LMFDB - Embedded newform 735.2.q.f.214.4

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			214.4
Root			$0.550552 + 0.147520i$ of defining polynomial
Character	$\chi$	$=$	735.214
Dual form			735.2.q.f.79.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.167954 - 0.0969683i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.981194 + 1.69948i) q^{4} +(-2.19130 - 0.445186i) q^{5} +0.193937 q^{6} +0.768452i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.167954 - 0.0969683i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.981194 + 1.69948i) q^{4} +(-2.19130 - 0.445186i) q^{5} +0.193937 q^{6} +0.768452i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.411207 + 0.137716i) 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} +(4.60362 + 1.95108i) q^{25} +(0.130933 + 0.226782i) q^{26} +1.00000i q^{27} -7.92478 q^{29} +(-0.424974 - 0.0863379i) 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} +(0.342104 - 1.68391i) q^{40} -3.73813 q^{41} +12.6253i q^{43} +(-1.96239 - 3.39896i) q^{44} +(-0.710109 - 2.12032i) 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} +(4.16089 - 1.39351i) q^{60} +(-4.35026 - 7.53487i) q^{61} -0.887166i q^{62} +7.11142 q^{64} +(0.601118 - 2.95883i) 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} +(3.01131 + 3.99149i) q^{75} +10.4993 q^{76} +0.261865i q^{78} +(5.35026 + 9.26693i) q^{79} +(2.68119 + 8.00578i) 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} +(3.79927 + 11.3443i) 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	−0.439443	−	0.898271i	$-0.644824\pi$
$2$	0.167954	−	0.0969683i	0.118761	−	0.0685669i	0.558204	+	0.829704i	$0.311491\pi$
$3$	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
$5$	−2.19130	−	0.445186i	−0.979981	−	0.199093i
$5$	−2.19130	−	0.445186i	−0.979981	−	0.199093i
$6$	0.193937			0.0791743
$7$		0			0
$7$		0			0
$8$			0.768452i			0.271689i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−0.411207	+	0.137716i	−0.130035	+	0.0435496i
$11$	−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	$-0.956340\pi$
$19$	−2.67513	−	4.63346i	−0.613717	−	1.06299i	0.376891	−	0.926258i	$-0.376993\pi$
$20$	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	−0.875934	−	0.482432i	$-0.839754\pi$
$23$	−4.29755	+	2.48119i	−0.896102	+	0.517365i	−0.0201686	+	0.999797i	$0.506420\pi$
$24$	−0.384226	+	0.665499i	−0.0784298	+	0.135844i
$25$	4.60362	+	1.95108i	0.920724	+	0.390215i
$26$	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	$0.763192\pi$
$30$	−0.424974	−	0.0863379i	−0.0775892	−	0.0157631i
$31$	2.28726	−	3.96165i	0.410804	−	0.711533i	−0.584174	−	0.811628i	$-0.698582\pi$
$31$	2.28726	−	3.96165i	0.410804	−	0.711533i	0.994978	+	0.100096i	$0.0319149\pi$
$32$	−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	−0.554205	−	0.832380i	$-0.686978\pi$
$37$	−0.671816	+	0.387873i	−0.110446	+	0.0637660i	0.443760	+	0.896146i	$0.353644\pi$
$38$	−0.898598	−	0.518806i	−0.145772	−	0.0841614i
$39$	−0.675131	+	1.16936i	−0.108107	+	0.187248i
$40$	0.342104	−	1.68391i	0.0540915	−	0.266250i
$41$	−3.73813			−0.583799			−0.291899	−	0.956449i	$-0.594287\pi$
$41$	−3.73813			−0.583799			−0.291899	+	0.956449i	$0.594287\pi$
$42$		0			0
$43$			12.6253i			1.92534i	0.270677	+	0.962670i	$0.412752\pi$
$43$			12.6253i			1.92534i	−0.270677	+	0.962670i	$0.587248\pi$
$44$	−1.96239	−	3.39896i	−0.295841	−	0.512412i
$45$	−0.710109	−	2.12032i	−0.105857	−	0.316078i
$46$	−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	0.914105	−	0.405477i	$-0.132894\pi$
$53$	7.42575	+	4.28726i	1.02000	+	0.588900i	0.105900	+	0.994377i	$0.466228\pi$
$54$	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	$-0.643573\pi$
$59$	4.31265	−	7.46973i	0.561459	−	0.972476i	0.997369	−	0.0724858i	$-0.0230932\pi$
$60$	4.16089	−	1.39351i	0.537168	−	0.179901i
$61$	−4.35026	−	7.53487i	−0.556994	−	0.964742i	−0.997745	−	0.0671126i	$-0.978621\pi$
$61$	−4.35026	−	7.53487i	−0.556994	−	0.964742i	0.440751	−	0.897629i	$-0.354712\pi$
$62$		−	0.887166i		−	0.112670i
$63$		0			0
$64$	7.11142			0.888927
$65$	0.601118	−	2.95883i	0.0745595	−	0.366998i
$66$	−0.193937	+	0.335908i	−0.0238719	+	0.0413474i
