LMFDB - Embedded newform 507.2.m.a.79.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(40,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("507.40");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.m (of order $13$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$15$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			79.5
Character	$\chi$	$=$	507.79
Dual form			507.2.m.a.430.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.890994 - 0.467630i) q^{2} +(0.970942 + 0.239316i) q^{3} +(-0.560937 - 0.812658i) q^{4} +(-1.54798 - 4.08168i) q^{5} +(-0.753192 - 0.667270i) q^{6} +(-0.324090 - 2.66912i) q^{7} +(0.362350 + 2.98422i) q^{8} +(0.885456 + 0.464723i) q^{9} +O(q^{10})$	\(q+(-0.890994 - 0.467630i) q^{2} +(0.970942 + 0.239316i) q^{3} +(-0.560937 - 0.812658i) q^{4} +(-1.54798 - 4.08168i) q^{5} +(-0.753192 - 0.667270i) q^{6} +(-0.324090 - 2.66912i) q^{7} +(0.362350 + 2.98422i) q^{8} +(0.885456 + 0.464723i) q^{9} +(-0.529477 + 4.36063i) q^{10} +(4.53045 - 2.37776i) q^{11} +(-0.350156 - 0.923284i) q^{12} +(-3.55448 + 0.604710i) q^{13} +(-0.959397 + 2.52972i) q^{14} +(-0.526186 - 4.33353i) q^{15} +(0.372346 - 0.981797i) q^{16} +(0.405256 + 3.33758i) q^{17} +(-0.571617 - 0.828131i) q^{18} -4.69861 q^{19} +(-2.44869 + 3.54754i) q^{20} +(0.324090 - 2.66912i) q^{21} -5.14852 q^{22} +5.66816 q^{23} +(-0.362350 + 2.98422i) q^{24} +(-10.5213 + 9.32109i) q^{25} +(3.44980 + 1.12339i) q^{26} +(0.748511 + 0.663123i) q^{27} +(-1.98729 + 1.76058i) q^{28} +(-4.48565 - 2.35425i) q^{29} +(-1.55766 + 4.10721i) q^{30} +(0.407265 + 0.360805i) q^{31} +(3.70938 - 3.28622i) q^{32} +(4.96784 - 1.22446i) q^{33} +(1.19967 - 3.16328i) q^{34} +(-10.3928 + 5.45457i) q^{35} +(-0.119024 - 0.980253i) q^{36} +(-0.581056 - 0.514770i) q^{37} +(4.18643 + 2.19721i) q^{38} +(-3.59591 - 0.263504i) q^{39} +(11.6197 - 6.09850i) q^{40} +(-3.17267 - 0.781994i) q^{41} +(-1.53692 + 2.22661i) q^{42} +(3.11859 - 2.76283i) q^{43} +(-4.47361 - 2.34793i) q^{44} +(0.526186 - 4.33353i) q^{45} +(-5.05030 - 2.65060i) q^{46} +(5.58868 - 8.09660i) q^{47} +(0.596486 - 0.864159i) q^{48} +(-0.222563 + 0.0548570i) q^{49} +(13.7333 - 3.38495i) q^{50} +(-0.405256 + 3.33758i) q^{51} +(2.48526 + 2.54937i) q^{52} +(-0.172948 - 1.42436i) q^{53} +(-0.356823 - 0.940864i) q^{54} +(-16.7183 - 14.8111i) q^{55} +(7.84780 - 1.93431i) q^{56} +(-4.56208 - 1.12445i) q^{57} +(2.89577 + 4.19524i) q^{58} +(3.60390 + 9.50270i) q^{59} +(-3.22652 + 2.85845i) q^{60} +(0.438888 - 3.61457i) q^{61} +(-0.194147 - 0.511925i) q^{62} +(0.953434 - 2.51400i) q^{63} +(-6.88080 + 1.69597i) q^{64} +(7.97049 + 13.5722i) q^{65} +(-4.99891 - 1.23212i) q^{66} +(5.48230 - 7.94248i) q^{67} +(2.48499 - 2.20151i) q^{68} +(5.50346 + 1.35648i) q^{69} +11.8106 q^{70} +(-7.93582 - 1.95600i) q^{71} +(-1.06599 + 2.81079i) q^{72} +(-9.30115 + 4.88162i) q^{73} +(0.276995 + 0.730376i) q^{74} +(-12.4463 + 6.53232i) q^{75} +(2.63562 + 3.81836i) q^{76} +(-7.81480 - 11.3217i) q^{77} +(3.08071 + 1.91633i) q^{78} +(-7.29242 + 10.5649i) q^{79} -4.58377 q^{80} +(0.568065 + 0.822984i) q^{81} +(2.46115 + 2.18039i) q^{82} +(7.14071 - 1.76003i) q^{83} +(-2.35087 + 1.23383i) q^{84} +(12.9956 - 6.82063i) q^{85} +(-4.07063 + 1.00332i) q^{86} +(-3.79189 - 3.35933i) q^{87} +(8.73737 + 12.6583i) q^{88} -0.922521 q^{89} +(-2.49532 + 3.61509i) q^{90} +(2.76601 + 9.29134i) q^{91} +(-3.17948 - 4.60628i) q^{92} +(0.309084 + 0.447786i) q^{93} +(-8.76568 + 4.60059i) q^{94} +(7.27334 + 19.1782i) q^{95} +(4.38803 - 2.30302i) q^{96} +(-0.329017 + 0.867548i) q^{97} +(0.223955 + 0.0552000i) q^{98} +5.11652 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9}+O(q^{10}) $ 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9	\( 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9} - 2 q^{10} - 4 q^{11} + 15 q^{12} - 14 q^{13} + 6 q^{14} + 2 q^{15} - 15 q^{16} - 2 q^{17} - q^{18} + 2 q^{20} - 4 q^{21} - 28 q^{22} - 52 q^{23} - 3 q^{24} - 67 q^{25} - 40 q^{26} + 15 q^{27} - 4 q^{28} - 27 q^{29} + 2 q^{30} + 22 q^{31} - 5 q^{32} - 9 q^{33} + 63 q^{34} - 31 q^{35} - 15 q^{36} + 2 q^{37} + 65 q^{38} + q^{39} + 45 q^{40} - 6 q^{41} + 59 q^{42} - 60 q^{43} - 35 q^{44} - 2 q^{45} - 156 q^{46} + 15 q^{48} + 59 q^{49} - 51 q^{50} + 2 q^{51} + 66 q^{52} + 50 q^{53} + q^{54} + 55 q^{55} - 14 q^{56} - 13 q^{57} + 36 q^{58} + 92 q^{59} - 15 q^{60} + 6 q^{61} + 61 q^{62} + 4 q^{63} - 203 q^{64} - 54 q^{65} + 54 q^{66} + 86 q^{67} + 32 q^{68} + 112 q^{70} + 39 q^{71} + 3 q^{72} - 158 q^{73} - 80 q^{74} + 15 q^{75} + 130 q^{76} - 64 q^{77} + 66 q^{78} - 10 q^{79} - 310 q^{80} - 15 q^{81} + 59 q^{82} - 82 q^{83} + 4 q^{84} + 22 q^{85} - q^{86} + 40 q^{87} + 10 q^{88} + 2 q^{89} - 2 q^{90} - 100 q^{91} - 54 q^{92} + 43 q^{93} + 65 q^{94} + 58 q^{95} - 60 q^{96} + 16 q^{97} - 113 q^{98} - 30 q^{99}+O(q^{100}) \) 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9 - 2 * q^10 - 4 * q^11 + 15 * q^12 - 14 * q^13 + 6 * q^14 + 2 * q^15 - 15 * q^16 - 2 * q^17 - q^18 + 2 * q^20 - 4 * q^21 - 28 * q^22 - 52 * q^23 - 3 * q^24 - 67 * q^25 - 40 * q^26 + 15 * q^27 - 4 * q^28 - 27 * q^29 + 2 * q^30 + 22 * q^31 - 5 * q^32 - 9 * q^33 + 63 * q^34 - 31 * q^35 - 15 * q^36 + 2 * q^37 + 65 * q^38 + q^39 + 45 * q^40 - 6 * q^41 + 59 * q^42 - 60 * q^43 - 35 * q^44 - 2 * q^45 - 156 * q^46 + 15 * q^48 + 59 * q^49 - 51 * q^50 + 2 * q^51 + 66 * q^52 + 50 * q^53 + q^54 + 55 * q^55 - 14 * q^56 - 13 * q^57 + 36 * q^58 + 92 * q^59 - 15 * q^60 + 6 * q^61 + 61 * q^62 + 4 * q^63 - 203 * q^64 - 54 * q^65 + 54 * q^66 + 86 * q^67 + 32 * q^68 + 112 * q^70 + 39 * q^71 + 3 * q^72 - 158 * q^73 - 80 * q^74 + 15 * q^75 + 130 * q^76 - 64 * q^77 + 66 * q^78 - 10 * q^79 - 310 * q^80 - 15 * q^81 + 59 * q^82 - 82 * q^83 + 4 * q^84 + 22 * q^85 - q^86 + 40 * q^87 + 10 * q^88 + 2 * q^89 - 2 * q^90 - 100 * q^91 - 54 * q^92 + 43 * q^93 + 65 * q^94 + 58 * q^95 - 60 * q^96 + 16 * q^97 - 113 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{2}{13}\right)$

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 $

$2$	−0.890994	−	0.467630i	−0.630028	−	0.330664i	0.119305	−	0.992858i	$-0.461933\pi$
$2$	−0.890994	−	0.467630i	−0.630028	−	0.330664i	−0.749333	+	0.662194i	$0.769626\pi$
$3$	0.970942	+	0.239316i	0.560574	+	0.138169i
$3$	0.970942	+	0.239316i	0.560574	+	0.138169i
$4$	−0.560937	−	0.812658i	−0.280469	−	0.406329i
$5$	−1.54798	−	4.08168i	−0.692277	−	1.82538i	−0.549237	−	0.835667i	$-0.685081\pi$
$5$	−1.54798	−	4.08168i	−0.692277	−	1.82538i	−0.143040	−	0.989717i	$-0.545688\pi$
$6$	−0.753192	−	0.667270i	−0.307489	−	0.272412i
$7$	−0.324090	−	2.66912i	−0.122494	−	1.00883i	−0.916253	−	0.400599i	$-0.868802\pi$
$7$	−0.324090	−	2.66912i	−0.122494	−	1.00883i	0.793759	−	0.608232i	$-0.208121\pi$
$8$	0.362350	+	2.98422i	0.128110	+	1.05508i
$9$	0.885456	+	0.464723i	0.295152	+	0.154908i
$10$	−0.529477	+	4.36063i	−0.167435	+	1.37895i
$11$	4.53045	−	2.37776i	1.36598	−	0.716923i	0.387233	−	0.921982i	$-0.373431\pi$
$11$	4.53045	−	2.37776i	1.36598	−	0.716923i	0.978750	+	0.205059i	$0.0657388\pi$
$12$	−0.350156	−	0.923284i	−0.101081	−	0.266529i
$13$	−3.55448	+	0.604710i	−0.985835	+	0.167716i
$13$	−3.55448	+	0.604710i	−0.985835	+	0.167716i
$14$	−0.959397	+	2.52972i	−0.256410	+	0.676096i
$15$	−0.526186	−	4.33353i	−0.135861	−	1.11891i
$16$	0.372346	−	0.981797i	0.0930866	−	0.245449i
$17$	0.405256	+	3.33758i	0.0982890	+	0.809483i	0.955596	+	0.294678i	$0.0952125\pi$
$17$	0.405256	+	3.33758i	0.0982890	+	0.809483i	−0.857307	+	0.514805i	$0.827864\pi$
$18$	−0.571617	−	0.828131i	−0.134732	−	0.195192i
$19$	−4.69861			−1.07793			−0.538967	−	0.842327i	$-0.681185\pi$
$19$	−4.69861			−1.07793			−0.538967	+	0.842327i	$0.681185\pi$
$20$	−2.44869	+	3.54754i	−0.547544	+	0.793255i
$21$	0.324090	−	2.66912i	0.0707221	−	0.582449i
$22$	−5.14852			−1.09767
$23$	5.66816			1.18189			0.590947	−	0.806710i	$-0.298754\pi$
$23$	5.66816			1.18189			0.590947	+	0.806710i	$0.298754\pi$
$24$	−0.362350	+	2.98422i	−0.0739643	+	0.609151i
$25$	−10.5213	+	9.32109i	−2.10427	+	1.86422i
$26$	3.44980	+	1.12339i	0.676561	+	0.220314i
$27$	0.748511	+	0.663123i	0.144051	+	0.127618i
$28$	−1.98729	+	1.76058i	−0.375562	+	0.332719i
$29$	−4.48565	−	2.35425i	−0.832964	−	0.437173i	−0.00637519	−	0.999980i	$-0.502029\pi$
$29$	−4.48565	−	2.35425i	−0.832964	−	0.437173i	−0.826589	+	0.562807i	$0.809722\pi$
$30$	−1.55766	+	4.10721i	−0.284388	+	0.749870i
$31$	0.407265	+	0.360805i	0.0731470	+	0.0648026i	0.698904	−	0.715215i	$-0.253671\pi$
$31$	0.407265	+	0.360805i	0.0731470	+	0.0648026i	−0.625757	+	0.780018i	$0.715210\pi$
$32$	3.70938	−	3.28622i	0.655731	−	0.580927i
$33$	4.96784	−	1.22446i	0.864790	−	0.213152i
$34$	1.19967	−	3.16328i	0.205742	−	0.542497i
$35$	−10.3928	+	5.45457i	−1.75671	+	0.921990i
$36$	−0.119024	−	0.980253i	−0.0198374	−	0.163376i
$37$	−0.581056	−	0.514770i	−0.0955249	−	0.0846277i	0.614009	−	0.789299i	$-0.289556\pi$
$37$	−0.581056	−	0.514770i	−0.0955249	−	0.0846277i	−0.709534	+	0.704671i	$0.751094\pi$
$38$	4.18643	+	2.19721i	0.679129	+	0.356434i
$39$	−3.59591	−	0.263504i	−0.575806	−	0.0421945i
$40$	11.6197	−	6.09850i	1.83724	−	0.964258i
$41$	−3.17267	−	0.781994i	−0.495488	−	0.122127i	−0.0163500	−	0.999866i	$-0.505205\pi$
$41$	−3.17267	−	0.781994i	−0.495488	−	0.122127i	−0.479138	+	0.877739i	$0.659051\pi$
$42$	−1.53692	+	2.22661i	−0.237152	+	0.343574i
$43$	3.11859	−	2.76283i	0.475581	−	0.421328i	−0.390980	−	0.920399i	$-0.627864\pi$
$43$	3.11859	−	2.76283i	0.475581	−	0.421328i	0.866561	+	0.499071i	$0.166325\pi$
$44$	−4.47361	−	2.34793i	−0.674421	−	0.353964i
$45$	0.526186	−	4.33353i	0.0784392	−	0.646005i
$46$	−5.05030	−	2.65060i	−0.744626	−	0.390810i
$47$	5.58868	−	8.09660i	0.815192	−	1.18101i	−0.165646	−	0.986185i	$-0.552971\pi$
$47$	5.58868	−	8.09660i	0.815192	−	1.18101i	0.980838	−	0.194825i	$-0.0624138\pi$
$48$	0.596486	−	0.864159i	0.0860953	−	0.124731i
