LMFDB - Embedded newform 375.2.l.b.368.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [375,2,Mod(32,375)] 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("375.32"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(375, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.l (of order $20$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [64,0,0,20,0,-6,20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			368.3
Character	$\chi$	$=$	375.368
Dual form			375.2.l.b.107.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.32314 + 0.674175i) q^{2} +(1.68525 - 0.399927i) q^{3} +(0.120624 - 0.166024i) q^{4} +(-1.96020 + 1.66531i) q^{6} +(1.72218 - 1.72218i) q^{7} +(0.416937 - 2.63243i) q^{8} +(2.68012 - 1.34795i) q^{9} +(-3.72206 - 1.20937i) q^{11} +(0.136883 - 0.328033i) q^{12} +(2.65113 - 5.20313i) q^{13} +(-1.11764 + 3.43974i) q^{14} +(1.34989 + 4.15452i) q^{16} +(-0.760813 - 0.120501i) q^{17} +(-2.63742 + 3.59040i) q^{18} +(2.08083 + 2.86402i) q^{19} +(2.21355 - 3.59105i) q^{21} +(5.74013 - 0.909148i) q^{22} +(0.471845 + 0.926047i) q^{23} +(-0.350141 - 4.60305i) q^{24} +8.67180i q^{26} +(3.97758 - 3.34348i) q^{27} +(-0.0781880 - 0.493660i) q^{28} +(0.111964 + 0.0813465i) q^{29} +(0.372717 - 0.270795i) q^{31} +(-0.817733 - 0.817733i) q^{32} +(-6.75624 - 0.549535i) q^{33} +(1.08790 - 0.353481i) q^{34} +(0.0994927 - 0.607559i) q^{36} +(-4.55581 - 2.32130i) q^{37} +(-4.68409 - 2.38666i) q^{38} +(2.38693 - 9.82881i) q^{39} +(6.18190 - 2.00862i) q^{41} +(-0.507853 + 6.24379i) q^{42} +(5.58451 + 5.58451i) q^{43} +(-0.649753 + 0.472073i) q^{44} +(-1.24864 - 0.907186i) q^{46} +(0.629748 + 3.97607i) q^{47} +(3.93640 + 6.46154i) q^{48} +1.06819i q^{49} +(-1.33035 + 0.101196i) q^{51} +(-0.544057 - 1.06777i) q^{52} +(2.90283 - 0.459763i) q^{53} +(-3.00881 + 7.10549i) q^{54} +(-3.81549 - 5.25157i) q^{56} +(4.65212 + 3.99440i) q^{57} +(-0.202986 - 0.0321498i) q^{58} +(0.855253 + 2.63220i) q^{59} +(1.24058 - 3.81812i) q^{61} +(-0.310595 + 0.609576i) q^{62} +(2.29423 - 6.93706i) q^{63} +(-6.67577 - 2.16909i) q^{64} +(9.30995 - 3.82778i) q^{66} +(-0.304459 + 1.92228i) q^{67} +(-0.111778 + 0.111778i) q^{68} +(1.16553 + 1.37191i) q^{69} +(-2.08859 + 2.87469i) q^{71} +(-2.43096 - 7.61724i) q^{72} +(-10.6846 + 5.44405i) q^{73} +7.59295 q^{74} +0.726495 q^{76} +(-8.49280 + 4.32730i) q^{77} +(3.46809 + 14.6141i) q^{78} +(-0.518361 + 0.713462i) q^{79} +(5.36605 - 7.22534i) q^{81} +(-6.82537 + 6.82537i) q^{82} +(1.49428 - 9.43448i) q^{83} +(-0.329194 - 0.800669i) q^{84} +(-11.1540 - 3.62417i) q^{86} +(0.221219 + 0.0923115i) q^{87} +(-4.73545 + 9.29383i) q^{88} +(-3.64270 + 11.2111i) q^{89} +(-4.39501 - 13.5264i) q^{91} +(0.210662 + 0.0333656i) q^{92} +(0.519822 - 0.605416i) q^{93} +(-3.51381 - 4.83635i) q^{94} +(-1.70512 - 1.05105i) q^{96} +(-16.0719 + 2.54554i) q^{97} +(-0.720145 - 1.41336i) q^{98} +(-11.6057 + 1.77590i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 20 q^{4} - 6 q^{6} + 20 q^{7} + 10 q^{9} + 40 q^{12} - 8 q^{16} + 10 q^{18} - 6 q^{21} - 30 q^{27} - 80 q^{28} - 12 q^{31} - 50 q^{33} - 20 q^{34} - 22 q^{36} - 120 q^{37} - 30 q^{39} + 60 q^{42}+ \cdots + 42 q^{96}+O(q^{100}) $ 64 * q + 20 * q^4 - 6 * q^6 + 20 * q^7 + 10 * q^9 + 40 * q^12 - 8 * q^16 + 10 * q^18 - 6 * q^21 - 30 * q^27 - 80 * q^28 - 12 * q^31 - 50 * q^33 - 20 * q^34 - 22 * q^36 - 120 * q^37 - 30 * q^39 + 60 * q^42 + 20 * q^43 - 12 * q^46 + 100 * q^48 - 16 * q^51 + 100 * q^52 - 120 * q^54 - 70 * q^57 + 120 * q^58 - 12 * q^61 - 70 * q^63 + 100 * q^64 - 30 * q^66 - 60 * q^67 + 80 * q^69 - 40 * q^72 - 80 * q^73 - 64 * q^76 + 70 * q^78 + 60 * q^79 + 14 * q^81 + 60 * q^82 + 130 * q^84 + 100 * q^87 + 60 * q^88 - 12 * q^91 + 20 * q^93 - 260 * q^94 + 42 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{7}{20}\right)$	$-1$

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 $

$2$	−1.32314	+	0.674175i	−0.935603	+	0.476714i	−0.854187	−	0.519967i	$-0.825944\pi$
$2$	−1.32314	+	0.674175i	−0.935603	+	0.476714i	−0.0814164	+	0.996680i	$0.525944\pi$
$3$	1.68525	−	0.399927i	0.972978	−	0.230898i
$3$	1.68525	−	0.399927i	0.972978	−	0.230898i
$4$	0.120624	−	0.166024i	0.0603118	−	0.0830121i
$5$		0			0
$5$		0			0
$6$	−1.96020	+	1.66531i	−0.800249	+	0.679861i
$7$	1.72218	−	1.72218i	0.650923	−	0.650923i	−0.302292	−	0.953215i	$-0.597752\pi$
$7$	1.72218	−	1.72218i	0.650923	−	0.650923i	0.953215	+	0.302292i	$0.0977518\pi$
$8$	0.416937	−	2.63243i	0.147409	−	0.930706i
$9$	2.68012	−	1.34795i	0.893372	−	0.449318i
$10$		0			0
$11$	−3.72206	−	1.20937i	−1.12224	−	0.364638i	−0.311619	−	0.950207i	$-0.600871\pi$
$11$	−3.72206	−	1.20937i	−1.12224	−	0.364638i	−0.810623	+	0.585569i	$0.800871\pi$
$12$	0.136883	−	0.328033i	0.0395147	−	0.0946949i
$13$	2.65113	−	5.20313i	0.735290	−	1.44309i	−0.155104	−	0.987898i	$-0.549571\pi$
$13$	2.65113	−	5.20313i	0.735290	−	1.44309i	0.890394	−	0.455190i	$-0.150429\pi$
$14$	−1.11764	+	3.43974i	−0.298702	+	0.919309i
$15$		0			0
$16$	1.34989	+	4.15452i	0.337471	+	1.03863i
$17$	−0.760813	−	0.120501i	−0.184524	−	0.0292258i	0.0634883	−	0.997983i	$-0.479777\pi$
$17$	−0.760813	−	0.120501i	−0.184524	−	0.0292258i	−0.248013	+	0.968757i	$0.579777\pi$
$18$	−2.63742	+	3.59040i	−0.621646	+	0.846265i
$19$	2.08083	+	2.86402i	0.477376	+	0.657051i	0.977998	−	0.208614i	$-0.0668954\pi$
$19$	2.08083	+	2.86402i	0.477376	+	0.657051i	−0.500622	+	0.865666i	$0.666895\pi$
$20$		0			0
$21$	2.21355	−	3.59105i	0.483037	−	0.783631i
$22$	5.74013	−	0.909148i	1.22380	−	0.193831i
$23$	0.471845	+	0.926047i	0.0983864	+	0.193094i	0.934953	−	0.354770i	$-0.115441\pi$
$23$	0.471845	+	0.926047i	0.0983864	+	0.193094i	−0.836567	+	0.547864i	$0.815441\pi$
$24$	−0.350141	−	4.60305i	−0.0714722	−	0.939593i
$25$		0			0
$26$			8.67180i			1.70068i
$27$	3.97758	−	3.34348i	0.765485	−	0.643454i
$28$	−0.0781880	−	0.493660i	−0.0147761	−	0.0932929i
$29$	0.111964	+	0.0813465i	0.0207912	+	0.0151057i	0.598132	−	0.801397i	$-0.295910\pi$
$29$	0.111964	+	0.0813465i	0.0207912	+	0.0151057i	−0.577341	+	0.816503i	$0.695910\pi$
$30$		0			0
$31$	0.372717	−	0.270795i	0.0669420	−	0.0486362i	−0.553811	−	0.832642i	$-0.686827\pi$
$31$	0.372717	−	0.270795i	0.0669420	−	0.0486362i	0.620753	+	0.784006i	$0.286827\pi$
$32$	−0.817733	−	0.817733i	−0.144556	−	0.144556i
$33$	−6.75624	−	0.549535i	−1.17611	−	0.0956617i
$34$	1.08790	−	0.353481i	0.186574	−	0.0606215i
$35$		0			0
$36$	0.0994927	−	0.607559i	0.0165821	−	0.101260i
$37$	−4.55581	−	2.32130i	−0.748970	−	0.381620i	0.0374602	−	0.999298i	$-0.488073\pi$
$37$	−4.55581	−	2.32130i	−0.748970	−	0.381620i	−0.786431	+	0.617679i	$0.788073\pi$
$38$	−4.68409	−	2.38666i	−0.759859	−	0.387168i
$39$	2.38693	−	9.82881i	0.382215	−	1.57387i
$40$		0			0
$41$	6.18190	−	2.00862i	0.965450	−	0.313694i	0.216472	−	0.976289i	$-0.430545\pi$
$41$	6.18190	−	2.00862i	0.965450	−	0.313694i	0.748978	+	0.662595i	$0.230545\pi$
$42$	−0.507853	+	6.24379i	−0.0783634	+	0.963437i
$43$	5.58451	+	5.58451i	0.851630	+	0.851630i	0.990334	−	0.138704i	$-0.0442938\pi$
$43$	5.58451	+	5.58451i	0.851630	+	0.851630i	−0.138704	+	0.990334i	$0.544294\pi$
$44$	−0.649753	+	0.472073i	−0.0979539	+	0.0711677i
$45$		0			0
$46$	−1.24864	−	0.907186i	−0.184101	−	0.133757i
$47$	0.629748	+	3.97607i	0.0918582	+	0.579970i	0.990089	+	0.140445i	$0.0448532\pi$
$47$	0.629748	+	3.97607i	0.0918582	+	0.579970i	−0.898230	+	0.439525i	$0.855147\pi$
$48$	3.93640	+	6.46154i	0.568170	+	0.932642i
$49$			1.06819i			0.152598i
$50$		0			0
$51$	−1.33035	+	0.101196i	−0.186286	+	0.0141703i
$52$	−0.544057	−	1.06777i	−0.0754471	−	0.148073i
$53$	2.90283	−	0.459763i	0.398734	−	0.0631533i	0.0461526	−	0.998934i	$-0.485304\pi$
$53$	2.90283	−	0.459763i	0.398734	−	0.0631533i	0.352581	+	0.935781i	$0.385304\pi$
$54$	−3.00881	+	7.10549i	−0.409447	+	0.966934i
$55$		0			0
$56$	−3.81549	−	5.25157i	−0.509866	−	0.701770i
$57$	4.65212	+	3.99440i	0.616188	+	0.529071i
$58$	−0.202986	−	0.0321498i	−0.0266533	−	0.00422147i
$59$	0.855253	+	2.63220i	0.111344	+	0.342683i	0.991167	−	0.132619i	$-0.0423388\pi$
$59$	0.855253	+	2.63220i	0.111344	+	0.342683i	−0.879823	+	0.475302i	$0.842339\pi$
$60$		0			0
$61$	1.24058	−	3.81812i	0.158840	−	0.488860i	−0.839689	−	0.543067i	$-0.817263\pi$
$61$	1.24058	−	3.81812i	0.158840	−	0.488860i	0.998530	+	0.0542065i	$0.0172629\pi$
$62$	−0.310595	+	0.609576i	−0.0394456	+	0.0774163i
$63$	2.29423	−	6.93706i	0.289045	−	0.873988i
$64$	−6.67577	−	2.16909i	−0.834471	−	0.271136i
$65$		0			0
$66$	9.30995	−	3.82778i	1.14598	−	0.471167i
$67$	−0.304459	+	1.92228i	−0.0371956	+	0.234844i	−0.999281	−	0.0379032i	$-0.987932\pi$
