LMFDB - Embedded newform 675.2.ba.b.32.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(32,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.32"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([10, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.ba (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [192] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			32.11
Character	$\chi$	$=$	675.32
Dual form			675.2.ba.b.443.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0909691 - 1.03978i) q^{2} +(-1.49497 + 0.874685i) q^{3} +(0.896746 + 0.158121i) q^{4} +(0.773485 + 1.63401i) q^{6} +(-0.397456 + 0.567627i) q^{7} +(0.786273 - 2.93441i) q^{8} +(1.46985 - 2.61525i) q^{9} +(0.597632 - 1.64198i) q^{11} +(-1.47891 + 0.547986i) q^{12} +(0.720360 - 0.0630233i) q^{13} +(0.554051 + 0.464904i) q^{14} +(-1.26829 - 0.461619i) q^{16} +(0.792096 + 2.95614i) q^{17} +(-2.58558 - 1.76623i) q^{18} +(-3.38781 + 1.95596i) q^{19} +(0.0976895 - 1.19623i) q^{21} +(-1.65293 - 0.770776i) q^{22} +(6.61310 - 4.63055i) q^{23} +(1.39123 + 5.07459i) q^{24} -0.754750i q^{26} +(0.0901428 + 5.19537i) q^{27} +(-0.446171 + 0.446171i) q^{28} +(5.68683 - 4.77181i) q^{29} +(0.764639 - 4.33648i) q^{31} +(1.97241 - 4.22984i) q^{32} +(0.542776 + 2.97745i) q^{33} +(3.14580 - 0.554689i) q^{34} +(1.73161 - 2.11280i) q^{36} +(10.6938 - 2.86540i) q^{37} +(1.72558 + 3.70052i) q^{38} +(-1.02179 + 0.724306i) q^{39} +(2.71443 - 3.23493i) q^{41} +(-1.23493 - 0.210396i) q^{42} +(-5.87799 + 2.74095i) q^{43} +(0.795555 - 1.37794i) q^{44} +(-4.21317 - 7.29742i) q^{46} +(3.32527 + 2.32838i) q^{47} +(2.29982 - 0.419248i) q^{48} +(2.22991 + 6.12663i) q^{49} +(-3.76985 - 3.72650i) q^{51} +(0.655945 + 0.0573878i) q^{52} +(-5.90884 - 5.90884i) q^{53} +(5.41025 + 0.378889i) q^{54} +(1.35314 + 1.61261i) q^{56} +(3.35382 - 5.88736i) q^{57} +(-4.44432 - 6.34714i) q^{58} +(-2.63750 + 0.959971i) q^{59} +(1.13591 + 6.44205i) q^{61} +(-4.43943 - 1.18954i) q^{62} +(0.900284 + 1.87378i) q^{63} +(-6.55640 - 3.78534i) q^{64} +(3.14527 - 0.293513i) q^{66} +(-0.978397 - 11.1831i) q^{67} +(0.242882 + 2.77616i) q^{68} +(-5.83610 + 12.7069i) q^{69} +(5.58689 + 3.22559i) q^{71} +(-6.51852 - 6.36945i) q^{72} +(-8.08612 - 2.16667i) q^{73} +(-2.00658 - 11.3799i) q^{74} +(-3.34729 + 1.21831i) q^{76} +(0.694499 + 0.991847i) q^{77} +(0.660168 + 1.12833i) q^{78} +(1.04738 + 1.24822i) q^{79} +(-4.67907 - 7.68806i) q^{81} +(-3.11669 - 3.11669i) q^{82} +(1.78607 + 0.156261i) q^{83} +(0.276752 - 1.05727i) q^{84} +(2.31528 + 6.36117i) q^{86} +(-4.32778 + 12.1079i) q^{87} +(-4.34834 - 3.04474i) q^{88} +(-2.78132 - 4.81739i) q^{89} +(-0.250538 + 0.433944i) q^{91} +(6.66246 - 3.10676i) q^{92} +(2.64995 + 7.15171i) q^{93} +(2.72350 - 3.24574i) q^{94} +(0.751097 + 8.04871i) q^{96} +(1.95866 + 4.20036i) q^{97} +(6.57321 - 1.76129i) q^{98} +(-3.41576 - 3.97642i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.0909691	−	1.03978i	0.0643248	−	0.735236i	−0.893721	−	0.448622i	$-0.851915\pi$
$2$	0.0909691	−	1.03978i	0.0643248	−	0.735236i	0.958046	−	0.286614i	$-0.0925296\pi$
$3$	−1.49497	+	0.874685i	−0.863119	+	0.505000i
$3$	−1.49497	+	0.874685i	−0.863119	+	0.505000i
$4$	0.896746	+	0.158121i	0.448373	+	0.0790603i
$5$		0			0
$5$		0			0
$6$	0.773485	+	1.63401i	0.315774	+	0.667081i
$7$	−0.397456	+	0.567627i	−0.150224	+	0.214543i	−0.887210	−	0.461366i	$-0.847360\pi$
$7$	−0.397456	+	0.567627i	−0.150224	+	0.214543i	0.736986	+	0.675908i	$0.236249\pi$
$8$	0.786273	−	2.93441i	0.277990	−	1.03747i
$9$	1.46985	−	2.61525i	0.489950	−	0.871750i
$10$		0			0
$11$	0.597632	−	1.64198i	0.180193	−	0.495076i	−0.816406	−	0.577478i	$-0.804037\pi$
$11$	0.597632	−	1.64198i	0.180193	−	0.495076i	0.996599	+	0.0824022i	$0.0262592\pi$
$12$	−1.47891	+	0.547986i	−0.426925	+	0.158190i
$13$	0.720360	−	0.0630233i	0.199792	−	0.0174795i	0.0131795	−	0.999913i	$-0.495805\pi$
$13$	0.720360	−	0.0630233i	0.199792	−	0.0174795i	0.186612	+	0.982434i	$0.440249\pi$
$14$	0.554051	+	0.464904i	0.148076	+	0.124251i
$15$		0			0
$16$	−1.26829	−	0.461619i	−0.317072	−	0.115405i
$17$	0.792096	+	2.95614i	0.192112	+	0.716970i	0.992996	+	0.118151i	$0.0376966\pi$
$17$	0.792096	+	2.95614i	0.192112	+	0.716970i	−0.800884	+	0.598819i	$0.795637\pi$
$18$	−2.58558	−	1.76623i	−0.609426	−	0.416304i
$19$	−3.38781	+	1.95596i	−0.777218	+	0.448727i	−0.835443	−	0.549576i	$-0.814789\pi$
$19$	−3.38781	+	1.95596i	−0.777218	+	0.448727i	0.0582254	+	0.998303i	$0.481456\pi$
$20$		0			0
$21$	0.0976895	−	1.19623i	0.0213176	−	0.261039i
$22$	−1.65293	−	0.770776i	−0.352407	−	0.164330i
$23$	6.61310	−	4.63055i	1.37893	−	0.965535i	0.379746	−	0.925091i	$-0.376011\pi$
$23$	6.61310	−	4.63055i	1.37893	−	0.965535i	0.999182	−	0.0404446i	$-0.0128774\pi$
$24$	1.39123	+	5.07459i	0.283985	+	1.03585i
$25$		0			0
$26$		−	0.754750i		−	0.148019i
$27$	0.0901428	+	5.19537i	0.0173480	+	0.999850i
$28$	−0.446171	+	0.446171i	−0.0843184	+	0.0843184i
$29$	5.68683	−	4.77181i	1.05602	−	0.886103i	0.0623035	−	0.998057i	$-0.480155\pi$
$29$	5.68683	−	4.77181i	1.05602	−	0.886103i	0.993713	+	0.111954i	$0.0357109\pi$
$30$		0			0
$31$	0.764639	−	4.33648i	0.137333	−	0.778855i	−0.835873	−	0.548922i	$-0.815038\pi$
$31$	0.764639	−	4.33648i	0.137333	−	0.778855i	0.973207	−	0.229933i	$-0.0738506\pi$
$32$	1.97241	−	4.22984i	0.348676	−	0.747738i
$33$	0.542776	+	2.97745i	0.0944852	+	0.518307i
$34$	3.14580	−	0.554689i	0.539500	−	0.0951284i
$35$		0			0
$36$	1.73161	−	2.11280i	0.288601	−	0.352134i
$37$	10.6938	−	2.86540i	1.75805	−	0.471069i	0.771739	−	0.635939i	$-0.219387\pi$
$37$	10.6938	−	2.86540i	1.75805	−	0.471069i	0.986315	+	0.164870i	$0.0527205\pi$
$38$	1.72558	+	3.70052i	0.279926	+	0.600303i
$39$	−1.02179	+	0.724306i	−0.163617	+	0.115982i
$40$		0			0
$41$	2.71443	−	3.23493i	0.423923	−	0.505212i	−0.511236	−	0.859441i	$-0.670812\pi$
$41$	2.71443	−	3.23493i	0.423923	−	0.505212i	0.935159	+	0.354229i	$0.115257\pi$
$42$	−1.23493	−	0.210396i	−0.190554	−	0.0324648i
$43$	−5.87799	+	2.74095i	−0.896385	+	0.417991i	−0.815517	−	0.578733i	$-0.803547\pi$
$43$	−5.87799	+	2.74095i	−0.896385	+	0.417991i	−0.0808685	+	0.996725i	$0.525769\pi$
$44$	0.795555	−	1.37794i	0.119934	−	0.207733i
$45$		0			0
$46$	−4.21317	−	7.29742i	−0.621197	−	1.07595i
$47$	3.32527	+	2.32838i	0.485040	+	0.339628i	0.790382	−	0.612614i	$-0.209882\pi$
$47$	3.32527	+	2.32838i	0.485040	+	0.339628i	−0.305342	+	0.952243i	$0.598771\pi$
$48$	2.29982	−	0.419248i	0.331950	−	0.0605132i
$49$	2.22991	+	6.12663i	0.318559	+	0.875234i
$50$		0			0
$51$	−3.76985	−	3.72650i	−0.527885	−	0.521815i
$52$	0.655945	+	0.0573878i	0.0909632	+	0.00795825i
$53$	−5.90884	−	5.90884i	−0.811642	−	0.811642i	0.173238	−	0.984880i	$-0.444577\pi$
$53$	−5.90884	−	5.90884i	−0.811642	−	0.811642i	−0.984880	+	0.173238i	$0.944577\pi$
$54$	5.41025	+	0.378889i	0.736241	+	0.0515603i
$55$		0			0
$56$	1.35314	+	1.61261i	0.180821	+	0.215494i
$57$	3.35382	−	5.88736i	0.444225	−	0.779800i
$58$	−4.44432	−	6.34714i	−0.583567	−	0.833420i
$59$	−2.63750	+	0.959971i	−0.343373	+	0.124978i	−0.507950	−	0.861387i	$-0.669596\pi$
$59$	−2.63750	+	0.959971i	−0.343373	+	0.124978i	0.164577	+	0.986364i	$0.447374\pi$
$60$		0			0
$61$	1.13591	+	6.44205i	0.145438	+	0.824820i	0.967014	+	0.254722i	$0.0819838\pi$
$61$	1.13591	+	6.44205i	0.145438	+	0.824820i	−0.821576	+	0.570098i	$0.806905\pi$
$62$	−4.43943	−	1.18954i	−0.563808	−	0.151072i
$63$	0.900284	+	1.87378i	0.113425	+	0.236073i
$64$	−6.55640	−	3.78534i	−0.819551	−	0.473168i
$65$		0			0
$66$	3.14527	−	0.293513i	0.387156	−	0.0361289i
$67$	−0.978397	−	11.1831i	−0.119530	−	1.36624i	−0.784853	−	0.619682i	$-0.787262\pi$
$67$	−0.978397	−	11.1831i	−0.119530	−	1.36624i	0.665323	−	0.746556i	$-0.268294\pi$
$68$	0.242882	+	2.77616i	0.0294538	+	0.336659i
$69$	−5.83610	+	12.7069i	−0.702584	+	1.52973i
$70$		0			0
$71$	5.58689	+	3.22559i	0.663042	+	0.382807i	0.793435	−	0.608655i	$-0.208291\pi$
$71$	5.58689	+	3.22559i	0.663042	+	0.382807i	−0.130393	+	0.991462i	$0.541624\pi$
$72$	−6.51852	−	6.36945i	−0.768215	−	0.750647i
$73$	−8.08612	−	2.16667i	−0.946409	−	0.253589i	−0.247571	−	0.968870i	$-0.579632\pi$
$73$	−8.08612	−	2.16667i	−0.946409	−	0.253589i	−0.698838	+	0.715280i	$0.746299\pi$
$74$	−2.00658	−	11.3799i	−0.233261	−	1.32289i
$75$		0			0
$76$	−3.34729	+	1.21831i	−0.383960	+	0.139750i
$77$	0.694499	+	0.991847i	0.0791455	+	0.113032i
$78$	0.660168	+	1.12833i	0.0747494	+	0.127758i