$49$	−0.222563	+	0.0548570i	−0.0317948	+	0.00783671i
$50$	13.7333	−	3.38495i	1.94218	−	0.478704i
$51$	−0.405256	+	3.33758i	−0.0567472	+	0.467355i
$52$	2.48526	+	2.54937i	0.344644	+	0.353534i
$53$	−0.172948	−	1.42436i	−0.0237563	−	0.195651i	0.975999	−	0.217775i	$-0.0698800\pi$
$53$	−0.172948	−	1.42436i	−0.0237563	−	0.195651i	−0.999755	+	0.0221247i	$0.992957\pi$
$54$	−0.356823	−	0.940864i	−0.0485574	−	0.128035i
$55$	−16.7183	−	14.8111i	−2.25430	−	1.99713i
$56$	7.84780	−	1.93431i	1.04871	−	0.258483i
$57$	−4.56208	−	1.12445i	−0.604262	−	0.148937i
$58$	2.89577	+	4.19524i	0.380233	+	0.550862i
$59$	3.60390	+	9.50270i	0.469188	+	1.23715i	0.935752	+	0.352659i	$0.114722\pi$
$59$	3.60390	+	9.50270i	0.469188	+	1.23715i	−0.466564	+	0.884487i	$0.654508\pi$
$60$	−3.22652	+	2.85845i	−0.416542	+	0.369024i
$61$	0.438888	−	3.61457i	0.0561939	−	0.462798i	−0.937266	−	0.348615i	$-0.886652\pi$
$61$	0.438888	−	3.61457i	0.0561939	−	0.462798i	0.993460	−	0.114183i	$-0.0364250\pi$
$62$	−0.194147	−	0.511925i	−0.0246567	−	0.0650145i
$63$	0.953434	−	2.51400i	0.120121	−	0.316734i
$64$	−6.88080	+	1.69597i	−0.860100	+	0.211996i
$65$	7.97049	+	13.5722i	0.988618	+	1.68342i
$66$	−4.99891	−	1.23212i	−0.615323	−	0.151664i
$67$	5.48230	−	7.94248i	0.669769	−	0.970329i	−0.329884	−	0.944021i	$-0.607010\pi$
$67$	5.48230	−	7.94248i	0.669769	−	0.970329i	0.999654	−	0.0263072i	$-0.00837481\pi$
$68$	2.48499	−	2.20151i	0.301349	−	0.266972i
$69$	5.50346	+	1.35648i	0.662539	+	0.163301i
$70$	11.8106			1.41164
$71$	−7.93582	−	1.95600i	−0.941808	−	0.232135i	−0.261619	−	0.965171i	$-0.584256\pi$
$71$	−7.93582	−	1.95600i	−0.941808	−	0.232135i	−0.680190	+	0.733036i	$0.738103\pi$
$72$	−1.06599	+	2.81079i	−0.125628	+	0.331254i
$73$	−9.30115	+	4.88162i	−1.08862	+	0.571350i	−0.910856	−	0.412724i	$-0.864578\pi$
$73$	−9.30115	+	4.88162i	−1.08862	+	0.571350i	−0.177760	+	0.984074i	$0.556885\pi$
$74$	0.276995	+	0.730376i	0.0322000	+	0.0849045i
$75$	−12.4463	+	6.53232i	−1.43717	+	0.754287i
$76$	2.63562	+	3.81836i	0.302327	+	0.437996i
$77$	−7.81480	−	11.3217i	−0.890579	−	1.29023i
$78$	3.08071	+	1.91633i	0.348822	+	0.216982i
$79$	−7.29242	+	10.5649i	−0.820461	+	1.18864i	0.159053	+	0.987270i	$0.449156\pi$
$79$	−7.29242	+	10.5649i	−0.820461	+	1.18864i	−0.979515	+	0.201374i	$0.935459\pi$
$80$	−4.58377			−0.512481
$81$	0.568065	+	0.822984i	0.0631183	+	0.0914427i
$82$	2.46115	+	2.18039i	0.271788	+	0.240784i
$83$	7.14071	−	1.76003i	0.783795	−	0.193188i	0.172942	−	0.984932i	$-0.444673\pi$
$83$	7.14071	−	1.76003i	0.783795	−	0.193188i	0.610853	+	0.791744i	$0.290827\pi$
$84$	−2.35087	+	1.23383i	−0.256501	+	0.134622i
$85$	12.9956	−	6.82063i	1.40957	−	0.739802i
$86$	−4.07063	+	1.00332i	−0.438947	+	0.108191i
$87$	−3.79189	−	3.35933i	−0.406534	−	0.360157i
$88$	8.73737	+	12.6583i	0.931407	+	1.34938i
$89$	−0.922521			−0.0977870			−0.0488935	−	0.998804i	$-0.515569\pi$
$89$	−0.922521			−0.0977870			−0.0488935	+	0.998804i	$0.515569\pi$
$90$	−2.49532	+	3.61509i	−0.263029	+	0.381064i
$91$	2.76601	+	9.29134i	0.289957	+	0.973998i
$92$	−3.17948	−	4.60628i	−0.331484	−	0.480238i
$93$	0.309084	+	0.447786i	0.0320506	+	0.0464332i
$94$	−8.76568	+	4.60059i	−0.904111	+	0.474514i
$95$	7.27334	+	19.1782i	0.746229	+	1.96764i
$96$	4.38803	−	2.30302i	0.447852	−	0.235051i
$97$	−0.329017	+	0.867548i	−0.0334067	+	0.0880861i	−0.950682	−	0.310168i	$-0.899615\pi$
$97$	−0.329017	+	0.867548i	−0.0334067	+	0.0880861i	0.917275	+	0.398254i	$0.130384\pi$
$98$	0.223955	+	0.0552000i	0.0226229	+	0.00557605i
$99$	5.11652			0.514229
$100$	13.4767	+	3.32170i	1.34767	+	0.332170i
$101$	2.48147	−	2.19839i	0.246916	−	0.218748i	−0.530583	−	0.847633i	$-0.678027\pi$
$101$	2.48147	−	2.19839i	0.246916	−	0.218748i	0.777498	+	0.628885i	$0.216488\pi$
$102$	1.92183	−	2.78426i	0.190290	−	0.275683i
$103$	−8.85148	−	2.18169i	−0.872163	−	0.214969i	−0.222261	−	0.974987i	$-0.571344\pi$
$103$	−8.85148	−	2.18169i	−0.872163	−	0.214969i	−0.649902	+	0.760018i	$0.725190\pi$
$104$	−3.09255	−	10.3882i	−0.303250	−	1.01865i
$105$	−11.3962	+	2.80890i	−1.11215	+	0.274121i
$106$	−0.511976	+	1.34997i	−0.0497275	+	0.131121i
$107$	−0.800299	−	2.11022i	−0.0773678	−	0.204002i	0.890752	−	0.454490i	$-0.150178\pi$
$107$	−0.800299	−	2.11022i	−0.0773678	−	0.204002i	−0.968120	+	0.250487i	$0.919409\pi$
$108$	0.119024	−	0.980253i	0.0114531	−	0.0943249i
$109$	9.63922	−	8.53960i	0.923270	−	0.817946i	−0.0603543	−	0.998177i	$-0.519223\pi$
$109$	9.63922	−	8.53960i	0.923270	−	0.817946i	0.983624	+	0.180231i	$0.0576846\pi$
$110$	7.96979	+	21.0146i	0.759889	+	2.00366i
$111$	−0.440979	−	0.638868i	−0.0418558	−	0.0606386i
$112$	−2.74120	−	0.675646i	−0.259019	−	0.0638426i
$113$	12.5362	−	3.08989i	1.17931	−	0.290673i	0.399523	−	0.916723i	$-0.369176\pi$
$113$	12.5362	−	3.08989i	1.17931	−	0.290673i	0.779783	+	0.626050i	$0.215330\pi$
$114$	3.53895	+	3.13524i	0.331453	+	0.293642i
$115$	−8.77419	−	23.1356i	−0.818198	−	2.15741i
$116$	0.602967	+	4.96588i	0.0559841	+	0.461071i
$117$	−3.42836	−	1.11640i	−0.316952	−	0.103212i
$118$	1.23269	−	10.1521i	0.113479	−	0.934580i
$119$	8.77707	−	2.16335i	0.804592	−	0.198314i
$120$	12.7415	−	3.14051i	1.16314	−	0.286688i
$121$	8.62251	−	12.4919i	0.783864	−	1.13562i
$122$	−2.08133	+	3.01532i	−0.188434	+	0.272994i
$123$	−2.89334	−	1.51854i	−0.260883	−	0.136922i
$124$	0.0647612	−	0.533356i	0.00581573	−	0.0478968i
$125$	35.0059	+	18.3725i	3.13102	+	1.64329i
$126$	−2.02512	+	1.79410i	−0.180412	+	0.159831i
$127$	6.78781	−	9.83384i	0.602320	−	0.872612i	−0.396650	−	0.917970i	$-0.629827\pi$
$127$	6.78781	−	9.83384i	0.602320	−	0.872612i	0.998971	+	0.0453579i	$0.0144428\pi$
$128$	−2.69951	−	0.665369i	−0.238605	−	0.0588108i
$129$	3.68916	−	1.93622i	0.324813	−	0.170475i
$130$	−0.754905	−	15.8200i	−0.0662095	−	1.38750i
$131$	−20.2179	−	10.6112i	−1.76645	−	0.927103i	−0.916201	−	0.400719i	$-0.868760\pi$
$131$	−20.2179	−	10.6112i	−1.76645	−	0.927103i	−0.850247	−	0.526384i	$-0.823547\pi$
$132$	−3.78171	−	3.35031i	−0.329156	−	0.291607i
$133$	1.52277	+	12.5411i	0.132041	+	1.08745i
$134$	−8.59883	+	4.51302i	−0.742826	+	0.389865i
$135$	1.54798	−	4.08168i	0.133229	−	0.351295i
$136$	−9.81324	+	2.41875i	−0.841478	+	0.207406i
$137$	8.51262	−	7.54152i	0.727282	−	0.644316i	−0.215967	−	0.976401i	$-0.569290\pi$
$137$	8.51262	−	7.54152i	0.727282	−	0.644316i	0.943250	+	0.332085i	$0.107752\pi$
$138$	−4.26922	−	3.78220i	−0.363420	−	0.321962i
$139$	4.42304	−	11.6626i	0.375157	−	0.989209i	−0.605908	−	0.795534i	$-0.707190\pi$
$139$	4.42304	−	11.6626i	0.375157	−	0.989209i	0.981066	−	0.193674i	$-0.0620406\pi$
$140$	10.2624	+	5.38613i	0.867332	+	0.455211i
$141$	7.36392	−	6.52387i	0.620154	−	0.549409i
$142$	6.15608	+	5.45381i	0.516607	+	0.457674i
$143$	−14.6655	+	11.1913i	−1.22639	+	0.935865i
$144$	0.785960	−	0.696300i	0.0654967	−	0.0580250i
$145$	−2.66561	+	21.9533i	−0.221367	+	1.82312i
$146$	10.5701			0.874784
$147$	−0.229224			−0.0189061
$148$	−0.0923964	+	0.760953i	−0.00759494	+	0.0625499i
$149$	2.80277	−	4.06052i	0.229612	−	0.332650i	−0.691195	−	0.722668i	$-0.742916\pi$
$149$	2.80277	−	4.06052i	0.229612	−	0.332650i	0.920807	+	0.390017i	$0.127531\pi$
$150$	14.1443			1.15488
$151$	−2.10380	−	3.04788i	−0.171205	−	0.248033i	0.727984	−	0.685594i	$-0.240458\pi$
$151$	−2.10380	−	3.04788i	−0.171205	−	0.248033i	−0.899188	+	0.437562i	$0.855842\pi$
$152$	−1.70254	−	14.0217i	−0.138094	−	1.13731i
$153$	−1.19222	+	3.14362i	−0.0963850	+	0.254146i
$154$	1.66858	+	13.7420i	0.134458	+	1.10736i
$155$	0.842256	−	2.22085i	0.0676516	−	0.178383i
$156$	1.80294	+	3.07005i	0.144351	+	0.245801i
$157$	5.78491	+	15.2536i	0.461686	+	1.21737i	0.940604	+	0.339507i	$0.110260\pi$
$157$	5.78491	+	15.2536i	0.461686	+	1.21737i	−0.478917	+	0.877860i	$0.658971\pi$
$158$	11.4380	−	6.00310i	0.909955	−	0.477581i
$159$	0.172948	−	1.42436i	0.0137157	−	0.112959i
$160$	−19.1553	−	10.0535i	−1.51436	−	0.794799i
$161$	−1.83699	−	15.1290i	−0.144775	−	1.19233i
$162$	−0.121291	−	0.998917i	−0.00952948	−	0.0784824i
$163$	0.322891	+	0.286057i	0.0252908	+	0.0224057i	0.675673	−	0.737201i	$-0.263853\pi$
$163$	0.322891	+	0.286057i	0.0252908	+	0.0224057i	−0.650383	+	0.759607i	$0.725391\pi$
$164$	1.14418	+	3.01695i	0.0893452	+	0.235584i
$165$	−12.6880	−	18.3817i	−0.987757	−	1.43101i
$166$	−7.18537	−	1.77103i	−0.557693	−	0.137459i
$167$	2.68372	+	1.40852i	0.207672	+	0.108995i	0.565353	−	0.824849i	$-0.308740\pi$
$167$	2.68372	+	1.40852i	0.207672	+	0.108995i	−0.357680	+	0.933844i	$0.616432\pi$
$168$	8.08266			0.623591
$169$	12.2687	−	4.29886i	0.943742	−	0.330682i
$170$	−14.7686			−1.13270
$171$	−4.16041	−	2.18355i	−0.318155	−	0.166980i
$172$	−3.99457	−	0.984573i	−0.304583	−	0.0750730i
$173$	−9.40054	−	13.6190i	−0.714710	−	1.03544i	−0.997097	−	0.0761353i	$-0.975742\pi$
$173$	−9.40054	−	13.6190i	−0.714710	−	1.03544i	0.282388	−	0.959300i	$-0.408873\pi$
$174$	1.80763	+	4.76634i	0.137036	+	0.361335i
$175$	28.2890	+	25.0618i	2.13844	+	1.89450i
$176$	−0.647584	−	5.33333i	−0.0488135	−	0.402015i
$177$	1.22503	+	10.0890i	0.0920790	+	0.758339i
$178$	0.821960	+	0.431398i	0.0616085	+	0.0323346i
$179$	−2.46245	+	20.2801i	−0.184052	+	1.51581i	0.549107	+	0.835752i	$0.314968\pi$
$179$	−2.46245	+	20.2801i	−0.184052	+	1.51581i	−0.733160	+	0.680057i	$0.761955\pi$
$180$	−3.81683	+	2.00323i	−0.284490	+	0.149312i
$181$	−4.91319	−	12.9550i	−0.365194	−	0.962939i	−0.984122	−	0.177491i	$-0.943202\pi$
$181$	−4.91319	−	12.9550i	−0.365194	−	0.962939i	0.618928	−	0.785448i	$-0.287567\pi$
$182$	1.88041	−	9.57200i	0.139385	−	0.709524i
$183$	1.29116	−	3.40450i	0.0954451	−	0.251668i
$184$	2.05386	+	16.9150i	0.151412	+	1.24699i
$185$	−1.20167	+	3.16854i	−0.0883484	+	0.232955i
$186$	−0.0659942	−	0.543512i	−0.00483893	−	0.0398522i
$187$	9.77198	+	14.1572i	0.714598	+	1.03527i
$188$	−9.71466			−0.708514
$189$	1.52737	−	2.21277i	0.111100	−	0.160956i
