LMFDB - Embedded newform 735.2.q.e.214.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(79,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("735.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			214.3
Root			$-0.147520 + 0.550552i$ of defining polynomial
Character	$\chi$	$=$	735.214
Dual form			735.2.q.e.79.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.167954 + 0.0969683i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.981194 + 1.69948i) q^{4} +(-0.710109 + 2.12032i) q^{5} -0.193937 q^{6} -0.768452i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.167954 + 0.0969683i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.981194 + 1.69948i) q^{4} +(-0.710109 + 2.12032i) q^{5} -0.193937 q^{6} -0.768452i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.0863379 - 0.424974i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(-1.69948 + 0.981194i) q^{12} +1.35026i q^{13} +(-1.67513 + 1.48119i) q^{15} +(-1.88787 - 3.26989i) q^{16} +(-2.90141 - 1.67513i) q^{17} +(-0.167954 - 0.0969683i) q^{18} +(2.67513 + 4.63346i) q^{19} +(-2.90668 - 3.28726i) q^{20} -0.387873i q^{22} +(4.29755 - 2.48119i) q^{23} +(0.384226 - 0.665499i) q^{24} +(-3.99149 - 3.01131i) q^{25} +(-0.130933 - 0.226782i) q^{26} +1.00000i q^{27} -7.92478 q^{29} +(0.137716 - 0.411207i) q^{30} +(-2.28726 + 3.96165i) q^{31} +(1.96515 + 1.13458i) q^{32} +(-1.73205 + 1.00000i) q^{33} +0.649738 q^{34} -1.96239 q^{36} +(0.671816 - 0.387873i) q^{37} +(-0.898598 - 0.518806i) q^{38} +(-0.675131 + 1.16936i) q^{39} +(1.62936 + 0.545685i) q^{40} +3.73813 q^{41} -12.6253i q^{43} +(-1.96239 - 3.39896i) q^{44} +(-2.19130 + 0.445186i) q^{45} +(-0.481194 + 0.833453i) q^{46} +(-8.59511 + 4.96239i) q^{47} -3.77575i q^{48} +(0.962389 + 0.118714i) q^{50} +(-1.67513 - 2.90141i) q^{51} +(-2.29474 - 1.32487i) q^{52} +(-7.42575 - 4.28726i) q^{53} +(-0.0969683 - 0.167954i) q^{54} +(-2.96239 - 3.35026i) q^{55} +5.35026i q^{57} +(1.33100 - 0.768452i) q^{58} +(-4.31265 + 7.46973i) q^{59} +(-0.873629 - 4.30019i) q^{60} +(4.35026 + 7.53487i) q^{61} -0.887166i q^{62} +7.11142 q^{64} +(-2.86298 - 0.958833i) q^{65} +(0.193937 - 0.335908i) q^{66} +(8.59511 + 4.96239i) q^{67} +(5.69370 - 3.28726i) q^{68} +4.96239 q^{69} +2.00000 q^{71} +(0.665499 - 0.384226i) q^{72} +(8.09756 + 4.67513i) q^{73} +(-0.0752228 + 0.130290i) q^{74} +(-1.95108 - 4.60362i) q^{75} -10.4993 q^{76} -0.261865i q^{78} +(5.35026 + 9.26693i) q^{79} +(8.27380 - 1.68091i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.627835 + 0.362481i) q^{82} +3.22425i q^{83} +(5.61213 - 4.96239i) q^{85} +(1.22425 + 2.12047i) q^{86} +(-6.86306 - 3.96239i) q^{87} +(1.33100 + 0.768452i) q^{88} +(0.518806 + 0.898598i) q^{89} +(0.324869 - 0.287258i) q^{90} +9.73813i q^{92} +(-3.96165 + 2.28726i) q^{93} +(0.962389 - 1.66691i) q^{94} +(-11.7240 + 2.38186i) q^{95} +(1.13458 + 1.96515i) q^{96} +18.4993i q^{97} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 10 q^{4} - 2 q^{5} - 4 q^{6} + 6 q^{9}+O(q^{10}) $ 12 * q + 10 * q^4 - 2 * q^5 - 4 * q^6 + 6 * q^9	$ 12 q + 10 q^{4} - 2 q^{5} - 4 q^{6} + 6 q^{9} + 12 q^{10} - 12 q^{11} - 26 q^{16} + 12 q^{19} - 60 q^{20} - 18 q^{24} + 2 q^{25} - 20 q^{26} - 8 q^{29} + 10 q^{30} - 4 q^{31} + 48 q^{34} + 20 q^{36} + 12 q^{39} - 4 q^{40} + 8 q^{41} + 20 q^{44} + 2 q^{45} + 16 q^{46} - 32 q^{50} - 2 q^{54} + 8 q^{55} + 32 q^{59} + 8 q^{60} + 12 q^{61} - 52 q^{64} - 32 q^{65} + 4 q^{66} + 16 q^{69} + 24 q^{71} - 88 q^{74} - 8 q^{75} + 8 q^{76} + 24 q^{79} - 46 q^{80} - 6 q^{81} + 64 q^{85} + 8 q^{86} + 28 q^{89} + 24 q^{90} - 32 q^{94} - 4 q^{95} + 58 q^{96} - 24 q^{99}+O(q^{100}) $ 12 * q + 10 * q^4 - 2 * q^5 - 4 * q^6 + 6 * q^9 + 12 * q^10 - 12 * q^11 - 26 * q^16 + 12 * q^19 - 60 * q^20 - 18 * q^24 + 2 * q^25 - 20 * q^26 - 8 * q^29 + 10 * q^30 - 4 * q^31 + 48 * q^34 + 20 * q^36 + 12 * q^39 - 4 * q^40 + 8 * q^41 + 20 * q^44 + 2 * q^45 + 16 * q^46 - 32 * q^50 - 2 * q^54 + 8 * q^55 + 32 * q^59 + 8 * q^60 + 12 * q^61 - 52 * q^64 - 32 * q^65 + 4 * q^66 + 16 * q^69 + 24 * q^71 - 88 * q^74 - 8 * q^75 + 8 * q^76 + 24 * q^79 - 46 * q^80 - 6 * q^81 + 64 * q^85 + 8 * q^86 + 28 * q^89 + 24 * q^90 - 32 * q^94 - 4 * q^95 + 58 * q^96 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

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 $

$2$	−0.167954	+	0.0969683i	−0.118761	+	0.0685669i	−0.558204	−	0.829704i	$-0.688509\pi$
$2$	−0.167954	+	0.0969683i	−0.118761	+	0.0685669i	0.439443	+	0.898271i	$0.355176\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−0.981194	+	1.69948i	−0.490597	+	0.849739i
$5$	−0.710109	+	2.12032i	−0.317570	+	0.948235i
$5$	−0.710109	+	2.12032i	−0.317570	+	0.948235i
$6$	−0.193937			−0.0791743
$7$		0			0
$7$		0			0
$8$		−	0.768452i		−	0.271689i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−0.0863379	−	0.424974i	−0.0273025	−	0.134389i
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$	−1.69948	+	0.981194i	−0.490597	+	0.283246i
$13$			1.35026i			0.374495i	0.982313	+	0.187248i	$0.0599567\pi$
$13$			1.35026i			0.374495i	−0.982313	+	0.187248i	$0.940043\pi$
$14$		0			0
$15$	−1.67513	+	1.48119i	−0.432517	+	0.382443i
$16$	−1.88787	−	3.26989i	−0.471968	−	0.817473i
$17$	−2.90141	−	1.67513i	−0.703696	−	0.406279i	0.105027	−	0.994469i	$-0.466507\pi$
$17$	−2.90141	−	1.67513i	−0.703696	−	0.406279i	−0.808722	+	0.588190i	$0.799841\pi$
$18$	−0.167954	−	0.0969683i	−0.0395871	−	0.0228556i
$19$	2.67513	+	4.63346i	0.613717	+	1.06299i	0.990608	+	0.136732i	$0.0436598\pi$
$19$	2.67513	+	4.63346i	0.613717	+	1.06299i	−0.376891	+	0.926258i	$0.623007\pi$
$20$	−2.90668	−	3.28726i	−0.649953	−	0.735053i
$21$		0			0
$22$		−	0.387873i		−	0.0826948i
$23$	4.29755	−	2.48119i	0.896102	−	0.517365i	0.0201686	−	0.999797i	$-0.493580\pi$
$23$	4.29755	−	2.48119i	0.896102	−	0.517365i	0.875934	+	0.482432i	$0.160246\pi$
$24$	0.384226	−	0.665499i	0.0784298	−	0.135844i
$25$	−3.99149	−	3.01131i	−0.798298	−	0.602262i
$26$	−0.130933	−	0.226782i	−0.0256780	−	0.0444756i
$27$			1.00000i			0.192450i
$28$		0			0
$29$	−7.92478			−1.47159			−0.735797	−	0.677202i	$-0.763192\pi$
$29$	−7.92478			−1.47159			−0.735797	+	0.677202i	$0.763192\pi$
$30$	0.137716	−	0.411207i	0.0251434	−	0.0750758i
$31$	−2.28726	+	3.96165i	−0.410804	+	0.711533i	−0.994978	−	0.100096i	$-0.968085\pi$
$31$	−2.28726	+	3.96165i	−0.410804	+	0.711533i	0.584174	+	0.811628i	$0.301418\pi$
$32$	1.96515	+	1.13458i	0.347393	+	0.200567i
$33$	−1.73205	+	1.00000i	−0.301511	+	0.174078i
$34$	0.649738			0.111429
$35$		0			0
$36$	−1.96239			−0.327065
$37$	0.671816	−	0.387873i	0.110446	−	0.0637660i	−0.443760	−	0.896146i	$-0.646356\pi$
$37$	0.671816	−	0.387873i	0.110446	−	0.0637660i	0.554205	+	0.832380i	$0.313022\pi$
$38$	−0.898598	−	0.518806i	−0.145772	−	0.0841614i
$39$	−0.675131	+	1.16936i	−0.108107	+	0.187248i
$40$	1.62936	+	0.545685i	0.257625	+	0.0862803i
$41$	3.73813			0.583799			0.291899	−	0.956449i	$-0.405713\pi$
$41$	3.73813			0.583799			0.291899	+	0.956449i	$0.405713\pi$
$42$		0			0
$43$		−	12.6253i		−	1.92534i	−0.270677	−	0.962670i	$-0.587248\pi$
$43$		−	12.6253i		−	1.92534i	0.270677	−	0.962670i	$-0.412752\pi$
$44$	−1.96239	−	3.39896i	−0.295841	−	0.512412i
$45$	−2.19130	+	0.445186i	−0.326660	+	0.0663645i
$46$	−0.481194	+	0.833453i	−0.0709482	+	0.122886i
$47$	−8.59511	+	4.96239i	−1.25373	+	0.723839i	−0.971847	−	0.235611i	$-0.924291\pi$
$47$	−8.59511	+	4.96239i	−1.25373	+	0.723839i	−0.281878	+	0.959450i	$0.590957\pi$
$48$		−	3.77575i		−	0.544982i
$49$		0			0
$50$	0.962389	+	0.118714i	0.136102	+	0.0167887i
$51$	−1.67513	−	2.90141i	−0.234565	−	0.406279i
$52$	−2.29474	−	1.32487i	−0.318223	−	0.183726i
$53$	−7.42575	−	4.28726i	−1.02000	−	0.588900i	−0.105900	−	0.994377i	$-0.533772\pi$
$53$	−7.42575	−	4.28726i	−1.02000	−	0.588900i	−0.914105	+	0.405477i	$0.867106\pi$
$54$	−0.0969683	−	0.167954i	−0.0131957	−	0.0228556i
$55$	−2.96239	−	3.35026i	−0.399448	−	0.451749i
$56$		0			0
$57$			5.35026i			0.708659i
$58$	1.33100	−	0.768452i	0.174769	−	0.100903i
$59$	−4.31265	+	7.46973i	−0.561459	+	0.972476i	0.435910	+	0.899990i	$0.356427\pi$
$59$	−4.31265	+	7.46973i	−0.561459	+	0.972476i	−0.997369	+	0.0724858i	$0.976907\pi$
$60$	−0.873629	−	4.30019i	−0.112785	−	0.555152i
$61$	4.35026	+	7.53487i	0.556994	+	0.964742i	0.997745	+	0.0671126i	$0.0213787\pi$
$61$	4.35026	+	7.53487i	0.556994	+	0.964742i	−0.440751	+	0.897629i	$0.645288\pi$
$62$		−	0.887166i		−	0.112670i
$63$		0			0
$64$	7.11142			0.888927
$65$	−2.86298	−	0.958833i	−0.355109	−	0.118929i
$66$	0.193937	−	0.335908i	0.0238719	−	0.0413474i