$67$	−0.304459	+	1.92228i	−0.0371956	+	0.234844i	0.962086	+	0.272747i	$0.0879322\pi$
$68$	−0.111778	+	0.111778i	−0.0135551	+	0.0135551i
$69$	1.16553	+	1.37191i	0.140313	+	0.165159i
$70$		0			0
$71$	−2.08859	+	2.87469i	−0.247870	+	0.341163i	−0.914764	−	0.403989i	$-0.867623\pi$
$71$	−2.08859	+	2.87469i	−0.247870	+	0.341163i	0.666894	+	0.745152i	$0.267623\pi$
$72$	−2.43096	−	7.61724i	−0.286491	−	0.897700i
$73$	−10.6846	+	5.44405i	−1.25053	+	0.637178i	−0.948698	−	0.316182i	$-0.897599\pi$
$73$	−10.6846	+	5.44405i	−1.25053	+	0.637178i	−0.301834	+	0.953360i	$0.597599\pi$
$74$	7.59295			0.882662
$75$		0			0
$76$	0.726495			0.0833347
$77$	−8.49280	+	4.32730i	−0.967845	+	0.493142i
$78$	3.46809	+	14.6141i	0.392684	+	1.65472i
$79$	−0.518361	+	0.713462i	−0.0583201	+	0.0802708i	−0.837181	−	0.546926i	$-0.815798\pi$
$79$	−0.518361	+	0.713462i	−0.0583201	+	0.0802708i	0.778861	+	0.627197i	$0.215798\pi$
$80$		0			0
$81$	5.36605	−	7.22534i	0.596228	−	0.802816i
$82$	−6.82537	+	6.82537i	−0.753736	+	0.753736i
$83$	1.49428	−	9.43448i	0.164018	−	1.03557i	−0.759078	−	0.651000i	$-0.774350\pi$
$83$	1.49428	−	9.43448i	0.164018	−	1.03557i	0.923096	−	0.384569i	$-0.125650\pi$
$84$	−0.329194	−	0.800669i	−0.0359180	−	0.0873601i
$85$		0			0
$86$	−11.1540	−	3.62417i	−1.20277	−	0.390804i
$87$	0.221219	+	0.0923115i	0.0237172	+	0.00989684i
$88$	−4.73545	+	9.29383i	−0.504800	+	0.990726i
$89$	−3.64270	+	11.2111i	−0.386125	+	1.18837i	0.549535	+	0.835470i	$0.314805\pi$
$89$	−3.64270	+	11.2111i	−0.386125	+	1.18837i	−0.935661	+	0.352901i	$0.885195\pi$
$90$		0			0
$91$	−4.39501	−	13.5264i	−0.460722	−	1.41796i
$92$	0.210662	+	0.0333656i	0.0219630	+	0.00347860i
$93$	0.519822	−	0.605416i	0.0539030	−	0.0627787i
$94$	−3.51381	−	4.83635i	−0.362422	−	0.498831i
$95$		0			0
$96$	−1.70512	−	1.05105i	−0.174028	−	0.107272i
$97$	−16.0719	+	2.54554i	−1.63186	+	0.258461i	−0.904083	−	0.427356i	$-0.859445\pi$
$97$	−16.0719	+	2.54554i	−1.63186	+	0.258461i	−0.727774	+	0.685817i	$0.759445\pi$
$98$	−0.720145	−	1.41336i	−0.0727456	−	0.142771i
$99$	−11.6057	+	1.77590i	−1.16642	+	0.178485i
$100$		0			0
$101$			14.8155i			1.47420i	0.675784	+	0.737100i	$0.263805\pi$
$101$			14.8155i			1.47420i	−0.675784	+	0.737100i	$0.736195\pi$
$102$	1.69202	−	1.03079i	0.167535	−	0.102063i
$103$	−1.39927	−	8.83465i	−0.137874	−	0.870504i	−0.955551	−	0.294826i	$-0.904738\pi$
$103$	−1.39927	−	8.83465i	−0.137874	−	0.870504i	0.817677	−	0.575678i	$-0.195262\pi$
$104$	−12.5915	−	9.14829i	−1.23470	−	0.897063i
$105$		0			0
$106$	−3.53089	+	2.56534i	−0.342951	+	0.249168i
$107$	−10.2862	−	10.2862i	−0.994405	−	0.994405i	0.00557906	−	0.999984i	$-0.498224\pi$
$107$	−10.2862	−	10.2862i	−0.994405	−	0.994405i	−0.999984	+	0.00557906i	$0.998224\pi$
$108$	−0.0753098	−	1.06368i	−0.00724668	−	0.102352i
$109$	−9.46329	+	3.07481i	−0.906419	+	0.294513i	−0.724884	−	0.688871i	$-0.758107\pi$
$109$	−9.46329	+	3.07481i	−0.906419	+	0.294513i	−0.181535	+	0.983384i	$0.558107\pi$
$110$		0			0
$111$	−8.60602	−	2.08997i	−0.816847	−	0.198372i
$112$	9.47958	+	4.83009i	0.895736	+	0.456400i
$113$	−4.31931	−	2.20080i	−0.406326	−	0.207034i	0.238868	−	0.971052i	$-0.423224\pi$
$113$	−4.31931	−	2.20080i	−0.406326	−	0.207034i	−0.645194	+	0.764018i	$0.723224\pi$
$114$	−8.84834	−	2.14882i	−0.828723	−	0.201256i
$115$		0			0
$116$	0.0270110	−	0.00877640i	0.00250791	−	0.000814868i
$117$	0.0917569	−	17.5186i	0.00848293	−	1.61959i
$118$	−2.90618	−	2.90618i	−0.267536	−	0.267536i
$119$	−1.51778	+	1.10273i	−0.139135	+	0.101087i
$120$		0			0
$121$	3.49193	+	2.53704i	0.317449	+	0.230640i
$122$	0.932613	+	5.88829i	0.0844349	+	0.533101i
$123$	9.61472	−	5.85733i	0.866930	−	0.528138i
$124$		−	0.0945443i		−	0.00849033i
$125$		0			0
$126$	1.64120	+	10.7254i	0.146210	+	0.955497i
$127$	5.18173	+	10.1697i	0.459804	+	0.902417i	0.998214	+	0.0597340i	$0.0190253\pi$
$127$	5.18173	+	10.1697i	0.459804	+	0.902417i	−0.538410	+	0.842683i	$0.680975\pi$
$128$	12.5798	−	1.99244i	1.11190	−	0.176108i
$129$	11.6447	+	7.17788i	1.02526	+	0.631977i
$130$		0			0
$131$	2.60417	+	3.58434i	0.227528	+	0.313165i	0.907483	−	0.420088i	$-0.138001\pi$
$131$	2.60417	+	3.58434i	0.227528	+	0.313165i	−0.679956	+	0.733253i	$0.738001\pi$
$132$	−0.906199	+	1.05541i	−0.0788745	+	0.0918619i
$133$	8.51593	+	1.34879i	0.738425	+	0.116955i
$134$	−0.893109	−	2.74871i	−0.0771529	−	0.237452i
$135$		0			0
$136$	−0.634422	+	1.95255i	−0.0544012	+	0.167430i
$137$	3.76412	−	7.38749i	0.321590	−	0.631156i	−0.672453	−	0.740139i	$-0.734759\pi$
$137$	3.76412	−	7.38749i	0.321590	−	0.631156i	0.994044	+	0.108983i	$0.0347595\pi$
$138$	−2.46707	−	1.02947i	−0.210011	−	0.0876343i
$139$	20.8266	+	6.76697i	1.76649	+	0.573967i	0.997839	−	0.0657043i	$-0.0209294\pi$
$139$	20.8266	+	6.76697i	1.76649	+	0.573967i	0.768649	+	0.639671i	$0.220929\pi$
$140$		0			0
$141$	2.65142	+	6.44881i	0.223290	+	0.543088i
$142$	0.825452	−	5.21170i	0.0692704	−	0.437356i
$143$	−16.1601	+	16.1601i	−1.35138	+	1.35138i
$144$	9.21794	+	9.31501i	0.768162	+	0.776251i
$145$		0			0
$146$	10.4669	−	14.4065i	0.866251	−	1.19229i
$147$	0.427197	+	1.80016i	0.0352346	+	0.148475i
$148$	−0.934931	+	0.476371i	−0.0768508	+	0.0391575i
$149$	5.61752			0.460205			0.230103	−	0.973166i	$-0.426094\pi$
$149$	5.61752			0.460205			0.230103	+	0.973166i	$0.426094\pi$
$150$		0			0
$151$	−14.6821			−1.19482			−0.597408	−	0.801938i	$-0.703803\pi$
$151$	−14.6821			−1.19482			−0.597408	+	0.801938i	$0.703803\pi$
$152$	8.40692	−	4.28354i	0.681891	−	0.347441i
$153$	−2.20150	+	0.702584i	−0.177981	+	0.0568005i
$154$	8.31983	−	11.4513i	0.670431	−	0.922769i
$155$		0			0
$156$	−1.34390	−	1.58188i	−0.107598	−	0.126651i
$157$	7.39864	−	7.39864i	0.590476	−	0.590476i	−0.347284	−	0.937760i	$-0.612896\pi$
$157$	7.39864	−	7.39864i	0.590476	−	0.590476i	0.937760	+	0.347284i	$0.112896\pi$
$158$	0.204867	−	1.29348i	0.0162983	−	0.102904i
$159$	4.70811	−	1.93573i	0.373377	−	0.153514i
$160$		0			0
$161$	2.40742	+	0.782219i	0.189731	+	0.0616475i
$162$	−2.22890	+	13.1778i	−0.175119	+	1.03535i
$163$	−3.88333	+	7.62146i	−0.304166	+	0.596959i	−0.991608	−	0.129280i	$-0.958733\pi$
$163$	−3.88333	+	7.62146i	−0.304166	+	0.596959i	0.687442	+	0.726239i	$0.258733\pi$
$164$	0.412204	−	1.26863i	0.0321877	−	0.0990635i
$165$		0			0
$166$	4.38335	+	13.4906i	0.340214	+	1.04707i
$167$	17.2815	+	2.73713i	1.33729	+	0.211805i	0.783779	−	0.621039i	$-0.213289\pi$
$167$	17.2815	+	2.73713i	1.33729	+	0.211805i	0.553507	+	0.832845i	$0.313289\pi$
$168$	−8.53028	−	7.32427i	−0.658126	−	0.565080i
$169$	−12.4029	−	17.0711i	−0.954066	−	1.31316i
$170$		0			0
$171$	9.43744	+	4.87104i	0.721699	+	0.372498i
$172$	1.60079	−	0.253540i	0.122059	−	0.0193322i
$173$	7.59919	+	14.9142i	0.577755	+	1.13391i	0.976232	+	0.216730i	$0.0695392\pi$
$173$	7.59919	+	14.9142i	0.577755	+	1.13391i	−0.398476	+	0.917179i	$0.630461\pi$
$174$	−0.354939	+	0.0269992i	−0.0269078	+	0.00204680i
$175$		0			0
$176$		−	17.0959i		−	1.28865i
$177$	2.49400	+	4.09386i	0.187460	+	0.307714i
$178$	−2.73841	−	17.2897i	−0.205253	−	1.29591i
$179$	7.83739	+	5.69420i	0.585794	+	0.425604i	0.840808	−	0.541333i	$-0.182080\pi$
$179$	7.83739	+	5.69420i	0.585794	+	0.425604i	−0.255014	+	0.966937i	$0.582080\pi$
$180$		0			0
$181$	7.76955	−	5.64491i	0.577506	−	0.419583i	−0.260318	−	0.965523i	$-0.583827\pi$
$181$	7.76955	−	5.64491i	0.577506	−	0.419583i	0.837824	+	0.545940i	$0.183827\pi$
$182$	14.9344	+	14.9344i	1.10701	+	1.10701i
$183$	0.563718	−	6.93062i	0.0416712	−	0.512326i
$184$	2.63449	−	0.855997i	0.194217	−	0.0631049i
$185$		0			0
$186$	−0.279643	+	1.15150i	−0.0205044	+	0.0844322i
$187$	2.68606	+	1.36862i	0.196424	+	0.100083i
$188$	0.736087	+	0.375055i	0.0536847	+	0.0273537i
$189$	1.09202	−	12.6082i	0.0794327	−	0.917111i
$190$		0			0
$191$	10.1420	−	3.29532i	0.733847	−	0.238441i	0.0818306	−	0.996646i	$-0.473923\pi$
$191$	10.1420	−	3.29532i	0.733847	−	0.238441i	0.652016	+	0.758205i	$0.273923\pi$
$192$	−12.1178	−	0.985629i	−0.874527	−	0.0711316i
$193$	−8.82760	−	8.82760i	−0.635425	−	0.635425i	0.313999	−	0.949423i	$-0.398331\pi$
$193$	−8.82760	−	8.82760i	−0.635425	−	0.635425i	−0.949423	+	0.313999i	$0.898331\pi$
$194$	19.5493	−	14.2034i	1.40356	−	1.01975i
$195$		0			0
$196$	0.177345	+	0.128849i	0.0126675	+	0.00920348i
$197$	−1.19701	−	7.55759i	−0.0852831	−	0.538456i	−0.992928	−	0.118718i	$-0.962122\pi$
$197$	−1.19701	−	7.55759i	−0.0852831	−	0.538456i	0.907645	−	0.419739i	$-0.137878\pi$
$198$	14.1587	−	10.1741i	1.00622	−	0.723038i
$199$			16.5759i			1.17503i	0.809212	+	0.587517i	$0.199895\pi$
$199$			16.5759i			1.17503i	−0.809212	+	0.587517i	$0.800105\pi$
$200$		0			0
$201$	0.255683	+	3.36128i	0.0180345	+	0.237086i
