LMFDB - Embedded newform 627.2.be.a.10.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [627,2,Mod(10,627)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(627, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 17]))

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

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

chi := DirichletCharacter("627.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 627 = 3 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	627.be (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:	$5.00662020673$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			10.18
Character	$\chi$	$=$	627.10
Dual form			627.2.be.a.439.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0377067 - 0.213846i) q^{2} +(-0.642788 - 0.766044i) q^{3} +(1.83508 - 0.667913i) q^{4} +(-2.08488 - 0.758835i) q^{5} +(-0.139578 + 0.166342i) q^{6} +(3.25299 + 1.87811i) q^{7} +(-0.429169 - 0.743343i) q^{8} +(-0.173648 + 0.984808i) q^{9} +(-0.0836593 + 0.474456i) q^{10} +(0.641700 + 3.25395i) q^{11} +(-1.69122 - 0.976424i) q^{12} +(2.75799 + 2.31423i) q^{13} +(0.278967 - 0.766455i) q^{14} +(0.758835 + 2.08488i) q^{15} +(2.84916 - 2.39073i) q^{16} +(3.82049 - 0.673656i) q^{17} +0.217144 q^{18} +(3.24043 - 2.91541i) q^{19} -4.33275 q^{20} +(-0.652262 - 3.69916i) q^{21} +(0.671647 - 0.259921i) q^{22} +(-1.93230 + 0.703298i) q^{23} +(-0.293569 + 0.806575i) q^{24} +(-0.0593218 - 0.0497769i) q^{25} +(0.390892 - 0.677045i) q^{26} +(0.866025 - 0.500000i) q^{27} +(7.22391 + 1.27377i) q^{28} +(0.228694 - 1.29699i) q^{29} +(0.417229 - 0.240887i) q^{30} +(-6.19662 - 3.57762i) q^{31} +(-1.93373 - 1.62259i) q^{32} +(2.08020 - 2.58317i) q^{33} +(-0.288117 - 0.791594i) q^{34} +(-5.35692 - 6.38413i) q^{35} +(0.339109 + 1.92318i) q^{36} -0.219776i q^{37} +(-0.745633 - 0.583021i) q^{38} -3.60030i q^{39} +(0.330693 + 1.87545i) q^{40} +(1.99086 - 1.67053i) q^{41} +(-0.766455 + 0.278967i) q^{42} +(0.722931 - 1.98624i) q^{43} +(3.35093 + 5.54266i) q^{44} +(1.10934 - 1.92144i) q^{45} +(0.223258 + 0.386694i) q^{46} +(0.203656 - 1.15499i) q^{47} +(-3.66281 - 0.645852i) q^{48} +(3.55463 + 6.15680i) q^{49} +(-0.00840774 + 0.0145626i) q^{50} +(-2.97181 - 2.49365i) q^{51} +(6.60682 + 2.40469i) q^{52} +(0.774672 + 2.12839i) q^{53} +(-0.139578 - 0.166342i) q^{54} +(1.13134 - 7.27105i) q^{55} -3.22412i q^{56} +(-4.31624 - 0.608324i) q^{57} -0.285978 q^{58} +(8.75698 - 1.54409i) q^{59} +(2.78504 + 3.31908i) q^{60} +(5.03183 + 13.8248i) q^{61} +(-0.531404 + 1.46002i) q^{62} +(-2.41446 + 2.87744i) q^{63} +(3.44524 - 5.96734i) q^{64} +(-3.99396 - 6.91774i) q^{65} +(-0.630837 - 0.347438i) q^{66} +(-10.9486 - 1.93053i) q^{67} +(6.56095 - 3.78797i) q^{68} +(1.78081 + 1.02815i) q^{69} +(-1.16323 + 1.38628i) q^{70} +(2.27176 - 6.24160i) q^{71} +(0.806575 - 0.293569i) q^{72} +(-3.42454 - 4.08121i) q^{73} +(-0.0469982 + 0.00828705i) q^{74} +0.0774392i q^{75} +(3.99920 - 7.51433i) q^{76} +(-4.02385 + 11.7903i) q^{77} +(-0.769907 + 0.135755i) q^{78} +(-12.1389 + 10.1858i) q^{79} +(-7.75433 + 2.82234i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(-0.432303 - 0.362746i) q^{82} +(15.0510 + 8.68972i) q^{83} +(-3.66767 - 6.35260i) q^{84} +(-8.47646 - 1.49463i) q^{85} +(-0.452007 - 0.0797011i) q^{86} +(-1.14055 + 0.658497i) q^{87} +(2.14341 - 1.87350i) q^{88} +(-7.29087 + 8.68892i) q^{89} +(-0.452720 - 0.164777i) q^{90} +(4.62532 + 12.7080i) q^{91} +(-3.07617 + 2.58121i) q^{92} +(1.24249 + 7.04654i) q^{93} -0.254668 q^{94} +(-8.96823 + 3.61933i) q^{95} +2.52431i q^{96} +(5.45706 - 0.962226i) q^{97} +(1.18257 - 0.992294i) q^{98} +(-3.31595 + 0.0669082i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 6 q^{11} - 48 q^{14} + 24 q^{15} - 216 q^{20} + 24 q^{26} - 36 q^{31} - 6 q^{33} - 132 q^{34} + 180 q^{38} + 12 q^{42} - 24 q^{44} - 12 q^{45} + 72 q^{47} + 48 q^{48} + 132 q^{49} + 108 q^{53} - 30 q^{55}+ \cdots - 12 q^{99}+O(q^{100}) $ 240 * q + 6 * q^11 - 48 * q^14 + 24 * q^15 - 216 * q^20 + 24 * q^26 - 36 * q^31 - 6 * q^33 - 132 * q^34 + 180 * q^38 + 12 * q^42 - 24 * q^44 - 12 * q^45 + 72 * q^47 + 48 * q^48 + 132 * q^49 + 108 * q^53 - 30 * q^55 - 24 * q^58 + 48 * q^60 - 120 * q^64 - 48 * q^66 + 48 * q^67 - 228 * q^70 - 84 * q^71 - 72 * q^77 + 84 * q^78 - 24 * q^80 - 156 * q^82 + 48 * q^86 + 108 * q^88 + 144 * q^89 - 24 * q^91 - 60 * q^92 - 24 * q^93 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/627\mathbb{Z}\right)^\times$.

$n$	$343$	$419$	$496$
$\chi(n)$	$-1$	$1$	$e\left(\frac{17}{18}\right)$

Coefficient data

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

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

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

$2$	−0.0377067	−	0.213846i	−0.0266627	−	0.151212i	0.968570	−	0.248741i	$-0.0800170\pi$
$2$	−0.0377067	−	0.213846i	−0.0266627	−	0.151212i	−0.995233	+	0.0975299i	$0.968906\pi$
$3$	−0.642788	−	0.766044i	−0.371114	−	0.442276i
$3$	−0.642788	−	0.766044i	−0.371114	−	0.442276i
$4$	1.83508	−	0.667913i	0.917539	−	0.333957i
$5$	−2.08488	−	0.758835i	−0.932387	−	0.339361i	−0.169232	−	0.985576i	$-0.554129\pi$
$5$	−2.08488	−	0.758835i	−0.932387	−	0.339361i	−0.763155	+	0.646215i	$0.776351\pi$
$6$	−0.139578	+	0.166342i	−0.0569824	+	0.0679090i
$7$	3.25299	+	1.87811i	1.22951	+	0.709861i	0.966928	−	0.255048i	$-0.0820913\pi$
$7$	3.25299	+	1.87811i	1.22951	+	0.709861i	0.262586	+	0.964909i	$0.415425\pi$
$8$	−0.429169	−	0.743343i	−0.151734	−	0.262812i
$9$	−0.173648	+	0.984808i	−0.0578827	+	0.328269i
$10$	−0.0836593	+	0.474456i	−0.0264554	+	0.150036i
$11$	0.641700	+	3.25395i	0.193480	+	0.981104i
$11$	0.641700	+	3.25395i	0.193480	+	0.981104i
$12$	−1.69122	−	0.976424i	−0.488212	−	0.281869i
$13$	2.75799	+	2.31423i	0.764928	+	0.641851i	0.939405	−	0.342810i	$-0.111379\pi$
$13$	2.75799	+	2.31423i	0.764928	+	0.641851i	−0.174477	+	0.984661i	$0.555823\pi$
$14$	0.278967	−	0.766455i	0.0745570	−	0.204844i
$15$	0.758835	+	2.08488i	0.195930	+	0.538314i
$16$	2.84916	−	2.39073i	0.712290	−	0.597682i
$17$	3.82049	−	0.673656i	0.926605	−	0.163386i	0.310071	−	0.950713i	$-0.399647\pi$
$17$	3.82049	−	0.673656i	0.926605	−	0.163386i	0.616534	+	0.787328i	$0.288536\pi$
$18$	0.217144			0.0511814
$19$	3.24043	−	2.91541i	0.743406	−	0.668841i
$19$	3.24043	−	2.91541i	0.743406	−	0.668841i
$20$	−4.33275			−0.968833
$21$	−0.652262	−	3.69916i	−0.142335	−	0.807224i
$22$	0.671647	−	0.259921i	0.143196	−	0.0554153i
$23$	−1.93230	+	0.703298i	−0.402912	+	0.146648i	−0.535524	−	0.844520i	$-0.679886\pi$
$23$	−1.93230	+	0.703298i	−0.402912	+	0.146648i	0.132612	+	0.991168i	$0.457664\pi$
$24$	−0.293569	+	0.806575i	−0.0599246	+	0.164641i
$25$	−0.0593218	−	0.0497769i	−0.0118644	−	0.00995539i
$26$	0.390892	−	0.677045i	0.0766603	−	0.132779i
$27$	0.866025	−	0.500000i	0.166667	−	0.0962250i
$28$	7.22391	+	1.27377i	1.36519	+	0.240720i
$29$	0.228694	−	1.29699i	0.0424673	−	0.240844i	−0.956184	−	0.292767i	$-0.905424\pi$
$29$	0.228694	−	1.29699i	0.0424673	−	0.240844i	0.998651	+	0.0519229i	$0.0165350\pi$
$30$	0.417229	−	0.240887i	0.0761753	−	0.0439798i
$31$	−6.19662	−	3.57762i	−1.11295	−	0.642560i	−0.173355	−	0.984859i	$-0.555461\pi$
$31$	−6.19662	−	3.57762i	−1.11295	−	0.642560i	−0.939591	+	0.342300i	$0.888794\pi$
$32$	−1.93373	−	1.62259i	−0.341839	−	0.286837i
$33$	2.08020	−	2.58317i	0.362116	−	0.449673i
$34$	−0.288117	−	0.791594i	−0.0494116	−	0.135757i
$35$	−5.35692	−	6.38413i	−0.905485	−	1.07911i
$36$	0.339109	+	1.92318i	0.0565181	+	0.320530i
$37$		−	0.219776i		−	0.0361310i	−0.999837	−	0.0180655i	$-0.994249\pi$
$37$		−	0.219776i		−	0.0361310i	0.999837	−	0.0180655i	$-0.00575074\pi$
$38$	−0.745633	−	0.583021i	−0.120958	−	0.0945785i
$39$		−	3.60030i		−	0.576509i
$40$	0.330693	+	1.87545i	0.0522871	+	0.296535i
$41$	1.99086	−	1.67053i	0.310919	−	0.260892i	−0.473952	−	0.880550i	$-0.657173\pi$
$41$	1.99086	−	1.67053i	0.310919	−	0.260892i	0.784872	+	0.619658i	$0.212729\pi$
$42$	−0.766455	+	0.278967i	−0.118267	+	0.0430455i
$43$	0.722931	−	1.98624i	0.110246	−	0.302898i	−0.872285	−	0.488998i	$-0.837363\pi$
$43$	0.722931	−	1.98624i	0.110246	−	0.302898i	0.982531	+	0.186100i	$0.0595847\pi$
$44$	3.35093	+	5.54266i	0.505172	+	0.835587i
$45$	1.10934	−	1.92144i	0.165371	−	0.286431i
$46$	0.223258	+	0.386694i	0.0329176	+	0.0570149i
$47$	0.203656	−	1.15499i	0.0297062	−	0.168472i	−0.966345	−	0.257248i	$-0.917184\pi$
$47$	0.203656	−	1.15499i	0.0297062	−	0.168472i	0.996052	+	0.0887756i	$0.0282954\pi$
$48$	−3.66281	−	0.645852i	−0.528681	−	0.0932207i
$49$	3.55463	+	6.15680i	0.507804	+	0.879542i
$50$	−0.00840774	+	0.0145626i	−0.00118903	+	0.00205947i
$51$	−2.97181	−	2.49365i	−0.416137	−	0.349181i
$52$	6.60682	+	2.40469i	0.916201	+	0.333470i
$53$	0.774672	+	2.12839i	0.106409	+	0.292357i	0.981458	−	0.191678i	$-0.0613929\pi$
$53$	0.774672	+	2.12839i	0.106409	+	0.292357i	−0.875048	+	0.484035i	$0.839171\pi$
$54$	−0.139578	−	0.166342i	−0.0189941	−	0.0226363i
$55$	1.13134	−	7.27105i	0.152550	−	0.980429i
$56$		−	3.22412i		−	0.430841i
$57$	−4.31624	−	0.608324i	−0.571700	−	0.0805745i
$58$	−0.285978			−0.0375507
$59$	8.75698	−	1.54409i	1.14006	−	0.201024i	0.428429	−	0.903575i	$-0.359067\pi$
$59$	8.75698	−	1.54409i	1.14006	−	0.201024i	0.711633	+	0.702552i	$0.247956\pi$
$60$	2.78504	+	3.31908i	0.359547	+	0.428492i
$61$	5.03183	+	13.8248i	0.644260	+	1.77009i	0.637912	+	0.770109i	$0.279798\pi$
$61$	5.03183	+	13.8248i	0.644260	+	1.77009i	0.00634771	+	0.999980i	$0.497979\pi$
$62$	−0.531404	+	1.46002i	−0.0674884	+	0.185423i
