LMFDB - Embedded newform 153.3.j.a.86.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,3,Mod(86,153)] 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("153.86"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	153.j (of order $6$, degree $2$, 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:	$4.16894804471$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			86.16
Character	$\chi$	$=$	153.86
Dual form			153.3.j.a.137.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0918678 + 0.0530399i) q^{2} +(-2.79064 + 1.10106i) q^{3} +(-1.99437 + 3.45436i) q^{4} +(-0.368715 - 0.212878i) q^{5} +(0.197970 - 0.249167i) q^{6} +(-3.49077 - 6.04619i) q^{7} -0.847445i q^{8} +(6.57534 - 6.14532i) q^{9} +0.0451640 q^{10} +(-0.977932 + 0.564609i) q^{11} +(1.76213 - 11.8358i) q^{12} +(7.30063 - 12.6451i) q^{13} +(0.641379 + 0.370300i) q^{14} +(1.26334 + 0.188088i) q^{15} +(-7.93255 - 13.7396i) q^{16} -4.12311i q^{17} +(-0.278115 + 0.913312i) q^{18} +8.85050 q^{19} +(1.47071 - 0.849115i) q^{20} +(16.3987 + 13.0292i) q^{21} +(0.0598936 - 0.103739i) q^{22} +(-35.3768 - 20.4248i) q^{23} +(0.933086 + 2.36491i) q^{24} +(-12.4094 - 21.4937i) q^{25} +1.54890i q^{26} +(-11.5830 + 24.3892i) q^{27} +27.8476 q^{28} +(-34.5797 + 19.9646i) q^{29} +(-0.126037 + 0.0497282i) q^{30} +(-8.41833 + 14.5810i) q^{31} +(4.39312 + 2.53637i) q^{32} +(2.10739 - 2.65238i) q^{33} +(0.218689 + 0.378781i) q^{34} +2.97243i q^{35} +(8.11443 + 34.9696i) q^{36} +60.2993 q^{37} +(-0.813076 + 0.469430i) q^{38} +(-6.45047 + 43.3262i) q^{39} +(-0.180402 + 0.312465i) q^{40} +(-0.494829 - 0.285690i) q^{41} +(-2.19758 - 0.327179i) q^{42} +(-12.5109 - 21.6695i) q^{43} -4.50417i q^{44} +(-3.73263 + 0.866127i) q^{45} +4.33332 q^{46} +(-14.7477 + 8.51462i) q^{47} +(37.2650 + 29.6080i) q^{48} +(0.129025 - 0.223479i) q^{49} +(2.28004 + 1.31638i) q^{50} +(4.53978 + 11.5061i) q^{51} +(29.1204 + 50.4380i) q^{52} -24.4489i q^{53} +(-0.229492 - 2.85495i) q^{54} +0.480770 q^{55} +(-5.12381 + 2.95824i) q^{56} +(-24.6986 + 9.74492i) q^{57} +(2.11784 - 3.66821i) q^{58} +(-41.7773 - 24.1201i) q^{59} +(-3.16930 + 3.98891i) q^{60} +(-30.4999 - 52.8275i) q^{61} -1.78603i q^{62} +(-60.1088 - 18.3039i) q^{63} +62.9223 q^{64} +(-5.38370 + 3.10828i) q^{65} +(-0.0529190 + 0.355444i) q^{66} +(17.2958 - 29.9572i) q^{67} +(14.2427 + 8.22301i) q^{68} +(121.213 + 18.0463i) q^{69} +(-0.157657 - 0.273070i) q^{70} +127.386i q^{71} +(-5.20782 - 5.57224i) q^{72} -104.409 q^{73} +(-5.53956 + 3.19827i) q^{74} +(58.2958 + 46.3176i) q^{75} +(-17.6512 + 30.5728i) q^{76} +(6.82747 + 3.94184i) q^{77} +(-1.70543 - 4.32242i) q^{78} +(-29.2711 - 50.6991i) q^{79} +6.75465i q^{80} +(5.47017 - 80.8151i) q^{81} +0.0606118 q^{82} +(-69.6131 + 40.1911i) q^{83} +(-77.7126 + 30.6619i) q^{84} +(-0.877717 + 1.52025i) q^{85} +(2.29869 + 1.32715i) q^{86} +(74.5173 - 93.7883i) q^{87} +(0.478475 + 0.828743i) q^{88} -22.9617i q^{89} +(0.296969 - 0.277547i) q^{90} -101.939 q^{91} +(141.109 - 81.4695i) q^{92} +(7.43801 - 49.9593i) q^{93} +(0.903229 - 1.56444i) q^{94} +(-3.26331 - 1.88407i) q^{95} +(-15.0523 - 2.24101i) q^{96} +(-3.86636 - 6.69674i) q^{97} +0.0273740i q^{98} +(-2.96053 + 9.72219i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 2 q^{3} + 64 q^{4} - 18 q^{5} - 22 q^{6} + 2 q^{7} - 6 q^{9} - 44 q^{12} - 10 q^{13} + 72 q^{14} - 36 q^{15} - 128 q^{16} - 38 q^{18} - 28 q^{19} - 18 q^{20} + 88 q^{21} + 144 q^{23} - 42 q^{24}+ \cdots + 58 q^{99}+O(q^{100}) $ 64 * q - 2 * q^3 + 64 * q^4 - 18 * q^5 - 22 * q^6 + 2 * q^7 - 6 * q^9 - 44 * q^12 - 10 * q^13 + 72 * q^14 - 36 * q^15 - 128 * q^16 - 38 * q^18 - 28 * q^19 - 18 * q^20 + 88 * q^21 + 144 * q^23 - 42 * q^24 + 154 * q^25 - 164 * q^27 + 32 * q^28 - 162 * q^29 - 220 * q^30 + 62 * q^31 + 126 * q^32 - 40 * q^33 + 12 * q^36 + 128 * q^37 - 36 * q^38 - 126 * q^39 - 144 * q^41 + 114 * q^42 - 64 * q^43 - 72 * q^45 - 48 * q^46 + 288 * q^47 - 10 * q^48 - 246 * q^49 + 62 * q^52 + 374 * q^54 - 84 * q^55 + 684 * q^56 + 232 * q^57 + 138 * q^58 - 432 * q^59 - 86 * q^60 + 110 * q^61 + 304 * q^63 - 260 * q^64 + 328 * q^66 - 148 * q^67 + 36 * q^69 - 216 * q^70 - 96 * q^72 - 196 * q^73 - 918 * q^74 + 314 * q^75 - 112 * q^76 - 504 * q^77 + 276 * q^78 + 86 * q^79 + 234 * q^81 - 396 * q^82 - 594 * q^83 + 592 * q^84 + 126 * q^86 + 462 * q^87 + 24 * q^88 - 338 * q^90 + 52 * q^91 - 36 * q^92 - 1006 * q^93 - 186 * q^94 - 144 * q^95 + 18 * q^96 + 140 * q^97 + 58 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.0918678	+	0.0530399i	−0.0459339	+	0.0265199i	−0.522791	−	0.852461i	$-0.675109\pi$
$2$	−0.0918678	+	0.0530399i	−0.0459339	+	0.0265199i	0.476857	+	0.878981i	$0.341776\pi$
$3$	−2.79064	+	1.10106i	−0.930213	+	0.367020i
$3$	−2.79064	+	1.10106i	−0.930213	+	0.367020i
$4$	−1.99437	+	3.45436i	−0.498593	+	0.863589i
$5$	−0.368715	−	0.212878i	−0.0737430	−	0.0425755i	0.462675	−	0.886528i	$-0.346890\pi$
$5$	−0.368715	−	0.212878i	−0.0737430	−	0.0425755i	−0.536418	+	0.843952i	$0.680223\pi$
$6$	0.197970	−	0.249167i	0.0329950	−	0.0415278i
$7$	−3.49077	−	6.04619i	−0.498682	−	0.863742i	0.501317	−	0.865264i	$-0.332849\pi$
$7$	−3.49077	−	6.04619i	−0.498682	−	0.863742i	−0.999999	+	0.00152160i	$0.999516\pi$
$8$		−	0.847445i		−	0.105931i
$9$	6.57534	−	6.14532i	0.730593	−	0.682813i
$10$	0.0451640			0.00451640
$11$	−0.977932	+	0.564609i	−0.0889029	+	0.0513281i	−0.543792	−	0.839220i	$-0.683012\pi$
$11$	−0.977932	+	0.564609i	−0.0889029	+	0.0513281i	0.454889	+	0.890548i	$0.349679\pi$
$12$	1.76213	−	11.8358i	0.146844	−	0.986316i
$13$	7.30063	−	12.6451i	0.561587	−	0.972697i	−0.435771	−	0.900057i	$-0.643524\pi$
$13$	7.30063	−	12.6451i	0.561587	−	0.972697i	0.997358	−	0.0726397i	$-0.0231423\pi$
$14$	0.641379	+	0.370300i	0.0458128	+	0.0264500i
$15$	1.26334	+	0.188088i	0.0842227	+	0.0125392i
$16$	−7.93255	−	13.7396i	−0.495784	−	0.858723i
$17$		−	4.12311i		−	0.242536i
$17$		−	4.12311i		−	0.242536i
$18$	−0.278115	+	0.913312i	−0.0154508	+	0.0507396i
$19$	8.85050			0.465816			0.232908	−	0.972499i	$-0.425176\pi$
$19$	8.85050			0.465816			0.232908	+	0.972499i	$0.425176\pi$
$20$	1.47071	−	0.849115i	0.0735355	−	0.0424557i
$21$	16.3987	+	13.0292i	0.780891	+	0.620438i
$22$	0.0598936	−	0.103739i	0.00272244	−	0.00471540i
$23$	−35.3768	−	20.4248i	−1.53812	−	0.888036i	−0.998949	−	0.0458416i	$-0.985403\pi$
$23$	−35.3768	−	20.4248i	−1.53812	−	0.888036i	−0.539174	−	0.842194i	$-0.681264\pi$
$24$	0.933086	+	2.36491i	0.0388786	+	0.0985380i
$25$	−12.4094	−	21.4937i	−0.496375	−	0.859746i
$26$			1.54890i			0.0595730i
$27$	−11.5830	+	24.3892i	−0.429002	+	0.903304i
$28$	27.8476			0.994558
$29$	−34.5797	+	19.9646i	−1.19240	+	0.688435i	−0.958851	−	0.283910i	$-0.908368\pi$
$29$	−34.5797	+	19.9646i	−1.19240	+	0.688435i	−0.233553	+	0.972344i	$0.575035\pi$
$30$	−0.126037	+	0.0497282i	−0.00420122	+	0.00165761i
$31$	−8.41833	+	14.5810i	−0.271559	+	0.470354i	−0.969261	−	0.246034i	$-0.920873\pi$
$31$	−8.41833	+	14.5810i	−0.271559	+	0.470354i	0.697702	+	0.716388i	$0.254206\pi$
$32$	4.39312	+	2.53637i	0.137285	+	0.0792616i
$33$	2.10739	−	2.65238i	0.0638602	−	0.0803752i
$34$	0.218689	+	0.378781i	0.00643203	+	0.0111406i
$35$			2.97243i			0.0849265i
$36$	8.11443	+	34.9696i	0.225401	+	0.971378i
$37$	60.2993			1.62971			0.814855	−	0.579664i	$-0.196816\pi$
$37$	60.2993			1.62971			0.814855	+	0.579664i	$0.196816\pi$
$38$	−0.813076	+	0.469430i	−0.0213967	+	0.0123534i
$39$	−6.45047	+	43.3262i	−0.165397	+	1.11093i
$40$	−0.180402	+	0.312465i	−0.00451005	+	0.00781163i
$41$	−0.494829	−	0.285690i	−0.0120690	−	0.00696804i	0.493953	−	0.869488i	$-0.335551\pi$
$41$	−0.494829	−	0.285690i	−0.0120690	−	0.00696804i	−0.506022	+	0.862520i	$0.668885\pi$
$42$	−2.19758	−	0.327179i	−0.0523233	−	0.00778997i
$43$	−12.5109	−	21.6695i	−0.290951	−	0.503941i	0.683084	−	0.730340i	$-0.260638\pi$
$43$	−12.5109	−	21.6695i	−0.290951	−	0.503941i	−0.974035	+	0.226398i	$0.927305\pi$
$44$		−	4.50417i		−	0.102367i
$45$	−3.73263	+	0.866127i	−0.0829472	+	0.0192473i
$46$	4.33332			0.0942026
$47$	−14.7477	+	8.51462i	−0.313782	+	0.181162i	−0.648618	−	0.761114i	$-0.724653\pi$
$47$	−14.7477	+	8.51462i	−0.313782	+	0.181162i	0.334836	+	0.942277i	$0.391319\pi$
$48$	37.2650	+	29.6080i	0.776353	+	0.616833i
$49$	0.129025	−	0.223479i	0.00263317	−	0.00456079i
$50$	2.28004	+	1.31638i	0.0456008	+	0.0263277i
$51$	4.53978	+	11.5061i	0.0890153	+	0.225610i
$52$	29.1204	+	50.4380i	0.560007	+	0.969961i
$53$		−	24.4489i		−	0.461300i	−0.973037	−	0.230650i	$-0.925915\pi$
$53$		−	24.4489i		−	0.461300i	0.973037	−	0.230650i	$-0.0740853\pi$
$54$	−0.229492	−	2.85495i	−0.00424984	−	0.0528694i
$55$	0.480770			0.00874128
$56$	−5.12381	+	2.95824i	−0.0914967	+	0.0528256i
$57$	−24.6986	+	9.74492i	−0.433308	+	0.170964i
$58$	2.11784	−	3.66821i	0.0365145	−	0.0632450i
$59$	−41.7773	−	24.1201i	−0.708089	−	0.408815i	0.102264	−	0.994757i	$-0.467391\pi$
$59$	−41.7773	−	24.1201i	−0.708089	−	0.408815i	−0.810353	+	0.585942i	$0.800725\pi$
$60$	−3.16930	+	3.98891i	−0.0528216	+	0.0664819i
$61$	−30.4999	−	52.8275i	−0.499999	−	0.866024i	0.500001	−	0.866025i	$-0.333333\pi$
