LMFDB - Embedded newform 555.2.bb.a.454.16

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			454.16
Character	$\chi$	$=$	555.454
Dual form			555.2.bb.a.544.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.331339 - 0.191298i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.926810 - 1.60528i) q^{4} +(1.22222 - 1.87248i) q^{5} -0.382597 q^{6} +(3.21815 - 1.85800i) q^{7} +1.47438i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.331339 - 0.191298i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.926810 - 1.60528i) q^{4} +(1.22222 - 1.87248i) q^{5} -0.382597 q^{6} +(3.21815 - 1.85800i) q^{7} +1.47438i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.763172 + 0.386614i) q^{10} +5.65186 q^{11} +(-1.60528 - 0.926810i) q^{12} +(-3.15837 + 1.82349i) q^{13} -1.42173 q^{14} +(0.122239 - 2.23272i) q^{15} +(-1.57157 + 2.72204i) q^{16} +(-3.02981 - 1.74926i) q^{17} +(-0.331339 + 0.191298i) q^{18} +(3.45663 + 5.98706i) q^{19} +(-4.13862 - 0.226585i) q^{20} +(1.85800 - 3.21815i) q^{21} +(-1.87268 - 1.08119i) q^{22} -0.722815i q^{23} +(0.737191 + 1.27685i) q^{24} +(-2.01234 - 4.57717i) q^{25} +1.39532 q^{26} -1.00000i q^{27} +(-5.96522 - 3.44402i) q^{28} -9.21176 q^{29} +(-0.467619 + 0.716403i) q^{30} +6.47062 q^{31} +(3.59515 - 2.07566i) q^{32} +(4.89465 - 2.82593i) q^{33} +(0.669262 + 1.15920i) q^{34} +(0.454240 - 8.29680i) q^{35} -1.85362 q^{36} +(-3.88125 + 4.68357i) q^{37} -2.64499i q^{38} +(-1.82349 + 3.15837i) q^{39} +(2.76075 + 1.80203i) q^{40} +(-1.35097 - 2.33994i) q^{41} +(-1.23125 + 0.710864i) q^{42} -0.141562i q^{43} +(-5.23820 - 9.07282i) q^{44} +(-1.01050 - 1.99472i) q^{45} +(-0.138273 + 0.239496i) q^{46} +4.29227i q^{47} +3.14315i q^{48} +(3.40432 - 5.89645i) q^{49} +(-0.208841 + 1.90155i) q^{50} -3.49853 q^{51} +(5.85442 + 3.38005i) q^{52} +(-2.55451 - 1.47484i) q^{53} +(-0.191298 + 0.331339i) q^{54} +(6.90784 - 10.5830i) q^{55} +(2.73940 + 4.74478i) q^{56} +(5.98706 + 3.45663i) q^{57} +(3.05221 + 1.76219i) q^{58} +(-1.37271 + 2.37760i) q^{59} +(-3.69744 + 1.87308i) q^{60} +(6.59581 + 11.4243i) q^{61} +(-2.14397 - 1.23782i) q^{62} -3.71600i q^{63} +4.69801 q^{64} +(-0.445802 + 8.14269i) q^{65} -2.16238 q^{66} +(-7.05243 + 4.07172i) q^{67} +6.48494i q^{68} +(-0.361407 - 0.625976i) q^{69} +(-1.73767 + 2.66215i) q^{70} +(-0.260271 - 0.450802i) q^{71} +(1.27685 + 0.737191i) q^{72} -12.2552i q^{73} +(2.18197 - 0.809371i) q^{74} +(-4.03132 - 2.95778i) q^{75} +(6.40728 - 11.0977i) q^{76} +(18.1885 - 10.5011i) q^{77} +(1.20838 - 0.697660i) q^{78} +(3.59575 + 6.22803i) q^{79} +(3.17615 + 6.26968i) q^{80} +(-0.500000 - 0.866025i) q^{81} +1.03375i q^{82} +(-14.5203 - 8.38329i) q^{83} -6.88805 q^{84} +(-6.97856 + 3.53526i) q^{85} +(-0.0270806 + 0.0469050i) q^{86} +(-7.97762 + 4.60588i) q^{87} +8.33300i q^{88} +(-0.300127 + 0.519835i) q^{89} +(-0.0467682 + 0.854233i) q^{90} +(-6.77607 + 11.7365i) q^{91} +(-1.16032 + 0.669912i) q^{92} +(5.60372 - 3.23531i) q^{93} +(0.821104 - 1.42219i) q^{94} +(15.4354 + 0.845071i) q^{95} +(2.07566 - 3.59515i) q^{96} +6.42270i q^{97} +(-2.25596 + 1.30248i) q^{98} +(2.82593 - 4.89465i) 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 $

$2$	−0.331339	−	0.191298i	−0.234292	−	0.135268i	0.378259	−	0.925700i	$-0.376523\pi$
$2$	−0.331339	−	0.191298i	−0.234292	−	0.135268i	−0.612550	+	0.790432i	$0.709856\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−0.926810	−	1.60528i	−0.463405	−	0.802641i
$5$	1.22222	−	1.87248i	0.546595	−	0.837397i
$5$	1.22222	−	1.87248i	0.546595	−	0.837397i
$6$	−0.382597			−0.156194
$7$	3.21815	−	1.85800i	1.21635	−	0.702257i	0.252211	−	0.967672i	$-0.418842\pi$
$7$	3.21815	−	1.85800i	1.21635	−	0.702257i	0.964134	+	0.265415i	$0.0855089\pi$
$8$			1.47438i			0.521273i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−0.763172	+	0.386614i	−0.241336	+	0.122258i
$11$	5.65186			1.70410			0.852049	−	0.523461i	$-0.175360\pi$
$11$	5.65186			1.70410			0.852049	+	0.523461i	$0.175360\pi$
$12$	−1.60528	−	0.926810i	−0.463405	−	0.267547i
$13$	−3.15837	+	1.82349i	−0.875975	+	0.505744i	−0.869329	−	0.494234i	$-0.835449\pi$
$13$	−3.15837	+	1.82349i	−0.875975	+	0.505744i	−0.00664561	+	0.999978i	$0.502115\pi$
$14$	−1.42173			−0.379973
$15$	0.122239	−	2.23272i	0.0315620	−	0.576487i
$16$	−1.57157	+	2.72204i	−0.392893	+	0.680511i
$17$	−3.02981	−	1.74926i	−0.734837	−	0.424259i	0.0853519	−	0.996351i	$-0.472799\pi$
$17$	−3.02981	−	1.74926i	−0.734837	−	0.424259i	−0.820189	+	0.572092i	$0.806132\pi$
$18$	−0.331339	+	0.191298i	−0.0780972	+	0.0450895i
$19$	3.45663	+	5.98706i	0.793006	+	1.37353i	0.924098	+	0.382156i	$0.124818\pi$
$19$	3.45663	+	5.98706i	0.793006	+	1.37353i	−0.131092	+	0.991370i	$0.541848\pi$
$20$	−4.13862	−	0.226585i	−0.925424	−	0.0506659i
$21$	1.85800	−	3.21815i	0.405448	−	0.702257i
$22$	−1.87268	−	1.08119i	−0.399256	−	0.230511i
$23$		−	0.722815i		−	0.150717i	−0.997156	−	0.0753587i	$-0.975990\pi$
$23$		−	0.722815i		−	0.150717i	0.997156	−	0.0753587i	$-0.0240102\pi$
$24$	0.737191	+	1.27685i	0.150479	+	0.260636i
$25$	−2.01234	−	4.57717i	−0.402467	−	0.915434i
$26$	1.39532			0.273645
$27$		−	1.00000i		−	0.192450i
$28$	−5.96522	−	3.44402i	−1.12732	−	0.650859i
$29$	−9.21176			−1.71058			−0.855290	−	0.518149i	$-0.826621\pi$
$29$	−9.21176			−1.71058			−0.855290	+	0.518149i	$0.826621\pi$
$30$	−0.467619	+	0.716403i	−0.0853752	+	0.130797i
$31$	6.47062			1.16216			0.581079	−	0.813847i	$-0.302631\pi$
$31$	6.47062			1.16216			0.581079	+	0.813847i	$0.302631\pi$
$32$	3.59515	−	2.07566i	0.635539	−	0.366928i
$33$	4.89465	−	2.82593i	0.852049	−	0.491931i
$34$	0.669262	+	1.15920i	0.114778	+	0.198801i
$35$	0.454240	−	8.29680i	0.0767805	−	1.40241i
$36$	−1.85362			−0.308937
$37$	−3.88125	+	4.68357i	−0.638074	+	0.769975i
$37$	−3.88125	+	4.68357i	−0.638074	+	0.769975i
$38$		−	2.64499i		−	0.429074i
$39$	−1.82349	+	3.15837i	−0.291992	+	0.505744i
$40$	2.76075	+	1.80203i	0.436512	+	0.284925i
$41$	−1.35097	−	2.33994i	−0.210985	−	0.365437i	0.741038	−	0.671463i	$-0.234334\pi$
$41$	−1.35097	−	2.33994i	−0.210985	−	0.365437i	−0.952023	+	0.306026i	$0.901001\pi$
$42$	−1.23125	+	0.710864i	−0.189986	+	0.109689i
$43$		−	0.141562i		−	0.0215880i	−0.999942	−	0.0107940i	$-0.996564\pi$
$43$		−	0.141562i		−	0.0215880i	0.999942	−	0.0107940i	$-0.00343591\pi$
$44$	−5.23820	−	9.07282i	−0.789688	−	1.36778i
$45$	−1.01050	−	1.99472i	−0.150636	−	0.297355i
$46$	−0.138273	+	0.239496i	−0.0203873	+	0.0353118i
$47$			4.29227i			0.626091i	0.949738	+	0.313046i	$0.101349\pi$
$47$			4.29227i			0.626091i	−0.949738	+	0.313046i	$0.898651\pi$
$48$			3.14315i			0.453674i
$49$	3.40432	−	5.89645i	0.486331	−	0.842350i
$50$	−0.208841	+	1.90155i	−0.0295346	+	0.268920i
$51$	−3.49853			−0.489892
$52$	5.85442	+	3.38005i	0.811862	+	0.468729i
$53$	−2.55451	−	1.47484i	−0.350888	−	0.202585i	0.314188	−	0.949361i	$-0.398268\pi$
$53$	−2.55451	−	1.47484i	−0.350888	−	0.202585i	−0.665076	+	0.746775i	$0.731601\pi$
$54$	−0.191298	+	0.331339i	−0.0260324	+	0.0450895i
$55$	6.90784	−	10.5830i	0.931452	−	1.42701i
$56$	2.73940	+	4.74478i	0.366068	+	0.634048i
$57$	5.98706	+	3.45663i	0.793006	+	0.457842i
$58$	3.05221	+	1.76219i	0.400775	+	0.231387i
$59$	−1.37271	+	2.37760i	−0.178711	+	0.309537i	−0.941439	−	0.337182i	$-0.890526\pi$
$59$	−1.37271	+	2.37760i	−0.178711	+	0.309537i	0.762728	+	0.646719i	$0.223859\pi$
$60$	−3.69744	+	1.87308i	−0.477338	+	0.241814i
$61$	6.59581	+	11.4243i	0.844507	+	1.46273i	0.886048	+	0.463593i	$0.153440\pi$
$61$	6.59581	+	11.4243i	0.844507	+	1.46273i	−0.0415413	+	0.999137i	$0.513227\pi$
$62$	−2.14397	−	1.23782i	−0.272284	−	0.157203i
$63$		−	3.71600i		−	0.468172i
$64$	4.69801			0.587251
$65$	−0.445802	+	8.14269i	−0.0552950	+	1.00998i
$66$	−2.16238			−0.266171
$67$	−7.05243	+	4.07172i	−0.861592	+	0.497440i	−0.864545	−	0.502555i	$-0.832393\pi$
$67$	−7.05243	+	4.07172i	−0.861592	+	0.497440i	0.00295326	+	0.999996i	$0.499060\pi$
$68$			6.48494i			0.786414i
$69$	−0.361407	−	0.625976i	−0.0435083	−	0.0753587i
$70$	−1.73767	+	2.66215i	−0.207691	+	0.318188i
$71$	−0.260271	−	0.450802i	−0.0308884	−	0.0535004i	0.850168	−	0.526512i	$-0.176500\pi$
$71$	−0.260271	−	0.450802i	−0.0308884	−	0.0535004i	−0.881056	+	0.473011i	$0.843167\pi$
$72$	1.27685	+	0.737191i	0.150479	+	0.0868788i
$73$		−	12.2552i		−	1.43436i	−0.696889	−	0.717179i	$-0.745433\pi$
$73$		−	12.2552i		−	1.43436i	0.696889	−	0.717179i	$-0.254567\pi$
$74$	2.18197	−	0.809371i	0.253649	−	0.0940875i
$75$	−4.03132	−	2.95778i	−0.465497	−	0.341535i
$76$	6.40728	−	11.0977i	0.734966	−	1.27300i
$77$	18.1885	−	10.5011i	2.07277	−	1.19672i
$78$	1.20838	−	0.697660i	0.136822	−	0.0789945i
