LMFDB - Embedded newform 375.2.l.b.107.6

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			107.6
Character	$\chi$	$=$	375.107
Dual form			375.2.l.b.368.6

$q$-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} +(-1.72635 - 0.140417i) q^{3} +(0.120624 + 0.166024i) q^{4} +(-2.18954 - 1.34965i) q^{6} +(1.72218 + 1.72218i) q^{7} +(-0.416937 - 2.63243i) q^{8} +(2.96057 + 0.484816i) q^{9} +(3.72206 - 1.20937i) q^{11} +(-0.184926 - 0.303553i) 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} +(3.59040 + 2.63742i) q^{18} +(2.08083 - 2.86402i) q^{19} +(-2.73126 - 3.21491i) q^{21} +(5.74013 + 0.909148i) q^{22} +(-0.471845 + 0.926047i) q^{23} +(0.350141 + 4.60305i) q^{24} +8.67180i q^{26} +(-5.04290 - 1.25268i) 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} +(-6.59538 + 1.56516i) q^{33} +(1.08790 + 0.353481i) q^{34} +(0.276623 + 0.550006i) q^{36} +(-4.55581 + 2.32130i) q^{37} +(4.68409 - 2.38666i) q^{38} +(-3.84616 - 9.35468i) q^{39} +(-6.18190 - 2.00862i) q^{41} +(-1.44644 - 6.09513i) 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} +(-2.91374 + 6.98261i) q^{48} -1.06819i q^{49} +(-1.33035 + 0.101196i) q^{51} +(-0.544057 + 1.06777i) q^{52} +(-2.90283 - 0.459763i) q^{53} +(-5.82795 - 5.05726i) q^{54} +(3.81549 - 5.25157i) q^{56} +(-3.99440 + 4.65212i) 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} +(4.26369 + 5.93357i) q^{63} +(-6.67577 + 2.16909i) q^{64} +(-9.78182 - 2.37552i) q^{66} +(-0.304459 - 1.92228i) q^{67} +(0.111778 + 0.111778i) q^{68} +(0.944601 - 1.53243i) q^{69} +(2.08859 + 2.87469i) q^{71} +(0.0418786 - 7.99563i) q^{72} +(-10.6846 - 5.44405i) q^{73} -7.59295 q^{74} +0.726495 q^{76} +(8.49280 + 4.32730i) q^{77} +(1.21766 - 14.9706i) q^{78} +(-0.518361 - 0.713462i) q^{79} +(8.52991 + 2.87066i) q^{81} +(-6.82537 - 6.82537i) q^{82} +(-1.49428 - 9.43448i) q^{83} +(0.204298 - 0.841250i) q^{84} +(11.1540 - 3.62417i) q^{86} +(0.204711 - 0.124711i) 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} +(-0.605416 - 0.519822i) q^{93} +(-3.51381 + 4.83635i) q^{94} +(-1.52652 + 1.29687i) 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 $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{13}{20}\right)$	$-1$

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	$-0.174056\pi$
$2$	1.32314	+	0.674175i	0.935603	+	0.476714i	0.0814164	+	0.996680i	$0.474056\pi$
$3$	−1.72635	−	0.140417i	−0.996708	−	0.0810696i
$3$	−1.72635	−	0.140417i	−0.996708	−	0.0810696i
$4$	0.120624	+	0.166024i	0.0603118	+	0.0830121i
$5$		0			0
$5$		0			0
$6$	−2.18954	−	1.34965i	−0.893876	−	0.550993i
$7$	1.72218	+	1.72218i	0.650923	+	0.650923i	0.953215	−	0.302292i	$-0.0977518\pi$
$7$	1.72218	+	1.72218i	0.650923	+	0.650923i	−0.302292	+	0.953215i	$0.597752\pi$
$8$	−0.416937	−	2.63243i	−0.147409	−	0.930706i
$9$	2.96057	+	0.484816i	0.986855	+	0.161605i
$10$		0			0
$11$	3.72206	−	1.20937i	1.12224	−	0.364638i	0.311619	−	0.950207i	$-0.399129\pi$
$11$	3.72206	−	1.20937i	1.12224	−	0.364638i	0.810623	+	0.585569i	$0.199129\pi$
$12$	−0.184926	−	0.303553i	−0.0533836	−	0.0876283i
$13$	2.65113	+	5.20313i	0.735290	+	1.44309i	0.890394	+	0.455190i	$0.150429\pi$
$13$	2.65113	+	5.20313i	0.735290	+	1.44309i	−0.155104	+	0.987898i	$0.549571\pi$
$14$	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	$-0.520223\pi$
$17$	0.760813	−	0.120501i	0.184524	−	0.0292258i	0.248013	+	0.968757i	$0.420223\pi$
$18$	3.59040	+	2.63742i	0.846265	+	0.621646i
$19$	2.08083	−	2.86402i	0.477376	−	0.657051i	−0.500622	−	0.865666i	$-0.666895\pi$
$19$	2.08083	−	2.86402i	0.477376	−	0.657051i	0.977998	+	0.208614i	$0.0668954\pi$
$20$		0			0
$21$	−2.73126	−	3.21491i	−0.596011	−	0.701551i
$22$	5.74013	+	0.909148i	1.22380	+	0.193831i
$23$	−0.471845	+	0.926047i	−0.0983864	+	0.193094i	−0.934953	−	0.354770i	$-0.884559\pi$
$23$	−0.471845	+	0.926047i	−0.0983864	+	0.193094i	0.836567	+	0.547864i	$0.184559\pi$
$24$	0.350141	+	4.60305i	0.0714722	+	0.939593i
$25$		0			0
$26$			8.67180i			1.70068i
$27$	−5.04290	−	1.25268i	−0.970506	−	0.241077i
$28$	−0.0781880	+	0.493660i	−0.0147761	+	0.0932929i
$29$	−0.111964	+	0.0813465i	−0.0207912	+	0.0151057i	−0.598132	−	0.801397i	$-0.704090\pi$
$29$	−0.111964	+	0.0813465i	−0.0207912	+	0.0151057i	0.577341	+	0.816503i	$0.304090\pi$
$30$		0			0
$31$	0.372717	+	0.270795i	0.0669420	+	0.0486362i	0.620753	−	0.784006i	$-0.286827\pi$
$31$	0.372717	+	0.270795i	0.0669420	+	0.0486362i	−0.553811	+	0.832642i	$0.686827\pi$
$32$	0.817733	−	0.817733i	0.144556	−	0.144556i
$33$	−6.59538	+	1.56516i	−1.14811	+	0.272459i
$34$	1.08790	+	0.353481i	0.186574	+	0.0606215i
$35$		0			0
$36$	0.276623	+	0.550006i	0.0461039	+	0.0916677i
$37$	−4.55581	+	2.32130i	−0.748970	+	0.381620i	−0.786431	−	0.617679i	$-0.788073\pi$
$37$	−4.55581	+	2.32130i	−0.748970	+	0.381620i	0.0374602	+	0.999298i	$0.488073\pi$
$38$	4.68409	−	2.38666i	0.759859	−	0.387168i
$39$	−3.84616	−	9.35468i	−0.615879	−	1.49795i
$40$		0			0
$41$	−6.18190	−	2.00862i	−0.965450	−	0.313694i	−0.216472	−	0.976289i	$-0.569455\pi$
$41$	−6.18190	−	2.00862i	−0.965450	−	0.313694i	−0.748978	+	0.662595i	$0.769455\pi$
$42$	−1.44644	−	6.09513i	−0.223191	−	0.940499i
$43$	5.58451	−	5.58451i	0.851630	−	0.851630i	−0.138704	−	0.990334i	$-0.544294\pi$
$43$	5.58451	−	5.58451i	0.851630	−	0.851630i	0.990334	+	0.138704i	$0.0442938\pi$
$44$	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	0.898230	+	0.439525i	$0.144853\pi$
$47$	−0.629748	+	3.97607i	−0.0918582	+	0.579970i	−0.990089	+	0.140445i	$0.955147\pi$
$48$	−2.91374	+	6.98261i	−0.420562	+	1.00785i
$49$		−	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	$-0.514696\pi$
$53$	−2.90283	−	0.459763i	−0.398734	−	0.0631533i	−0.352581	+	0.935781i	$0.614696\pi$
$54$	−5.82795	−	5.05726i	−0.793083	−	0.688206i
$55$		0			0
$56$	3.81549	−	5.25157i	0.509866	−	0.701770i
$57$	−3.99440	+	4.65212i	−0.529071	+	0.616188i
$58$	−0.202986	+	0.0321498i	−0.0266533	+	0.00422147i
$59$	−0.855253	+	2.63220i	−0.111344	+	0.342683i	−0.991167	−	0.132619i	$-0.957661\pi$
$59$	−0.855253	+	2.63220i	−0.111344	+	0.342683i	0.879823	+	0.475302i	$0.157661\pi$
$60$		0			0
$61$	1.24058	+	3.81812i	0.158840	+	0.488860i	0.998530	−	0.0542065i	$-0.0172629\pi$
$61$	1.24058	+	3.81812i	0.158840	+	0.488860i	−0.839689	+	0.543067i	$0.817263\pi$
$62$	0.310595	+	0.609576i	0.0394456	+	0.0774163i
$63$	4.26369	+	5.93357i	0.537174	+	0.747560i
$64$	−6.67577	+	2.16909i	−0.834471	+	0.271136i
$65$		0			0
$66$	−9.78182	−	2.37552i	−1.20406	−	0.292406i
$67$	−0.304459	−	1.92228i	−0.0371956	−	0.234844i	0.962086	−	0.272747i	$-0.0879322\pi$
$67$	−0.304459	−	1.92228i	−0.0371956	−	0.234844i	−0.999281	+	0.0379032i	$0.987932\pi$
$68$	0.111778	+	0.111778i	0.0135551	+	0.0135551i
$69$	0.944601	−	1.53243i	0.113717	−	0.184482i
$70$		0			0
$71$	2.08859	+	2.87469i	0.247870	+	0.341163i	0.914764	−	0.403989i	$-0.132377\pi$
$71$	2.08859	+	2.87469i	0.247870	+	0.341163i	−0.666894	+	0.745152i	$0.732377\pi$
$72$	0.0418786	−	7.99563i	0.00493545	−	0.942294i
$73$	−10.6846	−	5.44405i	−1.25053	−	0.637178i	−0.301834	−	0.953360i	$-0.597599\pi$
$73$	−10.6846	−	5.44405i	−1.25053	−	0.637178i	−0.948698	+	0.316182i	$0.897599\pi$
$74$	−7.59295			−0.882662
$75$		0			0
