LMFDB - Embedded newform 378.2.v.b.79.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(67,378)]

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([8, 12]))

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

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

chi := DirichletCharacter("378.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.v (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:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			79.6
Character	$\chi$	$=$	378.79
Dual form			378.2.v.b.67.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(-0.389111 + 1.68778i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.0926928 - 0.525687i) q^{5} +(-1.38296 + 1.04280i) q^{6} +(-2.63702 - 0.214772i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.69718 - 1.31347i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(-0.389111 + 1.68778i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.0926928 - 0.525687i) q^{5} +(-1.38296 + 1.04280i) q^{6} +(-2.63702 - 0.214772i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.69718 - 1.31347i) q^{9} +(0.266898 - 0.462282i) q^{10} +(-0.646545 + 3.66674i) q^{11} +(-1.72970 - 0.0901205i) q^{12} +(1.06859 + 6.06025i) q^{13} +(-1.88202 - 1.85957i) q^{14} +(0.923311 + 0.0481060i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-1.09213 + 1.89162i) q^{17} +(-1.22188 - 2.73989i) q^{18} +(-1.35938 - 2.35452i) q^{19} +(0.501605 - 0.182569i) q^{20} +(1.38858 - 4.36713i) q^{21} +(-2.85221 + 2.39329i) q^{22} +(-1.36672 + 1.14682i) q^{23} +(-1.26710 - 1.18087i) q^{24} +(4.43071 - 1.61265i) q^{25} +(-3.07687 + 5.32930i) q^{26} +(3.26635 - 4.04116i) q^{27} +(-0.246405 - 2.63425i) q^{28} +(1.83629 - 10.4141i) q^{29} +(0.676375 + 0.630344i) q^{30} +(0.267574 + 1.51749i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(-5.93706 - 2.51799i) q^{33} +(-2.05253 + 0.747059i) q^{34} +(0.131530 + 1.40616i) q^{35} +(0.825151 - 2.88429i) q^{36} +10.3983 q^{37} +(0.472108 - 2.67746i) q^{38} +(-10.6442 - 0.554578i) q^{39} +(0.501605 + 0.182569i) q^{40} +(1.45917 + 8.27535i) q^{41} +(3.87085 - 2.45285i) q^{42} +(4.99996 + 4.19547i) q^{43} -3.72330 q^{44} +(-0.440463 + 1.53962i) q^{45} -1.78413 q^{46} +(-1.81932 + 10.3179i) q^{47} +(-0.211609 - 1.71908i) q^{48} +(6.90775 + 1.13272i) q^{49} +(4.43071 + 1.61265i) q^{50} +(-2.76767 - 2.57932i) q^{51} +(-5.78263 + 2.10470i) q^{52} +(-3.95402 - 6.84856i) q^{53} +(5.09977 - 0.996143i) q^{54} +1.98749 q^{55} +(1.50451 - 2.17634i) q^{56} +(4.50285 - 1.37816i) q^{57} +(8.10076 - 6.79734i) q^{58} +(-2.66278 - 0.969171i) q^{59} +(0.112956 + 0.917637i) q^{60} +(-1.02770 + 5.82837i) q^{61} +(-0.770450 + 1.33446i) q^{62} +(6.83043 + 4.04292i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(3.08675 - 1.12348i) q^{65} +(-2.92951 - 5.74516i) q^{66} +(-2.89382 + 2.42820i) q^{67} +(-2.05253 - 0.747059i) q^{68} +(-1.40376 - 2.75296i) q^{69} +(-0.803101 + 1.16172i) q^{70} +(-4.58179 - 7.93590i) q^{71} +(2.48609 - 1.67910i) q^{72} +7.60381 q^{73} +(7.96558 + 6.68392i) q^{74} +(0.997748 + 8.10555i) q^{75} +(2.08269 - 1.74759i) q^{76} +(2.49246 - 9.53040i) q^{77} +(-7.79742 - 7.26676i) q^{78} +(11.3423 + 9.51730i) q^{79} +(0.266898 + 0.462282i) q^{80} +(5.54961 + 7.08533i) q^{81} +(-4.20150 + 7.27722i) q^{82} +(0.348371 - 1.97571i) q^{83} +(4.54191 + 0.609141i) q^{84} +(1.09563 + 0.398777i) q^{85} +(1.13340 + 6.42783i) q^{86} +(16.8622 + 7.15151i) q^{87} +(-2.85221 - 2.39329i) q^{88} +(-1.91914 - 3.32405i) q^{89} +(-1.32707 + 0.896297i) q^{90} +(-1.51631 - 16.2105i) q^{91} +(-1.36672 - 1.14682i) q^{92} +(-2.66530 - 0.138867i) q^{93} +(-8.02588 + 6.73451i) q^{94} +(-1.11173 + 0.932856i) q^{95} +(0.942899 - 1.45291i) q^{96} +(-5.72248 - 4.80173i) q^{97} +(4.56355 + 5.30792i) q^{98} +(6.55999 - 9.04065i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9}+O(q^{10}) $ 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9	$ 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9} - 6 q^{10} + 12 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} - 18 q^{19} - 30 q^{21} - 6 q^{22} + 30 q^{23} + 6 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} - 18 q^{35} + 9 q^{36} - 24 q^{39} - 6 q^{41} + 12 q^{42} + 24 q^{43} + 51 q^{45} + 45 q^{47} - 6 q^{48} - 12 q^{49} + 6 q^{50} - 51 q^{51} + 6 q^{52} - 15 q^{53} + 27 q^{54} + 72 q^{55} - 3 q^{56} - 63 q^{57} + 3 q^{58} - 30 q^{59} - 3 q^{60} + 9 q^{61} - 24 q^{62} - 39 q^{63} - 36 q^{64} + 9 q^{65} - 6 q^{67} + 9 q^{68} - 21 q^{69} - 33 q^{70} + 12 q^{71} - 12 q^{72} + 132 q^{73} - 18 q^{74} - 30 q^{75} - 33 q^{77} + 30 q^{78} - 9 q^{79} - 6 q^{80} + 36 q^{81} - 33 q^{82} - 18 q^{83} + 15 q^{84} + 21 q^{85} - 12 q^{86} - 39 q^{87} - 6 q^{88} - 36 q^{89} + 69 q^{90} + 39 q^{91} + 30 q^{92} - 66 q^{93} - 9 q^{94} - 33 q^{95} - 48 q^{97} - 12 q^{98} - 54 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9 - 6 * q^10 + 12 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 - 18 * q^19 - 30 * q^21 - 6 * q^22 + 30 * q^23 + 6 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 - 18 * q^35 + 9 * q^36 - 24 * q^39 - 6 * q^41 + 12 * q^42 + 24 * q^43 + 51 * q^45 + 45 * q^47 - 6 * q^48 - 12 * q^49 + 6 * q^50 - 51 * q^51 + 6 * q^52 - 15 * q^53 + 27 * q^54 + 72 * q^55 - 3 * q^56 - 63 * q^57 + 3 * q^58 - 30 * q^59 - 3 * q^60 + 9 * q^61 - 24 * q^62 - 39 * q^63 - 36 * q^64 + 9 * q^65 - 6 * q^67 + 9 * q^68 - 21 * q^69 - 33 * q^70 + 12 * q^71 - 12 * q^72 + 132 * q^73 - 18 * q^74 - 30 * q^75 - 33 * q^77 + 30 * q^78 - 9 * q^79 - 6 * q^80 + 36 * q^81 - 33 * q^82 - 18 * q^83 + 15 * q^84 + 21 * q^85 - 12 * q^86 - 39 * q^87 - 6 * q^88 - 36 * q^89 + 69 * q^90 + 39 * q^91 + 30 * q^92 - 66 * q^93 - 9 * q^94 - 33 * q^95 - 48 * q^97 - 12 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	−0.389111	+	1.68778i	−0.224654	+	0.974439i
$3$	−0.389111	+	1.68778i	−0.224654	+	0.974439i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−0.0926928	−	0.525687i	−0.0414535	−	0.235094i	0.957041	−	0.289954i	$-0.0936400\pi$
$5$	−0.0926928	−	0.525687i	−0.0414535	−	0.235094i	−0.998494	+	0.0548595i	$0.982529\pi$
$6$	−1.38296	+	1.04280i	−0.564591	+	0.425720i
$7$	−2.63702	−	0.214772i	−0.996700	−	0.0811761i
$7$	−2.63702	−	0.214772i	−0.996700	−	0.0811761i
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−2.69718	−	1.31347i	−0.899062	−	0.437822i
$10$	0.266898	−	0.462282i	0.0844007	−	0.146186i
$11$	−0.646545	+	3.66674i	−0.194941	+	1.10556i	0.717563	+	0.696494i	$0.245258\pi$
$11$	−0.646545	+	3.66674i	−0.194941	+	1.10556i	−0.912503	+	0.409069i	$0.865854\pi$
$12$	−1.72970	−	0.0901205i	−0.499323	−	0.0260156i
$13$	1.06859	+	6.06025i	0.296372	+	1.68081i	0.661572	+	0.749882i	$0.269890\pi$
$13$	1.06859	+	6.06025i	0.296372	+	1.68081i	−0.365199	+	0.930929i	$0.618999\pi$
$14$	−1.88202	−	1.85957i	−0.502991	−	0.496991i
$15$	0.923311	+	0.0481060i	0.238398	+	0.0124209i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−1.09213	+	1.89162i	−0.264880	+	0.458785i	−0.967532	−	0.252748i	$-0.918666\pi$
$17$	−1.09213	+	1.89162i	−0.264880	+	0.458785i	0.702652	+	0.711533i	$0.251999\pi$
$18$	−1.22188	−	2.73989i	−0.288001	−	0.645798i
$19$	−1.35938	−	2.35452i	−0.311863	−	0.540163i	0.666902	−	0.745145i	$-0.267620\pi$
$19$	−1.35938	−	2.35452i	−0.311863	−	0.540163i	−0.978766	+	0.204982i	$0.934286\pi$
$20$	0.501605	−	0.182569i	0.112162	−	0.0408237i
$21$	1.38858	−	4.36713i	0.303013	−	0.952986i
$22$	−2.85221	+	2.39329i	−0.608094	+	0.510252i
$23$	−1.36672	+	1.14682i	−0.284981	+	0.239128i	−0.774060	−	0.633112i	$-0.781777\pi$
$23$	−1.36672	+	1.14682i	−0.284981	+	0.239128i	0.489079	+	0.872239i	$0.337333\pi$
$24$	−1.26710	−	1.18087i	−0.258646	−	0.241044i
$25$	4.43071	−	1.61265i	0.886142	−	0.322529i
$26$	−3.07687	+	5.32930i	−0.603424	+	1.04516i
$27$	3.26635	−	4.04116i	0.628608	−	0.777722i
$28$	−0.246405	−	2.63425i	−0.0465661	−	0.497827i
$29$	1.83629	−	10.4141i	0.340991	−	1.93386i	−0.0163112	−	0.999867i	$-0.505192\pi$
$29$	1.83629	−	10.4141i	0.340991	−	1.93386i	0.357302	−	0.933989i	$-0.383697\pi$
$30$	0.676375	+	0.630344i	0.123489	+	0.115085i
$31$	0.267574	+	1.51749i	0.0480578	+	0.272549i	0.999362	−	0.0357030i	$-0.0113670\pi$
$31$	0.267574	+	1.51749i	0.0480578	+	0.272549i	−0.951305	+	0.308252i	$0.900256\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	−5.93706	−	2.51799i	−1.03351	−	0.438326i
$34$	−2.05253	+	0.747059i	−0.352005	+	0.128119i
$35$	0.131530	+	1.40616i	0.0222326	+	0.237684i
$36$	0.825151	−	2.88429i	0.137525	−	0.480715i
$37$	10.3983			1.70948			0.854738	−	0.519060i	$-0.173718\pi$
$37$	10.3983			1.70948			0.854738	+	0.519060i	$0.173718\pi$
$38$	0.472108	−	2.67746i	0.0765860	−	0.434341i
$39$	−10.6442	−	0.554578i	−1.70443	−	0.0888036i
$40$	0.501605	+	0.182569i	0.0793107	+	0.0288667i
$41$	1.45917	+	8.27535i	0.227884	+	1.29239i	0.857095	+	0.515158i	$0.172267\pi$
$41$	1.45917	+	8.27535i	0.227884	+	1.29239i	−0.629212	+	0.777234i	$0.716622\pi$
$42$	3.87085	−	2.45285i	0.597286	−	0.378484i
$43$	4.99996	+	4.19547i	0.762487	+	0.639803i	0.938773	−	0.344536i	$-0.111964\pi$
$43$	4.99996	+	4.19547i	0.762487	+	0.639803i	−0.176286	+	0.984339i	$0.556408\pi$
$44$	−3.72330			−0.561309
$45$	−0.440463	+	1.53962i	−0.0656604	+	0.229514i
$46$	−1.78413			−0.263056
$47$	−1.81932	+	10.3179i	−0.265375	+	1.50502i	0.502590	+	0.864525i	$0.332380\pi$
$47$	−1.81932	+	10.3179i	−0.265375	+	1.50502i	−0.767965	+	0.640492i	$0.778731\pi$
$48$	−0.211609	−	1.71908i	−0.0305431	−	0.248127i
$49$	6.90775	+	1.13272i	0.986821	+	0.161816i
$50$	4.43071	+	1.61265i	0.626597	+	0.228063i
$51$	−2.76767	−	2.57932i	−0.387552	−	0.361177i
$52$	−5.78263	+	2.10470i	−0.801906	+	0.291870i
$53$	−3.95402	−	6.84856i	−0.543126	−	0.940722i	−0.998722	−	0.0505354i	$-0.983907\pi$
$53$	−3.95402	−	6.84856i	−0.543126	−	0.940722i	0.455596	−	0.890187i	$-0.349426\pi$
