LMFDB - Embedded newform 187.2.j.a.16.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(16,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 5]))

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

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

chi := DirichletCharacter("187.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.j (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			16.8
Character	$\chi$	$=$	187.16
Dual form			187.2.j.a.152.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.150351 - 0.462733i) q^{2} +(1.01595 - 1.39834i) q^{3} +(1.42652 - 1.03643i) q^{4} +(-0.411135 - 0.133586i) q^{5} +(-0.799806 - 0.259873i) q^{6} +(-1.36610 - 1.88027i) q^{7} +(-1.48131 - 1.07624i) q^{8} +(0.00385940 + 0.0118780i) q^{9} +O(q^{10})$	\(q+(-0.150351 - 0.462733i) q^{2} +(1.01595 - 1.39834i) q^{3} +(1.42652 - 1.03643i) q^{4} +(-0.411135 - 0.133586i) q^{5} +(-0.799806 - 0.259873i) q^{6} +(-1.36610 - 1.88027i) q^{7} +(-1.48131 - 1.07624i) q^{8} +(0.00385940 + 0.0118780i) q^{9} +0.210330i q^{10} +(-0.896081 + 3.19328i) q^{11} -3.04771i q^{12} +(1.55373 + 4.78190i) q^{13} +(-0.664669 + 0.914838i) q^{14} +(-0.604491 + 0.439189i) q^{15} +(0.814469 - 2.50668i) q^{16} +(-1.54409 - 3.82306i) q^{17} +(0.00491608 - 0.00357174i) q^{18} +(3.47951 + 2.52801i) q^{19} +(-0.724943 + 0.235548i) q^{20} -4.01715 q^{21} +(1.61236 - 0.0654670i) q^{22} -2.37337i q^{23} +(-3.00989 + 0.977972i) q^{24} +(-3.89390 - 2.82908i) q^{25} +(1.97914 - 1.43793i) q^{26} +(4.95207 + 1.60902i) q^{27} +(-3.89752 - 1.26638i) q^{28} +(2.24111 + 3.08463i) q^{29} +(0.294113 + 0.213685i) q^{30} +(8.80885 - 2.86217i) q^{31} -4.94439 q^{32} +(3.55491 + 4.49725i) q^{33} +(-1.53690 + 1.28930i) q^{34} +(0.310472 + 0.955536i) q^{35} +(0.0178162 + 0.0129442i) q^{36} +(2.44435 + 3.36436i) q^{37} +(0.646646 - 1.99017i) q^{38} +(8.26523 + 2.68554i) q^{39} +(0.465250 + 0.640361i) q^{40} +(-6.87388 + 9.46108i) q^{41} +(0.603982 + 1.85886i) q^{42} -6.49757 q^{43} +(2.03132 + 5.48399i) q^{44} -0.00539902i q^{45} +(-1.09824 + 0.356838i) q^{46} +(-4.92926 - 3.58132i) q^{47} +(-2.67772 - 3.68557i) q^{48} +(0.493920 - 1.52013i) q^{49} +(-0.723658 + 2.22719i) q^{50} +(-6.91466 - 1.72488i) q^{51} +(7.17251 + 5.21114i) q^{52} +(2.57340 + 7.92012i) q^{53} -2.53340i q^{54} +(0.794987 - 1.19316i) q^{55} +4.25552i q^{56} +(7.07004 - 2.29719i) q^{57} +(1.09040 - 1.50081i) q^{58} +(-8.63769 + 6.27565i) q^{59} +(-0.407131 + 1.25302i) q^{60} +(-3.16977 - 1.02992i) q^{61} +(-2.64884 - 3.64581i) q^{62} +(0.0170616 - 0.0234832i) q^{63} +(-0.885545 - 2.72543i) q^{64} -2.17356i q^{65} +(1.54654 - 2.32114i) q^{66} +6.52631 q^{67} +(-6.16499 - 3.85332i) q^{68} +(-3.31877 - 2.41123i) q^{69} +(0.395478 - 0.287331i) q^{70} +(7.27416 + 2.36352i) q^{71} +(0.00706658 - 0.0217487i) q^{72} +(-4.94642 - 6.80816i) q^{73} +(1.18929 - 1.63691i) q^{74} +(-7.91203 + 2.57078i) q^{75} +7.58368 q^{76} +(7.22837 - 2.67746i) q^{77} -4.22837i q^{78} +(-3.58850 + 1.16598i) q^{79} +(-0.669713 + 0.921781i) q^{80} +(7.25071 - 5.26795i) q^{81} +(5.41145 + 1.75829i) q^{82} +(2.20955 - 6.80030i) q^{83} +(-5.73053 + 4.16347i) q^{84} +(0.124124 + 1.77806i) q^{85} +(0.976916 + 3.00664i) q^{86} +6.59022 q^{87} +(4.76411 - 3.76586i) q^{88} -9.25653 q^{89} +(-0.00249830 + 0.000811748i) q^{90} +(6.86872 - 9.45398i) q^{91} +(-2.45982 - 3.38565i) q^{92} +(4.94709 - 15.2256i) q^{93} +(-0.916074 + 2.81939i) q^{94} +(-1.09284 - 1.50417i) q^{95} +(-5.02326 + 6.91393i) q^{96} +(-17.9197 + 5.82245i) q^{97} -0.777675 q^{98} +(-0.0413881 + 0.00168049i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{2} - 20 q^{4} - 4 q^{8} + 30 q^{9}+O(q^{10}) $ 64 * q - 8 * q^2 - 20 * q^4 - 4 * q^8 + 30 * q^9	$ 64 q - 8 q^{2} - 20 q^{4} - 4 q^{8} + 30 q^{9} - 4 q^{13} - 34 q^{15} - 16 q^{16} - 14 q^{17} + 10 q^{18} - 72 q^{21} + 36 q^{25} + 22 q^{26} - 8 q^{30} + 84 q^{32} - 44 q^{33} - 44 q^{34} + 18 q^{35} - 32 q^{36} - 60 q^{38} - 10 q^{42} + 32 q^{43} + 16 q^{47} - 18 q^{49} + 4 q^{50} - 2 q^{51} + 44 q^{52} - 16 q^{53} + 22 q^{55} - 50 q^{59} + 68 q^{60} - 80 q^{64} - 172 q^{66} + 40 q^{67} + 18 q^{68} + 6 q^{69} + 128 q^{70} + 186 q^{72} - 116 q^{76} - 30 q^{77} + 48 q^{81} - 12 q^{83} + 68 q^{84} - 108 q^{85} - 16 q^{86} + 92 q^{87} - 40 q^{89} - 80 q^{93} - 188 q^{94} + 72 q^{98}+O(q^{100}) $ 64 * q - 8 * q^2 - 20 * q^4 - 4 * q^8 + 30 * q^9 - 4 * q^13 - 34 * q^15 - 16 * q^16 - 14 * q^17 + 10 * q^18 - 72 * q^21 + 36 * q^25 + 22 * q^26 - 8 * q^30 + 84 * q^32 - 44 * q^33 - 44 * q^34 + 18 * q^35 - 32 * q^36 - 60 * q^38 - 10 * q^42 + 32 * q^43 + 16 * q^47 - 18 * q^49 + 4 * q^50 - 2 * q^51 + 44 * q^52 - 16 * q^53 + 22 * q^55 - 50 * q^59 + 68 * q^60 - 80 * q^64 - 172 * q^66 + 40 * q^67 + 18 * q^68 + 6 * q^69 + 128 * q^70 + 186 * q^72 - 116 * q^76 - 30 * q^77 + 48 * q^81 - 12 * q^83 + 68 * q^84 - 108 * q^85 - 16 * q^86 + 92 * q^87 - 40 * q^89 - 80 * q^93 - 188 * q^94 + 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.150351	−	0.462733i	−0.106314	−	0.327201i	0.883722	−	0.468011i	$-0.155029\pi$
$2$	−0.150351	−	0.462733i	−0.106314	−	0.327201i	−0.990037	+	0.140810i	$0.955029\pi$
$3$	1.01595	−	1.39834i	0.586560	−	0.807331i	−0.407835	−	0.913056i	$-0.633716\pi$
$3$	1.01595	−	1.39834i	0.586560	−	0.807331i	0.994395	+	0.105724i	$0.0337161\pi$
$4$	1.42652	−	1.03643i	0.713259	−	0.518213i
$5$	−0.411135	−	0.133586i	−0.183865	−	0.0597414i	0.215637	−	0.976474i	$-0.430817\pi$
$5$	−0.411135	−	0.133586i	−0.183865	−	0.0597414i	−0.399502	+	0.916732i	$0.630817\pi$
$6$	−0.799806	−	0.259873i	−0.326520	−	0.106093i
$7$	−1.36610	−	1.88027i	−0.516336	−	0.710676i	0.468636	−	0.883392i	$-0.344746\pi$
$7$	−1.36610	−	1.88027i	−0.516336	−	0.710676i	−0.984972	+	0.172716i	$0.944746\pi$
$8$	−1.48131	−	1.07624i	−0.523724	−	0.380508i
$9$	0.00385940	+	0.0118780i	0.00128647	+	0.00395933i
$10$			0.210330i			0.0665122i
$11$	−0.896081	+	3.19328i	−0.270178	+	0.962810i
$11$	−0.896081	+	3.19328i	−0.270178	+	0.962810i
$12$		−	3.04771i		−	0.879799i
$13$	1.55373	+	4.78190i	0.430928	+	1.32626i	0.897202	+	0.441620i	$0.145596\pi$
$13$	1.55373	+	4.78190i	0.430928	+	1.32626i	−0.466274	+	0.884640i	$0.654404\pi$
$14$	−0.664669	+	0.914838i	−0.177640	+	0.244501i
$15$	−0.604491	+	0.439189i	−0.156079	+	0.113398i
$16$	0.814469	−	2.50668i	0.203617	−	0.626670i
$17$	−1.54409	−	3.82306i	−0.374498	−	0.927228i
$17$	−1.54409	−	3.82306i	−0.374498	−	0.927228i
$18$	0.00491608	−	0.00357174i	0.00115873	−	0.000841867i
$19$	3.47951	+	2.52801i	0.798255	+	0.579966i	0.910402	−	0.413726i	$-0.135773\pi$
$19$	3.47951	+	2.52801i	0.798255	+	0.579966i	−0.112147	+	0.993692i	$0.535773\pi$
$20$	−0.724943	+	0.235548i	−0.162102	+	0.0526702i
$21$	−4.01715			−0.876613
$22$	1.61236	−	0.0654670i	0.343757	−	0.0139576i
$23$		−	2.37337i		−	0.494882i	−0.968903	−	0.247441i	$-0.920410\pi$
$23$		−	2.37337i		−	0.494882i	0.968903	−	0.247441i	$-0.0795896\pi$
$24$	−3.00989	+	0.977972i	−0.614391	+	0.199628i
$25$	−3.89390	−	2.82908i	−0.778780	−	0.565817i
$26$	1.97914	−	1.43793i	0.388140	−	0.282001i
$27$	4.95207	+	1.60902i	0.953026	+	0.309657i
$28$	−3.89752	−	1.26638i	−0.736563	−	0.239324i
$29$	2.24111	+	3.08463i	0.416164	+	0.572801i	0.964708	−	0.263320i	$-0.0848177\pi$
$29$	2.24111	+	3.08463i	0.416164	+	0.572801i	−0.548544	+	0.836122i	$0.684818\pi$
$30$	0.294113	+	0.213685i	0.0536974	+	0.0390134i
$31$	8.80885	−	2.86217i	1.58212	−	0.514061i	0.619515	−	0.784985i	$-0.287329\pi$
$31$	8.80885	−	2.86217i	1.58212	−	0.514061i	0.962601	+	0.270924i	$0.0873292\pi$
$32$	−4.94439			−0.874053
$33$	3.55491	+	4.49725i	0.618831	+	0.782870i
$34$	−1.53690	+	1.28930i	−0.263576	+	0.221114i
$35$	0.310472	+	0.955536i	0.0524794	+	0.161515i
$36$	0.0178162	+	0.0129442i	0.00296936	+	0.00215737i
$37$	2.44435	+	3.36436i	0.401849	+	0.553097i	0.961207	−	0.275829i	$-0.0889523\pi$
$37$	2.44435	+	3.36436i	0.401849	+	0.553097i	−0.559358	+	0.828926i	$0.688952\pi$
$38$	0.646646	−	1.99017i	0.104900	−	0.322849i
$39$	8.26523	+	2.68554i	1.32350	+	0.430030i
$40$	0.465250	+	0.640361i	0.0735624	+	0.101250i
$41$	−6.87388	+	9.46108i	−1.07352	+	1.47757i	−0.207059	+	0.978329i	$0.566389\pi$
$41$	−6.87388	+	9.46108i	−1.07352	+	1.47757i	−0.866461	+	0.499245i	$0.833611\pi$
$42$	0.603982	+	1.85886i	0.0931964	+	0.286829i
$43$	−6.49757			−0.990870			−0.495435	−	0.868645i	$-0.664991\pi$
$43$	−6.49757			−0.990870			−0.495435	+	0.868645i	$0.664991\pi$
$44$	2.03132	+	5.48399i	0.306234	+	0.826743i
$45$		−	0.00539902i		−	0.000804838i
$46$	−1.09824	+	0.356838i	−0.161926	+	0.0526129i
$47$	−4.92926	−	3.58132i	−0.719007	−	0.522389i	0.167060	−	0.985947i	$-0.446573\pi$
$47$	−4.92926	−	3.58132i	−0.719007	−	0.522389i	−0.886067	+	0.463558i	$0.846573\pi$
$48$	−2.67772	−	3.68557i	−0.386496	−	0.531966i
$49$	0.493920	−	1.52013i	0.0705600	−	0.217161i
$50$	−0.723658	+	2.22719i	−0.102341	+	0.314972i
$51$	−6.91466	−	1.72488i	−0.968245	−	0.241532i
$52$	7.17251	+	5.21114i	0.994649	+	0.722654i
$53$	2.57340	+	7.92012i	0.353484	+	1.08791i	0.956883	+	0.290473i	$0.0938126\pi$
$53$	2.57340	+	7.92012i	0.353484	+	1.08791i	−0.603399	+	0.797439i	$0.706187\pi$
$54$		−	2.53340i		−	0.344752i
$55$	0.794987	−	1.19316i	0.107196	−	0.160886i
$56$			4.25552i			0.568668i
$57$	7.07004	−	2.29719i	0.936449	−	0.304271i
$58$	1.09040	−	1.50081i	0.143177	−	0.197066i
$59$	−8.63769	+	6.27565i	−1.12453	+	0.817020i	−0.984890	−	0.173182i	$-0.944595\pi$
