LMFDB - Embedded newform 465.2.bm.a.104.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [465,2,Mod(44,465)] 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("465.44"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(465, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([15, 15, 11])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 465 = 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	465.bm (of order $30$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-3,3,-3,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$3.71304369399$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{30}]$

Embedding invariants

Embedding label			104.1
Root			$0.913545 + 0.406737i$ of defining polynomial
Character	$\chi$	$=$	465.104
Dual form			465.2.bm.a.389.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.604528 - 1.86055i) q^{2} +(-1.28716 + 1.15897i) q^{3} +(-1.47815 + 1.07394i) q^{4} +(-1.11803 - 1.93649i) q^{5} +(2.93444 + 1.69420i) q^{6} +(-0.273659 - 0.198825i) q^{8} +(0.313585 - 2.98357i) q^{9} +(-2.92705 + 3.25082i) q^{10} +(0.657960 - 3.09546i) q^{12} +(3.68343 + 1.19682i) q^{15} +(-1.33369 + 4.10468i) q^{16} +(-0.166307 - 0.373532i) q^{17} +(-5.74064 + 1.22021i) q^{18} +(-3.01255 - 0.640337i) q^{19} +(3.73229 + 1.66172i) q^{20} +(-4.73745 + 6.52054i) q^{23} +(0.582676 - 0.0612417i) q^{24} +(-2.50000 + 4.33013i) q^{25} +(3.05422 + 4.20378i) q^{27} -7.57670i q^{30} +(-2.44736 + 5.00104i) q^{31} +7.76669 q^{32} +(-0.594437 + 0.535233i) q^{34} +(2.74064 + 4.74692i) q^{36} +(0.629795 + 5.99209i) q^{38} +(-0.0790627 + 0.752232i) q^{40} +(-6.12825 + 2.72847i) q^{45} +(14.9957 + 4.87240i) q^{46} +(-1.21878 + 3.75103i) q^{47} +(-3.04052 - 6.82911i) q^{48} +(-6.84703 + 1.45538i) q^{49} +(9.56773 + 2.03368i) q^{50} +(0.646976 + 0.288052i) q^{51} +(0.0284543 + 0.00299067i) q^{53} +(5.97496 - 8.22383i) q^{54} +(4.61978 - 2.66723i) q^{57} +(-6.72995 + 2.18669i) q^{60} -15.5692i q^{61} +(10.7842 + 1.53015i) q^{62} +(-2.02780 - 6.24093i) q^{64} +(0.646976 + 0.373532i) q^{68} +(-1.45922 - 13.8836i) q^{69} +(-0.679023 + 0.754131i) q^{72} +(-1.80057 - 8.47101i) q^{75} +(5.14068 - 2.28878i) q^{76} +(-6.94437 - 15.5973i) q^{79} +(9.43980 - 2.00649i) q^{80} +(-8.80333 - 1.87121i) q^{81} +(3.05530 + 2.75100i) q^{83} +(-0.537405 + 0.739674i) q^{85} +(8.78115 + 9.75246i) q^{90} -14.7260i q^{92} +(-2.64590 - 9.27358i) q^{93} +7.71576 q^{94} +(2.12813 + 6.54970i) q^{95} +(-9.99701 + 9.00135i) q^{96} +(6.84703 + 11.8594i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{6} + 4 q^{8} - 3 q^{9} - 10 q^{10} - 3 q^{12} - 3 q^{16} - 9 q^{17} - 27 q^{18} + 12 q^{19} - 5 q^{20} + 20 q^{23} - 6 q^{24} - 20 q^{25} - 8 q^{31} + 24 q^{34}+ \cdots - 7 q^{98}+O(q^{100}) $ 8 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^6 + 4 * q^8 - 3 * q^9 - 10 * q^10 - 3 * q^12 - 3 * q^16 - 9 * q^17 - 27 * q^18 + 12 * q^19 - 5 * q^20 + 20 * q^23 - 6 * q^24 - 20 * q^25 - 8 * q^31 + 24 * q^34 + 3 * q^36 - 22 * q^38 - 20 * q^40 - 15 * q^45 + 5 * q^46 + 18 * q^47 - 3 * q^48 + 7 * q^49 + 45 * q^50 + 9 * q^51 + 14 * q^53 + 39 * q^57 - 30 * q^60 + 38 * q^62 + 16 * q^64 + 9 * q^68 + 39 * q^69 - 24 * q^72 - 15 * q^75 + 23 * q^76 - 9 * q^79 + 30 * q^80 + 9 * q^81 - 23 * q^83 + 30 * q^90 - 48 * q^93 + 42 * q^94 + 35 * q^95 - 45 * q^96 - 7 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/465\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$406$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{23}{30}\right)$

Coefficient data

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

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

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

$2$	−0.604528	−	1.86055i	−0.427466	−	1.31561i	−0.900613	−	0.434622i	$-0.856882\pi$
$2$	−0.604528	−	1.86055i	−0.427466	−	1.31561i	0.473147	−	0.880984i	$-0.343118\pi$
$3$	−1.28716	+	1.15897i	−0.743145	+	0.669131i
$3$	−1.28716	+	1.15897i	−0.743145	+	0.669131i
$4$	−1.47815	+	1.07394i	−0.739074	+	0.536969i
$5$	−1.11803	−	1.93649i	−0.500000	−	0.866025i
$5$	−1.11803	−	1.93649i	−0.500000	−	0.866025i
$6$	2.93444	+	1.69420i	1.19798	+	0.691655i
$7$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$7$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$8$	−0.273659	−	0.198825i	−0.0967531	−	0.0702952i
$9$	0.313585	−	2.98357i	0.104528	−	0.994522i
$10$	−2.92705	+	3.25082i	−0.925615	+	1.02800i
$11$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$11$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$12$	0.657960	−	3.09546i	0.189937	−	0.893582i
$13$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$13$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$14$		0			0
$15$	3.68343	+	1.19682i	0.951057	+	0.309017i
$16$	−1.33369	+	4.10468i	−0.333423	+	1.02617i
$17$	−0.166307	−	0.373532i	−0.0403354	−	0.0905948i	0.892254	−	0.451534i	$-0.149123\pi$
$17$	−0.166307	−	0.373532i	−0.0403354	−	0.0905948i	−0.932589	+	0.360939i	$0.882456\pi$
$18$	−5.74064	+	1.22021i	−1.35308	+	0.287606i
$19$	−3.01255	−	0.640337i	−0.691126	−	0.146903i	−0.151058	−	0.988525i	$-0.548268\pi$
$19$	−3.01255	−	0.640337i	−0.691126	−	0.146903i	−0.540068	+	0.841621i	$0.681602\pi$
$20$	3.73229	+	1.66172i	0.834565	+	0.371572i
$21$		0			0
$22$		0			0
$23$	−4.73745	+	6.52054i	−0.987826	+	1.35963i	−0.0553214	+	0.998469i	$0.517618\pi$
$23$	−4.73745	+	6.52054i	−0.987826	+	1.35963i	−0.932505	+	0.361158i	$0.882382\pi$
$24$	0.582676	−	0.0612417i	0.118938	−	0.0125009i
$25$	−2.50000	+	4.33013i	−0.500000	+	0.866025i
$26$		0			0
$27$	3.05422	+	4.20378i	0.587785	+	0.809017i
$28$		0			0
$29$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$29$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$30$		−	7.57670i		−	1.38331i
$31$	−2.44736	+	5.00104i	−0.439558	+	0.898214i
$31$	−2.44736	+	5.00104i	−0.439558	+	0.898214i
$32$	7.76669			1.37297
$33$		0			0
$34$	−0.594437	+	0.535233i	−0.101945	+	0.0917917i
$35$		0			0
$36$	2.74064	+	4.74692i	0.456773	+	0.791154i
$37$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$37$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$38$	0.629795	+	5.99209i	0.102166	+	0.972046i
$39$		0			0
$40$	−0.0790627	+	0.752232i	−0.0125009	+	0.118938i
$41$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$41$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$42$		0			0
$43$		0			0		0.207912	−	0.978148i	$-0.433333\pi$
$43$		0			0		−0.207912	+	0.978148i	$0.566667\pi$
$44$		0			0
$45$	−6.12825	+	2.72847i	−0.913545	+	0.406737i
