LMFDB - Embedded newform 155.2.n.a.39.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [155,2,Mod(4,155)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("155.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(155, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 155 = 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	155.n (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.23768123133$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.10
Character	$\chi$	$=$	155.39
Dual form			155.2.n.a.4.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.03006 + 0.334686i) q^{2} +(-2.61471 + 0.849570i) q^{3} +(-0.669031 - 0.486079i) q^{4} +(-1.31324 - 1.80981i) q^{5} -2.97764 q^{6} +(-2.94133 + 4.04839i) q^{7} +(-1.79968 - 2.47704i) q^{8} +(3.68788 - 2.67940i) q^{9} +(-0.746995 - 2.30373i) q^{10} +(-1.13130 - 0.821939i) q^{11} +(2.16228 + 0.702567i) q^{12} +(0.605427 - 0.196715i) q^{13} +(-4.38467 + 3.18565i) q^{14} +(4.97130 + 3.61643i) q^{15} +(-0.513645 - 1.58084i) q^{16} +(1.41059 + 1.94151i) q^{17} +(4.69549 - 1.52566i) q^{18} +(-0.848048 + 2.61002i) q^{19} +(-0.00111178 + 1.84916i) q^{20} +(4.25132 - 13.0842i) q^{21} +(-0.890214 - 1.22527i) q^{22} +(-4.38062 - 6.02940i) q^{23} +(6.81005 + 4.94779i) q^{24} +(-1.55080 + 4.75342i) q^{25} +0.689462 q^{26} +(-2.51846 + 3.46636i) q^{27} +(3.93568 - 1.27878i) q^{28} +(-0.238536 + 0.734139i) q^{29} +(3.91035 + 5.38895i) q^{30} +(-3.70997 + 4.15164i) q^{31} +4.32332i q^{32} +(3.65632 + 1.18801i) q^{33} +(0.803191 + 2.47197i) q^{34} +(11.1895 + 0.00672754i) q^{35} -3.76971 q^{36} -7.89911i q^{37} +(-1.74708 + 2.40464i) q^{38} +(-1.41589 + 1.02871i) q^{39} +(-2.11956 + 6.51002i) q^{40} +(-2.21167 + 6.80681i) q^{41} +(8.75821 - 12.0546i) q^{42} +(-4.89908 - 1.59181i) q^{43} +(0.357348 + 1.09980i) q^{44} +(-9.69228 - 3.15566i) q^{45} +(-2.49433 - 7.67676i) q^{46} +(3.22464 - 1.04775i) q^{47} +(2.68606 + 3.69705i) q^{48} +(-5.57493 - 17.1579i) q^{49} +(-3.18832 + 4.37726i) q^{50} +(-5.33772 - 3.87808i) q^{51} +(-0.500668 - 0.162677i) q^{52} +(-0.788052 - 1.08466i) q^{53} +(-3.75430 + 2.72766i) q^{54} +(-0.00187998 + 3.12684i) q^{55} +15.3215 q^{56} -7.54493i q^{57} +(-0.491412 + 0.676370i) q^{58} +(-1.16069 - 3.57224i) q^{59} +(-1.56808 - 4.83595i) q^{60} -6.15910 q^{61} +(-5.21098 + 3.03475i) q^{62} +22.8110i q^{63} +(-2.47425 + 7.61494i) q^{64} +(-1.15109 - 0.837372i) q^{65} +(3.36861 + 2.44744i) q^{66} -3.34130i q^{67} -1.98459i q^{68} +(16.5764 + 12.0435i) q^{69} +(11.5235 + 3.75189i) q^{70} +(1.69553 - 1.23188i) q^{71} +(-13.2740 - 4.31298i) q^{72} +(-6.46222 + 8.89448i) q^{73} +(2.64372 - 8.13653i) q^{74} +(0.0165296 - 13.7463i) q^{75} +(1.83605 - 1.33397i) q^{76} +(6.65506 - 2.16236i) q^{77} +(-1.80274 + 0.585747i) q^{78} +(5.88488 - 4.27562i) q^{79} +(-2.18647 + 3.00562i) q^{80} +(-0.585816 + 1.80296i) q^{81} +(-4.55629 + 6.27119i) q^{82} +(8.25452 + 2.68206i) q^{83} +(-9.20423 + 6.68727i) q^{84} +(1.66131 - 5.10256i) q^{85} +(-4.51358 - 3.27931i) q^{86} -2.12221i q^{87} +4.28151i q^{88} +(-8.03470 - 5.83755i) q^{89} +(-8.92745 - 6.49437i) q^{90} +(-0.984379 + 3.02961i) q^{91} +6.16318i q^{92} +(6.17339 - 14.0072i) q^{93} +3.67223 q^{94} +(5.83733 - 1.89278i) q^{95} +(-3.67297 - 11.3042i) q^{96} +(-10.1356 + 13.9505i) q^{97} -19.5394i q^{98} -6.37441 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 2 q^{4} - 10 q^{5} - 4 q^{6} + 8 q^{9} + 4 q^{10} - 14 q^{11} - 16 q^{14} + 21 q^{15} - 22 q^{16} - 2 q^{19} - 29 q^{20} - 38 q^{21} - 30 q^{24} - 10 q^{25} + 12 q^{26} + 20 q^{29} - 30 q^{30} + 26 q^{31}+ \cdots - 52 q^{99}+O(q^{100}) $ 56 * q + 2 * q^4 - 10 * q^5 - 4 * q^6 + 8 * q^9 + 4 * q^10 - 14 * q^11 - 16 * q^14 + 21 * q^15 - 22 * q^16 - 2 * q^19 - 29 * q^20 - 38 * q^21 - 30 * q^24 - 10 * q^25 + 12 * q^26 + 20 * q^29 - 30 * q^30 + 26 * q^31 - 2 * q^34 + 24 * q^35 - 44 * q^36 - 18 * q^39 + 36 * q^40 - 20 * q^41 + 62 * q^44 + 8 * q^45 - 70 * q^46 - 42 * q^49 - 11 * q^50 + 10 * q^51 - 26 * q^54 - 30 * q^55 + 208 * q^56 - 50 * q^59 - 67 * q^60 + 56 * q^61 + 12 * q^64 - 27 * q^65 + 60 * q^66 + 34 * q^69 + 5 * q^70 - 8 * q^71 - 84 * q^74 - 38 * q^75 - 20 * q^76 + 122 * q^79 - 80 * q^80 + 42 * q^81 - 40 * q^84 - 18 * q^85 + 78 * q^86 - 28 * q^89 + 144 * q^90 - 20 * q^91 + 160 * q^94 + 9 * q^95 - 70 * q^96 - 52 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/155\mathbb{Z}\right)^\times$.

$n$	$32$	$96$
$\chi(n)$	$-1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	1.03006	+	0.334686i	0.728360	+	0.236659i	0.649644	−	0.760238i	$-0.274918\pi$
$2$	1.03006	+	0.334686i	0.728360	+	0.236659i	0.0787163	+	0.996897i	$0.474918\pi$
$3$	−2.61471	+	0.849570i	−1.50960	+	0.490500i	−0.942801	−	0.333355i	$-0.891819\pi$
$3$	−2.61471	+	0.849570i	−1.50960	+	0.490500i	−0.566801	+	0.823854i	$0.691819\pi$
$4$	−0.669031	−	0.486079i	−0.334515	−	0.243040i
$5$	−1.31324	−	1.80981i	−0.587299	−	0.809370i
$5$	−1.31324	−	1.80981i	−0.587299	−	0.809370i
$6$	−2.97764			−1.21562
$7$	−2.94133	+	4.04839i	−1.11172	+	1.53015i	−0.292855	+	0.956157i	$0.594605\pi$
$7$	−2.94133	+	4.04839i	−1.11172	+	1.53015i	−0.818862	+	0.573990i	$0.805395\pi$
$8$	−1.79968	−	2.47704i	−0.636282	−	0.875767i
$9$	3.68788	−	2.67940i	1.22929	−	0.893134i
$10$	−0.746995	−	2.30373i	−0.236221	−	0.728503i
$11$	−1.13130	−	0.821939i	−0.341100	−	0.247824i	0.404026	−	0.914748i	$-0.367611\pi$
$11$	−1.13130	−	0.821939i	−0.341100	−	0.247824i	−0.745126	+	0.666924i	$0.767611\pi$
$12$	2.16228	+	0.702567i	0.624196	+	0.202814i
$13$	0.605427	−	0.196715i	0.167915	−	0.0545590i	−0.223853	−	0.974623i	$-0.571864\pi$
$13$	0.605427	−	0.196715i	0.167915	−	0.0545590i	0.391768	+	0.920064i	$0.371864\pi$
$14$	−4.38467	+	3.18565i	−1.17185	+	0.851401i
$15$	4.97130	+	3.61643i	1.28358	+	0.933758i
$16$	−0.513645	−	1.58084i	−0.128411	−	0.395209i
$17$	1.41059	+	1.94151i	0.342118	+	0.470885i	0.945058	−	0.326901i	$-0.106004\pi$
$17$	1.41059	+	1.94151i	0.342118	+	0.470885i	−0.602941	+	0.797786i	$0.706004\pi$
$18$	4.69549	−	1.52566i	1.10674	−	0.359601i
$19$	−0.848048	+	2.61002i	−0.194556	+	0.598781i	0.805426	+	0.592697i	$0.201937\pi$
$19$	−0.848048	+	2.61002i	−0.194556	+	0.598781i	−0.999981	+	0.00608415i	$0.998063\pi$
$20$	−0.00111178	+	1.84916i	−0.000248602	+	0.413484i
$21$	4.25132	−	13.0842i	0.927714	−	2.85521i
$22$	−0.890214	−	1.22527i	−0.189794	−	0.261229i
$23$	−4.38062	−	6.02940i	−0.913422	−	1.25722i	−0.965985	−	0.258600i	$-0.916739\pi$
$23$	−4.38062	−	6.02940i	−0.913422	−	1.25722i	0.0525629	−	0.998618i	$-0.483261\pi$
$24$	6.81005	+	4.94779i	1.39010	+	1.00996i
$25$	−1.55080	+	4.75342i	−0.310160	+	0.950684i
$26$	0.689462			0.135215
$27$	−2.51846	+	3.46636i	−0.484678	+	0.667102i
$28$	3.93568	−	1.27878i	0.743773	−	0.241666i
$29$	−0.238536	+	0.734139i	−0.0442950	+	0.136326i	−0.970758	−	0.240059i	$-0.922833\pi$
$29$	−0.238536	+	0.734139i	−0.0442950	+	0.136326i	0.926463	+	0.376385i	$0.122833\pi$
$30$	3.91035	+	5.38895i	0.713930	+	0.983884i
$31$	−3.70997	+	4.15164i	−0.666331	+	0.745656i
$31$	−3.70997	+	4.15164i	−0.666331	+	0.745656i
$32$			4.32332i			0.764263i
$33$	3.65632	+	1.18801i	0.636484	+	0.206806i
$34$	0.803191	+	2.47197i	0.137746	+	0.423939i
$35$	11.1895	+	0.00672754i	1.89137	+	0.00113716i
$36$	−3.76971			−0.628285
$37$		−	7.89911i		−	1.29861i	−0.760530	−	0.649303i	$-0.775061\pi$
$37$		−	7.89911i		−	1.29861i	0.760530	−	0.649303i	$-0.224939\pi$
$38$	−1.74708	+	2.40464i	−0.283413	+	0.390085i
$39$	−1.41589	+	1.02871i	−0.226724	+	0.164725i
$40$	−2.11956	+	6.51002i	−0.335132	+	1.02932i
$41$	−2.21167	+	6.80681i	−0.345404	+	1.06305i	0.615963	+	0.787775i	$0.288767\pi$
$41$	−2.21167	+	6.80681i	−0.345404	+	1.06305i	−0.961367	+	0.275270i	$0.911233\pi$
$42$	8.75821	−	12.0546i	1.35142	−	1.86007i
$43$	−4.89908	−	1.59181i	−0.747103	−	0.242748i	−0.0893688	−	0.995999i	$-0.528485\pi$
$43$	−4.89908	−	1.59181i	−0.747103	−	0.242748i	−0.657734	+	0.753250i	$0.728485\pi$
$44$	0.357348	+	1.09980i	0.0538723	+	0.165802i
$45$	−9.69228	−	3.15566i	−1.44484	−	0.470417i
$46$	−2.49433	−	7.67676i	−0.367769	−	1.13188i
$47$	3.22464	−	1.04775i	0.470362	−	0.152830i	−0.0642386	−	0.997935i	$-0.520462\pi$
$47$	3.22464	−	1.04775i	0.470362	−	0.152830i	0.534601	+	0.845105i	$0.320462\pi$
$48$	2.68606	+	3.69705i	0.387700	+	0.533623i
$49$	−5.57493	−	17.1579i	−0.796419	−	2.45112i
$50$	−3.18832	+	4.37726i	−0.450896	+	0.619039i
$51$	−5.33772	−	3.87808i	−0.747431	−	0.543040i
$52$	−0.500668	−	0.162677i	−0.0694302	−	0.0225592i
$53$	−0.788052	−	1.08466i	−0.108247	−	0.148989i	0.751456	−	0.659783i	$-0.229352\pi$
$53$	−0.788052	−	1.08466i	−0.108247	−	0.148989i	−0.859704	+	0.510793i	$0.829352\pi$
$54$	−3.75430	+	2.72766i	−0.510896	+	0.371187i
$55$	−0.00187998	+	3.12684i	−0.000253496	+	0.421623i
$56$	15.3215			2.04742
$57$		−	7.54493i		−	0.999351i
$58$	−0.491412	+	0.676370i	−0.0645255	+	0.0888117i
$59$	−1.16069	−	3.57224i	−0.151109	−	0.465066i	0.846637	−	0.532171i	$-0.178624\pi$
$59$	−1.16069	−	3.57224i	−0.151109	−	0.465066i	−0.997746	+	0.0671049i	$0.978624\pi$
$60$	−1.56808	−	4.83595i	−0.202438	−	0.624318i
$61$	−6.15910			−0.788593			−0.394296	−	0.918983i	$-0.629012\pi$
$61$	−6.15910			−0.788593			−0.394296	+	0.918983i	$0.629012\pi$
$62$	−5.21098	+	3.03475i	−0.661795	+	0.385413i