$67$	−8.59511	−	4.96239i	−1.05006	−	0.606252i	−0.127394	−	0.991852i	$-0.540661\pi$
$67$	−8.59511	−	4.96239i	−1.05006	−	0.606252i	−0.922666	+	0.385600i	$0.873994\pi$
$68$	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
$75$	3.01131	+	3.99149i	0.347716	+	0.460898i
$76$	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	$0.627723\pi$
$80$	2.68119	+	8.00578i	0.299766	+	0.895073i
$81$	−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	0.837218	−	0.546869i	$-0.184180\pi$
$89$	−0.518806	−	0.898598i	−0.0549933	−	0.0952512i	−0.892212	+	0.451618i	$0.850847\pi$
$90$	−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
$95$	3.79927	+	11.3443i	0.389797	+	1.16390i
$96$	−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
$100$	−7.83286	+	5.90936i	−0.783286	+	0.590936i
$101$	−8.83146	+	15.2965i	−0.878763	+	1.52206i	−0.0260630	+	0.999660i	$0.508297\pi$
$101$	−8.83146	+	15.2965i	−0.878763	+	1.52206i	−0.852700	+	0.522401i	$0.825036\pi$
$102$	−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	0.201250	−	0.979540i	$-0.435500\pi$
$107$	11.8976	−	6.86907i	1.15018	−	0.664058i	0.948932	+	0.315482i	$0.102166\pi$
$108$	−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	$0.209107\pi$
$110$	0.172676	−	0.849948i	0.0164640	−	0.0810393i
$111$	−0.775746			−0.0736306
$112$		0			0
$113$		−	12.0508i		−	1.13364i	−0.823841	−	0.566821i	$-0.808173\pi$
$113$		−	12.0508i		−	1.13364i	0.823841	−	0.566821i	$-0.191827\pi$
$114$	−0.518806	−	0.898598i	−0.0485906	−	0.0841614i
$115$	10.5218	−	3.52384i	0.981167	−	0.328599i
$116$	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	$0.0382306\pi$
$127$			2.70052i			0.239633i	−0.992796	+	0.119816i	$0.961769\pi$
$128$	5.12469	−	2.95874i	0.452963	−	0.261518i
$129$	−6.31265	+	10.9338i	−0.555798	+	0.962670i
$130$	−0.185953	−	0.555237i	−0.0163091	−	0.0486975i
$131$	10.3127	+	17.8620i	0.901020	+	1.56061i	0.826172	+	0.563418i	$0.190514\pi$
$131$	10.3127	+	17.8620i	0.901020	+	1.56061i	0.0748486	+	0.997195i	$0.476153\pi$
$132$		−	3.92478i		−	0.341608i
$133$		0			0
$134$	−1.92478			−0.166275
$135$	0.445186	−	2.19130i	0.0383155	−	0.188597i
$136$	1.28726	−	2.22960i	0.110381	−	0.191186i
$137$	−19.4850	−	11.2496i	−1.66471	−	0.961122i	−0.970418	−	0.241431i	$-0.922383\pi$
$137$	−19.4850	−	11.2496i	−1.66471	−	0.961122i	−0.694294	−	0.719691i	$-0.744283\pi$
$138$	−0.833453	+	0.481194i	−0.0709482	+	0.0409620i
$139$	−3.27504			−0.277785			−0.138893	−	0.990307i	$-0.544354\pi$
$139$	−3.27504			−0.277785			−0.138893	+	0.990307i	$0.544354\pi$
$140$		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
$145$	17.3656	+	3.52800i	1.44213	+	0.292985i
$146$	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	$0.891661\pi$
$150$	0.892810	+	0.378385i	0.0728976	+	0.0308950i
$151$	−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	−0.668851	−	0.743397i	$-0.733214\pi$
$163$	−4.58948	+	2.64974i	−0.359476	+	0.207544i	0.309375	+	0.950940i	$0.399880\pi$
$164$	3.66784	−	6.35288i	0.286410	−	0.496077i
$165$	4.24063	−	1.42022i	0.330133	−	0.110564i
$166$	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
$170$	1.42377	+	0.289255i	0.109198	+	0.0221848i
$171$	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	$0.0447496\pi$
$180$	4.30019	+	0.873629i	0.320517	+	0.0651164i
$181$	−10.6253			−0.789772			−0.394886	−	0.918730i	$-0.629216\pi$
$181$	−10.6253			−0.789772			−0.394886	+	0.918730i	$0.629216\pi$
$182$		0			0
$183$		−	8.70052i		−	0.643161i
$184$	−1.90668	−	3.30246i	−0.140562	−	0.243461i
$185$	1.64483	−	0.550864i	0.120930	−	0.0405003i
$186$	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	0.894748	−	0.446572i	$-0.147355\pi$
$193$	13.2726	+	7.66291i	0.955379	+	0.551588i	0.0606314	+	0.998160i	$0.480689\pi$
$194$	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	$-0.993485\pi$
$197$		−	0.574515i		−	0.0409325i	0.999791	−	0.0204663i	$-0.00651507\pi$
$198$	−0.335908	+	0.193937i	−0.0238719	+	0.0137825i
$199$	0.100615	−	0.174271i	0.00713244	−	0.0123537i	−0.862437	−	0.506164i	$-0.831063\pi$
$199$	0.100615	−	0.174271i	0.00713244	−	0.0123537i	0.869570	+	0.493810i	$0.164396\pi$
$200$	−1.49931	+	3.53766i	−0.106017	+	0.250150i
