LMFDB - Embedded newform 555.2.bb.a.454.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [555,2,Mod(454,555)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(555, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("555.454");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 555 = 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	555.bb (of order $6$, degree $2$, 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:	$4.43169731218$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			454.17
Character	$\chi$	$=$	555.454
Dual form			555.2.bb.a.544.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.153667 - 0.0887196i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.984258 - 1.70478i) q^{4} +(2.22191 + 0.251234i) q^{5} -0.177439 q^{6} +(-1.07771 + 0.622215i) q^{7} +0.704171i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.153667 - 0.0887196i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.984258 - 1.70478i) q^{4} +(2.22191 + 0.251234i) q^{5} -0.177439 q^{6} +(-1.07771 + 0.622215i) q^{7} +0.704171i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.319145 - 0.235733i) q^{10} +1.60162 q^{11} +(-1.70478 - 0.984258i) q^{12} +(4.18407 - 2.41567i) q^{13} +0.220811 q^{14} +(2.04985 - 0.893380i) q^{15} +(-1.90604 + 3.30136i) q^{16} +(3.79020 + 2.18827i) q^{17} +(-0.153667 + 0.0887196i) q^{18} +(-3.05983 - 5.29977i) q^{19} +(-1.75863 - 4.03515i) q^{20} +(-0.622215 + 1.07771i) q^{21} +(-0.246116 - 0.142095i) q^{22} -5.94293i q^{23} +(0.352085 + 0.609830i) q^{24} +(4.87376 + 1.11644i) q^{25} -0.857270 q^{26} -1.00000i q^{27} +(2.12148 + 1.22484i) q^{28} -2.75303 q^{29} +(-0.394254 - 0.0445787i) q^{30} -8.35380 q^{31} +(1.80545 - 1.04238i) q^{32} +(1.38704 - 0.800808i) q^{33} +(-0.388285 - 0.672530i) q^{34} +(-2.55089 + 1.11175i) q^{35} -1.96852 q^{36} +(4.85655 + 3.66250i) q^{37} +1.08587i q^{38} +(2.41567 - 4.18407i) q^{39} +(-0.176911 + 1.56460i) q^{40} +(-2.39040 - 4.14029i) q^{41} +(0.191228 - 0.110405i) q^{42} +0.801301i q^{43} +(-1.57640 - 2.73041i) q^{44} +(1.32853 - 1.79861i) q^{45} +(-0.527255 + 0.913232i) q^{46} +1.04257i q^{47} +3.81208i q^{48} +(-2.72570 + 4.72105i) q^{49} +(-0.649886 - 0.603958i) q^{50} +4.37654 q^{51} +(-8.23640 - 4.75529i) q^{52} +(-4.49825 - 2.59707i) q^{53} +(-0.0887196 + 0.153667i) q^{54} +(3.55865 + 0.402380i) q^{55} +(-0.438145 - 0.758890i) q^{56} +(-5.29977 - 3.05983i) q^{57} +(0.423050 + 0.244248i) q^{58} +(3.61723 - 6.26522i) q^{59} +(-3.54060 - 2.61523i) q^{60} +(5.46984 + 9.47405i) q^{61} +(1.28370 + 0.741147i) q^{62} +1.24443i q^{63} +7.25425 q^{64} +(9.90352 - 4.31623i) q^{65} -0.284190 q^{66} +(5.32007 - 3.07154i) q^{67} -8.61529i q^{68} +(-2.97147 - 5.14673i) q^{69} +(0.490622 + 0.0554751i) q^{70} +(4.18274 + 7.24471i) q^{71} +(0.609830 + 0.352085i) q^{72} +7.83796i q^{73} +(-0.421356 - 0.993677i) q^{74} +(4.77902 - 1.47002i) q^{75} +(-6.02331 + 10.4327i) q^{76} +(-1.72608 + 0.996550i) q^{77} +(-0.742418 + 0.428635i) q^{78} +(4.34432 + 7.52458i) q^{79} +(-5.06446 + 6.85646i) q^{80} +(-0.500000 - 0.866025i) q^{81} +0.848300i q^{82} +(3.42666 + 1.97838i) q^{83} +2.44968 q^{84} +(7.87171 + 5.81436i) q^{85} +(0.0710911 - 0.123133i) q^{86} +(-2.38420 + 1.37652i) q^{87} +1.12781i q^{88} +(2.56056 - 4.43502i) q^{89} +(-0.363723 + 0.158521i) q^{90} +(-3.00613 + 5.20678i) q^{91} +(-10.1314 + 5.84938i) q^{92} +(-7.23461 + 4.17690i) q^{93} +(0.0924966 - 0.160209i) q^{94} +(-5.46717 - 12.5443i) q^{95} +(1.04238 - 1.80545i) q^{96} +9.76941i q^{97} +(0.837699 - 0.483646i) q^{98} +(0.800808 - 1.38704i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9}+O(q^{10}) $ 72 * q + 32 * q^4 - 2 * q^5 + 36 * q^9	$ 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9} - 8 q^{11} - 16 q^{14} - 24 q^{16} + 4 q^{19} + 4 q^{20} + 12 q^{21} + 10 q^{25} + 24 q^{26} + 16 q^{29} + 12 q^{30} + 24 q^{31} - 44 q^{34} - 2 q^{35} + 64 q^{36} - 8 q^{39} + 46 q^{40} - 48 q^{41} - 8 q^{44} - 4 q^{45} - 64 q^{46} + 32 q^{49} - 46 q^{50} - 8 q^{51} - 12 q^{55} - 72 q^{56} + 32 q^{59} - 68 q^{60} - 8 q^{61} - 136 q^{64} - 42 q^{65} - 32 q^{66} - 4 q^{69} + 4 q^{70} + 12 q^{71} - 96 q^{74} - 8 q^{75} + 8 q^{76} - 8 q^{79} - 44 q^{80} - 36 q^{81} + 136 q^{84} + 4 q^{85} + 8 q^{86} + 8 q^{91} - 28 q^{94} + 18 q^{95} - 20 q^{96} - 4 q^{99}+O(q^{100}) $ 72 * q + 32 * q^4 - 2 * q^5 + 36 * q^9 - 8 * q^11 - 16 * q^14 - 24 * q^16 + 4 * q^19 + 4 * q^20 + 12 * q^21 + 10 * q^25 + 24 * q^26 + 16 * q^29 + 12 * q^30 + 24 * q^31 - 44 * q^34 - 2 * q^35 + 64 * q^36 - 8 * q^39 + 46 * q^40 - 48 * q^41 - 8 * q^44 - 4 * q^45 - 64 * q^46 + 32 * q^49 - 46 * q^50 - 8 * q^51 - 12 * q^55 - 72 * q^56 + 32 * q^59 - 68 * q^60 - 8 * q^61 - 136 * q^64 - 42 * q^65 - 32 * q^66 - 4 * q^69 + 4 * q^70 + 12 * q^71 - 96 * q^74 - 8 * q^75 + 8 * q^76 - 8 * q^79 - 44 * q^80 - 36 * q^81 + 136 * q^84 + 4 * q^85 + 8 * q^86 + 8 * q^91 - 28 * q^94 + 18 * q^95 - 20 * q^96 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/555\mathbb{Z}\right)^\times$.

$n$	$76$	$112$	$371$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

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 $

$2$	−0.153667	−	0.0887196i	−0.108659	−	0.0627343i	0.444686	−	0.895687i	$-0.353315\pi$
$2$	−0.153667	−	0.0887196i	−0.108659	−	0.0627343i	−0.553345	+	0.832952i	$0.686649\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−0.984258	−	1.70478i	−0.492129	−	0.852392i
$5$	2.22191	+	0.251234i	0.993668	+	0.112355i
$5$	2.22191	+	0.251234i	0.993668	+	0.112355i
$6$	−0.177439			−0.0724393
$7$	−1.07771	+	0.622215i	−0.407335	+	0.235175i	−0.689644	−	0.724148i	$-0.742233\pi$
$7$	−1.07771	+	0.622215i	−0.407335	+	0.235175i	0.282309	+	0.959324i	$0.408900\pi$
$8$			0.704171i			0.248962i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−0.319145	−	0.235733i	−0.100922	−	0.0745454i
$11$	1.60162			0.482906			0.241453	−	0.970413i	$-0.422376\pi$
$11$	1.60162			0.482906			0.241453	+	0.970413i	$0.422376\pi$
$12$	−1.70478	−	0.984258i	−0.492129	−	0.284131i
$13$	4.18407	−	2.41567i	1.16045	−	0.669987i	0.209039	−	0.977907i	$-0.432966\pi$
$13$	4.18407	−	2.41567i	1.16045	−	0.669987i	0.951412	+	0.307920i	$0.0996330\pi$
$14$	0.220811			0.0590142
$15$	2.04985	−	0.893380i	0.529268	−	0.230670i
$16$	−1.90604	+	3.30136i	−0.476510	+	0.825340i
$17$	3.79020	+	2.18827i	0.919258	+	0.530734i	0.883398	−	0.468623i	$-0.155250\pi$
$17$	3.79020	+	2.18827i	0.919258	+	0.530734i	0.0358594	+	0.999357i	$0.488583\pi$
$18$	−0.153667	+	0.0887196i	−0.0362196	+	0.0209114i
$19$	−3.05983	−	5.29977i	−0.701972	−	1.21585i	−0.967773	−	0.251823i	$-0.918970\pi$
$19$	−3.05983	−	5.29977i	−0.701972	−	1.21585i	0.265801	−	0.964028i	$-0.414364\pi$
$20$	−1.75863	−	4.03515i	−0.393242	−	0.902288i
$21$	−0.622215	+	1.07771i	−0.135778	+	0.235175i
$22$	−0.246116	−	0.142095i	−0.0524720	−	0.0302947i
$23$		−	5.94293i		−	1.23919i	−0.784923	−	0.619593i	$-0.787297\pi$
$23$		−	5.94293i		−	1.23919i	0.784923	−	0.619593i	$-0.212703\pi$
$24$	0.352085	+	0.609830i	0.0718691	+	0.124481i
$25$	4.87376	+	1.11644i	0.974753	+	0.223287i
$26$	−0.857270			−0.168125
$27$		−	1.00000i		−	0.192450i
$28$	2.12148	+	1.22484i	0.400923	+	0.231473i
$29$	−2.75303			−0.511226			−0.255613	−	0.966779i	$-0.582277\pi$
$29$	−2.75303			−0.511226			−0.255613	+	0.966779i	$0.582277\pi$
$30$	−0.394254	−	0.0445787i	−0.0719806	−	0.00813892i
$31$	−8.35380			−1.50039			−0.750194	−	0.661218i	$-0.770040\pi$
$31$	−8.35380			−1.50039			−0.750194	+	0.661218i	$0.770040\pi$
$32$	1.80545	−	1.04238i	0.319162	−	0.184268i
$33$	1.38704	−	0.800808i	0.241453	−	0.139403i
$34$	−0.388285	−	0.672530i	−0.0665904	−	0.115338i
$35$	−2.55089	+	1.11175i	−0.431179	+	0.187920i
$36$	−1.96852			−0.328086
$37$	4.85655	+	3.66250i	0.798412	+	0.602111i
$37$	4.85655	+	3.66250i	0.798412	+	0.602111i
$38$			1.08587i			0.176151i
$39$	2.41567	−	4.18407i	0.386817	−	0.669987i
$40$	−0.176911	+	1.56460i	−0.0279721	+	0.247385i
$41$	−2.39040	−	4.14029i	−0.373317	−	0.646604i	0.616756	−	0.787154i	$-0.288446\pi$
$41$	−2.39040	−	4.14029i	−0.373317	−	0.646604i	−0.990074	+	0.140550i	$0.955113\pi$
$42$	0.191228	−	0.110405i	0.0295071	−	0.0170359i
$43$			0.801301i			0.122197i	0.998132	+	0.0610986i	$0.0194604\pi$
$43$			0.801301i			0.122197i	−0.998132	+	0.0610986i	$0.980540\pi$
$44$	−1.57640	−	2.73041i	−0.237652	−	0.411625i
$45$	1.32853	−	1.79861i	0.198045	−	0.268121i
$46$	−0.527255	+	0.913232i	−0.0777395	+	0.134649i
$47$			1.04257i			0.152075i	0.997105	+	0.0760374i	$0.0242268\pi$
$47$			1.04257i			0.152075i	−0.997105	+	0.0760374i	$0.975773\pi$
$48$			3.81208i			0.550227i
$49$	−2.72570	+	4.72105i	−0.389385	+	0.674435i
$50$	−0.649886	−	0.603958i	−0.0919078	−	0.0854126i
$51$	4.37654			0.612838
$52$	−8.23640	−	4.75529i	−1.14218	−	0.659440i
$53$	−4.49825	−	2.59707i	−0.617883	−	0.356735i	0.158162	−	0.987413i	$-0.449443\pi$
$53$	−4.49825	−	2.59707i	−0.617883	−	0.356735i	−0.776044	+	0.630679i	$0.782777\pi$
$54$	−0.0887196	+	0.153667i	−0.0120732	+	0.0209114i
$55$	3.55865	+	0.402380i	0.479848	+	0.0542569i
$56$	−0.438145	−	0.758890i	−0.0585497	−	0.101411i
$57$	−5.29977	−	3.05983i	−0.701972	−	0.405284i