$79$	1.04738	+	1.24822i	0.117840	+	0.140436i	0.821739	−	0.569863i	$-0.193004\pi$
$79$	1.04738	+	1.24822i	0.117840	+	0.140436i	−0.703899	+	0.710300i	$0.748559\pi$
$80$		0			0
$81$	−4.67907	−	7.68806i	−0.519897	−	0.854229i
$82$	−3.11669	−	3.11669i	−0.344181	−	0.344181i
$83$	1.78607	+	0.156261i	0.196046	+	0.0171518i	0.184756	−	0.982784i	$-0.440851\pi$
$83$	1.78607	+	0.156261i	0.196046	+	0.0171518i	0.0112903	+	0.999936i	$0.496406\pi$
$84$	0.276752	−	1.05727i	0.0301961	−	0.115358i
$85$		0			0
$86$	2.31528	+	6.36117i	0.249663	+	0.685942i
$87$	−4.32778	+	12.1079i	−0.463987	+	1.29810i
$88$	−4.34834	−	3.04474i	−0.463535	−	0.324571i
$89$	−2.78132	−	4.81739i	−0.294820	−	0.510643i	0.680123	−	0.733098i	$-0.261926\pi$
$89$	−2.78132	−	4.81739i	−0.294820	−	0.510643i	−0.974943	+	0.222455i	$0.928593\pi$
$90$		0			0
$91$	−0.250538	+	0.433944i	−0.0262635	+	0.0454897i
$92$	6.66246	−	3.10676i	0.694610	−	0.323902i
$93$	2.64995	+	7.15171i	0.274787	+	0.741598i
$94$	2.72350	−	3.24574i	0.280907	−	0.334772i
$95$		0			0
$96$	0.751097	+	8.04871i	0.0766585	+	0.821468i
$97$	1.95866	+	4.20036i	0.198872	+	0.426482i	0.980300	−	0.197513i	$-0.0632865\pi$
$97$	1.95866	+	4.20036i	0.198872	+	0.426482i	−0.781429	+	0.623995i	$0.785509\pi$
$98$	6.57321	−	1.76129i	0.663995	−	0.177917i
$99$	−3.41576	−	3.97642i	−0.343297	−	0.399646i
$100$		0			0
$101$	11.1359	−	1.96356i	1.10806	−	0.195381i	0.410469	−	0.911875i	$-0.365365\pi$
$101$	11.1359	−	1.96356i	1.10806	−	0.195381i	0.697594	+	0.716493i	$0.254254\pi$
$102$	−4.21769	+	3.58083i	−0.417613	+	0.354555i
$103$	2.08661	−	4.47475i	0.205600	−	0.440911i	−0.776287	−	0.630380i	$-0.782899\pi$
$103$	2.08661	−	4.47475i	0.205600	−	0.440911i	0.981887	+	0.189470i	$0.0606768\pi$
$104$	0.381463	−	2.16339i	0.0374055	−	0.212137i
$105$		0			0
$106$	−6.68142	+	5.60638i	−0.648957	+	0.544540i
$107$	−11.1511	+	11.1511i	−1.07801	+	1.07801i	−0.0813251	+	0.996688i	$0.525915\pi$
$107$	−11.1511	+	11.1511i	−1.07801	+	1.07801i	−0.996688	+	0.0813251i	$0.974085\pi$
$108$	−0.740660	+	4.67318i	−0.0712700	+	0.449677i
$109$			20.3152i			1.94584i	0.231133	+	0.972922i	$0.425757\pi$
$109$			20.3152i			1.94584i	−0.231133	+	0.972922i	$0.574243\pi$
$110$		0			0
$111$	−13.4806	+	13.6374i	−1.27952	+	1.29441i
$112$	0.766117	−	0.536441i	0.0723912	−	0.0506889i
$113$	0.110679	+	0.0516106i	0.0104118	+	0.00485512i	0.427817	−	0.903865i	$-0.359283\pi$
$113$	0.110679	+	0.0516106i	0.0104118	+	0.00485512i	−0.417405	+	0.908720i	$0.637060\pi$
$114$	−5.81647	−	4.02281i	−0.544763	−	0.376771i
$115$		0			0
$116$	5.85416	−	3.37990i	0.543545	−	0.313816i
$117$	0.894000	−	1.97656i	0.0826503	−	0.182733i
$118$	0.758229	+	2.82975i	0.0698006	+	0.260500i
$119$	−1.99281	−	0.725323i	−0.182681	−	0.0664903i
$120$		0			0
$121$	6.08755	+	5.10806i	0.553414	+	0.464369i
$122$	6.80165	−	0.595068i	0.615793	−	0.0538749i
$123$	−1.22844	+	7.21039i	−0.110764	+	0.650139i
$124$	1.37137	−	3.76782i	0.123153	−	0.338360i
$125$		0			0
$126$	2.03021	−	0.765643i	0.180866	−	0.0682089i
$127$	−4.29687	+	16.0361i	−0.381286	+	1.42298i	0.462654	+	0.886539i	$0.346897\pi$
$127$	−4.29687	+	16.0361i	−0.381286	+	1.42298i	−0.843939	+	0.536439i	$0.819769\pi$
$128$	0.821539	−	1.17328i	0.0726144	−	0.103704i
$129$	6.38993	−	9.23903i	0.562602	−	0.813451i
$130$		0			0
$131$	−22.1825	−	3.91138i	−1.93810	−	0.341739i	−0.938109	−	0.346341i	$-0.887424\pi$
$131$	−22.1825	−	3.91138i	−1.93810	−	0.341739i	−0.999989	+	0.00460251i	$0.998535\pi$
$132$	0.0159371	+	2.75584i	0.00138714	+	0.239865i
$133$	0.236256	−	2.70042i	0.0204860	−	0.234156i
$134$	−11.7170			−1.01220
$135$		0			0
$136$	9.29735			0.797241
$137$	0.454409	−	5.19392i	0.0388228	−	0.443747i	−0.951761	−	0.306840i	$-0.900728\pi$
$137$	0.454409	−	5.19392i	0.0388228	−	0.443747i	0.990584	−	0.136907i	$-0.0437161\pi$
$138$	12.6815	+	7.22420i	1.07952	+	0.614965i
$139$	−12.7974	−	2.25653i	−1.08546	−	0.191396i	−0.397833	−	0.917458i	$-0.630238\pi$
$139$	−12.7974	−	2.25653i	−1.08546	−	0.191396i	−0.687630	+	0.726061i	$0.741349\pi$
$140$		0			0
$141$	−7.00776	−	0.572284i	−0.590160	−	0.0481950i
$142$	3.86214	−	5.51571i	0.324104	−	0.462868i
$143$	0.327027	−	1.22048i	0.0273474	−	0.102062i
$144$	−3.07144	+	2.63838i	−0.255954	+	0.219865i
$145$		0			0
$146$	−2.98845	+	8.21069i	−0.247326	+	0.679522i
$147$	−8.69252	−	7.20864i	−0.716947	−	0.594559i
$148$	10.0427	−	0.878625i	0.825507	−	0.0722225i
$149$	8.70742	+	7.30639i	0.713340	+	0.598563i	0.925534	−	0.378664i	$-0.123617\pi$
$149$	8.70742	+	7.30639i	0.713340	+	0.598563i	−0.212194	+	0.977227i	$0.568061\pi$
$150$		0			0
$151$	−8.54652	−	3.11068i	−0.695506	−	0.253143i	−0.0300149	−	0.999549i	$-0.509555\pi$
$151$	−8.54652	−	3.11068i	−0.695506	−	0.253143i	−0.665491	+	0.746406i	$0.731778\pi$
$152$	3.07583	+	11.4792i	0.249483	+	0.931083i
$153$	8.89532	+	2.27356i	0.719144	+	0.183806i
$154$	1.09448	−	0.631900i	0.0881959	−	0.0509199i
$155$		0			0
$156$	−1.03081	+	0.487953i	−0.0825311	+	0.0390675i
$157$	−3.03444	−	1.41498i	−0.242175	−	0.112928i	0.297742	−	0.954646i	$-0.403767\pi$
$157$	−3.03444	−	1.41498i	−0.242175	−	0.112928i	−0.539917	+	0.841718i	$0.681544\pi$
$158$	1.39316	−	0.975501i	0.110834	−	0.0776067i
$159$	14.0019	+	3.66515i	1.11042	+	0.290665i
$160$		0			0
$161$			5.59421i			0.440886i
$162$	−8.41955	+	4.16584i	−0.661502	+	0.327299i
$163$	−9.97670	+	9.97670i	−0.781435	+	0.781435i	−0.980073	−	0.198638i	$-0.936348\pi$
$163$	−9.97670	+	9.97670i	−0.781435	+	0.781435i	0.198638	+	0.980073i	$0.436348\pi$
$164$	2.94567	−	2.47171i	0.230018	−	0.193008i
$165$		0			0
$166$	0.324953	−	1.84290i	0.0252213	−	0.143037i
$167$	−5.88249	+	12.6150i	−0.455201	+	0.976182i	0.536049	+	0.844187i	$0.319916\pi$
$167$	−5.88249	+	12.6150i	−0.455201	+	0.976182i	−0.991250	+	0.131995i	$0.957862\pi$
$168$	−3.43343	−	1.22723i	−0.264895	−	0.0946826i
$169$	−12.2876	+	2.16663i	−0.945196	+	0.166664i
$170$		0			0
$171$	0.135731	+	11.7350i	0.0103796	+	0.897394i
$172$	−5.70447	+	1.52851i	−0.434962	+	0.116548i
$173$	−1.31470	−	2.81939i	−0.0999551	−	0.214354i	0.849971	−	0.526830i	$-0.176620\pi$
$173$	−1.31470	−	2.81939i	−0.0999551	−	0.214354i	−0.949926	+	0.312476i	$0.898842\pi$
$174$	12.1959	+	5.60139i	0.924565	+	0.424640i
$175$		0			0
$176$	−1.51594	+	1.80663i	−0.114268	+	0.136180i
$177$	3.10330	−	3.74211i	0.233258	−	0.281274i
$178$	−5.26205	+	2.45373i	−0.394407	+	0.183915i
$179$	−2.53650	+	4.39334i	−0.189587	+	0.328374i	−0.945113	−	0.326745i	$-0.894048\pi$
$179$	−2.53650	+	4.39334i	−0.189587	+	0.328374i	0.755526	+	0.655119i	$0.227381\pi$
$180$		0			0
$181$	−4.66805	−	8.08530i	−0.346974	−	0.600976i	0.638737	−	0.769425i	$-0.279457\pi$
$181$	−4.66805	−	8.08530i	−0.346974	−	0.600976i	−0.985710	+	0.168449i	$0.946124\pi$
$182$	0.428416	+	0.299980i	0.0317563	+	0.0222360i
$183$	−7.33291	−	8.63709i	−0.542064	−	0.638472i
$184$	−8.38822	−	23.0464i	−0.618388	−	1.69901i
$185$		0			0
$186$	7.67728	−	2.10478i	0.562925	−	0.154330i
$187$	5.32731	+	0.466079i	0.389572	+	0.0340831i
$188$	2.61375	+	2.61375i	0.190628	+	0.190628i
$189$	−2.98486	−	2.01377i	−0.217117	−	0.146480i
$190$		0			0
$191$	0.729528	+	0.869417i	0.0527868	+	0.0629088i	0.791792	−	0.610791i	$-0.209148\pi$
$191$	0.729528	+	0.869417i	0.0527868	+	0.0629088i	−0.739005	+	0.673700i	$0.764704\pi$
$192$	13.1126	−	0.0758304i	0.946320	−	0.00547259i
$193$	7.90607	+	11.2910i	0.569091	+	0.812746i	0.995792	−	0.0916467i	$-0.0292130\pi$
$193$	7.90607	+	11.2910i	0.569091	+	0.812746i	−0.426701	+	0.904393i	$0.640324\pi$
$194$	4.54563	−	1.65447i	0.326357	−	0.118784i
$195$		0			0
$196$	1.03092	+	5.84663i	0.0736371	+	0.417617i
$197$	−1.93314	−	0.517983i	−0.137730	−	0.0369048i	0.189295	−	0.981920i	$-0.439380\pi$
$197$	−1.93314	−	0.517983i	−0.137730	−	0.0369048i	−0.327026	+	0.945015i	$0.606046\pi$
$198$	−4.44534	+	3.18991i	−0.315916	+	0.226697i
$199$	−16.0030	−	9.23931i	−1.13442	−	0.654957i	−0.189377	−	0.981905i	$-0.560647\pi$
$199$	−16.0030	−	9.23931i	−1.13442	−	0.654957i	−0.945043	+	0.326947i	$0.893980\pi$
$200$		0			0
$201$	11.2444	+	15.8626i	0.793118	+	1.11886i
$202$	−1.02865	−	11.7575i	−0.0723755	−	0.827256i
$203$	0.448343	+	5.12458i	0.0314675	+	0.359675i
$204$	−2.79136	−	3.93782i	−0.195435	−	0.275702i
$205$		0			0
$206$	−4.46295	−	2.57668i	−0.310948	−	0.179526i
$207$	−2.38976	−	24.1011i	−0.166100	−	1.67515i
$208$	−0.942717	−	0.252600i	−0.0653656	−	0.0175147i
$209$	1.18697	+	6.73167i	0.0821047	+	0.465639i
$210$		0			0