$54$	5.09977	−	0.996143i	0.693991	−	0.135558i
$55$	1.98749			0.267993
$56$	1.50451	−	2.17634i	0.201048	−	0.290826i
$57$	4.50285	−	1.37816i	0.596417	−	0.182542i
$58$	8.10076	−	6.79734i	1.06368	−	0.892535i
$59$	−2.66278	−	0.969171i	−0.346664	−	0.126175i	0.162819	−	0.986656i	$-0.447941\pi$
$59$	−2.66278	−	0.969171i	−0.346664	−	0.126175i	−0.509483	+	0.860481i	$0.670163\pi$
$60$	0.112956	+	0.917637i	0.0145826	+	0.118466i
$61$	−1.02770	+	5.82837i	−0.131583	+	0.746246i	0.845595	+	0.533825i	$0.179246\pi$
$61$	−1.02770	+	5.82837i	−0.131583	+	0.746246i	−0.977178	+	0.212421i	$0.931865\pi$
$62$	−0.770450	+	1.33446i	−0.0978472	+	0.169476i
$63$	6.83043	+	4.04292i	0.860554	+	0.509360i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	3.08675	−	1.12348i	0.382864	−	0.139351i
$66$	−2.92951	−	5.74516i	−0.360598	−	0.707180i
$67$	−2.89382	+	2.42820i	−0.353536	+	0.296652i	−0.802208	−	0.597045i	$-0.796342\pi$
$67$	−2.89382	+	2.42820i	−0.353536	+	0.296652i	0.448672	+	0.893696i	$0.351897\pi$
$68$	−2.05253	−	0.747059i	−0.248905	−	0.0905942i
$69$	−1.40376	−	2.75296i	−0.168993	−	0.331418i
$70$	−0.803101	+	1.16172i	−0.0959890	+	0.138853i
$71$	−4.58179	−	7.93590i	−0.543759	−	0.941818i	−0.998684	−	0.0512884i	$-0.983667\pi$
$71$	−4.58179	−	7.93590i	−0.543759	−	0.941818i	0.454925	−	0.890530i	$-0.349666\pi$
$72$	2.48609	−	1.67910i	0.292988	−	0.197883i
$73$	7.60381			0.889959			0.444980	−	0.895541i	$-0.353211\pi$
$73$	7.60381			0.889959			0.444980	+	0.895541i	$0.353211\pi$
$74$	7.96558	+	6.68392i	0.925980	+	0.776990i
$75$	0.997748	+	8.10555i	0.115210	+	0.935948i
$76$	2.08269	−	1.74759i	0.238901	−	0.200462i
$77$	2.49246	−	9.53040i	0.284042	−	1.08609i
$78$	−7.79742	−	7.26676i	−0.882884	−	0.822799i
$79$	11.3423	+	9.51730i	1.27611	+	1.07078i	0.993768	+	0.111464i	$0.0355541\pi$
$79$	11.3423	+	9.51730i	1.27611	+	1.07078i	0.282337	+	0.959315i	$0.408890\pi$
$80$	0.266898	+	0.462282i	0.0298401	+	0.0516847i
$81$	5.54961	+	7.08533i	0.616623	+	0.787258i
$82$	−4.20150	+	7.27722i	−0.463978	+	0.803634i
$83$	0.348371	−	1.97571i	0.0382386	−	0.216862i	−0.959701	−	0.281023i	$-0.909326\pi$
$83$	0.348371	−	1.97571i	0.0382386	−	0.216862i	0.997940	+	0.0641614i	$0.0204372\pi$
$84$	4.54191	+	0.609141i	0.495563	+	0.0664628i
$85$	1.09563	+	0.398777i	0.118838	+	0.0432535i
$86$	1.13340	+	6.42783i	0.122218	+	0.693130i
$87$	16.8622	+	7.15151i	1.80782	+	0.766722i
$88$	−2.85221	−	2.39329i	−0.304047	−	0.255126i
$89$	−1.91914	−	3.32405i	−0.203429	−	0.352349i	0.746202	−	0.665719i	$-0.231875\pi$
$89$	−1.91914	−	3.32405i	−0.203429	−	0.352349i	−0.949631	+	0.313370i	$0.898542\pi$
$90$	−1.32707	+	0.896297i	−0.139885	+	0.0944779i
$91$	−1.51631	−	16.2105i	−0.158953	−	1.69932i
$92$	−1.36672	−	1.14682i	−0.142491	−	0.119564i
$93$	−2.66530	−	0.138867i	−0.276379	−	0.0143998i
$94$	−8.02588	+	6.73451i	−0.827806	+	0.694612i
$95$	−1.11173	+	0.932856i	−0.114062	+	0.0957090i
$96$	0.942899	−	1.45291i	0.0962342	−	0.148287i
$97$	−5.72248	−	4.80173i	−0.581030	−	0.487542i	0.304255	−	0.952591i	$-0.401592\pi$
$97$	−5.72248	−	4.80173i	−0.581030	−	0.487542i	−0.885285	+	0.465049i	$0.846037\pi$
$98$	4.56355	+	5.30792i	0.460988	+	0.536181i
$99$	6.55999	−	9.04065i	0.659303	−	0.908619i
$100$	2.35753	+	4.08336i	0.235753	+	0.408336i
$101$	−1.33462	−	1.11988i	−0.132800	−	0.111433i	0.573968	−	0.818878i	$-0.305403\pi$
$101$	−1.33462	−	1.11988i	−0.132800	−	0.111433i	−0.706768	+	0.707445i	$0.749848\pi$
$102$	−0.462207	−	3.75490i	−0.0457653	−	0.371790i
$103$	−0.545966	−	3.09633i	−0.0537957	−	0.305090i	0.946024	−	0.324098i	$-0.105061\pi$
$103$	−0.545966	−	3.09633i	−0.0537957	−	0.305090i	−0.999819	+	0.0190071i	$0.993949\pi$
$104$	−5.78263	−	2.10470i	−0.567033	−	0.206383i
$105$	−2.42446	−	0.325158i	−0.236603	−	0.0317321i
$106$	1.37322	−	7.78789i	0.133379	−	0.756427i
$107$	−6.59506	+	11.4230i	−0.637569	+	1.10430i	0.348396	+	0.937347i	$0.386726\pi$
$107$	−6.59506	+	11.4230i	−0.637569	+	1.10430i	−0.985965	+	0.166954i	$0.946607\pi$
$108$	4.54696	+	2.51498i	0.437532	+	0.242004i
$109$	−7.15909	−	12.3999i	−0.685716	−	1.18769i	−0.973211	−	0.229913i	$-0.926156\pi$
$109$	−7.15909	−	12.3999i	−0.685716	−	1.18769i	0.287495	−	0.957782i	$-0.407177\pi$
$110$	1.52250	+	1.27753i	0.145165	+	0.121808i
$111$	−4.04611	+	17.5501i	−0.384040	+	1.66578i
$112$	2.55144	−	0.700094i	0.241089	−	0.0661527i
$113$	−10.5821	+	8.87944i	−0.995481	+	0.835308i	−0.986352	−	0.164651i	$-0.947350\pi$
$113$	−10.5821	+	8.87944i	−0.995481	+	0.835308i	−0.00912887	+	0.999958i	$0.502906\pi$
$114$	4.33525	+	1.83864i	0.406033	+	0.172205i
$115$	0.729552	+	0.612167i	0.0680311	+	0.0570849i
$116$	10.5748			0.981844
$117$	5.07777	−	17.7492i	0.469440	−	1.64091i
$118$	−1.41683	−	2.45403i	−0.130430	−	0.225912i
$119$	3.28623	−	4.75368i	0.301248	−	0.435769i
$120$	−0.503316	+	0.775558i	−0.0459463	+	0.0707984i
$121$	−2.69032	−	0.979195i	−0.244574	−	0.0890177i
$122$	−4.53366	+	3.80420i	−0.410459	+	0.344416i
$123$	−14.5347	−	0.757283i	−1.31055	−	0.0682819i
$124$	−1.44797	+	0.527019i	−0.130032	+	0.0473277i
$125$	−2.59293	−	4.49109i	−0.231919	−	0.401696i
$126$	2.63368	+	7.48757i	0.234627	+	0.667046i
$127$	10.2055	−	17.6765i	0.905592	−	1.56853i	0.0854719	−	0.996341i	$-0.472760\pi$
$127$	10.2055	−	17.6765i	0.905592	−	1.56853i	0.820120	−	0.572191i	$-0.193906\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	−9.02655	+	6.80632i	−0.794744	+	0.599263i
$130$	3.08675	+	1.12348i	0.270726	+	0.0985361i
$131$	−2.87687	+	2.41398i	−0.251354	+	0.210911i	−0.759755	−	0.650210i	$-0.774681\pi$
$131$	−2.87687	+	2.41398i	−0.251354	+	0.210911i	0.508401	+	0.861120i	$0.330237\pi$
$132$	1.44878	−	6.28410i	0.126100	−	0.546961i
$133$	3.07903	+	6.50086i	0.266986	+	0.563696i
$134$	−3.77761			−0.326336
$135$	−2.42715	−	1.34249i	−0.208896	−	0.115543i
$136$	−1.09213	−	1.89162i	−0.0936491	−	0.162205i
$137$	3.99593	−	1.45440i	0.341395	−	0.124258i	−0.165632	−	0.986188i	$-0.552966\pi$
$137$	3.99593	−	1.45440i	0.341395	−	0.124258i	0.507028	+	0.861930i	$0.330744\pi$
$138$	0.694225	−	3.01121i	0.0590964	−	0.256331i
$139$	2.40909	+	0.876837i	0.204336	+	0.0743723i	0.442161	−	0.896936i	$-0.354212\pi$
$139$	2.40909	+	0.876837i	0.204336	+	0.0743723i	−0.237824	+	0.971308i	$0.576434\pi$
$140$	−1.36195	+	0.373708i	−0.115106	+	0.0315841i
$141$	−16.7064	−	7.08541i	−1.40693	−	0.596699i
$142$	1.59124	−	9.02437i	0.133534	−	0.757309i
$143$	−22.9122			−1.91602
$144$	2.98376	+	0.311764i	0.248646	+	0.0259803i
$145$	−5.64479			−0.468774
$146$	5.82486	+	4.88764i	0.482069	+	0.404504i
$147$	−4.59965	+	11.2180i	−0.379373	+	0.925244i
$148$	1.80565	+	10.2404i	0.148424	+	0.841752i
$149$	10.4053	+	3.78722i	0.852436	+	0.310261i	0.731033	−	0.682342i	$-0.239039\pi$
$149$	10.4053	+	3.78722i	0.852436	+	0.310261i	0.121403	+	0.992603i	$0.461261\pi$
$150$	−4.44583	+	6.85055i	−0.363000	+	0.559345i
$151$	−0.252186	+	1.43022i	−0.0205226	+	0.116390i	−0.993348	−	0.115150i	$-0.963265\pi$
$151$	−0.252186	+	1.43022i	−0.0205226	+	0.116390i	0.972825	+	0.231540i	$0.0743763\pi$
$152$	2.71876			0.220521
$153$	5.43025	−	3.66757i	0.439009	−	0.296506i
$154$	8.03536	−	5.69858i	0.647508	−	0.459205i
$155$	0.772923	−	0.281321i	0.0620826	−	0.0225962i
$156$	−1.30219	−	10.5787i	−0.104258	−	0.846978i
$157$	11.7476	+	4.27579i	0.937563	+	0.341245i	0.765203	−	0.643789i	$-0.222639\pi$
$157$	11.7476	+	4.27579i	0.937563	+	0.341245i	0.172360	+	0.985034i	$0.444861\pi$
$158$	2.57108	+	14.5813i	0.204545	+	1.16003i
$159$	13.0974	−	4.00865i	1.03869	−	0.317906i
$160$	−0.0926928	+	0.525687i	−0.00732801	+	0.0415592i
$161$	3.85038	−	2.73064i	0.303452	−	0.215205i
$162$	−0.303112	+	8.99489i	−0.0238147	+	0.706706i
$163$	−0.994136	+	1.72189i	−0.0778668	+	0.134869i	−0.902329	−	0.431047i	$-0.858144\pi$
$163$	−0.994136	+	1.72189i	−0.0778668	+	0.134869i	0.824463	+	0.565916i	$0.191478\pi$
$164$	−7.89624	+	2.87400i	−0.616593	+	0.224422i
$165$	−0.773354	+	3.35443i	−0.0602055	+	0.261142i
$166$	1.53683	−	1.28955i	0.119281	−	0.100089i
$167$	12.6179	−	10.5876i	0.976400	−	0.819297i	−0.00714251	−	0.999974i	$-0.502274\pi$
$167$	12.6179	−	10.5876i	0.976400	−	0.819297i	0.983542	+	0.180678i	$0.0578291\pi$
$168$	3.08776	+	3.38611i	0.238226	+	0.261244i
$169$	−23.3688	+	8.50554i	−1.79760	+	0.654272i
$170$	0.582974	+	1.00974i	0.0447120	+	0.0774435i
$171$	0.573921	+	8.13607i	0.0438888	+	0.622181i
$172$	−3.26349	+	5.65254i	−0.248839	+	0.431002i
$173$	7.61347	−	2.77108i	0.578842	−	0.210681i	−0.0359730	−	0.999353i	$-0.511453\pi$
$173$	7.61347	−	2.77108i	0.578842	−	0.210681i	0.614815	+	0.788672i	$0.289231\pi$
$174$	8.32030	+	16.3172i	0.630761	+	1.23700i
$175$	−12.0302	+	3.30099i	−0.909399	+	0.249531i
$176$	−0.646545	−	3.66674i	−0.0487351	−	0.276391i
$177$	2.67186	−	4.11706i	0.200829	−	0.309457i
$178$	0.666512	−	3.77997i	0.0499572	−	0.283321i
$179$	2.26949	−	3.93087i	0.169630	−	0.293807i	−0.768660	−	0.639658i	$-0.779076\pi$
$179$	2.26949	−	3.93087i	0.169630	−	0.293807i	0.938290	+	0.345850i	$0.112410\pi$
$180$	−1.59272	−	0.166418i	−0.118714	−	0.0124041i
$181$	2.05546	−	3.56016i	0.152781	−	0.264625i	−0.779468	−	0.626442i	$-0.784510\pi$
$181$	2.05546	−	3.56016i	0.152781	−	0.264625i	0.932249	+	0.361818i	$0.117844\pi$
$182$	9.25835	−	13.3926i	0.686275	−	0.992728i
$183$	−9.43710	−	4.00241i	−0.697610	−	0.295867i
$184$	−0.309811	−	1.75702i	−0.0228396	−	0.129530i
$185$	−0.963851	−	5.46627i	−0.0708637	−	0.401888i
$186$	−1.95248	−	1.81960i	−0.143163	−	0.133420i
$187$	−6.22996	−	5.22756i	−0.455580	−	0.382277i
$188$	−10.4770			−0.764117
$189$	−9.48134	+	9.95510i	−0.689666	+	0.724127i
$190$	−1.45127			−0.105286
$191$	−11.3230	−	9.50114i	−0.819305	−	0.687478i	0.133504	−	0.991048i	$-0.457377\pi$
$191$	−11.3230	−	9.50114i	−0.819305	−	0.687478i	−0.952809	+	0.303570i	$0.901821\pi$
$192$	1.65621	−	0.506908i	0.119527	−	0.0365830i