$67$	8.59511	+	4.96239i	1.05006	+	0.606252i	0.922666	−	0.385600i	$-0.126006\pi$
$67$	8.59511	+	4.96239i	1.05006	+	0.606252i	0.127394	+	0.991852i	$0.459339\pi$
$68$	5.69370	−	3.28726i	0.690462	−	0.398639i
$69$	4.96239			0.597401
$70$		0			0
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$	0.665499	−	0.384226i	0.0784298	−	0.0452815i
$73$	8.09756	+	4.67513i	0.947748	+	0.547183i	0.892381	−	0.451283i	$-0.149034\pi$
$73$	8.09756	+	4.67513i	0.947748	+	0.547183i	0.0553675	+	0.998466i	$0.482367\pi$
$74$	−0.0752228	+	0.130290i	−0.00874447	+	0.0151459i
$75$	−1.95108	−	4.60362i	−0.225291	−	0.531580i
$76$	−10.4993			−1.20435
$77$		0			0
$78$		−	0.261865i		−	0.0296504i
$79$	5.35026	+	9.26693i	0.601951	+	1.04261i	0.992525	+	0.122039i	$0.0389433\pi$
$79$	5.35026	+	9.26693i	0.601951	+	1.04261i	−0.390574	+	0.920572i	$0.627723\pi$
$80$	8.27380	−	1.68091i	0.925039	−	0.187932i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.627835	+	0.362481i	−0.0693327	+	0.0400293i
$83$			3.22425i			0.353908i	0.984219	+	0.176954i	$0.0566244\pi$
$83$			3.22425i			0.353908i	−0.984219	+	0.176954i	$0.943376\pi$
$84$		0			0
$85$	5.61213	−	4.96239i	0.608721	−	0.538247i
$86$	1.22425	+	2.12047i	0.132015	+	0.228656i
$87$	−6.86306	−	3.96239i	−0.735797	−	0.424813i
$88$	1.33100	+	0.768452i	0.141885	+	0.0819173i
$89$	0.518806	+	0.898598i	0.0549933	+	0.0952512i	0.892212	−	0.451618i	$-0.149153\pi$
$89$	0.518806	+	0.898598i	0.0549933	+	0.0952512i	−0.837218	+	0.546869i	$0.815820\pi$
$90$	0.324869	−	0.287258i	0.0342442	−	0.0302796i
$91$		0			0
$92$			9.73813i			1.01527i
$93$	−3.96165	+	2.28726i	−0.410804	+	0.237178i
$94$	0.962389	−	1.66691i	0.0992628	−	0.171928i
$95$	−11.7240	+	2.38186i	−1.20286	+	0.244374i
$96$	1.13458	+	1.96515i	0.115798	+	0.200567i
$97$			18.4993i			1.87832i	0.343482	+	0.939159i	$0.388394\pi$
$97$			18.4993i			1.87832i	−0.343482	+	0.939159i	$0.611606\pi$
$98$		0			0
$99$	−2.00000			−0.201008
$100$	9.03409	−	3.82877i	0.903409	−	0.382877i
$101$	8.83146	−	15.2965i	0.878763	−	1.52206i	0.0260630	−	0.999660i	$-0.491703\pi$
$101$	8.83146	−	15.2965i	0.878763	−	1.52206i	0.852700	−	0.522401i	$-0.174964\pi$
$102$	0.562690	+	0.324869i	0.0557146	+	0.0321668i
$103$	5.80282	−	3.35026i	0.571769	−	0.330111i	−0.186086	−	0.982533i	$-0.559580\pi$
$103$	5.80282	−	3.35026i	0.571769	−	0.330111i	0.757856	+	0.652422i	$0.226247\pi$
$104$	1.03761			0.101746
$105$		0			0
$106$	1.66291			0.161516
$107$	−11.8976	+	6.86907i	−1.15018	+	0.664058i	−0.948932	−	0.315482i	$-0.897834\pi$
$107$	−11.8976	+	6.86907i	−1.15018	+	0.664058i	−0.201250	+	0.979540i	$0.564500\pi$
$108$	−1.69948	−	0.981194i	−0.163532	−	0.0944155i
$109$	−1.38787	+	2.40387i	−0.132934	+	0.230249i	−0.924806	−	0.380438i	$-0.875773\pi$
$109$	−1.38787	+	2.40387i	−0.132934	+	0.230249i	0.791872	+	0.610687i	$0.209107\pi$
$110$	0.822414	+	0.275432i	0.0784141	+	0.0262614i
$111$	0.775746			0.0736306
$112$		0			0
$113$			12.0508i			1.13364i	0.823841	+	0.566821i	$0.191827\pi$
$113$			12.0508i			1.13364i	−0.823841	+	0.566821i	$0.808173\pi$
$114$	−0.518806	−	0.898598i	−0.0485906	−	0.0841614i
$115$	2.20919	+	10.8741i	0.206008	+	1.01401i
$116$	7.77575	−	13.4680i	0.721960	−	1.25047i
$117$	−1.16936	+	0.675131i	−0.108107	+	0.0624159i
$118$		−	1.67276i		−	0.153990i
$119$		0			0
$120$	1.13823	+	1.28726i	0.103905	+	0.117510i
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−1.46129	−	0.843675i	−0.132299	−	0.0763827i
$123$	3.23732	+	1.86907i	0.291899	+	0.168528i
$124$	−4.48849	−	7.77429i	−0.403078	−	0.698152i
$125$	9.21933	−	6.32487i	0.824602	−	0.565713i
$126$		0			0
$127$		−	2.70052i		−	0.239633i	−0.992796	−	0.119816i	$-0.961769\pi$
$127$		−	2.70052i		−	0.239633i	0.992796	−	0.119816i	$-0.0382306\pi$
$128$	−5.12469	+	2.95874i	−0.452963	+	0.261518i
$129$	6.31265	−	10.9338i	0.555798	−	0.962670i
$130$	0.573826	−	0.116579i	0.0503279	−	0.0102246i
$131$	−10.3127	−	17.8620i	−0.901020	−	1.56061i	−0.826172	−	0.563418i	$-0.809486\pi$
$131$	−10.3127	−	17.8620i	−0.901020	−	1.56061i	−0.0748486	−	0.997195i	$-0.523847\pi$
$132$		−	3.92478i		−	0.341608i
$133$		0			0
$134$	−1.92478			−0.166275
$135$	−2.12032	−	0.710109i	−0.182488	−	0.0611164i
$136$	−1.28726	+	2.22960i	−0.110381	+	0.191186i
$137$	19.4850	+	11.2496i	1.66471	+	0.961122i	0.970418	+	0.241431i	$0.0776168\pi$
$137$	19.4850	+	11.2496i	1.66471	+	0.961122i	0.694294	+	0.719691i	$0.255717\pi$
$138$	−0.833453	+	0.481194i	−0.0709482	+	0.0409620i
$139$	3.27504			0.277785			0.138893	−	0.990307i	$-0.455646\pi$
$139$	3.27504			0.277785			0.138893	+	0.990307i	$0.455646\pi$
$140$		0			0
$141$	−9.92478			−0.835817
$142$	−0.335908	+	0.193937i	−0.0281888	+	0.0162748i
$143$	−2.33872	−	1.35026i	−0.195574	−	0.112915i
$144$	1.88787	−	3.26989i	0.157323	−	0.272491i
$145$	5.62745	−	16.8030i	0.467335	−	1.39542i
$146$	−1.81336			−0.150075
$147$		0			0
$148$			1.52232i			0.125134i
$149$	−2.22425	−	3.85252i	−0.182218	−	0.315611i	0.760418	−	0.649434i	$-0.224994\pi$
$149$	−2.22425	−	3.85252i	−0.182218	−	0.315611i	−0.942636	+	0.333824i	$0.891661\pi$
$150$	0.774096	+	0.584003i	0.0632047	+	0.0476837i
$151$	−0.649738	+	1.12538i	−0.0528749	+	0.0915821i	−0.891251	−	0.453510i	$-0.850172\pi$
$151$	−0.649738	+	1.12538i	−0.0528749	+	0.0915821i	0.838376	+	0.545092i	$0.183505\pi$
$152$	3.56059	−	2.05571i	0.288802	−	0.166740i
$153$		−	3.35026i		−	0.270853i
$154$		0			0
$155$	−6.77575	−	7.66291i	−0.544241	−	0.615500i
$156$	−1.32487	−	2.29474i	−0.106074	−	0.183726i
$157$	−2.29474	−	1.32487i	−0.183140	−	0.105736i	0.405627	−	0.914039i	$-0.367053\pi$
$157$	−2.29474	−	1.32487i	−0.183140	−	0.105736i	−0.588767	+	0.808303i	$0.700387\pi$
$158$	−1.79720	−	1.03761i	−0.142977	−	0.0825479i
$159$	−4.28726	−	7.42575i	−0.340002	−	0.588900i
$160$	−3.80114	+	3.36107i	−0.300506	+	0.265716i
$161$		0			0
$162$		−	0.193937i		−	0.0152371i
$163$	4.58948	−	2.64974i	0.359476	−	0.207544i	−0.309375	−	0.950940i	$-0.600120\pi$
$163$	4.58948	−	2.64974i	0.359476	−	0.207544i	0.668851	+	0.743397i	$0.266786\pi$
$164$	−3.66784	+	6.35288i	−0.286410	+	0.496077i
$165$	−0.890373	−	4.38261i	−0.0693154	−	0.341185i
$166$	−0.312650	−	0.541526i	−0.0242664	−	0.0420306i
$167$			14.5501i			1.12592i	0.826485	+	0.562959i	$0.190337\pi$
$167$			14.5501i			1.12592i	−0.826485	+	0.562959i	$0.809663\pi$
$168$		0			0
$169$	11.1768			0.859753
$170$	−0.461385	+	1.37765i	−0.0353866	+	0.105661i
$171$	−2.67513	+	4.63346i	−0.204572	+	0.354330i
$172$	21.4564	+	12.3879i	1.63604	+	0.944566i
$173$	−3.89650	+	2.24965i	−0.296246	+	0.171037i	−0.640755	−	0.767745i	$-0.721379\pi$
$173$	−3.89650	+	2.24965i	−0.296246	+	0.171037i	0.344509	+	0.938783i	$0.388045\pi$
$174$	1.53690			0.116512
$175$		0			0
$176$	7.55149			0.569215
$177$	−7.46973	+	4.31265i	−0.561459	+	0.324159i
$178$	−0.174271	−	0.100615i	−0.0130622	−	0.00754144i
$179$	5.00000	−	8.66025i	0.373718	−	0.647298i	−0.616417	−	0.787420i	$-0.711416\pi$
$179$	5.00000	−	8.66025i	0.373718	−	0.647298i	0.990134	+	0.140122i	$0.0447496\pi$
$180$	1.39351	−	4.16089i	0.103866	−	0.310134i
$181$	10.6253			0.789772			0.394886	−	0.918730i	$-0.370784\pi$
$181$	10.6253			0.789772			0.394886	+	0.918730i	$0.370784\pi$
$182$		0			0
$183$			8.70052i			0.643161i
$184$	−1.90668	−	3.30246i	−0.140562	−	0.243461i
$185$	0.345352	+	1.69990i	0.0253908	+	0.124979i
$186$	0.443583	−	0.768308i	0.0325251	−	0.0563351i
$187$	5.80282	−	3.35026i	0.424344	−	0.244995i
$188$		−	19.4763i		−	1.42045i
$189$		0			0
$190$	1.73813	−	1.53690i	0.126098	−	0.111499i
$191$	6.92478	+	11.9941i	0.501059	+	0.867860i	0.999999	+	0.00122360i	$0.000389484\pi$
$191$	6.92478	+	11.9941i	0.501059	+	0.867860i	−0.498940	+	0.866637i	$0.666277\pi$
$192$	6.15867	+	3.55571i	0.444464	+	0.256611i
$193$	−13.2726	−	7.66291i	−0.955379	−	0.551588i	−0.0606314	−	0.998160i	$-0.519311\pi$
$193$	−13.2726	−	7.66291i	−0.955379	−	0.551588i	−0.894748	+	0.446572i	$0.852645\pi$
$194$	−1.79384	−	3.10703i	−0.128791	−	0.223072i
$195$	−2.00000	−	2.26187i	−0.143223	−	0.161976i
$196$		0			0
$197$			0.574515i			0.0409325i	0.999791	+	0.0204663i	$0.00651507\pi$
$197$			0.574515i			0.0409325i	−0.999791	+	0.0204663i	$0.993485\pi$
$198$	0.335908	−	0.193937i	0.0238719	−	0.0137825i
$199$	−0.100615	+	0.174271i	−0.00713244	+	0.0123537i	−0.869570	−	0.493810i	$-0.835604\pi$
$199$	−0.100615	+	0.174271i	−0.00713244	+	0.0123537i	0.862437	+	0.506164i	$0.168937\pi$
$200$	−2.31405	+	3.06727i	−0.163628	+	0.216889i
$201$	4.96239	+	8.59511i	0.350020	+	0.606252i
$202$			3.42548i			0.241016i
$203$		0			0
$204$	6.57452			0.460308
$205$	−2.65448	+	7.92603i	−0.185397	+	0.553578i