$79$	3.59575	+	6.22803i	0.404554	+	0.700708i	0.994269	−	0.106903i	$-0.0340934\pi$
$79$	3.59575	+	6.22803i	0.404554	+	0.700708i	−0.589715	+	0.807611i	$0.700760\pi$
$80$	3.17615	+	6.26968i	0.355104	+	0.700972i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$			1.03375i			0.114159i
$83$	−14.5203	−	8.38329i	−1.59381	−	0.920185i	−0.992645	−	0.121058i	$-0.961371\pi$
$83$	−14.5203	−	8.38329i	−1.59381	−	0.920185i	−0.601162	−	0.799127i	$-0.705295\pi$
$84$	−6.88805			−0.751547
$85$	−6.97856	+	3.53526i	−0.756931	+	0.383453i
$86$	−0.0270806	+	0.0469050i	−0.00292018	+	0.00505790i
$87$	−7.97762	+	4.60588i	−0.855290	+	0.493802i
$88$			8.33300i			0.888301i
$89$	−0.300127	+	0.519835i	−0.0318134	+	0.0551024i	−0.881494	−	0.472196i	$-0.843462\pi$
$89$	−0.300127	+	0.519835i	−0.0318134	+	0.0551024i	0.849680	+	0.527298i	$0.176795\pi$
$90$	−0.0467682	+	0.854233i	−0.00492981	+	0.0900441i
$91$	−6.77607	+	11.7365i	−0.710325	+	1.23032i
$92$	−1.16032	+	0.669912i	−0.120972	+	0.0698432i
$93$	5.60372	−	3.23531i	0.581079	−	0.335486i
$94$	0.821104	−	1.42219i	0.0846904	−	0.146688i
$95$	15.4354	+	0.845071i	1.58364	+	0.0867024i
$96$	2.07566	−	3.59515i	0.211846	−	0.366928i
$97$			6.42270i			0.652126i	0.945348	+	0.326063i	$0.105722\pi$
$97$			6.42270i			0.652126i	−0.945348	+	0.326063i	$0.894278\pi$
$98$	−2.25596	+	1.30248i	−0.227887	+	0.131570i
$99$	2.82593	−	4.89465i	0.284016	−	0.491931i
$100$	−5.48260	+	7.47253i	−0.548260	+	0.747253i
$101$	−2.54463			−0.253200			−0.126600	−	0.991954i	$-0.540406\pi$
$101$	−2.54463			−0.253200			−0.126600	+	0.991954i	$0.540406\pi$
$102$	1.15920	+	0.669262i	0.114778	+	0.0662668i
$103$			8.48996i			0.836541i	0.908323	+	0.418271i	$0.137364\pi$
$103$			8.48996i			0.836541i	−0.908323	+	0.418271i	$0.862636\pi$
$104$	−2.68852	−	4.65665i	−0.263631	−	0.456622i
$105$	−3.75501	−	7.41236i	−0.366452	−	0.723372i
$106$	0.564271	+	0.977345i	0.0548068	+	0.0949282i
$107$	6.79587	−	3.92360i	0.656981	−	0.379308i	−0.134145	−	0.990962i	$-0.542829\pi$
$107$	6.79587	−	3.92360i	0.656981	−	0.379308i	0.791126	+	0.611654i	$0.209495\pi$
$108$	−1.60528	+	0.926810i	−0.154468	+	0.0891823i
$109$	−2.64822	+	4.58685i	−0.253653	+	0.439340i	−0.964529	−	0.263977i	$-0.914966\pi$
$109$	−2.64822	+	4.58685i	−0.253653	+	0.439340i	0.710876	+	0.703318i	$0.248299\pi$
$110$	−4.31334	+	2.18509i	−0.411261	+	0.208340i
$111$	−1.01948	+	5.99672i	−0.0967645	+	0.569184i
$112$			11.6799i			1.10365i
$113$	1.01737	+	0.587381i	0.0957064	+	0.0552561i	0.547089	−	0.837074i	$-0.315736\pi$
$113$	1.01737	+	0.587381i	0.0957064	+	0.0552561i	−0.451383	+	0.892330i	$0.649069\pi$
$114$	−1.32250	−	2.29063i	−0.123863	−	0.214537i
$115$	−1.35345	−	0.883442i	−0.126210	−	0.0823814i
$116$	8.53755	+	14.7875i	0.792691	+	1.37298i
$117$			3.64697i			0.337163i
$118$	0.909662	−	0.525194i	0.0837412	−	0.0483480i
$119$	−13.0005			−1.19175
$120$	3.29189	+	0.180227i	0.300507	+	0.0164524i
$121$	20.9435			1.90395
$122$		−	5.04707i		−	0.456940i
$123$	−2.33994	−	1.35097i	−0.210985	−	0.121812i
$124$	−5.99704	−	10.3872i	−0.538550	−	0.932795i
$125$	−11.0302	−	1.82628i	−0.986569	−	0.163347i
$126$	−0.710864	+	1.23125i	−0.0633288	+	0.109689i
$127$	2.62105	+	1.51327i	0.232581	+	0.134281i	0.611762	−	0.791042i	$-0.290461\pi$
$127$	2.62105	+	1.51327i	0.232581	+	0.134281i	−0.379181	+	0.925322i	$0.623794\pi$
$128$	−8.74693	−	5.05004i	−0.773127	−	0.446365i
$129$	−0.0707811	−	0.122596i	−0.00623193	−	0.0107940i
$130$	1.70539	−	2.61270i	0.149573	−	0.229149i
$131$	8.47216	−	14.6742i	0.740216	−	1.28209i	−0.212181	−	0.977230i	$-0.568057\pi$
$131$	8.47216	−	14.6742i	0.740216	−	1.28209i	0.952397	−	0.304861i	$-0.0986101\pi$
$132$	−9.07282	−	5.23820i	−0.789688	−	0.455926i
$133$	22.2479	+	12.8448i	1.92914	+	1.11379i
$134$	3.11566			0.269152
$135$	−1.87248	−	1.22222i	−0.161157	−	0.105192i
$136$	2.57908	−	4.46710i	0.221154	−	0.383051i
$137$			3.46094i			0.295688i	0.989011	+	0.147844i	$0.0472333\pi$
$137$			3.46094i			0.295688i	−0.989011	+	0.147844i	$0.952767\pi$
$138$			0.276547i			0.0235412i
$139$	1.11001	−	1.92259i	0.0941497	−	0.163072i	−0.815104	−	0.579315i	$-0.803320\pi$
$139$	1.11001	−	1.92259i	0.0941497	−	0.163072i	0.909253	+	0.416243i	$0.136653\pi$
$140$	−13.7397	+	6.96037i	−1.16122	+	0.588259i
$141$	2.14613	+	3.71721i	0.180737	+	0.313046i
$142$			0.199157i			0.0167129i
$143$	−17.8507	+	10.3061i	−1.49275	+	0.861838i
$144$	1.57157	+	2.72204i	0.130964	+	0.226837i
$145$	−11.2588	+	17.2488i	−0.934995	+	1.43243i
$146$	−2.34439	+	4.06060i	−0.194023	+	0.336058i
$147$		−	6.80863i		−	0.561567i
$148$	11.1156	+	1.88972i	0.913700	+	0.155334i
$149$	6.32425			0.518103			0.259051	−	0.965864i	$-0.416590\pi$
$149$	6.32425			0.518103			0.259051	+	0.965864i	$0.416590\pi$
$150$	0.769913	+	1.75121i	0.0628631	+	0.142986i
$151$	9.33718	+	16.1725i	0.759849	+	1.31610i	0.942928	+	0.332998i	$0.108060\pi$
$151$	9.33718	+	16.1725i	0.759849	+	1.31610i	−0.183079	+	0.983098i	$0.558606\pi$
$152$	−8.82722	+	5.09640i	−0.715982	+	0.413372i
$153$	−3.02981	+	1.74926i	−0.244946	+	0.141420i
$154$	−8.03540			−0.647511
$155$	7.90855	−	12.1161i	0.635230	−	0.973187i
$156$	6.76010			0.541241
$157$	−12.7425	−	7.35687i	−1.01696	−	0.587142i	−0.103738	−	0.994605i	$-0.533080\pi$
$157$	−12.7425	−	7.35687i	−1.01696	−	0.587142i	−0.913222	+	0.407463i	$0.866414\pi$
$158$		−	2.75145i		−	0.218893i
$159$	−2.94969			−0.233926
$160$	0.507453	−	9.26876i	0.0401177	−	0.732760i
$161$	−1.34299	−	2.32613i	−0.105842	−	0.183324i
$162$			0.382597i			0.0300596i
$163$	2.01979	+	1.16613i	0.158202	+	0.0913380i	0.577011	−	0.816736i	$-0.304219\pi$
$163$	2.01979	+	1.16613i	0.158202	+	0.0913380i	−0.418809	+	0.908074i	$0.637552\pi$
$164$	−2.50418	+	4.33736i	−0.195543	+	0.338691i
$165$	0.690877	−	12.6190i	0.0537847	−	0.982391i
$166$	3.20742	+	5.55541i	0.248944	+	0.431183i
$167$	14.3618	−	8.29181i	1.11135	−	0.641640i	0.172173	−	0.985067i	$-0.444921\pi$
$167$	14.3618	−	8.29181i	1.11135	−	0.641640i	0.939179	+	0.343427i	$0.111588\pi$
$168$	4.74478	+	2.73940i	0.366068	+	0.211349i
$169$	0.150208	−	0.260168i	0.0115544	−	0.0200129i
$170$	2.98856	+	0.163620i	0.229212	+	0.0125491i
$171$	6.91326			0.528671
$172$	−0.227247	+	0.131201i	−0.0173274	+	0.0100040i
$173$	20.9752	+	12.1100i	1.59471	+	0.920708i	0.992483	+	0.122385i	$0.0390542\pi$
$173$	20.9752	+	12.1100i	1.59471	+	0.920708i	0.602230	+	0.798323i	$0.294279\pi$
$174$	3.52439			0.267183
$175$	−14.9804	−	10.9911i	−1.13241	−	0.830849i
$176$	−8.88230	+	15.3846i	−0.669529	+	1.15966i
$177$			2.74542i			0.206358i
$178$	0.198887	−	0.114828i	0.0149072	−	0.00860669i
$179$	2.67322			0.199806			0.0999028	−	0.994997i	$-0.468147\pi$
$179$	2.67322			0.199806			0.0999028	+	0.994997i	$0.468147\pi$
$180$	−2.26554	+	3.47086i	−0.168863	+	0.258703i
$181$	2.06006	+	3.56814i	0.153123	+	0.265217i	0.932374	−	0.361495i	$-0.117733\pi$
$181$	2.06006	+	3.56814i	0.153123	+	0.265217i	−0.779251	+	0.626712i	$0.784400\pi$
$182$	4.49035	−	2.59250i	0.332847	−	0.192169i
$183$	11.4243	+	6.59581i	0.844507	+	0.487576i
$184$	1.06571			0.0785649
$185$	4.02612	+	12.9919i	0.296006	+	0.955186i
$186$	−2.47564			−0.181523
$187$	−17.1241	−	9.88658i	−1.25224	−	0.722978i
$188$	6.89030	−	3.97811i	0.502527	−	0.290134i
$189$	−1.85800	−	3.21815i	−0.135149	−	0.234086i
$190$	−4.95269	−	3.23277i	−0.359306	−	0.234530i
$191$	−13.4702			−0.974666			−0.487333	−	0.873216i	$-0.662030\pi$
$191$	−13.4702			−0.974666			−0.487333	+	0.873216i	$0.662030\pi$
$192$	4.06859	−	2.34900i	0.293626	−	0.169525i
$193$		−	7.16968i		−	0.516085i	−0.966134	−	0.258042i	$-0.916923\pi$
$193$		−	7.16968i		−	0.516085i	0.966134	−	0.258042i	$-0.0830774\pi$
$194$	1.22865	−	2.12809i	0.0882120	−	0.152788i
$195$	3.68527	+	7.27467i	0.263907	+	0.520950i
$196$	−12.6206			−0.901473
$197$	14.9553	+	8.63445i	1.06552	+	0.615179i	0.926954	−	0.375174i	$-0.122417\pi$
$197$	14.9553	+	8.63445i	1.06552	+	0.615179i	0.138567	+	0.990353i	$0.455750\pi$
$198$	−1.87268	+	1.08119i	−0.133085	+	0.0768369i
$199$	16.6180			1.17802			0.589009	−	0.808127i	$-0.299518\pi$
$199$	16.6180			1.17802			0.589009	+	0.808127i	$0.299518\pi$
$200$	6.74850	−	2.96695i	0.477191	−	0.209795i
$201$	−4.07172	+	7.05243i	−0.287197	+	0.497440i
$202$	0.843133	+	0.486783i	0.0593226	+	0.0342499i
$203$	−29.6448	+	17.1154i	−2.08066	+	1.20127i
$204$	3.24247	+	5.61612i	0.227018	+	0.393207i
$205$	−6.03267	−	0.330281i	−0.421340	−	0.0230679i
$206$	1.62412	−	2.81305i	0.113158	−	0.195995i
$207$	−0.625976	−	0.361407i	−0.0435083	−	0.0251196i
$208$		−	11.4630i		−	0.794814i
$209$	19.5364	+	33.8380i	1.35136	+	2.34062i
$210$	−0.173791	+	3.17433i	−0.0119927	+	0.219049i
$211$	−19.6211			−1.35078			−0.675388	−	0.737463i	$-0.736024\pi$
