LMFDB - Embedded newform 546.2.bx.b.223.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("546.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			223.6
Character	$\chi$	$=$	546.223
Dual form			546.2.bx.b.475.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.50346 - 2.50346i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(-0.691933 + 2.55367i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.50346 - 2.50346i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(-0.691933 + 2.55367i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.77021 - 3.06610i) q^{10} +(-0.883046 + 3.29557i) q^{11} -1.00000 q^{12} +(-1.87030 + 3.08253i) q^{13} +(-1.32929 + 2.28757i) q^{14} +(3.41979 + 0.916329i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.906845 - 1.57070i) q^{17} +(0.707107 - 0.707107i) q^{18} +(-6.44615 + 1.72724i) q^{19} +(-0.916329 - 3.41979i) q^{20} +(-0.677603 - 2.55751i) q^{21} +(-1.70591 + 2.95473i) q^{22} +(-5.86204 + 3.38445i) q^{23} +(-0.965926 - 0.258819i) q^{24} +7.53460i q^{25} +(-2.60439 + 2.49343i) q^{26} +1.00000i q^{27} +(-1.87607 + 1.86558i) q^{28} +(-2.24008 - 3.87993i) q^{29} +(3.06610 + 1.77021i) q^{30} +(6.69700 + 6.69700i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-0.883046 - 3.29557i) q^{33} +(1.28247 - 1.28247i) q^{34} +(8.12523 - 4.66078i) q^{35} +(0.866025 - 0.500000i) q^{36} +(0.544249 - 2.03117i) q^{37} -6.67355 q^{38} +(0.0784593 - 3.60470i) q^{39} -3.54042i q^{40} +(1.43414 - 5.35230i) q^{41} +(0.00741761 - 2.64574i) q^{42} +(-2.23136 - 1.28828i) q^{43} +(-2.41253 + 2.41253i) q^{44} +(-3.41979 + 0.916329i) q^{45} +(-6.53826 + 1.75192i) q^{46} +(-2.09068 + 2.09068i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(-6.04246 - 3.53394i) q^{49} +(-1.95010 + 7.27786i) q^{50} +1.81369i q^{51} +(-3.16099 + 1.73440i) q^{52} +12.2946 q^{53} +(-0.258819 + 0.965926i) q^{54} +(10.4610 - 6.03965i) q^{55} +(-2.29499 + 1.31645i) q^{56} +(4.71891 - 4.71891i) q^{57} +(-1.15955 - 4.32750i) q^{58} +(-0.202021 - 0.753954i) q^{59} +(2.50346 + 2.50346i) q^{60} +(3.49316 + 2.01678i) q^{61} +(4.73550 + 8.20212i) q^{62} +(1.86558 + 1.87607i) q^{63} +1.00000i q^{64} +(12.3992 - 3.03477i) q^{65} -3.41183i q^{66} +(-11.6954 - 3.13378i) q^{67} +(1.57070 - 0.906845i) q^{68} +(3.38445 - 5.86204i) q^{69} +(9.05467 - 2.39900i) q^{70} +(-1.20161 - 4.48447i) q^{71} +(0.965926 - 0.258819i) q^{72} +(-4.59840 + 4.59840i) q^{73} +(1.05141 - 1.82109i) q^{74} +(-3.76730 - 6.52515i) q^{75} +(-6.44615 - 1.72724i) q^{76} +(-7.80479 - 4.53532i) q^{77} +(1.00875 - 3.46156i) q^{78} +8.32488 q^{79} +(0.916329 - 3.41979i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.77055 - 4.79874i) q^{82} +(10.8432 + 10.8432i) q^{83} +(0.691933 - 2.55367i) q^{84} +(-6.20243 + 1.66194i) q^{85} +(-1.82190 - 1.82190i) q^{86} +(3.87993 + 2.24008i) q^{87} +(-2.95473 + 1.70591i) q^{88} +(6.87740 + 1.84280i) q^{89} -3.54042 q^{90} +(-6.57764 - 6.90902i) q^{91} -6.76890 q^{92} +(-9.14828 - 2.45127i) q^{93} +(-2.56055 + 1.47834i) q^{94} +(20.4617 + 11.8136i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(-1.49705 + 0.401134i) q^{97} +(-4.92192 - 4.97742i) q^{98} +(2.41253 + 2.41253i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q + 8 * q^7 + 20 * q^9	$ 40 q + 8 q^{7} + 20 q^{9} + 8 q^{11} - 40 q^{12} - 8 q^{14} + 20 q^{16} - 16 q^{17} - 16 q^{19} + 4 q^{21} + 8 q^{22} - 32 q^{26} - 8 q^{28} + 8 q^{33} - 16 q^{34} + 40 q^{35} + 40 q^{37} + 16 q^{38} - 16 q^{39} + 4 q^{41} - 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} - 20 q^{49} - 16 q^{50} + 8 q^{52} + 32 q^{53} + 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} - 84 q^{59} + 48 q^{61} + 4 q^{62} + 4 q^{63} - 16 q^{65} - 12 q^{68} + 8 q^{69} - 20 q^{70} - 40 q^{71} + 48 q^{73} + 8 q^{74} - 36 q^{75} - 16 q^{76} + 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} - 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} - 12 q^{89} + 32 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} - 8 q^{98} - 8 q^{99}+O(q^{100}) $ 40 * q + 8 * q^7 + 20 * q^9 + 8 * q^11 - 40 * q^12 - 8 * q^14 + 20 * q^16 - 16 * q^17 - 16 * q^19 + 4 * q^21 + 8 * q^22 - 32 * q^26 - 8 * q^28 + 8 * q^33 - 16 * q^34 + 40 * q^35 + 40 * q^37 + 16 * q^38 - 16 * q^39 + 4 * q^41 - 12 * q^42 + 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 - 20 * q^49 - 16 * q^50 + 8 * q^52 + 32 * q^53 + 72 * q^55 + 12 * q^56 + 8 * q^57 - 36 * q^58 - 84 * q^59 + 48 * q^61 + 4 * q^62 + 4 * q^63 - 16 * q^65 - 12 * q^68 + 8 * q^69 - 20 * q^70 - 40 * q^71 + 48 * q^73 + 8 * q^74 - 36 * q^75 - 16 * q^76 + 24 * q^77 - 8 * q^78 - 48 * q^79 - 20 * q^81 - 36 * q^83 - 8 * q^84 + 8 * q^85 - 8 * q^86 - 12 * q^89 + 32 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 - 8 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−2.50346	−	2.50346i	−1.11958	−	1.11958i	−0.991803	−	0.127777i	$-0.959216\pi$
$5$	−2.50346	−	2.50346i	−1.11958	−	1.11958i	−0.127777	−	0.991803i	$-0.540784\pi$
$6$	−0.965926	+	0.258819i	−0.394338	+	0.105662i
$7$	−0.691933	+	2.55367i	−0.261526	+	0.965196i
$7$	−0.691933	+	2.55367i	−0.261526	+	0.965196i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−1.77021	−	3.06610i	−0.559790	−	0.969585i
$11$	−0.883046	+	3.29557i	−0.266248	+	0.993652i	0.695234	+	0.718784i	$0.255301\pi$
$11$	−0.883046	+	3.29557i	−0.266248	+	0.993652i	−0.961482	+	0.274868i	$0.911366\pi$
$12$	−1.00000			−0.288675
$13$	−1.87030	+	3.08253i	−0.518727	+	0.854940i
$13$	−1.87030	+	3.08253i	−0.518727	+	0.854940i
$14$	−1.32929	+	2.28757i	−0.355269	+	0.611379i
$15$	3.41979	+	0.916329i	0.882985	+	0.236595i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.906845	−	1.57070i	0.219942	−	0.380951i	−0.734848	−	0.678232i	$-0.762746\pi$
$17$	0.906845	−	1.57070i	0.219942	−	0.380951i	0.954790	+	0.297281i	$0.0960798\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	−6.44615	+	1.72724i	−1.47885	+	0.396256i	−0.905955	−	0.423373i	$-0.860846\pi$
$19$	−6.44615	+	1.72724i	−1.47885	+	0.396256i	−0.572894	+	0.819630i	$0.694179\pi$
$20$	−0.916329	−	3.41979i	−0.204897	−	0.764687i
$21$	−0.677603	−	2.55751i	−0.147865	−	0.558094i
$22$	−1.70591	+	2.95473i	−0.363702	+	0.629950i
$23$	−5.86204	+	3.38445i	−1.22232	+	0.705707i	−0.965412	−	0.260729i	$-0.916037\pi$
$23$	−5.86204	+	3.38445i	−1.22232	+	0.705707i	−0.256908	+	0.966436i	$0.582704\pi$
$24$	−0.965926	−	0.258819i	−0.197169	−	0.0528312i
$25$			7.53460i			1.50692i
$26$	−2.60439	+	2.49343i	−0.510762	+	0.489001i
$27$			1.00000i			0.192450i
$28$	−1.87607	+	1.86558i	−0.354543	+	0.352561i
$29$	−2.24008	−	3.87993i	−0.415973	−	0.720486i	0.579557	−	0.814931i	$-0.303225\pi$
$29$	−2.24008	−	3.87993i	−0.415973	−	0.720486i	−0.995530	+	0.0944458i	$0.969892\pi$
$30$	3.06610	+	1.77021i	0.559790	+	0.323195i
$31$	6.69700	+	6.69700i	1.20282	+	1.20282i	0.973306	+	0.229511i	$0.0737128\pi$
$31$	6.69700	+	6.69700i	1.20282	+	1.20282i	0.229511	+	0.973306i	$0.426287\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	−0.883046	−	3.29557i	−0.153719	−	0.573685i
$34$	1.28247	−	1.28247i	0.219942	−	0.219942i
$35$	8.12523	−	4.66078i	1.37341	−	0.787815i
$36$	0.866025	−	0.500000i	0.144338	−	0.0833333i
$37$	0.544249	−	2.03117i	0.0894740	−	0.333922i	−0.906650	−	0.421884i	$-0.861369\pi$
$37$	0.544249	−	2.03117i	0.0894740	−	0.333922i	0.996124	+	0.0879625i	$0.0280356\pi$
$38$	−6.67355			−1.08259
$39$	0.0784593	−	3.60470i	0.0125635	−	0.577214i
$40$		−	3.54042i		−	0.559790i
$41$	1.43414	−	5.35230i	0.223976	−	0.835889i	−0.758837	−	0.651281i	$-0.774232\pi$
$41$	1.43414	−	5.35230i	0.223976	−	0.835889i	0.982812	−	0.184608i	$-0.0591015\pi$
$42$	0.00741761	−	2.64574i	0.00114456	−	0.408247i
$43$	−2.23136	−	1.28828i	−0.340279	−	0.196460i	0.320116	−	0.947378i	$-0.396278\pi$
$43$	−2.23136	−	1.28828i	−0.340279	−	0.196460i	−0.660396	+	0.750918i	$0.729611\pi$
$44$	−2.41253	+	2.41253i	−0.363702	+	0.363702i
$45$	−3.41979	+	0.916329i	−0.509792	+	0.136598i
$46$	−6.53826	+	1.75192i	−0.964013	+	0.258307i
$47$	−2.09068	+	2.09068i	−0.304958	+	0.304958i	−0.842950	−	0.537992i	$-0.819183\pi$
$47$	−2.09068	+	2.09068i	−0.304958	+	0.304958i	0.537992	+	0.842950i	$0.319183\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	−6.04246	−	3.53394i	−0.863208	−	0.504848i
$50$	−1.95010	+	7.27786i	−0.275785	+	1.02925i
$51$			1.81369i			0.253967i
$52$	−3.16099	+	1.73440i	−0.438350	+	0.240518i
$53$	12.2946			1.68880			0.844399	−	0.535714i	$-0.179958\pi$
$53$	12.2946			1.68880			0.844399	+	0.535714i	$0.179958\pi$
$54$	−0.258819	+	0.965926i	−0.0352208	+	0.131446i
$55$	10.4610	−	6.03965i	1.41056	−	0.814387i
$56$	−2.29499	+	1.31645i	−0.306681	+	0.175918i
$57$	4.71891	−	4.71891i	0.625035	−	0.625035i
$58$	−1.15955	−	4.32750i	−0.152257	−	0.568229i
$59$	−0.202021	−	0.753954i	−0.0263009	−	0.0981565i	0.951528	−	0.307563i	$-0.0995135\pi$
$59$	−0.202021	−	0.753954i	−0.0263009	−	0.0981565i	−0.977829	+	0.209407i	$0.932847\pi$
$60$	2.50346	+	2.50346i	0.323195	+	0.323195i
$61$	3.49316	+	2.01678i	0.447253	+	0.258222i	0.706670	−	0.707544i	$-0.250197\pi$
$61$	3.49316	+	2.01678i	0.447253	+	0.258222i	−0.259416	+	0.965766i	$0.583530\pi$
$62$	4.73550	+	8.20212i	0.601409	+	1.04167i
$63$	1.86558	+	1.87607i	0.235041	+	0.236362i
$64$			1.00000i			0.125000i
$65$	12.3992	−	3.03477i	1.53793	−	0.376417i
$66$		−	3.41183i		−	0.419967i
$67$	−11.6954	−	3.13378i	−1.42882	−	0.382852i	−0.540219	−	0.841524i	$-0.681659\pi$
