	−	0.277384i	−0.299084	−	0.954227i	$-0.596681\pi$
$5$	−2.31481	−	0.620250i	−1.03521	−	0.277384i	−0.736128	+	0.676842i	$0.763348\pi$
$6$	−0.965926	−	0.258819i	−0.394338	−	0.105662i
$7$	−2.57277	−	0.617120i	−0.972417	−	0.233249i
$7$	−2.57277	−	0.617120i	−0.972417	−	0.233249i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−1.19823	−	2.07540i	−0.378914	−	0.656298i
$11$	3.24561	+	0.869658i	0.978587	+	0.262212i	0.712450	−	0.701723i	$-0.247586\pi$
$11$	3.24561	+	0.869658i	0.978587	+	0.262212i	0.266138	+	0.963935i	$0.414252\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	2.14551	−	2.89772i	0.595058	−	0.803683i
$13$	2.14551	−	2.89772i	0.595058	−	0.803683i
$14$	−1.38286	−	2.25560i	−0.369584	−	0.602833i
$15$	2.31481	−	0.620250i	0.597680	−	0.160148i
$16$	−1.00000			−0.250000
$17$	−6.37060			−1.54510			−0.772548	−	0.634956i	$-0.781018\pi$
$17$	−6.37060			−1.54510			−0.772548	+	0.634956i	$0.781018\pi$
$18$	0.965926	−	0.258819i	0.227671	−	0.0610042i
$19$	−1.65086	−	6.16110i	−0.378734	−	1.41345i	−0.847812	−	0.530297i	$-0.822080\pi$
$19$	−1.65086	−	6.16110i	−0.378734	−	1.41345i	0.469078	−	0.883157i	$-0.344586\pi$
$20$	0.620250	−	2.31481i	0.138692	−	0.517606i
$21$	2.53665	−	0.751945i	0.553542	−	0.164088i
$22$	1.68005	+	2.90993i	0.358188	+	0.620400i
$23$		−	6.51073i		−	1.35758i	−0.734332	−	0.678790i	$-0.762505\pi$
$23$		−	6.51073i		−	1.35758i	0.734332	−	0.678790i	$-0.237495\pi$
$24$	0.258819	−	0.965926i	0.0528312	−	0.197169i
$25$	0.643487	+	0.371517i	0.128697	+	0.0743035i
$26$	3.56610	−	0.531892i	0.699370	−	0.104313i
$27$			1.00000i			0.192450i
$28$	0.617120	−	2.57277i	0.116625	−	0.486208i
$29$	1.87496	−	3.24753i	0.348172	−	0.603052i	−0.637753	−	0.770241i	$-0.720136\pi$
$29$	1.87496	−	3.24753i	0.348172	−	0.603052i	0.985925	+	0.167189i	$0.0534691\pi$
$30$	2.07540	+	1.19823i	0.378914	+	0.218766i
$31$	−1.56651	−	5.84629i	−0.281353	−	1.05002i	−0.951463	−	0.307762i	$-0.900420\pi$
$31$	−1.56651	−	5.84629i	−0.281353	−	1.05002i	0.670110	−	0.742262i	$-0.266247\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−3.24561	+	0.869658i	−0.564988	+	0.151388i
$34$	−4.50469	−	4.50469i	−0.772548	−	0.772548i
$35$	5.57270	+	3.02428i	0.941958	+	0.511196i
$36$	0.866025	+	0.500000i	0.144338	+	0.0833333i
$37$	−2.23541	+	2.23541i	−0.367500	+	0.367500i	−0.866565	−	0.499065i	$-0.833677\pi$
$37$	−2.23541	+	2.23541i	−0.367500	+	0.367500i	0.499065	+	0.866565i	$0.333677\pi$
$38$	3.18922	−	5.52389i	0.517360	−	0.896094i
$39$	−0.409207	+	3.58225i	−0.0655256	+	0.573620i
$40$	2.07540	−	1.19823i	0.328149	−	0.189457i
$41$	2.36414	+	8.82310i	0.369217	+	1.37794i	0.861613	+	0.507566i	$0.169455\pi$
$41$	2.36414	+	8.82310i	0.369217	+	1.37794i	−0.492396	+	0.870371i	$0.663879\pi$
$42$	2.32539	+	1.26197i	0.358815	+	0.194727i
$43$	−7.35081	+	4.24399i	−1.12099	+	0.647203i	−0.941653	−	0.336585i	$-0.890728\pi$
$43$	−7.35081	+	4.24399i	−1.12099	+	0.647203i	−0.179335	+	0.983788i	$0.557395\pi$
$44$	−0.869658	+	3.24561i	−0.131106	+	0.489294i
$45$	−1.69456	+	1.69456i	−0.252609	+	0.252609i
$46$	4.60378	−	4.60378i	0.678790	−	0.678790i
$47$	−2.14578	+	8.00816i	−0.312994	+	1.16811i	0.612848	+	0.790201i	$0.290024\pi$
$47$	−2.14578	+	8.00816i	−0.312994	+	1.16811i	−0.925842	+	0.377910i	$0.876643\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	6.23833	+	3.17542i	0.891189	+	0.453631i
$50$	0.192312	+	0.717716i	0.0271970	+	0.101500i
$51$	5.51710	−	3.18530i	0.772548	−	0.446031i
$52$	2.89772	+	2.14551i	0.401841	+	0.297529i
$53$	−4.65896	+	8.06956i	−0.639958	+	1.10844i	0.345484	+	0.938425i	$0.387715\pi$
$53$	−4.65896	+	8.06956i	−0.639958	+	1.10844i	−0.985442	+	0.170015i	$0.945618\pi$
$54$	−0.707107	+	0.707107i	−0.0962250	+	0.0962250i
$55$	−6.97354	−	4.02618i	−0.940312	−	0.542890i
$56$	2.25560	−	1.38286i	0.301417	−	0.184792i
$57$	4.51024	+	4.51024i	0.597396	+	0.597396i
$58$	3.62215	−	0.970553i	0.475612	−	0.127440i
$59$	−1.73579	−	1.73579i	−0.225980	−	0.225980i	0.585031	−	0.811011i	$-0.301082\pi$
$59$	−1.73579	−	1.73579i	−0.225980	−	0.225980i	−0.811011	+	0.585031i	$0.801082\pi$
$60$	0.620250	+	2.31481i	0.0800740	+	0.298840i
$61$	−6.53195	−	3.77122i	−0.836331	−	0.482856i	0.0196846	−	0.999806i	$-0.493734\pi$
$61$	−6.53195	−	3.77122i	−0.836331	−	0.482856i	−0.856015	+	0.516950i	$0.827067\pi$
$62$	3.02626	−	5.24164i	0.384335	−	0.665689i
$63$	−1.82083	+	1.91953i	−0.229403	+	0.241838i
$64$		−	1.00000i		−	0.125000i
$65$	−6.76375	+	5.37690i	−0.838940	+	0.666923i
$66$	−2.90993	−	1.68005i	−0.358188	−	0.206800i
$67$	1.93283	−	7.21342i	0.236133	−	0.881259i	−0.741502	−	0.670950i	$-0.765886\pi$
$67$	1.93283	−	7.21342i	0.236133	−	0.881259i	0.977635	−	0.210309i	$-0.0674469\pi$
$68$		−	6.37060i		−	0.772548i
$69$	3.25536	+	5.63845i	0.391900	+	0.678790i
$70$	1.80201	+	6.07898i	0.215381	+	0.726577i
$71$	0.165170	−	0.616423i	0.0196021	−	0.0731559i	−0.955432	−	0.295211i	$-0.904610\pi$
$71$	0.165170	−	0.616423i	0.0196021	−	0.0731559i	0.975034	+	0.222055i	$0.0712766\pi$
$72$	0.258819	+	0.965926i	0.0305021	+	0.113835i
$73$	10.6978	−	2.86646i	1.25208	−	0.335493i	0.428939	−	0.903333i	$-0.358887\pi$
$73$	10.6978	−	2.86646i	1.25208	−	0.335493i	0.823139	+	0.567840i	$0.192221\pi$
$74$	−3.16135			−0.367500
$75$	−0.743035			−0.0857983
$76$	6.16110	−	1.65086i	0.706727	−	0.189367i
$77$	−7.81353	−	4.24036i	−0.890434	−	0.483234i
$78$	−2.82239	+	2.24368i	−0.319573	+	0.254047i
$79$	−2.75688	−	4.77505i	−0.310173	−	0.537235i	0.668227	−	0.743958i	$-0.267054\pi$
$79$	−2.75688	−	4.77505i	−0.310173	−	0.537235i	−0.978400	+	0.206722i	$0.933720\pi$
$80$	2.31481	+	0.620250i	0.258803	+	0.0693461i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−4.56717	+	7.91058i	−0.504360	+	0.873577i
$83$	0.287435	−	0.287435i	0.0315501	−	0.0315501i	−0.691156	−	0.722706i	$-0.742898\pi$
$83$	0.287435	−	0.287435i	0.0315501	−	0.0315501i	0.722706	+	0.691156i	$0.242898\pi$
$84$	0.751945	+	2.53665i	0.0820439	+	0.276771i
$85$	14.7467	+	3.95136i	1.59950	+	0.428586i
$86$	−8.19877	−	2.19685i	−0.884096	−	0.236893i
$87$			3.74993i			0.402035i
$88$	−2.90993	+	1.68005i	−0.310200	+	0.179094i
$89$	−1.95367	−	1.95367i	−0.207088	−	0.207088i	0.595940	−	0.803029i	$-0.296779\pi$
$89$	−1.95367	−	1.95367i	−0.207088	−	0.207088i	−0.803029	+	0.595940i	$0.796779\pi$
$90$	−2.39646			−0.252609
$91$	−7.30815	+	6.13114i	−0.766103	+	0.642718i
$92$	6.51073			0.678790
$93$	4.27978	+	4.27978i	0.443792	+	0.443792i
$94$	−7.17992	+	4.14533i	−0.740552	+	0.427558i
$95$			15.2857i			1.56828i
$96$	0.965926	+	0.258819i	0.0985844	+	0.0264156i
$97$	−3.55971	−	0.953822i	−0.361434	−	0.0968460i	0.0735319	−	0.997293i	$-0.476573\pi$
$97$	−3.55971	−	0.953822i	−0.361434	−	0.0968460i	−0.434966	+	0.900447i	$0.643240\pi$
$98$	2.16580	+	6.65652i	0.218779	+	0.672410i
$99$	2.37595	−	2.37595i	0.238792	−	0.238792i
$100$	−0.371517	+	0.643487i	−0.0371517	+	0.0643487i
$101$	−2.42268	−	4.19620i	−0.241066	−	0.417538i	0.719953	−	0.694023i	$-0.244164\pi$
$101$	−2.42268	−	4.19620i	−0.241066	−	0.417538i	−0.961018	+	0.276485i	$0.910830\pi$
$102$	6.15352	+	1.64883i	0.609290	+	0.163259i
$103$	−8.89257	−	15.4024i	−0.876211	−	1.51764i	−0.855467	−	0.517857i	$-0.826730\pi$
$103$	−8.89257	−	15.4024i	−0.876211	−	1.51764i	−0.0207442	−	0.999785i	$-0.506604\pi$
$104$	0.531892	+	3.56610i	0.0521563	+	0.349685i
$105$	−6.33824	+	0.167251i	−0.618549	+	0.0163220i
$106$	−9.00043	+	2.41166i	−0.874199	+	0.234241i
$107$	−13.3757			−1.29308			−0.646540	−	0.762880i	$-0.723785\pi$
$107$	−13.3757			−1.29308			−0.646540	+	0.762880i	$0.723785\pi$
$108$	−1.00000			−0.0962250
$109$	9.91417	−	2.65649i	0.949605	−	0.254446i	0.249411	−	0.968398i	$-0.419763\pi$
$109$	9.91417	−	2.65649i	0.949605	−	0.254446i	0.700195	+	0.713952i	$0.253096\pi$
$110$	−2.08410	−	7.77798i	−0.198711	−	0.741601i
$111$	0.818218	−	3.05363i	0.0776619	−	0.289838i
$112$	2.57277	+	0.617120i	0.243104	+	0.0583124i
$113$	6.08846	+	10.5455i	0.572754	+	0.992040i	0.996282	+	0.0861564i	$0.0274585\pi$
$113$	6.08846	+	10.5455i	0.572754	+	0.992040i	−0.423527	+	0.905883i	$0.639208\pi$
$114$			6.37844i			0.597396i
$115$	−4.03828	+	15.0711i	−0.376572	+	1.40538i
$116$	3.24753	+	1.87496i	0.301526	+	0.174086i
$117$	−1.43674	−	3.30693i	−0.132827	−	0.305726i
$118$		−	2.45477i		−	0.225980i
$119$	16.3901	+	3.93142i	1.50248	+	0.360393i
$120$	−1.19823	+	2.07540i	−0.109383	+	0.189457i
$121$	0.251383	+	0.145136i	0.0228530	+	0.0131942i
$122$	−1.95213	−	7.28545i	−0.176737	−	0.659593i
$123$	−6.45896	−	6.45896i	−0.582385	−	0.582385i
$124$	5.84629	−	1.56651i	0.525012	−	0.140677i
$125$	7.21366	+	7.21366i	0.645210	+	0.645210i
$126$	−2.64483	+	0.0697906i	−0.235620	+	0.00621744i
$127$	3.36327	+	1.94179i	0.298442	+	0.172306i	0.641743	−	0.766920i	$-0.278212\pi$