$201$	−4.96239	−	8.59511i	−0.350020	−	0.606252i
$202$			3.42548i			0.241016i
$203$		0			0
$204$	6.57452			0.460308
$205$	8.19139	+	1.66417i	0.572111	+	0.116230i
$206$	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
$215$	5.62061	−	27.6659i	0.383323	−	1.88680i
$216$	−0.768452			−0.0522865
$217$		0			0
$218$			0.538319i			0.0364595i
$219$	4.67513	+	8.09756i	0.315916	+	0.547183i
$220$	2.78702	+	8.32177i	0.187901	+	0.561054i
$221$	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	0.816519	−	0.577319i	$-0.195901\pi$
$229$	−1.38787	−	2.40387i	−0.0917132	−	0.158852i	−0.908232	+	0.418467i	$0.862568\pi$
$230$	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	−0.498559	−	0.866856i	$-0.666137\pi$
$233$	0.0439813	−	0.0253926i	0.00288131	−	0.00166353i	0.501440	+	0.865192i	$0.332804\pi$
$234$	−0.130933	+	0.226782i	−0.00855933	+	0.0148252i
$235$	21.0437	−	7.04767i	1.37274	−	0.459739i
$236$	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	$0.560586\pi$
$240$	−1.68091	+	8.27380i	−0.108502	+	0.534072i
$241$	−0.0376114	+	0.0651448i	−0.00242276	+	0.00419635i	−0.867234	−	0.497900i	$-0.834105\pi$
$241$	−0.0376114	+	0.0651448i	−0.00242276	+	0.00419635i	0.864811	+	0.502097i	$0.167438\pi$
$242$	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
$250$	−2.16173	−	0.168305i	−0.136720	−	0.0106445i
$251$	−19.2243			−1.21342			−0.606712	−	0.794922i	$-0.707512\pi$
$251$	−19.2243			−1.21342			−0.606712	+	0.794922i	$0.707512\pi$
$252$		0			0
$253$		−	9.92478i		−	0.623965i
$254$	0.261865	+	0.453564i	0.0164309	+	0.0284591i
$255$	2.37905	+	7.10362i	0.148982	+	0.444846i
$256$	−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	0.112229	−	0.993682i	$-0.464201\pi$
$263$	−11.2258	−	6.48119i	−0.692210	−	0.399648i	−0.804439	+	0.594035i	$0.797534\pi$
$264$	−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	−0.921865	−	0.387510i	$-0.873335\pi$
$269$	−2.05571	+	3.56059i	−0.125339	+	0.217093i	0.796527	+	0.604604i	$0.206668\pi$
$270$	−0.137716	−	0.411207i	−0.00838113	−	0.0250253i
$271$	−8.21203	−	14.2237i	−0.498846	−	0.864026i	0.501154	−	0.865358i	$-0.332909\pi$
$271$	−8.21203	−	14.2237i	−0.498846	−	0.864026i	−0.999999	+	0.00133248i	$0.999576\pi$
$272$			12.6497i			0.767003i
$273$		0			0
$274$	−4.36344			−0.263605
$275$	−7.98298	+	6.02262i	−0.481392	+	0.363178i
$276$	4.86907	−	8.43347i	0.293083	−	0.507635i
$277$	9.59020	+	5.53690i	0.576219	+	0.332680i	0.759629	−	0.650356i	$-0.225380\pi$
$277$	9.59020	+	5.53690i	0.576219	+	0.332680i	−0.183410	+	0.983036i	$0.558714\pi$
$278$	−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
$285$	−2.38186	+	11.7240i	−0.141089	+	0.694472i
$286$	−0.523730			−0.0309688
$287$		0			0
$288$		−	2.26916i		−	0.133711i
$289$	−2.88787	−	5.00194i	−0.169875	−	0.294232i
$290$	3.25872	−	1.09137i	0.191359	−	0.0640874i
$291$	−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
$305$	6.17832	+	18.4479i	0.353769	+	1.05632i
$306$	−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
$310$	−0.394954	+	1.94405i	−0.0224319	+	0.110415i
$311$	4.12601	−	7.14646i	0.233964	−	0.405238i	−0.725007	−	0.688742i	$-0.758163\pi$
$311$	4.12601	−	7.14646i	0.233964	−	0.405238i	0.958971	+	0.283503i	$0.0914967\pi$
$312$	−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	−0.233089	−	0.972455i	$-0.574883\pi$
$317$	8.76938	−	5.06300i	0.492537	−	0.284367i	0.725627	+	0.688089i	$0.241550\pi$
$318$	1.44012	+	0.831456i	0.0807582	+	0.0466257i
$319$	7.92478	−	13.7261i	0.443702	−	0.768515i
$320$	−15.5833	−	3.16591i	−0.871132	−	0.176980i
$321$	13.7381			0.766788
$322$		0			0
$323$			17.9248i			0.997361i
$324$	−0.981194	−	1.69948i	−0.0545108	−	0.0944155i
$325$	−2.63446	+	6.21609i	−0.146134	+	0.344807i
$326$	−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	$-0.966564\pi$
$337$		−	3.84955i		−	0.209699i	0.994488	−	0.104849i	$-0.0334360\pi$
$338$	1.87719	−	1.08379i	0.102106	−	0.0589506i
$339$	6.02539	−	10.4363i	0.327254	−	0.566821i
$340$	−13.9401	+	4.66862i	−0.756006	+	0.253192i
$341$	4.57452	+	7.92329i	0.247724	+	0.429070i
$342$		−	1.03761i		−	0.0561076i
$343$		0			0
$344$	−9.70194			−0.523093
$345$	10.8741	+	2.20919i	0.585442	+	0.118939i
