LMFDB - Embedded newform 378.2.u.c.295.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(43,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("378.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.u (of order $9$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			295.3
Character	$\chi$	$=$	378.295
Dual form			378.2.u.c.337.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 + 0.984808i) q^{2} +(1.13330 + 1.30982i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(2.14766 - 1.80210i) q^{5} +(-1.48672 + 0.888630i) q^{6} +(0.939693 - 0.342020i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.431280 + 2.96884i) q^{9} +O(q^{10})$	\(q+(-0.173648 + 0.984808i) q^{2} +(1.13330 + 1.30982i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(2.14766 - 1.80210i) q^{5} +(-1.48672 + 0.888630i) q^{6} +(0.939693 - 0.342020i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.431280 + 2.96884i) q^{9} +(1.40179 + 2.42797i) q^{10} +(0.617661 + 0.518279i) q^{11} +(-0.616964 - 1.61844i) q^{12} +(0.0751565 + 0.426234i) q^{13} +(0.173648 + 0.984808i) q^{14} +(4.79438 + 0.770745i) q^{15} +(0.766044 + 0.642788i) q^{16} +(0.882551 + 1.52862i) q^{17} +(-2.84884 - 0.940261i) q^{18} +(2.43396 - 4.21574i) q^{19} +(-2.63450 + 0.958879i) q^{20} +(1.51294 + 0.843222i) q^{21} +(-0.617661 + 0.518279i) q^{22} +(2.01139 + 0.732085i) q^{23} +(1.70099 - 0.326551i) q^{24} +(0.496639 - 2.81658i) q^{25} -0.432809 q^{26} +(-4.37742 + 2.79967i) q^{27} -1.00000 q^{28} +(-1.34443 + 7.62462i) q^{29} +(-1.59157 + 4.58770i) q^{30} +(-9.12775 - 3.32223i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(0.0211381 + 1.39639i) q^{33} +(-1.65865 + 0.603701i) q^{34} +(1.40179 - 2.42797i) q^{35} +(1.42067 - 2.64229i) q^{36} +(-0.701181 - 1.21448i) q^{37} +(3.72904 + 3.12904i) q^{38} +(-0.473117 + 0.581491i) q^{39} +(-0.486836 - 2.76098i) q^{40} +(-0.0980363 - 0.555992i) q^{41} +(-1.09313 + 1.34353i) q^{42} +(-7.28801 - 6.11537i) q^{43} +(-0.403150 - 0.698276i) q^{44} +(4.42391 + 7.15327i) q^{45} +(-1.07024 + 1.85370i) q^{46} +(-7.86903 + 2.86409i) q^{47} +(0.0262162 + 1.73185i) q^{48} +(0.766044 - 0.642788i) q^{49} +(2.68755 + 0.978187i) q^{50} +(-1.00204 + 2.88837i) q^{51} +(0.0751565 - 0.426234i) q^{52} -0.683345 q^{53} +(-1.99701 - 4.79708i) q^{54} +2.26052 q^{55} +(0.173648 - 0.984808i) q^{56} +(8.28028 - 1.58962i) q^{57} +(-7.27533 - 2.64800i) q^{58} +(10.6623 - 8.94676i) q^{59} +(-4.24163 - 2.36404i) q^{60} +(0.529750 - 0.192813i) q^{61} +(4.85678 - 8.41218i) q^{62} +(0.610132 + 2.93730i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.929528 + 0.779967i) q^{65} +(-1.37885 - 0.221664i) q^{66} +(-2.22866 - 12.6394i) q^{67} +(-0.306507 - 1.73829i) q^{68} +(1.32059 + 3.46423i) q^{69} +(2.14766 + 1.80210i) q^{70} +(6.31380 + 10.9358i) q^{71} +(2.35545 + 1.85792i) q^{72} +(0.627254 - 1.08644i) q^{73} +(1.31779 - 0.479636i) q^{74} +(4.25206 - 2.54151i) q^{75} +(-3.72904 + 3.12904i) q^{76} +(0.757674 + 0.275771i) q^{77} +(-0.490501 - 0.566904i) q^{78} +(1.10100 - 6.24407i) q^{79} +2.80357 q^{80} +(-8.62799 - 2.56080i) q^{81} +0.564569 q^{82} +(0.124565 - 0.706444i) q^{83} +(-1.13330 - 1.30982i) q^{84} +(4.65016 + 1.69252i) q^{85} +(7.28801 - 6.11537i) q^{86} +(-11.5106 + 6.87999i) q^{87} +(0.757674 - 0.275771i) q^{88} +(3.20745 - 5.55547i) q^{89} +(-7.81280 + 3.11454i) q^{90} +(0.216405 + 0.374824i) q^{91} +(-1.63970 - 1.37587i) q^{92} +(-5.99291 - 15.7208i) q^{93} +(-1.45414 - 8.24682i) q^{94} +(-2.36988 - 13.4402i) q^{95} +(-1.71009 - 0.274915i) q^{96} +(9.94201 + 8.34234i) q^{97} +(0.500000 + 0.866025i) q^{98} +(-1.80507 + 1.61021i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9}+O(q^{10}) $ 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9	$ 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9} + 3 q^{10} - 9 q^{13} - 6 q^{18} + 15 q^{19} - 6 q^{20} - 3 q^{21} + 6 q^{23} + 3 q^{24} + 33 q^{25} + 18 q^{26} - 18 q^{27} - 24 q^{28} - 30 q^{29} + 15 q^{30} - 6 q^{33} - 3 q^{34} + 3 q^{35} - 12 q^{36} - 3 q^{37} + 15 q^{38} - 18 q^{39} - 3 q^{40} + 27 q^{41} + 18 q^{43} - 3 q^{44} + 12 q^{45} + 15 q^{46} + 3 q^{48} + 3 q^{50} + 24 q^{51} - 9 q^{52} + 6 q^{53} + 45 q^{54} - 66 q^{55} - 6 q^{57} + 3 q^{58} - 30 q^{59} - 30 q^{60} - 57 q^{61} - 18 q^{62} + 12 q^{63} - 12 q^{64} + 24 q^{65} - 54 q^{66} + 39 q^{67} + 3 q^{68} + 36 q^{69} + 3 q^{70} - 24 q^{71} - 6 q^{72} + 36 q^{73} - 12 q^{74} + 15 q^{75} - 15 q^{76} - 9 q^{77} + 18 q^{78} - 33 q^{79} + 6 q^{80} + 9 q^{81} - 15 q^{83} + 3 q^{84} + 36 q^{85} - 18 q^{86} - 84 q^{87} - 9 q^{88} - 3 q^{89} - 30 q^{90} - 9 q^{91} - 30 q^{92} - 45 q^{93} + 45 q^{94} + 63 q^{95} - 30 q^{97} + 12 q^{98} - 57 q^{99}+O(q^{100}) $ 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9 + 3 * q^10 - 9 * q^13 - 6 * q^18 + 15 * q^19 - 6 * q^20 - 3 * q^21 + 6 * q^23 + 3 * q^24 + 33 * q^25 + 18 * q^26 - 18 * q^27 - 24 * q^28 - 30 * q^29 + 15 * q^30 - 6 * q^33 - 3 * q^34 + 3 * q^35 - 12 * q^36 - 3 * q^37 + 15 * q^38 - 18 * q^39 - 3 * q^40 + 27 * q^41 + 18 * q^43 - 3 * q^44 + 12 * q^45 + 15 * q^46 + 3 * q^48 + 3 * q^50 + 24 * q^51 - 9 * q^52 + 6 * q^53 + 45 * q^54 - 66 * q^55 - 6 * q^57 + 3 * q^58 - 30 * q^59 - 30 * q^60 - 57 * q^61 - 18 * q^62 + 12 * q^63 - 12 * q^64 + 24 * q^65 - 54 * q^66 + 39 * q^67 + 3 * q^68 + 36 * q^69 + 3 * q^70 - 24 * q^71 - 6 * q^72 + 36 * q^73 - 12 * q^74 + 15 * q^75 - 15 * q^76 - 9 * q^77 + 18 * q^78 - 33 * q^79 + 6 * q^80 + 9 * q^81 - 15 * q^83 + 3 * q^84 + 36 * q^85 - 18 * q^86 - 84 * q^87 - 9 * q^88 - 3 * q^89 - 30 * q^90 - 9 * q^91 - 30 * q^92 - 45 * q^93 + 45 * q^94 + 63 * q^95 - 30 * q^97 + 12 * q^98 - 57 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$3$	1.13330	+	1.30982i	0.654309	+	0.756227i
$3$	1.13330	+	1.30982i	0.654309	+	0.756227i
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	2.14766	−	1.80210i	0.960464	−	0.805925i	−0.0205646	−	0.999789i	$-0.506546\pi$
$5$	2.14766	−	1.80210i	0.960464	−	0.805925i	0.981028	+	0.193864i	$0.0621019\pi$
$6$	−1.48672	+	0.888630i	−0.606951	+	0.362782i
$7$	0.939693	−	0.342020i	0.355170	−	0.129271i
$7$	0.939693	−	0.342020i	0.355170	−	0.129271i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−0.431280	+	2.96884i	−0.143760	+	0.989613i
$10$	1.40179	+	2.42797i	0.443284	+	0.767790i
$11$	0.617661	+	0.518279i	0.186232	+	0.156267i	0.731137	−	0.682230i	$-0.238990\pi$
$11$	0.617661	+	0.518279i	0.186232	+	0.156267i	−0.544905	+	0.838498i	$0.683434\pi$
$12$	−0.616964	−	1.61844i	−0.178102	−	0.467204i
$13$	0.0751565	+	0.426234i	0.0208447	+	0.118216i	0.993455	−	0.114227i	$-0.0364392\pi$
$13$	0.0751565	+	0.426234i	0.0208447	+	0.118216i	−0.972610	+	0.232443i	$0.925328\pi$
$14$	0.173648	+	0.984808i	0.0464094	+	0.263201i
$15$	4.79438	+	0.770745i	1.23790	+	0.199005i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	0.882551	+	1.52862i	0.214050	+	0.370746i	0.952978	−	0.303038i	$-0.0980011\pi$
$17$	0.882551	+	1.52862i	0.214050	+	0.370746i	−0.738928	+	0.673784i	$0.764668\pi$
$18$	−2.84884	−	0.940261i	−0.671479	−	0.221622i
$19$	2.43396	−	4.21574i	0.558389	−	0.967157i	−0.439243	−	0.898368i	$-0.644753\pi$
$19$	2.43396	−	4.21574i	0.558389	−	0.967157i	0.997631	−	0.0687889i	$-0.0219135\pi$
$20$	−2.63450	+	0.958879i	−0.589092	+	0.214412i
$21$	1.51294	+	0.843222i	0.330150	+	0.184006i
$22$	−0.617661	+	0.518279i	−0.131686	+	0.110498i
$23$	2.01139	+	0.732085i	0.419403	+	0.152650i	0.543097	−	0.839670i	$-0.317252\pi$
$23$	2.01139	+	0.732085i	0.419403	+	0.152650i	−0.123694	+	0.992320i	$0.539474\pi$
$24$	1.70099	−	0.326551i	0.347213	−	0.0666569i
$25$	0.496639	−	2.81658i	0.0993277	−	0.563316i
$26$	−0.432809			−0.0848809
$27$	−4.37742	+	2.79967i	−0.842436	+	0.538797i
$28$	−1.00000			−0.188982
$29$	−1.34443	+	7.62462i	−0.249654	+	1.41586i	0.559778	+	0.828643i	$0.310886\pi$
$29$	−1.34443	+	7.62462i	−0.249654	+	1.41586i	−0.809432	+	0.587214i	$0.800225\pi$
$30$	−1.59157	+	4.58770i	−0.290580	+	0.837596i
$31$	−9.12775	−	3.32223i	−1.63939	−	0.596690i	−0.652460	−	0.757823i	$-0.726263\pi$
$31$	−9.12775	−	3.32223i	−1.63939	−	0.596690i	−0.986933	+	0.161133i	$0.948485\pi$
$32$	−0.766044	+	0.642788i	−0.135419	+	0.113630i
$33$	0.0211381	+	1.39639i	0.00367968	+	0.243081i
$34$	−1.65865	+	0.603701i	−0.284457	+	0.103534i
$35$	1.40179	−	2.42797i	0.236945	−	0.410401i
$36$	1.42067	−	2.64229i	0.236779	−	0.440381i
$37$	−0.701181	−	1.21448i	−0.115273	−	0.199659i	0.802616	−	0.596497i	$-0.203441\pi$
$37$	−0.701181	−	1.21448i	−0.115273	−	0.199659i	−0.917889	+	0.396837i	$0.870108\pi$
$38$	3.72904	+	3.12904i	0.604930	+	0.507597i
$39$	−0.473117	+	0.581491i	−0.0757594	+	0.0931131i
$40$	−0.486836	−	2.76098i	−0.0769755	−	0.436550i
$41$	−0.0980363	−	0.555992i	−0.0153107	−	0.0868313i	0.976195	−	0.216895i	$-0.0695929\pi$
$41$	−0.0980363	−	0.555992i	−0.0153107	−	0.0868313i	−0.991506	+	0.130064i	$0.958482\pi$
$42$	−1.09313	+	1.34353i	−0.168674	+	0.207311i
$43$	−7.28801	−	6.11537i	−1.11141	−	0.932585i	−0.113273	−	0.993564i	$-0.536133\pi$
$43$	−7.28801	−	6.11537i	−1.11141	−	0.932585i	−0.998139	+	0.0609788i	$0.980578\pi$
$44$	−0.403150	−	0.698276i	−0.0607771	−	0.105269i
$45$	4.42391	+	7.15327i	0.659477	+	1.06635i
$46$	−1.07024	+	1.85370i	−0.157798	+	0.273314i
$47$	−7.86903	+	2.86409i	−1.14782	+	0.417771i	−0.844730	−	0.535193i	$-0.820239\pi$
$47$	−7.86903	+	2.86409i	−1.14782	+	0.417771i	−0.303085	+	0.952963i	$0.598017\pi$
$48$	0.0262162	+	1.73185i	0.00378399	+	0.249971i
$49$	0.766044	−	0.642788i	0.109435	−	0.0918268i
$50$	2.68755	+	0.978187i	0.380077	+	0.138337i
$51$	−1.00204	+	2.88837i	−0.140313	+	0.404453i
$52$	0.0751565	−	0.426234i	0.0104223	−	0.0591080i
$53$	−0.683345			−0.0938646			−0.0469323	−	0.998898i	$-0.514945\pi$
$53$	−0.683345			−0.0938646			−0.0469323	+	0.998898i	$0.514945\pi$