$63$			22.8110i			2.87391i
$64$	−2.47425	+	7.61494i	−0.309281	+	0.951868i
$65$	−1.15109	−	0.837372i	−0.142775	−	0.103863i
$66$	3.36861	+	2.44744i	0.414647	+	0.301259i
$67$		−	3.34130i		−	0.408205i	−0.978950	−	0.204102i	$-0.934572\pi$
$67$		−	3.34130i		−	0.408205i	0.978950	−	0.204102i	$-0.0654275\pi$
$68$		−	1.98459i		−	0.240666i
$69$	16.5764	+	12.0435i	1.99557	+	1.44987i
$70$	11.5235	+	3.75189i	1.37733	+	0.448436i
$71$	1.69553	−	1.23188i	0.201223	−	0.146197i	−0.482611	−	0.875835i	$-0.660311\pi$
$71$	1.69553	−	1.23188i	0.201223	−	0.146197i	0.683834	+	0.729638i	$0.260311\pi$
$72$	−13.2740	−	4.31298i	−1.56436	−	0.508290i
$73$	−6.46222	+	8.89448i	−0.756346	+	1.04102i	0.241163	+	0.970485i	$0.422471\pi$
$73$	−6.46222	+	8.89448i	−0.756346	+	1.04102i	−0.997509	+	0.0705361i	$0.977529\pi$
$74$	2.64372	−	8.13653i	0.307326	−	0.945853i
$75$	0.0165296	−	13.7463i	0.00190868	−	1.58729i
$76$	1.83605	−	1.33397i	0.210609	−	0.153017i
$77$	6.65506	−	2.16236i	0.758414	−	0.246424i
$78$	−1.80274	+	0.585747i	−0.204120	+	0.0663228i
$79$	5.88488	−	4.27562i	0.662101	−	0.481045i	−0.205271	−	0.978705i	$-0.565807\pi$
$79$	5.88488	−	4.27562i	0.662101	−	0.481045i	0.867372	+	0.497661i	$0.165807\pi$
$80$	−2.18647	+	3.00562i	−0.244455	+	0.336038i
$81$	−0.585816	+	1.80296i	−0.0650907	+	0.200329i
$82$	−4.55629	+	6.27119i	−0.503158	+	0.692537i
$83$	8.25452	+	2.68206i	0.906052	+	0.294394i	0.724733	−	0.689030i	$-0.241963\pi$
$83$	8.25452	+	2.68206i	0.906052	+	0.294394i	0.181319	+	0.983424i	$0.441963\pi$
$84$	−9.20423	+	6.68727i	−1.00426	+	0.729641i
$85$	1.66131	−	5.10256i	0.180195	−	0.553450i
$86$	−4.51358	−	3.27931i	−0.486712	−	0.353617i
$87$		−	2.12221i		−	0.227525i
$88$			4.28151i			0.456410i
$89$	−8.03470	−	5.83755i	−0.851676	−	0.618779i	0.0739315	−	0.997263i	$-0.476445\pi$
$89$	−8.03470	−	5.83755i	−0.851676	−	0.618779i	−0.925608	+	0.378484i	$0.876445\pi$
$90$	−8.92745	−	6.49437i	−0.941035	−	0.684567i
$91$	−0.984379	+	3.02961i	−0.103191	+	0.317589i
$92$			6.16318i			0.642556i
$93$	6.17339	−	14.0072i	0.640151	−	1.45248i
$94$	3.67223			0.378762
$95$	5.83733	−	1.89278i	0.598898	−	0.194196i
$96$	−3.67297	−	11.3042i	−0.374871	−	1.15373i
$97$	−10.1356	+	13.9505i	−1.02912	+	1.41646i	−0.123509	+	0.992343i	$0.539415\pi$
$97$	−10.1356	+	13.9505i	−1.02912	+	1.41646i	−0.905608	+	0.424115i	$0.860585\pi$
$98$		−	19.5394i		−	1.97378i
$99$	−6.37441			−0.640653
$100$	3.34807	−	2.42637i	0.334807	−	0.242637i
$101$	2.82366	−	2.05151i	0.280965	−	0.204133i	−0.438373	−	0.898793i	$-0.644445\pi$
$101$	2.82366	−	2.05151i	0.280965	−	0.204133i	0.719338	+	0.694660i	$0.244445\pi$
$102$	−4.20022	−	5.78111i	−0.415884	−	0.572415i
$103$	7.82683	+	2.54309i	0.771200	+	0.250578i	0.668079	−	0.744091i	$-0.267117\pi$
$103$	7.82683	+	2.54309i	0.771200	+	0.250578i	0.103122	+	0.994669i	$0.467117\pi$
$104$	−1.57684	−	1.14564i	−0.154622	−	0.112340i
$105$	−29.2629	+	9.48865i	−2.85577	+	0.925998i
$106$	−0.448718	−	1.38101i	−0.0435833	−	0.134136i
$107$	3.49058	+	4.80437i	0.337447	+	0.464456i	0.943694	−	0.330821i	$-0.107326\pi$
$107$	3.49058	+	4.80437i	0.337447	+	0.464456i	−0.606247	+	0.795277i	$0.707326\pi$
$108$	3.36985	−	1.09493i	0.324264	−	0.105360i
$109$	3.44220	+	10.5940i	0.329703	+	1.01472i	0.969273	+	0.245988i	$0.0791125\pi$
$109$	3.44220	+	10.5940i	0.329703	+	1.01472i	−0.639570	+	0.768733i	$0.720887\pi$
$110$	−1.04845	+	3.22020i	−0.0999654	+	0.307034i
$111$	6.71085	+	20.6539i	0.636966	+	1.96038i
$112$	7.91064	+	2.57032i	0.747485	+	0.242873i
$113$	−7.29991	+	10.0475i	−0.686718	+	0.945186i	−0.999990	−	0.00447704i	$-0.998575\pi$
$113$	−7.29991	+	10.0475i	−0.686718	+	0.945186i	0.313272	+	0.949664i	$0.398575\pi$
$114$	2.52518	−	7.77171i	0.236505	−	0.727887i
$115$	−5.15925	+	15.8461i	−0.481103	+	1.47766i
$116$	0.516437	−	0.375214i	0.0479500	−	0.0348377i
$117$	1.70566	−	2.34765i	0.157689	−	0.217040i
$118$		−	4.06808i		−	0.374497i
$119$	−12.0090			−1.10086
$120$	0.0113168	−	18.8225i	0.00103308	−	1.71825i
$121$	−2.79493	−	8.60190i	−0.254084	−	0.781991i
$122$	−6.34423	−	2.06137i	−0.574380	−	0.186627i
$123$		−	19.6768i		−	1.77420i
$124$	4.50011	−	0.974232i	0.404122	−	0.0874886i
$125$	10.6393	−	3.43573i	0.951612	−	0.307301i
$126$	−7.63451	+	23.4966i	−0.680137	+	2.09324i
$127$	−10.0823	+	3.27595i	−0.894662	+	0.290693i	−0.720032	−	0.693941i	$-0.755873\pi$
$127$	−10.0823	+	3.27595i	−0.894662	+	0.290693i	−0.174630	+	0.984634i	$0.555873\pi$
$128$	−0.0148564	+	0.0204481i	−0.00131313	+	0.00180737i
$129$	14.1620			1.24690
$130$	−0.905429	−	1.24779i	−0.0794114	−	0.109439i
$131$	3.13546	+	2.27805i	0.273947	+	0.199034i	0.716273	−	0.697820i	$-0.245847\pi$
$131$	3.13546	+	2.27805i	0.273947	+	0.199034i	−0.442326	+	0.896854i	$0.645847\pi$
$132$	−1.86872	−	2.57208i	−0.162651	−	0.223871i
$133$	−8.07201	−	11.1102i	−0.699932	−	0.963373i
$134$	1.11829	−	3.44173i	0.0966052	−	0.297320i
$135$	9.58079	+	0.00576034i	0.824583	+	0.000495771i
$136$	2.27059	−	6.98817i	0.194702	−	0.599231i
$137$	20.8193	−	6.76461i	1.77872	−	0.577940i	0.779869	−	0.625943i	$-0.215286\pi$
$137$	20.8193	−	6.76461i	1.77872	−	0.577940i	0.998847	+	0.0480027i	$0.0152856\pi$
$138$	13.0439	+	17.9534i	1.11037	+	1.52829i
$139$	−1.65531	−	5.09453i	−0.140402	−	0.432112i	0.855989	−	0.516994i	$-0.172949\pi$
$139$	−1.65531	−	5.09453i	−0.140402	−	0.432112i	−0.996391	+	0.0848813i	$0.972949\pi$
$140$	−7.48283	−	5.44347i	−0.632414	−	0.460057i
$141$	−7.54136	+	5.47912i	−0.635097	+	0.461425i
$142$	2.15879	−	0.701433i	0.181162	−	0.0588630i
$143$	−0.846608	−	0.275080i	−0.0707970	−	0.0230033i
$144$	−6.12996	−	4.45368i	−0.510830	−	0.371140i
$145$	1.64190	−	0.532396i	0.136353	−	0.0442131i
$146$	−9.63332	+	6.99901i	−0.797259	+	0.579242i
$147$	29.1536	+	40.1265i	2.40455	+	3.30958i
$148$	−3.83959	+	5.28475i	−0.315613	+	0.434404i
$149$	1.57437			0.128977			0.0644886	−	0.997918i	$-0.479458\pi$
$149$	1.57437			0.128977			0.0644886	+	0.997918i	$0.479458\pi$
$150$	4.61773	−	14.1540i	0.377036	−	1.15567i
$151$	6.94745	+	5.04761i	0.565375	+	0.410769i	0.833422	−	0.552637i	$-0.186378\pi$
$151$	6.94745	+	5.04761i	0.565375	+	0.410769i	−0.268047	+	0.963406i	$0.586378\pi$
$152$	7.99136	−	2.59655i	0.648185	−	0.210608i
$153$	10.4042	+	3.38052i	0.841127	+	0.273299i
$154$	7.57880			0.610717
$155$	12.3857	+	1.26224i	0.994847	+	0.101385i
$156$	1.44731			0.115877
$157$	−8.00189	−	2.59997i	−0.638620	−	0.207500i	−0.0282303	−	0.999601i	$-0.508987\pi$
$157$	−8.00189	−	2.59997i	−0.638620	−	0.207500i	−0.610390	+	0.792101i	$0.708987\pi$
$158$	7.49276	−	2.43454i	0.596092	−	0.193682i
$159$	2.98202	+	2.16656i	0.236490	+	0.171820i
$160$	7.82438	−	5.67756i	0.618572	−	0.448851i
$161$	37.2942			2.93919
$162$	−1.20685	+	1.66108i	−0.0948190	+	0.130507i
$163$	1.73630	+	2.38981i	0.135997	+	0.187184i	0.871584	−	0.490247i	$-0.163093\pi$
$163$	1.73630	+	2.38981i	0.135997	+	0.187184i	−0.735587	+	0.677431i	$0.763093\pi$
$164$	4.78832	−	3.47892i	0.373905	−	0.271658i
$165$	−2.65156	−	8.17737i	−0.206423	−	0.636608i
$166$	7.60498	+	5.52534i	0.590261	+	0.428850i
$167$	−9.95936	−	3.23599i	−0.770678	−	0.250409i	−0.102823	−	0.994700i	$-0.532787\pi$
$167$	−9.95936	−	3.23599i	−0.770678	−	0.250409i	−0.667855	+	0.744291i	$0.732787\pi$
$168$	−40.0612	+	13.0167i	−3.09079	+	1.00426i
$169$	−10.1894	+	7.40301i	−0.783798	+	0.569463i
$170$	3.41900	−	4.69991i	0.262225	−	0.360466i
$171$	3.86581	+	11.8977i	0.295626	+	0.909842i
$172$	2.50389	+	3.44631i	0.190920	+	0.262779i
$173$	−4.05518	+	1.31761i	−0.308310	+	0.100176i	−0.459086	−	0.888392i	$-0.651823\pi$
$173$	−4.05518	+	1.31761i	−0.308310	+	0.100176i	0.150776	+	0.988568i	$0.451823\pi$
$174$	0.710274	−	2.18600i	0.0538458	−	0.165720i
$175$	−14.6823	−	20.2596i	−1.10988	−	1.53148i
$176$	−0.718264	+	2.21059i	−0.0541411	+	0.166629i
$177$	6.06974	+	8.35429i	0.456230	+	0.627947i
$178$	−6.32245	−	8.70211i	−0.473888	−	0.652251i
$179$	−2.38375	−	1.73189i	−0.178170	−	0.129448i	0.495126	−	0.868821i	$-0.335122\pi$
$179$	−2.38375	−	1.73189i	−0.178170	−	0.129448i	−0.673296	+	0.739373i	$0.735122\pi$
$180$	4.95053	+	6.82245i	0.368991	+	0.508515i
$181$	0.445493			0.0331132			0.0165566	−	0.999863i	$-0.494730\pi$
$181$	0.445493			0.0331132			0.0165566	+	0.999863i	$0.494730\pi$
$182$	−2.02793	+	2.79121i	−0.150320	+	0.206898i
$183$	16.1043	−	5.23259i	1.19046	−	0.386804i
$184$	−7.05139	+	21.7019i	−0.519835	+	1.59989i
$185$	−14.2959	+	10.3734i	−1.05105	+	0.762669i
$186$	11.0470	−	12.3621i	0.810003	−	0.906432i
$187$		−	3.35585i		−	0.245404i
$188$	−2.66667	−	0.866455i	−0.194487	−	0.0631927i
$189$	−6.62557	−	20.3914i	−0.481939	−	1.48326i
$190$	6.64627	+	0.00399600i	0.482171	+	0.000289900i
$191$	−23.6564			−1.71172			−0.855858	−	0.517211i	$-0.826970\pi$
$191$	−23.6564			−1.71172			−0.855858	+	0.517211i	$0.826970\pi$
$192$		−	22.0129i		−	1.58864i
$193$	11.4037	−	15.6959i	0.820860	−	1.12982i	−0.168696	−	0.985668i	$-0.553956\pi$
$193$	11.4037	−	15.6959i	0.820860	−	1.12982i	0.989556	−	0.144148i	$-0.0460442\pi$
$194$	−15.1093	+	10.9776i	−1.08479	+	0.788143i
$195$	3.72116	+	1.21155i	0.266478	+	0.0867612i
$196$	−4.61029	+	14.1890i	−0.329306	+	1.01350i
$197$	6.44933	−	8.87674i	0.459496	−	0.632442i	−0.514908	−	0.857245i	$-0.672174\pi$
$197$	6.44933	−	8.87674i	0.459496	−	0.632442i	0.974404	+	0.224803i	$0.0721740\pi$