$211$	15.7638	−	5.73754i	1.08522	−	0.394989i	0.263374	−	0.964694i	$-0.415165\pi$
$211$	15.7638	−	5.73754i	1.08522	−	0.394989i	0.821849	+	0.569705i	$0.192943\pi$
$212$	−4.36442	−	6.23304i	−0.299750	−	0.428087i
$213$	−11.1736	+	0.0646171i	−0.765602	+	0.00442749i
$214$	10.5803	+	12.6091i	0.723251	+	0.861937i
$215$		0			0
$216$	15.3162	+	3.82046i	1.04214	+	0.259950i
$217$	2.15759	+	2.15759i	0.146467	+	0.146467i
$218$	21.1234	+	1.84806i	1.43066	+	0.125166i
$219$	13.9836	−	3.83371i	0.944926	−	0.259058i
$220$		0			0
$221$	0.756900	+	2.07957i	0.0509146	+	0.139887i
$222$	12.9536	+	15.2574i	0.869389	+	1.02401i
$223$	16.4615	+	11.5264i	1.10234	+	0.771868i	0.975488	−	0.220054i	$-0.0706233\pi$
$223$	16.4615	+	11.5264i	1.10234	+	0.771868i	0.126854	+	0.991921i	$0.459512\pi$
$224$	1.61703	+	2.80077i	0.108042	+	0.187134i
$225$		0			0
$226$	0.0637321	−	0.110387i	0.00423940	−	0.00734285i
$227$	4.22414	−	1.96975i	0.280366	−	0.130737i	−0.277349	−	0.960769i	$-0.589456\pi$
$227$	4.22414	−	1.96975i	0.280366	−	0.130737i	0.557715	+	0.830032i	$0.311678\pi$
$228$	3.93844	−	4.74916i	0.260830	−	0.314521i
$229$	15.6103	−	18.6036i	1.03156	−	1.22936i	0.0586205	−	0.998280i	$-0.481330\pi$
$229$	15.6103	−	18.6036i	1.03156	−	1.22936i	0.972935	−	0.231080i	$-0.0742258\pi$
$230$		0			0
$231$	−1.90581	−	0.875311i	−0.125393	−	0.0575912i
$232$	−9.53106	−	20.4394i	−0.625745	−	1.34191i
$233$	−6.84167	+	1.83322i	−0.448213	+	0.120098i	−0.475863	−	0.879519i	$-0.657864\pi$
$233$	−6.84167	+	1.83322i	−0.448213	+	0.120098i	0.0276501	+	0.999618i	$0.491198\pi$
$234$	−1.97386	−	1.10937i	−0.129035	−	0.0725218i
$235$		0			0
$236$	−2.51696	+	0.443808i	−0.163840	+	0.0288894i
$237$	−2.65761	−	0.949922i	−0.172630	−	0.0617041i
$238$	−0.935462	+	2.00610i	−0.0606370	+	0.130036i
$239$	−2.01666	+	11.4370i	−0.130447	+	0.739799i	0.847476	+	0.530833i	$0.178121\pi$
$239$	−2.01666	+	11.4370i	−0.130447	+	0.739799i	−0.977923	+	0.208966i	$0.932990\pi$
$240$		0			0
$241$	8.02324	−	6.73230i	0.516822	−	0.433665i	−0.346700	−	0.937976i	$-0.612698\pi$
$241$	8.02324	−	6.73230i	0.516822	−	0.433665i	0.863522	+	0.504311i	$0.168253\pi$
$242$	5.86505	−	5.86505i	0.377020	−	0.377020i
$243$	13.7197	+	7.40068i	0.880119	+	0.474754i
$244$			5.95649i			0.381325i
$245$		0			0
$246$	7.38548	+	1.93323i	0.470881	+	0.123258i
$247$	−2.31717	+	1.62250i	−0.147438	+	0.103237i
$248$	−12.1238	−	5.65342i	−0.769862	−	0.358993i
$249$	−2.80679	+	1.32864i	−0.177873	+	0.0841992i
$250$		0			0
$251$	−9.75413	+	5.63155i	−0.615675	+	0.355460i	−0.775183	−	0.631736i	$-0.782343\pi$
$251$	−9.75413	+	5.63155i	−0.615675	+	0.355460i	0.159508	+	0.987197i	$0.449009\pi$
$252$	0.511044	+	1.82265i	0.0321928	+	0.114816i
$253$	−3.65106	−	13.6259i	−0.229540	−	0.856656i
$254$	16.2832	+	5.92660i	1.02170	+	0.371868i
$255$		0			0
$256$	−12.7442	−	10.6936i	−0.796511	−	0.668352i
$257$	19.7620	−	1.72895i	1.23272	−	0.107849i	0.547890	−	0.836551i	$-0.315431\pi$
$257$	19.7620	−	1.72895i	1.23272	−	0.107849i	0.684832	+	0.728701i	$0.259876\pi$
$258$	−9.02528	−	7.48459i	−0.561889	−	0.465970i
$259$	−2.62385	+	7.20897i	−0.163038	+	0.447944i
$260$		0			0
$261$	−4.12070	−	21.8863i	−0.255065	−	1.35473i
$262$	−6.08491	+	22.7092i	−0.375927	+	1.40298i
$263$	9.68085	−	13.8257i	0.596947	−	0.852529i	−0.401033	−	0.916064i	$-0.631349\pi$
$263$	9.68085	−	13.8257i	0.596947	−	0.852529i	0.997980	+	0.0635351i	$0.0202375\pi$
$264$	9.16382	+	0.748357i	0.563994	+	0.0460582i
$265$		0			0
$266$	−2.78635	−	0.491310i	−0.170842	−	0.0301241i
$267$	8.37169	+	4.76906i	0.512339	+	0.291862i
$268$	0.890909	−	10.1831i	0.0544209	−	0.622034i
$269$	−30.5994			−1.86568			−0.932838	−	0.360296i	$-0.882676\pi$
$269$	−30.5994			−1.86568			−0.932838	+	0.360296i	$0.882676\pi$
$270$		0			0
$271$	−5.21670			−0.316892			−0.158446	−	0.987368i	$-0.550648\pi$
$271$	−5.21670			−0.316892			−0.158446	+	0.987368i	$0.550648\pi$
$272$	0.360006	−	4.11489i	0.0218286	−	0.249502i
$273$	−0.00501894	−	0.867874i	−0.000303760	−	0.0525262i
$274$	−5.35921	−	0.944973i	−0.323761	−	0.0570879i
$275$		0			0
$276$	−7.24272	+	10.4721i	−0.435961	+	0.630344i
$277$	−6.69422	+	9.56033i	−0.402216	+	0.574425i	−0.968258	−	0.249952i	$-0.919585\pi$
$277$	−6.69422	+	9.56033i	−0.402216	+	0.574425i	0.566042	+	0.824377i	$0.308474\pi$
$278$	−3.51047	+	13.1012i	−0.210544	+	0.785760i
$279$	−10.2171	−	8.37370i	−0.611681	−	0.501320i
$280$		0			0
$281$	4.68215	−	12.8641i	0.279313	−	0.767407i	−0.718127	−	0.695912i	$-0.755001\pi$
$281$	4.68215	−	12.8641i	0.279313	−	0.767407i	0.997441	−	0.0714958i	$-0.0227772\pi$
$282$	−1.23254	+	7.23447i	−0.0733966	+	0.430807i
$283$	−8.84093	+	0.773481i	−0.525539	+	0.0459787i	−0.346838	−	0.937925i	$-0.612745\pi$
$283$	−8.84093	+	0.773481i	−0.525539	+	0.0459787i	−0.178700	+	0.983904i	$0.557189\pi$
$284$	4.49999	+	3.77594i	0.267025	+	0.224061i
$285$		0			0
$286$	−1.23928	−	0.451062i	−0.0732804	−	0.0266719i
$287$	0.757366	+	2.82653i	0.0447059	+	0.166845i
$288$	−8.16295	−	11.3756i	−0.481007	−	0.670313i
$289$	6.61106	−	3.81690i	0.388886	−	0.224524i
$290$		0			0
$291$	−6.60212	−	4.56619i	−0.387023	−	0.267675i
$292$	−6.90860	−	3.22153i	−0.404295	−	0.188526i
$293$	−9.25201	+	6.47833i	−0.540508	+	0.378468i	−0.811716	−	0.584053i	$-0.801466\pi$
$293$	−9.25201	+	6.47833i	−0.540508	+	0.378468i	0.271207	+	0.962521i	$0.412577\pi$
$294$	−8.28616	+	8.38256i	−0.483259	+	0.488881i
$295$		0			0
$296$		−	33.6331i		−	1.95488i
$297$	8.58457	+	2.95691i	0.498127	+	0.171577i
$298$	8.38915	−	8.38915i	0.485971	−	0.485971i
$299$	4.47198	−	3.75244i	0.258621	−	0.217009i
$300$		0			0
$301$	0.780408	−	4.42591i	0.0449820	−	0.255105i
$302$	−4.01189	+	8.60353i	−0.230858	+	0.495078i
$303$	−14.9303	+	12.6759i	−0.857723	+	0.728209i
$304$	5.19963	−	0.916835i	0.298219	−	0.0525841i
$305$		0			0
$306$	3.17320	−	9.04236i	0.181400	−	0.516917i
$307$	8.24213	−	2.20847i	0.470403	−	0.126044i	−0.0158274	−	0.999875i	$-0.505038\pi$
$307$	8.24213	−	2.20847i	0.470403	−	0.126044i	0.486230	+	0.873831i	$0.338372\pi$
$308$	0.465958	+	0.999250i	0.0265504	+	0.0569376i
$309$	0.794586	+	8.51474i	0.0452024	+	0.484386i
$310$		0			0
$311$	−9.40563	+	11.2092i	−0.533344	+	0.635615i	−0.963682	−	0.267053i	$-0.913950\pi$
$311$	−9.40563	+	11.2092i	−0.533344	+	0.635615i	0.430338	+	0.902668i	$0.358394\pi$
$312$	1.32201	+	3.56785i	0.0748439	+	0.201990i
$313$	8.45186	−	3.94117i	0.477727	−	0.222768i	−0.168812	−	0.985648i	$-0.553993\pi$
$313$	8.45186	−	3.94117i	0.477727	−	0.222768i	0.646540	+	0.762880i	$0.276215\pi$
$314$	−1.74731	+	3.02644i	−0.0986067	+	0.170792i
$315$		0			0
$316$	0.741868	+	1.28495i	0.0417333	+	0.0722843i
$317$	−19.3542	−	13.5519i	−1.08704	−	0.761152i	−0.114390	−	0.993436i	$-0.536491\pi$
$317$	−19.3542	−	13.5519i	−1.08704	−	0.761152i	−0.972648	+	0.232283i	$0.925380\pi$
$318$	5.08469	−	14.2255i	0.285135	−	0.797726i
$319$	−4.43659	−	12.1894i	−0.248402	−	0.682478i
$320$		0			0
$321$	6.91679	−	26.4241i	0.386058	−	1.47485i
$322$	5.81676	+	0.508900i	0.324155	+	0.0283599i
$323$	−8.46556	−	8.46556i	−0.471036	−	0.471036i
$324$	−2.98030	−	7.63410i	−0.165572	−	0.424116i
$325$		0			0
$326$	9.46601	+	11.2812i	0.524274	+	0.624805i
$327$	−17.7694	−	30.3706i	−0.982651	−	1.67950i
$328$	−7.35834	−	10.5088i	−0.406297	−	0.580252i
$329$	−2.64330	+	0.962081i	−0.145730	+	0.0530413i
$330$		0			0
$331$	4.01625	+	22.7773i	0.220753	+	1.25195i	0.870639	+	0.491922i	$0.163705\pi$
$331$	4.01625	+	22.7773i	0.220753	+	1.25195i	−0.649886	+	0.760032i	$0.725183\pi$
$332$	1.57694	+	0.422540i	0.0865458	+	0.0231899i
$333$	8.22459	−	32.1788i	0.450705	−	1.76338i
$334$	12.5818	+	7.26408i	0.688443	+	0.397473i
$335$		0			0
$336$	−0.676102	+	1.47207i	−0.0368844	+	0.0803081i
$337$	1.08633	+	12.4168i	0.0591760	+	0.676384i	0.966621	+	0.256212i	$0.0824747\pi$
$337$	1.08633	+	12.4168i	0.0591760	+	0.676384i	−0.907445	+	0.420172i	$0.861970\pi$
$338$	1.13503	+	12.9735i	0.0617375	+	0.705663i
$339$	−0.210605	+	0.0196534i	−0.0114385	+	0.00106743i
$340$		0			0
$341$	−6.66344	−	3.84714i	−0.360846	−	0.208334i
$342$	12.2141	+	0.926386i	0.660464	+	0.0500932i
$343$	−9.04926	−	2.42474i	−0.488614	−	0.130924i
$344$	3.42137	+	19.4036i	0.184468	+	1.04617i
$345$		0			0
$346$	−3.05115	+	1.11053i	−0.164031	+	0.0597023i
$347$	−6.55983	−	9.36840i	−0.352150	−	0.502922i	0.603526	−	0.797343i	$-0.293762\pi$
$347$	−6.55983	−	9.36840i	−0.352150	−	0.502922i	−0.955676	+	0.294421i	$0.904873\pi$
$348$	−5.79543	+	10.1734i	−0.310667	+	0.545351i
