LMFDB - Embedded newform 675.2.ba.b.632.6

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			632.6
Character	$\chi$	$=$	675.632
Dual form			675.2.ba.b.518.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.03978 + 0.0909691i) q^{2} +(-0.874685 + 1.49497i) q^{3} +(-0.896746 + 0.158121i) q^{4} +(0.773485 - 1.63401i) q^{6} +(0.567627 - 0.397456i) q^{7} +(2.93441 - 0.786273i) q^{8} +(-1.46985 - 2.61525i) q^{9} +(0.597632 + 1.64198i) q^{11} +(0.547986 - 1.47891i) q^{12} +(0.0630233 - 0.720360i) q^{13} +(-0.554051 + 0.464904i) q^{14} +(-1.26829 + 0.461619i) q^{16} +(2.95614 + 0.792096i) q^{17} +(1.76623 + 2.58558i) q^{18} +(3.38781 + 1.95596i) q^{19} +(0.0976895 + 1.19623i) q^{21} +(-0.770776 - 1.65293i) q^{22} +(4.63055 - 6.61310i) q^{23} +(-1.39123 + 5.07459i) q^{24} +0.754750i q^{26} +(5.19537 + 0.0901428i) q^{27} +(-0.446171 + 0.446171i) q^{28} +(-5.68683 - 4.77181i) q^{29} +(0.764639 + 4.33648i) q^{31} +(-4.22984 + 1.97241i) q^{32} +(-2.97745 - 0.542776i) q^{33} +(-3.14580 - 0.554689i) q^{34} +(1.73161 + 2.11280i) q^{36} +(-2.86540 + 10.6938i) q^{37} +(-3.70052 - 1.72558i) q^{38} +(1.02179 + 0.724306i) q^{39} +(2.71443 + 3.23493i) q^{41} +(-0.210396 - 1.23493i) q^{42} +(-2.74095 + 5.87799i) q^{43} +(-0.795555 - 1.37794i) q^{44} +(-4.21317 + 7.29742i) q^{46} +(2.32838 + 3.32527i) q^{47} +(0.419248 - 2.29982i) q^{48} +(-2.22991 + 6.12663i) q^{49} +(-3.76985 + 3.72650i) q^{51} +(0.0573878 + 0.655945i) q^{52} +(5.90884 + 5.90884i) q^{53} +(-5.41025 + 0.378889i) q^{54} +(1.35314 - 1.61261i) q^{56} +(-5.88736 + 3.35382i) q^{57} +(6.34714 + 4.44432i) q^{58} +(2.63750 + 0.959971i) q^{59} +(1.13591 - 6.44205i) q^{61} +(-1.18954 - 4.43943i) q^{62} +(-1.87378 - 0.900284i) q^{63} +(6.55640 - 3.78534i) q^{64} +(3.14527 + 0.293513i) q^{66} +(-11.1831 - 0.978397i) q^{67} +(-2.77616 - 0.242882i) q^{68} +(5.83610 + 12.7069i) q^{69} +(5.58689 - 3.22559i) q^{71} +(-6.36945 - 6.51852i) q^{72} +(2.16667 + 8.08612i) q^{73} +(2.00658 - 11.3799i) q^{74} +(-3.34729 - 1.21831i) q^{76} +(0.991847 + 0.694499i) q^{77} +(-1.12833 - 0.660168i) q^{78} +(-1.04738 + 1.24822i) q^{79} +(-4.67907 + 7.68806i) q^{81} +(-3.11669 - 3.11669i) q^{82} +(-0.156261 - 1.78607i) q^{83} +(-0.276752 - 1.05727i) q^{84} +(2.31528 - 6.36117i) q^{86} +(12.1079 - 4.32778i) q^{87} +(3.04474 + 4.34834i) q^{88} +(2.78132 - 4.81739i) q^{89} +(-0.250538 - 0.433944i) q^{91} +(-3.10676 + 6.66246i) q^{92} +(-7.15171 - 2.64995i) q^{93} +(-2.72350 - 3.24574i) q^{94} +(0.751097 - 8.04871i) q^{96} +(4.20036 + 1.95866i) q^{97} +(1.76129 - 6.57321i) 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 $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.03978	+	0.0909691i	−0.735236	+	0.0643248i	−0.448622	−	0.893721i	$-0.648085\pi$
$2$	−1.03978	+	0.0909691i	−0.735236	+	0.0643248i	−0.286614	+	0.958046i	$0.592530\pi$
$3$	−0.874685	+	1.49497i	−0.505000	+	0.863119i
$3$	−0.874685	+	1.49497i	−0.505000	+	0.863119i
$4$	−0.896746	+	0.158121i	−0.448373	+	0.0790603i
$5$		0			0
$5$		0			0
$6$	0.773485	−	1.63401i	0.315774	−	0.667081i
$7$	0.567627	−	0.397456i	0.214543	−	0.150224i	−0.461366	−	0.887210i	$-0.652640\pi$
$7$	0.567627	−	0.397456i	0.214543	−	0.150224i	0.675908	+	0.736986i	$0.263751\pi$
$8$	2.93441	−	0.786273i	1.03747	−	0.277990i
$9$	−1.46985	−	2.61525i	−0.489950	−	0.871750i
$10$		0			0
$11$	0.597632	+	1.64198i	0.180193	+	0.495076i	0.996599	−	0.0824022i	$-0.0262592\pi$
$11$	0.597632	+	1.64198i	0.180193	+	0.495076i	−0.816406	+	0.577478i	$0.804037\pi$
$12$	0.547986	−	1.47891i	0.158190	−	0.426925i
$13$	0.0630233	−	0.720360i	0.0174795	−	0.199792i	−0.982434	−	0.186612i	$-0.940249\pi$
$13$	0.0630233	−	0.720360i	0.0174795	−	0.199792i	0.999913	−	0.0131795i	$-0.00419529\pi$
$14$	−0.554051	+	0.464904i	−0.148076	+	0.124251i
$15$		0			0
$16$	−1.26829	+	0.461619i	−0.317072	+	0.115405i
$17$	2.95614	+	0.792096i	0.716970	+	0.192112i	0.598819	−	0.800884i	$-0.295637\pi$
$17$	2.95614	+	0.792096i	0.716970	+	0.192112i	0.118151	+	0.992996i	$0.462303\pi$
$18$	1.76623	+	2.58558i	0.416304	+	0.609426i
$19$	3.38781	+	1.95596i	0.777218	+	0.448727i	0.835443	−	0.549576i	$-0.185211\pi$
$19$	3.38781	+	1.95596i	0.777218	+	0.448727i	−0.0582254	+	0.998303i	$0.518544\pi$
$20$		0			0
$21$	0.0976895	+	1.19623i	0.0213176	+	0.261039i
$22$	−0.770776	−	1.65293i	−0.164330	−	0.352407i
$23$	4.63055	−	6.61310i	0.965535	−	1.37893i	0.0404446	−	0.999182i	$-0.487123\pi$
$23$	4.63055	−	6.61310i	0.965535	−	1.37893i	0.925091	−	0.379746i	$-0.123989\pi$
$24$	−1.39123	+	5.07459i	−0.283985	+	1.03585i
$25$		0			0
$26$			0.754750i			0.148019i
$27$	5.19537	+	0.0901428i	0.999850	+	0.0173480i
$28$	−0.446171	+	0.446171i	−0.0843184	+	0.0843184i
$29$	−5.68683	−	4.77181i	−1.05602	−	0.886103i	−0.0623035	−	0.998057i	$-0.519845\pi$
$29$	−5.68683	−	4.77181i	−1.05602	−	0.886103i	−0.993713	+	0.111954i	$0.964289\pi$
$30$		0			0
$31$	0.764639	+	4.33648i	0.137333	+	0.778855i	0.973207	+	0.229933i	$0.0738506\pi$
$31$	0.764639	+	4.33648i	0.137333	+	0.778855i	−0.835873	+	0.548922i	$0.815038\pi$
$32$	−4.22984	+	1.97241i	−0.747738	+	0.348676i
$33$	−2.97745	−	0.542776i	−0.518307	−	0.0944852i
$34$	−3.14580	−	0.554689i	−0.539500	−	0.0951284i
$35$		0			0
$36$	1.73161	+	2.11280i	0.288601	+	0.352134i
$37$	−2.86540	+	10.6938i	−0.471069	+	1.75805i	0.164870	+	0.986315i	$0.447280\pi$
$37$	−2.86540	+	10.6938i	−0.471069	+	1.75805i	−0.635939	+	0.771739i	$0.719387\pi$
$38$	−3.70052	−	1.72558i	−0.600303	−	0.279926i
$39$	1.02179	+	0.724306i	0.163617	+	0.115982i
$40$		0			0
$41$	2.71443	+	3.23493i	0.423923	+	0.505212i	0.935159	−	0.354229i	$-0.115257\pi$
$41$	2.71443	+	3.23493i	0.423923	+	0.505212i	−0.511236	+	0.859441i	$0.670812\pi$
$42$	−0.210396	−	1.23493i	−0.0324648	−	0.190554i
$43$	−2.74095	+	5.87799i	−0.417991	+	0.896385i	0.578733	+	0.815517i	$0.303547\pi$
$43$	−2.74095	+	5.87799i	−0.417991	+	0.896385i	−0.996725	+	0.0808685i	$0.974231\pi$
$44$	−0.795555	−	1.37794i	−0.119934	−	0.207733i
$45$		0			0
$46$	−4.21317	+	7.29742i	−0.621197	+	1.07595i
$47$	2.32838	+	3.32527i	0.339628	+	0.485040i	0.952243	−	0.305342i	$-0.0987709\pi$
$47$	2.32838	+	3.32527i	0.339628	+	0.485040i	−0.612614	+	0.790382i	$0.709882\pi$
$48$	0.419248	−	2.29982i	0.0605132	−	0.331950i
$49$	−2.22991	+	6.12663i	−0.318559	+	0.875234i
$50$		0			0
$51$	−3.76985	+	3.72650i	−0.527885	+	0.521815i
$52$	0.0573878	+	0.655945i	0.00795825	+	0.0909632i
$53$	5.90884	+	5.90884i	0.811642	+	0.811642i	0.984880	−	0.173238i	$-0.0554230\pi$
$53$	5.90884	+	5.90884i	0.811642	+	0.811642i	−0.173238	+	0.984880i	$0.555423\pi$
$54$	−5.41025	+	0.378889i	−0.736241	+	0.0515603i
$55$		0			0
$56$	1.35314	−	1.61261i	0.180821	−	0.215494i
$57$	−5.88736	+	3.35382i	−0.779800	+	0.444225i
$58$	6.34714	+	4.44432i	0.833420	+	0.583567i
$59$	2.63750	+	0.959971i	0.343373	+	0.124978i	0.507950	−	0.861387i	$-0.330404\pi$
$59$	2.63750	+	0.959971i	0.343373	+	0.124978i	−0.164577	+	0.986364i	$0.552626\pi$
$60$		0			0
$61$	1.13591	−	6.44205i	0.145438	−	0.824820i	−0.821576	−	0.570098i	$-0.806905\pi$
$61$	1.13591	−	6.44205i	0.145438	−	0.824820i	0.967014	−	0.254722i	$-0.0819838\pi$
$62$	−1.18954	−	4.43943i	−0.151072	−	0.563808i
$63$	−1.87378	−	0.900284i	−0.236073	−	0.113425i
$64$	6.55640	−	3.78534i	0.819551	−	0.473168i
$65$		0			0
$66$	3.14527	+	0.293513i	0.387156	+	0.0361289i
$67$	−11.1831	−	0.978397i	−1.36624	−	0.119530i	−0.619682	−	0.784853i	$-0.712738\pi$
$67$	−11.1831	−	0.978397i	−1.36624	−	0.119530i	−0.746556	+	0.665323i	$0.768294\pi$
$68$	−2.77616	−	0.242882i	−0.336659	−	0.0294538i
$69$	5.83610	+	12.7069i	0.702584	+	1.52973i
$70$		0			0
$71$	5.58689	−	3.22559i	0.663042	−	0.382807i	−0.130393	−	0.991462i	$-0.541624\pi$
$71$	5.58689	−	3.22559i	0.663042	−	0.382807i	0.793435	+	0.608655i	$0.208291\pi$