$63$	−2.41446	+	2.87744i	−0.304193	+	0.362523i
$64$	3.44524	−	5.96734i	0.430655	−	0.745917i
$65$	−3.99396	−	6.91774i	−0.495390	−	0.858041i
$66$	−0.630837	−	0.347438i	−0.0776507	−	0.0427666i
$67$	−10.9486	−	1.93053i	−1.33758	−	0.235852i	−0.541327	−	0.840812i	$-0.682078\pi$
$67$	−10.9486	−	1.93053i	−1.33758	−	0.235852i	−0.796256	+	0.604960i	$0.793189\pi$
$68$	6.56095	−	3.78797i	0.795632	−	0.459359i
$69$	1.78081	+	1.02815i	0.214385	+	0.123775i
$70$	−1.16323	+	1.38628i	−0.139032	+	0.165692i
$71$	2.27176	−	6.24160i	0.269608	−	0.740742i	−0.728821	−	0.684705i	$-0.759931\pi$
$71$	2.27176	−	6.24160i	0.269608	−	0.740742i	0.998429	−	0.0560372i	$-0.0178465\pi$
$72$	0.806575	−	0.293569i	0.0950558	−	0.0345975i
$73$	−3.42454	−	4.08121i	−0.400812	−	0.477669i	0.527455	−	0.849583i	$-0.323146\pi$
$73$	−3.42454	−	4.08121i	−0.400812	−	0.477669i	−0.928267	+	0.371914i	$0.878702\pi$
$74$	−0.0469982	+	0.00828705i	−0.00546343	+	0.000963350i
$75$			0.0774392i			0.00894190i
$76$	3.99920	−	7.51433i	0.458739	−	0.861953i
$77$	−4.02385	+	11.7903i	−0.458561	+	1.34363i
$78$	−0.769907	+	0.135755i	−0.0871748	+	0.0153713i
$79$	−12.1389	+	10.1858i	−1.36574	+	1.14599i	−0.391572	+	0.920148i	$0.628068\pi$
$79$	−12.1389	+	10.1858i	−1.36574	+	1.14599i	−0.974164	+	0.225841i	$0.927487\pi$
$80$	−7.75433	+	2.82234i	−0.866960	+	0.315548i
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$	−0.432303	−	0.362746i	−0.0477399	−	0.0400585i
$83$	15.0510	+	8.68972i	1.65207	+	0.953820i	0.976221	+	0.216776i	$0.0695540\pi$
$83$	15.0510	+	8.68972i	1.65207	+	0.953820i	0.675844	+	0.737045i	$0.263779\pi$
$84$	−3.66767	−	6.35260i	−0.400176	−	0.693125i
$85$	−8.47646	−	1.49463i	−0.919402	−	0.162115i
$86$	−0.452007	−	0.0797011i	−0.0487412	−	0.00859439i
$87$	−1.14055	+	0.658497i	−0.122280	+	0.0705983i
$88$	2.14341	−	1.87350i	0.228488	−	0.199716i
$89$	−7.29087	+	8.68892i	−0.772831	+	0.921024i	−0.998586	−	0.0531601i	$-0.983071\pi$
$89$	−7.29087	+	8.68892i	−0.772831	+	0.921024i	0.225755	+	0.974184i	$0.427515\pi$
$90$	−0.452720	−	0.164777i	−0.0477209	−	0.0173690i
$91$	4.62532	+	12.7080i	0.484866	+	1.33216i
$92$	−3.07617	+	2.58121i	−0.320713	+	0.269110i
$93$	1.24249	+	7.04654i	0.128841	+	0.730692i
$94$	−0.254668			−0.0262670
$95$	−8.96823	+	3.61933i	−0.920121	+	0.371336i
$96$			2.52431i			0.257636i
$97$	5.45706	−	0.962226i	0.554080	−	0.0976993i	0.110405	−	0.993887i	$-0.464785\pi$
$97$	5.45706	−	0.962226i	0.554080	−	0.0976993i	0.443676	+	0.896187i	$0.353674\pi$
$98$	1.18257	−	0.992294i	0.119458	−	0.100237i
$99$	−3.31595	+	0.0669082i	−0.333265	+	0.00672453i
$100$	−0.142107	−	0.0517227i	−0.0142107	−	0.00517227i
$101$	3.68920	−	4.39662i	0.367089	−	0.437480i	−0.550606	−	0.834765i	$-0.685603\pi$
$101$	3.68920	−	4.39662i	0.367089	−	0.437480i	0.917695	+	0.397285i	$0.130048\pi$
$102$	−0.421198	+	0.729537i	−0.0417048	+	0.0722349i
$103$	7.95007	−	4.58998i	0.783344	−	0.452264i	−0.0542701	−	0.998526i	$-0.517283\pi$
$103$	7.95007	−	4.58998i	0.783344	−	0.452264i	0.837614	+	0.546262i	$0.183950\pi$
$104$	0.536621	−	3.04333i	0.0526200	−	0.298423i
$105$	−1.44716	+	8.20728i	−0.141229	+	0.800948i
$106$	0.425937	−	0.245915i	0.0413707	−	0.0238854i
$107$	−1.05075	+	1.81995i	−0.101580	+	0.175941i	−0.912336	−	0.409443i	$-0.865723\pi$
$107$	−1.05075	+	1.81995i	−0.101580	+	0.175941i	0.810756	+	0.585384i	$0.199056\pi$
$108$	1.25527	−	1.49597i	0.120788	−	0.143950i
$109$	−7.64338	−	2.78196i	−0.732103	−	0.266464i	−0.0510481	−	0.998696i	$-0.516256\pi$
$109$	−7.64338	−	2.78196i	−0.732103	−	0.266464i	−0.681055	+	0.732233i	$0.738478\pi$
$110$	−1.59754	+	0.0322347i	−0.152320	+	0.00307346i
$111$	−0.168358	+	0.141270i	−0.0159799	+	0.0134087i
$112$	13.7583	−	2.42597i	1.30004	−	0.229232i
$113$		−	18.6552i		−	1.75494i	−0.479634	−	0.877469i	$-0.659230\pi$
$113$		−	18.6552i		−	1.75494i	0.479634	−	0.877469i	$-0.340770\pi$
$114$	0.0326640	+	0.945947i	0.00305926	+	0.0885960i
$115$	4.56229			0.425436
$116$	−0.446604	−	2.53282i	−0.0414661	−	0.235166i
$117$	−2.75799	+	2.31423i	−0.254976	+	0.213950i
$118$	−0.660394	−	1.81442i	−0.0607942	−	0.167031i
$119$	13.6932	+	4.98393i	1.25526	+	0.456876i
$120$	1.22411	−	1.45884i	0.111746	−	0.133173i
$121$	−10.1764	+	4.17613i	−0.925131	+	0.379648i
$122$	2.76665	−	1.59732i	0.250480	−	0.144615i
$123$	−2.55939	−	0.451290i	−0.230773	−	0.0406915i
$124$	−13.7608	−	2.42640i	−1.23576	−	0.217897i
$125$	5.63262	+	9.75598i	0.503797	+	0.872601i
$126$	0.706369	+	0.407822i	0.0629283	+	0.0363317i
$127$	8.81473	+	7.39644i	0.782181	+	0.656328i	0.943797	−	0.330526i	$-0.107226\pi$
$127$	8.81473	+	7.39644i	0.782181	+	0.656328i	−0.161616	+	0.986854i	$0.551671\pi$
$128$	−6.15014	−	2.23847i	−0.543601	−	0.197855i
$129$	−1.98624	+	0.722931i	−0.174878	+	0.0636506i
$130$	−1.32873	+	1.11494i	−0.116537	+	0.0977864i
$131$	−16.8043	+	2.96306i	−1.46820	+	0.258883i	−0.849852	−	0.527021i	$-0.823309\pi$
$131$	−16.8043	+	2.96306i	−1.46820	+	0.258883i	−0.618348	+	0.785904i	$0.712198\pi$
$132$	2.09199	−	6.12971i	0.182084	−	0.533523i
$133$	16.0166	−	3.39790i	1.38881	−	0.294635i
$134$			2.41410i			0.208547i
$135$	−2.18498	+	0.385271i	−0.188053	+	0.0331588i
$136$	−2.14040	−	2.55082i	−0.183537	−	0.218731i
$137$	−14.8447	+	5.40304i	−1.26827	+	0.461613i	−0.886536	−	0.462659i	$-0.846895\pi$
$137$	−14.8447	+	5.40304i	−1.26827	+	0.461613i	−0.381734	+	0.924272i	$0.624673\pi$
$138$	0.152717	−	0.419587i	0.0130002	−	0.0357176i
$139$	−4.24929	+	5.06411i	−0.360420	+	0.429532i	−0.915533	−	0.402243i	$-0.868231\pi$
$139$	−4.24929	+	5.06411i	−0.360420	+	0.429532i	0.555113	+	0.831775i	$0.312675\pi$
$140$	−14.0944	−	8.13741i	−1.19119	−	0.687737i
$141$	−1.01568	+	0.586403i	−0.0855356	+	0.0493840i
$142$	−1.42040	−	0.250455i	−0.119197	−	0.0210177i
$143$	−5.76059	+	10.4594i	−0.481724	+	0.874659i
$144$	1.85966	+	3.22102i	0.154971	+	0.268418i
$145$	−1.46100	+	2.53052i	−0.121329	+	0.210148i
$146$	−0.743620	+	0.886212i	−0.0615424	+	0.0733434i
$147$	2.43151	−	6.68052i	0.200547	−	0.551000i
$148$	−0.146792	−	0.403307i	−0.0120662	−	0.0331516i
$149$	−2.60277	−	3.10186i	−0.213227	−	0.254114i	0.648821	−	0.760941i	$-0.275263\pi$
$149$	−2.60277	−	3.10186i	−0.213227	−	0.254114i	−0.862048	+	0.506827i	$0.830818\pi$
$150$	0.0165600	−	0.00291998i	0.00135212	−	0.000238415i
$151$	−18.0109			−1.46570			−0.732852	−	0.680388i	$-0.761811\pi$
$151$	−18.0109			−1.46570			−0.732852	+	0.680388i	$0.761811\pi$
$152$	−3.55784	−	1.15755i	−0.288579	−	0.0938895i
$153$			3.87943i			0.313633i
$154$	2.67302	+	0.415911i	0.215398	+	0.0335150i
$155$	10.2044	+	12.1611i	0.819637	+	0.976805i
$156$	−2.40469	−	6.60682i	−0.192529	−	0.528969i
$157$	14.7559	+	5.37071i	1.17765	+	0.428629i	0.855371	−	0.518016i	$-0.173329\pi$
$157$	14.7559	+	5.37071i	1.17765	+	0.428629i	0.322278	+	0.946645i	$0.395551\pi$
$158$	2.63590	+	2.21178i	0.209701	+	0.175960i
$159$	1.13250	−	1.96154i	0.0898127	−	0.155560i
$160$	2.80032	+	4.85030i	0.221385	+	0.383450i
$161$	−7.60661	−	1.34125i	−0.599485	−	0.105705i
$162$	−0.0377067	+	0.213846i	−0.00296252	+	0.0168013i
$163$	2.60867	+	4.51834i	0.204326	+	0.353904i	0.949918	−	0.312500i	$-0.101166\pi$
$163$	2.60867	+	4.51834i	0.204326	+	0.353904i	−0.745591	+	0.666403i	$0.767833\pi$
$164$	2.53761	−	4.39526i	0.198154	−	0.343212i
$165$	−6.29716	+	3.80708i	−0.490234	+	0.296381i
$166$	1.29073	−	3.54626i	0.100180	−	0.275243i
$167$	−19.6983	+	7.16958i	−1.52430	+	0.554799i	−0.962217	−	0.272284i	$-0.912221\pi$
$167$	−19.6983	+	7.16958i	−1.52430	+	0.554799i	−0.562080	+	0.827083i	$0.689999\pi$
$168$	−2.46982	+	2.07242i	−0.190551	+	0.159891i
$169$	−0.00657467	−	0.0372868i	−0.000505744	−	0.00286822i
$170$			1.86901i			0.143347i
$171$	2.30842	+	3.69746i	0.176530	+	0.282752i
$172$		−	4.12775i		−	0.314738i
$173$	−1.91724	−	10.8732i	−0.145765	−	0.826677i	−0.966749	−	0.255726i	$-0.917686\pi$
$173$	−1.91724	−	10.8732i	−0.145765	−	0.826677i	0.820984	−	0.570951i	$-0.193425\pi$
$174$	0.183823	+	0.219072i	0.0139356	+	0.0166078i
$175$	−0.0994866	−	0.273337i	−0.00752048	−	0.0206623i
$176$	9.60763	+	7.73690i	0.724202	+	0.583191i
$177$	−6.81172	−	5.71571i	−0.512000	−	0.429619i
$178$	2.13300	+	1.23149i	0.159875	+	0.0923040i
$179$	−1.95677	+	1.12974i	−0.146256	+	0.0844407i	−0.571342	−	0.820712i	$-0.693577\pi$
$179$	−1.95677	+	1.12974i	−0.146256	+	0.0844407i	0.425086	+	0.905153i	$0.360244\pi$
$180$	0.752375	−	4.26693i	0.0560787	−	0.318038i
$181$	−23.8266	−	4.20127i	−1.77102	−	0.312278i	−0.809520	−	0.587093i	$-0.800272\pi$
$181$	−23.8266	−	4.20127i	−1.77102	−	0.312278i	−0.961497	+	0.274815i	$0.911383\pi$
$182$	2.54314	−	1.46828i	0.188510	−	0.108836i
$183$	7.35604	−	12.7410i	0.543774	−	0.941845i
$184$	1.35207	+	1.13453i	0.0996763	+	0.0836383i
$185$	−0.166774	+	0.458208i	−0.0122615	+	0.0336881i
$186$	1.46002	−	0.531404i	0.107054	−	0.0389644i
$187$	4.64366	+	11.9994i	0.339578	+	0.877485i
$188$	−0.397708	−	2.25552i	−0.0290059	−	0.164500i
$189$	3.75623			0.273225
$190$	1.11214	+	1.78134i	0.0806832	+	0.129232i
$191$	−26.1276			−1.89053			−0.945264	−	0.326307i	$-0.894196\pi$
$191$	−26.1276			−1.89053			−0.945264	+	0.326307i	$0.894196\pi$
$192$	−6.78581	+	1.19652i	−0.489723	+	0.0863514i
$193$	7.65982	−	6.42735i	0.551366	−	0.462651i	−0.324037	−	0.946044i	$-0.605040\pi$
$193$	7.65982	−	6.42735i	0.551366	−	0.462651i	0.875403	+	0.483393i	$0.160596\pi$
$194$	−0.411536	−	1.13068i	−0.0295465	−	0.0811784i
$195$	−2.73203	+	7.50619i	−0.195645	+	0.537530i
$196$	10.6352	+	8.92401i	0.759659	+	0.637429i
$197$	6.14747	+	3.54924i	0.437989	+	0.252873i	0.702744	−	0.711443i	$-0.251958\pi$