$206$	−0.649738	+	1.12538i	−0.0452694	+	0.0784089i
$207$	4.29755	+	2.48119i	0.298701	+	0.172455i
$208$	4.41521	−	2.54912i	0.306140	−	0.176750i
$209$	−10.7005			−0.740171
$210$		0			0
$211$	6.44851			0.443934			0.221967	−	0.975054i	$-0.428752\pi$
$211$	6.44851			0.443934			0.221967	+	0.975054i	$0.428752\pi$
$212$	14.5722	−	8.41327i	1.00082	−	0.577825i
$213$	1.73205	+	1.00000i	0.118678	+	0.0685189i
$214$	1.33216	−	2.30737i	0.0910648	−	0.157729i
$215$	26.7696	+	8.96534i	1.82567	+	0.611431i
$216$	0.768452			0.0522865
$217$		0			0
$218$		−	0.538319i		−	0.0364595i
$219$	4.67513	+	8.09756i	0.315916	+	0.547183i
$220$	8.60038	−	1.74726i	0.579837	−	0.117800i
$221$	2.26187	−	3.91767i	0.152150	−	0.263531i
$222$	−0.130290	+	0.0752228i	−0.00874447	+	0.00504862i
$223$			1.55149i			0.103896i	0.998650	+	0.0519478i	$0.0165429\pi$
$223$			1.55149i			0.103896i	−0.998650	+	0.0519478i	$0.983457\pi$
$224$		0			0
$225$	0.612127	−	4.96239i	0.0408085	−	0.330826i
$226$	−1.16854	−	2.02398i	−0.0777304	−	0.134633i
$227$	−11.3874	−	6.57452i	−0.755808	−	0.436366i	0.0719807	−	0.997406i	$-0.477068\pi$
$227$	−11.3874	−	6.57452i	−0.755808	−	0.436366i	−0.827789	+	0.561040i	$0.810401\pi$
$228$	−9.09265	−	5.24965i	−0.602176	−	0.347666i
$229$	1.38787	+	2.40387i	0.0917132	+	0.158852i	0.908232	−	0.418467i	$-0.137432\pi$
$229$	1.38787	+	2.40387i	0.0917132	+	0.158852i	−0.816519	+	0.577319i	$0.804099\pi$
$230$	−1.42548	−	1.61213i	−0.0939937	−	0.106300i
$231$		0			0
$232$			6.08981i			0.399816i
$233$	−0.0439813	+	0.0253926i	−0.00288131	+	0.00166353i	−0.501440	−	0.865192i	$-0.667196\pi$
$233$	−0.0439813	+	0.0253926i	−0.00288131	+	0.00166353i	0.498559	+	0.866856i	$0.333863\pi$
$234$	0.130933	−	0.226782i	0.00855933	−	0.0148252i
$235$	−4.41838	−	21.7482i	−0.288223	−	1.41870i
$236$	−8.46310	−	14.6585i	−0.550901	−	0.954188i
$237$			10.7005i			0.695074i
$238$		0			0
$239$	−5.84955			−0.378376			−0.189188	−	0.981941i	$-0.560586\pi$
$239$	−5.84955			−0.378376			−0.189188	+	0.981941i	$0.560586\pi$
$240$	8.00578	+	2.68119i	0.516771	+	0.173070i
$241$	0.0376114	−	0.0651448i	0.00242276	−	0.00419635i	−0.864811	−	0.502097i	$-0.832562\pi$
$241$	0.0376114	−	0.0651448i	0.00242276	−	0.00419635i	0.867234	+	0.497900i	$0.165895\pi$
$242$	−1.17568	−	0.678778i	−0.0755754	−	0.0436335i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−17.0738			−1.09304
$245$		0			0
$246$	−0.724961			−0.0462218
$247$	−6.25639	+	3.61213i	−0.398084	+	0.229834i
$248$	3.04434	+	1.75765i	0.193315	+	0.111611i
$249$	−1.61213	+	2.79229i	−0.102164	+	0.176954i
$250$	−0.935111	+	1.95627i	−0.0591416	+	0.123725i
$251$	19.2243			1.21342			0.606712	−	0.794922i	$-0.292488\pi$
$251$	19.2243			1.21342			0.606712	+	0.794922i	$0.292488\pi$
$252$		0			0
$253$			9.92478i			0.623965i
$254$	0.261865	+	0.453564i	0.0164309	+	0.0284591i
$255$	7.34144	−	1.49149i	0.459739	−	0.0934008i
$256$	−6.53761	+	11.3235i	−0.408601	+	0.707717i
$257$	−6.36551	+	3.67513i	−0.397070	+	0.229248i	−0.685219	−	0.728337i	$-0.740293\pi$
$257$	−6.36551	+	3.67513i	−0.397070	+	0.229248i	0.288149	+	0.957586i	$0.406960\pi$
$258$			2.44851i			0.152437i
$259$		0			0
$260$	4.43866	−	3.92478i	0.275274	−	0.243404i
$261$	−3.96239	−	6.86306i	−0.245266	−	0.424813i
$262$	3.46410	+	2.00000i	0.214013	+	0.123560i
$263$	11.2258	+	6.48119i	0.692210	+	0.399648i	0.804439	−	0.594035i	$-0.202466\pi$
$263$	11.2258	+	6.48119i	0.692210	+	0.399648i	−0.112229	+	0.993682i	$0.535799\pi$
$264$	0.768452	+	1.33100i	0.0472950	+	0.0819173i
$265$	14.3634	−	12.7005i	0.882339	−	0.780187i
$266$		0			0
$267$			1.03761i			0.0635008i
$268$	−16.8669	+	9.73813i	−1.03031	+	0.594851i
$269$	2.05571	−	3.56059i	0.125339	−	0.217093i	−0.796527	−	0.604604i	$-0.793332\pi$
$269$	2.05571	−	3.56059i	0.125339	−	0.217093i	0.921865	+	0.387510i	$0.126665\pi$
$270$	0.424974	−	0.0863379i	0.0258631	−	0.00525436i
$271$	8.21203	+	14.2237i	0.498846	+	0.864026i	0.999999	−	0.00133248i	$-0.000424141\pi$
$271$	8.21203	+	14.2237i	0.498846	+	0.864026i	−0.501154	+	0.865358i	$0.667091\pi$
$272$			12.6497i			0.767003i
$273$		0			0
$274$	−4.36344			−0.263605
$275$	9.20724	−	3.90215i	0.555217	−	0.235309i
$276$	−4.86907	+	8.43347i	−0.293083	+	0.507635i
$277$	−9.59020	−	5.53690i	−0.576219	−	0.332680i	0.183410	−	0.983036i	$-0.441286\pi$
$277$	−9.59020	−	5.53690i	−0.576219	−	0.332680i	−0.759629	+	0.650356i	$0.774620\pi$
$278$	−0.550056	+	0.317575i	−0.0329902	+	0.0190469i
$279$	−4.57452			−0.273869
$280$		0			0
$281$	14.3733			0.857438			0.428719	−	0.903438i	$-0.358965\pi$
$281$	14.3733			0.857438			0.428719	+	0.903438i	$0.358965\pi$
$282$	1.66691	−	0.962389i	0.0992628	−	0.0573094i
$283$	−0.995090	−	0.574515i	−0.0591520	−	0.0341514i	0.470132	−	0.882596i	$-0.344206\pi$
$283$	−0.995090	−	0.574515i	−0.0591520	−	0.0341514i	−0.529284	+	0.848445i	$0.677540\pi$
$284$	−1.96239	+	3.39896i	−0.116446	+	0.201691i
$285$	−11.3443	−	3.79927i	−0.671976	−	0.225049i
$286$	0.523730			0.0309688
$287$		0			0
$288$			2.26916i			0.133711i
$289$	−2.88787	−	5.00194i	−0.169875	−	0.294232i
$290$	0.684209	+	3.36782i	0.0401781	+	0.197765i
$291$	−9.24965	+	16.0209i	−0.542224	+	0.939159i
$292$	−15.8906	+	9.17442i	−0.929925	+	0.536893i
$293$			0.649738i			0.0379581i	0.999820	+	0.0189791i	$0.00604158\pi$
$293$			0.649738i			0.0379581i	−0.999820	+	0.0189791i	$0.993958\pi$
$294$		0			0
$295$	−12.7757	−	14.4485i	−0.743833	−	0.841225i
$296$	−0.298062	−	0.516258i	−0.0173245	−	0.0300069i
$297$	−1.73205	−	1.00000i	−0.100504	−	0.0580259i
$298$	0.747145	+	0.431364i	0.0432809	+	0.0249883i
$299$	3.35026	+	5.80282i	0.193751	+	0.335586i
$300$	9.73813	+	1.20123i	0.562231	+	0.0693531i
$301$		0			0
$302$		−	0.252016i		−	0.0145019i
$303$	15.2965	−	8.83146i	0.878763	−	0.507354i
$304$	10.1006	−	17.4948i	0.579310	−	1.00339i
$305$	−19.0655	+	3.87336i	−1.09169	+	0.221788i
$306$	0.324869	+	0.562690i	0.0185715	+	0.0321668i
$307$		−	24.1016i		−	1.37555i	−0.725924	−	0.687775i	$-0.758588\pi$
$307$		−	24.1016i		−	1.37555i	0.725924	−	0.687775i	$-0.241412\pi$
$308$		0			0
$309$	6.70052			0.381179
$310$	1.88107	+	0.629984i	0.106838	+	0.0357807i
$311$	−4.12601	+	7.14646i	−0.233964	+	0.405238i	−0.958971	−	0.283503i	$-0.908503\pi$
$311$	−4.12601	+	7.14646i	−0.233964	+	0.405238i	0.725007	+	0.688742i	$0.241837\pi$
$312$	0.898598	+	0.518806i	0.0508731	+	0.0293716i
$313$	−12.9053	+	7.45088i	−0.729451	+	0.421148i	−0.818221	−	0.574904i	$-0.805040\pi$
$313$	−12.9053	+	7.45088i	−0.729451	+	0.421148i	0.0887706	+	0.996052i	$0.471706\pi$
$314$	0.513881			0.0290000
$315$		0			0
$316$	−20.9986			−1.18126
$317$	−8.76938	+	5.06300i	−0.492537	+	0.284367i	−0.725627	−	0.688089i	$-0.758450\pi$
$317$	−8.76938	+	5.06300i	−0.492537	+	0.284367i	0.233089	+	0.972455i	$0.425117\pi$
$318$	1.44012	+	0.831456i	0.0807582	+	0.0466257i
$319$	7.92478	−	13.7261i	0.443702	−	0.768515i
$320$	−5.04988	+	15.0785i	−0.282297	+	0.842912i
$321$	−13.7381			−0.766788
$322$		0			0
$323$		−	17.9248i		−	0.997361i
$324$	−0.981194	−	1.69948i	−0.0545108	−	0.0944155i
$325$	4.06606	−	5.38956i	0.225544	−	0.298959i
$326$	−0.513881	+	0.890068i	−0.0284612	+	0.0492963i
$327$	−2.40387	+	1.38787i	−0.132934	+	0.0767496i
$328$		−	2.87258i		−	0.158612i
$329$		0			0
$330$	0.574515	+	0.649738i	0.0316260	+	0.0357669i
$331$	−13.9248	−	24.1184i	−0.765375	−	1.32567i	−0.940048	−	0.341042i	$-0.889220\pi$
$331$	−13.9248	−	24.1184i	−0.765375	−	1.32567i	0.174673	−	0.984626i	$-0.444113\pi$
$332$	−5.47955	−	3.16362i	−0.300729	−	0.173626i
$333$	0.671816	+	0.387873i	0.0368153	+	0.0212553i
$334$	−1.41090	−	2.44374i	−0.0772008	−	0.133716i
$335$	−16.6253	+	14.7005i	−0.908337	+	0.803175i
$336$		0			0
$337$			3.84955i			0.209699i	0.994488	+	0.104849i	$0.0334360\pi$
$337$			3.84955i			0.209699i	−0.994488	+	0.104849i	$0.966564\pi$
$338$	−1.87719	+	1.08379i	−0.102106	+	0.0589506i
$339$	−6.02539	+	10.4363i	−0.327254	+	0.566821i
$340$	2.92689	+	14.4068i	0.158733	+	0.781316i
$341$	−4.57452	−	7.92329i	−0.247724	−	0.429070i
$342$		−	1.03761i		−	0.0561076i
$343$		0			0
$344$	−9.70194			−0.523093
$345$	−3.52384	+	10.5218i	−0.189717	+	0.566477i
$346$	0.436289	−	0.755674i	0.0234550	−	0.0406253i
$347$	8.30318	+	4.79384i	0.445738	+	0.257347i	0.706029	−	0.708183i	$-0.250485\pi$
$347$	8.30318	+	4.79384i	0.445738	+	0.257347i	−0.260290	+	0.965530i	$0.583818\pi$
$348$	13.4680	−	7.77575i	0.721960	−	0.416824i
$349$	15.1490			0.810909			0.405455	−	0.914115i	$-0.367113\pi$
$349$	15.1490			0.810909			0.405455	+	0.914115i	$0.367113\pi$
$350$		0			0
$351$	−1.35026			−0.0720716
$352$	−3.93030	+	2.26916i	−0.209486	+	0.120947i
