LMFDB - Embedded newform 169.2.k.a.127.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(4,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("169.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.k (of order $78$, degree $24$, 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:	$360$
Relative dimension:	$15$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			127.15
Character	$\chi$	$=$	169.127
Dual form			169.2.k.a.4.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.57861 - 0.103914i) q^{2} +(-0.381537 - 1.31722i) q^{3} +(4.64490 - 0.374975i) q^{4} +(-3.32428 + 1.26073i) q^{5} +(-1.12071 - 3.35694i) q^{6} +(0.633807 - 1.48760i) q^{7} +(6.81465 - 0.827448i) q^{8} +(0.946076 - 0.598262i) q^{9} +O(q^{10})$	\(q+(2.57861 - 0.103914i) q^{2} +(-0.381537 - 1.31722i) q^{3} +(4.64490 - 0.374975i) q^{4} +(-3.32428 + 1.26073i) q^{5} +(-1.12071 - 3.35694i) q^{6} +(0.633807 - 1.48760i) q^{7} +(6.81465 - 0.827448i) q^{8} +(0.946076 - 0.598262i) q^{9} +(-8.44101 + 3.59638i) q^{10} +(-2.92094 + 4.61910i) q^{11} +(-2.26613 - 5.97529i) q^{12} +(0.0292141 + 3.60543i) q^{13} +(1.47976 - 3.90180i) q^{14} +(2.92900 + 3.89779i) q^{15} +(8.28698 - 1.34677i) q^{16} +(0.607879 + 0.258993i) q^{17} +(2.37739 - 1.64099i) q^{18} +(-3.26641 - 1.88586i) q^{19} +(-14.9682 + 7.10251i) q^{20} +(-2.20131 - 0.267288i) q^{21} +(-7.05197 + 12.2144i) q^{22} +(-2.06885 - 3.58336i) q^{23} +(-3.68997 - 8.66068i) q^{24} +(5.71886 - 5.06647i) q^{25} +(0.449988 + 9.29396i) q^{26} +(-4.22844 - 3.74607i) q^{27} +(2.38616 - 7.14742i) q^{28} +(-0.0150965 - 0.374615i) q^{29} +(7.95778 + 9.74651i) q^{30} +(4.01307 - 4.52982i) q^{31} +(7.77699 - 1.58768i) q^{32} +(7.19881 + 2.08516i) q^{33} +(1.59439 + 0.604674i) q^{34} +(-0.231486 + 5.74426i) q^{35} +(4.17010 - 3.13363i) q^{36} +(8.68138 + 1.77232i) q^{37} +(-8.61876 - 4.52348i) q^{38} +(4.73800 - 1.41409i) q^{39} +(-21.6106 + 11.3421i) q^{40} +(-6.39824 + 1.85327i) q^{41} +(-5.70410 - 0.460483i) q^{42} +(-1.58264 - 7.75228i) q^{43} +(-11.8354 + 22.5505i) q^{44} +(-2.39078 + 3.18154i) q^{45} +(-5.70713 - 9.02510i) q^{46} +(7.99021 + 5.51524i) q^{47} +(-4.93577 - 10.4019i) q^{48} +(3.03783 + 3.16272i) q^{49} +(14.2202 - 13.6587i) q^{50} +(0.109222 - 0.899525i) q^{51} +(1.48765 + 16.7359i) q^{52} +(-0.387154 - 3.18850i) q^{53} +(-11.2928 - 9.22026i) q^{54} +(3.88658 - 19.0377i) q^{55} +(3.08826 - 10.6619i) q^{56} +(-1.23784 + 5.02211i) q^{57} +(-0.0778557 - 0.964416i) q^{58} +(0.599422 - 3.68839i) q^{59} +(15.0665 + 17.0066i) q^{60} +(-3.97645 - 2.98811i) q^{61} +(9.87743 - 12.0977i) q^{62} +(-0.290345 - 1.78656i) q^{63} +(3.58533 - 0.883705i) q^{64} +(-4.64261 - 11.9487i) q^{65} +(18.7796 + 4.62875i) q^{66} +(-0.700108 + 8.67239i) q^{67} +(2.92066 + 0.975058i) q^{68} +(-3.93073 + 4.09232i) q^{69} +14.8363i q^{70} +(0.998956 + 0.959510i) q^{71} +(5.95215 - 4.85978i) q^{72} +(-0.592291 - 1.12852i) q^{73} +(22.5700 + 3.66799i) q^{74} +(-8.85560 - 5.59994i) q^{75} +(-15.8793 - 7.53483i) q^{76} +(5.02006 + 7.27281i) q^{77} +(12.0705 - 4.13872i) q^{78} +(-2.22323 + 3.22090i) q^{79} +(-25.8504 + 14.9247i) q^{80} +(-1.88150 + 3.96518i) q^{81} +(-16.3060 + 5.44373i) q^{82} +(-1.29292 - 5.24558i) q^{83} +(-10.3251 - 0.416088i) q^{84} +(-2.34728 - 0.0945923i) q^{85} +(-4.88658 - 19.8256i) q^{86} +(-0.487690 + 0.162815i) q^{87} +(-16.0831 + 33.8945i) q^{88} +(2.98137 - 1.72129i) q^{89} +(-5.83426 + 8.45239i) q^{90} +(5.38196 + 2.24169i) q^{91} +(-10.9533 - 15.8686i) q^{92} +(-7.49791 - 3.55780i) q^{93} +(21.1767 + 13.3913i) q^{94} +(13.2361 + 2.15107i) q^{95} +(-5.05853 - 9.63823i) q^{96} +(-10.3543 + 8.45403i) q^{97} +(8.16202 + 7.83973i) q^{98} +6.11751i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q - 23 q^{2} - 24 q^{3} - 41 q^{4} - 26 q^{5} - 32 q^{6} - 26 q^{7} - 26 q^{8} - 11 q^{9}+O(q^{10}) $ 360 * q - 23 * q^2 - 24 * q^3 - 41 * q^4 - 26 * q^5 - 32 * q^6 - 26 * q^7 - 26 * q^8 - 11 * q^9	\( 360 q - 23 q^{2} - 24 q^{3} - 41 q^{4} - 26 q^{5} - 32 q^{6} - 26 q^{7} - 26 q^{8} - 11 q^{9} - 27 q^{10} - 26 q^{11} - 14 q^{12} - 34 q^{13} - 30 q^{14} - 84 q^{15} - 13 q^{16} - 31 q^{17} + 52 q^{18} - 33 q^{19} - 29 q^{20} - 26 q^{21} - 33 q^{22} + 57 q^{23} + 58 q^{24} + 2 q^{25} - 29 q^{26} - 30 q^{27} - 26 q^{28} - 19 q^{29} + 178 q^{30} - 78 q^{31} - 30 q^{32} - 26 q^{33} - 91 q^{34} - 18 q^{35} - 51 q^{36} - 41 q^{37} + 25 q^{38} + 12 q^{39} - 134 q^{40} - 17 q^{41} + 250 q^{42} - 28 q^{43} + 42 q^{45} + 18 q^{46} + 117 q^{47} - 57 q^{48} - 117 q^{49} - 20 q^{50} - 59 q^{51} + 37 q^{52} - 75 q^{53} + 118 q^{54} + 64 q^{55} - 42 q^{56} - 104 q^{57} - 87 q^{58} + 170 q^{59} + 78 q^{60} - 15 q^{61} + 19 q^{62} + 39 q^{63} + 32 q^{64} - 17 q^{65} + 73 q^{66} + 20 q^{67} - 76 q^{68} - 11 q^{69} + 46 q^{71} - 198 q^{72} - 26 q^{73} + 29 q^{74} - 70 q^{75} + 58 q^{76} + 6 q^{77} + 128 q^{78} - 54 q^{79} - 24 q^{80} - 7 q^{81} + 81 q^{82} + 234 q^{83} - 273 q^{84} - 74 q^{85} + 52 q^{86} - 112 q^{87} + 256 q^{88} - 27 q^{89} + 28 q^{90} - 78 q^{91} - 34 q^{92} + 51 q^{93} + 28 q^{94} - 11 q^{95} + 143 q^{96} + 40 q^{97} - 47 q^{98}+O(q^{100}) \) 360 * q - 23 * q^2 - 24 * q^3 - 41 * q^4 - 26 * q^5 - 32 * q^6 - 26 * q^7 - 26 * q^8 - 11 * q^9 - 27 * q^10 - 26 * q^11 - 14 * q^12 - 34 * q^13 - 30 * q^14 - 84 * q^15 - 13 * q^16 - 31 * q^17 + 52 * q^18 - 33 * q^19 - 29 * q^20 - 26 * q^21 - 33 * q^22 + 57 * q^23 + 58 * q^24 + 2 * q^25 - 29 * q^26 - 30 * q^27 - 26 * q^28 - 19 * q^29 + 178 * q^30 - 78 * q^31 - 30 * q^32 - 26 * q^33 - 91 * q^34 - 18 * q^35 - 51 * q^36 - 41 * q^37 + 25 * q^38 + 12 * q^39 - 134 * q^40 - 17 * q^41 + 250 * q^42 - 28 * q^43 + 42 * q^45 + 18 * q^46 + 117 * q^47 - 57 * q^48 - 117 * q^49 - 20 * q^50 - 59 * q^51 + 37 * q^52 - 75 * q^53 + 118 * q^54 + 64 * q^55 - 42 * q^56 - 104 * q^57 - 87 * q^58 + 170 * q^59 + 78 * q^60 - 15 * q^61 + 19 * q^62 + 39 * q^63 + 32 * q^64 - 17 * q^65 + 73 * q^66 + 20 * q^67 - 76 * q^68 - 11 * q^69 + 46 * q^71 - 198 * q^72 - 26 * q^73 + 29 * q^74 - 70 * q^75 + 58 * q^76 + 6 * q^77 + 128 * q^78 - 54 * q^79 - 24 * q^80 - 7 * q^81 + 81 * q^82 + 234 * q^83 - 273 * q^84 - 74 * q^85 + 52 * q^86 - 112 * q^87 + 256 * q^88 - 27 * q^89 + 28 * q^90 - 78 * q^91 - 34 * q^92 + 51 * q^93 + 28 * q^94 - 11 * q^95 + 143 * q^96 + 40 * q^97 - 47 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{77}{78}\right)$

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 $

$2$	2.57861	−	0.103914i	1.82335	−	0.0734785i	0.895196	−	0.445673i	$-0.147036\pi$
$2$	2.57861	−	0.103914i	1.82335	−	0.0734785i	0.928155	+	0.372194i	$0.121394\pi$
$3$	−0.381537	−	1.31722i	−0.220280	−	0.760496i	−0.992187	−	0.124760i	$-0.960184\pi$
$3$	−0.381537	−	1.31722i	−0.220280	−	0.760496i	0.771906	−	0.635736i	$-0.219303\pi$
$4$	4.64490	−	0.374975i	2.32245	−	0.187488i
$5$	−3.32428	+	1.26073i	−1.48666	+	0.563818i	−0.958442	−	0.285288i	$-0.907911\pi$
$5$	−3.32428	+	1.26073i	−1.48666	+	0.563818i	−0.528223	+	0.849106i	$0.677142\pi$
$6$	−1.12071	−	3.35694i	−0.457529	−	1.37047i
$7$	0.633807	−	1.48760i	0.239556	−	0.562260i	−0.756194	−	0.654347i	$-0.772944\pi$
$7$	0.633807	−	1.48760i	0.239556	−	0.562260i	0.995751	+	0.0920873i	$0.0293539\pi$
$8$	6.81465	−	0.827448i	2.40934	−	0.292547i
$9$	0.946076	−	0.598262i	0.315359	−	0.199421i
$10$	−8.44101	+	3.59638i	−2.66928	+	1.13728i
$11$	−2.92094	+	4.61910i	−0.880697	+	1.39271i	0.0386459	+	0.999253i	$0.487696\pi$
$11$	−2.92094	+	4.61910i	−0.880697	+	1.39271i	−0.919343	+	0.393458i	$0.871279\pi$
$12$	−2.26613	−	5.97529i	−0.654174	−	1.72492i
$13$	0.0292141	+	3.60543i	0.00810254	+	0.999967i
$13$	0.0292141	+	3.60543i	0.00810254	+	0.999967i
$14$	1.47976	−	3.90180i	0.395481	−	1.04280i
$15$	2.92900	+	3.89779i	0.756265	+	1.00641i
$16$	8.28698	−	1.34677i	2.07175	−	0.336691i
$17$	0.607879	+	0.258993i	0.147432	+	0.0628150i	0.464422	−	0.885614i	$-0.346262\pi$
$17$	0.607879	+	0.258993i	0.147432	+	0.0628150i	−0.316990	+	0.948429i	$0.602672\pi$
$18$	2.37739	−	1.64099i	0.560356	−	0.386786i
$19$	−3.26641	−	1.88586i	−0.749366	−	0.432647i	0.0760985	−	0.997100i	$-0.475754\pi$
