LMFDB - Embedded newform 169.2.g.a.27.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(14,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([18]))

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

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

chi := DirichletCharacter("169.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.g (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:	$1.34947179416$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$13$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			27.1
Character	$\chi$	$=$	169.27
Dual form			169.2.g.a.144.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.952850 - 2.51246i) q^{2} +(-0.297229 + 0.430610i) q^{3} +(-3.90751 + 3.46175i) q^{4} +(0.365684 + 3.01168i) q^{5} +(1.36511 + 0.336468i) q^{6} +(-2.17334 - 1.14066i) q^{7} +(7.66220 + 4.02143i) q^{8} +(0.966734 + 2.54907i) q^{9} +O(q^{10})$	\(q+(-0.952850 - 2.51246i) q^{2} +(-0.297229 + 0.430610i) q^{3} +(-3.90751 + 3.46175i) q^{4} +(0.365684 + 3.01168i) q^{5} +(1.36511 + 0.336468i) q^{6} +(-2.17334 - 1.14066i) q^{7} +(7.66220 + 4.02143i) q^{8} +(0.966734 + 2.54907i) q^{9} +(7.21828 - 3.78845i) q^{10} +(-0.241580 + 0.636994i) q^{11} +(-0.329241 - 2.71155i) q^{12} +(-0.756816 + 3.52523i) q^{13} +(-0.794988 + 6.54731i) q^{14} +(-1.40555 - 0.737691i) q^{15} +(1.54427 - 12.7182i) q^{16} +(-3.05039 - 1.60097i) q^{17} +(5.48328 - 4.85776i) q^{18} +4.57811 q^{19} +(-11.8546 - 10.5023i) q^{20} +(1.13716 - 0.596827i) q^{21} +1.83061 q^{22} -8.26888 q^{23} +(-4.00910 + 2.10414i) q^{24} +(-4.08178 + 1.00607i) q^{25} +(9.57812 - 1.45754i) q^{26} +(-2.90908 - 0.717023i) q^{27} +(12.4410 - 3.06644i) q^{28} +(2.79395 + 7.36704i) q^{29} +(-0.514137 + 4.23430i) q^{30} +(3.45540 + 0.851679i) q^{31} +(-16.6215 + 4.09682i) q^{32} +(-0.202492 - 0.293360i) q^{33} +(-1.11580 + 9.18946i) q^{34} +(2.64054 - 6.96253i) q^{35} +(-12.6018 - 6.61392i) q^{36} +(7.28687 + 1.79605i) q^{37} +(-4.36226 - 11.5023i) q^{38} +(-1.29305 - 1.37369i) q^{39} +(-9.30932 + 24.5467i) q^{40} +(-0.114022 + 0.165189i) q^{41} +(-2.58305 - 2.28838i) q^{42} +(0.943264 - 0.232494i) q^{43} +(-1.26114 - 3.32535i) q^{44} +(-7.32346 + 3.84365i) q^{45} +(7.87900 + 20.7752i) q^{46} +(4.26700 + 3.78023i) q^{47} +(5.01758 + 4.44518i) q^{48} +(-0.554136 - 0.802805i) q^{49} +(6.41703 + 9.29667i) q^{50} +(1.59606 - 0.837675i) q^{51} +(-9.24619 - 16.3948i) q^{52} +(-8.33843 - 4.37635i) q^{53} +(0.970423 + 7.99215i) q^{54} +(-2.00676 - 0.494623i) q^{55} +(-12.0655 - 17.4799i) q^{56} +(-1.36075 + 1.97138i) q^{57} +(15.8472 - 14.0394i) q^{58} +(-0.616927 - 5.08085i) q^{59} +(8.04591 - 1.98314i) q^{60} +(4.02471 - 2.11233i) q^{61} +(-1.15267 - 9.49307i) q^{62} +(0.806571 - 6.64271i) q^{63} +(11.5752 + 16.7696i) q^{64} +(-10.8936 - 0.990168i) q^{65} +(-0.544111 + 0.788280i) q^{66} +(-5.10800 - 4.52529i) q^{67} +(17.4616 - 4.30389i) q^{68} +(2.45775 - 3.56067i) q^{69} -20.0091 q^{70} +(1.92369 - 2.78694i) q^{71} +(-2.84360 + 23.4191i) q^{72} +(2.71442 - 7.15733i) q^{73} +(-2.43079 - 20.0193i) q^{74} +(0.779999 - 2.05669i) q^{75} +(-17.8890 + 15.8483i) q^{76} +(1.25163 - 1.10885i) q^{77} +(-2.21926 + 4.55766i) q^{78} +(8.54797 + 7.57284i) q^{79} +38.8678 q^{80} +(-4.94842 + 4.38392i) q^{81} +(0.523676 + 0.129075i) q^{82} +(9.48405 + 13.7400i) q^{83} +(-2.37739 + 6.26867i) q^{84} +(3.70612 - 9.77224i) q^{85} +(-1.48292 - 2.14838i) q^{86} +(-4.00276 - 0.986593i) q^{87} +(-4.41267 + 3.90928i) q^{88} -11.3874 q^{89} +(16.6352 + 14.7375i) q^{90} +(5.66590 - 6.79826i) q^{91} +(32.3107 - 28.6248i) q^{92} +(-1.39379 + 1.23479i) q^{93} +(5.43187 - 14.3227i) q^{94} +(1.67414 + 13.7878i) q^{95} +(3.17624 - 8.37507i) q^{96} +(0.552586 - 4.55096i) q^{97} +(-1.48901 + 2.15720i) q^{98} -1.85729 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9}+O(q^{10}) $ 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9} + q^{10} - q^{11} + 11 q^{12} - 65 q^{13} + 9 q^{14} - 41 q^{15} + 3 q^{17} - 13 q^{18} - 6 q^{19} + 29 q^{20} + 19 q^{21} - 22 q^{22} - 82 q^{23} - 31 q^{24} + 2 q^{25} + 26 q^{26} + 21 q^{27} + 43 q^{28} + 13 q^{29} - 81 q^{30} - 33 q^{31} - 93 q^{32} + 35 q^{33} - 24 q^{34} + 27 q^{35} + 54 q^{36} + 25 q^{37} - 56 q^{38} - 13 q^{39} - 52 q^{40} + 29 q^{41} - 63 q^{42} + 21 q^{43} + 45 q^{44} + 33 q^{46} - 69 q^{47} + 54 q^{48} - 54 q^{49} + 80 q^{50} - 16 q^{51} + 13 q^{52} - 45 q^{53} + 29 q^{54} - 83 q^{55} + 91 q^{56} - 11 q^{57} + 25 q^{58} - 57 q^{59} + 51 q^{60} + 39 q^{61} + 4 q^{62} + 26 q^{63} + 86 q^{64} + 65 q^{65} - 138 q^{66} - 101 q^{67} + 36 q^{68} + 32 q^{69} - 90 q^{70} + 20 q^{71} + 13 q^{72} + 61 q^{73} - 4 q^{74} - 67 q^{75} - 107 q^{76} + 67 q^{77} + 13 q^{78} + 57 q^{79} + 160 q^{80} + 78 q^{81} - 31 q^{82} - 59 q^{83} - 36 q^{84} - 61 q^{85} + 41 q^{86} - 9 q^{87} - 45 q^{88} - 66 q^{89} + 191 q^{90} + 39 q^{91} + 79 q^{92} - 80 q^{93} - 21 q^{94} - 28 q^{95} + 70 q^{96} + 7 q^{97} + 158 q^{98} + 130 q^{99}+O(q^{100}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9 + q^10 - q^11 + 11 * q^12 - 65 * q^13 + 9 * q^14 - 41 * q^15 + 3 * q^17 - 13 * q^18 - 6 * q^19 + 29 * q^20 + 19 * q^21 - 22 * q^22 - 82 * q^23 - 31 * q^24 + 2 * q^25 + 26 * q^26 + 21 * q^27 + 43 * q^28 + 13 * q^29 - 81 * q^30 - 33 * q^31 - 93 * q^32 + 35 * q^33 - 24 * q^34 + 27 * q^35 + 54 * q^36 + 25 * q^37 - 56 * q^38 - 13 * q^39 - 52 * q^40 + 29 * q^41 - 63 * q^42 + 21 * q^43 + 45 * q^44 + 33 * q^46 - 69 * q^47 + 54 * q^48 - 54 * q^49 + 80 * q^50 - 16 * q^51 + 13 * q^52 - 45 * q^53 + 29 * q^54 - 83 * q^55 + 91 * q^56 - 11 * q^57 + 25 * q^58 - 57 * q^59 + 51 * q^60 + 39 * q^61 + 4 * q^62 + 26 * q^63 + 86 * q^64 + 65 * q^65 - 138 * q^66 - 101 * q^67 + 36 * q^68 + 32 * q^69 - 90 * q^70 + 20 * q^71 + 13 * q^72 + 61 * q^73 - 4 * q^74 - 67 * q^75 - 107 * q^76 + 67 * q^77 + 13 * q^78 + 57 * q^79 + 160 * q^80 + 78 * q^81 - 31 * q^82 - 59 * q^83 - 36 * q^84 - 61 * q^85 + 41 * q^86 - 9 * q^87 - 45 * q^88 - 66 * q^89 + 191 * q^90 + 39 * q^91 + 79 * q^92 - 80 * q^93 - 21 * q^94 - 28 * q^95 + 70 * q^96 + 7 * q^97 + 158 * q^98 + 130 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{13}\right)$

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 $

$2$	−0.952850	−	2.51246i	−0.673767	−	1.77658i	−0.628772	−	0.777590i	$-0.716442\pi$
$2$	−0.952850	−	2.51246i	−0.673767	−	1.77658i	−0.0449953	−	0.998987i	$-0.514327\pi$
$3$	−0.297229	+	0.430610i	−0.171605	+	0.248613i	−0.899344	−	0.437241i	$-0.855956\pi$
$3$	−0.297229	+	0.430610i	−0.171605	+	0.248613i	0.727739	+	0.685854i	$0.240571\pi$
$4$	−3.90751	+	3.46175i	−1.95375	+	1.73088i
$5$	0.365684	+	3.01168i	0.163539	+	1.34686i	0.811126	+	0.584872i	$0.198855\pi$
$5$	0.365684	+	3.01168i	0.163539	+	1.34686i	−0.647587	+	0.761992i	$0.724222\pi$
$6$	1.36511	+	0.336468i	0.557302	+	0.137363i
$7$	−2.17334	−	1.14066i	−0.821446	−	0.431128i	0.000980315	−	1.00000i	$-0.499688\pi$
$7$	−2.17334	−	1.14066i	−0.821446	−	0.431128i	−0.822427	+	0.568871i	$0.807380\pi$
$8$	7.66220	+	4.02143i	2.70900	+	1.42179i
$9$	0.966734	+	2.54907i	0.322245	+	0.849690i
$10$	7.21828	−	3.78845i	2.28262	−	1.19801i
$11$	−0.241580	+	0.636994i	−0.0728391	+	0.192061i	−0.966491	−	0.256699i	$-0.917365\pi$
$11$	−0.241580	+	0.636994i	−0.0728391	+	0.192061i	0.893652	+	0.448760i	$0.148134\pi$
$12$	−0.329241	−	2.71155i	−0.0950438	−	0.782756i
$13$	−0.756816	+	3.52523i	−0.209903	+	0.977722i
$13$	−0.756816	+	3.52523i	−0.209903	+	0.977722i
$14$	−0.794988	+	6.54731i	−0.212469	+	1.74984i
$15$	−1.40555	−	0.737691i	−0.362912	−	0.190471i
$16$	1.54427	−	12.7182i	0.386066	−	3.17954i
$17$	−3.05039	−	1.60097i	−0.739828	−	0.388292i	0.0523125	−	0.998631i	$-0.483341\pi$
$17$	−3.05039	−	1.60097i	−0.739828	−	0.388292i	−0.792140	+	0.610339i	$0.791033\pi$
$18$	5.48328	−	4.85776i	1.29242	−	1.14499i
$19$	4.57811			1.05029			0.525146	−	0.851012i	$-0.324011\pi$
$19$	4.57811			1.05029			0.525146	+	0.851012i	$0.324011\pi$