$353$	17.6226	+	10.1744i	0.937957	+	0.541530i	0.889319	−	0.457287i	$-0.151179\pi$
$353$	17.6226	+	10.1744i	0.937957	+	0.541530i	0.0486379	+	0.998816i	$0.484512\pi$
$354$	0.836381	−	1.44865i	0.0444531	−	0.0769951i
$355$	−1.42022	+	4.24063i	−0.0753773	+	0.225070i
$356$	−2.03620			−0.107918
$357$		0			0
$358$			1.93937i			0.102499i
$359$	−15.7005	−	27.1941i	−0.828642	−	1.43525i	−0.899104	−	0.437735i	$-0.855781\pi$
$359$	−15.7005	−	27.1941i	−0.828642	−	1.43525i	0.0704619	−	0.997514i	$-0.477553\pi$
$360$	0.342104	+	1.68391i	0.0180305	+	0.0887499i
$361$	−4.81265	+	8.33575i	−0.253297	+	0.438724i
$362$	−1.78456	+	1.03032i	−0.0937945	+	0.0541523i
$363$			7.00000i			0.367405i
$364$		0			0
$365$	−15.6629	+	13.8496i	−0.819834	+	0.724919i
$366$	−0.843675	−	1.46129i	−0.0440996	−	0.0763827i
$367$	−25.4621	−	14.7005i	−1.32911	−	0.767361i	−0.343947	−	0.938989i	$-0.611764\pi$
$367$	−25.4621	−	14.7005i	−1.32911	−	0.767361i	−0.985162	+	0.171628i	$0.945097\pi$
$368$	−16.2265	−	9.36836i	−0.845864	−	0.488360i
$369$	1.86907	+	3.23732i	0.0972998	+	0.168528i
$370$	−0.222839	−	0.252016i	−0.0115849	−	0.0131017i
$371$		0			0
$372$		−	8.97698i		−	0.465435i
$373$	13.8564	−	8.00000i	0.717458	−	0.414224i	−0.0963587	−	0.995347i	$-0.530720\pi$
$373$	13.8564	−	8.00000i	0.717458	−	0.414224i	0.813816	+	0.581122i	$0.197386\pi$
$374$	−0.649738	+	1.12538i	−0.0335972	+	0.0581920i
$375$	11.1466	−	0.867833i	0.575608	−	0.0448147i
$376$	3.81336	+	6.60493i	0.196659	+	0.340623i
$377$		−	10.7005i		−	0.551105i
$378$		0			0
$379$	−10.7005			−0.549649			−0.274824	−	0.961494i	$-0.588620\pi$
$379$	−10.7005			−0.549649			−0.274824	+	0.961494i	$0.588620\pi$
$380$	7.45564	−	22.2618i	0.382466	−	1.14201i
$381$	1.35026	−	2.33872i	0.0691760	−	0.119816i
$382$	−2.32609	−	1.34297i	−0.119013	−	0.0687122i
$383$	−14.5282	+	8.38787i	−0.742357	+	0.428600i	−0.822926	−	0.568149i	$-0.807660\pi$
$383$	−14.5282	+	8.38787i	−0.742357	+	0.428600i	0.0805684	+	0.996749i	$0.474326\pi$
$384$	−5.91748			−0.301975
$385$		0			0
$386$	2.97224			0.151283
$387$	10.9338	−	6.31265i	0.555798	−	0.320890i
$388$	−31.4391	−	18.1514i	−1.59608	−	0.921498i
$389$	−14.6629	+	25.3969i	−0.743439	+	1.28767i	0.207481	+	0.978239i	$0.433473\pi$
$389$	−14.6629	+	25.3969i	−0.743439	+	1.28767i	−0.950920	+	0.309435i	$0.899860\pi$
$390$	0.555237	+	0.185953i	0.0281155	+	0.00941608i
$391$	−16.6253			−0.840778
$392$		0			0
$393$		−	20.6253i		−	1.04041i
$394$	−0.0557098	−	0.0964922i	−0.00280662	−	0.00486121i
$395$	−23.4481	+	4.76373i	−1.17980	+	0.239689i
$396$	1.96239	−	3.39896i	0.0986137	−	0.170804i
$397$	−15.8906	+	9.17442i	−0.797525	+	0.460451i	−0.842605	−	0.538532i	$-0.818979\pi$
$397$	−15.8906	+	9.17442i	−0.797525	+	0.460451i	0.0450802	+	0.998983i	$0.485646\pi$
$398$		−	0.0390260i		−	0.00195620i
$399$		0			0
$400$	−2.31124	+	18.7367i	−0.115562	+	0.936836i
$401$	18.6629	+	32.3251i	0.931981	+	1.61424i	0.779930	+	0.625866i	$0.215254\pi$
$401$	18.6629	+	32.3251i	0.931981	+	1.61424i	0.152051	+	0.988373i	$0.451412\pi$
$402$	−1.66691	−	0.962389i	−0.0831377	−	0.0479996i
$403$	−5.34926	−	3.08840i	−0.266466	−	0.153844i
$404$	17.3307	+	30.0177i	0.862237	+	1.49344i
$405$	−1.48119	−	1.67513i	−0.0736011	−	0.0832379i
$406$		0			0
$407$			1.55149i			0.0769046i
$408$	−2.22960	+	1.28726i	−0.110381	+	0.0637288i
$409$	−11.1866	+	19.3758i	−0.553144	+	0.958073i	0.444901	+	0.895580i	$0.353239\pi$
$409$	−11.1866	+	19.3758i	−0.553144	+	0.958073i	−0.998045	+	0.0624938i	$0.980095\pi$
$410$	−0.322743	−	1.58861i	−0.0159391	−	0.0784558i
$411$	11.2496	+	19.4850i	0.554904	+	0.961122i
$412$			13.1490i			0.647806i
$413$		0			0
$414$	−0.962389			−0.0472988
$415$	−6.83644	−	2.28957i	−0.335588	−	0.112391i
$416$	−1.53198	+	2.65347i	−0.0751115	+	0.130097i
$417$	2.83627	+	1.63752i	0.138893	+	0.0801897i
$418$	1.79720	−	1.03761i	0.0879037	−	0.0507512i
$419$	−23.4763			−1.14689			−0.573445	−	0.819244i	$-0.694394\pi$
$419$	−23.4763			−1.14689			−0.573445	+	0.819244i	$0.694394\pi$
$420$		0			0
$421$	−25.2243			−1.22935			−0.614677	−	0.788779i	$-0.710714\pi$
$421$	−25.2243			−1.22935			−0.614677	+	0.788779i	$0.710714\pi$
$422$	−1.08305	+	0.625301i	−0.0527222	+	0.0304392i
$423$	−8.59511	−	4.96239i	−0.417909	−	0.241280i
$424$	−3.29455	+	5.70633i	−0.159998	+	0.277124i
$425$	6.53662	+	15.4233i	0.317073	+	0.748141i
$426$	−0.387873			−0.0187925
$427$		0			0
$428$		−	26.9596i		−	1.30314i
$429$	−1.35026	−	2.33872i	−0.0651913	−	0.112915i
$430$	−5.36542	+	1.09004i	−0.258744	+	0.0525665i
$431$	9.70052	−	16.8018i	0.467258	−	0.809314i	−0.532042	−	0.846718i	$-0.678575\pi$
$431$	9.70052	−	16.8018i	0.467258	−	0.809314i	0.999300	+	0.0374035i	$0.0119087\pi$
$432$	3.26989	−	1.88787i	0.157323	−	0.0908303i
$433$			6.49929i			0.312336i	0.987731	+	0.156168i	$0.0499141\pi$
$433$			6.49929i			0.312336i	−0.987731	+	0.156168i	$0.950086\pi$
$434$		0			0
$435$	13.2750	−	11.7381i	0.636489	−	0.562800i
$436$	−2.72355	−	4.71732i	−0.130434	−	0.225919i
$437$	22.9930	+	13.2750i	1.09991	+	0.635031i
$438$	−1.57041	−	0.906679i	−0.0750373	−	0.0433228i
$439$	−7.32487	−	12.6870i	−0.349597	−	0.605520i	0.636581	−	0.771210i	$-0.280348\pi$
$439$	−7.32487	−	12.6870i	−0.349597	−	0.605520i	−0.986178	+	0.165690i	$0.947015\pi$
$440$	−2.57452	+	2.27645i	−0.122735	+	0.108526i
$441$		0			0
$442$			0.877317i			0.0417297i
$443$	16.5750	−	9.56959i	0.787503	−	0.454665i	−0.0515798	−	0.998669i	$-0.516426\pi$
$443$	16.5750	−	9.56959i	0.787503	−	0.454665i	0.839083	+	0.544004i	$0.183092\pi$
$444$	−0.761158	+	1.31836i	−0.0361230	+	0.0625668i
$445$	−2.27372	+	0.461931i	−0.107785	+	0.0218976i
$446$	−0.150446	−	0.260579i	−0.00712380	−	0.0123388i
$447$		−	4.44851i		−	0.210407i
$448$		0			0
$449$	32.8021			1.54803			0.774013	−	0.633169i	$-0.218246\pi$
$449$	32.8021			1.54803			0.774013	+	0.633169i	$0.218246\pi$
$450$	0.378385	+	0.892810i	0.0178372	+	0.0420875i
$451$	−3.73813	+	6.47464i	−0.176022	+	0.304879i
$452$	−20.4800	−	11.8242i	−0.963300	−	0.556162i
$453$	−1.12538	+	0.649738i	−0.0528749	+	0.0305274i
$454$	2.55008			0.119681
$455$		0			0
$456$	4.11142			0.192535
$457$	16.1951	−	9.35026i	0.757576	−	0.437387i	−0.0708487	−	0.997487i	$-0.522571\pi$
$457$	16.1951	−	9.35026i	0.757576	−	0.437387i	0.828425	+	0.560100i	$0.189237\pi$
$458$	−0.466198	−	0.269159i	−0.0217840	−	0.0125770i
$459$	1.67513	−	2.90141i	0.0781884	−	0.135426i
$460$	−20.6479	−	6.91513i	−0.962715	−	0.322420i
$461$	−6.96239			−0.324271			−0.162135	−	0.986769i	$-0.551838\pi$
$461$	−6.96239			−0.324271			−0.162135	+	0.986769i	$0.551838\pi$
$462$		0			0
$463$			5.29948i			0.246288i	0.992389	+	0.123144i	$0.0392976\pi$
$463$			5.29948i			0.246288i	−0.992389	+	0.123144i	$0.960702\pi$
$464$	14.9610	+	25.9132i	0.694546	+	1.20299i
$465$	−2.03651	−	10.0241i	−0.0944410	−	0.464859i
$466$	0.00492456	−	0.00852958i	0.000228126	−	0.000395125i
$467$	11.3874	−	6.57452i	0.526946	−	0.304232i	−0.212826	−	0.977090i	$-0.568267\pi$
$467$	11.3874	−	6.57452i	0.526946	−	0.304232i	0.739772	+	0.672858i	$0.234933\pi$
$468$		−	2.64974i		−	0.122484i
$469$		0			0
$470$	2.85097	+	3.22425i	0.131505	+	0.148724i
$471$	−1.32487	−	2.29474i	−0.0610467	−	0.105736i
$472$	5.74013	+	3.31406i	0.264211	+	0.152542i
$473$	21.8677	+	12.6253i	1.00548	+	0.580512i
$474$	−1.03761	−	1.79720i	−0.0476591	−	0.0825479i
$475$	3.27504	−	26.5501i	0.150269	−	1.21820i
$476$		0			0
$477$		−	8.57452i		−	0.392600i
$478$	0.982456	−	0.567221i	0.0449365	−	0.0259441i
$479$	2.57452	−	4.45919i	0.117633	−	0.203746i	−0.801196	−	0.598401i	$-0.795803\pi$
$479$	2.57452	−	4.45919i	0.117633	−	0.203746i	0.918829	+	0.394656i	$0.129136\pi$
$480$	−4.97242	+	1.01020i	−0.226959	+	0.0461091i
$481$	0.523730	+	0.907127i	0.0238800	+	0.0413614i
$482$			0.0145884i			0.000664486i
$483$		0			0
$484$	−13.7367			−0.624396
$485$	−39.2244	−	13.1365i	−1.78109	−	0.596498i
$486$	0.0969683	−	0.167954i	0.00439857	−	0.00761855i
$487$	−19.2057	−	11.0884i	−0.870292	−	0.502463i	−0.00284661	−	0.999996i	$-0.500906\pi$
$487$	−19.2057	−	11.0884i	−0.870292	−	0.502463i	−0.867445	+	0.497533i	$0.834239\pi$
$488$	5.79019	−	3.34297i	0.262110	−	0.151329i
$489$	5.29948			0.239651
$490$		0			0
$491$	2.00000			0.0902587			0.0451294	−	0.998981i	$-0.485630\pi$
$491$	2.00000			0.0902587			0.0451294	+	0.998981i	$0.485630\pi$
$492$	−6.35288	+	3.66784i	−0.286410	+	0.165359i
$493$	22.9930	+	13.2750i	1.03555	+	0.597878i
$494$	0.700523	−	1.21334i	0.0315180	−	0.0545908i
$495$	1.42022	−	4.24063i	0.0638340	−	0.190602i
$496$	17.2722			0.775545
$497$		0			0
$498$		−	0.625301i		−	0.0280204i