$67$	−11.6954	−	3.13378i	−1.42882	−	0.382852i	−0.888606	+	0.458672i	$0.848325\pi$
$68$	1.57070	−	0.906845i	0.190476	−	0.109971i
$69$	3.38445	−	5.86204i	0.407440	−	0.705707i
$70$	9.05467	−	2.39900i	1.08224	−	0.286736i
$71$	−1.20161	−	4.48447i	−0.142605	−	0.532209i	−0.999850	−	0.0173006i	$-0.994493\pi$
$71$	−1.20161	−	4.48447i	−0.142605	−	0.532209i	0.857245	−	0.514908i	$-0.172174\pi$
$72$	0.965926	−	0.258819i	0.113835	−	0.0305021i
$73$	−4.59840	+	4.59840i	−0.538202	+	0.538202i	−0.923001	−	0.384798i	$-0.874271\pi$
$73$	−4.59840	+	4.59840i	−0.538202	+	0.538202i	0.384798	+	0.923001i	$0.374271\pi$
$74$	1.05141	−	1.82109i	0.122224	−	0.211698i
$75$	−3.76730	−	6.52515i	−0.435010	−	0.753460i
$76$	−6.44615	−	1.72724i	−0.739425	−	0.198128i
$77$	−7.80479	−	4.53532i	−0.889438	−	0.516848i
$78$	1.00875	−	3.46156i	0.114218	−	0.391945i
$79$	8.32488			0.936622			0.468311	−	0.883564i	$-0.344863\pi$
$79$	8.32488			0.936622			0.468311	+	0.883564i	$0.344863\pi$
$80$	0.916329	−	3.41979i	0.102449	−	0.382344i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.77055	−	4.79874i	0.305957	−	0.529932i
$83$	10.8432	+	10.8432i	1.19020	+	1.19020i	0.977012	+	0.213186i	$0.0683839\pi$
$83$	10.8432	+	10.8432i	1.19020	+	1.19020i	0.213186	+	0.977012i	$0.431616\pi$
$84$	0.691933	−	2.55367i	0.0754961	−	0.278628i
$85$	−6.20243	+	1.66194i	−0.672748	+	0.180262i
$86$	−1.82190	−	1.82190i	−0.196460	−	0.196460i
$87$	3.87993	+	2.24008i	0.415973	+	0.240162i
$88$	−2.95473	+	1.70591i	−0.314975	+	0.181851i
$89$	6.87740	+	1.84280i	0.729003	+	0.195336i	0.604185	−	0.796844i	$-0.293499\pi$
$89$	6.87740	+	1.84280i	0.729003	+	0.195336i	0.124818	+	0.992180i	$0.460165\pi$
$90$	−3.54042			−0.373193
$91$	−6.57764	−	6.90902i	−0.689524	−	0.724262i
$92$	−6.76890			−0.705707
$93$	−9.14828	−	2.45127i	−0.948632	−	0.254185i
$94$	−2.56055	+	1.47834i	−0.264101	+	0.152479i
$95$	20.4617	+	11.8136i	2.09933	+	1.21205i
$96$	−0.707107	−	0.707107i	−0.0721688	−	0.0721688i
$97$	−1.49705	+	0.401134i	−0.152003	+	0.0407290i	−0.334018	−	0.942567i	$-0.608405\pi$
$97$	−1.49705	+	0.401134i	−0.152003	+	0.0407290i	0.182015	+	0.983296i	$0.441738\pi$
$98$	−4.92192	−	4.97742i	−0.497189	−	0.502796i
$99$	2.41253	+	2.41253i	0.242468	+	0.242468i
$100$	−3.76730	+	6.52515i	−0.376730	+	0.652515i
$101$	−1.55487	−	2.69311i	−0.154715	−	0.267975i	0.778240	−	0.627967i	$-0.216113\pi$
$101$	−1.55487	−	2.69311i	−0.154715	−	0.267975i	−0.932955	+	0.359992i	$0.882779\pi$
$102$	−0.469417	+	1.75189i	−0.0464793	+	0.173463i
$103$	11.4905			1.13220			0.566098	−	0.824338i	$-0.308452\pi$
$103$	11.4905			1.13220			0.566098	+	0.824338i	$0.308452\pi$
$104$	−3.50218	+	0.857178i	−0.343417	+	0.0840533i
$105$	−4.70626	+	8.09897i	−0.459284	+	0.790378i
$106$	11.8757	+	3.18209i	1.15347	+	0.309072i
$107$	−5.24739	−	9.08875i	−0.507284	−	0.878643i	−0.999964	−	0.00843193i	$-0.997316\pi$
$107$	−5.24739	−	9.08875i	−0.507284	−	0.878643i	0.492680	−	0.870211i	$-0.336017\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−8.23020	+	8.23020i	−0.788310	+	0.788310i	−0.981217	−	0.192907i	$-0.938208\pi$
$109$	−8.23020	+	8.23020i	−0.788310	+	0.788310i	0.192907	+	0.981217i	$0.438208\pi$
$110$	11.6677	−	3.12636i	1.11247	−	0.298086i
$111$	0.544249	+	2.03117i	0.0516579	+	0.192790i
$112$	−2.55751	+	0.677603i	−0.241662	+	0.0640275i
$113$	−8.71580	+	15.0962i	−0.819913	+	1.42013i	0.0858320	+	0.996310i	$0.472645\pi$
$113$	−8.71580	+	15.0962i	−0.819913	+	1.42013i	−0.905745	+	0.423822i	$0.860688\pi$
$114$	5.77946	−	3.33678i	0.541296	−	0.312518i
$115$	23.1482	+	6.20254i	2.15858	+	0.578390i
$116$		−	4.48016i		−	0.415973i
$117$	1.73440	+	3.16099i	0.160345	+	0.292234i
$118$		−	0.780551i		−	0.0718555i
$119$	3.38358	+	3.40260i	0.310172	+	0.311916i
$120$	1.77021	+	3.06610i	0.161597	+	0.279895i
$121$	−0.554739	−	0.320279i	−0.0504308	−	0.0291162i
$122$	2.85215	+	2.85215i	0.258222	+	0.258222i
$123$	1.43414	+	5.35230i	0.129312	+	0.482601i
$124$	2.45127	+	9.14828i	0.220131	+	0.821539i
$125$	6.34526	−	6.34526i	0.567537	−	0.567537i
$126$	1.31645	+	2.29499i	0.117278	+	0.204454i
$127$	0.620950	−	0.358506i	0.0551004	−	0.0318122i	−0.472197	−	0.881493i	$-0.656539\pi$
$127$	0.620950	−	0.358506i	0.0551004	−	0.0318122i	0.527297	+	0.849681i	$0.323205\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	2.57655			0.226853
$130$	12.7622	+	0.277779i	1.11932	+	0.0243629i
$131$		−	11.7074i		−	1.02288i	−0.859320	−	0.511438i	$-0.829113\pi$
$131$		−	11.7074i		−	1.02288i	0.859320	−	0.511438i	$-0.170887\pi$
$132$	0.883046	−	3.29557i	0.0768593	−	0.286843i
$133$	0.0495018	−	17.6565i	0.00429235	−	1.53101i
$134$	−10.4858	−	6.05400i	−0.905839	−	0.522986i
$135$	2.50346	−	2.50346i	0.215463	−	0.215463i
$136$	1.75189	−	0.469417i	0.150223	−	0.0402522i
$137$	−4.86220	+	1.30282i	−0.415406	+	0.111308i	−0.460468	−	0.887677i	$-0.652318\pi$
$137$	−4.86220	+	1.30282i	−0.415406	+	0.111308i	0.0450616	+	0.998984i	$0.485652\pi$
$138$	4.78634	−	4.78634i	0.407440	−	0.407440i
$139$	−11.2297	−	6.48345i	−0.952487	−	0.549919i	−0.0586347	−	0.998280i	$-0.518675\pi$
$139$	−11.2297	−	6.48345i	−0.952487	−	0.549919i	−0.893853	+	0.448361i	$0.852008\pi$
$140$	9.36704	+	0.0262615i	0.791660	+	0.00221950i
$141$	0.765243	−	2.85593i	0.0644451	−	0.240512i
$142$		−	4.64266i		−	0.389604i
$143$	−8.50714	−	8.88571i	−0.711403	−	0.743060i
$144$	1.00000			0.0833333
$145$	−4.10530	+	15.3212i	−0.340927	+	1.27236i
$146$	−5.63187	+	3.25156i	−0.466097	+	0.269101i
$147$	6.99989	+	0.0392501i	0.577341	+	0.00323730i
$148$	1.48692	−	1.48692i	0.122224	−	0.122224i
$149$	−0.893110	−	3.33313i	−0.0731664	−	0.273061i	0.919645	−	0.392751i	$-0.128477\pi$
$149$	−0.893110	−	3.33313i	−0.0731664	−	0.273061i	−0.992811	+	0.119690i	$0.961810\pi$
$150$	−1.95010	−	7.27786i	−0.159225	−	0.594235i
$151$	16.4384	+	16.4384i	1.33774	+	1.33774i	0.898249	+	0.439486i	$0.144839\pi$
$151$	16.4384	+	16.4384i	1.33774	+	1.33774i	0.439486	+	0.898249i	$0.355161\pi$
$152$	−5.77946	−	3.33678i	−0.468776	−	0.270648i
$153$	−0.906845	−	1.57070i	−0.0733141	−	0.126984i
$154$	−6.36502	−	6.40081i	−0.512908	−	0.515792i
$155$		−	33.5313i		−	2.69330i
$156$	1.87030	−	3.08253i	0.149744	−	0.246800i
$157$			9.99665i			0.797819i	0.916990	+	0.398910i	$0.130611\pi$
$157$			9.99665i			0.797819i	−0.916990	+	0.398910i	$0.869389\pi$
$158$	8.04122	+	2.15464i	0.639725	+	0.171414i
$159$	−10.6475	+	6.14732i	−0.844399	+	0.487514i
$160$	1.77021	−	3.06610i	0.139948	−	0.242396i
$161$	−4.58663	−	17.3115i	−0.361477	−	1.36434i
$162$	−0.258819	−	0.965926i	−0.0203347	−	0.0758903i
$163$	0.938913	−	0.251581i	0.0735414	−	0.0197053i	−0.221861	−	0.975078i	$-0.571213\pi$
$163$	0.938913	−	0.251581i	0.0735414	−	0.0197053i	0.295402	+	0.955373i	$0.404546\pi$
$164$	3.91816	−	3.91816i	0.305957	−	0.305957i
$165$	−6.03965	+	10.4610i	−0.470186	+	0.814387i
$166$	7.66731	+	13.2802i	0.595099	+	1.03074i
$167$	−2.52015	−	0.675271i	−0.195015	−	0.0522541i	0.159990	−	0.987119i	$-0.448854\pi$
$167$	−2.52015	−	0.675271i	−0.195015	−	0.0522541i	−0.355004	+	0.934865i	$0.615521\pi$
$168$	1.32929	−	2.28757i	0.102557	−	0.176490i
$169$	−6.00398	−	11.5305i	−0.461845	−	0.886961i
$170$	−6.42123			−0.492486
$171$	−1.72724	+	6.44615i	−0.132085	+	0.492950i
$172$	−1.28828	−	2.23136i	−0.0982302	−	0.170140i
$173$	−2.31596	+	4.01136i	−0.176079	+	0.304978i	−0.940534	−	0.339699i	$-0.889675\pi$
$173$	−2.31596	+	4.01136i	−0.176079	+	0.304978i	0.764455	+	0.644677i	$0.223008\pi$
$174$	3.16795	+	3.16795i	0.240162	+	0.240162i
$175$	−19.2409	−	5.21344i	−1.45447	−	0.394099i
$176$	−3.29557	+	0.883046i	−0.248413	+	0.0665621i
$177$	0.551933	+	0.551933i	0.0414858	+	0.0414858i
$178$	6.16611	+	3.56001i	0.462170	+	0.266834i
$179$	−10.3458	+	5.97314i	−0.773280	+	0.446453i	−0.834043	−	0.551699i	$-0.813980\pi$
$179$	−10.3458	+	5.97314i	−0.773280	+	0.446453i	0.0607637	+	0.998152i	$0.480646\pi$
$180$	−3.41979	−	0.916329i	−0.254896	−	0.0682991i
$181$	−16.2760			−1.20979			−0.604893	−	0.796306i	$-0.706784\pi$
$181$	−16.2760			−1.20979			−0.604893	+	0.796306i	$0.706784\pi$
$182$	−4.56533	−	8.37602i	−0.338405	−	0.620872i
$183$	−4.03356			−0.298169
$184$	−6.53826	−	1.75192i	−0.482007	−	0.129153i
$185$	−6.44744	+	3.72243i	−0.474025	+	0.273679i
$186$	−8.20212	−	4.73550i	−0.601409	−	0.347223i
$187$	4.37557	+	4.37557i	0.319974	+	0.319974i
$188$	−2.85593	+	0.765243i	−0.208290	+	0.0558111i
$189$	−2.55367	−	0.691933i	−0.185752	−	0.0503307i
$190$	16.7069	+	16.7069i	1.21205	+	1.21205i
$191$	10.2736	−	17.7943i	0.743369	−	1.28755i	−0.207584	−	0.978217i	$-0.566560\pi$
$191$	10.2736	−	17.7943i	0.743369	−	1.28755i	0.950953	−	0.309336i	$-0.100107\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−4.57901	+	17.0891i	−0.329604	+	1.23010i	0.579998	+	0.814618i	$0.303053\pi$
$193$	−4.57901	+	17.0891i	−0.329604	+	1.23010i	−0.909602	+	0.415481i	$0.863613\pi$
$194$	−1.54986			−0.111274
$195$	−9.22063	+	8.82779i	−0.660303	+	0.632171i
$196$	−3.46595	−	6.08171i	−0.247568	−	0.434408i
$197$	20.9228	+	5.60626i	1.49069	+	0.399429i	0.909970	−	0.414673i	$-0.136104\pi$
$197$	20.9228	+	5.60626i	1.49069	+	0.399429i	0.580721	+	0.814103i	$0.302771\pi$
$198$	1.70591	+	2.95473i	0.121234	+	0.209983i
$199$	11.0074	−	19.0653i	0.780292	−	1.35151i	−0.151480	−	0.988460i	$-0.548404\pi$
$199$	11.0074	−	19.0653i	0.780292	−	1.35151i	0.931772	−	0.363045i	$-0.118263\pi$
$200$	−5.32776	+	5.32776i	−0.376730	+	0.376730i
