LMFDB - Embedded newform 546.2.by.b.115.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(19,546)]

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, 5]))

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

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

chi := DirichletCharacter("546.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.by (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			115.6
Character	$\chi$	$=$	546.115
Dual form			546.2.by.b.19.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(-3.15172 - 0.844500i) q^{5} +(0.258819 + 0.965926i) q^{6} +(-2.64535 + 0.0462630i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(-3.15172 - 0.844500i) q^{5} +(0.258819 + 0.965926i) q^{6} +(-2.64535 + 0.0462630i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} -3.26290 q^{10} +(-0.954682 + 0.954682i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-3.41301 - 1.16248i) q^{13} +(-2.54324 + 0.729353i) q^{14} +(0.844500 - 3.15172i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.17710 - 2.03880i) q^{17} +(-0.965926 + 0.258819i) q^{18} +(-3.26997 + 3.26997i) q^{19} +(-3.15172 + 0.844500i) q^{20} +(-0.0462630 - 2.64535i) q^{21} +(-0.675062 + 1.16924i) q^{22} +(0.786006 + 0.453801i) q^{23} +(0.707107 + 0.707107i) q^{24} +(4.89002 + 2.82325i) q^{25} +(-3.59759 - 0.239513i) q^{26} -1.00000i q^{27} +(-2.26781 + 1.36274i) q^{28} +(-4.41535 - 7.64762i) q^{29} -3.26290i q^{30} +(0.496285 + 1.85216i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-0.954682 - 0.954682i) q^{33} +(-1.66467 - 1.66467i) q^{34} +(8.37645 + 2.08819i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(2.95086 + 11.0128i) q^{37} +(-2.31222 + 4.00488i) q^{38} +(1.16248 - 3.41301i) q^{39} +(-2.82575 + 1.63145i) q^{40} +(-2.56627 - 0.687631i) q^{41} +(-0.729353 - 2.54324i) q^{42} +(-1.72993 - 0.998773i) q^{43} +(-0.349438 + 1.30412i) q^{44} +(3.15172 + 0.844500i) q^{45} +(0.876676 + 0.234905i) q^{46} +(1.88337 - 7.02882i) q^{47} +(0.866025 + 0.500000i) q^{48} +(6.99572 - 0.244763i) q^{49} +(5.45410 + 1.46142i) q^{50} +(2.03880 - 1.17710i) q^{51} +(-3.53699 + 0.699772i) q^{52} +(3.56317 - 6.17160i) q^{53} +(-0.258819 - 0.965926i) q^{54} +(3.81512 - 2.20266i) q^{55} +(-1.83783 + 1.90326i) q^{56} +(-3.26997 - 3.26997i) q^{57} +(-6.24425 - 6.24425i) q^{58} +(-1.55838 + 5.81596i) q^{59} +(-0.844500 - 3.15172i) q^{60} -0.730890i q^{61} +(0.958748 + 1.66060i) q^{62} +(2.64535 - 0.0462630i) q^{63} -1.00000i q^{64} +(9.77514 + 6.54608i) q^{65} +(-1.16924 - 0.675062i) q^{66} +(8.73152 + 8.73152i) q^{67} +(-2.03880 - 1.17710i) q^{68} +(-0.453801 + 0.786006i) q^{69} +(8.63150 - 0.150951i) q^{70} +(-2.14989 + 0.576061i) q^{71} +(-0.707107 + 0.707107i) q^{72} +(-6.21032 + 1.66405i) q^{73} +(5.70063 + 9.87378i) q^{74} +(-2.82325 + 4.89002i) q^{75} +(-1.19689 + 4.46686i) q^{76} +(2.48130 - 2.56963i) q^{77} +(0.239513 - 3.59759i) q^{78} +(-6.18489 - 10.7125i) q^{79} +(-2.30722 + 2.30722i) q^{80} +1.00000 q^{81} -2.65680 q^{82} +(-2.48034 + 2.48034i) q^{83} +(-1.36274 - 2.26781i) q^{84} +(1.98812 + 7.41977i) q^{85} +(-1.92948 - 0.517003i) q^{86} +(7.64762 - 4.41535i) q^{87} +1.35012i q^{88} +(-4.45779 + 1.19446i) q^{89} +3.26290 q^{90} +(9.08238 + 2.91726i) q^{91} +0.907601 q^{92} +(-1.85216 + 0.496285i) q^{93} -7.27677i q^{94} +(13.0675 - 7.54453i) q^{95} +(0.965926 + 0.258819i) q^{96} +(-2.33821 - 8.72634i) q^{97} +(6.69400 - 2.04705i) q^{98} +(0.954682 - 0.954682i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) $ 40 * q - 4 * q^7 - 40 * q^9	$ 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{7}{12}\right)$

Coefficient data

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

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

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

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−3.15172	−	0.844500i	−1.40949	−	0.377672i	−0.527747	−	0.849401i	$-0.676963\pi$
$5$	−3.15172	−	0.844500i	−1.40949	−	0.377672i	−0.881743	+	0.471729i	$0.843630\pi$
$6$	0.258819	+	0.965926i	0.105662	+	0.394338i
$7$	−2.64535	+	0.0462630i	−0.999847	+	0.0174858i
$7$	−2.64535	+	0.0462630i	−0.999847	+	0.0174858i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−1.00000			−0.333333
$10$	−3.26290			−1.03182
$11$	−0.954682	+	0.954682i	−0.287847	+	0.287847i	−0.836229	−	0.548381i	$-0.815244\pi$
$11$	−0.954682	+	0.954682i	−0.287847	+	0.287847i	0.548381	+	0.836229i	$0.315244\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−3.41301	−	1.16248i	−0.946599	−	0.322413i
$13$	−3.41301	−	1.16248i	−0.946599	−	0.322413i
$14$	−2.54324	+	0.729353i	−0.679708	+	0.194928i
$15$	0.844500	−	3.15172i	0.218049	−	0.813770i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.17710	−	2.03880i	−0.285488	−	0.494480i	0.687239	−	0.726431i	$-0.258822\pi$
$17$	−1.17710	−	2.03880i	−0.285488	−	0.494480i	−0.972728	+	0.231951i	$0.925489\pi$
$18$	−0.965926	+	0.258819i	−0.227671	+	0.0610042i
$19$	−3.26997	+	3.26997i	−0.750183	+	0.750183i	−0.974513	−	0.224331i	$-0.927980\pi$
$19$	−3.26997	+	3.26997i	−0.750183	+	0.750183i	0.224331	+	0.974513i	$0.427980\pi$
$20$	−3.15172	+	0.844500i	−0.704745	+	0.188836i
$21$	−0.0462630	−	2.64535i	−0.0100954	−	0.577262i
$22$	−0.675062	+	1.16924i	−0.143924	+	0.249283i
$23$	0.786006	+	0.453801i	0.163894	+	0.0946240i	0.579703	−	0.814828i	$-0.303168\pi$
$23$	0.786006	+	0.453801i	0.163894	+	0.0946240i	−0.415810	+	0.909452i	$0.636502\pi$
$24$	0.707107	+	0.707107i	0.144338	+	0.144338i
$25$	4.89002	+	2.82325i	0.978003	+	0.564650i
$26$	−3.59759	−	0.239513i	−0.705545	−	0.0469724i
$27$		−	1.00000i		−	0.192450i
$28$	−2.26781	+	1.36274i	−0.428575	+	0.257533i
$29$	−4.41535	−	7.64762i	−0.819911	−	1.42013i	−0.905747	−	0.423818i	$-0.860690\pi$
$29$	−4.41535	−	7.64762i	−0.819911	−	1.42013i	0.0858368	−	0.996309i	$-0.472644\pi$
$30$		−	3.26290i		−	0.595721i
$31$	0.496285	+	1.85216i	0.0891353	+	0.332658i	0.996065	−	0.0886242i	$-0.0282470\pi$
$31$	0.496285	+	1.85216i	0.0891353	+	0.332658i	−0.906930	+	0.421282i	$0.861580\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−0.954682	−	0.954682i	−0.166189	−	0.166189i
$34$	−1.66467	−	1.66467i	−0.285488	−	0.285488i
$35$	8.37645	+	2.08819i	1.41588	+	0.352968i
$36$	−0.866025	+	0.500000i	−0.144338	+	0.0833333i
$37$	2.95086	+	11.0128i	0.485119	+	1.81049i	0.579526	+	0.814954i	$0.303238\pi$
$37$	2.95086	+	11.0128i	0.485119	+	1.81049i	−0.0944072	+	0.995534i	$0.530096\pi$
$38$	−2.31222	+	4.00488i	−0.375091	+	0.649677i
$39$	1.16248	−	3.41301i	0.186145	−	0.546519i
$40$	−2.82575	+	1.63145i	−0.446791	+	0.257955i
$41$	−2.56627	−	0.687631i	−0.400785	−	0.107390i	0.0527957	−	0.998605i	$-0.483187\pi$
$41$	−2.56627	−	0.687631i	−0.400785	−	0.107390i	−0.453580	+	0.891215i	$0.649853\pi$
$42$	−0.729353	−	2.54324i	−0.112542	−	0.392430i
$43$	−1.72993	−	0.998773i	−0.263811	−	0.152311i	0.362261	−	0.932077i	$-0.382005\pi$
$43$	−1.72993	−	0.998773i	−0.263811	−	0.152311i	−0.626072	+	0.779765i	$0.715338\pi$
$44$	−0.349438	+	1.30412i	−0.0526797	+	0.196603i
$45$	3.15172	+	0.844500i	0.469830	+	0.125891i
$46$	0.876676	+	0.234905i	0.129259	+	0.0346348i
$47$	1.88337	−	7.02882i	0.274717	−	1.02526i	−0.681313	−	0.731992i	$-0.738591\pi$
$47$	1.88337	−	7.02882i	0.274717	−	1.02526i	0.956031	−	0.293267i	$-0.0947424\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	6.99572	−	0.244763i	0.999388	−	0.0349662i
$50$	5.45410	+	1.46142i	0.771327	+	0.206676i
$51$	2.03880	−	1.17710i	0.285488	−	0.164827i
$52$	−3.53699	+	0.699772i	−0.490493	+	0.0970410i
$53$	3.56317	−	6.17160i	0.489439	−	0.847734i	−0.510487	−	0.859886i	$-0.670535\pi$
$53$	3.56317	−	6.17160i	0.489439	−	0.847734i	0.999926	+	0.0121516i	$0.00386808\pi$
$54$	−0.258819	−	0.965926i	−0.0352208	−	0.131446i
$55$	3.81512	−	2.20266i	0.514430	−	0.297006i
$56$	−1.83783	+	1.90326i	−0.245590	+	0.254333i
$57$	−3.26997	−	3.26997i	−0.433118	−	0.433118i
$58$	−6.24425	−	6.24425i	−0.819911	−	0.819911i
$59$	−1.55838	+	5.81596i	−0.202884	+	0.757174i	0.787200	+	0.616698i	$0.211530\pi$
$59$	−1.55838	+	5.81596i	−0.202884	+	0.757174i	−0.990084	+	0.140476i	$0.955137\pi$
$60$	−0.844500	−	3.15172i	−0.109024	−	0.406885i
$61$		−	0.730890i		−	0.0935808i	−0.998905	−	0.0467904i	$-0.985101\pi$
$61$		−	0.730890i		−	0.0935808i	0.998905	−	0.0467904i	$-0.0148993\pi$
$62$	0.958748	+	1.66060i	0.121761	+	0.210896i
$63$	2.64535	−	0.0462630i	0.333282	−	0.00582859i
$64$		−	1.00000i		−	0.125000i
$65$	9.77514	+	6.54608i	1.21246	+	0.811942i
$66$	−1.16924	−	0.675062i	−0.143924	−	0.0830944i
$67$	8.73152	+	8.73152i	1.06673	+	1.06673i	0.997609	+	0.0691170i	$0.0220182\pi$
$67$	8.73152	+	8.73152i	1.06673	+	1.06673i	0.0691170	+	0.997609i	$0.477982\pi$
$68$	−2.03880	−	1.17710i	−0.247240	−	0.142744i
$69$	−0.453801	+	0.786006i	−0.0546312	+	0.0946240i
$70$	8.63150	−	0.150951i	1.03166	−	0.0180422i
$71$	−2.14989	+	0.576061i	−0.255145	+	0.0683659i	−0.384124	−	0.923281i	$-0.625497\pi$
$71$	−2.14989	+	0.576061i	−0.255145	+	0.0683659i	0.128979	+	0.991647i	$0.458830\pi$
$72$	−0.707107	+	0.707107i	−0.0833333	+	0.0833333i