$349$	15.6113	+	18.6048i	0.835652	+	0.995891i	0.999955	+	0.00948135i	$0.00301805\pi$
$349$	15.6113	+	18.6048i	0.835652	+	0.995891i	−0.164303	+	0.986410i	$0.552538\pi$
$350$		0			0
$351$	0.392365	+	3.73686i	0.0209429	+	0.199459i
$352$	−5.76654	−	5.76654i	−0.307358	−	0.307358i
$353$	−33.3825	−	2.92059i	−1.77677	−	0.155447i	−0.848951	−	0.528472i	$-0.822765\pi$
$353$	−33.3825	−	2.92059i	−1.77677	−	0.155447i	−0.927822	+	0.373024i	$0.878321\pi$
$354$	−3.60867	−	3.56717i	−0.191799	−	0.189593i
$355$		0			0
$356$	−1.73241	−	4.75976i	−0.0918177	−	0.252267i
$357$	3.61361	−	0.658747i	0.191253	−	0.0348646i
$358$	4.33737	+	3.03706i	0.229237	+	0.160514i
$359$	−9.34241	−	16.1815i	−0.493073	−	0.854028i	0.506895	−	0.862008i	$-0.330793\pi$
$359$	−9.34241	−	16.1815i	−0.493073	−	0.854028i	−0.999968	+	0.00797981i	$0.997460\pi$
$360$		0			0
$361$	−1.84847	+	3.20165i	−0.0972881	+	0.168508i
$362$	−8.83159	+	4.11824i	−0.464178	+	0.216450i
$363$	−13.5686	−	2.31169i	−0.712169	−	0.121332i
$364$	−0.293285	+	0.349523i	−0.0153723	+	0.0183200i
$365$		0			0
$366$	−9.64775	+	6.83891i	−0.504296	+	0.357476i
$367$	3.00914	+	6.45312i	0.157076	+	0.336850i	0.969058	−	0.246831i	$-0.0793894\pi$
$367$	3.00914	+	6.45312i	0.157076	+	0.336850i	−0.811983	+	0.583682i	$0.801612\pi$
$368$	−10.5249	+	2.82013i	−0.548647	+	0.147009i
$369$	−4.47035	−	11.8538i	−0.232717	−	0.617084i
$370$		0			0
$371$	5.70252	−	1.00551i	0.296060	−	0.0522034i
$372$	1.24550	+	6.83228i	0.0645760	+	0.354237i
$373$	4.36650	−	9.36399i	0.226089	−	0.484849i	−0.760239	−	0.649643i	$-0.774918\pi$
$373$	4.36650	−	9.36399i	0.226089	−	0.484849i	0.986328	+	0.164794i	$0.0526960\pi$
$374$	0.969241	−	5.49684i	0.0501183	−	0.284235i
$375$		0			0
$376$	9.44698	−	7.92696i	0.487191	−	0.408802i
$377$	3.79582	−	3.79582i	0.195495	−	0.195495i
$378$	−2.36541	+	2.92041i	−0.121663	+	0.150210i
$379$		−	5.45309i		−	0.280106i	−0.990144	−	0.140053i	$-0.955273\pi$
$379$		−	5.45309i		−	0.280106i	0.990144	−	0.140053i	$-0.0447273\pi$
$380$		0			0
$381$	−7.60290	−	27.7319i	−0.389508	−	1.42075i
$382$	0.970368	−	0.679459i	0.0496483	−	0.0347641i
$383$	−4.05128	−	1.88914i	−0.207011	−	0.0965307i	0.316348	−	0.948643i	$-0.397543\pi$
$383$	−4.05128	−	1.88914i	−0.207011	−	0.0965307i	−0.523359	+	0.852113i	$0.675321\pi$
$384$	−0.201923	+	2.47260i	−0.0103044	+	0.126179i
$385$		0			0
$386$	12.4594	−	7.19344i	0.634167	−	0.366137i
$387$	−1.47149	+	19.4012i	−0.0748003	+	0.986219i
$388$	1.09226	+	4.07636i	0.0554510	+	0.206946i
$389$	9.10172	+	3.31276i	0.461476	+	0.167963i	0.562287	−	0.826942i	$-0.309922\pi$
$389$	9.10172	+	3.31276i	0.461476	+	0.167963i	−0.100811	+	0.994906i	$0.532144\pi$
$390$		0			0
$391$	18.9268	+	15.8814i	0.957168	+	0.803159i
$392$	19.7314	−	1.72627i	0.996586	−	0.0871899i
$393$	36.5834	−	13.5554i	1.84539	−	0.683778i
$394$	−0.714445	+	1.96292i	−0.0359932	+	0.0988906i
$395$		0			0
$396$	−2.43432	−	4.10595i	−0.122329	−	0.206332i
$397$	−0.263053	+	0.981728i	−0.0132023	+	0.0492715i	−0.972213	−	0.234099i	$-0.924786\pi$
$397$	−0.263053	+	0.981728i	−0.0132023	+	0.0492715i	0.959010	+	0.283371i	$0.0914527\pi$
$398$	−11.0626	+	15.7991i	−0.554520	+	0.791936i
$399$	2.00882	+	4.24369i	0.100567	+	0.212450i
$400$		0			0
$401$	8.07342	+	1.42356i	0.403168	+	0.0710893i	0.371555	−	0.928411i	$-0.378825\pi$
$401$	8.07342	+	1.42356i	0.403168	+	0.0710893i	0.0316124	+	0.999500i	$0.489936\pi$
$402$	17.5165	−	10.2487i	0.873646	−	0.511159i
$403$	0.277515	−	3.17202i	0.0138240	−	0.158009i
$404$	10.2965			0.512272
$405$		0			0
$406$	5.36923			0.266470
$407$	1.68604	−	19.2715i	0.0835738	−	0.955253i
$408$	−13.8992	+	8.13225i	−0.688114	+	0.402606i
$409$	28.0740	+	4.95021i	1.38817	+	0.244772i	0.817274	−	0.576249i	$-0.195484\pi$
$409$	28.0740	+	4.95021i	1.38817	+	0.244772i	0.570897	+	0.821021i	$0.306595\pi$
$410$		0			0
$411$	3.86372	+	8.16221i	0.190583	+	0.402612i
$412$	2.57871	−	3.68278i	0.127044	−	0.181438i
$413$	0.503386	−	1.87866i	0.0247700	−	0.0924429i
$414$	−25.2773	+	0.292368i	−1.24231	+	0.0143691i
$415$		0			0
$416$	1.15426	−	3.17132i	0.0565925	−	0.155487i
$417$	21.1055	−	7.82028i	1.03354	−	0.382961i
$418$	7.10744	−	0.621820i	0.347636	−	0.0304142i
$419$	19.6956	+	16.5265i	0.962192	+	0.807375i	0.981308	−	0.192443i	$-0.0616409\pi$
$419$	19.6956	+	16.5265i	0.962192	+	0.807375i	−0.0191165	+	0.999817i	$0.506085\pi$
$420$		0			0
$421$	−12.0396	−	4.38206i	−0.586775	−	0.213569i	0.0315356	−	0.999503i	$-0.489960\pi$
$421$	−12.0396	−	4.38206i	−0.586775	−	0.213569i	−0.618310	+	0.785934i	$0.712182\pi$
$422$	−4.53177	−	16.9128i	−0.220603	−	0.823303i
$423$	10.9769	−	5.27404i	0.533717	−	0.256432i
$424$	−21.9849	+	12.6930i	−1.06768	+	0.616427i
$425$		0			0
$426$	−0.949263	+	11.6240i	−0.0459920	+	0.563183i
$427$	−4.10815	−	1.91566i	−0.198807	−	0.0927054i
$428$	−11.7629	+	8.23645i	−0.568580	+	0.398124i
$429$	0.578643	+	2.11062i	0.0279371	+	0.101902i
$430$		0			0
$431$			5.16823i			0.248945i	0.992223	+	0.124473i	$0.0397239\pi$
$431$			5.16823i			0.248945i	−0.992223	+	0.124473i	$0.960276\pi$
$432$	2.28396	−	6.63084i	0.109887	−	0.319026i
$433$	2.74947	−	2.74947i	0.132131	−	0.132131i	−0.637948	−	0.770079i	$-0.720217\pi$
$433$	2.74947	−	2.74947i	0.132131	−	0.132131i	0.770079	+	0.637948i	$0.220217\pi$
$434$	2.43970	−	2.04715i	0.117109	−	0.0982663i
$435$		0			0
$436$	−3.21225	+	18.2176i	−0.153839	+	0.872464i
$437$	−13.3468	+	28.6224i	−0.638465	+	1.36919i
$438$	−2.71414	−	14.8887i	−0.129687	−	0.711408i
$439$	31.6512	−	5.58095i	1.51063	−	0.266364i	0.643886	−	0.765122i	$-0.277321\pi$
$439$	31.6512	−	5.58095i	1.51063	−	0.266364i	0.866742	+	0.498757i	$0.166210\pi$
$440$		0			0
$441$	19.3003	+	3.17346i	0.919063	+	0.151117i
$442$	2.23115	−	0.597834i	0.106125	−	0.0284361i
$443$	6.48333	+	13.9035i	0.308032	+	0.660577i	0.997997	−	0.0632661i	$-0.0201517\pi$
$443$	6.48333	+	13.9035i	0.308032	+	0.660577i	−0.689965	+	0.723843i	$0.742374\pi$
$444$	−14.2450	+	10.0977i	−0.676039	+	0.479218i
$445$		0			0
$446$	13.4825	−	16.0678i	0.638413	−	0.760831i
$447$	−19.4081	−	3.30656i	−0.917972	−	0.156395i
$448$	4.75455	−	2.21708i	0.224631	−	0.104747i
$449$	1.37821	−	2.38713i	0.0650416	−	0.112655i	−0.831671	−	0.555269i	$-0.812615\pi$
$449$	1.37821	−	2.38713i	0.0650416	−	0.112655i	0.896712	+	0.442614i	$0.145949\pi$
$450$		0			0
$451$	−3.68947	−	6.39034i	−0.173730	−	0.300910i
$452$	0.0910905	+	0.0637823i	0.00428454	+	0.00300007i
$453$	15.4976	−	2.82515i	0.728142	−	0.132737i
$454$	−1.66384	−	4.57137i	−0.0780879	−	0.214545i
$455$		0			0
$456$	−14.6389	−	14.4706i	−0.685530	−	0.677647i
$457$	34.1536	+	2.98806i	1.59764	+	0.139775i	0.850895	−	0.525335i	$-0.176060\pi$
$457$	34.1536	+	2.98806i	1.59764	+	0.139775i	0.746745	+	0.665111i	$0.231616\pi$
$458$	−17.9236	−	17.9236i	−0.837515	−	0.837515i
$459$	−15.2869	+	4.38171i	−0.713529	+	0.204521i
$460$		0			0
$461$	−1.95614	−	2.33124i	−0.0911067	−	0.108577i	0.718565	−	0.695460i	$-0.244799\pi$
$461$	−1.95614	−	2.33124i	−0.0911067	−	0.108577i	−0.809672	+	0.586883i	$0.800355\pi$
$462$	−1.08350	+	1.90200i	−0.0504090	+	0.0884889i
$463$	15.4489	+	22.0633i	0.717970	+	1.02537i	0.997863	+	0.0653361i	$0.0208119\pi$
$463$	15.4489	+	22.0633i	0.717970	+	1.02537i	−0.279894	+	0.960031i	$0.590299\pi$
$464$	−9.41529	+	3.42689i	−0.437094	+	0.159089i
$465$		0			0
$466$	1.28377	+	7.28061i	0.0594694	+	0.337268i
$467$	−16.6209	−	4.45355i	−0.769122	−	0.206086i	−0.147138	−	0.989116i	$-0.547006\pi$
$467$	−16.6209	−	4.45355i	−0.769122	−	0.206086i	−0.621983	+	0.783030i	$0.713673\pi$
$468$	1.11423	−	1.63111i	0.0515051	−	0.0753981i
$469$	6.73671	+	3.88944i	0.311073	+	0.179598i
$470$		0			0
$471$	5.77406	−	0.538829i	0.266055	−	0.0248279i
$472$	0.743156	+	8.49431i	0.0342065	+	0.390982i
$473$	0.987714	+	11.2896i	0.0454152	+	0.519098i
$474$	−1.22947	+	2.67692i	−0.0564715	+	0.122955i
$475$		0			0
$476$	−1.67236	−	0.965535i	−0.0766523	−	0.0442552i
$477$	−24.1382	+	6.76799i	−1.10521	+	0.309885i
$478$	11.7085	+	3.13729i	0.535536	+	0.143497i
$479$	−6.03903	−	34.2490i	−0.275930	−	1.56488i	−0.735991	−	0.676991i	$-0.763283\pi$
$479$	−6.03903	−	34.2490i	−0.275930	−	1.56488i	0.460061	−	0.887888i	$-0.347828\pi$
$480$		0			0
$481$	7.52282	−	2.73808i	0.343011	−	0.124846i
$482$	−6.27025	−	8.95484i	−0.285602	−	0.407882i
$483$	−4.89318	−	8.36316i	−0.222647	−	0.380537i
$484$	4.65130	+	5.54320i	0.211423	+	0.251964i
$485$		0			0
$486$	8.94315	−	13.5922i	0.405670	−	0.616557i
$487$	10.1713	+	10.1713i	0.460908	+	0.460908i	0.898953	−	0.438045i	$-0.144329\pi$