$193$	−0.882494	−	5.00487i	−0.0635233	−	0.360259i	−0.999956	−	0.00941065i	$-0.997004\pi$
$193$	−0.882494	−	5.00487i	−0.0635233	−	0.360259i	0.936432	−	0.350848i	$-0.114107\pi$
$194$	−1.29718	−	7.35668i	−0.0931322	−	0.528179i
$195$	0.695102	+	5.64690i	0.0497773	+	0.404383i
$196$	0.0840109	+	6.99950i	0.00600078	+	0.499964i
$197$	1.89075	−	3.27487i	0.134710	−	0.233325i	−0.790776	−	0.612105i	$-0.790323\pi$
$197$	1.89075	−	3.27487i	0.134710	−	0.233325i	0.925487	+	0.378780i	$0.123656\pi$
$198$	10.8365	−	2.70886i	0.770114	−	0.192510i
$199$	−10.5237	+	18.2276i	−0.746005	+	1.29212i	0.203718	+	0.979030i	$0.434697\pi$
$199$	−10.5237	+	18.2276i	−0.746005	+	1.29212i	−0.949724	+	0.313090i	$0.898636\pi$
$200$	−0.818762	+	4.64343i	−0.0578952	+	0.328340i
$201$	−2.97224	−	5.82896i	−0.209646	−	0.411143i
$202$	−0.302535	−	1.71576i	−0.0212863	−	0.120720i
$203$	−7.07900	+	27.0679i	−0.496849	+	1.89979i
$204$	2.05953	−	3.17352i	0.144196	−	0.222191i
$205$	4.21499	−	1.53413i	0.294388	−	0.107148i
$206$	1.57205	−	2.72287i	0.109530	−	0.189711i
$207$	5.19261	−	1.29803i	0.360911	−	0.0902194i
$208$	−3.07687	−	5.32930i	−0.213343	−	0.369520i
$209$	9.51229	−	3.46219i	0.657979	−	0.239485i
$210$	−1.64823	−	1.80750i	−0.113739	−	0.124729i
$211$	−0.403942	+	0.338947i	−0.0278085	+	0.0233341i	−0.656586	−	0.754251i	$-0.728000\pi$
$211$	−0.403942	+	0.338947i	−0.0278085	+	0.0233341i	0.628777	+	0.777585i	$0.283556\pi$
$212$	6.05791	−	5.08319i	0.416059	−	0.349115i
$213$	15.1769	−	4.64510i	1.03990	−	0.318277i
$214$	−12.3947	+	4.51129i	−0.847282	+	0.308385i
$215$	1.74204	−	3.01731i	0.118806	−	0.205779i
$216$	1.86658	+	4.84932i	0.127004	+	0.329954i
$217$	−0.379685	−	4.05912i	−0.0257747	−	0.275551i
$218$	2.48632	−	14.1006i	0.168395	−	0.955016i
$219$	−2.95873	+	12.8335i	−0.199933	+	0.867211i
$220$	0.345123	+	1.95729i	0.0232682	+	0.131961i
$221$	−12.6307	−	4.59721i	−0.849634	−	0.309241i
$222$	−14.3805	+	10.8433i	−0.965154	+	0.727757i
$223$	5.24765	−	1.90999i	0.351408	−	0.127902i	−0.160284	−	0.987071i	$-0.551241\pi$
$223$	5.24765	−	1.90999i	0.351408	−	0.127902i	0.511692	+	0.859169i	$0.329019\pi$
$224$	2.40453	+	1.10373i	0.160660	+	0.0737463i
$225$	−14.0686	−	1.46999i	−0.937906	−	0.0979990i
$226$	−13.8140			−0.918891
$227$	−0.0166532	+	0.0944448i	−0.00110531	+	0.00626852i	−0.985355	−	0.170513i	$-0.945458\pi$
$227$	−0.0166532	+	0.0944448i	−0.00110531	+	0.00626852i	0.984250	+	0.176782i	$0.0565686\pi$
$228$	2.13914	+	4.19513i	0.141668	+	0.277829i
$229$	−16.7729	−	6.10483i	−1.10838	−	0.403419i	−0.277983	−	0.960586i	$-0.589666\pi$
$229$	−16.7729	−	6.10483i	−1.10838	−	0.403419i	−0.830400	+	0.557167i	$0.811888\pi$
$230$	0.165376	+	0.937894i	0.0109046	+	0.0618429i
$231$	15.1153	+	7.91511i	0.994516	+	0.520776i
$232$	8.10076	+	6.79734i	0.531841	+	0.446267i
$233$	−2.26889			−0.148640			−0.0743200	−	0.997234i	$-0.523679\pi$
$233$	−2.26889			−0.148640			−0.0743200	+	0.997234i	$0.523679\pi$
$234$	15.2987	−	10.3327i	1.00011	−	0.675472i
$235$	5.59261			0.364822
$236$	0.492061	−	2.79062i	0.0320305	−	0.181654i
$237$	−20.4765	+	15.4399i	−1.33009	+	1.00293i
$238$	5.57300	−	1.52918i	0.361244	−	0.0991222i
$239$	15.4607	+	5.62725i	1.00007	+	0.363997i	0.789612	−	0.613606i	$-0.210282\pi$
$239$	15.4607	+	5.62725i	1.00007	+	0.363997i	0.210460	+	0.977602i	$0.432504\pi$
$240$	−0.884082	+	0.270586i	−0.0570672	+	0.0174663i
$241$	−16.8597	+	6.13641i	−1.08603	+	0.395281i	−0.822147	−	0.569275i	$-0.807224\pi$
$241$	−16.8597	+	6.13641i	−1.08603	+	0.395281i	−0.263879	+	0.964556i	$0.585002\pi$
$242$	−1.43149	−	2.47941i	−0.0920195	−	0.159382i
$243$	−14.1179	+	6.60952i	−0.905662	+	0.424001i
$244$	−5.91828			−0.378879
$245$	−0.0448448	−	3.73631i	−0.00286503	−	0.238704i
$246$	−10.6475	−	9.92285i	−0.678858	−	0.632658i
$247$	12.8163	−	10.7542i	0.815485	−	0.684273i
$248$	−1.44797	−	0.527019i	−0.0919463	−	0.0334657i
$249$	3.19900	+	1.35674i	0.202728	+	0.0859801i
$250$	0.900517	−	5.10708i	0.0569537	−	0.323000i
$251$	0.0690199	−	0.119546i	0.00435650	−	0.00754568i	−0.863839	−	0.503768i	$-0.831947\pi$
$251$	0.0690199	−	0.119546i	0.00435650	−	0.00754568i	0.868195	+	0.496222i	$0.165280\pi$
$252$	−2.79540	+	7.42871i	−0.176094	+	0.467965i
$253$	−3.32143	−	5.75288i	−0.208816	−	0.361680i
$254$	19.1801	−	6.98098i	1.20347	−	0.438025i
$255$	−1.09937	+	1.69401i	−0.0688453	+	0.106083i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	19.1542	+	6.97155i	1.19480	+	0.434873i	0.861408	−	0.507913i	$-0.169583\pi$
$257$	19.1542	+	6.97155i	1.19480	+	0.434873i	0.333397	+	0.942787i	$0.391805\pi$
$258$	−11.2898	−	0.588215i	−0.702870	−	0.0366207i
$259$	−27.4206	−	2.23327i	−1.70383	−	0.138769i
$260$	1.64242	+	2.84476i	0.101859	+	0.176425i
$261$	−18.6314	+	25.6769i	−1.15326	+	1.58936i
$262$	−3.75549			−0.232015
$263$	11.8569	+	9.94908i	0.731125	+	0.613487i	0.930438	−	0.366449i	$-0.119427\pi$
$263$	11.8569	+	9.94908i	0.731125	+	0.613487i	−0.199313	+	0.979936i	$0.563871\pi$
$264$	5.14917	−	3.88265i	0.316910	−	0.238960i
$265$	−3.23369	+	2.71339i	−0.198644	+	0.166682i
$266$	−1.82000	+	6.95911i	−0.111591	+	0.426691i
$267$	6.35702	−	1.94566i	0.389044	−	0.119072i
$268$	−2.89382	−	2.42820i	−0.176768	−	0.148326i
$269$	−13.6222	−	23.5944i	−0.830562	−	1.43858i	−0.897593	−	0.440825i	$-0.854686\pi$
$269$	−13.6222	−	23.5944i	−0.830562	−	1.43858i	0.0670304	−	0.997751i	$-0.478648\pi$
$270$	−0.996372	−	2.58855i	−0.0606373	−	0.157534i
$271$	3.21867	−	5.57491i	0.195521	−	0.338651i	−0.751551	−	0.659676i	$-0.770694\pi$
$271$	3.21867	−	5.57491i	0.195521	−	0.338651i	0.947071	+	0.321024i	$0.104027\pi$
$272$	0.379292	−	2.15107i	0.0229979	−	0.130428i
$273$	27.9497	+	3.74850i	1.69160	+	0.226869i
$274$	3.99593	+	1.45440i	0.241403	+	0.0878635i
$275$	3.04850	+	17.2889i	0.183831	+	1.04256i
$276$	2.46738	−	1.86048i	0.148519	−	0.111988i
$277$	0.383069	+	0.321433i	0.0230164	+	0.0193130i	0.654223	−	0.756301i	$-0.272996\pi$
$277$	0.383069	+	0.321433i	0.0230164	+	0.0193130i	−0.631207	+	0.775615i	$0.717440\pi$
$278$	1.28185	+	2.22023i	0.0768802	+	0.133160i
$279$	1.27148	−	4.44440i	0.0761212	−	0.266079i
$280$	−1.28353	−	0.589169i	−0.0767057	−	0.0352096i
$281$	−15.8449	−	13.2954i	−0.945226	−	0.793138i	0.0332615	−	0.999447i	$-0.489411\pi$
$281$	−15.8449	−	13.2954i	−0.945226	−	0.793138i	−0.978487	+	0.206308i	$0.933855\pi$
$282$	−8.24340	−	16.1664i	−0.490887	−	0.962694i
$283$	−17.5981	+	14.7666i	−1.04610	+	0.877782i	−0.992678	−	0.120790i	$-0.961457\pi$
$283$	−17.5981	+	14.7666i	−1.04610	+	0.877782i	−0.0534215	+	0.998572i	$0.517013\pi$
$284$	7.01972	−	5.89024i	0.416544	−	0.349522i
$285$	−1.14186	−	2.23934i	−0.0676382	−	0.132647i
$286$	−17.5518	−	14.7277i	−1.03786	−	0.870867i
$287$	−2.07054	−	22.1356i	−0.122220	−	1.30663i
$288$	2.08529	+	2.15675i	0.122877	+	0.127088i
$289$	6.11452	+	10.5907i	0.359678	+	0.622980i
$290$	−4.32416	−	3.62840i	−0.253923	−	0.213067i
$291$	10.3309	−	7.78986i	0.605610	−	0.456650i
$292$	1.32039	+	7.48830i	0.0772699	+	0.438219i
$293$	30.3169	+	11.0344i	1.77113	+	0.644639i	0.999968	+	0.00799968i	$0.00254641\pi$
$293$	30.3169	+	11.0344i	1.77113	+	0.644639i	0.771162	+	0.636639i	$0.219676\pi$
$294$	−10.7343	+	5.63687i	−0.626038	+	0.328749i
$295$	−0.262661	+	1.48962i	−0.0152927	+	0.0867292i
$296$	−5.19917	+	9.00522i	−0.302195	+	0.523418i
$297$	12.7060	+	14.5896i	0.737279	+	0.846575i
$298$	5.53655	+	9.58958i	0.320724	+	0.555509i
$299$	−8.41046	−	7.05721i	−0.486389	−	0.408129i
$300$	−7.80915	+	2.39010i	−0.450861	+	0.137993i
$301$	−12.2839	−	12.1374i	−0.708034	−	0.699587i
$302$	−1.11251	+	0.933510i	−0.0640180	+	0.0537175i
$303$	2.40943	−	1.81679i	0.138418	−	0.104372i
$304$	2.08269	+	1.74759i	0.119451	+	0.100231i
$305$	3.15916			0.180893
$306$	6.51728	+	0.680971i	0.372568	+	0.0389285i
$307$	−0.224919	−	0.389571i	−0.0128368	−	0.0222340i	0.859536	−	0.511076i	$-0.170753\pi$
$307$	−0.224919	−	0.389571i	−0.0128368	−	0.0222340i	−0.872372	+	0.488842i	$0.837420\pi$
$308$	9.81842	+	0.799660i	0.559456	+	0.0455649i
$309$	5.43836	+	0.283348i	0.309377	+	0.0161191i
$310$	0.772923	+	0.281321i	0.0438991	+	0.0159780i
$311$	12.5463	−	10.5276i	0.711438	−	0.596967i	−0.213564	−	0.976929i	$-0.568507\pi$
$311$	12.5463	−	10.5276i	0.711438	−	0.596967i	0.925002	+	0.379962i	$0.124063\pi$
$312$	5.80236	−	8.94082i	0.328494	−	0.506174i
$313$	9.03960	−	3.29015i	0.510948	−	0.185970i	−0.0736634	−	0.997283i	$-0.523469\pi$
$313$	9.03960	−	3.29015i	0.510948	−	0.185970i	0.584612	+	0.811313i	$0.301247\pi$
$314$	6.25078	+	10.8267i	0.352752	+	0.610985i
$315$	1.49218	−	3.96542i	0.0840747	−	0.223426i
$316$	−7.40314	+	12.8226i	−0.416459	+	0.721329i
$317$	−0.0144768	+	0.0821020i	−0.000813098	+	0.00461131i	−0.985212	−	0.171342i	$-0.945190\pi$
$317$	−0.0144768	+	0.0821020i	−0.000813098	+	0.00461131i	0.984399	+	0.175953i	$0.0563008\pi$
$318$	12.6099	+	5.34804i	0.707128	+	0.299903i
$319$	36.9986	+	13.4664i	2.07153	+	0.753974i
$320$	−0.408912	+	0.343118i	−0.0228589	+	0.0191809i
$321$	−16.7132	−	15.5758i	−0.932842	−	0.869357i
$322$	4.70478	+	0.383181i	0.262187	+	0.0213538i
$323$	5.93846			0.330425
$324$	−6.01400	+	6.69565i	−0.334111	+	0.371981i
$325$	14.5076	+	25.1280i	0.804739	+	1.39385i
$326$	−1.86837	+	0.680029i	−0.103479	+	0.0376633i
$327$	23.7140	−	7.25800i	1.31138	−	0.401368i
$328$	−7.89624	−	2.87400i	−0.435997	−	0.158690i
$329$	7.01357	−	26.8177i	0.386671	−	1.47851i
$330$	−2.74861	+	2.07254i	−0.151306	+	0.114090i
$331$	−1.93142	+	10.9536i	−0.106161	+	0.602066i	0.884590	+	0.466370i	$0.154438\pi$
$331$	−1.93142	+	10.9536i	−0.106161	+	0.602066i	−0.990750	+	0.135697i	$0.956673\pi$
$332$	2.00619			0.110104
$333$	−28.0462	−	13.6579i	−1.53692	−	0.748446i
$334$	16.4715			0.901278
$335$	1.54471	+	1.29617i	0.0843965	+	0.0708171i
$336$	0.188807	+	4.57868i	0.0103003	+	0.249788i
$337$	3.16376	+	17.9426i	0.172341	+	0.977393i	0.941169	+	0.337937i	$0.109729\pi$
