LMFDB - Embedded newform 459.2.l.a.325.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [459,2,Mod(298,459)] 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("459.298"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(459, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 459 = 3^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	459.l (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0,0,0,-16,0,0,0,0,0,-48,0,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)

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

Self dual:	no
Analytic conductor:	$3.66513345278$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			325.7
Character	$\chi$	$=$	459.325
Dual form			459.2.l.a.298.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.221411 + 0.221411i) q^{2} -1.90195i q^{4} +(-0.0227939 - 0.0550294i) q^{5} +(1.02440 - 2.47313i) q^{7} +(0.863936 - 0.863936i) q^{8} +(0.00713730 - 0.0172310i) q^{10} +(-5.01504 - 2.07730i) q^{11} +0.468997i q^{13} +(0.774391 - 0.320763i) q^{14} -3.42134 q^{16} +(1.35164 + 3.89526i) q^{17} +(-4.85739 - 4.85739i) q^{19} +(-0.104663 + 0.0433530i) q^{20} +(-0.650449 - 1.57032i) q^{22} +(4.86066 + 2.01335i) q^{23} +(3.53303 - 3.53303i) q^{25} +(-0.103841 + 0.103841i) q^{26} +(-4.70377 - 1.94837i) q^{28} +(-0.921784 - 2.22538i) q^{29} +(2.91521 - 1.20752i) q^{31} +(-2.48539 - 2.48539i) q^{32} +(-0.563186 + 1.16172i) q^{34} -0.159445 q^{35} +(6.93112 - 2.87096i) q^{37} -2.15096i q^{38} +(-0.0672344 - 0.0278494i) q^{40} +(0.852281 - 2.05759i) q^{41} +(-3.19320 + 3.19320i) q^{43} +(-3.95093 + 9.53839i) q^{44} +(0.630426 + 1.52198i) q^{46} -9.24764i q^{47} +(-0.117205 - 0.117205i) q^{49} +1.56450 q^{50} +0.892011 q^{52} +(9.14029 + 9.14029i) q^{53} +0.323325i q^{55} +(-1.25160 - 3.02164i) q^{56} +(0.288631 - 0.696818i) q^{58} +(-6.66815 + 6.66815i) q^{59} +(0.696537 - 1.68159i) q^{61} +(0.912817 + 0.378101i) q^{62} +5.74209i q^{64} +(0.0258086 - 0.0106903i) q^{65} +3.18673 q^{67} +(7.40861 - 2.57076i) q^{68} +(-0.0353029 - 0.0353029i) q^{70} +(3.99130 - 1.65325i) q^{71} +(4.56957 + 11.0319i) q^{73} +(2.17029 + 0.898963i) q^{74} +(-9.23854 + 9.23854i) q^{76} +(-10.2748 + 10.2748i) q^{77} +(9.86201 + 4.08498i) q^{79} +(0.0779858 + 0.188274i) q^{80} +(0.644277 - 0.266868i) q^{82} +(-6.15847 - 6.15847i) q^{83} +(0.183545 - 0.163168i) q^{85} -1.41402 q^{86} +(-6.12733 + 2.53802i) q^{88} -15.9437i q^{89} +(1.15989 + 0.480442i) q^{91} +(3.82930 - 9.24476i) q^{92} +(2.04753 - 2.04753i) q^{94} +(-0.156580 + 0.378019i) q^{95} +(1.33512 + 3.22326i) q^{97} -0.0519011i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 16 q^{10} - 48 q^{16} - 16 q^{19} - 24 q^{22} + 16 q^{25} + 24 q^{28} - 40 q^{31} + 64 q^{34} + 48 q^{37} - 48 q^{40} - 8 q^{43} + 24 q^{46} - 16 q^{49} + 32 q^{52} + 64 q^{58} - 24 q^{61} - 32 q^{67}+ \cdots - 88 q^{97}+O(q^{100}) $ 48 * q - 16 * q^10 - 48 * q^16 - 16 * q^19 - 24 * q^22 + 16 * q^25 + 24 * q^28 - 40 * q^31 + 64 * q^34 + 48 * q^37 - 48 * q^40 - 8 * q^43 + 24 * q^46 - 16 * q^49 + 32 * q^52 + 64 * q^58 - 24 * q^61 - 32 * q^67 + 96 * q^70 + 48 * q^73 + 96 * q^76 - 48 * q^79 + 112 * q^82 - 56 * q^85 - 160 * q^88 - 80 * q^91 - 40 * q^94 - 88 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/459\mathbb{Z}\right)^\times$.

$n$	$137$	$190$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$

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 $

$2$	0.221411	+	0.221411i	0.156561	+	0.156561i	0.781041	−	0.624480i	$-0.214689\pi$
$2$	0.221411	+	0.221411i	0.156561	+	0.156561i	−0.624480	+	0.781041i	$0.714689\pi$
$3$		0			0
$3$		0			0
$4$		−	1.90195i		−	0.950977i
$5$	−0.0227939	−	0.0550294i	−0.0101938	−	0.0246099i	0.918701	−	0.394954i	$-0.129240\pi$
$5$	−0.0227939	−	0.0550294i	−0.0101938	−	0.0246099i	−0.928894	+	0.370345i	$0.879240\pi$
$6$		0			0
$7$	1.02440	−	2.47313i	0.387188	−	0.934754i	−0.603345	−	0.797480i	$-0.706166\pi$
$7$	1.02440	−	2.47313i	0.387188	−	0.934754i	0.990533	−	0.137274i	$-0.0438340\pi$
$8$	0.863936	−	0.863936i	0.305447	−	0.305447i
$9$		0			0
$10$	0.00713730	−	0.0172310i	0.00225701	−	0.00544891i
$11$	−5.01504	−	2.07730i	−1.51209	−	0.626329i	−0.536104	−	0.844152i	$-0.680105\pi$
$11$	−5.01504	−	2.07730i	−1.51209	−	0.626329i	−0.975988	+	0.217822i	$0.930105\pi$
$12$		0			0
$13$			0.468997i			0.130076i	0.997883	+	0.0650382i	$0.0207169\pi$
$13$			0.468997i			0.130076i	−0.997883	+	0.0650382i	$0.979283\pi$
$14$	0.774391	−	0.320763i	0.206965	−	0.0857276i
$15$		0			0
$16$	−3.42134			−0.855335
$17$	1.35164	+	3.89526i	0.327821	+	0.944740i
$17$	1.35164	+	3.89526i	0.327821	+	0.944740i
$18$		0			0
$19$	−4.85739	−	4.85739i	−1.11436	−	1.11436i	−0.992554	−	0.121808i	$-0.961131\pi$
$19$	−4.85739	−	4.85739i	−1.11436	−	1.11436i	−0.121808	−	0.992554i	$-0.538869\pi$
$20$	−0.104663	+	0.0433530i	−0.0234035	+	0.00969403i
$21$		0			0
$22$	−0.650449	−	1.57032i	−0.138676	−	0.334794i
$23$	4.86066	+	2.01335i	1.01352	+	0.419813i	0.826737	−	0.562589i	$-0.190194\pi$
$23$	4.86066	+	2.01335i	1.01352	+	0.419813i	0.186781	+	0.982402i	$0.440194\pi$
$24$		0			0
$25$	3.53303	−	3.53303i	0.706605	−	0.706605i
$26$	−0.103841	+	0.103841i	−0.0203649	+	0.0203649i
$27$		0			0
$28$	−4.70377	−	1.94837i	−0.888930	−	0.368207i
$29$	−0.921784	−	2.22538i	−0.171171	−	0.413243i	0.814893	−	0.579612i	$-0.196796\pi$
$29$	−0.921784	−	2.22538i	−0.171171	−	0.413243i	−0.986064	+	0.166369i	$0.946796\pi$
$30$		0			0
$31$	2.91521	−	1.20752i	0.523587	−	0.216877i	−0.105205	−	0.994451i	$-0.533550\pi$
$31$	2.91521	−	1.20752i	0.523587	−	0.216877i	0.628792	+	0.777574i	$0.283550\pi$
$32$	−2.48539	−	2.48539i	−0.439360	−	0.439360i
$33$		0			0
$34$	−0.563186	+	1.16172i	−0.0965856	+	0.199234i
$35$	−0.159445			−0.0269511
$36$		0			0
$37$	6.93112	−	2.87096i	1.13947	−	0.471983i	0.268479	−	0.963285i	$-0.413479\pi$
$37$	6.93112	−	2.87096i	1.13947	−	0.471983i	0.870989	+	0.491302i	$0.163479\pi$
$38$		−	2.15096i		−	0.348932i
$39$		0			0
$40$	−0.0672344	−	0.0278494i	−0.0106307	−	0.00440338i
$41$	0.852281	−	2.05759i	0.133104	−	0.321341i	−0.843249	−	0.537523i	$-0.819360\pi$
$41$	0.852281	−	2.05759i	0.133104	−	0.321341i	0.976353	+	0.216181i	$0.0693603\pi$
$42$		0			0
$43$	−3.19320	+	3.19320i	−0.486959	+	0.486959i	−0.907345	−	0.420386i	$-0.861895\pi$
$43$	−3.19320	+	3.19320i	−0.486959	+	0.486959i	0.420386	+	0.907345i	$0.361895\pi$
$44$	−3.95093	+	9.53839i	−0.595625	+	1.43797i
$45$		0			0
$46$	0.630426	+	1.52198i	0.0929512	+	0.224404i
$47$		−	9.24764i		−	1.34891i	−0.738317	−	0.674453i	$-0.764379\pi$
$47$		−	9.24764i		−	1.34891i	0.738317	−	0.674453i	$-0.235621\pi$
$48$		0			0
$49$	−0.117205	−	0.117205i	−0.0167436	−	0.0167436i
$50$	1.56450			0.221254
$51$		0			0
$52$	0.892011			0.123700
$53$	9.14029	+	9.14029i	1.25552	+	1.25552i	0.953211	+	0.302305i	$0.0977560\pi$
$53$	9.14029	+	9.14029i	1.25552	+	1.25552i	0.302305	+	0.953211i	$0.402244\pi$
$54$		0			0
$55$			0.323325i			0.0435971i
$56$	−1.25160	−	3.02164i	−0.167253	−	0.403784i
$57$		0			0
$58$	0.288631	−	0.696818i	0.0378992	−	0.0914967i
$59$	−6.66815	+	6.66815i	−0.868119	+	0.868119i	−0.992264	−	0.124145i	$-0.960381\pi$
$59$	−6.66815	+	6.66815i	−0.868119	+	0.868119i	0.124145	+	0.992264i	$0.460381\pi$
$60$		0			0
$61$	0.696537	−	1.68159i	0.0891824	−	0.215305i	−0.872995	−	0.487729i	$-0.837825\pi$
$61$	0.696537	−	1.68159i	0.0891824	−	0.215305i	0.962177	+	0.272424i	$0.0878253\pi$
$62$	0.912817	+	0.378101i	0.115928	+	0.0480189i
$63$		0			0
$64$			5.74209i			0.717761i
$65$	0.0258086	−	0.0106903i	0.00320117	−	0.00132597i
$66$		0			0