$19$	−3.26641	−	1.88586i	−0.749366	−	0.432647i	−0.825465	+	0.564453i	$0.809087\pi$
$20$	−14.9682	+	7.10251i	−3.34700	+	1.58817i
$21$	−2.20131	−	0.267288i	−0.480366	−	0.0583270i
$22$	−7.05197	+	12.2144i	−1.50348	+	2.60411i
$23$	−2.06885	−	3.58336i	−0.431386	−	0.747183i	0.565607	−	0.824675i	$-0.308642\pi$
$23$	−2.06885	−	3.58336i	−0.431386	−	0.747183i	−0.996993	+	0.0774924i	$0.975309\pi$
$24$	−3.68997	−	8.66068i	−0.753212	−	1.76785i
$25$	5.71886	−	5.06647i	1.14377	−	1.01329i
$26$	0.449988	+	9.29396i	0.0882499	+	1.82270i
$27$	−4.22844	−	3.74607i	−0.813764	−	0.720932i
$28$	2.38616	−	7.14742i	0.450942	−	1.35073i
$29$	−0.0150965	−	0.374615i	−0.00280334	−	0.0695643i	0.997182	−	0.0750237i	$-0.0239032\pi$
$29$	−0.0150965	−	0.374615i	−0.00280334	−	0.0695643i	−0.999985	+	0.00545940i	$0.998262\pi$
$30$	7.95778	+	9.74651i	1.45288	+	1.77946i
$31$	4.01307	−	4.52982i	0.720769	−	0.813581i	−0.267938	−	0.963436i	$-0.586342\pi$
$31$	4.01307	−	4.52982i	0.720769	−	0.813581i	0.988708	+	0.149855i	$0.0478808\pi$
$32$	7.77699	−	1.58768i	1.37479	−	0.280665i
$33$	7.19881	+	2.08516i	1.25315	+	0.362980i
$34$	1.59439	+	0.604674i	0.273436	+	0.103701i
$35$	−0.231486	+	5.74426i	−0.0391283	+	0.970958i
$36$	4.17010	−	3.13363i	0.695016	−	0.522271i
$37$	8.68138	+	1.77232i	1.42721	+	0.291367i	0.850669	−	0.525701i	$-0.176197\pi$
$37$	8.68138	+	1.77232i	1.42721	+	0.291367i	0.576541	+	0.817068i	$0.304402\pi$
$38$	−8.61876	−	4.52348i	−1.39815	−	0.733805i
$39$	4.73800	−	1.41409i	0.758687	−	0.226435i
$40$	−21.6106	+	11.3421i	−3.41694	+	1.79335i
$41$	−6.39824	+	1.85327i	−0.999237	+	0.289433i	−0.737236	−	0.675635i	$-0.763870\pi$
$41$	−6.39824	+	1.85327i	−0.999237	+	0.289433i	−0.262001	+	0.965068i	$0.584382\pi$
$42$	−5.70410	−	0.460483i	−0.880162	−	0.0710540i
$43$	−1.58264	−	7.75228i	−0.241350	−	1.18221i	−0.902074	−	0.431582i	$-0.857956\pi$
$43$	−1.58264	−	7.75228i	−0.241350	−	1.18221i	0.660724	−	0.750629i	$-0.270249\pi$
$44$	−11.8354	+	22.5505i	−1.78426	+	3.39962i
$45$	−2.39078	+	3.18154i	−0.356396	+	0.474277i
$46$	−5.70713	−	9.02510i	−0.841470	−	1.33068i
$47$	7.99021	+	5.51524i	1.16549	+	0.804481i	0.983869	−	0.178888i	$-0.0572499\pi$
$47$	7.99021	+	5.51524i	1.16549	+	0.804481i	0.181622	+	0.983368i	$0.441865\pi$
$48$	−4.93577	−	10.4019i	−0.712418	−	1.50139i
$49$	3.03783	+	3.16272i	0.433976	+	0.451817i
$50$	14.2202	−	13.6587i	2.01104	−	1.93163i
$51$	0.109222	−	0.899525i	0.0152942	−	0.125959i
$52$	1.48765	+	16.7359i	0.206299	+	2.32086i
$53$	−0.387154	−	3.18850i	−0.0531798	−	0.437975i	−0.994844	−	0.101420i	$-0.967661\pi$
$53$	−0.387154	−	3.18850i	−0.0531798	−	0.437975i	0.941664	−	0.336555i	$-0.109262\pi$
$54$	−11.2928	−	9.22026i	−1.53675	−	1.25472i
$55$	3.88658	−	19.0377i	0.524066	−	2.56705i
$56$	3.08826	−	10.6619i	0.412686	−	1.42476i
$57$	−1.23784	+	5.02211i	−0.163956	+	0.665194i
$58$	−0.0778557	−	0.964416i	−0.0102230	−	0.126634i
$59$	0.599422	−	3.68839i	0.0780381	−	0.480188i	−0.918385	−	0.395687i	$-0.870506\pi$
$59$	0.599422	−	3.68839i	0.0780381	−	0.480188i	0.996423	−	0.0845005i	$-0.0269295\pi$
$60$	15.0665	+	17.0066i	1.94508	+	2.19554i
$61$	−3.97645	−	2.98811i	−0.509132	−	0.382588i	0.314905	−	0.949123i	$-0.398027\pi$
$61$	−3.97645	−	2.98811i	−0.509132	−	0.382588i	−0.824038	+	0.566535i	$0.808284\pi$
$62$	9.87743	−	12.0977i	1.25443	−	1.53640i
$63$	−0.290345	−	1.78656i	−0.0365800	−	0.225086i
$64$	3.58533	−	0.883705i	0.448167	−	0.110463i
$65$	−4.64261	−	11.9487i	−0.575845	−	1.48205i
$66$	18.7796	+	4.62875i	2.31161	+	0.569760i
$67$	−0.700108	+	8.67239i	−0.0855318	+	1.05950i	0.801562	+	0.597912i	$0.204003\pi$
$67$	−0.700108	+	8.67239i	−0.0855318	+	1.05950i	−0.887094	+	0.461590i	$0.847279\pi$
$68$	2.92066	+	0.975058i	0.354181	+	0.118243i
$69$	−3.93073	+	4.09232i	−0.473204	+	0.492657i
$70$			14.8363i			1.77327i
$71$	0.998956	+	0.959510i	0.118554	+	0.113873i	0.749658	−	0.661826i	$-0.230218\pi$
$71$	0.998956	+	0.959510i	0.118554	+	0.113873i	−0.631103	+	0.775699i	$0.717398\pi$
$72$	5.95215	−	4.85978i	0.701467	−	0.572730i
$73$	−0.592291	−	1.12852i	−0.0693224	−	0.132083i	0.848329	−	0.529470i	$-0.177609\pi$
$73$	−0.592291	−	1.12852i	−0.0693224	−	0.132083i	−0.917651	+	0.397387i	$0.869917\pi$
$74$	22.5700	+	3.66799i	2.62371	+	0.426395i
$75$	−8.85560	−	5.59994i	−1.02256	−	0.646626i
$76$	−15.8793	−	7.53483i	−1.82148	−	0.864304i
$77$	5.02006	+	7.27281i	0.572088	+	0.828813i
$78$	12.0705	−	4.13872i	1.36671	−	0.468618i
$79$	−2.22323	+	3.22090i	−0.250133	+	0.362380i	−0.927857	−	0.372936i	$-0.878351\pi$
$79$	−2.22323	+	3.22090i	−0.250133	+	0.362380i	0.677724	+	0.735316i	$0.262966\pi$
$80$	−25.8504	+	14.9247i	−2.89016	+	1.66863i
$81$	−1.88150	+	3.96518i	−0.209056	+	0.440575i
$82$	−16.3060	+	5.44373i	−1.80069	+	0.601160i
$83$	−1.29292	−	5.24558i	−0.141916	−	0.575777i	−0.998238	−	0.0593346i	$-0.981102\pi$
$83$	−1.29292	−	5.24558i	−0.141916	−	0.575777i	0.856322	−	0.516443i	$-0.172744\pi$
$84$	−10.3251	−	0.416088i	−1.12656	−	0.0453989i
$85$	−2.34728	−	0.0945923i	−0.254599	−	0.0102600i
$86$	−4.88658	−	19.8256i	−0.526933	−	2.13785i
$87$	−0.487690	+	0.162815i	−0.0522859	+	0.0174556i
$88$	−16.0831	+	33.8945i	−1.71447	+	3.61316i
$89$	2.98137	−	1.72129i	0.316025	−	0.182457i	−0.333595	−	0.942717i	$-0.608262\pi$
$89$	2.98137	−	1.72129i	0.316025	−	0.182457i	0.649619	+	0.760260i	$0.274928\pi$
$90$	−5.83426	+	8.45239i	−0.614985	+	0.890960i
$91$	5.38196	+	2.24169i	0.564182	+	0.234993i
$92$	−10.9533	−	15.8686i	−1.14196	−	1.65442i
$93$	−7.49791	−	3.55780i	−0.777497	−	0.368927i
$94$	21.1767	+	13.3913i	2.18421	+	1.38121i
$95$	13.2361	+	2.15107i	1.35799	+	0.220695i
$96$	−5.05853	−	9.63823i	−0.516284	−	0.983698i
$97$	−10.3543	+	8.45403i	−1.05132	+	0.858377i	−0.990186	−	0.139753i	$-0.955369\pi$
$97$	−10.3543	+	8.45403i	−1.05132	+	0.858377i	−0.0611345	+	0.998130i	$0.519472\pi$
$98$	8.16202	+	7.83973i	0.824489	+	0.791932i
$99$			6.11751i			0.614833i
$100$	24.6637	−	25.6777i	2.46637	−	2.56777i
$101$	2.13614	+	0.713148i	0.212554	+	0.0709609i	0.420951	−	0.907083i	$-0.361696\pi$
$101$	2.13614	+	0.713148i	0.212554	+	0.0709609i	−0.208397	+	0.978044i	$0.566825\pi$
$102$	0.188167	−	2.33087i	0.0186313	−	0.230791i
$103$	13.3753	+	3.29671i	1.31790	+	0.324834i	0.834715	−	0.550681i	$-0.185632\pi$
$103$	13.3753	+	3.29671i	1.31790	+	0.324834i	0.483189	+	0.875516i	$0.339478\pi$
$104$	3.18239	+	24.5456i	0.312059	+	2.40689i
$105$	7.65477	−	1.88673i	0.747029	−	0.184126i
$106$	−1.32965	−	8.18167i	−0.129147	−	0.794674i
$107$	1.54972	−	1.89807i	0.149817	−	0.183493i	−0.694244	−	0.719740i	$-0.744261\pi$
$107$	1.54972	−	1.89807i	0.149817	−	0.183493i	0.844061	+	0.536247i	$0.180158\pi$
$108$	−21.0454	−	15.8146i	−2.02509	−	1.52176i
$109$	−4.61348	−	5.20755i	−0.441892	−	0.498792i	0.484795	−	0.874628i	$-0.338894\pi$
$109$	−4.61348	−	5.20755i	−0.441892	−	0.498792i	−0.926686	+	0.375835i	$0.877356\pi$
$110$	8.04367	−	49.4947i	0.766934	−	4.71913i
$111$	−0.977739	−	12.1115i	−0.0928029	−	1.14957i
$112$	3.24890	−	13.1813i	0.306992	−	1.24552i
$113$	−5.45564	+	18.8350i	−0.513223	+	1.77185i	0.114508	+	0.993422i	$0.463471\pi$
$113$	−5.45564	+	18.8350i	−0.513223	+	1.77185i	−0.627731	+	0.778430i	$0.716016\pi$
$114$	−2.67003	+	13.0787i	−0.250071	+	1.22493i
$115$	11.3951	+	9.30383i	1.06260	+	0.867587i
$116$	−0.210593	−	1.73439i	−0.0195531	−	0.161034i
$117$	2.18463	+	3.39354i	0.201969	+	0.313733i
$118$	1.16240	−	9.57320i	0.107007	−	0.881285i
$119$	0.770556	−	0.740129i	0.0706367	−	0.0678475i
$120$	23.1853	+	24.1385i	2.11652	+	2.20353i
$121$	−8.08856	−	17.0463i	−0.735323	−	1.54966i
$122$	−10.5642	−	7.29195i	−0.956439	−	0.660182i
$123$	4.88233	+	7.72079i	0.440225	+	0.696160i
$124$	16.9418	−	22.5454i	1.52142	−	2.02464i
$125$	−4.36244	+	8.31193i	−0.390188	+	0.743441i
$126$	−0.934336	−	4.57668i	−0.0832372	−	0.407723i
$127$	0.594992	+	0.0480327i	0.0527970	+	0.00426222i	0.106837	−	0.994277i	$-0.465928\pi$
$127$	0.594992	+	0.0480327i	0.0527970	+	0.00426222i	−0.0540398	+	0.998539i	$0.517210\pi$
$128$	−6.09469	+	1.76535i	−0.538700	+	0.156036i
$129$	−9.60761	+	5.04246i	−0.845903	+	0.443964i
$130$	−13.2131	−	30.3284i	−1.15887	−	2.65998i
$131$	15.7024	+	8.24127i	1.37193	+	0.720043i	0.979821	−	0.199877i	$-0.0640541\pi$
