LMFDB - Embedded newform 684.2.bs.a.23.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(23,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 15, 2]))

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

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

chi := DirichletCharacter("684.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$684 = 2^{2} \cdot 3^{2} \cdot 19$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	684.bs (of order $18$ , degree $6$ , minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$696$
Relative dimension:	$116$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			23.6
Character	$\chi$	$=$	684.23
Dual form			684.2.bs.a.119.6

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40179 - 0.187006i) q^{2} +(1.60726 - 0.645527i) q^{3} +(1.93006 + 0.524287i) q^{4} +(-0.300003 + 0.0528987i) q^{5} +(-2.37377 + 0.604329i) q^{6} -4.64420i q^{7} +(-2.60750 - 1.09588i) q^{8} +(2.16659 - 2.07506i) q^{9} +(0.430435 - 0.0180508i) q^{10} +(-0.364450 + 0.631246i) q^{11} +(3.44055 - 0.403236i) q^{12} +(2.47855 + 2.07975i) q^{13} +(-0.868492 + 6.51022i) q^{14} +(-0.448037 + 0.278682i) q^{15} +(3.45025 + 2.02381i) q^{16} +(1.52304 - 4.18452i) q^{17} +(-3.42516 + 2.50365i) q^{18} +(-2.92871 - 3.22841i) q^{19} +(-0.606758 - 0.0551904i) q^{20} +(-2.99796 - 7.46446i) q^{21} +(0.628931 - 0.816723i) q^{22} +(-5.74828 + 2.09220i) q^{23} +(-4.89836 - 0.0781486i) q^{24} +(-4.61126 + 1.67836i) q^{25} +(-3.08549 - 3.37889i) q^{26} +(2.14277 - 4.73376i) q^{27} +(2.43490 - 8.96358i) q^{28} +(-2.86006 + 3.40849i) q^{29} +(0.680171 - 0.306870i) q^{30} +(3.50772 - 2.02518i) q^{31} +(-4.45807 - 3.48218i) q^{32} +(-0.178281 + 1.24984i) q^{33} +(-2.91752 + 5.58102i) q^{34} +(0.245672 + 1.39328i) q^{35} +(5.26957 - 2.86907i) q^{36} +7.38739 q^{37} +(3.50173 + 5.07326i) q^{38} +(5.32621 + 1.74274i) q^{39} +(0.840229 + 0.190833i) q^{40} +(-1.17176 + 3.21939i) q^{41} +(2.80662 + 11.0243i) q^{42} +(3.21117 - 8.82262i) q^{43} +(-1.03436 + 1.02726i) q^{44} +(-0.540216 + 0.737136i) q^{45} +(8.44916 - 1.85788i) q^{46} +(4.91052 + 4.12042i) q^{47} +(6.85188 + 1.02557i) q^{48} -14.5686 q^{49} +(6.77790 - 1.49039i) q^{50} +(-0.253292 - 7.70879i) q^{51} +(3.69336 + 5.31351i) q^{52} +(-0.546835 + 0.651692i) q^{53} +(-3.88897 + 6.23506i) q^{54} +(0.0759441 - 0.208655i) q^{55} +(-5.08947 + 12.1098i) q^{56} +(-6.79124 - 3.29834i) q^{57} +(4.64663 - 4.24315i) q^{58} +(8.62647 - 7.23847i) q^{59} +(-1.01085 + 0.302973i) q^{60} +(0.263390 - 1.49376i) q^{61} +(-5.29583 + 2.18293i) q^{62} +(-9.63701 - 10.0621i) q^{63} +(5.59812 + 5.71499i) q^{64} +(-0.853589 - 0.492820i) q^{65} +(0.483641 - 1.71868i) q^{66} +(-2.53541 - 0.447060i) q^{67} +(5.13345 - 7.27785i) q^{68} +(-7.88843 + 7.07339i) q^{69} +(-0.0838314 - 1.99903i) q^{70} +(1.43374 - 1.20305i) q^{71} +(-7.92340 + 3.03641i) q^{72} +(-0.632028 - 3.58441i) q^{73} +(-10.3556 - 1.38148i) q^{74} +(-6.32808 + 5.67426i) q^{75} +(-3.95997 - 7.76651i) q^{76} +(2.93163 + 1.69258i) q^{77} +(-7.14036 - 3.43899i) q^{78} +(2.28594 + 2.72428i) q^{79} +(-1.14214 - 0.424636i) q^{80} +(0.388230 - 8.99162i) q^{81} +(2.24461 - 4.29379i) q^{82} +4.06716 q^{83} +(-1.87271 - 15.9786i) q^{84} +(-0.235562 + 1.33594i) q^{85} +(-6.15128 + 11.7670i) q^{86} +(-2.39660 + 7.32458i) q^{87} +(1.64207 - 1.24658i) q^{88} +(-14.9076 - 2.62861i) q^{89} +(0.895121 - 0.932289i) q^{90} +(9.65878 - 11.5109i) q^{91} +(-12.1914 + 1.02432i) q^{92} +(4.33052 - 5.51933i) q^{93} +(-6.11300 - 6.69428i) q^{94} +(1.04940 + 0.813609i) q^{95} +(-9.41314 - 2.71898i) q^{96} +(2.32282 + 13.1734i) q^{97} +(20.4222 + 2.72442i) q^{98} +(0.520261 + 2.12391i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$696 q - 9 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{6} - 18 q^{9} - 12 q^{10} - 3 q^{12} - 6 q^{13} - 9 q^{14} - 3 q^{16} - 12 q^{18} - 18 q^{20} + 24 q^{21} + 9 q^{22} + 45 q^{24} - 6 q^{25} + 72 q^{26} - 18 q^{29}+ \cdots + 45 q^{98}+O(q^{100})$ 696 * q - 9 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^6 - 18 * q^9 - 12 * q^10 - 3 * q^12 - 6 * q^13 - 9 * q^14 - 3 * q^16 - 12 * q^18 - 18 * q^20 + 24 * q^21 + 9 * q^22 + 45 * q^24 - 6 * q^25 + 72 * q^26 - 18 * q^29 - 9 * q^32 + 12 * q^33 + 15 * q^34 - 66 * q^36 - 48 * q^37 - 9 * q^38 + 12 * q^40 - 108 * q^41 + 126 * q^42 + 135 * q^44 - 6 * q^45 - 6 * q^46 - 18 * q^48 - 564 * q^49 - 9 * q^50 - 3 * q^52 - 66 * q^54 + 45 * q^56 - 12 * q^57 - 6 * q^58 + 9 * q^60 - 6 * q^61 - 18 * q^62 + 12 * q^64 - 18 * q^65 - 18 * q^66 - 6 * q^69 + 18 * q^70 + 12 * q^72 + 12 * q^73 - 90 * q^74 - 3 * q^76 - 36 * q^77 - 21 * q^78 + 18 * q^81 - 12 * q^82 + 81 * q^84 - 6 * q^85 - 9 * q^86 + 90 * q^88 - 117 * q^90 - 9 * q^92 - 30 * q^93 - 6 * q^94 - 87 * q^96 + 12 * q^97 + 45 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$ .

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

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

)

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

$2$	−1.40179	−	0.187006i	−0.991219	−	0.132233i
$2$	−1.40179	−	0.187006i	−0.991219	−	0.132233i
$3$	1.60726	−	0.645527i	0.927954	−	0.372695i
$3$	1.60726	−	0.645527i	0.927954	−	0.372695i
$4$	1.93006	+	0.524287i	0.965029	+	0.262144i
$5$	−0.300003	+	0.0528987i	−0.134166	+	0.0236570i	−0.240328	−	0.970692i	$-0.577255\pi$
$5$	−0.300003	+	0.0528987i	−0.134166	+	0.0236570i	0.106162	+	0.994349i	$0.466144\pi$
$6$	−2.37377	+	0.604329i	−0.969088	+	0.246716i
$7$		−	4.64420i		−	1.75534i	−0.479262	−	0.877672i	$-0.659096\pi$
$7$		−	4.64420i		−	1.75534i	0.479262	−	0.877672i	$-0.340904\pi$
$8$	−2.60750	−	1.09588i	−0.921891	−	0.387450i
$9$	2.16659	−	2.07506i	0.722197	−	0.691688i
$10$	0.430435	−	0.0180508i	0.136116	−	0.00570815i
$11$	−0.364450	+	0.631246i	−0.109886	+	0.190328i	−0.915724	−	0.401808i	$-0.868382\pi$
$11$	−0.364450	+	0.631246i	−0.109886	+	0.190328i	0.805838	+	0.592136i	$0.201715\pi$
$12$	3.44055	−	0.403236i	0.993202	−	0.116404i
$13$	2.47855	+	2.07975i	0.687426	+	0.576819i	0.918166	−	0.396197i	$-0.129670\pi$
$13$	2.47855	+	2.07975i	0.687426	+	0.576819i	−0.230740	+	0.973015i	$0.574115\pi$
$14$	−0.868492	+	6.51022i	−0.232114	+	1.73993i
$15$	−0.448037	+	0.278682i	−0.115683	+	0.0719555i
$16$	3.45025	+	2.02381i	0.862561	+	0.505952i
$17$	1.52304	−	4.18452i	0.369391	−	1.01489i	−0.606202	−	0.795311i	$-0.707308\pi$
$17$	1.52304	−	4.18452i	0.369391	−	1.01489i	0.975594	−	0.219584i	$-0.0704700\pi$
$18$	−3.42516	+	2.50365i	−0.807319	+	0.590115i
$19$	−2.92871	−	3.22841i	−0.671893	−	0.740648i
$19$	−2.92871	−	3.22841i	−0.671893	−	0.740648i
$20$	−0.606758	−	0.0551904i	−0.135675	−	0.0123410i
$21$	−2.99796	−	7.46446i	−0.654208	−	1.62888i
$22$	0.628931	−	0.816723i	0.134088	−	0.174126i
$23$	−5.74828	+	2.09220i	−1.19860	+	0.436254i	−0.862735	−	0.505656i	$-0.831250\pi$
$23$	−5.74828	+	2.09220i	−1.19860	+	0.436254i	−0.335864	+	0.941910i	$0.609028\pi$
$24$	−4.89836	−	0.0781486i	−0.999873	−	0.0159520i
$25$	−4.61126	+	1.67836i	−0.922252	+	0.335672i
$26$	−3.08549	−	3.37889i	−0.605115	−	0.662654i
$27$	2.14277	−	4.73376i	0.412377	−	0.911013i
$28$	2.43490	−	8.96358i	0.460152	−	1.69396i
$29$	−2.86006	+	3.40849i	−0.531100	+	0.632940i	−0.963168	−	0.268901i	$-0.913340\pi$
$29$	−2.86006	+	3.40849i	−0.531100	+	0.632940i	0.432068	+	0.901841i	$0.357784\pi$
$30$	0.680171	−	0.306870i	0.124182	−	0.0560265i
$31$	3.50772	−	2.02518i	0.630005	−	0.363734i	−0.150749	−	0.988572i	$-0.548168\pi$
$31$	3.50772	−	2.02518i	0.630005	−	0.363734i	0.780754	+	0.624838i	$0.214835\pi$
$32$	−4.45807	−	3.48218i	−0.788083	−	0.615568i
$33$	−0.178281	+	1.24984i	−0.0310347	+	0.217569i
$34$	−2.91752	+	5.58102i	−0.500350	+	0.957137i
$35$	0.245672	+	1.39328i	0.0415262	+	0.235507i
$36$	5.26957	−	2.86907i	0.878262	−	0.478179i
$37$	7.38739			1.21448			0.607239	−	0.794519i	$-0.292277\pi$
$37$	7.38739			1.21448			0.607239	+	0.794519i	$0.292277\pi$
$38$	3.50173	+	5.07326i	0.568055	+	0.822991i
$39$	5.32621	+	1.74274i	0.852877	+	0.279061i
$40$	0.840229	+	0.190833i	0.132852	+	0.0301733i
$41$	−1.17176	+	3.21939i	−0.182998	+	0.502784i	−0.996941	−	0.0781619i	$-0.975095\pi$
$41$	−1.17176	+	3.21939i	−0.182998	+	0.502784i	0.813942	+	0.580946i	$0.197317\pi$
$42$	2.80662	+	11.0243i	0.433072	+	1.70108i
$43$	3.21117	−	8.82262i	0.489699	−	1.34544i	−0.411254	−	0.911521i	$-0.634909\pi$
$43$	3.21117	−	8.82262i	0.489699	−	1.34544i	0.900953	−	0.433916i	$-0.142869\pi$
$44$	−1.03436	+	1.02726i	−0.155936	+	0.154866i
$45$	−0.540216	+	0.737136i	−0.0805307	+	0.109886i
$46$	8.44916	−	1.85788i	1.24576	−	0.273929i
$47$	4.91052	+	4.12042i	0.716273	+	0.601025i	0.926352	−	0.376660i	$-0.122927\pi$
$47$	4.91052	+	4.12042i	0.716273	+	0.601025i	−0.210078	+	0.977685i	$0.567372\pi$
$48$	6.85188	+	1.02557i	0.988983	+	0.148028i
$49$	−14.5686			−2.08123
$50$	6.77790	−	1.49039i	0.958540	−	0.210772i
$51$	−0.253292	−	7.70879i	−0.0354679	−	1.07945i
$52$	3.69336	+	5.31351i	0.512176	+	0.736851i
$53$	−0.546835	+	0.651692i	−0.0751135	+	0.0895168i	−0.802293	−	0.596931i	$-0.796387\pi$
$53$	−0.546835	+	0.651692i	−0.0751135	+	0.0895168i	0.727179	+	0.686448i	$0.240831\pi$
$54$	−3.88897	+	6.23506i	−0.529222	+	0.848484i