$190$	2.48780	−	20.4889i	0.180484	−	1.48642i
$191$	21.6063			1.56338			0.781688	−	0.623670i	$-0.214359\pi$
$191$	21.6063			1.56338			0.781688	+	0.623670i	$0.214359\pi$
$192$	−7.08673			−0.511441
$193$	−1.81857	+	14.9773i	−0.130904	+	1.07809i	0.768155	+	0.640263i	$0.221175\pi$
$193$	−1.81857	+	14.9773i	−0.130904	+	1.07809i	−0.899059	+	0.437827i	$0.855748\pi$
$194$	0.698844	−	0.619121i	0.0501740	−	0.0444503i
$195$	4.49085	+	15.0853i	0.321596	+	1.08028i
$196$	0.169424	+	0.150097i	0.0121017	+	0.0107212i
$197$	11.7502	−	10.4098i	0.837169	−	0.741667i	−0.131156	−	0.991362i	$-0.541869\pi$
$197$	11.7502	−	10.4098i	0.837169	−	0.741667i	0.968325	+	0.249695i	$0.0803303\pi$
$198$	−4.55878	−	2.39263i	−0.323979	−	0.170037i
$199$	0.523720	−	1.38094i	0.0371255	−	0.0978920i	−0.915171	−	0.403065i	$-0.867945\pi$
$199$	0.523720	−	1.38094i	0.0371255	−	0.0978920i	0.952297	+	0.305173i	$0.0987142\pi$
$200$	−31.6286	−	28.0205i	−2.23648	−	1.98135i
$201$	7.22375	−	6.39969i	0.509524	−	0.451399i
$202$	−3.23901	+	0.798345i	−0.227896	+	0.0561713i
$203$	−4.83002	+	12.7357i	−0.339001	+	0.893872i
$204$	2.93964	−	1.54284i	0.205816	−	0.108020i
$205$	1.71938	+	14.1604i	0.120087	+	0.989002i
$206$	6.86639	+	6.08309i	0.478404	+	0.423829i
$207$	5.01891	+	2.63413i	0.348838	+	0.183085i
$208$	−0.729795	+	3.71494i	−0.0506022	+	0.257585i
$209$	−21.2868	+	11.1722i	−1.47244	+	0.772796i
$210$	11.4674	+	2.82647i	0.791329	+	0.195045i
$211$	−0.0364980	+	0.0528764i	−0.00251262	+	0.00364016i	−0.824238	−	0.566243i	$-0.808396\pi$
$211$	−0.0364980	+	0.0528764i	−0.00251262	+	0.00364016i	0.821726	+	0.569883i	$0.193012\pi$
$212$	−1.06050	+	0.939523i	−0.0728356	+	0.0645267i
$213$	−7.23712	−	3.79833i	−0.495879	−	0.260257i
$214$	−0.273738	+	2.25443i	−0.0187123	+	0.154110i
$215$	−16.1045	−	8.45230i	−1.09832	−	0.576442i
$216$	−1.70768	+	2.47400i	−0.116193	+	0.168335i
$217$	0.831042	−	1.20397i	0.0564148	−	0.0817309i
$218$	−12.5819	+	3.10115i	−0.852151	+	0.210036i
$219$	−10.1991	+	2.51386i	−0.689193	+	0.169871i
$220$	−2.65846	+	21.8944i	−0.179233	+	1.47612i
$221$	−3.45875	−	11.6183i	−0.232660	−	0.781532i
$222$	0.0941557	+	0.775442i	0.00631931	+	0.0520442i
$223$	−0.607771	−	1.60256i	−0.0406993	−	0.107315i	0.913126	−	0.407678i	$-0.133661\pi$
$223$	−0.607771	−	1.60256i	−0.0406993	−	0.107315i	−0.953825	+	0.300363i	$0.902892\pi$
$224$	−9.97348	−	8.83573i	−0.666381	−	0.590362i
$225$	−13.6479	+	3.36391i	−0.909861	+	0.224261i
$226$	−12.6146	−	3.10922i	−0.839110	−	0.206822i
$227$	−10.5384	−	15.2676i	−0.699460	−	1.01334i	−0.998256	−	0.0590262i	$-0.981200\pi$
$227$	−10.5384	−	15.2676i	−0.699460	−	1.01334i	0.298796	−	0.954317i	$-0.403415\pi$
$228$	1.64524	+	4.33815i	0.108959	+	0.287301i
$229$	2.14603	−	1.90122i	0.141814	−	0.125636i	−0.589234	−	0.807963i	$-0.700570\pi$
$229$	2.14603	−	1.90122i	0.141814	−	0.125636i	0.731047	+	0.682327i	$0.239032\pi$
$230$	−3.00116	+	24.7168i	−0.197891	+	1.62978i
$231$	−4.87826	−	12.8629i	−0.320966	−	0.846318i
$232$	5.40022	−	14.2392i	0.354542	−	0.934850i
$233$	−19.4557	+	4.79539i	−1.27458	+	0.314156i	−0.817841	−	0.575444i	$-0.804829\pi$
$233$	−19.4557	+	4.79539i	−1.27458	+	0.314156i	−0.456741	+	0.889600i	$0.650983\pi$
$234$	2.53258	+	2.59791i	0.165560	+	0.169831i
$235$	−41.6989	−	10.2779i	−2.72013	−	0.670453i
$236$	5.70088	−	8.25915i	0.371096	−	0.537625i
$237$	−9.60886	+	8.51271i	−0.624163	+	0.552960i
$238$	−8.83196	−	2.17688i	−0.572491	−	0.141106i
$239$	2.55860			0.165502			0.0827509	−	0.996570i	$-0.473629\pi$
$239$	2.55860			0.165502			0.0827509	+	0.996570i	$0.473629\pi$
$240$	−4.45057	−	1.09697i	−0.287283	−	0.0708089i
$241$	−2.04295	+	5.38682i	−0.131598	+	0.346996i	−0.984578	−	0.174949i	$-0.944024\pi$
$241$	−2.04295	+	5.38682i	−0.131598	+	0.346996i	0.852979	+	0.521945i	$0.174793\pi$
$242$	−13.5242	+	7.09803i	−0.869366	+	0.456278i
$243$	0.354605	+	0.935016i	0.0227479	+	0.0599813i
$244$	−3.18360	+	1.67088i	−0.203809	+	0.106967i
$245$	0.568432	+	0.823516i	0.0363158	+	0.0526125i
$246$	1.86783	+	2.70602i	0.119089	+	0.172530i
$247$	16.7011	−	2.84130i	1.06267	−	0.180787i
$248$	−0.929150	+	1.34611i	−0.0590011	+	0.0854778i
$249$	7.35442			0.466067
$250$	−22.5985	−	32.7396i	−1.42925	−	2.07063i
$251$	19.2408	+	17.0459i	1.21447	+	1.07593i	0.994955	+	0.100319i	$0.0319863\pi$
$251$	19.2408	+	17.0459i	1.21447	+	1.07593i	0.219516	+	0.975609i	$0.429552\pi$
$252$	−2.57784	+	0.635380i	−0.162388	+	0.0400252i
$253$	25.6793	−	13.4776i	1.61445	−	0.847327i
$254$	−10.6465	+	5.58771i	−0.668020	+	0.350604i
$255$	14.2503	−	3.51238i	0.892388	−	0.219954i
$256$	12.7031	+	11.2540i	0.793943	+	0.703372i
$257$	−3.55677	−	5.15287i	−0.221865	−	0.321427i	0.696206	−	0.717842i	$-0.254870\pi$
$257$	−3.55677	−	5.15287i	−0.221865	−	0.321427i	−0.918072	+	0.396414i	$0.870254\pi$
$258$	−4.19245			−0.261011
$259$	−1.18567	+	1.71774i	−0.0736739	+	0.106735i
$260$	6.55859	−	14.0904i	0.406747	−	0.873851i
$261$	−2.87777	−	4.16917i	−0.178129	−	0.258065i
$262$	13.0519	+	18.9090i	0.806351	+	1.16820i
$263$	7.37511	−	3.87076i	0.454769	−	0.238681i	−0.221754	−	0.975103i	$-0.571178\pi$
$263$	7.37511	−	3.87076i	0.454769	−	0.238681i	0.676523	+	0.736421i	$0.263486\pi$
$264$	5.45416	+	14.3814i	0.335680	+	0.885116i
$265$	−5.54606	+	2.91079i	−0.340691	+	0.178809i
$266$	4.50783	−	11.8862i	0.276393	−	0.728788i
$267$	−0.895714	−	0.220774i	−0.0548168	−	0.0135111i
$268$	−9.52974			−0.582122
$269$	0.180960	+	0.0446026i	0.0110333	+	0.00271947i	0.244828	−	0.969566i	$-0.421268\pi$
$269$	0.180960	+	0.0446026i	0.0110333	+	0.00271947i	−0.233795	+	0.972286i	$0.575115\pi$
$270$	−3.28795	+	2.91287i	−0.200099	+	0.177272i
$271$	−12.2498	+	17.7470i	−0.744125	+	1.07805i	0.249833	+	0.968289i	$0.419624\pi$
$271$	−12.2498	+	17.7470i	−0.744125	+	1.07805i	−0.993958	+	0.109762i	$0.964991\pi$
$272$	3.42773	+	0.844858i	0.207836	+	0.0512271i
$273$	0.462073	+	9.68331i	0.0279659	+	0.586060i
$274$	−11.1113	+	2.73870i	−0.671260	+	0.165451i
$275$	−25.5030	+	67.2460i	−1.53789	+	4.05509i
$276$	−1.98474	−	5.23333i	−0.119467	−	0.315009i
$277$	2.16070	−	17.7950i	0.129824	−	1.06920i	−0.771555	−	0.636163i	$-0.780521\pi$
$277$	2.16070	−	17.7950i	0.129824	−	1.06920i	0.901378	−	0.433032i	$-0.142556\pi$
$278$	−9.39468	+	8.32296i	−0.563455	+	0.499178i
$279$	0.192941	+	0.508743i	0.0115511	+	0.0304576i
$280$	−20.0434	−	29.0379i	−1.19783	−	1.73535i
$281$	−21.1453	−	5.21185i	−1.26142	−	0.310913i	−0.448763	−	0.893651i	$-0.648135\pi$
$281$	−21.1453	−	5.21185i	−1.26142	−	0.310913i	−0.812660	+	0.582738i	$0.801981\pi$
$282$	−9.61196	+	2.36914i	−0.572384	+	0.141080i
$283$	0.0469122	+	0.0415606i	0.00278864	+	0.00247052i	0.664516	−	0.747274i	$-0.268638\pi$
$283$	0.0469122	+	0.0415606i	0.00278864	+	0.00247052i	−0.661727	+	0.749745i	$0.730176\pi$
$284$	2.86193	+	7.54630i	0.169825	+	0.447790i
$285$	2.47234	+	20.3616i	0.146449	+	1.20612i
$286$	18.3003	−	3.11336i	1.08212	−	0.184097i
$287$	−1.05900	+	8.72168i	−0.0625110	+	0.514824i
$288$	4.81167	−	1.18597i	0.283530	−	0.0698840i
$289$	5.53077	−	1.36321i	0.325340	−	0.0801890i
$290$	12.6411	−	18.3137i	0.742309	−	1.07542i
$291$	−0.527075	+	0.763599i	−0.0308977	+	0.0447630i
$292$	9.18444	+	4.82037i	0.537479	+	0.282091i
$293$	1.91419	−	15.7648i	0.111828	−	0.920987i	−0.823527	−	0.567277i	$-0.807997\pi$
$293$	1.91419	−	15.7648i	0.111828	−	0.920987i	0.935355	−	0.353710i	$-0.115080\pi$
$294$	0.204237	+	0.107192i	0.0119114	+	0.00625157i
$295$	33.2083	−	29.4199i	1.93346	−	1.71290i
$296$	1.32564	−	1.92052i	0.0770514	−	0.111628i
$297$	4.96784	+	1.22446i	0.288263	+	0.0710505i
$298$	−4.39607	+	2.30724i	−0.254658	+	0.133655i
$299$	−20.1474	+	3.42760i	−1.16515	+	0.198223i
$300$	12.2901	+	6.45036i	0.709571	+	0.372411i
$301$	−8.38503	−	7.42849i	−0.483305	−	0.428171i
$302$	0.449193	+	3.69944i	0.0258481	+	0.212879i
$303$	2.93548	−	1.54066i	0.168639	−	0.0885084i
$304$	−1.74951	+	4.61308i	−0.100341	+	0.264578i
$305$	−15.4329	+	3.80387i	−0.883686	+	0.217809i
$306$	2.53231	−	2.24343i	0.144762	−	0.128248i
$307$	−2.67058	−	2.36593i	−0.152418	−	0.135031i	0.583468	−	0.812136i	$-0.301695\pi$
$307$	−2.67058	−	2.36593i	−0.152418	−	0.135031i	−0.735886	+	0.677106i	$0.763234\pi$
$308$	−4.81705	+	12.7015i	−0.274477	+	0.723736i
$309$	−8.07216	−	4.23660i	−0.459209	−	0.241012i
$310$	−1.78898	+	1.58490i	−0.101607	+	0.0900160i
$311$	12.6497	+	11.2066i	0.717296	+	0.635469i	0.940693	−	0.339259i	$-0.110176\pi$
$311$	12.6497	+	11.2066i	0.717296	+	0.635469i	−0.223397	+	0.974728i	$0.571715\pi$
$312$	−0.516623	−	10.8265i	−0.0292480	−	0.612928i
$313$	18.6005	−	16.4786i	1.05136	−	0.931425i	0.0536176	−	0.998562i	$-0.482925\pi$
$313$	18.6005	−	16.4786i	1.05136	−	0.931425i	0.997744	+	0.0671367i	$0.0213864\pi$
$314$	1.97870	−	16.2960i	0.111664	−	0.919638i
$315$	−11.7372			−0.661318
$316$	12.6762			0.713094
$317$	1.91452	−	15.7675i	0.107530	−	0.885592i	−0.834718	−	0.550678i	$-0.814369\pi$
$317$	1.91452	−	15.7675i	0.107530	−	0.885592i	0.942248	−	0.334915i	$-0.108708\pi$
$318$	−0.820168	+	1.18822i	−0.0459927	+	0.0666320i
$319$	−25.9199			−1.45123
$320$	17.5737	+	25.4599i	0.982401	+	1.42325i
$321$	−0.272036	−	2.24042i	−0.0151836	−	0.125048i
$322$	−5.43802	+	14.3389i	−0.303049	+	0.799074i
$323$	−1.90414	−	15.6820i	−0.105949	−	0.872570i
$324$	0.350156	−	0.923284i	0.0194531	−	0.0512936i
$325$	31.7613	−	39.4940i	1.76180	−	2.19073i
$326$	−0.153925	−	0.405868i	−0.00852514	−	0.0224790i
$327$	11.4028	−	5.98464i	0.630575	−	0.330951i
$328$	1.18402	−	9.75131i	0.0653767	−	0.538426i
$329$	−23.4220	−	12.2928i	−1.29130	−	0.677725i
$330$	2.70908	+	22.3113i	0.149130	+	1.22819i
$331$	1.08535	+	8.93869i	0.0596564	+	0.491315i	0.991662	+	0.128870i	$0.0411349\pi$
$331$	1.08535	+	8.93869i	0.0596564	+	0.491315i	−0.932005	+	0.362445i	$0.881942\pi$
$332$	−5.43579	−	4.81569i	−0.298328	−	0.264295i
$333$	−0.275273	−	0.725836i	−0.0150849	−	0.0397756i
$334$	−1.73251	−	2.50997i	−0.0947987	−	0.137340i
