LMFDB - Embedded newform 169.2.h.a.155.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [169,2,Mod(12,169)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			155.3
Character	$\chi$	$=$	169.155
Dual form			169.2.h.a.12.3

$q$-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} +(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} - 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}+ \cdots - 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

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{26}\right)$

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	−0.224142	−	0.974556i	$-0.571958\pi$
$2$	−1.71806	−	1.18589i	−1.21485	−	0.838551i	−0.990708	+	0.136006i	$0.956573\pi$
$3$	2.94692	−	1.54666i	1.70141	−	0.892967i	0.721784	−	0.692118i	$-0.243322\pi$
$3$	2.94692	−	1.54666i	1.70141	−	0.892967i	0.979622	−	0.200849i	$-0.0643701\pi$
$4$	0.836178	+	2.20482i	0.418089	+	1.10241i
$5$	−0.781452	+	0.882078i	−0.349476	+	0.394477i	−0.896794	−	0.442448i	$-0.854110\pi$
$5$	−0.781452	+	0.882078i	−0.349476	+	0.394477i	0.547318	+	0.836925i	$0.315649\pi$
$6$	−6.89716	−	0.837466i	−2.81575	−	0.341894i
$7$	0.664295	−	2.69515i	0.251080	−	1.01867i	−0.701083	−	0.713080i	$-0.747300\pi$
$7$	0.664295	−	2.69515i	0.251080	−	1.01867i	0.952163	−	0.305592i	$-0.0988543\pi$
$8$	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	−0.649802	−	0.760103i	$-0.725148\pi$
$11$	−0.562223	+	0.388074i	−0.169517	+	0.117009i	0.480286	+	0.877112i	$0.340533\pi$
$12$	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	0.457737	−	0.889088i	$-0.348660\pi$
$17$	1.85483	+	0.457175i	0.449863	+	0.110881i	−0.00787380	+	0.999969i	$0.502506\pi$
$18$	−15.7649	+	5.97882i	−3.71581	+	1.40922i
$19$		−	1.63338i		−	0.374722i	−0.982291	−	0.187361i	$-0.940007\pi$
$19$		−	1.63338i		−	0.374722i	0.982291	−	0.187361i	$-0.0599934\pi$
$20$	−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	0.163595	+	0.986528i	$0.447691\pi$
$29$	−4.39880	+	6.37276i	−0.816836	+	1.18339i	−0.980431	+	0.196864i	$0.936924\pi$
$30$	6.12851	−	5.42939i	1.11891	−	0.991266i
$31$	6.06341	+	0.736231i	1.08902	+	0.132231i	0.645296	−	0.763932i	$-0.276734\pi$
$31$	6.06341	+	0.736231i	1.08902	+	0.132231i	0.443724	+	0.896163i	$0.353657\pi$
$32$	−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	0.454343	−	0.890827i	$-0.349874\pi$
$37$	4.15024	+	0.503930i	0.682295	+	0.0828456i	0.227952	+	0.973672i	$0.426797\pi$
$38$	−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	0.933167	+	0.359444i	$0.117034\pi$
$41$	4.47504	+	8.52648i	0.698884	+	1.33161i	−0.234282	+	0.972169i	$0.575274\pi$
$42$	−6.83885	+	18.0326i	−1.05526	+	2.78248i
$43$	−0.509861	−	4.19909i	−0.0777531	−	0.640355i	−0.978535	−	0.206082i	$-0.933929\pi$
$43$	−0.509861	−	4.19909i	−0.0777531	−	0.640355i	0.900782	−	0.434272i	$-0.142994\pi$
$44$	−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	0.0768623	−	0.997042i	$-0.475510\pi$
$47$	−3.61133	−	1.36960i	−0.526766	−	0.199776i	−0.603629	+	0.797266i	$0.706279\pi$
$48$	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	0.842528	−	0.538653i	$-0.181067\pi$
$53$	9.74242	+	2.40129i	1.33822	+	0.329843i	0.495697	+	0.868496i	$0.334913\pi$
$54$	−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	−0.263092	−	0.964771i	$-0.584742\pi$
$59$	5.57925	−	6.29767i	0.726356	−	0.819887i	0.989449	+	0.144884i	$0.0462808\pi$
$60$	−9.18092	+	1.11477i	−1.18525	+	0.143916i
$61$	1.36238	−	0.335797i	0.174435	−	0.0429944i	−0.151131	−	0.988514i	$-0.548291\pi$
$61$	1.36238	−	0.335797i	0.174435	−	0.0429944i	0.325566	+	0.945519i	$0.394445\pi$
$62$	−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	0.254278	−	0.967131i	$-0.418162\pi$
$67$	−1.61021	−	0.610672i	−0.196718	−	0.0746055i	−0.450997	+	0.892526i	$0.648931\pi$
$68$	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	0.715685	−	0.698423i	$-0.246114\pi$
$71$	−2.23850	−	4.26510i	−0.265661	−	0.506175i	−0.981346	+	0.192248i	$0.938422\pi$
$72$	−4.00327	−	4.51876i	−0.471790	−	0.532541i
$73$	−9.42952	+	6.50872i	−1.10364	+	0.761789i	−0.973267	−	0.229676i	$-0.926233\pi$
$73$	−9.42952	+	6.50872i	−1.10364	+	0.761789i	−0.130374	+	0.991465i	$0.541618\pi$
$74$	−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	0.558499	+	0.829505i	$0.311378\pi$
$79$	−3.64067	+	9.59966i	−0.409607	+	1.08005i	−0.968106	+	0.250541i	$0.919392\pi$
$80$			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	−0.660352	−	0.750956i	$-0.729593\pi$
$83$	3.03191	−	5.77682i	0.332795	−	0.634089i	0.993148	+	0.116867i	$0.0372853\pi$
$84$	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	$0.166366\pi$
$89$			9.41856i			0.998365i	−0.866497	+	0.499183i	$0.833634\pi$
$90$	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	0.198395	−	0.980122i	$-0.436427\pi$
$97$	−7.86426	−	8.87691i	−0.798494	−	0.901314i	−0.996890	+	0.0788082i	$0.974889\pi$
$98$	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	−0.839103	−	0.543973i	$-0.816920\pi$
$101$	−1.55335	−	12.7930i	−0.154564	−	1.27295i	0.684539	−	0.728976i	$-0.260004\pi$