$337$	3.16376	+	17.9426i	0.172341	+	0.977393i	−0.768828	+	0.639456i	$0.779160\pi$
$338$	−23.3688	−	8.50554i	−1.27109	−	0.462640i
$339$	−10.8689	−	21.3153i	−0.590318	−	1.15769i
$340$	−0.202465	+	1.14823i	−0.0109802	+	0.0622717i
$341$	−5.73723			−0.310689
$342$	−4.79011	+	6.60150i	−0.259020	+	0.356968i
$343$	−17.9726	−	4.47058i	−0.970429	−	0.241389i
$344$	−6.13336	+	2.23236i	−0.330689	+	0.120361i
$345$	−1.31708	+	0.993120i	−0.0709091	+	0.0534678i
$346$	7.61347	+	2.77108i	0.409303	+	0.148974i
$347$	−2.15111	−	12.1995i	−0.115478	−	0.654906i	−0.986513	−	0.163685i	$-0.947662\pi$
$347$	−2.15111	−	12.1995i	−0.115478	−	0.654906i	0.871035	−	0.491221i	$-0.163449\pi$
$348$	−4.11477	+	17.8479i	−0.220575	+	0.956747i
$349$	−0.465111	+	2.63777i	−0.0248968	+	0.141197i	−0.994722	−	0.102603i	$-0.967283\pi$
$349$	−0.465111	+	2.63777i	−0.0248968	+	0.141197i	0.969826	+	0.243800i	$0.0783940\pi$
$350$	−11.3375	−	5.20417i	−0.606016	−	0.278175i
$351$	27.9808	+	15.4765i	1.49351	+	0.826077i
$352$	1.86165	−	3.22447i	0.0992263	−	0.171865i
$353$	−7.17389	+	2.61108i	−0.381828	+	0.138974i	−0.525801	−	0.850608i	$-0.676234\pi$
$353$	−7.17389	+	2.61108i	−0.381828	+	0.138974i	0.143973	+	0.989582i	$0.454012\pi$
$354$	4.69316	−	1.43641i	0.249439	−	0.0763443i
$355$	−3.74710	+	3.14419i	−0.198876	+	0.166876i
$356$	2.94030	−	2.46720i	0.155836	−	0.130762i
$357$	6.74444	+	7.39613i	0.356954	+	0.391445i
$358$	4.26525	−	1.55242i	0.225425	−	0.0820481i
$359$	2.93490	+	5.08339i	0.154898	+	0.268291i	0.933022	−	0.359820i	$-0.117162\pi$
$359$	2.93490	+	5.08339i	0.154898	+	0.268291i	−0.778124	+	0.628111i	$0.783828\pi$
$360$	−1.11312	−	1.15126i	−0.0586667	−	0.0606770i
$361$	5.80417	−	10.0531i	0.305483	−	0.529111i
$362$	3.86301	−	1.40602i	0.203035	−	0.0738987i
$363$	2.69950	−	4.15964i	0.141687	−	0.218324i
$364$	15.7009	−	4.30820i	0.822952	−	0.225811i
$365$	−0.704819	−	3.99723i	−0.0368919	−	0.209224i
$366$	−4.65654	−	9.13207i	−0.243401	−	0.477341i
$367$	5.59903	−	31.7537i	0.292267	−	1.65753i	−0.385839	−	0.922566i	$-0.626088\pi$
$367$	5.59903	−	31.7537i	0.292267	−	1.65753i	0.678106	−	0.734964i	$-0.262801\pi$
$368$	0.892065	−	1.54510i	0.0465021	−	0.0805440i
$369$	6.93375	−	24.2367i	0.360957	−	1.26171i
$370$	2.77530	−	4.80696i	0.144281	−	0.249902i
$371$	8.95594	+	18.9090i	0.464969	+	0.981706i
$372$	−0.326068	−	2.64892i	−0.0169058	−	0.137340i
$373$	−1.37095	−	7.77507i	−0.0709853	−	0.402578i	−0.999510	−	0.0313067i	$-0.990033\pi$
$373$	−1.37095	−	7.77507i	−0.0709853	−	0.402578i	0.928524	−	0.371271i	$-0.121078\pi$
$374$	−1.41222	−	8.00908i	−0.0730240	−	0.414140i
$375$	8.58891	−	2.62876i	0.443529	−	0.135749i
$376$	−8.02588	−	6.73451i	−0.413903	−	0.347306i
$377$	65.0745			3.35151
$378$	−13.6621	+	1.53156i	−0.702705	+	0.0787751i
$379$	7.39451			0.379830			0.189915	−	0.981801i	$-0.439179\pi$
$379$	7.39451			0.379830			0.189915	+	0.981801i	$0.439179\pi$
$380$	−1.11173	−	0.932856i	−0.0570308	−	0.0478545i
$381$	25.8628	+	24.1027i	1.32499	+	1.23482i
$382$	−2.56672	−	14.5566i	−0.131325	−	0.744780i
$383$	5.61357	+	31.8361i	0.286840	+	1.62675i	0.698639	+	0.715475i	$0.253789\pi$
$383$	5.61357	+	31.8361i	0.286840	+	1.62675i	−0.411799	+	0.911275i	$0.635099\pi$
$384$	1.59457	+	0.676279i	0.0813724	+	0.0345112i
$385$	−5.24104	−	0.426856i	−0.267108	−	0.0217546i
$386$	2.54104	−	4.40121i	0.129336	−	0.224016i
$387$	−7.97521	−	17.8832i	−0.405403	−	0.909056i
$388$	3.73508	−	6.46935i	0.189620	−	0.328432i
$389$	−2.95846	+	16.7783i	−0.150000	+	0.850691i	0.813216	+	0.581962i	$0.197715\pi$
$389$	−2.95846	+	16.7783i	−0.150000	+	0.850691i	−0.963216	+	0.268729i	$0.913396\pi$
$390$	−3.09728	+	4.77258i	−0.156837	+	0.241669i
$391$	−0.676705	−	3.83779i	−0.0342225	−	0.194085i
$392$	−4.43483	+	5.41593i	−0.223993	+	0.273546i
$393$	−2.95484	−	5.79483i	−0.149052	−	0.292311i
$394$	3.55344	−	1.29335i	0.179020	−	0.0651579i
$395$	3.95177	−	6.84467i	0.198835	−	0.344393i
$396$	10.0424	+	4.89043i	0.504651	+	0.245754i
$397$	−12.0904	−	20.9412i	−0.606799	−	1.05101i	−0.991764	−	0.128076i	$-0.959120\pi$
$397$	−12.0904	−	20.9412i	−0.606799	−	1.05101i	0.384965	−	0.922931i	$-0.374214\pi$
$398$	−19.7781	+	7.19864i	−0.991386	+	0.360835i
$399$	−12.1701	+	2.66716i	−0.609267	+	0.133525i
$400$	−3.61195	+	3.03078i	−0.180597	+	0.151539i
$401$	−12.6183	+	10.5880i	−0.630129	+	0.528741i	−0.900969	−	0.433883i	$-0.857143\pi$
$401$	−12.6183	+	10.5880i	−0.630129	+	0.528741i	0.270840	+	0.962624i	$0.412699\pi$
$402$	1.46991	−	6.37576i	0.0733125	−	0.317994i
$403$	−8.91044	+	3.24314i	−0.443861	+	0.161552i
$404$	0.871114	−	1.50881i	0.0433396	−	0.0750663i
$405$	3.21026	−	3.57412i	0.159519	−	0.177599i
$406$	−22.8217	+	16.1849i	−1.13262	+	0.803244i
$407$	−6.72298	+	38.1279i	−0.333246	+	1.88993i
$408$	3.61759	−	1.10722i	0.179097	−	0.0548154i
$409$	−1.77102	−	10.0439i	−0.0875711	−	0.496640i	−0.996772	−	0.0802830i	$-0.974418\pi$
$409$	−1.77102	−	10.0439i	−0.0875711	−	0.496640i	0.909201	−	0.416357i	$-0.136694\pi$
$410$	4.21499	+	1.53413i	0.208163	+	0.0757653i
$411$	0.899841	+	7.31016i	0.0443859	+	0.360584i
$412$	2.95448	−	1.07534i	0.145557	−	0.0529784i
$413$	6.81364	+	3.12761i	0.335277	+	0.153900i
$414$	4.81213	+	2.34340i	0.236503	+	0.115172i
$415$	−1.07090			−0.0525682
$416$	1.06859	−	6.06025i	0.0523917	−	0.297128i
$417$	−2.41731	+	3.72482i	−0.118376	+	0.182405i
$418$	9.51229	+	3.46219i	0.465261	+	0.169341i
$419$	−6.20977	−	35.2174i	−0.303367	−	1.72048i	−0.631092	−	0.775708i	$-0.717393\pi$
$419$	−6.20977	−	35.2174i	−0.303367	−	1.72048i	0.327725	−	0.944773i	$-0.393718\pi$
$420$	−0.100785	−	2.44409i	−0.00491779	−	0.119259i
$421$	25.2202	+	21.1622i	1.22916	+	1.03138i	0.998293	+	0.0583970i	$0.0185989\pi$
$421$	25.2202	+	21.1622i	1.22916	+	1.03138i	0.230862	+	0.972987i	$0.425846\pi$
$422$	−0.527308			−0.0256690
$423$	18.4592	−	25.4396i	0.897518	−	1.23692i
$424$	7.90803			0.384048
$425$	−1.78838	+	10.1424i	−0.0867493	+	0.491980i
$426$	14.6120	+	6.19715i	0.707952	+	0.300253i
$427$	3.96183	−	15.1488i	0.191726	−	0.733102i
$428$	−12.3947	−	4.51129i	−0.599119	−	0.218061i
$429$	8.91541	−	38.6707i	0.430440	−	1.86704i
$430$	3.27397	−	1.19163i	0.157885	−	0.0574654i
$431$	−1.03187	−	1.78725i	−0.0497034	−	0.0860888i	0.840103	−	0.542426i	$-0.182494\pi$
$431$	−1.03187	−	1.78725i	−0.0497034	−	0.0860888i	−0.889807	+	0.456338i	$0.849161\pi$
$432$	−1.68720	+	4.91461i	−0.0811755	+	0.236454i
$433$	29.0541			1.39625			0.698124	−	0.715977i	$-0.254018\pi$
$433$	29.0541			1.39625			0.698124	+	0.715977i	$0.254018\pi$
$434$	2.31830	−	3.35352i	0.111282	−	0.160974i
$435$	2.19645	−	9.52714i	0.105312	−	0.456792i
$436$	10.9684	−	9.20354i	0.525289	−	0.440770i
$437$	4.55809	+	1.65901i	0.218043	+	0.0793612i
$438$	−10.5158	+	7.92923i	−0.502463	+	0.378873i
$439$	6.11836	−	34.6990i	0.292014	−	1.65609i	−0.387085	−	0.922044i	$-0.626518\pi$
$439$	6.11836	−	34.6990i	0.292014	−	1.65609i	0.679098	−	0.734047i	$-0.262371\pi$
$440$	−0.993743	+	1.72121i	−0.0473748	+	0.0820556i
$441$	−17.1437	−	12.1282i	−0.816366	−	0.577535i
$442$	−6.72066	−	11.6405i	−0.319669	−	0.553684i
$443$	5.70933	−	2.07803i	0.271259	−	0.0987300i	−0.202810	−	0.979218i	$-0.565007\pi$
$443$	5.70933	−	2.07803i	0.271259	−	0.0987300i	0.474068	+	0.880488i	$0.342785\pi$
$444$	−17.9860	−	0.937103i	−0.853580	−	0.0444729i
$445$	−1.56952	+	1.31699i	−0.0744025	+	0.0624311i
$446$	5.24765	+	1.90999i	0.248483	+	0.0904405i
$447$	−10.4408	+	16.0882i	−0.493833	+	0.760945i
$448$	1.13251	+	2.39111i	0.0535062	+	0.112969i
$449$	8.11231	+	14.0509i	0.382843	+	0.663104i	0.991467	−	0.130355i	$-0.0416116\pi$
$449$	8.11231	+	14.0509i	0.382843	+	0.663104i	−0.608624	+	0.793459i	$0.708278\pi$
$450$	−9.83228	−	10.1692i	−0.463498	−	0.479380i
$451$	−31.2869			−1.47324
$452$	−10.5821	−	8.87944i	−0.497740	−	0.417654i
$453$	−2.31577	−	0.982150i	−0.108804	−	0.0461454i
$454$	−0.0734650	+	0.0616445i	−0.00344788	+	0.00289312i
$455$	−8.38110	+	2.29970i	−0.392912	+	0.107812i
$456$	−1.05790	+	4.58866i	−0.0495408	+	0.214884i
$457$	24.6907	+	20.7180i	1.15498	+	0.969146i	0.999824	−	0.0187433i	$-0.00596654\pi$
$457$	24.6907	+	20.7180i	1.15498	+	0.969146i	0.155159	+	0.987889i	$0.450411\pi$
$458$	−8.92467	−	15.4580i	−0.417022	−	0.722304i
$459$	4.07708	+	10.5921i	0.190302	+	0.494399i
$460$	−0.476181	+	0.824770i	−0.0222021	+	0.0384551i
$461$	4.89315	−	27.7504i	0.227896	−	1.29247i	−0.629173	−	0.777265i	$-0.716606\pi$
$461$	4.89315	−	27.7504i	0.227896	−	1.29247i	0.857070	−	0.515200i	$-0.172282\pi$
$462$	6.49129	+	15.7793i	0.302002	+	0.734118i
$463$	5.73184	+	2.08622i	0.266381	+	0.0969548i	0.471758	−	0.881728i	$-0.343620\pi$
$463$	5.73184	+	2.08622i	0.266381	+	0.0969548i	−0.205377	+	0.978683i	$0.565842\pi$
$464$	1.83629	+	10.4141i	0.0852477	+	0.483464i
$465$	0.174054	+	1.41399i	0.00807156	+	0.0655721i
$466$	−1.73807	−	1.45841i	−0.0805146	−	0.0675598i
$467$	2.76992	+	4.79765i	0.128177	+	0.222009i	0.922970	−	0.384871i	$-0.125754\pi$
$467$	2.76992	+	4.79765i	0.128177	+	0.222009i	−0.794793	+	0.606880i	$0.792421\pi$
$468$	18.3613	+	1.91851i	0.848750	+	0.0886833i
$469$	8.15256	−	5.78170i	0.376450	−	0.266974i
$470$	4.28419	+	3.59486i	0.197615	+	0.165819i
$471$	−11.7877	+	18.1636i	−0.543149	+	0.836936i
$472$	2.17071	−	1.82145i	0.0999153	−	0.0838389i
$473$	−18.6164	+	15.6210i	−0.855981	+	0.718254i
$474$	−25.6105	−	1.33435i	−1.17633	−	0.0612887i
$475$	−9.82002	−	8.23998i	−0.450573	−	0.378076i
$476$	5.25211	+	2.41083i	0.240730	+	0.110500i
$477$	1.66936	+	23.6653i	0.0764347	+	1.08356i
$478$	8.22649	+	14.2487i	0.376271	+	0.651720i
$479$	−19.8257	−	16.6358i	−0.905860	−	0.760107i	0.0654667	−	0.997855i	$-0.479146\pi$
$479$	−19.8257	−	16.6358i	−0.905860	−	0.760107i	−0.971327	+	0.237748i	$0.923591\pi$
$480$	−0.851175	−	0.360996i	−0.0388507	−	0.0164771i
$481$	11.1115	+	63.0165i	0.506641	+	2.87331i
$482$	−16.8597	−	6.13641i	−0.767937	−	0.279506i