$61$	−30.4999	−	52.8275i	−0.499999	−	0.866024i	−1.00000		9.53650e-7i	$1.00000\pi$
$62$		−	1.78603i		−	0.0288069i
$63$	−60.1088	−	18.3039i	−0.954108	−	0.290538i
$64$	62.9223			0.983160
$65$	−5.38370	+	3.10828i	−0.0828262	+	0.0478197i
$66$	−0.0529190	+	0.355444i	−0.000801803	+	0.00538551i
$67$	17.2958	−	29.9572i	0.258146	−	0.447122i	−0.707599	−	0.706614i	$-0.750222\pi$
$67$	17.2958	−	29.9572i	0.258146	−	0.447122i	0.965745	+	0.259492i	$0.0835550\pi$
$68$	14.2427	+	8.22301i	0.209451	+	0.120927i
$69$	121.213	+	18.0463i	1.75671	+	0.261541i
$70$	−0.157657	−	0.273070i	−0.00225225	−	0.00390101i
$71$			127.386i			1.79417i	0.441862	+	0.897083i	$0.354318\pi$
$71$			127.386i			1.79417i	−0.441862	+	0.897083i	$0.645682\pi$
$72$	−5.20782	−	5.57224i	−0.0723308	−	0.0773922i
$73$	−104.409			−1.43026			−0.715131	−	0.698990i	$-0.753633\pi$
$73$	−104.409			−1.43026			−0.715131	+	0.698990i	$0.753633\pi$
$74$	−5.53956	+	3.19827i	−0.0748590	+	0.0432198i
$75$	58.2958	+	46.3176i	0.777278	+	0.617568i
$76$	−17.6512	+	30.5728i	−0.232253	+	0.402273i
$77$	6.82747	+	3.94184i	0.0886685	+	0.0511928i
$78$	−1.70543	−	4.32242i	−0.0218645	−	0.0554156i
$79$	−29.2711	−	50.6991i	−0.370520	−	0.641760i	0.619125	−	0.785292i	$-0.287487\pi$
$79$	−29.2711	−	50.6991i	−0.370520	−	0.641760i	−0.989646	+	0.143532i	$0.954154\pi$
$80$			6.75465i			0.0844331i
$81$	5.47017	−	80.8151i	0.0675329	−	0.997717i
$82$	0.0606118			0.000739168
$83$	−69.6131	+	40.1911i	−0.838712	+	0.484231i	−0.856826	−	0.515605i	$-0.827567\pi$
$83$	−69.6131	+	40.1911i	−0.838712	+	0.484231i	0.0181143	+	0.999836i	$0.494234\pi$
$84$	−77.7126	+	30.6619i	−0.925151	+	0.365022i
$85$	−0.877717	+	1.52025i	−0.0103261	+	0.0178853i
$86$	2.29869	+	1.32715i	0.0267290	+	0.0154320i
$87$	74.5173	−	93.7883i	0.856521	−	1.07803i
$88$	0.478475	+	0.828743i	0.00543721	+	0.00941753i
$89$		−	22.9617i		−	0.257997i	−0.991645	−	0.128999i	$-0.958824\pi$
$89$		−	22.9617i		−	0.257997i	0.991645	−	0.128999i	$-0.0411763\pi$
$90$	0.296969	−	0.277547i	0.00329965	−	0.00308386i
$91$	−101.939			−1.12021
$92$	141.109	−	81.4695i	1.53380	−	0.885538i
$93$	7.43801	−	49.9593i	0.0799786	−	0.537197i
$94$	0.903229	−	1.56444i	0.00960882	−	0.0166430i
$95$	−3.26331	−	1.88407i	−0.0343506	−	0.0198324i
$96$	−15.0523	−	2.24101i	−0.156795	−	0.0233439i
$97$	−3.86636	−	6.69674i	−0.0398594	−	0.0690385i	0.845407	−	0.534122i	$-0.179358\pi$
$97$	−3.86636	−	6.69674i	−0.0398594	−	0.0690385i	−0.885267	+	0.465083i	$0.846024\pi$
$98$			0.0273740i			0.000279326i
$99$	−2.96053	+	9.72219i	−0.0299043	+	0.0982040i
$100$	98.9956			0.989956
$101$	24.9210	−	14.3881i	0.246742	−	0.142457i	−0.371529	−	0.928421i	$-0.621167\pi$
$101$	24.9210	−	14.3881i	0.246742	−	0.142457i	0.618272	+	0.785965i	$0.287833\pi$
$102$	−1.02734	−	0.816251i	−0.0100720	−	0.00800246i
$103$	16.4552	−	28.5013i	0.159760	−	0.276712i	−0.775022	−	0.631934i	$-0.782261\pi$
$103$	16.4552	−	28.5013i	0.159760	−	0.276712i	0.934782	+	0.355222i	$0.115595\pi$
$104$	−10.7160	−	6.18688i	−0.103038	−	0.0594892i
$105$	−3.27282	−	8.29498i	−0.0311697	−	0.0789998i
$106$	1.29677	+	2.24607i	0.0122337	+	0.0211893i
$107$		−	107.879i		−	1.00821i	−0.863641	−	0.504107i	$-0.831822\pi$
$107$		−	107.879i		−	1.00821i	0.863641	−	0.504107i	$-0.168178\pi$
$108$	−61.1481	−	88.6531i	−0.566186	−	0.820862i
$109$	36.1080			0.331266			0.165633	−	0.986187i	$-0.447033\pi$
$109$	36.1080			0.331266			0.165633	+	0.986187i	$0.447033\pi$
$110$	−0.0441673	+	0.0255000i	−0.000401521	+	0.000231818i
$111$	−168.274	+	66.3931i	−1.51598	+	0.598136i
$112$	−55.3814	+	95.9234i	−0.494477	+	0.856459i
$113$	153.812	+	88.8036i	1.36117	+	0.785872i	0.989780	−	0.142604i	$-0.0455476\pi$
$113$	153.812	+	88.8036i	1.36117	+	0.785872i	0.371391	+	0.928477i	$0.378881\pi$
$114$	1.75213	−	2.20525i	0.0153696	−	0.0193443i
$115$	8.69597	+	15.0619i	0.0756172	+	0.130973i
$116$		−	159.267i		−	1.37300i
$117$	−29.7038	−	128.010i	−0.253879	−	1.09410i
$118$	5.11731			0.0433671
$119$	−24.9291	+	14.3928i	−0.209488	+	0.120948i
$120$	0.159394	−	1.07061i	0.00132828	−	0.00892176i
$121$	−59.8624	+	103.685i	−0.494731	+	0.856899i
$122$	5.60393	+	3.23543i	0.0459338	+	0.0265199i
$123$	1.69545	+	0.252421i	0.0137841	+	0.00205220i
$124$	−33.5786	−	58.1598i	−0.270795	−	0.469031i
$125$			21.2106i			0.169685i
$126$	6.49290	−	1.50663i	0.0515309	−	0.0119574i
$127$	148.304			1.16775			0.583874	−	0.811844i	$-0.301536\pi$
$127$	148.304			1.16775			0.583874	+	0.811844i	$0.301536\pi$
$128$	−23.3530	+	13.4829i	−0.182446	+	0.105335i
$129$	58.7727	+	46.6965i	0.455603	+	0.361988i
$130$	0.329726	−	0.571102i	0.00253635	−	0.00439309i
$131$	−213.272	−	123.133i	−1.62803	−	0.939944i	−0.984680	−	0.174372i	$-0.944210\pi$
$131$	−213.272	−	123.133i	−1.62803	−	0.939944i	−0.643351	−	0.765572i	$-0.722456\pi$
$132$	4.95935	+	12.5695i	0.0375708	+	0.0952235i
$133$	−30.8951	−	53.5118i	−0.232294	−	0.402345i
$134$			3.66947i			0.0273841i
$135$	9.46276	−	6.52689i	0.0700945	−	0.0483473i
$136$	−3.49410			−0.0256919
$137$	196.455	−	113.423i	1.43398	−	0.827907i	0.436556	−	0.899677i	$-0.356198\pi$
$137$	196.455	−	113.423i	1.43398	−	0.827907i	0.997421	+	0.0717696i	$0.0228646\pi$
$138$	−12.0927	+	4.77124i	−0.0876285	+	0.0345742i
$139$	19.1414	−	33.1538i	0.137708	−	0.238517i	−0.788921	−	0.614495i	$-0.789360\pi$
$139$	19.1414	−	33.1538i	0.137708	−	0.238517i	0.926629	+	0.375978i	$0.122693\pi$
$140$	−10.2678	−	5.92813i	−0.0733416	−	0.0423438i
$141$	31.7806	−	39.9994i	0.225394	−	0.283683i
$142$	−6.75653	−	11.7026i	−0.0475812	−	0.0824130i
$143$			16.4880i			0.115301i
$144$	−136.593	−	41.5943i	−0.948564	−	0.288850i
$145$	17.0001			0.117242
$146$	9.59184	−	5.53785i	0.0656975	−	0.0379305i
$147$	−0.114000	+	0.765713i	−0.000775513	+	0.00520893i
$148$	−120.259	+	208.295i	−0.812563	+	1.40740i
$149$	174.259	+	100.608i	1.16952	+	0.675224i	0.953567	−	0.301180i	$-0.0973805\pi$
$149$	174.259	+	100.608i	1.16952	+	0.675224i	0.215954	+	0.976403i	$0.430714\pi$
$150$	−7.81219	−	1.16309i	−0.0520813	−	0.00775393i
$151$	62.8728	+	108.899i	0.416376	+	0.721185i	0.995572	−	0.0940039i	$-0.0299666\pi$
$151$	62.8728	+	108.899i	0.416376	+	0.721185i	−0.579196	+	0.815189i	$0.696633\pi$
$152$		−	7.50031i		−	0.0493441i
$153$	−25.3378	−	27.1108i	−0.165606	−	0.177195i
$154$	−0.836300			−0.00543052
$155$	6.20793	−	3.58415i	0.0400511	−	0.0231235i
$156$	−136.800	−	108.691i	−0.876921	−	0.696737i
$157$	−58.2102	+	100.823i	−0.370765	+	0.642184i	−0.989683	−	0.143271i	$-0.954238\pi$
$157$	−58.2102	+	100.823i	−0.370765	+	0.642184i	0.618918	+	0.785455i	$0.287571\pi$
$158$	5.37815	+	3.10507i	0.0340389	+	0.0196524i
$159$	26.9197	+	68.2281i	0.169306	+	0.429107i
$160$	−1.07987	−	1.87040i	−0.00674921	−	0.0116900i
$161$			285.194i			1.77139i
$162$	3.78389	+	7.71444i	0.0233574	+	0.0476200i
$163$	−133.191			−0.817123			−0.408561	−	0.912731i	$-0.633969\pi$
$163$	−133.191			−0.817123			−0.408561	+	0.912731i	$0.633969\pi$
$164$	1.97375	−	1.13954i	0.0120350	−	0.00694844i
$165$	−1.34166	+	0.529357i	−0.00813126	+	0.00320822i
$166$	4.26347	−	7.38454i	0.0256835	−	0.0444852i
$167$	152.573	+	88.0878i	0.913608	+	0.527472i	0.881590	−	0.472015i	$-0.156473\pi$
$167$	152.573	+	88.0878i	0.913608	+	0.527472i	0.0320179	+	0.999487i	$0.489807\pi$
$168$	11.0415	−	13.8970i	0.0657234	−	0.0827202i
$169$	−22.0984	−	38.2756i	−0.130760	−	0.226483i
$170$		−	0.186216i		−	0.00109539i
$171$	58.1950	−	54.3891i	0.340322	−	0.318065i
$172$	99.8055			0.580264
$173$	−5.03796	+	2.90867i	−0.0291212	+	0.0168131i	−0.514490	−	0.857496i	$-0.672019\pi$
$173$	−5.03796	+	2.90867i	−0.0291212	+	0.0168131i	0.485369	+	0.874310i	$0.338685\pi$
$174$	−1.87122	+	12.5685i	−0.0107541	+	0.0722328i
$175$	−86.6365	+	150.059i	−0.495066	+	0.857479i
$176$	15.5150	+	8.95757i	0.0881533	+	0.0508953i
$177$	143.143	+	21.3113i	0.808717	+	0.120403i
$178$	1.21789	+	2.10944i	0.00684207	+	0.0118508i
$179$			222.907i			1.24529i	0.782504	+	0.622646i	$0.213942\pi$
$179$			222.907i			1.24529i	−0.782504	+	0.622646i	$0.786058\pi$
$180$	4.45234	−	14.6212i	0.0247352	−	0.0812289i
$181$	188.421			1.04100			0.520501	−	0.853861i	$-0.325745\pi$
$181$	188.421			1.04100			0.520501	+	0.853861i	$0.325745\pi$
$182$	9.36494	−	5.40685i	0.0514557	−	0.0297080i
$183$	143.281	+	113.840i	0.782954	+	0.622077i
$184$	−17.3089	+	29.9799i	−0.0940701	+	0.162934i
$185$	−22.2332	−	12.8364i	−0.120180	−	0.0693858i
$186$	1.96652	+	4.98416i	0.0105727	+	0.0267966i
$187$	2.32794	+	4.03211i	0.0124489	+	0.0215621i
$188$		−	67.9253i		−	0.361305i
$189$	187.896	−	15.1038i	0.994157	−	0.0799142i
$190$	0.399724			0.00210381
$191$	−121.584	+	70.1965i	−0.636565	+	0.367521i	−0.783290	−	0.621656i	$-0.786460\pi$
$191$	−121.584	+	70.1965i	−0.636565	+	0.367521i	0.146725	+	0.989177i	$0.453127\pi$
$192$	−175.593	+	69.2811i	−0.914549	+	0.360839i
$193$	−26.8095	+	46.4354i	−0.138909	+	0.240598i	−0.927084	−	0.374854i	$-0.877693\pi$
$193$	−26.8095	+	46.4354i	−0.138909	+	0.240598i	0.788175	+	0.615451i	$0.211026\pi$
$194$	0.710389	+	0.410143i	0.00366180	+	0.00211414i
$195$	11.6016	−	14.6019i	0.0594952	−	0.0748814i
$196$	0.514650	+	0.891400i	0.00262576	+	0.00454796i
$197$		−	265.787i		−	1.34917i	−0.738196	−	0.674586i	$-0.764322\pi$
