LMFDB - Embedded newform 765.2.be.b.631.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [765,2,Mod(406,765)] 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("765.406"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(765, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 0, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 765 = 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	765.be (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.10855575463$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			631.3
Character	$\chi$	$=$	765.631
Dual form			765.2.be.b.451.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.213325 - 0.213325i) q^{2} -1.90899i q^{4} +(0.382683 + 0.923880i) q^{5} +(-0.960473 + 2.31879i) q^{7} +(-0.833883 + 0.833883i) q^{8} +(0.115451 - 0.278722i) q^{10} +(-2.25941 - 0.935880i) q^{11} +5.61335i q^{13} +(0.699548 - 0.289762i) q^{14} -3.46219 q^{16} +(-2.76113 + 3.06205i) q^{17} +(-5.04243 - 5.04243i) q^{19} +(1.76367 - 0.730537i) q^{20} +(0.282343 + 0.681636i) q^{22} +(-0.795280 - 0.329416i) q^{23} +(-0.707107 + 0.707107i) q^{25} +(1.19747 - 1.19747i) q^{26} +(4.42653 + 1.83353i) q^{28} +(1.43561 + 3.46587i) q^{29} +(-2.07626 + 0.860015i) q^{31} +(2.40634 + 2.40634i) q^{32} +(1.24223 - 0.0641935i) q^{34} -2.50984 q^{35} +(4.71693 - 1.95382i) q^{37} +2.15135i q^{38} +(-1.08952 - 0.451294i) q^{40} +(-4.72598 + 11.4095i) q^{41} +(-1.85272 + 1.85272i) q^{43} +(-1.78658 + 4.31319i) q^{44} +(0.0993804 + 0.239926i) q^{46} -2.30114i q^{47} +(0.495478 + 0.495478i) q^{49} +0.301687 q^{50} +10.7158 q^{52} +(-1.96204 - 1.96204i) q^{53} -2.44557i q^{55} +(-1.13268 - 2.73452i) q^{56} +(0.433105 - 1.04561i) q^{58} +(5.26206 - 5.26206i) q^{59} +(-0.346822 + 0.837303i) q^{61} +(0.626380 + 0.259455i) q^{62} +5.89773i q^{64} +(-5.18606 + 2.14814i) q^{65} -6.69889 q^{67} +(5.84541 + 5.27096i) q^{68} +(0.535411 + 0.535411i) q^{70} +(-0.222439 + 0.0921372i) q^{71} +(-2.47116 - 5.96591i) q^{73} +(-1.42304 - 0.589441i) q^{74} +(-9.62592 + 9.62592i) q^{76} +(4.34022 - 4.34022i) q^{77} +(13.5899 + 5.62912i) q^{79} +(-1.32492 - 3.19865i) q^{80} +(3.44210 - 1.42577i) q^{82} +(9.82767 + 9.82767i) q^{83} +(-3.88561 - 1.37916i) q^{85} +0.790460 q^{86} +(2.66450 - 1.10367i) q^{88} +0.395163i q^{89} +(-13.0162 - 5.39148i) q^{91} +(-0.628850 + 1.51818i) q^{92} +(-0.490889 + 0.490889i) q^{94} +(2.72894 - 6.58825i) q^{95} +(3.42855 + 8.27725i) q^{97} -0.211396i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{11} - 24 q^{16} + 8 q^{17} - 8 q^{19} - 32 q^{22} + 16 q^{23} - 16 q^{26} + 48 q^{28} + 8 q^{29} + 16 q^{34} + 32 q^{35} + 24 q^{37} + 16 q^{40} - 16 q^{41} + 8 q^{43} - 16 q^{44} + 8 q^{46}+ \cdots - 40 q^{97}+O(q^{100}) $ 24 * q + 8 * q^11 - 24 * q^16 + 8 * q^17 - 8 * q^19 - 32 * q^22 + 16 * q^23 - 16 * q^26 + 48 * q^28 + 8 * q^29 + 16 * q^34 + 32 * q^35 + 24 * q^37 + 16 * q^40 - 16 * q^41 + 8 * q^43 - 16 * q^44 + 8 * q^46 - 8 * q^50 - 48 * q^52 - 24 * q^53 - 64 * q^56 - 64 * q^58 - 32 * q^59 + 32 * q^61 + 32 * q^62 - 8 * q^65 + 16 * q^67 + 40 * q^68 + 24 * q^71 + 64 * q^74 - 8 * q^76 - 24 * q^77 + 32 * q^80 - 80 * q^82 + 96 * q^83 + 16 * q^86 - 8 * q^88 - 24 * q^91 - 80 * q^92 + 56 * q^94 + 16 * q^95 - 40 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/765\mathbb{Z}\right)^\times$.

$n$	$307$	$496$	$596$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.213325	−	0.213325i	−0.150843	−	0.150843i	0.627651	−	0.778495i	$-0.284016\pi$
$2$	−0.213325	−	0.213325i	−0.150843	−	0.150843i	−0.778495	+	0.627651i	$0.784016\pi$
$3$		0			0
$3$		0			0
$4$		−	1.90899i		−	0.954493i
$5$	0.382683	+	0.923880i	0.171141	+	0.413171i
$5$	0.382683	+	0.923880i	0.171141	+	0.413171i
$6$		0			0
$7$	−0.960473	+	2.31879i	−0.363025	+	0.876420i	0.631830	+	0.775107i	$0.282304\pi$
$7$	−0.960473	+	2.31879i	−0.363025	+	0.876420i	−0.994855	+	0.101312i	$0.967696\pi$
$8$	−0.833883	+	0.833883i	−0.294822	+	0.294822i
$9$		0			0
$10$	0.115451	−	0.278722i	0.0365087	−	0.0881397i
$11$	−2.25941	−	0.935880i	−0.681239	−	0.282179i	0.0151056	−	0.999886i	$-0.495192\pi$
$11$	−2.25941	−	0.935880i	−0.681239	−	0.282179i	−0.696345	+	0.717707i	$0.745192\pi$
$12$		0			0
$13$			5.61335i			1.55686i	0.627729	+	0.778432i	$0.283985\pi$
$13$			5.61335i			1.55686i	−0.627729	+	0.778432i	$0.716015\pi$
$14$	0.699548	−	0.289762i	0.186962	−	0.0774422i
$15$		0			0
$16$	−3.46219			−0.865549
$17$	−2.76113	+	3.06205i	−0.669673	+	0.742656i
$17$	−2.76113	+	3.06205i	−0.669673	+	0.742656i
$18$		0			0
$19$	−5.04243	−	5.04243i	−1.15681	−	1.15681i	−0.985157	−	0.171655i	$-0.945089\pi$
$19$	−5.04243	−	5.04243i	−1.15681	−	1.15681i	−0.171655	−	0.985157i	$-0.554911\pi$
$20$	1.76367	−	0.730537i	0.394369	−	0.163353i
$21$		0			0
$22$	0.282343	+	0.681636i	0.0601957	+	0.145325i
$23$	−0.795280	−	0.329416i	−0.165827	−	0.0686880i	0.298226	−	0.954495i	$-0.403605\pi$
$23$	−0.795280	−	0.329416i	−0.165827	−	0.0686880i	−0.464053	+	0.885807i	$0.653605\pi$
$24$		0			0
$25$	−0.707107	+	0.707107i	−0.141421	+	0.141421i
$26$	1.19747	−	1.19747i	0.234843	−	0.234843i
$27$		0			0
$28$	4.42653	+	1.83353i	0.836536	+	0.346505i
$29$	1.43561	+	3.46587i	0.266586	+	0.643597i	0.999318	−	0.0369210i	$-0.0117550\pi$
$29$	1.43561	+	3.46587i	0.266586	+	0.643597i	−0.732732	+	0.680518i	$0.761755\pi$
$30$		0			0
$31$	−2.07626	+	0.860015i	−0.372907	+	0.154463i	−0.561263	−	0.827638i	$-0.689684\pi$
$31$	−2.07626	+	0.860015i	−0.372907	+	0.154463i	0.188356	+	0.982101i	$0.439684\pi$
$32$	2.40634	+	2.40634i	0.425385	+	0.425385i
$33$		0			0
$34$	1.24223	−	0.0641935i	0.213041	−	0.0110091i
$35$	−2.50984			−0.424240
$36$		0			0
$37$	4.71693	−	1.95382i	0.775459	−	0.321206i	0.0403776	−	0.999184i	$-0.487144\pi$
$37$	4.71693	−	1.95382i	0.775459	−	0.321206i	0.735081	+	0.677979i	$0.237144\pi$
$38$			2.15135i			0.348995i
$39$		0			0
$40$	−1.08952	−	0.451294i	−0.172268	−	0.0713559i
$41$	−4.72598	+	11.4095i	−0.738074	+	1.78187i	−0.124518	+	0.992217i	$0.539738\pi$
$41$	−4.72598	+	11.4095i	−0.738074	+	1.78187i	−0.613556	+	0.789651i	$0.710262\pi$
$42$		0			0
$43$	−1.85272	+	1.85272i	−0.282536	+	0.282536i	−0.834120	−	0.551583i	$-0.814024\pi$
$43$	−1.85272	+	1.85272i	−0.282536	+	0.282536i	0.551583	+	0.834120i	$0.314024\pi$
$44$	−1.78658	+	4.31319i	−0.269337	+	0.650238i
$45$		0			0
$46$	0.0993804	+	0.239926i	0.0146528	+	0.0353751i
$47$		−	2.30114i		−	0.335655i	−0.985816	−	0.167828i	$-0.946325\pi$
$47$		−	2.30114i		−	0.335655i	0.985816	−	0.167828i	$-0.0536752\pi$
$48$		0			0
$49$	0.495478	+	0.495478i	0.0707826	+	0.0707826i
$50$	0.301687			0.0426650
$51$		0			0
$52$	10.7158			1.48602
$53$	−1.96204	−	1.96204i	−0.269507	−	0.269507i	0.559394	−	0.828902i	$-0.311034\pi$
$53$	−1.96204	−	1.96204i	−0.269507	−	0.269507i	−0.828902	+	0.559394i	$0.811034\pi$
$54$		0			0
$55$		−	2.44557i		−	0.329761i
$56$	−1.13268	−	2.73452i	−0.151360	−	0.365416i
$57$		0			0
$58$	0.433105	−	1.04561i	0.0568695	−	0.137295i
$59$	5.26206	−	5.26206i	0.685062	−	0.685062i	−0.276075	−	0.961136i	$-0.589034\pi$
$59$	5.26206	−	5.26206i	0.685062	−	0.685062i	0.961136	+	0.276075i	$0.0890337\pi$
$60$		0			0
$61$	−0.346822	+	0.837303i	−0.0444061	+	0.107206i	−0.944526	−	0.328436i	$-0.893478\pi$
$61$	−0.346822	+	0.837303i	−0.0444061	+	0.107206i	0.900120	+	0.435642i	$0.143478\pi$
$62$	0.626380	+	0.259455i	0.0795504	+	0.0329508i
$63$		0			0
$64$			5.89773i			0.737216i
$65$	−5.18606	+	2.14814i	−0.643252	+	0.266444i
$66$		0			0
$67$	−6.69889			−0.818399			−0.409200	−	0.912445i	$-0.634192\pi$
$67$	−6.69889			−0.818399			−0.409200	+	0.912445i	$0.634192\pi$
