LMFDB - Embedded newform 798.2.bu.a.611.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(53,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 12, 11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.53"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bu (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [162,0,0,0,0,0,0,-81] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$162$
Relative dimension:	$27$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			611.24
Character	$\chi$	$=$	798.611
Dual form			798.2.bu.a.431.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.939693 + 0.342020i) q^{2} +(1.62120 + 0.609683i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.36601 - 1.62795i) q^{5} +(-1.73195 - 0.0184316i) q^{6} +(-0.0385504 + 2.64547i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.25657 + 1.97683i) q^{9} +(-0.726838 + 1.99697i) q^{10} +4.02535i q^{11} +(1.63381 - 0.575043i) q^{12} +(-2.04188 + 5.61002i) q^{13} +(-0.868579 - 2.49911i) q^{14} +(3.20710 - 1.80639i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-6.67261 - 1.17656i) q^{17} +(-2.79660 - 1.08582i) q^{18} +(-3.87478 + 1.99651i) q^{19} -2.12513i q^{20} +(-1.67540 + 4.26533i) q^{21} +(-1.37675 - 3.78259i) q^{22} +(1.99655 - 5.48548i) q^{23} +(-1.33860 + 1.09916i) q^{24} +(0.0840125 + 0.476459i) q^{25} -5.97006i q^{26} +(2.45311 + 4.58064i) q^{27} +(1.67094 + 2.05133i) q^{28} +(2.43331 - 2.04179i) q^{29} +(-2.39587 + 2.79435i) q^{30} +(2.24232 + 1.29460i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-2.45419 + 6.52589i) q^{33} +(6.67261 - 1.17656i) q^{34} +(4.25402 + 3.67650i) q^{35} +(2.99932 + 0.0638452i) q^{36} +(8.07321 + 4.66107i) q^{37} +(2.95826 - 3.20136i) q^{38} +(-6.73063 + 7.85006i) q^{39} +(0.726838 + 1.99697i) q^{40} +(2.13288 - 0.776304i) q^{41} +(0.115528 - 4.58112i) q^{42} +(2.12461 - 12.0493i) q^{43} +(2.58745 + 3.08360i) q^{44} +(6.30068 - 0.973208i) q^{45} +5.83752i q^{46} +(2.66102 - 0.469209i) q^{47} +(0.881939 - 1.49070i) q^{48} +(-6.99703 - 0.203968i) q^{49} +(-0.241904 - 0.418991i) q^{50} +(-10.1003 - 5.97562i) q^{51} +(2.04188 + 5.61002i) q^{52} +(0.142441 - 0.119522i) q^{53} +(-3.87184 - 3.46538i) q^{54} +(6.55305 + 5.49867i) q^{55} +(-2.27177 - 1.35612i) q^{56} +(-7.49903 + 0.874349i) q^{57} +(-1.58823 + 2.75090i) q^{58} +(1.15106 - 6.52801i) q^{59} +(1.29566 - 3.44526i) q^{60} +(-1.22738 - 0.446730i) q^{61} +(-2.54987 - 0.449611i) q^{62} +(-5.31665 + 5.89349i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(6.34359 + 10.9874i) q^{65} +(0.0741935 - 6.97172i) q^{66} +(4.04730 - 11.1199i) q^{67} +(-5.86780 + 3.38777i) q^{68} +(6.58121 - 7.67579i) q^{69} +(-5.25491 - 1.99981i) q^{70} +(0.639621 - 3.62747i) q^{71} +(-2.84028 + 0.965833i) q^{72} +(10.4745 + 8.78913i) q^{73} +(-9.18052 - 1.61877i) q^{74} +(-0.154288 + 0.823655i) q^{75} +(-1.68493 + 4.02008i) q^{76} +(-10.6489 - 0.155179i) q^{77} +(3.63984 - 9.67866i) q^{78} +(-9.16534 - 1.61610i) q^{79} +(-1.36601 - 1.62795i) q^{80} +(1.18425 + 8.92175i) q^{81} +(-1.73874 + 1.45898i) q^{82} +(5.32128 - 3.07224i) q^{83} +(1.45827 + 4.34436i) q^{84} +(-11.0302 + 9.25546i) q^{85} +(2.12461 + 