$131$	15.7024	+	8.24127i	1.37193	+	0.720043i	0.392107	+	0.919920i	$0.371746\pi$
$132$	34.2197	+	6.98599i	2.97844	+	0.608053i
$133$	−4.87568	+	3.66384i	−0.422775	+	0.317695i
$134$	−0.904118	+	22.4355i	−0.0781039	+	1.93813i
$135$	18.7794	+	7.12207i	1.61627	+	0.612970i
$136$	4.35678	+	1.26196i	0.373591	+	0.108212i
$137$	−0.713145	+	0.145590i	−0.0609281	+	0.0124386i	−0.230393	−	0.973098i	$-0.574001\pi$
$137$	−0.713145	+	0.145590i	−0.0609281	+	0.0124386i	0.169465	+	0.985536i	$0.445796\pi$
$138$	−9.71055	+	10.9609i	−0.826617	+	0.933057i
$139$	−14.4527	−	17.7013i	−1.22586	−	1.50140i	−0.803872	−	0.594803i	$-0.797230\pi$
$139$	−14.4527	−	17.7013i	−1.22586	−	1.50140i	−0.421987	−	0.906602i	$-0.638667\pi$
$140$	1.07873	+	26.7684i	0.0911691	+	2.26234i
$141$	4.21622	−	12.6291i	0.355070	−	1.06356i
$142$	2.67562	+	2.37039i	0.224533	+	0.198919i
$143$	−16.7392	−	10.3963i	−1.39980	−	0.869383i
$144$	7.03440	−	6.23193i	0.586200	−	0.519328i
$145$	0.522475	+	1.22629i	0.0433892	+	0.101838i
$146$	−1.64455	−	2.84845i	−0.136104	−	0.235740i
$147$	3.00694	−	5.20818i	0.248009	−	0.429563i
$148$	40.9887	+	4.97693i	3.36925	+	0.409101i
$149$	−17.2271	+	8.17434i	−1.41130	+	0.669668i	−0.973348	−	0.229332i	$-0.926346\pi$
$149$	−17.2271	+	8.17434i	−1.41130	+	0.669668i	−0.437948	+	0.899001i	$0.644294\pi$
$150$	−23.4170	−	13.5198i	−1.91199	−	1.10389i
$151$	9.28831	−	6.41125i	0.755872	−	0.521741i	−0.126687	−	0.991943i	$-0.540434\pi$
$151$	9.28831	−	6.41125i	0.755872	−	0.521741i	0.882559	+	0.470202i	$0.155819\pi$
$152$	−23.8199	−	10.1487i	−1.93205	−	0.823169i
$153$	0.730046	−	0.118644i	0.0590207	−	0.00959180i
$154$	13.7005	+	18.2321i	1.10402	+	1.46918i
$155$	−7.62969	+	20.1178i	−0.612832	+	1.61590i
$156$	21.4773	−	8.34493i	1.71956	−	0.668129i
$157$	5.69361	+	15.0128i	0.454399	+	1.19815i	0.945088	+	0.326817i	$0.105976\pi$
$157$	5.69361	+	15.0128i	0.454399	+	1.19815i	−0.490688	+	0.871335i	$0.663255\pi$
$158$	−5.39813	+	8.53647i	−0.429452	+	0.679125i
$159$	−4.05224	+	1.72650i	−0.321364	+	0.136920i
$160$	−23.8513	+	15.0826i	−1.88561	+	1.19239i
$161$	−6.64186	+	0.806468i	−0.523452	+	0.0635586i
$162$	−4.43961	+	10.4202i	−0.348809	+	0.818684i
$163$	−0.106045	−	0.317643i	−0.00830607	−	0.0248797i	0.944302	−	0.329081i	$-0.106739\pi$
$163$	−0.106045	−	0.317643i	−0.00830607	−	0.0248797i	−0.952608	+	0.304201i	$0.901611\pi$
$164$	−29.0243	+	11.0075i	−2.26642	+	0.859538i
$165$	−26.5597	+	2.14412i	−2.06767	+	0.166920i
$166$	−3.87902	−	13.3919i	−0.301070	−	1.03942i
$167$	−6.28018	+	0.253083i	−0.485975	+	0.0195841i	−0.282045	−	0.959401i	$-0.591013\pi$
$167$	−6.28018	+	0.253083i	−0.485975	+	0.0195841i	−0.203930	+	0.978985i	$0.565372\pi$
$168$	−15.2223			−1.17443
$169$	−12.9983	+	0.210659i	−0.999869	+	0.0162045i
$170$	−6.06255			−0.464977
$171$	−4.21852	+	0.170000i	−0.322598	+	0.0130003i
$172$	−10.2581	−	35.4151i	−0.782174	−	2.70038i
$173$	20.1134	−	1.62372i	1.52920	−	0.123449i	0.712975	−	0.701190i	$-0.247347\pi$
$173$	20.1134	−	1.62372i	1.52920	−	0.123449i	0.816221	+	0.577740i	$0.196065\pi$
$174$	−1.24064	+	0.470514i	−0.0940529	+	0.0356695i
$175$	−3.91222	−	11.7185i	−0.295736	−	0.885838i
$176$	−17.9849	+	42.2122i	−1.35567	+	3.18187i
$177$	−5.08712	+	0.617688i	−0.382371	+	0.0464283i
$178$	7.50892	−	4.74835i	0.562817	−	0.355904i
$179$	−6.18386	+	2.63470i	−0.462204	+	0.196927i	−0.610500	−	0.792016i	$-0.709031\pi$
$179$	−6.18386	+	2.63470i	−0.462204	+	0.196927i	0.148296	+	0.988943i	$0.452621\pi$
$180$	−9.91192	+	15.6744i	−0.738791	+	1.16830i
$181$	0.654370	+	1.72543i	0.0486390	+	0.128250i	0.957134	−	0.289645i	$-0.0935372\pi$
$181$	0.654370	+	1.72543i	0.0486390	+	0.128250i	−0.908495	+	0.417895i	$0.862768\pi$
$182$	14.1109	+	5.22117i	1.04597	+	0.387019i
$183$	−2.41883	+	6.37793i	−0.178805	+	0.471470i
$184$	−17.0636	−	22.7075i	−1.25794	−	1.67402i
$185$	−31.0938	+	5.05323i	−2.28606	+	0.371521i
$186$	−19.7039	−	8.39503i	−1.44476	−	0.615554i
$187$	−2.97189	+	2.05135i	−0.217326	+	0.150010i
$188$	39.1818	+	22.6216i	2.85763	+	1.64985i
$189$	−8.25267	+	3.91594i	−0.600294	+	0.284843i
$190$	34.3541	+	4.17135i	2.49231	+	0.302621i
$191$	7.53238	−	13.0465i	0.545024	−	0.944009i	−0.453581	−	0.891215i	$-0.649854\pi$
$191$	7.53238	−	13.0465i	0.545024	−	0.944009i	0.998605	−	0.0527943i	$-0.0168128\pi$
$192$	−2.53197	−	4.38550i	−0.182729	−	0.316496i
$193$	−0.458739	−	1.07670i	−0.0330208	−	0.0775026i	0.902653	−	0.430370i	$-0.141617\pi$
$193$	−0.458739	−	1.07670i	−0.0330208	−	0.0775026i	−0.935673	+	0.352867i	$0.885207\pi$
$194$	−25.8212	+	22.8756i	−1.85385	+	1.64237i
$195$	−13.9677	+	10.6742i	−1.00024	+	0.764394i
$196$	15.2964	+	13.5514i	1.09260	+	0.967957i
$197$	0.657798	−	1.97034i	0.0468661	−	0.140381i	−0.922503	−	0.385990i	$-0.873860\pi$
$197$	0.657798	−	1.97034i	0.0468661	−	0.140381i	0.969369	+	0.245609i	$0.0789880\pi$
$198$	0.635697	+	15.7747i	0.0451770	+	1.12106i
$199$	−1.25696	−	1.53950i	−0.0891039	−	0.109132i	0.728129	−	0.685440i	$-0.240390\pi$
$199$	−1.25696	−	1.53950i	−0.0891039	−	0.109132i	−0.817233	+	0.576308i	$0.804493\pi$
$200$	34.7798	−	39.2582i	2.45930	−	2.77598i
$201$	11.6906	−	2.38664i	0.824588	−	0.168341i
$202$	5.58237	+	1.61695i	0.392774	+	0.113768i
$203$	−0.566845	−	0.214976i	−0.0397847	−	0.0150884i
$204$	0.170026	−	4.21916i	0.0119042	−	0.295400i
$205$	18.9331	−	14.2273i	1.32234	−	0.993677i
$206$	34.8322	+	7.11104i	2.42687	+	0.495449i
$207$	−4.10108	−	2.15242i	−0.285045	−	0.149603i
$208$	5.09777	+	29.8388i	0.353467	+	2.06895i
$209$	18.2520	−	9.57938i	1.26252	−	0.662620i
$210$	19.5426	−	5.66058i	1.34857	−	0.390617i
$211$	4.56596	+	0.368603i	0.314334	+	0.0253756i	0.236627	−	0.971601i	$-0.423958\pi$
$211$	4.56596	+	0.368603i	0.314334	+	0.0253756i	0.0777069	+	0.996976i	$0.475240\pi$
$212$	−2.99391	−	14.6651i	−0.205622	−	1.00720i
$213$	0.882746	−	1.68193i	0.0604848	−	0.115244i
$214$	3.79889	−	5.05541i	0.259687	−	0.345581i
$215$	15.0347	+	23.7755i	1.02536	+	1.62147i
$216$	−31.9150	−	22.0294i	−2.17154	−	1.49891i
$217$	−4.19505	−	8.84088i	−0.284779	−	0.600158i
$218$	−12.4375	−	12.9488i	−0.842374	−	0.877004i
$219$	−1.26052	+	1.21075i	−0.0851781	+	0.0818147i
$220$	10.9141	−	89.8858i	0.735829	−	6.06010i
$221$	−0.916023	+	2.19923i	−0.0616184	+	0.147936i
$222$	−3.77976	−	31.1291i	−0.253681	−	2.08925i
$223$	2.49454	+	2.03673i	0.167047	+	0.136390i	0.712281	−	0.701894i	$-0.247662\pi$
$223$	2.49454	+	2.03673i	0.167047	+	0.136390i	−0.545235	+	0.838284i	$0.683559\pi$
$224$	2.56727	−	12.5753i	0.171533	−	0.840224i
$225$	2.37940	−	8.21464i	0.158627	−	0.547643i
$226$	−12.1107	+	49.1351i	−0.805593	+	3.26842i
$227$	0.629942	+	7.80323i	0.0418107	+	0.517919i	0.983436	+	0.181256i	$0.0580162\pi$
$227$	0.629942	+	7.80323i	0.0418107	+	0.517919i	−0.941625	+	0.336663i	$0.890702\pi$
$228$	−3.86647	+	23.7914i	−0.256063	+	1.57562i
$229$	17.1729	+	19.3842i	1.13482	+	1.28094i	0.954789	+	0.297283i	$0.0960806\pi$
$229$	17.1729	+	19.3842i	1.13482	+	1.28094i	0.180029	+	0.983661i	$0.442381\pi$
$230$	30.3504	+	22.8068i	2.00124	+	1.50384i
$231$	7.66454	−	9.38735i	0.504290	−	0.617643i
$232$	−0.412852	−	2.54038i	−0.0271050	−	0.166784i
$233$	7.55195	−	1.86139i	0.494745	−	0.121944i	0.0159542	−	0.999873i	$-0.494921\pi$
$233$	7.55195	−	1.86139i	0.494745	−	0.121944i	0.478791	+	0.877929i	$0.341075\pi$
$234$	5.98595	+	8.52358i	0.391314	+	0.557204i
$235$	−33.5150	−	8.26070i	−2.18628	−	0.538869i
$236$	1.40120	−	17.3570i	0.0912104	−	1.12984i
$237$	5.09087	+	1.69958i	0.330688	+	0.110400i
$238$	1.91005	−	1.98857i	0.123810	−	0.128900i
$239$			3.83283i			0.247925i	0.992287	+	0.123963i	$0.0395603\pi$
$239$			3.83283i			0.247925i	−0.992287	+	0.123963i	$0.960440\pi$
$240$	29.5220	+	28.3562i	1.90564	+	1.83039i
$241$	−12.9967	+	10.6115i	−0.837192	+	0.683546i	−0.950741	−	0.309987i	$-0.899675\pi$
$241$	−12.9967	+	10.6115i	−0.837192	+	0.683546i	0.113549	+	0.993532i	$0.463778\pi$
$242$	−22.6286	−	43.1151i	−1.45462	−	2.77155i
$243$	−10.7871	−	1.75307i	−0.691992	−	0.112460i
$244$	−19.5907	−	12.3884i	−1.25417	−	0.793087i
$245$	−14.0860	−	6.68387i	−0.899919	−	0.427017i
$246$	13.3919	+	19.4015i	0.853837	+	1.23700i
$247$	6.70393	−	11.8319i	0.426561	−	0.752847i