$68$	5.84541	+	5.27096i	0.708860	+	0.639198i
$69$		0			0
$70$	0.535411	+	0.535411i	0.0639938	+	0.0639938i
$71$	−0.222439	+	0.0921372i	−0.0263986	+	0.0109347i	−0.395844	−	0.918318i	$-0.629548\pi$
$71$	−0.222439	+	0.0921372i	−0.0263986	+	0.0109347i	0.369445	+	0.929253i	$0.379548\pi$
$72$		0			0
$73$	−2.47116	−	5.96591i	−0.289228	−	0.698257i	0.710759	−	0.703436i	$-0.248352\pi$
$73$	−2.47116	−	5.96591i	−0.289228	−	0.698257i	−0.999987	+	0.00517825i	$0.998352\pi$
$74$	−1.42304	−	0.589441i	−0.165425	−	0.0685211i
$75$		0			0
$76$	−9.62592	+	9.62592i	−1.10417	+	1.10417i
$77$	4.34022	−	4.34022i	0.494614	−	0.494614i
$78$		0			0
$79$	13.5899	+	5.62912i	1.52898	+	0.633325i	0.979366	−	0.202093i	$-0.0647743\pi$
$79$	13.5899	+	5.62912i	1.52898	+	0.633325i	0.549615	+	0.835418i	$0.314774\pi$
$80$	−1.32492	−	3.19865i	−0.148131	−	0.357620i
$81$		0			0
$82$	3.44210	−	1.42577i	0.380117	−	0.157449i
$83$	9.82767	+	9.82767i	1.07873	+	1.07873i	0.996624	+	0.0821031i	$0.0261637\pi$
$83$	9.82767	+	9.82767i	1.07873	+	1.07873i	0.0821031	+	0.996624i	$0.473836\pi$
$84$		0			0
$85$	−3.88561	−	1.37916i	−0.421453	−	0.149591i
$86$	0.790460			0.0852375
$87$		0			0
$88$	2.66450	−	1.10367i	0.284037	−	0.117652i
$89$			0.395163i			0.0418872i	0.999781	+	0.0209436i	$0.00666704\pi$
$89$			0.395163i			0.0418872i	−0.999781	+	0.0209436i	$0.993333\pi$
$90$		0			0
$91$	−13.0162	−	5.39148i	−1.36447	−	0.565181i
$92$	−0.628850	+	1.51818i	−0.0655621	+	0.158281i
$93$		0			0
$94$	−0.490889	+	0.490889i	−0.0506314	+	0.0506314i
$95$	2.72894	−	6.58825i	0.279983	−	0.675940i
$96$		0			0
$97$	3.42855	+	8.27725i	0.348116	+	0.840427i	0.996842	+	0.0794052i	$0.0253021\pi$
$97$	3.42855	+	8.27725i	0.348116	+	0.840427i	−0.648726	+	0.761022i	$0.724698\pi$
$98$		−	0.211396i		−	0.0213542i
$99$		0			0
$100$	1.34986	+	1.34986i	0.134986	+	0.134986i
$101$	−15.2882			−1.52124			−0.760619	−	0.649199i	$-0.775104\pi$
$101$	−15.2882			−1.52124			−0.760619	+	0.649199i	$0.775104\pi$
$102$		0			0
$103$	−14.7746			−1.45579			−0.727894	−	0.685690i	$-0.759501\pi$
$103$	−14.7746			−1.45579			−0.727894	+	0.685690i	$0.759501\pi$
$104$	−4.68088	−	4.68088i	−0.458998	−	0.458998i
$105$		0			0
$106$			0.837105i			0.0813068i
$107$	−0.562841	−	1.35882i	−0.0544119	−	0.131362i	0.894336	−	0.447396i	$-0.147649\pi$
$107$	−0.562841	−	1.35882i	−0.0544119	−	0.131362i	−0.948748	+	0.316034i	$0.897649\pi$
$108$		0			0
$109$	3.61166	−	8.71931i	0.345934	−	0.835158i	−0.651157	−	0.758943i	$-0.725716\pi$
$109$	3.61166	−	8.71931i	0.345934	−	0.835158i	0.997091	−	0.0762157i	$-0.0242838\pi$
$110$	−0.521701	+	0.521701i	−0.0497423	+	0.0497423i
$111$		0			0
$112$	3.32535	−	8.02809i	0.314216	−	0.758584i
$113$	−13.8222	−	5.72534i	−1.30028	−	0.538595i	−0.378249	−	0.925704i	$-0.623474\pi$
$113$	−13.8222	−	5.72534i	−1.30028	−	0.538595i	−0.922034	+	0.387109i	$0.873474\pi$
$114$		0			0
$115$		−	0.860805i		−	0.0802705i
$116$	6.61630	−	2.74056i	0.614308	−	0.254455i
$117$		0			0
$118$	−2.24505			−0.206674
$119$	−4.44825	−	9.34350i	−0.407771	−	0.856517i
$120$		0			0
$121$	−3.54909	−	3.54909i	−0.322645	−	0.322645i
$122$	0.252603	−	0.104632i	0.0228696	−	0.00947291i
$123$		0			0
$124$	1.64176	+	3.96355i	0.147434	+	0.355937i
$125$	−0.923880	−	0.382683i	−0.0826343	−	0.0342282i
$126$		0			0
$127$	4.21071	−	4.21071i	0.373640	−	0.373640i	−0.495161	−	0.868801i	$-0.664891\pi$
$127$	4.21071	−	4.21071i	0.373640	−	0.373640i	0.868801	+	0.495161i	$0.164891\pi$
$128$	6.07081	−	6.07081i	0.536589	−	0.536589i
$129$		0			0
$130$	1.56457	+	0.648065i	0.137222	+	0.0568390i
$131$	1.60241	+	3.86856i	0.140003	+	0.337998i	0.978293	−	0.207228i	$-0.0664441\pi$
$131$	1.60241	+	3.86856i	0.140003	+	0.337998i	−0.838290	+	0.545225i	$0.816444\pi$
$132$		0			0
$133$	16.5354	−	6.84920i	1.43380	−	0.593901i
$134$	1.42904	+	1.42904i	0.123450	+	0.123450i
$135$		0			0
$136$	−0.250931	−	4.85585i	−0.0215172	−	0.416386i
$137$	−7.25998			−0.620262			−0.310131	−	0.950694i	$-0.600373\pi$
$137$	−7.25998			−0.620262			−0.310131	+	0.950694i	$0.600373\pi$
$138$		0			0
$139$	9.60207	−	3.97731i	0.814437	−	0.337351i	0.0637140	−	0.997968i	$-0.479705\pi$
$139$	9.60207	−	3.97731i	0.814437	−	0.337351i	0.750723	+	0.660617i	$0.229705\pi$
$140$			4.79124i			0.404934i
$141$		0			0
$142$	0.0671069	+	0.0277966i	0.00563149	+	0.00233264i
$143$	5.25343	−	12.6829i	0.439314	−	1.06060i
$144$		0			0
$145$	−2.65267	+	2.65267i	−0.220292	+	0.220292i
$146$	−0.745517	+	1.79984i	−0.0616994	+	0.148956i
$147$		0			0
$148$	−3.72981	−	9.00455i	−0.306588	−	0.740170i
$149$		−	6.01765i		−	0.492985i	−0.969145	−	0.246492i	$-0.920722\pi$
$149$		−	6.01765i		−	0.492985i	0.969145	−	0.246492i	$-0.0792781\pi$
$150$		0			0
$151$	7.36684	+	7.36684i	0.599505	+	0.599505i	0.940181	−	0.340676i	$-0.110656\pi$
$151$	7.36684	+	7.36684i	0.599505	+	0.599505i	−0.340676	+	0.940181i	$0.610656\pi$
$152$	8.40959			0.682108
$153$		0			0
$154$	−1.85175			−0.149218
$155$	−1.58910	−	1.58910i	−0.127640	−	0.127640i
$156$		0			0
$157$			13.4073i			1.07002i	0.844847	+	0.535008i	$0.179691\pi$
$157$			13.4073i			1.07002i	−0.844847	+	0.535008i	$0.820309\pi$
$158$	−1.69823	−	4.09989i	−0.135104	−	0.326170i
$159$		0			0
$160$	−1.30230	+	3.14403i	−0.102956	+	0.248558i
$161$	1.52769	−	1.52769i	0.120399	−	0.120399i
$162$		0			0
$163$	0.602777	−	1.45523i	0.0472132	−	0.113983i	−0.898513	−	0.438946i	$-0.855352\pi$
$163$	0.602777	−	1.45523i	0.0472132	−	0.113983i	0.945727	+	0.324963i	$0.105352\pi$
$164$	21.7806	+	9.02182i	1.70078	+	0.704486i
$165$		0			0
$166$		−	4.19297i		−	0.325438i
$167$	16.2648	−	6.73711i	1.25861	−	0.521333i	0.349127	−	0.937075i	$-0.386478\pi$
$167$	16.2648	−	6.73711i	1.25861	−	0.521333i	0.909482	+	0.415742i	$0.136478\pi$
$168$		0			0
$169$	−18.5098			−1.42383
$170$	0.534688	+	1.12310i	0.0410087	+	0.0861382i
$171$		0			0
$172$	3.53681	+	3.53681i	0.269679	+	0.269679i
$173$	17.4086	−	7.21087i	1.32355	−	0.548232i	0.394741	−	0.918792i	$-0.370834\pi$
$173$	17.4086	−	7.21087i	1.32355	−	0.548232i	0.928808	+	0.370560i	$0.120834\pi$
$174$		0			0
$175$	−0.960473	−	2.31879i	−0.0726050	−	0.175284i
$176$	7.82253	+	3.24020i	0.589646	+	0.244239i
$177$		0			0
$178$	0.0842980	−	0.0842980i	0.00631840	−	0.00631840i
$179$	−2.34324	+	2.34324i	−0.175142	+	0.175142i	−0.789234	−	0.614092i	$-0.789522\pi$
$179$	−2.34324	+	2.34324i	−0.175142	+	0.175142i	0.614092	+	0.789234i	$0.289522\pi$
$180$		0			0
$181$	−14.6575	−	6.07133i	−1.08948	−	0.451278i	−0.235656	−	0.971836i	$-0.575724\pi$
$181$	−14.6575	−	6.07133i	−1.08948	−	0.451278i	−0.853826	+	0.520558i	$0.825724\pi$
$182$	1.62654	+	3.92681i	0.120567	+	0.291075i
$183$		0			0
$184$	0.937865	−	0.388477i	0.0691404	−	0.0286389i
$185$	3.61018	+	3.61018i	0.265426	+	0.265426i
$186$		0			0
$187$	9.10425	−	4.33435i	0.665769	−	0.316959i
$188$	−4.39284			−0.320380
$189$		0			0
$190$	−1.98759	+	0.823286i	−0.144195	+	0.0597274i
$191$		−	27.4943i		−	1.98941i	−0.102748	−	0.994707i	$-0.532764\pi$
$191$		−	27.4943i		−	1.98941i	0.102748	−	0.994707i	$-0.467236\pi$
$192$		0			0
$193$	13.6376	+	5.64889i	0.981658	+	0.406616i	0.815040	−	0.579405i	$-0.196715\pi$
$193$	13.6376	+	5.64889i	0.981658	+	0.406616i	0.166619	+	0.986021i	$0.446715\pi$
$194$	1.03435	−	2.49714i	0.0742618	−	0.179284i
$195$		0			0
$196$	0.945861	−	0.945861i	0.0675615	−	0.0675615i
$197$	0.144044	−	0.347754i	0.0102627	−	0.0247764i	−0.918665	−	0.395037i	$-0.870732\pi$
$197$	0.144044	−	0.347754i	0.0102627	−	0.0247764i	0.928928	+	0.370261i	$0.120732\pi$
$198$		0			0
$199$	2.88162	+	6.95685i	0.204273	+	0.493158i	0.992503	−	0.122223i	$-0.0390022\pi$