$54$	−1.99701	−	4.79708i	−0.271758	−	0.652800i
$55$	2.26052			0.304809
$56$	0.173648	−	0.984808i	0.0232047	−	0.131600i
$57$	8.28028	−	1.58962i	1.09675	−	0.210551i
$58$	−7.27533	−	2.64800i	−0.955298	−	0.347700i
$59$	10.6623	−	8.94676i	1.38812	−	1.16477i	0.422022	−	0.906586i	$-0.361321\pi$
$59$	10.6623	−	8.94676i	1.38812	−	1.16477i	0.966096	−	0.258183i	$-0.0831238\pi$
$60$	−4.24163	−	2.36404i	−0.547592	−	0.305196i
$61$	0.529750	−	0.192813i	0.0678276	−	0.0246872i	−0.307884	−	0.951424i	$-0.599621\pi$
$61$	0.529750	−	0.192813i	0.0678276	−	0.0246872i	0.375711	+	0.926737i	$0.377398\pi$
$62$	4.85678	−	8.41218i	0.616811	−	1.06835i
$63$	0.610132	+	2.93730i	0.0768694	+	0.370065i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	0.929528	+	0.779967i	0.115294	+	0.0967430i
$66$	−1.37885	−	0.221664i	−0.169724	−	0.0272849i
$67$	−2.22866	−	12.6394i	−0.272275	−	1.54415i	−0.747488	−	0.664276i	$-0.768740\pi$
$67$	−2.22866	−	12.6394i	−0.272275	−	1.54415i	0.475213	−	0.879871i	$-0.342371\pi$
$68$	−0.306507	−	1.73829i	−0.0371694	−	0.210798i
$69$	1.32059	+	3.46423i	0.158981	+	0.417044i
$70$	2.14766	+	1.80210i	0.256695	+	0.215392i
$71$	6.31380	+	10.9358i	0.749310	+	1.29784i	0.948154	+	0.317811i	$0.102948\pi$
$71$	6.31380	+	10.9358i	0.749310	+	1.29784i	−0.198844	+	0.980031i	$0.563719\pi$
$72$	2.35545	+	1.85792i	0.277592	+	0.218958i
$73$	0.627254	−	1.08644i	0.0734145	−	0.127158i	−0.826981	−	0.562230i	$-0.809944\pi$
$73$	0.627254	−	1.08644i	0.0734145	−	0.127158i	0.900396	+	0.435072i	$0.143277\pi$
$74$	1.31779	−	0.479636i	0.153190	−	0.0557566i
$75$	4.25206	−	2.54151i	0.490986	−	0.293468i
$76$	−3.72904	+	3.12904i	−0.427750	+	0.358925i
$77$	0.757674	+	0.275771i	0.0863449	+	0.0314270i
$78$	−0.490501	−	0.566904i	−0.0555383	−	0.0641893i
$79$	1.10100	−	6.24407i	0.123872	−	0.702513i	−0.858099	−	0.513484i	$-0.828355\pi$
$79$	1.10100	−	6.24407i	0.123872	−	0.702513i	0.981971	−	0.189030i	$-0.0605342\pi$
$80$	2.80357			0.313449
$81$	−8.62799	−	2.56080i	−0.958666	−	0.284533i
$82$	0.564569			0.0623462
$83$	0.124565	−	0.706444i	0.0136728	−	0.0775424i	−0.977208	−	0.212285i	$-0.931910\pi$
$83$	0.124565	−	0.706444i	0.0136728	−	0.0775424i	0.990881	+	0.134742i	$0.0430207\pi$
$84$	−1.13330	−	1.30982i	−0.123653	−	0.142914i
$85$	4.65016	+	1.69252i	0.504381	+	0.183580i
$86$	7.28801	−	6.11537i	0.785887	−	0.659437i
$87$	−11.5106	+	6.87999i	−1.23406	+	0.737613i
$88$	0.757674	−	0.275771i	0.0807683	−	0.0293973i
$89$	3.20745	−	5.55547i	0.339990	−	0.588879i	−0.644441	−	0.764654i	$-0.722910\pi$
$89$	3.20745	−	5.55547i	0.339990	−	0.588879i	0.984430	+	0.175775i	$0.0562431\pi$
$90$	−7.81280	+	3.11454i	−0.823542	+	0.328302i
$91$	0.216405	+	0.374824i	0.0226854	+	0.0392922i
$92$	−1.63970	−	1.37587i	−0.170950	−	0.143444i
$93$	−5.99291	−	15.7208i	−0.621436	−	1.63017i
$94$	−1.45414	−	8.24682i	−0.149983	−	0.850595i
$95$	−2.36988	−	13.4402i	−0.243144	−	1.37894i
$96$	−1.71009	−	0.274915i	−0.174536	−	0.0280584i
$97$	9.94201	+	8.34234i	1.00946	+	0.847036i	0.988266	−	0.152740i	$-0.0488096\pi$
$97$	9.94201	+	8.34234i	1.00946	+	0.847036i	0.0211916	+	0.999775i	$0.493254\pi$
$98$	0.500000	+	0.866025i	0.0505076	+	0.0874818i
$99$	−1.80507	+	1.61021i	−0.181417	+	0.161832i
$100$	−1.43001	+	2.47686i	−0.143001	+	0.247686i
$101$	1.55844	−	0.567224i	0.155070	−	0.0564409i	−0.263319	−	0.964709i	$-0.584817\pi$
$101$	1.55844	−	0.567224i	0.155070	−	0.0564409i	0.418389	+	0.908268i	$0.362595\pi$
$102$	−2.67049	−	1.48837i	−0.264418	−	0.147371i
$103$	0.00934804	−	0.00784393i	0.000921089	−	0.000772886i	−0.642327	−	0.766431i	$-0.722031\pi$
$103$	0.00934804	−	0.00784393i	0.000921089	−	0.000772886i	0.643248	+	0.765658i	$0.277586\pi$
$104$	0.406708	+	0.148029i	0.0398810	+	0.0145155i
$105$	4.76885	−	0.915510i	0.465392	−	0.0893446i
$106$	0.118662	−	0.672963i	0.0115254	−	0.0653640i
$107$	−5.76724			−0.557540			−0.278770	−	0.960358i	$-0.589927\pi$
$107$	−5.76724			−0.557540			−0.278770	+	0.960358i	$0.589927\pi$
$108$	5.07098	−	1.13366i	0.487955	−	0.109087i
$109$	−9.47158			−0.907213			−0.453606	−	0.891202i	$-0.649863\pi$
$109$	−9.47158			−0.907213			−0.453606	+	0.891202i	$0.649863\pi$
$110$	−0.392535	+	2.22618i	−0.0374268	+	0.212258i
$111$	0.796111	−	2.29479i	0.0755635	−	0.217812i
$112$	0.939693	+	0.342020i	0.0887926	+	0.0323179i
$113$	−9.45672	+	7.93513i	−0.889613	+	0.746474i	−0.968133	−	0.250438i	$-0.919425\pi$
$113$	−9.45672	+	7.93513i	−0.889613	+	0.746474i	0.0785191	+	0.996913i	$0.474981\pi$
$114$	0.127618	+	8.43052i	0.0119526	+	0.789590i
$115$	5.63907	−	2.05245i	0.525846	−	0.191392i
$116$	3.87112	−	6.70498i	0.359425	−	0.622542i
$117$	−1.29783	+	0.0393014i	−0.119985	+	0.00363341i
$118$	6.95934	+	12.0539i	0.640660	+	1.10965i
$119$	1.35215	+	1.13459i	0.123951	+	0.104007i
$120$	3.06467	−	3.76668i	0.279765	−	0.343849i
$121$	−1.79724	−	10.1926i	−0.163385	−	0.926604i
$122$	0.0978939	+	0.555184i	0.00886289	+	0.0502640i
$123$	0.617147	−	0.758513i	0.0556463	−	0.0683928i
$124$	7.44101	+	6.24375i	0.668223	+	0.560705i
$125$	2.99978	+	5.19578i	0.268309	+	0.464725i
$126$	−2.99863	+	0.0908052i	−0.267139	+	0.00808957i
$127$	−6.33670	+	10.9755i	−0.562291	+	0.973917i	0.435005	+	0.900428i	$0.356747\pi$
$127$	−6.33670	+	10.9755i	−0.562291	+	0.973917i	−0.997296	+	0.0734888i	$0.976587\pi$
$128$	0.939693	−	0.342020i	0.0830579	−	0.0302306i
$129$	−0.249417	−	16.4765i	−0.0219599	−	1.45068i
$130$	−0.929528	+	0.779967i	−0.0815250	+	0.0684076i
$131$	−20.7787	−	7.56282i	−1.81544	−	0.660767i	−0.996178	−	0.0873505i	$-0.972160\pi$
$131$	−20.7787	−	7.56282i	−1.81544	−	0.660767i	−0.819264	−	0.573416i	$-0.805618\pi$
$132$	0.457731	−	1.31941i	0.0398404	−	0.114840i
$133$	0.845305	−	4.79396i	0.0732973	−	0.415689i
$134$	12.8344			1.10872
$135$	−4.35594	+	13.9013i	−0.374899	+	1.19643i
$136$	1.76510			0.151356
$137$	2.02654	−	11.4931i	0.173139	−	0.981919i	−0.767131	−	0.641490i	$-0.778317\pi$
$137$	2.02654	−	11.4931i	0.173139	−	0.981919i	0.940270	−	0.340429i	$-0.110572\pi$
$138$	−3.64092	+	0.698973i	−0.309936	+	0.0595005i
$139$	19.9468	+	7.26005i	1.69187	+	0.615790i	0.994859	−	0.101272i	$-0.0322914\pi$
$139$	19.9468	+	7.26005i	1.69187	+	0.615790i	0.697009	+	0.717062i	$0.254514\pi$
$140$	−2.14766	+	1.80210i	−0.181511	+	0.152305i
$141$	−12.6694	−	7.06118i	−1.06696	−	0.594659i
$142$	−11.8661	+	4.31889i	−0.995777	+	0.362433i
$143$	−0.174487	+	0.302220i	−0.0145913	+	0.0252729i
$144$	−2.23871	+	1.99704i	−0.186559	+	0.166420i
$145$	10.8530	+	18.7979i	0.901291	+	1.56108i
$146$	0.961009	+	0.806382i	0.0795337	+	0.0667367i
$147$	1.71009	+	0.274915i	0.141046	+	0.0226746i
$148$	0.243518	+	1.38106i	0.0200170	+	0.113522i
$149$	−2.08224	−	11.8089i	−0.170583	−	0.967427i	−0.943119	−	0.332455i	$-0.892123\pi$
$149$	−2.08224	−	11.8089i	−0.170583	−	0.967427i	0.772536	−	0.634971i	$-0.218988\pi$
$150$	1.76453	+	4.62879i	0.144074	+	0.377939i
$151$	−16.3212	−	13.6951i	−1.32820	−	1.11449i	−0.984495	−	0.175411i	$-0.943875\pi$
$151$	−16.3212	−	13.6951i	−1.32820	−	1.11449i	−0.343702	−	0.939079i	$-0.611681\pi$
$152$	−2.43396	−	4.21574i	−0.197420	−	0.341942i
$153$	−4.91886	+	1.96089i	−0.397667	+	0.158528i
$154$	−0.403150	+	0.698276i	−0.0324867	+	0.0562687i
$155$	−25.5903	+	9.31412i	−2.05547	+	0.748128i
$156$	0.643466	−	0.384607i	0.0515185	−	0.0307932i
$157$	−11.4048	+	9.56980i	−0.910206	+	0.763753i	−0.972158	−	0.234326i	$-0.924712\pi$
$157$	−11.4048	+	9.56980i	−0.910206	+	0.763753i	0.0619523	+	0.998079i	$0.480267\pi$
$158$	5.95803	+	2.16854i	0.473995	+	0.172520i
$159$	−0.774432	−	0.895062i	−0.0614164	−	0.0709830i
$160$	−0.486836	+	2.76098i	−0.0384877	+	0.218275i
$161$	2.14047			0.168693
$162$	4.02013	−	8.05224i	0.315851	−	0.632644i
$163$	−2.90481			−0.227522			−0.113761	−	0.993508i	$-0.536290\pi$
$163$	−2.90481			−0.227522			−0.113761	+	0.993508i	$0.536290\pi$
$164$	−0.0980363	+	0.555992i	−0.00765535	+	0.0434156i
$165$	2.56184	+	2.96089i	0.199439	+	0.230505i
$166$	0.674081	+	0.245346i	0.0523189	+	0.0190425i
$167$	−0.588666	+	0.493950i	−0.0455524	+	0.0382230i	−0.665280	−	0.746594i	$-0.731688\pi$
$167$	−0.588666	+	0.493950i	−0.0455524	+	0.0382230i	0.619727	+	0.784817i	$0.287243\pi$
$168$	1.48672	−	0.888630i	0.114703	−	0.0685593i
$169$	12.0400	−	4.38219i	0.926152	−	0.337092i
$170$	−2.47430	+	4.28561i	−0.189770	+	0.328691i
$171$	11.4661	+	9.04420i	0.876837	+	0.691627i
$172$	4.75691	+	8.23922i	0.362711	+	0.628234i
$173$	17.7038	+	14.8553i	1.34600	+	1.12942i	0.980042	+	0.198791i	$0.0637014\pi$
$173$	17.7038	+	14.8553i	1.34600	+	1.12942i	0.365953	+	0.930633i	$0.380743\pi$
$174$	−4.77668	−	12.5304i	−0.362119	−	0.949926i
$175$	−0.496639	−	2.81658i	−0.0375424	−	0.212913i
$176$	0.140012	+	0.794050i	0.0105538	+	0.0598538i
$177$	23.8023	+	3.82646i	1.78909	+	0.287614i
$178$	4.91411	+	4.12342i	0.368328	+	0.309064i
$179$	1.27660	+	2.21114i	0.0954178	+	0.165268i	0.909783	−	0.415084i	$-0.136248\pi$
$179$	1.27660	+	2.21114i	0.0954178	+	0.165268i	−0.814365	+	0.580353i	$0.802915\pi$
$180$	−1.71055	−	8.23494i	−0.127497	−	0.613796i
$181$	−4.33150	+	7.50238i	−0.321958	+	0.557648i	−0.980892	−	0.194553i	$-0.937674\pi$
$181$	−4.33150	+	7.50238i	−0.321958	+	0.557648i	0.658934	+	0.752201i	$0.271008\pi$
$182$	−0.406708	+	0.148029i	−0.0301472	+	0.0109727i
$183$	0.852915	+	0.475365i	0.0630493	+	0.0351400i
$184$	1.63970	−	1.37587i	0.120880	−	0.101430i
$185$	−3.69452	−	1.34470i	−0.271626	−	0.0988640i
$186$	16.5227	−	3.17197i	1.21150	−	0.232580i
$187$	−0.247136	+	1.40158i	−0.0180724	+	0.102494i
$188$	8.37404			0.610740
$189$	−3.15589	+	4.12800i	−0.229557	+	0.300268i
$190$	13.6476			0.990099
$191$	−2.13397	+	12.1024i	−0.154409	+	0.875695i	0.804916	+	0.593389i	$0.202210\pi$
$191$	−2.13397	+	12.1024i	−0.154409	+	0.875695i	−0.959324	+	0.282306i	$0.908901\pi$
$192$	0.567693	−	1.63638i	0.0409697	−	0.118095i