$20$	−11.8546	−	10.5023i	−2.65077	−	2.34838i
$21$	1.13716	−	0.596827i	0.248148	−	0.130238i
$22$	1.83061			0.390288
$23$	−8.26888			−1.72418			−0.862090	−	0.506755i	$-0.830845\pi$
$23$	−8.26888			−1.72418			−0.862090	+	0.506755i	$0.830845\pi$
$24$	−4.00910	+	2.10414i	−0.818354	+	0.429505i
$25$	−4.08178	+	1.00607i	−0.816355	+	0.201213i
$26$	9.57812	−	1.45754i	1.87842	−	0.285848i
$27$	−2.90908	−	0.717023i	−0.559852	−	0.137991i
$28$	12.4410	−	3.06644i	2.35113	−	0.579502i
$29$	2.79395	+	7.36704i	0.518823	+	1.36802i	0.896893	+	0.442247i	$0.145819\pi$
$29$	2.79395	+	7.36704i	0.518823	+	1.36802i	−0.378070	+	0.925777i	$0.623412\pi$
$30$	−0.514137	+	4.23430i	−0.0938682	+	0.773074i
$31$	3.45540	+	0.851679i	0.620608	+	0.152966i	0.537069	−	0.843538i	$-0.319532\pi$
$31$	3.45540	+	0.851679i	0.620608	+	0.152966i	0.0835390	+	0.996505i	$0.473378\pi$
$32$	−16.6215	+	4.09682i	−2.93829	+	0.724223i
$33$	−0.202492	−	0.293360i	−0.0352493	−	0.0510674i
$34$	−1.11580	+	9.18946i	−0.191358	+	1.57598i
$35$	2.64054	−	6.96253i	0.446333	−	1.17688i
$36$	−12.6018	−	6.61392i	−2.10029	−	1.10232i
$37$	7.28687	+	1.79605i	1.19795	+	0.295269i	0.787328	−	0.616534i	$-0.211464\pi$
$37$	7.28687	+	1.79605i	1.19795	+	0.295269i	0.410626	+	0.911804i	$0.365310\pi$
$38$	−4.36226	−	11.5023i	−0.707652	−	1.86592i
$39$	−1.29305	−	1.37369i	−0.207054	−	0.219967i
$40$	−9.30932	+	24.5467i	−1.47193	+	3.88117i
$41$	−0.114022	+	0.165189i	−0.0178072	+	0.0257982i	−0.831786	−	0.555096i	$-0.812682\pi$
$41$	−0.114022	+	0.165189i	−0.0178072	+	0.0257982i	0.813979	+	0.580894i	$0.197297\pi$
$42$	−2.58305	−	2.28838i	−0.398573	−	0.353105i
$43$	0.943264	−	0.232494i	0.143846	−	0.0354550i	−0.166735	−	0.986002i	$-0.553322\pi$
$43$	0.943264	−	0.232494i	0.143846	−	0.0354550i	0.310581	+	0.950547i	$0.399476\pi$
$44$	−1.26114	−	3.32535i	−0.190124	−	0.501315i
$45$	−7.32346	+	3.84365i	−1.09172	+	0.572977i
$46$	7.87900	+	20.7752i	1.16170	+	3.06314i
$47$	4.26700	+	3.78023i	0.622406	+	0.551404i	0.914295	−	0.405048i	$-0.132745\pi$
$47$	4.26700	+	3.78023i	0.622406	+	0.551404i	−0.291889	+	0.956452i	$0.594284\pi$
$48$	5.01758	+	4.44518i	0.724225	+	0.641607i
$49$	−0.554136	−	0.802805i	−0.0791623	−	0.114686i
$50$	6.41703	+	9.29667i	0.907504	+	1.31475i
$51$	1.59606	−	0.837675i	0.223493	−	0.117298i
$52$	−9.24619	−	16.3948i	−1.28222	−	2.27354i
$53$	−8.33843	−	4.37635i	−1.14537	−	0.601137i	−0.218248	−	0.975893i	$-0.570034\pi$
$53$	−8.33843	−	4.37635i	−1.14537	−	0.601137i	−0.927123	+	0.374756i	$0.877726\pi$
$54$	0.970423	+	7.99215i	0.132058	+	1.08759i
$55$	−2.00676	−	0.494623i	−0.270592	−	0.0666949i
$56$	−12.0655	−	17.4799i	−1.61232	−	2.33585i
$57$	−1.36075	+	1.97138i	−0.180235	+	0.261116i
$58$	15.8472	−	14.0394i	2.08084	−	1.84346i
$59$	−0.616927	−	5.08085i	−0.0803171	−	0.661471i	−0.976153	−	0.217085i	$-0.930345\pi$
$59$	−0.616927	−	5.08085i	−0.0803171	−	0.661471i	0.895836	−	0.444386i	$-0.146578\pi$
$60$	8.04591	−	1.98314i	1.03872	−	0.256022i
$61$	4.02471	−	2.11233i	0.515311	−	0.270456i	−0.186958	−	0.982368i	$-0.559863\pi$
$61$	4.02471	−	2.11233i	0.515311	−	0.270456i	0.702269	+	0.711912i	$0.252171\pi$
$62$	−1.15267	−	9.49307i	−0.146389	−	1.20562i
$63$	0.806571	−	6.64271i	0.101618	−	0.836903i
$64$	11.5752	+	16.7696i	1.44691	+	2.09620i
$65$	−10.8936	−	0.990168i	−1.35119	−	0.122815i
$66$	−0.544111	+	0.788280i	−0.0669754	+	0.0970306i
$67$	−5.10800	−	4.52529i	−0.624042	−	0.552853i	0.290740	−	0.956802i	$-0.406099\pi$
$67$	−5.10800	−	4.52529i	−0.624042	−	0.552853i	−0.914781	+	0.403950i	$0.867637\pi$
$68$	17.4616	−	4.30389i	2.11753	−	0.521923i
$69$	2.45775	−	3.56067i	0.295878	−	0.428654i
$70$	−20.0091			−2.39155
$71$	1.92369	−	2.78694i	0.228300	−	0.330749i	−0.692047	−	0.721852i	$-0.743291\pi$
$71$	1.92369	−	2.78694i	0.228300	−	0.330749i	0.920347	+	0.391103i	$0.127906\pi$
$72$	−2.84360	+	23.4191i	−0.335121	+	2.75997i
$73$	2.71442	−	7.15733i	0.317699	−	0.837703i	−0.677105	−	0.735887i	$-0.736766\pi$
$73$	2.71442	−	7.15733i	0.317699	−	0.837703i	0.994803	−	0.101816i	$-0.0324652\pi$
$74$	−2.43079	−	20.0193i	−0.282573	−	2.32720i
$75$	0.779999	−	2.05669i	0.0900665	−	0.237486i
$76$	−17.8890	+	15.8483i	−2.05201	+	1.81792i
$77$	1.25163	−	1.10885i	0.142636	−	0.126365i
$78$	−2.21926	+	4.55766i	−0.251282	+	0.516054i
$79$	8.54797	+	7.57284i	0.961722	+	0.852011i	0.989045	−	0.147616i	$-0.0471599\pi$
$79$	8.54797	+	7.57284i	0.961722	+	0.852011i	−0.0273232	+	0.999627i	$0.508698\pi$
$80$	38.8678			4.34555
$81$	−4.94842	+	4.38392i	−0.549824	+	0.487102i
$82$	0.523676	+	0.129075i	0.0578303	+	0.0142539i
$83$	9.48405	+	13.7400i	1.04101	+	1.50816i	0.850146	+	0.526547i	$0.176514\pi$
$83$	9.48405	+	13.7400i	1.04101	+	1.50816i	0.190864	+	0.981617i	$0.438871\pi$
$84$	−2.37739	+	6.26867i	−0.259395	+	0.683968i
$85$	3.70612	−	9.77224i	0.401985	−	1.05995i
$86$	−1.48292	−	2.14838i	−0.159907	−	0.231666i
$87$	−4.00276	−	0.986593i	−0.429141	−	0.105774i
$88$	−4.41267	+	3.90928i	−0.470392	+	0.416731i
$89$	−11.3874			−1.20707			−0.603533	−	0.797338i	$-0.706241\pi$
$89$	−11.3874			−1.20707			−0.603533	+	0.797338i	$0.706241\pi$
$90$	16.6352	+	14.7375i	1.75350	+	1.55347i
$91$	5.66590	−	6.79826i	0.593948	−	0.712651i
$92$	32.3107	−	28.6248i	3.36863	−	2.98434i
$93$	−1.39379	+	1.23479i	−0.144529	+	0.128041i
$94$	5.43187	−	14.3227i	0.560255	−	1.47727i
$95$	1.67414	+	13.7878i	0.171763	+	1.41460i
$96$	3.17624	−	8.37507i	0.324174	−	0.854777i
$97$	0.552586	−	4.55096i	0.0561066	−	0.462080i	−0.937396	−	0.348267i	$-0.886770\pi$
$97$	0.552586	−	4.55096i	0.0561066	−	0.462080i	0.993502	−	0.113813i	$-0.0363065\pi$
$98$	−1.48901	+	2.15720i	−0.150412	+	0.217910i
$99$	−1.85729			−0.186664
$100$	12.4668	−	18.0613i	1.24668	−	1.80613i
$101$	0.867962	−	0.213933i	0.0863654	−	0.0212872i	−0.195896	−	0.980625i	$-0.562762\pi$
$101$	0.867962	−	0.213933i	0.0863654	−	0.0212872i	0.282262	+	0.959337i	$0.408915\pi$
$102$	−3.62543	−	3.21185i	−0.358971	−	0.318020i
$103$	3.12548	−	4.52805i	0.307963	−	0.446162i	−0.638191	−	0.769878i	$-0.720317\pi$
$103$	3.12548	−	4.52805i	0.307963	−	0.446162i	0.946154	+	0.323716i	$0.104932\pi$
$104$	−19.9754	+	23.9675i	−1.95874	+	2.35021i
$105$	2.21329	+	3.20651i	0.215995	+	0.312923i
$106$	−3.05012	+	25.1200i	−0.296254	+	2.43987i
$107$	−0.263890	−	2.17333i	−0.0255112	−	0.210104i	0.974379	−	0.224912i	$-0.0722094\pi$
$107$	−0.263890	−	2.17333i	−0.0255112	−	0.210104i	−0.999890	+	0.0148080i	$0.995286\pi$
$108$	13.8494	−	7.26872i	1.33266	−	0.699433i
$109$	4.52333	−	1.11490i	0.433257	−	0.106788i	−0.0166548	−	0.999861i	$-0.505302\pi$
$109$	4.52333	−	1.11490i	0.433257	−	0.106788i	0.449912	+	0.893073i	$0.351455\pi$
$110$	0.669426	+	5.51322i	0.0638272	+	0.525664i
$111$	−2.93927	+	2.60396i	−0.278983	+	0.247157i
$112$	−17.8633	+	25.8795i	−1.68792	+	2.44538i
$113$	8.88874	+	12.8776i	0.836183	+	1.21142i	0.975243	+	0.221136i	$0.0709764\pi$
$113$	8.88874	+	12.8776i	0.836183	+	1.21142i	−0.139060	+	0.990284i	$0.544408\pi$
$114$	6.24961	+	1.54039i	0.585330	+	0.144271i
$115$	−3.02380	−	24.9032i	−0.281971	−	2.32224i
$116$	−36.4202	−	19.1148i	−3.38153	−	1.77477i
$117$	−9.71769	+	1.47878i	−0.898401	+	0.136713i
$118$	−12.1776	+	6.39130i	−1.12104	+	0.588367i
$119$	4.80338	+	6.95890i	0.440325	+	0.637921i
$120$	−7.80305	−	11.3047i	−0.712318	−	1.03197i
$121$	7.88622	+	6.98658i	0.716929	+	0.635144i
$122$	−9.14208	−	8.09918i	−0.827685	−	0.733265i
$123$	−0.0372415	−	0.0981978i	−0.00335795	−	0.00885420i
$124$	−16.4503	+	8.63378i	−1.47728	+	0.775336i
$125$	0.856407	+	2.25816i	0.0765994	+	0.201976i
$126$	−17.4581	+	4.30303i	−1.55529	+	0.383345i
$127$	5.92531	+	5.24937i	0.525786	+	0.465806i	0.883770	−	0.467922i	$-0.154997\pi$
$127$	5.92531	+	5.24937i	0.525786	+	0.465806i	−0.357983	+	0.933728i	$0.616536\pi$
$128$	11.6543	−	16.8841i	1.03010	−	1.49236i
$129$	−0.180251	+	0.475283i	−0.0158702	+	0.0418464i
$130$	7.89222	+	28.3132i	0.692194	+	2.48324i
$131$	−4.07142	−	10.7354i	−0.355721	−	0.937960i	−0.986757	−	0.162206i	$-0.948139\pi$