$483$	3.11049	+	7.56111i	0.141532	+	0.344042i
$484$	0.497150	−	2.81948i	0.0225977	−	0.128158i
$485$	−1.99378	+	3.45332i	−0.0905327	+	0.156807i
$486$	−15.0634	−	4.01160i	−0.683291	−	0.181970i
$487$	−13.3297	−	23.0877i	−0.604026	−	1.04620i	−0.992205	−	0.124620i	$-0.960229\pi$
$487$	−13.3297	−	23.0877i	−0.604026	−	1.04620i	0.388178	−	0.921584i	$-0.373105\pi$
$488$	−4.53366	−	3.80420i	−0.205229	−	0.172208i
$489$	−2.51935	−	2.34789i	−0.113929	−	0.106175i
$490$	2.36730	−	2.89100i	0.106944	−	0.130602i
$491$	6.83700	−	5.73692i	0.308549	−	0.258904i	−0.475343	−	0.879801i	$-0.657676\pi$
$491$	6.83700	−	5.73692i	0.308549	−	0.258904i	0.783892	+	0.620897i	$0.213232\pi$
$492$	−1.77815	−	14.4454i	−0.0801652	−	0.651249i
$493$	17.6941	+	14.8471i	0.796902	+	0.668681i
$494$	16.7306			0.752743
$495$	−5.36062	−	2.61050i	−0.240942	−	0.117333i
$496$	−0.770450	−	1.33446i	−0.0345942	−	0.0599189i
$497$	10.3779	+	21.9112i	0.465511	+	0.982850i
$498$	1.57848	+	3.09560i	0.0707333	+	0.138717i
$499$	−35.2419	−	12.8270i	−1.57764	−	0.574215i	−0.602952	−	0.797777i	$-0.706009\pi$
$499$	−35.2419	−	12.8270i	−1.57764	−	0.574215i	−0.974690	+	0.223563i	$0.928231\pi$
$500$	3.97261	−	3.33341i	0.177660	−	0.149075i
$501$	12.9598	+	25.4159i	0.579003	+	1.13550i
$502$	0.129715	−	0.0472124i	0.00578946	−	0.00210719i
$503$	0.558023	+	0.966525i	0.0248810	+	0.0430952i	0.878198	−	0.478298i	$-0.158746\pi$
$503$	0.558023	+	0.966525i	0.0248810	+	0.0430952i	−0.853317	+	0.521393i	$0.825413\pi$
$504$	−6.91649	+	3.89387i	−0.308085	+	0.173447i
$505$	−0.464998	+	0.805400i	−0.0206921	+	0.0358398i
$506$	1.15352	−	6.54193i	0.0512802	−	0.290824i
$507$	−5.26240	−	42.7509i	−0.233711	−	1.89863i
$508$	19.1801	+	6.98098i	0.850978	+	0.309731i
$509$	−24.0068	+	20.1441i	−1.06408	+	0.892870i	−0.994503	−	0.104707i	$-0.966610\pi$
$509$	−24.0068	+	20.1441i	−1.06408	+	0.892870i	−0.0695776	+	0.997577i	$0.522165\pi$
$510$	−1.93106	+	0.591028i	−0.0855087	+	0.0261712i
$511$	−20.0514	−	1.63309i	−0.887022	−	0.0722434i
$512$	1.00000			0.0441942
$513$	−13.9552	−	2.19719i	−0.616137	−	0.0970081i
$514$	10.1917	+	17.6526i	0.449538	+	0.778622i
$515$	−1.57709	+	0.574015i	−0.0694951	+	0.0252941i
$516$	−8.27036	−	7.70752i	−0.364082	−	0.339304i
$517$	−36.6566	−	13.3419i	−1.61216	−	0.586777i
$518$	−19.5699	−	19.3364i	−0.859851	−	0.849593i
$519$	1.71447	+	13.9281i	0.0752570	+	0.611376i
$520$	−0.570408	+	3.23494i	−0.0250140	+	0.141862i
$521$	−1.31511			−0.0576159			−0.0288080	−	0.999585i	$-0.509171\pi$
$521$	−1.31511			−0.0576159			−0.0288080	+	0.999585i	$0.509171\pi$
$522$	−30.7773	+	7.69361i	−1.34709	+	0.336740i
$523$	16.3519			0.715020			0.357510	−	0.933909i	$-0.383626\pi$
$523$	16.3519			0.715020			0.357510	+	0.933909i	$0.383626\pi$
$524$	−2.87687	−	2.41398i	−0.125677	−	0.105455i
$525$	−0.890238	−	21.5888i	−0.0388532	−	0.942211i
$526$	2.68773	+	15.2429i	0.117191	+	0.664621i
$527$	−3.16274	−	1.15114i	−0.137771	−	0.0501445i
$528$	6.44021	+	0.335546i	0.280274	+	0.0146028i
$529$	−3.44117	+	19.5158i	−0.149616	+	0.848514i
$530$	−4.22128			−0.183361
$531$	5.90902	+	6.11150i	0.256430	+	0.265217i
$532$	−5.86743	+	4.16112i	−0.254385	+	0.180407i
$533$	−48.5914	+	17.6858i	−2.10473	+	0.766059i
$534$	6.12041	+	2.59575i	0.264856	+	0.112329i
$535$	6.61623	+	2.40811i	0.286045	+	0.104112i
$536$	−0.655975	−	3.72022i	−0.0283338	−	0.160689i
$537$	5.75135	+	5.35994i	0.248189	+	0.231299i
$538$	4.73095	−	26.8306i	0.203966	−	1.15675i
$539$	−8.61953	+	24.5965i	−0.371270	+	1.05945i
$540$	0.900623	−	2.62340i	0.0387566	−	0.112893i
$541$	−3.48995	+	6.04477i	−0.150045	+	0.259885i	−0.931244	−	0.364397i	$-0.881275\pi$
$541$	−3.48995	+	6.04477i	−0.150045	+	0.259885i	0.781199	+	0.624282i	$0.214608\pi$
$542$	6.04913	−	2.20170i	0.259832	−	0.0945712i
$543$	5.20896	+	4.85446i	0.223538	+	0.208325i
$544$	1.67324	−	1.40401i	0.0717394	−	0.0601965i
$545$	−5.85487	+	4.91282i	−0.250795	+	0.210442i
$546$	19.0013	+	20.8373i	0.813179	+	0.891752i
$547$	18.8244	−	6.85153i	0.804875	−	0.292950i	0.0933697	−	0.995632i	$-0.470236\pi$
$547$	18.8244	−	6.85153i	0.804875	−	0.292950i	0.711505	+	0.702681i	$0.248014\pi$
$548$	2.12619	+	3.68267i	0.0908263	+	0.157316i
$549$	10.4273	−	14.3703i	0.445025	−	0.613311i
$550$	−8.77780	+	15.2036i	−0.374287	+	0.648283i
$551$	−27.0165	+	9.83319i	−1.15094	+	0.418908i
$552$	3.08602	+	0.160787i	0.131350	+	0.00684353i
$553$	−27.8658	−	27.5333i	−1.18497	−	1.17084i
$554$	0.0868347	+	0.492464i	0.00368925	+	0.0209228i
$555$	9.60089	+	0.500223i	0.407535	+	0.0212333i
$556$	−0.445182	+	2.52475i	−0.0188799	+	0.107073i
$557$	6.53924	−	11.3263i	0.277076	−	0.479910i	−0.693580	−	0.720379i	$-0.743968\pi$
$557$	6.53924	−	11.3263i	0.277076	−	0.479910i	0.970657	+	0.240469i	$0.0773011\pi$
$558$	3.83081	−	2.58732i	0.162171	−	0.109530i
$559$	−20.0827	+	34.7842i	−0.849407	+	1.47122i
$560$	−0.604531	−	1.27637i	−0.0255461	−	0.0539364i
$561$	11.2471	−	8.48068i	0.474853	−	0.358055i
$562$	−3.59174	−	20.3698i	−0.151508	−	0.859247i
$563$	1.06892	+	6.06215i	0.0450496	+	0.255489i	0.999012	−	0.0444366i	$-0.0141493\pi$
$563$	1.06892	+	6.06215i	0.0450496	+	0.255489i	−0.953963	+	0.299926i	$0.903038\pi$
$564$	4.07674	−	17.6829i	0.171662	−	0.744585i
$565$	5.64869	+	4.73982i	0.237642	+	0.199406i
$566$	−22.9727			−0.965615
$567$	−13.1127	−	19.8760i	−0.550682	−	0.834715i
$568$	9.16359			0.384496
$569$	8.36547	+	7.01946i	0.350699	+	0.294271i	0.801071	−	0.598570i	$-0.204264\pi$
$569$	8.36547	+	7.01946i	0.350699	+	0.294271i	−0.450372	+	0.892841i	$0.648709\pi$
$570$	0.564704	−	2.44941i	0.0236529	−	0.102595i
$571$	−7.59753	−	43.0878i	−0.317947	−	1.80317i	−0.555198	−	0.831718i	$-0.687357\pi$
$571$	−7.59753	−	43.0878i	−0.317947	−	1.80317i	0.237251	−	0.971448i	$-0.423754\pi$
$572$	−3.97867	−	22.5641i	−0.166356	−	0.943454i
$573$	20.4417	−	15.4137i	0.853965	−	0.643918i
$574$	12.6424	−	18.2878i	0.527683	−	0.763318i
$575$	−4.20614	+	7.28525i	−0.175408	+	0.303816i
$576$	0.211097	+	2.99256i	0.00879569	+	0.124690i
$577$	−15.4875	+	26.8251i	−0.644752	+	1.11674i	0.339607	+	0.940567i	$0.389706\pi$
$577$	−15.4875	+	26.8251i	−0.644752	+	1.11674i	−0.984359	+	0.176175i	$0.943628\pi$
$578$	−2.12355	+	12.0433i	−0.0883280	+	0.500933i
$579$	8.79050	+	0.458000i	0.365321	+	0.0190338i
$580$	−0.980207	−	5.55903i	−0.0407009	−	0.230826i
$581$	−1.34299	+	5.13516i	−0.0557165	+	0.213042i
$582$	12.9212	+	0.673215i	0.535600	+	0.0279057i
$583$	27.6683	−	10.0704i	1.14590	−	0.417075i
$584$	−3.80191	+	6.58510i	−0.157324	+	0.272493i
$585$	−9.80118	−	1.02410i	−0.405229	−	0.0423412i
$586$	16.1313	+	27.9402i	0.666376	+	1.15420i
$587$	−17.2058	+	6.26239i	−0.710158	+	0.258476i	−0.671742	−	0.740785i	$-0.734454\pi$
$587$	−17.2058	+	6.26239i	−0.710158	+	0.258476i	−0.0384165	+	0.999262i	$0.512231\pi$
$588$	−11.8463	−	2.58179i	−0.488532	−	0.106471i
$589$	3.20922	−	2.69285i	0.132234	−	0.110957i
$590$	−1.15872	+	0.972282i	−0.0477038	+	0.0400282i
$591$	4.79154	+	4.46545i	0.197098	+	0.183684i
$592$	−9.77123	+	3.55644i	−0.401595	+	0.146169i
$593$	4.86034	−	8.41836i	0.199590	−	0.345701i	−0.748805	−	0.662790i	$-0.769372\pi$
$593$	4.86034	−	8.41836i	0.199590	−	0.345701i	0.948396	+	0.317089i	$0.102706\pi$
$594$	0.355364	+	19.3436i	0.0145808	+	0.793677i
$595$	−2.80356	−	1.28690i	−0.114935	−	0.0527576i
$596$	−1.92282	+	10.9049i	−0.0787619	+	0.446681i
$597$	−26.6692	−	24.8542i	−1.09150	−	1.01722i
$598$	−1.90650	−	10.8123i	−0.0779624	−	0.442147i
$599$	11.3067	+	4.11529i	0.461978	+	0.168146i	0.562515	−	0.826787i	$-0.309834\pi$
$599$	11.3067	+	4.11529i	0.461978	+	0.168146i	−0.100537	+	0.994933i	$0.532056\pi$
$600$	−7.51848	−	3.18870i	−0.306941	−	0.130178i
$601$	−24.9525	+	9.08198i	−1.01784	+	0.370462i	−0.796437	−	0.604722i	$-0.793284\pi$
$601$	−24.9525	+	9.08198i	−1.01784	+	0.370462i	−0.221398	+	0.975183i	$0.571062\pi$
$602$	−1.60828	−	17.1937i	−0.0655486	−	0.700764i
$603$	10.9945	−	2.74837i	0.447731	−	0.111922i
$604$	−1.45228			−0.0590926
$605$	−0.265377	+	1.50503i	−0.0107891	+	0.0611881i
$606$	3.01354	+	0.157011i	0.122417	+	0.00637812i
$607$	14.2517	+	5.18721i	0.578460	+	0.210542i	0.614647	−	0.788803i	$-0.289299\pi$
$607$	14.2517	+	5.18721i	0.578460	+	0.210542i	−0.0361860	+	0.999345i	$0.511521\pi$
$608$	0.472108	+	2.67746i	0.0191465	+	0.108585i
$609$	−42.9300	−	22.4802i	−1.73961	−	0.910944i
$610$	2.42006	+	2.03067i	0.0979852	+	0.0822193i
$611$	−64.4730			−2.60830
$612$	4.55481	+	4.71088i	0.184117	+	0.190426i
$613$	2.76459			0.111661			0.0558304	−	0.998440i	$-0.482219\pi$
$613$	2.76459			0.111661			0.0558304	+	0.998440i	$0.482219\pi$
$614$	0.0781135	−	0.443004i	0.00315240	−	0.0178782i
$615$	0.949170	+	7.71091i	0.0382742	+	0.310934i
$616$	7.00733	+	6.92373i	0.282334	+	0.278965i
$617$	11.9987	+	4.36716i	0.483048	+	0.175815i	0.572054	−	0.820216i	$-0.306147\pi$
$617$	11.9987	+	4.36716i	0.483048	+	0.175815i	−0.0890059	+	0.996031i	$0.528369\pi$
$618$	3.98389	+	3.71277i	0.160256	+	0.149349i
$619$	20.0009	−	7.27972i	0.803903	−	0.292597i	0.0928001	−	0.995685i	$-0.470418\pi$
$619$	20.0009	−	7.27972i	0.803903	−	0.292597i	0.711103	+	0.703088i	$0.248196\pi$
$620$	0.411264	+	0.712329i	0.0165167	+	0.0286078i
$621$	0.170283	+	9.26904i	0.00683323	+	0.371954i
$622$	16.3781			0.656702
$623$	4.34691	+	9.17777i	0.174155	+	0.367700i
$624$	10.1919	−	3.11938i	0.408003	−	0.124875i
$625$	15.9392	−	13.3745i	0.637567	−	0.534982i
$626$	9.03960	+	3.29015i	0.361295	+	0.131501i
$627$	2.14207	+	17.4018i	0.0855459	+	0.694961i
$628$	−2.17087	+	12.3116i	−0.0866273	+	0.491288i
$629$	−11.3563	+	19.6697i	−0.452805	+	0.784281i
$630$	3.69200	−	2.07854i	0.147093	−	0.0828108i
$631$	22.3795	+	38.7625i	0.890916	+	1.54311i	0.838780	+	0.544471i	$0.183270\pi$
$631$	22.3795	+	38.7625i	0.890916	+	1.54311i	0.0521360	+	0.998640i	$0.483397\pi$
$632$	−13.9134	+	5.06405i	−0.553444	+	0.201437i