$197$		−	265.787i		−	1.34917i	0.738196	−	0.674586i	$-0.235678\pi$
$198$	−0.243687	−	1.05018i	−0.00123074	−	0.00530395i
$199$	−268.572			−1.34961			−0.674805	−	0.737996i	$-0.735772\pi$
$199$	−268.572			−1.34961			−0.674805	+	0.737996i	$0.735772\pi$
$200$	−18.2147	+	10.5162i	−0.0910734	+	0.0525812i
$201$	−15.2817	+	102.643i	−0.0760284	+	0.510664i
$202$	−1.52629	+	2.64361i	−0.00755589	+	0.0130872i
$203$	241.420	+	139.384i	1.18926	+	0.686619i
$204$	−48.8002	−	7.26544i	−0.239217	−	0.0356149i
$205$	0.121634	+	0.210676i	0.000593336	+	0.00102769i
$206$			3.49113i			0.0169473i
$207$	−358.132	+	83.1017i	−1.73010	+	0.401457i
$208$	−231.650			−1.11370
$209$	−8.65518	+	4.99707i	−0.0414124	+	0.0239094i
$210$	0.740631	+	0.588451i	0.00352682	+	0.00280215i
$211$	−38.7902	+	67.1866i	−0.183840	+	0.318420i	−0.943185	−	0.332268i	$-0.892186\pi$
$211$	−38.7902	+	67.1866i	−0.183840	+	0.318420i	0.759345	+	0.650688i	$0.225519\pi$
$212$	84.4552	+	48.7602i	0.398374	+	0.230001i
$213$	−140.259	−	355.488i	−0.658494	−	1.66896i
$214$	5.72188	+	9.91059i	0.0267378	+	0.0463112i
$215$			10.6531i			0.0495495i
$216$	20.6685	+	9.81599i	0.0956875	+	0.0454444i
$217$	117.546			0.541686
$218$	−3.31717	+	1.91517i	−0.0152164	+	0.00878517i
$219$	291.368	−	114.961i	1.33045	−	0.524934i
$220$	−0.958836	+	1.66075i	−0.00435835	+	0.00754888i
$221$	−52.1369	−	30.1013i	−0.235914	−	0.136205i
$222$	11.9374	−	15.0246i	0.0537723	−	0.0676784i
$223$	116.201	+	201.266i	0.521081	+	0.902539i	0.999699	+	0.0245162i	$0.00780454\pi$
$223$	116.201	+	201.266i	0.521081	+	0.902539i	−0.478618	+	0.878023i	$0.658862\pi$
$224$		−	35.4156i		−	0.158105i
$225$	−213.681	−	65.0686i	−0.949694	−	0.289194i
$226$	−18.8405			−0.0833652
$227$	−32.6237	+	18.8353i	−0.143717	+	0.0829749i	−0.570134	−	0.821552i	$-0.693109\pi$
$227$	−32.6237	+	18.8353i	−0.143717	+	0.0829749i	0.426417	+	0.904526i	$0.359775\pi$
$228$	15.5957	−	104.753i	0.0684023	−	0.459441i
$229$	151.296	−	262.053i	0.660682	−	1.14433i	−0.319755	−	0.947500i	$-0.603601\pi$
$229$	151.296	−	262.053i	0.660682	−	1.14433i	0.980437	−	0.196834i	$-0.0630661\pi$
$230$	−1.59776	−	0.922467i	−0.00694678	−	0.00401073i
$231$	−23.3932	−	3.48281i	−0.101269	−	0.0150771i
$232$	16.9189	+	29.3044i	0.0729263	+	0.126312i
$233$			152.352i			0.653870i	0.945047	+	0.326935i	$0.106016\pi$
$233$			152.352i			0.653870i	−0.945047	+	0.326935i	$0.893984\pi$
$234$	9.51847	+	10.1845i	0.0406772	+	0.0435236i
$235$	7.25028			0.0308523
$236$	166.639	−	96.2090i	0.706097	−	0.407665i
$237$	137.508	+	109.254i	0.580202	+	0.460986i
$238$	1.52679	−	2.64447i	0.00641507	−	0.0111112i
$239$	−164.111	−	94.7496i	−0.686658	−	0.396442i	0.115701	−	0.993284i	$-0.463089\pi$
$239$	−164.111	−	94.7496i	−0.686658	−	0.396442i	−0.802359	+	0.596842i	$0.796422\pi$
$240$	−7.43726	−	18.8498i	−0.0309886	−	0.0785408i
$241$	−165.351	−	286.396i	−0.686104	−	1.18837i	−0.973089	−	0.230431i	$-0.925986\pi$
$241$	−165.351	−	286.396i	−0.686104	−	1.18837i	0.286985	−	0.957935i	$-0.407347\pi$
$242$		−	12.7004i		−	0.0524809i
$243$	73.7169	+	231.549i	0.303362	+	0.952875i
$244$	243.313			0.997185
$245$	−0.0951472	+	0.0549333i	−0.000388356	+	0.000224217i
$246$	−0.169146	+	0.0667371i	−0.000687584	+	0.000271289i
$247$	64.6142	−	111.915i	0.261596	−	0.453098i
$248$	12.3566	+	7.13407i	0.0498249	+	0.0287664i
$249$	150.012	−	188.807i	0.602459	−	0.758261i
$250$	−1.12501	−	1.94857i	−0.00450003	−	0.00779428i
$251$		−	236.746i		−	0.943210i	−0.881810	−	0.471605i	$-0.843675\pi$
$251$		−	236.746i		−	0.943210i	0.881810	−	0.471605i	$-0.156325\pi$
$252$	183.107	−	171.132i	0.726617	−	0.679097i
$253$	46.1282			0.182325
$254$	−13.6244	+	7.86603i	−0.0536392	+	0.0309686i
$255$	0.775507	−	5.20889i	0.00304120	−	0.0204270i
$256$	−124.414	+	215.492i	−0.485993	+	0.841765i
$257$	−363.750	−	210.011i	−1.41537	−	0.817163i	−0.419481	−	0.907764i	$-0.637788\pi$
$257$	−363.750	−	210.011i	−1.41537	−	0.817163i	−0.995887	+	0.0906010i	$0.971121\pi$
$258$	−7.87610	−	1.17260i	−0.0305275	−	0.00454498i
$259$	−210.491	−	364.581i	−0.812707	−	1.40765i
$260$		−	24.7963i		−	0.0953704i
$261$	−104.684	+	343.777i	−0.401090	+	1.31715i
$262$	26.1238			0.0997090
$263$	253.584	−	146.407i	0.964198	−	0.556680i	0.0667353	−	0.997771i	$-0.478742\pi$
$263$	253.584	−	146.407i	0.964198	−	0.556680i	0.897462	+	0.441091i	$0.145408\pi$
$264$	−2.24775	−	1.78589i	−0.00851419	−	0.00676475i
$265$	−5.20462	+	9.01467i	−0.0196401	+	0.0340176i
$266$	5.67652	+	3.27734i	0.0213403	+	0.0123208i
$267$	25.2822	+	64.0779i	0.0946900	+	0.239992i
$268$	68.9886	+	119.492i	0.257420	+	0.445865i
$269$			29.9863i			0.111473i	0.998446	+	0.0557367i	$0.0177507\pi$
$269$			29.9863i			0.111473i	−0.998446	+	0.0557367i	$0.982249\pi$
$270$	−0.523137	+	1.10151i	−0.00193754	+	0.00407968i
$271$	213.417			0.787515			0.393758	−	0.919214i	$-0.371175\pi$
$271$	213.417			0.787515			0.393758	+	0.919214i	$0.371175\pi$
$272$	−56.6497	+	32.7067i	−0.208271	+	0.120245i
$273$	284.476	−	112.241i	1.04204	−	0.411140i
$274$	−12.0319	+	20.8399i	−0.0439121	+	0.0760580i
$275$	24.2710	+	14.0129i	0.0882583	+	0.0509559i
$276$	−304.082	+	382.721i	−1.10175	+	1.38667i
$277$	−108.677	−	188.235i	−0.392337	−	0.679548i	0.600420	−	0.799685i	$-0.295000\pi$
$277$	−108.677	−	188.235i	−0.392337	−	0.679548i	−0.992757	+	0.120137i	$0.961667\pi$
$278$			4.06102i			0.0146080i
$279$	34.2513	+	147.608i	0.122765	+	0.529061i
$280$	2.51897			0.00899632
$281$	−376.996	+	217.659i	−1.34162	+	0.774586i	−0.987045	−	0.160441i	$-0.948708\pi$
$281$	−376.996	+	217.659i	−1.34162	+	0.774586i	−0.354577	+	0.935027i	$0.615375\pi$
$282$	−0.798048	+	5.36029i	−0.00282996	+	0.0190081i
$283$	265.207	−	459.352i	0.937127	−	1.62315i	0.166330	−	0.986070i	$-0.446808\pi$
$283$	265.207	−	459.352i	0.937127	−	1.62315i	0.770796	−	0.637081i	$-0.219859\pi$
$284$	−440.036	−	254.055i	−1.54942	−	0.894559i
$285$	11.1812	+	1.66467i	0.0392323	+	0.00584096i
$286$	−0.874522	−	1.51472i	−0.00305777	−	0.00529621i
$287$			3.98911i			0.0138993i
$288$	44.4731	−	10.3196i	0.154420	−	0.0358321i
$289$	−17.0000			−0.0588235
$290$	−1.56176	+	0.901682i	−0.00538537	+	0.00310925i
$291$	18.1631	+	14.4311i	0.0624163	+	0.0495914i
$292$	208.231	−	360.666i	0.713119	−	1.23516i
$293$	−18.7053	−	10.7995i	−0.0638407	−	0.0368585i	0.467740	−	0.883866i	$-0.345068\pi$
$293$	−18.7053	−	10.7995i	−0.0638407	−	0.0368585i	−0.531581	+	0.847008i	$0.678402\pi$
$294$	−0.0301404	−	0.0763909i	−0.000102518	−	0.000259833i
$295$	10.2693	+	17.7869i	0.0348111	+	0.0602945i
$296$		−	51.1003i		−	0.172636i
$297$	−2.44294	−	30.3909i	−0.00822537	−	0.102326i
$298$	−21.3450			−0.0716276
$299$	−516.546	+	298.228i	−1.72758	+	0.997419i
$300$	−276.261	+	109.000i	−0.920871	+	0.363333i
$301$	−87.3453	+	151.286i	−0.290184	+	0.502613i
$302$	−11.5520	−	6.66953i	−0.0382516	−	0.0220845i
$303$	−53.7032	+	67.5915i	−0.177238	+	0.223074i
$304$	−70.2070	−	121.602i	−0.230944	−	0.400007i
$305$			25.9710i			0.0851509i
$306$	3.76568	+	1.14670i	0.0123061	+	0.00374738i
$307$	375.508			1.22315			0.611577	−	0.791185i	$-0.290536\pi$
$307$	375.508			1.22315			0.611577	+	0.791185i	$0.290536\pi$
$308$	−27.2331	+	15.7230i	−0.0884190	+	0.0510487i
$309$	−14.5390	+	97.6550i	−0.0470518	+	0.316036i
$310$	−0.380206	+	0.658535i	−0.00122647	+	0.00212431i
$311$	−41.2502	−	23.8158i	−0.132637	−	0.0765782i	0.432213	−	0.901771i	$-0.357733\pi$
$311$	−41.2502	−	23.8158i	−0.132637	−	0.0765782i	−0.564850	+	0.825193i	$0.691066\pi$
$312$	36.7166	+	5.46642i	0.117681	+	0.0175206i
$313$	11.0815	+	19.1937i	0.0354042	+	0.0613219i	0.883185	−	0.469026i	$-0.155395\pi$
$313$	11.0815	+	19.1937i	0.0354042	+	0.0613219i	−0.847780	+	0.530347i	$0.822061\pi$
$314$		−	12.3498i		−	0.0393307i
$315$	18.2665	+	19.5447i	0.0579889	+	0.0620467i
$316$	233.510			0.738956
$317$	311.395	−	179.784i	0.982318	−	0.567142i	0.0793491	−	0.996847i	$-0.474716\pi$
$317$	311.395	−	179.784i	0.982318	−	0.567142i	0.902969	+	0.429705i	$0.141382\pi$
$318$	−6.09186	−	4.84015i	−0.0191568	−	0.0152206i
$319$	22.5444	−	39.0480i	0.0706721	−	0.122408i
$320$	−23.2004	−	13.3947i	−0.0725011	−	0.0418586i
$321$	118.781	+	301.051i	0.370034	+	0.937853i
$322$	−15.1266	−	26.2001i	−0.0469771	−	0.0813668i
$323$		−	36.4915i		−	0.112977i
$324$	268.255	+	180.071i	0.827946	+	0.555776i
$325$	−362.385			−1.11503
$326$	12.2360	−	7.06444i	0.0375336	−	0.0216701i
$327$	−100.765	+	39.7571i	−0.308148	+	0.121581i
$328$	−0.242106	+	0.419340i	−0.000738128	+	0.00127848i
$329$	102.962	+	59.4452i	0.312955	+	0.180684i
$330$	0.0951781	−	0.119792i	0.000288418	−	0.000363007i
$331$	71.9604	+	124.639i	0.217403	+	0.376553i	0.954013	−	0.299765i	$-0.0969081\pi$
$331$	71.9604	+	124.639i	0.217403	+	0.376553i	−0.736610	+	0.676317i	$0.763575\pi$
$332$		−	320.625i		−	0.965737i
$333$	396.488	−	370.558i	1.19066	−	1.11279i
$334$	−18.6887			−0.0559541
$335$	−12.7544	+	7.36378i	−0.0380729	+	0.0219814i
$336$	48.9322	−	328.666i	0.145632	−	0.978172i
$337$	135.265	−	234.287i	0.401381	−	0.695212i	−0.592512	−	0.805562i	$-0.701864\pi$
$337$	135.265	−	234.287i	0.401381	−	0.695212i	0.993893	+	0.110349i	$0.0351970\pi$
$338$	4.06026	+	2.34419i	0.0120126	+	0.00693549i
