LMFDB - Embedded newform 637.2.bl.b.625.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$348$
Relative dimension:	$29$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			625.5
Character	$\chi$	$=$	637.625
Dual form			637.2.bl.b.53.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69736 + 1.15724i) q^{2} +(1.28266 - 1.19014i) q^{3} +(0.811150 - 2.06678i) q^{4} +(0.653901 + 0.201702i) q^{5} +(-0.799869 + 3.50445i) q^{6} +(-2.34964 + 1.21622i) q^{7} +(0.100685 + 0.441128i) q^{8} +(0.00460791 - 0.0614883i) q^{9} +O(q^{10})$	\(q+(-1.69736 + 1.15724i) q^{2} +(1.28266 - 1.19014i) q^{3} +(0.811150 - 2.06678i) q^{4} +(0.653901 + 0.201702i) q^{5} +(-0.799869 + 3.50445i) q^{6} +(-2.34964 + 1.21622i) q^{7} +(0.100685 + 0.441128i) q^{8} +(0.00460791 - 0.0614883i) q^{9} +(-1.34333 + 0.414361i) q^{10} +(0.294283 + 3.92694i) q^{11} +(-1.41932 - 3.61636i) q^{12} +(-0.900969 - 0.433884i) q^{13} +(2.58074 - 4.78347i) q^{14} +(1.07879 - 0.519518i) q^{15} +(2.57373 + 2.38807i) q^{16} +(-5.35944 - 0.807806i) q^{17} +(0.0633356 + 0.109700i) q^{18} +(-0.297407 + 0.515124i) q^{19} +(0.947285 - 1.18786i) q^{20} +(-1.56634 + 4.35640i) q^{21} +(-5.04393 - 6.32489i) q^{22} +(-3.45086 + 0.520133i) q^{23} +(0.654149 + 0.445991i) q^{24} +(-3.74429 - 2.55281i) q^{25} +(2.03138 - 0.306181i) q^{26} +(3.20560 + 4.01970i) q^{27} +(0.607733 + 5.84272i) q^{28} +(1.81431 - 2.27507i) q^{29} +(-1.22989 + 2.13023i) q^{30} +(0.831438 + 1.44009i) q^{31} +(-8.02698 - 1.20987i) q^{32} +(5.05107 + 4.68671i) q^{33} +(10.0317 - 4.83104i) q^{34} +(-1.78175 + 0.321358i) q^{35} +(-0.123345 - 0.0593997i) q^{36} +(3.23686 + 8.24739i) q^{37} +(-0.0913159 - 1.21853i) q^{38} +(-1.67202 + 0.515751i) q^{39} +(-0.0231386 + 0.308763i) q^{40} +(2.08928 + 9.15371i) q^{41} +(-2.38277 - 9.20703i) q^{42} +(0.0187464 - 0.0821334i) q^{43} +(8.35481 + 2.57712i) q^{44} +(0.0154154 - 0.0392778i) q^{45} +(5.25544 - 4.87633i) q^{46} +(-8.34061 + 5.68653i) q^{47} +6.14337 q^{48} +(4.04164 - 5.71534i) q^{49} +9.30965 q^{50} +(-7.83577 + 5.34234i) q^{51} +(-1.62756 + 1.51016i) q^{52} +(-4.69529 + 11.9634i) q^{53} +(-10.0928 - 3.11323i) q^{54} +(-0.599639 + 2.62719i) q^{55} +(-0.773080 - 0.914040i) q^{56} +(0.231596 + 1.01469i) q^{57} +(-0.446732 + 5.96123i) q^{58} +(1.08013 - 0.333177i) q^{59} +(-0.198667 - 2.65102i) q^{60} +(-4.00065 - 10.1935i) q^{61} +(-3.07779 - 1.48218i) q^{62} +(0.0639560 + 0.150080i) q^{63} +(8.69824 - 4.18885i) q^{64} +(-0.501630 - 0.465444i) q^{65} +(-13.9972 - 2.10973i) q^{66} +(1.57305 + 2.72461i) q^{67} +(-6.01686 + 10.4215i) q^{68} +(-3.80726 + 4.77416i) q^{69} +(2.65238 - 2.60738i) q^{70} +(4.70112 + 5.89502i) q^{71} +(0.0275882 - 0.00415825i) q^{72} +(-12.8769 - 8.77931i) q^{73} +(-15.0384 - 10.2530i) q^{74} +(-7.84087 + 1.18182i) q^{75} +(0.823405 + 1.03252i) q^{76} +(-5.46747 - 8.86899i) q^{77} +(2.24118 - 2.81035i) q^{78} +(3.08003 - 5.33476i) q^{79} +(1.20129 + 2.08069i) q^{80} +(9.07863 + 1.36838i) q^{81} +(-14.1393 - 13.1194i) q^{82} +(4.64925 - 2.23896i) q^{83} +(7.73316 + 6.77096i) q^{84} +(-3.34161 - 1.60923i) q^{85} +(0.0632288 + 0.161104i) q^{86} +(-0.380502 - 5.07744i) q^{87} +(-1.70266 + 0.525200i) q^{88} +(0.572244 - 7.63606i) q^{89} +(0.0192884 + 0.0845082i) q^{90} +(2.64465 - 0.0763007i) q^{91} +(-1.72416 + 7.55405i) q^{92} +(2.78037 + 0.857629i) q^{93} +(7.57635 - 19.3042i) q^{94} +(-0.298377 + 0.276853i) q^{95} +(-11.7358 + 8.00136i) q^{96} +6.03606 q^{97} +(-0.246091 + 14.3782i) q^{98} +0.242817 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) $ 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{16}{21}\right)$

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 $

$2$	−1.69736	+	1.15724i	−1.20022	+	0.818294i	−0.987314	−	0.158779i	$-0.949244\pi$
$2$	−1.69736	+	1.15724i	−1.20022	+	0.818294i	−0.212903	+	0.977073i	$0.568292\pi$
$3$	1.28266	−	1.19014i	0.740547	−	0.687127i	−0.216752	−	0.976227i	$-0.569546\pi$
$3$	1.28266	−	1.19014i	0.740547	−	0.687127i	0.957299	+	0.289100i	$0.0933558\pi$
$4$	0.811150	−	2.06678i	0.405575	−	1.03339i
$5$	0.653901	+	0.201702i	0.292434	+	0.0902038i	0.437501	−	0.899218i	$-0.355864\pi$
$5$	0.653901	+	0.201702i	0.292434	+	0.0902038i	−0.145067	+	0.989422i	$0.546340\pi$
$6$	−0.799869	+	3.50445i	−0.326545	+	1.43069i
$7$	−2.34964	+	1.21622i	−0.888081	+	0.459686i
$7$	−2.34964	+	1.21622i	−0.888081	+	0.459686i
$8$	0.100685	+	0.441128i	0.0355974	+	0.155962i
$9$	0.00460791	−	0.0614883i	0.00153597	−	0.0204961i
$10$	−1.34333	+	0.414361i	−0.424797	+	0.131033i
$11$	0.294283	+	3.92694i	0.0887298	+	1.18402i	0.846824	+	0.531872i	$0.178511\pi$
$11$	0.294283	+	3.92694i	0.0887298	+	1.18402i	−0.758095	+	0.652145i	$0.773870\pi$
$12$	−1.41932	−	3.61636i	−0.409722	−	1.04395i
$13$	−0.900969	−	0.433884i	−0.249884	−	0.120338i
$13$	−0.900969	−	0.433884i	−0.249884	−	0.120338i
$14$	2.58074	−	4.78347i	0.689732	−	1.27844i
$15$	1.07879	−	0.519518i	0.278542	−	0.134139i
$16$	2.57373	+	2.38807i	0.643433	+	0.597018i
$17$	−5.35944	−	0.807806i	−1.29986	−	0.195922i	−0.537601	−	0.843199i	$-0.680669\pi$
$17$	−5.35944	−	0.807806i	−1.29986	−	0.195922i	−0.762254	+	0.647278i	$0.775907\pi$
$18$	0.0633356	+	0.109700i	0.0149283	+	0.0258566i
$19$	−0.297407	+	0.515124i	−0.0682299	+	0.118178i	−0.898122	−	0.439746i	$-0.855068\pi$
$19$	−0.297407	+	0.515124i	−0.0682299	+	0.118178i	0.829892	+	0.557924i	$0.188402\pi$
$20$	0.947285	−	1.18786i	0.211819	−	0.265613i
$21$	−1.56634	+	4.35640i	−0.341803	+	0.950644i
$22$	−5.04393	−	6.32489i	−1.07537	−	1.34847i
$23$	−3.45086	+	0.520133i	−0.719553	+	0.108455i	−0.498604	−	0.866830i	$-0.666154\pi$
$23$	−3.45086	+	0.520133i	−0.719553	+	0.108455i	−0.220950	+	0.975285i	$0.570916\pi$
$24$	0.654149	+	0.445991i	0.133528	+	0.0910376i
$25$	−3.74429	−	2.55281i	−0.748858	−	0.510563i
$26$	2.03138	−	0.306181i	0.398386	−	0.0600471i
$27$	3.20560	+	4.01970i	0.616919	+	0.773592i
$28$	0.607733	+	5.84272i	0.114851	+	1.10417i
$29$	1.81431	−	2.27507i	0.336909	−	0.422471i	−0.584300	−	0.811537i	$-0.698631\pi$
$29$	1.81431	−	2.27507i	0.336909	−	0.422471i	0.921210	+	0.389067i	$0.127202\pi$
$30$	−1.22989	+	2.13023i	−0.224546	+	0.388925i
$31$	0.831438	+	1.44009i	0.149331	+	0.258648i	0.930980	−	0.365070i	$-0.118955\pi$
$31$	0.831438	+	1.44009i	0.149331	+	0.258648i	−0.781650	+	0.623718i	$0.785621\pi$
$32$	−8.02698	−	1.20987i	−1.41898	−	0.213877i
$33$	5.05107	+	4.68671i	0.879279	+	0.815852i
$34$	10.0317	−	4.83104i	1.72043	−	0.828516i
$35$	−1.78175	+	0.321358i	−0.301170	+	0.0543194i
$36$	−0.123345	−	0.0593997i	−0.0205575	−	0.00989995i
$37$	3.23686	+	8.24739i	0.532137	+	1.35586i	0.903983	+	0.427568i	$0.140630\pi$
$37$	3.23686	+	8.24739i	0.532137	+	1.35586i	−0.371846	+	0.928294i	$0.621275\pi$
$38$	−0.0913159	−	1.21853i	−0.0148134	−	0.197671i
$39$	−1.67202	+	0.515751i	−0.267738	+	0.0825862i
$40$	−0.0231386	+	0.308763i	−0.00365853	+	0.0488197i
$41$	2.08928	+	9.15371i	0.326290	+	1.42957i	0.826143	+	0.563460i	$0.190530\pi$
$41$	2.08928	+	9.15371i	0.326290	+	1.42957i	−0.499853	+	0.866110i	$0.666613\pi$
$42$	−2.38277	−	9.20703i	−0.367669	−	1.42067i
$43$	0.0187464	−	0.0821334i	0.00285880	−	0.0125252i	−0.973478	−	0.228779i	$-0.926527\pi$
$43$	0.0187464	−	0.0821334i	0.00285880	−	0.0125252i	0.976337	+	0.216254i	$0.0693838\pi$
$44$	8.35481	+	2.57712i	1.25954	+	0.388515i
$45$	0.0154154	−	0.0392778i	0.00229799	−	0.00585519i
$46$	5.25544	−	4.87633i	0.774872	−	0.718976i
$47$	−8.34061	+	5.68653i	−1.21660	+	0.829466i	−0.989518	−	0.144409i	$-0.953872\pi$
$47$	−8.34061	+	5.68653i	−1.21660	+	0.829466i	−0.227085	+	0.973875i	$0.572919\pi$
$48$	6.14337			0.886720
$49$	4.04164	−	5.71534i	0.577377	−	0.816478i
$50$	9.30965			1.31658
$51$	−7.83577	+	5.34234i	−1.09723	+	0.748077i
$52$	−1.62756	+	1.51016i	−0.225702	+	0.209421i
$53$	−4.69529	+	11.9634i	−0.644948	+	1.64330i	0.115038	+	0.993361i	$0.463301\pi$
$53$	−4.69529	+	11.9634i	−0.644948	+	1.64330i	−0.759986	+	0.649939i	$0.774794\pi$
$54$	−10.0928	−	3.11323i	−1.37346	−	0.423657i
$55$	−0.599639	+	2.62719i	−0.0808553	+	0.354250i
$56$	−0.773080	−	0.914040i	−0.103307	−	0.122144i
$57$	0.231596	+	1.01469i	0.0306756	+	0.134399i
$58$	−0.446732	+	5.96123i	−0.0586588	+	0.782747i
$59$	1.08013	−	0.333177i	0.140621	−	0.0433759i	−0.223646	−	0.974671i	$-0.571796\pi$
$59$	1.08013	−	0.333177i	0.140621	−	0.0433759i	0.364267	+	0.931295i	$0.381320\pi$
$60$	−0.198667	−	2.65102i	−0.0256478	−	0.342246i
$61$	−4.00065	−	10.1935i	−0.512231	−	1.30514i	−0.919950	−	0.392036i	$-0.871771\pi$
$61$	−4.00065	−	10.1935i	−0.512231	−	1.30514i	0.407719	−	0.913107i	$-0.366324\pi$
$62$	−3.07779	−	1.48218i	−0.390879	−	0.188238i
$63$	0.0639560	+	0.150080i	0.00805770	+	0.0189083i
$64$	8.69824	−	4.18885i	1.08728	−	0.523607i
$65$	−0.501630	−	0.465444i	−0.0622195	−	0.0577313i
$66$	−13.9972	−	2.10973i	−1.72293	−	0.259690i
$67$	1.57305	+	2.72461i	0.192179	+	0.332864i	0.945972	−	0.324248i	$-0.105111\pi$
$67$	1.57305	+	2.72461i	0.192179	+	0.332864i	−0.753793	+	0.657112i	$0.771778\pi$
$68$	−6.01686	+	10.4215i	−0.729652	+	1.26379i
$69$	−3.80726	+	4.77416i	−0.458341	+	0.574741i
$70$	2.65238	−	2.60738i	0.317021	−	0.311641i
$71$	4.70112	+	5.89502i	0.557920	+	0.699610i	0.978172	−	0.207798i	$-0.0666295\pi$
$71$	4.70112	+	5.89502i	0.557920	+	0.699610i	−0.420251	+	0.907408i	$0.638058\pi$
$72$	0.0275882	−	0.00415825i	0.00325130	−	0.000490054i
$73$	−12.8769	−	8.77931i	−1.50713	−	1.02754i	−0.984581	−	0.174928i	$-0.944031\pi$