$58$	0.423050	+	0.244248i	0.0555492	+	0.0320714i
$59$	3.61723	−	6.26522i	0.470923	−	0.815662i	−0.528524	−	0.848918i	$-0.677254\pi$
$59$	3.61723	−	6.26522i	0.470923	−	0.815662i	0.999447	+	0.0332559i	$0.0105876\pi$
$60$	−3.54060	−	2.61523i	−0.457089	−	0.337625i
$61$	5.46984	+	9.47405i	0.700342	+	1.21303i	0.968346	+	0.249610i	$0.0803024\pi$
$61$	5.46984	+	9.47405i	0.700342	+	1.21303i	−0.268005	+	0.963418i	$0.586364\pi$
$62$	1.28370	+	0.741147i	0.163031	+	0.0941257i
$63$			1.24443i			0.156783i
$64$	7.25425			0.906781
$65$	9.90352	−	4.31623i	1.22838	−	0.535362i
$66$	−0.284190			−0.0349813
$67$	5.32007	−	3.07154i	0.649950	−	0.375249i	−0.138487	−	0.990364i	$-0.544224\pi$
$67$	5.32007	−	3.07154i	0.649950	−	0.375249i	0.788437	+	0.615115i	$0.210891\pi$
$68$		−	8.61529i		−	1.04476i
$69$	−2.97147	−	5.14673i	−0.357722	−	0.619593i
$70$	0.490622	+	0.0554751i	0.0586405	+	0.00663054i
$71$	4.18274	+	7.24471i	0.496399	+	0.859789i	0.999991	−	0.00415264i	$-0.00132183\pi$
$71$	4.18274	+	7.24471i	0.496399	+	0.859789i	−0.503592	+	0.863942i	$0.667988\pi$
$72$	0.609830	+	0.352085i	0.0718691	+	0.0414936i
$73$			7.83796i			0.917364i	0.888600	+	0.458682i	$0.151678\pi$
$73$			7.83796i			0.917364i	−0.888600	+	0.458682i	$0.848322\pi$
$74$	−0.421356	−	0.993677i	−0.0489816	−	0.115513i
$75$	4.77902	−	1.47002i	0.551834	−	0.169743i
$76$	−6.02331	+	10.4327i	−0.690921	+	1.19671i
$77$	−1.72608	+	0.996550i	−0.196705	+	0.113567i
$78$	−0.742418	+	0.428635i	−0.0840623	+	0.0485334i
$79$	4.34432	+	7.52458i	0.488774	+	0.846582i	0.999917	−	0.0129142i	$-0.00411084\pi$
$79$	4.34432	+	7.52458i	0.488774	+	0.846582i	−0.511142	+	0.859496i	$0.670778\pi$
$80$	−5.06446	+	6.85646i	−0.566224	+	0.766576i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$			0.848300i			0.0936791i
$83$	3.42666	+	1.97838i	0.376125	+	0.217156i	0.676131	−	0.736781i	$-0.263655\pi$
$83$	3.42666	+	1.97838i	0.376125	+	0.217156i	−0.300006	+	0.953937i	$0.596989\pi$
$84$	2.44968			0.267282
$85$	7.87171	+	5.81436i	0.853806	+	0.630656i
$86$	0.0710911	−	0.123133i	0.00766595	−	0.0132778i
$87$	−2.38420	+	1.37652i	−0.255613	+	0.147578i
$88$			1.12781i			0.120225i
$89$	2.56056	−	4.43502i	0.271419	−	0.470111i	−0.697807	−	0.716286i	$-0.745841\pi$
$89$	2.56056	−	4.43502i	0.271419	−	0.470111i	0.969225	+	0.246175i	$0.0791739\pi$
$90$	−0.363723	+	0.158521i	−0.0383398	+	0.0167096i
$91$	−3.00613	+	5.20678i	−0.315129	+	0.545819i
$92$	−10.1314	+	5.84938i	−1.05627	+	0.609840i
$93$	−7.23461	+	4.17690i	−0.750194	+	0.433125i
$94$	0.0924966	−	0.160209i	0.00954030	−	0.0165243i
$95$	−5.46717	−	12.5443i	−0.560920	−	1.28702i
$96$	1.04238	−	1.80545i	0.106387	−	0.184268i
$97$			9.76941i			0.991934i	0.868341	+	0.495967i	$0.165186\pi$
$97$			9.76941i			0.991934i	−0.868341	+	0.495967i	$0.834814\pi$
$98$	0.837699	−	0.483646i	0.0846204	−	0.0488556i
$99$	0.800808	−	1.38704i	0.0804843	−	0.139403i
$100$	−2.89376	−	9.40758i	−0.289376	−	0.940758i
$101$	−4.65886			−0.463574			−0.231787	−	0.972767i	$-0.574457\pi$
$101$	−4.65886			−0.463574			−0.231787	+	0.972767i	$0.574457\pi$
$102$	−0.672530	−	0.388285i	−0.0665904	−	0.0384460i
$103$			7.68026i			0.756759i	0.925651	+	0.378379i	$0.123519\pi$
$103$			7.68026i			0.756759i	−0.925651	+	0.378379i	$0.876481\pi$
$104$	1.70105	+	2.94630i	0.166801	+	0.288908i
$105$	−1.65326	+	2.23825i	−0.161342	+	0.218431i
$106$	0.460822	+	0.798167i	0.0447590	+	0.0775248i
$107$	−2.78357	+	1.60710i	−0.269098	+	0.155364i	−0.628478	−	0.777828i	$-0.716322\pi$
$107$	−2.78357	+	1.60710i	−0.269098	+	0.155364i	0.359380	+	0.933191i	$0.382988\pi$
$108$	−1.70478	+	0.984258i	−0.164043	+	0.0947102i
$109$	−1.93720	+	3.35533i	−0.185550	+	0.321383i	−0.943762	−	0.330626i	$-0.892740\pi$
$109$	−1.93720	+	3.35533i	−0.185550	+	0.321383i	0.758212	+	0.652009i	$0.226073\pi$
$110$	−0.511147	−	0.377554i	−0.0487360	−	0.0359984i
$111$	6.03715	+	0.743542i	0.573021	+	0.0705739i
$112$		−	4.74387i		−	0.448254i
$113$	−9.47851	−	5.47242i	−0.891663	−	0.514802i	−0.0171769	−	0.999852i	$-0.505468\pi$
$113$	−9.47851	−	5.47242i	−0.891663	−	0.514802i	−0.874486	+	0.485051i	$0.838801\pi$
$114$	0.542933	+	0.940388i	0.0508504	+	0.0880754i
$115$	1.49306	−	13.2047i	0.139229	−	1.23134i
$116$	2.70969	+	4.69333i	0.251589	+	0.435765i
$117$		−	4.83134i		−	0.446658i
$118$	−1.11170	+	0.641838i	−0.102340	+	0.0590860i
$119$	−5.44630			−0.499261
$120$	0.629092	+	1.44344i	0.0574280	+	0.131768i
$121$	−8.43482			−0.766802
$122$		−	1.94113i		−	0.175742i
$123$	−4.14029	−	2.39040i	−0.373317	−	0.215535i
$124$	8.22230	+	14.2414i	0.738384	+	1.27892i
$125$	10.5486	+	3.70507i	0.943493	+	0.331392i
$126$	0.110405	−	0.191228i	0.00983569	−	0.0170359i
$127$	2.88400	+	1.66508i	0.255913	+	0.147752i	0.622469	−	0.782645i	$-0.286130\pi$
$127$	2.88400	+	1.66508i	0.255913	+	0.147752i	−0.366556	+	0.930396i	$0.619463\pi$
$128$	−4.72564	−	2.72835i	−0.417691	−	0.241154i
$129$	0.400650	+	0.693947i	0.0352753	+	0.0610986i
$130$	−1.90478	−	0.215375i	−0.167060	−	0.0188896i
$131$	−11.0040	+	19.0595i	−0.961424	+	1.66524i	−0.242494	+	0.970153i	$0.577965\pi$
$131$	−11.0040	+	19.0595i	−0.961424	+	1.66524i	−0.718930	+	0.695082i	$0.755368\pi$
$132$	−2.73041	−	1.57640i	−0.237652	−	0.137208i
$133$	6.59520	+	3.80774i	0.571876	+	0.330173i
$134$	−1.09003			−0.0941638
$135$	0.251234	−	2.22191i	0.0216227	−	0.191232i
$136$	−1.54092	+	2.66894i	−0.132132	+	0.228860i
$137$			15.6815i			1.33976i	0.742470	+	0.669880i	$0.233654\pi$
$137$			15.6815i			1.33976i	−0.742470	+	0.669880i	$0.766346\pi$
$138$			1.05451i			0.0897658i
$139$	−3.31933	+	5.74925i	−0.281542	+	0.487645i	−0.971765	−	0.235952i	$-0.924179\pi$
$139$	−3.31933	+	5.74925i	−0.281542	+	0.487645i	0.690223	+	0.723597i	$0.257512\pi$
$140$	4.40603	+	3.25447i	0.372377	+	0.275053i
$141$	0.521286	+	0.902894i	0.0439002	+	0.0760374i
$142$		−	1.48436i		−	0.124565i
$143$	6.70127	−	3.86898i	0.560388	−	0.323540i
$144$	1.90604	+	3.30136i	0.158837	+	0.275113i
$145$	−6.11699	−	0.691655i	−0.507989	−	0.0574388i
$146$	0.695381	−	1.20444i	0.0575502	−	0.0996798i
$147$			5.45139i			0.449623i
$148$	1.46367	−	11.8842i	0.120313	−	0.976877i
$149$	17.1563			1.40550			0.702751	−	0.711435i	$-0.251955\pi$
$149$	17.1563			1.40550			0.702751	+	0.711435i	$0.251955\pi$
$150$	−0.864797	−	0.198100i	−0.0706104	−	0.0161748i
$151$	−6.55972	−	11.3618i	−0.533822	−	0.924607i	−0.999219	−	0.0395053i	$-0.987422\pi$
$151$	−6.55972	−	11.3618i	−0.533822	−	0.924607i	0.465397	−	0.885102i	$-0.345912\pi$
$152$	3.73194	−	2.15464i	0.302701	−	0.174764i
$153$	3.79020	−	2.18827i	0.306419	−	0.176911i
$154$	0.353654			0.0284983
$155$	−18.5614	−	2.09876i	−1.49089	−	0.168576i
$156$	−9.51058			−0.761455
$157$	−11.1160	−	6.41781i	−0.887151	−	0.512197i	−0.0141412	−	0.999900i	$-0.504501\pi$
$157$	−11.1160	−	6.41781i	−0.887151	−	0.512197i	−0.873009	+	0.487703i	$0.837835\pi$
$158$		−	1.54171i		−	0.122652i
$159$	−5.19413			−0.411922
$160$	4.27343	−	1.86248i	0.337844	−	0.147242i
$161$	3.69778	+	6.40474i	0.291426	+	0.504765i
$162$			0.177439i			0.0139409i
$163$	−14.0212	−	8.09513i	−1.09822	−	0.634059i	−0.162469	−	0.986714i	$-0.551946\pi$
$163$	−14.0212	−	8.09513i	−1.09822	−	0.634059i	−0.935754	+	0.352654i	$0.885279\pi$
$164$	−4.70553	+	8.15022i	−0.367440	+	0.636425i
$165$	3.28307	−	1.43085i	0.255587	−	0.111392i
$166$	−0.351043	−	0.608024i	−0.0272462	−	0.0471918i
$167$	11.2105	−	6.47240i	0.867497	−	0.500849i	0.000981055	−	1.00000i	$-0.499688\pi$
$167$	11.2105	−	6.47240i	0.867497	−	0.500849i	0.866516	+	0.499150i	$0.166354\pi$
$168$	−0.758890	−	0.438145i	−0.0585497	−	0.0338037i
$169$	5.17094	−	8.95634i	0.397765	−	0.688949i
$170$	−0.693773	−	1.59185i	−0.0532099	−	0.122089i
$171$	−6.11965			−0.467981
$172$	1.36604	−	0.788686i	0.104160	−	0.0601368i
$173$	−8.56133	−	4.94288i	−0.650906	−	0.375801i	0.137897	−	0.990447i	$-0.455966\pi$
$173$	−8.56133	−	4.94288i	−0.650906	−	0.375801i	−0.788803	+	0.614646i	$0.789299\pi$
$174$	0.488496			0.0370328
$175$	−5.94716	+	1.82934i	−0.449563	+	0.138285i
$176$	−3.05275	+	5.28751i	−0.230110	+	0.398561i
$177$		−	7.23446i		−	0.543775i
$178$	−0.786946	+	0.454343i	−0.0589841	+	0.0340545i
$179$	18.2281			1.36243			0.681215	−	0.732083i	$-0.261452\pi$
$179$	18.2281			1.36243			0.681215	+	0.732083i	$0.261452\pi$
$180$	−4.37386	−	0.494557i	−0.326008	−	0.0368621i
$181$	6.86138	+	11.8843i	0.510003	+	0.883351i	0.999933	+	0.0115889i	$0.00368894\pi$
$181$	6.86138	+	11.8843i	0.510003	+	0.883351i	−0.489930	+	0.871762i	$0.662978\pi$
$182$	0.923887	−	0.533406i	0.0684831	−	0.0395387i
$183$	9.47405	+	5.46984i	0.700342	+	0.404343i
$184$	4.18484			0.308510
$185$	9.87068	+	9.35787i	0.725706	+	0.688004i
$186$	1.48229			0.108687
$187$	6.07044	+	3.50477i	0.443915	+	0.256294i
$188$	1.77736	−	1.02616i	0.129627	−	0.0748404i
$189$	0.622215	+	1.07771i	0.0452595	+	0.0783917i
$190$	−0.272806	+	2.41270i	−0.0197914	+	0.175035i
$191$	−26.2695			−1.90080			−0.950398	−	0.311037i	$-0.899324\pi$
$191$	−26.2695			−1.90080			−0.950398	+	0.311037i	$0.899324\pi$
$192$	6.28236	−	3.62712i	0.453391	−	0.261765i
$193$			21.8435i			1.57233i	0.618017	+	0.786164i	$0.287936\pi$