$127$	3.36327	+	1.94179i	0.298442	+	0.172306i	−0.343301	+	0.939226i	$0.611545\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	4.24399	−	7.35081i	0.373663	−	0.647203i
$130$	−8.58474	−	0.980649i	−0.752932	−	0.0860086i
$131$	−14.6139	+	8.43733i	−1.27682	+	0.737173i	−0.976263	−	0.216590i	$-0.930507\pi$
$131$	−14.6139	+	8.43733i	−1.27682	+	0.737173i	−0.300559	+	0.953763i	$0.597173\pi$
$132$	−0.869658	−	3.24561i	−0.0756940	−	0.282494i
$133$	0.445155	+	16.8699i	0.0385999	+	1.46281i
$134$	6.46737	−	3.73394i	0.558696	−	0.322563i
$135$	0.620250	−	2.31481i	0.0533826	−	0.199227i
$136$	4.50469	−	4.50469i	0.386274	−	0.386274i
$137$	0.206381	−	0.206381i	0.0176323	−	0.0176323i	−0.698236	−	0.715868i	$-0.746031\pi$
$137$	0.206381	−	0.206381i	0.0176323	−	0.0176323i	0.715868	+	0.698236i	$0.246031\pi$
$138$	−1.68510	+	6.28888i	−0.143445	+	0.535345i
$139$	7.59129	−	4.38283i	0.643884	−	0.371747i	−0.142225	−	0.989834i	$-0.545426\pi$
$139$	7.59129	−	4.38283i	0.643884	−	0.371747i	0.786109	+	0.618088i	$0.212092\pi$
$140$	−3.02428	+	5.57270i	−0.255598	+	0.470979i
$141$	−2.14578	−	8.00816i	−0.180707	−	0.674409i
$142$	0.552669	−	0.319084i	0.0463790	−	0.0267769i
$143$	9.48351	−	7.53900i	0.793051	−	0.630443i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−6.35446	+	6.35446i	−0.527709	+	0.527709i
$146$	9.59135	+	5.53757i	0.793786	+	0.458292i
$147$	−6.99026	+	0.369168i	−0.576547	+	0.0304485i
$148$	−2.23541	−	2.23541i	−0.183750	−	0.183750i
$149$	4.01080	−	1.07469i	0.328577	−	0.0880420i	−0.0907593	−	0.995873i	$-0.528929\pi$
$149$	4.01080	−	1.07469i	0.328577	−	0.0880420i	0.419337	+	0.907831i	$0.362263\pi$
$150$	−0.525405	−	0.525405i	−0.0428991	−	0.0428991i
$151$	−3.35695	−	12.5283i	−0.273185	−	1.01954i	−0.957048	−	0.289929i	$-0.906368\pi$
$151$	−3.35695	−	12.5283i	−0.273185	−	1.01954i	0.683864	−	0.729610i	$-0.260298\pi$
$152$	5.52389	+	3.18922i	0.448047	+	0.258680i
$153$	−3.18530	+	5.51710i	−0.257516	+	0.446031i
$154$	−2.52661	−	8.52339i	−0.203600	−	0.686834i
$155$			14.5046i			1.16504i
$156$	−3.58225	−	0.409207i	−0.286810	−	0.0327628i
$157$	−7.83081	−	4.52112i	−0.624966	−	0.360825i	0.153834	−	0.988097i	$-0.450838\pi$
$157$	−7.83081	−	4.52112i	−0.624966	−	0.360825i	−0.778800	+	0.627272i	$0.784171\pi$
$158$	1.42707	−	5.32588i	0.113531	−	0.423704i
$159$		−	9.31793i		−	0.738960i
$160$	1.19823	+	2.07540i	0.0947285	+	0.164075i
$161$	−4.01790	+	16.7506i	−0.316655	+	1.32013i
$162$	0.258819	−	0.965926i	0.0203347	−	0.0758903i
$163$	2.58647	+	9.65282i	0.202588	+	0.756068i	0.990171	+	0.139860i	$0.0446652\pi$
$163$	2.58647	+	9.65282i	0.202588	+	0.756068i	−0.787584	+	0.616208i	$0.788668\pi$
$164$	−8.82310	+	2.36414i	−0.688968	+	0.184609i
$165$	8.05236			0.626875
$166$	0.406494			0.0315501
$167$	9.35729	−	2.50728i	0.724089	−	0.194019i	0.122093	−	0.992519i	$-0.461039\pi$
$167$	9.35729	−	2.50728i	0.724089	−	0.194019i	0.601995	+	0.798500i	$0.294373\pi$
$168$	−1.26197	+	2.32539i	−0.0973635	+	0.179407i
$169$	−3.79356	−	12.4342i	−0.291813	−	0.956475i
$170$	7.63345	+	13.2215i	0.585459	+	1.01404i
$171$	−6.16110	−	1.65086i	−0.471151	−	0.126245i
$172$	−4.24399	−	7.35081i	−0.323601	−	0.560494i
$173$	−4.39738	+	7.61648i	−0.334326	+	0.579070i	−0.983355	−	0.181694i	$-0.941842\pi$
$173$	−4.39738	+	7.61648i	−0.334326	+	0.579070i	0.649029	+	0.760764i	$0.275175\pi$
$174$	−2.65160	+	2.65160i	−0.201017	+	0.201017i
$175$	−1.42628	−	1.35294i	−0.107816	−	0.102273i
$176$	−3.24561	−	0.869658i	−0.244647	−	0.0655529i
$177$	2.37113	+	0.635342i	0.178225	+	0.0477552i
$178$		−	2.76290i		−	0.207088i
$179$	11.4198	−	6.59322i	0.853555	−	0.492800i	−0.00829395	−	0.999966i	$-0.502640\pi$
$179$	11.4198	−	6.59322i	0.853555	−	0.492800i	0.861849	+	0.507166i	$0.169307\pi$
$180$	−1.69456	−	1.69456i	−0.126305	−	0.126305i
$181$	−1.53653			−0.114209			−0.0571046	−	0.998368i	$-0.518187\pi$
$181$	−1.53653			−0.114209			−0.0571046	+	0.998368i	$0.518187\pi$
$182$	−9.50302	−	0.832275i	−0.704410	−	0.0616924i
$183$	7.54245			0.557554
$184$	4.60378	+	4.60378i	0.339395	+	0.339395i
$185$	6.56107	−	3.78803i	0.482379	−	0.278502i
$186$			6.05252i			0.443792i
$187$	−20.6765	−	5.54024i	−1.51201	−	0.405142i
$188$	−8.00816	−	2.14578i	−0.584055	−	0.156497i
$189$	0.617120	−	2.57277i	0.0448889	−	0.187142i
$190$	−10.8086	+	10.8086i	−0.784140	+	0.784140i
$191$	13.6091	−	23.5717i	0.984722	−	1.70559i	0.341558	−	0.939861i	$-0.389046\pi$
$191$	13.6091	−	23.5717i	0.984722	−	1.70559i	0.643165	−	0.765728i	$-0.277621\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−2.07410	−	0.555754i	−0.149297	−	0.0400040i	0.183396	−	0.983039i	$-0.441291\pi$
$193$	−2.07410	−	0.555754i	−0.149297	−	0.0400040i	−0.332694	+	0.943035i	$0.607957\pi$
$194$	−1.84264	−	3.19155i	−0.132294	−	0.229140i
$195$	3.16913	−	8.03841i	0.226946	−	0.575643i
$196$	−3.17542	+	6.23833i	−0.226816	+	0.445595i
$197$	21.2058	−	5.68207i	1.51085	−	0.404831i	0.594132	−	0.804368i	$-0.297496\pi$
$197$	21.2058	−	5.68207i	1.51085	−	0.404831i	0.916717	+	0.399537i	$0.130829\pi$
$198$	3.36010			0.238792
$199$	25.0379			1.77489			0.887443	−	0.460917i	$-0.152479\pi$
$199$	25.0379			1.77489			0.887443	+	0.460917i	$0.152479\pi$
$200$	−0.717716	+	0.192312i	−0.0507502	+	0.0135985i
$201$	1.93283	+	7.21342i	0.136331	+	0.508795i
$202$	1.25407	−	4.68026i	0.0882361	−	0.329302i
$203$	−6.82798	+	7.19809i	−0.479230	+	0.505207i
$204$	3.18530	+	5.51710i	0.223015	+	0.386274i
$205$		−	21.8901i		−	1.52887i
$206$	4.60313	−	17.1791i	0.320716	−	1.19693i
$207$	−5.63845	−	3.25536i	−0.391900	−	0.226263i
$208$	−2.14551	+	2.89772i	−0.148764	+	0.200921i
$209$		−	21.4322i		−	1.48250i
$210$	−4.60008	−	4.36355i	−0.317435	−	0.301113i
$211$	−11.9314	+	20.6658i	−0.821392	+	1.42269i	0.0832538	+	0.996528i	$0.473469\pi$
$211$	−11.9314	+	20.6658i	−0.821392	+	1.42269i	−0.904646	+	0.426164i	$0.859865\pi$
$212$	−8.06956	−	4.65896i	−0.554220	−	0.319979i
$213$	0.165170	+	0.616423i	0.0113173	+	0.0422366i
$214$	−9.45806	−	9.45806i	−0.646540	−	0.646540i
$215$	19.6480	−	5.26468i	1.33998	−	0.359048i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	0.422409	+	16.0079i	0.0286750	+	1.08669i
$218$	8.88880	+	5.13195i	0.602026	+	0.347580i
$219$	−7.83130	+	7.83130i	−0.529190	+	0.529190i
$220$	4.02618	−	6.97354i	0.271445	−	0.470156i
$221$	−13.6682	+	18.4602i	−0.919421	+	1.24177i
$222$	2.73781	−	1.58068i	0.183750	−	0.106088i
$223$	−3.96426	−	14.7948i	−0.265467	−	0.990735i	−0.961964	−	0.273176i	$-0.911926\pi$
$223$	−3.96426	−	14.7948i	−0.265467	−	0.990735i	0.696498	−	0.717559i	$-0.254741\pi$
$224$	1.38286	+	2.25560i	0.0923959	+	0.150708i
$225$	0.643487	−	0.371517i	0.0428991	−	0.0247678i
$226$	−3.15162	+	11.7620i	−0.209643	+	0.782397i
$227$	−7.34882	+	7.34882i	−0.487758	+	0.487758i	−0.907598	−	0.419840i	$-0.862086\pi$
$227$	−7.34882	+	7.34882i	−0.487758	+	0.487758i	0.419840	+	0.907598i	$0.362086\pi$
$228$	−4.51024	+	4.51024i	−0.298698	+	0.298698i
$229$	−3.99160	+	14.8969i	−0.263773	+	0.984413i	0.699225	+	0.714902i	$0.253529\pi$
$229$	−3.99160	+	14.8969i	−0.263773	+	0.984413i	−0.962997	+	0.269511i	$0.913138\pi$
$230$	−13.5123	+	7.80136i	−0.890978	+	0.514406i
$231$	8.88690	−	0.234503i	0.584715	−	0.0154292i
$232$	0.970553	+	3.62215i	0.0637199	+	0.237806i
$233$	3.08882	−	1.78333i	0.202355	−	0.116830i	−0.395398	−	0.918510i	$-0.629393\pi$
$233$	3.08882	−	1.78333i	0.202355	−	0.116830i	0.597754	+	0.801680i	$0.296060\pi$
$234$	1.32242	−	3.35428i	0.0864493	−	0.219276i
$235$	9.93413	−	17.2064i	0.648031	−	1.12242i
$236$	1.73579	−	1.73579i	0.112990	−	0.112990i
$237$	4.77505	+	2.75688i	0.310173	+	0.179078i
$238$	8.80961	+	14.3695i	0.571042	+	0.931435i
$239$	−13.8603	−	13.8603i	−0.896550	−	0.896550i	0.0985792	−	0.995129i	$-0.468570\pi$
$239$	−13.8603	−	13.8603i	−0.896550	−	0.896550i	−0.995129	+	0.0985792i	$0.968570\pi$
$240$	−2.31481	+	0.620250i	−0.149420	+	0.0400370i
$241$	19.6223	+	19.6223i	1.26398	+	1.26398i	0.949145	+	0.314838i	$0.101950\pi$
$241$	19.6223	+	19.6223i	1.26398	+	1.26398i	0.314838	+	0.949145i	$0.398050\pi$
$242$	0.0751278	+	0.280381i	0.00482940	+	0.0180236i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	3.77122	−	6.53195i	0.241428	−	0.418165i
$245$	−12.4710	−	11.2198i	−0.796740	−	0.716807i
$246$		−	9.13435i		−	0.582385i
$247$	−21.3951	−	8.43498i	−1.36134	−	0.536705i
$248$	5.24164	+	3.02626i	0.332844	+	0.192168i
$249$	−0.105209	+	0.392643i	−0.00666732	+	0.0248828i
$250$			10.2017i			0.645210i
$251$	−10.3080	−	17.8540i	−0.650637	−	1.12694i	−0.982969	−	0.183774i	$-0.941169\pi$
$251$	−10.3080	−	17.8540i	−0.650637	−	1.12694i	0.332332	−	0.943163i	$-0.392165\pi$
$252$	−1.91953	−	1.82083i	−0.120919	−	0.114701i
$253$	5.66210	−	21.1313i	0.355973	−	1.32851i