$346$	−0.436289	+	0.755674i	−0.0234550	+	0.0406253i
$347$	−8.30318	−	4.79384i	−0.445738	−	0.257347i	0.260290	−	0.965530i	$-0.416182\pi$
$347$	−8.30318	−	4.79384i	−0.445738	−	0.257347i	−0.706029	+	0.708183i	$0.749515\pi$
$348$	13.4680	−	7.77575i	0.721960	−	0.416824i
$349$	−15.1490			−0.810909			−0.405455	−	0.914115i	$-0.632887\pi$
$349$	−15.1490			−0.810909			−0.405455	+	0.914115i	$0.632887\pi$
$350$		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
$355$	−4.38261	−	0.890373i	−0.232605	−	0.0472561i
$356$	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	$-0.477553\pi$
$360$	1.62936	−	0.545685i	0.0858749	−	0.0287601i
$361$	−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	−0.813816	−	0.581122i	$-0.802614\pi$
$373$	−13.8564	+	8.00000i	−0.717458	+	0.414224i	0.0963587	+	0.995347i	$0.469280\pi$
$374$	0.649738	−	1.12538i	0.0335972	−	0.0581920i
$375$	−4.82174	−	10.0872i	−0.248994	−	0.520899i
$376$	−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	$0.588620\pi$
$380$	−23.0071	−	4.67414i	−1.18024	−	0.239778i
$381$	−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	$0.899860\pi$
$390$	0.116579	−	0.573826i	0.00590320	−	0.0290568i
$391$	16.6253			0.840778
$392$		0			0
$393$			20.6253i			1.04041i
$394$	−0.0557098	−	0.0964922i	−0.00280662	−	0.00486121i
$395$	−7.59854	−	22.6885i	−0.382324	−	1.14158i
$396$	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	$-0.646761\pi$
$409$	11.1866	−	19.3758i	0.553144	−	0.958073i	0.998045	−	0.0624938i	$-0.0199054\pi$
$410$	1.53715	−	0.514801i	0.0759143	−	0.0254242i
$411$	−11.2496	−	19.4850i	−0.554904	−	0.961122i
$412$			13.1490i			0.647806i
$413$		0			0
$414$	−0.962389			−0.0472988
$415$	1.43539	−	7.06532i	0.0704607	−	0.346823i
$416$	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	$-0.305606\pi$
$419$	23.4763			1.14689			0.573445	+	0.819244i	$0.305606\pi$
$420$		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
$425$	−10.0887	−	13.3725i	−0.489373	−	0.648663i
$426$	0.387873			0.0187925
$427$		0			0
$428$			26.9596i			1.30314i
$429$	−1.35026	−	2.33872i	−0.0651913	−	0.112915i
$430$	−1.73871	−	5.19161i	−0.0838479	−	0.250362i
$431$	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	0.986178	−	0.165690i	$-0.0529852\pi$
$439$	7.32487	+	12.6870i	0.349597	+	0.605520i	−0.636581	+	0.771210i	$0.719652\pi$
$440$	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	−0.839083	−	0.544004i	$-0.816908\pi$
$443$	−16.5750	+	9.56959i	−0.787503	+	0.454665i	0.0515798	+	0.998669i	$0.483574\pi$
$444$	0.761158	−	1.31836i	0.0361230	−	0.0625668i
$445$	0.736817	+	2.20007i	0.0349285	+	0.104293i
$446$	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	$0.218246\pi$
$450$	0.584003	+	0.774096i	0.0275302	+	0.0364912i
$451$	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	−0.828425	−	0.560100i	$-0.810763\pi$
$457$	−16.1951	+	9.35026i	−0.757576	+	0.437387i	0.0708487	+	0.997487i	$0.477429\pi$
$458$	−0.466198	−	0.269159i	−0.0217840	−	0.0125770i
$459$	1.67513	−	2.90141i	0.0781884	−	0.135426i
$460$	−4.33529	+	21.3392i	−0.202134	+	0.994946i
$461$	6.96239			0.324271			0.162135	−	0.986769i	$-0.448162\pi$
$461$	6.96239			0.324271			0.162135	+	0.986769i	$0.448162\pi$
$462$		0			0
$463$		−	5.29948i		−	0.246288i	−0.992389	−	0.123144i	$-0.960702\pi$
$463$		−	5.29948i		−	0.246288i	0.992389	−	0.123144i	$-0.0392976\pi$
$464$	14.9610	+	25.9132i	0.694546	+	1.20299i
$465$	−9.69942	+	3.24840i	−0.449800	+	0.150641i
$466$	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	−0.918829	−	0.394656i	$-0.870864\pi$
$479$	−2.57452	+	4.45919i	−0.117633	+	0.203746i	0.801196	+	0.598401i	$0.204197\pi$
$480$	1.61135	+	4.81134i	0.0735477	+	0.219607i
$481$	−0.523730	−	0.907127i	−0.0238800	−	0.0413614i
$482$			0.0145884i			0.000664486i
$483$		0			0
$484$	−13.7367			−0.624396
$485$	8.23563	−	40.5376i	0.373961	−	1.84072i
$486$	−0.0969683	+	0.167954i	−0.00439857	+	0.00761855i
$487$	19.2057	+	11.0884i	0.870292	+	0.502463i	0.867445	−	0.497533i	$-0.165761\pi$
$487$	19.2057	+	11.0884i	0.870292	+	0.502463i	0.00284661	+	0.999996i	$0.499094\pi$
$488$	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
$495$	4.38261	+	0.890373i	0.196983	+	0.0400193i