$193$			21.8435i			1.57233i	−0.618017	+	0.786164i	$0.712064\pi$
$194$	0.866739	−	1.50124i	0.0622282	−	0.107782i
$195$	6.41858	−	8.68972i	0.459644	−	0.622284i
$196$	10.7312			0.766511
$197$	2.09682	+	1.21060i	0.149392	+	0.0862515i	0.572833	−	0.819672i	$-0.305844\pi$
$197$	2.09682	+	1.21060i	0.149392	+	0.0862515i	−0.423441	+	0.905924i	$0.639178\pi$
$198$	−0.246116	+	0.142095i	−0.0174907	+	0.0100982i
$199$	−19.7541			−1.40033			−0.700166	−	0.713980i	$-0.746891\pi$
$199$	−19.7541			−1.40033			−0.700166	+	0.713980i	$0.746891\pi$
$200$	−0.786162	+	3.43196i	−0.0555900	+	0.242676i
$201$	3.07154	−	5.32007i	0.216650	−	0.375249i
$202$	0.715912	+	0.413332i	0.0503714	+	0.0290819i
$203$	2.96697	−	1.71298i	0.208240	−	0.120228i
$204$	−4.30764	−	7.46106i	−0.301595	−	0.522379i
$205$	−4.27106	−	9.79989i	−0.298304	−	0.684454i
$206$	0.681390	−	1.18020i	0.0474747	−	0.0822286i
$207$	−5.14673	−	2.97147i	−0.357722	−	0.206531i
$208$			18.4175i			1.27702i
$209$	−4.90067	−	8.48820i	−0.338986	−	0.587141i
$210$	0.452628	−	0.197268i	0.0312343	−	0.0136128i
$211$	9.35301			0.643888			0.321944	−	0.946759i	$-0.395664\pi$
$211$	9.35301			0.643888			0.321944	+	0.946759i	$0.395664\pi$
$212$			10.2247i			0.702238i
$213$	7.24471	+	4.18274i	0.496399	+	0.286596i
$214$	0.570324			0.0389866
$215$	−0.201314	+	1.78042i	−0.0137295	+	0.121423i
$216$	0.704171			0.0479127
$217$	9.00296	−	5.19786i	0.611161	−	0.352854i
$218$	0.595368	−	0.343736i	0.0403234	−	0.0232807i
$219$	3.91898	+	6.78787i	0.264820	+	0.458682i
$220$	−2.81665	−	6.46277i	−0.189899	−	0.435720i
$221$	21.1446			1.42234
$222$	−0.861743	−	0.649871i	−0.0578364	−	0.0436165i
$223$			18.5715i			1.24364i	0.783161	+	0.621819i	$0.213606\pi$
$223$			18.5715i			1.24364i	−0.783161	+	0.621819i	$0.786394\pi$
$224$	−1.29717	+	2.24676i	−0.0866705	+	0.150118i
$225$	3.40374	−	3.66258i	0.226916	−	0.244172i
$226$	0.971022	+	1.68186i	0.0645914	+	0.111876i
$227$	17.6703	−	10.2019i	1.17282	−	0.677127i	0.218476	−	0.975842i	$-0.429892\pi$
$227$	17.6703	−	10.2019i	1.17282	−	0.677127i	0.954342	+	0.298716i	$0.0965582\pi$
$228$			12.0466i			0.797807i
$229$	−11.9999	−	20.7845i	−0.792976	−	1.37348i	−0.924116	−	0.382112i	$-0.875197\pi$
$229$	−11.9999	−	20.7845i	−0.792976	−	1.37348i	0.131140	−	0.991364i	$-0.458136\pi$
$230$	−1.40095	+	1.89665i	−0.0923757	+	0.125062i
$231$	−0.996550	+	1.72608i	−0.0655682	+	0.113567i
$232$		−	1.93861i		−	0.127276i
$233$		−	16.7836i		−	1.09953i	−0.835320	−	0.549764i	$-0.814718\pi$
$233$		−	16.7836i		−	1.09953i	0.835320	−	0.549764i	$-0.185282\pi$
$234$	−0.428635	+	0.742418i	−0.0280208	+	0.0485334i
$235$	−0.261929	+	2.31650i	−0.0170864	+	0.151112i
$236$	−14.2411			−0.927019
$237$	7.52458	+	4.34432i	0.488774	+	0.282194i
$238$	0.836916	+	0.483194i	0.0542492	+	0.0313208i
$239$	−11.9060	+	20.6218i	−0.770134	+	1.33391i	0.167355	+	0.985897i	$0.446477\pi$
$239$	−11.9060	+	20.6218i	−0.770134	+	1.33391i	−0.937489	+	0.348014i	$0.886856\pi$
$240$	−0.957723	+	8.47010i	−0.0618208	+	0.546743i
$241$	−6.04698	−	10.4737i	−0.389520	−	0.674669i	0.602865	−	0.797843i	$-0.294026\pi$
$241$	−6.04698	−	10.4737i	−0.389520	−	0.674669i	−0.992385	+	0.123174i	$0.960693\pi$
$242$	1.29615	+	0.748335i	0.0833199	+	0.0481048i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	10.7675	−	18.6498i	0.689317	−	1.19393i
$245$	−7.24234	+	9.80495i	−0.462696	+	0.626415i
$246$	0.424150	+	0.734650i	0.0270428	+	0.0468396i
$247$	−25.6050	−	14.7831i	−1.62921	−	0.940624i
$248$		−	5.88250i		−	0.373539i
$249$	3.95677			0.250750
$250$	−1.29225	−	1.50521i	−0.0817293	−	0.0951980i
$251$	9.17274			0.578978			0.289489	−	0.957181i	$-0.406515\pi$
$251$	9.17274			0.578978			0.289489	+	0.957181i	$0.406515\pi$
$252$	2.12148	−	1.22484i	0.133641	−	0.0771577i
$253$		−	9.51830i		−	0.598410i
$254$	−0.295450	−	0.511734i	−0.0185382	−	0.0321091i
$255$	9.72428	+	1.09953i	0.608958	+	0.0688555i
$256$	−6.77013	−	11.7262i	−0.423133	−	0.732888i
$257$	23.9296	+	13.8158i	1.49269	+	0.861804i	0.999965	−	0.00838187i	$-0.00266806\pi$
$257$	23.9296	+	13.8158i	1.49269	+	0.861804i	0.492724	+	0.870186i	$0.336001\pi$
$258$		−	0.142182i		−	0.00885188i
$259$	−7.51281	−	0.925286i	−0.466823	−	0.0574945i
$260$	−17.1058	−	12.6351i	−1.06086	−	0.783594i
$261$	−1.37652	+	2.38420i	−0.0852043	+	0.147578i
$262$	3.38190	−	1.95254i	0.208935	−	0.120628i
$263$	1.80239	−	1.04061i	0.111140	−	0.0641668i	−0.443399	−	0.896324i	$-0.646228\pi$
$263$	1.80239	−	1.04061i	0.111140	−	0.0641668i	0.554540	+	0.832157i	$0.312894\pi$
$264$	0.563906	+	0.976713i	0.0347060	+	0.0601125i
$265$	−9.34224	−	6.90056i	−0.573889	−	0.423898i
$266$	−0.675642	−	1.17025i	−0.0414263	−	0.0717524i
$267$		−	5.12111i		−	0.313407i
$268$	−10.4726	−	6.04638i	−0.639718	−	0.369342i
$269$	6.44316			0.392846			0.196423	−	0.980519i	$-0.437067\pi$
$269$	6.44316			0.392846			0.196423	+	0.980519i	$0.437067\pi$
$270$	−0.235733	+	0.319145i	−0.0143463	+	0.0194225i
$271$	2.90218	−	5.02673i	0.176295	−	0.305352i	−0.764314	−	0.644845i	$-0.776922\pi$
$271$	2.90218	−	5.02673i	0.176295	−	0.305352i	0.940609	+	0.339493i	$0.110255\pi$
$272$	−14.4485	+	8.34187i	−0.876072	+	0.505800i
$273$			6.01227i			0.363879i
$274$	1.39126	−	2.40973i	0.0840488	−	0.145577i
$275$	7.80590	+	1.78810i	0.470714	+	0.107827i
$276$	−5.84938	+	10.1314i	−0.352091	+	0.609840i
$277$	8.43689	−	4.87104i	0.506923	−	0.292672i	−0.224645	−	0.974441i	$-0.572122\pi$
$277$	8.43689	−	4.87104i	0.506923	−	0.292672i	0.731568	+	0.681768i	$0.238789\pi$
$278$	1.02014	−	0.588979i	0.0611841	−	0.0353246i
$279$	−4.17690	+	7.23461i	−0.250065	+	0.433125i
$280$	−0.782861	−	1.79626i	−0.0467849	−	0.107347i
$281$	8.04901	−	13.9413i	0.480163	−	0.831667i	−0.519578	−	0.854423i	$-0.673911\pi$
$281$	8.04901	−	13.9413i	0.480163	−	0.831667i	0.999741	+	0.0227558i	$0.00724402\pi$
$282$		−	0.184993i		−	0.0110162i
$283$	21.7959	−	12.5839i	1.29563	−	0.748035i	0.315987	−	0.948763i	$-0.397664\pi$
$283$	21.7959	−	12.5839i	1.29563	−	0.748035i	0.979647	+	0.200729i	$0.0643310\pi$
$284$	8.23378	−	14.2613i	0.488585	−	0.846254i
$285$	−11.0069	−	8.13013i	−0.651992	−	0.481588i
$286$	−1.37302			−0.0811883
$287$	5.15230	+	2.97468i	0.304131	+	0.175590i
$288$		−	2.08475i		−	0.122845i
$289$	1.07706	+	1.86552i	0.0633563	+	0.109736i
$290$	0.878616	+	0.648982i	0.0515941	+	0.0381095i
$291$	4.88471	+	8.46056i	0.286347	+	0.495967i
$292$	13.3620	−	7.71457i	0.781954	−	0.451461i
$293$	12.2546	−	7.07522i	0.715924	−	0.413339i	−0.0973269	−	0.995252i	$-0.531029\pi$
$293$	12.2546	−	7.07522i	0.715924	−	0.413339i	0.813250	+	0.581914i	$0.197696\pi$
$294$	0.483646	−	0.837699i	0.0282068	−	0.0488556i
$295$	9.61119	−	13.0120i	0.559585	−	0.757587i
$296$	−2.57902	+	3.41984i	−0.149903	+	0.198774i
$297$		−	1.60162i		−	0.0929352i
$298$	−2.63636	−	1.52211i	−0.152720	−	0.0881732i
$299$	−14.3562	−	24.8656i	−0.830239	−	1.43802i
$300$	−7.20985	−	6.70032i	−0.416261	−	0.386843i
$301$	−0.498581	−	0.863568i	−0.0287378	−	0.0497752i
$302$			2.32790i			0.133956i
$303$	−4.03469	+	2.32943i	−0.231787	+	0.133822i
$304$	23.3286			1.33799
$305$	9.77330	+	22.4247i	0.559618	+	1.28403i
$306$	−0.776570			−0.0443936
$307$		−	4.40153i		−	0.251209i	−0.992080	−	0.125604i	$-0.959913\pi$
$307$		−	4.40153i		−	0.251209i	0.992080	−	0.125604i	$-0.0400870\pi$
$308$	3.39781	+	1.96172i	0.193608	+	0.111780i
$309$	3.84013	+	6.65130i	0.218457	+	0.378379i
$310$	2.66607	+	1.96927i	0.151423	+	0.111847i
$311$	9.85030	−	17.0612i	0.558560	−	0.967454i	−0.439057	−	0.898459i	$-0.644688\pi$
$311$	9.85030	−	17.0612i	0.558560	−	0.967454i	0.997617	−	0.0689945i	$-0.0219791\pi$
$312$	2.94630	+	1.70105i	0.166801	+	0.0963027i
$313$	−4.18427	−	2.41579i	−0.236509	−	0.136548i	0.377062	−	0.926188i	$-0.376934\pi$
$313$	−4.18427	−	2.41579i	−0.236509	−	0.136548i	−0.613571	+	0.789639i	$0.710268\pi$
$314$	1.13877	+	1.97241i	0.0642646	+	0.111309i
$315$	−0.312643	+	2.76501i	−0.0176154	+	0.155791i
$316$	8.55186	−	14.8123i	0.481080	−	0.833255i
$317$	−29.9596	−	17.2972i	−1.68270	−	0.971505i	−0.959857	−	0.280489i	$-0.909503\pi$
$317$	−29.9596	−	17.2972i	−1.68270	−	0.971505i	−0.722839	−	0.691016i	$-0.757163\pi$
$318$	0.798167	+	0.460822i	0.0447590	+	0.0258416i
$319$	−4.40931			−0.246874
$320$	16.1183	+	1.82251i	0.901039	+	0.101881i
$321$	−1.60710	+	2.78357i	−0.0896994	+	0.155364i
$322$		−	1.31226i		−	0.0731296i
$323$		−	26.7829i		−	1.49024i
$324$	−0.984258	+	1.70478i	−0.0546810	+	0.0947102i
$325$	23.0891	−	7.10217i	1.28075	−	0.393957i
$326$	1.43639	+	2.48791i	0.0795545	+	0.137792i
$327$			3.87440i			0.214255i
$328$	2.91547	−	1.68325i	0.160980	−	0.0929417i
$329$	−0.648704	−	1.12359i	−0.0357642	−	0.0619454i
$330$	−0.631444	−	0.0713980i	−0.0347598	−	0.00393033i
$331$	−7.69562	+	13.3292i	−0.422989	+	0.732639i	−0.996230	−	0.0867477i	$-0.972353\pi$
$331$	−7.69562	+	13.3292i	−0.422989	+	0.732639i	0.573241	+	0.819387i	$0.305686\pi$
$332$		−	7.78896i		−	0.427475i
$333$	5.60009	−	2.37465i	0.306883	−	0.130130i
$334$	−2.29692			−0.125682
$335$	12.5924	−	5.48811i	0.687996	−	0.299848i
$336$	−2.37194	−	4.10831i	−0.129400	−	0.224127i
$337$	−11.8002	+	6.81286i	−0.642799	+	0.371120i	−0.785692	−	0.618618i	$-0.787693\pi$