$499$	−3.27504	−	5.67253i	−0.146611	−	0.253937i	0.783362	−	0.621566i	$-0.213503\pi$
$499$	−3.27504	−	5.67253i	−0.146611	−	0.253937i	−0.929973	+	0.367628i	$0.880170\pi$
$500$	1.70303	+	21.8740i	0.0761616	+	0.978234i
$501$	−7.27504	+	12.6007i	−0.325025	+	0.562959i
$502$	−3.22879	+	1.86414i	−0.144108	+	0.0832008i
$503$			8.77575i			0.391291i	0.980675	+	0.195646i	$0.0626802\pi$
$503$			8.77575i			0.391291i	−0.980675	+	0.195646i	$0.937320\pi$
$504$		0			0
$505$	26.1622	+	29.5877i	1.16420	+	1.31663i
$506$	−0.962389	−	1.66691i	−0.0427834	−	0.0741030i
$507$	9.67939	+	5.58840i	0.429877	+	0.248189i
$508$	4.58948	+	2.64974i	0.203625	+	0.117563i
$509$	6.56959	+	11.3789i	0.291192	+	0.504359i	0.974092	−	0.226153i	$-0.0726148\pi$
$509$	6.56959	+	11.3789i	0.291192	+	0.504359i	−0.682900	+	0.730512i	$0.739281\pi$
$510$	−1.08840	+	0.962389i	−0.0481950	+	0.0426153i
$511$		0			0
$512$		−	14.3707i		−	0.635103i
$513$	−4.63346	+	2.67513i	−0.204572	+	0.118110i
$514$	0.712742	−	1.23451i	0.0314377	−	0.0544517i
$515$	2.98298	+	14.6829i	0.131446	+	0.647005i
$516$	12.3879	+	21.4564i	0.545346	+	0.944566i
$517$		−	19.8496i		−	0.872982i
$518$		0			0
$519$	−4.49929			−0.197497
$520$	−0.736817	+	2.20007i	−0.0323116	+	0.0964793i
$521$	18.8315	−	32.6170i	0.825021	−	1.42898i	−0.0768821	−	0.997040i	$-0.524497\pi$
$521$	18.8315	−	32.6170i	0.825021	−	1.42898i	0.901903	−	0.431938i	$-0.142170\pi$
$522$	1.33100	+	0.768452i	0.0582562	+	0.0336342i
$523$	−3.46410	+	2.00000i	−0.151475	+	0.0874539i	−0.573822	−	0.818980i	$-0.694540\pi$
$523$	−3.46410	+	2.00000i	−0.151475	+	0.0874539i	0.422347	+	0.906434i	$0.361206\pi$
$524$	40.4749			1.76815
$525$		0			0
$526$	−2.51388			−0.109610
$527$	13.2726	−	7.66291i	0.578161	−	0.333802i
$528$	6.53978	+	3.77575i	0.284608	+	0.164318i
$529$	0.812650	−	1.40755i	0.0353326	−	0.0611979i
$530$	−1.18085	+	3.52590i	−0.0512928	+	0.153155i
$531$	−8.62530			−0.374306
$532$		0			0
$533$			5.04746i			0.218630i
$534$	−0.100615	−	0.174271i	−0.00435405	−	0.00754144i
$535$	−6.11603	−	30.1044i	−0.264419	−	1.30153i
$536$	3.81336	−	6.60493i	0.164712	−	0.285289i
$537$	8.66025	−	5.00000i	0.373718	−	0.215766i
$538$			0.797355i			0.0343764i
$539$		0			0
$540$	3.28726	−	2.90668i	0.141461	−	0.125084i
$541$	11.2374	+	19.4638i	0.483135	+	0.836814i	0.999812	−	0.0193660i	$-0.00616479\pi$
$541$	11.2374	+	19.4638i	0.483135	+	0.836814i	−0.516678	+	0.856180i	$0.672831\pi$
$542$	−2.75849	−	1.59261i	−0.118487	−	0.0684086i
$543$	9.20178	+	5.31265i	0.394886	+	0.227988i
$544$	−3.80114	−	6.58377i	−0.162972	−	0.282277i
$545$	−4.11142	−	4.64974i	−0.176114	−	0.199173i
$546$		0			0
$547$			25.9248i			1.10846i	0.832362	+	0.554232i	$0.186988\pi$
$547$			25.9248i			1.10846i	−0.832362	+	0.554232i	$0.813012\pi$
$548$	−38.2371	+	22.0762i	−1.63341	+	0.943048i
$549$	−4.35026	+	7.53487i	−0.185665	+	0.321581i
$550$	−1.16801	+	1.54819i	−0.0498040	+	0.0660151i
$551$	−21.1998	−	36.7192i	−0.903143	−	1.56429i
$552$		−	3.81336i		−	0.162307i
$553$		0			0
$554$	2.14762			0.0912435
$555$	−0.550864	+	1.64483i	−0.0233829	+	0.0698191i
$556$	−3.21345	+	5.56586i	−0.136281	+	0.236045i
$557$	−24.7039	−	14.2628i	−1.04674	−	0.604335i	−0.125004	−	0.992156i	$-0.539895\pi$
$557$	−24.7039	−	14.2628i	−1.04674	−	0.604335i	−0.921735	+	0.387821i	$0.873228\pi$
$558$	0.768308	−	0.443583i	0.0325251	−	0.0187784i
$559$	17.0475			0.721031
$560$		0			0
$561$	6.70052			0.282896
$562$	−2.41405	+	1.39375i	−0.101831	+	0.0587919i
$563$	10.0690	+	5.81336i	0.424359	+	0.245004i	0.696941	−	0.717129i	$-0.254544\pi$
$563$	10.0690	+	5.81336i	0.424359	+	0.245004i	−0.272582	+	0.962133i	$0.587877\pi$
$564$	9.73813	−	16.8669i	0.410049	−	0.710226i
$565$	−25.5515	−	8.55737i	−1.07496	−	0.360011i
$566$	0.222839			0.00936663
$567$		0			0
$568$		−	1.53690i		−	0.0644871i
$569$	4.66291	+	8.07640i	0.195479	+	0.338580i	0.947058	−	0.321064i	$-0.104040\pi$
$569$	4.66291	+	8.07640i	0.195479	+	0.338580i	−0.751578	+	0.659644i	$0.770707\pi$
$570$	2.27372	−	0.461931i	0.0952357	−	0.0193481i
$571$	9.84955	−	17.0599i	0.412191	−	0.713936i	−0.582938	−	0.812517i	$-0.698097\pi$
$571$	9.84955	−	17.0599i	0.412191	−	0.713936i	0.995129	+	0.0985808i	$0.0314303\pi$
$572$	4.58948	−	2.64974i	0.191896	−	0.110791i
$573$			13.8496i			0.578573i
$574$		0			0
$575$	−24.6253	−	3.03761i	−1.02695	−	0.126677i
$576$	3.55571	+	6.15867i	0.148155	+	0.256611i
$577$	28.4033	+	16.3987i	1.18245	+	0.682686i	0.956579	−	0.291472i	$-0.0941451\pi$
$577$	28.4033	+	16.3987i	1.18245	+	0.682686i	0.225867	+	0.974158i	$0.427478\pi$
$578$	0.970060	+	0.560064i	0.0403492	+	0.0232956i
$579$	−7.66291	−	13.2726i	−0.318460	−	0.551588i
$580$	23.0348	+	26.0508i	0.956467	+	1.08170i
$581$		0			0
$582$		−	3.58769i		−	0.148715i
$583$	14.8515	−	8.57452i	0.615086	−	0.355120i
$584$	3.59261	−	6.22259i	0.148663	−	0.257493i
$585$	−0.601118	−	2.95883i	−0.0248532	−	0.122333i
$586$	−0.0630040	−	0.109126i	−0.00260267	−	0.00450796i
$587$		−	18.8218i		−	0.776859i	−0.921479	−	0.388429i	$-0.873018\pi$
$587$		−	18.8218i		−	0.776859i	0.921479	−	0.388429i	$-0.126982\pi$
$588$		0			0
$589$	−24.4749			−1.00847
$590$	3.54678	+	1.18784i	0.146019	+	0.0489027i
$591$	−0.287258	+	0.497545i	−0.0118162	+	0.0204663i
$592$	−2.53661	−	1.46451i	−0.104254	−	0.0601910i
$593$	29.2283	−	16.8749i	1.20026	−	0.692971i	0.239648	−	0.970860i	$-0.422968\pi$
$593$	29.2283	−	16.8749i	1.20026	−	0.692971i	0.960613	+	0.277889i	$0.0896347\pi$
$594$	0.387873			0.0159146
$595$		0			0
$596$	8.72970			0.357582
$597$	−0.174271	+	0.100615i	−0.00713244	+	0.00411791i
$598$	−1.12538	−	0.649738i	−0.0460202	−	0.0265698i
$599$	−10.1490	+	17.5786i	−0.414678	+	0.718244i	−0.995395	−	0.0958622i	$-0.969439\pi$
$599$	−10.1490	+	17.5786i	−0.414678	+	0.718244i	0.580716	+	0.814106i	$0.302773\pi$
$600$	−3.53766	+	1.49931i	−0.144424	+	0.0612090i
$601$	−13.8496			−0.564935			−0.282468	−	0.959277i	$-0.591153\pi$
$601$	−13.8496			−0.564935			−0.282468	+	0.959277i	$0.591153\pi$
$602$		0			0
$603$			9.92478i			0.404168i
$604$	−1.27504	−	2.20843i	−0.0518806	−	0.0898598i
$605$	−15.3391	+	3.11631i	−0.623624	+	0.126696i
$606$	−1.71274	+	2.96656i	−0.0695754	+	0.120508i
$607$	21.8677	−	12.6253i	0.887581	−	0.512445i	0.0144305	−	0.999896i	$-0.495406\pi$
$607$	21.8677	−	12.6253i	0.887581	−	0.512445i	0.873150	+	0.487451i	$0.162073\pi$
$608$			12.1406i			0.492366i
$609$		0			0
$610$	2.82653	−	2.49929i	0.114443	−	0.101193i
$611$	−6.70052	−	11.6056i	−0.271074	−	0.469514i
$612$	5.69370	+	3.28726i	0.230154	+	0.132880i
$613$	7.92329	+	4.57452i	0.320019	+	0.184763i	0.651401	−	0.758734i	$-0.274182\pi$
$613$	7.92329	+	4.57452i	0.320019	+	0.184763i	−0.331382	+	0.943497i	$0.607515\pi$
$614$	2.33709	+	4.04796i	0.0943172	+	0.163362i
$615$	−6.26187	+	5.53690i	−0.252503	+	0.223270i
$616$		0			0
$617$		−	15.9492i		−	0.642091i	−0.947064	−	0.321046i	$-0.895966\pi$
$617$		−	15.9492i		−	0.642091i	0.947064	−	0.321046i	$-0.104034\pi$
$618$	−1.12538	+	0.649738i	−0.0452694	+	0.0261363i
$619$	5.58673	−	9.67651i	0.224550	−	0.388932i	−0.731634	−	0.681697i	$-0.761242\pi$
$619$	5.58673	−	9.67651i	0.224550	−	0.388932i	0.956184	+	0.292765i	$0.0945755\pi$
$620$	19.6713	−	3.99643i	0.790018	−	0.160500i
$621$	2.48119	+	4.29755i	0.0995669	+	0.172455i
$622$		−	1.60037i		−	0.0641689i
$623$		0			0
$624$	5.09825			0.204093
$625$	6.86400	+	24.0392i	0.274560	+	0.961570i
$626$	1.44500	−	2.50281i	0.0577537	−	0.100032i
$627$	−9.26693	−	5.35026i	−0.370085	−	0.213669i
$628$	4.50317	−	2.59991i	0.179696	−	0.103748i
$629$	−2.59895			−0.103627
$630$		0			0
$631$	−14.5501			−0.579229			−0.289615	−	0.957143i	$-0.593527\pi$
$631$	−14.5501			−0.579229			−0.289615	+	0.957143i	$0.593527\pi$
$632$	7.12119	−	4.11142i	0.283266	−	0.163543i
$633$	5.58457	+	3.22425i	0.221967	+	0.128153i
$634$	0.981902	−	1.70070i	0.0389963	−	0.0675436i
$635$	5.72597	+	1.91767i	0.227228	+	0.0761002i
$636$	16.8265			0.667215
$637$		0			0
$638$			3.07381i			0.121693i
$639$	1.00000	+	1.73205i	0.0395594	+	0.0685189i
$640$	−2.63438	−	12.9670i	−0.104133	−	0.512566i
$641$	19.3634	−	33.5385i	0.764810	−	1.32469i	−0.175537	−	0.984473i	$-0.556166\pi$
$641$	19.3634	−	33.5385i	0.764810	−	1.32469i	0.940347	−	0.340217i	$-0.110500\pi$
$642$	2.30737	−	1.33216i	0.0910648	−	0.0525763i
$643$		−	11.9511i		−	0.471306i	−0.971837	−	0.235653i	$-0.924277\pi$
$643$		−	11.9511i		−	0.471306i	0.971837	−	0.235653i	$-0.0757229\pi$
$644$		0			0
$645$	18.7005	+	21.1490i	0.736332	+	0.832742i
$646$	1.73813	+	3.01054i	0.0683860	+	0.118448i
$647$	−12.6007	−	7.27504i	−0.495386	−	0.286011i	0.231420	−	0.972854i	$-0.425663\pi$