$198$	−6.56601	−	2.13343i	−0.466626	−	0.151616i
$199$	−3.19700	−	9.83935i	−0.226629	−	0.697493i	−0.998122	−	0.0612552i	$-0.980490\pi$
$199$	−3.19700	−	9.83935i	−0.226629	−	0.697493i	0.771493	−	0.636238i	$-0.219510\pi$
$200$	14.5654	−	4.71322i	1.02993	−	0.333275i
$201$	2.83867	+	8.73652i	0.200224	+	0.616227i
$202$	3.59514	−	1.16813i	0.252953	−	0.0821895i
$203$	−2.27047	−	3.12503i	−0.159355	−	0.219334i
$204$	1.68605	+	5.18911i	0.118047	+	0.363311i
$205$	15.2235	−	4.93628i	1.06325	−	0.344765i
$206$	7.21095	+	5.23906i	0.502410	+	0.365022i
$207$	−32.3104	−	10.4983i	−2.24573	−	0.729681i
$208$	−0.621949	−	0.856039i	−0.0431244	−	0.0593557i
$209$	3.10468	−	2.25568i	0.214755	−	0.156029i
$210$	−33.3182	−	0.0200322i	−2.29917	−	0.00138235i
$211$	−14.8291			−1.02088			−0.510440	−	0.859913i	$-0.670518\pi$
$211$	−14.8291			−1.02088			−0.510440	+	0.859913i	$0.670518\pi$
$212$			1.10873i			0.0761476i
$213$	−3.38676	+	4.66148i	−0.232057	+	0.319399i
$214$	1.98754	+	6.11702i	0.135866	+	0.418151i
$215$	3.55280	+	10.9568i	0.242299	+	0.747249i
$216$	13.1187			0.892617
$217$	−5.89520	−	27.2307i	−0.400192	−	1.84854i
$218$			12.0645i			0.817110i
$219$	9.34034	−	28.7466i	0.631161	−	1.94252i
$220$	1.52115	−	2.09104i	0.102556	−	0.140978i
$221$	1.23593	+	0.897957i	0.0831378	+	0.0604031i
$222$			23.5207i			1.57861i
$223$		−	13.4811i		−	0.902758i	−0.892332	−	0.451379i	$-0.850932\pi$
$223$		−	13.4811i		−	0.902758i	0.892332	−	0.451379i	$-0.149068\pi$
$224$	−17.5025	−	12.7163i	−1.16943	−	0.849644i
$225$	7.01716	+	21.6853i	0.467810	+	1.44569i
$226$	−10.8821	+	7.90629i	−0.723865	+	0.525919i
$227$	−20.9487	−	6.80665i	−1.39042	−	0.451773i	−0.484336	−	0.874882i	$-0.660939\pi$
$227$	−20.9487	−	6.80665i	−1.39042	−	0.451773i	−0.906079	+	0.423109i	$0.860939\pi$
$228$	−3.66743	+	5.04779i	−0.242882	+	0.334298i
$229$	1.32263	−	4.07064i	0.0874019	−	0.268995i	−0.897797	−	0.440409i	$-0.854833\pi$
$229$	1.32263	−	4.07064i	0.0874019	−	0.268995i	0.985199	+	0.171414i	$0.0548334\pi$
$230$	−10.6178	+	14.5957i	−0.700117	+	0.962411i
$231$	−15.5640	+	11.3079i	−1.02403	+	0.744004i
$232$	2.24778	−	0.730348i	0.147574	−	0.0479497i
$233$	−15.7304	+	5.11113i	−1.03053	+	0.334841i	−0.775002	−	0.631959i	$-0.782251\pi$
$233$	−15.7304	+	5.11113i	−1.03053	+	0.334841i	−0.255533	+	0.966800i	$0.582251\pi$
$234$	2.54266	−	1.84735i	0.166219	−	0.120765i
$235$	−6.13095	−	4.46003i	−0.399939	−	0.290940i
$236$	−0.959855	+	2.95413i	−0.0624812	+	0.192297i
$237$	−11.7548	+	16.1791i	−0.763558	+	1.05095i
$238$	−12.3699	−	4.01923i	−0.801824	−	0.260528i
$239$	12.1116	−	8.79963i	0.783437	−	0.569201i	−0.122571	−	0.992460i	$-0.539114\pi$
$239$	12.1116	−	8.79963i	0.783437	−	0.569201i	0.906009	+	0.423259i	$0.139114\pi$
$240$	3.16350	−	9.71637i	0.204203	−	0.627189i
$241$	10.4677	+	7.60519i	0.674281	+	0.489894i	0.871455	−	0.490475i	$-0.163177\pi$
$241$	10.4677	+	7.60519i	0.674281	+	0.489894i	−0.197175	+	0.980368i	$0.563177\pi$
$242$		−	9.79587i		−	0.629703i
$243$		−	18.0659i		−	1.15893i
$244$	4.12063	+	2.99381i	0.263796	+	0.191659i
$245$	−23.7312	+	32.6219i	−1.51613	+	2.08414i
$246$	6.58555	−	20.2682i	0.419879	−	1.29225i
$247$			1.74700i			0.111159i
$248$	16.9605	+	1.71816i	1.07700	+	0.109103i
$249$	−23.8618			−1.51218
$250$	12.1090	+	0.0218413i	0.765842	+	0.00138136i
$251$	−4.44076	−	13.6673i	−0.280298	−	0.862670i	−0.987769	−	0.155927i	$-0.950164\pi$
$251$	−4.44076	−	13.6673i	−0.280298	−	0.862670i	0.707470	−	0.706743i	$-0.249836\pi$
$252$	11.0879	−	15.2612i	0.698475	−	0.961368i
$253$			10.4217i			0.655205i
$254$	−11.4818			−0.720432
$255$	−0.00887013	+	14.7531i	−0.000555469	+	0.923875i
$256$	12.9332	−	9.39650i	0.808323	−	0.587281i
$257$	11.6567	+	16.0441i	0.727128	+	1.00081i	0.999257	+	0.0385449i	$0.0122723\pi$
$257$	11.6567	+	16.0441i	0.727128	+	1.00081i	−0.272129	+	0.962261i	$0.587728\pi$
$258$	14.5877	+	4.73983i	0.908190	+	0.295089i
$259$	31.9787	+	23.2339i	1.98706	+	1.44368i
$260$	0.363084	+	1.11975i	0.0225175	+	0.0694438i
$261$	1.08736	+	3.34655i	0.0673059	+	0.207146i
$262$	2.46728	+	3.39592i	0.152429	+	0.209800i
$263$	0.0776412	−	0.0252272i	0.00478756	−	0.00155557i	−0.306622	−	0.951831i	$-0.599199\pi$
$263$	0.0776412	−	0.0252272i	0.00478756	−	0.00155557i	0.311410	+	0.950276i	$0.399199\pi$
$264$	−3.63744	−	11.1949i	−0.223869	−	0.688998i
$265$	−0.928124	+	2.85064i	−0.0570142	+	0.175113i
$266$	−4.59621	−	14.1457i	−0.281812	−	0.867328i
$267$	25.9678	+	8.43745i	1.58920	+	0.516364i
$268$	−1.62414	+	2.23543i	−0.0992099	+	0.136551i
$269$	3.59930	−	11.0775i	0.219453	−	0.675408i	−0.779354	−	0.626584i	$-0.784453\pi$
$269$	3.59930	−	11.0775i	0.219453	−	0.675408i	0.998807	−	0.0488240i	$-0.0155474\pi$
$270$	9.86683	+	3.21249i	0.600476	+	0.195506i
$271$	−5.81128	+	4.22214i	−0.353010	+	0.256477i	−0.750131	−	0.661290i	$-0.770009\pi$
$271$	−5.81128	+	4.22214i	−0.353010	+	0.256477i	0.397121	+	0.917766i	$0.370009\pi$
$272$	2.34466	−	3.22715i	0.142166	−	0.195675i
$273$		−	8.75784i		−	0.530049i
$274$	23.7091			1.43232
$275$	5.66145	−	4.10289i	0.341398	−	0.247414i
$276$	−5.23606	−	16.1149i	−0.315174	−	0.970005i
$277$	−14.8519	−	4.82569i	−0.892366	−	0.289947i	−0.173284	−	0.984872i	$-0.555438\pi$
$277$	−14.8519	−	4.82569i	−0.892366	−	0.289947i	−0.719083	+	0.694925i	$0.755438\pi$
$278$		−	5.80167i		−	0.347961i
$279$	−2.55803	+	25.2513i	−0.153145	+	1.51175i
$280$	−20.1208	−	27.7289i	−1.20245	−	1.65712i
$281$	−3.75049	+	11.5428i	−0.223735	+	0.688586i	0.774682	+	0.632351i	$0.217910\pi$
$281$	−3.75049	+	11.5428i	−0.223735	+	0.688586i	−0.998418	+	0.0562356i	$0.982090\pi$
$282$	−9.60182	+	3.11982i	−0.571780	+	0.185783i
$283$	−3.32278	+	4.57342i	−0.197519	+	0.271861i	−0.896275	−	0.443498i	$-0.853737\pi$
$283$	−3.32278	+	4.57342i	−0.197519	+	0.271861i	0.698756	+	0.715360i	$0.253737\pi$
$284$	−1.73315			−0.102844
$285$	−13.6549	+	9.90831i	−0.808845	+	0.586917i
$286$	−0.779990	−	0.566696i	−0.0461218	−	0.0335094i
$287$	−21.0514	−	28.9747i	−1.24262	−	1.71032i
$288$	11.5839	+	15.9439i	0.682590	+	0.939504i
$289$	3.47360	−	10.6906i	0.204329	−	0.628861i
$290$	1.86944	+	0.00112398i	0.109777	+	6.60023e-5i
$291$	14.6498	−	45.0874i	0.858786	−	2.64307i
$292$	8.64685	−	2.80953i	0.506019	−	0.164415i
$293$	9.74536	+	13.4133i	0.569330	+	0.783616i	0.992475	−	0.122446i	$-0.0390739\pi$
$293$	9.74536	+	13.4133i	0.569330	+	0.783616i	−0.423145	+	0.906062i	$0.639074\pi$
$294$	16.6001	+	51.0900i	0.968139	+	2.97963i
$295$	−4.94080	+	6.79184i	−0.287665	+	0.395436i
$296$	−19.5664	+	14.2158i	−1.13728	+	0.826279i
$297$	5.69828	−	1.85148i	0.330648	−	0.107434i
$298$	1.62169	+	0.526919i	0.0939419	+	0.0305236i
$299$	−3.83822	−	2.78863i	−0.221970	−	0.161271i
$300$	−6.69286	+	9.18868i	−0.386413	+	0.530509i
$301$	20.8541	−	15.1514i	1.20201	−	0.873310i
$302$	5.46690	+	7.52454i	0.314585	+	0.432989i
$303$	−5.64015	+	7.76299i	−0.324018	+	0.445972i
$304$	4.56162			0.261627
$305$	8.08838	+	11.1468i	0.463139	+	0.638263i
$306$	9.58547	+	6.96425i	0.547965	+	0.398120i
$307$	1.01481	−	0.329733i	0.0579185	−	0.0188189i	−0.279914	−	0.960025i	$-0.590306\pi$
$307$	1.01481	−	0.329733i	0.0579185	−	0.0188189i	0.337833	+	0.941206i	$0.390306\pi$
$308$	−5.50351	−	1.78820i	−0.313592	−	0.101892i
$309$	−22.6254			−1.28711
$310$	12.3356	+	5.44551i	0.700614	+	0.309284i
$311$	−20.0217			−1.13532			−0.567662	−	0.823262i	$-0.692152\pi$
$311$	−20.0217			−1.13532			−0.567662	+	0.823262i	$0.692152\pi$
$312$	5.09630	+	1.65589i	0.288521	+	0.0937461i
$313$	−18.3388	+	5.95865i	−1.03657	+	0.336803i	−0.777385	−	0.629025i	$-0.783454\pi$
$313$	−18.3388	+	5.95865i	−1.03657	+	0.336803i	−0.259187	+	0.965827i	$0.583454\pi$
$314$	−7.37223	−	5.35624i	−0.416039	−	0.302270i
$315$	41.2835	−	29.9563i	2.32606	−	1.68785i
$316$	−6.01546			−0.338396
$317$	13.7506	−	18.9260i	0.772309	−	1.06299i	−0.223781	−	0.974640i	$-0.571840\pi$
$317$	13.7506	−	18.9260i	0.772309	−	1.06299i	0.996089	−	0.0883523i	$-0.0281601\pi$
$318$	2.34653	+	3.22973i	0.131587	+	0.181114i
$319$	0.873273	−	0.634470i	0.0488939	−	0.0355235i
$320$	17.0309	−	5.52234i	0.952054	−	0.308708i
$321$	−13.2085	−	9.59654i	−0.737226	−	0.535626i
$322$	38.4151	+	12.4818i	2.14079	+	0.695586i
$323$	−6.26363	+	2.03518i	−0.348518	+	0.113240i
$324$	1.26831	−	0.921481i	0.0704616	−	0.0511934i
$325$	−0.00382738	+	3.18292i	−0.000212305	+	0.176556i
$326$	0.988649	+	3.04275i	0.0547562	+	0.168522i
$327$	−18.0007	−	24.7758i	−0.995441	−	1.37011i
$328$	20.8410	−	6.77167i	1.15075	−	0.373903i
$329$	−5.24303	+	16.1364i	−0.289057	+	0.889627i
$330$	0.00559789	−	9.31060i	0.000308154	−	0.512532i
$331$	−6.55241	+	20.1663i	−0.360153	+	1.10844i	0.592808	+	0.805344i	$0.298019\pi$
$331$	−6.55241	+	20.1663i	−0.360153	+	1.10844i	−0.952961	+	0.303094i	$0.901981\pi$
$332$	−4.21884	−	5.80673i	−0.231539	−	0.318686i
$333$	−21.1649	−	29.1310i	−1.15983	−	1.59637i
$334$	−9.17567	−	6.66651i	−0.502070	−	0.364775i
$335$	−6.04711	+	4.38793i	−0.330389	+	0.239738i
$336$	−22.8677			−1.24753
$337$	−7.51736	+	10.3468i	−0.409497	+	0.563624i	−0.963096	−	0.269160i	$-0.913254\pi$
$337$	−7.51736	+	10.3468i	−0.409497	+	0.563624i	0.553599	+	0.832783i	$0.313254\pi$
$338$	−12.9733	+	4.21529i	−0.705656	+	0.229281i
$339$	10.5511	−	32.4730i	0.573058	−	1.76369i
$340$	−3.59172	+	2.60624i	−0.194788	+	0.141343i