$339$	−527.013	−	78.4624i	−1.55461	−	0.231452i
$340$	−3.50099	−	6.06389i	−0.0102970	−	0.0178350i
$341$		−	19.0123i		−	0.0557544i
$342$	−2.46146	+	8.08327i	−0.00719724	+	0.0236353i
$343$	−343.897			−1.00262
$344$	−18.3637	+	10.6023i	−0.0533828	+	0.0308206i
$345$	−40.8513	−	32.4575i	−0.118410	−	0.0940796i
$346$	0.308551	−	0.534426i	0.000891765	−	0.00154458i
$347$	88.3900	+	51.0320i	0.254726	+	0.147066i	0.621926	−	0.783076i	$-0.286350\pi$
$347$	88.3900	+	51.0320i	0.254726	+	0.147066i	−0.367200	+	0.930142i	$0.619684\pi$
$348$	175.363	+	444.458i	0.503916	+	1.27718i
$349$	139.781	+	242.108i	0.400519	+	0.693720i	0.993789	−	0.111284i	$-0.0354964\pi$
$349$	139.781	+	242.108i	0.400519	+	0.693720i	−0.593269	+	0.805004i	$0.702163\pi$
$350$		−	18.3808i		−	0.0525165i
$351$	223.839	+	324.525i	0.637719	+	0.924572i
$352$	−5.72823			−0.0162734
$353$	−211.978	+	122.385i	−0.600503	+	0.346701i	−0.769240	−	0.638961i	$-0.779365\pi$
$353$	−211.978	+	122.385i	−0.600503	+	0.346701i	0.168736	+	0.985661i	$0.446031\pi$
$354$	−14.2806	+	5.63446i	−0.0403406	+	0.0159166i
$355$	27.1176	−	46.9690i	0.0763875	−	0.132307i
$356$	79.3180	+	45.7943i	0.222803	+	0.128636i
$357$	53.7208	−	67.6136i	0.150478	−	0.189394i
$358$	−11.8230	−	20.4780i	−0.0330251	−	0.0572011i
$359$		−	372.376i		−	1.03726i	−0.854999	−	0.518630i	$-0.826442\pi$
$359$		−	372.376i		−	1.03726i	0.854999	−	0.518630i	$-0.173558\pi$
$360$	0.733995	+	3.16319i	0.00203887	+	0.00878665i
$361$	−282.669			−0.783016
$362$	−17.3099	+	9.99386i	−0.0478173	+	0.0276073i
$363$	52.8914	−	355.259i	0.145706	−	0.978675i
$364$	203.305	−	352.135i	0.558531	−	0.967403i
$365$	38.4972	+	22.2264i	0.105472	+	0.0608942i
$366$	−19.2009	−	2.85866i	−0.0524616	−	0.00781055i
$367$	348.128	+	602.975i	0.948578	+	1.64298i	0.748424	+	0.663220i	$0.230811\pi$
$367$	348.128	+	602.975i	0.948578	+	1.64298i	0.200154	+	0.979765i	$0.435856\pi$
$368$			648.083i			1.76110i
$369$	−5.00932	+	1.16237i	−0.0135754	+	0.00315007i
$370$	2.72336			0.00736043
$371$	−147.823	+	85.3455i	−0.398444	+	0.230042i
$372$	157.743	+	125.331i	0.424041	+	0.336912i
$373$	244.349	−	423.225i	0.655091	−	1.13465i	−0.326779	−	0.945101i	$-0.605963\pi$
$373$	244.349	−	423.225i	0.655091	−	1.13465i	0.981871	−	0.189551i	$-0.0607032\pi$
$374$	−0.427726	−	0.246948i	−0.00114365	−	0.000660288i
$375$	−23.3541	−	59.1911i	−0.0622776	−	0.157843i
$376$	7.21567	+	12.4979i	0.0191906	+	0.0332391i
$377$			583.017i			1.54646i
$378$	−16.4605	+	11.3535i	−0.0435462	+	0.0300357i
$379$	39.1190			0.103216			0.0516082	−	0.998667i	$-0.483565\pi$
$379$	39.1190			0.103216			0.0516082	+	0.998667i	$0.483565\pi$
$380$	13.0165	−	7.51509i	0.0342540	−	0.0197766i
$381$	−413.863	+	163.291i	−1.08625	+	0.428586i
$382$	7.44643	−	12.8976i	0.0194933	−	0.0337633i
$383$	−406.860	−	234.901i	−1.06230	−	0.613318i	−0.136231	−	0.990677i	$-0.543499\pi$
$383$	−406.860	−	234.901i	−1.06230	−	0.613318i	−0.926067	+	0.377359i	$0.876832\pi$
$384$	50.3244	−	63.3389i	0.131053	−	0.164945i
$385$	−1.67826	−	2.90683i	−0.00435912	−	0.00755021i
$386$		−	5.68789i		−	0.0147355i
$387$	−215.429	−	65.6009i	−0.556664	−	0.169511i
$388$	30.8439			0.0794946
$389$	319.341	−	184.372i	0.820929	−	0.473964i	−0.0298077	−	0.999556i	$-0.509489\pi$
$389$	319.341	−	184.372i	0.820929	−	0.473964i	0.850737	+	0.525592i	$0.176156\pi$
$390$	−0.291329	+	1.95679i	−0.000746998	+	0.00501740i
$391$	−84.2137	+	145.862i	−0.215380	+	0.373050i
$392$	−0.189386	−	0.109342i	−0.000483127	−	0.000278933i
$393$	730.742	+	108.794i	1.85939	+	0.276829i
$394$	14.0973	+	24.4173i	0.0357800	+	0.0619727i
$395$			24.9247i			0.0631004i
$396$	−27.6795	−	29.6164i	−0.0698978	−	0.0747889i
$397$	−488.915			−1.23152			−0.615761	−	0.787933i	$-0.711151\pi$
$397$	−488.915			−1.23152			−0.615761	+	0.787933i	$0.711151\pi$
$398$	24.6731	−	14.2450i	0.0619928	−	0.0357916i
$399$	145.137	+	115.315i	0.363751	+	0.289010i
$400$	−196.876	+	340.999i	−0.492189	+	0.852497i
$401$	228.193	+	131.747i	0.569059	+	0.328546i	0.756773	−	0.653677i	$-0.226775\pi$
$401$	228.193	+	131.747i	0.569059	+	0.328546i	−0.187714	+	0.982224i	$0.560108\pi$
$402$	−4.04030	−	10.2402i	−0.0100505	−	0.0254730i
$403$	122.918	+	212.901i	0.305008	+	0.528289i
$404$			114.781i			0.284112i
$405$	−19.2207	+	28.6332i	−0.0474584	+	0.0706994i
$406$	−29.5716			−0.0728364
$407$	−58.9686	+	34.0455i	−0.144886	+	0.0836499i
$408$	9.75078	−	3.84721i	0.0238990	−	0.00942944i
$409$	26.3114	−	45.5727i	0.0643311	−	0.111425i	−0.832066	−	0.554677i	$-0.812842\pi$
$409$	26.3114	−	45.5727i	0.0643311	−	0.111425i	0.896397	+	0.443252i	$0.146175\pi$
$410$	−0.0223485	−	0.0129029i	−5.45084e−5	−	3.14705e-5i
$411$	−423.349	+	532.832i	−1.03005	+	1.29643i
$412$	65.6358	+	113.684i	0.159310	+	0.275933i
$413$			336.791i			0.815475i
$414$	28.4931	−	26.6296i	0.0688238	−	0.0643228i
$415$	34.2232			0.0824655
$416$	64.1452	−	37.0342i	0.154195	−	0.0890246i
$417$	−16.9123	+	113.596i	−0.0405572	+	0.272413i
$418$	0.530088	−	0.918140i	0.00126815	−	0.00219651i
$419$	117.264	+	67.7026i	0.279867	+	0.161581i	0.633363	−	0.773855i	$-0.281674\pi$
$419$	117.264	+	67.7026i	0.279867	+	0.161581i	−0.353496	+	0.935436i	$0.615007\pi$
$420$	35.1810	+	5.23780i	0.0837644	+	0.0124710i
$421$	−53.5411	−	92.7359i	−0.127176	−	0.220275i	0.795405	−	0.606078i	$-0.207258\pi$
$421$	−53.5411	−	92.7359i	−0.127176	−	0.220275i	−0.922581	+	0.385802i	$0.873925\pi$
$422$		−	8.22972i		−	0.0195017i
$423$	−44.6464	+	146.616i	−0.105547	+	0.346610i
$424$	−20.7191			−0.0488658
$425$	−88.6206	+	51.1651i	−0.208519	+	0.120389i
$426$	31.7403	+	25.2185i	0.0745078	+	0.0591984i
$427$	−212.937	+	368.817i	−0.498681	+	0.863741i
$428$	372.652	+	215.151i	0.870682	+	0.502688i
$429$	−18.1543	−	46.0121i	−0.0423176	−	0.107254i
$430$	−0.565042	−	0.978681i	−0.00131405	−	0.00227600i
$431$		−	169.107i		−	0.392359i	−0.980568	−	0.196179i	$-0.937147\pi$
$431$		−	169.107i		−	0.392359i	0.980568	−	0.196179i	$-0.0628535\pi$
$432$	426.980	−	34.3223i	0.988380	−	0.0794498i
$433$	−591.309			−1.36561			−0.682805	−	0.730601i	$-0.739240\pi$
$433$	−591.309			−1.36561			−0.682805	+	0.730601i	$0.739240\pi$
$434$	−10.7987	+	6.23462i	−0.0248817	+	0.0143655i
$435$	−47.4411	+	18.7181i	−0.109060	+	0.0430301i
$436$	−72.0129	+	124.730i	−0.165167	+	0.286078i
$437$	−313.103	−	180.770i	−0.716482	−	0.413661i
$438$	−20.6699	+	26.0153i	−0.0471915	+	0.0593957i
$439$	241.045	+	417.501i	0.549076	+	0.951028i	0.998338	+	0.0576279i	$0.0183537\pi$
$439$	241.045	+	417.501i	0.549076	+	0.951028i	−0.449262	+	0.893400i	$0.648313\pi$
$440$		−	0.407426i		−	0.000925969i
$441$	−0.524961	−	2.26235i	−0.00119039	−	0.00513005i
$442$	6.38627			0.0144486
$443$	236.134	−	136.332i	0.533034	−	0.307747i	−0.209217	−	0.977869i	$-0.567091\pi$
$443$	236.134	−	136.332i	0.533034	−	0.307747i	0.742251	+	0.670122i	$0.233758\pi$
$444$	106.255	−	713.690i	0.239313	−	1.60741i
$445$	−4.88804	+	8.46633i	−0.0109844	+	0.0190255i
$446$	−21.3503	−	12.3266i	−0.0478706	−	0.0276381i
$447$	−597.069	−	88.8925i	−1.33572	−	0.198865i
$448$	−219.647	−	380.440i	−0.490284	−	0.849197i
$449$			145.766i			0.324645i	0.986738	+	0.162323i	$0.0518985\pi$
$449$			145.766i			0.324645i	−0.986738	+	0.162323i	$0.948102\pi$
$450$	23.0816	−	5.35592i	0.0512925	−	0.0119020i
$451$	0.645212			0.00143062
$452$	−613.518	+	354.215i	−1.35734	+	0.783662i
$453$	−295.359	−	234.671i	−0.652008	−	0.518037i
$454$	1.99804	−	3.46071i	0.00440098	−	0.00762272i
$455$	37.5865	+	21.7006i	0.0826078	+	0.0476936i
$456$	8.25828	+	20.9307i	0.0181103	+	0.0459006i
$457$	298.290	+	516.653i	0.652713	+	1.13053i	0.982462	+	0.186463i	$0.0597026\pi$
$457$	298.290	+	516.653i	0.652713	+	1.13053i	−0.329749	+	0.944069i	$0.606964\pi$
$458$			32.0989i			0.0700850i
$459$	100.559	+	47.7581i	0.219083	+	0.104048i
$460$	−69.3721			−0.150809
$461$	−403.197	+	232.786i	−0.874613	+	0.504958i	−0.868879	−	0.495025i	$-0.835159\pi$
$461$	−403.197	+	232.786i	−0.874613	+	0.504958i	−0.00573478	+	0.999984i	$0.501825\pi$
$462$	2.33381	−	0.920815i	0.00505154	−	0.00199311i
$463$	425.247	−	736.550i	0.918460	−	1.59082i	0.116705	−	0.993167i	$-0.462767\pi$
$463$	425.247	−	736.550i	0.918460	−	1.59082i	0.801755	−	0.597653i	$-0.203900\pi$
$464$	548.610	+	316.740i	1.18235	+	0.682630i
$465$	−13.3777	+	16.8374i	−0.0287693	+	0.0362094i
$466$	−8.08072	−	13.9962i	−0.0173406	−	0.0300348i
$467$		−	407.155i		−	0.871852i	−0.899982	−	0.435926i	$-0.856421\pi$
$467$		−	407.155i		−	0.871852i	0.899982	−	0.435926i	$-0.143579\pi$
$468$	501.434	+	152.693i	1.07144	+	0.326267i
$469$	−241.503			−0.514931
$470$	−0.666068	+	0.384554i	−0.00141717	+	0.000818201i
$471$	51.4316	−	345.453i	0.109197	−	0.733447i
$472$	−20.4405	+	35.4039i	−0.0433061	+	0.0750083i
$473$	24.4696	+	14.1275i	0.0517327	+	0.0298679i
$474$	−18.4273	−	2.74349i	−0.0388762	−	0.00578795i
$475$	−109.829	−	190.230i	−0.231219	−	0.400483i
$476$		−	114.819i		−	0.241216i
$477$	−150.246	−	160.760i	−0.314982	−	0.337023i
$478$	20.1020			0.0420545
$479$	763.370	−	440.732i	1.59367	−	0.920108i	0.601005	−	0.799245i	$-0.294767\pi$
$479$	763.370	−	440.732i	1.59367	−	0.920108i	0.992669	−	0.120863i	$-0.0385663\pi$
$480$	5.07295	+	4.03060i	0.0105687	+	0.00839708i