$73$	−6.21032	+	1.66405i	−0.726863	+	0.194762i	−0.603232	−	0.797566i	$-0.706121\pi$
$73$	−6.21032	+	1.66405i	−0.726863	+	0.194762i	−0.123631	+	0.992328i	$0.539454\pi$
$74$	5.70063	+	9.87378i	0.662684	+	1.14780i
$75$	−2.82325	+	4.89002i	−0.326001	+	0.564650i
$76$	−1.19689	+	4.46686i	−0.137293	+	0.512384i
$77$	2.48130	−	2.56963i	0.282770	−	0.292837i
$78$	0.239513	−	3.59759i	0.0271195	−	0.407347i
$79$	−6.18489	−	10.7125i	−0.695854	−	1.20525i	−0.969892	−	0.243536i	$-0.921693\pi$
$79$	−6.18489	−	10.7125i	−0.695854	−	1.20525i	0.274038	−	0.961719i	$-0.411641\pi$
$80$	−2.30722	+	2.30722i	−0.257955	+	0.257955i
$81$	1.00000			0.111111
$82$	−2.65680			−0.293395
$83$	−2.48034	+	2.48034i	−0.272253	+	0.272253i	−0.830007	−	0.557754i	$-0.811663\pi$
$83$	−2.48034	+	2.48034i	−0.272253	+	0.272253i	0.557754	+	0.830007i	$0.311663\pi$
$84$	−1.36274	−	2.26781i	−0.148687	−	0.247438i
$85$	1.98812	+	7.41977i	0.215642	+	0.804787i
$86$	−1.92948	−	0.517003i	−0.208061	−	0.0557498i
$87$	7.64762	−	4.41535i	0.819911	−	0.473376i
$88$			1.35012i			0.143924i
$89$	−4.45779	+	1.19446i	−0.472525	+	0.126613i	−0.487220	−	0.873279i	$-0.661989\pi$
$89$	−4.45779	+	1.19446i	−0.472525	+	0.126613i	0.0146949	+	0.999892i	$0.495322\pi$
$90$	3.26290			0.343940
$91$	9.08238	+	2.91726i	0.952092	+	0.305811i
$92$	0.907601			0.0946240
$93$	−1.85216	+	0.496285i	−0.192060	+	0.0514623i
$94$		−	7.27677i		−	0.750541i
$95$	13.0675	−	7.54453i	1.34070	−	0.774053i
$96$	0.965926	+	0.258819i	0.0985844	+	0.0264156i
$97$	−2.33821	−	8.72634i	−0.237410	−	0.886025i	−0.977048	−	0.213020i	$-0.931670\pi$
$97$	−2.33821	−	8.72634i	−0.237410	−	0.886025i	0.739638	−	0.673005i	$-0.234997\pi$
$98$	6.69400	−	2.04705i	0.676196	−	0.206783i
$99$	0.954682	−	0.954682i	0.0959491	−	0.0959491i
$100$	5.64650			0.564650
$101$	−14.8000			−1.47266			−0.736329	−	0.676624i	$-0.763442\pi$
$101$	−14.8000			−1.47266			−0.736329	+	0.676624i	$0.763442\pi$
$102$	1.66467	−	1.66467i	0.164827	−	0.164827i
$103$	7.77373	+	13.4645i	0.765969	+	1.32670i	0.939733	+	0.341910i	$0.111074\pi$
$103$	7.77373	+	13.4645i	0.765969	+	1.32670i	−0.173764	+	0.984787i	$0.555593\pi$
$104$	−3.23536	+	1.59137i	−0.317253	+	0.156047i
$105$	−2.08819	+	8.37645i	−0.203786	+	0.817458i
$106$	1.84443	−	6.88352i	0.179147	−	0.668587i
$107$	−4.31566	+	7.47494i	−0.417210	+	0.722630i	−0.995658	−	0.0930901i	$-0.970326\pi$
$107$	−4.31566	+	7.47494i	−0.417210	+	0.722630i	0.578447	+	0.815720i	$0.303659\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	−13.9717	+	3.74371i	−1.33825	+	0.358582i	−0.855784	−	0.517334i	$-0.826924\pi$
$109$	−13.9717	+	3.74371i	−1.33825	+	0.358582i	−0.482463	+	0.875916i	$0.660258\pi$
$110$	3.11503	−	3.11503i	0.297006	−	0.297006i
$111$	−11.0128	+	2.95086i	−1.04529	+	0.280083i
$112$	−1.28261	+	2.31407i	−0.121195	+	0.218659i
$113$	1.28971	−	2.23384i	0.121326	−	0.210142i	−0.798965	−	0.601378i	$-0.794619\pi$
$113$	1.28971	−	2.23384i	0.121326	−	0.210142i	0.920291	+	0.391235i	$0.127952\pi$
$114$	−4.00488	−	2.31222i	−0.375091	−	0.216559i
$115$	−2.09403	−	2.09403i	−0.195270	−	0.195270i
$116$	−7.64762	−	4.41535i	−0.710063	−	0.409955i
$117$	3.41301	+	1.16248i	0.315533	+	0.107471i
$118$			6.02113i			0.554290i
$119$	3.20816	+	5.33886i	0.294091	+	0.489413i
$120$	−1.63145	−	2.82575i	−0.148930	−	0.257955i
$121$			9.17716i			0.834288i
$122$	−0.189168	−	0.705985i	−0.0171265	−	0.0639169i
$123$	0.687631	−	2.56627i	0.0620016	−	0.231393i
$124$	1.35587	+	1.35587i	0.121761	+	0.121761i
$125$	−1.49162	−	1.49162i	−0.133415	−	0.133415i
$126$	2.54324	−	0.729353i	0.226569	−	0.0649759i
$127$	8.75703	−	5.05587i	0.777061	−	0.448636i	−0.0583269	−	0.998298i	$-0.518577\pi$
$127$	8.75703	−	5.05587i	0.777061	−	0.448636i	0.835388	+	0.549661i	$0.185243\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	0.998773	−	1.72993i	0.0879370	−	0.152311i
$130$	11.1363	+	3.79304i	0.976719	+	0.332672i
$131$	14.4605	−	8.34878i	1.26342	−	0.729436i	0.289686	−	0.957122i	$-0.406449\pi$
$131$	14.4605	−	8.34878i	1.26342	−	0.729436i	0.973735	+	0.227686i	$0.0731159\pi$
$132$	−1.30412	−	0.349438i	−0.113509	−	0.0304147i
$133$	8.49893	−	8.80148i	0.736950	−	0.763185i
$134$	10.6939	+	6.17412i	0.923811	+	0.533363i
$135$	−0.844500	+	3.15172i	−0.0726830	+	0.271257i
$136$	−2.27398	−	0.609311i	−0.194992	−	0.0522480i
$137$	4.58235	+	1.22784i	0.391497	+	0.104901i	0.449197	−	0.893433i	$-0.351710\pi$
$137$	4.58235	+	1.22784i	0.391497	+	0.104901i	−0.0577003	+	0.998334i	$0.518377\pi$
$138$	−0.234905	+	0.876676i	−0.0199964	+	0.0746276i
$139$	−6.60535	−	3.81360i	−0.560258	−	0.323465i	0.192991	−	0.981201i	$-0.438181\pi$
$139$	−6.60535	−	3.81360i	−0.560258	−	0.323465i	−0.753249	+	0.657735i	$0.771515\pi$
$140$	8.29832	−	2.37980i	0.701336	−	0.201130i
$141$	7.02882	+	1.88337i	0.591933	+	0.158608i
$142$	−1.92754	+	1.11287i	−0.161755	+	0.0933896i
$143$	4.36814	−	2.14855i	0.365282	−	0.179670i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	7.45753	+	27.8319i	0.619315	+	2.31131i
$146$	−5.56802	+	3.21470i	−0.460813	+	0.266050i
$147$	0.244763	+	6.99572i	0.0201877	+	0.576997i
$148$	8.06190	+	8.06190i	0.662684	+	0.662684i
$149$	−10.8249	−	10.8249i	−0.886812	−	0.886812i	0.107404	−	0.994215i	$-0.465746\pi$
$149$	−10.8249	−	10.8249i	−0.886812	−	0.886812i	−0.994215	+	0.107404i	$0.965746\pi$
$150$	−1.46142	+	5.45410i	−0.119325	+	0.445326i
$151$	−5.93126	−	22.1358i	−0.482679	−	1.80138i	−0.590290	−	0.807191i	$-0.700987\pi$
$151$	−5.93126	−	22.1358i	−0.482679	−	1.80138i	0.107611	−	0.994193i	$-0.465680\pi$
$152$			4.62444i			0.375091i
$153$	1.17710	+	2.03880i	0.0951628	+	0.164827i
$154$	1.73168	−	3.12428i	0.139543	−	0.251762i
$155$		−	6.25660i		−	0.502542i
$156$	−0.699772	−	3.53699i	−0.0560266	−	0.283186i
$157$	−3.92065	−	2.26359i	−0.312902	−	0.180654i	0.335322	−	0.942103i	$-0.391155\pi$
$157$	−3.92065	−	2.26359i	−0.312902	−	0.180654i	−0.648224	+	0.761449i	$0.724488\pi$
$158$	−8.74675	−	8.74675i	−0.695854	−	0.695854i
$159$	6.17160	+	3.56317i	0.489439	+	0.282578i
$160$	−1.63145	+	2.82575i	−0.128977	+	0.223395i
$161$	−2.10025	−	1.16410i	−0.165523	−	0.0917437i
$162$	0.965926	−	0.258819i	0.0758903	−	0.0203347i
$163$	−10.9762	+	10.9762i	−0.859721	+	0.859721i	−0.991305	−	0.131584i	$-0.957994\pi$
$163$	−10.9762	+	10.9762i	−0.859721	+	0.859721i	0.131584	+	0.991305i	$0.457994\pi$
$164$	−2.56627	+	0.687631i	−0.200392	+	0.0536950i
$165$	2.20266	+	3.81512i	0.171477	+	0.297006i
$166$	−1.75387	+	3.03779i	−0.136126	+	0.235778i
$167$	6.07764	−	22.6820i	0.470302	−	1.75519i	−0.168384	−	0.985722i	$-0.553855\pi$
$167$	6.07764	−	22.6820i	0.470302	−	1.75519i	0.638685	−	0.769468i	$-0.279479\pi$
$168$	−1.90326	−	1.83783i	−0.146839	−	0.141792i
$169$	10.2973	+	7.93509i	0.792100	+	0.610391i
$170$	3.84075	+	6.65238i	0.294572	+	0.510214i
$171$	3.26997	−	3.26997i	0.250061	−	0.250061i
$172$	−1.99755			−0.152311
$173$	−8.06695			−0.613319			−0.306660	−	0.951819i	$-0.599211\pi$
$173$	−8.06695			−0.613319			−0.306660	+	0.951819i	$0.599211\pi$
$174$	6.24425	−	6.24425i	0.473376	−	0.473376i
$175$	−13.0664	−	7.24225i	−0.987727	−	0.547463i
$176$	0.349438	+	1.30412i	0.0263399	+	0.0983017i
$177$	−5.81596	−	1.55838i	−0.437154	−	0.117135i
$178$	−3.99675	+	2.30752i	−0.299569	+	0.172956i
$179$		−	17.7297i		−	1.32518i	−0.748982	−	0.662590i	$-0.769457\pi$
$179$		−	17.7297i		−	1.32518i	0.748982	−	0.662590i	$-0.230543\pi$
$180$	3.15172	−	0.844500i	0.234915	−	0.0629453i
$181$	4.90151			0.364327			0.182163	−	0.983268i	$-0.441690\pi$
$181$	4.90151			0.364327			0.182163	+	0.983268i	$0.441690\pi$
$182$	9.52795	+	0.467160i	0.706258	+	0.0346282i
$183$	0.730890			0.0540289
$184$	0.876676	−	0.234905i	0.0646294	−	0.0173174i
$185$		−	37.2011i		−	2.73508i
$186$	−1.66060	+	0.958748i	−0.121761	+	0.0702988i
$187$	3.07016	+	0.822646i	0.224512	+	0.0601578i
$188$	−1.88337	−	7.02882i	−0.137359	−	0.512629i
$189$	0.0462630	+	2.64535i	0.00336514	+	0.192421i
$190$	10.6696	−	10.6696i	0.774053	−	0.774053i
$191$	1.73630			0.125634			0.0628172	−	0.998025i	$-0.479991\pi$
$191$	1.73630			0.125634			0.0628172	+	0.998025i	$0.479991\pi$
$192$	1.00000			0.0721688
$193$	−14.7628	+	14.7628i	−1.06265	+	1.06265i	−0.0647507	+	0.997901i	$0.520625\pi$
$193$	−14.7628	+	14.7628i	−1.06265	+	1.06265i	−0.997901	+	0.0647507i	$0.979375\pi$
$194$	−4.51708	−	7.82382i	−0.324308	−	0.561717i
$195$	−6.54608	+	9.77514i	−0.468775	+	0.700012i
$196$	5.93609	−	3.70983i	0.424006	−	0.264988i
$197$	0.834638	−	3.11491i	0.0594655	−	0.221928i	−0.929798	−	0.368070i	$-0.880019\pi$
$197$	0.834638	−	3.11491i	0.0594655	−	0.221928i	0.989264	+	0.146141i	$0.0466855\pi$
$198$	0.675062	−	1.16924i	0.0479746	−	0.0830944i
$199$	1.64365	+	2.84688i	0.116515	+	0.201810i	0.918384	−	0.395689i	$-0.129494\pi$
$199$	1.64365	+	2.84688i	0.116515	+	0.201810i	−0.801869	+	0.597499i	$0.796161\pi$
$200$	5.45410	−	1.46142i	0.385663	−	0.103338i
$201$	−8.73152	+	8.73152i	−0.615874	+	0.615874i
$202$	−14.2957	+	3.83053i	−1.00584	+	0.269515i
$203$	12.0339	+	20.0263i	0.844617	+	1.40557i
$204$	1.17710	−	2.03880i	0.0824134	−	0.142744i
$205$	7.50747	+	4.33444i	0.524344	+	0.302730i
$206$	10.9937	+	10.9937i	0.765969	+	0.765969i
