LMFDB - Embedded newform 169.2.h.a.12.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(12,169)]

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([21]))

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

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

chi := DirichletCharacter("169.12");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.h (of order $26$, 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:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			12.3
Character	$\chi$	$=$	169.12
Dual form			169.2.h.a.155.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.71806 + 1.18589i) q^{2} +(2.94692 + 1.54666i) q^{3} +(0.836178 - 2.20482i) q^{4} +(-0.781452 - 0.882078i) q^{5} +(-6.89716 + 0.837466i) q^{6} +(0.664295 + 2.69515i) q^{7} +(0.178883 + 0.725755i) q^{8} +(4.58799 + 6.64685i) q^{9} +O(q^{10})$	\(q+(-1.71806 + 1.18589i) q^{2} +(2.94692 + 1.54666i) q^{3} +(0.836178 - 2.20482i) q^{4} +(-0.781452 - 0.882078i) q^{5} +(-6.89716 + 0.837466i) q^{6} +(0.664295 + 2.69515i) q^{7} +(0.178883 + 0.725755i) q^{8} +(4.58799 + 6.64685i) q^{9} +(2.38863 + 0.588744i) q^{10} +(-0.562223 - 0.388074i) q^{11} +(5.87427 - 5.20415i) q^{12} +(-1.84768 - 3.09614i) q^{13} +(-4.33745 - 3.84265i) q^{14} +(-0.938602 - 3.80806i) q^{15} +(2.36206 + 2.09261i) q^{16} +(1.85483 - 0.457175i) q^{17} +(-15.7649 - 5.97882i) q^{18} +1.63338i q^{19} +(-2.59826 + 0.985388i) q^{20} +(-2.21087 + 8.96985i) q^{21} +1.42614 q^{22} -6.28383 q^{23} +(-0.595347 + 2.41542i) q^{24} +(0.435291 - 3.58494i) q^{25} +(6.84610 + 3.12820i) q^{26} +(2.03651 + 16.7722i) q^{27} +(6.49780 + 0.788975i) q^{28} +(-4.39880 - 6.37276i) q^{29} +(6.12851 + 5.42939i) q^{30} +(6.06341 - 0.736231i) q^{31} +(-8.02381 - 0.974267i) q^{32} +(-1.05661 - 2.01320i) q^{33} +(-2.64455 + 2.98508i) q^{34} +(1.85822 - 2.69209i) q^{35} +(18.4915 - 4.55774i) q^{36} +(4.15024 - 0.503930i) q^{37} +(-1.93700 - 2.80623i) q^{38} +(-0.656278 - 11.9818i) q^{39} +(0.500384 - 0.724932i) q^{40} +(4.47504 - 8.52648i) q^{41} +(-6.83885 - 18.0326i) q^{42} +(-0.509861 + 4.19909i) q^{43} +(-1.32575 + 0.915101i) q^{44} +(2.27774 - 9.24116i) q^{45} +(10.7960 - 7.45192i) q^{46} +(-3.61133 + 1.36960i) q^{47} +(3.72426 + 9.82007i) q^{48} +(-0.624365 + 0.327692i) q^{49} +(3.50349 + 6.67534i) q^{50} +(6.17315 + 1.52154i) q^{51} +(-8.37142 + 1.48488i) q^{52} +(9.74242 - 2.40129i) q^{53} +(-23.3888 - 26.4005i) q^{54} +(0.0970387 + 0.799186i) q^{55} +(-1.83719 + 0.964232i) q^{56} +(-2.52628 + 4.81343i) q^{57} +(15.1148 + 5.73228i) q^{58} +(5.57925 + 6.29767i) q^{59} +(-9.18092 - 1.11477i) q^{60} +(1.36238 + 0.335797i) q^{61} +(-9.54420 + 8.45542i) q^{62} +(-14.8665 + 16.7808i) q^{63} +(9.35230 - 4.90847i) q^{64} +(-1.28716 + 4.04928i) q^{65} +(4.20274 + 2.20577i) q^{66} +(-1.61021 + 0.610672i) q^{67} +(0.542981 - 4.47185i) q^{68} +(-18.5180 - 9.71897i) q^{69} +6.82881i q^{70} +(-2.23850 + 4.26510i) q^{71} +(-4.00327 + 4.51876i) q^{72} +(-9.42952 - 6.50872i) q^{73} +(-6.53274 + 5.78751i) q^{74} +(6.82747 - 9.89130i) q^{75} +(3.60130 + 1.36579i) q^{76} +(0.672438 - 1.77307i) q^{77} +(15.3366 + 19.8072i) q^{78} +(-3.64067 - 9.59966i) q^{79} -3.71880i q^{80} +(-11.3476 + 29.9211i) q^{81} +(2.42308 + 19.9559i) q^{82} +(3.03191 + 5.77682i) q^{83} +(17.9282 + 12.3750i) q^{84} +(-1.85273 - 1.27885i) q^{85} +(-4.10368 - 7.81891i) q^{86} +(-3.10640 - 25.5835i) q^{87} +(0.181075 - 0.477456i) q^{88} -9.41856i q^{89} +(7.04570 + 18.5780i) q^{90} +(7.11716 - 7.03653i) q^{91} +(-5.25440 + 13.8547i) q^{92} +(19.0071 + 7.20844i) q^{93} +(4.58028 - 6.63568i) q^{94} +(1.44076 - 1.27641i) q^{95} +(-22.1387 - 15.2812i) q^{96} +(-7.86426 + 8.87691i) q^{97} +(0.684088 - 1.30342i) q^{98} -5.51749i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9}+O(q^{10}) $ 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9} - 9 q^{10} - 13 q^{11} - 9 q^{12} + 52 q^{13} - 15 q^{14} + 39 q^{15} - 31 q^{16} - 11 q^{17} + 26 q^{18} - 13 q^{20} - 13 q^{21} - 6 q^{22} - 102 q^{23} - 91 q^{24} + 3 q^{25} - 13 q^{26} - 19 q^{27} - 13 q^{28} - 17 q^{29} + 23 q^{30} + 39 q^{31} - 13 q^{33} + 52 q^{34} - 21 q^{35} + 11 q^{36} - 13 q^{37} - 40 q^{38} - 65 q^{39} + 53 q^{40} - 13 q^{41} + 101 q^{42} - 3 q^{43} - 39 q^{44} - 78 q^{45} - 39 q^{46} - 39 q^{47} + 8 q^{48} + 85 q^{49} - 13 q^{50} + 62 q^{51} - 78 q^{52} + 18 q^{53} + 65 q^{54} - 103 q^{55} + 3 q^{56} + 65 q^{57} + 39 q^{58} + 91 q^{59} - 117 q^{60} - 23 q^{61} - 64 q^{62} - 78 q^{63} + 15 q^{64} - 13 q^{65} + 134 q^{66} - 65 q^{67} + 40 q^{68} - 40 q^{69} + 26 q^{71} + 156 q^{72} - 13 q^{73} - 53 q^{74} + 35 q^{75} + 221 q^{76} + 3 q^{77} - 143 q^{78} - 23 q^{79} - 43 q^{81} - 129 q^{82} + 117 q^{83} + 234 q^{84} + 26 q^{85} - 91 q^{86} + 79 q^{87} + 95 q^{88} + 17 q^{90} + 39 q^{91} - 89 q^{92} + 52 q^{93} - 61 q^{94} + 122 q^{95} - 182 q^{96} - 91 q^{97} - 13 q^{98}+O(q^{100}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9 - 9 * q^10 - 13 * q^11 - 9 * q^12 + 52 * q^13 - 15 * q^14 + 39 * q^15 - 31 * q^16 - 11 * q^17 + 26 * q^18 - 13 * q^20 - 13 * q^21 - 6 * q^22 - 102 * q^23 - 91 * q^24 + 3 * q^25 - 13 * q^26 - 19 * q^27 - 13 * q^28 - 17 * q^29 + 23 * q^30 + 39 * q^31 - 13 * q^33 + 52 * q^34 - 21 * q^35 + 11 * q^36 - 13 * q^37 - 40 * q^38 - 65 * q^39 + 53 * q^40 - 13 * q^41 + 101 * q^42 - 3 * q^43 - 39 * q^44 - 78 * q^45 - 39 * q^46 - 39 * q^47 + 8 * q^48 + 85 * q^49 - 13 * q^50 + 62 * q^51 - 78 * q^52 + 18 * q^53 + 65 * q^54 - 103 * q^55 + 3 * q^56 + 65 * q^57 + 39 * q^58 + 91 * q^59 - 117 * q^60 - 23 * q^61 - 64 * q^62 - 78 * q^63 + 15 * q^64 - 13 * q^65 + 134 * q^66 - 65 * q^67 + 40 * q^68 - 40 * q^69 + 26 * q^71 + 156 * q^72 - 13 * q^73 - 53 * q^74 + 35 * q^75 + 221 * q^76 + 3 * q^77 - 143 * q^78 - 23 * q^79 - 43 * q^81 - 129 * q^82 + 117 * q^83 + 234 * q^84 + 26 * q^85 - 91 * q^86 + 79 * q^87 + 95 * q^88 + 17 * q^90 + 39 * q^91 - 89 * q^92 + 52 * q^93 - 61 * q^94 + 122 * q^95 - 182 * q^96 - 91 * q^97 - 13 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{21}{26}\right)$

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 $

$2$	−1.71806	+	1.18589i	−1.21485	+	0.838551i	−0.990708	−	0.136006i	$-0.956573\pi$
$2$	−1.71806	+	1.18589i	−1.21485	+	0.838551i	−0.224142	+	0.974556i	$0.571958\pi$
$3$	2.94692	+	1.54666i	1.70141	+	0.892967i	0.979622	+	0.200849i	$0.0643701\pi$
$3$	2.94692	+	1.54666i	1.70141	+	0.892967i	0.721784	+	0.692118i	$0.243322\pi$
$4$	0.836178	−	2.20482i	0.418089	−	1.10241i
$5$	−0.781452	−	0.882078i	−0.349476	−	0.394477i	0.547318	−	0.836925i	$-0.315649\pi$
$5$	−0.781452	−	0.882078i	−0.349476	−	0.394477i	−0.896794	+	0.442448i	$0.854110\pi$
$6$	−6.89716	+	0.837466i	−2.81575	+	0.341894i
$7$	0.664295	+	2.69515i	0.251080	+	1.01867i	0.952163	+	0.305592i	$0.0988543\pi$
$7$	0.664295	+	2.69515i	0.251080	+	1.01867i	−0.701083	+	0.713080i	$0.747300\pi$
$8$	0.178883	+	0.725755i	0.0632445	+	0.256593i
$9$	4.58799	+	6.64685i	1.52933	+	2.21562i
$10$	2.38863	+	0.588744i	0.755350	+	0.186177i
$11$	−0.562223	−	0.388074i	−0.169517	−	0.117009i	0.480286	−	0.877112i	$-0.340533\pi$
$11$	−0.562223	−	0.388074i	−0.169517	−	0.117009i	−0.649802	+	0.760103i	$0.725148\pi$
$12$	5.87427	−	5.20415i	1.69576	−	1.50231i
$13$	−1.84768	−	3.09614i	−0.512454	−	0.858715i
$13$	−1.84768	−	3.09614i	−0.512454	−	0.858715i
$14$	−4.33745	−	3.84265i	−1.15923	−	1.02699i
$15$	−0.938602	−	3.80806i	−0.242346	−	0.983237i
$16$	2.36206	+	2.09261i	0.590516	+	0.523152i
$17$	1.85483	−	0.457175i	0.449863	−	0.110881i	−0.00787380	−	0.999969i	$-0.502506\pi$
$17$	1.85483	−	0.457175i	0.449863	−	0.110881i	0.457737	+	0.889088i	$0.348660\pi$
$18$	−15.7649	−	5.97882i	−3.71581	−	1.40922i
$19$			1.63338i			0.374722i	0.982291	+	0.187361i	$0.0599934\pi$
$19$			1.63338i			0.374722i	−0.982291	+	0.187361i	$0.940007\pi$
$20$	−2.59826	+	0.985388i	−0.580988	+	0.220340i
$21$	−2.21087	+	8.96985i	−0.482451	+	1.95738i
$22$	1.42614			0.304055