$481$	440.223	−	762.488i	0.915224	−	1.58521i
$482$	30.3809	+	17.5404i	0.0630308	+	0.0363909i
$483$	−314.015	−	795.873i	−0.650134	−	1.64777i
$484$	−238.776	−	413.572i	−0.493339	−	0.854488i
$485$			3.29225i			0.00678814i
$486$	−19.0535	−	17.3619i	−0.0392048	−	0.0357241i
$487$	−190.530			−0.391233			−0.195616	−	0.980681i	$-0.562671\pi$
$487$	−190.530			−0.391233			−0.195616	+	0.980681i	$0.562671\pi$
$488$	−44.7683	+	25.8470i	−0.0917384	+	0.0529652i
$489$	371.688	−	146.651i	0.760098	−	0.299900i
$490$	0.00582731	−	0.0100932i	1.18925e−5	−	2.05984e-5i
$491$	−673.525	−	388.860i	−1.37174	−	0.791975i	−0.380594	−	0.924742i	$-0.624280\pi$
$491$	−673.525	−	388.860i	−1.37174	−	0.791975i	−0.991147	+	0.132767i	$0.957614\pi$
$492$	−4.25331	+	5.35327i	−0.00864494	+	0.0108806i
$493$	82.3162	+	142.576i	0.166970	+	0.289200i
$494$			13.7085i			0.0277501i
$495$	3.16123	−	2.95449i	0.00638632	−	0.00596866i
$496$	267.115			0.538539
$497$	770.199	−	444.675i	1.54970	−	0.894718i
$498$	−3.76699	+	25.3019i	−0.00756423	+	0.0508071i
$499$	74.7755	−	129.515i	0.149851	−	0.259549i	−0.781322	−	0.624129i	$-0.785454\pi$
$499$	74.7755	−	129.515i	0.149851	−	0.259549i	0.931172	+	0.364580i	$0.118787\pi$
$500$	−73.2689	−	42.3018i	−0.146538	−	0.0846037i
$501$	−522.765	−	77.8300i	−1.04344	−	0.155349i
$502$	12.5570	+	21.7493i	0.0250139	+	0.0433253i
$503$		−	913.509i		−	1.81612i	−0.418840	−	0.908060i	$-0.637563\pi$
$503$		−	913.509i		−	1.81612i	0.418840	−	0.908060i	$-0.362437\pi$
$504$	−15.5115	+	50.9389i	−0.0307768	+	0.101069i
$505$	−12.2516			−0.0242607
$506$	−4.23769	+	2.44663i	−0.00837489	+	0.00483524i
$507$	103.812	+	82.4817i	0.204758	+	0.162686i
$508$	−295.774	+	512.295i	−0.582231	+	1.00845i
$509$	469.072	+	270.819i	0.921555	+	0.532060i	0.884131	−	0.467239i	$-0.154751\pi$
$509$	469.072	+	270.819i	0.921555	+	0.532060i	0.0374244	+	0.999299i	$0.488085\pi$
$510$	0.205035	+	0.519662i	0.000402029	+	0.00101894i
$511$	364.469	+	631.278i	0.713246	+	1.23538i
$512$		−	134.259i		−	0.262224i
$513$	−102.516	+	215.857i	−0.199836	+	0.420773i
$514$	44.5558			0.0866845
$515$	−12.1346	+	7.00590i	−0.0235623	+	0.0136037i
$516$	−278.521	+	109.892i	−0.539770	+	0.212968i
$517$	9.61486	−	16.6534i	0.0185974	−	0.0322117i
$518$	38.6747	+	22.3288i	0.0746616	+	0.0431059i
$519$	10.8565	−	13.6641i	0.0209181	−	0.0263278i
$520$	2.63410	+	4.56239i	0.00506557	+	0.00877382i
$521$		−	716.530i		−	1.37530i	−0.726044	−	0.687649i	$-0.758643\pi$
$521$		−	716.530i		−	1.37530i	0.726044	−	0.687649i	$-0.241357\pi$
$522$	−8.61678	−	37.1345i	−0.0165072	−	0.0711389i
$523$	−337.220			−0.644780			−0.322390	−	0.946607i	$-0.604486\pi$
$523$	−337.220			−0.644780			−0.322390	+	0.946607i	$0.604486\pi$
$524$	850.688	−	491.145i	1.62345	−	0.937300i
$525$	76.5477	−	514.152i	0.145805	−	0.979337i
$526$	−15.5308	+	26.9001i	−0.0295262	+	0.0511409i
$527$	60.1189	+	34.7097i	0.114078	+	0.0658627i
$528$	−53.1595	−	7.91446i	−0.100681	−	0.0149895i
$529$	569.847	+	987.004i	1.07722	+	1.86579i
$530$		−	1.10421i		−	0.00208342i
$531$	−422.925	+	98.1366i	−0.796470	+	0.184815i
$532$	246.465			0.463281
$533$	−7.22513	+	4.17143i	−0.0135556	+	0.00782632i
$534$	−5.72131	−	4.54573i	−0.0107141	−	0.00851261i
$535$	−22.9650	+	39.7765i	−0.0429252	+	0.0743486i
$536$	−25.3871	−	14.6572i	−0.0473639	−	0.0273456i
$537$	−245.434	−	622.054i	−0.457047	−	1.15839i
$538$	−1.59047	−	2.75478i	−0.00295627	−	0.00512040i
$539$			0.291396i			0.000540623i
$540$	3.67393	+	45.7048i	0.00680357	+	0.0846385i
$541$	−147.530			−0.272699			−0.136349	−	0.990661i	$-0.543537\pi$
$541$	−147.530			−0.272699			−0.136349	+	0.990661i	$0.543537\pi$
$542$	−19.6061	+	11.3196i	−0.0361736	+	0.0208849i
$543$	−525.816	+	207.463i	−0.968354	+	0.382068i
$544$	10.4577	−	18.1133i	0.0192238	−	0.0332965i
$545$	−13.3136	−	7.68659i	−0.0244286	−	0.0141038i
$546$	−20.1809	+	25.3999i	−0.0369614	+	0.0465200i
$547$	−229.933	−	398.256i	−0.420353	−	0.728073i	0.575621	−	0.817717i	$-0.304761\pi$
$547$	−229.933	−	398.256i	−0.420353	−	0.728073i	−0.995974	+	0.0896437i	$0.971427\pi$
$548$			904.834i			1.65116i
$549$	−525.189	−	159.927i	−0.956628	−	0.291305i
$550$	−2.97297			−0.00540539
$551$	−306.048	+	176.697i	−0.555440	+	0.320684i
$552$	15.2933	−	102.721i	0.0277052	−	0.186089i
$553$	−204.358	+	353.958i	−0.369544	+	0.640068i
$554$	19.9679	+	11.5285i	0.0360432	+	0.0208095i
$555$	76.1786	+	11.3416i	0.137259	+	0.0204353i
$556$	76.3500	+	132.242i	0.137320	+	0.237846i
$557$		−	769.472i		−	1.38146i	−0.723114	−	0.690729i	$-0.757290\pi$
$557$		−	769.472i		−	1.38146i	0.723114	−	0.690729i	$-0.242710\pi$
$558$	−10.9757	−	11.7437i	−0.0196697	−	0.0210461i
$559$	−365.349			−0.653577
$560$	40.8399	−	23.5789i	0.0729284	−	0.0421052i
$561$	−10.9360	−	8.68898i	−0.0194938	−	0.0154884i
$562$	23.0892	−	39.9916i	0.0410840	−	0.0711595i
$563$	−535.297	−	309.054i	−0.950794	−	0.548941i	−0.0574662	−	0.998347i	$-0.518302\pi$
$563$	−535.297	−	309.054i	−0.950794	−	0.548941i	−0.893327	+	0.449407i	$0.851635\pi$
$564$	74.7898	+	189.555i	0.132606	+	0.336091i
$565$	−37.8086	−	65.4864i	−0.0669179	−	0.115905i
$566$			56.2662i			0.0994102i
$567$	−507.719	+	249.033i	−0.895448	+	0.439212i
$568$	107.952			0.190057
$569$	−274.325	+	158.382i	−0.482118	+	0.278351i	−0.721299	−	0.692624i	$-0.756454\pi$
$569$	−274.325	+	158.382i	−0.482118	+	0.278351i	0.239181	+	0.970975i	$0.423121\pi$
$570$	−1.11549	+	0.440120i	−0.00195699	+	0.000772140i
$571$	−129.845	+	224.898i	−0.227399	+	0.393866i	−0.957036	−	0.289968i	$-0.906355\pi$
$571$	−129.845	+	224.898i	−0.227399	+	0.393866i	0.729638	+	0.683834i	$0.239689\pi$
$572$	−56.9555	−	32.8832i	−0.0995725	−	0.0574882i
$573$	262.006	−	329.764i	0.457254	−	0.575504i
$574$	−0.211582	−	0.366471i	−0.000368610	−	0.000638450i
$575$			1013.84i			1.76319i
$576$	413.735	−	386.677i	0.718290	−	0.671315i
$577$	−470.615			−0.815624			−0.407812	−	0.913066i	$-0.633708\pi$
$577$	−470.615			−0.815624			−0.407812	+	0.913066i	$0.633708\pi$
$578$	1.56175	−	0.901678i	0.00270199	−	0.00156000i
$579$	23.6875	−	159.103i	0.0409111	−	0.274790i
$580$	−33.9045	+	58.7243i	−0.0584560	+	0.101249i
$581$	486.007	+	280.596i	0.836501	+	0.482954i
$582$	−2.43403	−	0.362382i	−0.00418218	−	0.000622649i
$583$	13.8041	+	23.9094i	0.0236777	+	0.0410109i
$584$			88.4810i			0.151509i
$585$	−16.2983	+	53.5226i	−0.0278603	+	0.0914915i
$586$	2.29122			0.00390994
$587$	965.284	−	557.307i	1.64444	−	0.949416i	0.665208	−	0.746658i	$-0.268343\pi$
$587$	965.284	−	557.307i	1.64444	−	0.949416i	0.979229	−	0.202757i	$-0.0649903\pi$
$588$	−2.41769	−	1.92092i	−0.00411171	−	0.00326686i
$589$	−74.5064	+	129.049i	−0.126496	+	0.219098i
$590$	−1.88683	−	1.08936i	−0.00319802	−	0.00184638i
$591$	292.647	+	741.716i	0.495173	+	1.25502i
$592$	−478.327	−	828.487i	−0.807985	−	1.39947i
$593$			560.788i			0.945680i	0.881148	+	0.472840i	$0.156771\pi$
$593$			560.788i			0.945680i	−0.881148	+	0.472840i	$0.843229\pi$
$594$	1.83635	+	2.66237i	0.00309151	+	0.00448210i
$595$	12.2556			0.0205977
$596$	−695.074	+	401.301i	−1.16623	+	0.673324i
$597$	749.489	−	295.714i	1.25542	−	0.495333i
$598$	31.6360	−	54.7951i	0.0529030	−	0.0916306i
$599$	813.259	+	469.535i	1.35769	+	0.783865i	0.989313	−	0.145809i	$-0.0465786\pi$
$599$	813.259	+	469.535i	1.35769	+	0.783865i	0.368382	+	0.929675i	$0.379912\pi$
$600$	39.2516	−	49.4025i	0.0654193	−	0.0823375i
$601$	270.710	+	468.883i	0.450433	+	0.780172i	0.998413	−	0.0563192i	$-0.0179365\pi$
$601$	270.710	+	468.883i	0.450433	+	0.780172i	−0.547980	+	0.836491i	$0.684603\pi$
$602$		−	18.5311i		−	0.0307826i
$603$	−70.3707	−	303.267i	−0.116701	−	0.502930i
$604$	−501.567			−0.830410
$605$	44.1443	−	25.4867i	0.0729658	−	0.0421268i
$606$	1.34855	−	9.05790i	0.00222533	−	0.0149470i
$607$	−264.278	+	457.743i	−0.435384	+	0.754106i	−0.997327	−	0.0730693i	$-0.976721\pi$
$607$	−264.278	+	457.743i	−0.435384	+	0.754106i	0.561943	+	0.827176i	$0.310054\pi$
$608$	38.8814	+	22.4482i	0.0639496	+	0.0369213i
$609$	−827.185	−	123.152i	−1.35827	−	0.202221i
$610$	−1.37750	−	2.38590i	−0.00225820	−	0.00391131i
$611$			248.648i			0.406953i
$612$	144.183	−	33.4567i	0.235594	−	0.0546677i
$613$	−582.529			−0.950292			−0.475146	−	0.879907i	$-0.657605\pi$
$613$	−582.529			−0.950292			−0.475146	+	0.879907i	$0.657605\pi$
$614$	−34.4971	+	19.9169i	−0.0561842	+	0.0324380i
$615$	−0.571403	−	0.453995i	−0.000929110	−	0.000738203i
$616$	3.34049	−	5.78590i	0.00542288	−	0.00939270i
$617$	569.239	+	328.650i	0.922592	+	0.532659i	0.884461	−	0.466614i	$-0.154526\pi$
$617$	569.239	+	328.650i	0.922592	+	0.532659i	0.0381309	+	0.999273i	$0.487860\pi$
$618$	−3.84394	−	9.74250i	−0.00621998	−	0.0157646i
$619$	61.4674	+	106.465i	0.0993011	+	0.171995i	0.911396	−	0.411531i	$-0.135006\pi$
$619$	61.4674	+	106.465i	0.0993011	+	0.171995i	−0.812094	+	0.583526i	$0.801673\pi$
$620$			28.5925i			0.0461170i
$621$	907.917	−	626.231i	1.46202	−	1.00842i
$622$	5.05276			0.00812340
$623$	−138.831	+	80.1542i	−0.222843	+	0.128658i
$624$	646.453	−	255.061i	1.03598	−	0.408751i
$625$	−305.719	+	529.521i	−0.489150	+	0.847233i
$626$	−2.03607	−	1.17552i	−0.00325251	−	0.00187783i
$627$	18.6514	−	23.4749i	0.0297471	−	0.0374400i