$254$	1.00514	+	3.75124i	0.0630682	+	0.235374i
$255$	−14.7467	+	3.95136i	−0.923473	+	0.247444i
$256$	1.00000			0.0625000
$257$	23.0075			1.43517			0.717586	−	0.696470i	$-0.245247\pi$
$257$	23.0075			1.43517			0.717586	+	0.696470i	$0.245247\pi$
$258$	8.19877	−	2.19685i	0.510433	−	0.136770i
$259$	7.13073	−	4.37170i	0.443082	−	0.271644i
$260$	−5.37690	−	6.76375i	−0.333461	−	0.419470i
$261$	−1.87496	−	3.24753i	−0.116057	−	0.201017i
$262$	−16.2997	−	4.36749i	−1.00700	−	0.269824i
$263$	−5.42117	−	9.38974i	−0.334284	−	0.578996i	0.649063	−	0.760734i	$-0.275161\pi$
$263$	−5.42117	−	9.38974i	−0.334284	−	0.578996i	−0.983347	+	0.181738i	$0.941828\pi$
$264$	1.68005	−	2.90993i	0.103400	−	0.179094i
$265$	15.7897	−	15.7897i	0.969956	−	0.969956i
$266$	−11.6141	+	12.2436i	−0.712103	+	0.750703i
$267$	2.66876	+	0.715092i	0.163325	+	0.0437629i
$268$	7.21342	+	1.93283i	0.440630	+	0.118066i
$269$			21.4209i			1.30605i	0.757335	+	0.653027i	$0.226501\pi$
$269$			21.4209i			1.30605i	−0.757335	+	0.653027i	$0.773499\pi$
$270$	2.07540	−	1.19823i	0.126305	−	0.0729220i
$271$	23.2139	+	23.2139i	1.41014	+	1.41014i	0.758686	+	0.651457i	$0.225842\pi$
$271$	23.2139	+	23.2139i	1.41014	+	1.41014i	0.651457	+	0.758686i	$0.274158\pi$
$272$	6.37060			0.386274
$273$	3.26348	−	8.96380i	0.197515	−	0.542514i
$274$	0.291867			0.0176323
$275$	1.76541	+	1.76541i	0.106458	+	0.106458i
$276$	−5.63845	+	3.25536i	−0.339395	+	0.195950i
$277$			17.9129i			1.07628i	0.842855	+	0.538140i	$0.180873\pi$
$277$			17.9129i			1.07628i	−0.842855	+	0.538140i	$0.819127\pi$
$278$	8.46698	+	2.26872i	0.507816	+	0.136069i
$279$	−5.84629	−	1.56651i	−0.350008	−	0.0937844i
$280$	−6.07898	+	1.80201i	−0.363289	+	0.107691i
$281$	−7.49939	+	7.49939i	−0.447376	+	0.447376i	−0.894481	−	0.447105i	$-0.852455\pi$
$281$	−7.49939	+	7.49939i	−0.447376	+	0.447376i	0.447105	+	0.894481i	$0.352455\pi$
$282$	4.14533	−	7.17992i	0.246851	−	0.427558i
$283$	−10.8689	−	18.8255i	−0.646088	−	1.11906i	−0.984049	−	0.177897i	$-0.943071\pi$
$283$	−10.8689	−	18.8255i	−0.646088	−	1.11906i	0.337961	−	0.941160i	$-0.390263\pi$
$284$	0.616423	+	0.165170i	0.0365780	+	0.00980103i
$285$	−7.64285	−	13.2378i	−0.452723	−	0.784140i
$286$	12.0367	+	1.37498i	0.711747	+	0.0813040i
$287$	−0.637491	−	24.1588i	−0.0376299	−	1.42605i
$288$	−0.965926	+	0.258819i	−0.0569177	+	0.0152511i
$289$	23.5845			1.38732
$290$	−8.98657			−0.527709
$291$	3.55971	−	0.953822i	0.208674	−	0.0559141i
$292$	2.86646	+	10.6978i	0.167747	+	0.626039i
$293$	0.450034	−	1.67955i	0.0262913	−	0.0981203i	−0.951533	−	0.307545i	$-0.900492\pi$
$293$	0.450034	−	1.67955i	0.0262913	−	0.0981203i	0.977825	+	0.209425i	$0.0671592\pi$
$294$	−5.20390	−	4.68182i	−0.303498	−	0.273049i
$295$	2.94139	+	5.09463i	0.171254	+	0.296621i
$296$		−	3.16135i		−	0.183750i
$297$	−0.869658	+	3.24561i	−0.0504627	+	0.188329i
$298$	3.59598	+	2.07614i	0.208310	+	0.120268i
$299$	−18.8663	−	13.9688i	−1.09106	−	0.807839i
$300$		−	0.743035i		−	0.0428991i
$301$	21.5310	−	6.38250i	1.24103	−	0.367881i
$302$	6.48513	−	11.2326i	0.373177	−	0.646362i
$303$	4.19620	+	2.42268i	0.241066	+	0.139179i
$304$	1.65086	+	6.16110i	0.0946835	+	0.353363i
$305$	12.7811	+	12.7811i	0.731843	+	0.731843i
$306$	−6.15352	+	1.64883i	−0.351773	+	0.0942574i
$307$	10.5367	+	10.5367i	0.601358	+	0.601358i	0.940673	−	0.339315i	$-0.110195\pi$
$307$	10.5367	+	10.5367i	0.601358	+	0.601358i	−0.339315	+	0.940673i	$0.610195\pi$
$308$	4.24036	−	7.81353i	0.241617	−	0.445217i
$309$	15.4024	+	8.89257i	0.876211	+	0.505881i
$310$	−10.2563	+	10.2563i	−0.582520	+	0.582520i
$311$	0.0418085	−	0.0724144i	0.00237074	−	0.00410624i	−0.864838	−	0.502052i	$-0.832579\pi$
$311$	0.0418085	−	0.0724144i	0.00237074	−	0.00410624i	0.867208	+	0.497945i	$0.165912\pi$
$312$	−2.24368	−	2.82239i	−0.127024	−	0.159786i
$313$	−21.7563	+	12.5610i	−1.22974	+	0.709991i	−0.966976	−	0.254869i	$-0.917968\pi$
$313$	−21.7563	+	12.5610i	−1.22974	+	0.709991i	−0.262765	+	0.964860i	$0.584634\pi$
$314$	−2.34030	−	8.73413i	−0.132071	−	0.492895i
$315$	5.40545	−	3.31396i	0.304563	−	0.186721i
$316$	4.77505	−	2.75688i	0.268618	−	0.155086i
$317$	5.17664	−	19.3195i	0.290749	−	1.08509i	−0.653786	−	0.756680i	$-0.726820\pi$
$317$	5.17664	−	19.3195i	0.290749	−	1.08509i	0.944535	−	0.328411i	$-0.106513\pi$
$318$	6.58877	−	6.58877i	0.369480	−	0.369480i
$319$	8.90964	−	8.90964i	0.498844	−	0.498844i
$320$	−0.620250	+	2.31481i	−0.0346730	+	0.129402i
$321$	11.5837	−	6.68786i	0.646540	−	0.373280i
$322$	−14.6856	+	9.00339i	−0.818394	+	0.501740i
$323$	10.5170	+	39.2499i	0.585180	+	2.18392i
$324$	0.866025	−	0.500000i	0.0481125	−	0.0277778i
$325$	2.45716	−	1.06755i	0.136299	−	0.0592170i
$326$	−4.99667	+	8.65449i	−0.276740	+	0.479328i
$327$	−7.25768	+	7.25768i	−0.401351	+	0.401351i
$328$	−7.91058	−	4.56717i	−0.436788	−	0.252180i
$329$	10.4626	−	19.2790i	0.576822	−	1.06288i
$330$	5.69387	+	5.69387i	0.313437	+	0.313437i
$331$	−11.0351	+	2.95685i	−0.606546	+	0.162523i	−0.549004	−	0.835820i	$-0.684993\pi$
$331$	−11.0351	+	2.95685i	−0.606546	+	0.162523i	−0.0575415	+	0.998343i	$0.518326\pi$
$332$	0.287435	+	0.287435i	0.0157750	+	0.0157750i
$333$	0.818218	+	3.05363i	0.0448381	+	0.167338i
$334$	8.38951	+	4.84369i	0.459054	+	0.265035i
$335$	−8.94825	+	15.4988i	−0.488895	+	0.846791i
$336$	−2.53665	+	0.751945i	−0.138385	+	0.0410220i
$337$		−	0.594432i		−	0.0323808i	−0.999869	−	0.0161904i	$-0.994846\pi$
$337$		−	0.594432i		−	0.0323808i	0.999869	−	0.0161904i	$-0.00515378\pi$
$338$	6.10984	−	11.4747i	0.332331	−	0.624144i
$339$	−10.5455	−	6.08846i	−0.572754	−	0.330680i
$340$	−3.95136	+	14.7467i	−0.214293	+	0.799751i
$341$		−	20.3371i		−	1.10131i
$342$	−3.18922	−	5.52389i	−0.172453	−	0.298698i
$343$	−14.0902	−	12.0194i	−0.760798	−	0.648988i
$344$	2.19685	−	8.19877i	0.118446	−	0.442048i
$345$	−4.03828	−	15.0711i	−0.217414	−	0.811399i
$346$	−8.49508	+	2.27625i	−0.456698	+	0.122372i
$347$	−27.1085			−1.45526			−0.727629	−	0.685971i	$-0.759378\pi$
$347$	−27.1085			−1.45526			−0.727629	+	0.685971i	$0.759378\pi$
$348$	−3.74993			−0.201017
$349$	−3.89257	+	1.04301i	−0.208365	+	0.0558311i	−0.361491	−	0.932375i	$-0.617732\pi$
$349$	−3.89257	+	1.04301i	−0.208365	+	0.0558311i	0.153127	+	0.988207i	$0.451066\pi$
$350$	−0.0518568	−	1.96520i	−0.00277186	−	0.105044i
$351$	2.89772	+	2.14551i	0.154669	+	0.114519i
$352$	−1.68005	−	2.90993i	−0.0895470	−	0.155100i
$353$	−18.2741	−	4.89653i	−0.972631	−	0.260616i	−0.262693	−	0.964879i	$-0.584611\pi$
$353$	−18.2741	−	4.89653i	−0.972631	−	0.260616i	−0.709939	+	0.704264i	$0.751277\pi$
$354$	1.22739	+	2.12590i	0.0652349	+	0.112990i
$355$	−0.764673	+	1.32445i	−0.0405846	+	0.0702946i
$356$	1.95367	−	1.95367i	0.103544	−	0.103544i
$357$	−16.1600	+	4.79034i	−0.855275	+	0.253532i
$358$	12.7371	+	3.41290i	0.673177	+	0.180377i
$359$	7.21299	+	1.93271i	0.380687	+	0.102005i	0.444088	−	0.895983i	$-0.353528\pi$
$359$	7.21299	+	1.93271i	0.380687	+	0.102005i	−0.0634006	+	0.997988i	$0.520195\pi$
$360$		−	2.39646i		−	0.126305i
$361$	−18.7794	+	10.8423i	−0.988387	+	0.570646i
$362$	−1.08649	−	1.08649i	−0.0571046	−	0.0571046i
$363$	−0.290272			−0.0152353
$364$	−6.13114	−	7.30815i	−0.321359	−	0.383051i
$365$	−26.5412			−1.38923
$366$	5.33332	+	5.33332i	0.278777	+	0.278777i
$367$	31.5624	−	18.2225i	1.64754	−	0.951209i	0.669498	−	0.742814i	$-0.266509\pi$
$367$	31.5624	−	18.2225i	1.64754	−	0.951209i	0.978045	−	0.208396i	$-0.0668241\pi$
$368$			6.51073i			0.339395i
$369$	8.82310	+	2.36414i	0.459312	+	0.123072i
$370$	7.31792	+	1.96083i	0.380440	+	0.101939i
$371$	16.9663	−	17.8860i	0.880849	−	0.928596i
$372$	−4.27978	+	4.27978i	−0.221896	+	0.221896i
$373$	6.36136	−	11.0182i	0.329379	−	0.570501i	−0.653010	−	0.757349i	$-0.726494\pi$
$373$	6.36136	−	11.0182i	0.329379	−	0.570501i	0.982389	+	0.186848i	$0.0598273\pi$
$374$	−10.7029	−	18.5380i	−0.553435	−	0.958577i
$375$	−9.85405	−	2.64038i	−0.508861	−	0.136349i
$376$	−4.14533	−	7.17992i	−0.213779	−	0.370276i
$377$	−5.38769	−	12.4007i	−0.277480	−	0.638671i
$378$	2.25560	−	1.38286i	0.116015	−	0.0711264i
$379$	−5.32301	+	1.42630i	−0.273425	+	0.0732640i	−0.392926	−	0.919570i	$-0.628537\pi$
$379$	−5.32301	+	1.42630i	−0.273425	+	0.0732640i	0.119501	+	0.992834i	$0.461870\pi$
$380$	−15.2857			−0.784140
$381$	−3.88357			−0.198961
$382$	26.2908	−	7.04460i	1.34516	−	0.360433i
$383$	−1.73622	−	6.47965i	−0.0887165	−	0.331095i	0.907275	−	0.420537i	$-0.138158\pi$
$383$	−1.73622	−	6.47965i	−0.0887165	−	0.331095i	−0.995992	+	0.0894422i	$0.971492\pi$
$384$	−0.258819	+	0.965926i	−0.0132078	+	0.0492922i
$385$	15.4567	+	14.6620i	0.787747	+	0.747242i
$386$	−1.07363	−	1.85959i	−0.0546465	−	0.0946505i
$387$			8.48799i			0.431469i