$23$	−6.28383			−1.31027			−0.655134	−	0.755513i	$-0.727388\pi$
$23$	−6.28383			−1.31027			−0.655134	+	0.755513i	$0.727388\pi$
$24$	−0.595347	+	2.41542i	−0.121525	+	0.493045i
$25$	0.435291	−	3.58494i	0.0870581	−	0.716988i
$26$	6.84610	+	3.12820i	1.34263	+	0.613491i
$27$	2.03651	+	16.7722i	0.391927	+	3.22781i
$28$	6.49780	+	0.788975i	1.22797	+	0.149102i
$29$	−4.39880	−	6.37276i	−0.816836	−	1.18339i	−0.980431	−	0.196864i	$-0.936924\pi$
$29$	−4.39880	−	6.37276i	−0.816836	−	1.18339i	0.163595	−	0.986528i	$-0.447691\pi$
$30$	6.12851	+	5.42939i	1.11891	+	0.991266i
$31$	6.06341	−	0.736231i	1.08902	−	0.132231i	0.443724	−	0.896163i	$-0.353657\pi$
$31$	6.06341	−	0.736231i	1.08902	−	0.132231i	0.645296	+	0.763932i	$0.276734\pi$
$32$	−8.02381	−	0.974267i	−1.41842	−	0.172228i
$33$	−1.05661	−	2.01320i	−0.183932	−	0.350452i
$34$	−2.64455	+	2.98508i	−0.453537	+	0.511937i
$35$	1.85822	−	2.69209i	0.314096	−	0.455047i
$36$	18.4915	−	4.55774i	3.08191	−	0.759624i
$37$	4.15024	−	0.503930i	0.682295	−	0.0828456i	0.227952	−	0.973672i	$-0.426797\pi$
$37$	4.15024	−	0.503930i	0.682295	−	0.0828456i	0.454343	+	0.890827i	$0.349874\pi$
$38$	−1.93700	−	2.80623i	−0.314223	−	0.455231i
$39$	−0.656278	−	11.9818i	−0.105089	−	1.91863i
$40$	0.500384	−	0.724932i	0.0791177	−	0.114622i
$41$	4.47504	−	8.52648i	0.698884	−	1.33161i	−0.234282	−	0.972169i	$-0.575274\pi$
$41$	4.47504	−	8.52648i	0.698884	−	1.33161i	0.933167	−	0.359444i	$-0.117034\pi$
$42$	−6.83885	−	18.0326i	−1.05526	−	2.78248i
$43$	−0.509861	+	4.19909i	−0.0777531	+	0.640355i	0.900782	+	0.434272i	$0.142994\pi$
$43$	−0.509861	+	4.19909i	−0.0777531	+	0.640355i	−0.978535	+	0.206082i	$0.933929\pi$
$44$	−1.32575	+	0.915101i	−0.199865	+	0.137957i
$45$	2.27774	−	9.24116i	0.339546	−	1.37759i
$46$	10.7960	−	7.45192i	1.59178	−	1.09873i
$47$	−3.61133	+	1.36960i	−0.526766	+	0.199776i	−0.603629	−	0.797266i	$-0.706279\pi$
$47$	−3.61133	+	1.36960i	−0.526766	+	0.199776i	0.0768623	+	0.997042i	$0.475510\pi$
$48$	3.72426	+	9.82007i	0.537551	+	1.41740i
$49$	−0.624365	+	0.327692i	−0.0891950	+	0.0468131i
$50$	3.50349	+	6.67534i	0.495468	+	0.944036i
$51$	6.17315	+	1.52154i	0.864413	+	0.213059i
$52$	−8.37142	+	1.48488i	−1.16091	+	0.205915i
$53$	9.74242	−	2.40129i	1.33822	−	0.329843i	0.495697	−	0.868496i	$-0.334913\pi$
$53$	9.74242	−	2.40129i	1.33822	−	0.329843i	0.842528	+	0.538653i	$0.181067\pi$
$54$	−23.3888	−	26.4005i	−3.18282	−	3.59266i
$55$	0.0970387	+	0.799186i	0.0130847	+	0.107762i
$56$	−1.83719	+	0.964232i	−0.245505	+	0.128851i
$57$	−2.52628	+	4.81343i	−0.334614	+	0.637555i
$58$	15.1148	+	5.73228i	1.98467	+	0.752685i
$59$	5.57925	+	6.29767i	0.726356	+	0.819887i	0.989449	−	0.144884i	$-0.0462808\pi$
$59$	5.57925	+	6.29767i	0.726356	+	0.819887i	−0.263092	+	0.964771i	$0.584742\pi$
$60$	−9.18092	−	1.11477i	−1.18525	−	0.143916i
$61$	1.36238	+	0.335797i	0.174435	+	0.0429944i	0.325566	−	0.945519i	$-0.394445\pi$
$61$	1.36238	+	0.335797i	0.174435	+	0.0429944i	−0.151131	+	0.988514i	$0.548291\pi$
$62$	−9.54420	+	8.45542i	−1.21211	+	1.07384i
$63$	−14.8665	+	16.7808i	−1.87300	+	2.11418i
$64$	9.35230	−	4.90847i	1.16904	−	0.613559i
$65$	−1.28716	+	4.04928i	−0.159653	+	0.502252i
$66$	4.20274	+	2.20577i	0.517321	+	0.271511i
$67$	−1.61021	+	0.610672i	−0.196718	+	0.0746055i	−0.450997	−	0.892526i	$-0.648931\pi$
$67$	−1.61021	+	0.610672i	−0.196718	+	0.0746055i	0.254278	+	0.967131i	$0.418162\pi$
$68$	0.542981	−	4.47185i	0.0658462	−	0.542292i
$69$	−18.5180	−	9.71897i	−2.22930	−	1.17003i
$70$			6.82881i			0.816199i
$71$	−2.23850	+	4.26510i	−0.265661	+	0.506175i	−0.981346	−	0.192248i	$-0.938422\pi$
$71$	−2.23850	+	4.26510i	−0.265661	+	0.506175i	0.715685	+	0.698423i	$0.246114\pi$
$72$	−4.00327	+	4.51876i	−0.471790	+	0.532541i
$73$	−9.42952	−	6.50872i	−1.10364	−	0.761789i	−0.130374	−	0.991465i	$-0.541618\pi$
$73$	−9.42952	−	6.50872i	−1.10364	−	0.761789i	−0.973267	+	0.229676i	$0.926233\pi$
$74$	−6.53274	+	5.78751i	−0.759416	+	0.672784i
$75$	6.82747	−	9.89130i	0.788368	−	1.14215i
$76$	3.60130	+	1.36579i	0.413097	+	0.156667i
$77$	0.672438	−	1.77307i	0.0766314	−	0.202060i
$78$	15.3366	+	19.8072i	1.73653	+	2.24272i
$79$	−3.64067	−	9.59966i	−0.409607	−	1.08005i	−0.968106	−	0.250541i	$-0.919392\pi$
$79$	−3.64067	−	9.59966i	−0.409607	−	1.08005i	0.558499	−	0.829505i	$-0.311378\pi$
$80$		−	3.71880i		−	0.415774i
$81$	−11.3476	+	29.9211i	−1.26084	+	3.32457i
$82$	2.42308	+	19.9559i	0.267585	+	2.20376i
$83$	3.03191	+	5.77682i	0.332795	+	0.634089i	0.993148	−	0.116867i	$-0.0372853\pi$
$83$	3.03191	+	5.77682i	0.332795	+	0.634089i	−0.660352	+	0.750956i	$0.729593\pi$
$84$	17.9282	+	12.3750i	1.95613	+	1.35022i
$85$	−1.85273	−	1.27885i	−0.200957	−	0.138710i
$86$	−4.10368	−	7.81891i	−0.442511	−	0.843135i
$87$	−3.10640	−	25.5835i	−0.333041	−	2.74284i
$88$	0.181075	−	0.477456i	0.0193027	−	0.0508970i
$89$		−	9.41856i		−	0.998365i	−0.866497	−	0.499183i	$-0.833634\pi$
$89$		−	9.41856i		−	0.998365i	0.866497	−	0.499183i	$-0.166366\pi$
$90$	7.04570	+	18.5780i	0.742682	+	1.95829i
$91$	7.11716	−	7.03653i	0.746081	−	0.737629i
$92$	−5.25440	+	13.8547i	−0.547809	+	1.44445i
$93$	19.0071	+	7.20844i	1.97095	+	0.747481i
$94$	4.58028	−	6.63568i	0.472420	−	0.684418i
$95$	1.44076	−	1.27641i	0.147819	−	0.130956i
$96$	−22.1387	−	15.2812i	−2.25952	−	1.55963i
$97$	−7.86426	+	8.87691i	−0.798494	+	0.901314i	−0.996890	−	0.0788082i	$-0.974889\pi$
$97$	−7.86426	+	8.87691i	−0.798494	+	0.901314i	0.198395	+	0.980122i	$0.436427\pi$
$98$	0.684088	−	1.30342i	0.0691033	−	0.131665i
$99$		−	5.51749i		−	0.554529i
$100$	−7.54017	−	3.95739i	−0.754017	−	0.395739i
$101$	−1.55335	+	12.7930i	−0.154564	+	1.27295i	0.684539	+	0.728976i	$0.260004\pi$
$101$	−1.55335	+	12.7930i	−0.154564	+	1.27295i	−0.839103	+	0.543973i	$0.816920\pi$
$102$	−12.4102	+	4.70657i	−1.22879	+	0.466020i
$103$	−16.2051	−	8.50508i	−1.59673	−	0.838030i	−0.999349	−	0.0360750i	$-0.988514\pi$
$103$	−16.2051	−	8.50508i	−1.59673	−	0.838030i	−0.597384	−	0.801955i	$-0.703793\pi$
$104$	1.91652	−	1.89481i	0.187930	−	0.185801i
$105$	9.63979	−	5.05935i	0.940747	−	0.493742i
$106$	−13.8904	+	15.6790i	−1.34915	+	1.52288i
$107$	−4.70163	+	4.16528i	−0.454523	+	0.402673i	−0.859081	−	0.511840i	$-0.828964\pi$
$107$	−4.70163	+	4.16528i	−0.454523	+	0.402673i	0.404557	+	0.914513i	$0.367426\pi$
$108$	38.6826	+	9.53440i	3.72223	+	0.917448i
$109$	−0.0587053	−	0.00712811i	−0.00562295	−	0.000682749i	0.117725	−	0.993046i	$-0.462440\pi$
$109$	−0.0587053	−	0.00712811i	−0.00562295	−	0.000682749i	−0.123348	+	0.992364i	$0.539363\pi$
$110$	−1.11446	−	1.25797i	−0.106260	−	0.119943i
$111$	13.0098	+	4.93398i	1.23484	+	0.468313i
$112$	−4.07078	+	7.75623i	−0.384653	+	0.732895i
$113$	−5.61202	+	2.94541i	−0.527934	+	0.277081i	−0.707559	−	0.706654i	$-0.750204\pi$
$113$	−5.61202	+	2.94541i	−0.527934	+	0.277081i	0.179625	+	0.983735i	$0.442511\pi$
$114$	−1.36790	−	11.2656i	−0.128115	−	1.05512i
$115$	4.91051	+	5.54282i	0.457908	+	0.516871i
$116$	−17.7290	+	4.36980i	−1.64609	+	0.405725i
$117$	12.1024	−	26.4863i	1.11887	−	2.44866i
$118$	−17.0538	−	4.20339i	−1.56993	−	0.386953i
$119$	2.46431	+	4.69536i	0.225903	+	0.430423i
$120$	2.59582	−	1.36239i	0.236965	−	0.124369i
$121$	−3.73516	−	9.84881i	−0.339560	−	0.895346i
$122$	−2.73887	+	1.03872i	−0.247966	+	0.0940410i
$123$	26.3752	−	18.2055i	2.37817	−	1.64153i
$124$	3.44683	−	13.9844i	0.309535	−	1.25583i
$125$	−8.35155	+	5.76466i	−0.746986	+	0.515607i
$126$	5.64131	−	46.4604i	0.502568	−	4.13902i
$127$	0.249279	+	0.657293i	0.0221199	+	0.0583254i	0.945621	−	0.325270i	$-0.105455\pi$
$127$	0.249279	+	0.657293i	0.0221199	+	0.0583254i	−0.923501	+	0.383595i	$0.874686\pi$
$128$	−2.73442	+	5.21000i	−0.241691	+	0.460503i
$129$	−7.99710	+	11.5858i	−0.704105	+	1.02007i
$130$	−2.59058	−	8.48333i	−0.227209	−	0.744037i
$131$	0.615944	+	0.892349i	0.0538153	+	0.0779649i	0.848968	−	0.528445i	$-0.177225\pi$
$131$	0.615944	+	0.892349i	0.0538153	+	0.0779649i	−0.795152	+	0.606410i	$0.792609\pi$