$46$	14.9957	+	4.87240i	2.21099	+	0.718396i
$47$	−1.21878	+	3.75103i	−0.177778	+	0.547144i	−0.999749	−	0.0223844i	$-0.992874\pi$
$47$	−1.21878	+	3.75103i	−0.177778	+	0.547144i	0.821972	+	0.569529i	$0.192874\pi$
$48$	−3.04052	−	6.82911i	−0.438861	−	0.985697i
$49$	−6.84703	+	1.45538i	−0.978148	+	0.207912i
$50$	9.56773	+	2.03368i	1.35308	+	0.287606i
$51$	0.646976	+	0.288052i	0.0905948	+	0.0403354i
$52$		0			0
$53$	0.0284543	+	0.00299067i	0.00390850	+	0.000410800i	0.106483	−	0.994315i	$-0.466041\pi$
$53$	0.0284543	+	0.00299067i	0.00390850	+	0.000410800i	−0.102574	+	0.994725i	$0.532708\pi$
$54$	5.97496	−	8.22383i	0.813089	−	1.11912i
$55$		0			0
$56$		0			0
$57$	4.61978	−	2.66723i	0.611905	−	0.353283i
$58$		0			0
$59$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$59$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$60$	−6.72995	+	2.18669i	−0.868833	+	0.282301i
$61$		−	15.5692i		−	1.99343i	−0.0809615	−	0.996717i	$-0.525799\pi$
$61$		−	15.5692i		−	1.99343i	0.0809615	−	0.996717i	$-0.474201\pi$
$62$	10.7842	+	1.53015i	1.36959	+	0.194330i
$63$		0			0
$64$	−2.02780	−	6.24093i	−0.253475	−	0.780116i
$65$		0			0
$66$		0			0
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$	0.646976	+	0.373532i	0.0784574	+	0.0452974i
$69$	−1.45922	−	13.8836i	−0.175670	−	1.67138i
$70$		0			0
$71$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$71$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$72$	−0.679023	+	0.754131i	−0.0800236	+	0.0888752i
$73$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$73$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$74$		0			0
$75$	−1.80057	−	8.47101i	−0.207912	−	0.978148i
$76$	5.14068	−	2.28878i	0.589676	−	0.262541i
$77$		0			0
$78$		0			0
$79$	−6.94437	−	15.5973i	−0.781303	−	1.75483i	−0.645022	−	0.764164i	$-0.723152\pi$
$79$	−6.94437	−	15.5973i	−0.781303	−	1.75483i	−0.136281	−	0.990670i	$-0.543515\pi$
$80$	9.43980	−	2.00649i	1.05540	−	0.224333i
$81$	−8.80333	−	1.87121i	−0.978148	−	0.207912i
$82$		0			0
$83$	3.05530	+	2.75100i	0.335363	+	0.301962i	0.819556	−	0.572999i	$-0.194220\pi$
$83$	3.05530	+	2.75100i	0.335363	+	0.301962i	−0.484193	+	0.874961i	$0.660887\pi$
$84$		0			0
$85$	−0.537405	+	0.739674i	−0.0582897	+	0.0802289i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$89$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$90$	8.78115	+	9.75246i	0.925615	+	1.02800i
$91$		0			0
$92$		−	14.7260i		−	1.53530i
$93$	−2.64590	−	9.27358i	−0.274367	−	0.961625i
$94$	7.71576			0.795820
$95$	2.12813	+	6.54970i	0.218341	+	0.671985i
$96$	−9.99701	+	9.00135i	−1.02032	+	0.918696i
$97$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$97$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$98$	6.84703	+	11.8594i	0.691655	+	1.19798i
$99$		0			0
$100$	−0.954915	−	9.08541i	−0.0954915	−	0.908541i
$101$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$101$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$102$	0.144820	−	1.37787i	0.0143393	−	0.136429i
$103$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$103$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$104$		0			0
$105$		0			0
$106$	−0.0116372	−	0.0547485i	−0.00113030	−	0.00531765i
$107$	−18.8013	+	8.37088i	−1.81759	+	0.809243i	−0.867369	+	0.497665i	$0.834191\pi$
$107$	−18.8013	+	8.37088i	−1.81759	+	0.809243i	−0.950221	+	0.311578i	$0.899143\pi$
$108$	−9.02918	−	2.93376i	−0.868833	−	0.282301i
$109$	−5.88985	+	18.1271i	−0.564145	+	1.73626i	0.106333	+	0.994331i	$0.466089\pi$
$109$	−5.88985	+	18.1271i	−0.564145	+	1.73626i	−0.670478	+	0.741929i	$0.733911\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−14.4011	−	6.41177i	−1.35474	−	0.603168i	−0.404456	−	0.914557i	$-0.632539\pi$
$113$	−14.4011	−	6.41177i	−1.35474	−	0.603168i	−0.950283	+	0.311389i	$0.899206\pi$
$114$	−7.75530	−	6.98290i	−0.726350	−	0.654009i
$115$	17.9236	+	1.88385i	1.67138	+	0.175670i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−0.770046	−	1.05988i	−0.0702952	−	0.0967531i
$121$	−7.36044	−	8.17459i	−0.669131	−	0.743145i
$122$	−28.9673	+	9.41204i	−2.62257	+	0.852126i
$123$		0			0
$124$	−1.75325	−	10.0206i	−0.157446	−	0.899875i
$125$	11.1803			1.00000
$126$		0			0
$127$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$127$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$128$	2.18109	−	1.58466i	0.192783	−	0.140065i
$129$		0			0
$130$		0			0
$131$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$131$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	4.72585	−	10.6144i	0.406737	−	0.913545i
$136$	−0.0287560	+	0.135286i	−0.00246581	+	0.0116007i
$137$	−4.47301	−	21.0439i	−0.382155	−	1.79790i	−0.576646	−	0.816994i	$-0.695639\pi$
$137$	−4.47301	−	21.0439i	−0.382155	−	1.79790i	0.194491	−	0.980904i	$-0.437694\pi$
$138$	−24.9489	+	11.1080i	−2.12379	+	0.945572i
$139$	21.7372	+	7.06284i	1.84372	+	0.599062i	0.997840	+	0.0656950i	$0.0209264\pi$
$139$	21.7372	+	7.06284i	1.84372	+	0.599062i	0.845884	+	0.533367i	$0.179074\pi$
$140$		0			0
$141$	−2.77855	−	6.24073i	−0.233996	−	0.525564i
$142$		0			0
$143$		0			0
$144$	11.8284	+	5.26633i	0.985697	+	0.438861i
$145$		0			0
$146$		0			0
$147$	7.12652	−	9.80881i	0.587785	−	0.809017i
$148$		0			0
$149$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$149$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$150$	−14.6722	+	8.47101i	−1.19798	+	0.691655i
$151$	−8.69297	−	11.9648i	−0.707424	−	0.973685i	−0.999849	−	0.0173966i	$-0.994462\pi$
$151$	−8.69297	−	11.9648i	−0.707424	−	0.973685i	0.292425	−	0.956288i	$-0.405538\pi$
$152$	0.697097	+	0.774204i	0.0565420	+	0.0627963i
$153$	−1.16661	+	0.379054i	−0.0943147	+	0.0306447i
$154$		0			0
$155$	12.4207	−	0.852048i	0.997655	−	0.0684382i
$156$		0			0
$157$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$157$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$158$	−24.8215	+	22.3493i	−1.97469	+	1.77802i
$159$	−0.0400915	+	0.0291281i	−0.00317946	+	0.00231001i
$160$	−8.68343	−	15.0401i	−0.686485	−	1.18903i
$161$		0			0
$162$	1.84040	+	17.5102i	0.144595	+	1.37573i
$163$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$163$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$164$		0			0
$165$		0			0
$166$	3.27136	−	7.34759i	0.253907	−	0.570284i
$167$	1.32244	−	6.22160i	0.102334	−	0.481442i	−0.896898	−	0.442238i	$-0.854185\pi$
$167$	1.32244	−	6.22160i	0.102334	−	0.481442i	0.999231	−	0.0392036i	$-0.0124821\pi$
$168$		0			0
$169$	−11.8761	+	5.28758i	−0.913545	+	0.406737i