$211$	−19.6211			−1.35078			−0.675388	+	0.737463i	$0.736024\pi$
$212$			5.46760i			0.375516i
$213$	−0.450802	−	0.260271i	−0.0308884	−	0.0178335i
$214$	−3.00231			−0.205234
$215$	−0.265072	−	0.173021i	−0.0180778	−	0.0117999i
$216$	1.47438			0.100319
$217$	20.8234	−	12.0224i	1.41359	−	0.816134i
$218$	1.75491	−	1.01320i	0.118858	−	0.0686225i
$219$	−6.12758	−	10.6133i	−0.414063	−	0.717179i
$220$	−23.3909	−	1.28062i	−1.57701	−	0.0863396i
$221$	12.7590			0.858265
$222$	1.48495	−	1.79192i	0.0996637	−	0.120266i
$223$		−	6.09719i		−	0.408298i	−0.978940	−	0.204149i	$-0.934557\pi$
$223$		−	6.09719i		−	0.408298i	0.978940	−	0.204149i	$-0.0654428\pi$
$224$	7.71315	−	13.3596i	0.515356	−	0.892624i
$225$	−4.97012	−	0.545852i	−0.331341	−	0.0363901i
$226$	−0.224730	−	0.389244i	−0.0149488	−	0.0258921i
$227$	−15.1967	+	8.77381i	−1.00864	+	0.582338i	−0.910793	−	0.412864i	$-0.864529\pi$
$227$	−15.1967	+	8.77381i	−1.00864	+	0.582338i	−0.0978461	+	0.995202i	$0.531195\pi$
$228$		−	12.8146i		−	0.848665i
$229$	−4.29051	−	7.43139i	−0.283525	−	0.491080i	0.688725	−	0.725022i	$-0.258171\pi$
$229$	−4.29051	−	7.43139i	−0.283525	−	0.491080i	−0.972250	+	0.233943i	$0.924837\pi$
$230$	0.279450	+	0.551632i	0.0184264	+	0.0363735i
$231$	10.5011	−	18.1885i	0.690924	−	1.19672i
$232$		−	13.5817i		−	0.891679i
$233$		−	1.61211i		−	0.105613i	−0.998605	−	0.0528063i	$-0.983183\pi$
$233$		−	1.61211i		−	0.105613i	0.998605	−	0.0528063i	$-0.0168166\pi$
$234$	0.697660	−	1.20838i	0.0456075	−	0.0789945i
$235$	8.03717	+	5.24611i	0.524287	+	0.342219i
$236$	5.08896			0.331263
$237$	6.22803	+	3.59575i	0.404554	+	0.233569i
$238$	4.30757	+	2.48698i	0.279218	+	0.161207i
$239$	10.8021	−	18.7098i	0.698730	−	1.21024i	−0.270177	−	0.962811i	$-0.587082\pi$
$239$	10.8021	−	18.7098i	0.698730	−	1.21024i	0.968907	−	0.247426i	$-0.0795846\pi$
$240$	5.88547	+	3.84163i	0.379905	+	0.247976i
$241$	−13.9703	−	24.1974i	−0.899909	−	1.55869i	−0.827609	−	0.561306i	$-0.810299\pi$
$241$	−13.9703	−	24.1974i	−0.899909	−	1.55869i	−0.0723006	−	0.997383i	$-0.523034\pi$
$242$	−6.93938	−	4.00645i	−0.446080	−	0.257545i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	12.2261	−	21.1763i	0.782698	−	1.35567i
$245$	−6.88012	−	13.5813i	−0.439555	−	0.867676i
$246$	0.516875	+	0.895254i	0.0329548	+	0.0570793i
$247$	−21.8347	−	12.6062i	−1.38931	−	0.802116i
$248$			9.54017i			0.605801i
$249$	−16.7666			−1.06254
$250$	3.30536	+	2.71517i	0.209049	+	0.171722i
$251$	14.3528			0.905939			0.452969	−	0.891526i	$-0.350365\pi$
$251$	14.3528			0.905939			0.452969	+	0.891526i	$0.350365\pi$
$252$	−5.96522	+	3.44402i	−0.375774	+	0.216953i
$253$		−	4.08525i		−	0.256837i
$254$	−0.578971	−	1.00281i	−0.0363279	−	0.0629217i
$255$	−4.27598	+	6.55091i	−0.267772	+	0.410234i
$256$	−2.76588	−	4.79064i	−0.172867	−	0.299415i
$257$	−13.0401	−	7.52870i	−0.813418	−	0.469627i	0.0347234	−	0.999397i	$-0.488945\pi$
$257$	−13.0401	−	7.52870i	−0.813418	−	0.469627i	−0.848141	+	0.529770i	$0.822278\pi$
$258$			0.0541613i			0.00337193i
$259$	−3.78837	+	22.2838i	−0.235398	+	1.38465i
$260$	13.4845	−	6.83108i	0.836272	−	0.423646i
$261$	−4.60588	+	7.97762i	−0.285097	+	0.493802i
$262$	−5.61431	+	3.24142i	−0.346853	+	0.200256i
$263$	11.2673	−	6.50516i	0.694770	−	0.401125i	−0.110627	−	0.993862i	$-0.535286\pi$
$263$	11.2673	−	6.50516i	0.694770	−	0.401125i	0.805396	+	0.592737i	$0.201952\pi$
$264$	4.16650	+	7.21659i	0.256430	+	0.444150i
$265$	−5.88379	+	2.98066i	−0.361438	+	0.183101i
$266$	−4.91439	−	8.51198i	−0.301321	−	0.521903i
$267$			0.600254i			0.0367350i
$268$	13.0725	+	7.54743i	0.798532	+	0.461033i
$269$	−18.5416			−1.13050			−0.565252	−	0.824918i	$-0.691221\pi$
$269$	−18.5416			−1.13050			−0.565252	+	0.824918i	$0.691221\pi$
$270$	0.386614	+	0.763172i	0.0235286	+	0.0464451i
$271$	10.3630	−	17.9493i	0.629509	−	1.09034i	−0.358141	−	0.933667i	$-0.616589\pi$
$271$	10.3630	−	17.9493i	0.629509	−	1.09034i	0.987650	−	0.156674i	$-0.0500772\pi$
$272$	9.52314	−	5.49819i	0.577425	−	0.333377i
$273$			13.5521i			0.820213i
$274$	0.662072	−	1.14674i	0.0399972	−	0.0692772i
$275$	−11.3734	−	25.8695i	−0.685844	−	1.55999i
$276$	−0.669912	+	1.16032i	−0.0403240	+	0.0698432i
$277$	16.0905	−	9.28984i	0.966783	−	0.558172i	0.0685287	−	0.997649i	$-0.478170\pi$
$277$	16.0905	−	9.28984i	0.966783	−	0.558172i	0.898254	+	0.439477i	$0.144836\pi$
$278$	−0.735577	+	0.424686i	−0.0441170	+	0.0254709i
$279$	3.23531	−	5.60372i	0.193693	−	0.335486i
$280$	12.2327	+	0.669723i	0.731041	+	0.0400236i
$281$	−9.35715	+	16.2071i	−0.558201	+	0.966832i	0.439446	+	0.898269i	$0.355175\pi$
$281$	−9.35715	+	16.2071i	−0.558201	+	0.966832i	−0.997647	+	0.0685631i	$0.978159\pi$
$282$		−	1.64221i		−	0.0977920i
$283$	4.15252	−	2.39746i	0.246842	−	0.142514i	−0.371476	−	0.928443i	$-0.621148\pi$
$283$	4.15252	−	2.39746i	0.246842	−	0.142514i	0.618317	+	0.785929i	$0.287815\pi$
$284$	−0.482443	+	0.835616i	−0.0286277	+	0.0495847i
$285$	13.7900	−	6.98585i	0.816849	−	0.413806i
$286$	7.88615			0.466318
$287$	−8.69521	−	5.02018i	−0.513262	−	0.296332i
$288$		−	4.15132i		−	0.244619i
$289$	−2.38016	−	4.12256i	−0.140009	−	0.242503i
$290$	7.03015	−	3.56139i	0.412825	−	0.209132i
$291$	3.21135	+	5.56222i	0.188253	+	0.326063i
$292$	−19.6730	+	11.3582i	−1.15127	+	0.664688i
$293$	2.37801	−	1.37294i	0.138925	−	0.0802083i	−0.428927	−	0.903339i	$-0.641108\pi$
$293$	2.37801	−	1.37294i	0.138925	−	0.0802083i	0.567851	+	0.823131i	$0.307775\pi$
$294$	−1.30248	+	2.25596i	−0.0759622	+	0.131570i
$295$	2.77424	+	5.47632i	0.161523	+	0.318844i
$296$	−6.90538	−	5.72245i	−0.401367	−	0.332611i
$297$		−	5.65186i		−	0.327954i
$298$	−2.09547	−	1.20982i	−0.121387	−	0.0700829i
$299$	1.31804	+	2.28292i	0.0762244	+	0.132025i
$300$	−1.01180	+	9.21270i	−0.0584164	+	0.531896i
$301$	−0.263022	−	0.455568i	−0.0151604	−	0.0262585i
$302$		−	7.14475i		−	0.411134i
$303$	−2.20371	+	1.27231i	−0.126600	+	0.0730925i
$304$	−21.7294			−1.24627
$305$	29.4533	+	1.61253i	1.68649	+	0.0923333i
$306$	1.33852			0.0765183
$307$		−	1.29752i		−	0.0740536i	−0.999314	−	0.0370268i	$-0.988211\pi$
$307$		−	1.29752i		−	0.0740536i	0.999314	−	0.0370268i	$-0.0117887\pi$
$308$	−33.7146	−	19.4651i	−1.92107	−	1.10913i
$309$	4.24498	+	7.35252i	0.241489	+	0.418271i
$310$	−4.93819	+	2.50163i	−0.280471	+	0.142083i
$311$	9.61740	−	16.6578i	0.545353	−	0.944579i	−0.453232	−	0.891393i	$-0.649729\pi$
$311$	9.61740	−	16.6578i	0.545353	−	0.944579i	0.998585	−	0.0531862i	$-0.0169377\pi$
$312$	−4.65665	−	2.68852i	−0.263631	−	0.152207i
$313$	−17.1282	−	9.88899i	−0.968145	−	0.558959i	−0.0694747	−	0.997584i	$-0.522132\pi$
$313$	−17.1282	−	9.88899i	−0.968145	−	0.558959i	−0.898670	+	0.438625i	$0.855466\pi$
$314$	2.81471	+	4.87523i	0.158843	+	0.275125i
$315$	−6.95812	−	4.54178i	−0.392045	−	0.255900i
$316$	6.66516	−	11.5444i	0.374945	−	0.649423i
$317$	−15.6137	−	9.01456i	−0.876951	−	0.506308i	−0.00729932	−	0.999973i	$-0.502323\pi$
$317$	−15.6137	−	9.01456i	−0.876951	−	0.506308i	−0.869652	+	0.493665i	$0.835657\pi$
$318$	0.977345	+	0.564271i	0.0548068	+	0.0316427i
$319$	−52.0635			−2.91500
$320$	5.74202	−	8.79691i	0.320989	−	0.491762i
$321$	3.92360	−	6.79587i	0.218994	−	0.379308i
$322$			1.02765i			0.0572685i
$323$		−	24.1862i		−	1.34576i
$324$	−0.926810	+	1.60528i	−0.0514894	+	0.0891823i
$325$	14.7021	+	10.7869i	0.815527	+	0.598352i
$326$	−0.446156	−	0.772764i	−0.0247103	−	0.0427995i
$327$			5.29644i			0.292894i
$328$	3.44997	−	1.99184i	0.190493	−	0.109981i
$329$	7.97502	+	13.8131i	0.439677	+	0.761543i
$330$	−2.64292	+	4.04901i	−0.145488	+	0.222891i
$331$	−7.85255	+	13.6010i	−0.431615	+	0.747579i	−0.997013	−	0.0772392i	$-0.975389\pi$
$331$	−7.85255	+	13.6010i	−0.431615	+	0.747579i	0.565397	+	0.824819i	$0.308723\pi$
$332$			31.0788i			1.70567i
$333$	2.11547	+	5.70305i	0.115927	+	0.312525i
$334$	−6.34484			−0.347174
$335$	−0.995447	+	18.1821i	−0.0543871	+	0.993393i
$336$	5.83996	+	10.1151i	0.318596	+	0.551824i
$337$	11.5819	−	6.68682i	0.630907	−	0.364254i	−0.150196	−	0.988656i	$-0.547991\pi$
$337$	11.5819	−	6.68682i	0.630907	−	0.364254i	0.781103	+	0.624402i	$0.214657\pi$
$338$	−0.0995392	+	0.0574690i	−0.00541422	+	0.00312590i
$339$	1.17476			0.0638043
$340$	12.1429	+	7.92605i	0.658541	+	0.429850i
$341$	36.5710			1.98043
$342$	−2.29063	−	1.32250i	−0.123863	−	0.0715124i
$343$			0.711121i			0.0383969i
$344$	0.208717			0.0112533
$345$	−1.61385	−	0.0883562i	−0.0868866	−	0.00475694i
$346$	−4.63325	−	8.02503i	−0.249085	−	0.431428i
$347$			1.18326i			0.0635206i	0.999496	+	0.0317603i	$0.0101113\pi$
$347$			1.18326i			0.0635206i	−0.999496	+	0.0317603i	$0.989889\pi$
$348$	14.7875	+	8.53755i	0.792691	+	0.457661i