$193$	4.95009	+	1.80168i	0.356315	+	0.129688i	0.513975	−	0.857805i	$-0.328173\pi$
$193$	4.95009	+	1.80168i	0.356315	+	0.129688i	−0.157659	+	0.987494i	$0.550395\pi$
$194$	−9.94201	+	8.34234i	−0.713795	+	0.598945i
$195$	0.0318111	+	2.10145i	0.00227804	+	0.150488i
$196$	−0.939693	+	0.342020i	−0.0671209	+	0.0244300i
$197$	−3.26296	+	5.65161i	−0.232476	+	0.402661i	−0.958536	−	0.284971i	$-0.908016\pi$
$197$	−3.26296	+	5.65161i	−0.232476	+	0.402661i	0.726060	+	0.687631i	$0.241349\pi$
$198$	−1.27230	−	2.05726i	−0.0904186	−	0.146203i
$199$	5.57483	+	9.65589i	0.395189	+	0.684488i	0.993125	−	0.117056i	$-0.0373457\pi$
$199$	5.57483	+	9.65589i	0.395189	+	0.684488i	−0.597936	+	0.801544i	$0.704012\pi$
$200$	−2.19091	−	1.83839i	−0.154921	−	0.129994i
$201$	14.0296	−	17.2433i	0.989574	−	1.21625i
$202$	0.287987	+	1.63326i	0.0202627	+	0.114916i
$203$	1.34443	+	7.62462i	0.0943603	+	0.535144i
$204$	1.92949	−	2.37146i	0.135091	−	0.166036i
$205$	−1.21250	−	1.01741i	−0.0846849	−	0.0710590i
$206$	0.00610150	+	0.0105681i	0.000425111	+	0.000736315i
$207$	−3.04091	+	5.65574i	−0.211358	+	0.393101i
$208$	−0.216405	+	0.374824i	−0.0150050	+	0.0259894i
$209$	3.68829	−	1.34243i	0.255125	−	0.0928578i
$210$	0.0734991	+	4.85538i	0.00507192	+	0.335053i
$211$	−14.9232	+	12.5221i	−1.02736	+	0.862055i	−0.990534	−	0.137267i	$-0.956168\pi$
$211$	−14.9232	+	12.5221i	−1.02736	+	0.862055i	−0.0368228	+	0.999322i	$0.511724\pi$
$212$	0.642134	+	0.233718i	0.0441019	+	0.0160518i
$213$	−7.16860	+	20.6635i	−0.491184	+	1.41584i
$214$	1.00147	−	5.67962i	0.0684591	−	0.388251i
$215$	−26.6727			−1.81906
$216$	0.235874	+	5.19080i	0.0160492	+	0.353189i
$217$	−9.71355			−0.659399
$218$	1.64472	−	9.32769i	0.111395	−	0.631751i
$219$	2.13391	−	0.409661i	0.144196	−	0.0276823i
$220$	−2.12419	−	0.773144i	−0.143213	−	0.0521253i
$221$	−0.585222	+	0.491059i	−0.0393663	+	0.0330322i
$222$	2.12168	+	1.18250i	0.142398	+	0.0793644i
$223$	25.2087	−	9.17523i	1.68810	−	0.614419i	0.693718	−	0.720247i	$-0.255971\pi$
$223$	25.2087	−	9.17523i	1.68810	−	0.614419i	0.994384	+	0.105828i	$0.0337492\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$	8.14777	+	2.68917i	0.543185	+	0.179278i
$226$	−6.17244	−	10.6910i	−0.410584	−	0.711153i
$227$	17.9860	+	15.0921i	1.19377	+	1.00170i	0.999786	+	0.0206917i	$0.00658685\pi$
$227$	17.9860	+	15.0921i	1.19377	+	1.00170i	0.193988	+	0.981004i	$0.437858\pi$
$228$	−8.32460	−	1.33826i	−0.551310	−	0.0886287i
$229$	−2.52610	−	14.3262i	−0.166929	−	0.946704i	−0.947053	−	0.321078i	$-0.895955\pi$
$229$	−2.52610	−	14.3262i	−0.166929	−	0.946704i	0.780123	−	0.625626i	$-0.215156\pi$
$230$	1.04206	+	5.90980i	0.0687113	+	0.389681i
$231$	0.497458	+	1.30495i	0.0327303	+	0.0858594i
$232$	5.93090	+	4.97662i	0.389383	+	0.326731i
$233$	5.70827	+	9.88701i	0.373961	+	0.647720i	0.990171	−	0.139862i	$-0.0446660\pi$
$233$	5.70827	+	9.88701i	0.373961	+	0.647720i	−0.616210	+	0.787582i	$0.711333\pi$
$234$	0.186662	−	1.28494i	0.0122025	−	0.0839992i
$235$	−11.7386	+	20.3319i	−0.765743	+	1.32631i
$236$	−13.0793	+	4.76047i	−0.851389	+	0.309880i
$237$	9.42640	−	5.63427i	0.612310	−	0.365985i
$238$	−1.35215	+	1.13459i	−0.0876467	+	0.0735443i
$239$	−22.2527	−	8.09931i	−1.43941	−	0.523901i	−0.499795	−	0.866144i	$-0.666591\pi$
$239$	−22.2527	−	8.09931i	−1.43941	−	0.523901i	−0.939612	+	0.342243i	$0.888813\pi$
$240$	3.17728	+	3.67219i	0.205093	+	0.237039i
$241$	−3.26856	+	18.5369i	−0.210546	+	1.19407i	0.677923	+	0.735132i	$0.262880\pi$
$241$	−3.26856	+	18.5369i	−0.210546	+	1.19407i	−0.888470	+	0.458935i	$0.848231\pi$
$242$	10.3499			0.665316
$243$	−6.42387	−	14.2033i	−0.412092	−	0.911142i
$244$	−0.563748			−0.0360903
$245$	0.486836	−	2.76098i	0.0311028	−	0.176393i
$246$	0.639823	+	0.739486i	0.0407936	+	0.0471479i
$247$	1.97982	+	0.720595i	0.125973	+	0.0458504i
$248$	−7.44101	+	6.24375i	−0.472505	+	0.396479i
$249$	1.06649	−	0.637452i	0.0675859	−	0.0403969i
$250$	−5.63775	+	2.05197i	−0.356563	+	0.129778i
$251$	0.486835	−	0.843223i	0.0307288	−	0.0532238i	−0.850252	−	0.526376i	$-0.823551\pi$
$251$	0.486835	−	0.843223i	0.0307288	−	0.0532238i	0.880981	+	0.473152i	$0.156884\pi$
$252$	0.431280	−	2.96884i	0.0271681	−	0.187019i
$253$	0.862931	+	1.49464i	0.0542520	+	0.0939672i
$254$	−9.70839	−	8.14630i	−0.609158	−	0.511145i
$255$	3.05310	+	8.00902i	0.191193	+	0.501544i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	0.288423	+	1.63573i	0.0179914	+	0.102034i	0.992481	−	0.122398i	$-0.0390584\pi$
$257$	0.288423	+	1.63573i	0.0179914	+	0.102034i	−0.974490	+	0.224432i	$0.927947\pi$
$258$	16.2695	+	2.61549i	1.01290	+	0.162834i
$259$	−1.07427	−	0.901421i	−0.0667520	−	0.0560116i
$260$	−0.606706	−	1.05085i	−0.0376263	−	0.0651707i
$261$	−22.0564	−	7.27973i	−1.36526	−	0.450604i
$262$	11.0561	−	19.1497i	0.683048	−	1.18307i
$263$	−9.60224	+	3.49493i	−0.592099	+	0.215507i	−0.620653	−	0.784086i	$-0.713132\pi$
$263$	−9.60224	+	3.49493i	−0.592099	+	0.215507i	0.0285532	+	0.999592i	$0.490910\pi$
$264$	1.21988	+	0.679890i	0.0750784	+	0.0418443i
$265$	−1.46759	+	1.23146i	−0.0901536	+	0.0756478i
$266$	4.57435	+	1.66493i	0.280471	+	0.102083i
$267$	10.9117	−	2.09479i	0.667785	−	0.128199i
$268$	−2.22866	+	12.6394i	−0.136137	+	0.772073i
$269$	6.24342			0.380668			0.190334	−	0.981719i	$-0.439043\pi$
$269$	6.24342			0.380668			0.190334	+	0.981719i	$0.439043\pi$
$270$	−12.9337	−	6.70370i	−0.787121	−	0.407974i
$271$	−11.4952			−0.698284			−0.349142	−	0.937070i	$-0.613527\pi$
$271$	−11.4952			−0.698284			−0.349142	+	0.937070i	$0.613527\pi$
$272$	−0.306507	+	1.73829i	−0.0185847	+	0.105399i
$273$	−0.245703	+	0.708238i	−0.0148706	+	0.0428645i
$274$	10.9666	+	3.99150i	0.662514	+	0.241135i
$275$	1.76653	−	1.48229i	0.106526	−	0.0893857i
$276$	−0.0561151	−	3.70698i	−0.00337773	−	0.223134i
$277$	7.03903	−	2.56200i	0.422934	−	0.153935i	−0.121780	−	0.992557i	$-0.538860\pi$
$277$	7.03903	−	2.56200i	0.422934	−	0.153935i	0.544714	+	0.838622i	$0.316638\pi$
$278$	−10.6135	+	18.3831i	−0.636555	+	1.10254i
$279$	13.7998	−	25.6660i	0.826171	−	1.53658i
$280$	−1.40179	−	2.42797i	−0.0837728	−	0.145099i
$281$	−16.1214	−	13.5274i	−0.961721	−	0.806980i	0.0195113	−	0.999810i	$-0.493789\pi$
$281$	−16.1214	−	13.5274i	−0.961721	−	0.806980i	−0.981232	+	0.192830i	$0.938233\pi$
$282$	9.15392	−	11.2508i	0.545108	−	0.669973i
$283$	−0.539321	−	3.05864i	−0.0320593	−	0.181817i	0.964573	−	0.263815i	$-0.0849810\pi$
$283$	−0.539321	−	3.05864i	−0.0320593	−	0.181817i	−0.996632	+	0.0819980i	$0.973870\pi$
$284$	−2.19276	−	12.4358i	−0.130116	−	0.737926i
$285$	14.9186	−	18.3359i	0.883700	−	1.08612i
$286$	−0.267330	−	0.224316i	−0.0158075	−	0.0132641i
$287$	−0.282284	−	0.488931i	−0.0166627	−	0.0288607i
$288$	−1.57795	−	2.55148i	−0.0929817	−	0.150348i
$289$	6.94221	−	12.0243i	0.408365	−	0.707309i
$290$	−20.3969	+	7.42388i	−1.19775	+	0.435945i
$291$	0.340244	+	22.4766i	0.0199454	+	1.31760i
$292$	−0.961009	+	0.806382i	−0.0562388	+	0.0471900i
$293$	8.02103	+	2.91941i	0.468593	+	0.170554i	0.565515	−	0.824738i	$-0.308677\pi$
$293$	8.02103	+	2.91941i	0.468593	+	0.170554i	−0.0969217	+	0.995292i	$0.530900\pi$
$294$	−0.567693	+	1.63638i	−0.0331085	+	0.0954354i
$295$	6.77611	−	38.4292i	0.394520	−	2.23744i
$296$	−1.40236			−0.0815106
$297$	−4.15478	−	0.539480i	−0.241085	−	0.0313038i
$298$	11.9911			0.694627
$299$	−0.160870	+	0.912342i	−0.00930338	+	0.0527621i
$300$	−4.86488	+	0.933945i	−0.280874	+	0.0539213i
$301$	−8.94007	−	3.25392i	−0.515297	−	0.187553i
$302$	16.3212	−	13.6951i	0.939177	−	0.788063i
$303$	2.50913	+	1.39844i	0.144146	+	0.0803385i
$304$	4.57435	−	1.66493i	0.262357	−	0.0954901i
$305$	0.790255	−	1.36876i	0.0452499	−	0.0783751i
$306$	−1.07695	−	5.18464i	−0.0615648	−	0.296386i
$307$	−12.9566	−	22.4415i	−0.739472	−	1.28080i	−0.952733	−	0.303808i	$-0.901742\pi$
$307$	−12.9566	−	22.4415i	−0.739472	−	1.28080i	0.213261	−	0.976995i	$-0.431592\pi$
$308$	−0.617661	−	0.518279i	−0.0351945	−	0.0295317i
$309$	0.0208683	+	0.00335479i	0.00118715	+	0.000190847i
$310$	−4.72890	−	26.8189i	−0.268584	−	1.52321i
$311$	−4.37045	−	24.7861i	−0.247826	−	1.40549i	−0.813838	−	0.581092i	$-0.802626\pi$
$311$	−4.37045	−	24.7861i	−0.247826	−	1.40549i	0.566012	−	0.824397i	$-0.308486\pi$
$312$	0.267028	+	0.700477i	0.0151175	+	0.0396567i
$313$	15.1333	+	12.6984i	0.855386	+	0.717754i	0.960969	−	0.276656i	$-0.0892263\pi$
$313$	15.1333	+	12.6984i	0.855386	+	0.717754i	−0.105583	+	0.994411i	$0.533671\pi$
$314$	−7.44398	−	12.8934i	−0.420088	−	0.727614i
$315$	6.60368	+	5.20881i	0.372075	+	0.293483i
$316$	−3.17020	+	5.49095i	−0.178338	+	0.308890i
$317$	32.0939	−	11.6812i	1.80257	−	0.656083i	0.804506	−	0.593944i	$-0.202430\pi$
$317$	32.0939	−	11.6812i	1.80257	−	0.656083i	0.998068	−	0.0621386i	$-0.0197921\pi$
$318$	1.01594	−	0.607241i	0.0569712	−	0.0340524i
$319$	−4.78209	+	4.01265i	−0.267745	+	0.224665i
$320$	−2.63450	−	0.958879i	−0.147273	−	0.0536030i
$321$	−6.53599	−	7.55407i	−0.364804	−	0.421627i
$322$	−0.371689	+	2.10795i	−0.0207134	+	0.117472i
$323$	8.59238			0.478093
$324$	7.23182	+	5.35731i	0.401768	+	0.297629i
$325$	1.23785			0.0686634
$326$	0.504415	−	2.86068i	0.0279370	−	0.158438i
$327$	−10.7341	−	12.4061i	−0.593597	−	0.686059i
$328$	−0.530521	−	0.193094i	−0.0292931	−	0.0106618i
$329$	−6.41489	+	5.38273i	−0.353664	+	0.296760i
$330$	−3.36076	+	2.00877i	−0.185004	+	0.110579i
$331$	0.983728	−	0.358048i	0.0540706	−	0.0196801i	−0.314843	−	0.949144i	$-0.601952\pi$
$331$	0.983728	−	0.358048i	0.0540706	−	0.0196801i	0.368914	+	0.929464i	$0.379730\pi$
$332$	−0.358671	+	0.621237i	−0.0196846	+	0.0340948i
$333$	3.90800	−	1.55791i	0.214157	−	0.0853730i
$334$	−0.384225	−	0.665497i	−0.0210238	−	0.0364144i
$335$	−27.5639	−	23.1288i	−1.50598	−	1.26366i
$336$	0.616964	+	1.61844i	0.0336581	+	0.0882933i
$337$	4.27458	+	24.2424i	0.232851	+	1.32057i	0.847092	+	0.531447i	$0.178351\pi$