$201$	11.6954	−	3.13378i	0.824932	−	0.221040i
$202$	−0.804859	−	3.00377i	−0.0566297	−	0.211345i
$203$	11.4581	−	3.03577i	0.804198	−	0.213069i
$204$	−0.906845	+	1.57070i	−0.0634918	+	0.109971i
$205$	−16.9896	+	9.80894i	−1.18660	+	0.685086i
$206$	11.0990	+	2.97397i	0.773304	+	0.207206i
$207$			6.76890i			0.470471i
$208$	−3.60470	−	0.0784593i	−0.249941	−	0.00544018i
$209$		−	22.7690i		−	1.57496i
$210$	−6.64207	+	6.60493i	−0.458346	+	0.455783i
$211$	2.64275	+	4.57737i	0.181934	+	0.315119i	0.942539	−	0.334096i	$-0.108431\pi$
$211$	2.64275	+	4.57737i	0.181934	+	0.315119i	−0.760605	+	0.649215i	$0.775098\pi$
$212$	10.6475	+	6.14732i	0.731271	+	0.422200i
$213$	3.28286	+	3.28286i	0.224938	+	0.224938i
$214$	−2.71625	−	10.1372i	−0.185679	−	0.692963i
$215$	2.36097	+	8.81126i	0.161017	+	0.600923i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	−21.7358	+	12.4681i	−1.47552	+	0.846387i
$218$	−10.0799	+	5.81963i	−0.682696	+	0.394155i
$219$	1.68313	−	6.28154i	0.113736	−	0.424467i
$220$	12.0793			0.814387
$221$	3.14567	+	5.73305i	0.211600	+	0.385647i
$222$			2.10282i			0.141132i
$223$	−4.02721	+	15.0297i	−0.269682	+	1.00647i	0.689641	+	0.724152i	$0.257769\pi$
$223$	−4.02721	+	15.0297i	−0.269682	+	1.00647i	−0.959322	+	0.282314i	$0.908898\pi$
$224$	−2.64574	−	0.00741761i	−0.176776	−	0.000495610i
$225$	6.52515	+	3.76730i	0.435010	+	0.251153i
$226$	−12.3260	+	12.3260i	−0.819913	+	0.819913i
$227$	−22.6358	+	6.06524i	−1.50239	+	0.402564i	−0.913900	−	0.405940i	$-0.866944\pi$
$227$	−22.6358	+	6.06524i	−1.50239	+	0.402564i	−0.588490	+	0.808504i	$0.700278\pi$
$228$	6.44615	−	1.72724i	0.426907	−	0.114389i
$229$	7.49070	−	7.49070i	0.494999	−	0.494999i	−0.414878	−	0.909877i	$-0.636176\pi$
$229$	7.49070	−	7.49070i	0.494999	−	0.494999i	0.909877	+	0.414878i	$0.136176\pi$
$230$	20.7541	+	11.9824i	1.36848	+	0.790095i
$231$	9.02681	+	0.0253076i	0.593920	+	0.00166512i
$232$	1.15955	−	4.32750i	0.0761283	−	0.284115i
$233$		−	6.30863i		−	0.413292i	−0.978416	−	0.206646i	$-0.933745\pi$
$233$		−	6.30863i		−	0.413292i	0.978416	−	0.206646i	$-0.0662549\pi$
$234$	0.857178	+	3.50218i	0.0560355	+	0.228944i
$235$	10.4679			0.682849
$236$	0.202021	−	0.753954i	0.0131505	−	0.0490782i
$237$	−7.20956	+	4.16244i	−0.468311	+	0.270380i
$238$	2.38763	+	4.16240i	0.154767	+	0.269808i
$239$	−9.24784	+	9.24784i	−0.598193	+	0.598193i	−0.939831	−	0.341638i	$-0.889018\pi$
$239$	−9.24784	+	9.24784i	−0.598193	+	0.598193i	0.341638	+	0.939831i	$0.389018\pi$
$240$	0.916329	+	3.41979i	0.0591488	+	0.220746i
$241$	1.37222	+	5.12118i	0.0883922	+	0.329884i	0.995935	−	0.0900755i	$-0.0287108\pi$
$241$	1.37222	+	5.12118i	0.0883922	+	0.329884i	−0.907543	+	0.419960i	$0.862044\pi$
$242$	−0.452942	−	0.452942i	−0.0291162	−	0.0291162i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	2.01678	+	3.49316i	0.129111	+	0.223627i
$245$	6.27997	+	23.9741i	0.401213	+	1.53165i
$246$			5.54111i			0.353288i
$247$	6.73195	−	23.1009i	0.428343	−	1.46988i
$248$			9.47099i			0.601409i
$249$	−14.8121	−	3.96889i	−0.938679	−	0.251518i
$250$	7.77132	−	4.48677i	0.491501	−	0.283768i
$251$	−10.4340	+	18.0722i	−0.658587	+	1.14071i	0.322394	+	0.946605i	$0.395512\pi$
$251$	−10.4340	+	18.0722i	−0.658587	+	1.14071i	−0.980982	+	0.194101i	$0.937821\pi$
$252$	0.677603	+	2.55751i	0.0426850	+	0.161108i
$253$	−5.97725	−	22.3074i	−0.375786	−	1.40245i
$254$	0.692580	−	0.185576i	0.0434563	−	0.0116441i
$255$	4.54050	−	4.54050i	0.284337	−	0.284337i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.88721	+	5.00080i	0.180099	+	0.311941i	0.941914	−	0.335854i	$-0.109025\pi$
$257$	2.88721	+	5.00080i	0.180099	+	0.311941i	−0.761815	+	0.647795i	$0.775691\pi$
$258$	2.48876	+	0.666861i	0.154943	+	0.0415170i
$259$	4.81034	+	2.79526i	0.298900	+	0.173689i
$260$	12.2554	+	3.57140i	0.760048	+	0.221489i
$261$	−4.48016			−0.277315
$262$	3.03009	−	11.3084i	0.187199	−	0.698638i
$263$	11.7845	+	20.4114i	0.726666	+	1.25862i	0.958285	+	0.285816i	$0.0922646\pi$
$263$	11.7845	+	20.4114i	0.726666	+	1.25862i	−0.231618	+	0.972807i	$0.574402\pi$
$264$	1.70591	−	2.95473i	0.104992	−	0.181851i
$265$	−30.7791	−	30.7791i	−1.89075	−	1.89075i
$266$	4.61765	−	17.0420i	0.283126	−	1.04491i
$267$	−6.87740	+	1.84280i	−0.420890	+	0.112777i
$268$	−8.56165	−	8.56165i	−0.522986	−	0.522986i
$269$	−27.5648	−	15.9146i	−1.68066	−	0.970328i	−0.961225	−	0.275766i	$-0.911069\pi$
$269$	−27.5648	−	15.9146i	−1.68066	−	0.970328i	−0.719433	−	0.694562i	$-0.755598\pi$
$270$	3.06610	−	1.77021i	0.186597	−	0.107732i
$271$	4.09003	+	1.09592i	0.248451	+	0.0665724i	0.380895	−	0.924618i	$-0.375616\pi$
$271$	4.09003	+	1.09592i	0.248451	+	0.0665724i	−0.132444	+	0.991190i	$0.542282\pi$
$272$	1.81369			0.109971
$273$	9.15092	+	2.69457i	0.553839	+	0.163083i
$274$	−5.03372			−0.304098
$275$	−24.8308	−	6.65339i	−1.49735	−	0.401215i
$276$	5.86204	−	3.38445i	0.352853	−	0.203720i
$277$	25.4445	+	14.6904i	1.52881	+	0.882660i	0.999412	+	0.0342884i	$0.0109165\pi$
$277$	25.4445	+	14.6904i	1.52881	+	0.882660i	0.529401	+	0.848372i	$0.322417\pi$
$278$	−9.16898	−	9.16898i	−0.549919	−	0.549919i
$279$	9.14828	−	2.45127i	0.547693	−	0.146754i
$280$	9.04107	+	2.44974i	0.540307	+	0.146400i
$281$	−1.65818	−	1.65818i	−0.0989186	−	0.0989186i	0.655916	−	0.754834i	$-0.272283\pi$
$281$	−1.65818	−	1.65818i	−0.0989186	−	0.0989186i	−0.754834	+	0.655916i	$0.772283\pi$
$282$	1.47834	−	2.56055i	0.0880337	−	0.152479i
$283$	−5.02109	−	8.69678i	−0.298473	−	0.516970i	0.677314	−	0.735694i	$-0.263144\pi$
$283$	−5.02109	−	8.69678i	−0.298473	−	0.516970i	−0.975787	+	0.218724i	$0.929810\pi$
$284$	1.20161	−	4.48447i	0.0713024	−	0.266104i
$285$	−23.6272			−1.39955
$286$	−5.91747	−	10.7847i	−0.349908	−	0.637715i
$287$	12.6757	+	7.36576i	0.748221	+	0.434787i
$288$	0.965926	+	0.258819i	0.0569177	+	0.0152511i
$289$	6.85526	+	11.8737i	0.403251	+	0.698451i
$290$	−7.93083	+	13.7366i	−0.465715	+	0.806641i
$291$	1.09592	−	1.09592i	0.0642439	−	0.0642439i
$292$	−6.28154	+	1.68313i	−0.367599	+	0.0984979i
$293$	1.87393	+	6.99358i	0.109476	+	0.408570i	0.998814	−	0.0486797i	$-0.0155014\pi$
$293$	1.87393	+	6.99358i	0.109476	+	0.408570i	−0.889339	+	0.457249i	$0.848835\pi$
$294$	6.75122	+	1.84962i	0.393739	+	0.107872i
$295$	−1.38174	+	2.39324i	−0.0804480	+	0.139340i
$296$	1.82109	−	1.05141i	0.105849	−	0.0611119i
$297$	−3.29557	−	0.883046i	−0.191228	−	0.0512395i
$298$		−	3.45071i		−	0.199894i
$299$	0.531083	−	24.3998i	0.0307133	−	1.41108i
$300$		−	7.53460i		−	0.435010i
$301$	4.83379	−	4.80676i	0.278615	−	0.277057i
$302$	11.6237	+	20.1328i	0.668868	+	1.15851i
$303$	2.69311	+	1.55487i	0.154715	+	0.0893248i
$304$	−4.71891	−	4.71891i	−0.270648	−	0.270648i
$305$	−3.69606	−	13.7939i	−0.211636	−	0.789836i
$306$	−0.469417	−	1.75189i	−0.0268348	−	0.100149i
$307$	−5.35959	+	5.35959i	−0.305888	+	0.305888i	−0.843312	−	0.537424i	$-0.819397\pi$
$307$	−5.35959	+	5.35959i	−0.305888	+	0.305888i	0.537424	+	0.843312i	$0.319397\pi$
$308$	−4.49149	−	7.83010i	−0.255926	−	0.446161i
$309$	−9.95109	+	5.74527i	−0.566098	+	0.326837i
$310$	8.67854	−	32.3888i	0.492908	−	1.83956i
$311$	12.8828			0.730517			0.365258	−	0.930906i	$-0.380981\pi$
$311$	12.8828			0.730517			0.365258	+	0.930906i	$0.380981\pi$
$312$	2.60439	−	2.49343i	0.147444	−	0.141163i
$313$			0.0590269i			0.00333640i	0.999999	+	0.00166820i	$0.000531005\pi$
$313$			0.0590269i			0.00333640i	−0.999999	+	0.00166820i	$0.999469\pi$
$314$	−2.58732	+	9.65602i	−0.146011	+	0.544921i
$315$	0.0262615	−	9.36704i	0.00147967	−	0.527773i
$316$	7.20956	+	4.16244i	0.405569	+	0.234156i
$317$	−8.94214	+	8.94214i	−0.502241	+	0.502241i	−0.912134	−	0.409893i	$-0.865566\pi$
$317$	−8.94214	+	8.94214i	−0.502241	+	0.502241i	0.409893	+	0.912134i	$0.365566\pi$
$318$	−11.8757	+	3.18209i	−0.665957	+	0.178443i
$319$	14.7647	−	3.95619i	0.826664	−	0.221504i
$320$	2.50346	−	2.50346i	0.139948	−	0.139948i
$321$	9.08875	+	5.24739i	0.507284	+	0.292881i
$322$	0.0502091	−	17.9088i	0.00279804	−	0.998016i
$323$	−3.13268	+	11.6913i	−0.174307	+	0.650523i
$324$		−	1.00000i		−	0.0555556i
$325$	−23.2256	−	14.0919i	−1.28833	−	0.781680i
$326$	0.972034			0.0538360
$327$	3.01246	−	11.2427i	0.166589	−	0.621720i
$328$	4.79874	−	2.77055i	0.264966	−	0.152978i
$329$	−3.89230	−	6.78553i	−0.214590	−	0.374098i
$330$	−8.54136	+	8.54136i	−0.470186	+	0.470186i
$331$	8.08323	+	30.1670i	0.444294	+	1.65813i	0.717793	+	0.696257i	$0.245152\pi$
$331$	8.08323	+	30.1670i	0.444294	+	1.65813i	−0.273499	+	0.961872i	$0.588181\pi$
$332$	3.96889	+	14.8121i	0.217821	+	0.812920i
$333$	−1.48692	−	1.48692i	−0.0814825	−	0.0814825i
$334$	−2.25950	−	1.30452i	−0.123634	−	0.0713804i
$335$	21.4337	+	37.1243i	1.17105	+	2.02832i
$336$	1.87607	−	1.86558i	0.102348	−	0.101776i
$337$		−	1.82207i		−	0.0992545i	−0.998768	−	0.0496273i	$-0.984197\pi$
$337$		−	1.82207i		−	0.0992545i	0.998768	−	0.0496273i	$-0.0158033\pi$
$338$	−2.81509	−	12.6915i	−0.153121	−	0.690329i
$339$		−	17.4316i		−	0.946754i
$340$	−6.20243	−	1.66194i	−0.336374	−	0.0901312i
$341$	−27.9842	+	16.1567i	−1.51543	+	0.874934i
$342$	−3.33678	+	5.77946i	−0.180432	+	0.312518i
$343$	13.2055	−	12.9852i	0.713029	−	0.701135i
$344$	−0.666861	−	2.48876i	−0.0359548	−	0.134185i
$345$	−23.1482	+	6.20254i	−1.24626	+	0.333934i
$346$	−3.27526	+	3.27526i	−0.176079	+	0.176079i
$347$	−15.8923	+	27.5263i	−0.853143	+	1.47769i	0.0252141	+	0.999682i	$0.491973\pi$