$170$	1.70107	+	0.552713i	0.130466	+	0.0423911i
$171$	−2.85518	+	8.78734i	−0.218341	+	0.671985i
$172$		0			0
$173$	9.72824	−	2.06780i	0.739625	−	0.157212i	0.177333	−	0.984151i	$-0.443253\pi$
$173$	9.72824	−	2.06780i	0.739625	−	0.157212i	0.562292	+	0.826939i	$0.309920\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$179$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$180$	6.12825	−	10.6144i	0.456773	−	0.791154i
$181$	0.344711	−	0.199019i	0.0256222	−	0.0147930i	−0.487134	−	0.873327i	$-0.661958\pi$
$181$	0.344711	−	0.199019i	0.0256222	−	0.0147930i	0.512756	+	0.858534i	$0.328624\pi$
$182$		0			0
$183$	18.0442	+	20.0401i	1.33387	+	1.48141i
$184$	2.59289	−	0.842481i	0.191150	−	0.0621086i
$185$		0			0
$186$	−15.6544	+	10.5290i	−1.14784	+	0.772021i
$187$		0			0
$188$	−2.22683	−	6.85348i	−0.162408	−	0.499841i
$189$		0			0
$190$	10.8995	−	7.91896i	0.790734	−	0.574502i
$191$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$191$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$192$	9.84315	+	5.68295i	0.710368	+	0.410131i
$193$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$193$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$194$		0			0
$195$		0			0
$196$	8.55794	−	9.50455i	0.611281	−	0.678897i
$197$	9.55747	−	21.4664i	0.680942	−	1.52942i	−0.159313	−	0.987228i	$-0.550928\pi$
$197$	9.55747	−	21.4664i	0.680942	−	1.52942i	0.840255	−	0.542192i	$-0.182405\pi$
$198$		0			0
$199$	5.29662	+	24.9187i	0.375468	+	1.76644i	0.608088	+	0.793869i	$0.291937\pi$
$199$	5.29662	+	24.9187i	0.375468	+	1.76644i	−0.232621	+	0.972568i	$0.574730\pi$
$200$	1.54508	−	0.687916i	0.109254	−	0.0486430i
$201$		0			0
$202$		0			0
$203$		0			0
$204$	−1.26568	+	0.269028i	−0.0886151	+	0.0188357i
$205$		0			0
$206$		0			0
$207$	17.9689	+	16.1792i	1.24892	+	1.12453i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	9.04976	−	15.6746i	0.623011	−	1.07909i	−0.365911	−	0.930650i	$-0.619243\pi$
$211$	9.04976	−	15.6746i	0.623011	−	1.07909i	0.988922	−	0.148437i	$-0.0474241\pi$
$212$	−0.0452714	+	0.0261375i	−0.00310926	+	0.00179513i
$213$		0			0
$214$	26.9403	+	29.9203i	1.84160	+	2.04531i
$215$		0			0
$216$		−	1.75766i		−	0.119593i
$217$		0			0
$218$	37.2869			2.52539
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$223$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$224$		0			0
$225$	12.1353	+	8.81678i	0.809017	+	0.587785i
$226$	−3.22354	+	30.6700i	−0.214427	+	2.04014i
$227$	20.0366	−	22.2529i	1.32988	−	1.47698i	0.581887	−	0.813269i	$-0.302314\pi$
$227$	20.0366	−	22.2529i	1.32988	−	1.47698i	0.747991	−	0.663709i	$-0.231019\pi$
$228$	−3.96428	+	8.90391i	−0.262541	+	0.589676i
$229$	−6.13646	+	28.8698i	−0.405509	+	1.90777i	0.0137585	+	0.999905i	$0.495620\pi$
$229$	−6.13646	+	28.8698i	−0.405509	+	1.90777i	−0.419267	+	0.907863i	$0.637713\pi$
$230$	−7.33034	−	34.4865i	−0.483348	−	2.27397i
$231$		0			0
$232$		0			0
$233$	−8.09421	+	24.9114i	−0.530269	+	1.63200i	0.223385	+	0.974730i	$0.428289\pi$
$233$	−8.09421	+	24.9114i	−0.530269	+	1.63200i	−0.753655	+	0.657271i	$0.771711\pi$
$234$		0			0
$235$	8.62648	−	1.83362i	0.562730	−	0.119612i
$236$		0			0
$237$	27.0153	+	12.0280i	1.75483	+	0.781303i
$238$		0			0
$239$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$239$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$240$	−9.82512	+	13.5231i	−0.634209	+	0.872913i
$241$	−22.0968	+	2.32247i	−1.42338	+	0.149603i	−0.784704	−	0.619871i	$-0.787185\pi$
$241$	−22.0968	+	2.32247i	−1.42338	+	0.149603i	−0.638678	+	0.769474i	$0.720518\pi$
$242$	−10.7596	+	18.6362i	−0.691655	+	1.19798i
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$	16.7204	+	23.0136i	1.07041	+	1.47330i
$245$	10.4736	+	11.6321i	0.669131	+	0.743145i
$246$		0			0
$247$		0			0
$248$	1.66407	−	0.881985i	0.105669	−	0.0560061i
$249$	−7.12100			−0.451275
$250$	−6.75883	−	20.8016i	−0.427466	−	1.31561i
$251$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$251$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−0.165530	−	1.57492i	−0.0103659	−	0.0986251i
$256$	−14.8846	−	10.8143i	−0.930285	−	0.675892i
$257$	1.65139	−	15.7119i	0.103011	−	0.980081i	−0.813904	−	0.580999i	$-0.802662\pi$
$257$	1.65139	−	15.7119i	0.103011	−	0.980081i	0.916915	−	0.399082i	$-0.130671\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−26.1620	−	8.50054i	−1.61322	−	0.524166i	−0.642888	−	0.765960i	$-0.722264\pi$
$263$	−26.1620	−	8.50054i	−1.61322	−	0.524166i	−0.970328	+	0.241794i	$0.922264\pi$
$264$		0			0
$265$	−0.0260215	−	0.0584452i	−0.00159849	−	0.00359026i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$269$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$270$	−22.6056	−	2.37594i	−1.37573	−	0.144595i
$271$	−8.36411	+	11.5122i	−0.508083	+	0.699317i	−0.983595	−	0.180393i	$-0.942263\pi$
$271$	−8.36411	+	11.5122i	−0.508083	+	0.699317i	0.475511	+	0.879710i	$0.342263\pi$
$272$	1.75503	−	0.184461i	0.106415	−	0.0111846i
$273$		0			0
$274$	−36.4490	+	21.0439i	−2.20197	+	1.27131i
$275$		0			0
$276$	17.0670	+	18.9548i	1.02731	+	1.14095i
$277$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$277$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$278$		−	44.7127i		−	2.68169i
$279$	14.1535	+	8.87011i	0.847347	+	0.531039i
$280$		0			0
$281$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$281$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$282$	−9.93145	+	8.94232i	−0.591409	+	0.532507i
$283$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$283$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$284$		0			0
$285$	−10.3301	−	5.96411i	−0.611905	−	0.353283i
$286$		0			0
$287$		0			0
$288$	2.43552	−	23.1724i	0.143514	−	1.36545i
$289$	11.2634	−	12.5092i	0.662550	−	0.735836i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−25.3417	+	11.2829i	−1.48048	+	0.659151i	−0.978597	−	0.205785i	$-0.934025\pi$
$293$	−25.3417	+	11.2829i	−1.48048	+	0.659151i	−0.501881	+	0.864937i	$0.667359\pi$
$294$	−22.5579	−	7.32952i	−1.31561	−	0.427466i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$	11.7588	+	10.5877i	0.678897	+	0.611281i
$301$		0			0
$302$	−17.0060	+	23.4068i	−0.978586	+	1.34691i
$303$		0			0
$304$	6.64620	−	11.5116i	0.381186	−	0.660233i
$305$	−30.1497	+	17.4069i	−1.72636	+	0.996717i
$306$	1.41050	+	1.94138i	0.0806327	+	0.110981i
$307$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$307$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$308$		0			0
$309$		0			0
$310$	−9.09395	−	22.5942i	−0.516502	−	1.28327i