$388$	0.953822	−	3.55971i	0.0484230	−	0.180717i
$389$	−21.4686	−	12.3949i	−1.08850	−	0.628446i	−0.155324	−	0.987864i	$-0.549642\pi$
$389$	−21.4686	−	12.3949i	−1.08850	−	0.628446i	−0.933177	+	0.359417i	$0.882975\pi$
$390$	7.92493	−	3.44310i	0.401294	−	0.174348i
$391$			41.4772i			2.09759i
$392$	−6.65652	+	2.16580i	−0.336205	+	0.109389i
$393$	8.43733	−	14.6139i	0.425607	−	0.737173i
$394$	19.0126	+	10.9769i	0.957840	+	0.553009i
$395$	3.41991	+	12.7633i	0.172074	+	0.642190i
$396$	2.37595	+	2.37595i	0.119396	+	0.119396i
$397$	−14.8401	+	3.97640i	−0.744805	+	0.199570i	−0.611213	−	0.791467i	$-0.709318\pi$
$397$	−14.8401	+	3.97640i	−0.744805	+	0.199570i	−0.133592	+	0.991036i	$0.542651\pi$
$398$	17.7044	+	17.7044i	0.887443	+	0.887443i
$399$	−8.82047	−	14.3872i	−0.441576	−	0.720260i
$400$	−0.643487	−	0.371517i	−0.0321743	−	0.0185759i
$401$	12.3604	−	12.3604i	0.617249	−	0.617249i	−0.327576	−	0.944825i	$-0.606232\pi$
$401$	12.3604	−	12.3604i	0.617249	−	0.617249i	0.944825	+	0.327576i	$0.106232\pi$
$402$	−3.73394	+	6.46737i	−0.186232	+	0.322563i
$403$	−20.3019	−	8.00397i	−1.01131	−	0.398706i
$404$	4.19620	−	2.42268i	0.208769	−	0.120533i
$405$	0.620250	+	2.31481i	0.0308205	+	0.115024i
$406$	−9.91793	+	0.261710i	−0.492219	+	0.0129884i
$407$	−9.19932	+	5.31123i	−0.455994	+	0.263268i
$408$	−1.64883	+	6.15352i	−0.0816293	+	0.304645i
$409$	19.7210	−	19.7210i	0.975139	−	0.975139i	−0.0245594	−	0.999698i	$-0.507818\pi$
$409$	19.7210	−	19.7210i	0.975139	−	0.975139i	0.999698	+	0.0245594i	$0.00781828\pi$
$410$	15.4787	−	15.4787i	0.764436	−	0.764436i
$411$	−0.0755407	+	0.281922i	−0.00372615	+	0.0139062i
$412$	15.4024	−	8.89257i	0.758821	−	0.438106i
$413$	3.39460	+	5.53698i	0.167037	+	0.272457i
$414$	−1.68510	−	6.28888i	−0.0828181	−	0.309082i
$415$	−0.843638	+	0.487074i	−0.0414125	+	0.0239095i
$416$	−3.56610	+	0.531892i	−0.174843	+	0.0260782i
$417$	−4.38283	+	7.59129i	−0.214628	+	0.371747i
$418$	15.1549	−	15.1549i	0.741248	−	0.741248i
$419$	13.7060	+	7.91317i	0.669583	+	0.386584i	0.795919	−	0.605404i	$-0.206988\pi$
$419$	13.7060	+	7.91317i	0.669583	+	0.386584i	−0.126336	+	0.991988i	$0.540322\pi$
$420$	−0.167251	−	6.33824i	−0.00816099	−	0.309274i
$421$	13.1569	+	13.1569i	0.641228	+	0.641228i	0.950857	−	0.309629i	$-0.100205\pi$
$421$	13.1569	+	13.1569i	0.641228	+	0.641228i	−0.309629	+	0.950857i	$0.600205\pi$
$422$	−23.0497	+	6.17615i	−1.12204	+	0.300650i
$423$	5.86238	+	5.86238i	0.285039	+	0.285039i
$424$	−2.41166	−	9.00043i	−0.117120	−	0.437099i
$425$	−4.09939	−	2.36679i	−0.198850	−	0.114806i
$426$	−0.319084	+	0.552669i	−0.0154597	+	0.0267769i
$427$	14.4779	+	13.7335i	0.700636	+	0.664611i
$428$		−	13.3757i		−	0.646540i
$429$	−4.44346	+	11.2707i	−0.214532	+	0.544156i
$430$	17.6159	+	10.1706i	0.849516	+	0.490469i
$431$	−1.50900	+	5.63168i	−0.0726861	+	0.271268i	−0.992699	−	0.120621i	$-0.961512\pi$
$431$	−1.50900	+	5.63168i	−0.0726861	+	0.271268i	0.920013	+	0.391889i	$0.128178\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	−15.2205	−	26.3626i	−0.731449	−	1.26691i	−0.956264	−	0.292506i	$-0.905511\pi$
$433$	−15.2205	−	26.3626i	−0.731449	−	1.26691i	0.224814	−	0.974402i	$-0.427822\pi$
$434$	−11.0206	+	11.6180i	−0.529006	+	0.557681i
$435$	2.32589	−	8.68036i	0.111518	−	0.416191i
$436$	2.65649	+	9.91417i	0.127223	+	0.474803i
$437$	−40.1133	+	10.7483i	−1.91888	+	0.514162i
$438$	−11.0751			−0.529190
$439$	0.406139			0.0193840			0.00969198	−	0.999953i	$-0.496915\pi$
$439$	0.406139			0.0193840			0.00969198	+	0.999953i	$0.496915\pi$
$440$	7.77798	−	2.08410i	0.370801	−	0.0993557i
$441$	5.86916	−	3.81484i	0.279484	−	0.181659i
$442$	−22.7182	+	3.38847i	−1.08059	+	0.161173i
$443$	−9.26476	−	16.0470i	−0.440182	−	0.762418i	0.557521	−	0.830163i	$-0.311753\pi$
$443$	−9.26476	−	16.0470i	−0.440182	−	0.762418i	−0.997703	+	0.0677454i	$0.978419\pi$
$444$	3.05363	+	0.818218i	0.144919	+	0.0388309i
$445$	3.31060	+	5.73412i	0.156937	+	0.271824i
$446$	7.65836	−	13.2647i	0.362634	−	0.628101i
$447$	−2.93611	+	2.93611i	−0.138873	+	0.138873i
$448$	−0.617120	+	2.57277i	−0.0291562	+	0.121552i
$449$	−3.33970	−	0.894870i	−0.157610	−	0.0422315i	0.179151	−	0.983822i	$-0.442665\pi$
$449$	−3.33970	−	0.894870i	−0.157610	−	0.0422315i	−0.336761	+	0.941590i	$0.609332\pi$
$450$	0.717716	+	0.192312i	0.0338335	+	0.00906565i
$451$			30.6923i			1.44524i
$452$	−10.5455	+	6.08846i	−0.496020	+	0.286377i
$453$	9.17136	+	9.17136i	0.430908	+	0.430908i
$454$	−10.3928			−0.487758
$455$	20.7198	−	9.65951i	0.971359	−	0.452845i
$456$	−6.37844			−0.298698
$457$	1.91462	+	1.91462i	0.0895620	+	0.0895620i	0.750468	−	0.660906i	$-0.229828\pi$
$457$	1.91462	+	1.91462i	0.0895620	+	0.0895620i	−0.660906	+	0.750468i	$0.729828\pi$
$458$	−13.3562	+	7.71119i	−0.624093	+	0.360320i
$459$		−	6.37060i		−	0.297354i
$460$	−15.0711	−	4.03828i	−0.702692	−	0.188286i
$461$	−5.81853	−	1.55907i	−0.270996	−	0.0726132i	0.120762	−	0.992682i	$-0.461466\pi$
$461$	−5.81853	−	1.55907i	−0.270996	−	0.0726132i	−0.391758	+	0.920068i	$0.628133\pi$
$462$	6.44980	+	6.11817i	0.300072	+	0.284643i
$463$	7.99091	−	7.99091i	0.371369	−	0.371369i	−0.496607	−	0.867976i	$-0.665421\pi$
$463$	7.99091	−	7.99091i	0.371369	−	0.371369i	0.867976	+	0.496607i	$0.165421\pi$
$464$	−1.87496	+	3.24753i	−0.0870430	+	0.150763i
$465$	−7.25232	−	12.5614i	−0.336318	−	0.582520i
$466$	3.44513	+	0.923120i	0.159593	+	0.0427627i
$467$	6.03438	+	10.4519i	0.279238	+	0.483654i	0.971196	−	0.238284i	$-0.0765848\pi$
$467$	6.03438	+	10.4519i	0.279238	+	0.483654i	−0.691958	+	0.721938i	$0.743251\pi$
$468$	3.30693	−	1.43674i	0.152863	−	0.0664135i
$469$	−9.42428	+	17.3657i	−0.435173	+	0.801873i
$470$	19.1913	−	5.14228i	0.885227	−	0.237196i
$471$	9.04224			0.416644
$472$	2.45477			0.112990
$473$	−27.5487	+	7.38164i	−1.26669	+	0.339408i
$474$	1.42707	+	5.32588i	0.0655473	+	0.244626i
$475$	1.22665	−	4.57791i	0.0562825	−	0.210049i
$476$	−3.93142	+	16.3901i	−0.180196	+	0.751239i
$477$	4.65896	+	8.06956i	0.213319	+	0.369480i
$478$		−	19.6015i		−	0.896550i
$479$	−0.0759633	+	0.283499i	−0.00347085	+	0.0129534i	−0.967640	−	0.252337i	$-0.918801\pi$
$479$	−0.0759633	+	0.283499i	−0.00347085	+	0.0129534i	0.964169	+	0.265290i	$0.0854677\pi$
$480$	−2.07540	−	1.19823i	−0.0947285	−	0.0546915i
$481$	1.68150	+	11.2737i	0.0766698	+	0.514037i
$482$			27.7501i			1.26398i
$483$	−4.89571	−	16.5154i	−0.222762	−	0.751477i
$484$	−0.145136	+	0.251383i	−0.00659708	+	0.0114265i
$485$	7.64843	+	4.41583i	0.347298	+	0.200512i
$486$	0.258819	+	0.965926i	0.0117403	+	0.0438153i
$487$	0.783166	+	0.783166i	0.0354886	+	0.0354886i	0.724628	−	0.689140i	$-0.242011\pi$
$487$	0.783166	+	0.783166i	0.0354886	+	0.0354886i	−0.689140	+	0.724628i	$0.742011\pi$
$488$	7.28545	−	1.95213i	0.329797	−	0.0883687i
$489$	−7.06636	−	7.06636i	−0.319552	−	0.319552i
$490$	−0.884699	−	16.7519i	−0.0399666	−	0.756774i
$491$	−7.42479	−	4.28670i	−0.335076	−	0.193456i	0.323017	−	0.946393i	$-0.395303\pi$
$491$	−7.42479	−	4.28670i	−0.335076	−	0.193456i	−0.658092	+	0.752937i	$0.728636\pi$
$492$	6.45896	−	6.45896i	0.291192	−	0.291192i
$493$	−11.9446	+	20.6887i	−0.537960	+	0.931773i
$494$	−9.16419	−	21.0930i	−0.412316	−	0.949021i
$495$	−6.97354	+	4.02618i	−0.313437	+	0.180963i
$496$	1.56651	+	5.84629i	0.0703383	+	0.262506i
$497$	−0.805352	+	1.48399i	−0.0361250	+	0.0665659i
$498$	−0.352035	+	0.203247i	−0.0157750	+	0.00910773i
$499$	3.23373	−	12.0684i	0.144762	−	0.540258i	−0.855004	−	0.518621i	$-0.826446\pi$
$499$	3.23373	−	12.0684i	0.144762	−	0.540258i	0.999766	−	0.0216369i	$-0.00688777\pi$
$500$	−7.21366	+	7.21366i	−0.322605	+	0.322605i
$501$	−6.85001	+	6.85001i	−0.306036	+	0.306036i
$502$	5.33583	−	19.9136i	0.238150	−	0.888787i
$503$	9.79693	−	5.65626i	0.436823	−	0.252200i	−0.265426	−	0.964131i	$-0.585513\pi$
$503$	9.79693	−	5.65626i	0.436823	−	0.252200i	0.702249	+	0.711931i	$0.252179\pi$
$504$	−0.0697906	−	2.64483i	−0.00310872	−	0.117810i
$505$	3.00533	+	11.2161i	0.133736	+	0.499108i
$506$	18.9458	−	10.9383i	0.842242	−	0.486269i
$507$	9.50241	+	8.87153i	0.422017	+	0.393999i
$508$	−1.94179	+	3.36327i	−0.0861528	+	0.149221i
$509$	4.69237	−	4.69237i	0.207986	−	0.207986i	−0.595425	−	0.803411i	$-0.703016\pi$
$509$	4.69237	−	4.69237i	0.207986	−	0.207986i	0.803411	+	0.595425i	$0.203016\pi$
$510$	−13.2215	−	7.63345i	−0.585459	−	0.338015i
$511$	−29.2919	+	0.772940i	−1.29580	+	0.0341929i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	6.16110	−	1.65086i	0.272019	−	0.0728874i
$514$	16.2688	+	16.2688i	0.717586	+	0.717586i
$515$	11.0312	+	41.1691i	0.486095	+	1.81413i
$516$	7.35081	+	4.24399i	0.323601	+	0.186831i
$517$	−13.9287	+	24.1253i	−0.612585	+	1.06103i
$518$	8.13345	+	1.95093i	0.357363	+	0.0857191i