12.0493i) q^{86} +(5.18973 - 1.82660i) q^{87} +(-3.48606 - 2.01268i) q^{88} +(1.04320 - 0.875346i) q^{89} +(-5.58785 + 3.06948i) q^{90} +(-14.7624 - 5.61800i) q^{91} +(-1.99655 - 5.48548i) q^{92} +(2.84595 + 3.46591i) q^{93} +(-2.34006 + 1.35103i) q^{94} +(-2.04278 + 9.03519i) q^{95} +(-0.318902 + 1.70244i) q^{96} +(-3.17345 + 3.78197i) q^{97} +(6.64482 - 2.20146i) q^{98} +(-7.95745 + 9.08350i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q - 81 q^{8} + 15 q^{13} + 6 q^{14} + 27 q^{15} - 6 q^{17} - 18 q^{18} + 9 q^{19} - 6 q^{22} - 6 q^{25} - 9 q^{27} + 9 q^{28} + 6 q^{29} - 24 q^{33} + 6 q^{34} + 24 q^{35} + 18 q^{37} - 9 q^{39} - 9 q^{43}+ \cdots - 57 q^{99}+O(q^{100}) $ 162 * q - 81 * q^8 + 15 * q^13 + 6 * q^14 + 27 * q^15 - 6 * q^17 - 18 * q^18 + 9 * q^19 - 6 * q^22 - 6 * q^25 - 9 * q^27 + 9 * q^28 + 6 * q^29 - 24 * q^33 + 6 * q^34 + 24 * q^35 + 18 * q^37 - 9 * q^39 - 9 * q^43 - 12 * q^44 - 63 * q^45 + 12 * q^47 - 48 * q^49 + 87 * q^50 - 24 * q^51 - 15 * q^52 - 18 * q^54 - 18 * q^57 - 48 * q^59 + 6 * q^60 + 45 * q^61 + 36 * q^62 - 15 * q^63 - 81 * q^64 + 36 * q^65 + 12 * q^66 + 9 * q^67 + 9 * q^69 - 24 * q^70 + 12 * q^71 + 102 * q^73 + 39 * q^74 - 6 * q^78 - 42 * q^79 + 84 * q^81 - 3 * q^84 - 6 * q^85 - 9 * q^86 + 60 * q^87 + 54 * q^89 + 36 * q^90 - 18 * q^91 - 21 * q^93 - 72 * q^94 - 12 * q^97 - 27 * q^98 - 57 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$3$	1.62120	+	0.609683i	0.936000	+	0.352000i
$3$	1.62120	+	0.609683i	0.936000	+	0.352000i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	1.36601	−	1.62795i	0.610898	−	0.728040i	−0.368579	−	0.929596i	$-0.620156\pi$
$5$	1.36601	−	1.62795i	0.610898	−	0.728040i	0.979477	+	0.201557i	$0.0646000\pi$
$6$	−1.73195	−	0.0184316i	−0.707067	−	0.00752465i
$7$	−0.0385504	+	2.64547i	−0.0145707	+	0.999894i
$7$	−0.0385504	+	2.64547i	−0.0145707	+	0.999894i
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	2.25657	+	1.97683i	0.752191	+	0.658945i
$10$	−0.726838	+	1.99697i	−0.229846	+	0.631498i
$11$			4.02535i			1.21369i	0.794821	+	0.606844i	$0.207565\pi$
$11$			4.02535i			1.21369i	−0.794821	+	0.606844i	$0.792435\pi$
$12$	1.63381	−	0.575043i	0.471640	−	0.166001i
$13$	−2.04188	+	5.61002i	−0.566316	+	1.55594i	0.243895	+	0.969802i	$0.421575\pi$
$13$	−2.04188	+	5.61002i	−0.566316	+	1.55594i	−0.810211	+	0.586138i	$0.800648\pi$
$14$	−0.868579	−	2.49911i	−0.232137	−	0.667916i
$15$	3.20710	−	1.80639i	0.828071	−	0.466409i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−6.67261	−	1.17656i	−1.61835	−	0.285358i	−0.710197	−	0.704003i	$-0.751394\pi$
$17$	−6.67261	−	1.17656i	−1.61835	−	0.285358i	−0.908150	+	0.418645i	$0.862505\pi$
$18$	−2.79660	−	1.08582i	−0.659166	−	0.255931i
$19$	−3.87478	+	1.99651i	−0.888936	+	0.458031i
$19$	−3.87478	+	1.99651i	−0.888936	+	0.458031i
$20$		−	2.12513i		−	0.475194i
$21$	−1.67540	+	4.26533i	−0.365601	+	0.930772i
$22$	−1.37675	−	3.78259i	−0.293524	−	0.806451i
$23$	1.99655	−	5.48548i	0.416309	−	1.14380i	−0.537467	−	0.843285i	$-0.680619\pi$
$23$	1.99655	−	5.48548i	0.416309	−	1.14380i	0.953777	−	0.300516i	$-0.0971590\pi$
$24$	−1.33860	+	1.09916i	−0.273241	+	0.224365i
$25$	0.0840125	+	0.476459i	0.0168025	+	0.0952917i