$349$	9.88411	−	17.1198i	0.529084	−	0.916401i	−0.470340	−	0.882485i	$-0.655869\pi$
$349$	9.88411	−	17.1198i	0.529084	−	0.916401i	0.999425	−	0.0339159i	$-0.0107978\pi$
$350$	2.86100	+	6.50750i	0.152927	+	0.347840i
$351$	1.82349	+	3.15837i	0.0973305	+	0.168581i
$352$	20.3193	−	11.7313i	1.08302	−	0.625282i
$353$	−22.4496	−	12.9613i	−1.19487	−	0.689861i	−0.235466	−	0.971883i	$-0.575662\pi$
$353$	−22.4496	−	12.9613i	−1.19487	−	0.689861i	−0.959408	+	0.282022i	$0.908995\pi$
$354$	0.525194	−	0.909662i	0.0279137	−	0.0483480i
$355$	−1.16223	−	0.0636305i	−0.0616845	−	0.00337715i
$356$	1.11264			0.0589699
$357$	−11.2588	+	6.50025i	−0.595877	+	0.344030i
$358$	−0.885739	−	0.511382i	−0.0468128	−	0.0270274i
$359$	15.1828			0.801318			0.400659	−	0.916227i	$-0.368781\pi$
$359$	15.1828			0.801318			0.400659	+	0.916227i	$0.368781\pi$
$360$	2.94097	−	1.48986i	0.155003	−	0.0785227i
$361$	−14.3966	+	24.9357i	−0.757717	+	1.31240i
$362$		−	1.57635i		−	0.0828510i
$363$	18.1376	−	10.4717i	0.951977	−	0.549624i
$364$	25.1205			1.31667
$365$	−22.9475	−	14.9785i	−1.20113	−	0.784013i
$366$	−2.52354	−	4.37089i	−0.131907	−	0.228470i
$367$	−14.7351	+	8.50730i	−0.769164	+	0.444077i	−0.832576	−	0.553910i	$-0.813135\pi$
$367$	−14.7351	+	8.50730i	−0.769164	+	0.444077i	0.0634120	+	0.997987i	$0.479802\pi$
$368$	1.96753	+	1.13596i	0.102565	+	0.0592158i
$369$	−2.70193			−0.140657
$370$	1.15133	−	5.07492i	0.0598546	−	0.263832i
$371$	−10.9610			−0.569069
$372$	−10.3872	−	5.99704i	−0.538550	−	0.310932i
$373$	8.28852	−	4.78538i	0.429163	−	0.247778i	−0.269827	−	0.962909i	$-0.586966\pi$
$373$	8.28852	−	4.78538i	0.429163	−	0.247778i	0.698990	+	0.715131i	$0.253633\pi$
$374$	3.78257	+	6.55161i	0.195592	+	0.338776i
$375$	−10.4655	+	3.93348i	−0.540439	+	0.203124i
$376$	−6.32844			−0.326364
$377$	29.0942	−	16.7975i	1.49843	−	0.865116i
$378$			1.42173i			0.0731258i
$379$	10.1865	−	17.6435i	0.523246	−	0.906288i	−0.476388	−	0.879235i	$-0.658054\pi$
$379$	10.1865	−	17.6435i	0.523246	−	0.906288i	0.999634	−	0.0270529i	$-0.00861226\pi$
$380$	−12.9491	−	25.5614i	−0.664276	−	1.31127i
$381$	3.02653			0.155054
$382$	4.46318	+	2.57682i	0.228356	+	0.131841i
$383$	−6.63957	+	3.83336i	−0.339266	+	0.195876i	−0.659948	−	0.751312i	$-0.729422\pi$
$383$	−6.63957	+	3.83336i	−0.339266	+	0.195876i	0.320681	+	0.947187i	$0.396088\pi$
$384$	−10.1001			−0.515418
$385$	2.56730	−	46.8923i	0.130842	−	2.38985i
$386$	−1.37155	+	2.37559i	−0.0698099	+	0.120914i
$387$	−0.122596	−	0.0707811i	−0.00623193	−	0.00359801i
$388$	10.3102	−	5.95262i	0.523423	−	0.302198i
$389$	−5.74156	−	9.94468i	−0.291109	−	0.504215i	0.682963	−	0.730453i	$-0.260691\pi$
$389$	−5.74156	−	9.94468i	−0.291109	−	0.504215i	−0.974072	+	0.226237i	$0.927357\pi$
$390$	0.170563	−	3.11537i	0.00863677	−	0.157753i
$391$	−1.26439	+	2.18999i	−0.0639431	+	0.110753i
$392$	8.69362	+	5.01926i	0.439094	+	0.253511i
$393$		−	16.9443i		−	0.854728i
$394$	−3.30351	−	5.72185i	−0.166429	−	0.288263i
$395$	16.0567	+	0.879083i	0.807898	+	0.0442315i
$396$	−10.4764			−0.526459
$397$			33.5781i			1.68523i	0.538513	+	0.842617i	$0.318986\pi$
$397$			33.5781i			1.68523i	−0.538513	+	0.842617i	$0.681014\pi$
$398$	−5.50618	−	3.17899i	−0.276000	−	0.159348i
$399$	25.6897			1.28609
$400$	15.6218	+	1.71569i	0.781090	+	0.0857846i
$401$	7.71210			0.385124			0.192562	−	0.981285i	$-0.438320\pi$
$401$	7.71210			0.385124			0.192562	+	0.981285i	$0.438320\pi$
$402$	2.69824	−	1.55783i	0.134576	−	0.0776974i
$403$	−20.4366	+	11.7991i	−1.01802	+	0.587755i
$404$	2.35839	+	4.08484i	0.117334	+	0.203229i
$405$	−2.23272	−	0.122239i	−0.110945	−	0.00607410i
$406$	13.0966			0.649974
$407$	−21.9363	+	26.4709i	−1.08734	+	1.31211i
$408$		−	5.15816i		−	0.255367i
$409$	−12.5667	+	21.7662i	−0.621385	+	1.07627i	0.367843	+	0.929888i	$0.380096\pi$
$409$	−12.5667	+	21.7662i	−0.621385	+	1.07627i	−0.989228	+	0.146383i	$0.953237\pi$
$410$	1.93567	+	1.26347i	0.0955961	+	0.0623986i
$411$	1.73047	+	2.99726i	0.0853577	+	0.147844i
$412$	13.6288	−	7.86858i	0.671442	−	0.387657i
$413$			10.2020i			0.502005i
$414$	0.138273	+	0.239496i	0.00679576	+	0.0117706i
$415$	−33.4445	+	16.9426i	−1.64173	+	0.831681i
$416$	−7.56988	+	13.1114i	−0.371144	+	0.642840i
$417$		−	2.22002i		−	0.108715i
$418$		−	14.9491i		−	0.731185i
$419$	−14.7397	+	25.5298i	−0.720079	+	1.24721i	0.240888	+	0.970553i	$0.422561\pi$
$419$	−14.7397	+	25.5298i	−0.720079	+	1.24721i	−0.960968	+	0.276661i	$0.910772\pi$
$420$	−8.41874	+	12.8977i	−0.410792	+	0.629343i
$421$	−14.2790			−0.695915			−0.347958	−	0.937510i	$-0.613125\pi$
$421$	−14.2790			−0.695915			−0.347958	+	0.937510i	$0.613125\pi$
$422$	6.50124	+	3.75349i	0.316475	+	0.182717i
$423$	3.71721	+	2.14613i	0.180737	+	0.104349i
$424$	2.17448	−	3.76632i	0.105602	−	0.182909i
$425$	−1.90968	+	17.3881i	−0.0926329	+	0.843445i
$426$	0.0995787	+	0.172475i	0.00482460	+	0.00835646i
$427$	42.4526	+	24.5100i	2.05443	+	1.18612i
$428$	−12.5970	−	7.27285i	−0.608897	−	0.351547i
$429$	−10.3061	+	17.8507i	−0.497583	+	0.861838i
$430$	0.0547299	+	0.108036i	0.00263931	+	0.00520997i
$431$	−3.12677	−	5.41572i	−0.150611	−	0.260866i	0.780841	−	0.624730i	$-0.214791\pi$
$431$	−3.12677	−	5.41572i	−0.150611	−	0.260866i	−0.931452	+	0.363864i	$0.881457\pi$
$432$	2.72204	+	1.57157i	0.130964	+	0.0756123i
$433$		−	7.89575i		−	0.379445i	−0.981838	−	0.189723i	$-0.939241\pi$
$433$		−	7.89575i		−	0.379445i	0.981838	−	0.189723i	$-0.0607589\pi$
$434$	−9.19947			−0.441588
$435$	−1.12604	+	20.5673i	−0.0539893	+	0.986127i
$436$	9.81758			0.470177
$437$	4.32754	−	2.49851i	0.207014	−	0.119520i
$438$			4.68878i			0.224039i
$439$	17.8672	+	30.9470i	0.852757	+	1.47702i	0.878710	+	0.477356i	$0.158405\pi$
$439$	17.8672	+	30.9470i	0.852757	+	1.47702i	−0.0259530	+	0.999663i	$0.508262\pi$
$440$	15.6033	+	10.1848i	0.743860	+	0.485541i
$441$	−3.40432	−	5.89645i	−0.162110	−	0.280783i
$442$	−4.22756	−	2.44078i	−0.201084	−	0.116096i
$443$			35.0976i			1.66754i	0.552115	+	0.833768i	$0.313821\pi$
$443$			35.0976i			1.66754i	−0.552115	+	0.833768i	$0.686179\pi$
$444$	10.5713	−	3.92127i	0.501691	−	0.186095i
$445$	0.606557	+	1.19734i	0.0287535	+	0.0567592i
$446$	−1.16638	+	2.02024i	−0.0552298	+	0.0956609i
$447$	5.47696	−	3.16212i	0.259051	−	0.149563i
$448$	15.1189	−	8.72889i	0.714300	−	0.412401i
$449$	−2.95036	−	5.11016i	−0.139236	−	0.241164i	0.787972	−	0.615711i	$-0.211131\pi$
$449$	−2.95036	−	5.11016i	−0.139236	−	0.241164i	−0.927208	+	0.374548i	$0.877798\pi$
$450$	1.54237	+	1.13164i	0.0727080	+	0.0533459i
$451$	−7.63546	−	13.2250i	−0.359540	−	0.622742i
$452$		−	2.17756i		−	0.102424i
$453$	16.1725	+	9.33718i	0.759849	+	0.438699i
$454$	6.71366			0.315088
$455$	13.6944	+	27.0327i	0.642005	+	1.26731i
$456$	−5.09640	+	8.82722i	−0.238661	+	0.413372i
$457$	−3.63004	+	2.09581i	−0.169806	+	0.0980377i	−0.582494	−	0.812835i	$-0.697923\pi$
$457$	−3.63004	+	2.09581i	−0.169806	+	0.0980377i	0.412688	+	0.910872i	$0.364590\pi$
$458$			3.28307i			0.153408i
$459$	−1.74926	+	3.02981i	−0.0816486	+	0.141420i
$460$	−0.163779	+	2.99146i	−0.00763622	+	0.139477i
$461$	−7.01524	+	12.1508i	−0.326732	+	0.565917i	−0.981861	−	0.189600i	$-0.939281\pi$
$461$	−7.01524	+	12.1508i	−0.326732	+	0.565917i	0.655129	+	0.755517i	$0.272614\pi$
$462$	−6.95886	+	4.01770i	−0.323756	+	0.186920i
$463$	−25.3482	+	14.6348i	−1.17803	+	0.680136i	−0.955558	−	0.294803i	$-0.904746\pi$
$463$	−25.3482	+	14.6348i	−1.17803	+	0.680136i	−0.222472	+	0.974939i	$0.571413\pi$
$464$	14.4769	−	25.0748i	0.672075	−	1.16407i
$465$	0.790962	−	14.4471i	0.0366800	−	0.669969i
$466$	−0.308394	+	0.534153i	−0.0142861	+	0.0247442i
$467$			24.8790i			1.15126i	0.817710	+	0.575631i	$0.195243\pi$
$467$			24.8790i			1.15126i	−0.817710	+	0.575631i	$0.804757\pi$
$468$	5.85442	−	3.38005i	0.270621	−	0.156243i
$469$	−15.1305	+	26.2068i	−0.698662	+	1.21012i
$470$	−1.65945	−	3.27574i	−0.0765447	−	0.151098i
$471$	−14.7137			−0.677973
$472$	−3.50549	−	2.02390i	−0.161353	−	0.0931574i
$473$		−	0.800090i		−	0.0367882i
$474$	−1.37572	−	2.38282i	−0.0631891	−	0.109447i
$475$	20.4479	−	27.8696i	0.938215	−	1.27874i
$476$	12.0490	+	20.8695i	0.552265	+	0.956551i
$477$	−2.55451	+	1.47484i	−0.116963	+	0.0675285i
$478$	−7.15831	+	4.13285i	−0.327413	+	0.189032i
$479$	−16.7492	+	29.0105i	−0.765291	+	1.32552i	0.174802	+	0.984604i	$0.444071\pi$
$479$	−16.7492	+	29.0105i	−0.765291	+	1.32552i	−0.940093	+	0.340918i	$0.889262\pi$
$480$	−4.19491	−	8.28071i	−0.191471	−	0.377961i
$481$	3.71800	−	21.8699i	0.169526	−	0.997181i
$482$			10.6900i			0.486917i
$483$	−2.32613	−	1.34299i	−0.105842	−	0.0611081i
$484$	−19.4106	−	33.6202i	−0.882301	−	1.52819i
$485$	12.0263	+	7.84998i	0.546088	+	0.356449i
$486$	0.191298	+	0.331339i	0.00867747	+	0.0150298i