$487$	10.1713	+	10.1713i	0.460908	+	0.460908i	−0.438045	+	0.898953i	$0.644329\pi$
$488$	19.7968	+	1.73199i	0.896157	+	0.0784036i
$489$	6.18836	−	23.6413i	0.279847	−	1.06910i
$490$		0			0
$491$	10.0702	+	27.6677i	0.454462	+	1.24863i	0.929553	+	0.368688i	$0.120193\pi$
$491$	10.0702	+	27.6677i	0.454462	+	1.24863i	−0.475091	+	0.879937i	$0.657585\pi$
$492$	−2.24171	+	6.27165i	−0.101064	+	0.282748i
$493$	18.6107	+	13.0313i	0.838183	+	0.586902i
$494$	1.47626	+	2.55695i	0.0664199	+	0.115043i
$495$		0			0
$496$	−2.97158	+	5.14694i	−0.133428	+	0.231104i
$497$	−4.05148	+	1.88923i	−0.181734	+	0.0847438i
$498$	1.12617	+	3.03931i	0.0504647	+	0.136195i
$499$	−11.3613	+	13.5399i	−0.508604	+	0.606130i	−0.957847	−	0.287279i	$-0.907249\pi$
$499$	−11.3613	+	13.5399i	−0.508604	+	0.606130i	0.449243	+	0.893410i	$0.351694\pi$
$500$		0			0
$501$	−2.24006	−	24.0044i	−0.100079	−	1.07244i
$502$	4.96826	+	10.6545i	0.221744	+	0.475532i
$503$	12.5537	−	3.36375i	0.559742	−	0.149982i	0.0321541	−	0.999483i	$-0.489763\pi$
$503$	12.5537	−	3.36375i	0.559742	−	0.149982i	0.527588	+	0.849501i	$0.323097\pi$
$504$	6.20630	−	1.16851i	0.276450	−	0.0520494i
$505$		0			0
$506$	−14.5001	+	2.55677i	−0.644610	+	0.113662i
$507$	16.4744	−	13.9868i	0.731652	−	0.621175i
$508$	−6.38885	+	13.7009i	−0.283459	+	0.607880i
$509$	0.0644329	−	0.365417i	0.00285594	−	0.0161968i	−0.983346	−	0.181741i	$-0.941827\pi$
$509$	0.0644329	−	0.365417i	0.00285594	−	0.0161968i	0.986202	+	0.165544i	$0.0529380\pi$
$510$		0			0
$511$	4.44374	−	3.72874i	0.196579	−	0.164950i
$512$	−10.2528	+	10.2528i	−0.453113	+	0.453113i
$513$	−10.4673	−	17.4246i	−0.462143	−	0.769317i
$514$		−	20.7055i		−	0.913279i
$515$		0			0
$516$	7.19103	−	7.27468i	0.316567	−	0.320250i
$517$	5.81043	−	4.06851i	0.255542	−	0.178933i
$518$	7.25707	+	3.38403i	0.318857	+	0.148686i
$519$	4.43152	+	3.06494i	0.194522	+	0.134536i
$520$		0			0
$521$	−2.40696	+	1.38966i	−0.105451	+	0.0608820i	−0.551798	−	0.833978i	$-0.686058\pi$
$521$	−2.40696	+	1.38966i	−0.105451	+	0.0608820i	0.446347	+	0.894860i	$0.352725\pi$
$522$	−23.1318	+	2.29365i	−1.01245	+	0.100390i
$523$	3.93462	+	14.6842i	0.172049	+	0.642096i	0.997035	+	0.0769434i	$0.0245161\pi$
$523$	3.93462	+	14.6842i	0.172049	+	0.642096i	−0.824986	+	0.565153i	$0.808817\pi$
$524$	−19.2736	−	7.01503i	−0.841973	−	0.306453i
$525$		0			0
$526$	−13.4950	−	11.3237i	−0.588411	−	0.493736i
$527$	13.4249	−	1.17453i	0.584799	−	0.0511633i
$528$	0.686049	−	4.02681i	0.0298565	−	0.175245i
$529$	14.4247	−	39.6316i	0.627162	−	1.72311i
$530$		0			0
$531$	−1.36617	+	8.30874i	−0.0592866	+	0.360569i
$532$	0.638854	−	2.38424i	0.0276978	−	0.103370i
$533$	1.75149	−	2.50139i	0.0758655	−	0.108347i
$534$	5.72034	−	8.27089i	0.247544	−	0.357916i
$535$		0			0
$536$	−33.5852	−	5.92198i	−1.45066	−	0.255790i
$537$	−0.0508127	−	8.78654i	−0.00219273	−	0.379167i
$538$	−2.78359	+	31.8166i	−0.120009	+	1.37171i
$539$	11.3925			0.490709
$540$		0			0
$541$	−16.6575			−0.716163			−0.358081	−	0.933690i	$-0.616569\pi$
$541$	−16.6575			−0.716163			−0.358081	+	0.933690i	$0.616569\pi$
$542$	−0.474558	+	5.42423i	−0.0203840	+	0.232990i
$543$	14.0507	+	8.00418i	0.602972	+	0.343492i
$544$	14.0664	+	2.48028i	0.603090	+	0.106341i
$545$		0			0
$546$	−0.902856	−	0.0737311i	−0.0386387	−	0.00315540i
$547$	0.222344	−	0.317541i	0.00950676	−	0.0135771i	−0.814371	−	0.580345i	$-0.802918\pi$
$547$	0.222344	−	0.317541i	0.00950676	−	0.0135771i	0.823877	+	0.566768i	$0.191806\pi$
$548$	1.22876	−	4.58578i	0.0524899	−	0.195895i
$549$	18.5172	+	6.49817i	0.790294	+	0.277335i
$550$		0			0
$551$	−9.93246	+	27.2892i	−0.423137	+	1.16256i
$552$	32.6985	+	27.1166i	1.39174	+	1.15416i
$553$	−1.12482	+	0.0984086i	−0.0478320	+	0.00418476i
$554$	9.33168	+	7.83021i	0.396465	+	0.332674i
$555$		0			0
$556$	−11.1192	−	4.04707i	−0.471561	−	0.171634i
$557$	−3.29185	−	12.2853i	−0.139480	−	0.520546i	−0.999939	−	0.0110271i	$-0.996490\pi$
$557$	−3.29185	−	12.2853i	−0.139480	−	0.520546i	0.860459	−	0.509519i	$-0.170177\pi$
$558$	−9.63626	+	9.86178i	−0.407935	+	0.417482i
$559$	−4.06152	+	2.34492i	−0.171784	+	0.0991797i
$560$		0			0
$561$	−8.37183	+	3.96295i	−0.353459	+	0.167316i
$562$	−12.9499	−	6.03864i	−0.546259	−	0.254725i
$563$	23.9613	−	16.7779i	1.00985	−	0.707102i	0.0532691	−	0.998580i	$-0.483036\pi$
$563$	23.9613	−	16.7779i	1.00985	−	0.707102i	0.956578	+	0.291478i	$0.0941470\pi$
$564$	−6.19369	−	1.62126i	−0.260801	−	0.0682675i
$565$		0			0
$566$			9.26299i			0.389353i
$567$	6.22368	+	0.399701i	0.261370	+	0.0167859i
$568$	13.8580	−	13.8580i	0.581470	−	0.581470i
$569$	3.92124	−	3.29031i	0.164387	−	0.137937i	−0.556884	−	0.830591i	$-0.688003\pi$
$569$	3.92124	−	3.29031i	0.164387	−	0.137937i	0.721270	+	0.692654i	$0.243559\pi$
$570$		0			0
$571$	1.16063	−	6.58228i	0.0485710	−	0.275460i	−0.950844	−	0.309671i	$-0.899781\pi$
$571$	1.16063	−	6.58228i	0.0485710	−	0.275460i	0.999415	+	0.0342116i	$0.0108920\pi$
$572$	0.486243	−	1.04275i	0.0203309	−	0.0435997i
$573$	−1.85109	−	0.661643i	−0.0773302	−	0.0276405i
$574$	3.00787	−	0.530368i	0.125546	−	0.0221372i
$575$		0			0
$576$	−19.5366	+	11.5828i	−0.814023	+	0.482615i
$577$	−44.6435	+	11.9622i	−1.85853	+	0.497992i	−0.999894	−	0.0145873i	$-0.995357\pi$
$577$	−44.6435	+	11.9622i	−1.85853	+	0.497992i	−0.858640	+	0.512580i	$0.828690\pi$
$578$	−3.36734	−	7.22128i	−0.140063	−	0.300366i
$579$	−21.6954	−	9.96440i	−0.901630	−	0.414106i
$580$		0			0
$581$	−0.798581	+	0.951712i	−0.0331307	+	0.0394837i
$582$	−5.34842	+	6.44938i	−0.221699	+	0.267335i
$583$	−13.2335	+	6.17089i	−0.548076	+	0.255572i
$584$	−12.7158	+	22.0244i	−0.526183	+	0.911376i
$585$		0			0
$586$	5.89440	+	10.2094i	0.243495	+	0.421746i
$587$	−1.45431	−	1.01832i	−0.0600260	−	0.0420306i	0.543178	−	0.839617i	$-0.317221\pi$
$587$	−1.45431	−	1.01832i	−0.0600260	−	0.0420306i	−0.603204	+	0.797587i	$0.706110\pi$
$588$	−6.65515	−	7.83879i	−0.274454	−	0.323266i
$589$	5.89151	+	16.1868i	0.242755	+	0.666965i
$590$		0			0
$591$	3.34305	−	0.916521i	0.137515	−	0.0377006i
$592$	−14.8856	−	1.30232i	−0.611794	−	0.0535250i
$593$	27.8118	+	27.8118i	1.14209	+	1.14209i	0.988066	+	0.154028i	$0.0492246\pi$
$593$	27.8118	+	27.8118i	1.14209	+	1.14209i	0.154028	+	0.988066i	$0.450775\pi$
$594$	3.85547	−	8.65708i	0.158192	−	0.355204i
$595$		0			0
$596$	6.65306	+	7.92880i	0.272520	+	0.324776i
$597$	32.0054	−	0.185088i	1.30989	−	0.00757514i
$598$	−3.49490	−	4.99124i	−0.142917	−	0.204107i
$599$	−37.7245	+	13.7306i	−1.54138	+	0.561017i	−0.966376	−	0.257133i	$-0.917222\pi$
$599$	−37.7245	+	13.7306i	−1.54138	+	0.561017i	−0.575005	+	0.818150i	$0.695000\pi$
$600$		0			0
$601$	3.13840	+	17.7988i	0.128018	+	0.726027i	0.979469	+	0.201593i	$0.0646119\pi$
$601$	3.13840	+	17.7988i	0.128018	+	0.726027i	−0.851451	+	0.524434i	$0.824277\pi$
$602$	−4.53099	−	1.21407i	−0.184669	−	0.0494820i
$603$	−30.6848	−	13.8788i	−1.24958	−	0.565188i
$604$	−7.17219	−	4.14087i	−0.291832	−	0.168490i
$605$		0			0
$606$	11.8219	+	16.6773i	0.480233	+	0.677471i
$607$	1.24916	+	14.2779i	0.0507016	+	0.579522i	0.978473	+	0.206374i	$0.0661663\pi$
$607$	1.24916	+	14.2779i	0.0507016	+	0.579522i	−0.927772	+	0.373149i	$0.878278\pi$
$608$	1.59123	+	18.1879i	0.0645330	+	0.737616i
$609$	−5.15265	−	7.26892i	−0.208796	−	0.294552i
$610$		0			0
$611$	2.54213	+	1.46770i	0.102844	+	0.0593767i
$612$	7.61735	+	3.44534i	0.307913	+	0.139270i
$613$	27.3956	+	7.34062i	1.10650	+	0.296485i	0.765408	−	0.643546i	$-0.222537\pi$
$613$	27.3956	+	7.34062i	1.10650	+	0.296485i	0.341090	+	0.940031i	$0.389204\pi$
$614$	−1.54655	−	8.77091i	−0.0624136	−	0.353965i
$615$		0			0
$616$	3.45655	−	1.25808i	0.139269	−	0.0506896i
$617$	−13.4838	−	19.2569i	−0.542839	−	0.775255i	0.450214	−	0.892921i	$-0.351348\pi$
$617$	−13.4838	−	19.2569i	−0.542839	−	0.775255i	−0.993053	+	0.117666i	$0.962459\pi$
$618$	8.92574	−	0.0516178i	0.359046	−	0.00207637i
$619$	−5.35313	−	6.37961i	−0.215160	−	0.256418i	0.647659	−	0.761930i	$-0.275748\pi$
$619$	−5.35313	−	6.37961i	−0.215160	−	0.256418i	−0.862820	+	0.505512i	$0.831304\pi$
$620$		0			0
$621$	24.6535	+	33.9401i	0.989312	+	1.36197i
$622$	10.7995	+	10.7995i	0.433020	+	0.433020i
$623$	3.83994	+	0.335951i	0.153844	+	0.0134596i
$624$	1.63028	−	0.446952i	0.0652633	−	0.0178924i
$625$		0			0
$626$	−3.32909	−	9.14661i	−0.133057	−	0.365572i
$627$	−7.66258	−	9.02539i	−0.306014	−	0.360439i
$628$	−2.49739	−	1.74869i	−0.0996566	−	0.0697803i