$202$	−9.98825	−	19.6030i	−0.702771	−	1.37927i
$203$	0.332915	−	0.0527286i	0.0233661	−	0.00370082i
$204$	−0.143671	+	0.233077i	−0.0100590	+	0.0163187i
$205$		0			0
$206$	7.80753	+	10.7461i	0.543976	+	0.748719i
$207$	2.51287	+	1.84589i	0.174656	+	0.128298i
$208$	25.1952	+	3.99053i	1.74697	+	0.276693i
$209$	−4.28132	−	13.1765i	−0.296145	−	0.911440i
$210$		0			0
$211$	−7.40904	+	22.8027i	−0.510059	+	1.56980i	0.282036	+	0.959404i	$0.408990\pi$
$211$	−7.40904	+	22.8027i	−0.510059	+	1.56980i	−0.792096	+	0.610397i	$0.791010\pi$
$212$	0.273818	−	0.537398i	0.0188059	−	0.0369086i
$213$	−2.37012	+	5.67985i	−0.162398	+	0.389177i
$214$	20.5448	+	6.67542i	1.40442	+	0.456322i
$215$		0			0
$216$	−7.14311	−	11.8647i	−0.486027	−	0.807292i
$217$	0.175529	−	1.10824i	0.0119157	−	0.0752325i
$218$	10.4483	−	10.4483i	0.707650	−	0.707650i
$219$	−15.8289	+	13.4476i	−1.06962	+	0.908706i
$220$		0			0
$221$	−2.64399	+	3.63914i	−0.177854	+	0.244795i
$222$	12.7960	−	3.03663i	0.858811	−	0.203805i
$223$	−2.11546	+	1.07788i	−0.141662	+	0.0721802i	−0.523385	−	0.852097i	$-0.675331\pi$
$223$	−2.11546	+	1.07788i	−0.141662	+	0.0721802i	0.381723	+	0.924277i	$0.375331\pi$
$224$	−2.81657			−0.188190
$225$		0			0
$226$	7.19878			0.478856
$227$	−10.8425	+	5.52455i	−0.719644	+	0.366677i	−0.775146	−	0.631782i	$-0.782324\pi$
$227$	−10.8425	+	5.52455i	−0.719644	+	0.366677i	0.0555024	+	0.998459i	$0.482324\pi$
$228$	1.22432	−	0.290545i	0.0810828	−	0.0192418i
$229$	8.52530	−	11.7341i	0.563368	−	0.775409i	−0.428382	−	0.903598i	$-0.640916\pi$
$229$	8.52530	−	11.7341i	0.563368	−	0.775409i	0.991750	+	0.128188i	$0.0409162\pi$
$230$		0			0
$231$	−12.5819	+	10.6891i	−0.827826	+	0.703289i
$232$	0.260821	−	0.260821i	0.0171237	−	0.0171237i
$233$	−3.38975	+	21.4020i	−0.222070	+	1.40209i	0.584710	+	0.811242i	$0.301208\pi$
$233$	−3.38975	+	21.4020i	−0.222070	+	1.40209i	−0.806780	+	0.590852i	$0.798792\pi$
$234$	11.6892	+	23.2414i	0.764145	+	1.51934i
$235$		0			0
$236$	0.540172	+	0.175513i	0.0351622	+	0.0114249i
$237$	−0.588233	+	1.40967i	−0.0382098	+	0.0915677i
$238$	1.26481	−	2.48232i	0.0819853	−	0.160905i
$239$	2.61133	−	8.03683i	0.168913	−	0.519859i	−0.830391	−	0.557182i	$-0.811883\pi$
$239$	2.61133	−	8.03683i	0.168913	−	0.519859i	0.999303	+	0.0373221i	$0.0118827\pi$
$240$		0			0
$241$	0.483477	+	1.48799i	0.0311435	+	0.0958498i	0.965420	−	0.260699i	$-0.0839532\pi$
$241$	0.483477	+	1.48799i	0.0311435	+	0.0958498i	−0.934277	+	0.356549i	$0.883953\pi$
$242$	−6.33073	−	1.00269i	−0.406955	−	0.0644553i
$243$	6.15351	−	14.3225i	0.394748	−	0.918790i
$244$	−0.484257	−	0.666523i	−0.0310014	−	0.0426698i
$245$		0			0
$246$	−8.77278	+	14.2321i	−0.559332	+	0.907405i
$247$	20.4184	−	3.23396i	1.29919	−	0.205772i
$248$	−0.557450	−	1.09406i	−0.0353981	−	0.0694727i
$249$	−1.25488	−	16.4970i	−0.0795250	−	1.04546i
$250$		0			0
$251$		−	8.41068i		−	0.530878i	−0.964128	−	0.265439i	$-0.914483\pi$
$251$		−	8.41068i		−	0.530878i	0.964128	−	0.265439i	$-0.0855168\pi$
$252$	−0.874983	−	1.21767i	−0.0551187	−	0.0767061i
$253$	−0.636299	−	4.01743i	−0.0400038	−	0.252574i
$254$	−13.7123	−	9.96260i	−0.860389	−	0.625109i
$255$		0			0
$256$	−3.94407	+	2.86553i	−0.246504	+	0.179096i
$257$	−10.6415	−	10.6415i	−0.663801	−	0.663801i	0.292473	−	0.956274i	$-0.405522\pi$
$257$	−10.6415	−	10.6415i	−0.663801	−	0.663801i	−0.956274	+	0.292473i	$0.905522\pi$
$258$	−20.2467	−	1.64681i	−1.26050	−	0.102526i
$259$	−11.8436	+	3.84823i	−0.735927	+	0.239117i
$260$		0			0
$261$	0.409727	+	0.0670961i	0.0253615	+	0.00415314i
$262$	−5.86216	−	2.98692i	−0.362165	−	0.184532i
$263$	1.66971	+	0.850760i	0.102959	+	0.0524601i	0.504711	−	0.863288i	$-0.331599\pi$
$263$	1.66971	+	0.850760i	0.102959	+	0.0524601i	−0.401753	+	0.915748i	$0.631599\pi$
$264$	−4.26354	+	17.5562i	−0.262403	+	1.08051i
$265$		0			0
$266$	−12.1771	+	3.95658i	−0.746627	+	0.242594i
$267$	−1.65523	+	20.3502i	−0.101299	+	1.24541i
$268$	0.282420	+	0.282420i	0.0172515	+	0.0172515i
$269$	−19.0018	+	13.8056i	−1.15856	+	0.841745i	−0.989596	−	0.143877i	$-0.954043\pi$
$269$	−19.0018	+	13.8056i	−1.15856	+	0.841745i	−0.168966	+	0.985622i	$0.554043\pi$
$270$		0			0
$271$	0.609720	+	0.442988i	0.0370379	+	0.0269096i	0.606150	−	0.795350i	$-0.292713\pi$
$271$	0.609720	+	0.442988i	0.0370379	+	0.0269096i	−0.569112	+	0.822260i	$0.692713\pi$
$272$	−0.526387	−	3.32348i	−0.0319169	−	0.201515i
$273$	−12.8163	−	21.0377i	−0.775676	−	1.27326i
$274$			12.3124i			0.743818i
$275$		0			0
$276$	0.368361	−	0.0280202i	0.0221727	−	0.00168662i
$277$	4.16594	+	8.17612i	0.250307	+	0.491255i	0.981635	−	0.190771i	$-0.0610989\pi$
$277$	4.16594	+	8.17612i	0.250307	+	0.491255i	−0.731327	+	0.682027i	$0.761099\pi$
$278$	−32.1187	+	5.08710i	−1.92635	+	0.305104i
$279$	0.633907	−	1.22817i	0.0379510	−	0.0735284i
$280$		0			0
$281$	−14.7500	−	20.3017i	−0.879913	−	1.21110i	−0.976445	−	0.215766i	$-0.930775\pi$
$281$	−14.7500	−	20.3017i	−0.879913	−	1.21110i	0.0965320	−	0.995330i	$-0.469225\pi$
$282$	−7.85583	−	6.74518i	−0.467808	−	0.401669i
$283$	23.3503	+	3.69832i	1.38803	+	0.219843i	0.805322	−	0.592838i	$-0.201993\pi$
$283$	23.3503	+	3.69832i	1.38803	+	0.219843i	0.582709	+	0.812681i	$0.301993\pi$
$284$	0.225336	+	0.693512i	0.0133712	+	0.0411524i
$285$		0			0
$286$	10.4874	−	32.2769i	0.620133	−	1.90857i
$287$	7.18714	−	14.1056i	0.424243	−	0.832624i
$288$	−3.29388	−	1.08935i	−0.194094	−	0.0641908i
$289$	−15.6036	−	5.06993i	−0.917861	−	0.298231i
$290$		0			0
$291$	−26.0671	+	10.7175i	−1.52808	+	0.628270i
$292$	−0.384966	+	2.43058i	−0.0225284	+	0.142239i
$293$	17.4959	−	17.4959i	1.02212	−	1.02212i	0.0223711	−	0.999750i	$-0.492878\pi$
$293$	17.4959	−	17.4959i	1.02212	−	1.02212i	0.999750	−	0.0223711i	$-0.00712154\pi$
$294$	−1.77887	−	2.09386i	−0.103746	−	0.122117i
$295$		0			0
$296$	−8.01016	+	11.0250i	−0.465581	+	0.640817i
$297$	−18.8483	+	7.63428i	−1.09369	+	0.442986i
$298$	−7.43278	+	3.78719i	−0.430569	+	0.219386i
$299$	6.06926			0.350994
$300$		0			0
$301$	19.2351			1.10869
$302$	19.4266	−	9.89833i	1.11787	−	0.569585i
$303$	5.92513	+	24.9678i	0.340390	+	1.43436i
$304$	−9.08974	+	12.5110i	−0.521333	+	0.717553i
$305$		0			0
$306$	2.43923	−	2.41381i	0.139442	−	0.137988i
$307$	4.00162	−	4.00162i	0.228384	−	0.228384i	−0.583633	−	0.812017i	$-0.698369\pi$
$307$	4.00162	−	4.00162i	0.228384	−	0.228384i	0.812017	+	0.583633i	$0.198369\pi$
$308$	−0.305997	+	1.93199i	−0.0174358	+	0.110085i
$309$	−5.89133	−	14.3290i	−0.335146	−	0.815146i
$310$		0			0
$311$	32.7389	+	10.6375i	1.85645	+	0.603198i	0.995528	+	0.0944627i	$0.0301133\pi$
$311$	32.7389	+	10.6375i	1.85645	+	0.603198i	0.860923	+	0.508735i	$0.169887\pi$
$312$	−24.8785	−	10.3814i	−1.40847	−	0.587733i
$313$	−8.86459	+	17.3977i	−0.501056	+	0.983378i	0.492530	+	0.870296i	$0.336072\pi$
$313$	−8.86459	+	17.3977i	−0.501056	+	0.983378i	−0.993586	+	0.113082i	$0.963928\pi$
$314$	−4.80148	+	14.7774i	−0.270963	+	0.833939i
$315$		0			0
$316$	0.0559255	+	0.172121i	0.00314605	+	0.00968256i
$317$	2.89957	+	0.459247i	0.162856	+	0.0257939i	0.237330	−	0.971429i	$-0.423728\pi$
$317$	2.89957	+	0.459247i	0.162856	+	0.0257939i	−0.0744738	+	0.997223i	$0.523728\pi$
$318$	−4.92448	+	5.73534i	−0.276151	+	0.321622i
$319$	−0.318358	−	0.438182i	−0.0178246	−	0.0245335i
$320$		0			0
$321$	−21.4485	−	13.2211i	−1.19714	−	0.737928i
$322$	−3.71271	+	0.588036i	−0.206901	+	0.0327700i
$323$	−1.23801	−	2.42973i	−0.0688846	−	0.135194i
$324$	−0.552309	−	1.76244i	−0.0306838	−	0.0979134i
$325$		0			0
$326$		−	12.7023i		−	0.703516i
$327$	−14.7183	+	8.96644i	−0.813923	+	0.495845i
$328$	−2.71010	−	17.1109i	−0.149640	−	0.944792i
$329$	7.93206	+	5.76298i	0.437308	+	0.317723i
$330$		0			0
$331$	3.26639	−	2.37317i	0.179537	−	0.130441i	−0.494387	−	0.869242i	$-0.664607\pi$
$331$	3.26639	−	2.37317i	0.179537	−	0.130441i	0.673924	+	0.738800i	$0.264607\pi$
$332$	−1.38611	−	1.38611i	−0.0760725	−	0.0760725i
$333$	−15.3391	−	0.0803415i	−0.840578	−	0.00440268i
$334$	−24.7112	+	8.02917i	−1.35214	+	0.439337i
$335$		0			0
$336$	17.9071	+	4.34875i	0.976913	+	0.237244i
$337$	−9.50552	−	4.84331i	−0.517799	−	0.263832i	0.175503	−	0.984479i	$-0.443845\pi$
$337$	−9.50552	−	4.84331i	−0.517799	−	0.263832i	−0.693302	+	0.720647i	$0.743845\pi$
$338$	27.9196	+	14.2258i	1.51863	+	0.773779i
$339$	−8.15926	−	1.98148i	−0.443150	−	0.107619i
$340$		0			0
$341$	−1.71476	+	0.557161i	−0.0928597	+	0.0301719i
$342$	−15.7710	−	0.0826036i	−0.852799	−	0.00446669i
$343$	13.8949	+	13.8949i	0.750253	+	0.750253i
$344$	17.0292	−	12.3725i	0.918155	−	0.667079i
$345$		0			0
$346$	−20.1096	−	14.6105i	−1.08110	−	0.785465i
$347$	3.88435	+	24.5248i	0.208523	+	1.31656i	0.840600	+	0.541656i	$0.182202\pi$