$59$	−8.63769	+	6.27565i	−1.12453	+	0.817020i	−0.139642	+	0.990202i	$0.544595\pi$
$60$	−0.407131	+	1.25302i	−0.0525604	+	0.161764i
$61$	−3.16977	−	1.02992i	−0.405848	−	0.131868i	0.0989772	−	0.995090i	$-0.468443\pi$
$61$	−3.16977	−	1.02992i	−0.405848	−	0.131868i	−0.504825	+	0.863222i	$0.668443\pi$
$62$	−2.64884	−	3.64581i	−0.336403	−	0.463019i
$63$	0.0170616	−	0.0234832i	0.00214955	−	0.00295861i
$64$	−0.885545	−	2.72543i	−0.110693	−	0.340679i
$65$		−	2.17356i		−	0.269597i
$66$	1.54654	−	2.32114i	0.190366	−	0.285712i
$67$	6.52631			0.797316			0.398658	−	0.917100i	$-0.369476\pi$
$67$	6.52631			0.797316			0.398658	+	0.917100i	$0.369476\pi$
$68$	−6.16499	−	3.85332i	−0.747615	−	0.467284i
$69$	−3.31877	−	2.41123i	−0.399533	−	0.290278i
$70$	0.395478	−	0.287331i	0.0472686	−	0.0343427i
$71$	7.27416	+	2.36352i	0.863284	+	0.280498i	0.706999	−	0.707214i	$-0.250048\pi$
$71$	7.27416	+	2.36352i	0.863284	+	0.280498i	0.156285	+	0.987712i	$0.450048\pi$
$72$	0.00706658	−	0.0217487i	0.000832804	−	0.00256311i
$73$	−4.94642	−	6.80816i	−0.578934	−	0.796835i	0.414644	−	0.909984i	$-0.363906\pi$
$73$	−4.94642	−	6.80816i	−0.578934	−	0.796835i	−0.993578	+	0.113149i	$0.963906\pi$
$74$	1.18929	−	1.63691i	0.138252	−	0.190288i
$75$	−7.91203	+	2.57078i	−0.913603	+	0.296848i
$76$	7.58368			0.869908
$77$	7.22837	−	2.67746i	0.823749	−	0.305124i
$78$		−	4.22837i		−	0.478768i
$79$	−3.58850	+	1.16598i	−0.403738	+	0.131182i	−0.503845	−	0.863794i	$-0.668082\pi$
$79$	−3.58850	+	1.16598i	−0.403738	+	0.131182i	0.100107	+	0.994977i	$0.468082\pi$
$80$	−0.669713	+	0.921781i	−0.0748762	+	0.103058i
$81$	7.25071	−	5.26795i	0.805635	−	0.585328i
$82$	5.41145	+	1.75829i	0.597594	+	0.194170i
$83$	2.20955	−	6.80030i	0.242530	−	0.746430i	−0.753503	−	0.657444i	$-0.771637\pi$
$83$	2.20955	−	6.80030i	0.242530	−	0.746430i	0.996033	−	0.0889858i	$-0.0283626\pi$
$84$	−5.73053	+	4.16347i	−0.625252	+	0.454272i
$85$	0.124124	+	1.77806i	0.0134631	+	0.192858i
$86$	0.976916	+	3.00664i	0.105344	+	0.324214i
$87$	6.59022			0.706546
$88$	4.76411	−	3.76586i	0.507855	−	0.401442i
$89$	−9.25653			−0.981190			−0.490595	−	0.871388i	$-0.663221\pi$
$89$	−9.25653			−0.981190			−0.490595	+	0.871388i	$0.663221\pi$
$90$	−0.00249830		0.000811748i	−0.000263344		8.55657e-5i
$91$	6.86872	−	9.45398i	0.720037	−	0.991046i
$92$	−2.45982	−	3.38565i	−0.256454	−	0.352979i
$93$	4.94709	−	15.2256i	0.512990	−	1.57882i
$94$	−0.916074	+	2.81939i	−0.0944858	+	0.290797i
$95$	−1.09284	−	1.50417i	−0.112123	−	0.154324i
$96$	−5.02326	+	6.91393i	−0.512685	+	0.705650i
$97$	−17.9197	+	5.82245i	−1.81947	+	0.591180i	−0.819633	+	0.572889i	$0.805822\pi$
$97$	−17.9197	+	5.82245i	−1.81947	+	0.591180i	−0.999833	+	0.0182907i	$0.994178\pi$
$98$	−0.777675			−0.0785570
$99$	−0.0413881	+	0.00168049i	−0.00415966	+	0.000168895i
$100$	−8.48685			−0.848685
$101$	−2.15273	−	6.62541i	−0.214204	−	0.659253i	−0.999209	−	0.0397636i	$-0.987340\pi$
$101$	−2.15273	−	6.62541i	−0.214204	−	0.659253i	0.785005	−	0.619490i	$-0.212660\pi$
$102$	0.241466	+	3.45897i	0.0239087	+	0.342490i
$103$	−1.27548	+	0.926687i	−0.125676	+	0.0913092i	−0.648848	−	0.760918i	$-0.724749\pi$
$103$	−1.27548	+	0.926687i	−0.125676	+	0.0913092i	0.523171	+	0.852228i	$0.324749\pi$
$104$	2.84489	−	8.75568i	0.278965	−	0.858565i
$105$	1.65159	+	0.536633i	0.161178	+	0.0523701i
$106$	3.27798	−	2.38159i	0.318386	−	0.231321i
$107$	3.70517	−	5.09974i	0.358193	−	0.493010i	−0.591451	−	0.806341i	$-0.701445\pi$
$107$	3.70517	−	5.09974i	0.358193	−	0.493010i	0.949644	+	0.313331i	$0.101445\pi$
$108$	8.73185	−	2.83715i	0.840222	−	0.273005i
$109$		−	1.62388i		−	0.155539i	−0.996971	−	0.0777697i	$-0.975220\pi$
$109$		−	1.62388i		−	0.155539i	0.996971	−	0.0777697i	$-0.0247799\pi$
$110$	−0.671643	−	0.188473i	−0.0640387	−	0.0179702i
$111$	7.18786			0.682241
$112$	−5.82588	+	1.89294i	−0.550494	+	0.178866i
$113$	−0.854036	+	1.17548i	−0.0803410	+	0.110580i	−0.847296	−	0.531121i	$-0.821771\pi$
$113$	−0.854036	+	1.17548i	−0.0803410	+	0.110580i	0.766955	+	0.641701i	$0.221771\pi$
$114$	−2.12597	−	2.92615i	−0.199116	−	0.274059i
$115$	−0.317048	+	0.975774i	−0.0295649	+	0.0909914i
$116$	6.39398	+	2.07753i	0.593666	+	0.192894i
$117$	−0.0508029	+	0.0369105i	−0.00469673	+	0.00341238i
$118$	4.20263	+	3.05339i	0.386884	+	0.281088i
$119$	−5.07901	+	8.12598i	−0.465592	+	0.744908i
$120$	1.36811			0.124891
$121$	−9.39408	−	5.72287i	−0.854007	−	0.520261i
$122$			1.62161i			0.146813i
$123$	6.24626	+	19.2240i	0.563207	+	1.73337i
$124$	9.59956	−	13.2127i	0.862066	−	1.18653i
$125$	2.49347	+	3.43196i	0.223023	+	0.306964i
$126$	−0.0134317	−	0.00436422i	−0.00119659	−	0.000388795i
$127$	0.314505	−	0.967948i	0.0279078	−	0.0858915i	−0.936132	−	0.351648i	$-0.885622\pi$
$127$	0.314505	−	0.967948i	0.0279078	−	0.0858915i	0.964040	+	0.265756i	$0.0856216\pi$
$128$	−9.12819	+	6.63202i	−0.806826	+	0.586193i
$129$	−6.60122	+	9.08581i	−0.581205	+	0.799961i
$130$	−1.00578	+	0.326797i	−0.0882125	+	0.0286620i
$131$		−	15.8013i		−	1.38056i	−0.723541	−	0.690281i	$-0.757487\pi$
$131$		−	15.8013i		−	1.38056i	0.723541	−	0.690281i	$-0.242513\pi$
$132$	9.73221	+	2.73100i	0.847080	+	0.237703i
$133$		−	9.99594i		−	0.866758i
$134$	−0.981237	−	3.01994i	−0.0847660	−	0.260883i
$135$	−1.82102	−	1.32305i	−0.156729	−	0.113870i
$136$	−1.82723	+	7.32496i	−0.156684	+	0.628110i
$137$	0.944546	−	2.90701i	0.0806980	−	0.248363i	−0.902565	−	0.430553i	$-0.858319\pi$
$137$	0.944546	−	2.90701i	0.0806980	−	0.248363i	0.983263	+	0.182190i	$0.0583186\pi$
$138$	−0.616774	+	1.89824i	−0.0525033	+	0.161589i
$139$	4.65678	+	6.40951i	0.394983	+	0.543648i	0.959476	−	0.281790i	$-0.0909282\pi$
$139$	4.65678	+	6.40951i	0.394983	+	0.543648i	−0.564493	+	0.825438i	$0.690928\pi$
$140$	1.43324	+	1.04131i	0.121131	+	0.0880065i
$141$	−10.0158	+	3.25433i	−0.843482	+	0.274064i
$142$		−	3.72135i		−	0.312289i
$143$	−16.6622	+	0.676538i	−1.39336	+	0.0565750i
$144$	0.0329177			0.00274314
$145$	−0.509337	−	1.56758i	−0.0422982	−	0.130180i
$146$	−2.40666	+	3.31248i	−0.199176	+	0.274143i
$147$	−1.62386	−	2.23505i	−0.133933	−	0.184343i
$148$	6.97382	+	2.26593i	0.573244	+	0.186258i
$149$	−1.90237	+	5.85489i	−0.155848	+	0.479651i	−0.998246	−	0.0592050i	$-0.981143\pi$
$149$	−1.90237	+	5.85489i	−0.155848	+	0.479651i	0.842398	+	0.538856i	$0.181143\pi$
$150$	2.37916	+	3.27464i	0.194258	+	0.267373i
$151$	17.0171	+	12.3637i	1.38483	+	1.00614i	0.996410	+	0.0846609i	$0.0269807\pi$
$151$	17.0171	+	12.3637i	1.38483	+	1.00614i	0.388425	+	0.921480i	$0.373019\pi$
$152$	−2.43351	−	7.48956i	−0.197383	−	0.607484i
$153$	0.0394510	−	0.0330954i	0.00318943	−	0.00267561i
$154$	−2.32574	−	2.94224i	−0.187413	−	0.237093i
$155$	−4.00397			−0.321606
$156$	14.5739	−	4.73534i	1.16684	−	0.379130i
$157$	−8.74166	−	6.35119i	−0.697661	−	0.506880i	0.181509	−	0.983389i	$-0.441902\pi$
$157$	−8.74166	−	6.35119i	−0.697661	−	0.506880i	−0.879170	+	0.476509i	$0.841902\pi$
$158$	1.07907	+	1.48521i	0.0858462	+	0.118157i
$159$	13.6895	+	4.44798i	1.08565	+	0.352748i
$160$	2.03281	+	0.660500i	0.160708	+	0.0522171i
$161$	−4.46258	+	3.24225i	−0.351700	+	0.255525i
$162$	−3.52781	−	2.56310i	−0.277171	−	0.201376i
$163$	2.98170	−	0.968814i	0.233545	−	0.0758833i	−0.189906	−	0.981802i	$-0.560818\pi$
$163$	2.98170	−	0.968814i	0.233545	−	0.0758833i	0.423451	+	0.905919i	$0.360818\pi$
$164$			20.6207i			1.61020i
$165$	−0.860780	−	2.32386i	−0.0670116	−	0.180912i
$166$	−3.47893			−0.270017
$167$	4.45699	−	1.44816i	0.344892	−	0.112062i	−0.131449	−	0.991323i	$-0.541963\pi$
$167$	4.45699	−	1.44816i	0.344892	−	0.112062i	0.476341	+	0.879261i	$0.341963\pi$
$168$	5.95066	+	4.32340i	0.459103	+	0.333558i
$169$	−9.93525	+	7.21838i	−0.764250	+	0.555260i
$170$	0.804105	−	0.324769i	0.0616720	−	0.0249087i
$171$	−0.0165989	+	0.0510862i	−0.00126935	+	0.00390666i
$172$	−9.26890	+	6.73425i	−0.706747	+	0.513482i
$173$	9.09639	−	12.5201i	0.691586	−	0.951886i	−0.308414	−	0.951252i	$-0.599798\pi$
$173$	9.09639	−	12.5201i	0.691586	−	0.951886i	1.00000		0.000633895i	$-0.000201775\pi$
$174$	−0.990846	−	3.04951i	−0.0751158	−	0.231183i
$175$			11.1864i			0.845611i
$176$	7.27470	+	4.84702i	0.548351	+	0.365358i
$177$			18.4542i			1.38710i
$178$	1.39173	+	4.28330i	0.104314	+	0.321047i
$179$	−0.490281	−	0.356210i	−0.0366454	−	0.0266244i	0.569312	−	0.822122i	$-0.307210\pi$
$179$	−0.490281	−	0.356210i	−0.0366454	−	0.0266244i	−0.605957	+	0.795497i	$0.707210\pi$
$180$	−0.00559568	−	0.00770180i	−0.000417078	−	0.000574058i
$181$	−20.0063	−	6.50043i	−1.48705	−	0.483173i	−0.550842	−	0.834610i	$-0.685693\pi$
$181$	−20.0063	−	6.50043i	−1.48705	−	0.483173i	−0.936212	+	0.351437i	$0.885693\pi$
$182$	−5.40738	−	1.75697i	−0.400822	−	0.130235i
$183$	−4.66052	+	3.38606i	−0.344515	+	0.250305i
$184$	−2.55431	+	3.51571i	−0.188306	+	0.259181i
$185$	−0.555527	−	1.70973i	−0.0408431	−	0.125702i
$186$	−7.78917			−0.571130
$187$	13.5917	−	1.50495i	0.993926	−	0.110053i
$188$	−10.7435			−0.783547
$189$	−3.73960	−	11.5093i	−0.272016	−	0.837179i
$190$	−0.531717	+	0.731846i	−0.0385748	+	0.0530937i
$191$	8.68366	−	6.30905i	0.628327	−	0.456507i	−0.227493	−	0.973780i	$-0.573053\pi$
$191$	8.68366	−	6.30905i	0.628327	−	0.456507i	0.855820	+	0.517273i	$0.173053\pi$
$192$	−4.71074	−	1.53061i	−0.339969	−	0.110463i
$193$	24.4865	+	7.95616i	1.76258	+	0.572697i	0.997462	−	0.0711942i	$-0.0226810\pi$
$193$	24.4865	+	7.95616i	1.76258	+	0.572697i	0.765117	+	0.643891i	$0.222681\pi$