$26$		−	5.97006i		−	1.17082i
$27$	2.45311	+	4.58064i	0.472102	+	0.881544i
$28$	1.67094	+	2.05133i	0.315779	+	0.387664i
$29$	2.43331	−	2.04179i	0.451855	−	0.379151i	−0.388269	−	0.921546i	$-0.626927\pi$
$29$	2.43331	−	2.04179i	0.451855	−	0.379151i	0.840124	+	0.542395i	$0.182482\pi$
$30$	−2.39587	+	2.79435i	−0.437424	+	0.510176i
$31$	2.24232	+	1.29460i	0.402732	+	0.232518i	0.687662	−	0.726031i	$-0.258637\pi$
$31$	2.24232	+	1.29460i	0.402732	+	0.232518i	−0.284930	+	0.958548i	$0.591970\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	−2.45419	+	6.52589i	−0.427219	+	1.13601i
$34$	6.67261	−	1.17656i	1.14434	−	0.201779i
$35$	4.25402	+	3.67650i	0.719061	+	0.621441i
$36$	2.99932	+	0.0638452i	0.499887	+	0.0106409i
$37$	8.07321	+	4.66107i	1.32723	+	0.766275i	0.984870	−	0.173294i	$-0.0554412\pi$
$37$	8.07321	+	4.66107i	1.32723	+	0.766275i	0.342358	+	0.939570i	$0.388775\pi$
$38$	2.95826	−	3.20136i	0.479893	−	0.519329i
$39$	−6.73063	+	7.85006i	−1.07776	+	1.25702i
$40$	0.726838	+	1.99697i	0.114923	+	0.315749i
$41$	2.13288	−	0.776304i	0.333100	−	0.121238i	−0.170055	−	0.985435i	$-0.554395\pi$
$41$	2.13288	−	0.776304i	0.333100	−	0.121238i	0.503155	+	0.864196i	$0.332172\pi$
$42$	0.115528	−	4.58112i	0.0178263	−	0.706882i
$43$	2.12461	−	12.0493i	0.324001	−	1.83750i	−0.192606	−	0.981276i	$-0.561694\pi$
$43$	2.12461	−	12.0493i	0.324001	−	1.83750i	0.516607	−	0.856223i	$-0.327195\pi$
$44$	2.58745	+	3.08360i	0.390072	+	0.464870i
$45$	6.30068	−	0.973208i	0.939250	−	0.145077i
$46$			5.83752i			0.860696i
$47$	2.66102	−	0.469209i	0.388149	−	0.0684411i	0.0238316	−	0.999716i	$-0.492413\pi$
$47$	2.66102	−	0.469209i	0.388149	−	0.0684411i	0.364317	+	0.931275i	$0.381302\pi$
$48$	0.881939	−	1.49070i	0.127297	−	0.215164i
$49$	−6.99703	−	0.203968i	−0.999575	−	0.0291382i
$50$	−0.241904	−	0.418991i	−0.0342104	−	0.0592542i
$51$	−10.1003	−	5.97562i	−1.41433	−	0.836754i
$52$	2.04188	+	5.61002i	0.283158	+	0.777970i
$53$	0.142441	−	0.119522i	0.0195657	−	0.0164176i	−0.632952	−	0.774191i	$-0.718157\pi$
$53$	0.142441	−	0.119522i	0.0195657	−	0.0164176i	0.652518	+	0.757773i	$0.273713\pi$
$54$	−3.87184	−	3.46538i	−0.526891	−	0.471578i
$55$	6.55305	+	5.49867i	0.883614	+	0.741440i
$56$	−2.27177	−	1.35612i	−0.303578	−	0.181219i
$57$	−7.49903	+	0.874349i	−0.993271	+	0.115810i
$58$	−1.58823	+	2.75090i	−0.208545	+	0.361211i
$59$	1.15106	−	6.52801i	0.149856	−	0.849874i	−0.813483	−	0.581588i	$-0.802432\pi$
$59$	1.15106	−	6.52801i	0.149856	−	0.849874i	0.963339	−	0.268286i	$-0.0864573\pi$
$60$	1.29566	−	3.44526i	0.167269	−	0.444782i
$61$	−1.22738	−	0.446730i	−0.157150	−	0.0571979i	0.262247	−	0.965001i	$-0.415536\pi$
$61$	−1.22738	−	0.446730i	−0.157150	−	0.0571979i	−0.419397	+	0.907803i	$0.637759\pi$
$62$	−2.54987	−	0.449611i	−0.323834	−	0.0571007i
$63$	−5.31665	+	5.89349i	−0.669835	+	0.742510i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	6.34359	+	10.9874i	0.786825	+	1.36282i
$66$	0.0741935	−	6.97172i	0.00913258	−	0.858159i
$67$	4.04730	−	11.1199i	0.494456	−	1.35851i	−0.402108	−	0.915592i	$-0.631722\pi$
$67$	4.04730	−	11.1199i	0.494456	−	1.35851i	0.896564	−	0.442915i	$-0.146056\pi$
$68$	−5.86780	+	3.38777i	−0.711575	+	0.410828i
