LMFDB - Embedded newform 546.2.z.b.131.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(131,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("546.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.z (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.16
Character	$\chi$	$=$	546.131
Dual form			546.2.z.b.521.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(1.70558 - 0.301663i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.737837 + 1.27797i) q^{5} +(1.62791 + 0.591542i) q^{6} +(2.24993 - 1.39206i) q^{7} +1.00000i q^{8} +(2.81800 - 1.02902i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(1.70558 - 0.301663i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.737837 + 1.27797i) q^{5} +(1.62791 + 0.591542i) q^{6} +(2.24993 - 1.39206i) q^{7} +1.00000i q^{8} +(2.81800 - 1.02902i) q^{9} +(-1.27797 + 0.737837i) q^{10} +(-0.616972 + 0.356209i) q^{11} +(1.11404 + 1.32624i) q^{12} +1.00000i q^{13} +(2.64452 - 0.0805913i) q^{14} +(-0.872923 + 2.40226i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.629942 - 1.09109i) q^{17} +(2.95497 + 0.517844i) q^{18} +(-1.83612 - 1.06009i) q^{19} -1.47567 q^{20} +(3.41750 - 3.05298i) q^{21} -0.712418 q^{22} +(-1.87219 - 1.08091i) q^{23} +(0.301663 + 1.70558i) q^{24} +(1.41119 + 2.44426i) q^{25} +(-0.500000 + 0.866025i) q^{26} +(4.49590 - 2.60516i) q^{27} +(2.33052 + 1.25247i) q^{28} +1.97689i q^{29} +(-1.95710 + 1.64395i) q^{30} +(-1.42876 + 0.824895i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.944840 + 0.793660i) q^{33} -1.25988i q^{34} +(0.118927 + 3.90245i) q^{35} +(2.30016 + 1.92595i) q^{36} +(0.738591 - 1.27928i) q^{37} +(-1.06009 - 1.83612i) q^{38} +(0.301663 + 1.70558i) q^{39} +(-1.27797 - 0.737837i) q^{40} -4.74235 q^{41} +(4.48613 - 0.935209i) q^{42} -8.19918 q^{43} +(-0.616972 - 0.356209i) q^{44} +(-0.764168 + 4.36057i) q^{45} +(-1.08091 - 1.87219i) q^{46} +(-1.02924 + 1.78269i) q^{47} +(-0.591542 + 1.62791i) q^{48} +(3.12436 - 6.26405i) q^{49} +2.82239i q^{50} +(-1.40356 - 1.67091i) q^{51} +(-0.866025 + 0.500000i) q^{52} +(11.4944 - 6.63632i) q^{53} +(5.19615 - 0.00817995i) q^{54} -1.05130i q^{55} +(1.39206 + 2.24993i) q^{56} +(-3.45144 - 1.25417i) q^{57} +(-0.988443 + 1.71203i) q^{58} +(-4.88092 - 8.45400i) q^{59} +(-2.51688 + 0.445155i) q^{60} +(-3.61623 - 2.08783i) q^{61} -1.64979 q^{62} +(4.90785 - 6.23803i) q^{63} -1.00000 q^{64} +(-1.27797 - 0.737837i) q^{65} +(-1.21509 + 0.214910i) q^{66} +(-3.50829 - 6.07654i) q^{67} +(0.629942 - 1.09109i) q^{68} +(-3.51925 - 1.27881i) q^{69} +(-1.84823 + 3.43909i) q^{70} +4.81777i q^{71} +(1.02902 + 2.81800i) q^{72} +(-1.31716 + 0.760465i) q^{73} +(1.27928 - 0.738591i) q^{74} +(3.14424 + 3.74317i) q^{75} -2.12017i q^{76} +(-0.892281 + 1.66030i) q^{77} +(-0.591542 + 1.62791i) q^{78} +(1.00421 - 1.73934i) q^{79} +(-0.737837 - 1.27797i) q^{80} +(6.88224 - 5.79955i) q^{81} +(-4.10699 - 2.37117i) q^{82} -16.6965 q^{83} +(4.35271 + 1.43315i) q^{84} +1.85918 q^{85} +(-7.10070 - 4.09959i) q^{86} +(0.596352 + 3.37173i) q^{87} +(-0.356209 - 0.616972i) q^{88} +(-1.87730 + 3.25158i) q^{89} +(-2.84207 + 3.39428i) q^{90} +(1.39206 + 2.24993i) q^{91} -2.16182i q^{92} +(-2.18802 + 1.83793i) q^{93} +(-1.78269 + 1.02924i) q^{94} +(2.70952 - 1.56434i) q^{95} +(-1.32624 + 1.11404i) q^{96} +5.98973i q^{97} +(5.83780 - 3.86265i) q^{98} +(-1.37208 + 1.63867i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) $ 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9	$ 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} + 24 q^{11} - 4 q^{14} - 12 q^{15} - 16 q^{16} - 4 q^{17} - 24 q^{18} + 4 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} - 16 q^{26} + 6 q^{27} - 2 q^{28} - 8 q^{30} - 6 q^{31} + 14 q^{33} - 48 q^{35} + 4 q^{36} - 16 q^{38} - 6 q^{39} + 6 q^{40} - 16 q^{41} + 14 q^{42} + 32 q^{43} + 24 q^{44} + 20 q^{45} + 16 q^{46} - 20 q^{47} - 26 q^{49} - 46 q^{51} + 60 q^{53} + 6 q^{54} - 8 q^{56} - 8 q^{57} - 10 q^{58} - 8 q^{59} - 6 q^{60} + 36 q^{61} - 36 q^{62} + 84 q^{63} - 32 q^{64} + 6 q^{65} + 36 q^{66} + 4 q^{68} + 36 q^{69} - 18 q^{70} - 24 q^{72} - 48 q^{73} + 84 q^{74} - 2 q^{75} - 52 q^{77} + 18 q^{79} - 74 q^{81} - 24 q^{83} + 8 q^{84} - 32 q^{85} + 24 q^{86} + 14 q^{87} - 6 q^{88} + 20 q^{89} + 6 q^{90} - 8 q^{91} - 40 q^{93} + 72 q^{95} - 6 q^{96} - 32 q^{98}+O(q^{100}) $ 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9 + 6 * q^10 + 24 * q^11 - 4 * q^14 - 12 * q^15 - 16 * q^16 - 4 * q^17 - 24 * q^18 + 4 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 - 16 * q^26 + 6 * q^27 - 2 * q^28 - 8 * q^30 - 6 * q^31 + 14 * q^33 - 48 * q^35 + 4 * q^36 - 16 * q^38 - 6 * q^39 + 6 * q^40 - 16 * q^41 + 14 * q^42 + 32 * q^43 + 24 * q^44 + 20 * q^45 + 16 * q^46 - 20 * q^47 - 26 * q^49 - 46 * q^51 + 60 * q^53 + 6 * q^54 - 8 * q^56 - 8 * q^57 - 10 * q^58 - 8 * q^59 - 6 * q^60 + 36 * q^61 - 36 * q^62 + 84 * q^63 - 32 * q^64 + 6 * q^65 + 36 * q^66 + 4 * q^68 + 36 * q^69 - 18 * q^70 - 24 * q^72 - 48 * q^73 + 84 * q^74 - 2 * q^75 - 52 * q^77 + 18 * q^79 - 74 * q^81 - 24 * q^83 + 8 * q^84 - 32 * q^85 + 24 * q^86 + 14 * q^87 - 6 * q^88 + 20 * q^89 + 6 * q^90 - 8 * q^91 - 40 * q^93 + 72 * q^95 - 6 * q^96 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	1.70558	−	0.301663i	0.984716	−	0.174165i
$3$	1.70558	−	0.301663i	0.984716	−	0.174165i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.737837	+	1.27797i	−0.329971	+	0.571526i	−0.982506	−	0.186233i	$-0.940372\pi$
$5$	−0.737837	+	1.27797i	−0.329971	+	0.571526i	0.652535	+	0.757759i	$0.273706\pi$
$6$	1.62791	+	0.591542i	0.664590	+	0.241496i
$7$	2.24993	−	1.39206i	0.850393	−	0.526148i
$7$	2.24993	−	1.39206i	0.850393	−	0.526148i
$8$			1.00000i			0.353553i
$9$	2.81800	−	1.02902i	0.939333	−	0.343006i
$10$	−1.27797	+	0.737837i	−0.404130	+	0.233324i
$11$	−0.616972	+	0.356209i	−0.186024	+	0.107401i	−0.590120	−	0.807316i	$-0.700920\pi$
$11$	−0.616972	+	0.356209i	−0.186024	+	0.107401i	0.404096	+	0.914717i	$0.367586\pi$
$12$	1.11404	+	1.32624i	0.321595	+	0.382854i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	2.64452	−	0.0805913i	0.706779	−	0.0215389i
$15$	−0.872923	+	2.40226i	−0.225388	+	0.620260i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.629942	−	1.09109i	−0.152783	−	0.264628i	0.779466	−	0.626444i	$-0.215490\pi$
$17$	−0.629942	−	1.09109i	−0.152783	−	0.264628i	−0.932250	+	0.361816i	$0.882157\pi$
$18$	2.95497	+	0.517844i	0.696493	+	0.122057i
$19$	−1.83612	−	1.06009i	−0.421236	−	0.243201i	0.274370	−	0.961624i	$-0.411531\pi$
$19$	−1.83612	−	1.06009i	−0.421236	−	0.243201i	−0.695606	+	0.718424i	$0.744864\pi$
$20$	−1.47567			−0.329971
$21$	3.41750	−	3.05298i	0.745760	−	0.666215i
$22$	−0.712418			−0.151888
$23$	−1.87219	−	1.08091i	−0.390379	−	0.225386i	0.291945	−	0.956435i	$-0.405698\pi$
$23$	−1.87219	−	1.08091i	−0.390379	−	0.225386i	−0.682325	+	0.731049i	$0.739031\pi$
$24$	0.301663	+	1.70558i	0.0615766	+	0.348150i
$25$	1.41119	+	2.44426i	0.282239	+	0.488852i
$26$	−0.500000	+	0.866025i	−0.0980581	+	0.169842i
$27$	4.49590	−	2.60516i	0.865237	−	0.501363i
$28$	2.33052	+	1.25247i	0.440427	+	0.236694i
$29$			1.97689i			0.367098i	0.983011	+	0.183549i	$0.0587587\pi$
$29$			1.97689i			0.367098i	−0.983011	+	0.183549i	$0.941241\pi$
$30$	−1.95710	+	1.64395i	−0.357316	+	0.300144i
$31$	−1.42876	+	0.824895i	−0.256613	+	0.148156i	−0.622789	−	0.782390i	$-0.714000\pi$
$31$	−1.42876	+	0.824895i	−0.256613	+	0.148156i	0.366176	+	0.930546i	$0.380667\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−0.944840	+	0.793660i	−0.164476	+	0.138158i
$34$		−	1.25988i		−	0.216068i
$35$	0.118927	+	3.90245i	0.0201023	+	0.659635i
$36$	2.30016	+	1.92595i	0.383359	+	0.320992i
$37$	0.738591	−	1.27928i	0.121424	−	0.210312i	−0.798906	−	0.601456i	$-0.794587\pi$
$37$	0.738591	−	1.27928i	0.121424	−	0.210312i	0.920329	+	0.391144i	$0.127921\pi$
$38$	−1.06009	−	1.83612i	−0.171969	−	0.297859i
$39$	0.301663	+	1.70558i	0.0483047	+	0.273111i
$40$	−1.27797	−	0.737837i	−0.202065	−	0.116662i
$41$	−4.74235			−0.740630			−0.370315	−	0.928906i	$-0.620750\pi$
$41$	−4.74235			−0.740630			−0.370315	+	0.928906i	$0.620750\pi$
$42$	4.48613	−	0.935209i	0.692225	−	0.144306i
$43$	−8.19918			−1.25036			−0.625182	−	0.780479i	$-0.714975\pi$
$43$	−8.19918			−1.25036			−0.625182	+	0.780479i	$0.714975\pi$
$44$	−0.616972	−	0.356209i	−0.0930121	−	0.0537005i
$45$	−0.764168	+	4.36057i	−0.113915	+	0.650035i
$46$	−1.08091	−	1.87219i	−0.159372	−	0.276040i
$47$	−1.02924	+	1.78269i	−0.150130	+	0.260032i	−0.931275	−	0.364317i	$-0.881302\pi$
$47$	−1.02924	+	1.78269i	−0.150130	+	0.260032i	0.781145	+	0.624349i	$0.214636\pi$
$48$	−0.591542	+	1.62791i	−0.0853817	+	0.234968i
$49$	3.12436	−	6.26405i	0.446337	−	0.894865i
$50$			2.82239i			0.399146i
$51$	−1.40356	−	1.67091i	−0.196537	−	0.233974i
$52$	−0.866025	+	0.500000i	−0.120096	+	0.0693375i
$53$	11.4944	−	6.63632i	1.57888	−	0.911568i	0.583867	−	0.811849i	$-0.301539\pi$
$53$	11.4944	−	6.63632i	1.57888	−	0.911568i	0.995016	−	0.0997187i	$-0.0317943\pi$
$54$	5.19615	−	0.00817995i	0.707106	−	0.00111315i
$55$		−	1.05130i		−	0.141757i
$56$	1.39206	+	2.24993i	0.186021	+	0.300659i
$57$	−3.45144	−	1.25417i	−0.457155	−	0.166119i
$58$	−0.988443	+	1.71203i	−0.129789	+	0.224801i