$194$	5.38847	+	7.41660i	0.386870	+	0.532481i
$195$	−3.03937	−	2.20823i	−0.217654	−	0.158135i
$196$	−0.870916	−	2.68040i	−0.0622083	−	0.191457i
$197$		−	9.70356i		−	0.691350i	−0.938354	−	0.345675i	$-0.887650\pi$
$197$		−	9.70356i		−	0.691350i	0.938354	−	0.345675i	$-0.112350\pi$
$198$	0.00700036	+	0.0188990i	0.000497494	+	0.00134309i
$199$			22.5370i			1.59761i	0.601592	+	0.798804i	$0.294533\pi$
$199$			22.5370i			1.59761i	−0.601592	+	0.798804i	$0.705467\pi$
$200$	2.72332	+	8.38152i	0.192568	+	0.592663i
$201$	6.63043	−	9.12600i	0.467674	−	0.643698i
$202$	−2.74213	+	1.99227i	−0.192936	+	0.140176i
$203$	2.73836	−	8.42781i	0.192195	−	0.591516i
$204$	−11.6516	+	4.70595i	−0.815775	+	0.329483i
$205$	4.08996	−	2.97153i	0.285655	−	0.207540i
$206$	0.620577	+	0.450876i	0.0432377	+	0.0314140i
$207$	0.0281909	−	0.00915977i	0.00195940	−	0.000636648i
$208$	13.2522			0.918872
$209$	−11.1906	+	8.84575i	−0.774068	+	0.611873i
$210$		−	0.844927i		−	0.0583055i
$211$	−7.10620	+	2.30894i	−0.489211	+	0.158954i	−0.543227	−	0.839586i	$-0.682798\pi$
$211$	−7.10620	+	2.30894i	−0.489211	+	0.158954i	0.0540162	+	0.998540i	$0.482798\pi$
$212$	11.8796	+	8.63105i	0.815896	+	0.592783i
$213$	10.6952	−	7.77052i	0.732823	−	0.532427i
$214$	−2.91689	−	0.947755i	−0.199395	−	0.0647872i
$215$	2.67138	+	0.867983i	0.182186	+	0.0591959i
$216$	−5.60388	−	7.71307i	−0.381295	−	0.524808i
$217$	−17.4154	−	12.6530i	−1.18223	−	0.858943i
$218$	−0.751421	+	0.244152i	−0.0508927	+	0.0165360i
$219$	−14.5454			−0.982889
$220$	−0.102564	−	2.52602i	−0.00691488	−	0.170304i
$221$	15.8824	−	13.3237i	1.06836	−	0.896250i
$222$	−1.08070	−	3.32606i	−0.0725319	−	0.223230i
$223$	−5.23252	−	3.80165i	−0.350396	−	0.254577i	0.398639	−	0.917108i	$-0.369483\pi$
$223$	−5.23252	−	3.80165i	−0.350396	−	0.254577i	−0.749035	+	0.662530i	$0.769483\pi$
$224$	6.75451	+	9.29679i	0.451305	+	0.621168i
$225$	0.0185758	−	0.0571703i	0.00123838	−	0.00381135i
$226$	0.672338	+	0.218456i	0.0447233	+	0.0145315i
$227$	−7.59451	−	10.4529i	−0.504065	−	0.693786i	0.478839	−	0.877903i	$-0.341058\pi$
$227$	−7.59451	−	10.4529i	−0.504065	−	0.693786i	−0.982904	+	0.184116i	$0.941058\pi$
$228$	7.70466	−	10.6046i	0.510254	−	0.702304i
$229$	6.35848	+	19.5694i	0.420180	+	1.29318i	0.907534	+	0.419978i	$0.137962\pi$
$229$	6.35848	+	19.5694i	0.420180	+	1.29318i	−0.487354	+	0.873205i	$0.662038\pi$
$230$	0.499191			0.0329157
$231$	3.59969	−	12.8279i	0.236842	−	0.844012i
$232$		−	6.98128i		−	0.458343i
$233$	−13.4025	+	4.35473i	−0.878026	+	0.285288i	−0.713138	−	0.701024i	$-0.752726\pi$
$233$	−13.4025	+	4.35473i	−0.878026	+	0.285288i	−0.164889	+	0.986312i	$0.552726\pi$
$234$	0.0247180	+	0.0179586i	0.00161586	+	0.00117399i
$235$	1.54818	+	2.13088i	0.100992	+	0.139004i
$236$	−5.81758	+	17.9047i	−0.378692	+	1.16549i
$237$	−2.01532	+	6.20252i	−0.130909	+	0.402897i
$238$	4.52379	+	1.12847i	0.293234	+	0.0731480i
$239$	−7.08356	−	5.14650i	−0.458197	−	0.332900i	0.334626	−	0.942351i	$-0.391390\pi$
$239$	−7.08356	−	5.14650i	−0.458197	−	0.332900i	−0.792824	+	0.609451i	$0.791390\pi$
$240$	0.608565	+	1.87297i	0.0392827	+	0.120900i
$241$		−	16.9328i		−	1.09073i	−0.838197	−	0.545367i	$-0.816390\pi$
$241$		−	16.9328i		−	1.09073i	0.838197	−	0.545367i	$-0.183610\pi$
$242$	−1.23575	+	5.20739i	−0.0794371	+	0.334743i
$243$			0.129791i			0.00832613i
$244$	−5.58917	+	1.81603i	−0.357810	+	0.116260i
$245$	−0.406135	+	0.558997i	−0.0259470	+	0.0357130i
$246$	7.95645	−	5.78070i	0.507285	−	0.368564i
$247$	−6.68247	+	20.5665i	−0.425195	+	1.30862i
$248$	−16.1290	−	5.24065i	−1.02420	−	0.332781i
$249$	−7.26433	−	9.99849i	−0.460358	−	0.633628i
$250$	1.21319	−	1.66981i	0.0767286	−	0.105608i
$251$	−0.580413	−	1.78633i	−0.0366354	−	0.112752i	0.931066	−	0.364850i	$-0.118880\pi$
$251$	−0.580413	−	1.78633i	−0.0366354	−	0.112752i	−0.967702	+	0.252098i	$0.918880\pi$
$252$		−	0.0511823i		−	0.00322418i
$253$	7.57883	+	2.12673i	0.476477	+	0.133706i
$254$	−0.495187			−0.0310708
$255$	2.61244	+	1.63286i	0.163597	+	0.102254i
$256$	−0.195492	−	0.142033i	−0.0122182	−	0.00887707i
$257$	0.660340	−	0.479765i	0.0411909	−	0.0299269i	−0.566999	−	0.823718i	$-0.691896\pi$
$257$	0.660340	−	0.479765i	0.0411909	−	0.0299269i	0.608190	+	0.793791i	$0.291896\pi$
$258$	5.19680	+	1.68854i	0.323539	+	0.105124i
$259$	2.98669	−	9.19208i	0.185584	−	0.571168i
$260$	−2.25274	−	3.10062i	−0.139709	−	0.192293i
$261$	−0.0279899	+	0.0385248i	−0.00173253	+	0.00238462i
$262$	−7.31176	+	2.37573i	−0.451722	+	0.146773i
$263$	16.9084			1.04262			0.521310	−	0.853368i	$-0.325444\pi$
$263$	16.9084			1.04262			0.521310	+	0.853368i	$0.325444\pi$
$264$	−0.425836	−	10.4878i	−0.0262084	−	0.645477i
$265$		−	3.60001i		−	0.221147i
$266$	−4.62545	+	1.50290i	−0.283604	+	0.0921486i
$267$	−9.40419	+	12.9438i	−0.575527	+	0.792145i
$268$	9.30990	−	6.76404i	0.568693	−	0.413180i
$269$	−1.26729	−	0.411767i	−0.0772680	−	0.0251059i	0.270128	−	0.962824i	$-0.412934\pi$
$269$	−1.26729	−	0.411767i	−0.0772680	−	0.0251059i	−0.347396	+	0.937719i	$0.612934\pi$
$270$	−0.338426	+	1.04157i	−0.0205960	+	0.0633879i
$271$	19.2539	−	13.9888i	1.16959	−	0.849757i	0.178630	−	0.983916i	$-0.442834\pi$
$271$	19.2539	−	13.9888i	1.16959	−	0.849757i	0.990960	+	0.134160i	$0.0428335\pi$
$272$	−10.8408	+	0.756781i	−0.657320	+	0.0458866i
$273$	−6.24157	−	19.2096i	−0.377757	−	1.16262i
$274$	−1.48718			−0.0898440
$275$	12.5233	−	9.89922i	0.755183	−	0.596946i
$276$	−7.23335			−0.435397
$277$	7.01052	−	2.27786i	0.421222	−	0.136863i	−0.0907339	−	0.995875i	$-0.528921\pi$
$277$	7.01052	−	2.27786i	0.421222	−	0.136863i	0.511955	+	0.859012i	$0.328921\pi$
$278$	2.26574	−	3.11852i	0.135890	−	0.187037i
$279$	0.0679937	+	0.0935853i	0.00407068	+	0.00560281i
$280$	0.568477	−	1.74959i	0.0339730	−	0.104558i
$281$	2.21473	−	6.81623i	0.132120	−	0.406622i	−0.863011	−	0.505185i	$-0.831424\pi$
$281$	2.21473	−	6.81623i	0.132120	−	0.406622i	0.995131	+	0.0985625i	$0.0314244\pi$
$282$	3.01177	+	4.14534i	0.179348	+	0.246852i
$283$	6.39909	−	8.80759i	0.380387	−	0.523557i	−0.575300	−	0.817942i	$-0.695115\pi$
$283$	6.39909	−	8.80759i	0.380387	−	0.523557i	0.955687	+	0.294385i	$0.0951148\pi$
$284$	12.8263	−	4.16753i	0.761103	−	0.247297i
$285$	−3.21361			−0.190358
$286$	2.81824	+	7.60843i	0.166646	+	0.449896i
$287$	27.1798			1.60437
$288$	−0.0190824	−	0.0587295i	−0.00112444	−	0.00346067i
$289$	−12.2316	+	11.8063i	−0.719503	+	0.694489i
$290$	−0.648791	+	0.471374i	−0.0380983	+	0.0276800i
$291$	−10.0638	+	30.9731i	−0.589948	+	1.81567i
$292$	−14.1123	−	4.58536i	−0.825860	−	0.268338i
$293$	2.65800	−	1.93115i	0.155282	−	0.112819i	−0.507431	−	0.861692i	$-0.669405\pi$
$293$	2.65800	−	1.93115i	0.155282	−	0.112819i	0.662713	+	0.748873i	$0.269405\pi$
$294$	−0.790080	+	1.08745i	−0.0460784	+	0.0634215i
$295$	4.38959	−	1.42627i	0.255572	−	0.0830404i
$296$		−	7.61437i		−	0.442577i
$297$	−9.57552	+	14.3715i	−0.555628	+	0.833920i
$298$	2.99527			0.173511
$299$	11.3492	−	3.68758i	0.656342	−	0.213258i
$300$	−8.62224	+	11.8675i	−0.497805	+	0.685170i
$301$	8.87631	+	12.2172i	0.511622	+	0.704188i
$302$	3.16253	−	9.73327i	0.181983	−	0.560087i
$303$	−11.4516	−	3.72086i	−0.657880	−	0.213758i
$304$	9.17087	−	6.66303i	0.525986	−	0.382151i
$305$	1.16562	+	0.846872i	0.0667432	+	0.0484918i
$306$	−0.0212458	−	0.0132793i	−0.00121454	−	0.000759130i
$307$	−13.5276			−0.772063			−0.386031	−	0.922486i	$-0.626154\pi$
$307$	−13.5276			−0.772063			−0.386031	+	0.922486i	$0.626154\pi$
$308$	7.53641	−	11.3111i	0.429427	−	0.644510i
$309$			2.72502i			0.155021i
$310$	0.602000	+	1.85277i	0.0341913	+	0.105230i
$311$	9.37788	−	12.9075i	0.531771	−	0.731920i	−0.455628	−	0.890170i	$-0.650585\pi$
$311$	9.37788	−	12.9075i	0.531771	−	0.731920i	0.987399	+	0.158250i	$0.0505853\pi$
$312$	−9.35313	−	12.8735i	−0.529517	−	0.728817i
$313$	−24.4433	−	7.94212i	−1.38162	−	0.448915i	−0.478418	−	0.878132i	$-0.658790\pi$
$313$	−24.4433	−	7.94212i	−1.38162	−	0.448915i	−0.903201	+	0.429217i	$0.858790\pi$
$314$	−1.62459	+	4.99996i	−0.0916807	+	0.282164i
$315$	−0.0101516	+	0.00737558i	−0.000571979	+	0.000415567i
$316$	−3.91062	+	5.38250i	−0.219989	+	0.302789i
$317$	26.7206	−	8.68205i	1.50078	−	0.487632i	0.560533	−	0.828132i	$-0.310596\pi$
$317$	26.7206	−	8.68205i	1.50078	−	0.487632i	0.940245	+	0.340500i	$0.110596\pi$
$318$		−	7.00332i		−	0.392727i
$319$	−11.8583	+	4.39243i	−0.663938	+	0.245929i
$320$			1.23881i			0.0692518i
$321$	−3.36688	−	10.3622i	−0.187921	−	0.578360i
$322$	2.17125	+	1.57750i	0.120999	+	0.0879109i
$323$	4.29205	−	17.2059i	0.238816	−	0.957360i
$324$	4.88343	−	15.0297i	0.271302	−	0.834981i
$325$	7.47831	−	23.0159i	0.414822	−	1.27669i
$326$	−0.896603	−	1.23407i	−0.0496583	−	0.0683487i
$327$	−2.27073	−	1.64978i	−0.125572	−	0.0912332i
$328$	20.3648	−	6.61691i	1.12446	−	0.365358i
$329$			14.1608i			0.780709i
$330$	−0.945906	+	0.747705i	−0.0520704	+	0.0411598i
$331$	−21.8272			−1.19973			−0.599865	−	0.800101i	$-0.704779\pi$
$331$	−21.8272			−1.19973			−0.599865	+	0.800101i	$0.704779\pi$
$332$	−3.89604	−	11.9908i	−0.213823	−	0.658080i
$333$	−0.0305281	+	0.0420184i	−0.00167293	+	0.00230259i
$334$	−1.34022	−	1.84466i	−0.0733338	−	0.100935i
$335$	−2.68319	−	0.871823i	−0.146599	−	0.0476328i
$336$	−3.27184	+	10.0697i	−0.178494	+	0.549347i
$337$	9.47586	+	13.0424i	0.516183	+	0.710465i	0.984947	−	0.172859i	$-0.0553004\pi$
$337$	9.47586	+	13.0424i	0.516183	+	0.710465i	−0.468764	+	0.883324i	$0.655300\pi$