$335$	−40.9052	−	10.0822i	−2.23489	−	0.550850i
$336$	−2.49986	−	1.31203i	−0.136378	−	0.0715769i
$337$	−9.02193			−0.491456			−0.245728	−	0.969339i	$-0.579027\pi$
$337$	−9.02193			−0.491456			−0.245728	+	0.969339i	$0.579027\pi$
$338$	−12.9416	−	1.90693i	−0.703928	−	0.103723i
$339$	12.9114			0.701250
$340$	−12.8326	−	6.73505i	−0.695944	−	0.365260i
$341$	2.70300	+	0.666231i	0.146376	+	0.0360784i
$342$	2.68581	+	3.89106i	0.145232	+	0.210405i
$343$	−6.45549	−	17.0217i	−0.348564	−	0.919086i
$344$	9.37492	+	8.30545i	0.505462	+	0.447800i
$345$	−2.98251	−	24.5632i	−0.160573	−	1.32244i
$346$	2.00716	+	16.5304i	0.107906	+	0.888682i
$347$	20.2552	+	10.6307i	1.08736	+	0.570688i	0.910484	−	0.413545i	$-0.135710\pi$
$347$	20.2552	+	10.6307i	1.08736	+	0.570688i	0.176872	+	0.984234i	$0.443402\pi$
$348$	−0.602967	+	4.96588i	−0.0323224	+	0.266199i
$349$	−24.0387	+	12.6165i	−1.28676	+	0.675346i	−0.962670	−	0.270679i	$-0.912752\pi$
$349$	−24.0387	+	12.6165i	−1.28676	+	0.675346i	−0.324094	+	0.946025i	$0.605060\pi$
$350$	−13.4856	−	35.5587i	−0.720837	−	1.90069i
$351$	−3.06156	−	1.90442i	−0.163414	−	0.101651i
$352$	8.99129	−	23.7081i	0.479237	−	1.26364i
$353$	−2.51072	−	20.6776i	−0.133632	−	1.10056i	−0.893051	−	0.449956i	$-0.851440\pi$
$353$	−2.51072	−	20.6776i	−0.133632	−	1.10056i	0.759419	−	0.650602i	$-0.225483\pi$
$354$	3.62644	−	9.56213i	0.192743	−	0.508222i
$355$	4.30069	+	35.4193i	0.228257	+	1.87986i
$356$	0.517476	+	0.749693i	0.0274262	+	0.0397337i
$357$	9.03975			0.478434
$358$	11.6776	−	16.9180i	0.617182	−	0.894142i
$359$	−1.15058	+	9.47591i	−0.0607255	+	0.500119i	0.930335	+	0.366710i	$0.119516\pi$
$359$	−1.15058	+	9.47591i	−0.0607255	+	0.500119i	−0.991061	+	0.133410i	$0.957407\pi$
$360$	13.1229			0.691636
$361$	3.07692			0.161943
$362$	−1.68053	+	13.8404i	−0.0883266	+	0.727435i
$363$	11.3614	−	10.0654i	0.596321	−	0.528295i
$364$	5.99912	−	7.45968i	0.314440	−	0.390994i
$365$	34.3232	+	30.4077i	1.79656	+	1.59161i
$366$	−2.74246	+	2.42961i	−0.143351	+	0.126998i
$367$	30.3205	+	15.9134i	1.58272	+	0.830675i	0.999836	+	0.0181188i	$0.00576770\pi$
$367$	30.3205	+	15.9134i	1.58272	+	0.830675i	0.582883	+	0.812556i	$0.301925\pi$
$368$	2.11052	−	5.56499i	0.110018	−	0.290095i
$369$	−2.44585	−	2.16684i	−0.127326	−	0.112801i
$370$	2.55238	−	2.26121i	0.132692	−	0.117555i
$371$	−3.74573	+	0.923239i	−0.194469	+	0.0479322i
$372$	0.190520	−	0.502360i	0.00987799	−	0.0260461i
$373$	−9.83795	+	5.16335i	−0.509390	+	0.267348i	−0.699778	−	0.714361i	$-0.746718\pi$
$373$	−9.83795	+	5.16335i	−0.509390	+	0.267348i	0.190388	+	0.981709i	$0.439025\pi$
$374$	−2.08647	−	17.1836i	−0.107889	−	0.888543i
$375$	29.5918	+	26.2161i	1.52812	+	1.35379i
$376$	26.1871	+	13.7440i	1.35049	+	0.708794i
$377$	17.3678	+	5.65562i	0.894486	+	0.291279i
$378$	−2.39563	+	1.25733i	−0.123218	+	0.0646699i
$379$	−8.60136	−	2.12004i	−0.441822	−	0.108899i	0.0121280	−	0.999926i	$-0.496139\pi$
$379$	−8.60136	−	2.12004i	−0.441822	−	0.108899i	−0.453950	+	0.891027i	$0.649986\pi$
$380$	11.5054	−	16.6685i	0.590217	−	0.855077i
$381$	8.94396	−	7.92365i	0.458213	−	0.405941i
$382$	−19.2511	−	10.1037i	−0.984970	−	0.516952i
$383$	−2.18366	+	17.9840i	−0.111580	+	0.918941i	0.824186	+	0.566319i	$0.191633\pi$
$383$	−2.18366	+	17.9840i	−0.111580	+	0.918941i	−0.935766	+	0.352622i	$0.885290\pi$
$384$	−2.46183	−	1.29207i	−0.125630	−	0.0659356i
$385$	−34.1144	+	49.4233i	−1.73863	+	2.51884i
$386$	8.62417	−	12.4943i	0.438959	−	0.635942i
$387$	4.04533	−	0.997084i	0.205636	−	0.0506846i
$388$	0.889577	−	0.219261i	0.0451615	−	0.0111313i
$389$	−4.50126	+	37.0712i	−0.228223	+	1.87958i	0.205671	+	0.978621i	$0.434062\pi$
$389$	−4.50126	+	37.0712i	−0.228223	+	1.87958i	−0.433894	+	0.900964i	$0.642861\pi$
$390$	3.05300	−	15.5409i	0.154594	−	0.786945i
$391$	2.29706	+	18.9180i	0.116167	+	0.956723i
$392$	−0.244351	−	0.644300i	−0.0123416	−	0.0325421i
$393$	−17.0910	−	15.1413i	−0.862127	−	0.763778i
$394$	−15.3373	+	3.78031i	−0.772682	+	0.190449i
$395$	54.4110	+	13.4111i	2.73772	+	0.674787i
$396$	−2.87004	−	4.15798i	−0.144225	−	0.208946i
$397$	6.76255	+	17.8314i	0.339403	+	0.894931i	0.990695	+	0.136104i	$0.0434581\pi$
$397$	6.76255	+	17.8314i	0.339403	+	0.894931i	−0.651292	+	0.758827i	$0.725773\pi$
$398$	−1.11240	+	0.985499i	−0.0557595	+	0.0493986i
$399$	−1.52277	+	12.5411i	−0.0762339	+	0.627842i
$400$	5.23384	+	13.8005i	0.261692	+	0.690025i
$401$	10.4571	−	27.5731i	0.522202	−	1.37693i	−0.371568	−	0.928406i	$-0.621180\pi$
$401$	10.4571	−	27.5731i	0.522202	−	1.37693i	0.893769	−	0.448527i	$-0.148051\pi$
$402$	−9.42900	+	2.32404i	−0.470276	+	0.115913i
$403$	−1.66580	−	1.03620i	−0.0829793	−	0.0516167i
$404$	−3.17849	−	0.783428i	−0.158136	−	0.0389770i
$405$	2.47981	−	3.59262i	0.123223	−	0.178519i
$406$	10.2591	−	9.08878i	0.509151	−	0.451069i
$407$	−3.85645	−	0.950528i	−0.191157	−	0.0471159i
$408$	−10.1069			−0.500367
$409$	30.4953	+	7.51641i	1.50790	+	0.371663i	0.904741	−	0.425962i	$-0.140064\pi$
$409$	30.4953	+	7.51641i	1.50790	+	0.371663i	0.603154	+	0.797625i	$0.293910\pi$
$410$	5.08984	−	13.4208i	0.251370	−	0.662807i
$411$	10.0701	−	5.28518i	0.496720	−	0.260699i
$412$	3.19215	+	8.41702i	0.157266	+	0.414677i
$413$	24.1958	−	12.6990i	1.19060	−	0.624875i
$414$	−3.24002	−	4.69398i	−0.159238	−	0.230697i
$415$	−18.2375	−	26.4216i	−0.895245	−	1.29699i
$416$	−11.1977	+	13.9239i	−0.549012	+	0.682675i
$417$	7.08556	−	10.2652i	0.346981	−	0.502689i
$418$	24.1909			1.18321
$419$	−10.9090	−	15.8044i	−0.532939	−	0.772096i	0.460352	−	0.887737i	$-0.347723\pi$
$419$	−10.9090	−	15.8044i	−0.532939	−	0.772096i	−0.993291	+	0.115641i	$0.963108\pi$
$420$	8.67521	+	7.68557i	0.423307	+	0.375017i
$421$	−8.86692	+	2.18550i	−0.432147	+	0.106515i	−0.449388	−	0.893337i	$-0.648358\pi$
$421$	−8.86692	+	2.18550i	−0.432147	+	0.106515i	0.0172407	+	0.999851i	$0.494512\pi$
$422$	0.0572460	−	0.0300450i	0.00278669	−	0.00146257i
$423$	8.71120	−	4.57199i	0.423553	−	0.222298i
$424$	4.18793	−	1.03223i	0.203384	−	0.0501296i
$425$	−35.3738	−	31.3384i	−1.71588	−	1.52014i
$426$	4.67201	+	6.76858i	0.226360	+	0.327939i
$427$	−9.78995			−0.473769
$428$	−1.26597	+	1.83407i	−0.0611927	+	0.0886530i
$429$	−16.9176	+	7.35643i	−0.816791	+	0.355172i
$430$	10.3965	+	15.0619i	0.501363	+	0.726349i
$431$	−2.57103	−	3.72477i	−0.123842	−	0.179416i	0.756159	−	0.654388i	$-0.227074\pi$
$431$	−2.57103	−	3.72477i	−0.123842	−	0.179416i	−0.880001	+	0.474972i	$0.842458\pi$
$432$	0.929757	−	0.487974i	0.0447329	−	0.0234777i
$433$	10.6552	+	28.0953i	0.512054	+	1.35018i	0.902952	+	0.429742i	$0.141396\pi$
$433$	10.6552	+	28.0953i	0.512054	+	1.35018i	−0.390897	+	0.920434i	$0.627835\pi$
$434$	−1.30347	+	0.684112i	−0.0625684	+	0.0328384i
$435$	−7.84193	+	20.6775i	−0.375992	+	0.991409i
$436$	−12.3468	−	3.04321i	−0.591303	−	0.145743i
$437$	−26.6325			−1.27400
$438$	10.2629	+	2.52958i	0.490381	+	0.120868i
$439$	−13.1323	+	11.6342i	−0.626770	+	0.555270i	−0.915590	−	0.402114i	$-0.868276\pi$
$439$	−13.1323	+	11.6342i	−0.626770	+	0.555270i	0.288820	+	0.957384i	$0.406737\pi$
$440$	38.1418	−	55.2579i	1.81834	−	2.63432i
$441$	−0.222563	−	0.0548570i	−0.0105983	−	0.00261224i
$442$	−2.35135	+	11.9693i	−0.111842	+	0.569319i
$443$	−7.78107	+	1.91786i	−0.369690	+	0.0911203i	−0.419784	−	0.907624i	$-0.637894\pi$
$443$	−7.78107	+	1.91786i	−0.369690	+	0.0911203i	0.0500940	+	0.998745i	$0.484048\pi$
$444$	−0.271820	+	0.716729i	−0.0129000	+	0.0340145i
$445$	1.42804	+	3.76544i	0.0676957	+	0.178499i
$446$	−0.207884	+	1.71208i	−0.00984361	+	0.0810694i
$447$	3.69307	−	3.27178i	0.174676	−	0.154750i
$448$	6.75673	+	17.8160i	0.319225	+	0.841728i
$449$	9.92828	+	14.3836i	0.468544	+	0.678804i	0.984011	−	0.178106i	$-0.0569969\pi$
$449$	9.92828	+	14.3836i	0.468544	+	0.678804i	−0.515467	+	0.856909i	$0.672382\pi$
$450$	13.7333	+	3.38495i	0.647392	+	0.159568i
$451$	−16.2330	+	4.00108i	−0.764384	+	0.188404i
$452$	−9.54304	−	8.45440i	−0.448867	−	0.397661i
$453$	−1.31326	−	3.46278i	−0.0617023	−	0.162696i
$454$	2.25012	+	18.5314i	0.105603	+	0.869721i
$455$	33.6426	−	25.6728i	1.57719	−	1.20356i
$456$	1.70254	−	14.0217i	0.0797287	−	0.656625i
$457$	7.28337	−	1.79519i	0.340702	−	0.0839754i	−0.0652527	−	0.997869i	$-0.520785\pi$
$457$	7.28337	−	1.79519i	0.340702	−	0.0839754i	0.405954	+	0.913893i	$0.366939\pi$
$458$	−2.80116	+	0.690425i	−0.130890	+	0.0322614i
$459$	−1.90989	+	2.76695i	−0.0891460	+	0.129150i
$460$	−13.8796	+	20.1081i	−0.647139	+	0.937543i
$461$	−6.13441	−	3.21959i	−0.285708	−	0.149951i	0.315781	−	0.948832i	$-0.397733\pi$
$461$	−6.13441	−	3.21959i	−0.285708	−	0.149951i	−0.601489	+	0.798881i	$0.705426\pi$
$462$	−1.66858	+	13.7420i	−0.0776294	+	0.639335i
$463$	−0.275226	−	0.144450i	−0.0127908	−	0.00671314i	0.458316	−	0.888790i	$-0.348453\pi$
$463$	−0.275226	−	0.144450i	−0.0127908	−	0.00671314i	−0.471106	+	0.882076i	$0.656145\pi$
$464$	−3.98161	+	3.52740i	−0.184842	+	0.163755i
$465$	1.34926	−	1.95475i	0.0625706	−	0.0906492i
$466$	19.5773	+	4.82538i	0.906902	+	0.223531i
$467$	5.39828	−	2.83324i	0.249803	−	0.131107i	−0.335175	−	0.942156i	$-0.608796\pi$
$467$	5.39828	−	2.83324i	0.249803	−	0.131107i	0.584978	+	0.811049i	$0.301103\pi$
$468$	1.01584	+	3.41231i	0.0469571	+	0.157734i
$469$	−22.9762	−	12.0588i	−1.06094	−	0.556825i
$470$	32.3472	+	28.6571i	1.49207	+	1.32185i
$471$	1.96640	+	16.1947i	0.0906068	+	0.746214i
$472$	−27.0523	+	14.1981i	−1.24518	+	0.653522i
$473$	7.55927	−	19.9322i	0.347575	−	0.916481i
$474$	12.5422	−	3.09138i	0.576084	−	0.141992i
$475$	49.4357	−	43.7962i	2.26826	−	2.00951i
$476$	−6.68145	−	5.91925i	−0.306244	−	0.271308i
$477$	0.508794	−	1.34158i	0.0232961	−	0.0614267i
$478$	−2.27969	−	1.19648i	−0.104271	−	0.0547255i
$479$	−1.23522	+	1.09431i	−0.0564387	+	0.0500003i	−0.690871	−	0.722978i	$-0.742773\pi$
$479$	−1.23522	+	1.09431i	−0.0564387	+	0.0500003i	0.634432	+	0.772979i	$0.281234\pi$