$102$	−12.4102	−	4.70657i	−1.22879	−	0.466020i
$103$	−16.2051	+	8.50508i	−1.59673	+	0.838030i	−0.597384	+	0.801955i	$0.703793\pi$
$103$	−16.2051	+	8.50508i	−1.59673	+	0.838030i	−0.999349	+	0.0360750i	$0.988514\pi$
$104$	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	0.404557	−	0.914513i	$-0.367426\pi$
$107$	−4.70163	−	4.16528i	−0.454523	−	0.402673i	−0.859081	+	0.511840i	$0.828964\pi$
$108$	38.6826	−	9.53440i	3.72223	−	0.917448i
$109$	−0.0587053	+	0.00712811i	−0.00562295	+	0.000682749i	−0.123348	−	0.992364i	$-0.539363\pi$
$109$	−0.0587053	+	0.00712811i	−0.00562295	+	0.000682749i	0.117725	+	0.993046i	$0.462440\pi$
$110$	−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	0.179625	−	0.983735i	$-0.442511\pi$
$113$	−5.61202	−	2.94541i	−0.527934	−	0.277081i	−0.707559	+	0.706654i	$0.750204\pi$
$114$	−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	−0.923501	−	0.383595i	$-0.874686\pi$
$127$	0.249279	−	0.657293i	0.0221199	−	0.0583254i	0.945621	+	0.325270i	$0.105455\pi$
$128$	−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	−0.795152	−	0.606410i	$-0.792609\pi$
$131$	0.615944	−	0.892349i	0.0538153	−	0.0779649i	0.848968	+	0.528445i	$0.177225\pi$
$132$	−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	0.737085	−	0.675800i	$-0.236202\pi$
$137$	18.8970	−	2.29451i	1.61448	−	0.196034i	0.877396	+	0.479766i	$0.159278\pi$
$138$	43.3405	+	5.26249i	3.68939	+	0.447973i
$139$	−3.90177	+	3.45667i	−0.330944	+	0.293191i	−0.812188	−	0.583396i	$-0.801724\pi$
$139$	−3.90177	+	3.45667i	−0.330944	+	0.293191i	0.481244	+	0.876587i	$0.340185\pi$
$140$	−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	−0.550450	−	0.834868i	$-0.685544\pi$
$149$	−18.5062	−	7.01848i	−1.51609	−	0.574976i	−0.965638	+	0.259892i	$0.916313\pi$
$150$		−	25.0904i		−	2.04863i
$151$	−11.1146	+	4.21522i	−0.904494	+	0.343029i	−0.762614	−	0.646854i	$-0.776084\pi$
$151$	−11.1146	+	4.21522i	−0.904494	+	0.343029i	−0.141881	+	0.989884i	$0.545315\pi$
$152$	−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	0.468206	−	0.883620i	$-0.344901\pi$
$157$	−4.41726	−	3.91335i	−0.352536	−	0.312319i	−0.820741	+	0.571300i	$0.806439\pi$
$158$	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	0.0636156	−	0.997974i	$-0.479737\pi$
$163$	−1.44841	−	0.175869i	−0.113448	−	0.0137751i	−0.177064	+	0.984199i	$0.556660\pi$
$164$	−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	0.664469	−	0.747316i	$-0.268658\pi$
$167$	2.60190	+	1.79596i	0.201341	+	0.138976i	−0.463128	+	0.886291i	$0.653273\pi$
$168$	−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	0.763635	−	0.645648i	$-0.223413\pi$
$173$	−3.10538	−	8.18821i	−0.236098	−	0.622538i	−0.999733	+	0.0231097i	$0.992643\pi$
$174$	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	−0.299496	−	0.954098i	$-0.596818\pi$
$179$	−1.62281	+	0.399988i	−0.121295	+	0.0298965i	0.178201	+	0.983994i	$0.442972\pi$
$180$	−18.4705	+	12.7493i	−1.37671	+	0.950274i
$181$	3.94330	+	3.49346i	0.293103	+	0.259667i	0.796840	−	0.604191i	$-0.206503\pi$
$181$	3.94330	+	3.49346i	0.293103	+	0.259667i	−0.503737	+	0.863857i	$0.668042\pi$
$182$	−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	0.901766	−	0.432224i	$-0.142271\pi$
$193$	−1.35552	−	5.49956i	−0.0975724	−	0.395867i	−0.999339	+	0.0363568i	$0.988425\pi$
$194$	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	−0.183867	−	0.982951i	$-0.558862\pi$
$197$	−1.78472	+	0.216704i	−0.127156	+	0.0154395i	0.0567113	+	0.998391i	$0.481939\pi$
$198$	6.54314	−	9.47937i	0.465000	−	0.673669i
$199$	−0.792846	+	0.702401i	−0.0562034	+	0.0497919i	−0.690757	−	0.723087i	$-0.742722\pi$
$199$	−0.792846	+	0.702401i	−0.0562034	+	0.0497919i	0.634553	+	0.772879i	$0.281184\pi$
$200$	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	−0.874949	−	0.484214i	$-0.839105\pi$
$211$	1.46788	−	3.87049i	0.101053	−	0.266455i	0.976003	+	0.217759i	$0.0698747\pi$
$212$	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	−0.412369	−	0.911017i	$-0.635299\pi$
$223$	8.08947	−	9.13113i	0.541711	−	0.611465i	0.954080	+	0.299551i	$0.0968370\pi$
$224$	−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	−0.199674	−	0.979862i	$-0.563988\pi$
$227$	4.52954	−	1.71783i	0.300636	−	0.114016i	0.500310	+	0.865846i	$0.333219\pi$
$228$	8.50033	−	9.59489i	0.562948	−	0.635437i
$229$	12.2540	−	1.48791i	0.809769	−	0.0983238i	0.294829	−	0.955550i	$-0.404737\pi$
$229$	12.2540	−	1.48791i	0.809769	−	0.0983238i	0.514940	+	0.857226i	$0.327814\pi$
$230$	−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	−0.244038	−	0.969766i	$-0.578472\pi$
$233$	−18.0237	−	9.45955i	−1.18077	−	0.619716i	−0.936731	+	0.350050i	$0.886165\pi$
$234$	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	$0.172658\pi$
$239$			15.9608i			1.03242i	−0.856462	+	0.516210i	$0.827342\pi$
$240$	5.75173	+	10.9590i	0.371272	+	0.707401i
$241$	−2.09977	−	2.37015i	−0.135258	−	0.152675i	0.676979	−	0.736002i	$-0.263289\pi$
$241$	−2.09977	−	2.37015i	−0.135258	−	0.152675i	−0.812237	+	0.583328i	$0.801750\pi$