$629$	16.9411	+	29.3428i	0.675485	+	1.16997i
$630$		0			0
$631$	10.7788	−	18.6694i	0.429097	−	0.743218i	−0.567696	−	0.823238i	$-0.692165\pi$
$631$	10.7788	−	18.6694i	0.429097	−	0.743218i	0.996793	+	0.0800204i	$0.0254985\pi$
$632$	4.48633	−	2.09201i	0.178457	−	0.0832158i
$633$	−18.5478	+	22.3658i	−0.737208	+	0.888960i
$634$	−15.8517	+	18.8913i	−0.629550	+	0.750269i
$635$		0			0
$636$	11.9766	+	5.50069i	0.474904	+	0.218117i
$637$	1.99246	+	4.27285i	0.0789442	+	0.169296i
$638$	−13.0779	+	3.50422i	−0.517761	+	0.138734i
$639$	16.6476	−	9.86998i	0.658570	−	0.390450i
$640$		0			0
$641$	−4.89330	+	0.862821i	−0.193274	+	0.0340794i	−0.269447	−	0.963015i	$-0.586841\pi$
$641$	−4.89330	+	0.862821i	−0.193274	+	0.0340794i	0.0761733	+	0.997095i	$0.475730\pi$
$642$	−26.8461	−	9.59572i	−1.05953	−	0.378713i
$643$	9.66776	−	20.7326i	0.381259	−	0.817613i	−0.618241	−	0.785989i	$-0.712154\pi$
$643$	9.66776	−	20.7326i	0.381259	−	0.817613i	0.999500	−	0.0316243i	$-0.0100680\pi$
$644$	−0.884560	+	5.01659i	−0.0348566	+	0.197681i
$645$		0			0
$646$	−9.57243	+	8.03223i	−0.376622	+	0.316024i
$647$	−8.15287	+	8.15287i	−0.320522	+	0.320522i	−0.848967	−	0.528445i	$-0.822775\pi$
$647$	−8.15287	+	8.15287i	−0.320522	+	0.320522i	0.528445	+	0.848967i	$0.322775\pi$
$648$	−26.2390	+	7.68542i	−1.03076	+	0.301912i
$649$			4.90443i			0.192516i
$650$		0			0
$651$	−5.11274	−	1.33831i	−0.200384	−	0.0524527i
$652$	−10.5241	+	7.36905i	−0.412155	+	0.288594i
$653$	−33.6553	−	15.6937i	−1.31703	−	0.614142i	−0.368148	−	0.929767i	$-0.620008\pi$
$653$	−33.6553	−	15.6937i	−1.31703	−	0.614142i	−0.948884	+	0.315625i	$0.897786\pi$
$654$	−33.1952	+	15.7135i	−1.29804	+	0.614447i
$655$		0			0
$656$	−4.93599	+	2.84980i	−0.192718	+	0.111266i
$657$	−17.5518	+	17.9626i	−0.684760	+	0.700786i
$658$	0.759896	+	2.83597i	0.0296238	+	0.110558i
$659$	−17.4051	−	6.33493i	−0.678005	−	0.246774i	−0.0200144	−	0.999800i	$-0.506371\pi$
$659$	−17.4051	−	6.33493i	−0.678005	−	0.246774i	−0.657991	+	0.753026i	$0.728593\pi$
$660$		0			0
$661$	32.6452	+	27.3925i	1.26975	+	1.06545i	0.994572	+	0.104053i	$0.0331813\pi$
$661$	32.6452	+	27.3925i	1.26975	+	1.06545i	0.275178	+	0.961393i	$0.411263\pi$
$662$	24.0488	−	2.10399i	0.934682	−	0.0817740i
$663$	−2.95051	−	2.44683i	−0.114588	−	0.0950271i
$664$	1.86287	−	5.11819i	0.0722933	−	0.198624i
$665$		0			0
$666$	−32.7107	−	11.4790i	−1.26751	−	0.444804i
$667$	15.5115	−	57.8896i	0.600607	−	2.24149i
$668$	−7.26980	+	10.3824i	−0.281277	+	0.401705i
$669$	−34.6914	−	2.83305i	−1.34125	−	0.109532i
$670$		0			0
$671$	11.2566	+	1.98484i	0.434555	+	0.0766238i
$672$	−4.86719	−	2.77267i	−0.187756	−	0.106958i
$673$	−0.827111	+	9.45392i	−0.0318828	+	0.364422i	0.963448	+	0.267896i	$0.0863285\pi$
$673$	−0.827111	+	9.45392i	−0.0318828	+	0.364422i	−0.995331	+	0.0965254i	$0.969227\pi$
$674$	13.0095			0.501109
$675$		0			0
$676$	−11.3614			−0.436977
$677$	−0.944208	+	10.7923i	−0.0362888	+	0.414783i	0.956223	+	0.292638i	$0.0945330\pi$
$677$	−0.944208	+	10.7923i	−0.0362888	+	0.414783i	−0.992512	+	0.122146i	$0.961023\pi$
$678$	0.00127672	+	0.220771i	4.90322e−5	+	0.00847865i
$679$	−3.16272	−	0.557672i	−0.121374	−	0.0214015i
$680$		0			0
$681$	−4.59204	+	6.63950i	−0.175967	+	0.254426i
$682$	−4.60635	+	6.57855i	−0.176386	+	0.251906i
$683$	0.586431	−	2.18859i	0.0224392	−	0.0837441i	−0.953798	−	0.300448i	$-0.902864\pi$
$683$	0.586431	−	2.18859i	0.0224392	−	0.0837441i	0.976237	+	0.216704i	$0.0695306\pi$
$684$	−1.73382	+	10.5447i	−0.0662943	+	0.403188i
$685$		0			0
$686$	−3.34440	+	9.18868i	−0.127690	+	0.350825i
$687$	−7.06454	+	41.4658i	−0.269529	+	1.58202i
$688$	8.72026	−	0.762924i	0.332457	−	0.0290862i
$689$	−4.62889	−	3.88410i	−0.176347	−	0.147972i
$690$		0			0
$691$	7.28698	+	2.65224i	0.277210	+	0.100896i	0.476884	−	0.878966i	$-0.341766\pi$
$691$	7.28698	+	2.65224i	0.277210	+	0.100896i	−0.199674	+	0.979862i	$0.563988\pi$
$692$	−0.733152	−	2.73616i	−0.0278703	−	0.104013i
$693$	3.61474	−	0.358421i	0.137313	−	0.0136153i
$694$	−10.3378	+	5.96855i	−0.392419	+	0.226563i
$695$		0			0
$696$	32.1267	+	22.2196i	1.21776	+	0.842231i
$697$	11.7130	+	5.46187i	0.443662	+	0.206883i
$698$	20.7650	−	14.5398i	0.785969	−	0.550341i
$699$	8.62458	−	8.72492i	0.326212	−	0.330007i
$700$		0			0
$701$		−	3.06270i		−	0.115677i	−0.998326	−	0.0578383i	$-0.981579\pi$
$701$		−	3.06270i		−	0.115677i	0.998326	−	0.0578383i	$-0.0184208\pi$
$702$	3.92120	−	0.0680353i	0.147996	−	0.00256783i
$703$	−30.6241	+	30.6241i	−1.15501	+	1.15501i
$704$	−10.1338	+	8.50324i	−0.381931	+	0.320478i
$705$		0			0
$706$	−6.07355	+	34.4448i	−0.228581	+	1.29635i
$707$	−3.31146	+	7.10146i	−0.124540	+	0.267078i
$708$	3.37458	−	2.86502i	0.126824	−	0.107674i
$709$	−45.6222	+	8.04442i	−1.71338	+	0.302114i	−0.942335	−	0.334671i	$-0.891375\pi$
$709$	−45.6222	+	8.04442i	−1.71338	+	0.302114i	−0.771041	+	0.636785i	$0.780264\pi$
$710$		0			0
$711$	4.80392	−	0.904469i	0.180161	−	0.0339203i
$712$	−16.3231	+	4.37376i	−0.611734	+	0.163914i
$713$	−15.0236	−	32.2183i	−0.562640	−	1.20658i
$714$	−0.356226	−	3.81729i	−0.0133314	−	0.142859i
$715$		0			0
$716$	−2.96927	+	3.53864i	−0.110967	+	0.132245i
$717$	−6.98896	−	18.8619i	−0.261008	−	0.704411i
$718$	−17.6751	+	8.24204i	−0.659629	+	0.307590i
$719$	25.2485	−	43.7317i	0.941610	−	1.63092i	0.179211	−	0.983811i	$-0.442646\pi$
$719$	25.2485	−	43.7317i	0.941610	−	1.63092i	0.762400	−	0.647106i	$-0.224021\pi$
$720$		0			0
$721$	1.71065	+	2.96294i	0.0637080	+	0.110346i
$722$	3.16086	+	2.21326i	0.117635	+	0.0823690i
$723$	−6.10583	+	17.0824i	−0.227078	+	0.635300i
$724$	−2.90761	−	7.98858i	−0.108060	−	0.296893i
$725$		0			0
$726$	−3.63798	+	13.8981i	−0.135018	+	0.515808i
$727$	10.5499	+	0.922993i	0.391273	+	0.0342319i	0.281095	−	0.959680i	$-0.409302\pi$
$727$	10.5499	+	0.922993i	0.391273	+	0.0342319i	0.110178	+	0.993912i	$0.464858\pi$
$728$	1.07638	+	1.07638i	0.0398933	+	0.0398933i
$729$	−26.9837	+	0.936651i	−0.999398	+	0.0346908i
$730$		0			0
$731$	−12.7586	−	15.2051i	−0.471893	−	0.562380i
$732$	−5.21006	−	8.90476i	−0.192569	−	0.329129i
$733$	−16.7312	−	23.8946i	−0.617981	−	0.882569i	0.381139	−	0.924518i	$-0.375532\pi$
$733$	−16.7312	−	23.8946i	−0.617981	−	0.882569i	−0.999120	+	0.0419494i	$0.986643\pi$
$734$	6.98357	−	2.54181i	0.257768	−	0.0938200i
$735$		0			0
$736$	−6.54274	−	37.1057i	−0.241169	−	1.36774i
$737$	−18.9472	−	5.07689i	−0.697929	−	0.187010i
$738$	−12.7320	+	3.56986i	−0.468672	+	0.131408i
$739$	−5.54415	−	3.20092i	−0.203945	−	0.117748i	0.394549	−	0.918875i	$-0.370901\pi$
$739$	−5.54415	−	3.20092i	−0.203945	−	0.117748i	−0.598494	+	0.801127i	$0.704234\pi$
$740$		0			0
$741$	2.04492	−	4.45239i	0.0751220	−	0.163563i
$742$	−0.526756	−	6.02085i	−0.0193378	−	0.221032i
$743$	2.60134	+	29.7334i	0.0954338	+	1.09081i	0.881345	+	0.472473i	$0.156639\pi$
$743$	2.60134	+	29.7334i	0.0954338	+	1.09081i	−0.785911	+	0.618339i	$0.787806\pi$
$744$	23.0696	−	2.15283i	0.845774	−	0.0789267i
$745$		0			0
$746$	−9.33928	−	5.39204i	−0.341935	−	0.197416i
$747$	3.03391	−	4.44133i	0.111005	−	0.162500i
$748$	4.70355	+	1.26031i	0.171979	+	0.0460816i
$749$	−1.89758	−	10.7617i	−0.0693359	−	0.393224i
$750$		0			0
$751$	−9.53000	+	3.46864i	−0.347755	+	0.126572i	−0.509991	−	0.860180i	$-0.670351\pi$
$751$	−9.53000	+	3.46864i	−0.347755	+	0.126572i	0.162237	+	0.986752i	$0.448129\pi$
$752$	−3.14257	−	4.48806i	−0.114598	−	0.163663i
$753$	9.65627	−	16.9508i	0.351894	−	0.617721i
$754$	−3.60152	−	4.29213i	−0.131160	−	0.156310i
$755$		0			0
$756$	−2.35824	−	2.27780i	−0.0857685	−	0.0828430i
$757$	−6.39851	−	6.39851i	−0.232558	−	0.232558i	0.581202	−	0.813760i	$-0.302583\pi$
$757$	−6.39851	−	6.39851i	−0.232558	−	0.232558i	−0.813760	+	0.581202i	$0.802583\pi$
$758$	−5.67002	−	0.496062i	−0.205944	−	0.0180178i
$759$	17.3766	+	17.1768i	0.630732	+	0.623479i
$760$		0			0
$761$	9.16585	+	25.1830i	0.332262	+	0.912882i	0.987522	+	0.157479i	$0.0503367\pi$
$761$	9.16585	+	25.1830i	0.332262	+	0.912882i	−0.655260	+	0.755403i	$0.727441\pi$
$762$	−29.5267	+	5.38260i	−1.06964	+	0.194991i
$763$	−11.5315	−	8.07441i	−0.417467	−	0.292313i
$764$	0.516728	+	0.895000i	0.0186946	+	0.0323800i
$765$		0			0
$766$	−2.33284	+	4.04059i	−0.0842888	+	0.145993i
$767$	−1.83945	+	0.857749i	−0.0664186	+	0.0309715i
$768$	28.4057	+	4.83948i	1.02500	+	0.174630i
$769$	8.41448	−	10.0280i	0.303434	−	0.361619i	−0.592684	−	0.805435i	$-0.701932\pi$
$769$	8.41448	−	10.0280i	0.303434	−	0.361619i	0.896117	+	0.443817i	$0.146376\pi$