$347$	−15.8923	+	27.5263i	−0.853143	+	1.47769i	−0.878357	+	0.478005i	$0.841360\pi$
$348$	2.24008	+	3.87993i	0.120081	+	0.207986i
$349$	17.1913	+	4.60639i	0.920229	+	0.246575i	0.687683	−	0.726011i	$-0.258628\pi$
$349$	17.1913	+	4.60639i	0.920229	+	0.246575i	0.232546	+	0.972585i	$0.425294\pi$
$350$	−17.2359	−	10.0157i	−0.921299	−	0.535362i
$351$	−3.08253	−	1.87030i	−0.164533	−	0.0998290i
$352$	−3.41183			−0.181851
$353$	3.62512	−	13.5291i	0.192946	−	0.720083i	−0.799844	−	0.600209i	$-0.795084\pi$
$353$	3.62512	−	13.5291i	0.192946	−	0.720083i	0.992789	−	0.119874i	$-0.0382491\pi$
$354$	0.390275	+	0.675977i	0.0207429	+	0.0359278i
$355$	−8.21850	+	14.2349i	−0.436193	+	0.755508i
$356$	5.03461	+	5.03461i	0.266834	+	0.266834i
$357$	−4.63156	−	1.25495i	−0.245128	−	0.0664191i
$358$	−11.5392	+	3.09192i	−0.609866	+	0.163413i
$359$	−12.5099	−	12.5099i	−0.660250	−	0.660250i	0.295189	−	0.955439i	$-0.404617\pi$
$359$	−12.5099	−	12.5099i	−0.660250	−	0.660250i	−0.955439	+	0.295189i	$0.904617\pi$
$360$	−3.06610	−	1.77021i	−0.161597	−	0.0932983i
$361$	22.1151	−	12.7681i	1.16395	−	0.672007i
$362$	−15.7214	−	4.21254i	−0.826300	−	0.221406i
$363$	0.640557			0.0336205
$364$	−2.24189	−	9.27221i	−0.117507	−	0.485996i
$365$	23.0238			1.20512
$366$	−3.89612	−	1.04396i	−0.203653	−	0.0545687i
$367$	−15.2317	+	8.79404i	−0.795089	+	0.459045i	−0.841751	−	0.539866i	$-0.818475\pi$
$367$	−15.2317	+	8.79404i	−0.795089	+	0.459045i	0.0466619	+	0.998911i	$0.485142\pi$
$368$	−5.86204	−	3.38445i	−0.305580	−	0.176427i
$369$	−3.91816	−	3.91816i	−0.203971	−	0.203971i
$370$	−7.19119	+	1.92687i	−0.373852	+	0.100173i
$371$	−8.50707	+	31.3964i	−0.441665	+	1.63002i
$372$	−6.69700	−	6.69700i	−0.347223	−	0.347223i
$373$	18.6281	−	32.2648i	0.964526	−	1.67061i	0.253644	−	0.967298i	$-0.418371\pi$
$373$	18.6281	−	32.2648i	0.964526	−	1.67061i	0.710883	−	0.703311i	$-0.248296\pi$
$374$	3.09400	+	5.35896i	0.159987	+	0.277105i
$375$	−2.32252	+	8.66778i	−0.119935	+	0.447602i
$376$	−2.95667			−0.152479
$377$	16.1496	+	0.351510i	0.831748	+	0.0181037i
$378$	−2.28757	−	1.32929i	−0.117660	−	0.0683715i
$379$	−3.57009	−	0.956604i	−0.183383	−	0.0491374i	0.165959	−	0.986133i	$-0.446928\pi$
$379$	−3.57009	−	0.956604i	−0.183383	−	0.0491374i	−0.349342	+	0.936995i	$0.613595\pi$
$380$	11.8136	+	20.4617i	0.606025	+	1.04967i
$381$	−0.358506	+	0.620950i	−0.0183668	+	0.0318122i
$382$	14.5290	−	14.5290i	0.743369	−	0.743369i
$383$	−4.06841	+	1.09013i	−0.207886	+	0.0557029i	−0.361259	−	0.932465i	$-0.617653\pi$
$383$	−4.06841	+	1.09013i	−0.207886	+	0.0557029i	0.153373	+	0.988168i	$0.450986\pi$
$384$	−0.258819	−	0.965926i	−0.0132078	−	0.0492922i
$385$	8.18498	+	30.8929i	0.417145	+	1.57445i
$386$	−8.84596	+	15.3217i	−0.450247	+	0.779851i
$387$	−2.23136	+	1.28828i	−0.113426	+	0.0654868i
$388$	−1.49705	−	0.401134i	−0.0760013	−	0.0203645i
$389$			6.27546i			0.318178i	0.987264	+	0.159089i	$0.0508558\pi$
$389$			6.27546i			0.318178i	−0.987264	+	0.159089i	$0.949144\pi$
$390$	−11.1912	+	6.14051i	−0.566690	+	0.310937i
$391$			12.2767i			0.620859i
$392$	−1.77379	−	6.77153i	−0.0895900	−	0.342014i
$393$	5.85368	+	10.1389i	0.295279	+	0.511438i
$394$	18.7589	+	10.8305i	0.945060	+	0.545631i
$395$	−20.8410	−	20.8410i	−1.04862	−	1.04862i
$396$	0.883046	+	3.29557i	0.0443747	+	0.165609i
$397$	9.50501	+	35.4732i	0.477043	+	1.78035i	0.613492	+	0.789701i	$0.289764\pi$
$397$	9.50501	+	35.4732i	0.477043	+	1.78035i	−0.136449	+	0.990647i	$0.543569\pi$
$398$	15.5668	−	15.5668i	0.780292	−	0.780292i
$399$	8.78537	+	15.3157i	0.439819	+	0.766745i
$400$	−6.52515	+	3.76730i	−0.326258	+	0.188365i
$401$	−6.81502	+	25.4340i	−0.340326	+	1.27011i	0.557652	+	0.830075i	$0.311702\pi$
$401$	−6.81502	+	25.4340i	−0.340326	+	1.27011i	−0.897978	+	0.440039i	$0.854964\pi$
$402$	12.1080			0.603892
$403$	−33.1691	+	8.11833i	−1.65227	+	0.404403i
$404$		−	3.10974i		−	0.154715i
$405$	−0.916329	+	3.41979i	−0.0455328	+	0.169931i
$406$	11.8533	+	0.0332321i	0.588272	+	0.00164928i
$407$	6.21325	+	3.58722i	0.307980	+	0.177812i
$408$	−1.28247	+	1.28247i	−0.0634918	+	0.0634918i
$409$	3.68919	−	0.988514i	0.182418	−	0.0488789i	−0.166453	−	0.986049i	$-0.553232\pi$
$409$	3.68919	−	0.988514i	0.182418	−	0.0488789i	0.348872	+	0.937170i	$0.386565\pi$
$410$	−18.9494	+	5.07748i	−0.935845	+	0.250759i
$411$	3.55938	−	3.55938i	0.175571	−	0.175571i
$412$	9.95109	+	5.74527i	0.490255	+	0.283049i
$413$	2.06514	+	0.00578982i	0.101619	+	0.000284898i
$414$	−1.75192	+	6.53826i	−0.0861022	+	0.321338i
$415$		−	54.2910i		−	2.66504i
$416$	−3.46156	−	1.00875i	−0.169717	−	0.0494581i
$417$	12.9669			0.634992
$418$	5.89305	−	21.9932i	0.288238	−	1.07572i
$419$	−4.51614	+	2.60739i	−0.220628	+	0.127379i	−0.606241	−	0.795281i	$-0.707323\pi$
$419$	−4.51614	+	2.60739i	−0.220628	+	0.127379i	0.385613	+	0.922661i	$0.373990\pi$
$420$	−8.12523	+	4.66078i	−0.396471	+	0.227423i
$421$	9.98812	−	9.98812i	0.486791	−	0.486791i	−0.420501	−	0.907292i	$-0.638146\pi$
$421$	9.98812	−	9.98812i	0.486791	−	0.486791i	0.907292	+	0.420501i	$0.138146\pi$
$422$	1.36799	+	5.10539i	0.0665925	+	0.248527i
$423$	0.765243	+	2.85593i	0.0372074	+	0.138860i
$424$	8.69362	+	8.69362i	0.422200	+	0.422200i
$425$	11.8346	+	6.83271i	0.574063	+	0.331435i
$426$	2.32133	+	4.02067i	0.112469	+	0.194802i
$427$	−7.56722	+	7.52490i	−0.366203	+	0.364156i
$428$		−	10.4948i		−	0.507284i
$429$	11.8103	+	3.44168i	0.570204	+	0.166166i
$430$			9.12209i			0.439906i
$431$	−33.9678	−	9.10166i	−1.63617	−	0.438411i	−0.680478	−	0.732769i	$-0.738228\pi$
$431$	−33.9678	−	9.10166i	−1.63617	−	0.438411i	−0.955695	+	0.294357i	$0.904894\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	10.0853	−	17.4682i	0.484668	−	0.839469i	−0.515177	−	0.857084i	$-0.672274\pi$
$433$	10.0853	−	17.4682i	0.484668	−	0.839469i	0.999845	+	0.0176146i	$0.00560719\pi$
$434$	−24.2222	+	6.41758i	−1.16270	+	0.308053i
$435$	−4.10530	−	15.3212i	−0.196834	−	0.734595i
$436$	−11.2427	+	3.01246i	−0.538426	+	0.144271i
$437$	31.9419	−	31.9419i	1.52799	−	1.52799i
$438$	3.25156	−	5.63187i	0.155366	−	0.269101i
$439$	−17.0504	−	29.5322i	−0.813773	−	1.40950i	−0.910205	−	0.414157i	$-0.864076\pi$
$439$	−17.0504	−	29.5322i	−0.813773	−	1.40950i	0.0964318	−	0.995340i	$-0.469257\pi$
$440$	11.6677	+	3.12636i	0.556237	+	0.149043i
$441$	−6.08171	+	3.46595i	−0.289605	+	0.165045i
$442$	1.55466	+	6.35186i	0.0739474	+	0.302127i
$443$	0.993699			0.0472121			0.0236060	−	0.999721i	$-0.492485\pi$
$443$	0.993699			0.0472121			0.0236060	+	0.999721i	$0.492485\pi$
$444$	−0.544249	+	2.03117i	−0.0258289	+	0.0963949i
$445$	−12.6039	−	21.8306i	−0.597484	−	1.03487i
$446$	−7.77996	+	13.4753i	−0.368392	+	0.638074i
$447$	2.44002	+	2.44002i	0.115409	+	0.115409i
$448$	−2.55367	−	0.691933i	−0.120650	−	0.0326908i
$449$	1.79245	−	0.480285i	0.0845908	−	0.0226660i	−0.216275	−	0.976332i	$-0.569391\pi$
$449$	1.79245	−	0.480285i	0.0845908	−	0.0226660i	0.300866	+	0.953666i	$0.402724\pi$
$450$	5.32776	+	5.32776i	0.251153	+	0.251153i
$451$	16.3725	+	9.45265i	0.770950	+	0.445108i
$452$	−15.0962	+	8.71580i	−0.710066	+	0.409957i
$453$	−22.4552	−	6.01686i	−1.05504	−	0.282697i
$454$	−23.4343			−1.09983
$455$	−0.829597	+	33.7633i	−0.0388921	+	1.58285i
$456$	6.67355			0.312518
$457$	−22.7983	−	6.10880i	−1.06646	−	0.285758i	−0.317423	−	0.948284i	$-0.602818\pi$
$457$	−22.7983	−	6.10880i	−1.06646	−	0.285758i	−0.749039	+	0.662526i	$0.769484\pi$
$458$	9.17420	−	5.29673i	0.428682	−	0.247500i
$459$	1.57070	+	0.906845i	0.0733141	+	0.0423279i
$460$	16.9457	+	16.9457i	0.790095	+	0.790095i
$461$	4.21637	−	1.12977i	0.196376	−	0.0526187i	−0.159290	−	0.987232i	$-0.550921\pi$
$461$	4.21637	−	1.12977i	0.196376	−	0.0526187i	0.355666	+	0.934613i	$0.384254\pi$
$462$	8.71268	+	2.36076i	0.405350	+	0.109832i
$463$	16.9243	+	16.9243i	0.786541	+	0.786541i	0.980925	−	0.194384i	$-0.0622709\pi$
$463$	16.9243	+	16.9243i	0.786541	+	0.786541i	−0.194384	+	0.980925i	$0.562271\pi$
$464$	2.24008	−	3.87993i	0.103993	−	0.180121i
$465$	16.7657	+	29.0390i	0.777489	+	1.34665i
$466$	1.63279	−	6.09367i	0.0756377	−	0.282284i
$467$	−2.54809			−0.117911			−0.0589557	−	0.998261i	$-0.518777\pi$
$467$	−2.54809			−0.117911			−0.0589557	+	0.998261i	$0.518777\pi$
$468$	−0.0784593	+	3.60470i	−0.00362678	+	0.166627i
$469$	16.0951	−	27.6979i	0.743203	−	1.27897i
$470$	10.1112	+	2.70929i	0.466394	+	0.124970i
$471$	−4.99832	−	8.65735i	−0.230311	−	0.398910i
$472$	0.390275	−	0.675977i	0.0179639	−	0.0311144i
$473$	6.21600	−	6.21600i	0.285812	−	0.285812i
$474$	−8.04122	+	2.15464i	−0.369345	+	0.0989658i
$475$	−13.0141	−	48.5692i	−0.597127	−	2.22851i
$476$	1.22896	+	4.63853i	0.0563294	+	0.212607i
$477$	6.14732	−	10.6475i	0.281466	−	0.487514i
$478$	−11.3262	+	6.53921i	−0.518050	+	0.299097i
$479$	−12.2119	−	3.27218i	−0.557978	−	0.149510i	−0.0312007	−	0.999513i	$-0.509933\pi$
$479$	−12.2119	−	3.27218i	−0.557978	−	0.149510i	−0.526777	+	0.850003i	$0.676600\pi$
$480$			3.54042i			0.161597i
$481$	5.24322	+	5.47655i	0.239070	+	0.249709i
$482$			5.30184i			0.241492i
$483$	12.6279	+	12.6989i	0.574589	+	0.577820i
$484$	−0.320279	−	0.554739i	−0.0145581	−	0.0252154i
$485$	4.75203	+	2.74358i	0.215778	+	0.124580i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	0.205325	+	0.766284i	0.00930417	+	0.0347236i	0.970422	−	0.241415i	$-0.0776116\pi$
$487$	0.205325	+	0.766284i	0.00930417	+	0.0347236i	−0.961118	+	0.276139i	$0.910945\pi$