$76$	0.726495			0.0833347
$77$	8.49280	+	4.32730i	0.967845	+	0.493142i
$78$	1.21766	−	14.9706i	0.137873	−	1.69508i
$79$	−0.518361	−	0.713462i	−0.0583201	−	0.0802708i	0.778861	−	0.627197i	$-0.215798\pi$
$79$	−0.518361	−	0.713462i	−0.0583201	−	0.0802708i	−0.837181	+	0.546926i	$0.815798\pi$
$80$		0			0
$81$	8.52991	+	2.87066i	0.947767	+	0.318962i
$82$	−6.82537	−	6.82537i	−0.753736	−	0.753736i
$83$	−1.49428	−	9.43448i	−0.164018	−	1.03557i	−0.923096	−	0.384569i	$-0.874350\pi$
$83$	−1.49428	−	9.43448i	−0.164018	−	1.03557i	0.759078	−	0.651000i	$-0.225650\pi$
$84$	0.204298	−	0.841250i	0.0222907	−	0.0917879i
$85$		0			0
$86$	11.1540	−	3.62417i	1.20277	−	0.390804i
$87$	0.204711	−	0.124711i	0.0219473	−	0.0133704i
$88$	−4.73545	−	9.29383i	−0.504800	−	0.990726i
$89$	3.64270	+	11.2111i	0.386125	+	1.18837i	0.935661	+	0.352901i	$0.114805\pi$
$89$	3.64270	+	11.2111i	0.386125	+	1.18837i	−0.549535	+	0.835470i	$0.685195\pi$
$90$		0			0
$91$	−4.39501	+	13.5264i	−0.460722	+	1.41796i
$92$	−0.210662	+	0.0333656i	−0.0219630	+	0.00347860i
$93$	−0.605416	−	0.519822i	−0.0627787	−	0.0539030i
$94$	−3.51381	+	4.83635i	−0.362422	+	0.498831i
$95$		0			0
$96$	−1.52652	+	1.29687i	−0.155799	+	0.132361i
$97$	−16.0719	−	2.54554i	−1.63186	−	0.258461i	−0.727774	−	0.685817i	$-0.759445\pi$
$97$	−16.0719	−	2.54554i	−1.63186	−	0.258461i	−0.904083	+	0.427356i	$0.859445\pi$
$98$	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	$0.736195\pi$
$102$	−1.82847	−	0.762992i	−0.181045	−	0.0755474i
$103$	−1.39927	+	8.83465i	−0.137874	+	0.870504i	0.817677	+	0.575678i	$0.195262\pi$
$103$	−1.39927	+	8.83465i	−0.137874	+	0.870504i	−0.955551	+	0.294826i	$0.904738\pi$
$104$	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	$-0.501776\pi$
$107$	10.2862	−	10.2862i	0.994405	−	0.994405i	0.999984	+	0.00557906i	$0.00177588\pi$
$108$	−0.400318	−	0.988345i	−0.0385206	−	0.0951036i
$109$	−9.46329	−	3.07481i	−0.906419	−	0.294513i	−0.181535	−	0.983384i	$-0.558107\pi$
$109$	−9.46329	−	3.07481i	−0.906419	−	0.294513i	−0.724884	+	0.688871i	$0.758107\pi$
$110$		0			0
$111$	8.19087	−	3.36767i	0.777443	−	0.319645i
$112$	9.47958	−	4.83009i	0.895736	−	0.456400i
$113$	4.31931	−	2.20080i	0.406326	−	0.207034i	−0.238868	−	0.971052i	$-0.576776\pi$
$113$	4.31931	−	2.20080i	0.406326	−	0.207034i	0.645194	+	0.764018i	$0.276776\pi$
$114$	−8.42150	+	3.46249i	−0.788746	+	0.324292i
$115$		0			0
$116$	−0.0270110	−	0.00877640i	−0.00250791	−	0.000814868i
$117$	5.32627	+	16.6895i	0.492414	+	1.54295i
$118$	−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
$123$	10.3901	+	4.33562i	0.936841	+	0.390930i
$124$			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	−0.538410	−	0.842683i	$-0.680975\pi$
$127$	5.18173	−	10.1697i	0.459804	−	0.902417i	0.998214	−	0.0597340i	$-0.0190253\pi$
$128$	−12.5798	−	1.99244i	−1.11190	−	0.176108i
$129$	−10.4250	+	8.85666i	−0.917868	+	0.779785i
$130$		0			0
$131$	−2.60417	+	3.58434i	−0.227528	+	0.313165i	−0.907483	−	0.420088i	$-0.861999\pi$
$131$	−2.60417	+	3.58434i	−0.227528	+	0.313165i	0.679956	+	0.733253i	$0.261999\pi$
$132$	−1.05541	−	0.906199i	−0.0918619	−	0.0788745i
$133$	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	$-0.265241\pi$
$137$	−3.76412	−	7.38749i	−0.321590	−	0.631156i	−0.994044	+	0.108983i	$0.965241\pi$
$138$	2.28296	−	1.39079i	0.194339	−	0.118392i
$139$	20.8266	−	6.76697i	1.76649	−	0.573967i	0.768649	−	0.639671i	$-0.220929\pi$
$139$	20.8266	−	6.76697i	1.76649	−	0.573967i	0.997839	+	0.0657043i	$0.0209294\pi$
$140$		0			0
$141$	1.64547	−	6.77566i	0.138574	−	0.570614i
$142$	0.825452	+	5.21170i	0.0692704	+	0.437356i
$143$	16.1601	+	16.1601i	1.35138	+	1.35138i
$144$	6.01060	−	11.6453i	0.500884	−	0.970440i
$145$		0			0
$146$	−10.4669	−	14.4065i	−0.866251	−	1.19229i
$147$	−0.149991	+	1.84406i	−0.0123711	+	0.152096i
$148$	−0.934931	−	0.476371i	−0.0768508	−	0.0391575i
$149$	−5.61752			−0.460205			−0.230103	−	0.973166i	$-0.573906\pi$
$149$	−5.61752			−0.460205			−0.230103	+	0.973166i	$0.573906\pi$
$150$		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
$153$	2.31086	+	0.0121036i	0.186822	+	0.000978515i
$154$	8.31983	+	11.4513i	0.670431	+	0.922769i
$155$		0			0
$156$	1.08917	−	1.76695i	0.0872030	−	0.141469i
$157$	7.39864	+	7.39864i	0.590476	+	0.590476i	0.937760	−	0.347284i	$-0.112896\pi$
$157$	7.39864	+	7.39864i	0.590476	+	0.590476i	−0.347284	+	0.937760i	$0.612896\pi$
$158$	−0.204867	−	1.29348i	−0.0162983	−	0.102904i
$159$	4.94674	+	1.20132i	0.392302	+	0.0952706i
$160$		0			0
$161$	−2.40742	+	0.782219i	−0.189731	+	0.0616475i
$162$	9.35095	+	9.54894i	0.734680	+	0.750236i
$163$	−3.88333	−	7.62146i	−0.304166	−	0.596959i	0.687442	−	0.726239i	$-0.258733\pi$
$163$	−3.88333	−	7.62146i	−0.304166	−	0.596959i	−0.991608	+	0.129280i	$0.958733\pi$
$164$	−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	$-0.786711\pi$
$167$	−17.2815	+	2.73713i	−1.33729	+	0.211805i	−0.553507	+	0.832845i	$0.686711\pi$
$168$	−7.32427	+	8.53028i	−0.565080	+	0.658126i
$169$	−12.4029	+	17.0711i	−0.954066	+	1.31316i
$170$		0			0
$171$	7.54897	−	7.47030i	0.577284	−	0.571268i
$172$	1.60079	+	0.253540i	0.122059	+	0.0193322i
$173$	−7.59919	+	14.9142i	−0.577755	+	1.13391i	0.398476	+	0.917179i	$0.369539\pi$
$173$	−7.59919	+	14.9142i	−0.577755	+	1.13391i	−0.976232	+	0.216730i	$0.930461\pi$
$174$	0.354939	−	0.0269992i	0.0269078	−	0.00204680i
$175$		0			0
$176$		−	17.0959i		−	1.28865i
$177$	1.84607	−	4.42400i	0.138759	−	0.332528i
$178$	−2.73841	+	17.2897i	−0.205253	+	1.29591i
$179$	−7.83739	+	5.69420i	−0.585794	+	0.425604i	−0.840808	−	0.541333i	$-0.817920\pi$
$179$	−7.83739	+	5.69420i	−0.585794	+	0.425604i	0.255014	+	0.966937i	$0.417920\pi$
$180$		0			0
$181$	7.76955	+	5.64491i	0.577506	+	0.419583i	0.837824	−	0.545940i	$-0.183827\pi$
$181$	7.76955	+	5.64491i	0.577506	+	0.419583i	−0.260318	+	0.965523i	$0.583827\pi$
$182$	−14.9344	+	14.9344i	−1.10701	+	1.10701i
$183$	−1.60555	−	6.76561i	−0.118686	−	0.500129i
$184$	2.63449	+	0.855997i	0.194217	+	0.0631049i
$185$		0			0
$186$	−0.450600	−	1.09595i	−0.0330396	−	0.0803593i
$187$	2.68606	−	1.36862i	0.196424	−	0.100083i
$188$	−0.736087	+	0.375055i	−0.0536847	+	0.0273537i
$189$	−6.52745	−	10.8421i	−0.474802	−	0.788648i
$190$		0			0
$191$	−10.1420	−	3.29532i	−0.733847	−	0.238441i	−0.0818306	−	0.996646i	$-0.526077\pi$
$191$	−10.1420	−	3.29532i	−0.733847	−	0.238441i	−0.652016	+	0.758205i	$0.726077\pi$
$192$	11.8293	−	2.80722i	0.853705	−	0.202593i
$193$	−8.82760	+	8.82760i	−0.635425	+	0.635425i	−0.949423	−	0.313999i	$-0.898331\pi$
$193$	−8.82760	+	8.82760i	−0.635425	+	0.635425i	0.313999	+	0.949423i	$0.398331\pi$
$194$	−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	−0.907645	−	0.419739i	$-0.862122\pi$
$197$	1.19701	−	7.55759i	0.0852831	−	0.538456i	0.992928	−	0.118718i	$-0.0378783\pi$
$198$	16.5533	+	5.47450i	1.17639	+	0.389056i
$199$		−	16.5759i		−	1.17503i	−0.809212	−	0.587517i	$-0.800105\pi$
$199$		−	16.5759i		−	1.17503i	0.809212	−	0.587517i	$-0.199895\pi$
$200$		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
$204$	−0.177273	−	0.208664i	−0.0124116	−	0.0146094i
$205$		0			0
$206$	−7.80753	+	10.7461i	−0.543976	+	0.748719i