$496$	−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	$0.880170\pi$
$500$	19.7949	−	9.46213i	0.885256	−	0.423159i
$501$	−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	0.682900	−	0.730512i	$-0.260719\pi$
$509$	−6.56959	−	11.3789i	−0.291192	−	0.504359i	−0.974092	+	0.226153i	$0.927385\pi$
$510$	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
$515$	−14.2072	+	4.75810i	−0.626046	+	0.209667i
$516$	−12.3879	−	21.4564i	−0.545346	−	0.944566i
$517$		−	19.8496i		−	0.872982i
$518$		0			0
$519$	−4.49929			−0.197497
$520$	2.27372	+	0.461931i	0.0997093	+	0.0202570i
$521$	−18.8315	+	32.6170i	−0.825021	+	1.42898i	0.0768821	+	0.997040i	$0.475503\pi$
$521$	−18.8315	+	32.6170i	−0.825021	+	1.42898i	−0.901903	+	0.431938i	$0.857830\pi$
$522$	−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
$530$	−3.64394	−	0.740306i	−0.158283	−	0.0321568i
$531$	8.62530			0.374306
$532$		0			0
$533$		−	5.04746i		−	0.218630i
$534$	−0.100615	−	0.174271i	−0.00435405	−	0.00754144i
$535$	−29.1292	+	9.75557i	−1.25937	+	0.421770i
$536$	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	$-0.813012\pi$
$547$		−	25.9248i		−	1.10846i	0.832362	−	0.554232i	$-0.186988\pi$
$548$	38.2371	−	22.0762i	1.63341	−	0.943048i
$549$	4.35026	−	7.53487i	0.185665	−	0.321581i
$550$	−0.756770	+	1.78562i	−0.0322688	+	0.0761391i
$551$	21.1998	+	36.7192i	0.903143	+	1.56429i
$552$		−	3.81336i		−	0.162307i
$553$		0			0
$554$	2.14762			0.0912435
$555$	1.69990	+	0.345352i	0.0721565	+	0.0146594i
$556$	3.21345	−	5.56586i	0.136281	−	0.236045i
$557$	24.7039	+	14.2628i	1.04674	+	0.604335i	0.921735	−	0.387821i	$-0.126772\pi$
$557$	24.7039	+	14.2628i	1.04674	+	0.604335i	0.125004	+	0.992156i	$0.460105\pi$
$558$	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
$565$	−5.36485	+	26.4069i	−0.225701	+	1.11095i
$566$	−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	$0.770707\pi$
$570$	0.736817	+	2.20007i	0.0308619	+	0.0921506i
$571$	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
$585$	2.86298	−	0.958833i	0.118370	−	0.0396429i
$586$	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
$590$	−0.744691	+	3.66553i	−0.0306584	+	0.150907i
$591$	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	$0.302773\pi$
$600$	−3.06727	+	2.31405i	−0.125221	+	0.0944706i
$601$	13.8496			0.564935			0.282468	−	0.959277i	$-0.408847\pi$
$601$	13.8496			0.564935			0.282468	+	0.959277i	$0.408847\pi$
$602$		0			0
$603$		−	9.92478i		−	0.404168i
$604$	−1.27504	−	2.20843i	−0.0518806	−	0.0898598i
$605$	−4.97076	−	14.8422i	−0.202090	−	0.603422i
$606$	−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	0.331382	−	0.943497i	$-0.392485\pi$
$613$	−7.92329	−	4.57452i	−0.320019	−	0.184763i	−0.651401	+	0.758734i	$0.725818\pi$
$614$	−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	$0.104034\pi$
$617$			15.9492i			0.642091i	−0.947064	+	0.321046i	$0.895966\pi$
$618$	1.12538	−	0.649738i	0.0452694	−	0.0261363i
$619$	−5.58673	+	9.67651i	−0.224550	+	0.388932i	−0.956184	−	0.292765i	$-0.905424\pi$
$619$	−5.58673	+	9.67651i	−0.224550	+	0.388932i	0.731634	+	0.681697i	$0.238758\pi$
$620$	−6.37463	−	19.0340i	−0.256011	−	0.764425i
$621$	−2.48119	−	4.29755i	−0.0995669	−	0.172455i
$622$		−	1.60037i		−	0.0641689i
$623$		0			0
$624$	5.09825			0.204093
$625$	17.3866	+	17.9640i	0.695464	+	0.718561i
$626$	−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
$635$	1.20224	−	5.91767i	0.0477093	−	0.234835i
$636$	−16.8265			−0.667215
$637$		0			0
$638$		−	3.07381i		−	0.121693i
$639$	1.00000	+	1.73205i	0.0395594	+	0.0685189i
$640$	−12.5469	+	4.20206i	−0.495961	+	0.166101i
$641$	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	$0.766209\pi$
$653$	−43.2801	+	24.9878i	−1.69368	+	0.977847i	−0.951500	+	0.307648i	$0.900458\pi$
$654$	−0.269159	+	0.466198i	−0.0105250	+	0.0182298i
$655$	−14.6462	−	43.7322i	−0.572275	−	1.70876i
$656$	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	$0.392888\pi$
$660$	−1.74726	+	8.60038i	−0.0680119	+	0.334769i
$661$	−7.82653	+	13.5560i	−0.304417	+	0.527265i	−0.977131	−	0.212637i	$-0.931795\pi$
$661$	−7.82653	+	13.5560i	−0.304417	+	0.527265i	0.672715	+	0.739902i	$0.265128\pi$