$131$	−4.07142	−	10.7354i	−0.355721	−	0.937960i	0.631036	−	0.775754i	$-0.282630\pi$
$132$	1.80678	+	0.445331i	0.157260	+	0.0387610i
$133$	−9.94981	−	5.22206i	−0.862758	−	0.452810i
$134$	−6.50246	+	17.1456i	−0.561727	+	1.48115i
$135$	1.09564	−	9.02341i	0.0942977	−	0.776611i
$136$	−16.9345	−	24.5339i	−1.45212	−	2.10376i
$137$	18.3408	−	4.52059i	1.56696	−	0.386220i	0.642126	−	0.766599i	$-0.278053\pi$
$137$	18.3408	−	4.52059i	1.56696	−	0.386220i	0.924831	+	0.380379i	$0.124207\pi$
$138$	−11.2879	−	2.78222i	−0.960889	−	0.236838i
$139$	1.93333	−	15.9224i	0.163983	−	1.35052i	−0.645673	−	0.763614i	$-0.723423\pi$
$139$	1.93333	−	15.9224i	0.163983	−	1.35052i	0.809656	−	0.586905i	$-0.199654\pi$
$140$	13.7846	+	36.3470i	1.16501	+	3.07189i
$141$	−2.89608	+	0.713821i	−0.243894	+	0.0601145i
$142$	−8.83507	−	2.17765i	−0.741423	−	0.182744i
$143$	−2.06272	−	1.33371i	−0.172493	−	0.111531i
$144$	33.9124	−	8.35866i	2.82603	−	0.696555i
$145$	−21.1654	+	11.1085i	−1.75769	+	0.922509i
$146$	−20.5689			−1.70230
$147$	0.510402			0.0420972
$148$	−34.6910	+	18.2072i	−2.85158	+	1.49663i
$149$	5.27855	+	4.67639i	0.432436	+	0.383105i	0.851072	−	0.525049i	$-0.175953\pi$
$149$	5.27855	+	4.67639i	0.432436	+	0.383105i	−0.418636	+	0.908154i	$0.637492\pi$
$150$	−5.91057			−0.482596
$151$	−6.31854	+	5.59774i	−0.514196	+	0.455538i	−0.879876	−	0.475203i	$-0.842375\pi$
$151$	−6.31854	+	5.59774i	−0.514196	+	0.455538i	0.365681	+	0.930740i	$0.380836\pi$
$152$	35.0784	+	18.4106i	2.84524	+	1.49330i
$153$	1.13206	−	9.32336i	0.0915217	−	0.753749i
$154$	−3.97855	−	2.08810i	−0.320600	−	0.168264i
$155$	−1.30140	+	10.7180i	−0.104531	+	0.860890i
$156$	9.80799	+	0.891492i	0.785268	+	0.0713765i
$157$	−0.0922946	−	0.760115i	−0.00736591	−	0.0606638i	0.988562	−	0.150812i	$-0.0481889\pi$
$157$	−0.0922946	−	0.760115i	−0.00736591	−	0.0606638i	−0.995928	+	0.0901485i	$0.971266\pi$
$158$	10.8815	−	28.6922i	0.865687	−	2.28263i
$159$	4.36292	−	2.28984i	0.346002	−	0.181596i
$160$	−18.4165	−	48.5604i	−1.45595	−	3.83903i
$161$	17.9711	+	9.43197i	1.41632	+	0.743343i
$162$	15.7295	+	8.25549i	1.23583	+	0.648612i
$163$	18.3481	+	4.52241i	1.43714	+	0.354222i	0.879514	−	0.475873i	$-0.157868\pi$
$163$	18.3481	+	4.52241i	1.43714	+	0.354222i	0.557622	+	0.830095i	$0.311714\pi$
$164$	−0.126302	−	1.04019i	−0.00986254	−	0.0812253i
$165$	0.809458	−	0.717117i	0.0630162	−	0.0558275i
$166$	25.4844	−	36.9205i	1.97797	−	2.86559i
$167$	−1.82658	−	4.81630i	−0.141345	−	0.372696i	0.845586	−	0.533839i	$-0.179251\pi$
$167$	−1.82658	−	4.81630i	−0.141345	−	0.372696i	−0.986931	+	0.161143i	$0.948482\pi$
$168$	11.1132			0.857406
$169$	−11.8545	−	5.33590i	−0.911881	−	0.410454i
$170$	−28.0837			−2.15392
$171$	4.42582	+	11.6699i	0.338451	+	0.892422i
$172$	−2.88098	+	4.17382i	−0.219673	+	0.318251i
$173$	−7.97824	+	7.06811i	−0.606575	+	0.537378i	−0.909536	−	0.415624i	$-0.863563\pi$
$173$	−7.97824	+	7.06811i	−0.606575	+	0.537378i	0.302962	+	0.953003i	$0.402025\pi$
$174$	1.33526	+	10.9969i	0.101226	+	0.833670i
$175$	10.0187	+	2.46938i	0.757341	+	0.186668i
$176$	7.72834	+	4.05615i	0.582545	+	0.305743i
$177$	2.37124	+	1.24452i	0.178233	+	0.0935439i
$178$	10.8505	+	28.6105i	0.813282	+	2.14445i
$179$	2.42435	−	1.27240i	0.181205	−	0.0951035i	−0.371682	−	0.928360i	$-0.621219\pi$
$179$	2.42435	−	1.27240i	0.181205	−	0.0951035i	0.552886	+	0.833257i	$0.313526\pi$
$180$	15.3107	−	40.3711i	1.14119	−	3.00908i
$181$	2.29585	+	18.9080i	0.170649	+	1.40542i	0.786515	+	0.617571i	$0.211883\pi$
$181$	2.29585	+	18.9080i	0.170649	+	1.40542i	−0.615866	+	0.787851i	$0.711194\pi$
$182$	−22.4791	−	7.75762i	−1.66626	−	0.575033i
$183$	−0.286668	+	2.36092i	−0.0211911	+	0.174525i
$184$	−63.3578	−	33.2528i	−4.67080	−	2.45143i
$185$	−2.74444	+	22.6025i	−0.201775	+	1.66177i
$186$	4.43042	+	2.32526i	0.324854	+	0.170497i
$187$	1.75672	−	1.55632i	0.128464	−	0.113809i
$188$	−29.7596			−2.17044
$189$	5.50454	+	4.87660i	0.400396	+	0.354720i
$190$	33.0461	−	17.3439i	2.39742	−	1.25826i
$191$	−5.44285			−0.393830			−0.196915	−	0.980421i	$-0.563092\pi$
$191$	−5.44285			−0.393830			−0.196915	+	0.980421i	$0.563092\pi$
$192$	−10.6617			−0.769440
$193$	5.44804	−	2.85935i	0.392159	−	0.205821i	−0.257106	−	0.966383i	$-0.582769\pi$
$193$	5.44804	−	2.85935i	0.392159	−	0.205821i	0.649265	+	0.760562i	$0.275077\pi$
$194$	−11.9606	+	2.94803i	−0.858723	+	0.211656i
$195$	3.66427	−	4.39659i	0.262404	−	0.314847i
$196$	4.94440	+	1.21869i	0.353172	+	0.0870490i
$197$	13.2517	−	3.26625i	0.944143	−	0.232710i	0.262946	−	0.964810i	$-0.415306\pi$
$197$	13.2517	−	3.26625i	0.944143	−	0.232710i	0.681197	+	0.732100i	$0.261460\pi$
$198$	1.76972	+	4.66636i	0.125768	+	0.331623i
$199$	−0.585634	+	4.82313i	−0.0415145	+	0.341903i	0.957121	+	0.289687i	$0.0935513\pi$
$199$	−0.585634	+	4.82313i	−0.0415145	+	0.341903i	−0.998636	+	0.0522154i	$0.983372\pi$
$200$	−35.3212	−	8.70590i	−2.49759	−	0.615600i
$201$	3.46688	−	0.854510i	0.244535	−	0.0602725i
$202$	−1.36454	−	1.97687i	−0.0960085	−	0.139092i
$203$	2.33106	−	19.1980i	0.163609	−	1.34744i
$204$	−3.33678	+	8.79837i	−0.233621	+	0.616009i
$205$	−0.539192	−	0.282990i	−0.0376588	−	0.0197649i
$206$	−14.3546	−	3.53810i	−1.00014	−	0.246511i
$207$	−7.99381	−	21.0779i	−0.555608	−	1.46502i
$208$	43.6657	+	15.0692i	3.02767	+	1.04486i
$209$	−1.10598	+	2.91623i	−0.0765023	+	0.201720i
$210$	5.94729	−	8.61613i	0.410402	−	0.594570i
$211$	13.5413	+	11.9966i	0.932223	+	0.825877i	0.984969	−	0.172731i	$-0.0552590\pi$
$211$	13.5413	+	11.9966i	0.932223	+	0.825877i	−0.0527463	+	0.998608i	$0.516797\pi$
$212$	47.7323	−	11.7650i	3.27827	−	0.808020i
$213$	0.628311	+	1.65672i	0.0430512	+	0.113517i
$214$	−5.20896	+	2.73387i	−0.356077	+	0.186884i
$215$	1.04513	+	2.75579i	0.0712775	+	0.187943i
$216$	−19.4065	−	17.1926i	−1.32044	−	1.16981i
$217$	−6.53829	−	5.79242i	−0.443848	−	0.393215i
$218$	−7.11121	−	10.3024i	−0.481632	−	0.697764i
$219$	2.27522	+	3.29622i	0.153745	+	0.222738i
$220$	9.55371	−	5.01417i	0.644111	−	0.338055i
$221$	7.95236	−	9.54167i	0.534933	−	0.641842i
$222$	9.34303	+	4.90360i	0.627063	+	0.329108i
$223$	−0.863529	−	7.11180i	−0.0578261	−	0.476241i	−0.992640	−	0.121103i	$-0.961357\pi$
$223$	−0.863529	−	7.11180i	−0.0578261	−	0.476241i	0.934814	−	0.355138i	$-0.115566\pi$
$224$	40.7972	+	10.0556i	2.72588	+	0.671868i
$225$	−6.51053	−	9.43213i	−0.434035	−	0.628809i
$226$	23.8847	−	34.6030i	1.58879	−	2.30176i
$227$	−18.3215	+	16.2315i	−1.21604	+	1.07732i	−0.221269	+	0.975213i	$0.571020\pi$
$227$	−18.3215	+	16.2315i	−1.21604	+	1.07732i	−0.994773	+	0.102107i	$0.967442\pi$
$228$	−1.50730	−	12.4138i	−0.0998237	−	0.822122i
$229$	−8.85652	+	2.18294i	−0.585255	+	0.144252i	−0.520816	−	0.853669i	$-0.674372\pi$
$229$	−8.85652	+	2.18294i	−0.585255	+	0.144252i	−0.0644396	+	0.997922i	$0.520526\pi$
$230$	−59.6871	+	31.3262i	−3.93565	+	2.06559i
$231$	0.105461	+	0.868545i	0.00693879	+	0.0571461i
$232$	−8.21826	+	67.6834i	−0.539555	+	4.44363i
$233$	8.33640	+	12.0774i	0.546136	+	0.791214i	0.994731	−	0.102521i	$-0.0326909\pi$
$233$	8.33640	+	12.0774i	0.546136	+	0.791214i	−0.448595	+	0.893735i	$0.648076\pi$
$234$	12.9749	+	23.0062i	0.848195	+	1.50397i
$235$	−9.82448	+	14.2332i	−0.640878	+	0.928472i
$236$	19.9993	+	17.7178i	1.30184	+	1.15333i
$237$	−5.80165	+	1.42998i	−0.376857	+	0.0928870i
$238$	12.9071	−	18.6991i	0.836640	−	1.21208i
$239$	−11.5632			−0.747964			−0.373982	−	0.927436i	$-0.622008\pi$
$239$	−11.5632			−0.747964			−0.373982	+	0.927436i	$0.622008\pi$
$240$	−11.5526	+	16.7369i	−0.745719	+	1.08036i
$241$	−1.88540	+	15.5277i	−0.121449	+	1.00023i	0.796806	+	0.604236i	$0.206521\pi$
$241$	−1.88540	+	15.5277i	−0.121449	+	1.00023i	−0.918255	+	0.395990i	$0.870402\pi$
$242$	10.0391	−	26.4710i	0.645339	−	1.70162i
$243$	−1.50038	−	12.3567i	−0.0962495	−	0.792686i
$244$	−8.41422	+	22.1865i	−0.538665	+	1.42034i
$245$	2.21515	−	1.96245i	0.141521	−	0.125377i
$246$	−0.211232	+	0.187136i	−0.0134677	+	0.0119313i