$59$	−4.88092	−	8.45400i	−0.635442	−	1.10062i	−0.986421	−	0.164234i	$-0.947485\pi$
$59$	−4.88092	−	8.45400i	−0.635442	−	1.10062i	0.350979	−	0.936383i	$-0.385849\pi$
$60$	−2.51688	+	0.445155i	−0.324928	+	0.0574693i
$61$	−3.61623	−	2.08783i	−0.463011	−	0.267319i	0.250299	−	0.968169i	$-0.419471\pi$
$61$	−3.61623	−	2.08783i	−0.463011	−	0.267319i	−0.713309	+	0.700849i	$0.752805\pi$
$62$	−1.64979			−0.209524
$63$	4.90785	−	6.23803i	0.618331	−	0.785918i
$64$	−1.00000			−0.125000
$65$	−1.27797	−	0.737837i	−0.158513	−	0.0915174i
$66$	−1.21509	+	0.214910i	−0.149567	+	0.0264536i
$67$	−3.50829	−	6.07654i	−0.428606	−	0.742368i	0.568143	−	0.822930i	$-0.307662\pi$
$67$	−3.50829	−	6.07654i	−0.428606	−	0.742368i	−0.996750	+	0.0805619i	$0.974329\pi$
$68$	0.629942	−	1.09109i	0.0763916	−	0.132314i
$69$	−3.51925	−	1.27881i	−0.423667	−	0.153951i
$70$	−1.84823	+	3.43909i	−0.220906	+	0.411050i
$71$			4.81777i			0.571764i	0.958265	+	0.285882i	$0.0922865\pi$
$71$			4.81777i			0.571764i	−0.958265	+	0.285882i	$0.907714\pi$
$72$	1.02902	+	2.81800i	0.121271	+	0.332104i
$73$	−1.31716	+	0.760465i	−0.154162	+	0.0890057i	−0.575097	−	0.818085i	$-0.695036\pi$
$73$	−1.31716	+	0.760465i	−0.154162	+	0.0890057i	0.420934	+	0.907091i	$0.361702\pi$
$74$	1.27928	−	0.738591i	0.148713	−	0.0858594i
$75$	3.14424	+	3.74317i	0.363066	+	0.432224i
$76$		−	2.12017i		−	0.243201i
$77$	−0.892281	+	1.66030i	−0.101685	+	0.189209i
$78$	−0.591542	+	1.62791i	−0.0669790	+	0.184324i
$79$	1.00421	−	1.73934i	0.112983	−	0.195692i	−0.803989	−	0.594644i	$-0.797293\pi$
$79$	1.00421	−	1.73934i	0.112983	−	0.195692i	0.916971	+	0.398953i	$0.130626\pi$
$80$	−0.737837	−	1.27797i	−0.0824927	−	0.142881i
$81$	6.88224	−	5.79955i	0.764694	−	0.644394i
$82$	−4.10699	−	2.37117i	−0.453542	−	0.261852i
$83$	−16.6965			−1.83268			−0.916342	−	0.400397i	$-0.868872\pi$
$83$	−16.6965			−1.83268			−0.916342	+	0.400397i	$0.868872\pi$
$84$	4.35271	+	1.43315i	0.474919	+	0.156370i
$85$	1.85918			0.201656
$86$	−7.10070	−	4.09959i	−0.765688	−	0.442070i
$87$	0.596352	+	3.37173i	0.0639357	+	0.361488i
$88$	−0.356209	−	0.616972i	−0.0379720	−	0.0657695i
$89$	−1.87730	+	3.25158i	−0.198994	+	0.344667i	−0.948202	−	0.317667i	$-0.897101\pi$
$89$	−1.87730	+	3.25158i	−0.198994	+	0.344667i	0.749209	+	0.662334i	$0.230434\pi$
$90$	−2.84207	+	3.39428i	−0.299581	+	0.357788i
$91$	1.39206	+	2.24993i	0.145927	+	0.235857i
$92$		−	2.16182i		−	0.225386i
$93$	−2.18802	+	1.83793i	−0.226887	+	0.190584i
$94$	−1.78269	+	1.02924i	−0.183871	+	0.106158i
$95$	2.70952	−	1.56434i	0.277991	−	0.160498i
$96$	−1.32624	+	1.11404i	−0.135359	+	0.113701i
$97$			5.98973i			0.608164i	0.952646	+	0.304082i	$0.0983498\pi$
$97$			5.98973i			0.608164i	−0.952646	+	0.304082i	$0.901650\pi$
$98$	5.83780	−	3.86265i	0.589707	−	0.390187i
$99$	−1.37208	+	1.63867i	−0.137899	+	0.164693i
$100$	−1.41119	+	2.44426i	−0.141119	+	0.244426i
$101$	−4.48679	−	7.77135i	−0.446453	−	0.773279i	0.551700	−	0.834043i	$-0.313980\pi$
$101$	−4.48679	−	7.77135i	−0.446453	−	0.773279i	−0.998152	+	0.0607643i	$0.980646\pi$
$102$	−0.380060	−	2.14883i	−0.0376315	−	0.212766i
$103$	4.95116	+	2.85856i	0.487853	+	0.281662i	0.723683	−	0.690132i	$-0.242448\pi$
$103$	4.95116	+	2.85856i	0.487853	+	0.281662i	−0.235830	+	0.971794i	$0.575781\pi$
$104$	−1.00000			−0.0980581
$105$	1.38006	+	6.62007i	0.134680	+	0.646052i
$106$	13.2726			1.28915
$107$	−2.23780	−	1.29199i	−0.216336	−	0.124902i	0.387916	−	0.921695i	$-0.373195\pi$
$107$	−2.23780	−	1.29199i	−0.216336	−	0.124902i	−0.604253	+	0.796793i	$0.706528\pi$
$108$	4.50408	+	2.59099i	0.433406	+	0.249318i
$109$	5.72625	+	9.91816i	0.548476	+	0.949987i	0.998379	+	0.0569104i	$0.0181249\pi$
$109$	5.72625	+	9.91816i	0.548476	+	0.949987i	−0.449904	+	0.893077i	$0.648542\pi$
$110$	0.525648	−	0.910449i	0.0501186	−	0.0868080i
$111$	0.873815	−	2.40471i	0.0829389	−	0.228245i
$112$	0.0805913	+	2.64452i	0.00761517	+	0.249884i
$113$			4.53409i			0.426532i	0.976994	+	0.213266i	$0.0684100\pi$
$113$			4.53409i			0.426532i	−0.976994	+	0.213266i	$0.931590\pi$
$114$	−2.36195	−	2.81187i	−0.221217	−	0.263356i
$115$	2.76275	−	1.59507i	0.257627	−	0.148741i
$116$	−1.71203	+	0.988443i	−0.158958	+	0.0917746i
$117$	1.02902	+	2.81800i	0.0951328	+	0.260524i
$118$		−	9.76184i		−	0.898650i
$119$	−2.93618	−	1.57796i	−0.269159	−	0.144652i
$120$	−2.40226	−	0.872923i	−0.219295	−	0.0796866i
$121$	−5.24623	+	9.08674i	−0.476930	+	0.826067i
$122$	−2.08783	−	3.61623i	−0.189023	−	0.327398i
$123$	−8.08845	+	1.43059i	−0.729311	+	0.128992i
$124$	−1.42876	−	0.824895i	−0.128306	−	0.0740778i
$125$	−11.5433			−1.03246
$126$	7.36934	−	2.94837i	0.656513	−	0.262662i
$127$	15.7161			1.39458			0.697289	−	0.716790i	$-0.254390\pi$
$127$	15.7161			1.39458			0.697289	+	0.716790i	$0.254390\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−13.9844	+	2.47339i	−1.23125	+	0.217770i
$130$	−0.737837	−	1.27797i	−0.0647126	−	0.112085i
$131$	7.04632	−	12.2046i	0.615640	−	1.06632i	−0.374632	−	0.927174i	$-0.622231\pi$
$131$	7.04632	−	12.2046i	0.615640	−	1.06632i	0.990272	−	0.139146i	$-0.0444357\pi$
$132$	−1.15975	−	0.421425i	−0.100943	−	0.0366804i
$133$	−5.60685	+	0.170868i	−0.486176	+	0.0148161i
$134$		−	7.01658i		−	0.606141i
$135$	0.0120709	+	7.66782i	0.00103890	+	0.659940i
$136$	1.09109	−	0.629942i	0.0935603	−	0.0540170i
$137$	12.1811	−	7.03277i	1.04070	−	0.600850i	0.120670	−	0.992693i	$-0.461496\pi$
$137$	12.1811	−	7.03277i	1.04070	−	0.600850i	0.920032	+	0.391843i	$0.128162\pi$
$138$	−2.40835	−	2.86710i	−0.205012	−	0.244064i
$139$			1.53247i			0.129983i	0.997886	+	0.0649913i	$0.0207020\pi$
$139$			1.53247i			0.129983i	−0.997886	+	0.0649913i	$0.979298\pi$
$140$	−3.32016	+	2.05422i	−0.280605	+	0.173613i
$141$	−1.21768	+	3.35101i	−0.102547	+	0.282206i
$142$	−2.40888	+	4.17231i	−0.202149	+	0.350132i
$143$	−0.356209	−	0.616972i	−0.0297877	−	0.0515938i
$144$	−0.517844	+	2.95497i	−0.0431536	+	0.246247i
$145$	−2.52640	−	1.45862i	−0.209806	−	0.121132i
$146$	−1.52093			−0.125873
$147$	3.43921	−	11.6263i	0.283662	−	0.958924i
$148$	1.47718			0.121424
$149$	−14.5145	−	8.37995i	−1.18907	−	0.686512i	−0.230978	−	0.972959i	$-0.574192\pi$
$149$	−14.5145	−	8.37995i	−1.18907	−	0.686512i	−0.958096	+	0.286447i	$0.907526\pi$
$150$	0.851409	+	4.81381i	0.0695172	+	0.393046i
$151$	7.58068	+	13.1301i	0.616907	+	1.06851i	0.990047	+	0.140739i	$0.0449479\pi$
$151$	7.58068	+	13.1301i	0.616907	+	1.06851i	−0.373140	+	0.927775i	$0.621719\pi$
$152$	1.06009	−	1.83612i	0.0859844	−	0.148929i
$153$	−2.89793	−	2.42647i	−0.234284	−	0.196169i
$154$	−1.60289	+	0.991726i	−0.129165	+	0.0799155i
$155$		−	2.43455i		−	0.195548i
$156$	−1.32624	+	1.11404i	−0.106184	+	0.0891943i
$157$	−13.4848	+	7.78544i	−1.07620	+	0.621345i	−0.929869	−	0.367890i	$-0.880080\pi$
$157$	−13.4848	+	7.78544i	−1.07620	+	0.621345i	−0.146333	+	0.989235i	$0.546747\pi$
$158$	1.73934	−	1.00421i	0.138375	−	0.0798907i
$159$	17.6027	−	14.7862i	1.39599	−	1.17262i
$160$		−	1.47567i		−	0.116662i
$161$	−5.71699	+	0.174224i	−0.450562	+	0.0137308i
$162$	8.85997	−	1.58143i	0.696105	−	0.124249i
$163$	11.7901	−	20.4210i	0.923468	−	1.59949i	0.129462	−	0.991584i	$-0.458675\pi$
$163$	11.7901	−	20.4210i	0.923468	−	1.59949i	0.794006	−	0.607910i	$-0.207992\pi$
$164$	−2.37117	−	4.10699i	−0.185158	−	0.320702i
$165$	−0.317137	−	1.79307i	−0.0246891	−	0.139590i
$166$	−14.4596	−	8.34827i	−1.12228	−	0.647951i
$167$	−13.6759			−1.05828			−0.529138	−	0.848536i	$-0.677485\pi$
$167$	−13.6759			−1.05828			−0.529138	+	0.848536i	$0.677485\pi$
$168$	3.05298	+	3.41750i	0.235543	+	0.263666i
$169$	−1.00000			−0.0769231
$170$	1.61009	+	0.929588i	0.123489	+	0.0712962i
$171$	−6.26505	−	1.09792i	−0.479100	−	0.0839599i
$172$	−4.09959	−	7.10070i	−0.312591	−	0.541423i
$173$	12.7552	−	22.0927i	0.969760	−	1.67967i	0.273517	−	0.961867i	$-0.411813\pi$
$173$	12.7552	−	22.0927i	0.969760	−	1.67967i	0.696243	−	0.717807i	$-0.254854\pi$
$174$	−1.16941	+	3.21818i	−0.0886528	+	0.243970i
$175$	6.57763	+	3.53495i	0.497222	+	0.267217i
$176$		−	0.712418i		−	0.0537005i
$177$	−10.8751	−	12.9466i	−0.817419	−	0.973125i
$178$	−3.25158	+	1.87730i	−0.243716	+	0.140710i
$179$	−5.27781	+	3.04714i	−0.394482	+	0.227754i	−0.684100	−	0.729388i	$-0.739805\pi$
$179$	−5.27781	+	3.04714i	−0.394482	+	0.227754i	0.289618	+	0.957142i	$0.406472\pi$
$180$	−4.15845	+	1.51850i	−0.309952	+	0.113182i
$181$			18.2078i			1.35338i	0.736270	+	0.676688i	$0.236585\pi$
$181$			18.2078i			1.35338i	−0.736270	+	0.676688i	$0.763415\pi$
$182$	0.0805913	+	2.64452i	0.00597383	+	0.196025i
$183$	−6.79758	−	2.47008i	−0.502492	−	0.182594i
$184$	1.08091	−	1.87219i	0.0796859	−	0.138020i
$185$	1.08992	+	1.88779i	0.0801324	+	0.138793i
$186$	−2.81385	+	0.497680i	−0.206321	+	0.0364917i
$187$	0.777313	+	0.448782i	0.0568427	+	0.0328182i
$188$	−2.05848			−0.150130
$189$	6.48894	−	12.1200i	0.472001	−	0.881598i
$190$	3.12869			0.226979
$191$	7.38111	+	4.26148i	0.534078	+	0.308350i	0.742676	−	0.669651i	$-0.233556\pi$
$191$	7.38111	+	4.26148i	0.534078	+	0.308350i	−0.208597	+	0.978002i	$0.566890\pi$
$192$	−1.70558	+	0.301663i	−0.123090	+	0.0217706i
$193$	5.24285	+	9.08089i	0.377389	+	0.653657i	0.990681	−	0.136199i	$-0.0434887\pi$
$193$	5.24285	+	9.08089i	0.377389	+	0.653657i	−0.613293	+	0.789856i	$0.710155\pi$
$194$	−2.99486	+	5.18725i	−0.215019	+	0.372423i
