LMFDB - Embedded newform 675.2.r.a.46.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(46,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.46"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([20, 18])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.r (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			46.24
Character	$\chi$	$=$	675.46
Dual form			675.2.r.a.631.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.30960 + 1.45446i) q^{2} +(-0.191342 + 1.82050i) q^{4} +(1.40249 - 1.74155i) q^{5} +(0.690014 - 1.19514i) q^{7} +(0.268345 - 0.194964i) q^{8} +(4.36974 - 0.240869i) q^{10} +(-1.65278 - 1.83560i) q^{11} +(2.15209 - 2.39014i) q^{13} +(2.64193 - 0.561560i) q^{14} +(4.21604 + 0.896147i) q^{16} +(-3.02773 + 2.19977i) q^{17} +(0.234784 - 0.170581i) q^{19} +(2.90214 + 2.88647i) q^{20} +(0.505323 - 4.80783i) q^{22} +(0.569918 - 0.121140i) q^{23} +(-1.06602 - 4.88504i) q^{25} +6.29476 q^{26} +(2.04372 + 1.48485i) q^{28} +(-3.40818 + 1.51742i) q^{29} +(7.82432 + 3.48361i) q^{31} +(3.88624 + 6.73116i) q^{32} +(-7.16461 - 1.52289i) q^{34} +(-1.11366 - 2.87787i) q^{35} +(2.37815 + 7.31918i) q^{37} +(0.555578 + 0.118092i) q^{38} +(0.0368121 - 0.740773i) q^{40} +(-4.25243 + 4.72280i) q^{41} +(-3.20269 + 5.54723i) q^{43} +(3.65796 - 2.65766i) q^{44} +(0.922560 + 0.670279i) q^{46} +(-6.56303 + 2.92205i) q^{47} +(2.54776 + 4.41285i) q^{49} +(5.70905 - 7.94795i) q^{50} +(3.93946 + 4.37521i) q^{52} +(-6.69073 - 4.86110i) q^{53} +(-5.51482 + 0.303989i) q^{55} +(-0.0478474 - 0.455238i) q^{56} +(-6.67040 - 2.96985i) q^{58} +(1.30177 - 1.44576i) q^{59} +(-8.77365 - 9.74413i) q^{61} +(5.17998 + 15.9423i) q^{62} +(-2.03692 + 6.26900i) q^{64} +(-1.14426 - 7.10014i) q^{65} +(9.24473 + 4.11602i) q^{67} +(-3.42535 - 5.93288i) q^{68} +(2.72731 - 5.38865i) q^{70} +(10.4571 + 7.59752i) q^{71} +(1.44065 - 4.43387i) q^{73} +(-7.53104 + 13.0442i) q^{74} +(0.265618 + 0.460064i) q^{76} +(-3.33424 + 0.708716i) q^{77} +(-14.5537 + 6.47975i) q^{79} +(7.47366 - 6.08562i) q^{80} -12.4381 q^{82} +(0.0211178 + 0.200922i) q^{83} +(-0.415350 + 8.35812i) q^{85} +(-12.2625 + 2.60647i) q^{86} +(-0.801393 - 0.170341i) q^{88} +(3.30633 - 10.1758i) q^{89} +(-1.37158 - 4.22128i) q^{91} +(0.111485 + 1.06071i) q^{92} +(-12.8450 - 5.71895i) q^{94} +(0.0322082 - 0.648128i) q^{95} +(10.0866 - 4.49085i) q^{97} +(-3.08177 + 9.48471i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28}+ \cdots - 146 q^{98}+O(q^{100}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Character values

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

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	1.30960	+	1.45446i	0.926030	+	1.02846i	0.999514	+	0.0311641i	$0.00992143\pi$
$2$	1.30960	+	1.45446i	0.926030	+	1.02846i	−0.0734844	+	0.997296i	$0.523412\pi$
$3$		0			0
$3$		0			0
$4$	−0.191342	+	1.82050i	−0.0956710	+	0.910248i
$5$	1.40249	−	1.74155i	0.627215	−	0.778846i
$5$	1.40249	−	1.74155i	0.627215	−	0.778846i
$6$		0			0
$7$	0.690014	−	1.19514i	0.260801	−	0.451720i	−0.705654	−	0.708556i	$-0.749347\pi$
$7$	0.690014	−	1.19514i	0.260801	−	0.451720i	0.966455	+	0.256836i	$0.0826801\pi$
$8$	0.268345	−	0.194964i	0.0948743	−	0.0689302i
$9$		0			0
$10$	4.36974	−	0.240869i	1.38183	−	0.0761696i
$11$	−1.65278	−	1.83560i	−0.498333	−	0.553455i	0.440533	−	0.897736i	$-0.354789\pi$
$11$	−1.65278	−	1.83560i	−0.498333	−	0.553455i	−0.938867	+	0.344281i	$0.888123\pi$
$12$		0			0
$13$	2.15209	−	2.39014i	0.596883	−	0.662906i	−0.366692	−	0.930342i	$-0.619510\pi$
$13$	2.15209	−	2.39014i	0.596883	−	0.662906i	0.963576	+	0.267436i	$0.0861765\pi$
$14$	2.64193	−	0.561560i	0.706086	−	0.150083i
$15$		0			0
$16$	4.21604	+	0.896147i	1.05401	+	0.224037i
$17$	−3.02773	+	2.19977i	−0.734332	+	0.533523i	−0.890931	−	0.454139i	$-0.849947\pi$
$17$	−3.02773	+	2.19977i	−0.734332	+	0.533523i	0.156599	+	0.987662i	$0.449947\pi$
$18$		0			0
$19$	0.234784	−	0.170581i	0.0538632	−	0.0391339i	−0.560528	−	0.828136i	$-0.689402\pi$
$19$	0.234784	−	0.170581i	0.0538632	−	0.0391339i	0.614391	+	0.789002i	$0.289402\pi$
$20$	2.90214	+	2.88647i	0.648937	+	0.645434i
$21$		0			0
$22$	0.505323	−	4.80783i	0.107735	−	1.02503i
$23$	0.569918	−	0.121140i	0.118836	−	0.0252594i	−0.148110	−	0.988971i	$-0.547319\pi$
$23$	0.569918	−	0.121140i	0.118836	−	0.0252594i	0.266946	+	0.963712i	$0.413986\pi$
$24$		0			0
$25$	−1.06602	−	4.88504i	−0.213203	−	0.977008i
$26$	6.29476			1.23450
$27$		0			0
$28$	2.04372	+	1.48485i	0.386227	+	0.280610i
$29$	−3.40818	+	1.51742i	−0.632884	+	0.281778i	−0.697998	−	0.716100i	$-0.745925\pi$
$29$	−3.40818	+	1.51742i	−0.632884	+	0.281778i	0.0651142	+	0.997878i	$0.479259\pi$
$30$		0			0
$31$	7.82432	+	3.48361i	1.40529	+	0.625675i	0.962582	−	0.270991i	$-0.0873515\pi$
$31$	7.82432	+	3.48361i	1.40529	+	0.625675i	0.442707	+	0.896666i	$0.354018\pi$
$32$	3.88624	+	6.73116i	0.686996	+	1.18991i
$33$		0			0
$34$	−7.16461	−	1.52289i	−1.22872	−	0.261173i
$35$	−1.11366	−	2.87787i	−0.188243	−	0.486449i
$36$		0			0
$37$	2.37815	+	7.31918i	0.390965	+	1.20327i	0.932060	+	0.362304i	$0.118010\pi$
$37$	2.37815	+	7.31918i	0.390965	+	1.20327i	−0.541095	+	0.840961i	$0.681990\pi$
$38$	0.555578	+	0.118092i	0.0901267	+	0.0191570i
$39$		0			0
$40$	0.0368121	−	0.740773i	0.00582050	−	0.117127i
$41$	−4.25243	+	4.72280i	−0.664118	+	0.737578i	−0.977240	−	0.212135i	$-0.931958\pi$
$41$	−4.25243	+	4.72280i	−0.664118	+	0.737578i	0.313122	+	0.949713i	$0.398625\pi$
$42$		0			0
$43$	−3.20269	+	5.54723i	−0.488406	+	0.845944i	−0.999911	−	0.0133363i	$-0.995755\pi$
$43$	−3.20269	+	5.54723i	−0.488406	+	0.845944i	0.511505	+	0.859280i	$0.329088\pi$
$44$	3.65796	−	2.65766i	0.551458	−	0.400657i
$45$		0			0
$46$	0.922560	+	0.670279i	0.136024	+	0.0988273i
$47$	−6.56303	+	2.92205i	−0.957316	+	0.426225i	−0.825094	−	0.564996i	$-0.808878\pi$
$47$	−6.56303	+	2.92205i	−0.957316	+	0.426225i	−0.132222	+	0.991220i	$0.542211\pi$
$48$		0			0
$49$	2.54776	+	4.41285i	0.363966	+	0.630407i
$50$	5.70905	−	7.94795i	0.807381	−	1.12401i
$51$		0			0
$52$	3.93946	+	4.37521i	0.546305	+	0.606733i
$53$	−6.69073	−	4.86110i	−0.919043	−	0.667724i	0.0242428	−	0.999706i	$-0.492283\pi$
$53$	−6.69073	−	4.86110i	−0.919043	−	0.667724i	−0.943286	+	0.331982i	$0.892283\pi$
$54$		0			0
$55$	−5.51482	+	0.303989i	−0.743618	+	0.0409899i
$56$	−0.0478474	−	0.455238i	−0.00639388	−	0.0608337i
$57$		0			0
$58$	−6.67040	−	2.96985i	−0.875867	−	0.389961i
$59$	1.30177	−	1.44576i	0.169476	−	0.188222i	−0.652424	−	0.757854i	$-0.726248\pi$
$59$	1.30177	−	1.44576i	0.169476	−	0.188222i	0.821900	+	0.569632i	$0.192914\pi$
$60$		0			0
$61$	−8.77365	−	9.74413i	−1.12335	−	1.24761i	−0.965573	−	0.260133i	$-0.916234\pi$
$61$	−8.77365	−	9.74413i	−1.12335	−	1.24761i	−0.157778	−	0.987475i	$-0.550433\pi$
$62$	5.17998	+	15.9423i	0.657858	+	2.02468i
$63$		0			0
$64$	−2.03692	+	6.26900i	−0.254615	+	0.783625i
$65$	−1.14426	−	7.10014i	−0.141928	−	0.880665i
$66$		0			0
$67$	9.24473	+	4.11602i	1.12942	+	0.502852i	0.884430	−	0.466673i	$-0.154547\pi$
$67$	9.24473	+	4.11602i	1.12942	+	0.502852i	0.244994	+	0.969525i	$0.421214\pi$
$68$	−3.42535	−	5.93288i	−0.415385	−	0.719467i
$69$		0			0
$70$	2.72731	−	5.38865i	0.325976	−	0.644067i
$71$	10.4571	+	7.59752i	1.24103	+	0.901659i	0.997666	−	0.0682765i	$-0.0217500\pi$
$71$	10.4571	+	7.59752i	1.24103	+	0.901659i	0.243361	+	0.969936i	$0.421750\pi$
$72$		0			0
$73$	1.44065	−	4.43387i	0.168615	−	0.518945i	−0.830669	−	0.556767i	$-0.812042\pi$
$73$	1.44065	−	4.43387i	0.168615	−	0.518945i	0.999285	+	0.0378214i	$0.0120418\pi$
$74$	−7.53104	+	13.0442i	−0.875466	+	1.51635i
$75$		0			0
$76$	0.265618	+	0.460064i	0.0304685	+	0.0527729i
$77$	−3.33424	+	0.708716i	−0.379972	+	0.0807656i