$337$	−11.8002	+	6.81286i	−0.642799	+	0.371120i	0.142893	+	0.989738i	$0.454360\pi$
$338$	−1.58921	+	0.917529i	−0.0864414	+	0.0499070i
$339$	−10.9448			−0.594442
$340$	2.16445	−	19.1424i	0.117384	−	1.03814i
$341$	−13.3796			−0.724546
$342$	0.940388	+	0.542933i	0.0508504	+	0.0293585i
$343$		−	15.4949i		−	0.836645i
$344$	−0.564252			−0.0304225
$345$	−5.30930	−	12.1821i	−0.285843	−	0.655862i
$346$	0.877062	+	1.51912i	0.0471511	+	0.0816682i
$347$		−	12.5571i		−	0.674102i	−0.941486	−	0.337051i	$-0.890570\pi$
$347$		−	12.5571i		−	0.674102i	0.941486	−	0.337051i	$-0.109430\pi$
$348$	4.69333	+	2.70969i	0.251589	+	0.145255i
$349$	−5.81744	+	10.0761i	−0.311400	+	0.539361i	−0.978666	−	0.205459i	$-0.934131\pi$
$349$	−5.81744	+	10.0761i	−0.311400	+	0.539361i	0.667265	+	0.744820i	$0.267465\pi$
$350$	1.07618	+	0.246521i	0.0575242	+	0.0131771i
$351$	−2.41567	−	4.18407i	−0.128939	−	0.223329i
$352$	2.89164	−	1.66949i	0.154125	−	0.0889841i
$353$	−5.28406	−	3.05075i	−0.281242	−	0.162375i	0.352743	−	0.935720i	$-0.385249\pi$
$353$	−5.28406	−	3.05075i	−0.281242	−	0.162375i	−0.633986	+	0.773345i	$0.718582\pi$
$354$	−0.641838	+	1.11170i	−0.0341133	+	0.0590860i
$355$	7.47355	+	17.1479i	0.396655	+	0.910118i
$356$	−10.0810			−0.534291
$357$	−4.71663	+	2.72315i	−0.249631	+	0.144124i
$358$	−2.80105	−	1.61719i	−0.148040	−	0.0854710i
$359$	−32.4063			−1.71034			−0.855169	−	0.518349i	$-0.826547\pi$
$359$	−32.4063			−1.71034			−0.855169	+	0.518349i	$0.826547\pi$
$360$	1.26653	+	0.935511i	0.0667520	+	0.0493058i
$361$	−9.22506	+	15.9783i	−0.485529	+	0.840962i
$362$		−	2.43496i		−	0.127979i
$363$	−7.30477	+	4.21741i	−0.383401	+	0.221357i
$364$	11.8352			0.620335
$365$	−1.96916	+	17.4152i	−0.103070	+	0.911555i
$366$	−0.970565	−	1.68107i	−0.0507323	−	0.0878709i
$367$	−13.9772	+	8.06976i	−0.729605	+	0.421238i	−0.818278	−	0.574823i	$-0.805071\pi$
$367$	−13.9772	+	8.06976i	−0.729605	+	0.421238i	0.0886724	+	0.996061i	$0.471738\pi$
$368$	19.6198	+	11.3275i	1.02275	+	0.590485i
$369$	−4.78079			−0.248878
$370$	−0.686569	−	2.31372i	−0.0356930	−	0.120284i
$371$	6.46374			0.335581
$372$	14.2414	+	8.22230i	0.738384	+	0.426306i
$373$	1.05343	−	0.608200i	0.0545447	−	0.0314914i	−0.472480	−	0.881342i	$-0.656641\pi$
$373$	1.05343	−	0.608200i	0.0545447	−	0.0314914i	0.527024	+	0.849850i	$0.323308\pi$
$374$	−0.621884	−	1.07713i	−0.0321569	−	0.0556973i
$375$	10.9879	−	2.06560i	0.567411	−	0.106667i
$376$	−0.734149			−0.0378608
$377$	−11.5189	+	6.65043i	−0.593252	+	0.342514i
$378$		−	0.220811i		−	0.0113573i
$379$	12.4476	−	21.5599i	0.639390	−	1.10746i	−0.346176	−	0.938169i	$-0.612520\pi$
$379$	12.4476	−	21.5599i	0.639390	−	1.10746i	0.985567	−	0.169287i	$-0.0541466\pi$
$380$	−16.0043	+	21.6672i	−0.821003	+	1.11150i
$381$	3.33015			0.170609
$382$	4.03676	+	2.33062i	0.206538	+	0.119245i
$383$	−5.62529	+	3.24776i	−0.287439	+	0.165953i	−0.636786	−	0.771040i	$-0.719737\pi$
$383$	−5.62529	+	3.24776i	−0.287439	+	0.165953i	0.349347	+	0.936993i	$0.386403\pi$
$384$	−5.45670			−0.278461
$385$	−4.08555	+	1.78060i	−0.208219	+	0.0907476i
$386$	1.93795	−	3.35662i	0.0986389	−	0.170848i
$387$	0.693947	+	0.400650i	0.0352753	+	0.0203662i
$388$	16.6547	−	9.61562i	0.845516	−	0.488159i
$389$	−9.53798	−	16.5203i	−0.483595	−	0.837610i	0.516228	−	0.856451i	$-0.327336\pi$
$389$	−9.53798	−	16.5203i	−0.483595	−	0.837610i	−0.999822	+	0.0188409i	$0.994002\pi$
$390$	−1.75727	+	0.765868i	−0.0889830	+	0.0387812i
$391$	13.0047	−	22.5249i	0.657678	−	1.13913i
$392$	−3.32442	−	1.91936i	−0.167909	−	0.0969421i
$393$			22.0080i			1.11016i
$394$	−0.214808	−	0.372058i	−0.0108218	−	0.0187440i
$395$	7.76226	+	17.8104i	0.390562	+	0.896138i
$396$	−3.15281			−0.158435
$397$			25.7684i			1.29328i	0.762796	+	0.646640i	$0.223826\pi$
$397$			25.7684i			1.29328i	−0.762796	+	0.646640i	$0.776174\pi$
$398$	3.03555	+	1.75258i	0.152159	+	0.0878488i
$399$	7.61548			0.381251
$400$	−12.9754	+	13.9621i	−0.648768	+	0.698104i
$401$	−11.3209			−0.565341			−0.282671	−	0.959217i	$-0.591220\pi$
$401$	−11.3209			−0.565341			−0.282671	+	0.959217i	$0.591220\pi$
$402$	−0.943990	+	0.545013i	−0.0470819	+	0.0271828i
$403$	−34.9529	+	20.1801i	−1.74113	+	1.00524i
$404$	4.58551	+	7.94234i	0.228138	+	0.395146i
$405$	−0.893380	−	2.04985i	−0.0443924	−	0.101858i
$406$	−0.607900			−0.0301695
$407$	7.77833	+	5.86592i	0.385558	+	0.290763i
$408$			3.08183i			0.152573i
$409$	−5.57330	+	9.65324i	−0.275582	+	0.477322i	−0.970282	−	0.241978i	$-0.922204\pi$
$409$	−5.57330	+	9.65324i	−0.275582	+	0.477322i	0.694700	+	0.719300i	$0.255537\pi$
$410$	−0.213122	+	1.88485i	−0.0105253	+	0.0930859i
$411$	7.84074	+	13.5806i	0.386755	+	0.669880i
$412$	13.0932	−	7.55936i	0.645055	−	0.372423i
$413$			9.00277i			0.442998i
$414$	0.527255	+	0.913232i	0.0259132	+	0.0448829i
$415$	7.11669	+	5.25668i	0.349345	+	0.258040i
$416$	5.03608	−	8.72275i	0.246914	−	0.427668i
$417$			6.63866i			0.325096i
$418$			1.73914i			0.0850642i
$419$	−3.68102	+	6.37572i	−0.179830	+	0.311474i	−0.941822	−	0.336112i	$-0.890888\pi$
$419$	−3.68102	+	6.37572i	−0.179830	+	0.311474i	0.761992	+	0.647586i	$0.224221\pi$
$420$	5.44297	+	0.615442i	0.265590	+	0.0300305i
$421$	4.27836			0.208514			0.104257	−	0.994550i	$-0.466753\pi$
$421$	4.27836			0.208514			0.104257	+	0.994550i	$0.466753\pi$
$422$	−1.43725	−	0.829796i	−0.0699642	−	0.0403938i
$423$	0.902894	+	0.521286i	0.0439002	+	0.0253458i
$424$	1.82878	−	3.16754i	0.0888133	−	0.153829i
$425$	16.0295	+	14.8966i	0.777543	+	0.722593i
$426$	−0.742182	−	1.28550i	−0.0359588	−	0.0622825i
$427$	−11.7898	−	6.80684i	−0.570548	−	0.329406i
$428$	5.47951	+	3.16360i	0.264862	+	0.152918i
$429$	3.86898	−	6.70127i	0.186796	−	0.323540i
$430$	0.188893	−	0.255731i	0.00910924	−	0.0123324i
$431$	16.0715	+	27.8367i	0.774139	+	1.34085i	0.935277	+	0.353916i	$0.115150\pi$
$431$	16.0715	+	27.8367i	0.774139	+	1.34085i	−0.161139	+	0.986932i	$0.551517\pi$
$432$	3.30136	+	1.90604i	0.158837	+	0.0917045i
$433$			23.6306i			1.13562i	0.823161	+	0.567808i	$0.192208\pi$
$433$			23.6306i			1.13562i	−0.823161	+	0.567808i	$0.807792\pi$
$434$	−1.84461			−0.0885441
$435$	−5.64330	+	2.45951i	−0.270575	+	0.117924i
$436$	7.62682			0.365259
$437$	−31.4962	+	18.1843i	−1.50667	+	0.869874i
$438$		−	1.39076i		−	0.0664532i
$439$	−7.48667	−	12.9673i	−0.357319	−	0.618895i	0.630193	−	0.776439i	$-0.282976\pi$
$439$	−7.48667	−	12.9673i	−0.357319	−	0.618895i	−0.987512	+	0.157544i	$0.949642\pi$
$440$	−0.283344	+	2.50589i	−0.0135079	+	0.119464i
$441$	2.72570	+	4.72105i	0.129795	+	0.224812i
$442$	−3.24922	−	1.87594i	−0.154550	−	0.0892293i
$443$		−	19.8436i		−	0.942797i	−0.881920	−	0.471398i	$-0.843749\pi$
$443$		−	19.8436i		−	0.942797i	0.881920	−	0.471398i	$-0.156251\pi$
$444$	−4.67453	−	11.0239i	−0.221843	−	0.523170i
$445$	6.80355	−	9.21090i	0.322519	−	0.436639i
$446$	1.64766	−	2.85382i	0.0780187	−	0.135132i
$447$	14.8578	−	8.57817i	0.702751	−	0.405734i
$448$	−7.81796	+	4.51370i	−0.369364	+	0.213252i
$449$	10.2766	+	17.7995i	0.484981	+	0.840011i	0.999851	−	0.0172569i	$-0.00549333\pi$
$449$	10.2766	+	17.7995i	0.484981	+	0.840011i	−0.514871	+	0.857268i	$0.672160\pi$
$450$	−0.847986	+	0.260839i	−0.0399745	+	0.0122961i
$451$	−3.82850	−	6.63115i	−0.180277	−	0.312249i
$452$			21.5451i			1.01340i
$453$	−11.3618	−	6.55972i	−0.533822	−	0.308202i
$454$	−3.62045			−0.169916
$455$	−7.98748	+	10.8137i	−0.374459	+	0.506956i
$456$	2.15464	−	3.73194i	0.100900	−	0.174764i
$457$	23.1673	−	13.3756i	1.08372	−	0.625685i	0.151821	−	0.988408i	$-0.451486\pi$
$457$	23.1673	−	13.3756i	1.08372	−	0.625685i	0.931897	+	0.362723i	$0.118153\pi$
$458$			4.25851i			0.198987i
$459$	2.18827	−	3.79020i	0.102140	−	0.176911i
$460$	−23.9806	+	10.4514i	−1.11810	+	0.487301i
$461$	16.4189	−	28.4384i	0.764705	−	1.32451i	−0.175697	−	0.984444i	$-0.556218\pi$
$461$	16.4189	−	28.4384i	0.764705	−	1.32451i	0.940402	−	0.340064i	$-0.110449\pi$
$462$	0.306274	−	0.176827i	0.0142491	−	0.00822674i
$463$	−19.8028	+	11.4332i	−0.920316	+	0.531345i	−0.883736	−	0.467986i	$-0.844980\pi$
$463$	−19.8028	+	11.4332i	−0.920316	+	0.531345i	−0.0365805	+	0.999331i	$0.511647\pi$
$464$	5.24740	−	9.08876i	0.243604	−	0.421935i
$465$	−17.1240	+	7.46312i	−0.794107	+	0.346094i
$466$	−1.48903	+	2.57908i	−0.0689781	+	0.119473i
$467$		−	21.3407i		−	0.987529i	−0.869596	−	0.493765i	$-0.835620\pi$
$467$		−	21.3407i		−	0.987529i	0.869596	−	0.493765i	$-0.164380\pi$
$468$	−8.23640	+	4.75529i	−0.380728	+	0.219813i
$469$	−3.82232	+	6.62045i	−0.176498	+	0.305704i
$470$	0.245769	−	0.332731i	0.0113365	−	0.0153478i
$471$	−12.8356			−0.591434
$472$	4.41179	+	2.54715i	0.203069	+	0.117242i
$473$			1.28338i			0.0590097i
$474$	−0.770853	−	1.33516i	−0.0354065	−	0.0613258i
$475$	−8.99600	−	29.2459i	−0.412765	−	1.34190i
$476$	5.36056	+	9.28477i	0.245701	+	0.425567i
$477$	−4.49825	+	2.59707i	−0.205961	+	0.118912i
$478$	3.65911	−	2.11259i	0.167364	−	0.0966276i
$479$	−14.6420	+	25.3607i	−0.669009	+	1.15876i	0.309172	+	0.951006i	$0.399948\pi$
$479$	−14.6420	+	25.3607i	−0.669009	+	1.15876i	−0.978182	+	0.207752i	$0.933385\pi$
$480$	2.76966	−	3.74967i	0.126417	−	0.171148i
