LMFDB - Embedded newform 900.2.o.b.299.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(299,900)] 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("900.299"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 1, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,6,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			299.11
Character	$\chi$	$=$	900.299
Dual form			900.2.o.b.599.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.228922 + 1.39556i) q^{2} +(0.654027 - 1.60382i) q^{3} +(-1.89519 - 0.638951i) q^{4} +(2.08851 + 1.27989i) q^{6} +(-0.604565 + 1.04714i) q^{7} +(1.32555 - 2.49858i) q^{8} +(-2.14450 - 2.09789i) q^{9} +(-1.52161 + 2.63550i) q^{11} +(-2.26427 + 2.62166i) q^{12} +(-4.39869 + 2.53958i) q^{13} +(-1.32295 - 1.08342i) q^{14} +(3.18348 + 2.42186i) q^{16} +2.23944 q^{17} +(3.41866 - 2.51253i) q^{18} -2.53835i q^{19} +(1.28402 + 1.65447i) q^{21} +(-3.32968 - 2.72682i) q^{22} +(-6.02870 + 3.48067i) q^{23} +(-3.14035 - 3.76008i) q^{24} +(-2.53719 - 6.72001i) q^{26} +(-4.76720 + 2.06732i) q^{27} +(1.81484 - 1.59824i) q^{28} +(4.84407 + 2.79673i) q^{29} +(-2.83759 + 1.63828i) q^{31} +(-4.10863 + 3.88833i) q^{32} +(3.23171 + 4.16408i) q^{33} +(-0.512657 + 3.12527i) q^{34} +(2.72378 + 5.34612i) q^{36} +10.3514i q^{37} +(3.54243 + 0.581085i) q^{38} +(1.19618 + 8.71567i) q^{39} +(3.70208 - 2.13740i) q^{41} +(-2.60286 + 1.41319i) q^{42} +(-2.15991 + 3.74108i) q^{43} +(4.56769 - 4.02254i) q^{44} +(-3.47739 - 9.21023i) q^{46} +(-8.92129 - 5.15071i) q^{47} +(5.96633 - 3.52178i) q^{48} +(2.76900 + 4.79605i) q^{49} +(1.46465 - 3.59166i) q^{51} +(9.95902 - 2.00245i) q^{52} -9.42683 q^{53} +(-1.79375 - 7.12618i) q^{54} +(1.81498 + 2.89859i) q^{56} +(-4.07106 - 1.66015i) q^{57} +(-5.01192 + 6.11997i) q^{58} +(-4.46335 - 7.73074i) q^{59} +(1.32896 - 2.30183i) q^{61} +(-1.63674 - 4.33508i) q^{62} +(3.49327 - 0.977274i) q^{63} +(-4.48585 - 6.62398i) q^{64} +(-6.55104 + 3.55680i) q^{66} +(7.20867 + 12.4858i) q^{67} +(-4.24416 - 1.43089i) q^{68} +(1.63945 + 11.9454i) q^{69} -3.49303 q^{71} +(-8.08438 + 2.57736i) q^{72} +5.10052i q^{73} +(-14.4461 - 2.36967i) q^{74} +(-1.62188 + 4.81065i) q^{76} +(-1.83982 - 3.18667i) q^{77} +(-12.4371 - 0.325865i) q^{78} +(-3.26472 - 1.88488i) q^{79} +(0.197735 + 8.99783i) q^{81} +(2.13538 + 5.65579i) q^{82} +(0.495665 + 0.286172i) q^{83} +(-1.37634 - 3.95596i) q^{84} +(-4.72646 - 3.87071i) q^{86} +(7.65361 - 5.93990i) q^{87} +(4.56806 + 7.29535i) q^{88} -2.40129i q^{89} -6.14138i q^{91} +(13.6495 - 2.74449i) q^{92} +(0.771656 + 5.62248i) q^{93} +(9.23042 - 11.2711i) q^{94} +(3.54904 + 9.13260i) q^{96} +(-10.0902 - 5.82556i) q^{97} +(-7.32708 + 2.76639i) q^{98} +(8.79207 - 2.45966i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{6} - 12 q^{8} - 4 q^{9} - 28 q^{12} + 30 q^{14} + 18 q^{18} - 4 q^{21} + 42 q^{22} + 28 q^{24} + 12 q^{29} + 48 q^{33} + 6 q^{34} + 42 q^{36} + 6 q^{38} - 60 q^{41} - 16 q^{42} - 12 q^{46} + 74 q^{48}+ \cdots - 84 q^{98}+O(q^{100}) $ 48 * q + 6 * q^6 - 12 * q^8 - 4 * q^9 - 28 * q^12 + 30 * q^14 + 18 * q^18 - 4 * q^21 + 42 * q^22 + 28 * q^24 + 12 * q^29 + 48 * q^33 + 6 * q^34 + 42 * q^36 + 6 * q^38 - 60 * q^41 - 16 * q^42 - 12 * q^46 + 74 * q^48 - 24 * q^49 + 90 * q^52 + 32 * q^54 - 42 * q^56 + 16 * q^57 - 84 * q^58 - 84 * q^62 + 48 * q^64 + 16 * q^66 - 6 * q^68 - 36 * q^69 + 80 * q^72 - 84 * q^74 + 6 * q^76 + 46 * q^78 - 50 * q^84 - 54 * q^86 - 114 * q^88 + 42 * q^92 + 24 * q^93 - 18 * q^94 - 18 * q^96 + 48 * q^97 - 84 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.228922	+	1.39556i	−0.161872	+	0.986812i
$2$	−0.228922	+	1.39556i	−0.161872	+	0.986812i
$3$	0.654027	−	1.60382i	0.377603	−	0.925968i
$3$	0.654027	−	1.60382i	0.377603	−	0.925968i
$4$	−1.89519	−	0.638951i	−0.947595	−	0.319475i
$5$		0			0
$5$		0			0
$6$	2.08851	+	1.27989i	0.852632	+	0.522511i
$7$	−0.604565	+	1.04714i	−0.228504	+	0.395781i	−0.957365	−	0.288881i	$-0.906717\pi$
$7$	−0.604565	+	1.04714i	−0.228504	+	0.395781i	0.728861	+	0.684662i	$0.240050\pi$
$8$	1.32555	−	2.49858i	0.468651	−	0.883383i
$9$	−2.14450	−	2.09789i	−0.714832	−	0.699296i
$10$		0			0
$11$	−1.52161	+	2.63550i	−0.458782	+	0.794634i	−0.998897	−	0.0469575i	$-0.985047\pi$
$11$	−1.52161	+	2.63550i	−0.458782	+	0.794634i	0.540115	+	0.841591i	$0.318381\pi$
$12$	−2.26427	+	2.62166i	−0.653638	+	0.756807i
$13$	−4.39869	+	2.53958i	−1.21998	+	0.704354i	−0.964913	−	0.262570i	$-0.915430\pi$
$13$	−4.39869	+	2.53958i	−1.21998	+	0.704354i	−0.255064	+	0.966924i	$0.582096\pi$
$14$	−1.32295	−	1.08342i	−0.353573	−	0.289557i
$15$		0			0
$16$	3.18348	+	2.42186i	0.795871	+	0.605466i
$17$	2.23944			0.543143			0.271572	−	0.962418i	$-0.412457\pi$
$17$	2.23944			0.543143			0.271572	+	0.962418i	$0.412457\pi$
$18$	3.41866	−	2.51253i	0.805785	−	0.592208i
$19$		−	2.53835i		−	0.582337i	−0.956672	−	0.291169i	$-0.905956\pi$
$19$		−	2.53835i		−	0.582337i	0.956672	−	0.291169i	$-0.0940441\pi$
$20$		0			0
$21$	1.28402	+	1.65447i	0.280197	+	0.361035i
$22$	−3.32968	−	2.72682i	−0.709890	−	0.581361i
$23$	−6.02870	+	3.48067i	−1.25707	+	0.725770i	−0.972504	−	0.232886i	$-0.925183\pi$
$23$	−6.02870	+	3.48067i	−1.25707	+	0.725770i	−0.284567	+	0.958656i	$0.591850\pi$
$24$	−3.14035	−	3.76008i	−0.641020	−	0.767524i
$25$		0			0
$26$	−2.53719	−	6.72001i	−0.497584	−	1.31790i
$27$	−4.76720	+	2.06732i	−0.917448	+	0.397856i
$28$	1.81484	−	1.59824i	0.342972	−	0.302038i
$29$	4.84407	+	2.79673i	0.899521	+	0.519339i	0.877045	−	0.480408i	$-0.159512\pi$
$29$	4.84407	+	2.79673i	0.899521	+	0.519339i	0.0224766	+	0.999747i	$0.492845\pi$
$30$		0			0
$31$	−2.83759	+	1.63828i	−0.509647	+	0.294245i	−0.732688	−	0.680564i	$-0.761735\pi$
$31$	−2.83759	+	1.63828i	−0.509647	+	0.294245i	0.223042	+	0.974809i	$0.428401\pi$
$32$	−4.10863	+	3.88833i	−0.726311	+	0.687367i
$33$	3.23171	+	4.16408i	0.562568	+	0.724873i
$34$	−0.512657	+	3.12527i	−0.0879199	+	0.535980i
$35$		0			0
$36$	2.72378	+	5.34612i	0.453964	+	0.891020i
$37$			10.3514i			1.70176i	0.525356	+	0.850882i	$0.323932\pi$
$37$			10.3514i			1.70176i	−0.525356	+	0.850882i	$0.676068\pi$
$38$	3.54243	+	0.581085i	0.574657	+	0.0942644i
$39$	1.19618	+	8.71567i	0.191542	+	1.39562i
$40$		0			0
$41$	3.70208	−	2.13740i	0.578168	−	0.333806i	−0.182237	−	0.983255i	$-0.558334\pi$
$41$	3.70208	−	2.13740i	0.578168	−	0.333806i	0.760405	+	0.649449i	$0.225000\pi$
$42$	−2.60286	+	1.41319i	−0.401630	+	0.218060i
$43$	−2.15991	+	3.74108i	−0.329384	+	0.570509i	−0.982390	−	0.186844i	$-0.940174\pi$
$43$	−2.15991	+	3.74108i	−0.329384	+	0.570509i	0.653006	+	0.757353i	$0.273508\pi$
$44$	4.56769	−	4.02254i	0.688605	−	0.606421i
$45$		0			0
$46$	−3.47739	−	9.21023i	−0.512713	−	1.35797i
$47$	−8.92129	−	5.15071i	−1.30130	−	0.751308i	−0.320677	−	0.947189i	$-0.603910\pi$
$47$	−8.92129	−	5.15071i	−1.30130	−	0.751308i	−0.980628	+	0.195880i	$0.937244\pi$
$48$	5.96633	−	3.52178i	0.861165	−	0.508325i
$49$	2.76900	+	4.79605i	0.395572	+	0.685150i
$50$		0			0
$51$	1.46465	−	3.59166i	0.205092	−	0.502933i
$52$	9.95902	−	2.00245i	1.38107	−	0.277690i
$53$	−9.42683			−1.29487			−0.647437	−	0.762119i	$-0.724159\pi$
$53$	−9.42683			−1.29487			−0.647437	+	0.762119i	$0.724159\pi$
$54$	−1.79375	−	7.12618i	−0.244099	−	0.969750i
$55$		0			0
$56$	1.81498	+	2.89859i	0.242537	+	0.387340i
$57$	−4.07106	−	1.66015i	−0.539226	−	0.219892i
$58$	−5.01192	+	6.11997i	−0.658098	+	0.803592i
$59$	−4.46335	−	7.73074i	−0.581078	−	1.00646i	−0.995352	−	0.0963045i	$-0.969298\pi$
$59$	−4.46335	−	7.73074i	−0.581078	−	1.00646i	0.414274	−	0.910152i	$-0.364036\pi$
$60$		0			0
$61$	1.32896	−	2.30183i	0.170156	−	0.294720i	−0.768318	−	0.640068i	$-0.778906\pi$
$61$	1.32896	−	2.30183i	0.170156	−	0.294720i	0.938474	+	0.345349i	$0.112239\pi$
$62$	−1.63674	−	4.33508i	−0.207866	−	0.550555i
$63$	3.49327	−	0.977274i	0.440110	−	0.123125i
$64$	−4.48585	−	6.62398i	−0.560732	−	0.827998i
$65$		0			0
$66$	−6.55104	+	3.55680i	−0.806378	+	0.437812i
$67$	7.20867	+	12.4858i	0.880679	+	1.52538i	0.850588	+	0.525833i	$0.176246\pi$
$67$	7.20867	+	12.4858i	0.880679	+	1.52538i	0.0300911	+	0.999547i	$0.490420\pi$
$68$	−4.24416	−	1.43089i	−0.514679	−	0.173521i
$69$	1.63945	+	11.9454i	0.197366	+	1.43806i
$70$		0			0
$71$	−3.49303			−0.414546			−0.207273	−	0.978283i	$-0.566459\pi$
$71$	−3.49303			−0.414546			−0.207273	+	0.978283i	$0.566459\pi$
$72$	−8.08438	+	2.57736i	−0.952753	+	0.303745i