$78$		0			0
$79$	−14.5537	+	6.47975i	−1.63742	+	0.729028i	−0.999168	−	0.0407952i	$-0.987011\pi$
$79$	−14.5537	+	6.47975i	−1.63742	+	0.729028i	−0.638257	+	0.769824i	$0.720344\pi$
$80$	7.47366	−	6.08562i	0.835581	−	0.680393i
$81$		0			0
$82$	−12.4381			−1.37356
$83$	0.0211178	+	0.200922i	0.00231797	+	0.0220541i	0.995620	−	0.0934950i	$-0.0298039\pi$
$83$	0.0211178	+	0.200922i	0.00231797	+	0.0220541i	−0.993302	+	0.115549i	$0.963137\pi$
$84$		0			0
$85$	−0.415350	+	8.35812i	−0.0450510	+	0.906565i
$86$	−12.2625	+	2.60647i	−1.32230	+	0.281063i
$87$		0			0
$88$	−0.801393	−	0.170341i	−0.0854288	−	0.0181584i
$89$	3.30633	−	10.1758i	0.350471	−	1.07864i	−0.608119	−	0.793846i	$-0.708076\pi$
$89$	3.30633	−	10.1758i	0.350471	−	1.07864i	0.958589	−	0.284792i	$-0.0919244\pi$
$90$		0			0
$91$	−1.37158	−	4.22128i	−0.143780	−	0.442510i
$92$	0.111485	+	1.06071i	0.0116232	+	0.110587i
$93$		0			0
$94$	−12.8450	−	5.71895i	−1.32486	−	0.589865i
$95$	0.0322082	−	0.648128i	0.00330449	−	0.0664966i
$96$		0			0
$97$	10.0866	−	4.49085i	1.02414	−	0.455977i	0.175238	−	0.984526i	$-0.443930\pi$
$97$	10.0866	−	4.49085i	1.02414	−	0.455977i	0.848903	+	0.528549i	$0.177264\pi$
$98$	−3.08177	+	9.48471i	−0.311306	+	0.958101i
$99$		0			0
$100$	9.09717	−	1.00597i	0.909717	−	0.100597i
$101$	−7.27293	+	12.5971i	−0.723684	+	1.25346i	0.235830	+	0.971794i	$0.424219\pi$
$101$	−7.27293	+	12.5971i	−0.723684	+	1.25346i	−0.959513	+	0.281663i	$0.909114\pi$
$102$		0			0
$103$	0.606222	−	5.76782i	0.0597328	−	0.568320i	−0.923195	−	0.384331i	$-0.874432\pi$
$103$	0.606222	−	5.76782i	0.0597328	−	0.568320i	0.982928	−	0.183989i	$-0.0589011\pi$
$104$	0.111512	−	1.06096i	0.0109346	−	0.104036i
$105$		0			0
$106$	−1.69192	−	16.0975i	−0.164334	−	1.56353i
$107$	12.8622			1.24344			0.621718	−	0.783241i	$-0.286435\pi$
$107$	12.8622			1.24344			0.621718	+	0.783241i	$0.286435\pi$
$108$		0			0
$109$	−4.92848	−	15.1683i	−0.472063	−	1.45286i	−0.849878	−	0.526979i	$-0.823325\pi$
$109$	−4.92848	−	15.1683i	−0.472063	−	1.45286i	0.377816	−	0.925881i	$-0.376675\pi$
$110$	−7.66437	−	7.62300i	−0.730769	−	0.726824i
$111$		0			0
$112$	3.98015	−	4.42040i	0.376089	−	0.417689i
$113$	−4.94877	+	5.49617i	−0.465542	+	0.517036i	−0.929501	−	0.368820i	$-0.879762\pi$
$113$	−4.94877	+	5.49617i	−0.465542	+	0.517036i	0.463959	+	0.885857i	$0.346428\pi$
$114$		0			0
$115$	0.588335	−	1.16244i	0.0548626	−	0.108398i
$116$	−2.11033	−	6.49493i	−0.195939	−	0.603039i
$117$		0			0
$118$	3.80761			0.350519
$119$	0.539861	+	5.13643i	0.0494889	+	0.470856i
$120$		0			0
$121$	0.512071	−	4.87203i	0.0465519	−	0.442912i
$122$	2.68246	−	25.5219i	0.242858	−	2.31064i
$123$		0			0
$124$	−7.83902	+	13.5776i	−0.703965	+	1.21930i
$125$	−10.0026	−	4.99472i	−0.894663	−	0.446741i
$126$		0			0
$127$	−4.27237	+	13.1490i	−0.379112	+	1.16679i	0.561551	+	0.827442i	$0.310205\pi$
$127$	−4.27237	+	13.1490i	−0.379112	+	1.16679i	−0.940663	+	0.339343i	$0.889795\pi$
$128$	2.41543	−	1.07542i	0.213496	−	0.0950544i
$129$		0			0
$130$	8.82837	−	10.9627i	0.774299	−	0.961489i
$131$	−6.74268	−	3.00204i	−0.589111	−	0.262289i	0.0904585	−	0.995900i	$-0.471167\pi$
$131$	−6.74268	−	3.00204i	−0.589111	−	0.262289i	−0.679570	+	0.733611i	$0.737833\pi$
$132$		0			0
$133$	−0.0418634	−	0.398303i	−0.00363001	−	0.0345373i
$134$	6.12034	+	18.8365i	0.528717	+	1.62722i
$135$		0			0
$136$	−0.383599	+	1.18060i	−0.0328933	+	0.101235i
$137$	−4.12212	−	0.876184i	−0.352177	−	0.0748574i	0.0284267	−	0.999596i	$-0.490950\pi$
$137$	−4.12212	−	0.876184i	−0.352177	−	0.0748574i	−0.380603	+	0.924738i	$0.624284\pi$
$138$		0			0
$139$	0.349017	−	0.0741858i	0.0296032	−	0.00629236i	−0.193086	−	0.981182i	$-0.561850\pi$
$139$	0.349017	−	0.0741858i	0.0296032	−	0.00629236i	0.222689	+	0.974889i	$0.428516\pi$
$140$	5.45225	−	1.47675i	0.460799	−	0.124808i
$141$		0			0
$142$	2.64434	+	25.1592i	0.221908	+	2.11131i
$143$	−7.94429			−0.664335
$144$		0			0
$145$	−2.13729	+	8.06371i	−0.177492	+	0.669654i
$146$	8.33558	−	3.71124i	0.689858	−	0.307144i
$147$		0			0
$148$	−13.7796	+	2.92894i	−1.13267	+	0.240757i
$149$	−11.6755	−	20.2226i	−0.956497	−	1.65670i	−0.730905	−	0.682479i	$-0.760902\pi$
$149$	−11.6755	−	20.2226i	−0.956497	−	1.65670i	−0.225591	−	0.974222i	$-0.572431\pi$
$150$		0			0
$151$	4.03983	−	6.99720i	0.328757	−	0.569424i	−0.653508	−	0.756919i	$-0.726704\pi$
$151$	4.03983	−	6.99720i	0.328757	−	0.569424i	0.982265	+	0.187495i	$0.0600369\pi$
$152$	0.0297461	−	0.0915490i	0.00241273	−	0.00742561i
$153$		0			0
$154$	−5.39734	−	3.92140i	−0.434930	−	0.315995i
$155$	17.0405	−	8.74072i	1.36872	−	0.702072i
$156$		0			0
$157$	8.40415	+	14.5564i	0.670724	+	1.16173i	0.977699	+	0.210011i	$0.0673500\pi$
$157$	8.40415	+	14.5564i	0.670724	+	1.16173i	−0.306975	+	0.951718i	$0.599317\pi$
$158$	−28.4842	−	12.6820i	−2.26608	−	1.00892i
$159$		0			0
$160$	17.1731	+	2.67233i	1.35765	+	0.211266i
$161$	0.248472	−	0.764719i	0.0195824	−	0.0602683i
$162$		0			0
$163$	1.89571	+	5.83439i	0.148483	+	0.456985i	0.997442	−	0.0714737i	$-0.0227702\pi$
$163$	1.89571	+	5.83439i	0.148483	+	0.456985i	−0.848959	+	0.528459i	$0.822770\pi$
$164$	−7.78418	−	8.64521i	−0.607842	−	0.675077i
$165$		0			0
$166$	−0.264578	+	0.293843i	−0.0205352	+	0.0228067i
$167$	18.6016	+	8.28195i	1.43943	+	0.640876i	0.970224	−	0.242211i	$-0.0778727\pi$
$167$	18.6016	+	8.28195i	1.43943	+	0.640876i	0.469208	+	0.883088i	$0.344539\pi$
$168$		0			0
$169$	0.277599	+	2.64118i	0.0213538	+	0.203167i
$170$	−12.7005	+	10.3417i	−0.974085	+	0.793174i
$171$		0			0
$172$	−9.48590	−	6.89191i	−0.723293	−	0.525503i
$173$	8.79105	+	9.76345i	0.668371	+	0.742301i	0.978011	−	0.208553i	$-0.0668752\pi$
$173$	8.79105	+	9.76345i	0.668371	+	0.742301i	−0.309640	+	0.950854i	$0.600209\pi$
$174$		0			0
$175$	−6.57387	−	2.09671i	−0.496938	−	0.158496i
$176$	−5.32323	−	9.22011i	−0.401254	−	0.694992i
$177$		0			0
$178$	19.1304	−	8.51739i	1.43388	−	0.638406i
$179$	−4.14235	−	3.00959i	−0.309614	−	0.224947i	0.422117	−	0.906541i	$-0.361287\pi$
$179$	−4.14235	−	3.00959i	−0.309614	−	0.224947i	−0.731731	+	0.681594i	$0.761287\pi$
$180$		0			0
$181$	−7.20858	+	5.23734i	−0.535810	+	0.389289i	−0.822526	−	0.568727i	$-0.807436\pi$
$181$	−7.20858	+	5.23734i	−0.535810	+	0.389289i	0.286717	+	0.958015i	$0.407436\pi$
$182$	4.34347	−	7.52312i	0.321960	−	0.557650i
$183$		0			0
$184$	0.129317	−	0.143621i	0.00953335	−	0.0105879i
$185$	16.0821	+	6.12344i	1.18238	+	0.450204i
$186$		0			0
$187$	9.04209	+	1.92196i	0.661223	+	0.140547i
$188$	−4.06380	−	12.5071i	−0.296383	−	0.912173i
$189$		0			0
$190$	0.984859	−	0.801946i	0.0714492	−	0.0581793i
$191$	−1.84219	−	0.391569i	−0.133296	−	0.0283329i	0.140781	−	0.990041i	$-0.455039\pi$
$191$	−1.84219	−	0.391569i	−0.133296	−	0.0283329i	−0.274076	+	0.961708i	$0.588372\pi$
$192$		0			0
$193$	−0.740550	−	1.28267i	−0.0533060	−	0.0923286i	0.838141	−	0.545453i	$-0.183643\pi$
$193$	−0.740550	−	1.28267i	−0.0533060	−	0.0923286i	−0.891447	+	0.453125i	$0.850309\pi$
$194$	19.7412	+	8.78937i	1.41734	+	0.631040i
$195$		0			0
$196$	−8.52108	+	3.79383i	−0.608648	+	0.270988i
$197$	−15.6165	−	11.3460i	−1.11263	−	0.808372i	−0.129553	−	0.991572i	$-0.541354\pi$
$197$	−15.6165	−	11.3460i	−1.11263	−	0.808372i	−0.983076	+	0.183200i	$0.941354\pi$
$198$		0			0
$199$	6.17381			0.437650			0.218825	−	0.975764i	$-0.429778\pi$
$199$	6.17381			0.437650			0.218825	+	0.975764i	$0.429778\pi$
$200$	−1.23847	−	1.10304i	−0.0875729	−	0.0779968i
$201$		0			0
$202$	−27.8467	+	5.91899i	−1.95928	+	0.416459i
$203$	−0.538165	+	5.12029i	−0.0377718	+	0.359374i
$204$		0			0
$205$	2.26100	+	14.0295i	0.157915	+	0.979866i
$206$	9.18299	−	6.67183i	0.639809	−	0.464848i
$207$		0			0
$208$	11.2152	−	8.14834i	0.777636	−	0.564986i