$628$	−232.186	−	402.157i	−0.369722	−	0.640378i
$629$		−	248.620i		−	0.395263i
$630$	−2.71475	−	0.826677i	−0.00430913	−	0.00131219i
$631$	536.175			0.849723			0.424861	−	0.905258i	$-0.360323\pi$
$631$	536.175			0.849723			0.424861	+	0.905258i	$0.360323\pi$
$632$	−42.9646	+	24.8056i	−0.0679820	+	0.0392494i
$633$	34.2731	−	230.204i	0.0541439	−	0.363671i
$634$	−19.0714	+	33.0327i	−0.0300811	+	0.0521021i
$635$	−54.6819	−	31.5706i	−0.0861132	−	0.0497175i
$636$	−289.372	−	43.0821i	−0.454987	−	0.0677392i
$637$	−1.88393	−	3.26307i	−0.00295751	−	0.00512256i
$638$			4.78301i			0.00749688i
$639$	782.826	+	837.605i	1.22508	+	1.31081i
$640$	11.4808			0.0179388
$641$	382.069	−	220.588i	0.596052	−	0.344131i	−0.171435	−	0.985195i	$-0.554840\pi$
$641$	382.069	−	220.588i	0.596052	−	0.344131i	0.767487	+	0.641065i	$0.221507\pi$
$642$	−26.8798	−	21.3568i	−0.0418689	−	0.0332660i
$643$	9.51552	−	16.4814i	0.0147986	−	0.0256320i	−0.858531	−	0.512761i	$-0.828623\pi$
$643$	9.51552	−	16.4814i	0.0147986	−	0.0256320i	0.873330	+	0.487129i	$0.161956\pi$
$644$	−985.160	−	568.783i	−1.52975	−	0.883203i
$645$	−11.7297	−	29.7291i	−0.0181856	−	0.0460916i
$646$	1.93551	+	3.35240i	0.00299614	+	0.00518947i
$647$			115.918i			0.179162i	0.995980	+	0.0895809i	$0.0285527\pi$
$647$			115.918i			0.179162i	−0.995980	+	0.0895809i	$0.971447\pi$
$648$	−68.4863	−	4.63566i	−0.105689	−	0.00715380i
$649$	54.4737			0.0839349
$650$	33.2915	−	19.2208i	0.0512177	−	0.0295705i
$651$	−328.028	+	129.425i	−0.503883	+	0.198809i
$652$	265.633	−	460.089i	0.407412	−	0.705658i
$653$	1080.89	+	624.054i	1.65527	+	0.955672i	0.974853	+	0.222850i	$0.0715361\pi$
$653$	1080.89	+	624.054i	1.65527	+	0.955672i	0.680420	+	0.732822i	$0.261797\pi$
$654$	7.14830	−	8.99693i	0.0109301	−	0.0137568i
$655$	52.4244	+	90.8017i	0.0800372	+	0.138628i
$656$			9.06498i			0.0138186i
$657$	−686.526	+	641.627i	−1.04494	+	0.976602i
$658$	−12.6119			−0.0191670
$659$	368.661	−	212.846i	0.559424	−	0.322984i	−0.193490	−	0.981102i	$-0.561981\pi$
$659$	368.661	−	212.846i	0.559424	−	0.322984i	0.752914	+	0.658118i	$0.228647\pi$
$660$	0.847179	−	5.69030i	0.00128361	−	0.00862166i
$661$	−201.761	+	349.460i	−0.305235	+	0.528683i	−0.977314	−	0.211797i	$-0.932068\pi$
$661$	−201.761	+	349.460i	−0.305235	+	0.528683i	0.672078	+	0.740480i	$0.265402\pi$
$662$	−13.2217	−	7.63354i	−0.0199723	−	0.0115310i
$663$	178.639	+	26.5960i	0.269440	+	0.0401146i
$664$	34.0598	+	58.9932i	0.0512948	+	0.0888452i
$665$			26.3075i			0.0395601i
$666$	−16.7701	+	55.0721i	−0.0251804	+	0.0826908i
$667$	1631.09			2.44542
$668$	−608.573	+	351.360i	−0.911038	+	0.525988i
$669$	−545.882	−	433.717i	−0.815966	−	0.648307i
$670$	0.781148	−	1.35299i	0.00116589	−	0.00201938i
$671$	59.6537	+	34.4411i	0.0889027	+	0.0513280i
$672$	38.9946	+	98.8321i	0.0580277	+	0.147072i
$673$	−260.614	−	451.396i	−0.387242	−	0.670722i	0.604836	−	0.796350i	$-0.293239\pi$
$673$	−260.614	−	451.396i	−0.387242	−	0.670722i	−0.992077	+	0.125628i	$0.959905\pi$
$674$			28.6978i			0.0425784i
$675$	667.951	−	53.6925i	0.989557	−	0.0795445i
$676$	176.290			0.260784
$677$	−739.406	+	426.896i	−1.09218	+	0.630571i	−0.934156	−	0.356865i	$-0.883846\pi$
$677$	−739.406	+	426.896i	−1.09218	+	0.630571i	−0.158024	+	0.987435i	$0.550512\pi$
$678$	52.5771	−	20.7445i	0.0775474	−	0.0305967i
$679$	−26.9932	+	46.7536i	−0.0397543	+	0.0688565i
$680$	1.28833	+	0.743816i	0.00189460	+	0.00109385i
$681$	70.3022	−	88.4831i	0.103234	−	0.129931i
$682$	1.00841	+	1.74661i	0.00147860	+	0.00256102i
$683$		−	582.940i		−	0.853499i	−0.904370	−	0.426750i	$-0.859659\pi$
$683$		−	582.940i		−	0.853499i	0.904370	−	0.426750i	$-0.140341\pi$
$684$	71.8168	+	309.499i	0.104995	+	0.452483i
$685$	−96.5811			−0.140994
$686$	31.5931	−	18.2403i	0.0460540	−	0.0265893i
$687$	−133.678	+	897.880i	−0.194582	+	1.30696i
$688$	−198.486	+	343.788i	−0.288498	+	0.499692i
$689$	−309.158	−	178.492i	−0.448705	−	0.259060i
$690$	5.47446	+	0.815046i	0.00793400	+	0.00118123i
$691$	−641.420	−	1110.97i	−0.928249	−	1.60777i	−0.786251	−	0.617907i	$-0.787981\pi$
$691$	−641.420	−	1110.97i	−0.928249	−	1.60777i	−0.141998	−	0.989867i	$-0.545353\pi$
$692$		−	23.2039i		−	0.0335316i
$693$	69.1168	−	16.0380i	0.0997357	−	0.0231429i
$694$	−10.8269			−0.0156008
$695$	−14.1154	+	8.14953i	−0.0203099	+	0.0117259i
$696$	−79.4804	−	63.1493i	−0.114196	−	0.0907317i
$697$	−1.17793	+	2.04023i	−0.00169000	+	0.00292716i
$698$	−25.6828	−	14.8280i	−0.0367948	−	0.0212435i
$699$	−167.748	−	425.159i	−0.239983	−	0.608239i
$700$	−345.571	−	598.547i	−0.493673	−	0.855067i
$701$			723.270i			1.03177i	0.856658	+	0.515884i	$0.172536\pi$
$701$			723.270i			1.03177i	−0.856658	+	0.515884i	$0.827464\pi$
$702$	−37.7764	−	17.9410i	−0.0538125	−	0.0255569i
$703$	533.679			0.759145
$704$	−61.5337	+	35.5265i	−0.0874058	+	0.0504637i
$705$	−20.2329	+	7.98299i	−0.0286992	+	0.0113234i
$706$	12.9826	−	22.4865i	0.0183890	−	0.0318506i
$707$	−173.987	−	100.451i	−0.246092	−	0.142081i
$708$	−359.097	+	451.964i	−0.507200	+	0.638367i
$709$	639.995	+	1108.50i	0.902673	+	1.56348i	0.824011	+	0.566574i	$0.191732\pi$
$709$	639.995	+	1108.50i	0.902673	+	1.56348i	0.0786623	+	0.996901i	$0.474935\pi$
$710$			5.75325i			0.00810317i
$711$	−504.029	−	153.483i	−0.708902	−	0.215870i
$712$	−19.4588			−0.0273298
$713$	595.628	−	343.886i	0.835382	−	0.482308i
$714$	−1.34899	+	9.06085i	−0.00188935	+	0.0126903i
$715$	3.50993	−	6.07937i	0.00490899	−	0.00850262i
$716$	−770.001	−	444.560i	−1.07542	−	0.620894i
$717$	562.300	+	83.7160i	0.784240	+	0.116759i
$718$	19.7508	+	34.2094i	0.0275081	+	0.0476453i
$719$			61.5730i			0.0856371i	0.999083	+	0.0428185i	$0.0136337\pi$
$719$			61.5730i			0.0856371i	−0.999083	+	0.0428185i	$0.986366\pi$
$720$	41.5094	+	44.4141i	0.0576520	+	0.0616862i
$721$	−229.766			−0.318677
$722$	25.9681	−	14.9927i	0.0359670	−	0.0207655i
$723$	776.774	+	617.168i	1.07438	+	0.853621i
$724$	−375.783	+	650.875i	−0.519037	+	0.898999i
$725$	858.224	+	495.496i	1.18376	+	0.683443i
$726$	13.9839	+	35.4422i	0.0192615	+	0.0488185i
$727$	371.772	+	643.929i	0.511379	+	0.885734i	0.999913	+	0.0131895i	$0.00419846\pi$
$727$	371.772	+	643.929i	0.511379	+	0.885734i	−0.488534	+	0.872545i	$0.662468\pi$
$728$			86.3879i			0.118665i
$729$	−460.666	−	565.002i	−0.631915	−	0.775038i
$730$	−4.71554			−0.00645964
$731$	−89.3456	+	51.5837i	−0.122224	+	0.0705659i
$732$	−678.999	+	267.902i	−0.927595	+	0.365986i
$733$	−625.594	+	1083.56i	−0.853470	+	1.47825i	0.0245867	+	0.999698i	$0.492173\pi$
$733$	−625.594	+	1083.56i	−0.853470	+	1.47825i	−0.878057	+	0.478556i	$0.841160\pi$
$734$	−63.9635	−	36.9293i	−0.0871437	−	0.0503125i
$735$	0.205037	−	0.258062i	0.000278962	−	0.000351104i
$736$	−103.610	−	179.458i	−0.140774	−	0.243828i
$737$			39.0615i			0.0530006i
$738$	0.398543	−	0.372479i	0.000540031	−	0.000504714i
$739$	1030.72			1.39475			0.697375	−	0.716707i	$-0.254351\pi$
$739$	1030.72			1.39475			0.697375	+	0.716707i	$0.254351\pi$
$740$	88.6828	−	51.2010i	0.119842	−	0.0691906i
$741$	−57.0899	+	383.459i	−0.0770444	+	0.517488i
$742$	9.05344	−	15.6810i	0.0122014	−	0.0211334i
$743$	−935.174	−	539.923i	−1.25865	−	0.726680i	−0.285835	−	0.958279i	$-0.592271\pi$
$743$	−935.174	−	539.923i	−1.25865	−	0.726680i	−0.972811	+	0.231599i	$0.925604\pi$
$744$	−42.3378	−	6.30330i	−0.0569056	−	0.00847218i
$745$	−42.8345	−	74.1916i	−0.0574960	−	0.0995860i
$746$			51.8410i			0.0694920i
$747$	−210.742	+	692.065i	−0.282118	+	0.926459i
$748$	−18.5711			−0.0248277
$749$	−652.256	+	376.580i	−0.870836	+	0.502777i
$750$	5.28498	+	4.19906i	0.00704664	+	0.00559874i
$751$	284.139	−	492.144i	0.378348	−	0.655318i	−0.612474	−	0.790491i	$-0.709826\pi$
$751$	284.139	−	492.144i	0.378348	−	0.655318i	0.990822	+	0.135173i	$0.0431589\pi$
$752$	233.974	+	135.085i	0.311136	+	0.179635i
$753$	260.671	+	660.672i	0.346177	+	0.877387i
$754$	−30.9231	−	53.5605i	−0.0410121	−	0.0710351i
$755$		−	53.5368i		−	0.0709097i
$756$	−322.560	+	679.181i	−0.426667	+	0.898387i
$757$	228.788			0.302230			0.151115	−	0.988516i	$-0.451714\pi$
$757$	228.788			0.302230			0.151115	+	0.988516i	$0.451714\pi$
$758$	−3.59378	+	2.07487i	−0.00474113	+	0.00273729i
$759$	−128.727	+	50.7898i	−0.169601	+	0.0669168i
$760$	−1.59665	+	2.76548i	−0.00210085	+	0.00363878i
$761$	−1005.67	−	580.622i	−1.32151	−	0.762973i	−0.337538	−	0.941312i	$-0.609594\pi$
$761$	−1005.67	−	580.622i	−1.32151	−	0.762973i	−0.983969	+	0.178339i	$0.942928\pi$
$762$	29.3597	−	36.9525i	0.0385298	−	0.0484941i
$763$	−126.045	−	218.316i	−0.165196	−	0.286129i
$764$		−	559.992i		−	0.732974i
$765$	3.57113	+	15.3900i	0.00466815	+	0.0201177i
$766$	49.8365			0.0650607
$767$	−610.001	+	352.184i	−0.795307	+	0.459171i
$768$	109.926	−	738.347i	0.143133	−	0.961390i
$769$	566.736	−	981.615i	0.736978	−	1.27648i	−0.216873	−	0.976200i	$-0.569586\pi$
$769$	566.736	−	981.615i	0.736978	−	1.27648i	0.953850	−	0.300283i	$-0.0970811\pi$
$770$	0.308356	+	0.178029i	0.000400462	+	0.000231207i
$771$	1246.33	+	185.555i	1.61651	+	0.240668i
$772$	−106.936	−	185.219i	−0.138518	−	0.239921i
$773$			795.299i			1.02885i	0.857536	+	0.514424i	$0.171994\pi$