$73$			5.10052i			0.596970i	0.954414	+	0.298485i	$0.0964813\pi$
$73$			5.10052i			0.596970i	−0.954414	+	0.298485i	$0.903519\pi$
$74$	−14.4461	−	2.36967i	−1.67932	−	0.275469i
$75$		0			0
$76$	−1.62188	+	4.81065i	−0.186042	+	0.551820i
$77$	−1.83982	−	3.18667i	−0.209667	−	0.363154i
$78$	−12.4371	−	0.325865i	−1.40822	−	0.0368970i
$79$	−3.26472	−	1.88488i	−0.367309	−	0.212066i	0.304973	−	0.952361i	$-0.401353\pi$
$79$	−3.26472	−	1.88488i	−0.367309	−	0.212066i	−0.672282	+	0.740295i	$0.734686\pi$
$80$		0			0
$81$	0.197735	+	8.99783i	0.0219706	+	0.999759i
$82$	2.13538	+	5.65579i	0.235814	+	0.624577i
$83$	0.495665	+	0.286172i	0.0544063	+	0.0314115i	0.526956	−	0.849892i	$-0.323333\pi$
$83$	0.495665	+	0.286172i	0.0544063	+	0.0314115i	−0.472550	+	0.881304i	$0.656666\pi$
$84$	−1.37634	−	3.95596i	−0.150171	−	0.431631i
$85$		0			0
$86$	−4.72646	−	3.87071i	−0.509667	−	0.417389i
$87$	7.65361	−	5.93990i	0.820553	−	0.636824i
$88$	4.56806	+	7.29535i	0.486957	+	0.777687i
$89$		−	2.40129i		−	0.254536i	−0.991868	−	0.127268i	$-0.959379\pi$
$89$		−	2.40129i		−	0.254536i	0.991868	−	0.127268i	$-0.0406208\pi$
$90$		0			0
$91$		−	6.14138i		−	0.643791i
$92$	13.6495	−	2.74449i	1.42306	−	0.286133i
$93$	0.771656	+	5.62248i	0.0800170	+	0.583024i
$94$	9.23042	−	11.2711i	0.952045	−	1.16253i
$95$		0			0
$96$	3.54904	+	9.13260i	0.362222	+	0.932092i
$97$	−10.0902	−	5.82556i	−1.02450	−	0.591496i	−0.109096	−	0.994031i	$-0.534796\pi$
$97$	−10.0902	−	5.82556i	−1.02450	−	0.591496i	−0.915404	+	0.402535i	$0.868129\pi$
$98$	−7.32708	+	2.76639i	−0.740146	+	0.279448i
$99$	8.79207	−	2.45966i	0.883636	−	0.247206i
$100$		0			0
$101$	−4.13758	−	2.38883i	−0.411704	−	0.237698i	0.279818	−	0.960053i	$-0.409726\pi$
$101$	−4.13758	−	2.38883i	−0.411704	−	0.237698i	−0.691522	+	0.722356i	$0.743059\pi$
$102$	4.67709	+	2.86622i	0.463101	+	0.283798i
$103$	−4.72945	−	8.19166i	−0.466007	−	0.807148i	0.533239	−	0.845964i	$-0.320975\pi$
$103$	−4.72945	−	8.19166i	−0.466007	−	0.807148i	−0.999246	+	0.0388166i	$0.987641\pi$
$104$	0.514701	+	14.3568i	0.0504706	+	1.40780i
$105$		0			0
$106$	2.15801	−	13.1557i	0.209605	−	1.27780i
$107$		−	18.3014i		−	1.76926i	−0.466294	−	0.884630i	$-0.654411\pi$
$107$		−	18.3014i		−	1.76926i	0.466294	−	0.884630i	$-0.345589\pi$
$108$	10.3557	−	0.871955i	0.996474	−	0.0839039i
$109$	10.2589			0.982625			0.491312	−	0.870983i	$-0.336517\pi$
$109$	10.2589			0.982625			0.491312	+	0.870983i	$0.336517\pi$
$110$		0			0
$111$	16.6019	+	6.77012i	1.57578	+	0.642591i
$112$	−4.46065	+	1.86937i	−0.421492	+	0.176639i
$113$	3.06731	+	5.31273i	0.288548	+	0.499780i	0.973463	−	0.228843i	$-0.0734942\pi$
$113$	3.06731	+	5.31273i	0.288548	+	0.499780i	−0.684915	+	0.728623i	$0.740161\pi$
$114$	3.24880	−	5.30138i	0.304278	−	0.496520i
$115$		0			0
$116$	−7.39346	−	8.39545i	−0.686466	−	0.779498i
$117$	14.7607	+	3.78182i	1.36463	+	0.349630i
$118$	11.8105	−	4.45914i	1.08724	−	0.410497i
$119$	−1.35389	+	2.34500i	−0.124110	+	0.214966i
$120$		0			0
$121$	0.869419	+	1.50588i	0.0790381	+	0.136898i
$122$	2.90812	+	2.38159i	0.263289	+	0.215619i
$123$	−1.00675	−	7.33540i	−0.0907753	−	0.661411i
$124$	6.42456	−	1.29178i	0.576942	−	0.116005i
$125$		0			0
$126$	0.564161	+	5.09879i	0.0502594	+	0.454236i
$127$	9.41213			0.835192			0.417596	−	0.908633i	$-0.362873\pi$
$127$	9.41213			0.835192			0.417596	+	0.908633i	$0.362873\pi$
$128$	10.2711	−	4.74391i	0.907845	−	0.419307i
$129$	4.58739	+	5.91088i	0.403897	+	0.520424i
$130$		0			0
$131$	−1.06630	−	1.84689i	−0.0931633	−	0.161364i	0.815677	−	0.578507i	$-0.196365\pi$
$131$	−1.06630	−	1.84689i	−0.0931633	−	0.161364i	−0.908841	+	0.417144i	$0.863031\pi$
$132$	−3.46405	−	9.95662i	−0.301507	−	0.866612i
$133$	2.65800	+	1.53460i	0.230478	+	0.133067i
$134$	−19.0749	+	7.20187i	−1.64782	+	0.622147i
$135$		0			0
$136$	2.96848	−	5.59542i	0.254545	−	0.479803i
$137$	8.24344	−	14.2781i	0.704285	−	1.21986i	−0.262665	−	0.964887i	$-0.584601\pi$
$137$	8.24344	−	14.2781i	0.704285	−	1.21986i	0.966949	−	0.254969i	$-0.0820654\pi$
$138$	−17.0459	−	0.446620i	−1.45104	−	0.0380188i
$139$	−17.4077	+	10.0504i	−1.47650	+	0.852460i	−0.999648	−	0.0265213i	$-0.991557\pi$
$139$	−17.4077	+	10.0504i	−1.47650	+	0.852460i	−0.476856	+	0.878981i	$0.658224\pi$
$140$		0			0
$141$	−14.0956	+	10.9395i	−1.18706	+	0.921270i
$142$	0.799631	−	4.87474i	0.0671036	−	0.409079i
$143$		−	15.4570i		−	1.29258i
$144$	−1.74617	−	11.8723i	−0.145514	−	0.989356i
$145$		0			0
$146$	−7.11809	−	1.16762i	−0.589097	−	0.0966331i
$147$	9.50302	−	1.30424i	0.783796	−	0.107572i
$148$	6.61405	−	19.6179i	0.543672	−	1.61258i
$149$	−1.63133	+	0.941851i	−0.133644	+	0.0771594i	−0.565331	−	0.824864i	$-0.691252\pi$
$149$	−1.63133	+	0.941851i	−0.133644	+	0.0771594i	0.431687	+	0.902023i	$0.357918\pi$
$150$		0			0
$151$	−5.35919	−	3.09413i	−0.436124	−	0.251796i	0.265828	−	0.964020i	$-0.414355\pi$
$151$	−5.35919	−	3.09413i	−0.436124	−	0.251796i	−0.701952	+	0.712224i	$0.747688\pi$
$152$	−6.34228	−	3.36470i	−0.514427	−	0.272913i
$153$	−4.80246	−	4.69809i	−0.388256	−	0.379818i
$154$	4.86837	−	1.83809i	0.392304	−	0.148117i
$155$		0			0
$156$	3.30189	−	17.2822i	0.264363	−	1.38368i
$157$	1.90546	−	1.10012i	0.152073	−	0.0877991i	−0.422033	−	0.906581i	$-0.638683\pi$
$157$	1.90546	−	1.10012i	0.152073	−	0.0877991i	0.574105	+	0.818781i	$0.305350\pi$
$158$	3.37784	−	4.12462i	0.268726	−	0.328137i
$159$	−6.16540	+	15.1190i	−0.488948	+	1.19901i
$160$		0			0
$161$		−	8.41717i		−	0.663366i
$162$	−12.6023	−	1.78385i	−0.990130	−	0.140153i
$163$	15.3649			1.20347			0.601737	−	0.798694i	$-0.294475\pi$
$163$	15.3649			1.20347			0.601737	+	0.798694i	$0.294475\pi$
$164$	−8.38184	+	1.68533i	−0.654512	+	0.131602i
$165$		0			0
$166$	−0.512840	+	0.626220i	−0.0398041	+	0.0486041i
$167$	−19.2472	+	11.1124i	−1.48939	+	0.859901i	−0.999927	−	0.0121218i	$-0.996141\pi$
$167$	−19.2472	+	11.1124i	−1.48939	+	0.859901i	−0.489465	+	0.872023i	$0.662808\pi$
$168$	5.83587	−	1.01516i	0.450247	−	0.0783211i
$169$	6.39897	−	11.0833i	0.492229	−	0.852565i
$170$		0			0
$171$	−5.32517	+	5.44348i	−0.407226	+	0.416274i
$172$	6.48381	−	5.70997i	0.494386	−	0.435381i
$173$	7.70532	−	13.3460i	0.585825	−	1.01468i	−0.408947	−	0.912558i	$-0.634104\pi$
$173$	7.70532	−	13.3460i	0.585825	−	1.01468i	0.994772	−	0.102120i	$-0.0325627\pi$
$174$	6.53742	+	12.0409i	0.495600	+	0.912815i
$175$		0			0
$176$	−11.2268	+	4.70495i	−0.846255	+	0.354649i
$177$	−15.3179	+	2.10230i	−1.15136	+	0.158019i
$178$	3.35115	+	0.549708i	0.251179	+	0.0412024i
$179$	12.8229			0.958425			0.479212	−	0.877699i	$-0.340922\pi$
$179$	12.8229			0.958425			0.479212	+	0.877699i	$0.340922\pi$
$180$		0			0
$181$	17.3649			1.29072			0.645360	−	0.763879i	$-0.276707\pi$
$181$	17.3649			1.29072			0.645360	+	0.763879i	$0.276707\pi$
$182$	8.57068	+	1.40590i	0.635301	+	0.104212i
$183$	−2.82255	−	3.63688i	−0.208649	−	0.268846i
$184$	0.705432	+	19.6770i	0.0520052	+	1.45061i
$185$		0			0
$186$	−8.02317	−	0.210216i	−0.588287	−	0.0154137i
$187$	−3.40754	+	5.90204i	−0.249184	+	0.431600i
$188$	13.6165	+	15.4618i	0.993085	+	1.12767i
$189$	0.717316	−	6.24174i	0.0521771	−	0.454020i
$190$		0			0
$191$	−8.91431	+	15.4400i	−0.645017	+	1.11720i	0.339281	+	0.940685i	$0.389816\pi$
$191$	−8.91431	+	15.4400i	−0.645017	+	1.11720i	−0.984298	+	0.176516i	$0.943517\pi$
$192$	−13.5576	+	2.86225i	−0.978433	+	0.206565i
$193$	−4.22934	+	2.44181i	−0.304434	+	0.175765i	−0.644433	−	0.764661i	$-0.722907\pi$
$193$	−4.22934	+	2.44181i	−0.304434	+	0.175765i	0.339999	+	0.940426i	$0.389573\pi$
$194$	10.4398	−	12.7479i	0.749533	−	0.915242i
$195$		0			0
$196$	−2.18334	−	10.8587i	−0.155953	−	0.775620i
$197$	16.8173			1.19818			0.599090	−	0.800682i	$-0.295529\pi$
$197$	16.8173			1.19818			0.599090	+	0.800682i	$0.295529\pi$
$198$	1.41991	+	12.8330i	0.100909	+	0.911998i
$199$		−	5.91492i		−	0.419297i	−0.977777	−	0.209649i	$-0.932768\pi$
$199$		−	5.91492i		−	0.419297i	0.977777	−	0.209649i	$-0.0672320\pi$
$200$		0			0
$201$	24.7396	−	3.39539i	1.74500	−	0.239492i
$202$	4.28095	−	5.22739i	0.301206	−	0.367798i
$203$	−5.85712	+	3.38161i	−0.411089	+	0.237342i
$204$	−5.07069	+	5.87103i	−0.355019	+	0.411055i
$205$		0			0
$206$	12.5146	−	4.72500i	0.871937	−	0.329206i
$207$	20.2306	+	5.18325i	1.40612	+	0.360260i
$208$	−20.1537	−	2.56830i	−1.39741	−	0.178080i
$209$	6.68983	+	3.86237i	0.462745	+	0.267166i
$210$		0			0