$242$	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	−0.675635	−	0.737237i	$-0.736130\pi$
$251$	2.48417	−	20.4590i	0.156800	−	1.29136i	0.832434	−	0.554124i	$-0.186947\pi$
$252$	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	0.845087	−	0.534628i	$-0.179548\pi$
$257$	−2.27633	−	6.00219i	−0.141994	−	0.374406i	−0.987081	+	0.160222i	$0.948779\pi$
$258$			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	0.645410	−	0.763836i	$-0.276686\pi$
$263$	−4.82714	−	6.99333i	−0.297654	−	0.431227i	−0.943065	+	0.332609i	$0.892071\pi$
$264$	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	−0.812604	−	0.582817i	$-0.801951\pi$
$269$	−13.0319	+	6.83965i	−0.794567	+	0.417021i	0.0180371	+	0.999837i	$0.494258\pi$
$270$	−5.01006	−	41.2615i	−0.304902	−	2.51110i
$271$	14.1519	+	5.36709i	0.859664	+	0.326028i	0.744747	−	0.667347i	$-0.232570\pi$
$271$	14.1519	+	5.36709i	0.859664	+	0.326028i	0.114918	+	0.993375i	$0.463340\pi$
$272$	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	0.229808	−	0.973236i	$-0.426190\pi$
$277$	14.7389	−	3.63282i	0.885577	−	0.218275i	0.655770	+	0.754961i	$0.272344\pi$
$278$	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	0.996912	−	0.0785223i	$-0.0250202\pi$
$281$	6.13493	+	11.6891i	0.365979	+	0.697315i	−0.630933	+	0.775837i	$0.717328\pi$
$282$	23.7609	+	12.4707i	1.41494	+	0.742619i
$283$	2.14414	−	17.6586i	0.127456	−	1.04970i	−0.778890	−	0.627160i	$-0.784217\pi$
$283$	2.14414	−	17.6586i	0.127456	−	1.04970i	0.906346	−	0.422535i	$-0.138860\pi$
$284$	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	−0.999735	−	0.0230129i	$-0.992674\pi$
$293$	−2.14322	−	8.69539i	−0.125208	−	0.507990i	0.874527	−	0.484977i	$-0.161172\pi$
$294$	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	−0.467705	−	0.883885i	$-0.654919\pi$
$307$	−19.8578	−	2.41118i	−1.13335	−	0.137613i	−0.665642	+	0.746272i	$0.731842\pi$
$308$	−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	−0.963551	−	0.267524i	$-0.913795\pi$
$311$	0.635282	−	5.23202i	0.0360235	−	0.296681i	0.999575	−	0.0291570i	$-0.00928227\pi$
$312$	8.57847	+	2.61964i	0.485660	+	0.148308i
$313$	2.42724	+	19.9901i	0.137196	+	1.12991i	0.884868	+	0.465842i	$0.154248\pi$
$313$	2.42724	+	19.9901i	0.137196	+	1.12991i	−0.747672	+	0.664068i	$0.768829\pi$
$314$	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	0.905974	−	0.423333i	$-0.139140\pi$
$317$	−1.65509	−	6.71495i	−0.0929590	−	0.377149i	−0.998933	+	0.0461840i	$0.985294\pi$
$318$	−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	0.568600	+	0.822614i	$0.307485\pi$
$331$	−5.77019	+	23.4106i	−0.317158	+	1.28676i	−0.885758	+	0.464147i	$0.846361\pi$
$332$	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	−0.829859	−	0.557973i	$-0.811579\pi$
$347$	−0.258425	+	0.374393i	−0.0138730	+	0.0200985i	0.815986	+	0.578072i	$0.196195\pi$
$348$	−59.0045	+	14.5433i	−3.16297	+	0.779603i
$349$	14.4032	−	9.94183i	0.770987	−	0.532174i	−0.116398	−	0.993203i	$-0.537135\pi$
$349$	14.4032	−	9.94183i	0.770987	−	0.532174i	0.887385	+	0.461029i	$0.152519\pi$
$350$	−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	−0.913119	−	0.407693i	$-0.866333\pi$
$353$	1.59460	−	6.46956i	0.0848722	−	0.344340i	0.997991	+	0.0633531i	$0.0201794\pi$
$354$	−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	0.986409	+	0.164308i	$0.0525391\pi$
$359$	3.58758	+	14.5554i	0.189345	+	0.768203i	−0.797064	+	0.603895i	$0.793615\pi$
$360$	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	0.101808	+	0.994804i	$0.467537\pi$
$367$	−16.5605	+	23.9920i	−0.864451	+	1.25237i	−0.966260	+	0.257570i	$0.917078\pi$
$368$	−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	0.925180	−	0.379529i	$-0.123914\pi$
$373$	4.67844	+	6.77789i	0.242240	+	0.350946i	−0.682939	+	0.730475i	$0.739299\pi$
$374$	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	0.862145	−	0.506661i	$-0.169120\pi$
$379$	−0.867937	−	1.65372i	−0.0445829	−	0.0849456i	−0.906728	+	0.421715i	$0.861428\pi$
$380$	−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	0.996450	−	0.0841870i	$-0.0268293\pi$
$383$	1.46805	+	5.95610i	0.0750137	+	0.304342i	−0.921436	+	0.388530i	$0.872983\pi$
$384$	−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	0.692263	−	0.721645i	$-0.256614\pi$
$389$	32.3576	−	7.97544i	1.64060	−	0.404371i	0.948334	+	0.317274i	$0.102768\pi$
$390$	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	−0.981284	−	0.192566i	$-0.938319\pi$
$397$	−13.3863	+	15.1101i	−0.671841	+	0.758352i	0.309443	+	0.950918i	$0.399857\pi$
$398$	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	0.546208	−	0.837650i	$-0.316071\pi$
$401$	−7.03223	−	7.93775i	−0.351173	−	0.396392i	−0.897381	+	0.441258i	$0.854533\pi$
$402$	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	0.985543	+	0.169428i	$0.0541921\pi$
$409$	11.4290	+	21.7761i	0.565127	+	1.07676i	−0.420415	+	0.907332i	$0.638116\pi$
$410$	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	0.627440	+	0.778665i	$0.284103\pi$
$419$	13.7994	+	36.3860i	0.674145	+	1.77757i	0.0467045	+	0.998909i	$0.485128\pi$