$647$	−12.6007	−	7.27504i	−0.495386	−	0.286011i	−0.726806	+	0.686843i	$0.758996\pi$
$648$	0.665499	+	0.384226i	0.0261433	+	0.0150938i
$649$	−8.62530	−	14.9395i	−0.338573	−	0.586425i
$650$	−0.160295	+	1.29948i	−0.00628727	+	0.0509697i
$651$		0			0
$652$			10.3996i			0.407281i
$653$	43.2801	−	24.9878i	1.69368	−	0.977847i	0.742181	−	0.670199i	$-0.233791\pi$
$653$	43.2801	−	24.9878i	1.69368	−	0.977847i	0.951500	−	0.307648i	$-0.0995420\pi$
$654$	0.269159	−	0.466198i	0.0105250	−	0.0182298i
$655$	45.1963	−	9.18210i	1.76596	−	0.358775i
$656$	−7.05712	−	12.2233i	−0.275534	−	0.477240i
$657$			9.35026i			0.364788i
$658$		0			0
$659$	16.9525			0.660377			0.330189	−	0.943915i	$-0.392888\pi$
$659$	16.9525			0.660377			0.330189	+	0.943915i	$0.392888\pi$
$660$	8.32177	+	2.78702i	0.323925	+	0.108485i
$661$	7.82653	−	13.5560i	0.304417	−	0.527265i	−0.672715	−	0.739902i	$-0.734872\pi$
$661$	7.82653	−	13.5560i	0.304417	−	0.527265i	0.977131	+	0.212637i	$0.0682051\pi$
$662$	4.67744	+	2.70052i	0.181794	+	0.104959i
$663$	3.91767	−	2.26187i	0.152150	−	0.0878436i
$664$	2.47768			0.0961528
$665$		0			0
$666$	−0.150446			−0.00582965
$667$	−34.0572	+	19.6629i	−1.31870	+	0.761351i
$668$	−24.7275	−	14.2765i	−0.956737	−	0.552373i
$669$	−0.775746	+	1.34363i	−0.0299921	+	0.0519478i
$670$	1.36680	−	4.08114i	0.0528041	−	0.157668i
$671$	−17.4010			−0.671760
$672$		0			0
$673$			26.0263i			1.00324i	0.865088	+	0.501621i	$0.167263\pi$
$673$			26.0263i			1.00324i	−0.865088	+	0.501621i	$0.832737\pi$
$674$	−0.373285	−	0.646548i	−0.0143784	−	0.0249041i
$675$	3.01131	−	3.99149i	0.115905	−	0.153633i
$676$	−10.9666	+	18.9947i	−0.421793	+	0.730566i
$677$	30.7022	−	17.7259i	1.17998	−	0.681262i	0.223971	−	0.974596i	$-0.428098\pi$
$677$	30.7022	−	17.7259i	1.17998	−	0.681262i	0.956010	+	0.293334i	$0.0947647\pi$
$678$		−	2.33709i		−	0.0897553i
$679$		0			0
$680$	−3.81336	−	4.31265i	−0.146236	−	0.165383i
$681$	−6.57452	−	11.3874i	−0.251936	−	0.436366i
$682$	1.53662	+	0.887166i	0.0588401	+	0.0339713i
$683$	20.4927	+	11.8315i	0.784131	+	0.452718i	0.837892	−	0.545836i	$-0.183788\pi$
$683$	20.4927	+	11.8315i	0.784131	+	0.452718i	−0.0537615	+	0.998554i	$0.517121\pi$
$684$	−5.24965	−	9.09265i	−0.200725	−	0.347666i
$685$	−37.6893	+	33.3258i	−1.44003	+	1.27331i
$686$		0			0
$687$			2.77575i			0.105901i
$688$	−41.2834	+	23.8350i	−1.57391	+	0.908700i
$689$	5.78892	−	10.0267i	0.220540	−	0.381987i
$690$	−0.428442	−	2.10889i	−0.0163105	−	0.0802839i
$691$	0.287258	+	0.497545i	0.0109278	+	0.0189275i	0.871438	−	0.490506i	$-0.163188\pi$
$691$	0.287258	+	0.497545i	0.0109278	+	0.0189275i	−0.860510	+	0.509434i	$0.829855\pi$
$692$		−	8.82936i		−	0.335642i
$693$		0			0
$694$	−1.85940			−0.0705820
$695$	−2.32563	+	6.94412i	−0.0882163	+	0.263406i
$696$	−3.04491	+	5.27393i	−0.115417	+	0.199908i
$697$	−10.8459	−	6.26187i	−0.410817	−	0.237185i
$698$	−2.54434	+	1.46898i	−0.0963047	+	0.0556015i
$699$	−0.0507852			−0.00192087
$700$		0			0
$701$	42.7269			1.61377			0.806886	−	0.590707i	$-0.201151\pi$
$701$	42.7269			1.61377			0.806886	+	0.590707i	$0.201151\pi$
$702$	0.226782	−	0.130933i	0.00855933	−	0.00494173i
$703$	3.59439	+	2.07522i	0.135565	+	0.0782685i
$704$	−7.11142	+	12.3173i	−0.268022	+	0.464227i
$705$	7.04767	−	21.0437i	0.265431	−	0.792551i
$706$	−3.94639			−0.148524
$707$		0			0
$708$		−	16.9262i		−	0.636125i
$709$	13.6253	+	23.5997i	0.511709	+	0.886306i	0.999908	+	0.0135735i	$0.00432070\pi$
$709$	13.6253	+	23.5997i	0.511709	+	0.886306i	−0.488199	+	0.872732i	$0.662346\pi$
$710$	−0.172676	−	0.849948i	−0.00648041	−	0.0318980i
$711$	−5.35026	+	9.26693i	−0.200650	+	0.347537i
$712$	0.690529	−	0.398677i	0.0258787	−	0.0149411i
$713$			22.7005i			0.850141i
$714$		0			0
$715$	4.52373	−	4.00000i	0.169178	−	0.149592i
$716$	9.81194	+	16.9948i	0.366690	+	0.635125i
$717$	−5.06586	−	2.92478i	−0.189188	−	0.109228i
$718$	5.27393	+	3.04491i	0.196821	+	0.113635i
$719$	−5.35026	−	9.26693i	−0.199531	−	0.345598i	0.748845	−	0.662745i	$-0.230609\pi$
$719$	−5.35026	−	9.26693i	−0.199531	−	0.345598i	−0.948376	+	0.317147i	$0.897275\pi$
$720$	5.59261	+	6.32487i	0.208424	+	0.235714i
$721$		0			0
$722$		−	1.86670i		−	0.0694713i
$723$	0.0651448	−	0.0376114i	0.00242276	−	0.00139878i
$724$	−10.4255	+	18.0575i	−0.387460	+	0.671101i
$725$	31.6317	+	23.8640i	1.17477	+	0.886286i
$726$	−0.678778	−	1.17568i	−0.0251918	−	0.0436335i
$727$		−	39.9511i		−	1.48171i	−0.671668	−	0.740853i	$-0.734422\pi$
$727$		−	39.9511i		−	1.48171i	0.671668	−	0.740853i	$-0.265578\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	1.28768	−	3.84489i	0.0476592	−	0.142306i
$731$	−21.1490	+	36.6312i	−0.782225	+	1.35485i
$732$	−14.7864	−	8.53690i	−0.546519	−	0.315533i
$733$	−26.2829	+	15.1744i	−0.970780	+	0.560480i	−0.899474	−	0.436974i	$-0.856050\pi$
$733$	−26.2829	+	15.1744i	−0.970780	+	0.560480i	−0.0713061	+	0.997454i	$0.522717\pi$
$734$	5.70194			0.210462
$735$		0			0
$736$	11.2605			0.415066
$737$	−17.1902	+	9.92478i	−0.633210	+	0.365584i
$738$	−0.627835	−	0.362481i	−0.0231109	−	0.0133431i
$739$	18.6253	−	32.2600i	0.685143	−	1.18670i	−0.288249	−	0.957555i	$-0.593073\pi$
$739$	18.6253	−	32.2600i	0.685143	−	1.18670i	0.973392	−	0.229147i	$-0.0735935\pi$
$740$	−3.22779	−	1.08101i	−0.118656	−	0.0397387i
$741$	−7.22425			−0.265390
$742$		0			0
$743$			26.3634i			0.967181i	0.875294	+	0.483590i	$0.160668\pi$
$743$			26.3634i			0.967181i	−0.875294	+	0.483590i	$0.839332\pi$
$744$	1.75765	+	3.04434i	0.0644385	+	0.111611i
$745$	9.74803	−	1.98042i	0.357140	−	0.0725568i
$746$	−1.55149	+	2.68726i	−0.0568042	+	0.0983877i
$747$	−2.79229	+	1.61213i	−0.102164	+	0.0589846i
$748$			13.1490i			0.480776i
$749$		0			0
$750$	−1.78797	+	1.22662i	−0.0652873	+	0.0447900i
$751$	−25.3258	−	43.8656i	−0.924152	−	1.60068i	−0.792919	−	0.609328i	$-0.791439\pi$
$751$	−25.3258	−	43.8656i	−0.924152	−	1.60068i	−0.131234	−	0.991351i	$-0.541894\pi$
$752$	32.4530	+	18.7367i	1.18344	+	0.683258i
$753$	16.6487	+	9.61213i	0.606712	+	0.350285i
$754$	1.03761	+	1.79720i	0.0377876	+	0.0654500i
$755$	−1.92478	−	2.17679i	−0.0700498	−	0.0792216i
$756$		0			0
$757$		−	38.9525i		−	1.41575i	−0.706336	−	0.707877i	$-0.749653\pi$
$757$		−	38.9525i		−	1.41575i	0.706336	−	0.707877i	$-0.250347\pi$
$758$	1.79720	−	1.03761i	0.0652771	−	0.0376877i
$759$	−4.96239	+	8.59511i	−0.180123	+	0.311983i
$760$	1.83035	+	9.00937i	0.0663937	+	0.326804i
$761$	−24.1065	−	41.7537i	−0.873860	−	1.51357i	−0.857972	−	0.513696i	$-0.828276\pi$
$761$	−24.1065	−	41.7537i	−0.873860	−	1.51357i	−0.0158873	−	0.999874i	$-0.505057\pi$
$762$			0.523730i			0.0189727i
$763$		0			0
$764$	−27.1782			−0.983273
$765$	7.10362	+	2.37905i	0.256832	+	0.0860147i
$766$	1.62672	−	2.81755i	0.0587756	−	0.101802i
$767$	−10.0861	−	5.82321i	−0.364188	−	0.210264i
$768$	−11.3235	+	6.53761i	−0.408601	+	0.235906i
$769$	−4.44851			−0.160417			−0.0802086	−	0.996778i	$-0.525559\pi$
$769$	−4.44851			−0.160417			−0.0802086	+	0.996778i	$0.525559\pi$
$770$		0			0
$771$	−7.35026			−0.264713
$772$	26.0459	−	15.0376i	0.937413	−	0.541215i
$773$	−34.0360	−	19.6507i	−1.22419	−	0.706786i	−0.258381	−	0.966043i	$-0.583189\pi$
$773$	−34.0360	−	19.6507i	−1.22419	−	0.706786i	−0.965808	+	0.259257i	$0.916522\pi$
$774$	−1.22425	+	2.12047i	−0.0440049	+	0.0762187i
$775$	21.0593	−	8.92523i	0.756473	−	0.320604i
$776$	14.2158			0.510318
$777$		0			0
$778$		−	5.68735i		−	0.203901i
$779$	10.0000	+	17.3205i	0.358287	+	0.620572i
$780$	5.80638	−	1.17963i	0.207902	−	0.0422374i
$781$	−2.00000	+	3.46410i	−0.0715656	+	0.123955i
$782$	2.79229	−	1.61213i	0.0998519	−	0.0576495i
$783$		−	7.92478i		−	0.283208i
$784$		0			0
$785$	4.43866	−	3.92478i	0.158423	−	0.140081i
$786$	2.00000	+	3.46410i	0.0713376	+	0.123560i
$787$	0.776838	+	0.448507i	0.0276913	+	0.0159876i	0.513782	−	0.857921i	$-0.328244\pi$
$787$	0.776838	+	0.448507i	0.0276913	+	0.0159876i	−0.486090	+	0.873909i	$0.661577\pi$
$788$	−0.976377	−	0.563711i	−0.0347820	−	0.0200814i
$789$	6.48119	+	11.2258i	0.230737	+	0.399648i
$790$	3.47627	−	3.07381i	0.123680	−	0.109361i
$791$		0			0
$792$			1.53690i			0.0546115i
$793$	−10.1741	+	5.87399i	−0.361291	+	0.208592i
$794$	1.77926	−	3.08176i	0.0631434	−	0.109368i
$795$	18.7894	−	3.81726i	0.666390	−	0.135384i
$796$	−0.197447	−	0.341987i	−0.00699831	−	0.0121214i
$797$		−	3.19982i		−	0.113343i	−0.998393	−	0.0566717i	$-0.981951\pi$
$797$		−	3.19982i		−	0.113343i	0.998393	−	0.0566717i	$-0.0180488\pi$
$798$		0			0
$799$	33.2506			1.17632
$800$	−4.42730	−	10.4463i	−0.156529	−	0.369334i
$801$	−0.518806	+	0.898598i	−0.0183311	+	0.0317504i