$207$	−0.786006	−	0.453801i	−0.0546312	−	0.0315413i
$208$	−2.71324	+	2.37452i	−0.188129	+	0.164643i
$209$		−	6.24356i		−	0.431876i
$210$	0.150951	+	8.63150i	0.0104166	+	0.595630i
$211$	−11.5477	−	20.0012i	−0.794977	−	1.37694i	−0.922854	−	0.385151i	$-0.874149\pi$
$211$	−11.5477	−	20.0012i	−0.794977	−	1.37694i	0.127876	−	0.991790i	$-0.459184\pi$
$212$		−	7.12635i		−	0.489439i
$213$	−0.576061	−	2.14989i	−0.0394711	−	0.147308i
$214$	−2.23395	+	8.33721i	−0.152710	+	0.569920i
$215$	4.60877	+	4.60877i	0.314316	+	0.314316i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	−1.39853	−	4.87664i	−0.0949385	−	0.331048i
$218$	−12.5267	+	7.23229i	−0.848414	+	0.489832i
$219$	−1.66405	−	6.21032i	−0.112446	−	0.419655i
$220$	2.20266	−	3.81512i	0.148503	−	0.257215i
$221$	1.64740	+	8.32678i	0.110816	+	0.560120i
$222$	−9.87378	+	5.70063i	−0.662684	+	0.382601i
$223$	−10.5430	−	2.82498i	−0.706009	−	0.189174i	−0.112088	−	0.993698i	$-0.535754\pi$
$223$	−10.5430	−	2.82498i	−0.706009	−	0.189174i	−0.593920	+	0.804524i	$0.702421\pi$
$224$	−0.639979	+	2.56718i	−0.0427604	+	0.171527i
$225$	−4.89002	−	2.82325i	−0.326001	−	0.188217i
$226$	0.667603	−	2.49153i	0.0444083	−	0.165734i
$227$	10.6877	+	2.86377i	0.709370	+	0.190075i	0.595424	−	0.803412i	$-0.296984\pi$
$227$	10.6877	+	2.86377i	0.709370	+	0.190075i	0.113946	+	0.993487i	$0.463651\pi$
$228$	−4.46686	−	1.19689i	−0.295825	−	0.0792661i
$229$	0.657930	−	2.45543i	0.0434773	−	0.162259i	−0.940774	−	0.339034i	$-0.889900\pi$
$229$	0.657930	−	2.45543i	0.0434773	−	0.162259i	0.984251	+	0.176775i	$0.0565664\pi$
$230$	−2.56466	−	1.48071i	−0.169108	−	0.0976348i
$231$	2.56963	+	2.48130i	0.169069	+	0.163257i
$232$	−8.52981	−	2.28556i	−0.560009	−	0.150054i
$233$	−22.7469	+	13.1329i	−1.49020	+	0.860365i	−0.999937	−	0.0112116i	$-0.996431\pi$
$233$	−22.7469	+	13.1329i	−1.49020	+	0.860365i	−0.490259	+	0.871577i	$0.663098\pi$
$234$	3.59759	+	0.239513i	0.235182	+	0.0156575i
$235$	−11.8717	+	20.5623i	−0.774423	+	1.34134i
$236$	1.55838	+	5.81596i	0.101442	+	0.378587i
$237$	10.7125	−	6.18489i	0.695854	−	0.401752i
$238$	4.48064	+	4.32661i	0.290437	+	0.280453i
$239$	−9.09071	−	9.09071i	−0.588029	−	0.588029i	0.349068	−	0.937097i	$-0.386498\pi$
$239$	−9.09071	−	9.09071i	−0.588029	−	0.588029i	−0.937097	+	0.349068i	$0.886498\pi$
$240$	−2.30722	−	2.30722i	−0.148930	−	0.148930i
$241$	−0.250209	+	0.933794i	−0.0161174	+	0.0601510i	−0.973516	−	0.228618i	$-0.926579\pi$
$241$	−0.250209	+	0.933794i	−0.0161174	+	0.0601510i	0.957399	+	0.288769i	$0.0932460\pi$
$242$	2.37522	+	8.86446i	0.152685	+	0.569829i
$243$			1.00000i			0.0641500i
$244$	−0.365445	−	0.632969i	−0.0233952	−	0.0405217i
$245$	−22.2552	−	5.13646i	−1.42183	−	0.328156i
$246$		−	2.65680i		−	0.169392i
$247$	14.9617	−	7.35918i	0.951991	−	0.468254i
$248$	1.66060	+	0.958748i	0.105448	+	0.0608806i
$249$	−2.48034	−	2.48034i	−0.157185	−	0.157185i
$250$	−1.82686	−	1.05474i	−0.115541	−	0.0667074i
$251$	−7.00072	+	12.1256i	−0.441882	+	0.765362i	−0.997829	−	0.0658558i	$-0.979022\pi$
$251$	−7.00072	+	12.1256i	−0.441882	+	0.765362i	0.555947	+	0.831217i	$0.312356\pi$
$252$	2.26781	−	1.36274i	0.142858	−	0.0858444i
$253$	−1.18362	+	0.317150i	−0.0744136	+	0.0199391i
$254$	7.15008	−	7.15008i	0.448636	−	0.448636i
$255$	−7.41977	+	1.98812i	−0.464644	+	0.124501i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−15.8191	+	27.3994i	−0.986767	+	1.70913i	−0.352963	+	0.935637i	$0.614826\pi$
$257$	−15.8191	+	27.3994i	−0.986767	+	1.70913i	−0.633805	+	0.773493i	$0.718508\pi$
$258$	0.517003	−	1.92948i	0.0321872	−	0.120124i
$259$	−8.31554	−	28.9961i	−0.516702	−	1.80173i
$260$	11.7386	+	0.781507i	0.727995	+	0.0484670i
$261$	4.41535	+	7.64762i	0.273304	+	0.473376i
$262$	11.8070	−	11.8070i	0.729436	−	0.729436i
$263$	12.1909			0.751720			0.375860	−	0.926676i	$-0.377347\pi$
$263$	12.1909			0.751720			0.375860	+	0.926676i	$0.377347\pi$
$264$	−1.35012			−0.0830944
$265$	−16.4420	+	16.4420i	−1.01003	+	1.01003i
$266$	5.93134	−	10.7013i	0.363674	−	0.656137i
$267$	−1.19446	−	4.45779i	−0.0730999	−	0.272812i
$268$	11.9275	+	3.19596i	0.728587	+	0.195224i
$269$	−13.8267	+	7.98287i	−0.843031	+	0.486724i	−0.858293	−	0.513159i	$-0.828475\pi$
$269$	−13.8267	+	7.98287i	−0.843031	+	0.486724i	0.0152621	+	0.999884i	$0.495142\pi$
$270$			3.26290i			0.198574i
$271$	26.0921	−	6.99135i	1.58498	−	0.424694i	0.644518	−	0.764589i	$-0.277058\pi$
$271$	26.0921	−	6.99135i	1.58498	−	0.424694i	0.940463	+	0.339895i	$0.110391\pi$
$272$	−2.35420			−0.142744
$273$	−2.91726	+	9.08238i	−0.176560	+	0.549691i
$274$	4.74400			0.286595
$275$	−7.36372	+	1.97310i	−0.444049	+	0.118983i
$276$			0.907601i			0.0546312i
$277$	−25.6243	+	14.7942i	−1.53962	+	0.888898i	−0.540755	+	0.841180i	$0.681861\pi$
$277$	−25.6243	+	14.7942i	−1.53962	+	0.888898i	−0.998861	+	0.0477173i	$0.984805\pi$
$278$	−7.36731	−	1.97406i	−0.441862	−	0.118397i
$279$	−0.496285	−	1.85216i	−0.0297118	−	0.110886i
$280$	7.39962	−	4.44648i	0.442212	−	0.265728i
$281$	−5.11259	+	5.11259i	−0.304992	+	0.304992i	−0.842963	−	0.537972i	$-0.819191\pi$
$281$	−5.11259	+	5.11259i	−0.304992	+	0.304992i	0.537972	+	0.842963i	$0.319191\pi$
$282$	7.27677			0.433325
$283$	−19.7916			−1.17649			−0.588245	−	0.808683i	$-0.700181\pi$
$283$	−19.7916			−1.17649			−0.588245	+	0.808683i	$0.700181\pi$
$284$	−1.57383	+	1.57383i	−0.0933896	+	0.0933896i
$285$	7.54453	+	13.0675i	0.446899	+	0.774053i
$286$	3.66321	−	3.20589i	0.216610	−	0.189568i
$287$	6.82050	+	1.70030i	0.402601	+	0.100365i
$288$	−0.258819	+	0.965926i	−0.0152511	+	0.0569177i
$289$	5.72888	−	9.92270i	0.336993	−	0.583689i
$290$	14.4068	+	24.9534i	0.845999	+	1.46531i
$291$	8.72634	−	2.33821i	0.511547	−	0.137069i
$292$	−4.54627	+	4.54627i	−0.266050	+	0.266050i
$293$	12.5810	−	3.37106i	0.734989	−	0.196940i	0.128139	−	0.991756i	$-0.459100\pi$
$293$	12.5810	−	3.37106i	0.734989	−	0.196940i	0.606850	+	0.794817i	$0.292433\pi$
$294$	2.04705	+	6.69400i	0.119386	+	0.390402i
$295$	9.82316	−	17.0142i	0.571926	−	0.990606i
$296$	9.87378	+	5.70063i	0.573902	+	0.331342i
$297$	0.954682	+	0.954682i	0.0553963	+	0.0553963i
$298$	−13.2578	−	7.65437i	−0.768001	−	0.443406i
$299$	−2.15512	−	2.46254i	−0.124634	−	0.142412i
$300$			5.64650i			0.326001i
$301$	4.62246	+	2.56207i	0.266434	+	0.147675i
$302$	−11.4583	−	19.8464i	−0.659352	−	1.14203i
$303$		−	14.8000i		−	0.850239i
$304$	1.19689	+	4.46686i	0.0686465	+	0.256192i
$305$	−0.617236	+	2.30356i	−0.0353428	+	0.131901i
$306$	1.66467	+	1.66467i	0.0951628	+	0.0951628i
$307$	13.3694	+	13.3694i	0.763033	+	0.763033i	0.976870	−	0.213836i	$-0.0685958\pi$
$307$	13.3694	+	13.3694i	0.763033	+	0.763033i	−0.213836	+	0.976870i	$0.568596\pi$
$308$	0.864052	−	3.46602i	0.0492339	−	0.197495i
$309$	−13.4645	+	7.77373i	−0.765969	+	0.442232i
$310$	−1.61933	−	6.04341i	−0.0919715	−	0.343242i
$311$	−13.3477	+	23.1190i	−0.756881	+	1.31096i	0.187553	+	0.982254i	$0.439944\pi$
$311$	−13.3477	+	23.1190i	−0.756881	+	1.31096i	−0.944434	+	0.328701i	$0.893389\pi$
$312$	−1.59137	−	3.23536i	−0.0900935	−	0.183166i
$313$	17.7118	−	10.2259i	1.00113	−	0.578002i	0.0925465	−	0.995708i	$-0.470499\pi$
$313$	17.7118	−	10.2259i	1.00113	−	0.578002i	0.908582	+	0.417707i	$0.137166\pi$
$314$	−4.37292	−	1.17172i	−0.246778	−	0.0661240i
$315$	−8.37645	−	2.08819i	−0.471960	−	0.117656i
$316$	−10.7125	−	6.18489i	−0.602627	−	0.347927i
$317$	−4.80051	+	17.9157i	−0.269623	+	1.00625i	0.689736	+	0.724061i	$0.257727\pi$
$317$	−4.80051	+	17.9157i	−0.269623	+	1.00625i	−0.959359	+	0.282187i	$0.908940\pi$
$318$	6.88352	+	1.84443i	0.386009	+	0.103431i
$319$	11.5163	+	3.08578i	0.644789	+	0.172771i
$320$	−0.844500	+	3.15172i	−0.0472090	+	0.176186i
$321$	−7.47494	−	4.31566i	−0.417210	−	0.240877i
$322$	−2.32998	−	0.580846i	−0.129845	−	0.0323693i
$323$	10.5159	+	2.81772i	0.585119	+	0.156782i
$324$	0.866025	−	0.500000i	0.0481125	−	0.0277778i
$325$	−13.4077	−	15.3203i	−0.743726	−	0.849818i
$326$	−7.76134	+	13.4430i	−0.429861	+	0.744540i
$327$	−3.74371	−	13.9717i	−0.207027	−	0.772637i
$328$	−2.30086	+	1.32840i	−0.127044	+	0.0733487i
$329$	−4.65698	+	18.6808i	−0.256748	+	1.02991i
$330$	3.11503	+	3.11503i	0.171477	+	0.171477i
$331$	4.13646	+	4.13646i	0.227360	+	0.227360i	0.811589	−	0.584229i	$-0.198603\pi$
$331$	4.13646	+	4.13646i	0.227360	+	0.227360i	−0.584229	+	0.811589i	$0.698603\pi$
$332$	−0.907868	+	3.38821i	−0.0498257	+	0.185952i
$333$	−2.95086	−	11.0128i	−0.161706	−	0.603496i
$334$		−	23.4822i		−	1.28489i
$335$	−20.1455	−	34.8931i	−1.10067	−	1.90641i
$336$	−2.31407	−	1.28261i	−0.126243	−	0.0699720i
$337$		−	4.58809i		−	0.249929i	−0.992161	−	0.124965i	$-0.960118\pi$
$337$		−	4.58809i		−	0.249929i	0.992161	−	0.124965i	$-0.0398818\pi$
$338$	12.0002	+	4.99957i	0.652724	+	0.271941i
$339$	2.23384	+	1.28971i	0.121326	+	0.0700475i
$340$	5.43165	+	5.43165i	0.294572	+	0.294572i
$341$	−2.24202	−	1.29443i	−0.121412	−	0.0700973i
$342$	2.31222	−	4.00488i	0.125030	−	0.216559i
$343$	−18.4948	+	0.971127i	−0.998624	+	0.0524359i
$344$	−1.92948	+	0.517003i	−0.104031	+	0.0278749i
$345$	2.09403	−	2.09403i	0.112739	−	0.112739i
$346$	−7.79208	+	2.08788i	−0.418905	+	0.112245i