$55$	0.0759441	−	0.208655i	0.0102403	−	0.0281350i
$56$	−5.08947	+	12.1098i	−0.680109	+	1.61823i
$57$	−6.79124	−	3.29834i	−0.899522	−	0.436876i
$58$	4.64663	−	4.24315i	0.610132	−	0.557153i
$59$	8.62647	−	7.23847i	1.12307	−	0.942368i	0.124315	−	0.992243i	$-0.460327\pi$
$59$	8.62647	−	7.23847i	1.12307	−	0.942368i	0.998755	+	0.0498747i	$0.0158822\pi$
$60$	−1.01085	+	0.302973i	−0.130500	+	0.0391136i
$61$	0.263390	−	1.49376i	0.0337237	−	0.191256i	−0.963292	−	0.268456i	$-0.913487\pi$
$61$	0.263390	−	1.49376i	0.0337237	−	0.191256i	0.997016	+	0.0771994i	$0.0245978\pi$
$62$	−5.29583	+	2.18293i	−0.672571	+	0.277232i
$63$	−9.63701	−	10.0621i	−1.21415	−	1.26770i
$64$	5.59812	+	5.71499i	0.699764	+	0.714374i
$65$	−0.853589	−	0.492820i	−0.105875	−	0.0611268i
$66$	0.483641	−	1.71868i	0.0595321	−	0.211555i
$67$	−2.53541	−	0.447060i	−0.309749	−	0.0546171i	0.0166128	−	0.999862i	$-0.494712\pi$
$67$	−2.53541	−	0.447060i	−0.309749	−	0.0546171i	−0.326362	+	0.945245i	$0.605823\pi$
$68$	5.13345	−	7.27785i	0.622522	−	0.882569i
$69$	−7.88843	+	7.07339i	−0.949655	+	0.851536i
$70$	−0.0838314	−	1.99903i	−0.0100198	−	0.238930i
$71$	1.43374	−	1.20305i	0.170154	−	0.142776i	−0.553734	−	0.832693i	$-0.686798\pi$
$71$	1.43374	−	1.20305i	0.170154	−	0.142776i	0.723888	+	0.689917i	$0.242353\pi$
$72$	−7.92340	+	3.03641i	−0.933781	+	0.357845i
$73$	−0.632028	−	3.58441i	−0.0739732	−	0.419523i	−0.999196	−	0.0400981i	$-0.987233\pi$
$73$	−0.632028	−	3.58441i	−0.0739732	−	0.419523i	0.925223	−	0.379425i	$-0.123878\pi$
$74$	−10.3556	−	1.38148i	−1.20381	−	0.160594i
$75$	−6.32808	+	5.67426i	−0.730704	+	0.655207i
$76$	−3.95997	−	7.76651i	−0.454240	−	0.890879i
$77$	2.93163	+	1.69258i	0.334091	+	0.192887i
$78$	−7.14036	−	3.43899i	−0.808486	−	0.389389i
$79$	2.28594	+	2.72428i	0.257188	+	0.306505i	0.879152	−	0.476541i	$-0.158109\pi$
$79$	2.28594	+	2.72428i	0.257188	+	0.306505i	−0.621964	+	0.783046i	$0.713665\pi$
$80$	−1.14214	−	0.424636i	−0.127695	−	0.0474758i
$81$	0.388230	−	8.99162i	0.0431366	−	0.999069i
$82$	2.24461	−	4.29379i	0.247876	−	0.474170i
$83$	4.06716			0.446428			0.223214	−	0.974769i	$-0.428345\pi$
$83$	4.06716			0.446428			0.223214	+	0.974769i	$0.428345\pi$
$84$	−1.87271	−	15.9786i	−0.204329	−	1.74341i
$85$	−0.235562	+	1.33594i	−0.0255502	+	0.144903i
$86$	−6.15128	+	11.7670i	−0.663310	+	1.26887i
$87$	−2.39660	+	7.32458i	−0.256943	+	0.785278i
$88$	1.64207	−	1.24658i	0.175045	−	0.132886i
$89$	−14.9076	−	2.62861i	−1.58020	−	0.278632i	−0.686444	−	0.727182i	$-0.740829\pi$
$89$	−14.9076	−	2.62861i	−1.58020	−	0.278632i	−0.893758	+	0.448550i	$0.851941\pi$
$90$	0.895121	−	0.932289i	0.0943540	−	0.0982719i
$91$	9.65878	−	11.5109i	1.01252	−	1.20667i
$92$	−12.1914	+	1.02432i	−1.27104	+	0.106793i
$93$	4.33052	−	5.51933i	0.449054	−	0.572328i
$94$	−6.11300	−	6.69428i	−0.630508	−	0.690462i
$95$	1.04940	+	0.813609i	0.107666	+	0.0834745i
$96$	−9.41314	−	2.71898i	−0.960724	−	0.277504i
$97$	2.32282	+	13.1734i	0.235847	+	1.33755i	0.840823	+	0.541310i	$0.182071\pi$
$97$	2.32282	+	13.1734i	0.235847	+	1.33755i	−0.604976	+	0.796243i	$0.706817\pi$
$98$	20.4222	+	2.72442i	2.06296	+	0.275208i
$99$	0.520261	+	2.12391i	0.0522882	+	0.213461i
$100$	−9.77994	+	0.821709i	−0.977994	+	0.0821709i
$101$	1.40642	+	3.86412i	0.139944	+	0.384494i	0.989789	−	0.142539i	$-0.0455266\pi$
$101$	1.40642	+	3.86412i	0.139944	+	0.384494i	−0.849845	+	0.527033i	$0.823304\pi$
$102$	−1.08652	+	10.8535i	−0.107582	+	1.07466i
$103$			6.74443i			0.664549i	0.943183	+	0.332274i	$0.107816\pi$
$103$			6.74443i			0.664549i	−0.943183	+	0.332274i	$0.892184\pi$
$104$	−4.18367	−	8.13913i	−0.410243	−	0.798107i
$105$	1.29426	+	2.08077i	0.126307	+	0.203063i
$106$	0.888420	−	0.811278i	0.0862910	−	0.0787983i
$107$	9.93237	−	17.2034i	0.960198	−	1.66311i	0.238201	−	0.971216i	$-0.423442\pi$
$107$	9.93237	−	17.2034i	0.960198	−	1.66311i	0.721997	−	0.691896i	$-0.243224\pi$
$108$	6.61753	−	8.01301i	0.636772	−	0.771052i
$109$	11.9395	−	10.0185i	1.14360	−	0.959594i	0.144049	−	0.989571i	$-0.453988\pi$
$109$	11.9395	−	10.0185i	1.14360	−	0.959594i	0.999551	+	0.0299768i	$0.00954335\pi$
$110$	−0.145478	+	0.278289i	−0.0138708	+	0.0265338i
$111$	11.8735	−	4.76875i	1.12698	−	0.452630i
$112$	9.39898	−	16.0236i	0.888120	−	1.51409i
$113$	6.19538	+	3.57691i	0.582813	+	0.336487i	0.762250	−	0.647282i	$-0.224095\pi$
$113$	6.19538	+	3.57691i	0.582813	+	0.336487i	−0.179438	+	0.983769i	$0.557428\pi$
$114$	8.90312	+	5.89360i	0.833853	+	0.551986i
$115$	1.61383	−	0.931744i	0.150490	−	0.0868856i
$116$	−7.30711	+	5.07909i	−0.678448	+	0.471581i
$117$	9.68561	−	0.637179i	0.895435	−	0.0589072i
$118$	−13.4462	+	8.53365i	−1.23782	+	0.785586i
$119$	−19.4338	−	7.07331i	−1.78149	−	0.648409i
$120$	1.47366	−	0.235672i	0.134526	−	0.0215138i
$121$	5.23435	+	9.06616i	0.475850	+	0.824197i
$122$	−0.648561	+	2.04469i	−0.0587179	+	0.185118i
$123$	0.194872	+	5.93080i	0.0175710	+	0.534763i
$124$	7.83188	−	2.06967i	0.703324	−	0.185862i
$125$	2.61370	−	1.50902i	0.233777	−	0.134971i
$126$	11.6274	+	15.9072i	1.03586	+	1.41712i
$127$	8.73955	+	1.54102i	0.775509	+	0.136743i	0.547376	−	0.836887i	$-0.315627\pi$
$127$	8.73955	+	1.54102i	0.775509	+	0.136743i	0.228133	+	0.973630i	$0.426738\pi$
$128$	−6.77867	−	9.05812i	−0.599156	−	0.800632i
$129$	−0.534039	−	16.2532i	−0.0470195	−	1.43101i
$130$	1.10440	+	0.850458i	0.0968620	+	0.0745901i
$131$	−8.70295	+	7.30264i	−0.760380	+	0.638035i	−0.938226	−	0.346024i	$-0.887532\pi$
$131$	−8.70295	+	7.30264i	−0.760380	+	0.638035i	0.177846	+	0.984058i	$0.443087\pi$
$132$	−0.999368	+	2.31879i	−0.0869838	+	0.201825i
$133$	−14.9934	+	13.6015i	−1.30009	+	1.17940i
$134$	3.47052	+	1.10082i	0.299807	+	0.0950966i
$135$	−0.392429	+	1.53349i	−0.0337749	+	0.131982i
$136$	−8.55704	+	9.24207i	−0.733760	+	0.792501i
$137$	12.2080	+	2.15261i	1.04300	+	0.183909i	0.668804	−	0.743439i	$-0.266807\pi$
$137$	12.2080	+	2.15261i	1.04300	+	0.183909i	0.374199	+	0.927349i	$0.377918\pi$
$138$	12.3807	−	8.44026i	1.05392	−	0.718483i
$139$	−13.4192	+	15.9924i	−1.13820	+	1.35646i	−0.212967	+	0.977059i	$0.568313\pi$
$139$	−13.4192	+	15.9924i	−1.13820	+	1.35646i	−0.925234	+	0.379396i	$0.876132\pi$
$140$	−0.256316	+	2.81791i	−0.0216626	+	0.238157i
$141$	10.5523	+	3.45272i	0.888667	+	0.290772i
$142$	−2.23479	+	1.41831i	−0.187539	+	0.119022i
$143$	−2.21614	+	0.806609i	−0.185323	+	0.0674520i
$144$	11.6748	−	2.77471i	0.972900	−	0.231226i
$145$	0.677723	−	1.17385i	0.0562819	−	0.0974831i
$146$	0.215669	+	5.14280i	0.0178489	+	0.425621i
$147$	−23.4156	+	9.40444i	−1.93129	+	0.775665i
$148$	14.2581	+	3.87311i	1.17201	+	0.318368i
$149$	−0.158410	+	0.435228i	−0.0129775	+	0.0356553i	−0.946012	−	0.324131i	$-0.894928\pi$
$149$	−0.158410	+	0.435228i	−0.0129775	+	0.0356553i	0.933035	+	0.359786i	$0.117150\pi$
$150$	9.93179	−	6.77076i	0.810927	−	0.552830i
$151$	−7.36041	+	4.24954i	−0.598982	+	0.345822i	−0.768641	−	0.639680i	$-0.779067\pi$
$151$	−7.36041	+	4.24954i	−0.598982	+	0.345822i	0.169659	+	0.985503i	$0.445733\pi$
$152$	4.09869	+	11.6276i	0.332448	+	0.943122i
$153$	−5.38333	−	12.2265i	−0.435217	−	0.988457i
$154$	−3.79303	−	2.92088i	−0.305651	−	0.235371i
$155$	−0.945199	+	0.793116i	−0.0759202	+	0.0637046i
$156$	9.36621	+	6.15605i	0.749897	+	0.492878i
$157$	3.99458	+	22.6544i	0.318803	+	1.80802i	0.550059	+	0.835126i	$0.314605\pi$
$157$	3.99458	+	22.6544i	0.318803	+	1.80802i	−0.231256	+	0.972893i	$0.574284\pi$
$158$	−2.69496	−	4.24636i	−0.214400	−	0.337822i
$159$	−0.458223	+	1.40044i	−0.0363394	+	0.111062i
$160$	1.52164	+	0.808840i	0.120296	+	0.0639444i
$161$	9.71661	+	26.6962i	0.765776	+	2.10395i
$162$	−2.22570	+	12.5318i	−0.174868	+	0.984592i
$163$	0.468730	−	0.270622i	0.0367138	−	0.0211967i	−0.481531	−	0.876429i	$-0.659919\pi$
$163$	0.468730	−	0.270622i	0.0367138	−	0.0211967i	0.518245	+	0.855232i	$0.326586\pi$
$164$	−3.94945	+	5.59926i	−0.308400	+	0.437229i
$165$	−0.0126300	−	0.384387i	−0.000983246	−	0.0299245i
$166$	−5.70132	−	0.760581i	−0.442508	−	0.0590325i
$167$	10.3393	−	3.76320i	0.800080	−	0.291205i	0.0905603	−	0.995891i	$-0.471134\pi$
$167$	10.3393	−	3.76320i	0.800080	−	0.291205i	0.709520	+	0.704686i	$0.248912\pi$
$168$	−0.362938	+	22.7490i	−0.0280013	+	1.75512i
$169$	−0.439579	−	2.49298i	−0.0338138	−	0.191768i
$170$	0.580037	−	1.82866i	0.0444868	−	0.140252i
$171$	−13.0445	−	0.917377i	−0.997536	−	0.0701536i
$172$	10.8233	−	15.3446i	0.825271	−	1.17001i
$173$	5.73919	−	1.01197i	0.436342	−	0.0769389i	0.0488378	−	0.998807i	$-0.484448\pi$
$173$	5.73919	−	1.01197i	0.436342	−	0.0769389i	0.387505	+	0.921868i	$0.373337\pi$
$174$	4.72928	−	9.81939i	0.358526	−	0.744406i
$175$	7.79465	+	21.4156i	0.589220	+	1.61887i
$176$	−2.53496	+	1.44038i	−0.191080	+	0.108572i
$177$	9.19238	−	17.2027i	0.690942	−	1.29304i
$178$	20.4058	+	6.47258i	1.52948	+	0.485140i
$179$	−3.72746	−	6.45616i	−0.278604	−	0.482556i	0.692434	−	0.721481i	$-0.256538\pi$
$179$	−3.72746	−	6.45616i	−0.278604	−	0.482556i	−0.971038	+	0.238925i	$0.923205\pi$
$180$	−1.42912	+	1.13949i	−0.106520	+	0.0849322i
$181$	−22.2545	+	8.09997i	−1.65416	+	0.602066i	−0.989429	−	0.145016i	$-0.953677\pi$
$181$	−22.2545	+	8.09997i	−1.65416	+	0.602066i	−0.664733	+	0.747081i	$0.731454\pi$