$662$	−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
$670$	4.21777	+	0.856885i	0.162947	+	0.0331043i
$671$	17.4010			0.671760
$672$		0			0
$673$		−	26.0263i		−	1.00324i	−0.865088	−	0.501621i	$-0.832737\pi$
$673$		−	26.0263i		−	1.00324i	0.865088	−	0.501621i	$-0.167263\pi$
$674$	−0.373285	−	0.646548i	−0.0143784	−	0.0249041i
$675$	−1.95108	+	4.60362i	−0.0750970	+	0.177193i
$676$	−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	0.0537615	−	0.998554i	$-0.482879\pi$
$683$	−20.4927	−	11.8315i	−0.784131	−	0.452718i	−0.837892	+	0.545836i	$0.816212\pi$
$684$	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
$690$	2.04057	−	0.683401i	0.0776831	−	0.0260166i
$691$	−0.287258	−	0.497545i	−0.0109278	−	0.0189275i	0.860510	−	0.509434i	$-0.170145\pi$
$691$	−0.287258	−	0.497545i	−0.0109278	−	0.0189275i	−0.871438	+	0.490506i	$0.836812\pi$
$692$		−	8.82936i		−	0.335642i
$693$		0			0
$694$	−1.85940			−0.0705820
$695$	7.17660	+	1.45800i	0.272224	+	0.0553052i
$696$	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
$705$	21.7482	+	4.41838i	0.819084	+	0.166406i
$706$	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	$0.662346\pi$
$710$	−0.822414	+	0.275432i	−0.0308647	+	0.0103368i
$711$	−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	0.948376	−	0.317147i	$-0.102725\pi$
$719$	5.35026	+	9.26693i	0.199531	+	0.345598i	−0.748845	+	0.662745i	$0.769391\pi$
$720$	−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
$725$	−36.4826	−	15.4618i	−1.35493	−	0.574239i
$726$	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
$730$	−3.97362	−	0.807282i	−0.147070	−	0.0298789i
$731$	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	$-0.0735935\pi$
$740$	−0.677714	+	3.33585i	−0.0249133	+	0.122628i
$741$	7.22425			0.265390
$742$		0			0
$743$		−	26.3634i		−	0.967181i	−0.875294	−	0.483590i	$-0.839332\pi$
$743$		−	26.3634i		−	0.967181i	0.875294	−	0.483590i	$-0.160668\pi$
$744$	1.75765	+	3.04434i	0.0644385	+	0.111611i
$745$	3.15892	+	9.43225i	0.115734	+	0.345571i
$746$	−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	$0.250347\pi$
$757$			38.9525i			1.41575i	−0.706336	+	0.707877i	$0.749653\pi$
$758$	−1.79720	+	1.03761i	−0.0652771	+	0.0376877i
$759$	4.96239	−	8.59511i	0.180123	−	0.311983i
$760$	−8.71751	+	2.91955i	−0.316217	+	0.105903i
$761$	24.1065	+	41.7537i	0.873860	+	1.51357i	0.857972	+	0.513696i	$0.171724\pi$
$761$	24.1065	+	41.7537i	0.873860	+	1.51357i	0.0158873	+	0.999874i	$0.494943\pi$
$762$			0.523730i			0.0189727i
$763$		0			0
$764$	−27.1782			−0.983273
$765$	−1.49149	+	7.34144i	−0.0539250	+	0.265430i
$766$	−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	$-0.474441\pi$
$769$	4.44851			0.160417			0.0802086	+	0.996778i	$0.474441\pi$
$770$		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
$775$	18.2591	−	13.7753i	0.655888	−	0.494823i
$776$	−14.2158			−0.510318
$777$		0			0
$778$			5.68735i			0.203901i
$779$	10.0000	+	17.3205i	0.358287	+	0.620572i
$780$	1.88160	+	5.61829i	0.0673722	+	0.201167i
$781$	−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
$795$	−6.08884	−	18.1807i	−0.215949	−	0.644803i
$796$	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
$800$	−6.83315	−	9.05733i	−0.241588	−	0.320225i
$801$	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	$0.141749\pi$
$810$	0.0863379	−	0.424974i	0.00303361	−	0.0149321i
$811$	−37.6747			−1.32294			−0.661468	−	0.749973i	$-0.730066\pi$
$811$	−37.6747			−1.32294			−0.661468	+	0.749973i	$0.730066\pi$
$812$		0			0
$813$		−	16.4241i		−	0.576017i
$814$	−0.150446	−	0.260579i	−0.00527311	−	0.00913330i
$815$	11.2366	−	3.76320i	0.393600	−	0.131819i
$816$	−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	0.0454565	−	0.998966i	$-0.485526\pi$
$823$	−22.8628	−	13.1998i	−0.796945	−	0.460117i	−0.842402	+	0.538850i	$0.818859\pi$
$824$	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	$0.0301367\pi$
$827$			5.43724i			0.189071i	−0.995521	+	0.0945357i	$0.969863\pi$
$828$	8.43347	−	4.86907i	0.293083	−	0.169212i
$829$	−11.3879	+	19.7244i	−0.395517	+	0.685056i	−0.993167	−	0.116701i	$-0.962768\pi$
$829$	−11.3879	+	19.7244i	−0.395517	+	0.685056i	0.597650	+	0.801757i	$0.296101\pi$