$338$	4.83396	+	3.51207i	0.262933	+	0.191032i
$339$	0.776059	+	2.38846i	0.0421497	+	0.129724i
$340$	2.01989	+	2.40779i	0.109544	+	0.130581i
$341$	1.24627	+	30.6939i	0.0674892	+	1.66217i
$342$	0.0261349			0.00141322
$343$	−19.0057	+	6.17534i	−1.02621	+	0.333437i
$344$	9.62494	+	6.99293i	0.518942	+	0.377034i
$345$	1.04236	+	1.43468i	0.0561186	+	0.0772406i
$346$	−7.16111	−	2.32679i	−0.384984	−	0.125089i
$347$	9.38945	+	3.05082i	0.504052	+	0.163776i	0.549995	−	0.835168i	$-0.314629\pi$
$347$	9.38945	+	3.05082i	0.504052	+	0.163776i	−0.0459435	+	0.998944i	$0.514629\pi$
$348$	9.40107	−	6.83028i	0.503950	−	0.366141i
$349$	0.171969	+	0.124943i	0.00920528	+	0.00668803i	0.592378	−	0.805660i	$-0.298189\pi$
$349$	0.171969	+	0.124943i	0.00920528	+	0.00668803i	−0.583173	+	0.812348i	$0.698189\pi$
$350$	5.17631	−	1.68188i	0.276685	−	0.0899005i
$351$			26.1803i			1.39740i
$352$	4.43057	−	15.7888i	0.236150	−	0.841547i
$353$	13.1041			0.697460			0.348730	−	0.937223i	$-0.386613\pi$
$353$	13.1041			0.697460			0.348730	+	0.937223i	$0.386613\pi$
$354$	8.53935	−	2.77460i	0.453861	−	0.147469i
$355$	−2.67493	−	1.94345i	−0.141970	−	0.103148i
$356$	−13.2046	+	9.59371i	−0.699843	+	0.508465i
$357$	6.20285	+	15.3578i	0.328289	+	0.812820i
$358$	−0.0911159	+	0.280426i	−0.00481562	+	0.0148210i
$359$	5.88826	−	4.27807i	0.310771	−	0.225788i	−0.421457	−	0.906849i	$-0.638481\pi$
$359$	5.88826	−	4.27807i	0.310771	−	0.225788i	0.732227	+	0.681061i	$0.238481\pi$
$360$	−0.00581063	+	0.00799764i	−0.000306247	+	0.000421513i
$361$	−0.155174	−	0.477576i	−0.00816705	−	0.0251356i
$362$			10.2349i			0.537934i
$363$	−17.5465	+	7.32194i	−0.920950	+	0.384302i
$364$		−	20.6052i		−	1.08001i
$365$	1.12417	+	3.45984i	0.0588418	+	0.181096i
$366$	2.26755	+	1.64747i	0.118527	+	0.0861149i
$367$	1.33546	+	1.83810i	0.0697103	+	0.0959479i	0.842448	−	0.538777i	$-0.181113\pi$
$367$	1.33546	+	1.83810i	0.0697103	+	0.0959479i	−0.772738	+	0.634725i	$0.781113\pi$
$368$	−5.94927	−	1.93304i	−0.310127	−	0.100766i
$369$	−0.138908	−	0.0451339i	−0.00723125	−	0.00234958i
$370$	−0.707626	+	0.514121i	−0.0367877	+	0.0267279i
$371$	11.3765	−	15.6583i	0.590636	−	0.812941i
$372$	−8.72307	−	26.8469i	−0.452270	−	1.39194i
$373$	−8.39745			−0.434803			−0.217402	−	0.976082i	$-0.569758\pi$
$373$	−8.39745			−0.434803			−0.217402	+	0.976082i	$0.569758\pi$
$374$	−2.73992	−	6.06307i	−0.141678	−	0.313514i
$375$	7.33229			0.378638
$376$	3.44744	+	10.6101i	0.177788	+	0.547175i
$377$	−11.2683	+	15.5095i	−0.580347	+	0.798778i
$378$	−4.76348	+	3.46087i	−0.245007	+	0.178008i
$379$	−22.5243	−	7.31858i	−1.15699	−	0.375930i	−0.333220	−	0.942849i	$-0.608135\pi$
$379$	−22.5243	−	7.31858i	−1.15699	−	0.375930i	−0.823773	+	0.566919i	$0.808135\pi$
$380$	−3.11791	−	1.01307i	−0.159946	−	0.0519695i
$381$	−1.03400	−	1.42317i	−0.0529732	−	0.0729114i
$382$	−4.22500	−	3.06964i	−0.216170	−	0.157056i
$383$	11.6049	+	35.7163i	0.592984	+	1.82502i	0.564515	+	0.825423i	$0.309063\pi$
$383$	11.6049	+	35.7163i	0.592984	+	1.82502i	0.0284693	+	0.999595i	$0.490937\pi$
$384$			19.5021i			0.995213i
$385$	−3.32950	+	0.135188i	−0.169687	+	0.00688983i
$386$		−	12.5269i		−	0.637604i
$387$	−0.0250767	−	0.0771782i	−0.00127472	−	0.00392319i
$388$	−19.5282	+	26.8782i	−0.991393	+	1.36454i
$389$	−27.7649	+	20.1724i	−1.40774	+	1.02278i	−0.414091	+	0.910235i	$0.635900\pi$
$389$	−27.7649	+	20.1724i	−1.40774	+	1.02278i	−0.993647	+	0.112546i	$0.964100\pi$
$390$	−0.564849	+	1.73843i	−0.0286023	+	0.0880287i
$391$	−9.07353	+	3.66470i	−0.458868	+	0.185332i
$392$	−2.36767	+	1.72021i	−0.119585	+	0.0868839i
$393$	−22.0955	−	16.0533i	−1.11457	−	0.809783i
$394$	−4.49015	+	1.45894i	−0.226211	+	0.0735003i
$395$	1.63112			0.0820703
$396$	−0.0572992	+	0.0452930i	−0.00287939	+	0.00227606i
$397$		−	3.29890i		−	0.165567i	−0.996568	−	0.0827836i	$-0.973619\pi$
$397$		−	3.29890i		−	0.165567i	0.996568	−	0.0827836i	$-0.0263810\pi$
$398$	10.4286	−	3.38846i	0.522739	−	0.169848i
$399$	−13.9777	−	10.1554i	−0.699760	−	0.508406i
$400$	−10.2631	+	7.45655i	−0.513153	+	0.372828i
$401$	27.6728	+	8.99142i	1.38191	+	0.449010i	0.903297	−	0.429015i	$-0.141139\pi$
$401$	27.6728	+	8.99142i	1.38191	+	0.449010i	0.478614	+	0.878025i	$0.341139\pi$
$402$	−5.21979	−	1.69601i	−0.260339	−	0.0845894i
$403$	27.3732	+	37.6760i	1.36356	+	1.87677i
$404$	−9.93766	−	7.22013i	−0.494417	−	0.359215i
$405$	−3.68474	+	1.19725i	−0.183096	+	0.0594916i
$406$	−4.31154			−0.213978
$407$	−12.9337	+	4.79076i	−0.641099	+	0.237469i
$408$	8.38640	+	9.99690i	0.415188	+	0.494921i
$409$	6.47525	+	19.9288i	0.320181	+	0.985414i	0.973569	+	0.228392i	$0.0733467\pi$
$409$	6.47525	+	19.9288i	0.320181	+	0.985414i	−0.653389	+	0.757023i	$0.726653\pi$
$410$	−1.98995	−	1.44578i	−0.0982767	−	0.0714022i
$411$	−3.10537	−	4.27418i	−0.153177	−	0.210830i
$412$	−0.859046	+	2.64387i	−0.0423222	+	0.130254i
$413$	23.5999	+	7.66806i	1.16127	+	0.377320i
$414$	−0.00847705	−	0.0116677i	−0.000416624	−	0.000573434i
$415$	−1.81685	+	2.50068i	−0.0891855	+	0.122753i
$416$	−7.68226	−	23.6436i	−0.376654	−	1.15922i
$417$	13.6937			0.670585
$418$	5.77573	+	3.84828i	0.282500	+	0.188225i
$419$			4.56386i			0.222959i	0.993767	+	0.111479i	$0.0355589\pi$
$419$			4.56386i			0.222959i	−0.993767	+	0.111479i	$0.964441\pi$
$420$	2.91220	−	0.946231i	0.142101	−	0.0461714i
$421$	16.6128	+	12.0699i	0.809657	+	0.588250i	0.913731	−	0.406319i	$-0.133188\pi$
$421$	16.6128	+	12.0699i	0.809657	+	0.588250i	−0.104074	+	0.994570i	$0.533188\pi$
$422$	2.13685	+	2.94112i	0.104020	+	0.143171i
$423$	0.0235149	−	0.0723715i	0.00114334	−	0.00351883i
$424$	4.71191	−	14.5018i	0.228831	−	0.704269i
$425$	−4.80321	+	19.2550i	−0.232990	+	0.934003i
$426$	−5.20371	−	3.78071i	−0.252120	−	0.183176i
$427$	2.39368	+	7.36700i	0.115838	+	0.356514i
$428$		−	11.1150i		−	0.537264i
$429$	−15.9820	+	23.9868i	−0.771618	+	1.15809i
$430$		−	1.36664i		−	0.0659050i
$431$	−0.0386660	+	0.0125633i	−0.00186247	+	0.000605155i	−0.309948	−	0.950753i	$-0.600312\pi$
$431$	−0.0386660	+	0.0125633i	−0.00186247	+	0.000605155i	0.308086	+	0.951359i	$0.400312\pi$
$432$	8.06661	−	11.1027i	0.388105	−	0.534181i
$433$	18.3957	−	13.3653i	0.884041	−	0.642293i	−0.0502768	−	0.998735i	$-0.516010\pi$
$433$	18.3957	−	13.3653i	0.884041	−	0.642293i	0.934317	+	0.356442i	$0.116010\pi$
$434$	−3.23655	+	9.96107i	−0.155359	+	0.478147i
$435$	−2.70947	−	0.880360i	−0.129909	−	0.0422100i
$436$	−1.68303	−	2.31649i	−0.0806025	−	0.110940i
$437$	5.99991	−	8.25816i	0.287014	−	0.395042i
$438$	2.18692	+	6.73065i	0.104495	+	0.321603i
$439$			13.6450i			0.651240i	0.945501	+	0.325620i	$0.105573\pi$
$439$			13.6450i			0.651240i	−0.945501	+	0.325620i	$0.894427\pi$
$440$	−2.46175	+	0.911857i	−0.117360	+	0.0434711i
$441$	0.0199623			0.000950587
$442$	−8.55324	−	5.34606i	−0.406836	−	0.254286i
$443$	14.6720	+	10.6598i	0.697086	+	0.506463i	0.878982	−	0.476855i	$-0.158223\pi$
$443$	14.6720	+	10.6598i	0.697086	+	0.506463i	−0.181896	+	0.983318i	$0.558223\pi$
$444$	10.2536	−	7.44968i	0.486615	−	0.353546i
$445$	3.80568	+	1.23654i	0.180407	+	0.0586176i
$446$	−0.972433	+	2.99284i	−0.0460460	+	0.141715i
$447$	6.25440	+	8.60845i	0.295823	+	0.407166i
$448$	−3.91480	+	5.38827i	−0.184957	+	0.254572i
$449$	5.67599	−	1.84424i	0.267867	−	0.0870351i	−0.172004	−	0.985096i	$-0.555024\pi$
$449$	5.67599	−	1.84424i	0.267867	−	0.0870351i	0.439871	+	0.898061i	$0.355024\pi$
$450$	−0.0292474			−0.00137874
$451$	−24.0523	−	30.4281i	−1.13258	−	1.43280i
$452$			2.56199i			0.120506i
$453$	34.5772	−	11.2348i	1.62458	−	0.527858i
$454$	−3.69508	+	5.08584i	−0.173419	+	0.238690i
$455$	−4.08688	+	2.96930i	−0.191596	+	0.139203i
$456$	−12.9453	−	4.20617i	−0.606218	−	0.196972i
$457$	−0.652637	+	2.00861i	−0.0305291	+	0.0939588i	−0.965160	−	0.261660i	$-0.915730\pi$
$457$	−0.652637	+	2.00861i	−0.0305291	+	0.0939588i	0.934631	+	0.355619i	$0.115730\pi$
$458$	8.09940	−	5.88456i	0.378460	−	0.274967i
$459$	−1.49506	−	21.4165i	−0.0697833	−	0.999638i
$460$	0.559043	+	1.72056i	0.0260655	+	0.0802214i
$461$	19.2191			0.895122			0.447561	−	0.894253i	$-0.352293\pi$
$461$	19.2191			0.895122			0.447561	+	0.894253i	$0.352293\pi$
$462$	−6.47709	+	0.262990i	−0.301342	+	0.0122354i
$463$	−14.8700			−0.691068			−0.345534	−	0.938406i	$-0.612302\pi$
$463$	−14.8700			−0.691068			−0.345534	+	0.938406i	$0.612302\pi$
$464$	9.55749	−	3.10542i	0.443695	−	0.144165i
$465$	−4.06784	+	5.59890i	−0.188642	+	0.259643i
$466$	4.03015	+	5.54703i	0.186693	+	0.256961i
$467$	−0.411246	+	1.26568i	−0.0190302	+	0.0585689i	−0.960121	−	0.279586i	$-0.909803\pi$
$467$	−0.411246	+	1.26568i	−0.0190302	+	0.0585689i	0.941090	+	0.338155i	$0.109803\pi$
$468$	−0.0342163	+	0.105307i	−0.00158165	+	0.00486782i
$469$	−8.91558	−	12.2712i	−0.411683	−	0.566633i
$470$	0.753260	−	1.03677i	0.0347453	−	0.0478228i
$471$	−17.7622	+	5.77130i	−0.818440	+	0.265927i
$472$	19.5492			0.899826
$473$	5.82235	−	20.7486i	0.267712	−	0.954020i
$474$	3.17311			0.145746
$475$	−6.39691	−	19.6877i	−0.293510	−	0.903331i
$476$	1.17669	+	16.8559i	0.0539333	+	0.772588i
$477$	−0.0841434	+	0.0611338i	−0.00385266	+	0.00279912i
$478$	−1.31644	+	4.05157i	−0.0602124	+	0.185315i
$479$	−22.9657	−	7.46201i	−1.04933	−	0.340948i	−0.266924	−	0.963717i	$-0.586007\pi$
$479$	−22.9657	−	7.46201i	−1.04933	−	0.340948i	−0.782405	+	0.622770i	$0.786007\pi$
$480$	2.98884	−	2.17152i	0.136421	−	0.0991159i
$481$	−12.2902	+	16.9160i	−0.560383	+	0.771301i