$182$	−15.6922	+	14.3297i	−1.16319	+	1.06218i
$183$	−0.540925	−	2.57089i	−0.0399863	−	0.190046i
$184$	17.2814	+	0.843977i	1.27400	+	0.0622188i
$185$	−2.21624	+	0.390783i	−0.162941	+	0.0287309i
$186$	−7.10265	+	6.92714i	−0.520792	+	0.507922i
$187$	2.08639	+	2.48646i	0.152572	+	0.181828i
$188$	7.31731	+	10.5272i	0.533670	+	0.767773i
$189$	−21.9846	−	9.95147i	−1.59914	−	0.723863i
$190$	−1.31890	−	1.33676i	−0.0956829	−	0.0969785i
$191$	2.75293	+	4.76822i	0.199195	+	0.345016i	0.948268	−	0.317472i	$-0.102834\pi$
$191$	2.75293	+	4.76822i	0.199195	+	0.345016i	−0.749072	+	0.662488i	$0.769501\pi$
$192$	12.6868	+	5.57176i	0.915593	+	0.402107i
$193$	4.31360	+	1.57002i	0.310500	+	0.113013i	0.492570	−	0.870273i	$-0.336058\pi$
$193$	4.31360	+	1.57002i	0.310500	+	0.113013i	−0.182070	+	0.983286i	$0.558280\pi$
$194$	−0.792623	−	18.9007i	−0.0569070	−	1.35699i
$195$	−1.69007	−	0.241077i	−0.121028	−	0.0172639i
$196$	−28.1183	−	7.63814i	−2.00845	−	0.545582i
$197$	7.99009	+	4.61308i	0.569270	+	0.328668i	0.756858	−	0.653579i	$-0.226733\pi$
$197$	7.99009	+	4.61308i	0.569270	+	0.328668i	−0.187587	+	0.982248i	$0.560067\pi$
$198$	−0.332116	−	3.07457i	−0.0236025	−	0.218501i
$199$	7.00208	+	19.2380i	0.496364	+	1.36375i	0.894765	+	0.446538i	$0.147343\pi$
$199$	7.00208	+	19.2380i	0.496364	+	1.36375i	−0.398401	+	0.917211i	$0.630435\pi$
$200$	13.8631	+	0.677037i	0.980272	+	0.0478737i
$201$	−4.36365	+	0.918128i	−0.307788	+	0.0647598i
$202$	−1.24891	−	5.67971i	−0.0878727	−	0.399623i
$203$	15.8297	+	13.2827i	1.11103	+	0.932263i
$204$	3.55275	−	15.0112i	0.248742	−	1.05099i
$205$	0.181231	−	1.02781i	0.0126577	−	0.0717854i
$206$	1.26125	−	9.45431i	0.0878753	−	0.658713i
$207$	−8.11272	+	16.4610i	−0.563873	+	1.14412i
$208$	4.34259	+	12.1918i	0.301104	+	0.845346i
$209$	3.10529	−	0.672145i	0.214797	−	0.0464932i
$210$	−1.42517	−	3.15885i	−0.0983458	−	0.217981i
$211$	4.48888	+	5.34964i	0.309027	+	0.368284i	0.898097	−	0.439798i	$-0.144950\pi$
$211$	4.48888	+	5.34964i	0.309027	+	0.368284i	−0.589070	+	0.808082i	$0.700506\pi$
$212$	−1.39710	+	0.971105i	−0.0959530	+	0.0666958i
$213$	1.52780	−	2.85914i	0.104683	−	0.195905i
$214$	−17.1403	+	22.2582i	−1.17168	+	1.52154i
$215$	−0.496657	+	2.81668i	−0.0338717	+	0.192096i
$216$	−10.7749	+	9.99508i	−0.733139	+	0.680079i
$217$	−9.40537	−	16.2906i	−0.638478	−	1.10588i
$218$	−18.6103	+	11.8111i	−1.26045	+	0.799946i
$219$	−3.32967	−	5.35310i	−0.224998	−	0.361729i
$220$	0.255972	−	0.362899i	0.0172576	−	0.0244667i
$221$	12.4777	−	7.20399i	0.839340	−	0.484593i
$222$	−17.5360	+	4.46441i	−1.17694	+	0.299631i
$223$	−3.88016	+	10.6607i	−0.259835	+	0.713890i	0.739342	+	0.673330i	$0.235137\pi$
$223$	−3.88016	+	10.6607i	−0.259835	+	0.713890i	−0.999177	+	0.0405604i	$0.987086\pi$
$224$	−16.1720	+	20.7042i	−1.08053	+	1.38336i
$225$	−6.50801	+	13.2050i	−0.433867	+	0.880332i
$226$	−8.01575	−	6.17266i	−0.533200	−	0.410599i
$227$	−0.416567	−	0.721515i	−0.0276485	−	0.0478886i	0.851870	−	0.523753i	$-0.175469\pi$
$227$	−0.416567	−	0.721515i	−0.0276485	−	0.0478886i	−0.879519	+	0.475865i	$0.842135\pi$
$228$	−11.3782	−	9.92655i	−0.753540	−	0.657402i
$229$	4.46586	−	7.73510i	0.295112	−	0.511149i	−0.679899	−	0.733306i	$-0.737976\pi$
$229$	4.46586	−	7.73510i	0.295112	−	0.511149i	0.975011	+	0.222157i	$0.0713096\pi$
$230$	−2.43650	+	1.00432i	−0.160658	+	0.0662228i
$231$	5.80451	+	0.827973i	0.381909	+	0.0544766i
$232$	11.1929	−	5.75337i	0.734849	−	0.377727i
$233$	−15.7924	−	18.8206i	−1.03459	−	1.23298i	−0.972010	−	0.234940i	$-0.924511\pi$
$233$	−15.7924	−	18.8206i	−1.03459	−	1.23298i	−0.0625830	−	0.998040i	$-0.519934\pi$
$234$	−13.6964	−	0.918071i	−0.895362	−	0.0600162i
$235$	−1.69114	−	0.976379i	−0.110318	−	0.0636919i
$236$	20.4446	−	9.44791i	1.33083	−	0.615007i
$237$	5.43270	+	2.90300i	0.352892	+	0.188570i
$238$	25.9194	+	13.5495i	1.68010	+	0.878287i
$239$	12.8606			0.831881			0.415941	−	0.909392i	$-0.363452\pi$
$239$	12.8606			0.831881			0.415941	+	0.909392i	$0.363452\pi$
$240$	−2.10984	+	0.0547811i	−0.136189	+	0.00353611i
$241$	21.0742	−	7.67039i	1.35751	−	0.494094i	0.442227	−	0.896903i	$-0.354189\pi$
$241$	21.0742	−	7.67039i	1.35751	−	0.494094i	0.915284	+	0.402810i	$0.131966\pi$
$242$	−5.64206	−	13.6878i	−0.362686	−	0.879882i
$243$	−5.18035	−	14.7025i	−0.332319	−	0.943167i
$244$	1.29152	−	2.74495i	0.0826810	−	0.175728i
$245$	4.37064	−	0.770661i	0.279230	−	0.0492357i
$246$	0.835924	−	8.35021i	0.0532966	−	0.532390i
$247$	−0.544677	−	14.0928i	−0.0346570	−	0.896701i
$248$	−11.3657	+	1.43664i	−0.721725	+	0.0912270i
$249$	6.53699	−	2.62546i	0.414265	−	0.166382i
$250$	−3.94607	+	1.62656i	−0.249571	+	0.102873i
$251$	6.01767	+	5.04942i	0.379832	+	0.318717i	0.812636	−	0.582771i	$-0.198032\pi$
$251$	6.01767	+	5.04942i	0.379832	+	0.318717i	−0.432805	+	0.901488i	$0.642476\pi$
$252$	−13.3246	−	24.4730i	−0.839369	−	1.54165i
$253$	0.774266	−	4.39108i	0.0486777	−	0.276065i
$254$	−11.9629	−	3.79454i	−0.750617	−	0.238090i
$255$	0.483773	+	2.29926i	0.0302950	+	0.143985i
$256$	7.80839	+	13.9653i	0.488024	+	0.872830i
$257$	−3.04287	−	0.536539i	−0.189809	−	0.0334684i	0.0779356	−	0.996958i	$-0.475167\pi$
$257$	−3.04287	−	0.536539i	−0.189809	−	0.0334684i	−0.267744	+	0.963490i	$0.586278\pi$
$258$	−2.29082	+	22.8835i	−0.142620	+	1.42466i
$259$		−	34.3085i		−	2.13183i
$260$	−1.38910	−	1.39870i	−0.0861481	−	0.0867435i
$261$	0.876245	+	13.3196i	0.0542382	+	0.824463i
$262$	13.5654	−	8.60930i	0.838072	−	0.531884i
$263$	−7.83546	+	6.57473i	−0.483155	+	0.405415i	−0.851566	−	0.524248i	$-0.824346\pi$
$263$	−7.83546	+	6.57473i	−0.483155	+	0.405415i	0.368411	+	0.929663i	$0.379902\pi$
$264$	1.83454	−	3.06359i	0.112908	−	0.188551i
$265$	0.129579	−	0.224437i	0.00795995	−	0.0137870i
$266$	23.5612	−	16.2627i	1.44463	−	0.997132i
$267$	−25.6573	+	5.39838i	−1.57020	+	0.330375i
$268$	−4.65909	−	2.19213i	−0.284599	−	0.133906i
$269$	11.2293	−	1.98003i	0.684663	−	0.120725i	0.179512	−	0.983756i	$-0.442548\pi$
$269$	11.2293	−	1.98003i	0.684663	−	0.120725i	0.505151	+	0.863031i	$0.331437\pi$
$270$	0.836878	−	2.07626i	0.0509307	−	0.126357i
$271$	0.874173	+	1.04180i	0.0531022	+	0.0632848i	0.791942	−	0.610597i	$-0.209070\pi$
$271$	0.874173	+	1.04180i	0.0531022	+	0.0632848i	−0.738840	+	0.673881i	$0.764626\pi$
$272$	13.7235	−	11.3553i	0.832111	−	0.688515i
$273$	8.09362	−	24.7360i	0.489848	−	1.49709i
$274$	−16.7106	−	5.30048i	−1.00952	−	0.320214i
$275$	0.621115	−	3.52252i	0.0374546	−	0.212416i
$276$	−18.9336	+	9.51625i	−1.13967	+	0.572811i
$277$	−12.9150	+	22.3695i	−0.775988	+	1.34405i	0.158249	+	0.987399i	$0.449415\pi$
$277$	−12.9150	+	22.3695i	−0.775988	+	1.34405i	−0.934237	+	0.356652i	$0.883918\pi$
$278$	21.8016	−	19.9086i	1.30757	−	1.19404i
$279$	3.39741	−	11.6665i	0.203398	−	0.698454i
$280$	0.886266	−	3.90219i	0.0529645	−	0.233201i
$281$	30.2796	+	5.33911i	1.80633	+	0.318505i	0.972392	−	0.233353i	$-0.0749697\pi$
$281$	30.2796	+	5.33911i	1.80633	+	0.318505i	0.833938	+	0.551858i	$0.186081\pi$
$282$	−14.1465	−	6.81336i	−0.842414	−	0.405729i
$283$	−12.1287	−	14.4544i	−0.720976	−	0.859226i	0.273749	−	0.961801i	$-0.411736\pi$
$283$	−12.1287	−	14.4544i	−0.720976	−	0.859226i	−0.994725	+	0.102575i	$0.967292\pi$
$284$	3.39795	−	1.57027i	0.201631	−	0.0931782i
$285$	2.21187	+	0.630266i	0.131020	+	0.0373337i
$286$	3.25741	−	0.716270i	0.192615	−	0.0423539i
$287$	14.9515	+	5.44189i	0.882558	+	0.321225i
$288$	−16.8846	+	1.70632i	−0.994932	+	0.100546i
$289$	−2.16779	−	1.81899i	−0.127517	−	0.106999i
$290$	−1.16955	+	1.51876i	−0.0686781	+	0.0891847i
$291$	12.2371	+	19.6736i	0.717354	+	1.15329i
$292$	0.659409	−	7.24948i	0.0385890	−	0.424244i
$293$			31.6191i			1.84721i	0.383346	+	0.923605i	$0.374772\pi$
$293$			31.6191i			1.84721i	−0.383346	+	0.923605i	$0.625228\pi$
$294$	34.5826	−	8.80424i	2.01690	−	0.513473i
$295$	−2.20506	+	2.62789i	−0.128384	+	0.153002i
$296$	−19.2626	−	8.09565i	−1.11962	−	0.470550i
$297$	2.20724	+	3.07784i	0.128077	+	0.178594i
$298$	0.303448	−	0.580477i	0.0175783	−	0.0336261i
$299$	−18.5987	−	6.76936i	−1.07559	−	0.391482i
$300$	−15.1885	+	7.63392i	−0.876909	+	0.440744i
$301$	−40.9740	−	14.9133i	−2.36170	−	0.859590i
$302$	11.1125	−	4.58054i	0.639451	−	0.263580i
$303$	4.75488	+	5.30277i	0.273161	+	0.304636i
$304$	−3.57110	−	17.0660i	−0.204816	−	0.978800i
$305$			0.462066i			0.0264578i
$306$	5.25990	+	18.1458i	0.300688	+	1.03733i
$307$	17.5711	−	3.09827i	1.00284	−	0.176827i	0.351964	−	0.936013i	$-0.385514\pi$
$307$	17.5711	−	3.09827i	1.00284	−	0.176827i	0.650874	+	0.759186i	$0.274403\pi$
$308$	4.77082	+	4.80379i	0.271843	+	0.273722i
$309$	4.35371	+	10.8401i	0.247674	+	0.616671i
$310$	1.47329	−	0.935028i	0.0836774	−	0.0531060i
$311$	−0.0917239	−	0.158870i	−0.00520119	−	0.00900872i	0.863413	−	0.504498i	$-0.168322\pi$
$311$	−0.0917239	−	0.158870i	−0.00520119	−	0.00900872i	−0.868614	+	0.495489i	$0.834989\pi$
$312$	−11.9783	−	10.3810i	−0.678137	−	0.587711i
$313$	11.1466	+	9.35308i	0.630041	+	0.528667i	0.900942	−	0.433940i	$-0.142877\pi$
$313$	11.1466	+	9.35308i	0.630041	+	0.528667i	−0.270901	+	0.962607i	$0.587321\pi$
$314$	−1.36308	−	32.5038i	−0.0769232	−	1.83430i
$315$	3.42341	+	2.50887i	0.192887	+	0.141359i
$316$	2.98369	+	6.45650i	0.167846	+	0.363207i