$481$	29.1675	+	3.59231i	1.32993	+	0.163795i
$482$			2.14594i			0.0977451i
$483$	6.40474	+	3.69778i	0.291426	+	0.168255i
$484$	8.30204	+	14.3796i	0.377365	+	0.653616i
$485$	−2.45440	+	21.7068i	−0.111449	+	0.985653i
$486$	0.0887196	+	0.153667i	0.00402440	+	0.00697047i
$487$			31.4888i			1.42689i	0.700709	+	0.713447i	$0.252867\pi$
$487$			31.4888i			1.42689i	−0.700709	+	0.713447i	$0.747133\pi$
$488$	−6.67135	+	3.85170i	−0.301998	+	0.174358i
$489$	−16.1903			−0.732149
$490$	1.98280	−	0.864159i	0.0895737	−	0.0390387i
$491$	1.06745			0.0481733			0.0240866	−	0.999710i	$-0.492332\pi$
$491$	1.06745			0.0481733			0.0240866	+	0.999710i	$0.492332\pi$
$492$			9.41106i			0.424283i
$493$	−10.4345	−	6.02438i	−0.469948	−	0.271325i
$494$	2.62310	+	4.54334i	0.118019	+	0.204414i
$495$	2.12779	−	2.88069i	0.0956373	−	0.129477i
$496$	15.9227	−	27.5789i	0.714950	−	1.23833i
$497$	−9.01554	−	5.20512i	−0.404402	−	0.233482i
$498$	−0.608024	−	0.351043i	−0.0272462	−	0.0157306i
$499$	0.795153	+	1.37725i	0.0355959	+	0.0616540i	0.883275	−	0.468856i	$-0.155334\pi$
$499$	0.795153	+	1.37725i	0.0355959	+	0.0616540i	−0.847679	+	0.530510i	$0.822000\pi$
$500$	−4.06616	−	21.6298i	−0.181844	−	0.967314i
$501$	6.47240	−	11.2105i	0.289166	−	0.500849i
$502$	−1.40955	−	0.813802i	−0.0629111	−	0.0363218i
$503$	11.2245	+	6.48046i	0.500475	+	0.288950i	0.728910	−	0.684610i	$-0.240027\pi$
$503$	11.2245	+	6.48046i	0.500475	+	0.288950i	−0.228434	+	0.973559i	$0.573361\pi$
$504$	−0.876291			−0.0390331
$505$	−10.3516	−	1.17046i	−0.460638	−	0.0520848i
$506$	−0.844460	+	1.46265i	−0.0375408	+	0.0650226i
$507$		−	10.3419i		−	0.459299i
$508$		−	6.55546i		−	0.290851i
$509$	−17.8623	+	30.9385i	−0.791734	+	1.37132i	0.133159	+	0.991095i	$0.457488\pi$
$509$	−17.8623	+	30.9385i	−0.791734	+	1.37132i	−0.924893	+	0.380228i	$0.875845\pi$
$510$	−1.39675	−	1.03170i	−0.0618491	−	0.0456843i
$511$	−4.87690	−	8.44703i	−0.215741	−	0.373675i
$512$			13.3160i			0.588488i
$513$	−5.29977	+	3.05983i	−0.233991	+	0.135095i
$514$	−2.45146	−	4.24605i	−0.108129	−	0.187285i
$515$	−1.92954	+	17.0648i	−0.0850257	+	0.751967i
$516$	0.788686	−	1.36604i	0.0347200	−	0.0601368i
$517$			1.66980i			0.0734378i
$518$	1.07238	+	0.808719i	0.0471176	+	0.0355331i
$519$	−9.88577			−0.433937
$520$	3.03936	+	6.97376i	0.133285	+	0.305820i
$521$	−1.36783	−	2.36915i	−0.0599256	−	0.103794i	0.834506	−	0.550999i	$-0.185753\pi$
$521$	−1.36783	−	2.36915i	−0.0599256	−	0.103794i	−0.894432	+	0.447204i	$0.852420\pi$
$522$	0.423050	−	0.244248i	0.0185164	−	0.0106905i
$523$	16.8387	−	9.72182i	0.736305	−	0.425106i	−0.0844196	−	0.996430i	$-0.526904\pi$
$523$	16.8387	−	9.72182i	0.736305	−	0.425106i	0.820724	+	0.571325i	$0.193570\pi$
$524$	43.3231			1.89258
$525$	−4.23572	+	4.55783i	−0.184862	+	0.198920i
$526$	−0.369291			−0.0161018
$527$	−31.6626	−	18.2804i	−1.37924	−	0.796306i
$528$			6.10550i			0.265708i
$529$	−12.3184			−0.535584
$530$	0.823378	+	1.88923i	0.0357653	+	0.0820628i
$531$	−3.61723	−	6.26522i	−0.156974	−	0.271887i
$532$		−	14.9912i		−	0.649950i
$533$	−20.0032	−	11.5488i	−0.866433	−	0.500235i
$534$	−0.454343	+	0.786946i	−0.0196614	+	0.0340545i
$535$	−6.58861	+	2.87150i	−0.284850	+	0.124146i
$536$	2.16289	+	3.74624i	0.0934227	+	0.161813i
$537$	15.7860	−	9.11404i	0.681215	−	0.393300i
$538$	−0.990100	−	0.571635i	−0.0426863	−	0.0246449i
$539$	−4.36552	+	7.56131i	−0.188036	+	0.325688i
$540$	−4.03515	+	1.75863i	−0.173645	+	0.0756795i
$541$	−4.22773			−0.181764			−0.0908822	−	0.995862i	$-0.528969\pi$
$541$	−4.22773			−0.181764			−0.0908822	+	0.995862i	$0.528969\pi$
$542$	−0.891939	+	0.514961i	−0.0383121	+	0.0221195i
$543$	11.8843	+	6.86138i	0.510003	+	0.294450i
$544$	9.12401			0.391189
$545$	−5.14726	+	6.96855i	−0.220484	+	0.298500i
$546$	0.533406	−	0.923887i	0.0228277	−	0.0395387i
$547$		−	15.1137i		−	0.646215i	−0.946362	−	0.323108i	$-0.895272\pi$
$547$		−	15.1137i		−	0.646215i	0.946362	−	0.323108i	$-0.104728\pi$
$548$	26.7335	−	15.4346i	1.14200	−	0.659334i
$549$	10.9397			0.466895
$550$	−1.04087	−	0.967309i	−0.0443828	−	0.0412462i
$551$	8.42380	+	14.5905i	0.358866	+	0.621574i
$552$	3.62418	−	2.09242i	0.154255	−	0.0890593i
$553$	−9.36382	−	5.40620i	−0.398190	−	0.229895i
$554$	−1.72863			−0.0734423
$555$	13.2272	+	3.16882i	0.561463	+	0.134509i
$556$	13.0683			0.554219
$557$	3.62446	+	2.09258i	0.153573	+	0.0886657i	0.574817	−	0.818282i	$-0.305073\pi$
$557$	3.62446	+	2.09258i	0.153573	+	0.0886657i	−0.421244	+	0.906947i	$0.638406\pi$
$558$	1.28370	−	0.741147i	0.0543435	−	0.0313752i
$559$	1.93568	+	3.35270i	0.0818705	+	0.141804i
$560$	1.19182	−	10.5405i	0.0503636	−	0.445415i
$561$	7.00954			0.295943
$562$	−2.47373	+	1.42821i	−0.104348	+	0.0602454i
$563$		−	16.2897i		−	0.686528i	−0.939239	−	0.343264i	$-0.888467\pi$
$563$		−	16.2897i		−	0.686528i	0.939239	−	0.343264i	$-0.111533\pi$
$564$	1.02616	−	1.77736i	0.0432091	−	0.0748404i
$565$	−19.6855	−	14.5405i	−0.828177	−	0.611725i
$566$	−4.46575			−0.187710
$567$	1.07771	+	0.622215i	0.0452595	+	0.0261306i
$568$	−5.10151	+	2.94536i	−0.214055	+	0.123585i
$569$	12.1047			0.507456			0.253728	−	0.967276i	$-0.418343\pi$
$569$	12.1047			0.507456			0.253728	+	0.967276i	$0.418343\pi$
$570$	0.970091	+	2.22586i	0.0406327	+	0.0932310i
$571$	11.4215	−	19.7827i	0.477976	−	0.827879i	−0.521705	−	0.853126i	$-0.674704\pi$
$571$	11.4215	−	19.7827i	0.477976	−	0.827879i	0.999681	+	0.0252471i	$0.00803724\pi$
$572$	−13.1916	−	7.61615i	−0.551567	−	0.318447i
$573$	−22.7501	+	13.1348i	−0.950398	+	0.548712i
$574$	−0.527825	−	0.914220i	−0.0220310	−	0.0381588i
$575$	6.63491	−	28.9644i	0.276695	−	1.20790i
$576$	3.62712	−	6.28236i	0.151130	−	0.261765i
$577$	−29.4438	−	16.9994i	−1.22576	−	0.707693i	−0.259620	−	0.965711i	$-0.583597\pi$
$577$	−29.4438	−	16.9994i	−1.22576	−	0.707693i	−0.966140	+	0.258018i	$0.916931\pi$
$578$		−	0.382225i		−	0.0158985i
$579$	10.9217	+	18.9170i	0.453892	+	0.786164i
$580$	4.84157	+	11.1089i	0.201035	+	0.461273i
$581$	−4.92392			−0.204279
$582$		−	1.73348i		−	0.0718550i
$583$	−7.20448	−	4.15951i	−0.298379	−	0.172269i
$584$	−5.51926			−0.228389
$585$	1.21380	−	10.7348i	0.0501843	−	0.443830i
$586$	−2.51084			−0.103722
$587$	−24.9562	+	14.4085i	−1.03005	+	0.594701i	−0.917000	−	0.398888i	$-0.869396\pi$
$587$	−24.9562	+	14.4085i	−1.03005	+	0.594701i	−0.113053	+	0.993589i	$0.536063\pi$
$588$	9.29345	−	5.36558i	0.383255	−	0.221273i
$589$	25.5612	+	44.2733i	1.05323	+	1.82425i
$590$	−2.63134	+	1.14681i	−0.108331	+	0.0472135i
$591$	2.42119			0.0995946
$592$	−21.3480	+	9.05235i	−0.877398	+	0.372049i
$593$		−	43.3361i		−	1.77960i	−0.456352	−	0.889800i	$-0.650844\pi$
$593$		−	43.3361i		−	1.77960i	0.456352	−	0.889800i	$-0.349156\pi$
$594$	−0.142095	+	0.246116i	−0.00583022	+	0.0100982i
$595$	−12.1012	−	1.36829i	−0.496100	−	0.0560946i
$596$	−16.8863	−	29.2479i	−0.691688	−	1.19804i
$597$	−17.1076	+	9.87705i	−0.700166	+	0.404241i
$598$			5.09470i			0.208338i
$599$	6.59205	+	11.4178i	0.269344	+	0.466517i	0.968693	−	0.248264i	$-0.0798599\pi$
$599$	6.59205	+	11.4178i	0.269344	+	0.466517i	−0.699349	+	0.714781i	$0.746527\pi$
$600$	1.03514	+	3.36525i	0.0422596	+	0.137386i
$601$	13.9191	−	24.1087i	0.567774	−	0.983413i	−0.429012	−	0.903299i	$-0.641138\pi$
$601$	13.9191	−	24.1087i	0.567774	−	0.983413i	0.996786	−	0.0801142i	$-0.0255285\pi$
$602$			0.176936i			0.00721137i
$603$		−	6.14309i		−	0.250166i
$604$	−12.9129	+	22.3658i	−0.525419	+	0.910052i
$605$	−18.7414	−	2.11911i	−0.761947	−	0.0861541i
$606$	0.826664			0.0335809
$607$	−14.1123	−	8.14776i	−0.572802	−	0.330708i	0.185466	−	0.982651i	$-0.440621\pi$
$607$	−14.1123	−	8.14776i	−0.572802	−	0.330708i	−0.758268	+	0.651943i	$0.773954\pi$
$608$	−11.0487	−	6.37898i	−0.448085	−	0.258702i
$609$	1.71298	−	2.96697i	0.0694134	−	0.120228i
$610$	0.487677	−	4.31302i	0.0197455	−	0.174629i
$611$	2.51851	+	4.36219i	0.101888	+	0.176475i
$612$	−7.46106	−	4.30764i	−0.301595	−	0.174126i
$613$	19.0027	+	10.9712i	0.767510	+	0.443122i	0.831986	−	0.554797i	$-0.187204\pi$
$613$	19.0027	+	10.9712i	0.767510	+	0.443122i	−0.0644754	+	0.997919i	$0.520537\pi$
$614$	−0.390502	+	0.676370i	−0.0157594	+	0.0272961i
$615$	−8.59880	−	6.35142i	−0.346737	−	0.256114i
$616$	−0.701741	−	1.21545i	−0.0282740	−	0.0489719i
$617$	38.6262	+	22.3008i	1.55503	+	0.897798i	0.997720	+	0.0674944i	$0.0215005\pi$
$617$	38.6262	+	22.3008i	1.55503	+	0.897798i	0.557312	+	0.830303i	$0.311833\pi$
$618$		−	1.36278i		−	0.0548191i
$619$	−21.1197			−0.848873			−0.424437	−	0.905458i	$-0.639528\pi$
$619$	−21.1197			−0.848873			−0.424437	+	0.905458i	$0.639528\pi$
$620$	14.6913	+	33.7089i	0.590016	+	1.35378i
$621$	−5.94293			−0.238482
$622$	−3.02733	+	1.74783i	−0.121385	+	0.0700816i
$623$			6.37287i			0.255324i
$624$	9.20874	+	15.9500i	0.368645	+	0.638511i
$625$	22.5071	+	10.8825i	0.900286	+	0.435300i
$626$	0.428656	+	0.742454i	0.0171325	+	0.0296744i
$627$	−8.48820	−	4.90067i	−0.338986	−	0.195714i
$628$			25.2671i			1.00827i
$629$	10.3927	+	24.5090i	0.414386	+	0.977240i
$630$	0.293354	−	0.397153i	0.0116875	−	0.0158230i
$631$	1.18357	−	2.05000i	0.0471171	−	0.0816092i	−0.841505	−	0.540249i	$-0.818330\pi$