$337$	4.27458	+	24.2424i	0.232851	+	1.32057i	−0.614240	+	0.789119i	$0.710537\pi$
$338$	2.22490	+	12.6180i	0.121018	+	0.686330i
$339$	−21.1109	−	3.39379i	−1.14659	−	0.184325i
$340$	−3.79085	−	3.18090i	−0.205587	−	0.172508i
$341$	−3.91602	−	6.78274i	−0.212064	−	0.367306i
$342$	−10.8979	+	9.72143i	−0.589289	+	0.525675i
$343$	0.500000	−	0.866025i	0.0269975	−	0.0467610i
$344$	−8.94007	+	3.25392i	−0.482016	+	0.175440i
$345$	9.07909	+	5.06015i	0.488802	+	0.272429i
$346$	−17.7038	+	14.8553i	−0.951762	+	0.798623i
$347$	4.67397	+	1.70119i	0.250912	+	0.0913245i	0.464414	−	0.885618i	$-0.346265\pi$
$347$	4.67397	+	1.70119i	0.250912	+	0.0913245i	−0.213502	+	0.976943i	$0.568487\pi$
$348$	13.1695	−	2.52824i	0.705958	−	0.135528i
$349$	−3.18468	+	18.0612i	−0.170472	+	0.966794i	0.772770	+	0.634687i	$0.218871\pi$
$349$	−3.18468	+	18.0612i	−0.170472	+	0.966794i	−0.943242	+	0.332107i	$0.892240\pi$
$350$	2.86003			0.152875
$351$	−1.52231	−	1.65539i	−0.0812547	−	0.0883583i
$352$	−0.806300			−0.0429759
$353$	1.65787	−	9.40226i	0.0882396	−	0.500432i	−0.908371	−	0.418166i	$-0.862673\pi$
$353$	1.65787	−	9.40226i	0.0882396	−	0.500432i	0.996610	−	0.0822661i	$-0.0262157\pi$
$354$	−7.90154	+	22.7762i	−0.419962	+	1.21054i
$355$	33.2674	+	12.1083i	1.76565	+	0.642644i
$356$	−4.91411	+	4.12342i	−0.260447	+	0.218541i
$357$	0.0462743	+	3.05690i	0.00244910	+	0.161788i
$358$	−2.39923	+	0.873248i	−0.126803	+	0.0461526i
$359$	0.437466	−	0.757714i	0.0230886	−	0.0399906i	−0.854250	−	0.519862i	$-0.825983\pi$
$359$	0.437466	−	0.757714i	0.0230886	−	0.0399906i	0.877339	+	0.479871i	$0.159317\pi$
$360$	8.40687	−	0.254579i	0.443081	−	0.0134175i
$361$	−2.34832	−	4.06740i	−0.123596	−	0.214074i
$362$	−6.63625	−	5.56847i	−0.348793	−	0.292672i
$363$	11.3138	−	13.9053i	0.593819	−	0.729841i
$364$	−0.0751565	−	0.426234i	−0.00393927	−	0.0223407i
$365$	−0.610739	−	3.46367i	−0.0319676	−	0.181297i
$366$	−0.616250	+	0.757411i	−0.0322119	+	0.0395905i
$367$	8.50936	+	7.14020i	0.444185	+	0.372715i	0.837273	−	0.546786i	$-0.184149\pi$
$367$	8.50936	+	7.14020i	0.444185	+	0.372715i	−0.393088	+	0.919501i	$0.628593\pi$
$368$	1.07024	+	1.85370i	0.0557899	+	0.0966310i
$369$	1.69293	−	0.0512658i	0.0881304	−	0.00266879i
$370$	1.96581	−	3.40489i	0.102198	−	0.177012i
$371$	−0.642134	+	0.233718i	−0.0333379	+	0.0121340i
$372$	0.254653	+	16.8224i	0.0132031	+	0.872203i
$373$	−16.0663	+	13.4812i	−0.831881	+	0.698031i	−0.955722	−	0.294271i	$-0.904923\pi$
$373$	−16.0663	+	13.4812i	−0.831881	+	0.698031i	0.123841	+	0.992302i	$0.460479\pi$
$374$	−1.33737	−	0.486764i	−0.0691539	−	0.0251700i
$375$	−3.40591	+	9.81755i	−0.175881	+	0.506976i
$376$	−1.45414	+	8.24682i	−0.0749914	+	0.425297i
$377$	−3.35092			−0.172581
$378$	−3.51727	−	3.82476i	−0.180909	−	0.196725i
$379$	33.2040			1.70558			0.852789	−	0.522256i	$-0.174910\pi$
$379$	33.2040			1.70558			0.852789	+	0.522256i	$0.174910\pi$
$380$	−2.36988	+	13.4402i	−0.121572	+	0.689469i
$381$	−21.5573	+	4.13851i	−1.10441	+	0.212022i
$382$	−11.5479	−	4.20310i	−0.590843	−	0.215049i
$383$	−11.2654	+	9.45280i	−0.575636	+	0.483016i	−0.883511	−	0.468411i	$-0.844827\pi$
$383$	−11.2654	+	9.45280i	−0.575636	+	0.483016i	0.307875	+	0.951427i	$0.400382\pi$
$384$	1.51294	+	0.843222i	0.0772067	+	0.0430305i
$385$	2.12419	−	0.773144i	0.108259	−	0.0394031i
$386$	−2.63389	+	4.56203i	−0.134061	+	0.232201i
$387$	21.2987	−	18.9995i	1.08267	−	0.965798i
$388$	−6.48919	−	11.2396i	−0.329438	−	0.570604i
$389$	29.4525	+	24.7136i	1.49330	+	1.25303i	0.890369	+	0.455239i	$0.150446\pi$
$389$	29.4525	+	24.7136i	1.49330	+	1.25303i	0.602934	+	0.797791i	$0.293998\pi$
$390$	−2.07505	−	0.333585i	−0.105074	−	0.0168918i
$391$	0.656069	+	3.72075i	0.0331789	+	0.188167i
$392$	−0.173648	−	0.984808i	−0.00877056	−	0.0497403i
$393$	−13.6424	−	35.7873i	−0.688170	−	1.80523i
$394$	−4.99914	−	4.19478i	−0.251853	−	0.211330i
$395$	−8.88789	−	15.3943i	−0.447198	−	0.774570i
$396$	2.24694	−	0.895734i	0.112913	−	0.0450123i
$397$	−3.84881	+	6.66633i	−0.193166	+	0.334573i	−0.946298	−	0.323296i	$-0.895209\pi$
$397$	−3.84881	+	6.66633i	−0.193166	+	0.334573i	0.753132	+	0.657870i	$0.228542\pi$
$398$	−10.4773	+	3.81341i	−0.525177	+	0.191149i
$399$	7.23723	−	4.32578i	0.362315	−	0.216560i
$400$	2.19091	−	1.83839i	0.109545	−	0.0919195i
$401$	−1.27378	−	0.463619i	−0.0636097	−	0.0231520i	0.310019	−	0.950730i	$-0.399664\pi$
$401$	−1.27378	−	0.463619i	−0.0636097	−	0.0231520i	−0.373629	+	0.927578i	$0.621887\pi$
$402$	14.5451	+	16.8108i	0.725445	+	0.838445i
$403$	0.730037	−	4.14025i	0.0363657	−	0.206240i
$404$	−1.65845			−0.0825111
$405$	−23.1448	+	10.0488i	−1.15008	+	0.499329i
$406$	−7.74225			−0.384241
$407$	0.196348	−	1.11355i	0.00973262	−	0.0551964i
$408$	2.00038	+	2.31197i	0.0990338	+	0.114460i
$409$	6.76887	+	2.46367i	0.334699	+	0.121821i	0.503902	−	0.863761i	$-0.331897\pi$
$409$	6.76887	+	2.46367i	0.334699	+	0.121821i	−0.169203	+	0.985581i	$0.554119\pi$
$410$	1.21250	−	1.01741i	0.0598812	−	0.0502463i
$411$	17.3506	−	10.3706i	0.855840	−	0.511546i
$412$	−0.0114671	+	0.00417367i	−0.000564942	+	0.000205622i
$413$	6.95934	−	12.0539i	0.342447	−	0.593135i
$414$	−5.04177	−	3.97682i	−0.247790	−	0.195450i
$415$	−1.00556	−	1.74168i	−0.0493611	−	0.0854959i
$416$	−0.331551	−	0.278204i	−0.0162556	−	0.0136401i
$417$	13.0963	+	34.3546i	0.641327	+	1.68235i
$418$	0.681569	+	3.86537i	0.0333366	+	0.189062i
$419$	3.69196	+	20.9381i	0.180364	+	1.02289i	0.931769	+	0.363053i	$0.118266\pi$
$419$	3.69196	+	20.9381i	0.180364	+	1.02289i	−0.751405	+	0.659842i	$0.770623\pi$
$420$	−4.79438	−	0.770745i	−0.233942	−	0.0376085i
$421$	0.221475	+	0.185840i	0.0107940	+	0.00905728i	0.648169	−	0.761497i	$-0.275535\pi$
$421$	0.221475	+	0.185840i	0.0107940	+	0.00905728i	−0.637375	+	0.770554i	$0.719980\pi$
$422$	−9.74044	−	16.8709i	−0.474157	−	0.821264i
$423$	−5.10927	−	24.5971i	−0.248421	−	1.19595i
$424$	−0.341672	+	0.591794i	−0.0165931	+	0.0287401i
$425$	4.74380	−	1.72660i	0.230108	−	0.0837525i
$426$	−19.1047	−	10.6479i	−0.925628	−	0.515891i
$427$	0.431856	−	0.362370i	0.0208990	−	0.0175363i
$428$	5.41943	+	1.97251i	0.261958	+	0.0953450i
$429$	−0.593601	+	0.113958i	−0.0286593	+	0.00550193i
$430$	4.63167	−	26.2675i	0.223359	−	1.26673i
$431$	−3.45298			−0.166324			−0.0831621	−	0.996536i	$-0.526502\pi$
$431$	−3.45298			−0.166324			−0.0831621	+	0.996536i	$0.526502\pi$
$432$	−5.15290	−	0.669082i	−0.247919	−	0.0321912i
$433$	−39.5597			−1.90112			−0.950558	−	0.310547i	$-0.899488\pi$
$433$	−39.5597			−1.90112			−0.950558	+	0.310547i	$0.899488\pi$
$434$	1.68674	−	9.56598i	0.0809662	−	0.459182i
$435$	−12.3223	+	35.5191i	−0.590810	+	1.70301i
$436$	8.90037	+	3.23947i	0.426251	+	0.155143i
$437$	7.98191	−	6.69762i	0.381827	−	0.320390i
$438$	0.0328885	+	2.17262i	0.00157147	+	0.103812i
$439$	22.5036	−	8.19065i	1.07404	−	0.390918i	0.256353	−	0.966583i	$-0.417479\pi$
$439$	22.5036	−	8.19065i	1.07404	−	0.390918i	0.817686	+	0.575665i	$0.195257\pi$
$440$	1.13026	−	1.95767i	0.0538831	−	0.0933282i
$441$	1.57795	+	2.55148i	0.0751406	+	0.121499i
$442$	−0.381976	−	0.661603i	−0.0181688	−	0.0314692i
$443$	9.24079	+	7.75395i	0.439043	+	0.368401i	0.835351	−	0.549717i	$-0.185264\pi$
$443$	9.24079	+	7.75395i	0.439043	+	0.368401i	−0.396308	+	0.918118i	$0.629709\pi$
$444$	−1.53296	+	1.88411i	−0.0727513	+	0.0894160i
$445$	−3.12301	−	17.7114i	−0.148045	−	0.839603i
$446$	4.65839	+	26.4190i	0.220581	+	1.25098i
$447$	13.1079	−	16.1104i	0.619980	−	0.761996i
$448$	−0.766044	−	0.642788i	−0.0361922	−	0.0303689i
$449$	10.7588	+	18.6348i	0.507739	+	0.879430i	0.999960	+	0.00895936i	$0.00285189\pi$
$449$	10.7588	+	18.6348i	0.507739	+	0.879430i	−0.492221	+	0.870470i	$0.663815\pi$
$450$	−4.06317	+	7.55702i	−0.191539	+	0.356241i
$451$	0.227606	−	0.394225i	0.0107175	−	0.0185633i
$452$	11.6004	−	4.22219i	0.545636	−	0.198595i
$453$	−0.558557	−	36.8984i	−0.0262433	−	1.73364i
$454$	−17.9860	+	15.0921i	−0.844126	+	0.708306i
$455$	1.14024	+	0.415012i	0.0534550	+	0.0194560i
$456$	2.76348	−	7.96574i	0.129412	−	0.373030i
$457$	0.811141	−	4.60021i	0.0379436	−	0.215189i	−0.959941	−	0.280203i	$-0.909598\pi$
$457$	0.811141	−	4.60021i	0.0379436	−	0.215189i	0.997884	+	0.0650143i	$0.0207093\pi$
$458$	14.5472			0.679748
$459$	−8.14295	−	4.22058i	−0.380080	−	0.197000i
$460$	−6.00097			−0.279797
$461$	2.71084	−	15.3739i	0.126256	−	0.716036i	−0.854297	−	0.519785i	$-0.826012\pi$
$461$	2.71084	−	15.3739i	0.126256	−	0.716036i	0.980554	−	0.196251i	$-0.0628767\pi$
$462$	−1.37151	+	0.263298i	−0.0638083	+	0.0122497i
$463$	3.55835	+	1.29513i	0.165370	+	0.0601899i	0.423379	−	0.905953i	$-0.360844\pi$
$463$	3.55835	+	1.29513i	0.165370	+	0.0601899i	−0.258008	+	0.966143i	$0.583066\pi$
$464$	−5.93090	+	4.97662i	−0.275335	+	0.231034i
$465$	−41.2013	−	22.9632i	−1.91066	−	1.06489i
$466$	−10.7280	+	3.90469i	−0.496967	+	0.180881i
$467$	−13.2539	+	22.9565i	−0.613319	+	1.06230i	0.377358	+	0.926068i	$0.376833\pi$
$467$	−13.2539	+	22.9565i	−0.613319	+	1.06230i	−0.990677	+	0.136232i	$0.956501\pi$
$468$	1.23301	+	0.406954i	0.0569957	+	0.0188114i
$469$	−6.41718	−	11.1149i	−0.296318	−	0.513238i
$470$	−17.9846	−	15.0909i	−0.829569	−	0.696091i
$471$	−25.4598	−	4.09293i	−1.17313	−	0.188592i
$472$	−2.41695	−	13.7072i	−0.111249	−	0.630926i
$473$	−1.33205	−	7.55446i	−0.0612479	−	0.347354i
$474$	3.91180	+	10.2616i	0.179675	+	0.471330i
$475$	−10.6652	−	8.94914i	−0.489351	−	0.410615i
$476$	−0.882551	−	1.52862i	−0.0404517	−	0.0700644i
$477$	0.294713	−	2.02874i	0.0134940	−	0.0928896i
$478$	11.8404	−	20.5082i	0.541568	−	0.938023i
$479$	−10.4039	+	3.78671i	−0.475367	+	0.173019i	−0.568582	−	0.822627i	$-0.692508\pi$
$479$	−10.4039	+	3.78671i	−0.475367	+	0.173019i	0.0932151	+	0.995646i	$0.470286\pi$
$480$	−4.16813	+	2.49134i	−0.190248	+	0.113714i
$481$	0.464955	−	0.390143i	0.0212001	−	0.0177890i