$199$	2.88162	+	6.95685i	0.204273	+	0.493158i	−0.788230	+	0.615381i	$0.789002\pi$
$200$		−	1.17929i		−	0.0833883i
$201$		0			0
$202$	3.26136	+	3.26136i	0.229469	+	0.229469i
$203$	−9.41549			−0.660838
$204$		0			0
$205$	−12.3496			−0.862532
$206$	3.15180	+	3.15180i	0.219596	+	0.219596i
$207$		0			0
$208$		−	19.4345i		−	1.34754i
$209$	6.67383	+	16.1120i	0.461638	+	1.11449i
$210$		0			0
$211$	3.32647	−	8.03080i	0.229003	−	0.552863i	−0.767053	−	0.641584i	$-0.778278\pi$
$211$	3.32647	−	8.03080i	0.229003	−	0.552863i	0.996057	+	0.0887204i	$0.0282778\pi$
$212$	−3.74551	+	3.74551i	−0.257243	+	0.257243i
$213$		0			0
$214$	−0.169802	+	0.409938i	−0.0116074	+	0.0280228i
$215$	−2.42069	−	1.00268i	−0.165090	−	0.0683824i
$216$		0			0
$217$		−	5.64043i		−	0.382897i
$218$	−2.63050	+	1.08959i	−0.178160	+	0.0737963i
$219$		0			0
$220$	−4.66856			−0.314754
$221$	−17.1884	−	15.4992i	−1.15622	−	1.04259i
$222$		0			0
$223$	4.57010	+	4.57010i	0.306037	+	0.306037i	0.843370	−	0.537333i	$-0.180568\pi$
$223$	4.57010	+	4.57010i	0.306037	+	0.306037i	−0.537333	+	0.843370i	$0.680568\pi$
$224$	−7.89101	+	3.26856i	−0.527241	+	0.218390i
$225$		0			0
$226$	1.72726	+	4.16997i	0.114896	+	0.277382i
$227$	−2.82763	−	1.17124i	−0.187676	−	0.0777381i	0.286866	−	0.957971i	$-0.407386\pi$
$227$	−2.82763	−	1.17124i	−0.187676	−	0.0777381i	−0.474543	+	0.880233i	$0.657386\pi$
$228$		0			0
$229$	5.34518	−	5.34518i	0.353219	−	0.353219i	−0.508087	−	0.861306i	$-0.669647\pi$
$229$	5.34518	−	5.34518i	0.353219	−	0.353219i	0.861306	+	0.508087i	$0.169647\pi$
$230$	−0.183631	+	0.183631i	−0.0121083	+	0.0121083i
$231$		0			0
$232$	−4.08727	−	1.69300i	−0.268342	−	0.111151i
$233$	−8.55214	−	20.6467i	−0.560270	−	1.35261i	−0.909551	−	0.415593i	$-0.863574\pi$
$233$	−8.55214	−	20.6467i	−0.560270	−	1.35261i	0.349281	−	0.937018i	$-0.386426\pi$
$234$		0			0
$235$	2.12597	−	0.880607i	0.138683	−	0.0574445i
$236$	−10.0452	−	10.0452i	−0.653886	−	0.653886i
$237$		0			0
$238$	−1.04428	+	2.94212i	−0.0676904	+	0.190709i
$239$	3.45981			0.223797			0.111898	−	0.993720i	$-0.464307\pi$
$239$	3.45981			0.223797			0.111898	+	0.993720i	$0.464307\pi$
$240$		0			0
$241$	−16.6541	+	6.89834i	−1.07278	+	0.444361i	−0.847972	−	0.530042i	$-0.822176\pi$
$241$	−16.6541	+	6.89834i	−1.07278	+	0.444361i	−0.224810	+	0.974403i	$0.572176\pi$
$242$			1.51422i			0.0973376i
$243$		0			0
$244$	1.59840	+	0.662079i	0.102327	+	0.0423853i
$245$	−0.268151	+	0.647374i	−0.0171315	+	0.0413592i
$246$		0			0
$247$	28.3049	−	28.3049i	1.80100	−	1.80100i
$248$	1.01421	−	2.44851i	0.0644022	−	0.155481i
$249$		0			0
$250$	0.115451	+	0.278722i	0.00730173	+	0.0176279i
$251$			24.0478i			1.51788i	0.651159	+	0.758941i	$0.274283\pi$
$251$			24.0478i			1.51788i	−0.651159	+	0.758941i	$0.725717\pi$
$252$		0			0
$253$	1.48857	+	1.48857i	0.0935859	+	0.0935859i
$254$	−1.79650			−0.112722
$255$		0			0
$256$	9.20534			0.575334
$257$	10.4664	+	10.4664i	0.652873	+	0.652873i	0.953684	−	0.300811i	$-0.0972573\pi$
$257$	10.4664	+	10.4664i	0.652873	+	0.652873i	−0.300811	+	0.953684i	$0.597257\pi$
$258$		0			0
$259$			12.8142i			0.796233i
$260$	4.10076	+	9.90012i	0.254319	+	0.613979i
$261$		0			0
$262$	0.483426	−	1.16709i	0.0298661	−	0.0721032i
$263$	−17.3357	+	17.3357i	−1.06896	+	1.06896i	−0.0715243	+	0.997439i	$0.522786\pi$
$263$	−17.3357	+	17.3357i	−1.06896	+	1.06896i	−0.997439	+	0.0715243i	$0.977214\pi$
$264$		0			0
$265$	1.06185	−	2.56353i	0.0652289	−	0.157477i
$266$	−4.98852	−	2.06631i	−0.305866	−	0.126694i
$267$		0			0
$268$			12.7881i			0.781156i
$269$	−6.09269	+	2.52367i	−0.371478	+	0.153871i	−0.560609	−	0.828081i	$-0.689433\pi$
$269$	−6.09269	+	2.52367i	−0.371478	+	0.153871i	0.189131	+	0.981952i	$0.439433\pi$
$270$		0			0
$271$	−26.1956			−1.59127			−0.795634	−	0.605778i	$-0.792862\pi$
$271$	−26.1956			−1.59127			−0.795634	+	0.605778i	$0.792862\pi$
$272$	9.55957	−	10.6014i	0.579634	−	0.642805i
$273$		0			0
$274$	1.54873	+	1.54873i	0.0935624	+	0.0935624i
$275$	2.25941	−	0.935880i	0.136248	−	0.0564357i
$276$		0			0
$277$	3.66038	+	8.83695i	0.219931	+	0.530961i	0.994880	−	0.101063i	$-0.0322245\pi$
$277$	3.66038	+	8.83695i	0.219931	+	0.530961i	−0.774949	+	0.632024i	$0.782224\pi$
$278$	−2.89682	−	1.19990i	−0.173740	−	0.0719653i
$279$		0			0
$280$	2.09291	−	2.09291i	0.125075	−	0.125075i
$281$	−8.78037	+	8.78037i	−0.523793	+	0.523793i	−0.918715	−	0.394922i	$-0.870772\pi$
$281$	−8.78037	+	8.78037i	−0.523793	+	0.523793i	0.394922	+	0.918715i	$0.370772\pi$
$282$		0			0
$283$	15.5612	+	6.44566i	0.925017	+	0.383155i	0.793786	−	0.608197i	$-0.208107\pi$
$283$	15.5612	+	6.44566i	0.925017	+	0.383155i	0.131231	+	0.991352i	$0.458107\pi$
$284$	0.175889	+	0.424633i	0.0104371	+	0.0251973i
$285$		0			0
$286$	−3.82626	+	1.58489i	−0.226252	+	0.0937165i
$287$	−21.9171	−	21.9171i	−1.29372	−	1.29372i
$288$		0			0
$289$	−1.75231	−	16.9094i	−0.103077	−	0.994673i
$290$	1.13176			0.0664591
$291$		0			0
$292$	−11.3888	+	4.71741i	−0.666482	+	0.276066i
$293$			20.8806i			1.21986i	0.792456	+	0.609930i	$0.208802\pi$
$293$			20.8806i			1.21986i	−0.792456	+	0.609930i	$0.791198\pi$
$294$		0			0
$295$	6.87521	+	2.84781i	0.400290	+	0.165806i
$296$	−2.30412	+	5.56263i	−0.133924	+	0.323321i
$297$		0			0
$298$	−1.28371	+	1.28371i	−0.0743635	+	0.0743635i
$299$	1.84913	−	4.46419i	0.106938	−	0.258171i
$300$		0			0
$301$	−2.51657	−	6.07554i	−0.145053	−	0.350188i
$302$		−	3.14306i		−	0.180863i
$303$		0			0
$304$	17.4579	+	17.4579i	1.00128	+	1.00128i
$305$	−0.906291			−0.0518941
$306$		0			0
$307$	−29.9529			−1.70950			−0.854751	−	0.519038i	$-0.826290\pi$
$307$	−29.9529			−1.70950			−0.854751	+	0.519038i	$0.826290\pi$
$308$	−8.28541	−	8.28541i	−0.472105	−	0.472105i
$309$		0			0
$310$			0.677989i			0.0385072i
$311$	−0.0804873	−	0.194314i	−0.00456402	−	0.0110185i	0.921581	−	0.388186i	$-0.126898\pi$
$311$	−0.0804873	−	0.194314i	−0.00456402	−	0.0110185i	−0.926145	+	0.377167i	$0.876898\pi$
$312$		0			0
$313$	−12.4082	+	29.9561i	−0.701354	+	1.69322i	0.0191979	+	0.999816i	$0.493889\pi$
$313$	−12.4082	+	29.9561i	−0.701354	+	1.69322i	−0.720551	+	0.693402i	$0.756111\pi$
$314$	2.86010	−	2.86010i	0.161405	−	0.161405i
$315$		0			0
$316$	10.7459	−	25.9429i	0.604504	−	1.45940i
$317$	30.8937	+	12.7966i	1.73516	+	0.718728i	0.999127	+	0.0417842i	$0.0133042\pi$
$317$	30.8937	+	12.7966i	1.73516	+	0.718728i	0.736035	+	0.676943i	$0.236696\pi$
$318$		0			0
$319$		−	9.17441i		−	0.513668i
$320$	−5.44879	+	2.25696i	−0.304596	+	0.126168i
$321$		0			0
$322$	−0.651789			−0.0363228
$323$	29.3630	−	1.51736i	1.63380	−	0.0844283i
$324$		0			0
$325$	−3.96924	−	3.96924i	−0.220174	−	0.220174i
$326$	−0.439025	+	0.181850i	−0.0243153	+	0.0100717i
$327$		0			0
$328$	−5.57330	−	13.4551i	−0.307734	−	0.742935i
$329$	5.33585	+	2.21018i	0.294175	+	0.121851i
$330$		0			0
$331$	0.626030	−	0.626030i	0.0344097	−	0.0344097i	−0.689693	−	0.724102i	$-0.742254\pi$
$331$	0.626030	−	0.626030i	0.0344097	−	0.0344097i	0.724102	+	0.689693i	$0.242254\pi$
$332$	18.7609	−	18.7609i	1.02964	−	1.02964i
$333$		0			0
$334$	−4.90688	−	2.03250i	−0.268493	−	0.111213i
$335$	−2.56355	−	6.18896i	−0.140062	−	0.338139i
$336$		0			0
$337$	15.8506	−	6.56551i	0.863434	−	0.357646i	0.0933847	−	0.995630i	$-0.470231\pi$
$337$	15.8506	−	6.56551i	0.863434	−	0.357646i	0.770050	+	0.637984i	$0.220231\pi$
$338$	3.94859	+	3.94859i	0.214775	+	0.214775i
$339$		0			0
$340$	−2.63279	+	7.41756i	−0.142783	+	0.402274i
$341$	5.49600			0.297625
$342$		0			0
$343$	−17.8563	+	7.39633i	−0.964151	+	0.399364i
$344$		−	3.08990i		−	0.166596i
$345$		0			0