$197$	6.14747	+	3.54924i	0.437989	+	0.252873i	−0.264755	+	0.964316i	$0.585291\pi$
$198$	0.139342	+	0.706578i	0.00990258	+	0.0502143i
$199$	−0.947198	+	5.37183i	−0.0671451	+	0.380799i	0.932654	+	0.360771i	$0.117486\pi$
$199$	−0.947198	+	5.37183i	−0.0671451	+	0.380799i	−0.999799	+	0.0200275i	$0.993625\pi$
$200$	−0.0115422	+	0.0654592i	−0.000816159	+	0.00462867i
$201$	5.55875	+	9.62803i	0.392084	+	0.679109i
$202$	−1.07930	−	0.623137i	−0.0759396	−	0.0438438i
$203$	3.17983	−	3.78957i	0.223180	−	0.265976i
$204$	−7.11905	−	2.59112i	−0.498433	−	0.181415i
$205$	−5.41835	+	1.97212i	−0.378434	+	0.137739i
$206$	−1.28132	−	1.52701i	−0.0892736	−	0.106392i
$207$	−0.357074	−	2.02507i	−0.0248183	−	0.140752i
$208$	13.3906			0.928473
$209$	11.5660	+	8.67339i	0.800037	+	0.599951i
$210$	1.80966			0.124878
$211$	3.42742	+	19.4379i	0.235953	+	1.33816i	0.840596	+	0.541662i	$0.182205\pi$
$211$	3.42742	+	19.4379i	0.235953	+	1.33816i	−0.604643	+	0.796497i	$0.706684\pi$
$212$	2.84317	+	3.38835i	0.195269	+	0.232713i
$213$	−6.24160	+	2.27176i	−0.427667	+	0.155658i
$214$	0.428808	+	0.156073i	0.0293127	+	0.0106690i
$215$	−3.01445	+	3.59248i	−0.205584	+	0.245005i
$216$	−0.743343	−	0.429169i	−0.0505781	−	0.0292013i
$217$	−13.4384	−	23.2759i	−0.912256	−	1.58007i
$218$	−0.306703	+	1.73940i	−0.0207726	+	0.117807i
$219$	−0.925135	+	5.24670i	−0.0625148	+	0.354539i
$220$	−2.78033	−	14.0986i	−0.187450	−	0.950526i
$221$	12.0959	+	6.98355i	0.813656	+	0.469764i
$222$	0.0365581	+	0.0306759i	0.00245362	+	0.00205883i
$223$	3.42391	−	9.40712i	0.229282	−	0.629947i	−0.770692	−	0.637208i	$-0.780089\pi$
$223$	3.42391	−	9.40712i	0.229282	−	0.629947i	0.999974	+	0.00726100i	$0.00231127\pi$
$224$	−3.24299	−	8.91004i	−0.216681	−	0.595327i
$225$	0.0593218	−	0.0497769i	0.00395479	−	0.00331846i
$226$	−3.98934	+	0.703428i	−0.265367	+	0.0467914i
$227$	−4.42566			−0.293741			−0.146871	−	0.989156i	$-0.546920\pi$
$227$	−4.42566			−0.293741			−0.146871	+	0.989156i	$0.546920\pi$
$228$	−8.32694	+	1.76655i	−0.551465	+	0.116993i
$229$	−6.32793			−0.418162			−0.209081	−	0.977898i	$-0.567047\pi$
$229$	−6.32793			−0.418162			−0.209081	+	0.977898i	$0.567047\pi$
$230$	−0.172029	−	0.975626i	−0.0113433	−	0.0643309i
$231$	11.6184	−	4.49619i	0.764432	−	0.295827i
$232$	−1.06225	+	0.386629i	−0.0697404	+	0.0253834i
$233$	9.00576	−	24.7431i	0.589987	−	1.62098i	−0.180539	−	0.983568i	$-0.557784\pi$
$233$	9.00576	−	24.7431i	0.589987	−	1.62098i	0.770526	−	0.637408i	$-0.219993\pi$
$234$	0.598882	+	0.502521i	0.0391501	+	0.0328508i
$235$	−1.30104	+	2.25347i	−0.0848707	+	0.147000i
$236$	15.0384	−	8.68243i	0.978918	−	0.565178i
$237$	15.6055	+	2.75167i	1.01369	+	0.178740i
$238$	0.549463	−	3.11616i	0.0356164	−	0.201991i
$239$	6.42125	−	3.70731i	0.415356	−	0.239806i	−0.277732	−	0.960658i	$-0.589583\pi$
$239$	6.42125	−	3.70731i	0.415356	−	0.239806i	0.693088	+	0.720853i	$0.256250\pi$
$240$	7.14643	+	4.12599i	0.461300	+	0.266332i
$241$	4.69931	+	3.94319i	0.302709	+	0.254003i	0.781471	−	0.623942i	$-0.214470\pi$
$241$	4.69931	+	3.94319i	0.302709	+	0.254003i	−0.478762	+	0.877945i	$0.658914\pi$
$242$	1.27677	+	2.01872i	0.0820737	+	0.129768i
$243$	0.342020	+	0.939693i	0.0219406	+	0.0602813i
$244$	18.4676	+	22.0088i	1.18227	+	1.40897i
$245$	−2.73899	−	15.5336i	−0.174987	−	0.992403i
$246$			0.564332i			0.0359805i
$247$	15.6840	−	0.541576i	0.997948	−	0.0344596i
$248$			6.14162i			0.389993i
$249$	−3.01791	−	17.1154i	−0.191252	−	1.08464i
$250$	1.87388	−	1.57238i	0.118515	−	0.0994458i
$251$	2.36384	−	0.860368i	0.149204	−	0.0543060i	−0.266338	−	0.963880i	$-0.585814\pi$
$251$	2.36384	−	0.860368i	0.149204	−	0.0543060i	0.415543	+	0.909574i	$0.363592\pi$
$252$	−2.50884	+	6.89297i	−0.158042	+	0.434216i
$253$	−3.52846	−	5.83630i	−0.221832	−	0.366925i
$254$	1.24932	−	2.16389i	0.0783893	−	0.135774i
$255$	4.30361	+	7.45408i	0.269503	+	0.466792i
$256$	2.14626	−	12.1720i	0.134141	−	0.760752i
$257$	3.88019	+	0.684182i	0.242040	+	0.0426781i	0.293352	−	0.956005i	$-0.405229\pi$
$257$	3.88019	+	0.684182i	0.242040	+	0.0426781i	−0.0513123	+	0.998683i	$0.516340\pi$
$258$	0.229490	+	0.397489i	0.0142874	+	0.0247466i
$259$	0.412765	−	0.714930i	0.0256480	−	0.0444236i
$260$	−11.9497	−	10.0270i	−0.741088	−	0.621847i
$261$	1.23757	+	0.450439i	0.0766036	+	0.0278814i
$262$	1.26727	+	3.48180i	0.0782923	+	0.215106i
$263$	12.0602	+	14.3728i	0.743663	+	0.886263i	0.996698	−	0.0811941i	$-0.0258734\pi$
$263$	12.0602	+	14.3728i	0.743663	+	0.886263i	−0.253035	+	0.967457i	$0.581429\pi$
$264$	−2.81294	−	0.437682i	−0.173125	−	0.0269374i
$265$		−	5.02530i		−	0.308702i
$266$	−1.33056	−	3.29695i	−0.0815817	−	0.202149i
$267$	11.3426			0.694155
$268$	−21.3809	+	3.77004i	−1.30605	+	0.230292i
$269$	−15.9613	−	19.0219i	−0.973178	−	1.15979i	−0.987136	−	0.159886i	$-0.948887\pi$
$269$	−15.9613	−	19.0219i	−0.973178	−	1.15979i	0.0139575	−	0.999903i	$-0.495557\pi$
$270$	0.164777	+	0.452720i	0.0100280	+	0.0275517i
$271$	8.65263	−	23.7729i	0.525610	−	1.44410i	−0.338581	−	0.940937i	$-0.609947\pi$
$271$	8.65263	−	23.7729i	0.525610	−	1.44410i	0.864191	−	0.503164i	$-0.167831\pi$
$272$	9.27466	−	11.0531i	0.562359	−	0.670193i
$273$	6.76177	−	11.7117i	0.409241	−	0.708826i
$274$	1.71516	+	2.97075i	0.103617	+	0.179469i
$275$	0.123905	−	0.224972i	0.00747176	−	0.0135664i
$276$	3.95465	+	0.697311i	0.238042	+	0.0419732i
$277$	−11.0076	+	6.35526i	−0.661385	+	0.381851i	−0.792804	−	0.609476i	$-0.791380\pi$
$277$	−11.0076	+	6.35526i	−0.661385	+	0.381851i	0.131420	+	0.991327i	$0.458046\pi$
$278$	1.24316	+	0.717741i	0.0745600	+	0.0430472i
$279$	4.59930	−	5.48123i	0.275353	−	0.328153i
$280$	−2.44657	+	6.72190i	−0.146211	+	0.401711i
$281$	24.9859	−	9.09413i	1.49053	−	0.542510i	0.536945	−	0.843617i	$-0.319578\pi$
$281$	24.9859	−	9.09413i	1.49053	−	0.542510i	0.953590	+	0.301107i	$0.0973562\pi$
$282$	0.163698	+	0.195087i	0.00974805	+	0.0116173i
$283$	3.65870	−	0.645127i	0.217487	−	0.0383488i	−0.0638428	−	0.997960i	$-0.520336\pi$
$283$	3.65870	−	0.645127i	0.217487	−	0.0383488i	0.281330	+	0.959611i	$0.409225\pi$
$284$		−	12.9712i		−	0.769697i
$285$	8.53723	+	4.54360i	0.505702	+	0.269140i
$286$	2.45391	+	0.837485i	0.145103	+	0.0495215i
$287$	9.61367	−	1.69515i	0.567477	−	0.100062i
$288$	1.93373	−	1.62259i	0.113946	−	0.0956122i
$289$	−1.83243	+	0.666951i	−0.107790	+	0.0392324i
$290$	0.596230	+	0.217010i	0.0350118	+	0.0127433i
$291$	−4.24484	−	3.56184i	−0.248837	−	0.208799i
$292$	−9.01019	−	5.20204i	−0.527281	−	0.304426i
$293$	13.2780	+	22.9981i	0.775708	+	1.34357i	0.934396	+	0.356237i	$0.115940\pi$
$293$	13.2780	+	22.9981i	0.775708	+	1.34357i	−0.158687	+	0.987329i	$0.550726\pi$
$294$	−1.52028	−	0.268067i	−0.0886647	−	0.0156340i
$295$	−19.4290	−	3.42585i	−1.13120	−	0.199461i
$296$	−0.163369	+	0.0943213i	−0.00949565	+	0.00548232i
$297$	2.18271	+	2.49716i	0.126653	+	0.144900i
$298$	−0.565176	+	0.673551i	−0.0327398	+	0.0390178i
$299$	−6.95684	−	2.53208i	−0.402324	−	0.146434i
$300$	0.0517227	+	0.142107i	0.00298621	+	0.00820454i
$301$	6.08207	−	5.10346i	0.350565	−	0.294159i
$302$	0.679131	+	3.85155i	0.0390796	+	0.221632i
$303$	−5.73938			−0.329719
$304$	2.26255	−	16.0535i	0.129766	−	0.920729i
$305$		−	32.6415i		−	1.86905i
$306$	0.829598	−	0.146281i	0.0474250	−	0.00836230i
$307$	2.55596	−	2.14471i	0.145876	−	0.122405i	−0.566929	−	0.823767i	$-0.691869\pi$
$307$	2.55596	−	2.14471i	0.145876	−	0.122405i	0.712805	+	0.701362i	$0.247424\pi$
$308$	0.490795	+	24.3236i	0.0279656	+	1.38597i
$309$	−8.62634	−	3.13973i	−0.490735	−	0.178613i
$310$	2.21583	−	2.64072i	0.125851	−	0.149983i
$311$	−13.1277	+	22.7379i	−0.744405	+	1.28935i	0.206068	+	0.978538i	$0.433933\pi$
$311$	−13.1277	+	22.7379i	−0.744405	+	1.28935i	−0.950472	+	0.310809i	$0.899400\pi$
$312$	−2.67626	+	1.54514i	−0.151513	+	0.0874762i
$313$	−2.03498	+	11.5409i	−0.115024	+	0.652332i	0.871715	+	0.490014i	$0.163008\pi$
$313$	−2.03498	+	11.5409i	−0.115024	+	0.652332i	−0.986738	+	0.162318i	$0.948103\pi$
$314$	0.592105	−	3.35799i	0.0334144	−	0.189503i
$315$	7.21736	−	4.16694i	0.406652	−	0.234781i
$316$	−15.4727	+	26.7994i	−0.870405	+	1.50759i
$317$	12.1253	−	14.4503i	0.681023	−	0.811612i	−0.309216	−	0.950992i	$-0.600066\pi$
$317$	12.1253	−	14.4503i	0.681023	−	0.811612i	0.990239	+	0.139380i	$0.0445109\pi$
$318$	−0.462169	−	0.168216i	−0.0259172	−	0.00943307i
$319$	4.36709	−	0.0881177i	0.244510	−	0.00493365i
$320$	−11.7111	+	9.82682i	−0.654673	+	0.549336i
$321$	2.06957	−	0.364921i	0.115512	−	0.0203679i
$322$			1.67721i			0.0934675i
$323$	10.4161	−	13.3212i	0.579565	−	0.741213i
$324$	−1.95285			−0.108492
$325$	−0.0484138	−	0.274568i	−0.00268551	−	0.0152303i
$326$	0.867863	−	0.728223i	0.0480665	−	0.0403326i
$327$	2.78196	+	7.64338i	0.153843	+	0.422680i
$328$	−2.09619	−	0.762951i	−0.115743	−	0.0421269i
$329$	2.83169	−	3.37468i	0.156116	−	0.186052i
$330$	1.05157	+	1.20307i	0.0578872	+	0.0662267i
$331$	−1.69795	+	0.980313i	−0.0933279	+	0.0538829i	−0.545938	−	0.837826i	$-0.683826\pi$
$331$	−1.69795	+	0.980313i	−0.0933279	+	0.0538829i	0.452610	+	0.891709i	$0.350493\pi$
$332$	33.4238	+	5.89351i	1.83437	+	0.323449i
$333$	0.216437	+	0.0381638i	0.0118607	+	0.00209136i
$334$	2.27594	+	3.94204i	0.124534	+	0.215699i
$335$	21.3616	+	12.3331i	1.16711	+	0.673829i
$336$	−10.7021	−	8.98012i	−0.583847	−	0.489906i
$337$	−20.1329	−	7.32778i	−1.09671	−	0.399170i	−0.270608	−	0.962690i	$-0.587225\pi$
$337$	−20.1329	−	7.32778i	−1.09671	−	0.399170i	−0.826102	+	0.563520i	$0.809447\pi$
$338$	−0.00772571	+	0.00281193i	−0.000420223	+	0.000152949i