$195$	−2.40226	−	0.872923i	−0.172029	−	0.0625113i
$196$	6.98701	−	0.426251i	0.499072	−	0.0304465i
$197$			27.5463i			1.96259i	0.192501	+	0.981297i	$0.438340\pi$
$197$			27.5463i			1.96259i	−0.192501	+	0.981297i	$0.561660\pi$
$198$	−2.00759	+	0.733091i	−0.142673	+	0.0520985i
$199$	15.6308	−	9.02443i	1.10804	−	0.639725i	0.169716	−	0.985493i	$-0.445715\pi$
$199$	15.6308	−	9.02443i	1.10804	−	0.639725i	0.938320	+	0.345768i	$0.112382\pi$
$200$	−2.44426	+	1.41119i	−0.172835	+	0.0997865i
$201$	−7.81673	−	9.30570i	−0.551350	−	0.656373i
$202$		−	8.97359i		−	0.631379i
$203$	2.75194	+	4.44785i	0.193148	+	0.312178i
$204$	0.745274	−	2.05097i	0.0521796	−	0.143597i
$205$	3.49908	−	6.06058i	0.244386	−	0.423289i
$206$	2.85856	+	4.95116i	0.199165	+	0.344964i
$207$	−6.38812	−	1.11949i	−0.444005	−	0.0778097i
$208$	−0.866025	−	0.500000i	−0.0600481	−	0.0346688i
$209$	1.51045			0.104480
$210$	−2.11486	+	6.42318i	−0.145940	+	0.443241i
$211$	−2.97983			−0.205140			−0.102570	−	0.994726i	$-0.532707\pi$
$211$	−2.97983			−0.205140			−0.102570	+	0.994726i	$0.532707\pi$
$212$	11.4944	+	6.63632i	0.789441	+	0.455784i
$213$	1.45334	+	8.21708i	0.0995812	+	0.563025i
$214$	−1.29199	−	2.23780i	−0.0883189	−	0.152973i
$215$	6.04966	−	10.4783i	0.412583	−	0.714615i
$216$	2.60516	+	4.49590i	0.177258	+	0.305908i
$217$	−2.06631	+	3.84487i	−0.140270	+	0.261007i
$218$			11.4525i			0.775662i
$219$	−2.01712	+	1.69437i	−0.136305	+	0.114495i
$220$	0.910449	−	0.525648i	0.0613825	−	0.0354392i
$221$	1.09109	−	0.629942i	0.0733947	−	0.0423745i
$222$	1.95910	−	1.64563i	0.131486	−	0.110448i
$223$		−	2.54971i		−	0.170741i	−0.996349	−	0.0853705i	$-0.972793\pi$
$223$		−	2.54971i		−	0.170741i	0.996349	−	0.0853705i	$-0.0272074\pi$
$224$	−1.25247	+	2.33052i	−0.0836840	+	0.155714i
$225$	6.49193	+	5.43578i	0.432795	+	0.362385i
$226$	−2.26705	+	3.92664i	−0.150802	+	0.261196i
$227$	4.12234	+	7.14010i	0.273609	+	0.473905i	0.969783	−	0.243968i	$-0.0784492\pi$
$227$	4.12234	+	7.14010i	0.273609	+	0.473905i	−0.696174	+	0.717873i	$0.745116\pi$
$228$	−0.639577	−	3.61612i	−0.0423570	−	0.239484i
$229$	−6.90443	−	3.98628i	−0.456258	−	0.263421i	0.254212	−	0.967149i	$-0.418184\pi$
$229$	−6.90443	−	3.98628i	−0.456258	−	0.263421i	−0.710469	+	0.703728i	$0.751517\pi$
$230$	3.19015			0.210352
$231$	−1.02100	+	3.10095i	−0.0671771	+	0.204027i
$232$	−1.97689			−0.129789
$233$	22.7059	+	13.1093i	1.48752	+	0.858818i	0.999899	−	0.0142398i	$-0.00453283\pi$
$233$	22.7059	+	13.1093i	1.48752	+	0.858818i	0.487617	+	0.873058i	$0.337866\pi$
$234$	−0.517844	+	2.95497i	−0.0338525	+	0.193172i
$235$	−1.51882	−	2.63067i	−0.0990768	−	0.171606i
$236$	4.88092	−	8.45400i	0.317721	−	0.550309i
$237$	1.18807	−	3.26952i	0.0771732	−	0.212378i
$238$	−1.75383	−	2.83465i	−0.113684	−	0.183743i
$239$			16.1711i			1.04602i	0.852325	+	0.523012i	$0.175192\pi$
$239$			16.1711i			1.04602i	−0.852325	+	0.523012i	$0.824808\pi$
$240$	−1.64395	−	1.95710i	−0.106117	−	0.126330i
$241$	−11.4305	+	6.59939i	−0.736302	+	0.425104i	−0.820723	−	0.571326i	$-0.806429\pi$
$241$	−11.4305	+	6.59939i	−0.736302	+	0.425104i	0.0844211	+	0.996430i	$0.473096\pi$
$242$	−9.08674	+	5.24623i	−0.584118	+	0.337240i
$243$	9.98870	−	11.9677i	0.640776	−	0.767728i
$244$		−	4.17566i		−	0.267319i
$245$	5.70001	+	8.61469i	0.364160	+	0.550372i
$246$	−7.72010	−	2.80530i	−0.492215	−	0.178859i
$247$	1.06009	−	1.83612i	0.0674517	−	0.116830i
$248$	−0.824895	−	1.42876i	−0.0523809	−	0.0907264i
$249$	−28.4773	+	5.03672i	−1.80467	+	0.319189i
$250$	−9.99678	−	5.77165i	−0.632252	−	0.365031i
$251$	10.1448			0.640337			0.320168	−	0.947361i	$-0.396260\pi$
$251$	10.1448			0.640337			0.320168	+	0.947361i	$0.396260\pi$
$252$	7.85622	+	1.13130i	0.494895	+	0.0712655i
$253$	1.54012			0.0968266
$254$	13.6105	+	7.85804i	0.854001	+	0.493058i
$255$	3.17097	−	0.560844i	0.198574	−	0.0351214i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−13.4826	+	23.3525i	−0.841020	+	1.45669i	0.0480126	+	0.998847i	$0.484711\pi$
$257$	−13.4826	+	23.3525i	−0.841020	+	1.45669i	−0.889033	+	0.457843i	$0.848622\pi$
$258$	−13.3475	−	4.85016i	−0.830979	−	0.301958i
$259$	−0.119048	−	3.90644i	−0.00739729	−	0.242734i
$260$		−	1.47567i		−	0.0915174i
$261$	2.03425	+	5.57086i	0.125917	+	0.344828i
$262$	12.2046	−	7.04632i	0.754002	−	0.435323i
$263$	24.6665	−	14.2412i	1.52100	−	0.878152i	0.521311	−	0.853367i	$-0.325443\pi$
$263$	24.6665	−	14.2412i	1.52100	−	0.878152i	0.999693	−	0.0247857i	$-0.00789034\pi$
$264$	−0.793660	−	0.944840i	−0.0488464	−	0.0581509i
$265$			19.5861i			1.20316i
$266$	−4.94111	−	2.65545i	−0.302959	−	0.162816i
$267$	−2.22101	+	6.11214i	−0.135923	+	0.374057i
$268$	3.50829	−	6.07654i	0.214303	−	0.371184i
$269$	1.07074	+	1.85458i	0.0652844	+	0.113076i	0.896820	−	0.442395i	$-0.145871\pi$
$269$	1.07074	+	1.85458i	0.0652844	+	0.113076i	−0.831536	+	0.555471i	$0.812538\pi$
$270$	−3.82345	+	6.64656i	−0.232688	+	0.404497i
$271$	18.3465	+	10.5924i	1.11447	+	0.643441i	0.939984	−	0.341219i	$-0.110840\pi$
$271$	18.3465	+	10.5924i	1.11447	+	0.643441i	0.174488	+	0.984659i	$0.444173\pi$
$272$	1.25988			0.0763916
$273$	3.05298	+	3.41750i	0.184775	+	0.206837i
$274$	14.0655			0.849730
$275$	−1.74133	−	1.00536i	−0.105006	−	0.0606255i
$276$	−0.652141	−	3.68716i	−0.0392543	−	0.221941i
$277$	9.41135	+	16.3009i	0.565473	+	0.979429i	0.997005	+	0.0773311i	$0.0246398\pi$
$277$	9.41135	+	16.3009i	0.565473	+	0.979429i	−0.431532	+	0.902098i	$0.642027\pi$
$278$	−0.766236	+	1.32716i	−0.0459558	+	0.0795977i
$279$	−3.17741	+	3.79478i	−0.190227	+	0.227187i
$280$	−3.90245	+	0.118927i	−0.233216	+	0.00710722i
$281$			21.8958i			1.30619i	0.757274	+	0.653097i	$0.226531\pi$
$281$			21.8958i			1.30619i	−0.757274	+	0.653097i	$0.773469\pi$
$282$	−2.73004	+	2.29322i	−0.162572	+	0.136559i
$283$	1.19367	−	0.689163i	0.0709561	−	0.0409665i	−0.464102	−	0.885782i	$-0.653623\pi$
$283$	1.19367	−	0.689163i	0.0709561	−	0.0409665i	0.535058	+	0.844815i	$0.320290\pi$
$284$	−4.17231	+	2.40888i	−0.247581	+	0.142941i
$285$	4.14940	−	3.48547i	0.245789	−	0.206461i
$286$		−	0.712418i		−	0.0421262i
$287$	−10.6699	+	6.60161i	−0.629827	+	0.389681i
$288$	−1.92595	+	2.30016i	−0.113488	+	0.135538i
$289$	7.70635	−	13.3478i	0.453315	−	0.785164i
$290$	−1.45862	−	2.52640i	−0.0856531	−	0.148355i
$291$	1.80688	+	10.2159i	0.105921	+	0.598870i
$292$	−1.31716	−	0.760465i	−0.0770812	−	0.0445029i
$293$	23.4405			1.36941			0.684703	−	0.728822i	$-0.259932\pi$
$293$	23.4405			1.36941			0.684703	+	0.728822i	$0.259932\pi$
$294$	8.79162	−	8.34910i	0.512738	−	0.486929i
$295$	14.4053			0.838709
$296$	1.27928	+	0.738591i	0.0743564	+	0.0429297i
$297$	−1.84587	+	3.20879i	−0.107108	+	0.186193i
$298$	−8.37995	−	14.5145i	−0.485437	−	0.840802i
$299$	1.08091	−	1.87219i	0.0625107	−	0.108272i
$300$	−1.66956	+	4.59458i	−0.0963922	+	0.265268i
$301$	−18.4476	+	11.4137i	−1.06330	+	0.657876i
$302$			15.1614i			0.872438i
$303$	−9.99691	−	11.9012i	−0.574307	−	0.683704i
$304$	1.83612	−	1.06009i	0.105309	−	0.0608002i
$305$	5.33637	−	3.08096i	0.305560	−	0.176415i
$306$	−1.29644	−	3.55035i	−0.0741127	−	0.202960i
$307$		−	7.51595i		−	0.428958i	−0.976729	−	0.214479i	$-0.931195\pi$
$307$		−	7.51595i		−	0.428958i	0.976729	−	0.214479i	$-0.0688054\pi$
$308$	−1.88401	+	0.0574147i	−0.107351	+	0.00327151i
$309$	9.30692	+	3.38191i	0.529452	+	0.192390i
$310$	1.21728	−	2.10838i	0.0691366	−	0.119748i
$311$	−3.07687	−	5.32930i	−0.174473	−	0.302197i	0.765505	−	0.643429i	$-0.222489\pi$
$311$	−3.07687	−	5.32930i	−0.174473	−	0.302197i	−0.939979	+	0.341233i	$0.889156\pi$
$312$	−1.70558	+	0.301663i	−0.0965594	+	0.0170783i
$313$	−22.5207	−	13.0024i	−1.27295	−	0.734936i	−0.297405	−	0.954751i	$-0.596121\pi$
$313$	−22.5207	−	13.0024i	−1.27295	−	0.734936i	−0.975542	+	0.219815i	$0.929455\pi$
$314$	−15.5709			−0.878715
$315$	4.35083	+	10.8747i	0.245142	+	0.612722i
$316$	2.00842			0.112983
$317$	11.8361	+	6.83359i	0.664783	+	0.383813i	0.794097	−	0.607791i	$-0.207944\pi$
$317$	11.8361	+	6.83359i	0.664783	+	0.383813i	−0.129314	+	0.991604i	$0.541277\pi$
$318$	22.6375	−	4.00386i	1.26945	−	0.224525i
$319$	−0.704185	−	1.21968i	−0.0394268	−	0.0682892i
$320$	0.737837	−	1.27797i	0.0412463	−	0.0714407i
$321$	−4.20649	−	1.52854i	−0.234783	−	0.0853147i
$322$	−5.03817	−	2.70761i	−0.280766	−	0.150889i
$323$			2.67117i			0.148628i
$324$	8.46368	+	3.06042i	0.470204	+	0.170023i
$325$	−2.44426	+	1.41119i	−0.135583	+	0.0782789i
$326$	20.4210	−	11.7901i	1.13101	−	0.652991i
$327$	12.7585	+	15.1888i	0.705547	+	0.839943i
$328$		−	4.74235i		−	0.261852i
$329$	0.165895	+	5.44369i	0.00914611	+	0.300120i
$330$	0.621886	−	1.71141i	0.0342337	−	0.0942101i
$331$	−3.55757	+	6.16188i	−0.195541	+	0.338688i	−0.947078	−	0.321004i	$-0.895980\pi$
$331$	−3.55757	+	6.16188i	−0.195541	+	0.338688i	0.751536	+	0.659692i	$0.229313\pi$
$332$	−8.34827	−	14.4596i	−0.458171	−	0.793575i
$333$	0.764949	−	4.36502i	0.0419189	−	0.239202i
$334$	−11.8437	−	6.83797i	−0.648059	−	0.374157i
$335$	10.3542			0.565710
$336$	0.935209	+	4.48613i	0.0510198	+	0.244739i
$337$	1.82826			0.0995918			0.0497959	−	0.998759i	$-0.484143\pi$
$337$	1.82826			0.0995918			0.0497959	+	0.998759i	$0.484143\pi$
$338$	−0.866025	−	0.500000i	−0.0471056	−	0.0271964i
$339$	1.36777	+	7.73326i	0.0742869	+	0.420013i