$73$	−12.8769	−	8.77931i	−1.50713	−	1.02754i	−0.522544	−	0.852612i	$-0.675017\pi$
$74$	−15.0384	−	10.2530i	−1.74817	−	1.19189i
$75$	−7.84087	+	1.18182i	−0.905386	+	0.136465i
$76$	0.823405	+	1.03252i	0.0944510	+	0.118438i
$77$	−5.46747	−	8.86899i	−0.623076	−	1.01072i
$78$	2.24118	−	2.81035i	0.253764	−	0.318210i
$79$	3.08003	−	5.33476i	0.346530	−	0.600208i	−0.639101	−	0.769123i	$-0.720693\pi$
$79$	3.08003	−	5.33476i	0.346530	−	0.600208i	0.985631	+	0.168916i	$0.0540266\pi$
$80$	1.20129	+	2.08069i	0.134308	+	0.232628i
$81$	9.07863	+	1.36838i	1.00874	+	0.152043i
$82$	−14.1393	−	13.1194i	−1.56143	−	1.44879i
$83$	4.64925	−	2.23896i	0.510321	−	0.245758i	−0.160959	−	0.986961i	$-0.551459\pi$
$83$	4.64925	−	2.23896i	0.510321	−	0.245758i	0.671281	+	0.741203i	$0.265745\pi$
$84$	7.73316	+	6.77096i	0.843757	+	0.738773i
$85$	−3.34161	−	1.60923i	−0.362449	−	0.174546i
$86$	0.0632288	+	0.161104i	0.00681813	+	0.0173723i
$87$	−0.380502	−	5.07744i	−0.0407940	−	0.544359i
$88$	−1.70266	+	0.525200i	−0.181504	+	0.0559865i
$89$	0.572244	−	7.63606i	0.0606577	−	0.809421i	−0.881057	−	0.473009i	$-0.843168\pi$
$89$	0.572244	−	7.63606i	0.0606577	−	0.809421i	0.941715	−	0.336411i	$-0.109213\pi$
$90$	0.0192884	+	0.0845082i	0.00203318	+	0.00890794i
$91$	2.64465	−	0.0763007i	0.277235	−	0.00799848i
$92$	−1.72416	+	7.55405i	−0.179756	+	0.787565i
$93$	2.78037	+	0.857629i	0.288310	+	0.0889320i
$94$	7.57635	−	19.3042i	0.781441	−	1.99108i
$95$	−0.298377	+	0.276853i	−0.0306128	+	0.0284045i
$96$	−11.7358	+	8.00136i	−1.19778	+	0.816635i
$97$	6.03606			0.612869			0.306435	−	0.951892i	$-0.400864\pi$
$97$	6.03606			0.612869			0.306435	+	0.951892i	$0.400864\pi$
$98$	−0.246091	+	14.3782i	−0.0248590	+	1.45241i
$99$	0.242817			0.0244040
$100$	−8.31327	+	5.66789i	−0.831327	+	0.566789i
$101$	−8.29897	+	7.70032i	−0.825778	+	0.766210i	−0.974908	−	0.222607i	$-0.928543\pi$
$101$	−8.29897	+	7.70032i	−0.825778	+	0.766210i	0.149130	+	0.988818i	$0.452353\pi$
$102$	7.11777	−	18.1358i	0.704764	−	1.79571i
$103$	−7.05363	−	2.17576i	−0.695015	−	0.214384i	−0.0729340	−	0.997337i	$-0.523236\pi$
$103$	−7.05363	−	2.17576i	−0.695015	−	0.214384i	−0.622081	+	0.782953i	$0.713712\pi$
$104$	0.100685	−	0.441128i	0.00987295	−	0.0432562i
$105$	−1.90292	+	2.53272i	−0.185706	+	0.247168i
$106$	−5.87495	−	25.7398i	−0.570626	−	2.50007i
$107$	−0.366786	+	4.89441i	−0.0354585	+	0.473161i	0.951005	+	0.309177i	$0.100054\pi$
$107$	−0.366786	+	4.89441i	−0.0354585	+	0.473161i	−0.986463	+	0.163984i	$0.947566\pi$
$108$	10.9080	−	3.36469i	1.04963	−	0.323767i
$109$	1.39443	+	18.6074i	0.133562	+	1.78226i	0.514332	+	0.857591i	$0.328040\pi$
$109$	1.39443	+	18.6074i	0.133562	+	1.78226i	−0.380770	+	0.924670i	$0.624341\pi$
$110$	−2.02249	−	5.15322i	−0.192837	−	0.491340i
$111$	13.9674	+	6.72632i	1.32572	+	0.638434i
$112$	−8.95176	−	2.48091i	−0.845862	−	0.234424i
$113$	−0.103664	+	0.0499218i	−0.00975185	+	0.00469624i	−0.438753	−	0.898608i	$-0.644580\pi$
$113$	−0.103664	+	0.0499218i	−0.00975185	+	0.00469624i	0.429001	+	0.903304i	$0.358866\pi$
$114$	−1.56734	−	1.45428i	−0.146795	−	0.136206i
$115$	−2.36143	−	0.355929i	−0.220205	−	0.0331905i
$116$	−3.23039	−	5.59520i	−0.299934	−	0.519501i
$117$	−0.0308303	+	0.0533997i	−0.00285027	+	0.00493681i
$118$	−1.44781	+	1.81550i	−0.133282	+	0.167130i
$119$	13.5752	−	4.62018i	1.24444	−	0.423531i
$120$	0.337792	+	0.423577i	0.0308360	+	0.0386671i
$121$	−4.45712	+	0.671802i	−0.405192	+	0.0610729i
$122$	18.5869	+	12.6723i	1.68278	+	1.14730i
$123$	13.5740	+	9.25462i	1.22393	+	0.834461i
$124$	3.65077	−	0.550265i	0.327849	−	0.0494152i
$125$	−4.06677	−	5.09957i	−0.363743	−	0.456119i
$126$	−0.282235	−	0.180727i	−0.0251435	−	0.0161004i
$127$	10.9690	−	13.7547i	0.973339	−	1.22053i	−0.00204131	−	0.999998i	$-0.500650\pi$
$127$	10.9690	−	13.7547i	0.973339	−	1.22053i	0.975380	−	0.220530i	$-0.0707788\pi$
$128$	−1.79892	+	3.11581i	−0.159003	+	0.275402i
$129$	−0.0737048	−	0.127660i	−0.00648934	−	0.0112399i
$130$	1.39008	+	0.209521i	0.121918	+	0.0183762i
$131$	7.13936	+	6.62435i	0.623768	+	0.578773i	0.927425	−	0.374009i	$-0.122017\pi$
$131$	7.13936	+	6.62435i	0.623768	+	0.578773i	−0.303657	+	0.952782i	$0.598208\pi$
$132$	13.7836	−	6.63781i	1.19970	−	0.577747i
$133$	0.0722983	−	1.57207i	0.00626906	−	0.136316i
$134$	−5.82307	−	2.80424i	−0.503037	−	0.242250i
$135$	1.28537	+	3.27506i	0.110627	+	0.281873i
$136$	−0.183268	−	2.44554i	−0.0157151	−	0.209703i
$137$	−15.2327	+	4.69866i	−1.30142	+	0.401434i	−0.866563	−	0.499068i	$-0.833676\pi$
$137$	−15.2327	+	4.69866i	−1.30142	+	0.401434i	−0.434853	+	0.900501i	$0.643200\pi$
$138$	0.937450	−	12.5094i	0.0798011	−	1.06487i
$139$	−1.65888	−	7.26804i	−0.140705	−	0.616467i	−0.995272	−	0.0971264i	$-0.969035\pi$
$139$	−1.65888	−	7.26804i	−0.140705	−	0.616467i	0.854568	−	0.519340i	$-0.173822\pi$
$140$	−0.781090	+	3.94314i	−0.0660141	+	0.333256i
$141$	−3.93044	+	17.2204i	−0.331003	+	1.45022i
$142$	−14.8015	−	4.56565i	−1.24211	−	0.383141i
$143$	1.43870	−	3.66574i	0.120310	−	0.306544i
$144$	0.158698	−	0.147250i	0.0132248	−	0.0122709i
$145$	1.64527	−	1.12172i	0.136632	−	0.0931541i
$146$	32.0165			2.64971
$147$	−1.61798	−	12.1410i	−0.133449	−	1.00137i
$148$	19.6711			1.61695
$149$	−9.02639	+	6.15409i	−0.739470	+	0.504162i	−0.873506	−	0.486814i	$-0.838159\pi$
$149$	−9.02639	+	6.15409i	−0.739470	+	0.504162i	0.134035	+	0.990977i	$0.457207\pi$
$150$	11.9412	−	11.0798i	0.974992	−	0.904660i
$151$	7.30163	−	18.6043i	0.594199	−	1.51399i	−0.244641	−	0.969614i	$-0.578670\pi$
$151$	7.30163	−	18.6043i	0.594199	−	1.51399i	0.838839	−	0.544379i	$-0.183235\pi$
$152$	−0.257180	−	0.0793297i	−0.0208601	−	0.00643448i
$153$	−0.0743664	+	0.325821i	−0.00601217	+	0.0263410i
$154$	19.5439	+	8.72672i	1.57489	+	0.703219i
$155$	0.253209	+	1.10938i	0.0203382	+	0.0891076i
$156$	−0.290320	+	3.87405i	−0.0232442	+	0.310172i
$157$	20.4992	−	6.32316i	1.63601	−	0.504643i	0.665644	−	0.746269i	$-0.268157\pi$
$157$	20.4992	−	6.32316i	1.63601	−	0.504643i	0.970370	+	0.241626i	$0.0776806\pi$
$158$	0.945691	+	12.6194i	0.0752351	+	1.00394i
$159$	8.21563	+	20.9331i	0.651542	+	1.66010i
$160$	−5.00482	−	2.41019i	−0.395666	−	0.190542i
$161$	7.47569	−	5.41911i	0.589167	−	0.427086i
$162$	−16.9933	+	8.18354i	−1.33512	+	0.642960i
$163$	15.2443	+	14.1446i	1.19402	+	1.10789i	0.991700	+	0.128573i	$0.0410395\pi$
$163$	15.2443	+	14.1446i	1.19402	+	1.10789i	0.202323	+	0.979319i	$0.435151\pi$
$164$	20.6134	+	3.10697i	1.60964	+	0.242614i
$165$	2.35759	+	4.08346i	0.183538	+	0.317897i
$166$	−5.30044	+	9.18064i	−0.411394	+	0.712556i
$167$	2.77526	−	3.48006i	0.214756	−	0.269295i	−0.662772	−	0.748821i	$-0.730620\pi$
$167$	2.77526	−	3.48006i	0.214756	−	0.269295i	0.877528	+	0.479526i	$0.159191\pi$
$168$	−2.07944	−	0.252334i	−0.160432	−	0.0194680i
$169$	0.623490	+	0.781831i	0.0479608	+	0.0601409i
$170$	7.53420	−	1.13560i	0.577847	−	0.0870964i
$171$	0.0303037	+	0.0206607i	0.00231738	+	0.00157996i
$172$	−0.154545	−	0.105367i	−0.0117840	−	0.00803416i
$173$	18.4395	−	2.77931i	1.40193	−	0.211307i	0.595841	−	0.803102i	$-0.296819\pi$
$173$	18.4395	−	2.77931i	1.40193	−	0.211307i	0.806088	+	0.591796i	$0.201581\pi$
$174$	6.52168	+	8.17793i	0.494407	+	0.619967i
$175$	11.9025	+	1.44434i	0.899746	+	0.109182i
$176$	−8.62041	+	10.8097i	−0.649788	+	0.814809i
$177$	0.988922	−	1.71286i	0.0743319	−	0.128747i
$178$	7.86547	+	13.6234i	0.589542	+	1.02112i
$179$	22.0991	+	3.33091i	1.65177	+	0.248964i	0.907846	−	0.419305i	$-0.137726\pi$
$179$	22.0991	+	3.33091i	1.65177	+	0.248964i	0.743920	+	0.668268i	$0.232964\pi$
$180$	−0.0686743	−	0.0637204i	−0.00511868	−	0.00474944i
$181$	−9.28910	+	4.47340i	−0.690453	+	0.332505i	−0.745995	−	0.665952i	$-0.768026\pi$
$181$	−9.28910	+	4.47340i	−0.690453	+	0.332505i	0.0555416	+	0.998456i	$0.482311\pi$
$182$	−4.40064	+	3.19001i	−0.326197	+	0.236460i
$183$	−17.2632	−	8.31351i	−1.27613	−	0.614552i
$184$	−0.576894	−	1.46990i	−0.0425292	−	0.108363i
$185$	0.453075	+	6.04586i	0.0333107	+	0.444501i
$186$	−5.71178	+	1.76185i	−0.418808	+	0.129185i
$187$	1.59501	−	21.2839i	0.116639	−	1.55644i
$188$	4.98730	+	21.8508i	0.363736	+	1.59363i
$189$	−12.4208	−	5.54615i	−0.903483	−	0.403423i
$190$	0.186067	−	0.815214i	0.0134987	−	0.0591419i
$191$	−8.90227	−	2.74599i	−0.644146	−	0.198693i	−0.0445646	−	0.999007i	$-0.514190\pi$
$191$	−8.90227	−	2.74599i	−0.644146	−	0.198693i	−0.599581	+	0.800314i	$0.704666\pi$
$192$	6.17161	−	15.7250i	0.445398	−	1.13486i
$193$	8.41661	−	7.80947i	0.605841	−	0.562138i	−0.316462	−	0.948605i	$-0.602495\pi$
$193$	8.41661	−	7.80947i	0.605841	−	0.562138i	0.922303	+	0.386467i	$0.126305\pi$
$194$	−10.2454	+	6.98519i	−0.735577	+	0.501508i
$195$	−1.19737			−0.0857452
$196$	−8.53396	−	12.9892i	−0.609569	−	0.927797i
$197$	−5.40689			−0.385225			−0.192612	−	0.981275i	$-0.561696\pi$
$197$	−5.40689			−0.385225			−0.192612	+	0.981275i	$0.561696\pi$
$198$	−0.412148	+	0.280998i	−0.0292901	+	0.0199697i
$199$	−0.371124	+	0.344353i	−0.0263083	+	0.0244105i	−0.693217	−	0.720729i	$-0.743807\pi$
$199$	−0.371124	+	0.344353i	−0.0263083	+	0.0244105i	0.666909	+	0.745139i	$0.267617\pi$
$200$	0.749126	−	1.90874i	0.0529712	−	0.134968i
$201$	5.26036	+	1.62261i	0.371037	+	0.114450i
$202$	5.17523	−	22.6742i	0.364128	−	1.59535i
$203$	−1.49600	+	7.55220i	−0.104999	+	0.530061i
$204$	4.68543	+	20.5282i	0.328046	+	1.43726i
$205$	−0.480141	+	6.40704i	−0.0335345	+	0.447487i
$206$	14.4905	−	4.46971i	1.00960	−	0.311420i