$482$	−17.6877	−	6.43780i	−0.805653	−	0.293234i
$483$	2.42579	+	2.80364i	0.110377	+	0.127570i
$484$	−1.79724	+	10.1926i	−0.0816926	+	0.463302i
$485$	36.3858			1.65220
$486$	15.1030	−	3.85990i	0.685087	−	0.175089i
$487$	21.4205			0.970654			0.485327	−	0.874333i	$-0.338701\pi$
$487$	21.4205			0.970654			0.485327	+	0.874333i	$0.338701\pi$
$488$	0.0978939	−	0.555184i	0.00443145	−	0.0251320i
$489$	−3.29201	−	3.80479i	−0.148870	−	0.172059i
$490$	2.63450	+	0.958879i	0.119014	+	0.0433177i
$491$	20.3874	−	17.1071i	0.920072	−	0.772032i	−0.0539367	−	0.998544i	$-0.517177\pi$
$491$	20.3874	−	17.1071i	0.920072	−	0.772032i	0.974008	+	0.226513i	$0.0727325\pi$
$492$	−0.839355	+	0.501693i	−0.0378411	+	0.0226181i
$493$	−12.8417	+	4.67400i	−0.578361	+	0.210506i
$494$	−1.05344	+	1.82461i	−0.0473965	+	0.0820932i
$495$	−0.974918	+	6.71112i	−0.0438193	+	0.301642i
$496$	−4.85678	−	8.41218i	−0.218076	−	0.377718i
$497$	9.67330	+	8.11686i	0.433907	+	0.364091i
$498$	0.442574	+	1.16098i	0.0198322	+	0.0520246i
$499$	4.09673	+	23.2337i	0.183395	+	1.04008i	0.928000	+	0.372579i	$0.121526\pi$
$499$	4.09673	+	23.2337i	0.183395	+	1.04008i	−0.744606	+	0.667505i	$0.767362\pi$
$500$	−1.04181	−	5.90842i	−0.0465913	−	0.264233i
$501$	−1.31412	−	0.211258i	−0.0587106	−	0.00943833i
$502$	0.745875	+	0.625863i	0.0332900	+	0.0279336i
$503$	3.10127	+	5.37156i	0.138279	+	0.239506i	0.926845	−	0.375444i	$-0.122510\pi$
$503$	3.10127	+	5.37156i	0.138279	+	0.239506i	−0.788566	+	0.614950i	$0.789176\pi$
$504$	2.84884	+	0.940261i	0.126898	+	0.0418826i
$505$	2.32480	−	4.02667i	0.103452	−	0.179184i
$506$	−1.62178	+	0.590280i	−0.0720969	+	0.0262411i
$507$	19.3848	+	10.8039i	0.860908	+	0.479820i
$508$	9.70839	−	8.14630i	0.430740	−	0.361434i
$509$	6.34574	+	2.30966i	0.281270	+	0.102374i	0.478803	−	0.877922i	$-0.341071\pi$
$509$	6.34574	+	2.30966i	0.281270	+	0.102374i	−0.197533	+	0.980296i	$0.563293\pi$
$510$	−8.41751	+	1.61597i	−0.372734	+	0.0715563i
$511$	0.217843	−	1.23545i	0.00963681	−	0.0546531i
$512$	−1.00000			−0.0441942
$513$	1.14821	+	25.2684i	0.0506949	+	1.11563i
$514$	−1.66096			−0.0732620
$515$	0.00594085	−	0.0336922i	0.000261785	−	0.00148466i
$516$	−5.40093	+	15.5682i	−0.237763	+	0.685351i
$517$	−6.34479	−	2.30932i	−0.279044	−	0.101564i
$518$	1.07427	−	0.901421i	0.0472008	−	0.0396062i
$519$	0.605874	+	40.0243i	0.0265949	+	1.75687i
$520$	1.14024	−	0.415012i	0.0500026	−	0.0181995i
$521$	1.14638	−	1.98558i	0.0502236	−	0.0869899i	−0.839821	−	0.542864i	$-0.817340\pi$
$521$	1.14638	−	1.98558i	0.0502236	−	0.0869899i	0.890044	+	0.455874i	$0.150673\pi$
$522$	10.9992	−	20.4572i	0.481422	−	0.895389i
$523$	9.35540	+	16.2040i	0.409083	+	0.708553i	0.994787	−	0.101972i	$-0.0325153\pi$
$523$	9.35540	+	16.2040i	0.409083	+	0.708553i	−0.585704	+	0.810525i	$0.699182\pi$
$524$	16.9389	+	14.2135i	0.739981	+	0.620918i
$525$	3.12638	−	3.84253i	0.136447	−	0.167702i
$526$	−1.77442	−	10.0632i	−0.0773685	−	0.438778i
$527$	−2.97727	−	16.8849i	−0.129692	−	0.735520i
$528$	−0.881391	+	1.08329i	−0.0383576	+	0.0471440i
$529$	−14.1093	−	11.8391i	−0.613448	−	0.514744i
$530$	−0.957904	−	1.65914i	−0.0416087	−	0.0720683i
$531$	21.9630	+	35.5133i	0.953114	+	1.54115i
$532$	−2.43396	+	4.21574i	−0.105526	+	0.182776i
$533$	0.229614	−	0.0835728i	0.00994570	−	0.00361994i
$534$	0.168175	+	11.1097i	0.00727763	+	0.480763i
$535$	−12.3861	+	10.3932i	−0.535497	+	0.449336i
$536$	−12.0604	−	4.38961i	−0.520928	−	0.189602i
$537$	−1.44944	+	4.17800i	−0.0625479	+	0.180294i
$538$	−1.08416	+	6.14857i	−0.0467414	+	0.265083i
$539$	0.806300			0.0347298
$540$	8.84777	−	11.5731i	0.380747	−	0.498029i
$541$	−29.9947			−1.28957			−0.644786	−	0.764363i	$-0.723054\pi$
$541$	−29.9947			−1.28957			−0.644786	+	0.764363i	$0.723054\pi$
$542$	1.99612	−	11.3206i	0.0857408	−	0.486260i
$543$	−14.7357	+	2.82891i	−0.632368	+	0.121400i
$544$	−1.65865	−	0.603701i	−0.0711142	−	0.0258835i
$545$	−20.3418	+	17.0688i	−0.871345	+	0.731145i
$546$	−0.654813	−	0.364954i	−0.0280234	−	0.0156186i
$547$	−21.7202	+	7.90551i	−0.928689	+	0.338015i	−0.761690	−	0.647942i	$-0.775630\pi$
$547$	−21.7202	+	7.90551i	−0.928689	+	0.338015i	−0.166999	+	0.985957i	$0.553408\pi$
$548$	−5.83518	+	10.1068i	−0.249267	+	0.431742i
$549$	0.343961	+	1.65590i	0.0146799	+	0.0706720i
$550$	1.15302	+	1.99709i	0.0491649	+	0.0851562i
$551$	28.8712	+	24.2258i	1.22995	+	1.03205i
$552$	3.66041	+	0.588448i	0.155797	+	0.0250460i
$553$	−1.10100	−	6.24407i	−0.0468192	−	0.265525i
$554$	1.30076	+	7.37698i	0.0552640	+	0.313418i
$555$	−2.42567	−	6.36311i	−0.102964	−	0.270099i
$556$	−16.2608	−	13.6444i	−0.689612	−	0.578653i
$557$	13.3437	+	23.1120i	0.565392	+	0.979288i	0.997013	+	0.0772330i	$0.0246085\pi$
$557$	13.3437	+	23.1120i	0.565392	+	0.979288i	−0.431621	+	0.902055i	$0.642058\pi$
$558$	22.8798	+	18.0470i	0.968578	+	0.763990i
$559$	2.05884	−	3.56601i	0.0870795	−	0.150826i
$560$	2.63450	−	0.958879i	0.111328	−	0.0405200i
$561$	−2.11590	+	1.26470i	−0.0893335	+	0.0533957i
$562$	16.1214	−	13.5274i	0.680039	−	0.570621i
$563$	39.3311	+	14.3154i	1.65761	+	0.603321i	0.989984	−	0.141177i	$-0.0450886\pi$
$563$	39.3311	+	14.3154i	1.65761	+	0.603321i	0.667625	+	0.744497i	$0.267311\pi$
$564$	9.49027	+	10.9685i	0.399612	+	0.461858i
$565$	−6.00992	+	34.0840i	−0.252839	+	1.43392i
$566$	3.10583			0.130548
$567$	−8.98351	+	0.544582i	−0.377272	+	0.0228703i
$568$	12.6276			0.529842
$569$	4.07029	−	23.0838i	0.170636	−	0.967722i	−0.772426	−	0.635105i	$-0.780957\pi$
$569$	4.07029	−	23.0838i	0.170636	−	0.967722i	0.943062	−	0.332618i	$-0.107932\pi$
$570$	15.4667	+	17.8759i	0.647830	+	0.748740i
$571$	37.3458	+	13.5927i	1.56287	+	0.568839i	0.971392	−	0.237481i	$-0.0763219\pi$
$571$	37.3458	+	13.5927i	1.56287	+	0.568839i	0.591479	+	0.806320i	$0.298544\pi$
$572$	0.267330	−	0.224316i	0.0111776	−	0.00937913i
$573$	−18.2704	+	10.9204i	−0.763256	+	0.456207i
$574$	0.530521	−	0.193094i	0.0221435	−	0.00805958i
$575$	3.06091	−	5.30164i	0.127649	−	0.221094i
$576$	2.78673	−	1.11092i	0.116114	−	0.0462883i
$577$	2.61781	+	4.53418i	0.108981	+	0.188760i	0.915358	−	0.402642i	$-0.131908\pi$
$577$	2.61781	+	4.53418i	0.108981	+	0.188760i	−0.806377	+	0.591402i	$0.798575\pi$
$578$	10.6361	+	8.92473i	0.442402	+	0.371220i
$579$	3.25002	+	8.52559i	0.135066	+	0.354311i
$580$	−3.76920	−	21.3762i	−0.156508	−	0.887598i
$581$	−0.124565	−	0.706444i	−0.00516784	−	0.0293083i
$582$	−22.1942	−	3.56795i	−0.919981	−	0.147896i
$583$	−0.422076	−	0.354163i	−0.0174806	−	0.0146680i
$584$	−0.627254	−	1.08644i	−0.0259560	−	0.0449570i
$585$	−2.71648	+	2.42323i	−0.112313	+	0.100188i
$586$	−4.26790	+	7.39222i	−0.176305	+	0.305370i
$587$	39.4446	−	14.3567i	1.62805	−	0.592563i	0.643162	−	0.765730i	$-0.277622\pi$
$587$	39.4446	−	14.3567i	1.62805	−	0.592563i	0.984893	+	0.173167i	$0.0553999\pi$
$588$	−1.51294	−	0.843222i	−0.0623924	−	0.0347739i
$589$	−36.2222	+	30.3941i	−1.49251	+	1.25237i
$590$	36.6688	+	13.3463i	1.50963	+	0.549460i
$591$	−11.1005	+	2.13104i	−0.456614	+	0.0876594i
$592$	0.243518	−	1.38106i	0.0100085	−	0.0567611i
$593$	−13.4079			−0.550595			−0.275297	−	0.961359i	$-0.588776\pi$
$593$	−13.4079			−0.550595			−0.275297	+	0.961359i	$0.588776\pi$
$594$	1.25275	−	3.99798i	0.0514011	−	0.164039i
$595$	4.94860			0.202873
$596$	−2.08224	+	11.8089i	−0.0852917	+	0.483713i
$597$	−6.32959	+	18.2450i	−0.259053	+	0.746719i
$598$	−0.870546	−	0.316853i	−0.0355993	−	0.0129571i
$599$	30.6811	−	25.7445i	1.25360	−	1.05189i	0.257262	−	0.966342i	$-0.417179\pi$
$599$	30.6811	−	25.7445i	1.25360	−	1.05189i	0.996334	−	0.0855507i	$-0.0272649\pi$
$600$	−0.0749791	−	4.95315i	−0.00306101	−	0.202211i
$601$	−10.1849	+	3.70701i	−0.415452	+	0.151212i	−0.541285	−	0.840839i	$-0.682062\pi$
$601$	−10.1849	+	3.70701i	−0.415452	+	0.151212i	0.125833	+	0.992051i	$0.459840\pi$
$602$	4.75691	−	8.23922i	0.193877	−	0.335805i
$603$	38.4855	−	1.16543i	1.56725	−	0.0474599i
$604$	10.6529	+	18.4513i	0.433460	+	0.750774i
$605$	−22.2281	−	18.6515i	−0.903699	−	0.758293i
$606$	−1.81291	+	2.22818i	−0.0736442	+	0.0905135i
$607$	−3.93973	−	22.3433i	−0.159909	−	0.906888i	−0.954160	−	0.299298i	$-0.903247\pi$
$607$	−3.93973	−	22.3433i	−0.159909	−	0.906888i	0.794251	−	0.607590i	$-0.207864\pi$
$608$	0.845305	+	4.79396i	0.0342817	+	0.194421i
$609$	−8.46328	+	10.4019i	−0.342950	+	0.421507i
$610$	1.21074	+	1.01593i	0.0490215	+	0.0411339i
$611$	−1.81218	−	3.13879i	−0.0733130	−	0.126982i
$612$	5.29288	−	0.160281i	0.213952	−	0.00647896i
$613$	1.23721	−	2.14292i	0.0499706	−	0.0865517i	−0.839958	−	0.542651i	$-0.817421\pi$
$613$	1.23721	−	2.14292i	0.0499706	−	0.0865517i	0.889929	+	0.456100i	$0.150754\pi$
$614$	24.3504	−	8.86284i	0.982704	−	0.357675i
$615$	−0.0414953	−	2.74119i	−0.00167325	−	0.110536i
$616$	0.617661	−	0.518279i	0.0248863	−	0.0208821i
$617$	−7.48415	−	2.72401i	−0.301301	−	0.109664i	0.186946	−	0.982370i	$-0.440141\pi$
$617$	−7.48415	−	2.72401i	−0.301301	−	0.109664i	−0.488247	+	0.872706i	$0.662363\pi$
$618$	−0.00692756	+	0.0199687i	−0.000278667	+	0.000803258i
$619$	4.84434	−	27.4736i	0.194710	−	1.10426i	−0.718120	−	0.695919i	$-0.754997\pi$
$619$	4.84434	−	27.4736i	0.194710	−	1.10426i	0.912830	−	0.408339i	$-0.133892\pi$
$620$	27.2327			1.09369
$621$	−10.8543	+	2.42657i	−0.435567	+	0.0973750i
$622$	25.1684			1.00916
$623$	1.11394	−	6.31745i	0.0446290	−	0.253103i
$624$	−0.736204	+	0.141334i	−0.0294717	+	0.00565790i
$625$	29.2436	+	10.6438i	1.16974	+	0.425752i
$626$	−15.1333	+	12.6984i	−0.604849	+	0.507529i
$627$	5.93828	+	3.30965i	0.237152	+	0.132175i
$628$	13.9901	−	5.09199i	0.558266	−	0.203192i
$629$	1.23766	−	2.14368i	0.0493486	−	0.0854743i
$630$	−6.27639	+	5.59885i	−0.250058	+	0.223064i
$631$	−17.9175	−	31.0341i	−0.713286	−	1.23545i	−0.963617	−	0.267287i	$-0.913873\pi$