$488$	1.04396	+	3.89612i	0.0472579	+	0.176369i
$489$	−0.687332	+	0.687332i	−0.0310822	+	0.0310822i
$490$	−0.138962	+	24.7826i	−0.00627767	+	1.11956i
$491$	28.3763	−	16.3831i	1.28060	−	0.739357i	0.303645	−	0.952785i	$-0.401796\pi$
$491$	28.3763	−	16.3831i	1.28060	−	0.739357i	0.976959	+	0.213428i	$0.0684629\pi$
$492$	−1.43414	+	5.35230i	−0.0646562	+	0.241300i
$493$	−8.12562			−0.365960
$494$	12.4815	−	20.5714i	0.561570	−	0.925552i
$495$		−	12.0793i		−	0.542925i
$496$	−2.45127	+	9.14828i	−0.110065	+	0.410770i
$497$	12.2833	+	0.0344375i	0.550981	+	0.00154473i
$498$	−13.2802	−	7.66731i	−0.595099	−	0.343580i
$499$	16.4023	−	16.4023i	0.734266	−	0.734266i	−0.237196	−	0.971462i	$-0.576228\pi$
$499$	16.4023	−	16.4023i	0.734266	−	0.734266i	0.971462	+	0.237196i	$0.0762284\pi$
$500$	8.66778	−	2.32252i	0.387635	−	0.103866i
$501$	2.52015	−	0.675271i	0.112592	−	0.0301689i
$502$	−14.7559	+	14.7559i	−0.658587	+	0.658587i
$503$	5.93660	+	3.42750i	0.264700	+	0.152825i	0.626477	−	0.779440i	$-0.284496\pi$
$503$	5.93660	+	3.42750i	0.264700	+	0.152825i	−0.361777	+	0.932265i	$0.617830\pi$
$504$	−0.00741761	+	2.64574i	−0.000330407	+	0.117851i
$505$	−2.84954	+	10.6346i	−0.126803	+	0.473235i
$506$		−	23.0943i		−	1.02667i
$507$	10.9648	+	6.98371i	0.486966	+	0.310157i
$508$	0.717011			0.0318122
$509$	2.80154	−	10.4555i	0.124176	−	0.463431i	−0.875633	−	0.482977i	$-0.839555\pi$
$509$	2.80154	−	10.4555i	0.124176	−	0.463431i	0.999809	+	0.0195460i	$0.00622209\pi$
$510$	5.56095	−	3.21061i	0.246243	−	0.142168i
$511$	−8.56102	−	14.9246i	−0.378717	−	0.660225i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−1.72724	−	6.44615i	−0.0762596	−	0.284605i
$514$	1.49453	+	5.57767i	0.0659210	+	0.246020i
$515$	−28.7661	−	28.7661i	−1.26758	−	1.26758i
$516$	2.23136	+	1.28828i	0.0982302	+	0.0567132i
$517$	−5.04383	−	8.73617i	−0.221827	−	0.384216i
$518$	3.92297	+	3.94503i	0.172365	+	0.173334i
$519$		−	4.63192i		−	0.203319i
$520$	10.9135	+	6.62164i	0.478587	+	0.290378i
$521$			15.6561i			0.685907i	0.939352	+	0.342953i	$0.111427\pi$
$521$			15.6561i			0.685907i	−0.939352	+	0.342953i	$0.888573\pi$
$522$	−4.32750	−	1.15955i	−0.189410	−	0.0507522i
$523$	27.6033	−	15.9368i	1.20701	−	0.696867i	0.244904	−	0.969547i	$-0.421244\pi$
$523$	27.6033	−	15.9368i	1.20701	−	0.696867i	0.962105	+	0.272680i	$0.0879102\pi$
$524$	5.85368	−	10.1389i	0.255719	−	0.442919i
$525$	19.2698	−	5.10547i	0.841003	−	0.222821i
$526$	6.10013	+	22.7660i	0.265978	+	0.992644i
$527$	16.5921	−	4.44585i	0.722765	−	0.193664i
$528$	2.41253	−	2.41253i	0.104992	−	0.104992i
$529$	11.4090	−	19.7610i	0.496044	−	0.859173i
$530$	−21.7641	−	37.6966i	−0.945373	−	1.63743i
$531$	−0.753954	−	0.202021i	−0.0327188	−	0.00876698i
$532$	8.87111	−	15.2662i	0.384612	−	0.661874i
$533$	13.8164	+	14.4312i	0.598453	+	0.625084i
$534$	−7.12001			−0.308113
$535$	−9.61667	+	35.8899i	−0.415765	+	1.55166i
$536$	−6.05400	−	10.4858i	−0.261493	−	0.452919i
$537$	5.97314	−	10.3458i	0.257760	−	0.446453i
$538$	−22.5066	−	22.5066i	−0.970328	−	0.970328i
$539$	16.9821	−	16.7927i	0.731471	−	0.723314i
$540$	3.41979	−	0.916329i	0.147164	−	0.0394325i
$541$	0.149689	+	0.149689i	0.00643565	+	0.00643565i	0.710317	−	0.703882i	$-0.248551\pi$
$541$	0.149689	+	0.149689i	0.00643565	+	0.00643565i	−0.703882	+	0.710317i	$0.748551\pi$
$542$	3.66702	+	2.11715i	0.157512	+	0.0909395i
$543$	14.0954	−	8.13801i	0.604893	−	0.349235i
$544$	1.75189	+	0.469417i	0.0751117	+	0.0201261i
$545$	41.2079			1.76515
$546$	8.14170	+	4.97119i	0.348433	+	0.212747i
$547$	34.4130			1.47139			0.735696	−	0.677311i	$-0.236855\pi$
$547$	34.4130			1.47139			0.735696	+	0.677311i	$0.236855\pi$
$548$	−4.86220	−	1.30282i	−0.207703	−	0.0556538i
$549$	3.49316	−	2.01678i	0.149084	−	0.0860740i
$550$	−22.2627	−	12.8534i	−0.949284	−	0.548069i
$551$	21.1415	+	21.1415i	0.900658	+	0.900658i
$552$	6.53826	−	1.75192i	0.278287	−	0.0745667i
$553$	−5.76026	+	21.2590i	−0.244951	+	0.904025i
$554$	20.7754	+	20.7754i	0.882660	+	0.882660i
$555$	3.72243	−	6.44744i	0.158008	−	0.273679i
$556$	−6.48345	−	11.2297i	−0.274959	−	0.476244i
$557$	6.72804	−	25.1094i	0.285076	−	1.06392i	−0.663707	−	0.747992i	$-0.731018\pi$
$557$	6.72804	−	25.1094i	0.285076	−	1.06392i	0.948784	−	0.315927i	$-0.102315\pi$
$558$	9.47099			0.400939
$559$	8.14446	−	4.46878i	0.344474	−	0.189009i
$560$	8.09897	+	4.70626i	0.342244	+	0.198876i
$561$	−5.97714	−	1.60157i	−0.252355	−	0.0676184i
$562$	−1.17251	−	2.03085i	−0.0494593	−	0.0856660i
$563$	20.3919	−	35.3197i	0.859414	−	1.48855i	−0.0130740	−	0.999915i	$-0.504162\pi$
$563$	20.3919	−	35.3197i	0.859414	−	1.48855i	0.872488	−	0.488635i	$-0.162505\pi$
$564$	2.09068	−	2.09068i	0.0880337	−	0.0880337i
$565$	59.6123	−	15.9731i	2.50791	−	0.671992i
$566$	−2.59911	−	9.69999i	−0.109249	−	0.407721i
$567$	2.55751	−	0.677603i	0.107405	−	0.0284567i
$568$	2.32133	−	4.02067i	0.0974009	−	0.168703i
$569$	−0.901570	+	0.520522i	−0.0377958	+	0.0218214i	−0.518779	−	0.854908i	$-0.673613\pi$
$569$	−0.901570	+	0.520522i	−0.0377958	+	0.0218214i	0.480983	+	0.876730i	$0.340280\pi$
$570$	−22.8221	−	6.11517i	−0.955913	−	0.256136i
$571$		−	16.8732i		−	0.706120i	−0.935601	−	0.353060i	$-0.885141\pi$
$571$		−	16.8732i		−	0.706120i	0.935601	−	0.353060i	$-0.114859\pi$
$572$	−2.92454	−	11.9488i	−0.122281	−	0.499605i
$573$			20.5471i			0.858369i
$574$	10.3374	+	10.3955i	0.431473	+	0.433899i
$575$	−25.5005	−	44.1681i	−1.06344	−	1.84194i
$576$	0.866025	+	0.500000i	0.0360844	+	0.0208333i
$577$	27.2510	+	27.2510i	1.13447	+	1.13447i	0.989425	+	0.145047i	$0.0463334\pi$
$577$	27.2510	+	27.2510i	1.13447	+	1.13447i	0.145047	+	0.989425i	$0.453667\pi$
$578$	3.54855	+	13.2434i	0.147600	+	0.550851i
$579$	−4.57901	−	17.0891i	−0.190297	−	0.710198i
$580$	−11.2159	+	11.2159i	−0.465715	+	0.465715i
$581$	−35.1928	+	20.1872i	−1.46004	+	0.837506i
$582$	1.34222	−	0.774931i	0.0556368	−	0.0321219i
$583$	−10.8567	+	40.5179i	−0.449640	+	1.67808i
$584$	−6.50312			−0.269101
$585$	3.57140	−	12.2554i	0.147659	−	0.506698i
$586$			7.24029i			0.299094i
$587$	−7.02605	+	26.2216i	−0.289996	+	1.08228i	0.655115	+	0.755530i	$0.272620\pi$
$587$	−7.02605	+	26.2216i	−0.289996	+	1.08228i	−0.945111	+	0.326751i	$0.894046\pi$
$588$	6.04246	+	3.53394i	0.249187	+	0.145737i
$589$	−54.7373	−	31.6026i	−2.25541	−	1.30216i
$590$	−1.95408	+	1.95408i	−0.0804480	+	0.0804480i
$591$	−20.9228	+	5.60626i	−0.860651	+	0.230611i
$592$	2.03117	−	0.544249i	0.0834804	−	0.0223685i
$593$	−1.53045	+	1.53045i	−0.0628482	+	0.0628482i	−0.737832	−	0.674984i	$-0.764150\pi$
$593$	−1.53045	+	1.53045i	−0.0628482	+	0.0628482i	0.674984	+	0.737832i	$0.264150\pi$
$594$	−2.95473	−	1.70591i	−0.121234	−	0.0699945i
$595$	0.0476302	−	16.9889i	0.00195265	−	0.696477i
$596$	0.893110	−	3.33313i	0.0365832	−	0.136530i
$597$			22.0147i			0.901003i
$598$	6.82813	−	23.4310i	0.279223	−	0.958164i
$599$	−10.0865			−0.412125			−0.206063	−	0.978539i	$-0.566065\pi$
$599$	−10.0865			−0.412125			−0.206063	+	0.978539i	$0.566065\pi$
$600$	1.95010	−	7.27786i	0.0796124	−	0.297117i
$601$	8.89524	−	5.13567i	0.362845	−	0.209488i	−0.307483	−	0.951553i	$-0.599487\pi$
$601$	8.89524	−	5.13567i	0.362845	−	0.209488i	0.670328	+	0.742065i	$0.266153\pi$
$602$	5.91316	−	3.39190i	0.241002	−	0.138243i
$603$	−8.56165	+	8.56165i	−0.348657	+	0.348657i
$604$	6.01686	+	22.4552i	0.244823	+	0.913690i
$605$	0.586961	+	2.19057i	0.0238634	+	0.0890593i
$606$	2.19892	+	2.19892i	0.0893248	+	0.0893248i
$607$	28.8044	+	16.6302i	1.16914	+	0.675001i	0.953476	−	0.301468i	$-0.0974765\pi$
$607$	28.8044	+	16.6302i	1.16914	+	0.675001i	0.215660	+	0.976469i	$0.430810\pi$
$608$	−3.33678	−	5.77946i	−0.135324	−	0.234388i
$609$	−8.40508	+	8.35808i	−0.340591	+	0.338687i
$610$		−	14.2805i		−	0.578200i
$611$	−2.53440	−	10.3548i	−0.102531	−	0.418910i
$612$		−	1.81369i		−	0.0733141i
$613$	−13.4448	−	3.60253i	−0.543032	−	0.145505i	−0.0231323	−	0.999732i	$-0.507364\pi$
$613$	−13.4448	−	3.60253i	−0.543032	−	0.145505i	−0.519899	+	0.854228i	$0.674031\pi$
$614$	−6.56413	+	3.78980i	−0.264907	+	0.152944i
$615$	9.80894	−	16.9896i	0.395534	−	0.685086i
$616$	−2.31186	−	8.72578i	−0.0931477	−	0.351572i
$617$	−9.24523	−	34.5037i	−0.372199	−	1.38907i	−0.857394	−	0.514660i	$-0.827918\pi$
$617$	−9.24523	−	34.5037i	−0.372199	−	1.38907i	0.485196	−	0.874406i	$-0.338748\pi$
$618$	−11.0990	+	2.97397i	−0.446467	+	0.119631i
$619$	3.83959	−	3.83959i	0.154326	−	0.154326i	−0.625721	−	0.780047i	$-0.715195\pi$
$619$	3.83959	−	3.83959i	0.154326	−	0.154326i	0.780047	+	0.625721i	$0.215195\pi$
$620$	16.7657	−	29.0390i	0.673325	−	1.16623i
$621$	−3.38445	−	5.86204i	−0.135813	−	0.235236i
$622$	12.4438	+	3.33432i	0.498952	+	0.133694i
$623$	−9.46459	+	16.2875i	−0.379191	+	0.652546i
$624$	3.16099	−	1.73440i	0.126541	−	0.0694316i
$625$	5.90283			0.236113
$626$	−0.0152773	+	0.0570156i	−0.000610603	+	0.00227880i
$627$	11.3845	+	19.7185i	0.454653	+	0.787482i
$628$	−4.99832	+	8.65735i	−0.199455	+	0.345466i
$629$	−2.69681	−	2.69681i	−0.107529	−	0.107529i
$630$	2.44974	−	9.04107i	0.0975998	−	0.360205i
$631$	14.2859	−	3.82788i	0.568711	−	0.152386i	0.0370056	−	0.999315i	$-0.488218\pi$
$631$	14.2859	−	3.82788i	0.568711	−	0.152386i	0.531705	+	0.846929i	$0.321551\pi$
$632$	5.88658	+	5.88658i	0.234156	+	0.234156i
$633$	−4.57737	−	2.64275i	−0.181934	−	0.105040i
$634$	−10.9518	+	6.32305i	−0.434953	+	0.251120i