$341$	7.60949	−	1.64738i	0.412077	−	0.0892108i
$342$			13.5492i			0.732655i
$343$	52.5453	+	17.0730i	2.83718	+	0.921855i
$344$	4.87379	+	15.0000i	0.262777	+	0.808744i
$345$	0.0275464	−	45.8161i	0.00148305	−	2.46666i
$346$	−4.61806			−0.248268
$347$			34.2904i			1.84080i	0.390974	+	0.920402i	$0.372138\pi$
$347$			34.2904i			1.84080i	−0.390974	+	0.920402i	$0.627862\pi$
$348$	−1.03156	+	1.41982i	−0.0552976	+	0.0761106i
$349$	0.843868	−	0.613106i	0.0451712	−	0.0328188i	−0.564971	−	0.825111i	$-0.691112\pi$
$349$	0.843868	−	0.613106i	0.0451712	−	0.0328188i	0.610142	+	0.792292i	$0.291112\pi$
$350$	−8.34298	−	25.7825i	−0.445951	−	1.37813i
$351$	−0.842858	+	2.59405i	−0.0449884	+	0.138460i
$352$	3.55351	−	4.89098i	0.189403	−	0.260690i
$353$	2.79985	+	0.909726i	0.149021	+	0.0484198i	0.382578	−	0.923923i	$-0.375036\pi$
$353$	2.79985	+	0.909726i	0.149021	+	0.0484198i	−0.233557	+	0.972343i	$0.575036\pi$
$354$	3.45612	+	10.6369i	0.183691	+	0.565342i
$355$	−4.45610	−	1.45084i	−0.236505	−	0.0770025i
$356$	2.53795	+	7.81100i	0.134511	+	0.413982i
$357$	31.4000	−	10.2025i	1.66186	−	0.539972i
$358$	−1.87576	−	2.58176i	−0.0991368	−	0.136450i
$359$	−1.18848	−	3.65778i	−0.0627258	−	0.193050i	0.914783	−	0.403946i	$-0.132362\pi$
$359$	−1.18848	−	3.65778i	−0.0627258	−	0.193050i	−0.977508	+	0.210896i	$0.932362\pi$
$360$	9.62627	+	29.6873i	0.507349	+	1.56466i
$361$	9.27828	+	6.74107i	0.488331	+	0.354793i
$362$	0.458883	+	0.149100i	0.0241183	+	0.00783653i
$363$	14.6158	+	20.1170i	0.767133	+	1.05587i
$364$	2.13121	−	1.54841i	0.111706	−	0.0811590i
$365$	24.5837	+	0.0147807i	1.28677	+	0.000773657i
$366$	18.3396			0.958626
$367$			5.51281i			0.287766i	0.989595	+	0.143883i	$0.0459589\pi$
$367$			5.51281i			0.287766i	−0.989595	+	0.143883i	$0.954041\pi$
$368$	−7.28142	+	10.0220i	−0.379570	+	0.522433i
$369$	10.0818	+	31.0287i	0.524839	+	1.61529i
$370$	−18.1974	+	5.90060i	−0.946038	+	0.306758i
$371$	6.70904			0.348316
$372$	−10.9388	+	6.37050i	−0.567151	+	0.330295i
$373$		−	0.532637i		−	0.0275789i	−0.999905	−	0.0137895i	$-0.995611\pi$
$373$		−	0.532637i		−	0.0275789i	0.999905	−	0.0137895i	$-0.00438946\pi$
$374$	1.12315	−	3.45671i	0.0580769	−	0.178742i
$375$	−24.8999	+	18.0223i	−1.28583	+	0.930668i
$376$	−8.39864	−	6.10197i	−0.433127	−	0.314685i
$377$			0.491391i			0.0253079i
$378$		−	23.2218i		−	1.19440i
$379$	−5.95047	−	4.32327i	−0.305655	−	0.222071i	0.424375	−	0.905487i	$-0.360494\pi$
$379$	−5.95047	−	4.32327i	−0.305655	−	0.222071i	−0.730030	+	0.683415i	$0.760494\pi$
$380$	−4.82540	−	1.57107i	−0.247538	−	0.0805944i
$381$	23.5792	−	17.1313i	1.20800	−	0.877663i
$382$	−24.3674	−	7.91746i	−1.24675	−	0.405092i
$383$	−2.39136	+	3.29142i	−0.122193	+	0.168184i	−0.865731	−	0.500510i	$-0.833146\pi$
$383$	−2.39136	+	3.29142i	−0.122193	+	0.168184i	0.743538	+	0.668693i	$0.233146\pi$
$384$	0.0214731	−	0.0660873i	0.00109579	−	0.00337250i
$385$	−12.6531	−	9.20467i	−0.644864	−	0.469113i
$386$	16.9997	−	12.3510i	0.865263	−	0.628650i
$387$	−22.3323	+	7.25622i	−1.13522	+	0.368854i
$388$	13.5621	−	4.40659i	0.688511	−	0.223711i
$389$	−27.8933	+	20.2656i	−1.41424	+	1.02751i	−0.421556	+	0.906802i	$0.638516\pi$
$389$	−27.8933	+	20.2656i	−1.41424	+	1.02751i	−0.992688	+	0.120707i	$0.961484\pi$
$390$	3.42752	+	2.49339i	0.173559	+	0.126258i
$391$	5.52688	−	17.0100i	0.279507	−	0.860233i
$392$	−32.4677	+	44.6880i	−1.63987	+	2.25708i
$393$	−10.1337	−	3.29264i	−0.511177	−	0.166092i
$394$	9.61410	−	6.98505i	0.484351	−	0.351902i
$395$	−15.4663	−	5.03559i	−0.778194	−	0.253368i
$396$	4.26468	+	3.09847i	0.214308	+	0.155704i
$397$		−	1.88725i		−	0.0947182i	−0.998878	−	0.0473591i	$-0.984919\pi$
$397$		−	1.88725i		−	0.0947182i	0.998878	−	0.0473591i	$-0.0150805\pi$
$398$		−	11.2051i		−	0.561660i
$399$	30.5448	+	22.1921i	1.52915	+	1.11100i
$400$	8.31094	+	0.00999372i	0.415547	+	0.000499686i
$401$	6.21445	−	19.1261i	0.310335	−	0.955113i	−0.667297	−	0.744791i	$-0.732549\pi$
$401$	6.21445	−	19.1261i	0.310335	−	0.955113i	0.977632	−	0.210321i	$-0.0674510\pi$
$402$			9.94918i			0.496220i
$403$	−1.42943	+	3.24332i	−0.0712049	+	0.161561i
$404$	−2.88631			−0.143599
$405$	4.03232	−	1.30750i	0.200368	−	0.0649703i
$406$	−1.29281	−	3.97885i	−0.0641609	−	0.197467i
$407$	−6.49258	+	8.93628i	−0.321825	+	0.442955i
$408$			20.2011i			1.00010i
$409$	11.8662			0.586745			0.293373	−	0.955998i	$-0.405222\pi$
$409$	11.8662			0.586745			0.293373	+	0.955998i	$0.405222\pi$
$410$	17.3331	+	0.0104214i	0.856023	+	0.000514674i
$411$	−48.6895	+	35.3750i	−2.40168	+	1.74492i
$412$	−4.00025	−	5.50587i	−0.197078	−	0.271255i
$413$	17.8758	+	5.80820i	0.879611	+	0.285803i
$414$	−29.7679	−	21.6277i	−1.46301	−	1.06294i
$415$	−5.98616	−	18.4613i	−0.293849	−	0.906228i
$416$	0.850463	+	2.61746i	0.0416974	+	0.128331i
$417$	8.65632	+	11.9144i	0.423902	+	0.583451i
$418$	3.95294	−	1.28439i	0.193345	−	0.0628215i
$419$	−4.55963	−	14.0331i	−0.222752	−	0.685561i	−0.998512	−	0.0545326i	$-0.982633\pi$
$419$	−4.55963	−	14.0331i	−0.222752	−	0.685561i	0.775760	−	0.631028i	$-0.217367\pi$
$420$	24.1900	+	7.87590i	1.18035	+	0.384305i
$421$	−3.13553	−	9.65018i	−0.152817	−	0.470321i	0.845117	−	0.534582i	$-0.179531\pi$
$421$	−3.13553	−	9.65018i	−0.152817	−	0.470321i	−0.997933	+	0.0642610i	$0.979531\pi$
$422$	−15.2749	−	4.96311i	−0.743569	−	0.241600i
$423$	9.08476	−	12.5041i	0.441716	−	0.607970i
$424$	−1.26851	+	3.90407i	−0.0616043	+	0.189599i
$425$	−11.4163	+	3.69422i	−0.553774	+	0.179196i
$426$	−5.04869	+	3.66809i	−0.244610	+	0.177719i
$427$	18.1159	−	24.9345i	0.876692	−	1.20666i
$428$		−	4.91097i		−	0.237381i
$429$	2.44733			0.118158
$430$	−0.00750058	+	12.4752i	−0.000361710	+	0.601609i
$431$	7.62147	+	23.4565i	0.367113	+	1.12986i	0.948647	+	0.316336i	$0.102453\pi$
$431$	7.62147	+	23.4565i	0.367113	+	1.12986i	−0.581534	+	0.813522i	$0.697547\pi$
$432$	6.77335	+	2.20079i	0.325883	+	0.105886i
$433$			15.8754i			0.762922i	0.924385	+	0.381461i	$0.124579\pi$
$433$			15.8754i			0.762922i	−0.924385	+	0.381461i	$0.875421\pi$
$434$	3.04135	−	30.0223i	0.145989	−	1.44111i
$435$	−3.84079	+	2.78697i	−0.184152	+	0.133625i
$436$	2.84659	−	8.76090i	0.136327	−	0.419571i
$437$	19.4519	−	6.32029i	0.930509	−	0.302341i
$438$	19.2422	−	26.4846i	0.919426	−	1.26548i
$439$	1.64657			0.0785864			0.0392932	−	0.999228i	$-0.487489\pi$
$439$	1.64657			0.0785864			0.0392932	+	0.999228i	$0.487489\pi$
$440$	7.74870	−	5.62265i	0.369405	−	0.268049i
$441$	−66.5325	−	48.3387i	−3.16822	−	2.30184i
$442$	0.972547	+	1.33860i	0.0462593	+	0.0636705i
$443$	−10.5950	−	14.5828i	−0.503383	−	0.692848i	0.479403	−	0.877595i	$-0.340853\pi$
$443$	−10.5950	−	14.5828i	−0.503383	−	0.692848i	−0.982786	+	0.184747i	$0.940853\pi$
$444$	5.54965	−	17.0801i	0.263375	−	0.810585i
$445$	−0.0133519	+	22.2074i	−0.000632941	+	1.05273i
$446$	4.51192	−	13.8863i	0.213646	−	0.657533i
$447$	−4.11651	+	1.33754i	−0.194704	+	0.0632633i
$448$	−23.5507	−	32.4147i	−1.11267	−	1.53145i
$449$	−1.49885	−	4.61297i	−0.0707349	−	0.217700i	0.909440	−	0.415836i	$-0.136511\pi$
$449$	−1.49885	−	4.61297i	−0.0707349	−	0.217700i	−0.980174	+	0.198137i	$0.936511\pi$
$450$	−0.0296839	+	24.6856i	−0.00139931	+	1.16369i
$451$	8.09684	−	5.88270i	0.381265	−	0.277006i
$452$	9.76773	−	3.17373i	0.459436	−	0.149280i
$453$	−22.4539	−	7.29570i	−1.05497	−	0.342782i
$454$	−19.3003	−	14.0225i	−0.905807	−	0.658108i
$455$	6.77573	−	2.19707i	0.317651	−	0.103000i
$456$	−18.6891	+	13.5784i	−0.875198	+	0.635869i
$457$	2.41462	+	3.32344i	0.112951	+	0.155464i	0.861750	−	0.507334i	$-0.169369\pi$
$457$	2.41462	+	3.32344i	0.112951	+	0.155464i	−0.748798	+	0.662798i	$0.769369\pi$
$458$	2.72477	−	3.75032i	0.127320	−	0.175241i
$459$	−10.2825			−0.479945
$460$	11.1542	−	8.09374i	0.520066	−	0.377372i
$461$	−18.8029	−	13.6611i	−0.875738	−	0.636261i	0.0563827	−	0.998409i	$-0.482043\pi$
$461$	−18.8029	−	13.6611i	−0.875738	−	0.636261i	−0.932120	+	0.362149i	$0.882043\pi$
$462$	−19.8164	+	6.43872i	−0.921940	+	0.299557i
$463$	29.2711	+	9.51077i	1.36035	+	0.442003i	0.896158	−	0.443734i	$-0.146347\pi$
$463$	29.2711	+	9.51077i	1.36035	+	0.442003i	0.464187	+	0.885737i	$0.346347\pi$
$464$	1.28308			0.0595653
$465$	−33.4575	+	7.22218i	−1.55155	+	0.334920i
$466$	−17.9139			−0.829844
$467$	15.8854	+	5.16147i	0.735088	+	0.238844i	0.652552	−	0.757744i	$-0.273698\pi$
$467$	15.8854	+	5.16147i	0.735088	+	0.238844i	0.0825353	+	0.996588i	$0.473698\pi$
$468$	−2.28228	+	0.741559i	−0.105499	+	0.0342786i
$469$	13.5269	+	9.82785i	0.624613	+	0.453808i
$470$	−4.82252	−	6.64603i	−0.222446	−	0.306559i
$471$	23.1315			1.06584
$472$	−6.75973	+	9.30397i	−0.311142	+	0.428250i
$473$	4.23397	+	5.82756i	0.194678	+	0.267952i
$474$	−17.5231	+	12.7312i	−0.804861	+	0.584766i
$475$	−11.0914	−	8.07876i	−0.508908	−	0.370679i
$476$	8.03437	+	5.83731i	0.368255	+	0.267553i
$477$	−5.81248	−	1.88859i	−0.266135	−	0.0864726i
$478$	15.4208	−	5.01052i	0.705331	−	0.229176i
$479$	−3.66602	+	2.66352i	−0.167505	+	0.121699i	−0.668379	−	0.743820i	$-0.733012\pi$
$479$	−3.66602	+	2.66352i	−0.167505	+	0.121699i	0.500875	+	0.865520i	$0.333012\pi$
$480$	−15.6350	+	21.4925i	−0.713637	+	0.980996i
$481$	−1.55387	−	4.78233i	−0.0708506	−	0.218056i
$482$	8.23693	+	11.3372i	0.375182	+	0.516393i
