LMFDB - Embedded newform 429.2.x.a.248.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(248,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 9, 0]))

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

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

chi := DirichletCharacter("429.248");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.x (of order $10$, degree $4$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			248.4
Character	$\chi$	$=$	429.248
Dual form			429.2.x.a.365.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.759437 - 2.33731i) q^{2} +(0.0396224 + 1.73160i) q^{3} +(-3.26823 + 2.37451i) q^{4} +(-0.541474 - 0.175936i) q^{5} +(4.01719 - 1.40765i) q^{6} +(0.184926 + 0.254529i) q^{7} +(4.05551 + 2.94650i) q^{8} +(-2.99686 + 0.137220i) q^{9} +O(q^{10})$	\(q+(-0.759437 - 2.33731i) q^{2} +(0.0396224 + 1.73160i) q^{3} +(-3.26823 + 2.37451i) q^{4} +(-0.541474 - 0.175936i) q^{5} +(4.01719 - 1.40765i) q^{6} +(0.184926 + 0.254529i) q^{7} +(4.05551 + 2.94650i) q^{8} +(-2.99686 + 0.137220i) q^{9} +1.39920i q^{10} +(0.654561 - 3.25139i) q^{11} +(-4.24119 - 5.56517i) q^{12} +(-0.951057 + 0.309017i) q^{13} +(0.454472 - 0.625527i) q^{14} +(0.283195 - 0.944586i) q^{15} +(1.31026 - 4.03258i) q^{16} +(2.30750 - 7.10176i) q^{17} +(2.59665 + 6.90037i) q^{18} +(4.82965 - 6.64744i) q^{19} +(2.18742 - 0.710737i) q^{20} +(-0.433414 + 0.330302i) q^{21} +(-8.09660 + 0.939318i) q^{22} -0.163019i q^{23} +(-4.94146 + 7.13925i) q^{24} +(-3.78284 - 2.74840i) q^{25} +(1.44454 + 1.98823i) q^{26} +(-0.356353 - 5.18392i) q^{27} +(-1.20876 - 0.392750i) q^{28} +(-6.84622 + 4.97407i) q^{29} +(-2.42286 + 0.0554399i) q^{30} +(-1.50927 - 4.64507i) q^{31} -0.394677 q^{32} +(5.65604 + 1.00461i) q^{33} -18.3514 q^{34} +(-0.0553519 - 0.170356i) q^{35} +(9.46860 - 7.56453i) q^{36} +(2.39151 - 1.73753i) q^{37} +(-19.2049 - 6.24006i) q^{38} +(-0.572776 - 1.63460i) q^{39} +(-1.67756 - 2.30896i) q^{40} +(3.19372 + 2.32037i) q^{41} +(1.10117 + 0.762178i) q^{42} +3.85370i q^{43} +(5.58120 + 12.1806i) q^{44} +(1.64686 + 0.452953i) q^{45} +(-0.381025 + 0.123803i) q^{46} +(-2.98658 + 4.11068i) q^{47} +(7.03472 + 2.10907i) q^{48} +(2.13253 - 6.56326i) q^{49} +(-3.55102 + 10.9289i) q^{50} +(12.3888 + 3.71427i) q^{51} +(2.37451 - 3.26823i) q^{52} +(3.98280 - 1.29409i) q^{53} +(-11.8458 + 4.76977i) q^{54} +(-0.926464 + 1.64538i) q^{55} +1.57713i q^{56} +(11.7021 + 8.09962i) q^{57} +(16.8252 + 12.2242i) q^{58} +(0.567088 + 0.780530i) q^{59} +(1.31738 + 3.75957i) q^{60} +(7.37582 + 2.39655i) q^{61} +(-9.71076 + 7.05528i) q^{62} +(-0.589123 - 0.737411i) q^{63} +(-2.32079 - 7.14267i) q^{64} +0.569340 q^{65} +(-1.94733 - 13.9828i) q^{66} -7.53188 q^{67} +(9.32173 + 28.6893i) q^{68} +(0.282283 - 0.00645920i) q^{69} +(-0.356137 + 0.258749i) q^{70} +(-2.23907 - 0.727518i) q^{71} +(-12.5581 - 8.27374i) q^{72} +(-3.39229 - 4.66909i) q^{73} +(-5.87736 - 4.27015i) q^{74} +(4.60923 - 6.65926i) q^{75} +33.1934i q^{76} +(0.948617 - 0.434662i) q^{77} +(-3.38558 + 2.58013i) q^{78} +(-6.38654 + 2.07511i) q^{79} +(-1.41895 + 1.95301i) q^{80} +(8.96234 - 0.822459i) q^{81} +(2.99800 - 9.22689i) q^{82} +(2.00370 - 6.16674i) q^{83} +(0.632191 - 2.10865i) q^{84} +(-2.49890 + 3.43945i) q^{85} +(9.00729 - 2.92665i) q^{86} +(-8.88436 - 11.6578i) q^{87} +(12.2348 - 11.2574i) q^{88} +11.2748i q^{89} +(-0.191999 - 4.19322i) q^{90} +(-0.254529 - 0.184926i) q^{91} +(0.387089 + 0.532783i) q^{92} +(7.98359 - 2.79751i) q^{93} +(11.8760 + 3.85876i) q^{94} +(-3.78465 + 2.74971i) q^{95} +(-0.0156381 - 0.683422i) q^{96} +(1.20038 + 3.69440i) q^{97} -16.9599 q^{98} +(-1.51547 + 9.83379i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 6 q^{3} - 48 q^{4} - 10 q^{6} - 14 q^{9}+O(q^{10}) $ 192 * q + 6 * q^3 - 48 * q^4 - 10 * q^6 - 14 * q^9	$ 192 q + 6 q^{3} - 48 q^{4} - 10 q^{6} - 14 q^{9} - 20 q^{12} + 6 q^{15} - 28 q^{16} - 10 q^{18} - 60 q^{19} + 4 q^{22} + 30 q^{24} - 12 q^{25} + 30 q^{27} - 20 q^{28} + 12 q^{31} - 32 q^{33} + 56 q^{34} + 44 q^{36} + 60 q^{40} - 108 q^{42} - 40 q^{45} - 28 q^{48} - 24 q^{49} + 10 q^{51} + 20 q^{52} - 20 q^{55} + 50 q^{57} - 60 q^{58} + 36 q^{60} + 20 q^{61} - 30 q^{63} + 64 q^{64} - 30 q^{66} - 120 q^{67} - 16 q^{69} + 20 q^{70} + 150 q^{72} - 20 q^{73} + 18 q^{75} + 40 q^{78} - 160 q^{79} - 46 q^{81} + 88 q^{82} - 40 q^{85} + 72 q^{88} - 80 q^{90} + 8 q^{91} - 72 q^{93} - 120 q^{94} - 140 q^{96} - 88 q^{97} + 62 q^{99}+O(q^{100}) $ 192 * q + 6 * q^3 - 48 * q^4 - 10 * q^6 - 14 * q^9 - 20 * q^12 + 6 * q^15 - 28 * q^16 - 10 * q^18 - 60 * q^19 + 4 * q^22 + 30 * q^24 - 12 * q^25 + 30 * q^27 - 20 * q^28 + 12 * q^31 - 32 * q^33 + 56 * q^34 + 44 * q^36 + 60 * q^40 - 108 * q^42 - 40 * q^45 - 28 * q^48 - 24 * q^49 + 10 * q^51 + 20 * q^52 - 20 * q^55 + 50 * q^57 - 60 * q^58 + 36 * q^60 + 20 * q^61 - 30 * q^63 + 64 * q^64 - 30 * q^66 - 120 * q^67 - 16 * q^69 + 20 * q^70 + 150 * q^72 - 20 * q^73 + 18 * q^75 + 40 * q^78 - 160 * q^79 - 46 * q^81 + 88 * q^82 - 40 * q^85 + 72 * q^88 - 80 * q^90 + 8 * q^91 - 72 * q^93 - 120 * q^94 - 140 * q^96 - 88 * q^97 + 62 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$	$-1$

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 $

$2$	−0.759437	−	2.33731i	−0.537003	−	1.65273i	−0.739280	−	0.673398i	$-0.764834\pi$
$2$	−0.759437	−	2.33731i	−0.537003	−	1.65273i	0.202277	−	0.979328i	$-0.435166\pi$
$3$	0.0396224	+	1.73160i	0.0228760	+	0.999738i
$3$	0.0396224	+	1.73160i	0.0228760	+	0.999738i
$4$	−3.26823	+	2.37451i	−1.63411	+	1.18725i
$5$	−0.541474	−	0.175936i	−0.242155	−	0.0786808i	0.185425	−	0.982658i	$-0.440634\pi$
$5$	−0.541474	−	0.175936i	−0.242155	−	0.0786808i	−0.427580	+	0.903978i	$0.640634\pi$
$6$	4.01719	−	1.40765i	1.64001	−	0.574671i
$7$	0.184926	+	0.254529i	0.0698954	+	0.0962027i	0.842533	−	0.538644i	$-0.181063\pi$
$7$	0.184926	+	0.254529i	0.0698954	+	0.0962027i	−0.772638	+	0.634847i	$0.781063\pi$
$8$	4.05551	+	2.94650i	1.43384	+	1.04174i
$9$	−2.99686	+	0.137220i	−0.998953	+	0.0457401i
$10$			1.39920i			0.442467i
$11$	0.654561	−	3.25139i	0.197358	−	0.980332i
$11$	0.654561	−	3.25139i	0.197358	−	0.980332i
$12$	−4.24119	−	5.56517i	−1.22433	−	1.60653i
$13$	−0.951057	+	0.309017i	−0.263776	+	0.0857059i
$13$	−0.951057	+	0.309017i	−0.263776	+	0.0857059i
$14$	0.454472	−	0.625527i	0.121463	−	0.167179i
$15$	0.283195	−	0.944586i	0.0731207	−	0.243891i
$16$	1.31026	−	4.03258i	0.327566	−	1.00814i
$17$	2.30750	−	7.10176i	0.559651	−	1.72243i	−0.123682	−	0.992322i	$-0.539470\pi$
$17$	2.30750	−	7.10176i	0.559651	−	1.72243i	0.683333	−	0.730107i	$-0.260530\pi$
$18$	2.59665	+	6.90037i	0.612037	+	1.62643i
$19$	4.82965	−	6.64744i	1.10800	−	1.52503i	0.283663	−	0.958924i	$-0.408450\pi$
$19$	4.82965	−	6.64744i	1.10800	−	1.52503i	0.824334	−	0.566104i	$-0.191550\pi$
$20$	2.18742	−	0.710737i	0.489122	−	0.158926i
$21$	−0.433414	+	0.330302i	−0.0945786	+	0.0720778i
$22$	−8.09660	+	0.939318i	−1.72620	+	0.200263i
$23$		−	0.163019i		−	0.0339918i	−0.999856	−	0.0169959i	$-0.994590\pi$
$23$		−	0.163019i		−	0.0339918i	0.999856	−	0.0169959i	$-0.00541022\pi$
$24$	−4.94146	+	7.13925i	−1.00867	+	1.45729i
$25$	−3.78284	−	2.74840i	−0.756569	−	0.549679i
$26$	1.44454	+	1.98823i	0.283297	+	0.389925i
$27$	−0.356353	−	5.18392i	−0.0685802	−	0.997646i
$28$	−1.20876	−	0.392750i	−0.228434	−	0.0742227i
$29$	−6.84622	+	4.97407i	−1.27131	+	0.923662i	−0.999254	−	0.0386188i	$-0.987704\pi$
$29$	−6.84622	+	4.97407i	−1.27131	+	0.923662i	−0.272058	+	0.962281i	$0.587704\pi$
$30$	−2.42286	+	0.0554399i	−0.442351	+	0.0101219i
$31$	−1.50927	−	4.64507i	−0.271074	−	0.834279i	−0.990232	−	0.139433i	$-0.955472\pi$
$31$	−1.50927	−	4.64507i	−0.271074	−	0.834279i	0.719158	−	0.694847i	$-0.244528\pi$
$32$	−0.394677			−0.0697698
$33$	5.65604	+	1.00461i	0.984590	+	0.174880i
$34$	−18.3514			−3.14724
$35$	−0.0553519	−	0.170356i	−0.00935618	−	0.0287954i
$36$	9.46860	−	7.56453i	1.57810	−	1.26076i
$37$	2.39151	−	1.73753i	0.393162	−	0.285649i	−0.373588	−	0.927595i	$-0.621873\pi$
$37$	2.39151	−	1.73753i	0.393162	−	0.285649i	0.766750	+	0.641946i	$0.221873\pi$
$38$	−19.2049	−	6.24006i	−3.11545	−	1.01227i
$39$	−0.572776	−	1.63460i	−0.0917176	−	0.261746i
$40$	−1.67756	−	2.30896i	−0.265245	−	0.365079i
$41$	3.19372	+	2.32037i	0.498775	+	0.362381i	0.808549	−	0.588429i	$-0.200253\pi$
$41$	3.19372	+	2.32037i	0.498775	+	0.362381i	−0.309774	+	0.950810i	$0.600253\pi$
$42$	1.10117	+	0.762178i	0.169914	+	0.117607i
$43$			3.85370i			0.587684i	0.955854	+	0.293842i	$0.0949340\pi$
$43$			3.85370i			0.587684i	−0.955854	+	0.293842i	$0.905066\pi$
$44$	5.58120	+	12.1806i	0.841397	+	1.83629i
$45$	1.64686	+	0.452953i	0.245500	+	0.0675223i
$46$	−0.381025	+	0.123803i	−0.0561791	+	0.0182537i
$47$	−2.98658	+	4.11068i	−0.435638	+	0.599604i	−0.969236	−	0.246134i	$-0.920840\pi$
$47$	−2.98658	+	4.11068i	−0.435638	+	0.599604i	0.533598	+	0.845738i	$0.320840\pi$
$48$	7.03472	+	2.10907i	1.01537	+	0.304418i
$49$	2.13253	−	6.56326i	0.304647	−	0.937608i
$50$	−3.55102	+	10.9289i	−0.502190	+	1.54558i
$51$	12.3888	+	3.71427i	1.73478	+	0.520102i
$52$	2.37451	−	3.26823i	0.329285	−	0.453222i
$53$	3.98280	−	1.29409i	0.547080	−	0.177757i	−0.0224197	−	0.999749i	$-0.507137\pi$
$53$	3.98280	−	1.29409i	0.547080	−	0.177757i	0.569500	+	0.821992i	$0.307137\pi$
$54$	−11.8458	+	4.76977i	−1.61201	+	0.649083i
$55$	−0.926464	+	1.64538i	−0.124924	+	0.221864i
$56$			1.57713i			0.210752i
$57$	11.7021	+	8.09962i	1.54998	+	1.07282i