$339$	−14.2907	+	11.9914i	−0.776167	+	0.651281i
$340$	−16.5533	+	2.91878i	−0.897726	+	0.158293i
$341$	7.66504	−	22.4593i	0.415085	−	1.21624i
$342$	0.703641	−	0.633065i	0.0380486	−	0.0342322i
$343$			0.410392i			0.0221591i
$344$	−1.78672	+	0.315046i	−0.0963333	+	0.0169862i
$345$	−2.93259	−	3.49492i	−0.157885	−	0.188160i
$346$	−2.25290	+	0.819988i	−0.121117	+	0.0440829i
$347$	−10.7764	+	29.6079i	−0.578508	+	1.58944i	0.212188	+	0.977229i	$0.431941\pi$
$347$	−10.7764	+	29.6079i	−0.578508	+	1.58944i	−0.790696	+	0.612209i	$0.790281\pi$
$348$	−1.65318	+	1.97018i	−0.0886197	+	0.105613i
$349$	−15.8077	−	9.12656i	−0.846165	−	0.488533i	0.0131903	−	0.999913i	$-0.495801\pi$
$349$	−15.8077	−	9.12656i	−0.846165	−	0.488533i	−0.859355	+	0.511380i	$0.829135\pi$
$350$	−0.0547006	+	0.0315814i	−0.00292387	+	0.00168810i
$351$	3.54560	+	0.625185i	0.189250	+	0.0333699i
$352$	4.03897	−	7.33349i	0.215278	−	0.390876i
$353$	0.934288	+	1.61824i	0.0497272	+	0.0861300i	0.889818	−	0.456316i	$-0.150831\pi$
$353$	0.934288	+	1.61824i	0.0497272	+	0.0861300i	−0.840090	+	0.542446i	$0.817498\pi$
$354$	−0.965432	+	1.67218i	−0.0513121	+	0.0888752i
$355$	−9.47269	+	11.2891i	−0.502758	+	0.599164i
$356$	−7.57586	+	20.8145i	−0.401520	+	1.10317i
$357$	−4.98393	−	13.6932i	−0.263777	−	0.724722i
$358$	0.315373	+	0.375847i	0.0166680	+	0.0198641i
$359$	−20.3351	+	3.58563i	−1.07325	+	0.189242i	−0.682228	−	0.731140i	$-0.738989\pi$
$359$	−20.3351	+	3.58563i	−1.07325	+	0.189242i	−0.391020	+	0.920382i	$0.627878\pi$
$360$	−1.90438			−0.100370
$361$	2.00077	−	18.8944i	0.105304	−	0.994440i
$362$			5.25363i			0.276124i
$363$	9.74039	+	5.11124i	0.511238	+	0.268271i
$364$	16.9756	+	20.2308i	0.889766	+	1.06038i
$365$	4.04280	+	11.1075i	0.211610	+	0.581393i
$366$	−3.00199	−	1.09263i	−0.156916	−	0.0571129i
$367$	2.03328	+	1.70613i	0.106137	+	0.0890591i	0.694312	−	0.719675i	$-0.255709\pi$
$367$	2.03328	+	1.70613i	0.106137	+	0.0890591i	−0.588175	+	0.808734i	$0.700153\pi$
$368$	−3.82402	+	6.62340i	−0.199341	+	0.345269i
$369$	1.29944	+	2.25069i	0.0676461	+	0.117166i
$370$	0.104274	+	0.0183863i	0.00542096	+	0.000955861i
$371$	−1.47737	+	8.37857i	−0.0767011	+	0.434994i
$372$	6.98655	+	12.1011i	0.362236	+	0.627411i
$373$	1.25034	−	2.16565i	0.0647402	−	0.112133i	−0.831839	−	0.555018i	$-0.812711\pi$
$373$	1.25034	−	2.16565i	0.0647402	−	0.112133i	0.896579	+	0.442884i	$0.146045\pi$
$374$	2.39093	−	1.44548i	0.123632	−	0.0747442i
$375$	3.85294	−	10.5859i	0.198965	−	0.546651i
$376$	−0.945955	+	0.344300i	−0.0487839	+	0.0177559i
$377$	3.63225	−	3.04782i	0.187071	−	0.156971i
$378$	−0.141635	−	0.803253i	−0.00728492	−	0.0413149i
$379$			9.01018i			0.462822i	0.972856	+	0.231411i	$0.0743342\pi$
$379$			9.01018i			0.462822i	−0.972856	+	0.231411i	$0.925666\pi$
$380$	−14.0400	+	12.6318i	−0.720236	+	0.647995i
$381$		−	11.5068i		−	0.589512i
$382$	0.985187	+	5.58727i	0.0504066	+	0.285870i
$383$	−4.43215	−	5.28203i	−0.226472	−	0.269899i	0.640828	−	0.767685i	$-0.278591\pi$
$383$	−4.43215	−	5.28203i	−0.226472	−	0.269899i	−0.867300	+	0.497785i	$0.834147\pi$
$384$	2.23847	+	6.15014i	0.114231	+	0.313848i
$385$	17.3361	−	21.5279i	0.883531	−	1.09716i
$386$	−1.66329	−	1.39566i	−0.0846591	−	0.0710374i
$387$	1.83053	+	1.05686i	0.0930509	+	0.0537230i
$388$	9.37144	−	5.41060i	0.475763	−	0.274682i
$389$	−2.36957	+	13.4385i	−0.120142	+	0.681358i	0.863934	+	0.503606i	$0.167994\pi$
$389$	−2.36957	+	13.4385i	−0.120142	+	0.681358i	−0.984075	+	0.177752i	$0.943118\pi$
$390$	1.70818	+	0.301198i	0.0864971	+	0.0152518i
$391$	−6.90854	+	3.98865i	−0.349380	+	0.201715i
$392$	3.05108	−	5.28462i	0.154103	−	0.266914i
$393$	13.0714	+	10.9682i	0.659367	+	0.553275i
$394$	0.527188	−	1.44844i	0.0265594	−	0.0729713i
$395$	33.0375	−	12.0247i	1.66230	−	0.605027i
$396$	−6.04033	+	2.33755i	−0.303538	+	0.117466i
$397$	−4.39085	−	24.9018i	−0.220371	−	1.24978i	−0.871340	−	0.490680i	$-0.836748\pi$
$397$	−4.39085	−	24.9018i	−0.220371	−	1.24978i	0.650969	−	0.759104i	$-0.274363\pi$
$398$	1.18446			0.0593715
$399$	−12.8982	−	10.0853i	−0.645717	−	0.504895i
$400$	−0.288021			−0.0144010
$401$	−15.0902	+	2.66081i	−0.753568	+	0.132874i	−0.537220	−	0.843442i	$-0.680526\pi$
$401$	−15.0902	+	2.66081i	−0.753568	+	0.132874i	−0.216348	+	0.976316i	$0.569414\pi$
$402$	1.84931	−	1.55175i	0.0922351	−	0.0773945i
$403$	−8.81078	−	24.2074i	−0.438896	−	1.20586i
$404$	3.83341	−	10.5322i	0.190719	−	0.523997i
$405$	1.69961	+	1.42614i	0.0844543	+	0.0708656i
$406$	−0.930283	−	0.537099i	−0.0461692	−	0.0266558i
$407$	0.715142	−	0.141031i	0.0354483	−	0.00699063i
$408$	−0.578225	+	3.27928i	−0.0286264	+	0.162348i
$409$	1.15771	−	6.56570i	0.0572451	−	0.324653i	−0.942715	−	0.333599i	$-0.891737\pi$
$409$	1.15771	−	6.56570i	0.0572451	−	0.324653i	0.999960	+	0.00894652i	$0.00284780\pi$
$410$	0.626037	+	1.08433i	0.0309178	+	0.0535511i
$411$	13.6810	+	7.89871i	0.674833	+	0.389615i
$412$	11.5233	−	13.7329i	0.567712	−	0.676573i
$413$	31.3864	+	11.4237i	1.54442	+	0.562123i
$414$	−0.419587	+	0.152717i	−0.0206216	+	0.00750564i
$415$	−24.7856	−	29.5383i	−1.21668	−	1.44998i
$416$	−1.57816	−	8.95018i	−0.0773756	−	0.438819i
$417$	6.61072			0.323728
$418$	1.41865	−	2.80038i	0.0693884	−	0.136971i
$419$	−3.54084			−0.172981			−0.0864906	−	0.996253i	$-0.527565\pi$
$419$	−3.54084			−0.172981			−0.0864906	+	0.996253i	$0.527565\pi$
$420$	2.82609	+	16.0276i	0.137899	+	0.782065i
$421$	−10.6880	−	12.7375i	−0.520903	−	0.620789i	0.439891	−	0.898051i	$-0.355017\pi$
$421$	−10.6880	−	12.7375i	−0.520903	−	0.620789i	−0.960794	+	0.277263i	$0.910573\pi$
$422$	4.02747	−	1.46588i	0.196054	−	0.0713578i
$423$	1.10208	+	0.401123i	0.0535848	+	0.0195033i
$424$	1.24966	−	1.48929i	0.0606890	−	0.0723263i
$425$	−0.260171	−	0.150210i	−0.0126202	−	0.00728625i
$426$	0.721155	+	1.24908i	0.0349401	+	0.0605180i
$427$	−9.59614	+	54.4224i	−0.464390	+	2.63368i
$428$	−0.712635	+	4.04155i	−0.0344465	+	0.195356i
$429$	11.7152	−	2.31031i	0.565615	−	0.111543i
$430$	0.881902	+	0.509166i	0.0425291	+	0.0245542i
$431$	9.42865	+	7.91158i	0.454162	+	0.381087i	0.840978	−	0.541070i	$-0.181981\pi$
$431$	9.42865	+	7.91158i	0.454162	+	0.381087i	−0.386816	+	0.922157i	$0.626425\pi$
$432$	1.27208	−	3.49501i	0.0612030	−	0.168154i
$433$	1.59774	+	4.38977i	0.0767827	+	0.210959i	0.972145	−	0.234379i	$-0.0753057\pi$
$433$	1.59774	+	4.38977i	0.0767827	+	0.210959i	−0.895363	+	0.445338i	$0.853084\pi$
$434$	−4.47074	+	3.75139i	−0.214602	+	0.180073i
$435$	2.87760	−	0.507399i	0.137970	−	0.0243279i
$436$	−15.8843			−0.760720
$437$	−4.21107	+	7.91242i	−0.201443	+	0.378503i
$438$	1.15687			0.0552772
$439$	2.32305	+	13.1747i	0.110873	+	0.628793i	0.988711	+	0.149835i	$0.0478742\pi$
$439$	2.32305	+	13.1747i	0.110873	+	0.628793i	−0.877838	+	0.478958i	$0.841015\pi$
$440$	−5.89043	+	2.27954i	−0.280815	+	0.108673i
$441$	−6.68052	+	2.43151i	−0.318120	+	0.115786i
$442$	1.03730	−	2.84997i	0.0493396	−	0.135559i
$443$	5.72196	+	4.80129i	0.271858	+	0.228116i	0.768516	−	0.639830i	$-0.220995\pi$
$443$	5.72196	+	4.80129i	0.271858	+	0.228116i	−0.496658	+	0.867946i	$0.665440\pi$
$444$	−0.214595	+	0.371689i	−0.0101842	+	0.0176396i
$445$	21.7941	−	12.5828i	1.03314	−	0.596482i
$446$	−2.14078	−	0.377476i	−0.101369	−	0.0178740i
$447$	−0.703134	+	3.98767i	−0.0332571	+	0.188610i
$448$	22.4147	−	12.9411i	1.05899	−	0.611411i
$449$	−21.4566	−	12.3880i	−1.01260	−	0.584625i	−0.100648	−	0.994922i	$-0.532092\pi$
$449$	−21.4566	−	12.3880i	−1.01260	−	0.584625i	−0.911952	+	0.410297i	$0.865425\pi$
$450$	−0.0128814	−	0.0108088i	−0.000607235	−	0.000509531i
$451$	6.71335	+	5.40618i	0.316119	+	0.254567i
$452$	−12.4601	−	34.2338i	−0.586073	−	1.61022i
$453$	11.5772	+	13.7971i	0.543943	+	0.648246i
$454$	0.166877	+	0.946407i	0.00783193	+	0.0444171i
$455$		−	30.0045i		−	1.40663i
$456$	1.40021	+	3.46952i	0.0655706	+	0.162475i
$457$		−	29.7206i		−	1.39027i	−0.718880	−	0.695134i	$-0.755345\pi$
$457$		−	29.7206i		−	1.39027i	0.718880	−	0.695134i	$-0.244655\pi$
$458$	0.238606	+	1.35320i	0.0111493	+	0.0632309i
$459$	2.97181	−	2.49365i	0.138712	−	0.116394i
$460$	8.37216	−	3.04722i	0.390354	−	0.142077i
$461$	5.83587	−	16.0339i	0.271803	−	0.746774i	−0.726423	−	0.687248i	$-0.758819\pi$
$461$	5.83587	−	16.0339i	0.271803	−	0.746774i	0.998227	−	0.0595263i	$-0.0189590\pi$
$462$	−1.39958	−	2.31500i	−0.0651143	−	0.107703i
$463$	−4.90409	+	8.49413i	−0.227912	+	0.394756i	−0.957189	−	0.289463i	$-0.906523\pi$
$463$	−4.90409	+	8.49413i	−0.227912	+	0.394756i	0.729277	+	0.684219i	$0.239857\pi$
$464$	−2.44916	−	4.24206i	−0.113699	−	0.196933i
$465$	2.75670	−	15.6340i	0.127839	−	0.725011i
$466$	−5.63078	−	0.992859i	−0.260841	−	0.0459933i
$467$	10.0747	+	17.4500i	0.466204	+	0.807488i	0.999255	−	0.0385946i	$-0.0122881\pi$
$467$	10.0747	+	17.4500i	0.466204	+	0.807488i	−0.533051	+	0.846083i	$0.678955\pi$
$468$	−3.51542	+	6.08888i	−0.162500	+	0.281459i
$469$	−31.9899	−	26.8427i	−1.47716	−	1.23948i
$470$	0.530953	+	0.193251i	0.0244910	+	0.00891401i
$471$	−5.37071	−	14.7559i	−0.247469	−	0.679916i
$472$	−4.90602	−	5.84677i	−0.225818	−	0.269119i
$473$	6.92703	+	1.07782i	0.318505	+	0.0495581i
$474$		−	3.44092i		−	0.158047i
$475$	−0.337348	+	0.0116488i	−0.0154786	+	0.000534484i
$476$	28.4569			1.30432
$477$	−2.23058	+	0.393311i	−0.102131	+	0.0180085i
$478$	−1.03492	−	1.23336i	−0.0473359	−	0.0564128i
$479$	−4.97949	−	13.6810i	−0.227519	−	0.625103i	0.772431	−	0.635098i	$-0.219040\pi$
$479$	−4.97949	−	13.6810i	−0.227519	−	0.625103i	−0.999950	+	0.00999556i	$0.996818\pi$
$480$	1.91553	−	5.26288i	0.0874316	−	0.240216i