$72$	−6.36945	−	6.51852i	−0.750647	−	0.768215i
$73$	2.16667	+	8.08612i	0.253589	+	0.946409i	0.968870	+	0.247571i	$0.0796324\pi$
$73$	2.16667	+	8.08612i	0.253589	+	0.946409i	−0.715280	+	0.698838i	$0.753701\pi$
$74$	2.00658	−	11.3799i	0.233261	−	1.32289i
$75$		0			0
$76$	−3.34729	−	1.21831i	−0.383960	−	0.139750i
$77$	0.991847	+	0.694499i	0.113032	+	0.0791455i
$78$	−1.12833	−	0.660168i	−0.127758	−	0.0747494i
$79$	−1.04738	+	1.24822i	−0.117840	+	0.140436i	−0.821739	−	0.569863i	$-0.806996\pi$
$79$	−1.04738	+	1.24822i	−0.117840	+	0.140436i	0.703899	+	0.710300i	$0.251441\pi$
$80$		0			0
$81$	−4.67907	+	7.68806i	−0.519897	+	0.854229i
$82$	−3.11669	−	3.11669i	−0.344181	−	0.344181i
$83$	−0.156261	−	1.78607i	−0.0171518	−	0.196046i	−0.999936	−	0.0112903i	$-0.996406\pi$
$83$	−0.156261	−	1.78607i	−0.0171518	−	0.196046i	0.982784	−	0.184756i	$-0.0591494\pi$
$84$	−0.276752	−	1.05727i	−0.0301961	−	0.115358i
$85$		0			0
$86$	2.31528	−	6.36117i	0.249663	−	0.685942i
$87$	12.1079	−	4.32778i	1.29810	−	0.463987i
$88$	3.04474	+	4.34834i	0.324571	+	0.463535i
$89$	2.78132	−	4.81739i	0.294820	−	0.510643i	−0.680123	−	0.733098i	$-0.738074\pi$
$89$	2.78132	−	4.81739i	0.294820	−	0.510643i	0.974943	+	0.222455i	$0.0714071\pi$
$90$		0			0
$91$	−0.250538	−	0.433944i	−0.0262635	−	0.0454897i
$92$	−3.10676	+	6.66246i	−0.323902	+	0.694610i
$93$	−7.15171	−	2.64995i	−0.741598	−	0.274787i
$94$	−2.72350	−	3.24574i	−0.280907	−	0.334772i
$95$		0			0
$96$	0.751097	−	8.04871i	0.0766585	−	0.821468i
$97$	4.20036	+	1.95866i	0.426482	+	0.198872i	0.623995	−	0.781429i	$-0.285509\pi$
$97$	4.20036	+	1.95866i	0.426482	+	0.198872i	−0.197513	+	0.980300i	$0.563286\pi$
$98$	1.76129	−	6.57321i	0.177917	−	0.663995i
$99$	3.41576	−	3.97642i	0.343297	−	0.399646i
$100$		0			0
$101$	11.1359	+	1.96356i	1.10806	+	0.195381i	0.697594	−	0.716493i	$-0.254254\pi$
$101$	11.1359	+	1.96356i	1.10806	+	0.195381i	0.410469	+	0.911875i	$0.365365\pi$
$102$	3.58083	−	4.21769i	0.354555	−	0.417613i
$103$	4.47475	−	2.08661i	0.440911	−	0.205600i	−0.189470	−	0.981887i	$-0.560677\pi$
$103$	4.47475	−	2.08661i	0.440911	−	0.205600i	0.630380	+	0.776287i	$0.282899\pi$
$104$	−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	$-0.474085\pi$
$107$	11.1511	−	11.1511i	1.07801	−	1.07801i	0.996688	−	0.0813251i	$-0.0259152\pi$
$108$	−4.67318	+	0.740660i	−0.449677	+	0.0712700i
$109$			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
$112$	−0.536441	+	0.766117i	−0.0506889	+	0.0723912i
$113$	−0.0516106	−	0.110679i	−0.00485512	−	0.0104118i	0.903865	−	0.427817i	$-0.140717\pi$
$113$	−0.0516106	−	0.110679i	−0.00485512	−	0.0104118i	−0.908720	+	0.417405i	$0.862940\pi$
$114$	5.81647	−	4.02281i	0.544763	−	0.376771i
$115$		0			0
$116$	5.85416	+	3.37990i	0.543545	+	0.313816i
$117$	−1.97656	+	0.894000i	−0.182733	+	0.0826503i
$118$	−2.82975	−	0.758229i	−0.260500	−	0.0698006i
$119$	1.99281	−	0.725323i	0.182681	−	0.0664903i
$120$		0			0
$121$	6.08755	−	5.10806i	0.553414	−	0.464369i
$122$	−0.595068	+	6.80165i	−0.0538749	+	0.615793i
$123$	−7.21039	+	1.22844i	−0.650139	+	0.110764i
$124$	−1.37137	−	3.76782i	−0.123153	−	0.338360i
$125$		0			0
$126$	2.03021	+	0.765643i	0.180866	+	0.0682089i
$127$	16.0361	−	4.29687i	1.42298	−	0.381286i	0.536439	−	0.843939i	$-0.319769\pi$
$127$	16.0361	−	4.29687i	1.42298	−	0.381286i	0.886539	+	0.462654i	$0.153103\pi$
$128$	1.17328	−	0.821539i	0.103704	−	0.0726144i
$129$	−6.38993	−	9.23903i	−0.562602	−	0.813451i
$130$		0			0
$131$	−22.1825	+	3.91138i	−1.93810	+	0.341739i	−0.999989	−	0.00460251i	$-0.998535\pi$
$131$	−22.1825	+	3.91138i	−1.93810	+	0.341739i	−0.938109	+	0.346341i	$0.887424\pi$
$132$	2.75584	+	0.0159371i	0.239865	+	0.00138714i
$133$	2.70042	−	0.236256i	0.234156	−	0.0204860i
$134$	11.7170			1.01220
$135$		0			0
$136$	9.29735			0.797241
$137$	−5.19392	+	0.454409i	−0.443747	+	0.0388228i	−0.306840	−	0.951761i	$-0.599272\pi$
$137$	−5.19392	+	0.454409i	−0.443747	+	0.0388228i	−0.136907	+	0.990584i	$0.543716\pi$
$138$	−7.22420	−	12.6815i	−0.614965	−	1.07952i
$139$	12.7974	−	2.25653i	1.08546	−	0.191396i	0.397833	−	0.917458i	$-0.369762\pi$
$139$	12.7974	−	2.25653i	1.08546	−	0.191396i	0.687630	+	0.726061i	$0.258651\pi$
$140$		0			0
$141$	−7.00776	+	0.572284i	−0.590160	+	0.0481950i
$142$	−5.51571	+	3.86214i	−0.462868	+	0.324104i
$143$	1.22048	−	0.327027i	0.102062	−	0.0273474i
$144$	3.07144	+	2.63838i	0.255954	+	0.219865i
$145$		0			0
$146$	−2.98845	−	8.21069i	−0.247326	−	0.679522i
$147$	−7.20864	−	8.69252i	−0.594559	−	0.716947i
$148$	0.878625	−	10.0427i	0.0722225	−	0.825507i
$149$	−8.70742	+	7.30639i	−0.713340	+	0.598563i	−0.925534	−	0.378664i	$-0.876383\pi$
$149$	−8.70742	+	7.30639i	−0.713340	+	0.598563i	0.212194	+	0.977227i	$0.431939\pi$
$150$		0			0
$151$	−8.54652	+	3.11068i	−0.695506	+	0.253143i	−0.665491	−	0.746406i	$-0.731778\pi$
$151$	−8.54652	+	3.11068i	−0.695506	+	0.253143i	−0.0300149	+	0.999549i	$0.509555\pi$
$152$	11.4792	+	3.07583i	0.931083	+	0.249483i
$153$	−2.27356	−	8.89532i	−0.183806	−	0.719144i
$154$	−1.09448	−	0.631900i	−0.0881959	−	0.0509199i
$155$		0			0
$156$	−1.03081	−	0.487953i	−0.0825311	−	0.0390675i
$157$	−1.41498	−	3.03444i	−0.112928	−	0.242175i	0.841718	−	0.539917i	$-0.181544\pi$
$157$	−1.41498	−	3.03444i	−0.112928	−	0.242175i	−0.954646	+	0.297742i	$0.903767\pi$
$158$	0.975501	−	1.39316i	0.0776067	−	0.110834i
$159$	−14.0019	+	3.66515i	−1.11042	+	0.290665i
$160$		0			0
$161$		−	5.59421i		−	0.440886i
$162$	4.16584	−	8.41955i	0.327299	−	0.661502i
$163$	−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
$167$	12.6150	−	5.88249i	0.976182	−	0.455201i	0.131995	−	0.991250i	$-0.457862\pi$
$167$	12.6150	−	5.88249i	0.976182	−	0.455201i	0.844187	+	0.536049i	$0.180084\pi$
$168$	1.22723	+	3.43343i	0.0946826	+	0.264895i
$169$	12.2876	+	2.16663i	0.945196	+	0.166664i
$170$		0			0
$171$	0.135731	−	11.7350i	0.0103796	−	0.897394i
$172$	1.52851	−	5.70447i	0.116548	−	0.434962i
$173$	2.81939	+	1.31470i	0.214354	+	0.0999551i	0.526830	−	0.849971i	$-0.323380\pi$
$173$	2.81939	+	1.31470i	0.214354	+	0.0999551i	−0.312476	+	0.949926i	$0.601158\pi$
$174$	−12.1959	+	5.60139i	−0.924565	+	0.424640i
$175$		0			0
$176$	−1.51594	−	1.80663i	−0.114268	−	0.136180i
$177$	−3.74211	+	3.10330i	−0.281274	+	0.233258i
$178$	−2.45373	+	5.26205i	−0.183915	+	0.394407i
$179$	2.53650	+	4.39334i	0.189587	+	0.328374i	0.945113	−	0.326745i	$-0.105952\pi$
$179$	2.53650	+	4.39334i	0.189587	+	0.328374i	−0.755526	+	0.655119i	$0.772619\pi$
$180$		0			0
$181$	−4.66805	+	8.08530i	−0.346974	+	0.600976i	−0.985710	−	0.168449i	$-0.946124\pi$
$181$	−4.66805	+	8.08530i	−0.346974	+	0.600976i	0.638737	+	0.769425i	$0.279457\pi$
$182$	0.299980	+	0.428416i	0.0222360	+	0.0317563i
$183$	8.63709	+	7.33291i	0.638472	+	0.542064i
$184$	8.38822	−	23.0464i	0.618388	−	1.69901i
$185$		0			0
$186$	7.67728	+	2.10478i	0.562925	+	0.154330i
$187$	0.466079	+	5.32731i	0.0340831	+	0.389572i
$188$	−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	−0.739005	−	0.673700i	$-0.764704\pi$
$191$	0.729528	−	0.869417i	0.0527868	−	0.0629088i	0.791792	+	0.610791i	$0.209148\pi$
$192$	−0.0758304	+	13.1126i	−0.00547259	+	0.946320i
$193$	−11.2910	−	7.90607i	−0.812746	−	0.569091i	0.0916467	−	0.995792i	$-0.470787\pi$
$193$	−11.2910	−	7.90607i	−0.812746	−	0.569091i	−0.904393	+	0.426701i	$0.859676\pi$
$194$	−4.54563	−	1.65447i	−0.326357	−	0.118784i
$195$		0			0
$196$	1.03092	−	5.84663i	0.0736371	−	0.417617i
$197$	−0.517983	−	1.93314i	−0.0369048	−	0.137730i	0.945015	−	0.327026i	$-0.106046\pi$
$197$	−0.517983	−	1.93314i	−0.0369048	−	0.137730i	−0.981920	+	0.189295i	$0.939380\pi$
$198$	−3.18991	+	4.44534i	−0.226697	+	0.315916i
$199$	16.0030	−	9.23931i	1.13442	−	0.654957i	0.189377	−	0.981905i	$-0.439353\pi$