$132$	−5.32225	+	0.646238i	−0.463242	+	0.0562478i
$133$	−4.40220	+	1.08504i	−0.381719	+	0.0940852i
$134$	2.04224	−	2.95870i	0.176423	−	0.255593i
$135$	13.2029	−	14.9030i	1.13633	−	1.28265i
$136$	0.663595	+	1.26437i	0.0569028	+	0.108419i
$137$	18.8970	+	2.29451i	1.61448	+	0.196034i	0.877396	−	0.479766i	$-0.159278\pi$
$137$	18.8970	+	2.29451i	1.61448	+	0.196034i	0.737085	+	0.675800i	$0.236202\pi$
$138$	43.3405	−	5.26249i	3.68939	−	0.447973i
$139$	−3.90177	−	3.45667i	−0.330944	−	0.293191i	0.481244	−	0.876587i	$-0.340185\pi$
$139$	−3.90177	−	3.45667i	−0.330944	−	0.293191i	−0.812188	+	0.583396i	$0.801724\pi$
$140$	−4.38178	−	6.34811i	−0.370328	−	0.536513i
$141$	−12.7606	−	1.54942i	−1.07464	−	0.130485i
$142$	−1.21207	−	9.98231i	−0.101715	−	0.837697i
$143$	−0.162725	+	2.45776i	−0.0136078	+	0.205528i
$144$	−3.07211	+	25.3011i	−0.256010	+	2.10843i
$145$	−2.18382	+	8.86009i	−0.181356	+	0.735790i
$146$	23.9191			1.97956
$147$	−2.34678			−0.193560
$148$	2.35926	−	9.57191i	0.193930	−	0.786806i
$149$	−18.5062	+	7.01848i	−1.51609	+	0.574976i	−0.965638	−	0.259892i	$-0.916313\pi$
$149$	−18.5062	+	7.01848i	−1.51609	+	0.574976i	−0.550450	+	0.834868i	$0.685544\pi$
$150$			25.0904i			2.04863i
$151$	−11.1146	−	4.21522i	−0.904494	−	0.343029i	−0.141881	−	0.989884i	$-0.545315\pi$
$151$	−11.1146	−	4.21522i	−0.904494	−	0.343029i	−0.762614	+	0.646854i	$0.776084\pi$
$152$	−1.18543	+	0.292182i	−0.0961511	+	0.0236991i
$153$	11.5487	+	10.2313i	0.933659	+	0.827150i
$154$	0.947381	+	3.84368i	0.0763422	+	0.309732i
$155$	−5.38768	−	4.77307i	−0.432749	−	0.383382i
$156$	−26.9665	−	8.57196i	−2.15905	−	0.686306i
$157$	−4.41726	+	3.91335i	−0.352536	+	0.312319i	−0.820741	−	0.571300i	$-0.806439\pi$
$157$	−4.41726	+	3.91335i	−0.352536	+	0.312319i	0.468206	+	0.883620i	$0.344901\pi$
$158$	17.6390	+	12.1753i	1.40328	+	0.968618i
$159$	32.4242	+	7.99184i	2.57140	+	0.633794i
$160$	5.41085	+	7.83897i	0.427765	+	0.619725i
$161$	−4.17432	−	16.9359i	−0.328982	−	1.33473i
$162$	−15.9874	−	64.8632i	−1.25609	−	5.09614i
$163$	−1.44841	+	0.175869i	−0.113448	+	0.0137751i	−0.177064	−	0.984199i	$-0.556660\pi$
$163$	−1.44841	+	0.175869i	−0.113448	+	0.0137751i	0.0636156	+	0.997974i	$0.479737\pi$
$164$	−15.0574	−	16.9963i	−1.17579	−	1.32719i
$165$	−0.950107	+	2.50523i	−0.0739657	+	0.195032i
$166$	−12.0597	−	6.32940i	−0.936012	−	0.491257i
$167$	2.60190	−	1.79596i	0.201341	−	0.138976i	−0.463128	−	0.886291i	$-0.653273\pi$
$167$	2.60190	−	1.79596i	0.201341	−	0.138976i	0.664469	+	0.747316i	$0.268658\pi$
$168$	−6.90540			−0.532763
$169$	−6.17216	+	11.4413i	−0.474782	+	0.880104i
$170$	4.69966			0.360448
$171$	−10.8568	+	7.49391i	−0.830240	+	0.573074i
$172$	8.83189	+	4.63534i	0.673426	+	0.353441i
$173$	−3.10538	+	8.18821i	−0.236098	+	0.622538i	−0.999733	−	0.0231097i	$-0.992643\pi$
$173$	−3.10538	+	8.18821i	−0.236098	+	0.622538i	0.763635	+	0.645648i	$0.223413\pi$
$174$	35.6762	+	40.2701i	2.70460	+	3.05287i
$175$	9.95112	−	1.20829i	0.752234	−	0.0913378i
$176$	−0.515920	−	2.09317i	−0.0388889	−	0.157778i
$177$	6.70123	+	27.1880i	0.503696	+	2.04357i
$178$	11.1694	+	16.1816i	0.837180	+	1.21286i
$179$	−1.62281	−	0.399988i	−0.121295	−	0.0298965i	0.178201	−	0.983994i	$-0.442972\pi$
$179$	−1.62281	−	0.399988i	−0.121295	−	0.0298965i	−0.299496	+	0.954098i	$0.596818\pi$
$180$	−18.4705	−	12.7493i	−1.37671	−	0.950274i
$181$	3.94330	−	3.49346i	0.293103	−	0.259667i	−0.503737	−	0.863857i	$-0.668042\pi$
$181$	3.94330	−	3.49346i	0.293103	−	0.259667i	0.796840	+	0.604191i	$0.206503\pi$
$182$	−3.88315	+	20.5293i	−0.287838	+	1.52174i
$183$	3.49547	+	3.09672i	0.258393	+	0.228916i
$184$	−1.12407	−	4.56052i	−0.0828673	−	0.336206i
$185$	−3.68772	−	3.26703i	−0.271127	−	0.240197i
$186$	−41.2037	+	10.1558i	−3.02120	+	0.744660i
$187$	−1.22025	−	0.462779i	−0.0892333	−	0.0338417i
$188$			9.10756i			0.664237i
$189$	−43.8508	+	16.6304i	−3.18968	+	1.20968i
$190$	−0.961640	+	3.90153i	−0.0697647	+	0.283046i
$191$	15.3410			1.11004			0.555019	−	0.831838i	$-0.312711\pi$
$191$	15.3410			1.11004			0.555019	+	0.831838i	$0.312711\pi$
$192$	35.1523			2.53690
$193$	−1.35552	+	5.49956i	−0.0975724	+	0.395867i	−0.999339	−	0.0363568i	$-0.988425\pi$
$193$	−1.35552	+	5.49956i	−0.0975724	+	0.395867i	0.901766	+	0.432224i	$0.142271\pi$
$194$	2.98421	−	24.5772i	0.214254	−	1.76454i
$195$	−10.0560	+	9.94211i	−0.720129	+	0.711970i
$196$	0.200422	+	1.65062i	0.0143158	+	0.117902i
$197$	−1.78472	−	0.216704i	−0.127156	−	0.0154395i	0.0567113	−	0.998391i	$-0.481939\pi$
$197$	−1.78472	−	0.216704i	−0.127156	−	0.0154395i	−0.183867	+	0.982951i	$0.558862\pi$
$198$	6.54314	+	9.47937i	0.465000	+	0.673669i
$199$	−0.792846	−	0.702401i	−0.0562034	−	0.0497919i	0.634553	−	0.772879i	$-0.281184\pi$
$199$	−0.792846	−	0.702401i	−0.0562034	−	0.0497919i	−0.690757	+	0.723087i	$0.742722\pi$
$200$	2.67966	−	0.325369i	0.189480	−	0.0230071i
$201$	−5.68967	−	0.690851i	−0.401318	−	0.0487289i
$202$	−12.5023	−	23.8212i	−0.879660	−	1.67605i
$203$	14.2535	−	16.0888i	1.00040	−	1.12921i
$204$	8.51658	−	12.3384i	0.596280	−	0.863861i
$205$	−11.0181	+	2.71571i	−0.769534	+	0.189673i
$206$	37.9273	−	4.60521i	2.64252	−	0.320860i
$207$	−28.8301	−	41.7676i	−2.00383	−	2.90305i
$208$	2.11467	−	11.1797i	0.146626	−	0.775176i
$209$	0.633871	−	0.918321i	0.0438458	−	0.0635216i
$210$	−10.5619	+	20.1240i	−0.728839	+	1.38869i
$211$	1.46788	+	3.87049i	0.101053	+	0.266455i	0.976003	−	0.217759i	$-0.0698747\pi$
$211$	1.46788	+	3.87049i	0.101053	+	0.266455i	−0.874949	+	0.484214i	$0.839105\pi$
$212$	2.85198	−	23.4882i	0.195875	−	1.61318i
$213$	−13.1934	+	9.10673i	−0.903995	+	0.623983i
$214$	3.13811	−	12.7318i	0.214516	−	0.870327i
$215$	4.10235	−	2.83165i	0.279778	−	0.193117i
$216$	−11.8082	+	4.47827i	−0.803447	+	0.304707i
$217$	6.01215	+	15.8527i	0.408131	+	1.07615i
$218$	0.109312	−	0.0573715i	0.00740356	−	0.00388569i
$219$	−17.7212	−	33.7650i	−1.19749	−	2.28163i
$220$	1.84320	+	0.454309i	0.124269	+	0.0306295i
$221$	−4.84261	−	4.89811i	−0.325749	−	0.329482i
$222$	−28.2028	+	6.95137i	−1.89285	+	0.466545i
$223$	8.08947	+	9.13113i	0.541711	+	0.611465i	0.954080	−	0.299551i	$-0.0968370\pi$
$223$	8.08947	+	9.13113i	0.541711	+	0.611465i	−0.412369	+	0.911017i	$0.635299\pi$
$224$	−2.70438	−	22.2726i	−0.180694	−	1.48815i
$225$	25.8257	−	13.5544i	1.72171	−	0.903624i
$226$	6.14883	−	11.7156i	0.409014	−	0.779311i
$227$	4.52954	+	1.71783i	0.300636	+	0.114016i	0.500310	−	0.865846i	$-0.333219\pi$
$227$	4.52954	+	1.71783i	0.300636	+	0.114016i	−0.199674	+	0.979862i	$0.563988\pi$
$228$	8.50033	+	9.59489i	0.562948	+	0.635437i
$229$	12.2540	+	1.48791i	0.809769	+	0.0983238i	0.514940	−	0.857226i	$-0.327814\pi$
$229$	12.2540	+	1.48791i	0.809769	+	0.0983238i	0.294829	+	0.955550i	$0.404737\pi$
$230$	−15.0097	−	3.69956i	−0.989711	−	0.243942i
$231$	4.72397	−	4.18507i	0.310814	−	0.275358i
$232$	3.83819	−	4.33243i	0.251990	−	0.284438i
$233$	−18.0237	+	9.45955i	−1.18077	+	0.619716i	−0.936731	−	0.350050i	$-0.886165\pi$
$233$	−18.0237	+	9.45955i	−1.18077	+	0.619716i	−0.244038	+	0.969766i	$0.578472\pi$
$234$	10.6171	+	59.8571i	0.694063	+	3.91298i
$235$	4.03017	+	2.11520i	0.262899	+	0.137980i
$236$	18.5505	−	7.03527i	1.20753	−	0.457957i
$237$	4.11868	−	33.9203i	0.267537	−	2.20336i
$238$	−9.80201	−	5.14449i	−0.635370	−	0.333468i
$239$		−	15.9608i		−	1.03242i	−0.856462	−	0.516210i	$-0.827342\pi$
$239$		−	15.9608i		−	1.03242i	0.856462	−	0.516210i	$-0.172658\pi$
$240$	5.75173	−	10.9590i	0.371272	−	0.707401i
$241$	−2.09977	+	2.37015i	−0.135258	+	0.152675i	−0.812237	−	0.583328i	$-0.801750\pi$
$241$	−2.09977	+	2.37015i	−0.135258	+	0.152675i	0.676979	+	0.736002i	$0.263289\pi$
$242$	18.0968	+	12.4913i	1.16331	+	0.802973i
$243$	−41.7793	+	37.0132i	−2.68014	+	2.37440i
$244$	1.87957	−	2.72302i	0.120327	−	0.174324i
$245$	0.776961	+	0.294662i	0.0496382	+	0.0188253i
$246$	−23.7244	+	62.5562i	−1.51261	+	3.98844i
$247$	5.05716	−	3.01795i	0.321779	−	0.192028i