$481$	0.508612	−	0.606141i	0.0231907	−	0.0276376i
$482$	0.666038	−	1.15361i	0.0303372	−	0.0525456i
$483$	3.86198	+	6.68914i	0.175726	+	0.304367i
$484$	−15.8853	+	14.4605i	−0.722057	+	0.657295i
$485$	−12.1075	−	2.13488i	−0.549773	−	0.0969397i
$486$	0.188053	−	0.108572i	0.00853024	−	0.00492494i
$487$	7.46275	+	4.30862i	0.338169	+	0.195242i	0.659462	−	0.751738i	$-0.270784\pi$
$487$	7.46275	+	4.30862i	0.338169	+	0.195242i	−0.321293	+	0.946980i	$0.604117\pi$
$488$	8.11709	−	9.67358i	0.367444	−	0.437902i
$489$	1.78443	−	4.90269i	0.0806948	−	0.221707i
$490$	−3.21851	+	1.17144i	−0.145397	+	0.0529203i
$491$	11.4392	+	13.6328i	0.516245	+	0.615237i	0.959689	−	0.281065i	$-0.0906877\pi$
$491$	11.4392	+	13.6328i	0.516245	+	0.615237i	−0.443443	+	0.896302i	$0.646243\pi$
$492$	−4.99811	+	0.881302i	−0.225332	+	0.0397321i
$493$		−	5.10918i		−	0.230106i
$494$	−0.707205	−	3.33353i	−0.0318187	−	0.149983i
$495$	6.96413	+	2.37676i	0.313015	+	0.106828i
$496$	−26.2083	+	4.62123i	−1.17679	+	0.207499i
$497$	19.1124	−	16.0372i	0.857310	−	0.719369i
$498$	−3.54626	+	1.29073i	−0.158912	+	0.0578391i
$499$	14.1992	+	5.16810i	0.635645	+	0.231356i	0.639687	−	0.768636i	$-0.279064\pi$
$499$	14.1992	+	5.16810i	0.635645	+	0.231356i	−0.00404128	+	0.999992i	$0.501286\pi$
$500$	16.8524	+	14.1409i	0.753664	+	0.632399i
$501$	18.1540	+	10.4812i	0.811061	+	0.468266i
$502$	−0.273119	−	0.473056i	−0.0121899	−	0.0211135i
$503$	14.5307	+	2.56215i	0.647890	+	0.114240i	0.487930	−	0.872883i	$-0.337752\pi$
$503$	14.5307	+	2.56215i	0.647890	+	0.114240i	0.159960	+	0.987123i	$0.448863\pi$
$504$	3.17514	+	0.559862i	0.141432	+	0.0249382i
$505$	−11.0279	+	6.36693i	−0.490733	+	0.283325i
$506$	−1.11502	+	0.974612i	−0.0495687	+	0.0433268i
$507$	−0.0243372	+	0.0290040i	−0.00108085	+	0.00128811i
$508$	21.1159	+	7.68556i	0.936866	+	0.340992i
$509$	8.30762	+	22.8250i	0.368229	+	1.01170i	0.976035	+	0.217615i	$0.0698277\pi$
$509$	8.30762	+	22.8250i	0.368229	+	1.01170i	−0.607806	+	0.794086i	$0.707950\pi$
$510$	1.43175	−	1.20138i	0.0633988	−	0.0531979i
$511$	−3.47502	−	19.7078i	−0.153726	−	0.871822i
$512$	−15.7735			−0.697099
$513$	1.34859	−	4.14503i	0.0595417	−	0.183008i
$514$		−	0.855559i		−	0.0377371i
$515$	−20.0580	+	3.53677i	−0.883861	+	0.155849i
$516$	−3.16204	+	2.65327i	−0.139201	+	0.116804i
$517$	3.88896	−	0.0784703i	0.171036	−	0.00345112i
$518$	−0.168449	−	0.0613103i	−0.00740121	−	0.00269382i
$519$	−7.09700	+	8.45788i	−0.311524	+	0.371260i
$520$	−3.42817	+	5.93777i	−0.150335	+	0.260388i
$521$	23.1613	−	13.3722i	1.01471	−	0.585845i	0.102145	−	0.994770i	$-0.467429\pi$
$521$	23.1613	−	13.3722i	1.01471	−	0.585845i	0.912568	+	0.408925i	$0.134096\pi$
$522$	0.0496595	−	0.281633i	0.00217354	−	0.0123268i
$523$	−5.31941	+	30.1679i	−0.232601	+	1.31915i	0.615005	+	0.788523i	$0.289154\pi$
$523$	−5.31941	+	30.1679i	−0.232601	+	1.31915i	−0.847607	+	0.530625i	$0.821957\pi$
$524$	−28.8582	+	16.6613i	−1.26067	+	0.727851i
$525$	−0.145440	+	0.251909i	−0.00634751	+	0.0109942i
$526$	2.61880	−	3.12097i	0.114185	−	0.136081i
$527$	−26.0842	−	9.49388i	−1.13625	−	0.413560i
$528$	−0.248853	−	12.3331i	−0.0108299	−	0.536727i
$529$	−14.3799	+	12.0662i	−0.625212	+	0.524615i
$530$	−1.07464	+	0.189488i	−0.0466793	+	0.00823081i
$531$			8.89207i			0.385883i
$532$	27.1221	−	16.9331i	1.17589	−	0.734142i
$533$	9.35673			0.405285
$534$	−0.427692	−	2.42556i	−0.0185080	−	0.104964i
$535$	3.57172	−	2.99703i	0.154419	−	0.129573i
$536$	3.26375	+	8.96709i	0.140973	+	0.387319i
$537$	2.12322	+	0.772787i	0.0916235	+	0.0333482i
$538$	−3.46591	+	4.13051i	−0.149426	+	0.178079i
$539$	−17.7529	+	15.5174i	−0.764673	+	0.668382i
$540$	−3.75228	+	2.16638i	−0.161472	+	0.0932260i
$541$	−0.623720	−	0.109979i	−0.0268158	−	0.00472835i	0.160224	−	0.987081i	$-0.448778\pi$
$541$	−0.623720	−	0.109979i	−0.0268158	−	0.00472835i	−0.187040	+	0.982352i	$0.559889\pi$
$542$	−5.40999	−	0.953927i	−0.232379	−	0.0409747i
$543$	12.0971	+	20.9528i	0.519135	+	0.899169i
$544$	−8.48087	−	4.89643i	−0.363614	−	0.209933i
$545$	13.8245	+	11.6001i	0.592176	+	0.496895i
$546$	−2.75947	−	1.00436i	−0.118094	−	0.0429828i
$547$	1.32644	−	0.482786i	0.0567147	−	0.0206424i	−0.313507	−	0.949586i	$-0.601504\pi$
$547$	1.32644	−	0.482786i	0.0567147	−	0.0206424i	0.370222	+	0.928943i	$0.379282\pi$
$548$	−23.6325	+	19.8300i	−1.00953	+	0.847095i
$549$	−14.4886	+	2.55473i	−0.618357	+	0.109033i
$550$	−0.0527814	−	0.0180136i	−0.00225061	−	0.000768101i
$551$	−3.04018	−	4.86953i	−0.129516	−	0.207449i
$552$		−	1.76501i		−	0.0751237i
$553$	−58.6178	+	10.3359i	−2.49268	+	0.439527i
$554$	1.77411	+	2.11430i	0.0753746	+	0.0898279i
$555$	0.458208	−	0.166774i	0.0194498	−	0.00707916i
$556$	−4.41539	+	12.1312i	−0.187254	+	0.514477i
$557$	7.31641	−	8.71936i	0.310006	−	0.369451i	−0.588435	−	0.808544i	$-0.700256\pi$
$557$	7.31641	−	8.71936i	0.310006	−	0.369451i	0.898442	+	0.439093i	$0.144700\pi$
$558$	−1.34556	−	0.776860i	−0.0569622	−	0.0328871i
$559$	6.59044	−	3.80499i	0.278746	−	0.160934i
$560$	−30.5254	−	5.38246i	−1.28993	−	0.227450i
$561$	6.20720	−	11.2703i	0.262068	−	0.475834i
$562$	−2.88688	−	5.00022i	−0.121776	−	0.210921i
$563$	−3.32120	+	5.75249i	−0.139972	+	0.242438i	−0.927486	−	0.373858i	$-0.878035\pi$
$563$	−3.32120	+	5.75249i	−0.139972	+	0.242438i	0.787514	+	0.616297i	$0.211368\pi$
$564$	−1.47218	+	1.75448i	−0.0619901	+	0.0738769i
$565$	−14.1562	+	38.8940i	−0.595558	+	1.63628i
$566$	−0.275915	−	0.758070i	−0.0115976	−	0.0318641i
$567$	−2.41446	−	2.87744i	−0.101398	−	0.120841i
$568$	−5.61462	+	0.990009i	−0.235584	+	0.0415399i
$569$	−32.2213			−1.35079			−0.675393	−	0.737458i	$-0.736026\pi$
$569$	−32.2213			−1.35079			−0.675393	+	0.737458i	$0.736026\pi$
$570$	0.649717	−	1.99697i	0.0272136	−	0.0836440i
$571$			28.9368i			1.21097i	0.795857	+	0.605484i	$0.207020\pi$
$571$			28.9368i			1.21097i	−0.795857	+	0.605484i	$0.792980\pi$
$572$	−3.58514	+	23.0414i	−0.149902	+	0.963409i
$573$	16.7945	+	20.0149i	0.701601	+	0.836135i
$574$	−0.725000	−	1.99192i	−0.0302609	−	0.0831412i
$575$	0.149635	+	0.0544628i	0.00624023	+	0.00227126i
$576$	5.27842	+	4.42912i	0.219934	+	0.184547i
$577$	−18.3138	+	31.7205i	−0.762415	+	1.32054i	0.179188	+	0.983815i	$0.442653\pi$
$577$	−18.3138	+	31.7205i	−0.762415	+	1.32054i	−0.941603	+	0.336726i	$0.890680\pi$
$578$	0.211719	+	0.366709i	0.00880637	+	0.0152531i
$579$	−9.84727	−	1.73634i	−0.409239	−	0.0721598i
$580$	−0.990873	+	5.61952i	−0.0411438	+	0.233338i
$581$	32.6406	+	56.5351i	1.35416	+	2.34547i
$582$	−0.601625	+	1.04204i	−0.0249381	+	0.0431941i
$583$	−6.42859	+	3.88654i	−0.266245	+	0.160964i
$584$	−1.56403	+	4.29714i	−0.0647201	+	0.177817i
$585$	7.50619	−	2.73203i	0.310343	−	0.112956i
$586$	4.41738	−	3.70662i	0.182480	−	0.153119i
$587$	−2.23997	−	12.7035i	−0.0924535	−	0.524330i	−0.995498	−	0.0947827i	$-0.969784\pi$
$587$	−2.23997	−	12.7035i	−0.0924535	−	0.524330i	0.903045	−	0.429547i	$-0.141327\pi$
$588$		−	13.8833i		−	0.572538i
$589$	−30.5099	+	6.47266i	−1.25714	+	0.266701i
$590$			4.28398i			0.176369i
$591$	−1.23264	−	6.99064i	−0.0507040	−	0.287557i
$592$	−0.525426	−	0.626178i	−0.0215949	−	0.0257358i
$593$	−10.3049	−	28.3124i	−0.423170	−	1.16265i	−0.949883	−	0.312607i	$-0.898798\pi$
$593$	−10.3049	−	28.3124i	−0.423170	−	1.16265i	0.526712	−	0.850044i	$-0.323425\pi$
$594$	0.451703	−	0.560922i	0.0185336	−	0.0230149i
$595$	−24.7668	−	20.7818i	−1.01534	−	0.851970i
$596$	−6.84805	−	3.95372i	−0.280507	−	0.161951i
$597$	4.72391	−	2.72735i	0.193337	−	0.111623i
$598$	−0.279155	+	1.58317i	−0.0114155	+	0.0647404i
$599$	7.02375	+	1.23848i	0.286983	+	0.0506028i	0.315286	−	0.948997i	$-0.397899\pi$
$599$	7.02375	+	1.23848i	0.286983	+	0.0506028i	−0.0283036	+	0.999599i	$0.509011\pi$
$600$	0.0575639	−	0.0332345i	0.00235004	−	0.00135679i
$601$	−0.433823	+	0.751403i	−0.0176960	+	0.0306504i	−0.874738	−	0.484597i	$-0.838966\pi$
$601$	−0.433823	+	0.751403i	−0.0176960	+	0.0306504i	0.857042	+	0.515247i	$0.172300\pi$
$602$	−1.32069	−	1.10819i	−0.0538272	−	0.0451664i
$603$	3.80241	−	10.4470i	0.154846	−	0.425436i
$604$	−33.0514	+	12.0297i	−1.34484	+	0.489482i
$605$	24.3857	−	0.984494i	0.991418	−	0.0400254i
$606$	0.216413	+	1.22734i	0.00879119	+	0.0498573i
$607$	−33.9163			−1.37662			−0.688311	−	0.725416i	$-0.741647\pi$
$607$	−33.9163			−1.37662			−0.688311	+	0.725416i	$0.741647\pi$
$608$	−10.9966	+	0.379719i	−0.445973	+	0.0153997i
$609$	−4.94693			−0.200460
$610$	−6.98023	+	1.23080i	−0.282621	+	0.0498338i
$611$	3.23458	−	2.71414i	0.130857	−	0.109802i
$612$	2.59112	+	7.11905i	0.104740	+	0.287771i
$613$	−4.52557	+	12.4339i	−0.182786	+	0.502201i	−0.996915	−	0.0784829i	$-0.974992\pi$
$613$	−4.52557	+	12.4339i	−0.182786	+	0.502201i	0.814129	+	0.580683i	$0.197215\pi$
$614$	−0.555012	−	0.465711i	−0.0223985	−	0.0187946i
$615$	4.99358	+	2.88304i	0.201361	+	0.116256i
$616$	10.4911	−	2.06892i	0.422700	−	0.0833591i
$617$	0.175574	−	0.995730i	0.00706835	−	0.0400866i	−0.981070	−	0.193655i	$-0.937966\pi$
$617$	0.175574	−	0.995730i	0.00706835	−	0.0400866i	0.988138	+	0.153569i	$0.0490767\pi$
$618$	−0.346146	+	1.96309i	−0.0139240	+	0.0789671i
$619$	−9.63592	−	16.6899i	−0.387300	−	0.670824i	0.604785	−	0.796389i	$-0.293259\pi$
$619$	−9.63592	−	16.6899i	−0.387300	−	0.670824i	−0.992085	+	0.125565i	$0.959926\pi$
$620$	26.8484	+	15.5010i	1.07826	+	0.622533i
$621$	−1.32177	+	1.57522i	−0.0530407	+	0.0632115i
$622$	5.35740	+	1.94993i	0.214812	+	0.0781852i
$623$	−40.0359	+	14.5719i	−1.60401	+	0.583810i
$624$	−8.60733	−	10.2578i	−0.344569	−	0.410641i