$347$	3.88435	+	24.5248i	0.208523	+	1.31656i	−0.632077	+	0.774905i	$0.717798\pi$
$348$	0.0420103	−	0.0255928i	0.00225199	−	0.00137192i
$349$			3.68396i			0.197198i	0.995127	+	0.0985990i	$0.0314361\pi$
$349$			3.68396i			0.197198i	−0.995127	+	0.0985990i	$0.968564\pi$
$350$		0			0
$351$	−6.85152	−	29.5598i	−0.365707	−	1.57779i
$352$	2.05471	+	4.03259i	0.109516	+	0.214938i
$353$	0.544691	−	0.0862706i	0.0289910	−	0.00459172i	−0.141922	−	0.989878i	$-0.545328\pi$
$353$	0.544691	−	0.0862706i	0.0289910	−	0.00459172i	0.170913	+	0.985286i	$0.445328\pi$
$354$	−6.05990	−	3.73537i	−0.322080	−	0.198533i
$355$		0			0
$356$	1.42191	+	1.95710i	0.0753613	+	0.103726i
$357$	−2.11683	+	2.46538i	−0.112034	+	0.130482i
$358$	−14.2089	−	2.25046i	−0.750962	−	0.118941i
$359$	−0.0579467	−	0.178342i	−0.00305831	−	0.00941251i	0.949516	−	0.313719i	$-0.101575\pi$
$359$	−0.0579467	−	0.178342i	−0.00305831	−	0.00941251i	−0.952574	+	0.304307i	$0.901575\pi$
$360$		0			0
$361$	1.99857	−	6.15098i	0.105188	−	0.323736i
$362$	−6.47457	+	12.7071i	−0.340296	+	0.667868i
$363$	6.89940	+	2.87902i	0.362125	+	0.151109i
$364$	−2.77586	−	0.901931i	−0.145495	−	0.0472741i
$365$		0			0
$366$	3.92657	+	9.55025i	0.205245	+	0.499199i
$367$	−3.24722	+	20.5021i	−0.169503	+	1.07020i	0.745426	+	0.666589i	$0.232246\pi$
$367$	−3.24722	+	20.5021i	−0.169503	+	1.07020i	−0.914929	+	0.403614i	$0.867754\pi$
$368$	−3.21034	+	3.21034i	−0.167351	+	0.167351i
$369$	13.8607	−	13.7162i	0.721558	−	0.714039i
$370$		0			0
$371$	4.20740	−	5.79099i	0.218437	−	0.300653i
$372$	−0.0378109	−	0.159331i	−0.00196040	−	0.00826091i
$373$	−4.29685	+	2.18936i	−0.222483	+	0.113361i	−0.561680	−	0.827355i	$-0.689845\pi$
$373$	−4.29685	+	2.18936i	−0.222483	+	0.113361i	0.339197	+	0.940715i	$0.389845\pi$
$374$	−4.47672			−0.231486
$375$		0			0
$376$	10.7293			0.553322
$377$	0.720086	−	0.366902i	0.0370863	−	0.0188964i
$378$	7.05523	+	17.4186i	0.362882	+	0.895918i
$379$	−4.09975	+	5.64282i	−0.210590	+	0.289852i	−0.901225	−	0.433351i	$-0.857331\pi$
$379$	−4.09975	+	5.64282i	−0.210590	+	0.289852i	0.690635	+	0.723203i	$0.257331\pi$
$380$		0			0
$381$	12.7997	+	15.0662i	0.655746	+	0.771864i
$382$	−11.1976	+	11.1976i	−0.572921	+	0.572921i
$383$	−1.60030	+	10.1039i	−0.0817714	+	0.516284i	0.912472	+	0.409139i	$0.134171\pi$
$383$	−1.60030	+	10.1039i	−0.0817714	+	0.516284i	−0.994243	+	0.107145i	$0.965829\pi$
$384$	20.4032	−	8.38874i	1.04119	−	0.428086i
$385$		0			0
$386$	17.6315	+	5.72883i	0.897421	+	0.291590i
$387$	22.4948	+	7.43948i	1.14347	+	0.378170i
$388$	−1.51603	+	2.97538i	−0.0769650	+	0.151052i
$389$	9.90598	−	30.4875i	0.502253	−	1.54578i	−0.303087	−	0.952963i	$-0.598017\pi$
$389$	9.90598	−	30.4875i	0.502253	−	1.54578i	0.805340	−	0.592813i	$-0.201983\pi$
$390$		0			0
$391$	−0.247396	−	0.761407i	−0.0125114	−	0.0385060i
$392$	2.81193	+	0.445366i	0.142024	+	0.0224944i
$393$	5.82215	+	4.99901i	0.293688	+	0.252167i
$394$	6.67895	+	9.19278i	0.336481	+	0.463126i
$395$		0			0
$396$	−1.10508	+	2.14105i	−0.0555324	+	0.107592i
$397$	−10.1301	+	1.60445i	−0.508414	+	0.0805249i	−0.405371	−	0.914152i	$-0.632858\pi$
$397$	−10.1301	+	1.60445i	−0.508414	+	0.0805249i	−0.103043	+	0.994677i	$0.532858\pi$
$398$	−11.1751	−	21.9323i	−0.560155	−	1.09937i
$399$	14.8909	−	1.13271i	0.745476	−	0.0567063i
$400$		0			0
$401$		−	14.6016i		−	0.729167i	−0.931171	−	0.364584i	$-0.881211\pi$
$401$		−	14.6016i		−	0.729167i	0.931171	−	0.364584i	$-0.118789\pi$
$402$	−2.60439	−	4.27507i	−0.129895	−	0.213221i
$403$	−0.420860	−	2.65721i	−0.0209645	−	0.132365i
$404$	2.45974	+	1.78710i	0.122376	+	0.0889117i
$405$		0			0
$406$	−0.404946	+	0.294210i	−0.0200971	+	0.0146014i
$407$	14.1497	+	14.1497i	0.701373	+	0.701373i
$408$	−0.288280	+	3.54425i	−0.0142720	+	0.175467i
$409$	15.6748	−	5.09306i	0.775070	−	0.251835i	0.105336	−	0.994437i	$-0.466408\pi$
$409$	15.6748	−	5.09306i	0.775070	−	0.251835i	0.669734	+	0.742601i	$0.266408\pi$
$410$		0			0
$411$	3.38901	−	13.9551i	0.167167	−	0.688356i
$412$	−1.63555	−	0.833355i	−0.0805778	−	0.0410564i
$413$	6.00602	+	3.06022i	0.295537	+	0.150584i
$414$	−4.56933	−	0.748265i	−0.224570	−	0.0367752i
$415$		0			0
$416$	−6.42268	+	2.08686i	−0.314898	+	0.102317i
$417$	37.8042	+	3.07489i	1.85128	+	0.150578i
$418$	14.5481	+	14.5481i	0.711570	+	0.711570i
$419$	−0.887321	+	0.644676i	−0.0433484	+	0.0314945i	−0.609248	−	0.792979i	$-0.708529\pi$
$419$	−0.887321	+	0.644676i	−0.0433484	+	0.0314945i	0.565900	+	0.824474i	$0.308529\pi$
$420$		0			0
$421$	23.5246	+	17.0916i	1.14652	+	0.832996i	0.988014	−	0.154362i	$-0.0493324\pi$
$421$	23.5246	+	17.0916i	1.14652	+	0.832996i	0.158506	+	0.987358i	$0.449332\pi$
$422$	−5.56977	−	35.1662i	−0.271132	−	1.71186i
$423$	7.04736	+	9.80747i	0.342654	+	0.476855i
$424$		−	7.83319i		−	0.380414i
$425$		0			0
$426$	−0.693210	−	9.11312i	−0.0335861	−	0.441532i
$427$	−4.43899	−	8.71201i	−0.214818	−	0.421603i
$428$	−2.94852	+	0.467000i	−0.142522	+	0.0225733i
$429$	−20.7709	+	33.6967i	−1.00283	+	1.62689i
$430$		0			0
$431$	15.6969	+	21.6049i	0.756091	+	1.04067i	0.997529	+	0.0702534i	$0.0223808\pi$
$431$	15.6969	+	21.6049i	0.756091	+	1.04067i	−0.241439	+	0.970416i	$0.577619\pi$
$432$	19.2598	+	12.0116i	0.926640	+	0.577908i
$433$	−26.4272	−	4.18566i	−1.27001	−	0.201150i	−0.515187	−	0.857078i	$-0.672277\pi$
$433$	−26.4272	−	4.18566i	−1.27001	−	0.201150i	−0.754823	+	0.655928i	$0.772277\pi$
$434$	0.514901	+	1.58470i	0.0247160	+	0.0760681i
$435$		0			0
$436$	−0.631004	+	1.94203i	−0.0302196	+	0.0930064i
$437$	−1.67039	+	3.27832i	−0.0799055	+	0.156823i
$438$	11.8778	−	28.4646i	0.567545	−	1.36009i
$439$	−19.2932	−	6.26873i	−0.920812	−	0.299190i	−0.190012	−	0.981782i	$-0.560853\pi$
$439$	−19.2932	−	6.26873i	−0.920812	−	0.299190i	−0.730800	+	0.682592i	$0.760853\pi$
$440$		0			0
$441$	1.43987	+	2.86287i	0.0685650	+	0.136327i
$442$	1.04496	−	6.59762i	0.0497037	−	0.313817i
$443$	−12.0174	+	12.0174i	−0.570962	+	0.570962i	−0.932397	−	0.361435i	$-0.882287\pi$
$443$	−12.0174	+	12.0174i	−0.570962	+	0.570962i	0.361435	+	0.932397i	$0.382287\pi$
$444$	−1.38508	+	1.17671i	−0.0657328	+	0.0558441i
$445$		0			0
$446$	2.07237	−	2.85238i	0.0981298	−	0.135064i
$447$	9.46691	−	2.24660i	0.447770	−	0.106261i
$448$	−15.2324	+	7.76132i	−0.719665	+	0.366688i
$449$	−23.5930			−1.11342			−0.556711	−	0.830706i	$-0.687937\pi$
$449$	−23.5930			−1.11342			−0.556711	+	0.830706i	$0.687937\pi$
$450$		0			0
$451$	−25.4385			−1.19785
$452$	−0.886396	+	0.451642i	−0.0416926	+	0.0212434i
$453$	−24.7430	+	5.87179i	−1.16253	+	0.275881i
$454$	10.6217	−	14.6195i	0.498501	−	0.686128i
$455$		0			0
$456$	12.4546	−	10.5810i	0.583242	−	0.495500i
$457$	1.82957	−	1.82957i	0.0855837	−	0.0855837i	−0.663019	−	0.748603i	$-0.730725\pi$
$457$	1.82957	−	1.82957i	0.0855837	−	0.0855837i	0.748603	+	0.663019i	$0.230725\pi$
$458$	−3.36937	+	21.2734i	−0.157441	+	0.994040i
$459$	−3.42909	+	2.06447i	−0.160056	+	0.0963610i
$460$		0			0
$461$	−24.9186	−	8.09654i	−1.16057	−	0.377094i	−0.335458	−	0.942055i	$-0.608891\pi$
$461$	−24.9186	−	8.09654i	−1.16057	−	0.377094i	−0.825117	+	0.564962i	$0.808891\pi$
$462$	9.44130	−	22.6255i	0.439249	−	1.05264i
$463$	9.73607	−	19.1081i	0.452474	−	0.888030i	−0.546255	−	0.837619i	$-0.683947\pi$
$463$	9.73607	−	19.1081i	0.452474	−	0.888030i	0.998729	−	0.0504107i	$-0.0160530\pi$
$464$	−0.186817	+	0.574964i	−0.00867277	+	0.0266920i
$465$		0			0
$466$	−9.94359	−	30.6032i	−0.460628	−	1.41767i
$467$	−29.2023	−	4.62519i	−1.35132	−	0.214028i	−0.561556	−	0.827439i	$-0.689797\pi$
$467$	−29.2023	−	4.62519i	−1.35132	−	0.214028i	−0.789764	+	0.613411i	$0.789797\pi$
$468$	−2.89744	−	2.12839i	−0.133934	−	0.0983848i
$469$	2.78618	+	3.83484i	0.128654	+	0.177077i
$470$		0			0
$471$	9.50963	−	15.4275i	0.438180	−	0.710860i
$472$	7.28567	−	1.15394i	0.335350	−	0.0531142i
$473$	−14.0321	−	27.5396i	−0.645197	−	1.26627i
$474$	−0.172046	−	2.26176i	−0.00790233	−	0.103886i
$475$		0			0
$476$			0.385004i			0.0176467i
$477$	7.16018	−	5.14509i	0.327842	−	0.235578i
$478$	1.96307	+	12.3944i	0.0897889	+	0.566905i
$479$	24.4450	+	17.7603i	1.11692	+	0.811489i	0.983739	−	0.179603i	$-0.0574813\pi$
$479$	24.4450	+	17.7603i	1.11692	+	0.811489i	0.133180	+	0.991092i	$0.457481\pi$
$480$		0			0
$481$	−24.1560	+	17.5504i	−1.10142	+	0.800229i
$482$	−1.64287	−	1.64287i	−0.0748309	−	0.0748309i
$483$	4.36993	+	0.355438i	0.198839	+	0.0161730i
$484$	0.842420	−	0.273719i	0.0382918	−	0.0124418i
$485$		0			0
$486$	1.51391	+	23.0993i	0.0686723	+	1.04780i
$487$	−13.4191	−	6.83736i	−0.608076	−	0.309830i	0.122704	−	0.992443i	$-0.460843\pi$