$67$	3.18673			0.389321			0.194661	−	0.980871i	$-0.437639\pi$
$67$	3.18673			0.389321			0.194661	+	0.980871i	$0.437639\pi$
$68$	7.40861	−	2.57076i	0.898426	−	0.311750i
$69$		0			0
$70$	−0.0353029	−	0.0353029i	−0.00421950	−	0.00421950i
$71$	3.99130	−	1.65325i	0.473681	−	0.196205i	−0.133055	−	0.991109i	$-0.542479\pi$
$71$	3.99130	−	1.65325i	0.473681	−	0.196205i	0.606736	+	0.794904i	$0.292479\pi$
$72$		0			0
$73$	4.56957	+	11.0319i	0.534827	+	1.29119i	0.928293	+	0.371848i	$0.121276\pi$
$73$	4.56957	+	11.0319i	0.534827	+	1.29119i	−0.393466	+	0.919339i	$0.628724\pi$
$74$	2.17029	+	0.898963i	0.252291	+	0.104502i
$75$		0			0
$76$	−9.23854	+	9.23854i	−1.05973	+	1.05973i
$77$	−10.2748	+	10.2748i	−1.17093	+	1.17093i
$78$		0			0
$79$	9.86201	+	4.08498i	1.10956	+	0.459596i	0.860787	−	0.508965i	$-0.169972\pi$
$79$	9.86201	+	4.08498i	1.10956	+	0.459596i	0.248776	+	0.968561i	$0.419972\pi$
$80$	0.0779858	+	0.188274i	0.00871908	+	0.0210497i
$81$		0			0
$82$	0.644277	−	0.266868i	0.0711485	−	0.0294707i
$83$	−6.15847	−	6.15847i	−0.675980	−	0.675980i	0.283108	−	0.959088i	$-0.408635\pi$
$83$	−6.15847	−	6.15847i	−0.675980	−	0.675980i	−0.959088	+	0.283108i	$0.908635\pi$
$84$		0			0
$85$	0.183545	−	0.163168i	0.0199082	−	0.0176981i
$86$	−1.41402			−0.152478
$87$		0			0
$88$	−6.12733	+	2.53802i	−0.653176	+	0.270554i
$89$		−	15.9437i		−	1.69003i	−0.534740	−	0.845017i	$-0.679590\pi$
$89$		−	15.9437i		−	1.69003i	0.534740	−	0.845017i	$-0.320410\pi$
$90$		0			0
$91$	1.15989	+	0.480442i	0.121589	+	0.0503640i
$92$	3.82930	−	9.24476i	0.399233	−	0.963833i
$93$		0			0
$94$	2.04753	−	2.04753i	0.211187	−	0.211187i
$95$	−0.156580	+	0.378019i	−0.0160648	+	0.0387839i
$96$		0			0
$97$	1.33512	+	3.22326i	0.135561	+	0.327273i	0.977053	−	0.212997i	$-0.0683223\pi$
$97$	1.33512	+	3.22326i	0.135561	+	0.327273i	−0.841492	+	0.540269i	$0.818322\pi$
$98$		−	0.0519011i		−	0.00524280i
$99$		0			0
$100$	−6.71965	−	6.71965i	−0.671965	−	0.671965i
$101$	−4.40807			−0.438619			−0.219310	−	0.975655i	$-0.570380\pi$
$101$	−4.40807			−0.438619			−0.219310	+	0.975655i	$0.570380\pi$
$102$		0			0
$103$	0.977534			0.0963192			0.0481596	−	0.998840i	$-0.484664\pi$
$103$	0.977534			0.0963192			0.0481596	+	0.998840i	$0.484664\pi$
$104$	0.405183	+	0.405183i	0.0397315	+	0.0397315i
$105$		0			0
$106$			4.04752i			0.393130i
$107$	6.71232	+	16.2050i	0.648904	+	1.56659i	0.814350	+	0.580375i	$0.197094\pi$
$107$	6.71232	+	16.2050i	0.648904	+	1.56659i	−0.165445	+	0.986219i	$0.552906\pi$
$108$		0			0
$109$	−4.41765	+	10.6651i	−0.423134	+	1.02154i	0.558283	+	0.829650i	$0.311460\pi$
$109$	−4.41765	+	10.6651i	−0.423134	+	1.02154i	−0.981417	+	0.191886i	$0.938540\pi$
$110$	−0.0715877	+	0.0715877i	−0.00682562	+	0.00682562i
$111$		0			0
$112$	−3.50483	+	8.46140i	−0.331175	+	0.799527i
$113$	−4.20973	−	1.74373i	−0.396018	−	0.164036i	0.175782	−	0.984429i	$-0.443755\pi$
$113$	−4.20973	−	1.74373i	−0.396018	−	0.164036i	−0.571800	+	0.820393i	$0.693755\pi$
$114$		0			0
$115$		−	0.313372i		−	0.0292221i
$116$	−4.23258	+	1.75319i	−0.392985	+	0.162780i
$117$		0			0
$118$	−2.95280			−0.271828
$119$	11.0181	+	0.647539i	1.01003	+	0.0593598i
$120$		0			0
$121$	13.0573	+	13.0573i	1.18703	+	1.18703i
$122$	0.526543	−	0.218101i	0.0476710	−	0.0197460i
$123$		0			0
$124$	−2.29665	−	5.54459i	−0.206245	−	0.497919i
$125$	−0.550099	−	0.227859i	−0.0492024	−	0.0203803i
$126$		0			0
$127$	3.92206	−	3.92206i	0.348027	−	0.348027i	−0.511347	−	0.859374i	$-0.670853\pi$
$127$	3.92206	−	3.92206i	0.348027	−	0.348027i	0.859374	+	0.511347i	$0.170853\pi$
$128$	−6.24215	+	6.24215i	−0.551733	+	0.551733i
$129$		0			0
$130$	0.00808127	+	0.00334737i	0.000708774	+	0.000293584i
$131$	2.40754	+	5.81231i	0.210348	+	0.507824i	0.993477	−	0.114035i	$-0.0363776\pi$
$131$	2.40754	+	5.81231i	0.210348	+	0.507824i	−0.783129	+	0.621859i	$0.786378\pi$
$132$		0			0
$133$	−16.9889	+	7.03702i	−1.47312	+	0.610187i
$134$	0.705577	+	0.705577i	0.0609526	+	0.0609526i
$135$		0			0
$136$	4.53299	+	2.19753i	0.388700	+	0.188436i
$137$	−8.44606			−0.721595			−0.360798	−	0.932644i	$-0.617495\pi$
$137$	−8.44606			−0.721595			−0.360798	+	0.932644i	$0.617495\pi$
$138$		0			0
$139$	−5.11432	+	2.11842i	−0.433791	+	0.179682i	−0.588884	−	0.808218i	$-0.700432\pi$
$139$	−5.11432	+	2.11842i	−0.433791	+	0.179682i	0.155093	+	0.987900i	$0.450432\pi$
$140$			0.303257i			0.0256299i
$141$		0			0
$142$	1.24977	+	0.517670i	0.104878	+	0.0434419i
$143$	0.974247	−	2.35204i	0.0814707	−	0.196688i
$144$		0			0
$145$	−0.101451	+	0.101451i	−0.00842501	+	0.00842501i
$146$	−1.43083	+	3.45434i	−0.118417	+	0.285883i
$147$		0			0
$148$	−5.46044	−	13.1827i	−0.448845	−	1.08361i
$149$		−	22.6720i		−	1.85736i	−0.370882	−	0.928680i	$-0.620945\pi$
$149$		−	22.6720i		−	1.85736i	0.370882	−	0.928680i	$-0.379055\pi$
$150$		0			0
$151$	8.99660	+	8.99660i	0.732133	+	0.732133i	0.971042	−	0.238909i	$-0.0767898\pi$
$151$	8.99660	+	8.99660i	0.732133	+	0.732133i	−0.238909	+	0.971042i	$0.576790\pi$
$152$	−8.39295			−0.680758
$153$		0			0
$154$	−4.54993			−0.366644
$155$	−0.132898	−	0.132898i	−0.0106746	−	0.0106746i
$156$		0			0
$157$			2.50104i			0.199605i	0.995007	+	0.0998023i	$0.0318210\pi$
$157$			2.50104i			0.199605i	−0.995007	+	0.0998023i	$0.968179\pi$
$158$	1.27910	+	3.08802i	0.101760	+	0.245670i
$159$		0			0
$160$	−0.0801179	+	0.193422i	−0.00633388	+	0.0152913i
$161$	9.95855	−	9.95855i	0.784844	−	0.784844i
$162$		0			0
$163$	4.11319	−	9.93011i	0.322170	−	0.777786i	−0.676958	−	0.736022i	$-0.736702\pi$
$163$	4.11319	−	9.93011i	0.322170	−	0.777786i	0.999127	−	0.0417646i	$-0.0132980\pi$
$164$	−3.91344	−	1.62100i	−0.305588	−	0.126579i
$165$		0			0
$166$		−	2.72711i		−	0.211665i
$167$	8.52287	−	3.53029i	0.659519	−	0.273182i	−0.0277171	−	0.999616i	$-0.508824\pi$
$167$	8.52287	−	3.53029i	0.659519	−	0.273182i	0.687236	+	0.726434i	$0.258824\pi$
$168$		0			0
$169$	12.7800			0.983080
$170$	0.0767662	+	0.00451159i	0.00588770	+	0.000346023i
$171$		0			0
$172$	6.07333	+	6.07333i	0.463087	+	0.463087i
$173$	−1.46148	+	0.605364i	−0.111114	+	0.0460250i	−0.437548	−	0.899195i	$-0.644153\pi$
$173$	−1.46148	+	0.605364i	−0.111114	+	0.0460250i	0.326434	+	0.945220i	$0.394153\pi$
$174$		0			0
$175$	−5.11838	−	12.3569i	−0.386913	−	0.934091i
$176$	17.1582	+	7.10715i	1.29335	+	0.535721i
$177$		0			0
$178$	3.53012	−	3.53012i	0.264594	−	0.264594i
$179$	−4.70314	+	4.70314i	−0.351529	+	0.351529i	−0.860678	−	0.509149i	$-0.829960\pi$
$179$	−4.70314	+	4.70314i	−0.351529	+	0.351529i	0.509149	+	0.860678i	$0.329960\pi$
$180$		0			0
$181$	15.7739	+	6.53377i	1.17247	+	0.485652i	0.882007	−	0.471236i	$-0.156192\pi$
$181$	15.7739	+	6.53377i	1.17247	+	0.485652i	0.290459	+	0.956887i	$0.406192\pi$
$182$	0.150437	+	0.363187i	0.0111511	+	0.0269212i
$183$		0			0
$184$	5.93871	−	2.45989i	0.437807	−	0.181346i
$185$	−0.315975	−	0.315975i	−0.0232309	−	0.0232309i
$186$		0			0
$187$	1.31309	−	22.3427i	0.0960227	−	1.63386i
$188$	−17.5886			−1.28278
$189$		0			0
$190$	−0.118366	+	0.0490289i	−0.00858718	+	0.00355693i
$191$			4.76822i			0.345016i	0.985008	+	0.172508i	$0.0551871\pi$
$191$			4.76822i			0.345016i	−0.985008	+	0.172508i	$0.944813\pi$
$192$		0			0
$193$	−7.14171	−	2.95820i	−0.514072	−	0.212936i	0.110539	−	0.993872i	$-0.464742\pi$
$193$	−7.14171	−	2.95820i	−0.514072	−	0.212936i	−0.624611	+	0.780936i	$0.714742\pi$
$194$	−0.418056	+	1.00928i	−0.0300147	+	0.0724618i
$195$		0			0
$196$	−0.222919	+	0.222919i	−0.0159228	+	0.0159228i
$197$	−0.727234	+	1.75570i	−0.0518132	+	0.125088i	−0.947667	−	0.319261i	$-0.896565\pi$