$420$	−3.09438	+	25.4845i	−0.150990	+	1.24352i
$421$	5.16794	−	9.84669i	0.251870	−	0.479898i	−0.726389	−	0.687283i	$-0.758803\pi$
$421$	5.16794	−	9.84669i	0.251870	−	0.479898i	0.978259	+	0.207385i	$0.0664953\pi$
$422$	−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	0.0974518	−	0.995240i	$-0.468931\pi$
$431$	17.2388	−	6.53780i	0.830362	−	0.314915i	0.732910	+	0.680325i	$0.238162\pi$
$432$	−30.2872	−	43.8786i	−1.45720	−	2.11111i
$433$	0.222728	+	0.197320i	0.0107036	+	0.00948259i	0.668458	−	0.743750i	$-0.266955\pi$
$433$	0.222728	+	0.197320i	0.0107036	+	0.00948259i	−0.657754	+	0.753233i	$0.728493\pi$
$434$	−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	−0.985365	−	0.170459i	$-0.945475\pi$
$439$	−1.45464	−	11.9801i	−0.0694264	−	0.571777i	0.915938	−	0.401319i	$-0.131448\pi$
$440$	−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	0.271053	−	0.962564i	$-0.412628\pi$
$443$	−7.72754	−	4.05573i	−0.367147	−	0.192693i	−0.638199	+	0.769871i	$0.720320\pi$
$444$	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	−0.999255	−	0.0386056i	$-0.987708\pi$
$449$	−36.4802	+	13.8351i	−1.72161	+	0.652919i	−0.722353	+	0.691525i	$0.756939\pi$
$450$	−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	−0.861367	−	0.507983i	$-0.830391\pi$
$457$	0.983520	−	1.87394i	0.0460071	−	0.0876592i	0.907374	+	0.420324i	$0.138084\pi$
$458$	−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	0.0887498	−	0.996054i	$-0.471713\pi$
$461$	−17.4152	−	12.0208i	−0.811106	−	0.559866i	−0.899856	+	0.436188i	$0.856328\pi$
$462$	−3.15302	−	12.7923i	−0.146692	−	0.595152i
$463$	−25.4055	−	17.5362i	−1.18069	−	0.814975i	−0.194555	−	0.980892i	$-0.562326\pi$
$463$	−25.4055	−	17.5362i	−1.18069	−	0.814975i	−0.986140	+	0.165917i	$0.946942\pi$
$464$	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	0.780840	−	0.624731i	$-0.214791\pi$
$467$	−1.73276	−	2.51034i	−0.0801828	−	0.116165i	−0.861023	+	0.508566i	$0.830176\pi$
$468$	−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	−0.120292	−	0.992739i	$-0.538383\pi$
$479$	0.0107135	−	0.00130086i	0.000489513	−	5.94376e-5i	0.120781	+	0.992679i	$0.461460\pi$
$480$	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	0.676163	−	0.736752i	$-0.263641\pi$
$487$	15.3091	+	5.80598i	0.693722	+	0.263094i	0.0175585	+	0.999846i	$0.494411\pi$
$488$		−	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	−0.251045	−	0.967975i	$-0.580774\pi$
$491$	15.0592	−	13.3413i	0.679613	−	0.602084i	0.930658	+	0.365891i	$0.119236\pi$
$492$	−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	−0.867724	−	0.497047i	$-0.834418\pi$
$499$	2.93964	−	11.9266i	0.131596	−	0.533908i	0.999320	−	0.0368614i	$-0.0117360\pi$
$500$	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	0.909255	−	0.416240i	$-0.136652\pi$
$503$	−1.06196	−	2.80015i	−0.0473504	−	0.124853i	−0.956605	+	0.291387i	$0.905883\pi$
$504$	−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	0.975570	−	0.219690i	$-0.0705047\pi$
$509$	25.1803	+	17.3807i	1.11610	+	0.770386i	0.140528	+	0.990077i	$0.455120\pi$
$510$	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	−0.717148	−	0.696921i	$-0.754553\pi$
$521$	−2.55075	+	2.25977i	−0.111750	+	0.0990022i	0.605397	+	0.795923i	$0.293014\pi$
$522$	31.2448	−	126.765i	1.36755	−	5.54836i
$523$	30.4081	−	26.9392i	1.32965	−	1.17797i	0.360147	−	0.932895i	$-0.382726\pi$
$523$	30.4081	−	26.9392i	1.32965	−	1.17797i	0.969505	−	0.245073i	$-0.0788120\pi$
$524$	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	0.592078	−	0.805880i	$-0.298308\pi$
$541$	−6.49620	−	7.33269i	−0.279293	−	0.315257i	−0.871372	+	0.490623i	$0.836769\pi$
$542$	−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	0.625142	−	0.780511i	$-0.285041\pi$
$547$	−7.63215	−	11.0571i	−0.326327	−	0.472767i	−0.951469	+	0.307745i	$0.900426\pi$
$548$	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	0.522166	+	0.852844i	$0.325124\pi$
$557$	−11.2419	+	21.4197i	−0.476335	+	0.907580i	−0.998501	+	0.0547363i	$0.982568\pi$
$558$	−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	0.733457	−	0.679736i	$-0.237906\pi$
$563$	14.0158	+	7.35607i	0.590697	+	0.310022i	−0.142760	+	0.989757i	$0.545598\pi$
$564$	−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	0.903717	−	0.428130i	$-0.140828\pi$
$569$	14.0174	+	12.4183i	0.587639	+	0.520603i	−0.316078	+	0.948733i	$0.602366\pi$
$570$	−8.86823	−	10.0102i	−0.371449	−	0.419279i
$571$	26.0765	+	13.6860i	1.09127	+	0.572741i	0.911638	−	0.410993i	$-0.134818\pi$
$571$	26.0765	+	13.6860i	1.09127	+	0.572741i	0.179629	+	0.983734i	$0.442510\pi$
$572$	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	$-0.844336\pi$
$577$		−	22.5686i		−	0.939545i	0.882788	−	0.469772i	$-0.155664\pi$
$578$	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	$-0.986509\pi$
$587$		−	2.05306i		−	0.0847388i	0.999102	−	0.0423694i	$-0.0134906\pi$
$588$	−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	−0.724602	−	0.689168i	$-0.757976\pi$
$593$	6.19000	−	11.7941i	0.254193	−	0.484324i	0.978795	+	0.204844i	$0.0656686\pi$