$211$	23.9485	−	13.8267i	1.64868	−	0.951868i	0.671089	−	0.741377i	$-0.265827\pi$
$211$	23.9485	−	13.8267i	1.64868	−	0.951868i	0.977596	−	0.210491i	$-0.0675063\pi$
$212$	17.8656	+	6.02328i	1.22702	+	0.413681i
$213$	−2.28453	+	5.60220i	−0.156534	+	0.383856i
$214$	25.5407	+	4.18959i	1.74593	+	0.286394i
$215$		0			0
$216$	−1.15377	+	14.6516i	−0.0785043	+	0.996914i
$217$		−	3.96180i		−	0.268945i
$218$	−2.34849	+	14.3169i	−0.159060	+	0.969665i
$219$	8.18033	+	3.33588i	0.552775	+	0.225418i
$220$		0			0
$221$	−9.85058	+	5.68724i	−0.662622	+	0.382565i
$222$	−13.2487	+	21.6191i	−0.889192	+	1.45098i
$223$	−11.9737	+	20.7390i	−0.801815	+	1.38878i	0.116605	+	0.993178i	$0.462799\pi$
$223$	−11.9737	+	20.7390i	−0.801815	+	1.38878i	−0.918420	+	0.395606i	$0.870535\pi$
$224$	−1.58768	−	6.65306i	−0.106082	−	0.444526i
$225$		0			0
$226$	−8.11643	+	3.06442i	−0.539897	+	0.203842i
$227$	−5.99253	−	3.45979i	−0.397739	−	0.229634i	0.287769	−	0.957700i	$-0.407086\pi$
$227$	−5.99253	−	3.45979i	−0.397739	−	0.229634i	−0.685508	+	0.728065i	$0.740420\pi$
$228$	6.65468	+	5.74751i	0.440717	+	0.380638i
$229$	−7.65837	−	13.2647i	−0.506080	−	0.876556i	−0.999975	−	0.00703439i	$-0.997761\pi$
$229$	−7.65837	−	13.2647i	−0.506080	−	0.876556i	0.493896	−	0.869521i	$-0.335572\pi$
$230$		0			0
$231$	−6.31414	+	0.866584i	−0.415440	+	0.0570170i
$232$	13.4089	−	8.39613i	0.880337	−	0.551233i
$233$	−6.61050			−0.433068			−0.216534	−	0.976275i	$-0.569475\pi$
$233$	−6.61050			−0.433068			−0.216534	+	0.976275i	$0.569475\pi$
$234$	−8.65683	+	19.7338i	−0.565915	+	1.29004i
$235$		0			0
$236$	3.51932	+	17.5031i	0.229088	+	1.13935i
$237$	−5.15823	+	4.00326i	−0.335063	+	0.260040i
$238$	−2.96266	−	2.42625i	−0.192041	−	0.157271i
$239$	4.11060	+	7.11976i	0.265892	+	0.460539i	0.967797	−	0.251732i	$-0.0810001\pi$
$239$	4.11060	+	7.11976i	0.265892	+	0.460539i	−0.701905	+	0.712271i	$0.747667\pi$
$240$		0			0
$241$	−7.30777	+	12.6574i	−0.470735	+	0.815337i	−0.999440	−	0.0334691i	$-0.989344\pi$
$241$	−7.30777	+	12.6574i	−0.470735	+	0.815337i	0.528705	+	0.848806i	$0.322678\pi$
$242$	−2.30058	+	0.868600i	−0.147887	+	0.0558357i
$243$	14.5602	+	5.56769i	0.934040	+	0.357168i
$244$	−3.98940	+	3.51327i	−0.255395	+	0.224914i
$245$		0			0
$246$	10.4675	+	0.274259i	0.667382	+	0.0174861i
$247$	6.44635	+	11.1654i	0.410172	+	0.710438i
$248$	0.332033	+	9.26159i	0.0210841	+	0.588111i
$249$	0.783148	−	0.607794i	0.0496300	−	0.0385174i
$250$		0			0
$251$	−2.39191			−0.150976			−0.0754880	−	0.997147i	$-0.524051\pi$
$251$	−2.39191			−0.150976			−0.0754880	+	0.997147i	$0.524051\pi$
$252$	−7.24483	−	0.379905i	−0.456381	−	0.0239318i
$253$		−	21.1849i		−	1.33188i
$254$	−2.15465	+	13.1352i	−0.135195	+	0.824177i
$255$		0			0
$256$	4.26915	+	15.4199i	0.266822	+	0.963746i
$257$	−4.22474	−	7.31747i	−0.263532	−	0.456451i	0.703646	−	0.710551i	$-0.251554\pi$
$257$	−4.22474	−	7.31747i	−0.263532	−	0.456451i	−0.967178	+	0.254100i	$0.918221\pi$
$258$	−9.29916	+	5.04885i	−0.578941	+	0.314328i
$259$	−10.8394	−	6.25812i	−0.673526	−	0.388860i
$260$		0			0
$261$	−4.52088	−	16.1599i	−0.279835	−	1.00027i
$262$	2.82155	−	1.06530i	0.174316	−	0.0658143i
$263$	5.59733	+	3.23162i	0.345146	+	0.199270i	0.662545	−	0.749022i	$-0.269476\pi$
$263$	5.59733	+	3.23162i	0.345146	+	0.199270i	−0.317399	+	0.948292i	$0.602810\pi$
$264$	14.6881	−	2.55501i	0.903989	−	0.157250i
$265$		0			0
$266$	−2.75010	+	3.35810i	−0.168620	+	0.205899i
$267$	−3.85124	−	1.57051i	−0.235692	−	0.0961135i
$268$	−5.68399	−	28.2689i	−0.347205	−	1.72680i
$269$			6.14888i			0.374904i	0.982274	+	0.187452i	$0.0600229\pi$
$269$			6.14888i			0.374904i	−0.982274	+	0.187452i	$0.939977\pi$
$270$		0			0
$271$			0.446839i			0.0271436i	0.999908	+	0.0135718i	$0.00432016\pi$
$271$			0.446839i			0.0271436i	−0.999908	+	0.0135718i	$0.995680\pi$
$272$	7.12921	+	5.42361i	0.432272	+	0.328855i
$273$	−9.84968	−	4.01663i	−0.596130	−	0.243097i
$274$	18.0388	+	14.7728i	1.08976	+	0.892457i
$275$		0			0
$276$	4.52547	−	23.6864i	0.272401	−	1.42575i
$277$	5.91710	+	3.41624i	0.355524	+	0.205262i	0.667115	−	0.744954i	$-0.267529\pi$
$277$	5.91710	+	3.41624i	0.355524	+	0.205262i	−0.311592	+	0.950216i	$0.600862\pi$
$278$	−10.0409	−	26.5943i	−0.602212	−	1.59502i
$279$	9.52214	+	2.43965i	0.570076	+	0.146058i
$280$		0			0
$281$	−2.85059	−	1.64579i	−0.170052	−	0.0981794i	0.412559	−	0.910931i	$-0.364635\pi$
$281$	−2.85059	−	1.64579i	−0.170052	−	0.0981794i	−0.582610	+	0.812752i	$0.697969\pi$
$282$	−12.0399	−	22.1756i	−0.716967	−	1.32054i
$283$	11.7187	+	20.2974i	0.696603	+	1.20655i	0.969637	+	0.244548i	$0.0786395\pi$
$283$	11.7187	+	20.2974i	0.696603	+	1.20655i	−0.273034	+	0.962004i	$0.588027\pi$
$284$	6.61994	+	2.23187i	0.392821	+	0.132437i
$285$		0			0
$286$	21.5712	+	3.53845i	1.27553	+	0.209233i
$287$			5.16879i			0.305104i
$288$	16.9682	+	0.280933i	0.999863	+	0.0165541i
$289$	−11.9849			−0.704996
$290$		0			0
$291$	−15.9424	+	12.3728i	−0.934560	+	0.725304i
$292$	3.25898	−	9.66644i	0.190717	−	0.565686i
$293$	13.9565	+	24.1734i	0.815349	+	1.41223i	0.909077	+	0.416628i	$0.136788\pi$
$293$	13.9565	+	24.1734i	0.815349	+	1.41223i	−0.0937278	+	0.995598i	$0.529878\pi$
$294$	−0.355303	+	13.5606i	−0.0207217	+	0.790872i
$295$		0			0
$296$	25.8639	+	13.7213i	1.50331	+	0.797535i
$297$	1.80539	−	15.7096i	0.104759	−	0.911564i
$298$	−0.940963	−	2.49224i	−0.0545085	−	0.144371i
$299$	17.6789	−	30.6208i	1.02240	−	1.77085i
$300$		0			0
$301$	−2.61162	−	4.52345i	−0.150531	−	0.260727i
$302$	5.54488	−	6.77076i	0.319072	−	0.389614i
$303$	−6.53735	+	5.07358i	−0.375561	+	0.291470i
$304$	6.14754	−	8.08080i	0.352586	−	0.463466i
$305$		0			0
$306$	7.65586	−	5.62664i	0.437657	−	0.321654i
$307$	−22.5939			−1.28950			−0.644750	−	0.764393i	$-0.723039\pi$
$307$	−22.5939			−1.28950			−0.644750	+	0.764393i	$0.723039\pi$
$308$	1.45069	+	7.21489i	0.0826607	+	0.411107i
$309$	−16.2312	+	2.22764i	−0.923358	+	0.126726i
$310$		0			0
$311$	−2.94543	−	5.10164i	−0.167020	−	0.289287i	0.770351	−	0.637620i	$-0.220081\pi$
$311$	−2.94543	−	5.10164i	−0.167020	−	0.289287i	−0.937371	+	0.348333i	$0.886748\pi$
$312$	23.3624	+	8.56427i	1.32264	+	0.484856i
$313$	−6.72675	−	3.88369i	−0.380218	−	0.219519i	0.297695	−	0.954661i	$-0.403782\pi$
$313$	−6.72675	−	3.88369i	−0.380218	−	0.219519i	−0.677913	+	0.735142i	$0.737115\pi$
$314$	1.09908	+	2.91104i	0.0620249	+	0.164279i
$315$		0			0
$316$	4.98291	+	5.65820i	0.280310	+	0.318299i
$317$	−5.88545	+	10.1939i	−0.330560	+	0.572547i	−0.982622	−	0.185619i	$-0.940571\pi$
$317$	−5.88545	+	10.1939i	−0.330560	+	0.572547i	0.652062	+	0.758166i	$0.273904\pi$
$318$	−19.6881	−	12.0653i	−1.10405	−	0.676587i
$319$	−14.7416	+	8.51104i	−0.825369	+	0.476527i
$320$		0			0
$321$	−29.3522	−	11.9696i	−1.63828	−	0.668077i
$322$	11.7467	+	1.92688i	0.654618	+	0.107381i
$323$		−	5.68447i		−	0.316293i
$324$	5.37442	−	17.1789i	0.298579	−	0.954385i
$325$		0			0
$326$	−3.51737	+	21.4427i	−0.194809	+	1.18760i
$327$	6.70960	−	16.4535i	0.371042	−	0.909879i
$328$	−0.433190	−	12.0832i	−0.0239189	−	0.667183i
$329$	10.7870	−	6.22788i	0.594707	−	0.343354i
$330$		0			0
$331$	3.74464	+	2.16197i	0.205824	+	0.118833i	0.599369	−	0.800473i	$-0.295418\pi$
$331$	3.74464	+	2.16197i	0.205824	+	0.118833i	−0.393545	+	0.919305i	$0.628751\pi$
$332$	−0.756529	−	0.859056i	−0.0415199	−	0.0471468i
$333$	21.7161	−	22.1986i	1.19004	−	1.21648i
$334$	−11.1019	−	29.4045i	−0.607469	−	1.60894i
$335$		0			0
$336$	0.0807555	+	8.37671i	0.00440557	+	0.456987i
$337$	−6.72910	+	3.88505i	−0.366558	+	0.211632i	−0.671953	−	0.740593i	$-0.734545\pi$
$337$	−6.72910	+	3.88505i	−0.366558	+	0.211632i	0.305396	+	0.952225i	$0.401211\pi$
$338$	14.0026	+	11.4674i	0.761643	+	0.623744i
$339$	10.5268	−	1.44475i	0.571737	−	0.0784679i
$340$		0			0
$341$		−	9.97131i		−	0.539977i
$342$	−6.37767	−	8.67775i	−0.344865	−	0.469239i
$343$	−15.1601			−0.818568
$344$	6.48434	+	10.3557i	0.349612	+	0.558342i
$345$		0			0
$346$	16.8613	+	13.8085i	0.906468	+	0.742347i
$347$	9.75677	−	5.63307i	0.523771	−	0.302399i	−0.214705	−	0.976679i	$-0.568879\pi$
$347$	9.75677	−	5.63307i	0.523771	−	0.302399i	0.738476	+	0.674280i	$0.235546\pi$
$348$	−18.3003	+	6.36696i	−0.981001	+	0.341305i
$349$	−11.1403	+	19.2956i	−0.596326	+	1.03287i	0.397032	+	0.917805i	$0.370040\pi$
$349$	−11.1403	+	19.2956i	−0.596326	+	1.03287i	−0.993358	+	0.115063i	$0.963293\pi$
$350$		0			0