$482$	−7.83534	+	2.54586i	−0.356890	+	0.115961i
$483$			9.53417i			0.433820i
$484$	−19.3322	+	1.57249i	−0.878734	+	0.0714766i
$485$	8.14519			0.369854
$486$	0.0600587	−	0.0195143i	0.00272432	−	0.000885185i
$487$	25.2340	−	34.7316i	1.14346	−	1.57384i	0.383933	−	0.923361i	$-0.374570\pi$
$487$	25.2340	−	34.7316i	1.14346	−	1.57384i	0.759527	−	0.650476i	$-0.225430\pi$
$488$	3.58699	+	4.93706i	0.162375	+	0.223490i
$489$	1.67454	−	5.15370i	0.0757252	−	0.233058i
$490$	0.319729	+	0.103886i	0.0144439	+	0.00469310i
$491$	27.5131	−	19.9894i	1.24165	−	0.902111i	0.243942	−	0.969790i	$-0.421559\pi$
$491$	27.5131	−	19.9894i	1.24165	−	0.902111i	0.997707	+	0.0676791i	$0.0215594\pi$
$492$	28.8347	+	20.9496i	1.29997	+	0.944482i
$493$	8.33223	−	13.3309i	0.375265	−	0.600392i
$494$	10.5215			0.473386
$495$	0.0172406	+	0.00483796i	0.000774907	+	0.000217450i
$496$		−	24.4121i		−	1.09614i
$497$	−5.49315	−	16.9062i	−0.246402	−	0.758346i
$498$	−3.53443	+	4.86472i	−0.158382	+	0.217993i
$499$	−1.55800	−	2.14441i	−0.0697458	−	0.0959968i	0.772719	−	0.634748i	$-0.218896\pi$
$499$	−1.55800	−	2.14441i	−0.0697458	−	0.0959968i	−0.842465	+	0.538751i	$0.818896\pi$
$500$	7.11395	+	2.31146i	0.318146	+	0.103372i
$501$	2.50306	−	7.70364i	0.111829	−	0.344173i
$502$	−0.739327	+	0.537152i	−0.0329978	+	0.0239743i
$503$	13.1596	−	18.1127i	0.586759	−	0.807604i	−0.407657	−	0.913135i	$-0.633654\pi$
$503$	13.1596	−	18.1127i	0.586759	−	0.807604i	0.994416	+	0.105531i	$0.0336542\pi$
$504$	−0.0505471	+	0.0164237i	−0.00225154	+	0.000731571i
$505$			3.01151i			0.134011i
$506$	−0.155377	−	3.82673i	−0.00690736	−	0.170119i
$507$			21.2264i			0.942697i
$508$	−0.554559	−	1.70676i	−0.0246046	−	0.0757251i
$509$	29.3065	+	21.2924i	1.29899	+	0.943771i	0.999945	−	0.0104688i	$-0.00333237\pi$
$509$	29.3065	+	21.2924i	1.29899	+	0.943771i	0.299044	+	0.954239i	$0.403332\pi$
$510$	0.362795	−	1.45436i	0.0160648	−	0.0644002i
$511$	−6.04390	+	18.6012i	−0.267366	+	0.822869i
$512$	−7.00965	+	21.5735i	−0.309786	+	0.953422i
$513$	13.1631	+	18.1175i	0.581167	+	0.799908i
$514$	−0.321286	−	0.233428i	−0.0141713	−	0.0102961i
$515$	0.648185	−	0.210608i	0.0285624	−	0.00928049i
$516$			19.8027i			0.871767i
$517$	15.8532	−	12.5314i	0.697222	−	0.551129i
$518$	−4.70253			−0.206617
$519$	−8.26585	−	25.4397i	−0.362831	−	1.11668i
$520$	−2.33927	+	3.21973i	−0.102584	+	0.141194i
$521$	−16.8220	−	23.1535i	−0.736986	−	1.01437i	−0.998786	−	0.0492520i	$-0.984316\pi$
$521$	−16.8220	−	23.1535i	−0.736986	−	1.01437i	0.261801	−	0.965122i	$-0.415684\pi$
$522$	0.0220350	+	0.00715960i	0.000964445	+	0.000313367i
$523$	1.68993	−	5.20106i	0.0738954	−	0.227427i	−0.907286	−	0.420514i	$-0.861850\pi$
$523$	1.68993	−	5.20106i	0.0738954	−	0.227427i	0.981182	+	0.193087i	$0.0618499\pi$
$524$	−16.3768	−	22.5408i	−0.715425	−	0.984699i
$525$	15.6424	+	11.3648i	0.682689	+	0.496002i
$526$	−2.54220	−	7.82409i	−0.110845	−	0.341147i
$527$	−24.5439	−	29.2573i	−1.06915	−	1.27447i
$528$	14.1685	−	5.24815i	0.616606	−	0.228397i
$529$	17.3671			0.755092
$530$	−1.66584	+	0.541264i	−0.0723595	+	0.0235110i
$531$	−0.107878	−	0.0783783i	−0.00468153	−	0.00340133i
$532$	−10.3600	−	14.2594i	−0.449165	−	0.618223i
$533$	−55.9221	−	18.1702i	−2.42226	−	0.787039i
$534$	7.40343	+	2.40552i	0.320378	+	0.104097i
$535$	−2.20458	+	1.60172i	−0.0953122	+	0.0692484i
$536$	−9.66752	−	7.02387i	−0.417573	−	0.303385i
$537$	−0.996205	+	0.323687i	−0.0429894	+	0.0139681i
$538$			0.648325i			0.0279513i
$539$	4.41161	+	2.93938i	0.190021	+	0.126608i
$540$	−3.96897			−0.170797
$541$	−18.9962	+	6.17225i	−0.816712	+	0.265366i	−0.687438	−	0.726243i	$-0.741265\pi$
$541$	−18.9962	+	6.17225i	−0.816712	+	0.265366i	−0.129274	+	0.991609i	$0.541265\pi$
$542$	−9.36789	−	6.80617i	−0.402385	−	0.292350i
$543$	−29.4152	+	21.3714i	−1.26233	+	0.917135i
$544$	7.63459	+	18.9027i	0.327331	+	0.810446i
$545$	−0.216927	+	0.667633i	−0.00929213	+	0.0285982i
$546$	−7.95048	+	5.77636i	−0.340249	+	0.247205i
$547$	−16.3436	+	22.4950i	−0.698801	+	0.961816i	0.301166	+	0.953572i	$0.402624\pi$
$547$	−16.3436	+	22.4950i	−0.698801	+	0.961816i	−0.999966	+	0.00824449i	$0.997376\pi$
$548$	−1.66549	−	5.12586i	−0.0711463	−	0.218966i
$549$		−	0.0416254i		−	0.00177653i
$550$	−6.46358	−	4.30658i	−0.275608	−	0.183633i
$551$			16.3986i			0.698602i
$552$	2.32109	+	7.14358i	0.0987921	+	0.304051i
$553$	7.09459	+	5.15452i	0.301693	+	0.219193i
$554$	−2.10808	−	2.90152i	−0.0895636	−	0.123274i
$555$	−2.95518	−	0.960195i	−0.125440	−	0.0407580i
$556$	13.2860	+	4.31687i	0.563451	+	0.183076i
$557$	5.05501	−	3.67268i	0.214188	−	0.155616i	−0.475519	−	0.879706i	$-0.657740\pi$
$557$	5.05501	−	3.67268i	0.214188	−	0.155616i	0.689706	+	0.724089i	$0.257740\pi$
$558$	0.0330821	−	0.0455335i	0.00140047	−	0.00192759i
$559$	−10.0955	−	31.0707i	−0.426994	−	1.31415i
$560$	2.64809			0.111902
$561$	11.7041	−	20.5348i	0.494148	−	0.866980i
$562$	−3.48708			−0.147093
$563$	4.40932	+	13.5705i	0.185831	+	0.571929i	0.999962	−	0.00875291i	$-0.00278617\pi$
$563$	4.40932	+	13.5705i	0.185831	+	0.571929i	−0.814131	+	0.580681i	$0.802786\pi$
$564$	−10.9148	+	15.0230i	−0.459598	+	0.632582i
$565$	0.508151	−	0.369193i	0.0213781	−	0.0155321i
$566$	−5.03767	−	1.63684i	−0.211749	−	0.0688015i
$567$	−19.8104	−	6.43678i	−0.831957	−	0.270319i
$568$	−8.23161	−	11.3298i	−0.345391	−	0.475389i
$569$	−4.01514	−	2.91717i	−0.168323	−	0.122294i	0.500434	−	0.865774i	$-0.333174\pi$
$569$	−4.01514	−	2.91717i	−0.168323	−	0.122294i	−0.668758	+	0.743480i	$0.733174\pi$
$570$	0.483169	+	1.48704i	0.0202377	+	0.0622853i
$571$		−	38.4471i		−	1.60896i	−0.593979	−	0.804481i	$-0.702444\pi$
$571$		−	38.4471i		−	1.60896i	0.593979	−	0.804481i	$-0.297556\pi$
$572$	−23.0678	+	18.2342i	−0.964512	+	0.762412i
$573$		−	18.5524i		−	0.775037i
$574$	−4.08651	−	12.5770i	−0.170568	−	0.524953i
$575$	−6.71446	+	9.24166i	−0.280012	+	0.385404i
$576$	0.0289550	−	0.0210370i	0.00120646	−	0.000876542i
$577$	−5.60013	+	17.2354i	−0.233136	+	0.717520i	0.764227	+	0.644948i	$0.223121\pi$
$577$	−5.60013	+	17.2354i	−0.233136	+	0.717520i	−0.997363	+	0.0725722i	$0.976879\pi$
$578$	7.30219	+	3.88485i	0.303731	+	0.161588i
$579$	36.0026	−	26.1574i	1.49622	−	1.08706i
$580$	−2.35126	−	1.70829i	−0.0976307	−	0.0709328i
$581$	−15.8049	+	5.13532i	−0.655697	+	0.213049i
$582$	15.8454			0.656811
$583$	−27.5971	+	1.12053i	−1.14296	+	0.0464076i
$584$			15.4085i			0.637610i
$585$	0.0258176	−	0.00838864i	0.00106742	−	0.000346827i
$586$	−1.29324	−	0.939593i	−0.0534232	−	0.0388142i
$587$	−8.87203	+	6.44590i	−0.366188	+	0.266051i	−0.755628	−	0.655001i	$-0.772668\pi$
$587$	−8.87203	+	6.44590i	−0.366188	+	0.266051i	0.389441	+	0.921052i	$0.372668\pi$
$588$	−4.63292	−	1.50533i	−0.191058	−	0.0620786i
$589$	37.8861	+	12.3099i	1.56107	+	0.507222i
$590$	−1.31996	−	1.81677i	−0.0543418	−	0.0747951i
$591$	−13.5689	−	9.85835i	−0.558148	−	0.405519i
$592$	10.4242	−	3.38703i	0.428433	−	0.139206i
$593$	−42.7682			−1.75628			−0.878139	−	0.478405i	$-0.841215\pi$
$593$	−42.7682			−1.75628			−0.878139	+	0.478405i	$0.841215\pi$
$594$	8.08986	+	2.27013i	0.331931	+	0.0931447i
$595$	3.17367	−	2.66239i	0.130108	−	0.109147i
$596$	3.35440	+	10.3238i	0.137401	+	0.422878i
$597$	31.5144	+	22.8965i	1.28980	+	0.937093i
$598$	−3.41273	−	4.69722i	−0.139557	−	0.192084i
$599$	13.7751	−	42.3955i	0.562837	−	1.73223i	−0.111456	−	0.993769i	$-0.535551\pi$
$599$	13.7751	−	42.3955i	0.562837	−	1.73223i	0.674293	−	0.738464i	$-0.264449\pi$
$600$	14.4870	+	4.70710i	0.591428	+	0.192167i
$601$	6.06596	+	8.34908i	0.247436	+	0.340566i	0.914611	−	0.404334i	$-0.132497\pi$
$601$	6.06596	+	8.34908i	0.247436	+	0.340566i	−0.667175	+	0.744901i	$0.732497\pi$
$602$	4.31873	−	5.94423i	0.176018	−	0.242269i
$603$	0.0251876	+	0.0775196i	0.00102572	+	0.00315684i
$604$	37.0893			1.50914
$605$	3.09774	+	3.60779i	0.125941	+	0.146677i
$606$			5.85848i			0.237985i
$607$	22.0916	−	7.17800i	0.896671	−	0.291346i	0.175809	−	0.984424i	$-0.443746\pi$
$607$	22.0916	−	7.17800i	0.896671	−	0.291346i	0.720862	+	0.693078i	$0.243746\pi$
$608$	−17.2041	−	12.4995i	−0.697717	−	0.506921i
$609$	−9.00288	−	12.3914i	−0.364815	−	0.502125i
$610$	0.216623	−	0.666698i	0.00877083	−	0.0269938i
$611$	9.46675	−	29.1357i	0.382984	−	1.17870i
$612$	0.0219766	−	0.0880993i	0.000888353	−	0.00356120i
$613$	10.6769	+	7.75721i	0.431235	+	0.313311i	0.782143	−	0.623099i	$-0.214127\pi$
$613$	10.6769	+	7.75721i	0.431235	+	0.313311i	−0.350907	+	0.936410i	$0.614127\pi$
$614$	2.03389	+	6.25968i	0.0820812	+	0.252620i
$615$		−	8.73808i		−	0.352353i
$616$	−13.5891	−	3.81329i	−0.547519	−	0.153642i
$617$			20.5128i			0.825812i	0.910774	+	0.412906i	$0.135486\pi$
$617$			20.5128i			0.825812i	−0.910774	+	0.412906i	$0.864514\pi$
$618$	1.26095	−	0.409709i	0.0507230	−	0.0164809i
$619$	5.06950	−	6.97756i	0.203760	−	0.280452i	−0.694892	−	0.719115i	$-0.744548\pi$
$619$	5.06950	−	6.97756i	0.203760	−	0.280452i	0.898652	+	0.438663i	$0.144548\pi$
$620$	−5.71173	+	4.14982i	−0.229389	+	0.166661i
$621$	3.81881	−	11.7531i	0.153244	−	0.471635i
$622$	−7.38272	−	2.39879i	−0.296020	−	0.0961827i
$623$	12.6453	+	17.4048i	0.506624	+	0.697308i
$624$	13.4636	−	18.5310i	0.538974	−	0.741834i
$625$	6.86999	+	21.1437i	0.274800	+	0.845747i
$626$			12.5048i			0.499794i
$627$	1.00026	+	24.6351i	0.0399466	+	0.983830i
$628$	−19.0527			−0.760285
$629$	9.08784	−	14.5398i	0.362356	−	0.579739i
$630$	0.00493923	+	0.00358856i	0.000196784	+	0.000142972i