$802$	−6.26902	−	3.61942i	−0.221367	−	0.127806i
$803$	−16.1951	+	9.35026i	−0.571514	+	0.329964i
$804$	−19.4763			−0.686875
$805$		0			0
$806$	1.19791			0.0421944
$807$	3.56059	−	2.05571i	0.125339	−	0.0723644i
$808$	−11.7547	−	6.78655i	−0.413527	−	0.238750i
$809$	2.22425	−	3.85252i	0.0782006	−	0.135447i	−0.824273	−	0.566193i	$-0.808416\pi$
$809$	2.22425	−	3.85252i	0.0782006	−	0.135447i	0.902474	+	0.430745i	$0.141749\pi$
$810$	0.411207	+	0.137716i	0.0144483	+	0.00483885i
$811$	37.6747			1.32294			0.661468	−	0.749973i	$-0.269934\pi$
$811$	37.6747			1.32294			0.661468	+	0.749973i	$0.269934\pi$
$812$		0			0
$813$			16.4241i			0.576017i
$814$	−0.150446	−	0.260579i	−0.00527311	−	0.00913330i
$815$	2.35926	+	11.6128i	0.0826411	+	0.406777i
$816$	−6.32487	+	10.9550i	−0.221415	+	0.383502i
$817$	58.4989	−	33.7743i	2.04662	−	1.18161i
$818$		−	4.33900i		−	0.151710i
$819$		0			0
$820$	−10.8656	−	12.2882i	−0.379442	−	0.429123i
$821$	0.374699	+	0.648998i	0.0130771	+	0.0226502i	0.872490	−	0.488632i	$-0.162504\pi$
$821$	0.374699	+	0.648998i	0.0130771	+	0.0226502i	−0.859413	+	0.511282i	$0.829171\pi$
$822$	−3.77885	−	2.18172i	−0.131802	−	0.0760961i
$823$	22.8628	+	13.1998i	0.796945	+	0.460117i	0.842402	−	0.538850i	$-0.181141\pi$
$823$	22.8628	+	13.1998i	0.796945	+	0.460117i	−0.0454565	+	0.998966i	$0.514474\pi$
$824$	−2.57452	−	4.45919i	−0.0896875	−	0.155343i
$825$	9.92478	+	1.22425i	0.345536	+	0.0426230i
$826$		0			0
$827$		−	5.43724i		−	0.189071i	−0.995521	−	0.0945357i	$-0.969863\pi$
$827$		−	5.43724i		−	0.189071i	0.995521	−	0.0945357i	$-0.0301367\pi$
$828$	−8.43347	+	4.86907i	−0.293083	+	0.169212i
$829$	11.3879	−	19.7244i	0.395517	−	0.685056i	−0.597650	−	0.801757i	$-0.703899\pi$
$829$	11.3879	−	19.7244i	0.395517	−	0.685056i	0.993167	+	0.116701i	$0.0372320\pi$
$830$	1.37022	−	0.278375i	0.0475611	−	0.00966255i
$831$	−5.53690	−	9.59020i	−0.192073	−	0.332680i
$832$			9.60228i			0.332899i
$833$		0			0
$834$	−0.635150			−0.0219934
$835$	−30.8508	−	10.3321i	−1.06764	−	0.357558i
$836$	10.4993	−	18.1853i	0.363126	−	0.628952i
$837$	−3.96165	−	2.28726i	−0.136935	−	0.0790592i
$838$	3.94293	−	2.27645i	0.136206	−	0.0786388i
$839$	−15.8496			−0.547187			−0.273594	−	0.961845i	$-0.588212\pi$
$839$	−15.8496			−0.547187			−0.273594	+	0.961845i	$0.588212\pi$
$840$		0			0
$841$	33.8021			1.16559
$842$	4.23651	−	2.44595i	0.146000	−	0.0842931i
$843$	12.4476	+	7.18664i	0.428719	+	0.247521i
$844$	−6.32724	+	10.9591i	−0.217793	+	0.377228i
$845$	−7.93674	+	23.6983i	−0.273032	+	0.815248i
$846$	1.92478			0.0661752
$847$		0			0
$848$			32.3752i			1.11177i
$849$	−0.574515	−	0.995090i	−0.0197173	−	0.0341514i
$850$	−2.59342	−	1.95656i	−0.0889537	−	0.0671096i
$851$	1.92478	−	3.33381i	0.0659805	−	0.114282i
$852$	−3.39896	+	1.96239i	−0.116446	+	0.0672303i
$853$		−	21.0494i		−	0.720717i	−0.932814	−	0.360358i	$-0.882654\pi$
$853$		−	21.0494i		−	0.720717i	0.932814	−	0.360358i	$-0.117346\pi$
$854$		0			0
$855$	−7.92478	−	8.96239i	−0.271022	−	0.306507i
$856$	5.27855	+	9.14271i	0.180417	+	0.312492i
$857$	43.4332	+	25.0762i	1.48365	+	0.856586i	0.999827	−	0.0185800i	$-0.00591453\pi$
$857$	43.4332	+	25.0762i	1.48365	+	0.856586i	0.483823	+	0.875166i	$0.339248\pi$
$858$	0.453564	+	0.261865i	0.0154844	+	0.00893993i
$859$	−2.67513	−	4.63346i	−0.0912743	−	0.158092i	0.816773	−	0.576959i	$-0.195761\pi$
$859$	−2.67513	−	4.63346i	−0.0912743	−	0.158092i	−0.908048	+	0.418867i	$0.862427\pi$
$860$	−41.5026	+	36.6977i	−1.41523	+	1.25138i
$861$		0			0
$862$			3.76257i			0.128154i
$863$	−29.1758	+	16.8446i	−0.993154	+	0.573398i	−0.906216	−	0.422816i	$-0.861042\pi$
$863$	−29.1758	+	16.8446i	−0.993154	+	0.573398i	−0.0869386	+	0.996214i	$0.527708\pi$
$864$	−1.13458	+	1.96515i	−0.0385992	+	0.0668557i
$865$	−2.00302	−	9.85931i	−0.0681049	−	0.335227i
$866$	−0.630225	−	1.09158i	−0.0214159	−	0.0370935i
$867$		−	5.77575i		−	0.196155i
$868$		0			0
$869$	−21.4010			−0.725981
$870$	−1.09137	+	3.25872i	−0.0370009	+	0.110481i
$871$	−6.70052	+	11.6056i	−0.227039	+	0.393242i
$872$	1.84726	+	1.06651i	0.0625560	+	0.0361167i
$873$	−16.0209	+	9.24965i	−0.542224	+	0.313053i
$874$	−5.14903			−0.174169
$875$		0			0
$876$	−18.3488			−0.619950
$877$	18.6218	−	10.7513i	0.628814	−	0.363046i	−0.151479	−	0.988461i	$-0.548403\pi$
$877$	18.6218	−	10.7513i	0.628814	−	0.363046i	0.780293	+	0.625415i	$0.215070\pi$
$878$	2.46048	+	1.42056i	0.0830372	+	0.0479416i
$879$	−0.324869	+	0.562690i	−0.0109576	+	0.0189791i
$880$	−5.36238	+	16.0116i	−0.180766	+	0.539750i
$881$	32.3634			1.09035			0.545176	−	0.838322i	$-0.316463\pi$
$881$	32.3634			1.09035			0.545176	+	0.838322i	$0.316463\pi$
$882$		0			0
$883$		−	2.59895i		−	0.0874617i	−0.999043	−	0.0437309i	$-0.986076\pi$
$883$		−	2.59895i		−	0.0874617i	0.999043	−	0.0437309i	$-0.0139244\pi$
$884$	4.43866	+	7.68798i	0.149288	+	0.258575i
$885$	−3.83987	−	18.9006i	−0.129076	−	0.635338i
$886$	−1.85589	+	3.21450i	−0.0623500	+	0.107993i
$887$	−33.1500	+	19.1392i	−1.11307	+	0.642631i	−0.939623	−	0.342212i	$-0.888824\pi$
$887$	−33.1500	+	19.1392i	−1.11307	+	0.642631i	−0.173447	+	0.984843i	$0.555490\pi$
$888$		−	0.596124i		−	0.0200046i
$889$		0			0
$890$	0.337088	−	0.298062i	0.0112992	−	0.00999106i
$891$	−1.00000	−	1.73205i	−0.0335013	−	0.0580259i
$892$	−2.63673	−	1.52232i	−0.0882842	−	0.0509709i
$893$	−45.9861	−	26.5501i	−1.53887	−	0.888464i
$894$	0.431364	+	0.747145i	0.0144270	+	0.0249883i
$895$	14.8119	+	16.7513i	0.495109	+	0.559934i
$896$		0			0
$897$			6.70052i			0.223724i
$898$	−5.50924	+	3.18076i	−0.183846	+	0.106143i
$899$	18.1260	−	31.3952i	0.604536	−	1.04709i
$900$	7.83286	+	5.90936i	0.261095	+	0.196979i
$901$	14.3634	+	24.8782i	0.478515	+	0.828813i
$902$		−	1.44992i		−	0.0482771i
$903$		0			0
$904$	9.26045			0.307998
$905$	−7.54512	+	22.5290i	−0.250808	+	0.748890i
$906$	0.126008	−	0.218252i	0.00418634	−	0.00725095i
$907$	−43.2988	−	24.9986i	−1.43771	−	0.830064i	−0.440023	−	0.897986i	$-0.645030\pi$
$907$	−43.2988	−	24.9986i	−1.43771	−	0.830064i	−0.997691	+	0.0679221i	$0.978363\pi$
$908$	22.3465	−	12.9018i	0.741594	−	0.428160i
$909$	17.6629			0.585842
$910$		0			0
$911$	−24.9525			−0.826715			−0.413357	−	0.910569i	$-0.635644\pi$
$911$	−24.9525			−0.826715			−0.413357	+	0.910569i	$0.635644\pi$
$912$	17.4948	−	10.1006i	0.579310	−	0.334465i
$913$	−5.58457	−	3.22425i	−0.184822	−	0.106707i
$914$	−1.81336	+	3.14083i	−0.0599805	+	0.103889i
$915$	−18.4479	−	6.17832i	−0.609868	−	0.204249i
$916$	−5.44709			−0.179977
$917$		0			0
$918$			0.649738i			0.0214446i
$919$	−5.84955	−	10.1317i	−0.192959	−	0.334215i	0.753271	−	0.657711i	$-0.228475\pi$
$919$	−5.84955	−	10.1317i	−0.192959	−	0.334215i	−0.946230	+	0.323496i	$0.895142\pi$
$920$	8.35622	−	1.69766i	0.275496	−	0.0559700i
$921$	12.0508	−	20.8726i	0.397087	−	0.687775i
$922$	1.16936	−	0.675131i	0.0385109	−	0.0222343i
$923$			2.70052i			0.0888888i
$924$		0			0
$925$	−3.84955	−	0.474855i	−0.126573	−	0.0156131i
$926$	−0.513881	−	0.890068i	−0.0168872	−	0.0292495i
$927$	5.80282	+	3.35026i	0.190590	+	0.110037i
$928$	−15.5734	−	8.99129i	−0.511221	−	0.295154i
$929$	11.8545	+	20.5326i	0.388933	+	0.673651i	0.992306	−	0.123807i	$-0.0395105\pi$
$929$	11.8545	+	20.5326i	0.388933	+	0.673651i	−0.603373	+	0.797459i	$0.706177\pi$
$930$	1.31406	+	1.48612i	0.0430899	+	0.0487318i
$931$		0			0
$932$		−	0.0996603i		−	0.00326448i
$933$	−7.14646	+	4.12601i	−0.233964	+	0.135079i
$934$	−1.27504	+	2.20843i	−0.0417205	+	0.0722621i
$935$	2.98298	+	14.6829i	0.0975540	+	0.480181i
$936$	0.518806	+	0.898598i	0.0169577	+	0.0293716i
$937$			19.9003i			0.650116i	0.945694	+	0.325058i	$0.105384\pi$
$937$			19.9003i			0.650116i	−0.945694	+	0.325058i	$0.894616\pi$
$938$		0			0
$939$	−14.9018			−0.486300
$940$	41.2959	+	13.8303i	1.34692	+	0.451094i
$941$	3.14411	−	5.44575i	0.102495	−	0.177526i	−0.810217	−	0.586130i	$-0.800651\pi$
$941$	3.14411	−	5.44575i	0.102495	−	0.177526i	0.912712	+	0.408604i	$0.133984\pi$
$942$	0.445034	+	0.256941i	0.0145000	+	0.00837158i
$943$	16.0648	−	9.27504i	0.523143	−	0.302037i
$944$	32.5669			1.05996
$945$		0			0
$946$	−4.89701			−0.159216
$947$	34.6724	−	20.0181i	1.12670	−	0.650501i	0.183597	−	0.983002i	$-0.441226\pi$
$947$	34.6724	−	20.0181i	1.12670	−	0.650501i	0.943103	+	0.332501i	$0.107892\pi$
$948$	−18.1853	−	10.4993i	−0.590631	−	0.341001i
$949$	−6.31265	+	10.9338i	−0.204917	+	0.354927i
$950$	2.02446	+	4.77677i	0.0656821	+	0.154979i
$951$	−10.1260			−0.328358
$952$		0			0
$953$			40.9478i			1.32643i	0.748429	+	0.663215i	$0.230808\pi$
$953$			40.9478i			1.32643i	−0.748429	+	0.663215i	$0.769192\pi$