$248$	23.5995	−	34.1898i	1.49857	−	2.17105i
$249$	−6.41628	+	3.70444i	−0.406615	+	0.234759i
$250$	−10.3853	+	21.8865i	−0.656823	+	1.38422i
$251$	−10.4189	+	3.47833i	−0.657633	+	0.219550i	−0.625848	−	0.779945i	$-0.715247\pi$
$251$	−10.4189	+	3.47833i	−0.657633	+	0.219550i	−0.0317842	+	0.999495i	$0.510119\pi$
$252$	−2.01854	−	8.18955i	−0.127156	−	0.515893i
$253$	22.5949	+	0.910544i	1.42053	+	0.0572454i
$254$	1.53924	+	0.0620293i	0.0965807	+	0.00389207i
$255$	0.770977	+	3.12798i	0.0482804	+	0.195881i
$256$	−22.5376	+	7.52414i	−1.40860	+	0.470259i
$257$	−1.46728	+	3.09222i	−0.0915262	+	0.192887i	−0.944051	−	0.329799i	$-0.893019\pi$
$257$	−1.46728	+	3.09222i	−0.0915262	+	0.192887i	0.852525	+	0.522687i	$0.175070\pi$
$258$	−24.2503	+	14.0009i	−1.50976	+	0.871658i
$259$	8.13881	−	11.7911i	0.505721	−	0.732664i
$260$	−26.0449	−	53.7595i	−1.61524	−	3.33402i
$261$	−0.238401	−	0.345383i	−0.0147566	−	0.0213787i
$262$	41.3468	+	19.6193i	2.55441	+	1.21208i
$263$	−18.5638	−	11.7391i	−1.14469	−	0.723861i	−0.179079	−	0.983835i	$-0.557312\pi$
$263$	−18.5638	−	11.7391i	−1.14469	−	0.723861i	−0.965616	+	0.259974i	$0.916286\pi$
$264$	50.7827	+	8.25299i	3.12546	+	0.507937i
$265$	5.30687	+	10.1114i	0.325998	+	0.621138i
$266$	−12.1917	+	9.95426i	−0.747524	+	0.610335i
$267$	−3.40482	−	3.27038i	−0.208372	−	0.200144i
$268$			40.5450i			2.47668i
$269$	7.20348	−	7.49962i	0.439204	−	0.457260i	−0.464402	−	0.885625i	$-0.653731\pi$
$269$	7.20348	−	7.49962i	0.439204	−	0.457260i	0.903606	+	0.428365i	$0.140910\pi$
$270$	49.1647	+	16.4136i	2.99207	+	0.998898i
$271$	0.979373	−	12.1317i	0.0594927	−	0.736949i	−0.896402	−	0.443241i	$-0.853829\pi$
$271$	0.979373	−	12.1317i	0.0594927	−	0.736949i	0.955895	−	0.293708i	$-0.0948894\pi$
$272$	5.38629	+	1.32760i	0.326592	+	0.0804976i
$273$	0.899379	−	7.94450i	0.0544329	−	0.480823i
$274$	−1.82379	+	0.449524i	−0.110179	+	0.0271568i
$275$	6.69806	+	41.2148i	0.403908	+	2.48535i
$276$	−16.7233	+	20.4824i	−1.00663	+	1.23289i
$277$	19.1789	+	14.4120i	1.15235	+	0.865934i	0.992625	−	0.121228i	$-0.0386832\pi$
$277$	19.1789	+	14.4120i	1.15235	+	0.865934i	0.159724	+	0.987162i	$0.448940\pi$
$278$	−39.1072	−	44.1429i	−2.34549	−	2.64751i
$279$	1.08665	−	6.68643i	0.0650561	−	0.400306i
$280$	3.17559	+	39.3367i	0.189778	+	2.35082i
$281$	0.950183	−	3.85504i	0.0566832	−	0.229973i	−0.935767	−	0.352618i	$-0.885292\pi$
$281$	0.950183	−	3.85504i	0.0566832	−	0.229973i	0.992451	+	0.122645i	$0.0391377\pi$
$282$	9.55963	−	33.0037i	0.569268	−	1.96534i
$283$	0.0492759	−	0.241369i	0.00292915	−	0.0143479i	−0.978300	−	0.207194i	$-0.933567\pi$
$283$	0.0492759	−	0.241369i	0.00292915	−	0.0143479i	0.981229	+	0.192846i	$0.0617719\pi$
$284$	4.99985	+	4.08225i	0.296686	+	0.242237i
$285$	−2.21662	−	18.2555i	−0.131301	−	1.08136i
$286$	−44.2441	−	25.0686i	−2.61621	−	1.48234i
$287$	−1.29832	+	10.6926i	−0.0766375	+	0.631166i
$288$	6.40777	−	6.15475i	0.377582	−	0.362672i
$289$	−11.4739	−	11.9456i	−0.674934	−	0.702681i
$290$	1.47469	+	3.10784i	0.0865966	+	0.182499i
$291$	15.0864	+	10.4134i	0.884378	+	0.610442i
$292$	−3.17430	−	5.01975i	−0.185762	−	0.293759i
$293$	12.4734	−	16.5991i	0.728707	−	0.969732i	−0.271267	−	0.962504i	$-0.587443\pi$
$293$	12.4734	−	16.5991i	0.728707	−	0.969732i	0.999974	−	0.00722828i	$-0.00230085\pi$
$294$	7.21252	−	13.7423i	0.420643	−	0.801468i
$295$	2.65743	+	13.0170i	0.154722	+	0.757877i
$296$	60.6270	+	4.89432i	3.52388	+	0.284477i
$297$	29.6545	−	8.58954i	1.72073	−	0.498416i
$298$	−43.5724	+	22.8686i	−2.52408	+	1.32474i
$299$	12.8591	−	7.56380i	0.743663	−	0.437426i
$300$	−43.2332	−	22.6906i	−2.49607	−	1.31004i
$301$	−12.5354	−	2.55911i	−0.722526	−	0.147505i
$302$	23.2847	−	17.4973i	1.33988	−	1.00686i
$303$	0.124356	−	3.08585i	0.00714405	−	0.177278i
$304$	−29.6085	−	11.2290i	−1.69816	−	0.644029i
$305$	16.9861	+	4.92007i	0.972619	+	0.281723i
$306$	1.87017	−	0.381798i	0.106911	−	0.0218260i
$307$	−2.44358	+	2.75824i	−0.139463	+	0.157421i	−0.814092	−	0.580736i	$-0.802765\pi$
$307$	−2.44358	+	2.75824i	−0.139463	+	0.157421i	0.674629	+	0.738157i	$0.264303\pi$
$308$	26.0448	+	31.8991i	1.48404	+	1.81762i
$309$	−0.760676	−	18.8760i	−0.0432733	−	1.07382i
$310$	−17.5834	+	52.6689i	−0.998673	+	2.99139i
$311$	2.36566	+	2.09579i	0.134144	+	0.118842i	0.727527	−	0.686079i	$-0.240670\pi$
$311$	2.36566	+	2.09579i	0.134144	+	0.118842i	−0.593383	+	0.804920i	$0.702208\pi$
$312$	31.1177	−	13.5570i	1.76169	−	0.767511i
$313$	15.8786	−	14.0672i	0.897513	−	0.795127i	−0.0819741	−	0.996634i	$-0.526122\pi$
$313$	15.8786	−	14.0672i	0.897513	−	0.795127i	0.979487	+	0.201507i	$0.0645840\pi$
$314$	16.2416	+	38.1205i	0.916568	+	2.15126i
$315$	3.21757	+	5.57300i	0.181290	+	0.314003i
$316$	−9.11892	+	15.7944i	−0.512979	+	0.888506i
$317$	2.03005	+	0.246493i	0.114019	+	0.0138444i	0.177347	−	0.984148i	$-0.443248\pi$
$317$	2.03005	+	0.246493i	0.114019	+	0.0138444i	−0.0633281	+	0.997993i	$0.520171\pi$
$318$	−10.2697	+	4.87305i	−0.575898	+	0.273267i
$319$	1.77448	+	1.02450i	0.0993518	+	0.0573608i
$320$	−10.8045	+	7.45784i	−0.603993	+	0.416906i
$321$	−3.09145	−	1.31714i	−0.172548	−	0.0735157i
$322$	−17.0429	+	2.76975i	−0.949766	+	0.154352i
$323$	−1.49716	−	1.99236i	−0.0833041	−	0.110858i
$324$	−7.25254	+	19.1234i	−0.402919	+	1.06241i
$325$	18.4339	+	20.4709i	1.02253	+	1.13552i
$326$	−0.306456	−	0.808057i	−0.0169730	−	0.0447542i
$327$	−5.09926	+	8.06384i	−0.281990	+	0.445931i
$328$	−42.0683	+	17.9236i	−2.32283	+	0.989666i
$329$	13.2687	−	8.39063i	0.731528	−	0.462590i
$330$	−68.2643	+	8.28878i	−3.75783	+	0.456283i
$331$	12.6917	−	29.7885i	0.697599	−	1.63733i	−0.0709066	−	0.997483i	$-0.522589\pi$
$331$	12.6917	−	29.7885i	0.697599	−	1.63733i	0.768506	−	0.639843i	$-0.221001\pi$
$332$	−7.97245	−	23.8804i	−0.437545	−	1.31061i
$333$	9.27356	−	3.51700i	0.508188	−	0.192730i
$334$	−16.1678	+	1.30520i	−0.884664	+	0.0714174i
$335$	−8.60623	−	29.7121i	−0.470209	−	1.62335i
$336$	−18.6022	+	0.749644i	−1.01483	+	0.0408964i
$337$	−31.0373			−1.69071			−0.845354	−	0.534207i	$-0.820610\pi$
$337$	−31.0373			−1.69071			−0.845354	+	0.534207i	$0.820610\pi$
$338$	−33.4956	+	1.89392i	−1.82192	+	0.103015i
$339$	26.8914			1.46054
$340$	−10.9384	+	0.440802i	−0.593217	+	0.0239058i
$341$	9.20175	+	31.7681i	0.498303	+	1.72034i
$342$	−10.8602	+	0.876729i	−0.587254	+	0.0474081i
$343$	17.2136	−	6.52828i	0.929450	−	0.352494i
$344$	−17.1997	−	51.5195i	−0.927347	−	2.77774i
$345$	7.90752	−	18.5596i	0.425727	−	0.999217i
$346$	51.6959	−	6.27702i	2.77919	−	0.337455i
$347$	−9.28103	+	5.86897i	−0.498232	+	0.315063i	−0.759838	−	0.650112i	$-0.774722\pi$
$347$	−9.28103	+	5.86897i	−0.498232	+	0.315063i	0.261607	+	0.965175i	$0.415748\pi$
$348$	−2.20422	+	0.939131i	−0.118159	+	0.0503427i
$349$	−4.90223	+	7.75225i	−0.262410	+	0.414969i	−0.950532	−	0.310627i	$-0.899461\pi$
$349$	−4.90223	+	7.75225i	−0.262410	+	0.414969i	0.688122	+	0.725595i	$0.258435\pi$
$350$	−11.3058	−	29.8110i	−0.604321	−	1.59346i
$351$	13.3827	−	15.3548i	0.714315	−	0.819579i
$352$	−15.3825	+	40.5602i	−0.819888	+	2.16187i
$353$	−9.11776	−	12.1335i	−0.485289	−	0.645803i	0.488685	−	0.872460i	$-0.337477\pi$
$353$	−9.11776	−	12.1335i	−0.485289	−	0.645803i	−0.973975	+	0.226657i	$0.927220\pi$
$354$	−13.0535	+	2.12140i	−0.693786	+	0.112751i
$355$	−4.53050	−	1.93027i	−0.240454	−	0.102448i
$356$	13.2027	−	9.11319i	0.699743	−	0.482998i
$357$	−1.26891	−	0.732604i	−0.0671577	−	0.0387735i
$358$	−15.6720	+	7.43645i	−0.828290	+	0.393028i
$359$	−11.1571	−	1.35471i	−0.588848	−	0.0714991i	−0.179311	−	0.983792i	$-0.557387\pi$
$359$	−11.1571	−	1.35471i	−0.588848	−	0.0714991i	−0.409537	+	0.912293i	$0.634310\pi$
$360$	−13.6597	+	23.6594i	−0.719931	+	1.24696i
$361$	−2.38703	−	4.13446i	−0.125633	−	0.217603i
$362$	1.86666	+	4.38122i	0.0981096	+	0.230272i
$363$	−19.3676	+	17.1582i	−1.01653	+	0.900571i
$364$	25.8392	+	8.39433i	1.35434	+	0.439982i
$365$	3.39170	+	3.00479i	0.177530	+	0.157278i
$366$	−5.57445	+	16.6975i	−0.291381	+	0.872794i
$367$	−0.389655	−	9.66919i	−0.0203398	−	0.504727i	−0.976964	−	0.213403i	$-0.931545\pi$
$367$	−0.389655	−	9.66919i	−0.0203398	−	0.504727i	0.956624	−	0.291324i	$-0.0940958\pi$