$340$	0.929588	+	1.61009i	0.0504140	+	0.0873196i
$341$	0.587670	−	1.01787i	0.0318241	−	0.0551210i
$342$	−4.87673	−	4.08335i	−0.263703	−	0.220802i
$343$	−1.69032	−	18.4430i	−0.0912689	−	0.995826i
$344$		−	8.19918i		−	0.442070i
$345$	4.23091	−	3.55394i	0.227785	−	0.191338i
$346$	22.0927	−	12.7552i	1.18771	−	0.685724i
$347$	−18.1042	+	10.4525i	−0.971884	+	0.561117i	−0.899810	−	0.436282i	$-0.856295\pi$
$347$	−18.1042	+	10.4525i	−0.971884	+	0.561117i	−0.0720736	+	0.997399i	$0.522962\pi$
$348$	−2.62183	+	2.20232i	−0.140545	+	0.118057i
$349$			30.2526i			1.61939i	0.586853	+	0.809694i	$0.300367\pi$
$349$			30.2526i			1.61939i	−0.586853	+	0.809694i	$0.699633\pi$
$350$	3.92892	+	6.35017i	0.210010	+	0.339431i
$351$	2.60516	+	4.49590i	0.139053	+	0.239974i
$352$	0.356209	−	0.616972i	0.0189860	−	0.0328847i
$353$	−3.37558	−	5.84667i	−0.179664	−	0.311187i	0.762102	−	0.647457i	$-0.224168\pi$
$353$	−3.37558	−	5.84667i	−0.179664	−	0.311187i	−0.941765	+	0.336271i	$0.890834\pi$
$354$	−2.94478	−	16.6496i	−0.156513	−	0.884916i
$355$	−6.15697	−	3.55473i	−0.326778	−	0.188665i
$356$	−3.75460			−0.198994
$357$	−5.48391	−	1.80560i	−0.290239	−	0.0955627i
$358$	−6.09429			−0.322093
$359$	6.61905	+	3.82151i	0.349340	+	0.201692i	0.664395	−	0.747382i	$-0.268689\pi$
$359$	6.61905	+	3.82151i	0.349340	+	0.201692i	−0.315054	+	0.949074i	$0.602023\pi$
$360$	−4.36057	−	0.764168i	−0.229822	−	0.0402752i
$361$	−7.25243	−	12.5616i	−0.381707	−	0.661136i
$362$	−9.10391	+	15.7684i	−0.478491	+	0.828770i
$363$	−6.20673	+	17.0807i	−0.325769	+	0.896506i
$364$	−1.25247	+	2.33052i	−0.0656471	+	0.122152i
$365$		−	2.24440i		−	0.117477i
$366$	−4.65184	−	5.53794i	−0.243156	−	0.289473i
$367$	16.0066	−	9.24140i	0.835537	−	0.482397i	−0.0202079	−	0.999796i	$-0.506433\pi$
$367$	16.0066	−	9.24140i	0.835537	−	0.482397i	0.855745	+	0.517398i	$0.173099\pi$
$368$	1.87219	−	1.08091i	0.0975949	−	0.0563464i
$369$	−13.3639	+	4.87996i	−0.695699	+	0.254041i
$370$			2.17984i			0.113324i
$371$	16.6235	−	30.9321i	0.863051	−	1.60592i
$372$	−2.68570	−	0.975921i	−0.139247	−	0.0505991i
$373$	2.56061	−	4.43510i	0.132583	−	0.229641i	−0.792088	−	0.610406i	$-0.791006\pi$
$373$	2.56061	−	4.43510i	0.132583	−	0.229641i	0.924672	+	0.380765i	$0.124339\pi$
$374$	0.448782	+	0.777313i	0.0232060	+	0.0401939i
$375$	−19.6880	+	3.48218i	−1.01668	+	0.179819i
$376$	−1.78269	−	1.02924i	−0.0919353	−	0.0530789i
$377$	−1.97689			−0.101815
$378$	11.6796	−	7.25173i	0.600732	−	0.372989i
$379$	−17.1215			−0.879471			−0.439736	−	0.898127i	$-0.644928\pi$
$379$	−17.1215			−0.879471			−0.439736	+	0.898127i	$0.644928\pi$
$380$	2.70952	+	1.56434i	0.138995	+	0.0802491i
$381$	26.8050	−	4.74095i	1.37326	−	0.242886i
$382$	4.26148	+	7.38111i	0.218036	+	0.377650i
$383$	8.37015	−	14.4975i	0.427695	−	0.740789i	−0.568973	−	0.822356i	$-0.692659\pi$
$383$	8.37015	−	14.4975i	0.427695	−	0.740789i	0.996668	+	0.0815673i	$0.0259926\pi$
$384$	−1.62791	−	0.591542i	−0.0830737	−	0.0301870i
$385$	−1.46346	−	2.36534i	−0.0745850	−	0.120549i
$386$			10.4857i			0.533709i
$387$	−23.1053	+	8.43711i	−1.17451	+	0.428882i
$388$	−5.18725	+	2.99486i	−0.263343	+	0.152041i
$389$	17.2918	−	9.98343i	0.876729	−	0.506180i	0.00715063	−	0.999974i	$-0.497724\pi$
$389$	17.2918	−	9.98343i	0.876729	−	0.506180i	0.869579	+	0.493795i	$0.164391\pi$
$390$	−1.64395	−	1.95710i	−0.0832449	−	0.0991017i
$391$			2.72364i			0.137741i
$392$	6.26405	+	3.12436i	0.316383	+	0.157804i
$393$	8.33639	−	22.9415i	0.420515	−	1.15725i
$394$	−13.7732	+	23.8558i	−0.693882	+	1.20184i
$395$	1.48189	+	2.56670i	0.0745618	+	0.129145i
$396$	−2.10517	−	0.368921i	−0.105789	−	0.0185390i
$397$	7.52672	+	4.34555i	0.377755	+	0.218097i	0.676841	−	0.736129i	$-0.263348\pi$
$397$	7.52672	+	4.34555i	0.377755	+	0.218097i	−0.299086	+	0.954226i	$0.596682\pi$
$398$	18.0489			0.904707
$399$	−9.51138	+	1.98281i	−0.476165	+	0.0992644i
$400$	−2.82239			−0.141119
$401$	−9.22909	−	5.32841i	−0.460879	−	0.266088i	0.251535	−	0.967848i	$-0.419065\pi$
$401$	−9.22909	−	5.32841i	−0.460879	−	0.266088i	−0.712414	+	0.701760i	$0.752398\pi$
$402$	−2.11664	−	11.9673i	−0.105568	−	0.596877i
$403$	−0.824895	−	1.42876i	−0.0410910	−	0.0711716i
$404$	4.48679	−	7.77135i	0.223226	−	0.386639i
$405$	2.33368	+	13.0744i	0.115962	+	0.649673i
$406$	0.159320	+	5.22792i	0.00790691	+	0.259457i
$407$			1.05237i			0.0521641i
$408$	1.67091	−	1.40356i	0.0827225	−	0.0694864i
$409$	−17.2644	+	9.96762i	−0.853671	+	0.492867i	−0.861888	−	0.507099i	$-0.830718\pi$
$409$	−17.2644	+	9.96762i	−0.853671	+	0.492867i	0.00821693	+	0.999966i	$0.497384\pi$
$410$	6.06058	−	3.49908i	0.299311	−	0.172807i
$411$	18.6543	−	15.6695i	0.920150	−	0.772921i
$412$			5.71711i			0.281662i
$413$	−22.7502	−	12.2264i	−1.11946	−	0.601621i
$414$	−4.97253	−	4.16356i	−0.244387	−	0.204628i
$415$	12.3193	−	21.3377i	0.604732	−	1.04743i
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$	0.462289	+	2.61375i	0.0226384	+	0.127996i
$418$	1.30809	+	0.755225i	0.0639807	+	0.0369393i
$419$	20.2944			0.991446			0.495723	−	0.868481i	$-0.334903\pi$
$419$	20.2944			0.991446			0.495723	+	0.868481i	$0.334903\pi$
$420$	−5.04311	+	4.50520i	−0.246079	+	0.219831i
$421$	−18.9286			−0.922523			−0.461261	−	0.887264i	$-0.652603\pi$
$421$	−18.9286			−0.922523			−0.461261	+	0.887264i	$0.652603\pi$
$422$	−2.58061	−	1.48992i	−0.125622	−	0.0725280i
$423$	−1.06597	+	6.08273i	−0.0518292	+	0.295753i
$424$	6.63632	+	11.4944i	0.322288	+	0.558219i
$425$	1.77794	−	3.07948i	0.0862427	−	0.149377i
$426$	−2.84991	+	7.84287i	−0.138079	+	0.379988i
$427$	−11.0426	+	0.336522i	−0.534391	+	0.0162855i
$428$		−	2.58399i		−	0.124902i
$429$	−0.793660	−	0.944840i	−0.0383183	−	0.0456173i
$430$	10.4783	−	6.04966i	0.505309	−	0.291740i
$431$	2.25497	−	1.30191i	0.108618	−	0.0627107i	−0.444707	−	0.895676i	$-0.646692\pi$
$431$	2.25497	−	1.30191i	0.108618	−	0.0627107i	0.553325	+	0.832966i	$0.313359\pi$
$432$	0.00817995	+	5.19615i	0.000393558	+	0.250000i
$433$			28.2873i			1.35940i	0.733489	+	0.679701i	$0.237890\pi$
$433$			28.2873i			1.35940i	−0.733489	+	0.679701i	$0.762110\pi$
$434$	−3.71191	+	2.29660i	−0.178177	+	0.110240i
$435$	−4.74899	−	1.72567i	−0.227697	−	0.0827395i
$436$	−5.72625	+	9.91816i	−0.274238	+	0.474994i
$437$	2.29172	+	3.96938i	0.109628	+	0.189881i
$438$	−2.59407	+	0.458808i	−0.123949	+	0.0219227i
$439$	34.5408	+	19.9421i	1.64854	+	0.951785i	0.977653	+	0.210227i	$0.0674203\pi$
$439$	34.5408	+	19.9421i	1.64854	+	0.951785i	0.670888	+	0.741559i	$0.265913\pi$
$440$	1.05130			0.0501186
$441$	2.35862	−	20.8671i	0.112315	−	0.993673i
$442$	1.25988			0.0599265
$443$	12.0320	+	6.94666i	0.571656	+	0.330046i	0.757810	−	0.652475i	$-0.226269\pi$
$443$	12.0320	+	6.94666i	0.571656	+	0.330046i	−0.186154	+	0.982520i	$0.559602\pi$
$444$	2.51945	−	0.445610i	0.119568	−	0.0211477i
$445$	−2.77029	−	4.79828i	−0.131324	−	0.227460i
$446$	1.27485	−	2.20811i	0.0603661	−	0.104557i
$447$	−27.2835	−	9.91419i	−1.29047	−	0.468925i
$448$	−2.24993	+	1.39206i	−0.106299	+	0.0657685i
$449$		−	21.7353i		−	1.02575i	−0.858463	−	0.512875i	$-0.828580\pi$
$449$		−	21.7353i		−	1.02575i	0.858463	−	0.512875i	$-0.171420\pi$
$450$	2.90429	+	7.95349i	0.136909	+	0.374931i
$451$	2.92590	−	1.68927i	0.137775	−	0.0795445i
$452$	−3.92664	+	2.26705i	−0.184694	+	0.106633i
$453$	16.8903	+	20.1077i	0.793576	+	0.944740i
$454$			8.24468i			0.386942i
$455$	−3.90245	+	0.118927i	−0.182950	+	0.00557536i
$456$	1.25417	−	3.45144i	0.0587320	−	0.161629i
$457$	4.34511	−	7.52596i	0.203256	−	0.352050i	−0.746320	−	0.665588i	$-0.768181\pi$
$457$	4.34511	−	7.52596i	0.203256	−	0.352050i	0.949576	+	0.313538i	$0.101514\pi$
$458$	−3.98628	−	6.90443i	−0.186267	−	0.322623i
$459$	−5.67462	−	3.26434i	−0.264869	−	0.152367i
$460$	2.76275	+	1.59507i	0.128814	+	0.0743706i
$461$	35.1161			1.63552			0.817760	−	0.575559i	$-0.195215\pi$
$461$	35.1161			1.63552			0.817760	+	0.575559i	$0.195215\pi$
$462$	−2.43469	+	2.17500i	−0.113272	+	0.101190i
$463$	−20.9880			−0.975395			−0.487698	−	0.873013i	$-0.662163\pi$
$463$	−20.9880			−0.975395			−0.487698	+	0.873013i	$0.662163\pi$
$464$	−1.71203	−	0.988443i	−0.0794791	−	0.0458873i
$465$	−0.734413	−	4.15232i	−0.0340576	−	0.192559i
$466$	13.1093	+	22.7059i	0.607276	+	1.05183i
$467$	−17.2987	+	29.9621i	−0.800486	+	1.38648i	0.118810	+	0.992917i	$0.462092\pi$
$467$	−17.2987	+	29.9621i	−0.800486	+	1.38648i	−0.919297	+	0.393566i	$0.871241\pi$
$468$	−1.92595	+	2.30016i	−0.0890271	+	0.106325i
$469$	−16.3523	−	8.78805i	−0.755079	−	0.405794i
$470$		−	3.03764i		−	0.140116i
$471$	−20.6508	+	17.3465i	−0.951537	+	0.799286i
$472$	8.45400	−	4.88092i	0.389127	−	0.224663i
$473$	5.05867	−	2.92062i	0.232598	−	0.134290i
$474$	2.66366	−	2.23746i	0.122346	−	0.102770i
$475$		−	5.98395i		−	0.274563i
$476$	−0.101536	−	3.33179i	−0.00465388	−	0.152712i
$477$	25.5624	−	30.5291i	1.17042	−	1.39783i
$478$	−8.08557	+	14.0046i	−0.369825	+	0.640556i
$479$	−19.4526	−	33.6929i	−0.888813	−	1.53947i	−0.841280	−	0.540599i	$-0.818198\pi$
$479$	−19.4526	−	33.6929i	−0.888813	−	1.53947i	−0.0475326	−	0.998870i	$-0.515136\pi$
$480$	−0.445155	−	2.51688i	−0.0203185	−	0.114879i
$481$	1.27928	+	0.738591i	0.0583300	+	0.0336768i
$482$	−13.1988			−0.601188
$483$	−9.69823	+	2.02176i	−0.441285	+	0.0919931i
$484$	−10.4925			−0.476930
$485$	−7.65469	−	4.41944i	−0.347582	−	0.200676i