$633$	−0.414889	−	0.813652i	−0.0164904	−	0.0323398i
$634$	−0.0638640	+	0.0535883i	−0.00253636	+	0.00212826i
$635$	−10.2383	−	3.72642i	−0.406293	−	0.147879i
$636$	6.22209	+	12.2023i	0.246722	+	0.483854i
$637$	0.516982	+	43.0731i	0.0204836	+	1.70662i
$638$	19.6866	+	34.0981i	0.779398	+	1.34996i
$639$	1.93440	+	27.4226i	0.0765238	+	1.08482i
$640$	−0.533797			−0.0211002
$641$	11.3281	+	9.50542i	0.447434	+	0.375442i	0.838483	−	0.544928i	$-0.183443\pi$
$641$	11.3281	+	9.50542i	0.447434	+	0.375442i	−0.391049	+	0.920370i	$0.627888\pi$
$642$	−2.79115	−	22.6748i	−0.110158	−	0.894904i
$643$	−5.58511	+	4.68647i	−0.220255	+	0.184816i	−0.746238	−	0.665679i	$-0.768142\pi$
$643$	−5.58511	+	4.68647i	−0.220255	+	0.184816i	0.525983	+	0.850495i	$0.323698\pi$
$644$	3.35777	+	3.31771i	0.132315	+	0.130736i
$645$	4.41469	+	4.11425i	0.173828	+	0.161998i
$646$	4.54913	+	3.81717i	0.178983	+	0.150185i
$647$	9.57823	+	16.5900i	0.376559	+	0.652219i	0.990559	−	0.137087i	$-0.0437738\pi$
$647$	9.57823	+	16.5900i	0.376559	+	0.652219i	−0.614000	+	0.789306i	$0.710441\pi$
$648$	−8.91088	+	1.26344i	−0.350052	+	0.0496326i
$649$	5.27530	−	9.13709i	0.207074	−	0.358662i
$650$	−5.03845	+	28.5745i	−0.197624	+	1.12078i
$651$	6.99863	+	0.938626i	0.274298	+	0.0367876i
$652$	−1.86837	−	0.680029i	−0.0731708	−	0.0266320i
$653$	5.70137	+	32.3341i	0.223112	+	1.26533i	0.866262	+	0.499591i	$0.166516\pi$
$653$	5.70137	+	32.3341i	0.223112	+	1.26533i	−0.643150	+	0.765741i	$0.722373\pi$
$654$	22.8313	+	9.68308i	0.892774	+	0.378639i
$655$	1.53567	+	1.28858i	0.0600034	+	0.0503489i
$656$	−4.20150	−	7.27722i	−0.164041	−	0.284128i
$657$	−20.5089	−	9.98736i	−0.800128	−	0.389644i
$658$	22.6108	−	16.0353i	0.881460	−	0.625121i
$659$	−19.8827	−	16.6836i	−0.774522	−	0.649901i	0.167341	−	0.985899i	$-0.446482\pi$
$659$	−19.8827	−	16.6836i	−0.774522	−	0.649901i	−0.941863	+	0.335998i	$0.890926\pi$
$660$	−3.43776	−	0.179113i	−0.133815	−	0.00697198i
$661$	−0.174022	+	0.146022i	−0.00676867	+	0.00567959i	−0.646166	−	0.763197i	$-0.723629\pi$
$661$	−0.174022	+	0.146022i	−0.00676867	+	0.00567959i	0.639397	+	0.768877i	$0.279184\pi$
$662$	−8.52042	+	7.14948i	−0.331155	+	0.277872i
$663$	12.6738	−	19.5290i	0.492210	−	0.758444i
$664$	1.53683	+	1.28955i	0.0596405	+	0.0500443i
$665$	3.13202	−	2.22119i	0.121454	−	0.0861341i
$666$	−12.7055	−	28.4903i	−0.492330	−	1.10398i
$667$	9.43339	+	16.3391i	0.365262	+	0.632653i
$668$	12.6179	+	10.5876i	0.488200	+	0.409648i
$669$	1.18171	+	9.60005i	0.0456877	+	0.371160i
$670$	0.350157	+	1.98584i	0.0135278	+	0.0767197i
$671$	−20.7066	−	7.53660i	−0.799371	−	0.290947i
$672$	−2.79849	+	3.62884i	−0.107954	+	0.139985i
$673$	2.17438	−	12.3315i	0.0838161	−	0.475345i	−0.913790	−	0.406188i	$-0.866858\pi$
$673$	2.17438	−	12.3315i	0.0838161	−	0.475345i	0.997606	−	0.0691572i	$-0.0220310\pi$
$674$	−9.10967	+	15.7784i	−0.350892	+	0.607762i
$675$	7.95526	−	23.1727i	0.306198	−	0.891916i
$676$	−12.4343	−	21.5368i	−0.478241	−	0.828338i
$677$	−2.31278	−	1.94065i	−0.0888872	−	0.0745852i	0.597261	−	0.802047i	$-0.296256\pi$
$677$	−2.31278	−	1.94065i	−0.0888872	−	0.0745852i	−0.686148	+	0.727462i	$0.740700\pi$
$678$	5.37517	−	23.3149i	0.206432	−	0.895403i
$679$	14.0590	+	13.8913i	0.539536	+	0.533099i
$680$	−0.893168	+	0.749457i	−0.0342514	+	0.0287403i
$681$	−0.152922	−	0.0648564i	−0.00585998	−	0.00248530i
$682$	−4.39498	−	3.68782i	−0.168292	−	0.141214i
$683$	−33.7273			−1.29054			−0.645270	−	0.763955i	$-0.723255\pi$
$683$	−33.7273			−1.29054			−0.645270	+	0.763955i	$0.723255\pi$
$684$	−7.91280	+	1.97802i	−0.302554	+	0.0756313i
$685$	−1.13495	−	1.96580i	−0.0433643	−	0.0751092i
$686$	−10.8942	−	14.9772i	−0.415941	−	0.571833i
$687$	16.8301	−	25.9334i	0.642109	−	0.989422i
$688$	−6.13336	−	2.23236i	−0.233832	−	0.0851080i
$689$	37.2788	−	31.2806i	1.42021	−	1.19170i
$690$	−1.64731	−	0.0858274i	−0.0627119	−	0.00326739i
$691$	−12.7944	+	4.65679i	−0.486723	+	0.177153i	−0.573713	−	0.819056i	$-0.694498\pi$
$691$	−12.7944	+	4.65679i	−0.486723	+	0.177153i	0.0869896	+	0.996209i	$0.472275\pi$
$692$	4.05104	+	7.01662i	0.153998	+	0.266732i
$693$	−19.2405	+	22.4315i	−0.730886	+	0.852101i
$694$	6.19387	−	10.7281i	0.235116	−	0.407233i
$695$	0.237637	−	1.34770i	0.00901407	−	0.0511213i
$696$	−14.6245	+	11.0274i	−0.554340	+	0.417991i
$697$	−17.2474	−	6.27754i	−0.653292	−	0.237779i
$698$	−2.05182	+	1.72168i	−0.0776626	+	0.0651667i
$699$	0.882851	−	3.82938i	0.0333925	−	0.144841i
$700$	−5.33986	−	11.2742i	−0.201828	−	0.426126i
$701$	24.7530			0.934907			0.467454	−	0.884018i	$-0.345171\pi$
$701$	24.7530			0.934907			0.467454	+	0.884018i	$0.345171\pi$
$702$	11.4864	+	29.8415i	0.433527	+	1.12629i
$703$	−14.1353	−	24.4830i	−0.533123	−	0.923395i
$704$	3.49876	−	1.27344i	0.131864	−	0.0479947i
$705$	−2.17615	+	9.43908i	−0.0819585	+	0.355496i
$706$	−7.17389	−	2.61108i	−0.269993	−	0.0982694i
$707$	3.27891	+	3.23979i	0.123316	+	0.121845i
$708$	4.51847	+	1.91635i	0.169815	+	0.0720209i
$709$	1.57640	−	8.94022i	0.0592030	−	0.335757i	−0.940792	−	0.338985i	$-0.889916\pi$
$709$	1.57640	−	8.94022i	0.0592030	−	0.335757i	0.999995	+	0.00322800i	$0.00102750\pi$
$710$	−4.89149			−0.183575
$711$	−18.0915	−	40.5676i	−0.678486	−	1.52140i
$712$	3.83829			0.143846
$713$	−2.10598	−	1.76713i	−0.0788696	−	0.0661795i
$714$	0.412403	+	10.0010i	0.0154338	+	0.374278i
$715$	2.12380	+	12.0447i	0.0794256	+	0.450445i
$716$	4.26525	+	1.55242i	0.159400	+	0.0580168i
$717$	−15.5135	+	23.9047i	−0.579362	+	0.892736i
$718$	−1.01928	+	5.78062i	−0.0380392	+	0.215731i
$719$	43.1185			1.60805			0.804024	−	0.594597i	$-0.202688\pi$
$719$	43.1185			1.60805			0.804024	+	0.594597i	$0.202688\pi$
$720$	−0.112683	−	1.59742i	−0.00419943	−	0.0595324i
$721$	0.774720	+	8.28234i	0.0288521	+	0.308450i
$722$	10.9083	−	3.97028i	0.405964	−	0.147759i
$723$	−3.79661	−	30.8431i	−0.141198	−	1.14707i
$724$	3.86301	+	1.40602i	0.143567	+	0.0522543i
$725$	−8.65823	−	49.1033i	−0.321559	−	1.82365i
$726$	4.74170	−	1.45127i	0.175981	−	0.0538615i
$727$	8.91327	−	50.5497i	0.330575	−	1.87478i	−0.136611	−	0.990625i	$-0.543621\pi$
$727$	8.91327	−	50.5497i	0.330575	−	1.87478i	0.467186	−	0.884159i	$-0.345268\pi$
$728$	14.7969	+	6.79209i	0.548408	+	0.251732i
$729$	−5.66198	−	26.3997i	−0.209703	−	0.977765i
$730$	2.02945	−	3.51510i	0.0751132	−	0.130100i
$731$	−13.3968	+	4.87604i	−0.495499	+	0.180347i
$732$	2.30287	−	9.98874i	0.0851165	−	0.369194i
$733$	11.2832	−	9.46773i	0.416755	−	0.349699i	−0.410172	−	0.912008i	$-0.634531\pi$
$733$	11.2832	−	9.46773i	0.416755	−	0.349699i	0.826927	+	0.562309i	$0.190087\pi$
$734$	24.7000	−	20.7258i	0.911694	−	0.765002i
$735$	6.32351	+	1.37815i	0.233246	+	0.0508339i
$736$	1.67653	−	0.610208i	0.0617978	−	0.0224926i
$737$	−7.03259	−	12.1808i	−0.259049	−	0.448686i
$738$	20.8906	−	14.1095i	0.768994	−	0.519377i
$739$	11.3518	−	19.6618i	0.417582	−	0.723273i	−0.578114	−	0.815956i	$-0.696211\pi$
$739$	11.3518	−	19.6618i	0.417582	−	0.723273i	0.995696	+	0.0926834i	$0.0295445\pi$
$740$	5.21585	−	1.89842i	0.191739	−	0.0697871i
$741$	13.1637	+	25.8157i	0.483580	+	0.948364i
$742$	−5.29382	+	20.2419i	−0.194342	+	0.743104i
$743$	0.754568	+	4.27937i	0.0276824	+	0.156995i	0.995516	−	0.0945983i	$-0.0301567\pi$
$743$	0.754568	+	4.27937i	0.0276824	+	0.156995i	−0.967833	+	0.251593i	$0.919046\pi$
$744$	1.45291	−	2.23879i	0.0532664	−	0.0820778i
$745$	1.02640	−	5.82098i	0.0376043	−	0.213264i
$746$	3.94751	−	6.83728i	0.144528	−	0.250331i
$747$	−3.53465	+	4.87127i	−0.129326	+	0.178231i
$748$	4.06632	−	7.04307i	0.148679	−	0.257520i
$749$	19.8446	−	28.7062i	0.725108	−	1.04890i
$750$	8.26922	+	3.50710i	0.301949	+	0.128061i
$751$	−0.799961	−	4.53681i	−0.0291910	−	0.165550i	0.966727	−	0.255809i	$-0.0823418\pi$
$751$	−0.799961	−	4.53681i	−0.0291910	−	0.165550i	−0.995918	+	0.0902585i	$0.971231\pi$
$752$	−1.81932	−	10.3179i	−0.0663437	−	0.376254i
$753$	0.174911	+	0.163007i	0.00637410	+	0.00594030i
$754$	49.8500	+	41.8291i	1.81543	+	1.52333i
$755$	0.775225			0.0282133
$756$	−11.4503	−	7.60862i	−0.416443	−	0.276723i
$757$	−19.5732			−0.711398			−0.355699	−	0.934600i	$-0.615757\pi$
$757$	−19.5732			−0.711398			−0.355699	+	0.934600i	$0.615757\pi$
$758$	5.66452	+	4.75310i	0.205745	+	0.172640i
$759$	11.0020	−	3.36732i	0.399347	−	0.122226i
$760$	−0.252010	−	1.42922i	−0.00914135	−	0.0518432i
$761$	−4.78963	−	27.1633i	−0.173624	−	0.984670i	−0.939720	−	0.341944i	$-0.888915\pi$
$761$	−4.78963	−	27.1633i	−0.173624	−	0.984670i	0.766096	−	0.642726i	$-0.222196\pi$
$762$	4.31915	+	35.0881i	0.156466	+	1.27111i
$763$	16.2155	+	34.2363i	0.587041	+	1.23944i
$764$	7.39057	−	12.8008i	0.267382	−	0.463118i
$765$	−2.43134	−	2.51465i	−0.0879053	−	0.0909175i
$766$	−16.1636	+	27.9962i	−0.584015	+	1.01154i
$767$	3.02802	−	17.1727i	0.109335	−	0.620072i
$768$	0.786806	+	1.54303i	0.0283914	+	0.0556792i
$769$	6.13303	+	34.7821i	0.221163	+	1.25428i	0.869886	+	0.493252i	$0.164192\pi$
$769$	6.13303	+	34.7821i	0.221163	+	1.25428i	−0.648724	+	0.761024i	$0.724697\pi$
$770$	−3.74049	−	3.69587i	−0.134798	−	0.133190i
$771$	−19.2195	+	29.6153i	−0.692175	+	1.06657i
$772$	4.77560	−	1.73817i	0.171877	−	0.0625583i
$773$	−8.38835	+	14.5290i	−0.301708	+	0.522573i	−0.976523	−	0.215414i	$-0.930890\pi$
$773$	−8.38835	+	14.5290i	−0.301708	+	0.522573i	0.674815	+	0.737987i	$0.264223\pi$
$774$	5.38575	−	18.8257i	0.193587	−	0.676676i
$775$	3.63272	+	6.29205i	0.130491	+	0.226017i
$776$	7.01966	−	2.55495i	0.251991	−	0.0917173i
$777$	14.4389	−	45.4109i	0.517994	−	1.62911i
$778$	−13.0512	+	10.9512i	−0.467907	+	0.392621i
$779$	17.5009	−	14.6850i	0.627034	−	0.526144i
$780$	−5.44041	+	1.66512i	−0.194798	+	0.0596207i
$781$	32.0612	−	11.6693i	1.14724	−	0.417561i
$782$	1.94850	−	3.37489i	0.0696781	−	0.120686i
$783$	−36.0872	−	41.4369i	−1.28965	−	1.48083i
$784$	−6.87857	+	1.29818i	−0.245663	+	0.0463637i