$346$	−5.25194	−	2.17542i	−0.282346	−	0.116951i
$347$	−11.8288	+	28.5572i	−0.635003	+	1.53303i	0.198257	+	0.980150i	$0.436472\pi$
$347$	−11.8288	+	28.5572i	−0.635003	+	1.53303i	−0.833260	+	0.552882i	$0.813528\pi$
$348$		0			0
$349$	2.38415	−	2.38415i	0.127621	−	0.127621i	−0.640411	−	0.768032i	$-0.721236\pi$
$349$	2.38415	−	2.38415i	0.127621	−	0.127621i	0.768032	+	0.640411i	$0.221236\pi$
$350$	−0.289762	+	0.699548i	−0.0154884	+	0.0373924i
$351$		0			0
$352$	−3.18487	−	7.68896i	−0.169754	−	0.409823i
$353$			23.7918i			1.26631i	0.774025	+	0.633155i	$0.218240\pi$
$353$			23.7918i			1.26631i	−0.774025	+	0.633155i	$0.781760\pi$
$354$		0			0
$355$	−0.170247	−	0.170247i	−0.00903579	−	0.00903579i
$356$	0.754360			0.0399810
$357$		0			0
$358$	0.999743			0.0528381
$359$	−22.4244	−	22.4244i	−1.18351	−	1.18351i	−0.978827	−	0.204688i	$-0.934382\pi$
$359$	−22.4244	−	22.4244i	−1.18351	−	1.18351i	−0.204688	−	0.978827i	$-0.565618\pi$
$360$		0			0
$361$			31.8521i			1.67643i
$362$	1.83164	+	4.42197i	0.0962689	+	0.232414i
$363$		0			0
$364$	−10.2923	+	24.8477i	−0.539461	+	1.30237i
$365$	4.56611	−	4.56611i	0.239001	−	0.239001i
$366$		0			0
$367$	−1.72853	+	4.17304i	−0.0902286	+	0.217831i	−0.962551	−	0.271099i	$-0.912613\pi$
$367$	−1.72853	+	4.17304i	−0.0902286	+	0.217831i	0.872323	+	0.488930i	$0.162613\pi$
$368$	2.75341	+	1.14050i	0.143532	+	0.0594528i
$369$		0			0
$370$		−	1.54028i		−	0.0800755i
$371$	6.43405	−	2.66507i	0.334039	−	0.138364i
$372$		0			0
$373$	−5.12748			−0.265491			−0.132745	−	0.991150i	$-0.542379\pi$
$373$	−5.12748			−0.265491			−0.132745	+	0.991150i	$0.542379\pi$
$374$	−2.86679	−	1.01754i	−0.148238	−	0.0526156i
$375$		0			0
$376$	1.91888	+	1.91888i	0.0989586	+	0.0989586i
$377$	−19.4552	+	8.05860i	−1.00199	+	0.415039i
$378$		0			0
$379$	2.11629	+	5.10917i	0.108706	+	0.262441i	0.968867	−	0.247584i	$-0.0796365\pi$
$379$	2.11629	+	5.10917i	0.108706	+	0.262441i	−0.860160	+	0.510024i	$0.829636\pi$
$380$	−12.5769	−	5.20951i	−0.645180	−	0.267242i
$381$		0			0
$382$	−5.86521	+	5.86521i	−0.300090	+	0.300090i
$383$	−14.4493	+	14.4493i	−0.738326	+	0.738326i	−0.972254	−	0.233928i	$-0.924842\pi$
$383$	−14.4493	+	14.4493i	−0.738326	+	0.738326i	0.233928	+	0.972254i	$0.424842\pi$
$384$		0			0
$385$	5.67077	+	2.34891i	0.289009	+	0.119711i
$386$	−1.70420	−	4.11429i	−0.0867413	−	0.209412i
$387$		0			0
$388$	15.8011	−	6.54505i	0.802181	−	0.332274i
$389$	3.66726	+	3.66726i	0.185937	+	0.185937i	0.793937	−	0.608000i	$-0.208028\pi$
$389$	3.66726	+	3.66726i	0.185937	+	0.185937i	−0.608000	+	0.793937i	$0.708028\pi$
$390$		0			0
$391$	3.20456	−	1.52563i	0.162062	−	0.0771543i
$392$	−0.826343			−0.0417366
$393$		0			0
$394$	−0.104913	+	0.0434563i	−0.00528543	+	0.00218930i
$395$			14.7096i			0.740120i
$396$		0			0
$397$	−5.70360	−	2.36251i	−0.286255	−	0.118571i	0.234936	−	0.972011i	$-0.424512\pi$
$397$	−5.70360	−	2.36251i	−0.286255	−	0.118571i	−0.521191	+	0.853440i	$0.674512\pi$
$398$	0.869348	−	2.09879i	0.0435765	−	0.105203i
$399$		0			0
$400$	2.44814	−	2.44814i	0.122407	−	0.122407i
$401$	3.63413	−	8.77356i	0.181480	−	0.438131i	−0.806792	−	0.590835i	$-0.798798\pi$
$401$	3.63413	−	8.77356i	0.181480	−	0.438131i	0.988272	+	0.152705i	$0.0487983\pi$
$402$		0			0
$403$	−4.82757	−	11.6548i	−0.240478	−	0.580566i
$404$			29.1850i			1.45201i
$405$		0			0
$406$	2.00856	+	2.00856i	0.0996831	+	0.0996831i
$407$	−12.4860			−0.618910
$408$		0			0
$409$	14.3886			0.711469			0.355734	−	0.934587i	$-0.384231\pi$
$409$	14.3886			0.711469			0.355734	+	0.934587i	$0.384231\pi$
$410$	2.63447	+	2.63447i	0.130107	+	0.130107i
$411$		0			0
$412$			28.2046i			1.38954i
$413$	7.14753	+	17.2557i	0.351707	+	0.849096i
$414$		0			0
$415$	−5.31870	+	12.8405i	−0.261085	+	0.630314i
$416$	−13.5076	+	13.5076i	−0.662266	+	0.662266i
$417$		0			0
$418$	2.01340	−	4.86079i	0.0984789	−	0.237749i
$419$	−19.6078	−	8.12181i	−0.957903	−	0.396776i	−0.151707	−	0.988425i	$-0.548477\pi$
$419$	−19.6078	−	8.12181i	−0.957903	−	0.396776i	−0.806196	+	0.591649i	$0.798477\pi$
$420$		0			0
$421$			20.1672i			0.982887i	0.870909	+	0.491444i	$0.163531\pi$
$421$			20.1672i			0.982887i	−0.870909	+	0.491444i	$0.836469\pi$
$422$	−2.42279	+	1.00355i	−0.117939	+	0.0488521i
$423$		0			0
$424$	3.27223			0.158914
$425$	−0.212782	−	4.11761i	−0.0103214	−	0.199733i
$426$		0			0
$427$	−1.60842	−	1.60842i	−0.0778367	−	0.0778367i
$428$	−2.59397	+	1.07446i	−0.125384	+	0.0519358i
$429$		0			0
$430$	0.302496	+	0.730290i	0.0145877	+	0.0352177i
$431$	18.4485	+	7.64163i	0.888635	+	0.368085i	0.779839	−	0.625980i	$-0.215301\pi$
$431$	18.4485	+	7.64163i	0.888635	+	0.368085i	0.108795	+	0.994064i	$0.465301\pi$
$432$		0			0
$433$	12.8860	−	12.8860i	0.619263	−	0.619263i	−0.326080	−	0.945342i	$-0.605728\pi$
$433$	12.8860	−	12.8860i	0.619263	−	0.619263i	0.945342	+	0.326080i	$0.105728\pi$
$434$	−1.20324	+	1.20324i	−0.0577575	+	0.0577575i
$435$		0			0
$436$	−16.6450	−	6.89460i	−0.797152	−	0.330191i
$437$	2.34909	+	5.67120i	0.112372	+	0.271290i
$438$		0			0
$439$	13.6117	−	5.63815i	0.649651	−	0.269094i	−0.0334251	−	0.999441i	$-0.510642\pi$
$439$	13.6117	−	5.63815i	0.649651	−	0.269094i	0.683077	+	0.730347i	$0.260642\pi$
$440$	2.03932	+	2.03932i	0.0972209	+	0.0972209i
$441$		0			0
$442$	0.360341	+	6.97307i	0.0171397	+	0.331675i
$443$	23.3335			1.10861			0.554305	−	0.832314i	$-0.312984\pi$
$443$	23.3335			1.10861			0.554305	+	0.832314i	$0.312984\pi$
$444$		0			0
$445$	−0.365083	+	0.151222i	−0.0173066	+	0.00716862i
$446$		−	1.94983i		−	0.0923272i
$447$		0			0
$448$	−13.6756	−	5.66461i	−0.646110	−	0.267628i
$449$	0.655009	−	1.58133i	0.0309118	−	0.0746277i	−0.907670	−	0.419685i	$-0.862141\pi$
$449$	0.655009	−	1.58133i	0.0309118	−	0.0746277i	0.938582	+	0.345057i	$0.112141\pi$
$450$		0			0
$451$	21.3559	−	21.3559i	1.00561	−	1.00561i
$452$	−10.9296	+	26.3864i	−0.514085	+	1.24111i
$453$		0			0
$454$	0.353348	+	0.853058i	0.0165835	+	0.0400360i
$455$		−	14.0886i		−	0.660484i
$456$		0			0
$457$	9.34572	+	9.34572i	0.437174	+	0.437174i	0.891060	−	0.453886i	$-0.149963\pi$
$457$	9.34572	+	9.34572i	0.437174	+	0.437174i	−0.453886	+	0.891060i	$0.649963\pi$
$458$	−2.28052			−0.106562
$459$		0			0
$460$	−1.64326			−0.0766176
$461$	20.7116	+	20.7116i	0.964634	+	0.964634i	0.999396	−	0.0347616i	$-0.0110672\pi$
$461$	20.7116	+	20.7116i	0.964634	+	0.964634i	−0.0347616	+	0.999396i	$0.511067\pi$
$462$		0			0
$463$			9.80371i			0.455617i	0.973706	+	0.227808i	$0.0731560\pi$
$463$			9.80371i			0.455617i	−0.973706	+	0.227808i	$0.926844\pi$
$464$	−4.97037	−	11.9995i	−0.230744	−	0.557064i
$465$		0			0
$466$	−2.58007	+	6.22884i	−0.119519	+	0.288545i
$467$	9.67459	−	9.67459i	0.447687	−	0.447687i	−0.446898	−	0.894585i	$-0.647471\pi$
$467$	9.67459	−	9.67459i	0.447687	−	0.447687i	0.894585	+	0.446898i	$0.147471\pi$
$468$		0			0
$469$	6.43410	−	15.5333i	0.297099	−	0.717261i
$470$	−0.641378	−	0.265667i	−0.0295846	−	0.0122543i
$471$		0			0
$472$			8.77589i			0.403943i
$473$	5.91997	−	2.45213i	0.272201	−	0.112749i
$474$		0			0
$475$	7.13107			0.327196
$476$	−17.8366	+	8.49165i	−0.817539	+	0.389214i
$477$		0			0
$478$	−0.738063	−	0.738063i	−0.0337582	−	0.0337582i
$479$	10.1719	−	4.21334i	0.464766	−	0.192513i	−0.137997	−	0.990433i	$-0.544066\pi$
$479$	10.1719	−	4.21334i	0.464766	−	0.192513i	0.602763	+	0.797920i	$0.294066\pi$
$480$		0			0
$481$	10.9675	+	26.4778i	0.500074	+	1.20728i
$482$	5.02431	+	2.08114i	0.228851	+	0.0947932i
$483$		0			0
$484$	−6.77516	+	6.77516i	−0.307962	+	0.307962i
$485$	−6.33513	+	6.33513i	−0.287663	+	0.287663i
$486$		0			0