$317$	−4.45282	−	12.2340i	−0.250095	−	0.687131i	−0.999682	−	0.0252246i	$-0.991970\pi$
$317$	−4.45282	−	12.2340i	−0.250095	−	0.687131i	0.749587	−	0.661906i	$-0.230252\pi$
$318$	0.904224	−	1.87744i	0.0507064	−	0.105281i
$319$	−1.10924	−	3.04763i	−0.0621058	−	0.170634i
$320$	−1.98177	−	1.41838i	−0.110784	−	0.0792900i
$321$	4.85870	−	34.0619i	0.271186	−	1.90115i
$322$	−8.62836	−	39.2396i	−0.480840	−	2.18674i
$323$	−17.9699	+	7.33826i	−0.999872	+	0.408312i
$324$	5.46350	−	17.1508i	0.303528	−	0.952823i
$325$	−14.9198	−	5.43036i	−0.827602	−	0.301222i
$326$	−0.707672	+	0.291701i	−0.0391943	+	0.0161558i
$327$	12.7228	−	23.8096i	0.703572	−	1.31667i
$328$	6.58341	−	7.11045i	0.363508	−	0.392609i
$329$	19.1361	−	22.8055i	1.05500	−	1.25731i
$330$	−0.0541779	+	0.541194i	−0.00298239	+	0.0297917i
$331$	−16.2026	−	9.35460i	−0.890578	−	0.514175i	−0.0164465	−	0.999865i	$-0.505235\pi$
$331$	−16.2026	−	9.35460i	−0.890578	−	0.514175i	−0.874132	+	0.485689i	$0.838569\pi$
$332$	7.84984	+	2.13236i	0.430816	+	0.117028i
$333$	16.0054	−	15.3293i	0.877093	−	0.840040i
$334$	−15.1973	+	3.34173i	−0.831561	+	0.182851i
$335$	0.784279			0.0428497
$336$	4.76295	−	31.8215i	0.259840	−	1.73601i
$337$	1.94718	+	11.0430i	0.106070	+	0.601551i	0.990788	+	0.135424i	$0.0432398\pi$
$337$	1.94718	+	11.0430i	0.106070	+	0.601551i	−0.884718	+	0.466127i	$0.845649\pi$
$338$	0.149999	+	3.57685i	0.00815886	+	0.194555i
$339$	12.2666	+	1.74974i	0.666230	+	0.0950331i
$340$	−1.15506	+	2.45493i	−0.0626420	+	0.133137i
$341$			2.95231i			0.159877i
$342$	18.1141	+	3.72537i	0.979500	+	0.201445i
$343$			35.1502i			1.89793i
$344$	−18.0416	+	19.4859i	−0.972739	+	1.05061i
$345$	1.99238	−	2.53933i	0.107266	−	0.136713i
$346$	−8.23441	+	0.345319i	−0.442684	+	0.0185644i
$347$	5.05444	+	28.6651i	0.271336	+	1.53883i	0.750364	+	0.661025i	$0.229878\pi$
$347$	5.05444	+	28.6651i	0.271336	+	1.53883i	−0.479027	+	0.877800i	$0.659011\pi$
$348$	−8.46577	+	12.8804i	−0.453813	+	0.690460i
$349$	−21.8215			−1.16808			−0.584040	−	0.811725i	$-0.698529\pi$
$349$	−21.8215			−1.16808			−0.584040	+	0.811725i	$0.698529\pi$
$350$	−6.92166	−	31.4780i	−0.369978	−	1.68257i
$351$	15.1560	−	7.27644i	0.808968	−	0.388387i
$352$	3.82286	−	1.54506i	0.203759	−	0.0823519i
$353$	15.5973	+	9.00511i	0.830161	+	0.479294i	0.853908	−	0.520424i	$-0.174226\pi$
$353$	15.5973	+	9.00511i	0.830161	+	0.479294i	−0.0237465	+	0.999718i	$0.507559\pi$
$354$	−16.1028	+	22.3957i	−0.855857	+	1.19032i
$355$	−0.366487	+	0.436763i	−0.0194511	+	0.0231810i
$356$	−27.3944	−	12.8892i	−1.45190	−	0.683128i
$357$	−35.8012	+	1.17634i	−1.89480	+	0.0622584i
$358$	4.01780	+	9.74726i	0.212347	+	0.515159i
$359$	−32.7644	−	11.9253i	−1.72924	−	0.629392i	−0.730665	−	0.682736i	$-0.760790\pi$
$359$	−32.7644	−	11.9253i	−1.72924	−	0.629392i	−0.998576	+	0.0533437i	$0.983012\pi$
$360$	2.21642	−	1.33007i	0.116816	−	0.0701009i
$361$	−1.84526	+	18.9102i	−0.0971192	+	0.995273i
$362$	32.7109	−	7.19278i	1.71925	−	0.378044i
$363$	14.2654	+	11.1928i	0.748741	+	0.587470i
$364$	24.6770	−	17.1527i	1.29343	−	0.899046i
$365$	0.379221	+	1.04190i	0.0198493	+	0.0545356i
$366$	0.277494	+	3.70502i	0.0145048	+	0.193664i
$367$	−6.55914	−	18.0211i	−0.342385	−	0.940694i	−0.984701	−	0.174254i	$-0.944249\pi$
$367$	−6.55914	−	18.0211i	−0.342385	−	0.940694i	0.642316	−	0.766440i	$-0.277974\pi$
$368$	−24.0672	−	4.41481i	−1.25459	−	0.230138i
$369$	4.14170	+	9.40657i	0.215608	+	0.489686i
$370$	3.17979	−	0.133348i	0.165310	−	0.00693243i
$371$	3.02659	+	2.53961i	0.157133	+	0.131850i
$372$	11.2519	−	8.38219i	0.583382	−	0.434596i
$373$	−0.115884	−	0.200717i	−0.00600025	−	0.0103927i	0.863010	−	0.505187i	$-0.168577\pi$
$373$	−0.115884	−	0.200717i	−0.00600025	−	0.0103927i	−0.869010	+	0.494795i	$0.835243\pi$
$374$	−2.45971	−	3.87567i	−0.127188	−	0.200406i
$375$	3.22679	−	4.11261i	0.166631	−	0.212374i
$376$	−8.28873	−	16.1253i	−0.427458	−	0.831599i
$377$	−14.1776	+	2.49989i	−0.730184	+	0.128751i
$378$	28.9569	+	18.0612i	1.48938	+	0.928966i
$379$			7.19225i			0.369441i	0.982791	+	0.184720i	$0.0591380\pi$
$379$			7.19225i			0.369441i	−0.982791	+	0.184720i	$0.940862\pi$
$380$	1.59884	+	2.12050i	0.0820189	+	0.108779i
$381$	15.0415	−	3.16479i	0.770600	−	0.162137i
$382$	−2.96736	−	7.19888i	−0.151824	−	0.368327i
$383$	−8.02869	−	2.92220i	−0.410247	−	0.149318i	0.128649	−	0.991690i	$-0.458936\pi$
$383$	−8.02869	−	2.92220i	−0.410247	−	0.149318i	−0.538896	+	0.842373i	$0.681158\pi$
$384$	−16.7424	−	10.1830i	−0.854381	−	0.519648i
$385$	−0.969035	−	0.352700i	−0.0493866	−	0.0179753i
$386$	−5.75318	−	3.00751i	−0.292829	−	0.153078i
$387$	−11.3502	−	25.7784i	−0.576963	−	1.31039i
$388$	−2.42345	+	26.6432i	−0.123032	+	1.35260i
$389$	−13.5627	+	16.1635i	−0.687659	+	0.819520i	−0.991070	−	0.133340i	$-0.957430\pi$
$389$	−13.5627	+	16.1635i	−0.687659	+	0.819520i	0.303412	+	0.952860i	$0.401874\pi$
$390$	2.32405	+	0.653993i	0.117683	+	0.0331162i
$391$			27.2403i			1.37760i
$392$	37.9877	+	15.9654i	1.91867	+	0.806374i
$393$	−9.27388	+	17.3553i	−0.467805	+	0.875457i
$394$	−10.3378	−	7.96079i	−0.520811	−	0.401059i
$395$	−0.829900	−	0.696369i	−0.0417568	−	0.0350381i
$396$	−0.109404	+	4.37203i	−0.00549777	+	0.219703i
$397$	−4.82177	−	1.75498i	−0.241998	−	0.0880799i	0.218174	−	0.975910i	$-0.429990\pi$
$397$	−4.82177	−	1.75498i	−0.241998	−	0.0880799i	−0.460172	+	0.887830i	$0.652212\pi$
$398$	−6.21785	−	28.2772i	−0.311673	−	1.41741i
$399$	−15.3182	+	31.5399i	−0.766868	+	1.57897i
$400$	−19.3067	−	3.54155i	−0.965333	−	0.177078i
$401$	−15.0786	−	17.9700i	−0.752991	−	0.897380i	0.244392	−	0.969677i	$-0.421412\pi$
$401$	−15.0786	−	17.9700i	−0.752991	−	0.897380i	−0.997383	+	0.0722965i	$0.976967\pi$
$402$	6.28864	−	0.470999i	0.313649	−	0.0234913i
$403$	12.9059	+	2.27566i	0.642890	+	0.113359i
$404$	0.688571	+	8.19534i	0.0342577	+	0.407733i
$405$	0.359175	+	2.71805i	0.0178475	+	0.135061i
$406$	−19.7061	−	21.5799i	−0.977996	−	1.07099i
$407$	−2.69233	+	4.66326i	−0.133454	+	0.231149i
$408$	−7.78741	+	20.3782i	−0.385534	+	1.00887i
$409$	3.74747	−	21.2530i	0.185300	−	1.05089i	−0.740268	−	0.672312i	$-0.765302\pi$
$409$	3.74747	−	21.2530i	0.185300	−	1.05089i	0.925569	−	0.378580i	$-0.123587\pi$
$410$	−0.446255	+	1.40689i	−0.0220390	+	0.0694813i
$411$	21.0111	−	4.42081i	1.03640	−	0.218062i
$412$	−3.53602	+	13.0171i	−0.174207	+	0.641309i
$413$	−33.6169	−	40.0631i	−1.65418	−	1.97138i
$414$	14.4507	−	21.5578i	0.710211	−	1.05951i
$415$	−1.22016	+	0.215147i	−0.0598953	+	0.0105612i
$416$	−3.80749	−	17.9024i	−0.186677	−	0.877739i
$417$	−11.2447	+	34.3664i	−0.550654	+	1.68293i
$418$	−4.47867	+	0.361502i	−0.219059	+	0.0176816i
$419$	19.3011	−	33.4306i	0.942923	−	1.63319i	0.183065	−	0.983101i	$-0.441398\pi$
$419$	19.3011	−	33.4306i	0.942923	−	1.63319i	0.759858	−	0.650089i	$-0.225269\pi$
$420$	1.40707	+	4.69458i	0.0686579	+	0.229072i
$421$	18.0094	−	15.1117i	0.877723	−	0.736497i	−0.0879868	−	0.996122i	$-0.528043\pi$
$421$	18.0094	−	15.1117i	0.877723	−	0.736497i	0.965710	+	0.259625i	$0.0835989\pi$
$422$	−5.29207	−	8.33854i	−0.257614	−	0.405914i
$423$	19.1892	−	1.26238i	0.933012	−	0.0613792i
$424$	2.14005	−	1.10003i	0.103930	−	0.0534220i
$425$			21.8521i			1.05998i
$426$	−2.67633	+	3.72222i	−0.129669	+	0.180342i
$427$	−6.93733	−	1.22324i	−0.335721	−	0.0591966i
$428$	28.1895	−	27.9961i	1.36259	−	1.35324i
$429$	−3.04123	+	2.72701i	−0.146832	+	0.131661i
$430$	1.22295	−	3.85553i	0.0589757	−	0.185930i
$431$	−2.06553	+	11.7142i	−0.0994932	+	0.564254i	0.893784	+	0.448497i	$0.148041\pi$
$431$	−2.06553	+	11.7142i	−0.0994932	+	0.564254i	−0.993278	+	0.115757i	$0.963071\pi$
$432$	16.9733	−	11.9961i	0.816630	−	0.577162i
$433$	−4.88668	−	4.10041i	−0.234839	−	0.197053i	0.517772	−	0.855518i	$-0.326761\pi$
$433$	−4.88668	−	4.10041i	−0.234839	−	0.197053i	−0.752611	+	0.658465i	$0.771206\pi$
$434$	10.1380	+	24.5949i	0.486638	+	1.18059i
$435$	0.331528	−	2.32418i	0.0158955	−	0.111436i
$436$	28.2965	−	13.0765i	1.35516	−	0.626248i
$437$	23.5896	+	12.4303i	1.12844	+	0.594624i
$438$	3.66645	+	8.12661i	0.175190	+	0.388304i
$439$	0.997619	−	0.175907i	0.0476138	−	0.00839559i	−0.149791	−	0.988718i	$-0.547860\pi$
$439$	0.997619	−	0.175907i	0.0476138	−	0.00839559i	0.197404	+	0.980322i	$0.436749\pi$
$440$	−0.426684	+	0.460842i	−0.0203414	+	0.0219698i
$441$	−31.5642	+	30.2308i	−1.50306	+	1.43956i
$442$	−18.8383	+	7.76512i	−0.896048	+	0.369349i
$443$	13.3972	−	4.87620i	0.636522	−	0.231675i	−0.00354531	−	0.999994i	$-0.501129\pi$
$443$	13.3972	−	4.87620i	0.636522	−	0.231675i	0.640068	+	0.768319i	$0.278906\pi$
$444$	25.4167	−	2.97886i	1.20622	−	0.141370i
$445$	4.61138			0.218600
$446$	7.43279	−	14.2184i	0.351953	−	0.673263i
$447$	0.0263447	+	0.801784i	0.00124606	+	0.0379231i
$448$	26.5416	−	25.9988i	1.25397	−	1.22833i
$449$	18.9558	+	10.9441i	0.894580	+	0.516486i	0.875438	−	0.483331i	$-0.160573\pi$
$449$	18.9558	+	10.9441i	0.894580	+	0.516486i	0.0191423	+	0.999817i	$0.493906\pi$
$450$	11.5923	−	17.2936i	0.546466	−	0.815230i
$451$	−1.60518	−	1.91297i	−0.0755848	−	0.0900784i
$452$	10.0821	+	10.1518i	0.474223	+	0.477500i
$453$	−9.08693	+	11.5815i	−0.426941	+	0.544145i
$454$	0.449014	+	1.08932i	0.0210733	+	0.0511242i