$631$	1.18357	−	2.05000i	0.0471171	−	0.0816092i	0.888622	+	0.458640i	$0.151663\pi$
$632$	−5.29859	+	3.05914i	−0.210767	+	0.121686i
$633$	8.09995	−	4.67651i	0.321944	−	0.185874i
$634$	3.06920	+	5.31600i	0.121893	+	0.211125i
$635$	5.98966	+	4.42421i	0.237692	+	0.175569i
$636$	5.11237	+	8.85488i	0.202719	+	0.351119i
$637$			26.3376i			1.04353i
$638$	0.677564	+	0.391192i	0.0268250	+	0.0154874i
$639$	8.36547			0.330933
$640$	−9.81449	−	7.24938i	−0.387952	−	0.286557i
$641$	9.01153	−	15.6084i	0.355934	−	0.616496i	−0.631343	−	0.775503i	$-0.717496\pi$
$641$	9.01153	−	15.6084i	0.355934	−	0.616496i	0.987277	+	0.159008i	$0.0508295\pi$
$642$	0.493915	−	0.285162i	0.0194933	−	0.0112545i
$643$			47.0743i			1.85643i	0.372045	+	0.928215i	$0.378657\pi$
$643$			47.0743i			1.85643i	−0.372045	+	0.928215i	$0.621343\pi$
$644$	7.27914	−	12.6078i	0.286838	−	0.496818i
$645$	0.715866	+	1.64254i	0.0281872	+	0.0646751i
$646$	−2.37617	+	4.11565i	−0.0934891	+	0.161928i
$647$	27.8879	−	16.1011i	1.09639	−	0.632999i	0.161116	−	0.986935i	$-0.448491\pi$
$647$	27.8879	−	16.1011i	1.09639	−	0.632999i	0.935269	+	0.353937i	$0.115157\pi$
$648$	0.609830	−	0.352085i	0.0239564	−	0.0138312i
$649$	5.79341	−	10.0345i	0.227411	−	0.393888i
$650$	−4.17813	−	0.957088i	−0.163880	−	0.0375401i
$651$	5.19786	−	9.00296i	0.203720	−	0.352854i
$652$			31.8708i			1.24816i
$653$	38.0205	−	21.9511i	1.48786	−	0.859014i	0.487952	−	0.872871i	$-0.337744\pi$
$653$	38.0205	−	21.9511i	1.48786	−	0.859014i	0.999904	+	0.0138568i	$0.00441088\pi$
$654$	0.343736	−	0.595368i	0.0134411	−	0.0232807i
$655$	−29.2383	+	39.5839i	−1.14243	+	1.54667i
$656$	18.2248			0.711558
$657$	6.78787	+	3.91898i	0.264820	+	0.152894i
$658$			0.230211i			0.00897457i
$659$	−24.2484	−	41.9995i	−0.944584	−	1.63607i	−0.756582	−	0.653899i	$-0.773132\pi$
$659$	−24.2484	−	41.9995i	−0.944584	−	1.63607i	−0.188002	−	0.982169i	$-0.560201\pi$
$660$	−5.67068	−	4.18860i	−0.220731	−	0.163041i
$661$	−9.98085	−	17.2873i	−0.388210	−	0.672400i	0.603999	−	0.796985i	$-0.293573\pi$
$661$	−9.98085	−	17.2873i	−0.388210	−	0.672400i	−0.992209	+	0.124586i	$0.960240\pi$
$662$	2.36512	−	1.36551i	0.0919232	−	0.0530719i
$663$	18.3117	−	10.5723i	0.711169	−	0.410594i
$664$	−1.39312	+	2.41295i	−0.0540635	+	0.0936408i
$665$	13.6973	+	10.1174i	0.531158	+	0.392335i
$666$	−1.07123	−	0.131934i	−0.0415092	−	0.00511232i
$667$			16.3611i			0.633504i
$668$	−22.0681	−	12.7410i	−0.853840	−	0.492965i
$669$	9.28574	+	16.0834i	0.359007	+	0.621819i
$670$	−2.42194	−	0.273851i	−0.0935676	−	0.0105798i
$671$	8.76060	+	15.1738i	0.338199	+	0.585778i
$672$			2.59433i			0.100078i
$673$	9.82786	−	5.67412i	0.378836	−	0.218721i	−0.298476	−	0.954417i	$-0.596478\pi$
$673$	9.82786	−	5.67412i	0.378836	−	0.218721i	0.677312	+	0.735696i	$0.263145\pi$
$674$	2.41774			0.0931278
$675$	1.11644	−	4.87376i	0.0429717	−	0.187591i
$676$	−20.3582			−0.783006
$677$			33.0734i			1.27111i	0.772054	+	0.635557i	$0.219230\pi$
$677$			33.0734i			1.27111i	−0.772054	+	0.635557i	$0.780770\pi$
$678$	1.68186	+	0.971022i	0.0645914	+	0.0372919i
$679$	−6.07868	−	10.5286i	−0.233278	−	0.404050i
$680$	−4.09430	+	5.54302i	−0.157009	+	0.212565i
$681$	10.2019	−	17.6703i	0.390939	−	0.677127i
$682$	2.05600	+	1.18703i	0.0787284	+	0.0454538i
$683$	−19.1732	−	11.0697i	−0.733643	−	0.423569i	0.0861104	−	0.996286i	$-0.472556\pi$
$683$	−19.1732	−	11.0697i	−0.733643	−	0.423569i	−0.819753	+	0.572717i	$0.805890\pi$
$684$	6.02331	+	10.4327i	0.230307	+	0.398904i
$685$	−3.93971	+	34.8428i	−0.150529	+	1.33128i
$686$	−1.37470	+	2.38105i	−0.0524863	+	0.0909090i
$687$	−20.7845	−	11.9999i	−0.792976	−	0.457825i
$688$	−2.64538	−	1.52731i	−0.100854	−	0.0582282i
$689$	−25.0947			−0.956030
$690$	−0.264928	+	2.34302i	−0.0100856	+	0.0891974i
$691$	−7.63229	+	13.2195i	−0.290346	+	0.502894i	−0.973892	−	0.227014i	$-0.927104\pi$
$691$	−7.63229	+	13.2195i	−0.290346	+	0.502894i	0.683545	+	0.729908i	$0.260437\pi$
$692$			19.4603i			0.739769i
$693$			1.99310i			0.0757116i
$694$	−1.11406	+	1.92962i	−0.0422893	+	0.0732473i
$695$	−8.81965	+	11.9404i	−0.334548	+	0.452924i
$696$	−0.969303	−	1.67888i	−0.0367413	−	0.0636378i
$697$		−	20.9233i		−	0.792528i
$698$	1.78790	−	1.03224i	0.0676729	−	0.0390710i
$699$	−8.39178	−	14.5350i	−0.317406	−	0.549764i
$700$	8.97216	+	8.33808i	0.339116	+	0.315150i
$701$	14.0645	−	24.3604i	0.531209	−	0.920080i	−0.468128	−	0.883661i	$-0.655071\pi$
$701$	14.0645	−	24.3604i	0.531209	−	0.920080i	0.999337	−	0.0364195i	$-0.0115953\pi$
$702$			0.857270i			0.0323556i
$703$	4.55022	−	36.9452i	0.171615	−	1.39342i
$704$	11.6185			0.437890
$705$	0.931413	+	2.13711i	0.0350790	+	0.0804883i
$706$	0.541324	+	0.937600i	0.0203730	+	0.0352870i
$707$	5.02089	−	2.89881i	0.188830	−	0.109021i
$708$	−12.3332	+	7.12057i	−0.463510	+	0.267607i
$709$	−19.9315			−0.748544			−0.374272	−	0.927319i	$-0.622107\pi$
$709$	−19.9315			−0.748544			−0.374272	+	0.927319i	$0.622107\pi$
$710$	0.372922	−	3.29812i	0.0139955	−	0.123776i
$711$	8.68864			0.325849
$712$	3.12301	+	1.80307i	0.117040	+	0.0675729i
$713$			49.6461i			1.85926i
$714$	0.966388			0.0361661
$715$	15.8616	−	6.91294i	0.593192	−	0.258529i
$716$	−17.9411	−	31.0749i	−0.670491	−	1.16132i
$717$			23.8120i			0.889274i
$718$	4.97978	+	2.87507i	0.185844	+	0.107297i
$719$	2.31804	−	4.01497i	0.0864484	−	0.149733i	−0.819559	−	0.572995i	$-0.805782\pi$
$719$	2.31804	−	4.01497i	0.0864484	−	0.149733i	0.906007	+	0.423262i	$0.139115\pi$
$720$	3.40564	+	7.81419i	0.126921	+	0.291218i
$721$	−4.77878	−	8.27708i	−0.177971	−	0.308255i
$722$	2.83517	−	1.63689i	0.105514	−	0.0609187i
$723$	−10.4737	−	6.04698i	−0.389520	−	0.224890i
$724$	13.5067	−	23.3944i	0.501974	−	0.869445i
$725$	−13.4176	−	3.07359i	−0.498318	−	0.114150i
$726$	1.49667			0.0555466
$727$	27.0716	−	15.6298i	1.00403	−	0.579677i	0.0945921	−	0.995516i	$-0.469845\pi$
$727$	27.0716	−	15.6298i	1.00403	−	0.579677i	0.909438	+	0.415839i	$0.136512\pi$
$728$	−3.66646	−	2.11683i	−0.135888	−	0.0784550i
$729$	−1.00000			−0.0370370
$730$	1.84767	−	2.50144i	0.0683853	−	0.0925826i
$731$	−1.75346	+	3.03709i	−0.0648542	+	0.112331i
$732$		−	21.5349i		−	0.795955i
$733$	11.3299	−	6.54131i	0.418479	−	0.241609i	−0.275948	−	0.961173i	$-0.588992\pi$
$733$	11.3299	−	6.54131i	0.418479	−	0.241609i	0.694426	+	0.719564i	$0.255658\pi$
$734$	2.86378			0.105704
$735$	−1.36957	+	12.1125i	−0.0505175	+	0.446776i
$736$	−6.19478	−	10.7297i	−0.228342	−	0.395501i
$737$	8.52071	−	4.91944i	0.313865	−	0.181210i
$738$	0.734650	+	0.424150i	0.0270428	+	0.0156132i
$739$	−10.9578			−0.403090			−0.201545	−	0.979479i	$-0.564596\pi$
$739$	−10.9578			−0.403090			−0.201545	+	0.979479i	$0.564596\pi$
$740$	6.23786	−	26.0379i	0.229308	−	0.957173i
$741$	−29.5661			−1.08614
$742$	−0.993263	−	0.573460i	−0.0364638	−	0.0210524i
$743$	−16.4226	+	9.48160i	−0.602487	+	0.347846i	−0.770019	−	0.638020i	$-0.779754\pi$
$743$	−16.4226	+	9.48160i	−0.602487	+	0.347846i	0.167532	+	0.985867i	$0.446420\pi$
$744$	−2.94125	−	5.09440i	−0.107832	−	0.186770i
$745$	38.1199	+	4.31025i	1.39660	+	0.157915i
$746$	−0.215837			−0.00790236
$747$	3.42666	−	1.97838i	0.125375	−	0.0723853i
$748$		−	13.7984i		−	0.504519i
$749$	1.99992	−	3.46396i	0.0730755	−	0.126570i
$750$	−1.87173	−	0.657426i	−0.0683460	−	0.0240058i
$751$	−42.7462			−1.55983			−0.779915	−	0.625886i	$-0.784738\pi$
$751$	−42.7462			−1.55983			−0.779915	+	0.625886i	$0.784738\pi$
$752$	−3.44191	−	1.98719i	−0.125513	−	0.0724652i
$753$	7.94382	−	4.58637i	0.289489	−	0.167137i
$754$	2.36009			0.0859496
$755$	−11.7206	−	26.8928i	−0.426558	−	0.978730i
$756$	1.22484	−	2.12148i	0.0445470	−	0.0771577i
$757$	14.4844	+	8.36259i	0.526446	+	0.303944i	0.739568	−	0.673082i	$-0.235030\pi$
$757$	14.4844	+	8.36259i	0.526446	+	0.303944i	−0.213122	+	0.977026i	$0.568363\pi$
$758$	−3.82557	+	2.20869i	−0.138951	+	0.0802234i
$759$	−4.75915	−	8.24309i	−0.172746	−	0.299205i
$760$	8.83336	−	3.84982i	0.320420	−	0.139648i
$761$	2.70413	−	4.68369i	0.0980245	−	0.169783i	−0.812842	−	0.582484i	$-0.802081\pi$
$761$	2.70413	−	4.68369i	0.0980245	−	0.169783i	0.910867	+	0.412700i	$0.135414\pi$
$762$	−0.511734	−	0.295450i	−0.0185382	−	0.0107030i
$763$		−	4.82142i		−	0.174547i
$764$	25.8560	+	44.7839i	0.935436	+	1.62022i
$765$	8.97124	−	3.90991i	0.324356	−	0.141363i
$766$	1.15256			0.0416437
$767$		−	34.9521i		−	1.26205i
$768$	−11.7262	−	6.77013i	−0.423133	−	0.244296i
$769$	32.7744			1.18187			0.590937	−	0.806718i	$-0.298758\pi$
$769$	32.7744			1.18187			0.590937	+	0.806718i	$0.298758\pi$
$770$	0.785788	+	0.0888498i	0.0283178	+	0.00320193i
$771$	27.6315			0.995126
$772$	37.2384	−	21.4996i	1.34024	−	0.773788i
$773$	−5.45043	+	3.14681i	−0.196038	+	0.113183i	−0.594806	−	0.803869i	$-0.702771\pi$
$773$	−5.45043	+	3.14681i	−0.196038	+	0.113183i	0.398768	+	0.917052i	$0.369438\pi$
$774$	−0.0710911	−	0.123133i	−0.00255532	−	0.00442594i
$775$	−40.7145	−	9.32649i	−1.46251	−	0.335018i
$776$	−6.87933			−0.246954
$777$	−6.96892	+	2.95508i	−0.250009	+	0.106013i
$778$			3.38482i			0.121352i
$779$	−14.6284	+	25.3371i	−0.524116	+	0.907796i