$487$	9.32586	+	3.86290i	0.422595	+	0.175045i	0.583838	−	0.811870i	$-0.301550\pi$
$487$	9.32586	+	3.86290i	0.422595	+	0.175045i	−0.161243	+	0.986915i	$0.551550\pi$
$488$	−0.409004	−	0.987423i	−0.0185147	−	0.0446985i
$489$		0			0
$490$	0.195304	−	0.0808976i	0.00882294	−	0.00365458i
$491$	12.0793	+	12.0793i	0.545132	+	0.545132i	0.925029	−	0.379897i	$-0.124041\pi$
$491$	12.0793	+	12.0793i	0.545132	+	0.545132i	−0.379897	+	0.925029i	$0.624041\pi$
$492$		0			0
$493$	−14.5766	−	5.17382i	−0.656497	−	0.233017i
$494$	−12.0763			−0.543338
$495$		0			0
$496$	7.18841	−	2.97754i	0.322769	−	0.133695i
$497$		−	0.604284i		−	0.0271059i
$498$		0			0
$499$	−28.9724	−	12.0008i	−1.29698	−	0.537227i	−0.375923	−	0.926651i	$-0.622674\pi$
$499$	−28.9724	−	12.0008i	−1.29698	−	0.537227i	−0.921059	+	0.389424i	$0.872674\pi$
$500$	−0.730537	+	1.76367i	−0.0326706	+	0.0788738i
$501$		0			0
$502$	5.12999	−	5.12999i	0.228963	−	0.228963i
$503$	3.31991	−	8.01498i	0.148028	−	0.357370i	−0.832422	−	0.554143i	$-0.813046\pi$
$503$	3.31991	−	8.01498i	0.148028	−	0.357370i	0.980449	+	0.196773i	$0.0630461\pi$
$504$		0			0
$505$	−5.85056	−	14.1245i	−0.260346	−	0.628532i
$506$		−	0.635099i		−	0.0282336i
$507$		0			0
$508$	−8.03817	−	8.03817i	−0.356636	−	0.356636i
$509$	14.1196			0.625840			0.312920	−	0.949780i	$-0.398693\pi$
$509$	14.1196			0.625840			0.312920	+	0.949780i	$0.398693\pi$
$510$		0			0
$511$	16.2072			0.716963
$512$	−14.1053	−	14.1053i	−0.623374	−	0.623374i
$513$		0			0
$514$		−	4.46546i		−	0.196963i
$515$	−5.65401	−	13.6500i	−0.249145	−	0.601490i
$516$		0			0
$517$	−2.15359	+	5.19922i	−0.0947147	+	0.228662i
$518$	2.73358	−	2.73358i	0.120106	−	0.120106i
$519$		0			0
$520$	2.53328	−	6.11587i	0.111091	−	0.268199i
$521$	16.2808	+	6.74373i	0.713275	+	0.295448i	0.709659	−	0.704545i	$-0.248849\pi$
$521$	16.2808	+	6.74373i	0.713275	+	0.295448i	0.00361608	+	0.999993i	$0.498849\pi$
$522$		0			0
$523$			26.3853i			1.15375i	0.816833	+	0.576875i	$0.195728\pi$
$523$			26.3853i			1.15375i	−0.816833	+	0.576875i	$0.804272\pi$
$524$	7.38502	−	3.05898i	0.322616	−	0.133632i
$525$		0			0
$526$	7.39626			0.322492
$527$	3.09942	−	8.73223i	0.135013	−	0.380382i
$528$		0			0
$529$	−15.7395	−	15.7395i	−0.684326	−	0.684326i
$530$	−0.773384	+	0.320346i	−0.0335937	+	0.0139150i
$531$		0			0
$532$	−13.0750	−	31.5659i	−0.566874	−	1.36856i
$533$	−64.0457	−	26.5286i	−2.77413	−	1.14908i
$534$		0			0
$535$	1.04000	−	1.04000i	0.0449629	−	0.0449629i
$536$	5.58609	−	5.58609i	0.241282	−	0.241282i
$537$		0			0
$538$	1.83808	+	0.761359i	0.0792454	+	0.0328245i
$539$	−0.655783	−	1.58320i	−0.0282466	−	0.0681932i
$540$		0			0
$541$	−4.07266	+	1.68695i	−0.175097	+	0.0725277i	−0.468510	−	0.883458i	$-0.655209\pi$
$541$	−4.07266	+	1.68695i	−0.175097	+	0.0725277i	0.293413	+	0.955986i	$0.405209\pi$
$542$	5.58816	+	5.58816i	0.240032	+	0.240032i
$543$		0			0
$544$	−14.0125	+	0.724113i	−0.600783	+	0.0310461i
$545$	9.43771			0.404267
$546$		0			0
$547$	−20.9386	+	8.67306i	−0.895271	+	0.370833i	−0.782400	−	0.622776i	$-0.786005\pi$
$547$	−20.9386	+	8.67306i	−0.895271	+	0.370833i	−0.112871	+	0.993610i	$0.536005\pi$
$548$			13.8592i			0.592035i
$549$		0			0
$550$	−0.681636	−	0.282343i	−0.0290650	−	0.0120391i
$551$	10.2374	−	24.7154i	0.436130	−	1.05291i
$552$		0			0
$553$	−26.1055	+	26.1055i	−1.11012	+	1.11012i
$554$	1.10429	−	2.66599i	0.0469167	−	0.113267i
$555$		0			0
$556$	−7.59262	−	18.3302i	−0.321999	−	0.777374i
$557$			11.4954i			0.487076i	0.969891	+	0.243538i	$0.0783080\pi$
$557$			11.4954i			0.487076i	−0.969891	+	0.243538i	$0.921692\pi$
$558$		0			0
$559$	−10.4000	−	10.4000i	−0.439871	−	0.439871i
$560$	8.68955			0.367200
$561$		0			0
$562$	3.74614			0.158021
$563$	−9.57715	−	9.57715i	−0.403629	−	0.403629i	0.475881	−	0.879510i	$-0.342129\pi$
$563$	−9.57715	−	9.57715i	−0.403629	−	0.403629i	−0.879510	+	0.475881i	$0.842129\pi$
$564$		0			0
$565$		−	14.9610i		−	0.629415i
$566$	−1.94457	−	4.69461i	−0.0817364	−	0.197329i
$567$		0			0
$568$	0.108656	−	0.262320i	0.00455912	−	0.0110067i
$569$	11.2263	−	11.2263i	0.470632	−	0.470632i	−0.431487	−	0.902119i	$-0.642011\pi$
$569$	11.2263	−	11.2263i	0.470632	−	0.470632i	0.902119	+	0.431487i	$0.142011\pi$
$570$		0			0
$571$	1.35486	−	3.27093i	0.0566993	−	0.136884i	−0.892991	−	0.450074i	$-0.851398\pi$
$571$	1.35486	−	3.27093i	0.0566993	−	0.136884i	0.949691	+	0.313190i	$0.101398\pi$
$572$	−24.2115	−	10.0287i	−1.01233	−	0.419322i
$573$		0			0
$574$			9.35092i			0.390300i
$575$	0.795280	−	0.329416i	0.0331655	−	0.0137376i
$576$		0			0
$577$	18.5078			0.770492			0.385246	−	0.922814i	$-0.374117\pi$
$577$	18.5078			0.770492			0.385246	+	0.922814i	$0.374117\pi$
$578$	−3.23339	+	3.98101i	−0.134491	+	0.165588i
$579$		0			0
$580$	5.06390	+	5.06390i	0.210267	+	0.210267i
$581$	−32.2275	+	13.3491i	−1.33702	+	0.553813i
$582$		0			0
$583$	2.59683	+	6.26931i	0.107550	+	0.259648i
$584$	7.03554	+	2.91422i	0.291133	+	0.120591i
$585$		0			0
$586$	4.45436	−	4.45436i	0.184008	−	0.184008i
$587$	9.70579	−	9.70579i	0.400601	−	0.400601i	−0.477844	−	0.878445i	$-0.658582\pi$
$587$	9.70579	−	9.70579i	0.400601	−	0.400601i	0.878445	+	0.477844i	$0.158582\pi$
$588$		0			0
$589$	14.8059	+	6.13282i	0.610068	+	0.252699i
$590$	−0.859145	−	2.07416i	−0.0353705	−	0.0853918i
$591$		0			0
$592$	−16.3309	+	6.76450i	−0.671197	+	0.278019i
$593$	14.3711	+	14.3711i	0.590150	+	0.590150i	0.937672	−	0.347522i	$-0.112977\pi$
$593$	14.3711	+	14.3711i	0.590150	+	0.590150i	−0.347522	+	0.937672i	$0.612977\pi$
$594$		0			0
$595$	6.92999	−	7.68525i	0.284102	−	0.315065i
$596$	−11.4876			−0.470550
$597$		0			0
$598$	−1.34679	+	0.557858i	−0.0550742	+	0.0228125i
$599$			26.7277i			1.09206i	0.837764	+	0.546032i	$0.183862\pi$
$599$			26.7277i			1.09206i	−0.837764	+	0.546032i	$0.816138\pi$
$600$		0			0
$601$	25.5537	+	10.5847i	1.04236	+	0.431758i	0.837157	−	0.546962i	$-0.184216\pi$
$601$	25.5537	+	10.5847i	1.04236	+	0.431758i	0.205199	+	0.978720i	$0.434216\pi$
$602$	−0.759216	+	1.83291i	−0.0309433	+	0.0747038i
$603$		0			0
$604$	14.0632	−	14.0632i	0.572223	−	0.572223i
$605$	1.92075	−	4.63711i	0.0780898	−	0.188525i
$606$		0			0
$607$	−9.03844	−	21.8207i	−0.366859	−	0.885676i	−0.994261	−	0.106981i	$-0.965882\pi$
$607$	−9.03844	−	21.8207i	−0.366859	−	0.885676i	0.627402	−	0.778696i	$-0.284118\pi$
$608$		−	24.2676i		−	0.984180i
$609$		0			0
$610$	0.193334	+	0.193334i	0.00782788	+	0.00782788i
$611$	12.9171			0.522570
$612$		0			0
$613$	12.0396			0.486275			0.243137	−	0.969992i	$-0.421823\pi$
$613$	12.0396			0.486275			0.243137	+	0.969992i	$0.421823\pi$
$614$	6.38969	+	6.38969i	0.257867	+	0.257867i
$615$		0			0
$616$			7.23847i			0.291646i
$617$	−5.94989	−	14.3643i	−0.239534	−	0.578285i	0.757701	−	0.652602i	$-0.226322\pi$
$617$	−5.94989	−	14.3643i	−0.239534	−	0.578285i	−0.997235	+	0.0743165i	$0.976322\pi$
$618$		0			0
$619$	12.8172	−	30.9434i	0.515166	−	1.24372i	−0.425676	−	0.904876i	$-0.639964\pi$
$619$	12.8172	−	30.9434i	0.515166	−	1.24372i	0.940842	−	0.338845i	$-0.110036\pi$
$620$	−3.03357	+	3.03357i	−0.121831	+	0.121831i
$621$		0			0
$622$	−0.0242820	+	0.0586218i	−0.000973618	+	0.00235052i
$623$	−0.916299	−	0.379543i	−0.0367107	−	0.0152061i
$624$		0			0
$625$		−	1.00000i		−	0.0400000i
$626$	9.03735	−	3.74339i	0.361205	−	0.149616i
$627$		0			0
$628$	25.5942			1.02132
$629$	−7.04138	+	19.8382i	−0.280758	+	0.791002i
$630$		0			0
$631$	−0.385100	−	0.385100i	−0.0153306	−	0.0153306i	0.699400	−	0.714731i	$-0.253451\pi$
$631$	−0.385100	−	0.385100i	−0.0153306	−	0.0153306i	−0.714731	+	0.699400i	$0.753451\pi$
$632$	−16.0264	+	6.63836i	−0.637496	+	0.264060i