$207$	0.0160808	+	0.214584i	0.00111770	+	0.0149146i
$208$	−1.28271	−	3.26828i	−0.0889396	−	0.226614i
$209$	−2.11038	−	1.01631i	−0.145978	−	0.0702995i
$210$	0.298981	−	6.50110i	0.0206316	−	0.448618i
$211$	4.02478	−	1.93823i	0.277078	−	0.133434i	−0.290185	−	0.956971i	$-0.593717\pi$
$211$	4.02478	−	1.93823i	0.277078	−	0.133434i	0.567262	+	0.823537i	$0.308003\pi$
$212$	20.9171	+	19.4082i	1.43659	+	1.33296i
$213$	13.0459	+	1.96635i	0.893887	+	0.134732i
$214$	−5.04146	−	8.73206i	−0.344627	−	0.596911i
$215$	0.0288247	−	0.0499259i	0.00196583	−	0.00340492i
$216$	−1.45045	+	1.81881i	−0.0986905	+	0.123754i
$217$	−3.70504	−	2.37249i	−0.251515	−	0.161055i
$218$	−23.9001	−	29.9697i	−1.61872	−	2.02981i
$219$	−26.9653	+	4.06437i	−1.82215	+	0.274645i
$220$	4.94341	+	3.37036i	0.333285	+	0.227230i
$221$	4.47820	+	3.05318i	0.301236	+	0.205379i
$222$	−31.4917	+	4.74660i	−2.11358	+	0.318571i
$223$	−7.46015	−	9.35473i	−0.499569	−	0.626439i	0.466563	−	0.884488i	$-0.345492\pi$
$223$	−7.46015	−	9.35473i	−0.499569	−	0.626439i	−0.966132	+	0.258049i	$0.916921\pi$
$224$	20.3320	−	6.91977i	1.35849	−	0.462346i
$225$	−0.174221	+	0.218467i	−0.0116148	+	0.0145645i
$226$	0.118183	−	0.204699i	0.00786143	−	0.0136164i
$227$	−8.56837	−	14.8408i	−0.568702	−	0.985021i	−0.996695	−	0.0812390i	$-0.974112\pi$
$227$	−8.56837	−	14.8408i	−0.568702	−	0.985021i	0.427992	−	0.903782i	$-0.359221\pi$
$228$	2.28499	+	0.344407i	0.151327	+	0.0228089i
$229$	−11.4782	−	10.6503i	−0.758504	−	0.703789i	0.202818	−	0.979216i	$-0.434990\pi$
$229$	−11.4782	−	10.6503i	−0.758504	−	0.703789i	−0.961322	+	0.275428i	$0.911181\pi$
$230$	4.42010	−	2.12861i	0.291453	−	0.140356i
$231$	−17.5683	−	4.86890i	−1.15591	−	0.320350i
$232$	1.18627	+	0.571279i	0.0778827	+	0.0375063i
$233$	1.34313	+	3.42223i	0.0879911	+	0.224198i	0.968095	−	0.250583i	$-0.0806225\pi$
$233$	1.34313	+	3.42223i	0.0879911	+	0.224198i	−0.880104	+	0.474781i	$0.842527\pi$
$234$	−0.00946614	−	0.126317i	−0.000618821	−	0.00825760i
$235$	−6.60092	+	2.03611i	−0.430597	+	0.132821i
$236$	0.187548	−	2.50265i	0.0122083	−	0.162909i
$237$	−2.39847	−	10.5084i	−0.155797	−	0.682592i
$238$	−17.6954	+	23.5520i	−1.14703	+	1.52665i
$239$	−1.66252	+	7.28397i	−0.107539	+	0.471161i	0.892267	+	0.451507i	$0.149113\pi$
$239$	−1.66252	+	7.28397i	−0.107539	+	0.471161i	−0.999807	+	0.0196536i	$0.993744\pi$
$240$	4.01716	+	1.23913i	0.259307	+	0.0799855i
$241$	3.46923	−	8.83946i	0.223473	−	0.569400i	−0.774532	−	0.632535i	$-0.782015\pi$
$241$	3.46923	−	8.83946i	0.223473	−	0.569400i	0.998005	+	0.0631349i	$0.0201098\pi$
$242$	6.78791	−	6.29826i	0.436343	−	0.404867i
$243$	0.529368	−	0.360917i	0.0339590	−	0.0231528i
$244$	−24.3128			−1.55647
$245$	3.79563	−	2.92206i	0.242494	−	0.186684i
$246$	−33.7499			−2.15182
$247$	0.491459	−	0.335071i	0.0312708	−	0.0213201i
$248$	−0.551553	+	0.511766i	−0.0350236	+	0.0324972i
$249$	3.29875	−	8.40509i	0.209050	−	0.532651i
$250$	12.8042	+	3.94958i	0.809810	+	0.249793i
$251$	2.17898	−	9.54673i	0.137536	−	0.602584i	−0.858436	−	0.512920i	$-0.828564\pi$
$251$	2.17898	−	9.54673i	0.137536	−	0.602584i	0.995972	−	0.0896637i	$-0.0285792\pi$
$252$	0.362059	−	0.0104457i	0.0228076	−	0.000658020i
$253$	−3.05806	−	13.3982i	−0.192259	−	0.842340i
$254$	−2.70086	+	36.0404i	−0.169467	+	2.26138i
$255$	−6.20138	+	1.91287i	−0.388346	+	0.119789i
$256$	0.890598	+	11.8842i	0.0556623	+	0.742762i
$257$	2.42449	+	6.17749i	0.151235	+	0.385342i	0.986334	−	0.164759i	$-0.0526846\pi$
$257$	2.42449	+	6.17749i	0.151235	+	0.385342i	−0.835098	+	0.550101i	$0.814589\pi$
$258$	0.272838	+	0.131392i	0.0169861	+	0.00818010i
$259$	−17.6361	−	15.4417i	−1.09585	−	0.959500i
$260$	−1.36887	+	0.659211i	−0.0848935	+	0.0408825i
$261$	−0.131530	−	0.122042i	−0.00814151	−	0.00755422i
$262$	−19.7841	−	2.98197i	−1.22226	−	0.184227i
$263$	1.64659	+	2.85197i	0.101533	+	0.175860i	0.912316	−	0.409486i	$-0.134292\pi$
$263$	1.64659	+	2.85197i	0.101533	+	0.175860i	−0.810784	+	0.585346i	$0.800959\pi$
$264$	−1.55888	+	2.70005i	−0.0959422	+	0.166177i
$265$	−5.48330	+	6.87584i	−0.336836	+	0.422380i
$266$	1.69655	+	2.75204i	0.104022	+	0.168738i
$267$	−8.35398	−	10.4756i	−0.511255	−	0.641094i
$268$	6.90713	−	1.04108i	0.421920	−	0.0635942i
$269$	23.2335	+	15.8403i	1.41657	+	0.965802i	0.998348	+	0.0574578i	$0.0182995\pi$
$269$	23.2335	+	15.8403i	1.41657	+	0.965802i	0.418223	+	0.908344i	$0.362653\pi$
$270$	−5.97178	−	4.07149i	−0.363431	−	0.247783i
$271$	4.13665	−	0.623500i	0.251284	−	0.0378749i	−0.0221924	−	0.999754i	$-0.507065\pi$
$271$	4.13665	−	0.623500i	0.251284	−	0.0378749i	0.273476	+	0.961879i	$0.411827\pi$
$272$	−11.8647	−	14.8778i	−0.719401	−	0.902100i
$273$	3.30139	−	3.24537i	0.199809	−	0.196419i
$274$	20.4179	−	25.6033i	1.23349	−	1.54675i
$275$	8.92286	−	15.4549i	0.538069	−	0.931963i
$276$	6.77885	+	11.7413i	0.408039	+	0.706744i
$277$	−19.6594	−	2.96318i	−1.18122	−	0.178040i	−0.471074	−	0.882094i	$-0.656133\pi$
$277$	−19.6594	−	2.96318i	−1.18122	−	0.178040i	−0.710147	+	0.704054i	$0.751371\pi$
$278$	11.2266	+	10.4168i	0.673327	+	0.624756i
$279$	0.0923800	−	0.0444878i	0.00553064	−	0.00266342i
$280$	−0.321155	−	0.753624i	−0.0191927	−	0.0450376i
$281$	−5.05884	−	2.43621i	−0.301785	−	0.145332i	0.276863	−	0.960909i	$-0.410705\pi$
$281$	−5.05884	−	2.43621i	−0.301785	−	0.145332i	−0.578648	+	0.815577i	$0.696419\pi$
$282$	−13.2568	−	33.7778i	−0.789431	−	2.01144i
$283$	1.87470	+	25.0161i	0.111439	+	1.48705i	0.720238	+	0.693727i	$0.244032\pi$
$283$	1.87470	+	25.0161i	0.111439	+	1.48705i	−0.608799	+	0.793324i	$0.708348\pi$
$284$	15.9970	−	4.93442i	0.949247	−	0.292804i
$285$	−0.0532236	+	0.710219i	−0.00315269	+	0.0420698i
$286$	1.80016	+	7.88701i	0.106446	+	0.466368i
$287$	−16.0419	−	18.9669i	−0.946926	−	1.11958i
$288$	−0.111381	+	0.487990i	−0.00656316	+	0.0287551i
$289$	11.8263	+	3.64794i	0.695667	+	0.214585i
$290$	−1.49451	+	3.80795i	−0.0877606	+	0.223610i
$291$	7.74225	−	7.18376i	0.453859	−	0.421119i
$292$	−28.5899	+	19.4923i	−1.67310	+	1.14070i
$293$	−10.6698			−0.623338			−0.311669	−	0.950191i	$-0.600888\pi$
$293$	−10.6698			−0.623338			−0.311669	+	0.950191i	$0.600888\pi$
$294$	16.7964	+	18.7353i	0.979584	+	1.09266i
$295$	0.773503			0.0450351
$296$	−3.31226	+	2.25826i	−0.192521	+	0.131259i
$297$	−14.8418	+	13.7711i	−0.861207	+	0.799083i
$298$	8.19929	−	20.8914i	0.474972	−	1.21021i
$299$	3.33479	+	1.02865i	0.192856	+	0.0594882i
$300$	−3.91756	+	17.1640i	−0.226181	+	0.990962i
$301$	0.0558445	+	0.215784i	0.00321882	+	0.0124376i
$302$	9.13612	+	40.0280i	0.525725	+	2.30335i
$303$	−1.48035	+	19.7539i	−0.0850437	+	1.13483i
$304$	−1.99560	+	0.615561i	−0.114456	+	0.0353049i
$305$	−0.559985	−	7.47248i	−0.0320646	−	0.427873i
$306$	−0.250827	−	0.639096i	−0.0143388	−	0.0365347i
$307$	27.0697	+	13.0361i	1.54495	+	0.744007i	0.995786	−	0.0917096i	$-0.0292332\pi$
$307$	27.0697	+	13.0361i	1.54495	+	0.744007i	0.549161	+	0.835717i	$0.314947\pi$
$308$	−22.7652	+	4.10595i	−1.29717	+	0.233958i
$309$	−11.6369	+	5.60403i	−0.662000	+	0.318802i
$310$	−1.71361	−	1.59000i	−0.0973265	−	0.0903058i
$311$	1.45981	+	0.220031i	0.0827781	+	0.0124768i	0.190301	−	0.981726i	$-0.439054\pi$
$311$	1.45981	+	0.220031i	0.0827781	+	0.0124768i	−0.107523	+	0.994203i	$0.534292\pi$
$312$	−0.395860	−	0.685649i	−0.0224111	−	0.0388172i
$313$	2.00999	−	3.48140i	0.113611	−	0.196781i	−0.803612	−	0.595153i	$-0.797091\pi$
$313$	2.00999	−	3.48140i	0.113611	−	0.196781i	0.917224	+	0.398372i	$0.130425\pi$
$314$	−27.4771	+	34.4553i	−1.55063	+	1.94442i
$315$	0.0115496	+	0.111037i	0.000650746	+	0.00625625i
$316$	−8.52739	−	10.6930i	−0.479703	−	0.601529i
$317$	−25.8533	+	3.89675i	−1.45206	+	0.218864i	−0.827217	−	0.561883i	$-0.810077\pi$
$317$	−25.8533	+	3.89675i	−1.45206	+	0.218864i	−0.624848	+	0.780746i	$0.714839\pi$
$318$	−38.1696	−	26.0236i	−2.14044	−	1.45933i
$319$	9.46800	+	6.45517i	0.530106	+	0.361420i
$320$	6.53269	−	0.984645i	0.365189	−	0.0550433i
$321$	5.35457	+	6.71442i	0.298863	+	0.374762i
$322$	−6.41773	+	17.8494i	−0.357646	+	0.994708i
$323$	2.01006	−	2.52053i	0.111843	−	0.140246i
$324$	10.1923	−	17.6535i	0.566237	−	0.980752i
$325$	2.26586	+	3.92459i	0.125688	+	0.217697i
$326$	−42.2438	−	6.36723i	−2.33967	−	0.352648i
$327$	23.9339	+	22.2074i	1.32355	+	1.22807i
$328$	−3.82761	+	1.84328i	−0.211344	+	0.101778i
$329$	12.6814	−	23.5053i	0.699148	−	1.29589i
$330$	−8.72723	−	4.20281i	−0.480418	−	0.231357i
$331$	−4.71913	−	12.0241i	−0.259387	−	0.660907i	0.740552	−	0.671999i	$-0.234564\pi$
$331$	−4.71913	−	12.0241i	−0.259387	−	0.660907i	−0.999938	+	0.0110926i	$0.996469\pi$
$332$	−0.856192	−	11.4251i	−0.0469896	−	0.627033i
$333$	0.522033	−	0.161026i	0.0286072	−	0.00882416i
$334$	−0.683342	+	9.11857i	−0.0373908	+	0.498946i
$335$	0.479063	+	2.09891i	0.0261740	+	0.114676i
$336$	−14.4347	+	7.47167i	−0.787479	+	0.407613i
$337$	−2.70582	+	11.8550i	−0.147396	+	0.645782i	0.846208	+	0.532853i	$0.178880\pi$
$337$	−2.70582	+	11.8550i	−0.147396	+	0.645782i	−0.993603	+	0.112929i	$0.963977\pi$
$338$	−1.96306	−	0.605523i	−0.106776	−	0.0329361i
$339$	−0.0735518	+	0.187407i	−0.00399479	+	0.0101786i
$340$	−6.03647	+	5.60103i	−0.327374	+	0.303759i
$341$	−5.41048	+	3.68880i	−0.292994	+	0.199760i
$342$	−0.0753458			−0.00407424
$343$	−2.54532	+	18.3445i	−0.137434	+	0.990511i
$344$	0.0381188			0.00205523
$345$	−3.45253	+	2.35390i	−0.185878	+	0.126729i
$346$	−28.0822	+	26.0565i	−1.50971	+	1.40080i