$207$	−1.84589	+	2.51287i	−0.128298	+	0.174656i
$208$	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	−0.792096	−	0.610397i	$-0.791010\pi$
$211$	−7.40904	−	22.8027i	−0.510059	−	1.56980i	0.282036	−	0.959404i	$-0.408990\pi$
$212$	−0.273818	−	0.537398i	−0.0188059	−	0.0369086i
$213$	−3.20197	−	5.25599i	−0.219396	−	0.360135i
$214$	20.5448	−	6.67542i	1.40442	−	0.456322i
$215$		0			0
$216$	−1.19502	+	13.7974i	−0.0813106	+	0.938793i
$217$	0.175529	+	1.10824i	0.0119157	+	0.0752325i
$218$	−10.4483	−	10.4483i	−0.707650	−	0.707650i
$219$	17.6808	+	10.8986i	1.19476	+	0.736461i
$220$		0			0
$221$	2.64399	+	3.63914i	0.177854	+	0.244795i
$222$	13.1081	+	1.06618i	0.879757	+	0.0715570i
$223$	−2.11546	−	1.07788i	−0.141662	−	0.0721802i	0.381723	−	0.924277i	$-0.375331\pi$
$223$	−2.11546	−	1.07788i	−0.141662	−	0.0721802i	−0.523385	+	0.852097i	$0.675331\pi$
$224$	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	$-0.217676\pi$
$227$	10.8425	+	5.52455i	0.719644	+	0.366677i	−0.0555024	+	0.998459i	$0.517676\pi$
$228$	−1.25418	−	0.102012i	−0.0830604	−	0.00675590i
$229$	8.52530	+	11.7341i	0.563368	+	0.775409i	0.991750	−	0.128188i	$-0.0409162\pi$
$229$	8.52530	+	11.7341i	0.563368	+	0.775409i	−0.428382	+	0.903598i	$0.640916\pi$
$230$		0			0
$231$	−14.0539	−	8.66296i	−0.924680	−	0.569981i
$232$	0.260821	+	0.260821i	0.0171237	+	0.0171237i
$233$	3.38975	+	21.4020i	0.222070	+	1.40209i	0.806780	+	0.590852i	$0.201208\pi$
$233$	3.38975	+	21.4020i	0.222070	+	1.40209i	−0.584710	+	0.811242i	$0.698792\pi$
$234$	−4.20423	+	25.6734i	−0.274839	+	1.67833i
$235$		0			0
$236$	−0.540172	+	0.175513i	−0.0351622	+	0.0114249i
$237$	0.794690	+	1.30447i	0.0516206	+	0.0847345i
$238$	1.26481	+	2.48232i	0.0819853	+	0.160905i
$239$	−2.61133	−	8.03683i	−0.168913	−	0.519859i	0.830391	−	0.557182i	$-0.188117\pi$
$239$	−2.61133	−	8.03683i	−0.168913	−	0.519859i	−0.999303	+	0.0373221i	$0.988117\pi$
$240$		0			0
$241$	0.483477	−	1.48799i	0.0311435	−	0.0958498i	−0.934277	−	0.356549i	$-0.883953\pi$
$241$	0.483477	−	1.48799i	0.0311435	−	0.0958498i	0.965420	+	0.260699i	$0.0839532\pi$
$242$	6.33073	−	1.00269i	0.406955	−	0.0644553i
$243$	−14.3225	−	6.15351i	−0.918790	−	0.394748i
$244$	−0.484257	+	0.666523i	−0.0310014	+	0.0426698i
$245$		0			0
$246$	10.8246	+	12.7414i	0.690150	+	0.812360i
$247$	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	$-0.0855168\pi$
$252$	−0.470815	+	1.42361i	−0.0296586	+	0.0896787i
$253$	−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	$-0.594478\pi$
$257$	10.6415	−	10.6415i	0.663801	−	0.663801i	0.956274	+	0.292473i	$0.0944781\pi$
$258$	−19.7647	+	4.69036i	−1.23049	+	0.292009i
$259$	−11.8436	−	3.84823i	−0.735927	−	0.239117i
$260$		0			0
$261$	−0.370914	+	0.186550i	−0.0229590	+	0.0115471i
$262$	−5.86216	+	2.98692i	−0.362165	+	0.184532i
$263$	−1.66971	+	0.850760i	−0.102959	+	0.0524601i	−0.504711	−	0.863288i	$-0.668401\pi$
$263$	−1.66971	+	0.850760i	−0.102959	+	0.0524601i	0.401753	+	0.915748i	$0.368401\pi$
$264$	6.87003	+	16.7093i	0.422821	+	1.02839i
$265$		0			0
$266$	12.1771	+	3.95658i	0.746627	+	0.242594i
$267$	−4.71435	−	19.8657i	−0.288514	−	1.21576i
$268$	0.282420	−	0.282420i	0.0172515	−	0.0172515i
$269$	19.0018	+	13.8056i	1.15856	+	0.841745i	0.989596	−	0.143877i	$-0.0459571\pi$
$269$	19.0018	+	13.8056i	1.15856	+	0.841745i	0.168966	+	0.985622i	$0.445957\pi$
$270$		0			0
$271$	0.609720	−	0.442988i	0.0370379	−	0.0269096i	−0.569112	−	0.822260i	$-0.692713\pi$
$271$	0.609720	−	0.442988i	0.0370379	−	0.0269096i	0.606150	+	0.795350i	$0.292713\pi$
$272$	0.526387	−	3.32348i	0.0319169	−	0.201515i
$273$	9.48666	−	22.7342i	0.574159	−	1.37594i
$274$		−	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	−0.731327	−	0.682027i	$-0.761099\pi$
$277$	4.16594	−	8.17612i	0.250307	−	0.491255i	0.981635	+	0.190771i	$0.0610989\pi$
$278$	32.1187	+	5.08710i	1.92635	+	0.305104i
$279$	0.972168	+	0.982405i	0.0582022	+	0.0588151i
$280$		0			0
$281$	14.7500	−	20.3017i	0.879913	−	1.21110i	−0.0965320	−	0.995330i	$-0.530775\pi$
$281$	14.7500	−	20.3017i	0.879913	−	1.21110i	0.976445	−	0.215766i	$-0.0692250\pi$
$282$	6.74518	−	7.85583i	0.401669	−	0.467808i
$283$	23.3503	−	3.69832i	1.38803	−	0.219843i	0.582709	−	0.812681i	$-0.301993\pi$
$283$	23.3503	−	3.69832i	1.38803	−	0.219843i	0.805322	+	0.592838i	$0.201993\pi$
$284$	−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
$288$	2.81740	−	2.02450i	0.166017	−	0.119295i
$289$	−15.6036	+	5.06993i	−0.917861	+	0.298231i
$290$		0			0
$291$	27.3883	+	6.65127i	1.60553	+	0.389904i
$292$	−0.384966	−	2.43058i	−0.0225284	−	0.142239i
$293$	−17.4959	−	17.4959i	−1.02212	−	1.02212i	−0.999750	−	0.0223711i	$-0.992878\pi$
$293$	−17.4959	−	17.4959i	−1.02212	−	1.02212i	−0.0223711	−	0.999750i	$-0.507122\pi$
$294$	−1.44168	+	2.33884i	−0.0840806	+	0.136404i
$295$		0			0
$296$	8.01016	+	11.0250i	0.465581	+	0.640817i
$297$	−20.2849	+	1.43620i	−1.17705	+	0.0833366i
$298$	−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
$303$	2.08035	−	25.5768i	0.119513	−	1.46935i
$304$	−9.08974	−	12.5110i	−0.521333	−	0.717553i
$305$		0			0
$306$	3.04944	+	1.57394i	0.174325	+	0.0899760i
$307$	4.00162	+	4.00162i	0.228384	+	0.228384i	0.812017	−	0.583633i	$-0.198369\pi$
$307$	4.00162	+	4.00162i	0.228384	+	0.228384i	−0.583633	+	0.812017i	$0.698369\pi$
$308$	0.305997	+	1.93199i	0.0174358	+	0.110085i
$309$	3.65616	−	15.0552i	0.207992	−	0.856461i
$310$		0			0
$311$	−32.7389	+	10.6375i	−1.85645	+	0.603198i	−0.860923	+	0.508735i	$0.830113\pi$
$311$	−32.7389	+	10.6375i	−1.85645	+	0.603198i	−0.995528	+	0.0944627i	$0.969887\pi$
$312$	−23.0220	+	14.0251i	−1.30336	+	0.794014i
$313$	−8.86459	−	17.3977i	−0.501056	−	0.983378i	−0.993586	−	0.113082i	$-0.963928\pi$
$313$	−8.86459	−	17.3977i	−0.501056	−	0.983378i	0.492530	−	0.870296i	$-0.336072\pi$
$314$	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	$-0.576272\pi$
$317$	−2.89957	+	0.459247i	−0.162856	+	0.0257939i	0.0744738	+	0.997223i	$0.476272\pi$
$318$	5.73534	+	4.92448i	0.321622	+	0.276151i
$319$	−0.318358	+	0.438182i	−0.0178246	+	0.0245335i
$320$		0			0
$321$	−19.2019	+	16.3132i	−1.07175	+	0.910516i
$322$	−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
$327$	15.9052	+	6.63700i	0.879559	+	0.367027i
$328$	−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	0.673924	−	0.738800i	$-0.264607\pi$
$331$	3.26639	+	2.37317i	0.179537	+	0.130441i	−0.494387	+	0.869242i	$0.664607\pi$
$332$	1.38611	−	1.38611i	0.0760725	−	0.0760725i
$333$	−14.6132	+	4.66363i	−0.800797	+	0.255566i
$334$	−24.7112	−	8.02917i	−1.35214	−	0.439337i
$335$		0			0
$336$	−17.0433	+	7.00733i	−0.929788	+	0.382281i
$337$	−9.50552	+	4.84331i	−0.517799	+	0.263832i	−0.693302	−	0.720647i	$-0.743845\pi$
$337$	−9.50552	+	4.84331i	−0.517799	+	0.263832i	0.175503	+	0.984479i	$0.443845\pi$
$338$	−27.9196	+	14.2258i	−1.51863	+	0.773779i
$339$	−7.76566	+	3.19284i	−0.421773	+	0.173411i
$340$		0			0
$341$	1.71476	+	0.557161i	0.0928597	+	0.0301719i
$342$	15.0246	−	4.79495i	0.812440	−	0.259281i
$343$	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	0.632077	+	0.774905i	$0.282202\pi$
$347$	−3.88435	+	24.5248i	−0.208523	+	1.31656i	−0.840600	+	0.541656i	$0.817798\pi$