$633$		0			0
$634$	−3.86056	−	9.32021i	−0.153322	−	0.370153i
$635$	5.50155	+	2.27882i	0.218322	+	0.0904321i
$636$		0			0
$637$	−2.78130	+	2.78130i	−0.110199	+	0.110199i
$638$	−1.95713	+	1.95713i	−0.0774835	+	0.0774835i
$639$		0			0
$640$	7.93189	+	3.28550i	0.313536	+	0.129871i
$641$	−4.75450	−	11.4784i	−0.187792	−	0.453369i	0.801742	−	0.597670i	$-0.203907\pi$
$641$	−4.75450	−	11.4784i	−0.187792	−	0.453369i	−0.989534	+	0.144301i	$0.953907\pi$
$642$		0			0
$643$	35.4438	−	14.6813i	1.39777	−	0.578975i	0.448597	−	0.893734i	$-0.351924\pi$
$643$	35.4438	−	14.6813i	1.39777	−	0.578975i	0.949171	+	0.314760i	$0.101924\pi$
$644$	−2.91634	−	2.91634i	−0.114920	−	0.114920i
$645$		0			0
$646$	−6.58754	−	5.94016i	−0.259183	−	0.233712i
$647$	−19.6602			−0.772923			−0.386462	−	0.922305i	$-0.626303\pi$
$647$	−19.6602			−0.772923			−0.386462	+	0.922305i	$0.626303\pi$
$648$		0			0
$649$	−16.8138	+	6.96452i	−0.660001	+	0.273381i
$650$			1.69348i			0.0664236i
$651$		0			0
$652$	−2.77802	−	1.15069i	−0.108796	−	0.0450646i
$653$	−11.9119	+	28.7578i	−0.466147	+	1.12538i	0.499684	+	0.866208i	$0.333449\pi$
$653$	−11.9119	+	28.7578i	−0.466147	+	1.12538i	−0.965831	+	0.259171i	$0.916551\pi$
$654$		0			0
$655$	−2.96087	+	2.96087i	−0.115691	+	0.115691i
$656$	16.3623	−	39.5020i	0.638839	−	1.54229i
$657$		0			0
$658$	−0.666782	−	1.60975i	−0.0259939	−	0.0627548i
$659$		−	4.15956i		−	0.162033i	−0.996713	−	0.0810167i	$-0.974183\pi$
$659$		−	4.15956i		−	0.162033i	0.996713	−	0.0810167i	$-0.0258167\pi$
$660$		0			0
$661$	4.85106	+	4.85106i	0.188685	+	0.188685i	0.795127	−	0.606443i	$-0.207404\pi$
$661$	4.85106	+	4.85106i	0.188685	+	0.188685i	−0.606443	+	0.795127i	$0.707404\pi$
$662$	−0.267095			−0.0103810
$663$		0			0
$664$	−16.3903			−0.636066
$665$	12.6557	+	12.6557i	0.490766	+	0.490766i
$666$		0			0
$667$		−	3.22925i		−	0.125037i
$668$	−12.8610	−	31.0493i	−0.497608	−	1.20133i
$669$		0			0
$670$	−0.773390	+	1.86713i	−0.0298787	+	0.0721335i
$671$	1.56723	−	1.56723i	0.0605023	−	0.0605023i
$672$		0			0
$673$	−6.61298	+	15.9651i	−0.254912	+	0.615411i	−0.998588	−	0.0531290i	$-0.983081\pi$
$673$	−6.61298	+	15.9651i	−0.254912	+	0.615411i	0.743676	+	0.668540i	$0.233081\pi$
$674$	−4.78190	−	1.98073i	−0.184192	−	0.0762948i
$675$		0			0
$676$			35.3348i			1.35903i
$677$	−7.51469	+	3.11269i	−0.288813	+	0.119630i	−0.522386	−	0.852709i	$-0.674958\pi$
$677$	−7.51469	+	3.11269i	−0.288813	+	0.119630i	0.233573	+	0.972339i	$0.424958\pi$
$678$		0			0
$679$	−22.4862			−0.862942
$680$	4.39020	−	2.09009i	0.168356	−	0.0801511i
$681$		0			0
$682$	−1.17243	−	1.17243i	−0.0448948	−	0.0448948i
$683$	26.9190	−	11.1502i	1.03003	−	0.426652i	0.197306	−	0.980342i	$-0.436781\pi$
$683$	26.9190	−	11.1502i	1.03003	−	0.426652i	0.832723	+	0.553690i	$0.186781\pi$
$684$		0			0
$685$	−2.77827	−	6.70735i	−0.106152	−	0.256275i
$686$	5.38702	+	2.23138i	0.205677	+	0.0851943i
$687$		0			0
$688$	6.41446	−	6.41446i	0.244549	−	0.244549i
$689$	11.0136	−	11.0136i	0.419587	−	0.419587i
$690$		0			0
$691$	34.5393	+	14.3066i	1.31394	+	0.544250i	0.926031	−	0.377448i	$-0.123198\pi$
$691$	34.5393	+	14.3066i	1.31394	+	0.544250i	0.387906	+	0.921699i	$0.373198\pi$
$692$	−13.7654	−	33.2327i	−0.523283	−	1.26332i
$693$		0			0
$694$	8.61534	−	3.56859i	0.327034	−	0.135462i
$695$	7.34910	+	7.34910i	0.278767	+	0.278767i
$696$		0			0
$697$	−21.8875	−	45.9744i	−0.829048	−	1.74140i
$698$	−1.01720			−0.0385015
$699$		0			0
$700$	−4.42653	+	1.83353i	−0.167307	+	0.0693009i
$701$		−	14.6423i		−	0.553031i	−0.961009	−	0.276515i	$-0.910820\pi$
$701$		−	14.6423i		−	0.553031i	0.961009	−	0.276515i	$-0.0891797\pi$
$702$		0			0
$703$	−33.6368	−	13.9328i	−1.26863	−	0.525486i
$704$	5.51956	−	13.3254i	0.208026	−	0.502220i
$705$		0			0
$706$	5.07538	−	5.07538i	0.191014	−	0.191014i
$707$	14.6840	−	35.4502i	0.552247	−	1.33324i
$708$		0			0
$709$	−10.8526	−	26.2006i	−0.407579	−	0.983983i	−0.985773	−	0.168083i	$-0.946242\pi$
$709$	−10.8526	−	26.2006i	−0.407579	−	0.983983i	0.578194	−	0.815899i	$-0.303758\pi$
$710$			0.0726360i			0.00272598i
$711$		0			0
$712$	−0.329520	−	0.329520i	−0.0123493	−	0.0123493i
$713$	1.93451			0.0724480
$714$		0			0
$715$	13.7279			0.513393
$716$	4.47321	+	4.47321i	0.167172	+	0.167172i
$717$		0			0
$718$			9.56736i			0.357051i
$719$	4.83536	+	11.6736i	0.180329	+	0.435352i	0.988034	−	0.154234i	$-0.0492910\pi$
$719$	4.83536	+	11.6736i	0.180329	+	0.435352i	−0.807706	+	0.589586i	$0.799291\pi$
$720$		0			0
$721$	14.1906	−	34.2593i	0.528487	−	1.27588i
$722$	6.79485	−	6.79485i	0.252878	−	0.252878i
$723$		0			0
$724$	−11.5901	+	27.9809i	−0.430742	+	1.03990i
$725$	−3.46587	−	1.43561i	−0.128719	−	0.0533173i
$726$		0			0
$727$			15.0242i			0.557218i	0.960405	+	0.278609i	$0.0898734\pi$
$727$			15.0242i			0.557218i	−0.960405	+	0.278609i	$0.910127\pi$
$728$	15.3498	−	6.35811i	0.568903	−	0.235647i
$729$		0			0
$730$	−1.94813			−0.0721035
$731$	−0.557517	−	10.7887i	−0.0206205	−	0.399035i
$732$		0			0
$733$	−1.24931	−	1.24931i	−0.0461442	−	0.0461442i	0.683658	−	0.729802i	$-0.260388\pi$
$733$	−1.24931	−	1.24931i	−0.0461442	−	0.0461442i	−0.729802	+	0.683658i	$0.760388\pi$
$734$	1.25895	−	0.521475i	0.0464688	−	0.0192480i
$735$		0			0
$736$	−1.12103	−	2.70640i	−0.0413216	−	0.0997592i
$737$	15.1356	+	6.26935i	0.557526	+	0.230935i
$738$		0			0
$739$	−13.9406	+	13.9406i	−0.512812	+	0.512812i	−0.915387	−	0.402575i	$-0.868115\pi$
$739$	−13.9406	+	13.9406i	−0.512812	+	0.512812i	0.402575	+	0.915387i	$0.368115\pi$
$740$	6.89179	−	6.89179i	0.253347	−	0.253347i
$741$		0			0
$742$	−1.94107	−	0.804017i	−0.0712589	−	0.0295164i
$743$	10.8535	+	26.2027i	0.398176	+	0.961282i	0.988099	+	0.153822i	$0.0491583\pi$
$743$	10.8535	+	26.2027i	0.398176	+	0.961282i	−0.589922	+	0.807460i	$0.700842\pi$
$744$		0			0
$745$	5.55958	−	2.30285i	0.203687	−	0.0843700i
$746$	1.09382	+	1.09382i	0.0400475	+	0.0400475i
$747$		0			0
$748$	−8.27422	−	17.3799i	−0.302535	−	0.635472i
$749$	3.69141			0.134881
$750$		0			0
$751$	16.5853	−	6.86987i	0.605207	−	0.250685i	−0.0589704	−	0.998260i	$-0.518782\pi$
$751$	16.5853	−	6.86987i	0.605207	−	0.250685i	0.664178	+	0.747575i	$0.268782\pi$
$752$			7.96698i			0.290526i
$753$		0			0
$754$	5.86937	+	2.43117i	0.213750	+	0.0885381i
$755$	−3.98690	+	9.62524i	−0.145098	+	0.350298i
$756$		0			0
$757$	−31.0649	+	31.0649i	−1.12907	+	1.12907i	−0.138743	+	0.990328i	$0.544306\pi$
$757$	−31.0649	+	31.0649i	−1.12907	+	1.12907i	−0.990328	+	0.138743i	$0.955694\pi$
$758$	0.638456	−	1.54137i	0.0231898	−	0.0559851i
$759$		0			0
$760$	3.21821	+	7.76945i	0.116737	+	0.281828i
$761$			13.2781i			0.481331i	0.970608	+	0.240666i	$0.0773657\pi$
$761$			13.2781i			0.481331i	−0.970608	+	0.240666i	$0.922634\pi$
$762$		0			0
$763$	16.7493	+	16.7493i	0.606367	+	0.606367i
$764$	−52.4861			−1.89888
$765$		0			0
$766$	6.16480			0.222743
$767$	29.5378	+	29.5378i	1.06655	+	1.06655i
$768$		0			0
$769$			24.8906i			0.897578i	0.893638	+	0.448789i	$0.148144\pi$
$769$			24.8906i			0.897578i	−0.893638	+	0.448789i	$0.851856\pi$
$770$	−0.708635	−	1.71080i	−0.0255374	−	0.0616528i
$771$		0			0
$772$	10.7836	−	26.0340i	0.388112	−	0.936985i
$773$	37.9750	−	37.9750i	1.36587	−	1.36587i	0.499624	−	0.866242i	$-0.333471\pi$
$773$	37.9750	−	37.9750i	1.36587	−	1.36587i	0.866242	−	0.499624i	$-0.166529\pi$
$774$		0			0
$775$	0.860015	−	2.07626i	0.0308926	−	0.0745814i
$776$	−9.76127	−	4.04325i	−0.350409	−	0.145144i
$777$		0			0
$778$		−	1.56463i		−	0.0560949i
$779$	81.3621	−	33.7013i	2.91510	−	1.20747i
$780$		0			0
$781$	0.588811			0.0210693