$347$	10.3457	−	26.3605i	0.555388	−	1.41510i	−0.327200	−	0.944955i	$-0.606105\pi$
$347$	10.3457	−	26.3605i	0.555388	−	1.41510i	0.882587	−	0.470149i	$-0.155800\pi$
$348$	−10.8026	−	3.33215i	−0.579079	−	0.178622i
$349$	−5.58935	+	24.4885i	−0.299191	+	1.31084i	0.572144	+	0.820153i	$0.306112\pi$
$349$	−5.58935	+	24.4885i	−0.299191	+	1.31084i	−0.871335	+	0.490688i	$0.836745\pi$
$350$	−21.8743	+	11.3225i	−1.16923	+	0.605215i
$351$	−1.14407	−	5.01248i	−0.0610658	−	0.267547i
$352$	2.38889	−	31.8775i	0.127328	−	1.69908i
$353$	12.5545	−	3.87256i	0.668210	−	0.206115i	0.0579534	−	0.998319i	$-0.481543\pi$
$353$	12.5545	−	3.87256i	0.668210	−	0.206115i	0.610257	+	0.792204i	$0.291066\pi$
$354$	0.303638	+	4.05177i	0.0161382	+	0.215349i
$355$	1.88503	+	4.80299i	0.100047	+	0.254916i
$356$	−15.3178	−	7.37669i	−0.811844	−	0.390964i
$357$	11.9138	−	22.0826i	0.630546	−	1.16873i
$358$	−41.3649	+	19.9203i	−2.18620	+	1.05282i
$359$	−14.5860	−	13.5338i	−0.769819	−	0.714287i	0.193955	−	0.981011i	$-0.437869\pi$
$359$	−14.5860	−	13.5338i	−0.769819	−	0.714287i	−0.963773	+	0.266723i	$0.914059\pi$
$360$	0.0188787	+	0.00284550i	0.000994993	+	0.000149971i
$361$	9.32310	+	16.1481i	0.490689	+	0.849899i
$362$	10.5902	−	18.3427i	0.556607	−	0.964072i
$363$	−4.91745	+	6.16629i	−0.258099	+	0.323646i
$364$	1.98751	−	5.52779i	0.104174	−	0.289735i
$365$	−6.64941	−	8.33809i	−0.348046	−	0.436436i
$366$	38.9226	−	5.86664i	2.03452	−	0.306654i
$367$	10.3915	+	7.08479i	0.542431	+	0.369823i	0.803322	−	0.595545i	$-0.203064\pi$
$367$	10.3915	+	7.08479i	0.542431	+	0.369823i	−0.260891	+	0.965368i	$0.584016\pi$
$368$	−10.1237	−	6.90222i	−0.527734	−	0.359803i
$369$	0.572473	−	0.0862865i	0.0298018	−	0.00449189i
$370$	−7.76556	−	9.73771i	−0.403712	−	0.506239i
$371$	−3.51783	−	33.8202i	−0.182636	−	1.75586i
$372$	4.02782	−	5.05073i	0.208833	−	0.261868i
$373$	−12.1292	+	21.0084i	−0.628026	+	1.08777i	0.359922	+	0.932983i	$0.382803\pi$
$373$	−12.1292	+	21.0084i	−0.628026	+	1.08777i	−0.987947	+	0.154790i	$0.950530\pi$
$374$	21.9234	+	37.9724i	1.13363	+	1.96351i
$375$	−11.2855	−	1.70102i	−0.582781	−	0.0878400i
$376$	−3.34826	−	3.10673i	−0.172673	−	0.160218i
$377$	−2.62176	+	1.26257i	−0.135027	+	0.0650257i
$378$	27.5009	−	4.96010i	1.41450	−	0.255120i
$379$	23.3163	+	11.2285i	1.19768	+	0.576771i	0.923013	−	0.384769i	$-0.125719\pi$
$379$	23.3163	+	11.2285i	1.19768	+	0.576771i	0.274664	+	0.961540i	$0.411433\pi$
$380$	0.330165	+	0.841247i	0.0169371	+	0.0431550i
$381$	−2.30044	−	30.6972i	−0.117855	−	1.57267i
$382$	18.2882	−	5.64115i	0.935704	−	0.288627i
$383$	2.32079	−	30.9688i	0.118587	−	1.58243i	−0.547660	−	0.836701i	$-0.684481\pi$
$383$	2.32079	−	30.9688i	0.118587	−	1.58243i	0.666247	−	0.745732i	$-0.267900\pi$
$384$	1.40085	+	6.13751i	0.0714866	+	0.313203i
$385$	−1.78629	−	6.90225i	−0.0910378	−	0.351771i
$386$	−5.24859	+	22.9956i	−0.267146	+	1.17044i
$387$	−0.00496386	−	0.00153115i	−0.000252327	−	7.78326e-5i
$388$	4.89615	−	12.4752i	0.248564	−	0.633332i
$389$	−22.7994	+	21.1548i	−1.15598	+	1.07259i	−0.159630	+	0.987177i	$0.551030\pi$
$389$	−22.7994	+	21.1548i	−1.15598	+	1.07259i	−0.996346	+	0.0854115i	$0.972780\pi$
$390$	2.03237	−	1.38564i	0.102913	−	0.0701648i
$391$	18.9148			0.956564
$392$	2.92813	+	1.20743i	0.147893	+	0.0609847i
$393$	17.0413			0.859620
$394$	9.17745	−	6.25708i	0.462353	−	0.315227i
$395$	3.09006	−	2.86716i	0.155478	−	0.144263i
$396$	0.196961	−	0.501848i	0.00989765	−	0.0252188i
$397$	7.71796	+	2.38068i	0.387353	+	0.119483i	0.482314	−	0.875998i	$-0.339796\pi$
$397$	7.71796	+	2.38068i	0.387353	+	0.119483i	−0.0949608	+	0.995481i	$0.530273\pi$
$398$	0.231433	−	1.01397i	0.0116007	−	0.0508259i
$399$	−1.77825	−	2.10248i	−0.0890237	−	0.105256i
$400$	−3.54049	−	15.5119i	−0.177024	−	0.775595i
$401$	−0.361598	+	4.82520i	−0.0180574	+	0.240959i	0.980870	+	0.194662i	$0.0623610\pi$
$401$	−0.361598	+	4.82520i	−0.0180574	+	0.240959i	−0.998928	+	0.0462967i	$0.985258\pi$
$402$	−10.8065	+	3.33336i	−0.538979	+	0.166253i
$403$	−0.124267	−	1.65823i	−0.00619017	−	0.0826021i
$404$	9.18312	+	23.3982i	0.456877	+	1.16410i
$405$	5.66053	+	2.72597i	0.281274	+	0.135454i
$406$	−6.20047	−	14.5501i	−0.307724	−	0.722108i
$407$	−31.4345	+	15.1380i	−1.55815	+	0.750365i
$408$	−3.14560	−	2.91869i	−0.155730	−	0.144497i
$409$	4.54774	+	0.685461i	0.224871	+	0.0338939i	0.260511	−	0.965471i	$-0.416109\pi$
$409$	4.54774	+	0.685461i	0.224871	+	0.0338939i	−0.0356401	+	0.999365i	$0.511347\pi$
$410$	−6.59952	−	11.4307i	−0.325927	−	0.564523i
$411$	−13.9464	+	24.1558i	−0.687924	+	1.19152i
$412$	−10.2184	+	12.8134i	−0.503422	+	0.631271i
$413$	−2.13271	+	2.09652i	−0.104944	+	0.103163i
$414$	−0.275621	−	0.345618i	−0.0135460	−	0.0169862i
$415$	3.49175	−	0.526297i	0.171403	−	0.0258349i
$416$	6.70711	+	4.57283i	0.328843	+	0.224202i
$417$	−10.7778	−	7.34815i	−0.527789	−	0.359841i
$418$	4.75821	−	0.717184i	0.232731	−	0.0350786i
$419$	−6.70871	−	8.41246i	−0.327742	−	0.410975i	0.590473	−	0.807057i	$-0.298941\pi$
$419$	−6.70871	−	8.41246i	−0.327742	−	0.410975i	−0.918215	+	0.396082i	$0.870370\pi$
$420$	3.69101	+	5.98734i	0.180103	+	0.292152i
$421$	14.1989	−	17.8049i	0.692014	−	0.867758i	−0.304385	−	0.952549i	$-0.598451\pi$
$421$	14.1989	−	17.8049i	0.692014	−	0.867758i	0.996399	+	0.0847914i	$0.0270224\pi$
$422$	−4.58851	+	7.94754i	−0.223365	+	0.386880i
$423$	0.311222	+	0.539053i	0.0151321	+	0.0262096i
$424$	−5.75014	−	0.866695i	−0.279252	−	0.0420904i
$425$	18.0051	+	16.7063i	0.873377	+	0.810376i
$426$	−24.4191	+	11.7596i	−1.18311	+	0.569755i
$427$	21.7976	+	19.0854i	1.05486	+	0.923608i
$428$	9.81814	+	4.72817i	0.474578	+	0.228545i
$429$	−2.51737	−	6.41416i	−0.121540	−	0.309678i
$430$	0.00885035	+	0.118100i	0.000426802	+	0.00569527i
$431$	12.8497	−	3.96361i	0.618949	−	0.190921i	0.0306056	−	0.999532i	$-0.490256\pi$
$431$	12.8497	−	3.96361i	0.618949	−	0.190921i	0.588344	+	0.808611i	$0.299780\pi$
$432$	−1.34898	+	18.0008i	−0.0649027	+	0.866066i
$433$	−1.67778	−	7.35082i	−0.0806288	−	0.353258i	0.918480	−	0.395467i	$-0.129417\pi$
$433$	−1.67778	−	7.35082i	−0.0806288	−	0.353258i	−0.999109	+	0.0422097i	$0.986560\pi$
$434$	9.03436	−	0.260650i	0.433663	−	0.0125116i
$435$	0.775319	−	3.39689i	0.0371737	−	0.162869i
$436$	39.5883	+	12.2114i	1.89594	+	0.584819i
$437$	0.758377	−	1.93231i	0.0362781	−	0.0924350i
$438$	41.0665	−	38.1041i	1.96223	−	1.82069i
$439$	−25.2827	+	17.2374i	−1.20668	+	0.822697i	−0.988204	−	0.153146i	$-0.951059\pi$
$439$	−25.2827	+	17.2374i	−1.20668	+	0.822697i	−0.218472	+	0.975843i	$0.570107\pi$
$440$	−1.21930			−0.0581280
$441$	−0.332803	−	0.274849i	−0.0158478	−	0.0130881i
$442$	−11.1344			−0.529609
$443$	−3.46985	+	2.36571i	−0.164858	+	0.112398i	−0.642939	−	0.765918i	$-0.722285\pi$
$443$	−3.46985	+	2.36571i	−0.164858	+	0.112398i	0.478081	+	0.878316i	$0.341333\pi$
$444$	25.2314	−	23.4113i	1.19743	−	1.11105i
$445$	1.91440	−	4.87781i	0.0907512	−	0.231230i
$446$	23.4883	+	7.24518i	1.11220	+	0.343069i
$447$	−4.25361	+	18.6363i	−0.201189	+	0.881466i
$448$	−15.3432	+	20.4212i	−0.724899	+	0.964813i
$449$	0.0130632	+	0.0572335i	0.000616489	+	0.00270102i	0.975235	−	0.221170i	$-0.0709876\pi$
$449$	0.0130632	+	0.0572335i	0.000616489	+	0.00270102i	−0.974619	+	0.223871i	$0.928130\pi$
$450$	0.0428980	−	0.572434i	0.00202223	−	0.0269848i
$451$	−35.3312	+	10.8982i	−1.66368	+	0.513178i
$452$	0.0190904	+	0.254743i	0.000897936	+	0.0119821i
$453$	−12.7761	−	32.5530i	−0.600274	−	1.52947i
$454$	31.7181	+	15.2746i	1.48860	+	0.716874i
$455$	1.74473	+	0.483538i	0.0817942	+	0.0226686i
$456$	−0.424290	+	0.204327i	−0.0198692	+	0.00956849i
$457$	−23.6019	−	21.8994i	−1.10405	−	1.02441i	−0.999553	−	0.0298847i	$-0.990486\pi$
$457$	−23.6019	−	21.8994i	−1.10405	−	1.02441i	−0.104498	−	0.994525i	$-0.533324\pi$
$458$	31.8077	+	4.79424i	1.48628	+	0.224020i
$459$	−13.9331	−	24.1329i	−0.650342	−	1.12643i
$460$	−2.65110	+	4.59184i	−0.123608	+	0.214096i
$461$	−7.67647	+	9.62599i	−0.357529	+	0.448327i	−0.927771	−	0.373149i	$-0.878278\pi$
$461$	−7.67647	+	9.62599i	−0.357529	+	0.448327i	0.570242	+	0.821477i	$0.306849\pi$
$462$	35.4542	−	12.0665i	1.64948	−	0.561382i
$463$	13.0286	+	16.3374i	0.605491	+	0.759262i	0.986223	−	0.165424i	$-0.0528991\pi$
$463$	13.0286	+	16.3374i	0.605491	+	0.759262i	−0.380731	+	0.924686i	$0.624328\pi$
$464$	10.1026	−	1.52272i	0.469001	−	0.0706905i
$465$	1.64510	+	1.12161i	0.0762897	+	0.0520134i
$466$	−6.24012	−	4.25444i	−0.289068	−	0.197083i
$467$	20.8655	−	3.14496i	0.965538	−	0.145532i	0.352697	−	0.935738i	$-0.385265\pi$
$467$	20.8655	−	3.14496i	0.965538	−	0.145532i	0.612841	+	0.790206i	$0.290026\pi$
$468$	0.0853572	+	0.107035i	0.00394564	+	0.00494768i
$469$	−7.00982	−	4.48868i	−0.323683	−	0.207268i
$470$	8.84788	−	11.0949i	0.408122	−	0.511769i
$471$	18.7682	−	32.5074i	0.864791	−	1.49786i
$472$	0.255727	+	0.442932i	0.0117708	+	0.0203876i
$473$	0.328050	+	0.0494455i	0.0150837	+	0.00227351i
$474$	16.2318	+	15.0609i	0.745552	+	0.691771i
$475$	2.42860	−	1.16955i	0.111432	−	0.0536626i
$476$	1.46267	−	31.8046i	0.0670415	−	1.45776i
$477$	0.713974	+	0.343832i	0.0326906	+	0.0157430i
$478$	−5.60742	−	14.2875i	−0.256478	−	0.653494i
$479$	1.55656	+	20.7709i	0.0711211	+	0.949046i	0.912626	+	0.408796i	$0.134051\pi$
$479$	1.55656	+	20.7709i	0.0711211	+	0.949046i	−0.841505	+	0.540250i	$0.818330\pi$
$480$	−9.28797	+	2.86496i	−0.423936	+	0.130767i
$481$	0.662097	−	8.83506i	0.0301890	−	0.402844i