$483$	−97.5134	+	31.6840i	−4.43702	+	1.44167i
$484$	−2.31131	+	7.11349i	−0.105060	+	0.323341i
$485$	38.5582	+	0.0231827i	1.75084	+	0.00105267i
$486$	6.04640	−	18.6089i	0.274270	−	0.844116i
$487$	−8.81591	−	12.1341i	−0.399487	−	0.549847i	0.561128	−	0.827729i	$-0.310367\pi$
$487$	−8.81591	−	12.1341i	−0.399487	−	0.549847i	−0.960615	+	0.277882i	$0.910367\pi$
$488$	11.0844	+	15.2564i	0.501767	+	0.690623i
$489$	−6.57021	−	4.77354i	−0.297115	−	0.215867i
$490$	−35.3626	+	25.6600i	−1.59752	+	1.15920i
$491$	40.2267			1.81541			0.907703	−	0.419613i	$-0.137834\pi$
$491$	40.2267			1.81541			0.907703	+	0.419613i	$0.137834\pi$
$492$	−9.56448	+	13.1644i	−0.431200	+	0.593496i
$493$	−1.76181	+	0.572447i	−0.0793480	+	0.0257817i
$494$	−0.584697	+	1.79951i	−0.0263068	+	0.0809639i
$495$	8.37113	+	11.5365i	0.376254	+	0.518525i
$496$	8.46867	+	3.73239i	0.380255	+	0.167589i
$497$			10.4875i			0.470430i
$498$	−24.5790	−	7.98620i	−1.10141	−	0.357870i
$499$	12.6135	+	38.8202i	0.564656	+	1.73783i	0.668972	+	0.743288i	$0.266735\pi$
$499$	12.6135	+	38.8202i	0.564656	+	1.73783i	−0.104316	+	0.994544i	$0.533265\pi$
$500$	−8.78809	−	2.87296i	−0.393015	−	0.128483i
$501$	28.7900			1.28624
$502$		−	15.5643i		−	0.694670i
$503$	4.29417	−	5.91042i	0.191468	−	0.263533i	−0.702480	−	0.711703i	$-0.747924\pi$
$503$	4.29417	−	5.91042i	0.191468	−	0.263533i	0.893948	+	0.448170i	$0.147924\pi$
$504$	56.5038	−	41.0524i	2.51688	−	1.82862i
$505$	−7.42097	−	2.41615i	−0.330229	−	0.107517i
$506$	−3.48799	+	10.7349i	−0.155060	+	0.477225i
$507$	20.3529	−	28.0133i	0.903903	−	1.24412i
$508$	8.33776	+	2.70910i	0.369928	+	0.120197i
$509$	−6.40708	−	19.7190i	−0.283989	−	0.874028i	−0.986700	−	0.162553i	$-0.948027\pi$
$509$	−6.40708	−	19.7190i	−0.283989	−	0.874028i	0.702711	−	0.711475i	$-0.251973\pi$
$510$	−4.94679	+	15.1936i	−0.219048	+	0.672783i
$511$	−17.0008	−	52.3232i	−0.752072	−	2.31464i
$512$	16.5149	−	5.36600i	0.729861	−	0.237146i
$513$	−6.91152	−	9.51289i	−0.305151	−	0.420004i
$514$	6.63737	+	20.4277i	0.292762	+	0.901028i
$515$	−5.67600	−	17.5047i	−0.250114	−	0.771351i
$516$	−9.47483	−	6.88387i	−0.417106	−	0.303045i
$517$	−4.50923	−	1.46514i	−0.198316	−	0.0644367i
$518$	25.1638	+	34.6350i	1.10563	+	1.52178i
$519$	9.48373	−	6.89033i	0.416289	−	0.302452i
$520$	−0.00262037	+	4.35829i	−0.000114911	+	0.191124i
$521$	−5.07858			−0.222497			−0.111248	−	0.993793i	$-0.535485\pi$
$521$	−5.07858			−0.222497			−0.111248	+	0.993793i	$0.535485\pi$
$522$			3.81106i			0.166806i
$523$	−9.62516	+	13.2479i	−0.420879	+	0.579290i	−0.965830	−	0.259178i	$-0.916548\pi$
$523$	−9.62516	+	13.2479i	−0.420879	+	0.579290i	0.544951	+	0.838468i	$0.316548\pi$
$524$	−0.990410	−	3.04817i	−0.0432663	−	0.133160i
$525$	55.6019	+	40.4994i	2.42666	+	1.76754i
$526$	0.0884181			0.00385521
$527$	−13.2937	−	1.34669i	−0.579082	−	0.0586628i
$528$		−	6.39026i		−	0.278100i
$529$	−10.0565	+	30.9507i	−0.437239	+	1.34568i
$530$	−1.91009	+	2.62569i	−0.0829690	+	0.114053i
$531$	−13.8520	−	10.0640i	−0.601125	−	0.436743i
$532$			11.3567i			0.492374i
$533$			4.55609i			0.197346i
$534$	23.9244	+	17.3821i	1.03531	+	0.752198i
$535$	4.11101	−	12.6266i	0.177735	−	0.545894i
$536$	−8.27654	+	6.01326i	−0.357492	+	0.259733i
$537$	7.70417	+	2.50324i	0.332460	+	0.108023i
$538$	7.41497	−	10.2058i	0.319682	−	0.440005i
$539$	−7.79579	+	23.9930i	−0.335789	+	1.03345i
$540$	−6.40704	−	4.66088i	−0.275715	−	0.200572i
$541$	34.4222	−	25.0092i	1.47993	−	1.07523i	0.502347	−	0.864666i	$-0.332470\pi$
$541$	34.4222	−	25.0092i	1.47993	−	1.07523i	0.977580	−	0.210563i	$-0.0675299\pi$
$542$	−7.39904	+	2.40409i	−0.317816	+	0.103265i
$543$	−1.16483	+	0.378477i	−0.0499878	+	0.0162420i
$544$	−8.39377	+	6.09843i	−0.359880	+	0.261468i
$545$	14.6527	−	20.1422i	0.627651	−	0.862796i
$546$	2.93113	−	9.02108i	0.125441	−	0.386066i
$547$	6.21198	−	8.55006i	0.265605	−	0.365574i	−0.655295	−	0.755373i	$-0.727456\pi$
$547$	6.21198	−	8.55006i	0.265605	−	0.365574i	0.920900	+	0.389799i	$0.127456\pi$
$548$	−17.2169	−	5.59412i	−0.735470	−	0.238969i
$549$	−22.7141	+	16.5027i	−0.969412	+	0.704319i
$550$	7.20479	−	2.33140i	0.307213	−	0.0994114i
$551$	−1.71383	−	1.24517i	−0.0730116	−	0.0530460i
$552$		−	62.7349i		−	2.67018i
$553$			36.4003i			1.54790i
$554$	−13.6833	−	9.94147i	−0.581346	−	0.422372i
$555$	28.5666	−	39.2688i	1.21258	−	1.66687i
$556$	−1.36889	+	4.21301i	−0.0580539	+	0.178671i
$557$		−	23.2668i		−	0.985845i	−0.870073	−	0.492923i	$-0.835929\pi$
$557$		−	23.2668i		−	0.985845i	0.870073	−	0.492923i	$-0.164071\pi$
$558$	−11.0862	+	25.1541i	−0.469315	+	1.06486i
$559$	−3.27917			−0.138694
$560$	−5.73678	−	17.6922i	−0.242423	−	0.747631i
$561$	2.85103	+	8.77456i	0.120371	+	0.370462i
$562$	−7.72643	+	10.6345i	−0.325920	+	0.448590i
$563$		−	4.65782i		−	0.196304i	−0.995171	−	0.0981519i	$-0.968707\pi$
$563$		−	4.65782i		−	0.196304i	0.995171	−	0.0981519i	$-0.0312931\pi$
$564$	7.70869			0.324594
$565$	27.7705	+	0.0166967i	1.16831	+	0.000702436i
$566$	−4.95331	+	3.59879i	−0.208203	+	0.151269i
$567$	−5.57600	−	7.67470i	−0.234170	−	0.322307i
$568$	−6.10283	−	1.98293i	−0.256069	−	0.0832018i
$569$	−4.77950	−	3.47251i	−0.200367	−	0.145575i	0.483078	−	0.875578i	$-0.339519\pi$
$569$	−4.77950	−	3.47251i	−0.200367	−	0.145575i	−0.683445	+	0.730002i	$0.739519\pi$
$570$	−17.3815	+	5.63603i	−0.728030	+	0.236067i
$571$	14.4553	+	44.4889i	0.604936	+	1.86180i	0.497229	+	0.867620i	$0.334351\pi$
$571$	14.4553	+	44.4889i	0.604936	+	1.86180i	0.107708	+	0.994183i	$0.465649\pi$
$572$	0.432696	+	0.595556i	0.0180919	+	0.0249014i
$573$	61.8545	−	20.0978i	2.58401	−	0.839596i
$574$	−11.9867	−	36.8912i	−0.500315	−	1.53981i
$575$	35.4538	−	11.4725i	1.47852	−	0.478437i
$576$	11.2788	+	34.7125i	0.469949	+	1.44636i
$577$	16.6370	+	5.40567i	0.692605	+	0.225041i	0.634106	−	0.773246i	$-0.281368\pi$
$577$	16.6370	+	5.40567i	0.692605	+	0.225041i	0.0584996	+	0.998287i	$0.481368\pi$
$578$	7.15601	−	9.84940i	0.297651	−	0.409681i
$579$	−16.4827	+	50.7285i	−0.684998	+	2.10821i
$580$	−1.35727	−	0.441906i	−0.0563576	−	0.0183492i
$581$	−35.1373	+	25.5287i	−1.45774	+	1.05911i
$582$	30.1802	−	41.5396i	1.25101	−	1.72187i
$583$			1.87481i			0.0776466i
$584$	33.6619			1.39294
$585$	−6.48873	−	0.00390127i	−0.268276	−	0.000161298i
$586$	5.54903	+	17.0781i	0.229228	+	0.705492i
$587$	−31.9580	−	10.3838i	−1.31905	−	0.428584i	−0.436879	−	0.899520i	$-0.643916\pi$
$587$	−31.9580	−	10.3838i	−1.31905	−	0.428584i	−0.882167	+	0.470936i	$0.843916\pi$
$588$		−	41.0169i		−	1.69151i
$589$	−7.68964	−	13.2039i	−0.316846	−	0.544058i
$590$	−7.36244	+	5.34237i	−0.303107	+	0.219942i
$591$	−9.32171	+	28.6893i	−0.383444	+	1.18012i
$592$	−12.4872	+	4.05734i	−0.513221	+	0.166756i
$593$	−13.7638	+	18.9442i	−0.565211	+	0.777946i	−0.991977	−	0.126416i	$-0.959653\pi$
$593$	−13.7638	+	18.9442i	−0.565211	+	0.777946i	0.426767	+	0.904362i	$0.359653\pi$
$594$	6.48922			0.266256
$595$	15.7707	+	21.7339i	0.646534	+	0.891004i
$596$	−1.05330	−	0.765268i	−0.0431449	−	0.0313466i
$597$	16.7184	+	23.0110i	0.684240	+	0.941776i
$598$	−3.02027	−	4.15704i	−0.123508	−	0.169994i
$599$	−1.12006	+	3.44720i	−0.0457645	+	0.140849i	−0.971328	−	0.237744i	$-0.923592\pi$
$599$	−1.12006	+	3.44720i	−0.0457645	+	0.140849i	0.925563	+	0.378593i	$0.123592\pi$
$600$	−34.0800	+	24.6980i	−1.39131	+	1.00829i
$601$	−8.53432	+	26.2659i	−0.348122	+	1.07141i	0.611769	+	0.791036i	$0.290458\pi$
$601$	−8.53432	+	26.2659i	−0.348122	+	1.07141i	−0.959891	+	0.280373i	$0.909542\pi$
$602$	26.5518	−	8.62721i	1.08217	−	0.351619i
$603$	−8.95269	−	12.3223i	−0.364582	−	0.501804i
$604$	−2.19451	−	6.75402i	−0.0892935	−	0.274817i
$605$	−11.8974	+	16.3546i	−0.483697	+	0.664911i
$606$	−8.40784	+	6.10865i	−0.341545	+	0.248147i
$607$	25.9484	−	8.43114i	1.05321	−	0.342209i	0.269284	−	0.963061i	$-0.413213\pi$
$607$	25.9484	−	8.43114i	1.05321	−	0.342209i	0.783928	+	0.620851i	$0.213213\pi$
$608$	−11.2840	−	3.66639i	−0.457626	−	0.148692i
$609$	8.59154	+	6.24212i	0.348147	+	0.252943i
$610$	4.60082	+	14.1889i	0.186282	+	0.574492i
$611$	1.74618	−	1.26867i	0.0706428	−	0.0513250i
$612$	−5.31750	−	7.31892i	−0.214947	−	0.295850i
$613$	−27.0308	+	37.2047i	−1.09176	+	1.50268i	−0.245892	+	0.969297i	$0.579081\pi$
$613$	−27.0308	+	37.2047i	−1.09176	+	1.50268i	−0.845872	+	0.533387i	$0.820919\pi$
$614$	1.15567			0.0466392
$615$	−35.6112	+	25.8404i	−1.43598	+	1.04198i
$616$	−17.3332	−	12.5933i	−0.698375	−	0.507399i
$617$	−15.5311	+	5.04636i	−0.625259	+	0.203159i	−0.604474	−	0.796625i	$-0.706617\pi$
$617$	−15.5311	+	5.04636i	−0.625259	+	0.203159i	−0.0207851	+	0.999784i	$0.506617\pi$
$618$	−23.3055	−	7.57241i	−0.937484	−	0.304607i
$619$	−7.49401			−0.301210			−0.150605	−	0.988594i	$-0.548122\pi$
$619$	−7.49401			−0.301210			−0.150605	+	0.988594i	$0.548122\pi$
$620$	−7.67290	−	6.86493i	−0.308151	−	0.275702i
$621$	31.9325			1.28141
$622$	−20.6234	−	6.70096i	−0.826925	−	0.268684i
$623$	47.2653	−	15.3574i	1.89365	−	0.615283i
$624$	2.35348	+	1.70990i	0.0942147	+	0.0684510i
$625$	−20.1900	−	14.7432i	−0.807601	−	0.589729i
$626$	−20.8843			−0.834705
$627$	−6.20147	+	8.53559i	−0.247663	+	0.340879i
$628$	4.08972	+	5.62901i	0.163197	+	0.224622i
$629$	15.3362	−	11.1424i	0.611493	−	0.444276i
$630$	52.5503	−	17.0397i	2.09365	−	0.678878i