$487$	−13.4191	−	6.83736i	−0.608076	−	0.309830i	−0.730780	+	0.682613i	$0.760843\pi$
$488$	−9.53371	−	4.85767i	−0.431571	−	0.219896i
$489$	−3.49634	+	14.3971i	−0.158110	+	0.651059i
$490$		0			0
$491$	−31.9571	+	10.3835i	−1.44220	+	0.468601i	−0.922584	−	0.385797i	$-0.873927\pi$
$491$	−31.9571	+	10.3835i	−1.44220	+	0.468601i	−0.519621	+	0.854397i	$0.673927\pi$
$492$	0.187304	−	2.30281i	0.00844433	−	0.103819i
$493$	−0.0753812	−	0.0753812i	−0.00339500	−	0.00339500i
$494$	−24.8362	+	18.0446i	−1.11743	+	0.811863i
$495$		0			0
$496$	1.62815	+	1.18292i	0.0731060	+	0.0531146i
$497$	1.35382	+	8.54766i	0.0607270	+	0.383415i
$498$	12.7823	+	20.9819i	0.572787	+	0.940222i
$499$		−	32.3318i		−	1.44737i	−0.690131	−	0.723684i	$-0.742447\pi$
$499$		−	32.3318i		−	1.44737i	0.690131	−	0.723684i	$-0.257553\pi$
$500$		0			0
$501$	30.2183	−	2.29862i	1.35006	−	0.102695i
$502$	5.67027	+	11.1285i	0.253077	+	0.496691i
$503$	0.646326	−	0.102368i	0.0288182	−	0.00456436i	−0.142009	−	0.989865i	$-0.545356\pi$
$503$	0.646326	−	0.102368i	0.0288182	−	0.00456436i	0.170827	+	0.985301i	$0.445356\pi$
$504$	−17.3048	−	8.93172i	−0.770818	−	0.397850i
$505$		0			0
$506$	3.55037	+	4.88666i	0.157833	+	0.217238i
$507$	−27.7291	−	23.8087i	−1.23149	−	1.05738i
$508$	2.31346	+	0.366416i	0.102643	+	0.0162571i
$509$	7.29902	+	22.4641i	0.323523	+	0.995703i	0.972103	+	0.234556i	$0.0753635\pi$
$509$	7.29902	+	22.4641i	0.323523	+	0.995703i	−0.648579	+	0.761147i	$0.724636\pi$
$510$		0			0
$511$	−9.02509	+	27.7764i	−0.399247	+	1.22875i
$512$	−8.27787	+	16.2462i	−0.365834	+	0.717989i
$513$	17.8525	+	4.43463i	0.788206	+	0.195794i
$514$	21.2545	+	6.90601i	0.937497	+	0.304611i
$515$		0			0
$516$	2.59633	−	1.06748i	0.114297	−	0.0469930i
$517$	2.46458	−	15.5608i	0.108392	−	0.684361i
$518$	13.0764	−	13.0764i	0.574545	−	0.574545i
$519$	18.7711	+	22.0951i	0.823961	+	0.969866i
$520$		0			0
$521$	−20.7338	+	28.5376i	−0.908365	+	1.25026i	0.0593574	+	0.998237i	$0.481095\pi$
$521$	−20.7338	+	28.5376i	−0.908365	+	1.25026i	−0.967722	+	0.252020i	$0.918905\pi$
$522$	−0.587362	+	0.187450i	−0.0257081	+	0.00820447i
$523$	2.26510	−	1.15413i	0.0990460	−	0.0504664i	−0.403766	−	0.914862i	$-0.632299\pi$
$523$	2.26510	−	1.15413i	0.0990460	−	0.0504664i	0.502812	+	0.864396i	$0.332299\pi$
$524$	0.909212			0.0397191
$525$		0			0
$526$	−2.78282			−0.121337
$527$	−0.316199	+	0.161111i	−0.0137738	+	0.00701813i
$528$	−6.83710	−	28.8108i	−0.297547	−	1.25383i
$529$	12.8841	−	17.7335i	0.560180	−	0.771021i
$530$		0			0
$531$	5.84025	+	5.90175i	0.253445	+	0.256114i
$532$	1.25116	−	1.25116i	0.0542445	−	0.0542445i
$533$	5.93788	−	37.4903i	0.257198	−	1.62389i
$534$	−11.5295	−	28.0422i	−0.498931	−	1.21350i
$535$		0			0
$536$	4.93333	+	1.60294i	0.213087	+	0.0692363i
$537$	15.4852	+	6.46174i	0.668236	+	0.278845i
$538$	15.8347	−	31.0774i	0.682683	−	1.33984i
$539$	1.29183	−	3.97585i	0.0556432	−	0.171252i
$540$		0			0
$541$	3.34503	+	10.2949i	0.143814	+	0.442614i	0.996857	−	0.0792273i	$-0.0252453\pi$
$541$	3.34503	+	10.2949i	0.143814	+	0.442614i	−0.853043	+	0.521841i	$0.825245\pi$
$542$	−1.10540	−	0.175078i	−0.0474809	−	0.00752024i
$543$	10.8361	−	12.6203i	0.465020	−	0.541590i
$544$	0.523604	+	0.720680i	0.0224494	+	0.0308989i
$545$		0			0
$546$	31.1408	+	19.1955i	1.33271	+	0.821491i
$547$	22.7658	−	3.60575i	0.973396	−	0.154171i	0.350574	−	0.936535i	$-0.385986\pi$
$547$	22.7658	−	3.60575i	0.973396	−	0.154171i	0.622821	+	0.782364i	$0.285986\pi$
$548$	−0.772462	−	1.51604i	−0.0329979	−	0.0647621i
$549$	−1.82174	−	11.9053i	−0.0777500	−	0.508104i
$550$		0			0
$551$			0.489935i			0.0208719i
$552$	4.09743	−	2.49617i	0.174398	−	0.106244i
$553$	0.336000	+	2.12142i	0.0142882	+	0.0902120i
$554$	−11.0243	−	8.00960i	−0.468376	−	0.340295i
$555$		0			0
$556$	3.63566	−	2.64146i	0.154186	−	0.112023i
$557$	−6.52436	−	6.52436i	−0.276446	−	0.276446i	0.555242	−	0.831689i	$-0.312625\pi$
$557$	−6.52436	−	6.52436i	−0.276446	−	0.276446i	−0.831689	+	0.555242i	$0.812625\pi$
$558$	−0.0107498	+	2.05240i	−0.000455077	+	0.0868851i
$559$	43.8621	−	14.2517i	1.85517	−	0.602782i
$560$		0			0
$561$	5.07402	+	1.23223i	0.214225	+	0.0520247i
$562$	33.2033	+	16.9179i	1.40060	+	0.713639i
$563$	−9.63388	−	4.90871i	−0.406020	−	0.206877i	0.239040	−	0.971010i	$-0.423167\pi$
$563$	−9.63388	−	4.90871i	−0.406020	−	0.206877i	−0.645059	+	0.764132i	$0.723167\pi$
$564$	1.39048	+	0.337679i	0.0585499	+	0.0142189i
$565$		0			0
$566$	−33.3891	+	10.8488i	−1.40345	+	0.456008i
$567$	−3.20204	−	21.6846i	−0.134473	−	0.910669i
$568$	6.69663	+	6.69663i	0.280984	+	0.280984i
$569$	−15.4318	+	11.2119i	−0.646937	+	0.470027i	−0.862226	−	0.506523i	$-0.830930\pi$
$569$	−15.4318	+	11.2119i	−0.646937	+	0.470027i	0.215290	+	0.976550i	$0.430930\pi$
$570$		0			0
$571$	−7.63086	−	5.54414i	−0.319342	−	0.232015i	0.416553	−	0.909111i	$-0.363238\pi$
$571$	−7.63086	−	5.54414i	−0.319342	−	0.232015i	−0.735894	+	0.677096i	$0.763238\pi$
$572$	0.733679	+	4.63227i	0.0306767	+	0.193685i
$573$	15.7738	−	9.60948i	0.658961	−	0.401442i
$574$			23.5090i			0.981248i
$575$		0			0
$576$	−20.8157	+	3.18521i	−0.867319	+	0.132717i
$577$	3.02469	+	5.93629i	0.125920	+	0.247131i	0.945357	−	0.326038i	$-0.105714\pi$
$577$	3.02469	+	5.93629i	0.125920	+	0.247131i	−0.819437	+	0.573169i	$0.805714\pi$
$578$	24.0639	−	3.81134i	1.00092	−	0.158531i
$579$	−18.4071	−	11.3463i	−0.764973	−	0.471536i
$580$		0			0
$581$	−13.6745	−	18.8213i	−0.567313	−	0.780839i
$582$	27.2651	−	31.7546i	1.13017	−	1.31627i
$583$	−11.3605	−	1.79933i	−0.470504	−	0.0745205i
$584$	9.87633	+	30.3962i	0.408685	+	1.25780i
$585$		0			0
$586$	−11.3543	+	34.9448i	−0.469040	+	1.44356i
$587$	−7.27726	+	14.2824i	−0.300365	+	0.589499i	−0.991024	−	0.133681i	$-0.957320\pi$
$587$	−7.27726	+	14.2824i	−0.300365	+	0.589499i	0.690660	+	0.723180i	$0.257320\pi$
$588$	0.350400	+	0.146217i	0.0144503	+	0.00602988i
$589$	1.55112	+	0.503991i	0.0639129	+	0.0207666i
$590$		0			0
$591$	−5.03974	−	12.2577i	−0.207307	−	0.504214i
$592$	3.49407	−	22.0607i	0.143605	−	0.906689i
$593$	19.4509	−	19.4509i	0.798754	−	0.798754i	−0.184145	−	0.982899i	$-0.558952\pi$
$593$	19.4509	−	19.4509i	0.798754	−	0.798754i	0.982899	+	0.184145i	$0.0589517\pi$
$594$	19.7921	−	22.8083i	0.812080	−	0.935834i
$595$		0			0
$596$	0.677606	−	0.932645i	0.0277558	−	0.0382026i
$597$	6.62915	+	27.9345i	0.271313	+	1.14328i
$598$	−8.03050	+	4.09174i	−0.328391	+	0.167324i
$599$	−8.83948			−0.361171			−0.180586	−	0.983559i	$-0.557799\pi$
$599$	−8.83948			−0.361171			−0.180586	+	0.983559i	$0.557799\pi$
$600$		0			0
$601$	−18.4292			−0.751744			−0.375872	−	0.926672i	$-0.622657\pi$
$601$	−18.4292			−0.751744			−0.375872	+	0.926672i	$0.622657\pi$
$602$	−25.4507	+	12.9678i	−1.03729	+	0.528528i
$603$	1.77515	+	5.56233i	0.0722899	+	0.226515i
$604$	−1.77101	+	2.43759i	−0.0720615	+	0.0991842i
$605$		0			0
$606$	−24.6725	−	29.0414i	−1.00225	−	1.17973i
$607$	−11.7369	+	11.7369i	−0.476386	+	0.476386i	−0.903974	−	0.427588i	$-0.859363\pi$
$607$	−11.7369	+	11.7369i	−0.476386	+	0.476386i	0.427588	+	0.903974i	$0.359363\pi$
$608$	0.640439	−	4.04357i	0.0259732	−	0.163988i
$609$	0.539957	−	0.222003i	0.0218802	−	0.00899600i
$610$		0			0
$611$	22.3576	+	7.26441i	0.904490	+	0.293887i
$612$	−0.148907	+	0.450250i	−0.00601920	+	0.0182003i
$613$	6.54078	−	12.8370i	0.264180	−	0.518482i	−0.720369	−	0.693591i	$-0.756028\pi$
$613$	6.54078	−	12.8370i	0.264180	−	0.518482i	0.984549	+	0.175109i	$0.0560277\pi$
$614$	−2.59692	+	7.99250i	−0.104803	+	0.322551i
$615$		0			0
$616$	7.85037	+	24.1610i	0.316300	+	0.973473i
$617$	−13.5321	−	2.14327i	−0.544782	−	0.0862849i	−0.122023	−	0.992527i	$-0.538938\pi$
$617$	−13.5321	−	2.14327i	−0.544782	−	0.0862849i	−0.422759	+	0.906242i	$0.638938\pi$
$618$	17.4553	+	14.9875i	0.702155	+	0.602884i
$619$	5.41760	+	7.45669i	0.217752	+	0.299710i	0.903893	−	0.427759i	$-0.140697\pi$
$619$	5.41760	+	7.45669i	0.217752	+	0.299710i	−0.686141	+	0.727468i	$0.740697\pi$
$620$		0			0
$621$	4.97302	+	2.10582i	0.199560	+	0.0845035i
$622$	−50.4897	+	7.99679i	−2.02445	+	0.320642i
$623$	13.0341	+	25.5809i	0.522201	+	1.02488i
$624$	44.0561	−	3.35122i	1.76365	−	0.134156i
$625$		0			0
$626$		−	28.9960i		−	1.15891i
$627$	−12.4847	−	20.4935i	−0.498592	−	0.818432i
$628$	−0.335903	−	2.12081i	−0.0134040	−	0.0846294i
$629$	3.18640	+	2.31506i	0.127050	+	0.0923073i
$630$		0			0
$631$	32.6151	−	23.6962i	1.29839	−	0.943333i	0.298448	−	0.954426i	$-0.403531\pi$
$631$	32.6151	−	23.6962i	1.29839	−	0.943333i	0.999938	+	0.0110933i	$0.00353119\pi$
$632$	1.66202	+	1.66202i	0.0661115	+	0.0661115i
$633$	−3.36665	+	41.3912i	−0.133812	+	1.64515i
$634$	−4.14616	+	1.34717i	−0.164665	+	0.0535029i