$773$			795.299i			1.02885i	−0.857536	+	0.514424i	$0.828006\pi$
$774$	23.2705	−	5.39973i	0.0300652	−	0.00697640i
$775$	417.865			0.539180
$776$	−5.67511	+	3.27653i	−0.00731329	+	0.00422233i
$777$	988.830	+	785.652i	1.27263	+	1.01113i
$778$	−19.5581	+	33.8757i	−0.0251390	+	0.0435420i
$779$	−4.37948	−	2.52850i	−0.00562193	−	0.00324582i
$780$	27.3022	+	69.1975i	0.0350028	+	0.0887148i
$781$	−71.9232	−	124.575i	−0.0920911	−	0.159506i
$782$		−	17.8667i		−	0.0228475i
$783$	−86.3823	−	1074.62i	−0.110322	−	1.37244i
$784$	−4.09400			−0.00522194
$785$	42.9259	−	24.7833i	0.0546827	−	0.0315711i
$786$	−72.9020	+	28.7638i	−0.0927507	+	0.0365952i
$787$	675.973	−	1170.82i	0.858924	−	1.48770i	−0.0140323	−	0.999902i	$-0.504467\pi$
$787$	675.973	−	1170.82i	0.858924	−	1.48770i	0.872956	−	0.487798i	$-0.162200\pi$
$788$	918.123	+	530.079i	1.16513	+	0.672688i
$789$	−546.459	+	687.779i	−0.692597	+	0.871710i
$790$	−1.32200	−	2.28977i	−0.00167342	−	0.00289845i
$791$		−	1239.97i		−	1.56760i
$792$	8.23902	+	2.50889i	0.0104028	+	0.00316778i
$793$	−890.675			−1.12317
$794$	44.9155	−	25.9320i	0.0565686	−	0.0326599i
$795$	4.59854	−	30.8873i	0.00578433	−	0.0388520i
$796$	535.634	−	927.745i	0.672907	−	1.16551i
$797$	−1118.56	−	645.799i	−1.40346	−	0.810288i	−0.408714	−	0.912663i	$-0.634023\pi$
$797$	−1118.56	−	645.799i	−1.40346	−	0.810288i	−0.994746	+	0.102375i	$0.967356\pi$
$798$	−19.4497	−	2.89570i	−0.0243730	−	0.00362869i
$799$	35.1067	+	60.8065i	0.0439383	+	0.0761033i
$800$		−	125.899i		−	0.157374i
$801$	−141.107	−	150.981i	−0.176164	−	0.188491i
$802$	−27.9514			−0.0348521
$803$	102.105	−	58.9504i	0.127154	−	0.0734126i
$804$	−324.090	−	257.498i	−0.403097	−	0.320271i
$805$	60.7113	−	105.155i	0.0754178	−	0.130627i
$806$	−22.5844	−	13.0391i	−0.0280204	−	0.0161776i
$807$	−33.0167	−	83.6810i	−0.0409129	−	0.103694i
$808$	−12.1931	−	21.1191i	−0.0150905	−	0.0261375i
$809$		−	660.551i		−	0.816503i	−0.912869	−	0.408252i	$-0.866139\pi$
$809$		−	660.551i		−	0.816503i	0.912869	−	0.408252i	$-0.133861\pi$
$810$	0.247055	−	3.64993i	0.000305006	−	0.00450609i
$811$	1318.41			1.62565			0.812827	−	0.582505i	$-0.197927\pi$
$811$	1318.41			1.62565			0.812827	+	0.582505i	$0.197927\pi$
$812$	−962.962	+	555.966i	−1.18591	+	0.684688i
$813$	−595.569	+	234.984i	−0.732557	+	0.289033i
$814$	3.61154	−	6.25537i	0.00443678	−	0.00768474i
$815$	49.1095	+	28.3534i	0.0602571	+	0.0347894i
$816$	122.077	−	153.647i	0.149604	−	0.188293i
$817$	−110.728	−	191.786i	−0.135529	−	0.234744i
$818$			5.58222i			0.00682423i
$819$	−670.286	+	626.449i	−0.818420	+	0.764896i
$820$	−0.970333			−0.00118333
$821$	1277.87	−	737.780i	1.55648	−	0.898635i	0.558893	−	0.829240i	$-0.311226\pi$
$821$	1277.87	−	737.780i	1.55648	−	0.898635i	0.997589	−	0.0693956i	$-0.0221071\pi$
$822$	10.6308	−	71.4045i	0.0129328	−	0.0868668i
$823$	83.6675	−	144.916i	0.101662	−	0.176083i	−0.810708	−	0.585451i	$-0.800917\pi$
$823$	83.6675	−	144.916i	0.101662	−	0.176083i	0.912369	+	0.409368i	$0.134251\pi$
$824$	−24.1533	−	13.9449i	−0.0293122	−	0.0169234i
$825$	−83.1607	−	12.3811i	−0.100801	−	0.0150074i
$826$	−17.8634	−	30.9403i	−0.0216264	−	0.0374579i
$827$		−	780.858i		−	0.944205i	−0.881544	−	0.472103i	$-0.843495\pi$
$827$		−	780.858i		−	0.944205i	0.881544	−	0.472103i	$-0.156505\pi$
$828$	427.185	−	1402.85i	0.515924	−	1.69426i
$829$	−769.558			−0.928297			−0.464148	−	0.885757i	$-0.653640\pi$
$829$	−769.558			−0.928297			−0.464148	+	0.885757i	$0.653640\pi$
$830$	−3.14401	+	1.81519i	−0.00378796	+	0.00218698i
$831$	510.537	+	405.635i	0.614365	+	0.488129i
$832$	459.372	−	795.656i	0.552130	−	0.956317i
$833$	−0.921426	−	0.531986i	−0.00110615	−	0.000638638i
$834$	−4.47142	−	11.3328i	−0.00536142	−	0.0135885i
$835$	−37.5038	−	64.9586i	−0.0449148	−	0.0777947i
$836$		−	39.8641i		−	0.0476844i
$837$	−258.108	−	374.208i	−0.308373	−	0.447083i
$838$	−14.3638			−0.0171405
$839$	−741.579	+	428.151i	−0.883884	+	0.510311i	−0.871937	−	0.489618i	$-0.837136\pi$
$839$	−741.579	+	428.151i	−0.883884	+	0.510311i	−0.0119468	+	0.999929i	$0.503803\pi$
$840$	−7.02953	+	2.77353i	−0.00836849	+	0.00330182i
$841$	376.671	−	652.413i	0.447884	−	0.775758i
$842$	9.83741	+	5.67963i	0.0116834	+	0.00674540i
$843$	812.405	−	1022.50i	0.963707	−	1.21293i
$844$	−154.724	−	267.991i	−0.183323	−	0.317524i
$845$			18.8170i			0.0222687i
$846$	−3.67493	−	15.8373i	−0.00434389	−	0.0187203i
$847$	835.864			0.986853
$848$	−335.917	+	193.942i	−0.396129	+	0.228705i
$849$	−234.324	+	1573.89i	−0.275999	+	1.85382i
$850$	5.42759	−	9.40085i	0.00638539	−	0.0110598i
$851$	−2133.20	−	1231.60i	−2.50670	−	1.44724i
$852$	1507.71	+	224.470i	1.76961	+	0.263463i
$853$	−83.7978	−	145.142i	−0.0982389	−	0.170155i	0.812717	−	0.582659i	$-0.197988\pi$
$853$	−83.7978	−	145.142i	−0.0982389	−	0.170155i	−0.910956	+	0.412504i	$0.864654\pi$
$854$		−	45.1766i		−	0.0529000i
$855$	−33.0356	+	7.66566i	−0.0386381	+	0.00896568i
$856$	−91.4213			−0.106801
$857$	−371.896	+	214.714i	−0.433951	+	0.250542i	−0.701028	−	0.713133i	$-0.747275\pi$
$857$	−371.896	+	214.714i	−0.433951	+	0.250542i	0.267078	+	0.963675i	$0.413942\pi$
$858$	4.10827	+	3.26413i	0.00478819	+	0.00380435i
$859$	71.9865	−	124.684i	0.0838027	−	0.145151i	−0.821078	−	0.570816i	$-0.806627\pi$
$859$	71.9865	−	124.684i	0.0838027	−	0.145151i	0.904880	+	0.425666i	$0.139960\pi$
$860$	−36.7998	−	21.2464i	−0.0427904	−	0.0247051i
$861$	−4.39224	−	11.1322i	−0.00510133	−	0.0129293i
$862$	8.96939	+	15.5354i	0.0104053	+	0.0180226i
$863$			1085.72i			1.25808i	0.777374	+	0.629038i	$0.216551\pi$
$863$			1085.72i			1.25808i	−0.777374	+	0.629038i	$0.783449\pi$
$864$	−112.746	+	77.7659i	−0.130493	+	0.0900068i
$865$	2.47676			0.00286331
$866$	54.3223	−	31.3630i	0.0627278	−	0.0362159i
$867$	47.4409	−	18.7180i	0.0547184	−	0.0215894i
$868$	−234.430	+	406.045i	−0.270081	+	0.467794i
$869$	57.2503	+	33.0535i	0.0658807	+	0.0380362i
$870$	3.36550	−	4.23586i	0.00386839	−	0.00486880i
$871$	−252.540	−	437.413i	−0.289943	−	0.502196i
$872$		−	30.5996i		−	0.0350912i
$873$	−66.5762	−	20.2733i	−0.0762614	−	0.0232226i
$874$	38.3521			0.0438811
$875$	128.243	−	74.0413i	0.146564	−	0.0846186i
$876$	−183.982	+	1235.76i	−0.210026	+	1.41069i
$877$	54.9266	−	95.1356i	0.0626301	−	0.108478i	−0.833010	−	0.553258i	$-0.813385\pi$
$877$	54.9266	−	95.1356i	0.0626301	−	0.108478i	0.895640	+	0.444779i	$0.146718\pi$
$878$	−44.2885	−	25.5699i	−0.0504424	−	0.0291229i
$879$	64.0908	+	9.54192i	0.0729133	+	0.0108554i
$880$	−3.81373	−	6.60558i	−0.00433379	−	0.00750634i
$881$		−	331.425i		−	0.376192i	−0.982151	−	0.188096i	$-0.939768\pi$
$881$		−	331.425i		−	0.376192i	0.982151	−	0.188096i	$-0.0602316\pi$
$882$	0.168222	+	0.179993i	0.000190728	+	0.000204074i
$883$	−870.249			−0.985559			−0.492779	−	0.870154i	$-0.664019\pi$
$883$	−870.249			−0.985559			−0.492779	+	0.870154i	$0.664019\pi$
$884$	207.961	−	120.066i	0.235250	−	0.135822i
$885$	−48.2422	−	38.3297i	−0.0545110	−	0.0433104i
$886$	−14.4621	+	25.0491i	−0.0163229	+	0.0282721i
$887$	910.537	+	525.699i	1.02654	+	0.592671i	0.915990	−	0.401200i	$-0.131407\pi$
$887$	910.537	+	525.699i	1.02654	+	0.592671i	0.110545	+	0.993871i	$0.464740\pi$
$888$	56.2644	+	142.603i	0.0633609	+	0.160588i
$889$	−517.695	−	896.675i	−0.582335	−	1.00863i
$890$		−	1.03704i		−	0.00116522i
$891$	40.2795	+	82.1201i	0.0452070	+	0.0921662i
$892$	−926.994			−1.03923
$893$	−130.525	+	75.3586i	−0.146165	+	0.0843882i
$894$	59.5663	−	23.5021i	0.0666289	−	0.0262887i
$895$	47.4520	−	82.1892i	0.0530190	−	0.0918315i
$896$	163.040	+	94.1313i	0.181964	+	0.105057i
$897$	1113.13	−	1401.00i	1.24095	−	1.56187i
$898$	−7.73139	−	13.3912i	−0.00860957	−	0.0149122i
$899$		−	672.274i		−	0.747802i
$900$	650.930	−	608.360i	0.723255	−	0.675955i
$901$	−100.805			−0.111882
$902$	−0.0592742	+	0.0342220i	−6.57142e−5	+	3.79401e-5i
$903$	77.1739	−	518.358i	0.0854639	−	0.574040i
$904$	75.2561	−	130.347i	0.0832479	−	0.144190i
$905$	−69.4738	−	40.1107i	−0.0767666	−	0.0443212i
$906$	39.5809	+	5.89287i	0.0436876	+	0.00650427i
$907$	−5.14923	−	8.91872i	−0.00567721	−	0.00983321i	0.863173	−	0.504909i	$-0.168474\pi$
$907$	−5.14923	−	8.91872i	−0.00567721	−	0.00983321i	−0.868850	+	0.495075i	$0.835140\pi$
$908$		−	150.258i		−	0.165483i
$909$	75.4442	−	247.754i	0.0829969	−	0.272557i
$910$	−4.60399			−0.00505933
$911$	229.132	−	132.290i	0.251518	−	0.145214i	−0.368941	−	0.929453i	$-0.620280\pi$
$911$	229.132	−	132.290i	0.251518	−	0.145214i	0.620459	+	0.784239i	$0.286946\pi$
$912$	329.813	+	262.046i	0.361638	+	0.287331i
$913$	45.3846	−	78.6084i	0.0497093	−	0.0860990i
$914$	−54.8065	−	31.6425i	−0.0599633	−	0.0346198i
$915$	−28.5956	−	72.4758i	−0.0312521	−	0.0792085i
$916$	603.482	+	1045.26i	0.658823	+	1.14112i
$917$			1719.31i			1.87493i
$918$	−11.7712	+	0.946218i	−0.0128227	+	0.00103074i
$919$	68.7028			0.0747583			0.0373791	−	0.999301i	$-0.488099\pi$
$919$	68.7028			0.0747583			0.0373791	+	0.999301i	$0.488099\pi$
$920$	12.7641	−	7.36936i	0.0138740	−	0.00801017i
$921$	−1047.91	+	413.456i	−1.13779	+	0.448921i
$922$	24.6939	−	42.7710i	0.0267829	−	0.0463894i
$923$	1610.80	+	929.996i	1.74518	+	1.00758i
$924$	58.6857	−	73.8625i	0.0635126	−	0.0799377i