$785$	1.15881	−	6.57192i	0.0413596	−	0.234562i
$786$	1.46131	−	6.33844i	0.0521230	−	0.226084i
$787$	−1.05981	−	6.01048i	−0.0377781	−	0.214250i	0.960075	−	0.279743i	$-0.0902493\pi$
$787$	−1.05981	−	6.01048i	−0.0377781	−	0.214250i	−0.997853	+	0.0654926i	$0.979138\pi$
$788$	3.55344	+	1.29335i	0.126586	+	0.0460736i
$789$	−21.4055	+	16.1404i	−0.762055	+	0.574615i
$790$	7.42691	−	2.70317i	0.264237	−	0.0961746i
$791$	29.8123	−	21.1425i	1.06000	−	0.751742i
$792$	4.54944	+	10.2014i	0.161657	+	0.362492i
$793$	−36.4196			−1.29330
$794$	4.19895	−	23.8134i	0.149015	−	0.845107i
$795$	−3.32133	−	6.51356i	−0.117795	−	0.231012i
$796$	−19.7781	−	7.19864i	−0.701016	−	0.255149i
$797$	−9.28900	−	52.6805i	−0.329033	−	1.86604i	−0.479667	−	0.877451i	$-0.659243\pi$
$797$	−9.28900	−	52.6805i	−0.329033	−	1.86604i	0.150634	−	0.988590i	$-0.451869\pi$
$798$	−11.0372	−	5.77963i	−0.390714	−	0.204597i
$799$	−17.5306	−	14.7099i	−0.620186	−	0.520398i
$800$	−4.71506			−0.166703
$801$	0.810249	+	11.4863i	0.0286287	+	0.405849i
$802$	−16.4721			−0.581648
$803$	−4.91620	+	27.8812i	−0.173489	+	0.983906i
$804$	5.22428	−	3.93928i	0.184246	−	0.138928i
$805$	−1.79237	−	1.77098i	−0.0631726	−	0.0624190i
$806$	−8.91044	−	3.24314i	−0.313857	−	0.114235i
$807$	45.1227	−	13.8104i	1.58839	−	0.486151i
$808$	1.63716	−	0.595877i	0.0575951	−	0.0209629i
$809$	22.7376	+	39.3827i	0.799411	+	1.38462i	0.920000	+	0.391918i	$0.128188\pi$
$809$	22.7376	+	39.3827i	0.799411	+	1.38462i	−0.120589	+	0.992703i	$0.538478\pi$
$810$	4.75660	−	0.674420i	0.167130	−	0.0236967i
$811$	22.6718			0.796114			0.398057	−	0.917361i	$-0.369685\pi$
$811$	22.6718			0.796114			0.398057	+	0.917361i	$0.369685\pi$
$812$	−27.8859	−	2.27117i	−0.978604	−	0.0797023i
$813$	8.15678	+	7.60166i	0.286071	+	0.266602i
$814$	−29.6583	+	24.8862i	−1.03952	+	0.872262i
$815$	0.997327	+	0.362998i	0.0349349	+	0.0127152i
$816$	3.48294	+	1.47717i	0.121927	+	0.0517111i
$817$	3.08144	−	17.4757i	0.107806	−	0.611398i
$818$	5.09944	−	8.83249i	0.178298	−	0.308821i
$819$	−17.2022	+	45.7144i	−0.601093	+	1.59739i
$820$	2.24275	+	3.88456i	0.0783202	+	0.135655i
$821$	8.80522	−	3.20484i	0.307304	−	0.111850i	−0.183765	−	0.982970i	$-0.558828\pi$
$821$	8.80522	−	3.20484i	0.307304	−	0.111850i	0.491069	+	0.871121i	$0.336606\pi$
$822$	−4.00956	+	6.17832i	−0.139850	+	0.215494i
$823$	8.95468	−	7.51387i	0.312140	−	0.261917i	−0.473236	−	0.880936i	$-0.656914\pi$
$823$	8.95468	−	7.51387i	0.312140	−	0.261917i	0.785376	+	0.619019i	$0.212470\pi$
$824$	2.95448	+	1.07534i	0.102924	+	0.0374614i
$825$	−30.3660	−	1.58212i	−1.05721	−	0.0550823i
$826$	3.20916	+	6.77562i	0.111661	+	0.235754i
$827$	−20.2574	−	35.0868i	−0.704417	−	1.22009i	−0.966901	−	0.255150i	$-0.917875\pi$
$827$	−20.2574	−	35.0868i	−0.704417	−	1.22009i	0.262484	−	0.964936i	$-0.415458\pi$
$828$	2.18000	+	4.88832i	0.0757601	+	0.169881i
$829$	49.1599			1.70739			0.853697	−	0.520771i	$-0.174355\pi$
$829$	49.1599			1.70739			0.853697	+	0.520771i	$0.174355\pi$
$830$	−0.820354	−	0.688358i	−0.0284749	−	0.0238933i
$831$	−0.691564	+	0.521462i	−0.0239901	+	0.0180893i
$832$	4.71404	−	3.95555i	0.163430	−	0.137134i
$833$	−9.68680	+	11.8298i	−0.335628	+	0.409877i
$834$	−4.24603	+	1.29956i	−0.147028	+	0.0450001i
$835$	−6.73538	−	5.65165i	−0.233087	−	0.195583i
$836$	5.06138	+	8.76658i	0.175052	+	0.303198i
$837$	7.00641	+	3.87533i	0.242177	+	0.133951i
$838$	17.8803	−	30.9696i	0.617666	−	1.06983i
$839$	−7.70527	+	43.6987i	−0.266015	+	1.50865i	0.500113	+	0.865960i	$0.333292\pi$
$839$	−7.70527	+	43.6987i	−0.266015	+	1.50865i	−0.766128	+	0.642688i	$0.777819\pi$
$840$	1.49382	−	1.93706i	0.0515418	−	0.0668350i
$841$	−77.8311	−	28.3282i	−2.68383	−	0.976835i
$842$	5.71694	+	32.4224i	0.197019	+	1.11735i
$843$	28.6051	−	21.5692i	0.985213	−	0.742883i
$844$	−0.403942	−	0.338947i	−0.0139042	−	0.0116670i
$845$	6.63737	+	11.4963i	0.228332	+	0.395483i
$846$	30.4928	−	7.62250i	1.04837	−	0.262067i
$847$	6.88411	+	3.15996i	0.236541	+	0.108578i
$848$	6.05791	+	5.08319i	0.208029	+	0.174557i
$849$	−18.0751	−	35.4475i	−0.620334	−	1.21656i
$850$	−7.88941	+	6.62000i	−0.270604	+	0.227064i
$851$	−14.2116	+	11.9250i	−0.487168	+	0.408783i
$852$	7.20996	+	14.1397i	0.247009	+	0.484417i
$853$	16.8048	+	14.1009i	0.575385	+	0.482806i	0.883428	−	0.468567i	$-0.155230\pi$
$853$	16.8048	+	14.1009i	0.575385	+	0.482806i	−0.308043	+	0.951373i	$0.599674\pi$
$854$	12.7724	−	9.05804i	0.437062	−	0.309960i
$855$	4.22383	−	1.05586i	0.144452	−	0.0361096i
$856$	−6.59506	−	11.4230i	−0.225415	−	0.390430i
$857$	−8.70095	−	7.30096i	−0.297219	−	0.249396i	0.481967	−	0.876189i	$-0.339923\pi$
$857$	−8.70095	−	7.30096i	−0.297219	−	0.249396i	−0.779185	+	0.626793i	$0.784367\pi$
$858$	31.6867	−	23.8928i	1.08177	−	0.815687i
$859$	−6.12958	−	34.7626i	−0.209139	−	1.18608i	−0.890793	−	0.454409i	$-0.849850\pi$
$859$	−6.12958	−	34.7626i	−0.209139	−	1.18608i	0.681655	−	0.731674i	$-0.261261\pi$
$860$	3.27397	+	1.19163i	0.111641	+	0.0406341i
$861$	38.1657	+	5.11862i	1.30068	+	0.174442i
$862$	0.358364	−	2.03238i	0.0122059	−	0.0692233i
$863$	2.87507	−	4.97977i	0.0978685	−	0.169513i	−0.812934	−	0.582356i	$-0.802131\pi$
$863$	2.87507	−	4.97977i	0.0978685	−	0.169513i	0.910802	+	0.412843i	$0.135464\pi$
$864$	−4.45152	+	2.68029i	−0.151444	+	0.0911855i
$865$	−2.16243	−	3.74545i	−0.0735250	−	0.127349i
$866$	22.2567	+	18.6756i	0.756313	+	0.634622i
$867$	−20.2539	+	6.19900i	−0.687859	+	0.210529i
$868$	3.93152	−	1.07878i	0.133444	−	0.0366160i
$869$	−42.2307	+	35.4358i	−1.43258	+	1.20208i
$870$	7.80651	−	5.88636i	0.264665	−	0.199566i
$871$	−17.8078	−	14.9425i	−0.603394	−	0.506308i
$872$	14.3182			0.484874
$873$	9.12767	+	20.4674i	0.308925	+	0.692718i
$874$	2.42531	+	4.20076i	0.0820374	+	0.142093i
$875$	5.87306	+	12.4000i	0.198546	+	0.419196i
$876$	−13.1524	−	0.685260i	−0.444377	−	0.0231528i
$877$	7.71825	+	2.80922i	0.260627	+	0.0948605i	0.469029	−	0.883183i	$-0.344604\pi$
$877$	7.71825	+	2.80922i	0.260627	+	0.0948605i	−0.208402	+	0.978043i	$0.566826\pi$
$878$	26.9910	−	22.6481i	0.910902	−	0.764338i
$879$	−30.4203	+	46.8745i	−1.02605	+	1.58104i
$880$	−1.86763	+	0.679760i	−0.0629577	+	0.0229147i
$881$	25.0282	+	43.3501i	0.843221	+	1.46050i	0.887157	+	0.461468i	$0.152677\pi$
$881$	25.0282	+	43.3501i	0.843221	+	1.46050i	−0.0439356	+	0.999034i	$0.513990\pi$
$882$	−5.33694	−	20.3105i	−0.179704	−	0.683891i
$883$	−1.24292	+	2.15280i	−0.0418276	+	0.0724474i	−0.886181	−	0.463339i	$-0.846651\pi$
$883$	−1.24292	+	2.15280i	−0.0418276	+	0.0724474i	0.844354	+	0.535786i	$0.179985\pi$
$884$	2.33406	−	13.2371i	0.0785030	−	0.445213i
$885$	−2.41195	−	1.02294i	−0.0810767	−	0.0343858i
$886$	5.70933	+	2.07803i	0.191809	+	0.0698127i
$887$	36.2006	−	30.3759i	1.21550	−	1.01992i	0.216448	−	0.976294i	$-0.430553\pi$
$887$	36.2006	−	30.3759i	1.21550	−	1.01992i	0.999048	−	0.0436284i	$-0.0138918\pi$
$888$	−13.1757	−	12.2791i	−0.442149	−	0.412059i
$889$	−30.7085	+	44.4213i	−1.02993	+	1.48984i
$890$	−2.04887			−0.0686781
$891$	−29.5681	+	15.7680i	−0.990568	+	0.528247i
$892$	2.79221	+	4.83626i	0.0934902	+	0.161930i
$893$	26.7667	−	9.74230i	0.895715	−	0.326014i
$894$	−18.3394	+	5.61304i	−0.613362	+	0.187728i
$895$	−2.27678	−	0.828678i	−0.0761042	−	0.0276997i
$896$	−0.669423	+	2.55966i	−0.0223638	+	0.0855123i
$897$	15.1836	−	11.4489i	0.506966	−	0.382269i
$898$	−2.81737	+	15.9781i	−0.0940170	+	0.533197i
$899$	16.2947			0.543458
$900$	−0.995333	−	14.1101i	−0.0331778	−	0.470337i
$901$	17.2732			0.575452
$902$	−23.9672	−	20.1109i	−0.798020	−	0.669618i
$903$	25.2650	−	16.0097i	0.840767	−	0.532771i
$904$	−2.39877	−	13.6041i	−0.0797819	−	0.452465i
$905$	−2.06206	−	0.750528i	−0.0685452	−	0.0249484i
$906$	−1.14267	−	2.24092i	−0.0379625	−	0.0744494i
$907$	−0.426444	+	2.41849i	−0.0141599	+	0.0803045i	−0.991069	−	0.133352i	$-0.957426\pi$
$907$	−0.426444	+	2.41849i	−0.0141599	+	0.0803045i	0.976909	+	0.213656i	$0.0685372\pi$
$908$	−0.0959017			−0.00318261
$909$	2.12880	+	4.77352i	0.0706078	+	0.158328i
$910$	−7.89852	−	3.62560i	−0.261833	−	0.120187i
$911$	29.9239	−	10.8914i	0.991422	−	0.360848i	0.205151	−	0.978730i	$-0.434231\pi$
$911$	29.9239	−	10.8914i	0.991422	−	0.360848i	0.786271	+	0.617882i	$0.212009\pi$
$912$	−3.75994	+	2.83511i	−0.124504	+	0.0938800i
$913$	7.01916	+	2.55477i	0.232300	+	0.0845504i
$914$	5.59693	+	31.7418i	0.185130	+	1.04992i
$915$	−1.22926	+	5.33196i	−0.0406382	+	0.176269i
$916$	3.09950	−	17.5782i	0.102410	−	0.580799i
$917$	8.10483	−	5.74785i	0.267645	−	0.189811i
$918$	−3.68528	+	10.7347i	−0.121632	+	0.354299i
$919$	−9.85716	+	17.0731i	−0.325158	+	0.563190i	−0.981544	−	0.191235i	$-0.938751\pi$
$919$	−9.85716	+	17.0731i	−0.325158	+	0.563190i	0.656387	+	0.754425i	$0.272084\pi$
$920$	−0.894928	+	0.325727i	−0.0295049	+	0.0107389i
$921$	0.745027	−	0.228026i	0.0245495	−	0.00751373i
$922$	21.5860	−	18.1128i	0.710896	−	0.596513i
$923$	43.1975	−	36.2470i	1.42186	−	1.19309i
$924$	−5.17011	+	16.2601i	−0.170084	+	0.534920i
$925$	46.0720	−	16.7688i	1.51484	−	0.551356i
$926$	3.04985	+	5.28249i	0.100224	+	0.173593i
$927$	−2.59435	+	9.06848i	−0.0852098	+	0.297848i
$928$	−5.28739	+	9.15803i	−0.173567	+	0.300627i
$929$	2.86304	−	1.04206i	0.0939333	−	0.0341889i	−0.294626	−	0.955613i	$-0.595195\pi$
$929$	2.86304	−	1.04206i	0.0939333	−	0.0341889i	0.388559	+	0.921424i	$0.372973\pi$
$930$	−0.775560	+	1.19506i	−0.0254316	+	0.0391874i
$931$	−6.72326	−	17.8042i	−0.220346	−	0.583509i
$932$	−0.393989	−	2.23442i	−0.0129055	−	0.0731909i
$933$	12.8864	+	25.2719i	0.421881	+	0.827364i
$934$	−0.961985	+	5.45569i	−0.0314771	+	0.178516i
$935$	−2.17059	+	3.75957i	−0.0709858	+	0.122951i
$936$	12.8323	+	13.2721i	0.419438	+	0.433811i
$937$	−25.2760	+	43.7794i	−0.825732	+	1.43021i	0.0756261	+	0.997136i	$0.475904\pi$