$635$		0			0
$636$	0.246531	−	1.01516i	0.00977558	−	0.0402535i
$637$	5.55791	+	2.83190i	0.220213	+	0.112204i
$638$	0.716643	+	0.365148i	0.0283722	+	0.0144563i
$639$	−1.72270	+	10.5198i	−0.0681491	+	0.416158i
$640$		0			0
$641$	41.3915	−	13.4489i	1.63487	−	0.531201i	0.659484	−	0.751718i	$-0.270775\pi$
$641$	41.3915	−	13.4489i	1.63487	−	0.531201i	0.975383	+	0.220518i	$0.0707748\pi$
$642$	37.2928	+	3.03329i	1.47183	+	0.119715i
$643$	−19.6168	−	19.6168i	−0.773612	−	0.773612i	0.205124	−	0.978736i	$-0.434240\pi$
$643$	−19.6168	−	19.6168i	−0.773612	−	0.773612i	−0.978736	+	0.205124i	$0.934240\pi$
$644$	0.420259	−	0.305336i	0.0165605	−	0.0120319i
$645$		0			0
$646$	3.27612	+	2.38024i	0.128897	+	0.0936494i
$647$	−4.20028	−	26.5196i	−0.165130	−	1.04259i	−0.921481	−	0.388425i	$-0.873019\pi$
$647$	−4.20028	−	26.5196i	−0.165130	−	1.04259i	0.756350	−	0.654167i	$-0.226981\pi$
$648$	−16.7829	−	17.1383i	−0.659296	−	0.673255i
$649$		−	10.8315i		−	0.425173i
$650$		0			0
$651$	−0.147408	−	1.93786i	−0.00577737	−	0.0759508i
$652$	0.796926	+	1.56406i	0.0312100	+	0.0612531i
$653$	−20.1993	+	3.19926i	−0.790460	+	0.125197i	−0.538594	−	0.842566i	$-0.681044\pi$
$653$	−20.1993	+	3.19926i	−0.790460	+	0.125197i	−0.251866	+	0.967762i	$0.581044\pi$
$654$	13.4294	−	21.7866i	0.525133	−	0.851922i
$655$		0			0
$656$	16.6897	+	22.9714i	0.651623	+	0.896883i
$657$	−21.2975	+	28.9930i	−0.830896	+	1.13112i
$658$	−14.3805	−	2.27765i	−0.560610	−	0.0887919i
$659$	−2.65726	−	8.17820i	−0.103512	−	0.318578i	0.885866	−	0.463941i	$-0.153565\pi$
$659$	−2.65726	−	8.17820i	−0.103512	−	0.318578i	−0.989378	+	0.145363i	$0.953565\pi$
$660$		0			0
$661$	12.9264	−	39.7835i	0.502781	−	1.54740i	−0.301689	−	0.953406i	$-0.597551\pi$
$661$	12.9264	−	39.7835i	0.502781	−	1.54740i	0.804470	−	0.593993i	$-0.202449\pi$
$662$	−2.72197	+	5.34217i	−0.105792	+	0.207629i
$663$	−3.00039	+	7.19026i	−0.116525	+	0.279247i
$664$	−24.2126	−	7.86716i	−0.939632	−	0.305305i
$665$		0			0
$666$	20.3500	−	10.2349i	0.788546	−	0.396596i
$667$	−0.0225011	+	0.142067i	−0.000871248	+	0.00550084i
$668$	2.53899	−	2.53899i	0.0982366	−	0.0982366i
$669$	−3.13400	+	2.66253i	−0.121167	+	0.102939i
$670$		0			0
$671$	−9.23504	+	12.7109i	−0.356515	+	0.490700i
$672$	−4.74661	+	1.12642i	−0.183105	+	0.0434527i
$673$	20.5969	−	10.4947i	0.793954	−	0.404540i	−0.00946407	−	0.999955i	$-0.503013\pi$
$673$	20.5969	−	10.4947i	0.793954	−	0.404540i	0.803418	+	0.595416i	$0.203013\pi$
$674$	15.8424			0.610226
$675$		0			0
$676$	−4.33029			−0.166550
$677$	18.1854	−	9.26592i	0.698921	−	0.356118i	−0.0681543	−	0.997675i	$-0.521711\pi$
$677$	18.1854	−	9.26592i	0.698921	−	0.356118i	0.767076	+	0.641557i	$0.221711\pi$
$678$	12.1317	−	2.87899i	0.465916	−	0.110567i
$679$	−23.2949	+	32.0627i	−0.893976	+	1.23045i
$680$		0			0
$681$	−16.0629	+	13.6464i	−0.615533	+	0.522933i
$682$	1.89325	−	1.89325i	0.0724964	−	0.0724964i
$683$	0.339136	−	2.14122i	0.0129767	−	0.0819315i	−0.980350	−	0.197266i	$-0.936794\pi$
$683$	0.339136	−	2.14122i	0.0129767	−	0.0819315i	0.993327	+	0.115334i	$0.0367939\pi$
$684$	1.94709	−	0.979280i	0.0744489	−	0.0374437i
$685$		0			0
$686$	−27.7525	−	9.01733i	−1.05959	−	0.344283i
$687$	9.67447	−	23.1843i	0.369104	−	0.884537i
$688$	−15.6625	+	30.7394i	−0.597127	+	1.17193i
$689$	5.30356	−	16.3227i	0.202049	−	0.621844i
$690$		0			0
$691$	4.06682	+	12.5164i	0.154709	+	0.476146i	0.998131	−	0.0611055i	$-0.0194626\pi$
$691$	4.06682	+	12.5164i	0.154709	+	0.476146i	−0.843422	+	0.537251i	$0.819463\pi$
$692$	3.39277	+	0.537362i	0.128974	+	0.0204274i
$693$	−16.9287	+	23.0456i	−0.643068	+	0.875429i
$694$	−21.6736	−	29.8311i	−0.822717	−	1.13237i
$695$		0			0
$696$	0.335238	−	0.543857i	0.0127072	−	0.0206149i
$697$	−4.94531	+	0.783260i	−0.187317	+	0.0296681i
$698$	−2.48363	−	4.87441i	−0.0940069	−	0.184499i
$699$	2.84669	+	37.4234i	0.107672	+	1.41548i
$700$		0			0
$701$			21.8766i			0.826268i	0.910670	+	0.413134i	$0.135566\pi$
$701$			21.8766i			0.826268i	−0.910670	+	0.413134i	$0.864434\pi$
$702$	28.9940	+	34.4927i	1.09431	+	1.30184i
$703$	−2.83162	−	17.8782i	−0.106797	−	0.674288i
$704$	22.2243	+	16.1469i	0.837612	+	0.608560i
$705$		0			0
$706$	−0.662542	+	0.481365i	−0.0249351	+	0.0181164i
$707$	25.5150	+	25.5150i	0.959591	+	0.959591i
$708$	0.980516	+	0.0797525i	0.0368500	+	0.00299728i
$709$	−24.3739	+	7.91956i	−0.915381	+	0.297425i	−0.728570	−	0.684971i	$-0.759815\pi$
$709$	−24.3739	+	7.91956i	−0.915381	+	0.297425i	−0.186810	+	0.982396i	$0.559815\pi$
$710$		0			0
$711$	−0.427554	+	2.61089i	−0.0160345	+	0.0979159i
$712$	27.9936	+	14.2635i	1.04911	+	0.534546i
$713$	0.426633	+	0.217380i	0.0159775	+	0.00814096i
$714$	1.13876	−	4.68916i	0.0426172	−	0.175487i
$715$		0			0
$716$	1.89075	−	0.614342i	0.0706606	−	0.0229590i
$717$	1.18658	−	14.5884i	0.0443136	−	0.544813i
$718$	0.196905	+	0.196905i	0.00734844	+	0.00734844i
$719$	5.09685	−	3.70308i	0.190081	−	0.138102i	−0.488675	−	0.872466i	$-0.662520\pi$
$719$	5.09685	−	3.70308i	0.190081	−	0.138102i	0.678756	+	0.734364i	$0.262520\pi$
$720$		0			0
$721$	−17.6247	−	12.8051i	−0.656376	−	0.476885i
$722$	1.50244	+	9.48601i	0.0559149	+	0.353033i
$723$	1.40987	+	2.31427i	0.0524335	+	0.0860688i
$724$		−	1.97084i		−	0.0732459i
$725$		0			0
$726$	−11.0699	+	0.842053i	−0.410841	+	0.0312515i
$727$	−7.14311	−	14.0192i	−0.264923	−	0.519942i	0.719775	−	0.694207i	$-0.244245\pi$
$727$	−7.14311	−	14.0192i	−0.264923	−	0.519942i	−0.984699	+	0.174266i	$0.944245\pi$
$728$	−37.4399	+	5.92990i	−1.38762	+	0.219777i
$729$	4.64222	−	26.5979i	0.171934	−	0.985108i
$730$		0			0
$731$	−3.57583	−	4.92171i	−0.132257	−	0.182036i
$732$	−1.08265	−	0.929588i	−0.0400160	−	0.0343586i
$733$	22.0161	+	3.48700i	0.813182	+	0.128795i	0.549155	−	0.835720i	$-0.314949\pi$
$733$	22.0161	+	3.48700i	0.813182	+	0.128795i	0.264026	+	0.964516i	$0.414949\pi$
$734$	−9.52549	−	29.3164i	−0.351592	−	1.08209i
$735$		0			0
$736$	0.371416	−	1.14310i	0.0136906	−	0.0421353i
$737$	3.45796	−	6.78662i	0.127375	−	0.249988i
$738$	−9.09251	+	27.4931i	−0.334700	+	1.01203i
$739$	34.2550	+	11.1301i	1.26009	+	0.409428i	0.861526	−	0.507713i	$-0.169509\pi$
$739$	34.2550	+	11.1301i	1.26009	+	0.409428i	0.398563	+	0.917141i	$0.369509\pi$
$740$		0			0
$741$	33.1167	−	13.6159i	1.21657	−	0.500193i
$742$	−1.66285	+	10.4988i	−0.0610452	+	0.385424i
$743$	−21.4863	+	21.4863i	−0.788255	+	0.788255i	−0.981208	−	0.192953i	$-0.938194\pi$
$743$	−21.4863	+	21.4863i	−0.788255	+	0.788255i	0.192953	+	0.981208i	$0.438194\pi$
$744$	−1.37698	−	1.62082i	−0.0504827	−	0.0594221i
$745$		0			0
$746$	4.20934	−	5.79366i	0.154115	−	0.212121i
$747$	−8.71240	−	27.2997i	−0.318770	−	0.998845i
$748$	0.551226	−	0.280863i	0.0201548	−	0.0102694i
$749$	−35.4294			−1.29456
$750$		0			0
$751$	44.7068			1.63137			0.815686	−	0.578494i	$-0.196360\pi$
$751$	44.7068			1.63137			0.815686	+	0.578494i	$0.196360\pi$
$752$	−15.6686	+	7.98354i	−0.571374	+	0.291130i
$753$	−3.36366	−	14.1741i	−0.122579	−	0.516532i
$754$	−0.705420	+	0.970928i	−0.0256899	+	0.0353591i
$755$		0			0
$756$	−1.96154	−	1.70215i	−0.0713406	−	0.0619065i
$757$	33.8318	−	33.8318i	1.22964	−	1.22964i	0.265539	−	0.964100i	$-0.414450\pi$
$757$	33.8318	−	33.8318i	1.22964	−	1.22964i	0.964100	−	0.265539i	$-0.0855498\pi$
$758$	1.62031	−	10.2302i	0.0588521	−	0.371578i
$759$	−2.67900	−	6.51589i	−0.0972416	−	0.236512i
$760$		0			0
$761$	−1.37065	−	0.445350i	−0.0496859	−	0.0161439i	0.284069	−	0.958804i	$-0.408316\pi$
$761$	−1.37065	−	0.445350i	−0.0496859	−	0.0161439i	−0.333755	+	0.942660i	$0.608316\pi$
$762$	−27.0930	−	11.3055i	−0.981476	−	0.409555i
$763$	−11.0021	+	21.5929i	−0.398303	+	0.781714i
$764$	0.676257	−	2.08131i	0.0244661	−	0.0752990i
$765$		0			0
$766$	−4.69436	−	14.4477i	−0.169614	−	0.522018i
$767$	15.9630	+	2.52830i	0.576392	+	0.0912915i
$768$	−5.50072	+	6.40647i	−0.198490	+	0.231173i
$769$	13.9798	+	19.2415i	0.504124	+	0.693867i	0.982915	−	0.184062i	$-0.0589248\pi$
$769$	13.9798	+	19.2415i	0.504124	+	0.693867i	−0.478791	+	0.877929i	$0.658925\pi$
$770$		0			0
$771$	−22.1895	−	13.6778i	−0.799134	−	0.492593i
$772$	−2.53041	+	0.400778i	−0.0910716	+	0.0144243i
$773$	1.97202	+	3.87030i	0.0709285	+	0.139205i	0.923748	−	0.383001i	$-0.125109\pi$
$773$	1.97202	+	3.87030i	0.0709285	+	0.139205i	−0.852820	+	0.522206i	$0.825109\pi$
$774$	−34.7793	+	5.32192i	−1.25012	+	0.191293i
$775$		0			0
$776$			43.3696i			1.55688i
$777$	−18.4204	+	11.2218i	−0.660829	+	0.402580i
$778$	7.44686	+	47.0176i	0.266983	+	1.68566i
$779$	18.6162	+	13.5255i	0.666995	+	0.484601i
$780$		0			0
$781$	11.2504	−	8.17389i	0.402571	−	0.292485i
$782$	0.840661	+	0.840661i	0.0300620	+	0.0300620i