$351$	15.7193	−	21.2002i	0.839034	−	1.13158i
$352$	−3.99598	−	16.7448i	−0.212986	−	0.892502i
$353$	11.0323	−	19.1084i	0.587188	−	1.01704i	−0.407411	−	0.913245i	$-0.633568\pi$
$353$	11.0323	−	19.1084i	0.587188	−	1.01704i	0.994599	−	0.103794i	$-0.0330983\pi$
$354$	0.572712	−	21.8583i	0.0304393	−	1.16176i
$355$		0			0
$356$	−1.53431	+	4.55090i	−0.0813180	+	0.241197i
$357$	2.87548	+	3.70509i	0.152187	+	0.196094i
$358$	−2.93544	+	17.8951i	−0.155143	+	0.945785i
$359$	−1.70332			−0.0898978			−0.0449489	−	0.998989i	$-0.514313\pi$
$359$	−1.70332			−0.0898978			−0.0449489	+	0.998989i	$0.514313\pi$
$360$		0			0
$361$	12.5568			0.660883
$362$	−3.97520	+	24.2337i	−0.208932	+	1.27370i
$363$	2.98379	−	0.409509i	0.156608	−	0.0214937i
$364$	−3.92404	+	11.6391i	−0.205675	+	0.610053i
$365$		0			0
$366$	5.72164	−	3.10649i	0.299075	−	0.162379i
$367$	−4.71076	+	8.15927i	−0.245900	+	0.425910i	−0.962384	−	0.271692i	$-0.912417\pi$
$367$	−4.71076	+	8.15927i	−0.245900	+	0.425910i	0.716485	+	0.697603i	$0.245750\pi$
$368$	−27.6220	−	3.52003i	−1.43990	−	0.183494i
$369$	−12.4231	−	3.18291i	−0.646722	−	0.165696i
$370$		0			0
$371$	5.69914	−	9.87119i	0.295884	−	0.512487i
$372$	2.13005	−	11.1487i	0.110438	−	0.578034i
$373$	12.6314	−	7.29277i	0.654031	−	0.377605i	−0.135968	−	0.990713i	$-0.543414\pi$
$373$	12.6314	−	7.29277i	0.654031	−	0.377605i	0.789999	+	0.613108i	$0.210081\pi$
$374$	−7.45660	−	6.10655i	−0.385572	−	0.315762i
$375$		0			0
$376$	−24.6951	+	15.4631i	−1.27355	+	0.797449i
$377$	−28.4101			−1.46319
$378$	8.54654	+	2.42993i	0.439586	+	0.124982i
$379$			9.46065i			0.485961i	0.970031	+	0.242980i	$0.0781251\pi$
$379$			9.46065i			0.485961i	−0.970031	+	0.242980i	$0.921875\pi$
$380$		0			0
$381$	6.15579	−	15.0954i	0.315371	−	0.773361i
$382$	−19.5068	−	15.9750i	−0.998057	−	0.817354i
$383$	5.94105	−	3.43007i	0.303573	−	0.175268i	−0.340474	−	0.940254i	$-0.610587\pi$
$383$	5.94105	−	3.43007i	0.303573	−	0.175268i	0.644047	+	0.764986i	$0.277254\pi$
$384$	−0.890825	−	19.5757i	−0.0454597	−	0.998966i
$385$		0			0
$386$	−2.43951	−	6.46129i	−0.124168	−	0.328871i
$387$	12.4803	−	3.49148i	0.634409	−	0.177482i
$388$	15.4005	+	17.4876i	0.781843	+	0.887801i
$389$	−7.11643	−	4.10868i	−0.360818	−	0.208318i	0.308622	−	0.951185i	$-0.400132\pi$
$389$	−7.11643	−	4.10868i	−0.360818	−	0.208318i	−0.669439	+	0.742867i	$0.733466\pi$
$390$		0			0
$391$	−13.5009	+	7.79474i	−0.682769	+	0.394197i
$392$	15.6538	−	0.561197i	0.790635	−	0.0283447i
$393$	−3.65948	+	0.502244i	−0.184596	+	0.0253349i
$394$	−3.84984	+	23.4695i	−0.193952	+	1.18238i
$395$		0			0
$396$	−18.2342	−	0.956169i	−0.916305	−	0.0480493i
$397$			7.07936i			0.355303i	0.984093	+	0.177651i	$0.0568499\pi$
$397$			7.07936i			0.355303i	−0.984093	+	0.177651i	$0.943150\pi$
$398$	8.25463	+	1.35406i	0.413767	+	0.0678727i
$399$	4.19963	−	3.25930i	0.210244	−	0.163169i
$400$		0			0
$401$	−15.3220	+	8.84615i	−0.765143	+	0.441755i	−0.831139	−	0.556064i	$-0.812311\pi$
$401$	−15.3220	+	8.84615i	−0.765143	+	0.441755i	0.0659963	+	0.997820i	$0.478977\pi$
$402$	−0.924976	+	35.3030i	−0.0461336	+	1.76075i
$403$	8.32112	−	14.4126i	0.414505	−	0.717943i
$404$	6.31514	+	7.17099i	0.314190	+	0.356770i
$405$		0			0
$406$	−3.37842	−	8.94810i	−0.167668	−	0.444087i
$407$	−27.2812	−	15.7508i	−1.35228	−	0.780739i
$408$	−7.03260	−	8.42047i	−0.348166	−	0.416875i
$409$	−11.3542	−	19.6660i	−0.561428	−	0.972422i	−0.997372	−	0.0724482i	$-0.976919\pi$
$409$	−11.3542	−	19.6660i	−0.561428	−	0.972422i	0.435944	−	0.899974i	$-0.356415\pi$
$410$		0			0
$411$	−17.5080	−	22.5593i	−0.863608	−	1.11277i
$412$	3.72915	+	18.5466i	0.183722	+	0.913727i
$413$	10.7935			0.531115
$414$	−11.8648	+	27.0465i	−0.583122	+	1.32926i
$415$		0			0
$416$	8.19785	−	27.5378i	0.401933	−	1.35015i
$417$	4.73387	+	34.4921i	0.231818	+	1.68909i
$418$	−6.92163	+	8.45189i	−0.338548	+	0.413395i
$419$	−13.1805	−	22.8292i	−0.643908	−	1.11528i	−0.984553	−	0.175089i	$-0.943979\pi$
$419$	−13.1805	−	22.8292i	−0.643908	−	1.11528i	0.340645	−	0.940192i	$-0.389355\pi$
$420$		0			0
$421$	−8.57768	+	14.8570i	−0.418050	+	0.724084i	−0.995743	−	0.0921697i	$-0.970620\pi$
$421$	−8.57768	+	14.8570i	−0.418050	+	0.724084i	0.577693	+	0.816254i	$0.303953\pi$
$422$	13.8137	+	36.5869i	0.672438	+	1.78102i
$423$	8.32607	+	29.7616i	0.404828	+	1.44706i
$424$	−12.4957	+	23.5537i	−0.606845	+	1.14387i
$425$		0			0
$426$	−7.29523	−	4.47068i	−0.353455	−	0.216605i
$427$	1.60689	+	2.78322i	0.0777629	+	0.134689i
$428$	−11.6937	+	34.6846i	−0.565235	+	1.67654i
$429$	−24.7903	−	10.1093i	−1.19689	−	0.488082i
$430$		0			0
$431$	12.5816			0.606037			0.303018	−	0.952985i	$-0.402006\pi$
$431$	12.5816			0.606037			0.303018	+	0.952985i	$0.402006\pi$
$432$	−20.1831	−	4.96424i	−0.971058	−	0.238842i
$433$		−	11.7433i		−	0.564346i	−0.959364	−	0.282173i	$-0.908945\pi$
$433$		−	11.7433i		−	0.564346i	0.959364	−	0.282173i	$-0.0910553\pi$
$434$	5.52894	+	0.906944i	0.265398	+	0.0435347i
$435$		0			0
$436$	−19.4426	−	6.55493i	−0.931130	−	0.313924i
$437$	8.83516	+	15.3030i	0.422643	+	0.732039i
$438$	−6.52808	+	10.6525i	−0.311924	+	0.508996i
$439$	−1.45738	−	0.841421i	−0.0695571	−	0.0401588i	0.464818	−	0.885406i	$-0.346120\pi$
$439$	−1.45738	−	0.841421i	−0.0695571	−	0.0401588i	−0.534375	+	0.845247i	$0.679453\pi$
$440$		0			0
$441$	4.12346	−	16.0942i	0.196355	−	0.766389i
$442$	−5.68188	−	15.0490i	−0.270259	−	0.715810i
$443$	−0.657331	−	0.379510i	−0.0312307	−	0.0180311i	0.484303	−	0.874900i	$-0.339073\pi$
$443$	−0.657331	−	0.379510i	−0.0312307	−	0.0180311i	−0.515534	+	0.856869i	$0.672406\pi$
$444$	−27.1379	−	23.4384i	−1.28791	−	1.11234i
$445$		0			0
$446$	−26.2015	−	21.4576i	−1.24068	−	1.01605i
$447$	0.443626	+	3.23237i	0.0209828	+	0.152886i
$448$	9.64821	−	0.692678i	0.455835	−	0.0327260i
$449$		−	17.4579i		−	0.823887i	−0.911209	−	0.411943i	$-0.864850\pi$
$449$		−	17.4579i		−	0.823887i	0.911209	−	0.411943i	$-0.135150\pi$
$450$		0			0
$451$			13.0091i			0.612576i
$452$	−2.41856	−	12.0285i	−0.113759	−	0.565773i
$453$	−8.46749	+	6.57154i	−0.397837	+	0.308758i
$454$	6.20018	−	7.57093i	0.290989	−	0.355322i
$455$		0			0
$456$	−9.54441	+	7.97130i	−0.446958	+	0.373290i
$457$	−30.1929	−	17.4319i	−1.41237	−	0.815430i	−0.416756	−	0.909019i	$-0.636833\pi$
$457$	−30.1929	−	17.4319i	−1.41237	−	0.815430i	−0.995611	+	0.0935884i	$0.970166\pi$
$458$	20.2649	−	7.65116i	0.946916	−	0.357515i
$459$	−10.6758	+	4.62963i	−0.498306	+	0.216093i
$460$		0			0
$461$	27.0906	+	15.6407i	1.26173	+	0.728462i	0.973410	−	0.229071i	$-0.0735688\pi$
$461$	27.0906	+	15.6407i	1.26173	+	0.728462i	0.288324	+	0.957533i	$0.406902\pi$
$462$	0.236076	−	9.01016i	0.0109832	−	0.419191i
$463$	−5.14137	−	8.90511i	−0.238940	−	0.413856i	0.721471	−	0.692445i	$-0.243466\pi$
$463$	−5.14137	−	8.90511i	−0.238940	−	0.413856i	−0.960410	+	0.278589i	$0.910133\pi$
$464$	8.64773	+	20.6350i	0.401461	+	0.957957i
$465$		0			0
$466$	1.51329	−	9.22537i	0.0701018	−	0.427357i
$467$			2.90585i			0.134467i	0.997737	+	0.0672333i	$0.0214172\pi$
$467$			2.90585i			0.134467i	−0.997737	+	0.0672333i	$0.978583\pi$
$468$	−25.5580	−	16.5987i	−1.18142	−	0.767273i
$469$	−17.4324			−0.804955
$470$		0			0
$471$	−0.518173	−	3.77554i	−0.0238761	−	0.173967i
$472$	−25.2323	+	0.904592i	−1.16141	+	0.0416372i
$473$	−6.57308	−	11.3849i	−0.302231	−	0.523479i
$474$	−4.40597	−	8.11507i	−0.202373	−	0.372738i
$475$		0			0
$476$	4.06421	−	3.57915i	0.186283	−	0.164050i
$477$	20.2158	+	19.7764i	0.925618	+	0.905501i
$478$	−10.8771	+	4.10672i	−0.497506	+	0.187837i
$479$	9.42773	−	16.3293i	0.430764	−	0.746105i	−0.566175	−	0.824285i	$-0.691578\pi$
$479$	9.42773	−	16.3293i	0.430764	−	0.746105i	0.996939	+	0.0781799i	$0.0249109\pi$
$480$		0			0
$481$	−26.2883	−	45.5327i	−1.19864	−	2.07611i
$482$	−15.9913	−	13.0960i	−0.728385	−	0.596507i
$483$	−13.4997	−	5.50506i	−0.614256	−	0.250489i
$484$	−0.685532	−	3.40944i	−0.0311605	−	0.154975i
$485$		0			0
$486$	−11.1032	+	19.0452i	−0.503653	+	0.863906i
$487$	11.5696			0.524268			0.262134	−	0.965031i	$-0.415574\pi$
$487$	11.5696			0.524268			0.262134	+	0.965031i	$0.415574\pi$
$488$	−3.98972	−	6.37172i	−0.180606	−	0.288434i
$489$	10.0491	−	24.6426i	0.454435	−	1.11438i
$490$		0			0
$491$	0.747617	+	1.29491i	0.0337395	+	0.0584385i	0.882402	−	0.470496i	$-0.155925\pi$
$491$	0.747617	+	1.29491i	0.0337395	+	0.0584385i	−0.848663	+	0.528935i	$0.822592\pi$