$631$	−17.9175	−	31.0341i	−0.713286	−	1.23545i	0.250331	−	0.968160i	$-0.419461\pi$
$632$	−4.85703	−	4.07553i	−0.193202	−	0.162116i
$633$	−33.3141	−	5.35559i	−1.32412	−	0.212866i
$634$	5.93071	+	33.6348i	0.235539	+	1.33581i
$635$	6.16986	+	34.9910i	0.244844	+	1.38858i
$636$	0.421599	+	1.10595i	0.0167175	+	0.0438539i
$637$	0.331551	+	0.278204i	0.0131365	+	0.0110229i
$638$	−3.12128	−	5.40622i	−0.123573	−	0.214034i
$639$	−35.1897	+	14.0282i	−1.39208	+	0.554948i
$640$	1.40179	−	2.42797i	0.0554105	−	0.0959738i
$641$	18.2864	−	6.65572i	0.722271	−	0.262885i	0.0453814	−	0.998970i	$-0.485550\pi$
$641$	18.2864	−	6.65572i	0.722271	−	0.262885i	0.676890	+	0.736085i	$0.263327\pi$
$642$	8.57427	−	5.12494i	0.338400	−	0.202265i
$643$	38.0548	−	31.9318i	1.50074	−	1.25927i	0.620995	−	0.783815i	$-0.286729\pi$
$643$	38.0548	−	31.9318i	1.50074	−	1.25927i	0.879742	−	0.475452i	$-0.157716\pi$
$644$	−2.01139	−	0.732085i	−0.0792597	−	0.0288482i
$645$	−30.2281	−	34.9366i	−1.19023	−	1.37563i
$646$	−1.49205	+	8.46184i	−0.0587039	+	0.332927i
$647$	18.3387			0.720967			0.360484	−	0.932766i	$-0.382612\pi$
$647$	18.3387			0.720967			0.360484	+	0.932766i	$0.382612\pi$
$648$	−6.53172	+	6.19166i	−0.256590	+	0.243231i
$649$	11.2226			0.440527
$650$	−0.214950	+	1.21904i	−0.00843103	+	0.0478147i
$651$	−11.0083	−	12.7231i	−0.431451	−	0.498656i
$652$	2.72963	+	0.993504i	0.106901	+	0.0389086i
$653$	−14.2325	+	11.9425i	−0.556963	+	0.467347i	−0.877291	−	0.479960i	$-0.840651\pi$
$653$	−14.2325	+	11.9425i	−0.556963	+	0.467347i	0.320328	+	0.947307i	$0.396207\pi$
$654$	14.0816	−	8.41673i	0.550634	−	0.329120i
$655$	−58.2546	+	21.2029i	−2.27619	+	0.828467i
$656$	0.282284	−	0.488931i	0.0110213	−	0.0190895i
$657$	2.95493	+	2.33077i	0.115283	+	0.0909322i
$658$	−4.18702	−	7.25213i	−0.163227	−	0.282718i
$659$	−12.8281	−	10.7641i	−0.499713	−	0.419309i	0.357779	−	0.933806i	$-0.383534\pi$
$659$	−12.8281	−	10.7641i	−0.499713	−	0.419309i	−0.857492	+	0.514497i	$0.827979\pi$
$660$	−1.39466	−	3.65852i	−0.0542870	−	0.142408i
$661$	4.02128	+	22.8058i	0.156410	+	0.887044i	0.957486	+	0.288481i	$0.0931503\pi$
$661$	4.02128	+	22.8058i	0.156410	+	0.887044i	−0.801076	+	0.598563i	$0.795739\pi$
$662$	0.181786	+	1.03096i	0.00706529	+	0.0400693i
$663$	−1.30643	−	0.210022i	−0.0507376	−	0.00815659i
$664$	−0.549516	−	0.461099i	−0.0213254	−	0.0178941i
$665$	−6.82379	−	11.8191i	−0.264615	−	0.458327i
$666$	0.855625	+	4.11916i	0.0331548	+	0.159614i
$667$	−8.28603	+	14.3518i	−0.320836	+	0.555705i
$668$	0.722106	−	0.262825i	0.0279391	−	0.0101690i
$669$	40.5869	+	22.6208i	1.56918	+	0.874570i
$670$	27.5639	−	23.1288i	1.06489	−	0.893545i
$671$	0.427137	+	0.155465i	0.0164895	+	0.00600167i
$672$	−1.70099	+	0.326551i	−0.0656171	+	0.0125970i
$673$	4.43250	−	25.1380i	0.170860	−	0.968997i	−0.771954	−	0.635679i	$-0.780720\pi$
$673$	4.43250	−	25.1380i	0.170860	−	0.968997i	0.942814	−	0.333319i	$-0.108169\pi$
$674$	−24.6163			−0.948186
$675$	5.71149	+	13.7198i	0.219835	+	0.528075i
$676$	−12.8127			−0.492795
$677$	7.66302	−	43.4592i	0.294514	−	1.67027i	−0.374658	−	0.927163i	$-0.622240\pi$
$677$	7.66302	−	43.4592i	0.294514	−	1.67027i	0.669171	−	0.743108i	$-0.266649\pi$
$678$	7.00810	−	20.2008i	0.269144	−	0.775809i
$679$	12.1957	+	4.43886i	0.468027	+	0.170348i
$680$	3.79085	−	3.18090i	0.145372	−	0.121982i
$681$	0.615533	+	40.6623i	0.0235873	+	1.55818i
$682$	7.35971	−	2.67871i	0.281818	−	0.102573i
$683$	−18.2401	+	31.5928i	−0.697939	+	1.20887i	0.271241	+	0.962511i	$0.412566\pi$
$683$	−18.2401	+	31.5928i	−0.697939	+	1.20887i	−0.969180	+	0.246354i	$0.920767\pi$
$684$	−7.68134	−	12.4204i	−0.293704	−	0.474906i
$685$	−16.3594	−	28.3353i	−0.625059	−	1.08263i
$686$	0.766044	+	0.642788i	0.0292477	+	0.0245417i
$687$	15.9020	−	19.5446i	0.606700	−	0.745674i
$688$	−1.65206	−	9.36929i	−0.0629841	−	0.357201i
$689$	−0.0513578	−	0.291265i	−0.00195658	−	0.0110963i
$690$	−6.55985	+	8.06247i	−0.249729	+	0.306933i
$691$	12.6357	+	10.6026i	0.480684	+	0.403342i	0.850674	−	0.525694i	$-0.176194\pi$
$691$	12.6357	+	10.6026i	0.480684	+	0.403342i	−0.369989	+	0.929036i	$0.620639\pi$
$692$	−11.5553	−	20.0144i	−0.439268	−	0.760834i
$693$	−1.14549	+	2.13048i	−0.0435135	+	0.0809301i
$694$	−2.48697	+	4.30756i	−0.0944041	+	0.163513i
$695$	55.9224	−	20.3541i	2.12126	−	0.772075i
$696$	0.202972	+	13.4084i	0.00769365	+	0.508245i
$697$	0.763380	−	0.640552i	0.0289151	−	0.0242626i
$698$	−17.2338	−	6.27259i	−0.652309	−	0.237421i
$699$	−6.48109	+	18.6817i	−0.245137	+	0.706608i
$700$	−0.496639	+	2.81658i	−0.0187712	+	0.106457i
$701$	−13.8223			−0.522063			−0.261031	−	0.965330i	$-0.584063\pi$
$701$	−13.8223			−0.522063			−0.261031	+	0.965330i	$0.584063\pi$
$702$	1.89459	−	1.21172i	0.0715067	−	0.0457336i
$703$	−6.82658			−0.257469
$704$	0.140012	−	0.794050i	0.00527692	−	0.0299269i
$705$	−39.9346	+	7.66652i	−1.50402	+	0.288738i
$706$	8.97153	+	3.26537i	0.337648	+	0.122894i
$707$	1.27045	−	1.06603i	0.0477801	−	0.0400923i
$708$	−21.0581	−	11.7365i	−0.791411	−	0.441086i
$709$	−29.9225	+	10.8909i	−1.12376	+	0.409017i	−0.836025	−	0.548692i	$-0.815126\pi$
$709$	−29.9225	+	10.8909i	−1.12376	+	0.409017i	−0.287740	+	0.957709i	$0.592904\pi$
$710$	−17.7012	+	30.6594i	−0.664314	+	1.15063i
$711$	18.0628	+	5.96163i	0.677408	+	0.223579i
$712$	−3.20745	−	5.55547i	−0.120204	−	0.208200i
$713$	−15.9273	−	13.3646i	−0.596481	−	0.500507i
$714$	−3.01849	−	0.485253i	−0.112964	−	0.0181602i
$715$	0.169893	+	0.963511i	0.00635364	+	0.0360333i
$716$	−0.443360	−	2.51442i	−0.0165691	−	0.0939682i
$717$	−14.6102	−	38.3260i	−0.545628	−	1.43131i
$718$	0.670237	+	0.562396i	0.0250130	+	0.0209884i
$719$	−19.9773	−	34.6016i	−0.745026	−	1.29042i	−0.950182	−	0.311694i	$-0.899104\pi$
$719$	−19.9773	−	34.6016i	−0.745026	−	1.29042i	0.205156	−	0.978729i	$-0.434230\pi$
$720$	−1.20913	+	8.32336i	−0.0450615	+	0.310193i
$721$	0.00610150	−	0.0105681i	0.000227232	−	0.000393577i
$722$	4.41339	−	1.60634i	0.164249	−	0.0597819i
$723$	−27.9843	+	16.7266i	−1.04075	+	0.622068i
$724$	6.63625	−	5.56847i	0.246634	−	0.206951i
$725$	20.8077	+	7.57337i	0.772777	+	0.281268i
$726$	11.7295	+	13.5565i	0.435322	+	0.503130i
$727$	−3.68736	+	20.9121i	−0.136757	+	0.775586i	0.836863	+	0.547412i	$0.184387\pi$
$727$	−3.68736	+	20.9121i	−0.136757	+	0.775586i	−0.973620	+	0.228175i	$0.926724\pi$
$728$	0.432809			0.0160410
$729$	11.3237	−	24.5107i	0.419396	−	0.907803i
$730$	3.51711			0.130174
$731$	2.91605	−	16.5378i	0.107854	−	0.611671i
$732$	−0.638894	−	0.738411i	−0.0236142	−	0.0272925i
$733$	25.2128	+	9.17672i	0.931257	+	0.338950i	0.762708	−	0.646743i	$-0.223869\pi$
$733$	25.2128	+	9.17672i	0.931257	+	0.338950i	0.168549	+	0.985693i	$0.446092\pi$
$734$	−8.50936	+	7.14020i	−0.314086	+	0.263550i
$735$	4.16813	−	2.49134i	0.153744	−	0.0918945i
$736$	−2.01139	+	0.732085i	−0.0741407	+	0.0269850i
$737$	5.17417	−	8.96193i	0.190593	−	0.330117i
$738$	−0.243487	+	1.67611i	−0.00896289	+	0.0616986i
$739$	−13.7206	−	23.7648i	−0.504721	−	0.874203i	−0.999985	−	0.00546036i	$-0.998262\pi$
$739$	−13.7206	−	23.7648i	−0.504721	−	0.874203i	0.495264	−	0.868743i	$-0.335071\pi$
$740$	3.01180	+	2.52720i	0.110716	+	0.0929017i
$741$	1.29987	+	3.40986i	0.0477519	+	0.125264i
$742$	−0.118662	−	0.672963i	−0.00435620	−	0.0247053i
$743$	0.346750	+	1.96651i	0.0127210	+	0.0721444i	0.990507	−	0.137459i	$-0.0438937\pi$
$743$	0.346750	+	1.96651i	0.0127210	+	0.0721444i	−0.977786	+	0.209604i	$0.932783\pi$
$744$	−16.6111	−	2.67040i	−0.608992	−	0.0979017i
$745$	−25.7529	−	21.6092i	−0.943513	−	0.791701i
$746$	−10.4865	−	18.1632i	−0.383939	−	0.665002i
$747$	2.04360	+	0.674489i	0.0747713	+	0.0246783i
$748$	0.711601	−	1.23253i	0.0260187	−	0.0450657i
$749$	−5.41943	+	1.97251i	−0.198022	+	0.0720741i
$750$	−9.07697	−	5.05897i	−0.331444	−	0.184727i
$751$	−5.19936	+	4.36278i	−0.189727	+	0.159200i	−0.732704	−	0.680548i	$-0.761742\pi$
$751$	−5.19936	+	4.36278i	−0.189727	+	0.159200i	0.542976	+	0.839748i	$0.317297\pi$
$752$	−7.86903	−	2.86409i	−0.286954	−	0.104443i
$753$	1.65620	−	0.317953i	0.0603554	−	0.0115869i
$754$	0.581880	−	3.30001i	0.0211908	−	0.120179i
$755$	−59.7323			−2.17388
$756$	4.37742	−	2.79967i	0.159205	−	0.101823i
$757$	27.1509			0.986815			0.493408	−	0.869798i	$-0.335751\pi$
$757$	27.1509			0.986815			0.493408	+	0.869798i	$0.335751\pi$
$758$	−5.76582	+	32.6996i	−0.209424	+	1.18770i
$759$	−0.979760	+	2.82416i	−0.0355630	+	0.102510i
$760$	−12.8245	−	4.66774i	−0.465194	−	0.169317i
$761$	19.2333	−	16.1387i	0.697207	−	0.585026i	−0.223771	−	0.974642i	$-0.571837\pi$
$761$	19.2333	−	16.1387i	0.697207	−	0.585026i	0.920978	+	0.389616i	$0.127392\pi$
$762$	−0.332249	−	21.9485i	−0.0120361	−	0.795109i
$763$	−8.90037	+	3.23947i	−0.322215	+	0.117277i
$764$	6.14452	−	10.6426i	0.222301	−	0.385037i
$765$	−7.03034	+	13.0756i	−0.254182	+	0.472750i
$766$	−7.35297	−	12.7357i	−0.265674	−	0.460160i
$767$	4.61476	+	3.87224i	0.166629	+	0.139819i
$768$	−1.09313	+	1.34353i	−0.0394449	+	0.0484804i
$769$	−3.70994	−	21.0401i	−0.133784	−	0.758726i	−0.975699	−	0.219116i	$-0.929683\pi$
$769$	−3.70994	−	21.0401i	−0.133784	−	0.758726i	0.841915	−	0.539610i	$-0.181428\pi$
$770$	0.392535	+	2.22618i	0.0141460	+	0.0802259i
$771$	−1.81565	+	2.23155i	−0.0653891	+	0.0803673i
$772$	−4.03535	−	3.38606i	−0.145235	−	0.121867i
$773$	22.6507	+	39.2322i	0.814690	+	1.41108i	0.909550	+	0.415594i	$0.136426\pi$
$773$	22.6507	+	39.2322i	0.814690	+	1.41108i	−0.0948603	+	0.995491i	$0.530240\pi$
$774$	15.0124	+	24.2744i	0.539608	+	0.872524i
$775$	−13.8905	+	24.0591i	−0.498962	+	0.864228i
$776$	12.1957	−	4.43886i	0.437799	−	0.159346i
$777$	−0.0367646	−	2.42868i	−0.00131892	−	0.0871285i
$778$	−29.4525	+	24.7136i	−1.05592	+	0.886026i
$779$	−2.58253	−	0.939965i	−0.0925288	−	0.0336777i
$780$	0.688846	−	1.98560i	0.0246647	−	0.0710958i
$781$	−1.76802	+	10.0269i	−0.0632647	+	0.358792i