$782$	−1.00907	−	0.358158i	−0.0360841	−	0.0128077i
$783$		0			0
$784$	−1.71544	−	1.71544i	−0.0612658	−	0.0612658i
$785$	−12.3867	+	5.13073i	−0.442100	+	0.183124i
$786$		0			0
$787$	19.6997	+	47.5592i	0.702217	+	1.69530i	0.718588	+	0.695436i	$0.244789\pi$
$787$	19.6997	+	47.5592i	0.702217	+	1.69530i	−0.0163714	+	0.999866i	$0.505211\pi$
$788$	−0.663857	−	0.274979i	−0.0236489	−	0.00979571i
$789$		0			0
$790$	3.13792	−	3.13792i	0.111642	−	0.111642i
$791$	26.5517	−	26.5517i	0.944070	−	0.944070i
$792$		0			0
$793$	−4.70008	−	1.94684i	−0.166905	−	0.0691342i
$794$	0.712737	+	1.72070i	0.0252941	+	0.0610654i
$795$		0			0
$796$	13.2805	−	5.50097i	0.470716	−	0.194977i
$797$	−13.3772	−	13.3772i	−0.473846	−	0.473846i	0.429311	−	0.903157i	$-0.358756\pi$
$797$	−13.3772	−	13.3772i	−0.473846	−	0.473846i	−0.903157	+	0.429311i	$0.858756\pi$
$798$		0			0
$799$	7.04620	+	6.35374i	0.249276	+	0.224779i
$800$	−3.40308			−0.120317
$801$		0			0
$802$	−2.64687	+	1.09637i	−0.0934642	+	0.0387141i
$803$			15.7922i			0.557294i
$804$		0			0
$805$	1.99602	+	0.826780i	0.0703506	+	0.0291402i
$806$	−1.45641	+	3.51609i	−0.0513000	+	0.123849i
$807$		0			0
$808$	12.7486	−	12.7486i	0.448495	−	0.448495i
$809$	−11.5703	+	27.9333i	−0.406791	+	0.982081i	0.579185	+	0.815196i	$0.303371\pi$
$809$	−11.5703	+	27.9333i	−0.406791	+	0.982081i	−0.985976	+	0.166885i	$0.946629\pi$
$810$		0			0
$811$	−6.57121	−	15.8643i	−0.230746	−	0.557071i	0.765519	−	0.643413i	$-0.222482\pi$
$811$	−6.57121	−	15.8643i	−0.230746	−	0.557071i	−0.996266	+	0.0863422i	$0.972482\pi$
$812$			17.9740i			0.630765i
$813$		0			0
$814$	2.66358	+	2.66358i	0.0933586	+	0.0933586i
$815$	1.57513			0.0551745
$816$		0			0
$817$	18.6844			0.653683
$818$	−3.06944	−	3.06944i	−0.107320	−	0.107320i
$819$		0			0
$820$			23.5752i			0.823280i
$821$	16.7555	+	40.4514i	0.584771	+	1.41176i	0.888443	+	0.458986i	$0.151787\pi$
$821$	16.7555	+	40.4514i	0.584771	+	1.41176i	−0.303672	+	0.952777i	$0.598213\pi$
$822$		0			0
$823$	9.67025	−	23.3460i	0.337084	−	0.813792i	−0.660909	−	0.750466i	$-0.729829\pi$
$823$	9.67025	−	23.3460i	0.337084	−	0.813792i	0.997993	−	0.0633260i	$-0.0201708\pi$
$824$	12.3203	−	12.3203i	0.429199	−	0.429199i
$825$		0			0
$826$	2.15632	−	5.20581i	0.0750278	−	0.181133i
$827$	20.3879	+	8.44496i	0.708958	+	0.293660i	0.707874	−	0.706339i	$-0.249655\pi$
$827$	20.3879	+	8.44496i	0.708958	+	0.293660i	0.00108492	+	0.999999i	$0.499655\pi$
$828$		0			0
$829$			20.9555i			0.727816i	0.931435	+	0.363908i	$0.118558\pi$
$829$			20.9555i			0.727816i	−0.931435	+	0.363908i	$0.881442\pi$
$830$	3.87380	−	1.60458i	0.134462	−	0.0556958i
$831$		0			0
$832$	−33.1060			−1.14774
$833$	−2.88526	+	0.149099i	−0.0999684	+	0.00516597i
$834$		0			0
$835$	12.4486	+	12.4486i	0.430800	+	0.430800i
$836$	30.7576	−	12.7402i	1.06378	−	0.440630i
$837$		0			0
$838$	2.45024	+	5.91541i	0.0846422	+	0.204344i
$839$	−18.6855	−	7.73980i	−0.645096	−	0.267207i	0.0360558	−	0.999350i	$-0.488521\pi$
$839$	−18.6855	−	7.73980i	−0.645096	−	0.267207i	−0.681152	+	0.732142i	$0.738521\pi$
$840$		0			0
$841$	10.5548	−	10.5548i	0.363958	−	0.363958i
$842$	4.30216	−	4.30216i	0.148262	−	0.148262i
$843$		0			0
$844$	−15.3307	−	6.35018i	−0.527704	−	0.218582i
$845$	−7.08338	−	17.1008i	−0.243676	−	0.588285i
$846$		0			0
$847$	11.6384	−	4.82078i	0.399900	−	0.165644i
$848$	6.79298	+	6.79298i	0.233272	+	0.233272i
$849$		0			0
$850$	−0.832997	+	0.923780i	−0.0285716	+	0.0316854i
$851$	−4.39490			−0.150655
$852$		0			0
$853$	10.6192	−	4.39863i	0.363595	−	0.150606i	−0.193404	−	0.981119i	$-0.561953\pi$
$853$	10.6192	−	4.39863i	0.363595	−	0.150606i	0.556999	+	0.830513i	$0.311953\pi$
$854$			0.686230i			0.0234823i
$855$		0			0
$856$	1.60244	+	0.663753i	0.0547703	+	0.0226866i
$857$	10.7482	−	25.9484i	0.367151	−	0.886380i	−0.627064	−	0.778968i	$-0.715744\pi$
$857$	10.7482	−	25.9484i	0.367151	−	0.886380i	0.994215	−	0.107412i	$-0.0342565\pi$
$858$		0			0
$859$	−2.22749	+	2.22749i	−0.0760011	+	0.0760011i	−0.744086	−	0.668084i	$-0.767115\pi$
$859$	−2.22749	+	2.22749i	−0.0760011	+	0.0760011i	0.668084	+	0.744086i	$0.267115\pi$
$860$	−1.91411	+	4.62106i	−0.0652705	+	0.157577i
$861$		0			0
$862$	−2.30538	−	5.56568i	−0.0785216	−	0.189568i
$863$		−	34.5368i		−	1.17565i	−0.808989	−	0.587823i	$-0.799985\pi$
$863$		−	34.5368i		−	1.17565i	0.808989	−	0.587823i	$-0.200015\pi$
$864$		0			0
$865$	13.3239	+	13.3239i	0.453028	+	0.453028i
$866$	−5.49781			−0.186823
$867$		0			0
$868$	−10.7675			−0.365473
$869$	−25.4370	−	25.4370i	−0.862892	−	0.862892i
$870$		0			0
$871$		−	37.6032i		−	1.27414i
$872$	4.25919	+	10.2826i	0.144234	+	0.348212i
$873$		0			0
$874$	0.708688	−	1.71093i	0.0239717	−	0.0578729i
$875$	1.77472	−	1.77472i	0.0599966	−	0.0599966i
$876$		0			0
$877$	−6.05591	+	14.6203i	−0.204493	+	0.493691i	−0.992539	−	0.121926i	$-0.961093\pi$
$877$	−6.05591	+	14.6203i	−0.204493	+	0.493691i	0.788046	+	0.615617i	$0.211093\pi$
$878$	−4.10647	−	1.70096i	−0.138587	−	0.0574045i
$879$		0			0
$880$			8.46705i			0.285424i
$881$	−29.1623	+	12.0794i	−0.982504	+	0.406967i	−0.815353	−	0.578965i	$-0.803457\pi$
$881$	−29.1623	+	12.0794i	−0.982504	+	0.406967i	−0.167152	+	0.985931i	$0.553457\pi$
$882$		0			0
$883$	−20.2779			−0.682406			−0.341203	−	0.939990i	$-0.610834\pi$
$883$	−20.2779			−0.682406			−0.341203	+	0.939990i	$0.610834\pi$
$884$	−29.5878	+	32.8124i	−0.995144	+	1.10360i
$885$		0			0
$886$	−4.97762	−	4.97762i	−0.167226	−	0.167226i
$887$	−45.1215	+	18.6899i	−1.51503	+	0.627547i	−0.976589	−	0.215115i	$-0.930987\pi$
$887$	−45.1215	+	18.6899i	−1.51503	+	0.627547i	−0.538443	+	0.842662i	$0.680987\pi$
$888$		0			0
$889$	5.71946	+	13.8080i	0.191825	+	0.463106i
$890$	0.110141	+	0.0456218i	0.00369192	+	0.00152925i
$891$		0			0
$892$	8.72426	−	8.72426i	0.292110	−	0.292110i
$893$	−11.6033	+	11.6033i	−0.388290	+	0.388290i
$894$		0			0
$895$	−3.06159	−	1.26815i	−0.102338	−	0.0423897i
$896$	8.24607	+	19.9078i	0.275482	+	0.665072i
$897$		0			0
$898$	−0.477067	+	0.197608i	−0.0159199	+	0.00659425i
$899$	−5.96141	−	5.96141i	−0.198824	−	0.198824i
$900$		0			0
$901$	11.4253	−	0.590416i	0.380633	−	0.0196696i
$902$	−9.11148			−0.303379
$903$		0			0
$904$	16.3004	−	6.75183i	0.542142	−	0.224563i
$905$		−	15.8652i		−	0.527375i
$906$		0			0
$907$	−38.5317	−	15.9603i	−1.27942	−	0.529955i	−0.363608	−	0.931552i	$-0.618455\pi$
$907$	−38.5317	−	15.9603i	−1.27942	−	0.529955i	−0.915816	+	0.401598i	$0.868455\pi$
$908$	−2.23588	+	5.39790i	−0.0742004	+	0.179136i
$909$		0			0
$910$	−3.00545	+	3.00545i	−0.0996297	+	0.0996297i
$911$	−2.44973	+	5.91417i	−0.0811632	+	0.195945i	−0.959252	−	0.282553i	$-0.908819\pi$
$911$	−2.44973	+	5.91417i	−0.0811632	+	0.195945i	0.878088	+	0.478498i	$0.158819\pi$
$912$		0			0
$913$	−13.0073	−	31.4023i	−0.430478	−	1.03926i
$914$		−	3.98735i		−	0.131890i
$915$		0			0
$916$	−10.2039	−	10.2039i	−0.337145	−	0.337145i
$917$	−10.5094			−0.347052
$918$		0			0
$919$	−23.6812			−0.781170			−0.390585	−	0.920567i	$-0.627727\pi$
$919$	−23.6812			−0.781170			−0.390585	+	0.920567i	$0.627727\pi$
$920$	0.717811	+	0.717811i	0.0236655	+	0.0236655i
$921$		0			0
$922$		−	8.83658i		−	0.291017i
$923$	−0.517199	−	1.24863i	−0.0170238	−	0.0410991i
$924$		0			0
$925$	−1.95382	+	4.71693i	−0.0642411	+	0.155092i
$926$	2.09137	−	2.09137i	0.0687268	−	0.0687268i
$927$		0			0
$928$	−4.88550	+	11.7946i	−0.160374	+	0.387178i
$929$	−50.7164	−	21.0074i	−1.66395	−	0.689232i	−0.665583	−	0.746324i	$-0.731817\pi$
$929$	−50.7164	−	21.0074i	−1.66395	−	0.689232i	−0.998369	+	0.0570920i	$0.981817\pi$
$930$		0			0
$931$		−	4.99683i		−	0.163764i