$197$	−0.727234	+	1.75570i	−0.0518132	+	0.125088i	0.895853	+	0.444350i	$0.146565\pi$
$198$		0			0
$199$	−3.28003	−	7.91870i	−0.232515	−	0.561342i	0.763957	−	0.645268i	$-0.223254\pi$
$199$	−3.28003	−	7.91870i	−0.232515	−	0.561342i	−0.996472	+	0.0839259i	$0.973254\pi$
$200$		−	6.10461i		−	0.431661i
$201$		0			0
$202$	−0.975995	−	0.975995i	−0.0686708	−	0.0686708i
$203$	−6.44793			−0.452556
$204$		0			0
$205$	−0.132655			−0.00926501
$206$	0.216437	+	0.216437i	0.0150799	+	0.0150799i
$207$		0			0
$208$		−	1.60460i		−	0.111259i
$209$	14.2698	+	34.4503i	0.987061	+	2.38298i
$210$		0			0
$211$	7.53937	−	18.2016i	0.519032	−	1.25305i	−0.419467	−	0.907771i	$-0.637783\pi$
$211$	7.53937	−	18.2016i	0.519032	−	1.25305i	0.938499	−	0.345283i	$-0.112217\pi$
$212$	17.3844	−	17.3844i	1.19397	−	1.19397i
$213$		0			0
$214$	−2.10178	+	5.07414i	−0.143675	+	0.346861i
$215$	0.248506	+	0.102935i	0.0169480	+	0.00702008i
$216$		0			0
$217$		−	8.44666i		−	0.573397i
$218$	−3.33950	+	1.38327i	−0.226179	+	0.0936865i
$219$		0			0
$220$	0.614949			0.0414599
$221$	−1.82687	+	0.633915i	−0.122888	+	0.0426418i
$222$		0			0
$223$	−15.1388	−	15.1388i	−1.01377	−	1.01377i	−0.999904	−	0.0138641i	$-0.995587\pi$
$223$	−15.1388	−	15.1388i	−1.01377	−	1.01377i	−0.0138641	−	0.999904i	$-0.504413\pi$
$224$	−8.69274	+	3.60065i	−0.580808	+	0.240578i
$225$		0			0
$226$	−0.546000	−	1.31816i	−0.0363194	−	0.0876827i
$227$	7.55429	+	3.12909i	0.501396	+	0.207685i	0.619023	−	0.785373i	$-0.287529\pi$
$227$	7.55429	+	3.12909i	0.501396	+	0.207685i	−0.117627	+	0.993058i	$0.537529\pi$
$228$		0			0
$229$	−14.4527	+	14.4527i	−0.955059	+	0.955059i	−0.999033	−	0.0439732i	$-0.985998\pi$
$229$	−14.4527	+	14.4527i	−0.955059	+	0.955059i	0.0439732	+	0.999033i	$0.485998\pi$
$230$	0.0693840	−	0.0693840i	0.00457504	−	0.00457504i
$231$		0			0
$232$	−2.71895	−	1.12623i	−0.178508	−	0.0739404i
$233$	−5.69335	−	13.7450i	−0.372983	−	0.900462i	−0.993242	−	0.116064i	$-0.962972\pi$
$233$	−5.69335	−	13.7450i	−0.372983	−	0.900462i	0.620258	−	0.784398i	$-0.287028\pi$
$234$		0			0
$235$	−0.508892	+	0.210790i	−0.0331965	+	0.0137504i
$236$	12.6825	+	12.6825i	0.825561	+	0.825561i
$237$		0			0
$238$	2.29616	+	2.58290i	0.148838	+	0.167425i
$239$	−21.0979			−1.36471			−0.682356	−	0.731020i	$-0.739045\pi$
$239$	−21.0979			−1.36471			−0.682356	+	0.731020i	$0.739045\pi$
$240$		0			0
$241$	−10.7508	+	4.45313i	−0.692521	+	0.286852i	−0.701050	−	0.713112i	$-0.747285\pi$
$241$	−10.7508	+	4.45313i	−0.692521	+	0.286852i	0.00852904	+	0.999964i	$0.497285\pi$
$242$			5.78207i			0.371686i
$243$		0			0
$244$	−3.19830	−	1.32478i	−0.204750	−	0.0848104i
$245$	−0.00377817	+	0.00912132i	−0.000241379	+	0.000582740i
$246$		0			0
$247$	2.27810	−	2.27810i	0.144952	−	0.144952i
$248$	1.47533	−	3.56177i	0.0936838	−	0.226173i
$249$		0			0
$250$	−0.0713476	−	0.172248i	−0.00451242	−	0.0108939i
$251$		−	25.8214i		−	1.62983i	−0.579580	−	0.814915i	$-0.696784\pi$
$251$		−	25.8214i		−	1.62983i	0.579580	−	0.814915i	$-0.303216\pi$
$252$		0			0
$253$	−20.1941	−	20.1941i	−1.26959	−	1.26959i
$254$	1.73678			0.108975
$255$		0			0
$256$	8.72002			0.545001
$257$	8.88366	+	8.88366i	0.554148	+	0.554148i	0.927635	−	0.373488i	$-0.121838\pi$
$257$	8.88366	+	8.88366i	0.554148	+	0.554148i	−0.373488	+	0.927635i	$0.621838\pi$
$258$		0			0
$259$		−	20.0825i		−	1.24787i
$260$	−0.0203324	−	0.0490869i	−0.00126096	−	0.00304424i
$261$		0			0
$262$	−0.753855	+	1.81997i	−0.0465733	+	0.112438i
$263$	4.54105	−	4.54105i	0.280013	−	0.280013i	−0.553101	−	0.833114i	$-0.686556\pi$
$263$	4.54105	−	4.54105i	0.280013	−	0.280013i	0.833114	+	0.553101i	$0.186556\pi$
$264$		0			0
$265$	0.294642	−	0.711329i	0.0180997	−	0.0436966i
$266$	−5.31960	−	2.20345i	−0.326165	−	0.135102i
$267$		0			0
$268$		−	6.06102i		−	0.370236i
$269$	23.0379	−	9.54260i	1.40464	−	0.581823i	0.453692	−	0.891159i	$-0.350107\pi$
$269$	23.0379	−	9.54260i	1.40464	−	0.581823i	0.950953	+	0.309336i	$0.100107\pi$
$270$		0			0
$271$	−8.88651			−0.539817			−0.269909	−	0.962886i	$-0.586993\pi$
$271$	−8.88651			−0.539817			−0.269909	+	0.962886i	$0.586993\pi$
$272$	−4.62442	−	13.3270i	−0.280397	−	0.808069i
$273$		0			0
$274$	−1.87005	−	1.87005i	−0.112974	−	0.112974i
$275$	−25.0574	+	10.3791i	−1.51102	+	0.625885i
$276$		0			0
$277$	5.29180	+	12.7755i	0.317954	+	0.767608i	0.999362	+	0.0357049i	$0.0113676\pi$
$277$	5.29180	+	12.7755i	0.317954	+	0.767608i	−0.681409	+	0.731903i	$0.738632\pi$
$278$	−1.60141	−	0.663326i	−0.0960462	−	0.0397836i
$279$		0			0
$280$	−0.137750	+	0.137750i	−0.00823215	+	0.00823215i
$281$	−11.9649	+	11.9649i	−0.713764	+	0.713764i	−0.967321	−	0.253556i	$-0.918400\pi$
$281$	−11.9649	+	11.9649i	−0.713764	+	0.713764i	0.253556	+	0.967321i	$0.418400\pi$
$282$		0			0
$283$	−23.3011	−	9.65163i	−1.38511	−	0.573730i	−0.439264	−	0.898358i	$-0.644761\pi$
$283$	−23.3011	−	9.65163i	−1.38511	−	0.573730i	−0.945842	+	0.324628i	$0.894761\pi$
$284$	−3.14441	−	7.59128i	−0.186586	−	0.450459i
$285$		0			0
$286$	0.736477	−	0.305059i	0.0435488	−	0.0180385i
$287$	−4.21560	−	4.21560i	−0.248839	−	0.248839i
$288$		0			0
$289$	−13.3461	+	10.5300i	−0.785067	+	0.619411i
$290$	−0.0449246			−0.00263806
$291$		0			0
$292$	20.9822	−	8.69111i	1.22789	−	0.508609i
$293$			1.93377i			0.112972i	0.998403	+	0.0564859i	$0.0179896\pi$
$293$			1.93377i			0.112972i	−0.998403	+	0.0564859i	$0.982010\pi$
$294$		0			0
$295$	0.518938	+	0.214951i	0.0302137	+	0.0125149i
$296$	3.50771	−	8.46837i	0.203882	−	0.492214i
$297$		0			0
$298$	5.01982	−	5.01982i	0.290791	−	0.290791i
$299$	−0.944256	+	2.27964i	−0.0546078	+	0.131835i
$300$		0			0
$301$	4.62607	+	11.1683i	0.266642	+	0.643732i
$302$			3.98389i			0.229247i
$303$		0			0
$304$	16.6188	+	16.6188i	0.953152	+	0.953152i
$305$	−0.108414			−0.00620775
$306$		0			0
$307$	−0.791215			−0.0451570			−0.0225785	−	0.999745i	$-0.507188\pi$
$307$	−0.791215			−0.0451570			−0.0225785	+	0.999745i	$0.507188\pi$
$308$	19.5423	+	19.5423i	1.11353	+	1.11353i
$309$		0			0
$310$		−	0.0588503i		−	0.00334247i
$311$	11.8767	+	28.6728i	0.673464	+	1.62589i	0.775682	+	0.631124i	$0.217406\pi$
$311$	11.8767	+	28.6728i	0.673464	+	1.62589i	−0.102217	+	0.994762i	$0.532594\pi$
$312$		0			0
$313$	3.51406	−	8.48369i	0.198626	−	0.479527i	−0.792913	−	0.609335i	$-0.791436\pi$
$313$	3.51406	−	8.48369i	0.198626	−	0.479527i	0.991539	+	0.129809i	$0.0414363\pi$
$314$	−0.553758	+	0.553758i	−0.0312504	+	0.0312504i
$315$		0			0
$316$	7.76944	−	18.7571i	0.437065	−	1.05517i
$317$	18.4989	+	7.66249i	1.03900	+	0.430368i	0.835953	−	0.548801i	$-0.184915\pi$
$317$	18.4989	+	7.66249i	1.03900	+	0.430368i	0.203048	+	0.979169i	$0.434915\pi$
$318$		0			0
$319$			13.0752i			0.732072i
$320$	0.315984	−	0.130885i	0.0176640	−	0.00731669i
$321$		0			0
$322$	4.40987			0.245752
$323$	12.3554	−	25.4863i	0.687471	−	1.41809i
$324$		0			0
$325$	1.65698	+	1.65698i	0.0919126	+	0.0919126i
$326$	3.10934	−	1.28793i	0.172211	−	0.0713319i
$327$		0			0
$328$	−1.04131	−	2.51394i	−0.0574966	−	0.138809i
$329$	−22.8706	−	9.47330i	−1.26090	−	0.522280i
$330$		0			0
$331$	17.4538	−	17.4538i	0.959350	−	0.959350i	−0.0398555	−	0.999205i	$-0.512690\pi$
$331$	17.4538	−	17.4538i	0.959350	−	0.959350i	0.999205	+	0.0398555i	$0.0126898\pi$
$332$	−11.7131	+	11.7131i	−0.642842	+	0.642842i
$333$		0			0
$334$	2.66870	+	1.10541i	0.146025	+	0.0604855i
$335$	−0.0726382	−	0.175364i	−0.00396865	−	0.00958116i
$336$		0			0
$337$	25.4443	−	10.5394i	1.38604	−	0.574117i	0.439952	−	0.898021i	$-0.354995\pi$
$337$	25.4443	−	10.5394i	1.38604	−	0.574117i	0.946090	+	0.323904i	$0.104995\pi$