$347$	14.3810	+	24.9086i	0.772011	+	1.33716i	0.936459	+	0.350776i	$0.114082\pi$
$347$	14.3810	+	24.9086i	0.772011	+	1.33716i	−0.164449	+	0.986386i	$0.552584\pi$
$348$	4.41535	−	7.64762i	0.236688	−	0.409955i
$349$	4.39591	−	16.4058i	0.235308	−	0.878180i	−0.742702	−	0.669622i	$-0.766456\pi$
$349$	4.39591	−	16.4058i	0.235308	−	0.878180i	0.978010	−	0.208558i	$-0.0668771\pi$
$350$	−14.4956	−	3.61365i	−0.774823	−	0.193158i
$351$	−1.16248	+	3.41301i	−0.0620484	+	0.182173i
$352$	0.675062	+	1.16924i	0.0359809	+	0.0623208i
$353$	20.3834	−	20.3834i	1.08490	−	1.08490i	0.0888567	−	0.996044i	$-0.471679\pi$
$353$	20.3834	−	20.3834i	1.08490	−	1.08490i	0.996044	−	0.0888567i	$-0.0283213\pi$
$354$	−6.02113			−0.320019
$355$	7.26233			0.385445
$356$	−3.26333	+	3.26333i	−0.172956	+	0.172956i
$357$	−5.33886	+	3.20816i	−0.282563	+	0.169794i
$358$	−4.58878	−	17.1256i	−0.242525	−	0.905115i
$359$	−25.8590	−	6.92891i	−1.36479	−	0.365694i	−0.499216	−	0.866478i	$-0.666379\pi$
$359$	−25.8590	−	6.92891i	−1.36479	−	0.365694i	−0.865572	+	0.500784i	$0.833045\pi$
$360$	2.82575	−	1.63145i	0.148930	−	0.0859849i
$361$		−	2.38540i		−	0.125548i
$362$	4.73450	−	1.26861i	0.248840	−	0.0666764i
$363$	−9.17716			−0.481676
$364$	9.32420	−	2.01477i	0.488721	−	0.105603i
$365$	20.9785			1.09806
$366$	0.705985	−	0.189168i	0.0369024	−	0.00988798i
$367$		−	11.5334i		−	0.602040i	−0.953618	−	0.301020i	$-0.902673\pi$
$367$		−	11.5334i		−	0.602040i	0.953618	−	0.301020i	$-0.0973272\pi$
$368$	0.786006	−	0.453801i	0.0409734	−	0.0236560i
$369$	2.56627	+	0.687631i	0.133595	+	0.0357966i
$370$	−9.62836	−	35.9335i	−0.500555	−	1.86810i
$371$	−9.14031	+	16.4909i	−0.474541	+	0.856163i
$372$	−1.35587	+	1.35587i	−0.0702988	+	0.0702988i
$373$	−6.42675			−0.332765			−0.166382	−	0.986061i	$-0.553209\pi$
$373$	−6.42675			−0.332765			−0.166382	+	0.986061i	$0.553209\pi$
$374$	3.17846			0.164354
$375$	1.49162	−	1.49162i	0.0770271	−	0.0770271i
$376$	−3.63838	−	6.30187i	−0.187635	−	0.324994i
$377$	6.17948	+	31.2342i	0.318260	+	1.60864i
$378$	0.729353	+	2.54324i	0.0375139	+	0.130810i
$379$	4.98986	−	18.6224i	0.256312	−	0.956568i	−0.711044	−	0.703147i	$-0.751778\pi$
$379$	4.98986	−	18.6224i	0.256312	−	0.956568i	0.967356	−	0.253421i	$-0.0815558\pi$
$380$	7.54453	−	13.0675i	0.387026	−	0.670349i
$381$	5.05587	+	8.75703i	0.259020	+	0.448636i
$382$	1.67714	−	0.449388i	0.0858099	−	0.0229927i
$383$	−7.66992	+	7.66992i	−0.391915	+	0.391915i	−0.875369	−	0.483455i	$-0.839382\pi$
$383$	−7.66992	+	7.66992i	−0.391915	+	0.391915i	0.483455	+	0.875369i	$0.339382\pi$
$384$	0.965926	−	0.258819i	0.0492922	−	0.0132078i
$385$	−9.99041	+	6.00330i	−0.509158	+	0.305956i
$386$	−10.4389	+	18.0807i	−0.531326	+	0.920284i
$387$	1.72993	+	0.998773i	0.0879370	+	0.0507705i
$388$	−6.38812	−	6.38812i	−0.324308	−	0.324308i
$389$	−4.57588	−	2.64188i	−0.232006	−	0.133949i	0.379491	−	0.925195i	$-0.376099\pi$
$389$	−4.57588	−	2.64188i	−0.232006	−	0.133949i	−0.611497	+	0.791247i	$0.709432\pi$
$390$	−3.79304	+	11.1363i	−0.192068	+	0.563909i
$391$		−	2.13667i		−	0.108056i
$392$	4.77365	−	5.11979i	0.241106	−	0.258589i
$393$	8.34878	+	14.4605i	0.421140	+	0.729436i
$394$		−	3.22479i		−	0.162463i
$395$	10.4463	+	38.9860i	0.525609	+	1.96160i
$396$	0.349438	−	1.30412i	0.0175599	−	0.0655345i
$397$	−14.7011	−	14.7011i	−0.737828	−	0.737828i	0.234329	−	0.972157i	$-0.424711\pi$
$397$	−14.7011	−	14.7011i	−0.737828	−	0.737828i	−0.972157	+	0.234329i	$0.924711\pi$
$398$	2.32447	+	2.32447i	0.116515	+	0.116515i
$399$	8.80148	+	8.49893i	0.440625	+	0.425478i
$400$	4.89002	−	2.82325i	0.244501	−	0.141163i
$401$	−9.52069	−	35.5317i	−0.475441	−	1.77437i	−0.619711	−	0.784830i	$-0.712750\pi$
$401$	−9.52069	−	35.5317i	−0.475441	−	1.77437i	0.144270	−	0.989538i	$-0.453917\pi$
$402$	−6.17412	+	10.6939i	−0.307937	+	0.533363i
$403$	0.459265	−	6.89836i	0.0228776	−	0.343632i
$404$	−12.8172	+	7.40001i	−0.637679	+	0.368164i
$405$	−3.15172	−	0.844500i	−0.156610	−	0.0419635i
$406$	16.8071	+	16.2293i	0.834122	+	0.805449i
$407$	−13.3308	−	7.69655i	−0.660784	−	0.381504i
$408$	0.609311	−	2.27398i	0.0301654	−	0.112579i
$409$	−9.23579	−	2.47472i	−0.456681	−	0.122367i	0.0231430	−	0.999732i	$-0.492633\pi$
$409$	−9.23579	−	2.47472i	−0.456681	−	0.122367i	−0.479824	+	0.877365i	$0.659299\pi$
$410$	8.37349	+	2.24367i	0.413537	+	0.110807i
$411$	−1.22784	+	4.58235i	−0.0605648	+	0.226031i
$412$	13.4645	+	7.77373i	0.663348	+	0.382984i
$413$	3.85340	−	15.4573i	0.189613	−	0.760605i
$414$	−0.876676	−	0.234905i	−0.0430863	−	0.0115449i
$415$	9.91198	−	5.72269i	0.486560	−	0.280916i
$416$	−2.00622	+	2.99585i	−0.0983629	+	0.146883i
$417$	3.81360	−	6.60535i	0.186753	−	0.323465i
$418$	−1.61595	−	6.03082i	−0.0790388	−	0.294977i
$419$	14.0813	−	8.12987i	0.687919	−	0.397170i	−0.114913	−	0.993376i	$-0.536659\pi$
$419$	14.0813	−	8.12987i	0.687919	−	0.397170i	0.802832	+	0.596205i	$0.203326\pi$
$420$	2.37980	+	8.29832i	0.116123	+	0.404916i
$421$	14.9294	+	14.9294i	0.727614	+	0.727614i	0.970144	−	0.242530i	$-0.0779774\pi$
$421$	14.9294	+	14.9294i	0.727614	+	0.727614i	−0.242530	+	0.970144i	$0.577977\pi$
$422$	−16.3309	−	16.3309i	−0.794977	−	0.794977i
$423$	−1.88337	+	7.02882i	−0.0915724	+	0.341753i
$424$	−1.84443	−	6.88352i	−0.0895736	−	0.334293i
$425$		−	13.2930i		−	0.644804i
$426$	−1.11287	−	1.92754i	−0.0539185	−	0.0933896i
$427$	0.0338132	+	1.93346i	0.00163633	+	0.0935665i
$428$			8.63132i			0.417210i
$429$	2.14855	+	4.36814i	0.103733	+	0.210896i
$430$	5.64457	+	3.25889i	0.272205	+	0.157158i
$431$	12.9074	+	12.9074i	0.621729	+	0.621729i	0.945973	−	0.324244i	$-0.105110\pi$
$431$	12.9074	+	12.9074i	0.621729	+	0.621729i	−0.324244	+	0.945973i	$0.605110\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$	0.272369	−	0.471756i	0.0130892	−	0.0226712i	−0.859407	−	0.511293i	$-0.829167\pi$
$433$	0.272369	−	0.471756i	0.0130892	−	0.0226712i	0.872496	+	0.488622i	$0.162500\pi$
$434$	−2.61305	−	4.34851i	−0.125430	−	0.208735i
$435$	−27.8319	+	7.45753i	−1.33444	+	0.357561i
$436$	−10.2280	+	10.2280i	−0.489832	+	0.489832i
$437$	−4.05413	+	1.08630i	−0.193935	+	0.0519648i
$438$	−3.21470	−	5.56802i	−0.153604	−	0.266050i
$439$	5.09124	−	8.81828i	0.242991	−	0.420874i	−0.718574	−	0.695451i	$-0.755205\pi$
$439$	5.09124	−	8.81828i	0.242991	−	0.420874i	0.961565	+	0.274577i	$0.0885380\pi$
$440$	1.14018	−	4.25521i	0.0543560	−	0.202859i
$441$	−6.99572	+	0.244763i	−0.333129	+	0.0116554i
$442$	3.74640	+	7.61667i	0.178198	+	0.362288i
$443$	−8.99848	−	15.5858i	−0.427531	−	0.740505i	0.569122	−	0.822253i	$-0.307283\pi$
$443$	−8.99848	−	15.5858i	−0.427531	−	0.740505i	−0.996653	+	0.0817479i	$0.973950\pi$
$444$	−8.06190	+	8.06190i	−0.382601	+	0.382601i
$445$	15.0584			0.713838
$446$	−10.9149			−0.516834
$447$	10.8249	−	10.8249i	0.512001	−	0.512001i
$448$	0.0462630	+	2.64535i	0.00218572	+	0.124981i
$449$	−7.09485	−	26.4783i	−0.334826	−	1.24959i	−0.904057	−	0.427411i	$-0.859426\pi$
$449$	−7.09485	−	26.4783i	−0.334826	−	1.24959i	0.569231	−	0.822178i	$-0.307241\pi$
$450$	−5.45410	−	1.46142i	−0.257109	−	0.0688921i
$451$	3.10644	−	1.79351i	0.146277	−	0.0844529i
$452$		−	2.57942i		−	0.121326i
$453$	22.1358	−	5.93126i	1.04003	−	0.278675i
$454$	11.0648			0.519295
$455$	−26.1615	−	16.8644i	−1.22647	−	0.790617i
$456$	−4.62444			−0.216559
$457$	38.5451	−	10.3281i	1.80306	−	0.483129i	0.808613	−	0.588340i	$-0.200219\pi$
$457$	38.5451	−	10.3281i	1.80306	−	0.483129i	0.994450	+	0.105211i	$0.0335518\pi$
$458$		−	2.54205i		−	0.118782i
$459$	−2.03880	+	1.17710i	−0.0951628	+	0.0549423i
$460$	−2.86050	−	0.766470i	−0.133372	−	0.0357368i
$461$	6.42732	+	23.9871i	0.299350	+	1.11719i	0.937701	+	0.347444i	$0.112950\pi$
$461$	6.42732	+	23.9871i	0.299350	+	1.11719i	−0.638350	+	0.769746i	$0.720383\pi$
$462$	3.12428	+	1.73168i	0.145355	+	0.0805651i
$463$	−0.812272	+	0.812272i	−0.0377495	+	0.0377495i	−0.725730	−	0.687980i	$-0.758498\pi$
$463$	−0.812272	+	0.812272i	−0.0377495	+	0.0377495i	0.687980	+	0.725730i	$0.258498\pi$
$464$	−8.83071			−0.409955
$465$	6.25660			0.290143
$466$	−18.5727	+	18.5727i	−0.860365	+	0.860365i
$467$	16.3896	+	28.3876i	0.758421	+	1.31362i	0.943656	+	0.330929i	$0.107362\pi$
$467$	16.3896	+	28.3876i	0.758421	+	1.31362i	−0.185235	+	0.982694i	$0.559305\pi$
$468$	3.53699	−	0.699772i	0.163498	−	0.0323470i
$469$	−23.5019	−	22.6940i	−1.08521	−	1.04791i
$470$	−6.14523	+	22.9343i	−0.283458	+	1.05788i
$471$	2.26359	−	3.92065i	0.104301	−	0.180654i
$472$	3.01056	+	5.21445i	0.138572	+	0.240014i
$473$	2.60504	−	0.698018i	0.119780	−	0.0320949i
$474$	8.74675	−	8.74675i	0.401752	−	0.401752i
$475$	−25.2221	+	6.75825i	−1.15727	+	0.310090i
$476$	5.44778	+	3.01951i	0.249698	+	0.138399i
$477$	−3.56317	+	6.17160i	−0.163146	+	0.282578i
$478$	−11.1338	−	6.42810i	−0.509248	−	0.294015i
$479$	−1.49287	−	1.49287i	−0.0682108	−	0.0682108i	0.672178	−	0.740389i	$-0.265359\pi$
$479$	−1.49287	−	1.49287i	−0.0682108	−	0.0682108i	−0.740389	+	0.672178i	$0.765359\pi$
$480$	−2.82575	−	1.63145i	−0.128977	−	0.0744651i
$481$	2.73075	−	41.0170i	0.124511	−	1.87021i
$482$			0.966735i			0.0440336i