$625$	−4.27293	−	24.2330i	−0.170917	−	0.969319i
$626$	2.54471			0.101707
$627$	−0.790275	−	14.4352i	−0.0315605	−	0.576487i
$628$	30.6654			1.22368
$629$	−0.148054	−	0.839654i	−0.00590328	−	0.0334792i
$630$	−1.16323	−	1.38628i	−0.0463440	−	0.0552306i
$631$	−2.31048	+	0.840948i	−0.0919790	+	0.0334776i	−0.387600	−	0.921828i	$-0.626696\pi$
$631$	−2.31048	+	0.840948i	−0.0919790	+	0.0334776i	0.295621	+	0.955305i	$0.404474\pi$
$632$	12.7812	+	4.65197i	0.508408	+	0.185045i
$633$	12.6872	−	15.1200i	0.504270	−	0.600965i
$634$	−3.54735	−	2.04806i	−0.140883	−	0.0813389i
$635$	−12.7650	−	22.1096i	−0.506564	−	0.877394i
$636$	0.768077	−	4.35598i	0.0304563	−	0.172726i
$637$	−4.44460	+	25.2066i	−0.176101	+	0.998721i
$638$	−0.183512	−	0.930559i	−0.00726532	−	0.0368412i
$639$	5.75229	+	3.32109i	0.227557	+	0.131380i
$640$	11.1237	+	9.33388i	0.439702	+	0.368954i
$641$	5.22558	−	14.3572i	0.206398	−	0.567074i	−0.792697	−	0.609616i	$-0.791324\pi$
$641$	5.22558	−	14.3572i	0.206398	−	0.567074i	0.999095	+	0.0425425i	$0.0135458\pi$
$642$	−0.156073	−	0.428808i	−0.00615972	−	0.0169237i
$643$	24.0824	−	20.2075i	0.949717	−	0.796907i	−0.0295327	−	0.999564i	$-0.509402\pi$
$643$	24.0824	−	20.2075i	0.949717	−	0.796907i	0.979250	+	0.202656i	$0.0649575\pi$
$644$	−14.8546	+	2.61926i	−0.585352	+	0.103213i
$645$	4.68966			0.184655
$646$	−3.24144	−	1.72513i	−0.127533	−	0.0678742i
$647$	8.77766			0.345085			0.172543	−	0.985002i	$-0.444802\pi$
$647$	8.77766			0.345085			0.172543	+	0.985002i	$0.444802\pi$
$648$	0.149049	+	0.845299i	0.00585520	+	0.0332065i
$649$	10.6438	+	27.5040i	0.417804	+	1.07963i
$650$	−0.0568897	+	0.0207062i	−0.00223140	+	0.000812162i
$651$	−9.19238	+	25.2559i	−0.360278	+	0.989855i
$652$	7.80496	+	6.54914i	0.305666	+	0.256484i
$653$	−9.46954	+	16.4017i	−0.370572	+	0.641849i	−0.989654	−	0.143477i	$-0.954172\pi$
$653$	−9.46954	+	16.4017i	−0.370572	+	0.641849i	0.619082	+	0.785326i	$0.287505\pi$
$654$	1.52960	−	0.883117i	0.0598122	−	0.0345326i
$655$	37.2835	+	6.57408i	1.45679	+	0.256871i
$656$	1.67849	−	9.51919i	0.0655340	−	0.371662i
$657$	4.61387	−	2.66382i	0.180004	−	0.103925i
$658$	−0.828433	−	0.478296i	−0.0322957	−	0.0186459i
$659$	−26.1563	−	21.9478i	−1.01891	−	0.854964i	−0.0294167	−	0.999567i	$-0.509365\pi$
$659$	−26.1563	−	21.9478i	−1.01891	−	0.854964i	−0.989490	+	0.144603i	$0.953809\pi$
$660$	−9.01298	+	11.1923i	−0.350830	+	0.435658i
$661$	6.39151	+	17.5605i	0.248601	+	0.683026i	0.999738	+	0.0228797i	$0.00728347\pi$
$661$	6.39151	+	17.5605i	0.248601	+	0.683026i	−0.751137	+	0.660146i	$0.770494\pi$
$662$	0.273660	+	0.326135i	0.0106361	+	0.0126756i
$663$	−2.42536	−	13.7549i	−0.0941932	−	0.534196i
$664$		−	14.9174i		−	0.578909i
$665$	−35.9711	−	5.06970i	−1.39490	−	0.196595i
$666$		−	0.0477232i		−	0.00184924i
$667$	0.470264	+	2.66700i	0.0182087	+	0.103267i
$668$	−31.3592	+	26.3135i	−1.21332	+	1.01810i
$669$	−9.40712	+	3.42391i	−0.363700	+	0.132376i
$670$	1.83190	−	5.03312i	0.0707726	−	0.194446i
$671$	−41.7565	+	25.2447i	−1.61199	+	0.974563i
$672$	−4.74094	+	8.21154i	−0.182886	+	0.316767i
$673$	−6.84011	−	11.8474i	−0.263667	−	0.456684i	0.703547	−	0.710649i	$-0.251599\pi$
$673$	−6.84011	−	11.8474i	−0.263667	−	0.456684i	−0.967213	+	0.253965i	$0.918265\pi$
$674$	−0.807867	+	4.58164i	−0.0311179	+	0.176478i
$675$	−0.0762627	−	0.0134472i	−0.00293535	−	0.000517582i
$676$	−0.0369694	−	0.0640329i	−0.00142190	−	0.00246280i
$677$	−14.2616	+	24.7018i	−0.548118	+	0.949368i	0.450285	+	0.892885i	$0.351322\pi$
$677$	−14.2616	+	24.7018i	−0.548118	+	0.949368i	−0.998404	+	0.0564837i	$0.982011\pi$
$678$	3.10316	+	2.60386i	0.119176	+	0.100001i
$679$	19.5589	+	7.11886i	0.750602	+	0.273197i
$680$	2.52682	+	6.94237i	0.0968990	+	0.266228i
$681$	2.84476	+	3.39025i	0.109011	+	0.129915i
$682$	−5.09184	−	0.792269i	−0.194977	−	0.0303375i
$683$		−	41.9580i		−	1.60548i	−0.596331	−	0.802739i	$-0.703375\pi$
$683$		−	41.9580i		−	1.60548i	0.596331	−	0.802739i	$-0.296625\pi$
$684$	6.70572	+	5.24329i	0.256399	+	0.200482i
$685$	35.0495			1.33917
$686$	0.0877605	−	0.0154745i	0.00335071	−	0.000590821i
$687$	4.06752	+	4.84748i	0.155185	+	0.184943i
$688$	−2.68881	−	7.38744i	−0.102510	−	0.281644i
$689$	−2.78905	+	7.66285i	−0.106254	+	0.291931i
$690$	−0.636795	+	0.758903i	−0.0242424	+	0.0288909i
$691$	21.0823	−	36.5157i	0.802010	−	1.38912i	−0.116281	−	0.993216i	$-0.537097\pi$
$691$	21.0823	−	36.5157i	0.802010	−	1.38912i	0.918291	−	0.395906i	$-0.129569\pi$
$692$	−10.7807	−	18.6727i	−0.409820	−	0.709829i
$693$	−10.9124	−	6.01008i	−0.414528	−	0.228304i
$694$	6.73787	+	1.18807i	0.255766	+	0.0450984i
$695$	12.7021	−	7.33355i	0.481817	−	0.278177i
$696$	0.978979	+	0.565214i	0.0371081	+	0.0214244i
$697$	6.48069	−	7.72338i	0.245474	−	0.292544i
$698$	−1.35562	+	3.72453i	−0.0513109	+	0.140976i
$699$	−24.7431	+	9.00576i	−0.935871	+	0.340629i
$700$	−0.365131	−	0.435146i	−0.0138007	−	0.0164470i
$701$	31.9852	−	5.63986i	1.20807	−	0.213015i	0.466884	−	0.884319i	$-0.345377\pi$
$701$	31.9852	−	5.63986i	1.20807	−	0.213015i	0.741182	+	0.671304i	$0.234266\pi$
$702$		−	0.781784i		−	0.0295066i
$703$	−0.640738	−	0.712170i	−0.0241659	−	0.0268600i
$704$	21.6283	+	7.38142i	0.815146	+	0.278198i
$705$	2.56255	−	0.451847i	0.0965114	−	0.0170176i
$706$	0.310823	−	0.260812i	0.0116980	−	0.00981578i
$707$	20.2583	−	7.37341i	0.761891	−	0.277306i
$708$	−16.3176	−	5.93913i	−0.613254	−	0.223206i
$709$	1.07665	+	0.903420i	0.0404346	+	0.0339286i	0.662781	−	0.748813i	$-0.269376\pi$
$709$	1.07665	+	0.903420i	0.0404346	+	0.0339286i	−0.622346	+	0.782742i	$0.713820\pi$
$710$	2.77131	+	1.60002i	0.104005	+	0.0600475i
$711$	−7.92312	−	13.7232i	−0.297140	−	0.514662i
$712$	9.58787	+	1.69060i	0.359321	+	0.0633579i
$713$	14.4898	+	2.55495i	0.542649	+	0.0956836i
$714$	−2.74031	+	1.58212i	−0.102553	+	0.0592092i
$715$	19.9471	−	17.4353i	0.745979	−	0.652043i
$716$	−2.83625	+	3.38011i	−0.105996	+	0.126321i
$717$	−6.96746	−	2.53595i	−0.260205	−	0.0947067i
$718$	1.53354	+	4.21337i	0.0572313	+	0.157242i
$719$	−39.9898	+	33.5554i	−1.49137	+	1.25141i	−0.598471	+	0.801144i	$0.704225\pi$
$719$	−39.9898	+	33.5554i	−1.49137	+	1.25141i	−0.892897	+	0.450262i	$0.851331\pi$
$720$	−1.43294	−	8.12662i	−0.0534026	−	0.302861i
$721$	34.4820			1.28418
$722$	−4.11592	+	0.284589i	−0.153179	+	0.0105913i
$723$		−	6.13451i		−	0.228145i
$724$	−46.5297	+	8.20444i	−1.72926	+	0.304916i
$725$	−0.0781265	+	0.0655559i	−0.00290155	+	0.00243469i
$726$	0.725738	−	2.27567i	0.0269347	−	0.0844579i
$727$	35.6104	+	12.9611i	1.32072	+	0.480701i	0.903688	−	0.428192i	$-0.140849\pi$
$727$	35.6104	+	12.9611i	1.32072	+	0.480701i	0.417029	+	0.908893i	$0.363072\pi$
$728$	7.46134	−	8.89208i	0.276536	−	0.329562i
$729$	0.500000	−	0.866025i	0.0185185	−	0.0320750i
$730$	2.22285	−	1.28336i	0.0822713	−	0.0474993i
$731$	1.42391	−	8.07541i	0.0526653	−	0.298680i
$732$	4.98899	−	28.2940i	0.184399	−	1.04578i
$733$	29.7611	−	17.1826i	1.09925	−	0.634652i	0.163226	−	0.986589i	$-0.447810\pi$
$733$	29.7611	−	17.1826i	1.09925	−	0.634652i	0.936024	+	0.351936i	$0.114477\pi$
$734$	0.288179	−	0.499141i	0.0106369	−	0.0184236i
$735$	−10.1388	+	12.0830i	−0.373976	+	0.445687i
$736$	4.87771	+	1.77534i	0.179795	+	0.0654399i
$737$	−0.743852	−	36.8650i	−0.0274001	−	1.35794i
$738$	0.432303	−	0.362746i	0.0159133	−	0.0133528i
$739$	−12.5576	+	2.21425i	−0.461940	+	0.0814524i	−0.399775	−	0.916613i	$-0.630912\pi$
$739$	−12.5576	+	2.21425i	−0.461940	+	0.0814524i	−0.0621651	+	0.998066i	$0.519801\pi$
$740$			0.952237i			0.0350049i
$741$	−10.4963	−	11.6665i	−0.385593	−	0.428580i
$742$	1.84743			0.0678211
$743$	1.35313	+	7.67400i	0.0496416	+	0.281532i	0.999516	−	0.0310992i	$-0.00990079\pi$
$743$	1.35313	+	7.67400i	0.0496416	+	0.281532i	−0.949875	+	0.312631i	$0.898790\pi$
$744$	4.70476	−	3.94776i	0.172485	−	0.144732i
$745$	3.07266	+	8.44207i	0.112574	+	0.309294i
$746$	−0.510262	−	0.185720i	−0.0186820	−	0.00679969i
$747$	−11.1713	+	13.3134i	−0.408736	+	0.487113i
$748$	16.5360	+	18.9183i	0.604618	+	0.691722i
$749$	−6.83614	+	3.94685i	−0.249787	+	0.144215i
$750$	−2.40902	−	0.424775i	−0.0879650	−	0.0155106i
$751$	−10.7316	−	1.89226i	−0.391600	−	0.0690496i	−0.0256185	−	0.999672i	$-0.508156\pi$
$751$	−10.7316	−	1.89226i	−0.391600	−	0.0690496i	−0.365981	+	0.930622i	$0.619267\pi$
$752$	−2.18102	−	3.77763i	−0.0795334	−	0.137756i
$753$	−2.17853	−	1.25777i	−0.0793900	−	0.0458359i
$754$	−0.788724	−	0.661818i	−0.0287236	−	0.0241020i
$755$	37.5506	+	13.6673i	1.36660	+	0.497403i
$756$	6.89297	−	2.50884i	0.250695	−	0.0912455i
$757$	2.93854	−	2.46573i	0.106803	−	0.0896186i	−0.587822	−	0.808990i	$-0.700015\pi$
$757$	2.93854	−	2.46573i	0.106803	−	0.0896186i	0.694625	+	0.719372i	$0.255570\pi$
$758$	1.92679	−	0.339744i	0.0699840	−	0.0123401i
$759$	−2.20281	+	6.45445i	−0.0799571	+	0.234282i
$760$	6.53930	+	5.11316i	0.237205	+	0.185474i
$761$		−	38.9898i		−	1.41338i	−0.707523	−	0.706690i	$-0.750187\pi$
$761$		−	38.9898i		−	1.41338i	0.707523	−	0.706690i	$-0.249813\pi$
$762$	−2.46068	+	0.433885i	−0.0891411	+	0.0157180i
$763$	−19.6390	−	23.4048i	−0.710979	−	0.847312i
$764$	−47.9462	+	17.4510i	−1.73463	+	0.631354i
$765$	2.94385	−	8.08815i	0.106435	−	0.292428i
$766$	−0.962417	+	1.14696i	−0.0347735	+	0.0414415i
$767$	27.7250	+	16.0070i	1.00109	+	0.577981i
$768$	−10.7039	+	6.17990i	−0.386244	+	0.222998i
$769$	9.83110	+	1.73349i	0.354519	+	0.0625112i	0.348071	−	0.937468i	$-0.386837\pi$
$769$	9.83110	+	1.73349i	0.354519	+	0.0625112i	0.00644716	+	0.999979i	$0.497948\pi$
$770$	−5.25733	−	2.89551i	−0.189461	−	0.104347i