$338$	2.82964	+	2.82964i	0.153912	+	0.153912i
$339$		0			0
$340$	−0.310339	−	0.349094i	−0.0168305	−	0.0189323i
$341$	−17.1283			−0.927548
$342$		0			0
$343$	16.9020	−	7.00102i	0.912620	−	0.378019i
$344$			5.51745i			0.297481i
$345$		0			0
$346$	−0.457621	−	0.189553i	−0.0246019	−	0.0101904i
$347$	8.81253	−	21.2753i	0.473082	−	1.14212i	−0.489713	−	0.871884i	$-0.662898\pi$
$347$	8.81253	−	21.2753i	0.473082	−	1.14212i	0.962794	−	0.270236i	$-0.0871017\pi$
$348$		0			0
$349$	−13.4894	+	13.4894i	−0.722069	+	0.722069i	−0.969026	−	0.246957i	$-0.920569\pi$
$349$	−13.4894	+	13.4894i	−0.722069	+	0.722069i	0.246957	+	0.969026i	$0.420569\pi$
$350$	1.60268	−	3.86921i	0.0856668	−	0.206818i
$351$		0			0
$352$	7.30145	+	17.6273i	0.389169	+	0.939537i
$353$			7.27281i			0.387093i	0.981091	+	0.193546i	$0.0619990\pi$
$353$			7.27281i			0.387093i	−0.981091	+	0.193546i	$0.938001\pi$
$354$		0			0
$355$	−0.181955	−	0.181955i	−0.00965717	−	0.00965717i
$356$	−30.3243			−1.60718
$357$		0			0
$358$	−2.08265			−0.110072
$359$	−18.7916	−	18.7916i	−0.991783	−	0.991783i	0.00818396	−	0.999967i	$-0.497395\pi$
$359$	−18.7916	−	18.7916i	−0.991783	−	0.991783i	−0.999967	+	0.00818396i	$0.997395\pi$
$360$		0			0
$361$			28.1885i			1.48361i
$362$	2.04587	+	4.93917i	0.107529	+	0.259597i
$363$		0			0
$364$	0.913778	−	2.20606i	0.0478950	−	0.115629i
$365$	0.502922	−	0.502922i	0.0263241	−	0.0263241i
$366$		0			0
$367$	−11.1747	+	26.9782i	−0.583316	+	1.40825i	0.306475	+	0.951879i	$0.400851\pi$
$367$	−11.1747	+	26.9782i	−0.583316	+	1.40825i	−0.889790	+	0.456370i	$0.849149\pi$
$368$	−16.6300	−	6.88836i	−0.866897	−	0.359081i
$369$		0			0
$370$		−	0.139921i		−	0.00727413i
$371$	31.9684	−	13.2418i	1.65972	−	0.687478i
$372$		0			0
$373$	−16.7965			−0.869689			−0.434844	−	0.900506i	$-0.643197\pi$
$373$	−16.7965			−0.869689			−0.434844	+	0.900506i	$0.643197\pi$
$374$	5.23765	−	4.65618i	0.270832	−	0.240765i
$375$		0			0
$376$	−7.98937	−	7.98937i	−0.412020	−	0.412020i
$377$	1.04370	−	0.432314i	0.0537532	−	0.0222653i
$378$		0			0
$379$	3.70421	+	8.94276i	0.190273	+	0.459359i	0.990011	−	0.140990i	$-0.0450285\pi$
$379$	3.70421	+	8.94276i	0.190273	+	0.459359i	−0.799738	+	0.600349i	$0.795028\pi$
$380$	0.718974	+	0.297809i	0.0368826	+	0.0152773i
$381$		0			0
$382$	−1.05574	+	1.05574i	−0.0540162	+	0.0540162i
$383$	−3.69319	+	3.69319i	−0.188713	+	0.188713i	−0.795140	−	0.606427i	$-0.792602\pi$
$383$	−3.69319	+	3.69319i	−0.188713	+	0.188713i	0.606427	+	0.795140i	$0.292602\pi$
$384$		0			0
$385$	0.799623	+	0.331215i	0.0407526	+	0.0168803i
$386$	−0.926277	−	2.23623i	−0.0471463	−	0.113821i
$387$		0			0
$388$	6.13050	−	2.53934i	0.311229	−	0.128915i
$389$	0.947715	+	0.947715i	0.0480511	+	0.0480511i	0.730724	−	0.682673i	$-0.239183\pi$
$389$	0.947715	+	0.947715i	0.0480511	+	0.0480511i	−0.682673	+	0.730724i	$0.739183\pi$
$390$		0			0
$391$	−1.27267	+	21.6549i	−0.0643616	+	1.09513i
$392$	−0.202516			−0.0102286
$393$		0			0
$394$	−0.549748	+	0.227713i	−0.0276959	+	0.0114720i
$395$		−	0.635814i		−	0.0319913i
$396$		0			0
$397$	−11.9156	−	4.93561i	−0.598028	−	0.247711i	0.0630721	−	0.998009i	$-0.479910\pi$
$397$	−11.9156	−	4.93561i	−0.598028	−	0.247711i	−0.661100	+	0.750298i	$0.729910\pi$
$398$	1.02705	−	2.47952i	0.0514815	−	0.124287i
$399$		0			0
$400$	−12.0877	+	12.0877i	−0.604384	+	0.604384i
$401$	−4.79470	+	11.5754i	−0.239436	+	0.578049i	−0.997225	−	0.0744507i	$-0.976280\pi$
$401$	−4.79470	+	11.5754i	−0.239436	+	0.578049i	0.757789	+	0.652500i	$0.226280\pi$
$402$		0			0
$403$	0.566323	+	1.36722i	0.0282105	+	0.0681063i
$404$			8.38395i			0.417117i
$405$		0			0
$406$	−1.42764	−	1.42764i	−0.0708528	−	0.0708528i
$407$	−40.7237			−2.01860
$408$		0			0
$409$	−0.156286			−0.00772787			−0.00386393	−	0.999993i	$-0.501230\pi$
$409$	−0.156286			−0.00772787			−0.00386393	+	0.999993i	$0.501230\pi$
$410$	−0.0293712	−	0.0293712i	−0.00145054	−	0.00145054i
$411$		0			0
$412$		−	1.85922i		−	0.0915974i
$413$	9.66030	+	23.3220i	0.475353	+	1.14760i
$414$		0			0
$415$	−0.198522	+	0.479273i	−0.00974504	+	0.0235266i
$416$	1.16564	−	1.16564i	0.0571503	−	0.0571503i
$417$		0			0
$418$	−4.46819	+	10.7872i	−0.218546	+	0.527617i
$419$	24.5021	+	10.1491i	1.19700	+	0.495815i	0.890030	−	0.455902i	$-0.150683\pi$
$419$	24.5021	+	10.1491i	1.19700	+	0.495815i	0.306974	+	0.951718i	$0.400683\pi$
$420$		0			0
$421$			26.6269i			1.29772i	0.760909	+	0.648859i	$0.224753\pi$
$421$			26.6269i			1.29772i	−0.760909	+	0.648859i	$0.775247\pi$
$422$	5.69935	−	2.36075i	0.277440	−	0.114919i
$423$		0			0
$424$	15.7933			0.766988
$425$	18.5374	+	8.98668i	0.899198	+	0.435918i
$426$		0			0
$427$	−3.44525	−	3.44525i	−0.166727	−	0.166727i
$428$	30.8211	−	12.7665i	1.48979	−	0.617093i
$429$		0			0
$430$	0.0322311	+	0.0778128i	0.00155432	+	0.00375247i
$431$	29.4298	+	12.1902i	1.41758	+	0.587182i	0.954252	−	0.299003i	$-0.0966541\pi$
$431$	29.4298	+	12.1902i	1.41758	+	0.587182i	0.463331	+	0.886185i	$0.346654\pi$
$432$		0			0
$433$	−24.1537	+	24.1537i	−1.16075	+	1.16075i	−0.176442	+	0.984311i	$0.556459\pi$
$433$	−24.1537	+	24.1537i	−1.16075	+	1.16075i	−0.984311	+	0.176442i	$0.943541\pi$
$434$	1.87018	−	1.87018i	0.0897717	−	0.0897717i
$435$		0			0
$436$	20.2846	+	8.40217i	0.971457	+	0.402391i
$437$	−13.8305	−	33.3898i	−0.661603	−	1.59725i
$438$		0			0
$439$	−27.4308	+	11.3622i	−1.30920	+	0.542288i	−0.924651	−	0.380816i	$-0.875643\pi$
$439$	−27.4308	+	11.3622i	−1.30920	+	0.542288i	−0.384549	+	0.923105i	$0.625643\pi$
$440$	0.279332	+	0.279332i	0.0133166	+	0.0133166i
$441$		0			0
$442$	−0.544844	−	0.264133i	−0.0259156	−	0.0125635i
$443$	−15.6384			−0.743002			−0.371501	−	0.928432i	$-0.621157\pi$
$443$	−15.6384			−0.743002			−0.371501	+	0.928432i	$0.621157\pi$
$444$		0			0
$445$	−0.877375	+	0.363421i	−0.0415916	+	0.0172278i
$446$		−	6.70379i		−	0.317434i
$447$		0			0
$448$	14.2009	+	5.88221i	0.670930	+	0.277908i
$449$	−3.22717	+	7.79108i	−0.152300	+	0.367684i	−0.981553	−	0.191188i	$-0.938766\pi$
$449$	−3.22717	+	7.79108i	−0.152300	+	0.367684i	0.829254	+	0.558872i	$0.188766\pi$
$450$		0			0
$451$	−8.54845	+	8.54845i	−0.402531	+	0.402531i
$452$	−3.31649	+	8.00671i	−0.155994	+	0.376604i
$453$		0			0
$454$	0.979788	+	2.36542i	0.0459837	+	0.111015i
$455$		−	0.0747792i		−	0.00350570i
$456$		0			0
$457$	16.8560	+	16.8560i	0.788491	+	0.788491i	0.981247	−	0.192756i	$-0.0617425\pi$
$457$	16.8560	+	16.8560i	0.788491	+	0.788491i	−0.192756	+	0.981247i	$0.561743\pi$
$458$	−6.39996			−0.299051
$459$		0			0
$460$	−0.596019			−0.0277895
$461$	−2.57453	−	2.57453i	−0.119908	−	0.119908i	0.644607	−	0.764515i	$-0.277021\pi$
$461$	−2.57453	−	2.57453i	−0.119908	−	0.119908i	−0.764515	+	0.644607i	$0.777021\pi$
$462$		0			0
$463$		−	20.7505i		−	0.964359i	−0.876072	−	0.482180i	$-0.839845\pi$
$463$		−	20.7505i		−	0.964359i	0.876072	−	0.482180i	$-0.160155\pi$
$464$	3.15374	+	7.61379i	0.146409	+	0.353461i
$465$		0			0
$466$	1.78271	−	4.30385i	0.0825827	−	0.199372i
$467$	−25.6578	+	25.6578i	−1.18730	+	1.18730i	−0.209491	+	0.977811i	$0.567181\pi$
$467$	−25.6578	+	25.6578i	−1.18730	+	1.18730i	−0.977811	+	0.209491i	$0.932819\pi$
$468$		0			0
$469$	3.26449	−	7.88119i	0.150740	−	0.363919i
$470$	−0.159346	−	0.0660031i	−0.00735007	−	0.00304450i
$471$		0			0
$472$			11.5217i			0.530329i
$473$	22.6473	−	9.38082i	1.04132	−	0.431331i
$474$		0			0
$475$	−34.3226			−1.57483
$476$	1.23159	−	20.9559i	0.0564498	−	0.960513i
$477$		0			0
$478$	−4.67132	−	4.67132i	−0.213661	−	0.213661i