$519$		−	8.79475i		−	0.386047i
$520$	0.980649	−	8.58474i	0.0430043	−	0.376466i
$521$	−6.78078	−	3.91489i	−0.297071	−	0.171514i	0.344055	−	0.938949i	$-0.388199\pi$
$521$	−6.78078	−	3.91489i	−0.297071	−	0.171514i	−0.641127	+	0.767435i	$0.721533\pi$
$522$	0.970553	−	3.62215i	0.0424800	−	0.158537i
$523$			17.8376i			0.779984i	0.920818	+	0.389992i	$0.127522\pi$
$523$			17.8376i			0.779984i	−0.920818	+	0.389992i	$0.872478\pi$
$524$	−8.43733	−	14.6139i	−0.368587	−	0.638411i
$525$	1.91166	+	0.458542i	0.0834317	+	0.0200124i
$526$	2.80620	−	10.4729i	0.122356	−	0.456640i
$527$	9.97959	+	37.2443i	0.434718	+	1.62239i
$528$	3.24561	−	0.869658i	0.141247	−	0.0378470i
$529$	−19.3896			−0.843024
$530$	22.3301			0.969956
$531$	−2.37113	+	0.635342i	−0.102898	+	0.0275715i
$532$	−16.8699	+	0.445155i	−0.731403	+	0.0192999i
$533$	30.6392	+	12.0794i	1.32713	+	0.523218i
$534$	1.38145	+	2.39274i	0.0597813	+	0.103544i
$535$	30.9622	+	8.29629i	1.33861	+	0.358680i
$536$	3.73394	+	6.46737i	0.161282	+	0.279348i
$537$	−6.59322	+	11.4198i	−0.284518	+	0.492800i
$538$	−15.1468	+	15.1468i	−0.653027	+	0.653027i
$539$	17.4856	+	15.7314i	0.753159	+	0.677598i
$540$	2.31481	+	0.620250i	0.0996134	+	0.0266913i
$541$	9.30908	+	2.49436i	0.400229	+	0.107241i	0.453318	−	0.891349i	$-0.350240\pi$
$541$	9.30908	+	2.49436i	0.400229	+	0.107241i	−0.0530895	+	0.998590i	$0.516907\pi$
$542$			32.8294i			1.41014i
$543$	1.33067	−	0.768263i	0.0571046	−	0.0329693i
$544$	4.50469	+	4.50469i	0.193137	+	0.193137i
$545$	−24.5971			−1.05362
$546$	8.64599	−	4.03074i	0.370014	−	0.172500i
$547$	−1.49793			−0.0640470			−0.0320235	−	0.999487i	$-0.510195\pi$
$547$	−1.49793			−0.0640470			−0.0320235	+	0.999487i	$0.510195\pi$
$548$	0.206381	+	0.206381i	0.00881616	+	0.00881616i
$549$	−6.53195	+	3.77122i	−0.278777	+	0.160952i
$550$			2.49667i			0.106458i
$551$	−23.1037	−	6.19062i	−0.984251	−	0.263729i
$552$	−6.28888	−	1.68510i	−0.267672	−	0.0717226i
$553$	4.14604	+	13.9865i	0.176308	+	0.594764i
$554$	−12.6663	+	12.6663i	−0.538140	+	0.538140i
$555$	−3.78803	+	6.56107i	−0.160793	+	0.278502i
$556$	4.38283	+	7.59129i	0.185873	+	0.321942i
$557$	15.4723	+	4.14579i	0.655583	+	0.175663i	0.571252	−	0.820775i	$-0.306458\pi$
$557$	15.4723	+	4.14579i	0.655583	+	0.175663i	0.0843310	+	0.996438i	$0.473125\pi$
$558$	−3.02626	−	5.24164i	−0.128112	−	0.221896i
$559$	−3.47334	+	30.4061i	−0.146907	+	1.28604i
$560$	−5.57270	−	3.02428i	−0.235490	−	0.127799i
$561$	20.6765	−	5.54024i	0.872960	−	0.233909i
$562$	−10.6057			−0.447376
$563$	15.5033			0.653385			0.326692	−	0.945131i	$-0.394066\pi$
$563$	15.5033			0.653385			0.326692	+	0.945131i	$0.394066\pi$
$564$	8.00816	−	2.14578i	0.337204	−	0.0903537i
$565$	−7.55274	−	28.1872i	−0.317746	−	1.18585i
$566$	5.62615	−	20.9971i	0.236485	−	0.882573i
$567$	0.751945	+	2.53665i	0.0315787	+	0.106529i
$568$	0.319084	+	0.552669i	0.0133885	+	0.0231895i
$569$			35.1935i			1.47539i	0.675136	+	0.737694i	$0.264085\pi$
$569$			35.1935i			1.47539i	−0.675136	+	0.737694i	$0.735915\pi$
$570$	3.95623	−	14.7649i	0.165708	−	0.618432i
$571$	−0.873557	−	0.504348i	−0.0365572	−	0.0211063i	0.481610	−	0.876386i	$-0.340052\pi$
$571$	−0.873557	−	0.504348i	−0.0365572	−	0.0211063i	−0.518167	+	0.855279i	$0.673386\pi$
$572$	7.53900	+	9.48351i	0.315221	+	0.396526i
$573$			27.2183i			1.13706i
$574$	16.6321	−	17.5336i	0.694209	−	0.731839i
$575$	2.41885	−	4.18957i	0.100873	−	0.174717i
$576$	−0.866025	−	0.500000i	−0.0360844	−	0.0208333i
$577$	6.65759	+	24.8465i	0.277159	+	1.03437i	0.954381	+	0.298592i	$0.0965171\pi$
$577$	6.65759	+	24.8465i	0.277159	+	1.03437i	−0.677222	+	0.735779i	$0.736816\pi$
$578$	16.6767	+	16.6767i	0.693661	+	0.693661i
$579$	2.07410	−	0.555754i	0.0861967	−	0.0230963i
$580$	−6.35446	−	6.35446i	−0.263855	−	0.263855i
$581$	−0.916887	+	0.562123i	−0.0380389	+	0.0233208i
$582$	3.19155	+	1.84264i	0.132294	+	0.0763800i
$583$	−22.1389	+	22.1389i	−0.916901	+	0.916901i
$584$	−5.53757	+	9.59135i	−0.229146	+	0.396893i
$585$	1.27466	+	8.54603i	0.0527007	+	0.353335i
$586$	1.50584	−	0.869398i	0.0622058	−	0.0359145i
$587$	3.90487	+	14.5732i	0.161171	+	0.601499i	0.998498	+	0.0547955i	$0.0174507\pi$
$587$	3.90487	+	14.5732i	0.161171	+	0.601499i	−0.837327	+	0.546703i	$0.815883\pi$
$588$	−0.369168	−	6.99026i	−0.0152243	−	0.288273i
$589$	−33.4335	+	19.3028i	−1.37760	+	0.795359i
$590$	−1.52257	+	5.68232i	−0.0626834	+	0.233938i
$591$	−15.5237	+	15.5237i	−0.638560	+	0.638560i
$592$	2.23541	−	2.23541i	0.0918750	−	0.0918750i
$593$	7.61104	−	28.4048i	0.312548	−	1.16644i	−0.613703	−	0.789537i	$-0.710321\pi$
$593$	7.61104	−	28.4048i	0.312548	−	1.16644i	0.926251	−	0.376908i	$-0.123013\pi$
$594$	−2.90993	+	1.68005i	−0.119396	+	0.0689333i
$595$	−35.5014	−	19.2664i	−1.45542	−	0.789847i
$596$	1.07469	+	4.01080i	0.0440210	+	0.164289i
$597$	−21.6834	+	12.5189i	−0.887443	+	0.512366i
$598$	−3.46300	−	23.2179i	−0.141613	−	0.949451i
$599$	12.3677	−	21.4216i	0.505332	−	0.875261i	−0.494649	−	0.869093i	$-0.664703\pi$
$599$	12.3677	−	21.4216i	0.505332	−	0.875261i	0.999981	−	0.00616822i	$-0.00196342\pi$
$600$	0.525405	−	0.525405i	0.0214496	−	0.0214496i
$601$	7.62030	+	4.39958i	0.310838	+	0.179463i	0.647302	−	0.762234i	$-0.275897\pi$
$601$	7.62030	+	4.39958i	0.310838	+	0.179463i	−0.336463	+	0.941697i	$0.609231\pi$
$602$	19.7378	+	10.7116i	0.804454	+	0.436573i
$603$	−5.28059	−	5.28059i	−0.215042	−	0.215042i
$604$	12.5283	−	3.35695i	0.509769	−	0.136592i
$605$	−0.491881	−	0.491881i	−0.0199978	−	0.0199978i
$606$	1.25407	+	4.68026i	0.0509432	+	0.190122i
$607$	19.6033	+	11.3180i	0.795673	+	0.459382i	0.841956	−	0.539547i	$-0.181404\pi$
$607$	19.6033	+	11.3180i	0.795673	+	0.459382i	−0.0462832	+	0.998928i	$0.514738\pi$
$608$	−3.18922	+	5.52389i	−0.129340	+	0.224023i
$609$	2.31416	−	9.64772i	0.0937744	−	0.390945i
$610$			18.0752i			0.731843i
$611$	18.6016	+	23.3995i	0.752541	+	0.946641i
$612$	−5.51710	−	3.18530i	−0.223015	−	0.128758i
$613$	9.13560	−	34.0945i	0.368983	−	1.37707i	−0.492956	−	0.870054i	$-0.664084\pi$
$613$	9.13560	−	34.0945i	0.368983	−	1.37707i	0.861940	−	0.507011i	$-0.169250\pi$
$614$			14.9011i			0.601358i
$615$	10.9451	+	18.9574i	0.441347	+	0.764436i
$616$	8.52339	−	2.52661i	0.343417	−	0.101800i
$617$	9.32719	−	34.8095i	0.375498	−	1.40138i	−0.477117	−	0.878840i	$-0.658318\pi$
$617$	9.32719	−	34.8095i	0.375498	−	1.40138i	0.852615	−	0.522539i	$-0.175015\pi$
$618$	4.60313	+	17.1791i	0.185165	+	0.691046i
$619$	18.5078	−	4.95915i	0.743892	−	0.199325i	0.133085	−	0.991105i	$-0.457512\pi$
$619$	18.5078	−	4.95915i	0.743892	−	0.199325i	0.610807	+	0.791779i	$0.290845\pi$
$620$	−14.5046			−0.582520
$621$	6.51073			0.261266
$622$	0.0807678	−	0.0216417i	0.00323849	−	0.000867752i
$623$	3.82070	+	6.23199i	0.153073	+	0.249680i
$624$	0.409207	−	3.58225i	0.0163814	−	0.143405i
$625$	−14.0815	−	24.3899i	−0.563261	−	0.975597i
$626$	−24.2660	−	6.50206i	−0.969866	−	0.259875i
$627$	10.7161	+	18.5608i	0.427960	+	0.741248i
$628$	4.52112	−	7.83081i	0.180412	−	0.312483i
$629$	14.2409	−	14.2409i	0.567823	−	0.567823i
$630$	6.16556	+	1.47891i	0.245642	+	0.0589210i
$631$	−22.0223	−	5.90086i	−0.876694	−	0.234910i	−0.207714	−	0.978190i	$-0.566602\pi$
$631$	−22.0223	−	5.90086i	−0.876694	−	0.234910i	−0.668980	+	0.743280i	$0.733269\pi$
$632$	5.32588	+	1.42707i	0.211852	+	0.0567656i
$633$		−	23.8628i		−	0.948462i
$634$	17.3214	−	10.0005i	0.687920	−	0.397171i
$635$	−6.58093	−	6.58093i	−0.261156	−	0.261156i
$636$	9.31793			0.369480
$637$	22.5859	−	11.2640i	0.894885	−	0.446297i
$638$	12.6001			0.498844
$639$	−0.451253	−	0.451253i	−0.0178513	−	0.0178513i
$640$	−2.07540	+	1.19823i	−0.0820373	+	0.0473643i
$641$			10.0458i			0.396786i	0.980123	+	0.198393i	$0.0635723\pi$
$641$			10.0458i			0.396786i	−0.980123	+	0.198393i	$0.936428\pi$
$642$	12.9199	+	3.46189i	0.509910	+	0.136630i
$643$	19.2831	+	5.16690i	0.760452	+	0.203763i	0.618149	−	0.786061i	$-0.287883\pi$
$643$	19.2831	+	5.16690i	0.760452	+	0.203763i	0.142303	+	0.989823i	$0.454549\pi$
$644$	−16.7506	−	4.01790i	−0.660067	−	0.158327i
$645$	−14.3834	+	14.3834i	−0.566344	+	0.566344i
$646$	−20.3172	+	35.1905i	−0.799371	+	1.38455i
$647$	2.96052	+	5.12778i	0.116390	+	0.201594i	0.918335	−	0.395805i	$-0.129534\pi$
$647$	2.96052	+	5.12778i	0.116390	+	0.201594i	−0.801944	+	0.597399i	$0.796201\pi$
$648$	0.965926	+	0.258819i	0.0379452	+	0.0101674i
$649$	−4.12414	−	7.14323i	−0.161887	−	0.280396i
$650$	2.49235	+	0.982603i	0.0977579	+	0.0385409i
$651$	−8.36976	−	13.6520i	−0.328037	−	0.535066i
$652$	−9.65282	+	2.58647i	−0.378034	+	0.101294i
$653$	−21.2347			−0.830979			−0.415490	−	0.909598i	$-0.636390\pi$
$653$	−21.2347			−0.830979			−0.415490	+	0.909598i	$0.636390\pi$