$248$	1.61896	+	4.26885i	0.102804	+	0.271072i
$249$			21.7132i			1.37602i
$250$	7.51220	−	19.8080i	0.475113	−	1.25277i
$251$	2.48417	+	20.4590i	0.156800	+	1.29136i	0.832434	+	0.554124i	$0.186947\pi$
$251$	2.48417	+	20.4590i	0.156800	+	1.29136i	−0.675635	+	0.737237i	$0.736130\pi$
$252$	24.5676	+	46.8097i	1.54761	+	2.94873i
$253$	3.53291	+	2.43859i	0.222112	+	0.153313i
$254$	−1.20775	−	0.833651i	−0.0757811	−	0.0523079i
$255$	−3.48190	−	6.63421i	−0.218045	−	0.415450i
$256$	1.06565	+	8.77645i	0.0666033	+	0.548528i
$257$	−2.27633	+	6.00219i	−0.141994	+	0.374406i	−0.987081	−	0.160222i	$-0.948779\pi$
$257$	−2.27633	+	6.00219i	−0.141994	+	0.374406i	0.845087	+	0.534628i	$0.179548\pi$
$258$		−	29.3887i		−	1.82966i
$259$	4.11515	+	10.8508i	0.255703	+	0.674234i
$260$	7.85164	+	6.22388i	0.486938	+	0.385989i
$261$	22.1771	−	58.4763i	1.37273	−	3.61959i
$262$	−2.11646	−	0.802666i	−0.130755	−	0.0495889i
$263$	−4.82714	+	6.99333i	−0.297654	+	0.431227i	−0.943065	−	0.332609i	$-0.892071\pi$
$263$	−4.82714	+	6.99333i	−0.297654	+	0.431227i	0.645410	+	0.763836i	$0.276686\pi$
$264$	1.27208	−	1.12696i	0.0782910	−	0.0693598i
$265$	−9.73136	−	6.71708i	−0.597793	−	0.412627i
$266$	6.27648	−	7.08469i	0.384836	−	0.434390i
$267$	14.5674	−	27.7558i	0.891507	−	1.69863i
$268$			4.06085i			0.248056i
$269$	−13.0319	−	6.83965i	−0.794567	−	0.417021i	0.0180371	−	0.999837i	$-0.494258\pi$
$269$	−13.0319	−	6.83965i	−0.794567	−	0.417021i	−0.812604	+	0.582817i	$0.801951\pi$
$270$	−5.01006	+	41.2615i	−0.304902	+	2.51110i
$271$	14.1519	−	5.36709i	0.859664	−	0.326028i	0.114918	−	0.993375i	$-0.463340\pi$
$271$	14.1519	−	5.36709i	0.859664	−	0.326028i	0.744747	+	0.667347i	$0.232570\pi$
$272$	5.33792	+	2.80156i	0.323659	+	0.169869i
$273$	31.8569	−	9.72824i	1.92807	−	0.588780i
$274$	−35.1872	+	18.4677i	−2.12574	+	1.11567i
$275$	−1.63595	+	1.84661i	−0.0986518	+	0.111355i
$276$	−36.9129	+	32.7020i	−2.22189	+	1.96843i
$277$	14.7389	+	3.63282i	0.885577	+	0.218275i	0.655770	−	0.754961i	$-0.272344\pi$
$277$	14.7389	+	3.63282i	0.885577	+	0.218275i	0.229808	+	0.973236i	$0.426190\pi$
$278$	10.8027	+	1.31168i	0.647903	+	0.0786696i
$279$	32.7125	+	36.9248i	1.95844	+	2.21063i
$280$	2.28620	+	0.867043i	0.136627	+	0.0518157i
$281$	6.13493	−	11.6891i	0.365979	−	0.697315i	−0.630933	−	0.775837i	$-0.717328\pi$
$281$	6.13493	−	11.6891i	0.365979	−	0.697315i	0.996912	+	0.0785223i	$0.0250202\pi$
$282$	23.7609	−	12.4707i	1.41494	−	0.742619i
$283$	2.14414	+	17.6586i	0.127456	+	1.04970i	0.906346	+	0.422535i	$0.138860\pi$
$283$	2.14414	+	17.6586i	0.127456	+	1.04970i	−0.778890	+	0.627160i	$0.784217\pi$
$284$	7.53201	+	8.50188i	0.446942	+	0.504494i
$285$	6.21999	−	1.53309i	0.368440	−	0.0908124i
$286$	−2.63506	−	4.41554i	−0.155814	−	0.261097i
$287$	25.9529	+	6.39682i	1.53195	+	0.377592i
$288$	−30.3374	−	57.8030i	−1.78765	−	3.40607i
$289$	−11.8214	+	6.20433i	−0.695374	+	0.364960i
$290$	−6.75516	−	17.8119i	−0.396677	−	1.04595i
$291$	−36.9050	+	13.9962i	−2.16341	+	0.820472i
$292$	−22.2353	+	15.3479i	−1.30122	+	0.898170i
$293$	−2.14322	+	8.69539i	−0.125208	+	0.507990i	0.874527	+	0.484977i	$0.161172\pi$
$293$	−2.14322	+	8.69539i	−0.125208	+	0.507990i	−0.999735	+	0.0230129i	$0.992674\pi$
$294$	4.03191	−	2.78303i	0.235146	−	0.162309i
$295$	1.19512	−	9.84266i	0.0695823	−	0.573062i
$296$	1.10814	+	2.92191i	0.0644091	+	0.169833i
$297$	5.36389	−	10.2200i	0.311244	−	0.593027i
$298$	23.4716	−	34.0045i	1.35967	−	1.96983i
$299$	11.6105	+	19.4556i	0.671452	+	1.12515i
$300$	−16.0996	−	23.3242i	−0.929508	−	1.34662i
$301$	−11.6559	+	1.41528i	−0.671833	+	0.0815753i
$302$	24.0943	−	5.93872i	1.38647	−	0.341735i
$303$	−24.3640	+	35.2974i	−1.39968	+	2.02778i
$304$	−3.41801	+	3.85814i	−0.196036	+	0.221279i
$305$	−0.768438	−	1.46414i	−0.0440006	−	0.0838362i
$306$	−31.9745	−	3.88241i	−1.82786	−	0.221943i
$307$	−19.8578	+	2.41118i	−1.13335	+	0.137613i	−0.665642	−	0.746272i	$-0.731842\pi$
$307$	−19.8578	+	2.41118i	−1.13335	+	0.137613i	−0.467705	+	0.883885i	$0.654919\pi$
$308$	−3.34703	−	2.96521i	−0.190715	−	0.168958i
$309$	−34.6006	−	50.1276i	−1.96836	−	2.85166i
$310$	14.9167	+	1.81121i	0.847210	+	0.102870i
$311$	0.635282	+	5.23202i	0.0360235	+	0.296681i	0.999575	+	0.0291570i	$0.00928227\pi$
$311$	0.635282	+	5.23202i	0.0360235	+	0.296681i	−0.963551	+	0.267524i	$0.913795\pi$
$312$	8.57847	−	2.61964i	0.485660	−	0.148308i
$313$	2.42724	−	19.9901i	0.137196	−	1.12991i	−0.747672	−	0.664068i	$-0.768829\pi$
$313$	2.42724	−	19.9901i	0.137196	−	1.12991i	0.884868	−	0.465842i	$-0.154248\pi$
$314$	2.94830	−	11.9617i	0.166382	−	0.675040i
$315$	26.4194			1.48857
$316$	−24.2098			−1.36191
$317$	−1.65509	+	6.71495i	−0.0929590	+	0.377149i	−0.998933	−	0.0461840i	$-0.985294\pi$
$317$	−1.65509	+	6.71495i	−0.0929590	+	0.377149i	0.905974	+	0.423333i	$0.139140\pi$
$318$	−65.1840	+	24.7210i	−3.65534	+	1.38629i
$319$			5.28997i			0.296182i
$320$	−11.6380	−	4.41372i	−0.650586	−	0.246735i
$321$	−20.2976	+	5.00291i	−1.13290	+	0.279235i
$322$	27.2558	+	24.1465i	1.51891	+	1.34563i
$323$	0.746739	+	3.02964i	0.0415497	+	0.168574i
$324$	56.4821	+	50.0388i	3.13790	+	2.77993i
$325$	−11.9038	+	5.27610i	−0.660302	+	0.292665i
$326$	2.27989	−	2.01981i	0.126271	−	0.111867i
$327$	−0.161975	−	0.111803i	−0.00895724	−	0.00618274i
$328$	6.98865	+	1.72255i	0.385883	+	0.0951117i
$329$	−6.09026	−	8.82326i	−0.335767	−	0.486442i
$330$	−1.33858	−	5.43084i	−0.0736865	−	0.298958i
$331$	−5.77019	−	23.4106i	−0.317158	−	1.28676i	−0.885758	−	0.464147i	$-0.846361\pi$
$331$	−5.77019	−	23.4106i	−0.317158	−	1.28676i	0.568600	−	0.822614i	$-0.307485\pi$
$332$	15.2721	−	1.85437i	0.838164	−	0.101772i
$333$	22.3908	+	25.2740i	1.22701	+	1.38501i
$334$	−2.34040	+	6.17113i	−0.128061	+	0.337669i
$335$	1.79696	+	0.943119i	0.0981785	+	0.0515281i
$336$	−23.9926	+	16.5609i	−1.30890	+	0.903470i
$337$	33.8161			1.84208			0.921039	−	0.389470i	$-0.127342\pi$
$337$	33.8161			1.84208			0.921039	+	0.389470i	$0.127342\pi$
$338$	−2.96404	−	26.9764i	−0.161222	−	1.46732i
$339$	−21.0937			−1.14565
$340$	−4.36884	+	3.01559i	−0.236933	+	0.163543i
$341$	−3.69470	−	1.93913i	−0.200079	−	0.105010i
$342$	9.76566	−	25.7499i	0.528067	−	1.39240i
$343$	11.5870	+	13.0790i	0.625638	+	0.706200i
$344$	−3.13871	+	0.381109i	−0.169228	+	0.0205480i
$345$	5.89801	+	23.9292i	0.317538	+	1.28830i
$346$	−4.37509	−	17.7504i	−0.235206	−	0.954270i
$347$	−0.258425	−	0.374393i	−0.0138730	−	0.0200985i	0.815986	−	0.578072i	$-0.196195\pi$
$347$	−0.258425	−	0.374393i	−0.0138730	−	0.0200985i	−0.829859	+	0.557973i	$0.811579\pi$
$348$	−59.0045	−	14.5433i	−3.16297	−	0.779603i
$349$	14.4032	+	9.94183i	0.770987	+	0.532174i	0.887385	−	0.461029i	$-0.152519\pi$
$349$	14.4032	+	9.94183i	0.770987	+	0.532174i	−0.116398	+	0.993203i	$0.537135\pi$
$350$	−15.6637	+	13.8768i	−0.837261	+	0.741748i
$351$	48.1663	−	37.2950i	2.57092	−	1.99066i
$352$	4.13308	+	3.66159i	0.220294	+	0.195164i
$353$	1.59460	+	6.46956i	0.0848722	+	0.344340i	0.997991	−	0.0633531i	$-0.0201794\pi$
$353$	1.59460	+	6.46956i	0.0848722	+	0.344340i	−0.913119	+	0.407693i	$0.866333\pi$
$354$	−43.7550	−	38.7636i	−2.32555	−	2.06026i
$355$	5.51143	−	1.35845i	0.292517	−	0.0720988i
$356$	−20.7662	−	7.87559i	−1.10061	−	0.417406i
$357$			17.6483i			0.934048i
$358$	3.26243	−	1.23728i	0.172425	−	0.0653921i
$359$	3.58758	−	14.5554i	0.189345	−	0.768203i	−0.797064	−	0.603895i	$-0.793615\pi$
$359$	3.58758	−	14.5554i	0.189345	−	0.768203i	0.986409	−	0.164308i	$-0.0525391\pi$
$360$	7.11427			0.374955
$361$	16.3321			0.859583
$362$	−2.63196	+	10.6783i	−0.138333	+	0.561238i
$363$	4.22557	−	34.8007i	0.221785	−	1.82656i
$364$	−9.56306	−	21.5759i	−0.501241	−	1.13088i
$365$	1.62752	+	13.4038i	0.0851882	+	0.701588i
$366$	−9.67778	−	1.17510i	−0.505866	−	0.0614232i
$367$	−16.5605	−	23.9920i	−0.864451	−	1.25237i	−0.966260	−	0.257570i	$-0.917078\pi$
$367$	−16.5605	−	23.9920i	−0.864451	−	1.25237i	0.101808	−	0.994804i	$-0.467537\pi$