$58$	16.8252	+	12.2242i	2.20926	+	1.60512i
$59$	0.567088	+	0.780530i	0.0738286	+	0.101616i	0.844334	−	0.535817i	$-0.179996\pi$
$59$	0.567088	+	0.780530i	0.0738286	+	0.101616i	−0.770506	+	0.637433i	$0.779996\pi$
$60$	1.31738	+	3.75957i	0.170073	+	0.485359i
$61$	7.37582	+	2.39655i	0.944377	+	0.306847i	0.740429	−	0.672135i	$-0.234623\pi$
$61$	7.37582	+	2.39655i	0.944377	+	0.306847i	0.203948	+	0.978982i	$0.434623\pi$
$62$	−9.71076	+	7.05528i	−1.23327	+	0.896022i
$63$	−0.589123	−	0.737411i	−0.0742225	−	0.0929050i
$64$	−2.32079	−	7.14267i	−0.290099	−	0.892834i
$65$	0.569340			0.0706179
$66$	−1.94733	−	13.9828i	−0.239699	−	1.72117i
$67$	−7.53188			−0.920166			−0.460083	−	0.887876i	$-0.652180\pi$
$67$	−7.53188			−0.920166			−0.460083	+	0.887876i	$0.652180\pi$
$68$	9.32173	+	28.6893i	1.13043	+	3.47909i
$69$	0.282283	−	0.00645920i	0.0339829	−	0.000777596i
$70$	−0.356137	+	0.258749i	−0.0425665	+	0.0309264i
$71$	−2.23907	−	0.727518i	−0.265729	−	0.0863405i	0.173122	−	0.984900i	$-0.444614\pi$
$71$	−2.23907	−	0.727518i	−0.265729	−	0.0863405i	−0.438851	+	0.898560i	$0.644614\pi$
$72$	−12.5581	−	8.27374i	−1.47999	−	0.975070i
$73$	−3.39229	−	4.66909i	−0.397038	−	0.546476i	0.562959	−	0.826485i	$-0.309663\pi$
$73$	−3.39229	−	4.66909i	−0.397038	−	0.546476i	−0.959998	+	0.280008i	$0.909663\pi$
$74$	−5.87736	−	4.27015i	−0.683229	−	0.496395i
$75$	4.60923	−	6.65926i	0.532228	−	0.768945i
$76$			33.1934i			3.80754i
$77$	0.948617	−	0.434662i	0.108105	−	0.0495343i
$78$	−3.38558	+	2.58013i	−0.383342	+	0.292143i
$79$	−6.38654	+	2.07511i	−0.718542	+	0.233469i	−0.645391	−	0.763852i	$-0.723306\pi$
$79$	−6.38654	+	2.07511i	−0.718542	+	0.233469i	−0.0731513	+	0.997321i	$0.523306\pi$
$80$	−1.41895	+	1.95301i	−0.158643	+	0.218354i
$81$	8.96234	−	0.822459i	0.995816	−	0.0913844i
$82$	2.99800	−	9.22689i	0.331073	−	1.01894i
$83$	2.00370	−	6.16674i	0.219934	−	0.676888i	−0.778832	−	0.627232i	$-0.784188\pi$
$83$	2.00370	−	6.16674i	0.219934	−	0.676888i	0.998766	−	0.0496557i	$-0.0158124\pi$
$84$	0.632191	−	2.10865i	0.0689777	−	0.230072i
$85$	−2.49890	+	3.43945i	−0.271044	+	0.373060i
$86$	9.00729	−	2.92665i	0.971281	−	0.315588i
$87$	−8.88436	−	11.6578i	−0.952503	−	1.24985i
$88$	12.2348	−	11.2574i	1.30423	−	1.20004i
$89$			11.2748i			1.19513i	0.801820	+	0.597565i	$0.203865\pi$
$89$			11.2748i			1.19513i	−0.801820	+	0.597565i	$0.796135\pi$
$90$	−0.191999	−	4.19322i	−0.0202385	−	0.442004i
$91$	−0.254529	−	0.184926i	−0.0266818	−	0.0193855i
$92$	0.387089	+	0.532783i	0.0403568	+	0.0555464i
$93$	7.98359	−	2.79751i	0.827860	−	0.290088i
$94$	11.8760	+	3.85876i	1.22492	+	0.398001i
$95$	−3.78465	+	2.74971i	−0.388297	+	0.282114i
$96$	−0.0156381	−	0.683422i	−0.00159605	−	0.0697515i
$97$	1.20038	+	3.69440i	0.121880	+	0.375109i	0.993320	−	0.115394i	$-0.0368130\pi$
$97$	1.20038	+	3.69440i	0.121880	+	0.375109i	−0.871439	+	0.490503i	$0.836813\pi$
$98$	−16.9599			−1.71321
$99$	−1.51547	+	9.83379i	−0.152311	+	0.988333i
$100$	18.8893			1.88893
$101$	−5.87614	−	18.0849i	−0.584697	−	1.79951i	−0.600482	−	0.799638i	$-0.705025\pi$
$101$	−5.87614	−	18.0849i	−0.584697	−	1.79951i	0.0157845	−	0.999875i	$-0.494975\pi$
$102$	−0.727127	−	31.7772i	−0.0719963	−	3.14641i
$103$	−2.80843	+	2.04045i	−0.276723	+	0.201051i	−0.717487	−	0.696572i	$-0.754708\pi$
$103$	−2.80843	+	2.04045i	−0.276723	+	0.201051i	0.440764	+	0.897623i	$0.354708\pi$
$104$	−4.76753	−	1.54907i	−0.467495	−	0.151898i
$105$	0.292794	−	0.102597i	0.0285738	−	0.0100125i
$106$	−6.04938	−	8.32625i	−0.587567	−	0.808717i
$107$	−1.88059	−	1.36633i	−0.181803	−	0.132088i	0.493162	−	0.869938i	$-0.335841\pi$
$107$	−1.88059	−	1.36633i	−0.181803	−	0.132088i	−0.674965	+	0.737850i	$0.735841\pi$
$108$	13.4739	+	16.0961i	1.29653	+	1.54885i
$109$			3.39710i			0.325383i	0.986677	+	0.162692i	$0.0520175\pi$
$109$			3.39710i			0.325383i	−0.986677	+	0.162692i	$0.947982\pi$
$110$	4.54936	+	0.915864i	0.433765	+	0.0873243i
$111$	3.10347	+	4.07229i	0.294568	+	0.386525i
$112$	1.26871	−	0.412228i	0.119882	−	0.0389519i
$113$	8.81466	−	12.1323i	0.829214	−	1.14131i	−0.158855	−	0.987302i	$-0.550780\pi$
$113$	8.81466	−	12.1323i	0.829214	−	1.14131i	0.988069	−	0.154013i	$-0.0492197\pi$
$114$	10.0443	−	33.5025i	0.940738	−	3.13779i
$115$	−0.0286808	+	0.0882704i	−0.00267450	+	0.00823126i
$116$	10.5641	−	32.5128i	0.980848	−	3.01874i
$117$	2.80778	−	1.05658i	0.259579	−	0.0976813i
$118$	1.39367	−	1.91822i	0.128298	−	0.176587i
$119$	2.23432	−	0.725973i	0.204819	−	0.0665498i
$120$	3.93172	−	2.99634i	0.358915	−	0.273527i
$121$	−10.1431	−	4.25647i	−0.922100	−	0.386952i
$122$		−	19.0596i		−	1.72557i
$123$	−3.89141	+	5.62218i	−0.350877	+	0.506935i
$124$	15.9624	+	11.5974i	1.43347	+	1.04147i
$125$	3.23802	+	4.45675i	0.289617	+	0.398624i
$126$	−1.27615	+	1.93698i	−0.113689	+	0.172560i
$127$	15.7998	+	5.13368i	1.40201	+	0.455540i	0.909840	−	0.414959i	$-0.136204\pi$
$127$	15.7998	+	5.13368i	1.40201	+	0.455540i	0.492169	+	0.870500i	$0.336204\pi$
$128$	−15.5707	+	11.3128i	−1.37627	+	0.999919i
$129$	−6.67307	+	0.152693i	−0.587531	+	0.0134439i
$130$	−0.432378	−	1.33072i	−0.0379220	−	0.116712i
$131$	−8.50276			−0.742890			−0.371445	−	0.928455i	$-0.621138\pi$
$131$	−8.50276			−0.742890			−0.371445	+	0.928455i	$0.621138\pi$
$132$	−20.8707	+	10.1470i	−1.81656	+	0.883184i
$133$	2.58509			0.224156
$134$	5.71999	+	17.6043i	0.494132	+	1.52078i
$135$	−0.719080	+	2.86965i	−0.0618886	+	0.246980i
$136$	30.2834	−	22.0022i	2.59678	−	1.88667i
$137$	17.3470	+	5.63639i	1.48206	+	0.481550i	0.934727	−	0.355367i	$-0.115644\pi$
$137$	17.3470	+	5.63639i	1.48206	+	0.481550i	0.547331	+	0.836916i	$0.315644\pi$
$138$	−0.229473	−	0.654877i	−0.0195341	−	0.0557468i
$139$	5.17106	+	7.11735i	0.438603	+	0.603686i	0.969901	−	0.243500i	$-0.0782954\pi$
$139$	5.17106	+	7.11735i	0.438603	+	0.603686i	−0.531298	+	0.847185i	$0.678295\pi$
$140$	0.585414	+	0.425328i	0.0494765	+	0.0359468i
$141$	−7.23638	−	5.00868i	−0.609413	−	0.421807i
$142$			5.78590i			0.485542i
$143$	0.382211	+	3.29453i	0.0319621	+	0.275502i
$144$	−3.37333	+	12.2649i	−0.281111	+	1.02207i
$145$	4.58217	−	1.48884i	0.380528	−	0.123641i
$146$	−8.33687	+	11.4747i	−0.689965	+	0.949655i
$147$	11.4494	+	3.43263i	0.944332	+	0.283119i
$148$	−3.69022	+	11.3573i	−0.303334	+	0.933566i
$149$	−1.68667	+	5.19102i	−0.138177	+	0.425265i	−0.996071	−	0.0885622i	$-0.971773\pi$
$149$	−1.68667	+	5.19102i	−0.138177	+	0.425265i	0.857894	+	0.513827i	$0.171773\pi$
$150$	−19.0652	−	5.71590i	−1.55666	−	0.466702i
$151$	−6.11565	+	8.41747i	−0.497684	+	0.685004i	−0.981782	−	0.190010i	$-0.939148\pi$
$151$	−6.11565	+	8.41747i	−0.497684	+	0.685004i	0.484098	+	0.875014i	$0.339148\pi$
$152$	39.1733	−	12.7282i	3.17738	−	1.03239i
$153$	−5.94075	+	21.5996i	−0.480281	+	1.74622i
$154$	−1.73635	−	1.88711i	−0.139919	−	0.152068i
$155$			2.78072i			0.223353i
$156$	5.75334	+	3.98220i	0.460636	+	0.318831i
$157$	0.261652	+	0.190102i	0.0208821	+	0.0151718i	0.598177	−	0.801364i	$-0.295892\pi$
$157$	0.261652	+	0.190102i	0.0208821	+	0.0151718i	−0.577295	+	0.816535i	$0.695892\pi$
$158$	9.70036	+	13.3514i	0.771719	+	1.06218i
$159$	2.39865	+	6.84534i	0.190226	+	0.542870i
$160$	0.213708	+	0.0694378i	0.0168951	+	0.00548954i
$161$	0.0414929	−	0.0301464i	0.00327010	−	0.00237587i
$162$	−8.72868	−	20.3231i	−0.685790	−	1.59674i
$163$	−5.18317	−	15.9521i	−0.405977	−	1.24947i	−0.920077	−	0.391738i	$-0.871874\pi$
$163$	−5.18317	−	15.9521i	−0.405977	−	1.24947i	0.514100	−	0.857730i	$-0.328126\pi$
$164$	−15.9476			−1.24529
$165$	−2.88585	−	1.53907i	−0.224663	−	0.119816i
$166$	−15.9353			−1.23682
$167$	−3.66132	−	11.2684i	−0.283321	−	0.871973i	−0.986897	−	0.161353i	$-0.948414\pi$
$167$	−3.66132	−	11.2684i	−0.283321	−	0.871973i	0.703576	−	0.710621i	$-0.251586\pi$
$168$	−2.73095	+	0.0624895i	−0.210697	+	0.00482117i
$169$	0.809017	−	0.587785i	0.0622321	−	0.0452143i
$170$	9.93680	+	3.22866i	0.762118	+	0.247627i
$171$	−13.5616	+	20.5842i	−1.03708	+	1.57411i
$172$	−9.15065	−	12.5948i	−0.697731	−	0.960344i
$173$	14.4477	+	10.4969i	1.09844	+	0.798064i	0.980805	−	0.194992i	$-0.0624682\pi$
$173$	14.4477	+	10.4969i	1.09844	+	0.798064i	0.117637	+	0.993057i	$0.462468\pi$
$174$	−20.5008	+	29.6189i	−1.55416	+	2.24540i
$175$		−	1.47109i		−	0.111204i
$176$	−12.2538	−	6.89975i	−0.923668	−	0.520088i
$177$	−1.32909	+	1.01289i	−0.0999008	+	0.0761338i
$178$	26.3528	−	8.56253i	1.97522	−	0.641789i
$179$	−8.38147	+	11.5361i	−0.626460	+	0.862248i	−0.997803	−	0.0662473i	$-0.978897\pi$
$179$	−8.38147	+	11.5361i	−0.626460	+	0.862248i	0.371343	+	0.928496i	$0.378897\pi$
$180$	−6.45787	+	2.43014i	−0.481341	+	0.181132i
$181$	−4.78823	+	14.7367i	−0.355906	+	1.09537i	0.599576	+	0.800318i	$0.295336\pi$
$181$	−4.78823	+	14.7367i	−0.355906	+	1.09537i	−0.955482	+	0.295049i	$0.904664\pi$
$182$	−0.238930	+	0.735351i	−0.0177107	+	0.0545078i
$183$	−3.85761	+	12.8669i	−0.285163	+	0.951149i
$184$	0.480334	−	0.661123i	0.0354107	−	0.0487387i
$185$	−1.60064	+	0.520078i	−0.117681	+	0.0382369i
$186$	−12.6017	−	16.5356i	−0.923999	−	1.21245i
$187$	−21.5802	−	12.1511i	−1.57810	−	0.888578i
$188$		−	20.5263i		−	1.49703i
$189$	1.25356	−	1.04934i	0.0911828	−	0.0763284i
$190$	9.30113	+	6.75766i	0.674775	+	0.490252i
$191$	−10.5949	−	14.5826i	−0.766619	−	1.05516i	−0.996635	−	0.0819736i	$-0.973878\pi$
$191$	−10.5949	−	14.5826i	−0.766619	−	1.05516i	0.230015	−	0.973187i	$-0.426122\pi$
$192$	12.2763	−	4.30169i	0.885964	−	0.310448i
$193$	−1.16920	−	0.379897i	−0.0841610	−	0.0273456i	0.266634	−	0.963798i	$-0.414089\pi$