$482$	4.34085	+	19.0185i	0.197720	+	0.866270i
$483$	3.13930	−	15.8480i	0.142843	−	0.721110i
$484$	−2.22692	+	9.75679i	−0.101224	+	0.443491i
$485$	3.94699	+	1.21749i	0.179224	+	0.0552832i
$486$	−0.480861	+	1.22521i	−0.0218123	+	0.0555768i
$487$	−21.7493	+	20.1804i	−0.985554	+	0.914460i	−0.996340	−	0.0854816i	$-0.972757\pi$
$487$	−21.7493	+	20.1804i	−0.985554	+	0.914460i	0.0107860	+	0.999942i	$0.496567\pi$
$488$	4.09384	−	2.79113i	0.185319	−	0.126349i
$489$	36.3873			1.64549
$490$	−3.06102	+	9.35227i	−0.138283	+	0.422493i
$491$	18.1131			0.817431			0.408715	−	0.912662i	$-0.365977\pi$
$491$	18.1131			0.817431			0.408715	+	0.912662i	$0.365977\pi$
$492$	30.1378	−	20.5476i	1.35872	−	0.926358i
$493$	−11.5615	+	10.7275i	−0.520704	+	0.483143i
$494$	−0.446426	+	1.13747i	−0.0200856	+	0.0511774i
$495$	0.158778	+	0.0489766i	0.00713655	+	0.00220133i
$496$	−1.29915	+	5.69194i	−0.0583335	+	0.255576i
$497$	−18.2156	−	8.13361i	−0.817080	−	0.364842i
$498$	4.12754	+	18.0839i	0.184960	+	0.810361i
$499$	0.967904	−	12.9158i	0.0433293	−	0.578190i	−0.932714	−	0.360616i	$-0.882567\pi$
$499$	0.967904	−	12.9158i	0.0433293	−	0.578190i	0.976044	−	0.217574i	$-0.0698144\pi$
$500$	−13.8384	+	4.26859i	−0.618873	+	0.190897i
$501$	−0.582033	−	7.76669i	−0.0260033	−	0.346990i
$502$	7.34936	+	18.7259i	0.328018	+	0.835777i
$503$	9.35480	+	4.50503i	0.417110	+	0.200870i	0.630654	−	0.776064i	$-0.282787\pi$
$503$	9.35480	+	4.50503i	0.417110	+	0.200870i	−0.213545	+	0.976933i	$0.568501\pi$
$504$	−0.0597650	+	0.0433236i	−0.00266215	+	0.00192978i
$505$	−6.97987	+	3.36133i	−0.310600	+	0.149577i
$506$	20.6957	+	19.2028i	0.920034	+	0.853667i
$507$	1.73022	+	0.260788i	0.0768416	+	0.0115820i
$508$	−19.5303	−	33.8275i	−0.866517	−	1.50085i
$509$	1.77772	−	3.07911i	0.0787962	−	0.136479i	−0.823935	−	0.566685i	$-0.808226\pi$
$509$	1.77772	−	3.07911i	0.0787962	−	0.136479i	0.902731	+	0.430206i	$0.141559\pi$
$510$	8.31234	−	10.4233i	0.368077	−	0.461553i
$511$	40.9336	+	4.96718i	1.81080	+	0.219735i
$512$	−19.7510	−	24.7670i	−0.872879	−	1.09456i
$513$	−3.02402	+	0.455797i	−0.133514	+	0.0201239i
$514$	−11.2641	−	7.67973i	−0.496838	−	0.338738i
$515$	−4.17352	−	2.84546i	−0.183907	−	0.125386i
$516$	−0.323631	+	0.0487795i	−0.0142471	+	0.00214740i
$517$	−24.7852	−	31.0796i	−1.09005	−	1.36688i
$518$	47.8046	+	5.80095i	2.10041	+	0.254879i
$519$	20.3439	−	25.5105i	0.893000	−	1.11979i
$520$	0.154814	−	0.268146i	0.00678906	−	0.0117590i
$521$	−1.40762	−	2.43806i	−0.0616688	−	0.106814i	0.833543	−	0.552455i	$-0.186309\pi$
$521$	−1.40762	−	2.43806i	−0.0616688	−	0.106814i	−0.895211	+	0.445642i	$0.852976\pi$
$522$	0.364487	+	0.0549376i	0.0159532	+	0.00240455i
$523$	10.3993	+	9.64918i	0.454732	+	0.421929i	0.873995	−	0.485935i	$-0.161521\pi$
$523$	10.3993	+	9.64918i	0.454732	+	0.421929i	−0.419263	+	0.907865i	$0.637711\pi$
$524$	19.4821	−	9.38211i	0.851081	−	0.409859i
$525$	16.9859	−	12.3131i	0.741326	−	0.537386i
$526$	−6.09527	−	2.93533i	−0.265767	−	0.127986i
$527$	−3.29273	−	8.38973i	−0.143433	−	0.365462i
$528$	1.80789	+	24.1247i	0.0786785	+	1.04989i
$529$	−10.3403	+	3.18956i	−0.449578	+	0.138677i
$530$	1.35014	−	18.0163i	0.0586461	−	0.782578i
$531$	−0.0155093	−	0.0679507i	−0.000673047	−	0.00294881i
$532$	−3.19047	−	1.42461i	−0.138324	−	0.0617646i
$533$	2.08928	−	9.15371i	0.0904966	−	0.396491i
$534$	26.3025	+	8.11325i	1.13822	+	0.351095i
$535$	−1.22705	+	3.12648i	−0.0530502	+	0.135170i
$536$	−1.04352	+	0.968244i	−0.0450732	+	0.0418218i
$537$	32.3100	−	22.0286i	1.39428	−	0.950604i
$538$	−57.7668			−2.49050
$539$	23.6332	+	14.1893i	1.01795	+	0.611178i
$540$	7.81145			0.336151
$541$	−21.0077	+	14.3228i	−0.903193	+	0.615786i	−0.923329	−	0.384011i	$-0.874542\pi$
$541$	−21.0077	+	14.3228i	−0.903193	+	0.615786i	0.0201360	+	0.999797i	$0.493590\pi$
$542$	−6.29986	+	5.84542i	−0.270602	+	0.251082i
$543$	−6.59084	+	16.7932i	−0.282840	+	0.720665i
$544$	42.0428	+	12.9685i	1.80257	+	0.556019i
$545$	−2.84132	+	12.4486i	−0.121709	+	0.533241i
$546$	−1.84798	+	9.32909i	−0.0790863	+	0.399248i
$547$	0.319778	+	1.40104i	0.0136727	+	0.0599042i	0.981304	−	0.192464i	$-0.0616478\pi$
$547$	0.319778	+	1.40104i	0.0136727	+	0.0599042i	−0.967631	+	0.252368i	$0.918791\pi$
$548$	−2.64491	+	35.2939i	−0.112985	+	1.50768i
$549$	−0.645215	+	0.199022i	−0.0275371	+	0.00849407i
$550$	2.73968	+	36.5584i	0.116820	+	1.55886i
$551$	0.632357	+	1.61122i	0.0269393	+	0.0686403i
$552$	−2.48935	−	1.19881i	−0.105954	−	0.0510246i
$553$	−0.748740	+	16.2808i	−0.0318397	+	0.692328i
$554$	36.7983	−	17.7211i	1.56341	−	0.752899i
$555$	7.77656	+	7.21559i	0.330097	+	0.306285i
$556$	−16.3670	−	2.46693i	−0.694115	−	0.104621i
$557$	−1.31155	−	2.27167i	−0.0555721	−	0.0962538i	0.836901	−	0.547354i	$-0.184365\pi$
$557$	−1.31155	−	2.27167i	−0.0555721	−	0.0962538i	−0.892473	+	0.451100i	$0.851032\pi$
$558$	−0.105319	+	0.182418i	−0.00445851	+	0.00772237i
$559$	−0.0525263	+	0.0658658i	−0.00222162	+	0.00278583i
$560$	−5.35316	−	3.42786i	−0.226212	−	0.144853i
$561$	−23.2850	−	29.1984i	−0.983093	−	1.23276i
$562$	11.4060	−	1.71917i	0.481132	−	0.0725190i
$563$	18.2474	+	12.4409i	0.769036	+	0.524320i	0.883118	−	0.469151i	$-0.155440\pi$
$563$	18.2474	+	12.4409i	0.769036	+	0.524320i	−0.114082	+	0.993471i	$0.536393\pi$
$564$	32.4025	+	22.0917i	1.36439	+	0.930227i
$565$	−0.0778551	+	0.0117348i	−0.00327539	+	0.000493685i
$566$	−32.1317	−	40.2919i	−1.35060	−	1.69359i
$567$	−22.9958	+	7.82636i	−0.965733	+	0.328676i
$568$	−2.12713	+	2.66734i	−0.0892524	+	0.111919i
$569$	15.5352	−	26.9078i	0.651270	−	1.12803i	−0.331546	−	0.943439i	$-0.607570\pi$
$569$	15.5352	−	26.9078i	0.651270	−	1.12803i	0.982815	−	0.184593i	$-0.0590966\pi$
$570$	−0.731556	−	1.26709i	−0.0306415	−	0.0530727i
$571$	4.11039	+	0.619541i	0.172014	+	0.0259270i	0.234485	−	0.972120i	$-0.424660\pi$
$571$	4.11039	+	0.619541i	0.172014	+	0.0259270i	−0.0624703	+	0.998047i	$0.519898\pi$
$572$	−6.40926	−	5.94692i	−0.267984	−	0.248653i
$573$	−14.6867	+	7.07276i	−0.613548	+	0.295469i
$574$	49.1784	+	13.6294i	2.05267	+	0.568879i
$575$	14.2488	+	6.86187i	0.594217	+	0.286160i
$576$	−0.217485	−	0.554142i	−0.00906186	−	0.0230892i
$577$	−1.84044	−	24.5590i	−0.0766186	−	1.02240i	−0.894515	−	0.447038i	$-0.852479\pi$
$577$	−1.84044	−	24.5590i	−0.0766186	−	1.02240i	0.817896	−	0.575366i	$-0.195140\pi$
$578$	−24.2951	+	7.49406i	−1.01054	+	0.311712i
$579$	1.50133	−	20.0339i	0.0623932	−	0.832579i
$580$	−0.983794	−	4.31028i	−0.0408498	−	0.178975i
$581$	−8.20101	+	10.9152i	−0.340235	+	0.452841i
$582$	−4.82806	+	21.1531i	−0.200129	+	0.876825i
$583$	−48.3613	−	14.9175i	−2.00292	−	0.617820i
$584$	2.57630	−	6.56430i	0.106608	−	0.271633i
$585$	−0.0309308	+	0.0286996i	−0.00127883	+	0.00118658i
$586$	18.1106	−	12.3476i	0.748141	−	0.510074i
$587$	−28.2226			−1.16487			−0.582436	−	0.812877i	$-0.697900\pi$
$587$	−28.2226			−1.16487			−0.582436	+	0.812877i	$0.697900\pi$
$588$	−26.4051	−	6.50415i	−1.08893	−	0.268226i
$589$	−0.989102			−0.0407552
$590$	−1.31292	+	0.895131i	−0.0540519	+	0.0368519i
$591$	−6.93522	+	6.43495i	−0.285277	+	0.264698i
$592$	−11.3646	+	28.9564i	−0.467081	+	1.19010i
$593$	−0.766351	−	0.236388i	−0.0314702	−	0.00970728i	0.278980	−	0.960297i	$-0.410004\pi$
$593$	−0.766351	−	0.236388i	−0.0314702	−	0.00970728i	−0.310450	+	0.950590i	$0.600480\pi$
$594$	9.25531	−	40.5502i	0.379750	−	1.66379i
$595$	9.80877	−	0.282992i	0.402120	−	0.0116015i
$596$	5.39737	+	23.6474i	0.221085	+	0.968635i
$597$	−0.0662001	+	0.883379i	−0.00270939	+	0.0361543i
$598$	−6.85075	+	2.11318i	−0.280148	+	0.0864142i
$599$	3.12932	+	41.7578i	0.127860	+	1.70618i	0.580316	+	0.814392i	$0.302929\pi$
$599$	3.12932	+	41.7578i	0.127860	+	1.70618i	−0.452455	+	0.891787i	$0.649452\pi$
$600$	−1.31079	−	3.33984i	−0.0535128	−	0.136348i
$601$	−4.07386	−	1.96187i	−0.166176	−	0.0800262i	0.348947	−	0.937143i	$-0.386539\pi$
$601$	−4.07386	−	1.96187i	−0.166176	−	0.0800262i	−0.515123	+	0.857116i	$0.672254\pi$
$602$	−0.344503	−	0.301638i	−0.0140409	−	0.0122938i
$603$	0.174780	−	0.0841695i	0.00711758	−	0.00342765i
$604$	−32.5281	−	30.1817i	−1.32355	−	1.22808i
$605$	−3.05002	−	0.459716i	−0.124001	−	0.0186901i
$606$	−20.3473	−	35.2426i	−0.826553	−	1.43163i
$607$	−18.1210	+	31.3865i	−0.735509	+	1.27394i	0.218991	+	0.975727i	$0.429723\pi$
$607$	−18.1210	+	31.3865i	−0.735509	+	1.27394i	−0.954500	+	0.298212i	$0.903610\pi$
$608$	3.01052	−	3.77507i	0.122093	−	0.153099i
$609$	7.06930	+	11.4674i	0.286463	+	0.464682i
$610$	9.59797	+	12.0355i	0.388610	+	0.487302i
$611$	9.98192	−	1.50453i	0.403825	−	0.0608669i
$612$	0.613076	+	0.417988i	0.0247821	+	0.0168962i
$613$	12.5462	+	8.55387i	0.506737	+	0.345488i	0.789549	−	0.613688i	$-0.210315\pi$
$613$	12.5462	+	8.55387i	0.506737	+	0.345488i	−0.282812	+	0.959175i	$0.591267\pi$
$614$	−61.0329	+	9.19923i	−2.46309	+	0.371251i
$615$	7.00941	+	8.78952i	0.282647	+	0.354428i
$616$	3.36188	−	3.30483i	0.135454	−	0.133155i
$617$	−4.70151	+	5.89550i	−0.189275	+	0.237344i	−0.867410	−	0.497594i	$-0.834217\pi$
$617$	−4.70151	+	5.89550i	−0.189275	+	0.237344i	0.678135	+	0.734938i	$0.262789\pi$
$618$	13.2668	−	22.9788i	0.533670	−	0.924343i
$619$	21.1670	+	36.6624i	0.850775	+	1.47358i	0.880510	+	0.474027i	$0.157200\pi$
$619$	21.1670	+	36.6624i	0.850775	+	1.47358i	−0.0297357	+	0.999558i	$0.509467\pi$
$620$	2.49823	+	0.376548i	0.100331	+	0.0151225i
$621$	−13.1529	−	12.2041i	−0.527806	−	0.489732i
$622$	−2.73245	+	1.31588i	−0.109561	+	0.0527620i