$487$		−	32.8083i		−	1.48669i	−0.668910	−	0.743343i	$-0.733239\pi$
$487$		−	32.8083i		−	1.48669i	0.668910	−	0.743343i	$-0.266761\pi$
$488$	−16.8438	+	9.72475i	−0.762481	+	0.440219i
$489$	2.33225			0.105468
$490$	−0.318428	+	5.81616i	−0.0143851	+	0.262747i
$491$	−5.26642			−0.237670			−0.118835	−	0.992914i	$-0.537916\pi$
$491$	−5.26642			−0.237670			−0.118835	+	0.992914i	$0.537916\pi$
$492$			5.00835i			0.225794i
$493$	27.9099	+	16.1138i	1.25700	+	0.725728i
$494$	4.82311	+	8.35387i	0.217002	+	0.375858i
$495$	−5.71120	−	11.2738i	−0.256699	−	0.506722i
$496$	−10.1691	+	17.6133i	−0.456604	+	0.790861i
$497$	−1.67518	−	0.967165i	−0.0751420	−	0.0433833i
$498$	5.55541	+	3.20742i	0.248944	+	0.143728i
$499$	−2.66400	−	4.61418i	−0.119257	−	0.206559i	0.800216	−	0.599711i	$-0.204718\pi$
$499$	−2.66400	−	4.61418i	−0.119257	−	0.206559i	−0.919473	+	0.393152i	$0.871385\pi$
$500$	7.29118	+	19.3991i	0.326072	+	0.867556i
$501$	8.29181	−	14.3618i	0.370451	−	0.641640i
$502$	−4.75563	−	2.74566i	−0.212254	−	0.122545i
$503$	−3.36554	−	1.94309i	−0.150062	−	0.0866382i	0.423089	−	0.906088i	$-0.360946\pi$
$503$	−3.36554	−	1.94309i	−0.150062	−	0.0866382i	−0.573151	+	0.819450i	$0.694279\pi$
$504$	5.47880			0.244045
$505$	−3.11010	+	4.76475i	−0.138398	+	0.212029i
$506$	−0.781501	+	1.35360i	−0.0347420	+	0.0601748i
$507$		−	0.300416i		−	0.0133419i
$508$		−	5.61004i		−	0.248905i
$509$	0.771972	−	1.33709i	0.0342170	−	0.0592657i	−0.848410	−	0.529340i	$-0.822440\pi$
$509$	0.771972	−	1.33709i	0.0342170	−	0.0592657i	0.882627	+	0.470074i	$0.155773\pi$
$510$	2.66998	−	1.35258i	0.118228	−	0.0598932i
$511$	−22.7701	−	39.4389i	−1.00729	−	1.74467i
$512$			22.3166i			0.986264i
$513$	5.98706	−	3.45663i	0.264335	−	0.152614i
$514$	2.88045	+	4.98909i	0.127051	+	0.220059i
$515$	15.8973	+	10.3766i	0.700517	+	0.457249i
$516$	−0.131201	+	0.227247i	−0.00577581	+	0.0100040i
$517$			24.2593i			1.06692i
$518$	5.51809	−	6.65877i	0.242451	−	0.292570i
$519$	24.2200			1.06314
$520$	−12.0054	−	0.657283i	−0.526473	−	0.0288238i
$521$	−20.3435	−	35.2360i	−0.891265	−	1.54372i	−0.838361	−	0.545116i	$-0.816486\pi$
$521$	−20.3435	−	35.2360i	−0.891265	−	1.54372i	−0.0529042	−	0.998600i	$-0.516848\pi$
$522$	3.05221	−	1.76219i	0.133592	−	0.0771292i
$523$	−5.95119	+	3.43592i	−0.260227	+	0.150242i	−0.624438	−	0.781074i	$-0.714672\pi$
$523$	−5.95119	+	3.43592i	−0.260227	+	0.150242i	0.364211	+	0.931317i	$0.381339\pi$
$524$	−31.4083			−1.37208
$525$	−18.4689	−	2.02838i	−0.806050	−	0.0885259i
$526$	−4.97771			−0.217038
$527$	−19.6048	−	11.3188i	−0.853997	−	0.493055i
$528$			17.7646i			0.773105i
$529$	22.4775			0.977284
$530$	2.51972	+	0.137952i	0.109450	+	0.00599224i
$531$	1.37271	+	2.37760i	0.0595704	+	0.103179i
$532$		−	47.6189i		−	2.06454i
$533$	8.53370	+	4.92694i	0.369636	+	0.213409i
$534$	0.114828	−	0.198887i	0.00496908	−	0.00860669i
$535$	0.959233	−	17.5206i	0.0414712	−	0.757482i
$536$	−6.00328	−	10.3980i	−0.259302	−	0.449124i
$537$	2.31507	−	1.33661i	0.0999028	−	0.0576789i
$538$	6.14356	+	3.54699i	0.264868	+	0.152921i
$539$	19.2407	−	33.3259i	0.828756	−	1.43545i
$540$	−0.226585	+	4.13862i	−0.00975065	+	0.178098i
$541$	−42.0044			−1.80591			−0.902954	−	0.429737i	$-0.858606\pi$
$541$	−42.0044			−1.80591			−0.902954	+	0.429737i	$0.858606\pi$
$542$	−6.86734	+	3.96486i	−0.294977	+	0.170305i
$543$	3.56814	+	2.06006i	0.153123	+	0.0884058i
$544$	−14.5235			−0.622690
$545$	5.35205	+	10.5649i	0.229257	+	0.452550i
$546$	2.59250	−	4.49035i	0.110949	−	0.192169i
$547$			24.3668i			1.04185i	0.853603	+	0.520924i	$0.174413\pi$
$547$			24.3668i			1.04185i	−0.853603	+	0.520924i	$0.825587\pi$
$548$	5.55578	−	3.20763i	0.237331	−	0.137023i
$549$	13.1916			0.563005
$550$	−1.18034	+	10.7473i	−0.0503299	+	0.458266i
$551$	−31.8417	−	55.1514i	−1.35650	−	2.34953i
$552$	0.922928	−	0.532853i	0.0392824	−	0.0226797i
$553$	23.1433	+	13.3618i	0.984155	+	0.568202i
$554$	−7.10852			−0.302012
$555$	9.98269	+	9.23828i	0.423742	+	0.392143i
$556$	−4.11507			−0.174518
$557$	38.2305	+	22.0724i	1.61988	+	0.935237i	0.986950	+	0.161025i	$0.0514801\pi$
$557$	38.2305	+	22.0724i	1.61988	+	0.935237i	0.632927	+	0.774211i	$0.281853\pi$
$558$	−2.14397	+	1.23782i	−0.0907613	+	0.0524011i
$559$	0.258137	+	0.447106i	0.0109180	+	0.0189106i
$560$	21.8704	+	14.2755i	0.924192	+	0.603249i
$561$	−19.7732			−0.834824
$562$	6.20077	−	3.58002i	0.261564	−	0.151014i
$563$		−	40.4449i		−	1.70455i	−0.523095	−	0.852274i	$-0.675223\pi$
$563$		−	40.4449i		−	1.70455i	0.523095	−	0.852274i	$-0.324777\pi$
$564$	3.97811	−	6.89030i	0.167509	−	0.290134i
$565$	2.34331	−	1.18710i	0.0985840	−	0.0499415i
$566$	−1.83452			−0.0771106
$567$	−3.21815	−	1.85800i	−0.135149	−	0.0780286i
$568$	0.664655	−	0.383739i	0.0278883	−	0.0161013i
$569$	2.30974			0.0968294			0.0484147	−	0.998827i	$-0.484583\pi$
$569$	2.30974			0.0968294			0.0484147	+	0.998827i	$0.484583\pi$
$570$	−5.90554	−	0.323321i	−0.247356	−	0.0135424i
$571$	8.17331	−	14.1566i	0.342042	−	0.592435i	−0.642769	−	0.766060i	$-0.722215\pi$
$571$	8.17331	−	14.1566i	0.342042	−	0.592435i	0.984812	+	0.173625i	$0.0555480\pi$
$572$	33.0883	+	19.1036i	1.38349	+	0.798760i
$573$	−11.6655	+	6.73508i	−0.487333	+	0.281362i
$574$	1.92071	+	3.32676i	0.0801687	+	0.138856i
$575$	−3.30845	+	1.45455i	−0.137972	+	0.0606588i
$576$	2.34900	−	4.06859i	0.0978752	−	0.169525i
$577$	−5.08390	−	2.93519i	−0.211646	−	0.122194i	0.390430	−	0.920632i	$-0.372326\pi$
$577$	−5.08390	−	2.93519i	−0.211646	−	0.122194i	−0.602076	+	0.798439i	$0.705660\pi$
$578$			1.82128i			0.0757554i
$579$	−3.58484	−	6.20912i	−0.148981	−	0.258042i
$580$	38.1240	+	2.08724i	1.58301	+	0.0866680i
$581$	−62.3045			−2.58483
$582$		−	2.45730i		−	0.101858i
$583$	−14.4377	−	8.33561i	−0.597948	−	0.345226i
$584$	18.0688			0.747692
$585$	6.82887	+	4.45742i	0.282339	+	0.184292i
$586$	−1.05057			−0.0433986
$587$	18.0002	−	10.3924i	0.742946	−	0.428940i	−0.0801935	−	0.996779i	$-0.525554\pi$
$587$	18.0002	−	10.3924i	0.742946	−	0.428940i	0.823139	+	0.567839i	$0.192220\pi$
$588$	−10.9298	+	6.31031i	−0.450736	+	0.260233i
$589$	22.3666	+	38.7400i	0.921598	+	1.59625i
$590$	0.128398	−	2.34522i	0.00528607	−	0.0965514i
$591$	17.2689			0.710348
$592$	−6.64922	−	17.9255i	−0.273281	−	0.736734i
$593$			20.7753i			0.853137i	0.904455	+	0.426569i	$0.140278\pi$
$593$			20.7753i			0.853137i	−0.904455	+	0.426569i	$0.859722\pi$
$594$	−1.08119	+	1.87268i	−0.0443618	+	0.0768369i
$595$	−15.8895	+	24.3431i	−0.651408	+	0.997972i
$596$	−5.86138	−	10.1522i	−0.240091	−	0.415850i
$597$	14.3916	−	8.30899i	0.589009	−	0.340064i
$598$		−	1.00856i		−	0.0412430i
$599$	−2.81627	−	4.87793i	−0.115070	−	0.199307i	0.802738	−	0.596332i	$-0.203376\pi$
$599$	−2.81627	−	4.87793i	−0.115070	−	0.199307i	−0.917808	+	0.397025i	$0.870043\pi$
$600$	4.36090	−	5.94371i	0.178033	−	0.242651i
$601$	−10.7531	+	18.6249i	−0.438628	+	0.759727i	−0.997584	−	0.0694710i	$-0.977869\pi$
$601$	−10.7531	+	18.6249i	−0.438628	+	0.759727i	0.558956	+	0.829198i	$0.311202\pi$
$602$			0.201263i			0.00820287i
$603$			8.14345i			0.331627i
$604$	17.3076	−	29.9776i	0.704235	−	1.21977i
$605$	25.5976	−	39.2162i	1.04069	−	1.59436i
$606$	0.973566			0.0395484
$607$	−27.9164	−	16.1175i	−1.13309	−	0.654190i	−0.188381	−	0.982096i	$-0.560324\pi$
$607$	−27.9164	−	16.1175i	−1.13309	−	0.654190i	−0.944710	+	0.327906i	$0.893657\pi$
$608$	24.8542	+	14.3496i	1.00797	+	0.581953i
$609$	−17.1154	+	29.6448i	−0.693552	+	1.20127i
$610$	−9.45052	−	6.16865i	−0.382641	−	0.249762i
$611$	−7.82689	−	13.5566i	−0.316642	−	0.548440i
$612$	5.61612	+	3.24247i	0.227018	+	0.131069i
$613$	37.1747	+	21.4628i	1.50147	+	0.866875i	0.999999	+	0.00170077i	$0.000541371\pi$
$613$	37.1747	+	21.4628i	1.50147	+	0.866875i	0.501472	+	0.865174i	$0.332792\pi$
$614$	−0.248214	+	0.429919i	−0.0100171	+	0.0173501i
$615$	−5.38958	+	2.73030i	−0.217329	+	0.110096i
$616$	15.4827	+	26.8168i	0.623816	+	1.08048i
$617$	−20.6188	−	11.9043i	−0.830082	−	0.479248i	0.0237985	−	0.999717i	$-0.492424\pi$
$617$	−20.6188	−	11.9043i	−0.830082	−	0.479248i	−0.853881	+	0.520468i	$0.825757\pi$
$618$		−	3.24823i		−	0.130663i
$619$	−1.08114			−0.0434547			−0.0217274	−	0.999764i	$-0.506917\pi$
$619$	−1.08114			−0.0434547			−0.0217274	+	0.999764i	$0.506917\pi$
$620$	−26.7795	−	1.46614i	−1.07549	−	0.0588817i
$621$	−0.722815			−0.0290056
$622$	−6.37323	+	3.67959i	−0.255543	+	0.147538i
$623$			2.23054i			0.0893648i
$624$	−5.73148	−	9.92722i	−0.229443	−	0.397407i
$625$	−16.9010	+	18.4216i	−0.676040	+	0.736865i
$626$	3.78349	+	6.55321i	0.151219	+	0.261919i
$627$	33.8380	+	19.5364i	1.35136	+	0.780208i
$628$			27.2737i			1.08834i