$348$	0.0453980	+	0.0189439i	0.00243359	+	0.00101550i
$349$		−	3.68396i		−	0.197198i	−0.995127	−	0.0985990i	$-0.968564\pi$
$349$		−	3.68396i		−	0.197198i	0.995127	−	0.0985990i	$-0.0314361\pi$
$350$		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	$-0.454672\pi$
$353$	−0.544691	−	0.0862706i	−0.0289910	−	0.00459172i	−0.170913	+	0.985286i	$0.554672\pi$
$354$	5.42516	−	4.60901i	0.288344	−	0.244966i
$355$		0			0
$356$	−1.42191	+	1.95710i	−0.0753613	+	0.103726i
$357$	−2.46538	−	2.11683i	−0.130482	−	0.112034i
$358$	−14.2089	+	2.25046i	−0.750962	+	0.118941i
$359$	0.0579467	−	0.178342i	0.00305831	−	0.00941251i	−0.949516	−	0.313719i	$-0.898425\pi$
$359$	0.0579467	−	0.178342i	0.00305831	−	0.00941251i	0.952574	+	0.304307i	$0.0984249\pi$
$360$		0			0
$361$	1.99857	+	6.15098i	0.105188	+	0.323736i
$362$	6.47457	+	12.7071i	0.340296	+	0.667868i
$363$	−6.38454	+	3.88949i	−0.335101	+	0.204145i
$364$	−2.77586	+	0.901931i	−0.145495	+	0.0472741i
$365$		0			0
$366$	2.43683	−	10.0343i	0.127375	−	0.524501i
$367$	−3.24722	−	20.5021i	−0.169503	−	1.07020i	−0.914929	−	0.403614i	$-0.867754\pi$
$367$	−3.24722	−	20.5021i	−0.169503	−	1.07020i	0.745426	−	0.666589i	$-0.232246\pi$
$368$	3.21034	+	3.21034i	0.167351	+	0.167351i
$369$	−17.3281	−	8.94374i	−0.902065	−	0.465592i
$370$		0			0
$371$	−4.20740	−	5.79099i	−0.218437	−	0.300653i
$372$	0.0132756	−	0.163217i	0.000688308	−	0.00846239i
$373$	−4.29685	−	2.18936i	−0.222483	−	0.113361i	0.339197	−	0.940715i	$-0.389845\pi$
$373$	−4.29685	−	2.18936i	−0.222483	−	0.113361i	−0.561680	+	0.827355i	$0.689845\pi$
$374$	4.47672			0.231486
$375$		0			0
$376$	10.7293			0.553322
$377$	−0.720086	−	0.366902i	−0.0370863	−	0.0188964i
$378$	−1.32726	−	18.7463i	−0.0682670	−	0.964205i
$379$	−4.09975	−	5.64282i	−0.210590	−	0.289852i	0.690635	−	0.723203i	$-0.257331\pi$
$379$	−4.09975	−	5.64282i	−0.210590	−	0.289852i	−0.901225	+	0.433351i	$0.857331\pi$
$380$		0			0
$381$	−10.3735	+	16.8289i	−0.531450	+	0.862171i
$382$	−11.1976	−	11.1976i	−0.572921	−	0.572921i
$383$	1.60030	+	10.1039i	0.0817714	+	0.516284i	0.994243	+	0.107145i	$0.0341709\pi$
$383$	1.60030	+	10.1039i	0.0817714	+	0.516284i	−0.912472	+	0.409139i	$0.865829\pi$
$384$	21.4373	+	5.20605i	1.09397	+	0.265670i
$385$		0			0
$386$	−17.6315	+	5.72883i	−0.897421	+	0.291590i
$387$	19.2408	−	13.8258i	0.978063	−	0.702807i
$388$	−1.51603	−	2.97538i	−0.0769650	−	0.151052i
$389$	−9.90598	−	30.4875i	−0.502253	−	1.54578i	−0.805340	−	0.592813i	$-0.798017\pi$
$389$	−9.90598	−	30.4875i	−0.502253	−	1.54578i	0.303087	−	0.952963i	$-0.401983\pi$
$390$		0			0
$391$	−0.247396	+	0.761407i	−0.0125114	+	0.0385060i
$392$	−2.81193	+	0.445366i	−0.142024	+	0.0224944i
$393$	4.99901	−	5.82215i	0.252167	−	0.293688i
$394$	6.67895	−	9.19278i	0.336481	−	0.463126i
$395$		0			0
$396$	1.69477	+	1.71261i	0.0851652	+	0.0860621i
$397$	−10.1301	−	1.60445i	−0.508414	−	0.0805249i	−0.103043	−	0.994677i	$-0.532858\pi$
$397$	−10.1301	−	1.60445i	−0.508414	−	0.0805249i	−0.405371	+	0.914152i	$0.632858\pi$
$398$	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	$-0.118789\pi$
$402$	−1.92778	+	4.61982i	−0.0961490	+	0.230416i
$403$	−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
$408$	0.821063	+	3.45987i	0.0406487	+	0.171289i
$409$	15.6748	+	5.09306i	0.775070	+	0.251835i	0.669734	−	0.742601i	$-0.266408\pi$
$409$	15.6748	+	5.09306i	0.775070	+	0.251835i	0.105336	+	0.994437i	$0.466408\pi$
$410$		0			0
$411$	5.46085	+	13.2819i	0.269364	+	0.655150i
$412$	−1.63555	+	0.833355i	−0.0805778	+	0.0410564i
$413$	−6.00602	+	3.06022i	−0.295537	+	0.150584i
$414$	−4.13649	+	2.08043i	−0.203297	+	0.102247i
$415$		0			0
$416$	6.42268	+	2.08686i	0.314898	+	0.102317i
$417$	−36.9042	+	8.75775i	−1.80720	+	0.428869i
$418$	14.5481	−	14.5481i	0.711570	−	0.711570i
$419$	0.887321	+	0.644676i	0.0433484	+	0.0314945i	0.609248	−	0.792979i	$-0.291471\pi$
$419$	0.887321	+	0.644676i	0.0433484	+	0.0314945i	−0.565900	+	0.824474i	$0.691471\pi$
$420$		0			0
$421$	23.5246	−	17.0916i	1.14652	−	0.832996i	0.158506	−	0.987358i	$-0.449332\pi$
$421$	23.5246	−	17.0916i	1.14652	−	0.832996i	0.988014	+	0.154362i	$0.0493324\pi$
$422$	5.56977	−	35.1662i	0.271132	−	1.71186i
$423$	−3.79208	+	11.4661i	−0.184377	+	0.557502i
$424$			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
$429$	−25.6289	−	30.1672i	−1.23737	−	1.45649i
$430$		0			0
$431$	−15.6969	+	21.6049i	−0.756091	+	1.04067i	0.241439	+	0.970416i	$0.422381\pi$
$431$	−15.6969	+	21.6049i	−0.756091	+	1.04067i	−0.997529	+	0.0702534i	$0.977619\pi$
$432$	−12.0116	+	19.2598i	−0.577908	+	0.926640i
$433$	−26.4272	+	4.18566i	−1.27001	+	0.201150i	−0.754823	−	0.655928i	$-0.772277\pi$
$433$	−26.4272	+	4.18566i	−1.27001	+	0.201150i	−0.515187	+	0.857078i	$0.672277\pi$
$434$	−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
$438$	16.0467	+	26.3404i	0.766741	+	1.25859i
$439$	−19.2932	+	6.26873i	−0.920812	+	0.299190i	−0.730800	−	0.682592i	$-0.760853\pi$
$439$	−19.2932	+	6.26873i	−0.920812	+	0.299190i	−0.190012	+	0.981782i	$0.560853\pi$
$440$		0			0
$441$	0.517875	−	3.16244i	0.0246607	−	0.150592i
$442$	1.04496	+	6.59762i	0.0497037	+	0.313817i
$443$	12.0174	+	12.0174i	0.570962	+	0.570962i	0.932397	−	0.361435i	$-0.117713\pi$
$443$	12.0174	+	12.0174i	0.570962	+	0.570962i	−0.361435	+	0.932397i	$0.617713\pi$
$444$	1.54713	+	0.953663i	0.0734234	+	0.0452588i
$445$		0			0
$446$	−2.07237	−	2.85238i	−0.0981298	−	0.135064i
$447$	9.69781	+	0.788793i	0.458691	+	0.0373086i
$448$	−15.2324	−	7.76132i	−0.719665	−	0.366688i
$449$	23.5930			1.11342			0.556711	−	0.830706i	$-0.312063\pi$
$449$	23.5930			1.11342			0.556711	+	0.830706i	$0.312063\pi$
$450$		0			0
$451$	−25.4385			−1.19785
$452$	0.886396	+	0.451642i	0.0416926	+	0.0212434i
$453$	25.3465	+	2.06162i	1.19088	+	0.0968632i
$454$	10.6217	+	14.6195i	0.498501	+	0.686128i
$455$		0			0
$456$	13.9118	+	8.57536i	0.651480	+	0.401578i
$457$	1.82957	+	1.82957i	0.0855837	+	0.0855837i	0.748603	−	0.663019i	$-0.230725\pi$
$457$	1.82957	+	1.82957i	0.0855837	+	0.0855837i	−0.663019	+	0.748603i	$0.730725\pi$
$458$	3.36937	+	21.2734i	0.157441	+	0.994040i
$459$	−3.98765	−	0.345378i	−0.186128	−	0.0161209i
$460$		0			0
$461$	24.9186	−	8.09654i	1.16057	−	0.377094i	0.335458	−	0.942055i	$-0.391109\pi$
$461$	24.9186	−	8.09654i	1.16057	−	0.377094i	0.825117	+	0.564962i	$0.191109\pi$
$462$	−12.7550	−	20.9371i	−0.593416	−	0.974084i
$463$	9.73607	+	19.1081i	0.452474	+	0.888030i	0.998729	+	0.0504107i	$0.0160530\pi$
$463$	9.73607	+	19.1081i	0.452474	+	0.888030i	−0.546255	+	0.837619i	$0.683947\pi$
$464$	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	$-0.310203\pi$
$467$	29.2023	−	4.62519i	1.35132	−	0.214028i	0.789764	+	0.613411i	$0.210203\pi$
$468$	−2.12839	+	2.89744i	−0.0983848	+	0.133934i
$469$	2.78618	−	3.83484i	0.128654	−	0.177077i
$470$		0			0
$471$	−11.7338	−	13.8115i	−0.540663	−	0.636402i
$472$	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
$477$	−8.37111	−	2.76850i	−0.383287	−	0.126761i
$478$	1.96307	−	12.3944i	0.0897889	−	0.566905i
$479$	−24.4450	+	17.7603i	−1.11692	+	0.811489i	−0.983739	−	0.179603i	$-0.942519\pi$
$479$	−24.4450	+	17.7603i	−1.11692	+	0.811489i	−0.133180	+	0.991092i	$0.542519\pi$