$483$	1.16410	−	2.10025i	0.0529683	−	0.0955648i
$484$	4.58858	+	7.94766i	0.208572	+	0.361257i
$485$			29.4776i			1.33851i
$486$	0.258819	+	0.965926i	0.0117403	+	0.0438153i
$487$	−4.15962	+	15.5239i	−0.188490	+	0.703456i	0.805366	+	0.592778i	$0.201969\pi$
$487$	−4.15962	+	15.5239i	−0.188490	+	0.703456i	−0.993856	+	0.110678i	$0.964698\pi$
$488$	−0.516817	−	0.516817i	−0.0233952	−	0.0233952i
$489$	−10.9762	−	10.9762i	−0.496360	−	0.496360i
$490$	−22.8263	+	0.798638i	−1.03119	+	0.0360788i
$491$	6.53085	−	3.77059i	0.294733	−	0.170164i	−0.345341	−	0.938477i	$-0.612237\pi$
$491$	6.53085	−	3.77059i	0.294733	−	0.170164i	0.640074	+	0.768313i	$0.278904\pi$
$492$	−0.687631	−	2.56627i	−0.0310008	−	0.115697i
$493$	−10.3946	+	18.0040i	−0.468150	+	0.810860i
$494$	12.5472	−	10.9808i	0.564525	−	0.494050i
$495$	−3.81512	+	2.20266i	−0.171477	+	0.0990021i
$496$	1.85216	+	0.496285i	0.0831644	+	0.0222838i
$497$	5.66056	−	1.62334i	0.253911	−	0.0728169i
$498$	−3.03779	−	1.75387i	−0.136126	−	0.0785926i
$499$	−10.5818	+	39.4920i	−0.473708	+	1.76790i	0.152559	+	0.988294i	$0.451249\pi$
$499$	−10.5818	+	39.4920i	−0.473708	+	1.76790i	−0.626267	+	0.779609i	$0.715418\pi$
$500$	−2.03760	−	0.545972i	−0.0911240	−	0.0244166i
$501$	22.6820	+	6.07764i	1.01336	+	0.271529i
$502$	−3.62384	+	13.5244i	−0.161740	+	0.603622i
$503$	22.5080	+	12.9950i	1.00358	+	0.579419i	0.909307	−	0.416127i	$-0.136613\pi$
$503$	22.5080	+	12.9950i	1.00358	+	0.579419i	0.0942768	+	0.995546i	$0.469946\pi$
$504$	1.83783	−	1.90326i	0.0818634	−	0.0847777i
$505$	46.6455	+	12.4986i	2.07570	+	0.556181i
$506$	−1.06121	+	0.612687i	−0.0471763	+	0.0272373i
$507$	−7.93509	+	10.2973i	−0.352410	+	0.457319i
$508$	5.05587	−	8.75703i	0.224318	−	0.388530i
$509$	−5.84240	−	21.8041i	−0.258960	−	0.966451i	−0.965844	−	0.259122i	$-0.916567\pi$
$509$	−5.84240	−	21.8041i	−0.258960	−	0.966451i	0.706885	−	0.707329i	$-0.250100\pi$
$510$	−6.65238	+	3.84075i	−0.294572	+	0.170071i
$511$	16.3515	−	4.68930i	0.723346	−	0.207442i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	3.26997	+	3.26997i	0.144373	+	0.144373i
$514$	−8.18856	+	30.5601i	−0.361182	+	1.34795i
$515$	−13.1298	−	49.0012i	−0.578570	−	2.15925i
$516$		−	1.99755i		−	0.0879370i
$517$	4.91227	+	8.50830i	0.216041	+	0.374195i
$518$	−15.5369	−	25.8558i	−0.682653	−	1.13604i
$519$		−	8.06695i		−	0.354100i
$520$	11.5408	−	2.28329i	0.506100	−	0.100129i
$521$	38.5169	+	22.2377i	1.68746	+	0.974253i	0.956457	+	0.291875i	$0.0942791\pi$
$521$	38.5169	+	22.2377i	1.68746	+	0.974253i	0.730999	+	0.682378i	$0.239054\pi$
$522$	6.24425	+	6.24425i	0.273304	+	0.273304i
$523$	14.5874	+	8.42202i	0.637861	+	0.368269i	0.783790	−	0.621026i	$-0.213284\pi$
$523$	14.5874	+	8.42202i	0.637861	+	0.368269i	−0.145929	+	0.989295i	$0.546617\pi$
$524$	8.34878	−	14.4605i	0.364718	−	0.631710i
$525$	7.24225	−	13.0664i	0.316078	−	0.570264i
$526$	11.7755	−	3.15523i	0.513435	−	0.137574i
$527$	3.19200	−	3.19200i	0.139046	−	0.139046i
$528$	−1.30412	+	0.349438i	−0.0567545	+	0.0152073i
$529$	−11.0881	−	19.2052i	−0.482093	−	0.835009i
$530$	−11.6263	+	20.1373i	−0.505013	+	0.874708i
$531$	1.55838	−	5.81596i	0.0676280	−	0.252391i
$532$	2.95954	−	11.8718i	0.128313	−	0.514707i
$533$	7.95937	+	5.33012i	0.344759	+	0.230873i
$534$	−2.30752	−	3.99675i	−0.0998563	−	0.172956i
$535$	19.9143	−	19.9143i	0.860971	−	0.860971i
$536$	12.3482			0.533363
$537$	17.7297			0.765093
$538$	−11.2895	+	11.2895i	−0.486724	+	0.486724i
$539$	−6.44502	+	6.91236i	−0.277606	+	0.297736i
$540$	0.844500	+	3.15172i	0.0363415	+	0.135628i
$541$	19.0927	+	5.11588i	0.820860	+	0.219949i	0.644722	−	0.764417i	$-0.276973\pi$
$541$	19.0927	+	5.11588i	0.820860	+	0.219949i	0.176137	+	0.984366i	$0.443640\pi$
$542$	23.3935	−	13.5063i	1.00484	−	0.580143i
$543$			4.90151i			0.210344i
$544$	−2.27398	+	0.609311i	−0.0974961	+	0.0261240i
$545$	47.1964			2.02167
$546$	−0.467160	+	9.52795i	−0.0199926	+	0.407758i
$547$	14.9388			0.638737			0.319368	−	0.947631i	$-0.396529\pi$
$547$	14.9388			0.638737			0.319368	+	0.947631i	$0.396529\pi$
$548$	4.58235	−	1.22784i	0.195748	−	0.0524506i
$549$			0.730890i			0.0311936i
$550$	−6.60213	+	3.81174i	−0.281516	+	0.162533i
$551$	39.4456	+	10.5694i	1.68044	+	0.450272i
$552$	0.234905	+	0.876676i	0.00999820	+	0.0373138i
$553$	16.8568	+	28.0522i	0.716823	+	1.19290i
$554$	−20.9222	+	20.9222i	−0.888898	+	0.888898i
$555$	37.2011			1.57910
$556$	−7.62720			−0.323465
$557$	−13.4150	+	13.4150i	−0.568411	+	0.568411i	−0.931683	−	0.363272i	$-0.881659\pi$
$557$	−13.4150	+	13.4150i	−0.568411	+	0.568411i	0.363272	+	0.931683i	$0.381659\pi$
$558$	−0.958748	−	1.66060i	−0.0405870	−	0.0702988i
$559$	4.74321	+	5.41982i	0.200616	+	0.229234i
$560$	5.99665	−	6.21013i	0.253405	−	0.262426i
$561$	−0.822646	+	3.07016i	−0.0347321	+	0.129622i
$562$	−3.61515	+	6.26162i	−0.152496	+	0.264130i
$563$	2.58062	+	4.46976i	0.108760	+	0.188378i	0.915268	−	0.402845i	$-0.131979\pi$
$563$	2.58062	+	4.46976i	0.108760	+	0.188378i	−0.806508	+	0.591223i	$0.798645\pi$
$564$	7.02882	−	1.88337i	0.295967	−	0.0793040i
$565$	−5.95128	+	5.95128i	−0.250372	+	0.250372i
$566$	−19.1172	+	5.12245i	−0.803558	+	0.215313i
$567$	−2.64535	+	0.0462630i	−0.111094	+	0.00194286i
$568$	−1.11287	+	1.92754i	−0.0466948	+	0.0808777i
$569$	27.5895	+	15.9288i	1.15661	+	0.667771i	0.950490	−	0.310755i	$-0.100582\pi$
$569$	27.5895	+	15.9288i	1.15661	+	0.667771i	0.206123	+	0.978526i	$0.433915\pi$
$570$	10.6696	+	10.6696i	0.446899	+	0.446899i
$571$	28.2961	+	16.3367i	1.18415	+	0.683672i	0.956972	−	0.290181i	$-0.0937154\pi$
$571$	28.2961	+	16.3367i	1.18415	+	0.683672i	0.227182	+	0.973852i	$0.427049\pi$
$572$	2.70864	−	4.04476i	0.113254	−	0.169120i
$573$			1.73630i			0.0725350i
$574$	7.02816	−	0.122912i	0.293350	−	0.00513023i
$575$	2.56239	+	4.43818i	0.106859	+	0.185085i
$576$			1.00000i			0.0416667i
$577$	−7.85175	−	29.3031i	−0.326873	−	1.21991i	−0.912416	−	0.409264i	$-0.865785\pi$
$577$	−7.85175	−	29.3031i	−0.326873	−	1.21991i	0.585543	−	0.810641i	$-0.300881\pi$
$578$	2.96548	−	11.0673i	0.123348	−	0.460341i
$579$	−14.7628	−	14.7628i	−0.613523	−	0.613523i
$580$	20.3744	+	20.3744i	0.845999	+	0.845999i
$581$	6.44662	−	6.67611i	0.267451	−	0.276972i
$582$	7.82382	−	4.51708i	0.324308	−	0.187239i
$583$	2.49022	+	9.29361i	0.103134	+	0.384902i
$584$	−3.21470	+	5.56802i	−0.133025	+	0.230406i
$585$	−9.77514	−	6.54608i	−0.404152	−	0.270647i
$586$	11.2798	−	6.51239i	0.465964	−	0.269025i
$587$	−6.73302	−	1.80411i	−0.277902	−	0.0744635i	0.117176	−	0.993111i	$-0.462616\pi$
$587$	−6.73302	−	1.80411i	−0.277902	−	0.0744635i	−0.395078	+	0.918648i	$0.629282\pi$
$588$	3.70983	+	5.93609i	0.152991	+	0.244800i
$589$	−7.67934	−	4.43367i	−0.316422	−	0.182686i
$590$	5.08484	−	18.9769i	0.209340	−	0.781266i
$591$	3.11491	+	0.834638i	0.128130	+	0.0343324i
$592$	11.0128	+	2.95086i	0.452622	+	0.121280i
$593$	6.58817	−	24.5874i	0.270544	−	1.00968i	−0.688226	−	0.725497i	$-0.741610\pi$
$593$	6.58817	−	24.5874i	0.270544	−	1.00968i	0.958769	−	0.284186i	$-0.0917232\pi$
$594$	1.16924	+	0.675062i	0.0479746	+	0.0276981i
$595$	−5.60253	−	19.5359i	−0.229681	−	0.800893i
$596$	−14.7871	−	3.96219i	−0.605704	−	0.162298i
$597$	−2.84688	+	1.64365i	−0.116515	+	0.0672700i
$598$	−2.71903	−	1.82085i	−0.111190	−	0.0744599i
$599$	−6.75437	+	11.6989i	−0.275976	+	0.478004i	−0.970381	−	0.241580i	$-0.922334\pi$
$599$	−6.75437	+	11.6989i	−0.275976	+	0.478004i	0.694405	+	0.719584i	$0.255668\pi$
$600$	1.46142	+	5.45410i	0.0596623	+	0.222663i
$601$	36.4625	−	21.0516i	1.48734	−	0.858714i	0.487440	−	0.873157i	$-0.337931\pi$
$601$	36.4625	−	21.0516i	1.48734	−	0.858714i	0.999896	+	0.0144430i	$0.00459751\pi$
$602$	5.12806	+	1.27839i	0.209004	+	0.0521032i
$603$	−8.73152	−	8.73152i	−0.355575	−	0.355575i
$604$	−16.2045	−	16.2045i	−0.659352	−	0.659352i
$605$	7.75012	−	28.9238i	0.315087	−	1.17592i
$606$	−3.83053	−	14.2957i	−0.155605	−	0.580724i
$607$			22.9576i			0.931820i	0.884832	+	0.465910i	$0.154273\pi$
$607$			22.9576i			0.931820i	−0.884832	+	0.465910i	$0.845727\pi$
$608$	2.31222	+	4.00488i	0.0937728	+	0.162419i
$609$	−20.0263	+	12.0339i	−0.811508	+	0.487640i
$610$			2.38482i			0.0965585i
$611$	−14.5988	+	21.8001i	−0.590604	+	0.881936i
$612$	2.03880	+	1.17710i	0.0824134	+	0.0475814i
$613$	4.96217	+	4.96217i	0.200420	+	0.200420i	0.800180	−	0.599760i	$-0.204737\pi$
$613$	4.96217	+	4.96217i	0.200420	+	0.200420i	−0.599760	+	0.800180i	$0.704737\pi$
$614$	16.3741	+	9.45361i	0.660806	+	0.381517i
$615$	−4.33444	+	7.50747i	−0.174781	+	0.302730i
$616$	−0.0624608	−	3.57155i	−0.00251662	−	0.143902i
$617$	−11.9872	+	3.21195i	−0.482585	+	0.129308i	−0.491906	−	0.870648i	$-0.663700\pi$
$617$	−11.9872	+	3.21195i	−0.482585	+	0.129308i	0.00932104	+	0.999957i	$0.497033\pi$
$618$	−10.9937	+	10.9937i	−0.442232	+	0.442232i
$619$	−4.03018	+	1.07988i	−0.161987	+	0.0434042i	−0.338901	−	0.940822i	$-0.610055\pi$
$619$	−4.03018	+	1.07988i	−0.161987	+	0.0434042i	0.176914	+	0.984226i	$0.443388\pi$
$620$	−3.12830	−	5.41837i	−0.125635	−	0.217607i
$621$	0.453801	−	0.786006i	0.0182104	−	0.0315413i
$622$	−6.90930	+	25.7858i	−0.277038	+	1.03392i