$69$	6.58121	−	7.67579i	0.792284	−	0.924056i
$70$	−5.25491	−	1.99981i	−0.628082	−	0.239023i
$71$	0.639621	−	3.62747i	0.0759090	−	0.430501i	−0.923042	−	0.384700i	$-0.874305\pi$
$71$	0.639621	−	3.62747i	0.0759090	−	0.430501i	0.998951	−	0.0458012i	$-0.0145841\pi$
$72$	−2.84028	+	0.965833i	−0.334730	+	0.113825i
$73$	10.4745	+	8.78913i	1.22595	+	1.02869i	0.998492	+	0.0549013i	$0.0174844\pi$
$73$	10.4745	+	8.78913i	1.22595	+	1.02869i	0.227454	+	0.973789i	$0.426960\pi$
$74$	−9.18052	−	1.61877i	−1.06721	−	0.188179i
$75$	−0.154288	+	0.823655i	−0.0178156	+	0.0951075i
$76$	−1.68493	+	4.02008i	−0.193274	+	0.461135i
$77$	−10.6489	−	0.155179i	−1.21356	−	0.0176843i
$78$	3.63984	−	9.67866i	0.412131	−	1.09589i
$79$	−9.16534	−	1.61610i	−1.03118	−	0.181825i	−0.367643	−	0.929967i	$-0.619835\pi$
$79$	−9.16534	−	1.61610i	−1.03118	−	0.181825i	−0.663539	+	0.748142i	$0.730946\pi$
$80$	−1.36601	−	1.62795i	−0.152724	−	0.182010i
$81$	1.18425	+	8.92175i	0.131584	+	0.991305i
$82$	−1.73874	+	1.45898i	−0.192012	+	0.161117i
$83$	5.32128	−	3.07224i	0.584087	−	0.337223i	−0.178669	−	0.983909i	$-0.557179\pi$
$83$	5.32128	−	3.07224i	0.584087	−	0.337223i	0.762756	+	0.646687i	$0.223846\pi$
$84$	1.45827	+	4.34436i	0.159111	+	0.474008i
$85$	−11.0302	+	9.25546i	−1.19640	+	1.00390i
$86$	2.12461	+	12.0493i	0.229103	+	1.29931i
$87$	5.18973	−	1.82660i	0.556397	−	0.195832i
$88$	−3.48606	−	2.01268i	−0.371615	−	0.214552i
$89$	1.04320	−	0.875346i	0.110579	−	0.0927865i	−0.585822	−	0.810440i	$-0.699228\pi$
$89$	1.04320	−	0.875346i	0.110579	−	0.0927865i	0.696401	+	0.717653i	$0.254784\pi$
$90$	−5.58785	+	3.06948i	−0.589011	+	0.323551i
$91$	−14.7624	−	5.61800i	−1.54752	−	0.588927i
$92$	−1.99655	−	5.48548i	−0.208155	−	0.571900i
$93$	2.84595	+	3.46591i	0.295111	+	0.359399i
$94$	−2.34006	+	1.35103i	−0.241359	+	0.139348i
$95$	−2.04278	+	9.03519i	−0.209585	+	0.926991i
$96$	−0.318902	+	1.70244i	−0.0325478	+	0.173755i
$97$	−3.17345	+	3.78197i	−0.322215	+	0.384001i	−0.902700	−	0.430270i	$-0.858418\pi$
$97$	−3.17345	+	3.78197i	−0.322215	+	0.384001i	0.580485	+	0.814271i	$0.302863\pi$
$98$	6.64482	−	2.20146i	0.671228	−	0.222381i
$99$	−7.95745	+	9.08350i	−0.799754	+	0.912926i
$100$	0.370619	+	0.310986i	0.0370619	+	0.0310986i
$101$	1.35248	−	0.238478i	0.134576	−	0.0237295i	−0.105954	−	0.994371i	$-0.533790\pi$
$101$	1.35248	−	0.238478i	0.134576	−	0.0237295i	0.240531	+	0.970642i	$0.422679\pi$
$102$	11.5350	+	2.16074i	1.14213	+	0.213945i
$103$	1.71233	−	0.988614i	0.168721	−	0.0974110i	−0.413262	−	0.910612i	$-0.635611\pi$
$103$	1.71233	−	0.988614i	0.168721	−	0.0974110i	0.581983	+	0.813201i	$0.302277\pi$
$104$	−3.83748	−	4.57333i	−0.376296	−	0.448452i
$105$	4.65513	+	8.55394i	0.454294	+	0.834779i
$106$	−0.0929716	+	0.161032i	−0.00903020	+	0.0156408i
$107$	2.91395			0.281702			0.140851	−	0.990031i	$-0.455016\pi$
$107$	2.91395			0.281702			0.140851	+	0.990031i	$0.455016\pi$
$108$	4.82357	+	1.93214i	0.464148	+	0.185920i
$109$	−2.32444	−	6.38634i	−0.222641	−	0.611700i	0.777205	−	0.629247i	$-0.216637\pi$
$109$	−2.32444	−	6.38634i	−0.222641	−	0.611700i	−0.999846	+	0.0175468i	$0.994414\pi$
$110$	−8.03851	−	2.92578i	−0.766442	−	0.278962i