$780$	−21.1316	−	2.38938i	−0.756634	−	0.0855534i
$781$	6.69914	+	11.6032i	0.239714	+	0.415197i
$782$	−3.99680	+	2.30755i	−0.142925	+	0.0825179i
$783$			2.75303i			0.0983854i
$784$	−10.3906	−	17.9970i	−0.371092	−	0.642751i
$785$	−23.0863	−	17.0525i	−0.823985	−	0.608629i
$786$	1.95254	−	3.38190i	0.0696449	−	0.120628i
$787$		−	30.9101i		−	1.10182i	−0.834563	−	0.550912i	$-0.814280\pi$
$787$		−	30.9101i		−	1.10182i	0.834563	−	0.550912i	$-0.185720\pi$
$788$		−	4.76616i		−	0.169787i
$789$	1.04061	−	1.80239i	0.0370467	−	0.0641668i
$790$	0.387328	−	3.42553i	0.0137805	−	0.121875i
$791$	13.6201			0.484274
$792$	0.976713	+	0.563906i	0.0347060	+	0.0200375i
$793$	45.7724	+	26.4267i	1.62543	+	0.938440i
$794$	2.28616	−	3.95975i	0.0811329	−	0.140526i
$795$	−11.5409	−	1.30494i	−0.409313	−	0.0462815i
$796$	19.4431	+	33.6765i	0.689144	+	1.19363i
$797$	39.5836	+	22.8536i	1.40212	+	0.809516i	0.994610	−	0.103684i	$-0.0330632\pi$
$797$	39.5836	+	22.8536i	1.40212	+	0.809516i	0.407512	+	0.913200i	$0.366397\pi$
$798$	−1.17025	−	0.675642i	−0.0414263	−	0.0239175i
$799$	−2.28143	+	3.95155i	−0.0807112	+	0.139796i
$800$	9.96309	−	3.06463i	0.352248	−	0.108351i
$801$	−2.56056	−	4.43502i	−0.0904728	−	0.156704i
$802$	1.73966	+	1.00439i	0.0614294	+	0.0354663i
$803$			12.5534i			0.443000i
$804$	−12.0928			−0.426479
$805$	6.60705	+	15.1598i	0.232868	+	0.534312i
$806$	7.16147			0.252252
$807$	5.57994	−	3.22158i	0.196423	−	0.113405i
$808$		−	3.28063i		−	0.115412i
$809$	−24.4396	−	42.3305i	−0.859249	−	1.48826i	−0.872646	−	0.488353i	$-0.837598\pi$
$809$	−24.4396	−	42.3305i	−0.859249	−	1.48826i	0.0133975	−	0.999910i	$-0.495735\pi$
$810$	−0.0445787	+	0.394254i	−0.00156634	+	0.0138527i
$811$	24.1524	+	41.8331i	0.848104	+	1.46896i	0.882898	+	0.469565i	$0.155589\pi$
$811$	24.1524	+	41.8331i	0.848104	+	1.46896i	−0.0347943	+	0.999394i	$0.511078\pi$
$812$	−5.84052	−	3.37203i	−0.204962	−	0.118335i
$813$		−	5.80437i		−	0.203568i
$814$	−0.674850	−	1.59149i	−0.0236535	−	0.0557817i
$815$	−29.1200	−	21.5092i	−1.02003	−	0.753436i
$816$	−8.34187	+	14.4485i	−0.292024	+	0.505800i
$817$	4.24671	−	2.45184i	0.148574	−	0.0857790i
$818$	1.71286	−	0.988922i	0.0598889	−	0.0345769i
$819$	3.00613	+	5.20678i	0.105043	+	0.181940i
$820$	−12.5029	+	16.9269i	−0.436619	+	0.591112i
$821$	−24.5031	−	42.4406i	−0.855163	−	1.48119i	−0.876493	−	0.481414i	$-0.840123\pi$
$821$	−24.5031	−	42.4406i	−0.855163	−	1.48119i	0.0213300	−	0.999772i	$-0.493210\pi$
$822$		−	2.78251i		−	0.0970512i
$823$	5.74068	+	3.31438i	0.200108	+	0.115532i	0.596706	−	0.802460i	$-0.296476\pi$
$823$	5.74068	+	3.31438i	0.200108	+	0.115532i	−0.396598	+	0.917992i	$0.629809\pi$
$824$	−5.40822			−0.188404
$825$	7.65416	−	2.35441i	0.266484	−	0.0819699i
$826$	0.798723	−	1.38343i	0.0277911	−	0.0481356i
$827$	26.7238	−	15.4290i	0.929277	−	0.536518i	0.0426943	−	0.999088i	$-0.486406\pi$
$827$	26.7238	−	15.4290i	0.929277	−	0.536518i	0.886583	+	0.462570i	$0.153073\pi$
$828$			11.6988i			0.406560i
$829$	−27.9779	+	48.4591i	−0.971712	+	1.68305i	−0.281327	+	0.959612i	$0.590774\pi$
$829$	−27.9779	+	48.4591i	−0.971712	+	1.68305i	−0.690385	+	0.723442i	$0.742559\pi$
$830$	−0.627230	−	1.43917i	−0.0217715	−	0.0499543i
$831$	4.87104	−	8.43689i	0.168974	−	0.292672i
$832$	30.3523	−	17.5239i	1.05228	−	0.607531i
$833$	−20.6619	+	11.9291i	−0.715891	+	0.413320i
$834$	0.588979	−	1.02014i	0.0203947	−	0.0353246i
$835$	26.5349	−	11.5646i	0.918277	−	0.400210i
$836$	−9.64704	+	16.7092i	−0.333650	+	0.577898i
$837$			8.35380i			0.288750i
$838$	1.13130	−	0.653158i	0.0390802	−	0.0225630i
$839$	1.16379	−	2.01574i	0.0401785	−	0.0695911i	−0.845237	−	0.534392i	$-0.820541\pi$
$839$	1.16379	−	2.01574i	0.0401785	−	0.0695911i	0.885415	+	0.464801i	$0.153874\pi$
$840$	−1.57611	−	1.16418i	−0.0543809	−	0.0401680i
$841$	−21.4208			−0.738648
$842$	−0.657442	−	0.379574i	−0.0226569	−	0.0130810i
$843$		−	16.0980i		−	0.554445i
$844$	−9.20578	−	15.9449i	−0.316876	−	0.548845i
$845$	13.7395	−	18.6011i	0.472653	−	0.639896i
$846$	−0.0924966	−	0.160209i	−0.00318010	−	0.00550809i
$847$	9.09028	−	5.24827i	0.312346	−	0.180333i
$848$	17.1477	−	9.90024i	0.588855	−	0.339976i
$849$	12.5839	−	21.7959i	0.431878	−	0.748035i
$850$	−1.14157	−	3.71125i	−0.0391556	−	0.127295i
$851$	21.7660	−	28.8622i	0.746128	−	0.989382i
$852$		−	16.4676i		−	0.564169i
$853$	−10.6887	−	6.17110i	−0.365973	−	0.211294i	0.305725	−	0.952120i	$-0.401101\pi$
$853$	−10.6887	−	6.17110i	−0.365973	−	0.211294i	−0.671698	+	0.740825i	$0.734435\pi$
$854$	1.20780	+	2.09197i	0.0413301	+	0.0715858i
$855$	−13.5973	−	1.53746i	−0.465018	−	0.0525801i
$856$	−1.13167	−	1.96011i	−0.0386797	−	0.0669952i
$857$		−	51.8109i		−	1.76983i	−0.465755	−	0.884914i	$-0.654217\pi$
$857$		−	51.8109i		−	1.76983i	0.465755	−	0.884914i	$-0.345783\pi$
$858$	−1.18907	+	0.686509i	−0.0405941	+	0.0234370i
$859$	−38.8385			−1.32515			−0.662577	−	0.748994i	$-0.730537\pi$
$859$	−38.8385			−1.32515			−0.662577	+	0.748994i	$0.730537\pi$
$860$	3.23337	−	1.40919i	0.110257	−	0.0480531i
$861$	5.94936			0.202754
$862$		−	5.70344i		−	0.194260i
$863$	4.86208	+	2.80713i	0.165507	+	0.0955557i	0.580466	−	0.814285i	$-0.302871\pi$
$863$	4.86208	+	2.80713i	0.165507	+	0.0955557i	−0.414958	+	0.909840i	$0.636204\pi$
$864$	−1.04238	−	1.80545i	−0.0354624	−	0.0614227i
$865$	−17.7807	−	13.1335i	−0.604561	−	0.446554i
$866$	2.09650	−	3.63124i	0.0712420	−	0.123395i
$867$	1.86552	+	1.07706i	0.0633563	+	0.0365788i
$868$	−17.7225	−	10.2321i	−0.601540	−	0.347299i
$869$	6.95794	+	12.0515i	0.236032	+	0.408819i
$870$	1.08539	+	0.122727i	0.0367983	+	0.00416082i
$871$	14.8397	−	25.7031i	0.502824	−	0.870916i
$872$	−2.36273	−	1.36412i	−0.0800120	−	0.0461949i
$873$	8.46056	+	4.88471i	0.286347	+	0.165322i
$874$	6.45323			0.218284
$875$	−13.6736	+	2.57049i	−0.462253	+	0.0868985i
$876$	7.71457	−	13.3620i	0.260651	−	0.451461i
$877$			40.4165i			1.36477i	0.730994	+	0.682384i	$0.239057\pi$
$877$			40.4165i			1.36477i	−0.730994	+	0.682384i	$0.760943\pi$
$878$			2.65686i			0.0896646i
$879$	7.07522	−	12.2546i	0.238641	−	0.413339i
$880$	−8.11133	+	10.9814i	−0.273433	+	0.370184i
$881$	−19.7507	−	34.2093i	−0.665419	−	1.15254i	−0.979171	−	0.203035i	$-0.934919\pi$
$881$	−19.7507	−	34.2093i	−0.665419	−	1.15254i	0.313752	−	0.949505i	$-0.398414\pi$
$882$		−	0.967292i		−	0.0325704i
$883$	17.5289	−	10.1203i	0.589895	−	0.340576i	−0.175161	−	0.984540i	$-0.556045\pi$
$883$	17.5289	−	10.1203i	0.589895	−	0.340576i	0.765056	+	0.643964i	$0.222711\pi$
$884$	−20.8117	−	36.0469i	−0.699974	−	1.21239i
$885$	1.81754	−	16.0743i	0.0610959	−	0.540332i
$886$	−1.76052	+	3.04930i	−0.0591457	+	0.102443i
$887$		−	32.4058i		−	1.08808i	−0.839059	−	0.544041i	$-0.816894\pi$
$887$		−	32.4058i		−	1.08808i	0.839059	−	0.544041i	$-0.183106\pi$
$888$	−0.523580	+	4.25118i	−0.0175702	+	0.142660i
$889$	−4.14414			−0.138990
$890$	−1.86267	+	0.811803i	−0.0624368	+	0.0272117i
$891$	−0.800808	−	1.38704i	−0.0268281	−	0.0464676i
$892$	31.6604	−	18.2791i	1.06007	−	0.612030i
$893$	5.52539	−	3.19009i	0.184900	−	0.106752i
$894$	−3.04421			−0.101814
$895$	40.5011	+	4.57950i	1.35380	+	0.153076i
$896$	6.79048			0.226854
$897$	−24.8656	−	14.3562i	−0.830239	−	0.479339i
$898$		−	3.64693i		−	0.121700i
$899$	22.9983			0.767037
$900$	−9.59408	−	2.19772i	−0.319803	−	0.0732574i
$901$	−11.3662	−	19.6868i	−0.378662	−	0.655862i
$902$			1.35865i			0.0452382i
$903$	−0.863568	−	0.498581i	−0.0287378	−	0.0165917i
$904$	3.85352	−	6.67449i	0.128166	−	0.221990i
$905$	12.2596	+	28.1296i	0.407525	+	0.935059i
$906$	1.16395	+	2.01602i	0.0386697	+	0.0669779i
$907$	−24.6627	+	14.2390i	−0.818912	+	0.472799i	−0.850041	−	0.526716i	$-0.823423\pi$
$907$	−24.6627	+	14.2390i	−0.818912	+	0.472799i	0.0311289	+	0.999515i	$0.490090\pi$
$908$	−34.7842	−	20.0827i	−1.15435	−	0.666467i
$909$	−2.32943	+	4.03469i	−0.0772623	+	0.133822i
$910$	2.18680	−	0.953069i	0.0724918	−	0.0315939i
$911$	7.24946			0.240185			0.120093	−	0.992763i	$-0.461681\pi$
$911$	7.24946			0.240185			0.120093	+	0.992763i	$0.461681\pi$
$912$	20.2032	−	11.6643i	0.668994	−	0.386244i
$913$	5.48820	+	3.16861i	0.181633	+	0.104866i
$914$	−4.74672			−0.157008
$915$	19.6763	+	14.5337i	0.650477	+	0.480469i
$916$	−23.6220	+	40.9145i	−0.780493	+	1.35185i
$917$		−	27.3874i		−	0.904412i
$918$	−0.672530	+	0.388285i	−0.0221968	+	0.0128153i
$919$	6.69221			0.220756			0.110378	−	0.993890i	$-0.464794\pi$
$919$	6.69221			0.220756			0.110378	+	0.993890i	$0.464794\pi$
$920$	9.29833	+	1.05137i	0.306557	+	0.0346627i
$921$	−2.20076	−	3.81184i	−0.0725177	−	0.125604i
$922$	−5.04609	+	2.91336i	−0.166184	+	0.0959464i
$923$	35.0017	+	20.2082i	1.15209	+	0.665162i
$924$	3.92345			0.129072
$925$	19.5807	+	23.2722i	0.643811	+	0.765185i
$926$	4.05739			0.133334
$927$	6.65130	+	3.84013i	0.218457	+	0.126126i
$928$	−4.97047	+	2.86970i	−0.163164	+	0.0942025i
$929$	3.47037	+	6.01085i	0.113859	+	0.197210i	0.917323	−	0.398144i	$-0.130345\pi$
$929$	3.47037	+	6.01085i	0.113859	+	0.197210i	−0.803464	+	0.595353i	$0.797012\pi$
$930$	3.29352	+	0.372402i	0.107999	+	0.0122115i
$931$	33.3606			1.09335
$932$	−28.6123	+	16.5193i	−0.937229	+	0.541109i