$629$	19.9523	−	7.40102i	0.795549	−	0.295098i
$630$	1.43666	+	2.83594i	0.0572378	+	0.112987i
$631$	0.878737	−	1.52202i	0.0349820	−	0.0605905i	−0.848004	−	0.529989i	$-0.822196\pi$
$631$	0.878737	−	1.52202i	0.0349820	−	0.0605905i	0.882986	+	0.469399i	$0.155529\pi$
$632$	−9.18250	+	5.30152i	−0.365260	+	0.210883i
$633$	−16.9924	+	9.81057i	−0.675388	+	0.389935i
$634$	3.44894	+	5.97374i	0.136975	+	0.237248i
$635$	6.03707	−	3.05831i	0.239574	−	0.121365i
$636$	2.73380	+	4.73508i	0.108402	+	0.187758i
$637$			24.8309i			0.983836i
$638$	17.2507	+	9.95967i	0.682960	+	0.394307i
$639$	−0.520541			−0.0205923
$640$	−20.1468	+	10.2061i	−0.796372	+	0.403433i
$641$	−5.61405	+	9.72382i	−0.221742	+	0.384068i	−0.955337	−	0.295519i	$-0.904508\pi$
$641$	−5.61405	+	9.72382i	−0.221742	+	0.384068i	0.733595	+	0.679587i	$0.237841\pi$
$642$	−2.60008	+	1.50115i	−0.102617	+	0.0592459i
$643$			2.75746i			0.108744i	0.998521	+	0.0543718i	$0.0173156\pi$
$643$			2.75746i			0.108744i	−0.998521	+	0.0543718i	$0.982684\pi$
$644$	−2.48939	+	4.31175i	−0.0980957	+	0.169907i
$645$	−0.316069	−	0.0173044i	−0.0124452	−	0.000681361i
$646$	−4.62679	+	8.01383i	−0.182038	+	0.315300i
$647$	−0.787453	+	0.454636i	−0.0309580	+	0.0178736i	−0.515399	−	0.856950i	$-0.672356\pi$
$647$	−0.787453	+	0.454636i	−0.0309580	+	0.0178736i	0.484441	+	0.874824i	$0.339023\pi$
$648$	1.27685	−	0.737191i	0.0501595	−	0.0289596i
$649$	−7.75835	+	13.4379i	−0.304542	+	0.527482i
$650$	−2.80785	−	6.38662i	−0.110133	−	0.250504i
$651$	12.0224	−	20.8234i	0.471195	−	0.816134i
$652$		−	4.32311i		−	0.169306i
$653$	−32.0252	+	18.4897i	−1.25324	+	0.723559i	−0.971752	−	0.236005i	$-0.924162\pi$
$653$	−32.0252	+	18.4897i	−1.25324	+	0.723559i	−0.281490	+	0.959564i	$0.590828\pi$
$654$	1.01320	−	1.75491i	0.0396192	−	0.0686225i
$655$	−17.1222	−	33.7991i	−0.669021	−	1.32064i
$656$	8.49256			0.331579
$657$	−10.6133	−	6.12758i	−0.414063	−	0.239060i
$658$		−	6.10244i		−	0.237898i
$659$	−19.5435	−	33.8503i	−0.761306	−	1.31862i	−0.942178	−	0.335114i	$-0.891225\pi$
$659$	−19.5435	−	33.8503i	−0.761306	−	1.31862i	0.180872	−	0.983507i	$-0.442108\pi$
$660$	−20.8974	+	10.5864i	−0.813431	+	0.412075i
$661$	−10.8770	−	18.8396i	−0.423068	−	0.732775i	0.573170	−	0.819436i	$-0.305713\pi$
$661$	−10.8770	−	18.8396i	−0.423068	−	0.732775i	−0.996238	+	0.0866618i	$0.972380\pi$
$662$	5.20370	−	3.00436i	0.202248	−	0.116768i
$663$	11.0496	−	6.37951i	0.429133	−	0.247760i
$664$	12.3602	−	21.4084i	0.479668	−	0.830809i
$665$	51.2436	−	25.9594i	1.98714	−	1.00666i
$666$	0.390048	−	2.29433i	0.0151141	−	0.0889033i
$667$			6.65840i			0.257814i
$668$	−26.6214	−	15.3699i	−1.03001	−	0.594678i
$669$	−3.04860	−	5.28032i	−0.117866	−	0.204149i
$670$	3.80803	−	5.83399i	0.147117	−	0.225387i
$671$	37.2786	+	64.5684i	1.43912	+	2.49264i
$672$		−	15.4263i		−	0.595082i
$673$	34.5125	−	19.9258i	1.33036	−	0.768084i	0.345005	−	0.938601i	$-0.387877\pi$
$673$	34.5125	−	19.9258i	1.33036	−	0.768084i	0.985355	+	0.170517i	$0.0545439\pi$
$674$	−5.11671			−0.197088
$675$	−4.57717	+	2.01234i	−0.176175	+	0.0774548i
$676$	−0.556856			−0.0214175
$677$		−	12.4383i		−	0.478042i	−0.971014	−	0.239021i	$-0.923174\pi$
$677$		−	12.4383i		−	0.478042i	0.971014	−	0.239021i	$-0.0768265\pi$
$678$	−0.389244	−	0.224730i	−0.0149488	−	0.00863070i
$679$	11.9334	+	20.6692i	0.457960	+	0.793211i
$680$	−5.21233	−	10.2891i	−0.199884	−	0.394568i
$681$	−8.77381	+	15.1967i	−0.336213	+	0.582338i
$682$	−12.1174	−	6.99598i	−0.463999	−	0.267890i
$683$	−6.75160	−	3.89804i	−0.258343	−	0.149154i	0.365236	−	0.930915i	$-0.380988\pi$
$683$	−6.75160	−	3.89804i	−0.258343	−	0.149154i	−0.623578	+	0.781761i	$0.714322\pi$
$684$	−6.40728	−	11.0977i	−0.244989	−	0.424333i
$685$	6.48052	+	4.23004i	0.247608	+	0.161622i
$686$	0.136036	−	0.235622i	0.00519389	−	0.00899608i
$687$	−7.43139	−	4.29051i	−0.283525	−	0.163693i
$688$	0.385339	+	0.222475i	0.0146909	+	0.00848179i
$689$	10.7574			0.409826
$690$	0.517827	+	0.338002i	0.0197133	+	0.0128675i
$691$	−15.0865	+	26.1306i	−0.573917	+	0.994054i	0.422241	+	0.906484i	$0.361244\pi$
$691$	−15.0865	+	26.1306i	−0.573917	+	0.994054i	−0.996158	+	0.0875704i	$0.972090\pi$
$692$		−	44.8947i		−	1.70664i
$693$		−	21.0023i		−	0.797811i
$694$	0.226355	−	0.392059i	0.00859233	−	0.0148824i
$695$	−2.24333	−	4.42830i	−0.0850942	−	0.167975i
$696$	−6.79083	−	11.7621i	−0.257406	−	0.445840i
$697$			9.45278i			0.358049i
$698$	−6.54997	+	3.78163i	−0.247920	+	0.143137i
$699$	−0.806054	−	1.39613i	−0.0304878	−	0.0528063i
$700$	−3.75985	+	34.2344i	−0.142109	+	1.29394i
$701$	−11.7446	+	20.3423i	−0.443588	+	0.768317i	−0.997953	−	0.0639567i	$-0.979628\pi$
$701$	−11.7446	+	20.3423i	−0.443588	+	0.768317i	0.554364	+	0.832274i	$0.312961\pi$
$702$		−	1.39532i		−	0.0526630i
$703$	−41.4569	−	7.04791i	−1.56358	−	0.265817i
$704$	26.5525			1.00073
$705$	9.58345	+	0.524682i	0.360933	+	0.0197607i
$706$	4.95895	+	8.58916i	0.186633	+	0.323257i
$707$	−8.18899	+	4.72791i	−0.307979	+	0.177811i
$708$	4.40717	−	2.54448i	0.165631	−	0.0956273i
$709$	24.3654			0.915061			0.457531	−	0.889194i	$-0.348734\pi$
$709$	24.3654			0.915061			0.457531	+	0.889194i	$0.348734\pi$
$710$	0.372918	+	0.243415i	0.0139953	+	0.00913520i
$711$	7.19151			0.269703
$712$	−0.766436	−	0.442502i	−0.0287234	−	0.0165835i
$713$		−	4.67706i		−	0.175157i
$714$	4.97395			0.186145
$715$	−2.51961	+	46.0213i	−0.0942281	+	1.72110i
$716$	−2.47756	−	4.29126i	−0.0925909	−	0.160372i
$717$		−	21.6042i		−	0.806824i
$718$	−5.03065	−	2.90445i	−0.187742	−	0.108393i
$719$	−14.9756	+	25.9385i	−0.558495	+	0.967342i	0.439127	+	0.898425i	$0.355288\pi$
$719$	−14.9756	+	25.9385i	−0.558495	+	0.967342i	−0.997622	+	0.0689175i	$0.978045\pi$
$720$	7.01778	+	0.384215i	0.261537	+	0.0143188i
$721$	15.7743	+	27.3220i	0.587467	+	1.01752i
$722$	9.54031	−	5.50810i	0.355053	−	0.204990i
$723$	−24.1974	−	13.9703i	−0.899909	−	0.519563i
$724$	3.81858	−	6.61397i	0.141916	−	0.245806i
$725$	18.5372	+	42.1638i	0.688453	+	1.56592i
$726$	−8.01291			−0.297387
$727$	−26.7017	+	15.4162i	−0.990312	+	0.571757i	−0.905368	−	0.424629i	$-0.860405\pi$
$727$	−26.7017	+	15.4162i	−0.990312	+	0.571757i	−0.0849444	+	0.996386i	$0.527071\pi$
$728$	−17.3041	−	9.99052i	−0.641332	−	0.370273i
$729$	−1.00000			−0.0370370
$730$	4.73801	+	9.35279i	0.175362	+	0.346162i
$731$	−0.247630	+	0.428907i	−0.00915891	+	0.0158637i
$732$		−	24.4523i		−	0.903781i
$733$	45.9255	−	26.5151i	1.69630	−	0.979357i	0.747081	−	0.664734i	$-0.231455\pi$
$733$	45.9255	−	26.5151i	1.69630	−	0.979357i	0.949216	−	0.314624i	$-0.101878\pi$
$734$	6.50973			0.240278
$735$	−12.7490	−	8.32168i	−0.470254	−	0.306950i
$736$	−1.50032	−	2.59863i	−0.0553025	−	0.0957867i
$737$	−39.8593	+	23.0128i	−1.46824	+	0.847687i
$738$	0.895254	+	0.516875i	0.0329548	+	0.0190264i
$739$	−32.0215			−1.17793			−0.588964	−	0.808159i	$-0.700464\pi$
$739$	−32.0215			−1.17793			−0.588964	+	0.808159i	$0.700464\pi$
$740$	17.1243	−	18.5041i	0.629501	−	0.680225i
$741$	−25.2125			−0.926204
$742$	3.63181	+	2.09683i	0.133328	+	0.0769770i
$743$	6.19568	−	3.57708i	0.227298	−	0.131230i	−0.382027	−	0.924151i	$-0.624774\pi$
$743$	6.19568	−	3.57708i	0.227298	−	0.131230i	0.609325	+	0.792921i	$0.291441\pi$
$744$	4.77009	+	8.26203i	0.174880	+	0.302901i
$745$	7.72965	−	11.8420i	0.283192	−	0.433858i
$746$	−3.66174			−0.134066
$747$	−14.5203	+	8.38329i	−0.531269	+	0.306728i
$748$			36.6519i			1.34013i
$749$	14.5801	−	25.2534i	0.532744	−	0.922740i
$750$	4.22011	+	0.698728i	0.154097	+	0.0255140i
$751$	19.9372			0.727517			0.363759	−	0.931493i	$-0.381493\pi$
$751$	19.9372			0.727517			0.363759	+	0.931493i	$0.381493\pi$
$752$	−11.6837	−	6.74561i	−0.426062	−	0.245987i
$753$	12.4299	−	7.17639i	0.452969	−	0.261522i
$754$	−12.8534			−0.468091
$755$	41.6947	+	2.28273i	1.51742	+	0.0830772i
$756$	−3.44402	+	5.96522i	−0.125258	+	0.216953i
$757$	13.3780	+	7.72381i	0.486233	+	0.280727i	0.723010	−	0.690837i	$-0.242758\pi$
$757$	13.3780	+	7.72381i	0.486233	+	0.280727i	−0.236777	+	0.971564i	$0.576091\pi$
$758$	−6.75036	+	3.89732i	−0.245184	+	0.141557i
$759$	−2.04262	−	3.53793i	−0.0741425	−	0.128419i
$760$	−1.24596	+	22.7577i	−0.0451956	+	0.825509i
$761$	16.2842	−	28.2050i	0.590300	−	1.02243i	−0.403892	−	0.914807i	$-0.632343\pi$
$761$	16.2842	−	28.2050i	0.590300	−	1.02243i	0.994192	−	0.107623i	$-0.0343240\pi$
$762$	−1.00281	−	0.578971i	−0.0363279	−	0.0209739i
$763$			19.6815i			0.712520i
$764$	12.4843	+	21.6234i	0.451665	+	0.782307i
$765$	−0.427656	+	7.81124i	−0.0154619	+	0.282416i
$766$	2.93326			0.105983
$767$		−	10.0125i		−	0.361529i
$768$	−4.79064	−	2.76588i	−0.172867	−	0.0998050i
$769$	20.7063			0.746687			0.373343	−	0.927693i	$-0.378211\pi$