$193$	−1.16920	−	0.379897i	−0.0841610	−	0.0273456i	−0.350795	+	0.936452i	$0.614089\pi$
$194$	7.72333	−	5.61133i	0.554503	−	0.402870i
$195$	0.0225586	+	0.985867i	0.00161546	+	0.0705994i
$196$	8.61490	+	26.5139i	0.615350	+	1.89385i
$197$	22.9126			1.63246			0.816229	−	0.577729i	$-0.196061\pi$
$197$	22.9126			1.63246			0.816229	+	0.577729i	$0.196061\pi$
$198$	24.1355	−	3.92602i	1.71523	−	0.279010i
$199$	−9.06665			−0.642718			−0.321359	−	0.946957i	$-0.604140\pi$
$199$	−9.06665			−0.642718			−0.321359	+	0.946957i	$0.604140\pi$
$200$	−7.24320	−	22.2923i	−0.512172	−	1.57630i
$201$	−0.298431	−	13.0422i	−0.0210497	−	0.919925i
$202$	−37.8074	+	27.4687i	−2.66012	+	1.93269i
$203$	−2.53209	−	0.822725i	−0.177718	−	0.0577440i
$204$	−49.3090	+	17.2782i	−3.45232	+	1.20972i
$205$	−1.32108	−	1.81831i	−0.0922683	−	0.126996i
$206$	6.90198	+	5.01459i	0.480884	+	0.349383i
$207$	0.0223695	+	0.488544i	0.00155479	+	0.0339562i
$208$			4.24010i			0.293998i
$209$	−18.4521	−	20.0542i	−1.27636	−	1.38718i
$210$	−0.462160	−	0.606434i	−0.0318921	−	0.0418479i
$211$	−15.9822	+	5.19294i	−1.10026	+	0.357497i	−0.802204	−	0.597051i	$-0.796339\pi$
$211$	−15.9822	+	5.19294i	−1.10026	+	0.357497i	−0.298059	+	0.954547i	$0.596339\pi$
$212$	−9.94388	+	13.6866i	−0.682949	+	0.939998i
$213$	1.17105	−	3.90600i	0.0802391	−	0.267634i
$214$	−1.76534	+	5.43315i	−0.120676	+	0.371402i
$215$	0.678004	−	2.08668i	0.0462395	−	0.142310i
$216$	13.8292	−	22.0734i	0.940959	−	1.50190i
$217$	0.903199	−	1.24315i	0.0613131	−	0.0843903i
$218$	7.94007	−	2.57988i	0.537769	−	0.174732i
$219$	7.95058	−	6.05909i	0.537250	−	0.409435i
$220$	−0.879082	−	7.57739i	−0.0592677	−	0.510867i
$221$			7.46723i			0.502300i
$222$	7.16131	−	10.3464i	0.480635	−	0.694406i
$223$	5.08249	+	3.69265i	0.340349	+	0.247278i	0.744809	−	0.667278i	$-0.232541\pi$
$223$	5.08249	+	3.69265i	0.340349	+	0.247278i	−0.404460	+	0.914556i	$0.632541\pi$
$224$	−0.0729860	−	0.100457i	−0.00487658	−	0.00671204i
$225$	11.7138	+	7.71748i	0.780919	+	0.514499i
$226$	−35.0512	−	11.3888i	−2.33157	−	0.757574i
$227$	9.65997	−	7.01838i	0.641155	−	0.465826i	−0.219092	−	0.975704i	$-0.570309\pi$
$227$	9.65997	−	7.01838i	0.641155	−	0.465826i	0.860247	+	0.509878i	$0.170309\pi$
$228$	−57.4776	+	1.31520i	−3.80655	+	0.0871015i
$229$	1.63359	+	5.02769i	0.107951	+	0.332239i	0.990412	−	0.138147i	$-0.0441147\pi$
$229$	1.63359	+	5.02769i	0.107951	+	0.332239i	−0.882461	+	0.470386i	$0.844115\pi$
$230$	0.228096			0.0150402
$231$	0.790246	+	1.62540i	0.0519944	+	0.106944i
$232$	−42.4210			−2.78507
$233$	6.38324	+	19.6456i	0.418180	+	1.28703i	0.909376	+	0.415976i	$0.136560\pi$
$233$	6.38324	+	19.6456i	0.418180	+	1.28703i	−0.491196	+	0.871049i	$0.663440\pi$
$234$	−4.60190	−	5.76024i	−0.300835	−	0.376558i
$235$	2.34037	−	1.70038i	0.152669	−	0.110921i
$236$	−3.70675	−	1.20440i	−0.241289	−	0.0783995i
$237$	−3.84631	−	10.9767i	−0.249845	−	0.713014i
$238$	−3.39365	−	4.67095i	−0.219977	−	0.302773i
$239$	5.44007	+	3.95244i	0.351889	+	0.255662i	0.749661	−	0.661822i	$-0.230217\pi$
$239$	5.44007	+	3.95244i	0.351889	+	0.255662i	−0.397772	+	0.917484i	$0.630217\pi$
$240$	−3.43806	−	2.37966i	−0.221926	−	0.153607i
$241$		−	16.5551i		−	1.06641i	−0.845986	−	0.533205i	$-0.820988\pi$
$241$		−	16.5551i		−	1.06641i	0.845986	−	0.533205i	$-0.179012\pi$
$242$	−2.24563	+	26.9401i	−0.144355	+	1.73177i
$243$	1.77928	+	15.4866i	0.114141	+	0.993465i
$244$	−29.7965	+	9.68147i	−1.90752	+	0.619792i
$245$	−2.30942	+	3.17865i	−0.147544	+	0.203076i
$246$	16.0960	+	4.82573i	1.02625	+	0.307677i
$247$	−2.53910	+	7.81454i	−0.161559	+	0.497227i
$248$	7.56581	−	23.2852i	0.480430	−	1.47861i
$249$	10.7577	+	3.22525i	0.681742	+	0.204392i
$250$	7.95773	−	10.9529i	0.503291	−	0.692720i
$251$	5.44649	−	1.76967i	0.343779	−	0.111701i	−0.132038	−	0.991245i	$-0.542152\pi$
$251$	5.44649	−	1.76967i	0.343779	−	0.111701i	0.475818	+	0.879544i	$0.342152\pi$
$252$	3.67638	+	1.01115i	0.231590	+	0.0636965i
$253$	−0.530038	−	0.106706i	−0.0333232	−	0.00670853i
$254$		−	40.8278i		−	2.56176i
$255$	−6.05475	−	4.19082i	−0.379163	−	0.262439i
$256$	26.1146	+	18.9734i	1.63217	+	1.18584i
$257$	−1.58358	−	2.17961i	−0.0987807	−	0.135960i	0.756765	−	0.653687i	$-0.226778\pi$
$257$	−1.58358	−	2.17961i	−0.0987807	−	0.135960i	−0.855546	+	0.517726i	$0.826778\pi$
$258$	5.42467	+	15.4810i	0.337725	+	0.963808i
$259$	0.884504	+	0.287393i	0.0549604	+	0.0178577i
$260$	−1.86073	+	1.35190i	−0.115398	+	0.0838414i
$261$	19.8346	−	15.8460i	1.22773	−	0.980845i
$262$	6.45732	+	19.8736i	0.398934	+	1.22779i
$263$	−12.8544			−0.792637			−0.396319	−	0.918113i	$-0.629712\pi$
$263$	−12.8544			−0.792637			−0.396319	+	0.918113i	$0.629712\pi$
$264$	19.9780	+	20.7397i	1.22956	+	1.27644i
$265$	−2.38426			−0.146464
$266$	−1.96321	−	6.04215i	−0.120372	−	0.370468i
$267$	−19.5235	+	0.446736i	−1.19482	+	0.0273398i
$268$	24.6159	−	17.8845i	1.50366	−	1.09247i
$269$	4.52610	+	1.47062i	0.275961	+	0.0896652i	0.443728	−	0.896162i	$-0.353656\pi$
$269$	4.52610	+	1.47062i	0.275961	+	0.0896652i	−0.167767	+	0.985827i	$0.553656\pi$
$270$	7.25336	−	0.498611i	0.441425	−	0.0303445i
$271$	10.5213	+	14.4813i	0.639123	+	0.879678i	0.998568	−	0.0534883i	$-0.0170340\pi$
$271$	10.5213	+	14.4813i	0.639123	+	0.879678i	−0.359445	+	0.933166i	$0.617034\pi$
$272$	−25.6149	−	18.6103i	−1.55313	−	1.12842i
$273$	0.310132	−	0.448068i	0.0187700	−	0.0271183i
$274$		−	44.8259i		−	2.70803i
$275$	−11.4122	+	10.5005i	−0.688183	+	0.633205i
$276$	−0.907228	+	0.691393i	−0.0546087	+	0.0416170i
$277$	19.2277	−	6.24745i	1.15528	−	0.375373i	0.332150	−	0.943227i	$-0.392226\pi$
$277$	19.2277	−	6.24745i	1.15528	−	0.375373i	0.823129	+	0.567854i	$0.192226\pi$
$278$	12.7083	−	17.4915i	0.762196	−	1.04907i
$279$	5.16048	+	13.7135i	0.308950	+	0.821007i
$280$	0.277472	−	0.853972i	0.0165822	−	0.0510346i
$281$	−5.64969	+	17.3880i	−0.337032	+	1.03728i	0.628680	+	0.777664i	$0.283595\pi$
$281$	−5.64969	+	17.3880i	−0.337032	+	1.03728i	−0.965712	+	0.259614i	$0.916405\pi$
$282$	−6.21126	+	20.7174i	−0.369875	+	1.23370i
$283$	2.19840	−	3.02584i	0.130682	−	0.179868i	−0.738662	−	0.674076i	$-0.764542\pi$
$283$	2.19840	−	3.02584i	0.130682	−	0.179868i	0.869344	+	0.494208i	$0.164542\pi$
$284$	9.04530	−	2.93900i	0.536740	−	0.174397i
$285$	−4.91135	−	6.44454i	−0.290923	−	0.381742i
$286$	7.41006	−	3.39533i	0.438166	−	0.200770i
$287$			1.24199i			0.0733123i
$288$	1.18279	−	0.0541577i	0.0696967	−	0.00319127i
$289$	−31.3571	−	22.7823i	−1.84453	−	1.34013i
$290$	−6.95974	−	9.57926i	−0.408690	−	0.562514i
$291$	−6.34965	+	2.22496i	−0.372223	+	0.130429i
$292$	22.1736	+	7.20464i	1.29761	+	0.421620i
$293$	6.14229	−	4.46264i	0.358837	−	0.260710i	−0.393730	−	0.919226i	$-0.628816\pi$
$293$	6.14229	−	4.46264i	0.358837	−	0.260710i	0.752567	+	0.658516i	$0.228816\pi$
$294$	−0.671992	−	29.3677i	−0.0391913	−	1.71276i
$295$	−0.169741	−	0.522408i	−0.00988268	−	0.0304158i
$296$	14.8184			0.861304
$297$	−17.0882	−	2.23455i	−0.991558	−	0.129662i
$298$	13.4139			0.777048
$299$	0.0503756	+	0.155040i	0.00291329	+	0.00896620i
$300$	0.748440	+	32.7087i	0.0432112	+	1.88843i
$301$	−0.980878	+	0.712649i	−0.0565368	+	0.0410764i
$302$	24.3187	+	7.90162i	1.39938	+	0.454687i
$303$	31.0829	−	10.8917i	1.78567	−	0.625710i
$304$	−20.4782	−	28.1858i	−1.17451	−	1.61657i
$305$	−3.57218	−	2.59534i	−0.204542	−	0.148609i
$306$	54.9966	−	2.51818i	3.14394	−	0.143955i
$307$			29.2060i			1.66687i	0.552615	+	0.833437i	$0.313630\pi$
$307$			29.2060i			1.66687i	−0.552615	+	0.833437i	$0.686370\pi$
$308$	−2.06819	+	3.67307i	−0.117846	+	0.209293i
$309$	−3.64451	−	4.78223i	−0.207329	−	0.272052i
$310$	6.49940	−	2.11178i	0.369141	−	0.119941i
$311$	−6.81835	+	9.38466i	−0.386633	+	0.532155i	−0.957327	−	0.289008i	$-0.906675\pi$
$311$	−6.81835	+	9.38466i	−0.386633	+	0.532155i	0.570693	+	0.821163i	$0.306675\pi$
$312$	2.49346	−	8.31683i	0.141164	−	0.470848i
$313$	−2.71492	+	8.35568i	−0.153457	+	0.472291i	−0.998001	−	0.0631944i	$-0.979871\pi$
$313$	−2.71492	+	8.35568i	−0.153457	+	0.472291i	0.844545	+	0.535485i	$0.179871\pi$
$314$	0.245617	−	0.755932i	0.0138610	−	0.0426597i
$315$	0.189258	+	0.502937i	0.0106635	+	0.0283373i
$316$	15.9453	−	21.9468i	0.896994	−	1.23461i
$317$	14.1115	−	4.58510i	0.792581	−	0.257525i	0.115378	−	0.993322i	$-0.463192\pi$
$317$	14.1115	−	4.58510i	0.792581	−	0.257525i	0.677203	+	0.735797i	$0.263192\pi$
$318$	14.1780	−	10.8050i	0.795064	−	0.605914i
$319$	11.6914	+	25.5156i	0.654592	+	1.42860i
$320$			4.27588i			0.239029i
$321$	2.29141	−	3.31056i	0.127894	−	0.184777i
$322$	−0.101973	−	0.0740874i	−0.00568271	−	0.00412873i
$323$	−36.0641	−	49.6380i	−2.00666	−	2.76193i
$324$	−27.3381	+	23.9691i	−1.51878	+	1.33162i
$325$	4.44700	+	1.44492i	0.246675	+	0.0801496i
$326$	−33.3488	+	24.2293i	−1.84702	+	1.34194i
$327$	−5.88241	+	0.134601i	−0.325298	+	0.00744347i
$328$	6.11518	+	18.8206i	0.337654	+	1.03919i
$329$	−1.59858			−0.0881326
$330$	−1.40565	+	7.91395i	−0.0773786	+	0.435649i
$331$	4.45755			0.245009			0.122505	−	0.992468i	$-0.460907\pi$
$331$	4.45755			0.245009			0.122505	+	0.992468i	$0.460907\pi$
$332$	8.09444	+	24.9121i	0.444240	+	1.36723i
$333$	−6.92860	+	5.53531i	−0.379685	+	0.303333i
$334$	−23.5571	+	17.1153i	−1.28899	+	0.936505i
$335$	4.07832	+	1.32513i	0.222822	+	0.0723994i
$336$	0.764082	+	2.18056i	0.0416841	+	0.118959i
$337$	2.41532	+	3.32441i	0.131571	+	0.181092i	0.869720	−	0.493546i	$-0.164300\pi$
$337$	2.41532	+	3.32441i	0.131571	+	0.181092i	−0.738148	+	0.674638i	$0.764300\pi$