$368$	−14.8428	−	13.1496i	−0.773734	−	0.685469i
$369$	77.2057	−	9.37447i	4.01917	−	0.488015i
$370$	10.2101	+	1.23973i	0.530796	+	0.0644503i
$371$	12.9437	+	24.6621i	0.672003	+	1.28039i
$372$	31.7866	−	35.8797i	1.64806	−	1.86028i
$373$	4.67844	−	6.77789i	0.242240	−	0.350946i	−0.682939	−	0.730475i	$-0.739299\pi$
$373$	4.67844	−	6.77789i	0.242240	−	0.350946i	0.925180	+	0.379529i	$0.123914\pi$
$374$	2.64526	−	0.651998i	0.136783	−	0.0337140i
$375$	−33.5274	+	4.07096i	−1.73135	+	0.210224i
$376$	−1.64000	−	2.37594i	−0.0845763	−	0.122530i
$377$	−11.6034	+	25.3941i	−0.597605	+	1.30786i
$378$	55.6164	−	80.5742i	2.86060	−	4.14429i
$379$	−0.867937	+	1.65372i	−0.0445829	+	0.0849456i	−0.906728	−	0.421715i	$-0.861428\pi$
$379$	−0.867937	+	1.65372i	−0.0445829	+	0.0849456i	0.862145	+	0.506661i	$0.169120\pi$
$380$	−1.60951	−	4.24393i	−0.0825661	−	0.217709i
$381$	−0.282008	+	2.32254i	−0.0144477	+	0.118987i
$382$	−26.3568	+	18.1928i	−1.34853	+	0.930823i
$383$	1.46805	−	5.95610i	0.0750137	−	0.304342i	−0.921436	−	0.388530i	$-0.872983\pi$
$383$	1.46805	−	5.95610i	0.0750137	−	0.304342i	0.996450	+	0.0841870i	$0.0268293\pi$
$384$	−16.1162	+	11.1242i	−0.822429	+	0.567682i
$385$	−2.08947	+	0.792430i	−0.106489	+	0.0403860i
$386$	−4.19301	−	11.0561i	−0.213418	−	0.562738i
$387$	−30.2499	+	15.8764i	−1.53769	+	0.807042i
$388$	12.9961	+	24.7620i	0.659776	+	1.25710i
$389$	32.3576	+	7.97544i	1.64060	+	0.404371i	0.948334	−	0.317274i	$-0.102768\pi$
$389$	32.3576	+	7.97544i	1.64060	+	0.404371i	0.692263	+	0.721645i	$0.256614\pi$
$390$	5.48662	−	29.0065i	0.277826	−	1.46880i
$391$	−11.6554	+	2.87281i	−0.589441	+	0.145284i
$392$	−0.349512	−	0.394518i	−0.0176530	−	0.0199261i
$393$	0.434975	+	3.58234i	0.0219416	+	0.180705i
$394$	3.32324	−	1.74417i	0.167422	−	0.0878700i
$395$	−5.62263	+	10.7130i	−0.282905	+	0.539031i
$396$	−12.1651	−	4.61361i	−0.611318	−	0.231842i
$397$	−13.3863	−	15.1101i	−0.671841	−	0.758352i	0.309443	−	0.950918i	$-0.399857\pi$
$397$	−13.3863	−	15.1101i	−0.671841	−	0.758352i	−0.981284	+	0.192566i	$0.938319\pi$
$398$	2.19513	+	0.266536i	0.110032	+	0.0133603i
$399$	−14.6511	−	3.61118i	−0.733474	−	0.180785i
$400$	8.53005	−	7.55697i	0.426503	−	0.377848i
$401$	−7.03223	+	7.93775i	−0.351173	+	0.396392i	−0.897381	−	0.441258i	$-0.854533\pi$
$401$	−7.03223	+	7.93775i	−0.351173	+	0.396392i	0.546208	+	0.837650i	$0.316071\pi$
$402$	10.5944	−	5.56040i	0.528403	−	0.277327i
$403$	−13.4827	−	17.4128i	−0.671622	−	0.867396i
$404$	26.9073	+	14.1221i	1.33869	+	0.702599i
$405$	35.2604	−	13.3725i	1.75210	−	0.664485i
$406$	−5.40869	+	44.5445i	−0.268429	+	2.21071i
$407$	−2.52892	−	1.32728i	−0.125354	−	0.0657909i
$408$			4.75237i			0.235277i
$409$	11.4290	−	21.7761i	0.565127	−	1.07676i	−0.420415	−	0.907332i	$-0.638116\pi$
$409$	11.4290	−	21.7761i	0.565127	−	1.07676i	0.985543	−	0.169428i	$-0.0541921\pi$
$410$	15.7091	−	17.7319i	0.775818	−	0.875718i
$411$	52.1392	+	35.9891i	2.57184	+	1.77521i
$412$	−32.3025	+	28.6175i	−1.59143	+	1.40988i
$413$	−13.2669	+	19.2204i	−0.652822	+	0.945776i
$414$	99.0636	+	37.5699i	4.86871	+	1.84646i
$415$	2.72631	−	7.18869i	0.133829	−	0.352879i
$416$	11.8090	+	26.6430i	0.578982	+	1.30628i
$417$	−6.15191	−	16.2213i	−0.301261	−	0.794359i
$418$			2.32943i			0.113936i
$419$	13.7994	−	36.3860i	0.674145	−	1.77757i	0.0467045	−	0.998909i	$-0.485128\pi$
$419$	13.7994	−	36.3860i	0.674145	−	1.77757i	0.627440	−	0.778665i	$-0.284103\pi$
$420$	−3.09438	−	25.4845i	−0.150990	−	1.24352i
$421$	5.16794	+	9.84669i	0.251870	+	0.479898i	0.978259	−	0.207385i	$-0.0664953\pi$
$421$	5.16794	+	9.84669i	0.251870	+	0.479898i	−0.726389	+	0.687283i	$0.758803\pi$
$422$	−7.11188	−	4.90898i	−0.346201	−	0.238965i
$423$	−25.6722	−	17.7203i	−1.24823	−	0.861589i
$424$	3.48550	+	6.64106i	0.169271	+	0.322519i
$425$	−0.831555	−	6.84847i	−0.0403363	−	0.332200i
$426$	11.8674	−	31.2918i	0.574977	−	1.51609i
$427$			3.89490i			0.188487i
$428$	5.25229	+	13.8492i	0.253879	+	0.669424i
$429$	−4.28087	+	6.99114i	−0.206682	+	0.337535i
$430$	−3.69005	+	9.72987i	−0.177950	+	0.469216i
$431$	17.2388	+	6.53780i	0.830362	+	0.314915i	0.732910	−	0.680325i	$-0.238162\pi$
$431$	17.2388	+	6.53780i	0.830362	+	0.314915i	0.0974518	+	0.995240i	$0.468931\pi$
$432$	−30.2872	+	43.8786i	−1.45720	+	2.11111i
$433$	0.222728	−	0.197320i	0.0107036	−	0.00948259i	−0.657754	−	0.753233i	$-0.728493\pi$
$433$	0.222728	−	0.197320i	0.0107036	−	0.00948259i	0.668458	+	0.743750i	$0.266955\pi$
$434$	−29.1288	−	20.1062i	−1.39823	−	0.965127i
$435$	−20.1391	+	22.7324i	−0.965597	+	1.08993i
$436$	−0.0648043	+	0.123474i	−0.00310356	+	0.00591334i
$437$		−	10.2639i		−	0.490987i
$438$	70.4877	+	36.9948i	3.36803	+	1.76768i
$439$	−1.45464	+	11.9801i	−0.0694264	+	0.571777i	0.915938	+	0.401319i	$0.131448\pi$
$439$	−1.45464	+	11.9801i	−0.0694264	+	0.571777i	−0.985365	+	0.170459i	$0.945475\pi$
$440$	−0.562655	+	0.213387i	−0.0268235	+	0.0101728i
$441$	−5.04270	−	2.64661i	−0.240128	−	0.126029i
$442$	14.1285	+	2.67243i	0.672025	+	0.127114i
$443$	−7.72754	+	4.05573i	−0.367147	+	0.192693i	−0.638199	−	0.769871i	$-0.720320\pi$
$443$	−7.72754	+	4.05573i	−0.367147	+	0.192693i	0.271053	+	0.962564i	$0.412628\pi$
$444$	21.7571	−	24.5587i	1.03255	−	1.16550i
$445$	−8.30790	+	7.36016i	−0.393832	+	0.348905i
$446$	−24.7267	−	6.09458i	−1.17084	−	0.288587i
$447$	−65.3916	−	7.93998i	−3.09292	−	0.375548i
$448$	19.4418	+	21.9452i	0.918537	+	1.03681i
$449$	−36.4802	−	13.8351i	−1.72161	−	0.652919i	−0.722353	−	0.691525i	$-0.756939\pi$
$449$	−36.4802	−	13.8351i	−1.72161	−	0.652919i	−0.999255	+	0.0386056i	$0.987708\pi$
$450$	−28.2960	+	53.9136i	−1.33389	+	2.54151i
$451$	−5.82488	+	3.05713i	−0.274283	+	0.143955i
$452$	1.80146	+	14.8364i	0.0847337	+	0.697844i
$453$	−26.2344	−	29.6125i	−1.23260	−	1.39132i
$454$	−9.81916	+	2.42020i	−0.460836	+	0.113586i
$455$	−11.7685	−	0.779178i	−0.551715	−	0.0365284i
$456$	−3.94528	−	0.972425i	−0.184755	−	0.0455380i
$457$	0.983520	+	1.87394i	0.0460071	+	0.0876592i	0.907374	−	0.420324i	$-0.138084\pi$
$457$	0.983520	+	1.87394i	0.0460071	+	0.0876592i	−0.861367	+	0.507983i	$0.830391\pi$
$458$	−22.8176	+	11.9756i	−1.06620	+	0.559584i
$459$	11.4452	+	30.1786i	0.534218	+	1.40862i
$460$	16.3270	−	6.19201i	0.761250	−	0.288704i
$461$	−17.4152	+	12.0208i	−0.811106	+	0.559866i	−0.899856	−	0.436188i	$-0.856328\pi$
$461$	−17.4152	+	12.0208i	−0.811106	+	0.559866i	0.0887498	+	0.996054i	$0.471713\pi$
$462$	−3.15302	+	12.7923i	−0.146692	+	0.595152i
$463$	−25.4055	+	17.5362i	−1.18069	+	0.814975i	−0.986140	−	0.165917i	$-0.946942\pi$
$463$	−25.4055	+	17.5362i	−1.18069	+	0.814975i	−0.194555	+	0.980892i	$0.562326\pi$
$464$	2.94543	−	24.2578i	0.136738	−	1.12614i
$465$	−8.49474	−	22.3988i	−0.393934	−	1.03872i
$466$	19.7477	−	37.6261i	0.914795	−	1.74300i
$467$	−1.73276	+	2.51034i	−0.0801828	+	0.116165i	−0.861023	−	0.508566i	$-0.830176\pi$
$467$	−1.73276	+	2.51034i	−0.0801828	+	0.116165i	0.780840	+	0.624731i	$0.214791\pi$
$468$	−48.2777	−	48.8310i	−2.23164	−	2.25721i
$469$	−2.71551	−	3.93409i	−0.125391	−	0.181660i
$470$	−9.43246	+	1.14531i	−0.435087	+	0.0528291i
$471$	−19.0700	+	4.70032i	−0.878697	+	0.216579i
$472$	−3.57254	+	5.17571i	−0.164439	+	0.238231i
$473$	1.91621	−	2.16296i	0.0881076	−	0.0994529i
$474$	33.1497	+	63.1614i	1.52261	+	2.90110i
$475$	5.85556	+	0.710993i	0.268671	+	0.0326226i
$476$	12.4130	−	1.50721i	0.568950	−	0.0690830i
$477$	60.6591	+	53.7393i	2.77739	+	2.46055i
$478$	18.9278	+	27.4216i	0.865736	+	1.25424i
$479$	0.0107135	+	0.00130086i	0.000489513	+	5.94376e-5i	0.120781	−	0.992679i	$-0.461460\pi$
$479$	0.0107135	+	0.00130086i	0.000489513	+	5.94376e-5i	−0.120292	+	0.992739i	$0.538383\pi$
$480$	3.82110	+	31.4696i	0.174409	+	1.43638i
$481$	−9.22855	−	11.9186i	−0.420786	−	0.543442i
$482$	0.796788	−	6.56214i	0.0362927	−	0.298897i
$483$	13.8927	−	56.3650i	0.632140	−	2.56469i
$484$	−24.8381			−1.12901
$485$	13.9757			0.634602
$486$	27.8856	−	113.137i	1.26492	−	5.13198i