$209$	−0.701167	−	0.149038i	−0.0485007	−	0.0103091i
$210$		0			0
$211$	−27.6930	+	5.88633i	−1.90647	+	0.405232i	−0.999860	−	0.0167456i	$-0.994669\pi$
$211$	−27.6930	+	5.88633i	−1.90647	+	0.405232i	−0.906606	+	0.421977i	$0.861336\pi$
$212$	10.1298	−	11.2503i	0.695720	−	0.772675i
$213$		0			0
$214$	16.8444	+	18.7076i	1.15146	+	1.27883i
$215$	5.16903	+	13.3576i	0.352525	+	0.910982i
$216$		0			0
$217$	9.56229	−	6.94741i	0.649130	−	0.471621i
$218$	15.6074	−	27.0328i	1.05706	−	1.83089i
$219$		0			0
$220$	0.501806	−	10.0979i	0.0338317	−	0.680799i
$221$	−1.25818	+	11.9708i	−0.0846345	+	0.805244i
$222$		0			0
$223$	0.0705652	+	0.0783706i	0.00472540	+	0.00524809i	0.745503	−	0.666502i	$-0.232209\pi$
$223$	0.0705652	+	0.0783706i	0.00472540	+	0.00524809i	−0.740777	+	0.671750i	$0.765543\pi$
$224$	10.7262			0.716677
$225$		0			0
$226$	−14.4749			−0.962857
$227$	6.70838	+	7.45041i	0.445251	+	0.494501i	0.923433	−	0.383760i	$-0.125371\pi$
$227$	6.70838	+	7.45041i	0.445251	+	0.494501i	−0.478182	+	0.878261i	$0.658704\pi$
$228$		0			0
$229$	1.83314	−	17.4412i	0.121137	−	1.15255i	−0.749977	−	0.661464i	$-0.769935\pi$
$229$	1.83314	−	17.4412i	0.121137	−	1.15255i	0.871114	−	0.491081i	$-0.163398\pi$
$230$	2.46121	−	0.666625i	0.162288	−	0.0439559i
$231$		0			0
$232$	−0.618726	+	1.07167i	−0.0406214	+	0.0703583i
$233$	7.01516	−	5.09682i	0.459579	−	0.333903i	−0.333787	−	0.942648i	$-0.608327\pi$
$233$	7.01516	−	5.09682i	0.459579	−	0.333903i	0.793366	+	0.608745i	$0.208327\pi$
$234$		0			0
$235$	−4.11571	+	15.5280i	−0.268479	+	1.01294i
$236$	2.38292	+	2.64650i	0.155115	+	0.172273i
$237$		0			0
$238$	−6.76374	+	7.51190i	−0.438428	+	0.486924i
$239$	−9.90950	+	2.10633i	−0.640992	+	0.136247i	−0.516930	−	0.856027i	$-0.672925\pi$
$239$	−9.90950	+	2.10633i	−0.640992	+	0.136247i	−0.124062	+	0.992275i	$0.539592\pi$
$240$		0			0
$241$	7.96968	+	1.69401i	0.513372	+	0.109121i	0.457311	−	0.889307i	$-0.348813\pi$
$241$	7.96968	+	1.69401i	0.513372	+	0.109121i	0.0560610	+	0.998427i	$0.482146\pi$
$242$	7.75680	−	5.63564i	0.498626	−	0.362273i
$243$		0			0
$244$	19.4179	−	14.1079i	1.24310	−	0.903168i
$245$	11.2584	+	1.75194i	0.719275	+	0.111927i
$246$		0			0
$247$	0.0975655	−	0.928274i	0.00620794	−	0.0590646i
$248$	2.77880	−	0.590651i	0.176454	−	0.0375064i
$249$		0			0
$250$	−5.83487	−	21.0896i	−0.369030	−	1.33382i
$251$	−23.5790			−1.48829			−0.744146	−	0.668017i	$-0.767143\pi$
$251$	−23.5790			−1.48829			−0.744146	+	0.668017i	$0.767143\pi$
$252$		0			0
$253$	−1.16432	−	0.845925i	−0.0731999	−	0.0531828i
$254$	−24.7199	+	11.0060i	−1.55106	+	0.690577i
$255$		0			0
$256$	16.7709	+	7.46688i	1.04818	+	0.466680i
$257$	6.51124	+	11.2778i	0.406160	+	0.703490i	0.994456	−	0.105156i	$-0.0335342\pi$
$257$	6.51124	+	11.2778i	0.406160	+	0.703490i	−0.588296	+	0.808646i	$0.700201\pi$
$258$		0			0
$259$	10.3884	+	2.20812i	0.645503	+	0.137206i
$260$	13.1447	−	0.724566i	0.815202	−	0.0449357i
$261$		0			0
$262$	−4.46390	−	13.7385i	−0.275780	−	0.848765i
$263$	−11.0211	−	2.34260i	−0.679589	−	0.144451i	−0.144831	−	0.989456i	$-0.546264\pi$
$263$	−11.0211	−	2.34260i	−0.679589	−	0.144451i	−0.534758	+	0.845005i	$0.679597\pi$
$264$		0			0
$265$	−17.8496	+	4.83460i	−1.09649	+	0.296987i
$266$	0.524493	−	0.582508i	0.0321587	−	0.0357159i
$267$		0			0
$268$	−9.26210	+	16.0424i	−0.565773	+	0.979948i
$269$	17.7014	−	12.8608i	1.07927	−	0.784136i	0.101715	−	0.994814i	$-0.467567\pi$
$269$	17.7014	−	12.8608i	1.07927	−	0.784136i	0.977556	+	0.210677i	$0.0675670\pi$
$270$		0			0
$271$	−9.50877	−	6.90853i	−0.577617	−	0.419663i	0.260247	−	0.965542i	$-0.416196\pi$
$271$	−9.50877	−	6.90853i	−0.577617	−	0.419663i	−0.837864	+	0.545879i	$0.816196\pi$
$272$	−14.7363	+	6.56104i	−0.893522	+	0.397822i
$273$		0			0
$274$	−4.12397	−	7.14292i	−0.249138	−	0.431520i
$275$	−7.20509	+	10.0307i	−0.434484	+	0.604874i
$276$		0			0
$277$	−14.7246	−	16.3533i	−0.884714	−	0.982575i	0.115228	−	0.993339i	$-0.463240\pi$
$277$	−14.7246	−	16.3533i	−0.884714	−	0.982575i	−0.999942	+	0.0107642i	$0.996574\pi$
$278$	0.564974	+	0.410478i	0.0338849	+	0.0246188i
$279$		0			0
$280$	−0.859926	−	0.555139i	−0.0513904	−	0.0331759i
$281$	0.134587	+	1.28051i	0.00802878	+	0.0763888i	0.997803	−	0.0662570i	$-0.0211057\pi$
$281$	0.134587	+	1.28051i	0.00802878	+	0.0763888i	−0.989774	+	0.142646i	$0.954439\pi$
$282$		0			0
$283$	7.02505	+	3.12775i	0.417596	+	0.185926i	0.604768	−	0.796401i	$-0.293266\pi$
$283$	7.02505	+	3.12775i	0.417596	+	0.185926i	−0.187173	+	0.982327i	$0.559932\pi$
$284$	−15.8321	+	17.5834i	−0.939464	+	1.04338i
$285$		0			0
$286$	−10.4039	−	11.5547i	−0.615194	−	0.683242i
$287$	2.71017	+	8.34105i	0.159976	+	0.492356i
$288$		0			0
$289$	−0.925154	+	2.84733i	−0.0544209	+	0.167490i
$290$	−14.5274	+	7.45166i	−0.853076	+	0.437576i
$291$		0			0
$292$	7.79619	+	3.47109i	0.456237	+	0.203130i
$293$	5.62660	+	9.74556i	0.328710	+	0.569342i	0.982256	−	0.187545i	$-0.0600529\pi$
$293$	5.62660	+	9.74556i	0.328710	+	0.569342i	−0.653546	+	0.756886i	$0.726720\pi$
$294$		0			0
$295$	−0.692147	−	4.29478i	−0.0402983	−	0.250052i
$296$	2.06514	+	1.50041i	0.120034	+	0.0872097i
$297$		0			0
$298$	14.1227	−	43.4652i	0.818107	−	2.51787i
$299$	0.936975	−	1.62289i	0.0541867	−	0.0938540i
$300$		0			0
$301$	4.41980	+	7.65533i	0.254753	+	0.441246i
$302$	15.4677	−	3.28777i	0.890069	−	0.189190i
$303$		0			0
$304$	1.14273	−	0.508774i	0.0655398	−	0.0291802i
$305$	−29.2749	+	1.61370i	−1.67628	+	0.0924000i
$306$		0			0
$307$	22.3350			1.27473			0.637363	−	0.770563i	$-0.280025\pi$
$307$	22.3350			1.27473			0.637363	+	0.770563i	$0.280025\pi$
$308$	−0.652234	−	6.20559i	−0.0371645	−	0.353596i
$309$		0			0
$310$	35.0293	+	13.3378i	1.98953	+	0.757537i
$311$	−16.3623	+	3.47792i	−0.927823	+	0.197215i	−0.646952	−	0.762531i	$-0.723957\pi$
$311$	−16.3623	+	3.47792i	−0.927823	+	0.197215i	−0.280871	+	0.959746i	$0.590623\pi$
$312$		0			0
$313$	−14.3725	−	3.05496i	−0.812380	−	0.172677i	−0.217053	−	0.976160i	$-0.569644\pi$
$313$	−14.3725	−	3.05496i	−0.812380	−	0.172677i	−0.595327	+	0.803483i	$0.702978\pi$
$314$	−10.1657	+	31.2867i	−0.573681	+	1.76561i
$315$		0			0
$316$	−9.01161	−	27.7349i	−0.506943	−	1.56021i
$317$	0.308856	+	2.93857i	0.0173471	+	0.165047i	0.999766	−	0.0216446i	$-0.00689024\pi$
$317$	0.308856	+	2.93857i	0.0173471	+	0.165047i	−0.982419	+	0.186691i	$0.940224\pi$
$318$		0			0
$319$	8.41837	+	3.74810i	0.471338	+	0.209853i
$320$	8.06103	+	12.3397i	0.450625	+	0.689808i
$321$		0			0
$322$	1.43766	−	0.640086i	0.0801174	−	0.0356706i
$323$	−0.335624	+	1.03294i	−0.0186746	+	0.0574746i
$324$		0			0
$325$	−13.9701	−	7.96512i	−0.774922	−	0.441826i
$326$	−6.00328	+	10.3980i	−0.332491	+	0.575891i
$327$		0			0
$328$	−0.220342	+	2.09641i	−0.0121663	+	0.115755i
$329$	−1.03633	+	9.85999i	−0.0571345	+	0.543599i
$330$		0			0
$331$	1.21002	+	11.5126i	0.0665087	+	0.632788i	0.976106	+	0.217296i	$0.0697238\pi$
$331$	1.21002	+	11.5126i	0.0665087	+	0.632788i	−0.909597	+	0.415492i	$0.863610\pi$
$332$	−0.369819			−0.0202964
$333$		0			0
$334$	12.3149	+	37.9013i	0.673841	+	2.07387i
$335$	20.1340	−	10.3275i	1.10004	−	0.564251i
$336$		0			0
$337$	−13.5141	+	15.0089i	−0.736158	+	0.817586i	−0.988685	−	0.150004i	$-0.952071\pi$
$337$	−13.5141	+	15.0089i	−0.736158	+	0.817586i	0.252528	+	0.967590i	$0.418738\pi$
$338$	−3.47795	+	3.86265i	−0.189175	+	0.210101i
$339$		0			0
$340$	−15.1365	−	2.35540i	−0.820890	−	0.127740i
$341$	−6.53738	−	20.1200i	−0.354019	−	1.08956i
$342$		0			0
$343$	16.6922			0.901292
$344$	0.222083	+	2.11298i	0.0119739	+	0.113924i
$345$		0			0
$346$	−2.68778	+	25.5725i	−0.144496	+	1.37479i
$347$	0.262376	−	2.49634i	0.0140851	−	0.134010i	−0.985220	−	0.171296i	$-0.945204\pi$