$631$	−3.09596	−	2.24935i	−0.123248	−	0.0895452i	0.524453	−	0.851439i	$-0.324270\pi$
$631$	−3.09596	−	2.24935i	−0.123248	−	0.0895452i	−0.647702	+	0.761894i	$0.724270\pi$
$632$	−21.1818	−	6.88238i	−0.842566	−	0.273766i
$633$	38.7739	−	12.5984i	1.54112	−	0.500742i
$634$	20.4981	−	14.8928i	0.814085	−	0.591468i
$635$	19.1694	+	13.9450i	0.760713	+	0.553389i
$636$	−0.941941	−	2.89900i	−0.0373504	−	0.114953i
$637$	−6.75043	−	9.29117i	−0.267462	−	0.368129i
$638$	1.11187	−	0.361268i	0.0440193	−	0.0143027i
$639$	2.95223	−	9.08604i	0.116789	−	0.359438i
$640$	0.0565170		3.39802e-5i	0.00223403		1.34319e-6i
$641$	8.53249	−	26.2603i	0.337013	−	1.03722i	−0.628709	−	0.777641i	$-0.716416\pi$
$641$	8.53249	−	26.2603i	0.337013	−	1.03722i	0.965722	−	0.259579i	$-0.0835837\pi$
$642$	−10.3937	−	14.3057i	−0.410206	−	0.564600i
$643$	−18.3754	−	25.2916i	−0.724655	−	0.997401i	−0.999356	−	0.0358720i	$-0.988579\pi$
$643$	−18.3754	−	25.2916i	−0.724655	−	0.997401i	0.274702	−	0.961529i	$-0.411421\pi$
$644$	−24.9510	−	18.1279i	−0.983205	−	0.714341i
$645$	−18.5981	−	25.6305i	−0.732301	−	1.00920i
$646$	−7.13304			−0.280646
$647$	19.3386	−	26.6173i	0.760280	−	1.04644i	−0.236911	−	0.971531i	$-0.576135\pi$
$647$	19.3386	−	26.6173i	0.760280	−	1.04644i	0.997191	−	0.0749042i	$-0.0238651\pi$
$648$	5.52028	−	1.79365i	0.216857	−	0.0704612i
$649$	−1.62307	+	4.99530i	−0.0637112	+	0.196083i
$650$	−1.06922	+	3.27730i	−0.0419382	+	0.128546i
$651$	38.5487	+	66.1921i	1.51084	+	2.59427i
$652$		−	2.44283i		−	0.0956686i
$653$	−18.4108	−	5.98202i	−0.720469	−	0.234095i	−0.0742426	−	0.997240i	$-0.523654\pi$
$653$	−18.4108	−	5.98202i	−0.720469	−	0.234095i	−0.646227	+	0.763146i	$0.723654\pi$
$654$	−10.2496	−	31.5451i	−0.400792	−	1.23351i
$655$	0.00521046	−	8.66621i	0.000203589	−	0.338617i
$656$	11.8965			0.464479
$657$			50.1167i			1.95524i
$658$	−10.8012	+	14.8666i	−0.421076	+	0.579562i
$659$	−2.78409	+	2.02276i	−0.108453	+	0.0787957i	−0.640690	−	0.767800i	$-0.721352\pi$
$659$	−2.78409	+	2.02276i	−0.108453	+	0.0787957i	0.532237	+	0.846595i	$0.321352\pi$
$660$	−2.20088	+	6.75978i	−0.0856691	+	0.263124i
$661$	−5.48729	+	16.8881i	−0.213431	+	0.656873i	0.785830	+	0.618442i	$0.212236\pi$
$661$	−5.48729	+	16.8881i	−0.213431	+	0.656873i	−0.999261	+	0.0384307i	$0.987764\pi$
$662$	−13.4987	+	18.5794i	−0.524643	+	0.722109i
$663$	−3.99448	−	1.29789i	−0.155133	−	0.0504057i
$664$	−8.21190	−	25.2736i	−0.318684	−	0.980807i
$665$	−9.50677	+	29.1991i	−0.368657	+	1.13229i
$666$	−12.0513	−	37.0902i	−0.466979	−	1.43722i
$667$	5.47135	−	1.77775i	0.211852	−	0.0688347i
$668$	5.09017	+	7.00601i	0.196944	+	0.271071i
$669$	11.4531	+	35.2490i	0.442803	+	1.36281i
$670$	−7.69744	+	2.49594i	−0.297378	+	0.0964264i
$671$	6.96781	+	5.06241i	0.268989	+	0.195432i
$672$	56.5673	+	18.3798i	2.18213	+	0.709018i
$673$	−9.09980	−	12.5248i	−0.350771	−	0.482795i	0.596777	−	0.802407i	$-0.296448\pi$
$673$	−9.09980	−	12.5248i	−0.350771	−	0.482795i	−0.947549	+	0.319611i	$0.896448\pi$
$674$	−11.2062	+	8.14180i	−0.431648	+	0.313610i
$675$	−12.5715	−	17.3469i	−0.483875	−	0.667684i
$676$	10.4155			0.400595
$677$			26.4473i			1.01645i	0.861223	+	0.508227i	$0.169699\pi$
$677$			26.4473i			1.01645i	−0.861223	+	0.508227i	$0.830301\pi$
$678$	21.7365	−	29.9177i	0.834786	−	1.14898i
$679$	−26.6648	−	82.0659i	−1.02330	−	3.14940i
$680$	−15.6291	+	5.06781i	−0.599348	+	0.194342i
$681$	60.5575			2.32057
$682$	8.38957	+	0.849890i	0.321253	+	0.0325440i
$683$		−	35.7929i		−	1.36958i	−0.728742	−	0.684789i	$-0.759894\pi$
$683$		−	35.7929i		−	1.36958i	0.728742	−	0.684789i	$-0.240106\pi$
$684$	3.19690	−	9.83903i	0.122236	−	0.376205i
$685$	−39.5834	−	28.7954i	−1.51241	−	1.10022i
$686$	48.4105	+	35.1723i	1.84832	+	1.34289i
$687$			11.7672i			0.448947i
$688$			8.56227i			0.326434i
$689$	−0.690477	−	0.501661i	−0.0263051	−	0.0191118i
$690$	15.3624	−	47.1840i	0.584836	−	1.79627i
$691$	−36.9543	+	26.8488i	−1.40581	+	1.02138i	−0.411891	+	0.911233i	$0.635132\pi$
$691$	−36.9543	+	26.8488i	−1.40581	+	1.02138i	−0.993916	+	0.110145i	$0.964868\pi$
$692$	3.35351	+	1.08962i	0.127481	+	0.0414211i
$693$	18.7492	−	25.8061i	0.712224	−	0.980293i
$694$	−11.4765	+	35.3210i	−0.435642	+	1.34077i
$695$	−7.04629	+	9.68613i	−0.267281	+	0.367416i
$696$	−5.25681	+	3.81930i	−0.199259	+	0.144770i
$697$	−16.3352	+	5.30763i	−0.618741	+	0.201041i
$698$	1.07443	−	0.349104i	0.0406678	−	0.0132138i
$699$	36.7882	−	26.7282i	1.39146	−	1.01095i
$700$	−0.0248805	+	20.6911i	−0.000940396	+	0.782048i
$701$	−3.29087	+	10.1283i	−0.124295	+	0.382539i	−0.993772	−	0.111433i	$-0.964456\pi$
$701$	−3.29087	+	10.1283i	−0.124295	+	0.382539i	0.869477	+	0.493973i	$0.164456\pi$
$702$	−1.73638	+	2.38993i	−0.0655356	+	0.0902020i
$703$	20.6169	+	6.69883i	0.777580	+	0.252651i
$704$	9.05814	−	6.58112i	0.341391	−	0.248035i
$705$	19.8198	+	6.45301i	0.746456	+	0.243034i
$706$	2.57953	+	1.87414i	0.0970820	+	0.0705342i
$707$			17.4654i			0.656855i
$708$		−	8.53965i		−	0.320940i
$709$	0.118571	+	0.0861468i	0.00445303	+	0.00323531i	0.590010	−	0.807396i	$-0.299124\pi$
$709$	0.118571	+	0.0861468i	0.00445303	+	0.00323531i	−0.585557	+	0.810632i	$0.699124\pi$
$710$	−4.10447	−	2.98584i	−0.154038	−	0.112057i
$711$	10.2467	−	31.5360i	0.384279	−	1.18269i
$712$			30.4080i			1.13959i
$713$	41.2839	+	4.18219i	1.54609	+	0.156624i
$714$	35.7584			1.33822
$715$	0.613959	+	1.89344i	0.0229608	+	0.0708108i
$716$	0.752962	+	2.31738i	0.0281395	+	0.0866046i
$717$	−24.1925	+	33.2982i	−0.903487	+	1.24354i
$718$		−	4.16549i		−	0.155455i
$719$	28.0309			1.04538			0.522688	−	0.852524i	$-0.324929\pi$
$719$	28.0309			1.04538			0.522688	+	0.852524i	$0.324929\pi$
$720$	−0.0101867	+	16.9428i	−0.000379634	+	0.631421i
$721$	−33.3167	+	24.2060i	−1.24078	+	0.901478i
$722$	7.30102	+	10.0490i	0.271716	+	0.373985i
$723$	−33.8310	−	10.9924i	−1.25819	−	0.408810i
$724$	−0.298048	−	0.216545i	−0.0110769	−	0.00804782i
$725$	−3.11975	−	2.27237i	−0.115865	−	0.0843935i
$726$	8.32228	+	25.6134i	0.308869	+	0.950601i
$727$	20.3106	+	27.9552i	0.753280	+	1.03680i	0.997743	+	0.0671425i	$0.0213882\pi$
$727$	20.3106	+	27.9552i	0.753280	+	1.03680i	−0.244463	+	0.969659i	$0.578612\pi$
$728$	9.27603	−	3.01397i	0.343793	−	0.111705i
$729$	13.5908	+	41.8282i	0.503363	+	1.54919i
$730$	25.3177	+	8.24306i	0.937051	+	0.305089i
$731$	−3.82008	−	11.7570i	−0.141291	−	0.434848i
$732$	−13.3177	−	4.32718i	−0.492237	−	0.159937i
$733$	−10.1184	+	13.9267i	−0.373730	+	0.514396i	−0.953910	−	0.300093i	$-0.902982\pi$
$733$	−10.1184	+	13.9267i	−0.373730	+	0.514396i	0.580180	+	0.814488i	$0.302982\pi$
$734$	−1.84506	+	5.67851i	−0.0681024	+	0.209597i
$735$	34.3356	−	105.458i	1.26649	−	3.88989i
$736$	26.0671	−	18.9388i	0.960845	−	0.698094i
$737$	−2.74634	+	3.78002i	−0.101163	+	0.139239i
$738$			35.3355i			1.30072i
$739$	−31.0347			−1.14163			−0.570816	−	0.821078i	$-0.693373\pi$
$739$	−31.0347			−1.14163			−0.570816	+	0.821078i	$0.693373\pi$
$740$	14.6067	+	0.00878210i	0.536952	+	0.000322836i
$741$	−1.48420	−	4.56791i	−0.0545235	−	0.167806i
$742$	6.91070	+	2.24542i	0.253700	+	0.0824320i
$743$			31.9364i			1.17163i	0.810443	+	0.585817i	$0.199226\pi$
$743$			31.9364i			1.17163i	−0.810443	+	0.585817i	$0.800774\pi$
$744$	−45.8066	+	9.91669i	−1.67935	+	0.363564i
$745$	−2.06752	−	2.84930i	−0.0757482	−	0.104390i
$746$	0.178266	−	0.548647i	0.00652679	−	0.0200874i
$747$	37.6280	−	12.2261i	1.37674	−	0.447329i
$748$	−1.63121	+	2.24516i	−0.0596429	+	0.0820914i
$749$	−29.7169			−1.08583
$750$	−31.6801	+	10.2304i	−1.15680	+	0.373560i
$751$	4.73561	+	3.44062i	0.172805	+	0.125550i	0.670826	−	0.741615i	$-0.265940\pi$
$751$	4.73561	+	3.44062i	0.172805	+	0.125550i	−0.498021	+	0.867165i	$0.665940\pi$
$752$	−3.31264	−	4.55946i	−0.120800	−	0.166266i
$753$	23.2226	+	31.9632i	0.846279	+	1.16480i
$754$	−0.164462	+	0.506161i	−0.00598934	+	0.0184333i
$755$	0.0115451	−	19.2023i	0.000420171	−	0.698842i
$756$	−5.47913	+	16.8630i	−0.199274	+	0.613303i
$757$	−36.4227	+	11.8344i	−1.32380	+	0.430130i	−0.883800	−	0.467866i	$-0.845023\pi$
$757$	−36.4227	+	11.8344i	−1.32380	+	0.430130i	−0.440004	+	0.897996i	$0.645023\pi$
$758$	−4.68239	−	6.44475i	−0.170072	−	0.234084i
$759$	−8.85394	−	27.2496i	−0.321378	−	0.989099i
$760$	−15.1938	−	11.0529i	−0.551138	−	0.400931i
$761$	6.46626	−	4.69801i	0.234402	−	0.170303i	−0.464384	−	0.885634i	$-0.653724\pi$
$761$	6.46626	−	4.69801i	0.234402	−	0.170303i	0.698786	+	0.715331i	$0.253724\pi$
$762$	30.0216	−	9.75459i	1.08757	−	0.353372i
$763$	−53.0133	−	17.2251i	−1.91921	−	0.623589i
$764$	15.8268	+	11.4989i	0.572595	+	0.416015i
$765$	−7.54508	−	23.2690i	−0.272793	−	0.841291i
$766$	−3.56482	+	2.59000i	−0.128802	+	0.0935804i
$767$	−1.40543	−	1.93441i	−0.0507471	−	0.0698474i
$768$	−25.8335	+	35.5568i	−0.932186	+	1.28304i
$769$	−4.92944			−0.177760			−0.0888800	−	0.996042i	$-0.528329\pi$
$769$	−4.92944			−0.177760			−0.0888800	+	0.996042i	$0.528329\pi$
$770$	−9.95278	−	13.7162i	−0.358673	−	0.494296i
$771$	−44.1096	−	32.0475i	−1.58857	−	1.15416i
$772$	−15.2589	+	4.95792i	−0.549180	+	0.178440i
$773$	−40.3080	−	13.0969i	−1.44978	−	0.471062i	−0.524848	−	0.851196i	$-0.675878\pi$
$773$	−40.3080	−	13.0969i	−1.44978	−	0.471062i	−0.924931	+	0.380135i	$0.875878\pi$
$774$	−25.4321			−0.914139