$479$	−23.3776	+	9.68333i	−1.06815	+	0.442443i	−0.846338	−	0.532646i	$-0.821198\pi$
$479$	−23.3776	+	9.68333i	−1.06815	+	0.442443i	−0.221813	+	0.975089i	$0.571198\pi$
$480$		0			0
$481$	1.34647	+	3.25067i	0.0613939	+	0.148218i
$482$	−3.36632	−	1.39438i	−0.153332	−	0.0635121i
$483$		0			0
$484$	24.8344	−	24.8344i	1.12884	−	1.12884i
$485$	0.146942	−	0.146942i	0.00667228	−	0.00667228i
$486$		0			0
$487$	−19.1193	−	7.91949i	−0.866380	−	0.358866i	−0.0951805	−	0.995460i	$-0.530343\pi$
$487$	−19.1193	−	7.91949i	−0.866380	−	0.358866i	−0.771199	+	0.636594i	$0.780343\pi$
$488$	−0.851021	−	2.05455i	−0.0385239	−	0.0930050i
$489$		0			0
$490$	−0.00285609	+	0.00118303i	−0.000129025	+	5.34439e-5i
$491$	11.7349	+	11.7349i	0.529587	+	0.529587i	0.920449	−	0.390862i	$-0.127823\pi$
$491$	11.7349	+	11.7349i	0.529587	+	0.529587i	−0.390862	+	0.920449i	$0.627823\pi$
$492$		0			0
$493$	7.42253	−	6.59851i	0.334294	−	0.297182i
$494$	1.00879			0.0453878
$495$		0			0
$496$	−9.97391	+	4.13133i	−0.447842	+	0.185502i
$497$		−	11.5646i		−	0.518743i
$498$		0			0
$499$	26.3968	+	10.9339i	1.18168	+	0.489470i	0.885039	−	0.465518i	$-0.154132\pi$
$499$	26.3968	+	10.9339i	1.18168	+	0.489470i	0.296646	+	0.954987i	$0.404132\pi$
$500$	−0.433377	+	1.04626i	−0.0193812	+	0.0467903i
$501$		0			0
$502$	5.71714	−	5.71714i	0.255168	−	0.255168i
$503$	4.58354	−	11.0656i	0.204370	−	0.493392i	−0.788149	−	0.615484i	$-0.788960\pi$
$503$	4.58354	−	11.0656i	0.204370	−	0.493392i	0.992519	+	0.122092i	$0.0389604\pi$
$504$		0			0
$505$	0.100477	+	0.242574i	0.00447118	+	0.0107944i
$506$		−	8.94240i		−	0.397538i
$507$		0			0
$508$	−7.45959	−	7.45959i	−0.330966	−	0.330966i
$509$	−24.8636			−1.10206			−0.551031	−	0.834485i	$-0.685765\pi$
$509$	−24.8636			−1.10206			−0.551031	+	0.834485i	$0.685765\pi$
$510$		0			0
$511$	31.9644			1.41402
$512$	14.4150	+	14.4150i	0.637059	+	0.637059i
$513$		0			0
$514$			3.93388i			0.173516i
$515$	−0.0222818	−	0.0537931i	−0.000981855	−	0.00237041i
$516$		0			0
$517$	−19.2101	+	46.3773i	−0.844860	+	2.03967i
$518$	4.44650	−	4.44650i	0.195368	−	0.195368i
$519$		0			0
$520$	0.0130613	−	0.0315327i	0.000572775	−	0.00138280i
$521$	−23.6260	−	9.78620i	−1.03507	−	0.428741i	−0.200532	−	0.979687i	$-0.564267\pi$
$521$	−23.6260	−	9.78620i	−1.03507	−	0.428741i	−0.834541	+	0.550946i	$0.814267\pi$
$522$		0			0
$523$		−	15.9637i		−	0.698043i	−0.937115	−	0.349022i	$-0.886514\pi$
$523$		−	15.9637i		−	0.698043i	0.937115	−	0.349022i	$-0.113486\pi$
$524$	11.0548	−	4.57903i	0.482929	−	0.200036i
$525$		0			0
$526$	2.01088			0.0876784
$527$	8.64391	+	9.72337i	0.376535	+	0.423557i
$528$		0			0
$529$	3.30900	+	3.30900i	0.143869	+	0.143869i
$530$	0.222733	−	0.0922590i	0.00967491	−	0.00400748i
$531$		0			0
$532$	13.3841	+	32.3120i	0.580274	+	1.40090i
$533$	0.965003	+	0.399717i	0.0417989	+	0.0173137i
$534$		0			0
$535$	0.738750	−	0.738750i	0.0319390	−	0.0319390i
$536$	2.75313	−	2.75313i	0.118917	−	0.118917i
$537$		0			0
$538$	7.21368	+	2.98800i	0.311004	+	0.128822i
$539$	0.344319	+	0.831261i	0.0148309	+	0.0358049i
$540$		0			0
$541$	22.6178	−	9.36862i	0.972417	−	0.402788i	0.160806	−	0.986986i	$-0.448591\pi$
$541$	22.6178	−	9.36862i	0.972417	−	0.402788i	0.811611	+	0.584198i	$0.198591\pi$
$542$	−1.96757	−	1.96757i	−0.0845145	−	0.0845145i
$543$		0			0
$544$	6.32190	−	13.0406i	0.271049	−	0.559112i
$545$	0.687593			0.0294532
$546$		0			0
$547$	−34.4829	+	14.2833i	−1.47438	+	0.610708i	−0.967853	−	0.251516i	$-0.919071\pi$
$547$	−34.4829	+	14.2833i	−1.47438	+	0.610708i	−0.506527	+	0.862224i	$0.669071\pi$
$548$			16.0640i			0.686221i
$549$		0			0
$550$	−7.84605	−	3.24994i	−0.334556	−	0.138578i
$551$	−6.33209	+	15.2870i	−0.269756	+	0.651249i
$552$		0			0
$553$	20.2053	−	20.2053i	0.859218	−	0.859218i
$554$	−1.65698	+	4.00031i	−0.0703985	+	0.169957i
$555$		0			0
$556$	4.02914	+	9.72721i	0.170874	+	0.412526i
$557$		−	13.6266i		−	0.577378i	−0.957423	−	0.288689i	$-0.906781\pi$
$557$		−	13.6266i		−	0.577378i	0.957423	−	0.288689i	$-0.0932193\pi$
$558$		0			0
$559$	−1.49760	−	1.49760i	−0.0633419	−	0.0633419i
$560$	0.545515			0.0230522
$561$		0			0
$562$	−5.29831			−0.223496
$563$	27.3487	+	27.3487i	1.15261	+	1.15261i	0.986028	+	0.166581i	$0.0532726\pi$
$563$	27.3487	+	27.3487i	1.15261	+	1.15261i	0.166581	+	0.986028i	$0.446727\pi$
$564$		0			0
$565$			0.271405i			0.0114181i
$566$	−3.02214	−	7.29609i	−0.127030	−	0.306678i
$567$		0			0
$568$	2.01993	−	4.87653i	0.0847542	−	0.204615i
$569$	8.31984	−	8.31984i	0.348786	−	0.348786i	−0.510871	−	0.859657i	$-0.670677\pi$
$569$	8.31984	−	8.31984i	0.348786	−	0.348786i	0.859657	+	0.510871i	$0.170677\pi$
$570$		0			0
$571$	4.90353	−	11.8382i	0.205206	−	0.495411i	−0.787450	−	0.616378i	$-0.788599\pi$
$571$	4.90353	−	11.8382i	0.205206	−	0.495411i	0.992657	+	0.120967i	$0.0385994\pi$
$572$	−4.47347	−	1.85297i	−0.187045	−	0.0774767i
$573$		0			0
$574$		−	1.86676i		−	0.0779170i
$575$	24.2861	−	10.0596i	1.01280	−	0.419515i
$576$		0			0
$577$	30.7966			1.28208			0.641040	−	0.767508i	$-0.278503\pi$
$577$	30.7966			1.28208			0.641040	+	0.767508i	$0.278503\pi$
$578$	−5.28644	−	0.623527i	−0.219887	−	0.0259353i
$579$		0			0
$580$	0.192954	+	0.192954i	0.00801199	+	0.00801199i
$581$	−21.5394	+	8.92193i	−0.893607	+	0.370144i
$582$		0			0
$583$	−26.8519	−	64.8261i	−1.11209	−	2.68482i
$584$	13.4787	+	5.58305i	0.557752	+	0.231028i
$585$		0			0
$586$	−0.428157	+	0.428157i	−0.0176870	+	0.0176870i
$587$	13.3240	−	13.3240i	0.549939	−	0.549939i	−0.376484	−	0.926423i	$-0.622867\pi$
$587$	13.3240	−	13.3240i	0.549939	−	0.549939i	0.926423	+	0.376484i	$0.122867\pi$
$588$		0			0
$589$	−20.0257	−	8.29492i	−0.825144	−	0.341786i
$590$	0.0673060	+	0.162491i	0.00277095	+	0.00668965i
$591$		0			0
$592$	−23.7137	+	9.82253i	−0.974627	+	0.403704i
$593$	20.0409	+	20.0409i	0.822982	+	0.822982i	0.986535	−	0.163553i	$-0.0522955\pi$
$593$	20.0409	+	20.0409i	0.822982	+	0.822982i	−0.163553	+	0.986535i	$0.552295\pi$
$594$		0			0
$595$	−0.215512	−	0.621080i	−0.00883514	−	0.0254618i
$596$	−43.1210			−1.76631
$597$		0			0
$598$	−0.713805	+	0.295668i	−0.0291897	+	0.0120908i
$599$		−	20.3955i		−	0.833339i	−0.909058	−	0.416669i	$-0.863197\pi$
$599$		−	20.3955i		−	0.833339i	0.909058	−	0.416669i	$-0.136803\pi$
$600$		0			0
$601$	24.8984	+	10.3132i	1.01563	+	0.420686i	0.827504	−	0.561460i	$-0.189760\pi$
$601$	24.8984	+	10.3132i	1.01563	+	0.420686i	0.188122	+	0.982146i	$0.439760\pi$
$602$	−1.44853	+	3.49705i	−0.0590376	+	0.142529i
$603$		0			0
$604$	17.1111	−	17.1111i	0.696241	−	0.696241i
$605$	0.420909	−	1.01617i	0.0171124	−	0.0413130i
$606$		0			0
$607$	−14.2003	−	34.2826i	−0.576372	−	1.39149i	−0.896047	−	0.443959i	$-0.853574\pi$
$607$	−14.2003	−	34.2826i	−0.576372	−	1.39149i	0.319675	−	0.947527i	$-0.396426\pi$
$608$			24.1451i			0.979211i
$609$		0			0
$610$	−0.0240040	−	0.0240040i	−0.000971893	−	0.000971893i
$611$	4.33711			0.175461
$612$		0			0
$613$	−43.2999			−1.74887			−0.874433	−	0.485147i	$-0.838766\pi$
$613$	−43.2999			−1.74887			−0.874433	+	0.485147i	$0.838766\pi$
$614$	−0.175184	−	0.175184i	−0.00706984	−	0.00706984i
$615$		0			0
$616$			17.7536i			0.715314i
$617$	−2.23750	−	5.40179i	−0.0900782	−	0.217468i	0.872420	−	0.488758i	$-0.162550\pi$
$617$	−2.23750	−	5.40179i	−0.0900782	−	0.217468i	−0.962498	+	0.271290i	$0.912550\pi$
$618$		0			0
$619$	1.75427	−	4.23518i	0.0705101	−	0.170226i	−0.884696	−	0.466169i	$-0.845634\pi$
$619$	1.75427	−	4.23518i	0.0705101	−	0.170226i	0.955206	+	0.295943i	$0.0956338\pi$
$620$	−0.252766	+	0.252766i	−0.0101513	+	0.0101513i
$621$		0			0