$347$	0.262376	−	2.49634i	0.0140851	−	0.134010i	0.999305	+	0.0372857i	$0.0118712\pi$
$348$		0			0
$349$	−4.09655	+	7.09543i	−0.219283	+	0.379810i	−0.954589	−	0.297926i	$-0.903705\pi$
$349$	−4.09655	+	7.09543i	−0.219283	+	0.379810i	0.735306	+	0.677735i	$0.237039\pi$
$350$	−5.55958	−	12.3073i	−0.297172	−	0.657853i
$351$		0			0
$352$	5.93263	−	18.2587i	0.316210	−	0.973194i
$353$	17.6248	−	7.84707i	0.938074	−	0.417658i	0.120002	−	0.992774i	$-0.461710\pi$
$353$	17.6248	−	7.84707i	0.938074	−	0.417658i	0.818072	+	0.575116i	$0.195043\pi$
$354$		0			0
$355$	27.8975	−	7.55609i	1.48064	−	0.401036i
$356$	17.8925	+	7.96624i	0.948298	+	0.422210i
$357$		0			0
$358$	−1.04750	−	9.96626i	−0.0553619	−	0.526733i
$359$	8.64746	+	26.6141i	0.456395	+	1.40464i	0.869489	+	0.493952i	$0.164448\pi$
$359$	8.64746	+	26.6141i	0.456395	+	1.40464i	−0.413094	+	0.910688i	$0.635552\pi$
$360$		0			0
$361$	−5.84530	+	17.9900i	−0.307647	+	0.946841i
$362$	−17.0579	−	3.62577i	−0.896544	−	0.190566i
$363$		0			0
$364$	7.94727	−	1.68924i	0.416550	−	0.0885405i
$365$	−5.70131	−	8.72745i	−0.298420	−	0.456816i
$366$		0			0
$367$	−0.335149	−	3.18873i	−0.0174947	−	0.166450i	0.982286	−	0.187387i	$-0.0600019\pi$
$367$	−0.335149	−	3.18873i	−0.0174947	−	0.166450i	−0.999781	+	0.0209366i	$0.993335\pi$
$368$	2.51136			0.130913
$369$		0			0
$370$	12.1548	+	31.4101i	0.631900	+	1.63293i
$371$	−10.4264	+	4.64213i	−0.541311	+	0.241007i
$372$		0			0
$373$	−14.9713	+	3.18225i	−0.775186	+	0.164771i	−0.578485	−	0.815693i	$-0.696356\pi$
$373$	−14.9713	+	3.18225i	−0.775186	+	0.164771i	−0.196700	+	0.980464i	$0.563023\pi$
$374$	9.04614	+	15.6684i	0.467765	+	0.810193i
$375$		0			0
$376$	−1.19146	+	2.06367i	−0.0614449	+	0.106426i
$377$	−3.70788	+	11.4117i	−0.190965	+	0.587731i
$378$		0			0
$379$	5.89428	+	4.28245i	0.302769	+	0.219975i	0.728788	−	0.684740i	$-0.240084\pi$
$379$	5.89428	+	4.28245i	0.302769	+	0.219975i	−0.426019	+	0.904714i	$0.640084\pi$
$380$	1.17375	+	0.182649i	0.0602123	+	0.00936970i
$381$		0			0
$382$	−1.84301	−	3.19219i	−0.0942968	−	0.163327i
$383$	27.1725	+	12.0980i	1.38845	+	0.618178i	0.958609	−	0.284726i	$-0.0919026\pi$
$383$	27.1725	+	12.0980i	1.38845	+	0.618178i	0.429842	+	0.902904i	$0.358569\pi$
$384$		0			0
$385$	−3.44199	+	6.80074i	−0.175420	+	0.346598i
$386$	0.895769	−	2.75689i	0.0455934	−	0.140322i
$387$		0			0
$388$	6.24559	+	19.2219i	0.317072	+	0.975846i
$389$	3.01469	+	3.34816i	0.152851	+	0.169758i	0.814707	−	0.579873i	$-0.196898\pi$
$389$	3.01469	+	3.34816i	0.152851	+	0.169758i	−0.661856	+	0.749631i	$0.730231\pi$
$390$		0			0
$391$	−1.45908	+	1.62047i	−0.0737886	+	0.0819506i
$392$	1.54403	+	0.687445i	0.0779851	+	0.0347212i
$393$		0			0
$394$	−3.94902	−	37.5724i	−0.198949	−	1.89287i
$395$	−9.12673	+	34.4339i	−0.459216	+	1.73256i
$396$		0			0
$397$	−20.0082	−	14.5368i	−1.00418	−	0.729582i	−0.0412026	−	0.999151i	$-0.513119\pi$
$397$	−20.0082	−	14.5368i	−1.00418	−	0.729582i	−0.962981	+	0.269569i	$0.913119\pi$
$398$	8.08525	+	8.97958i	0.405277	+	0.450106i
$399$		0			0
$400$	−0.116659	−	21.5508i	−0.00583293	−	1.07754i
$401$	−7.15907	−	12.3999i	−0.357507	−	0.619220i	0.630037	−	0.776565i	$-0.283040\pi$
$401$	−7.15907	−	12.3999i	−0.357507	−	0.619220i	−0.987544	+	0.157345i	$0.949706\pi$
$402$		0			0
$403$	25.1650	−	11.2042i	1.25356	−	0.558119i
$404$	−21.5413	−	15.6507i	−1.07172	−	0.778651i
$405$		0			0
$406$	−8.15206	+	5.92282i	−0.404580	+	0.293945i
$407$	9.50454	−	16.4624i	0.471123	−	0.816009i
$408$		0			0
$409$	14.6532	−	16.2740i	0.724552	−	0.804697i	−0.262528	−	0.964924i	$-0.584556\pi$
$409$	14.6532	−	16.2740i	0.724552	−	0.804697i	0.987080	+	0.160227i	$0.0512228\pi$
$410$	−17.4444	+	21.6617i	−0.861519	+	1.06979i
$411$		0			0
$412$	10.3843	+	2.20725i	0.511598	+	0.108743i
$413$	−0.829648	−	2.55339i	−0.0408243	−	0.125644i
$414$		0			0
$415$	0.379534	+	0.245014i	0.0186306	+	0.0120273i
$416$	24.4520	+	5.19743i	1.19886	+	0.254825i
$417$		0			0
$418$	−0.701481	−	1.21500i	−0.0343106	−	0.0594276i
$419$	1.08241	+	0.481918i	0.0528790	+	0.0235432i	0.433006	−	0.901391i	$-0.357453\pi$
$419$	1.08241	+	0.481918i	0.0528790	+	0.0235432i	−0.380127	+	0.924934i	$0.624120\pi$
$420$		0			0
$421$	−10.8468	+	4.82933i	−0.528643	+	0.235367i	−0.653661	−	0.756787i	$-0.726768\pi$
$421$	−10.8468	+	4.82933i	−0.528643	+	0.235367i	0.125018	+	0.992154i	$0.460101\pi$
$422$	−44.8283	−	32.5697i	−2.18221	−	1.58547i
$423$		0			0
$424$	−2.74316			−0.133220
$425$	13.9736	+	12.4456i	0.677819	+	0.603699i
$426$		0			0
$427$	−17.6995	+	3.76215i	−0.856540	+	0.182063i
$428$	−2.46108	+	23.4156i	−0.118961	+	1.13184i
$429$		0			0
$430$	−12.6588	+	25.0113i	−0.610460	+	1.20615i
$431$	16.7241	−	12.1508i	0.805573	−	0.585283i	−0.106971	−	0.994262i	$-0.534115\pi$
$431$	16.7241	−	12.1508i	0.805573	−	0.585283i	0.912544	+	0.408979i	$0.134115\pi$
$432$		0			0
$433$	−10.6992	+	7.77342i	−0.514170	+	0.373566i	−0.814403	−	0.580299i	$-0.802936\pi$
$433$	−10.6992	+	7.77342i	−0.514170	+	0.373566i	0.300233	+	0.953866i	$0.402936\pi$
$434$	22.6276	+	4.80964i	1.08616	+	0.230870i
$435$		0			0
$436$	28.5569	−	6.06995i	1.36763	−	0.290698i
$437$	0.113144	−	0.125659i	0.00541240	−	0.00601108i
$438$		0			0
$439$	−9.35778	−	10.3929i	−0.446623	−	0.496025i	0.477227	−	0.878780i	$-0.341642\pi$
$439$	−9.35778	−	10.3929i	−0.446623	−	0.496025i	−0.923850	+	0.382755i	$0.874975\pi$
$440$	−1.42061	+	1.15677i	−0.0677248	+	0.0551466i
$441$		0			0
$442$	−19.0588	+	13.8470i	−0.906536	+	0.658637i
$443$	−0.0129892	+	0.0224980i	−0.000617136	+	0.00106891i	−0.866334	−	0.499465i	$-0.833530\pi$
$443$	−0.0129892	+	0.0224980i	−0.000617136	+	0.00106891i	0.865717	+	0.500534i	$0.166863\pi$
$444$		0			0
$445$	−13.0847	−	20.0297i	−0.620273	−	0.949500i
$446$	−0.0215746	+	0.205269i	−0.00102159	+	0.00971977i
$447$		0			0
$448$	6.08683	+	6.76011i	0.287576	+	0.319385i
$449$	32.1952			1.51939			0.759693	−	0.650282i	$-0.225349\pi$
$449$	32.1952			1.51939			0.759693	+	0.650282i	$0.225349\pi$
$450$		0			0
$451$	15.6975			0.739168
$452$	−9.05885	−	10.0609i	−0.426093	−	0.473224i
$453$		0			0
$454$	−2.05102	+	19.5142i	−0.0962592	+	0.915845i
$455$	−9.27522	−	3.53165i	−0.434829	−	0.165566i
$456$		0			0
$457$	5.72265	−	9.91192i	0.267694	−	0.463660i	−0.700572	−	0.713582i	$-0.747072\pi$
$457$	5.72265	−	9.91192i	0.267694	−	0.463660i	0.968266	+	0.249922i	$0.0804050\pi$
$458$	27.7682	−	20.1748i	1.29752	−	0.942707i
$459$		0			0
$460$	2.00365	+	1.29349i	0.0934205	+	0.0603091i
$461$	−1.73257	−	1.92422i	−0.0806940	−	0.0896197i	0.701446	−	0.712723i	$-0.252538\pi$
$461$	−1.73257	−	1.92422i	−0.0806940	−	0.0896197i	−0.782140	+	0.623103i	$0.785872\pi$
$462$		0			0
$463$	19.0782	−	21.1885i	0.886641	−	0.984714i	−0.113320	−	0.993559i	$-0.536149\pi$
$463$	19.0782	−	21.1885i	0.886641	−	0.984714i	0.999961	+	0.00884437i	$0.00281529\pi$
$464$	−15.7289	+	3.34327i	−0.730194	+	0.155208i
$465$		0			0
$466$	16.6002	+	3.52848i	0.768990	+	0.163454i
$467$	19.1318	−	13.9001i	0.885316	−	0.643220i	−0.0493364	−	0.998782i	$-0.515711\pi$
$467$	19.1318	−	13.9001i	0.885316	−	0.643220i	0.934653	+	0.355562i	$0.115711\pi$
$468$		0			0
$469$	11.2982	−	8.20863i	0.521703	−	0.379039i
$470$	−27.9749	+	14.3494i	−1.29038	+	0.661889i
$471$		0			0
$472$	0.0674518	−	0.641761i	0.00310472	−	0.0295395i
$473$	15.4759	−	3.28950i	0.711581	−	0.151251i
$474$		0			0
$475$	−1.08358	−	0.965089i	−0.0497180	−	0.0442813i
$476$	−9.45415			−0.433330
$477$		0			0
$478$	−16.0411	−	11.6545i	−0.733703	−	0.533066i
$479$	24.7354	−	11.0129i	1.13019	−	0.503192i	0.245510	−	0.969394i	$-0.421045\pi$
$479$	24.7354	−	11.0129i	1.13019	−	0.503192i	0.884678	+	0.466202i	$0.154378\pi$
$480$		0			0
$481$	22.6119	+	10.0674i	1.03101	+	0.459036i
$482$	7.97326	+	13.8101i	0.363172	+	0.629032i