$937$	−25.2760	+	43.7794i	−0.825732	+	1.43021i	−0.901358	+	0.433074i	$0.857429\pi$
$938$	9.96163	+	0.811324i	0.325259	+	0.0264907i
$939$	2.03562	+	16.5371i	0.0664300	+	0.539667i
$940$	0.971147	+	5.50765i	0.0316753	+	0.179640i
$941$	3.75274	+	21.2828i	0.122336	+	0.693800i	0.982855	+	0.184382i	$0.0590283\pi$
$941$	3.75274	+	21.2828i	0.122336	+	0.693800i	−0.860519	+	0.509418i	$0.829861\pi$
$942$	−20.7053	+	6.33715i	−0.674614	+	0.206475i
$943$	−11.4846	−	9.63671i	−0.373989	−	0.313814i
$944$	2.83367			0.0922280
$945$	6.11212	+	4.06145i	0.198827	+	0.132119i
$946$	−24.3019			−0.790124
$947$	18.9453	+	15.8970i	0.615640	+	0.516583i	0.896430	−	0.443186i	$-0.146152\pi$
$947$	18.9453	+	15.8970i	0.615640	+	0.516583i	−0.280790	+	0.959769i	$0.590596\pi$
$948$	−18.7611	−	17.4843i	−0.609332	−	0.567863i
$949$	8.12533	+	46.0810i	0.263759	+	1.49585i
$950$	−2.22602	−	12.6244i	−0.0722216	−	0.409589i
$951$	−0.132937	−	0.0563804i	−0.00431077	−	0.00182826i
$952$	2.47369	+	5.22279i	0.0801729	+	0.169272i
$953$	−6.49025	+	11.2414i	−0.210240	+	0.364146i	−0.951790	−	0.306752i	$-0.900758\pi$
$953$	−6.49025	+	11.2414i	−0.210240	+	0.364146i	0.741550	+	0.670898i	$0.234091\pi$
$954$	−13.9330	+	19.2017i	−0.451096	+	0.621678i
$955$	−3.94506	+	6.83305i	−0.127659	+	0.221112i
$956$	−2.85703	+	16.2030i	−0.0924030	+	0.524043i
$957$	−37.1249	+	57.2055i	−1.20008	+	1.84919i
$958$	−4.49413	−	25.4875i	−0.145199	−	0.823462i
$959$	−10.8497	+	2.97707i	−0.350355	+	0.0961345i
$960$	−0.419994	−	0.823664i	−0.0135553	−	0.0265836i
$961$	26.8993	−	9.79054i	0.867719	−	0.315824i
$962$	−31.9943	+	55.4158i	−1.03154	+	1.78668i
$963$	32.7918	−	22.1475i	1.05670	−	0.713693i
$964$	−8.97084	−	15.5379i	−0.288931	−	0.500444i
$965$	−2.54920	+	0.927832i	−0.0820616	+	0.0298680i
$966$	−2.47741	+	7.79153i	−0.0797093	+	0.250688i
$967$	−2.16173	+	1.81391i	−0.0695166	+	0.0583314i	−0.676884	−	0.736090i	$-0.736670\pi$
$967$	−2.16173	+	1.81391i	−0.0695166	+	0.0583314i	0.607367	+	0.794421i	$0.292226\pi$
$968$	2.19317	−	1.84028i	0.0704910	−	0.0591490i
$969$	−2.31072	+	10.0228i	−0.0742312	+	0.321979i
$970$	−3.74707	+	1.36382i	−0.120311	+	0.0437897i
$971$	23.0863	−	39.9867i	0.740875	−	1.28323i	−0.211222	−	0.977438i	$-0.567744\pi$
$971$	23.0863	−	39.9867i	0.740875	−	1.28323i	0.952097	−	0.305795i	$-0.0989224\pi$
$972$	−8.96065	−	12.7557i	−0.287413	−	0.409138i
$973$	−6.16450	−	2.82964i	−0.197625	−	0.0907141i
$974$	4.62936	−	26.2544i	0.148334	−	0.841245i
$975$	−48.0555	+	14.7081i	−1.53901	+	0.471035i
$976$	−1.02770	−	5.82837i	−0.0328958	−	0.186561i
$977$	−41.5867	−	15.1363i	−1.33048	−	0.484254i	−0.423676	−	0.905814i	$-0.639261\pi$
$977$	−41.5867	−	15.1363i	−1.33048	−	0.484254i	−0.906801	+	0.421560i	$0.861483\pi$
$978$	−0.420736	−	3.41799i	−0.0134536	−	0.109295i
$979$	13.4292	−	4.88784i	0.429200	−	0.156216i
$980$	3.67176	−	0.692967i	0.117290	−	0.0221360i
$981$	3.02252	+	42.8480i	0.0965015	+	1.36803i
$982$	8.92506			0.284810
$983$	−0.434096	+	2.46188i	−0.0138455	+	0.0785218i	−0.990948	−	0.134249i	$-0.957138\pi$
$983$	−0.434096	+	2.46188i	−0.0138455	+	0.0785218i	0.977102	+	0.212771i	$0.0682488\pi$
$984$	7.92319	−	12.2088i	0.252582	−	0.389202i
$985$	−1.89682	−	0.690385i	−0.0604376	−	0.0219975i
$986$	4.01093	+	22.7471i	0.127734	+	0.724415i
$987$	42.5332	+	22.2724i	1.35385	+	0.708939i
$988$	12.8163	+	10.7542i	0.407742	+	0.342136i
$989$	−11.6450			−0.370289
$990$	−2.42848	−	5.44550i	−0.0771820	−	0.173069i
$991$	−7.54664			−0.239727			−0.119863	−	0.992790i	$-0.538246\pi$
$991$	−7.54664			−0.239727			−0.119863	+	0.992790i	$0.538246\pi$
$992$	0.267574	−	1.51749i	0.00849550	−	0.0481803i
$993$	−17.7358	−	7.52199i	−0.562827	−	0.238703i
$994$	−6.13431	+	23.4557i	−0.194569	+	0.743970i
$995$	10.5575	+	3.84261i	0.334695	+	0.121819i
$996$	−0.780630	+	3.38600i	−0.0247352	+	0.107289i
$997$	9.57943	−	3.48663i	0.303384	−	0.110423i	−0.185843	−	0.982580i	$-0.559501\pi$
$997$	9.57943	−	3.48663i	0.303384	−	0.110423i	0.489226	+	0.872157i	$0.337279\pi$
$998$	−18.7518	−	32.4791i	−0.593578	−	1.02811i
$999$	33.9645	−	42.0213i	1.07459	−	1.32950i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.v.b.79.6	yes	72
7.4	even	3		378.2.w.a.25.11	yes	72
27.13	even	9		378.2.w.a.121.11	yes	72
189.67	even	9	inner	378.2.v.b.67.6	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.b.67.6	✓	72	189.67	even	9	inner
378.2.v.b.79.6	yes	72	1.1	even	1	trivial
378.2.w.a.25.11	yes	72	7.4	even	3
378.2.w.a.121.11	yes	72	27.13	even	9

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.v (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(-0.389111 + 1.68778i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.0926928 - 0.525687i) q^{5} +(-1.38296 + 1.04280i) q^{6} +(-2.63702 - 0.214772i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.69718 - 1.31347i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(-0.389111 + 1.68778i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.0926928 - 0.525687i) q^{5} +(-1.38296 + 1.04280i) q^{6} +(-2.63702 - 0.214772i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.69718 - 1.31347i) q^{9} +(0.266898 - 0.462282i) q^{10} +(-0.646545 + 3.66674i) q^{11} +(-1.72970 - 0.0901205i) q^{12} +(1.06859 + 6.06025i) q^{13} +(-1.88202 - 1.85957i) q^{14} +(0.923311 + 0.0481060i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-1.09213 + 1.89162i) q^{17} +(-1.22188 - 2.73989i) q^{18} +(-1.35938 - 2.35452i) q^{19} +(0.501605 - 0.182569i) q^{20} +(1.38858 - 4.36713i) q^{21} +(-2.85221 + 2.39329i) q^{22} +(-1.36672 + 1.14682i) q^{23} +(-1.26710 - 1.18087i) q^{24} +(4.43071 - 1.61265i) q^{25} +(-3.07687 + 5.32930i) q^{26} +(3.26635 - 4.04116i) q^{27} +(-0.246405 - 2.63425i) q^{28} +(1.83629 - 10.4141i) q^{29} +(0.676375 + 0.630344i) q^{30} +(0.267574 + 1.51749i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(-5.93706 - 2.51799i) q^{33} +(-2.05253 + 0.747059i) q^{34} +(0.131530 + 1.40616i) q^{35} +(0.825151 - 2.88429i) q^{36} +10.3983 q^{37} +(0.472108 - 2.67746i) q^{38} +(-10.6442 - 0.554578i) q^{39} +(0.501605 + 0.182569i) q^{40} +(1.45917 + 8.27535i) q^{41} +(3.87085 - 2.45285i) q^{42} +(4.99996 + 4.19547i) q^{43} -3.72330 q^{44} +(-0.440463 + 1.53962i) q^{45} -1.78413 q^{46} +(-1.81932 + 10.3179i) q^{47} +(-0.211609 - 1.71908i) q^{48} +(6.90775 + 1.13272i) q^{49} +(4.43071 + 1.61265i) q^{50} +(-2.76767 - 2.57932i) q^{51} +(-5.78263 + 2.10470i) q^{52} +(-3.95402 - 6.84856i) q^{53} +(5.09977 - 0.996143i) q^{54} +1.98749 q^{55} +(1.50451 - 2.17634i) q^{56} +(4.50285 - 1.37816i) q^{57} +(8.10076 - 6.79734i) q^{58} +(-2.66278 - 0.969171i) q^{59} +(0.112956 + 0.917637i) q^{60} +(-1.02770 + 5.82837i) q^{61} +(-0.770450 + 1.33446i) q^{62} +(6.83043 + 4.04292i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(3.08675 - 1.12348i) q^{65} +(-2.92951 - 5.74516i) q^{66} +(-2.89382 + 2.42820i) q^{67} +(-2.05253 - 0.747059i) q^{68} +(-1.40376 - 2.75296i) q^{69} +(-0.803101 + 1.16172i) q^{70} +(-4.58179 - 7.93590i) q^{71} +(2.48609 - 1.67910i) q^{72} +7.60381 q^{73} +(7.96558 + 6.68392i) q^{74} +(0.997748 + 8.10555i) q^{75} +(2.08269 - 1.74759i) q^{76} +(2.49246 - 9.53040i) q^{77} +(-7.79742 - 7.26676i) q^{78} +(11.3423 + 9.51730i) q^{79} +(0.266898 + 0.462282i) q^{80} +(5.54961 + 7.08533i) q^{81} +(-4.20150 + 7.27722i) q^{82} +(0.348371 - 1.97571i) q^{83} +(4.54191 + 0.609141i) q^{84} +(1.09563 + 0.398777i) q^{85} +(1.13340 + 6.42783i) q^{86} +(16.8622 + 7.15151i) q^{87} +(-2.85221 - 2.39329i) q^{88} +(-1.91914 - 3.32405i) q^{89} +(-1.32707 + 0.896297i) q^{90} +(-1.51631 - 16.2105i) q^{91} +(-1.36672 - 1.14682i) q^{92} +(-2.66530 - 0.138867i) q^{93} +(-8.02588 + 6.73451i) q^{94} +(-1.11173 + 0.932856i) q^{95} +(0.942899 - 1.45291i) q^{96} +(-5.72248 - 4.80173i) q^{97} +(4.56355 + 5.30792i) q^{98} +(6.55999 - 9.04065i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9}+O(q^{10}) \) 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9	\( 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9} - 6 q^{10} + 12 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} - 18 q^{19} - 30 q^{21} - 6 q^{22} + 30 q^{23} + 6 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} - 18 q^{35} + 9 q^{36} - 24 q^{39} - 6 q^{41} + 12 q^{42} + 24 q^{43} + 51 q^{45} + 45 q^{47} - 6 q^{48} - 12 q^{49} + 6 q^{50} - 51 q^{51} + 6 q^{52} - 15 q^{53} + 27 q^{54} + 72 q^{55} - 3 q^{56} - 63 q^{57} + 3 q^{58} - 30 q^{59} - 3 q^{60} + 9 q^{61} - 24 q^{62} - 39 q^{63} - 36 q^{64} + 9 q^{65} - 6 q^{67} + 9 q^{68} - 21 q^{69} - 33 q^{70} + 12 q^{71} - 12 q^{72} + 132 q^{73} - 18 q^{74} - 30 q^{75} - 33 q^{77} + 30 q^{78} - 9 q^{79} - 6 q^{80} + 36 q^{81} - 33 q^{82} - 18 q^{83} + 15 q^{84} + 21 q^{85} - 12 q^{86} - 39 q^{87} - 6 q^{88} - 36 q^{89} + 69 q^{90} + 39 q^{91} + 30 q^{92} - 66 q^{93} - 9 q^{94} - 33 q^{95} - 48 q^{97} - 12 q^{98} - 54 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9 - 6 * q^10 + 12 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 - 18 * q^19 - 30 * q^21 - 6 * q^22 + 30 * q^23 + 6 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 - 18 * q^35 + 9 * q^36 - 24 * q^39 - 6 * q^41 + 12 * q^42 + 24 * q^43 + 51 * q^45 + 45 * q^47 - 6 * q^48 - 12 * q^49 + 6 * q^50 - 51 * q^51 + 6 * q^52 - 15 * q^53 + 27 * q^54 + 72 * q^55 - 3 * q^56 - 63 * q^57 + 3 * q^58 - 30 * q^59 - 3 * q^60 + 9 * q^61 - 24 * q^62 - 39 * q^63 - 36 * q^64 + 9 * q^65 - 6 * q^67 + 9 * q^68 - 21 * q^69 - 33 * q^70 + 12 * q^71 - 12 * q^72 + 132 * q^73 - 18 * q^74 - 30 * q^75 - 33 * q^77 + 30 * q^78 - 9 * q^79 - 6 * q^80 + 36 * q^81 - 33 * q^82 - 18 * q^83 + 15 * q^84 + 21 * q^85 - 12 * q^86 - 39 * q^87 - 6 * q^88 - 36 * q^89 + 69 * q^90 + 39 * q^91 + 30 * q^92 - 66 * q^93 - 9 * q^94 - 33 * q^95 - 48 * q^97 - 12 * q^98 - 54 * q^99

Introduction

L-functions

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