$247$	−3.46479	+	16.1389i	−0.220459	+	1.02689i
$248$	23.0510	+	20.4214i	1.46374	+	1.29676i
$249$	−8.73553			−0.553592
$250$	4.85751	−	4.30338i	0.307216	−	0.272169i
$251$	−15.0781	−	3.71642i	−0.951721	−	0.234578i	−0.267257	−	0.963625i	$-0.586117\pi$
$251$	−15.0781	−	3.71642i	−0.951721	−	0.234578i	−0.684464	+	0.729047i	$0.739964\pi$
$252$	19.8437	+	28.7486i	1.25004	+	1.81099i
$253$	1.99760	−	5.26723i	0.125588	−	0.331148i
$254$	7.54289	−	19.8890i	0.473283	−	1.24794i
$255$	3.10646	+	4.50048i	0.194534	+	0.281831i
$256$	−13.9564	−	3.43994i	−0.872275	−	0.214996i
$257$	−5.39152	+	4.77647i	−0.336314	+	0.297948i	−0.814329	−	0.580404i	$-0.802895\pi$
$257$	−5.39152	+	4.77647i	−0.336314	+	0.297948i	0.478015	+	0.878351i	$0.341356\pi$
$258$	1.36588			0.0850361
$259$	−13.7882	−	12.2153i	−0.856756	−	0.759020i
$260$	45.9946	−	33.8419i	2.85246	−	2.09878i
$261$	−16.0781	+	14.2439i	−0.995208	+	0.881678i
$262$	−23.0929	+	20.4585i	−1.42669	+	1.26393i
$263$	−0.564641	+	1.48884i	−0.0348172	+	0.0918055i	−0.951297	−	0.308275i	$-0.900248\pi$
$263$	−0.564641	+	1.48884i	−0.0348172	+	0.0918055i	0.916480	+	0.400080i	$0.131018\pi$
$264$	−0.371805	−	3.06209i	−0.0228830	−	0.188459i
$265$	10.1309	−	26.7130i	0.622337	−	1.64097i
$266$	−3.63954	+	29.9743i	−0.223155	+	1.83785i
$267$	3.38468	−	4.90355i	0.207139	−	0.300092i
$268$	35.6250			2.17614
$269$	7.39844	−	10.7185i	0.451091	−	0.653518i	−0.529790	−	0.848129i	$-0.677729\pi$
$269$	7.39844	−	10.7185i	0.451091	−	0.653518i	0.980880	+	0.194611i	$0.0623446\pi$
$270$	−23.7149	+	5.84520i	−1.44324	+	0.355728i
$271$	−2.71084	−	2.40159i	−0.164672	−	0.145886i	0.576763	−	0.816912i	$-0.304316\pi$
$271$	−2.71084	−	2.40159i	−0.164672	−	0.145886i	−0.741434	+	0.671025i	$0.765854\pi$
$272$	−25.0720	+	36.3230i	−1.52021	+	2.20241i
$273$	1.24333	+	4.46043i	0.0752498	+	0.269958i
$274$	−28.8338	−	41.7730i	−1.74191	−	2.52360i
$275$	0.345216	−	2.84311i	0.0208173	−	0.171446i
$276$	2.72246	+	22.4214i	0.163873	+	1.34961i
$277$	−3.13801	+	1.64696i	−0.188545	+	0.0989560i	−0.556354	−	0.830945i	$-0.687800\pi$
$277$	−3.13801	+	1.64696i	−0.188545	+	0.0989560i	0.367809	+	0.929901i	$0.380108\pi$
$278$	−41.8465	+	10.3142i	−2.50979	+	0.618607i
$279$	1.16946	+	9.63140i	0.0700139	+	0.576617i
$280$	48.2317	−	42.7296i	2.88240	−	2.55358i
$281$	18.0685	−	26.1767i	1.07788	−	1.56157i	0.278795	−	0.960351i	$-0.410065\pi$
$281$	18.0685	−	26.1767i	1.07788	−	1.56157i	0.799082	−	0.601223i	$-0.205319\pi$
$282$	4.55298	+	6.59613i	0.271126	+	0.392794i
$283$	−12.7489	−	3.14232i	−0.757843	−	0.186791i	−0.158583	−	0.987346i	$-0.550692\pi$
$283$	−12.7489	−	3.14232i	−0.757843	−	0.186791i	−0.599260	+	0.800554i	$0.704539\pi$
$284$	2.13087	+	17.5493i	0.126444	+	1.04136i
$285$	−6.43478	−	3.37723i	−0.381163	−	0.200050i
$286$	−1.38544	+	6.45332i	−0.0819226	+	0.381593i
$287$	0.436232	−	0.228952i	0.0257500	−	0.0135146i
$288$	−26.5116	−	38.4087i	−1.56221	−	2.26325i
$289$	−2.91533	−	4.22359i	−0.171490	−	0.248446i
$290$	48.0771	+	42.5926i	2.82319	+	2.50112i
$291$	1.79544	+	1.59062i	0.105251	+	0.0932441i
$292$	14.1703	+	37.3640i	0.829254	+	2.18656i
$293$	15.1728	−	7.96330i	0.886404	−	0.465221i	0.0408836	−	0.999164i	$-0.486983\pi$
$293$	15.1728	−	7.96330i	0.886404	−	0.465221i	0.845520	+	0.533943i	$0.179290\pi$
$294$	−0.486336	−	1.28236i	−0.0283637	−	0.0747889i
$295$	15.0763	−	3.71597i	0.877776	−	0.216352i
$296$	48.6108	+	43.0654i	2.82544	+	2.50313i
$297$	1.15951	−	1.67985i	0.0672818	−	0.0974746i
$298$	6.71957	−	17.7181i	0.389254	−	1.02638i
$299$	6.25802	−	29.1497i	0.361911	−	1.68577i
$300$	4.07189	+	10.7367i	0.235090	+	0.619883i
$301$	−2.31523	−	0.570654i	−0.133448	−	0.0328919i
$302$	20.0847	+	10.5413i	1.15575	+	0.606582i
$303$	−0.165861	+	0.437341i	−0.00952849	+	0.0251246i
$304$	7.06983	−	58.2253i	0.405482	−	3.33945i
$305$	7.83343	+	11.3487i	0.448541	+	0.649823i
$306$	−24.5032	+	6.03951i	−1.40076	+	0.345256i
$307$	−12.9102	−	3.18207i	−0.736823	−	0.181610i	−0.146992	−	0.989138i	$-0.546959\pi$
$307$	−12.9102	−	3.18207i	−0.736823	−	0.181610i	−0.589830	+	0.807527i	$0.700805\pi$
$308$	−1.05220	+	8.66565i	−0.0599547	+	0.493771i
$309$	1.02084	+	2.69173i	0.0580735	+	0.153127i
$310$	28.1686	−	6.94293i	1.59987	−	0.394332i
$311$	−9.53011	−	2.34896i	−0.540403	−	0.133197i	−0.0403393	−	0.999186i	$-0.512844\pi$
$311$	−9.53011	−	2.34896i	−0.540403	−	0.133197i	−0.500064	+	0.865989i	$0.666690\pi$
$312$	−4.38341	−	15.7254i	−0.248162	−	0.890277i
$313$	−13.0341	+	3.21261i	−0.736730	+	0.181588i	−0.589789	−	0.807558i	$-0.700789\pi$
$313$	−13.0341	+	3.21261i	−0.736730	+	0.181588i	−0.146941	+	0.989145i	$0.546943\pi$
$314$	−1.82181	+	0.956162i	−0.102811	+	0.0539593i
$315$	20.3007			1.14381
$316$	−59.6165			−3.35369
$317$	5.72106	−	3.00265i	0.321327	−	0.168645i	−0.296346	−	0.955081i	$-0.595768\pi$
$317$	5.72106	−	3.00265i	0.321327	−	0.168645i	0.617673	+	0.786435i	$0.288076\pi$
$318$	−9.91034	−	8.77979i	−0.555744	−	0.492346i
$319$	−5.36772			−0.300535
$320$	−46.2719	+	40.9933i	−2.58668	+	2.29160i
$321$	1.01429	+	0.532343i	0.0566124	+	0.0297125i
$322$	6.57366	−	54.1389i	0.366336	−	3.01704i
$323$	−13.9650	−	7.32941i	−0.777035	−	0.407819i
$324$	4.15996	−	34.2604i	0.231109	−	1.90335i
$325$	−0.457462	−	15.1506i	−0.0253754	−	0.840404i
$326$	−6.12065	−	50.4081i	−0.338991	−	2.79185i
$327$	−0.864377	+	2.27918i	−0.0478002	+	0.126039i
$328$	−1.53795	+	0.807180i	−0.0849193	+	0.0445691i
$329$	−4.96170	−	13.0829i	−0.273547	−	0.721285i
$330$	−2.57302	−	1.35043i	−0.141640	−	0.0743385i
$331$	−14.7236	−	7.72754i	−0.809282	−	0.424744i	0.00871794	−	0.999962i	$-0.497225\pi$
$331$	−14.7236	−	7.72754i	−0.809282	−	0.424744i	−0.818000	+	0.575218i	$0.804917\pi$
$332$	−84.6235	−	20.8578i	−4.64432	−	1.14472i
$333$	2.46621	+	20.3110i	0.135147	+	1.11304i
$334$	−10.3603	+	9.17842i	−0.566890	+	0.502221i
$335$	11.7608	−	17.0385i	0.642562	−	0.930912i
$336$	−5.83448	−	15.3842i	−0.318297	−	0.839280i
$337$	2.35775			0.128435			0.0642174	−	0.997936i	$-0.479545\pi$
$337$	2.35775			0.128435			0.0642174	+	0.997936i	$0.479545\pi$
$338$	−2.11071	+	34.8682i	−0.114807	+	1.89658i
$339$	−8.18721			−0.444668
$340$	19.3473	+	51.0148i	1.04926	+	2.76666i
$341$	−1.37727	+	1.99532i	−0.0745833	+	0.108053i
$342$	25.1031	−	22.2394i	1.35742	−	1.20257i
$343$	2.35959	+	19.4330i	0.127406	+	1.04928i
$344$	8.16244	+	2.01186i	0.440089	+	0.108472i
$345$	11.6223	+	6.09987i	0.625726	+	0.328406i
$346$	25.3604	+	13.3102i	1.36338	+	0.715559i
$347$	−7.57742	−	19.9800i	−0.406777	−	1.07258i	−0.969317	−	0.245813i	$-0.920945\pi$
$347$	−7.57742	−	19.9800i	−0.406777	−	1.07258i	0.562540	−	0.826770i	$-0.309824\pi$
$348$	19.0562	−	10.0015i	1.02152	−	0.536134i
$349$	2.27701	−	6.00398i	0.121885	−	0.321386i	−0.860162	−	0.510022i	$-0.829637\pi$
$349$	2.27701	−	6.00398i	0.121885	−	0.321386i	0.982047	+	0.188636i	$0.0604066\pi$
$350$	−3.34208	−	27.5245i	−0.178641	−	1.47124i
$351$	4.72931	−	9.71250i	0.252432	−	0.518415i
$352$	1.40576	−	11.5775i	0.0749273	−	0.617082i
$353$	−23.5170	−	12.3427i	−1.25169	−	0.656935i	−0.297093	−	0.954849i	$-0.596017\pi$
$353$	−23.5170	−	12.3427i	−1.25169	−	0.656935i	−0.954593	+	0.297913i	$0.903709\pi$
$354$	0.867375	−	7.14348i	0.0461005	−	0.379672i
$355$	9.09684	+	4.77439i	0.482810	+	0.253398i
$356$	44.4965	−	39.4205i	2.35831	−	2.08928i
$357$	−4.42428			−0.234158
$358$	−5.50690	−	4.87868i	−0.291048	−	0.257846i
$359$	−13.1159	+	6.88377i	−0.692232	+	0.363312i	−0.773865	−	0.633351i	$-0.781679\pi$
$359$	−13.1159	+	6.88377i	−0.692232	+	0.363312i	0.0816324	+	0.996663i	$0.473987\pi$
$360$	−71.5708			−3.77211
$361$	1.95913			0.103112
$362$	45.3181	−	23.7847i	2.38186	−	1.25010i
$363$	−5.35250	+	1.31927i	−0.280934	+	0.0692439i
$364$	1.39432	+	46.1782i	0.0730822	+	2.42039i
$365$	22.5482	+	5.55764i	1.18023	+	0.290900i
$366$	6.20488	−	1.52937i	0.324334	−	0.0799412i
$367$	13.0849	+	34.5021i	0.683028	+	1.80100i	0.593224	+	0.805037i	$0.297855\pi$
$367$	13.0849	+	34.5021i	0.683028	+	1.80100i	0.0898037	+	0.995959i	$0.471376\pi$