$199$	16.0030	−	9.23931i	1.13442	−	0.654957i	0.945043	+	0.326947i	$0.106020\pi$
$200$		0			0
$201$	11.2444	−	15.8626i	0.793118	−	1.11886i
$202$	−11.7575	−	1.02865i	−0.827256	−	0.0723755i
$203$	−5.12458	−	0.448343i	−0.359675	−	0.0314675i
$204$	2.79136	−	3.93782i	0.195435	−	0.275702i
$205$		0			0
$206$	−4.46295	+	2.57668i	−0.310948	+	0.179526i
$207$	−24.1011	−	2.38976i	−1.67515	−	0.166100i
$208$	0.252600	+	0.942717i	0.0175147	+	0.0653656i
$209$	−1.18697	+	6.73167i	−0.0821047	+	0.465639i
$210$		0			0
$211$	15.7638	+	5.73754i	1.08522	+	0.394989i	0.821849	−	0.569705i	$-0.192943\pi$
$211$	15.7638	+	5.73754i	1.08522	+	0.394989i	0.263374	+	0.964694i	$0.415165\pi$
$212$	−6.23304	−	4.36442i	−0.428087	−	0.299750i
$213$	−0.0646171	+	11.1736i	−0.00442749	+	0.765602i
$214$	−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
$218$	−1.84806	−	21.1234i	−0.125166	−	1.43066i
$219$	−13.9836	−	3.83371i	−0.944926	−	0.259058i
$220$		0			0
$221$	0.756900	−	2.07957i	0.0509146	−	0.139887i
$222$	15.2574	+	12.9536i	1.02401	+	0.869389i
$223$	−11.5264	−	16.4615i	−0.771868	−	1.10234i	−0.991921	−	0.126854i	$-0.959512\pi$
$223$	−11.5264	−	16.4615i	−0.771868	−	1.10234i	0.220054	−	0.975488i	$-0.429377\pi$
$224$	−1.61703	+	2.80077i	−0.108042	+	0.187134i
$225$		0			0
$226$	0.0637321	+	0.110387i	0.00423940	+	0.00734285i
$227$	−1.96975	+	4.22414i	−0.130737	+	0.280366i	−0.960769	−	0.277349i	$-0.910544\pi$
$227$	−1.96975	+	4.22414i	−0.130737	+	0.280366i	0.830032	+	0.557715i	$0.188322\pi$
$228$	4.74916	−	3.93844i	0.314521	−	0.260830i
$229$	−15.6103	−	18.6036i	−1.03156	−	1.22936i	−0.972935	−	0.231080i	$-0.925774\pi$
$229$	−15.6103	−	18.6036i	−1.03156	−	1.22936i	−0.0586205	−	0.998280i	$-0.518670\pi$
$230$		0			0
$231$	−1.90581	+	0.875311i	−0.125393	+	0.0575912i
$232$	−20.4394	−	9.53106i	−1.34191	−	0.625745i
$233$	−1.83322	+	6.84167i	−0.120098	+	0.448213i	−0.999618	−	0.0276501i	$-0.991198\pi$
$233$	−1.83322	+	6.84167i	−0.120098	+	0.448213i	0.879519	+	0.475863i	$0.157864\pi$
$234$	1.97386	−	1.10937i	0.129035	−	0.0725218i
$235$		0			0
$236$	−2.51696	−	0.443808i	−0.163840	−	0.0288894i
$237$	−0.949922	−	2.65761i	−0.0617041	−	0.172630i
$238$	−2.00610	+	0.935462i	−0.130036	+	0.0606370i
$239$	2.01666	+	11.4370i	0.130447	+	0.739799i	0.977923	+	0.208966i	$0.0670098\pi$
$239$	2.01666	+	11.4370i	0.130447	+	0.739799i	−0.847476	+	0.530833i	$0.821879\pi$
$240$		0			0
$241$	8.02324	+	6.73230i	0.516822	+	0.433665i	0.863522	−	0.504311i	$-0.168253\pi$
$241$	8.02324	+	6.73230i	0.516822	+	0.433665i	−0.346700	+	0.937976i	$0.612698\pi$
$242$	−5.86505	+	5.86505i	−0.377020	+	0.377020i
$243$	−7.40068	−	13.7197i	−0.474754	−	0.880119i
$244$			5.95649i			0.381325i
$245$		0			0
$246$	7.38548	−	1.93323i	0.470881	−	0.123258i
$247$	1.62250	−	2.31717i	0.103237	−	0.147438i
$248$	5.65342	+	12.1238i	0.358993	+	0.769862i
$249$	2.80679	+	1.32864i	0.177873	+	0.0841992i
$250$		0			0
$251$	−9.75413	−	5.63155i	−0.615675	−	0.355460i	0.159508	−	0.987197i	$-0.449009\pi$
$251$	−9.75413	−	5.63155i	−0.615675	−	0.355460i	−0.775183	+	0.631736i	$0.782343\pi$
$252$	1.82265	+	0.511044i	0.114816	+	0.0321928i
$253$	13.6259	+	3.65106i	0.856656	+	0.229540i
$254$	−16.2832	+	5.92660i	−1.02170	+	0.371868i
$255$		0			0
$256$	−12.7442	+	10.6936i	−0.796511	+	0.668352i
$257$	−1.72895	+	19.7620i	−0.107849	+	1.23272i	0.728701	+	0.684832i	$0.240124\pi$
$257$	−1.72895	+	19.7620i	−0.107849	+	1.23272i	−0.836551	+	0.547890i	$0.815431\pi$
$258$	7.48459	+	9.02528i	0.465970	+	0.561889i
$259$	2.62385	+	7.20897i	0.163038	+	0.447944i
$260$		0			0
$261$	−4.12070	+	21.8863i	−0.255065	+	1.35473i
$262$	22.7092	−	6.08491i	1.40298	−	0.375927i
$263$	13.8257	−	9.68085i	0.852529	−	0.596947i	−0.0635351	−	0.997980i	$-0.520237\pi$
$263$	13.8257	−	9.68085i	0.852529	−	0.596947i	0.916064	+	0.401033i	$0.131349\pi$
$264$	−9.16382	+	0.748357i	−0.563994	+	0.0460582i
$265$		0			0
$266$	−2.78635	+	0.491310i	−0.170842	+	0.0301241i
$267$	4.76906	+	8.37169i	0.291862	+	0.512339i
$268$	10.1831	−	0.890909i	0.622034	−	0.0544209i
$269$	30.5994			1.86568			0.932838	−	0.360296i	$-0.117324\pi$
$269$	30.5994			1.86568			0.932838	+	0.360296i	$0.117324\pi$
$270$		0			0
$271$	−5.21670			−0.316892			−0.158446	−	0.987368i	$-0.550648\pi$
$271$	−5.21670			−0.316892			−0.158446	+	0.987368i	$0.550648\pi$
$272$	−4.11489	+	0.360006i	−0.249502	+	0.0218286i
$273$	0.867874	+	0.00501894i	0.0525262	+	0.000303760i
$274$	5.35921	−	0.944973i	0.323761	−	0.0570879i
$275$		0			0
$276$	−7.24272	−	10.4721i	−0.435961	−	0.630344i
$277$	9.56033	−	6.69422i	0.574425	−	0.402216i	−0.249952	−	0.968258i	$-0.580415\pi$
$277$	9.56033	−	6.69422i	0.574425	−	0.402216i	0.824377	+	0.566042i	$0.191526\pi$
$278$	−13.1012	+	3.51047i	−0.785760	+	0.210544i
$279$	10.2171	−	8.37370i	0.611681	−	0.501320i
$280$		0			0
$281$	4.68215	+	12.8641i	0.279313	+	0.767407i	0.997441	+	0.0714958i	$0.0227772\pi$
$281$	4.68215	+	12.8641i	0.279313	+	0.767407i	−0.718127	+	0.695912i	$0.755001\pi$
$282$	7.23447	−	1.23254i	0.430807	−	0.0733966i
$283$	−0.773481	+	8.84093i	−0.0459787	+	0.525539i	0.937925	+	0.346838i	$0.112745\pi$
$283$	−0.773481	+	8.84093i	−0.0459787	+	0.525539i	−0.983904	+	0.178700i	$0.942811\pi$
$284$	−4.49999	+	3.77594i	−0.267025	+	0.224061i
$285$		0			0
$286$	−1.23928	+	0.451062i	−0.0732804	+	0.0266719i
$287$	2.82653	+	0.757366i	0.166845	+	0.0447059i
$288$	11.3756	+	8.16295i	0.670313	+	0.481007i
$289$	−6.61106	−	3.81690i	−0.388886	−	0.224524i
$290$		0			0
$291$	−6.60212	+	4.56619i	−0.387023	+	0.267675i
$292$	−3.22153	−	6.90860i	−0.188526	−	0.404295i
$293$	−6.47833	+	9.25201i	−0.378468	+	0.540508i	−0.962521	−	0.271207i	$-0.912577\pi$
$293$	−6.47833	+	9.25201i	−0.378468	+	0.540508i	0.584053	+	0.811716i	$0.301466\pi$
$294$	8.28616	+	8.38256i	0.483259	+	0.488881i
$295$		0			0
$296$			33.6331i			1.95488i
$297$	2.95691	+	8.58457i	0.171577	+	0.498127i
$298$	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
$302$	8.60353	−	4.01189i	0.495078	−	0.230858i
$303$	−12.6759	+	14.9303i	−0.728209	+	0.857723i
$304$	−5.19963	−	0.916835i	−0.298219	−	0.0525841i
$305$		0			0
$306$	3.17320	+	9.04236i	0.181400	+	0.516917i
$307$	−2.20847	+	8.24213i	−0.126044	+	0.470403i	−0.999875	−	0.0158274i	$-0.994962\pi$
$307$	−2.20847	+	8.24213i	−0.126044	+	0.470403i	0.873831	+	0.486230i	$0.161628\pi$
$308$	−0.999250	−	0.465958i	−0.0569376	−	0.0265504i
$309$	−0.794586	+	8.51474i	−0.0452024	+	0.484386i
$310$		0			0
$311$	−9.40563	−	11.2092i	−0.533344	−	0.635615i	0.430338	−	0.902668i	$-0.358394\pi$
$311$	−9.40563	−	11.2092i	−0.533344	−	0.635615i	−0.963682	+	0.267053i	$0.913950\pi$
$312$	3.56785	+	1.32201i	0.201990	+	0.0748439i
$313$	3.94117	−	8.45186i	0.222768	−	0.477727i	−0.762880	−	0.646540i	$-0.776215\pi$
$313$	3.94117	−	8.45186i	0.222768	−	0.477727i	0.985648	+	0.168812i	$0.0539932\pi$
$314$	1.74731	+	3.02644i	0.0986067	+	0.170792i
$315$		0			0
$316$	0.741868	−	1.28495i	0.0417333	−	0.0722843i
$317$	−13.5519	−	19.3542i	−0.761152	−	1.08704i	−0.993436	−	0.114390i	$-0.963509\pi$
$317$	−13.5519	−	19.3542i	−0.761152	−	1.08704i	0.232283	−	0.972648i	$-0.425380\pi$
$318$	14.2255	−	5.08469i	0.797726	−	0.285135i
$319$	4.43659	−	12.1894i	0.248402	−	0.682478i
$320$		0			0
$321$	6.91679	+	26.4241i	0.386058	+	1.47485i
$322$	0.508900	+	5.81676i	0.0283599	+	0.324155i
$323$	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
$327$	−30.3706	−	17.7694i	−1.67950	−	0.982651i
$328$	10.5088	+	7.35834i	0.580252	+	0.406297i
$329$	2.64330	+	0.962081i	0.145730	+	0.0530413i
$330$		0			0
$331$	4.01625	−	22.7773i	0.220753	−	1.25195i	−0.649886	−	0.760032i	$-0.725183\pi$
$331$	4.01625	−	22.7773i	0.220753	−	1.25195i	0.870639	−	0.491922i	$-0.163705\pi$
$332$	0.422540	+	1.57694i	0.0231899	+	0.0865458i