$455$	−2.28876	+	3.96424i	−0.107299	+	0.185846i
$456$	14.0936	+	16.0428i	0.659993	+	0.751272i
$457$	−12.4699	−	21.5985i	−0.583318	−	1.01034i	−0.995083	−	0.0990458i	$-0.968421\pi$
$457$	−12.4699	−	21.5985i	−0.583318	−	1.01034i	0.411765	−	0.911290i	$-0.364912\pi$
$458$	−7.70673	+	10.0079i	−0.360112	+	0.467637i
$459$	−16.5450	−	16.1762i	−0.772254	−	0.755040i
$460$	3.60328	−	0.952210i	0.168004	−	0.0443970i
$461$	10.6748	−	29.3289i	0.497176	−	1.36598i	−0.396816	−	0.917898i	$-0.629885\pi$
$461$	10.6748	−	29.3289i	0.497176	−	1.36598i	0.893992	−	0.448083i	$-0.147893\pi$
$462$	−7.98190	−	2.24613i	−0.371352	−	0.104499i
$463$	−25.9003	+	14.9535i	−1.20369	+	0.694949i	−0.961373	−	0.275249i	$-0.911240\pi$
$463$	−25.9003	+	14.9535i	−1.20369	+	0.694949i	−0.242314	+	0.970198i	$0.577907\pi$
$464$	−16.7660	+	5.97190i	−0.778344	+	0.277239i
$465$	−1.00721	+	1.88490i	−0.0467080	+	0.0874100i
$466$	18.6181	+	29.3359i	0.862467	+	1.35896i
$467$	−13.1426	−	22.7637i	−0.608168	−	1.05338i	−0.991542	−	0.129785i	$-0.958571\pi$
$467$	−13.1426	−	22.7637i	−0.608168	−	1.05338i	0.383374	−	0.923593i	$-0.374762\pi$
$468$	19.0279	+	3.84825i	0.879563	+	0.177885i
$469$	−2.07624	+	11.7749i	−0.0958718	+	0.543716i
$470$	2.18804	+	1.68494i	0.100927	+	0.0777203i
$471$	21.0444	+	33.8330i	0.969674	+	1.55894i
$472$	−30.4260	+	9.42077i	−1.40047	+	0.433626i
$473$	4.39893	+	5.24244i	0.202263	+	0.241048i
$474$	−7.07266	−	5.08535i	−0.324858	−	0.233578i
$475$	18.9235	+	9.97160i	0.868270	+	0.457528i
$476$	−33.7998	−	23.8408i	−1.54921	−	1.09274i
$477$	0.167535	+	2.54667i	0.00767092	+	0.116604i
$478$	−18.0279	−	2.40500i	−0.824576	−	0.110002i
$479$	3.65255	−	20.7147i	0.166889	−	0.946477i	−0.780206	−	0.625523i	$-0.784886\pi$
$479$	3.65255	−	20.7147i	0.166889	−	0.946477i	0.947095	−	0.320953i	$-0.104003\pi$
$480$	2.96780	+	0.317760i	0.135461	+	0.0145037i
$481$	18.3100	+	15.3639i	0.834864	+	0.700534i
$482$	−30.9762	+	6.81132i	−1.41093	+	0.310247i
$483$	32.8503	+	36.6355i	1.49474	+	1.66697i
$484$	5.34933	+	20.2425i	0.243151	+	0.920115i
$485$	−1.39371	−	3.82918i	−0.0632850	−	0.173874i
$486$	4.51233	+	21.5787i	0.204683	+	0.978828i
$487$	4.64077	+	2.67935i	0.210293	+	0.121413i	0.601448	−	0.798912i	$-0.294591\pi$
$487$	4.64077	+	2.67935i	0.210293	+	0.121413i	−0.391154	+	0.920325i	$0.627924\pi$
$488$	−2.32376	+	3.60634i	−0.105192	+	0.163251i
$489$	0.578680	−	0.737538i	0.0261688	−	0.0333526i
$490$	−6.27085	+	0.262975i	−0.283288	+	0.0118800i
$491$	−22.7118	−	8.26643i	−1.02497	−	0.373059i	−0.225807	−	0.974172i	$-0.572502\pi$
$491$	−22.7118	−	8.26643i	−1.02497	−	0.373059i	−0.799164	+	0.601113i	$0.794724\pi$
$492$	−2.73333	+	11.5490i	−0.123228	+	0.520667i
$493$	9.90689	+	17.1592i	0.446184	+	0.772814i
$494$	−1.87190	+	19.8570i	−0.0842208	+	0.893410i
$495$	−0.268432	−	0.609658i	−0.0120651	−	0.0274021i
$496$	16.2011	+	0.111577i	0.727450	+	0.00500998i
$497$	−5.58722	−	6.65859i	−0.250621	−	0.298678i
$498$	−9.65449	+	2.45790i	−0.432628	+	0.110141i
$499$	−17.9430	+	3.16384i	−0.803239	+	0.141633i	−0.560172	−	0.828377i	$-0.689265\pi$
$499$	−17.9430	+	3.16384i	−0.803239	+	0.141633i	−0.243068	+	0.970009i	$0.578154\pi$
$500$	5.83576	−	1.54217i	0.260983	−	0.0689679i
$501$	14.1887	−	12.7228i	0.633907	−	0.568411i
$502$	−7.49126	−	8.20359i	−0.334351	−	0.366144i
$503$	9.56357	−	3.48085i	0.426418	−	0.155204i	−0.119891	−	0.992787i	$-0.538255\pi$
$503$	9.56357	−	3.48085i	0.426418	−	0.155204i	0.546309	+	0.837583i	$0.316032\pi$
$504$	14.1017	+	36.7979i	0.628141	+	1.63911i
$505$	−0.626339	−	1.08485i	−0.0278717	−	0.0482752i
$506$	−1.90652	+	6.01060i	−0.0847551	+	0.267204i
$507$	−2.31580	−	3.72311i	−0.102848	−	0.165349i
$508$	16.0599	+	7.55629i	0.712542	+	0.335256i
$509$	−5.28058	−	14.5083i	−0.234058	−	0.643068i	−1.00000		0.000159039i	$-0.999949\pi$
$509$	−5.28058	−	14.5083i	−0.234058	−	0.643068i	0.765942	−	0.642909i	$-0.222273\pi$
$510$	−0.248175	−	3.31356i	−0.0109894	−	0.146727i
$511$	−16.6467	+	2.93527i	−0.736407	+	0.129848i
$512$	−8.33418	−	21.0367i	−0.368322	−	0.929698i
$513$	−21.5581	+	6.94609i	−0.951813	+	0.306677i
$514$	4.16514	+	1.32115i	0.183716	+	0.0582735i
$515$	−0.356772	−	2.02335i	−0.0157212	−	0.0891596i
$516$	7.49060	−	31.6495i	0.329755	−	1.39329i
$517$	−4.39064	+	1.59806i	−0.193100	+	0.0702826i
$518$	−6.41589	+	48.0935i	−0.281898	+	2.11311i
$519$	8.57113	−	5.33131i	0.376231	−	0.234018i
$520$	1.68566	+	2.22045i	0.0739213	+	0.0973734i
$521$	−37.6728	+	21.7504i	−1.65047	+	0.952901i	−0.673596	+	0.739100i	$0.735251\pi$
$521$	−37.6728	+	21.7504i	−1.65047	+	0.952901i	−0.976877	+	0.213801i	$0.931415\pi$
$522$	1.26253	−	18.8352i	0.0552593	−	0.824395i
$523$	4.37854	+	12.0299i	0.191460	+	0.526033i	0.997864	−	0.0653332i	$-0.0208110\pi$
$523$	4.37854	+	12.0299i	0.191460	+	0.526033i	−0.806403	+	0.591366i	$0.798589\pi$
$524$	−20.6259	+	9.53167i	−0.901045	+	0.416393i
$525$	26.3524	+	29.3889i	1.15011	+	1.28264i
$526$	12.2132	−	7.75115i	0.532521	−	0.337966i
$527$	−3.13202	−	17.7626i	−0.136433	−	0.773749i
$528$	−3.14455	+	3.95145i	−0.136849	+	0.171965i
$529$	11.0464	−	9.26902i	0.480278	−	0.403001i
$530$	−0.223614	+	0.290382i	−0.00971315	+	0.0126134i
$531$	3.66975	−	33.5833i	0.159254	−	1.45739i
$532$	−36.0692	+	18.3909i	−1.56380	+	0.797348i
$533$	−9.59978	+	5.54244i	−0.415813	+	0.240070i
$534$	36.9758	−	2.76937i	1.60010	−	0.119842i
$535$	−2.06971	+	5.68648i	−0.0894813	+	0.245848i
$536$	6.12115	+	3.94420i	0.264393	+	0.170363i
$537$	−10.1586	−	7.97056i	−0.438377	−	0.343955i
$538$	−16.1115	+	0.675651i	−0.694614	+	0.0291294i
$539$	5.30953	−	9.19638i	0.228698	−	0.396116i
$540$	−1.56140	+	2.75399i	−0.0671921	+	0.118513i
$541$	0.0229040	−	0.00833637i	0.000984719	−	0.000358408i	−0.341528	−	0.939872i	$-0.610944\pi$
$541$	0.0229040	−	0.00833637i	0.000984719	−	0.000358408i	0.342512	+	0.939513i	$0.388722\pi$
$542$	−1.03059	−	1.62386i	−0.0442676	−	0.0697509i
$543$	−30.5401	+	27.3846i	−1.31060	+	1.17519i
$544$	−21.3611	+	13.3514i	−0.915849	+	0.572436i
$545$	−3.05194	+	3.63715i	−0.130731	+	0.155799i
$546$	−15.9714	+	33.1613i	−0.683512	+	1.41917i
$547$	12.3416	+	2.17616i	0.527690	+	0.0930460i	0.431145	−	0.902283i	$-0.358110\pi$
$547$	12.3416	+	2.17616i	0.527690	+	0.0930460i	0.0965451	+	0.995329i	$0.469221\pi$
$548$	22.4336	+	10.5552i	0.958317	+	0.450894i
$549$	−2.52899	−	3.78292i	−0.107935	−	0.161451i
$550$	−1.52941	+	4.82169i	−0.0652141	+	0.205598i
$551$	19.3803	−	0.749038i	0.825629	−	0.0319101i
$552$	28.3206	−	9.79913i	1.20541	−	0.417079i
$553$	12.6521	−	10.6164i	0.538022	−	0.451454i
$554$	22.2874	−	28.9422i	0.946902	−	1.22964i
$555$	−3.30982	+	2.05873i	−0.140494	+	0.0873884i
$556$	−34.2844	+	23.8307i	−1.45398	+	1.01065i
$557$	35.7848	+	6.30982i	1.51625	+	0.267356i	0.868958	−	0.494886i	$-0.164790\pi$
$557$	35.7848	+	6.30982i	1.51625	+	0.267356i	0.647292	+	0.762242i	$0.275901\pi$
$558$	−6.94418	+	15.7187i	−0.293970	+	0.665425i
$559$	26.3079	−	15.1889i	1.11270	−	0.642420i
$560$	−1.97210	+	5.30434i	−0.0833363	+	0.224149i
$561$	4.95845	+	2.64958i	0.209346	+	0.111865i
$562$	−41.4474	−	13.1468i	−1.74835	−	0.554564i
$563$	6.13503	+	10.6262i	0.258561	+	0.447840i	0.965857	−	0.259077i	$-0.0834185\pi$
$563$	6.13503	+	10.6262i	0.258561	+	0.447840i	−0.707296	+	0.706918i	$0.750085\pi$
$564$	18.5564	+	12.1964i	0.781366	+	0.513562i
$565$	−2.04785	−	0.745356i	−0.0861537	−	0.0313574i
$566$	14.2989	+	22.5303i	0.601027	+	0.947018i
$567$	−41.7589	−	1.80302i	−1.75371	−	0.0757196i
$568$	−5.05688	+	1.56576i	−0.212182	+	0.0656977i
$569$	35.5590	−	20.5300i	1.49071	−	0.860663i	0.490768	−	0.871290i	$-0.336716\pi$
$569$	35.5590	−	20.5300i	1.49071	−	0.860663i	0.999944	+	0.0106278i	$0.00338301\pi$
$570$	−2.98273	−	1.29714i	−0.124933	−	0.0543311i
$571$	−32.2837	−	18.6390i	−1.35103	−	0.780017i	−0.362636	−	0.931931i	$-0.618123\pi$
$571$	−32.2837	−	18.6390i	−1.35103	−	0.780017i	−0.988394	+	0.151914i	$0.951456\pi$
$572$	−4.70017	+	0.394908i	−0.196524	+	0.0165119i
$573$	7.50270	+	5.88670i	0.313430	+	0.245920i
$574$	−19.9412	−	10.4244i	−0.832332	−	0.435107i
$575$	22.9953	−	19.2954i	0.958972	−	0.804673i
$576$	23.9878	+	0.765600i	0.999491	+	0.0319000i
$577$	−2.49339	+	4.31867i	−0.103801	+	0.179789i	−0.913248	−	0.407405i	$-0.866434\pi$
$577$	−2.49339	+	4.31867i	−0.103801	+	0.179789i	0.809447	+	0.587193i	$0.199767\pi$
$578$	2.69863	+	2.95524i	0.112248	+	0.122922i
$579$	7.94658	−	0.261105i	0.330248	−	0.0108512i
$580$	1.92348	−	1.91028i	0.0798682	−	0.0793200i
$581$		−	18.8887i		−	0.783635i
$582$	−13.4749	−	29.8668i	−0.558552	−	1.23802i
$583$	−0.212084	−	0.582696i	−0.00878363	−	0.0241328i
$584$	−2.28005	+	10.0390i	−0.0943491	+	0.415415i
$585$	−2.87201	+	0.703512i	−0.118743	+	0.0290866i
$586$	5.91296	−	44.3235i	0.244262	−	1.83099i
$587$	−4.66642	−	26.4646i	−0.192604	−	1.09231i	−0.915790	−	0.401658i	$-0.868434\pi$
$587$	−4.66642	−	26.4646i	−0.192604	−	1.09231i	0.723186	−	0.690653i	$-0.242677\pi$
$588$	−50.1241	+	5.87459i	−2.06708	+	0.242264i
$589$	−16.8112	−	5.39318i	−0.692695	−	0.222222i
$590$	3.58248	−	3.27141i	0.147488	−	0.134682i
$591$	15.8200	+	2.25662i	0.650750	+	0.0928249i
$592$	25.4883	+	14.9507i	1.04756	+	0.614468i
$593$	−1.21757	+	1.45105i	−0.0499997	+	0.0595873i	−0.790465	−	0.612508i	$-0.790161\pi$