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$		0			0
$313$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$313$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$314$		0			0
$315$		0			0
$316$	27.0153	+	15.5973i	1.51973	+	0.877417i
$317$	3.31348	+	31.5257i	0.186104	+	1.77066i	0.546116	+	0.837710i	$0.316106\pi$
$317$	3.31348	+	31.5257i	0.186104	+	1.77066i	−0.360012	+	0.932948i	$0.617227\pi$
$318$	0.0784307	+	0.0569833i	0.00439818	+	0.00319546i
$319$		0			0
$320$	−9.81836	+	10.9044i	−0.548863	+	0.609574i
$321$	14.4988	−	32.5648i	0.809243	−	1.81759i
$322$		0			0
$323$	0.261822	+	1.23178i	0.0145682	+	0.0685379i
$324$	15.0222	−	6.68830i	0.834565	−	0.371572i
$325$		0			0
$326$		0			0
$327$	−13.4275	−	30.1587i	−0.742543	−	1.66778i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	12.5655	+	11.3140i	0.690663	+	0.621876i	0.937829	−	0.347097i	$-0.112833\pi$
$331$	12.5655	+	11.3140i	0.690663	+	0.621876i	−0.247166	+	0.968973i	$0.579499\pi$
$332$	−7.47059	−	0.785191i	−0.410002	−	0.0430929i
$333$		0			0
$334$	−12.3750	+	1.30067i	−0.677132	+	0.0711694i
$335$		0			0
$336$		0			0
$337$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$337$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$338$	17.0172	+	18.8995i	0.925615	+	1.02800i
$339$	25.9676	−	8.43738i	1.41037	−	0.458256i
$340$		−	1.67049i		−	0.0905948i
$341$		0			0
$342$	18.0753			0.977400
$343$		0			0
$344$		0			0
$345$	−25.2539	+	18.3481i	−1.35963	+	0.987826i
$346$	−9.72824	−	16.8498i	−0.522994	−	0.905852i
$347$	−31.7549	−	18.3337i	−1.70469	−	0.984204i	−0.940864	−	0.338784i	$-0.889984\pi$
$347$	−31.7549	−	18.3337i	−1.70469	−	0.984204i	−0.763828	−	0.645420i	$-0.776682\pi$
$348$		0			0
$349$	−20.0308	−	14.5532i	−1.07222	−	0.779016i	−0.0959126	−	0.995390i	$-0.530577\pi$
$349$	−20.0308	−	14.5532i	−1.07222	−	0.779016i	−0.976311	+	0.216374i	$0.930577\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	6.59507	−	31.0274i	0.351020	−	1.65142i	−0.348870	−	0.937171i	$-0.613435\pi$
$353$	6.59507	−	31.0274i	0.351020	−	1.65142i	0.699891	−	0.714250i	$-0.253232\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$359$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$360$	2.21954	+	0.471778i	0.116980	+	0.0248649i
$361$	−8.69194	−	3.86990i	−0.457470	−	0.203679i
$362$	−0.578672	−	0.521039i	−0.0304143	−	0.0273852i
$363$	18.9482	+	1.99153i	0.994522	+	0.104528i
$364$		0			0
$365$		0			0
$366$	26.3774	−	45.6870i	1.37877	−	2.38810i
$367$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$367$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$368$	−20.4465	−	28.1421i	−1.06584	−	1.46701i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	13.8703	+	10.8662i	0.719140	+	0.563386i
$373$		0			0		1.00000			$0$
$373$		0			0		−1.00000			$\pi$
$374$		0			0
$375$	−14.3909	+	12.9577i	−0.743145	+	0.669131i
$376$	1.07933	−	0.784179i	0.0556622	−	0.0404409i
$377$		0			0
$378$		0			0
$379$	3.97943	+	37.8618i	0.204410	+	1.94483i	0.310733	+	0.950497i	$0.399425\pi$
$379$	3.97943	+	37.8618i	0.204410	+	1.94483i	−0.106323	+	0.994332i	$0.533908\pi$
$380$	−10.1796	−	7.39595i	−0.522205	−	0.379404i
$381$		0			0
$382$		0			0
$383$	−14.4037	+	32.3512i	−0.735994	+	1.65307i	0.0211115	+	0.999777i	$0.493280\pi$
$383$	−14.4037	+	32.3512i	−0.735994	+	1.65307i	−0.757106	+	0.653293i	$0.773387\pi$
$384$	−0.970858	+	4.56753i	−0.0495439	+	0.233086i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$389$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$390$		0			0
$391$	3.22350	+	0.685176i	0.163019	+	0.0346509i
$392$	2.16312	+	0.963083i	0.109254	+	0.0486430i
$393$		0			0
$394$	−45.7171	−	4.80506i	−2.30319	−	0.242075i
$395$	−22.4400	+	30.8860i	−1.12908	+	1.55405i
$396$		0			0
$397$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$397$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$398$	43.1604	−	24.9187i	2.16343	−	1.24906i
$399$		0			0
$400$	−14.4396	−	16.0368i	−0.721979	−	0.801839i
$401$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$401$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	6.21885	+	19.1396i	0.309017	+	0.951057i
$406$		0			0
$407$		0			0
$408$	−0.119779	−	0.207463i	−0.00592994	−	0.0102710i
$409$	33.6713	+	19.4402i	1.66494	+	0.961254i	0.970302	+	0.241895i	$0.0777690\pi$
$409$	33.6713	+	19.4402i	1.66494	+	0.961254i	0.694639	+	0.719359i	$0.255564\pi$
$410$		0			0
$411$	30.1467	+	21.9028i	1.48703	+	1.08039i
$412$		0			0
$413$		0			0
$414$	19.2395	−	43.2127i	0.945572	−	2.12379i
$415$	1.91137	−	8.99228i	0.0938254	−	0.441414i
$416$		0			0
$417$	−36.1649	+	16.1017i	−1.77100	+	0.788502i
$418$		0			0
$419$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$419$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$420$		0			0
$421$	−31.7080	+	6.73975i	−1.54535	+	0.328475i	−0.900166	−	0.435548i	$-0.856555\pi$
$421$	−31.7080	+	6.73975i	−1.54535	+	0.328475i	−0.645189	+	0.764023i	$0.723221\pi$
$422$	−34.6342	−	7.36173i	−1.68597	−	0.358364i
$423$	10.8093	+	4.81259i	0.525564	+	0.233996i
$424$	−0.00719216	−	0.00647585i	−0.000349282	−	0.000314495i
$425$	2.03321	+	0.213699i	0.0986251	+	0.0103659i
$426$		0			0
$427$		0			0
$428$	18.8013	−	32.5648i	0.908795	−	1.57408i
$429$		0			0
$430$		0			0
$431$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$431$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$432$	−21.3286	+	6.93007i	−1.02617	+	0.333423i
$433$		0			0			−	1.00000i	$-0.5\pi$
$433$		0			0				1.00000i	$0.5\pi$
$434$		0			0
$435$		0			0
$436$	−10.7613	−	33.1198i	−0.515372	−	1.58615i
$437$	18.4471	−	16.6099i	0.882447	−	0.794559i
$438$		0			0
$439$	−4.91028	−	8.50485i	−0.234355	−	0.405914i	0.724730	−	0.689033i	$-0.241964\pi$
$439$	−4.91028	−	8.50485i	−0.234355	−	0.405914i	−0.959085	+	0.283118i	$0.908631\pi$
$440$		0			0
$441$	2.19510	+	20.8850i	0.104528	+	0.994522i
$442$		0			0
$443$	2.65713	−	25.2809i	0.126244	−	1.20113i	−0.729592	−	0.683883i	$-0.760290\pi$
$443$	2.65713	−	25.2809i	0.126244	−	1.20113i	0.855836	−	0.517248i	$-0.173043\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$449$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$450$	9.06793	−	27.9082i	0.427466	−	1.31561i
$451$		0			0
$452$	28.1727	−	5.98830i	1.32513	−	0.281666i
$453$	25.0562	+	5.32585i	1.17724	+	0.250230i
$454$	−53.5153	−	23.8266i	−2.51160	−	1.11824i
$455$		0			0
$456$	−1.79456	−	0.188615i	−0.0840378	−	0.00883273i
$457$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$457$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$458$	57.4232	−	6.03543i	2.68321	−	0.282017i