$783$	0.717325	−	0.0507876i	0.0256351	−	0.00181500i
$784$	−4.43781	+	1.44193i	−0.158493	+	0.0514975i
$785$		0			0
$786$	−11.0737	−	2.68926i	−0.394987	−	0.0959227i
$787$	−32.5272	−	16.5734i	−1.15947	−	0.590779i	−0.234985	−	0.971999i	$-0.575504\pi$
$787$	−32.5272	−	16.5734i	−1.15947	−	0.590779i	−0.924484	+	0.381220i	$0.875504\pi$
$788$	−1.39913	−	0.712893i	−0.0498420	−	0.0253958i
$789$	3.15412	+	0.765978i	0.112290	+	0.0272695i
$790$		0			0
$791$	−11.2288	+	3.64846i	−0.399250	+	0.129724i
$792$	−0.163896	+	31.2917i	−0.00582380	+	1.11190i
$793$	−16.5772	−	16.5772i	−0.588675	−	0.588675i
$794$	12.3219	−	8.95235i	0.437286	−	0.317707i
$795$		0			0
$796$	2.75200	+	1.99945i	0.0975421	+	0.0708685i
$797$	−3.74172	−	23.6243i	−0.132539	−	0.836816i	−0.960955	−	0.276703i	$-0.910758\pi$
$797$	−3.74172	−	23.6243i	−0.132539	−	0.836816i	0.828417	−	0.560112i	$-0.189242\pi$
$798$	−18.9391	+	11.5378i	−0.670437	+	0.408433i
$799$		−	3.10093i		−	0.109703i
$800$		0			0
$801$	5.34914	+	34.9572i	0.189003	+	1.23515i
$802$	9.84400	+	19.3199i	0.347604	+	0.682211i
$803$	46.3524	−	7.34149i	1.63574	−	0.259076i
$804$	0.588895	+	0.363000i	0.0207687	+	0.0128020i
$805$		0			0
$806$	2.34828	+	3.23213i	0.0827146	+	0.113847i
$807$	−26.5015	+	30.8653i	−0.932898	+	1.08651i
$808$	39.0009	+	6.17713i	1.37205	+	0.217311i
$809$	1.75262	+	5.39400i	0.0616187	+	0.189643i	0.977127	−	0.212656i	$-0.0682113\pi$
$809$	1.75262	+	5.39400i	0.0616187	+	0.189643i	−0.915508	+	0.402299i	$0.868211\pi$
$810$		0			0
$811$	5.70569	−	17.5603i	0.200354	−	0.616625i	−0.799518	−	0.600641i	$-0.794912\pi$
$811$	5.70569	−	17.5603i	0.200354	−	0.616625i	0.999872	−	0.0159840i	$-0.00508808\pi$
$812$	0.0314032	−	0.0616323i	0.00110204	−	0.00216287i
$813$	1.20469	+	0.502700i	0.0422504	+	0.0176305i
$814$	−28.2614	−	9.18267i	−0.990560	−	0.321853i
$815$		0			0
$816$	−2.21624	−	5.39036i	−0.0775839	−	0.188700i
$817$	−4.37372	+	27.6146i	−0.153017	+	0.966112i
$818$	−17.3064	+	17.3064i	−0.605104	+	0.605104i
$819$	−30.0121	−	30.3282i	−1.04871	−	1.05975i
$820$		0			0
$821$	15.0984	−	20.7812i	0.526938	−	0.725268i	−0.459722	−	0.888063i	$-0.652051\pi$
$821$	15.0984	−	20.7812i	0.526938	−	0.725268i	0.986660	+	0.162795i	$0.0520508\pi$
$822$	4.92406	+	20.7494i	0.171746	+	0.723718i
$823$	−1.75544	+	0.894443i	−0.0611909	+	0.0311783i	−0.484318	−	0.874892i	$-0.660932\pi$
$823$	−1.75544	+	0.894443i	−0.0611909	+	0.0311783i	0.423127	+	0.906070i	$0.360932\pi$
$824$	−23.8400			−0.830507
$825$		0			0
$826$	−10.0099			−0.348290
$827$	37.8448	−	19.2829i	1.31599	−	0.670532i	0.351885	−	0.936043i	$-0.385541\pi$
$827$	37.8448	−	19.2829i	1.31599	−	0.670532i	0.964108	+	0.265511i	$0.0855407\pi$
$828$	0.609574	−	0.194539i	0.0211841	−	0.00676069i
$829$	−18.3344	+	25.2352i	−0.636781	+	0.876453i	−0.998439	−	0.0558574i	$-0.982211\pi$
$829$	−18.3344	+	25.2352i	−0.636781	+	0.876453i	0.361658	+	0.932311i	$0.382211\pi$
$830$		0			0
$831$	10.2905	+	12.1127i	0.356973	+	0.420185i
$832$	−28.9843	+	28.9843i	−1.00485	+	1.00485i
$833$	0.128718	−	0.812691i	0.00445980	−	0.0281581i
$834$	−52.0934	+	21.4181i	−1.80385	+	0.741650i
$835$		0			0
$836$	−2.70405	−	0.878600i	−0.0935216	−	0.0303870i
$837$	0.577112	−	2.32328i	0.0199479	−	0.0803043i
$838$	0.739427	−	1.45121i	0.0255431	−	0.0501311i
$839$	3.12345	−	9.61299i	0.107833	−	0.331877i	−0.882552	−	0.470216i	$-0.844176\pi$
$839$	3.12345	−	9.61299i	0.107833	−	0.331877i	0.990385	+	0.138338i	$0.0441762\pi$
$840$		0			0
$841$	−8.95557	−	27.5624i	−0.308813	−	0.950428i
$842$	−42.6492	−	6.75497i	−1.46979	−	0.232792i
$843$	−32.9766	−	28.3144i	−1.13578	−	0.975200i
$844$	2.89209	+	3.98062i	0.0995499	+	0.137019i
$845$		0			0
$846$	−15.9366	−	8.22553i	−0.547912	−	0.282799i
$847$	10.3830	−	1.64450i	0.356763	−	0.0565058i
$848$	5.82858	+	11.4392i	0.200154	+	0.392825i
$849$	40.8301	−	3.10583i	1.40128	−	0.106592i
$850$		0			0
$851$		−	5.31419i		−	0.182168i
$852$	0.657101	+	1.07862i	0.0225119	+	0.0369529i
$853$	2.37400	+	14.9888i	0.0812842	+	0.513208i	0.994415	+	0.105541i	$0.0336575\pi$
$853$	2.37400	+	14.9888i	0.0812842	+	0.513208i	−0.913131	+	0.407667i	$0.866342\pi$
$854$	11.7468	+	8.53457i	0.401968	+	0.292047i
$855$		0			0
$856$	−31.3665	+	22.7891i	−1.07208	+	0.778914i
$857$	−26.4246	−	26.4246i	−0.902648	−	0.902648i	0.0930163	−	0.995665i	$-0.470349\pi$
$857$	−26.4246	−	26.4246i	−0.902648	−	0.902648i	−0.995665	+	0.0930163i	$0.970349\pi$
$858$	4.76545	−	58.5888i	0.162690	−	2.00019i
$859$	−42.0699	+	13.6693i	−1.43541	+	0.466392i	−0.920462	−	0.390832i	$-0.872187\pi$
$859$	−42.0699	+	13.6693i	−1.43541	+	0.466392i	−0.514944	+	0.857224i	$0.672187\pi$
$860$		0			0
$861$	6.47091	−	26.6457i	0.220528	−	0.908082i
$862$	−35.3346	−	18.0039i	−1.20350	−	0.613215i
$863$	−48.4015	−	24.6618i	−1.64760	−	0.839496i	−0.996773	−	0.0802746i	$-0.974420\pi$
$863$	−48.4015	−	24.6618i	−1.64760	−	0.839496i	−0.650832	−	0.759222i	$-0.725580\pi$
$864$	−5.98667	−	0.518517i	−0.203671	−	0.0176403i
$865$		0			0
$866$	37.7888	−	12.2783i	1.28412	−	0.417235i
$867$	−28.3236	−	2.30377i	−0.961920	−	0.0782400i
$868$	−0.162822	−	0.162822i	−0.00552655	−	0.00552655i
$869$	2.79221	−	2.02866i	0.0947191	−	0.0688174i
$870$		0			0
$871$	9.19470	+	6.68034i	0.311551	+	0.226355i
$872$	4.14864	+	26.1935i	0.140491	+	0.887023i
$873$	−39.6434	+	28.4866i	−1.34173	+	0.964124i
$874$		−	5.46382i		−	0.184816i
$875$		0			0
$876$	0.323292	+	4.25008i	0.0109230	+	0.143597i
$877$	−22.0243	−	43.2252i	−0.743709	−	1.45961i	−0.883007	−	0.469360i	$-0.844485\pi$
$877$	−22.0243	−	43.2252i	−0.743709	−	1.45961i	0.139298	−	0.990250i	$-0.455515\pi$
$878$	29.7538	−	4.71254i	1.00414	−	0.159041i
$879$	22.4878	−	36.4820i	0.758495	−	1.23051i
$880$		0			0
$881$	−31.2390	−	42.9968i	−1.05247	−	1.44860i	−0.886649	−	0.462443i	$-0.846973\pi$
$881$	−31.2390	−	42.9968i	−1.05247	−	1.44860i	−0.165820	−	0.986156i	$-0.553027\pi$
$882$	−3.83522	−	2.81726i	−0.129139	−	0.0948620i
$883$	9.36055	+	1.48257i	0.315008	+	0.0498923i	0.311936	−	0.950103i	$-0.399022\pi$
$883$	9.36055	+	1.48257i	0.315008	+	0.0498923i	0.00307116	+	0.999995i	$0.499022\pi$
$884$	0.285258	+	0.877934i	0.00959427	+	0.0295281i
$885$		0			0
$886$	7.79887	−	24.0025i	0.262008	−	0.806379i
$887$	−12.2915	+	24.1235i	−0.412709	+	0.809986i	0.587291	+	0.809376i	$0.300194\pi$
$887$	−12.2915	+	24.1235i	−0.412709	+	0.809986i	−1.00000		0.000610667i	$0.999806\pi$
$888$	−9.08988	+	21.7834i	−0.305036	+	0.731003i
$889$	26.4380	+	8.59022i	0.886702	+	0.288107i
$890$		0			0
$891$	−28.7108	+	20.4036i	−0.961849	+	0.683546i
$892$	−0.0762202	+	0.481236i	−0.00255204	+	0.0161130i
$893$	−10.0772	+	10.0772i	−0.337219	+	0.337219i
$894$	−11.0115	+	9.35492i	−0.368279	+	0.312875i
$895$		0			0
$896$	18.2333	−	25.0960i	0.609131	−	0.838397i
$897$	10.2282	−	2.42726i	0.341510	−	0.0810439i
$898$	31.2169	−	15.9058i	1.04172	−	0.530784i
$899$	0.0637590			0.00212648
$900$		0			0
$901$	−2.26391			−0.0754218
$902$	33.6588	−	17.1500i	1.12072	−	0.571033i
$903$	32.4158	−	7.69263i	1.07873	−	0.255995i
$904$	−7.59433	+	10.4527i	−0.252584	+	0.347652i
$905$		0			0
$906$	28.7799	−	24.4503i	0.956150	−	0.812308i
$907$	5.89173	−	5.89173i	0.195632	−	0.195632i	−0.602493	−	0.798124i	$-0.705826\pi$
$907$	5.89173	−	5.89173i	0.195632	−	0.195632i	0.798124	+	0.602493i	$0.205826\pi$
$908$	−0.390657	+	2.46651i	−0.0129644	+	0.0818541i
$909$	19.9706	+	39.7073i	0.662384	+	1.31701i
$910$		0			0
$911$	−48.7073	−	15.8260i	−1.61374	−	0.524337i	−0.643290	−	0.765623i	$-0.722431\pi$
$911$	−48.7073	−	15.8260i	−1.61374	−	0.524337i	−0.970454	+	0.241286i	$0.922431\pi$
$912$	−10.3150	+	24.7193i	−0.341564	+	0.818538i
$913$	−16.9715	+	33.3085i	−0.561676	+	1.10235i
$914$	−1.18733	+	3.65423i	−0.0392735	+	0.120871i
$915$		0			0
$916$	−0.919787	−	2.83081i	−0.0303906	−	0.0935327i
$917$	10.6577	+	1.68802i	0.351949	+	0.0557433i
$918$	3.14536	−	5.04339i	0.103812	−	0.166457i
$919$	−9.10877	−	12.5372i	−0.300471	−	0.413562i	0.631909	−	0.775042i	$-0.282272\pi$
$919$	−9.10877	−	12.5372i	−0.300471	−	0.413562i	−0.932380	+	0.361480i	$0.882272\pi$
$920$		0			0
$921$	5.14336	−	8.34407i	0.169479	−	0.274946i
$922$	38.4293	−	6.08661i	1.26560	−	0.200452i
$923$	9.42028	+	18.4883i	0.310072	+	0.608551i
$924$	0.256974	+	3.37825i	0.00845383	+	0.111136i
$925$		0			0
$926$			31.8466i			1.04654i
$927$	−15.6589	−	21.7917i	−0.514305	−	0.715734i
$928$	−0.0250368	−	0.158076i	−0.000821874	−	0.00518911i
$929$	−33.7506	−	24.5213i	−1.10732	−	0.804517i	−0.125083	−	0.992146i	$-0.539920\pi$
$929$	−33.7506	−	24.5213i	−1.10732	−	0.804517i	−0.982240	+	0.187629i	$0.939920\pi$
$930$		0			0
$931$	−3.05931	+	2.22272i	−0.100265	+	0.0728467i
$932$	3.14437	+	3.14437i	0.102997	+	0.102997i