$483$		0			0
$484$	8.77154	+	1.86445i	0.398706	+	0.0847476i
$485$	6.32537	−	23.8648i	0.287220	−	1.08364i
$486$		0			0
$487$	1.88824	+	5.81140i	0.0855643	+	0.263340i	0.984680	−	0.174371i	$-0.0557893\pi$
$487$	1.88824	+	5.81140i	0.0855643	+	0.263340i	−0.899116	+	0.437711i	$0.855789\pi$
$488$	−4.25412	−	0.904241i	−0.192575	−	0.0409331i
$489$		0			0
$490$	12.1960	+	18.6693i	0.550958	+	0.843394i
$491$	16.1290	−	17.9131i	0.727894	−	0.808408i	−0.259658	−	0.965701i	$-0.583610\pi$
$491$	16.1290	−	17.9131i	0.727894	−	0.808408i	0.987552	+	0.157293i	$0.0502766\pi$
$492$		0			0
$493$	6.98107	−	12.0916i	0.314411	−	0.544577i
$494$	1.47791	−	1.07377i	0.0664944	−	0.0483110i
$495$		0			0
$496$	29.8658	+	21.6988i	1.34101	+	0.974304i
$497$	16.2956	−	7.25528i	0.730959	−	0.325444i
$498$		0			0
$499$	−4.18052	−	7.24087i	−0.187146	−	0.324146i	0.757152	−	0.653239i	$-0.226590\pi$
$499$	−4.18052	−	7.24087i	−0.187146	−	0.324146i	−0.944298	+	0.329093i	$0.893257\pi$
$500$	11.0068	−	17.2541i	0.492238	−	0.771626i
$501$		0			0
$502$	−30.8791	−	34.2947i	−1.37820	−	1.53065i
$503$	−21.1533	−	15.3688i	−0.943178	−	0.685259i	0.00600579	−	0.999982i	$-0.498088\pi$
$503$	−21.1533	−	15.3688i	−0.943178	−	0.685259i	−0.949183	+	0.314723i	$0.898088\pi$
$504$		0			0
$505$	11.7383	+	30.3335i	0.522345	+	1.34983i
$506$	−0.294426	−	2.80128i	−0.0130888	−	0.124532i
$507$		0			0
$508$	−23.1202	−	10.2938i	−1.02579	−	0.456713i
$509$	21.7833	−	24.1929i	0.965530	−	1.07233i	−0.0318141	−	0.999494i	$-0.510128\pi$
$509$	21.7833	−	24.1929i	0.965530	−	1.07233i	0.997344	−	0.0728357i	$-0.0232049\pi$
$510$		0			0
$511$	−4.30502	−	4.78121i	−0.190443	−	0.211508i
$512$	9.46884	+	29.1421i	0.418468	+	1.28791i
$513$		0			0
$514$	−7.87599	+	24.2398i	−0.347395	+	1.06917i
$515$	−9.19474	−	9.14510i	−0.405169	−	0.402981i
$516$		0			0
$517$	16.2110	+	7.21760i	0.712958	+	0.317430i
$518$	10.3931	+	18.0013i	0.456645	+	0.790931i
$519$		0			0
$520$	−1.69133	−	1.68220i	−0.0741697	−	0.0737693i
$521$	−12.7402	−	9.25627i	−0.558157	−	0.405525i	0.272627	−	0.962120i	$-0.412107\pi$
$521$	−12.7402	−	9.25627i	−0.558157	−	0.405525i	−0.830784	+	0.556595i	$0.812107\pi$
$522$		0			0
$523$	−4.06035	+	12.4965i	−0.177547	+	0.546432i	−0.999741	−	0.0227752i	$-0.992750\pi$
$523$	−4.06035	+	12.4965i	−0.177547	+	0.546432i	0.822194	+	0.569207i	$0.192750\pi$
$524$	6.75536	−	11.7006i	0.295109	−	0.511144i
$525$		0			0
$526$	−11.0260	−	19.0976i	−0.480757	−	0.832696i
$527$	−31.3531	+	6.66430i	−1.36576	+	0.290301i
$528$		0			0
$529$	−20.7014	+	9.21686i	−0.900061	+	0.400733i
$530$	−30.4076	−	19.6301i	−1.32082	−	0.852679i
$531$		0			0
$532$	0.733120			0.0317848
$533$	2.13654	+	20.3278i	0.0925438	+	0.880496i
$534$		0			0
$535$	18.0392	−	22.4002i	0.779902	−	0.968446i
$536$	3.28325	−	0.697877i	0.141815	−	0.0301437i
$537$		0			0
$538$	41.8873	+	8.90342i	1.80589	+	0.383854i
$539$	3.88934	−	11.9702i	0.167526	−	0.515592i
$540$		0			0
$541$	−10.0048	−	30.7916i	−0.430139	−	1.32383i	−0.897987	−	0.440023i	$-0.854970\pi$
$541$	−10.0048	−	30.7916i	−0.430139	−	1.32383i	0.467847	−	0.883809i	$-0.345030\pi$
$542$	−2.40453	−	22.8776i	−0.103283	−	0.982677i
$543$		0			0
$544$	−26.5735	−	11.8313i	−1.13933	−	0.507262i
$545$	−33.3286	−	12.6902i	−1.42764	−	0.543591i
$546$		0			0
$547$	12.8061	−	5.70165i	0.547550	−	0.243785i	−0.114267	−	0.993450i	$-0.536452\pi$
$547$	12.8061	−	5.70165i	0.547550	−	0.243785i	0.661818	+	0.749665i	$0.269785\pi$
$548$	2.38382	−	7.33666i	0.101832	−	0.313406i
$549$		0			0
$550$	−24.0251	+	2.65670i	−1.02443	+	0.113282i
$551$	−0.541345	+	0.937637i	−0.0230621	+	0.0399447i
$552$		0			0
$553$	−2.29809	+	21.8649i	−0.0977247	+	0.929789i
$554$	4.50190	−	42.8327i	0.191267	−	1.81979i
$555$		0			0
$556$	0.0682735	+	0.649579i	0.00289544	+	0.0275483i
$557$	4.26938			0.180900			0.0904498	−	0.995901i	$-0.471170\pi$
$557$	4.26938			0.180900			0.0904498	+	0.995901i	$0.471170\pi$
$558$		0			0
$559$	6.36616	+	19.5930i	0.269260	+	0.828697i
$560$	−2.11623	−	13.1312i	−0.0894270	−	0.554896i
$561$		0			0
$562$	−1.68620	+	1.87271i	−0.0711279	+	0.0789956i
$563$	8.16098	−	9.06369i	0.343944	−	0.381989i	−0.546210	−	0.837648i	$-0.683930\pi$
$563$	8.16098	−	9.06369i	0.343944	−	0.381989i	0.890154	+	0.455660i	$0.150597\pi$
$564$		0			0
$565$	2.63125	+	16.3269i	0.110697	+	0.686878i
$566$	4.65083	+	14.3138i	0.195489	+	0.601654i
$567$		0			0
$568$	4.28735			0.179893
$569$	−1.73671	−	16.5237i	−0.0728068	−	0.692711i	−0.968665	−	0.248371i	$-0.920105\pi$
$569$	−1.73671	−	16.5237i	−0.0728068	−	0.692711i	0.895858	−	0.444340i	$-0.146562\pi$
$570$		0			0
$571$	1.74493	−	16.6019i	0.0730232	−	0.694769i	−0.895367	−	0.445329i	$-0.853087\pi$
$571$	1.74493	−	16.6019i	0.0730232	−	0.694769i	0.968390	−	0.249440i	$-0.0802466\pi$
$572$	1.52008	−	14.4626i	0.0635576	−	0.604710i
$573$		0			0
$574$	−8.58249	+	14.8653i	−0.358226	+	0.620466i
$575$	−1.19931	−	2.65493i	−0.0500149	−	0.110718i
$576$		0			0
$577$	9.92545	−	30.5474i	0.413202	−	1.27171i	−0.500647	−	0.865651i	$-0.666905\pi$
$577$	9.92545	−	30.5474i	0.413202	−	1.27171i	0.913849	−	0.406054i	$-0.133095\pi$
$578$	−5.35293	+	2.38328i	−0.222652	+	0.0991312i
$579$		0			0
$580$	−14.2710	−	5.43385i	−0.592571	−	0.225628i
$581$	0.254701	+	0.113400i	0.0105668	+	0.00470464i
$582$		0			0
$583$	2.13528	+	20.3159i	0.0884344	+	0.841398i
$584$	−0.477853	−	1.47068i	−0.0197737	−	0.0608572i
$585$		0			0
$586$	−6.80594	+	20.9465i	−0.281151	+	0.865293i
$587$	10.5912	+	2.25124i	0.437147	+	0.0929185i	0.421228	−	0.906955i	$-0.361599\pi$
$587$	10.5912	+	2.25124i	0.437147	+	0.0929185i	0.0159191	+	0.999873i	$0.494933\pi$
$588$		0			0
$589$	2.43127	−	0.516781i	0.100179	−	0.0212936i
$590$	5.34015	−	6.63116i	0.219851	−	0.273000i
$591$		0			0
$592$	3.46730	+	32.9891i	0.142505	+	1.35584i
$593$	−8.57810			−0.352260			−0.176130	−	0.984367i	$-0.556358\pi$
$593$	−8.57810			−0.352260			−0.176130	+	0.984367i	$0.556358\pi$
$594$		0			0
$595$	9.70252	+	6.26362i	0.397765	+	0.256783i
$596$	39.0492	−	17.3858i	1.59952	−	0.712151i
$597$		0			0
$598$	3.58750	−	0.762546i	0.146704	−	0.0311828i
$599$	−6.67217	−	11.5565i	−0.272617	−	0.472187i	0.696914	−	0.717155i	$-0.254556\pi$
$599$	−6.67217	−	11.5565i	−0.272617	−	0.472187i	−0.969531	+	0.244968i	$0.921223\pi$
$600$		0			0
$601$	−3.48996	+	6.04478i	−0.142358	+	0.246572i	−0.928384	−	0.371622i	$-0.878802\pi$
$601$	−3.48996	+	6.04478i	−0.142358	+	0.246572i	0.786026	+	0.618194i	$0.212135\pi$
$602$	−5.34619	+	16.4539i	−0.217895	+	0.670610i
$603$		0			0
$604$	11.9654	+	8.69336i	0.486865	+	0.353728i
$605$	−7.76673	−	7.72480i	−0.315762	−	0.314058i
$606$		0			0
$607$	2.00295	+	3.46922i	0.0812974	+	0.140811i	0.903807	−	0.427939i	$-0.140760\pi$
$607$	2.00295	+	3.46922i	0.0812974	+	0.140811i	−0.822510	+	0.568751i	$0.807427\pi$
$608$	2.06064	+	0.917454i	0.0835698	+	0.0372077i
$609$		0			0
$610$	−40.6856	−	40.4660i	−1.64731	−	1.63842i
$611$	−7.14014	+	21.9751i	−0.288859	+	0.889017i
$612$		0			0
$613$	−11.1550	−	34.3317i	−0.450548	−	1.38664i	−0.876283	−	0.481796i	$-0.839985\pi$
$613$	−11.1550	−	34.3317i	−0.450548	−	1.38664i	0.425735	−	0.904848i	$-0.360015\pi$
$614$	29.2500	+	32.4855i	1.18044	+	1.31101i
$615$		0			0
$616$	−0.756554	+	0.840238i	−0.0304824	+	0.0338542i
$617$	−41.2361	−	18.3595i	−1.66010	−	0.739126i	−0.660176	−	0.751111i	$-0.729518\pi$
$617$	−41.2361	−	18.3595i	−1.66010	−	0.739126i	−0.999928	+	0.0119846i	$0.996185\pi$
$618$		0			0
$619$	−1.22908	−	11.6939i	−0.0494010	−	0.470019i	−0.991057	−	0.133441i	$-0.957397\pi$
$619$	−1.22908	−	11.6939i	−0.0494010	−	0.470019i	0.941656	−	0.336578i	$-0.109269\pi$
$620$	12.6519	+	32.6946i	0.508113	+	1.31305i
$621$		0			0
$622$	−26.4867	−	19.2437i	−1.06202	−	0.771602i