$111$	10.2465	+	12.4786i	0.972556	+	1.18442i
$112$	2.59859	+	0.497346i	0.245543	+	0.0469948i
$113$	15.8970			1.49547			0.747734	−	0.663998i	$-0.231142\pi$
$113$	15.8970			1.49547			0.747734	+	0.663998i	$0.231142\pi$
$114$	6.74774	−	3.38644i	0.631984	−	0.317169i
$115$	−6.20276	−	10.7435i	−0.578410	−	1.00184i
$116$	0.551587	−	3.12821i	0.0512136	−	0.290447i
$117$	−15.6977	+	8.62297i	−1.45126	+	0.797194i
$118$	1.15106	+	6.52801i	0.105964	+	0.600952i
$119$	3.36979	−	17.6068i	0.308908	−	1.61402i
$120$	−0.0391695	+	3.68063i	−0.00357567	+	0.335994i
$121$	−5.20344			−0.473040
$122$	1.30615			0.118253
$123$	3.93112	+	0.0418352i	0.354457	+	0.00377216i
$124$	2.54987	−	0.449611i	0.228985	−	0.0403763i
$125$	10.0925	+	5.82691i	0.902701	+	0.521175i
$126$	2.98032	−	7.35647i	0.265508	−	0.655367i
$127$	−5.40357	+	14.8462i	−0.479489	+	1.31739i	0.430439	+	0.902620i	$0.358359\pi$
$127$	−5.40357	+	14.8462i	−0.479489	+	1.31739i	−0.909928	+	0.414766i	$0.863863\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	10.7907	−	18.2390i	0.950065	−	1.60585i
$130$	−9.71894	−	8.15516i	−0.852407	−	0.715255i
$131$	−0.722404	−	1.98479i	−0.0631167	−	0.173412i	0.904126	−	0.427267i	$-0.140524\pi$
$131$	−0.722404	−	1.98479i	−0.0631167	−	0.173412i	−0.967242	+	0.253855i	$0.918301\pi$
$132$	2.31475	+	6.57665i	0.201473	+	0.572424i
$133$	−5.13233	−	10.3276i	−0.445029	−	0.895516i
$134$			11.8335i			1.02226i
$135$	10.8080	+	2.26365i	0.930205	+	0.194824i
$136$	4.35524	−	5.19037i	0.373459	−	0.445071i
$137$	0.143043	+	0.170472i	0.0122210	+	0.0145644i	0.772120	−	0.635476i	$-0.219196\pi$
$137$	0.143043	+	0.170472i	0.0122210	+	0.0145644i	−0.759899	+	0.650041i	$0.774752\pi$
$138$	−3.55904	+	9.46379i	−0.302965	+	0.805611i
$139$	11.4179	+	4.15576i	0.968450	+	0.352487i	0.777339	−	0.629081i	$-0.216569\pi$
$139$	11.4179	+	4.15576i	0.968450	+	0.352487i	0.191111	+	0.981568i	$0.438791\pi$
$140$	5.62198	+	0.0819247i	0.475144	+	0.00692390i
$141$	4.60010	+	0.861694i	0.387399	+	0.0725677i
$142$	0.639621	+	3.62747i	0.0536758	+	0.304410i
$143$	−22.5823	−	8.21928i	−1.88843	−	0.687331i
$144$	2.33865	−	1.87902i	0.194888	−	0.156585i
$145$		−	6.75041i		−	0.560591i
$146$	−12.8489	−	4.67660i	−1.06338	−	0.387038i
$147$	−11.2192	−	4.59664i	−0.925346	−	0.379124i
$148$	9.18052	−	1.61877i	0.754634	−	0.133062i
$149$	−13.7531	−	2.42505i	−1.12670	−	0.198668i	−0.420919	−	0.907098i	$-0.638292\pi$
$149$	−13.7531	−	2.42505i	−1.12670	−	0.198668i	−0.705780	+	0.708431i	$0.749403\pi$
$150$	−0.136724	−	0.826752i	−0.0111635	−	0.0675040i
$151$	12.8483	−	7.41799i	1.04558	−	0.603667i	0.124173	−	0.992261i	$-0.460372\pi$
$151$	12.8483	−	7.41799i	1.04558	−	0.603667i	0.921409	+	0.388593i	$0.127039\pi$
$152$	0.208365	−	4.35392i	0.0169006	−	0.353149i
$153$	−12.7314	−	15.8457i	−1.02927	−	1.28104i
$154$	10.0598	−	3.49633i	0.810643	−	0.281743i
$155$	5.17057	−	1.88194i	0.415311	−	0.151161i
$156$	−0.110037	+	10.3399i	−0.00881005	+	0.827851i
$157$	−7.42646	+	2.70301i	−0.592696	+	0.215724i	−0.620915	−	0.783878i	$-0.713239\pi$
$157$	−7.42646	+	2.70301i	−0.592696	+	0.215724i	0.0282188	+	0.999602i	$0.491016\pi$
$158$	9.16534	−	1.61610i	0.729155	−	0.128570i