$492$	−2.77899	+	14.5452i	−0.125286	+	0.655750i
$493$	10.8480	+	6.26309i	0.488569	+	0.282075i
$494$	−17.0577	+	6.44028i	−0.767464	+	0.289762i
$495$		0			0
$496$	−13.0011	−	1.65681i	−0.583768	−	0.0743930i
$497$	2.11176	−	3.65768i	0.0947255	−	0.164069i
$498$	0.668935	+	1.23207i	0.0299757	+	0.0552103i
$499$	27.2612	−	15.7393i	1.22038	−	0.704586i	0.255380	−	0.966841i	$-0.417799\pi$
$499$	27.2612	−	15.7393i	1.22038	−	0.704586i	0.964999	+	0.262254i	$0.0844660\pi$
$500$		0			0
$501$	5.23409	+	38.1369i	0.233842	+	1.70383i
$502$	0.547562	−	3.33806i	0.0244389	−	0.148985i
$503$			1.90449i			0.0849171i	0.999098	+	0.0424585i	$0.0135190\pi$
$503$			1.90449i			0.0849171i	−0.999098	+	0.0424585i	$0.986481\pi$
$504$	2.18868	−	10.0236i	0.0974917	−	0.446489i
$505$		0			0
$506$	29.5648	+	4.84969i	1.31432	+	0.215595i
$507$	−13.5906	−	17.5116i	−0.603581	−	0.777719i
$508$	−17.8378	−	6.01389i	−0.791423	−	0.266823i
$509$	−27.2228	+	15.7171i	−1.20663	+	0.696647i	−0.962021	−	0.272975i	$-0.911992\pi$
$509$	−27.2228	+	15.7171i	−1.20663	+	0.696647i	−0.244607	+	0.969622i	$0.578659\pi$
$510$		0			0
$511$	−5.34094	−	3.08360i	−0.236269	−	0.136410i
$512$	−22.4968	+	2.42789i	−0.994227	+	0.107299i
$513$	5.24758	+	12.1008i	0.231686	+	0.534264i
$514$	11.1791	−	4.22076i	0.493090	−	0.186170i
$515$		0			0
$516$	−4.91720	−	14.1334i	−0.216468	−	0.622186i
$517$	27.1494	−	15.6747i	1.19403	−	0.689374i
$518$	11.2150	−	13.6944i	0.492757	−	0.601698i
$519$	−16.3652	−	21.0866i	−0.718350	−	0.925600i
$520$		0			0
$521$			23.2742i			1.01966i	0.860275	+	0.509831i	$0.170292\pi$
$521$			23.2742i			1.01966i	−0.860275	+	0.509831i	$0.829708\pi$
$522$	23.5871	−	2.60981i	1.03238	−	0.114228i
$523$	−10.8804			−0.475769			−0.237884	−	0.971293i	$-0.576454\pi$
$523$	−10.8804			−0.475769			−0.237884	+	0.971293i	$0.576454\pi$
$524$	0.840774	+	4.18152i	0.0367294	+	0.182671i
$525$		0			0
$526$	−5.79128	+	7.07163i	−0.252512	+	0.308338i
$527$	−6.35461	+	3.66883i	−0.276811	+	0.159817i
$528$	0.203250	+	21.0830i	0.00884534	+	0.917521i
$529$	12.7302	−	22.0493i	0.553485	−	0.958664i
$530$		0			0
$531$	−6.64660	+	25.9422i	−0.288438	+	1.12579i
$532$	−4.05689	−	4.60669i	−0.175888	−	0.199725i
$533$	−10.8562	+	18.8035i	−0.470235	+	0.814470i
$534$	3.07338	−	5.01513i	0.132998	−	0.217026i
$535$		0			0
$536$	40.7522	−	1.46099i	1.76023	−	0.0631052i
$537$	8.38649	−	20.5656i	0.361904	−	0.887471i
$538$	−8.58115	−	1.40762i	−0.369960	−	0.0606867i
$539$	−16.8533			−0.725925
$540$		0			0
$541$	−6.53795			−0.281088			−0.140544	−	0.990074i	$-0.544885\pi$
$541$	−6.53795			−0.281088			−0.140544	+	0.990074i	$0.544885\pi$
$542$	−0.623592	−	0.102291i	−0.0267856	−	0.00439379i
$543$	11.3571	−	27.8502i	0.487379	−	1.19516i
$544$	−9.20102	+	8.70767i	−0.394491	+	0.373338i
$545$		0			0
$546$	7.86027	−	12.8264i	0.336388	−	0.548917i
$547$	−13.2886	+	23.0165i	−0.568178	+	0.984113i	0.428569	+	0.903509i	$0.359018\pi$
$547$	−13.2886	+	23.0165i	−0.568178	+	0.984113i	−0.996746	+	0.0806034i	$0.974315\pi$
$548$	−24.7458	+	21.7925i	−1.05709	+	0.930928i
$549$	−7.67895	+	2.14826i	−0.327729	+	0.0916854i
$550$		0			0
$551$	7.09907	−	12.2959i	0.302431	−	0.523825i
$552$	32.0198	+	11.7379i	1.36285	+	0.499599i
$553$	3.94747	−	2.27907i	0.167863	−	0.0969160i
$554$	−6.12213	+	7.47562i	−0.260104	+	0.317609i
$555$		0			0
$556$	39.4126	−	7.92465i	1.67147	−	0.336080i
$557$	8.68248			0.367889			0.183944	−	0.982937i	$-0.441113\pi$
$557$	8.68248			0.367889			0.183944	+	0.982937i	$0.441113\pi$
$558$	−5.58452	+	12.7303i	−0.236412	+	0.538915i
$559$		−	21.9411i		−	0.928010i
$560$		0			0
$561$	7.23720	+	9.32519i	0.305555	+	0.393710i
$562$	2.94936	−	3.60141i	0.124411	−	0.151916i
$563$	−27.4226	+	15.8324i	−1.15572	+	0.667257i	−0.950275	−	0.311411i	$-0.899199\pi$
$563$	−27.4226	+	15.8324i	−1.15572	+	0.667257i	−0.205448	+	0.978668i	$0.565865\pi$
$564$	33.7036	−	11.7260i	1.41918	−	0.493753i
$565$		0			0
$566$	−31.0089	+	11.7076i	−1.30340	+	0.492109i
$567$	−9.54151	−	5.23272i	−0.400706	−	0.219754i
$568$	−4.63017	+	8.72762i	−0.194278	+	0.366203i
$569$	−27.9697	−	16.1483i	−1.17255	−	0.676973i	−0.218272	−	0.975888i	$-0.570042\pi$
$569$	−27.9697	−	16.1483i	−1.17255	−	0.676973i	−0.954280	+	0.298915i	$0.903375\pi$
$570$		0			0
$571$	−12.7245	+	7.34651i	−0.532505	+	0.307442i	−0.742036	−	0.670360i	$-0.766140\pi$
$571$	−12.7245	+	7.34651i	−0.532505	+	0.307442i	0.209531	+	0.977802i	$0.432806\pi$
$572$	−9.87626	+	29.2939i	−0.412947	+	1.22484i
$573$	18.9329	+	24.3952i	0.790932	+	1.01912i
$574$	−7.21337	−	1.18325i	−0.301080	−	0.0493879i
$575$		0			0
$576$	−4.27647	+	23.6159i	−0.178186	+	0.983997i
$577$			22.4886i			0.936214i	0.883672	+	0.468107i	$0.155064\pi$
$577$			22.4886i			0.936214i	−0.883672	+	0.468107i	$0.844936\pi$
$578$	2.74362	−	16.7257i	0.114119	−	0.695698i
$579$	1.15013	+	8.38012i	0.0477977	+	0.348266i
$580$		0			0
$581$	−0.599324	+	0.346020i	−0.0248641	+	0.0143553i
$582$	−13.6174	−	25.0810i	−0.564459	−	1.03964i
$583$	14.3439	−	24.8444i	0.594065	−	1.02895i
$584$	12.7441	+	6.76097i	0.527354	+	0.279771i
$585$		0			0
$586$	−36.9305	+	13.9434i	−1.52558	+	0.575996i
$587$	29.8752	+	17.2484i	1.23308	+	0.711919i	0.967671	−	0.252217i	$-0.0811597\pi$
$587$	29.8752	+	17.2484i	1.23308	+	0.711919i	0.265409	+	0.964136i	$0.414493\pi$
$588$	−18.8434	−	3.60018i	−0.777087	−	0.148469i
$589$	4.15854	+	7.20280i	0.171350	+	0.296786i
$590$		0			0
$591$	10.9989	−	26.9719i	0.452436	−	1.10948i
$592$	−25.0698	+	32.9536i	−1.03036	+	1.35439i
$593$	−11.5133			−0.472794			−0.236397	−	0.971656i	$-0.575967\pi$
$593$	−11.5133			−0.472794			−0.236397	+	0.971656i	$0.575967\pi$
$594$	21.5105	+	6.11581i	0.882585	+	0.250935i
$595$		0			0
$596$	3.69348	−	0.742644i	0.151291	−	0.0304199i
$597$	−9.48648	−	3.86852i	−0.388256	−	0.158328i
$598$	38.6861	+	31.6818i	1.58199	+	1.29557i
$599$	17.8060	+	30.8410i	0.727535	+	1.26013i	0.957922	+	0.287028i	$0.0926674\pi$
$599$	17.8060	+	30.8410i	0.727535	+	1.26013i	−0.230387	+	0.973099i	$0.573999\pi$
$600$		0			0
$601$	−20.4137	+	35.3576i	−0.832693	+	1.44227i	0.0632021	+	0.998001i	$0.479869\pi$
$601$	−20.4137	+	35.3576i	−0.832693	+	1.44227i	−0.895895	+	0.444266i	$0.853465\pi$
$602$	6.91062	−	2.60916i	0.281656	−	0.106341i
$603$	10.7348	−	41.8987i	0.437155	−	1.70625i
$604$	8.17968	+	9.28821i	0.332826	+	0.377932i
$605$		0			0
$606$	−5.58395	−	10.2847i	−0.226833	−	0.417789i
$607$	1.09711	+	1.90026i	0.0445304	+	0.0771290i	0.887432	−	0.460940i	$-0.152487\pi$
$607$	1.09711	+	1.90026i	0.0445304	+	0.0771290i	−0.842901	+	0.538069i	$0.819154\pi$
$608$	9.86995	+	10.4292i	0.400279	+	0.422958i
$609$	1.59279	+	11.6054i	0.0645430	+	0.470276i
$610$		0			0
$611$	52.3227			2.11675
$612$	6.09973	+	11.9723i	0.246567	+	0.483951i
$613$			38.7673i			1.56580i	0.622149	+	0.782899i	$0.286260\pi$
$613$			38.7673i			1.56580i	−0.622149	+	0.782899i	$0.713740\pi$
$614$	5.17224	−	31.5312i	0.208735	−	1.27249i
$615$		0			0
$616$	−10.4009	+	0.372879i	−0.419065	+	0.0150237i
$617$	7.42778	+	12.8653i	0.299031	+	0.517937i	0.975915	−	0.218153i	$-0.0700033\pi$
$617$	7.42778	+	12.8653i	0.299031	+	0.517937i	−0.676884	+	0.736090i	$0.736670\pi$
$618$	0.606857	−	23.1616i	0.0244114	−	0.931694i
$619$	12.3383	+	7.12352i	0.495918	+	0.286318i	0.727026	−	0.686610i	$-0.240902\pi$
$619$	12.3383	+	7.12352i	0.495918	+	0.286318i	−0.231108	+	0.972928i	$0.574235\pi$
$620$		0			0
$621$	21.5444	−	29.0563i	0.864545	−	1.16599i
$622$	7.79393	−	2.94266i	0.312508	−	0.117990i
$623$	2.51448	+	1.45174i	0.100741	+	0.0581626i
$624$	−17.3002	+	30.6432i	−0.692561	+	1.22671i
$625$		0			0
$626$	6.95983	−	8.49853i	0.278171	−	0.339670i
$627$	10.5699	−	8.20320i	0.422121	−	0.327604i
$628$	−4.31414	+	0.867439i	−0.172153	+	0.0346146i
$629$			23.1814i			0.924302i
$630$		0			0
$631$			38.8200i			1.54540i	0.634772	+	0.772700i	$0.281094\pi$
$631$			38.8200i			1.54540i	−0.634772	+	0.772700i	$0.718906\pi$
$632$	−9.03707	+	5.65867i	−0.359476	+	0.225090i
$633$	−6.51258	−	47.4522i	−0.258852	−	1.88606i
$634$	−12.8789	−	10.5471i	−0.511487	−	0.418880i
$635$		0			0
$636$	21.3449	−	24.7139i	0.846380	−	0.979971i
$637$	−24.3599	−	14.0642i	−0.965176	−	0.557245i
$638$	−8.50302	−	22.5211i	−0.336638	−	0.891620i
$639$	7.49078	+	7.32798i	0.296331	+	0.289890i
$640$		0			0
$641$	16.5595	+	9.56061i	0.654060	+	0.377621i	0.790010	−	0.613094i	$-0.210075\pi$
$641$	16.5595	+	9.56061i	0.654060	+	0.377621i	−0.135950	+	0.990716i	$0.543409\pi$