$459$	1.06231	−	1.83997i	0.0495842	−	0.0858823i
$460$	−28.5169	+	16.4642i	−1.32961	+	0.767648i
$461$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$461$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$462$		0			0
$463$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$463$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$464$		0			0
$465$	−15.0000	+	15.4919i	−0.695608	+	0.718421i
$466$	51.2420			2.37374
$467$	−10.5429	−	32.4478i	−0.487868	−	1.50150i	−0.827783	−	0.561048i	$-0.810398\pi$
$467$	−10.5429	−	32.4478i	−0.487868	−	1.50150i	0.339915	−	0.940456i	$-0.389602\pi$
$468$		0			0
$469$		0			0
$470$	−8.62648	−	14.9415i	−0.397910	−	0.689200i
$471$		0			0
$472$		0			0
$473$		0			0
$474$	6.04713	−	57.5346i	0.277754	−	2.64265i
$475$	10.3041	−	11.4439i	0.472785	−	0.525081i
$476$		0			0
$477$	0.0178457	−	0.0839574i	0.000817099	−	0.00384415i
$478$		0			0
$479$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$479$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$480$	28.6080	+	9.29531i	1.30577	+	0.424271i
$481$		0			0
$482$	17.6792	+	39.7082i	0.805267	+	1.80866i
$483$		0			0
$484$	19.6588	+	4.17861i	0.893582	+	0.189937i
$485$		0			0
$486$	−22.6627	−	20.4056i	−1.02800	−	0.925615i
$487$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$487$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$488$	−3.09555	+	4.26066i	−0.140129	+	0.192871i
$489$		0			0
$490$	15.3104	−	26.5184i	0.691655	−	1.19798i
$491$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$491$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−17.2637	−	16.7155i	−0.775162	−	0.750548i
$497$		0			0
$498$	4.30485	+	13.2490i	0.192905	+	0.593700i
$499$	32.8768	−	29.6024i	1.47177	−	1.32519i	0.642578	−	0.766220i	$-0.277865\pi$
$499$	32.8768	−	29.6024i	1.47177	−	1.32519i	0.829191	−	0.558966i	$-0.188802\pi$
$500$	−16.5262	+	12.0070i	−0.739074	+	0.536969i
$501$	5.50844	+	9.54089i	0.246099	+	0.426256i
$502$		0			0
$503$	1.78892	+	17.0205i	0.0797641	+	0.758905i	0.959170	+	0.282831i	$0.0912737\pi$
$503$	1.78892	+	17.0205i	0.0797641	+	0.758905i	−0.879406	+	0.476073i	$0.842060\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	9.15835	−	20.5700i	0.406737	−	0.913545i
$508$		0			0
$509$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$509$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$510$	−2.83014	+	1.26006i	−0.125321	+	0.0557964i
$511$		0			0
$512$	−9.45611	+	29.1029i	−0.417905	+	1.28618i
$513$	−6.50916	−	14.6198i	−0.287387	−	0.645481i
$514$	−30.2310	+	6.42581i	−1.33343	+	0.283430i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−10.1253	+	13.9363i	−0.444453	+	0.611737i
$520$		0			0
$521$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$521$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$522$		0			0
$523$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$523$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$524$		0			0
$525$		0			0
$526$			53.8144i			2.34642i
$527$	2.27506	+	0.0824572i	0.0991033	+	0.00359189i
$528$		0			0
$529$	−12.9666	−	39.9071i	−0.563766	−	1.73509i
$530$	−0.0930093	+	0.0837460i	−0.00404007	+	0.00363769i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	37.2306	+	27.0496i	1.60962	+	1.16946i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$	4.41373	+	20.7650i	0.189937	+	0.893582i
$541$	42.0342	−	18.7148i	1.80719	−	0.804613i	0.843728	−	0.536771i	$-0.180356\pi$
$541$	42.0342	−	18.7148i	1.80719	−	0.804613i	0.963463	−	0.267842i	$-0.0863106\pi$
$542$	26.4754	+	8.60236i	1.13721	+	0.369503i
$543$	−0.213043	+	0.655680i	−0.00914256	+	0.0281379i
$544$	−1.29166	−	2.90111i	−0.0553793	−	0.124384i
$545$	41.6880	−	8.86106i	1.78572	−	0.379566i
$546$		0			0
$547$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$547$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$548$	29.2116	+	26.3022i	1.24786	+	1.12357i
$549$	−46.4518	−	4.88228i	−1.98251	−	0.208371i
$550$		0			0
$551$		0			0
$552$	−2.36107	+	4.08949i	−0.100494	+	0.174060i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−39.7158	+	12.9044i	−1.68433	+	0.547270i
$557$			36.0118i			1.52587i	0.646476	+	0.762934i	$0.276242\pi$
$557$			36.0118i			1.52587i	−0.646476	+	0.762934i	$0.723758\pi$
$558$	7.94707	−	31.6955i	0.336426	−	1.34178i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	14.2566	+	24.6932i	0.600845	+	1.04069i	0.992693	+	0.120664i	$0.0385023\pi$
$563$	14.2566	+	24.6932i	0.600845	+	1.04069i	−0.391849	+	0.920030i	$0.628164\pi$
$564$	10.8093	+	6.24073i	0.455152	+	0.262782i
$565$	3.68455	+	35.0561i	0.155010	+	1.47482i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$569$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$570$	−4.85164	+	22.8252i	−0.203213	+	0.956042i
$571$	−3.04828	−	14.3410i	−0.127566	−	0.600153i	−0.994765	−	0.102190i	$-0.967415\pi$
$571$	−3.04828	−	14.3410i	−0.127566	−	0.600153i	0.867198	−	0.497963i	$-0.165918\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−16.3911	−	36.8151i	−0.683558	−	1.53530i
$576$	−19.2561	+	4.09301i	−0.802338	+	0.170542i
$577$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$577$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$578$	−30.0830	−	13.3938i	−1.25129	−	0.557109i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	36.3121	+	40.3286i	1.50004	+	1.66596i
$587$	−16.0152	+	5.20366i	−0.661019	+	0.214778i	−0.620266	−	0.784391i	$-0.712975\pi$
$587$	−16.0152	+	5.20366i	−0.661019	+	0.214778i	−0.0407524	+	0.999169i	$0.512975\pi$
$588$			22.1523i			0.913545i
$589$	10.5751	−	13.4988i	0.435741	−	0.556207i
$590$		0			0
$591$	12.5769	+	38.7076i	0.517343	+	1.59222i
$592$		0			0
$593$	19.2636	−	13.9959i	0.791063	−	0.574741i	−0.117216	−	0.993106i	$-0.537397\pi$
$593$	19.2636	−	13.9959i	0.791063	−	0.574741i	0.908279	+	0.418365i	$0.137397\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−35.6976	−	25.9358i	−1.46100	−	1.06148i
$598$		0			0
$599$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$599$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$600$	−1.19151	+	2.67617i	−0.0486430	+	0.109254i
$601$	7.18400	−	33.7981i	0.293042	−	1.37865i	−0.547455	−	0.836835i	$-0.684403\pi$
$601$	7.18400	−	33.7981i	0.293042	−	1.37865i	0.840497	−	0.541817i	$-0.182263\pi$
$602$		0			0
$603$		0			0
$604$	25.6990	+	8.35010i	1.04568	+	0.339761i
$605$	−7.60081	+	23.3929i	−0.309017	+	0.951057i
$606$		0			0
$607$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$607$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$608$	−23.3976	−	4.97330i	−0.948896	−	0.201694i