$480$		0			0
$481$	−24.1560	−	17.5504i	−1.10142	−	0.800229i
$482$	1.64287	−	1.64287i	0.0748309	−	0.0748309i
$483$	4.26589	−	1.01234i	0.194105	−	0.0460631i
$484$	0.842420	+	0.273719i	0.0382918	+	0.0124418i
$485$		0			0
$486$	−14.8022	−	17.7978i	−0.671441	−	0.807326i
$487$	−13.4191	+	6.83736i	−0.608076	+	0.309830i	−0.730780	−	0.682613i	$-0.760843\pi$
$487$	−13.4191	+	6.83736i	−0.608076	+	0.309830i	0.122704	+	0.992443i	$0.460843\pi$
$488$	9.53371	−	4.85767i	0.431571	−	0.219896i
$489$	5.63380	+	13.7026i	0.254769	+	0.619653i
$490$		0			0
$491$	31.9571	+	10.3835i	1.44220	+	0.468601i	0.922584	−	0.385797i	$-0.126073\pi$
$491$	31.9571	+	10.3835i	1.44220	+	0.468601i	0.519621	+	0.854397i	$0.326073\pi$
$492$	0.533470	+	2.24798i	0.0240507	+	0.101347i
$493$	−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
$498$	−9.46149	+	22.6739i	−0.423980	+	1.01604i
$499$			32.3318i			1.44737i	0.690131	+	0.723684i	$0.257553\pi$
$499$			32.3318i			1.44737i	−0.690131	+	0.723684i	$0.742447\pi$
$500$		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	$-0.454644\pi$
$503$	−0.646326	−	0.102368i	−0.0288182	−	0.00456436i	−0.170827	+	0.985301i	$0.554644\pi$
$504$	13.8420	−	13.6978i	0.616574	−	0.610149i
$505$		0			0
$506$	−3.55037	+	4.88666i	−0.157833	+	0.217238i
$507$	23.8087	−	27.7291i	1.05738	−	1.23149i
$508$	2.31346	−	0.366416i	0.102643	−	0.0162571i
$509$	−7.29902	+	22.4641i	−0.323523	+	0.995703i	0.648579	+	0.761147i	$0.275364\pi$
$509$	−7.29902	+	22.4641i	−0.323523	+	0.995703i	−0.972103	+	0.234556i	$0.924636\pi$
$510$		0			0
$511$	−9.02509	−	27.7764i	−0.399247	−	1.22875i
$512$	8.27787	+	16.2462i	0.365834	+	0.717989i
$513$	−14.0811	+	11.8364i	−0.621696	+	0.522588i
$514$	21.2545	−	6.90601i	0.937497	−	0.304611i
$515$		0			0
$516$	−2.72792	−	0.662476i	−0.120090	−	0.0291639i
$517$	2.46458	+	15.5608i	0.108392	+	0.684361i
$518$	−13.0764	−	13.0764i	−0.574545	−	0.574545i
$519$	15.2131	−	24.6801i	0.667779	−	1.08334i
$520$		0			0
$521$	20.7338	+	28.5376i	0.908365	+	1.25026i	0.967722	+	0.252020i	$0.0810948\pi$
$521$	20.7338	+	28.5376i	0.908365	+	1.25026i	−0.0593574	+	0.998237i	$0.518905\pi$
$522$	−0.616540	−	0.00322924i	−0.0269852	−	0.000141340i
$523$	2.26510	+	1.15413i	0.0990460	+	0.0504664i	0.502812	−	0.864396i	$-0.332299\pi$
$523$	2.26510	+	1.15413i	0.0990460	+	0.0504664i	−0.403766	+	0.914862i	$0.632299\pi$
$524$	−0.909212			−0.0397191
$525$		0			0
$526$	−2.78282			−0.121337
$527$	0.316199	+	0.161111i	0.0137738	+	0.00701813i
$528$	−2.40054	+	29.5134i	−0.104470	+	1.28441i
$529$	12.8841	+	17.7335i	0.560180	+	0.771021i
$530$		0			0
$531$	−3.80816	+	7.37815i	−0.165260	+	0.320185i
$532$	1.25116	+	1.25116i	0.0542445	+	0.0542445i
$533$	−5.93788	−	37.4903i	−0.257198	−	1.62389i
$534$	7.15521	−	29.4635i	0.309636	−	1.27501i
$535$		0			0
$536$	−4.93333	+	1.60294i	−0.213087	+	0.0692363i
$537$	14.3296	−	8.72967i	0.618369	−	0.376713i
$538$	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	−0.853043	−	0.521841i	$-0.825245\pi$
$541$	3.34503	−	10.2949i	0.143814	−	0.442614i	0.996857	+	0.0792273i	$0.0252453\pi$
$542$	1.10540	−	0.175078i	0.0474809	−	0.00752024i
$543$	−12.6203	−	10.8361i	−0.541590	−	0.465020i
$544$	0.523604	−	0.720680i	0.0224494	−	0.0308989i
$545$		0			0
$546$	27.8790	−	23.6850i	1.19311	−	1.01362i
$547$	22.7658	+	3.60575i	0.973396	+	0.154171i	0.622821	−	0.782364i	$-0.285986\pi$
$547$	22.7658	+	3.60575i	0.973396	+	0.154171i	0.350574	+	0.936535i	$0.385986\pi$
$548$	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
$552$	−4.42785	−	1.84768i	−0.188462	−	0.0786423i
$553$	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	$-0.687375\pi$
$557$	6.52436	−	6.52436i	0.276446	−	0.276446i	0.831689	+	0.555242i	$0.187375\pi$
$558$	0.624004	+	1.95527i	0.0264162	+	0.0827733i
$559$	43.8621	+	14.2517i	1.85517	+	0.602782i
$560$		0			0
$561$	−4.82925	+	1.98554i	−0.203891	+	0.0838296i
$562$	33.2033	−	16.9179i	1.40060	−	0.713639i
$563$	9.63388	−	4.90871i	0.406020	−	0.206877i	−0.239040	−	0.971010i	$-0.576833\pi$
$563$	9.63388	−	4.90871i	0.406020	−	0.206877i	0.645059	+	0.764132i	$0.276833\pi$
$564$	1.32341	−	0.544117i	0.0557255	−	0.0229115i
$565$		0			0
$566$	33.3891	+	10.8488i	1.40345	+	0.456008i
$567$	9.74624	+	19.6338i	0.409304	+	0.824544i
$568$	6.69663	−	6.69663i	0.280984	−	0.280984i
$569$	15.4318	+	11.2119i	0.646937	+	0.470027i	0.862226	−	0.506523i	$-0.169070\pi$
$569$	15.4318	+	11.2119i	0.646937	+	0.470027i	−0.215290	+	0.976550i	$0.569070\pi$
$570$		0			0
$571$	−7.63086	+	5.54414i	−0.319342	+	0.232015i	−0.735894	−	0.677096i	$-0.763238\pi$
$571$	−7.63086	+	5.54414i	−0.319342	+	0.232015i	0.416553	+	0.909111i	$0.363238\pi$
$572$	−0.733679	+	4.63227i	−0.0306767	+	0.193685i
$573$	17.0459	+	7.11298i	0.712101	+	0.297149i
$574$		−	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	−0.819437	−	0.573169i	$-0.805714\pi$
$577$	3.02469	−	5.93629i	0.125920	−	0.247131i	0.945357	+	0.326038i	$0.105714\pi$
$578$	−24.0639	−	3.81134i	−1.00092	−	0.158531i
$579$	16.4791	−	14.0000i	0.684847	−	0.581820i
$580$		0			0
$581$	13.6745	−	18.8213i	0.567313	−	0.780839i
$582$	31.7546	+	27.2651i	1.31627	+	1.13017i
$583$	−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	$-0.0426798\pi$
$587$	7.27726	+	14.2824i	0.300365	+	0.589499i	−0.690660	+	0.723180i	$0.742680\pi$
$588$	−0.324252	+	0.197536i	−0.0133719	+	0.00814624i
$589$	1.55112	−	0.503991i	0.0639129	−	0.0207666i
$590$		0			0
$591$	−3.12766	+	12.8790i	−0.128655	+	0.529770i
$592$	3.49407	+	22.0607i	0.143605	+	0.906689i
$593$	−19.4509	−	19.4509i	−0.798754	−	0.798754i	0.184145	−	0.982899i	$-0.441048\pi$
$593$	−19.4509	−	19.4509i	−0.798754	−	0.798754i	−0.982899	+	0.184145i	$0.941048\pi$
$594$	−27.8080	−	11.7753i	−1.14098	−	0.483145i
$595$		0			0
$596$	−0.677606	−	0.932645i	−0.0277558	−	0.0382026i
$597$	−2.32753	+	28.6158i	−0.0952595	+	1.17117i
$598$	−8.03050	−	4.09174i	−0.328391	−	0.167324i
$599$	8.83948			0.361171			0.180586	−	0.983559i	$-0.442201\pi$
$599$	8.83948			0.361171			0.180586	+	0.983559i	$0.442201\pi$
$600$		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
$603$	0.0305810	−	5.83864i	0.00124535	−	0.237768i
$604$	−1.77101	−	2.43759i	−0.0720615	−	0.0991842i
$605$		0			0
$606$	19.9958	−	32.4392i	0.812274	−	1.31775i
$607$	−11.7369	−	11.7369i	−0.476386	−	0.476386i	0.427588	−	0.903974i	$-0.359363\pi$
$607$	−11.7369	−	11.7369i	−0.476386	−	0.476386i	−0.903974	+	0.427588i	$0.859363\pi$
$608$	−0.640439	−	4.04357i	−0.0259732	−	0.163988i
$609$	0.567324	+	0.137775i	0.0229891	+	0.00558292i
$610$		0			0
$611$	−22.3576	+	7.26441i	−0.904490	+	0.293887i
$612$	0.276735	+	0.385119i	0.0111863	+	0.0155675i
$613$	6.54078	+	12.8370i	0.264180	+	0.518482i	0.984549	−	0.175109i	$-0.0560277\pi$
$613$	6.54078	+	12.8370i	0.264180	+	0.518482i	−0.720369	+	0.693591i	$0.756028\pi$
$614$	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	$-0.461062\pi$
$617$	13.5321	−	2.14327i	0.544782	−	0.0862849i	0.422759	+	0.906242i	$0.361062\pi$
$618$	14.9875	−	17.4553i	0.602884	−	0.702155i
$619$	5.41760	−	7.45669i	0.217752	−	0.299710i	−0.686141	−	0.727468i	$-0.740697\pi$
$619$	5.41760	−	7.45669i	0.217752	−	0.299710i	0.903893	+	0.427759i	$0.140697\pi$