$487$	15.3091	−	5.80598i	0.693722	−	0.263094i	0.0175585	−	0.999846i	$-0.494411\pi$
$487$	15.3091	−	5.80598i	0.693722	−	0.263094i	0.676163	+	0.736752i	$0.263641\pi$
$488$			1.04882i			0.0474781i
$489$	−4.54036	−	1.72193i	−0.205322	−	0.0778685i
$490$	−1.68430	+	0.415143i	−0.0760890	+	0.0187542i
$491$	15.0592	+	13.3413i	0.679613	+	0.602084i	0.930658	−	0.365891i	$-0.119236\pi$
$491$	15.0592	+	13.3413i	0.679613	+	0.602084i	−0.251045	+	0.967975i	$0.580774\pi$
$492$	−18.0855	−	73.3756i	−0.815356	−	3.30803i
$493$	−11.0725	−	9.80938i	−0.498680	−	0.441792i
$494$	−5.10953	+	11.1823i	−0.229889	+	0.503113i
$495$	−4.86686	+	4.31166i	−0.218749	+	0.193795i
$496$	15.8628	+	10.9493i	0.712261	+	0.491638i
$497$	−12.9821	−	3.19981i	−0.582328	−	0.143531i
$498$	−25.7495	−	37.3045i	−1.15386	−	1.67166i
$499$	2.93964	+	11.9266i	0.131596	+	0.533908i	0.999320	+	0.0368614i	$0.0117360\pi$
$499$	2.93964	+	11.9266i	0.131596	+	0.533908i	−0.867724	+	0.497047i	$0.834418\pi$
$500$	5.72666	+	23.2340i	0.256104	+	1.03905i
$501$	10.4453	−	1.26830i	0.466664	−	0.0566632i
$502$	−28.5301	−	32.2038i	−1.27336	−	1.43733i
$503$	−1.06196	+	2.80015i	−0.0473504	+	0.124853i	−0.956605	−	0.291387i	$-0.905883\pi$
$503$	−1.06196	+	2.80015i	−0.0473504	+	0.124853i	0.909255	+	0.416240i	$0.136652\pi$
$504$	−14.8381	−	7.78764i	−0.660942	−	0.346889i
$505$	12.4983	−	8.62693i	0.556166	−	0.383893i
$506$	−8.96165			−0.398394
$507$	−35.8848	+	24.1705i	−1.59370	+	1.07345i
$508$	1.65766			0.0735466
$509$	25.1803	−	17.3807i	1.11610	−	0.770386i	0.140528	−	0.990077i	$-0.455120\pi$
$509$	25.1803	−	17.3807i	1.11610	−	0.770386i	0.975570	+	0.219690i	$0.0705047\pi$
$510$	13.8495	+	7.26880i	0.613268	+	0.321868i
$511$	11.2780	−	29.7377i	0.498910	−	1.31552i
$512$	−20.0423	−	22.6231i	−0.885755	−	0.999811i
$513$	−27.3953	+	3.32639i	−1.20953	+	0.146864i
$514$	−3.20707	−	13.0116i	−0.141458	−	0.573916i
$515$	5.16136	+	20.9404i	0.227437	+	0.922746i
$516$	18.8576	+	27.3200i	0.830160	+	1.20269i
$517$	2.56188	+	0.631446i	0.112671	+	0.0277710i
$518$	−19.9379	−	13.7621i	−0.876020	−	0.604673i
$519$	−21.8157	+	19.3270i	−0.957604	+	0.848363i
$520$	−3.16904	−	0.209818i	−0.138972	−	0.00920115i
$521$	−2.55075	−	2.25977i	−0.111750	−	0.0990022i	0.605397	−	0.795923i	$-0.293014\pi$
$521$	−2.55075	−	2.25977i	−0.111750	−	0.0990022i	−0.717148	+	0.696921i	$0.754553\pi$
$522$	31.2448	+	126.765i	1.36755	+	5.54836i
$523$	30.4081	+	26.9392i	1.32965	+	1.17797i	0.969505	+	0.245073i	$0.0788120\pi$
$523$	30.4081	+	26.9392i	1.32965	+	1.17797i	0.360147	+	0.932895i	$0.382726\pi$
$524$	2.48251	−	0.611884i	0.108449	−	0.0267303i
$525$	31.1940	+	11.8303i	1.36142	+	0.516318i
$526$		−	17.7394i		−	0.773474i
$527$	10.9100	−	4.13763i	0.475248	−	0.180238i
$528$	1.71705	−	6.96636i	0.0747251	−	0.303172i
$529$	16.4865			0.716803
$530$	24.6848			1.07224
$531$	−16.2621	+	65.9781i	−0.705716	+	2.86320i
$532$	−1.28869	+	10.6133i	−0.0558719	+	0.460147i
$533$	−34.6676	+	1.89884i	−1.50162	+	0.0822480i
$534$	7.88773	+	64.9613i	0.341335	+	2.81115i
$535$	7.34819	+	0.892232i	0.317690	+	0.0385746i
$536$	−0.731237	−	1.05938i	−0.0315846	−	0.0457582i
$537$	−4.16366	−	3.68868i	−0.179675	−	0.159178i
$538$	30.5006	−	3.70344i	1.31497	−	0.159667i
$539$	0.478201	+	0.0580641i	0.0205976	+	0.00250100i
$540$	−21.8185	−	41.5717i	−0.938920	−	1.78896i
$541$	−6.49620	+	7.33269i	−0.279293	+	0.315257i	−0.871372	−	0.490623i	$-0.836769\pi$
$541$	−6.49620	+	7.33269i	−0.279293	+	0.315257i	0.592078	+	0.805880i	$0.298308\pi$
$542$	−17.9489	+	26.0035i	−0.770973	+	1.11695i
$543$	17.0238	−	4.19599i	0.730561	−	0.180067i
$544$	−15.3282	+	1.86119i	−0.657193	+	0.0797977i
$545$	0.0395878	+	0.0573529i	0.00169576	+	0.00245673i
$546$	−43.1953	+	54.4924i	−1.84859	+	2.33206i
$547$	−7.63215	+	11.0571i	−0.326327	+	0.472767i	−0.951469	−	0.307745i	$-0.900426\pi$
$547$	−7.63215	+	11.0571i	−0.326327	+	0.472767i	0.625142	+	0.780511i	$0.285041\pi$
$548$	20.8603	−	39.7459i	0.891107	−	1.69786i
$549$	4.01860	+	10.5962i	0.171510	+	0.452234i
$550$	0.620787	−	5.11264i	0.0264705	−	0.218004i
$551$	10.4091	−	7.18489i	0.443443	−	0.306087i
$552$	3.74105	−	15.1781i	0.159230	−	0.646021i
$553$	23.4541	−	16.1892i	0.997368	−	0.688433i
$554$	−29.6305	+	11.2374i	−1.25888	+	0.477430i
$555$	−5.81442	−	15.3314i	−0.246808	−	0.650780i
$556$	−10.8839	+	5.71232i	−0.461581	+	0.242256i
$557$	−11.2419	−	21.4197i	−0.476335	−	0.907580i	−0.998501	−	0.0547363i	$-0.982568\pi$
$557$	−11.2419	−	21.4197i	−0.476335	−	0.907580i	0.522166	−	0.852844i	$-0.325124\pi$
$558$	−99.9906	−	24.6455i	−4.23294	−	1.04333i
$559$	13.9430	−	6.17996i	0.589727	−	0.261384i
$560$	10.0227	−	2.47038i	0.423537	−	0.104393i
$561$	−2.88021	−	3.25109i	−0.121603	−	0.137261i
$562$	3.32185	+	27.3579i	0.140124	+	1.15402i
$563$	14.0158	−	7.35607i	0.590697	−	0.310022i	−0.142760	−	0.989757i	$-0.545598\pi$
$563$	14.0158	−	7.35607i	0.590697	−	0.310022i	0.733457	+	0.679736i	$0.237906\pi$
$564$	−14.0863	+	26.8393i	−0.593142	+	1.13014i
$565$	6.98361	+	2.64853i	0.293803	+	0.111425i
$566$	−24.6249	−	27.7958i	−1.03506	−	1.16834i
$567$	−88.1802	−	10.7070i	−3.70322	−	0.449652i
$568$	−3.49585	−	0.861650i	−0.146683	−	0.0361540i
$569$	14.0174	−	12.4183i	0.587639	−	0.520603i	−0.316078	−	0.948733i	$-0.602366\pi$
$569$	14.0174	−	12.4183i	0.587639	−	0.520603i	0.903717	+	0.428130i	$0.140828\pi$
$570$	−8.86823	+	10.0102i	−0.371449	+	0.419279i
$571$	26.0765	−	13.6860i	1.09127	−	0.572741i	0.179629	−	0.983734i	$-0.442510\pi$
$571$	26.0765	−	13.6860i	1.09127	−	0.572741i	0.911638	+	0.410993i	$0.134818\pi$
$572$	5.28285	+	2.41390i	0.220887	+	0.100930i
$573$	45.2088	+	23.7274i	1.88863	+	0.991228i
$574$	−52.1745	+	19.7872i	−2.17772	+	0.825901i
$575$	−2.73529	+	22.5271i	−0.114070	+	0.939447i
$576$	75.5341	+	39.6434i	3.14725	+	1.65181i
$577$			22.5686i			0.939545i	0.882788	+	0.469772i	$0.155664\pi$
$577$			22.5686i			0.939545i	−0.882788	+	0.469772i	$0.844336\pi$
$578$	12.9521	−	24.6782i	0.538737	−	1.02648i
$579$	−12.5006	+	14.1102i	−0.519506	+	0.586401i
$580$	17.7088	+	12.2235i	0.735320	+	0.507554i
$581$	−13.5553	+	12.0090i	−0.562370	+	0.498216i
$582$	46.8069	−	67.8115i	1.94021	−	2.81088i
$583$	−6.40929	−	2.43072i	−0.265446	−	0.100670i
$584$	3.03696	−	8.00782i	0.125670	−	0.331366i
$585$	−32.8205	+	10.0225i	−1.35696	+	0.414379i
$586$	−6.62959	−	17.4808i	−0.273866	−	0.722125i
$587$			2.05306i			0.0847388i	0.999102	+	0.0423694i	$0.0134906\pi$
$587$			2.05306i			0.0847388i	−0.999102	+	0.0423694i	$0.986509\pi$
$588$	−1.96233	+	5.17424i	−0.0809251	+	0.213382i
$589$	1.20254	+	9.90383i	0.0495499	+	0.408080i
$590$	9.61903	+	18.3275i	0.396009	+	0.754533i
$591$	−4.92426	−	3.39897i	−0.202557	−	0.139815i
$592$	10.8577	+	7.49450i	0.446247	+	0.308022i
$593$	6.19000	+	11.7941i	0.254193	+	0.484324i	0.978795	−	0.204844i	$-0.0656686\pi$
$593$	6.19000	+	11.7941i	0.254193	+	0.484324i	−0.724602	+	0.689168i	$0.757976\pi$
$594$	2.90436	+	23.9196i	0.119167	+	0.981433i
$595$	2.21593	−	5.84291i	0.0908441	−	0.239536i
$596$			46.6716i			1.91174i
$597$	−1.25008	−	3.29619i	−0.0511623	−	0.134904i
$598$	−43.0197	−	19.6571i	−1.75921	−	0.803838i
$599$	−1.83443	+	4.83700i	−0.0749529	+	0.197634i	−0.967256	−	0.253802i	$-0.918319\pi$
$599$	−1.83443	+	4.83700i	−0.0749529	+	0.197634i	0.892303	+	0.451436i	$0.149088\pi$
$600$	8.39997	+	3.18569i	0.342928	+	0.130055i
$601$	2.38770	−	3.45919i	0.0973965	−	0.141103i	−0.771256	−	0.636525i	$-0.780371\pi$
$601$	2.38770	−	3.45919i	0.0973965	−	0.141103i	0.868652	+	0.495422i	$0.164987\pi$
$602$	18.3471	−	16.2541i	0.747772	−	0.662468i
$603$	−11.4467	−	7.90106i	−0.466144	−	0.321756i
$604$	−18.5876	+	20.9810i	−0.756318	+	0.853707i
$605$	−5.76856	+	10.9911i	−0.234525	+	0.446851i
$606$		−	89.5360i		−	3.63715i
$607$	2.09806	+	1.10114i	0.0851575	+	0.0446941i	0.506764	−	0.862085i	$-0.330841\pi$
$607$	2.09806	+	1.10114i	0.0851575	+	0.0446941i	−0.421607	+	0.906779i	$0.638534\pi$
$608$	1.59134	−	13.1059i	0.0645375	−	0.531514i