$593$	−1.21757	+	1.45105i	−0.0499997	+	0.0595873i	0.740465	+	0.672095i	$0.234605\pi$
$594$	−2.51852	−	4.72726i	−0.103336	−	0.193962i
$595$	6.20436	+	1.09400i	0.254354	+	0.0448495i
$596$	−0.533925	+	0.756963i	−0.0218704	+	0.0310064i
$597$	23.6729	+	26.4006i	0.968865	+	1.08050i
$598$	24.8056	+	12.9673i	1.01438	+	0.530272i
$599$	−2.98608	+	16.9349i	−0.122008	+	0.691942i	0.861032	+	0.508551i	$0.169819\pi$
$599$	−2.98608	+	16.9349i	−0.122008	+	0.691942i	−0.983040	+	0.183391i	$0.941292\pi$
$600$	22.7188	−	7.86085i	0.927489	−	0.320918i
$601$	−3.39556			−0.138508			−0.0692540	−	0.997599i	$-0.522062\pi$
$601$	−3.39556			−0.138508			−0.0692540	+	0.997599i	$0.522062\pi$
$602$	54.6483	+	28.5678i	2.22730	+	1.16434i
$603$	−6.42087	+	4.29253i	−0.261478	+	0.174805i
$604$	−16.4340	+	4.34288i	−0.668690	+	0.176709i
$605$	−2.04991	−	2.44299i	−0.0833407	−	0.0993216i
$606$	−5.67372	−	8.32259i	−0.230479	−	0.338082i
$607$	−13.4845	−	7.78527i	−0.547319	−	0.315995i	0.200721	−	0.979648i	$-0.435671\pi$
$607$	−13.4845	−	7.78527i	−0.547319	−	0.315995i	−0.748040	+	0.663654i	$0.769005\pi$
$608$	1.81451	+	24.5908i	0.0735882	+	0.997289i
$609$	34.0169	+	11.1303i	1.37843	+	0.451023i
$610$	0.0864090	−	0.647722i	0.00349860	−	0.0262255i
$611$	3.60153	+	20.4253i	0.145702	+	0.826320i
$612$	−3.97992	−	26.4203i	−0.160879	−	1.06798i
$613$	30.4586	−	25.5578i	1.23021	−	1.03227i	0.231987	−	0.972719i	$-0.425477\pi$
$613$	30.4586	−	25.5578i	1.23021	−	1.03227i	0.998225	−	0.0595521i	$-0.0189672\pi$
$614$	−25.2105	+	1.05723i	−1.01741	+	0.0426663i
$615$	−0.372194	−	1.76895i	−0.0150083	−	0.0713310i
$616$	−5.78938	−	7.62611i	−0.233261	−	0.307265i
$617$	−33.6221	−	5.92848i	−1.35357	−	0.238672i	−0.550641	−	0.834742i	$-0.685617\pi$
$617$	−33.6221	−	5.92848i	−1.35357	−	0.238672i	−0.802932	+	0.596070i	$0.796728\pi$
$618$	−4.07585	−	16.0097i	−0.163955	−	0.644006i
$619$	0.664725	+	0.383779i	0.0267176	+	0.0154254i	0.513299	−	0.858210i	$-0.328423\pi$
$619$	0.664725	+	0.383779i	0.0267176	+	0.0154254i	−0.486582	+	0.873635i	$0.661756\pi$
$620$	−2.24011	+	1.03520i	−0.0899649	+	0.0415748i
$621$	−2.41327	+	31.6941i	−0.0968410	+	1.27184i
$622$	0.0988684	+	0.239857i	0.00396426	+	0.00961738i
$623$	−12.2078	+	69.2339i	−0.489095	+	2.77380i
$624$	14.8498	+	16.7921i	0.594467	+	0.672222i
$625$	18.0914	−	15.1805i	0.723655	−	0.607219i
$626$	−13.8761	−	15.1956i	−0.554601	−	0.607337i
$627$	4.55713	−	3.08486i	0.181994	−	0.123197i
$628$	−4.16764	+	45.8186i	−0.166307	+	1.82836i
$629$	11.2513	−	30.9127i	0.448618	−	1.23257i
$630$	−4.32974	−	4.15712i	−0.172501	−	0.165624i
$631$	−7.68470	+	9.15827i	−0.305923	+	0.364585i	−0.897000	−	0.442030i	$-0.854258\pi$
$631$	−7.68470	+	9.15827i	−0.305923	+	0.364585i	0.591077	+	0.806615i	$0.298703\pi$
$632$	−2.97512	−	9.60866i	−0.118344	−	0.382212i
$633$	10.6681	+	5.70058i	0.424021	+	0.226578i
$634$	3.95411	+	17.9823i	0.157038	+	0.714168i
$635$	−2.70341			−0.107282
$636$	−1.61863	+	2.46269i	−0.0641828	+	0.0976518i
$637$	−36.1090	−	30.2991i	−1.43069	−	1.20049i
$638$	0.985010	+	4.47958i	0.0389969	+	0.177348i
$639$	0.609923	−	5.58162i	0.0241282	−	0.220806i
$640$	2.51279	+	2.35888i	0.0993267	+	0.0932431i
$641$	−11.9312	+	32.7806i	−0.471252	+	1.29475i	0.445494	+	0.895285i	$0.353028\pi$
$641$	−11.9312	+	32.7806i	−0.471252	+	1.29475i	−0.916746	+	0.399470i	$0.869194\pi$
$642$	−13.1807	+	46.8393i	−0.520200	+	1.84860i
$643$	5.34663	−	14.6897i	0.210850	−	0.579307i	−0.788512	−	0.615020i	$-0.789148\pi$
$643$	5.34663	−	14.6897i	0.210850	−	0.579307i	0.999362	+	0.0357130i	$0.0113702\pi$
$644$	4.75716	+	56.6195i	0.187458	+	2.23112i
$645$	1.01998	+	4.84775i	0.0401619	+	0.190880i
$646$	26.5624	−	6.92626i	1.04508	−	0.272510i
$647$	−42.7677			−1.68137			−0.840686	−	0.541523i	$-0.817848\pi$
$647$	−42.7677			−1.68137			−0.840686	+	0.541523i	$0.817848\pi$
$648$	−10.8660	+	23.0202i	−0.426857	+	0.904319i
$649$	1.42534	+	8.08348i	0.0559493	+	0.317304i
$650$	19.8990	+	10.4023i	0.780503	+	0.408014i
$651$	−25.6329	−	20.1118i	−1.00463	−	0.788245i
$652$	1.04656	−	0.276566i	0.0409865	−	0.0108312i
$653$	0.143559	−	0.0828837i	0.00561789	−	0.00324349i	−0.497188	−	0.867643i	$-0.665634\pi$
$653$	0.143559	−	0.0828837i	0.00561789	−	0.00324349i	0.502806	+	0.864399i	$0.332301\pi$
$654$	−22.2873	+	30.9969i	−0.871501	+	1.21208i
$655$	2.22461	−	2.65119i	0.0869228	−	0.103591i
$656$	−10.5583	+	8.73625i	−0.412232	+	0.341093i
$657$	−8.80721	−	6.45445i	−0.343602	−	0.251812i
$658$	−31.0896	+	28.3900i	−1.21200	+	1.10676i
$659$	−11.6054	+	4.22402i	−0.452082	+	0.164544i	−0.558019	−	0.829828i	$-0.688438\pi$
$659$	−11.6054	+	4.22402i	−0.452082	+	0.164544i	0.105936	+	0.994373i	$0.466216\pi$
$660$	0.177153	−	0.748511i	0.00689566	−	0.0291358i
$661$	5.75176	−	2.09347i	0.223717	−	0.0814265i	−0.227730	−	0.973724i	$-0.573130\pi$
$661$	5.75176	−	2.09347i	0.223717	−	0.0814265i	0.451447	+	0.892298i	$0.350908\pi$
$662$	20.9634	+	16.1432i	0.814767	+	0.627424i
$663$	15.4045	−	19.6334i	0.598263	−	0.762498i
$664$	−10.6051	−	4.45709i	−0.411558	−	0.172969i
$665$	3.77856	−	4.87364i	0.146526	−	0.188992i
$666$	−25.3030	+	18.4954i	−0.980472	+	0.716683i
$667$	9.30918	−	25.5768i	0.360453	−	0.990337i
$668$	21.9285	−	1.84243i	0.848438	−	0.0712856i
$669$	0.645297	+	19.6392i	0.0249486	+	0.759296i
$670$	−1.09940	−	0.146665i	−0.0424735	−	0.00566615i
$671$	0.846937	+	0.710665i	0.0326957	+	0.0274349i
$672$	−12.6275	+	43.7165i	−0.487116	+	1.68640i
$673$	18.4338	−	31.9282i	0.710570	−	1.23074i	−0.254074	−	0.967185i	$-0.581771\pi$
$673$	18.4338	−	31.9282i	0.710570	−	1.23074i	0.964643	−	0.263558i	$-0.0848961\pi$
$674$	−0.664442	−	15.8442i	−0.0255933	−	0.610295i
$675$	−1.93592	+	25.4250i	−0.0745135	+	0.978607i
$676$	0.458623	−	5.04206i	0.0176394	−	0.193925i
$677$			11.9363i			0.458750i	0.973338	+	0.229375i	$0.0736682\pi$
$677$			11.9363i			0.458750i	−0.973338	+	0.229375i	$0.926332\pi$
$678$	−16.8680	−	4.74671i	−0.647813	−	0.182296i
$679$	61.1798	−	10.7877i	2.34787	−	0.413992i
$680$	2.07825	−	3.22531i	0.0796971	−	0.123685i
$681$	−1.13529	−	0.890760i	−0.0435044	−	0.0341340i
$682$	0.552099	−	4.13854i	0.0211410	−	0.158473i
$683$	−0.833395			−0.0318890			−0.0159445	−	0.999873i	$-0.505076\pi$
$683$	−0.833395			−0.0318890			−0.0159445	+	0.999873i	$0.505076\pi$
$684$	−24.6956	−	8.60964i	−0.944261	−	0.329198i
$685$	−3.77632			−0.144286
$686$	6.57329	−	49.2734i	0.250969	−	1.88127i
$687$	2.18460	−	15.3152i	0.0833477	−	0.584310i
$688$	28.9346	−	23.9414i	1.10312	−	0.912757i
$689$	−2.71071	+	0.477972i	−0.103270	+	0.0182093i
$690$	−3.26778	+	3.18703i	−0.124402	+	0.121328i
$691$			18.0324i			0.685983i	0.939339	+	0.342991i	$0.111440\pi$
$691$			18.0324i			0.685983i	−0.939339	+	0.342991i	$0.888560\pi$
$692$	11.6075	+	1.05582i	0.441252	+	0.0401361i
$693$	9.86386	−	2.41620i	0.374697	−	0.0917837i
$694$	−1.72474	−	41.1278i	−0.0654702	−	1.56119i
$695$	3.17983	−	5.50762i	0.120618	−	0.208916i
$696$	14.2760	−	16.4725i	0.541129	−	0.624388i
$697$	11.6869	+	9.80651i	0.442674	+	0.371448i
$698$	30.5893	+	4.08075i	1.15782	+	0.154459i
$699$	−37.5317	−	20.0553i	−1.41958	−	0.758561i
$700$	3.81619	+	45.4200i	0.144238	+	1.71672i
$701$	8.81994	−	24.2326i	0.333124	−	0.915252i	−0.654170	−	0.756348i	$-0.726982\pi$
$701$	8.81994	−	24.2326i	0.333124	−	0.915252i	0.987294	−	0.158904i	$-0.0507960\pi$
$702$	−22.6064	+	7.36581i	−0.853222	+	0.278005i
$703$	−21.6355	−	23.8495i	−0.816000	−	0.899501i
$704$	−5.64780	+	1.45096i	−0.212859	+	0.0546851i
$705$	−3.34838	−	0.477623i	−0.126107	−	0.0179883i
$706$	−20.1802	−	15.5401i	−0.759493	−	0.584860i
$707$	17.9457	−	6.53172i	0.674919	−	0.245651i
$708$	26.7610	−	28.3828i	1.00574	−	1.06669i
$709$	21.5640	−	7.84864i	0.809852	−	0.294762i	0.0962892	−	0.995353i	$-0.469303\pi$
$709$	21.5640	−	7.84864i	0.809852	−	0.294762i	0.713563	+	0.700591i	$0.247080\pi$
$710$	0.595417	−	0.543716i	0.0223456	−	0.0204053i
$711$	10.6057	+	1.15892i	0.397746	+	0.0434631i
$712$	35.9909	+	23.1910i	1.34882	+	0.869118i
$713$	−15.9263	+	18.9802i	−0.596443	+	0.710814i
$714$	50.4059	+	5.04604i	1.88639	+	0.188843i
$715$	0.622181	−	0.359216i	0.0232682	−	0.0134339i
$716$	−3.80934	−	14.4150i	−0.142362	−	0.538714i
$717$	20.6703	−	8.30184i	0.771948	−	0.310038i
$718$	43.6989	+	22.8439i	1.63083	+	0.852528i
$719$	2.90789	+	16.4915i	0.108446	+	0.615027i	0.989788	+	0.142548i	$0.0455296\pi$
$719$	2.90789	+	16.4915i	0.108446	+	0.615027i	−0.881342	+	0.472479i	$0.843359\pi$
$720$	−3.35570	+	1.45000i	−0.125060	+	0.0540384i
$721$	31.3225			1.16651
$722$	6.12299	−	26.1631i	0.227874	−	0.973691i
$723$	28.9204	−	25.9323i	1.07556	−	0.964434i
$724$	−47.1991	+	3.96566i	−1.75414	+	0.147383i
$725$	7.46781	−	20.5176i	0.277348	−	0.762006i
$726$	−17.9041	−	18.3577i	−0.664483	−	0.681319i
$727$	14.1097	−	38.7662i	0.523301	−	1.43776i	−0.343523	−	0.939144i	$-0.611620\pi$
$727$	14.1097	−	38.7662i	0.523301	−	1.43776i	0.866824	−	0.498614i	$-0.166158\pi$
$728$	−37.7998	+	19.4298i	−1.40095	+	0.720117i
$729$	−17.8170	−	20.2868i	−0.659891	−	0.751362i
$730$	−0.336748	−	1.53145i	−0.0124636	−	0.0566814i
$731$	−32.0277	−	26.8744i	−1.18459	−	0.993986i
$732$	0.303870	−	5.24557i	0.0112314	−	0.193882i
$733$	19.7465			0.729354			0.364677	−	0.931134i	$-0.381179\pi$