$480$	−16.1928	−	14.3455i	−0.739095	−	0.654781i
$481$	2.37664	+	1.47837i	0.108365	+	0.0674079i
$482$	4.33930	−	3.84428i	0.197650	−	0.175102i
$483$	1.83699	−	15.1290i	0.0835861	−	0.688393i
$484$	−14.9883			−0.681286
$485$	4.05037			0.183918
$486$	0.121291	−	0.998917i	0.00550185	−	0.0453118i
$487$	−19.6720	+	28.4999i	−0.891425	+	1.29145i	0.0645236	+	0.997916i	$0.479447\pi$
$487$	−19.6720	+	28.4999i	−0.891425	+	1.29145i	−0.955948	+	0.293535i	$0.905168\pi$
$488$	10.9457			0.495488
$489$	0.245051	+	0.355017i	0.0110816	+	0.0160544i
$490$	−0.121369	−	0.999563i	−0.00548289	−	0.0451557i
$491$	0.000858833	−	0.00226456i	3.87586e−5	−	0.000102198i	−0.934997	−	0.354656i	$-0.884598\pi$
$491$	0.000858833	−	0.00226456i	3.87586e−5	−	0.000102198i	0.935036	+	0.354554i	$0.115367\pi$
$492$	0.388927	+	3.20310i	0.0175342	+	0.144407i
$493$	6.03967	−	15.9253i	0.272013	−	0.717240i
$494$	−16.2093	−	5.27835i	−0.729289	−	0.237484i
$495$	−7.92025	−	20.8840i	−0.355989	−	0.938666i
$496$	0.505881	−	0.265507i	0.0227147	−	0.0119216i
$497$	−2.64889	+	21.8156i	−0.118819	+	0.978561i
$498$	−6.55274	−	3.43914i	−0.293635	−	0.154112i
$499$	−3.15587	−	25.9909i	−0.141276	−	1.16351i	−0.875020	−	0.484086i	$-0.839152\pi$
$499$	−3.15587	−	25.9909i	−0.141276	−	1.16351i	0.733744	−	0.679426i	$-0.237771\pi$
$500$	−4.70554	−	38.7536i	−0.210438	−	1.73311i
$501$	2.26865	+	2.00985i	0.101356	+	0.0897936i
$502$	−9.17231	−	24.1854i	−0.409380	−	1.07945i
$503$	3.19564	+	4.62968i	0.142486	+	0.206427i	0.887729	−	0.460366i	$-0.152282\pi$
$503$	3.19564	+	4.62968i	0.142486	+	0.206427i	−0.745243	+	0.666793i	$0.767666\pi$
$504$	7.84780	+	1.93431i	0.349569	+	0.0861609i
$505$	−12.8144	−	6.72552i	−0.570234	−	0.299282i
$506$	−29.1826			−1.29733
$507$	12.9409	−	1.23786i	0.574727	−	0.0549754i
$508$	−11.7991			−0.523499
$509$	13.3984	+	7.03204i	0.593875	+	0.311690i	0.734750	−	0.678338i	$-0.237299\pi$
$509$	13.3984	+	7.03204i	0.593875	+	0.311690i	−0.140875	+	0.990027i	$0.544992\pi$
$510$	−14.3394	−	3.53435i	−0.634960	−	0.156504i
$511$	16.0440	+	23.2438i	0.709746	+	1.02824i
$512$	−4.08388	−	10.7683i	−0.180483	−	0.475896i
$513$	−3.51696	−	3.11575i	−0.155278	−	0.137564i
$514$	0.759425	+	6.25443i	0.0334968	+	0.275871i
$515$	4.79692	+	39.5062i	0.211377	+	1.74085i
$516$	−3.64287	−	1.91193i	−0.160369	−	0.0841679i
$517$	6.06743	−	49.9698i	0.266845	−	2.19767i
$518$	1.85969	−	0.976040i	0.0817100	−	0.0428847i
$519$	−5.86813	−	15.4730i	−0.257582	−	0.679188i
$520$	−37.6142	+	28.7036i	−1.64949	+	1.25873i
$521$	−11.8499	+	31.2457i	−0.519155	+	1.36890i	0.377435	+	0.926036i	$0.376806\pi$
$521$	−11.8499	+	31.2457i	−0.519155	+	1.36890i	−0.896590	+	0.442862i	$0.853963\pi$
$522$	0.614448	+	5.06043i	0.0268937	+	0.221489i
$523$	−6.98533	+	18.4188i	−0.305447	+	0.805398i	0.691130	+	0.722731i	$0.257113\pi$
$523$	−6.98533	+	18.4188i	−0.305447	+	0.805398i	−0.996577	+	0.0826677i	$0.973656\pi$
$524$	2.71772	+	22.3825i	0.118724	+	0.977782i
$525$	21.4692	+	31.1036i	0.936995	+	1.35747i
$526$	−8.38126			−0.365440
$527$	−1.03917	+	1.50550i	−0.0452670	+	0.0655806i
$528$	0.647584	−	5.33333i	0.0281825	−	0.232104i
$529$	9.12809			0.396874
$530$	6.30267			0.273771
$531$	−1.22503	+	10.0890i	−0.0531618	+	0.437827i
$532$	9.33747	−	8.27228i	0.404831	−	0.358649i
$533$	11.7501	+	0.861033i	0.508953	+	0.0372955i
$534$	0.694835	+	0.615570i	0.0300685	+	0.0266383i
$535$	−7.37438	+	6.53313i	−0.318822	+	0.282452i
$536$	25.6886	+	13.4824i	1.10958	+	0.582352i
$537$	−7.24425	+	19.1015i	−0.312613	+	0.824292i
$538$	−0.140377	−	0.124363i	−0.00605207	−	0.00536167i
$539$	−0.877876	+	0.777730i	−0.0378128	+	0.0334992i
$540$	−4.18533	+	1.03159i	−0.180108	+	0.0443926i
$541$	2.41698	−	6.37304i	0.103914	−	0.273998i	−0.872968	−	0.487777i	$-0.837808\pi$
$541$	2.41698	−	6.37304i	0.103914	−	0.273998i	0.976882	+	0.213779i	$0.0685771\pi$
$542$	19.2135	−	10.0840i	0.825292	−	0.433147i
$543$	−1.67008	−	13.7544i	−0.0716701	−	0.590256i
$544$	12.4713	+	11.0486i	0.534702	+	0.473705i
$545$	−49.7773	−	26.1251i	−2.13222	−	1.11908i
$546$	4.11650	−	8.84384i	0.176170	−	0.378482i
$547$	8.93994	−	4.69204i	0.382244	−	0.200617i	−0.262646	−	0.964892i	$-0.584595\pi$
$547$	8.93994	−	4.69204i	0.382244	−	0.200617i	0.644891	+	0.764275i	$0.276903\pi$
$548$	−10.9037	−	2.68753i	−0.465784	−	0.114805i
$549$	2.06839	−	2.99658i	0.0882767	−	0.127891i
$550$	54.1693	−	47.9898i	2.30979	−	2.04629i
$551$	21.0763	+	11.0617i	0.897881	+	0.471244i
$552$	−2.05386	+	16.9150i	−0.0874180	+	0.719952i
$553$	30.5623	+	16.0404i	1.29964	+	0.682105i
$554$	−10.2466	+	14.8448i	−0.435337	+	0.630695i
$555$	−1.92503	+	2.78889i	−0.0817130	+	0.118382i
$556$	−11.9587	+	2.94757i	−0.507164	+	0.125005i
$557$	40.9267	−	10.0875i	1.73412	−	0.427422i	0.759357	−	0.650674i	$-0.225513\pi$
$557$	40.9267	−	10.0875i	1.73412	−	0.427422i	0.974761	+	0.223252i	$0.0716673\pi$
$558$	0.0659942	−	0.543512i	0.00279376	−	0.0230087i
$559$	−9.41426	+	11.7063i	−0.398181	+	0.495123i
$560$	1.48555	+	12.2346i	0.0627760	+	0.517007i
$561$	6.09999	+	16.0844i	0.257542	+	0.679082i
$562$	16.4031	+	14.5319i	0.691923	+	0.612991i
$563$	33.2912	−	8.20555i	1.40306	−	0.345823i	0.536079	−	0.844168i	$-0.319905\pi$
$563$	33.2912	−	8.20555i	1.40306	−	0.345823i	0.866979	+	0.498345i	$0.166059\pi$
$564$	−9.43237	−	2.32487i	−0.397174	−	0.0978947i
$565$	−32.0177	−	46.3857i	−1.34700	−	1.95146i
$566$	−0.0223635	−	0.0589677i	−0.000940008	−	0.00247860i
$567$	2.01254	−	1.78295i	0.0845186	−	0.0748770i
$568$	2.96160	−	24.3910i	0.124266	−	1.02342i
$569$	11.9598	+	31.5355i	0.501382	+	1.32204i	0.911986	+	0.410222i	$0.134549\pi$
$569$	11.9598	+	31.5355i	0.501382	+	1.32204i	−0.410604	+	0.911814i	$0.634682\pi$
$570$	7.31883	−	19.2982i	0.306552	−	0.808311i
$571$	11.1284	−	2.74291i	0.465710	−	0.114787i	0.000523366	−	1.00000i	$-0.499833\pi$
$571$	11.1284	−	2.74291i	0.465710	−	0.114787i	0.465187	+	0.885213i	$0.345987\pi$
$572$	17.3212	+	5.64043i	0.724234	+	0.235838i
$573$	20.9784	+	5.17072i	0.876387	+	0.216010i
$574$	5.02208	−	7.27574i	0.209618	−	0.303683i
$575$	−59.6367	+	52.8335i	−2.48702	+	2.20331i
$576$	−6.88080	−	1.69597i	−0.286700	−	0.0706652i
$577$	−42.7329			−1.77900			−0.889498	−	0.456940i	$-0.848946\pi$
$577$	−42.7329			−1.77900			−0.889498	+	0.456940i	$0.848946\pi$
$578$	−5.56536	−	1.37174i	−0.231489	−	0.0570568i
$579$	−5.35004	+	14.1069i	−0.222340	+	0.586262i
$580$	19.3358	−	10.1482i	0.802874	−	0.421381i
$581$	−7.01195	−	18.4890i	−0.290905	−	0.767053i
$582$	0.826702	−	0.433887i	0.0342679	−	0.0179852i
$583$	−4.17032	−	6.04175i	−0.172717	−	0.250224i
$584$	−17.9381	−	25.9878i	−0.742283	−	1.07538i
$585$	0.750213	+	15.7216i	0.0310175	+	0.650010i
$586$	−9.07760	+	13.1512i	−0.374992	+	0.543270i
$587$	22.4106			0.924984			0.462492	−	0.886624i	$-0.346955\pi$
$587$	22.4106			0.924984			0.462492	+	0.886624i	$0.346955\pi$
$588$	0.128580	+	0.186281i	0.00530257	+	0.00768209i
$589$	−1.91358	−	1.69528i	−0.0788477	−	0.0698529i
$590$	−43.3460	+	10.6838i	−1.78453	+	0.439846i
$591$	13.9000	−	7.29529i	0.571770	−	0.300088i
$592$	−0.721754	+	0.378806i	−0.0296639	+	0.0155688i
$593$	37.9193	−	9.34627i	1.55716	−	0.383805i	0.635593	−	0.772024i	$-0.280756\pi$
$593$	37.9193	−	9.34627i	1.55716	−	0.383805i	0.921567	+	0.388219i	$0.126910\pi$
$594$	−3.85372	−	3.41410i	−0.158120	−	0.140082i
$595$	−22.4168	−	32.4764i	−0.919000	−	1.33140i
$596$	−4.87199			−0.199564
$597$	0.838981	−	1.21547i	0.0343372	−	0.0497461i
$598$	19.5540	+	6.36754i	0.799624	+	0.260388i
$599$	−4.16632	−	6.03596i	−0.170231	−	0.246623i	0.728578	−	0.684963i	$-0.240182\pi$
$599$	−4.16632	−	6.03596i	−0.170231	−	0.246623i	−0.898809	+	0.438341i	$0.855566\pi$
$600$	−24.0038	−	34.7755i	−0.979950	−	1.41970i
$601$	−22.6225	+	11.8732i	−0.922790	+	0.484318i	−0.858040	−	0.513584i	$-0.828318\pi$
$601$	−22.6225	+	11.8732i	−0.922790	+	0.484318i	−0.0647510	+	0.997901i	$0.520625\pi$
$602$	3.99723	+	10.5398i	0.162915	+	0.429571i
$603$	8.54539	−	4.48497i	0.347995	−	0.182642i
$604$	−1.29678	+	3.41933i	−0.0527653	+	0.139131i
$605$	−64.3352	−	15.8572i	−2.61560	−	0.644687i
$606$	−3.33595			−0.135514
$607$	−7.99634	−	1.97092i	−0.324561	−	0.0799972i	0.0736687	−	0.997283i	$-0.476529\pi$
$607$	−7.99634	−	1.97092i	−0.324561	−	0.0799972i	−0.398230	+	0.917286i	$0.630375\pi$
$608$	−17.4289	+	15.4407i	−0.706835	+	0.626201i
$609$	−7.73752	+	11.2097i	−0.313540	+	0.454241i
$610$	15.5294	+	3.82766i	0.628768	+	0.154977i
$611$	−14.9687	+	32.1587i	−0.605571	+	1.30100i
$612$	3.22344	−	0.794507i	0.130300	−	0.0321160i
$613$	3.09097	−	8.15023i	0.124843	−	0.329185i	−0.857994	−	0.513660i	$-0.828289\pi$
$613$	3.09097	−	8.15023i	0.124843	−	0.329185i	0.982837	+	0.184475i	$0.0590586\pi$
$614$	1.27309	+	3.35687i	0.0513778	+	0.135472i
$615$	−1.71938	+	14.1604i	−0.0693320	+	0.571001i
$616$	30.9547	−	27.4235i	1.24720	−	1.10492i
$617$	7.94916	+	20.9602i	0.320021	+	0.843826i	0.994423	+	0.105462i	$0.0336321\pi$
$617$	7.94916	+	20.9602i	0.320021	+	0.843826i	−0.674402	+	0.738364i	$0.735599\pi$
$618$	5.21109	+	7.54956i	0.209621	+	0.303688i
$619$	1.02493	+	0.252622i	0.0411953	+	0.0101537i	0.259859	−	0.965646i	$-0.416324\pi$
$619$	1.02493	+	0.252622i	0.0411953	+	0.0101537i	−0.218664	+	0.975800i	$0.570170\pi$
$620$	−2.27724	+	0.561289i	−0.0914561	+	0.0225419i
$621$	4.24268	+	3.75869i	0.170253	+	0.150831i
$622$	−6.03022	−	15.9004i	−0.241790	−	0.637547i
$623$	0.298979	+	2.46232i	0.0119784	+	0.0986506i
$624$	−1.59763	+	3.43234i	−0.0639564	+	0.137403i
$625$	12.3308	−	101.554i	0.493234	−	4.06215i
$626$	−24.2788	+	5.98418i	−0.970376	+	0.239176i
$627$	−23.3419	+	5.75327i	−0.932187	+	0.229763i
$628$	9.15095	−	13.2574i	0.365163	−	0.529030i
$629$	1.48261	−	2.14794i	0.0591157	−	0.0856438i
$630$	10.4578	+	5.48868i	0.416649	+	0.218674i
$631$	0.480824	−	3.95994i	0.0191413	−	0.157643i	−0.980004	−	0.198978i	$-0.936238\pi$
$631$	0.480824	−	3.95994i	0.0191413	−	0.157643i	0.999145	+	0.0413347i	$0.0131610\pi$