$782$	−3.77815			−0.135106
$783$	−15.4613	−	37.1402i	−0.552542	−	1.32728i
$784$	1.00000			0.0357143
$785$	−7.24799	+	41.1054i	−0.258692	+	1.46711i
$786$	37.6126	−	7.22076i	1.34160	−	0.257556i
$787$	0.325968	+	0.118643i	0.0116195	+	0.00422915i	0.347823	−	0.937560i	$-0.386921\pi$
$787$	0.325968	+	0.118643i	0.0116195	+	0.00422915i	−0.336204	+	0.941789i	$0.609143\pi$
$788$	4.99914	−	4.19478i	0.178087	−	0.149433i
$789$	−15.4599	−	8.61646i	−0.550388	−	0.306754i
$790$	16.7038	−	6.07967i	0.594293	−	0.216305i
$791$	−6.17244	+	10.6910i	−0.219467	+	0.380127i
$792$	0.491949	+	2.36835i	0.0174806	+	0.0841555i
$793$	0.121998	+	0.211306i	0.00433227	+	0.00750371i
$794$	−5.89671	−	4.94793i	−0.209267	−	0.175595i
$795$	−3.27621	−	0.526684i	−0.116195	−	0.0186796i
$796$	−1.93612	−	10.9803i	−0.0686239	−	0.389185i
$797$	6.37670	+	36.1641i	0.225874	+	1.28100i	0.861007	+	0.508594i	$0.169834\pi$
$797$	6.37670	+	36.1641i	0.225874	+	1.28100i	−0.635132	+	0.772403i	$0.719054\pi$
$798$	3.00333	+	7.87845i	0.106317	+	0.278894i
$799$	−11.3229	−	9.50107i	−0.400577	−	0.336124i
$800$	1.43001	+	2.47686i	0.0505586	+	0.0875701i
$801$	15.1100	+	11.9184i	0.533885	+	0.421115i
$802$	0.677766	−	1.17393i	0.0239328	−	0.0414527i
$803$	0.950508	−	0.345957i	0.0335427	−	0.0122085i
$804$	−19.0811	+	11.4050i	−0.672939	+	0.402223i
$805$	4.59701	−	3.85735i	0.162023	−	0.135954i
$806$	3.95058	+	1.43789i	0.139153	+	0.0506476i
$807$	7.07564	+	8.17778i	0.249074	+	0.287872i
$808$	0.287987	−	1.63326i	0.0101314	−	0.0574578i
$809$	−48.3092			−1.69846			−0.849230	−	0.528023i	$-0.822934\pi$
$809$	−48.3092			−1.69846			−0.849230	+	0.528023i	$0.822934\pi$
$810$	−5.87707	−	24.5382i	−0.206499	−	0.862184i
$811$	−19.4735			−0.683808			−0.341904	−	0.939735i	$-0.611072\pi$
$811$	−19.4735			−0.683808			−0.341904	+	0.939735i	$0.611072\pi$
$812$	1.34443	−	7.62462i	0.0471801	−	0.267572i
$813$	−13.0275	−	15.0567i	−0.456894	−	0.528062i
$814$	1.06253	+	0.386730i	0.0372418	+	0.0135549i
$815$	−6.23856	+	5.23477i	−0.218527	+	0.183366i
$816$	−2.62421	+	1.56852i	−0.0918659	+	0.0549093i
$817$	−43.5195	+	15.8398i	−1.52256	+	0.554165i
$818$	−3.60164	+	6.23823i	−0.125928	+	0.218114i
$819$	−1.20612	+	0.480816i	−0.0421453	+	0.0168011i
$820$	0.791405	+	1.37075i	0.0276371	+	0.0478688i
$821$	−33.5470	−	28.1492i	−1.17080	−	0.982415i	−0.170801	−	0.985306i	$-0.554635\pi$
$821$	−33.5470	−	28.1492i	−1.17080	−	0.982415i	−0.999996	+	0.00289051i	$0.999080\pi$
$822$	7.20019	+	18.8878i	0.251135	+	0.658788i
$823$	−8.09357	−	45.9009i	−0.282124	−	1.60001i	−0.715381	−	0.698735i	$-0.753747\pi$
$823$	−8.09357	−	45.9009i	−0.282124	−	1.60001i	0.433257	−	0.901271i	$-0.357364\pi$
$824$	−0.00211903	−	0.0120176i	−7.38198e−5	−	0.000418653i
$825$	3.94355	+	0.633965i	0.137297	+	0.0220718i
$826$	10.6623	+	8.94676i	0.370990	+	0.311298i
$827$	9.53705	+	16.5187i	0.331636	+	0.574410i	0.982833	−	0.184499i	$-0.0590662\pi$
$827$	9.53705	+	16.5187i	0.331636	+	0.574410i	−0.651197	+	0.758909i	$0.725733\pi$
$828$	4.79190	−	4.27461i	0.166530	−	0.148553i
$829$	26.7838	−	46.3908i	0.930238	−	1.61122i	0.147326	−	0.989088i	$-0.452933\pi$
$829$	26.7838	−	46.3908i	0.930238	−	1.61122i	0.782912	−	0.622132i	$-0.213733\pi$
$830$	1.88984	−	0.687845i	0.0655972	−	0.0238754i
$831$	11.3331	+	6.31639i	0.393140	+	0.219113i
$832$	0.331551	−	0.278204i	0.0114945	−	0.00964500i
$833$	1.65865	+	0.603701i	0.0574690	+	0.0209170i
$834$	−36.1069	+	6.93169i	−1.25028	+	0.240025i
$835$	−0.374109	+	2.12168i	−0.0129466	+	0.0734236i
$836$	−3.92500			−0.135749
$837$	49.2572	−	11.0119i	1.70258	−	0.380627i
$838$	−21.2611			−0.734454
$839$	−6.43731	+	36.5078i	−0.222241	+	1.26039i	0.645650	+	0.763634i	$0.276587\pi$
$839$	−6.43731	+	36.5078i	−0.222241	+	1.26039i	−0.867891	+	0.496755i	$0.834525\pi$
$840$	1.59157	−	4.58770i	0.0549144	−	0.158291i
$841$	−29.0763	−	10.5829i	−1.00263	−	0.364928i
$842$	−0.221475	+	0.185840i	−0.00763255	+	0.00640447i
$843$	−0.551720	−	36.4468i	−0.0190022	−	1.25529i
$844$	18.3060	−	6.66285i	0.630120	−	0.229345i
$845$	17.9606	−	31.1087i	0.617865	−	1.07017i
$846$	25.1106	−	0.760407i	0.863321	−	0.0261433i
$847$	−5.17494	−	8.96326i	−0.177813	−	0.307981i
$848$	−0.523472	−	0.439245i	−0.0179761	−	0.0150838i
$849$	3.39507	−	4.17276i	0.116519	−	0.143209i
$850$	0.876618	+	4.97155i	0.0300678	+	0.170523i
$851$	−0.521243	−	2.95611i	−0.0178680	−	0.101334i
$852$	13.8036	−	16.9655i	0.472904	−	0.581229i
$853$	16.0299	+	13.4507i	0.548853	+	0.460542i	0.874552	−	0.484931i	$-0.161155\pi$
$853$	16.0299	+	13.4507i	0.548853	+	0.460542i	−0.325700	+	0.945473i	$0.605600\pi$
$854$	0.281874	+	0.488220i	0.00964554	+	0.0167066i
$855$	40.9240	−	1.23927i	1.39957	−	0.0423822i
$856$	−2.88362	+	4.99458i	−0.0985601	+	0.170711i
$857$	−41.7697	+	15.2029i	−1.42682	+	0.519322i	−0.936020	−	0.351948i	$-0.885519\pi$
$857$	−41.7697	+	15.2029i	−1.42682	+	0.519322i	−0.490805	+	0.871269i	$0.663297\pi$
$858$	−0.00914878	−	0.604371i	−0.000312334	−	0.0206329i
$859$	30.3244	−	25.4452i	1.03466	−	0.868180i	0.0432587	−	0.999064i	$-0.486226\pi$
$859$	30.3244	−	25.4452i	1.03466	−	0.868180i	0.991398	+	0.130884i	$0.0417816\pi$
$860$	25.0642	+	9.12261i	0.854681	+	0.311078i
$861$	0.320502	−	0.923846i	0.0109227	−	0.0314846i
$862$	0.599604	−	3.40052i	0.0204226	−	0.115822i
$863$	−39.0352			−1.32877			−0.664387	−	0.747389i	$-0.731307\pi$
$863$	−39.0352			−1.32877			−0.664387	+	0.747389i	$0.731307\pi$
$864$	1.55371	−	4.95843i	0.0528582	−	0.168689i
$865$	64.7925			2.20301
$866$	6.86946	−	38.9587i	0.233434	−	1.32387i
$867$	23.6172	−	4.53397i	0.802083	−	0.153982i
$868$	9.12775	+	3.32223i	0.309816	+	0.112764i
$869$	3.91622	−	3.28610i	0.132849	−	0.111473i
$870$	−32.8397	−	18.3029i	−1.11337	−	0.620528i
$871$	5.21984	−	1.89986i	0.176867	−	0.0643745i
$872$	−4.73579	+	8.20263i	−0.160374	+	0.277776i
$873$	−29.0548	+	25.9183i	−0.983357	+	0.877202i
$874$	5.20982	+	9.02368i	0.176225	+	0.305230i
$875$	4.59594	+	3.85645i	0.155371	+	0.130372i
$876$	−2.14533	−	0.344883i	−0.0724839	−	0.0116525i
$877$	−3.12210	−	17.7063i	−0.105426	−	0.597899i	−0.991049	−	0.133495i	$-0.957380\pi$
$877$	−3.12210	−	17.7063i	−0.105426	−	0.597899i	0.885624	−	0.464403i	$-0.153731\pi$
$878$	4.15850	+	23.5840i	0.140343	+	0.795923i
$879$	5.26628	+	13.8147i	0.177627	+	0.465958i
$880$	1.73166	+	1.45303i	0.0583742	+	0.0489818i
$881$	−10.8767	−	18.8389i	−0.366444	−	0.634700i	0.622563	−	0.782570i	$-0.286092\pi$
$881$	−10.8767	−	18.8389i	−0.366444	−	0.634700i	−0.989007	+	0.147870i	$0.952758\pi$
$882$	−2.78673	+	1.11092i	−0.0938340	+	0.0374066i
$883$	19.2499	−	33.3418i	0.647810	−	1.12204i	−0.335834	−	0.941921i	$-0.609018\pi$
$883$	19.2499	−	33.3418i	0.647810	−	1.12204i	0.983645	−	0.180120i	$-0.0576485\pi$
$884$	0.717881	−	0.261287i	0.0241449	−	0.00878804i
$885$	58.0149	−	34.6762i	1.95015	−	1.16563i
$886$	−9.24079	+	7.75395i	−0.310451	+	0.260499i
$887$	−25.2599	−	9.19385i	−0.848144	−	0.308699i	−0.118861	−	0.992911i	$-0.537924\pi$
$887$	−25.2599	−	9.19385i	−0.848144	−	0.308699i	−0.729283	+	0.684212i	$0.760146\pi$
$888$	−1.58929	−	1.83685i	−0.0533331	−	0.0616406i
$889$	−2.20071	+	12.4809i	−0.0738095	+	0.418595i
$890$	17.9847			0.602848
$891$	−4.00197	−	6.05342i	−0.134071	−	0.202797i
$892$	−26.8266			−0.898221
$893$	−7.07862	+	40.1449i	−0.236877	+	1.34340i
$894$	13.5895	+	15.7063i	0.454501	+	0.525296i
$895$	6.72642	+	2.44822i	0.224839	+	0.0818348i
$896$	0.766044	−	0.642788i	0.0255917	−	0.0214740i
$897$	−1.37732	+	0.823241i	−0.0459874	+	0.0274872i
$898$	−20.2199	+	7.35945i	−0.674748	+	0.245588i
$899$	37.6024	−	65.1292i	1.25411	−	2.17218i
$900$	−6.73665	−	5.31370i	−0.224555	−	0.177123i
$901$	−0.603087	−	1.04458i	−0.0200917	−	0.0347999i
$902$	0.348712	+	0.292604i	0.0116108	+	0.00974266i
$903$	−5.86968	−	15.3976i	−0.195331	−	0.512399i
$904$	2.14366	+	12.1573i	0.0712972	+	0.404347i
$905$	4.21746	+	23.9184i	0.140193	+	0.795074i
$906$	36.4349	+	5.85728i	1.21047	+	0.194595i
$907$	−11.7159	−	9.83082i	−0.389021	−	0.326427i	0.427211	−	0.904152i	$-0.359496\pi$
$907$	−11.7159	−	9.83082i	−0.389021	−	0.326427i	−0.816232	+	0.577725i	$0.803941\pi$
$908$	−11.7395	−	20.3335i	−0.389590	−	0.674790i
$909$	1.01187	+	4.87138i	0.0335618	+	0.161573i
$910$	−0.606706	+	1.05085i	−0.0201121	+	0.0348352i
$911$	−32.1858	+	11.7147i	−1.06636	+	0.388124i	−0.814815	−	0.579721i	$-0.803162\pi$
$911$	−32.1858	+	11.7147i	−1.06636	+	0.388124i	−0.251547	+	0.967845i	$0.580939\pi$
$912$	7.36485	+	4.10474i	0.243875	+	0.135921i
$913$	0.443075	−	0.371784i	0.0146636	−	0.0123043i
$914$	4.38947	+	1.59764i	0.145191	+	0.0528451i
$915$	2.68843	−	0.516117i	0.0888768	−	0.0170623i
$916$	−2.52610	+	14.3262i	−0.0834647	+	0.473352i
$917$	−22.1122			−0.730210
$918$	5.57047	−	7.28634i	0.183853	−	0.240485i
$919$	−56.2448			−1.85535			−0.927673	−	0.373395i	$-0.878194\pi$
$919$	−56.2448			−1.85535			−0.927673	+	0.373395i	$0.878194\pi$
$920$	1.04206	−	5.90980i	0.0343556	−	0.194840i
$921$	14.7108	−	42.4037i	0.484736	−	1.39725i
$922$	14.6696	+	5.33931i	0.483119	+	0.175841i
$923$	−4.18669	+	3.51305i	−0.137807	+	0.115634i
$924$	−0.0211381	−	1.39639i	−0.000695393	−	0.0459379i
$925$	−3.76891	+	1.37177i	−0.123921	+	0.0451036i
$926$	−1.89336	+	3.27939i	−0.0622195	+	0.107767i
$927$	0.0192557	+	0.0311357i	0.000632442	+	0.00102263i
$928$	−3.87112	−	6.70498i	−0.127076	−	0.220102i
$929$	−13.8035	−	11.5825i	−0.452879	−	0.380011i	0.387624	−	0.921818i	$-0.373296\pi$
$929$	−13.8035	−	11.5825i	−0.452879	−	0.380011i	−0.840503	+	0.541807i	$0.817740\pi$
$930$	29.7689	−	36.5878i	0.976159	−	1.19976i
$931$	−0.845305	−	4.79396i	−0.0277038	−	0.157116i
$932$	−1.98246	−	11.2431i	−0.0649377	−	0.368280i
$933$	27.5124	−	33.8145i	0.900715	−	1.10704i
$934$	−20.3062	−	17.0389i	−0.664439	−	0.557531i
$935$	1.99503	+	3.45549i	0.0652443	+	0.113006i
$936$	−0.614880	+	1.14361i	−0.0200980	+	0.0373800i