$932$	−39.4142	+	16.3259i	−1.29106	+	0.534773i
$933$		0			0
$934$	−4.12766			−0.135061
$935$	7.48847	+	6.75255i	0.244899	+	0.220832i
$936$		0			0
$937$	4.78966	+	4.78966i	0.156471	+	0.156471i	0.781001	−	0.624530i	$-0.214709\pi$
$937$	4.78966	+	4.78966i	0.156471	+	0.156471i	−0.624530	+	0.781001i	$0.714709\pi$
$938$	−4.68619	+	1.94108i	−0.153010	+	0.0633786i
$939$		0			0
$940$	−1.68107	−	4.05845i	−0.0548303	−	0.132372i
$941$	23.2992	+	9.65084i	0.759532	+	0.314608i	0.728624	−	0.684914i	$-0.240160\pi$
$941$	23.2992	+	9.65084i	0.759532	+	0.314608i	0.0309078	+	0.999522i	$0.490160\pi$
$942$		0			0
$943$	7.51696	−	7.51696i	0.244786	−	0.244786i
$944$	−18.2183	+	18.2183i	−0.592954	+	0.592954i
$945$		0			0
$946$	−1.78598	−	0.739776i	−0.0580671	−	0.0240522i
$947$	−9.37621	−	22.6362i	−0.304686	−	0.735577i	−0.999860	−	0.0167354i	$-0.994673\pi$
$947$	−9.37621	−	22.6362i	−0.304686	−	0.735577i	0.695174	−	0.718841i	$-0.255327\pi$
$948$		0			0
$949$	33.4888	−	13.8715i	1.08709	−	0.450288i
$950$	−1.52123	−	1.52123i	−0.0493553	−	0.0493553i
$951$		0			0
$952$	11.5007	+	4.08206i	0.372740	+	0.132300i
$953$	−30.3936			−0.984545			−0.492272	−	0.870441i	$-0.663834\pi$
$953$	−30.3936			−0.984545			−0.492272	+	0.870441i	$0.663834\pi$
$954$		0			0
$955$	25.4014	−	10.5216i	0.821969	−	0.340471i
$956$		−	6.60473i		−	0.213612i
$957$		0			0
$958$	−3.06873	−	1.27111i	−0.0991462	−	0.0410677i
$959$	6.97302	−	16.8344i	0.225171	−	0.543610i
$960$		0			0
$961$	−18.3491	+	18.3491i	−0.591906	+	0.591906i
$962$	3.30874	−	7.98801i	0.106678	−	0.257544i
$963$		0			0
$964$	13.1688	+	31.7923i	0.424139	+	1.02396i
$965$			14.7613i			0.475182i
$966$		0			0
$967$	−31.0785	−	31.0785i	−0.999416	−	0.999416i	0.000584066	−	1.00000i	$-0.499814\pi$
$967$	−31.0785	−	31.0785i	−0.999416	−	0.999416i	−1.00000		0.000584066i	$0.999814\pi$
$968$	5.91906			0.190246
$969$		0			0
$970$	2.70288			0.0867843
$971$	−29.9769	−	29.9769i	−0.962005	−	0.962005i	0.0372988	−	0.999304i	$-0.488125\pi$
$971$	−29.9769	−	29.9769i	−0.962005	−	0.962005i	−0.999304	+	0.0372988i	$0.988125\pi$
$972$		0			0
$973$			26.0853i			0.836255i
$974$	−1.16538	−	2.81349i	−0.0373413	−	0.0901500i
$975$		0			0
$976$	1.20077	−	2.89891i	0.0384356	−	0.0927918i
$977$	−16.7792	+	16.7792i	−0.536813	+	0.536813i	−0.922591	−	0.385778i	$-0.873933\pi$
$977$	−16.7792	+	16.7792i	−0.536813	+	0.536813i	0.385778	+	0.922591i	$0.373933\pi$
$978$		0			0
$979$	0.369825	−	0.892837i	0.0118197	−	0.0285352i
$980$	1.23583	+	0.511896i	0.0394770	+	0.0163519i
$981$		0			0
$982$		−	5.15363i		−	0.164459i
$983$	25.9264	−	10.7391i	0.826925	−	0.342524i	0.0712405	−	0.997459i	$-0.477304\pi$
$983$	25.9264	−	10.7391i	0.826925	−	0.342524i	0.755685	+	0.654935i	$0.227304\pi$
$984$		0			0
$985$	0.376406			0.0119933
$986$	2.00585	+	4.21325i	0.0638791	+	0.134177i
$987$		0			0
$988$	−54.0337	−	54.0337i	−1.71904	−	1.71904i
$989$	2.08374	−	0.863114i	0.0662591	−	0.0274454i
$990$		0			0
$991$	17.0472	+	41.1557i	0.541523	+	1.30735i	0.923648	+	0.383242i	$0.125193\pi$
$991$	17.0472	+	41.1557i	0.541523	+	1.30735i	−0.382124	+	0.924111i	$0.624807\pi$
$992$	−7.06567	−	2.92670i	−0.224335	−	0.0929227i
$993$		0			0
$994$	−0.128909	+	0.128909i	−0.00408874	+	0.00408874i
$995$	−5.32454	+	5.32454i	−0.168799	+	0.168799i
$996$		0			0
$997$	−18.9837	−	7.86332i	−0.601221	−	0.249034i	0.0612487	−	0.998123i	$-0.480492\pi$
$997$	−18.9837	−	7.86332i	−0.601221	−	0.249034i	−0.662470	+	0.749089i	$0.730492\pi$
$998$	3.62047	+	8.74058i	0.114604	+	0.276678i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	765.2.be.b.631.3		24
3.2	odd	2		85.2.l.a.36.4	yes	24
15.2	even	4		425.2.n.c.274.3		24
15.8	even	4		425.2.n.f.274.4		24
15.14	odd	2		425.2.m.b.376.3		24
17.9	even	8	inner	765.2.be.b.451.3		24
51.5	even	16		1445.2.d.j.866.12		24
51.14	even	16		1445.2.a.q.1.7		12
51.20	even	16		1445.2.a.p.1.7		12
51.26	odd	8		85.2.l.a.26.4	✓	24
51.29	even	16		1445.2.d.j.866.11		24
255.14	even	16		7225.2.a.bq.1.6		12
255.77	even	8		425.2.n.f.349.4		24
255.128	even	8		425.2.n.c.349.3		24
255.179	odd	8		425.2.m.b.26.3		24
255.224	even	16		7225.2.a.bs.1.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.26.4	✓	24	51.26	odd	8
85.2.l.a.36.4	yes	24	3.2	odd	2
425.2.m.b.26.3		24	255.179	odd	8
425.2.m.b.376.3		24	15.14	odd	2
425.2.n.c.274.3		24	15.2	even	4
425.2.n.c.349.3		24	255.128	even	8
425.2.n.f.274.4		24	15.8	even	4
425.2.n.f.349.4		24	255.77	even	8
765.2.be.b.451.3		24	17.9	even	8	inner
765.2.be.b.631.3		24	1.1	even	1	trivial
1445.2.a.p.1.7		12	51.20	even	16
1445.2.a.q.1.7		12	51.14	even	16
1445.2.d.j.866.11		24	51.29	even	16
1445.2.d.j.866.12		24	51.5	even	16
7225.2.a.bq.1.6		12	255.14	even	16
7225.2.a.bs.1.6		12	255.224	even	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:	\( N \)	\(=\)	\( 765 = 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	765.be (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.213325 - 0.213325i) q^{2} -1.90899i q^{4} +(0.382683 + 0.923880i) q^{5} +(-0.960473 + 2.31879i) q^{7} +(-0.833883 + 0.833883i) q^{8} +(0.115451 - 0.278722i) q^{10} +(-2.25941 - 0.935880i) q^{11} +5.61335i q^{13} +(0.699548 - 0.289762i) q^{14} -3.46219 q^{16} +(-2.76113 + 3.06205i) q^{17} +(-5.04243 - 5.04243i) q^{19} +(1.76367 - 0.730537i) q^{20} +(0.282343 + 0.681636i) q^{22} +(-0.795280 - 0.329416i) q^{23} +(-0.707107 + 0.707107i) q^{25} +(1.19747 - 1.19747i) q^{26} +(4.42653 + 1.83353i) q^{28} +(1.43561 + 3.46587i) q^{29} +(-2.07626 + 0.860015i) q^{31} +(2.40634 + 2.40634i) q^{32} +(1.24223 - 0.0641935i) q^{34} -2.50984 q^{35} +(4.71693 - 1.95382i) q^{37} +2.15135i q^{38} +(-1.08952 - 0.451294i) q^{40} +(-4.72598 + 11.4095i) q^{41} +(-1.85272 + 1.85272i) q^{43} +(-1.78658 + 4.31319i) q^{44} +(0.0993804 + 0.239926i) q^{46} -2.30114i q^{47} +(0.495478 + 0.495478i) q^{49} +0.301687 q^{50} +10.7158 q^{52} +(-1.96204 - 1.96204i) q^{53} -2.44557i q^{55} +(-1.13268 - 2.73452i) q^{56} +(0.433105 - 1.04561i) q^{58} +(5.26206 - 5.26206i) q^{59} +(-0.346822 + 0.837303i) q^{61} +(0.626380 + 0.259455i) q^{62} +5.89773i q^{64} +(-5.18606 + 2.14814i) q^{65} -6.69889 q^{67} +(5.84541 + 5.27096i) q^{68} +(0.535411 + 0.535411i) q^{70} +(-0.222439 + 0.0921372i) q^{71} +(-2.47116 - 5.96591i) q^{73} +(-1.42304 - 0.589441i) q^{74} +(-9.62592 + 9.62592i) q^{76} +(4.34022 - 4.34022i) q^{77} +(13.5899 + 5.62912i) q^{79} +(-1.32492 - 3.19865i) q^{80} +(3.44210 - 1.42577i) q^{82} +(9.82767 + 9.82767i) q^{83} +(-3.88561 - 1.37916i) q^{85} +0.790460 q^{86} +(2.66450 - 1.10367i) q^{88} +0.395163i q^{89} +(-13.0162 - 5.39148i) q^{91} +(-0.628850 + 1.51818i) q^{92} +(-0.490889 + 0.490889i) q^{94} +(2.72894 - 6.58825i) q^{95} +(3.42855 + 8.27725i) q^{97} -0.211396i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{11} - 24 q^{16} + 8 q^{17} - 8 q^{19} - 32 q^{22} + 16 q^{23} - 16 q^{26} + 48 q^{28} + 8 q^{29} + 16 q^{34} + 32 q^{35} + 24 q^{37} + 16 q^{40} - 16 q^{41} + 8 q^{43} - 16 q^{44} + 8 q^{46}+ \cdots - 40 q^{97}+O(q^{100}) \) 24 * q + 8 * q^11 - 24 * q^16 + 8 * q^17 - 8 * q^19 - 32 * q^22 + 16 * q^23 - 16 * q^26 + 48 * q^28 + 8 * q^29 + 16 * q^34 + 32 * q^35 + 24 * q^37 + 16 * q^40 - 16 * q^41 + 8 * q^43 - 16 * q^44 + 8 * q^46 - 8 * q^50 - 48 * q^52 - 24 * q^53 - 64 * q^56 - 64 * q^58 - 32 * q^59 + 32 * q^61 + 32 * q^62 - 8 * q^65 + 16 * q^67 + 40 * q^68 + 24 * q^71 + 64 * q^74 - 8 * q^76 - 24 * q^77 + 32 * q^80 - 80 * q^82 + 96 * q^83 + 16 * q^86 - 8 * q^88 - 24 * q^91 - 80 * q^92 + 56 * q^94 + 16 * q^95 - 40 * q^97

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