$623$	−9.88014	−	10.9730i	−0.395839	−	0.439624i
$624$		0			0
$625$	−22.7272	+	10.4151i	−0.909089	+	0.416603i
$626$	−14.3789	−	24.9050i	−0.574697	−	0.995405i
$627$		0			0
$628$	−28.1080	+	12.5145i	−1.12163	+	0.499382i
$629$	−23.3009	−	16.9291i	−0.929068	−	0.675008i
$630$		0			0
$631$	−28.9418	+	21.0275i	−1.15216	+	0.837090i	−0.988766	−	0.149472i	$-0.952243\pi$
$631$	−28.9418	+	21.0275i	−1.15216	+	0.837090i	−0.163390	+	0.986562i	$0.552243\pi$
$632$	−2.64211	+	4.57626i	−0.105097	+	0.182034i
$633$		0			0
$634$	−3.86956	+	4.29759i	−0.153680	+	0.170679i
$635$	16.9077	+	25.8820i	0.670962	+	1.02709i
$636$		0			0
$637$	16.0304	+	3.40736i	0.635146	+	0.135004i
$638$	5.57326	+	17.1527i	0.220648	+	0.679083i
$639$		0			0
$640$	1.51473	−	5.71486i	0.0598748	−	0.225900i
$641$	−38.8290	−	8.25337i	−1.53365	−	0.325988i	−0.637753	−	0.770241i	$-0.720136\pi$
$641$	−38.8290	−	8.25337i	−1.53365	−	0.325988i	−0.895902	+	0.444252i	$0.853469\pi$
$642$		0			0
$643$	−16.4497	−	28.4917i	−0.648712	−	1.12360i	−0.983431	−	0.181284i	$-0.941975\pi$
$643$	−16.4497	−	28.4917i	−0.648712	−	1.12360i	0.334718	−	0.942318i	$-0.391359\pi$
$644$	1.34463	+	0.598666i	0.0529857	+	0.0235907i
$645$		0			0
$646$	−1.94191	+	0.864596i	−0.0764036	+	0.0340171i
$647$	25.9334	+	18.8417i	1.01955	+	0.740745i	0.966190	−	0.257831i	$-0.0830077\pi$
$647$	25.9334	+	18.8417i	1.01955	+	0.740745i	0.0533576	+	0.998575i	$0.483008\pi$
$648$		0			0
$649$	−4.80539			−0.188628
$650$	−6.71032	−	30.7501i	−0.263201	−	1.20612i
$651$		0			0
$652$	−10.9842	+	2.33477i	−0.430175	+	0.0914366i
$653$	−2.94310	+	28.0017i	−0.115172	+	1.09579i	0.772404	+	0.635132i	$0.219054\pi$
$653$	−2.94310	+	28.0017i	−0.115172	+	1.09579i	−0.887576	+	0.460661i	$0.847613\pi$
$654$		0			0
$655$	−14.6848	+	7.53241i	−0.573782	+	0.294315i
$656$	−22.1607	+	16.1007i	−0.865232	+	0.628628i
$657$		0			0
$658$	−15.6982	+	11.4054i	−0.611978	+	0.444628i
$659$	−26.4346	−	5.61884i	−1.02974	−	0.218879i	−0.338094	−	0.941112i	$-0.609782\pi$
$659$	−26.4346	−	5.61884i	−1.02974	−	0.218879i	−0.691649	+	0.722233i	$0.743116\pi$
$660$		0			0
$661$	9.57615	−	2.03547i	0.372469	−	0.0791707i	−0.0178739	−	0.999840i	$-0.505690\pi$
$661$	9.57615	−	2.03547i	0.372469	−	0.0791707i	0.390343	+	0.920669i	$0.372356\pi$
$662$	−15.1600	+	16.8368i	−0.589208	+	0.654382i
$663$		0			0
$664$	0.0448394	+	0.0497992i	0.00174011	+	0.00193258i
$665$	−0.752380	−	0.485711i	−0.0291760	−	0.0188351i
$666$		0			0
$667$	−1.75856	+	1.27767i	−0.0680919	+	0.0494716i
$668$	−18.6365	+	32.2794i	−0.721068	+	1.24893i
$669$		0			0
$670$	41.3885	+	15.7591i	1.59898	+	0.608829i
$671$	−3.38539	+	32.2099i	−0.130692	+	1.24345i
$672$		0			0
$673$	−2.93780	−	3.26275i	−0.113244	−	0.125770i	0.683857	−	0.729616i	$-0.260301\pi$
$673$	−2.93780	−	3.26275i	−0.113244	−	0.125770i	−0.797101	+	0.603846i	$0.793634\pi$
$674$	−39.5279			−1.52256
$675$		0			0
$676$	−4.86137			−0.186976
$677$	4.50954	+	5.00836i	0.173316	+	0.192487i	0.823544	−	0.567252i	$-0.191993\pi$
$677$	4.50954	+	5.00836i	0.173316	+	0.192487i	−0.650228	+	0.759739i	$0.725327\pi$
$678$		0			0
$679$	1.59271	−	15.1537i	0.0611228	−	0.581544i
$680$	1.51808	+	2.32384i	0.0582156	+	0.0891151i
$681$		0			0
$682$	20.7024	−	35.8576i	0.792736	−	1.37306i
$683$	−14.2153	+	10.3280i	−0.543933	+	0.395191i	−0.825544	−	0.564338i	$-0.809131\pi$
$683$	−14.2153	+	10.3280i	−0.543933	+	0.395191i	0.281611	+	0.959529i	$0.409131\pi$
$684$		0			0
$685$	−7.30717	+	5.95005i	−0.279193	+	0.227340i
$686$	21.8601	+	24.2781i	0.834623	+	0.926943i
$687$		0			0
$688$	−18.4738	+	20.5172i	−0.704307	+	0.782213i
$689$	−26.0178	+	5.53025i	−0.991199	+	0.210686i
$690$		0			0
$691$	40.1370	+	8.53139i	1.52688	+	0.324549i	0.893420	−	0.449222i	$-0.148299\pi$
$691$	40.1370	+	8.53139i	1.52688	+	0.324549i	0.633465	+	0.773772i	$0.281632\pi$
$692$	−19.4564	+	14.1359i	−0.739622	+	0.537367i
$693$		0			0
$694$	3.97444	−	2.88760i	0.150868	−	0.109612i
$695$	0.360296	−	0.711877i	0.0136668	−	0.0270030i
$696$		0			0
$697$	2.48611	−	23.6537i	0.0941681	−	0.895949i
$698$	−15.6849	+	3.33393i	−0.593682	+	0.126191i
$699$		0			0
$700$	5.07490	−	11.5665i	0.191813	−	0.437173i
$701$	30.2765			1.14353			0.571763	−	0.820419i	$-0.306260\pi$
$701$	30.2765			1.14353			0.571763	+	0.820419i	$0.306260\pi$
$702$		0			0
$703$	1.80686	+	1.31276i	0.0681472	+	0.0495118i
$704$	14.8740	−	6.62233i	0.560585	−	0.249588i
$705$		0			0
$706$	34.4948	+	15.3581i	1.29823	+	0.578009i
$707$	10.0368	+	17.3843i	0.377475	+	0.653805i
$708$		0			0
$709$	10.8221	+	2.30030i	0.406431	+	0.0863896i	0.406591	−	0.913610i	$-0.366717\pi$
$709$	10.8221	+	2.30030i	0.406431	+	0.0863896i	−0.000159608		1.00000i	$0.500051\pi$
$710$	47.5247	+	30.6804i	1.78357	+	1.15141i
$711$		0			0
$712$	−1.09669	−	3.37525i	−0.0411001	−	0.126493i
$713$	4.88122	+	1.03754i	0.182803	+	0.0388560i
$714$		0			0
$715$	−11.1418	+	13.8354i	−0.416681	+	0.517415i
$716$	6.27156	−	6.96527i	0.234379	−	0.260304i
$717$		0			0
$718$	−27.3845	+	47.4314i	−1.02198	+	1.77012i
$719$	−1.95143	+	1.41780i	−0.0727761	+	0.0528749i	−0.623578	−	0.781761i	$-0.714322\pi$
$719$	−1.95143	+	1.41780i	−0.0727761	+	0.0528749i	0.550802	+	0.834636i	$0.314322\pi$
$720$		0			0
$721$	−6.47504	−	4.70439i	−0.241143	−	0.175201i
$722$	−33.8208	+	15.0580i	−1.25868	+	0.560400i
$723$		0			0
$724$	−8.15526	−	14.1253i	−0.303088	−	0.524964i
$725$	11.0458	+	15.0315i	0.410232	+	0.558256i
$726$		0			0
$727$	14.5405	+	16.1489i	0.539279	+	0.598930i	0.949775	−	0.312932i	$-0.101311\pi$
$727$	14.5405	+	16.1489i	0.539279	+	0.598930i	−0.410497	+	0.911862i	$0.634645\pi$
$728$	−1.19105	−	0.865351i	−0.0441434	−	0.0320721i
$729$		0			0
$730$	5.22729	−	19.7219i	0.193470	−	0.729939i
$731$	−2.50576	−	23.8407i	−0.0926788	−	0.881780i
$732$		0			0
$733$	27.8246	+	12.3883i	1.02772	+	0.457572i	0.850153	−	0.526536i	$-0.176509\pi$
$733$	27.8246	+	12.3883i	1.02772	+	0.457572i	0.177571	+	0.984108i	$0.443176\pi$
$734$	4.19898	−	4.66344i	0.154987	−	0.172131i
$735$		0			0
$736$	3.03025	+	3.36543i	0.111696	+	0.124051i
$737$	−7.72417	−	23.7725i	−0.284523	−	0.875673i
$738$		0			0
$739$	13.7160	−	42.2135i	0.504551	−	1.55285i	−0.296973	−	0.954886i	$-0.595977\pi$
$739$	13.7160	−	42.2135i	0.504551	−	1.55285i	0.801524	−	0.597962i	$-0.204023\pi$
$740$	−14.2249	+	28.1057i	−0.522917	+	1.03319i
$741$		0			0
$742$	−20.4062	−	9.08545i	−0.749137	−	0.333537i
$743$	−12.5838	−	21.7958i	−0.461655	−	0.799609i	0.537389	−	0.843335i	$-0.319411\pi$
$743$	−12.5838	−	21.7958i	−0.461655	−	0.799609i	−0.999044	+	0.0437252i	$0.986077\pi$
$744$		0			0
$745$	−51.5936	−	8.02854i	−1.89024	−	0.294143i
$746$	−24.2350	−	17.6077i	−0.887305	−	0.644665i
$747$		0			0
$748$	−5.22904	+	16.0933i	−0.191193	+	0.588431i
$749$	8.87511	−	15.3721i	0.324289	−	0.561686i
$750$		0			0
$751$	−25.2077	−	43.6611i	−0.919844	−	1.59322i	−0.799651	−	0.600465i	$-0.794982\pi$
$751$	−25.2077	−	43.6611i	−0.919844	−	1.59322i	−0.120193	−	0.992751i	$-0.538351\pi$
$752$	−30.2886	+	6.43804i	−1.10451	+	0.234771i
$753$		0			0
$754$	−21.4537	+	9.55180i	−0.781297	+	0.347856i
$755$	−6.52015	−	16.8491i	−0.237293	−	0.613202i
$756$		0			0
$757$	8.34393			0.303265			0.151633	−	0.988437i	$-0.451547\pi$
$757$	8.34393			0.303265			0.151633	+	0.988437i	$0.451547\pi$
$758$	1.49052	+	14.1813i	0.0541380	+	0.515089i
$759$		0			0
$760$	−0.117719	−	0.180201i	−0.00427011	−	0.00653659i
$761$	7.20785	−	1.53207i	0.261284	−	0.0555377i	−0.0754068	−	0.997153i	$-0.524026\pi$
$761$	7.20785	−	1.53207i	0.261284	−	0.0555377i	0.336691	+	0.941615i	$0.390692\pi$
$762$		0			0
$763$	−21.5290	−	4.57612i	−0.779400	−	0.165667i
$764$	1.06534	−	3.27877i	0.0385426	−	0.118622i
$765$		0			0
$766$	17.9892	+	55.3650i	0.649975	+	2.00042i