$333$	32.1788	−	8.22459i	1.76338	−	0.450705i
$334$	−12.5818	+	7.26408i	−0.688443	+	0.397473i
$335$		0			0
$336$	−0.676102	−	1.47207i	−0.0368844	−	0.0803081i
$337$	12.4168	+	1.08633i	0.676384	+	0.0591760i	0.420172	−	0.907445i	$-0.361970\pi$
$337$	12.4168	+	1.08633i	0.676384	+	0.0591760i	0.256212	+	0.966621i	$0.417525\pi$
$338$	−12.9735	−	1.13503i	−0.705663	−	0.0617375i
$339$	0.210605	+	0.0196534i	0.0114385	+	0.00106743i
$340$		0			0
$341$	−6.66344	+	3.84714i	−0.360846	+	0.208334i
$342$	0.926386	+	12.2141i	0.0500932	+	0.660464i
$343$	2.42474	+	9.04926i	0.130924	+	0.488614i
$344$	−3.42137	+	19.4036i	−0.184468	+	1.04617i
$345$		0			0
$346$	−3.05115	−	1.11053i	−0.164031	−	0.0597023i
$347$	−9.36840	−	6.55983i	−0.502922	−	0.352150i	0.294421	−	0.955676i	$-0.404873\pi$
$347$	−9.36840	−	6.55983i	−0.502922	−	0.352150i	−0.797343	+	0.603526i	$0.793762\pi$
$348$	−10.1734	+	5.79543i	−0.545351	+	0.310667i
$349$	−15.6113	+	18.6048i	−0.835652	+	0.995891i	0.164303	+	0.986410i	$0.447462\pi$
$349$	−15.6113	+	18.6048i	−0.835652	+	0.995891i	−0.999955	+	0.00948135i	$0.996982\pi$
$350$		0			0
$351$	0.392365	−	3.73686i	0.0209429	−	0.199459i
$352$	−5.76654	−	5.76654i	−0.307358	−	0.307358i
$353$	2.92059	+	33.3825i	0.155447	+	1.77677i	0.528472	+	0.848951i	$0.322765\pi$
$353$	2.92059	+	33.3825i	0.155447	+	1.77677i	−0.373024	+	0.927822i	$0.621679\pi$
$354$	3.60867	−	3.56717i	0.191799	−	0.189593i
$355$		0			0
$356$	−1.73241	+	4.75976i	−0.0918177	+	0.252267i
$357$	−0.658747	+	3.61361i	−0.0348646	+	0.191253i
$358$	−3.03706	−	4.33737i	−0.160514	−	0.229237i
$359$	9.34241	−	16.1815i	0.493073	−	0.854028i	−0.506895	−	0.862008i	$-0.669207\pi$
$359$	9.34241	−	16.1815i	0.493073	−	0.854028i	0.999968	+	0.00797981i	$0.00254008\pi$
$360$		0			0
$361$	−1.84847	−	3.20165i	−0.0972881	−	0.168508i
$362$	4.11824	−	8.83159i	0.216450	−	0.464178i
$363$	2.31169	+	13.5686i	0.121332	+	0.712169i
$364$	0.293285	+	0.349523i	0.0153723	+	0.0183200i
$365$		0			0
$366$	−9.64775	−	6.83891i	−0.504296	−	0.357476i
$367$	6.45312	+	3.00914i	0.336850	+	0.157076i	0.583682	−	0.811983i	$-0.301612\pi$
$367$	6.45312	+	3.00914i	0.336850	+	0.157076i	−0.246831	+	0.969058i	$0.579389\pi$
$368$	−2.82013	+	10.5249i	−0.147009	+	0.548647i
$369$	4.47035	−	11.8538i	0.232717	−	0.617084i
$370$		0			0
$371$	5.70252	+	1.00551i	0.296060	+	0.0522034i
$372$	6.83228	+	1.24550i	0.354237	+	0.0645760i
$373$	9.36399	−	4.36650i	0.484849	−	0.226089i	−0.164794	−	0.986328i	$-0.552696\pi$
$373$	9.36399	−	4.36650i	0.484849	−	0.226089i	0.649643	+	0.760239i	$0.274918\pi$
$374$	−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
$378$	−2.92041	+	2.36541i	−0.150210	+	0.121663i
$379$		−	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
$382$	−0.679459	+	0.970368i	−0.0347641	+	0.0496483i
$383$	1.88914	+	4.05128i	0.0965307	+	0.207011i	0.948643	−	0.316348i	$-0.102457\pi$
$383$	1.88914	+	4.05128i	0.0965307	+	0.207011i	−0.852113	+	0.523359i	$0.824679\pi$
$384$	0.201923	+	2.47260i	0.0103044	+	0.126179i
$385$		0			0
$386$	12.4594	+	7.19344i	0.634167	+	0.366137i
$387$	19.4012	−	1.47149i	0.986219	−	0.0748003i
$388$	−4.07636	−	1.09226i	−0.206946	−	0.0554510i
$389$	−9.10172	+	3.31276i	−0.461476	+	0.167963i	−0.562287	−	0.826942i	$-0.690078\pi$
$389$	−9.10172	+	3.31276i	−0.461476	+	0.167963i	0.100811	+	0.994906i	$0.467856\pi$
$390$		0			0
$391$	18.9268	−	15.8814i	0.957168	−	0.803159i
$392$	−1.72627	+	19.7314i	−0.0871899	+	0.996586i
$393$	13.5554	−	36.5834i	0.683778	−	1.84539i
$394$	0.714445	+	1.96292i	0.0359932	+	0.0988906i
$395$		0			0
$396$	−2.43432	+	4.10595i	−0.122329	+	0.206332i
$397$	0.981728	−	0.263053i	0.0492715	−	0.0132023i	−0.234099	−	0.972213i	$-0.575214\pi$
$397$	0.981728	−	0.263053i	0.0492715	−	0.0132023i	0.283371	+	0.959010i	$0.408547\pi$
$398$	−15.7991	+	11.0626i	−0.791936	+	0.554520i
$399$	−2.00882	+	4.24369i	−0.100567	+	0.212450i
$400$		0			0
$401$	8.07342	−	1.42356i	0.403168	−	0.0710893i	0.0316124	−	0.999500i	$-0.489936\pi$
$401$	8.07342	−	1.42356i	0.403168	−	0.0710893i	0.371555	+	0.928411i	$0.378825\pi$
$402$	−10.2487	+	17.5165i	−0.511159	+	0.873646i
$403$	3.17202	−	0.277515i	0.158009	−	0.0138240i
$404$	−10.2965			−0.512272
$405$		0			0
$406$	5.36923			0.266470
$407$	−19.2715	+	1.68604i	−0.955253	+	0.0835738i
$408$	−8.13225	+	13.8992i	−0.402606	+	0.688114i
$409$	−28.0740	+	4.95021i	−1.38817	+	0.244772i	−0.817274	−	0.576249i	$-0.804516\pi$
$409$	−28.0740	+	4.95021i	−1.38817	+	0.244772i	−0.570897	+	0.821021i	$0.693405\pi$
$410$		0			0
$411$	3.86372	−	8.16221i	0.190583	−	0.402612i
$412$	−3.68278	+	2.57871i	−0.181438	+	0.127044i
$413$	1.87866	−	0.503386i	0.0924429	−	0.0247700i
$414$	25.2773	+	0.292368i	1.24231	+	0.0143691i
$415$		0			0
$416$	1.15426	+	3.17132i	0.0565925	+	0.155487i
$417$	−7.82028	+	21.1055i	−0.382961	+	1.03354i
$418$	0.621820	−	7.10744i	0.0304142	−	0.347636i
$419$	−19.6956	+	16.5265i	−0.962192	+	0.807375i	−0.981308	−	0.192443i	$-0.938359\pi$
$419$	−19.6956	+	16.5265i	−0.962192	+	0.807375i	0.0191165	+	0.999817i	$0.493915\pi$
$420$		0			0
$421$	−12.0396	+	4.38206i	−0.586775	+	0.213569i	−0.618310	−	0.785934i	$-0.712182\pi$
$421$	−12.0396	+	4.38206i	−0.586775	+	0.213569i	0.0315356	+	0.999503i	$0.489960\pi$
$422$	−16.9128	−	4.53177i	−0.823303	−	0.220603i
$423$	5.27404	−	10.9769i	0.256432	−	0.533717i
$424$	21.9849	+	12.6930i	1.06768	+	0.616427i
$425$		0			0
$426$	−0.949263	−	11.6240i	−0.0459920	−	0.563183i
$427$	−1.91566	−	4.10815i	−0.0927054	−	0.198807i
$428$	−8.23645	+	11.7629i	−0.398124	+	0.568580i
$429$	−0.578643	+	2.11062i	−0.0279371	+	0.101902i
$430$		0			0
$431$		−	5.16823i		−	0.248945i	−0.992223	−	0.124473i	$-0.960276\pi$
$431$		−	5.16823i		−	0.248945i	0.992223	−	0.124473i	$-0.0397239\pi$
$432$	−6.63084	+	2.28396i	−0.319026	+	0.109887i
$433$	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
$437$	28.6224	−	13.3468i	1.36919	−	0.638465i
$438$	14.8887	+	2.71414i	0.711408	+	0.129687i
$439$	−31.6512	−	5.58095i	−1.51063	−	0.266364i	−0.643886	−	0.765122i	$-0.722679\pi$
$439$	−31.6512	−	5.58095i	−1.51063	−	0.266364i	−0.866742	+	0.498757i	$0.833790\pi$
$440$		0			0
$441$	19.3003	−	3.17346i	0.919063	−	0.151117i
$442$	−0.597834	+	2.23115i	−0.0284361	+	0.106125i
$443$	−13.9035	−	6.48333i	−0.660577	−	0.308032i	0.0632661	−	0.997997i	$-0.479848\pi$
$443$	−13.9035	−	6.48333i	−0.660577	−	0.308032i	−0.723843	+	0.689965i	$0.757626\pi$
$444$	14.2450	+	10.0977i	0.676039	+	0.479218i
$445$		0			0
$446$	13.4825	+	16.0678i	0.638413	+	0.760831i
$447$	−3.30656	−	19.4081i	−0.156395	−	0.917972i
$448$	2.21708	−	4.75455i	0.104747	−	0.224631i
$449$	−1.37821	−	2.38713i	−0.0650416	−	0.112655i	0.831671	−	0.555269i	$-0.187385\pi$
$449$	−1.37821	−	2.38713i	−0.0650416	−	0.112655i	−0.896712	+	0.442614i	$0.854051\pi$
$450$		0			0
$451$	−3.68947	+	6.39034i	−0.173730	+	0.300910i
$452$	0.0637823	+	0.0910905i	0.00300007	+	0.00428454i
$453$	2.82515	−	15.4976i	0.132737	−	0.728142i
$454$	1.66384	−	4.57137i	0.0780879	−	0.214545i
$455$		0			0
$456$	−14.6389	+	14.4706i	−0.685530	+	0.677647i
$457$	2.98806	+	34.1536i	0.139775	+	1.59764i	0.665111	+	0.746745i	$0.268384\pi$
$457$	2.98806	+	34.1536i	0.139775	+	1.59764i	−0.525335	+	0.850895i	$0.676060\pi$
$458$	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	−0.809672	−	0.586883i	$-0.800355\pi$
$461$	−1.95614	+	2.33124i	−0.0911067	+	0.108577i	0.718565	+	0.695460i	$0.244799\pi$
$462$	1.90200	−	1.08350i	0.0884889	−	0.0504090i
$463$	−22.0633	−	15.4489i	−1.02537	−	0.717970i	−0.0653361	−	0.997863i	$-0.520812\pi$
$463$	−22.0633	−	15.4489i	−1.02537	−	0.717970i	−0.960031	+	0.279894i	$0.909701\pi$
$464$	9.41529	+	3.42689i	0.437094	+	0.159089i
$465$		0			0
$466$	1.28377	−	7.28061i	0.0594694	−	0.337268i