$623$	7.94253	+	18.6380i	0.318211	+	0.746715i
$624$	−5.53499	−	2.66551i	−0.221577	−	0.106706i
$625$	6.64746	+	16.9375i	0.265898	+	0.677498i
$626$	0.617147	+	8.23525i	0.0246661	+	0.329147i
$627$	−3.91646	+	1.20807i	−0.156409	+	0.0482456i
$628$	3.55935	−	47.4963i	0.142034	−	1.89531i
$629$	−10.6855	−	46.8162i	−0.426058	−	1.86668i
$630$	−0.148101	−	0.175105i	−0.00590049	−	0.00697635i
$631$	−7.22254	+	31.6440i	−0.287525	+	1.25973i	0.600385	+	0.799711i	$0.295014\pi$
$631$	−7.22254	+	31.6440i	−0.287525	+	1.25973i	−0.887910	+	0.460018i	$0.847843\pi$
$632$	2.66343	+	0.821558i	0.105945	+	0.0326798i
$633$	2.85568	−	7.27616i	0.113503	−	0.289201i
$634$	39.3729	−	36.5327i	1.56370	−	1.45090i
$635$	9.94697	−	6.78173i	0.394733	−	0.269125i
$636$	49.9281			1.97978
$637$	−6.12119	+	3.39574i	−0.242530	+	0.134544i
$638$	−23.5408			−0.931991
$639$	0.384137	−	0.261900i	0.0151962	−	0.0103606i
$640$	−1.80478	+	1.67459i	−0.0713402	+	0.0661940i
$641$	4.60958	−	11.7450i	0.182068	−	0.463900i	−0.810479	−	0.585768i	$-0.800793\pi$
$641$	4.60958	−	11.7450i	0.182068	−	0.463900i	0.992546	+	0.121867i	$0.0388883\pi$
$642$	−16.8589	−	5.20027i	−0.665366	−	0.205238i
$643$	3.45169	−	15.1228i	0.136121	−	0.596386i	−0.860145	−	0.510050i	$-0.829627\pi$
$643$	3.45169	−	15.1228i	0.136121	−	0.596386i	0.996266	−	0.0863361i	$-0.0275159\pi$
$644$	−5.13619	−	19.8463i	−0.202394	−	0.782053i
$645$	−0.0224463	−	0.0983437i	−0.000883823	−	0.00387228i
$646$	−0.494930	+	6.60438i	−0.0194728	+	0.259846i
$647$	26.8472	−	8.28125i	1.05547	−	0.325570i	0.282008	−	0.959412i	$-0.408999\pi$
$647$	26.8472	−	8.28125i	1.05547	−	0.325570i	0.773462	+	0.633842i	$0.218523\pi$
$648$	0.310446	+	4.14262i	0.0121955	+	0.162737i
$649$	1.62623	+	4.14357i	0.0638351	+	0.162649i
$650$	−8.38770	−	4.03930i	−0.328993	−	0.158435i
$651$	−7.57593	+	1.36640i	−0.296924	+	0.0535535i
$652$	41.5991	−	20.0331i	1.62915	−	0.784556i
$653$	−28.8949	−	26.8105i	−1.13074	−	1.04918i	−0.998317	−	0.0579852i	$-0.981532\pi$
$653$	−28.8949	−	26.8105i	−1.13074	−	1.04918i	−0.132427	−	0.991193i	$-0.542277\pi$
$654$	−66.3240	−	9.99673i	−2.59347	−	0.390903i
$655$	3.33229	+	5.77170i	0.130203	+	0.225519i
$656$	−16.4825	+	28.5485i	−0.643534	+	1.11463i
$657$	−0.599160	+	0.751323i	−0.0233755	+	0.0293119i
$658$	5.67638	+	54.5725i	0.221288	+	2.12746i
$659$	4.17158	+	5.23100i	0.162502	+	0.203771i	0.856415	−	0.516288i	$-0.172686\pi$
$659$	4.17158	+	5.23100i	0.162502	+	0.203771i	−0.693914	+	0.720058i	$0.744115\pi$
$660$	10.3519	−	1.56030i	0.402949	−	0.0607348i
$661$	−7.24951	−	4.94263i	−0.281973	−	0.192246i	0.414072	−	0.910244i	$-0.364106\pi$
$661$	−7.24951	−	4.94263i	−0.281973	−	0.192246i	−0.696045	+	0.717998i	$0.745059\pi$
$662$	21.9249	+	14.9482i	0.852137	+	0.580977i
$663$	9.37774	−	1.41347i	0.364201	−	0.0548945i
$664$	1.45578	+	1.82549i	0.0564951	+	0.0708426i
$665$	0.364365	−	1.01340i	0.0141295	−	0.0392978i
$666$	−0.699734	+	0.877438i	−0.0271141	+	0.0340000i
$667$	−5.07759	+	8.79464i	−0.196605	+	0.340530i
$668$	−4.94136	−	8.55868i	−0.191187	−	0.331145i
$669$	−20.7023	−	3.12037i	−0.800398	−	0.120641i
$670$	−3.24209	−	3.00822i	−0.125253	−	0.116218i
$671$	38.8519	−	18.7101i	1.49986	−	0.722295i
$672$	17.8436	−	33.0736i	0.688334	−	1.27584i
$673$	13.8593	+	6.67429i	0.534237	+	0.257275i	0.681495	−	0.731823i	$-0.261330\pi$
$673$	13.8593	+	6.67429i	0.534237	+	0.257275i	−0.147257	+	0.989098i	$0.547045\pi$
$674$	−9.12633	−	23.2535i	−0.351533	−	0.895692i
$675$	−1.74117	−	23.2342i	−0.0670175	−	0.894286i
$676$	2.12161	−	0.654431i	0.0816005	−	0.0251704i
$677$	−3.22346	+	43.0141i	−0.123888	+	1.65317i	0.495888	+	0.868386i	$0.334843\pi$
$677$	−3.22346	+	43.0141i	−0.123888	+	1.65317i	−0.619776	+	0.784779i	$0.712776\pi$
$678$	−0.0920312	−	0.403215i	−0.00353444	−	0.0154854i
$679$	−14.1826	+	7.34116i	−0.544278	+	0.281728i
$680$	0.373430	−	1.63610i	0.0143204	−	0.0627418i
$681$	−28.6530	−	8.83828i	−1.09799	−	0.338684i
$682$	4.91471	−	12.5225i	0.188194	−	0.479510i
$683$	−19.5766	+	18.1644i	−0.749077	+	0.695042i	−0.959230	−	0.282627i	$-0.908794\pi$
$683$	−19.5766	+	18.1644i	−0.749077	+	0.695042i	0.210153	+	0.977669i	$0.432604\pi$
$684$	0.0672819	−	0.0458720i	0.00257259	−	0.00175396i
$685$	−10.9084			−0.416789
$686$	−16.9087	−	34.0829i	−0.645578	−	1.30129i
$687$	−27.3980			−1.04530
$688$	0.244389	−	0.166621i	0.00931723	−	0.00635238i
$689$	9.42104	−	8.74145i	0.358913	−	0.333023i
$690$	3.13617	−	7.99083i	0.119392	−	0.304206i
$691$	14.5350	+	4.48346i	0.552938	+	0.170559i	0.558618	−	0.829425i	$-0.311332\pi$
$691$	14.5350	+	4.48346i	0.552938	+	0.170559i	−0.00567989	+	0.999984i	$0.501808\pi$
$692$	9.21299	−	40.3647i	0.350225	−	1.53444i
$693$	−0.570533	+	0.295318i	−0.0216727	+	0.0112182i
$694$	12.9450	+	56.7158i	0.491386	+	2.15290i
$695$	0.381231	−	5.08718i	0.0144609	−	0.192968i
$696$	2.20149	−	0.679071i	0.0834474	−	0.0257401i
$697$	−3.80293	−	50.7465i	−0.144046	−	1.92216i
$698$	−18.8520	−	48.0342i	−0.713560	−	1.81812i
$699$	5.79571	+	2.79107i	0.219214	+	0.105568i
$700$	12.6398	−	23.4283i	0.477741	−	0.885505i
$701$	−42.1553	+	20.3009i	−1.59218	+	0.766755i	−0.999258	−	0.0385032i	$-0.987741\pi$
$701$	−42.1553	+	20.3009i	−1.59218	+	0.766755i	−0.592924	+	0.805258i	$0.702027\pi$
$702$	7.74256	+	7.18404i	0.292224	+	0.271144i
$703$	−5.21110	−	0.785447i	−0.196540	−	0.0296237i
$704$	19.0091	+	32.9248i	0.716433	+	1.24090i
$705$	−6.04351	+	10.4677i	−0.227612	+	0.394235i
$706$	−16.8281	+	21.1018i	−0.633334	+	0.794176i
$707$	10.1344	−	28.1863i	0.381142	−	1.06006i
$708$	−2.73794	−	3.43327i	−0.102898	−	0.129030i
$709$	−6.70202	+	1.01017i	−0.251700	+	0.0379376i	−0.273680	−	0.961821i	$-0.588241\pi$
$709$	−6.70202	+	1.01017i	−0.251700	+	0.0379376i	0.0219803	+	0.999758i	$0.493003\pi$
$710$	−8.75781	−	5.97097i	−0.328675	−	0.224087i
$711$	−0.313833	−	0.213968i	−0.0117696	−	0.00802441i
$712$	3.42610	−	0.516401i	0.128399	−	0.0193530i
$713$	−3.61821	−	4.53709i	−0.135503	−	0.169915i
$714$	5.33280	+	51.2693i	0.199575	+	1.91871i
$715$	1.68015	−	2.10684i	0.0628341	−	0.0787914i
$716$	24.8099	−	42.9721i	0.927191	−	1.60594i
$717$	6.53648	+	11.3215i	0.244109	+	0.422810i
$718$	40.4196	+	6.09228i	1.50845	+	0.227362i
$719$	6.57462	+	6.10036i	0.245192	+	0.227505i	0.793189	−	0.608975i	$-0.208419\pi$
$719$	6.57462	+	6.10036i	0.245192	+	0.227505i	−0.547997	+	0.836480i	$0.684610\pi$
$720$	0.133474	−	0.0642775i	0.00497426	−	0.00239548i
$721$	19.2197	−	3.46648i	0.715779	−	0.129099i
$722$	−34.5119	−	16.6201i	−1.28440	−	0.618535i
$723$	−6.07033	−	15.4669i	−0.225758	−	0.575222i
$724$	1.71065	+	22.8271i	0.0635759	+	0.848362i
$725$	−12.6011	+	3.88694i	−0.467995	+	0.144357i
$726$	1.21081	−	16.1571i	0.0449373	−	0.599647i
$727$	−4.83178	−	21.1694i	−0.179201	−	0.785130i	−0.982000	−	0.188881i	$-0.939514\pi$
$727$	−4.83178	−	21.1694i	−0.179201	−	0.785130i	0.802799	−	0.596249i	$-0.203343\pi$
$728$	0.299934	+	1.15895i	0.0111163	+	0.0429535i
$729$	−5.87955	+	25.7600i	−0.217761	+	0.954074i
$730$	20.9357	+	6.45780i	0.774864	+	0.239014i
$731$	−0.166818	+	0.425046i	−0.00616999	+	0.0157209i
$732$	−31.1852	+	28.9356i	−1.15264	+	1.06949i
$733$	−15.3810	+	10.4866i	−0.568110	+	0.387331i	−0.813038	−	0.582210i	$-0.802188\pi$
$733$	−15.3810	+	10.4866i	−0.568110	+	0.387331i	0.244928	+	0.969541i	$0.421236\pi$
$734$	−25.8369			−0.953659
$735$	1.39086	−	8.26536i	0.0513025	−	0.304872i
$736$	28.3292			1.04423
$737$	−10.2364	+	6.97909i	−0.377064	+	0.257078i
$738$	−0.871841	+	0.808950i	−0.0320929	+	0.0297779i
$739$	−18.6817	+	47.6001i	−0.687216	+	1.75100i	−0.0273359	+	0.999626i	$0.508702\pi$
$739$	−18.6817	+	47.6001i	−0.687216	+	1.75100i	−0.659880	+	0.751371i	$0.729393\pi$
$740$	12.8630	+	3.96770i	0.472852	+	0.145855i
$741$	0.231596	−	1.01469i	0.00850789	−	0.0372755i
$742$	45.1092	+	53.3342i	1.65601	+	1.95796i
$743$	2.49473	+	10.9301i	0.0915226	+	0.400987i	0.999851	−	0.0172712i	$-0.00549788\pi$
$743$	2.49473	+	10.9301i	0.0915226	+	0.400987i	−0.908328	+	0.418258i	$0.862641\pi$
$744$	−0.0983844	+	1.31285i	−0.00360695	+	0.0481314i
$745$	−7.14366	+	2.20353i	−0.261723	+	0.0807310i
$746$	−3.72415	−	49.6953i	−0.136351	−	1.81947i
$747$	−0.116246	−	0.296191i	−0.00425323	−	0.0108371i
$748$	−42.6953	−	20.5610i	−1.56110	−	0.751784i
$749$	−5.09085	−	11.9462i	−0.186015	−	0.436505i
$750$	21.1241	−	10.1728i	0.771342	−	0.371459i
$751$	−22.9813	−	21.3235i	−0.838598	−	0.778105i	0.138619	−	0.990346i	$-0.455734\pi$
$751$	−22.9813	−	21.3235i	−0.838598	−	0.778105i	−0.977217	+	0.212240i	$0.931924\pi$
$752$	−35.0463	−	5.28239i	−1.27801	−	0.192629i
$753$	−8.56704	−	14.8385i	−0.312200	−	0.540746i
$754$	2.98897	−	5.17705i	0.108852	−	0.188537i
$755$	8.52706	−	10.6926i	0.310332	−	0.389143i
$756$	−21.5378	+	21.1723i	−0.783323	+	0.770031i
$757$	−4.39005	−	5.50495i	−0.159559	−	0.200081i	0.695625	−	0.718405i	$-0.255127\pi$
$757$	−4.39005	−	5.50495i	−0.159559	−	0.200081i	−0.855184	+	0.518324i	$0.826556\pi$
$758$	−52.5704	+	7.92371i	−1.90944	+	0.287802i
$759$	−19.8682	−	13.5459i	−0.721171	−	0.491686i
$760$	−0.152170	−	0.103748i	−0.00551978	−	0.00376332i
$761$	26.5552	−	4.00255i	0.962625	−	0.145092i	0.351118	−	0.936331i	$-0.385802\pi$
$761$	26.5552	−	4.00255i	0.962625	−	0.145092i	0.611507	+	0.791239i	$0.290564\pi$
$762$	39.4288	+	49.4422i	1.42836	+	1.79110i
$763$	−25.9070	−	42.0247i	−0.937895	−	1.52140i
$764$	−12.8964	+	16.1716i	−0.466576	+	0.585068i
$765$	−0.114347	+	0.198055i	−0.00413422	+	0.00716068i