$368$	−21.9705	−	26.9090i	−1.14529	−	1.40273i
$369$	−4.94448	+	5.58116i	−0.257399	+	0.290544i
$370$	−79.6536	+	16.2614i	−4.14099	+	0.845390i
$371$	−4.98860	−	1.44496i	−0.258995	−	0.0750188i
$372$	−36.1611	−	13.7141i	−1.87487	−	0.711043i
$373$	−1.51600	+	37.6192i	−0.0784957	+	1.94785i	0.184020	+	0.982922i	$0.441089\pi$
$373$	−1.51600	+	37.6192i	−0.0784957	+	1.94785i	−0.262516	+	0.964928i	$0.584552\pi$
$374$	−7.45018	+	5.59845i	−0.385240	+	0.289489i
$375$	12.6131	+	2.57497i	0.651335	+	0.132971i
$376$	59.0140	+	30.9730i	3.04342	+	1.59731i
$377$	1.35021	−	0.0653734i	0.0695393	−	0.00336690i
$378$	−20.8735	+	10.9552i	−1.07362	+	0.563477i
$379$	19.8251	−	5.74240i	1.01835	−	0.294967i	0.273263	−	0.961939i	$-0.411897\pi$
$379$	19.8251	−	5.74240i	1.01835	−	0.294967i	0.745083	+	0.666972i	$0.232410\pi$
$380$	62.2868	+	5.02831i	3.19525	+	0.257947i
$381$	−0.163742	−	0.802061i	−0.00838875	−	0.0410908i
$382$	18.0673	−	34.4244i	0.924405	−	1.76131i
$383$	−8.37806	+	11.1492i	−0.428099	+	0.569696i	−0.961023	−	0.276467i	$-0.910836\pi$
$383$	−8.37806	+	11.1492i	−0.428099	+	0.569696i	0.532925	+	0.846163i	$0.321093\pi$
$384$	4.65070	+	7.35449i	0.237330	+	0.375307i
$385$	−25.8572	−	17.8479i	−1.31780	−	0.909614i
$386$	−1.29479	−	2.72872i	−0.0659032	−	0.138888i
$387$	−6.13519	−	6.38741i	−0.311869	−	0.324690i
$388$	−44.9247	+	43.1508i	−2.28071	+	2.19065i
$389$	0.0438925	−	0.361487i	0.00222544	−	0.0183281i	−0.991554	−	0.129696i	$-0.958600\pi$
$389$	0.0438925	−	0.361487i	0.00222544	−	0.0183281i	0.993779	+	0.111367i	$0.0355231\pi$
$390$	−34.9079	+	28.9760i	−1.76763	+	1.46726i
$391$	−0.329548	−	2.71407i	−0.0166659	−	0.137256i
$392$	23.3187	+	19.0392i	1.17777	+	0.961622i
$393$	4.86450	−	23.8279i	0.245381	−	1.20196i
$394$	1.49146	−	5.14910i	0.0751384	−	0.259408i
$395$	3.32994	−	13.5101i	0.167547	−	0.679766i
$396$	2.29391	+	28.4152i	0.115274	+	1.42792i
$397$	0.766347	−	4.71552i	0.0384618	−	0.236665i	−0.960701	−	0.277587i	$-0.910465\pi$
$397$	0.766347	−	4.71552i	0.0384618	−	0.236665i	0.999162	+	0.0409218i	$0.0130294\pi$
$398$	−3.40119	−	3.83915i	−0.170486	−	0.192439i
$399$	6.68633	+	5.02445i	0.334735	+	0.251537i
$400$	40.5687	−	49.6877i	2.02844	−	2.48438i
$401$	1.59975	+	9.84367i	0.0798878	+	0.491569i	0.995903	+	0.0904262i	$0.0288229\pi$
$401$	1.59975	+	9.84367i	0.0798878	+	0.491569i	−0.916015	+	0.401143i	$0.868613\pi$
$402$	29.8973	−	7.36903i	1.49114	−	0.367534i
$403$	16.4492	+	14.3365i	0.819394	+	0.714154i
$404$	10.1896	+	2.51150i	0.506950	+	0.124952i
$405$	1.25560	−	15.5535i	0.0623915	−	0.772857i
$406$	−1.48401	−	0.495436i	−0.0736502	−	0.0245881i
$407$	−33.5443	+	34.9233i	−1.66273	+	1.73108i
$408$		−	6.22032i		−	0.307952i
$409$	14.8237	+	14.2383i	0.732983	+	0.704040i	0.963106	−	0.269122i	$-0.0867334\pi$
$409$	14.8237	+	14.2383i	0.732983	+	0.704040i	−0.230123	+	0.973162i	$0.573913\pi$
$410$	47.3426	−	38.6540i	2.33808	−	1.90899i
$411$	0.463864	+	0.883820i	0.0228807	+	0.0435956i
$412$	63.3630	+	10.2975i	3.12167	+	0.507321i
$413$	−5.10693	−	3.22943i	−0.251296	−	0.158910i
$414$	−10.7988	−	5.12407i	−0.530730	−	0.251834i
$415$	10.9113	+	15.8078i	0.535615	+	0.775973i
$416$	5.95148	+	27.9930i	0.291795	+	1.37247i
$417$	−17.8023	+	25.7910i	−0.871780	+	1.26299i
$418$	46.0693	−	26.5981i	2.25332	−	1.30096i
$419$	8.69914	−	18.3330i	0.424981	−	0.895628i	−0.572166	−	0.820138i	$-0.693897\pi$
$419$	8.69914	−	18.3330i	0.424981	−	0.895628i	0.997147	−	0.0754899i	$-0.0240521\pi$
$420$	34.8482	−	11.6340i	1.70042	−	0.567683i
$421$	−8.93777	−	36.2620i	−0.435600	−	1.76730i	−0.620157	−	0.784478i	$-0.712931\pi$
$421$	−8.93777	−	36.2620i	−0.435600	−	1.76730i	0.184557	−	0.982822i	$-0.440915\pi$
$422$	11.8121	+	0.476012i	0.575005	+	0.0231719i
$423$	10.8589	+	0.437599i	0.527978	+	0.0212768i
$424$	−5.27664	−	21.4082i	−0.256256	−	1.03967i
$425$	4.78855	−	1.59865i	0.232279	−	0.0775461i
$426$	2.10148	−	4.42877i	0.101817	−	0.214575i
$427$	−6.96541	+	4.02148i	−0.337080	+	0.194613i
$428$	6.48659	−	9.39745i	0.313541	−	0.454243i
$429$	−7.30760	+	26.0157i	−0.352814	+	1.25605i
$430$	41.2392	+	59.7453i	1.98873	+	2.88117i
$431$	−7.53081	−	3.57342i	−0.362746	−	0.172125i	0.238592	−	0.971120i	$-0.423314\pi$
$431$	−7.53081	−	3.57342i	−0.362746	−	0.172125i	−0.601338	+	0.798995i	$0.705366\pi$
$432$	−40.0861	−	25.3489i	−1.92864	−	1.21960i
$433$	−11.3924	−	1.85145i	−0.547485	−	0.0889750i	−0.119624	−	0.992819i	$-0.538169\pi$
$433$	−11.3924	−	1.85145i	−0.547485	−	0.0889750i	−0.427862	+	0.903844i	$0.640733\pi$
$434$	−11.7361	−	22.3612i	−0.563350	−	1.07337i
$435$	1.41595	−	1.15609i	0.0678898	−	0.0554303i
$436$	−23.3819	−	22.4586i	−1.11979	−	1.07557i
$437$			15.6063i			0.746551i
$438$	−3.12458	+	3.25303i	−0.149298	+	0.155436i
$439$	−21.3518	−	7.12829i	−1.01907	−	0.340215i	−0.242435	−	0.970168i	$-0.577946\pi$
$439$	−21.3518	−	7.12829i	−1.01907	−	0.340215i	−0.776633	+	0.629953i	$0.783074\pi$
$440$	10.7329	−	132.951i	0.511673	−	6.33821i
$441$	4.76615	+	1.17475i	0.226960	+	0.0559405i
$442$	−2.13353	+	5.76615i	−0.101482	+	0.274268i
$443$	−8.88196	+	2.18921i	−0.421995	+	0.104012i	−0.444594	−	0.895732i	$-0.646652\pi$
$443$	−8.88196	+	2.18921i	−0.421995	+	0.104012i	0.0225992	+	0.999745i	$0.492806\pi$
$444$	−9.08301	−	55.8900i	−0.431061	−	2.65242i
$445$	−7.74082	+	9.48079i	−0.366950	+	0.449433i
$446$	6.64409	+	4.99271i	0.314607	+	0.236412i
$447$	17.3402	+	19.5730i	0.820161	+	0.925771i
$448$	0.957809	−	5.89364i	0.0452522	−	0.278448i
$449$	−1.27920	−	15.8458i	−0.0603694	−	0.747809i	−0.954155	−	0.299314i	$-0.903242\pi$
$449$	−1.27920	−	15.8458i	−0.0603694	−	0.747809i	0.893785	−	0.448495i	$-0.148040\pi$
$450$	5.28192	−	21.4296i	0.248992	−	1.01020i
$451$	10.1284	−	34.9674i	0.476929	−	1.64655i
$452$	−18.2782	+	89.5327i	−0.859736	+	4.21126i
$453$	−11.9889	−	9.78860i	−0.563286	−	0.459908i
$454$	2.43524	+	20.0560i	0.114291	+	0.941275i
$455$	−20.7173	−	0.666793i	−0.971243	−	0.0312598i
$456$	−4.27990	+	35.2481i	−0.200425	+	1.65064i
$457$	−2.75153	+	2.64288i	−0.128711	+	0.123629i	−0.754316	−	0.656511i	$-0.772032\pi$
$457$	−2.75153	+	2.64288i	−0.128711	+	0.123629i	0.625605	+	0.780140i	$0.284852\pi$
$458$	46.2965	+	48.1998i	2.16329	+	2.25223i
$459$	−1.60018	−	3.37230i	−0.0746898	−	0.157405i
$460$	56.4180	+	38.9425i	2.63050	+	1.81570i
$461$	−10.2751	−	16.2488i	−0.478560	−	0.756782i	0.516476	−	0.856302i	$-0.327244\pi$
$461$	−10.2751	−	16.2488i	−0.478560	−	0.756782i	−0.995036	+	0.0995201i	$0.968269\pi$
$462$	18.7884	−	25.0028i	0.874113	−	1.16323i
$463$	−18.5768	+	35.3952i	−0.863339	+	1.64496i	−0.103701	+	0.994608i	$0.533069\pi$
$463$	−18.5768	+	35.3952i	−0.863339	+	1.64496i	−0.759638	+	0.650347i	$0.774624\pi$
$464$	−0.629623	−	3.08410i	−0.0292295	−	0.143176i
$465$	29.4106	+	2.37427i	1.36388	+	0.110104i
$466$	19.2801	−	5.58455i	0.893133	−	0.258699i
$467$	7.41643	−	3.89244i	0.343192	−	0.180121i	−0.284317	−	0.958730i	$-0.591767\pi$
$467$	7.41643	−	3.89244i	0.343192	−	0.180121i	0.627509	+	0.778609i	$0.284075\pi$
$468$	11.4199	+	14.9435i	0.527885	+	0.690762i
$469$	12.4573	+	6.53810i	0.575225	+	0.301902i
$470$	−87.2804	−	17.8184i	−4.02594	−	0.821902i
$471$	17.6028	−	13.2277i	0.811095	−	0.609499i
$472$	1.03290	−	25.6311i	0.0475430	−	1.17977i
$473$	40.4313	+	15.3336i	1.85903	+	0.705039i
$474$	13.3040	+	3.85354i	0.611072	+	0.176999i
$475$	−28.2348	+	5.76418i	−1.29550	+	0.264479i
$476$	3.30163	−	3.72677i	0.151330	−	0.170816i
$477$	−2.27384	−	2.78495i	−0.104112	−	0.127514i
$478$	0.398286	+	9.88336i	0.0182172	+	0.452054i
$479$	5.50913	−	16.5018i	0.251718	−	0.753989i	−0.744541	−	0.667577i	$-0.767332\pi$
$479$	5.50913	−	16.5018i	0.251718	−	0.753989i	0.996259	−	0.0864120i	$-0.0275401\pi$
$480$	28.9673	+	25.6627i	1.32217	+	1.17134i
$481$	−6.13635	+	31.3519i	−0.279793	+	1.42952i
$482$	−32.4107	+	28.7134i	−1.47627	+	1.30786i
$483$	3.59641	+	8.44108i	0.163642	+	0.384083i
$484$	−43.9625	−	76.1453i	−1.99830	−	3.46115i
$485$	23.7624	−	41.1576i	1.07899	−	1.86887i
$486$	−27.9979	−	3.39955i	−1.27001	−	0.154207i
$487$	−17.2844	+	8.20153i	−0.783229	+	0.371647i	−0.777939	−	0.628339i	$-0.783735\pi$