$338$	−1.98823	−	1.44454i	−0.108146	−	0.0785724i
$339$	21.3576	+	14.7827i	1.15999	+	0.802888i
$340$		−	17.1746i		−	0.931421i
$341$	−16.0909	+	1.86676i	−0.871369	+	0.101091i
$342$	58.4108	+	16.0653i	3.15849	+	0.868711i
$343$	4.15941	−	1.35147i	0.224587	−	0.0729727i
$344$	−11.3549	+	15.6287i	−0.612217	+	0.842644i
$345$	−0.153985	−	0.0461661i	−0.00829029	−	0.00248550i
$346$	13.5623	−	41.7406i	0.729115	−	2.24399i
$347$	3.82501	−	11.7722i	0.205338	−	0.631964i	−0.794362	−	0.607445i	$-0.792195\pi$
$347$	3.82501	−	11.7722i	0.205338	−	0.631964i	0.999699	−	0.0245190i	$-0.00780543\pi$
$348$	56.7177	+	17.0045i	3.04039	+	0.911535i
$349$	21.3496	−	29.3853i	1.14282	−	1.57296i	0.381779	−	0.924254i	$-0.375311\pi$
$349$	21.3496	−	29.3853i	1.14282	−	1.57296i	0.761041	−	0.648704i	$-0.224689\pi$
$350$	−3.43839	+	1.11720i	−0.183790	+	0.0597169i
$351$	1.94083	+	4.82008i	0.103594	+	0.257277i
$352$	−0.258340	+	1.28325i	−0.0137696	+	0.0683975i
$353$		−	14.2080i		−	0.756216i	−0.925761	−	0.378108i	$-0.876575\pi$
$353$		−	14.2080i		−	0.756216i	0.925761	−	0.378108i	$-0.123425\pi$
$354$	3.37681	+	2.33727i	0.179475	+	0.124225i
$355$	1.08440	+	0.787865i	0.0575541	+	0.0418155i
$356$	−26.7722	−	36.8487i	−1.41892	−	1.95298i
$357$	1.34562	+	3.84017i	0.0712179	+	0.203243i
$358$	33.3286	+	10.8291i	1.76147	+	0.572337i
$359$	18.0992	−	13.1498i	0.955237	−	0.694020i	0.00319708	−	0.999995i	$-0.498982\pi$
$359$	18.0992	−	13.1498i	0.955237	−	0.694020i	0.952040	+	0.305975i	$0.0989823\pi$
$360$	5.34424	+	6.68944i	0.281666	+	0.352564i
$361$	−14.9916	−	46.1395i	−0.789034	−	2.42840i
$362$	38.0805			2.00146
$363$	6.96860	−	17.7324i	0.365757	−	0.930711i
$364$	1.27097			0.0666167
$365$	1.01538	+	3.12502i	0.0531474	+	0.163571i
$366$	33.0035	−	0.755187i	1.72512	−	0.0394743i
$367$	−21.0887	+	15.3218i	−1.10082	+	0.799792i	−0.981193	−	0.193027i	$-0.938169\pi$
$367$	−21.0887	+	15.3218i	−1.10082	+	0.799792i	−0.119626	+	0.992819i	$0.538169\pi$
$368$	−0.657386	−	0.213598i	−0.0342686	−	0.0111345i
$369$	−9.88954	−	6.51559i	−0.514829	−	0.339188i
$370$	2.43117	+	3.34621i	0.126390	+	0.173961i
$371$	1.06591	+	0.774426i	0.0553391	+	0.0402062i
$372$	−19.4495	+	28.1000i	−1.00841	+	1.45692i
$373$		−	35.0550i		−	1.81508i	−0.419968	−	0.907539i	$-0.637959\pi$
$373$		−	35.0550i		−	1.81508i	0.419968	−	0.907539i	$-0.362041\pi$
$374$	−12.0121	+	59.6676i	−0.621131	+	3.08534i
$375$	−7.58900	+	5.78353i	−0.391894	+	0.298660i
$376$	−24.2242	+	7.87092i	−1.24927	+	0.405912i
$377$	4.97407	−	6.84622i	0.256178	−	0.352598i
$378$	−3.40463	−	2.13304i	−0.175115	−	0.109712i
$379$	7.70615	−	23.7171i	0.395838	−	1.21826i	−0.532469	−	0.846450i	$-0.678736\pi$
$379$	7.70615	−	23.7171i	0.395838	−	1.21826i	0.928307	−	0.371815i	$-0.121264\pi$
$380$	5.83990	−	17.9734i	0.299581	−	0.922014i
$381$	−8.26344	+	27.5624i	−0.423349	+	1.41206i
$382$	−26.0379	+	35.8381i	−1.33221	+	1.83364i
$383$	−6.74861	+	2.19276i	−0.344838	+	0.112045i	−0.476315	−	0.879275i	$-0.658028\pi$
$383$	−6.74861	+	2.19276i	−0.344838	+	0.112045i	0.131478	+	0.991319i	$0.458028\pi$
$384$	−20.2062	−	26.5140i	−1.03114	−	1.35304i
$385$	−0.590124	+	0.0684626i	−0.0300755	+	0.00348918i
$386$			3.02129i			0.153780i
$387$	−0.528806	−	11.5490i	−0.0268807	−	0.587069i
$388$	−12.6955	−	9.22382i	−0.644516	−	0.468269i
$389$	−13.1853	−	18.1481i	−0.668523	−	0.920143i	0.331203	−	0.943560i	$-0.392546\pi$
$389$	−13.1853	−	18.1481i	−0.668523	−	0.920143i	−0.999726	+	0.0234167i	$0.992546\pi$
$390$	2.28714	−	0.801431i	0.115814	−	0.0405820i
$391$	−1.15772	−	0.376166i	−0.0585484	−	0.0190235i
$392$	27.9871	−	20.3338i	1.41356	−	1.02701i
$393$	−0.336900	−	14.7234i	−0.0169944	−	0.742695i
$394$	−17.4007	−	53.5539i	−0.876635	−	2.69800i
$395$	3.82324			0.192368
$396$	−18.3975	−	35.7376i	−0.924509	−	1.79588i
$397$	15.8055			0.793254			0.396627	−	0.917980i	$-0.370181\pi$
$397$	15.8055			0.793254			0.396627	+	0.917980i	$0.370181\pi$
$398$	6.88555	+	21.1916i	0.345142	+	1.06224i
$399$	0.102428	+	4.47634i	0.00512779	+	0.224097i
$400$	−16.0396	+	11.6535i	−0.801982	+	0.582674i
$401$	−19.5105	−	6.33933i	−0.974306	−	0.316571i	−0.221753	−	0.975103i	$-0.571178\pi$
$401$	−19.5105	−	6.33933i	−0.974306	−	0.316571i	−0.752553	+	0.658532i	$0.771178\pi$
$402$	−30.2570	+	10.6022i	−1.50908	+	0.528792i
$403$	2.87081	+	3.95133i	0.143005	+	0.196830i
$404$	62.1473	+	45.1526i	3.09194	+	2.24643i
$405$	−4.99758	−	1.13145i	−0.248332	−	0.0562224i
$406$			6.54307i			0.324727i
$407$	−4.08402	−	8.91306i	−0.202437	−	0.441804i
$408$	39.2988	+	51.5669i	1.94558	+	2.55294i
$409$	−22.3498	+	7.26189i	−1.10513	+	0.359077i	−0.804073	−	0.594530i	$-0.797338\pi$
$409$	−22.3498	+	7.26189i	−1.10513	+	0.359077i	−0.301053	+	0.953607i	$0.597338\pi$
$410$	−3.24668	+	4.46867i	−0.160342	+	0.220692i
$411$	−9.07264	+	30.2614i	−0.447520	+	1.49269i
$412$	4.33355	−	13.3373i	0.213499	−	0.657082i
$413$	−0.0937979	+	0.288680i	−0.00461549	+	0.0142050i
$414$	1.12489	−	0.423303i	0.0552853	−	0.0208042i
$415$	−2.16990	+	2.98661i	−0.106516	+	0.146607i
$416$	0.375360	−	0.121962i	0.0184036	−	0.00597968i
$417$	−12.1195	+	9.23620i	−0.593494	+	0.452298i
$418$	−32.8597	+	58.3583i	−1.60722	+	2.85440i
$419$		−	22.3183i		−	1.09032i	−0.838333	−	0.545159i	$-0.816469\pi$
$419$		−	22.3183i		−	1.09032i	0.838333	−	0.545159i	$-0.183531\pi$
$420$	−0.713301	+	1.03055i	−0.0348055	+	0.0502858i
$421$	2.87286	+	2.08726i	0.140015	+	0.101727i	0.655588	−	0.755119i	$-0.272421\pi$
$421$	2.87286	+	2.08726i	0.140015	+	0.101727i	−0.515573	+	0.856846i	$0.672421\pi$
$422$	24.2750	+	33.4117i	1.18169	+	1.62646i
$423$	8.38630	−	12.7289i	0.407756	−	0.618903i
$424$	19.9653	+	6.48712i	0.969601	+	0.315043i
$425$	−28.2474	+	20.5229i	−1.37020	+	0.995507i
$426$	−10.0189	+	0.229252i	−0.485415	+	0.0111073i
$427$	0.753989	+	2.32054i	0.0364881	+	0.112299i
$428$	9.39054			0.453909
$429$	−5.68965	+	0.792372i	−0.274699	+	0.0382561i
$430$	−5.39212			−0.260031
$431$	−9.63986	−	29.6684i	−0.464336	−	1.42908i	−0.859816	−	0.510604i	$-0.829422\pi$
$431$	−9.63986	−	29.6684i	−0.464336	−	1.42908i	0.395480	−	0.918474i	$-0.370578\pi$
$432$	−21.3715	−	5.35528i	−1.02824	−	0.257656i
$433$	−17.9133	+	13.0148i	−0.860859	+	0.625451i	−0.928119	−	0.372285i	$-0.878574\pi$
$433$	−17.9133	+	13.0148i	−0.860859	+	0.625451i	0.0672596	+	0.997736i	$0.478574\pi$
$434$	−3.59154	−	1.16696i	−0.172399	−	0.0560160i
$435$	2.75962	+	7.87548i	0.132314	+	0.377600i
$436$	−8.06644	−	11.1025i	−0.386312	−	0.531713i
$437$	−1.08366	−	0.787323i	−0.0518384	−	0.0376628i
$438$	−20.1999	−	13.9815i	−0.965190	−	0.668060i
$439$			40.9771i			1.95573i	0.209234	+	0.977866i	$0.432903\pi$
$439$			40.9771i			1.95573i	−0.209234	+	0.977866i	$0.567097\pi$
$440$	−8.60540	+	3.94304i	−0.410246	+	0.187977i
$441$	−5.49029	+	19.9618i	−0.261442	+	0.950562i
$442$	17.4532	−	5.67089i	0.830165	−	0.269737i
$443$	11.6622	−	16.0517i	0.554090	−	0.762639i	−0.436470	−	0.899719i	$-0.643772\pi$
$443$	11.6622	−	16.0517i	0.554090	−	0.762639i	0.990560	+	0.137080i	$0.0437717\pi$
$444$	−19.8125	−	5.93997i	−0.940261	−	0.281898i
$445$	1.98364	−	6.10503i	0.0940338	−	0.289406i
$446$	4.77102	−	14.6837i	0.225914	−	0.695293i
$447$	−9.05559	−	2.71494i	−0.428315	−	0.128412i
$448$	1.38884	−	1.91157i	0.0656165	−	0.0903133i
$449$	5.86379	−	1.90526i	0.276730	−	0.0899149i	−0.167364	−	0.985895i	$-0.553526\pi$
$449$	5.86379	−	1.90526i	0.276730	−	0.0899149i	0.444094	+	0.895980i	$0.353526\pi$
$450$	9.14223	−	33.2397i	0.430969	−	1.56693i
$451$	9.63493	−	8.86521i	0.453691	−	0.417446i
$452$			60.5818i			2.84953i
$453$	−14.8180	−	10.2563i	−0.696210	−	0.481884i
$454$	−23.7403	−	17.2483i	−1.11419	−	0.809503i
$455$	0.105286	+	0.144913i	0.00493586	+	0.00679363i
$456$	23.5922	+	67.3281i	1.10481	+	3.15293i
$457$	16.2060	+	5.26564i	0.758083	+	0.246316i	0.662456	−	0.749101i	$-0.269514\pi$
$457$	16.2060	+	5.26564i	0.758083	+	0.246316i	0.0956273	+	0.995417i	$0.469514\pi$
$458$	10.5106	−	7.63643i	0.491130	−	0.356827i
$459$	−37.6372	−	9.43116i	−1.75675	−	0.440209i
$460$	−0.115863	−	0.356591i	−0.00540216	−	0.0166261i
$461$	40.1732			1.87105			0.935526	−	0.353259i	$-0.114927\pi$
$461$	40.1732			1.87105			0.935526	+	0.353259i	$0.114927\pi$
$462$	3.19892	−	3.08144i	0.148827	−	0.143361i
$463$	36.1593			1.68046			0.840232	−	0.542227i	$-0.182419\pi$
$463$	36.1593			1.68046			0.840232	+	0.542227i	$0.182419\pi$
$464$	11.0880	+	34.1253i	0.514746	+	1.58423i
$465$	−4.81509	+	0.110179i	−0.223294	+	0.00510942i
$466$	41.0701	−	29.8392i	1.90254	−	1.38227i
$467$	−2.82105	−	0.916615i	−0.130543	−	0.0424159i	0.243017	−	0.970022i	$-0.421863\pi$
$467$	−2.82105	−	0.916615i	−0.130543	−	0.0424159i	−0.373560	+	0.927606i	$0.621863\pi$
$468$	−6.66760	+	10.1203i	−0.308210	+	0.467809i
$469$	−1.39284	−	1.91708i	−0.0643153	−	0.0885224i
$470$	−5.75168	−	4.17884i	−0.265305	−	0.192755i
$471$	−0.318812	+	0.460609i	−0.0146901	+	0.0212237i
$472$			4.83637i			0.222612i
$473$	12.5299	+	2.52249i	0.576126	+	0.115984i
$474$	−22.7349	+	17.3261i	−1.04425	+	0.795816i
$475$	−36.5396	+	11.8724i	−1.67655	+	0.544745i
$476$	−5.57843	+	7.67805i	−0.255687	+	0.351923i
$477$	−11.7583	+	4.42473i	−0.538377	+	0.202594i
$478$	5.10668	−	15.7167i	0.233574	−	0.718867i
$479$	−6.73441	+	20.7264i	−0.307703	+	0.947012i	0.670952	+	0.741501i	$0.265886\pi$
$479$	−6.73441	+	20.7264i	−0.307703	+	0.947012i	−0.978655	+	0.205511i	$0.934114\pi$
$480$	−0.111771	+	0.372807i	−0.00510161	+	0.0170162i
$481$	−1.73753	+	2.39151i	−0.0792248	+	0.109044i