$486$	14.6343	−	5.36998i	0.663826	−	0.243587i
$487$	−13.4920	−	23.3688i	−0.611381	−	1.05894i	−0.991008	−	0.133803i	$-0.957281\pi$
$487$	−13.4920	−	23.3688i	−0.611381	−	1.05894i	0.379627	−	0.925140i	$-0.376052\pi$
$488$	2.08783	−	3.61623i	0.0945117	−	0.163699i
$489$	13.9486	−	38.3862i	0.630779	−	1.73588i
$490$	0.629008	+	10.3105i	0.0284157	+	0.465783i
$491$			27.1248i			1.22413i	0.790809	+	0.612063i	$0.209660\pi$
$491$			27.1248i			1.22413i	−0.790809	+	0.612063i	$0.790340\pi$
$492$	−5.28315	−	6.28951i	−0.238183	−	0.283553i
$493$	2.15696	−	1.24532i	0.0971447	−	0.0560865i
$494$	1.83612	−	1.06009i	0.0826112	−	0.0476956i
$495$	−1.08180	−	2.96255i	−0.0486235	−	0.133157i
$496$		−	1.64979i		−	0.0740778i
$497$	6.70660	+	10.8396i	0.300832	+	0.486224i
$498$	−27.1804	−	9.87671i	−1.21798	−	0.442586i
$499$	21.1584	−	36.6475i	0.947182	−	1.64057i	0.195860	−	0.980632i	$-0.437250\pi$
$499$	21.1584	−	36.6475i	0.947182	−	1.64057i	0.751322	−	0.659936i	$-0.229416\pi$
$500$	−5.77165	−	9.99678i	−0.258116	−	0.447070i
$501$	−23.3254	+	4.12552i	−1.04210	+	0.184314i
$502$	8.78569	+	5.07242i	0.392125	+	0.226393i
$503$	−35.3532			−1.57632			−0.788160	−	0.615471i	$-0.788966\pi$
$503$	−35.3532			−1.57632			−0.788160	+	0.615471i	$0.788966\pi$
$504$	6.23803	+	4.90785i	0.277864	+	0.218613i
$505$	13.2421			0.589265
$506$	1.33378	+	0.770061i	0.0592940	+	0.0342334i
$507$	−1.70558	+	0.301663i	−0.0757474	+	0.0133973i
$508$	7.85804	+	13.6105i	0.348644	+	0.603870i
$509$	3.45844	−	5.99019i	0.153293	−	0.265511i	−0.779143	−	0.626846i	$-0.784346\pi$
$509$	3.45844	−	5.99019i	0.153293	−	0.265511i	0.932436	+	0.361335i	$0.117679\pi$
$510$	3.02656	+	1.09978i	0.134019	+	0.0486991i
$511$	−1.90492	+	3.54456i	−0.0842685	+	0.156802i
$512$		−	1.00000i		−	0.0441942i
$513$	−11.0167	+	0.0173429i	−0.486401	+	0.000765709i
$514$	−23.3525	+	13.4826i	−1.03004	+	0.594691i
$515$	−7.30630	+	4.21830i	−0.321954	+	0.185880i
$516$	−9.13419	−	10.8741i	−0.402110	−	0.478706i
$517$		−	1.46650i		−	0.0644964i
$518$	1.85012	−	3.44260i	0.0812897	−	0.151259i
$519$	15.0905	−	41.5285i	0.662398	−	1.82290i
$520$	0.737837	−	1.27797i	0.0323563	−	0.0560427i
$521$	−2.68088	−	4.64342i	−0.117452	−	0.203432i	0.801306	−	0.598255i	$-0.204139\pi$
$521$	−2.68088	−	4.64342i	−0.117452	−	0.203432i	−0.918757	+	0.394823i	$0.870806\pi$
$522$	−1.02372	+	5.84163i	−0.0448069	+	0.255681i
$523$	−10.4865	−	6.05436i	−0.458541	−	0.264739i	0.252890	−	0.967495i	$-0.418619\pi$
$523$	−10.4865	−	6.05436i	−0.458541	−	0.264739i	−0.711430	+	0.702757i	$0.751952\pi$
$524$	14.0926			0.615640
$525$	12.2850	+	4.04491i	0.536163	+	0.176534i
$526$	28.4825			1.24189
$527$	1.80007	+	1.03927i	0.0784123	+	0.0452714i
$528$	−0.214910	−	1.21509i	−0.00935275	−	0.0528798i
$529$	−9.16326	−	15.8712i	−0.398403	−	0.690054i
$530$	−9.79304	+	16.9620i	−0.425382	+	0.736784i
$531$	−22.4538	−	18.8008i	−0.974410	−	0.815886i
$532$	−2.95140	−	4.77024i	−0.127959	−	0.206816i
$533$		−	4.74235i		−	0.205414i
$534$	−4.97952	+	4.18277i	−0.215485	+	0.181006i
$535$	3.30226	−	1.90656i	0.142769	−	0.0824278i
$536$	6.07654	−	3.50829i	0.262467	−	0.151535i
$537$	−8.08251	+	6.78926i	−0.348786	+	0.292978i
$538$			2.14149i			0.0923260i
$539$	0.303669	+	4.97767i	0.0130800	+	0.214404i
$540$	−6.63449	+	3.84436i	−0.285503	+	0.165435i
$541$	−6.78137	+	11.7457i	−0.291554	+	0.504986i	−0.974177	−	0.225784i	$-0.927506\pi$
$541$	−6.78137	+	11.7457i	−0.291554	+	0.504986i	0.682624	+	0.730770i	$0.260839\pi$
$542$	10.5924	+	18.3465i	0.454981	+	0.788050i
$543$	5.49261	+	31.0549i	0.235711	+	1.33269i
$544$	1.09109	+	0.629942i	0.0467801	+	0.0270085i
$545$	−16.9002			−0.723923
$546$	0.935209	+	4.48613i	0.0400232	+	0.191989i
$547$	−33.1898			−1.41909			−0.709547	−	0.704658i	$-0.751101\pi$
$547$	−33.1898			−1.41909			−0.709547	+	0.704658i	$0.751101\pi$
$548$	12.1811	+	7.03277i	0.520351	+	0.300425i
$549$	−12.3389	−	2.16234i	−0.526613	−	0.0922864i
$550$	−1.00536	−	1.74133i	−0.0428687	−	0.0742508i
$551$	2.09567	−	3.62981i	0.0892786	−	0.154635i
$552$	1.27881	−	3.51925i	0.0544297	−	0.149789i
$553$	−0.161861	−	5.31132i	−0.00688305	−	0.225860i
$554$			18.8227i			0.799700i
$555$	2.42842	+	2.89100i	0.103081	+	0.122716i
$556$	−1.32716	+	0.766236i	−0.0562841	+	0.0324956i
$557$	−21.4609	+	12.3905i	−0.909329	+	0.525001i	−0.880215	−	0.474575i	$-0.842602\pi$
$557$	−21.4609	+	12.3905i	−0.909329	+	0.525001i	−0.0291135	+	0.999576i	$0.509268\pi$
$558$	−4.64911	+	1.69766i	−0.196812	+	0.0718679i
$559$		−	8.19918i		−	0.346789i
$560$	−3.43909	−	1.84823i	−0.145328	−	0.0781021i
$561$	1.46115	+	0.530947i	0.0616898	+	0.0224166i
$562$	−10.9479	+	18.9623i	−0.461809	+	0.799878i
$563$	−6.39650	−	11.0791i	−0.269580	−	0.466927i	0.699173	−	0.714952i	$-0.253552\pi$
$563$	−6.39650	−	11.0791i	−0.269580	−	0.466927i	−0.968753	+	0.248026i	$0.920218\pi$
$564$	−3.51089	+	0.620965i	−0.147835	+	0.0261473i
$565$	−5.79444	−	3.34542i	−0.243774	−	0.140743i
$566$	1.37833			0.0579354
$567$	7.41126	−	22.6290i	0.311244	−	0.950330i
$568$	−4.81777			−0.202149
$569$	−25.9976	−	15.0097i	−1.08988	−	0.629240i	−0.156333	−	0.987704i	$-0.549967\pi$
$569$	−25.9976	−	15.0097i	−1.08988	−	0.629240i	−0.933544	+	0.358464i	$0.883301\pi$
$570$	5.33622	−	0.943807i	0.223510	−	0.0395317i
$571$	−11.1007	−	19.2270i	−0.464551	−	0.804626i	0.534630	−	0.845086i	$-0.320451\pi$
$571$	−11.1007	−	19.2270i	−0.464551	−	0.804626i	−0.999181	+	0.0404599i	$0.987118\pi$
$572$	0.356209	−	0.616972i	0.0148938	−	0.0257969i
$573$	13.8746	+	5.04169i	0.579619	+	0.210620i
$574$	−12.5413	+	0.382192i	−0.523462	+	0.0159524i
$575$		−	6.10150i		−	0.254450i
$576$	−2.81800	+	1.02902i	−0.117417	+	0.0428758i
$577$	10.9229	−	6.30634i	0.454727	−	0.262536i	−0.255098	−	0.966915i	$-0.582108\pi$
$577$	10.9229	−	6.30634i	0.454727	−	0.262536i	0.709824	+	0.704379i	$0.248774\pi$
$578$	13.3478	−	7.70635i	0.555195	−	0.320542i
$579$	11.6815	+	13.9066i	0.485465	+	0.577939i
$580$		−	2.91724i		−	0.121132i
$581$	−37.5660	+	23.2425i	−1.55850	+	0.964262i
$582$	−3.54317	+	9.75071i	−0.146869	+	0.404180i
$583$	−4.72783	+	8.18885i	−0.195807	+	0.339147i
$584$	−0.760465	−	1.31716i	−0.0314683	−	0.0545046i
$585$	−4.36057	−	0.764168i	−0.180287	−	0.0315945i
$586$	20.3000	+	11.7202i	0.838587	+	0.484158i
$587$	23.0865			0.952884			0.476442	−	0.879206i	$-0.341926\pi$
$587$	23.0865			0.952884			0.476442	+	0.879206i	$0.341926\pi$
$588$	11.7883	−	2.83472i	0.486142	−	0.116902i
$589$	3.49784			0.144126
$590$	12.4753	+	7.20265i	0.513602	+	0.296528i
$591$	8.30969	+	46.9824i	0.341815	+	1.93260i
$592$	0.738591	+	1.27928i	0.0303559	+	0.0525779i
$593$	−11.8378	+	20.5037i	−0.486122	+	0.841987i	−0.999873	−	0.0159520i	$-0.994922\pi$
$593$	−11.8378	+	20.5037i	−0.486122	+	0.841987i	0.513751	+	0.857939i	$0.328255\pi$
$594$	−3.20296	+	1.85596i	−0.131419	+	0.0761510i
$595$	4.18301	−	2.58808i	0.171487	−	0.106101i
$596$		−	16.7599i		−	0.686512i
$597$	23.9372	−	20.1071i	0.979684	−	0.822929i
$598$	1.87219	−	1.08091i	0.0765597	−	0.0442018i
$599$	−1.09795	+	0.633902i	−0.0448611	+	0.0259005i	−0.522263	−	0.852785i	$-0.674912\pi$
$599$	−1.09795	+	0.633902i	−0.0448611	+	0.0259005i	0.477402	+	0.878685i	$0.341579\pi$
$600$	−3.74317	+	3.14424i	−0.152814	+	0.128363i
$601$		−	25.2631i		−	1.03050i	−0.857040	−	0.515251i	$-0.827699\pi$
$601$		−	25.2631i		−	1.03050i	0.857040	−	0.515251i	$-0.172301\pi$
$602$	−21.6829	+	0.660783i	−0.883730	+	0.0269315i
$603$	−16.1392	−	13.5136i	−0.657241	−	0.550316i
$604$	−7.58068	+	13.1301i	−0.308454	+	0.534257i
$605$	−7.74172	−	13.4091i	−0.314746	−	0.545156i
$606$	−2.70699	−	15.3052i	−0.109964	−	0.621730i
$607$	13.9578	+	8.05855i	0.566530	+	0.327086i	0.755762	−	0.654846i	$-0.227267\pi$
$607$	13.9578	+	8.05855i	0.566530	+	0.327086i	−0.189232	+	0.981932i	$0.560600\pi$
$608$	2.12017			0.0859844
$609$	6.03539	+	6.75601i	0.244566	+	0.273767i
$610$	6.16191			0.249489
$611$	−1.78269	−	1.02924i	−0.0721200	−	0.0416385i
$612$	0.652422	−	3.72292i	0.0263726	−	0.150490i
$613$	−9.56329	−	16.5641i	−0.386258	−	0.669018i	0.605685	−	0.795704i	$-0.292899\pi$
$613$	−9.56329	−	16.5641i	−0.386258	−	0.669018i	−0.991943	+	0.126687i	$0.959566\pi$
$614$	3.75798	−	6.50900i	0.151660	−	0.262682i
$615$	4.13970	−	11.3923i	0.166929	−	0.459384i
$616$	−1.66030	−	0.892281i	−0.0668956	−	0.0359510i
$617$			4.04245i			0.162743i	0.996684	+	0.0813715i	$0.0259300\pi$
$617$			4.04245i			0.162743i	−0.996684	+	0.0813715i	$0.974070\pi$
$618$	6.36907	+	7.58228i	0.256202	+	0.305004i
$619$	−38.4517	+	22.2001i	−1.54550	+	0.892297i	−0.547027	+	0.837115i	$0.684240\pi$
$619$	−38.4517	+	22.2001i	−1.54550	+	0.892297i	−0.998476	+	0.0551818i	$0.982426\pi$
$620$	2.10838	−	1.21728i	0.0846747	−	0.0488870i
$621$	−11.2331	+	0.0176836i	−0.450771	+	0.000709619i
$622$		−	6.15375i		−	0.246743i
$623$	0.302589	+	9.92914i	0.0121230	+	0.397803i
$624$	−1.62791	−	0.591542i	−0.0651684	−	0.0236806i
$625$	1.46109	−	2.53069i	0.0584438	−	0.101228i
$626$	−13.0024	−	22.5207i	−0.519678	−	0.900109i
$627$	2.57619	−	0.455646i	0.102883	−	0.0181968i
$628$	−13.4848	−	7.78544i	−0.538101	−	0.310673i
$629$	−1.86108			−0.0742060
$630$	−1.66944	+	11.5932i	−0.0665119	+	0.461885i
$631$	12.5677			0.500314			0.250157	−	0.968205i	$-0.419518\pi$
$631$	12.5677			0.500314			0.250157	+	0.968205i	$0.419518\pi$
$632$	1.73934	+	1.00421i	0.0691874	+	0.0399454i