$769$	20.7063			0.746687			0.373343	+	0.927693i	$0.378211\pi$
$770$	−9.82107	+	15.0461i	−0.353927	+	0.542224i
$771$	−15.0574			−0.542279
$772$	−11.5094	+	6.64493i	−0.414231	+	0.239156i
$773$	−40.9282	+	23.6299i	−1.47208	+	0.849908i	−0.999507	−	0.0313820i	$-0.990009\pi$
$773$	−40.9282	+	23.6299i	−1.47208	+	0.849908i	−0.472576	+	0.881290i	$0.656676\pi$
$774$	0.0270806	+	0.0469050i	0.000973393	+	0.00168597i
$775$	−13.0211	−	29.6171i	−0.467730	−	1.06388i
$776$	−9.46951			−0.339936
$777$	7.86107	+	21.1925i	0.282014	+	0.760277i
$778$			4.39341i			0.157511i
$779$	9.33958	−	16.1766i	0.334625	−	0.579588i
$780$	8.26236	−	12.6581i	0.295840	−	0.453234i
$781$	−1.47101	−	2.54787i	−0.0526370	−	0.0911699i
$782$	0.837884	−	0.483753i	0.0299627	−	0.0172990i
$783$			9.21176i			0.329201i
$784$	10.7003	+	18.5334i	0.382152	+	0.661907i
$785$	−29.3497	+	14.8682i	−1.04754	+	0.530670i
$786$	−3.24142	+	5.61431i	−0.115618	+	0.200256i
$787$		−	6.58396i		−	0.234693i	−0.993091	−	0.117346i	$-0.962561\pi$
$787$		−	6.58396i		−	0.234693i	0.993091	−	0.117346i	$-0.0374388\pi$
$788$		−	32.0100i		−	1.14031i
$789$	6.50516	−	11.2673i	0.231590	−	0.401125i
$790$	−5.15202	−	3.36289i	−0.183301	−	0.119646i
$791$	4.36541			0.155216
$792$	7.21659	+	4.16650i	0.256430	+	0.148050i
$793$	−41.6641	−	24.0548i	−1.47953	−	0.854209i
$794$	6.42343	−	11.1257i	0.227959	−	0.394836i
$795$	−3.60518	+	5.52322i	−0.127863	+	0.195889i
$796$	−15.4017	−	26.6765i	−0.545899	−	0.945525i
$797$	−12.4858	−	7.20870i	−0.442271	−	0.255345i	0.262289	−	0.964989i	$-0.415522\pi$
$797$	−12.4858	−	7.20870i	−0.442271	−	0.255345i	−0.704560	+	0.709644i	$0.748856\pi$
$798$	−8.51198	−	4.91439i	−0.301321	−	0.173968i
$799$	7.50830	−	13.0048i	0.265625	−	0.460075i
$800$	−16.7353	−	12.2787i	−0.591682	−	0.434117i
$801$	0.300127	+	0.519835i	0.0106045	+	0.0183675i
$802$	−2.55532	−	1.47531i	−0.0902314	−	0.0520951i
$803$		−	69.2644i		−	2.44429i
$804$	15.0949			0.532354
$805$	−5.99705	−	0.328331i	−0.211368	−	0.0115722i
$806$	9.02859			0.318018
$807$	−16.0575	+	9.27082i	−0.565252	+	0.326348i
$808$		−	3.75175i		−	0.131986i
$809$	−8.15320	−	14.1218i	−0.286651	−	0.496495i	0.686357	−	0.727265i	$-0.259209\pi$
$809$	−8.15320	−	14.1218i	−0.286651	−	0.496495i	−0.973008	+	0.230770i	$0.925875\pi$
$810$	0.716403	+	0.467619i	0.0251718	+	0.0164305i
$811$	−19.7864	−	34.2711i	−0.694795	−	1.20342i	−0.970250	−	0.242107i	$-0.922162\pi$
$811$	−19.7864	−	34.2711i	−0.694795	−	1.20342i	0.275454	−	0.961314i	$-0.411172\pi$
$812$	54.9502	+	31.7255i	1.92837	+	1.11335i
$813$		−	20.7260i		−	0.726894i
$814$	12.3322	−	4.57445i	0.432243	−	0.160334i
$815$	4.65218	−	2.35674i	0.162959	−	0.0825530i
$816$	5.49819	−	9.52314i	0.192475	−	0.333377i
$817$	0.847542	−	0.489329i	0.0296517	−	0.0171194i
$818$	8.32769	−	4.80799i	0.291171	−	0.168108i
$819$	6.77607	+	11.7365i	0.236775	+	0.410106i
$820$	5.06094	+	9.99024i	0.176736	+	0.348874i
$821$	−11.9853	−	20.7592i	−0.418291	−	0.724502i	0.577476	−	0.816407i	$-0.304038\pi$
$821$	−11.9853	−	20.7592i	−0.418291	−	0.724502i	−0.995768	+	0.0919055i	$0.970704\pi$
$822$		−	1.32414i		−	0.0461848i
$823$	4.76743	+	2.75248i	0.166182	+	0.0959453i	0.580784	−	0.814057i	$-0.302746\pi$
$823$	4.76743	+	2.75248i	0.166182	+	0.0959453i	−0.414602	+	0.910003i	$0.636079\pi$
$824$	−12.5175			−0.436066
$825$	−22.7844	−	16.7169i	−0.793253	−	0.582009i
$826$	1.95162	−	3.38030i	0.0679055	−	0.117616i
$827$	7.08825	−	4.09240i	0.246482	−	0.142307i	−0.371670	−	0.928365i	$-0.621215\pi$
$827$	7.08825	−	4.09240i	0.246482	−	0.142307i	0.618153	+	0.786058i	$0.287881\pi$
$828$			1.33982i			0.0465621i
$829$	18.9578	−	32.8358i	0.658431	−	1.14044i	−0.322591	−	0.946538i	$-0.604554\pi$
$829$	18.9578	−	32.8358i	0.658431	−	1.14044i	0.981022	−	0.193897i	$-0.0621128\pi$
$830$	14.3226	+	0.784143i	0.497143	+	0.0272180i
$831$	9.28984	−	16.0905i	0.322261	−	0.558172i
$832$	−14.8381	+	8.56676i	−0.514417	+	0.296999i
$833$	−20.6289	+	11.9101i	−0.714748	+	0.412660i
$834$	−0.424686	+	0.735577i	−0.0147057	+	0.0254709i
$835$	2.02717	−	37.0267i	0.0701530	−	1.28136i
$836$	36.2130	−	62.7228i	1.25245	−	2.16931i
$837$		−	6.47062i		−	0.223657i
$838$	9.76763	−	5.63934i	0.337417	−	0.194808i
$839$	−25.6394	+	44.4088i	−0.885172	+	1.53316i	−0.0396553	+	0.999213i	$0.512626\pi$
$839$	−25.6394	+	44.4088i	−0.885172	+	1.53316i	−0.845517	+	0.533949i	$0.820707\pi$
$840$	10.9286	−	5.53633i	0.377074	−	0.191021i
$841$	55.8565			1.92609
$842$	4.73118	+	2.73155i	0.163047	+	0.0941353i
$843$			18.7143i			0.644555i
$844$	18.1851	+	31.4975i	0.625956	+	1.08419i
$845$	−0.303570	−	0.599244i	−0.0104431	−	0.0206146i
$846$	−0.821104	−	1.42219i	−0.0282301	−	0.0488960i
$847$	67.3992	−	38.9130i	2.31586	−	1.33707i
$848$	8.02918	−	4.63565i	0.275723	−	0.159189i
$849$	2.39746	−	4.15252i	0.0822805	−	0.142514i
$850$	3.95906	−	5.39602i	0.135795	−	0.185082i
$851$	3.38536	+	2.80543i	0.116049	+	0.0961688i
$852$			0.964886i			0.0330564i
$853$	6.09582	+	3.51943i	0.208717	+	0.120503i	0.600715	−	0.799463i	$-0.294883\pi$
$853$	6.09582	+	3.51943i	0.208717	+	0.120503i	−0.391998	+	0.919966i	$0.628216\pi$
$854$	−9.37745	−	16.2422i	−0.320890	−	0.555797i
$855$	8.44956	−	12.9449i	0.288969	−	0.442707i
$856$	5.78488	+	10.0197i	0.197723	+	0.342466i
$857$		−	38.9191i		−	1.32945i	−0.747087	−	0.664726i	$-0.768548\pi$
$857$		−	38.9191i		−	1.32945i	0.747087	−	0.664726i	$-0.231452\pi$
$858$	6.82961	−	3.94307i	0.233159	−	0.134614i
$859$	−17.4357			−0.594897			−0.297449	−	0.954738i	$-0.596136\pi$
$859$	−17.4357			−0.594897			−0.297449	+	0.954738i	$0.596136\pi$
$860$	−0.0320758	+	0.585873i	−0.00109378	+	0.0199781i
$861$	−10.0404			−0.342175
$862$			2.39258i			0.0814917i
$863$	15.6796	+	9.05264i	0.533741	+	0.308155i	0.742538	−	0.669803i	$-0.233622\pi$
$863$	15.6796	+	9.05264i	0.533741	+	0.308155i	−0.208798	+	0.977959i	$0.566955\pi$
$864$	−2.07566	−	3.59515i	−0.0706154	−	0.122309i
$865$	48.3121	−	24.4743i	1.64266	−	0.832153i
$866$	−1.51044	+	2.61617i	−0.0513270	+	0.0889009i
$867$	−4.12256	−	2.38016i	−0.140009	−	0.0808345i
$868$	−38.5987	−	22.2850i	−1.31013	−	0.756401i
$869$	20.3227	+	35.1999i	0.689400	+	1.19408i
$870$	4.30759	−	6.59933i	0.146041	−	0.223738i
$871$	14.8495	−	25.7200i	0.503155	−	0.871490i
$872$	−6.76277	−	3.90449i	−0.229016	−	0.132223i
$873$	5.56222	+	3.21135i	0.188253	+	0.108688i
$874$	−1.91184			−0.0646690
$875$	−38.8899	+	14.6168i	−1.31472	+	0.494138i
$876$	−11.3582	+	19.6730i	−0.383758	+	0.664688i
$877$			40.4893i			1.36723i	0.729844	+	0.683614i	$0.239593\pi$
$877$			40.4893i			1.36723i	−0.729844	+	0.683614i	$0.760407\pi$
$878$		−	13.6719i		−	0.461404i
$879$	1.37294	−	2.37801i	0.0463083	−	0.0802083i
$880$	17.9511	+	35.4353i	0.605133	+	1.19453i
$881$	−6.31163	−	10.9321i	−0.212644	−	0.368311i	0.739897	−	0.672720i	$-0.234874\pi$
$881$	−6.31163	−	10.9321i	−0.212644	−	0.368311i	−0.952541	+	0.304410i	$0.901541\pi$
$882$			2.60496i			0.0877136i
$883$	36.2910	−	20.9526i	1.22129	−	0.705112i	0.256096	−	0.966651i	$-0.417564\pi$
$883$	36.2910	−	20.9526i	1.22129	−	0.705112i	0.965193	+	0.261540i	$0.0842302\pi$
$884$	−11.8252	−	20.4818i	−0.397724	−	0.688879i
$885$	5.14073	+	3.35551i	0.172804	+	0.112794i
$886$	6.71411	−	11.6292i	0.225565	−	0.390690i
$887$		−	24.6802i		−	0.828680i	−0.910122	−	0.414340i	$-0.864012\pi$
$887$		−	24.6802i		−	0.828680i	0.910122	−	0.414340i	$-0.135988\pi$
$888$	−8.84146	−	1.50310i	−0.296700	−	0.0504407i
$889$	11.2466			0.377198
$890$	0.0280728	−	0.512757i	0.000941003	−	0.0171876i
$891$	−2.82593	−	4.89465i	−0.0946722	−	0.163977i
$892$	−9.78771	+	5.65094i	−0.327717	+	0.189207i
$893$	−25.6981	+	14.8368i	−0.859953	+	0.496494i
$894$	−2.41964			−0.0809248
$895$	3.26727	−	5.00553i	0.109213	−	0.167317i
$896$	−37.5319			−1.25385
$897$	2.28292	+	1.31804i	0.0762244	+	0.0440082i
$898$			2.25759i			0.0753368i
$899$	−59.6058			−1.98796
$900$	3.73011	+	8.48434i	0.124337	+	0.282811i
$901$	5.15978	+	8.93700i	0.171897	+	0.297735i
$902$			5.84261i			0.194538i
$903$	−0.455568	−	0.263022i	−0.0151604	−	0.00875284i
$904$	−0.866024	+	1.50000i	−0.0288035	+	0.0498892i
$905$	9.19911	+	0.503640i	0.305789	+	0.0167416i
$906$	−3.57237	−	6.18753i	−0.118684	−	0.205567i
$907$	−26.3476	+	15.2118i	−0.874859	+	0.505100i	−0.868960	−	0.494883i	$-0.835211\pi$
$907$	−26.3476	+	15.2118i	−0.874859	+	0.505100i	−0.00589878	+	0.999983i	$0.501878\pi$
$908$	28.1689	+	16.2633i	0.934817	+	0.539717i
$909$	−1.27231	+	2.20371i	−0.0422000	+	0.0730925i
$910$	0.633810	−	11.5767i	0.0210106	−	0.383763i
$911$	41.1983			1.36496			0.682479	−	0.730905i	$-0.260902\pi$
$911$	41.1983			1.36496			0.682479	+	0.730905i	$0.260902\pi$
$912$	−18.8182	+	10.8647i	−0.623133	+	0.359766i
$913$	−82.0665	−	47.3811i	−2.71601	−	1.56809i