$482$	−38.6944	+	12.5726i	−1.76248	+	0.572665i
$483$	0.0538454	+	0.0706546i	0.00245005	+	0.00321489i
$484$	43.2570	−	10.1737i	1.96623	−	0.462443i
$485$		−	2.21161i		−	0.100424i
$486$	34.8457	−	15.9198i	1.58063	−	0.722137i
$487$	10.1089	+	7.34453i	0.458077	+	0.332812i	0.792776	−	0.609513i	$-0.208635\pi$
$487$	10.1089	+	7.34453i	0.458077	+	0.332812i	−0.334700	+	0.942325i	$0.608635\pi$
$488$	22.8512	+	31.4520i	1.03443	+	1.42377i
$489$	27.4173	−	9.60722i	1.23985	−	0.434454i
$490$	9.18334	+	2.98385i	0.414861	+	0.134796i
$491$	−3.80455	+	2.76417i	−0.171697	+	0.124745i	−0.670315	−	0.742077i	$-0.733841\pi$
$491$	−3.80455	+	2.76417i	−0.171697	+	0.124745i	0.498618	+	0.866822i	$0.333841\pi$
$492$	−0.631881	−	27.6147i	−0.0284874	−	1.24497i
$493$	19.5270	+	60.0979i	0.879451	+	2.70667i
$494$	20.1933			0.908538
$495$	2.55070	−	5.05812i	0.114646	−	0.227345i
$496$	−20.7092			−0.929868
$497$	−0.228888	−	0.704444i	−0.0102670	−	0.0315986i
$498$	−0.631394	−	27.5935i	−0.0282934	−	1.23649i
$499$	8.12469	−	5.90294i	0.363711	−	0.264252i	−0.390887	−	0.920439i	$-0.627832\pi$
$499$	8.12469	−	5.90294i	0.363711	−	0.264252i	0.754598	+	0.656187i	$0.227832\pi$
$500$	−21.1652	−	6.87698i	−0.946535	−	0.307548i
$501$	19.3672	−	6.78641i	0.865264	−	0.303194i
$502$	−8.27253	−	11.3862i	−0.369221	−	0.508190i
$503$	9.61580	+	6.98628i	0.428747	+	0.311503i	0.781148	−	0.624346i	$-0.214635\pi$
$503$	9.61580	+	6.98628i	0.428747	+	0.311503i	−0.352401	+	0.935849i	$0.614635\pi$
$504$	−0.216413	−	4.72642i	−0.00963982	−	0.210532i
$505$			10.8263i			0.481765i
$506$	0.153126	+	1.31990i	0.00680730	+	0.0586766i
$507$	1.04986	+	1.37760i	0.0466260	+	0.0611815i
$508$	−63.8275	+	20.7388i	−2.83189	+	0.920135i
$509$	0.777080	−	1.06956i	0.0344435	−	0.0474073i	−0.791448	−	0.611237i	$-0.790672\pi$
$509$	0.777080	−	1.06956i	0.0344435	−	0.0474073i	0.825891	+	0.563829i	$0.190672\pi$
$510$	−5.19703	+	17.3345i	−0.230128	+	0.767583i
$511$	0.561095	−	1.72687i	0.0248214	−	0.0763923i
$512$	12.6193	−	38.8381i	0.557698	−	1.71642i
$513$	−36.1809	−	22.6677i	−1.59742	−	1.00080i
$514$	−3.89178	+	5.35658i	−0.171659	+	0.236269i
$515$	1.87968	−	0.610746i	0.0828287	−	0.0269127i
$516$	21.4465	−	16.3443i	0.944131	−	0.719517i
$517$	11.4105	+	12.4012i	0.501834	+	0.545406i
$518$		−	2.28562i		−	0.100424i
$519$	−17.6039	+	25.4336i	−0.772727	+	1.11641i
$520$	2.30896	+	1.67756i	0.101255	+	0.0735658i
$521$	5.08875	+	7.00406i	0.222942	+	0.306854i	0.905806	−	0.423692i	$-0.139266\pi$
$521$	5.08875	+	7.00406i	0.222942	+	0.306854i	−0.682864	+	0.730545i	$0.739266\pi$
$522$	−52.1002	−	34.3256i	−2.28037	−	1.50239i
$523$	33.5086	+	10.8876i	1.46523	+	0.476082i	0.929663	−	0.368411i	$-0.120098\pi$
$523$	33.5086	+	10.8876i	1.46523	+	0.476082i	0.535567	+	0.844493i	$0.320098\pi$
$524$	27.7890	−	20.1899i	1.21397	−	0.881999i
$525$	2.54734	−	0.0582882i	0.111175	−	0.00254391i
$526$	9.76212	+	30.0447i	0.425649	+	1.31001i
$527$	−36.4708			−1.58869
$528$	11.4621	−	21.4921i	0.498822	−	0.935324i
$529$	22.9734			0.998845
$530$	1.81070	+	5.57275i	0.0786517	+	0.242065i
$531$	−1.80659	−	2.26132i	−0.0783992	−	0.0981330i
$532$	−8.44867	+	6.13832i	−0.366296	+	0.266130i
$533$	−3.75444	−	1.21989i	−0.162623	−	0.0528394i
$534$	15.8710	+	45.2931i	0.686806	+	1.96002i
$535$	0.777903	+	1.07069i	0.0336317	+	0.0462901i
$536$	−30.5456	−	22.1927i	−1.31937	−	0.958577i
$537$	−20.3080	−	14.0562i	−0.876354	−	0.606571i
$538$		−	11.6957i		−	0.504239i
$539$	−19.9439	−	11.2297i	−0.859042	−	0.483700i
$540$	−4.46390	−	11.0861i	−0.192095	−	0.477072i
$541$	−34.4917	+	11.2070i	−1.48291	+	0.481828i	−0.934982	−	0.354694i	$-0.884585\pi$
$541$	−34.4917	+	11.2070i	−1.48291	+	0.481828i	−0.547933	+	0.836522i	$0.684585\pi$
$542$	25.8571	−	35.5892i	1.11066	−	1.52869i
$543$	−25.7077	−	7.70738i	−1.10322	−	0.330755i
$544$	−0.910718	+	2.80290i	−0.0390467	+	0.120173i
$545$	0.597671	−	1.83944i	0.0256014	−	0.0787930i
$546$	−1.28280	−	0.384594i	−0.0548987	−	0.0164591i
$547$	13.5745	−	18.6837i	0.580405	−	0.798859i	−0.413335	−	0.910579i	$-0.635636\pi$
$547$	13.5745	−	18.6837i	0.580405	−	0.798859i	0.993740	+	0.111720i	$0.0356361\pi$
$548$	−70.0778	+	22.7696i	−2.99357	+	0.972671i
$549$	−22.4332	−	6.17001i	−0.957424	−	0.263330i
$550$	33.2098	+	18.6994i	1.41607	+	0.797345i
$551$			69.5329i			2.96220i
$552$	1.16383	+	0.805550i	0.0495360	+	0.0342865i
$553$	−1.70921	−	1.24182i	−0.0726831	−	0.0528074i
$554$	−29.2044	−	40.1964i	−1.24078	−	1.70778i
$555$	−0.963987	−	2.75105i	−0.0409190	−	0.116776i
$556$	−33.8004	−	10.9824i	−1.43346	−	0.465758i
$557$	20.8561	−	15.1528i	0.883700	−	0.642045i	−0.0505279	−	0.998723i	$-0.516090\pi$
$557$	20.8561	−	15.1528i	0.883700	−	0.642045i	0.934228	+	0.356677i	$0.116090\pi$
$558$	28.1337	−	22.4762i	1.19099	−	0.951493i
$559$	−1.19086	−	3.66509i	−0.0503680	−	0.155017i
$560$	−0.759498			−0.0320946
$561$	20.1858	−	37.8497i	0.852245	−	1.59801i
$562$	44.9316			1.89532
$563$	0.792315	+	2.43850i	0.0333921	+	0.102770i	0.966363	−	0.257180i	$-0.0827935\pi$
$563$	0.792315	+	2.43850i	0.0333921	+	0.102770i	−0.932971	+	0.359951i	$0.882793\pi$
$564$	35.5433	−	0.813302i	1.49664	−	0.0342462i
$565$	−6.90742	+	5.01854i	−0.290597	+	0.211131i
$566$	−8.74188	−	2.84041i	−0.367449	−	0.119391i
$567$	1.86671	+	2.12908i	0.0783943	+	0.0894128i
$568$	−6.93694	−	9.54787i	−0.291067	−	0.400620i
$569$	−2.52687	−	1.83588i	−0.105932	−	0.0769640i	0.533558	−	0.845763i	$-0.320855\pi$
$569$	−2.52687	−	1.83588i	−0.105932	−	0.0769640i	−0.639490	+	0.768799i	$0.720855\pi$
$570$	−11.3330	+	16.3736i	−0.474688	+	0.685813i
$571$		−	3.12912i		−	0.130950i	−0.997854	−	0.0654749i	$-0.979144\pi$
$571$		−	3.12912i		−	0.130950i	0.997854	−	0.0654749i	$-0.0208562\pi$
$572$	−9.07203	−	9.85971i	−0.379321	−	0.412255i
$573$	24.8314	−	18.9239i	1.03735	−	0.790556i
$574$	2.90291	−	0.943213i	0.121165	−	0.0393690i
$575$	−0.448040	+	0.616674i	−0.0186846	+	0.0257171i
$576$	7.93522	+	21.0871i	0.330634	+	0.878630i
$577$	7.18233	−	22.1049i	0.299004	−	0.920241i	−0.682843	−	0.730565i	$-0.739257\pi$
$577$	7.18233	−	22.1049i	0.299004	−	0.920241i	0.981847	−	0.189675i	$-0.0607435\pi$
$578$	−29.4354	+	90.5929i	−1.22435	+	3.76817i
$579$	0.611502	−	2.03964i	0.0254132	−	0.0847646i
$580$	−11.4403	+	15.7463i	−0.475034	+	0.653828i
$581$	1.94015	−	0.630392i	0.0804909	−	0.0261531i
$582$	10.0226	+	13.1514i	0.415449	+	0.545141i
$583$	−1.60061	−	13.7967i	−0.0662905	−	0.571401i
$584$		−	28.9309i		−	1.19717i
$585$	−1.70623	+	0.0781249i	−0.0705440	+	0.00323007i
$586$	−15.0952	−	10.9673i	−0.623579	−	0.453056i
$587$	0.895074	+	1.23196i	0.0369437	+	0.0508486i	0.827089	−	0.562071i	$-0.189995\pi$
$587$	0.895074	+	1.23196i	0.0369437	+	0.0508486i	−0.790146	+	0.612919i	$0.789995\pi$
$588$	−45.5701	+	15.9681i	−1.87928	+	0.658513i
$589$	−38.1671	−	12.4012i	−1.57265	−	0.510984i
$590$	−1.09212	+	0.793472i	−0.0449619	+	0.0326667i
$591$	0.907854	+	39.6754i	0.0373441	+	1.63203i
$592$	−3.87323	−	11.9206i	−0.159189	−	0.489933i
$593$	36.4518			1.49690			0.748449	−	0.663193i	$-0.230799\pi$
$593$	36.4518			1.49690			0.748449	+	0.663193i	$0.230799\pi$
$594$	7.75460	+	41.6374i	0.318175	+	1.70840i
$595$	−1.33755			−0.0548341
$596$	−6.81371	−	20.9705i	−0.279101	−	0.858983i
$597$	−0.359243	−	15.6998i	−0.0147028	−	0.642550i
$598$	0.324119	−	0.235486i	0.0132542	−	0.00962976i
$599$	−20.9743	−	6.81495i	−0.856985	−	0.278451i	−0.152616	−	0.988286i	$-0.548770\pi$
$599$	−20.9743	−	6.81495i	−0.856985	−	0.278451i	−0.704369	+	0.709834i	$0.748770\pi$
$600$	38.3143	−	13.4256i	1.56417	−	0.548097i
$601$	12.4512	+	17.1376i	0.507895	+	0.699057i	0.983562	−	0.180568i	$-0.0577936\pi$
$601$	12.4512	+	17.1376i	0.507895	+	0.699057i	−0.475668	+	0.879625i	$0.657794\pi$
$602$	2.41060	+	1.75140i	0.0982486	+	0.0713818i
$603$	22.5720	−	1.03353i	0.919202	−	0.0420884i
$604$		−	42.0319i		−	1.71025i
$605$	4.74336	+	4.08930i	0.192845	+	0.166254i
$606$	−49.0627	−	64.3788i	−1.99304	−	2.61521i
$607$	29.6653	−	9.63884i	1.20408	−	0.391228i	0.362818	−	0.931860i	$-0.381815\pi$
$607$	29.6653	−	9.63884i	1.20408	−	0.391228i	0.841259	+	0.540632i	$0.181815\pi$
$608$	−1.90615	+	2.62359i	−0.0773047	+	0.106401i
$609$	1.32430	−	4.41715i	0.0536634	−	0.178992i
$610$	−3.35326	+	10.3203i	−0.135770	+	0.417856i
$611$	1.57014	−	4.83239i	0.0635210	−	0.195498i
$612$	−31.8727	−	84.6988i	−1.28838	−	3.42375i
$613$	20.7707	−	28.5884i	0.838920	−	1.15467i	−0.147277	−	0.989095i	$-0.547051\pi$
$613$	20.7707	−	28.5884i	0.838920	−	1.15467i	0.986197	−	0.165578i	$-0.0529491\pi$
$614$	68.2634	−	22.1801i	2.75489	−	0.895117i
$615$	3.09624	−	2.35963i	0.124852	−	0.0951493i
$616$	5.12785	+	1.03232i	0.206607	+	0.0415935i
$617$			16.3761i			0.659276i	0.944107	+	0.329638i	$0.106927\pi$
$617$			16.3761i			0.659276i	−0.944107	+	0.329638i	$0.893073\pi$
$618$	−8.40977	+	12.1501i	−0.338291	+	0.488751i
$619$	5.07876	+	3.68993i	0.204133	+	0.148311i	0.685155	−	0.728397i	$-0.259734\pi$
$619$	5.07876	+	3.68993i	0.204133	+	0.148311i	−0.481022	+	0.876708i	$0.659734\pi$
$620$	−6.60284	−	9.08803i	−0.265177	−	0.364984i
$621$	−0.845076	+	0.0580922i	−0.0339117	+	0.00233116i
$622$	27.1129	+	8.80953i	1.08713	+	0.353230i
$623$	−2.86977	+	2.08501i	−0.114975	+	0.0835341i
$624$	−7.34215	+	0.168003i	−0.293921	+	0.00672551i
$625$	6.25539	+	19.2521i	0.250215	+	0.770084i
$626$	21.5916			0.862974
$627$	33.9948	−	32.7463i	1.35762	−	1.30776i
$628$	−1.30654			−0.0521365
$629$	−6.82113	−	20.9933i	−0.271976	−	0.837057i
$630$	1.03179	−	0.824303i	0.0411074	−	0.0328410i