$633$	−5.08234	+	0.898904i	−0.202005	+	0.0357282i
$634$	6.83359	+	11.8361i	0.271397	+	0.470073i
$635$	−11.5959	+	20.0847i	−0.460170	+	0.797037i
$636$	21.6066	+	7.85132i	0.856757	+	0.311325i
$637$	6.26405	+	3.12436i	0.248191	+	0.123792i
$638$		−	1.40837i		−	0.0557579i
$639$	4.95757	+	13.5765i	0.196118	+	0.537077i
$640$	1.27797	−	0.737837i	0.0505162	−	0.0291656i
$641$	20.6913	−	11.9462i	0.817259	−	0.471845i	−0.0322113	−	0.999481i	$-0.510255\pi$
$641$	20.6913	−	11.9462i	0.817259	−	0.471845i	0.849470	+	0.527636i	$0.176922\pi$
$642$	−2.87866	−	3.42700i	−0.113612	−	0.135253i
$643$		−	23.9933i		−	0.946205i	−0.881007	−	0.473103i	$-0.843134\pi$
$643$		−	23.9933i		−	0.946205i	0.881007	−	0.473103i	$-0.156866\pi$
$644$	−3.00938	−	4.86395i	−0.118586	−	0.191666i
$645$	7.15726	−	19.6966i	0.281817	−	0.775551i
$646$	−1.33559	+	2.31330i	−0.0525479	+	0.0910157i
$647$	3.31341	+	5.73900i	0.130264	+	0.225623i	0.923778	−	0.382928i	$-0.125084\pi$
$647$	3.31341	+	5.73900i	0.130264	+	0.225623i	−0.793514	+	0.608551i	$0.791751\pi$
$648$	5.79955	+	6.88224i	0.227828	+	0.270360i
$649$	6.02279	+	3.47726i	0.236415	+	0.136494i
$650$	−2.82239			−0.110703
$651$	−2.36440	+	7.18106i	−0.0926682	+	0.281448i
$652$	23.5801			0.923468
$653$	−13.2630	−	7.65742i	−0.519023	−	0.299658i	0.217512	−	0.976058i	$-0.430206\pi$
$653$	−13.2630	−	7.65742i	−0.519023	−	0.299658i	−0.736535	+	0.676400i	$0.763539\pi$
$654$	3.45479	+	19.5332i	0.135093	+	0.763807i
$655$	10.3981	+	18.0100i	0.406286	+	0.703708i
$656$	2.37117	−	4.10699i	0.0925788	−	0.160351i
$657$	−2.92924	+	3.49838i	−0.114280	+	0.136485i
$658$	−2.57817	+	4.79732i	−0.100508	+	0.187019i
$659$		−	25.8336i		−	1.00633i	−0.864189	−	0.503167i	$-0.832168\pi$
$659$		−	25.8336i		−	1.00633i	0.864189	−	0.503167i	$-0.167832\pi$
$660$	1.39428	−	1.17118i	0.0542721	−	0.0455882i
$661$	−18.6895	+	10.7904i	−0.726936	+	0.419697i	−0.817300	−	0.576212i	$-0.804530\pi$
$661$	−18.6895	+	10.7904i	−0.726936	+	0.419697i	0.0903641	+	0.995909i	$0.471197\pi$
$662$	−6.16188	+	3.55757i	−0.239488	+	0.138269i
$663$	1.67091	−	1.40356i	0.0648928	−	0.0545096i
$664$		−	16.6965i		−	0.647951i
$665$	3.91858	−	7.29146i	0.151956	−	0.282751i
$666$	2.84498	−	3.39775i	0.110241	−	0.131660i
$667$	2.13684	−	3.70111i	0.0827387	−	0.143308i
$668$	−6.83797	−	11.8437i	−0.264569	−	0.458247i
$669$	−0.769151	−	4.34873i	−0.0297371	−	0.168132i
$670$	8.96699	+	5.17709i	0.346425	+	0.200009i
$671$	2.97482			0.114842
$672$	−1.43315	+	4.35271i	−0.0552850	+	0.167909i
$673$	−23.3592			−0.900431			−0.450216	−	0.892920i	$-0.648653\pi$
$673$	−23.3592			−0.900431			−0.450216	+	0.892920i	$0.648653\pi$
$674$	1.58332	+	0.914131i	0.0609873	+	0.0352110i
$675$	12.7123	+	7.31278i	0.489296	+	0.281469i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	−10.1408	+	17.5644i	−0.389743	+	0.675054i	−0.992415	−	0.122935i	$-0.960769\pi$
$677$	−10.1408	+	17.5644i	−0.389743	+	0.675054i	0.602672	+	0.797989i	$0.294103\pi$
$678$	−2.68211	+	7.38108i	−0.103006	+	0.283469i
$679$	8.33803	+	13.4765i	0.319984	+	0.517179i
$680$			1.85918i			0.0712962i
$681$	9.18488	+	10.9345i	0.351965	+	0.419009i
$682$	1.01787	−	0.587670i	0.0389764	−	0.0225031i
$683$	16.7121	−	9.64873i	0.639470	−	0.369198i	−0.144940	−	0.989440i	$-0.546299\pi$
$683$	16.7121	−	9.64873i	0.639470	−	0.369198i	0.784410	+	0.620242i	$0.212966\pi$
$684$	−2.18170	−	5.97465i	−0.0834193	−	0.228446i
$685$			20.7561i			0.793051i
$686$	7.75762	−	16.8172i	0.296187	−	0.642085i
$687$	−12.9786	−	4.71610i	−0.495163	−	0.179931i
$688$	4.09959	−	7.10070i	0.156295	−	0.270712i
$689$	6.63632	+	11.4944i	0.252824	+	0.437903i
$690$	5.44105	−	0.962347i	0.207137	−	0.0366359i
$691$	5.44524	+	3.14381i	0.207147	+	0.119596i	0.599985	−	0.800011i	$-0.295173\pi$
$691$	5.44524	+	3.14381i	0.207147	+	0.119596i	−0.392838	+	0.919608i	$0.628507\pi$
$692$	25.5104			0.969760
$693$	−0.805962	+	5.59691i	−0.0306160	+	0.212609i
$694$	−20.9049			−0.793540
$695$	−1.95845	−	1.13071i	−0.0742884	−	0.0428904i
$696$	−3.37173	+	0.596352i	−0.127805	+	0.0226047i
$697$	2.98740	+	5.17433i	0.113156	+	0.195992i
$698$	−15.1263	+	26.1996i	−0.572540	+	0.991668i
$699$	42.6814	+	15.5094i	1.61436	+	0.586619i
$700$	0.227460	+	7.46387i	0.00859718	+	0.282108i
$701$		−	34.1003i		−	1.28795i	−0.765046	−	0.643976i	$-0.777284\pi$
$701$		−	34.1003i		−	1.28795i	0.765046	−	0.643976i	$-0.222716\pi$
$702$	0.00817995	+	5.19615i	0.000308732	+	0.196116i
$703$	−2.71229	+	1.56594i	−0.102296	+	0.0590606i
$704$	0.616972	−	0.356209i	0.0232530	−	0.0134251i
$705$	−3.38404	−	4.02865i	−0.127450	−	0.151728i
$706$		−	6.75115i		−	0.254083i
$707$	−20.9131	−	11.2391i	−0.786519	−	0.422691i
$708$	5.77454	−	15.8914i	0.217021	−	0.597234i
$709$	23.4010	−	40.5318i	0.878844	−	1.52220i	0.0262328	−	0.999656i	$-0.491649\pi$
$709$	23.4010	−	40.5318i	0.878844	−	1.52220i	0.852611	−	0.522546i	$-0.175018\pi$
$710$	−3.55473	−	6.15697i	−0.133406	−	0.231067i
$711$	1.04005	−	5.93482i	0.0390049	−	0.222573i
$712$	−3.25158	−	1.87730i	−0.121858	−	0.0703549i
$713$	3.56656			0.133569
$714$	−3.84640	−	4.30565i	−0.143948	−	0.161135i
$715$	1.05130			0.0393163
$716$	−5.27781	−	3.04714i	−0.197241	−	0.113877i
$717$	4.87823	+	27.5811i	0.182181	+	1.03004i
$718$	3.82151	+	6.61905i	0.142618	+	0.247021i
$719$	10.4968	−	18.1810i	0.391465	−	0.678037i	−0.601178	−	0.799115i	$-0.705302\pi$
$719$	10.4968	−	18.1810i	0.391465	−	0.678037i	0.992643	+	0.121078i	$0.0386351\pi$
$720$	−3.39428	−	2.84207i	−0.126497	−	0.105918i
$721$	15.1190	−	0.460750i	0.563062	−	0.0171592i
$722$		−	14.5049i		−	0.539815i
$723$	−17.5048	+	14.7039i	−0.651011	+	0.546845i
$724$	−15.7684	+	9.10391i	−0.586029	+	0.338344i
$725$	−4.83202	+	2.78977i	−0.179457	+	0.103609i
$726$	−13.9156	+	11.6890i	−0.516455	+	0.433819i
$727$		−	17.4752i		−	0.648121i	−0.946036	−	0.324060i	$-0.894952\pi$
$727$		−	17.4752i		−	0.648121i	0.946036	−	0.324060i	$-0.105048\pi$
$728$	−2.24993	+	1.39206i	−0.0833879	+	0.0515930i
$729$	13.4263	−	23.4251i	0.497271	−	0.867595i
$730$	1.12220	−	1.94370i	0.0415344	−	0.0719397i
$731$	5.16501	+	8.94605i	0.191035	+	0.330882i
$732$	−1.25964	−	7.12192i	−0.0465577	−	0.263234i
$733$	13.0692	+	7.54551i	0.482722	+	0.278700i	0.721550	−	0.692362i	$-0.243430\pi$
$733$	13.0692	+	7.54551i	0.482722	+	0.278700i	−0.238828	+	0.971062i	$0.576763\pi$
$734$	18.4828			0.682213
$735$	12.3205	+	12.9736i	0.454450	+	0.478537i
$736$	2.16182			0.0796859
$737$	4.32904	+	2.49937i	0.159462	+	0.0920655i
$738$	−14.0135	−	2.45579i	−0.515844	−	0.0903991i
$739$	−25.1280	−	43.5229i	−0.924348	−	1.60102i	−0.792607	−	0.609733i	$-0.791277\pi$
$739$	−25.1280	−	43.5229i	−0.924348	−	1.60102i	−0.131740	−	0.991284i	$-0.542057\pi$
$740$	−1.08992	+	1.88779i	−0.0400662	+	0.0693967i
$741$	1.25417	−	3.45144i	0.0460732	−	0.126792i
$742$	29.8625	−	18.4762i	1.09629	−	0.678284i
$743$		−	11.2555i		−	0.412925i	−0.978455	−	0.206462i	$-0.933805\pi$
$743$		−	11.2555i		−	0.412925i	0.978455	−	0.206462i	$-0.0661951\pi$
$744$	−1.83793	−	2.18802i	−0.0673817	−	0.0802168i
$745$	21.4187	−	12.3661i	0.784719	−	0.453058i
$746$	4.43510	−	2.56061i	0.162381	−	0.0937505i
$747$	−47.0508	+	17.1810i	−1.72150	+	0.628622i
$748$			0.897564i			0.0328182i
$749$	−6.83342	+	0.208247i	−0.249688	+	0.00760918i
$750$	−18.7914	−	6.82834i	−0.686165	−	0.249336i
$751$	−20.0363	+	34.7039i	−0.731136	+	1.26636i	0.225262	+	0.974298i	$0.427676\pi$
$751$	−20.0363	+	34.7039i	−0.731136	+	1.26636i	−0.956398	+	0.292066i	$0.905657\pi$
$752$	−1.02924	−	1.78269i	−0.0375324	−	0.0650081i
$753$	17.3028	−	3.06032i	0.630550	−	0.111524i
$754$	−1.71203	−	0.988443i	−0.0623486	−	0.0359970i
$755$	−22.3732			−0.814245
$756$	13.7407	−	0.440396i	0.499743	−	0.0160171i
$757$	7.74903			0.281643			0.140822	−	0.990035i	$-0.455026\pi$
$757$	7.74903			0.281643			0.140822	+	0.990035i	$0.455026\pi$
$758$	−14.8276	−	8.56074i	−0.538564	−	0.310940i
$759$	2.62680	−	0.464597i	0.0953468	−	0.0168638i
$760$	1.56434	+	2.70952i	0.0567447	+	0.0982847i
$761$	−13.4912	+	23.3675i	−0.489057	+	0.847071i	−0.999921	−	0.0125906i	$-0.995992\pi$
$761$	−13.4912	+	23.3675i	−0.489057	+	0.847071i	0.510864	+	0.859661i	$0.329326\pi$
$762$	25.5843	+	9.29673i	0.926822	+	0.336785i
$763$	26.6903	+	14.3439i	0.966254	+	0.519284i
$764$			8.52297i			0.308350i
$765$	5.23916	−	1.91313i	0.189422	−	0.0691692i
$766$	14.4975	−	8.37015i	0.523817	−	0.302426i
$767$	8.45400	−	4.88092i	0.305256	−	0.176240i
$768$	−1.11404	−	1.32624i	−0.0401993	−	0.0478567i
$769$		−	17.8098i		−	0.642236i	−0.947039	−	0.321118i	$-0.895941\pi$
$769$		−	17.8098i		−	0.642236i	0.947039	−	0.321118i	$-0.104059\pi$
$770$	−0.0847254	−	2.78018i	−0.00305329	−	0.100191i
$771$	−15.9510	+	43.8968i	−0.574462	+	1.58090i
$772$	−5.24285	+	9.08089i	−0.188694	+	0.326828i
$773$	2.47459	+	4.28611i	0.0890047	+	0.154161i	0.907091	−	0.420935i	$-0.138298\pi$
$773$	2.47459	+	4.28611i	0.0890047	+	0.154161i	−0.818086	+	0.575096i	$0.804965\pi$
$774$	−24.2283	−	4.24589i	−0.870869	−	0.152616i
$775$	−4.03252	−	2.32817i	−0.144852	−	0.0836305i
$776$	−5.98973			−0.215019
$777$	−1.38147	−	6.62683i	−0.0495601	−	0.237736i
$778$	19.9669			0.715846
$779$	8.70754	+	5.02730i	0.311980	+	0.180122i
$780$	−0.445155	−	2.51688i	−0.0159391	−	0.0901187i
$781$	−1.71613	−	2.97243i	−0.0614080	−	0.106362i
$782$	−1.36182	+	2.35875i	−0.0486987	+	0.0843486i