$609$	66.8878	−	25.3672i	2.71043	−	1.02793i
$610$	3.05652	+	1.60419i	0.123755	+	0.0649517i
$611$	10.9130	+	8.65061i	0.441494	+	0.349966i
$612$	32.2149	−	16.9077i	1.30221	−	0.683453i
$613$	−16.3721	+	18.4802i	−0.661261	+	0.746409i	−0.979465	−	0.201613i	$-0.935382\pi$
$613$	−16.3721	+	18.4802i	−0.661261	+	0.746409i	0.318204	+	0.948022i	$0.396920\pi$
$614$	31.2575	−	27.6917i	1.26145	−	1.11755i
$615$	−36.6696	−	9.03825i	−1.47866	−	0.364457i
$616$	1.40710	+	0.170853i	0.0566938	+	0.00688388i
$617$	−16.3897	−	18.5001i	−0.659823	−	0.744786i	0.319390	−	0.947623i	$-0.396522\pi$
$617$	−16.3897	−	18.5001i	−0.659823	−	0.744786i	−0.979212	+	0.202838i	$0.934984\pi$
$618$	118.892	+	45.0896i	4.78252	+	1.81377i
$619$	16.0853	−	30.6480i	0.646522	−	1.23185i	−0.312877	−	0.949794i	$-0.601293\pi$
$619$	16.0853	−	30.6480i	0.646522	−	1.23185i	0.959399	−	0.282052i	$-0.0910150\pi$
$620$	−15.0288	+	7.88773i	−0.603572	+	0.316779i
$621$	−12.7971	−	105.394i	−0.513530	−	4.22930i
$622$	−7.29605	−	8.23554i	−0.292545	−	0.330215i
$623$	25.3845	−	6.25671i	1.01701	−	0.250670i
$624$	23.5231	−	29.6752i	0.941676	−	1.18796i
$625$	−5.92045	−	1.45926i	−0.236818	−	0.0583704i
$626$	19.5360	+	37.2227i	0.780814	+	1.48772i
$627$	3.28830	−	1.72584i	0.131322	−	0.0689232i
$628$	4.93462	+	13.0115i	0.196913	+	0.519216i
$629$	7.46762	−	2.83209i	0.297753	−	0.112923i
$630$	−45.3901	+	31.3305i	−1.80838	+	1.24824i
$631$	−11.5283	+	46.7723i	−0.458936	+	1.86198i	0.0461941	+	0.998932i	$0.485291\pi$
$631$	−11.5283	+	46.7723i	−0.458936	+	1.86198i	−0.505130	+	0.863043i	$0.668555\pi$
$632$	6.31575	−	4.35945i	0.251227	−	0.173410i
$633$	−1.66061	+	13.6764i	−0.0660033	+	0.543586i
$634$	−5.11966	−	13.4994i	−0.203328	−	0.536131i
$635$	0.384984	−	0.733527i	0.0152776	−	0.0291091i
$636$	44.7329	−	64.8068i	1.77378	−	2.56976i
$637$	2.16821	+	1.32765i	0.0859074	+	0.0526035i
$638$	−6.27332	−	9.08847i	−0.248363	−	0.359816i
$639$	−38.6197	+	4.68928i	−1.52777	+	0.185505i
$640$	6.73244	−	1.65940i	0.266123	−	0.0655935i
$641$	14.5296	−	21.0497i	0.573883	−	0.831413i	−0.423333	−	0.905974i	$-0.639140\pi$
$641$	14.5296	−	21.0497i	0.573883	−	0.831413i	0.997216	+	0.0745608i	$0.0237555\pi$
$642$	28.9396	−	32.6660i	1.14215	−	1.28922i
$643$	−15.7498	−	30.0087i	−0.621111	−	1.18343i	−0.969272	−	0.245993i	$-0.920886\pi$
$643$	−15.7498	−	30.0087i	−0.621111	−	1.18343i	0.348161	−	0.937435i	$-0.386806\pi$
$644$	−40.8310	−	4.95778i	−1.60897	−	0.195364i
$645$	16.4689	−	1.99969i	0.648463	−	0.0787377i
$646$	−4.87576	−	4.31954i	−0.191834	−	0.169950i
$647$	−0.297211	−	0.430585i	−0.0116846	−	0.0169280i	0.817098	−	0.576499i	$-0.195581\pi$
$647$	−0.297211	−	0.430585i	−0.0116846	−	0.0169280i	−0.828783	+	0.559571i	$0.810966\pi$
$648$	−23.7453	−	2.88320i	−0.932804	−	0.113263i
$649$	−0.692817	−	5.70586i	−0.0271954	−	0.223975i
$650$	14.1945	−	23.1812i	0.556753	−	0.909241i
$651$	−6.80152	+	56.0156i	−0.266573	+	2.19542i
$652$	−0.823369	+	3.34054i	−0.0322456	+	0.130826i
$653$	24.2882			0.950470			0.475235	−	0.879859i	$-0.342363\pi$
$653$	24.2882			0.950470			0.475235	+	0.879859i	$0.342363\pi$
$654$	0.410869			0.0160662
$655$	0.305790	−	1.24064i	0.0119482	−	0.0484758i
$656$	28.4129	−	10.7756i	1.10934	−	0.420716i
$657$		−	92.5385i		−	3.61027i
$658$	20.9268	+	7.93650i	0.815813	+	0.309397i
$659$	−6.88578	+	1.69719i	−0.268232	+	0.0661132i	−0.371138	−	0.928578i	$-0.621032\pi$
$659$	−6.88578	+	1.69719i	−0.268232	+	0.0661132i	0.102906	+	0.994691i	$0.467186\pi$
$660$	4.72911	+	4.18963i	0.184081	+	0.163081i
$661$	−5.95474	−	24.1593i	−0.231613	−	0.939690i	−0.965497	−	0.260415i	$-0.916141\pi$
$661$	−5.95474	−	24.1593i	−0.231613	−	0.939690i	0.733884	−	0.679275i	$-0.237705\pi$
$662$	37.6759	+	33.3779i	1.46431	+	1.29727i
$663$	−6.69508	−	21.9242i	−0.260015	−	0.851467i
$664$	−3.65020	+	3.23380i	−0.141655	+	0.125496i
$665$	4.39720	+	3.03517i	0.170516	+	0.117699i
$666$	−68.4408	−	16.8691i	−2.65203	−	0.653666i
$667$	27.6413	+	40.0453i	1.07027	+	1.55056i
$668$	−1.78412	−	7.23847i	−0.0690297	−	0.280065i
$669$	9.71626	+	39.4204i	0.375652	+	1.52408i
$670$	−4.20572	+	0.510667i	−0.162481	+	0.0197288i
$671$	−0.635648	−	0.717499i	−0.0245389	−	0.0276987i
$672$	26.4786	−	69.8184i	1.02144	−	2.69330i
$673$	−15.6687	−	8.22355i	−0.603982	−	0.316994i	0.134868	−	0.990864i	$-0.456939\pi$
$673$	−15.6687	−	8.22355i	−0.603982	−	0.316994i	−0.738851	+	0.673869i	$0.764631\pi$
$674$	−58.0979	+	40.1021i	−2.23785	+	1.54468i
$675$	61.0138			2.34842
$676$	20.0651	+	23.1755i	0.771734	+	0.891366i
$677$	39.4430			1.51592			0.757958	−	0.652303i	$-0.226197\pi$
$677$	39.4430			1.51592			0.757958	+	0.652303i	$0.226197\pi$
$678$	36.2403	−	25.0148i	1.39180	−	0.960689i
$679$	−29.1488	−	15.2985i	−1.11863	−	0.587102i
$680$	0.596708	−	1.57339i	0.0228827	−	0.0603368i
$681$	10.6913	+	12.0680i	0.409691	+	0.462446i
$682$	8.64730	−	1.04997i	0.331122	−	0.0402055i
$683$	1.68997	+	6.85649i	0.0646650	+	0.262356i	0.994372	−	0.105943i	$-0.0337862\pi$
$683$	1.68997	+	6.85649i	0.0646650	+	0.262356i	−0.929707	+	0.368300i	$0.879940\pi$
$684$	7.44450	+	30.2035i	0.284648	+	1.15486i
$685$	−12.7432	−	18.4617i	−0.486892	−	0.705385i
$686$	−35.4174	−	8.72960i	−1.35224	−	0.333298i
$687$	33.8104	+	23.3376i	1.28995	+	0.890386i
$688$	−9.99136	+	8.85157i	−0.380917	+	0.337463i
$689$	−25.4356	−	25.7271i	−0.969019	−	0.980124i
$690$	−38.5105	−	34.1173i	−1.46607	−	1.29882i
$691$	−9.32311	−	37.8253i	−0.354668	−	1.43894i	−0.829322	−	0.558771i	$-0.811273\pi$
$691$	−9.32311	−	37.8253i	−0.354668	−	1.43894i	0.474654	−	0.880172i	$-0.342573\pi$
$692$	15.4569	+	13.6936i	0.587582	+	0.520553i
$693$	14.8705	−	3.66524i	0.564883	−	0.139231i
$694$	0.887979	+	0.336766i	0.0337072	+	0.0127835i
$695$			6.14289i			0.233013i
$696$	18.0117	−	6.83092i	0.682731	−	0.258926i
$697$	4.40236	−	17.8611i	0.166751	−	0.676537i
$698$	−36.5355			−1.38289
$699$	−67.7451			−2.56235
$700$	5.65686	−	22.9508i	0.213809	−	0.867458i
$701$	−3.04060	+	25.0416i	−0.114842	+	0.945807i	0.815410	+	0.578884i	$0.196512\pi$
$701$	−3.04060	+	25.0416i	−0.114842	+	0.945807i	−0.930251	+	0.366923i	$0.880411\pi$
$702$	−38.5247	+	121.195i	−1.45402	+	4.57420i
$703$	0.823107	+	6.77890i	0.0310441	+	0.255671i
$704$	−7.16293	−	0.869737i	−0.269963	−	0.0327795i
$705$	8.60511	+	12.4666i	0.324087	+	0.469521i
$706$	−10.4118	−	9.22406i	−0.391854	−	0.347152i
$707$	−35.5109	+	4.31180i	−1.33553	+	0.162162i
$708$	65.5480	+	7.95897i	2.46345	+	0.299116i
$709$	4.09557	+	7.80346i	0.153812	+	0.293065i	0.950153	−	0.311783i	$-0.100926\pi$
$709$	4.09557	+	7.80346i	0.153812	+	0.293065i	−0.796341	+	0.604848i	$0.793234\pi$
$710$	−7.85799	+	8.86984i	−0.294905	+	0.332879i
$711$	47.1041	−	68.2421i	1.76654	−	2.55928i
$712$	6.83557	−	1.68482i	0.256174	−	0.0631412i
$713$	−38.1014	+	4.62635i	−1.42691	+	0.173258i
$714$	−20.9290	−	30.3208i	−0.783247	−	1.13473i
$715$	2.29509	−	1.77708i	0.0858317	−	0.0664592i
$716$	−2.23886	+	3.24355i	−0.0836703	+	0.121217i
$717$	24.6860	−	47.0353i	0.921917	−	1.75657i
$718$	11.0974	+	29.2614i	0.414151	+	1.09203i
$719$	1.70788	−	14.0657i	0.0636933	−	0.524562i	−0.925587	−	0.378534i	$-0.876428\pi$
$719$	1.70788	−	14.0657i	0.0636933	−	0.524562i	0.989281	−	0.146027i	$-0.0466487\pi$
$720$	24.7183	−	17.0618i	0.921196	−	0.635855i
$721$	12.1575	−	49.3250i	0.452770	−	1.83696i
$722$	−28.0595	+	19.3680i	−1.04426	+	0.720804i
$723$	−9.85367	+	3.73700i	−0.366462	+	0.138981i
$724$	−4.40514	−	11.6154i	−0.163716	−	0.431683i
$725$	−24.7607	+	12.9954i	−0.919590	+	0.482638i
$726$	34.0100	+	64.8007i	1.26223	+	2.40498i
$727$	−24.4721	−	6.03182i	−0.907619	−	0.223708i	−0.242242	−	0.970216i	$-0.577883\pi$
$727$	−24.4721	−	6.03182i	−0.907619	−	0.223708i	−0.665377	+	0.746508i	$0.731729\pi$
$728$	6.37993	+	3.90661i	0.236456	+	0.144788i
$729$	−87.1551	+	21.4818i	−3.22797	+	0.795622i
$730$	−18.6916	−	21.0985i	−0.691808	−	0.780890i
$731$	0.974011	+	8.02170i	0.0360251	+	0.296693i
$732$	9.75054	−	5.11748i	0.360390	−	0.189147i