$609$		0			0
$610$	50.6127	+	45.5719i	2.04925	+	1.84515i
$611$		0			0
$612$	1.31734	−	1.81316i	0.0532503	−	0.0732928i
$613$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$613$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	5.76290	+	6.40034i	0.232005	+	0.257668i	0.847895	−	0.530164i	$-0.177870\pi$
$617$	5.76290	+	6.40034i	0.232005	+	0.257668i	−0.615889	+	0.787833i	$0.711203\pi$
$618$		0			0
$619$		−	41.3299i		−	1.66119i	−0.556877	−	0.830595i	$-0.688000\pi$
$619$		−	41.3299i		−	1.66119i	0.556877	−	0.830595i	$-0.312000\pi$
$620$	−17.4446	+	14.5985i	−0.700592	+	0.586290i
$621$	−41.8801			−1.68059
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−11.2977	+	25.3749i	−0.449752	+	1.01016i	0.536346	+	0.843998i	$0.319804\pi$
$631$	−11.2977	+	25.3749i	−0.449752	+	1.01016i	−0.986098	+	0.166162i	$0.946862\pi$
$632$	−1.20074	+	5.64906i	−0.0477631	+	0.224708i
$633$	6.51788	+	30.6642i	0.259062	+	1.21879i
$634$	56.6519	−	25.2230i	2.24993	−	1.00174i
$635$		0			0
$636$	0.0279793	−	0.0861114i	0.00110945	−	0.00341454i
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−5.50721	−	2.45197i	−0.217691	−	0.0969225i
$641$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$641$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$642$	−69.3533	−	7.28932i	−2.73716	−	0.287687i
$643$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$643$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$644$		0			0
$645$		0			0
$646$	2.13350	−	1.23178i	0.0839414	−	0.0484636i
$647$	19.4069	+	26.7112i	0.762962	+	1.05013i	0.996962	+	0.0778907i	$0.0248185\pi$
$647$	19.4069	+	26.7112i	0.762962	+	1.05013i	−0.234000	+	0.972237i	$0.575181\pi$
$648$	2.03707	+	2.26239i	0.0800236	+	0.0888752i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−3.89261	−	11.9802i	−0.152330	−	0.468822i	0.845551	−	0.533895i	$-0.179272\pi$
$653$	−3.89261	−	11.9802i	−0.152330	−	0.468822i	−0.997881	+	0.0650725i	$0.979272\pi$
$654$	−47.9943	+	43.2143i	−1.87673	+	1.68981i
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$659$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$660$		0			0
$661$	26.0970	−	28.9837i	1.01506	−	1.12734i	0.0232321	−	0.999730i	$-0.492604\pi$
$661$	26.0970	−	28.9837i	1.01506	−	1.12734i	0.991825	−	0.127605i	$-0.0407290\pi$
$662$	13.4541	−	30.2184i	0.522908	−	1.17447i
$663$		0			0
$664$	−0.289142	−	1.36031i	−0.0112209	−	0.0527902i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	4.72684	+	10.6167i	0.182887	+	0.410771i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$673$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$674$		0			0
$675$	−25.8384	+	2.71573i	−0.994522	+	0.104528i
$676$	11.8761	−	20.5700i	0.456773	−	0.791154i
$677$	13.1892	−	7.61481i	0.506903	−	0.292661i	−0.224656	−	0.974438i	$-0.572126\pi$
$677$	13.1892	−	7.61481i	0.506903	−	0.292661i	0.731560	+	0.681777i	$0.238793\pi$
$678$	−31.3963	−	43.2133i	−1.20577	−	1.65960i
$679$		0			0
$680$	0.294131	−	0.0955691i	0.0112794	−	0.00366491i
$681$			51.8650i			1.98747i
$682$		0			0
$683$	−52.2572			−1.99956			−0.999782	−	0.0208588i	$-0.993360\pi$
$683$	−52.2572			−1.99956			−0.999782	+	0.0208588i	$0.993360\pi$
$684$	−5.21667	−	16.0553i	−0.199465	−	0.613889i
$685$	−35.7503	+	32.1897i	−1.36595	+	1.22991i
$686$		0			0
$687$	−25.5605	−	44.2721i	−0.975194	−	1.68909i
$688$		0			0
$689$		0			0
$690$	49.4042	+	35.8942i	1.88078	+	1.36647i
$691$	0.237076	−	2.25563i	0.00901880	−	0.0858082i	−0.989087	−	0.147335i	$-0.952930\pi$
$691$	0.237076	−	2.25563i	0.00901880	−	0.0858082i	0.998105	+	0.0615271i	$0.0195971\pi$
$692$	−12.1591	+	13.5040i	−0.462219	+	0.513347i
$693$		0			0
$694$	−14.9140	+	70.1647i	−0.566127	+	2.66342i
$695$	−10.6258	−	49.9904i	−0.403059	−	1.89624i
$696$		0			0
$697$		0			0
$698$	−14.9678	+	46.0661i	−0.566538	+	1.74363i
$699$	−18.4530	−	41.4460i	−0.697955	−	1.56763i
$700$		0			0
$701$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$701$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−8.97860	+	12.3580i	−0.338154	+	0.465429i
$706$	−61.7148	+	6.48649i	−2.32267	+	0.244122i
$707$		0			0
$708$		0			0
$709$	12.3432	+	16.9890i	0.463559	+	0.638034i	0.975242	−	0.221140i	$-0.0709778\pi$
$709$	12.3432	+	16.9890i	0.463559	+	0.638034i	−0.511683	+	0.859174i	$0.670978\pi$
$710$		0			0
$711$	−48.7132	+	15.8279i	−1.82689	+	0.593592i
$712$		0			0
$713$	−21.0153	−	39.6503i	−0.787028	−	1.48491i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$719$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$720$	−3.02632	−	28.7935i	−0.112784	−	1.07307i
$721$		0			0
$722$	−1.94561	+	18.5112i	−0.0724080	+	0.688916i
$723$	25.7506	−	28.5989i	0.957675	−	1.06361i
$724$	−0.295800	+	0.664378i	−0.0109933	+	0.0246914i
$725$		0			0
$726$	−7.74937	−	36.4579i	−0.287606	−	1.35308i
$727$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$727$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$728$		0			0
$729$	−8.34346	+	25.6785i	−0.309017	+	0.951057i
$730$		0			0
$731$		0			0
$732$	−48.1939	−	10.2439i	−1.78130	−	0.378627i
$733$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$733$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$734$		0			0
$735$	−26.9624	−	2.83386i	−0.994522	−	0.104528i
$736$	−36.7943	+	50.6430i	−1.35626	+	1.86673i
$737$		0			0
$738$		0			0
$739$	20.4787	−	11.8234i	0.753322	−	0.434930i	−0.0735712	−	0.997290i	$-0.523440\pi$
$739$	20.4787	−	11.8234i	0.753322	−	0.434930i	0.826893	+	0.562360i	$0.190106\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			32.8983i			1.20692i	0.797392	+	0.603462i	$0.206212\pi$
$743$			32.8983i			1.20692i	−0.797392	+	0.603462i	$0.793788\pi$
$744$	−1.11974	+	3.06387i	−0.0410518	+	0.112327i
$745$		0			0
$746$		0			0
$747$	9.16590	−	8.25301i	0.335363	−	0.301962i
$748$		0			0
$749$		0			0
$750$	32.8081	+	18.9417i	1.19798	+	0.691655i
$751$	5.72408	+	54.4610i	0.208875	+	1.98731i	0.145962	+	0.989290i	$0.453372\pi$
$751$	5.72408	+	54.4610i	0.208875	+	1.98731i	0.0629125	+	0.998019i	$0.479961\pi$
$752$	−13.7713	−	10.0054i	−0.502188	−	0.364861i
$753$		0			0
$754$		0			0
$755$	−13.4508	+	30.2110i	−0.489524	+	1.09949i
$756$		0			0
$757$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$757$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$758$	68.0379	−	30.2924i	2.47125	−	1.10027i
$759$		0			0
$760$	0.719862	−	2.21551i	0.0261122	−	0.0803649i
$761$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$761$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	2.03834	+	1.83533i	0.0736965	+	0.0663566i