$770$		0			0
$771$	−28.0313	+	19.8703i	−1.00952	+	0.715611i
$772$	5.30439	+	11.3753i	0.190909	+	0.409406i
$773$	12.5218	−	3.35520i	0.450377	−	0.120678i	−0.0264987	−	0.999649i	$-0.508436\pi$
$773$	12.5218	−	3.35520i	0.450377	−	0.120678i	0.476876	+	0.878971i	$0.341769\pi$
$774$	20.0392	+	3.29494i	0.720293	+	0.118434i
$775$		0			0
$776$	13.8656	−	2.44488i	0.497747	−	0.0877662i
$777$	−2.38301	−	13.0722i	−0.0854901	−	0.468963i
$778$	4.27252	−	9.16244i	0.153177	−	0.328489i
$779$	−2.86861	+	16.2687i	−0.102778	+	0.582886i
$780$		0			0
$781$	8.63526	−	7.24584i	0.308994	−	0.259277i
$782$	18.2350	−	18.2350i	0.652082	−	0.652082i
$783$	25.3040	+	29.1150i	0.904290	+	1.04049i
$784$		−	8.79971i		−	0.314275i
$785$		0			0
$786$	−10.7667	−	39.2718i	−0.384034	−	1.40078i
$787$	−10.2457	+	7.17412i	−0.365220	+	0.255730i	−0.741753	−	0.670673i	$-0.766005\pi$
$787$	−10.2457	+	7.17412i	−0.365220	+	0.255730i	0.376533	+	0.926403i	$0.377116\pi$
$788$	−1.65163	−	0.770169i	−0.0588370	−	0.0274361i
$789$	−2.37942	+	29.1367i	−0.0847098	+	1.03729i
$790$		0			0
$791$	−0.0732857	+	0.0423115i	−0.00260574	+	0.00150443i
$792$	−14.3542	+	6.89669i	−0.510054	+	0.245063i
$793$	1.22426	+	4.56900i	0.0434748	+	0.162250i
$794$	0.996853	+	0.362825i	0.0353770	+	0.0128762i
$795$		0			0
$796$	−12.8897	−	10.8157i	−0.456862	−	0.383353i
$797$	6.53273	−	0.571540i	0.231401	−	0.0202450i	0.0291347	−	0.999575i	$-0.490725\pi$
$797$	6.53273	−	0.571540i	0.231401	−	0.0202450i	0.202267	+	0.979331i	$0.435169\pi$
$798$	4.59525	−	1.70269i	0.162670	−	0.0602747i
$799$	−4.24908	+	11.6743i	−0.150322	+	0.413006i
$800$		0			0
$801$	−16.6868	+	0.193007i	−0.589600	+	0.00681957i
$802$	2.21462	−	8.26509i	0.0782011	−	0.291851i
$803$	−8.39015	+	11.9824i	−0.296082	+	0.422849i
$804$	7.57516	+	16.0027i	0.267155	+	0.564372i
$805$		0			0
$806$	−3.27296	−	0.577111i	−0.115285	−	0.0203279i
$807$	45.7450	−	26.7648i	1.61030	−	0.942166i
$808$	2.99397	−	34.2212i	0.105327	−	1.20390i
$809$	21.1375			0.743156			0.371578	−	0.928402i	$-0.378817\pi$
$809$	21.1375			0.743156			0.371578	+	0.928402i	$0.378817\pi$
$810$		0			0
$811$	−48.6371			−1.70788			−0.853940	−	0.520371i	$-0.825794\pi$
$811$	−48.6371			−1.70788			−0.853940	+	0.520371i	$0.825794\pi$
$812$	−0.408252	+	4.66634i	−0.0143268	+	0.163756i
$813$	7.79879	−	4.56297i	0.273516	−	0.160030i
$814$	−19.8848	−	3.50622i	−0.696961	−	0.122893i
$815$		0			0
$816$	3.06104	+	6.46651i	0.107158	+	0.226373i
$817$	14.5524	−	20.7829i	0.509123	−	0.727103i
$818$	7.70100	−	28.7405i	0.269259	−	1.00489i
$819$	0.766620	+	1.29305i	0.0267879	+	0.0451829i
$820$		0			0
$821$	8.00089	−	21.9823i	0.279233	−	0.767186i	−0.718217	−	0.695819i	$-0.755042\pi$
$821$	8.00089	−	21.9823i	0.279233	−	0.767186i	0.997450	−	0.0713672i	$-0.0227362\pi$
$822$	8.83839	−	3.27492i	0.308274	−	0.114226i
$823$	3.34570	−	0.292711i	0.116624	−	0.0102033i	−0.0286943	−	0.999588i	$-0.509135\pi$
$823$	3.34570	−	0.292711i	0.116624	−	0.0102033i	0.145318	+	0.989385i	$0.453579\pi$
$824$	−11.4901	−	9.64136i	−0.400277	−	0.335873i
$825$		0			0
$826$	−1.90760	−	0.694311i	−0.0663740	−	0.0241582i
$827$	5.60974	+	20.9358i	0.195070	+	0.728010i	0.992249	+	0.124267i	$0.0396580\pi$
$827$	5.60974	+	20.9358i	0.195070	+	0.728010i	−0.797179	+	0.603743i	$0.793675\pi$
$828$	1.66788	−	21.9905i	0.0579628	−	0.764222i
$829$	4.62453	−	2.66997i	0.160617	−	0.0927320i	−0.417537	−	0.908660i	$-0.637107\pi$
$829$	4.62453	−	2.66997i	0.160617	−	0.0927320i	0.578154	+	0.815928i	$0.303773\pi$
$830$		0			0
$831$	1.64535	−	20.1477i	0.0570765	−	0.698916i
$832$	−4.96154	−	2.31360i	−0.172010	−	0.0802097i
$833$	−16.3449	+	11.4448i	−0.566317	+	0.396540i
$834$	−6.21143	−	22.6565i	−0.215084	−	0.784529i
$835$		0			0
$836$			6.22428i			0.215271i
$837$	22.5986	+	3.58168i	0.781120	+	0.123801i
$838$	18.9757	−	18.9757i	0.655504	−	0.655504i
$839$	−0.256169	+	0.214952i	−0.00884395	+	0.00742095i	−0.647199	−	0.762321i	$-0.724060\pi$
$839$	−0.256169	+	0.214952i	−0.00884395	+	0.00742095i	0.638355	+	0.769742i	$0.279615\pi$
$840$		0			0
$841$	4.53398	−	25.7135i	0.156344	−	0.886673i
$842$	−5.65161	+	12.1199i	−0.194767	+	0.417680i
$843$	4.25238	+	23.3268i	0.146460	+	0.803417i
$844$	15.0433	−	2.65254i	0.517813	−	0.0913043i
$845$		0			0
$846$	−4.48528	−	11.8934i	−0.154207	−	0.408903i
$847$	−5.31901	+	1.42522i	−0.182763	+	0.0489713i
$848$	4.76648	+	10.2217i	0.163682	+	0.351016i
$849$	12.5403	−	8.88936i	0.430383	−	0.305082i
$850$		0			0
$851$	57.4510	−	68.4675i	1.96940	−	2.34703i
$852$	−10.0301	−	1.70883i	−0.343625	−	0.0585435i
$853$	−15.6720	+	7.30797i	−0.536598	+	0.250220i	−0.671974	−	0.740574i	$-0.734554\pi$
$853$	−15.6720	+	7.30797i	−0.536598	+	0.250220i	0.135376	+	0.990794i	$0.456776\pi$
$854$	−2.36558	+	4.09731i	−0.0809486	+	0.140207i
$855$		0			0
$856$	23.9540	+	41.4895i	0.818731	+	1.41808i
$857$	8.96957	+	6.28056i	0.306395	+	0.214540i	0.716654	−	0.697429i	$-0.245673\pi$
$857$	8.96957	+	6.28056i	0.306395	+	0.214540i	−0.410259	+	0.911969i	$0.634562\pi$
$858$	2.24723	−	0.409660i	0.0767190	−	0.0139856i
$859$	9.19021	+	25.2499i	0.313566	+	0.861515i	0.991930	+	0.126789i	$0.0404671\pi$
$859$	9.19021	+	25.2499i	0.313566	+	0.861515i	−0.678364	+	0.734726i	$0.737311\pi$
$860$		0			0
$861$	−3.60456	−	3.56311i	−0.122843	−	0.121430i
$862$	5.37383	+	0.470149i	0.183033	+	0.0160133i
$863$	14.0569	+	14.0569i	0.478502	+	0.478502i	0.904652	−	0.426150i	$-0.140131\pi$
$863$	14.0569	+	14.0569i	0.478502	+	0.478502i	−0.426150	+	0.904652i	$0.640131\pi$
$864$	22.1534	+	9.86610i	0.753674	+	0.335652i
$865$		0			0
$866$	−2.60873	−	3.10897i	−0.0886484	−	0.105647i
$867$	−6.54473	+	11.4887i	−0.222271	+	0.390178i
$868$	1.59365	+	2.27597i	0.0540921	+	0.0772515i
$869$	2.67551	−	0.973806i	0.0907605	−	0.0330341i
$870$		0			0
$871$	−1.40960	−	7.99422i	−0.0477623	−	0.270874i
$872$	59.6132	+	15.9733i	2.01876	+	0.540924i
$873$	13.8639	+	1.05152i	0.469223	+	0.0355884i
$874$	28.5469	+	16.4815i	0.965612	+	0.557496i
$875$		0			0
$876$	13.1460	−	1.22677i	0.444161	−	0.0414486i
$877$	2.71444	+	31.0262i	0.0916602	+	1.04768i	0.893176	+	0.449708i	$0.148472\pi$
$877$	2.71444	+	31.0262i	0.0916602	+	1.04768i	−0.801516	+	0.597974i	$0.795973\pi$
$878$	−2.92369	−	33.4180i	−0.0986699	−	1.12780i
$879$	8.16495	−	17.7775i	0.275397	−	0.599620i
$880$		0			0
$881$	−10.7039	−	6.17988i	−0.360623	−	0.208206i	0.308731	−	0.951149i	$-0.400096\pi$
$881$	−10.7039	−	6.17988i	−0.360623	−	0.208206i	−0.669354	+	0.742944i	$0.733429\pi$
$882$	5.05544	−	19.7794i	0.170225	−	0.666008i
$883$	−34.5714	−	9.26338i	−1.16342	−	0.311738i	−0.375089	−	0.926989i	$-0.622388\pi$
$883$	−34.5714	−	9.26338i	−1.16342	−	0.311738i	−0.788331	+	0.615251i	$0.789055\pi$
$884$	0.349925	+	1.98452i	0.0117693	+	0.0667468i
$885$		0			0
$886$	15.0464	−	5.47645i	0.505494	−	0.183985i
$887$	−1.34433	−	1.91991i	−0.0451383	−	0.0644642i	0.795949	−	0.605364i	$-0.206973\pi$
$887$	−1.34433	−	1.91991i	−0.0451383	−	0.0644642i	−0.841087	+	0.540900i	$0.818084\pi$
$888$	29.4184	+	50.2803i	0.987215	+	1.68730i
$889$	−7.39472	−	8.81269i	−0.248011	−	0.295568i
$890$		0			0
$891$	−15.4200	+	3.08832i	−0.516590	+	0.103463i
$892$	12.9392	+	12.9392i	0.433236	+	0.433236i
$893$	−15.8196	−	1.38403i	−0.529382	−	0.0463149i
$894$	−5.20364	+	19.8794i	−0.174036	+	0.664866i
$895$		0			0
$896$	0.339458	+	0.932655i	0.0113405	+	0.0311578i
$897$	−3.40326	+	9.52135i	−0.113632	+	0.317909i
$898$	−2.35671	−	1.65019i	−0.0786446	−	0.0550675i
$899$	−16.3445	−	28.3095i	−0.545120	−	0.944175i
$900$		0			0
$901$	12.7870	−	22.1478i	0.425997	−	0.737849i
$902$	−6.98019	+	3.25491i	−0.232415	+	0.108377i
$903$	2.70460	+	7.29921i	0.0900034	+	0.242902i
$904$	0.238471	−	0.284198i	0.00793142	−	0.00945230i
$905$		0			0
$906$	−1.52774	−	16.3711i	−0.0507556	−	0.543895i
$907$	−23.6471	−	50.7113i	−0.785188	−	1.68384i	−0.728099	−	0.685472i	$-0.759596\pi$
$907$	−23.6471	−	50.7113i	−0.785188	−	1.68384i	−0.0570890	−	0.998369i	$-0.518182\pi$
$908$	4.09944	−	1.09844i	0.136045	−	0.0364530i
$909$	11.2329	−	32.0093i	0.372572	−	1.06168i
$910$		0			0
$911$	−26.4465	+	4.66323i	−0.876211	+	0.154500i	−0.593625	−	0.804742i	$-0.702304\pi$
$911$	−26.4465	+	4.66323i	−0.876211	+	0.154500i	−0.282587	+	0.959242i	$0.591192\pi$
$912$	−6.97133	+	5.91868i	−0.230844	+	0.195987i
$913$	1.32399	−	2.83930i	0.0438176	−	0.0939671i
$914$	6.21385	−	35.2405i	0.205536	−	1.16565i
$915$		0			0
$916$	16.9401	−	14.2144i	0.559715	−	0.469657i