$159$	0.303795	−	0.106925i	0.0240925	−	0.00847973i
$160$	1.84042	+	1.06257i	0.145498	+	0.0840033i
$161$	14.4347	+	5.49328i	1.13761	+	0.432931i
$162$	−4.16425	−	7.97866i	−0.327174	−	0.626863i
$163$	7.99260	+	13.8436i	0.626029	+	1.08431i	0.988341	+	0.152257i	$0.0486542\pi$
$163$	7.99260	+	13.8436i	0.626029	+	1.08431i	−0.362312	+	0.932057i	$0.618013\pi$
$164$	1.13488	−	1.96567i	0.0886193	−	0.153493i
$165$	7.27137	+	12.9097i	0.566075	+	1.00502i
$166$	−3.94960	+	4.70695i	−0.306548	+	0.365330i
$167$	3.15045	+	17.8671i	0.243789	+	1.38260i	0.823288	+	0.567624i	$0.192137\pi$
$167$	3.15045	+	17.8671i	0.243789	+	1.38260i	−0.579499	+	0.814973i	$0.696752\pi$
$168$	−2.85619	−	3.58360i	−0.220360	−	0.276481i
$169$	−17.3445	−	14.5537i	−1.33419	−	1.11952i
$170$	7.19947	−	12.4699i	0.552174	−	0.956394i
$171$	−12.6905	−	3.15454i	−0.970467	−	0.241233i
$172$	−6.11758	−	10.5960i	−0.466461	−	0.807935i
$173$	3.41664	−	1.24356i	0.259762	−	0.0945457i	−0.208856	−	0.977946i	$-0.566974\pi$
$173$	3.41664	−	1.24356i	0.259762	−	0.0945457i	0.468619	+	0.883401i	$0.344752\pi$
$174$	−4.25202	+	3.49144i	−0.322345	+	0.264685i
$175$	−1.26370	+	0.203885i	−0.0955264	+	0.0154123i
$176$	3.96420	+	0.698995i	0.298813	+	0.0526887i
$177$	5.84612	−	9.88142i	0.439421	−	0.742733i
$178$	−0.680898	+	1.17935i	−0.0510355	+	0.0883960i
$179$	7.38466			0.551955			0.275978	−	0.961164i	$-0.410998\pi$
$179$	7.38466			0.551955			0.275978	+	0.961164i	$0.410998\pi$
$180$	4.20104	−	4.79552i	0.313127	−	0.357437i
$181$	−0.453714	−	0.540715i	−0.0337243	−	0.0401910i	0.748919	−	0.662662i	$-0.230573\pi$
$181$	−0.453714	−	0.540715i	−0.0337243	−	0.0401910i	−0.782643	+	0.622471i	$0.786129\pi$
$182$	15.7936	+	0.230148i	1.17070	+	0.0170597i
$183$	−1.71746	−	1.47255i	−0.126959	−	0.108854i
$184$	3.75229	+	4.47180i	0.276622	+	0.329666i
$185$	18.6161	−	6.77569i	1.36868	−	0.498159i
$186$	−3.85973	−	2.28352i	−0.283009	−	0.167436i
$187$	4.73607	−	26.8596i	0.346336	−	1.96417i
$188$	1.73685	−	2.06990i	0.126673	−	0.150963i
$189$	−12.2125	+	6.31306i	−0.888329	+	0.459207i
$190$	−1.17063	−	9.18897i	−0.0849264	−	0.666638i
$191$	−21.1226	−	12.1951i	−1.52838	−	0.882408i	−0.999430	−	0.0337522i	$-0.989254\pi$
$191$	−21.1226	−	12.1951i	−1.52838	−	0.882408i	−0.528945	−	0.848656i	$-0.677412\pi$
$192$	−0.282599	−	1.70884i	−0.0203948	−	0.123325i
$193$	11.4209	−	13.6109i	0.822093	−	0.979732i	−0.177898	−	0.984049i	$-0.556930\pi$
$193$	11.4209	−	13.6109i	0.822093	−	0.979732i	0.999991	+	0.00431673i	$0.00137406\pi$
$194$	1.68856	−	4.63927i	0.121231	−	0.333080i
$195$	3.58538	+	21.6804i	0.256754	+	1.55256i
$196$	−5.49114	+	4.34135i	−0.392224	+	0.310097i
$197$	−9.04201	+	5.22041i	−0.644217	+	0.371939i	−0.786237	−	0.617925i	$-0.787973\pi$
$197$	−9.04201	+	5.22041i	−0.644217	+	0.371939i	0.142020	+	0.989864i	$0.454640\pi$
$198$	4.37082	−	11.2573i	0.310620	−	0.800022i
$199$	−3.15833	−	1.14954i	−0.223888	−	0.0814885i	0.227641	−	0.973745i	$-0.426899\pi$
$199$	−3.15833	−	1.14954i	−0.223888	−	0.0814885i	−0.451528	+	0.892257i	$0.649121\pi$
$200$	−0.454631	−	0.165472i	−0.0321473	−	0.0117007i
$201$	13.3411	−	15.5599i	0.941006	−	1.09751i
$202$	−1.18935	+	0.686671i	−0.0836823	+	0.0483140i
$203$	5.30770	+	6.51597i	0.372527	+	0.457331i