$467$	−4.45355	−	16.6209i	−0.206086	−	0.769122i	−0.989116	−	0.147138i	$-0.952994\pi$
$467$	−4.45355	−	16.6209i	−0.206086	−	0.769122i	0.783030	−	0.621983i	$-0.213673\pi$
$468$	1.63111	−	1.11423i	0.0753981	−	0.0515051i
$469$	−6.73671	+	3.88944i	−0.311073	+	0.179598i
$470$		0			0
$471$	5.77406	+	0.538829i	0.266055	+	0.0248279i
$472$	8.49431	+	0.743156i	0.390982	+	0.0342065i
$473$	−11.2896	−	0.987714i	−0.519098	−	0.0454152i
$474$	1.22947	+	2.67692i	0.0564715	+	0.122955i
$475$		0			0
$476$	−1.67236	+	0.965535i	−0.0766523	+	0.0442552i
$477$	6.76799	−	24.1382i	0.309885	−	1.10521i
$478$	−3.13729	−	11.7085i	−0.143497	−	0.535536i
$479$	6.03903	−	34.2490i	0.275930	−	1.56488i	−0.460061	−	0.887888i	$-0.652172\pi$
$479$	6.03903	−	34.2490i	0.275930	−	1.56488i	0.735991	−	0.676991i	$-0.236717\pi$
$480$		0			0
$481$	7.52282	+	2.73808i	0.343011	+	0.124846i
$482$	−8.95484	−	6.27025i	−0.407882	−	0.285602i
$483$	8.36316	+	4.89318i	0.380537	+	0.222647i
$484$	−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	$0.644329\pi$
$488$	−1.73199	−	19.7968i	−0.0784036	−	0.896157i
$489$	−6.18836	−	23.6413i	−0.279847	−	1.06910i
$490$		0			0
$491$	10.0702	−	27.6677i	0.454462	−	1.24863i	−0.475091	−	0.879937i	$-0.657585\pi$
$491$	10.0702	−	27.6677i	0.454462	−	1.24863i	0.929553	−	0.368688i	$-0.120193\pi$
$492$	6.27165	−	2.24171i	0.282748	−	0.101064i
$493$	−13.0313	−	18.6107i	−0.586902	−	0.838183i
$494$	−1.47626	+	2.55695i	−0.0664199	+	0.115043i
$495$		0			0
$496$	−2.97158	−	5.14694i	−0.133428	−	0.231104i
$497$	1.88923	−	4.05148i	0.0847438	−	0.181734i
$498$	−3.03931	−	1.12617i	−0.136195	−	0.0504647i
$499$	11.3613	+	13.5399i	0.508604	+	0.606130i	0.957847	−	0.287279i	$-0.0927507\pi$
$499$	11.3613	+	13.5399i	0.508604	+	0.606130i	−0.449243	+	0.893410i	$0.648306\pi$
$500$		0			0
$501$	−2.24006	+	24.0044i	−0.100079	+	1.07244i
$502$	10.6545	+	4.96826i	0.475532	+	0.221744i
$503$	3.36375	−	12.5537i	0.149982	−	0.559742i	−0.849501	−	0.527588i	$-0.823097\pi$
$503$	3.36375	−	12.5537i	0.149982	−	0.559742i	0.999483	−	0.0321541i	$-0.0102367\pi$
$504$	−6.20630	−	1.16851i	−0.276450	−	0.0520494i
$505$		0			0
$506$	−14.5001	−	2.55677i	−0.644610	−	0.113662i
$507$	−13.9868	+	16.4744i	−0.621175	+	0.731652i
$508$	−13.7009	+	6.38885i	−0.607880	+	0.283459i
$509$	−0.0644329	−	0.365417i	−0.00285594	−	0.0161968i	0.983346	−	0.181741i	$-0.0581732\pi$
$509$	−0.0644329	−	0.365417i	−0.00285594	−	0.0161968i	−0.986202	+	0.165544i	$0.947062\pi$
$510$		0			0
$511$	4.44374	+	3.72874i	0.196579	+	0.164950i
$512$	10.2528	−	10.2528i	0.453113	−	0.453113i
$513$	17.4246	+	10.4673i	0.769317	+	0.462143i
$514$		−	20.7055i		−	0.913279i
$515$		0			0
$516$	7.19103	+	7.27468i	0.316567	+	0.320250i
$517$	−4.06851	+	5.81043i	−0.178933	+	0.255542i
$518$	−3.38403	−	7.25707i	−0.148686	−	0.318857i
$519$	−4.43152	+	3.06494i	−0.194522	+	0.134536i
$520$		0			0
$521$	−2.40696	−	1.38966i	−0.105451	−	0.0608820i	0.446347	−	0.894860i	$-0.352725\pi$
$521$	−2.40696	−	1.38966i	−0.105451	−	0.0608820i	−0.551798	+	0.833978i	$0.686058\pi$
$522$	2.29365	−	23.1318i	0.100390	−	1.01245i
$523$	−14.6842	−	3.93462i	−0.642096	−	0.172049i	−0.0769434	−	0.997035i	$-0.524516\pi$
$523$	−14.6842	−	3.93462i	−0.642096	−	0.172049i	−0.565153	+	0.824986i	$0.691183\pi$
$524$	19.2736	−	7.01503i	0.841973	−	0.306453i
$525$		0			0
$526$	−13.4950	+	11.3237i	−0.588411	+	0.493736i
$527$	−1.17453	+	13.4249i	−0.0511633	+	0.584799i
$528$	4.02681	−	0.686049i	0.175245	−	0.0298565i
$529$	−14.4247	−	39.6316i	−0.627162	−	1.72311i
$530$		0			0
$531$	−1.36617	−	8.30874i	−0.0592866	−	0.360569i
$532$	−2.38424	+	0.638854i	−0.103370	+	0.0276978i
$533$	2.50139	−	1.75149i	0.108347	−	0.0758655i
$534$	−5.72034	−	8.27089i	−0.247544	−	0.357916i
$535$		0			0
$536$	−33.5852	+	5.92198i	−1.45066	+	0.255790i
$537$	−8.78654	−	0.0508127i	−0.379167	−	0.00219273i
$538$	−31.8166	+	2.78359i	−1.37171	+	0.120009i
$539$	−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	$0.616569\pi$
$542$	5.42423	−	0.474558i	0.232990	−	0.0203840i
$543$	−8.00418	−	14.0507i	−0.343492	−	0.602972i
$544$	−14.0664	+	2.48028i	−0.603090	+	0.106341i
$545$		0			0
$546$	−0.902856	+	0.0737311i	−0.0386387	+	0.00315540i
$547$	−0.317541	+	0.222344i	−0.0135771	+	0.00950676i	−0.580345	−	0.814371i	$-0.697082\pi$
$547$	−0.317541	+	0.222344i	−0.0135771	+	0.00950676i	0.566768	+	0.823877i	$0.308194\pi$
$548$	4.58578	−	1.22876i	0.195895	−	0.0524899i
$549$	−18.5172	+	6.49817i	−0.790294	+	0.277335i
$550$		0			0
$551$	−9.93246	−	27.2892i	−0.423137	−	1.16256i
$552$	27.1166	+	32.6985i	1.15416	+	1.39174i
$553$	−0.0984086	+	1.12482i	−0.00418476	+	0.0478320i
$554$	−9.33168	+	7.83021i	−0.396465	+	0.332674i
$555$		0			0
$556$	−11.1192	+	4.04707i	−0.471561	+	0.171634i
$557$	−12.2853	−	3.29185i	−0.520546	−	0.139480i	−0.0110271	−	0.999939i	$-0.503510\pi$
$557$	−12.2853	−	3.29185i	−0.520546	−	0.139480i	−0.509519	+	0.860459i	$0.670177\pi$
$558$	−9.86178	+	9.63626i	−0.417482	+	0.407935i
$559$	4.06152	+	2.34492i	0.171784	+	0.0991797i
$560$		0			0
$561$	−8.37183	−	3.96295i	−0.353459	−	0.167316i
$562$	−6.03864	−	12.9499i	−0.254725	−	0.546259i
$563$	16.7779	−	23.9613i	0.707102	−	1.00985i	−0.291478	−	0.956578i	$-0.594147\pi$
$563$	16.7779	−	23.9613i	0.707102	−	1.00985i	0.998580	−	0.0532691i	$-0.0169641\pi$
$564$	6.19369	−	1.62126i	0.260801	−	0.0682675i
$565$		0			0
$566$		−	9.26299i		−	0.389353i
$567$	0.399701	+	6.22368i	0.0167859	+	0.261370i
$568$	13.8580	−	13.8580i	0.581470	−	0.581470i
$569$	−3.92124	−	3.29031i	−0.164387	−	0.137937i	0.556884	−	0.830591i	$-0.311997\pi$
$569$	−3.92124	−	3.29031i	−0.164387	−	0.137937i	−0.721270	+	0.692654i	$0.756441\pi$
$570$		0			0
$571$	1.16063	+	6.58228i	0.0485710	+	0.275460i	0.999415	−	0.0342116i	$-0.0108920\pi$
$571$	1.16063	+	6.58228i	0.0485710	+	0.275460i	−0.950844	+	0.309671i	$0.899781\pi$
$572$	−1.04275	+	0.486243i	−0.0435997	+	0.0203309i
$573$	0.661643	+	1.85109i	0.0276405	+	0.0773302i
$574$	−3.00787	−	0.530368i	−0.125546	−	0.0221372i
$575$		0			0
$576$	−19.5366	−	11.5828i	−0.814023	−	0.482615i
$577$	11.9622	−	44.6435i	0.497992	−	1.85853i	−0.0145873	−	0.999894i	$-0.504643\pi$
$577$	11.9622	−	44.6435i	0.497992	−	1.85853i	0.512580	−	0.858640i	$-0.328690\pi$
$578$	7.22128	+	3.36734i	0.300366	+	0.140063i
$579$	21.6954	−	9.96440i	0.901630	−	0.414106i
$580$		0			0
$581$	−0.798581	−	0.951712i	−0.0331307	−	0.0394837i
$582$	6.44938	−	5.34842i	0.267335	−	0.221699i
$583$	−6.17089	+	13.2335i	−0.255572	+	0.548076i
$584$	12.7158	+	22.0244i	0.526183	+	0.911376i
$585$		0			0
$586$	5.89440	−	10.2094i	0.243495	−	0.421746i
$587$	−1.01832	−	1.45431i	−0.0420306	−	0.0600260i	0.797587	−	0.603204i	$-0.206110\pi$
$587$	−1.01832	−	1.45431i	−0.0420306	−	0.0600260i	−0.839617	+	0.543178i	$0.817221\pi$
$588$	7.83879	+	6.65515i	0.323266	+	0.274454i
$589$	−5.89151	+	16.1868i	−0.242755	+	0.666965i
$590$		0			0
$591$	3.34305	+	0.916521i	0.137515	+	0.0377006i
$592$	−1.30232	−	14.8856i	−0.0535250	−	0.611794i
$593$	−27.8118	−	27.8118i	−1.14209	−	1.14209i	−0.988066	−	0.154028i	$-0.950775\pi$
$593$	−27.8118	−	27.8118i	−1.14209	−	1.14209i	−0.154028	−	0.988066i	$-0.549225\pi$
$594$	−3.85547	−	8.65708i	−0.158192	−	0.355204i
$595$		0			0
$596$	6.65306	−	7.92880i	0.272520	−	0.324776i
$597$	−0.185088	+	32.0054i	−0.00757514	+	1.30989i
$598$	4.99124	+	3.49490i	0.204107	+	0.142917i
$599$	37.7245	+	13.7306i	1.54138	+	0.561017i	0.966376	−	0.257133i	$-0.0827779\pi$
$599$	37.7245	+	13.7306i	1.54138	+	0.561017i	0.575005	+	0.818150i	$0.305000\pi$
$600$		0			0
$601$	3.13840	−	17.7988i	0.128018	−	0.726027i	−0.851451	−	0.524434i	$-0.824277\pi$
$601$	3.13840	−	17.7988i	0.128018	−	0.726027i	0.979469	−	0.201593i	$-0.0646119\pi$
$602$	−1.21407	−	4.53099i	−0.0494820	−	0.184669i