$594$	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	0.892303	−	0.451436i	$-0.149088\pi$
$599$	−1.83443	−	4.83700i	−0.0749529	−	0.197634i	−0.967256	+	0.253802i	$0.918319\pi$
$600$	8.39997	−	3.18569i	0.342928	−	0.130055i
$601$	2.38770	+	3.45919i	0.0973965	+	0.141103i	0.868652	−	0.495422i	$-0.164987\pi$
$601$	2.38770	+	3.45919i	0.0973965	+	0.141103i	−0.771256	+	0.636525i	$0.780371\pi$
$602$	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	−0.421607	−	0.906779i	$-0.638534\pi$
$607$	2.09806	−	1.10114i	0.0851575	−	0.0446941i	0.506764	+	0.862085i	$0.330841\pi$
$608$	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	0.318204	−	0.948022i	$-0.396920\pi$
$613$	−16.3721	−	18.4802i	−0.661261	−	0.746409i	−0.979465	+	0.201613i	$0.935382\pi$
$614$	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	−0.979212	−	0.202838i	$-0.934984\pi$
$617$	−16.3897	+	18.5001i	−0.659823	+	0.744786i	0.319390	+	0.947623i	$0.396522\pi$
$618$	118.892	−	45.0896i	4.78252	−	1.81377i
$619$	16.0853	+	30.6480i	0.646522	+	1.23185i	0.959399	+	0.282052i	$0.0910150\pi$
$619$	16.0853	+	30.6480i	0.646522	+	1.23185i	−0.312877	+	0.949794i	$0.601293\pi$
$620$	−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	−0.505130	−	0.863043i	$-0.668555\pi$
$631$	−11.5283	−	46.7723i	−0.458936	−	1.86198i	0.0461941	−	0.998932i	$-0.485291\pi$
$632$	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	0.997216	−	0.0745608i	$-0.0237555\pi$
$641$	14.5296	+	21.0497i	0.573883	+	0.831413i	−0.423333	+	0.905974i	$0.639140\pi$
$642$	28.9396	+	32.6660i	1.14215	+	1.28922i
$643$	−15.7498	+	30.0087i	−0.621111	+	1.18343i	0.348161	+	0.937435i	$0.386806\pi$
$643$	−15.7498	+	30.0087i	−0.621111	+	1.18343i	−0.969272	+	0.245993i	$0.920886\pi$
$644$	−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	−0.828783	−	0.559571i	$-0.810966\pi$
$647$	−0.297211	+	0.430585i	−0.0116846	+	0.0169280i	0.817098	+	0.576499i	$0.195581\pi$
$648$	−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	0.102906	−	0.994691i	$-0.467186\pi$
$659$	−6.88578	−	1.69719i	−0.268232	−	0.0661132i	−0.371138	+	0.928578i	$0.621032\pi$
$660$	4.72911	−	4.18963i	0.184081	−	0.163081i
$661$	−5.95474	+	24.1593i	−0.231613	+	0.939690i	0.733884	+	0.679275i	$0.237705\pi$
$661$	−5.95474	+	24.1593i	−0.231613	+	0.939690i	−0.965497	+	0.260415i	$0.916141\pi$
$662$	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	−0.738851	−	0.673869i	$-0.764631\pi$
$673$	−15.6687	+	8.22355i	−0.603982	+	0.316994i	0.134868	+	0.990864i	$0.456939\pi$
$674$	−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	−0.929707	−	0.368300i	$-0.879940\pi$
$683$	1.68997	−	6.85649i	0.0646650	−	0.262356i	0.994372	+	0.105943i	$0.0337862\pi$
$684$	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	0.474654	+	0.880172i	$0.342573\pi$
$691$	−9.32311	+	37.8253i	−0.354668	+	1.43894i	−0.829322	+	0.558771i	$0.811273\pi$
$692$	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	−0.930251	−	0.366923i	$-0.880411\pi$
$701$	−3.04060	−	25.0416i	−0.114842	−	0.945807i	0.815410	−	0.578884i	$-0.196512\pi$
$702$	−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	−0.796341	−	0.604848i	$-0.793234\pi$
$709$	4.09557	−	7.80346i	0.153812	−	0.293065i	0.950153	+	0.311783i	$0.100926\pi$
$710$	−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	0.989281	+	0.146027i	$0.0466487\pi$
$719$	1.70788	+	14.0657i	0.0636933	+	0.524562i	−0.925587	+	0.378534i	$0.876428\pi$
$720$	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	−0.665377	−	0.746508i	$-0.731729\pi$
$727$	−24.4721	+	6.03182i	−0.907619	+	0.223708i	−0.242242	+	0.970216i	$0.577883\pi$
$728$	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	0.997922	+	0.0644376i	$0.0205254\pi$
$733$	13.1057	+	24.9708i	0.484069	+	0.922316i	−0.513853	+	0.857878i	$0.671782\pi$
$734$	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	0.999702	+	0.0244204i	$0.00777403\pi$
$739$	24.5597	+	27.7222i	0.903443	+	1.01978i	−0.0962584	+	0.995356i	$0.530688\pi$
$740$	−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	−0.107314	−	0.994225i	$-0.534225\pi$
$743$	−23.0857	−	8.75526i	−0.846933	−	0.321200i	−0.739619	+	0.673026i	$0.764994\pi$
$744$	−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	0.437700	−	0.899121i	$-0.355793\pi$
$751$	−15.2972	−	22.1618i	−0.558203	−	0.808697i	−0.995903	+	0.0904240i	$0.971178\pi$
$752$	−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	−0.952995	−	0.302985i	$-0.902017\pi$
$757$	−12.1221	−	31.9633i	−0.440584	−	1.16173i	0.512411	−	0.858740i	$-0.328753\pi$
$758$	−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	−0.999746	−	0.0225320i	$-0.992827\pi$
$761$	−36.7778	+	25.3859i	−1.33319	+	0.920237i	−0.333447	+	0.942769i	$0.608212\pi$
$762$	−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
$768$	−10.4338	−	27.5117i	−0.376498	−	0.992744i
$769$	−23.4835	+	8.90611i	−0.846836	+	0.321163i	−0.739580	−	0.673069i	$-0.764976\pi$
$769$	−23.4835	+	8.90611i	−0.846836	+	0.321163i	−0.107256	+	0.994231i	$0.534207\pi$