$766$	31.8992	+	55.2511i	1.15257	+	1.99630i
$767$	−1.11773	−	0.168470i	−0.0403588	−	0.00608310i
$768$	15.2862	+	14.1835i	0.551593	+	0.511803i
$769$	−32.5900	+	15.6945i	−1.17523	+	0.565959i	−0.916517	−	0.399996i	$-0.869011\pi$
$769$	−32.5900	+	15.6945i	−1.17523	+	0.565959i	−0.258709	+	0.965955i	$0.583297\pi$
$770$	11.0196	+	9.64845i	0.397117	+	0.347706i
$771$	10.4619	+	5.03818i	0.376776	+	0.181446i
$772$	−9.31330	−	23.7299i	−0.335193	−	0.854058i
$773$	−1.08770	−	14.5144i	−0.0391219	−	0.522046i	−0.981997	−	0.188898i	$-0.939508\pi$
$773$	−1.08770	−	14.5144i	−0.0391219	−	0.522046i	0.942875	−	0.333148i	$-0.108111\pi$
$774$	0.0101974	−	0.00314547i	0.000366537	−	0.000113062i
$775$	0.563144	−	7.51463i	0.0202287	−	0.269933i
$776$	0.607739	+	2.66268i	0.0218166	+	0.0955846i
$777$	−40.9989	+	1.18286i	−1.47083	+	0.0424348i
$778$	14.2177	−	62.2917i	0.509729	−	2.23327i
$779$	−5.33667	−	1.64614i	−0.191206	−	0.0589792i
$780$	−0.971243	+	2.47469i	−0.0347761	+	0.0886080i
$781$	−21.7659	+	20.1958i	−0.778846	+	0.722664i
$782$	−32.1054	+	21.8891i	−1.14808	+	0.782751i
$783$	14.9611			0.534665
$784$	24.0508	−	5.05802i	0.858955	−	0.180644i
$785$	14.6798			0.523946
$786$	−28.9253	+	19.7209i	−1.03173	+	0.703422i
$787$	6.47444	−	6.00740i	0.230789	−	0.214141i	−0.556298	−	0.830983i	$-0.687779\pi$
$787$	6.47444	−	6.00740i	0.230789	−	0.214141i	0.787087	+	0.616842i	$0.211588\pi$
$788$	−4.38579	+	11.1748i	−0.156237	+	0.398087i
$789$	5.50626	+	1.69846i	0.196028	+	0.0604666i
$790$	−1.92696	+	8.44257i	−0.0685582	+	0.300373i
$791$	0.182857	−	0.243376i	0.00650164	−	0.00865344i
$792$	0.0244479	+	0.107113i	0.000868719	+	0.00380611i
$793$	−0.818329	+	10.9198i	−0.0290597	+	0.387775i
$794$	−15.8552	+	4.89068i	−0.562680	+	0.173564i
$795$	1.14997	+	15.3453i	0.0407852	+	0.544241i
$796$	0.410663	+	1.04635i	0.0145556	+	0.0370870i
$797$	28.6356	+	13.7902i	1.01432	+	0.488473i	0.865776	−	0.500432i	$-0.166825\pi$
$797$	28.6356	+	13.7902i	1.01432	+	0.488473i	0.148549	+	0.988905i	$0.452540\pi$
$798$	5.45142	+	1.51082i	0.192978	+	0.0534823i
$799$	49.2946	−	23.7390i	1.74392	−	0.839827i
$800$	26.9668	+	25.0215i	0.953419	+	0.884643i
$801$	−0.466891	−	0.0703725i	−0.0164968	−	0.00248649i
$802$	−4.97016	−	8.60857i	−0.175502	−	0.303979i
$803$	30.6864	−	53.1504i	1.08290	−	1.87564i
$804$	7.62050	−	9.55581i	0.268754	−	0.337007i
$805$	5.98141	−	2.03571i	0.210817	−	0.0717492i
$806$	2.12990	+	2.67080i	0.0750224	+	0.0940751i
$807$	48.6530	−	7.33326i	1.71267	−	0.258143i
$808$	−4.23241	−	2.88561i	−0.148896	−	0.101515i
$809$	−5.18328	−	3.53390i	−0.182234	−	0.124245i	0.468767	−	0.883322i	$-0.344698\pi$
$809$	−5.18328	−	3.53390i	−0.182234	−	0.124245i	−0.651001	+	0.759077i	$0.725651\pi$
$810$	−12.7626	+	1.92365i	−0.448431	+	0.0675901i
$811$	12.3499	+	15.4863i	0.433663	+	0.543797i	0.949861	−	0.312673i	$-0.101224\pi$
$811$	12.3499	+	15.4863i	0.433663	+	0.543797i	−0.516197	+	0.856470i	$0.672653\pi$
$812$	14.3952	+	9.21787i	0.505174	+	0.323484i
$813$	4.56389	−	5.72293i	0.160063	−	0.200712i
$814$	35.8373	−	62.0720i	1.25610	−	2.17562i
$815$	7.11525	+	12.3240i	0.249236	+	0.431690i
$816$	−32.9251	−	4.96265i	−1.15261	−	0.173728i
$817$	0.0367336	+	0.0340838i	0.00128515	+	0.00119244i
$818$	−8.51241	+	4.09936i	−0.297629	+	0.143331i
$819$	0.00749471	−	0.162967i	0.000261886	−	0.00569451i
$820$	12.8524	+	6.18941i	0.448827	+	0.216144i
$821$	3.50107	+	8.92059i	0.122188	+	0.311331i	0.978860	−	0.204531i	$-0.0655670\pi$
$821$	3.50107	+	8.92059i	0.122188	+	0.311331i	−0.856672	+	0.515862i	$0.827472\pi$
$822$	−4.28209	−	57.1406i	−0.149355	−	1.99301i
$823$	15.8879	−	4.90076i	0.553816	−	0.170830i	−0.00520005	−	0.999986i	$-0.501655\pi$
$823$	15.8879	−	4.90076i	0.553816	−	0.170830i	0.559016	+	0.829157i	$0.311179\pi$
$824$	0.249596	−	3.33062i	0.00869507	−	0.116028i
$825$	−6.94838	−	30.4429i	−0.241912	−	1.05988i
$826$	1.19380	−	6.02662i	0.0415377	−	0.209693i
$827$	−9.77683	+	42.8351i	−0.339974	+	1.48952i	0.459151	+	0.888358i	$0.348154\pi$
$827$	−9.77683	+	42.8351i	−0.339974	+	1.48952i	−0.799125	+	0.601165i	$0.794704\pi$
$828$	0.456541	+	0.140824i	0.0158659	+	0.00489398i
$829$	−5.93062	+	15.1110i	−0.205979	+	0.524825i	−0.996111	−	0.0881115i	$-0.971917\pi$
$829$	−5.93062	+	15.1110i	−0.205979	+	0.524825i	0.790132	+	0.612937i	$0.210012\pi$
$830$	−5.31772	+	4.93412i	−0.184581	+	0.171266i
$831$	−28.7431	+	19.5967i	−0.997086	+	0.679801i
$832$	−9.65432			−0.334703
$833$	−26.2778	+	27.3662i	−0.910473	+	0.948182i
$834$	26.7974			0.927917
$835$	2.51668	−	1.71584i	0.0870932	−	0.0593792i
$836$	−3.81232	+	3.53731i	−0.131852	+	0.122341i
$837$	−3.12348	+	7.95849i	−0.107963	+	0.275086i
$838$	21.1224	+	6.51539i	0.729660	+	0.225070i
$839$	−8.69788	+	38.1079i	−0.300284	+	1.31563i	0.569416	+	0.822050i	$0.307170\pi$
$839$	−8.69788	+	38.1079i	−0.300284	+	1.31563i	−0.869700	+	0.493581i	$0.835688\pi$
$840$	−1.30885	−	0.584428i	−0.0451597	−	0.0201647i
$841$	4.56887	+	20.0175i	0.157547	+	0.690260i
$842$	−3.49616	+	46.6530i	−0.120486	+	1.60777i
$843$	−9.38822	+	2.89588i	−0.323347	+	0.0997395i
$844$	−0.741192	−	9.89052i	−0.0255129	−	0.340446i
$845$	0.250004	+	0.637000i	0.00860040	+	0.0219135i
$846$	−1.15207	−	0.554809i	−0.0396091	−	0.0190747i
$847$	9.65557	−	6.99931i	0.331769	−	0.240499i
$848$	−40.6539	+	19.5779i	−1.39606	+	0.672308i
$849$	32.1772	+	29.8561i	1.10432	+	1.02466i
$850$	−49.8945	−	7.52039i	−1.71137	−	0.257947i
$851$	−15.4597	−	26.7770i	−0.529951	−	0.917903i
$852$	14.6461	−	25.3679i	0.501769	−	0.869089i
$853$	27.1597	−	34.0572i	0.929930	−	1.16610i	−0.0559152	−	0.998436i	$-0.517808\pi$
$853$	27.1597	−	34.0572i	0.929930	−	1.16610i	0.985845	−	0.167659i	$-0.0536209\pi$
$854$	−59.0849	−	7.16978i	−2.02184	−	0.245345i
$855$	0.0156483	+	0.0196224i	0.000535161	+	0.000671071i
$856$	−2.19599	+	0.330993i	−0.0750576	+	0.0113131i
$857$	33.9406	+	23.1403i	1.15939	+	0.790458i	0.981096	−	0.193519i	$-0.0619902\pi$
$857$	33.9406	+	23.1403i	1.15939	+	0.790458i	0.178293	+	0.983977i	$0.442943\pi$
$858$	11.6956	+	7.97395i	0.399282	+	0.272226i
$859$	4.60915	−	0.694718i	0.157262	−	0.0237035i	−0.0699392	−	0.997551i	$-0.522281\pi$
$859$	4.60915	−	0.694718i	0.157262	−	0.0237035i	0.227201	+	0.973848i	$0.427042\pi$
$860$	−0.0798045	−	0.100072i	−0.00272131	−	0.00341242i
$861$	−43.1497	−	5.23610i	−1.47054	−	0.178446i
$862$	−17.2238	+	21.5979i	−0.586644	+	0.735629i
$863$	−21.1660	+	36.6606i	−0.720499	+	1.24794i	0.240301	+	0.970698i	$0.422754\pi$
$863$	−21.1660	+	36.6606i	−0.720499	+	1.24794i	−0.960800	+	0.277243i	$0.910579\pi$
$864$	−20.8680	−	36.1444i	−0.709943	−	1.22966i
$865$	12.6182	+	1.90189i	0.429032	+	0.0646662i
$866$	11.3545	+	10.5354i	0.385841	+	0.358008i
$867$	19.5108	−	9.39590i	0.662621	−	0.319101i
$868$	−7.90876	+	5.73305i	−0.268441	+	0.194592i
$869$	21.8557	+	10.5251i	0.741403	+	0.357041i
$870$	2.61503	+	6.66299i	0.0886579	+	0.225897i
$871$	−0.235109	−	3.13731i	−0.00796635	−	0.106304i
$872$	−8.06783	+	2.48860i	−0.273211	+	0.0842745i
$873$	0.0278136	−	0.371147i	0.000941349	−	0.0125614i
$874$	0.948914	+	4.15746i	0.0320975	+	0.140628i
$875$	15.7576	+	7.03609i	0.532705	+	0.237863i
$876$	−13.4728	+	59.0281i	−0.455203	+	1.99437i
$877$	7.16546	+	2.21025i	0.241960	+	0.0746349i	0.413363	−	0.910566i	$-0.364354\pi$
$877$	7.16546	+	2.21025i	0.241960	+	0.0746349i	−0.171403	+	0.985201i	$0.554830\pi$
$878$	22.9660	−	58.5163i	0.775064	−	1.97483i
$879$	−13.6858	+	12.6986i	−0.461611	+	0.428312i
$880$	−7.81723	+	5.32970i	−0.263519	+	0.179664i
$881$	−10.2574			−0.345581			−0.172791	−	0.984959i	$-0.555278\pi$
$881$	−10.2574			−0.345581			−0.172791	+	0.984959i	$0.555278\pi$
$882$	0.882955	+	0.0813850i	0.0297306	+	0.00274038i
$883$	29.7694			1.00182			0.500909	−	0.865500i	$-0.332999\pi$
$883$	29.7694			1.00182			0.500909	+	0.865500i	$0.332999\pi$
$884$	9.94273	−	6.77884i	0.334410	−	0.227997i
$885$	0.992145	−	0.920576i	0.0333506	−	0.0309448i
$886$	3.15191	−	8.03093i	0.105890	−	0.269804i
$887$	27.9221	+	8.61283i	0.937533	+	0.289191i	0.725618	−	0.688097i	$-0.241554\pi$
$887$	27.9221	+	8.61283i	0.937533	+	0.289191i	0.211915	+	0.977288i	$0.432030\pi$
$888$	−1.56087	+	6.83863i	−0.0523795	+	0.229490i
$889$	−9.04454	+	45.6592i	−0.303344	+	1.53136i
$890$	2.39538	+	10.4948i	0.0802933	+	0.351788i
$891$	−2.70187	+	36.0539i	−0.0905160	+	1.20785i
$892$	−25.3854	+	7.83037i	−0.849967	+	0.262180i
$893$	−0.448714	−	5.98767i	−0.0150156	−	0.200370i
$894$	−14.3468	−	36.5550i	−0.479828	−	1.22258i
$895$	13.7788	+	6.63552i	0.460574	+	0.221801i
$896$	0.437308	−	9.50892i	0.0146094	−	0.317671i
$897$	5.50165	−	2.64946i	0.183695	−	0.0884628i
$898$	−0.0884060	−	0.0820288i	−0.00295015	−	0.00273734i
$899$	4.78480	+	0.721193i	0.159582	+	0.0240531i
$900$	0.310202	+	0.537286i	0.0103401	+	0.0179095i
$901$	34.8283	−	60.3243i	1.16030	−	2.00969i
$902$	47.3581	−	59.3851i	1.57685	−	1.97731i
$903$	0.328442	+	0.210315i	0.0109299	+	0.00699886i
$904$	−0.0324593	−	0.0407026i	−0.00107958	−	0.00135375i
$905$	−6.97645	+	1.05153i	−0.231905	+	0.0349541i
$906$	59.3574	+	40.4692i	1.97202	+	1.34450i
$907$	17.4443	+	11.8934i	0.579230	+	0.394912i	0.817195	−	0.576361i	$-0.195528\pi$
$907$	17.4443	+	11.8934i	0.579230	+	0.394912i	−0.237965	+	0.971274i	$0.576480\pi$
$908$	−37.6229	+	5.67074i	−1.24856	+	0.188190i
$909$	0.435238	+	0.545772i	0.0144359	+	0.0181021i
$910$	−3.52101	+	1.19834i	−0.116720	+	0.0397245i
$911$	34.0836	−	42.7395i	1.12924	−	1.41602i	0.232988	−	0.972480i	$-0.425150\pi$