$631$	25.6204	−	18.6143i	1.01993	−	0.741024i	0.0536635	−	0.998559i	$-0.482910\pi$
$631$	25.6204	−	18.6143i	1.01993	−	0.741024i	0.966269	+	0.257535i	$0.0829102\pi$
$632$	6.57057	+	2.13491i	0.261363	+	0.0849220i
$633$	−3.99087	+	12.2826i	−0.158623	+	0.488191i
$634$	−8.03493	−	11.0591i	−0.319108	−	0.439214i
$635$	−0.258608	+	0.355944i	−0.0102625	+	0.0141252i
$636$	24.1383	−	7.84300i	0.957145	−	0.310995i
$637$	8.03652			0.318419
$638$	3.81543	+	4.82682i	0.151054	+	0.191096i
$639$			0.0955243i			0.00377888i
$640$	4.63886	−	1.50726i	0.183367	−	0.0595795i
$641$	−1.12464	+	1.54793i	−0.0444205	+	0.0611395i	−0.830649	−	0.556796i	$-0.812031\pi$
$641$	−1.12464	+	1.54793i	−0.0444205	+	0.0611395i	0.786229	+	0.617935i	$0.212031\pi$
$642$	−4.28871	+	3.11593i	−0.169262	+	0.122976i
$643$	−5.22194	−	1.69671i	−0.205933	−	0.0669118i	0.204234	−	0.978922i	$-0.434530\pi$
$643$	−5.22194	−	1.69671i	−0.205933	−	0.0669118i	−0.410167	+	0.912010i	$0.634530\pi$
$644$	−3.00559	+	9.25026i	−0.118437	+	0.364511i
$645$	3.92773	−	2.85366i	0.154654	−	0.112363i
$646$	−8.60703	+	0.600845i	−0.338639	+	0.0236399i
$647$	−12.8537	−	39.5596i	−0.505330	−	1.55525i	−0.800215	−	0.599714i	$-0.795281\pi$
$647$	−12.8537	−	39.5596i	−0.505330	−	1.55525i	0.294885	−	0.955533i	$-0.404719\pi$
$648$	−16.4102			−0.644652
$649$	−12.2998	−	33.2061i	−0.482811	−	1.30345i
$650$	−11.7746			−0.461836
$651$	−35.3864	+	11.4978i	−1.38690	+	0.450632i
$652$	3.24935	−	4.47234i	0.127254	−	0.175150i
$653$	9.35578	+	12.8771i	0.366120	+	0.503921i	0.951841	−	0.306592i	$-0.0991886\pi$
$653$	9.35578	+	12.8771i	0.366120	+	0.503921i	−0.585721	+	0.810513i	$0.699189\pi$
$654$	−0.422002	+	1.29879i	−0.0165016	+	0.0507866i
$655$	−2.11082	+	6.49645i	−0.0824767	+	0.253837i
$656$	18.1173	+	24.9364i	0.707363	+	0.973602i
$657$	0.0617771	−	0.0850289i	0.00241016	−	0.00331729i
$658$	6.55266	−	2.12909i	0.255449	−	0.0830005i
$659$	34.0981			1.32827			0.664137	−	0.747611i	$-0.268799\pi$
$659$	34.0981			1.32827			0.664137	+	0.747611i	$0.268799\pi$
$660$	−3.63643	−	2.42289i	−0.141548	−	0.0943110i
$661$	−38.4017			−1.49365			−0.746827	−	0.665019i	$-0.768423\pi$
$661$	−38.4017			−1.49365			−0.746827	+	0.665019i	$0.768423\pi$
$662$	3.28174	+	10.1001i	0.127548	+	0.392553i
$663$	−2.49532	−	35.7452i	−0.0969103	−	1.38823i
$664$	−10.5918	+	7.69538i	−0.411041	+	0.298639i
$665$	−1.33531	+	4.10968i	−0.0517813	+	0.159366i
$666$	0.0240332	+	0.00780887i	0.000931268	+	0.000302587i
$667$	7.32096	−	5.31899i	0.283469	−	0.205952i
$668$	4.85706	−	6.68517i	0.187925	−	0.258657i
$669$	−10.6320	+	3.45454i	−0.411057	+	0.133560i
$670$			1.37268i			0.0530313i
$671$	6.12920	−	9.19908i	0.236615	−	0.355126i
$672$	19.8623			0.766206
$673$	−15.6547	+	5.08652i	−0.603444	+	0.196071i	−0.594776	−	0.803891i	$-0.702759\pi$
$673$	−15.6547	+	5.08652i	−0.603444	+	0.196071i	−0.00866831	+	0.999962i	$0.502759\pi$
$674$	4.61044	−	6.34573i	0.177587	−	0.244428i
$675$	−14.7308	−	20.2752i	−0.566988	−	0.780392i
$676$	−6.69150	+	20.5943i	−0.257365	+	0.792089i
$677$	−4.19943	−	1.36448i	−0.161397	−	0.0524411i	0.227204	−	0.973847i	$-0.427042\pi$
$677$	−4.19943	−	1.36448i	−0.161397	−	0.0524411i	−0.388601	+	0.921406i	$0.627042\pi$
$678$	0.988539	−	0.718216i	0.0379646	−	0.0275829i
$679$	35.4278	+	25.7398i	1.35959	+	0.987802i
$680$	1.72975	−	2.76745i	0.0663329	−	0.106127i
$681$	−22.3324			−0.855780
$682$	14.0157	−	5.19154i	0.536688	−	0.198794i
$683$			44.8445i			1.71593i	0.513710	+	0.857964i	$0.328271\pi$
$683$			44.8445i			1.71593i	−0.513710	+	0.857964i	$0.671729\pi$
$684$	0.0292684	+	0.0900790i	0.00111911	+	0.00344426i
$685$	−0.776671	+	1.06900i	−0.0296751	+	0.0408442i
$686$	5.71506	+	7.86611i	0.218202	+	0.300329i
$687$	33.8246	+	10.9903i	1.29049	+	0.419305i
$688$	−5.29207	+	16.2873i	−0.201758	+	0.620948i
$689$	−33.8748	+	24.6115i	−1.29053	+	0.937624i
$690$	0.507154	−	0.698038i	0.0193070	−	0.0265739i
$691$	11.8901	−	3.86334i	0.452322	−	0.146968i	−0.0739914	−	0.997259i	$-0.523574\pi$
$691$	11.8901	−	3.86334i	0.452322	−	0.146968i	0.526314	+	0.850290i	$0.323574\pi$
$692$		−	27.2879i		−	1.03733i
$693$	0.0597000	+	0.0755252i	0.00226781	+	0.00286896i
$694$		−	4.80350i		−	0.182338i
$695$	−1.05835	−	3.25725i	−0.0401453	−	0.123555i
$696$	−9.76219	−	7.09265i	−0.370035	−	0.268846i
$697$	46.7842	+	11.6705i	1.77208	+	0.442050i
$698$	0.0319594	−	0.0983608i	0.00120968	−	0.00372301i
$699$	−7.52690	+	23.1654i	−0.284694	+	0.876197i
$700$	11.5939	+	15.9576i	0.438207	+	0.603140i
$701$	6.68679	+	4.85824i	0.252557	+	0.183493i	0.706859	−	0.707354i	$-0.250111\pi$
$701$	6.68679	+	4.85824i	0.252557	+	0.183493i	−0.454302	+	0.890848i	$0.650111\pi$
$702$	12.1145	−	3.93623i	0.457231	−	0.148563i
$703$			17.8857i			0.674571i
$704$	9.49658	−	0.385591i	0.357916	−	0.0145325i
$705$	4.55257			0.171460
$706$	−1.97021	−	6.06369i	−0.0741499	−	0.228210i
$707$	−9.51674	+	13.0987i	−0.357914	+	0.492626i
$708$	19.1264	+	26.3252i	0.718814	+	0.989362i
$709$	28.5788	+	9.28582i	1.07330	+	0.348736i	0.791772	−	0.610817i	$-0.209159\pi$
$709$	28.5788	+	9.28582i	1.07330	+	0.348736i	0.281528	+	0.959553i	$0.409159\pi$
$710$	−0.497119	+	1.52998i	−0.0186565	+	0.0574190i
$711$	−0.0276989	−	0.0381243i	−0.00103879	−	0.00142977i
$712$	13.7118	+	9.96222i	0.513872	+	0.373350i
$713$	−6.79298	−	20.9067i	−0.254399	−	0.782960i
$714$	6.17394	−	5.17932i	0.231054	−	0.193831i
$715$	6.94079	+	1.94769i	0.259571	+	0.0728393i
$716$	−1.06858			−0.0399347
$717$	−14.3931	+	4.67661i	−0.537521	+	0.174651i
$718$	−2.86491	−	2.08148i	−0.106917	−	0.0776801i
$719$	−15.8654	−	21.8368i	−0.591679	−	0.814377i	0.403236	−	0.915096i	$-0.367885\pi$
$719$	−15.8654	−	21.8368i	−0.591679	−	0.814377i	−0.994915	+	0.100720i	$0.967885\pi$
$720$	−0.0135336	−	0.00439734i	−0.000504368	−	0.000163879i
$721$	3.48485	+	1.13230i	0.129783	+	0.0421689i
$722$	−0.197660	+	0.143608i	−0.00735613	+	0.00534454i
$723$	−23.6777	−	17.2029i	−0.880584	−	0.639782i
$724$	−35.2765	+	11.4620i	−1.31104	+	0.425983i
$725$		−	18.3515i		−	0.681559i
$726$	6.02622	+	7.01846i	0.223654	+	0.260479i
$727$	−26.3795			−0.978362			−0.489181	−	0.872182i	$-0.662704\pi$
$727$	−26.3795			−0.978362			−0.489181	+	0.872182i	$0.662704\pi$
$728$	−20.3495	+	6.61194i	−0.754201	+	0.245055i
$729$	21.9336	+	15.9357i	0.812357	+	0.590212i
$730$	1.43196	−	1.04038i	0.0529993	−	0.0385062i
$731$	10.0329	+	24.8406i	0.371078	+	0.918763i
$732$	−3.13891	+	9.66056i	−0.116017	+	0.357065i
$733$	−23.0019	+	16.7119i	−0.849596	+	0.617267i	−0.925035	−	0.379883i	$-0.875964\pi$
$733$	−23.0019	+	16.7119i	−0.849596	+	0.617267i	0.0754389	+	0.997150i	$0.475964\pi$
$734$	0.649761	−	0.894319i	0.0239831	−	0.0330099i
$735$	0.369053	+	1.13583i	0.0136127	+	0.0418957i
$736$			11.7349i			0.432553i
$737$	−5.84810	+	20.8403i	−0.215418	+	0.767664i
$738$			0.0710631i			0.00261587i
$739$	5.49181	+	16.9021i	0.202020	+	0.621752i	0.999823	+	0.0188342i	$0.00599548\pi$
$739$	5.49181	+	16.9021i	0.202020	+	0.621752i	−0.797803	+	0.602918i	$0.794005\pi$
$740$	−2.56448	−	1.86321i	−0.0942722	−	0.0684928i
$741$	21.9699	+	30.2390i	0.807084	+	1.11086i
$742$	−8.95609	−	2.91001i	−0.328788	−	0.106830i
$743$	−41.8740	−	13.6057i	−1.53621	−	0.499145i	−0.585882	−	0.810396i	$-0.699252\pi$
$743$	−41.8740	−	13.6057i	−1.53621	−	0.499145i	−0.950328	+	0.311252i	$0.899252\pi$
$744$	−23.7145	+	17.2296i	−0.869417	+	0.631669i
$745$	1.56426	−	2.15302i	0.0573101	−	0.0788805i
$746$	1.26256	+	3.88577i	0.0462258	+	0.142268i
$747$	0.0893016			0.00326737
$748$	17.8291	−	16.2337i	0.651896	−	0.593561i
$749$	−14.6505			−0.535318
$750$	−1.10242	−	3.39289i	−0.0402546	−	0.123891i
$751$	−14.4313	+	19.8630i	−0.526606	+	0.724812i	−0.986609	−	0.163106i	$-0.947849\pi$
$751$	−14.4313	+	19.8630i	−0.526606	+	0.724812i	0.460002	+	0.887918i	$0.347849\pi$
$752$	−12.9920	+	9.43921i	−0.473768	+	0.344212i
$753$	−3.08756	−	1.00321i	−0.112517	−	0.0365590i
$754$	8.87094	+	2.88234i	0.323060	+	0.104969i
$755$	−5.34472	−	7.35638i	−0.194514	−	0.267726i
$756$	−17.2632	−	12.5424i	−0.627855	−	0.456163i
$757$	11.2965	+	34.7671i	0.410579	+	1.26363i	0.916146	+	0.400845i	$0.131283\pi$
$757$	11.2965	+	34.7671i	0.410579	+	1.26363i	−0.505567	+	0.862787i	$0.668717\pi$
$758$			11.5231i			0.418537i
$759$	10.6736	−	8.43712i	0.387428	−	0.306248i
$760$			3.40430i			0.123487i
$761$	9.15395	+	28.1730i	0.331831	+	1.02127i	0.968262	+	0.249936i	$0.0804097\pi$
$761$	9.15395	+	28.1730i	0.331831	+	1.02127i	−0.636432	+	0.771333i	$0.719590\pi$
$762$	−0.503087	+	0.692440i	−0.0182249	+	0.0250844i
$763$	−3.05333	+	2.21838i	−0.110538	+	0.0803106i
$764$	5.84853	−	17.9999i	0.211593	−	0.651215i
$765$	−0.0206408	+	0.00833659i	−0.000746268	+	0.000301410i
$766$	14.7823	−	10.7400i	0.534106	−	0.388050i
$767$	−43.4302	−	31.5539i	−1.56817	−	1.13934i
$768$	−0.397221	+	0.129065i	−0.0143335	+	0.00465723i
$769$	−15.0515			−0.542772			−0.271386	−	0.962471i	$-0.587482\pi$
$769$	−15.0515			−0.542772			−0.271386	+	0.962471i	$0.587482\pi$
$770$	0.563150	+	1.52034i	0.0202945	+	0.0547894i
$771$		−	1.41080i		−	0.0508086i
$772$	43.1765	−	14.0289i	1.55395	−	0.504910i
$773$	−12.9534	−	9.41121i	−0.465902	−	0.338498i	0.329940	−	0.944002i	$-0.392971\pi$
$773$	−12.9534	−	9.41121i	−0.465902	−	0.338498i	−0.795842	+	0.605504i	$0.792971\pi$
$774$	−0.0319426	+	0.0232076i	−0.00114815	+	0.000834181i
$775$	−42.3981	−	13.7760i	−1.52298	−	0.494847i
$776$	32.8110	+	10.6609i	1.17785	+	0.382705i