$766$	68.8984	+	7.24151i	2.48940	+	0.261647i
$767$		0			0
$768$	31.6923	−	3.33099i	1.14360	−	0.120197i
$769$	−26.9028	+	46.5969i	−0.970138	+	1.68033i	−0.275012	+	0.961441i	$0.588682\pi$
$769$	−26.9028	+	46.5969i	−0.970138	+	1.68033i	−0.695126	+	0.718888i	$0.744652\pi$
$770$		0			0
$771$	16.0840	+	22.1377i	0.579250	+	0.797270i
$772$		0			0
$773$	45.1456	−	14.6687i	1.62378	−	0.527597i	0.650947	−	0.759123i	$-0.274372\pi$
$773$	45.1456	−	14.6687i	1.62378	−	0.527597i	0.972829	+	0.231527i	$0.0743720\pi$
$774$		0			0
$775$	−15.5368	−	23.1000i	−0.558097	−	0.829776i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	−0.673895	−	6.41169i	−0.0240984	−	0.229281i
$783$		0			0
$784$	3.15796	−	30.0459i	0.112784	−	1.07307i
$785$		0			0
$786$		0			0
$787$		0			0		0.207912	−	0.978148i	$-0.433333\pi$
$787$		0			0		−0.207912	+	0.978148i	$0.566667\pi$
$788$	8.92624	+	41.9947i	0.317984	+	1.49600i
$789$	43.5266	−	19.3793i	1.54959	−	0.689921i
$790$	71.0306	+	23.0792i	2.52715	+	0.821122i
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	0.101230	+	0.0450705i	0.00359026	+	0.00159849i
$796$	−34.5903	−	31.1452i	−1.22602	−	1.10391i
$797$	51.5369	+	5.41675i	1.82553	+	0.191871i	0.954269	−	0.298948i	$-0.0966357\pi$
$797$	51.5369	+	5.41675i	1.82553	+	0.191871i	0.871262	+	0.490819i	$0.163302\pi$
$798$		0			0
$799$	1.60382	−	0.168569i	0.0567392	−	0.00596353i
$800$	−19.4167	+	33.6308i	−0.686485	+	1.18903i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$809$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$810$	31.8507	−	23.1409i	1.11912	−	0.813089i
$811$	−19.0847	−	33.0557i	−0.670155	−	1.16074i	−0.977860	−	0.209261i	$-0.932894\pi$
$811$	−19.0847	−	33.0557i	−0.670155	−	1.16074i	0.307705	−	0.951482i	$-0.400439\pi$
$812$		0			0
$813$	−2.57630	−	24.5118i	−0.0903547	−	0.859668i
$814$		0			0
$815$		0			0
$816$	−2.04523	+	2.27146i	−0.0715975	+	0.0795170i
$817$		0			0
$818$	15.8141	−	74.3993i	0.552925	−	2.60131i
$819$		0			0
$820$		0			0
$821$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$821$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$822$	22.5267	−	69.3302i	0.785710	−	2.41817i
$823$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$823$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	27.2071	+	24.4974i	0.946083	+	0.851857i	0.989104	−	0.147217i	$-0.0470315\pi$
$827$	27.2071	+	24.4974i	0.946083	+	0.851857i	−0.0430208	+	0.999074i	$0.513698\pi$
$828$	−43.9361	−	4.61787i	−1.52689	−	0.160482i
$829$	33.1307	−	45.6005i	1.15068	−	1.58377i	0.409729	−	0.912207i	$-0.365623\pi$
$829$	33.1307	−	45.6005i	1.15068	−	1.58377i	0.740947	−	0.671563i	$-0.234377\pi$
$830$	−17.8860	+	1.87990i	−0.620833	+	0.0652522i
$831$		0			0
$832$		0			0
$833$	1.68234	+	2.31555i	0.0582897	+	0.0802289i
$834$	51.8206	+	57.5527i	1.79440	+	1.99289i
$835$	−13.5266	+	4.39506i	−0.468108	+	0.152097i
$836$		0			0
$837$	−28.4980	+	4.98615i	−0.985036	+	0.172347i
$838$		0			0
$839$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$839$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$840$		0			0
$841$	23.4615	−	17.0458i	0.809017	−	0.587785i
$842$	31.7080	+	54.9199i	1.09273	+	1.89267i
$843$		0			0
$844$	3.45670	+	32.8883i	0.118984	+	1.13206i
$845$	23.5172	+	17.0863i	0.809017	+	0.587785i
$846$	2.41955	−	23.0205i	0.0831858	−	0.791460i
$847$		0			0
$848$	−0.0502250	+	0.112807i	−0.00172474	+	0.00387382i
$849$		0			0
$850$	−0.831536	−	3.91207i	−0.0285214	−	0.134183i
$851$		0			0
$852$		0			0
$853$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$853$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$854$		0			0
$855$	20.2088	−	4.29551i	0.691126	−	0.146903i
$856$	6.80948	+	1.44740i	0.232743	+	0.0494711i
$857$	46.6883	+	20.7870i	1.59484	+	0.710070i	0.995878	−	0.0907053i	$-0.0289121\pi$
$857$	46.6883	+	20.7870i	1.59484	+	0.710070i	0.598965	+	0.800775i	$0.295579\pi$
$858$		0			0
$859$	−6.74590	−	0.709022i	−0.230167	−	0.0241915i	−0.0112573	−	0.999937i	$-0.503583\pi$
$859$	−6.74590	−	0.709022i	−0.230167	−	0.0241915i	−0.218910	+	0.975745i	$0.570250\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−50.0410	+	28.8912i	−1.70342	+	0.983468i	−0.761166	+	0.648557i	$0.775373\pi$
$863$	−50.0410	+	28.8912i	−1.70342	+	0.983468i	−0.942250	+	0.334911i	$0.891294\pi$
$864$	23.7212	+	32.6494i	0.807012	+	1.11076i
$865$	−14.8808	−	16.5268i	−0.505962	−	0.561928i
$866$		0			0
$867$			29.1553i			0.990166i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	5.21593	−	3.78959i	0.176634	−	0.128332i
$873$		0			0
$874$	−42.0553	−	24.2806i	−1.42254	−	0.821305i
$875$		0			0
$876$		0			0
$877$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$877$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$878$	−12.8553	+	14.2772i	−0.433844	+	0.481833i
$879$	19.5425	−	43.8931i	0.659151	−	1.48048i
$880$		0			0
$881$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$881$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$882$	37.5305	−	16.7096i	1.26372	−	0.562643i
$883$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$883$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$884$		0			0
$885$		0			0
$886$	−48.6426	+	10.3393i	−1.63418	+	0.347356i
$887$	40.9360	+	8.70123i	1.37450	+	0.292159i	0.835195	−	0.549953i	$-0.185355\pi$
$887$	40.9360	+	8.70123i	1.37450	+	0.292159i	0.539303	+	0.842112i	$0.318688\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	6.07357	−	10.5197i	0.203244	−	0.352030i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−27.4064			−0.913545
$901$	−0.00361504	−	0.0111260i	−0.000120435	−	0.000370660i
$902$		0			0
$903$		0			0
$904$	2.66616	+	4.61793i	0.0886753	+	0.153590i
$905$	−0.770798	−	0.445020i	−0.0256222	−	0.0147930i
$906$	−5.23816	−	49.8378i	−0.174026	−	1.65575i
$907$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$907$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$908$	−5.71885	+	54.4112i	−0.189787	+	1.80570i
$909$		0			0
$910$		0			0
$911$		0			0		0.207912	−	0.978148i	$-0.433333\pi$
$911$		0			0		−0.207912	+	0.978148i	$0.566667\pi$
$912$	4.78677	+	22.5200i	0.158506	+	0.745712i
$913$		0			0
$914$		0			0
$915$	18.6335	−	57.3481i	0.616005	−	1.89587i
$916$	−21.9337	−	49.2640i	−0.724711	−	1.62773i
$917$		0			0
$918$	−4.06554	−	0.864157i	−0.134183	−	0.0285214i
$919$	−54.4543	−	24.2446i	−1.79628	−	0.799757i	−0.972519	−	0.232824i	$-0.925203\pi$
$919$	−54.4543	−	24.2446i	−1.79628	−	0.799757i	−0.823764	−	0.566933i	$-0.808130\pi$