$771$	−1.97002	−	3.41218i	−0.0709487	−	0.122887i
$772$	9.76345	−	16.9108i	0.351394	−	0.608632i
$773$	−2.64944	+	3.15748i	−0.0952937	+	0.113567i	−0.811584	−	0.584236i	$-0.801394\pi$
$773$	−2.64944	+	3.15748i	−0.0952937	+	0.113567i	0.716290	+	0.697803i	$0.245839\pi$
$774$	0.156981	−	0.431300i	0.00564255	−	0.0155028i
$775$	0.189512	+	0.520680i	0.00680747	+	0.0187034i
$776$	−3.05727	−	3.64351i	−0.109749	−	0.130794i
$777$	−0.812989	+	0.143352i	−0.0291658	+	0.00514272i
$778$	2.96311			0.106232
$779$	1.58096	−	11.2174i	0.0566438	−	0.401905i
$780$			15.5992i			0.558541i
$781$	21.7677	+	3.38696i	0.778909	+	0.121195i
$782$	1.11345	+	1.32696i	0.0398170	+	0.0474520i
$783$	−0.450439	−	1.23757i	−0.0160974	−	0.0442271i
$784$	24.8469	+	9.04354i	0.887390	+	0.322984i
$785$	−26.6888	−	22.3946i	−0.952565	−	0.799297i
$786$	1.85263	−	3.20885i	0.0660811	−	0.114456i
$787$	−18.7340	−	32.4482i	−0.667794	−	1.15665i	−0.978520	−	0.206154i	$-0.933905\pi$
$787$	−18.7340	−	32.4482i	−0.667794	−	1.15665i	0.310725	−	0.950500i	$-0.399428\pi$
$788$	13.6517	+	2.40716i	0.486320	+	0.0857514i
$789$	3.25804	−	18.4773i	0.115989	−	0.657808i
$790$	−3.81716	−	6.61152i	−0.135809	−	0.235227i
$791$	35.0367	−	60.6853i	1.24576	−	2.15772i
$792$	1.47284	+	2.43617i	0.0523351	+	0.0865657i
$793$	−18.1161	+	49.7735i	−0.643321	+	1.76751i
$794$	−5.15957	+	1.87793i	−0.183106	+	0.0666452i
$795$	−3.84960	+	3.23020i	−0.136531	+	0.114563i
$796$	1.84973	+	10.4904i	0.0655621	+	0.371821i
$797$			17.2739i			0.611873i	0.952052	+	0.305937i	$0.0989695\pi$
$797$			17.2739i			0.611873i	−0.952052	+	0.305937i	$0.901030\pi$
$798$	−1.67034	+	3.13850i	−0.0591294	+	0.111102i
$799$		−	4.54981i		−	0.160961i
$800$	0.0339448	+	0.192510i	0.00120013	+	0.00680627i
$801$	−7.29087	−	8.68892i	−0.257610	−	0.307008i
$802$	1.13800	+	3.12664i	0.0401843	+	0.110405i
$803$	11.0825	−	13.7622i	0.391094	−	0.485658i
$804$	16.6314	+	13.9554i	0.586545	+	0.492170i
$805$	14.8411	+	8.56851i	0.523080	+	0.302000i
$806$	−4.84442	+	2.79693i	−0.170637	+	0.0985176i
$807$	−4.31192	+	24.4541i	−0.151787	+	0.860826i
$808$	−4.85149	−	0.855449i	−0.170675	−	0.0300946i
$809$	35.3102	−	20.3863i	1.24144	−	0.716745i	0.272052	−	0.962283i	$-0.412298\pi$
$809$	35.3102	−	20.3863i	1.24144	−	0.716745i	0.969387	+	0.245537i	$0.0789644\pi$
$810$	0.240887	−	0.417229i	0.00846392	−	0.0146599i
$811$	38.8293	+	32.5817i	1.36348	+	1.14410i	0.974890	+	0.222688i	$0.0714832\pi$
$811$	38.8293	+	32.5817i	1.36348	+	1.14410i	0.388593	+	0.921410i	$0.372961\pi$
$812$	3.30412	−	9.07800i	0.115952	−	0.318575i
$813$	−23.7729	+	8.65263i	−0.833752	+	0.303461i
$814$	−0.0571244	−	0.147612i	−0.00200221	−	0.00517380i
$815$	−2.01008	−	11.3998i	−0.0704102	−	0.399316i
$816$	−14.4288			−0.505109
$817$	−3.44809	−	8.54391i	−0.120633	−	0.298913i
$818$	−1.44770			−0.0506176
$819$	−13.3181	+	2.34834i	−0.465372	+	0.0820576i
$820$	−8.62589	+	7.23798i	−0.301229	+	0.252761i
$821$	14.8021	+	40.6685i	0.516597	+	1.41934i	0.874246	+	0.485483i	$0.161356\pi$
$821$	14.8021	+	40.6685i	0.516597	+	1.41934i	−0.357649	+	0.933856i	$0.616421\pi$
$822$	1.17324	−	3.22345i	0.0409214	−	0.112431i
$823$	−29.1376	−	24.4494i	−1.01567	−	0.852252i	−0.0265964	−	0.999646i	$-0.508467\pi$
$823$	−29.1376	−	24.4494i	−1.01567	−	0.852252i	−0.989078	+	0.147394i	$0.952911\pi$
$824$	−6.82386	−	3.93976i	−0.237720	−	0.137248i
$825$	−0.251984	+	0.0496927i	−0.00877294	+	0.00173008i
$826$	1.25943	−	7.14258i	0.0438212	−	0.248522i
$827$	7.49007	−	42.4783i	0.260455	−	1.47712i	−0.521216	−	0.853425i	$-0.674521\pi$
$827$	7.49007	−	42.4783i	0.260455	−	1.47712i	0.781671	−	0.623691i	$-0.214368\pi$
$828$	−2.00783	−	3.47766i	−0.0697768	−	0.120857i
$829$	−21.7386	−	12.5508i	−0.755012	−	0.435907i	0.0724898	−	0.997369i	$-0.476906\pi$
$829$	−21.7386	−	12.5508i	−0.755012	−	0.435907i	−0.827502	+	0.561463i	$0.810239\pi$
$830$	−5.38205	+	6.41407i	−0.186814	+	0.222636i
$831$	11.9440	+	4.34726i	0.414332	+	0.150805i
$832$	23.3117	−	8.48477i	0.808188	−	0.294156i
$833$	17.7280	+	21.1274i	0.614238	+	0.732021i
$834$	−0.249269	−	1.41367i	−0.00863147	−	0.0489515i
$835$	46.5090			1.60951
$836$	27.0176	+	8.19126i	0.934422	+	0.283301i
$837$	−7.15524			−0.247321
$838$	0.133513	+	0.757192i	0.00461214	+	0.0261568i
$839$	4.27855	+	5.09898i	0.147712	+	0.176036i	0.834827	−	0.550512i	$-0.185568\pi$
$839$	4.27855	+	5.09898i	0.147712	+	0.176036i	−0.687115	+	0.726549i	$0.741123\pi$
$840$	6.72190	−	2.44657i	0.231928	−	0.0844148i
$841$	25.6212	+	9.32536i	0.883490	+	0.321564i
$842$	−2.32085	+	2.76588i	−0.0799818	+	0.0953185i
$843$	−23.0271	−	13.2947i	−0.793097	−	0.457895i
$844$	19.2724	+	33.3808i	0.663384	+	1.14901i
$845$	−0.0145871	+	0.0827277i	−0.000501812	+	0.00284592i
$846$	0.0442227	−	0.250799i	0.00152041	−	0.00862265i
$847$	−40.9471	−	5.52762i	−1.40696	−	0.189931i
$848$	7.29558	+	4.21210i	0.250531	+	0.144644i
$849$	−2.84596	−	2.38804i	−0.0976731	−	0.0819575i
$850$	−0.0223115	+	0.0613003i	−0.000765278	+	0.00210258i
$851$	0.154568	+	0.424673i	0.00529853	+	0.0145576i
$852$	−9.93648	+	8.33770i	−0.340418	+	0.285645i
$853$	33.5728	−	5.91979i	1.14951	−	0.202690i	0.433749	−	0.901034i	$-0.357190\pi$
$853$	33.5728	−	5.91979i	1.14951	−	0.202690i	0.715762	+	0.698344i	$0.246079\pi$
$854$	11.9998			0.410626
$855$	−2.00703	−	9.46047i	−0.0686390	−	0.323541i
$856$	1.80379			0.0616524
$857$	−5.51703	−	31.2886i	−0.188458	−	1.06880i	−0.921431	−	0.388541i	$-0.872979\pi$
$857$	−5.51703	−	31.2886i	−0.188458	−	1.06880i	0.732973	−	0.680257i	$-0.238132\pi$
$858$	−0.935792	−	2.41813i	−0.0319474	−	0.0825536i
$859$	46.0997	−	16.7789i	1.57290	−	0.572489i	0.599256	−	0.800558i	$-0.295463\pi$
$859$	46.0997	−	16.7789i	1.57290	−	0.572489i	0.973645	+	0.228068i	$0.0732410\pi$
$860$	−3.13228	+	8.60588i	−0.106810	+	0.293458i
$861$	−7.47811	−	6.27488i	−0.254853	−	0.213847i
$862$	1.33633	−	2.31459i	0.0455156	−	0.0788354i
$863$	41.9223	−	24.2038i	1.42705	−	0.823908i	0.430163	−	0.902751i	$-0.358456\pi$
$863$	41.9223	−	24.2038i	1.42705	−	0.823908i	0.996887	+	0.0788435i	$0.0251227\pi$
$864$	−2.48596	−	0.438341i	−0.0845739	−	0.0149127i
$865$	−4.25376	+	24.1243i	−0.144632	+	0.820250i
$866$	0.878486	−	0.507194i	0.0298522	−	0.0172352i
$867$	1.68878	+	0.975017i	0.0573539	+	0.0331133i
$868$	−40.2067	−	33.7375i	−1.36471	−	1.14512i
$869$	−40.9336	−	32.9633i	−1.38858	−	1.11820i
$870$	−0.217010	−	0.596230i	−0.00735733	−	0.0202141i
$871$	−25.7284	−	30.6619i	−0.871773	−	1.03894i
$872$	1.21235	+	6.87559i	0.0410554	+	0.232837i
$873$			5.54124i			0.187543i
$874$	1.85082	+	0.602166i	0.0626050	+	0.0203686i
$875$			42.3148i			1.43050i
$876$	1.80665	+	10.2460i	0.0610410	+	0.346181i
$877$	10.7478	−	9.01846i	0.362927	−	0.304532i	−0.443029	−	0.896507i	$-0.646096\pi$
$877$	10.7478	−	9.01846i	0.362927	−	0.304532i	0.805956	+	0.591975i	$0.201652\pi$
$878$	2.72975	−	0.993548i	0.0921246	−	0.0335306i
$879$	9.08268	−	24.9545i	0.306351	−	0.841693i
$880$	−14.1597	−	23.4211i	−0.477325	−	0.789526i
$881$	25.4224	−	44.0329i	0.856503	−	1.48351i	−0.0187397	−	0.999824i	$-0.505965\pi$
$881$	25.4224	−	44.0329i	0.856503	−	1.48351i	0.875243	−	0.483683i	$-0.160701\pi$
$882$	0.771868	+	1.33691i	0.0259901	+	0.0450162i
$883$	8.06045	−	45.7131i	0.271256	−	1.53837i	−0.479354	−	0.877621i	$-0.659129\pi$
$883$	8.06045	−	45.7131i	0.271256	−	1.53837i	0.750610	−	0.660745i	$-0.229760\pi$
$884$	26.8612	+	4.73636i	0.903441	+	0.159301i
$885$	9.86435	+	17.0856i	0.331587	+	0.574325i
$886$	0.810978	−	1.40466i	0.0272453	−	0.0471903i
$887$	20.2376	+	16.9814i	0.679512	+	0.570179i	0.915864	−	0.401489i	$-0.131507\pi$
$887$	20.2376	+	16.9814i	0.679512	+	0.570179i	−0.236351	+	0.971668i	$0.575952\pi$
$888$	0.177266	+	0.0645196i	0.00594866	+	0.00216514i
$889$	14.7829	+	40.6156i	0.495802	+	1.36220i
$890$	−3.51256	−	4.18611i	−0.117741	−	0.140319i
$891$	0.509917	−	3.27719i	0.0170829	−	0.109790i
$892$		−	19.5497i		−	0.654571i
$893$	−2.70733	−	4.33640i	−0.0905974	−	0.145112i
$894$	0.879258			0.0294068
$895$	4.93691	−	0.870511i	0.165023	−	0.0290980i
$896$	−15.8022	−	18.8324i	−0.527916	−	0.629146i
$897$	2.53208	+	6.95684i	0.0845438	+	0.232282i
$898$	−1.84006	+	5.05551i	−0.0614034	+	0.168705i
$899$	−6.05725	+	7.21875i	−0.202021	+	0.240759i
$900$	0.0756135	−	0.130966i	0.00252045	−	0.00436555i
$901$	4.39343	+	7.60965i	0.146366	+	0.253514i
$902$	0.902948	−	1.63947i	0.0300649	−	0.0545884i
$903$	−7.81896	−	1.37869i	−0.260199	−	0.0458800i
$904$	−13.8673	+	8.00626i	−0.461218	+	0.266284i
$905$	46.4875	+	26.8396i	1.54530	+	0.892178i
$906$	2.51392	−	2.99597i	0.0835193	−	0.0995345i
$907$	−9.39753	+	25.8195i	−0.312040	+	0.857323i	0.680205	+	0.733022i	$0.261891\pi$
$907$	−9.39753	+	25.8195i	−0.312040	+	0.857323i	−0.992245	+	0.124300i	$0.960331\pi$
$908$	−8.12143	+	2.95596i	−0.269519	+	0.0980969i
$909$	3.68920	+	4.39662i	0.122363	+	0.145827i
$910$	−6.41632	+	1.13137i	−0.212699	+	0.0375046i
$911$			58.5420i			1.93958i	0.243935	+	0.969791i	$0.421561\pi$
$911$			58.5420i			1.93958i	−0.243935	+	0.969791i	$0.578439\pi$
$912$	−13.7520	+	8.58575i	−0.455374	+	0.284303i
$913$	−18.6177	+	54.5516i	−0.616156	+	1.80539i
$914$	−6.35561	+	1.12067i	−0.210225	+	0.0370683i
$915$	−25.0048	+	20.9815i	−0.826634	+	0.693628i
$916$	−11.6122	+	4.22651i	−0.383679	+	0.139648i
$917$	−60.2292	−	21.9217i	−1.98894	−	0.723917i
$918$	−0.645313	−	0.541482i	−0.0212985	−	0.0178716i
$919$	−0.677193	−	0.390978i	−0.0223385	−	0.0128972i	0.488789	−	0.872402i	$-0.337439\pi$
$919$	−0.677193	−	0.390978i	−0.0223385	−	0.0128972i	−0.511128	+	0.859505i	$0.670772\pi$