$642$	23.4237	−	38.2227i	0.924459	−	1.50853i
$643$	3.28595	+	5.69143i	0.129585	+	0.224448i	0.923516	−	0.383560i	$-0.125302\pi$
$643$	3.28595	+	5.69143i	0.129585	+	0.224448i	−0.793931	+	0.608008i	$0.791969\pi$
$644$	−5.37816	+	15.9521i	−0.211929	+	0.628602i
$645$		0			0
$646$	7.93304	+	1.30130i	0.312121	+	0.0511991i
$647$		−	12.7191i		−	0.500040i	−0.968241	−	0.250020i	$-0.919563\pi$
$647$		−	12.7191i		−	0.500040i	0.968241	−	0.250020i	$-0.0804373\pi$
$648$	22.7439	+	11.4330i	0.893466	+	0.449130i
$649$	27.1658			1.06635
$650$		0			0
$651$	−6.35403	−	2.59112i	−0.249034	−	0.101554i
$652$	−29.1195	−	9.81743i	−1.14041	−	0.384480i
$653$	−22.0410	−	38.1762i	−0.862532	−	1.49395i	−0.869477	−	0.493974i	$-0.835544\pi$
$653$	−22.0410	−	38.1762i	−0.862532	−	1.49395i	0.00694441	−	0.999976i	$-0.497790\pi$
$654$	21.4259	+	13.1302i	0.837817	+	0.513433i
$655$		0			0
$656$	16.9620	+	2.16157i	0.662256	+	0.0843951i
$657$	10.7003	−	10.9380i	0.417459	−	0.426734i
$658$	6.22201	+	16.4796i	0.242559	+	0.642444i
$659$	−10.8929	+	18.8671i	−0.424328	+	0.734957i	−0.996357	−	0.0852757i	$-0.972823\pi$
$659$	−10.8929	+	18.8671i	−0.424328	+	0.734957i	0.572030	+	0.820233i	$0.306156\pi$
$660$		0			0
$661$	−10.2756	−	17.7979i	−0.399676	−	0.692260i	0.594009	−	0.804458i	$-0.297544\pi$
$661$	−10.2756	−	17.7979i	−0.399676	−	0.692260i	−0.993686	+	0.112198i	$0.964211\pi$
$662$	−3.87439	+	4.73096i	−0.150583	+	0.183874i
$663$	2.67877	+	19.5182i	0.104035	+	0.758024i
$664$	1.37205	−	0.859126i	0.0532460	−	0.0333406i
$665$		0			0
$666$	26.0082	+	35.3880i	1.00780	+	1.37126i
$667$	−38.9379			−1.50768
$668$	43.5773	−	8.76204i	1.68606	−	0.339014i
$669$	25.4305	+	32.7675i	0.983202	+	1.26686i
$670$		0			0
$671$	4.04432	+	7.00497i	0.156129	+	0.270424i
$672$	−11.7087	−	1.80492i	−0.451673	−	0.0696262i
$673$	1.88576	+	1.08874i	0.0726906	+	0.0419680i	0.535905	−	0.844278i	$-0.319971\pi$
$673$	1.88576	+	1.08874i	0.0726906	+	0.0419680i	−0.463214	+	0.886246i	$0.653304\pi$
$674$	−3.88139	−	10.2803i	−0.149505	−	0.395981i
$675$		0			0
$676$	−19.2090	+	16.9164i	−0.738807	+	0.650631i
$677$	1.11336	−	1.92840i	0.0427899	−	0.0741143i	−0.843837	−	0.536599i	$-0.819709\pi$
$677$	1.11336	−	1.92840i	0.0427899	−	0.0741143i	0.886627	+	0.462485i	$0.153042\pi$
$678$	−0.393580	+	15.0215i	−0.0151153	+	0.576898i
$679$	12.2003	−	7.04386i	0.468205	−	0.270319i
$680$		0			0
$681$	−9.46817	+	7.34817i	−0.362821	+	0.281582i
$682$	13.9156	+	2.28265i	0.532855	+	0.0874073i
$683$			12.9800i			0.496665i	0.968675	+	0.248333i	$0.0798826\pi$
$683$			12.9800i			0.496665i	−0.968675	+	0.248333i	$0.920117\pi$
$684$	13.5703	−	6.91391i	0.518874	−	0.264360i
$685$		0			0
$686$	3.47048	−	21.1568i	0.132504	−	0.807772i
$687$	−26.2830	+	3.60721i	−1.00276	+	0.137624i
$688$	−15.9364	+	6.67865i	−0.607571	+	0.254621i
$689$	41.4657	−	23.9402i	1.57972	−	0.912050i
$690$		0			0
$691$	24.1859	+	13.9637i	0.920074	+	0.531205i	0.883659	−	0.468132i	$-0.155073\pi$
$691$	24.1859	+	13.9637i	0.920074	+	0.531205i	0.0364156	+	0.999337i	$0.488406\pi$
$692$	−23.1305	+	20.3699i	−0.879289	+	0.774347i
$693$	−2.73977	+	10.6935i	−0.104075	+	0.406214i
$694$	5.62776	+	14.9057i	0.213627	+	0.565813i
$695$		0			0
$696$	−4.69613	−	26.9968i	−0.178006	−	1.02331i
$697$	8.29058	−	4.78657i	0.314028	−	0.181304i
$698$	−24.3779	−	19.9642i	−0.922717	−	0.755655i
$699$	−4.32345	+	10.6021i	−0.163528	+	0.401007i
$700$		0			0
$701$		−	31.0643i		−	1.17328i	−0.809847	−	0.586641i	$-0.800450\pi$
$701$		−	31.0643i		−	1.17328i	0.809847	−	0.586641i	$-0.199550\pi$
$702$	25.9877	+	26.7905i	0.980842	+	1.01114i
$703$	26.2756			0.991001
$704$	24.2832	−	1.74338i	0.915208	−	0.0657060i
$705$		0			0
$706$	24.1415	+	19.7705i	0.908576	+	0.744074i
$707$	5.00287	−	2.88841i	0.188152	−	0.108630i
$708$	30.3736	+	5.80311i	1.14151	+	0.218094i
$709$	−21.7239	+	37.6269i	−0.815859	+	1.41311i	0.0928511	+	0.995680i	$0.470402\pi$
$709$	−21.7239	+	37.6269i	−0.815859	+	1.41311i	−0.908710	+	0.417429i	$0.862931\pi$
$710$		0			0
$711$	3.04690	+	10.8911i	0.114268	+	0.408449i
$712$	−5.99982	−	3.18302i	−0.224853	−	0.119289i
$713$	11.4047	−	19.7535i	0.427108	−	0.739773i
$714$	−5.82894	+	3.16474i	−0.218143	+	0.118438i
$715$		0			0
$716$	−24.3017	−	8.19317i	−0.908198	−	0.306193i
$717$	14.1073	−	1.93615i	0.526846	−	0.0723069i
$718$	0.389928	−	2.37709i	0.0145520	−	0.0887122i
$719$	12.6495			0.471747			0.235874	−	0.971784i	$-0.424205\pi$
$719$	12.6495			0.471747			0.235874	+	0.971784i	$0.424205\pi$
$720$		0			0
$721$	11.4371			0.425938
$722$	−2.87453	+	17.5238i	−0.106979	+	0.652167i
$723$	15.5208	+	19.9987i	0.577225	+	0.743759i
$724$	−32.9097	−	11.0953i	−1.22308	−	0.412353i
$725$		0			0
$726$	−0.111559	+	4.25780i	−0.00414034	+	0.158022i
$727$	25.0590	−	43.4035i	0.929389	−	1.60975i	0.145042	−	0.989425i	$-0.453668\pi$
$727$	25.0590	−	43.4035i	0.929389	−	1.60975i	0.784347	−	0.620323i	$-0.212998\pi$
$728$	−15.3448	−	8.14068i	−0.568714	−	0.301714i
$729$	18.4524	−	19.7106i	0.683422	−	0.730024i
$730$		0			0
$731$	−4.83699	+	8.37791i	−0.178902	+	0.309868i
$732$	3.02549	+	8.69606i	0.111825	+	0.321415i
$733$	−25.5178	+	14.7327i	−0.942523	+	0.544166i	−0.890750	−	0.454493i	$-0.849821\pi$
$733$	−25.5178	+	14.7327i	−0.942523	+	0.544166i	−0.0517728	+	0.998659i	$0.516487\pi$
$734$	−10.3084	−	8.44199i	−0.380489	−	0.311600i
$735$		0			0
$736$	11.2357	−	37.7424i	0.414154	−	1.39120i
$737$	−43.8751			−1.61616
$738$	7.28588	−	16.6086i	0.268197	−	0.611372i
$739$			45.3131i			1.66687i	0.552618	+	0.833435i	$0.313629\pi$
$739$			45.3131i			1.66687i	−0.552618	+	0.833435i	$0.686371\pi$
$740$		0			0
$741$	22.1234	−	3.03633i	0.812725	−	0.111542i
$742$	12.4712	+	10.2132i	0.457832	+	0.374940i
$743$	6.99366	−	4.03779i	0.256573	−	0.148132i	−0.366197	−	0.930537i	$-0.619341\pi$
$743$	6.99366	−	4.03779i	0.256573	−	0.148132i	0.622770	+	0.782405i	$0.286007\pi$
$744$	15.0711	+	5.52481i	0.552534	+	0.202549i
$745$		0			0
$746$	7.28589	+	19.2974i	0.266756	+	0.706530i
$747$	−0.462595	−	1.65354i	−0.0169255	−	0.0605000i
$748$	10.2291	−	9.00823i	0.374011	−	0.329373i
$749$	19.1641	+	11.0644i	0.700239	+	0.404283i
$750$		0			0
$751$	9.71367	−	5.60819i	0.354457	−	0.204646i	−0.312190	−	0.950020i	$-0.601062\pi$
$751$	9.71367	−	5.60819i	0.354457	−	0.204646i	0.666646	+	0.745374i	$0.267729\pi$
$752$	−15.9265	−	38.0034i	−0.580779	−	1.38584i
$753$	−1.56437	+	3.83620i	−0.0570090	+	0.139799i
$754$	6.50370	−	39.6480i	0.236851	−	1.44390i
$755$		0			0
$756$	−5.34762	+	11.3710i	−0.194491	+	0.413558i
$757$			26.9148i			0.978236i	0.872218	+	0.489118i	$0.162681\pi$
$757$			26.9148i			0.978236i	−0.872218	+	0.489118i	$0.837319\pi$
$758$	−13.2029	−	2.16575i	−0.479552	−	0.0786637i
$759$	−33.9768	−	13.8555i	−1.23328	−	0.502922i
$760$		0			0
$761$	6.74550	−	3.89451i	0.244524	−	0.141176i	−0.372730	−	0.927940i	$-0.621578\pi$
$761$	6.74550	−	3.89451i	0.244524	−	0.141176i	0.617254	+	0.786764i	$0.288245\pi$
$762$	19.6574	+	12.0465i	0.712111	+	0.436397i
$763$	−6.20218	+	10.7425i	−0.224534	+	0.388904i
$764$	26.7597	−	23.5660i	0.968132	−	0.852587i
$765$		0			0
$766$	3.42683	+	9.07632i	0.123816	+	0.327941i
$767$	39.2657	+	22.6701i	1.41780	+	0.818569i
$768$	27.5230	+	3.23810i	0.993150	+	0.116845i
$769$	3.36491	+	5.82819i	0.121342	+	0.210170i	0.920297	−	0.391220i	$-0.127947\pi$
$769$	3.36491	+	5.82819i	0.121342	+	0.210170i	−0.798955	+	0.601390i	$0.794614\pi$
$770$		0			0
$771$	−14.4990	+	1.98992i	−0.522170	+	0.0716651i
$772$	9.57559	−	1.92535i	0.344633	−	0.0692950i
$773$	16.5270			0.594435			0.297217	−	0.954810i	$-0.403941\pi$
$773$	16.5270			0.594435			0.297217	+	0.954810i	$0.403941\pi$
$774$	2.01556	+	18.2163i	0.0724478	+	0.654771i
$775$		0			0
$776$	−27.9306	+	17.4891i	−1.00265	+	0.627821i
$777$	−17.1262	+	13.2915i	−0.614398	+	0.476829i
$778$	7.36302	−	8.99086i	0.263977	−	0.322338i
$779$	−5.42547	−	9.39719i	−0.194388	−	0.336689i
$780$		0			0
$781$	5.31502	−	9.20588i	0.190186	−	0.329412i
$782$	−7.78740	−	20.6257i	−0.278477	−	0.737574i
$783$	−28.8744	−	3.31831i	−1.03189	−	0.118587i
$784$	−2.80031	+	21.9743i	−0.100011	+	0.784796i
$785$		0			0
$786$	0.136822	−	5.22200i	0.00488028	−	0.186263i
$787$	−1.37971	−	2.38973i	−0.0491814	−	0.0851847i	0.840387	−	0.541987i	$-0.182328\pi$
$787$	−1.37971	−	2.38973i	−0.0491814	−	0.0851847i	−0.889568	+	0.456803i	$0.848995\pi$
$788$	−31.8719	−	10.7454i	−1.13539	−	0.382789i