$654$	−10.2639			−0.401351
$655$	39.0616	−	10.4665i	1.52626	−	0.408961i
$656$	−2.36414	−	8.82310i	−0.0923043	−	0.344484i
$657$	2.86646	−	10.6978i	0.111831	−	0.417359i
$658$	21.0305	−	6.23412i	0.819853	−	0.243031i
$659$	−18.8111	−	32.5818i	−0.732776	−	1.26920i	−0.955692	−	0.294367i	$-0.904891\pi$
$659$	−18.8111	−	32.5818i	−0.732776	−	1.26920i	0.222917	−	0.974838i	$-0.428442\pi$
$660$			8.05236i			0.313437i
$661$	−6.36003	+	23.7360i	−0.247377	+	0.923222i	0.724797	+	0.688962i	$0.241933\pi$
$661$	−6.36003	+	23.7360i	−0.247377	+	0.923222i	−0.972174	+	0.234260i	$0.924733\pi$
$662$	−9.89383	−	5.71220i	−0.384534	−	0.222011i
$663$	2.60689	−	22.8211i	0.101243	−	0.886298i
$664$			0.406494i			0.0157750i
$665$	9.43311	−	39.3266i	0.365800	−	1.52502i
$666$	−1.58068	+	2.73781i	−0.0612500	+	0.106088i
$667$	−21.1438	−	12.2074i	−0.818691	−	0.472672i
$668$	2.50728	+	9.35729i	0.0970095	+	0.362044i
$669$	10.8306	+	10.8306i	0.418734	+	0.418734i
$670$	−17.2867	+	4.63195i	−0.667843	+	0.178948i
$671$	−17.9205	−	17.9205i	−0.691812	−	0.691812i
$672$	−2.32539	−	1.26197i	−0.0897037	−	0.0486817i
$673$	−19.5012	−	11.2590i	−0.751715	−	0.434003i	0.0745983	−	0.997214i	$-0.476233\pi$
$673$	−19.5012	−	11.2590i	−0.751715	−	0.434003i	−0.826313	+	0.563211i	$0.809566\pi$
$674$	0.420327	−	0.420327i	0.0161904	−	0.0161904i
$675$	−0.371517	+	0.643487i	−0.0142997	+	0.0247678i
$676$	12.4342	−	3.79356i	0.478238	−	0.145906i
$677$	−32.8385	+	18.9593i	−1.26209	+	0.728666i	−0.973478	−	0.228781i	$-0.926526\pi$
$677$	−32.8385	+	18.9593i	−1.26209	+	0.728666i	−0.288609	+	0.957447i	$0.593193\pi$
$678$	−3.15162	−	11.7620i	−0.121037	−	0.451717i
$679$	8.56971	+	4.65074i	0.328875	+	0.178479i
$680$	−13.2215	+	7.63345i	−0.507022	+	0.292729i
$681$	2.68985	−	10.0387i	0.103075	−	0.384683i
$682$	14.3805	−	14.3805i	0.550657	−	0.550657i
$683$	8.92222	−	8.92222i	0.341399	−	0.341399i	−0.515494	−	0.856893i	$-0.672391\pi$
$683$	8.92222	−	8.92222i	0.341399	−	0.341399i	0.856893	+	0.515494i	$0.172391\pi$
$684$	1.65086	−	6.16110i	0.0631223	−	0.235576i
$685$	−0.605740	+	0.349724i	−0.0231441	+	0.0133623i
$686$	−1.46424	−	18.4623i	−0.0559050	−	0.704893i
$687$	−3.99160	−	14.8969i	−0.152289	−	0.568351i
$688$	7.35081	−	4.24399i	0.280247	−	0.161801i
$689$	13.3875	+	30.8137i	0.510022	+	1.17391i
$690$	7.80136	−	13.5123i	0.296993	−	0.514406i
$691$	−3.22936	+	3.22936i	−0.122851	+	0.122851i	−0.765859	−	0.643008i	$-0.777686\pi$
$691$	−3.22936	+	3.22936i	−0.122851	+	0.122851i	0.643008	+	0.765859i	$0.277686\pi$
$692$	−7.61648	−	4.39738i	−0.289535	−	0.167163i
$693$	−7.57903	+	4.64653i	−0.287903	+	0.176507i
$694$	−19.1686	−	19.1686i	−0.727629	−	0.727629i
$695$	−20.2908	+	5.43690i	−0.769674	+	0.206234i
$696$	−2.65160	−	2.65160i	−0.100509	−	0.100509i
$697$	−15.0610	−	56.2084i	−0.570476	−	2.12905i
$698$	−3.48998	−	2.01494i	−0.132098	−	0.0762667i
$699$	−1.78333	+	3.08882i	−0.0674518	+	0.116830i
$700$	1.35294	−	1.42628i	0.0511363	−	0.0539081i
$701$		−	35.0204i		−	1.32270i	−0.750077	−	0.661350i	$-0.769984\pi$
$701$		−	35.0204i		−	1.32270i	0.750077	−	0.661350i	$-0.230016\pi$
$702$	0.531892	+	3.56610i	0.0200750	+	0.134594i
$703$	17.4630	+	10.0823i	0.658629	+	0.380260i
$704$	0.869658	−	3.24561i	0.0327765	−	0.122323i
$705$			19.8683i			0.748282i
$706$	−9.45936	−	16.3841i	−0.356008	−	0.616624i
$707$	3.64344	+	12.2910i	0.137026	+	0.462249i
$708$	−0.635342	+	2.37113i	−0.0238776	+	0.0891125i
$709$	−12.7524	−	47.5926i	−0.478926	−	1.78738i	−0.605979	−	0.795481i	$-0.707218\pi$
$709$	−12.7524	−	47.5926i	−0.478926	−	1.78738i	0.127052	−	0.991896i	$-0.459448\pi$
$710$	−1.47723	+	0.395824i	−0.0554396	+	0.0148550i
$711$	−5.51376			−0.206782
$712$	2.76290			0.103544
$713$	−38.0636	+	10.1991i	−1.42549	+	0.381959i
$714$	−14.8141	−	8.03953i	−0.554403	−	0.300872i
$715$	−26.6286	+	11.5692i	−0.995851	+	0.432662i
$716$	6.59322	+	11.4198i	0.246400	+	0.426777i
$717$	18.9336	+	5.07323i	0.707087	+	0.189463i
$718$	3.73372	+	6.46699i	0.139341	+	0.241346i
$719$	16.0766	−	27.8454i	0.599554	−	1.03846i	−0.393333	−	0.919396i	$-0.628678\pi$
$719$	16.0766	−	27.8454i	0.599554	−	1.03846i	0.992887	−	0.119062i	$-0.0379888\pi$
$720$	1.69456	−	1.69456i	0.0631523	−	0.0631523i
$721$	13.3735	+	45.1146i	0.498053	+	1.68016i
$722$	−20.9457	−	5.61237i	−0.779517	−	0.208871i
$723$	−26.8046	−	7.18226i	−0.996872	−	0.267111i
$724$		−	1.53653i		−	0.0571046i
$725$	2.41303	−	1.39316i	0.0896177	−	0.0517408i
$726$	−0.205253	−	0.205253i	−0.00761766	−	0.00761766i
$727$	−19.7580			−0.732783			−0.366392	−	0.930461i	$-0.619407\pi$
$727$	−19.7580			−0.732783			−0.366392	+	0.930461i	$0.619407\pi$
$728$	0.832275	−	9.50302i	0.0308462	−	0.352205i
$729$	−1.00000			−0.0370370
$730$	−18.7674	−	18.7674i	−0.694614	−	0.694614i
$731$	46.8290	−	27.0368i	1.73203	−	0.999991i
$732$			7.54245i			0.278777i
$733$	−0.868590	−	0.232738i	−0.0320821	−	0.00859637i	0.242742	−	0.970091i	$-0.421953\pi$
$733$	−0.868590	−	0.232738i	−0.0320821	−	0.00859637i	−0.274824	+	0.961494i	$0.588620\pi$
$734$	35.2033	+	9.43268i	1.29938	+	0.348167i
$735$	16.4101	+	3.48116i	0.605294	+	0.128404i
$736$	−4.60378	+	4.60378i	−0.169698	+	0.169698i
$737$	12.5464	−	21.7310i	0.462153	−	0.800472i
$738$	4.56717	+	7.91058i	0.168120	+	0.291192i
$739$	8.73543	+	2.34065i	0.321338	+	0.0861023i	0.415882	−	0.909418i	$-0.363473\pi$
$739$	8.73543	+	2.34065i	0.321338	+	0.0861023i	−0.0945444	+	0.995521i	$0.530139\pi$
$740$	3.78803	+	6.56107i	0.139251	+	0.241190i
$741$	22.7462	−	3.39264i	0.835602	−	0.124632i
$742$	24.6443	−	0.650303i	0.904722	−	0.0238734i
$743$	−10.6974	+	2.86636i	−0.392450	+	0.105157i	−0.449647	−	0.893206i	$-0.648450\pi$
$743$	−10.6974	+	2.86636i	−0.392450	+	0.105157i	0.0571974	+	0.998363i	$0.481784\pi$
$744$	−6.05252			−0.221896
$745$	−9.95079			−0.364569
$746$	12.2892	−	3.29288i	0.449940	−	0.120561i
$747$	−0.105209	−	0.392643i	−0.00384938	−	0.0143661i
$748$	5.54024	−	20.6765i	0.202571	−	0.756006i
$749$	34.4127	+	8.25442i	1.25741	+	0.301610i
$750$	−5.10083	−	8.83490i	−0.186256	−	0.322605i
$751$			4.91530i			0.179362i	0.995971	+	0.0896810i	$0.0285848\pi$
$751$			4.91530i			0.179362i	−0.995971	+	0.0896810i	$0.971415\pi$
$752$	2.14578	−	8.00816i	0.0782486	−	0.292028i
$753$	17.8540	+	10.3080i	0.650637	+	0.375645i
$754$	4.95898	−	12.5783i	0.180595	−	0.458075i
$755$			31.0827i			1.13122i
$756$	2.57277	+	0.617120i	0.0935709	+	0.0224444i
$757$	−13.0641	+	22.6277i	−0.474822	+	0.822416i	−0.999584	−	0.0288326i	$-0.990821\pi$
$757$	−13.0641	+	22.6277i	−0.474822	+	0.822416i	0.524762	+	0.851249i	$0.324154\pi$
$758$	−4.77248	−	2.75540i	−0.173344	−	0.100080i
$759$	5.66210	+	21.1313i	0.205521	+	0.767016i
$760$	−10.8086	−	10.8086i	−0.392070	−	0.392070i
$761$	−12.0319	+	3.22395i	−0.436158	+	0.116868i	−0.470215	−	0.882552i	$-0.655824\pi$
$761$	−12.0319	+	3.22395i	−0.436158	+	0.116868i	0.0340575	+	0.999420i	$0.489157\pi$
$762$	−2.74610	−	2.74610i	−0.0994807	−	0.0994807i
$763$	−27.1463	+	0.716324i	−0.982762	+	0.0259327i
$764$	23.5717	+	13.6091i	0.852794	+	0.492361i
$765$	10.7953	−	10.7953i	0.390306	−	0.390306i
$766$	3.35411	−	5.80950i	0.121189	−	0.209906i
$767$	−8.75398	+	1.30568i	−0.316088	+	0.0471452i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	9.34074	+	34.8601i	0.336836	+	1.25709i	0.901865	+	0.432017i	$0.142198\pi$
$769$	9.34074	+	34.8601i	0.336836	+	1.25709i	−0.565030	+	0.825070i	$0.691135\pi$
$770$	0.561978	+	21.2971i	0.0202523	+	0.767495i
$771$	−19.9251	+	11.5038i	−0.717586	+	0.414298i
$772$	0.555754	−	2.07410i	0.0200020	−	0.0746485i
$773$	18.1883	−	18.1883i	0.654186	−	0.654186i	−0.299812	−	0.953998i	$-0.596924\pi$
$773$	18.1883	−	18.1883i	0.654186	−	0.654186i	0.953998	+	0.299812i	$0.0969239\pi$
$774$	−6.00191	+	6.00191i	−0.215734	+	0.215734i
$775$	1.16397	−	4.34399i	0.0418110	−	0.156041i
$776$	3.19155	−	1.84264i	0.114570	−	0.0661470i
$777$	−3.98955	+	7.35137i	−0.143124	+	0.263729i
$778$	−6.41607	−	23.9451i	−0.230027	−	0.858474i
$779$	50.4572	−	29.1315i	1.80782	−	1.04374i
$780$	8.03841	+	3.16913i	0.287821	+	0.113473i
$781$	1.07215	−	1.85702i	0.0383647	−	0.0664496i
$782$	−29.3288	+	29.3288i	−1.04880	+	1.04880i
$783$	3.24753	+	1.87496i	0.116057	+	0.0670058i
$784$	−6.23833	−	3.17542i	−0.222797	−	0.113408i
$785$	15.3226	+	15.3226i	0.546886	+	0.546886i
$786$	16.2997	−	4.36749i	0.581390	−	0.155783i
$787$	−13.7002	−	13.7002i	−0.488358	−	0.488358i	0.419430	−	0.907788i	$-0.362230\pi$
$787$	−13.7002	−	13.7002i	−0.488358	−	0.488358i	−0.907788	+	0.419430i	$0.862230\pi$
$788$	5.68207	+	21.2058i	0.202415	+	0.755424i
$789$	9.38974	+	5.42117i	0.334284	+	0.192999i
$790$	−6.60676	+	11.4432i	−0.235058	+	0.407132i
$791$	−9.15638	−	30.8886i	−0.325563	−	1.09827i
$792$			3.36010i			0.119396i