$917$	11.0368	−	11.0368i	0.364467	−	0.364467i
$918$	3.16539	+	16.2936i	0.104473	+	0.537768i
$919$		−	30.8687i		−	1.01826i	−0.860688	−	0.509132i	$-0.829967\pi$
$919$		−	30.8687i		−	1.01826i	0.860688	−	0.509132i	$-0.170033\pi$
$920$		0			0
$921$	−10.3900	+	10.5109i	−0.342362	+	0.346345i
$922$	−2.60193	+	1.82189i	−0.0856900	+	0.0600008i
$923$	4.22786	+	1.97148i	0.139162	+	0.0648921i
$924$	−1.57062	−	1.08628i	−0.0516696	−	0.0357360i
$925$		0			0
$926$	24.3463	−	14.0564i	0.800070	−	0.461921i
$927$	−8.63559	−	12.0342i	−0.283630	−	0.395256i
$928$	−8.96728	−	33.4663i	−0.294365	−	1.09859i
$929$	14.1178	+	5.13847i	0.463191	+	0.168588i	0.563065	−	0.826412i	$-0.309622\pi$
$929$	14.1178	+	5.13847i	0.463191	+	0.168588i	−0.0998747	+	0.995000i	$0.531844\pi$
$930$		0			0
$931$	−19.5380	−	16.3943i	−0.640331	−	0.537301i
$932$	−6.42512	+	0.562125i	−0.210462	+	0.0184130i
$933$	4.25659	−	24.9843i	0.139354	−	0.817950i
$934$	−6.14270	+	16.8769i	−0.200995	+	0.552230i
$935$		0			0
$936$	−5.09710	−	4.17748i	−0.166604	−	0.136545i
$937$	12.0470	−	44.9601i	0.393559	−	1.46878i	−0.430660	−	0.902514i	$-0.641719\pi$
$937$	12.0470	−	44.9601i	0.393559	−	1.46878i	0.824220	−	0.566270i	$-0.191614\pi$
$938$	4.65700	−	6.65089i	0.152057	−	0.217159i
$939$	−9.18797	+	13.2846i	−0.299838	+	0.433528i
$940$		0			0
$941$	−13.0261	−	2.29686i	−0.424640	−	0.0748755i	−0.0427555	−	0.999086i	$-0.513614\pi$
$941$	−13.0261	−	2.29686i	−0.424640	−	0.0748755i	−0.381884	+	0.924210i	$0.624725\pi$
$942$	−0.0350033	−	6.05277i	−0.00114047	−	0.197210i
$943$	2.97131	−	33.9623i	0.0967593	−	1.10596i
$944$	3.78825			0.123297
$945$		0			0
$946$	11.8286			0.384581
$947$	−2.93767	+	33.5777i	−0.0954614	+	1.09113i	0.785794	+	0.618488i	$0.212255\pi$
$947$	−2.93767	+	33.5777i	−0.0954614	+	1.09113i	−0.881255	+	0.472640i	$0.843301\pi$
$948$	−2.23300	−	1.27206i	−0.0725244	−	0.0413146i
$949$	−5.96147	−	1.05117i	−0.193517	−	0.0341223i
$950$		0			0
$951$	40.7875	+	3.33089i	1.32263	+	0.108011i
$952$	−3.69529	+	5.27742i	−0.119765	+	0.171042i
$953$	−10.1544	+	37.8969i	−0.328935	+	1.22760i	0.581362	+	0.813645i	$0.302520\pi$
$953$	−10.1544	+	37.8969i	−0.328935	+	1.22760i	−0.910297	+	0.413956i	$0.864147\pi$
$954$	4.84139	+	25.7141i	0.156746	+	0.832526i
$955$		0			0
$956$	−3.61686	+	9.93723i	−0.116977	+	0.321393i
$957$	17.2945	+	14.3422i	0.559051	+	0.463617i
$958$	−36.1609	+	3.16367i	−1.16830	+	0.102213i
$959$	2.76760	+	2.32229i	0.0893705	+	0.0749908i
$960$		0			0
$961$	10.9101	+	3.97094i	0.351938	+	0.128095i
$962$	−2.16266	−	8.07116i	−0.0697270	−	0.260225i
$963$	12.7724	+	45.5532i	0.411585	+	1.46793i
$964$	8.25932	−	4.76852i	0.266015	−	0.153584i
$965$		0			0
$966$	−9.14099	+	4.32704i	−0.294106	+	0.139220i
$967$	23.1190	+	10.7806i	0.743457	+	0.346680i	0.757163	−	0.653226i	$-0.226585\pi$
$967$	23.1190	+	10.7806i	0.743457	+	0.346680i	−0.0137056	+	0.999906i	$0.504363\pi$
$968$	19.7756	−	13.8471i	0.635613	−	0.445061i
$969$	20.0604	+	5.25103i	0.644434	+	0.168687i
$970$		0			0
$971$			23.0327i			0.739156i	0.929200	+	0.369578i	$0.120498\pi$
$971$			23.0327i			0.739156i	−0.929200	+	0.369578i	$0.879502\pi$
$972$	11.1329	+	8.80589i	0.357087	+	0.282449i
$973$	6.36728	−	6.36728i	0.204126	−	0.204126i
$974$	11.5013	−	9.65070i	0.368524	−	0.309228i
$975$		0			0
$976$	1.53312	−	8.69473i	0.0490738	−	0.278312i
$977$	−0.117212	+	0.251362i	−0.00374994	+	0.00804177i	−0.908174	−	0.418593i	$-0.862523\pi$
$977$	−0.117212	+	0.251362i	−0.00374994	+	0.00804177i	0.904424	+	0.426635i	$0.140301\pi$
$978$	−24.0188	−	8.58517i	−0.768038	−	0.274523i
$979$	−9.57227	+	1.68785i	−0.305931	+	0.0539439i
$980$		0			0
$981$	53.1294	+	29.8603i	1.69629	+	0.953367i
$982$	29.6844	−	7.95391i	0.947268	−	0.253820i
$983$	3.52521	+	7.55984i	0.112437	+	0.241122i	0.954472	−	0.298302i	$-0.0964201\pi$
$983$	3.52521	+	7.55984i	0.112437	+	0.241122i	−0.842035	+	0.539423i	$0.818642\pi$
$984$	20.1924	+	9.27408i	0.643709	+	0.295647i
$985$		0			0
$986$	15.2427	−	18.1656i	0.485427	−	0.578510i
$987$	3.11012	−	3.75033i	0.0989963	−	0.119374i
$988$	−2.33447	+	1.08858i	−0.0742694	+	0.0346324i
$989$	−26.1797	+	45.3445i	−0.832465	+	1.44187i
$990$		0			0
$991$	−3.48806	−	6.04150i	−0.110802	−	0.191914i	0.805292	−	0.592878i	$-0.202009\pi$
$991$	−3.48806	−	6.04150i	−0.110802	−	0.191914i	−0.916094	+	0.400964i	$0.868675\pi$
$992$	−16.8345	−	11.7876i	−0.534494	−	0.374257i
$993$	−25.9271	−	30.5383i	−0.822773	−	0.969105i
$994$	1.59583	+	4.38451i	0.0506167	+	0.139068i
$995$		0			0
$996$	−2.72706	+	0.747643i	−0.0864103	+	0.0236900i
$997$	−54.9810	−	4.81022i	−1.74127	−	0.152341i	−0.828276	−	0.560321i	$-0.810678\pi$
$997$	−54.9810	−	4.81022i	−1.74127	−	0.152341i	−0.912991	+	0.407980i	$0.866233\pi$
$998$	13.0450	+	13.0450i	0.412933	+	0.412933i
$999$	15.8508	+	55.3001i	0.501497	+	1.74962i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.ba.b.32.11		192
5.2	odd	4		135.2.q.a.113.11	yes	192
5.3	odd	4	inner	675.2.ba.b.518.6		192
5.4	even	2		135.2.q.a.32.6	✓	192
15.2	even	4		405.2.r.a.368.6		192
15.14	odd	2		405.2.r.a.287.11		192
27.11	odd	18	inner	675.2.ba.b.632.6		192
135.38	even	36	inner	675.2.ba.b.443.11		192
135.92	even	36		135.2.q.a.38.6	yes	192
135.97	odd	36		405.2.r.a.278.11		192
135.119	odd	18		135.2.q.a.92.11	yes	192
135.124	even	18		405.2.r.a.197.6		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.6	✓	192	5.4	even	2
135.2.q.a.38.6	yes	192	135.92	even	36
135.2.q.a.92.11	yes	192	135.119	odd	18
135.2.q.a.113.11	yes	192	5.2	odd	4
405.2.r.a.197.6		192	135.124	even	18
405.2.r.a.278.11		192	135.97	odd	36
405.2.r.a.287.11		192	15.14	odd	2
405.2.r.a.368.6		192	15.2	even	4
675.2.ba.b.32.11		192	1.1	even	1	trivial
675.2.ba.b.443.11		192	135.38	even	36	inner
675.2.ba.b.518.6		192	5.3	odd	4	inner
675.2.ba.b.632.6		192	27.11	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.ba (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0909691 - 1.03978i) q^{2} +(-1.49497 + 0.874685i) q^{3} +(0.896746 + 0.158121i) q^{4} +(0.773485 + 1.63401i) q^{6} +(-0.397456 + 0.567627i) q^{7} +(0.786273 - 2.93441i) q^{8} +(1.46985 - 2.61525i) q^{9} +(0.597632 - 1.64198i) q^{11} +(-1.47891 + 0.547986i) q^{12} +(0.720360 - 0.0630233i) q^{13} +(0.554051 + 0.464904i) q^{14} +(-1.26829 - 0.461619i) q^{16} +(0.792096 + 2.95614i) q^{17} +(-2.58558 - 1.76623i) q^{18} +(-3.38781 + 1.95596i) q^{19} +(0.0976895 - 1.19623i) q^{21} +(-1.65293 - 0.770776i) q^{22} +(6.61310 - 4.63055i) q^{23} +(1.39123 + 5.07459i) q^{24} -0.754750i q^{26} +(0.0901428 + 5.19537i) q^{27} +(-0.446171 + 0.446171i) q^{28} +(5.68683 - 4.77181i) q^{29} +(0.764639 - 4.33648i) q^{31} +(1.97241 - 4.22984i) q^{32} +(0.542776 + 2.97745i) q^{33} +(3.14580 - 0.554689i) q^{34} +(1.73161 - 2.11280i) q^{36} +(10.6938 - 2.86540i) q^{37} +(1.72558 + 3.70052i) q^{38} +(-1.02179 + 0.724306i) q^{39} +(2.71443 - 3.23493i) q^{41} +(-1.23493 - 0.210396i) q^{42} +(-5.87799 + 2.74095i) q^{43} +(0.795555 - 1.37794i) q^{44} +(-4.21317 - 7.29742i) q^{46} +(3.32527 + 2.32838i) q^{47} +(2.29982 - 0.419248i) q^{48} +(2.22991 + 6.12663i) q^{49} +(-3.76985 - 3.72650i) q^{51} +(0.655945 + 0.0573878i) q^{52} +(-5.90884 - 5.90884i) q^{53} +(5.41025 + 0.378889i) q^{54} +(1.35314 + 1.61261i) q^{56} +(3.35382 - 5.88736i) q^{57} +(-4.44432 - 6.34714i) q^{58} +(-2.63750 + 0.959971i) q^{59} +(1.13591 + 6.44205i) q^{61} +(-4.43943 - 1.18954i) q^{62} +(0.900284 + 1.87378i) q^{63} +(-6.55640 - 3.78534i) q^{64} +(3.14527 - 0.293513i) q^{66} +(-0.978397 - 11.1831i) q^{67} +(0.242882 + 2.77616i) q^{68} +(-5.83610 + 12.7069i) q^{69} +(5.58689 + 3.22559i) q^{71} +(-6.51852 - 6.36945i) q^{72} +(-8.08612 - 2.16667i) q^{73} +(-2.00658 - 11.3799i) q^{74} +(-3.34729 + 1.21831i) q^{76} +(0.694499 + 0.991847i) q^{77} +(0.660168 + 1.12833i) q^{78} +(1.04738 + 1.24822i) q^{79} +(-4.67907 - 7.68806i) q^{81} +(-3.11669 - 3.11669i) q^{82} +(1.78607 + 0.156261i) q^{83} +(0.276752 - 1.05727i) q^{84} +(2.31528 + 6.36117i) q^{86} +(-4.32778 + 12.1079i) q^{87} +(-4.34834 - 3.04474i) q^{88} +(-2.78132 - 4.81739i) q^{89} +(-0.250538 + 0.433944i) q^{91} +(6.66246 - 3.10676i) q^{92} +(2.64995 + 7.15171i) q^{93} +(2.72350 - 3.24574i) q^{94} +(0.751097 + 8.04871i) q^{96} +(1.95866 + 4.20036i) q^{97} +(6.57321 - 1.76129i) q^{98} +(-3.41576 - 3.97642i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Introduction

L-functions

Modular forms

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