$622$	−3.71885	+	8.97811i	−0.149112	+	0.359989i
$623$	−39.4309	−	16.3328i	−1.57977	−	0.654360i
$624$		0			0
$625$		−	24.9468i		−	0.997872i
$626$	2.65644	−	1.10033i	0.106173	−	0.0439781i
$627$		0			0
$628$	4.75686			0.189819
$629$	20.5515	+	23.1180i	0.819443	+	0.921775i
$630$		0			0
$631$	29.8822	+	29.8822i	1.18959	+	1.18959i	0.977180	+	0.212414i	$0.0681324\pi$
$631$	29.8822	+	29.8822i	1.18959	+	1.18959i	0.212414	+	0.977180i	$0.431868\pi$
$632$	12.0493	−	4.99099i	0.479296	−	0.198531i
$633$		0			0
$634$	2.39930	+	5.79242i	0.0952883	+	0.230046i
$635$	−0.305228	−	0.126430i	−0.0121126	−	0.00501721i
$636$		0			0
$637$	0.0549690	−	0.0549690i	0.00217795	−	0.00217795i
$638$	−2.89500	+	2.89500i	−0.114614	+	0.114614i
$639$		0			0
$640$	0.485785	+	0.201219i	0.0192023	+	0.00795387i
$641$	−14.0727	−	33.9746i	−0.555839	−	1.34192i	−0.913033	−	0.407885i	$-0.866266\pi$
$641$	−14.0727	−	33.9746i	−0.555839	−	1.34192i	0.357194	−	0.934030i	$-0.383734\pi$
$642$		0			0
$643$	−20.2367	+	8.38232i	−0.798058	+	0.330567i	−0.744178	−	0.667981i	$-0.767159\pi$
$643$	−20.2367	+	8.38232i	−0.798058	+	0.330567i	−0.0538797	+	0.998547i	$0.517159\pi$
$644$	−18.9407	−	18.9407i	−0.746368	−	0.746368i
$645$		0			0
$646$	8.37855	−	2.90732i	0.329650	−	0.114387i
$647$	13.3204			0.523681			0.261840	−	0.965111i	$-0.415671\pi$
$647$	13.3204			0.523681			0.261840	+	0.965111i	$0.415671\pi$
$648$		0			0
$649$	47.2928	−	19.5893i	1.85640	−	0.768948i
$650$			0.733747i			0.0287799i
$651$		0			0
$652$	−18.8866	−	7.82309i	−0.739657	−	0.306376i
$653$	3.92953	−	9.48672i	0.153774	−	0.371244i	−0.828153	−	0.560502i	$-0.810608\pi$
$653$	3.92953	−	9.48672i	0.153774	−	0.371244i	0.981927	+	0.189258i	$0.0606082\pi$
$654$		0			0
$655$	0.264971	−	0.264971i	0.0103533	−	0.0103533i
$656$	−2.91594	+	7.03970i	−0.113848	+	0.274854i
$657$		0			0
$658$	−2.96630	−	7.16129i	−0.115639	−	0.279176i
$659$		−	22.3839i		−	0.871954i	−0.899958	−	0.435977i	$-0.856403\pi$
$659$		−	22.3839i		−	0.871954i	0.899958	−	0.435977i	$-0.143597\pi$
$660$		0			0
$661$	−22.1866	−	22.1866i	−0.862958	−	0.862958i	0.128722	−	0.991681i	$-0.458912\pi$
$661$	−22.1866	−	22.1866i	−0.862958	−	0.862958i	−0.991681	+	0.128722i	$0.958912\pi$
$662$	7.72895			0.300394
$663$		0			0
$664$	−10.6411			−0.412953
$665$	0.774486	+	0.774486i	0.0300333	+	0.0300333i
$666$		0			0
$667$		−	12.6727i		−	0.490690i
$668$	−6.71444	−	16.2101i	−0.259790	−	0.627188i
$669$		0			0
$670$	0.0227446	−	0.0549104i	0.000878702	−	0.00212137i
$671$	−6.98632	+	6.98632i	−0.269704	+	0.269704i
$672$		0			0
$673$	3.79549	−	9.16311i	0.146305	−	0.353212i	−0.833690	−	0.552233i	$-0.813776\pi$
$673$	3.79549	−	9.16311i	0.146305	−	0.353212i	0.979995	+	0.199020i	$0.0637760\pi$
$674$	7.96720	+	3.30012i	0.306885	+	0.127116i
$675$		0			0
$676$		−	24.3071i		−	0.934887i
$677$	−1.12058	+	0.464158i	−0.0430673	+	0.0178390i	−0.404113	−	0.914709i	$-0.632420\pi$
$677$	−1.12058	+	0.464158i	−0.0430673	+	0.0178390i	0.361046	+	0.932548i	$0.382420\pi$
$678$		0			0
$679$	9.33924			0.358407
$680$	0.0176040	−	0.299538i	0.000675083	−	0.0114868i
$681$		0			0
$682$	−3.79239	−	3.79239i	−0.145218	−	0.145218i
$683$	−28.5239	+	11.8150i	−1.09144	+	0.452088i	−0.854507	−	0.519440i	$-0.826141\pi$
$683$	−28.5239	+	11.8150i	−1.09144	+	0.452088i	−0.236929	+	0.971527i	$0.576141\pi$
$684$		0			0
$685$	0.192519	+	0.464782i	0.00735577	+	0.0177584i
$686$	5.29238	+	2.19218i	0.202064	+	0.0836977i
$687$		0			0
$688$	10.9250	−	10.9250i	0.416513	−	0.416513i
$689$	−4.28677	+	4.28677i	−0.163313	+	0.163313i
$690$		0			0
$691$	23.8070	+	9.86119i	0.905661	+	0.375137i	0.786394	−	0.617725i	$-0.211945\pi$
$691$	23.8070	+	9.86119i	0.905661	+	0.375137i	0.119267	+	0.992862i	$0.461945\pi$
$692$	1.15137	+	2.77966i	0.0437687	+	0.105667i
$693$		0			0
$694$	6.66179	−	2.75940i	0.252878	−	0.104745i
$695$	0.233151	+	0.233151i	0.00884393	+	0.00884393i
$696$		0			0
$697$	9.16682	+	0.538739i	0.347218	+	0.0204062i
$698$	−5.97339			−0.226096
$699$		0			0
$700$	−23.5022	+	9.73492i	−0.888299	+	0.367945i
$701$			25.4354i			0.960683i	0.877081	+	0.480342i	$0.159487\pi$
$701$			25.4354i			0.960683i	−0.877081	+	0.480342i	$0.840513\pi$
$702$		0			0
$703$	−47.6125	−	19.7218i	−1.79574	−	0.743820i
$704$	11.9280	−	28.7968i	0.449555	−	1.08532i
$705$		0			0
$706$	−1.61028	+	1.61028i	−0.0606037	+	0.0606037i
$707$	−4.51564	+	10.9017i	−0.169828	+	0.410001i
$708$		0			0
$709$	−15.3766	−	37.1224i	−0.577480	−	1.39416i	−0.895067	−	0.445932i	$-0.852872\pi$
$709$	−15.3766	−	37.1224i	−0.577480	−	1.39416i	0.317587	−	0.948229i	$-0.397128\pi$
$710$		−	0.0805737i		−	0.00302388i
$711$		0			0
$712$	−13.7744	−	13.7744i	−0.516216	−	0.516216i
$713$	16.6010			0.621712
$714$		0			0
$715$	−0.151638			−0.00567096
$716$	8.94516	+	8.94516i	0.334296	+	0.334296i
$717$		0			0
$718$		−	8.32133i		−	0.310549i
$719$	7.61734	+	18.3899i	0.284079	+	0.685827i	0.999923	−	0.0124334i	$-0.00395779\pi$
$719$	7.61734	+	18.3899i	0.284079	+	0.685827i	−0.715844	+	0.698260i	$0.753958\pi$
$720$		0			0
$721$	1.00139	−	2.41756i	0.0372936	−	0.0900348i
$722$	−6.24125	+	6.24125i	−0.232275	+	0.232275i
$723$		0			0
$724$	12.4269	−	30.0013i	0.461843	−	1.11499i
$725$	−11.1190	−	4.60565i	−0.412950	−	0.171050i
$726$		0			0
$727$		−	3.61240i		−	0.133977i	−0.997754	−	0.0669883i	$-0.978661\pi$
$727$		−	3.61240i		−	0.133977i	0.997754	−	0.0669883i	$-0.0213390\pi$
$728$	1.41714	−	0.586999i	0.0525227	−	0.0217556i
$729$		0			0
$730$	0.222705			0.00824267
$731$	−16.7544	−	8.12231i	−0.619685	−	0.300414i
$732$		0			0
$733$	6.03103	+	6.03103i	0.222761	+	0.222761i	0.809660	−	0.586899i	$-0.199651\pi$
$733$	6.03103	+	6.03103i	0.222761	+	0.222761i	−0.586899	+	0.809660i	$0.699651\pi$
$734$	−8.44747	+	3.49906i	−0.311802	+	0.129153i
$735$		0			0
$736$	−7.07669	−	17.0846i	−0.260850	−	0.629748i
$737$	−15.9816	−	6.61979i	−0.588690	−	0.243843i
$738$		0			0
$739$	−15.6825	+	15.6825i	−0.576890	+	0.576890i	−0.934045	−	0.357155i	$-0.883747\pi$
$739$	−15.6825	+	15.6825i	−0.576890	+	0.576890i	0.357155	+	0.934045i	$0.383747\pi$
$740$	−0.600970	+	0.600970i	−0.0220921	+	0.0220921i
$741$		0			0
$742$	10.0100	+	4.14629i	0.367480	+	0.152215i
$743$	9.91023	+	23.9254i	0.363571	+	0.877738i	0.994772	+	0.102119i	$0.0325623\pi$
$743$	9.91023	+	23.9254i	0.363571	+	0.877738i	−0.631201	+	0.775619i	$0.717438\pi$
$744$		0			0
$745$	−1.24763	+	0.516783i	−0.0457095	+	0.0189335i
$746$	−3.71893	−	3.71893i	−0.136160	−	0.136160i
$747$		0			0
$748$	−42.4947	−	2.49744i	−1.55376	−	0.0913154i
$749$	46.9530			1.71563
$750$		0			0
$751$	−3.91962	+	1.62356i	−0.143029	+	0.0592445i	−0.453050	−	0.891485i	$-0.649664\pi$
$751$	−3.91962	+	1.62356i	−0.143029	+	0.0592445i	0.310021	+	0.950730i	$0.399664\pi$
$752$			31.6393i			1.15377i
$753$		0			0
$754$	0.326805	+	0.135367i	0.0119016	+	0.00492979i
$755$	0.290010	−	0.700146i	0.0105545	−	0.0254809i
$756$		0			0
$757$	5.57075	−	5.57075i	0.202472	−	0.202472i	−0.598586	−	0.801058i	$-0.704271\pi$
$757$	5.57075	−	5.57075i	0.202472	−	0.202472i	0.801058	+	0.598586i	$0.204271\pi$
$758$	−1.15987	+	2.80018i	−0.0421285	+	0.101707i
$759$		0			0
$760$	0.191308	+	0.461859i	0.00693948	+	0.0167534i
$761$		−	45.9699i		−	1.66641i	−0.552965	−	0.833205i	$-0.686504\pi$
$761$		−	45.9699i		−	1.66641i	0.552965	−	0.833205i	$-0.313496\pi$
$762$		0			0
$763$	21.8508	+	21.8508i	0.791052	+	0.791052i
$764$	9.06893			0.328102
$765$		0			0
$766$	−1.63542			−0.0590903
$767$	−3.12734	−	3.12734i	−0.112922	−	0.112922i
$768$		0			0
$769$			17.5627i			0.633328i	0.948538	+	0.316664i	$0.102563\pi$