$925$	−748.276	−	1296.05i	−0.808947	−	1.40114i
$926$			90.2202i			0.0974301i
$927$	−66.9508	−	288.528i	−0.0722231	−	0.311250i
$928$	−202.551			−0.218266
$929$	−1540.88	+	889.625i	−1.65864	+	0.957616i	−0.685295	+	0.728265i	$0.740327\pi$
$929$	−1540.88	+	889.625i	−1.65864	+	0.957616i	−0.973344	+	0.229350i	$0.926340\pi$
$930$	0.335931	−	2.25636i	0.000361216	−	0.00242620i
$931$	1.14194	−	1.97790i	0.00122657	−	0.00212449i
$932$	−526.277	−	303.846i	−0.564675	−	0.326015i
$933$	141.337	+	21.0425i	0.151487	+	0.0225536i
$934$	21.5955	+	37.4044i	0.0231215	+	0.0400476i
$935$		−	1.98227i		−	0.00212007i
$936$	−108.482	+	25.1723i	−0.115899	+	0.0268935i
$937$	−431.455			−0.460465			−0.230232	−	0.973136i	$-0.573949\pi$
$937$	−431.455			−0.460465			−0.230232	+	0.973136i	$0.573949\pi$
$938$	22.1863	−	12.8093i	0.0236528	−	0.0136559i
$939$	−52.0580	−	41.3614i	−0.0554398	−	0.0440484i
$940$	−14.4598	+	25.0451i	−0.0153827	+	0.0266437i
$941$	1282.13	+	740.238i	1.36252	+	0.786650i	0.989959	−	0.141358i	$-0.0451468\pi$
$941$	1282.13	+	740.238i	1.36252	+	0.786650i	0.372560	+	0.928008i	$0.378480\pi$
$942$	13.5979	+	34.4640i	0.0144351	+	0.0365859i
$943$	11.6703	+	20.2136i	0.0123757	+	0.0214354i
$944$			765.336i			0.810737i
$945$	−72.4952	−	34.4298i	−0.0767144	−	0.0364336i
$946$	−2.99729			−0.00316838
$947$	278.744	−	160.933i	0.294345	−	0.169940i	−0.345555	−	0.938399i	$-0.612309\pi$
$947$	278.744	−	160.933i	0.294345	−	0.169940i	0.639900	+	0.768459i	$0.278976\pi$
$948$	−651.643	+	257.108i	−0.687387	+	0.271211i
$949$	−762.253	+	1320.26i	−0.803217	+	1.39121i
$950$	20.1795	+	11.6506i	0.0212416	+	0.0122638i
$951$	−671.038	+	844.576i	−0.705613	+	0.888093i
$952$	12.1971	+	21.1260i	0.0128121	+	0.0221912i
$953$			196.608i			0.206305i	0.994666	+	0.103152i	$0.0328929\pi$
$953$			196.608i			0.206305i	−0.994666	+	0.103152i	$0.967107\pi$
$954$	22.3295	+	6.79960i	0.0234062	+	0.00712747i
$955$	59.7730			0.0625896
$956$	654.598	−	377.932i	0.684726	−	0.395327i
$957$	−19.9191	+	133.792i	−0.0208141	+	0.139803i
$958$	−46.7527	+	80.9781i	−0.0488024	+	0.0845283i
$959$	−1371.56	−	791.870i	−1.43020	−	0.825724i
$960$	79.4923	+	11.8349i	0.0828044	+	0.0123280i
$961$	338.763	+	586.756i	0.352511	+	0.610568i
$962$			93.3975i			0.0970868i
$963$	−662.949	−	709.340i	−0.688421	−	0.736594i
$964$	1319.09			1.36835
$965$	19.7701	−	11.4143i	0.0204872	−	0.0118283i
$966$	71.0608	+	56.4597i	0.0735620	+	0.0584469i
$967$	−407.918	+	706.534i	−0.421839	+	0.730646i	−0.996119	−	0.0880126i	$-0.971948\pi$
$967$	−407.918	+	706.534i	−0.421839	+	0.730646i	0.574281	+	0.818658i	$0.305282\pi$
$968$	87.8671	+	50.7301i	0.0907718	+	0.0524071i
$969$	40.1793	+	101.835i	0.0414647	+	0.105093i
$970$	−0.174621	−	0.302452i	−0.000180021	−	0.000311806i
$971$		−	1415.72i		−	1.45800i	−0.684512	−	0.729001i	$-0.739985\pi$
$971$		−	1415.72i		−	1.45800i	0.684512	−	0.729001i	$-0.260015\pi$
$972$	−946.871	−	207.150i	−0.974147	−	0.213118i
$973$	−267.272			−0.274689
$974$	17.5036	−	10.1057i	0.0179708	−	0.0103755i
$975$	1011.29	−	399.007i	1.03722	−	0.409238i
$976$	−483.884	+	838.113i	−0.495783	+	0.858722i
$977$	−1002.00	−	578.507i	−1.02559	−	0.592126i	−0.109873	−	0.993946i	$-0.535044\pi$
$977$	−1002.00	−	578.507i	−1.02559	−	0.592126i	−0.915719	+	0.401820i	$0.868378\pi$
$978$	−26.3678	+	33.1868i	−0.0269609	+	0.0339333i
$979$	12.9644	+	22.4550i	0.0132425	+	0.0229367i
$980$		−	0.438230i		−	0.000447173i
$981$	237.423	−	221.895i	0.242021	−	0.226193i
$982$	82.5003			0.0840126
$983$	202.732	−	117.048i	0.206238	−	0.119072i	−0.393324	−	0.919400i	$-0.628675\pi$
$983$	202.732	−	117.048i	0.206238	−	0.119072i	0.599562	+	0.800328i	$0.295341\pi$
$984$	0.213913	−	1.43680i	0.000217391	−	0.00146016i
$985$	−56.5801	+	97.9996i	−0.0574417	+	0.0994920i
$986$	−15.1244	−	8.73208i	−0.0153392	−	0.00885607i
$987$	−352.783	−	52.5228i	−0.357429	−	0.0532146i
$988$	257.730	+	446.401i	0.260860	+	0.451823i
$989$			1022.13i			1.03350i
$990$	−0.133709	+	0.439093i	−0.000135060	+	0.000443529i
$991$	1623.25			1.63799			0.818994	−	0.573802i	$-0.194532\pi$
$991$	1623.25			1.63799			0.818994	+	0.573802i	$0.194532\pi$
$992$	−73.9655	+	42.7040i	−0.0745620	+	0.0430484i
$993$	−338.050	−	268.590i	−0.340433	−	0.270483i
$994$	−47.1710	+	81.7025i	−0.0474557	+	0.0821957i
$995$	99.0266	+	57.1730i	0.0995242	+	0.0574603i
$996$	353.026	+	894.748i	0.354444	+	0.898341i
$997$	417.690	+	723.460i	0.418947	+	0.725637i	0.995834	−	0.0911869i	$-0.0290661\pi$
$997$	417.690	+	723.460i	0.418947	+	0.725637i	−0.576887	+	0.816824i	$0.695733\pi$
$998$			15.8643i			0.0158961i
$999$	−698.450	+	1470.65i	−0.699149	+	1.47212i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.3.j.a.86.16	✓	64
3.2	odd	2		459.3.j.a.341.17		64
9.2	odd	6	inner	153.3.j.a.137.16	yes	64
9.7	even	3		459.3.j.a.35.17		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.j.a.86.16	✓	64	1.1	even	1	trivial
153.3.j.a.137.16	yes	64	9.2	odd	6	inner
459.3.j.a.35.17		64	9.7	even	3
459.3.j.a.341.17		64	3.2	odd	2

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	153.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0918678 + 0.0530399i) q^{2} +(-2.79064 + 1.10106i) q^{3} +(-1.99437 + 3.45436i) q^{4} +(-0.368715 - 0.212878i) q^{5} +(0.197970 - 0.249167i) q^{6} +(-3.49077 - 6.04619i) q^{7} -0.847445i q^{8} +(6.57534 - 6.14532i) q^{9} +0.0451640 q^{10} +(-0.977932 + 0.564609i) q^{11} +(1.76213 - 11.8358i) q^{12} +(7.30063 - 12.6451i) q^{13} +(0.641379 + 0.370300i) q^{14} +(1.26334 + 0.188088i) q^{15} +(-7.93255 - 13.7396i) q^{16} -4.12311i q^{17} +(-0.278115 + 0.913312i) q^{18} +8.85050 q^{19} +(1.47071 - 0.849115i) q^{20} +(16.3987 + 13.0292i) q^{21} +(0.0598936 - 0.103739i) q^{22} +(-35.3768 - 20.4248i) q^{23} +(0.933086 + 2.36491i) q^{24} +(-12.4094 - 21.4937i) q^{25} +1.54890i q^{26} +(-11.5830 + 24.3892i) q^{27} +27.8476 q^{28} +(-34.5797 + 19.9646i) q^{29} +(-0.126037 + 0.0497282i) q^{30} +(-8.41833 + 14.5810i) q^{31} +(4.39312 + 2.53637i) q^{32} +(2.10739 - 2.65238i) q^{33} +(0.218689 + 0.378781i) q^{34} +2.97243i q^{35} +(8.11443 + 34.9696i) q^{36} +60.2993 q^{37} +(-0.813076 + 0.469430i) q^{38} +(-6.45047 + 43.3262i) q^{39} +(-0.180402 + 0.312465i) q^{40} +(-0.494829 - 0.285690i) q^{41} +(-2.19758 - 0.327179i) q^{42} +(-12.5109 - 21.6695i) q^{43} -4.50417i q^{44} +(-3.73263 + 0.866127i) q^{45} +4.33332 q^{46} +(-14.7477 + 8.51462i) q^{47} +(37.2650 + 29.6080i) q^{48} +(0.129025 - 0.223479i) q^{49} +(2.28004 + 1.31638i) q^{50} +(4.53978 + 11.5061i) q^{51} +(29.1204 + 50.4380i) q^{52} -24.4489i q^{53} +(-0.229492 - 2.85495i) q^{54} +0.480770 q^{55} +(-5.12381 + 2.95824i) q^{56} +(-24.6986 + 9.74492i) q^{57} +(2.11784 - 3.66821i) q^{58} +(-41.7773 - 24.1201i) q^{59} +(-3.16930 + 3.98891i) q^{60} +(-30.4999 - 52.8275i) q^{61} -1.78603i q^{62} +(-60.1088 - 18.3039i) q^{63} +62.9223 q^{64} +(-5.38370 + 3.10828i) q^{65} +(-0.0529190 + 0.355444i) q^{66} +(17.2958 - 29.9572i) q^{67} +(14.2427 + 8.22301i) q^{68} +(121.213 + 18.0463i) q^{69} +(-0.157657 - 0.273070i) q^{70} +127.386i q^{71} +(-5.20782 - 5.57224i) q^{72} -104.409 q^{73} +(-5.53956 + 3.19827i) q^{74} +(58.2958 + 46.3176i) q^{75} +(-17.6512 + 30.5728i) q^{76} +(6.82747 + 3.94184i) q^{77} +(-1.70543 - 4.32242i) q^{78} +(-29.2711 - 50.6991i) q^{79} +6.75465i q^{80} +(5.47017 - 80.8151i) q^{81} +0.0606118 q^{82} +(-69.6131 + 40.1911i) q^{83} +(-77.7126 + 30.6619i) q^{84} +(-0.877717 + 1.52025i) q^{85} +(2.29869 + 1.32715i) q^{86} +(74.5173 - 93.7883i) q^{87} +(0.478475 + 0.828743i) q^{88} -22.9617i q^{89} +(0.296969 - 0.277547i) q^{90} -101.939 q^{91} +(141.109 - 81.4695i) q^{92} +(7.43801 - 49.9593i) q^{93} +(0.903229 - 1.56444i) q^{94} +(-3.26331 - 1.88407i) q^{95} +(-15.0523 - 2.24101i) q^{96} +(-3.86636 - 6.69674i) q^{97} +0.0273740i q^{98} +(-2.96053 + 9.72219i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 2 q^{3} + 64 q^{4} - 18 q^{5} - 22 q^{6} + 2 q^{7} - 6 q^{9} - 44 q^{12} - 10 q^{13} + 72 q^{14} - 36 q^{15} - 128 q^{16} - 38 q^{18} - 28 q^{19} - 18 q^{20} + 88 q^{21} + 144 q^{23} - 42 q^{24}+ \cdots + 58 q^{99}+O(q^{100}) \) 64 * q - 2 * q^3 + 64 * q^4 - 18 * q^5 - 22 * q^6 + 2 * q^7 - 6 * q^9 - 44 * q^12 - 10 * q^13 + 72 * q^14 - 36 * q^15 - 128 * q^16 - 38 * q^18 - 28 * q^19 - 18 * q^20 + 88 * q^21 + 144 * q^23 - 42 * q^24 + 154 * q^25 - 164 * q^27 + 32 * q^28 - 162 * q^29 - 220 * q^30 + 62 * q^31 + 126 * q^32 - 40 * q^33 + 12 * q^36 + 128 * q^37 - 36 * q^38 - 126 * q^39 - 144 * q^41 + 114 * q^42 - 64 * q^43 - 72 * q^45 - 48 * q^46 + 288 * q^47 - 10 * q^48 - 246 * q^49 + 62 * q^52 + 374 * q^54 - 84 * q^55 + 684 * q^56 + 232 * q^57 + 138 * q^58 - 432 * q^59 - 86 * q^60 + 110 * q^61 + 304 * q^63 - 260 * q^64 + 328 * q^66 - 148 * q^67 + 36 * q^69 - 216 * q^70 - 96 * q^72 - 196 * q^73 - 918 * q^74 + 314 * q^75 - 112 * q^76 - 504 * q^77 + 276 * q^78 + 86 * q^79 + 234 * q^81 - 396 * q^82 - 594 * q^83 + 592 * q^84 + 126 * q^86 + 462 * q^87 + 24 * q^88 - 338 * q^90 + 52 * q^91 - 36 * q^92 - 1006 * q^93 - 186 * q^94 - 144 * q^95 + 18 * q^96 + 140 * q^97 + 58 * q^99

Introduction

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