$632$	−34.1704	−	17.9340i	−1.35922	−	0.713376i
$633$	−0.0480916	+	0.0426054i	−0.00191147	+	0.00169341i
$634$	−9.07919	+	13.1535i	−0.360581	+	0.522391i
$635$	−50.6460	−	12.4831i	−2.00982	−	0.495377i
$636$	−1.25453	+	0.658427i	−0.0497453	+	0.0261083i
$637$	0.757925	−	0.329574i	0.0300301	−	0.0130582i
$638$	23.0944	+	12.1209i	0.914317	+	0.479871i
$639$	−6.11782	−	5.41991i	−0.242017	−	0.214409i
$640$	1.46295	+	12.0485i	0.0578283	+	0.476259i
$641$	27.8761	−	14.6305i	1.10104	−	0.577871i	0.186537	−	0.982448i	$-0.440273\pi$
$641$	27.8761	−	14.6305i	1.10104	−	0.577871i	0.914504	+	0.404577i	$0.132581\pi$
$642$	−0.805304	+	2.12341i	−0.0317828	+	0.0838044i
$643$	18.0648	−	4.45257i	0.712405	−	0.175592i	0.133573	−	0.991039i	$-0.457355\pi$
$643$	18.0648	−	4.45257i	0.712405	−	0.175592i	0.578832	+	0.815447i	$0.303509\pi$
$644$	−11.2643	+	9.97926i	−0.443874	+	0.393238i
$645$	−13.6138	−	12.0608i	−0.536042	−	0.474892i
$646$	−5.63679	+	14.8630i	−0.221777	+	0.584777i
$647$	35.4522	+	18.6068i	1.39377	+	0.731507i	0.983577	−	0.180491i	$-0.0577687\pi$
$647$	35.4522	+	18.6068i	1.39377	+	0.731507i	0.410194	+	0.911998i	$0.365461\pi$
$648$	−2.25013	+	1.99344i	−0.0883933	+	0.0783096i
$649$	38.9225	+	34.4823i	1.52784	+	1.35355i
$650$	−46.7677	+	20.3364i	−1.83438	+	0.797658i
$651$	1.09502	−	0.970105i	0.0429173	−	0.0380214i
$652$	0.0513445	−	0.422860i	0.00201080	−	0.0165605i
$653$	36.7753			1.43913			0.719564	−	0.694427i	$-0.244342\pi$
$653$	36.7753			1.43913			0.719564	+	0.694427i	$0.244342\pi$
$654$	−12.9584			−0.506714
$655$	−12.0146	+	98.9490i	−0.469449	+	3.86626i
$656$	−1.94909	+	2.82375i	−0.0760993	+	0.110249i
$657$	−10.5044			−0.409814
$658$	15.1204	+	21.9056i	0.589453	+	0.853971i
$659$	5.58407	+	45.9890i	0.217525	+	1.79148i	0.536693	+	0.843778i	$0.319673\pi$
$659$	5.58407	+	45.9890i	0.217525	+	1.79148i	−0.319168	+	0.947698i	$0.603403\pi$
$660$	−7.82088	+	20.6220i	−0.304427	+	0.802709i
$661$	3.39888	+	27.9923i	0.132201	+	1.08877i	0.896229	+	0.443591i	$0.146296\pi$
$661$	3.39888	+	27.9923i	0.132201	+	1.08877i	−0.764028	+	0.645183i	$0.776781\pi$
$662$	3.21295	−	8.47186i	0.124875	−	0.329268i
$663$	−0.577797	−	12.1084i	−0.0224398	−	0.470253i
$664$	7.83974	+	20.6717i	0.304241	+	0.802217i
$665$	48.8317	−	25.6289i	1.89361	−	0.993845i
$666$	−0.0941557	+	0.775442i	−0.00364846	+	0.0300478i
$667$	−25.4254	−	13.3443i	−0.984475	−	0.516692i
$668$	−0.360749	−	2.97104i	−0.0139578	−	0.114953i
$669$	−0.206592	−	1.70144i	−0.00798732	−	0.0657815i
$670$	31.7315	+	28.1117i	1.22589	+	1.08605i
$671$	−6.60623	−	17.4192i	−0.255031	−	0.672461i
$672$	−7.56914	−	10.9658i	−0.291986	−	0.423015i
$673$	36.5990	+	9.02085i	1.41079	+	0.347728i	0.869843	−	0.493329i	$-0.164220\pi$
$673$	36.5990	+	9.02085i	1.41079	+	0.347728i	0.540946	+	0.841057i	$0.318066\pi$
$674$	8.03848	+	4.21892i	0.309631	+	0.162507i
$675$	−14.0564			−0.541030
$676$	−10.3754	−	7.55882i	−0.399055	−	0.290724i
$677$	21.6193			0.830897			0.415448	−	0.909617i	$-0.363625\pi$
$677$	21.6193			0.830897			0.415448	+	0.909617i	$0.363625\pi$
$678$	−11.5040	−	6.03774i	−0.441807	−	0.231878i
$679$	2.42222	+	0.597023i	0.0929562	+	0.0229116i
$680$	25.0632	+	36.3103i	0.961131	+	1.39244i
$681$	−6.57844	−	17.3459i	−0.252086	−	0.664697i
$682$	−2.09681	−	1.85761i	−0.0802910	−	0.0711317i
$683$	−1.08583	−	8.94261i	−0.0415481	−	0.342180i	−0.998628	−	0.0523568i	$-0.983327\pi$
$683$	−1.08583	−	8.94261i	−0.0415481	−	0.342180i	0.957080	−	0.289823i	$-0.0935964\pi$
$684$	0.559248	+	4.60583i	0.0213834	+	0.176108i
$685$	−43.9595	−	23.0717i	−1.67960	−	0.881524i
$686$	−2.20806	+	18.1850i	−0.0843042	+	0.694307i
$687$	2.53866	−	1.33239i	0.0968559	−	0.0508339i
$688$	−1.55134	−	4.09055i	−0.0591444	−	0.155951i
$689$	1.47606	+	4.95827i	0.0562336	+	0.188895i
$690$	−8.82907	+	23.2803i	−0.336117	+	0.886267i
$691$	−3.34973	−	27.5875i	−0.127430	−	1.04948i	−0.906401	−	0.422418i	$-0.861181\pi$
$691$	−3.34973	−	27.5875i	−0.127430	−	1.04948i	0.778971	−	0.627059i	$-0.215742\pi$
$692$	−5.79450	+	15.2788i	−0.220274	+	0.580814i
$693$	−1.65821	−	13.6566i	−0.0629902	−	0.518771i
$694$	−13.0760	−	18.9439i	−0.496358	−	0.719099i
$695$	−54.4498			−2.06540
$696$	8.65097	−	12.5331i	0.327914	−	0.475066i
$697$	1.32422	−	10.9060i	0.0501586	−	0.413093i
$698$	27.3182			1.03401
$699$	−20.0379			−0.757904
$700$	4.49836	−	37.0473i	0.170022	−	1.40026i
$701$	32.1180	−	28.4541i	1.21308	−	1.07470i	0.217968	−	0.975956i	$-0.430057\pi$
$701$	32.1180	−	28.4541i	1.21308	−	1.07470i	0.995113	−	0.0987403i	$-0.0314813\pi$
$702$	1.83727	+	3.12851i	0.0693432	+	0.118078i
$703$	2.73015	+	2.41870i	0.102970	+	0.0912231i
$704$	−27.1405	+	24.0444i	−1.02290	+	0.906208i
$705$	−38.0275	−	19.9584i	−1.43220	−	0.751676i
$706$	−7.43243	+	19.5977i	−0.279723	+	0.737569i
$707$	−6.67199	−	5.91087i	−0.250926	−	0.222301i
$708$	7.51177	−	6.65485i	0.282310	−	0.250105i
$709$	30.5994	−	7.54207i	1.14918	−	0.283249i	0.381681	−	0.924294i	$-0.375345\pi$
$709$	30.5994	−	7.54207i	1.14918	−	0.283249i	0.767503	+	0.641045i	$0.221499\pi$
$710$	12.7312	−	33.5695i	0.477795	−	1.25984i
$711$	−11.3669	+	5.96579i	−0.426291	+	0.223735i
$712$	−0.334275	−	2.75300i	−0.0125275	−	0.103173i
$713$	2.30845	+	2.04510i	0.0864520	+	0.0765898i
$714$	−8.05436	−	4.22725i	−0.301427	−	0.158201i
$715$	68.3813	+	42.5361i	2.55732	+	1.59076i
$716$	17.8621	−	9.37475i	0.667538	−	0.350351i
$717$	2.48425	+	0.612312i	0.0927760	+	0.0228672i
$718$	5.45638	−	7.90493i	0.203630	−	0.295009i
$719$	−22.3583	+	19.8077i	−0.833824	+	0.738704i	−0.967649	−	0.252301i	$-0.918813\pi$
$719$	−22.3583	+	19.8077i	−0.833824	+	0.738704i	0.133825	+	0.991005i	$0.457274\pi$
$720$	−4.05872	−	2.13018i	−0.151260	−	0.0793872i
$721$	−2.95453	+	24.3327i	−0.110032	+	0.906198i
$722$	−2.74152	−	1.43886i	−0.102029	−	0.0535488i
$723$	−3.27274	+	4.74138i	−0.121715	+	0.176334i
$724$	−7.77200	+	11.2597i	−0.288844	+	0.418463i
$725$	69.1392	−	17.0413i	2.56777	−	0.632897i
$726$	−14.8298	+	3.65523i	−0.550387	+	0.135658i
$727$	0.812224	−	6.68926i	0.0301237	−	0.248091i	−0.969866	−	0.243637i	$-0.921659\pi$
$727$	0.812224	−	6.68926i	0.0301237	−	0.248091i	0.999990	−	0.00445358i	$-0.00141762\pi$
$728$	−26.7251	+	11.6211i	−0.990500	+	0.430707i
$729$	0.120537	+	0.992709i	0.00446432	+	0.0367670i
$730$	−16.3622	−	43.1436i	−0.605592	−	1.59682i
$731$	10.4850	+	9.28891i	0.387802	+	0.343563i
$732$	−3.49095	+	0.860443i	−0.129029	+	0.0318029i
$733$	−21.4072	−	5.27639i	−0.790692	−	0.194888i	−0.176767	−	0.984253i	$-0.556564\pi$
$733$	−21.4072	−	5.27639i	−0.790692	−	0.194888i	−0.613924	+	0.789365i	$0.710410\pi$
$734$	−19.5738	−	28.3576i	−0.722482	−	1.04670i
$735$	0.354834	+	0.935621i	0.0130883	+	0.0345109i
$736$	21.0254	−	18.6268i	0.775005	−	0.686594i
$737$	5.95194	−	49.0186i	0.219242	−	1.80562i
$738$	1.16596	+	3.07439i	0.0429197	+	0.113170i
$739$	7.12210	−	18.7794i	0.261991	−	0.690813i	−0.737883	−	0.674928i	$-0.764174\pi$
$739$	7.12210	−	18.7794i	0.261991	−	0.690813i	0.999874	−	0.0158841i	$-0.00505628\pi$
$740$	3.24900	−	0.800806i	0.119435	−	0.0294382i
$741$	16.8958	+	1.23810i	0.620682	+	0.0454829i
$742$	3.76915	+	0.929013i	0.138370	+	0.0341051i
$743$	1.92238	−	2.78504i	0.0705252	−	0.102173i	−0.786134	−	0.618056i	$-0.787921\pi$
$743$	1.92238	−	2.78504i	0.0705252	−	0.102173i	0.856659	+	0.515883i	$0.172536\pi$
$744$	−1.22429	+	1.08463i	−0.0448848	+	0.0397645i
$745$	−20.9124	−	5.15444i	−0.766170	−	0.188844i
$746$	11.1801			0.409332
$747$	7.14071	+	1.76003i	0.261265	+	0.0643960i
$748$	6.02346	−	15.8825i	0.220239	−	0.580723i
$749$	−5.37304	+	2.81999i	−0.196327	+	0.103040i
$750$	−14.1067	−	37.1964i	−0.515105	−	1.35822i
$751$	−17.4885	+	9.17867i	−0.638164	+	0.334934i	−0.752582	−	0.658498i	$-0.771192\pi$
$751$	−17.4885	+	9.17867i	−0.638164	+	0.334934i	0.114418	+	0.993433i	$0.463500\pi$
$752$	−5.86829	−	8.50168i	−0.213994	−	0.310024i
$753$	14.6024	+	21.1552i	0.532141	+	0.770939i
$754$	−12.8299	−	13.1608i	−0.467236	−	0.479288i
$755$	−9.18383	+	13.3051i	−0.334234	+	0.484221i
$756$	−2.65499			−0.0965609
$757$	−5.90091	−	8.54894i	−0.214472	−	0.310717i	0.700951	−	0.713209i	$-0.252759\pi$
$757$	−5.90091	−	8.54894i	−0.214472	−	0.310717i	−0.915423	+	0.402493i	$0.868144\pi$
$758$	6.67236	+	5.91120i	0.242351	+	0.214704i
$759$	28.1585	−	6.94046i	1.02209	−	0.251923i
$760$	−54.5965	+	28.6545i	−1.98042	+	1.03941i
$761$	3.76359	−	1.97528i	0.136430	−	0.0716040i	−0.395127	−	0.918626i	$-0.629299\pi$
$761$	3.76359	−	1.97528i	0.136430	−	0.0716040i	0.531557	+	0.847023i	$0.321607\pi$
$762$	−11.6743	+	2.87747i	−0.422917	+	0.104240i
$763$	−25.9172	−	22.9606i	−0.938265	−	0.831230i
$764$	−12.1198	−	17.5585i	−0.438478	−	0.635244i
$765$	14.6768			0.530640
$766$	10.3555	−	15.0025i	0.374159	−	0.542063i
$767$	−18.5564	−	31.5978i	−0.670032	−	1.14093i
$768$	9.64071	+	13.9670i	0.347879	+	0.503990i
$769$	1.02378	+	1.48320i	0.0369183	+	0.0534854i	0.841008	−	0.541022i	$-0.181962\pi$
$769$	1.02378	+	1.48320i	0.0369183	+	0.0534854i	−0.804090	+	0.594507i	$0.797347\pi$
$770$	53.5075	−	28.0829i	1.92828	−	1.01204i
$771$	−2.22026	−	5.85433i	−0.0799606	−	0.210839i
$772$	13.1915	−	6.92345i	0.474774	−	0.249180i
$773$	−5.64658	+	14.8888i	−0.203093	+	0.535513i	−0.997405	−	0.0719977i	$-0.977063\pi$
$773$	−5.64658	+	14.8888i	−0.203093	+	0.535513i	0.794312	+	0.607511i	$0.207832\pi$
$774$	−4.07063	−	1.00332i	−0.146316	−	0.0360636i
$775$	−7.64808			−0.274727
$776$	−2.70817	−	0.667504i	−0.0972177	−	0.0239620i
$777$	−1.56230	+	1.38407i	−0.0560471	+	0.0496534i
$778$	21.3462	−	30.9253i	0.765298	−	1.10873i
$779$	14.9071	+	3.67428i	0.534104	+	0.131645i
$780$	9.74007	−	12.1114i	0.348750	−	0.433658i
$781$	−40.6037	+	10.0079i	−1.45292	+	0.358112i
$782$	6.79994	−	17.9300i	0.243165	−	0.641175i
$783$	−1.79640	−	4.73672i	−0.0641981	−	0.169276i
$784$	−0.0290123	+	0.238938i	−0.00103615	+	0.00853349i
$785$	53.3053	−	47.2244i	1.90255	−	1.68551i