$620$		0			0
$621$	3.53950	−	4.07889i	0.142035	−	0.163680i
$622$	−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
$627$	−9.24125	+	22.1461i	−0.369060	+	0.884432i
$628$	−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	0.999938	−	0.0110933i	$-0.00353119\pi$
$631$	32.6151	+	23.6962i	1.29839	+	0.943333i	0.298448	+	0.954426i	$0.403531\pi$
$632$	−1.66202	+	1.66202i	−0.0661115	+	0.0661115i
$633$	9.58872	+	40.4057i	0.381117	+	1.60598i
$634$	−4.14616	−	1.34717i	−0.164665	−	0.0535029i
$635$		0			0
$636$	0.397246	+	0.966186i	0.0157518	+	0.0383117i
$637$	5.55791	−	2.83190i	0.220213	−	0.112204i
$638$	−0.716643	+	0.365148i	−0.0283722	+	0.0144563i
$639$	4.78970	+	9.52330i	0.189478	+	0.376736i
$640$		0			0
$641$	−41.3915	−	13.4489i	−1.63487	−	0.531201i	−0.659484	−	0.751718i	$-0.729225\pi$
$641$	−41.3915	−	13.4489i	−1.63487	−	0.531201i	−0.975383	+	0.220518i	$0.929225\pi$
$642$	−36.4049	+	8.63927i	−1.43679	+	0.340965i
$643$	−19.6168	+	19.6168i	−0.773612	+	0.773612i	−0.978736	−	0.205124i	$-0.934240\pi$
$643$	−19.6168	+	19.6168i	−0.773612	+	0.773612i	0.205124	+	0.978736i	$0.434240\pi$
$644$	−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	−0.756350	−	0.654167i	$-0.773019\pi$
$647$	4.20028	−	26.5196i	0.165130	−	1.04259i	0.921481	−	0.388425i	$-0.126981\pi$
$648$	4.00040	−	23.6513i	0.157150	−	0.929111i
$649$			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	$-0.318956\pi$
$653$	20.1993	+	3.19926i	0.790460	+	0.125197i	0.251866	+	0.967762i	$0.418956\pi$
$654$	16.5703	+	19.5046i	0.647952	+	0.762689i
$655$		0			0
$656$	−16.6897	+	22.9714i	−0.651623	+	0.896883i
$657$	−28.9930	−	21.2975i	−1.13112	−	0.830896i
$658$	−14.3805	+	2.27765i	−0.560610	+	0.0887919i
$659$	2.65726	−	8.17820i	0.103512	−	0.318578i	−0.885866	−	0.463941i	$-0.846435\pi$
$659$	2.65726	−	8.17820i	0.103512	−	0.318578i	0.989378	+	0.145363i	$0.0464351\pi$
$660$		0			0
$661$	12.9264	+	39.7835i	0.502781	+	1.54740i	0.804470	+	0.593993i	$0.202449\pi$
$661$	12.9264	+	39.7835i	0.502781	+	1.54740i	−0.301689	+	0.953406i	$0.597551\pi$
$662$	2.72197	+	5.34217i	0.105792	+	0.207629i
$663$	−4.05346	−	6.65370i	−0.157423	−	0.258408i
$664$	−24.2126	+	7.86716i	−0.939632	+	0.305305i
$665$		0			0
$666$	−22.4794	−	3.68118i	−0.871060	−	0.142643i
$667$	−0.0225011	−	0.142067i	−0.000871248	−	0.00550084i
$668$	−2.53899	−	2.53899i	−0.0982366	−	0.0982366i
$669$	3.50067	+	2.15784i	0.135344	+	0.0834271i
$670$		0			0
$671$	9.23504	+	12.7109i	0.356515	+	0.490700i
$672$	−4.86238	−	0.395493i	−0.187570	−	0.0152565i
$673$	20.5969	+	10.4947i	0.793954	+	0.404540i	0.803418	−	0.595416i	$-0.203013\pi$
$673$	20.5969	+	10.4947i	0.793954	+	0.404540i	−0.00946407	+	0.999955i	$0.503013\pi$
$674$	−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	$-0.478289\pi$
$677$	−18.1854	−	9.26592i	−0.698921	−	0.356118i	−0.767076	+	0.641557i	$0.778289\pi$
$678$	−12.4276	−	1.01083i	−0.477280	−	0.0388206i
$679$	−23.2949	−	32.0627i	−0.893976	−	1.23045i
$680$		0			0
$681$	−17.9423	−	11.0598i	−0.687549	−	0.423811i
$682$	1.89325	+	1.89325i	0.0724964	+	0.0724964i
$683$	−0.339136	−	2.14122i	−0.0129767	−	0.0819315i	0.980350	−	0.197266i	$-0.0632061\pi$
$683$	−0.339136	−	2.14122i	−0.0129767	−	0.0819315i	−0.993327	+	0.115334i	$0.963206\pi$
$684$	2.15084	+	0.352216i	0.0822393	+	0.0134673i
$685$		0			0
$686$	27.7525	−	9.01733i	1.05959	−	0.344283i
$687$	−13.0700	−	21.4542i	−0.498651	−	0.818529i
$688$	−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	−0.843422	−	0.537251i	$-0.819463\pi$
$691$	4.06682	−	12.5164i	0.154709	−	0.476146i	0.998131	+	0.0611055i	$0.0194626\pi$
$692$	−3.39277	+	0.537362i	−0.128974	+	0.0204274i
$693$	23.0456	+	16.9287i	0.875429	+	0.643068i
$694$	−21.6736	+	29.8311i	−0.822717	+	1.13237i
$695$		0			0
$696$	−0.413645	−	0.486892i	−0.0156792	−	0.0184556i
$697$	−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	$0.864434\pi$
$702$	10.8629	−	43.7310i	0.409996	−	1.65052i
$703$	−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
$708$	0.957171	−	0.227147i	0.0359727	−	0.00853671i
$709$	−24.3739	−	7.91956i	−0.915381	−	0.297425i	−0.186810	−	0.982396i	$-0.559815\pi$
$709$	−24.3739	−	7.91956i	−0.915381	−	0.297425i	−0.728570	+	0.684971i	$0.759815\pi$
$710$		0			0
$711$	−1.18874	−	2.36356i	−0.0445813	−	0.0886405i
$712$	27.9936	−	14.2635i	1.04911	−	0.534546i
$713$	−0.426633	+	0.217380i	−0.0159775	+	0.00814096i
$714$	−1.83494	−	4.46296i	−0.0686709	−	0.167022i
$715$		0			0
$716$	−1.89075	−	0.614342i	−0.0706606	−	0.0229590i
$717$	3.37956	+	14.2411i	0.126212	+	0.531842i
$718$	0.196905	−	0.196905i	0.00734844	−	0.00734844i
$719$	−5.09685	−	3.70308i	−0.190081	−	0.138102i	0.488675	−	0.872466i	$-0.337480\pi$
$719$	−5.09685	−	3.70308i	−0.190081	−	0.138102i	−0.678756	+	0.734364i	$0.737480\pi$
$720$		0			0
$721$	−17.6247	+	12.8051i	−0.656376	+	0.476885i
$722$	−1.50244	+	9.48601i	−0.0559149	+	0.353033i
$723$	−1.04359	+	2.50090i	−0.0388115	+	0.0930096i
$724$			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	−0.984699	−	0.174266i	$-0.944245\pi$
$727$	−7.14311	+	14.0192i	−0.264923	+	0.519942i	0.719775	+	0.694207i	$0.244245\pi$
$728$	37.4399	+	5.92990i	1.38762	+	0.219777i
$729$	23.8616	+	12.6342i	0.883763	+	0.467934i
$730$		0			0
$731$	3.57583	−	4.92171i	0.132257	−	0.182036i
$732$	0.929588	−	1.08265i	0.0343586	−	0.0400160i
$733$	22.0161	−	3.48700i	0.813182	−	0.128795i	0.264026	−	0.964516i	$-0.414949\pi$
$733$	22.0161	−	3.48700i	0.813182	−	0.128795i	0.549155	+	0.835720i	$0.314949\pi$
$734$	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
$738$	−16.8979	−	23.5160i	−0.622021	−	0.865636i
$739$	34.2550	−	11.1301i	1.26009	−	0.409428i	0.398563	−	0.917141i	$-0.369509\pi$
$739$	34.2550	−	11.1301i	1.26009	−	0.409428i	0.861526	+	0.507713i	$0.169509\pi$
$740$		0			0
$741$	−34.7952	−	8.45003i	−1.27823	−	0.310420i
$742$	−1.66285	−	10.4988i	−0.0610452	−	0.385424i
$743$	21.4863	+	21.4863i	0.788255	+	0.788255i	0.981208	−	0.192953i	$-0.0618065\pi$
$743$	21.4863	+	21.4863i	0.788255	+	0.788255i	−0.192953	+	0.981208i	$0.561806\pi$
$744$	−1.11598	+	1.81045i	−0.0409137	+	0.0663743i
$745$		0			0
$746$	−4.20934	−	5.79366i	−0.154115	−	0.212121i
$747$	0.150090	−	28.6559i	0.00549152	−	1.04846i
$748$	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
$753$	−1.18100	+	14.5198i	−0.0430380	+	0.529130i
$754$	−0.705420	−	0.970928i	−0.0256899	−	0.0353591i
$755$		0			0
$756$	1.01269	−	2.39153i	0.0368311	−	0.0869791i
$757$	33.8318	+	33.8318i	1.22964	+	1.22964i	0.964100	+	0.265539i	$0.0855498\pi$
$757$	33.8318	+	33.8318i	1.22964	+	1.22964i	0.265539	+	0.964100i	$0.414450\pi$
$758$	−1.62031	−	10.2302i	−0.0588521	−	0.371578i
$759$	1.66259	−	6.84615i	0.0603481	−	0.248499i
$760$		0			0
$761$	1.37065	−	0.445350i	0.0496859	−	0.0161439i	−0.284069	−	0.958804i	$-0.591684\pi$
$761$	1.37065	−	0.445350i	0.0496859	−	0.0161439i	0.333755	+	0.942660i	$0.391684\pi$
$762$	−25.0712	+	15.2735i	−0.908234	+	0.553300i
$763$	−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
$768$	6.40647	+	5.50072i	0.231173	+	0.198490i
$769$	13.9798	−	19.2415i	0.504124	−	0.693867i	−0.478791	−	0.877929i	$-0.658925\pi$