$793$	−24.9423	+	10.8366i	−0.885728	+	0.384818i
$794$	−13.3053	−	7.68182i	−0.472187	−	0.272617i
$795$	−5.77945	+	21.5692i	−0.204976	+	0.764980i
$796$			25.0379i			0.887443i
$797$	−26.4379	−	45.7917i	−0.936477	−	1.62203i	−0.771978	−	0.635649i	$-0.780733\pi$
$797$	−26.4379	−	45.7917i	−0.936477	−	1.62203i	−0.164499	−	0.986377i	$-0.552601\pi$
$798$	3.93627	−	16.4103i	0.139342	−	0.580918i
$799$	13.6699	−	51.0168i	0.483606	−	1.80484i
$800$	−0.192312	−	0.717716i	−0.00679924	−	0.0253751i
$801$	−2.66876	+	0.715092i	−0.0942960	+	0.0252665i
$802$	17.4802			0.617249
$803$	37.2136			1.31324
$804$	−7.21342	+	1.93283i	−0.254398	+	0.0681656i
$805$	19.6902	−	36.2823i	0.693990	−	1.27878i
$806$	−8.69592	−	20.0152i	−0.306301	−	0.705007i
$807$	−10.7104	−	18.5510i	−0.377025	−	0.653027i
$808$	4.68026	+	1.25407i	0.164651	+	0.0441181i
$809$	−18.8244	−	32.6048i	−0.661830	−	1.14632i	−0.980134	−	0.198334i	$-0.936447\pi$
$809$	−18.8244	−	32.6048i	−0.661830	−	1.14632i	0.318305	−	0.947988i	$-0.396886\pi$
$810$	−1.19823	+	2.07540i	−0.0421016	+	0.0729220i
$811$	9.93129	−	9.93129i	0.348735	−	0.348735i	−0.510903	−	0.859638i	$-0.670689\pi$
$811$	9.93129	−	9.93129i	0.348735	−	0.348735i	0.859638	+	0.510903i	$0.170689\pi$
$812$	−7.19809	−	6.82798i	−0.252603	−	0.239615i
$813$	−31.7107	−	8.49687i	−1.11214	−	0.297998i
$814$	−10.2605	−	2.74930i	−0.359631	−	0.0963628i
$815$		−	23.9487i		−	0.838885i
$816$	−5.51710	+	3.18530i	−0.193137	+	0.111508i
$817$	38.2829	+	38.2829i	1.33935	+	1.33935i
$818$	27.8897			0.975139
$819$	1.65565	+	9.39462i	0.0578529	+	0.328275i
$820$	21.8901			0.764436
$821$	−16.4516	−	16.4516i	−0.574163	−	0.574163i	0.359126	−	0.933289i	$-0.383075\pi$
$821$	−16.4516	−	16.4516i	−0.574163	−	0.574163i	−0.933289	+	0.359126i	$0.883075\pi$
$822$	−0.252764	+	0.145933i	−0.00881616	+	0.00509001i
$823$		−	2.08894i		−	0.0728159i	−0.999337	−	0.0364079i	$-0.988408\pi$
$823$		−	2.08894i		−	0.0728159i	0.999337	−	0.0364079i	$-0.0115916\pi$
$824$	17.1791	+	4.60313i	0.598463	+	0.160358i
$825$	−2.41160	−	0.646186i	−0.0839611	−	0.0224973i
$826$	−1.51489	+	6.31558i	−0.0527098	+	0.219747i
$827$	−28.8903	+	28.8903i	−1.00461	+	1.00461i	−0.00462441	+	0.999989i	$0.501472\pi$
$827$	−28.8903	+	28.8903i	−1.00461	+	1.00461i	−0.999989	+	0.00462441i	$0.998528\pi$
$828$	3.25536	−	5.63845i	0.113132	−	0.195950i
$829$	−28.0319	−	48.5526i	−0.973587	−	1.68630i	−0.684520	−	0.728994i	$-0.739988\pi$
$829$	−28.0319	−	48.5526i	−0.973587	−	1.68630i	−0.289067	−	0.957309i	$-0.593345\pi$
$830$	−0.940956	−	0.252128i	−0.0326610	−	0.00875150i
$831$	−8.95644	−	15.5130i	−0.310695	−	0.538140i
$832$	−2.89772	−	2.14551i	−0.100460	−	0.0743822i
$833$	−39.7418	−	20.2293i	−1.37697	−	0.700904i
$834$	−8.46698	+	2.26872i	−0.293187	+	0.0785594i
$835$	−23.2154			−0.803403
$836$	21.4322			0.741248
$837$	5.84629	−	1.56651i	0.202077	−	0.0541464i
$838$	4.09616	+	15.2871i	0.141500	+	0.528083i
$839$	−7.10574	+	26.5190i	−0.245317	+	0.915537i	0.727906	+	0.685677i	$0.240494\pi$
$839$	−7.10574	+	26.5190i	−0.245317	+	0.915537i	−0.973224	+	0.229860i	$0.926173\pi$
$840$	4.36355	−	4.60008i	0.150557	−	0.158718i
$841$	7.46902	+	12.9367i	0.257552	+	0.446094i
$842$			18.6067i			0.641228i
$843$	2.74497	−	10.2444i	0.0945417	−	0.352834i
$844$	−20.6658	−	11.9314i	−0.711346	−	0.410696i
$845$	1.06906	+	31.1357i	0.0367768	+	1.07110i
$846$			8.29066i			0.285039i
$847$	−0.557184	−	0.528535i	−0.0191451	−	0.0181607i
$848$	4.65896	−	8.06956i	0.159989	−	0.277110i
$849$	18.8255	+	10.8689i	0.646088	+	0.373019i
$850$	−1.22514	−	4.57228i	−0.0420219	−	0.156828i
$851$	14.5542	+	14.5542i	0.498911	+	0.498911i
$852$	−0.616423	+	0.165170i	−0.0211183	+	0.00565863i
$853$	2.37750	+	2.37750i	0.0814041	+	0.0814041i	0.746636	−	0.665232i	$-0.231668\pi$
$853$	2.37750	+	2.37750i	0.0814041	+	0.0814041i	−0.665232	+	0.746636i	$0.731668\pi$
$854$	0.526392	+	19.9485i	0.0180128	+	0.682624i
$855$	13.2378	+	7.64285i	0.452723	+	0.261380i
$856$	9.45806	−	9.45806i	0.323270	−	0.323270i
$857$	−0.305713	+	0.529511i	−0.0104430	+	0.0180878i	−0.871200	−	0.490929i	$-0.836657\pi$
$857$	−0.305713	+	0.529511i	−0.0104430	+	0.0180878i	0.860757	+	0.509017i	$0.169991\pi$
$858$	−11.1116	+	4.82760i	−0.379344	+	0.164812i
$859$	36.0041	−	20.7870i	1.22844	−	0.709243i	0.261740	−	0.965138i	$-0.415704\pi$
$859$	36.0041	−	20.7870i	1.22844	−	0.709243i	0.966704	+	0.255896i	$0.0823704\pi$
$860$	5.26468	+	19.6480i	0.179524	+	0.669992i
$861$	12.6315	+	20.6034i	0.430480	+	0.702162i
$862$	−5.04922	+	2.91517i	−0.171977	+	0.0992911i
$863$	−5.26746	+	19.6584i	−0.179306	+	0.669180i	0.816472	+	0.577386i	$0.195927\pi$
$863$	−5.26746	+	19.6584i	−0.179306	+	0.669180i	−0.995778	+	0.0917948i	$0.970740\pi$
$864$	0.707107	−	0.707107i	0.0240563	−	0.0240563i
$865$	14.9032	−	14.9032i	0.506724	−	0.506724i
$866$	7.87870	−	29.4037i	0.267729	−	0.999179i
$867$	−20.4248	+	11.7922i	−0.693661	+	0.400486i
$868$	−16.0079	+	0.422409i	−0.543343	+	0.0143375i
$869$	−4.79508	−	17.8955i	−0.162662	−	0.607063i
$870$	7.78260	−	4.49328i	0.263855	−	0.152337i
$871$	−16.7556	−	21.0773i	−0.567740	−	0.714176i
$872$	−5.13195	+	8.88880i	−0.173790	+	0.301013i
$873$	−2.60589	+	2.60589i	−0.0881960	+	0.0881960i
$874$	−35.9646	−	20.7641i	−1.21652	−	0.702358i
$875$	−14.1074	−	23.0108i	−0.476918	−	0.777908i
$876$	−7.83130	−	7.83130i	−0.264595	−	0.264595i
$877$	−35.9775	+	9.64015i	−1.21488	+	0.325525i	−0.808673	−	0.588258i	$-0.799814\pi$
$877$	−35.9775	+	9.64015i	−1.21488	+	0.325525i	−0.406202	+	0.913783i	$0.633147\pi$
$878$	0.287184	+	0.287184i	0.00969198	+	0.00969198i
$879$	0.450034	+	1.67955i	0.0151793	+	0.0566498i
$880$	6.97354	+	4.02618i	0.235078	+	0.135722i
$881$	−20.6694	+	35.8005i	−0.696371	+	1.20615i	0.273346	+	0.961916i	$0.411870\pi$
$881$	−20.6694	+	35.8005i	−0.696371	+	1.20615i	−0.969716	+	0.244233i	$0.921464\pi$
$882$	6.84762	+	1.45262i	0.230571	+	0.0489123i
$883$			5.80574i			0.195379i	0.995217	+	0.0976894i	$0.0311452\pi$
$883$			5.80574i			0.195379i	−0.995217	+	0.0976894i	$0.968855\pi$
$884$	−18.4602	−	13.6682i	−0.620884	−	0.459711i
$885$	−5.09463	−	2.94139i	−0.171254	−	0.0988737i
$886$	4.79579	−	17.8981i	0.161118	−	0.601300i
$887$			22.0847i			0.741532i	0.928726	+	0.370766i	$0.120905\pi$
$887$			22.0847i			0.741532i	−0.928726	+	0.370766i	$0.879095\pi$
$888$	1.58068	+	2.73781i	0.0530440	+	0.0918750i
$889$	−7.45462	−	7.07132i	−0.250020	−	0.237164i
$890$	−1.71369	+	6.39559i	−0.0574431	+	0.214380i
$891$	−0.869658	−	3.24561i	−0.0291346	−	0.108732i
$892$	14.7948	−	3.96426i	0.495367	−	0.132733i
$893$	52.8815			1.76961
$894$	−4.15228			−0.138873
$895$	−30.5240	+	8.17889i	−1.02031	+	0.273390i
$896$	−2.25560	+	1.38286i	−0.0753541	+	0.0461980i
$897$	23.3231	+	2.66423i	0.778735	+	0.0889562i
$898$	−1.72876	−	2.99429i	−0.0576893	−	0.0999208i
$899$	−21.9232	−	5.87429i	−0.731178	−	0.195919i
$900$	0.371517	+	0.643487i	0.0123839	+	0.0214496i
$901$	29.6804	−	51.4079i	0.988797	−	1.71265i
$902$	−21.7027	+	21.7027i	−0.722622	+	0.722622i
$903$	−15.4552	+	16.2929i	−0.514316	+	0.542194i
$904$	−11.7620	−	3.15162i	−0.391199	−	0.104821i
$905$	3.55676	+	0.953031i	0.118231	+	0.0316798i
$906$			12.9703i			0.430908i
$907$	8.29878	−	4.79131i	0.275557	−	0.159093i	−0.355854	−	0.934542i	$-0.615810\pi$
$907$	8.29878	−	4.79131i	0.275557	−	0.159093i	0.631410	+	0.775449i	$0.282476\pi$
$908$	−7.34882	−	7.34882i	−0.243879	−	0.243879i
$909$	−4.84536			−0.160710
$910$	21.4814	+	7.82080i	0.712102	+	0.259257i
$911$	34.0329			1.12756			0.563780	−	0.825925i	$-0.309347\pi$
$911$	34.0329			1.12756			0.563780	+	0.825925i	$0.309347\pi$
$912$	−4.51024	−	4.51024i	−0.149349	−	0.149349i
$913$	1.18287	−	0.682931i	0.0391473	−	0.0226017i
$914$			2.70768i			0.0895620i
$915$	−17.4593	−	4.67821i	−0.577187	−	0.154657i
$916$	−14.8969	−	3.99160i	−0.492206	−	0.131886i
$917$	42.8051	−	12.6888i	1.41355	−	0.419022i
$918$	4.50469	−	4.50469i	0.148677	−	0.148677i
$919$	18.7467	−	32.4703i	0.618398	−	1.07110i	−0.371380	−	0.928481i	$-0.621115\pi$
$919$	18.7467	−	32.4703i	0.618398	−	1.07110i	0.989778	−	0.142616i	$-0.0455514\pi$
$920$	−7.80136	−	13.5123i	−0.257203	−	0.445489i
$921$	−14.3933	−	3.85668i	−0.474276	−	0.127082i
$922$	−3.01189	−	5.21675i	−0.0991914	−	0.171805i
$923$	−1.43185	−	1.80116i	−0.0471298	−	0.0592858i
$924$	0.234503	+	8.88690i	0.00771459	+	0.292357i
$925$	−2.26896	+	0.607965i	−0.0746028	+	0.0199898i
$926$	11.3009			0.371369
$927$	−17.7851			−0.584141
$928$	−3.62215	+	0.970553i	−0.118903	+	0.0318600i
$929$	9.34416	+	34.8729i	0.306572	+	1.14414i	0.931584	+	0.363527i	$0.118427\pi$
$929$	9.34416	+	34.8729i	0.306572	+	1.14414i	−0.625012	+	0.780615i	$0.714906\pi$
$930$	3.75408	−	14.0104i	0.123101	−	0.459419i