$933$	59.4273	+	4.83366i	1.94556	+	0.158247i
$934$	41.7570	−	13.5677i	1.36633	−	0.443947i
$935$		0			0
$936$	−46.0782	−	7.54568i	−1.50611	−	0.246638i
$937$	−0.722614	−	0.368190i	−0.0236068	−	0.0120282i	0.442147	−	0.896942i	$-0.354217\pi$
$937$	−0.722614	−	0.368190i	−0.0236068	−	0.0120282i	−0.465754	+	0.884914i	$0.654217\pi$
$938$	−6.27186	−	3.19567i	−0.204784	−	0.104342i
$939$	−7.98119	+	32.8647i	−0.260456	+	1.07250i
$940$		0			0
$941$	16.0740	−	5.22276i	0.523998	−	0.170257i	−0.0350611	−	0.999385i	$-0.511163\pi$
$941$	16.0740	−	5.22276i	0.523998	−	0.170257i	0.559059	+	0.829128i	$0.311163\pi$
$942$	−2.18178	+	26.8239i	−0.0710863	+	0.873969i
$943$	4.77697	+	4.77697i	0.155560	+	0.155560i
$944$	−9.78102	+	7.10633i	−0.318345	+	0.231291i
$945$		0			0
$946$	37.1330	+	26.9787i	1.20730	+	0.877153i
$947$	4.90398	+	30.9625i	0.159358	+	1.00615i	0.929647	+	0.368452i	$0.120112\pi$
$947$	4.90398	+	30.9625i	0.159358	+	1.00615i	−0.770289	+	0.637695i	$0.779888\pi$
$948$	0.163084	+	0.267700i	0.00529672	+	0.00869450i
$949$			70.0260i			2.27314i
$950$		0			0
$951$	5.07016	−	0.385673i	0.164411	−	0.0125063i
$952$	2.27005	+	4.45523i	0.0735729	+	0.144395i
$953$	25.1408	−	3.98191i	0.814391	−	0.128987i	0.264674	−	0.964338i	$-0.414736\pi$
$953$	25.1408	−	3.98191i	0.814391	−	0.128987i	0.549717	+	0.835351i	$0.314736\pi$
$954$	−6.00524	+	11.6349i	−0.194427	+	0.376694i
$955$		0			0
$956$	−1.01932	−	1.40298i	−0.0329672	−	0.0453755i
$957$	−0.711752	−	0.611124i	−0.0230077	−	0.0197548i
$958$	−44.3177	−	7.01924i	−1.43184	−	0.226781i
$959$	−6.24011	−	19.2051i	−0.201504	−	0.620165i
$960$		0			0
$961$	−9.51394	+	29.2809i	−0.306901	+	0.944545i
$962$	20.1299	−	39.5071i	0.649013	−	1.27376i
$963$	−41.4336	−	13.7029i	−1.33518	−	0.441570i
$964$	0.305361	+	0.0992179i	0.00983502	+	0.00319559i
$965$		0			0
$966$	−6.02167	+	2.47580i	−0.193744	+	0.0796576i
$967$	−8.00363	+	50.5329i	−0.257379	+	1.62503i	0.432869	+	0.901457i	$0.357501\pi$
$967$	−8.00363	+	50.5329i	−0.257379	+	1.62503i	−0.690249	+	0.723572i	$0.742499\pi$
$968$	8.13450	−	8.13450i	0.261453	−	0.261453i
$969$	−3.05806	−	3.59958i	−0.0982392	−	0.115635i
$970$		0			0
$971$	18.5870	−	25.5828i	0.596485	−	0.820991i	−0.398896	−	0.916996i	$-0.630607\pi$
$971$	18.5870	−	25.5828i	0.596485	−	0.820991i	0.995381	+	0.0960053i	$0.0306066\pi$
$972$	−1.63563	−	2.74927i	−0.0524627	−	0.0881827i
$973$	47.5211	−	24.2132i	1.52346	−	0.776240i
$974$	22.3649			0.716618
$975$		0			0
$976$	17.5371			0.561349
$977$	−39.7795	+	20.2687i	−1.27266	+	0.648452i	−0.954111	−	0.299454i	$-0.903195\pi$
$977$	−39.7795	+	20.2687i	−1.27266	+	0.648452i	−0.318549	+	0.947906i	$0.603195\pi$
$978$	−5.08000	−	21.4065i	−0.162441	−	0.684506i
$979$	27.1166	−	37.3229i	0.866652	−	1.19284i
$980$		0			0
$981$	−21.2180	+	20.9969i	−0.677439	+	0.670380i
$982$	35.2835	−	35.2835i	1.12594	−	1.12594i
$983$	7.45579	−	47.0740i	0.237803	−	1.50143i	−0.522938	−	0.852371i	$-0.675164\pi$
$983$	7.45579	−	47.0740i	0.237803	−	1.50143i	0.760740	−	0.649056i	$-0.224836\pi$
$984$	−11.4103	−	27.7523i	−0.363747	−	0.884710i
$985$		0			0
$986$	0.150560	+	0.0489200i	0.00479481	+	0.00155793i
$987$	15.6722	+	6.53979i	0.498853	+	0.208164i
$988$	1.92603	−	3.78004i	0.0612751	−	0.120259i
$989$	−2.53650	+	7.80654i	−0.0806559	+	0.248233i
$990$		0			0
$991$	1.87960	+	5.78480i	0.0597073	+	0.183760i	0.976462	−	0.215691i	$-0.0692005\pi$
$991$	1.87960	+	5.78480i	0.0597073	+	0.183760i	−0.916754	+	0.399452i	$0.869201\pi$
$992$	−0.526221	−	0.0833452i	−0.0167075	−	0.00264621i
$993$	4.55559	−	5.30571i	0.144567	−	0.168372i
$994$	−7.55391	−	10.3971i	−0.239595	−	0.329775i
$995$		0			0
$996$	−2.89028	−	1.78159i	−0.0915819	−	0.0564519i
$997$	24.4690	−	3.87551i	0.774942	−	0.122739i	0.243577	−	0.969882i	$-0.421679\pi$
$997$	24.4690	−	3.87551i	0.774942	−	0.122739i	0.531365	+	0.847143i	$0.321679\pi$
$998$	21.7973	+	42.7795i	0.689980	+	1.35416i
$999$	−25.8823	+	5.99913i	−0.818880	+	0.189804i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.l.b.368.3		64
3.2	odd	2	inner	375.2.l.b.368.6		64
5.2	odd	4		375.2.l.c.257.3		64
5.3	odd	4		75.2.l.a.47.6	yes	64
5.4	even	2		375.2.l.a.368.6		64
15.2	even	4		375.2.l.c.257.6		64
15.8	even	4		75.2.l.a.47.3	yes	64
15.14	odd	2		375.2.l.a.368.3		64
25.6	even	5		375.2.l.c.143.6		64
25.8	odd	20		375.2.l.a.107.3		64
25.17	odd	20	inner	375.2.l.b.107.6		64
25.19	even	10		75.2.l.a.8.3	✓	64
75.8	even	20		375.2.l.a.107.6		64
75.17	even	20	inner	375.2.l.b.107.3		64
75.44	odd	10		75.2.l.a.8.6	yes	64
75.56	odd	10		375.2.l.c.143.3		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.l.a.8.3	✓	64	25.19	even	10
75.2.l.a.8.6	yes	64	75.44	odd	10
75.2.l.a.47.3	yes	64	15.8	even	4
75.2.l.a.47.6	yes	64	5.3	odd	4
375.2.l.a.107.3		64	25.8	odd	20
375.2.l.a.107.6		64	75.8	even	20
375.2.l.a.368.3		64	15.14	odd	2
375.2.l.a.368.6		64	5.4	even	2
375.2.l.b.107.3		64	75.17	even	20	inner
375.2.l.b.107.6		64	25.17	odd	20	inner
375.2.l.b.368.3		64	1.1	even	1	trivial
375.2.l.b.368.6		64	3.2	odd	2	inner
375.2.l.c.143.3		64	75.56	odd	10
375.2.l.c.143.6		64	25.6	even	5
375.2.l.c.257.3		64	5.2	odd	4
375.2.l.c.257.6		64	15.2	even	4

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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.l (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.32314 + 0.674175i) q^{2} +(1.68525 - 0.399927i) q^{3} +(0.120624 - 0.166024i) q^{4} +(-1.96020 + 1.66531i) q^{6} +(1.72218 - 1.72218i) q^{7} +(0.416937 - 2.63243i) q^{8} +(2.68012 - 1.34795i) q^{9} +(-3.72206 - 1.20937i) q^{11} +(0.136883 - 0.328033i) q^{12} +(2.65113 - 5.20313i) q^{13} +(-1.11764 + 3.43974i) q^{14} +(1.34989 + 4.15452i) q^{16} +(-0.760813 - 0.120501i) q^{17} +(-2.63742 + 3.59040i) q^{18} +(2.08083 + 2.86402i) q^{19} +(2.21355 - 3.59105i) q^{21} +(5.74013 - 0.909148i) q^{22} +(0.471845 + 0.926047i) q^{23} +(-0.350141 - 4.60305i) q^{24} +8.67180i q^{26} +(3.97758 - 3.34348i) q^{27} +(-0.0781880 - 0.493660i) q^{28} +(0.111964 + 0.0813465i) q^{29} +(0.372717 - 0.270795i) q^{31} +(-0.817733 - 0.817733i) q^{32} +(-6.75624 - 0.549535i) q^{33} +(1.08790 - 0.353481i) q^{34} +(0.0994927 - 0.607559i) q^{36} +(-4.55581 - 2.32130i) q^{37} +(-4.68409 - 2.38666i) q^{38} +(2.38693 - 9.82881i) q^{39} +(6.18190 - 2.00862i) q^{41} +(-0.507853 + 6.24379i) q^{42} +(5.58451 + 5.58451i) q^{43} +(-0.649753 + 0.472073i) q^{44} +(-1.24864 - 0.907186i) q^{46} +(0.629748 + 3.97607i) q^{47} +(3.93640 + 6.46154i) q^{48} +1.06819i q^{49} +(-1.33035 + 0.101196i) q^{51} +(-0.544057 - 1.06777i) q^{52} +(2.90283 - 0.459763i) q^{53} +(-3.00881 + 7.10549i) q^{54} +(-3.81549 - 5.25157i) q^{56} +(4.65212 + 3.99440i) q^{57} +(-0.202986 - 0.0321498i) q^{58} +(0.855253 + 2.63220i) q^{59} +(1.24058 - 3.81812i) q^{61} +(-0.310595 + 0.609576i) q^{62} +(2.29423 - 6.93706i) q^{63} +(-6.67577 - 2.16909i) q^{64} +(9.30995 - 3.82778i) q^{66} +(-0.304459 + 1.92228i) q^{67} +(-0.111778 + 0.111778i) q^{68} +(1.16553 + 1.37191i) q^{69} +(-2.08859 + 2.87469i) q^{71} +(-2.43096 - 7.61724i) q^{72} +(-10.6846 + 5.44405i) q^{73} +7.59295 q^{74} +0.726495 q^{76} +(-8.49280 + 4.32730i) q^{77} +(3.46809 + 14.6141i) q^{78} +(-0.518361 + 0.713462i) q^{79} +(5.36605 - 7.22534i) q^{81} +(-6.82537 + 6.82537i) q^{82} +(1.49428 - 9.43448i) q^{83} +(-0.329194 - 0.800669i) q^{84} +(-11.1540 - 3.62417i) q^{86} +(0.221219 + 0.0923115i) q^{87} +(-4.73545 + 9.29383i) q^{88} +(-3.64270 + 11.2111i) q^{89} +(-4.39501 - 13.5264i) q^{91} +(0.210662 + 0.0333656i) q^{92} +(0.519822 - 0.605416i) q^{93} +(-3.51381 - 4.83635i) q^{94} +(-1.70512 - 1.05105i) q^{96} +(-16.0719 + 2.54554i) q^{97} +(-0.720145 - 1.41336i) q^{98} +(-11.6057 + 1.77590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 20 q^{4} - 6 q^{6} + 20 q^{7} + 10 q^{9} + 40 q^{12} - 8 q^{16} + 10 q^{18} - 6 q^{21} - 30 q^{27} - 80 q^{28} - 12 q^{31} - 50 q^{33} - 20 q^{34} - 22 q^{36} - 120 q^{37} - 30 q^{39} + 60 q^{42}+ \cdots + 42 q^{96}+O(q^{100}) \) 64 * q + 20 * q^4 - 6 * q^6 + 20 * q^7 + 10 * q^9 + 40 * q^12 - 8 * q^16 + 10 * q^18 - 6 * q^21 - 30 * q^27 - 80 * q^28 - 12 * q^31 - 50 * q^33 - 20 * q^34 - 22 * q^36 - 120 * q^37 - 30 * q^39 + 60 * q^42 + 20 * q^43 - 12 * q^46 + 100 * q^48 - 16 * q^51 + 100 * q^52 - 120 * q^54 - 70 * q^57 + 120 * q^58 - 12 * q^61 - 70 * q^63 + 100 * q^64 - 30 * q^66 - 60 * q^67 + 80 * q^69 - 40 * q^72 - 80 * q^73 - 64 * q^76 + 70 * q^78 + 60 * q^79 + 14 * q^81 + 60 * q^82 + 130 * q^84 + 100 * q^87 + 60 * q^88 - 12 * q^91 + 20 * q^93 - 260 * q^94 + 42 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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