$733$	13.1057	−	24.9708i	0.484069	−	0.922316i	−0.513853	−	0.857878i	$-0.671782\pi$
$733$	13.1057	−	24.9708i	0.484069	−	0.922316i	0.997922	−	0.0644376i	$-0.0205254\pi$
$734$	56.9038	+	21.5808i	2.10036	+	0.796561i
$735$	1.83390	+	2.07005i	0.0676444	+	0.0763548i
$736$	50.4202	+	6.12213i	1.85851	+	0.225665i
$737$	1.14228	+	0.281547i	0.0420765	+	0.0103709i
$738$	−121.527	+	107.663i	−4.47346	+	3.96314i
$739$	24.5597	−	27.7222i	0.903443	−	1.01978i	−0.0962584	−	0.995356i	$-0.530688\pi$
$739$	24.5597	−	27.7222i	0.903443	−	1.01978i	0.999702	−	0.0244204i	$-0.00777403\pi$
$740$	−10.2868	+	5.39894i	−0.378151	+	0.198469i
$741$	19.5708	−	1.07195i	0.718952	−	0.0393790i
$742$	−51.4846	−	27.0212i	−1.89006	−	0.991979i
$743$	−23.0857	+	8.75526i	−0.846933	+	0.321200i	−0.739619	−	0.673026i	$-0.764994\pi$
$743$	−23.0857	+	8.75526i	−0.846933	+	0.321200i	−0.107314	+	0.994225i	$0.534225\pi$
$744$	−1.83153	+	15.0840i	−0.0671470	+	0.553005i
$745$	20.6526	+	10.8393i	0.756651	+	0.397121i
$746$			17.1929i			0.629477i
$747$	−24.4873	+	46.6566i	−0.895943	+	1.70708i
$748$	−2.04069	+	2.30346i	−0.0746150	+	0.0842229i
$749$	−14.3493	−	9.90462i	−0.524313	−	0.361907i
$750$	52.7743	−	46.7539i	1.92704	−	1.70721i
$751$	−15.2972	+	22.1618i	−0.558203	+	0.808697i	−0.995903	−	0.0904240i	$-0.971178\pi$
$751$	−15.2972	+	22.1618i	−0.558203	+	0.808697i	0.437700	+	0.899121i	$0.355793\pi$
$752$	−11.3962	−	4.32201i	−0.415577	−	0.157608i
$753$	−24.3225	+	64.1333i	−0.886363	+	2.33715i
$754$	−10.1793	−	57.3889i	−0.370709	−	2.08998i
$755$	4.96739	+	13.0979i	0.180782	+	0.476683i
$756$			110.589i			4.02209i
$757$	−12.1221	+	31.9633i	−0.440584	+	1.16173i	0.512411	+	0.858740i	$0.328753\pi$
$757$	−12.1221	+	31.9633i	−0.440584	+	1.16173i	−0.952995	+	0.302985i	$0.902017\pi$
$758$	−0.469958	−	3.87045i	−0.0170697	−	0.140581i
$759$	6.63953	+	12.6506i	0.241000	+	0.459187i
$760$	1.18409	+	0.817315i	0.0429513	+	0.0296471i
$761$	−36.7778	−	25.3859i	−1.33319	−	0.920237i	−0.333447	−	0.942769i	$-0.608212\pi$
$761$	−36.7778	−	25.3859i	−1.33319	−	0.920237i	−0.999746	+	0.0225320i	$0.992827\pi$
$762$	−2.26977	−	4.32469i	−0.0822252	−	0.156667i
$763$	−0.0197863	−	0.162955i	−0.000716312	−	0.00589936i
$764$	12.8278	−	33.8242i	0.464095	−	1.22372i
$765$		−	18.1821i		−	0.657376i
$766$	4.54109	+	11.9739i	0.164076	+	0.432633i
$767$	9.18981	−	28.9102i	0.331825	−	1.04389i

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.h (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.71806 + 1.18589i) q^{2} +(2.94692 + 1.54666i) q^{3} +(0.836178 - 2.20482i) q^{4} +(-0.781452 - 0.882078i) q^{5} +(-6.89716 + 0.837466i) q^{6} +(0.664295 + 2.69515i) q^{7} +(0.178883 + 0.725755i) q^{8} +(4.58799 + 6.64685i) q^{9} +O(q^{10})\)	\(q+(-1.71806 + 1.18589i) q^{2} +(2.94692 + 1.54666i) q^{3} +(0.836178 - 2.20482i) q^{4} +(-0.781452 - 0.882078i) q^{5} +(-6.89716 + 0.837466i) q^{6} +(0.664295 + 2.69515i) q^{7} +(0.178883 + 0.725755i) q^{8} +(4.58799 + 6.64685i) q^{9} +(2.38863 + 0.588744i) q^{10} +(-0.562223 - 0.388074i) q^{11} +(5.87427 - 5.20415i) q^{12} +(-1.84768 - 3.09614i) q^{13} +(-4.33745 - 3.84265i) q^{14} +(-0.938602 - 3.80806i) q^{15} +(2.36206 + 2.09261i) q^{16} +(1.85483 - 0.457175i) q^{17} +(-15.7649 - 5.97882i) q^{18} +1.63338i q^{19} +(-2.59826 + 0.985388i) q^{20} +(-2.21087 + 8.96985i) q^{21} +1.42614 q^{22} -6.28383 q^{23} +(-0.595347 + 2.41542i) q^{24} +(0.435291 - 3.58494i) q^{25} +(6.84610 + 3.12820i) q^{26} +(2.03651 + 16.7722i) q^{27} +(6.49780 + 0.788975i) q^{28} +(-4.39880 - 6.37276i) q^{29} +(6.12851 + 5.42939i) q^{30} +(6.06341 - 0.736231i) q^{31} +(-8.02381 - 0.974267i) q^{32} +(-1.05661 - 2.01320i) q^{33} +(-2.64455 + 2.98508i) q^{34} +(1.85822 - 2.69209i) q^{35} +(18.4915 - 4.55774i) q^{36} +(4.15024 - 0.503930i) q^{37} +(-1.93700 - 2.80623i) q^{38} +(-0.656278 - 11.9818i) q^{39} +(0.500384 - 0.724932i) q^{40} +(4.47504 - 8.52648i) q^{41} +(-6.83885 - 18.0326i) q^{42} +(-0.509861 + 4.19909i) q^{43} +(-1.32575 + 0.915101i) q^{44} +(2.27774 - 9.24116i) q^{45} +(10.7960 - 7.45192i) q^{46} +(-3.61133 + 1.36960i) q^{47} +(3.72426 + 9.82007i) q^{48} +(-0.624365 + 0.327692i) q^{49} +(3.50349 + 6.67534i) q^{50} +(6.17315 + 1.52154i) q^{51} +(-8.37142 + 1.48488i) q^{52} +(9.74242 - 2.40129i) q^{53} +(-23.3888 - 26.4005i) q^{54} +(0.0970387 + 0.799186i) q^{55} +(-1.83719 + 0.964232i) q^{56} +(-2.52628 + 4.81343i) q^{57} +(15.1148 + 5.73228i) q^{58} +(5.57925 + 6.29767i) q^{59} +(-9.18092 - 1.11477i) q^{60} +(1.36238 + 0.335797i) q^{61} +(-9.54420 + 8.45542i) q^{62} +(-14.8665 + 16.7808i) q^{63} +(9.35230 - 4.90847i) q^{64} +(-1.28716 + 4.04928i) q^{65} +(4.20274 + 2.20577i) q^{66} +(-1.61021 + 0.610672i) q^{67} +(0.542981 - 4.47185i) q^{68} +(-18.5180 - 9.71897i) q^{69} +6.82881i q^{70} +(-2.23850 + 4.26510i) q^{71} +(-4.00327 + 4.51876i) q^{72} +(-9.42952 - 6.50872i) q^{73} +(-6.53274 + 5.78751i) q^{74} +(6.82747 - 9.89130i) q^{75} +(3.60130 + 1.36579i) q^{76} +(0.672438 - 1.77307i) q^{77} +(15.3366 + 19.8072i) q^{78} +(-3.64067 - 9.59966i) q^{79} -3.71880i q^{80} +(-11.3476 + 29.9211i) q^{81} +(2.42308 + 19.9559i) q^{82} +(3.03191 + 5.77682i) q^{83} +(17.9282 + 12.3750i) q^{84} +(-1.85273 - 1.27885i) q^{85} +(-4.10368 - 7.81891i) q^{86} +(-3.10640 - 25.5835i) q^{87} +(0.181075 - 0.477456i) q^{88} -9.41856i q^{89} +(7.04570 + 18.5780i) q^{90} +(7.11716 - 7.03653i) q^{91} +(-5.25440 + 13.8547i) q^{92} +(19.0071 + 7.20844i) q^{93} +(4.58028 - 6.63568i) q^{94} +(1.44076 - 1.27641i) q^{95} +(-22.1387 - 15.2812i) q^{96} +(-7.86426 + 8.87691i) q^{97} +(0.684088 - 1.30342i) q^{98} -5.51749i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9}+O(q^{10}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9} - 9 q^{10} - 13 q^{11} - 9 q^{12} + 52 q^{13} - 15 q^{14} + 39 q^{15} - 31 q^{16} - 11 q^{17} + 26 q^{18} - 13 q^{20} - 13 q^{21} - 6 q^{22} - 102 q^{23} - 91 q^{24} + 3 q^{25} - 13 q^{26} - 19 q^{27} - 13 q^{28} - 17 q^{29} + 23 q^{30} + 39 q^{31} - 13 q^{33} + 52 q^{34} - 21 q^{35} + 11 q^{36} - 13 q^{37} - 40 q^{38} - 65 q^{39} + 53 q^{40} - 13 q^{41} + 101 q^{42} - 3 q^{43} - 39 q^{44} - 78 q^{45} - 39 q^{46} - 39 q^{47} + 8 q^{48} + 85 q^{49} - 13 q^{50} + 62 q^{51} - 78 q^{52} + 18 q^{53} + 65 q^{54} - 103 q^{55} + 3 q^{56} + 65 q^{57} + 39 q^{58} + 91 q^{59} - 117 q^{60} - 23 q^{61} - 64 q^{62} - 78 q^{63} + 15 q^{64} - 13 q^{65} + 134 q^{66} - 65 q^{67} + 40 q^{68} - 40 q^{69} + 26 q^{71} + 156 q^{72} - 13 q^{73} - 53 q^{74} + 35 q^{75} + 221 q^{76} + 3 q^{77} - 143 q^{78} - 23 q^{79} - 43 q^{81} - 129 q^{82} + 117 q^{83} + 234 q^{84} + 26 q^{85} - 91 q^{86} + 79 q^{87} + 95 q^{88} + 17 q^{90} + 39 q^{91} - 89 q^{92} + 52 q^{93} - 61 q^{94} + 122 q^{95} - 182 q^{96} - 91 q^{97} - 13 q^{98}+O(q^{100}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9 - 9 * q^10 - 13 * q^11 - 9 * q^12 + 52 * q^13 - 15 * q^14 + 39 * q^15 - 31 * q^16 - 11 * q^17 + 26 * q^18 - 13 * q^20 - 13 * q^21 - 6 * q^22 - 102 * q^23 - 91 * q^24 + 3 * q^25 - 13 * q^26 - 19 * q^27 - 13 * q^28 - 17 * q^29 + 23 * q^30 + 39 * q^31 - 13 * q^33 + 52 * q^34 - 21 * q^35 + 11 * q^36 - 13 * q^37 - 40 * q^38 - 65 * q^39 + 53 * q^40 - 13 * q^41 + 101 * q^42 - 3 * q^43 - 39 * q^44 - 78 * q^45 - 39 * q^46 - 39 * q^47 + 8 * q^48 + 85 * q^49 - 13 * q^50 + 62 * q^51 - 78 * q^52 + 18 * q^53 + 65 * q^54 - 103 * q^55 + 3 * q^56 + 65 * q^57 + 39 * q^58 + 91 * q^59 - 117 * q^60 - 23 * q^61 - 64 * q^62 - 78 * q^63 + 15 * q^64 - 13 * q^65 + 134 * q^66 - 65 * q^67 + 40 * q^68 - 40 * q^69 + 26 * q^71 + 156 * q^72 - 13 * q^73 - 53 * q^74 + 35 * q^75 + 221 * q^76 + 3 * q^77 - 143 * q^78 - 23 * q^79 - 43 * q^81 - 129 * q^82 + 117 * q^83 + 234 * q^84 + 26 * q^85 - 91 * q^86 + 79 * q^87 + 95 * q^88 + 17 * q^90 + 39 * q^91 - 89 * q^92 + 52 * q^93 - 61 * q^94 + 122 * q^95 - 182 * q^96 - 91 * q^97 - 13 * q^98

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