$733$	19.7465			0.729354			0.364677	+	0.931134i	$0.381179\pi$
$734$	5.82453	+	26.4885i	0.214987	+	0.977708i
$735$	6.52728	−	4.06002i	0.240762	−	0.149756i
$736$	32.9117	+	10.6894i	1.21314	+	0.394015i
$737$	1.20623	−	1.43753i	0.0444322	−	0.0529522i
$738$	−4.04674	−	13.9606i	−0.148962	−	0.513897i
$739$	−5.76543	+	15.8404i	−0.212085	+	0.582698i	−0.999428	−	0.0338165i	$-0.989234\pi$
$739$	−5.76543	+	15.8404i	−0.212085	+	0.582698i	0.787343	+	0.616515i	$0.211456\pi$
$740$	−4.48235	−	0.407713i	−0.164775	−	0.0149878i
$741$	−9.97270	−	22.2992i	−0.366356	−	0.819181i
$742$	−3.76774	−	4.12600i	−0.138318	−	0.151470i
$743$	−33.1934	+	27.8526i	−1.21775	+	1.02181i	−0.218810	+	0.975767i	$0.570218\pi$
$743$	−33.1934	+	27.8526i	−1.21775	+	1.02181i	−0.998939	+	0.0460458i	$0.985338\pi$
$744$	−17.3403	+	9.64595i	−0.635728	+	0.353638i
$745$	0.0245006	−	0.138950i	0.000897631	−	0.00509072i
$746$	0.124911	+	0.303035i	0.00457330	+	0.0110949i
$747$	8.81186	−	8.43960i	0.322409	−	0.308789i
$748$	2.72323	+	5.89288i	0.0995711	+	0.215465i
$749$	−79.8959	−	46.1279i	−2.91933	−	1.68548i
$750$	−5.29239	+	5.16161i	−0.193251	+	0.188475i
$751$	8.58951	+	1.51456i	0.313436	+	0.0552672i	0.328153	−	0.944625i	$-0.393574\pi$
$751$	8.58951	+	1.51456i	0.313436	+	0.0552672i	−0.0147175	+	0.999892i	$0.504685\pi$
$752$	8.60357	+	24.1544i	0.313740	+	0.880821i
$753$	12.9315	+	4.23119i	0.471250	+	0.154193i
$754$	20.3416	−	0.853046i	0.740797	−	0.0310661i
$755$	1.98335	−	1.66423i	0.0721816	−	0.0605676i
$756$	−37.2140	−	30.7331i	−1.35346	−	1.11775i
$757$	1.39931	+	7.93588i	0.0508588	+	0.288435i	0.999620	−	0.0275588i	$-0.00877336\pi$
$757$	1.39931	+	7.93588i	0.0508588	+	0.288435i	−0.948761	+	0.315993i	$0.897662\pi$
$758$	1.34499	−	10.0821i	0.0488523	−	0.366197i
$759$	−1.59011	−	7.55743i	−0.0577174	−	0.274317i
$760$	−1.84470	−	3.27150i	−0.0669145	−	0.118670i
$761$	−11.5931	−	6.69328i	−0.420249	−	0.242631i	0.274935	−	0.961463i	$-0.411344\pi$
$761$	−11.5931	−	6.69328i	−0.420249	−	0.242631i	−0.695184	+	0.718832i	$0.744677\pi$
$762$	−21.6770	+	1.62353i	−0.785273	+	0.0588145i
$763$	−46.5277	−	55.4496i	−1.68442	−	2.00741i
$764$	2.81340	+	10.6463i	0.101785	+	0.385169i
$765$	2.26179	+	3.38323i	0.0817750	+	0.122321i
$766$	10.7081	+	5.59774i	0.386900	+	0.202255i
$767$	36.4353			1.31560
$768$	21.5651	+	17.4054i	0.778164	+	0.628062i
$769$	−3.95175	+	22.4115i	−0.142504	+	0.808180i	0.826834	+	0.562447i	$0.190140\pi$
$769$	−3.95175	+	22.4115i	−0.142504	+	0.808180i	−0.969338	+	0.245733i	$0.920971\pi$
$770$	1.29243	+	0.675628i	0.0465760	+	0.0243479i
$771$	−5.23704	+	1.10189i	−0.188607	+	0.0396836i
$772$	7.50235	+	5.29179i	0.270015	+	0.190456i
$773$	21.4876	+	3.78885i	0.772856	+	0.136275i	0.546150	−	0.837688i	$-0.316093\pi$
$773$	21.4876	+	3.78885i	0.772856	+	0.136275i	0.226707	+	0.973963i	$0.427204\pi$
$774$	11.0899	+	38.2586i	0.398620	+	1.37518i
$775$	−12.7760	+	15.2259i	−0.458928	+	0.546930i
$776$	8.37961	−	36.8951i	0.300811	−	1.32446i
$777$	−22.1471	−	55.1428i	−0.794522	−	1.97824i
$778$	22.0348	−	20.1215i	0.789988	−	0.721392i
$779$	13.8253	−	5.64574i	0.495341	−	0.202280i
$780$	−3.13554	−	1.35137i	−0.112270	−	0.0483870i
$781$	0.236895	+	1.34350i	0.00847675	+	0.0480740i
$782$	5.09409	−	38.1853i	0.182164	−	1.36550i
$783$	10.0065	+	20.8425i	0.357604	+	0.744849i
$784$	−50.2653	−	29.4841i	−1.79519	−	1.05300i
$785$	−2.39678	−	6.58509i	−0.0855446	−	0.235032i
$786$	16.2456	−	22.5942i	0.579462	−	0.805910i
$787$			11.3091i			0.403127i	0.979475	+	0.201563i	$0.0646022\pi$
$787$			11.3091i			0.403127i	−0.979475	+	0.201563i	$0.935398\pi$
$788$	13.0028	+	13.0926i	0.463204	+	0.466405i
$789$	−8.34948	+	15.6253i	−0.297249	+	0.556276i
$790$	1.03312	+	1.13136i	0.0367569	+	0.0402521i
$791$	16.6119	−	28.7726i	0.590650	−	1.02304i
$792$	0.970957	−	6.10823i	0.0345015	−	0.217047i
$793$	3.75947	−	3.15457i	0.133503	−	0.112022i
$794$	6.43094	+	3.36182i	0.228225	+	0.119307i
$795$	0.0633870	−	0.444375i	0.00224811	−	0.0157604i
$796$	3.42815	+	40.8016i	0.121508	+	1.44618i
$797$	−21.7076	−	12.5329i	−0.768923	−	0.443938i	0.0635673	−	0.997978i	$-0.479752\pi$
$797$	−21.7076	−	12.5329i	−0.768923	−	0.443938i	−0.832490	+	0.554040i	$0.813086\pi$
$798$	27.3711	−	41.3479i	0.968925	−	1.46370i
$799$	24.7209	−	14.2726i	0.874562	−	0.504929i
$800$	26.4017	+	8.57498i	0.933441	+	0.303171i
$801$	−37.7532	+	25.2391i	−1.33394	+	0.891779i
$802$	17.7767	+	28.0101i	0.627716	+	0.989070i
$803$	2.49298	+	0.907372i	0.0879755	+	0.0320205i
$804$	−8.90347	−	0.515768i	−0.314001	−	0.0181897i
$805$	−4.32721	−	7.49495i	−0.152514	−	0.264162i
$806$	−17.6659	−	5.60350i	−0.622255	−	0.197375i
$807$	16.7703	−	10.4312i	0.590342	−	0.367197i
$808$	0.567339	−	11.6170i	0.0199589	−	0.408683i
$809$	−45.9589	+	26.5344i	−1.61583	+	0.932900i	−0.627847	+	0.778337i	$0.716064\pi$
$809$	−45.9589	+	26.5344i	−1.61583	+	0.932900i	−0.987983	+	0.154563i	$0.950603\pi$
$810$	0.00480210	−	3.87732i	0.000168729	−	0.136235i
$811$	−38.4268	−	6.77569i	−1.34935	−	0.237927i	−0.548178	−	0.836362i	$-0.684678\pi$
$811$	−38.4268	−	6.77569i	−1.34935	−	0.237927i	−0.801171	+	0.598435i	$0.795789\pi$
$812$	23.5883	+	33.9357i	0.827787	+	1.19091i
$813$	2.07754	+	1.11014i	0.0728624	+	0.0389344i
$814$	4.64615	−	6.03345i	0.162848	−	0.211472i
$815$	−0.126305	+	0.105983i	−0.00442428	+	0.00371241i
$816$	14.7272	−	27.1098i	0.515555	−	0.949034i
$817$	−37.8876	+	15.4720i	−1.32552	+	0.541295i
$818$	−9.22761	+	29.0915i	−0.322636	+	1.01716i
$819$	−2.95919	−	44.9820i	−0.103402	−	1.57180i
$820$	0.888654	−	1.88872i	0.0310332	−	0.0659569i
$821$	−33.3586	−	5.88203i	−1.16422	−	0.205284i	−0.442047	−	0.896992i	$-0.645748\pi$
$821$	−33.3586	−	5.88203i	−1.16422	−	0.205284i	−0.722178	+	0.691708i	$0.756859\pi$
$822$	−30.2799	+	2.26787i	−1.05613	+	0.0791011i
$823$	−2.88275	+	3.43553i	−0.100486	+	0.119755i	−0.813944	−	0.580944i	$-0.802684\pi$
$823$	−2.88275	+	3.43553i	−0.100486	+	0.119755i	0.713458	+	0.700698i	$0.247128\pi$
$824$	7.39106	−	17.5861i	0.257480	−	0.612641i
$825$	−1.27558	−	6.06256i	−0.0444101	−	0.211071i
$826$	39.6320	+	62.4468i	1.37897	+	2.17280i
$827$	42.9191	−	15.6213i	1.49244	−	0.543205i	0.538352	−	0.842720i	$-0.319047\pi$
$827$	42.9191	−	15.6213i	1.49244	−	0.543205i	0.954092	+	0.299515i	$0.0968249\pi$
$828$	−24.2883	+	27.5173i	−0.844077	+	0.956291i
$829$	2.62117	−	4.53999i	0.0910369	−	0.157680i	−0.816911	−	0.576764i	$-0.804315\pi$
$829$	2.62117	−	4.53999i	0.0910369	−	0.157680i	0.907948	+	0.419084i	$0.137649\pi$
$830$	1.75065	−	0.0734153i	0.0607659	−	0.00254828i
$831$	−6.31775	+	44.2906i	−0.219160	+	1.53642i
$832$	1.98946	+	25.8076i	0.0689721	+	0.894716i
$833$	−22.1886	+	60.9627i	−0.768789	+	2.11223i
$834$	22.1894	−	46.0718i	0.768358	−	1.59534i
$835$	−2.90276	+	1.67591i	−0.100454	+	0.0579972i
$836$	6.34579	+	0.330786i	0.219474	+	0.0114405i
$837$	−2.07049	−	20.9442i	−0.0715667	−	0.723939i
$838$	−33.3080	+	43.2534i	−1.15060	+	1.49416i
$839$	−5.09154	+	4.27231i	−0.175779	+	0.147496i	−0.726433	−	0.687238i	$-0.758823\pi$
$839$	−5.09154	+	4.27231i	−0.175779	+	0.147496i	0.550653	+	0.834734i	$0.314379\pi$
$840$	−1.09451	−	6.84396i	−0.0377641	−	0.236139i
$841$	1.59795	+	9.06245i	0.0551019	+	0.312498i
$842$	−28.0714	+	17.8156i	−0.967404	+	0.613966i
$843$	52.1139	−	10.9649i	1.79490	−	0.377653i
$844$	5.85905	+	12.6786i	0.201677	+	0.436414i
$845$	0.263750	+	0.724648i	0.00907329	+	0.0249287i
$846$	−27.1354	−	1.81889i	−0.932935	−	0.0625347i
$847$	42.1051	−	24.3094i	1.44675	−	0.835281i
$848$	−3.20562	+	1.14181i	−0.110081	+	0.0392099i
$849$	−28.8247	−	15.4027i	−0.989262	−	0.528618i
$850$	4.08647	−	30.6322i	0.140165	−	1.05068i
$851$	−42.4648	+	15.4559i	−1.45567	+	0.529822i
$852$	4.44775	−	4.71730i	0.152377	−	0.161612i
$853$	−0.443662	−	2.51613i	−0.0151907	−	0.0861508i	0.976270	−	0.216557i	$-0.0694828\pi$
$853$	−0.443662	−	2.51613i	−0.0151907	−	0.0861508i	−0.991461	+	0.130407i	$0.958372\pi$
$854$	9.49596	+	3.01205i	0.324945	+	0.103070i
$855$	3.96192	−	0.414820i	0.135495	−	0.0141865i
$856$	−44.7514	+	33.9731i	−1.52957	+	1.16118i
$857$	0.746294	−	0.131592i	0.0254929	−	0.00449509i	−0.160887	−	0.986973i	$-0.551436\pi$
$857$	0.746294	−	0.131592i	0.0254929	−	0.00449509i	0.186380	+	0.982478i	$0.440324\pi$
$858$	4.77315	−	3.25398i	0.162953	−	0.111089i
$859$	−5.99365	−	16.4674i	−0.204501	−	0.561861i	0.794466	−	0.607309i	$-0.207751\pi$
$859$	−5.99365	−	16.4674i	−0.204501	−	0.561861i	−0.998967	+	0.0454473i	$0.985529\pi$
$860$	−2.43533	+	5.17597i	−0.0830439	+	0.176499i
$861$	27.5439	−	0.905024i	0.938692	−	0.0308431i
$862$	5.08608	−	16.0347i	0.173233	−	0.546143i
$863$	23.3064	+	40.3679i	0.793359	+	1.37414i	0.923876	+	0.382692i	$0.125003\pi$
$863$	23.3064	+	40.3679i	0.793359	+	1.37414i	−0.130517	+	0.991446i	$0.541664\pi$
$864$	−26.0365	+	13.6419i	−0.885778	+	0.464108i
$865$	−1.66824	+	0.607191i	−0.0567220	+	0.0206451i
$866$	6.08332	+	6.66177i	0.206720	+	0.226376i
$867$	−4.65841	−	1.52423i	−0.158208	−	0.0517656i
$868$	−9.61196	−	36.3729i	−0.326251	−	1.23458i
$869$	−2.55280	+	0.450127i	−0.0865978	+	0.0152695i
$870$	−0.899368	+	3.19602i	−0.0304914	+	0.108355i
$871$	−5.35435	−	6.38107i	−0.181425	−	0.216214i
$872$	−42.1113	+	13.0389i	−1.42607	+	0.441553i