$931$	9.26547	−	43.6772i	0.303664	−	1.43146i
$932$	1.78333	+	3.08882i	0.0584149	+	0.101178i
$933$			0.0836170i			0.00273750i
$934$	−3.12363	+	11.6575i	−0.102208	+	0.381446i
$935$	44.4256	+	25.6491i	1.45287	+	0.838817i
$936$	3.35428	+	1.32242i	0.109638	+	0.0432246i
$937$		−	40.1007i		−	1.31003i	−0.755615	−	0.655016i	$-0.772662\pi$
$937$		−	40.1007i		−	1.31003i	0.755615	−	0.655016i	$-0.227338\pi$
$938$	−18.9434	+	5.61543i	−0.618523	+	0.183350i
$939$	12.5610	−	21.7563i	0.409914	−	0.709991i
$940$	17.2064	+	9.93413i	0.561211	+	0.324016i
$941$	−3.73995	−	13.9577i	−0.121919	−	0.455007i	0.877792	−	0.479041i	$-0.159016\pi$
$941$	−3.73995	−	13.9577i	−0.121919	−	0.455007i	−0.999711	+	0.0240342i	$0.992349\pi$
$942$	6.39383	+	6.39383i	0.208322	+	0.208322i
$943$	57.4448	−	15.3923i	1.87066	−	0.501242i
$944$	1.73579	+	1.73579i	0.0564951	+	0.0564951i
$945$	−3.02428	+	5.57270i	−0.0983797	+	0.181280i
$946$	−24.6995	−	14.2602i	−0.803049	−	0.463640i
$947$	−1.82834	+	1.82834i	−0.0594130	+	0.0594130i	−0.736189	−	0.676776i	$-0.763377\pi$
$947$	−1.82834	+	1.82834i	−0.0594130	+	0.0594130i	0.676776	+	0.736189i	$0.263377\pi$
$948$	−2.75688	+	4.77505i	−0.0895392	+	0.155086i
$949$	14.6460	−	37.1491i	0.475428	−	1.20591i
$950$	4.10444	−	2.36970i	0.133166	−	0.0768833i
$951$	5.17664	+	19.3195i	0.167864	+	0.626477i
$952$	−14.3695	+	8.80961i	−0.465718	+	0.285521i
$953$	−10.9952	+	6.34808i	−0.356169	+	0.205634i	−0.667399	−	0.744700i	$-0.732592\pi$
$953$	−10.9952	+	6.34808i	−0.356169	+	0.205634i	0.311230	+	0.950335i	$0.399259\pi$
$954$	−2.41166	+	9.00043i	−0.0780803	+	0.291400i
$955$	−46.1228	+	46.1228i	−1.49250	+	1.49250i
$956$	13.8603	−	13.8603i	0.448275	−	0.448275i
$957$	−3.26116	+	12.1708i	−0.105418	+	0.393426i
$958$	−0.254178	+	0.146750i	−0.00821212	+	0.00474127i
$959$	−0.658333	+	0.403610i	−0.0212587	+	0.0130332i
$960$	−0.620250	−	2.31481i	−0.0200185	−	0.0747100i
$961$	−4.87833	+	2.81650i	−0.157365	+	0.0908550i
$962$	−6.78272	+	9.16072i	−0.218684	+	0.295353i
$963$	−6.68786	+	11.5837i	−0.215513	+	0.373280i
$964$	−19.6223	+	19.6223i	−0.631992	+	0.631992i
$965$	4.45643	+	2.57292i	0.143458	+	0.0828253i
$966$	8.21637	−	15.1400i	0.264357	−	0.487120i
$967$	−32.9354	−	32.9354i	−1.05913	−	1.05913i	−0.998138	−	0.0609945i	$-0.980573\pi$
$967$	−32.9354	−	32.9354i	−1.05913	−	1.05913i	−0.0609945	−	0.998138i	$-0.519427\pi$
$968$	−0.280381	+	0.0751278i	−0.00901178	+	0.00241470i
$969$	−28.7329	−	28.7329i	−0.923034	−	0.923034i
$970$	2.28580	+	8.53072i	0.0733926	+	0.273905i
$971$	27.4791	+	15.8651i	0.881847	+	0.509135i	0.871267	−	0.490809i	$-0.163299\pi$
$971$	27.4791	+	15.8651i	0.881847	+	0.509135i	0.0105803	+	0.999944i	$0.496632\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	−22.2354	+	6.59130i	−0.712834	+	0.211307i
$974$			1.10756i			0.0354886i
$975$	−1.59419	+	2.15311i	−0.0510549	+	0.0689546i
$976$	6.53195	+	3.77122i	0.209083	+	0.120714i
$977$	−14.8911	+	55.5742i	−0.476407	+	1.77798i	0.139569	+	0.990212i	$0.455428\pi$
$977$	−14.8911	+	55.5742i	−0.476407	+	1.77798i	−0.615977	+	0.787764i	$0.711239\pi$
$978$		−	9.99334i		−	0.319552i
$979$	−4.64182	−	8.03986i	−0.148353	−	0.256955i
$980$	11.2198	−	12.4710i	0.358403	−	0.398370i
$981$	2.65649	−	9.91417i	0.0848153	−	0.316535i
$982$	−2.21896	−	8.28127i	−0.0708099	−	0.264266i
$983$	28.4616	−	7.62627i	0.907785	−	0.243240i	0.225429	−	0.974260i	$-0.427622\pi$
$983$	28.4616	−	7.62627i	0.907785	−	0.243240i	0.682357	+	0.731019i	$0.260955\pi$
$984$	9.13435			0.291192
$985$	−52.6116			−1.67634
$986$	−23.0753	+	6.18300i	−0.734866	+	0.196907i
$987$	0.578610	+	21.9274i	0.0184174	+	0.697957i
$988$	8.43498	−	21.3951i	0.268352	−	0.680669i
$989$	27.6315	+	47.8591i	0.878630	+	1.52183i
$990$	−7.77798	−	2.08410i	−0.247200	−	0.0662371i
$991$	−24.3070	−	42.1009i	−0.772137	−	1.33738i	−0.936390	−	0.350962i	$-0.885855\pi$
$991$	−24.3070	−	42.1009i	−0.772137	−	1.33738i	0.164253	−	0.986418i	$-0.447479\pi$
$992$	−3.02626	+	5.24164i	−0.0960839	+	0.166422i
$993$	8.07828	−	8.07828i	0.256356	−	0.256356i
$994$	−1.61881	+	0.479867i	−0.0513454	+	0.0152205i
$995$	−57.9578	−	15.5297i	−1.83738	−	0.492326i
$996$	−0.392643	−	0.105209i	−0.0124414	−	0.00333366i
$997$		−	10.7862i		−	0.341603i	−0.985305	−	0.170801i	$-0.945364\pi$
$997$		−	10.7862i		−	0.341603i	0.985305	−	0.170801i	$-0.0546356\pi$
$998$	10.8203	−	6.24709i	0.342510	−	0.197748i
$999$	−2.23541	−	2.23541i	−0.0707254	−	0.0707254i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.cg.b.241.6	yes	40
7.5	odd	6		546.2.by.b.397.6	✓	40
13.2	odd	12		546.2.by.b.535.6	yes	40
91.54	even	12	inner	546.2.cg.b.145.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.397.6	✓	40	7.5	odd	6
546.2.by.b.535.6	yes	40	13.2	odd	12
546.2.cg.b.145.6	yes	40	91.54	even	12	inner
546.2.cg.b.241.6	yes	40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(-2.31481 - 0.620250i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(-2.57277 - 0.617120i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(-2.31481 - 0.620250i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(-2.57277 - 0.617120i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.19823 - 2.07540i) q^{10} +(3.24561 + 0.869658i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(2.14551 - 2.89772i) q^{13} +(-1.38286 - 2.25560i) q^{14} +(2.31481 - 0.620250i) q^{15} -1.00000 q^{16} -6.37060 q^{17} +(0.965926 - 0.258819i) q^{18} +(-1.65086 - 6.16110i) q^{19} +(0.620250 - 2.31481i) q^{20} +(2.53665 - 0.751945i) q^{21} +(1.68005 + 2.90993i) q^{22} -6.51073i q^{23} +(0.258819 - 0.965926i) q^{24} +(0.643487 + 0.371517i) q^{25} +(3.56610 - 0.531892i) q^{26} +1.00000i q^{27} +(0.617120 - 2.57277i) q^{28} +(1.87496 - 3.24753i) q^{29} +(2.07540 + 1.19823i) q^{30} +(-1.56651 - 5.84629i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.24561 + 0.869658i) q^{33} +(-4.50469 - 4.50469i) q^{34} +(5.57270 + 3.02428i) q^{35} +(0.866025 + 0.500000i) q^{36} +(-2.23541 + 2.23541i) q^{37} +(3.18922 - 5.52389i) q^{38} +(-0.409207 + 3.58225i) q^{39} +(2.07540 - 1.19823i) q^{40} +(2.36414 + 8.82310i) q^{41} +(2.32539 + 1.26197i) q^{42} +(-7.35081 + 4.24399i) q^{43} +(-0.869658 + 3.24561i) q^{44} +(-1.69456 + 1.69456i) q^{45} +(4.60378 - 4.60378i) q^{46} +(-2.14578 + 8.00816i) q^{47} +(0.866025 - 0.500000i) q^{48} +(6.23833 + 3.17542i) q^{49} +(0.192312 + 0.717716i) q^{50} +(5.51710 - 3.18530i) q^{51} +(2.89772 + 2.14551i) q^{52} +(-4.65896 + 8.06956i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(-6.97354 - 4.02618i) q^{55} +(2.25560 - 1.38286i) q^{56} +(4.51024 + 4.51024i) q^{57} +(3.62215 - 0.970553i) q^{58} +(-1.73579 - 1.73579i) q^{59} +(0.620250 + 2.31481i) q^{60} +(-6.53195 - 3.77122i) q^{61} +(3.02626 - 5.24164i) q^{62} +(-1.82083 + 1.91953i) q^{63} -1.00000i q^{64} +(-6.76375 + 5.37690i) q^{65} +(-2.90993 - 1.68005i) q^{66} +(1.93283 - 7.21342i) q^{67} -6.37060i q^{68} +(3.25536 + 5.63845i) q^{69} +(1.80201 + 6.07898i) q^{70} +(0.165170 - 0.616423i) q^{71} +(0.258819 + 0.965926i) q^{72} +(10.6978 - 2.86646i) q^{73} -3.16135 q^{74} -0.743035 q^{75} +(6.16110 - 1.65086i) q^{76} +(-7.81353 - 4.24036i) q^{77} +(-2.82239 + 2.24368i) q^{78} +(-2.75688 - 4.77505i) q^{79} +(2.31481 + 0.620250i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.56717 + 7.91058i) q^{82} +(0.287435 - 0.287435i) q^{83} +(0.751945 + 2.53665i) q^{84} +(14.7467 + 3.95136i) q^{85} +(-8.19877 - 2.19685i) q^{86} +3.74993i q^{87} +(-2.90993 + 1.68005i) q^{88} +(-1.95367 - 1.95367i) q^{89} -2.39646 q^{90} +(-7.30815 + 6.13114i) q^{91} +6.51073 q^{92} +(4.27978 + 4.27978i) q^{93} +(-7.17992 + 4.14533i) q^{94} +15.2857i q^{95} +(0.965926 + 0.258819i) q^{96} +(-3.55971 - 0.953822i) q^{97} +(2.16580 + 6.65652i) q^{98} +(2.37595 - 2.37595i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q + 4 * q^7 + 20 * q^9	\( 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q + 4 * q^7 + 20 * q^9 + 8 * q^11 - 20 * q^12 + 4 * q^14 - 40 * q^16 + 16 * q^17 + 4 * q^19 + 4 * q^21 - 4 * q^22 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 8 * q^33 - 8 * q^34 - 32 * q^35 + 40 * q^37 + 8 * q^38 + 20 * q^39 + 20 * q^41 + 12 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 + 4 * q^47 + 32 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^52 - 4 * q^53 + 24 * q^55 + 12 * q^56 + 8 * q^57 + 12 * q^58 + 24 * q^59 + 60 * q^61 + 32 * q^62 - 4 * q^63 + 44 * q^65 - 12 * q^67 - 8 * q^69 - 24 * q^70 - 28 * q^71 + 60 * q^73 - 40 * q^74 - 72 * q^75 + 4 * q^76 - 12 * q^77 + 4 * q^78 - 20 * q^81 - 24 * q^82 + 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 - 16 * q^92 - 24 * q^93 - 48 * q^97 - 88 * q^98 + 4 * q^99

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