$775$	−13.9810	−	24.0734i	−0.502214	−	0.864743i
$776$	52.7968			1.89530
$777$	−103.354	−	33.5817i	−3.70779	−	1.20474i
$778$	−35.5143	+	11.5393i	−1.27325	+	0.413704i
$779$	−15.8903	−	11.5450i	−0.569331	−	0.413643i
$780$	−1.90066	−	2.61935i	−0.0680546	−	0.0937877i
$781$	−2.93069			−0.104868
$782$	11.3860	−	15.6715i	0.407163	−	0.560412i
$783$	−1.94405	−	2.67575i	−0.0694746	−	0.0956235i
$784$	−24.2603	+	17.6261i	−0.866438	+	0.629504i
$785$	5.80295	+	17.8963i	0.207116	+	0.638745i
$786$	−9.33628	−	6.78321i	−0.333014	−	0.241949i
$787$	35.0337	+	11.3831i	1.24882	+	0.405765i	0.857497	−	0.514489i	$-0.172018\pi$
$787$	35.0337	+	11.3831i	1.24882	+	0.405765i	0.391320	+	0.920255i	$0.372018\pi$
$788$	−8.62960	+	2.80393i	−0.307417	+	0.0998858i
$789$	−0.181577	+	0.131923i	−0.00646431	+	0.00469660i
$790$	−14.2458	−	10.3633i	−0.506844	−	0.368710i
$791$	−19.2046	−	59.1058i	−0.682838	−	2.10156i
$792$	11.4719	+	15.7897i	0.407636	+	0.561062i
$793$	−3.72889	+	1.21159i	−0.132417	+	0.0430248i
$794$	0.631635	−	1.94397i	0.0224159	−	0.0689890i
$795$	0.00495547	−	8.24210i	0.000175752	−	0.292317i
$796$	−2.64381	+	8.13682i	−0.0937075	+	0.288402i
$797$	−19.9309	−	27.4325i	−0.705989	−	0.971710i	−0.999874	−	0.0158697i	$-0.994948\pi$
$797$	−19.9309	−	27.4325i	−0.705989	−	0.971710i	0.293885	−	0.955841i	$-0.405052\pi$
$798$	24.0355	+	33.0821i	0.850848	+	1.17109i
$799$	6.58285	+	4.78272i	0.232885	+	0.169201i
$800$	−20.5506	−	6.70462i	−0.726573	−	0.237044i
$801$	−45.2722			−1.59961
$802$	12.8025	−	17.6211i	0.452071	−	0.622223i
$803$	14.6214	−	4.75079i	0.515980	−	0.167652i
$804$	2.34749	−	7.22482i	0.0827895	−	0.254800i
$805$	−48.9762	−	67.4953i	−1.72618	−	2.37890i
$806$	−2.55789	+	2.86240i	−0.0900977	+	0.100824i
$807$			32.0223i			1.12724i
$808$	−10.1633	−	3.30227i	−0.357545	−	0.116174i
$809$	14.0661	+	43.2912i	0.494539	+	1.52204i	0.817673	+	0.575683i	$0.195264\pi$
$809$	14.0661	+	43.2912i	0.494539	+	1.52204i	−0.323134	+	0.946353i	$0.604736\pi$
$810$	4.59112	+	0.00276036i	0.161316	+	9.69892e-5i
$811$	−50.5430			−1.77480			−0.887402	−	0.460997i	$-0.847492\pi$
$811$	−50.5430			−1.77480			−0.887402	+	0.460997i	$0.847492\pi$
$812$			3.19437i			0.112100i
$813$	11.6078	−	15.9768i	0.407103	−	0.560329i
$814$	−9.67858	+	7.03190i	−0.339234	+	0.246468i
$815$	2.04491	−	6.28075i	0.0716302	−	0.220005i
$816$	−3.38892	+	10.4300i	−0.118636	+	0.365124i
$817$	8.30932	−	11.4368i	0.290706	−	0.400123i
$818$	12.2228	+	3.97144i	0.427362	+	0.138858i
$819$	4.48727	+	13.8104i	0.156798	+	0.482574i
$820$	−12.5844	−	4.09728i	−0.439466	−	0.143083i
$821$	−6.25705	−	19.2572i	−0.218372	−	0.672081i	−0.998897	−	0.0469561i	$-0.985048\pi$
$821$	−6.25705	−	19.2572i	−0.218372	−	0.672081i	0.780525	−	0.625125i	$-0.214952\pi$
$822$	−61.9925	+	20.1426i	−2.16224	+	0.702553i
$823$	14.9590	+	20.5894i	0.521440	+	0.717700i	0.985796	−	0.167948i	$-0.0537142\pi$
$823$	14.9590	+	20.5894i	0.521440	+	0.717700i	−0.464356	+	0.885649i	$0.653714\pi$
$824$	−7.78642	−	23.9641i	−0.271253	−	0.834830i
$825$	−11.3173	+	15.5377i	−0.394019	+	0.540952i
$826$	16.4692	+	11.9656i	0.573036	+	0.416335i
$827$	−21.1568	−	6.87427i	−0.735695	−	0.239042i	−0.0828805	−	0.996559i	$-0.526412\pi$
$827$	−21.1568	−	6.87427i	−0.735695	−	0.239042i	−0.652815	+	0.757518i	$0.726412\pi$
$828$	16.5136	+	22.7291i	0.573889	+	0.789890i
$829$	11.9991	−	8.71789i	0.416747	−	0.302785i	−0.359580	−	0.933114i	$-0.617080\pi$
$829$	11.9991	−	8.71789i	0.416747	−	0.302785i	0.776328	+	0.630329i	$0.217080\pi$
$830$	0.0126378	−	21.0197i	0.000438665	−	0.729603i
$831$	42.9333			1.48934
$832$			5.09701i			0.176707i
$833$	25.4482	−	35.0264i	0.881728	−	1.21359i
$834$	4.92892	+	15.1697i	0.170675	+	0.525283i
$835$	7.22251	+	22.2741i	0.249945	+	0.770829i
$836$	−3.17357			−0.109760
$837$	−5.04766	−	23.3158i	−0.174473	−	0.805914i
$838$		−	15.9809i		−	0.552052i
$839$	9.12565	−	28.0859i	0.315052	−	0.969632i	−0.660680	−	0.750667i	$-0.729732\pi$
$839$	9.12565	−	28.0859i	0.315052	−	0.969632i	0.975733	−	0.218964i	$-0.0702679\pi$
$840$	76.1676	+	55.4090i	2.62803	+	1.91179i
$841$	22.9794	+	16.6955i	0.792394	+	0.575708i
$842$		−	10.9897i		−	0.378729i
$843$		−	33.3674i		−	1.14923i
$844$	9.92115	+	7.20814i	0.341500	+	0.248114i
$845$	26.7791	+	8.71887i	0.921230	+	0.299938i
$846$	13.5428	−	9.83939i	0.465610	−	0.338285i
$847$	43.0446	+	13.9860i	1.47903	+	0.480566i
$848$	−1.30989	+	1.80291i	−0.0449819	+	0.0619122i
$849$	4.80267	−	14.7811i	0.164827	−	0.507286i
$850$	−12.9959	−	0.0156273i	−0.445755	−	0.000536011i
$851$	−47.6269	+	34.6030i	−1.63263	+	1.18617i
$852$	4.53169	−	1.47244i	0.155253	−	0.0504449i
$853$	19.1989	−	6.23811i	0.657359	−	0.213589i	0.0387029	−	0.999251i	$-0.487677\pi$
$853$	19.1989	−	6.23811i	0.657359	−	0.213589i	0.618656	+	0.785662i	$0.287677\pi$
$854$	27.0057	−	19.6208i	0.924115	−	0.671409i
$855$	16.4559	−	22.6209i	0.562778	−	0.773620i
$856$	5.61871	−	17.2926i	0.192044	−	0.591050i
$857$	15.7602	−	21.6920i	0.538357	−	0.740984i	−0.450019	−	0.893019i	$-0.648583\pi$
$857$	15.7602	−	21.6920i	0.538357	−	0.740984i	0.988375	+	0.152035i	$0.0485826\pi$
$858$	2.52089	+	0.819088i	0.0860619	+	0.0279632i
$859$	−37.3251	+	27.1183i	−1.27352	+	0.925263i	−0.999337	−	0.0364157i	$-0.988406\pi$
$859$	−37.3251	+	27.1183i	−1.27352	+	0.925263i	−0.274179	+	0.961679i	$0.588406\pi$
$860$	2.94895	−	9.05739i	0.100558	−	0.308855i
$861$	79.6593	+	57.8759i	2.71478	+	1.97240i
$862$			26.7123i			0.909825i
$863$		−	9.35901i		−	0.318585i	−0.987231	−	0.159292i	$-0.949079\pi$
$863$		−	9.35901i		−	0.318585i	0.987231	−	0.159292i	$-0.0509212\pi$
$864$	−14.9862	−	10.8881i	−0.509841	−	0.370421i
$865$	7.71005	+	5.60876i	0.262150	+	0.190704i
$866$	−5.31327	+	16.3526i	−0.180552	+	0.555682i
$867$			30.9039i			1.04955i
$868$	−9.29223	+	21.0837i	−0.315399	+	0.715629i
$869$	−10.1719			−0.345057
$870$	−4.88900	+	1.58528i	−0.165753	+	0.0537461i
$871$	−0.657284	−	2.02291i	−0.0222712	−	0.0685438i
$872$	20.0469	−	27.5923i	0.678875	−	0.934392i
$873$			78.6052i			2.66038i
$874$	22.1518			0.749297
$875$	−17.3846	+	53.1778i	−0.587708	+	1.79774i
$876$	−20.2221	+	14.6922i	−0.683241	+	0.496404i
$877$	25.8923	+	35.6378i	0.874322	+	1.20340i	0.977961	+	0.208787i	$0.0669514\pi$
$877$	25.8923	+	35.6378i	0.874322	+	1.20340i	−0.103639	+	0.994615i	$0.533049\pi$
$878$	1.69606	+	0.551083i	0.0572392	+	0.0185981i
$879$	−36.8769	−	26.7926i	−1.24383	−	0.903692i
$880$	4.94399	−	1.60311i	0.166662	−	0.0540410i
$881$	3.08166	+	9.48436i	0.103824	+	0.319536i	0.989453	−	0.144857i	$-0.0462723\pi$
$881$	3.08166	+	9.48436i	0.103824	+	0.319536i	−0.885629	+	0.464394i	$0.846272\pi$
$882$	−52.3540	−	72.0592i	−1.76285	−	2.42636i
$883$	−23.7680	+	7.72270i	−0.799858	+	0.259890i	−0.680296	−	0.732937i	$-0.738149\pi$
$883$	−23.7680	+	7.72270i	−0.799858	+	0.259890i	−0.119562	+	0.992827i	$0.538149\pi$
$884$	−0.390398	−	1.20152i	−0.0131305	−	0.0404115i
$885$	7.14861	−	21.9562i	0.240298	−	0.738051i
$886$	−6.03281	−	18.5671i	−0.202676	−	0.623773i
$887$	7.82050	+	2.54103i	0.262587	+	0.0853196i	0.437352	−	0.899291i	$-0.355917\pi$
$887$	7.82050	+	2.54103i	0.262587	+	0.0853196i	−0.174765	+	0.984610i	$0.555917\pi$
$888$	39.0832	−	53.7934i	1.31154	−	1.80519i
$889$	16.3931	−	50.4528i	0.549808	−	1.69213i
$890$	−7.44624	+	22.8704i	−0.249599	+	0.766617i
$891$	2.14466	−	1.55818i	0.0718487	−	0.0522011i
$892$	−6.55286	+	9.01924i	−0.219406	+	0.301987i
$893$			9.30494i			0.311378i
$894$	−4.68790			−0.156787
$895$	−0.00396127	+	6.58851i	−0.000132411	+	0.220230i
$896$	−0.0390842	−	0.120289i	−0.00130571	−	0.00401857i
$897$	12.4050	+	4.03062i	0.414190	+	0.134578i
$898$		−	5.25327i		−	0.175304i
$899$	−2.16291	−	3.71395i	−0.0721372	−	0.123867i
$900$	5.84607	−	17.9190i	0.194869	−	0.597300i
$901$	0.994259	−	3.06002i	0.0331236	−	0.101944i
$902$	10.3091	−	3.34962i	0.343254	−	0.111530i
$903$	−41.6551	+	57.3334i	−1.38620	+	1.90794i
$904$	38.0255			1.26471
$905$	−0.585039	−	0.806256i	−0.0194473	−	0.0268008i
$906$	−20.6870	−	15.0300i	−0.687279	−	0.499337i
$907$	−9.84777	−	13.5543i	−0.326990	−	0.450063i	0.613595	−	0.789621i	$-0.289723\pi$
$907$	−9.84777	−	13.5543i	−0.326990	−	0.450063i	−0.940585	+	0.339558i	$0.889723\pi$
$908$	10.7068	+	14.7366i	0.355316	+	0.489051i
$909$	4.91650	−	15.1314i	0.163070	−	0.501878i
$910$	7.71472	+	0.00463838i	0.255740	+	0.000153761i
$911$	5.47419	−	16.8478i	0.181368	−	0.558193i	−0.818499	−	0.574508i	$-0.805193\pi$
$911$	5.47419	−	16.8478i	0.181368	−	0.558193i	0.999867	+	0.0163147i	$0.00519337\pi$
$912$	−11.9273	+	3.87542i	−0.394953	+	0.128328i
$913$	−7.13387	−	9.81893i	−0.236097	−	0.324959i
$914$	1.37489	+	4.23147i	0.0454773	+	0.139965i
$915$	−30.6187	−	22.2740i	−1.01222	−	0.736354i
$916$	−2.86353	+	2.08048i	−0.0946138	+	0.0687410i
$917$	−18.4449	+	5.99310i	−0.609103	+	0.197909i
$918$	−10.5915	−	3.44140i	−0.349573	−	0.113583i
$919$	−0.480867	−	0.349370i	−0.0158623	−	0.0115247i	0.579826	−	0.814740i	$-0.303121\pi$
$919$	−0.480867	−	0.349370i	−0.0158623	−	0.0115247i	−0.595688	+	0.803216i	$0.703121\pi$
$920$	48.5365	−	15.7382i	1.60020	−	0.518873i
$921$	−2.37331	+	1.72431i	−0.0782033	+	0.0568180i
$922$	−14.7959	−	20.3648i	−0.487276	−	0.670678i
$923$	0.784193	−	1.07935i	0.0258120	−	0.0355272i
$924$	15.9093			0.523377
$925$	37.5478	+	12.2500i	1.23456	+	0.402776i