$368$	−12.7693	+	105.165i	−0.665648	+	5.48211i
$369$	−0.531307	−	0.130955i	−0.0276587	−	0.00681726i
$370$	59.4029	−	14.6415i	3.08821	−	0.761176i
$371$	13.1303	+	19.0226i	0.681694	+	0.987604i
$372$	1.17171	−	9.64988i	0.0607502	−	0.500323i
$373$	−9.29785	+	24.5164i	−0.481425	+	1.26941i	0.445876	+	0.895095i	$0.352892\pi$
$373$	−9.29785	+	24.5164i	−0.481425	+	1.26941i	−0.927301	+	0.374318i	$0.877877\pi$
$374$	−5.58408	−	2.93075i	−0.288746	−	0.151545i
$375$	−1.22694	−	0.302412i	−0.0633587	−	0.0156165i
$376$	17.4927	+	46.1244i	0.902116	+	2.37868i
$377$	−28.0850	+	4.27381i	−1.44645	+	0.220112i
$378$	7.00725	−	18.4766i	0.360414	−	0.950334i
$379$	13.9448	−	20.2026i	0.716299	−	1.03774i	−0.280660	−	0.959807i	$-0.590553\pi$
$379$	13.9448	−	20.2026i	0.716299	−	1.03774i	0.996959	−	0.0779306i	$-0.0248312\pi$
$380$	−54.2717	−	48.0805i	−2.78408	−	2.46648i
$381$	−4.02161	+	0.991237i	−0.206033	+	0.0507826i
$382$	5.18622	+	13.6749i	0.265350	+	0.699670i
$383$	8.93410	−	4.68898i	0.456511	−	0.239595i	−0.220761	−	0.975328i	$-0.570854\pi$
$383$	8.93410	−	4.68898i	0.456511	−	0.239595i	0.677272	+	0.735732i	$0.263162\pi$
$384$	3.80649	+	10.0369i	0.194249	+	0.512193i
$385$	3.79719	+	3.36402i	0.193523	+	0.171446i
$386$	−12.3752	−	10.9634i	−0.629880	−	0.558025i
$387$	1.50453	+	2.17969i	0.0764795	+	0.110800i
$388$	13.5950	+	19.6958i	0.690184	+	0.999904i
$389$	4.38026	−	2.29894i	0.222088	−	0.116561i	−0.350010	−	0.936746i	$-0.613822\pi$
$389$	4.38026	−	2.29894i	0.222088	−	0.116561i	0.572098	+	0.820185i	$0.306130\pi$
$390$	−14.5378	−	5.01704i	−0.736148	−	0.254048i
$391$	25.2233	+	13.2382i	1.27560	+	0.669485i
$392$	−1.01748	−	8.37968i	−0.0513904	−	0.423238i
$393$	5.83294	+	1.43769i	0.294233	+	0.0725218i
$394$	−20.8332	−	30.1821i	−1.04956	−	1.52055i
$395$	−19.6811	+	28.5130i	−0.990264	+	1.43464i
$396$	7.25736	−	6.42946i	0.364696	−	0.323093i
$397$	−3.58494	−	29.5246i	−0.179923	−	1.48180i	−0.750673	−	0.660674i	$-0.770271\pi$
$397$	−3.58494	−	29.5246i	−0.179923	−	1.48180i	0.570751	−	0.821123i	$-0.306652\pi$
$398$	12.6759	−	3.12434i	0.635388	−	0.156609i
$399$	5.20605	−	2.73234i	0.260628	−	0.136788i
$400$	6.49199	+	53.4664i	0.324600	+	2.67332i
$401$	−2.51184	+	20.6869i	−0.125435	+	1.03305i	0.785027	+	0.619461i	$0.212649\pi$
$401$	−2.51184	+	20.6869i	−0.125435	+	1.03305i	−0.910463	+	0.413591i	$0.864274\pi$
$402$	−5.45034	−	7.89619i	−0.271838	−	0.393826i
$403$	−5.61746	+	11.5365i	−0.279826	+	0.574674i
$404$	−2.65098	+	3.84061i	−0.131891	+	0.191078i
$405$	−15.0125	−	13.2999i	−0.745977	−	0.660878i
$406$	−50.4554	+	12.4362i	−2.50406	+	0.617196i
$407$	−2.90444	+	4.20780i	−0.143968	+	0.208573i
$408$	15.5980			0.772214
$409$	14.2740	−	20.6794i	0.705803	−	1.02253i	−0.292008	−	0.956416i	$-0.594324\pi$
$409$	14.2740	−	20.6794i	0.705803	−	1.02253i	0.997812	−	0.0661170i	$-0.0210611\pi$
$410$	−0.197231	+	1.62434i	−0.00974055	+	0.0802207i
$411$	−3.50479	+	9.24137i	−0.172878	+	0.455843i
$412$	3.46211	+	28.5130i	0.170566	+	1.40474i
$413$	−4.45472	+	11.7461i	−0.219203	+	0.577990i
$414$	−45.3406	+	40.1683i	−2.22837	+	1.97416i
$415$	−37.9124	+	33.5874i	−1.86104	+	1.64874i
$416$	−1.86284	−	61.6950i	−0.0913331	−	3.02484i
$417$	6.28171	+	5.56511i	0.307616	+	0.272524i
$418$	8.38075			0.409916
$419$	0.537094	−	0.475823i	0.0262387	−	0.0232455i	−0.649901	−	0.760019i	$-0.725190\pi$
$419$	0.537094	−	0.475823i	0.0262387	−	0.0232455i	0.676140	+	0.736773i	$0.263651\pi$
$420$	−19.7486	−	4.86759i	−0.963633	−	0.237514i
$421$	−4.04410	−	5.85889i	−0.197098	−	0.285545i	0.711956	−	0.702224i	$-0.247809\pi$
$421$	−4.04410	−	5.85889i	−0.197098	−	0.285545i	−0.909054	+	0.416679i	$0.863194\pi$
$422$	17.2380	−	45.4529i	0.839134	−	2.21261i
$423$	−5.51102	+	14.5314i	−0.267955	+	0.706539i
$424$	−46.2916	−	67.0649i	−2.24812	−	3.25696i
$425$	14.0617	+	3.46589i	0.682092	+	0.168120i
$426$	3.56376	−	3.15721i	0.172665	−	0.152967i
$427$	−11.1565			−0.539901
$428$	8.55468	+	7.57879i	0.413506	+	0.366334i
$429$	1.18741	−	0.491810i	0.0573287	−	0.0237448i
$430$	5.92796	−	5.25171i	0.285871	−	0.253260i
$431$	−11.4026	+	10.1018i	−0.549244	+	0.486588i	−0.891501	−	0.453018i	$-0.850347\pi$
$431$	−11.4026	+	10.1018i	−0.549244	+	0.486588i	0.342257	+	0.939606i	$0.388809\pi$
$432$	−13.6116	+	35.8909i	−0.654889	+	1.72680i
$433$	−1.01581	−	8.36599i	−0.0488169	−	0.402044i	−0.996551	−	0.0829824i	$-0.973555\pi$
$433$	−1.01581	−	8.36599i	−0.0488169	−	0.402044i	0.947734	−	0.319061i	$-0.103368\pi$
$434$	−8.32321	+	21.9465i	−0.399527	+	1.05347i
$435$	1.50755	−	12.4158i	0.0722817	−	0.595293i
$436$	−13.8155	+	20.0151i	−0.661640	+	0.958551i
$437$	−37.8559			−1.81089
$438$	6.11369	−	8.85720i	0.292123	−	0.423213i
$439$	5.05476	−	1.24589i	0.241251	−	0.0594629i	−0.116836	−	0.993151i	$-0.537275\pi$
$439$	5.05476	−	1.24589i	0.241251	−	0.0594629i	0.358087	+	0.933688i	$0.383429\pi$
$440$	−13.3871	−	11.8600i	−0.638207	−	0.565402i
$441$	1.51070	−	2.18863i	0.0719382	−	0.104221i
$442$	−31.5505	−	10.8882i	−1.50070	−	0.517898i
$443$	−6.91823	−	10.0228i	−0.328695	−	0.476197i	0.623442	−	0.781870i	$-0.285734\pi$
$443$	−6.91823	−	10.0228i	−0.328695	−	0.476197i	−0.952137	+	0.305673i	$0.901119\pi$
$444$	2.47094	−	20.3500i	0.117266	−	0.965769i
$445$	−4.16421	−	34.2953i	−0.197402	−	1.62575i
$446$	−17.0453	+	8.94606i	−0.807118	+	0.423608i
$447$	−3.58264	+	0.883042i	−0.169453	+	0.0417664i
$448$	−6.02855	−	49.6496i	−0.284822	−	2.34572i
$449$	11.8384	−	10.4879i	0.558689	−	0.494955i	−0.335868	−	0.941909i	$-0.609030\pi$
$449$	11.8384	−	10.4879i	0.558689	−	0.494955i	0.894557	+	0.446954i	$0.147491\pi$
$450$	−17.4943	+	25.3448i	−0.824688	+	1.19477i
$451$	−0.0776790	−	0.112537i	−0.00365776	−	0.00529918i
$452$	−79.3118	−	19.5486i	−3.73051	−	0.919489i
$453$	−0.532392	−	4.38464i	−0.0250139	−	0.206008i
$454$	58.2386	+	30.5660i	2.73327	+	1.43453i
$455$	22.5461	+	14.5779i	1.05698	+	0.683421i
$456$	−18.3541	+	9.63298i	−0.859510	+	0.451106i
$457$	5.07686	+	7.35511i	0.237486	+	0.344057i	0.923546	−	0.383487i	$-0.125277\pi$
$457$	5.07686	+	7.35511i	0.237486	+	0.344057i	−0.686061	+	0.727544i	$0.740662\pi$
$458$	13.9235	+	20.1716i	0.650601	+	0.942559i
$459$	7.72588	+	6.84453i	0.360613	+	0.319475i
$460$	98.0242	+	86.8419i	4.57040	+	4.04902i
$461$	−2.41605	−	6.37061i	−0.112527	−	0.296709i	0.866908	−	0.498467i	$-0.166104\pi$
$461$	−2.41605	−	6.37061i	−0.112527	−	0.296709i	−0.979435	+	0.201758i	$0.935334\pi$
$462$	2.08170	−	1.09256i	0.0968493	−	0.0508304i
$463$	6.28520	+	16.5727i	0.292098	+	0.770199i	0.998078	+	0.0619674i	$0.0197375\pi$
$463$	6.28520	+	16.5727i	0.292098	+	0.770199i	−0.705980	+	0.708232i	$0.749493\pi$
$464$	98.0099	−	24.1573i	4.54999	−	1.12147i
$465$	−4.22847	−	3.74609i	−0.196090	−	0.173721i
$466$	22.4005	−	32.4528i	1.03768	−	1.50335i
$467$	6.68848	−	17.6361i	0.309506	−	0.816099i	−0.686526	−	0.727105i	$-0.740865\pi$
$467$	6.68848	−	17.6361i	0.309506	−	0.816099i	0.996032	−	0.0889946i	$-0.0283654\pi$
$468$	32.8528	−	39.4186i	1.51862	−	1.82212i
$469$	5.93962	+	15.6615i	0.274266	+	0.723181i
$470$	45.1216	+	11.1215i	2.08131	+	0.512996i
$471$	0.354746	+	0.186185i	0.0163458	+	0.00857895i
$472$	15.7053	−	41.4115i	0.722895	−	1.90612i
$473$	−0.0797766	+	0.657020i	−0.00366813	+	0.0302098i
$474$	9.12086	+	13.2138i	0.418935	+	0.606932i
$475$	−18.6868	+	4.60589i	−0.857411	+	0.211333i
$476$	−42.8592	−	10.5639i	−1.96445	−	0.484193i
$477$	3.09456	−	25.4860i	0.141690	−	1.16692i
$478$	11.0180	+	29.0522i	0.503954	+	1.32882i
$479$	31.5996	−	7.78861i	1.44382	−	0.355871i	0.561878	−	0.827220i	$-0.310079\pi$
$479$	31.5996	−	7.78861i	1.44382	−	0.355871i	0.881947	+	0.471349i	$0.156233\pi$
$480$	26.3845	+	6.50320i	1.20428	+	0.296829i
$481$	−11.8463	+	24.3286i	−0.540146	+	1.10929i
$482$	40.8092	−	10.0586i	1.85881	−	0.458155i
$483$	−9.40303	+	4.93509i	−0.427853	+	0.224554i
$484$	−55.0013			−2.50006
$485$	13.9081			0.631534
$486$	−29.6162	+	15.5438i	−1.34342	+	0.705080i