$204$	−11.5783	+	1.91476i	−0.810646	+	0.134060i
$205$	1.64975	−	4.53265i	0.115224	−	0.316574i
$206$	−1.27094	+	1.51464i	−0.0885504	+	0.105530i
$207$	15.3492	−	8.43153i	1.06685	−	0.586032i
$208$	5.17022	+	2.98503i	0.358490	+	0.206975i
$209$	−8.03665	−	15.5974i	−0.555906	−	1.07889i
$210$	−7.30001	−	6.44592i	−0.503748	−	0.444811i
$211$	14.2096	−	16.9344i	0.978233	−	1.16581i	−0.00791948	−	0.999969i	$-0.502521\pi$
$211$	14.2096	−	16.9344i	0.978233	−	1.16581i	0.986152	−	0.165844i	$-0.0530347\pi$
$212$	0.0322887	−	0.183118i	0.00221760	−	0.0125766i
$213$	3.24856	−	5.49088i	0.222588	−	0.376229i
$214$	−2.73822	+	0.996630i	−0.187181	+	0.0681283i
$215$	−16.7133	−	19.9182i	−1.13984	−	1.35841i
$216$	−5.19350	−	0.165859i	−0.353373	−	0.0112853i
$217$	−3.51128	+	5.88208i	−0.238361	+	0.399302i
$218$	4.36851	+	5.20619i	0.295873	+	0.352608i
$219$	11.6226	+	20.6350i	0.785385	+	1.39439i
$220$	8.55441			0.576738
$221$	20.2252	−	35.0311i	1.36050	−	2.35645i
$222$	−13.8965	−	8.22156i	−0.932673	−	0.551795i
$223$	9.56900	+	1.68727i	0.640787	+	0.112988i	0.484595	−	0.874739i	$-0.338967\pi$
$223$	9.56900	+	1.68727i	0.640787	+	0.112988i	0.156192	+	0.987727i	$0.450078\pi$
$224$	−2.61197	+	0.421416i	−0.174520	+	0.0281571i
$225$	−0.752299	+	1.24124i	−0.0501533	+	0.0827495i
$226$	−14.9383	+	5.43711i	−0.993683	+	0.361671i
$227$	6.90589	+	11.9613i	0.458360	+	0.793902i	0.998874	−	0.0474323i	$-0.0151038\pi$
$227$	6.90589	+	11.9613i	0.458360	+	0.793902i	−0.540515	+	0.841335i	$0.681770\pi$
$228$	−5.18257	+	5.49008i	−0.343224	+	0.363589i
$229$	3.25244	−	5.63339i	0.214927	−	0.372265i	−0.738323	−	0.674447i	$-0.764382\pi$
$229$	3.25244	−	5.63339i	0.214927	−	0.372265i	0.953250	+	0.302183i	$0.0977153\pi$
$230$	9.50317	+	7.97411i	0.626621	+	0.525797i
$231$	−17.1695	−	6.74405i	−1.12967	−	0.443726i
$232$	0.551587	+	3.12821i	0.0362135	+	0.205377i
$233$	−14.5017	+	17.2825i	−0.950040	+	1.13221i	0.0410689	+	0.999156i	$0.486924\pi$
$233$	−14.5017	+	17.2825i	−0.950040	+	1.13221i	−0.991108	+	0.133057i	$0.957521\pi$
$234$	11.8018	−	13.4719i	0.771509	−	0.880684i
$235$	2.87113	−	4.97293i	0.187292	−	0.324398i
$236$	−3.31436	−	5.74063i	−0.215746	−	0.373683i
$237$	−13.8735	−	8.20796i	−0.901183	−	0.533164i
$238$	2.85533	+	17.6976i	0.185083	+	1.14716i
$239$	−21.2196	−	12.2511i	−1.37258	−	0.792459i	−0.381327	−	0.924440i	$-0.624533\pi$
$239$	−21.2196	−	12.2511i	−1.37258	−	0.792459i	−0.991252	+	0.131981i	$0.957866\pi$
$240$	−1.22204	−	3.47206i	−0.0788825	−	0.224120i
$241$	1.01107	−	0.178279i	0.0651289	−	0.0114840i	−0.140989	−	0.990011i	$-0.545028\pi$
$241$	1.01107	−	0.178279i	0.0651289	−	0.0114840i	0.206118	+	0.978527i	$0.433917\pi$
$242$	4.88964	−	1.77968i	0.314318	−	0.114402i
$243$	−3.51953	+	15.1859i	−0.225778	+	0.974179i
$244$	−1.22738	+	0.446730i	−0.0785749	+	0.0285989i
$245$	−9.89005	+	11.1122i	−0.631852	+	0.709930i
$246$	−3.70835	+	1.30521i	−0.236436	+	0.0832172i
$247$	−3.28861	−	25.8143i	−0.209249	−	1.64252i
$248$	−2.24232	+	1.29460i	−0.142387	+	0.0822074i
$249$	10.5000	−	1.73643i	0.665407	−	0.110041i
$250$	−11.4768	−	2.02367i	−0.725855	−	0.127988i
$251$	−28.5760	+	5.03872i	−1.80370	+	0.318041i	−0.971609	−	0.236593i	$-0.923969\pi$