$603$	13.8788	+	30.6848i	0.565188	+	1.24958i
$604$	7.17219	−	4.14087i	0.291832	−	0.168490i
$605$		0			0
$606$	11.8219	−	16.6773i	0.480233	−	0.677471i
$607$	14.2779	+	1.24916i	0.579522	+	0.0507016i	0.373149	−	0.927772i	$-0.378278\pi$
$607$	14.2779	+	1.24916i	0.579522	+	0.0507016i	0.206374	+	0.978473i	$0.433834\pi$
$608$	−18.1879	−	1.59123i	−0.737616	−	0.0645330i
$609$	5.15265	−	7.26892i	0.208796	−	0.294552i
$610$		0			0
$611$	2.54213	−	1.46770i	0.102844	−	0.0593767i
$612$	3.44534	+	7.61735i	0.139270	+	0.307913i
$613$	−7.34062	−	27.3956i	−0.296485	−	1.10650i	−0.940031	−	0.341090i	$-0.889204\pi$
$613$	−7.34062	−	27.3956i	−0.296485	−	1.10650i	0.643546	−	0.765408i	$-0.277463\pi$
$614$	1.54655	−	8.77091i	0.0624136	−	0.353965i
$615$		0			0
$616$	3.45655	+	1.25808i	0.139269	+	0.0506896i
$617$	−19.2569	−	13.4838i	−0.775255	−	0.542839i	0.117666	−	0.993053i	$-0.462459\pi$
$617$	−19.2569	−	13.4838i	−0.775255	−	0.542839i	−0.892921	+	0.450214i	$0.851348\pi$
$618$	0.0516178	−	8.92574i	0.00207637	−	0.359046i
$619$	5.35313	−	6.37961i	0.215160	−	0.256418i	−0.647659	−	0.761930i	$-0.724252\pi$
$619$	5.35313	−	6.37961i	0.215160	−	0.256418i	0.862820	+	0.505512i	$0.168696\pi$
$620$		0			0
$621$	24.6535	−	33.9401i	0.989312	−	1.36197i
$622$	10.7995	+	10.7995i	0.433020	+	0.433020i
$623$	−0.335951	−	3.83994i	−0.0134596	−	0.153844i
$624$	−1.63028	−	0.446952i	−0.0652633	−	0.0178924i
$625$		0			0
$626$	−3.32909	+	9.14661i	−0.133057	+	0.365572i
$627$	−9.02539	−	7.66258i	−0.360439	−	0.306014i
$628$	1.74869	+	2.49739i	0.0697803	+	0.0996566i
$629$	−16.9411	+	29.3428i	−0.675485	+	1.16997i
$630$		0			0
$631$	10.7788	+	18.6694i	0.429097	+	0.743218i	0.996793	−	0.0800204i	$-0.0254985\pi$
$631$	10.7788	+	18.6694i	0.429097	+	0.743218i	−0.567696	+	0.823238i	$0.692165\pi$
$632$	−2.09201	+	4.48633i	−0.0832158	+	0.178457i
$633$	−22.3658	+	18.5478i	−0.888960	+	0.737208i
$634$	15.8517	+	18.8913i	0.629550	+	0.750269i
$635$		0			0
$636$	11.9766	−	5.50069i	0.474904	−	0.218117i
$637$	4.27285	+	1.99246i	0.169296	+	0.0789442i
$638$	−3.50422	+	13.0779i	−0.138734	+	0.517761i
$639$	−16.6476	−	9.86998i	−0.658570	−	0.390450i
$640$		0			0
$641$	−4.89330	−	0.862821i	−0.193274	−	0.0340794i	0.0761733	−	0.997095i	$-0.475730\pi$
$641$	−4.89330	−	0.862821i	−0.193274	−	0.0340794i	−0.269447	+	0.963015i	$0.586841\pi$
$642$	−9.59572	−	26.8461i	−0.378713	−	1.05953i
$643$	20.7326	−	9.66776i	0.817613	−	0.381259i	0.0316243	−	0.999500i	$-0.489932\pi$
$643$	20.7326	−	9.66776i	0.817613	−	0.381259i	0.785989	+	0.618241i	$0.212154\pi$
$644$	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	−0.528445	−	0.848967i	$-0.677225\pi$
$647$	8.15287	−	8.15287i	0.320522	−	0.320522i	0.848967	+	0.528445i	$0.177225\pi$
$648$	−7.68542	+	26.2390i	−0.301912	+	1.03076i
$649$			4.90443i			0.192516i
$650$		0			0
$651$	−5.11274	+	1.33831i	−0.200384	+	0.0524527i
$652$	7.36905	−	10.5241i	0.288594	−	0.412155i
$653$	15.6937	+	33.6553i	0.614142	+	1.31703i	0.929767	+	0.368148i	$0.120008\pi$
$653$	15.6937	+	33.6553i	0.614142	+	1.31703i	−0.315625	+	0.948884i	$0.602214\pi$
$654$	33.1952	+	15.7135i	1.29804	+	0.614447i
$655$		0			0
$656$	−4.93599	−	2.84980i	−0.192718	−	0.111266i
$657$	17.9626	−	17.5518i	0.700786	−	0.684760i
$658$	−2.83597	−	0.759896i	−0.110558	−	0.0296238i
$659$	17.4051	−	6.33493i	0.678005	−	0.246774i	0.0200144	−	0.999800i	$-0.493629\pi$
$659$	17.4051	−	6.33493i	0.678005	−	0.246774i	0.657991	+	0.753026i	$0.271407\pi$
$660$		0			0
$661$	32.6452	−	27.3925i	1.26975	−	1.06545i	0.275178	−	0.961393i	$-0.411263\pi$
$661$	32.6452	−	27.3925i	1.26975	−	1.06545i	0.994572	−	0.104053i	$-0.0331813\pi$
$662$	−2.10399	+	24.0488i	−0.0817740	+	0.934682i
$663$	2.44683	+	2.95051i	0.0950271	+	0.114588i
$664$	−1.86287	−	5.11819i	−0.0722933	−	0.198624i
$665$		0			0
$666$	−32.7107	+	11.4790i	−1.26751	+	0.444804i
$667$	−57.8896	+	15.5115i	−2.24149	+	0.600607i
$668$	−10.3824	+	7.26980i	−0.401705	+	0.281277i
$669$	34.6914	−	2.83305i	1.34125	−	0.109532i
$670$		0			0
$671$	11.2566	−	1.98484i	0.434555	−	0.0766238i
$672$	−2.77267	−	4.86719i	−0.106958	−	0.187756i
$673$	−9.45392	+	0.827111i	−0.364422	+	0.0318828i	−0.267896	−	0.963448i	$-0.586328\pi$
$673$	−9.45392	+	0.827111i	−0.364422	+	0.0318828i	−0.0965254	+	0.995331i	$0.530773\pi$
$674$	−13.0095			−0.501109
$675$		0			0
$676$	−11.3614			−0.436977
$677$	10.7923	−	0.944208i	0.414783	−	0.0362888i	0.122146	−	0.992512i	$-0.461023\pi$
$677$	10.7923	−	0.944208i	0.414783	−	0.0362888i	0.292638	+	0.956223i	$0.405467\pi$
$678$	−0.220771	−	0.00127672i	−0.00847865	−	4.90322e-5i
$679$	3.16272	−	0.557672i	0.121374	−	0.0214015i
$680$		0			0
$681$	−4.59204	−	6.63950i	−0.175967	−	0.254426i
$682$	6.57855	−	4.60635i	0.251906	−	0.176386i
$683$	2.18859	−	0.586431i	0.0837441	−	0.0224392i	−0.216704	−	0.976237i	$-0.569531\pi$
$683$	2.18859	−	0.586431i	0.0837441	−	0.0224392i	0.300448	+	0.953798i	$0.402864\pi$
$684$	1.73382	+	10.5447i	0.0662943	+	0.403188i
$685$		0			0
$686$	−3.34440	−	9.18868i	−0.127690	−	0.350825i
$687$	41.4658	−	7.06454i	1.58202	−	0.269529i
$688$	0.762924	−	8.72026i	0.0290862	−	0.332457i
$689$	4.62889	−	3.88410i	0.176347	−	0.147972i
$690$		0			0
$691$	7.28698	−	2.65224i	0.277210	−	0.100896i	−0.199674	−	0.979862i	$-0.563988\pi$
$691$	7.28698	−	2.65224i	0.277210	−	0.100896i	0.476884	+	0.878966i	$0.341766\pi$
$692$	−2.73616	−	0.733152i	−0.104013	−	0.0278703i
$693$	0.358421	−	3.61474i	0.0136153	−	0.137313i
$694$	10.3378	+	5.96855i	0.392419	+	0.226563i
$695$		0			0
$696$	32.1267	−	22.2196i	1.21776	−	0.842231i
$697$	5.46187	+	11.7130i	0.206883	+	0.443662i
$698$	14.5398	−	20.7650i	0.550341	−	0.785969i
$699$	−8.62458	−	8.72492i	−0.326212	−	0.330007i
$700$		0			0
$701$			3.06270i			0.115677i	0.998326	+	0.0578383i	$0.0184208\pi$
$701$			3.06270i			0.115677i	−0.998326	+	0.0578383i	$0.981579\pi$
$702$	−0.0680353	+	3.92120i	−0.00256783	+	0.147996i
$703$	−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
$707$	7.10146	−	3.31146i	0.267078	−	0.124540i
$708$	2.86502	−	3.37458i	0.107674	−	0.126824i
$709$	45.6222	+	8.04442i	1.71338	+	0.302114i	0.942335	−	0.334671i	$-0.108625\pi$
$709$	45.6222	+	8.04442i	1.71338	+	0.302114i	0.771041	+	0.636785i	$0.219736\pi$
$710$		0			0
$711$	4.80392	+	0.904469i	0.180161	+	0.0339203i
$712$	4.37376	−	16.3231i	0.163914	−	0.611734i
$713$	32.2183	+	15.0236i	1.20658	+	0.562640i
$714$	0.356226	−	3.81729i	0.0133314	−	0.142859i
$715$		0			0
$716$	−2.96927	−	3.53864i	−0.110967	−	0.132245i
$717$	−18.8619	−	6.98896i	−0.704411	−	0.261008i
$718$	−8.24204	+	17.6751i	−0.307590	+	0.659629i
$719$	−25.2485	−	43.7317i	−0.941610	−	1.63092i	−0.762400	−	0.647106i	$-0.775979\pi$
$719$	−25.2485	−	43.7317i	−0.941610	−	1.63092i	−0.179211	−	0.983811i	$-0.557354\pi$
$720$		0			0
$721$	1.71065	−	2.96294i	0.0637080	−	0.110346i
$722$	2.21326	+	3.16086i	0.0823690	+	0.117635i
$723$	−17.0824	+	6.10583i	−0.635300	+	0.227078i
$724$	2.90761	−	7.98858i	0.108060	−	0.296893i
$725$		0			0
$726$	−3.63798	−	13.8981i	−0.135018	−	0.515808i
$727$	0.922993	+	10.5499i	0.0342319	+	0.391273i	0.993912	+	0.110178i	$0.0351420\pi$
$727$	0.922993	+	10.5499i	0.0342319	+	0.391273i	−0.959680	+	0.281095i	$0.909302\pi$
$728$	−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
$732$	−8.90476	−	5.21006i	−0.329129	−	0.192569i
$733$	23.8946	+	16.7312i	0.882569	+	0.617981i	0.924518	−	0.381139i	$-0.124468\pi$
$733$	23.8946	+	16.7312i	0.882569	+	0.617981i	−0.0419494	+	0.999120i	$0.513357\pi$
$734$	−6.98357	−	2.54181i	−0.257768	−	0.0938200i
$735$		0			0
$736$	−6.54274	+	37.1057i	−0.241169	+	1.36774i
$737$	−5.07689	−	18.9472i	−0.187010	−	0.697929i
$738$	−3.56986	+	12.7320i	−0.131408	+	0.468672i
$739$	5.54415	−	3.20092i	0.203945	−	0.117748i	−0.394549	−	0.918875i	$-0.629099\pi$