$933$		−	19.7006i		−	0.644969i
$934$	−1.89334	+	3.27936i	−0.0619519	+	0.107304i
$935$	12.6075	+	9.31238i	0.412308	+	0.304547i
$936$	3.40209			0.111201
$937$	1.45856	+	0.842097i	0.0476489	+	0.0275101i	0.523635	−	0.851943i	$-0.324575\pi$
$937$	1.45856	+	0.842097i	0.0476489	+	0.0275101i	−0.475986	+	0.879453i	$0.657909\pi$
$938$	1.17473	−	0.678230i	0.0383563	−	0.0221450i
$939$	−4.83158			−0.157673
$940$	4.20694	−	1.83350i	0.137215	−	0.0598022i
$941$	−10.6905	+	18.5165i	−0.348500	+	0.603619i	−0.985983	−	0.166845i	$-0.946642\pi$
$941$	−10.6905	+	18.5165i	−0.348500	+	0.603619i	0.637483	+	0.770464i	$0.279975\pi$
$942$	1.97241	+	1.13877i	0.0642646	+	0.0371032i
$943$	−24.6054	+	14.2060i	−0.801263	+	0.462610i
$944$	13.7892	+	23.8835i	0.448799	+	0.777343i
$945$	1.11175	+	2.55089i	0.0361652	+	0.0829805i
$946$	0.113861	−	0.197213i	0.00370193	−	0.00641193i
$947$	16.6493	+	9.61247i	0.541029	+	0.312363i	0.745496	−	0.666510i	$-0.232213\pi$
$947$	16.6493	+	9.61247i	0.541029	+	0.312363i	−0.204467	+	0.978874i	$0.565546\pi$
$948$		−	17.1037i		−	0.555503i
$949$	18.9339	+	32.7946i	0.614622	+	1.06456i
$950$	−1.21230	+	5.29226i	−0.0393322	+	0.171703i
$951$	−34.5943			−1.12180
$952$		−	3.83512i		−	0.124297i
$953$	5.55632	+	3.20794i	0.179987	+	0.103915i	0.587286	−	0.809379i	$-0.300196\pi$
$953$	5.55632	+	3.20794i	0.179987	+	0.103915i	−0.407300	+	0.913295i	$0.633530\pi$
$954$	0.921644			0.0298393
$955$	−58.3685	−	6.59978i	−1.88876	−	0.213564i
$956$	46.8742			1.51602
$957$	−3.81857	+	2.20465i	−0.123437	+	0.0712663i
$958$	4.49998	−	2.59806i	0.145388	−	0.0839396i
$959$	−9.75725	−	16.9001i	−0.315078	−	0.545731i
$960$	14.8701	−	6.48080i	0.479930	−	0.209167i
$961$	38.7861			1.25116
$962$	−4.16338	−	3.13975i	−0.134233	−	0.101230i
$963$			3.21419i			0.103576i
$964$	−11.9036	+	20.6176i	−0.383388	+	0.664048i
$965$	−5.48782	+	48.5343i	−0.176659	+	1.56237i
$966$	−0.656132	−	1.13645i	−0.0211107	−	0.0365648i
$967$	−7.59016	+	4.38218i	−0.244083	+	0.140922i	−0.617052	−	0.786922i	$-0.711673\pi$
$967$	−7.59016	+	4.38218i	−0.244083	+	0.140922i	0.372969	+	0.927844i	$0.378340\pi$
$968$		−	5.93955i		−	0.190905i
$969$	−13.3915	−	23.1947i	−0.430195	−	0.745120i
$970$	2.30298	−	3.11786i	0.0739441	−	0.100108i
$971$	12.5732	−	21.7774i	0.403493	−	0.698871i	−0.590652	−	0.806927i	$-0.701129\pi$
$971$	12.5732	−	21.7774i	0.403493	−	0.698871i	0.994145	+	0.108056i	$0.0344626\pi$
$972$			1.96852i			0.0631402i
$973$		−	8.26134i		−	0.264847i
$974$	2.79368	−	4.83879i	0.0895152	−	0.155045i
$975$	16.4447	−	17.6952i	0.526651	−	0.566700i
$976$	−41.7030			−1.33488
$977$	23.1627	+	13.3730i	0.741042	+	0.427841i	0.822448	−	0.568840i	$-0.192608\pi$
$977$	23.1627	+	13.3730i	0.741042	+	0.427841i	−0.0814063	+	0.996681i	$0.525941\pi$
$978$	2.48791	+	1.43639i	0.0795545	+	0.0459308i
$979$	4.10103	−	7.10319i	0.131070	−	0.227019i
$980$	23.8436	+	2.69603i	0.761657	+	0.0861214i
$981$	1.93720	+	3.35533i	0.0618501	+	0.107128i
$982$	−0.164032	−	0.0947037i	−0.00523446	−	0.00302212i
$983$	−39.4131	−	22.7552i	−1.25708	−	0.725777i	−0.284576	−	0.958654i	$-0.591853\pi$
$983$	−39.4131	−	22.7552i	−1.25708	−	0.725777i	−0.972506	+	0.232877i	$0.925186\pi$
$984$	1.68325	−	2.91547i	0.0536599	−	0.0929417i
$985$	4.35479	+	3.21663i	0.138755	+	0.102490i
$986$	1.06896	+	1.85150i	0.0340427	+	0.0589637i
$987$	−1.12359	−	0.648704i	−0.0357642	−	0.0206485i
$988$			58.2014i			1.85163i
$989$	4.76208			0.151425
$990$	−0.582545	+	0.253889i	−0.0185145	+	0.00806914i
$991$	16.0012			0.508295			0.254148	−	0.967165i	$-0.418205\pi$
$991$	16.0012			0.508295			0.254148	+	0.967165i	$0.418205\pi$
$992$	−15.0824	+	8.70782i	−0.478866	+	0.276473i
$993$			15.3912i			0.488426i
$994$	0.923593	+	1.59971i	0.0292946	+	0.0507397i
$995$	−43.8918	−	4.96290i	−1.39146	−	0.157334i
$996$	−3.89448	−	6.74543i	−0.123401	−	0.213737i
$997$	−4.30981	−	2.48827i	−0.136493	−	0.0788042i	0.430199	−	0.902734i	$-0.358444\pi$
$997$	−4.30981	−	2.48827i	−0.136493	−	0.0788042i	−0.566692	+	0.823930i	$0.691777\pi$
$998$		−	0.282183i		−	0.00893234i
$999$	3.66250	−	4.85655i	0.115876	−	0.153654i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	555.2.bb.a.454.17	✓	72
5.4	even	2	inner	555.2.bb.a.454.20	yes	72
37.26	even	3	inner	555.2.bb.a.544.20	yes	72
185.174	even	6	inner	555.2.bb.a.544.17	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
555.2.bb.a.454.17	✓	72	1.1	even	1	trivial
555.2.bb.a.454.20	yes	72	5.4	even	2	inner
555.2.bb.a.544.17	yes	72	185.174	even	6	inner
555.2.bb.a.544.20	yes	72	37.26	even	3	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:	\( N \)	\(=\)	\( 555 = 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	555.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.153667 - 0.0887196i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.984258 - 1.70478i) q^{4} +(2.22191 + 0.251234i) q^{5} -0.177439 q^{6} +(-1.07771 + 0.622215i) q^{7} +0.704171i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.153667 - 0.0887196i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.984258 - 1.70478i) q^{4} +(2.22191 + 0.251234i) q^{5} -0.177439 q^{6} +(-1.07771 + 0.622215i) q^{7} +0.704171i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.319145 - 0.235733i) q^{10} +1.60162 q^{11} +(-1.70478 - 0.984258i) q^{12} +(4.18407 - 2.41567i) q^{13} +0.220811 q^{14} +(2.04985 - 0.893380i) q^{15} +(-1.90604 + 3.30136i) q^{16} +(3.79020 + 2.18827i) q^{17} +(-0.153667 + 0.0887196i) q^{18} +(-3.05983 - 5.29977i) q^{19} +(-1.75863 - 4.03515i) q^{20} +(-0.622215 + 1.07771i) q^{21} +(-0.246116 - 0.142095i) q^{22} -5.94293i q^{23} +(0.352085 + 0.609830i) q^{24} +(4.87376 + 1.11644i) q^{25} -0.857270 q^{26} -1.00000i q^{27} +(2.12148 + 1.22484i) q^{28} -2.75303 q^{29} +(-0.394254 - 0.0445787i) q^{30} -8.35380 q^{31} +(1.80545 - 1.04238i) q^{32} +(1.38704 - 0.800808i) q^{33} +(-0.388285 - 0.672530i) q^{34} +(-2.55089 + 1.11175i) q^{35} -1.96852 q^{36} +(4.85655 + 3.66250i) q^{37} +1.08587i q^{38} +(2.41567 - 4.18407i) q^{39} +(-0.176911 + 1.56460i) q^{40} +(-2.39040 - 4.14029i) q^{41} +(0.191228 - 0.110405i) q^{42} +0.801301i q^{43} +(-1.57640 - 2.73041i) q^{44} +(1.32853 - 1.79861i) q^{45} +(-0.527255 + 0.913232i) q^{46} +1.04257i q^{47} +3.81208i q^{48} +(-2.72570 + 4.72105i) q^{49} +(-0.649886 - 0.603958i) q^{50} +4.37654 q^{51} +(-8.23640 - 4.75529i) q^{52} +(-4.49825 - 2.59707i) q^{53} +(-0.0887196 + 0.153667i) q^{54} +(3.55865 + 0.402380i) q^{55} +(-0.438145 - 0.758890i) q^{56} +(-5.29977 - 3.05983i) q^{57} +(0.423050 + 0.244248i) q^{58} +(3.61723 - 6.26522i) q^{59} +(-3.54060 - 2.61523i) q^{60} +(5.46984 + 9.47405i) q^{61} +(1.28370 + 0.741147i) q^{62} +1.24443i q^{63} +7.25425 q^{64} +(9.90352 - 4.31623i) q^{65} -0.284190 q^{66} +(5.32007 - 3.07154i) q^{67} -8.61529i q^{68} +(-2.97147 - 5.14673i) q^{69} +(0.490622 + 0.0554751i) q^{70} +(4.18274 + 7.24471i) q^{71} +(0.609830 + 0.352085i) q^{72} +7.83796i q^{73} +(-0.421356 - 0.993677i) q^{74} +(4.77902 - 1.47002i) q^{75} +(-6.02331 + 10.4327i) q^{76} +(-1.72608 + 0.996550i) q^{77} +(-0.742418 + 0.428635i) q^{78} +(4.34432 + 7.52458i) q^{79} +(-5.06446 + 6.85646i) q^{80} +(-0.500000 - 0.866025i) q^{81} +0.848300i q^{82} +(3.42666 + 1.97838i) q^{83} +2.44968 q^{84} +(7.87171 + 5.81436i) q^{85} +(0.0710911 - 0.123133i) q^{86} +(-2.38420 + 1.37652i) q^{87} +1.12781i q^{88} +(2.56056 - 4.43502i) q^{89} +(-0.363723 + 0.158521i) q^{90} +(-3.00613 + 5.20678i) q^{91} +(-10.1314 + 5.84938i) q^{92} +(-7.23461 + 4.17690i) q^{93} +(0.0924966 - 0.160209i) q^{94} +(-5.46717 - 12.5443i) q^{95} +(1.04238 - 1.80545i) q^{96} +9.76941i q^{97} +(0.837699 - 0.483646i) q^{98} +(0.800808 - 1.38704i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9}+O(q^{10}) \) 72 * q + 32 * q^4 - 2 * q^5 + 36 * q^9	\( 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9} - 8 q^{11} - 16 q^{14} - 24 q^{16} + 4 q^{19} + 4 q^{20} + 12 q^{21} + 10 q^{25} + 24 q^{26} + 16 q^{29} + 12 q^{30} + 24 q^{31} - 44 q^{34} - 2 q^{35} + 64 q^{36} - 8 q^{39} + 46 q^{40} - 48 q^{41} - 8 q^{44} - 4 q^{45} - 64 q^{46} + 32 q^{49} - 46 q^{50} - 8 q^{51} - 12 q^{55} - 72 q^{56} + 32 q^{59} - 68 q^{60} - 8 q^{61} - 136 q^{64} - 42 q^{65} - 32 q^{66} - 4 q^{69} + 4 q^{70} + 12 q^{71} - 96 q^{74} - 8 q^{75} + 8 q^{76} - 8 q^{79} - 44 q^{80} - 36 q^{81} + 136 q^{84} + 4 q^{85} + 8 q^{86} + 8 q^{91} - 28 q^{94} + 18 q^{95} - 20 q^{96} - 4 q^{99}+O(q^{100}) \) 72 * q + 32 * q^4 - 2 * q^5 + 36 * q^9 - 8 * q^11 - 16 * q^14 - 24 * q^16 + 4 * q^19 + 4 * q^20 + 12 * q^21 + 10 * q^25 + 24 * q^26 + 16 * q^29 + 12 * q^30 + 24 * q^31 - 44 * q^34 - 2 * q^35 + 64 * q^36 - 8 * q^39 + 46 * q^40 - 48 * q^41 - 8 * q^44 - 4 * q^45 - 64 * q^46 + 32 * q^49 - 46 * q^50 - 8 * q^51 - 12 * q^55 - 72 * q^56 + 32 * q^59 - 68 * q^60 - 8 * q^61 - 136 * q^64 - 42 * q^65 - 32 * q^66 - 4 * q^69 + 4 * q^70 + 12 * q^71 - 96 * q^74 - 8 * q^75 + 8 * q^76 - 8 * q^79 - 44 * q^80 - 36 * q^81 + 136 * q^84 + 4 * q^85 + 8 * q^86 + 8 * q^91 - 28 * q^94 + 18 * q^95 - 20 * q^96 - 4 * q^99

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