$920$	−1.95800	−	3.39135i	−0.0645533	−	0.111810i
$921$	−3.28588	−	0.579389i	−0.108273	−	0.0190915i
$922$	−3.64883	−	0.643388i	−0.120168	−	0.0211888i
$923$	20.7100	−	11.9569i	0.681676	−	0.393566i
$924$	18.3175	−	16.0109i	0.602602	−	0.526720i
$925$	−0.0109398	+	0.0130375i	−0.000359698	+	0.000428672i
$926$	2.00135	+	0.728432i	0.0657684	+	0.0239377i
$927$	3.13973	+	8.62634i	0.103122	+	0.283326i
$928$	−2.54671	+	2.13695i	−0.0835999	+	0.0701487i
$929$	−4.48938	−	25.4605i	−0.147292	−	0.835332i	−0.965499	−	0.260409i	$-0.916143\pi$
$929$	−4.48938	−	25.4605i	−0.147292	−	0.835332i	0.818207	−	0.574924i	$-0.194968\pi$
$930$	−3.44722			−0.113039
$931$	29.4681	+	9.58747i	0.965778	+	0.314217i
$932$		−	51.4206i		−	1.68434i
$933$	25.8566	−	4.55921i	0.846506	−	0.149262i
$934$	3.35171	−	2.81242i	0.109671	−	0.0920252i
$935$	−0.575894	−	28.5411i	−0.0188338	−	0.933395i
$936$	2.90391	+	1.05694i	0.0949172	+	0.0345470i
$937$	10.8583	−	12.9405i	0.354727	−	0.422747i	−0.558942	−	0.829207i	$-0.688793\pi$
$937$	10.8583	−	12.9405i	0.354727	−	0.422747i	0.913669	+	0.406460i	$0.133237\pi$
$938$	−4.53396	+	7.85305i	−0.148039	+	0.256411i
$939$	10.1489	−	5.85948i	0.331198	−	0.191217i
$940$	−0.882389	+	5.00428i	−0.0287804	+	0.163222i
$941$	−6.95344	+	39.4349i	−0.226676	+	1.28554i	0.632780	+	0.774331i	$0.281914\pi$
$941$	−6.95344	+	39.4349i	−0.226676	+	1.28554i	−0.859456	+	0.511210i	$0.829197\pi$
$942$	−2.95297	+	1.70490i	−0.0962130	+	0.0555486i
$943$	−2.67204	+	4.62812i	−0.0870137	+	0.150712i
$944$	21.2585	−	25.3349i	0.691906	−	0.824582i
$945$	−7.83129	−	2.85036i	−0.254752	−	0.0927221i
$946$	−0.0307096	−	1.52196i	−0.000998454	−	0.0494831i
$947$	−38.8908	+	32.6332i	−1.26378	+	1.06044i	−0.268511	+	0.963277i	$0.586532\pi$
$947$	−38.8908	+	32.6332i	−1.26378	+	1.06044i	−0.995269	+	0.0971607i	$0.969024\pi$
$948$	30.4752	−	5.37360i	0.989788	−	0.174526i
$949$		−	19.1811i		−	0.622644i
$950$	0.0152114	+	0.0717012i	0.000493521	+	0.00232629i
$951$	−18.8636			−0.611694
$952$	−2.17195	−	12.3177i	−0.0703932	−	0.399219i
$953$	−16.4119	+	13.7712i	−0.531634	+	0.446094i	−0.868665	−	0.495399i	$-0.835022\pi$
$953$	−16.4119	+	13.7712i	−0.531634	+	0.446094i	0.337031	+	0.941494i	$0.390577\pi$
$954$	0.168216	+	0.462169i	0.00544619	+	0.0149633i
$955$	54.4730	+	19.8265i	1.76270	+	0.641572i
$956$	9.30732	−	11.0920i	0.301020	−	0.358742i
$957$	−2.87461	−	3.28874i	−0.0929230	−	0.106310i
$958$	−2.73787	+	1.58071i	−0.0884566	+	0.0510704i
$959$	−58.4373	−	10.3041i	−1.88704	−	0.332736i
$960$	15.0556	+	2.65470i	0.485916	+	0.0856801i
$961$	10.0987	+	17.4915i	0.325766	+	0.564243i
$962$	−0.148799	−	0.0859089i	−0.00479746	−	0.00276981i
$963$	−1.60984	−	1.35081i	−0.0518763	−	0.0435294i
$964$	11.2573	+	4.09732i	0.362573	+	0.131966i
$965$	−20.8471	+	7.58773i	−0.671092	+	0.244258i
$966$	1.28482	−	1.07809i	0.0413384	−	0.0346871i
$967$	−12.9619	+	2.28553i	−0.416826	+	0.0734977i	−0.378128	−	0.925753i	$-0.623432\pi$
$967$	−12.9619	+	2.28553i	−0.416826	+	0.0734977i	−0.0386979	+	0.999251i	$0.512321\pi$
$968$	7.47172	+	5.77232i	0.240150	+	0.185530i
$969$	−16.9000	+	0.583564i	−0.542905	+	0.0187468i
$970$			2.66963i			0.0857167i
$971$	−4.78251	+	0.843285i	−0.153478	+	0.0270623i	−0.249859	−	0.968282i	$-0.580384\pi$
$971$	−4.78251	+	0.843285i	−0.153478	+	0.0270623i	0.0963812	+	0.995344i	$0.469273\pi$
$972$	1.25527	+	1.49597i	0.0402627	+	0.0479832i
$973$	−23.3339	+	8.49283i	−0.748049	+	0.272268i
$974$	0.639983	−	1.75834i	0.0205064	−	0.0563408i
$975$	−0.179212	+	0.213576i	−0.00573937	+	0.00683991i
$976$	47.3879	+	27.3594i	1.51685	+	0.875754i
$977$	14.4169	−	8.32362i	0.461238	−	0.266296i	−0.251327	−	0.967902i	$-0.580867\pi$
$977$	14.4169	−	8.32362i	0.461238	−	0.266296i	0.712565	+	0.701606i	$0.247533\pi$
$978$	−1.11570	−	0.196729i	−0.0356762	−	0.00629068i
$979$	−32.9519	−	18.1485i	−1.05315	−	0.580028i
$980$	−15.4013	−	26.6759i	−0.491977	−	0.852130i
$981$	4.06696	−	7.04418i	0.129848	−	0.224903i
$982$	2.48397	−	2.96028i	0.0792665	−	0.0944662i
$983$	2.03229	−	5.58368i	0.0648201	−	0.178092i	−0.903054	−	0.429527i	$-0.858680\pi$
$983$	2.03229	−	5.58368i	0.0648201	−	0.178092i	0.967874	+	0.251435i	$0.0809025\pi$
$984$	0.762951	+	2.09619i	0.0243220	+	0.0668241i
$985$	−10.1235	−	12.0647i	−0.322560	−	0.384412i
$986$	−1.09258	+	0.192651i	−0.0347947	+	0.00613525i
$987$	−4.40533			−0.140223
$988$	28.4196	−	11.4694i	0.904148	−	0.364889i
$989$			4.34644i			0.138209i
$990$	0.245665	−	1.57887i	0.00780775	−	0.0501797i
$991$	23.5068	+	28.0143i	0.746719	+	0.889905i	0.996931	−	0.0782860i	$-0.0249447\pi$
$991$	23.5068	+	28.0143i	0.746719	+	0.889905i	−0.250212	+	0.968191i	$0.580500\pi$
$992$	6.17757	+	16.9727i	0.196138	+	0.538885i
$993$	1.84239	+	0.670574i	0.0584664	+	0.0212800i
$994$	−4.15016	−	3.48240i	−0.131635	−	0.110455i
$995$	6.05113	−	10.4809i	0.191834	−	0.332265i
$996$	−16.9697	−	29.3924i	−0.537706	−	0.931333i
$997$	−15.6075	−	2.75202i	−0.494294	−	0.0871573i	−0.0790558	−	0.996870i	$-0.525191\pi$
$997$	−15.6075	−	2.75202i	−0.494294	−	0.0871573i	−0.415238	+	0.909713i	$0.636302\pi$
$998$	0.569768	−	3.23132i	0.0180357	−	0.102286i
$999$	−0.109888	−	0.190332i	−0.00347671	−	0.00602184i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	627.2.be.a.10.18	✓	240
11.10	odd	2	inner	627.2.be.a.10.23	yes	240
19.2	odd	18	inner	627.2.be.a.439.23	yes	240
209.21	even	18	inner	627.2.be.a.439.18	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
627.2.be.a.10.18	✓	240	1.1	even	1	trivial
627.2.be.a.10.23	yes	240	11.10	odd	2	inner
627.2.be.a.439.18	yes	240	209.21	even	18	inner
627.2.be.a.439.23	yes	240	19.2	odd	18	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:	\( N \)	\(=\)	\( 627 = 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	627.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0377067 - 0.213846i) q^{2} +(-0.642788 - 0.766044i) q^{3} +(1.83508 - 0.667913i) q^{4} +(-2.08488 - 0.758835i) q^{5} +(-0.139578 + 0.166342i) q^{6} +(3.25299 + 1.87811i) q^{7} +(-0.429169 - 0.743343i) q^{8} +(-0.173648 + 0.984808i) q^{9} +(-0.0836593 + 0.474456i) q^{10} +(0.641700 + 3.25395i) q^{11} +(-1.69122 - 0.976424i) q^{12} +(2.75799 + 2.31423i) q^{13} +(0.278967 - 0.766455i) q^{14} +(0.758835 + 2.08488i) q^{15} +(2.84916 - 2.39073i) q^{16} +(3.82049 - 0.673656i) q^{17} +0.217144 q^{18} +(3.24043 - 2.91541i) q^{19} -4.33275 q^{20} +(-0.652262 - 3.69916i) q^{21} +(0.671647 - 0.259921i) q^{22} +(-1.93230 + 0.703298i) q^{23} +(-0.293569 + 0.806575i) q^{24} +(-0.0593218 - 0.0497769i) q^{25} +(0.390892 - 0.677045i) q^{26} +(0.866025 - 0.500000i) q^{27} +(7.22391 + 1.27377i) q^{28} +(0.228694 - 1.29699i) q^{29} +(0.417229 - 0.240887i) q^{30} +(-6.19662 - 3.57762i) q^{31} +(-1.93373 - 1.62259i) q^{32} +(2.08020 - 2.58317i) q^{33} +(-0.288117 - 0.791594i) q^{34} +(-5.35692 - 6.38413i) q^{35} +(0.339109 + 1.92318i) q^{36} -0.219776i q^{37} +(-0.745633 - 0.583021i) q^{38} -3.60030i q^{39} +(0.330693 + 1.87545i) q^{40} +(1.99086 - 1.67053i) q^{41} +(-0.766455 + 0.278967i) q^{42} +(0.722931 - 1.98624i) q^{43} +(3.35093 + 5.54266i) q^{44} +(1.10934 - 1.92144i) q^{45} +(0.223258 + 0.386694i) q^{46} +(0.203656 - 1.15499i) q^{47} +(-3.66281 - 0.645852i) q^{48} +(3.55463 + 6.15680i) q^{49} +(-0.00840774 + 0.0145626i) q^{50} +(-2.97181 - 2.49365i) q^{51} +(6.60682 + 2.40469i) q^{52} +(0.774672 + 2.12839i) q^{53} +(-0.139578 - 0.166342i) q^{54} +(1.13134 - 7.27105i) q^{55} -3.22412i q^{56} +(-4.31624 - 0.608324i) q^{57} -0.285978 q^{58} +(8.75698 - 1.54409i) q^{59} +(2.78504 + 3.31908i) q^{60} +(5.03183 + 13.8248i) q^{61} +(-0.531404 + 1.46002i) q^{62} +(-2.41446 + 2.87744i) q^{63} +(3.44524 - 5.96734i) q^{64} +(-3.99396 - 6.91774i) q^{65} +(-0.630837 - 0.347438i) q^{66} +(-10.9486 - 1.93053i) q^{67} +(6.56095 - 3.78797i) q^{68} +(1.78081 + 1.02815i) q^{69} +(-1.16323 + 1.38628i) q^{70} +(2.27176 - 6.24160i) q^{71} +(0.806575 - 0.293569i) q^{72} +(-3.42454 - 4.08121i) q^{73} +(-0.0469982 + 0.00828705i) q^{74} +0.0774392i q^{75} +(3.99920 - 7.51433i) q^{76} +(-4.02385 + 11.7903i) q^{77} +(-0.769907 + 0.135755i) q^{78} +(-12.1389 + 10.1858i) q^{79} +(-7.75433 + 2.82234i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(-0.432303 - 0.362746i) q^{82} +(15.0510 + 8.68972i) q^{83} +(-3.66767 - 6.35260i) q^{84} +(-8.47646 - 1.49463i) q^{85} +(-0.452007 - 0.0797011i) q^{86} +(-1.14055 + 0.658497i) q^{87} +(2.14341 - 1.87350i) q^{88} +(-7.29087 + 8.68892i) q^{89} +(-0.452720 - 0.164777i) q^{90} +(4.62532 + 12.7080i) q^{91} +(-3.07617 + 2.58121i) q^{92} +(1.24249 + 7.04654i) q^{93} -0.254668 q^{94} +(-8.96823 + 3.61933i) q^{95} +2.52431i q^{96} +(5.45706 - 0.962226i) q^{97} +(1.18257 - 0.992294i) q^{98} +(-3.31595 + 0.0669082i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 6 q^{11} - 48 q^{14} + 24 q^{15} - 216 q^{20} + 24 q^{26} - 36 q^{31} - 6 q^{33} - 132 q^{34} + 180 q^{38} + 12 q^{42} - 24 q^{44} - 12 q^{45} + 72 q^{47} + 48 q^{48} + 132 q^{49} + 108 q^{53} - 30 q^{55}+ \cdots - 12 q^{99}+O(q^{100}) \) 240 * q + 6 * q^11 - 48 * q^14 + 24 * q^15 - 216 * q^20 + 24 * q^26 - 36 * q^31 - 6 * q^33 - 132 * q^34 + 180 * q^38 + 12 * q^42 - 24 * q^44 - 12 * q^45 + 72 * q^47 + 48 * q^48 + 132 * q^49 + 108 * q^53 - 30 * q^55 - 24 * q^58 + 48 * q^60 - 120 * q^64 - 48 * q^66 + 48 * q^67 - 228 * q^70 - 84 * q^71 - 72 * q^77 + 84 * q^78 - 24 * q^80 - 156 * q^82 + 48 * q^86 + 108 * q^88 + 144 * q^89 - 24 * q^91 - 60 * q^92 - 24 * q^93 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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