$830$	−0.444031	−	1.32584i	−0.0154126	−	0.0460204i
$831$	5.53690	+	9.59020i	0.192073	+	0.332680i
$832$			9.60228i			0.332899i
$833$		0			0
$834$	−0.635150			−0.0219934
$835$	6.47750	−	31.8836i	0.224163	−	1.10338i
$836$	−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	$-0.411788\pi$
$839$	15.8496			0.547187			0.273594	+	0.961845i	$0.411788\pi$
$840$		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
$845$	−24.4917	−	4.97576i	−0.842542	−	0.171171i
$846$	−1.92478			−0.0661752
$847$		0			0
$848$		−	32.3752i		−	1.11177i
$849$	−0.574515	−	0.995090i	−0.0197173	−	0.0341514i
$850$	−2.99115	−	1.26769i	−0.102595	−	0.0434814i
$851$	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	0.908048	−	0.418867i	$-0.137573\pi$
$859$	2.67513	+	4.63346i	0.0912743	+	0.158092i	−0.816773	+	0.576959i	$0.804239\pi$
$860$	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	0.0869386	−	0.996214i	$-0.472292\pi$
$863$	29.1758	−	16.8446i	0.993154	−	0.573398i	0.906216	+	0.422816i	$0.138958\pi$
$864$	1.13458	−	1.96515i	0.0385992	−	0.0668557i
$865$	9.53993	−	3.19499i	0.324367	−	0.108633i
$866$	0.630225	+	1.09158i	0.0214159	+	0.0370935i
$867$		−	5.77575i		−	0.196155i
$868$		0			0
$869$	−21.4010			−0.725981
$870$	3.36782	+	0.684209i	0.114180	+	0.0231969i
$871$	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	−0.780293	−	0.625415i	$-0.784930\pi$
$877$	−18.6218	+	10.7513i	−0.628814	+	0.363046i	0.151479	+	0.988461i	$0.451597\pi$
$878$	2.46048	+	1.42056i	0.0830372	+	0.0479416i
$879$	−0.324869	+	0.562690i	−0.0109576	+	0.0189791i
$880$	−16.5476	−	3.36182i	−0.557820	−	0.113327i
$881$	−32.3634			−1.09035			−0.545176	−	0.838322i	$-0.683537\pi$
$881$	−32.3634			−1.09035			−0.545176	+	0.838322i	$0.683537\pi$
$882$		0			0
$883$			2.59895i			0.0874617i	0.999043	+	0.0437309i	$0.0139244\pi$
$883$			2.59895i			0.0874617i	−0.999043	+	0.0437309i	$0.986076\pi$
$884$	4.43866	+	7.68798i	0.149288	+	0.258575i
$885$	−18.2884	+	6.12490i	−0.614757	+	0.205886i
$886$	−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
$900$	−9.03409	−	3.82877i	−0.301136	−	0.127626i
$901$	−14.3634	−	24.8782i	−0.478515	−	0.828813i
$902$		−	1.44992i		−	0.0482771i
$903$		0			0
$904$	9.26045			0.307998
$905$	23.2833	+	4.73024i	0.773962	+	0.157238i
$906$	−0.126008	+	0.218252i	−0.00418634	+	0.00725095i
$907$	43.2988	+	24.9986i	1.43771	+	0.830064i	0.997691	−	0.0679221i	$-0.0216369\pi$
$907$	43.2988	+	24.9986i	1.43771	+	0.830064i	0.440023	+	0.897986i	$0.354970\pi$
$908$	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
$915$	−3.87336	+	19.0655i	−0.128049	+	0.630285i
$916$	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	$0.895142\pi$
$920$	2.70790	+	8.08553i	0.0892768	+	0.266572i
$921$	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	0.603373	−	0.797459i	$-0.293823\pi$
$929$	−11.8545	−	20.5326i	−0.388933	−	0.673651i	−0.992306	+	0.123807i	$0.960490\pi$
$930$	−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
$935$	−14.2072	+	4.75810i	−0.464626	+	0.155607i
$936$	−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
$940$	−8.67057	+	42.6784i	−0.282803	+	1.39202i
$941$	−3.14411	+	5.44575i	−0.102495	+	0.177526i	−0.912712	−	0.408604i	$-0.866016\pi$
$941$	−3.14411	+	5.44575i	−0.102495	+	0.177526i	0.810217	+	0.586130i	$0.199349\pi$
$942$	−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	−0.943103	−	0.332501i	$-0.892108\pi$
$947$	−34.6724	+	20.0181i	−1.12670	+	0.650501i	−0.183597	+	0.983002i	$0.558774\pi$
$948$	−18.1853	−	10.4993i	−0.590631	−	0.341001i
$949$	−6.31265	+	10.9338i	−0.204917	+	0.354927i
$950$	−3.12457	−	4.14162i	−0.101374	−	0.134372i
$951$	10.1260			0.328358
$952$		0			0
$953$		−	40.9478i		−	1.32643i	−0.748429	−	0.663215i	$-0.769192\pi$
$953$		−	40.9478i		−	1.32643i	0.748429	−	0.663215i	$-0.230808\pi$
$954$	0.831456	+	1.44012i	0.0269194	+	0.0466257i
$955$	−9.83469	−	29.3655i	−0.318243	−	0.950244i
$956$	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	$0.211036\pi$
$967$			38.2784i			1.23095i	−0.788157	+	0.615475i	$0.788964\pi$
$968$	−4.65849	+	2.68958i	−0.149730	+	0.0864464i
$969$	−8.96239	+	15.5233i	−0.287913	+	0.498681i