$770$	2.65009	+	3.83931i	0.0955025	+	0.138359i
$771$	−15.9915	−	14.1673i	−0.575921	−	0.510222i
$772$	10.9921	−	7.58729i	0.395614	−	0.273072i
$773$	−16.3885	−	18.4988i	−0.589454	−	0.665356i	0.375791	−	0.926705i	$-0.377371\pi$
$773$	−16.3885	−	18.4988i	−0.589454	−	0.665356i	−0.965244	+	0.261349i	$0.915833\pi$
$774$	33.1435	+	63.1496i	1.19132	+	2.26987i
$775$			22.0574i			0.792327i
$776$	−7.84924	+	4.11960i	−0.281771	+	0.147885i
$777$	−4.65546	−	38.3411i	−0.167014	−	1.37548i
$778$	−65.0503	−	24.6703i	−2.33216	−	0.884473i
$779$	13.9269	−	7.30943i	0.498985	−	0.261887i
$780$	13.5119	−	30.4852i	0.483805	−	1.09154i
$781$	2.91371	+	1.52923i	0.104261	+	0.0547203i
$782$	16.6179	+	18.7577i	0.594255	+	0.670775i
$783$	97.9270	+	86.7557i	3.49962	+	3.10040i
$784$	−2.16052	+	0.532520i	−0.0771614	+	0.0190186i
$785$	6.90375	−	0.838268i	0.246406	−	0.0299191i
$786$	−4.99558	+	5.63884i	−0.178186	+	0.201131i
$787$	15.7647	−	5.97875i	0.561950	−	0.213120i	−0.0572403	−	0.998360i	$-0.518230\pi$
$787$	15.7647	−	5.97875i	0.561950	−	0.213120i	0.619190	+	0.785241i	$0.287461\pi$
$788$	−1.97014	−	3.75378i	−0.0701832	−	0.133723i
$789$	−25.0415	−	13.1428i	−0.891503	−	0.467897i
$790$	−3.04446	+	25.0734i	−0.108317	+	0.892072i
$791$	−11.6664	+	13.1686i	−0.414808	+	0.468222i
$792$	4.00435	+	0.986983i	0.142288	+	0.0350709i
$793$	−1.47757	+	4.83857i	−0.0524701	+	0.171823i
$794$	40.9173	−	10.0852i	1.45210	−	0.357911i
$795$	−18.2885	+	34.8459i	−0.648627	+	1.23586i
$796$	−2.21163	−	1.16075i	−0.0783891	−	0.0411418i
$797$	9.51858	−	25.0984i	0.337165	−	0.889032i	−0.654011	−	0.756485i	$-0.726915\pi$
$797$	9.51858	−	25.0984i	0.337165	−	0.889032i	0.991177	−	0.132547i	$-0.0423156\pi$
$798$	29.4539	+	11.1704i	1.04266	+	0.395428i
$799$	−6.07227	−	4.19138i	−0.214821	−	0.148280i
$800$	−6.98538	−	28.3408i	−0.246971	−	1.00200i
$801$	62.6037	+	43.2122i	2.21199	+	1.52683i
$802$	2.66849	+	21.9770i	0.0942275	+	0.776034i
$803$	2.77562	−	7.31871i	0.0979495	−	0.258272i
$804$	−6.28078	−	11.9670i	−0.221506	−	0.422044i
$805$	−11.6767	−	16.9166i	−0.411550	−	0.596233i
$806$	43.8138	−	13.9273i	1.54327	−	0.490567i
$807$	−27.8253	+	40.3118i	−0.979495	+	1.41904i
$808$	−9.56244	−	1.16109i	−0.336405	−	0.0408470i
$809$	−23.1782	−	5.71292i	−0.814903	−	0.200855i	−0.190227	−	0.981740i	$-0.560922\pi$
$809$	−23.1782	−	5.71292i	−0.814903	−	0.200855i	−0.624675	+	0.780885i	$0.714769\pi$
$810$	−44.7210	−	64.7896i	−1.57134	−	2.27648i
$811$	−36.0154	−	40.6530i	−1.26467	−	1.42752i	−0.857759	−	0.514052i	$-0.828144\pi$
$811$	−36.0154	−	40.6530i	−1.26467	−	1.42752i	−0.406913	−	0.913467i	$-0.633395\pi$
$812$	−23.5545	+	44.8794i	−0.826602	+	1.57496i
$813$	50.0055	−	6.07177i	1.75377	−	0.212946i
$814$	5.91884	+	0.718677i	0.207455	+	0.0251896i
$815$	1.28699	−	1.14018i	0.0450814	−	0.0399386i
$816$	11.3974	−	16.5119i	0.398988	−	0.578034i
$817$	−6.85868	+	0.832795i	−0.239955	+	0.0291358i
$818$	6.18841	−	50.9661i	0.216373	−	1.78199i
$819$	79.4242	−	15.0232i	2.77531	−	0.524953i
$820$	−3.22541	−	26.5636i	−0.112636	−	0.927642i
$821$	−3.88043	−	15.7435i	−0.135428	−	0.549452i	−0.998978	−	0.0451900i	$-0.985611\pi$
$821$	−3.88043	−	15.7435i	−0.135428	−	0.549452i	0.863551	−	0.504262i	$-0.168235\pi$
$822$	−132.257			−4.61300
$823$	36.6075			1.27606			0.638029	−	0.770012i	$-0.279750\pi$
$823$	36.6075			1.27606			0.638029	+	0.770012i	$0.279750\pi$
$824$	3.27380	+	13.2823i	0.114048	+	0.462712i
$825$	−7.67712	−	2.91155i	−0.267283	−	0.101367i
$826$			48.7549i			1.69640i
$827$	−14.4740	+	5.48928i	−0.503311	+	0.190881i	−0.593175	−	0.805073i	$-0.702126\pi$
$827$	−14.4740	+	5.48928i	−0.503311	+	0.190881i	0.0898640	+	0.995954i	$0.471357\pi$
$828$	−116.197	−	28.6401i	−4.03813	−	0.995311i
$829$	3.19196	−	2.82783i	0.110861	−	0.0982146i	−0.605871	−	0.795563i	$-0.707175\pi$
$829$	3.19196	−	2.82783i	0.110861	−	0.0982146i	0.716733	+	0.697348i	$0.245637\pi$
$830$	3.84103	−	15.5837i	0.133324	−	0.540918i
$831$	37.8158	−	33.5019i	1.31181	−	1.16217i
$832$	−32.4774	+	19.8868i	−1.12595	+	0.689450i
$833$	−1.00828	−	0.893258i	−0.0349348	−	0.0309496i
$834$	29.8060	−	20.5736i	1.03210	−	0.712405i
$835$	−3.61744	+	0.891619i	−0.125187	+	0.0308557i
$836$	−1.49470	+	2.16545i	−0.0516954	+	0.0748937i
$837$	24.6964	−	100.197i	0.853634	−	3.46333i
$838$	19.4416	−	78.8778i	0.671600	−	2.72479i
$839$	42.1160	+	5.11381i	1.45401	+	0.176548i	0.809081	−	0.587697i	$-0.199965\pi$
$839$	42.1160	+	5.11381i	1.45401	+	0.176548i	0.644925	+	0.764246i	$0.276888\pi$
$840$	5.39624	−	6.09110i	0.186188	−	0.210163i
$841$	−10.9791	−	28.9495i	−0.378589	−	0.998257i
$842$	−20.5559	+	10.7886i	−0.708403	+	0.371799i
$843$	36.1583	+	24.9583i	1.24536	+	0.859609i
$844$	9.76115			0.335992
$845$	14.9154	+	3.49654i	0.513106	+	0.120285i
$846$	65.1207			2.23889
$847$	24.0628	+	16.6093i	0.826807	+	0.570704i
$848$	28.0372	−	14.7150i	0.962801	−	0.505317i
$849$	−20.9933	−	55.3548i	−0.720489	−	1.89977i
$850$	9.55019	−	10.7799i	0.327569	−	0.369749i
$851$	−26.0794	−	3.16661i	−0.893990	−	0.108550i
$852$	9.04669	−	36.7039i	0.309934	−	1.25745i