$789$	8.84375	−	6.86356i	0.314846	−	0.244349i
$790$		0			0
$791$	−7.41755			−0.263738
$792$	5.50862	−	25.2281i	0.195740	−	0.896443i
$793$			13.5001i			0.479401i
$794$	−9.87968	−	1.62062i	−0.350617	−	0.0575137i
$795$		0			0
$796$	−3.77934	+	11.2099i	−0.133955	+	0.397324i
$797$	−2.62123	−	4.54011i	−0.0928488	−	0.160819i	0.815860	−	0.578250i	$-0.196264\pi$
$797$	−2.62123	−	4.54011i	−0.0928488	−	0.160819i	−0.908709	+	0.417431i	$0.862931\pi$
$798$	3.58716	+	6.60697i	0.126984	+	0.233884i
$799$	−19.9787	−	11.5347i	−0.706794	−	0.408068i
$800$		0			0
$801$	−5.03763	+	5.14956i	−0.177996	+	0.181951i
$802$	−8.83781	−	23.4079i	−0.312074	−	0.826560i
$803$	−13.4424	−	7.76099i	−0.474373	−	0.273879i
$804$	−49.0558	−	9.37250i	−1.73006	−	0.330543i
$805$		0			0
$806$	18.2088	+	14.9120i	0.641378	+	0.525253i
$807$	9.86172	+	4.02154i	0.347149	+	0.141565i
$808$	−11.4532	+	7.17158i	−0.402924	+	0.252295i
$809$			47.1813i			1.65881i	0.558650	+	0.829403i	$0.311319\pi$
$809$			47.1813i			1.65881i	−0.558650	+	0.829403i	$0.688681\pi$
$810$		0			0
$811$			18.8666i			0.662495i	0.943544	+	0.331247i	$0.107469\pi$
$811$			18.8666i			0.662495i	−0.943544	+	0.331247i	$0.892531\pi$
$812$	13.2610	−	2.66638i	0.465371	−	0.0935715i
$813$	0.716651	+	0.292245i	0.0251341	+	0.0102495i
$814$	28.2265	−	34.4669i	0.989339	−	1.20807i
$815$		0			0
$816$	13.3612	−	7.88680i	0.467736	−	0.276093i
$817$	9.49617	+	5.48261i	0.332229	+	0.191812i
$818$	30.0444	−	11.3435i	1.05048	−	0.396615i
$819$	−12.8839	+	13.1702i	−0.450201	+	0.460203i
$820$		0			0
$821$	1.12399	+	0.648938i	0.0392277	+	0.0226481i	0.519486	−	0.854479i	$-0.326124\pi$
$821$	1.12399	+	0.648938i	0.0392277	+	0.0226481i	−0.480258	+	0.877127i	$0.659457\pi$
$822$	35.4908	−	19.2693i	1.23788	−	0.672092i
$823$	3.33531	+	5.77693i	0.116262	+	0.201371i	0.918283	−	0.395924i	$-0.129576\pi$
$823$	3.33531	+	5.77693i	0.116262	+	0.201371i	−0.802022	+	0.597295i	$0.796242\pi$
$824$	−26.7367	+	0.958525i	−0.931416	+	0.0333918i
$825$		0			0
$826$	−2.47088	+	15.0631i	−0.0859729	+	0.524111i
$827$			37.4924i			1.30374i	0.758331	+	0.651869i	$0.226015\pi$
$827$			37.4924i			1.30374i	−0.758331	+	0.651869i	$0.773985\pi$
$828$	−35.0290	−	22.7496i	−1.21734	−	0.790602i
$829$	22.9261			0.796255			0.398127	−	0.917330i	$-0.369660\pi$
$829$	22.9261			0.796255			0.398127	+	0.917330i	$0.369660\pi$
$830$		0			0
$831$	9.34898	−	7.25566i	0.324313	−	0.251696i
$832$	36.5540	+	17.7446i	1.26728	+	0.615184i
$833$	6.20100	+	10.7405i	0.214852	+	0.372135i
$834$	−49.2196	−	1.28961i	−1.70434	−	0.0446554i
$835$		0			0
$836$	−10.2106	−	11.5944i	−0.353142	−	0.401001i
$837$	10.1405	−	13.6762i	0.350507	−	0.472720i
$838$	34.8769	−	13.1680i	1.20480	−	0.454882i
$839$	−9.11048	+	15.7798i	−0.314529	+	0.544780i	−0.979337	−	0.202234i	$-0.935180\pi$
$839$	−9.11048	+	15.7798i	−0.314529	+	0.544780i	0.664808	+	0.747014i	$0.268513\pi$
$840$		0			0
$841$	1.14335	+	1.98034i	0.0394259	+	0.0682877i
$842$	−18.7702	−	15.3718i	−0.646864	−	0.529746i
$843$	−4.50391	+	3.49545i	−0.155123	+	0.120390i
$844$	−54.2216	+	10.9023i	−1.86638	+	0.375271i
$845$		0			0
$846$	−43.4401	+	4.80648i	−1.49350	+	0.165250i
$847$	−2.10248			−0.0722422
$848$	−30.0102	−	22.8305i	−1.03055	−	0.784003i
$849$	40.2177	−	5.51967i	1.38027	−	0.189435i
$850$		0			0
$851$	−36.0299	−	62.4057i	−1.23509	−	2.13924i
$852$	7.90915	−	9.15752i	0.270963	−	0.313731i
$853$	1.68958	+	0.975478i	0.0578500	+	0.0333997i	0.528646	−	0.848842i	$-0.322700\pi$
$853$	1.68958	+	0.975478i	0.0578500	+	0.0333997i	−0.470796	+	0.882242i	$0.656033\pi$
$854$	−4.25201	+	1.60538i	−0.145501	+	0.0549349i
$855$		0			0
$856$	−45.7275	−	24.2593i	−1.56293	−	0.829166i
$857$	6.51166	−	11.2785i	0.222434	−	0.385267i	−0.733113	−	0.680107i	$-0.761933\pi$
$857$	6.51166	−	11.2785i	0.222434	−	0.385267i	0.955546	+	0.294840i	$0.0952665\pi$
$858$	19.7832	−	32.2822i	0.675388	−	1.10210i
$859$	−3.50034	+	2.02092i	−0.119430	+	0.0689530i	−0.558525	−	0.829488i	$-0.688633\pi$
$859$	−3.50034	+	2.02092i	−0.119430	+	0.0689530i	0.439095	+	0.898441i	$0.355299\pi$
$860$		0			0
$861$	8.28982	+	3.38053i	0.282516	+	0.115208i
$862$	−2.88022	+	17.5585i	−0.0981006	+	0.598044i
$863$		−	10.6258i		−	0.361705i	−0.983510	−	0.180853i	$-0.942114\pi$
$863$		−	10.6258i		−	0.361705i	0.983510	−	0.180853i	$-0.0578857\pi$
$864$	11.5483	−	27.0303i	0.392880	−	0.919590i
$865$		0			0
$866$	16.3885	+	2.68830i	0.556903	+	0.0913521i
$867$	−7.83847	+	19.2217i	−0.266208	+	0.652803i
$868$	−2.53139	+	7.50836i	−0.0859211	+	0.254850i
$869$	9.93523	−	5.73611i	0.337030	−	0.194584i
$870$		0			0
$871$	−63.4174	−	36.6140i	−2.14882	−	1.24062i
$872$	13.5986	−	25.6327i	0.460508	−	0.868034i
$873$	9.41696	+	33.6609i	0.318716	+	1.13925i
$874$	−23.3788	+	8.82684i	−0.790799	+	0.298572i
$875$		0			0
$876$	−13.3718	−	11.5489i	−0.451791	−	0.390203i
$877$	45.9911	−	26.5530i	1.55301	−	0.896631i	0.555115	−	0.831774i	$-0.312674\pi$
$877$	45.9911	−	26.5530i	1.55301	−	0.896631i	0.997895	−	0.0648570i	$-0.0206591\pi$
$878$	1.50788	−	1.84125i	0.0508886	−	0.0621392i
$879$	47.8978	−	6.57373i	1.61555	−	0.221727i
$880$		0			0
$881$		−	10.8244i		−	0.364685i	−0.983235	−	0.182342i	$-0.941632\pi$
$881$		−	10.8244i		−	0.364685i	0.983235	−	0.182342i	$-0.0583679\pi$
$882$	21.5165	+	9.43886i	0.724497	+	0.317823i
$883$	−21.6083			−0.727178			−0.363589	−	0.931559i	$-0.618449\pi$
$883$	−21.6083			−0.727178			−0.363589	+	0.931559i	$0.618449\pi$
$884$	22.3026	−	4.48435i	0.750117	−	0.150825i
$885$		0			0
$886$	0.680108	−	0.830468i	0.0228487	−	0.0279001i
$887$	0.457306	−	0.264026i	0.0153548	−	0.00886511i	−0.492303	−	0.870424i	$-0.663845\pi$
$887$	0.457306	−	0.264026i	0.0153548	−	0.00886511i	0.507658	+	0.861559i	$0.330511\pi$
$888$	38.9223	−	32.5071i	1.30615	−	1.09087i
$889$	−5.69025	+	9.85580i	−0.190845	+	0.330553i
$890$		0			0
$891$	−24.0147	−	13.1700i	−0.804522	−	0.441213i
$892$	35.9435	−	31.6537i	1.20348	−	1.05984i
$893$	−13.0743	+	22.6454i	−0.437515	+	0.757798i
$894$	−4.61252	−	0.120853i	−0.154266	−	0.00404193i
$895$		0			0
$896$	−1.24201	+	13.6233i	−0.0414928	+	0.455121i
$897$	−37.5478	−	48.3807i	−1.25369	−	1.61538i
$898$	24.3635	+	3.99649i	0.813021	+	0.133365i
$899$	−18.3273			−0.611251
$900$		0			0
$901$	−21.1108			−0.703302
$902$	−18.1551	−	2.97808i	−0.604497	−	0.0991592i
$903$	−8.96289	+	1.23011i	−0.298266	+	0.0409355i
$904$	17.3402	−	0.621656i	0.576726	−	0.0206760i
$905$		0			0
$906$	−7.23260	−	13.3213i	−0.240287	−	0.442570i
$907$	23.6647	−	40.9884i	0.785773	−	1.36100i	−0.142763	−	0.989757i	$-0.545599\pi$
$907$	23.6647	−	40.9884i	0.785773	−	1.36100i	0.928536	−	0.371242i	$-0.121068\pi$
$908$	9.14635	+	10.3859i	0.303532	+	0.344668i
$909$	3.86152	+	13.8030i	0.128079	+	0.457817i
$910$		0			0
$911$	−18.8160	+	32.5902i	−0.623401	+	1.07976i	0.365447	+	0.930832i	$0.380916\pi$
$911$	−18.8160	+	32.5902i	−0.623401	+	1.07976i	−0.988848	+	0.148930i	$0.952417\pi$
$912$	−8.93951	−	15.1446i	−0.296017	−	0.501489i
$913$	−1.50841	+	0.870884i	−0.0499213	+	0.0288220i
$914$	31.2392	−	38.1456i	1.03330	−	1.26174i
$915$		0			0
$916$	6.03859	+	30.0324i	0.199520	+	0.992299i
$917$	2.57860			0.0851528
$918$	−4.01700	−	15.9586i	−0.132581	−	0.526713i
$919$			42.9157i			1.41566i	0.706383	+	0.707830i	$0.250326\pi$
$919$			42.9157i			1.41566i	−0.706383	+	0.707830i	$0.749674\pi$
$920$		0			0
$921$	−14.7770	+	36.2366i	−0.486919	+	1.19404i
$922$	−28.0293	+	34.2261i	−0.923095	+	1.12718i
$923$	15.3647	−	8.87083i	0.505736	−	0.291987i
$924$	12.5202	+	2.39208i	0.411884	+	0.0786938i
$925$		0			0
$926$	13.6046	−	5.13652i	0.447075	−	0.168797i
$927$	−7.04287	+	27.4888i	−0.231318	+	0.902852i
$928$	−30.7771	+	7.34464i	−1.01031	+	0.241100i
$929$	25.1609	+	14.5267i	0.825503	+	0.476605i	0.852311	−	0.523036i	$-0.175201\pi$
$929$	25.1609	+	14.5267i	0.825503	+	0.476605i	−0.0268072	+	0.999641i	$0.508534\pi$
$930$		0			0
$931$	12.1741	−	7.02870i	0.398989	−	0.230356i
$932$	12.5282	+	4.22378i	0.410373	+	0.138355i
$933$	−10.1085	+	1.38734i	−0.330938	+	0.0454196i
$934$	−4.05529	−	0.665213i	−0.132693	−	0.0217665i
$935$		0			0
$936$	29.0152	−	31.8680i	0.948393	−	1.04164i
$937$		−	51.0143i		−	1.66656i	−0.552848	−	0.833282i	$-0.686459\pi$
$937$		−	51.0143i		−	1.66656i	0.552848	−	0.833282i	$-0.313541\pi$
$938$	3.99067	−	24.3281i	0.130300	−	0.794339i
$939$	−10.6282	+	8.24847i	−0.346839	+	0.269179i
$940$		0			0