$631$	−3.95349	+	2.87238i	−0.157386	+	0.114347i	−0.663691	−	0.748007i	$-0.731011\pi$
$631$	−3.95349	+	2.87238i	−0.157386	+	0.114347i	0.506305	+	0.862354i	$0.331011\pi$
$632$	−32.0150	−	10.4023i	−1.27349	−	0.413781i
$633$	−9.62534	−	27.4690i	−0.382573	−	1.09180i
$634$	−21.4336	−	29.5008i	−0.851237	−	1.17163i
$635$	−7.65201	−	5.55951i	−0.303661	−	0.220622i
$636$	−24.0936	−	16.6765i	−0.955375	−	0.661266i
$637$			6.90102i			0.273428i
$638$	50.7589	−	46.7039i	2.00956	−	1.84902i
$639$	6.81001	+	1.87302i	0.269400	+	0.0740957i
$640$	10.4215	−	3.38614i	0.411945	−	0.133849i
$641$	−16.1543	+	22.2344i	−0.638055	+	0.878207i	−0.998510	−	0.0545692i	$-0.982621\pi$
$641$	−16.1543	+	22.2344i	−0.638055	+	0.878207i	0.360455	+	0.932777i	$0.382621\pi$
$642$	−9.47797	−	2.84158i	−0.374066	−	0.112148i
$643$	5.83505	−	17.9584i	0.230112	−	0.708211i	−0.767621	−	0.640905i	$-0.778559\pi$
$643$	5.83505	−	17.9584i	0.230112	−	0.708211i	0.997732	−	0.0673066i	$-0.0214406\pi$
$644$	−0.0640256	+	0.197051i	−0.00252296	+	0.00776488i
$645$	3.64016	+	1.09135i	0.143331	+	0.0429719i
$646$	−88.6308	+	121.990i	−3.48713	+	4.79962i
$647$	−30.4993	+	9.90983i	−1.19905	+	0.389596i	−0.839412	−	0.543495i	$-0.817101\pi$
$647$	−30.4993	+	9.90983i	−1.19905	+	0.389596i	−0.359640	+	0.933091i	$0.617101\pi$
$648$	38.7702	+	23.0720i	1.52304	+	0.906355i
$649$	2.90900	−	1.33292i	0.114188	−	0.0523217i
$650$		−	11.4913i		−	0.450727i
$651$	2.18842	+	1.51472i	0.0857708	+	0.0593666i
$652$	54.8183	+	39.8278i	2.14685	+	1.55978i
$653$	18.1022	+	24.9156i	0.708395	+	0.975022i	0.999830	+	0.0184312i	$0.00586718\pi$
$653$	18.1022	+	24.9156i	0.708395	+	0.975022i	−0.291435	+	0.956591i	$0.594133\pi$
$654$	4.78193	+	13.6468i	0.186988	+	0.533631i
$655$	4.60403	+	1.49594i	0.179894	+	0.0584512i
$656$	13.5417	−	9.83862i	0.528715	−	0.384134i
$657$	10.8069	+	13.5271i	0.421618	+	0.527744i
$658$	1.21402	+	3.73638i	0.0473275	+	0.145659i
$659$	30.3435			1.18201			0.591007	−	0.806667i	$-0.298731\pi$
$659$	30.3435			1.18201			0.591007	+	0.806667i	$0.298731\pi$
$660$	13.0862	−	1.82245i	0.509378	−	0.0709388i
$661$	10.5952			0.412107			0.206054	−	0.978541i	$-0.433938\pi$
$661$	10.5952			0.412107			0.206054	+	0.978541i	$0.433938\pi$
$662$	−3.38523	−	10.4187i	−0.131571	−	0.404933i
$663$	−12.9302	+	0.295870i	−0.502169	+	0.0114906i
$664$	26.2963	−	19.1054i	1.02049	−	0.741433i
$665$	−1.39976	−	0.454809i	−0.0542803	−	0.0176368i
$666$	18.1996	+	11.9906i	0.705219	+	0.464624i
$667$	0.810867	+	1.11606i	0.0313969	+	0.0432141i
$668$	38.7229	+	28.1338i	1.49823	+	1.08853i
$669$	−6.19280	+	8.94714i	−0.239427	+	0.345917i
$670$		−	10.5386i		−	0.407143i
$671$	12.6200	−	22.4130i	0.487191	−	0.865244i
$672$	0.171059	−	0.130363i	0.00659873	−	0.00502885i
$673$	−12.0390	+	3.91172i	−0.464071	+	0.150786i	−0.531714	−	0.846924i	$-0.678452\pi$
$673$	−12.0390	+	3.91172i	−0.464071	+	0.150786i	0.0676433	+	0.997710i	$0.478452\pi$
$674$	5.93588	−	8.17004i	0.228642	−	0.314698i
$675$	−12.8994	+	20.5894i	−0.496500	+	0.792485i
$676$	−1.24835	+	3.84203i	−0.0480136	+	0.147771i
$677$	7.17369	−	22.0784i	0.275707	−	0.848540i	−0.713324	−	0.700834i	$-0.752811\pi$
$677$	7.17369	−	22.0784i	0.275707	−	0.848540i	0.989031	−	0.147706i	$-0.0471889\pi$
$678$	18.3321	−	61.1458i	0.704038	−	2.34829i
$679$	−0.718348	+	0.988721i	−0.0275677	+	0.0379436i
$680$	−20.2686	+	6.58568i	−0.777267	+	0.252549i
$681$	12.5358	+	16.4491i	0.480371	+	0.630331i
$682$	16.5832	+	36.1916i	0.635003	+	1.38585i
$683$			19.9298i			0.762593i	0.924453	+	0.381296i	$0.124522\pi$
$683$			19.9298i			0.762593i	−0.924453	+	0.381296i	$0.875478\pi$
$684$	−4.55481	−	99.4760i	−0.174157	−	3.80356i
$685$	−8.40133	−	6.10392i	−0.320998	−	0.233219i
$686$	−6.31762	−	8.69546i	−0.241208	−	0.331994i
$687$	−8.64120	+	3.02794i	−0.329683	+	0.115523i
$688$	15.5404	+	5.04937i	0.592471	+	0.192505i
$689$	−3.38797	+	2.46151i	−0.129072	+	0.0937759i
$690$	0.00903774	+	0.394971i	0.000344061	+	0.0150363i
$691$	0.823665	+	2.53498i	0.0313337	+	0.0964352i	0.965500	−	0.260402i	$-0.0838551\pi$
$691$	0.823665	+	2.53498i	0.0313337	+	0.0964352i	−0.934167	+	0.356837i	$0.883855\pi$
$692$	−72.1435			−2.74248
$693$	−2.78323	+	1.43279i	−0.105726	+	0.0544272i
$694$	−30.4201			−1.15473
$695$	−1.54780	−	4.76363i	−0.0587113	−	0.180695i
$696$	−1.68082	−	73.4561i	−0.0637114	−	2.78435i
$697$	23.8482	−	17.3268i	0.903316	−	0.656298i
$698$	−84.8961	−	27.5844i	−3.21337	−	1.04409i
$699$	−33.7653	+	11.8316i	−1.27712	+	0.447512i
$700$	3.49312	+	4.80786i	0.132027	+	0.181720i
$701$	11.1837	+	8.12545i	0.422403	+	0.306894i	0.778604	−	0.627516i	$-0.215928\pi$
$701$	11.1837	+	8.12545i	0.422403	+	0.306894i	−0.356201	+	0.934409i	$0.615928\pi$
$702$	9.79207	−	8.19687i	0.369578	−	0.309371i
$703$		−	24.2891i		−	0.916081i
$704$	−24.7427	+	2.87050i	−0.932527	+	0.108186i
$705$	3.03710	+	3.98521i	0.114384	+	0.150092i
$706$	−33.2085	+	10.7901i	−1.24982	+	0.406091i
$707$	3.51647	−	4.84001i	0.132250	−	0.182027i
$708$	1.93866	−	6.46632i	0.0728592	−	0.243019i
$709$	−7.14500	+	21.9900i	−0.268336	+	0.825853i	0.722570	+	0.691298i	$0.242961\pi$
$709$	−7.14500	+	21.9900i	−0.268336	+	0.825853i	−0.990906	+	0.134556i	$0.957039\pi$
$710$	1.01795	−	3.13292i	0.0382029	−	0.117576i
$711$	18.8548	−	7.09519i	0.707112	−	0.266090i
$712$	−33.2213	+	45.7252i	−1.24502	+	1.71362i
$713$	−0.757234	+	0.246040i	−0.0283586	+	0.00921427i
$714$	7.95375	−	6.06150i	0.297661	−	0.226846i
$715$	0.372668	−	1.85115i	0.0139370	−	0.0692289i
$716$		−	57.6045i		−	2.15278i
$717$	−6.62849	+	9.57662i	−0.247545	+	0.357645i
$718$	−44.4803	−	32.3168i	−1.65999	−	1.20605i
$719$	−11.1173	−	15.3017i	−0.414607	−	0.570657i	0.549728	−	0.835344i	$-0.314731\pi$
$719$	−11.1173	−	15.3017i	−0.414607	−	0.570657i	−0.964334	+	0.264687i	$0.914731\pi$
$720$	3.98440	−	6.04762i	0.148490	−	0.225381i
$721$	−1.03870	−	0.337495i	−0.0386834	−	0.0125690i
$722$	−96.4571	+	70.0802i	−3.58976	+	2.60811i
$723$	28.6668	−	0.655954i	1.06613	−	0.0243952i
$724$	−19.3433	−	59.5325i	−0.718887	−	2.21251i
$725$	39.5689			1.46955
$726$	−46.7383	−	2.82110i	−1.73462	−	0.104701i
$727$	−47.0734			−1.74586			−0.872929	−	0.487848i	$-0.837782\pi$
$727$	−47.0734			−1.74586			−0.872929	+	0.487848i	$0.837782\pi$
$728$	−0.487358	−	1.49994i	−0.0180627	−	0.0555913i
$729$	−26.7460	+	3.69461i	−0.990594	+	0.136837i
$730$	6.53301	−	4.74651i	0.241798	−	0.175676i
$731$	27.3681	+	8.89242i	1.01224	+	0.328898i
$732$	−17.9450	−	51.2119i	−0.663267	−	1.89285i
$733$	11.1079	+	15.2888i	0.410281	+	0.564703i	0.963287	−	0.268474i	$-0.0865194\pi$
$733$	11.1079	+	15.2888i	0.410281	+	0.564703i	−0.553006	+	0.833177i	$0.686519\pi$
$734$	51.8273	+	37.6547i	1.91298	+	1.38986i
$735$	−5.59564	−	3.87304i	−0.206398	−	0.142859i
$736$			0.0643398i			0.00237160i
$737$	−4.93008	+	24.4891i	−0.181602	+	0.902067i
$738$	−7.71846	+	28.0631i	−0.284121	+	1.03302i
$739$	22.2364	−	7.22506i	0.817981	−	0.265778i	0.130007	−	0.991513i	$-0.458500\pi$
$739$	22.2364	−	7.22506i	0.817981	−	0.265778i	0.687974	+	0.725735i	$0.258500\pi$
$740$	3.99632	−	5.50046i	0.146907	−	0.202201i
$741$	−13.6322	−	4.08706i	−0.500793	−	0.150142i
$742$	1.00058	−	3.07948i	0.0367326	−	0.113051i
$743$	−2.66419	+	8.19954i	−0.0977397	+	0.300812i	−0.987958	−	0.154722i	$-0.950552\pi$
$743$	−2.66419	+	8.19954i	−0.0977397	+	0.300812i	0.890218	+	0.455534i	$0.150552\pi$
$744$	40.6203	+	12.1783i	1.48921	+	0.446479i
$745$	1.82657	−	2.51406i	0.0669204	−	0.0921080i
$746$	−81.9343	+	26.6221i	−2.99983	+	0.974703i
$747$	−5.15860	+	18.7558i	−0.188743	+	0.686240i
$748$	99.3819	−	11.5297i	3.63376	−	0.421567i
$749$		−	0.731332i		−	0.0267223i
$750$	19.2813	+	13.3456i	0.704052	+	0.487312i
$751$	−9.89731	−	7.19082i	−0.361158	−	0.262397i	0.392377	−	0.919805i	$-0.371653\pi$
$751$	−9.89731	−	7.19082i	−0.361158	−	0.262397i	−0.753535	+	0.657408i	$0.771653\pi$
$752$	12.6634	+	17.4297i	0.461787	+	0.635596i
$753$	3.28016	+	9.36101i	0.119536	+	0.341134i
$754$	−19.7792	−	6.42666i	−0.720317	−	0.234045i
$755$	4.79240	−	3.48188i	0.174413	−	0.126719i
$756$	−1.60524	+	6.40607i	−0.0583819	+	0.232987i
$757$	6.34006	+	19.5127i	0.230433	+	0.709201i	0.997694	+	0.0678659i	$0.0216190\pi$
$757$	6.34006	+	19.5127i	0.230433	+	0.709201i	−0.767261	+	0.641335i	$0.778381\pi$
$758$	−61.2865			−2.22602
$759$	0.163770	−	0.922040i	0.00594447	−	0.0334679i
$760$	−23.4507			−0.850646
$761$	5.72051	+	17.6059i	0.207368	+	0.638214i	0.999608	+	0.0280035i	$0.00891496\pi$
$761$	5.72051	+	17.6059i	0.207368	+	0.638214i	−0.792240	+	0.610210i	$0.791085\pi$
$762$	70.6973	−	1.61770i	2.56109	−	0.0586030i
$763$	−0.864659	+	0.628211i	−0.0313027	+	0.0227428i
$764$	69.2530	+	22.5017i	2.50549	+	0.814082i
$765$	7.01690	−	10.6504i	0.253697	−	0.385067i
$766$	10.2503	+	14.1083i	0.370358	+	0.509754i
$767$	−0.780530	−	0.567088i	−0.0281833	−	0.0204764i
$768$	−31.8196	+	45.9718i	−1.14819	+	1.65887i
$769$			7.72003i			0.278391i	0.990265	+	0.139196i	$0.0444517\pi$
$769$			7.72003i			0.278391i	−0.990265	+	0.139196i	$0.955548\pi$
$770$	0.608180	+	1.32731i	0.0219173	+	0.0478329i
$771$	3.71145	−	2.82848i	0.133665	−	0.101865i
$772$	4.72329	−	1.53469i	0.169995	−	0.0552347i
$773$	−24.0521	+	33.1049i	−0.865095	+	1.19070i	0.115235	+	0.993338i	$0.463238\pi$
$773$	−24.0521	+	33.1049i	−0.865095	+	1.19070i	−0.980330	+	0.197363i	$0.936762\pi$
$774$	−26.5920	+	10.0067i	−0.955830	+	0.359685i
$775$	−7.05715	+	21.7197i	−0.253500	+	0.780193i
$776$	−6.01737	+	18.5196i	−0.216011	+	0.664814i
$777$	−0.462603	+	1.54299i	−0.0165958	+	0.0553546i
$778$	−32.4042	+	44.6005i	−1.16175	+	1.59901i