$786$	8.14745	+	21.4831i	0.290610	+	0.766276i
$787$	−7.45905	−	10.8063i	−0.265886	−	0.385203i	0.667186	−	0.744891i	$-0.267498\pi$
$787$	−7.45905	−	10.8063i	−0.265886	−	0.385203i	−0.933073	+	0.359688i	$0.882883\pi$
$788$	−15.0507	−	3.70967i	−0.536160	−	0.132152i
$789$	8.08714	−	1.99330i	0.287910	−	0.0709634i
$790$	−42.2085	−	37.3934i	−1.50171	−	1.33040i
$791$	−12.3101	−	32.4592i	−0.437698	−	1.15412i
$792$	1.85397	+	15.2688i	0.0658779	+	0.542553i
$793$	0.625748	+	13.1133i	0.0222210	+	0.465667i
$794$	2.31309	−	19.0500i	0.0820885	−	0.676060i
$795$	−6.08150	+	1.49895i	−0.215688	+	0.0531624i
$796$	−1.41600	+	0.349013i	−0.0501889	+	0.0123704i
$797$	20.8099	−	30.1484i	0.737125	−	1.06791i	−0.257692	−	0.966227i	$-0.582962\pi$
$797$	20.8099	−	30.1484i	0.737125	−	1.06791i	0.994817	−	0.101683i	$-0.0324227\pi$
$798$	7.22139	−	10.4620i	0.255634	−	0.370350i
$799$	29.2879	+	15.3715i	1.03613	+	0.543804i
$800$	−8.39644	+	69.1509i	−0.296859	+	2.44485i
$801$	−0.816851	−	0.428717i	−0.0288620	−	0.0151480i
$802$	−22.2112	+	19.6774i	−0.784304	+	0.694832i
$803$	−30.5310	+	44.2319i	−1.07742	+	1.56091i
$804$	−9.25283	−	2.28062i	−0.326322	−	0.0804312i
$805$	−58.9081	+	30.9174i	−2.07624	+	1.08969i
$806$	0.999659	+	1.70222i	0.0352115	+	0.0599582i
$807$	0.165028	+	0.0866131i	0.00580924	+	0.00304893i
$808$	7.45965	+	6.60867i	0.262429	+	0.232492i
$809$	2.68793	+	22.1371i	0.0945026	+	0.778299i	0.960506	+	0.278260i	$0.0897577\pi$
$809$	2.68793	+	22.1371i	0.0945026	+	0.778299i	−0.866003	+	0.500039i	$0.833319\pi$
$810$	−3.88951	+	2.04137i	−0.136663	+	0.0717265i
$811$	1.96915	−	5.19221i	0.0691461	−	0.182323i	−0.895989	−	0.444077i	$-0.853532\pi$
$811$	1.96915	−	5.19221i	0.0691461	−	0.182323i	0.965135	+	0.261754i	$0.0843009\pi$
$812$	13.0591	−	3.21878i	0.458285	−	0.112957i
$813$	−16.1410	+	14.2997i	−0.566090	+	0.501512i
$814$	2.99157	+	2.65030i	0.104855	+	0.0928931i
$815$	0.667764	−	1.76075i	0.0233907	−	0.0616763i
$816$	3.12593	+	1.64062i	0.109430	+	0.0574331i
$817$	−14.6530	+	12.9815i	−0.512645	+	0.454164i
$818$	−23.6562	−	20.9576i	−0.827120	−	0.732765i
$819$	−1.86872	+	9.51251i	−0.0652984	+	0.332394i
$820$	10.5431	−	9.34033i	0.368179	−	0.326179i
$821$	−4.72284	+	38.8961i	−0.164828	+	1.35748i	0.642003	+	0.766702i	$0.278104\pi$
$821$	−4.72284	+	38.8961i	−0.164828	+	1.35748i	−0.806831	+	0.590782i	$0.798819\pi$
$822$	−11.4439			−0.399151
$823$	−35.5437			−1.23898			−0.619488	−	0.785006i	$-0.712660\pi$
$823$	−35.5437			−1.23898			−0.619488	+	0.785006i	$0.712660\pi$
$824$	3.30332	−	27.2053i	0.115077	−	0.947742i
$825$	−40.8550	+	59.1887i	−1.42239	+	2.06069i
$826$	−27.4968			−0.956735
$827$	11.3282	+	16.4118i	0.393921	+	0.570694i	0.968893	−	0.247480i	$-0.0796023\pi$
$827$	11.3282	+	16.4118i	0.393921	+	0.570694i	−0.574972	+	0.818173i	$0.694987\pi$
$828$	−0.674649	−	5.55624i	−0.0234457	−	0.193093i
$829$	6.24723	−	16.4726i	0.216975	−	0.572117i	−0.781696	−	0.623660i	$-0.785645\pi$
$829$	6.24723	−	16.4726i	0.216975	−	0.572117i	0.998671	+	0.0515437i	$0.0164141\pi$
$830$	3.89399	+	32.0699i	0.135162	+	1.11316i
$831$	6.35653	−	16.7608i	0.220505	−	0.581425i
$832$	23.4321	−	10.1892i	0.812362	−	0.353246i
$833$	−0.273285	−	0.720593i	−0.00946876	−	0.0249671i
$834$	−11.1135	+	5.83282i	−0.384829	+	0.201974i
$835$	1.59481	−	13.1345i	0.0551907	−	0.454537i
$836$	21.0197	+	11.0320i	0.726982	+	0.381550i
$837$	0.0655841	+	0.540134i	0.00226692	+	0.0186697i
$838$	2.32924	+	19.1830i	0.0804622	+	0.662666i
$839$	−33.5553	−	29.7274i	−1.15846	−	1.02630i	−0.999237	−	0.0390608i	$-0.987563\pi$
$839$	−33.5553	−	29.7274i	−1.15846	−	1.02630i	−0.159221	−	0.987243i	$-0.550898\pi$
$840$	−12.5118	−	32.9909i	−0.431698	−	1.13829i
$841$	−1.89533	−	2.74586i	−0.0653563	−	0.0946850i
$842$	8.92238	+	2.19917i	0.307485	+	0.0757884i
$843$	−19.2836	−	10.1208i	−0.664162	−	0.348579i
$844$	0.0634435			0.00218382
$845$	−36.5382	−	43.4222i	−1.25695	−	1.49377i
$846$	−9.89963			−0.340356
$847$	−36.1367	−	18.9660i	−1.24167	−	0.651680i
$848$	−1.46283	−	0.360554i	−0.0502337	−	0.0123815i
$849$	0.0356029	+	0.0515797i	0.00122189	+	0.00177021i
$850$	16.8630	+	44.4642i	0.578397	+	1.52511i
$851$	−3.29352	−	2.91780i	−0.112900	−	0.100021i
$852$	0.972824	+	8.01192i	0.0333284	+	0.274484i
$853$	2.26534	+	18.6567i	0.0775637	+	0.638794i	0.978705	+	0.205270i	$0.0658072\pi$
$853$	2.26534	+	18.6567i	0.0775637	+	0.638794i	−0.901142	+	0.433525i	$0.857270\pi$
$854$	8.72278	+	4.57807i	0.298488	+	0.156658i
$855$	−2.47234	+	20.3616i	−0.0845523	+	0.696351i
$856$	6.00735	−	3.15290i	0.205327	−	0.107764i
$857$	3.05844	+	8.06446i	0.104474	+	0.275477i	0.977053	−	0.212998i	$-0.0683228\pi$
$857$	3.05844	+	8.06446i	0.104474	+	0.275477i	−0.872578	+	0.488474i	$0.837554\pi$
$858$	18.5136	+	1.35666i	0.632044	+	0.0463155i
$859$	−14.5116	+	38.2640i	−0.495130	+	1.30555i	0.421868	+	0.906657i	$0.361375\pi$
$859$	−14.5116	+	38.2640i	−0.495130	+	1.30555i	−0.916998	+	0.398893i	$0.869395\pi$
$860$	2.16479	+	17.8287i	0.0738188	+	0.607953i
$861$	−3.11546	+	8.21480i	−0.106175	+	0.279960i
$862$	0.548953	+	4.52104i	0.0186974	+	0.153987i
$863$	−14.7858	−	21.4210i	−0.503315	−	0.729178i	0.486162	−	0.873869i	$-0.338397\pi$
$863$	−14.7858	−	21.4210i	−0.503315	−	0.729178i	−0.989477	+	0.144691i	$0.953781\pi$
$864$	4.95567			0.168595
$865$	−41.0367	+	59.4520i	−1.39529	+	2.02143i
$866$	3.64454	−	30.0154i	0.123846	−	1.01997i
$867$	5.69630			0.193456
$868$	−1.44458			−0.0490322
$869$	−7.91712	+	65.2034i	−0.268570	+	2.21187i
$870$	16.6565	−	14.7564i	0.564708	−	0.500288i
$871$	−14.6838	+	31.5466i	−0.497542	+	1.06892i
$872$	28.9768	+	25.6712i	0.981279	+	0.869337i
$873$	−0.694500	+	0.615273i	−0.0235053	+	0.0208238i
$874$	23.7294	+	12.4541i	0.802658	+	0.421268i
$875$	37.6933	−	99.3891i	1.27427	−	3.35997i
$876$	7.76397	+	6.87828i	0.262320	+	0.232395i
$877$	−10.0077	+	8.86608i	−0.337937	+	0.299386i	−0.814975	−	0.579497i	$-0.803249\pi$
$877$	−10.0077	+	8.86608i	−0.337937	+	0.299386i	0.477037	+	0.878883i	$0.341711\pi$
$878$	17.1413	−	4.22495i	0.578490	−	0.142585i
$879$	5.63132	−	14.8486i	0.189940	−	0.500830i
$880$	−20.7665	+	10.8991i	−0.700039	+	0.367409i
$881$	0.150939	+	1.24309i	0.00508526	+	0.0418809i	0.995031	−	0.0995694i	$-0.0317465\pi$
$881$	0.150939	+	1.24309i	0.00508526	+	0.0418809i	−0.989945	+	0.141450i	$0.954823\pi$
$882$	0.172650	+	0.152954i	0.00581342	+	0.00515024i
$883$	47.6787	+	25.0237i	1.60452	+	0.842115i	0.998926	+	0.0463373i	$0.0147549\pi$
$883$	47.6787	+	25.0237i	1.60452	+	0.842115i	0.605589	+	0.795777i	$0.292937\pi$
$884$	−7.50157	+	9.32792i	−0.252305	+	0.313732i
$885$	39.2839	−	20.6178i	1.32052	−	0.693060i
$886$	7.82973	+	1.92985i	0.263045	+	0.0648347i
$887$	−9.42379	+	13.6527i	−0.316420	+	0.458413i	−0.948632	−	0.316382i	$-0.897532\pi$
$887$	−9.42379	+	13.6527i	−0.316420	+	0.458413i	0.632212	+	0.774796i	$0.282147\pi$
$888$	1.74673	−	1.54747i	0.0586165	−	0.0519297i
$889$	−28.4475	−	14.9304i	−0.954099	−	0.500750i
$890$	0.488453	−	4.02277i	0.0163730	−	0.134844i
$891$	4.53045	+	2.37776i	0.151776	+	0.0796581i
$892$	−0.961411	+	1.39284i	−0.0321904	+	0.0466359i
$893$	−26.2590	+	38.0427i	−0.878724	+	1.27305i
$894$	−4.82049	+	1.18814i	−0.161221	+	0.0397375i
$895$	86.5889	−	21.3422i	2.89435	−	0.713393i
$896$	−0.901065	+	7.42094i	−0.0301025	+	0.247916i
$897$	−20.3822	−	1.49359i	−0.680542	−	0.0498694i
$898$	−2.11984	−	17.4584i	−0.0707400	−	0.582596i
$899$	−0.977422	−	2.57725i	−0.0325988	−	0.0859561i
$900$	10.3893	+	9.20414i	0.346311	+	0.306805i
$901$	4.68383	−	1.15446i	0.156041	−	0.0384606i
$902$	16.3346	+	4.02611i	0.543881	+	0.134055i
$903$	−6.36362	−	9.21930i	−0.211768	−	0.306799i
$904$	13.7634	+	36.2911i	0.457764	+	1.20702i
$905$	−45.2727	+	40.1081i	−1.50492	+	1.33324i
$906$	−0.449193	+	3.69944i	−0.0149234	+	0.122906i
$907$	2.58726	+	6.82204i	0.0859085	+	0.226522i	0.971085	−	0.238733i	$-0.0767320\pi$
$907$	2.58726	+	6.82204i	0.0859085	+	0.226522i	−0.885177	+	0.465255i	$0.845963\pi$
$908$	−6.49590	+	17.1283i	−0.215574	+	0.568422i
$909$	3.21888	−	0.793383i	0.106764	−	0.0263148i
$910$	−41.9807	+	7.14202i	−1.39165	+	0.236756i
$911$	−2.68553	−	0.661923i	−0.0889755	−	0.0219305i	0.194577	−	0.980887i	$-0.437667\pi$
$911$	−2.68553	−	0.661923i	−0.0889755	−	0.0219305i	−0.283552	+	0.958957i	$0.591513\pi$
$912$	−2.80265	+	4.06035i	−0.0928051	+	0.134451i
$913$	28.1657	−	24.9526i	0.932149	−	0.825812i
$914$	−7.32892	−	1.80642i	−0.242419	−	0.0597509i
$915$	−15.8948			−0.525465
$916$	−2.74882	−	0.677524i	−0.0908237	−	0.0223860i
$917$	−21.7701	+	57.4030i	−0.718911	+	1.89561i
$918$	2.99561	−	1.57222i	0.0988698	−	0.0518909i
$919$	2.85102	+	7.51753i	0.0940466	+	0.247980i	0.973782	−	0.227483i	$-0.0730496\pi$
$919$	2.85102	+	7.51753i	0.0940466	+	0.247980i	−0.879735	+	0.475463i	$0.842280\pi$
$920$	65.8625	−	34.5673i	2.17142	−	1.13965i
$921$	−2.02677	−	2.93629i	−0.0667845	−	0.0967540i
$922$	3.96015	+	5.73727i	0.130421	+	0.188947i
$923$	29.3905	+	2.15371i	0.967401	+	0.0708901i
$924$	−7.71675	+	11.1796i	−0.253862	+	0.367783i
$925$	10.9117			0.358775
$926$	0.177675	+	0.257407i	0.00583878	+	0.00845893i
$927$	−6.82372	−	6.04528i	−0.224120	−	0.198553i
$928$	−24.3755	+	6.00803i	−0.800166	+	0.197223i
$929$	−12.1332	+	6.36802i	−0.398079	+	0.208928i	−0.651869	−	0.758331i	$-0.726015\pi$
$929$	−12.1332	+	6.36802i	−0.398079	+	0.208928i	0.253791	+	0.967259i	$0.418323\pi$
$930$	−2.11628	+	1.11071i	−0.0693957	+	0.0364217i
$931$	1.04574	−	0.257751i	0.0342727	−	0.00844746i
$932$	14.8104	+	13.1209i	0.485131	+	0.429789i
$933$	9.60016	+	13.9082i	0.314295	+	0.455335i
$934$	−6.13474			−0.200735
$935$	42.6582	−	61.8011i	1.39507	−	2.02111i
$936$	2.08933	−	10.6355i	0.0682919	−	0.347632i
$937$	−26.2735	−	38.0638i	−0.858318	−	1.24349i	−0.968359	−	0.249562i	$-0.919713\pi$
$937$	−26.2735	−	38.0638i	−0.858318	−	1.24349i	0.110041	−	0.993927i	$-0.464902\pi$
$938$	14.8326	+	21.4887i	0.484300	+	0.701630i