$623$	11.7371	−	3.36600i	0.470239	−	0.134856i
$624$	−2.37452	−	2.71324i	−0.0950568	−	0.108617i
$625$	−10.6748	−	18.4892i	−0.426990	−	0.739569i
$626$	14.4616	−	14.4616i	0.578002	−	0.578002i
$627$	6.24356			0.249344
$628$	−4.52718			−0.180654
$629$	18.9793	−	18.9793i	0.756755	−	0.756755i
$630$	−8.63150	+	0.150951i	−0.343887	+	0.00601405i
$631$	10.4658	+	39.0589i	0.416637	+	1.55491i	0.781534	+	0.623862i	$0.214437\pi$
$631$	10.4658	+	39.0589i	0.416637	+	1.55491i	−0.364897	+	0.931048i	$0.618896\pi$
$632$	−11.9483	−	3.20153i	−0.475277	−	0.127350i
$633$	20.0012	−	11.5477i	0.794977	−	0.458980i
$634$			18.5477i			0.736625i
$635$	−31.8694	+	8.53937i	−1.26470	+	0.338875i
$636$	7.12635			0.282578
$637$	−24.1610	−	7.29697i	−0.957294	−	0.289117i
$638$	11.9226			0.472018
$639$	2.14989	−	0.576061i	0.0850484	−	0.0227886i
$640$			3.26290i			0.128977i
$641$	−4.89745	+	2.82754i	−0.193438	+	0.111681i	−0.593591	−	0.804767i	$-0.702290\pi$
$641$	−4.89745	+	2.82754i	−0.193438	+	0.111681i	0.400153	+	0.916448i	$0.368957\pi$
$642$	−8.33721	−	2.23395i	−0.329043	−	0.0881669i
$643$	−6.61282	−	24.6794i	−0.260784	−	0.973259i	−0.964781	−	0.263056i	$-0.915270\pi$
$643$	−6.61282	−	24.6794i	−0.260784	−	0.973259i	0.703997	−	0.710203i	$-0.251397\pi$
$644$	−2.40092	+	0.0419884i	−0.0946095	+	0.00165457i
$645$	−4.60877	+	4.60877i	−0.181470	+	0.181470i
$646$	10.8868			0.428337
$647$	21.9265			0.862018			0.431009	−	0.902348i	$-0.358158\pi$
$647$	21.9265			0.862018			0.431009	+	0.902348i	$0.358158\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	−4.06463	−	7.04015i	−0.159551	−	0.276350i
$650$	−16.9161	−	11.3281i	−0.663502	−	0.444325i
$651$	4.87664	−	1.39853i	0.191131	−	0.0548128i
$652$	−4.01756	+	14.9937i	−0.157340	+	0.587201i
$653$	−19.8235	+	34.3354i	−0.775754	+	1.34365i	0.158615	+	0.987341i	$0.449297\pi$
$653$	−19.8235	+	34.3354i	−0.775754	+	1.34365i	−0.934369	+	0.356306i	$0.884036\pi$
$654$	−7.23229	−	12.5267i	−0.282805	−	0.489832i
$655$	−52.6260	+	14.1011i	−2.05627	+	0.550975i
$656$	−1.87864	+	1.87864i	−0.0733487	+	0.0733487i
$657$	6.21032	−	1.66405i	0.242288	−	0.0649208i
$658$	0.336645	+	19.2496i	0.0131238	+	0.750427i
$659$	−10.7732	+	18.6598i	−0.419666	+	0.726883i	−0.995906	−	0.0903977i	$-0.971186\pi$
$659$	−10.7732	+	18.6598i	−0.419666	+	0.726883i	0.576240	+	0.817281i	$0.304520\pi$
$660$	3.81512	+	2.20266i	0.148503	+	0.0857384i
$661$	−18.8289	−	18.8289i	−0.732360	−	0.732360i	0.238727	−	0.971087i	$-0.423270\pi$
$661$	−18.8289	−	18.8289i	−0.732360	−	0.732360i	−0.971087	+	0.238727i	$0.923270\pi$
$662$	5.06611	+	2.92492i	0.196900	+	0.113680i
$663$	−8.32678	+	1.64740i	−0.323385	+	0.0639798i
$664$			3.50773i			0.136126i
$665$	−34.2191	+	20.5624i	−1.32696	+	0.797377i
$666$	−5.70063	−	9.87378i	−0.220895	−	0.382601i
$667$		−	8.01476i		−	0.310333i
$668$	−6.07764	−	22.6820i	−0.235151	−	0.877595i
$669$	2.82498	−	10.5430i	0.109220	−	0.407614i
$670$	−28.4901	−	28.4901i	−1.10067	−	1.10067i
$671$	0.697767	+	0.697767i	0.0269370	+	0.0269370i
$672$	−2.56718	−	0.639979i	−0.0990312	−	0.0246877i
$673$	−11.5158	+	6.64864i	−0.443901	+	0.256286i	−0.705251	−	0.708958i	$-0.749166\pi$
$673$	−11.5158	+	6.64864i	−0.443901	+	0.256286i	0.261350	+	0.965244i	$0.415832\pi$
$674$	−1.18749	−	4.43176i	−0.0457402	−	0.170705i
$675$	2.82325	−	4.89002i	0.108667	−	0.188217i
$676$	12.8853	+	1.72334i	0.495587	+	0.0662822i
$677$	−5.69857	+	3.29007i	−0.219014	+	0.126448i	−0.605494	−	0.795850i	$-0.707024\pi$
$677$	−5.69857	+	3.29007i	−0.219014	+	0.126448i	0.386480	+	0.922298i	$0.373691\pi$
$678$	2.49153	+	0.667603i	0.0956866	+	0.0256391i
$679$	6.58909	+	22.9760i	0.252866	+	0.881738i
$680$	6.65238	+	3.84075i	0.255107	+	0.147286i
$681$	−2.86377	+	10.6877i	−0.109740	+	0.409555i
$682$	−2.50065	−	0.670046i	−0.0957547	−	0.0256574i
$683$	−26.4973	−	7.09993i	−1.01389	−	0.271671i	−0.286637	−	0.958039i	$-0.592537\pi$
$683$	−26.4973	−	7.09993i	−1.01389	−	0.271671i	−0.727254	+	0.686368i	$0.759204\pi$
$684$	1.19689	−	4.46686i	0.0457643	−	0.170795i
$685$	−13.4054	−	7.73959i	−0.512193	−	0.295715i
$686$	−17.6132	+	5.72484i	−0.672477	+	0.218575i
$687$	2.45543	+	0.657930i	0.0936805	+	0.0251016i
$688$	−1.72993	+	0.998773i	−0.0659528	+	0.0380779i
$689$	−19.3355	+	16.9216i	−0.736623	+	0.644663i
$690$	1.48071	−	2.56466i	0.0563695	−	0.0976348i
$691$	−5.80273	−	21.6561i	−0.220746	−	0.823836i	−0.984064	−	0.177813i	$-0.943098\pi$
$691$	−5.80273	−	21.6561i	−0.220746	−	0.823836i	0.763318	−	0.646023i	$-0.223569\pi$
$692$	−6.98619	+	4.03348i	−0.265575	+	0.153330i
$693$	−2.48130	+	2.56963i	−0.0942567	+	0.0976122i
$694$	20.3378	+	20.3378i	0.772011	+	0.772011i
$695$	17.5976	+	17.5976i	0.667515	+	0.667515i
$696$	2.28556	−	8.52981i	0.0866338	−	0.323322i
$697$	1.61882	+	6.04152i	0.0613172	+	0.228839i
$698$		−	16.9845i		−	0.642872i
$699$	−13.1329	−	22.7469i	−0.496732	−	0.860365i
$700$	−14.9370	+	0.261224i	−0.564564	+	0.00987335i
$701$			0.0631558i			0.00238536i	0.999999	+	0.00119268i	$0.000379642\pi$
$701$			0.0631558i			0.00238536i	−0.999999	+	0.00119268i	$0.999620\pi$
$702$	−0.239513	+	3.59759i	−0.00903984	+	0.135782i
$703$	−45.6606	−	26.3622i	−1.72212	−	0.994269i
$704$	0.954682	+	0.954682i	0.0359809	+	0.0359809i
$705$	−20.5623	−	11.8717i	−0.774423	−	0.447113i
$706$	14.4133	−	24.9645i	0.542451	−	0.939552i
$707$	39.1512	−	0.684694i	1.47243	−	0.0257506i
$708$	−5.81596	+	1.55838i	−0.218577	+	0.0585676i
$709$	−4.89726	+	4.89726i	−0.183920	+	0.183920i	−0.793062	−	0.609141i	$-0.791514\pi$
$709$	−4.89726	+	4.89726i	−0.183920	+	0.183920i	0.609141	+	0.793062i	$0.291514\pi$
$710$	7.01487	−	1.87963i	0.263263	−	0.0705412i
$711$	6.18489	+	10.7125i	0.231951	+	0.401752i
$712$	−2.30752	+	3.99675i	−0.0864781	+	0.149784i
$713$	−0.450429	+	1.68102i	−0.0168687	+	0.0629548i
$714$	−4.32661	+	4.48064i	−0.161919	+	0.167684i
$715$	−15.5816	+	3.08272i	−0.582718	+	0.115287i
$716$	−8.86485	−	15.3544i	−0.331295	−	0.573820i
$717$	9.09071	−	9.09071i	0.339499	−	0.339499i
$718$	−26.7713			−0.999094
$719$	10.3766			0.386983			0.193491	−	0.981102i	$-0.438019\pi$
$719$	10.3766			0.386983			0.193491	+	0.981102i	$0.438019\pi$
$720$	2.30722	−	2.30722i	0.0859849	−	0.0859849i
$721$	−21.1871	−	35.2586i	−0.789050	−	1.31310i
$722$	−0.617388	−	2.30412i	−0.0229768	−	0.0857506i
$723$	−0.933794	−	0.250209i	−0.0347282	−	0.00930539i
$724$	4.24484	−	2.45076i	0.157758	−	0.0910817i
$725$		−	49.8626i		−	1.85185i
$726$	−8.86446	+	2.37522i	−0.328991	+	0.0881529i
$727$	50.1687			1.86065			0.930327	−	0.366730i	$-0.119523\pi$
$727$	50.1687			1.86065			0.930327	+	0.366730i	$0.119523\pi$
$728$	8.48502	−	4.35940i	0.314476	−	0.161570i
$729$	−1.00000			−0.0370370
$730$	20.2636	−	5.42963i	0.749991	−	0.200959i
$731$			4.70262i			0.173933i
$732$	0.632969	−	0.365445i	0.0233952	−	0.0135072i
$733$	−13.8923	−	3.72244i	−0.513125	−	0.137491i	−0.00704017	−	0.999975i	$-0.502241\pi$
$733$	−13.8923	−	3.72244i	−0.513125	−	0.137491i	−0.506085	+	0.862484i	$0.668908\pi$
$734$	−2.98507	−	11.1404i	−0.110181	−	0.411201i
$735$	5.13646	−	22.2552i	0.189461	−	0.820897i
$736$	0.641771	−	0.641771i	0.0236560	−	0.0236560i
$737$	−16.6717			−0.614108
$738$	2.65680			0.0977982
$739$	−24.4423	+	24.4423i	−0.899126	+	0.899126i	−0.995359	−	0.0962327i	$-0.969321\pi$
$739$	−24.4423	+	24.4423i	−0.899126	+	0.899126i	0.0962327	+	0.995359i	$0.469321\pi$
$740$	−18.6006	−	32.2171i	−0.683770	−	1.18432i
$741$	7.35918	+	14.9617i	0.270346	+	0.549632i
$742$	−4.56072	+	18.2946i	−0.167429	+	0.671617i
$743$	−0.470553	+	1.75613i	−0.0172629	+	0.0644261i	−0.974020	−	0.226462i	$-0.927284\pi$
$743$	−0.470553	+	1.75613i	−0.0172629	+	0.0644261i	0.956757	+	0.290888i	$0.0939507\pi$
$744$	−0.958748	+	1.66060i	−0.0351494	+	0.0608806i
$745$	24.9754	+	43.2587i	0.915029	+	1.58488i
$746$	−6.20777	+	1.66337i	−0.227283	+	0.0609002i
$747$	2.48034	−	2.48034i	0.0907509	−	0.0907509i
$748$	3.07016	−	0.822646i	0.112256	−	0.0300789i
$749$	11.0706	−	19.9735i	0.404511	−	0.729814i
$750$	1.05474	−	1.82686i	0.0385135	−	0.0667074i
$751$	−19.0010	−	10.9702i	−0.693357	−	0.400310i	0.111511	−	0.993763i	$-0.464431\pi$
$751$	−19.0010	−	10.9702i	−0.693357	−	0.400310i	−0.804869	+	0.593453i	$0.797764\pi$
$752$	−5.14545	−	5.14545i	−0.187635	−	0.187635i
$753$	−12.1256	−	7.00072i	−0.441882	−	0.255121i
$754$	14.0529	+	28.5705i	0.511777	+	1.04048i
$755$			74.7747i			2.72133i
$756$	1.36274	+	2.26781i	0.0495623	+	0.0824793i
$757$	3.21431	+	5.56735i	0.116826	+	0.202349i	0.918508	−	0.395402i	$-0.129395\pi$
$757$	3.21431	+	5.56735i	0.116826	+	0.202349i	−0.801682	+	0.597751i	$0.796061\pi$
$758$		−	19.2793i		−	0.700256i
$759$	−0.317150	−	1.18362i	−0.0115118	−	0.0429627i
$760$	3.90534	−	14.5749i	0.141661	−	0.528688i
$761$	1.13229	+	1.13229i	0.0410455	+	0.0410455i	0.727332	−	0.686286i	$-0.240760\pi$
$761$	1.13229	+	1.13229i	0.0410455	+	0.0410455i	−0.686286	+	0.727332i	$0.740760\pi$
$762$	7.15008	+	7.15008i	0.259020	+	0.259020i
$763$	36.7868	−	10.5498i	1.33177	−	0.381928i
$764$	1.50368	−	0.868151i	0.0544013	−	0.0314086i
$765$	−1.98812	−	7.41977i	−0.0718806	−	0.268262i
$766$	−5.42345	+	9.39369i	−0.195957	+	0.339408i