$739$	5.54415	−	3.20092i	0.203945	−	0.117748i	0.598494	+	0.801127i	$0.295766\pi$
$740$		0			0
$741$	2.04492	+	4.45239i	0.0751220	+	0.163563i
$742$	−6.02085	−	0.526756i	−0.221032	−	0.0193378i
$743$	−29.7334	−	2.60134i	−1.09081	−	0.0954338i	−0.472473	−	0.881345i	$-0.656639\pi$
$743$	−29.7334	−	2.60134i	−1.09081	−	0.0954338i	−0.618339	+	0.785911i	$0.712194\pi$
$744$	−23.0696	−	2.15283i	−0.845774	−	0.0789267i
$745$		0			0
$746$	−9.33928	+	5.39204i	−0.341935	+	0.197416i
$747$	−4.44133	+	3.03391i	−0.162500	+	0.111005i
$748$	−1.26031	−	4.70355i	−0.0460816	−	0.171979i
$749$	1.89758	−	10.7617i	0.0693359	−	0.393224i
$750$		0			0
$751$	−9.53000	−	3.46864i	−0.347755	−	0.126572i	0.162237	−	0.986752i	$-0.448129\pi$
$751$	−9.53000	−	3.46864i	−0.347755	−	0.126572i	−0.509991	+	0.860180i	$0.670351\pi$
$752$	−4.48806	−	3.14257i	−0.163663	−	0.114598i
$753$	16.9508	−	9.65627i	0.617721	−	0.351894i
$754$	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	$0.802583\pi$
$758$	0.496062	+	5.67002i	0.0180178	+	0.205944i
$759$	−17.3766	+	17.1768i	−0.630732	+	0.623479i
$760$		0			0
$761$	9.16585	−	25.1830i	0.332262	−	0.912882i	−0.655260	−	0.755403i	$-0.727441\pi$
$761$	9.16585	−	25.1830i	0.332262	−	0.912882i	0.987522	−	0.157479i	$-0.0503367\pi$
$762$	5.38260	−	29.5267i	0.194991	−	1.06964i
$763$	8.07441	+	11.5315i	0.292313	+	0.417467i
$764$	−0.516728	+	0.895000i	−0.0186946	+	0.0323800i
$765$		0			0
$766$	−2.33284	−	4.04059i	−0.0842888	−	0.145993i
$767$	0.857749	−	1.83945i	0.0309715	−	0.0664186i
$768$	−4.83948	−	28.4057i	−0.174630	−	1.02500i
$769$	−8.41448	−	10.0280i	−0.303434	−	0.361619i	0.592684	−	0.805435i	$-0.298068\pi$
$769$	−8.41448	−	10.0280i	−0.303434	−	0.361619i	−0.896117	+	0.443817i	$0.853624\pi$
$770$		0			0
$771$	−28.0313	−	19.8703i	−1.00952	−	0.715611i
$772$	11.3753	+	5.30439i	0.409406	+	0.190909i
$773$	3.35520	−	12.5218i	0.120678	−	0.450377i	−0.878971	−	0.476876i	$-0.841769\pi$
$773$	3.35520	−	12.5218i	0.120678	−	0.450377i	0.999649	+	0.0264987i	$0.00843577\pi$
$774$	−20.0392	+	3.29494i	−0.720293	+	0.118434i
$775$		0			0
$776$	13.8656	+	2.44488i	0.497747	+	0.0877662i
$777$	−13.0722	−	2.38301i	−0.468963	−	0.0854901i
$778$	9.16244	−	4.27252i	0.328489	−	0.153177i
$779$	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
$783$	−29.1150	−	25.3040i	−1.04049	−	0.904290i
$784$		−	8.79971i		−	0.314275i
$785$		0			0
$786$	−10.7667	+	39.2718i	−0.384034	+	1.40078i
$787$	7.17412	−	10.2457i	0.255730	−	0.365220i	−0.670673	−	0.741753i	$-0.733995\pi$
$787$	7.17412	−	10.2457i	0.255730	−	0.365220i	0.926403	+	0.376533i	$0.122884\pi$
$788$	0.770169	+	1.65163i	0.0274361	+	0.0588370i
$789$	2.37942	+	29.1367i	0.0847098	+	1.03729i
$790$		0			0
$791$	−0.0732857	−	0.0423115i	−0.00260574	−	0.00150443i
$792$	6.89669	−	14.3542i	0.245063	−	0.510054i
$793$	−4.56900	−	1.22426i	−0.162250	−	0.0434748i
$794$	−0.996853	+	0.362825i	−0.0353770	+	0.0128762i
$795$		0			0
$796$	−12.8897	+	10.8157i	−0.456862	+	0.383353i
$797$	−0.571540	+	6.53273i	−0.0202450	+	0.231401i	0.979331	+	0.202267i	$0.0648307\pi$
$797$	−0.571540	+	6.53273i	−0.0202450	+	0.231401i	−0.999575	+	0.0291347i	$0.990725\pi$
$798$	1.70269	−	4.59525i	0.0602747	−	0.162670i
$799$	4.24908	+	11.6743i	0.150322	+	0.413006i
$800$		0			0
$801$	−16.6868	−	0.193007i	−0.589600	−	0.00681957i
$802$	−8.26509	+	2.21462i	−0.291851	+	0.0782011i
$803$	−11.9824	+	8.39015i	−0.422849	+	0.296082i
$804$	−7.57516	+	16.0027i	−0.267155	+	0.564372i
$805$		0			0
$806$	−3.27296	+	0.577111i	−0.115285	+	0.0203279i
$807$	−26.7648	+	45.7450i	−0.942166	+	1.61030i
$808$	34.2212	−	2.99397i	1.20390	−	0.105327i
$809$	−21.1375			−0.743156			−0.371578	−	0.928402i	$-0.621183\pi$
$809$	−21.1375			−0.743156			−0.371578	+	0.928402i	$0.621183\pi$
$810$		0			0
$811$	−48.6371			−1.70788			−0.853940	−	0.520371i	$-0.825794\pi$
$811$	−48.6371			−1.70788			−0.853940	+	0.520371i	$0.825794\pi$
$812$	4.66634	−	0.408252i	0.163756	−	0.0143268i
$813$	4.56297	−	7.79879i	0.160030	−	0.273516i
$814$	19.8848	−	3.50622i	0.696961	−	0.122893i
$815$		0			0
$816$	3.06104	−	6.46651i	0.107158	−	0.226373i
$817$	−20.7829	+	14.5524i	−0.727103	+	0.509123i
$818$	28.7405	−	7.70100i	1.00489	−	0.269259i
$819$	−0.766620	+	1.29305i	−0.0267879	+	0.0451829i
$820$		0			0
$821$	8.00089	+	21.9823i	0.279233	+	0.767186i	0.997450	+	0.0713672i	$0.0227362\pi$
$821$	8.00089	+	21.9823i	0.279233	+	0.767186i	−0.718217	+	0.695819i	$0.755042\pi$
$822$	−3.27492	+	8.83839i	−0.114226	+	0.308274i
$823$	0.292711	−	3.34570i	0.0102033	−	0.116624i	−0.989385	−	0.145318i	$-0.953579\pi$
$823$	0.292711	−	3.34570i	0.0102033	−	0.116624i	0.999588	+	0.0286943i	$0.00913494\pi$
$824$	11.4901	−	9.64136i	0.400277	−	0.335873i
$825$		0			0
$826$	−1.90760	+	0.694311i	−0.0663740	+	0.0241582i
$827$	20.9358	+	5.60974i	0.728010	+	0.195070i	0.603743	−	0.797179i	$-0.293675\pi$
$827$	20.9358	+	5.60974i	0.728010	+	0.195070i	0.124267	+	0.992249i	$0.460342\pi$
$828$	21.9905	−	1.66788i	0.764222	−	0.0579628i
$829$	−4.62453	−	2.66997i	−0.160617	−	0.0927320i	0.417537	−	0.908660i	$-0.362893\pi$
$829$	−4.62453	−	2.66997i	−0.160617	−	0.0927320i	−0.578154	+	0.815928i	$0.696227\pi$
$830$		0			0
$831$	1.64535	+	20.1477i	0.0570765	+	0.698916i
$832$	−2.31360	−	4.96154i	−0.0802097	−	0.172010i
$833$	−11.4448	+	16.3449i	−0.396540	+	0.566317i
$834$	6.21143	−	22.6565i	0.215084	−	0.784529i
$835$		0			0
$836$		−	6.22428i		−	0.215271i
$837$	3.58168	+	22.5986i	0.123801	+	0.781120i
$838$	18.9757	−	18.9757i	0.655504	−	0.655504i
$839$	0.256169	+	0.214952i	0.00884395	+	0.00742095i	0.647199	−	0.762321i	$-0.275940\pi$
$839$	0.256169	+	0.214952i	0.00884395	+	0.00742095i	−0.638355	+	0.769742i	$0.720385\pi$
$840$		0			0
$841$	4.53398	+	25.7135i	0.156344	+	0.886673i
$842$	12.1199	−	5.65161i	0.417680	−	0.194767i
$843$	−23.3268	−	4.25238i	−0.803417	−	0.146460i
$844$	−15.0433	−	2.65254i	−0.517813	−	0.0913043i
$845$		0			0
$846$	−4.48528	+	11.8934i	−0.154207	+	0.408903i
$847$	1.42522	−	5.31901i	0.0489713	−	0.182763i
$848$	−10.2217	−	4.76648i	−0.351016	−	0.163682i
$849$	−12.5403	−	8.88936i	−0.430383	−	0.305082i
$850$		0			0
$851$	57.4510	+	68.4675i	1.96940	+	2.34703i
$852$	−1.70883	−	10.0301i	−0.0585435	−	0.343625i
$853$	−7.30797	+	15.6720i	−0.250220	+	0.536598i	−0.990794	−	0.135376i	$-0.956776\pi$
$853$	−7.30797	+	15.6720i	−0.250220	+	0.536598i	0.740574	+	0.671974i	$0.234554\pi$
$854$	2.36558	+	4.09731i	0.0809486	+	0.140207i
$855$		0			0
$856$	23.9540	−	41.4895i	0.818731	−	1.41808i
$857$	6.28056	+	8.96957i	0.214540	+	0.306395i	0.911969	−	0.410259i	$-0.134562\pi$
$857$	6.28056	+	8.96957i	0.214540	+	0.306395i	−0.697429	+	0.716654i	$0.745673\pi$
$858$	0.409660	−	2.24723i	0.0139856	−	0.0767190i
$859$	−9.19021	+	25.2499i	−0.313566	+	0.861515i	0.678364	+	0.734726i	$0.262689\pi$
$859$	−9.19021	+	25.2499i	−0.313566	+	0.861515i	−0.991930	+	0.126789i	$0.959533\pi$
$860$		0			0
$861$	−3.60456	+	3.56311i	−0.122843	+	0.121430i
$862$	0.470149	+	5.37383i	0.0160133	+	0.183033i
$863$	−14.0569	−	14.0569i	−0.478502	−	0.478502i	0.426150	−	0.904652i	$-0.359869\pi$
$863$	−14.0569	−	14.0569i	−0.478502	−	0.478502i	−0.904652	+	0.426150i	$0.859869\pi$
$864$	−22.1534	+	9.86610i	−0.753674	+	0.335652i
$865$		0			0
$866$	−2.60873	+	3.10897i	−0.0886484	+	0.105647i
$867$	11.4887	−	6.54473i	0.390178	−	0.222271i
$868$	−2.27597	−	1.59365i	−0.0772515	−	0.0540921i
$869$	−2.67551	−	0.973806i	−0.0907605	−	0.0330341i
$870$		0			0
$871$	−1.40960	+	7.99422i	−0.0477623	+	0.270874i
$872$	15.9733	+	59.6132i	0.540924	+	2.01876i
$873$	−1.05152	−	13.8639i	−0.0355884	−	0.469223i
$874$	−28.5469	+	16.4815i	−0.965612	+	0.557496i
$875$		0			0
$876$	13.1460	+	1.22677i	0.444161	+	0.0414486i
$877$	31.0262	+	2.71444i	1.04768	+	0.0916602i	0.597974	−	0.801516i	$-0.295973\pi$