$487$	2.08951	+	1.85115i	0.0946849	+	0.0838835i	0.709137	−	0.705070i	$-0.249085\pi$
$487$	2.08951	+	1.85115i	0.0946849	+	0.0838835i	−0.614452	+	0.788954i	$0.710623\pi$
$488$	39.3327			1.78051
$489$	−7.40098	+	6.55670i	−0.334684	+	0.296504i
$490$	−7.04130	−	3.69556i	−0.318093	−	0.166948i
$491$	−4.56515	+	37.5974i	−0.206022	+	1.69675i	0.412482	+	0.910966i	$0.364662\pi$
$491$	−4.56515	+	37.5974i	−0.206022	+	1.69675i	−0.618504	+	0.785782i	$0.712261\pi$
$492$	0.485458	+	0.254788i	0.0218861	+	0.0114867i
$493$	3.27176	−	26.9453i	0.147352	−	1.21356i
$494$	43.8498	−	6.67280i	1.97289	−	0.300224i
$495$	−0.679180	−	5.59355i	−0.0305269	−	0.251411i
$496$	16.1679	−	42.6311i	0.725958	−	1.91419i
$497$	−7.35978	+	3.86271i	−0.330131	+	0.173266i
$498$	8.32365	+	21.9477i	0.372992	+	0.983498i
$499$	−5.30215	−	2.78278i	−0.237357	−	0.124574i	0.341852	−	0.939754i	$-0.388946\pi$
$499$	−5.30215	−	2.78278i	−0.237357	−	0.124574i	−0.579208	+	0.815179i	$0.696638\pi$
$500$	−11.1636	−	5.85911i	−0.499251	−	0.262027i
$501$	2.61686	+	0.644998i	0.116913	+	0.0288164i
$502$	5.02982	+	41.4243i	0.224492	+	1.84886i
$503$	16.0747	−	14.2410i	0.716737	−	0.634974i	−0.223812	−	0.974632i	$-0.571850\pi$
$503$	16.0747	−	14.2410i	0.716737	−	0.634974i	0.940549	+	0.339659i	$0.110312\pi$
$504$	32.8934	−	47.6543i	1.46519	−	2.12269i
$505$	0.961698	+	2.53579i	0.0427950	+	0.112841i
$506$	−15.1371			−0.672927
$507$	5.82118	−	3.51867i	0.258528	−	0.156270i
$508$	−41.3252			−1.83351
$509$	5.53466	+	14.5937i	0.245320	+	0.646855i	0.999957	−	0.00928744i	$-0.00295633\pi$
$509$	5.53466	+	14.5937i	0.245320	+	0.646855i	−0.754637	+	0.656142i	$0.772187\pi$
$510$	8.34729	−	12.0931i	0.369624	−	0.535493i
$511$	−14.0634	+	12.4591i	−0.622130	+	0.551159i
$512$	−0.290157	−	2.38966i	−0.0128233	−	0.105609i
$513$	−13.3181	−	3.28261i	−0.588008	−	0.144931i
$514$	17.1380	+	8.99471i	0.755924	+	0.396740i
$515$	14.7800	+	7.75712i	0.651283	+	0.341820i
$516$	−0.940979	−	2.48116i	−0.0414243	−	0.109227i
$517$	−3.43881	+	1.80483i	−0.151239	+	0.0793762i
$518$	−17.5523	+	46.2816i	−0.771203	+	2.03350i
$519$	−0.672236	−	5.53636i	−0.0295079	−	0.243019i
$520$	−79.4872	−	51.3948i	−3.48574	−	2.25381i
$521$	−0.905787	+	7.45983i	−0.0396833	+	0.326821i	0.959325	+	0.282303i	$0.0910983\pi$
$521$	−0.905787	+	7.45983i	−0.0396833	+	0.326821i	−0.999009	+	0.0445181i	$0.985825\pi$
$522$	51.1073	+	26.8232i	2.23691	+	1.17402i
$523$	2.30011	−	18.9431i	0.100577	−	0.828326i	−0.851898	−	0.523708i	$-0.824548\pi$
$523$	2.30011	−	18.9431i	0.100577	−	0.828326i	0.952475	−	0.304618i	$-0.0985287\pi$
$524$	53.0725	+	27.8546i	2.31848	+	1.21683i
$525$	−4.04118	+	3.58017i	−0.176372	+	0.156252i
$526$	4.27866			0.186558
$527$	−9.17679	−	8.12993i	−0.399747	−	0.354145i
$528$	−4.04370	+	2.12230i	−0.175980	+	0.0923612i
$529$	45.3744			1.97280
$530$	−76.7687			−3.33462
$531$	12.3550	−	6.48443i	0.536163	−	0.281400i
$532$	56.9565	−	14.0385i	2.46938	−	0.608646i
$533$	−0.496035	−	0.526970i	−0.0214857	−	0.0228256i
$534$	−15.5451	−	3.83151i	−0.672701	−	0.165806i
$535$	6.44887	−	1.58950i	0.278809	−	0.0687203i
$536$	−20.9404	−	55.2152i	−0.904486	−	2.38493i
$537$	−0.172680	+	1.42214i	−0.00745168	+	0.0613701i
$538$	−33.9794	−	8.37516i	−1.46495	−	0.361079i
$539$	0.645251	−	0.159040i	0.0277929	−	0.00685034i
$540$	26.9556	+	39.0519i	1.15998	+	1.68053i
$541$	0.728698	−	6.00137i	0.0313292	−	0.258019i	−0.968626	−	0.248524i	$-0.920055\pi$
$541$	0.728698	−	6.00137i	0.0313292	−	0.258019i	0.999955	−	0.00949494i	$-0.00302238\pi$
$542$	−3.45088	+	9.09923i	−0.148228	+	0.390845i
$543$	−8.82438	−	4.63139i	−0.378691	−	0.198752i
$544$	57.2608	+	14.1135i	2.45504	+	0.605112i
$545$	5.01184	+	13.2151i	0.214684	+	0.566074i
$546$	10.0220	−	7.37394i	0.428900	−	0.315576i
$547$	8.50983	−	22.4386i	0.363854	−	0.959405i	−0.620657	−	0.784082i	$-0.713134\pi$
$547$	8.50983	−	22.4386i	0.363854	−	0.959405i	0.984511	−	0.175322i	$-0.0560968\pi$
$548$	−56.0175	+	81.1553i	−2.39295	+	3.46678i
$549$	9.27529	+	8.21719i	0.395860	+	0.350701i
$550$	−7.47215	+	1.84172i	−0.318613	+	0.0785312i
$551$	12.7910	+	33.7271i	0.544916	+	1.43682i
$552$	33.1508	−	17.3989i	1.41099	−	0.740545i
$553$	−9.93964	−	26.2087i	−0.422677	−	1.11451i
$554$	7.12797	+	6.31483i	0.302838	+	0.268291i
$555$	−8.91715	−	7.89990i	−0.378512	−	0.335332i
$556$	47.5648	+	68.9096i	2.01720	+	2.92242i
$557$	8.33074	+	12.0692i	0.352985	+	0.511387i	0.958748	−	0.284259i	$-0.0917474\pi$
$557$	8.33074	+	12.0692i	0.352985	+	0.511387i	−0.605763	+	0.795645i	$0.707132\pi$
$558$	23.0842	−	12.1155i	0.977231	−	0.512890i
$559$	0.105716	+	3.50118i	0.00447130	+	0.148084i
$560$	−84.4730	−	44.3348i	−3.56963	−	1.87349i
$561$	0.148019	+	1.21904i	0.00624936	+	0.0514681i
$562$	−82.9846	−	20.4539i	−3.50049	−	0.862794i
$563$	−4.37097	−	6.33244i	−0.184214	−	0.266881i	0.719986	−	0.693988i	$-0.244148\pi$
$563$	−4.37097	−	6.33244i	−0.184214	−	0.266881i	−0.904201	+	0.427107i	$0.859533\pi$
$564$	8.84540	−	12.8148i	0.372459	−	0.539600i
$565$	−35.5326	+	31.4792i	−1.49487	+	1.32434i
$566$	4.25283	+	35.0252i	0.178760	+	1.47222i
$567$	15.7552	−	3.88330i	0.661654	−	0.163083i
$568$	25.9472	−	13.6181i	1.08872	−	0.571405i
$569$	−0.151545	−	1.24809i	−0.00635311	−	0.0523225i	0.989188	−	0.146656i	$-0.0468511\pi$
$569$	−0.151545	−	1.24809i	−0.00635311	−	0.0523225i	−0.995541	+	0.0943335i	$0.969928\pi$
$570$	−2.35378	+	19.3851i	−0.0985890	+	0.811953i
$571$	12.6401	+	18.3124i	0.528973	+	0.766350i	0.992827	−	0.119562i	$-0.0381491\pi$
$571$	12.6401	+	18.3124i	0.528973	+	0.766350i	−0.463854	+	0.885912i	$0.653534\pi$
$572$	12.6771	−	1.92912i	0.530055	−	0.0806607i
$573$	1.61777	−	2.34375i	0.0675833	−	0.0979114i
$574$	−0.990897	−	0.877858i	−0.0413593	−	0.0366411i
$575$	33.7517	−	8.31905i	1.40754	−	0.346928i
$576$	−31.5568	+	45.7179i	−1.31487	+	1.90491i
$577$	−5.15901			−0.214773			−0.107386	−	0.994217i	$-0.534248\pi$
$577$	−5.15901			−0.214773			−0.107386	+	0.994217i	$0.534248\pi$
$578$	−7.83372	+	11.3491i	−0.325840	+	0.472060i
$579$	−0.388048	+	3.19586i	−0.0161267	+	0.132816i
$580$	44.2494	−	116.676i	1.83735	−	4.84471i
$581$	−4.93943	−	40.6798i	−0.204922	−	1.68768i
$582$	2.28559	−	6.02661i	0.0947408	−	0.249811i
$583$	4.80210	−	4.25429i	0.198883	−	0.176195i
$584$	49.5812	−	43.9251i	2.05168	−	1.81763i
$585$	−8.00722	−	28.7258i	−0.331058	−	1.18767i
$586$	−34.4649	−	30.5332i	−1.42373	−	1.26131i
$587$	−42.2942			−1.74567			−0.872834	−	0.488017i	$-0.837720\pi$
$587$	−42.2942			−1.74567			−0.872834	+	0.488017i	$0.837720\pi$
$588$	−1.99440	+	1.76688i	−0.0822476	+	0.0728650i
$589$	15.8192	+	3.89908i	0.651819	+	0.160659i
$590$	−23.7017	−	34.3378i	−0.975783	−	1.41367i
$591$	−2.53230	+	6.67713i	−0.104165	+	0.274661i
$592$	34.0954	−	89.9021i	1.40131	−	3.69495i
$593$	15.1904	+	22.0071i	0.623796	+	0.903725i	0.999737	−	0.0229186i	$-0.00729585\pi$
$593$	15.1904	+	22.0071i	0.623796	+	0.903725i	−0.375941	+	0.926644i	$0.622680\pi$
$594$	−5.32539	−	1.31259i	−0.218503	−	0.0538562i
$595$	−19.2015	+	17.0110i	−0.787183	+	0.697383i
$596$	−36.8145			−1.50798
$597$	−1.90282	−	1.68575i	−0.0778773	−	0.0689933i
$598$	−79.2004	+	12.0523i	−3.23874	+	0.492853i
$599$	−1.61190	+	1.42802i	−0.0658605	+	0.0583473i	−0.695411	−	0.718612i	$-0.744778\pi$
$599$	−1.61190	+	1.42802i	−0.0658605	+	0.0583473i	0.629550	+	0.776960i	$0.283239\pi$
$600$	14.2473	−	12.6220i	0.581645	−	0.515293i
$601$	6.45417	−	17.0183i	0.263271	−	0.694189i	−0.736570	−	0.676362i	$-0.763556\pi$
$601$	6.45417	−	17.0183i	0.263271	−	0.694189i	0.999841	−	0.0178278i	$-0.00567506\pi$
$602$	0.772326	+	6.36068i	0.0314777	+	0.259242i
$603$	6.59721	−	17.3954i	0.268659	−	0.708396i
$604$	5.31178	−	43.7464i	0.216133	−	1.78002i
$605$	−18.1575	+	26.3056i	−0.738206	+	1.06948i
$606$	1.25684			0.0510557
$607$	−15.7717	+	22.8492i	−0.640152	+	0.927420i	−0.999984	−	0.00559715i	$-0.998218\pi$
$607$	−15.7717	+	22.8492i	−0.640152	+	0.927420i	0.359833	+	0.933017i	$0.382834\pi$
$608$	−76.0949	+	18.7557i	−3.08606	+	0.760645i