$769$			17.5627i			0.633328i	−0.948538	+	0.316664i	$0.897437\pi$
$770$	0.103711	+	0.250380i	0.00373748	+	0.00902307i
$771$		0			0
$772$	−5.62635	+	13.5832i	−0.202497	+	0.488871i
$773$	12.3939	−	12.3939i	0.445776	−	0.445776i	−0.448172	−	0.893948i	$-0.647925\pi$
$773$	12.3939	−	12.3939i	0.445776	−	0.445776i	0.893948	+	0.448172i	$0.147925\pi$
$774$		0			0
$775$	6.03331	−	14.5657i	0.216723	−	0.523215i
$776$	3.93815	+	1.63124i	0.141371	+	0.0585579i
$777$		0			0
$778$			0.419669i			0.0150459i
$779$	−14.1344	+	5.85465i	−0.506416	+	0.209765i
$780$		0			0
$781$	−23.4509			−0.839138
$782$	−5.07641	+	4.51285i	−0.181532	+	0.161379i
$783$		0			0
$784$	0.400999	+	0.400999i	0.0143214	+	0.0143214i
$785$	0.137631	−	0.0570085i	0.00491225	−	0.00203472i
$786$		0			0
$787$	12.2537	+	29.5830i	0.436797	+	1.05452i	0.977048	+	0.213018i	$0.0683292\pi$
$787$	12.2537	+	29.5830i	0.436797	+	1.05452i	−0.540251	+	0.841504i	$0.681671\pi$
$788$	3.33926	+	1.38317i	0.118956	+	0.0492732i
$789$		0			0
$790$	0.140776	−	0.140776i	0.00500859	−	0.00500859i
$791$	−8.62491	+	8.62491i	−0.306667	+	0.306667i
$792$		0			0
$793$	0.788660	+	0.326674i	0.0280061	+	0.0116005i
$794$	−1.54545	−	3.73105i	−0.0548460	−	0.132410i
$795$		0			0
$796$	−15.0610	+	6.23847i	−0.533823	+	0.221117i
$797$	3.77414	+	3.77414i	0.133687	+	0.133687i	0.770784	−	0.637097i	$-0.219865\pi$
$797$	3.77414	+	3.77414i	0.133687	+	0.133687i	−0.637097	+	0.770784i	$0.719865\pi$
$798$		0			0
$799$	36.0220	−	12.4995i	1.27437	−	0.442200i
$800$	−17.5619			−0.620908
$801$		0			0
$802$	−3.62453	+	1.50133i	−0.127986	+	0.0530137i
$803$		−	64.8179i		−	2.28737i
$804$		0			0
$805$	−0.775008	−	0.321019i	−0.0273154	−	0.0113144i
$806$	−0.177328	+	0.428109i	−0.00624613	+	0.0150795i
$807$		0			0
$808$	−3.80829	+	3.80829i	−0.133975	+	0.133975i
$809$	−15.5314	+	37.4960i	−0.546054	+	1.31829i	0.374338	+	0.927293i	$0.377870\pi$
$809$	−15.5314	+	37.4960i	−0.546054	+	1.31829i	−0.920391	+	0.390998i	$0.872130\pi$
$810$		0			0
$811$	8.29520	+	20.0264i	0.291284	+	0.703221i	0.999997	−	0.00227504i	$-0.000724170\pi$
$811$	8.29520	+	20.0264i	0.291284	+	0.703221i	−0.708714	+	0.705496i	$0.750724\pi$
$812$			12.2637i			0.430371i
$813$		0			0
$814$	−9.01668	−	9.01668i	−0.316034	−	0.316034i
$815$	−0.640204			−0.0224254
$816$		0			0
$817$	31.0213			1.08530
$818$	−0.0346035	−	0.0346035i	−0.00120988	−	0.00120988i
$819$		0			0
$820$			0.252303i			0.00881081i
$821$	−1.16146	−	2.80401i	−0.0405353	−	0.0978608i	0.902315	−	0.431077i	$-0.141866\pi$
$821$	−1.16146	−	2.80401i	−0.0405353	−	0.0978608i	−0.942851	+	0.333216i	$0.891866\pi$
$822$		0			0
$823$	−2.32792	+	5.62009i	−0.0811462	+	0.195904i	−0.959245	−	0.282574i	$-0.908812\pi$
$823$	−2.32792	+	5.62009i	−0.0811462	+	0.195904i	0.878099	+	0.478479i	$0.158812\pi$
$824$	0.844526	−	0.844526i	0.0294205	−	0.0294205i
$825$		0			0
$826$	−3.02486	+	7.30266i	−0.105248	+	0.254092i
$827$	21.1076	+	8.74304i	0.733982	+	0.304025i	0.718187	−	0.695850i	$-0.244972\pi$
$827$	21.1076	+	8.74304i	0.733982	+	0.304025i	0.0157948	+	0.999875i	$0.494972\pi$
$828$		0			0
$829$		−	5.37918i		−	0.186827i	−0.995627	−	0.0934133i	$-0.970222\pi$
$829$		−	5.37918i		−	0.186827i	0.995627	−	0.0934133i	$-0.0297778\pi$
$830$	−0.150071	+	0.0621616i	−0.00520905	+	0.00215766i
$831$		0			0
$832$	−2.69302			−0.0933638
$833$	0.298126	−	0.614965i	0.0103295	−	0.0213073i
$834$		0			0
$835$	−0.388539	−	0.388539i	−0.0134460	−	0.0134460i
$836$	65.5229	−	27.1405i	2.26616	−	0.938673i
$837$		0			0
$838$	3.17791	+	7.67215i	0.109779	+	0.265030i
$839$	1.41160	+	0.584702i	0.0487337	+	0.0201862i	0.406917	−	0.913465i	$-0.366604\pi$
$839$	1.41160	+	0.584702i	0.0487337	+	0.0201862i	−0.358183	+	0.933651i	$0.616604\pi$
$840$		0			0
$841$	16.4034	−	16.4034i	0.565636	−	0.565636i
$842$	−5.89550	+	5.89550i	−0.203172	+	0.203172i
$843$		0			0
$844$	−34.6187	−	14.3395i	−1.19162	−	0.493587i
$845$	−0.291308	−	0.703279i	−0.0100213	−	0.0241935i
$846$		0			0
$847$	45.6684	−	18.9165i	1.56918	−	0.649977i
$848$	−31.2720	−	31.2720i	−1.07389	−	1.07389i
$849$		0			0
$850$	2.11464	+	6.09414i	0.0725317	+	0.209027i
$851$	39.4701			1.35302
$852$		0			0
$853$	−19.7045	+	8.16188i	−0.674670	+	0.279457i	−0.693597	−	0.720364i	$-0.743975\pi$
$853$	−19.7045	+	8.16188i	−0.674670	+	0.279457i	0.0189270	+	0.999821i	$0.493975\pi$
$854$		−	1.52563i		−	0.0522060i
$855$		0			0
$856$	19.7991	+	8.20104i	0.676718	+	0.280306i
$857$	−1.76691	+	4.26569i	−0.0603564	+	0.145713i	−0.951181	−	0.308635i	$-0.900128\pi$
$857$	−1.76691	+	4.26569i	−0.0603564	+	0.145713i	0.890824	+	0.454348i	$0.150128\pi$
$858$		0			0
$859$	26.2760	−	26.2760i	0.896525	−	0.896525i	−0.0986015	−	0.995127i	$-0.531437\pi$
$859$	26.2760	−	26.2760i	0.896525	−	0.896525i	0.995127	+	0.0986015i	$0.0314369\pi$
$860$	0.195777	−	0.472647i	0.00667594	−	0.0161171i
$861$		0			0
$862$	3.81703	+	9.21513i	0.130009	+	0.313869i
$863$			32.4840i			1.10577i	0.833258	+	0.552884i	$0.186473\pi$
$863$			32.4840i			1.10577i	−0.833258	+	0.552884i	$0.813527\pi$
$864$		0			0
$865$	0.0666257	+	0.0666257i	0.00226534	+	0.00226534i
$866$	−10.6958			−0.363458
$867$		0			0
$868$	−16.0652			−0.545287
$869$	−40.9727	−	40.9727i	−1.38990	−	1.38990i
$870$		0			0
$871$			1.49457i			0.0506415i
$872$	5.39744	+	13.0306i	0.182780	+	0.441271i
$873$		0			0
$874$	4.33064	−	10.4551i	0.146486	−	0.353649i
$875$	−1.12705	+	1.12705i	−0.0381011	+	0.0381011i
$876$		0			0
$877$	−1.06535	+	2.57197i	−0.0359741	+	0.0868493i	−0.940846	−	0.338836i	$-0.889967\pi$
$877$	−1.06535	+	2.57197i	−0.0359741	+	0.0868493i	0.904871	+	0.425685i	$0.139967\pi$
$878$	−8.58919	−	3.55776i	−0.289871	−	0.120069i
$879$		0			0
$880$		−	1.10620i		−	0.0372901i
$881$	−47.0398	+	19.4845i	−1.58481	+	0.656450i	−0.989167	−	0.146797i	$-0.953103\pi$
$881$	−47.0398	+	19.4845i	−1.58481	+	0.656450i	−0.595645	+	0.803248i	$0.703103\pi$
$882$		0			0
$883$	36.5258			1.22919			0.614596	−	0.788842i	$-0.289319\pi$
$883$	36.5258			1.22919			0.614596	+	0.788842i	$0.289319\pi$
$884$	1.20568	+	3.47462i	0.0405513	+	0.116864i
$885$		0			0
$886$	−3.46251	−	3.46251i	−0.116325	−	0.116325i
$887$	24.1541	−	10.0049i	0.811014	−	0.335933i	0.0616555	−	0.998097i	$-0.480362\pi$
$887$	24.1541	−	10.0049i	0.811014	−	0.335933i	0.749359	+	0.662164i	$0.230362\pi$
$888$		0			0
$889$	−5.68199	−	13.7175i	−0.190568	−	0.460071i
$890$	−0.274726	−	0.113795i	−0.00920884	−	0.00381442i
$891$		0			0
$892$	−28.7933	+	28.7933i	−0.964070	+	0.964070i
$893$	−44.9194	+	44.9194i	−1.50317	+	1.50317i
$894$		0			0
$895$	0.366014	+	0.151608i	0.0122345	+	0.00506770i
$896$	9.04315	+	21.8321i	0.302110	+	0.729359i
$897$		0			0
$898$	−2.43956	+	1.01050i	−0.0814093	+	0.0337208i
$899$	−5.37439	−	5.37439i	−0.179246	−	0.179246i
$900$		0			0
$901$	−23.2495	+	47.9582i	−0.774552	+	1.59772i
$902$	−3.78544			−0.126041
$903$		0			0
$904$	−5.14340	+	2.13047i	−0.171067	+	0.0708583i
$905$		−	1.01696i		−	0.0338049i
$906$		0			0
$907$	43.9800	+	18.2171i	1.46033	+	0.604890i	0.964631	−	0.263603i	$-0.0849108\pi$
$907$	43.9800	+	18.2171i	1.46033	+	0.604890i	0.495702	+	0.868493i	$0.334911\pi$
$908$	5.95138	−	14.3679i	0.197504	−	0.476816i
$909$		0			0
$910$	0.0165569	−	0.0165569i	0.000548857	−	0.000548857i
$911$	13.8928	−	33.5403i	0.460290	−	1.11124i	−0.507988	−	0.861364i	$-0.669611\pi$
$911$	13.8928	−	33.5403i	0.460290	−	1.11124i	0.968278	−	0.249875i	$-0.0803894\pi$
$912$		0			0
$913$	18.0920	+	43.6780i	0.598759	+	1.44553i
$914$			7.46421i			0.246894i
$915$		0			0
$916$	27.4883	+	27.4883i	0.908240	+	0.908240i
$917$	16.8409			0.556135
$918$		0			0