$487$	−17.2844	+	8.20153i	−0.783229	+	0.371647i	−0.00528942	+	0.999986i	$0.501684\pi$
$488$	−29.5706	−	17.0726i	−1.33860	−	0.772841i
$489$	−0.377945	+	0.260877i	−0.0170913	+	0.0117973i
$490$	−37.0167	−	15.7713i	−1.67224	−	0.712477i
$491$	−8.90765	+	1.44763i	−0.401997	+	0.0653308i	−0.358048	−	0.933703i	$-0.616558\pi$
$491$	−8.90765	+	1.44763i	−0.401997	+	0.0653308i	−0.0439481	+	0.999034i	$0.513994\pi$
$492$	25.5731	+	34.0316i	1.15292	+	1.53426i
$493$	0.0878459	−	0.231631i	0.00395638	−	0.0104321i
$494$	16.0573	−	31.2065i	0.722452	−	1.40405i
$495$	−7.71255	−	20.3363i	−0.346654	−	0.914050i
$496$	27.1557	−	42.9432i	1.21933	−	1.92821i
$497$	2.06051	−	0.877902i	0.0924266	−	0.0393793i
$498$	−16.1601	+	10.2190i	−0.724152	+	0.457926i
$499$	11.5227	−	1.39911i	0.515826	−	0.0626326i	0.141516	−	0.989936i	$-0.454802\pi$
$499$	11.5227	−	1.39911i	0.515826	−	0.0626326i	0.374311	+	0.927303i	$0.377879\pi$
$500$	−17.1463	+	40.2439i	−0.766807	+	1.79976i
$501$	2.72949	+	8.17581i	0.121944	+	0.365268i
$502$	−26.5047	+	10.0519i	−1.18296	+	0.448639i
$503$	24.5403	−	1.98109i	1.09420	−	0.0883326i	0.479836	−	0.877358i	$-0.340696\pi$
$503$	24.5403	−	1.98109i	1.09420	−	0.0883326i	0.614360	+	0.789026i	$0.289414\pi$
$504$	−3.45689	−	11.9346i	−0.153982	−	0.531608i
$505$	−8.00022	+	0.322398i	−0.356005	+	0.0143465i
$506$	58.3580			2.59433
$507$	5.23681	+	17.0412i	0.232575	+	0.756827i
$508$	2.78169			0.123418
$509$	−31.7793	+	1.28066i	−1.40859	+	0.0567643i	−0.732858	−	0.680382i	$-0.761814\pi$
$509$	−31.7793	+	1.28066i	−1.40859	+	0.0567643i	−0.675733	+	0.737146i	$0.736173\pi$
$510$	2.31309	+	7.98571i	0.102425	+	0.353613i
$511$	−2.05418	+	0.165830i	−0.0908715	+	0.00733590i
$512$	−45.4679	+	17.2437i	−2.00942	+	0.762071i
$513$	6.74725	+	20.2105i	0.297899	+	0.892315i
$514$	−3.46220	+	8.12609i	−0.152711	+	0.358426i
$515$	−48.6195	+	5.90347i	−2.14243	+	0.260138i
$516$	−42.7356	+	27.0244i	−1.88133	+	1.18968i
$517$	−48.8144	+	20.7979i	−2.14685	+	0.914689i
$518$	19.7615	−	31.2504i	0.868272	−	1.37306i
$519$	−9.81282	−	25.8743i	−0.430735	−	1.13575i
$520$	−41.5246	−	77.5843i	−1.82098	−	3.40230i
$521$	−5.20813	+	13.7327i	−0.228172	+	0.601641i	−0.999390	−	0.0349309i	$-0.988879\pi$
$521$	−5.20813	+	13.7327i	−0.228172	+	0.601641i	0.771217	+	0.636572i	$0.219648\pi$
$522$	−0.650632	−	0.865833i	−0.0284774	−	0.0378965i
$523$	−6.87206	+	1.11682i	−0.300494	+	0.0488350i	−0.308789	−	0.951131i	$-0.599924\pi$
$523$	−6.87206	+	1.11682i	−0.300494	+	0.0488350i	0.00829494	+	0.999966i	$0.497360\pi$
$524$	76.0265	+	32.3919i	3.32123	+	1.41505i
$525$	−13.9432	+	9.62430i	−0.608531	+	0.420039i
$526$	−49.0887	−	28.3414i	−2.14037	−	1.23574i
$527$	3.61266	−	1.71423i	0.157370	−	0.0746729i
$528$	62.4646	+	7.58458i	2.71842	+	0.330076i
$529$	2.93968	−	5.09167i	0.127812	−	0.221377i
$530$	14.7350	+	25.5219i	0.640050	+	1.10860i
$531$	−1.63953	−	3.84811i	−0.0711494	−	0.166994i
$532$	−21.2732	+	18.8464i	−0.922312	+	0.817097i
$533$	−6.86877	−	23.0143i	−0.297519	−	0.996859i
$534$	−9.11954	−	8.07921i	−0.394641	−	0.349622i
$535$	−2.75876	+	8.26350i	−0.119272	+	0.357262i
$536$	2.40497	+	59.6786i	0.103879	+	2.57772i
$537$	5.82985	+	7.14027i	0.251576	+	0.308125i
$538$	17.7956	−	20.0871i	0.767224	−	0.866017i
$539$	−23.4822	+	4.79393i	−1.01145	+	0.206489i
$540$	89.8989	+	26.0395i	3.86863	+	1.12056i
$541$	14.3700	+	5.44983i	0.617815	+	0.234306i	0.643601	−	0.765361i	$-0.277440\pi$
$541$	14.3700	+	5.44983i	0.617815	+	0.234306i	−0.0257859	+	0.999667i	$0.508209\pi$
$542$	1.26476	−	31.3847i	0.0543261	−	1.34809i
$543$	2.02311	−	1.52027i	0.0868198	−	0.0652408i
$544$	5.13867	+	1.04907i	0.220318	+	0.0449783i
$545$	21.9019	+	11.4950i	0.938173	+	0.492391i
$546$	1.49360	−	20.5792i	0.0639201	−	0.880708i
$547$	−6.13271	+	3.21870i	−0.262216	+	0.137621i	−0.590709	−	0.806885i	$-0.701152\pi$
$547$	−6.13271	+	3.21870i	−0.262216	+	0.137621i	0.328493	+	0.944507i	$0.393459\pi$
$548$	−3.25790	+	0.943661i	−0.139170	+	0.0403112i
$549$	−5.54970	−	0.448018i	−0.236855	−	0.0191209i
$550$	21.5545	+	105.581i	0.919086	+	4.50198i
$551$	−0.657162	+	1.25212i	−0.0279960	+	0.0533420i
$552$	−23.4003	+	31.1402i	−0.995984	+	1.32541i
$553$	3.38231	+	5.34870i	0.143831	+	0.227450i
$554$	50.9525	+	35.1700i	2.16476	+	1.49423i
$555$	18.5196	+	39.0293i	0.786115	+	1.65670i
$556$	−73.7688	−	76.8014i	−3.12849	−	3.25711i
$557$	17.8106	−	17.1073i	0.754659	−	0.724860i	−0.213019	−	0.977048i	$-0.568330\pi$
$557$	17.8106	−	17.1073i	0.754659	−	0.724860i	0.967678	+	0.252188i	$0.0811501\pi$
$558$	2.10723	−	17.3546i	0.0892061	−	0.734679i
$559$	27.9041	−	5.93257i	1.18022	−	0.250921i
$560$	5.81786	+	47.9144i	0.245849	+	2.02475i
$561$	3.83596	+	3.13197i	0.161954	+	0.132232i
$562$	2.04955	−	10.0394i	0.0864553	−	0.423486i
$563$	−2.63546	+	9.09868i	−0.111072	+	0.383463i	−0.996723	−	0.0808865i	$-0.974225\pi$
$563$	−2.63546	+	9.09868i	−0.111072	+	0.383463i	0.885652	+	0.464350i	$0.153712\pi$
$564$	14.8483	−	60.2420i	0.625227	−	2.53665i
$565$	−5.60991	−	69.4912i	−0.236011	−	2.92352i
$566$	0.101981	−	0.627517i	0.00428660	−	0.0263765i
$567$	4.70609	+	5.31208i	0.197637	+	0.223086i
$568$	7.60148	+	5.71214i	0.318951	+	0.239676i
$569$	25.5911	−	31.3434i	1.07283	−	1.31398i	0.126081	−	0.992020i	$-0.459760\pi$
$569$	25.5911	−	31.3434i	1.07283	−	1.31398i	0.946753	−	0.321962i	$-0.104342\pi$
$570$	−7.61279	−	46.8434i	−0.318865	−	1.96205i
$571$	28.5365	−	7.03363i	1.19422	−	0.294348i	0.408398	−	0.912804i	$-0.366088\pi$
$571$	28.5365	−	7.03363i	1.19422	−	0.294348i	0.785819	+	0.618456i	$0.212242\pi$
$572$	−81.6502	−	42.0131i	−3.41397	−	1.75666i
$573$	−20.0589	−	4.94408i	−0.837974	−	0.206542i
$574$	−2.23674	+	27.7070i	−0.0933598	+	1.15647i
$575$	−29.9865	−	10.0110i	−1.25052	−	0.417486i
$576$	2.86331	−	2.98102i	0.119305	−	0.124209i
$577$			33.4826i			1.39390i	0.717121	+	0.696949i	$0.245460\pi$
$577$			33.4826i			1.39390i	−0.717121	+	0.696949i	$0.754540\pi$
$578$	−30.8279	−	29.6106i	−1.28227	−	1.23164i
$579$	−1.24322	+	1.01506i	−0.0516666	+	0.0421845i
$580$	2.88668	+	5.50010i	0.119863	+	0.228379i
$581$	−8.62278	−	1.40134i	−0.357733	−	0.0581373i
$582$	39.9839	+	25.2843i	1.65739	+	1.04807i
$583$	15.8589	+	7.52513i	0.656807	+	0.311659i
$584$	−4.97004	−	7.20035i	−0.205662	−	0.297953i
$585$	−11.5407	−	8.52684i	−0.477149	−	0.352541i
$586$	30.4392	−	44.0988i	1.25743	−	1.82171i
$587$	0.00406777	−	0.00234853i	0.000167895	−	9.69340e-5i	−0.499916	−	0.866074i	$-0.666636\pi$
$587$	0.00406777	−	0.00234853i	0.000167895	−	9.69340e-5i	0.500084	+	0.865977i	$0.333302\pi$
$588$	12.0140	−	25.3190i	0.495450	−	1.04414i
$589$	−21.6510	+	7.22816i	−0.892114	+	0.297831i
$590$	8.20513	+	33.2895i	0.337800	+	1.37051i
$591$	−2.84635	−	0.114704i	−0.117083	−	0.00471829i
$592$	74.3293	+	2.99537i	3.05492	+	0.123109i
$593$	−6.99047	−	28.3614i	−0.287064	−	1.16466i	−0.920460	−	0.390837i	$-0.872186\pi$
$593$	−6.99047	−	28.3614i	−0.287064	−	1.16466i	0.633396	−	0.773828i	$-0.281660\pi$
$594$	75.5748	−	25.2306i	3.10087	−	1.03522i
$595$	−1.62844	+	3.43186i	−0.0667595	+	0.140693i
$596$	−76.9528	+	44.4287i	−3.15211	+	1.81987i
$597$	−1.54828	+	2.24307i	−0.0633670	+	0.0918029i
$598$	32.3727	−	20.8403i	1.32382	−	0.852224i
$599$	−14.6978	−	21.2935i	−0.600538	−	0.870029i	0.398348	−	0.917235i	$-0.369584\pi$
$599$	−14.6978	−	21.2935i	−0.600538	−	0.870029i	−0.998885	+	0.0472056i	$0.984968\pi$
$600$	−64.9815	−	30.8341i	−2.65286	−	1.25880i
$601$	6.71705	+	4.24761i	0.273994	+	0.173264i	0.664395	−	0.747381i	$-0.268689\pi$
$601$	6.71705	+	4.24761i	0.273994	+	0.173264i	−0.390401	+	0.920645i	$0.627664\pi$
$602$	−32.5897	−	5.29634i	−1.32826	−	0.215863i
$603$	4.52601	+	8.62359i	0.184313	+	0.351180i
$604$	40.7392	−	33.2625i	1.65766	−	1.35343i
$605$	48.3795	+	46.4691i	1.96691	+	1.88924i
$606$		−	7.97013i		−	0.323764i
$607$	9.20130	−	9.57957i	0.373469	−	0.388823i	−0.507770	−	0.861492i	$-0.669530\pi$
$607$	9.20130	−	9.57957i	0.373469	−	0.388823i	0.881240	+	0.472670i	$0.156710\pi$
$608$	−28.3970	−	9.48031i	−1.15165	−	0.384477i
$609$	−0.0668980	+	0.828680i	−0.00271084	+	0.0335798i
$610$	44.3117	+	10.9218i	1.79413	+	0.442213i
$611$	−19.6514	+	28.9693i	−0.795011	+	1.17197i