$767$	12.0797	−	18.0384i	0.436172	−	0.651328i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	−25.2697	−	6.77100i	−0.911249	−	0.244168i	−0.227408	−	0.973800i	$-0.573025\pi$
$769$	−25.2697	−	6.77100i	−0.911249	−	0.244168i	−0.683841	+	0.729631i	$0.739692\pi$
$770$	−8.09622	+	8.38444i	−0.291768	+	0.302154i
$771$	−27.3994	−	15.8191i	−0.986767	−	0.569710i
$772$	−5.40357	+	20.1664i	−0.194479	+	0.725805i
$773$	0.0523937	+	0.0140389i	0.00188447	+	0.000504943i	0.259761	−	0.965673i	$-0.416356\pi$
$773$	0.0523937	+	0.0140389i	0.00188447	+	0.000504943i	−0.257877	+	0.966178i	$0.583023\pi$
$774$	1.92948	+	0.517003i	0.0693537	+	0.0185833i
$775$	−2.80227	+	10.4582i	−0.100661	+	0.375670i
$776$	−7.82382	−	4.51708i	−0.280859	−	0.162154i
$777$	28.9961	−	8.31554i	1.04023	−	0.298318i
$778$	−5.10373	−	1.36754i	−0.182977	−	0.0490287i
$779$	10.6402	−	6.14310i	0.381224	−	0.220100i
$780$	−0.781507	+	11.7386i	−0.0279824	+	0.420308i
$781$	1.50251	−	2.60242i	0.0537639	−	0.0931218i
$782$	−0.553012	−	2.06387i	−0.0197757	−	0.0738038i
$783$	−7.64762	+	4.41535i	−0.273304	+	0.157792i
$784$	3.28589	−	6.18085i	0.117353	−	0.220745i
$785$	10.4452	+	10.4452i	0.372805	+	0.372805i
$786$	11.8070	+	11.8070i	0.421140	+	0.421140i
$787$	8.38264	−	31.2844i	0.298809	−	1.11517i	−0.639336	−	0.768927i	$-0.720791\pi$
$787$	8.38264	−	31.2844i	0.298809	−	1.11517i	0.938145	−	0.346243i	$-0.112543\pi$
$788$	−0.834638	−	3.11491i	−0.0297327	−	0.110964i
$789$			12.1909i			0.434006i
$790$	20.1807	+	34.9539i	0.717995	+	1.24360i
$791$	−3.30839	+	5.96896i	−0.117633	+	0.212232i
$792$		−	1.35012i		−	0.0479746i
$793$	−0.849641	+	2.49453i	−0.0301717	+	0.0885835i
$794$	−18.0051	−	10.3953i	−0.638978	−	0.368914i
$795$	−16.4420	−	16.4420i	−0.583139	−	0.583139i
$796$	2.84688	+	1.64365i	0.100905	+	0.0582575i
$797$	12.7099	−	22.0142i	0.450209	−	0.779784i	−0.548190	−	0.836354i	$-0.684683\pi$
$797$	12.7099	−	22.0142i	0.450209	−	0.779784i	0.998399	+	0.0565694i	$0.0180162\pi$
$798$	10.7013	+	5.93134i	0.378821	+	0.209967i
$799$	−16.5472	+	4.43382i	−0.585399	+	0.156857i
$800$	3.99268	−	3.99268i	0.141163	−	0.141163i
$801$	4.45779	−	1.19446i	0.157508	−	0.0422042i
$802$	−18.3926	−	31.8569i	−0.649464	−	1.12490i
$803$	4.34024	−	7.51752i	0.153164	−	0.265287i
$804$	−3.19596	+	11.9275i	−0.112713	+	0.420650i
$805$	5.63632	+	5.44257i	0.198654	+	0.191825i
$806$	−1.34181	−	6.78217i	−0.0472633	−	0.238892i
$807$	−7.98287	−	13.8267i	−0.281010	−	0.486724i
$808$	−10.4652	+	10.4652i	−0.368164	+	0.368164i
$809$	−21.2591			−0.747430			−0.373715	−	0.927544i	$-0.621916\pi$
$809$	−21.2591			−0.747430			−0.373715	+	0.927544i	$0.621916\pi$
$810$	−3.26290			−0.114647
$811$	−12.7475	+	12.7475i	−0.447627	+	0.447627i	−0.894565	−	0.446938i	$-0.852514\pi$
$811$	−12.7475	+	12.7475i	−0.447627	+	0.447627i	0.446938	+	0.894565i	$0.352514\pi$
$812$	20.4349	+	11.3263i	0.717123	+	0.397477i
$813$	6.99135	+	26.0921i	0.245197	+	0.915089i
$814$	−14.8686	−	3.98403i	−0.521144	−	0.139640i
$815$	43.8632	−	25.3244i	1.53646	−	0.887077i
$816$		−	2.35420i		−	0.0824134i
$817$	8.92276	−	2.39085i	0.312168	−	0.0836451i
$818$	−9.56160			−0.334313
$819$	−9.08238	−	2.91726i	−0.317364	−	0.101937i
$820$	8.66887			0.302730
$821$	−14.9767	+	4.01300i	−0.522691	+	0.140055i	−0.510511	−	0.859871i	$-0.670544\pi$
$821$	−14.9767	+	4.01300i	−0.522691	+	0.140055i	−0.0121801	+	0.999926i	$0.503877\pi$
$822$			4.74400i			0.165466i
$823$	25.1368	−	14.5127i	0.876213	−	0.505882i	0.00680487	−	0.999977i	$-0.497834\pi$
$823$	25.1368	−	14.5127i	0.876213	−	0.505882i	0.869408	+	0.494095i	$0.164501\pi$
$824$	15.0177	+	4.02398i	0.523166	+	0.140182i
$825$	−1.97310	−	7.36372i	−0.0686946	−	0.256372i
$826$	−0.278555	−	15.9280i	−0.00969218	−	0.554205i
$827$	−9.10517	+	9.10517i	−0.316618	+	0.316618i	−0.847467	−	0.530849i	$-0.821873\pi$
$827$	−9.10517	+	9.10517i	−0.316618	+	0.316618i	0.530849	+	0.847467i	$0.321873\pi$
$828$	−0.907601			−0.0315413
$829$	5.46690			0.189873			0.0949367	−	0.995483i	$-0.469735\pi$
$829$	5.46690			0.189873			0.0949367	+	0.995483i	$0.469735\pi$
$830$	8.09310	−	8.09310i	0.280916	−	0.280916i
$831$	−14.7942	−	25.6243i	−0.513205	−	0.888898i
$832$	−1.16248	+	3.41301i	−0.0403016	+	0.118325i
$833$	−8.73368	−	13.9747i	−0.302604	−	0.484196i
$834$	1.97406	−	7.36731i	0.0683563	−	0.255109i
$835$	−38.3100	+	66.3548i	−1.32577	+	2.29630i
$836$	−3.12178	−	5.40708i	−0.107969	−	0.187008i
$837$	1.85216	−	0.496285i	0.0640200	−	0.0171541i
$838$	11.4974	−	11.4974i	0.397170	−	0.397170i
$839$	−39.3013	+	10.5308i	−1.35683	+	0.363562i	−0.862652	−	0.505798i	$-0.831198\pi$
$839$	−39.3013	+	10.5308i	−1.35683	+	0.363562i	−0.494180	+	0.869360i	$0.664532\pi$
$840$	4.44648	+	7.39962i	0.153418	+	0.255311i
$841$	−24.4907	+	42.4191i	−0.844507	+	1.46273i
$842$	18.2847	+	10.5567i	0.630132	+	0.363807i
$843$	−5.11259	−	5.11259i	−0.176087	−	0.176087i
$844$	−20.0012	−	11.5477i	−0.688470	−	0.397489i
$845$	−25.7530	−	33.7052i	−0.885930	−	1.15950i
$846$			7.27677i			0.250180i
$847$	−0.424563	−	24.2768i	−0.0145882	−	0.834160i
$848$	−3.56317	−	6.17160i	−0.122360	−	0.211933i
$849$		−	19.7916i		−	0.679247i
$850$	−3.44048	−	12.8400i	−0.118007	−	0.440410i
$851$	−2.67821	+	9.99520i	−0.0918077	+	0.342631i
$852$	−1.57383	−	1.57383i	−0.0539185	−	0.0539185i
$853$	24.1236	+	24.1236i	0.825975	+	0.825975i	0.986957	−	0.160982i	$-0.0514662\pi$
$853$	24.1236	+	24.1236i	0.825975	+	0.825975i	−0.160982	+	0.986957i	$0.551466\pi$
$854$	0.533076	+	1.85882i	0.0182415	+	0.0636076i
$855$	−13.0675	+	7.54453i	−0.446899	+	0.258018i
$856$	2.23395	+	8.33721i	0.0763548	+	0.284960i
$857$	−5.67732	+	9.83340i	−0.193934	+	0.335903i	−0.946550	−	0.322556i	$-0.895458\pi$
$857$	−5.67732	+	9.83340i	−0.193934	+	0.335903i	0.752617	+	0.658459i	$0.228791\pi$
$858$	3.20589	+	3.66321i	0.109447	+	0.125060i
$859$	10.0106	−	5.77961i	0.341557	−	0.197198i	−0.319404	−	0.947619i	$-0.603483\pi$
$859$	10.0106	−	5.77961i	0.341557	−	0.197198i	0.660960	+	0.750421i	$0.270149\pi$
$860$	6.29570	+	1.68693i	0.214682	+	0.0575237i
$861$	−1.70030	+	6.82050i	−0.0579460	+	0.232442i
$862$	15.8083	+	9.12693i	0.538433	+	0.310864i
$863$	8.23379	−	30.7289i	0.280281	−	1.04602i	−0.671938	−	0.740608i	$-0.734538\pi$
$863$	8.23379	−	30.7289i	0.280281	−	1.04602i	0.952219	−	0.305416i	$-0.0987956\pi$
$864$	−0.965926	−	0.258819i	−0.0328615	−	0.00880520i
$865$	25.4248	+	6.81254i	0.864468	+	0.231633i
$866$	0.140988	−	0.526176i	0.00479098	−	0.0178802i
$867$	9.92270	+	5.72888i	0.336993	+	0.194563i
$868$	−3.64949	−	3.52403i	−0.123872	−	0.119613i
$869$	16.1317	+	4.32247i	0.547229	+	0.146630i
$870$	−24.9534	+	14.4068i	−0.845999	+	0.488438i
$871$	−19.6506	−	39.9510i	−0.665836	−	1.35369i
$872$	−7.23229	+	12.5267i	−0.244916	+	0.424207i
$873$	2.33821	+	8.72634i	0.0791366	+	0.295342i
$874$	−3.63483	+	2.09857i	−0.122950	+	0.0709853i
$875$	4.01487	+	3.87685i	0.135727	+	0.131062i
$876$	−4.54627	−	4.54627i	−0.153604	−	0.153604i
$877$	19.3180	+	19.3180i	0.652323	+	0.652323i	0.953552	−	0.301229i	$-0.0973967\pi$
$877$	19.3180	+	19.3180i	0.652323	+	0.652323i	−0.301229	+	0.953552i	$0.597397\pi$
$878$	2.63542	−	9.83551i	0.0889411	−	0.331933i
$879$	3.37106	+	12.5810i	0.113703	+	0.424346i
$880$		−	4.40532i		−	0.148503i
$881$	−2.63093	−	4.55691i	−0.0886384	−	0.153526i	0.818297	−	0.574795i	$-0.194918\pi$
$881$	−2.63093	−	4.55691i	−0.0886384	−	0.153526i	−0.906936	+	0.421269i	$0.861585\pi$
$882$	−6.69400	+	2.04705i	−0.225399	+	0.0689277i
$883$		−	23.4641i		−	0.789630i	−0.918761	−	0.394815i	$-0.870809\pi$
$883$		−	23.4641i		−	0.789630i	0.918761	−	0.394815i	$-0.129191\pi$
$884$	5.59008	+	6.38750i	0.188015	+	0.214835i
$885$	17.0142	+	9.82316i	0.571926	+	0.330202i
$886$	−12.7258	−	12.7258i	−0.427531	−	0.427531i
$887$	−19.2357	−	11.1057i	−0.645872	−	0.372894i	0.141001	−	0.990009i	$-0.454968\pi$
$887$	−19.2357	−	11.1057i	−0.645872	−	0.372894i	−0.786873	+	0.617115i	$0.788301\pi$
$888$	−5.70063	+	9.87378i	−0.191301	+	0.331342i
$889$	−22.9315	+	13.7797i	−0.769097	+	0.462155i
$890$	14.5453	−	3.89741i	0.487560	−	0.130641i
$891$	−0.954682	+	0.954682i	−0.0319830	+	0.0319830i
$892$	−10.5430	+	2.82498i	−0.353004	+	0.0945872i
$893$	16.8255	+	29.1426i	0.563043	+	0.975219i
$894$	7.65437	−	13.2578i	0.256000	−	0.443406i
$895$	−14.9727	+	55.8790i	−0.500483	+	1.86783i
$896$	0.729353	+	2.54324i	0.0243660	+	0.0849635i
$897$	2.46254	−	2.15512i	0.0822218	−	0.0719572i
$898$	−13.7062	−	23.7398i	−0.457381	−	0.792208i
$899$	11.9733	−	11.9733i	0.399333	−	0.399333i
$900$	−5.64650			−0.188217
$901$	−16.7768			−0.558917
$902$	2.53640	−	2.53640i	0.0844529	−	0.0844529i
$903$	−2.56207	+	4.62246i	−0.0852603	+	0.153826i
$904$	−0.667603	−	2.49153i	−0.0222042	−	0.0828670i
$905$	−15.4482	−	4.13933i	−0.513515	−	0.137596i
$906$	19.8464	−	11.4583i	0.659352	−	0.380677i
$907$			34.6022i			1.14895i	0.818523	+	0.574474i	$0.194793\pi$
$907$			34.6022i			1.14895i	−0.818523	+	0.574474i	$0.805207\pi$
$908$	10.6877	−	2.86377i	0.354685	−	0.0950376i
$909$	14.8000			0.490886
$910$	−29.6349	−	9.51871i	−0.982387	−	0.315542i
$911$	−39.6228			−1.31276			−0.656381	−	0.754430i	$-0.727914\pi$