$919$	−1.14473			−0.0377611			−0.0188806	−	0.999822i	$-0.506010\pi$
$919$	−1.14473			−0.0377611			−0.0188806	+	0.999822i	$0.506010\pi$
$920$	−0.270733	−	0.270733i	−0.00892581	−	0.00892581i
$921$		0			0
$922$		−	1.14006i		−	0.0375459i
$923$	0.775370	+	1.87191i	0.0255216	+	0.0616146i
$924$		0			0
$925$	14.3446	−	34.6310i	0.471648	−	1.13866i
$926$	4.59440	−	4.59440i	0.150981	−	0.150981i
$927$		0			0
$928$	−3.23996	+	7.82195i	−0.106357	+	0.256768i
$929$	40.8677	+	16.9279i	1.34083	+	0.555388i	0.933724	−	0.357995i	$-0.116540\pi$
$929$	40.8677	+	16.9279i	1.34083	+	0.555388i	0.407102	+	0.913383i	$0.366540\pi$
$930$		0			0
$931$			1.13862i			0.0373169i
$932$	−26.1423	+	10.8285i	−0.856319	+	0.354699i
$933$		0			0
$934$	−11.3618			−0.371771
$935$	−1.25944	+	0.437019i	−0.0411880	+	0.0142921i
$936$		0			0
$937$	3.40623	+	3.40623i	0.111277	+	0.111277i	0.760553	−	0.649276i	$-0.224928\pi$
$937$	3.40623	+	3.40623i	0.111277	+	0.111277i	−0.649276	+	0.760553i	$0.724928\pi$
$938$	2.46778	−	1.02219i	0.0805758	−	0.0333756i
$939$		0			0
$940$	0.400913	+	0.967890i	0.0130763	+	0.0315691i
$941$	46.5982	+	19.3016i	1.51906	+	0.629214i	0.977403	−	0.211386i	$-0.0677978\pi$
$941$	46.5982	+	19.3016i	1.51906	+	0.629214i	0.541655	+	0.840601i	$0.317798\pi$
$942$		0			0
$943$	8.28530	−	8.28530i	0.269806	−	0.269806i
$944$	22.8140	−	22.8140i	0.742532	−	0.742532i
$945$		0			0
$946$	7.09138	+	2.93735i	0.230561	+	0.0955014i
$947$	8.78638	+	21.2122i	0.285519	+	0.689304i	0.999946	−	0.0104062i	$-0.00331245\pi$
$947$	8.78638	+	21.2122i	0.285519	+	0.689304i	−0.714427	+	0.699710i	$0.753312\pi$
$948$		0			0
$949$	−5.17393	+	2.14311i	−0.167953	+	0.0695684i
$950$	−7.59940	−	7.59940i	−0.246557	−	0.246557i
$951$		0			0
$952$	10.0784	−	8.95950i	0.326642	−	0.290379i
$953$	22.2611			0.721108			0.360554	−	0.932738i	$-0.382588\pi$
$953$	22.2611			0.721108			0.360554	+	0.932738i	$0.382588\pi$
$954$		0			0
$955$	0.262392	−	0.108686i	0.00849082	−	0.00351701i
$956$			40.1273i			1.29781i
$957$		0			0
$958$	−7.32006	−	3.03207i	−0.236500	−	0.0979617i
$959$	−8.65216	+	20.8882i	−0.279393	+	0.674514i
$960$		0			0
$961$	−14.8800	+	14.8800i	−0.479999	+	0.479999i
$962$	−0.421611	+	1.01786i	−0.0135933	+	0.0328171i
$963$		0			0
$964$	8.46966	+	20.4476i	0.272789	+	0.658572i
$965$			0.460434i			0.0148219i
$966$		0			0
$967$	28.6694	+	28.6694i	0.921944	+	0.921944i	0.997167	−	0.0752224i	$-0.0239667\pi$
$967$	28.6694	+	28.6694i	0.921944	+	0.921944i	−0.0752224	+	0.997167i	$0.523967\pi$
$968$	22.5614			0.725150
$969$		0			0
$970$	0.0650691			0.00208924
$971$	5.27642	+	5.27642i	0.169328	+	0.169328i	0.786684	−	0.617356i	$-0.211796\pi$
$971$	5.27642	+	5.27642i	0.169328	+	0.169328i	−0.617356	+	0.786684i	$0.711796\pi$
$972$		0			0
$973$			14.8185i			0.475059i
$974$	−2.47977	−	5.98669i	−0.0794570	−	0.191826i
$975$		0			0
$976$	−2.38309	+	5.75328i	−0.0762808	+	0.184158i
$977$	−1.22888	+	1.22888i	−0.0393153	+	0.0393153i	−0.726491	−	0.687176i	$-0.758850\pi$
$977$	−1.22888	+	1.22888i	−0.0393153	+	0.0393153i	0.687176	+	0.726491i	$0.258850\pi$
$978$		0			0
$979$	−33.1199	+	79.9586i	−1.05852	+	2.55549i
$980$	0.0173483	+	0.00718591i	0.000554172	+	0.000229546i
$981$		0			0
$982$			5.19645i			0.165826i
$983$	−49.9069	+	20.6721i	−1.59178	+	0.659338i	−0.990223	−	0.139491i	$-0.955454\pi$
$983$	−49.9069	+	20.6721i	−1.59178	+	0.659338i	−0.601559	+	0.798828i	$0.705454\pi$
$984$		0			0
$985$	0.113192			0.00360658
$986$	3.10441	+	0.182448i	0.0988647	+	0.00581033i
$987$		0			0
$988$	−4.33285	−	4.33285i	−0.137846	−	0.137846i
$989$	−21.9501	+	9.09205i	−0.697974	+	0.289110i
$990$		0			0
$991$	−2.66540	−	6.43485i	−0.0846692	−	0.204410i	0.875874	−	0.482539i	$-0.160285\pi$
$991$	−2.66540	−	6.43485i	−0.0846692	−	0.204410i	−0.960544	+	0.278130i	$0.910285\pi$
$992$	−10.2466	−	4.24428i	−0.325330	−	0.134756i
$993$		0			0
$994$	2.56053	−	2.56053i	0.0812150	−	0.0812150i
$995$	−0.360997	+	0.360997i	−0.0114444	+	0.0114444i
$996$		0			0
$997$	−43.1441	−	17.8709i	−1.36639	−	0.565976i	−0.425581	−	0.904920i	$-0.639930\pi$
$997$	−43.1441	−	17.8709i	−1.36639	−	0.565976i	−0.940807	+	0.338944i	$0.889930\pi$
$998$	3.42366	+	8.26545i	0.108374	+	0.261638i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.2.l.a.325.7	yes	48
3.2	odd	2	inner	459.2.l.a.325.6	yes	48
17.3	odd	16		7803.2.a.cd.1.14		24
17.9	even	8	inner	459.2.l.a.298.7	yes	48
17.14	odd	16		7803.2.a.cg.1.14		24
51.14	even	16		7803.2.a.cd.1.11		24
51.20	even	16		7803.2.a.cg.1.11		24
51.26	odd	8	inner	459.2.l.a.298.6	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
459.2.l.a.298.6	✓	48	51.26	odd	8	inner
459.2.l.a.298.7	yes	48	17.9	even	8	inner
459.2.l.a.325.6	yes	48	3.2	odd	2	inner
459.2.l.a.325.7	yes	48	1.1	even	1	trivial
7803.2.a.cd.1.11		24	51.14	even	16
7803.2.a.cd.1.14		24	17.3	odd	16
7803.2.a.cg.1.11		24	51.20	even	16
7803.2.a.cg.1.14		24	17.14	odd	16

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:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	459.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.221411 + 0.221411i) q^{2} -1.90195i q^{4} +(-0.0227939 - 0.0550294i) q^{5} +(1.02440 - 2.47313i) q^{7} +(0.863936 - 0.863936i) q^{8} +(0.00713730 - 0.0172310i) q^{10} +(-5.01504 - 2.07730i) q^{11} +0.468997i q^{13} +(0.774391 - 0.320763i) q^{14} -3.42134 q^{16} +(1.35164 + 3.89526i) q^{17} +(-4.85739 - 4.85739i) q^{19} +(-0.104663 + 0.0433530i) q^{20} +(-0.650449 - 1.57032i) q^{22} +(4.86066 + 2.01335i) q^{23} +(3.53303 - 3.53303i) q^{25} +(-0.103841 + 0.103841i) q^{26} +(-4.70377 - 1.94837i) q^{28} +(-0.921784 - 2.22538i) q^{29} +(2.91521 - 1.20752i) q^{31} +(-2.48539 - 2.48539i) q^{32} +(-0.563186 + 1.16172i) q^{34} -0.159445 q^{35} +(6.93112 - 2.87096i) q^{37} -2.15096i q^{38} +(-0.0672344 - 0.0278494i) q^{40} +(0.852281 - 2.05759i) q^{41} +(-3.19320 + 3.19320i) q^{43} +(-3.95093 + 9.53839i) q^{44} +(0.630426 + 1.52198i) q^{46} -9.24764i q^{47} +(-0.117205 - 0.117205i) q^{49} +1.56450 q^{50} +0.892011 q^{52} +(9.14029 + 9.14029i) q^{53} +0.323325i q^{55} +(-1.25160 - 3.02164i) q^{56} +(0.288631 - 0.696818i) q^{58} +(-6.66815 + 6.66815i) q^{59} +(0.696537 - 1.68159i) q^{61} +(0.912817 + 0.378101i) q^{62} +5.74209i q^{64} +(0.0258086 - 0.0106903i) q^{65} +3.18673 q^{67} +(7.40861 - 2.57076i) q^{68} +(-0.0353029 - 0.0353029i) q^{70} +(3.99130 - 1.65325i) q^{71} +(4.56957 + 11.0319i) q^{73} +(2.17029 + 0.898963i) q^{74} +(-9.23854 + 9.23854i) q^{76} +(-10.2748 + 10.2748i) q^{77} +(9.86201 + 4.08498i) q^{79} +(0.0779858 + 0.188274i) q^{80} +(0.644277 - 0.266868i) q^{82} +(-6.15847 - 6.15847i) q^{83} +(0.183545 - 0.163168i) q^{85} -1.41402 q^{86} +(-6.12733 + 2.53802i) q^{88} -15.9437i q^{89} +(1.15989 + 0.480442i) q^{91} +(3.82930 - 9.24476i) q^{92} +(2.04753 - 2.04753i) q^{94} +(-0.156580 + 0.378019i) q^{95} +(1.33512 + 3.22326i) q^{97} -0.0519011i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 16 q^{10} - 48 q^{16} - 16 q^{19} - 24 q^{22} + 16 q^{25} + 24 q^{28} - 40 q^{31} + 64 q^{34} + 48 q^{37} - 48 q^{40} - 8 q^{43} + 24 q^{46} - 16 q^{49} + 32 q^{52} + 64 q^{58} - 24 q^{61} - 32 q^{67}+ \cdots - 88 q^{97}+O(q^{100}) \) 48 * q - 16 * q^10 - 48 * q^16 - 16 * q^19 - 24 * q^22 + 16 * q^25 + 24 * q^28 - 40 * q^31 + 64 * q^34 + 48 * q^37 - 48 * q^40 - 8 * q^43 + 24 * q^46 - 16 * q^49 + 32 * q^52 + 64 * q^58 - 24 * q^61 - 32 * q^67 + 96 * q^70 + 48 * q^73 + 96 * q^76 - 48 * q^79 + 112 * q^82 - 56 * q^85 - 160 * q^88 - 80 * q^91 - 40 * q^94 - 88 * q^97

Introduction

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