$877$	31.0262	+	2.71444i	1.04768	+	0.0916602i	0.449708	+	0.893176i	$0.351528\pi$
$878$	33.4180	+	2.92369i	1.12780	+	0.0986699i
$879$	−8.16495	−	17.7775i	−0.275397	−	0.599620i
$880$		0			0
$881$	−10.7039	+	6.17988i	−0.360623	+	0.208206i	−0.669354	−	0.742944i	$-0.733429\pi$
$881$	−10.7039	+	6.17988i	−0.360623	+	0.208206i	0.308731	+	0.951149i	$0.400096\pi$
$882$	−19.7794	+	5.05544i	−0.666008	+	0.170225i
$883$	9.26338	+	34.5714i	0.311738	+	1.16342i	0.926989	+	0.375089i	$0.122388\pi$
$883$	9.26338	+	34.5714i	0.311738	+	1.16342i	−0.615251	+	0.788331i	$0.710945\pi$
$884$	−0.349925	+	1.98452i	−0.0117693	+	0.0667468i
$885$		0			0
$886$	15.0464	+	5.47645i	0.505494	+	0.183985i
$887$	−1.91991	−	1.34433i	−0.0644642	−	0.0451383i	0.540900	−	0.841087i	$-0.318084\pi$
$887$	−1.91991	−	1.34433i	−0.0644642	−	0.0451383i	−0.605364	+	0.795949i	$0.706973\pi$
$888$	−50.2803	−	29.4184i	−1.68730	−	0.987215i
$889$	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
$893$	1.38403	+	15.8196i	0.0463149	+	0.529382i
$894$	5.20364	+	19.8794i	0.174036	+	0.664866i
$895$		0			0
$896$	0.339458	−	0.932655i	0.0113405	−	0.0311578i
$897$	9.52135	−	3.40326i	0.317909	−	0.113632i
$898$	1.65019	+	2.35671i	0.0550675	+	0.0786446i
$899$	16.3445	−	28.3095i	0.545120	−	0.944175i
$900$		0			0
$901$	12.7870	+	22.1478i	0.425997	+	0.737849i
$902$	3.25491	−	6.98019i	0.108377	−	0.232415i
$903$	−7.29921	−	2.70460i	−0.242902	−	0.0900034i
$904$	−0.238471	−	0.284198i	−0.00793142	−	0.00945230i
$905$		0			0
$906$	−1.52774	+	16.3711i	−0.0507556	+	0.543895i
$907$	−50.7113	−	23.6471i	−1.68384	−	0.785188i	−0.998369	−	0.0570890i	$-0.981818\pi$
$907$	−50.7113	−	23.6471i	−1.68384	−	0.785188i	−0.685472	−	0.728099i	$-0.740404\pi$
$908$	1.09844	−	4.09944i	0.0364530	−	0.136045i
$909$	−11.2329	−	32.0093i	−0.372572	−	1.06168i
$910$		0			0
$911$	−26.4465	−	4.66323i	−0.876211	−	0.154500i	−0.282587	−	0.959242i	$-0.591192\pi$
$911$	−26.4465	−	4.66323i	−0.876211	−	0.154500i	−0.593625	+	0.804742i	$0.702304\pi$
$912$	5.91868	−	6.97133i	0.195987	−	0.230844i
$913$	2.83930	−	1.32399i	0.0939671	−	0.0438176i
$914$	−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
$918$	−16.2936	−	3.16539i	−0.537768	−	0.104473i
$919$		−	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
$922$	1.82189	−	2.60193i	0.0600008	−	0.0856900i
$923$	−1.97148	−	4.22786i	−0.0648921	−	0.139162i
$924$	1.57062	−	1.08628i	0.0516696	−	0.0357360i
$925$		0			0
$926$	24.3463	+	14.0564i	0.800070	+	0.461921i
$927$	−12.0342	−	8.63559i	−0.395256	−	0.283630i
$928$	33.4663	+	8.96728i	1.09859	+	0.294365i
$929$	−14.1178	+	5.13847i	−0.463191	+	0.168588i	−0.563065	−	0.826412i	$-0.690378\pi$
$929$	−14.1178	+	5.13847i	−0.463191	+	0.168588i	0.0998747	+	0.995000i	$0.468156\pi$
$930$		0			0
$931$	−19.5380	+	16.3943i	−0.640331	+	0.537301i
$932$	0.562125	−	6.42512i	0.0184130	−	0.210462i
$933$	24.9843	−	4.25659i	0.817950	−	0.139354i
$934$	6.14270	+	16.8769i	0.200995	+	0.552230i
$935$		0			0
$936$	−5.09710	+	4.17748i	−0.166604	+	0.136545i
$937$	−44.9601	+	12.0470i	−1.46878	+	0.393559i	−0.902514	−	0.430660i	$-0.858281\pi$
$937$	−44.9601	+	12.0470i	−1.46878	+	0.393559i	−0.566270	+	0.824220i	$0.691614\pi$
$938$	6.65089	−	4.65700i	0.217159	−	0.152057i
$939$	9.18797	+	13.2846i	0.299838	+	0.433528i
$940$		0			0
$941$	−13.0261	+	2.29686i	−0.424640	+	0.0748755i	−0.381884	−	0.924210i	$-0.624725\pi$
$941$	−13.0261	+	2.29686i	−0.424640	+	0.0748755i	−0.0427555	+	0.999086i	$0.513614\pi$
$942$	−6.05277	−	0.0350033i	−0.197210	−	0.00114047i
$943$	33.9623	−	2.97131i	1.10596	−	0.0967593i
$944$	−3.78825			−0.123297
$945$		0			0
$946$	11.8286			0.384581
$947$	33.5777	−	2.93767i	1.09113	−	0.0954614i	0.472640	−	0.881255i	$-0.343301\pi$
$947$	33.5777	−	2.93767i	1.09113	−	0.0954614i	0.618488	+	0.785794i	$0.287745\pi$
$948$	1.27206	+	2.23300i	0.0413146	+	0.0725244i
$949$	5.96147	−	1.05117i	0.193517	−	0.0341223i
$950$		0			0
$951$	40.7875	−	3.33089i	1.32263	−	0.108011i
$952$	5.27742	−	3.69529i	0.171042	−	0.119765i
$953$	−37.8969	+	10.1544i	−1.22760	+	0.328935i	−0.813645	−	0.581362i	$-0.802520\pi$
$953$	−37.8969	+	10.1544i	−1.22760	+	0.328935i	−0.413956	+	0.910297i	$0.635853\pi$
$954$	−4.84139	+	25.7141i	−0.156746	+	0.832526i
$955$		0			0
$956$	−3.61686	−	9.93723i	−0.116977	−	0.321393i
$957$	14.3422	+	17.2945i	0.463617	+	0.559051i
$958$	−3.16367	+	36.1609i	−0.102213	+	1.16830i
$959$	−2.76760	+	2.32229i	−0.0893705	+	0.0749908i
$960$		0			0
$961$	10.9101	−	3.97094i	0.351938	−	0.128095i
$962$	−8.07116	−	2.16266i	−0.260225	−	0.0697270i
$963$	−45.5532	−	12.7724i	−1.46793	−	0.411585i
$964$	−8.25932	−	4.76852i	−0.266015	−	0.153584i
$965$		0			0
$966$	−9.14099	−	4.32704i	−0.294106	−	0.139220i
$967$	10.7806	+	23.1190i	0.346680	+	0.743457i	0.999906	−	0.0137056i	$-0.00436278\pi$
$967$	10.7806	+	23.1190i	0.346680	+	0.743457i	−0.653226	+	0.757163i	$0.726585\pi$
$968$	13.8471	−	19.7756i	0.445061	−	0.635613i
$969$	−20.0604	+	5.25103i	−0.644434	+	0.168687i
$970$		0			0
$971$		−	23.0327i		−	0.739156i	−0.929200	−	0.369578i	$-0.879502\pi$
$971$		−	23.0327i		−	0.739156i	0.929200	−	0.369578i	$-0.120498\pi$
$972$	8.80589	+	11.1329i	0.282449	+	0.357087i
$973$	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
$977$	0.251362	−	0.117212i	0.00804177	−	0.00374994i	−0.418593	−	0.908174i	$-0.637477\pi$
$977$	0.251362	−	0.117212i	0.00804177	−	0.00374994i	0.426635	+	0.904424i	$0.359699\pi$
$978$	8.58517	+	24.0188i	0.274523	+	0.768038i
$979$	9.57227	+	1.68785i	0.305931	+	0.0539439i
$980$		0			0
$981$	53.1294	−	29.8603i	1.69629	−	0.953367i
$982$	−7.95391	+	29.6844i	−0.253820	+	0.947268i
$983$	−7.55984	−	3.52521i	−0.241122	−	0.112437i	0.298302	−	0.954472i	$-0.403580\pi$
$983$	−7.55984	−	3.52521i	−0.241122	−	0.112437i	−0.539423	+	0.842035i	$0.681358\pi$
$984$	−20.1924	+	9.27408i	−0.643709	+	0.295647i
$985$		0			0
$986$	15.2427	+	18.1656i	0.485427	+	0.578510i
$987$	−3.75033	+	3.11012i	−0.119374	+	0.0989963i
$988$	−1.08858	+	2.33447i	−0.0346324	+	0.0742694i
$989$	26.1797	+	45.3445i	0.832465	+	1.44187i
$990$		0			0
$991$	−3.48806	+	6.04150i	−0.110802	+	0.191914i	−0.916094	−	0.400964i	$-0.868675\pi$
$991$	−3.48806	+	6.04150i	−0.110802	+	0.191914i	0.805292	+	0.592878i	$0.202009\pi$
$992$	−11.7876	−	16.8345i	−0.374257	−	0.534494i
$993$	30.5383	+	25.9271i	0.969105	+	0.822773i
$994$	−1.59583	+	4.38451i	−0.0506167	+	0.139068i
$995$		0			0
$996$	−2.72706	−	0.747643i	−0.0864103	−	0.0236900i
$997$	−4.81022	−	54.9810i	−0.152341	−	1.74127i	−0.560321	−	0.828276i	$-0.689322\pi$
$997$	−4.81022	−	54.9810i	−0.152341	−	1.74127i	0.407980	−	0.912991i	$-0.366233\pi$
$998$	−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.632.6		192
5.2	odd	4		135.2.q.a.38.6	yes	192
5.3	odd	4	inner	675.2.ba.b.443.11		192
5.4	even	2		135.2.q.a.92.11	yes	192
15.2	even	4		405.2.r.a.278.11		192
15.14	odd	2		405.2.r.a.197.6		192
27.5	odd	18	inner	675.2.ba.b.32.11		192
135.22	odd	36		405.2.r.a.368.6		192
135.32	even	36		135.2.q.a.113.11	yes	192
135.49	even	18		405.2.r.a.287.11		192
135.59	odd	18		135.2.q.a.32.6	✓	192
135.113	even	36	inner	675.2.ba.b.518.6		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.6	✓	192	135.59	odd	18
135.2.q.a.38.6	yes	192	5.2	odd	4
135.2.q.a.92.11	yes	192	5.4	even	2
135.2.q.a.113.11	yes	192	135.32	even	36
405.2.r.a.197.6		192	15.14	odd	2
405.2.r.a.278.11		192	15.2	even	4
405.2.r.a.287.11		192	135.49	even	18
405.2.r.a.368.6		192	135.22	odd	36
675.2.ba.b.32.11		192	27.5	odd	18	inner
675.2.ba.b.443.11		192	5.3	odd	4	inner
675.2.ba.b.518.6		192	135.113	even	36	inner
675.2.ba.b.632.6		192	1.1	even	1	trivial

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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more