$783$	5.15010	+	8.88789i	0.184049	+	0.317627i
$784$	3.86265	+	5.83780i	0.137952	+	0.208493i
$785$		−	22.9775i		−	0.820103i
$786$	18.6903	−	15.6997i	0.666660	−	0.559991i
$787$	−22.3467	+	12.9019i	−0.796575	+	0.459903i	−0.842272	−	0.539053i	$-0.818782\pi$
$787$	−22.3467	+	12.9019i	−0.796575	+	0.459903i	0.0456973	+	0.998955i	$0.485449\pi$
$788$	−23.8558	+	13.7732i	−0.849828	+	0.490648i
$789$	37.7747	−	31.7305i	1.34481	−	1.12964i
$790$			2.96377i			0.105446i
$791$	6.31171	+	10.2014i	0.224419	+	0.362720i
$792$	−1.63867	−	1.37208i	−0.0582277	−	0.0487548i
$793$	2.08783	−	3.61623i	0.0741410	−	0.128416i
$794$	4.34555	+	7.52672i	0.154218	+	0.267113i
$795$	5.90838	+	33.4056i	0.209549	+	1.18477i
$796$	15.6308	+	9.02443i	0.554018	+	0.319862i
$797$	25.3698			0.898645			0.449323	−	0.893370i	$-0.351665\pi$
$797$	25.3698			0.898645			0.449323	+	0.893370i	$0.351665\pi$
$798$	−9.22850	−	3.03853i	−0.326685	−	0.107563i
$799$	2.59344			0.0917493
$800$	−2.44426	−	1.41119i	−0.0864176	−	0.0498932i
$801$	−1.94430	+	11.0947i	−0.0686984	+	0.392013i
$802$	−5.32841	−	9.22909i	−0.188153	−	0.325890i
$803$	0.541769	−	0.938372i	0.0191186	−	0.0331144i
$804$	4.15061	−	11.4223i	0.146381	−	0.402835i
$805$	3.99555	−	7.43470i	0.140825	−	0.262039i
$806$		−	1.64979i		−	0.0581114i
$807$	2.38569	+	2.84013i	0.0839804	+	0.0999774i
$808$	7.77135	−	4.48679i	0.273395	−	0.157845i
$809$	−22.2087	+	12.8222i	−0.780816	+	0.450804i	−0.836719	−	0.547632i	$-0.815529\pi$
$809$	−22.2087	+	12.8222i	−0.780816	+	0.450804i	0.0559033	+	0.998436i	$0.482196\pi$
$810$	−4.51619	+	12.4896i	−0.158683	+	0.438841i
$811$		−	25.6113i		−	0.899333i	−0.893196	−	0.449667i	$-0.851543\pi$
$811$		−	25.6113i		−	0.899333i	0.893196	−	0.449667i	$-0.148457\pi$
$812$	−2.47599	+	4.60717i	−0.0868901	+	0.161680i
$813$	34.4868	+	12.5317i	1.20950	+	0.439505i
$814$	−0.526185	+	0.911380i	−0.0184428	+	0.0319438i
$815$	17.3983	+	30.1347i	0.609435	+	1.05557i
$816$	2.14883	−	0.380060i	0.0752241	−	0.0133047i
$817$	15.0547	+	8.69185i	0.526698	+	0.304089i
$818$	−19.9352			−0.697019
$819$	6.23803	+	4.90785i	0.217974	+	0.171494i
$820$	6.99816			0.244386
$821$	−14.5678	−	8.41070i	−0.508418	−	0.293536i	0.223765	−	0.974643i	$-0.428165\pi$
$821$	−14.5678	−	8.41070i	−0.508418	−	0.293536i	−0.732183	+	0.681108i	$0.761499\pi$
$822$	23.9899	−	4.24304i	0.836743	−	0.147993i
$823$	−7.99185	−	13.8423i	−0.278578	−	0.482512i	0.692453	−	0.721463i	$-0.256530\pi$
$823$	−7.99185	−	13.8423i	−0.278578	−	0.482512i	−0.971032	+	0.238951i	$0.923196\pi$
$824$	−2.85856	+	4.95116i	−0.0995825	+	0.172482i
$825$	−3.27326	−	1.18943i	−0.113960	−	0.0414105i
$826$	−13.5890	−	21.9635i	−0.472823	−	0.764206i
$827$			49.9019i			1.73526i	0.497210	+	0.867630i	$0.334358\pi$
$827$			49.9019i			1.73526i	−0.497210	+	0.867630i	$0.665642\pi$
$828$	−2.22456	−	6.09202i	−0.0773087	−	0.211712i
$829$	31.7041	−	18.3044i	1.10113	−	0.635737i	0.164611	−	0.986359i	$-0.447363\pi$
$829$	31.7041	−	18.3044i	1.10113	−	0.635737i	0.936517	+	0.350622i	$0.114030\pi$
$830$	21.3377	−	12.3193i	0.740642	−	0.427610i
$831$	20.9692	+	24.9635i	0.727413	+	0.865974i
$832$		−	1.00000i		−	0.0346688i
$833$	−8.80282	+	0.537027i	−0.305000	+	0.0186069i
$834$	−0.906521	+	2.49472i	−0.0313903	+	0.0863851i
$835$	10.0906	−	17.4774i	0.349200	−	0.604832i
$836$	0.755225	+	1.30809i	0.0261200	+	0.0452412i
$837$	−4.27459	+	7.43080i	−0.147751	+	0.256846i
$838$	17.5755	+	10.1472i	0.607134	+	0.350529i
$839$	41.4486			1.43097			0.715483	−	0.698630i	$-0.246207\pi$
$839$	41.4486			1.43097			0.715483	+	0.698630i	$0.246207\pi$
$840$	−6.62007	+	1.38006i	−0.228414	+	0.0476167i
$841$	25.0919			0.865239
$842$	−16.3926	−	9.46429i	−0.564927	−	0.326161i
$843$	6.60514	+	37.3450i	0.227493	+	1.28623i
$844$	−1.48992	−	2.58061i	−0.0512850	−	0.0888283i
$845$	0.737837	−	1.27797i	0.0253824	−	0.0439635i
$846$	−3.96452	+	4.73482i	−0.136303	+	0.162786i
$847$	0.845602	+	27.7476i	0.0290552	+	0.953417i
$848$			13.2726i			0.455784i
$849$	1.82800	−	1.53551i	0.0627367	−	0.0526985i
$850$	3.07948	−	1.77794i	0.105625	−	0.0609828i
$851$	−2.76557	+	1.59670i	−0.0948025	+	0.0547343i
$852$	−6.38953	+	5.36717i	−0.218902	+	0.183876i
$853$			34.2914i			1.17412i	0.809545	+	0.587058i	$0.199714\pi$
$853$			34.2914i			1.17412i	−0.809545	+	0.587058i	$0.800286\pi$
$854$	−9.73146	−	5.22988i	−0.333004	−	0.178963i
$855$	6.02569	−	7.19646i	0.206074	−	0.246114i
$856$	1.29199	−	2.23780i	0.0441594	−	0.0764864i
$857$	0.370855	+	0.642339i	0.0126682	+	0.0219419i	0.872290	−	0.488989i	$-0.162634\pi$
$857$	0.370855	+	0.642339i	0.0126682	+	0.0219419i	−0.859622	+	0.510931i	$0.829301\pi$
$858$	−0.214910	−	1.21509i	−0.00733690	−	0.0414823i
$859$	10.0183	+	5.78405i	0.341819	+	0.197349i	0.661076	−	0.750319i	$-0.270100\pi$
$859$	10.0183	+	5.78405i	0.341819	+	0.197349i	−0.319257	+	0.947668i	$0.603433\pi$
$860$	12.0993			0.412583
$861$	−16.2070	+	14.4783i	−0.552332	+	0.493419i
$862$	2.60381			0.0886863
$863$	22.7050	+	13.1087i	0.772886	+	0.446226i	0.833903	−	0.551911i	$-0.186101\pi$
$863$	22.7050	+	13.1087i	0.772886	+	0.446226i	−0.0610174	+	0.998137i	$0.519435\pi$
$864$	−2.59099	+	4.50408i	−0.0881472	+	0.153232i
$865$	18.8225	+	32.6015i	0.639985	+	1.10849i
$866$	−14.1437	+	24.4975i	−0.480621	+	0.832460i
$867$	9.11726	−	25.0904i	0.309638	−	0.852115i
$868$	−4.36291	+	0.132959i	−0.148087	+	0.00451292i
$869$			1.43084i			0.0485378i
$870$	−3.24991	−	3.86897i	−0.110182	−	0.131170i
$871$	6.07654	−	3.50829i	0.205896	−	0.118874i
$872$	−9.91816	+	5.72625i	−0.335871	+	0.193915i
$873$	6.16354	+	16.8790i	0.208604	+	0.571269i
$874$			4.58344i			0.155037i
$875$	−25.9716	+	16.0689i	−0.878000	+	0.543228i
$876$	−2.47593	−	0.899694i	−0.0836540	−	0.0303979i
$877$	−8.17596	+	14.1612i	−0.276083	+	0.478189i	−0.970408	−	0.241472i	$-0.922370\pi$
$877$	−8.17596	+	14.1612i	−0.276083	+	0.478189i	0.694325	+	0.719662i	$0.255703\pi$
$878$	19.9421	+	34.5408i	0.673014	+	1.16569i
$879$	39.9796	−	7.07111i	1.34848	−	0.238503i
$880$	0.910449	+	0.525648i	0.0306912	+	0.0177196i
$881$	52.8947			1.78207			0.891033	−	0.453938i	$-0.149981\pi$
$881$	52.8947			1.78207			0.891033	+	0.453938i	$0.149981\pi$
$882$	12.4762	−	16.8922i	0.420095	−	0.568788i
$883$	−54.9388			−1.84884			−0.924419	−	0.381378i	$-0.875450\pi$
$883$	−54.9388			−1.84884			−0.924419	+	0.381378i	$0.875450\pi$
$884$	1.09109	+	0.629942i	0.0366974	+	0.0211872i
$885$	24.5694	−	4.34554i	0.825890	−	0.146074i
$886$	6.94666	+	12.0320i	0.233378	+	0.404222i
$887$	−16.1173	+	27.9160i	−0.541166	+	0.937328i	0.457671	+	0.889122i	$0.348684\pi$
$887$	−16.1173	+	27.9160i	−0.541166	+	0.937328i	−0.998837	+	0.0482060i	$0.984650\pi$
$888$	2.40471	+	0.873815i	0.0806969	+	0.0293233i
$889$	35.3601	−	21.8777i	1.18594	−	0.733754i
$890$		−	5.54057i		−	0.185720i
$891$	−2.18030	+	6.02968i	−0.0730428	+	0.202002i
$892$	2.20811	−	1.27485i	0.0739330	−	0.0426853i
$893$	3.77962	−	2.18216i	0.126480	−	0.0730233i
$894$	−18.6711	−	22.2277i	−0.624456	−	0.743406i
$895$		−	8.99318i		−	0.300609i
$896$	−2.64452	+	0.0805913i	−0.0883473	+	0.00269237i
$897$	1.27881	−	3.51925i	0.0426982	−	0.117504i
$898$	10.8676	−	18.8233i	0.362657	−	0.628141i
$899$	−1.63072	−	2.82450i	−0.0543877	−	0.0942022i
$900$	−1.46156	+	8.34007i	−0.0487185	+	0.278002i
$901$	−14.4816	−	8.36098i	−0.482454	−	0.278545i
$902$	3.37853			0.112493
$903$	−28.0207	+	25.0319i	−0.932471	+	0.833011i
$904$	−4.53409			−0.150802
$905$	−23.2691	−	13.4344i	−0.773489	−	0.446574i
$906$	4.57361	+	25.8589i	0.151948	+	0.859104i
$907$	11.4807	+	19.8851i	0.381210	+	0.660274i	0.991235	−	0.132107i	$-0.0421743\pi$
$907$	11.4807	+	19.8851i	0.381210	+	0.660274i	−0.610026	+	0.792382i	$0.708841\pi$
$908$	−4.12234	+	7.14010i	−0.136805	+	0.236953i
$909$	−20.6406	−	17.2827i	−0.684607	−	0.573230i
$910$	−3.43909	−	1.84823i	−0.114005	−	0.0612683i
$911$		−	14.0418i		−	0.465225i	−0.972570	−	0.232612i	$-0.925273\pi$
$911$		−	14.0418i		−	0.465225i	0.972570	−	0.232612i	$-0.0747274\pi$
$912$	2.81187	−	2.36195i	0.0931102	−	0.0782121i
$913$	10.3013	−	5.94746i	0.340923	−	0.196832i
$914$	7.52596	−	4.34511i	0.248937	−	0.143724i
$915$	8.17220	−	6.86460i	0.270165	−	0.226937i
$916$		−	7.97255i		−	0.263421i
$917$	−1.13574	−	37.2683i	−0.0375056	−	1.23071i
$918$	−3.28219	−	5.66431i	−0.108329	−	0.186950i
$919$	4.86603	−	8.42821i	0.160516	−	0.278021i	−0.774538	−	0.632527i	$-0.782018\pi$
$919$	4.86603	−	8.42821i	0.160516	−	0.278021i	0.935054	+	0.354506i	$0.115351\pi$
$920$	1.59507	+	2.76275i	0.0525880	+	0.0910851i
$921$	−2.26728	−	12.8190i	−0.0747094	−	0.422402i
$922$	30.4115	+	17.5581i	1.00155	+	0.578244i
$923$	−4.81777			−0.158579
$924$	−3.19600	+	0.666259i	−0.105141	+	0.0219183i
$925$	4.16918			0.137082
$926$	−18.1761	−	10.4940i	−0.597305	−	0.344854i
$927$	16.8939	+	2.96057i	0.554868	+	0.0972379i
$928$	−0.988443	−	1.71203i	−0.0324472	−	0.0562002i
$929$	8.24313	−	14.2775i	0.270448	−	0.468430i	−0.698528	−	0.715582i	$-0.746161\pi$
$929$	8.24313	−	14.2775i	0.270448	−	0.468430i	0.968977	+	0.247152i	$0.0794947\pi$
$930$	1.44014	−	3.96322i	0.0472241	−	0.129959i
$931$	−12.3772	+	8.18949i	−0.405645	+	0.268400i
$932$			26.2186i			0.858818i
$933$	−6.85550	−	8.16136i	−0.224439	−	0.267191i
$934$	−29.9621	+	17.2987i	−0.980391	+	0.566029i
$935$	−1.14706	+	0.662255i	−0.0375129	+	0.0216581i