$970$	−2.54765	−	7.60704i	−0.0818001	−	0.244247i
$971$	−14.3634	−	24.8782i	−0.460945	−	0.798379i	0.538064	−	0.842904i	$-0.319156\pi$
$971$	−14.3634	−	24.8782i	−0.460945	−	0.798379i	−0.999008	+	0.0445247i	$0.985823\pi$
$972$		−	1.96239i		−	0.0629436i
$973$		0			0
$974$	4.30089			0.137809
$975$	−5.38956	+	4.06606i	−0.172604	+	0.130218i
$976$	−16.4255	+	28.4498i	−0.525767	+	0.910655i
$977$	35.7681	+	20.6507i	1.14432	+	0.660674i	0.947497	−	0.319765i	$-0.103604\pi$
$977$	35.7681	+	20.6507i	1.14432	+	0.660674i	0.196824	+	0.980439i	$0.436937\pi$
$978$	−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
$985$	−0.255767	+	1.25894i	−0.00814940	+	0.0401131i
$986$	5.14903			0.163979
$987$		0			0
$988$			14.1768i			0.451024i
$989$	−31.3258	−	54.2579i	−0.996103	−	1.72530i
$990$	0.822414	−	0.275432i	0.0261380	−	0.00875381i
$991$	−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.f.214.4		12
5.4	even	2	inner	735.2.q.f.214.3		12
7.2	even	3	inner	735.2.q.f.79.3		12
7.3	odd	6		105.2.d.b.64.4	yes	6
7.4	even	3		735.2.d.b.589.4		6
7.5	odd	6		735.2.q.e.79.3		12
7.6	odd	2		735.2.q.e.214.4		12
21.11	odd	6		2205.2.d.l.1324.3		6
21.17	even	6		315.2.d.e.64.3		6
28.3	even	6		1680.2.t.k.1009.1		6
35.3	even	12		525.2.a.k.1.2		3
35.4	even	6		735.2.d.b.589.3		6
35.9	even	6	inner	735.2.q.f.79.4		12
35.17	even	12		525.2.a.j.1.2		3
35.18	odd	12		3675.2.a.bj.1.2		3
35.19	odd	6		735.2.q.e.79.4		12
35.24	odd	6		105.2.d.b.64.3	✓	6
35.32	odd	12		3675.2.a.bi.1.2		3
35.34	odd	2		735.2.q.e.214.3		12
84.59	odd	6		5040.2.t.v.1009.5		6
105.17	odd	12		1575.2.a.x.1.2		3
105.38	odd	12		1575.2.a.w.1.2		3
105.59	even	6		315.2.d.e.64.4		6
105.74	odd	6		2205.2.d.l.1324.4		6
140.3	odd	12		8400.2.a.dj.1.3		3
140.59	even	6		1680.2.t.k.1009.4		6
140.87	odd	12		8400.2.a.dg.1.1		3
420.59	odd	6		5040.2.t.v.1009.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.d.b.64.3	✓	6	35.24	odd	6
105.2.d.b.64.4	yes	6	7.3	odd	6
315.2.d.e.64.3		6	21.17	even	6
315.2.d.e.64.4		6	105.59	even	6
525.2.a.j.1.2		3	35.17	even	12
525.2.a.k.1.2		3	35.3	even	12
735.2.d.b.589.3		6	35.4	even	6
735.2.d.b.589.4		6	7.4	even	3
735.2.q.e.79.3		12	7.5	odd	6
735.2.q.e.79.4		12	35.19	odd	6
735.2.q.e.214.3		12	35.34	odd	2
735.2.q.e.214.4		12	7.6	odd	2
735.2.q.f.79.3		12	7.2	even	3	inner
735.2.q.f.79.4		12	35.9	even	6	inner
735.2.q.f.214.3		12	5.4	even	2	inner
735.2.q.f.214.4		12	1.1	even	1	trivial
1575.2.a.w.1.2		3	105.38	odd	12
1575.2.a.x.1.2		3	105.17	odd	12
1680.2.t.k.1009.1		6	28.3	even	6
1680.2.t.k.1009.4		6	140.59	even	6
2205.2.d.l.1324.3		6	21.11	odd	6
2205.2.d.l.1324.4		6	105.74	odd	6
3675.2.a.bi.1.2		3	35.32	odd	12
3675.2.a.bj.1.2		3	35.18	odd	12
5040.2.t.v.1009.5		6	84.59	odd	6
5040.2.t.v.1009.6		6	420.59	odd	6
8400.2.a.dg.1.1		3	140.87	odd	12
8400.2.a.dj.1.3		3	140.3	odd	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)

\(f(q)\)	\(=\)	\(q+(0.167954 - 0.0969683i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.981194 + 1.69948i) q^{4} +(-2.19130 - 0.445186i) q^{5} +0.193937 q^{6} +0.768452i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.167954 - 0.0969683i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.981194 + 1.69948i) q^{4} +(-2.19130 - 0.445186i) q^{5} +0.193937 q^{6} +0.768452i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.411207 + 0.137716i) 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} +(4.60362 + 1.95108i) q^{25} +(0.130933 + 0.226782i) q^{26} +1.00000i q^{27} -7.92478 q^{29} +(-0.424974 - 0.0863379i) 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} +(0.342104 - 1.68391i) q^{40} -3.73813 q^{41} +12.6253i q^{43} +(-1.96239 - 3.39896i) q^{44} +(-0.710109 - 2.12032i) 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} +(4.16089 - 1.39351i) q^{60} +(-4.35026 - 7.53487i) q^{61} -0.887166i q^{62} +7.11142 q^{64} +(0.601118 - 2.95883i) 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} +(3.01131 + 3.99149i) q^{75} +10.4993 q^{76} +0.261865i q^{78} +(5.35026 + 9.26693i) q^{79} +(2.68119 + 8.00578i) 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} +(3.79927 + 11.3443i) 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