$954$	0.831456	+	1.44012i	0.0269194	+	0.0466257i
$955$	−30.3486	+	6.16563i	−0.982057	+	0.199515i
$956$	5.73955	−	9.94119i	0.185630	−	0.321521i
$957$	13.7261	−	7.92478i	0.443702	−	0.256172i
$958$			0.998585i			0.0322628i
$959$		0			0
$960$	−11.9126	+	10.5334i	−0.384476	+	0.339964i
$961$	5.03690	+	8.72417i	0.162481	+	0.281425i
$962$	−0.175925	−	0.101570i	−0.00567206	−	0.00327476i
$963$	−11.8976	−	6.86907i	−0.383394	−	0.221353i
$964$	0.0738082	+	0.127839i	0.00237720	+	0.00411743i
$965$	25.6728	−	22.7005i	0.826435	−	0.730756i
$966$		0			0
$967$		−	38.2784i		−	1.23095i	−0.788157	−	0.615475i	$-0.788964\pi$
$967$		−	38.2784i		−	1.23095i	0.788157	−	0.615475i	$-0.211036\pi$
$968$	4.65849	−	2.68958i	0.149730	−	0.0864464i
$969$	8.96239	−	15.5233i	0.287913	−	0.498681i
$970$	7.86171	−	1.59719i	0.252424	−	0.0512827i
$971$	14.3634	+	24.8782i	0.460945	+	0.798379i	0.999008	−	0.0445247i	$-0.0141774\pi$
$971$	14.3634	+	24.8782i	0.460945	+	0.798379i	−0.538064	+	0.842904i	$0.680844\pi$
$972$		−	1.96239i		−	0.0629436i
$973$		0			0
$974$	4.30089			0.137809
$975$	6.21609	−	2.63446i	0.199074	−	0.0843704i
$976$	16.4255	−	28.4498i	0.525767	−	0.910655i
$977$	−35.7681	−	20.6507i	−1.14432	−	0.660674i	−0.196824	−	0.980439i	$-0.563063\pi$
$977$	−35.7681	−	20.6507i	−1.14432	−	0.660674i	−0.947497	+	0.319765i	$0.896396\pi$
$978$	−0.890068	+	0.513881i	−0.0284612	+	0.0164321i
$979$	−2.07522			−0.0663244
$980$		0			0
$981$	−2.77575			−0.0886228
$982$	−0.335908	+	0.193937i	−0.0107193	+	0.00618876i
$983$	20.7846	+	12.0000i	0.662926	+	0.382741i	0.793391	−	0.608712i	$-0.208314\pi$
$983$	20.7846	+	12.0000i	0.662926	+	0.382741i	−0.130465	+	0.991453i	$0.541647\pi$
$984$	1.43629	−	2.48772i	0.0457872	−	0.0793058i
$985$	−1.21816	−	0.407968i	−0.0388136	−	0.0129990i
$986$	−5.14903			−0.163979
$987$		0			0
$988$		−	14.1768i		−	0.451024i
$989$	−31.3258	−	54.2579i	−0.996103	−	1.72530i
$990$	0.172676	+	0.849948i	0.00548800	+	0.0270131i
$991$	−12.5501	+	21.7374i	−0.398666	+	0.690510i	−0.993562	−	0.113293i	$-0.963860\pi$
$991$	−12.5501	+	21.7374i	−0.398666	+	0.690510i	0.594895	+	0.803803i	$0.297194\pi$
$992$	−8.98961	+	5.19015i	−0.285420	+	0.164787i
$993$		−	27.8496i		−	0.883779i
$994$		0			0
$995$	−0.298062	−	0.337088i	−0.00944920	−	0.0106864i
$996$	−3.16362	−	5.47955i	−0.100243	−	0.173626i
$997$	28.4033	+	16.3987i	0.899543	+	0.519351i	0.877052	−	0.480396i	$-0.159507\pi$
$997$	28.4033	+	16.3987i	0.899543	+	0.519351i	0.0224910	+	0.999747i	$0.492840\pi$
$998$	1.10011	+	0.635150i	0.0348234	+	0.0201053i
$999$	0.387873	+	0.671816i	0.0122718	+	0.0212553i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.q.e.214.3		12
5.4	even	2	inner	735.2.q.e.214.4		12
7.2	even	3	inner	735.2.q.e.79.4		12
7.3	odd	6		735.2.d.b.589.3		6
7.4	even	3		105.2.d.b.64.3	✓	6
7.5	odd	6		735.2.q.f.79.4		12
7.6	odd	2		735.2.q.f.214.3		12
21.11	odd	6		315.2.d.e.64.4		6
21.17	even	6		2205.2.d.l.1324.4		6
28.11	odd	6		1680.2.t.k.1009.4		6
35.3	even	12		3675.2.a.bi.1.2		3
35.4	even	6		105.2.d.b.64.4	yes	6
35.9	even	6	inner	735.2.q.e.79.3		12
35.17	even	12		3675.2.a.bj.1.2		3
35.18	odd	12		525.2.a.j.1.2		3
35.19	odd	6		735.2.q.f.79.3		12
35.24	odd	6		735.2.d.b.589.4		6
35.32	odd	12		525.2.a.k.1.2		3
35.34	odd	2		735.2.q.f.214.4		12
84.11	even	6		5040.2.t.v.1009.6		6
105.32	even	12		1575.2.a.w.1.2		3
105.53	even	12		1575.2.a.x.1.2		3
105.59	even	6		2205.2.d.l.1324.3		6
105.74	odd	6		315.2.d.e.64.3		6
140.39	odd	6		1680.2.t.k.1009.1		6
140.67	even	12		8400.2.a.dj.1.3		3
140.123	even	12		8400.2.a.dg.1.1		3
420.179	even	6		5040.2.t.v.1009.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.d.b.64.3	✓	6	7.4	even	3
105.2.d.b.64.4	yes	6	35.4	even	6
315.2.d.e.64.3		6	105.74	odd	6
315.2.d.e.64.4		6	21.11	odd	6
525.2.a.j.1.2		3	35.18	odd	12
525.2.a.k.1.2		3	35.32	odd	12
735.2.d.b.589.3		6	7.3	odd	6
735.2.d.b.589.4		6	35.24	odd	6
735.2.q.e.79.3		12	35.9	even	6	inner
735.2.q.e.79.4		12	7.2	even	3	inner
735.2.q.e.214.3		12	1.1	even	1	trivial
735.2.q.e.214.4		12	5.4	even	2	inner
735.2.q.f.79.3		12	35.19	odd	6
735.2.q.f.79.4		12	7.5	odd	6
735.2.q.f.214.3		12	7.6	odd	2
735.2.q.f.214.4		12	35.34	odd	2
1575.2.a.w.1.2		3	105.32	even	12
1575.2.a.x.1.2		3	105.53	even	12
1680.2.t.k.1009.1		6	140.39	odd	6
1680.2.t.k.1009.4		6	28.11	odd	6
2205.2.d.l.1324.3		6	105.59	even	6
2205.2.d.l.1324.4		6	21.17	even	6
3675.2.a.bi.1.2		3	35.3	even	12
3675.2.a.bj.1.2		3	35.17	even	12
5040.2.t.v.1009.5		6	420.179	even	6
5040.2.t.v.1009.6		6	84.11	even	6
8400.2.a.dg.1.1		3	140.123	even	12
8400.2.a.dj.1.3		3	140.67	even	12

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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.167954 + 0.0969683i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.981194 + 1.69948i) q^{4} +(-0.710109 + 2.12032i) q^{5} -0.193937 q^{6} -0.768452i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.167954 + 0.0969683i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.981194 + 1.69948i) q^{4} +(-0.710109 + 2.12032i) q^{5} -0.193937 q^{6} -0.768452i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.0863379 - 0.424974i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(-1.69948 + 0.981194i) q^{12} +1.35026i q^{13} +(-1.67513 + 1.48119i) q^{15} +(-1.88787 - 3.26989i) q^{16} +(-2.90141 - 1.67513i) q^{17} +(-0.167954 - 0.0969683i) q^{18} +(2.67513 + 4.63346i) q^{19} +(-2.90668 - 3.28726i) q^{20} -0.387873i q^{22} +(4.29755 - 2.48119i) q^{23} +(0.384226 - 0.665499i) q^{24} +(-3.99149 - 3.01131i) q^{25} +(-0.130933 - 0.226782i) q^{26} +1.00000i q^{27} -7.92478 q^{29} +(0.137716 - 0.411207i) q^{30} +(-2.28726 + 3.96165i) q^{31} +(1.96515 + 1.13458i) q^{32} +(-1.73205 + 1.00000i) q^{33} +0.649738 q^{34} -1.96239 q^{36} +(0.671816 - 0.387873i) q^{37} +(-0.898598 - 0.518806i) q^{38} +(-0.675131 + 1.16936i) q^{39} +(1.62936 + 0.545685i) q^{40} +3.73813 q^{41} -12.6253i q^{43} +(-1.96239 - 3.39896i) q^{44} +(-2.19130 + 0.445186i) q^{45} +(-0.481194 + 0.833453i) q^{46} +(-8.59511 + 4.96239i) q^{47} -3.77575i q^{48} +(0.962389 + 0.118714i) q^{50} +(-1.67513 - 2.90141i) q^{51} +(-2.29474 - 1.32487i) q^{52} +(-7.42575 - 4.28726i) q^{53} +(-0.0969683 - 0.167954i) q^{54} +(-2.96239 - 3.35026i) q^{55} +5.35026i q^{57} +(1.33100 - 0.768452i) q^{58} +(-4.31265 + 7.46973i) q^{59} +(-0.873629 - 4.30019i) q^{60} +(4.35026 + 7.53487i) q^{61} -0.887166i q^{62} +7.11142 q^{64} +(-2.86298 - 0.958833i) q^{65} +(0.193937 - 0.335908i) q^{66} +(8.59511 + 4.96239i) q^{67} +(5.69370 - 3.28726i) q^{68} +4.96239 q^{69} +2.00000 q^{71} +(0.665499 - 0.384226i) q^{72} +(8.09756 + 4.67513i) q^{73} +(-0.0752228 + 0.130290i) q^{74} +(-1.95108 - 4.60362i) q^{75} -10.4993 q^{76} -0.261865i q^{78} +(5.35026 + 9.26693i) q^{79} +(8.27380 - 1.68091i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.627835 + 0.362481i) q^{82} +3.22425i q^{83} +(5.61213 - 4.96239i) q^{85} +(1.22425 + 2.12047i) q^{86} +(-6.86306 - 3.96239i) q^{87} +(1.33100 + 0.768452i) q^{88} +(0.518806 + 0.898598i) q^{89} +(0.324869 - 0.287258i) q^{90} +9.73813i q^{92} +(-3.96165 + 2.28726i) q^{93} +(0.962389 - 1.66691i) q^{94} +(-11.7240 + 2.38186i) q^{95} +(1.13458 + 1.96515i) q^{96} +18.4993i q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 10 q^{4} - 2 q^{5} - 4 q^{6} + 6 q^{9}+O(q^{10}) \) 12 * q + 10 * q^4 - 2 * q^5 - 4 * q^6 + 6 * q^9	\( 12 q + 10 q^{4} - 2 q^{5} - 4 q^{6} + 6 q^{9} + 12 q^{10} - 12 q^{11} - 26 q^{16} + 12 q^{19} - 60 q^{20} - 18 q^{24} + 2 q^{25} - 20 q^{26} - 8 q^{29} + 10 q^{30} - 4 q^{31} + 48 q^{34} + 20 q^{36} + 12 q^{39} - 4 q^{40} + 8 q^{41} + 20 q^{44} + 2 q^{45} + 16 q^{46} - 32 q^{50} - 2 q^{54} + 8 q^{55} + 32 q^{59} + 8 q^{60} + 12 q^{61} - 52 q^{64} - 32 q^{65} + 4 q^{66} + 16 q^{69} + 24 q^{71} - 88 q^{74} - 8 q^{75} + 8 q^{76} + 24 q^{79} - 46 q^{80} - 6 q^{81} + 64 q^{85} + 8 q^{86} + 28 q^{89} + 24 q^{90} - 32 q^{94} - 4 q^{95} + 58 q^{96} - 24 q^{99}+O(q^{100}) \) 12 * q + 10 * q^4 - 2 * q^5 - 4 * q^6 + 6 * q^9 + 12 * q^10 - 12 * q^11 - 26 * q^16 + 12 * q^19 - 60 * q^20 - 18 * q^24 + 2 * q^25 - 20 * q^26 - 8 * q^29 + 10 * q^30 - 4 * q^31 + 48 * q^34 + 20 * q^36 + 12 * q^39 - 4 * q^40 + 8 * q^41 + 20 * q^44 + 2 * q^45 + 16 * q^46 - 32 * q^50 - 2 * q^54 + 8 * q^55 + 32 * q^59 + 8 * q^60 + 12 * q^61 - 52 * q^64 - 32 * q^65 + 4 * q^66 + 16 * q^69 + 24 * q^71 - 88 * q^74 - 8 * q^75 + 8 * q^76 + 24 * q^79 - 46 * q^80 - 6 * q^81 + 64 * q^85 + 8 * q^86 + 28 * q^89 + 24 * q^90 - 32 * q^94 - 4 * q^95 + 58 * q^96 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more