$779$	30.8491	−	10.0235i	1.10528	−	0.359128i
$780$	−2.41468	−	3.16847i	−0.0864593	−	0.113450i
$781$	−3.83106	+	6.80389i	−0.137086	+	0.243462i
$782$			2.99162i			0.106980i
$783$	28.2249	+	33.7177i	1.00867	+	1.20497i
$784$	−23.6727	−	17.1992i	−0.845452	−	0.614257i
$785$	−0.108232	−	0.148969i	−0.00386298	−	0.00531693i
$786$	−34.1572	+	11.9689i	−1.21835	+	0.426917i
$787$	−28.4408	−	9.24096i	−1.01380	−	0.329405i	−0.245436	−	0.969413i	$-0.578931\pi$
$787$	−28.4408	−	9.24096i	−1.01380	−	0.329405i	−0.768368	+	0.640008i	$0.778931\pi$
$788$	−74.8837	+	54.4062i	−2.66762	+	1.93814i
$789$	−0.509323	−	22.2587i	−0.0181324	−	0.792430i
$790$	−2.90351	−	8.93608i	−0.103302	−	0.317931i
$791$	4.71809			0.167756
$792$	−35.1212	+	35.4156i	−1.24798	+	1.25844i
$793$	−7.75539			−0.275402
$794$	−12.0033	−	36.9422i	−0.425980	−	1.31103i
$795$	−0.0944702	−	4.12858i	−0.00335051	−	0.146426i
$796$	29.6319	−	21.5288i	1.05027	−	0.763069i
$797$	−7.51411	−	2.44148i	−0.266163	−	0.0864817i	0.172895	−	0.984940i	$-0.444688\pi$
$797$	−7.51411	−	2.44148i	−0.266163	−	0.0864817i	−0.439058	+	0.898459i	$0.644688\pi$
$798$	10.3848	−	3.63890i	0.367617	−	0.128816i
$799$	22.3015	+	30.6954i	0.788970	+	1.08592i
$800$	1.49300	+	1.08473i	0.0527856	+	0.0383510i
$801$	−1.54714	−	33.7891i	−0.0546653	−	1.19388i
$802$			50.4163i			1.78026i
$803$	−17.4015	+	7.97347i	−0.614086	+	0.281378i
$804$	31.9441	+	41.9162i	1.12658	+	1.47827i
$805$	−0.0277712	+	0.00902340i	−0.000978805	+	0.000318033i
$806$	7.05528	−	9.71076i	0.248512	−	0.342047i
$807$	−2.36718	+	7.89565i	−0.0833288	+	0.277940i
$808$	29.4564	−	90.6574i	1.03627	−	3.18932i
$809$	7.40434	−	22.7882i	0.260323	−	0.801191i	−0.732411	−	0.680862i	$-0.761605\pi$
$809$	7.40434	−	22.7882i	0.260323	−	0.801191i	0.992734	−	0.120328i	$-0.0383948\pi$
$810$	1.15079	+	12.5401i	0.0404346	+	0.440616i
$811$	18.5815	−	25.5752i	0.652483	−	0.898066i	−0.346721	−	0.937968i	$-0.612705\pi$
$811$	18.5815	−	25.5752i	0.652483	−	0.898066i	0.999204	+	0.0399026i	$0.0127048\pi$
$812$	10.2290	−	3.32361i	0.358968	−	0.116636i
$813$	−24.6590	+	18.7924i	−0.864827	+	0.659080i
$814$	−17.7310	+	16.3145i	−0.621472	+	0.571824i
$815$			9.54958i			0.334507i
$816$	31.2107	−	45.0922i	1.09259	−	1.57854i
$817$	25.6173	+	18.6120i	0.896235	+	0.651153i
$818$	33.9465	+	46.7234i	1.18691	+	1.63365i
$819$	0.788162	+	0.519270i	0.0275406	+	0.0181448i
$820$	8.63519	+	2.80574i	0.301554	+	0.0979808i
$821$	−16.2573	+	11.8116i	−0.567383	+	0.412228i	−0.834154	−	0.551532i	$-0.814043\pi$
$821$	−16.2573	+	11.8116i	−0.567383	+	0.412228i	0.266771	+	0.963760i	$0.414043\pi$
$822$	77.6204	−	1.77611i	2.70732	−	0.0619489i
$823$	10.0755	+	31.0093i	0.351210	+	1.08091i	0.958174	+	0.286185i	$0.0923873\pi$
$823$	10.0755	+	31.0093i	0.351210	+	1.08091i	−0.606964	+	0.794729i	$0.707613\pi$
$824$	−17.4018			−0.606220
$825$	−18.6348	−	19.3453i	−0.648782	−	0.673517i
$826$	0.745968			0.0259555
$827$	4.33766	+	13.3500i	0.150835	+	0.464223i	0.997715	−	0.0675610i	$-0.0215217\pi$
$827$	4.33766	+	13.3500i	0.150835	+	0.464223i	−0.846880	+	0.531784i	$0.821522\pi$
$828$	−1.23316	−	1.54356i	−0.0428553	−	0.0536424i
$829$	37.4595	−	27.2159i	1.30102	−	0.945247i	0.301055	−	0.953607i	$-0.402661\pi$
$829$	37.4595	−	27.2159i	1.30102	−	0.945247i	0.999965	+	0.00835991i	$0.00266107\pi$
$830$	8.62853	+	2.80358i	0.299501	+	0.0973137i
$831$	11.5799	+	33.0471i	0.401703	+	1.14639i
$832$	4.41441	+	6.07592i	0.153042	+	0.210645i
$833$	−41.6898	−	30.2894i	−1.44447	−	1.04947i
$834$	30.7918	+	21.3127i	1.06623	+	0.737998i
$835$			6.74569i			0.233444i
$836$	107.925	+	21.7271i	3.73266	+	0.751448i
$837$	−23.5418	+	9.47924i	−0.813725	+	0.327651i
$838$	−52.1646	+	16.9493i	−1.80200	+	0.585505i
$839$	2.42018	−	3.33109i	0.0835539	−	0.115002i	−0.765194	−	0.643800i	$-0.777357\pi$
$839$	2.42018	−	3.33109i	0.0835539	−	0.115002i	0.848748	+	0.528798i	$0.177357\pi$
$840$	1.48973	+	0.446634i	0.0514006	+	0.0154103i
$841$	13.1679	−	40.5266i	0.454065	−	1.39747i
$842$	2.69680	−	8.29990i	0.0929379	−	0.286033i
$843$	−30.3328	−	9.09403i	−1.04472	−	0.313215i
$844$	39.9029	−	54.9217i	1.37352	−	1.89048i
$845$	−0.541474	+	0.175936i	−0.0186273	+	0.00605237i
$846$	−36.1203	−	9.93453i	−1.24184	−	0.341556i
$847$	−0.792328	−	3.36884i	−0.0272247	−	0.115755i
$848$		−	17.7566i		−	0.609763i
$849$	5.32665	+	3.68686i	0.182810	+	0.126533i
$850$	69.4205	+	50.4369i	2.38110	+	1.72997i
$851$	−0.283251	−	0.389861i	−0.00970971	−	0.0133643i
$852$	5.44755	+	15.5464i	0.186630	+	0.532610i
$853$	−12.7535	−	4.14388i	−0.436673	−	0.141884i	0.0824271	−	0.996597i	$-0.473733\pi$
$853$	−12.7535	−	4.14388i	−0.436673	−	0.141884i	−0.519100	+	0.854713i	$0.673733\pi$
$854$	4.85121	−	3.52461i	0.166005	−	0.120610i
$855$	10.9648	−	8.75983i	0.374987	−	0.299580i
$856$	−3.60085	−	11.0823i	−0.123075	−	0.378785i
$857$	39.9562			1.36488			0.682439	−	0.730943i	$-0.260919\pi$
$857$	39.9562			1.36488			0.682439	+	0.730943i	$0.260919\pi$
$858$	6.17295	+	12.6967i	0.210741	+	0.433459i
$859$	−38.7627			−1.32257			−0.661283	−	0.750137i	$-0.729988\pi$
$859$	−38.7627			−1.32257			−0.661283	+	0.750137i	$0.729988\pi$
$860$	2.73897	+	8.42968i	0.0933981	+	0.287450i
$861$	−2.15063	+	0.0492107i	−0.0732932	+	0.00167709i
$862$	−62.0234	+	45.0626i	−2.11253	+	1.53484i
$863$	4.00029	+	1.29977i	0.136171	+	0.0442448i	0.376310	−	0.926494i	$-0.377193\pi$
$863$	4.00029	+	1.29977i	0.136171	+	0.0442448i	−0.240138	+	0.970739i	$0.577193\pi$
$864$	0.140644	+	2.04598i	0.00478482	+	0.0696055i
$865$	−5.97630	−	8.22567i	−0.203200	−	0.279681i
$866$	44.0236	+	31.9850i	1.49598	+	1.08690i
$867$	38.2073	−	55.2005i	1.29759	−	1.87471i
$868$			6.20754i			0.210698i
$869$	2.56663	+	22.1234i	0.0870668	+	0.750487i
$870$	16.3117	−	12.4310i	0.553017	−	0.421451i
$871$	7.16324	−	2.32748i	0.242717	−	0.0788636i
$872$	−10.0095	+	13.7770i	−0.338966	+	0.466547i
$873$	−4.10432	−	10.9069i	−0.138910	−	0.369142i
$874$	−1.01725	+	3.13076i	−0.0344089	+	0.105900i
$875$	−0.535577	+	1.64834i	−0.0181058	+	0.0557239i
$876$	−11.5970	+	38.6812i	−0.391825	+	1.30692i
$877$	15.9220	−	21.9148i	0.537648	−	0.740009i	−0.450624	−	0.892714i	$-0.648798\pi$
$877$	15.9220	−	21.9148i	0.537648	−	0.740009i	0.988272	+	0.152705i	$0.0487984\pi$
$878$	95.7761	−	31.1196i	3.23229	−	1.05023i
$879$	7.97086	+	10.4592i	0.268851	+	0.352779i
$880$	5.42123	+	5.89192i	0.182750	+	0.198617i
$881$			27.2472i			0.917981i	0.888441	+	0.458990i	$0.151789\pi$
$881$			27.2472i			0.917981i	−0.888441	+	0.458990i	$0.848211\pi$
$882$	50.8264	−	2.32724i	1.71141	−	0.0783622i
$883$	−39.0337	−	28.3596i	−1.31359	−	0.954377i	−0.999988	−	0.00482141i	$-0.998465\pi$
$883$	−39.0337	−	28.3596i	−1.31359	−	0.954377i	−0.313599	−	0.949556i	$-0.601535\pi$
$884$	−17.7310	−	24.4046i	−0.596358	−	0.820816i
$885$	0.897874	−	0.314621i	0.0301817	−	0.0105759i
$886$	−46.3745	−	15.0680i	−1.55798	−	0.506219i
$887$	−14.4031	+	10.4645i	−0.483608	+	0.351362i	−0.802721	−	0.596355i	$-0.796615\pi$
$887$	−14.4031	+	10.4645i	−0.483608	+	0.351362i	0.319113	+	0.947717i	$0.396615\pi$
$888$	0.587142	+	25.6596i	0.0197032	+	0.861078i
$889$	1.61513	+	4.97086i	0.0541697	+	0.166717i
$890$	−15.7758			−0.528806
$891$	3.19226	−	29.6784i	0.106945	−	0.994265i
$892$	−25.3790			−0.849751
$893$	12.9013	+	39.7063i	0.431727	+	1.32872i
$894$	0.531493	+	23.2275i	0.0177758	+	0.776845i
$895$	6.56796	−	4.77190i	0.219543	−	0.159507i
$896$	−5.75886	−	1.87117i	−0.192390	−	0.0625113i
$897$	−0.266471	+	0.0933733i	−0.00889721	+	0.00311764i
$898$	−8.90637	−	12.2586i	−0.297209	−	0.409074i
$899$	33.4378	+	24.2939i	1.11521	+	0.810249i
$900$	−56.6086	+	2.59199i	−1.88695	+	0.0863997i
$901$		−	31.2710i		−	1.04179i
$902$	−28.0379	−	15.7872i	−0.933558	−	0.525657i
$903$	−1.27289	−	1.67025i	−0.0423590	−	0.0555824i
$904$	71.4958	−	23.2304i	2.37792	−	0.772632i
$905$	5.18540	−	7.13710i	0.172369	−	0.237245i
$906$	−12.7189	+	42.4232i	−0.422556	+	1.40942i
$907$	−8.87674	+	27.3198i	−0.294747	+	0.907139i	0.688559	+	0.725180i	$0.258244\pi$
$907$	−8.87674	+	27.3198i	−0.294747	+	0.907139i	−0.983306	+	0.181958i	$0.941756\pi$
$908$	−14.9058	+	45.8754i	−0.494667	+	1.52243i
$909$	20.0916	+	53.3916i	0.666395	+	1.77089i
$910$	0.258749	−	0.356137i	0.00857744	−	0.0118058i
$911$	−34.6369	+	11.2542i	−1.14757	+	0.372869i	−0.820228	−	0.572037i	$-0.806154\pi$
$911$	−34.6369	+	11.2542i	−1.14757	+	0.372869i	−0.327344	+	0.944905i	$0.606154\pi$
$912$	47.9951	−	36.5768i	1.58928	−	1.21118i
$913$	−18.7390	−	10.5513i	−0.620169	−	0.349198i
$914$		−	41.8772i		−	1.38518i
$915$	4.35254	−	6.28841i	0.143891	−	0.207888i
$916$	−17.2772	−	12.5527i	−0.570856	−	0.414751i
$917$	−1.57238	−	2.16420i	−0.0519246	−	0.0714680i
$918$	6.53957	+	95.1321i	0.215838	+	3.13983i
$919$	6.62453	+	2.15244i	0.218523	+	0.0710025i	0.416233	−	0.909258i	$-0.363350\pi$
$919$	6.62453	+	2.15244i	0.218523	+	0.0710025i	−0.197709	+	0.980261i	$0.563350\pi$
$920$	−0.376404	+	0.273473i	−0.0124097	+	0.00901615i
$921$	−50.5730	+	1.15721i	−1.66644	+	0.0381314i
$922$	−30.5090	−	93.8971i	−1.00476	−	3.09234i
$923$	2.35430			0.0774927
$924$	−6.44223	−	3.43574i	−0.211934	−	0.113027i
$925$	−13.8222			−0.454470
$926$	−27.4607	−	84.5153i	−0.902414	−	2.77735i
$927$	8.13650	−	6.50031i	0.267238	−	0.213498i
$928$	2.70205	−	1.96315i	0.0886991	−	0.0644437i
$929$	33.7818	+	10.9764i	1.10834	+	0.360123i	0.805308	−	0.592856i	$-0.202000\pi$
$929$	33.7818	+	10.9764i	1.10834	+	0.360123i	0.303036	+	0.952979i	$0.402000\pi$
$930$	3.91428	+	11.1707i	0.128354	+	0.366301i