$911$	−39.6228			−1.31276			−0.656381	+	0.754430i	$0.727914\pi$
$912$	−4.46686	+	1.19689i	−0.147913	+	0.0396331i
$913$		−	4.73587i		−	0.156735i
$914$	34.5586	−	19.9524i	1.14310	−	0.659967i
$915$	−2.30356	−	0.617236i	−0.0761533	−	0.0204052i
$916$	−0.657930	−	2.45543i	−0.0217386	−	0.0811297i
$917$	−37.8668	+	22.7544i	−1.25047	+	0.751416i
$918$	−1.66467	+	1.66467i	−0.0549423	+	0.0549423i
$919$	5.46913			0.180410			0.0902050	−	0.995923i	$-0.471248\pi$
$919$	5.46913			0.180410			0.0902050	+	0.995923i	$0.471248\pi$
$920$	−2.96141			−0.0976348
$921$	−13.3694	+	13.3694i	−0.440538	+	0.440538i
$922$	12.4166	+	21.5062i	0.408920	+	0.708270i
$923$	8.00726	+	0.533091i	0.263562	+	0.0175469i
$924$	3.46602	+	0.864052i	0.114024	+	0.0284252i
$925$	−16.6620	+	62.1836i	−0.547845	+	2.04458i
$926$	−0.574363	+	0.994827i	−0.0188748	+	0.0326920i
$927$	−7.77373	−	13.4645i	−0.255323	−	0.442232i
$928$	−8.52981	+	2.28556i	−0.280005	+	0.0750270i
$929$	15.2246	−	15.2246i	0.499502	−	0.499502i	−0.411781	−	0.911283i	$-0.635093\pi$
$929$	15.2246	−	15.2246i	0.499502	−	0.499502i	0.911283	+	0.411781i	$0.135093\pi$
$930$	6.04341	−	1.61933i	0.198171	−	0.0530998i
$931$	−22.0754	+	23.6762i	−0.723493	+	0.775955i
$932$	−13.1329	+	22.7469i	−0.430183	+	0.745098i
$933$	−23.1190	−	13.3477i	−0.756881	−	0.436985i
$934$	23.1784	+	23.1784i	0.758421	+	0.758421i
$935$	−8.98154	−	5.18549i	−0.293728	−	0.169584i
$936$	3.23536	−	1.59137i	0.105751	−	0.0520155i
$937$			9.49034i			0.310036i	0.987912	+	0.155018i	$0.0495435\pi$
$937$			9.49034i			0.310036i	−0.987912	+	0.155018i	$0.950456\pi$
$938$	−28.5747	−	15.8380i	−0.932996	−	0.517128i
$939$	10.2259	+	17.7118i	0.333710	+	0.578002i
$940$			23.7434i			0.774423i
$941$	−13.1769	−	49.1768i	−0.429554	−	1.60312i	−0.753773	−	0.657135i	$-0.771768\pi$
$941$	−13.1769	−	49.1768i	−0.429554	−	1.60312i	0.324219	−	0.945982i	$-0.394898\pi$
$942$	1.17172	−	4.37292i	0.0381767	−	0.142477i
$943$	−1.70506	−	1.70506i	−0.0555244	−	0.0555244i
$944$	4.25758	+	4.25758i	0.138572	+	0.138572i
$945$	2.08819	−	8.37645i	0.0679288	−	0.272486i
$946$	2.33561	−	1.34847i	0.0759373	−	0.0438424i
$947$	−0.878781	−	3.27965i	−0.0285565	−	0.106574i	0.950177	−	0.311712i	$-0.100902\pi$
$947$	−0.878781	−	3.27965i	−0.0285565	−	0.106574i	−0.978733	+	0.205138i	$0.934236\pi$
$948$	6.18489	−	10.7125i	0.200876	−	0.347927i
$949$	23.1303	+	1.53992i	0.750842	+	0.0499880i
$950$	−22.6136	+	13.0559i	−0.733681	+	0.423591i
$951$	−17.9157	−	4.80051i	−0.580958	−	0.155667i
$952$	6.04366	+	1.50664i	0.195876	+	0.0488304i
$953$	−40.7371	−	23.5196i	−1.31960	−	0.761873i	−0.335938	−	0.941884i	$-0.609053\pi$
$953$	−40.7371	−	23.5196i	−1.31960	−	0.761873i	−0.983665	+	0.180011i	$0.942387\pi$
$954$	−1.84443	+	6.88352i	−0.0597158	+	0.222862i
$955$	−5.47233	−	1.46631i	−0.177080	−	0.0474486i
$956$	−12.4181	−	3.32743i	−0.401631	−	0.107617i
$957$	−3.08578	+	11.5163i	−0.0997492	+	0.372269i
$958$	−1.82838	−	1.05562i	−0.0590723	−	0.0341054i
$959$	−12.1787	−	3.03606i	−0.393271	−	0.0980396i
$960$	−3.15172	−	0.844500i	−0.101721	−	0.0272561i
$961$	23.6626	−	13.6616i	0.763309	−	0.440697i
$962$	−7.97828	−	40.3262i	−0.257230	−	1.30017i
$963$	4.31566	−	7.47494i	0.139070	−	0.240877i
$964$	0.250209	+	0.933794i	0.00805870	+	0.0300755i
$965$	58.9955	−	34.0611i	1.89913	−	1.09646i
$966$	0.580846	−	2.32998i	0.0186884	−	0.0749658i
$967$	−17.3419	−	17.3419i	−0.557679	−	0.557679i	0.370967	−	0.928646i	$-0.379026\pi$
$967$	−17.3419	−	17.3419i	−0.557679	−	0.557679i	−0.928646	+	0.370967i	$0.879026\pi$
$968$	6.48924	+	6.48924i	0.208572	+	0.208572i
$969$	−2.81772	+	10.5159i	−0.0905182	+	0.337819i
$970$	7.62936	+	28.4731i	0.244964	+	0.914217i
$971$		−	34.1823i		−	1.09696i	−0.836163	−	0.548481i	$-0.815206\pi$
$971$		−	34.1823i		−	1.09696i	0.836163	−	0.548481i	$-0.184794\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	17.6499	+	9.78271i	0.565829	+	0.313619i
$974$			16.0715i			0.514965i
$975$	15.3203	−	13.4077i	0.490643	−	0.429391i
$976$	−0.632969	−	0.365445i	−0.0202608	−	0.0116976i
$977$	−10.2646	−	10.2646i	−0.328393	−	0.328393i	0.523582	−	0.851975i	$-0.324595\pi$
$977$	−10.2646	−	10.2646i	−0.328393	−	0.328393i	−0.851975	+	0.523582i	$0.824595\pi$
$978$	−13.4430	−	7.76134i	−0.429861	−	0.248180i
$979$	3.11544	−	5.39610i	0.0995700	−	0.172460i
$980$	−21.8418	+	6.67931i	−0.697712	+	0.213363i
$981$	13.9717	−	3.74371i	0.446082	−	0.119527i
$982$	5.33241	−	5.33241i	0.170164	−	0.170164i
$983$	−36.3649	+	9.74394i	−1.15986	+	0.310784i	−0.786910	−	0.617068i	$-0.788320\pi$
$983$	−36.3649	+	9.74394i	−1.15986	+	0.310784i	−0.372950	+	0.927851i	$0.621654\pi$
$984$	−1.32840	−	2.30086i	−0.0423479	−	0.0733487i
$985$	−5.26108	+	9.11247i	−0.167632	+	0.290347i
$986$	−5.38065	+	20.0809i	−0.171355	+	0.639505i
$987$	−18.6808	−	4.65698i	−0.594616	−	0.148233i
$988$	9.27763	−	13.8541i	0.295161	−	0.440757i
$989$	−0.906488	−	1.57008i	−0.0288246	−	0.0499257i
$990$	−3.11503	+	3.11503i	−0.0990021	+	0.0990021i
$991$	31.2388			0.992334			0.496167	−	0.868227i	$-0.334740\pi$
$991$	31.2388			0.992334			0.496167	+	0.868227i	$0.334740\pi$
$992$	1.91750			0.0608806
$993$	−4.13646	+	4.13646i	−0.131267	+	0.131267i
$994$	5.04752	−	3.03309i	0.160098	−	0.0962037i
$995$	−2.77612	−	10.3606i	−0.0880089	−	0.328454i
$996$	−3.38821	−	0.907868i	−0.107360	−	0.0287669i
$997$	−50.6477	+	29.2415i	−1.60403	+	0.926087i	−0.613360	+	0.789803i	$0.710183\pi$
$997$	−50.6477	+	29.2415i	−1.60403	+	0.926087i	−0.990670	+	0.136284i	$0.956484\pi$
$998$			40.8851i			1.29419i
$999$	11.0128	−	2.95086i	0.348428	−	0.0933611i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.by.b.115.6	yes	40
7.5	odd	6		546.2.cg.b.271.1	yes	40
13.6	odd	12		546.2.cg.b.409.1	yes	40
91.19	even	12	inner	546.2.by.b.19.6	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.19.6	✓	40	91.19	even	12	inner
546.2.by.b.115.6	yes	40	1.1	even	1	trivial
546.2.cg.b.271.1	yes	40	7.5	odd	6
546.2.cg.b.409.1	yes	40	13.6	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(-3.15172 - 0.844500i) q^{5} +(0.258819 + 0.965926i) q^{6} +(-2.64535 + 0.0462630i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(-3.15172 - 0.844500i) q^{5} +(0.258819 + 0.965926i) q^{6} +(-2.64535 + 0.0462630i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} -3.26290 q^{10} +(-0.954682 + 0.954682i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-3.41301 - 1.16248i) q^{13} +(-2.54324 + 0.729353i) q^{14} +(0.844500 - 3.15172i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.17710 - 2.03880i) q^{17} +(-0.965926 + 0.258819i) q^{18} +(-3.26997 + 3.26997i) q^{19} +(-3.15172 + 0.844500i) q^{20} +(-0.0462630 - 2.64535i) q^{21} +(-0.675062 + 1.16924i) q^{22} +(0.786006 + 0.453801i) q^{23} +(0.707107 + 0.707107i) q^{24} +(4.89002 + 2.82325i) q^{25} +(-3.59759 - 0.239513i) q^{26} -1.00000i q^{27} +(-2.26781 + 1.36274i) q^{28} +(-4.41535 - 7.64762i) q^{29} -3.26290i q^{30} +(0.496285 + 1.85216i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-0.954682 - 0.954682i) q^{33} +(-1.66467 - 1.66467i) q^{34} +(8.37645 + 2.08819i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(2.95086 + 11.0128i) q^{37} +(-2.31222 + 4.00488i) q^{38} +(1.16248 - 3.41301i) q^{39} +(-2.82575 + 1.63145i) q^{40} +(-2.56627 - 0.687631i) q^{41} +(-0.729353 - 2.54324i) q^{42} +(-1.72993 - 0.998773i) q^{43} +(-0.349438 + 1.30412i) q^{44} +(3.15172 + 0.844500i) q^{45} +(0.876676 + 0.234905i) q^{46} +(1.88337 - 7.02882i) q^{47} +(0.866025 + 0.500000i) q^{48} +(6.99572 - 0.244763i) q^{49} +(5.45410 + 1.46142i) q^{50} +(2.03880 - 1.17710i) q^{51} +(-3.53699 + 0.699772i) q^{52} +(3.56317 - 6.17160i) q^{53} +(-0.258819 - 0.965926i) q^{54} +(3.81512 - 2.20266i) q^{55} +(-1.83783 + 1.90326i) q^{56} +(-3.26997 - 3.26997i) q^{57} +(-6.24425 - 6.24425i) q^{58} +(-1.55838 + 5.81596i) q^{59} +(-0.844500 - 3.15172i) q^{60} -0.730890i q^{61} +(0.958748 + 1.66060i) q^{62} +(2.64535 - 0.0462630i) q^{63} -1.00000i q^{64} +(9.77514 + 6.54608i) q^{65} +(-1.16924 - 0.675062i) q^{66} +(8.73152 + 8.73152i) q^{67} +(-2.03880 - 1.17710i) q^{68} +(-0.453801 + 0.786006i) q^{69} +(8.63150 - 0.150951i) q^{70} +(-2.14989 + 0.576061i) q^{71} +(-0.707107 + 0.707107i) q^{72} +(-6.21032 + 1.66405i) q^{73} +(5.70063 + 9.87378i) q^{74} +(-2.82325 + 4.89002i) q^{75} +(-1.19689 + 4.46686i) q^{76} +(2.48130 - 2.56963i) q^{77} +(0.239513 - 3.59759i) q^{78} +(-6.18489 - 10.7125i) q^{79} +(-2.30722 + 2.30722i) q^{80} +1.00000 q^{81} -2.65680 q^{82} +(-2.48034 + 2.48034i) q^{83} +(-1.36274 - 2.26781i) q^{84} +(1.98812 + 7.41977i) q^{85} +(-1.92948 - 0.517003i) q^{86} +(7.64762 - 4.41535i) q^{87} +1.35012i q^{88} +(-4.45779 + 1.19446i) q^{89} +3.26290 q^{90} +(9.08238 + 2.91726i) q^{91} +0.907601 q^{92} +(-1.85216 + 0.496285i) q^{93} -7.27677i q^{94} +(13.0675 - 7.54453i) q^{95} +(0.965926 + 0.258819i) q^{96} +(-2.33821 - 8.72634i) q^{97} +(6.69400 - 2.04705i) q^{98} +(0.954682 - 0.954682i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) \) 40 * q - 4 * q^7 - 40 * q^9	\( 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

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