$767$	−0.654046	−	6.22283i	−0.0236162	−	0.224693i
$768$		0			0
$769$	−12.7161	−	5.66158i	−0.458555	−	0.204162i	0.164441	−	0.986387i	$-0.447418\pi$
$769$	−12.7161	−	5.66158i	−0.458555	−	0.204162i	−0.622996	+	0.782225i	$0.714085\pi$
$770$	−14.3991	+	3.90002i	−0.518906	+	0.140547i
$771$		0			0
$772$	2.47680	−	1.10274i	0.0891418	−	0.0396885i
$773$	−7.27997	+	22.4054i	−0.261842	+	0.805867i	0.730562	+	0.682847i	$0.239258\pi$
$773$	−7.27997	+	22.4054i	−0.261842	+	0.805867i	−0.992404	+	0.123021i	$0.960742\pi$
$774$		0			0
$775$	8.67672	−	41.9357i	0.311677	−	1.50637i
$776$	1.83114	−	3.17162i	0.0657340	−	0.113855i
$777$		0			0
$778$	−0.921714	+	8.76952i	−0.0330450	+	0.314403i
$779$	−0.192785	+	1.83422i	−0.00690723	+	0.0657179i
$780$		0			0
$781$	−3.33728	−	31.7521i	−0.119417	−	1.13618i
$782$	−4.26772			−0.152613
$783$		0			0
$784$	6.78690	+	20.8879i	0.242389	+	0.745998i
$785$	37.1376	+	5.77902i	1.32550	+	0.206262i
$786$		0			0
$787$	−19.0981	+	21.2106i	−0.680776	+	0.756078i	−0.980193	−	0.198044i	$-0.936541\pi$
$787$	−19.0981	+	21.2106i	−0.680776	+	0.756078i	0.299418	+	0.954122i	$0.403208\pi$
$788$	23.6435	−	26.2588i	0.842266	−	0.935431i
$789$		0			0
$790$	−62.0353	+	31.8203i	−2.20712	+	1.13212i
$791$	3.15397	+	9.70691i	0.112142	+	0.345138i
$792$		0			0
$793$	−42.1715			−1.49756
$794$	−5.05958	−	48.1387i	−0.179558	−	1.70838i
$795$		0			0
$796$	−1.18131	+	11.2394i	−0.0418704	+	0.398370i
$797$	−0.874613	+	8.32139i	−0.0309804	+	0.294759i	0.968051	+	0.250754i	$0.0806784\pi$
$797$	−0.874613	+	8.32139i	−0.0309804	+	0.294759i	−0.999031	+	0.0440050i	$0.985988\pi$
$798$		0			0
$799$	13.4432	−	23.2843i	0.475587	−	0.823741i
$800$	28.7392	−	26.1600i	1.01608	−	0.924894i
$801$		0			0
$802$	8.65961	−	26.6515i	0.305781	−	0.941098i
$803$	−10.5199	+	4.68376i	−0.371239	+	0.165286i
$804$		0			0
$805$	−0.983318	−	1.50524i	−0.0346574	−	0.0530528i
$806$	49.2522	+	21.9285i	1.73483	+	0.772398i
$807$		0			0
$808$	0.504324	+	4.79833i	0.0177421	+	0.168805i
$809$	−12.4306	−	38.2574i	−0.437036	−	1.34506i	−0.890986	−	0.454030i	$-0.849986\pi$
$809$	−12.4306	−	38.2574i	−0.437036	−	1.34506i	0.453951	−	0.891027i	$-0.350014\pi$
$810$		0			0
$811$	3.05198	−	9.39304i	0.107170	−	0.329834i	−0.883064	−	0.469253i	$-0.844523\pi$
$811$	3.05198	−	9.39304i	0.107170	−	0.329834i	0.990234	+	0.139418i	$0.0445233\pi$
$812$	−9.21851	−	1.95945i	−0.323506	−	0.0687634i
$813$		0			0
$814$	36.3911	−	7.73516i	1.27551	−	0.271117i
$815$	12.8196	+	4.88123i	0.449052	+	0.170982i
$816$		0			0
$817$	0.194308	+	1.84872i	0.00679799	+	0.0646785i
$818$	42.8598			1.49856
$819$		0			0
$820$	−25.9734	+	1.43171i	−0.907029	+	0.0499974i
$821$	15.3567	−	6.83725i	0.535953	−	0.238622i	−0.120867	−	0.992669i	$-0.538568\pi$
$821$	15.3567	−	6.83725i	0.535953	−	0.238622i	0.656820	+	0.754047i	$0.271901\pi$
$822$		0			0
$823$	−30.3417	+	6.44934i	−1.05765	+	0.224810i	−0.703730	−	0.710467i	$-0.748484\pi$
$823$	−30.3417	+	6.44934i	−1.05765	+	0.224810i	−0.353917	+	0.935277i	$0.615150\pi$
$824$	−0.961840	−	1.66596i	−0.0335073	−	0.0580363i
$825$		0			0
$826$	2.62730	−	4.55063i	0.0914156	−	0.158337i
$827$	12.1795	−	37.4846i	0.423522	−	1.30347i	−0.480880	−	0.876787i	$-0.659683\pi$
$827$	12.1795	−	37.4846i	0.423522	−	1.30347i	0.904402	−	0.426681i	$-0.140317\pi$
$828$		0			0
$829$	−19.1615	−	13.9216i	−0.665505	−	0.483518i	0.203012	−	0.979176i	$-0.434927\pi$
$829$	−19.1615	−	13.9216i	−0.665505	−	0.483518i	−0.868518	+	0.495658i	$0.834927\pi$
$830$	0.140675	+	0.872890i	0.00488290	+	0.0302985i
$831$		0			0
$832$	10.6002	+	18.3600i	0.367494	+	0.636519i
$833$	−17.4212	−	7.75642i	−0.603609	−	0.268744i
$834$		0			0
$835$	40.5120	−	20.7802i	1.40198	−	0.719129i
$836$	0.405485	−	1.24795i	0.0140240	−	0.0431614i
$837$		0			0
$838$	0.716591	+	2.20544i	0.0247542	+	0.0761856i
$839$	1.39459	+	1.54884i	0.0481465	+	0.0534721i	0.766737	−	0.641961i	$-0.221879\pi$
$839$	1.39459	+	1.54884i	0.0481465	+	0.0534721i	−0.718591	+	0.695433i	$0.755212\pi$
$840$		0			0
$841$	−10.0916	+	11.2079i	−0.347988	+	0.386480i
$842$	−21.2291	−	9.45183i	−0.731605	−	0.325731i
$843$		0			0
$844$	−5.41721	−	51.5414i	−0.186468	−	1.77413i
$845$	4.98908	+	3.22078i	0.171630	+	0.110798i
$846$		0			0
$847$	−5.46942	−	3.97377i	−0.187932	−	0.136540i
$848$	−23.8521	−	26.4905i	−0.819086	−	0.909687i
$849$		0			0
$850$	0.198246	+	36.6228i	0.00679979	+	1.25615i
$851$	2.24199	+	3.88324i	0.0768545	+	0.133116i
$852$		0			0
$853$	−39.5591	+	17.6129i	−1.35448	+	0.603053i	−0.950217	−	0.311590i	$-0.899138\pi$
$853$	−39.5591	+	17.6129i	−1.35448	+	0.603053i	−0.404262	+	0.914643i	$0.632472\pi$
$854$	−28.6513	−	20.8164i	−0.980427	−	0.712322i
$855$		0			0
$856$	3.45151	−	2.50767i	0.117970	−	0.0857103i
$857$	7.87916	−	13.6471i	0.269147	−	0.466176i	−0.699495	−	0.714638i	$-0.746592\pi$
$857$	7.87916	−	13.6471i	0.269147	−	0.466176i	0.968642	+	0.248462i	$0.0799250\pi$
$858$		0			0
$859$	0.341216	−	0.378959i	0.0116422	−	0.0129299i	−0.737296	−	0.675570i	$-0.763898\pi$
$859$	0.341216	−	0.378959i	0.0116422	−	0.0129299i	0.748938	+	0.662640i	$0.230564\pi$
$860$	−25.3065	+	6.85433i	−0.862946	+	0.233731i
$861$		0			0
$862$	39.5749	+	8.41190i	1.34793	+	0.286510i
$863$	17.2401	+	53.0596i	0.586860	+	1.80617i	0.591668	+	0.806182i	$0.298470\pi$
$863$	17.2401	+	53.0596i	0.586860	+	1.80617i	−0.00480758	+	0.999988i	$0.501530\pi$
$864$		0			0
$865$	29.3330	−	1.61690i	0.997351	−	0.0549761i
$866$	−25.3178	−	5.38147i	−0.860335	−	0.182870i
$867$		0			0
$868$	10.8181	+	18.7374i	0.367189	+	0.635990i
$869$	35.9484	+	16.0053i	1.21947	+	0.542942i
$870$		0			0
$871$	29.7334	−	13.2382i	1.00748	−	0.448558i
$872$	−4.27981	−	3.10946i	−0.144933	−	0.105300i
$873$		0			0
$874$	0.330940			0.0111942
$875$	−12.8713	+	8.50813i	−0.435131	+	0.287627i
$876$		0			0
$877$	−0.609512	+	0.129556i	−0.0205818	+	0.00437479i	−0.218191	−	0.975906i	$-0.570016\pi$
$877$	−0.609512	+	0.129556i	−0.0205818	+	0.00437479i	0.197609	+	0.980281i	$0.436682\pi$
$878$	2.86105	−	27.2211i	0.0965559	−	0.918668i
$879$		0			0
$880$	−23.5231	−	3.66046i	−0.792964	−	0.123394i
$881$	−0.224011	+	0.162753i	−0.00754711	+	0.00548330i	−0.591552	−	0.806267i	$-0.701485\pi$
$881$	−0.224011	+	0.162753i	−0.00754711	+	0.00548330i	0.584005	+	0.811750i	$0.301485\pi$
$882$		0			0
$883$	−11.9127	+	8.65510i	−0.400895	+	0.291267i	−0.769906	−	0.638158i	$-0.779697\pi$
$883$	−11.9127	+	8.65510i	−0.400895	+	0.291267i	0.369010	+	0.929425i	$0.379697\pi$
$884$	−21.5521	−	4.58104i	−0.724875	−	0.154077i
$885$		0			0
$886$	−0.0497331	+	0.0105711i	−0.00167082	+	0.000355143i
$887$	−9.05574	+	10.0574i	−0.304062	+	0.337695i	−0.875740	−	0.482783i	$-0.839626\pi$
$887$	−9.05574	+	10.0574i	−0.304062	+	0.337695i	0.571678	+	0.820478i	$0.306293\pi$
$888$		0			0
$889$	12.7669	+	14.1791i	0.428188	+	0.475551i
$890$	11.9968	−	45.2622i	0.402132	−	1.51719i
$891$		0			0
$892$	−0.156176	+	0.113468i	−0.00522915	+	0.00379920i
$893$	−1.04245	+	1.80558i	−0.0348843	+	0.0604214i
$894$		0			0
$895$	−11.0510	+	2.99318i	−0.369394	+	0.100051i
$896$	0.381405	−	3.62883i	0.0127418	−	0.121231i
$897$		0			0
$898$	42.1630	+	46.8268i	1.40700	+	1.56263i
$899$	−31.9528			−1.06569
$900$		0			0
$901$	30.9510			1.03113
$902$	20.5576	+	22.8315i	0.684492	+	0.760205i
$903$		0			0
$904$	−0.256423	+	2.43970i	−0.00852851	+	0.0811433i
$905$	−0.988888	+	19.8995i	−0.0328717	+	0.661481i
$906$		0			0
$907$	3.57179	−	6.18652i	0.118599	−	0.205420i	−0.800614	−	0.599181i	$-0.795493\pi$
$907$	3.57179	−	6.18652i	0.118599	−	0.205420i	0.919213	+	0.393761i	$0.128826\pi$
$908$	−14.8470	+	10.7870i	−0.492716	+	0.357979i
$909$		0			0
$910$	−7.01021	−	18.1155i	−0.232386	−	0.600524i
$911$	8.43433	+	9.36728i	0.279442	+	0.310352i	0.866484	−	0.499205i	$-0.166374\pi$