$635$	−2.45203	−	0.657018i	−0.0973057	−	0.0260730i
$636$	−12.2946			−0.487514
$637$	22.1947	−	12.0165i	0.879384	−	0.476113i
$638$	15.2855			0.605160
$639$	−4.48447	−	1.20161i	−0.177403	−	0.0475350i
$640$	3.06610	−	1.77021i	0.121198	−	0.0699738i
$641$	11.0179	+	6.36116i	0.435179	+	0.251251i	0.701551	−	0.712620i	$-0.252491\pi$
$641$	11.0179	+	6.36116i	0.435179	+	0.251251i	−0.266371	+	0.963870i	$0.585825\pi$
$642$	7.42093	+	7.42093i	0.292881	+	0.292881i
$643$	−22.6514	+	6.06942i	−0.893283	+	0.239354i	−0.676129	−	0.736783i	$-0.736344\pi$
$643$	−22.6514	+	6.06942i	−0.893283	+	0.239354i	−0.217154	+	0.976137i	$0.569677\pi$
$644$	4.68363	−	17.2855i	0.184561	−	0.681146i
$645$	−6.45029	−	6.45029i	−0.253980	−	0.253980i
$646$	−6.05188	+	10.4822i	−0.238108	+	0.412415i
$647$	25.3809	+	43.9610i	0.997825	+	1.72828i	0.555996	+	0.831185i	$0.312337\pi$
$647$	25.3809	+	43.9610i	0.997825	+	1.72828i	0.441830	+	0.897099i	$0.354330\pi$
$648$	0.258819	−	0.965926i	0.0101674	−	0.0379452i
$649$	2.66310			0.104536
$650$	−18.7870	−	19.6230i	−0.736885	−	0.769677i
$651$	12.5897	−	21.6656i	0.493431	−	0.849140i
$652$	0.938913	+	0.251581i	0.0367707	+	0.00985267i
$653$	8.70883	+	15.0841i	0.340803	+	0.590288i	0.984582	−	0.174923i	$-0.0559678\pi$
$653$	8.70883	+	15.0841i	0.340803	+	0.590288i	−0.643779	+	0.765211i	$0.722634\pi$
$654$	5.81963	−	10.0799i	0.227565	−	0.394155i
$655$	−29.3089	+	29.3089i	−1.14519	+	1.14519i
$656$	5.35230	−	1.43414i	0.208972	−	0.0559939i
$657$	1.68313	+	6.28154i	0.0656653	+	0.245066i
$658$	−2.00345	−	7.56172i	−0.0781027	−	0.294787i
$659$	−15.8994	+	27.5386i	−0.619352	+	1.07275i	0.370252	+	0.928931i	$0.379271\pi$
$659$	−15.8994	+	27.5386i	−0.619352	+	1.07275i	−0.989604	+	0.143818i	$0.954062\pi$
$660$	−10.4610	+	6.03965i	−0.407193	+	0.235093i
$661$	37.4947	+	10.0467i	1.45837	+	0.390770i	0.898928	−	0.438096i	$-0.144347\pi$
$661$	37.4947	+	10.0467i	1.45837	+	0.390770i	0.559447	+	0.828866i	$0.311014\pi$
$662$			31.2312i			1.21383i
$663$	−5.59075	−	3.39214i	−0.217127	−	0.131740i
$664$			15.3346i			0.595099i
$665$	−44.3262	+	44.0783i	−1.71890	+	1.70928i
$666$	−1.05141	−	1.82109i	−0.0407413	−	0.0705659i
$667$	26.2629	+	15.1629i	1.01690	+	0.587109i
$668$	−1.84488	−	1.84488i	−0.0713804	−	0.0713804i
$669$	−4.02721	−	15.0297i	−0.155701	−	0.581083i
$670$	11.0949	+	41.4068i	0.428634	+	1.59968i
$671$	−9.73105	+	9.73105i	−0.375663	+	0.375663i
$672$	2.29499	−	1.31645i	0.0885311	−	0.0507830i
$673$	−17.3471	+	10.0154i	−0.668682	+	0.386064i	−0.795577	−	0.605853i	$-0.792832\pi$
$673$	−17.3471	+	10.0154i	−0.668682	+	0.386064i	0.126895	+	0.991916i	$0.459499\pi$
$674$	0.471587	−	1.75999i	0.0181648	−	0.0677921i
$675$	−7.53460			−0.290007
$676$	0.565644	−	12.9877i	0.0217556	−	0.499526i
$677$		−	28.2440i		−	1.08551i	−0.839892	−	0.542753i	$-0.817382\pi$
$677$		−	28.2440i		−	1.08551i	0.839892	−	0.542753i	$-0.182618\pi$
$678$	4.51163	−	16.8376i	0.173268	−	0.646645i
$679$	0.0114963	−	4.10053i	0.000441186	−	0.157364i
$680$	−5.56095	−	3.21061i	−0.213253	−	0.123121i
$681$	16.5705	−	16.5705i	0.634985	−	0.634985i
$682$	−31.2123	+	8.36332i	−1.19518	+	0.320248i
$683$	−20.0724	+	5.37838i	−0.768048	+	0.205798i	−0.621509	−	0.783407i	$-0.713480\pi$
$683$	−20.0724	+	5.37838i	−0.768048	+	0.205798i	−0.146539	+	0.989205i	$0.546813\pi$
$684$	−4.71891	+	4.71891i	−0.180432	+	0.180432i
$685$	15.4339	+	8.91075i	0.589698	+	0.340462i
$686$	16.1163	−	9.12490i	0.615324	−	0.348390i
$687$	−2.74179	+	10.2325i	−0.104606	+	0.390394i
$688$		−	2.57655i		−	0.0982302i
$689$	−22.9946	+	37.8986i	−0.876025	+	1.44382i
$690$	−23.9648			−0.912323
$691$	1.68554	−	6.29053i	0.0641211	−	0.239303i	−0.926426	−	0.376477i	$-0.877135\pi$
$691$	1.68554	−	6.29053i	0.0641211	−	0.239303i	0.990547	+	0.137174i	$0.0438020\pi$
$692$	−4.01136	+	2.31596i	−0.152489	+	0.0880395i
$693$	−7.83010	+	4.49149i	−0.297441	+	0.170617i
$694$	−22.4751	+	22.4751i	−0.853143	+	0.853143i
$695$	11.8819	+	44.3440i	0.450708	+	1.68206i
$696$	1.15955	+	4.32750i	0.0439527	+	0.164034i
$697$	−7.10632	−	7.10632i	−0.269171	−	0.269171i
$698$	15.4133	+	8.89887i	0.583402	+	0.336827i
$699$	3.15432	+	5.46344i	0.119307	+	0.206646i
$700$	−14.0564	−	14.1354i	−0.531281	−	0.534268i
$701$			1.66268i			0.0627986i	0.999507	+	0.0313993i	$0.00999635\pi$
$701$			1.66268i			0.0627986i	−0.999507	+	0.0313993i	$0.990004\pi$
$702$	−2.49343	−	2.60439i	−0.0941083	−	0.0982962i
$703$			14.0333i			0.529274i
$704$	−3.29557	−	0.883046i	−0.124207	−	0.0332810i
$705$	−9.06545	+	5.23394i	−0.341424	+	0.197121i
$706$	7.00319	−	12.1299i	0.263569	−	0.456514i
$707$	7.95318	−	2.10717i	0.299110	−	0.0792482i
$708$	0.202021	+	0.753954i	0.00759243	+	0.0283353i
$709$	−39.6753	+	10.6310i	−1.49004	+	0.399255i	−0.909750	−	0.415157i	$-0.863727\pi$
$709$	−39.6753	+	10.6310i	−1.49004	+	0.399255i	−0.580288	+	0.814411i	$0.697060\pi$
$710$	−11.6227	+	11.6227i	−0.436193	+	0.436193i
$711$	4.16244	−	7.20956i	0.156104	−	0.270380i
$712$	3.56001	+	6.16611i	0.133417	+	0.231085i
$713$	−61.9238	−	16.5924i	−2.31906	−	0.621391i
$714$	−4.14894	−	2.41093i	−0.155270	−	0.0902267i
$715$	−0.947734	+	43.5423i	−0.0354433	+	1.62839i
$716$	−11.9463			−0.446453
$717$	3.38494	−	12.6328i	0.126413	−	0.471780i
$718$	−8.84587	−	15.3215i	−0.330125	−	0.571793i
$719$	4.27213	−	7.39955i	0.159324	−	0.275957i	−0.775301	−	0.631592i	$-0.782402\pi$
$719$	4.27213	−	7.39955i	0.159324	−	0.275957i	0.934625	+	0.355635i	$0.115735\pi$
$720$	−2.50346	−	2.50346i	−0.0932983	−	0.0932983i
$721$	−7.95068	+	29.3430i	−0.296099	+	1.09279i
$722$	24.6661	−	6.60927i	0.917979	−	0.245972i
$723$	−3.74897	−	3.74897i	−0.139426	−	0.139426i
$724$	−14.0954	−	8.13801i	−0.523853	−	0.302447i
$725$	29.2337	−	16.8781i	1.08571	−	0.626837i
$726$	0.618731	+	0.165788i	0.0229633	+	0.00615298i
$727$	−34.2833			−1.27150			−0.635748	−	0.771897i	$-0.719308\pi$
$727$	−34.2833			−1.27150			−0.635748	+	0.771897i	$0.719308\pi$
$728$	0.234321	−	9.53651i	0.00868453	−	0.353447i
$729$	−1.00000			−0.0370370
$730$	22.2393	+	5.95900i	0.823113	+	0.220553i
$731$	−4.04700	+	2.33654i	−0.149684	+	0.0864199i
$732$	−3.49316	−	2.01678i	−0.129111	−	0.0745422i
$733$	8.57075	+	8.57075i	0.316568	+	0.316568i	0.847447	−	0.530879i	$-0.178138\pi$
$733$	8.57075	+	8.57075i	0.316568	+	0.316568i	−0.530879	+	0.847447i	$0.678138\pi$
$734$	−16.9888	+	4.55213i	−0.627067	+	0.168022i
$735$	−17.4257	−	17.6222i	−0.642755	−	0.650004i
$736$	−4.78634	−	4.78634i	−0.176427	−	0.176427i
$737$	20.6552	−	35.7759i	0.760844	−	1.31782i
$738$	−2.77055	−	4.79874i	−0.101986	−	0.176644i
$739$	1.85839	−	6.93561i	0.0683620	−	0.255131i	−0.923284	−	0.384117i	$-0.874506\pi$
$739$	1.85839	−	6.93561i	0.0683620	−	0.255131i	0.991646	+	0.128987i	$0.0411725\pi$
$740$	−7.44486			−0.273679
$741$	5.72042	+	23.3720i	0.210145	+	0.858590i
$742$	−16.3432	+	28.1249i	−0.599978	+	1.03250i
$743$	21.2104	+	5.68331i	0.778134	+	0.208500i	0.625962	−	0.779854i	$-0.284707\pi$
$743$	21.2104	+	5.68331i	0.778134	+	0.208500i	0.152172	+	0.988354i	$0.451373\pi$
$744$	−4.73550	−	8.20212i	−0.173612	−	0.300704i
$745$	−6.10849	+	10.5802i	−0.223798	+	0.387629i
$746$	26.3441	−	26.3441i	0.964526	−	0.964526i
$747$	14.8121	−	3.96889i	0.541947	−	0.145214i
$748$	1.60157	+	5.97714i	0.0585592	+	0.218546i
$749$	26.8405	−	7.11130i	0.980731	−	0.259841i
$750$	−4.48677	+	7.77132i	−0.163834	+	0.283768i
$751$	−4.50756	+	2.60244i	−0.164483	+	0.0949645i	−0.579982	−	0.814629i	$-0.696940\pi$
$751$	−4.50756	+	2.60244i	−0.164483	+	0.0949645i	0.415499	+	0.909594i	$0.363607\pi$
$752$	−2.85593	−	0.765243i	−0.104145	−	0.0279056i
$753$		−	20.8680i		−	0.760471i
$754$	15.5084	+	4.51936i	0.564781	+	0.164586i
$755$		−	82.3055i		−	2.99540i
$756$	−1.86558	−	1.87607i	−0.0678504	−	0.0682319i
$757$	−23.3580	−	40.4572i	−0.848960	−	1.47044i	−0.882138	−	0.470992i	$-0.843896\pi$
$757$	−23.3580	−	40.4572i	−0.848960	−	1.47044i	0.0331779	−	0.999449i	$-0.489437\pi$
$758$	−3.20086	−	1.84802i	−0.116260	−	0.0671230i
$759$	16.3301	+	16.3301i	0.592747	+	0.592747i
$760$	6.11517	+	22.8221i	0.221820	+	0.827845i
$761$	2.16748	+	8.08914i	0.0785710	+	0.293231i	0.994019	−	0.109205i	$-0.0348304\pi$
$761$	2.16748	+	8.08914i	0.0785710	+	0.293231i	−0.915448	+	0.402436i	$0.868164\pi$
$762$	−0.507004	+	0.507004i	−0.0183668	+	0.0183668i
$763$	−15.3225	−	26.7119i	−0.554710	−	0.967037i
$764$	17.7943	−	10.2736i	0.643777	−	0.371685i
$765$	−1.66194	+	6.20243i	−0.0600874	+	0.224249i
$766$	−4.21192			−0.152183
$767$	2.70193	+	0.787381i	0.0975609	+	0.0284307i
$768$		−	1.00000i		−	0.0360844i
$769$	6.46254	−	24.1185i	0.233045	−	0.869737i	−0.745975	−	0.665974i	$-0.768016\pi$
$769$	6.46254	−	24.1185i	0.233045	−	0.869737i	0.979020	−	0.203763i	$-0.0653171\pi$
$770$	−0.0895996	+	31.9587i	−0.00322894	+	1.15171i
$771$	−5.00080	−	2.88721i	−0.180099	−	0.103980i
$772$	−12.5101	+	12.5101i	−0.450247	+	0.450247i
$773$	6.16839	−	1.65282i	0.221862	−	0.0594477i	−0.146176	−	0.989259i	$-0.546696\pi$
$773$	6.16839	−	1.65282i	0.221862	−	0.0594477i	0.368037	+	0.929811i	$0.380030\pi$
$774$	−2.48876	+	0.666861i	−0.0894566	+	0.0239698i
$775$	−50.4592	+	50.4592i	−1.81255	+	1.81255i
$776$	−1.34222	−	0.774931i	−0.0481829	−	0.0278184i
$777$	−5.56351	−	0.0155979i	−0.199590	−	0.000559571i
$778$	−1.62421	+	6.06163i	−0.0582307	+	0.217320i
$779$			36.9789i			1.32491i
$780$	−12.3992	+	3.03477i	−0.443962	+	0.108662i
$781$	15.8400			0.566798
$782$	−3.17744	+	11.8584i	−0.113625	+	0.424054i