$853$	−4.96036	+	20.1250i	−0.169839	+	0.689065i	0.822839	+	0.568275i	$0.192389\pi$
$853$	−4.96036	+	20.1250i	−0.169839	+	0.689065i	−0.992678	+	0.120790i	$0.961457\pi$
$854$	−4.61892	+	6.69166i	−0.158056	+	0.228984i
$855$	15.0943	−	3.72041i	0.516214	−	0.127235i
$856$	−3.86401	+	2.66713i	−0.132069	+	0.0911608i
$857$	31.1296	+	27.5784i	1.06337	+	0.942060i	0.998440	−	0.0558304i	$-0.0177806\pi$
$857$	31.1296	+	27.5784i	1.06337	+	0.942060i	0.0649253	+	0.997890i	$0.479319\pi$
$858$	−0.935948	+	17.0878i	−0.0319527	+	0.583368i
$859$	−24.9950	+	22.1436i	−0.852819	+	0.755531i	−0.971409	−	0.237412i	$-0.923701\pi$
$859$	−24.9950	+	22.1436i	−0.852819	+	0.755531i	0.118590	+	0.992943i	$0.462162\pi$
$860$	−2.81298	+	11.4127i	−0.0959218	+	0.389170i
$861$	66.5875	−	58.9914i	2.26930	−	2.01042i
$862$	−37.3703	−	9.21095i	−1.27284	−	0.313726i
$863$	8.52768	−	3.23412i	0.290286	−	0.110091i	−0.205164	−	0.978728i	$-0.565773\pi$
$863$	8.52768	−	3.23412i	0.290286	−	0.110091i	0.495449	+	0.868637i	$0.335003\pi$
$864$			136.561i			4.64590i
$865$	9.64934	+	3.65951i	0.328087	+	0.124427i
$866$	−0.148660	−	0.603138i	−0.00505168	−	0.0204955i
$867$	−44.4326			−1.50901
$868$	39.9797			1.35700
$869$	−1.67851	−	6.81000i	−0.0569397	−	0.231013i
$870$	7.64209	+	62.9383i	0.259091	+	2.13381i
$871$	4.86588	−	3.85711i	0.164874	−	0.130693i
$872$	−0.00532809	+	0.0438808i	−0.000180432	+	0.00148599i
$873$	−95.0846	+	11.5454i	−3.21813	+	0.390751i
$874$	12.1718	−	17.6339i	0.411717	−	0.596475i
$875$	−21.0845	+	18.6793i	−0.712788	+	0.631475i
$876$	−89.2639	−	10.8386i	−3.01595	−	0.366202i
$877$	30.0309	−	3.64641i	1.01407	−	0.123130i	0.403407	−	0.915021i	$-0.367826\pi$
$877$	30.0309	−	3.64641i	1.01407	−	0.123130i	0.610664	+	0.791890i	$0.290903\pi$
$878$	−11.7079	+	22.3075i	−0.395122	+	0.752841i
$879$	−19.7647	−	22.3098i	−0.666648	−	0.752490i
$880$	−1.44317	−	2.09079i	−0.0486492	−	0.0704806i
$881$	−17.7790	−	4.38213i	−0.598989	−	0.147638i	−0.0718484	−	0.997416i	$-0.522890\pi$
$881$	−17.7790	−	4.38213i	−0.598989	−	0.147638i	−0.527141	+	0.849778i	$0.676736\pi$
$882$	11.8022	+	1.43305i	0.397402	+	0.0482533i
$883$	−29.4872	+	42.7197i	−0.992325	+	1.43763i	−0.0954047	+	0.995439i	$0.530415\pi$
$883$	−29.4872	+	42.7197i	−0.992325	+	1.43763i	−0.896920	+	0.442192i	$0.854201\pi$
$884$	−14.8487	−	6.58140i	−0.499417	−	0.221357i
$885$	18.7452	+	27.1571i	0.630113	+	0.912877i
$886$	8.46672	+	16.1320i	0.284445	+	0.541965i
$887$	−1.34235	+	3.53949i	−0.0450718	+	0.118844i	−0.955662	−	0.294466i	$-0.904858\pi$
$887$	−1.34235	+	3.53949i	−0.0450718	+	0.118844i	0.910590	+	0.413310i	$0.135628\pi$
$888$	−1.25363	−	10.3246i	−0.0420690	−	0.346470i
$889$	−1.60591	−	1.10848i	−0.0538605	−	0.0371772i
$890$	5.54512	+	22.4974i	0.185873	+	0.754115i
$891$	17.9915	+	12.4186i	0.602738	+	0.416040i
$892$	26.8967	+	10.2006i	0.900569	+	0.341541i
$893$	−2.23707	+	5.89866i	−0.0748605	+	0.197391i
$894$	121.762	+	63.9059i	4.07235	+	2.13733i
$895$	0.915332	−	1.74402i	0.0305962	−	0.0582962i
$896$	−15.8582	+	3.90870i	−0.529786	+	0.130580i
$897$	4.12394	−	75.2917i	0.137694	−	2.51392i
$898$	79.0820	+	19.4920i	2.63900	+	0.650455i
$899$	−31.3635	+	35.4021i	−1.04603	+	1.18073i
$900$	−8.29006	+	68.2748i	−0.276335	+	2.27583i
$901$	16.9728	+	8.90799i	0.565444	+	0.296768i
$902$	6.38206	+	12.1600i	0.212499	+	0.404884i
$903$	−36.5379	+	13.8570i	−1.21591	+	0.461132i
$904$	−3.14154	+	3.54607i	−0.104486	+	0.117940i
$905$	−6.16300	+	0.748323i	−0.204865	+	0.0248751i
$906$	80.1893	−	19.7649i	2.66411	−	0.656644i
$907$	14.5299	+	12.8724i	0.482457	+	0.427419i	0.868970	−	0.494864i	$-0.164782\pi$
$907$	14.5299	+	12.8724i	0.482457	+	0.427419i	−0.386513	+	0.922284i	$0.626321\pi$
$908$	7.57500	+	8.55041i	0.251385	+	0.283755i
$909$	−92.1597	−	48.3692i	−3.05675	−	1.60430i
$910$	21.1430	+	12.6175i	0.700882	+	0.418265i
$911$	13.1460	−	6.89958i	0.435548	−	0.228593i	−0.232675	−	0.972555i	$-0.574748\pi$
$911$	13.1460	−	6.89958i	0.435548	−	0.228593i	0.668223	+	0.743961i	$0.267055\pi$
$912$	−16.0399	−	6.08312i	−0.531133	−	0.201432i
$913$	0.537228	+	4.42447i	0.0177796	+	0.146429i
$914$	−3.91203	+	2.05319i	−0.129398	+	0.0679135i
$915$			5.50321i			0.181931i
$916$	13.5271	+	25.7738i	0.446949	+	0.851589i
$917$	−1.99585	−	2.25285i	−0.0659087	−	0.0743956i
$918$	−55.4520	+	38.2758i	−1.83019	+	1.26329i
$919$	−16.9144	−	14.9849i	−0.557955	−	0.494305i	0.336366	−	0.941731i	$-0.390802\pi$
$919$	−16.9144	−	14.9849i	−0.557955	−	0.494305i	−0.894321	+	0.447426i	$0.852341\pi$
$920$	−3.14433	−	4.55534i	−0.103665	−	0.150185i
$921$	−62.2488	+	23.6078i	−2.05117	+	0.777905i
$922$	15.6649	+	41.3050i	0.515896	+	1.36031i
$923$	17.3414	+	0.949836i	0.570799	+	0.0312642i
$924$	−5.27725	+	13.9150i	−0.173609	+	0.457769i
$925$			15.0977i			0.496410i
$926$	22.8522	+	60.2563i	0.750970	+	1.98014i
$927$	−17.8167	+	146.734i	−0.585178	+	4.81937i
$928$	29.0864	−	55.4194i	0.954806	−	1.81923i
$929$	24.8733	−	17.1688i	0.816066	−	0.563290i	−0.0852961	−	0.996356i	$-0.527184\pi$
$929$	24.8733	−	17.1688i	0.816066	−	0.563290i	0.901362	+	0.433066i	$0.142568\pi$