$609$	7.57401	+	6.70999i	0.306914	+	0.271903i
$610$	21.0490	−	30.4948i	0.852249	−	1.23470i
$611$	−16.5555	+	12.1812i	−0.669765	+	0.492799i
$612$	27.8516	+	40.3500i	1.12583	+	1.63105i
$613$	2.29621	−	18.9110i	0.0927429	−	0.763807i	−0.869937	−	0.493163i	$-0.835840\pi$
$613$	2.29621	−	18.9110i	0.0927429	−	0.763807i	0.962680	−	0.270643i	$-0.0872364\pi$
$614$	4.30663	+	35.4683i	0.173802	+	1.43139i
$615$	0.282122	−	0.148069i	0.0113762	−	0.00597071i
$616$	14.0494	−	3.46286i	0.566066	−	0.139523i
$617$	−0.170683	−	1.40570i	−0.00687144	−	0.0565914i	0.988870	−	0.148783i	$-0.0475357\pi$
$617$	−0.170683	−	1.40570i	−0.00687144	−	0.0565914i	−0.995741	+	0.0921920i	$0.970613\pi$
$618$	5.79016	−	5.12963i	0.232914	−	0.206344i
$619$	1.88353	−	2.72876i	0.0757053	−	0.109678i	−0.783302	−	0.621641i	$-0.786466\pi$
$619$	1.88353	−	2.72876i	0.0757053	−	0.109678i	0.859007	+	0.511963i	$0.171082\pi$
$620$	−32.0178	−	46.3858i	−1.28587	−	1.86290i
$621$	24.0548	+	5.92898i	0.965286	+	0.237922i
$622$	3.17910	+	26.1822i	0.127470	+	1.04981i
$623$	24.7488	+	12.9892i	0.991541	+	0.520401i
$624$	−19.4677	+	14.3239i	−0.779331	+	0.573415i
$625$	−25.0997	+	13.1733i	−1.00399	+	0.526933i
$626$	20.4911	+	29.6865i	0.818989	+	1.18651i
$627$	−0.927030	−	1.34304i	−0.0370220	−	0.0536357i
$628$	2.99197	+	2.65065i	0.119393	+	0.105773i
$629$	−19.3524	−	17.1447i	−0.771629	−	0.683604i
$630$	−19.3435	−	51.0046i	−0.770663	−	2.03207i
$631$	−11.2187	+	5.88804i	−0.446610	+	0.234399i	−0.673007	−	0.739636i	$-0.734998\pi$
$631$	−11.2187	+	5.88804i	−0.446610	+	0.234399i	0.226397	+	0.974035i	$0.427305\pi$
$632$	35.0426	+	92.3997i	1.39392	+	3.67546i
$633$	−9.19071	+	2.26531i	−0.365298	+	0.0900379i
$634$	−12.9953	−	11.5129i	−0.516111	−	0.457235i
$635$	−13.6426	+	19.7647i	−0.541391	+	0.784340i
$636$	−9.12131	+	24.0509i	−0.361683	+	0.953680i
$637$	3.24945	−	1.34588i	0.128748	−	0.0533257i
$638$	5.11464	+	13.4862i	0.202490	+	0.533923i
$639$	8.96381	+	2.20938i	0.354603	+	0.0874017i
$640$	55.1113	+	28.9247i	2.17847	+	1.14335i
$641$	0.502519	−	1.32503i	0.0198483	−	0.0523356i	−0.924726	−	0.380634i	$-0.875706\pi$
$641$	0.502519	−	1.32503i	0.0198483	−	0.0523356i	0.944574	+	0.328298i	$0.106475\pi$
$642$	0.371019	−	3.05562i	0.0146430	−	0.120596i
$643$	−18.4665	−	26.7534i	−0.728249	−	1.05505i	−0.995804	−	0.0915081i	$-0.970831\pi$
$643$	−18.4665	−	26.7534i	−0.728249	−	1.05505i	0.267555	−	0.963542i	$-0.413784\pi$
$644$	−102.873	+	25.3560i	−4.05378	+	0.999167i
$645$	−1.49732	−	0.369055i	−0.0589567	−	0.0145315i
$646$	−5.10827	+	42.0704i	−0.200982	+	1.65524i
$647$	6.09033	+	16.0589i	0.239435	+	0.631339i	0.999836	−	0.0181151i	$-0.00576652\pi$
$647$	6.09033	+	16.0589i	0.239435	+	0.631339i	−0.760400	+	0.649455i	$0.774997\pi$
$648$	−55.5454	+	13.6907i	−2.18203	+	0.537822i
$649$	3.38551	+	0.834454i	0.132893	+	0.0327552i
$650$	−37.6294	+	15.5856i	−1.47595	+	0.611318i
$651$	4.43764	−	1.09378i	0.173925	−	0.0428686i
$652$	−87.3509	+	45.8453i	−3.42092	+	1.79544i
$653$	40.8704			1.59938			0.799691	−	0.600411i	$-0.204996\pi$
$653$	40.8704			1.59938			0.799691	+	0.600411i	$0.204996\pi$
$654$	6.54996			0.256124
$655$	30.8429	−	16.1876i	1.20513	−	0.632501i
$656$	1.92482	+	1.70524i	0.0751516	+	0.0665785i
$657$	20.8687			0.814164
$658$	−28.1426	+	24.9322i	−1.09711	+	0.971957i
$659$	−20.9109	−	10.9749i	−0.814574	−	0.427521i	0.00535583	−	0.999986i	$-0.498295\pi$
$659$	−20.9109	−	10.9749i	−0.814574	−	0.427521i	−0.819930	+	0.572464i	$0.805987\pi$
$660$	−0.680483	+	5.60428i	−0.0264878	+	0.218146i
$661$	−24.3942	−	12.8030i	−0.948823	−	0.497981i	−0.0820196	−	0.996631i	$-0.526137\pi$
$661$	−24.3942	−	12.8030i	−0.948823	−	0.497981i	−0.866803	+	0.498650i	$0.833829\pi$
$662$	−5.38575	+	44.3556i	−0.209323	+	1.72393i
$663$	1.74507	+	6.26043i	0.0677730	+	0.243135i
$664$	17.4141	+	143.418i	0.675800	+	5.56571i
$665$	12.0887	−	31.8753i	0.468779	−	1.23607i
$666$	48.6808	−	25.5496i	1.88634	−	0.990028i
$667$	−23.1028	−	60.9171i	−0.894545	−	2.35872i
$668$	23.8102	+	12.4966i	0.921244	+	0.483506i
$669$	3.31908	+	1.74199i	0.128323	+	0.0673491i
$670$	−54.0148	−	13.3135i	−2.08677	−	0.514344i
$671$	0.373252	+	3.07401i	0.0144093	+	0.118671i
$672$	−16.4562	+	14.5789i	−0.634810	+	0.562392i
$673$	9.13442	−	13.2335i	0.352106	−	0.510114i	−0.606410	−	0.795152i	$-0.707391\pi$
$673$	9.13442	−	13.2335i	0.352106	−	0.510114i	0.958516	+	0.285038i	$0.0920063\pi$
$674$	−2.24658	−	5.92375i	−0.0865351	−	0.228174i
$675$	12.5956			0.484804
$676$	64.7929	−	20.1871i	2.49204	−	0.776427i
$677$	37.2856			1.43300			0.716501	−	0.697586i	$-0.245742\pi$
$677$	37.2856			1.43300			0.716501	+	0.697586i	$0.245742\pi$
$678$	7.80118	+	20.5700i	0.299603	+	0.789987i
$679$	−6.39205	+	9.26048i	−0.245304	+	0.355384i
$680$	67.6955	−	59.9729i	2.59600	−	2.29986i
$681$	−1.54375	−	12.7139i	−0.0591565	−	0.487198i
$682$	6.32549	+	1.55909i	0.242216	+	0.0597008i
$683$	7.34152	+	3.85313i	0.280916	+	0.147436i	0.599297	−	0.800527i	$-0.295447\pi$
$683$	7.34152	+	3.85313i	0.280916	+	0.147436i	−0.318381	+	0.947963i	$0.603139\pi$
$684$	−57.6923	−	30.2793i	−2.20592	−	1.15776i
$685$	20.3215	+	53.5833i	0.776444	+	2.04731i
$686$	46.5763	−	24.4451i	1.77829	−	0.933319i
$687$	1.69242	−	4.46254i	0.0645698	−	0.170257i
$688$	−1.50025	−	12.3556i	−0.0571963	−	0.471054i
$689$	21.7383	−	26.0828i	0.828162	−	0.993674i
$690$	4.25134	−	35.0129i	0.161846	−	1.33292i
$691$	45.6331	+	23.9501i	1.73597	+	0.911105i	0.959849	+	0.280516i	$0.0905056\pi$
$691$	45.6331	+	23.9501i	1.73597	+	0.911105i	0.776117	+	0.630589i	$0.217187\pi$
$692$	6.70703	−	55.2374i	0.254963	−	2.09981i
$693$	4.03652	+	2.11853i	0.153335	+	0.0804762i
$694$	−42.9788	+	38.0759i	−1.63145	+	1.44534i
$695$	48.6601			1.84578
$696$	−26.7025	−	23.6563i	−1.01215	−	0.896691i
$697$	0.612272	−	0.321345i	0.0231915	−	0.0121718i
$698$	−17.2544			−0.653089
$699$	−7.67845			−0.290426
$700$	−47.6964	+	25.0330i	−1.80276	+	0.946159i
$701$	43.1966	−	10.6470i	1.63151	−	0.402132i	0.685970	−	0.727630i	$-0.259378\pi$
$701$	43.1966	−	10.6470i	1.63151	−	0.402132i	0.945543	+	0.325498i	$0.105532\pi$
$702$	−28.9086	−	2.62763i	−1.09108	−	0.0991735i
$703$	33.3601	+	8.22253i	1.25820	+	0.310119i
$704$	−13.4785	+	3.32215i	−0.507990	+	0.125208i
$705$	−3.20885	−	8.46104i	−0.120852	−	0.318661i
$706$	−8.60230	+	70.8464i	−0.323752	+	2.66634i
$707$	−2.13040	−	0.525097i	−0.0801221	−	0.0197483i
$708$	−13.5738	+	3.34565i	−0.510136	+	0.125737i
$709$	−11.1495	−	16.1529i	−0.418730	−	0.606635i	0.555685	−	0.831393i	$-0.312456\pi$
$709$	−11.1495	−	16.1529i	−0.418730	−	0.606635i	−0.974415	+	0.224758i	$0.927841\pi$
$710$	3.32754	−	27.4047i	0.124880	−	1.02848i
$711$	−11.0401	+	29.1103i	−0.414035	+	1.09172i
$712$	−87.2529	−	45.7939i	−3.26994	−	1.71620i
$713$	−28.5723	−	7.04243i	−1.07004	−	0.263741i
$714$	4.21567	+	11.1158i	0.157768	+	0.415999i
$715$	3.26241	−	6.69996i	0.122007	−	0.250564i
$716$	−5.06845	+	13.3644i	−0.189417	+	0.499452i
$717$	3.43693	−	4.97925i	0.128355	−	0.185954i
$718$	29.7927	+	26.3940i	1.11185	+	0.985017i
$719$	−19.1707	+	4.72514i	−0.714945	+	0.176218i	−0.579978	−	0.814632i	$-0.696939\pi$
$719$	−19.1707	+	4.72514i	−0.714945	+	0.176218i	−0.134967	+	0.990850i	$0.543093\pi$
$720$	37.5748	+	99.0766i	1.40033	+	3.69237i
$721$	−11.9577	+	6.27588i	−0.445328	+	0.233726i
$722$	−1.86676	−	4.92224i	−0.0694737	−	0.183187i
$723$	−6.12598	−	5.42715i	−0.227828	−	0.201838i
$724$	−74.4259	−	65.9356i	−2.76602	−	2.45048i
$725$	−18.8160	−	27.2597i	−0.698809	−	1.01240i
$726$	8.41476	+	12.1909i	0.312301	+	0.452446i
$727$	−22.5136	+	11.8160i	−0.834982	+	0.438232i	−0.827315	−	0.561738i	$-0.810133\pi$
$727$	−22.5136	+	11.8160i	−0.834982	+	0.438232i	−0.00766681	+	0.999971i	$0.502440\pi$
$728$	70.7520	−	29.3046i	2.62224	−	1.08610i
$729$	−11.7944	−	6.19018i	−0.436830	−	0.229266i
$730$	−7.52174	−	61.9471i	−0.278392	−	2.29276i
$731$	−3.24954	−	0.800939i	−0.120188	−	0.0296238i
$732$	−7.05277	−	10.2177i	−0.260678	−	0.377657i