$939$	22.0036	−	11.5484i	0.718059	−	0.376867i
$940$	15.0381	+	39.6521i	0.490488	+	1.29331i
$941$	−32.3212	+	16.9635i	−1.05364	+	0.552993i	−0.900340	−	0.435187i	$-0.856682\pi$
$941$	−32.3212	+	16.9635i	−1.05364	+	0.552993i	−0.153300	+	0.988180i	$0.548990\pi$
$942$	5.82109	−	15.3490i	0.189661	−	0.500096i
$943$	−17.9832	−	4.43247i	−0.585615	−	0.144341i
$944$	10.6716			0.347332
$945$	−11.3962	−	2.80890i	−0.370718	−	0.0913737i
$946$	−16.0561	+	14.2245i	−0.522030	+	0.462478i
$947$	9.57627	−	13.8736i	0.311187	−	0.450832i	−0.635918	−	0.771757i	$-0.719378\pi$
$947$	9.57627	−	13.8736i	0.311187	−	0.450832i	0.947105	+	0.320925i	$0.103994\pi$
$948$	12.3079	+	3.03362i	0.399741	+	0.0985274i
$949$	30.1088	−	22.9761i	0.977372	−	0.745836i
$950$	−64.5272	+	15.9045i	−2.09354	+	0.516011i
$951$	5.63231	−	14.8512i	0.182640	−	0.481582i
$952$	9.63628	+	25.4088i	0.312314	+	0.823504i
$953$	−5.10432	+	42.0379i	−0.165345	+	1.36174i	0.639745	+	0.768587i	$0.279040\pi$
$953$	−5.10432	+	42.0379i	−0.165345	+	1.36174i	−0.805090	+	0.593153i	$0.797883\pi$
$954$	−1.08069	+	0.957412i	−0.0349888	+	0.0309973i
$955$	−33.4460	−	88.1900i	−1.08229	−	2.85376i
$956$	−1.43521	−	2.07926i	−0.0464181	−	0.0672482i
$957$	−25.1667	−	6.20303i	−0.813523	−	0.200515i
$958$	1.61231	−	0.397398i	0.0520913	−	0.0128393i
$959$	−22.8881	−	20.2771i	−0.739094	−	0.654780i
$960$	10.9701	+	28.9258i	0.354059	+	0.933576i
$961$	−3.70095	−	30.4801i	−0.119386	−	0.983229i
$962$	−1.42624	−	2.42860i	−0.0459838	−	0.0783013i
$963$	0.272036	−	2.24042i	0.00876625	−	0.0721965i
$964$	5.52361	−	1.36145i	0.177904	−	0.0438493i
$965$	63.9477	−	15.7617i	2.05855	−	0.507387i
$966$	−8.71152	+	12.6208i	−0.280288	+	0.406068i
$967$	−0.355412	+	0.514903i	−0.0114293	+	0.0165582i	−0.828657	−	0.559757i	$-0.810895\pi$
$967$	−0.355412	+	0.514903i	−0.0114293	+	0.0165582i	0.817228	+	0.576315i	$0.195510\pi$
$968$	40.4028	+	21.2050i	1.29859	+	0.681555i
$969$	1.90414	−	15.6820i	0.0611698	−	0.503778i
$970$	−3.60885	−	1.89407i	−0.115873	−	0.0608150i
$971$	−19.3197	+	17.1157i	−0.619998	+	0.549270i	−0.913578	−	0.406664i	$-0.866692\pi$
$971$	−19.3197	+	17.1157i	−0.619998	+	0.549270i	0.293580	+	0.955935i	$0.405153\pi$
$972$	0.560937	−	0.812658i	0.0179921	−	0.0260660i
$973$	−32.5623	−	8.02589i	−1.04390	−	0.257298i
$974$	30.8550	−	16.1940i	0.988659	−	0.518888i
$975$	40.2899	−	30.7454i	1.29031	−	0.984641i
$976$	−3.38535	−	1.77677i	−0.108363	−	0.0568730i
$977$	15.9537	+	14.1337i	0.510404	+	0.452178i	0.878592	−	0.477573i	$-0.158483\pi$
$977$	15.9537	+	14.1337i	0.510404	+	0.452178i	−0.368188	+	0.929751i	$0.620022\pi$
$978$	−0.0523221	−	0.430911i	−0.00167308	−	0.0137790i
$979$	−4.17943	+	2.19354i	−0.133575	+	0.0701057i
$980$	0.350382	−	0.923881i	0.0111925	−	0.0295123i
$981$	12.5037	−	3.08188i	0.399211	−	0.0983967i
$982$	−0.00182419	+	0.00161609i	−5.82122e−5	+	5.15715e-5i
$983$	−28.4037	−	25.1635i	−0.905936	−	0.802590i	0.0749467	−	0.997188i	$-0.476121\pi$
$983$	−28.4037	−	25.1635i	−0.905936	−	0.802590i	−0.980883	+	0.194598i	$0.937660\pi$
$984$	3.48326	−	9.18459i	0.111042	−	0.292794i
$985$	−60.6785	−	31.8466i	−1.93338	−	1.01472i
$986$	−12.8285	+	11.3650i	−0.408541	+	0.361936i
$987$	−19.7995	−	17.5409i	−0.630226	−	0.558332i
$988$	−11.6773	−	11.9785i	−0.371504	−	0.381087i
$989$	17.6767	−	15.6602i	0.562086	−	0.497965i
$990$	−2.70908	+	22.3113i	−0.0861001	+	0.709098i
$991$	21.5246			0.683751			0.341875	−	0.939745i	$-0.388938\pi$
$991$	21.5246			0.683751			0.341875	+	0.939745i	$0.388938\pi$
$992$	2.69639			0.0856103
$993$	−1.08535	+	8.93869i	−0.0344427	+	0.283661i
$994$	12.5617	−	18.1988i	0.398434	−	0.577232i
$995$	−6.44725			−0.204392
$996$	−4.12536	−	5.97662i	−0.130717	−	0.189377i
$997$	5.42121	+	44.6477i	0.171692	+	1.41401i	0.782708	+	0.622389i	$0.213838\pi$
$997$	5.42121	+	44.6477i	0.171692	+	1.41401i	−0.611016	+	0.791618i	$0.709239\pi$
$998$	−9.34225	+	24.6335i	−0.295724	+	0.779760i
$999$	−0.0935705	−	0.770622i	−0.00296044	−	0.0243814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.m.a.79.5	✓	180
169.92	even	13	inner	507.2.m.a.430.5	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.m.a.79.5	✓	180	1.1	even	1	trivial
507.2.m.a.430.5	yes	180	169.92	even	13	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.m (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.890994 - 0.467630i) q^{2} +(0.970942 + 0.239316i) q^{3} +(-0.560937 - 0.812658i) q^{4} +(-1.54798 - 4.08168i) q^{5} +(-0.753192 - 0.667270i) q^{6} +(-0.324090 - 2.66912i) q^{7} +(0.362350 + 2.98422i) q^{8} +(0.885456 + 0.464723i) q^{9} +O(q^{10})\)	\(q+(-0.890994 - 0.467630i) q^{2} +(0.970942 + 0.239316i) q^{3} +(-0.560937 - 0.812658i) q^{4} +(-1.54798 - 4.08168i) q^{5} +(-0.753192 - 0.667270i) q^{6} +(-0.324090 - 2.66912i) q^{7} +(0.362350 + 2.98422i) q^{8} +(0.885456 + 0.464723i) q^{9} +(-0.529477 + 4.36063i) q^{10} +(4.53045 - 2.37776i) q^{11} +(-0.350156 - 0.923284i) q^{12} +(-3.55448 + 0.604710i) q^{13} +(-0.959397 + 2.52972i) q^{14} +(-0.526186 - 4.33353i) q^{15} +(0.372346 - 0.981797i) q^{16} +(0.405256 + 3.33758i) q^{17} +(-0.571617 - 0.828131i) q^{18} -4.69861 q^{19} +(-2.44869 + 3.54754i) q^{20} +(0.324090 - 2.66912i) q^{21} -5.14852 q^{22} +5.66816 q^{23} +(-0.362350 + 2.98422i) q^{24} +(-10.5213 + 9.32109i) q^{25} +(3.44980 + 1.12339i) q^{26} +(0.748511 + 0.663123i) q^{27} +(-1.98729 + 1.76058i) q^{28} +(-4.48565 - 2.35425i) q^{29} +(-1.55766 + 4.10721i) q^{30} +(0.407265 + 0.360805i) q^{31} +(3.70938 - 3.28622i) q^{32} +(4.96784 - 1.22446i) q^{33} +(1.19967 - 3.16328i) q^{34} +(-10.3928 + 5.45457i) q^{35} +(-0.119024 - 0.980253i) q^{36} +(-0.581056 - 0.514770i) q^{37} +(4.18643 + 2.19721i) q^{38} +(-3.59591 - 0.263504i) q^{39} +(11.6197 - 6.09850i) q^{40} +(-3.17267 - 0.781994i) q^{41} +(-1.53692 + 2.22661i) q^{42} +(3.11859 - 2.76283i) q^{43} +(-4.47361 - 2.34793i) q^{44} +(0.526186 - 4.33353i) q^{45} +(-5.05030 - 2.65060i) q^{46} +(5.58868 - 8.09660i) q^{47} +(0.596486 - 0.864159i) q^{48} +(-0.222563 + 0.0548570i) q^{49} +(13.7333 - 3.38495i) q^{50} +(-0.405256 + 3.33758i) q^{51} +(2.48526 + 2.54937i) q^{52} +(-0.172948 - 1.42436i) q^{53} +(-0.356823 - 0.940864i) q^{54} +(-16.7183 - 14.8111i) q^{55} +(7.84780 - 1.93431i) q^{56} +(-4.56208 - 1.12445i) q^{57} +(2.89577 + 4.19524i) q^{58} +(3.60390 + 9.50270i) q^{59} +(-3.22652 + 2.85845i) q^{60} +(0.438888 - 3.61457i) q^{61} +(-0.194147 - 0.511925i) q^{62} +(0.953434 - 2.51400i) q^{63} +(-6.88080 + 1.69597i) q^{64} +(7.97049 + 13.5722i) q^{65} +(-4.99891 - 1.23212i) q^{66} +(5.48230 - 7.94248i) q^{67} +(2.48499 - 2.20151i) q^{68} +(5.50346 + 1.35648i) q^{69} +11.8106 q^{70} +(-7.93582 - 1.95600i) q^{71} +(-1.06599 + 2.81079i) q^{72} +(-9.30115 + 4.88162i) q^{73} +(0.276995 + 0.730376i) q^{74} +(-12.4463 + 6.53232i) q^{75} +(2.63562 + 3.81836i) q^{76} +(-7.81480 - 11.3217i) q^{77} +(3.08071 + 1.91633i) q^{78} +(-7.29242 + 10.5649i) q^{79} -4.58377 q^{80} +(0.568065 + 0.822984i) q^{81} +(2.46115 + 2.18039i) q^{82} +(7.14071 - 1.76003i) q^{83} +(-2.35087 + 1.23383i) q^{84} +(12.9956 - 6.82063i) q^{85} +(-4.07063 + 1.00332i) q^{86} +(-3.79189 - 3.35933i) q^{87} +(8.73737 + 12.6583i) q^{88} -0.922521 q^{89} +(-2.49532 + 3.61509i) q^{90} +(2.76601 + 9.29134i) q^{91} +(-3.17948 - 4.60628i) q^{92} +(0.309084 + 0.447786i) q^{93} +(-8.76568 + 4.60059i) q^{94} +(7.27334 + 19.1782i) q^{95} +(4.38803 - 2.30302i) q^{96} +(-0.329017 + 0.867548i) q^{97} +(0.223955 + 0.0552000i) q^{98} +5.11652 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9}+O(q^{10}) \) 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9	\( 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9} - 2 q^{10} - 4 q^{11} + 15 q^{12} - 14 q^{13} + 6 q^{14} + 2 q^{15} - 15 q^{16} - 2 q^{17} - q^{18} + 2 q^{20} - 4 q^{21} - 28 q^{22} - 52 q^{23} - 3 q^{24} - 67 q^{25} - 40 q^{26} + 15 q^{27} - 4 q^{28} - 27 q^{29} + 2 q^{30} + 22 q^{31} - 5 q^{32} - 9 q^{33} + 63 q^{34} - 31 q^{35} - 15 q^{36} + 2 q^{37} + 65 q^{38} + q^{39} + 45 q^{40} - 6 q^{41} + 59 q^{42} - 60 q^{43} - 35 q^{44} - 2 q^{45} - 156 q^{46} + 15 q^{48} + 59 q^{49} - 51 q^{50} + 2 q^{51} + 66 q^{52} + 50 q^{53} + q^{54} + 55 q^{55} - 14 q^{56} - 13 q^{57} + 36 q^{58} + 92 q^{59} - 15 q^{60} + 6 q^{61} + 61 q^{62} + 4 q^{63} - 203 q^{64} - 54 q^{65} + 54 q^{66} + 86 q^{67} + 32 q^{68} + 112 q^{70} + 39 q^{71} + 3 q^{72} - 158 q^{73} - 80 q^{74} + 15 q^{75} + 130 q^{76} - 64 q^{77} + 66 q^{78} - 10 q^{79} - 310 q^{80} - 15 q^{81} + 59 q^{82} - 82 q^{83} + 4 q^{84} + 22 q^{85} - q^{86} + 40 q^{87} + 10 q^{88} + 2 q^{89} - 2 q^{90} - 100 q^{91} - 54 q^{92} + 43 q^{93} + 65 q^{94} + 58 q^{95} - 60 q^{96} + 16 q^{97} - 113 q^{98} - 30 q^{99}+O(q^{100}) \) 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9 - 2 * q^10 - 4 * q^11 + 15 * q^12 - 14 * q^13 + 6 * q^14 + 2 * q^15 - 15 * q^16 - 2 * q^17 - q^18 + 2 * q^20 - 4 * q^21 - 28 * q^22 - 52 * q^23 - 3 * q^24 - 67 * q^25 - 40 * q^26 + 15 * q^27 - 4 * q^28 - 27 * q^29 + 2 * q^30 + 22 * q^31 - 5 * q^32 - 9 * q^33 + 63 * q^34 - 31 * q^35 - 15 * q^36 + 2 * q^37 + 65 * q^38 + q^39 + 45 * q^40 - 6 * q^41 + 59 * q^42 - 60 * q^43 - 35 * q^44 - 2 * q^45 - 156 * q^46 + 15 * q^48 + 59 * q^49 - 51 * q^50 + 2 * q^51 + 66 * q^52 + 50 * q^53 + q^54 + 55 * q^55 - 14 * q^56 - 13 * q^57 + 36 * q^58 + 92 * q^59 - 15 * q^60 + 6 * q^61 + 61 * q^62 + 4 * q^63 - 203 * q^64 - 54 * q^65 + 54 * q^66 + 86 * q^67 + 32 * q^68 + 112 * q^70 + 39 * q^71 + 3 * q^72 - 158 * q^73 - 80 * q^74 + 15 * q^75 + 130 * q^76 - 64 * q^77 + 66 * q^78 - 10 * q^79 - 310 * q^80 - 15 * q^81 + 59 * q^82 - 82 * q^83 + 4 * q^84 + 22 * q^85 - q^86 + 40 * q^87 + 10 * q^88 + 2 * q^89 - 2 * q^90 - 100 * q^91 - 54 * q^92 + 43 * q^93 + 65 * q^94 + 58 * q^95 - 60 * q^96 + 16 * q^97 - 113 * q^98 - 30 * q^99

Introduction

L-functions

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