$777$	−9.81931	−	13.5151i	−0.352266	−	0.484852i
$778$	13.5089	+	9.81480i	0.484318	+	0.351878i
$779$	−47.8355	+	15.5427i	−1.71388	+	0.556875i
$780$	−6.62439			−0.237191
$781$	−14.0656	+	21.1105i	−0.503307	+	0.755394i
$782$	3.05999	+	3.64763i	0.109425	+	0.130439i
$783$	6.13491	+	18.8813i	0.219244	+	0.674763i
$784$	−3.40819	−	2.47620i	−0.121721	−	0.0884356i
$785$	2.74557	+	3.77896i	0.0979937	+	0.134877i
$786$	−4.10632	+	12.6379i	−0.146468	+	0.450781i
$787$	1.37275	+	0.446033i	0.0489332	+	0.0158994i	0.333381	−	0.942792i	$-0.391810\pi$
$787$	1.37275	+	0.446033i	0.0489332	+	0.0158994i	−0.284448	+	0.958691i	$0.591810\pi$
$788$	−10.0570	−	13.8423i	−0.358266	−	0.493112i
$789$	17.1782	−	23.6437i	0.611559	−	0.841739i
$790$	−0.245240	−	0.754770i	−0.00872524	−	0.0268535i
$791$	3.37692			0.120069
$792$	0.0631174	+	0.0420541i	0.00224278	+	0.00149433i
$793$		−	16.7577i		−	0.595085i
$794$	−1.52651	+	0.495993i	−0.0541738	+	0.0176021i
$795$	−5.03403	−	3.65743i	−0.178539	−	0.129716i
$796$	23.3580	+	32.1495i	0.827901	+	1.13951i
$797$	6.05723	−	18.6422i	0.214558	−	0.660342i	−0.784627	−	0.619969i	$-0.787145\pi$
$797$	6.05723	−	18.6422i	0.214558	−	0.660342i	0.999185	−	0.0403733i	$-0.0128547\pi$
$798$	−2.59767	+	7.99481i	−0.0919566	+	0.283013i
$799$	−6.08036	+	24.3748i	−0.215107	+	0.862317i
$800$	19.2529	+	13.9881i	0.680694	+	0.494553i
$801$	−0.0357246	−	0.109949i	−0.00126227	−	0.00388486i
$802$		−	14.1570i		−	0.499899i
$803$	26.1727	−	9.69463i	0.923616	−	0.342116i
$804$		−	19.8903i		−	0.701478i
$805$	2.26784	−	0.736866i	0.0799308	−	0.0259711i
$806$	13.3183	−	18.3311i	0.469118	−	0.645685i
$807$	−1.86330	+	1.35376i	−0.0655911	+	0.0476547i
$808$	−3.94166	+	12.1312i	−0.138667	+	0.426773i
$809$	28.4666	+	9.24937i	1.00083	+	0.325191i	0.763199	−	0.646164i	$-0.223628\pi$
$809$	28.4666	+	9.24937i	1.00083	+	0.325191i	0.237635	+	0.971354i	$0.423628\pi$
$810$	1.10801	+	1.52504i	0.0389315	+	0.0535846i
$811$	−19.9896	+	27.5133i	−0.701930	+	0.966124i	0.298003	+	0.954565i	$0.403679\pi$
$811$	−19.9896	+	27.5133i	−0.701930	+	0.966124i	−0.999933	+	0.0115590i	$0.996321\pi$
$812$	−4.82848	−	14.8605i	−0.169446	−	0.521502i
$813$		−	41.1354i		−	1.44268i
$814$	4.16143	+	5.26454i	0.145858	+	0.184522i
$815$	−1.35530			−0.0474741
$816$	−9.95550	+	15.9280i	−0.348512	+	0.557590i
$817$	−22.6084	−	16.4259i	−0.790967	−	0.574671i
$818$	8.24813	−	5.99262i	0.288389	−	0.209527i
$819$	0.138803	+	0.0451000i	0.00485019	+	0.00157592i
$820$	2.75463	−	8.47787i	0.0961958	−	0.296060i
$821$	−12.5262	−	17.2409i	−0.437168	−	0.601710i	0.532412	−	0.846485i	$-0.321286\pi$
$821$	−12.5262	−	17.2409i	−0.437168	−	0.601710i	−0.969580	+	0.244775i	$0.921286\pi$
$822$	−1.51091	+	2.07959i	−0.0526989	+	0.0725339i
$823$	13.5786	−	4.41196i	0.473321	−	0.153791i	−0.0626363	−	0.998036i	$-0.519951\pi$
$823$	13.5786	−	4.41196i	0.473321	−	0.153791i	0.535957	+	0.844245i	$0.319951\pi$
$824$	2.88672			0.100564
$825$	−1.11939	−	27.5690i	−0.0389720	−	0.959828i
$826$		−	12.0733i		−	0.420085i
$827$	−27.7348	+	9.01159i	−0.964434	+	0.313364i	−0.748567	−	0.663059i	$-0.769258\pi$
$827$	−27.7348	+	9.01159i	−0.964434	+	0.313364i	−0.215867	+	0.976423i	$0.569258\pi$
$828$	0.0307214	−	0.0422843i	0.00106764	−	0.00146948i
$829$	44.1754	−	32.0953i	1.53428	−	1.11472i	0.580473	−	0.814279i	$-0.302868\pi$
$829$	44.1754	−	32.0953i	1.53428	−	1.11472i	0.953802	−	0.300437i	$-0.0971324\pi$
$830$	1.43031	+	0.464736i	0.0496467	+	0.0161312i
$831$	3.93714	−	12.1173i	0.136578	−	0.420344i
$832$	11.6568	−	8.46918i	0.404128	−	0.293616i
$833$	−6.57420	+	0.458936i	−0.227783	+	0.0159012i
$834$	−2.05887	−	6.33654i	−0.0712927	−	0.219416i
$835$	−2.02588			−0.0701083
$836$	−6.79559	+	24.2168i	−0.235030	+	0.837556i
$837$	48.2273			1.66698
$838$	2.11184	−	0.686180i	0.0729525	−	0.0237037i
$839$	4.43885	−	6.10956i	0.153246	−	0.210925i	−0.725490	−	0.688232i	$-0.758387\pi$
$839$	4.43885	−	6.10956i	0.153246	−	0.210925i	0.878737	+	0.477307i	$0.158387\pi$
$840$	−1.86898	−	2.57242i	−0.0644858	−	0.0887571i
$841$	4.46915	−	13.7546i	0.154109	−	0.474298i
$842$	3.08739	−	9.50199i	0.106398	−	0.327460i
$843$	−7.28134	−	10.0219i	−0.250783	−	0.345173i
$844$	−7.74407	+	10.6588i	−0.266562	+	0.366891i
$845$	5.04900	−	1.64052i	0.173691	−	0.0564356i
$846$	−0.0370242			−0.00127292
$847$	2.07267	+	25.4814i	0.0712177	+	0.875552i
$848$	21.9492			0.753737
$849$	−5.81483	−	17.8962i	−0.199564	−	0.614196i
$850$	9.63207	−	0.672401i	0.330377	−	0.0230632i
$851$	7.98487	−	5.80134i	0.273718	−	0.198868i
$852$	7.20333	−	22.1696i	0.246782	−	0.759517i
$853$	−33.0282	−	10.7315i	−1.13087	−	0.367440i	−0.316960	−	0.948439i	$-0.602662\pi$
$853$	−33.0282	−	10.7315i	−1.13087	−	0.367440i	−0.813905	+	0.580998i	$0.802662\pi$
$854$	3.04906	−	2.21527i	0.104337	−	0.0758050i
$855$	0.0136488	−	0.0187859i	0.000466779	−	0.000642466i
$856$	−10.9771	+	3.56666i	−0.375188	+	0.121906i
$857$			46.0372i			1.57260i	0.617845	+	0.786300i	$0.288006\pi$
$857$			46.0372i			1.57260i	−0.617845	+	0.786300i	$0.711994\pi$
$858$	13.5024	+	3.78896i	0.460963	+	0.129353i
$859$	9.09216			0.310221			0.155110	−	0.987897i	$-0.450427\pi$
$859$	9.09216			0.310221			0.155110	+	0.987897i	$0.450427\pi$
$860$	4.71037	−	1.53049i	0.160622	−	0.0521893i
$861$	27.6134	−	38.0066i	0.941062	−	1.29526i
$862$	0.0116269	+	0.0160031i	0.000396015	+	0.000545068i
$863$	−5.52961	+	17.0184i	−0.188230	+	0.579313i	−0.999989	−	0.00467989i	$-0.998510\pi$
$863$	−5.52961	+	17.0184i	−0.188230	+	0.579313i	0.811759	+	0.583993i	$0.198510\pi$
$864$	−24.4849	−	7.95564i	−0.832995	−	0.270656i
$865$	−5.41235	+	3.93230i	−0.184025	+	0.133702i
$866$	−8.95035	−	6.50281i	−0.304145	−	0.220974i
$867$	4.08255	+	29.0985i	0.138651	+	0.988237i
$868$	−37.9573			−1.28835
$869$	−0.507698	−	12.5039i	−0.0172225	−	0.424166i
$870$			1.38612i			0.0469940i
$871$	10.1402	+	31.2082i	0.343586	+	1.05745i
$872$	−1.74768	+	2.40547i	−0.0591839	+	0.0814596i
$873$	−0.138318	−	0.190379i	−0.00468136	−	0.00644334i
$874$	−4.72341	−	1.53473i	−0.159772	−	0.0519130i
$875$	3.04670	−	9.37679i	0.102997	−	0.316993i
$876$	−20.7493	+	15.0753i	−0.701055	+	0.509346i
$877$	13.1557	−	18.1073i	0.444237	−	0.611440i	−0.526910	−	0.849921i	$-0.676650\pi$
$877$	13.1557	−	18.1073i	0.444237	−	0.611440i	0.971147	+	0.238481i	$0.0766495\pi$
$878$	6.31398	−	2.05154i	0.213087	−	0.0692360i
$879$		−	5.67874i		−	0.191539i
$880$	−2.34339	−	2.96457i	−0.0789956	−	0.0999357i
$881$		−	23.8954i		−	0.805056i	−0.915408	−	0.402528i	$-0.868132\pi$
$881$		−	23.8954i		−	0.805056i	0.915408	−	0.402528i	$-0.131868\pi$
$882$	−0.00300135	−	0.00923722i	−0.000101061	−	0.000311033i
$883$	−23.9384	−	17.3922i	−0.805590	−	0.585295i	0.106959	−	0.994263i	$-0.465889\pi$
$883$	−23.9384	−	17.3922i	−0.805590	−	0.585295i	−0.912549	+	0.408968i	$0.865889\pi$
$884$	8.84745	−	35.4674i	0.297572	−	1.19290i
$885$	2.46522	−	7.58715i	0.0828673	−	0.255039i
$886$	2.72670	−	8.39191i	0.0916052	−	0.281932i
$887$	−2.20228	−	3.03118i	−0.0739453	−	0.101777i	0.770442	−	0.637510i	$-0.220035\pi$
$887$	−2.20228	−	3.03118i	−0.0739453	−	0.101777i	−0.844388	+	0.535733i	$0.820035\pi$
$888$	−10.6475	−	7.73584i	−0.357306	−	0.259598i
$889$	−2.24965	+	0.730956i	−0.0754508	+	0.0245155i
$890$		−	1.94693i		−	0.0652611i
$891$	10.3248	+	27.8741i	0.345895	+	0.933817i
$892$	−11.4044			−0.381848
$893$	−8.09781	−	24.9225i	−0.270983	−	0.833999i
$894$	3.04305	−	4.18841i	0.101775	−	0.140081i
$895$	0.153987	+	0.211945i	0.00514722	+	0.00708454i
$896$	24.9400	+	8.10349i	0.833187	+	0.270719i
$897$	6.37377	−	19.6164i	0.212814	−	0.654974i
$898$	−1.70678	−	2.34918i	−0.0569560	−	0.0783933i
$899$	28.5704	+	20.7576i	0.952875	+	0.692304i
$900$	−0.0327541	−	0.100807i	−0.00109180	−	0.00336023i
$901$	26.3055	−	22.0677i	0.876364	−	0.735181i
$902$	−10.4638	+	15.7047i	−0.348406	+	0.522909i
$903$	26.1017			0.868610
$904$	2.53019	−	0.822109i	0.0841529	−	0.0273429i
$905$	7.35690	+	5.34510i	0.244552	+	0.177677i
$906$	−10.3974	−	14.3108i	−0.345431	−	0.475446i
$907$	9.74714	+	3.16704i	0.323649	+	0.105160i	0.466335	−	0.884608i	$-0.345574\pi$
$907$	9.74714	+	3.16704i	0.323649	+	0.105160i	−0.142687	+	0.989768i	$0.545574\pi$
$908$	−21.6674	−	7.04017i	−0.719058	−	0.233636i
$909$	0.0703885	−	0.0511402i	0.00233464	−	0.00169621i
$910$	1.98846	+	1.44470i	0.0659167	+	0.0478913i
$911$	3.94005	−	1.28020i	0.130540	−	0.0424149i	−0.243019	−	0.970022i	$-0.578138\pi$
$911$	3.94005	−	1.28020i	0.130540	−	0.0424149i	0.373558	+	0.927607i	$0.378138\pi$
$912$		−	19.5933i		−	0.648799i
$913$	19.7353	+	13.1493i	0.653144	+	0.435180i
$914$	1.02757			0.0339891
$915$	2.36843	−	0.769549i	0.0782979	−	0.0254405i
$916$	29.3527	+	21.3260i	0.969841	+	0.704631i
$917$	−29.7107	+	21.5861i	−0.981132	+	0.712834i
$918$	−9.68534	+	3.91181i	−0.319664	+	0.129109i
$919$	7.20155	−	22.1641i	0.237557	−	0.731126i	−0.759215	−	0.650840i	$-0.774417\pi$
$919$	7.20155	−	22.1641i	0.237557	−	0.731126i	0.996772	−	0.0802855i	$-0.0255832\pi$
$920$	1.51981	−	1.10421i	0.0501068	−	0.0364047i
$921$	−13.7434	+	18.9162i	−0.452862	+	0.623310i
$922$	−2.88961	−	8.89330i	−0.0951641	−	0.292885i
$923$			38.4566i			1.26581i
$924$	−8.16012	−	22.0300i	−0.268448	−	0.724734i
$925$		−	20.0157i		−	0.658113i
$926$	2.23572	+	6.88084i	0.0734703	+	0.226118i
$927$	−0.0159298	−	0.0115737i	−0.000523202	−	0.000380129i
$928$	−11.0809	−	15.2516i	−0.363750	−	0.500658i
$929$	22.5710	+	7.33375i	0.740529	+	0.240613i	0.654901	−	0.755715i	$-0.272710\pi$