$937$	15.8020	−	27.3699i	0.516230	−	0.894137i	−0.483592	−	0.875293i	$-0.660668\pi$
$937$	15.8020	−	27.3699i	0.516230	−	0.894137i	0.999822	−	0.0188434i	$-0.00599841\pi$
$938$	12.0604	−	4.38961i	0.393785	−	0.143326i
$939$	0.517906	+	34.2130i	0.0169012	+	1.11650i
$940$	17.9846	−	15.0909i	0.586594	−	0.492210i
$941$	32.0289	+	11.6576i	1.04411	+	0.380026i	0.806438	−	0.591319i	$-0.201392\pi$
$941$	32.0289	+	11.6576i	1.04411	+	0.380026i	0.237675	+	0.971345i	$0.423615\pi$
$942$	8.45180	−	24.3623i	0.275374	−	0.793767i
$943$	0.209844	−	1.19008i	0.00683346	−	0.0387545i
$944$	13.9187			0.453015
$945$	0.661290	+	14.5528i	0.0215118	+	0.473402i
$946$	7.67099			0.249406
$947$	1.84369	−	10.4561i	0.0599117	−	0.339776i	−0.940088	−	0.340933i	$-0.889257\pi$
$947$	1.84369	−	10.4561i	0.0599117	−	0.339776i	0.999999	+	0.00115666i	$0.000368176\pi$
$948$	−10.7850	+	2.07046i	−0.350279	+	0.0672455i
$949$	0.510218	+	0.185704i	0.0165624	+	0.00602821i
$950$	10.6652	−	8.94914i	0.346024	−	0.290348i
$951$	51.6723	+	28.7991i	1.67559	+	0.933875i
$952$	1.65865	−	0.603701i	0.0537573	−	0.0195661i
$953$	−5.74371	+	9.94839i	−0.186057	+	0.322260i	−0.943932	−	0.330140i	$-0.892904\pi$
$953$	−5.74371	+	9.94839i	−0.186057	+	0.322260i	0.757875	+	0.652399i	$0.226238\pi$
$954$	1.94674	+	0.642523i	0.0630281	+	0.0208024i
$955$	17.2266	+	29.8374i	0.557441	+	0.965516i
$956$	18.1406	+	15.2217i	0.586707	+	0.492306i
$957$	−10.6754	−	1.71618i	−0.345086	−	0.0554761i
$958$	−1.92257	−	10.9034i	−0.0621153	−	0.352273i
$959$	−2.02654	−	11.4931i	−0.0654403	−	0.371130i
$960$	−1.72970	−	4.53742i	−0.0558259	−	0.146445i
$961$	48.5313	+	40.7226i	1.56553	+	1.31363i
$962$	0.303478	+	0.525639i	0.00978451	+	0.0169473i
$963$	2.48730	−	17.1220i	0.0801520	−	0.551749i
$964$	9.41144	−	16.3011i	0.303122	−	0.525023i
$965$	13.8779	−	5.05116i	0.446747	−	0.162603i
$966$	−3.18228	+	1.90209i	−0.102388	+	0.0611987i
$967$	−4.76190	+	3.99571i	−0.153132	+	0.128493i	−0.716135	−	0.697962i	$-0.754091\pi$
$967$	−4.76190	+	3.99571i	−0.153132	+	0.128493i	0.563003	+	0.826455i	$0.309646\pi$
$968$	−9.72571	−	3.53987i	−0.312596	−	0.113776i
$969$	9.73771	+	11.2545i	0.312820	+	0.361547i
$970$	−6.31833	+	35.8330i	−0.202869	+	1.15053i
$971$	−42.9596			−1.37864			−0.689320	−	0.724457i	$-0.742091\pi$
$971$	−42.9596			−1.37864			−0.689320	+	0.724457i	$0.742091\pi$
$972$	1.17865	+	15.5438i	0.0378052	+	0.498569i
$973$	21.2270			0.680506
$974$	−3.71963	+	21.0950i	−0.119184	+	0.675929i
$975$	1.40285	+	1.62136i	0.0449271	+	0.0519251i
$976$	0.529750	+	0.192813i	0.0169569	+	0.00617180i
$977$	−24.6954	+	20.7219i	−0.790076	+	0.662953i	−0.945764	−	0.324853i	$-0.894685\pi$
$977$	−24.6954	+	20.7219i	−0.790076	+	0.662953i	0.155688	+	0.987806i	$0.450241\pi$
$978$	4.31864	−	2.58130i	0.138095	−	0.0825410i
$979$	4.86041	−	1.76904i	0.155339	−	0.0565389i
$980$	−1.40179	+	2.42797i	−0.0447784	+	0.0775585i
$981$	4.08490	−	28.1196i	0.130421	−	0.897789i
$982$	13.3069	+	23.0483i	0.424642	+	0.735501i
$983$	2.71688	+	2.27973i	0.0866549	+	0.0727121i	0.685086	−	0.728462i	$-0.259765\pi$
$983$	2.71688	+	2.27973i	0.0866549	+	0.0727121i	−0.598431	+	0.801174i	$0.704209\pi$
$984$	−0.348318	−	0.913722i	−0.0111040	−	0.0291284i
$985$	3.17705	+	18.0179i	0.101229	+	0.574099i
$986$	−2.37305	−	13.4582i	−0.0755734	−	0.428598i
$987$	−14.3204	−	2.30215i	−0.455823	−	0.0732783i
$988$	−1.61396	−	1.35428i	−0.0513470	−	0.0430853i
$989$	−10.1820	−	17.6358i	−0.323770	−	0.560786i
$990$	−6.43987	−	2.12548i	−0.204673	−	0.0675522i
$991$	0.480315	−	0.831931i	0.0152577	−	0.0264272i	−0.858296	−	0.513155i	$-0.828476\pi$
$991$	0.480315	−	0.831931i	0.0152577	−	0.0264272i	0.873553	+	0.486728i	$0.161810\pi$
$992$	9.12775	−	3.32223i	0.289807	−	0.105481i
$993$	1.58383	+	0.882737i	0.0502615	+	0.0280128i
$994$	−9.67330	+	8.11686i	−0.306818	+	0.257451i
$995$	29.3738	+	10.6912i	0.931211	+	0.338933i
$996$	−1.22019	+	0.234249i	−0.0386633	+	0.00742246i
$997$	−3.58578	+	20.3360i	−0.113563	+	0.644046i	0.873889	+	0.486126i	$0.161590\pi$
$997$	−3.58578	+	20.3360i	−0.113563	+	0.644046i	−0.987452	+	0.157921i	$0.949521\pi$
$998$	−23.5921			−0.746796
$999$	6.46951	+	3.35322i	0.204686	+	0.106091i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.c.295.3	✓	24
27.13	even	9	inner	378.2.u.c.337.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.c.295.3	✓	24	1.1	even	1	trivial
378.2.u.c.337.3	yes	24	27.13	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(1.13330 + 1.30982i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(2.14766 - 1.80210i) q^{5} +(-1.48672 + 0.888630i) q^{6} +(0.939693 - 0.342020i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.431280 + 2.96884i) q^{9} +O(q^{10})\)	\(q+(-0.173648 + 0.984808i) q^{2} +(1.13330 + 1.30982i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(2.14766 - 1.80210i) q^{5} +(-1.48672 + 0.888630i) q^{6} +(0.939693 - 0.342020i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.431280 + 2.96884i) q^{9} +(1.40179 + 2.42797i) q^{10} +(0.617661 + 0.518279i) q^{11} +(-0.616964 - 1.61844i) q^{12} +(0.0751565 + 0.426234i) q^{13} +(0.173648 + 0.984808i) q^{14} +(4.79438 + 0.770745i) q^{15} +(0.766044 + 0.642788i) q^{16} +(0.882551 + 1.52862i) q^{17} +(-2.84884 - 0.940261i) q^{18} +(2.43396 - 4.21574i) q^{19} +(-2.63450 + 0.958879i) q^{20} +(1.51294 + 0.843222i) q^{21} +(-0.617661 + 0.518279i) q^{22} +(2.01139 + 0.732085i) q^{23} +(1.70099 - 0.326551i) q^{24} +(0.496639 - 2.81658i) q^{25} -0.432809 q^{26} +(-4.37742 + 2.79967i) q^{27} -1.00000 q^{28} +(-1.34443 + 7.62462i) q^{29} +(-1.59157 + 4.58770i) q^{30} +(-9.12775 - 3.32223i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(0.0211381 + 1.39639i) q^{33} +(-1.65865 + 0.603701i) q^{34} +(1.40179 - 2.42797i) q^{35} +(1.42067 - 2.64229i) q^{36} +(-0.701181 - 1.21448i) q^{37} +(3.72904 + 3.12904i) q^{38} +(-0.473117 + 0.581491i) q^{39} +(-0.486836 - 2.76098i) q^{40} +(-0.0980363 - 0.555992i) q^{41} +(-1.09313 + 1.34353i) q^{42} +(-7.28801 - 6.11537i) q^{43} +(-0.403150 - 0.698276i) q^{44} +(4.42391 + 7.15327i) q^{45} +(-1.07024 + 1.85370i) q^{46} +(-7.86903 + 2.86409i) q^{47} +(0.0262162 + 1.73185i) q^{48} +(0.766044 - 0.642788i) q^{49} +(2.68755 + 0.978187i) q^{50} +(-1.00204 + 2.88837i) q^{51} +(0.0751565 - 0.426234i) q^{52} -0.683345 q^{53} +(-1.99701 - 4.79708i) q^{54} +2.26052 q^{55} +(0.173648 - 0.984808i) q^{56} +(8.28028 - 1.58962i) q^{57} +(-7.27533 - 2.64800i) q^{58} +(10.6623 - 8.94676i) q^{59} +(-4.24163 - 2.36404i) q^{60} +(0.529750 - 0.192813i) q^{61} +(4.85678 - 8.41218i) q^{62} +(0.610132 + 2.93730i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.929528 + 0.779967i) q^{65} +(-1.37885 - 0.221664i) q^{66} +(-2.22866 - 12.6394i) q^{67} +(-0.306507 - 1.73829i) q^{68} +(1.32059 + 3.46423i) q^{69} +(2.14766 + 1.80210i) q^{70} +(6.31380 + 10.9358i) q^{71} +(2.35545 + 1.85792i) q^{72} +(0.627254 - 1.08644i) q^{73} +(1.31779 - 0.479636i) q^{74} +(4.25206 - 2.54151i) q^{75} +(-3.72904 + 3.12904i) q^{76} +(0.757674 + 0.275771i) q^{77} +(-0.490501 - 0.566904i) q^{78} +(1.10100 - 6.24407i) q^{79} +2.80357 q^{80} +(-8.62799 - 2.56080i) q^{81} +0.564569 q^{82} +(0.124565 - 0.706444i) q^{83} +(-1.13330 - 1.30982i) q^{84} +(4.65016 + 1.69252i) q^{85} +(7.28801 - 6.11537i) q^{86} +(-11.5106 + 6.87999i) q^{87} +(0.757674 - 0.275771i) q^{88} +(3.20745 - 5.55547i) q^{89} +(-7.81280 + 3.11454i) q^{90} +(0.216405 + 0.374824i) q^{91} +(-1.63970 - 1.37587i) q^{92} +(-5.99291 - 15.7208i) q^{93} +(-1.45414 - 8.24682i) q^{94} +(-2.36988 - 13.4402i) q^{95} +(-1.71009 - 0.274915i) q^{96} +(9.94201 + 8.34234i) q^{97} +(0.500000 + 0.866025i) q^{98} +(-1.80507 + 1.61021i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9}+O(q^{10}) \) 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9	\( 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9} + 3 q^{10} - 9 q^{13} - 6 q^{18} + 15 q^{19} - 6 q^{20} - 3 q^{21} + 6 q^{23} + 3 q^{24} + 33 q^{25} + 18 q^{26} - 18 q^{27} - 24 q^{28} - 30 q^{29} + 15 q^{30} - 6 q^{33} - 3 q^{34} + 3 q^{35} - 12 q^{36} - 3 q^{37} + 15 q^{38} - 18 q^{39} - 3 q^{40} + 27 q^{41} + 18 q^{43} - 3 q^{44} + 12 q^{45} + 15 q^{46} + 3 q^{48} + 3 q^{50} + 24 q^{51} - 9 q^{52} + 6 q^{53} + 45 q^{54} - 66 q^{55} - 6 q^{57} + 3 q^{58} - 30 q^{59} - 30 q^{60} - 57 q^{61} - 18 q^{62} + 12 q^{63} - 12 q^{64} + 24 q^{65} - 54 q^{66} + 39 q^{67} + 3 q^{68} + 36 q^{69} + 3 q^{70} - 24 q^{71} - 6 q^{72} + 36 q^{73} - 12 q^{74} + 15 q^{75} - 15 q^{76} - 9 q^{77} + 18 q^{78} - 33 q^{79} + 6 q^{80} + 9 q^{81} - 15 q^{83} + 3 q^{84} + 36 q^{85} - 18 q^{86} - 84 q^{87} - 9 q^{88} - 3 q^{89} - 30 q^{90} - 9 q^{91} - 30 q^{92} - 45 q^{93} + 45 q^{94} + 63 q^{95} - 30 q^{97} + 12 q^{98} - 57 q^{99}+O(q^{100}) \) 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9 + 3 * q^10 - 9 * q^13 - 6 * q^18 + 15 * q^19 - 6 * q^20 - 3 * q^21 + 6 * q^23 + 3 * q^24 + 33 * q^25 + 18 * q^26 - 18 * q^27 - 24 * q^28 - 30 * q^29 + 15 * q^30 - 6 * q^33 - 3 * q^34 + 3 * q^35 - 12 * q^36 - 3 * q^37 + 15 * q^38 - 18 * q^39 - 3 * q^40 + 27 * q^41 + 18 * q^43 - 3 * q^44 + 12 * q^45 + 15 * q^46 + 3 * q^48 + 3 * q^50 + 24 * q^51 - 9 * q^52 + 6 * q^53 + 45 * q^54 - 66 * q^55 - 6 * q^57 + 3 * q^58 - 30 * q^59 - 30 * q^60 - 57 * q^61 - 18 * q^62 + 12 * q^63 - 12 * q^64 + 24 * q^65 - 54 * q^66 + 39 * q^67 + 3 * q^68 + 36 * q^69 + 3 * q^70 - 24 * q^71 - 6 * q^72 + 36 * q^73 - 12 * q^74 + 15 * q^75 - 15 * q^76 - 9 * q^77 + 18 * q^78 - 33 * q^79 + 6 * q^80 + 9 * q^81 - 15 * q^83 + 3 * q^84 + 36 * q^85 - 18 * q^86 - 84 * q^87 - 9 * q^88 - 3 * q^89 - 30 * q^90 - 9 * q^91 - 30 * q^92 - 45 * q^93 + 45 * q^94 + 63 * q^95 - 30 * q^97 + 12 * q^98 - 57 * q^99

Introduction

L-functions

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