$914$	1.60370			0.0530456
$915$	26.3135	−	13.3301i	0.869899	−	0.440681i
$916$	−7.95298	+	13.7750i	−0.262774	+	0.455138i
$917$		−	62.9650i		−	2.07929i
$918$	1.15920	−	0.669262i	0.0382592	−	0.0220889i
$919$	32.5857			1.07490			0.537451	−	0.843295i	$-0.319387\pi$
$919$	32.5857			1.07490			0.537451	+	0.843295i	$0.319387\pi$
$920$	1.30253	−	1.99551i	0.0429432	−	0.0657900i
$921$	−0.648762	−	1.12369i	−0.0213774	−	0.0370268i
$922$	4.64884	−	2.68401i	0.153101	−	0.0883931i
$923$	1.64406	+	0.949200i	0.0541150	+	0.0312433i
$924$	−38.9302			−1.28071
$925$	29.2479	+	8.34024i	0.961665	+	0.274225i
$926$	11.1984			0.368004
$927$	7.35252	+	4.24498i	0.241489	+	0.139424i
$928$	−33.1177	+	19.1205i	−1.08714	+	0.627661i
$929$	−5.96375	−	10.3295i	−0.195664	−	0.338900i	0.751454	−	0.659786i	$-0.229353\pi$
$929$	−5.96375	−	10.3295i	−0.195664	−	0.338900i	−0.947118	+	0.320885i	$0.896020\pi$
$930$	−3.02579	+	4.63558i	−0.0992194	+	0.152006i
$931$	47.0699			1.54265
$932$	−2.58789	+	1.49412i	−0.0847690	+	0.0489414i
$933$		−	19.2348i		−	0.629719i
$934$	4.75931	−	8.24336i	0.155729	−	0.269731i
$935$	−39.4418	+	19.9808i	−1.28989	+	0.653441i
$936$	−5.37703			−0.175754
$937$	−18.4958	−	10.6786i	−0.604233	−	0.348854i	0.166472	−	0.986046i	$-0.446762\pi$
$937$	−18.4958	−	10.6786i	−0.604233	−	0.348854i	−0.770705	+	0.637192i	$0.780096\pi$
$938$	10.0266	−	5.78888i	0.327381	−	0.189014i
$939$	−19.7780			−0.645430
$940$	0.972562	−	17.7641i	0.0317215	−	0.579400i
$941$	−26.7147	+	46.2712i	−0.870875	+	1.50840i	−0.00978152	+	0.999952i	$0.503114\pi$
$941$	−26.7147	+	46.2712i	−0.870875	+	1.50840i	−0.861093	+	0.508447i	$0.830220\pi$
$942$	4.87523	+	2.81471i	0.158843	+	0.0917083i
$943$	−1.69134	+	0.976498i	−0.0550778	+	0.0317992i
$944$	−4.31462	−	7.47314i	−0.140429	−	0.243230i
$945$	−8.29680	−	0.454240i	−0.269895	−	0.0147764i
$946$	−0.153056	+	0.265100i	−0.00497627	+	0.00861916i
$947$	−28.0360	−	16.1866i	−0.911048	−	0.525994i	−0.0302795	−	0.999541i	$-0.509640\pi$
$947$	−28.0360	−	16.1866i	−0.911048	−	0.525994i	−0.880768	+	0.473548i	$0.842973\pi$
$948$		−	13.3303i		−	0.432949i
$949$	22.3471	+	38.7063i	0.725418	+	1.25646i
$950$	−12.1066	+	5.32261i	−0.392790	+	0.172688i
$951$	−18.0291			−0.584634
$952$		−	19.1677i		−	0.621229i
$953$	14.7990	+	8.54422i	0.479387	+	0.276774i	0.720161	−	0.693807i	$-0.244068\pi$
$953$	14.7990	+	8.54422i	0.479387	+	0.276774i	−0.240774	+	0.970581i	$0.577401\pi$
$954$	1.12854			0.0365379
$955$	−16.4635	+	25.2225i	−0.532748	+	0.816182i
$956$	−40.0460			−1.29518
$957$	−45.0883	+	26.0318i	−1.45750	+	0.841488i
$958$	11.0993	−	6.40819i	0.358602	−	0.207039i
$959$	6.43042	+	11.1378i	0.207649	+	0.359659i
$960$	0.574280	−	10.4894i	0.0185348	−	0.338543i
$961$	10.8689			0.350611
$962$	−5.41559	+	6.53509i	−0.174606	+	0.210700i
$963$		−	7.84719i		−	0.252872i
$964$	−25.8957	+	44.8527i	−0.834045	+	1.44461i
$965$	−13.4251	−	8.76295i	−0.432168	−	0.282089i
$966$	0.513823	+	0.889968i	0.0165320	+	0.0286342i
$967$	5.14391	−	2.96984i	0.165417	−	0.0955035i	−0.415006	−	0.909819i	$-0.636221\pi$
$967$	5.14391	−	2.96984i	0.165417	−	0.0955035i	0.580423	+	0.814315i	$0.302887\pi$
$968$			30.8787i			0.992479i
$969$	−12.0931	−	20.9459i	−0.388487	−	0.672879i
$970$	−2.48310	−	4.90162i	−0.0797277	−	0.157382i
$971$	12.4177	−	21.5081i	0.398504	−	0.690229i	−0.595038	−	0.803698i	$-0.702863\pi$
$971$	12.4177	−	21.5081i	0.398504	−	0.690229i	0.993542	+	0.113469i	$0.0361963\pi$
$972$			1.85362i			0.0594549i
$973$		−	8.24957i		−	0.264469i
$974$	−6.27617	+	10.8707i	−0.201102	+	0.348318i
$975$	18.1259	+	1.99071i	0.580493	+	0.0637537i
$976$	−41.4632			−1.32720
$977$	32.8675	+	18.9760i	1.05152	+	0.607097i	0.923075	−	0.384619i	$-0.125667\pi$
$977$	32.8675	+	18.9760i	1.05152	+	0.607097i	0.128448	+	0.991716i	$0.459001\pi$
$978$	−0.772764	−	0.446156i	−0.0247103	−	0.0142665i
$979$	−1.69628	+	2.93803i	−0.0542132	+	0.0939000i
$980$	−15.4252	+	23.6318i	−0.492741	+	0.754890i
$981$	2.64822	+	4.58685i	0.0845511	+	0.146447i
$982$	1.74497	+	1.00746i	0.0556841	+	0.0321492i
$983$	40.2614	+	23.2449i	1.28414	+	0.741398i	0.977602	−	0.210460i	$-0.0674963\pi$
$983$	40.2614	+	23.2449i	1.28414	+	0.741398i	0.306537	+	0.951859i	$0.400830\pi$
$984$	1.99184	−	3.44997i	0.0634975	−	0.109981i
$985$	34.4465	−	17.4502i	1.09756	−	0.556010i
$986$	−6.16508	−	10.6782i	−0.196336	−	0.340064i
$987$	13.8131	+	7.97502i	0.439677	+	0.253848i
$988$			46.7344i			1.48682i
$989$	−0.102323			−0.00325369
$990$	−0.264327	+	4.82800i	−0.00840088	+	0.153444i
$991$	−2.46689			−0.0783634			−0.0391817	−	0.999232i	$-0.512475\pi$
$991$	−2.46689			−0.0783634			−0.0391817	+	0.999232i	$0.512475\pi$
$992$	23.2629	−	13.4308i	0.738596	−	0.426429i
$993$			15.7051i			0.498386i
$994$	0.370034	+	0.640918i	0.0117368	+	0.0203287i
$995$	20.3109	−	31.1168i	0.643899	−	0.986468i
$996$	15.5394	+	26.9151i	0.492385	+	0.852837i
$997$	−23.3700	−	13.4927i	−0.740136	−	0.427318i	0.0819830	−	0.996634i	$-0.473875\pi$
$997$	−23.3700	−	13.4927i	−0.740136	−	0.427318i	−0.822119	+	0.569316i	$0.807208\pi$
$998$			2.03848i			0.0645268i
$999$	4.68357	+	3.88125i	0.148182	+	0.122797i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	555.2.bb.a.454.16	✓	72
5.4	even	2	inner	555.2.bb.a.454.21	yes	72
37.26	even	3	inner	555.2.bb.a.544.21	yes	72
185.174	even	6	inner	555.2.bb.a.544.16	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
555.2.bb.a.454.16	✓	72	1.1	even	1	trivial
555.2.bb.a.454.21	yes	72	5.4	even	2	inner
555.2.bb.a.544.16	yes	72	185.174	even	6	inner
555.2.bb.a.544.21	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)

\(f(q)\)	\(=\)	\(q+(-0.331339 - 0.191298i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.926810 - 1.60528i) q^{4} +(1.22222 - 1.87248i) q^{5} -0.382597 q^{6} +(3.21815 - 1.85800i) q^{7} +1.47438i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.331339 - 0.191298i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.926810 - 1.60528i) q^{4} +(1.22222 - 1.87248i) q^{5} -0.382597 q^{6} +(3.21815 - 1.85800i) q^{7} +1.47438i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.763172 + 0.386614i) q^{10} +5.65186 q^{11} +(-1.60528 - 0.926810i) q^{12} +(-3.15837 + 1.82349i) q^{13} -1.42173 q^{14} +(0.122239 - 2.23272i) q^{15} +(-1.57157 + 2.72204i) q^{16} +(-3.02981 - 1.74926i) q^{17} +(-0.331339 + 0.191298i) q^{18} +(3.45663 + 5.98706i) q^{19} +(-4.13862 - 0.226585i) q^{20} +(1.85800 - 3.21815i) q^{21} +(-1.87268 - 1.08119i) q^{22} -0.722815i q^{23} +(0.737191 + 1.27685i) q^{24} +(-2.01234 - 4.57717i) q^{25} +1.39532 q^{26} -1.00000i q^{27} +(-5.96522 - 3.44402i) q^{28} -9.21176 q^{29} +(-0.467619 + 0.716403i) q^{30} +6.47062 q^{31} +(3.59515 - 2.07566i) q^{32} +(4.89465 - 2.82593i) q^{33} +(0.669262 + 1.15920i) q^{34} +(0.454240 - 8.29680i) q^{35} -1.85362 q^{36} +(-3.88125 + 4.68357i) q^{37} -2.64499i q^{38} +(-1.82349 + 3.15837i) q^{39} +(2.76075 + 1.80203i) q^{40} +(-1.35097 - 2.33994i) q^{41} +(-1.23125 + 0.710864i) q^{42} -0.141562i q^{43} +(-5.23820 - 9.07282i) q^{44} +(-1.01050 - 1.99472i) q^{45} +(-0.138273 + 0.239496i) q^{46} +4.29227i q^{47} +3.14315i q^{48} +(3.40432 - 5.89645i) q^{49} +(-0.208841 + 1.90155i) q^{50} -3.49853 q^{51} +(5.85442 + 3.38005i) q^{52} +(-2.55451 - 1.47484i) q^{53} +(-0.191298 + 0.331339i) q^{54} +(6.90784 - 10.5830i) q^{55} +(2.73940 + 4.74478i) q^{56} +(5.98706 + 3.45663i) q^{57} +(3.05221 + 1.76219i) q^{58} +(-1.37271 + 2.37760i) q^{59} +(-3.69744 + 1.87308i) q^{60} +(6.59581 + 11.4243i) q^{61} +(-2.14397 - 1.23782i) q^{62} -3.71600i q^{63} +4.69801 q^{64} +(-0.445802 + 8.14269i) q^{65} -2.16238 q^{66} +(-7.05243 + 4.07172i) q^{67} +6.48494i q^{68} +(-0.361407 - 0.625976i) q^{69} +(-1.73767 + 2.66215i) q^{70} +(-0.260271 - 0.450802i) q^{71} +(1.27685 + 0.737191i) q^{72} -12.2552i q^{73} +(2.18197 - 0.809371i) q^{74} +(-4.03132 - 2.95778i) q^{75} +(6.40728 - 11.0977i) q^{76} +(18.1885 - 10.5011i) q^{77} +(1.20838 - 0.697660i) q^{78} +(3.59575 + 6.22803i) q^{79} +(3.17615 + 6.26968i) q^{80} +(-0.500000 - 0.866025i) q^{81} +1.03375i q^{82} +(-14.5203 - 8.38329i) q^{83} -6.88805 q^{84} +(-6.97856 + 3.53526i) q^{85} +(-0.0270806 + 0.0469050i) q^{86} +(-7.97762 + 4.60588i) q^{87} +8.33300i q^{88} +(-0.300127 + 0.519835i) q^{89} +(-0.0467682 + 0.854233i) q^{90} +(-6.77607 + 11.7365i) q^{91} +(-1.16032 + 0.669912i) q^{92} +(5.60372 - 3.23531i) q^{93} +(0.821104 - 1.42219i) q^{94} +(15.4354 + 0.845071i) q^{95} +(2.07566 - 3.59515i) q^{96} +6.42270i q^{97} +(-2.25596 + 1.30248i) q^{98} +(2.82593 - 4.89465i) 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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