$911$	34.0836	−	42.7395i	1.12924	−	1.41602i	0.896253	−	0.443543i	$-0.146279\pi$
$912$	−1.82708	+	3.16460i	−0.0605008	+	0.104790i
$913$	10.1605	+	17.5984i	0.336262	+	0.582423i
$914$	65.4039	+	9.85806i	2.16337	+	0.326076i
$915$	−9.61156	−	8.91823i	−0.317748	−	0.294828i
$916$	−31.3223	+	15.0840i	−1.03492	+	0.498390i
$917$	−24.8316	−	6.88187i	−0.820011	−	0.227259i
$918$	51.5771	+	24.8382i	1.70230	+	0.819784i
$919$	−11.3425	−	28.9002i	−0.374154	−	0.953329i	−0.986650	−	0.162855i	$-0.947930\pi$
$919$	−11.3425	−	28.9002i	−0.374154	−	0.953329i	0.612496	−	0.790474i	$-0.290166\pi$
$920$	−0.0807498	−	1.07753i	−0.00266224	−	0.0355252i
$921$	50.2360	−	15.4958i	1.65533	−	0.510603i
$922$	1.89015	−	25.2223i	0.0622489	−	0.830654i
$923$	−1.67781	−	7.35097i	−0.0552258	−	0.241960i
$924$	−24.3134	+	32.3603i	−0.799853	+	1.06457i
$925$	8.93430	−	39.1437i	0.293758	−	1.28704i
$926$	−41.0206	−	12.6532i	−1.34802	−	0.415809i
$927$	−0.166286	+	0.423690i	−0.00546155	+	0.0139158i
$928$	−17.3160	+	16.0669i	−0.568425	+	0.527421i
$929$	−10.5276	+	7.17760i	−0.345400	+	0.235489i	−0.723577	−	0.690244i	$-0.757503\pi$
$929$	−10.5276	+	7.17760i	−0.345400	+	0.235489i	0.378177	+	0.925733i	$0.376551\pi$
$930$	−4.09031			−0.134126
$931$	1.74210	+	3.78173i	0.0570950	+	0.123941i
$932$	8.16246			0.267370
$933$	2.13431	−	1.45515i	0.0698742	−	0.0476395i
$934$	−31.7768	+	29.4846i	−1.03977	+	0.964764i
$935$	5.33599	−	13.5959i	0.174505	−	0.444633i
$936$	−0.0266603	−	0.00822361i	−0.000871419	−	0.000268797i
$937$	0.533319	−	2.33662i	0.0174228	−	0.0763341i	−0.965469	−	0.260517i	$-0.916107\pi$
$937$	0.533319	−	2.33662i	0.0174228	−	0.0763341i	0.982892	+	0.184183i	$0.0589640\pi$
$938$	17.0927	−	0.493141i	0.558096	−	0.0161016i
$939$	−1.56521	−	6.85764i	−0.0510788	−	0.223791i
$940$	−1.14614	+	15.2942i	−0.0373831	+	0.498842i
$941$	−53.1100	+	16.3823i	−1.73134	+	0.534047i	−0.990485	−	0.137622i	$-0.956054\pi$
$941$	−53.1100	+	16.3823i	−1.73134	+	0.534047i	−0.740852	+	0.671668i	$0.765578\pi$
$942$	5.76257	+	76.8962i	0.187755	+	2.50541i
$943$	−11.9709	−	30.5015i	−0.389827	−	0.993264i
$944$	3.57562	+	1.72193i	0.116377	+	0.0560440i
$945$	−7.00334	−	6.13194i	−0.227819	−	0.199472i
$946$	−0.614040	+	0.295706i	−0.0199642	+	0.00961423i
$947$	10.3788	+	9.63008i	0.337264	+	0.312935i	0.830563	−	0.556924i	$-0.188019\pi$
$947$	10.3788	+	9.63008i	0.337264	+	0.312935i	−0.493299	+	0.869860i	$0.664209\pi$
$948$	−23.6640	−	3.56677i	−0.768570	−	0.115843i
$949$	7.79247	+	13.4970i	0.252954	+	0.438130i
$950$	−2.76876	+	4.79563i	−0.0898303	+	0.155591i
$951$	−28.5234	+	35.7672i	−0.924935	+	1.15983i
$952$	3.40491	+	5.52324i	0.110354	+	0.179009i
$953$	−30.9497	−	38.8097i	−1.00256	−	1.25717i	−0.966190	−	0.257832i	$-0.916992\pi$
$953$	−30.9497	−	38.8097i	−1.00256	−	1.25717i	−0.0363698	−	0.999338i	$-0.511579\pi$
$954$	−1.60977	+	0.242634i	−0.0521182	+	0.00785556i
$955$	−5.26734	−	3.59121i	−0.170447	−	0.116209i
$956$	13.7058	+	9.34444i	0.443277	+	0.302221i
$957$	19.8268	−	2.98841i	0.640910	−	0.0966017i
$958$	−26.6790	−	33.4544i	−0.861959	−	1.08086i
$959$	30.0768	−	29.5664i	0.971230	−	0.954749i
$960$	7.20739	−	9.03778i	0.232618	−	0.291693i
$961$	14.1174	−	24.4521i	0.455401	−	0.788777i
$962$	9.10050	+	15.7625i	0.293412	+	0.508204i
$963$	0.299259	+	0.0451060i	0.00964348	+	0.00145352i
$964$	−15.4551	−	14.3403i	−0.497776	−	0.461869i
$965$	7.07882	−	3.40898i	0.227875	−	0.109739i
$966$	13.0115	+	30.5328i	0.418637	+	0.982376i
$967$	−6.52508	−	3.14231i	−0.209832	−	0.101050i	0.326016	−	0.945364i	$-0.394294\pi$
$967$	−6.52508	−	3.14231i	−0.209832	−	0.101050i	−0.535848	+	0.844314i	$0.680008\pi$
$968$	−0.745114	−	1.89852i	−0.0239489	−	0.0610208i
$969$	−0.421554	−	5.62525i	−0.0135423	−	0.180709i
$970$	−8.10840	+	2.50111i	−0.260345	+	0.0803059i
$971$	−0.000781586		0.0104295i	−2.50823e−5		0.000334700i	−0.997216	−	0.0745627i	$-0.976244\pi$
$971$	−0.000781586		0.0104295i	−2.50823e−5		0.000334700i	0.997191	+	0.0748974i	$0.0238629\pi$
$972$	−0.316538	−	1.38684i	−0.0101529	−	0.0444830i
$973$	12.7373	+	15.0597i	0.408338	+	0.482793i
$974$	13.5628	−	59.4226i	0.434581	−	1.90402i
$975$	7.57716	+	2.33724i	0.242663	+	0.0748517i
$976$	14.0462	−	35.7892i	0.449608	−	1.14558i
$977$	−43.8820	+	40.7166i	−1.40391	+	1.30264i	−0.505951	+	0.862562i	$0.668858\pi$
$977$	−43.8820	+	40.7166i	−1.40391	+	1.30264i	−0.897960	+	0.440077i	$0.854951\pi$
$978$	−61.7625	+	42.1090i	−1.97495	+	1.34650i
$979$	30.1548			0.963750
$980$	−2.96043	−	10.2149i	−0.0945674	−	0.326305i
$981$	1.15056			0.0367345
$982$	−30.7444	+	20.9612i	−0.981094	+	0.668899i
$983$	9.43254	−	8.75212i	0.300851	−	0.279149i	−0.515272	−	0.857026i	$-0.672309\pi$
$983$	9.43254	−	8.75212i	0.300851	−	0.279149i	0.816124	+	0.577877i	$0.196119\pi$
$984$	−2.71578	+	6.91969i	−0.0865759	+	0.220592i
$985$	−3.53557	−	1.09058i	−0.112653	−	0.0347487i
$986$	7.20975	−	31.5880i	0.229605	−	1.00597i
$987$	−11.7086	−	45.2421i	−0.372688	−	1.44007i
$988$	−0.293870	−	1.28753i	−0.00934925	−	0.0409617i
$989$	−0.0219709	+	0.293181i	−0.000698633	+	0.00932262i
$990$	−0.326182	+	0.100614i	−0.0103668	+	0.00319772i
$991$	−1.75850	−	23.4656i	−0.0558606	−	0.745408i	−0.952867	−	0.303390i	$-0.901882\pi$
$991$	−1.75850	−	23.4656i	−0.0558606	−	0.745408i	0.897006	−	0.442019i	$-0.145737\pi$
$992$	−4.93160	−	12.5655i	−0.156579	−	0.398956i
$993$	−20.3635	−	9.80653i	−0.646215	−	0.311201i
$994$	40.3310	−	7.27414i	1.27922	−	0.230722i
$995$	−0.312135	+	0.150316i	−0.00989535	+	0.00476535i
$996$	−14.6956	−	13.6356i	−0.465649	−	0.432060i
$997$	14.5480	+	2.19276i	0.460740	+	0.0694454i	0.375311	−	0.926899i	$-0.377536\pi$
$997$	14.5480	+	2.19276i	0.460740	+	0.0694454i	0.0854290	+	0.996344i	$0.472774\pi$
$998$	13.3038	+	23.0429i	0.421125	+	0.729409i
$999$	−22.7759	+	39.4491i	−0.720599	+	1.24811i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.b.625.5	yes	348
49.4	even	21	inner	637.2.bl.b.53.5	✓	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.b.53.5	✓	348	49.4	even	21	inner
637.2.bl.b.625.5	yes	348	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.69736 + 1.15724i) q^{2} +(1.28266 - 1.19014i) q^{3} +(0.811150 - 2.06678i) q^{4} +(0.653901 + 0.201702i) q^{5} +(-0.799869 + 3.50445i) q^{6} +(-2.34964 + 1.21622i) q^{7} +(0.100685 + 0.441128i) q^{8} +(0.00460791 - 0.0614883i) q^{9} +O(q^{10})\)	\(q+(-1.69736 + 1.15724i) q^{2} +(1.28266 - 1.19014i) q^{3} +(0.811150 - 2.06678i) q^{4} +(0.653901 + 0.201702i) q^{5} +(-0.799869 + 3.50445i) q^{6} +(-2.34964 + 1.21622i) q^{7} +(0.100685 + 0.441128i) q^{8} +(0.00460791 - 0.0614883i) q^{9} +(-1.34333 + 0.414361i) q^{10} +(0.294283 + 3.92694i) q^{11} +(-1.41932 - 3.61636i) q^{12} +(-0.900969 - 0.433884i) q^{13} +(2.58074 - 4.78347i) q^{14} +(1.07879 - 0.519518i) q^{15} +(2.57373 + 2.38807i) q^{16} +(-5.35944 - 0.807806i) q^{17} +(0.0633356 + 0.109700i) q^{18} +(-0.297407 + 0.515124i) q^{19} +(0.947285 - 1.18786i) q^{20} +(-1.56634 + 4.35640i) q^{21} +(-5.04393 - 6.32489i) q^{22} +(-3.45086 + 0.520133i) q^{23} +(0.654149 + 0.445991i) q^{24} +(-3.74429 - 2.55281i) q^{25} +(2.03138 - 0.306181i) q^{26} +(3.20560 + 4.01970i) q^{27} +(0.607733 + 5.84272i) q^{28} +(1.81431 - 2.27507i) q^{29} +(-1.22989 + 2.13023i) q^{30} +(0.831438 + 1.44009i) q^{31} +(-8.02698 - 1.20987i) q^{32} +(5.05107 + 4.68671i) q^{33} +(10.0317 - 4.83104i) q^{34} +(-1.78175 + 0.321358i) q^{35} +(-0.123345 - 0.0593997i) q^{36} +(3.23686 + 8.24739i) q^{37} +(-0.0913159 - 1.21853i) q^{38} +(-1.67202 + 0.515751i) q^{39} +(-0.0231386 + 0.308763i) q^{40} +(2.08928 + 9.15371i) q^{41} +(-2.38277 - 9.20703i) q^{42} +(0.0187464 - 0.0821334i) q^{43} +(8.35481 + 2.57712i) q^{44} +(0.0154154 - 0.0392778i) q^{45} +(5.25544 - 4.87633i) q^{46} +(-8.34061 + 5.68653i) q^{47} +6.14337 q^{48} +(4.04164 - 5.71534i) q^{49} +9.30965 q^{50} +(-7.83577 + 5.34234i) q^{51} +(-1.62756 + 1.51016i) q^{52} +(-4.69529 + 11.9634i) q^{53} +(-10.0928 - 3.11323i) q^{54} +(-0.599639 + 2.62719i) q^{55} +(-0.773080 - 0.914040i) q^{56} +(0.231596 + 1.01469i) q^{57} +(-0.446732 + 5.96123i) q^{58} +(1.08013 - 0.333177i) q^{59} +(-0.198667 - 2.65102i) q^{60} +(-4.00065 - 10.1935i) q^{61} +(-3.07779 - 1.48218i) q^{62} +(0.0639560 + 0.150080i) q^{63} +(8.69824 - 4.18885i) q^{64} +(-0.501630 - 0.465444i) q^{65} +(-13.9972 - 2.10973i) q^{66} +(1.57305 + 2.72461i) q^{67} +(-6.01686 + 10.4215i) q^{68} +(-3.80726 + 4.77416i) q^{69} +(2.65238 - 2.60738i) q^{70} +(4.70112 + 5.89502i) q^{71} +(0.0275882 - 0.00415825i) q^{72} +(-12.8769 - 8.77931i) q^{73} +(-15.0384 - 10.2530i) q^{74} +(-7.84087 + 1.18182i) q^{75} +(0.823405 + 1.03252i) q^{76} +(-5.46747 - 8.86899i) q^{77} +(2.24118 - 2.81035i) q^{78} +(3.08003 - 5.33476i) q^{79} +(1.20129 + 2.08069i) q^{80} +(9.07863 + 1.36838i) q^{81} +(-14.1393 - 13.1194i) q^{82} +(4.64925 - 2.23896i) q^{83} +(7.73316 + 6.77096i) q^{84} +(-3.34161 - 1.60923i) q^{85} +(0.0632288 + 0.161104i) q^{86} +(-0.380502 - 5.07744i) q^{87} +(-1.70266 + 0.525200i) q^{88} +(0.572244 - 7.63606i) q^{89} +(0.0192884 + 0.0845082i) q^{90} +(2.64465 - 0.0763007i) q^{91} +(-1.72416 + 7.55405i) q^{92} +(2.78037 + 0.857629i) q^{93} +(7.57635 - 19.3042i) q^{94} +(-0.298377 + 0.276853i) q^{95} +(-11.7358 + 8.00136i) q^{96} +6.03606 q^{97} +(-0.246091 + 14.3782i) q^{98} +0.242817 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Introduction

L-functions

Modular forms

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