$911$	8.43433	+	9.36728i	0.279442	+	0.310352i	−0.587042	+	0.809556i	$0.699708\pi$
$912$		0			0
$913$	0.333910	−	0.370845i	0.0110508	−	0.0122732i
$914$	21.9109	−	4.65731i	0.724749	−	0.154050i
$915$		0			0
$916$	31.4009	+	6.67446i	1.03751	+	0.220530i
$917$	−8.24040	+	5.98700i	−0.272122	+	0.197708i
$918$		0			0
$919$	32.7101	−	23.7653i	1.07901	−	0.783945i	0.101498	−	0.994836i	$-0.467637\pi$
$919$	32.7101	−	23.7653i	1.07901	−	0.783945i	0.977510	+	0.210891i	$0.0676365\pi$
$920$	−0.0687572	−	0.426639i	−0.00226686	−	0.0140659i
$921$		0			0
$922$	0.529717	−	5.03992i	0.0174453	−	0.165981i
$923$	40.6637	−	8.64335i	1.33846	−	0.284499i
$924$		0			0
$925$	33.2193	−	19.4197i	1.09224	−	0.638516i
$926$	55.8028			1.83380
$927$		0			0
$928$	−23.4590	−	17.0440i	−0.770080	−	0.559496i
$929$	−39.4258	+	17.5535i	−1.29352	+	0.575912i	−0.934016	−	0.357232i	$-0.883721\pi$
$929$	−39.4258	+	17.5535i	−1.29352	+	0.575912i	−0.359503	+	0.933144i	$0.617054\pi$
$930$		0			0
$931$	1.35092	+	0.601470i	0.0442747	+	0.0197124i
$932$	7.93644	+	13.7463i	0.259967	+	0.450276i
$933$		0			0
$934$	45.2723	+	9.62293i	1.48136	+	0.314872i
$935$	16.0287	−	13.0517i	0.524194	−	0.426838i
$936$		0			0
$937$	4.03157	+	12.4079i	0.131706	+	0.405348i	0.995063	−	0.0992446i	$-0.0316426\pi$
$937$	4.03157	+	12.4079i	0.131706	+	0.405348i	−0.863357	+	0.504593i	$0.831643\pi$
$938$	26.7353	+	5.68277i	0.872939	+	0.185549i
$939$		0			0
$940$	−27.4812	−	10.4638i	−0.896338	−	0.341291i
$941$	37.1901	−	41.3038i	1.21236	−	1.34647i	0.291506	−	0.956569i	$-0.405844\pi$
$941$	37.1901	−	41.3038i	1.21236	−	1.34647i	0.920858	−	0.389898i	$-0.127490\pi$
$942$		0			0
$943$	−1.85142	+	3.20675i	−0.0602904	+	0.104426i
$944$	6.78393	−	4.92881i	0.220798	−	0.160419i
$945$		0			0
$946$	25.0517	+	18.2011i	0.814501	+	0.591770i
$947$	17.1941	−	7.65530i	0.558732	−	0.248764i	−0.107885	−	0.994163i	$-0.534408\pi$
$947$	17.1941	−	7.65530i	0.558732	−	0.248764i	0.666618	+	0.745400i	$0.267741\pi$
$948$		0			0
$949$	−7.49716	−	12.9855i	−0.243368	−	0.421526i
$950$	−0.0153730	−	2.83991i	−0.000498764	−	0.0921388i
$951$		0			0
$952$	1.14629	+	1.27308i	0.0371514	+	0.0412608i
$953$	24.1648	+	17.5568i	0.782775	+	0.568720i	0.905811	−	0.423683i	$-0.139263\pi$
$953$	24.1648	+	17.5568i	0.782775	+	0.568720i	−0.123035	+	0.992402i	$0.539263\pi$
$954$		0			0
$955$	−3.26560	+	2.65909i	−0.105672	+	0.0860463i
$956$	−1.93846	−	18.4432i	−0.0626944	−	0.596497i
$957$		0			0
$958$	48.4114	+	21.5541i	1.56410	+	0.696383i
$959$	−3.89148	+	4.32193i	−0.125663	+	0.139562i
$960$		0			0
$961$	28.3413	+	31.4763i	0.914237	+	1.01536i
$962$	14.9699	+	46.0725i	0.482648	+	1.48544i
$963$		0			0
$964$	−4.60887	+	14.1846i	−0.148442	+	0.456857i
$965$	−3.27246	−	0.509231i	−0.105344	−	0.0163927i
$966$		0			0
$967$	35.2090	+	15.6761i	1.13225	+	0.504108i	0.885346	−	0.464933i	$-0.153922\pi$
$967$	35.2090	+	15.6761i	1.13225	+	0.504108i	0.246900	+	0.969041i	$0.420588\pi$
$968$	−0.812459	−	1.40722i	−0.0261134	−	0.0452298i
$969$		0			0
$970$	42.9942	−	22.0534i	1.38046	−	0.708092i
$971$	22.5194	+	16.3613i	0.722682	+	0.525059i	0.887240	−	0.461308i	$-0.152620\pi$
$971$	22.5194	+	16.3613i	0.722682	+	0.525059i	−0.164558	+	0.986367i	$0.552620\pi$
$972$		0			0
$973$	0.152164	−	0.468313i	0.00487816	−	0.0150134i
$974$	−5.97962	+	10.3570i	−0.191599	+	0.331860i
$975$		0			0
$976$	−28.2579	−	48.9441i	−0.904513	−	1.56666i
$977$	−1.23727	+	0.262990i	−0.0395838	+	0.00841380i	−0.227661	−	0.973740i	$-0.573108\pi$
$977$	−1.23727	+	0.262990i	−0.0395838	+	0.00841380i	0.188077	+	0.982154i	$0.439774\pi$
$978$		0			0
$979$	−24.1435	+	10.7494i	−0.771629	+	0.343551i
$980$	−5.34361	+	20.1607i	−0.170695	+	0.644011i
$981$		0			0
$982$	47.1766			1.50547
$983$	5.12307	+	48.7427i	0.163401	+	1.55465i	0.702053	+	0.712124i	$0.252267\pi$
$983$	5.12307	+	48.7427i	0.163401	+	1.55465i	−0.538653	+	0.842528i	$0.681067\pi$
$984$		0			0
$985$	−41.6618	+	11.2842i	−1.32745	+	0.359544i
$986$	26.7292	−	5.68146i	0.851230	−	0.180935i
$987$		0			0
$988$	1.67125	+	0.355235i	0.0531696	+	0.0113015i
$989$	−1.15328	+	3.54944i	−0.0366722	+	0.112866i
$990$		0			0
$991$	−16.1594	−	49.7336i	−0.513321	−	1.57984i	−0.786316	−	0.617824i	$-0.788014\pi$
$991$	−16.1594	−	49.7336i	−0.513321	−	1.57984i	0.272995	−	0.962015i	$-0.411986\pi$
$992$	6.95841	+	66.2049i	0.220930	+	2.10201i
$993$		0			0
$994$	31.8933	+	14.1998i	1.01160	+	0.450391i
$995$	8.65874	−	10.7520i	0.274500	−	0.340862i
$996$		0			0
$997$	−16.6365	+	7.40706i	−0.526884	+	0.234584i	−0.652900	−	0.757444i	$-0.726448\pi$
$997$	−16.6365	+	7.40706i	−0.526884	+	0.234584i	0.126016	+	0.992028i	$0.459781\pi$
$998$	5.05675	−	15.5631i	0.160069	−	0.492641i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.r.a.46.24		224
3.2	odd	2		225.2.q.a.196.5	yes	224
9.4	even	3	inner	675.2.r.a.496.5		224
9.5	odd	6		225.2.q.a.121.24	yes	224
25.6	even	5	inner	675.2.r.a.181.5		224
75.56	odd	10		225.2.q.a.106.24	yes	224
225.31	even	15	inner	675.2.r.a.631.24		224
225.131	odd	30		225.2.q.a.31.5	✓	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.5	✓	224	225.131	odd	30
225.2.q.a.106.24	yes	224	75.56	odd	10
225.2.q.a.121.24	yes	224	9.5	odd	6
225.2.q.a.196.5	yes	224	3.2	odd	2
675.2.r.a.46.24		224	1.1	even	1	trivial
675.2.r.a.181.5		224	25.6	even	5	inner
675.2.r.a.496.5		224	9.4	even	3	inner
675.2.r.a.631.24		224	225.31	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.r (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.30960 + 1.45446i) q^{2} +(-0.191342 + 1.82050i) q^{4} +(1.40249 - 1.74155i) q^{5} +(0.690014 - 1.19514i) q^{7} +(0.268345 - 0.194964i) q^{8} +(4.36974 - 0.240869i) q^{10} +(-1.65278 - 1.83560i) q^{11} +(2.15209 - 2.39014i) q^{13} +(2.64193 - 0.561560i) q^{14} +(4.21604 + 0.896147i) q^{16} +(-3.02773 + 2.19977i) q^{17} +(0.234784 - 0.170581i) q^{19} +(2.90214 + 2.88647i) q^{20} +(0.505323 - 4.80783i) q^{22} +(0.569918 - 0.121140i) q^{23} +(-1.06602 - 4.88504i) q^{25} +6.29476 q^{26} +(2.04372 + 1.48485i) q^{28} +(-3.40818 + 1.51742i) q^{29} +(7.82432 + 3.48361i) q^{31} +(3.88624 + 6.73116i) q^{32} +(-7.16461 - 1.52289i) q^{34} +(-1.11366 - 2.87787i) q^{35} +(2.37815 + 7.31918i) q^{37} +(0.555578 + 0.118092i) q^{38} +(0.0368121 - 0.740773i) q^{40} +(-4.25243 + 4.72280i) q^{41} +(-3.20269 + 5.54723i) q^{43} +(3.65796 - 2.65766i) q^{44} +(0.922560 + 0.670279i) q^{46} +(-6.56303 + 2.92205i) q^{47} +(2.54776 + 4.41285i) q^{49} +(5.70905 - 7.94795i) q^{50} +(3.93946 + 4.37521i) q^{52} +(-6.69073 - 4.86110i) q^{53} +(-5.51482 + 0.303989i) q^{55} +(-0.0478474 - 0.455238i) q^{56} +(-6.67040 - 2.96985i) q^{58} +(1.30177 - 1.44576i) q^{59} +(-8.77365 - 9.74413i) q^{61} +(5.17998 + 15.9423i) q^{62} +(-2.03692 + 6.26900i) q^{64} +(-1.14426 - 7.10014i) q^{65} +(9.24473 + 4.11602i) q^{67} +(-3.42535 - 5.93288i) q^{68} +(2.72731 - 5.38865i) q^{70} +(10.4571 + 7.59752i) q^{71} +(1.44065 - 4.43387i) q^{73} +(-7.53104 + 13.0442i) q^{74} +(0.265618 + 0.460064i) q^{76} +(-3.33424 + 0.708716i) q^{77} +(-14.5537 + 6.47975i) q^{79} +(7.47366 - 6.08562i) q^{80} -12.4381 q^{82} +(0.0211178 + 0.200922i) q^{83} +(-0.415350 + 8.35812i) q^{85} +(-12.2625 + 2.60647i) q^{86} +(-0.801393 - 0.170341i) q^{88} +(3.30633 - 10.1758i) q^{89} +(-1.37158 - 4.22128i) q^{91} +(0.111485 + 1.06071i) q^{92} +(-12.8450 - 5.71895i) q^{94} +(0.0322082 - 0.648128i) q^{95} +(10.0866 - 4.49085i) q^{97} +(-3.08177 + 9.48471i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28}+ \cdots - 146 q^{98}+O(q^{100}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Introduction

L-functions

Modular forms

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Database

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