$769$	13.9798	−	19.2415i	0.504124	−	0.693867i	0.982915	+	0.184062i	$0.0589248\pi$
$770$		0			0
$771$	−19.8653	+	16.8768i	−0.715430	+	0.607802i
$772$	−2.53041	−	0.400778i	−0.0910716	−	0.0144243i
$773$	−1.97202	+	3.87030i	−0.0709285	+	0.139205i	−0.923748	−	0.383001i	$-0.874891\pi$
$773$	−1.97202	+	3.87030i	−0.0709285	+	0.139205i	0.852820	+	0.522206i	$0.174891\pi$
$774$	34.7793	−	5.32192i	1.25012	−	0.191293i
$775$		0			0
$776$			43.3696i			1.55688i
$777$	19.9059	+	8.30643i	0.714120	+	0.297991i
$778$	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
$783$	0.666523	−	0.269968i	0.0238196	−	0.00964785i
$784$	−4.43781	−	1.44193i	−0.158493	−	0.0514975i
$785$		0			0
$786$	10.5395	−	4.33332i	0.375933	−	0.154564i
$787$	−32.5272	+	16.5734i	−1.15947	+	0.590779i	−0.924484	−	0.381220i	$-0.875504\pi$
$787$	−32.5272	+	16.5734i	−1.15947	+	0.590779i	−0.234985	+	0.971999i	$0.575504\pi$
$788$	1.39913	−	0.712893i	0.0498420	−	0.0253958i
$789$	3.00196	−	1.23425i	0.106873	−	0.0439406i
$790$		0			0
$791$	11.2288	+	3.64846i	0.399250	+	0.129724i
$792$	−9.51380	−	29.8108i	−0.338058	−	1.05928i
$793$	−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	−0.828417	−	0.560112i	$-0.810758\pi$
$797$	3.74172	−	23.6243i	0.132539	−	0.836816i	0.960955	−	0.276703i	$-0.0892420\pi$
$798$	−20.4664	−	8.54031i	−0.724502	−	0.302324i
$799$			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
$804$	−0.527212	+	0.447899i	−0.0185933	+	0.0157962i
$805$		0			0
$806$	−2.34828	+	3.23213i	−0.0827146	+	0.113847i
$807$	−30.8653	−	26.5015i	−1.08651	−	0.932898i
$808$	39.0009	−	6.17713i	1.37205	−	0.217311i
$809$	−1.75262	+	5.39400i	−0.0616187	+	0.189643i	−0.977127	−	0.212656i	$-0.931789\pi$
$809$	−1.75262	+	5.39400i	−0.0616187	+	0.189643i	0.915508	+	0.402299i	$0.131789\pi$
$810$		0			0
$811$	5.70569	+	17.5603i	0.200354	+	0.616625i	0.999872	+	0.0159840i	$0.00508808\pi$
$811$	5.70569	+	17.5603i	0.200354	+	0.616625i	−0.799518	+	0.600641i	$0.794912\pi$
$812$	−0.0314032	−	0.0616323i	−0.00110204	−	0.00216287i
$813$	−1.11479	+	0.679137i	−0.0390975	+	0.0238184i
$814$	−28.2614	+	9.18267i	−0.990560	+	0.321853i
$815$		0			0
$816$	−1.37540	+	5.66357i	−0.0481486	+	0.198265i
$817$	−4.37372	−	27.6146i	−0.153017	−	0.966112i
$818$	17.3064	+	17.3064i	0.605104	+	0.605104i
$819$	−19.5696	+	37.9152i	−0.683815	+	1.32486i
$820$		0			0
$821$	−15.0984	−	20.7812i	−0.526938	−	0.725268i	0.459722	−	0.888063i	$-0.347949\pi$
$821$	−15.0984	−	20.7812i	−0.526938	−	0.725268i	−0.986660	+	0.162795i	$0.947949\pi$
$822$	−1.72886	+	21.2555i	−0.0603010	+	0.741370i
$823$	−1.75544	−	0.894443i	−0.0611909	−	0.0311783i	0.423127	−	0.906070i	$-0.360932\pi$
$823$	−1.75544	−	0.894443i	−0.0611909	−	0.0311783i	−0.484318	+	0.874892i	$0.660932\pi$
$824$	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	$-0.614459\pi$
$827$	−37.8448	−	19.2829i	−1.31599	−	0.670532i	−0.964108	+	0.265511i	$0.914459\pi$
$828$	−0.639855	−	0.00335136i	−0.0222365	−	0.000116468i
$829$	−18.3344	−	25.2352i	−0.636781	−	0.876453i	0.361658	−	0.932311i	$-0.382211\pi$
$829$	−18.3344	−	25.2352i	−0.636781	−	0.876453i	−0.998439	+	0.0558574i	$0.982211\pi$
$830$		0			0
$831$	−8.33993	+	13.5299i	−0.289309	+	0.469346i
$832$	−28.9843	−	28.9843i	−1.00485	−	1.00485i
$833$	−0.128718	−	0.812691i	−0.00445980	−	0.0281581i
$834$	−54.7337	−	13.2921i	−1.89527	−	0.460268i
$835$		0			0
$836$	2.70405	−	0.878600i	0.0935216	−	0.0303870i
$837$	−1.54036	−	1.83248i	−0.0532425	−	0.0633399i
$838$	0.739427	+	1.45121i	0.0255431	+	0.0501311i
$839$	−3.12345	−	9.61299i	−0.107833	−	0.331877i	0.882552	−	0.470216i	$-0.155824\pi$
$839$	−3.12345	−	9.61299i	−0.107833	−	0.331877i	−0.990385	+	0.138338i	$0.955824\pi$
$840$		0			0
$841$	−8.95557	+	27.5624i	−0.308813	+	0.950428i
$842$	42.6492	−	6.75497i	1.46979	−	0.232792i
$843$	−28.3144	+	32.9766i	−0.975200	+	1.13578i
$844$	2.89209	−	3.98062i	0.0995499	−	0.137019i
$845$		0			0
$846$	−12.7476	+	12.6148i	−0.438272	+	0.433705i
$847$	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
$852$	0.486389	−	1.16560i	0.0166634	−	0.0399329i
$853$	2.37400	−	14.9888i	0.0812842	−	0.513208i	−0.913131	−	0.407667i	$-0.866342\pi$
$853$	2.37400	−	14.9888i	0.0812842	−	0.513208i	0.994415	−	0.105541i	$-0.0336575\pi$
$854$	−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	$-0.529651\pi$
$857$	26.4246	−	26.4246i	0.902648	−	0.902648i	0.995665	+	0.0930163i	$0.0296509\pi$
$858$	−13.5727	−	57.1939i	−0.463365	−	1.95257i
$859$	−42.0699	−	13.6693i	−1.43541	−	0.466392i	−0.514944	−	0.857224i	$-0.672187\pi$
$859$	−42.0699	−	13.6693i	−1.43541	−	0.466392i	−0.920462	+	0.390832i	$0.872187\pi$
$860$		0			0
$861$	10.4269	+	25.3603i	0.355346	+	0.864277i
$862$	−35.3346	+	18.0039i	−1.20350	+	0.613215i
$863$	48.4015	−	24.6618i	1.64760	−	0.839496i	0.650832	−	0.759222i	$-0.274420\pi$
$863$	48.4015	−	24.6618i	1.64760	−	0.839496i	0.996773	−	0.0802746i	$-0.0255797\pi$
$864$	−5.14810	+	3.09939i	−0.175142	+	0.105443i
$865$		0			0
$866$	−37.7888	−	12.2783i	−1.28412	−	0.417235i
$867$	27.6492	−	6.56146i	0.939018	−	0.222839i
$868$	−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
$873$	−46.3479	−	15.3282i	−1.56864	−	0.518781i
$874$			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	0.139298	+	0.990250i	$0.455515\pi$
$877$	−22.0243	+	43.2252i	−0.743709	+	1.45961i	−0.883007	+	0.469360i	$0.844485\pi$
$878$	−29.7538	−	4.71254i	−1.00414	−	0.159041i
$879$	27.7473	+	32.6607i	0.935894	+	1.10162i
$880$		0			0
$881$	31.2390	−	42.9968i	1.05247	−	1.44860i	0.165820	−	0.986156i	$-0.446973\pi$
$881$	31.2390	−	42.9968i	1.05247	−	1.44860i	0.886649	−	0.462443i	$-0.153027\pi$
$882$	2.81726	−	3.83522i	0.0948620	−	0.129139i
$883$	9.36055	−	1.48257i	0.315008	−	0.0498923i	0.00307116	−	0.999995i	$-0.499022\pi$
$883$	9.36055	−	1.48257i	0.315008	−	0.0498923i	0.311936	+	0.950103i	$0.399022\pi$
$884$	−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	1.00000		0.000610667i	$0.000194381\pi$
$887$	12.2915	+	24.1235i	0.412709	+	0.809986i	−0.587291	+	0.809376i	$0.699806\pi$
$888$	−12.2802	−	20.1578i	−0.412098	−	0.676452i
$889$	26.4380	−	8.59022i	0.886702	−	0.288107i
$890$		0			0
$891$	35.2205	+	0.368958i	1.17993	+	0.0123606i
$892$	−0.0762202	−	0.481236i	−0.00255204	−	0.0161130i
$893$	10.0772	+	10.0772i	0.337219	+	0.337219i
$894$	12.2998	+	7.58170i	0.411367	+	0.253570i
$895$		0			0
$896$	−18.2333	−	25.0960i	−0.609131	−	0.838397i
$897$	10.4777	+	0.852225i	0.349839	+	0.0284550i
$898$	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
$903$	−33.2064	−	2.70092i	−1.10504	−	0.0898811i
$904$	−7.59433	−	10.4527i	−0.252584	−	0.347652i
$905$		0			0
$906$	32.1472	+	19.8158i	1.06802	+	0.658335i
$907$	5.89173	+	5.89173i	0.195632	+	0.195632i	0.798124	−	0.602493i	$-0.205826\pi$
$907$	5.89173	+	5.89173i	0.195632	+	0.195632i	−0.602493	+	0.798124i	$0.705826\pi$
$908$	0.390657	+	2.46651i	0.0129644	+	0.0818541i
$909$	−7.18281	+	43.8623i	−0.238239	+	1.45482i
$910$		0			0
$911$	48.7073	−	15.8260i	1.61374	−	0.524337i	0.643290	−	0.765623i	$-0.277569\pi$
$911$	48.7073	−	15.8260i	1.61374	−	0.524337i	0.970454	+	0.241286i	$0.0775691\pi$
$912$	13.9353	+	22.8746i	0.461445	+	0.757455i
$913$	−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