$920$	−4.53040	−	4.07919i	−0.149363	−	0.134487i
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0			−	1.00000i	$-0.5\pi$
$929$		0			0				1.00000i	$0.5\pi$
$930$	37.8914	+	18.5429i	1.24251	+	0.608045i
$931$	21.5590			0.706567
$932$	−14.7889	−	45.5154i	−0.484425	−	1.49091i
$933$		0			0
$934$	−53.9971	+	39.2312i	−1.76684	+	1.28368i
$935$		0			0
$936$		0			0
$937$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$937$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$938$		0			0
$939$		0			0
$940$	−10.7820	+	11.9747i	−0.351671	+	0.390570i
$941$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$941$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	9.73980	+	21.8759i	0.316501	+	0.710873i	0.999815	−	0.0192522i	$-0.00612855\pi$
$947$	9.73980	+	21.8759i	0.316501	+	0.710873i	−0.683314	+	0.730125i	$0.739462\pi$
$948$	−52.8500	+	11.2336i	−1.71649	+	0.364851i
$949$		0			0
$950$	−27.5210	−	12.2531i	−0.892900	−	0.397545i
$951$	−40.8022	−	36.7385i	−1.32310	−	1.19133i
$952$		0			0
$953$	19.0548	−	26.2267i	0.617245	−	0.849565i	−0.379904	−	0.925026i	$-0.624043\pi$
$953$	19.0548	−	26.2267i	0.617245	−	0.849565i	0.997149	+	0.0754611i	$0.0240429\pi$
$954$	−0.166995	+	0.0175519i	−0.00540666	+	0.000568263i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		−	25.4149i		−	0.820263i
$961$	−19.0209	−	24.4787i	−0.613577	−	0.789635i
$962$		0			0
$963$	19.0792	+	58.7199i	0.614820	+	1.89222i
$964$	30.1682	−	27.1636i	0.971652	−	0.874879i
$965$		0			0
$966$		0			0
$967$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$967$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$968$	0.388937	+	3.70049i	0.0125009	+	0.118938i
$969$	−1.76460	−	1.28206i	−0.0566871	−	0.0411856i
$970$		0			0
$971$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$971$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$972$	−11.5845	+	26.0192i	−0.371572	+	0.834565i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	63.9067	+	20.7646i	2.04560	+	0.664657i
$977$	13.3945	−	41.2240i	0.428528	−	1.31887i	−0.471048	−	0.882108i	$-0.656124\pi$
$977$	13.3945	−	41.2240i	0.428528	−	1.31887i	0.899576	−	0.436765i	$-0.143876\pi$
$978$		0			0
$979$		0			0
$980$	−27.9736	−	5.94596i	−0.893582	−	0.189937i
$981$	52.2364	+	23.2571i	1.66778	+	0.742543i
$982$		0			0
$983$	48.5786	+	5.10581i	1.54942	+	0.162850i	0.840253	−	0.542194i	$-0.182406\pi$
$983$	48.5786	+	5.10581i	1.54942	+	0.162850i	0.709163	+	0.705045i	$0.249073\pi$
$984$		0			0
$985$	−52.2551	+	5.49224i	−1.66499	+	0.174997i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		−	36.5185i		−	1.16005i	−0.814600	−	0.580024i	$-0.803043\pi$
$991$		−	36.5185i		−	1.16005i	0.814600	−	0.580024i	$-0.196957\pi$
$992$	−19.0079	+	38.8416i	−0.603501	+	1.23322i
$993$	−29.2865			−0.929379
$994$		0			0
$995$	42.3330	−	38.1168i	1.34205	−	1.20838i
$996$	10.5259	−	7.64751i	0.333526	−	0.242321i
$997$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$997$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$998$	−74.9517	−	43.2734i	−2.37255	−	1.36979i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.bm.a.104.1	✓	8
3.2	odd	2		465.2.bm.c.104.1	yes	8
5.4	even	2		465.2.bm.c.104.1	yes	8
15.14	odd	2	CM	465.2.bm.a.104.1	✓	8
31.17	odd	30	inner	465.2.bm.a.389.1	yes	8
93.17	even	30		465.2.bm.c.389.1	yes	8
155.79	odd	30		465.2.bm.c.389.1	yes	8
465.389	even	30	inner	465.2.bm.a.389.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.bm.a.104.1	✓	8	1.1	even	1	trivial
465.2.bm.a.104.1	✓	8	15.14	odd	2	CM
465.2.bm.a.389.1	yes	8	31.17	odd	30	inner
465.2.bm.a.389.1	yes	8	465.389	even	30	inner
465.2.bm.c.104.1	yes	8	3.2	odd	2
465.2.bm.c.104.1	yes	8	5.4	even	2
465.2.bm.c.389.1	yes	8	93.17	even	30
465.2.bm.c.389.1	yes	8	155.79	odd	30

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:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.bm (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.604528 - 1.86055i) q^{2} +(-1.28716 + 1.15897i) q^{3} +(-1.47815 + 1.07394i) q^{4} +(-1.11803 - 1.93649i) q^{5} +(2.93444 + 1.69420i) q^{6} +(-0.273659 - 0.198825i) q^{8} +(0.313585 - 2.98357i) q^{9} +(-2.92705 + 3.25082i) q^{10} +(0.657960 - 3.09546i) q^{12} +(3.68343 + 1.19682i) q^{15} +(-1.33369 + 4.10468i) q^{16} +(-0.166307 - 0.373532i) q^{17} +(-5.74064 + 1.22021i) q^{18} +(-3.01255 - 0.640337i) q^{19} +(3.73229 + 1.66172i) q^{20} +(-4.73745 + 6.52054i) q^{23} +(0.582676 - 0.0612417i) q^{24} +(-2.50000 + 4.33013i) q^{25} +(3.05422 + 4.20378i) q^{27} -7.57670i q^{30} +(-2.44736 + 5.00104i) q^{31} +7.76669 q^{32} +(-0.594437 + 0.535233i) q^{34} +(2.74064 + 4.74692i) q^{36} +(0.629795 + 5.99209i) q^{38} +(-0.0790627 + 0.752232i) q^{40} +(-6.12825 + 2.72847i) q^{45} +(14.9957 + 4.87240i) q^{46} +(-1.21878 + 3.75103i) q^{47} +(-3.04052 - 6.82911i) q^{48} +(-6.84703 + 1.45538i) q^{49} +(9.56773 + 2.03368i) q^{50} +(0.646976 + 0.288052i) q^{51} +(0.0284543 + 0.00299067i) q^{53} +(5.97496 - 8.22383i) q^{54} +(4.61978 - 2.66723i) q^{57} +(-6.72995 + 2.18669i) q^{60} -15.5692i q^{61} +(10.7842 + 1.53015i) q^{62} +(-2.02780 - 6.24093i) q^{64} +(0.646976 + 0.373532i) q^{68} +(-1.45922 - 13.8836i) q^{69} +(-0.679023 + 0.754131i) q^{72} +(-1.80057 - 8.47101i) q^{75} +(5.14068 - 2.28878i) q^{76} +(-6.94437 - 15.5973i) q^{79} +(9.43980 - 2.00649i) q^{80} +(-8.80333 - 1.87121i) q^{81} +(3.05530 + 2.75100i) q^{83} +(-0.537405 + 0.739674i) q^{85} +(8.78115 + 9.75246i) q^{90} -14.7260i q^{92} +(-2.64590 - 9.27358i) q^{93} +7.71576 q^{94} +(2.12813 + 6.54970i) q^{95} +(-9.99701 + 9.00135i) q^{96} +(6.84703 + 11.8594i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{6} + 4 q^{8} - 3 q^{9} - 10 q^{10} - 3 q^{12} - 3 q^{16} - 9 q^{17} - 27 q^{18} + 12 q^{19} - 5 q^{20} + 20 q^{23} - 6 q^{24} - 20 q^{25} - 8 q^{31} + 24 q^{34}+ \cdots - 7 q^{98}+O(q^{100}) \) 8 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^6 + 4 * q^8 - 3 * q^9 - 10 * q^10 - 3 * q^12 - 3 * q^16 - 9 * q^17 - 27 * q^18 + 12 * q^19 - 5 * q^20 + 20 * q^23 - 6 * q^24 - 20 * q^25 - 8 * q^31 + 24 * q^34 + 3 * q^36 - 22 * q^38 - 20 * q^40 - 15 * q^45 + 5 * q^46 + 18 * q^47 - 3 * q^48 + 7 * q^49 + 45 * q^50 + 9 * q^51 + 14 * q^53 + 39 * q^57 - 30 * q^60 + 38 * q^62 + 16 * q^64 + 9 * q^68 + 39 * q^69 - 24 * q^72 - 15 * q^75 + 23 * q^76 - 9 * q^79 + 30 * q^80 + 9 * q^81 - 23 * q^83 + 30 * q^90 - 48 * q^93 + 42 * q^94 + 35 * q^95 - 45 * q^96 - 7 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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