$941$	7.54730	−	4.35743i	0.246035	−	0.142048i	−0.371912	−	0.928268i	$-0.621298\pi$
$941$	7.54730	−	4.35743i	0.246035	−	0.142048i	0.617947	+	0.786220i	$0.287964\pi$
$942$	5.38762	+	0.141161i	0.175538	+	0.00459928i
$943$	−14.8792	+	25.7715i	−0.484532	+	0.839235i
$944$	4.51382	−	35.4203i	0.146912	−	1.15283i
$945$		0			0
$946$	17.3931	−	6.56689i	0.565498	−	0.213508i
$947$	33.0481	+	19.0803i	1.07392	+	0.620028i	0.929250	−	0.369452i	$-0.120455\pi$
$947$	33.0481	+	19.0803i	1.07392	+	0.620028i	0.144670	+	0.989480i	$0.453788\pi$
$948$	12.3337	−	4.29108i	0.400580	−	0.139368i
$949$	−12.9532	−	22.4356i	−0.420478	−	0.728290i
$950$		0			0
$951$	12.5000	+	16.1063i	0.405339	+	0.522283i
$952$	4.06454	+	6.49120i	0.131732	+	0.210381i
$953$	−40.4395			−1.30996			−0.654982	−	0.755645i	$-0.727324\pi$
$953$	−40.4395			−1.30996			−0.654982	+	0.755645i	$0.727324\pi$
$954$	−32.2271	+	23.6852i	−1.04339	+	0.766835i
$955$		0			0
$956$	−3.24118	−	16.1198i	−0.104827	−	0.521350i
$957$	4.00883	+	29.2093i	0.129587	+	0.944202i
$958$	20.6303	+	16.8951i	0.666536	+	0.545857i
$959$	9.96739	+	17.2640i	0.321864	+	0.557485i
$960$		0			0
$961$	−10.1320	+	17.5492i	−0.326840	+	0.566104i
$962$	69.5617	−	26.2636i	2.24276	−	0.846771i
$963$	−38.3942	+	39.2472i	−1.23724	+	1.26472i
$964$	21.9371	−	19.3189i	0.706546	−	0.622220i
$965$		0			0
$966$	10.7730	−	17.5794i	0.346616	−	0.565607i
$967$	−8.41511	−	14.5754i	−0.270612	−	0.468713i	0.698407	−	0.715701i	$-0.253893\pi$
$967$	−8.41511	−	14.5754i	−0.270612	−	0.468713i	−0.969019	+	0.246988i	$0.920559\pi$
$968$	4.91502	−	0.176206i	0.157975	−	0.00566349i
$969$	−9.11689	−	3.71780i	−0.292877	−	0.119433i
$970$		0			0
$971$	−34.0951			−1.09416			−0.547082	−	0.837079i	$-0.684262\pi$
$971$	−34.0951			−1.09416			−0.547082	+	0.837079i	$0.684262\pi$
$972$	−24.0369	−	19.8551i	−0.770985	−	0.636853i
$973$		−	24.3044i		−	0.779163i
$974$	−2.64854	+	16.1461i	−0.0848646	+	0.517354i
$975$		0			0
$976$	9.80546	−	4.10928i	0.313865	−	0.131535i
$977$	−0.431943	−	0.748148i	−0.0138191	−	0.0239354i	0.859033	−	0.511920i	$-0.171066\pi$
$977$	−0.431943	−	0.748148i	−0.0138191	−	0.0239354i	−0.872852	+	0.487985i	$0.837732\pi$
$978$	32.0899	+	19.6654i	1.02612	+	0.628829i
$979$	6.32860	+	3.65382i	0.202263	+	0.116777i
$980$		0			0
$981$	−22.0002	−	21.5220i	−0.702412	−	0.687145i
$982$	−1.97828	+	0.746913i	−0.0631293	+	0.0238349i
$983$	31.8882	+	18.4107i	1.01708	+	0.587209i	0.913256	−	0.407387i	$-0.133560\pi$
$983$	31.8882	+	18.4107i	1.01708	+	0.587209i	0.103821	+	0.994596i	$0.466893\pi$
$984$	−19.6626	−	7.20798i	−0.626821	−	0.229782i
$985$		0			0
$986$	−11.2239	+	13.7053i	−0.357441	+	0.436465i
$987$	−2.93343	−	21.3737i	−0.0933720	−	0.680331i
$988$	−5.08291	−	25.2795i	−0.161709	−	0.804247i
$989$		−	30.0718i		−	0.956227i
$990$		0			0
$991$		−	35.9773i		−	1.14286i	−0.820652	−	0.571428i	$-0.806390\pi$
$991$		−	35.9773i		−	1.14286i	0.820652	−	0.571428i	$-0.193610\pi$
$992$	5.28843	−	17.7646i	0.167908	−	0.564027i
$993$	5.91651	−	4.59175i	0.187755	−	0.145715i
$994$	4.62109	+	3.78442i	0.146572	+	0.120035i
$995$		0			0
$996$	−1.87256	+	0.651492i	−0.0593345	+	0.0206433i
$997$	−28.9811	−	16.7322i	−0.917840	−	0.529915i	−0.0348944	−	0.999391i	$-0.511109\pi$
$997$	−28.9811	−	16.7322i	−0.917840	−	0.529915i	−0.882945	+	0.469476i	$0.844443\pi$
$998$	15.7244	+	41.6478i	0.497748	+	1.31834i
$999$	−21.3997	−	49.3473i	−0.677057	−	1.56128i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.o.b.299.11		48
4.3	odd	2	inner	900.2.o.b.299.6		48
5.2	odd	4		180.2.q.a.11.1	✓	48
5.3	odd	4		900.2.r.f.551.24		48
5.4	even	2		900.2.o.c.299.14		48
9.5	odd	6		900.2.o.c.599.19		48
15.2	even	4		540.2.q.a.251.24		48
20.3	even	4		900.2.r.f.551.17		48
20.7	even	4		180.2.q.a.11.8	yes	48
20.19	odd	2		900.2.o.c.299.19		48
36.23	even	6		900.2.o.c.599.14		48
45.2	even	12		1620.2.e.b.971.17		48
45.7	odd	12		1620.2.e.b.971.32		48
45.14	odd	6	inner	900.2.o.b.599.6		48
45.22	odd	12		540.2.q.a.71.17		48
45.23	even	12		900.2.r.f.851.17		48
45.32	even	12		180.2.q.a.131.8	yes	48
60.47	odd	4		540.2.q.a.251.17		48
180.7	even	12		1620.2.e.b.971.18		48
180.23	odd	12		900.2.r.f.851.24		48
180.47	odd	12		1620.2.e.b.971.31		48
180.59	even	6	inner	900.2.o.b.599.11		48
180.67	even	12		540.2.q.a.71.24		48
180.167	odd	12		180.2.q.a.131.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.q.a.11.1	✓	48	5.2	odd	4
180.2.q.a.11.8	yes	48	20.7	even	4
180.2.q.a.131.1	yes	48	180.167	odd	12
180.2.q.a.131.8	yes	48	45.32	even	12
540.2.q.a.71.17		48	45.22	odd	12
540.2.q.a.71.24		48	180.67	even	12
540.2.q.a.251.17		48	60.47	odd	4
540.2.q.a.251.24		48	15.2	even	4
900.2.o.b.299.6		48	4.3	odd	2	inner
900.2.o.b.299.11		48	1.1	even	1	trivial
900.2.o.b.599.6		48	45.14	odd	6	inner
900.2.o.b.599.11		48	180.59	even	6	inner
900.2.o.c.299.14		48	5.4	even	2
900.2.o.c.299.19		48	20.19	odd	2
900.2.o.c.599.14		48	36.23	even	6
900.2.o.c.599.19		48	9.5	odd	6
900.2.r.f.551.17		48	20.3	even	4
900.2.r.f.551.24		48	5.3	odd	4
900.2.r.f.851.17		48	45.23	even	12
900.2.r.f.851.24		48	180.23	odd	12
1620.2.e.b.971.17		48	45.2	even	12
1620.2.e.b.971.18		48	180.7	even	12
1620.2.e.b.971.31		48	180.47	odd	12
1620.2.e.b.971.32		48	45.7	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.228922 + 1.39556i) q^{2} +(0.654027 - 1.60382i) q^{3} +(-1.89519 - 0.638951i) q^{4} +(2.08851 + 1.27989i) q^{6} +(-0.604565 + 1.04714i) q^{7} +(1.32555 - 2.49858i) q^{8} +(-2.14450 - 2.09789i) q^{9} +(-1.52161 + 2.63550i) q^{11} +(-2.26427 + 2.62166i) q^{12} +(-4.39869 + 2.53958i) q^{13} +(-1.32295 - 1.08342i) q^{14} +(3.18348 + 2.42186i) q^{16} +2.23944 q^{17} +(3.41866 - 2.51253i) q^{18} -2.53835i q^{19} +(1.28402 + 1.65447i) q^{21} +(-3.32968 - 2.72682i) q^{22} +(-6.02870 + 3.48067i) q^{23} +(-3.14035 - 3.76008i) q^{24} +(-2.53719 - 6.72001i) q^{26} +(-4.76720 + 2.06732i) q^{27} +(1.81484 - 1.59824i) q^{28} +(4.84407 + 2.79673i) q^{29} +(-2.83759 + 1.63828i) q^{31} +(-4.10863 + 3.88833i) q^{32} +(3.23171 + 4.16408i) q^{33} +(-0.512657 + 3.12527i) q^{34} +(2.72378 + 5.34612i) q^{36} +10.3514i q^{37} +(3.54243 + 0.581085i) q^{38} +(1.19618 + 8.71567i) q^{39} +(3.70208 - 2.13740i) q^{41} +(-2.60286 + 1.41319i) q^{42} +(-2.15991 + 3.74108i) q^{43} +(4.56769 - 4.02254i) q^{44} +(-3.47739 - 9.21023i) q^{46} +(-8.92129 - 5.15071i) q^{47} +(5.96633 - 3.52178i) q^{48} +(2.76900 + 4.79605i) q^{49} +(1.46465 - 3.59166i) q^{51} +(9.95902 - 2.00245i) q^{52} -9.42683 q^{53} +(-1.79375 - 7.12618i) q^{54} +(1.81498 + 2.89859i) q^{56} +(-4.07106 - 1.66015i) q^{57} +(-5.01192 + 6.11997i) q^{58} +(-4.46335 - 7.73074i) q^{59} +(1.32896 - 2.30183i) q^{61} +(-1.63674 - 4.33508i) q^{62} +(3.49327 - 0.977274i) q^{63} +(-4.48585 - 6.62398i) q^{64} +(-6.55104 + 3.55680i) q^{66} +(7.20867 + 12.4858i) q^{67} +(-4.24416 - 1.43089i) q^{68} +(1.63945 + 11.9454i) q^{69} -3.49303 q^{71} +(-8.08438 + 2.57736i) q^{72} +5.10052i q^{73} +(-14.4461 - 2.36967i) q^{74} +(-1.62188 + 4.81065i) q^{76} +(-1.83982 - 3.18667i) q^{77} +(-12.4371 - 0.325865i) q^{78} +(-3.26472 - 1.88488i) q^{79} +(0.197735 + 8.99783i) q^{81} +(2.13538 + 5.65579i) q^{82} +(0.495665 + 0.286172i) q^{83} +(-1.37634 - 3.95596i) q^{84} +(-4.72646 - 3.87071i) q^{86} +(7.65361 - 5.93990i) q^{87} +(4.56806 + 7.29535i) q^{88} -2.40129i q^{89} -6.14138i q^{91} +(13.6495 - 2.74449i) q^{92} +(0.771656 + 5.62248i) q^{93} +(9.23042 - 11.2711i) q^{94} +(3.54904 + 9.13260i) q^{96} +(-10.0902 - 5.82556i) q^{97} +(-7.32708 + 2.76639i) q^{98} +(8.79207 - 2.45966i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{6} - 12 q^{8} - 4 q^{9} - 28 q^{12} + 30 q^{14} + 18 q^{18} - 4 q^{21} + 42 q^{22} + 28 q^{24} + 12 q^{29} + 48 q^{33} + 6 q^{34} + 42 q^{36} + 6 q^{38} - 60 q^{41} - 16 q^{42} - 12 q^{46} + 74 q^{48}+ \cdots - 84 q^{98}+O(q^{100}) \) 48 * q + 6 * q^6 - 12 * q^8 - 4 * q^9 - 28 * q^12 + 30 * q^14 + 18 * q^18 - 4 * q^21 + 42 * q^22 + 28 * q^24 + 12 * q^29 + 48 * q^33 + 6 * q^34 + 42 * q^36 + 6 * q^38 - 60 * q^41 - 16 * q^42 - 12 * q^46 + 74 * q^48 - 24 * q^49 + 90 * q^52 + 32 * q^54 - 42 * q^56 + 16 * q^57 - 84 * q^58 - 84 * q^62 + 48 * q^64 + 16 * q^66 - 6 * q^68 - 36 * q^69 + 80 * q^72 - 84 * q^74 + 6 * q^76 + 46 * q^78 - 50 * q^84 - 54 * q^86 - 114 * q^88 + 42 * q^92 + 24 * q^93 - 18 * q^94 - 18 * q^96 + 48 * q^97 - 84 * q^98

Introduction

L-functions

Modular forms

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