$612$	3.34650	−	0.824839i	0.135274	−	0.0333421i
$613$	−5.57502	−	34.3045i	−0.225173	−	1.38554i	−0.815676	−	0.578509i	$-0.803635\pi$
$613$	−5.57502	−	34.3045i	−0.225173	−	1.38554i	0.590503	−	0.807036i	$-0.298929\pi$
$614$	−6.01443	+	7.36633i	−0.242722	+	0.297281i
$615$	−25.9641	−	19.5108i	−1.04697	−	0.786750i
$616$	40.2278	+	45.4078i	1.62082	+	1.82953i
$617$	−7.72887	+	47.5576i	−0.311153	+	1.91460i	0.0849367	+	0.996386i	$0.472931\pi$
$617$	−7.72887	+	47.5576i	−0.311153	+	1.91460i	−0.396089	+	0.918212i	$0.629633\pi$
$618$	−3.92297	−	48.5947i	−0.157805	−	1.95476i
$619$	−4.29688	+	17.4331i	−0.172706	+	0.700697i	0.819177	+	0.573541i	$0.194431\pi$
$619$	−4.29688	+	17.4331i	−0.172706	+	0.700697i	−0.991883	+	0.127155i	$0.959415\pi$
$620$	−27.8955	+	96.3064i	−1.12031	+	3.86776i
$621$	−4.67550	+	22.9021i	−0.187621	+	0.919031i
$622$	6.31790	+	5.15840i	0.253325	+	0.206833i
$623$	−0.670984	−	5.52605i	−0.0268824	−	0.221397i
$624$	37.3592	−	18.0995i	1.49557	−	0.724559i
$625$	−0.581850	+	4.79196i	−0.0232740	+	0.191679i
$626$	39.4830	−	37.9239i	1.57806	−	1.51574i
$627$	−19.5820	−	20.3870i	−0.782028	−	0.814177i
$628$	32.0757	+	67.5981i	1.27996	+	2.69746i
$629$	4.81821	+	3.32577i	0.192115	+	0.132607i
$630$	8.87597	+	14.0362i	0.353627	+	0.559217i
$631$	−16.2303	+	21.5986i	−0.646118	+	0.859827i	−0.997064	−	0.0765688i	$-0.975604\pi$
$631$	−16.2303	+	21.5986i	−0.646118	+	0.859827i	0.350946	+	0.936396i	$0.385860\pi$
$632$	−12.4854	+	23.7889i	−0.496642	+	0.946272i
$633$	−1.25655	−	6.15501i	−0.0499435	−	0.244639i
$634$	5.26033	+	0.424658i	0.208914	+	0.0168653i
$635$	−2.03848	+	0.590453i	−0.0808946	+	0.0234314i
$636$	−18.1749	+	9.53891i	−0.720681	+	0.378242i
$637$	−11.3142	+	11.0451i	−0.448285	+	0.437622i
$638$	4.68215	+	2.45738i	0.185368	+	0.0972886i
$639$	1.51913	+	0.310132i	0.0600958	+	0.0122686i
$640$	18.0348	−	13.5523i	0.712890	−	0.535702i
$641$	1.11405	−	27.6448i	0.0440021	−	1.09190i	−0.814848	−	0.579675i	$-0.803180\pi$
$641$	1.11405	−	27.6448i	0.0440021	−	1.09190i	0.858850	−	0.512227i	$-0.171179\pi$
$642$	−8.10850	−	3.07515i	−0.320017	−	0.121366i
$643$	−38.2119	−	11.0682i	−1.50693	−	0.436488i	−0.580912	−	0.813966i	$-0.697304\pi$
$643$	−38.2119	−	11.0682i	−1.50693	−	0.436488i	−0.926018	+	0.377479i	$0.876791\pi$
$644$	−30.5484	+	6.23650i	−1.20378	+	0.245752i
$645$	25.5812	−	28.8752i	1.00726	−	1.13696i
$646$	−4.06762	−	4.98193i	−0.160038	−	0.196011i
$647$	0.935352	+	23.2105i	0.0367725	+	0.912500i	0.907326	+	0.420427i	$0.138120\pi$
$647$	0.935352	+	23.2105i	0.0367725	+	0.912500i	−0.870554	+	0.492073i	$0.836239\pi$
$648$	−9.54078	+	28.5781i	−0.374797	+	1.12266i
$649$	15.2862	+	13.5424i	0.600035	+	0.531584i
$650$	49.6610	+	50.8710i	1.94786	+	1.99532i
$651$	−10.0448	+	8.89892i	−0.393687	+	0.348776i
$652$	−0.611676	−	1.43566i	−0.0239551	−	0.0562247i
$653$	8.52200	+	14.7605i	0.333492	+	0.577624i	0.983194	−	0.182564i	$-0.0584398\pi$
$653$	8.52200	+	14.7605i	0.333492	+	0.577624i	−0.649702	+	0.760189i	$0.725106\pi$
$654$	−12.3110	+	21.3234i	−0.481400	+	0.833809i
$655$	−62.5894	−	7.59973i	−2.44557	−	0.296946i
$656$	−50.5262	+	23.9750i	−1.97272	+	0.936065i
$657$	−1.23550	−	0.713317i	−0.0482015	−	0.0278291i
$658$	33.3429	−	23.0149i	1.29984	−	0.897216i
$659$	−19.5057	−	8.31060i	−0.759834	−	0.323735i	−0.0229343	−	0.999737i	$-0.507301\pi$
$659$	−19.5057	−	8.31060i	−0.759834	−	0.323735i	−0.736900	+	0.676002i	$0.763711\pi$
$660$	−122.563	+	19.9185i	−4.77077	+	0.775326i
$661$	−7.91508	−	10.5331i	−0.307861	−	0.409689i	0.618823	−	0.785531i	$-0.287610\pi$
$661$	−7.91508	−	10.5331i	−0.307861	−	0.409689i	−0.926684	+	0.375842i	$0.877354\pi$
$662$	29.6315	−	78.1318i	1.15166	−	3.03668i
$663$	3.24637	+	0.367514i	0.126078	+	0.0142731i
$664$	−13.1512	−	34.6770i	−0.510367	−	1.34573i
$665$	11.5890	−	18.3266i	0.449403	−	0.710674i
$666$	23.5474	−	10.0326i	0.912443	−	0.388756i
$667$	−1.31115	+	0.829120i	−0.0507679	+	0.0321037i
$668$	−29.0759	+	3.53046i	−1.12498	+	0.136597i
$669$	1.73106	−	4.06295i	0.0669266	−	0.157083i
$670$	−25.2796	−	75.7217i	−0.976636	−	2.92538i
$671$	25.4174	−	9.63953i	0.981226	−	0.372130i
$672$	−17.5440	+	1.41629i	−0.676773	+	0.0546348i
$673$	12.4232	+	42.8899i	0.478879	+	1.65328i	0.728581	+	0.684960i	$0.240180\pi$
$673$	12.4232	+	42.8899i	0.478879	+	1.65328i	−0.249702	+	0.968323i	$0.580333\pi$
$674$	−80.0329	+	3.22522i	−3.08275	+	0.124231i
$675$	−43.1612			−1.66128
$676$	−60.2968	+	5.85253i	−2.31911	+	0.225097i
$677$	27.6346			1.06208			0.531042	−	0.847346i	$-0.321801\pi$
$677$	27.6346			1.06208			0.531042	+	0.847346i	$0.321801\pi$
$678$	69.3424	−	2.79440i	2.66308	−	0.107318i
$679$	6.01358	+	20.7613i	0.230780	+	0.796745i
$680$	−16.0742	+	1.29764i	−0.616417	+	0.0497623i
$681$	10.0382	−	3.80699i	0.384665	−	0.145884i
$682$	27.0289	+	80.9614i	1.03499	+	3.10017i
$683$	0.498629	−	1.17033i	0.0190795	−	0.0447813i	−0.910167	−	0.414241i	$-0.864047\pi$
$683$	0.498629	−	1.17033i	0.0190795	−	0.0447813i	0.929247	+	0.369460i	$0.120457\pi$
$684$	−19.5309	+	2.37148i	−0.746781	+	0.0906756i
$685$	2.18715	−	1.38307i	0.0835666	−	0.0528443i
$686$	43.7089	−	18.6226i	1.66881	−	0.711014i
$687$	18.9811	−	30.0163i	0.724176	−	1.14519i
$688$	−23.5558	−	62.1115i	−0.898056	−	2.36798i
$689$	11.4846	−	1.48901i	0.437529	−	0.0567267i
$690$	18.4618	−	48.6797i	0.702828	−	1.85320i
$691$	−2.53276	−	3.37050i	−0.0963509	−	0.128220i	0.748693	−	0.662917i	$-0.230682\pi$
$691$	−2.53276	−	3.37050i	−0.0963509	−	0.128220i	−0.845043	+	0.534698i	$0.820426\pi$
$692$	92.8161	−	15.0841i	3.52834	−	0.573411i
$693$	9.10040	+	3.87732i	0.345696	+	0.147287i
$694$	−23.3223	+	16.0982i	−0.885301	+	0.611079i
$695$	70.3614	+	40.6232i	2.66896	+	1.54092i
$696$	−3.18872	+	1.51306i	−0.120868	+	0.0573525i
$697$	−4.36934	−	0.530534i	−0.165501	−	0.0200954i
$698$	−11.8354	+	20.4994i	−0.447975	+	0.775915i
$699$	−5.33321	−	9.23738i	−0.201720	−	0.349390i
$700$	−22.5660	−	52.9644i	−0.852916	−	2.00187i
$701$	6.70840	−	5.94313i	0.253373	−	0.224469i	−0.526869	−	0.849946i	$-0.676634\pi$
$701$	6.70840	−	5.94313i	0.253373	−	0.224469i	0.780242	+	0.625477i	$0.215096\pi$
$702$	32.9131	−	40.9847i	1.24223	−	1.54687i
$703$	−25.0146	−	22.1610i	−0.943444	−	0.835818i
$704$	−6.39063	+	19.1423i	−0.240856	+	0.721451i
$705$	1.90606	+	47.2983i	0.0717862	+	1.78136i
$706$	−24.7720	−	30.3401i	−0.932305	−	1.14187i
$707$	2.41478	−	2.72572i	0.0908171	−	0.102511i
$708$	−23.3976	+	4.77665i	−0.879334	+	0.179517i
$709$	13.4418	+	3.89345i	0.504816	+	0.146222i	0.520847	−	0.853650i	$-0.325616\pi$
$709$	13.4418	+	3.89345i	0.504816	+	0.146222i	−0.0160316	+	0.999871i	$0.505103\pi$
$710$	−11.8830	−	4.50661i	−0.445960	−	0.169130i
$711$	−0.176399	+	4.37729i	−0.00661547	+	0.164161i
$712$	18.8927	−	14.1969i	0.708034	−	0.532053i
$713$	−24.5345	−	5.00875i	−0.918823	−	0.187579i
$714$	−3.34814	−	1.75724i	−0.125301	−	0.0657630i
$715$	68.7528	+	13.4566i	2.57121	+	0.503250i
$716$	−27.7355	+	14.5567i	−1.03652	+	0.544010i
$717$	5.04867	−	1.46237i	0.188546	−	0.0546131i
$718$	−28.9105	−	2.33390i	−1.07893	−	0.0871003i
$719$	5.38127	+	26.3592i	0.200687	+	0.983032i	0.947930	+	0.318480i	$0.103172\pi$
$719$	5.38127	+	26.3592i	0.200687	+	0.983032i	−0.747242	+	0.664552i	$0.768622\pi$
$720$	−15.5275	+	29.5852i	−0.578677	+	1.10258i
$721$	13.3815	−	17.8076i	0.498354	−	0.663189i
$722$	−6.58485	−	10.4131i	−0.245063	−	0.387536i
$723$	18.9364	+	13.0708i	0.704251	+	0.486109i
$724$	3.68648	+	7.76910i	0.137007	+	0.288736i
$725$	−1.98431	−	2.06588i	−0.0736954	−	0.0767250i
$726$	−48.1584	+	46.2568i	−1.78733	+	1.71675i
$727$	1.14208	−	9.40585i	0.0423573	−	0.348843i	−0.956087	−	0.293083i	$-0.905319\pi$
$727$	1.14208	−	9.40585i	0.0423573	−	0.348843i	0.998444	−	0.0557602i	$-0.0177582\pi$
$728$	38.5310	+	10.8230i	1.42805	+	0.401128i
$729$	3.39357	+	27.9486i	0.125688	+	1.03513i
$730$	9.05811	+	7.39572i	0.335256	+	0.273728i
$731$	1.04573	−	5.12234i	0.0386778	−	0.189457i
$732$	−8.84366	+	30.5319i	−0.326871	+	1.12849i
$733$	11.5030	−	46.6694i	0.424872	−	1.72377i	−0.234644	−	0.972081i	$-0.575392\pi$
$733$	11.5030	−	46.6694i	0.424872	−	1.72377i	0.659515	−	0.751691i	$-0.270762\pi$
$734$	−2.00953	−	24.8925i	−0.0741733	−	0.918801i