$873$	32.3682	+	23.7213i	1.09550	+	0.802845i
$874$	−30.7432	−	21.8362i	−1.03990	−	0.738619i
$875$	−7.00820	−	12.1386i	−0.236921	−	0.410358i
$876$	−3.61989	−	12.0775i	−0.122305	−	0.408060i
$877$	2.13307	+	0.776374i	0.0720286	+	0.0262163i	0.377783	−	0.925894i	$-0.376686\pi$
$877$	2.13307	+	0.776374i	0.0720286	+	0.0262163i	−0.305755	+	0.952110i	$0.598909\pi$
$878$	−1.43135	+	0.0600253i	−0.0483058	+	0.00202576i
$879$	20.4110	+	50.8203i	0.688446	+	1.71413i
$880$	0.684303	−	0.566214i	0.0230679	−	0.0190871i
$881$	8.74157	+	5.04695i	0.294511	+	0.170036i	0.639974	−	0.768396i	$-0.278945\pi$
$881$	8.74157	+	5.04695i	0.294511	+	0.170036i	−0.345463	+	0.938432i	$0.612278\pi$
$882$	49.8999	−	36.4747i	1.68022	−	1.22817i
$883$	9.04875	+	24.8612i	0.304515	+	0.836648i	0.993701	+	0.112063i	$0.0357459\pi$
$883$	9.04875	+	24.8612i	0.304515	+	0.836648i	−0.689186	+	0.724584i	$0.742032\pi$
$884$	27.8596	−	7.36223i	0.937020	−	0.247619i
$885$	−1.84774	+	5.64714i	−0.0621112	+	0.189827i
$886$	−19.6921	+	4.33007i	−0.661568	+	0.145472i
$887$	−6.14276	−	5.15439i	−0.206254	−	0.173067i	0.533809	−	0.845605i	$-0.320760\pi$
$887$	−6.14276	−	5.15439i	−0.206254	−	0.173067i	−0.740063	+	0.672537i	$0.765204\pi$
$888$	−36.1860	−	0.577314i	−1.21432	−	0.0193734i
$889$	7.15680	−	40.5882i	0.240031	−	1.36129i
$890$	−6.46421	−	0.862354i	−0.216681	−	0.0289062i
$891$	5.53443	+	3.52206i	0.185411	+	0.117994i
$892$	−13.0782	+	18.5414i	−0.437890	+	0.620811i
$893$	−1.07912	−	27.9207i	−0.0361114	−	0.934331i
$894$	0.113008	−	1.12886i	0.00377956	−	0.0377548i
$895$	1.45977	+	1.73969i	0.0487948	+	0.0581514i
$896$	−42.0678	+	31.4815i	−1.40539	+	1.05172i
$897$	−34.2627	+	1.12579i	−1.14400	+	0.0375890i
$898$	−24.5255	−	18.8863i	−0.818428	−	0.630244i
$899$	−3.12948	+	17.7482i	−0.104374	+	0.591935i
$900$	−19.4840	+	22.0743i	−0.649468	+	0.735810i
$901$	1.89417	+	3.28079i	0.0631039	+	0.109299i
$902$	1.89239	+	2.98177i	0.0630097	+	0.0992822i
$903$	−75.4830	+	2.48019i	−2.51192	+	0.0825354i
$904$	−12.2346	−	16.1161i	−0.406917	−	0.536015i
$905$	6.24794	−	3.60725i	0.207688	−	0.119909i
$906$	14.9038	−	14.5355i	0.495146	−	0.482911i
$907$	−14.2268	+	39.0879i	−0.472394	+	1.29789i	0.443430	+	0.896309i	$0.353762\pi$
$907$	−14.2268	+	39.0879i	−0.472394	+	1.29789i	−0.915823	+	0.401582i	$0.868461\pi$
$908$	−0.425717	−	1.61097i	−0.0141279	−	0.0534618i
$909$	11.0654	+	5.45354i	0.367017	+	0.180883i
$910$	3.94970	−	5.12904i	0.130931	−	0.170026i
$911$	17.3391	+	30.0322i	0.574469	+	0.995010i	0.996099	+	0.0882417i	$0.0281248\pi$
$911$	17.3391	+	30.0322i	0.574469	+	0.995010i	−0.421630	+	0.906768i	$0.638542\pi$
$912$	−16.7562	−	25.1243i	−0.554854	−	0.831948i
$913$	−1.48227	+	2.56737i	−0.0490561	+	0.0849677i
$914$	13.4412	+	32.6086i	0.444596	+	1.07860i
$915$	0.298276	+	0.742662i	0.00986070	+	0.0245516i
$916$	12.6748	−	12.5878i	0.418786	−	0.415912i
$917$	33.9149	+	40.4183i	1.11997	+	1.33473i
$918$	20.1676	+	25.7697i	0.665632	+	0.850527i
$919$	−9.62605	−	5.55760i	−0.317534	−	0.183328i	0.332759	−	0.943012i	$-0.392021\pi$
$919$	−9.62605	−	5.55760i	−0.317534	−	0.183328i	−0.650293	+	0.759684i	$0.725354\pi$
$920$	−5.22913	+	0.660969i	−0.172399	+	0.0217915i
$921$	26.2414	−	16.3224i	0.864685	−	0.537840i
$922$	−20.4486	+	39.1168i	−0.673438	+	1.28824i
$923$	6.05565			0.199324
$924$	10.7689	+	4.64127i	0.354272	+	0.152687i
$925$	−34.0652	+	12.3987i	−1.12006	+	0.407667i
$926$	39.1033	−	16.1183i	1.28501	−	0.529679i
$927$	13.9951	+	14.6124i	0.459660	+	0.479935i
$928$	24.6193	−	5.23604i	0.808169	−	0.171881i
$929$	−21.0564	+	3.71281i	−0.690837	+	0.121813i	−0.508035	−	0.861336i	$-0.669628\pi$
$929$	−21.0564	+	3.71281i	−0.690837	+	0.121813i	−0.182802	+	0.983150i	$0.558517\pi$
$930$	1.76438	−	2.45389i	0.0578564	−	0.0804661i
$931$	42.6673	+	47.0335i	1.39837	+	1.54146i
$932$	−20.6128	−	44.6046i	−0.675194	−	1.46107i
$933$	−0.249980	−	0.196136i	−0.00818397	−	0.00642122i
$934$	14.1663	+	34.3678i	0.463536	+	1.12455i
$935$	−0.757454	−	0.635579i	−0.0247714	−	0.0207857i
$936$	−25.9535	−	8.95278i	−0.848317	−	0.292631i
$937$	−4.63304	+	26.2753i	−0.151355	+	0.858377i	0.810688	+	0.585478i	$0.199093\pi$
$937$	−4.63304	+	26.2753i	−0.151355	+	0.858377i	−0.962043	+	0.272898i	$0.912018\pi$
$938$	5.11244	−	16.1178i	0.166927	−	0.526264i
$939$	23.9531	+	7.83746i	0.781681	+	0.255766i
$940$	−2.75209	−	2.77111i	−0.0897633	−	0.0903836i
$941$	−0.800012	−	0.141064i	−0.0260796	−	0.00459855i	0.160593	−	0.987021i	$-0.448659\pi$
$941$	−0.800012	−	0.141064i	−0.0260796	−	0.00459855i	−0.186673	+	0.982422i	$0.559770\pi$
$942$	−23.1729	−	51.3623i	−0.755015	−	1.67348i
$943$		−	20.9575i		−	0.682470i
$944$	44.4127	−	7.51616i	1.44551	−	0.244630i
$945$	7.12186	+	1.82252i	0.231674	+	0.0592866i
$946$	−5.18603	−	8.17145i	−0.168612	−	0.265677i
$947$	−34.6414	+	29.0676i	−1.12570	+	0.944571i	−0.998878	−	0.0473556i	$-0.984921\pi$
$947$	−34.6414	+	29.0676i	−1.12570	+	0.944571i	−0.126817	+	0.991926i	$0.540476\pi$
$948$	8.96342	+	8.45124i	0.291118	+	0.274484i
$949$	5.88816	−	10.1986i	0.191138	−	0.331060i
$950$	−24.6621	−	17.5169i	−0.800145	−	0.568324i
$951$	−15.0542	−	16.7889i	−0.488167	−	0.544417i
$952$	42.9221	+	39.7406i	1.39111	+	1.28800i
$953$	17.6899	−	3.11921i	0.573033	−	0.101041i	0.120380	−	0.992728i	$-0.461589\pi$
$953$	17.6899	−	3.11921i	0.573033	−	0.101041i	0.452653	+	0.891687i	$0.350478\pi$
$954$	0.241391	−	3.60123i	0.00781532	−	0.116594i
$955$	−1.07812	−	1.28486i	−0.0348872	−	0.0415770i
$956$	24.8217	+	6.74264i	0.802790	+	0.218072i
$957$	−3.75017	−	4.18229i	−0.121226	−	0.135194i
$958$	−8.99389	+	28.3546i	−0.290579	+	0.916097i
$959$	9.99714	−	56.6966i	0.322824	−	1.83083i
$960$	−4.10083	−	1.00043i	−0.132354	−	0.0322887i
$961$	−7.29726	+	12.6392i	−0.235395	+	0.407717i
$962$	−22.7937	−	24.9611i	−0.734899	−	0.804779i
$963$	−14.1787	−	57.8829i	−0.456902	−	1.86525i
$964$	44.6960	−	3.75535i	1.43956	−	0.120952i
$965$	−1.37715	−	0.242828i	−0.0443319	−	0.00781691i
$966$	−39.1983	−	57.4986i	−1.26118	−	1.84999i
$967$	−26.6354	−	31.7428i	−0.856536	−	1.02078i	−0.999518	−	0.0310545i	$-0.990113\pi$
$967$	−26.6354	−	31.7428i	−0.856536	−	1.02078i	0.142982	−	0.989725i	$-0.454331\pi$
$968$	−3.71319	−	29.3762i	−0.119347	−	0.944188i
$969$	−24.1453	+	23.3946i	−0.775659	+	0.751542i
$970$	1.23761	+	5.62836i	0.0397374	+	0.180716i
$971$	14.5865	+	5.30905i	0.468103	+	0.170376i	0.565293	−	0.824890i	$-0.308763\pi$
$971$	14.5865	+	5.30905i	0.468103	+	0.170376i	−0.0971899	+	0.995266i	$0.530985\pi$
$972$	−2.29002	−	31.0927i	−0.0734525	−	0.997299i
$973$	74.2718	+	62.3215i	2.38105	+	1.99793i
$974$	−6.00435	−	4.62375i	−0.192392	−	0.148154i
$975$	−27.4855	+	0.903106i	−0.880240	+	0.0289225i
$976$	3.93185	−	4.62079i	0.125855	−	0.147908i
$977$			36.0526i			1.15342i	0.816948	+	0.576712i	$0.195664\pi$
$977$			36.0526i			1.15342i	−0.816948	+	0.576712i	$0.804336\pi$
$978$	−0.949114	+	0.925661i	−0.0303493	+	0.0295994i
$979$	7.09237	−	8.45236i	0.226673	−	0.270139i
$980$	8.83963	+	0.804048i	0.282372	+	0.0256844i
$981$	5.07915	−	46.4812i	0.162165	−	1.48403i
$982$	30.2915	+	15.8351i	0.966639	+	0.505318i
$983$	38.6671	+	14.0737i	1.23329	+	0.448880i	0.874723	−	0.484624i	$-0.161043\pi$
$983$	38.6671	+	14.0737i	1.23329	+	0.448880i	0.358566	+	0.933504i	$0.383266\pi$
$984$	5.99129	−	15.6781i	0.190995	−	0.499800i
$985$	−2.64108	−	0.961275i	−0.0841518	−	0.0306288i
$986$	−10.6786	−	25.9064i	−0.340075	−	0.825027i
$987$	16.0351	−	49.0072i	0.510404	−	1.55992i
$988$	6.33740	−	27.4854i	0.201620	−	0.874428i
$989$			57.4333i			1.82627i
$990$	0.262277	+	0.904814i	0.00833571	+	0.0287569i
$991$	3.07566	−	0.542321i	0.0977014	−	0.0172274i	−0.124584	−	0.992209i	$-0.539760\pi$
$991$	3.07566	−	0.542321i	0.0977014	−	0.0172274i	0.222285	+	0.974982i	$0.428648\pi$
$992$	−22.6897	−	3.18610i	−0.720400	−	0.101159i
$993$	−32.0806	−	4.57607i	−1.01805	−	0.145217i
$994$	6.58694	+	10.3788i	0.208925	+	0.329196i
$995$	−3.11831	−	5.40108i	−0.0988572	−	0.171226i
$996$	13.9933	−	1.64002i	0.443393	−	0.0519661i
$997$	4.79296	+	4.02177i	0.151795	+	0.127371i	0.715522	−	0.698590i	$-0.246189\pi$
$997$	4.79296	+	4.02177i	0.151795	+	0.127371i	−0.563728	+	0.825961i	$0.690633\pi$
$998$	25.7441	−	1.07960i	0.814914	−	0.0341743i
$999$	15.8295	−	34.9701i	0.500823	−	1.10641i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.bs.a.23.6	✓	696
4.3	odd	2	inner	684.2.bs.a.23.18	yes	696
9.2	odd	6		684.2.ch.a.479.44	yes	696
19.5	even	9		684.2.ch.a.347.22	yes	696
36.11	even	6		684.2.ch.a.479.22	yes	696
76.43	odd	18		684.2.ch.a.347.44	yes	696
171.119	odd	18	inner	684.2.bs.a.119.18	yes	696
684.119	even	18	inner	684.2.bs.a.119.6	yes	696

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.bs.a.23.6	✓	696	1.1	even	1	trivial
684.2.bs.a.23.18	yes	696	4.3	odd	2	inner
684.2.bs.a.119.6	yes	696	684.119	even	18	inner
684.2.bs.a.119.18	yes	696	171.119	odd	18	inner
684.2.ch.a.347.22	yes	696	19.5	even	9
684.2.ch.a.347.44	yes	696	76.43	odd	18
684.2.ch.a.479.22	yes	696	36.11	even	6
684.2.ch.a.479.44	yes	696	9.2	odd	6

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	684.2.bs.a.23.6

Level	$684$
Weight	$2$
Character	684.23
Analytic conductor	$5.462$
Analytic rank	$0$
Dimension	$696$
Inner twists	$4$