$783$	3.87993	−	2.24008i	0.138658	−	0.0800540i
$784$	0.0392501	−	6.99989i	0.00140179	−	0.249996i
$785$	25.0262	−	25.0262i	0.893223	−	0.893223i
$786$	3.03009	+	11.3084i	0.108080	+	0.403359i
$787$	−13.0527	−	48.7135i	−0.465280	−	1.73645i	−0.655959	−	0.754796i	$-0.727736\pi$
$787$	−13.0527	−	48.7135i	−0.465280	−	1.73645i	0.190679	−	0.981652i	$-0.438931\pi$
$788$	15.3166	+	15.3166i	0.545631	+	0.545631i
$789$	−20.4114	−	11.7845i	−0.726666	−	0.419541i
$790$	−14.7368	−	25.5249i	−0.524312	−	0.908135i
$791$	−32.5200	−	32.7028i	−1.15628	−	1.16278i
$792$			3.41183i			0.121234i
$793$	−12.7500	+	6.99580i	−0.452767	+	0.248428i
$794$			36.7245i			1.30331i
$795$	42.0450	+	11.2659i	1.49118	+	0.399562i
$796$	19.0653	−	11.0074i	0.675753	−	0.390146i
$797$	−12.9386	+	22.4103i	−0.458308	+	0.793812i	−0.998872	−	0.0474906i	$-0.984878\pi$
$797$	−12.9386	+	22.4103i	−0.458308	+	0.793812i	0.540564	+	0.841303i	$0.318211\pi$
$798$	4.52202	+	17.0677i	0.160078	+	0.604189i
$799$	1.38791	+	5.17977i	0.0491009	+	0.183247i
$800$	−7.27786	+	1.95010i	−0.257311	+	0.0689463i
$801$	5.03461	−	5.03461i	0.177889	−	0.177889i
$802$	−13.1656	+	22.8035i	−0.464894	+	0.805220i
$803$	−11.0938	−	19.2150i	−0.391490	−	0.678081i
$804$	11.6954	+	3.13378i	0.412466	+	0.110520i
$805$	−31.8562	+	54.8211i	−1.12278	+	1.93219i
$806$	−34.1401	−	0.743088i	−1.20253	−	0.0261742i
$807$	31.8291			1.12044
$808$	0.804859	−	3.00377i	0.0283148	−	0.105672i
$809$	0.0481878	+	0.0834637i	0.00169419	+	0.00293443i	0.866871	−	0.498532i	$-0.166127\pi$
$809$	0.0481878	+	0.0834637i	0.00169419	+	0.00293443i	−0.865177	+	0.501466i	$0.832794\pi$
$810$	−1.77021	+	3.06610i	−0.0621989	+	0.107732i
$811$	−12.0995	−	12.0995i	−0.424872	−	0.424872i	0.462005	−	0.886877i	$-0.347130\pi$
$811$	−12.0995	−	12.0995i	−0.424872	−	0.424872i	−0.886877	+	0.462005i	$0.847130\pi$
$812$	11.4409	+	3.09997i	0.401495	+	0.108788i
$813$	−4.09003	+	1.09592i	−0.143444	+	0.0384356i
$814$	5.07310	+	5.07310i	0.177812	+	0.177812i
$815$	−2.98035	−	1.72071i	−0.104397	−	0.0602737i
$816$	−1.57070	+	0.906845i	−0.0549856	+	0.0317459i
$817$	16.6089	+	4.45033i	0.581071	+	0.155697i
$818$	3.81933			0.133540
$819$	−9.27221	+	2.24189i	−0.323997	+	0.0783381i
$820$	−19.6179			−0.685086
$821$	−14.6844	−	3.93467i	−0.512489	−	0.137321i	−0.00669872	−	0.999978i	$-0.502132\pi$
$821$	−14.6844	−	3.93467i	−0.512489	−	0.137321i	−0.505790	+	0.862657i	$0.668799\pi$
$822$	4.35933	−	2.51686i	0.152049	−	0.0877856i
$823$	−18.8208	−	10.8662i	−0.656051	−	0.378771i	0.134719	−	0.990884i	$-0.456987\pi$
$823$	−18.8208	−	10.8662i	−0.656051	−	0.378771i	−0.790771	+	0.612112i	$0.790320\pi$
$824$	8.12503	+	8.12503i	0.283049	+	0.283049i
$825$	24.8308	−	6.65339i	0.864497	−	0.231641i
$826$	1.99327	+	0.540089i	0.0693547	+	0.0187921i
$827$	−11.5690	−	11.5690i	−0.402294	−	0.402294i	0.476746	−	0.879041i	$-0.341816\pi$
$827$	−11.5690	−	11.5690i	−0.402294	−	0.402294i	−0.879041	+	0.476746i	$0.841816\pi$
$828$	−3.38445	+	5.86204i	−0.117618	+	0.203720i
$829$	−0.943315	−	1.63387i	−0.0327627	−	0.0567467i	0.849179	−	0.528105i	$-0.177097\pi$
$829$	−0.943315	−	1.63387i	−0.0327627	−	0.0567467i	−0.881942	+	0.471358i	$0.843764\pi$
$830$	14.0516	−	52.4411i	0.487737	−	1.82026i
$831$	−29.3808			−1.01921
$832$	−3.08253	−	1.87030i	−0.106867	−	0.0648409i
$833$	−11.0303	+	6.28616i	−0.382178	+	0.217803i
$834$	12.5251	+	3.35608i	0.433707	+	0.116212i
$835$	4.61857	+	7.99959i	0.159832	+	0.276837i
$836$	11.3845	−	19.7185i	0.393741	−	0.681980i
$837$	−6.69700	+	6.69700i	−0.231482	+	0.231482i
$838$	−5.03710	+	1.34969i	−0.174004	+	0.0466241i
$839$	−0.770611	−	2.87596i	−0.0266044	−	0.0992891i	0.951347	−	0.308122i	$-0.0997003\pi$
$839$	−0.770611	−	2.87596i	−0.0266044	−	0.0992891i	−0.977951	+	0.208832i	$0.933034\pi$
$840$	−9.05467	+	2.39900i	−0.312416	+	0.0827734i
$841$	4.46408	−	7.73201i	0.153934	−	0.266621i
$842$	12.2329	−	7.06267i	0.421573	−	0.243396i
$843$	2.26511	+	0.606935i	0.0780146	+	0.0209040i
$844$			5.28549i			0.181934i
$845$	−13.8354	+	43.8968i	−0.475951	+	1.51010i
$846$			2.95667i			0.101653i
$847$	1.20173	−	1.19501i	0.0412919	−	0.0410610i
$848$	6.14732	+	10.6475i	0.211100	+	0.365636i
$849$	8.69678	+	5.02109i	0.298473	+	0.172323i
$850$	9.66291	+	9.66291i	0.331435	+	0.331435i
$851$	3.68397	+	13.7488i	0.126285	+	0.471301i
$852$	1.20161	+	4.48447i	0.0411665	+	0.153635i
$853$	−32.2414	+	32.2414i	−1.10392	+	1.10392i	−0.109992	+	0.993932i	$0.535083\pi$
$853$	−32.2414	+	32.2414i	−1.10392	+	1.10392i	−0.993932	+	0.109992i	$0.964917\pi$
$854$	−9.25696	+	5.30996i	−0.316767	+	0.181703i
$855$	20.4617	−	11.8136i	0.699777	−	0.404016i
$856$	2.71625	−	10.1372i	0.0928395	−	0.346482i
$857$	−36.4709			−1.24582			−0.622911	−	0.782293i	$-0.714050\pi$
$857$	−36.4709			−1.24582			−0.622911	+	0.782293i	$0.714050\pi$
$858$	10.5171	+	6.38113i	0.359046	+	0.217848i
$859$		−	4.27424i		−	0.145835i	−0.997338	−	0.0729177i	$-0.976769\pi$
$859$		−	4.27424i		−	0.145835i	0.997338	−	0.0729177i	$-0.0232310\pi$
$860$	−2.36097	+	8.81126i	−0.0805085	+	0.300462i
$861$	−14.6603	−	0.0411018i	−0.499623	−	0.00140074i
$862$	−30.4547	−	17.5830i	−1.03729	−	0.598881i
$863$	−0.453840	+	0.453840i	−0.0154489	+	0.0154489i	−0.714789	−	0.699340i	$-0.753477\pi$
$863$	−0.453840	+	0.453840i	−0.0154489	+	0.0154489i	0.699340	+	0.714789i	$0.253477\pi$
$864$	−0.965926	+	0.258819i	−0.0328615	+	0.00880520i
$865$	15.8402	−	4.24436i	0.538582	−	0.144313i
$866$	14.2627	−	14.2627i	0.484668	−	0.484668i
$867$	−11.8737	−	6.85526i	−0.403251	−	0.232817i
$868$	−25.0578	−	0.0702521i	−0.850517	−	0.00238451i
$869$	−7.35125	+	27.4352i	−0.249374	+	0.930677i
$870$		−	15.8617i		−	0.537761i
$871$	31.5339	−	30.1904i	1.06849	−	1.02296i
$872$	−11.6393			−0.394155
$873$	−0.401134	+	1.49705i	−0.0135763	+	0.0506675i
$874$	39.1206	−	22.5863i	1.32327	−	0.763993i
$875$	11.8132	+	20.5942i	0.399359	+	0.696210i
$876$	4.59840	−	4.59840i	0.155366	−	0.155366i
$877$	4.62763	+	17.2705i	0.156264	+	0.583185i	0.998994	+	0.0448481i	$0.0142804\pi$
$877$	4.62763	+	17.2705i	0.156264	+	0.583185i	−0.842730	+	0.538337i	$0.819053\pi$
$878$	−8.82596	−	32.9389i	−0.297862	−	1.11164i
$879$	−5.11966	−	5.11966i	−0.172682	−	0.172682i
$880$	10.4610	+	6.03965i	0.352640	+	0.203597i
$881$	−1.09999	−	1.90524i	−0.0370597	−	0.0641892i	0.846901	−	0.531751i	$-0.178466\pi$
$881$	−1.09999	−	1.90524i	−0.0370597	−	0.0641892i	−0.883960	+	0.467562i	$0.845132\pi$
$882$	−6.77153	+	1.77379i	−0.228009	+	0.0597267i
$883$		−	16.9663i		−	0.570962i	−0.958384	−	0.285481i	$-0.907847\pi$
$883$		−	16.9663i		−	0.570962i	0.958384	−	0.285481i	$-0.0921533\pi$
$884$	−0.142301	+	6.53780i	−0.00478610	+	0.219890i
$885$		−	2.76348i		−	0.0928934i
$886$	0.959840	+	0.257188i	0.0322465	+	0.00864041i
$887$	−28.5094	+	16.4599i	−0.957250	+	0.552669i	−0.895326	−	0.445412i	$-0.853057\pi$
$887$	−28.5094	+	16.4599i	−0.957250	+	0.552669i	−0.0619246	+	0.998081i	$0.519724\pi$
$888$	−1.05141	+	1.82109i	−0.0352830	+	0.0611119i
$889$	0.485849	+	1.83376i	0.0162949	+	0.0615024i
$890$	−6.52427	−	24.3489i	−0.218694	−	0.816178i
$891$	3.29557	−	0.883046i	0.110406	−	0.0295831i
$892$	−11.0025	+	11.0025i	−0.368392	+	0.368392i
$893$	9.86575	−	17.0880i	0.330145	−	0.571828i
$894$	1.72536	+	2.98840i	0.0577045	+	0.0999471i
$895$	40.8537	+	10.9467i	1.36559	+	0.365908i
$896$	−2.28757	−	1.32929i	−0.0764224	−	0.0444086i
$897$	11.7400	+	21.3964i	0.391987	+	0.714406i
$898$	1.85568			0.0619248
$899$	10.9821	−	40.9858i	0.366274	−	1.36695i
$900$	3.76730	+	6.52515i	0.125577	+	0.217505i
$901$	11.1493	−	19.3112i	0.371438	−	0.643350i
$902$	13.3681	+	13.3681i	0.445108	+	0.445108i
$903$	−1.78280	+	6.57967i	−0.0593280	+	0.218958i
$904$	−16.8376	+	4.51163i	−0.560011	+	0.150055i
$905$	40.7463	+	40.7463i	1.35445	+	1.35445i
$906$	−20.1328	−	11.6237i	−0.668868	−	0.386171i
$907$	−27.5955	+	15.9323i	−0.916293	+	0.529022i	−0.882451	−	0.470405i	$-0.844108\pi$
$907$	−27.5955	+	15.9323i	−0.916293	+	0.529022i	−0.0338425	+	0.999427i	$0.510774\pi$
$908$	−22.6358	−	6.06524i	−0.751195	−	0.201282i
$909$	−3.10974			−0.103143
$910$	−9.53991	+	32.3981i	−0.316245	+	1.07399i
$911$	−34.6918			−1.14939			−0.574695	−	0.818368i	$-0.694879\pi$
$911$	−34.6918			−1.14939			−0.574695	+	0.818368i	$0.694879\pi$
$912$	6.44615	+	1.72724i	0.213454	+	0.0571947i
$913$	−45.3096	+	26.1595i	−1.49953	+	0.865754i
$914$	−20.4404	−	11.8013i	−0.676110	−	0.390352i
$915$	10.0978	+	10.0978i	0.333824	+	0.333824i
$916$	10.2325	−	2.74179i	0.338091	−	0.0905912i
$917$	29.8967	+	8.10071i	0.987277	+	0.267509i
$918$	1.28247	+	1.28247i	0.0423279	+	0.0423279i
$919$	−11.1493	+	19.3111i	−0.367780	+	0.637014i	−0.989218	−	0.146449i	$-0.953216\pi$
$919$	−11.1493	+	19.3111i	−0.367780	+	0.637014i	0.621438	+	0.783464i	$0.286549\pi$
$920$	11.9824	+	20.7541i	0.395048	+	0.684242i
$921$	1.96175	−	7.32133i	0.0646417	−	0.241246i
$922$	4.36511			0.143757
$923$	16.0709	+	4.68329i	0.528979	+	0.154152i
$924$	7.80479	+	4.53532i	0.256759	+	0.149201i
$925$	15.3040	+	4.10070i	0.503193	+	0.134830i
$926$	11.9673	+	20.7280i	0.393270	+	0.681164i
$927$	5.74527	−	9.95109i	0.188699	−	0.326837i
$928$	3.16795	−	3.16795i	0.103993	−	0.103993i
$929$	37.6772	−	10.0956i	1.23615	−	0.331225i	0.419178	−	0.907904i	$-0.362318\pi$
$929$	37.6772	−	10.0956i	1.23615	−	0.331225i	0.816971	+	0.576679i	$0.195652\pi$
$930$	8.67854	+	32.3888i	0.284581	+	1.06207i
$931$	45.0546	+	12.3435i	1.47660	+	0.404542i