$936$	−2.81800	+	1.02902i	−0.0921092	+	0.0336345i
$937$			20.8956i			0.682629i	0.939949	+	0.341315i	$0.110872\pi$
$937$			20.8956i			0.682629i	−0.939949	+	0.341315i	$0.889128\pi$
$938$	−9.76748	−	15.7868i	−0.318919	−	0.515458i
$939$	−42.3332	−	15.3829i	−1.38149	−	0.502001i
$940$	1.51882	−	2.63067i	0.0495384	−	0.0858031i
$941$	−9.05103	−	15.6768i	−0.295055	−	0.511051i	0.679943	−	0.733265i	$-0.262005\pi$
$941$	−9.05103	−	15.6768i	−0.295055	−	0.511051i	−0.974998	+	0.222215i	$0.928671\pi$
$942$	−26.5574	+	4.69715i	−0.865285	+	0.153041i
$943$	8.87860	+	5.12606i	0.289127	+	0.166927i
$944$	9.76184			0.317721
$945$	10.7012	+	17.2352i	0.348110	+	0.560662i
$946$	5.84125			0.189915
$947$	33.3244	+	19.2399i	1.08290	+	0.625212i	0.931677	−	0.363288i	$-0.118346\pi$
$947$	33.3244	+	19.2399i	1.08290	+	0.625212i	0.151222	+	0.988500i	$0.451679\pi$
$948$	3.42552	−	0.605865i	0.111256	−	0.0196776i
$949$	−0.760465	−	1.31716i	−0.0246857	−	0.0427570i
$950$	2.99198	−	5.18226i	0.0970726	−	0.168135i
$951$	22.2489	+	8.08471i	0.721470	+	0.262165i
$952$	1.57796	−	2.93618i	0.0511421	−	0.0951623i
$953$		−	37.1230i		−	1.20253i	−0.799049	−	0.601265i	$-0.794663\pi$
$953$		−	37.1230i		−	1.20253i	0.799049	−	0.601265i	$-0.205337\pi$
$954$	37.4023	−	13.6578i	1.21094	−	0.442187i
$955$	−10.8921	+	6.28856i	−0.352460	+	0.203493i
$956$	−14.0046	+	8.08557i	−0.452942	+	0.261506i
$957$	−1.56898	−	1.86784i	−0.0507178	−	0.0603787i
$958$		−	38.9052i		−	1.25697i
$959$	17.6166	−	32.7800i	0.568870	−	1.05852i
$960$	0.872923	−	2.40226i	0.0281735	−	0.0775325i
$961$	−14.1391	+	24.4896i	−0.456100	+	0.789988i
$962$	0.738591	+	1.27928i	0.0238131	+	0.0412455i
$963$	−7.63560	−	1.33810i	−0.246054	−	0.0431197i
$964$	−11.4305	−	6.59939i	−0.368151	−	0.212552i
$965$	−15.4735			−0.498109
$966$	−9.40979	−	3.09822i	−0.302755	−	0.0996836i
$967$	−44.8131			−1.44109			−0.720545	−	0.693408i	$-0.756109\pi$
$967$	−44.8131			−1.44109			−0.720545	+	0.693408i	$0.756109\pi$
$968$	−9.08674	−	5.24623i	−0.292059	−	0.168620i
$969$	0.805792	+	4.55590i	0.0258858	+	0.146356i
$970$	−4.41944	−	7.65469i	−0.141900	−	0.245777i
$971$	7.29756	−	12.6397i	0.234190	−	0.405629i	−0.724847	−	0.688910i	$-0.758090\pi$
$971$	7.29756	−	12.6397i	0.234190	−	0.405629i	0.959037	+	0.283281i	$0.0914230\pi$
$972$	15.3587	+	2.66662i	0.492630	+	0.0855319i
$973$	2.13329	+	3.44795i	0.0683900	+	0.110536i
$974$		−	26.9840i		−	0.864623i
$975$	−3.74317	+	3.14424i	−0.119877	+	0.100696i
$976$	3.61623	−	2.08783i	0.115753	−	0.0668298i
$977$	−2.96708	+	1.71305i	−0.0949254	+	0.0548052i	−0.546711	−	0.837321i	$-0.684120\pi$
$977$	−2.96708	+	1.71305i	−0.0949254	+	0.0548052i	0.451786	+	0.892126i	$0.350787\pi$
$978$	31.2730	−	26.2691i	0.999999	−	0.839993i
$979$		−	2.67485i		−	0.0854885i
$980$	−4.61054	+	9.24370i	−0.147278	+	0.295279i
$981$	26.3425	+	22.0570i	0.841053	+	0.704224i
$982$	−13.5624	+	23.4908i	−0.432794	+	0.749621i
$983$	3.81097	+	6.60079i	0.121551	+	0.210533i	0.920380	−	0.391026i	$-0.127880\pi$
$983$	3.81097	+	6.60079i	0.121551	+	0.210533i	−0.798828	+	0.601559i	$0.794547\pi$
$984$	−1.43059	−	8.08845i	−0.0456055	−	0.257850i
$985$	−35.2034	−	20.3247i	−1.12167	−	0.647598i
$986$	2.49065			0.0793183
$987$	1.92510	+	9.23460i	0.0612767	+	0.293940i
$988$	2.12017			0.0674517
$989$	15.3505	+	8.86259i	0.488116	+	0.281814i
$990$	0.544407	−	3.10655i	0.0173024	−	0.0987326i
$991$	14.0329	+	24.3057i	0.445770	+	0.772096i	0.998106	−	0.0615255i	$-0.0195966\pi$
$991$	14.0329	+	24.3057i	0.445770	+	0.772096i	−0.552335	+	0.833622i	$0.686263\pi$
$992$	0.824895	−	1.42876i	0.0261904	−	0.0453632i
$993$	−4.20890	+	11.5828i	−0.133565	+	0.367568i
$994$	0.388270	+	12.7407i	0.0123152	+	0.404110i
$995$			26.6342i			0.844362i
$996$	−18.6006	−	22.1437i	−0.589381	−	0.701649i
$997$	31.0262	−	17.9130i	0.982609	−	0.567309i	0.0795519	−	0.996831i	$-0.474651\pi$
$997$	31.0262	−	17.9130i	0.982609	−	0.567309i	0.903057	+	0.429521i	$0.141318\pi$
$998$	36.6475	−	21.1584i	1.16006	−	0.669759i
$999$	−0.0120833	−	7.67565i	−0.000382298	−	0.242847i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.z.b.131.16	yes	32
3.2	odd	2		546.2.z.a.131.7	✓	32
7.3	odd	6		546.2.z.a.521.7	yes	32
21.17	even	6	inner	546.2.z.b.521.16	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.z.a.131.7	✓	32	3.2	odd	2
546.2.z.a.521.7	yes	32	7.3	odd	6
546.2.z.b.131.16	yes	32	1.1	even	1	trivial
546.2.z.b.521.16	yes	32	21.17	even	6	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.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.70558 - 0.301663i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.737837 + 1.27797i) q^{5} +(1.62791 + 0.591542i) q^{6} +(2.24993 - 1.39206i) q^{7} +1.00000i q^{8} +(2.81800 - 1.02902i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.70558 - 0.301663i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.737837 + 1.27797i) q^{5} +(1.62791 + 0.591542i) q^{6} +(2.24993 - 1.39206i) q^{7} +1.00000i q^{8} +(2.81800 - 1.02902i) q^{9} +(-1.27797 + 0.737837i) q^{10} +(-0.616972 + 0.356209i) q^{11} +(1.11404 + 1.32624i) q^{12} +1.00000i q^{13} +(2.64452 - 0.0805913i) q^{14} +(-0.872923 + 2.40226i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.629942 - 1.09109i) q^{17} +(2.95497 + 0.517844i) q^{18} +(-1.83612 - 1.06009i) q^{19} -1.47567 q^{20} +(3.41750 - 3.05298i) q^{21} -0.712418 q^{22} +(-1.87219 - 1.08091i) q^{23} +(0.301663 + 1.70558i) q^{24} +(1.41119 + 2.44426i) q^{25} +(-0.500000 + 0.866025i) q^{26} +(4.49590 - 2.60516i) q^{27} +(2.33052 + 1.25247i) q^{28} +1.97689i q^{29} +(-1.95710 + 1.64395i) q^{30} +(-1.42876 + 0.824895i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.944840 + 0.793660i) q^{33} -1.25988i q^{34} +(0.118927 + 3.90245i) q^{35} +(2.30016 + 1.92595i) q^{36} +(0.738591 - 1.27928i) q^{37} +(-1.06009 - 1.83612i) q^{38} +(0.301663 + 1.70558i) q^{39} +(-1.27797 - 0.737837i) q^{40} -4.74235 q^{41} +(4.48613 - 0.935209i) q^{42} -8.19918 q^{43} +(-0.616972 - 0.356209i) q^{44} +(-0.764168 + 4.36057i) q^{45} +(-1.08091 - 1.87219i) q^{46} +(-1.02924 + 1.78269i) q^{47} +(-0.591542 + 1.62791i) q^{48} +(3.12436 - 6.26405i) q^{49} +2.82239i q^{50} +(-1.40356 - 1.67091i) q^{51} +(-0.866025 + 0.500000i) q^{52} +(11.4944 - 6.63632i) q^{53} +(5.19615 - 0.00817995i) q^{54} -1.05130i q^{55} +(1.39206 + 2.24993i) q^{56} +(-3.45144 - 1.25417i) q^{57} +(-0.988443 + 1.71203i) q^{58} +(-4.88092 - 8.45400i) q^{59} +(-2.51688 + 0.445155i) q^{60} +(-3.61623 - 2.08783i) q^{61} -1.64979 q^{62} +(4.90785 - 6.23803i) q^{63} -1.00000 q^{64} +(-1.27797 - 0.737837i) q^{65} +(-1.21509 + 0.214910i) q^{66} +(-3.50829 - 6.07654i) q^{67} +(0.629942 - 1.09109i) q^{68} +(-3.51925 - 1.27881i) q^{69} +(-1.84823 + 3.43909i) q^{70} +4.81777i q^{71} +(1.02902 + 2.81800i) q^{72} +(-1.31716 + 0.760465i) q^{73} +(1.27928 - 0.738591i) q^{74} +(3.14424 + 3.74317i) q^{75} -2.12017i q^{76} +(-0.892281 + 1.66030i) q^{77} +(-0.591542 + 1.62791i) q^{78} +(1.00421 - 1.73934i) q^{79} +(-0.737837 - 1.27797i) q^{80} +(6.88224 - 5.79955i) q^{81} +(-4.10699 - 2.37117i) q^{82} -16.6965 q^{83} +(4.35271 + 1.43315i) q^{84} +1.85918 q^{85} +(-7.10070 - 4.09959i) q^{86} +(0.596352 + 3.37173i) q^{87} +(-0.356209 - 0.616972i) q^{88} +(-1.87730 + 3.25158i) q^{89} +(-2.84207 + 3.39428i) q^{90} +(1.39206 + 2.24993i) q^{91} -2.16182i q^{92} +(-2.18802 + 1.83793i) q^{93} +(-1.78269 + 1.02924i) q^{94} +(2.70952 - 1.56434i) q^{95} +(-1.32624 + 1.11404i) q^{96} +5.98973i q^{97} +(5.83780 - 3.86265i) q^{98} +(-1.37208 + 1.63867i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} + 24 q^{11} - 4 q^{14} - 12 q^{15} - 16 q^{16} - 4 q^{17} - 24 q^{18} + 4 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} - 16 q^{26} + 6 q^{27} - 2 q^{28} - 8 q^{30} - 6 q^{31} + 14 q^{33} - 48 q^{35} + 4 q^{36} - 16 q^{38} - 6 q^{39} + 6 q^{40} - 16 q^{41} + 14 q^{42} + 32 q^{43} + 24 q^{44} + 20 q^{45} + 16 q^{46} - 20 q^{47} - 26 q^{49} - 46 q^{51} + 60 q^{53} + 6 q^{54} - 8 q^{56} - 8 q^{57} - 10 q^{58} - 8 q^{59} - 6 q^{60} + 36 q^{61} - 36 q^{62} + 84 q^{63} - 32 q^{64} + 6 q^{65} + 36 q^{66} + 4 q^{68} + 36 q^{69} - 18 q^{70} - 24 q^{72} - 48 q^{73} + 84 q^{74} - 2 q^{75} - 52 q^{77} + 18 q^{79} - 74 q^{81} - 24 q^{83} + 8 q^{84} - 32 q^{85} + 24 q^{86} + 14 q^{87} - 6 q^{88} + 20 q^{89} + 6 q^{90} - 8 q^{91} - 40 q^{93} + 72 q^{95} - 6 q^{96} - 32 q^{98}+O(q^{100}) \) 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9 + 6 * q^10 + 24 * q^11 - 4 * q^14 - 12 * q^15 - 16 * q^16 - 4 * q^17 - 24 * q^18 + 4 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 - 16 * q^26 + 6 * q^27 - 2 * q^28 - 8 * q^30 - 6 * q^31 + 14 * q^33 - 48 * q^35 + 4 * q^36 - 16 * q^38 - 6 * q^39 + 6 * q^40 - 16 * q^41 + 14 * q^42 + 32 * q^43 + 24 * q^44 + 20 * q^45 + 16 * q^46 - 20 * q^47 - 26 * q^49 - 46 * q^51 + 60 * q^53 + 6 * q^54 - 8 * q^56 - 8 * q^57 - 10 * q^58 - 8 * q^59 - 6 * q^60 + 36 * q^61 - 36 * q^62 + 84 * q^63 - 32 * q^64 + 6 * q^65 + 36 * q^66 + 4 * q^68 + 36 * q^69 - 18 * q^70 - 24 * q^72 - 48 * q^73 + 84 * q^74 - 2 * q^75 - 52 * q^77 + 18 * q^79 - 74 * q^81 - 24 * q^83 + 8 * q^84 - 32 * q^85 + 24 * q^86 + 14 * q^87 - 6 * q^88 + 20 * q^89 + 6 * q^90 - 8 * q^91 - 40 * q^93 + 72 * q^95 - 6 * q^96 - 32 * q^98

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