$733$	21.4374	−	31.0574i	0.791809	−	1.14713i	−0.194286	−	0.980945i	$-0.562239\pi$
$733$	21.4374	−	31.0574i	0.791809	−	1.14713i	0.986094	−	0.166188i	$-0.0531458\pi$
$734$	74.2172	−	65.7507i	2.73941	−	2.42690i
$735$	0.186646	+	1.53717i	0.00688453	+	0.0566992i
$736$	137.441	−	33.8761i	5.06614	−	1.24869i
$737$	4.11658	−	2.16055i	0.151636	−	0.0795848i
$738$	0.177236	+	1.45967i	0.00652414	+	0.0537311i
$739$	1.11097	−	9.14966i	0.0408677	−	0.336576i	−0.957907	−	0.287080i	$-0.907315\pi$
$739$	1.11097	−	9.14966i	0.0408677	−	0.336576i	0.998774	−	0.0494958i	$-0.0157614\pi$
$740$	−67.5203	−	97.8201i	−2.48210	−	3.59594i
$741$	−5.91974	−	6.28892i	−0.217467	−	0.231029i
$742$	35.2822	−	51.1152i	1.29525	−	1.87650i
$743$	−24.2689	−	21.5004i	−0.890340	−	0.788772i	0.0879259	−	0.996127i	$-0.471976\pi$
$743$	−24.2689	−	21.5004i	−0.890340	−	0.788772i	−0.978266	+	0.207355i	$0.933515\pi$
$744$	−15.6451	+	3.85617i	−0.573577	+	0.141374i
$745$	−12.1535	+	17.6074i	−0.445270	+	0.645085i
$746$	70.4560			2.57958
$747$	−25.8557	+	37.4585i	−0.946011	+	1.37053i
$748$	−1.47681	+	12.1626i	−0.0539976	+	0.444710i
$749$	−1.90550	+	5.02440i	−0.0696256	+	0.183588i
$750$	0.409287	+	3.37078i	0.0149450	+	0.123083i
$751$	6.39054	−	16.8505i	0.233194	−	0.614883i	−0.766429	−	0.642329i	$-0.777968\pi$
$751$	6.39054	−	16.8505i	0.233194	−	0.614883i	0.999623	+	0.0274464i	$0.00873756\pi$
$752$	54.6671	−	48.4308i	1.99350	−	1.76609i
$753$	6.08197	−	5.38816i	0.221639	−	0.196355i
$754$	37.4986	+	66.4901i	1.36562	+	2.42143i
$755$	−19.1692	−	16.9824i	−0.697638	−	0.618053i
$756$	−38.3906			−1.39625
$757$	−38.1260	+	33.7767i	−1.38571	+	1.22763i	−0.441936	+	0.897046i	$0.645708\pi$
$757$	−38.1260	+	33.7767i	−1.38571	+	1.22763i	−0.943775	+	0.330587i	$0.892753\pi$
$758$	−64.0456	−	15.7858i	−2.32624	−	0.573367i
$759$	1.67438	+	2.42576i	0.0607761	+	0.0880494i
$760$	−42.6192	+	112.377i	−1.54596	+	4.07636i
$761$	16.0813	−	42.4029i	0.582947	−	1.53711i	−0.241050	−	0.970513i	$-0.577492\pi$
$761$	16.0813	−	42.4029i	0.582947	−	1.53711i	0.823998	−	0.566593i	$-0.191739\pi$
$762$	6.32243	+	9.15962i	0.229037	+	0.331818i
$763$	−11.1025	−	2.73651i	−0.401937	−	0.0990685i
$764$	21.2680	−	18.8418i	0.769448	−	0.681671i
$765$	28.4929			1.03016
$766$	−20.2937	−	17.9787i	−0.733242	−	0.649596i
$767$	18.3781	+	1.67046i	0.663593	+	0.0603169i
$768$

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	169.g (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.952850 - 2.51246i) q^{2} +(-0.297229 + 0.430610i) q^{3} +(-3.90751 + 3.46175i) q^{4} +(0.365684 + 3.01168i) q^{5} +(1.36511 + 0.336468i) q^{6} +(-2.17334 - 1.14066i) q^{7} +(7.66220 + 4.02143i) q^{8} +(0.966734 + 2.54907i) q^{9} +O(q^{10})\)	\(q+(-0.952850 - 2.51246i) q^{2} +(-0.297229 + 0.430610i) q^{3} +(-3.90751 + 3.46175i) q^{4} +(0.365684 + 3.01168i) q^{5} +(1.36511 + 0.336468i) q^{6} +(-2.17334 - 1.14066i) q^{7} +(7.66220 + 4.02143i) q^{8} +(0.966734 + 2.54907i) q^{9} +(7.21828 - 3.78845i) q^{10} +(-0.241580 + 0.636994i) q^{11} +(-0.329241 - 2.71155i) q^{12} +(-0.756816 + 3.52523i) q^{13} +(-0.794988 + 6.54731i) q^{14} +(-1.40555 - 0.737691i) q^{15} +(1.54427 - 12.7182i) q^{16} +(-3.05039 - 1.60097i) q^{17} +(5.48328 - 4.85776i) q^{18} +4.57811 q^{19} +(-11.8546 - 10.5023i) q^{20} +(1.13716 - 0.596827i) q^{21} +1.83061 q^{22} -8.26888 q^{23} +(-4.00910 + 2.10414i) q^{24} +(-4.08178 + 1.00607i) q^{25} +(9.57812 - 1.45754i) q^{26} +(-2.90908 - 0.717023i) q^{27} +(12.4410 - 3.06644i) q^{28} +(2.79395 + 7.36704i) q^{29} +(-0.514137 + 4.23430i) q^{30} +(3.45540 + 0.851679i) q^{31} +(-16.6215 + 4.09682i) q^{32} +(-0.202492 - 0.293360i) q^{33} +(-1.11580 + 9.18946i) q^{34} +(2.64054 - 6.96253i) q^{35} +(-12.6018 - 6.61392i) q^{36} +(7.28687 + 1.79605i) q^{37} +(-4.36226 - 11.5023i) q^{38} +(-1.29305 - 1.37369i) q^{39} +(-9.30932 + 24.5467i) q^{40} +(-0.114022 + 0.165189i) q^{41} +(-2.58305 - 2.28838i) q^{42} +(0.943264 - 0.232494i) q^{43} +(-1.26114 - 3.32535i) q^{44} +(-7.32346 + 3.84365i) q^{45} +(7.87900 + 20.7752i) q^{46} +(4.26700 + 3.78023i) q^{47} +(5.01758 + 4.44518i) q^{48} +(-0.554136 - 0.802805i) q^{49} +(6.41703 + 9.29667i) q^{50} +(1.59606 - 0.837675i) q^{51} +(-9.24619 - 16.3948i) q^{52} +(-8.33843 - 4.37635i) q^{53} +(0.970423 + 7.99215i) q^{54} +(-2.00676 - 0.494623i) q^{55} +(-12.0655 - 17.4799i) q^{56} +(-1.36075 + 1.97138i) q^{57} +(15.8472 - 14.0394i) q^{58} +(-0.616927 - 5.08085i) q^{59} +(8.04591 - 1.98314i) q^{60} +(4.02471 - 2.11233i) q^{61} +(-1.15267 - 9.49307i) q^{62} +(0.806571 - 6.64271i) q^{63} +(11.5752 + 16.7696i) q^{64} +(-10.8936 - 0.990168i) q^{65} +(-0.544111 + 0.788280i) q^{66} +(-5.10800 - 4.52529i) q^{67} +(17.4616 - 4.30389i) q^{68} +(2.45775 - 3.56067i) q^{69} -20.0091 q^{70} +(1.92369 - 2.78694i) q^{71} +(-2.84360 + 23.4191i) q^{72} +(2.71442 - 7.15733i) q^{73} +(-2.43079 - 20.0193i) q^{74} +(0.779999 - 2.05669i) q^{75} +(-17.8890 + 15.8483i) q^{76} +(1.25163 - 1.10885i) q^{77} +(-2.21926 + 4.55766i) q^{78} +(8.54797 + 7.57284i) q^{79} +38.8678 q^{80} +(-4.94842 + 4.38392i) q^{81} +(0.523676 + 0.129075i) q^{82} +(9.48405 + 13.7400i) q^{83} +(-2.37739 + 6.26867i) q^{84} +(3.70612 - 9.77224i) q^{85} +(-1.48292 - 2.14838i) q^{86} +(-4.00276 - 0.986593i) q^{87} +(-4.41267 + 3.90928i) q^{88} -11.3874 q^{89} +(16.6352 + 14.7375i) q^{90} +(5.66590 - 6.79826i) q^{91} +(32.3107 - 28.6248i) q^{92} +(-1.39379 + 1.23479i) q^{93} +(5.43187 - 14.3227i) q^{94} +(1.67414 + 13.7878i) q^{95} +(3.17624 - 8.37507i) q^{96} +(0.552586 - 4.55096i) q^{97} +(-1.48901 + 2.15720i) q^{98} -1.85729 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9}+O(q^{10}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9} + q^{10} - q^{11} + 11 q^{12} - 65 q^{13} + 9 q^{14} - 41 q^{15} + 3 q^{17} - 13 q^{18} - 6 q^{19} + 29 q^{20} + 19 q^{21} - 22 q^{22} - 82 q^{23} - 31 q^{24} + 2 q^{25} + 26 q^{26} + 21 q^{27} + 43 q^{28} + 13 q^{29} - 81 q^{30} - 33 q^{31} - 93 q^{32} + 35 q^{33} - 24 q^{34} + 27 q^{35} + 54 q^{36} + 25 q^{37} - 56 q^{38} - 13 q^{39} - 52 q^{40} + 29 q^{41} - 63 q^{42} + 21 q^{43} + 45 q^{44} + 33 q^{46} - 69 q^{47} + 54 q^{48} - 54 q^{49} + 80 q^{50} - 16 q^{51} + 13 q^{52} - 45 q^{53} + 29 q^{54} - 83 q^{55} + 91 q^{56} - 11 q^{57} + 25 q^{58} - 57 q^{59} + 51 q^{60} + 39 q^{61} + 4 q^{62} + 26 q^{63} + 86 q^{64} + 65 q^{65} - 138 q^{66} - 101 q^{67} + 36 q^{68} + 32 q^{69} - 90 q^{70} + 20 q^{71} + 13 q^{72} + 61 q^{73} - 4 q^{74} - 67 q^{75} - 107 q^{76} + 67 q^{77} + 13 q^{78} + 57 q^{79} + 160 q^{80} + 78 q^{81} - 31 q^{82} - 59 q^{83} - 36 q^{84} - 61 q^{85} + 41 q^{86} - 9 q^{87} - 45 q^{88} - 66 q^{89} + 191 q^{90} + 39 q^{91} + 79 q^{92} - 80 q^{93} - 21 q^{94} - 28 q^{95} + 70 q^{96} + 7 q^{97} + 158 q^{98} + 130 q^{99}+O(q^{100}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9 + q^10 - q^11 + 11 * q^12 - 65 * q^13 + 9 * q^14 - 41 * q^15 + 3 * q^17 - 13 * q^18 - 6 * q^19 + 29 * q^20 + 19 * q^21 - 22 * q^22 - 82 * q^23 - 31 * q^24 + 2 * q^25 + 26 * q^26 + 21 * q^27 + 43 * q^28 + 13 * q^29 - 81 * q^30 - 33 * q^31 - 93 * q^32 + 35 * q^33 - 24 * q^34 + 27 * q^35 + 54 * q^36 + 25 * q^37 - 56 * q^38 - 13 * q^39 - 52 * q^40 + 29 * q^41 - 63 * q^42 + 21 * q^43 + 45 * q^44 + 33 * q^46 - 69 * q^47 + 54 * q^48 - 54 * q^49 + 80 * q^50 - 16 * q^51 + 13 * q^52 - 45 * q^53 + 29 * q^54 - 83 * q^55 + 91 * q^56 - 11 * q^57 + 25 * q^58 - 57 * q^59 + 51 * q^60 + 39 * q^61 + 4 * q^62 + 26 * q^63 + 86 * q^64 + 65 * q^65 - 138 * q^66 - 101 * q^67 + 36 * q^68 + 32 * q^69 - 90 * q^70 + 20 * q^71 + 13 * q^72 + 61 * q^73 - 4 * q^74 - 67 * q^75 - 107 * q^76 + 67 * q^77 + 13 * q^78 + 57 * q^79 + 160 * q^80 + 78 * q^81 - 31 * q^82 - 59 * q^83 - 36 * q^84 - 61 * q^85 + 41 * q^86 - 9 * q^87 - 45 * q^88 - 66 * q^89 + 191 * q^90 + 39 * q^91 + 79 * q^92 - 80 * q^93 - 21 * q^94 - 28 * q^95 + 70 * q^96 + 7 * q^97 + 158 * q^98 + 130 * q^99

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