$735$	−3.42980	+	21.1044i	−0.126510	+	0.778448i
$736$	−21.7787	−	24.5831i	−0.802774	−	0.906144i
$737$	−38.0137	−	28.5654i	−1.40025	−	1.05222i
$738$	−12.1699	+	14.9054i	−0.447981	+	0.548677i
$739$	6.89519	+	42.4278i	0.253644	+	1.56073i	0.731220	+	0.682141i	$0.238951\pi$
$739$	6.89519	+	42.4278i	0.253644	+	1.56073i	−0.477577	+	0.878590i	$0.658485\pi$
$740$	−142.533	+	35.1312i	−5.23961	+	1.29145i
$741$	−18.1430	−	4.31622i	−0.666501	−	0.158560i
$742$	−13.0138	−	3.20761i	−0.477751	−	0.117755i
$743$	0.652198	−	8.07892i	0.0239268	−	0.296387i	−0.973716	−	0.227766i	$-0.926858\pi$
$743$	0.652198	−	8.07892i	0.0239268	−	0.296387i	0.997643	−	0.0686211i	$-0.0218600\pi$
$744$	−54.0395	−	18.0410i	−1.98118	−	0.661416i
$745$	46.9620	−	48.8926i	1.72055	−	1.79129i
$746$			97.1628i			3.55738i
$747$	−4.36143	−	4.18921i	−0.159576	−	0.153275i
$748$	−13.0350	+	10.6427i	−0.476605	+	0.389136i
$749$	−1.84134	−	3.50838i	−0.0672810	−	0.128193i
$750$	32.7917	+	5.32917i	1.19738	+	0.194594i
$751$	35.9846	+	22.7553i	1.31310	+	0.830351i	0.993123	−	0.117076i	$-0.0373520\pi$
$751$	35.9846	+	22.7553i	1.31310	+	0.830351i	0.319972	+	0.947427i	$0.396326\pi$
$752$	73.6424	+	34.9438i	2.68546	+	1.27427i
$753$	8.55690	+	12.3968i	0.311831	+	0.451765i
$754$	3.47486	−	0.308878i	0.126547	−	0.0112487i
$755$	−22.7941	+	33.0229i	−0.829561	+	1.20183i
$756$	−36.8645	+	21.2837i	−1.34075	+	0.774082i
$757$	−3.14650	+	6.63111i	−0.114361	+	0.241012i	−0.952558	−	0.304356i	$-0.901559\pi$
$757$	−3.14650	+	6.63111i	−0.114361	+	0.241012i	0.838197	+	0.545368i	$0.183610\pi$
$758$	50.5244	−	16.8675i	1.83513	−	0.612656i
$759$	−7.42141	−	30.1098i	−0.269380	−	1.09292i
$760$	91.9790	+	3.70663i	3.33643	+	0.134453i
$761$	−40.9851	−	1.65164i	−1.48571	−	0.0598721i	−0.715926	−	0.698176i	$-0.753995\pi$
$761$	−40.9851	−	1.65164i	−1.48571	−	0.0598721i	−0.769784	+	0.638304i	$0.779636\pi$
$762$	−0.505572	−	2.05118i	−0.0183149	−	0.0743066i
$763$	−10.6708	+	3.56244i	−0.386309	+	0.128969i
$764$	30.0951	−	63.4240i	1.08880	−	2.29460i
$765$	−2.27730	+	1.31480i	−0.0823360	+	0.0475367i
$766$	−20.4452	+	29.6199i	−0.738714	+	1.07021i

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.k (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(2.57861 - 0.103914i) q^{2} +(-0.381537 - 1.31722i) q^{3} +(4.64490 - 0.374975i) q^{4} +(-3.32428 + 1.26073i) q^{5} +(-1.12071 - 3.35694i) q^{6} +(0.633807 - 1.48760i) q^{7} +(6.81465 - 0.827448i) q^{8} +(0.946076 - 0.598262i) q^{9} +O(q^{10})\)	\(q+(2.57861 - 0.103914i) q^{2} +(-0.381537 - 1.31722i) q^{3} +(4.64490 - 0.374975i) q^{4} +(-3.32428 + 1.26073i) q^{5} +(-1.12071 - 3.35694i) q^{6} +(0.633807 - 1.48760i) q^{7} +(6.81465 - 0.827448i) q^{8} +(0.946076 - 0.598262i) q^{9} +(-8.44101 + 3.59638i) q^{10} +(-2.92094 + 4.61910i) q^{11} +(-2.26613 - 5.97529i) q^{12} +(0.0292141 + 3.60543i) q^{13} +(1.47976 - 3.90180i) q^{14} +(2.92900 + 3.89779i) q^{15} +(8.28698 - 1.34677i) q^{16} +(0.607879 + 0.258993i) q^{17} +(2.37739 - 1.64099i) q^{18} +(-3.26641 - 1.88586i) q^{19} +(-14.9682 + 7.10251i) q^{20} +(-2.20131 - 0.267288i) q^{21} +(-7.05197 + 12.2144i) q^{22} +(-2.06885 - 3.58336i) q^{23} +(-3.68997 - 8.66068i) q^{24} +(5.71886 - 5.06647i) q^{25} +(0.449988 + 9.29396i) q^{26} +(-4.22844 - 3.74607i) q^{27} +(2.38616 - 7.14742i) q^{28} +(-0.0150965 - 0.374615i) q^{29} +(7.95778 + 9.74651i) q^{30} +(4.01307 - 4.52982i) q^{31} +(7.77699 - 1.58768i) q^{32} +(7.19881 + 2.08516i) q^{33} +(1.59439 + 0.604674i) q^{34} +(-0.231486 + 5.74426i) q^{35} +(4.17010 - 3.13363i) q^{36} +(8.68138 + 1.77232i) q^{37} +(-8.61876 - 4.52348i) q^{38} +(4.73800 - 1.41409i) q^{39} +(-21.6106 + 11.3421i) q^{40} +(-6.39824 + 1.85327i) q^{41} +(-5.70410 - 0.460483i) q^{42} +(-1.58264 - 7.75228i) q^{43} +(-11.8354 + 22.5505i) q^{44} +(-2.39078 + 3.18154i) q^{45} +(-5.70713 - 9.02510i) q^{46} +(7.99021 + 5.51524i) q^{47} +(-4.93577 - 10.4019i) q^{48} +(3.03783 + 3.16272i) q^{49} +(14.2202 - 13.6587i) q^{50} +(0.109222 - 0.899525i) q^{51} +(1.48765 + 16.7359i) q^{52} +(-0.387154 - 3.18850i) q^{53} +(-11.2928 - 9.22026i) q^{54} +(3.88658 - 19.0377i) q^{55} +(3.08826 - 10.6619i) q^{56} +(-1.23784 + 5.02211i) q^{57} +(-0.0778557 - 0.964416i) q^{58} +(0.599422 - 3.68839i) q^{59} +(15.0665 + 17.0066i) q^{60} +(-3.97645 - 2.98811i) q^{61} +(9.87743 - 12.0977i) q^{62} +(-0.290345 - 1.78656i) q^{63} +(3.58533 - 0.883705i) q^{64} +(-4.64261 - 11.9487i) q^{65} +(18.7796 + 4.62875i) q^{66} +(-0.700108 + 8.67239i) q^{67} +(2.92066 + 0.975058i) q^{68} +(-3.93073 + 4.09232i) q^{69} +14.8363i q^{70} +(0.998956 + 0.959510i) q^{71} +(5.95215 - 4.85978i) q^{72} +(-0.592291 - 1.12852i) q^{73} +(22.5700 + 3.66799i) q^{74} +(-8.85560 - 5.59994i) q^{75} +(-15.8793 - 7.53483i) q^{76} +(5.02006 + 7.27281i) q^{77} +(12.0705 - 4.13872i) q^{78} +(-2.22323 + 3.22090i) q^{79} +(-25.8504 + 14.9247i) q^{80} +(-1.88150 + 3.96518i) q^{81} +(-16.3060 + 5.44373i) q^{82} +(-1.29292 - 5.24558i) q^{83} +(-10.3251 - 0.416088i) q^{84} +(-2.34728 - 0.0945923i) q^{85} +(-4.88658 - 19.8256i) q^{86} +(-0.487690 + 0.162815i) q^{87} +(-16.0831 + 33.8945i) q^{88} +(2.98137 - 1.72129i) q^{89} +(-5.83426 + 8.45239i) q^{90} +(5.38196 + 2.24169i) q^{91} +(-10.9533 - 15.8686i) q^{92} +(-7.49791 - 3.55780i) q^{93} +(21.1767 + 13.3913i) q^{94} +(13.2361 + 2.15107i) q^{95} +(-5.05853 - 9.63823i) q^{96} +(-10.3543 + 8.45403i) q^{97} +(8.16202 + 7.83973i) q^{98} +6.11751i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q - 23 q^{2} - 24 q^{3} - 41 q^{4} - 26 q^{5} - 32 q^{6} - 26 q^{7} - 26 q^{8} - 11 q^{9}+O(q^{10}) \) 360 * q - 23 * q^2 - 24 * q^3 - 41 * q^4 - 26 * q^5 - 32 * q^6 - 26 * q^7 - 26 * q^8 - 11 * q^9	\( 360 q - 23 q^{2} - 24 q^{3} - 41 q^{4} - 26 q^{5} - 32 q^{6} - 26 q^{7} - 26 q^{8} - 11 q^{9} - 27 q^{10} - 26 q^{11} - 14 q^{12} - 34 q^{13} - 30 q^{14} - 84 q^{15} - 13 q^{16} - 31 q^{17} + 52 q^{18} - 33 q^{19} - 29 q^{20} - 26 q^{21} - 33 q^{22} + 57 q^{23} + 58 q^{24} + 2 q^{25} - 29 q^{26} - 30 q^{27} - 26 q^{28} - 19 q^{29} + 178 q^{30} - 78 q^{31} - 30 q^{32} - 26 q^{33} - 91 q^{34} - 18 q^{35} - 51 q^{36} - 41 q^{37} + 25 q^{38} + 12 q^{39} - 134 q^{40} - 17 q^{41} + 250 q^{42} - 28 q^{43} + 42 q^{45} + 18 q^{46} + 117 q^{47} - 57 q^{48} - 117 q^{49} - 20 q^{50} - 59 q^{51} + 37 q^{52} - 75 q^{53} + 118 q^{54} + 64 q^{55} - 42 q^{56} - 104 q^{57} - 87 q^{58} + 170 q^{59} + 78 q^{60} - 15 q^{61} + 19 q^{62} + 39 q^{63} + 32 q^{64} - 17 q^{65} + 73 q^{66} + 20 q^{67} - 76 q^{68} - 11 q^{69} + 46 q^{71} - 198 q^{72} - 26 q^{73} + 29 q^{74} - 70 q^{75} + 58 q^{76} + 6 q^{77} + 128 q^{78} - 54 q^{79} - 24 q^{80} - 7 q^{81} + 81 q^{82} + 234 q^{83} - 273 q^{84} - 74 q^{85} + 52 q^{86} - 112 q^{87} + 256 q^{88} - 27 q^{89} + 28 q^{90} - 78 q^{91} - 34 q^{92} + 51 q^{93} + 28 q^{94} - 11 q^{95} + 143 q^{96} + 40 q^{97} - 47 q^{98}+O(q^{100}) \) 360 * q - 23 * q^2 - 24 * q^3 - 41 * q^4 - 26 * q^5 - 32 * q^6 - 26 * q^7 - 26 * q^8 - 11 * q^9 - 27 * q^10 - 26 * q^11 - 14 * q^12 - 34 * q^13 - 30 * q^14 - 84 * q^15 - 13 * q^16 - 31 * q^17 + 52 * q^18 - 33 * q^19 - 29 * q^20 - 26 * q^21 - 33 * q^22 + 57 * q^23 + 58 * q^24 + 2 * q^25 - 29 * q^26 - 30 * q^27 - 26 * q^28 - 19 * q^29 + 178 * q^30 - 78 * q^31 - 30 * q^32 - 26 * q^33 - 91 * q^34 - 18 * q^35 - 51 * q^36 - 41 * q^37 + 25 * q^38 + 12 * q^39 - 134 * q^40 - 17 * q^41 + 250 * q^42 - 28 * q^43 + 42 * q^45 + 18 * q^46 + 117 * q^47 - 57 * q^48 - 117 * q^49 - 20 * q^50 - 59 * q^51 + 37 * q^52 - 75 * q^53 + 118 * q^54 + 64 * q^55 - 42 * q^56 - 104 * q^57 - 87 * q^58 + 170 * q^59 + 78 * q^60 - 15 * q^61 + 19 * q^62 + 39 * q^63 + 32 * q^64 - 17 * q^65 + 73 * q^66 + 20 * q^67 - 76 * q^68 - 11 * q^69 + 46 * q^71 - 198 * q^72 - 26 * q^73 + 29 * q^74 - 70 * q^75 + 58 * q^76 + 6 * q^77 + 128 * q^78 - 54 * q^79 - 24 * q^80 - 7 * q^81 + 81 * q^82 + 234 * q^83 - 273 * q^84 - 74 * q^85 + 52 * q^86 - 112 * q^87 + 256 * q^88 - 27 * q^89 + 28 * q^90 - 78 * q^91 - 34 * q^92 + 51 * q^93 + 28 * q^94 - 11 * q^95 + 143 * q^96 + 40 * q^97 - 47 * q^98

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