$926$	26.9678	+	19.5933i	0.886218	+	0.643875i
$927$	35.6784	−	11.5926i	1.17183	−	0.380751i
$928$	−3.17392	−	1.03127i	−0.104189	−	0.0338531i
$929$	51.7518			1.69792			0.848960	−	0.528457i	$-0.177229\pi$
$929$	51.7518			1.69792			0.848960	+	0.528457i	$0.177229\pi$
$930$	−36.8803	−	3.75849i	−1.20935	−	0.123246i
$931$	49.5103			1.62263
$932$	13.0086	+	4.22674i	0.426109	+	0.138451i
$933$	52.3508	−	17.0098i	1.71389	−	0.556876i
$934$	14.6354	+	10.6332i	0.478884	+	0.347930i
$935$	−6.07344	+	4.40703i	−0.198623	+	0.144125i
$936$	−8.88486			−0.290411
$937$	−10.3939	+	14.3059i	−0.339552	+	0.467354i	−0.944311	−	0.329055i	$-0.893270\pi$
$937$	−10.3939	+	14.3059i	−0.339552	+	0.467354i	0.604758	+	0.796409i	$0.293270\pi$
$938$	10.6442	+	14.6505i	0.347546	+	0.478356i
$939$	42.8884	−	31.1603i	1.39961	−	1.01688i
$940$	1.93387	+	5.96403i	0.0630758	+	0.194525i
$941$	18.4855	+	13.4305i	0.602610	+	0.437822i	0.846804	−	0.531904i	$-0.178523\pi$
$941$	18.4855	+	13.4305i	0.602610	+	0.437822i	−0.244194	+	0.969726i	$0.578523\pi$
$942$	23.8267	+	7.74178i	0.776317	+	0.252241i
$943$	50.7295	−	16.4830i	1.65198	−	0.536760i
$944$	−5.05095	+	3.66973i	−0.164394	+	0.119440i
$945$	−28.2036	+	38.7698i	−0.917462	+	1.26118i
$946$	2.41083	+	7.41977i	0.0783828	+	0.241238i
$947$	−17.1954	−	23.6674i	−0.558774	−	0.769086i	0.432396	−	0.901684i	$-0.357668\pi$
$947$	−17.1954	−	23.6674i	−0.558774	−	0.769086i	−0.991170	+	0.132597i	$0.957668\pi$
$948$	15.7287	−	5.11055i	0.510843	−	0.165983i
$949$	−2.16272	+	6.65618i	−0.0702050	+	0.216069i
$950$	−8.72092	−	12.0337i	−0.282944	−	0.390425i
$951$	−19.8747	+	61.1681i	−0.644482	+	1.98351i
$952$	21.6123	+	29.7467i	0.700458	+	0.964097i
$953$	−16.3742	−	22.5372i	−0.530414	−	0.730052i	0.456780	−	0.889580i	$-0.349003\pi$
$953$	−16.3742	−	22.5372i	−0.530414	−	0.730052i	−0.987193	+	0.159528i	$0.949003\pi$
$954$	−5.35511	−	3.89071i	−0.173378	−	0.125966i
$955$	31.0665	+	42.8135i	1.00529	+	1.38541i
$956$	−12.3804			−0.400410
$957$	−1.74433	+	2.40086i	−0.0563861	+	0.0776088i
$958$	−4.66766	+	1.51661i	−0.150805	+	0.0489995i
$959$	−33.8507	+	104.182i	−1.09310	+	3.36420i
$960$	−39.8391	+	28.9082i	−1.28580	+	0.933009i
$961$	−3.47219	−	30.8049i	−0.112006	−	0.993708i
$962$		−	5.44614i		−	0.175591i
$963$	25.7457	+	8.36528i	0.829643	+	0.269567i
$964$	−3.30645	−	10.1762i	−0.106494	−	0.327754i
$965$	−43.3824	−	0.0260832i	−1.39653	−	0.000839647i
$966$	−111.049			−3.57293
$967$		−	30.6100i		−	0.984352i	−0.870496	−	0.492176i	$-0.836202\pi$
$967$		−	30.6100i		−	0.984352i	0.870496	−	0.492176i	$-0.163798\pi$
$968$	−16.2773	+	22.4038i	−0.523173	+	0.720085i
$969$	14.6485	−	10.6428i	0.470579	−	0.341896i
$970$	39.7094	+	12.9288i	1.27499	+	0.415118i
$971$	13.3831	−	41.1888i	0.429483	−	1.32181i	−0.469153	−	0.883117i	$-0.655441\pi$
$971$	13.3831	−	41.1888i	0.429483	−	1.32181i	0.898636	−	0.438695i	$-0.144559\pi$
$972$	−8.78145	+	12.0866i	−0.281665	+	0.387679i
$973$	25.4934	+	8.28332i	0.817282	+	0.265551i
$974$	−5.01979	−	15.4493i	−0.160845	−	0.495029i
$975$	−2.69410	−	8.32565i	−0.0862804	−	0.266634i
$976$	3.16359	+	9.73654i	0.101264	+	0.311659i
$977$	15.7510	−	5.11780i	0.503918	−	0.163733i	−0.0460166	−	0.998941i	$-0.514653\pi$
$977$	15.7510	−	5.11780i	0.503918	−	0.163733i	0.549934	+	0.835208i	$0.314653\pi$
$978$	−5.17006	−	7.11598i	−0.165320	−	0.227544i
$979$	4.29156	+	13.2081i	0.137159	+	0.422131i
$980$	31.7338	−	10.2898i	1.01370	−	0.328697i
$981$	41.0800	+	29.8464i	1.31158	+	0.952922i
$982$	41.4358	+	13.4633i	1.32227	+	0.429632i
$983$	−14.2962	−	19.6770i	−0.455977	−	0.627598i	0.517692	−	0.855567i	$-0.326792\pi$
$983$	−14.2962	−	19.6770i	−0.455977	−	0.627598i	−0.973668	+	0.227969i	$0.926792\pi$
$984$	−48.7403	+	35.4119i	−1.55378	+	1.12889i
$985$	−24.5347	−	0.0147512i	−0.781741	−	0.000470013i
$986$	−2.00636			−0.0638954
$987$		−	46.6463i		−	1.48477i
$988$	0.849182	−	1.16880i	0.0270161	−	0.0371844i
$989$	11.8633	+	36.5116i	0.377233	+	1.16100i
$990$	4.76166	+	14.6849i	0.151335	+	0.466717i
$991$	25.7566			0.818186			0.409093	−	0.912493i	$-0.365845\pi$
$991$	25.7566			0.818186			0.409093	+	0.912493i	$0.365845\pi$
$992$	−17.9489	−	16.0394i	−0.569877	−	0.509252i
$993$		−	58.2956i		−	1.84996i
$994$	−3.51003	+	10.8028i	−0.111331	+	0.342643i
$995$	−13.6089	+	18.7074i	−0.431431	+	0.593064i
$996$	15.9643	+	11.5987i	0.505847	+	0.367519i
$997$		−	27.2866i		−	0.864175i	−0.901832	−	0.432087i	$-0.857777\pi$
$997$		−	27.2866i		−	0.864175i	0.901832	−	0.432087i	$-0.142223\pi$
$998$			44.2086i			1.39940i
$999$	27.3812	+	19.8936i	0.866302	+	0.629405i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	155.2.n.a.39.10	yes	56
5.2	odd	4		775.2.k.h.101.5		56
5.3	odd	4		775.2.k.h.101.10		56
5.4	even	2	inner	155.2.n.a.39.5	yes	56
31.4	even	5	inner	155.2.n.a.4.5	✓	56
155.4	even	10	inner	155.2.n.a.4.10	yes	56
155.97	odd	20		775.2.k.h.376.5		56
155.128	odd	20		775.2.k.h.376.10		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.n.a.4.5	✓	56	31.4	even	5	inner
155.2.n.a.4.10	yes	56	155.4	even	10	inner
155.2.n.a.39.5	yes	56	5.4	even	2	inner
155.2.n.a.39.10	yes	56	1.1	even	1	trivial
775.2.k.h.101.5		56	5.2	odd	4
775.2.k.h.101.10		56	5.3	odd	4
775.2.k.h.376.5		56	155.97	odd	20
775.2.k.h.376.10		56	155.128	odd	20

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 155 = 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	155.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.03006 + 0.334686i) q^{2} +(-2.61471 + 0.849570i) q^{3} +(-0.669031 - 0.486079i) q^{4} +(-1.31324 - 1.80981i) q^{5} -2.97764 q^{6} +(-2.94133 + 4.04839i) q^{7} +(-1.79968 - 2.47704i) q^{8} +(3.68788 - 2.67940i) q^{9} +(-0.746995 - 2.30373i) q^{10} +(-1.13130 - 0.821939i) q^{11} +(2.16228 + 0.702567i) q^{12} +(0.605427 - 0.196715i) q^{13} +(-4.38467 + 3.18565i) q^{14} +(4.97130 + 3.61643i) q^{15} +(-0.513645 - 1.58084i) q^{16} +(1.41059 + 1.94151i) q^{17} +(4.69549 - 1.52566i) q^{18} +(-0.848048 + 2.61002i) q^{19} +(-0.00111178 + 1.84916i) q^{20} +(4.25132 - 13.0842i) q^{21} +(-0.890214 - 1.22527i) q^{22} +(-4.38062 - 6.02940i) q^{23} +(6.81005 + 4.94779i) q^{24} +(-1.55080 + 4.75342i) q^{25} +0.689462 q^{26} +(-2.51846 + 3.46636i) q^{27} +(3.93568 - 1.27878i) q^{28} +(-0.238536 + 0.734139i) q^{29} +(3.91035 + 5.38895i) q^{30} +(-3.70997 + 4.15164i) q^{31} +4.32332i q^{32} +(3.65632 + 1.18801i) q^{33} +(0.803191 + 2.47197i) q^{34} +(11.1895 + 0.00672754i) q^{35} -3.76971 q^{36} -7.89911i q^{37} +(-1.74708 + 2.40464i) q^{38} +(-1.41589 + 1.02871i) q^{39} +(-2.11956 + 6.51002i) q^{40} +(-2.21167 + 6.80681i) q^{41} +(8.75821 - 12.0546i) q^{42} +(-4.89908 - 1.59181i) q^{43} +(0.357348 + 1.09980i) q^{44} +(-9.69228 - 3.15566i) q^{45} +(-2.49433 - 7.67676i) q^{46} +(3.22464 - 1.04775i) q^{47} +(2.68606 + 3.69705i) q^{48} +(-5.57493 - 17.1579i) q^{49} +(-3.18832 + 4.37726i) q^{50} +(-5.33772 - 3.87808i) q^{51} +(-0.500668 - 0.162677i) q^{52} +(-0.788052 - 1.08466i) q^{53} +(-3.75430 + 2.72766i) q^{54} +(-0.00187998 + 3.12684i) q^{55} +15.3215 q^{56} -7.54493i q^{57} +(-0.491412 + 0.676370i) q^{58} +(-1.16069 - 3.57224i) q^{59} +(-1.56808 - 4.83595i) q^{60} -6.15910 q^{61} +(-5.21098 + 3.03475i) q^{62} +22.8110i q^{63} +(-2.47425 + 7.61494i) q^{64} +(-1.15109 - 0.837372i) q^{65} +(3.36861 + 2.44744i) q^{66} -3.34130i q^{67} -1.98459i q^{68} +(16.5764 + 12.0435i) q^{69} +(11.5235 + 3.75189i) q^{70} +(1.69553 - 1.23188i) q^{71} +(-13.2740 - 4.31298i) q^{72} +(-6.46222 + 8.89448i) q^{73} +(2.64372 - 8.13653i) q^{74} +(0.0165296 - 13.7463i) q^{75} +(1.83605 - 1.33397i) q^{76} +(6.65506 - 2.16236i) q^{77} +(-1.80274 + 0.585747i) q^{78} +(5.88488 - 4.27562i) q^{79} +(-2.18647 + 3.00562i) q^{80} +(-0.585816 + 1.80296i) q^{81} +(-4.55629 + 6.27119i) q^{82} +(8.25452 + 2.68206i) q^{83} +(-9.20423 + 6.68727i) q^{84} +(1.66131 - 5.10256i) q^{85} +(-4.51358 - 3.27931i) q^{86} -2.12221i q^{87} +4.28151i q^{88} +(-8.03470 - 5.83755i) q^{89} +(-8.92745 - 6.49437i) q^{90} +(-0.984379 + 3.02961i) q^{91} +6.16318i q^{92} +(6.17339 - 14.0072i) q^{93} +3.67223 q^{94} +(5.83733 - 1.89278i) q^{95} +(-3.67297 - 11.3042i) q^{96} +(-10.1356 + 13.9505i) q^{97} -19.5394i q^{98} -6.37441 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{4} - 10 q^{5} - 4 q^{6} + 8 q^{9} + 4 q^{10} - 14 q^{11} - 16 q^{14} + 21 q^{15} - 22 q^{16} - 2 q^{19} - 29 q^{20} - 38 q^{21} - 30 q^{24} - 10 q^{25} + 12 q^{26} + 20 q^{29} - 30 q^{30} + 26 q^{31}+ \cdots - 52 q^{99}+O(q^{100}) \) 56 * q + 2 * q^4 - 10 * q^5 - 4 * q^6 + 8 * q^9 + 4 * q^10 - 14 * q^11 - 16 * q^14 + 21 * q^15 - 22 * q^16 - 2 * q^19 - 29 * q^20 - 38 * q^21 - 30 * q^24 - 10 * q^25 + 12 * q^26 + 20 * q^29 - 30 * q^30 + 26 * q^31 - 2 * q^34 + 24 * q^35 - 44 * q^36 - 18 * q^39 + 36 * q^40 - 20 * q^41 + 62 * q^44 + 8 * q^45 - 70 * q^46 - 42 * q^49 - 11 * q^50 + 10 * q^51 - 26 * q^54 - 30 * q^55 + 208 * q^56 - 50 * q^59 - 67 * q^60 + 56 * q^61 + 12 * q^64 - 27 * q^65 + 60 * q^66 + 34 * q^69 + 5 * q^70 - 8 * q^71 - 84 * q^74 - 38 * q^75 - 20 * q^76 + 122 * q^79 - 80 * q^80 + 42 * q^81 - 40 * q^84 - 18 * q^85 + 78 * q^86 - 28 * q^89 + 144 * q^90 - 20 * q^91 + 160 * q^94 + 9 * q^95 - 70 * q^96 - 52 * q^99

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