$918$	−5.04339	−	3.14536i	−0.166457	−	0.103812i
$919$	−9.10877	+	12.5372i	−0.300471	+	0.413562i	−0.932380	−	0.361480i	$-0.882272\pi$
$919$	−9.10877	+	12.5372i	−0.300471	+	0.413562i	0.631909	+	0.775042i	$0.282272\pi$
$920$		0			0
$921$	−6.34630	−	7.47008i	−0.209118	−	0.246148i
$922$	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
$927$	−8.42581	+	25.4772i	−0.276740	+	0.836780i
$928$	−0.0250368	+	0.158076i	−0.000821874	+	0.00518911i
$929$	33.7506	−	24.5213i	1.10732	−	0.804517i	0.125083	−	0.992146i	$-0.460080\pi$
$929$	33.7506	−	24.5213i	1.10732	−	0.804517i	0.982240	+	0.187629i	$0.0600803\pi$
$930$		0			0
$931$	−3.05931	−	2.22272i	−0.100265	−	0.0728467i
$932$	−3.14437	+	3.14437i	−0.102997	+	0.102997i
$933$	58.0124	−	13.7670i	1.89924	−	0.450710i
$934$	41.7570	+	13.5677i	1.36633	+	0.443947i
$935$		0			0
$936$	41.7133	−	20.9795i	1.36344	−	0.685737i
$937$	−0.722614	+	0.368190i	−0.0236068	+	0.0120282i	−0.465754	−	0.884914i	$-0.654217\pi$
$937$	−0.722614	+	0.368190i	−0.0236068	+	0.0120282i	0.442147	+	0.896942i	$0.354217\pi$
$938$	6.27186	−	3.19567i	0.204784	−	0.104342i
$939$	12.8604	+	31.2793i	0.419685	+	1.02076i
$940$		0			0
$941$	−16.0740	−	5.22276i	−0.523998	−	0.170257i	0.0350611	−	0.999385i	$-0.488837\pi$
$941$	−16.0740	−	5.22276i	−0.523998	−	0.170257i	−0.559059	+	0.829128i	$0.688837\pi$
$942$	−6.21404	−	26.1852i	−0.202464	−	0.853161i
$943$	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	0.770289	+	0.637695i	$0.220112\pi$
$947$	−4.90398	+	30.9625i	−0.159358	+	1.00615i	−0.929647	+	0.368452i	$0.879888\pi$
$948$	−0.120716	+	0.289288i	−0.00392066	+	0.00939564i
$949$		−	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	$-0.585264\pi$
$953$	−25.1408	−	3.98191i	−0.814391	−	0.128987i	−0.549717	+	0.835351i	$0.685264\pi$
$954$	−9.20972	−	9.30671i	−0.298176	−	0.301316i
$955$		0			0
$956$	1.01932	−	1.40298i	0.0329672	−	0.0453755i
$957$	0.611124	−	0.711752i	0.0197548	−	0.0230077i
$958$	−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
$963$	35.4399	−	25.4661i	1.14204	−	0.820633i
$964$	0.305361	−	0.0992179i	0.00983502	−	0.00319559i
$965$		0			0
$966$	6.32687	+	1.53648i	0.203564	+	0.0494355i
$967$	−8.00363	−	50.5329i	−0.257379	−	1.62503i	−0.690249	−	0.723572i	$-0.742499\pi$
$967$	−8.00363	−	50.5329i	−0.257379	−	1.62503i	0.432869	−	0.901457i	$-0.357501\pi$
$968$	−8.13450	−	8.13450i	−0.261453	−	0.261453i
$969$	−2.47841	+	4.02072i	−0.0796180	+	0.129164i
$970$		0			0
$971$	−18.5870	−	25.5828i	−0.596485	−	0.820991i	0.398896	−	0.916996i	$-0.369393\pi$
$971$	−18.5870	−	25.5828i	−0.596485	−	0.820991i	−0.995381	+	0.0960053i	$0.969393\pi$
$972$	−0.706003	−	3.12014i	−0.0226450	−	0.100079i
$973$	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	$-0.0968045\pi$
$977$	39.7795	+	20.2687i	1.27266	+	0.648452i	0.318549	+	0.947906i	$0.396805\pi$
$978$	−1.78362	+	21.9286i	−0.0570338	+	0.701201i
$979$	27.1166	+	37.3229i	0.866652	+	1.19284i
$980$		0			0
$981$	−26.5260	−	13.6911i	−0.846909	−	0.437124i
$982$	35.2835	+	35.2835i	1.12594	+	1.12594i
$983$	−7.45579	−	47.0740i	−0.237803	−	1.50143i	−0.760740	−	0.649056i	$-0.775164\pi$
$983$	−7.45579	−	47.0740i	−0.237803	−	1.50143i	0.522938	−	0.852371i	$-0.324836\pi$
$984$	7.08124	−	29.1589i	0.225742	−	0.929550i
$985$		0			0
$986$	−0.150560	+	0.0489200i	−0.00479481	+	0.00155793i
$987$	14.5027	−	8.83512i	0.461627	−	0.281225i
$988$	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	−0.916754	−	0.399452i	$-0.869201\pi$
$991$	1.87960	−	5.78480i	0.0597073	−	0.183760i	0.976462	+	0.215691i	$0.0692005\pi$
$992$	0.526221	−	0.0833452i	0.0167075	−	0.00264621i
$993$	−5.30571	−	4.55559i	−0.168372	−	0.144567i
$994$	−7.55391	+	10.3971i	−0.239595	+	0.329775i
$995$		0			0
$996$	−2.58754	+	2.19827i	−0.0819893	+	0.0696550i
$997$	24.4690	+	3.87551i	0.774942	+	0.122739i	0.531365	−	0.847143i	$-0.321679\pi$
$997$	24.4690	+	3.87551i	0.774942	+	0.122739i	0.243577	+	0.969882i	$0.421679\pi$
$998$	−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.107.6		64
3.2	odd	2	inner	375.2.l.b.107.3		64
5.2	odd	4		75.2.l.a.8.3	✓	64
5.3	odd	4		375.2.l.c.143.6		64
5.4	even	2		375.2.l.a.107.3		64
15.2	even	4		75.2.l.a.8.6	yes	64
15.8	even	4		375.2.l.c.143.3		64
15.14	odd	2		375.2.l.a.107.6		64
25.3	odd	20	inner	375.2.l.b.368.3		64
25.4	even	10		75.2.l.a.47.6	yes	64
25.21	even	5		375.2.l.c.257.3		64
25.22	odd	20		375.2.l.a.368.6		64
75.29	odd	10		75.2.l.a.47.3	yes	64
75.47	even	20		375.2.l.a.368.3		64
75.53	even	20	inner	375.2.l.b.368.6		64
75.71	odd	10		375.2.l.c.257.6		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.l.a.8.3	✓	64	5.2	odd	4
75.2.l.a.8.6	yes	64	15.2	even	4
75.2.l.a.47.3	yes	64	75.29	odd	10
75.2.l.a.47.6	yes	64	25.4	even	10
375.2.l.a.107.3		64	5.4	even	2
375.2.l.a.107.6		64	15.14	odd	2
375.2.l.a.368.3		64	75.47	even	20
375.2.l.a.368.6		64	25.22	odd	20
375.2.l.b.107.3		64	3.2	odd	2	inner
375.2.l.b.107.6		64	1.1	even	1	trivial
375.2.l.b.368.3		64	25.3	odd	20	inner
375.2.l.b.368.6		64	75.53	even	20	inner
375.2.l.c.143.3		64	15.8	even	4
375.2.l.c.143.6		64	5.3	odd	4
375.2.l.c.257.3		64	25.21	even	5
375.2.l.c.257.6		64	75.71	odd	10

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} +(-1.72635 - 0.140417i) q^{3} +(0.120624 + 0.166024i) q^{4} +(-2.18954 - 1.34965i) q^{6} +(1.72218 + 1.72218i) q^{7} +(-0.416937 - 2.63243i) q^{8} +(2.96057 + 0.484816i) q^{9} +(3.72206 - 1.20937i) q^{11} +(-0.184926 - 0.303553i) 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} +(3.59040 + 2.63742i) q^{18} +(2.08083 - 2.86402i) q^{19} +(-2.73126 - 3.21491i) q^{21} +(5.74013 + 0.909148i) q^{22} +(-0.471845 + 0.926047i) q^{23} +(0.350141 + 4.60305i) q^{24} +8.67180i q^{26} +(-5.04290 - 1.25268i) 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} +(-6.59538 + 1.56516i) q^{33} +(1.08790 + 0.353481i) q^{34} +(0.276623 + 0.550006i) q^{36} +(-4.55581 + 2.32130i) q^{37} +(4.68409 - 2.38666i) q^{38} +(-3.84616 - 9.35468i) q^{39} +(-6.18190 - 2.00862i) q^{41} +(-1.44644 - 6.09513i) 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} +(-2.91374 + 6.98261i) q^{48} -1.06819i q^{49} +(-1.33035 + 0.101196i) q^{51} +(-0.544057 + 1.06777i) q^{52} +(-2.90283 - 0.459763i) q^{53} +(-5.82795 - 5.05726i) q^{54} +(3.81549 - 5.25157i) q^{56} +(-3.99440 + 4.65212i) 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} +(4.26369 + 5.93357i) q^{63} +(-6.67577 + 2.16909i) q^{64} +(-9.78182 - 2.37552i) q^{66} +(-0.304459 - 1.92228i) q^{67} +(0.111778 + 0.111778i) q^{68} +(0.944601 - 1.53243i) q^{69} +(2.08859 + 2.87469i) q^{71} +(0.0418786 - 7.99563i) q^{72} +(-10.6846 - 5.44405i) q^{73} -7.59295 q^{74} +0.726495 q^{76} +(8.49280 + 4.32730i) q^{77} +(1.21766 - 14.9706i) q^{78} +(-0.518361 - 0.713462i) q^{79} +(8.52991 + 2.87066i) q^{81} +(-6.82537 - 6.82537i) q^{82} +(-1.49428 - 9.43448i) q^{83} +(0.204298 - 0.841250i) q^{84} +(11.1540 - 3.62417i) q^{86} +(0.204711 - 0.124711i) 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} +(-0.605416 - 0.519822i) q^{93} +(-3.51381 + 4.83635i) q^{94} +(-1.52652 + 1.29687i) 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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