$932$	3.15432	−	5.46344i	0.103323	−	0.178961i
$933$	−11.1568	+	6.44140i	−0.365258	+	0.210882i
$934$	−2.46126	−	0.659493i	−0.0805349	−	0.0215793i
$935$		−	21.9081i		−	0.716472i
$936$	−1.00875	+	3.46156i	−0.0329720	+	0.113145i
$937$			43.7145i			1.42809i	0.700100	+	0.714045i	$0.253139\pi$
$937$			43.7145i			1.42809i	−0.700100	+	0.714045i	$0.746861\pi$
$938$	22.7154	−	22.5884i	0.741685	−	0.737538i
$939$	−0.0295135	−	0.0511188i	−0.000963135	−	0.00166820i
$940$	9.06545	+	5.23394i	0.295682	+	0.170712i
$941$	−30.2503	−	30.2503i	−0.986130	−	0.986130i	0.0137749	−	0.999905i	$-0.495615\pi$
$941$	−30.2503	−	30.2503i	−0.986130	−	0.986130i	−0.999905	+	0.0137749i	$0.995615\pi$
$942$	−2.58732	−	9.65602i	−0.0842995	−	0.314610i
$943$	9.70758	+	36.2292i	0.316122	+	1.17978i
$944$	0.551933	−	0.551933i	0.0179639	−	0.0179639i
$945$	4.66078	+	8.12523i	0.151615	+	0.264314i
$946$	7.61302	−	4.39538i	0.247521	−	0.142906i
$947$	1.29971	−	4.85057i	0.0422348	−	0.157622i	−0.941588	−	0.336767i	$-0.890666\pi$
$947$	1.29971	−	4.85057i	0.0422348	−	0.157622i	0.983823	+	0.179145i	$0.0573331\pi$
$948$	−8.32488			−0.270380
$949$	−5.57434	−	22.7751i	−0.180951	−	0.739311i
$950$		−	50.2825i		−	1.63138i
$951$	3.27305	−	12.2152i	0.106136	−	0.396105i
$952$	−0.0134532	+	4.79855i	−0.000436022	+	0.155522i
$953$	1.79888	+	1.03858i	0.0582715	+	0.0336430i	0.528853	−	0.848714i	$-0.322622\pi$
$953$	1.79888	+	1.03858i	0.0582715	+	0.0336430i	−0.470581	+	0.882357i	$0.655956\pi$
$954$	8.69362	−	8.69362i	0.281466	−	0.281466i
$955$	−70.2668	+	18.8279i	−2.27378	+	0.609258i
$956$	−12.6328	+	3.38494i	−0.408573	+	0.109477i
$957$	−10.8085	+	10.8085i	−0.349389	+	0.349389i
$958$	−10.9489	−	6.32137i	−0.353744	−	0.204234i
$959$	0.0373382	−	13.3179i	0.00120571	−	0.430058i
$960$	−0.916329	+	3.41979i	−0.0295744	+	0.110373i
$961$			58.6997i			1.89354i
$962$	3.64713	+	6.64698i	0.117588	+	0.214307i
$963$	−10.4948			−0.338190
$964$	−1.37222	+	5.12118i	−0.0441961	+	0.164942i
$965$	54.2451	−	31.3184i	1.74621	−	1.00818i
$966$	8.91090	+	15.5345i	0.286703	+	0.499816i
$967$	7.21243	−	7.21243i	0.231936	−	0.231936i	−0.581564	−	0.813500i	$-0.697559\pi$
$967$	7.21243	−	7.21243i	0.231936	−	0.231936i	0.813500	+	0.581564i	$0.197559\pi$
$968$	−0.165788	−	0.618731i	−0.00532864	−	0.0198868i
$969$	−3.13268	−	11.6913i	−0.100636	−	0.375579i
$970$	3.88001	+	3.88001i	0.124580	+	0.124580i
$971$	−39.3887	−	22.7411i	−1.26404	−	0.729796i	−0.290189	−	0.956969i	$-0.593718\pi$
$971$	−39.3887	−	22.7411i	−1.26404	−	0.729796i	−0.973854	+	0.227173i	$0.927052\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	24.3268	−	24.1907i	0.779880	−	0.775519i
$974$			0.793315i			0.0254195i
$975$	27.1599	+	0.591159i	0.869814	+	0.0189323i
$976$			4.03356i			0.129111i
$977$	−20.3607	−	5.45564i	−0.651397	−	0.174541i	−0.0820365	−	0.996629i	$-0.526142\pi$
$977$	−20.3607	−	5.45564i	−0.651397	−	0.174541i	−0.569360	+	0.822088i	$0.692809\pi$
$978$	−0.841807	+	0.486017i	−0.0269180	+	0.0155411i
$979$	−12.1461	+	21.0377i	−0.388192	+	0.672368i
$980$	−6.54843	+	23.9022i	−0.209182	+	0.763527i
$981$	3.01246	+	11.2427i	0.0961805	+	0.358950i
$982$	31.6496	−	8.48050i	1.00998	−	0.270624i
$983$	−0.728046	+	0.728046i	−0.0232210	+	0.0232210i	−0.718622	−	0.695401i	$-0.755227\pi$
$983$	−0.728046	+	0.728046i	−0.0232210	+	0.0232210i	0.695401	+	0.718622i	$0.255227\pi$
$984$	−2.77055	+	4.79874i	−0.0883221	+	0.152978i
$985$	−38.3444	−	66.4145i	−1.22175	−	2.11614i
$986$	−7.84875	−	2.10307i	−0.249955	−	0.0669753i
$987$	6.76360	+	3.93029i	0.215288	+	0.125102i
$988$	17.3805	−	16.6400i	0.552947	−	0.529389i
$989$	17.4404			0.554574
$990$	3.12636	−	11.6677i	0.0993621	−	0.370824i
$991$	18.0841	+	31.3226i	0.574460	+	0.994994i	0.996100	+	0.0882305i	$0.0281212\pi$
$991$	18.0841	+	31.3226i	0.574460	+	0.994994i	−0.421640	+	0.906763i	$0.638545\pi$
$992$	−4.73550	+	8.20212i	−0.150352	+	0.260418i
$993$	−22.0838	−	22.0838i	−0.700808	−	0.700808i
$994$	11.8558	+	3.21241i	0.376044	+	0.101892i
$995$	−75.2857	+	20.1727i	−2.38672	+	0.639519i
$996$	−10.8432	−	10.8432i	−0.343580	−	0.343580i
$997$	53.3925	+	30.8262i	1.69096	+	0.976274i	0.953747	+	0.300610i	$0.0971902\pi$
$997$	53.3925	+	30.8262i	1.69096	+	0.976274i	0.737209	+	0.675664i	$0.236143\pi$
$998$	20.0886	−	11.5981i	0.635893	−	0.367133i
$999$	2.03117	+	0.544249i	0.0642632	+	0.0172193i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bx.b.223.6	yes	40
7.6	odd	2		546.2.bx.a.223.10	✓	40
13.7	odd	12		546.2.bx.a.475.10	yes	40
91.20	even	12	inner	546.2.bx.b.475.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bx.a.223.10	✓	40	7.6	odd	2
546.2.bx.a.475.10	yes	40	13.7	odd	12
546.2.bx.b.223.6	yes	40	1.1	even	1	trivial
546.2.bx.b.475.6	yes	40	91.20	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.50346 - 2.50346i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(-0.691933 + 2.55367i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.50346 - 2.50346i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(-0.691933 + 2.55367i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.77021 - 3.06610i) q^{10} +(-0.883046 + 3.29557i) q^{11} -1.00000 q^{12} +(-1.87030 + 3.08253i) q^{13} +(-1.32929 + 2.28757i) q^{14} +(3.41979 + 0.916329i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.906845 - 1.57070i) q^{17} +(0.707107 - 0.707107i) q^{18} +(-6.44615 + 1.72724i) q^{19} +(-0.916329 - 3.41979i) q^{20} +(-0.677603 - 2.55751i) q^{21} +(-1.70591 + 2.95473i) q^{22} +(-5.86204 + 3.38445i) q^{23} +(-0.965926 - 0.258819i) q^{24} +7.53460i q^{25} +(-2.60439 + 2.49343i) q^{26} +1.00000i q^{27} +(-1.87607 + 1.86558i) q^{28} +(-2.24008 - 3.87993i) q^{29} +(3.06610 + 1.77021i) q^{30} +(6.69700 + 6.69700i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-0.883046 - 3.29557i) q^{33} +(1.28247 - 1.28247i) q^{34} +(8.12523 - 4.66078i) q^{35} +(0.866025 - 0.500000i) q^{36} +(0.544249 - 2.03117i) q^{37} -6.67355 q^{38} +(0.0784593 - 3.60470i) q^{39} -3.54042i q^{40} +(1.43414 - 5.35230i) q^{41} +(0.00741761 - 2.64574i) q^{42} +(-2.23136 - 1.28828i) q^{43} +(-2.41253 + 2.41253i) q^{44} +(-3.41979 + 0.916329i) q^{45} +(-6.53826 + 1.75192i) q^{46} +(-2.09068 + 2.09068i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(-6.04246 - 3.53394i) q^{49} +(-1.95010 + 7.27786i) q^{50} +1.81369i q^{51} +(-3.16099 + 1.73440i) q^{52} +12.2946 q^{53} +(-0.258819 + 0.965926i) q^{54} +(10.4610 - 6.03965i) q^{55} +(-2.29499 + 1.31645i) q^{56} +(4.71891 - 4.71891i) q^{57} +(-1.15955 - 4.32750i) q^{58} +(-0.202021 - 0.753954i) q^{59} +(2.50346 + 2.50346i) q^{60} +(3.49316 + 2.01678i) q^{61} +(4.73550 + 8.20212i) q^{62} +(1.86558 + 1.87607i) q^{63} +1.00000i q^{64} +(12.3992 - 3.03477i) q^{65} -3.41183i q^{66} +(-11.6954 - 3.13378i) q^{67} +(1.57070 - 0.906845i) q^{68} +(3.38445 - 5.86204i) q^{69} +(9.05467 - 2.39900i) q^{70} +(-1.20161 - 4.48447i) q^{71} +(0.965926 - 0.258819i) q^{72} +(-4.59840 + 4.59840i) q^{73} +(1.05141 - 1.82109i) q^{74} +(-3.76730 - 6.52515i) q^{75} +(-6.44615 - 1.72724i) q^{76} +(-7.80479 - 4.53532i) q^{77} +(1.00875 - 3.46156i) q^{78} +8.32488 q^{79} +(0.916329 - 3.41979i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.77055 - 4.79874i) q^{82} +(10.8432 + 10.8432i) q^{83} +(0.691933 - 2.55367i) q^{84} +(-6.20243 + 1.66194i) q^{85} +(-1.82190 - 1.82190i) q^{86} +(3.87993 + 2.24008i) q^{87} +(-2.95473 + 1.70591i) q^{88} +(6.87740 + 1.84280i) q^{89} -3.54042 q^{90} +(-6.57764 - 6.90902i) q^{91} -6.76890 q^{92} +(-9.14828 - 2.45127i) q^{93} +(-2.56055 + 1.47834i) q^{94} +(20.4617 + 11.8136i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(-1.49705 + 0.401134i) q^{97} +(-4.92192 - 4.97742i) q^{98} +(2.41253 + 2.41253i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q + 8 * q^7 + 20 * q^9	\( 40 q + 8 q^{7} + 20 q^{9} + 8 q^{11} - 40 q^{12} - 8 q^{14} + 20 q^{16} - 16 q^{17} - 16 q^{19} + 4 q^{21} + 8 q^{22} - 32 q^{26} - 8 q^{28} + 8 q^{33} - 16 q^{34} + 40 q^{35} + 40 q^{37} + 16 q^{38} - 16 q^{39} + 4 q^{41} - 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} - 20 q^{49} - 16 q^{50} + 8 q^{52} + 32 q^{53} + 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} - 84 q^{59} + 48 q^{61} + 4 q^{62} + 4 q^{63} - 16 q^{65} - 12 q^{68} + 8 q^{69} - 20 q^{70} - 40 q^{71} + 48 q^{73} + 8 q^{74} - 36 q^{75} - 16 q^{76} + 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} - 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} - 12 q^{89} + 32 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} - 8 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q + 8 * q^7 + 20 * q^9 + 8 * q^11 - 40 * q^12 - 8 * q^14 + 20 * q^16 - 16 * q^17 - 16 * q^19 + 4 * q^21 + 8 * q^22 - 32 * q^26 - 8 * q^28 + 8 * q^33 - 16 * q^34 + 40 * q^35 + 40 * q^37 + 16 * q^38 - 16 * q^39 + 4 * q^41 - 12 * q^42 + 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 - 20 * q^49 - 16 * q^50 + 8 * q^52 + 32 * q^53 + 72 * q^55 + 12 * q^56 + 8 * q^57 - 36 * q^58 - 84 * q^59 + 48 * q^61 + 4 * q^62 + 4 * q^63 - 16 * q^65 - 12 * q^68 + 8 * q^69 - 20 * q^70 - 40 * q^71 + 48 * q^73 + 8 * q^74 - 36 * q^75 - 16 * q^76 + 24 * q^77 - 8 * q^78 - 48 * q^79 - 20 * q^81 - 36 * q^83 - 8 * q^84 + 8 * q^85 - 8 * q^86 - 12 * q^89 + 32 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 - 8 * q^98 - 8 * q^99

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