$931$	−33.3295	−	45.8741i	−1.09233	−	1.50346i
$932$	−67.5105	−	49.0492i	−2.21138	−	1.60666i
$933$	−16.5206	−	11.4348i	−0.540861	−	0.374359i
$934$			7.28978i			0.238529i
$935$	9.54730	+	10.3762i	0.312230	+	0.339339i
$936$	14.5002	+	3.98813i	0.473954	+	0.130356i
$937$	−30.8518	+	10.0244i	−1.00789	+	0.327482i	−0.766012	−	0.642826i	$-0.777762\pi$
$937$	−30.8518	+	10.0244i	−1.00789	+	0.327482i	−0.241873	+	0.970308i	$0.577762\pi$
$938$	−3.42303	+	4.71139i	−0.111766	+	0.153832i
$939$	−14.5762	−	4.37008i	−0.475678	−	0.142612i
$940$	−3.61131	+	11.1145i	−0.117788	+	0.362514i
$941$	−17.4466	+	53.6951i	−0.568743	+	1.75041i	0.0878172	+	0.996137i	$0.472011\pi$
$941$	−17.4466	+	53.6951i	−0.568743	+	1.75041i	−0.656560	+	0.754274i	$0.727989\pi$
$942$	1.31870	+	0.395359i	0.0429657	+	0.0128815i
$943$	0.378264	−	0.520636i	0.0123180	−	0.0169542i
$944$	3.89058	−	1.26413i	0.126628	−	0.0411438i
$945$	−0.863385	+	0.347647i	−0.0280859	+	0.0113089i
$946$	−3.61985	−	31.2019i	−0.117692	−	1.01446i
$947$		−	23.2144i		−	0.754365i	−0.926139	−	0.377183i	$-0.876893\pi$
$947$		−	23.2144i		−	0.754365i	0.926139	−	0.377183i	$-0.123107\pi$
$948$	38.6349	+	26.7413i	1.25480	+	0.868517i
$949$	4.66909	+	3.39229i	0.151565	+	0.110119i
$950$	55.4991	+	76.3880i	1.80063	+	2.47835i
$951$	8.49869	+	24.2538i	0.275589	+	0.786482i
$952$	11.2004	+	3.63922i	0.363006	+	0.117948i
$953$	6.34414	−	4.60929i	0.205507	−	0.149310i	−0.480272	−	0.877120i	$-0.659462\pi$
$953$	6.34414	−	4.60929i	0.205507	−	0.149310i	0.685778	+	0.727810i	$0.259462\pi$
$954$	19.2717	+	24.1225i	0.623943	+	0.780995i
$955$	3.17126	+	9.76012i	0.102619	+	0.315830i
$956$	−27.1645			−0.878563
$957$	−43.7195	+	21.2558i	−1.41325	+	0.687101i
$958$	53.5583			1.73039
$959$	1.77329	+	5.45763i	0.0572626	+	0.176236i
$960$	−7.40411	+	0.169421i	−0.238967	+	0.00546803i
$961$	5.78076	−	4.19997i	0.186476	−	0.135483i
$962$	6.90925	+	2.24495i	0.222763	+	0.0723801i
$963$	5.82334	+	3.83663i	0.187655	+	0.123634i
$964$	39.3103	+	54.1059i	1.26610	+	1.74263i
$965$	0.566256	+	0.411409i	0.0182284	+	0.0132437i
$966$	0.124249	−	0.179511i	0.00399765	−	0.00577567i
$967$		−	29.9298i		−	0.962477i	−0.876590	−	0.481238i	$-0.840187\pi$
$967$		−	29.9298i		−	0.962477i	0.876590	−	0.481238i	$-0.159813\pi$
$968$	−28.5937	−	47.1487i	−0.919037	−	1.51542i
$969$	84.5240	−	64.4153i	2.71530	−	2.06932i
$970$	−5.16921	+	1.67958i	−0.165973	+	0.0539281i
$971$	−9.73461	+	13.3985i	−0.312398	+	0.429980i	−0.936127	−	0.351661i	$-0.885617\pi$
$971$	−9.73461	+	13.3985i	−0.312398	+	0.429980i	0.623729	+	0.781641i	$0.285617\pi$
$972$	−42.5881	−	46.3888i	−1.36601	−	1.48792i
$973$	−0.855307	+	2.63236i	−0.0274199	+	0.0843897i
$974$	9.48937	−	29.2053i	0.304059	−	0.935797i
$975$	−2.32582	+	7.75767i	−0.0744857	+	0.248444i
$976$	19.3285	−	26.6034i	0.618691	−	0.851556i
$977$	−40.2488	+	13.0776i	−1.28767	+	0.418391i	−0.871277	−	0.490792i	$-0.836708\pi$
$977$	−40.2488	+	13.0776i	−1.28767	+	0.418391i	−0.416398	+	0.909183i	$0.636708\pi$
$978$	−43.2768	−	56.7867i	−1.38384	−	1.81584i
$979$	36.6589	+	7.38007i	1.17162	+	0.235868i
$980$		−	15.8723i		−	0.507022i
$981$	−0.466151	−	10.1806i	−0.0148830	−	0.325043i
$982$	9.35002	+	6.79319i	0.298371	+	0.216779i
$983$	−21.3241	−	29.3500i	−0.680132	−	0.936121i	0.319804	−	0.947484i	$-0.396383\pi$
$983$	−21.3241	−	29.3500i	−0.680132	−	0.936121i	−0.999935	+	0.0113628i	$0.996383\pi$
$984$	−32.3474	+	11.3347i	−1.03120	+	0.361338i
$985$	−12.4066	−	4.03115i	−0.395307	−	0.128443i
$986$	125.638	−	91.2812i	4.00112	−	2.90698i
$987$	−0.0633397	−	2.76810i	−0.00201612	−	0.0881096i
$988$	−10.2573	−	31.5688i	−0.326329	−	1.00434i
$989$	0.628226			0.0199764
$990$	−13.7595	−	2.12045i	−0.437305	−	0.0673924i
$991$	−20.4585			−0.649886			−0.324943	−	0.945734i	$-0.605345\pi$
$991$	−20.4585			−0.649886			−0.324943	+	0.945734i	$0.605345\pi$
$992$	0.595677	+	1.83330i	0.0189128	+	0.0582075i
$993$	0.176619	+	7.71868i	0.00560483	+	0.244945i
$994$	−1.47268	+	1.06996i	−0.0467105	+	0.0339372i
$995$	4.90936	+	1.59515i	0.155637	+	0.0505696i
$996$	−42.8171	+	15.0034i	−1.35671	+	0.475401i
$997$	−8.56964	−	11.7951i	−0.271403	−	0.373555i	0.651460	−	0.758683i	$-0.274157\pi$
$997$	−8.56964	−	11.7951i	−0.271403	−	0.373555i	−0.922863	+	0.385129i	$0.874157\pi$
$998$	−19.9672	−	14.5070i	−0.632050	−	0.459211i
$999$	−9.85946	−	11.7782i	−0.311940	−	0.372647i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.x.a.248.4	✓	192
3.2	odd	2	inner	429.2.x.a.248.45	yes	192
11.2	odd	10	inner	429.2.x.a.365.45	yes	192
33.2	even	10	inner	429.2.x.a.365.4	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.x.a.248.4	✓	192	1.1	even	1	trivial
429.2.x.a.248.45	yes	192	3.2	odd	2	inner
429.2.x.a.365.4	yes	192	33.2	even	10	inner
429.2.x.a.365.45	yes	192	11.2	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.x (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.759437 - 2.33731i) q^{2} +(0.0396224 + 1.73160i) q^{3} +(-3.26823 + 2.37451i) q^{4} +(-0.541474 - 0.175936i) q^{5} +(4.01719 - 1.40765i) q^{6} +(0.184926 + 0.254529i) q^{7} +(4.05551 + 2.94650i) q^{8} +(-2.99686 + 0.137220i) q^{9} +O(q^{10})\)	\(q+(-0.759437 - 2.33731i) q^{2} +(0.0396224 + 1.73160i) q^{3} +(-3.26823 + 2.37451i) q^{4} +(-0.541474 - 0.175936i) q^{5} +(4.01719 - 1.40765i) q^{6} +(0.184926 + 0.254529i) q^{7} +(4.05551 + 2.94650i) q^{8} +(-2.99686 + 0.137220i) q^{9} +1.39920i q^{10} +(0.654561 - 3.25139i) q^{11} +(-4.24119 - 5.56517i) q^{12} +(-0.951057 + 0.309017i) q^{13} +(0.454472 - 0.625527i) q^{14} +(0.283195 - 0.944586i) q^{15} +(1.31026 - 4.03258i) q^{16} +(2.30750 - 7.10176i) q^{17} +(2.59665 + 6.90037i) q^{18} +(4.82965 - 6.64744i) q^{19} +(2.18742 - 0.710737i) q^{20} +(-0.433414 + 0.330302i) q^{21} +(-8.09660 + 0.939318i) q^{22} -0.163019i q^{23} +(-4.94146 + 7.13925i) q^{24} +(-3.78284 - 2.74840i) q^{25} +(1.44454 + 1.98823i) q^{26} +(-0.356353 - 5.18392i) q^{27} +(-1.20876 - 0.392750i) q^{28} +(-6.84622 + 4.97407i) q^{29} +(-2.42286 + 0.0554399i) q^{30} +(-1.50927 - 4.64507i) q^{31} -0.394677 q^{32} +(5.65604 + 1.00461i) q^{33} -18.3514 q^{34} +(-0.0553519 - 0.170356i) q^{35} +(9.46860 - 7.56453i) q^{36} +(2.39151 - 1.73753i) q^{37} +(-19.2049 - 6.24006i) q^{38} +(-0.572776 - 1.63460i) q^{39} +(-1.67756 - 2.30896i) q^{40} +(3.19372 + 2.32037i) q^{41} +(1.10117 + 0.762178i) q^{42} +3.85370i q^{43} +(5.58120 + 12.1806i) q^{44} +(1.64686 + 0.452953i) q^{45} +(-0.381025 + 0.123803i) q^{46} +(-2.98658 + 4.11068i) q^{47} +(7.03472 + 2.10907i) q^{48} +(2.13253 - 6.56326i) q^{49} +(-3.55102 + 10.9289i) q^{50} +(12.3888 + 3.71427i) q^{51} +(2.37451 - 3.26823i) q^{52} +(3.98280 - 1.29409i) q^{53} +(-11.8458 + 4.76977i) q^{54} +(-0.926464 + 1.64538i) q^{55} +1.57713i q^{56} +(11.7021 + 8.09962i) q^{57} +(16.8252 + 12.2242i) q^{58} +(0.567088 + 0.780530i) q^{59} +(1.31738 + 3.75957i) q^{60} +(7.37582 + 2.39655i) q^{61} +(-9.71076 + 7.05528i) q^{62} +(-0.589123 - 0.737411i) q^{63} +(-2.32079 - 7.14267i) q^{64} +0.569340 q^{65} +(-1.94733 - 13.9828i) q^{66} -7.53188 q^{67} +(9.32173 + 28.6893i) q^{68} +(0.282283 - 0.00645920i) q^{69} +(-0.356137 + 0.258749i) q^{70} +(-2.23907 - 0.727518i) q^{71} +(-12.5581 - 8.27374i) q^{72} +(-3.39229 - 4.66909i) q^{73} +(-5.87736 - 4.27015i) q^{74} +(4.60923 - 6.65926i) q^{75} +33.1934i q^{76} +(0.948617 - 0.434662i) q^{77} +(-3.38558 + 2.58013i) q^{78} +(-6.38654 + 2.07511i) q^{79} +(-1.41895 + 1.95301i) q^{80} +(8.96234 - 0.822459i) q^{81} +(2.99800 - 9.22689i) q^{82} +(2.00370 - 6.16674i) q^{83} +(0.632191 - 2.10865i) q^{84} +(-2.49890 + 3.43945i) q^{85} +(9.00729 - 2.92665i) q^{86} +(-8.88436 - 11.6578i) q^{87} +(12.2348 - 11.2574i) q^{88} +11.2748i q^{89} +(-0.191999 - 4.19322i) q^{90} +(-0.254529 - 0.184926i) q^{91} +(0.387089 + 0.532783i) q^{92} +(7.98359 - 2.79751i) q^{93} +(11.8760 + 3.85876i) q^{94} +(-3.78465 + 2.74971i) q^{95} +(-0.0156381 - 0.683422i) q^{96} +(1.20038 + 3.69440i) q^{97} -16.9599 q^{98} +(-1.51547 + 9.83379i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 6 q^{3} - 48 q^{4} - 10 q^{6} - 14 q^{9}+O(q^{10}) \) 192 * q + 6 * q^3 - 48 * q^4 - 10 * q^6 - 14 * q^9	\( 192 q + 6 q^{3} - 48 q^{4} - 10 q^{6} - 14 q^{9} - 20 q^{12} + 6 q^{15} - 28 q^{16} - 10 q^{18} - 60 q^{19} + 4 q^{22} + 30 q^{24} - 12 q^{25} + 30 q^{27} - 20 q^{28} + 12 q^{31} - 32 q^{33} + 56 q^{34} + 44 q^{36} + 60 q^{40} - 108 q^{42} - 40 q^{45} - 28 q^{48} - 24 q^{49} + 10 q^{51} + 20 q^{52} - 20 q^{55} + 50 q^{57} - 60 q^{58} + 36 q^{60} + 20 q^{61} - 30 q^{63} + 64 q^{64} - 30 q^{66} - 120 q^{67} - 16 q^{69} + 20 q^{70} + 150 q^{72} - 20 q^{73} + 18 q^{75} + 40 q^{78} - 160 q^{79} - 46 q^{81} + 88 q^{82} - 40 q^{85} + 72 q^{88} - 80 q^{90} + 8 q^{91} - 72 q^{93} - 120 q^{94} - 140 q^{96} - 88 q^{97} + 62 q^{99}+O(q^{100}) \) 192 * q + 6 * q^3 - 48 * q^4 - 10 * q^6 - 14 * q^9 - 20 * q^12 + 6 * q^15 - 28 * q^16 - 10 * q^18 - 60 * q^19 + 4 * q^22 + 30 * q^24 - 12 * q^25 + 30 * q^27 - 20 * q^28 + 12 * q^31 - 32 * q^33 + 56 * q^34 + 44 * q^36 + 60 * q^40 - 108 * q^42 - 40 * q^45 - 28 * q^48 - 24 * q^49 + 10 * q^51 + 20 * q^52 - 20 * q^55 + 50 * q^57 - 60 * q^58 + 36 * q^60 + 20 * q^61 - 30 * q^63 + 64 * q^64 - 30 * q^66 - 120 * q^67 - 16 * q^69 + 20 * q^70 + 150 * q^72 - 20 * q^73 + 18 * q^75 + 40 * q^78 - 160 * q^79 - 46 * q^81 + 88 * q^82 - 40 * q^85 + 72 * q^88 - 80 * q^90 + 8 * q^91 - 72 * q^93 - 120 * q^94 - 140 * q^96 - 88 * q^97 + 62 * q^99

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