$930$	41.1570	−	28.4086i	1.34959	−	0.931555i
$931$	−0.535244	+	1.01982i	−0.0175419	+	0.0334233i
$932$	5.78561	−	47.6488i	0.189514	−	1.56079i
$933$	−6.22005	−	16.4009i	−0.203635	−	0.536942i
$934$			6.36778i			0.208360i
$935$	0.545359	−	1.43799i	0.0178351	−	0.0470274i
$936$	21.3875	−	4.04547i	0.699072	−	0.132230i
$937$	−10.5809	−	27.8995i	−0.345663	−	0.911437i	−0.989272	−	0.146083i	$-0.953333\pi$
$937$	−10.5809	−	27.8995i	−0.345663	−	0.911437i	0.643610	−	0.765354i	$-0.277436\pi$
$938$	9.33080	−	3.53871i	0.304661	−	0.115543i
$939$	38.0709	+	55.1553i	1.24240	+	1.79992i
$940$	8.03357	+	7.11712i	0.262026	+	0.232135i
$941$	2.27954	−	1.57345i	0.0743108	−	0.0512930i	−0.530330	−	0.847791i	$-0.677932\pi$
$941$	2.27954	−	1.57345i	0.0743108	−	0.0512930i	0.604641	+	0.796498i	$0.293317\pi$
$942$	27.1892	+	30.6903i	0.885873	+	0.999943i
$943$	−28.1204	−	53.5789i	−0.915726	−	1.74477i
$944$		−	26.5507i		−	0.864151i
$945$	48.9366	−	25.6839i	1.59191	−	0.835498i
$946$	−0.727136	−	5.98850i	−0.0236412	−	0.194703i
$947$	18.9268	+	7.17799i	0.615038	+	0.233253i	0.642396	−	0.766373i	$-0.277940\pi$
$947$	18.9268	+	7.17799i	0.615038	+	0.233253i	−0.0273583	+	0.999626i	$0.508710\pi$
$948$	−71.3443	+	37.4444i	−2.31716	+	1.21614i
$949$	−2.72920	−	41.2211i	−0.0885937	−	1.33809i
$950$	−10.9033	−	5.72251i	−0.353751	−	0.185663i
$951$	−15.2632	−	17.2286i	−0.494943	−	0.558675i
$952$	−2.96686	−	2.62841i	−0.0961564	−	0.0851871i
$953$	5.74333	−	1.41560i	0.186045	−	0.0458559i	−0.145192	−	0.989403i	$-0.546380\pi$
$953$	5.74333	−	1.41560i	0.186045	−	0.0458559i	0.331237	+	0.943548i	$0.392534\pi$
$954$	−167.945	+	20.3922i	−5.43741	+	0.660221i
$955$	−11.9883	+	13.5320i	−0.387932	+	0.437885i
$956$	−35.1907	+	13.3461i	−1.13815	+	0.431643i
$957$	−8.18181	−	15.5891i	−0.264480	−	0.503925i
$958$	−0.0199491	−	0.0104701i	−0.000644526	−	0.000338273i
$959$	6.36914	−	52.4546i	0.205670	−	1.69385i
$960$	−27.4698	+	31.0070i	−0.886585	+	1.00075i
$961$	6.12372	+	1.50936i	0.197539	+	0.0486891i
$962$	29.9893	−	9.53283i	0.966895	−	0.307351i
$963$	−49.2570	+	12.1408i	−1.58728	+	0.391230i
$964$	3.46997	−	6.61147i	0.111760	−	0.212941i
$965$	5.91031	+	3.10197i	0.190260	+	0.0998559i
$966$	42.9741	−	113.313i	1.38267	−	3.64580i
$967$	41.2578	+	15.6470i	1.32676	+	0.503175i	0.913278	−	0.407336i	$-0.133542\pi$
$967$	41.2578	+	15.6470i	1.32676	+	0.503175i	0.413484	+	0.910511i	$0.364312\pi$
$968$	6.47967	+	4.47259i	0.208264	+	0.143755i
$969$	−2.48525	−	10.0831i	−0.0798378	−	0.323915i
$970$	−24.0110	−	16.5736i	−0.770947	−	0.532146i
$971$	−2.21865	−	18.2722i	−0.0711998	−	0.586383i	−0.984025	−	0.178032i	$-0.943027\pi$
$971$	−2.21865	−	18.2722i	−0.0711998	−	0.586383i	0.912825	−	0.408351i	$-0.133896\pi$
$972$	46.6726	−	123.066i	1.49702	−	3.94733i
$973$	6.72432	+	12.8121i	0.215572	+	0.410738i
$974$	−19.4167	−	28.1299i	−0.622150	−	0.901340i
$975$	−43.2398	+	2.86286i	−1.38478	+	0.0916848i
$976$	2.51534	−	3.64410i	0.0805142	−	0.116645i
$977$	29.6305	+	3.59780i	0.947964	+	0.115104i	0.579892	−	0.814694i	$-0.303095\pi$
$977$	29.6305	+	3.59780i	0.947964	+	0.115104i	0.368072	+	0.929797i	$0.380018\pi$
$978$	9.84262	+	2.42599i	0.314732	+	0.0775746i
$979$	−3.65510	−	5.29533i	−0.116818	−	0.169239i
$980$	1.29936	+	1.46667i	0.0415064	+	0.0468510i
$981$	−0.221960	+	0.422909i	−0.00708663	+	0.0135024i
$982$	−41.6939	+	5.06256i	−1.33051	+	0.161553i
$983$	−5.81382	−	0.705926i	−0.185432	−	0.0225155i	0.0272937	−	0.999627i	$-0.491311\pi$
$983$	−5.81382	−	0.705926i	−0.185432	−	0.0225155i	−0.212726	+	0.977112i	$0.568234\pi$
$984$	17.9308	−	15.8853i	0.571613	−	0.506405i
$985$	1.20352	−	1.74360i	0.0383474	−	0.0555558i
$986$	30.6560	−	3.72232i	0.976287	−	0.118543i
$987$	−4.30090	+	35.4211i	−0.136899	+	1.12746i
$988$	−2.42536	+	13.6737i	−0.0771610	+	0.435018i
$989$	3.20388	+	26.3863i	0.101877	+	0.839036i
$990$	3.24839	+	13.1792i	0.103241	+	0.418863i
$991$	3.59335			0.114146			0.0570732	−	0.998370i	$-0.481823\pi$
$991$	3.59335			0.114146			0.0570732	+	0.998370i	$0.481823\pi$
$992$	−49.3690			−1.56747
$993$	19.2040	+	77.9137i	0.609420	+	2.47252i
$994$	26.0987	+	9.89792i	0.827799	+	0.313943i
$995$		−	1.24824i		−	0.0395720i
$996$	47.8737	−	18.1561i	1.51694	−	0.575298i
$997$	−39.9163	−	9.83849i	−1.26416	−	0.311588i	−0.450422	−	0.892816i	$-0.648726\pi$
$997$	−39.9163	−	9.83849i	−1.26416	−	0.311588i	−0.813741	+	0.581228i	$0.802573\pi$
$998$	−19.1941	+	17.0045i	−0.607579	+	0.538268i
$999$	16.9040	−	68.5824i	0.534820	−	2.16985i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.2.h.a.155.3	yes	168
169.12	even	26	inner	169.2.h.a.12.3	✓	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.2.h.a.12.3	✓	168	169.12	even	26	inner
169.2.h.a.155.3	yes	168	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9} - 9 q^{10} - 13 q^{11} - 9 q^{12} + 52 q^{13} - 15 q^{14} + 39 q^{15} - 31 q^{16} - 11 q^{17} + 26 q^{18} - 13 q^{20}+ \cdots - 13 q^{98}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

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