$929$	22.5710	+	7.33375i	0.740529	+	0.240613i	0.0856282	+	0.996327i	$0.472710\pi$
$930$	3.20240	+	1.04052i	0.105011	+	0.0341201i
$931$	5.56151	−	4.04067i	0.182271	−	0.132428i
$932$	−14.6055	+	20.1028i	−0.478420	+	0.658489i
$933$	−8.52164	−	26.2269i	−0.278986	−	0.858630i
$934$	0.647505			0.0211870
$935$	−5.78907	−	1.19692i	−0.189323	−	0.0391436i
$936$	0.114980			0.00375823
$937$	−9.09071	−	27.9783i	−0.296981	−	0.914012i	−0.982549	−	0.186004i	$-0.940446\pi$
$937$	−9.09071	−	27.9783i	−0.296981	−	0.914012i	0.685568	−	0.728008i	$-0.259554\pi$
$938$	−4.33784	+	5.97052i	−0.141635	+	0.194944i
$939$	−35.9391	+	26.1113i	−1.17283	+	0.852109i
$940$	4.41701	+	1.43517i	0.144067	+	0.0468102i
$941$	−1.86778	−	0.606877i	−0.0608877	−	0.0197836i	0.278415	−	0.960461i	$-0.410191\pi$
$941$	−1.86778	−	0.606877i	−0.0608877	−	0.0197836i	−0.339303	+	0.940677i	$0.610191\pi$
$942$	5.34114	+	7.35144i	0.174024	+	0.239523i
$943$	22.4546	+	16.3143i	0.731224	+	0.531265i
$944$	8.69591	+	26.7632i	0.283028	+	0.871070i
$945$			5.23144i			0.170179i
$946$	−10.4764	+	0.425376i	−0.340618	+	0.0138302i
$947$		−	13.7588i		−	0.447101i	−0.974692	−	0.223550i	$-0.928235\pi$
$947$		−	13.7588i		−	0.447101i	0.974692	−	0.223550i	$-0.0717647\pi$
$948$	3.55356	+	10.9367i	0.115414	+	0.355209i
$949$	24.8705	−	34.2313i	0.807331	−	1.11120i
$950$	−8.14834	+	5.92011i	−0.264367	+	0.192074i
$951$	15.0064	−	46.1850i	0.486616	−	1.49765i
$952$	16.2691	−	6.57091i	0.527284	−	0.212965i
$953$	−30.1926	+	21.9362i	−0.978034	+	0.710583i	−0.957268	−	0.289201i	$-0.906610\pi$
$953$	−30.1926	+	21.9362i	−0.978034	+	0.710583i	−0.0207656	+	0.999784i	$0.506610\pi$
$954$	0.0409396	+	0.0297444i	0.00132547	+	0.000963010i
$955$	−4.41295	+	1.43385i	−0.142800	+	0.0463985i
$956$	−15.4388			−0.499326
$957$	−5.90537	+	21.0444i	−0.190894	+	0.680270i
$958$			11.7489i			0.379590i
$959$	−6.75631	+	2.19526i	−0.218173	+	0.0708886i
$960$	1.73228	+	1.25858i	0.0559092	+	0.0406204i
$961$	44.3243	−	32.2035i	1.42982	−	1.03882i
$962$	9.67540	+	3.14373i	0.311947	+	0.101358i
$963$	0.0748744	+	0.0243282i	0.00241279	+	0.000783964i
$964$	−17.5495	−	24.1549i	−0.565233	−	0.777976i
$965$	−9.00444	−	6.54211i	−0.289863	−	0.210598i
$966$	4.41177	−	1.43347i	0.141946	−	0.0461212i
$967$	−24.9069			−0.800953			−0.400477	−	0.916307i	$-0.631155\pi$
$967$	−24.9069			−0.800953			−0.400477	+	0.916307i	$0.631155\pi$
$968$	7.75641	+	18.5876i	0.249300	+	0.597429i
$969$	−19.6991	−	23.4821i	−0.632826	−	0.754353i
$970$	−1.22464	−	3.76904i	−0.0393207	−	0.121017i
$971$	−46.3823	−	33.6987i	−1.48848	−	1.08144i	−0.974700	−	0.223519i	$-0.928246\pi$
$971$	−46.3823	−	33.6987i	−1.48848	−	1.08144i	−0.513778	−	0.857923i	$-0.671754\pi$
$972$	0.134519	+	0.185150i	0.00431471	+	0.00593868i
$973$	5.69000	−	17.5120i	0.182413	−	0.561410i
$974$	−19.8654	−	6.45465i	−0.636528	−	0.206820i
$975$	−24.5864	−	33.8402i	−0.787394	−	1.08376i
$976$	−5.16336	+	7.10676i	−0.165275	+	0.227482i
$977$	11.9044	+	36.6379i	0.380855	+	1.17215i	0.939443	+	0.342706i	$0.111343\pi$
$977$	11.9044	+	36.6379i	0.380855	+	1.17215i	−0.558588	+	0.829445i	$0.688657\pi$
$978$	−2.63655			−0.0843076
$979$	8.29460	−	29.5587i	0.265096	−	0.944700i
$980$			1.21835i			0.0389187i
$981$	0.0192884	−	0.00626719i	0.000615832	−	0.000200096i
$982$	−13.3864	−	9.72578i	−0.427177	−	0.310362i
$983$	−16.5294	−	22.7507i	−0.527205	−	0.725635i	0.459497	−	0.888180i	$-0.348030\pi$
$983$	−16.5294	−	22.7507i	−0.527205	−	0.725635i	−0.986701	+	0.162545i	$0.948030\pi$
$984$	11.4369	−	35.1993i	0.364596	−	1.12211i
$985$	−1.29626	+	3.98947i	−0.0413022	+	0.127115i
$986$	−7.42138	−	1.85129i	−0.236345	−	0.0589570i
$987$	19.8016	+	14.3867i	0.630291	+	0.457933i
$988$	11.7830	+	36.2644i	0.374868	+	1.15372i
$989$			15.4211i			0.490364i
$990$	−0.000353457	−	0.00870517i	−1.12336e−5	−	0.000276668i
$991$		−	17.3331i		−	0.550604i	−0.961358	−	0.275302i	$-0.911222\pi$
$991$		−	17.3331i		−	0.550604i	0.961358	−	0.275302i	$-0.0887779\pi$
$992$	−43.5544	+	14.1517i	−1.38285	+	0.449316i
$993$	−22.1754	+	30.5218i	−0.703714	+	0.968580i
$994$	−6.99715	+	5.08372i	−0.221936	+	0.161246i
$995$	3.01063	−	9.26575i	0.0954432	−	0.293744i
$996$	−20.7254	−	6.73409i	−0.656709	−	0.213378i
$997$	−17.2055	−	23.6814i	−0.544904	−	0.749996i	0.444406	−	0.895826i	$-0.353415\pi$
$997$	−17.2055	−	23.6814i	−0.544904	−	0.749996i	−0.989310	+	0.145829i	$0.953415\pi$
$998$	−0.758040	+	1.04335i	−0.0239953	+	0.0330267i
$999$	6.69125	+	20.5936i	0.211702	+	0.651551i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.j.a.16.8	yes	64
11.9	even	5	inner	187.2.j.a.152.7	yes	64
17.16	even	2	inner	187.2.j.a.16.7	✓	64
187.152	even	10	inner	187.2.j.a.152.8	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.j.a.16.7	✓	64	17.16	even	2	inner
187.2.j.a.16.8	yes	64	1.1	even	1	trivial
187.2.j.a.152.7	yes	64	11.9	even	5	inner
187.2.j.a.152.8	yes	64	187.152	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.150351 - 0.462733i) q^{2} +(1.01595 - 1.39834i) q^{3} +(1.42652 - 1.03643i) q^{4} +(-0.411135 - 0.133586i) q^{5} +(-0.799806 - 0.259873i) q^{6} +(-1.36610 - 1.88027i) q^{7} +(-1.48131 - 1.07624i) q^{8} +(0.00385940 + 0.0118780i) q^{9} +O(q^{10})\)	\(q+(-0.150351 - 0.462733i) q^{2} +(1.01595 - 1.39834i) q^{3} +(1.42652 - 1.03643i) q^{4} +(-0.411135 - 0.133586i) q^{5} +(-0.799806 - 0.259873i) q^{6} +(-1.36610 - 1.88027i) q^{7} +(-1.48131 - 1.07624i) q^{8} +(0.00385940 + 0.0118780i) q^{9} +0.210330i q^{10} +(-0.896081 + 3.19328i) q^{11} -3.04771i q^{12} +(1.55373 + 4.78190i) q^{13} +(-0.664669 + 0.914838i) q^{14} +(-0.604491 + 0.439189i) q^{15} +(0.814469 - 2.50668i) q^{16} +(-1.54409 - 3.82306i) q^{17} +(0.00491608 - 0.00357174i) q^{18} +(3.47951 + 2.52801i) q^{19} +(-0.724943 + 0.235548i) q^{20} -4.01715 q^{21} +(1.61236 - 0.0654670i) q^{22} -2.37337i q^{23} +(-3.00989 + 0.977972i) q^{24} +(-3.89390 - 2.82908i) q^{25} +(1.97914 - 1.43793i) q^{26} +(4.95207 + 1.60902i) q^{27} +(-3.89752 - 1.26638i) q^{28} +(2.24111 + 3.08463i) q^{29} +(0.294113 + 0.213685i) q^{30} +(8.80885 - 2.86217i) q^{31} -4.94439 q^{32} +(3.55491 + 4.49725i) q^{33} +(-1.53690 + 1.28930i) q^{34} +(0.310472 + 0.955536i) q^{35} +(0.0178162 + 0.0129442i) q^{36} +(2.44435 + 3.36436i) q^{37} +(0.646646 - 1.99017i) q^{38} +(8.26523 + 2.68554i) q^{39} +(0.465250 + 0.640361i) q^{40} +(-6.87388 + 9.46108i) q^{41} +(0.603982 + 1.85886i) q^{42} -6.49757 q^{43} +(2.03132 + 5.48399i) q^{44} -0.00539902i q^{45} +(-1.09824 + 0.356838i) q^{46} +(-4.92926 - 3.58132i) q^{47} +(-2.67772 - 3.68557i) q^{48} +(0.493920 - 1.52013i) q^{49} +(-0.723658 + 2.22719i) q^{50} +(-6.91466 - 1.72488i) q^{51} +(7.17251 + 5.21114i) q^{52} +(2.57340 + 7.92012i) q^{53} -2.53340i q^{54} +(0.794987 - 1.19316i) q^{55} +4.25552i q^{56} +(7.07004 - 2.29719i) q^{57} +(1.09040 - 1.50081i) q^{58} +(-8.63769 + 6.27565i) q^{59} +(-0.407131 + 1.25302i) q^{60} +(-3.16977 - 1.02992i) q^{61} +(-2.64884 - 3.64581i) q^{62} +(0.0170616 - 0.0234832i) q^{63} +(-0.885545 - 2.72543i) q^{64} -2.17356i q^{65} +(1.54654 - 2.32114i) q^{66} +6.52631 q^{67} +(-6.16499 - 3.85332i) q^{68} +(-3.31877 - 2.41123i) q^{69} +(0.395478 - 0.287331i) q^{70} +(7.27416 + 2.36352i) q^{71} +(0.00706658 - 0.0217487i) q^{72} +(-4.94642 - 6.80816i) q^{73} +(1.18929 - 1.63691i) q^{74} +(-7.91203 + 2.57078i) q^{75} +7.58368 q^{76} +(7.22837 - 2.67746i) q^{77} -4.22837i q^{78} +(-3.58850 + 1.16598i) q^{79} +(-0.669713 + 0.921781i) q^{80} +(7.25071 - 5.26795i) q^{81} +(5.41145 + 1.75829i) q^{82} +(2.20955 - 6.80030i) q^{83} +(-5.73053 + 4.16347i) q^{84} +(0.124124 + 1.77806i) q^{85} +(0.976916 + 3.00664i) q^{86} +6.59022 q^{87} +(4.76411 - 3.76586i) q^{88} -9.25653 q^{89} +(-0.00249830 + 0.000811748i) q^{90} +(6.86872 - 9.45398i) q^{91} +(-2.45982 - 3.38565i) q^{92} +(4.94709 - 15.2256i) q^{93} +(-0.916074 + 2.81939i) q^{94} +(-1.09284 - 1.50417i) q^{95} +(-5.02326 + 6.91393i) q^{96} +(-17.9197 + 5.82245i) q^{97} -0.777675 q^{98} +(-0.0413881 + 0.00168049i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{2} - 20 q^{4} - 4 q^{8} + 30 q^{9}+O(q^{10}) \) 64 * q - 8 * q^2 - 20 * q^4 - 4 * q^8 + 30 * q^9	\( 64 q - 8 q^{2} - 20 q^{4} - 4 q^{8} + 30 q^{9} - 4 q^{13} - 34 q^{15} - 16 q^{16} - 14 q^{17} + 10 q^{18} - 72 q^{21} + 36 q^{25} + 22 q^{26} - 8 q^{30} + 84 q^{32} - 44 q^{33} - 44 q^{34} + 18 q^{35} - 32 q^{36} - 60 q^{38} - 10 q^{42} + 32 q^{43} + 16 q^{47} - 18 q^{49} + 4 q^{50} - 2 q^{51} + 44 q^{52} - 16 q^{53} + 22 q^{55} - 50 q^{59} + 68 q^{60} - 80 q^{64} - 172 q^{66} + 40 q^{67} + 18 q^{68} + 6 q^{69} + 128 q^{70} + 186 q^{72} - 116 q^{76} - 30 q^{77} + 48 q^{81} - 12 q^{83} + 68 q^{84} - 108 q^{85} - 16 q^{86} + 92 q^{87} - 40 q^{89} - 80 q^{93} - 188 q^{94} + 72 q^{98}+O(q^{100}) \) 64 * q - 8 * q^2 - 20 * q^4 - 4 * q^8 + 30 * q^9 - 4 * q^13 - 34 * q^15 - 16 * q^16 - 14 * q^17 + 10 * q^18 - 72 * q^21 + 36 * q^25 + 22 * q^26 - 8 * q^30 + 84 * q^32 - 44 * q^33 - 44 * q^34 + 18 * q^35 - 32 * q^36 - 60 * q^38 - 10 * q^42 + 32 * q^43 + 16 * q^47 - 18 * q^49 + 4 * q^50 - 2 * q^51 + 44 * q^52 - 16 * q^53 + 22 * q^55 - 50 * q^59 + 68 * q^60 - 80 * q^64 - 172 * q^66 + 40 * q^67 + 18 * q^68 + 6 * q^69 + 128 * q^70 + 186 * q^72 - 116 * q^76 - 30 * q^77 + 48 * q^81 - 12 * q^83 + 68 * q^84 - 108 * q^85 - 16 * q^86 + 92 * q^87 - 40 * q^89 - 80 * q^93 - 188 * q^94 + 72 * q^98

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