$251$	−28.5760	+	5.03872i	−1.80370	+	0.318041i	−0.832094	+	0.554635i	$0.812858\pi$
$252$	−0.284525	+	7.93215i	−0.0179234	+	0.499679i
$253$	22.0810	+	8.03681i	1.38822	+	0.505270i
$254$		−	15.7990i		−	0.991316i
$255$	−23.5251	+	8.28001i	−1.47320	+	0.518514i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	1.41076	+	8.00080i	0.0880006	+	0.499076i	0.996669	+	0.0815570i	$0.0259893\pi$
$257$	1.41076	+	8.00080i	0.0880006	+	0.499076i	−0.908668	+	0.417519i	$0.862900\pi$
$258$	−3.90182	+	20.8296i	−0.242917	+	1.29680i
$259$	−12.6419	+	21.1778i	−0.785533	+	1.31592i
$260$	11.9220	+	4.33927i	0.739374	+	0.269110i
$261$	9.52723	+	0.202802i	0.589721	+	0.0125531i
$262$	1.35768	+	1.61801i	0.0838775	+	0.0999613i
$263$	−1.07012	+	1.27532i	−0.0659863	+	0.0786394i	−0.798028	−	0.602621i	$-0.794123\pi$
$263$	−1.07012	+	1.27532i	−0.0659863	+	0.0786394i	0.732042	+	0.681260i	$0.238568\pi$
$264$	−4.42450	−	5.38834i	−0.272309	−	0.331629i
$265$		−	0.395154i		−	0.0242741i
$266$	8.35506	+	7.94940i	0.512281	+	0.487409i
$267$	2.22491	−	0.783091i	0.136162	−	0.0479244i
$268$	−4.04730	−	11.1199i	−0.247228	−	0.679254i
$269$	11.5353	+	9.67925i	0.703318	+	0.590154i	0.922716	−	0.385482i	$-0.125965\pi$
$269$	11.5353	+	9.67925i	0.703318	+	0.590154i	−0.219397	+	0.975636i	$0.570409\pi$
$270$	−10.9304	+	1.56942i	−0.665204	+	0.0955118i
$271$	2.55521	+	2.14408i	0.155218	+	0.130244i	0.717089	−	0.696981i	$-0.245474\pi$
$271$	2.55521	+	2.14408i	0.155218	+	0.130244i	−0.561871	+	0.827225i	$0.689918\pi$
$272$	−2.31737	+	6.36693i	−0.140511	+	0.386052i
$273$	−20.5076	−	18.1083i	−1.24118	−	1.09596i
$274$	−0.192722	−	0.111268i	−0.0116427	−	0.00672194i
$275$	−1.91791	+	0.338180i	−0.115654	+	0.0203930i
$276$	0.107595	−	10.1103i	0.00647643	−	0.608569i
$277$	−9.44946			−0.567763			−0.283881	−	0.958859i	$-0.591622\pi$
$277$	−9.44946			−0.567763			−0.283881	+	0.958859i	$0.591622\pi$
$278$	−12.1506			−0.728747
$279$	2.50074	+	7.35406i	0.149716	+	0.440276i
$280$	−5.31095	+	1.84585i	−0.317390	+	0.110310i
$281$	−4.18902	−	23.7571i	−0.249896	−	1.41723i	−0.808842	−	0.588027i	$-0.799905\pi$
$281$	−4.18902	−	23.7571i	−0.249896	−	1.41723i	0.558946	−	0.829204i	$-0.311206\pi$
$282$	−4.61740	+	0.763601i	−0.274962	+	0.0454718i
$283$	5.30044	−	30.0603i	0.315078	−	1.78690i	−0.256701	−	0.966491i	$-0.582636\pi$
$283$	5.30044	−	30.0603i	0.315078	−	1.78690i	0.571779	−	0.820407i	$-0.306253\pi$
$284$	−1.84171	−	3.18994i	−0.109286	−	0.189288i
$285$	−8.82036	+	13.4024i	−0.522473	+	0.793889i
$286$	24.0316			1.42102
$287$	1.97147	+	5.67239i	0.116372	+	0.334831i
$288$	−1.55495	+	2.56557i	−0.0916264	+	0.151177i
$289$	27.1647	+	9.88714i	1.59792	+	0.581597i
$290$	2.30878	+	6.34331i	0.135576	+	0.372492i
$291$	−7.45059	+	4.19653i	−0.436761	+	0.246005i
$292$	13.6735			0.800179
$293$	−1.11981	+	1.93957i	−0.0654199	+	0.113311i	−0.896880	−	0.442274i	$-0.854172\pi$
$293$	−1.11981	+	1.93957i	−0.0654199	+	0.113311i	0.831460	+	0.555584i	$0.187505\pi$
$294$	12.1148	+	0.482229i	0.706547	+	0.0281241i
$295$	−9.05488	−	10.7912i	−0.527196	−	0.628287i
$296$	−8.07321	+	4.66107i	−0.469246	+	0.270919i
$297$	−18.4387	+	9.87464i	−1.06992	+	0.572985i
$298$	13.7531	−	2.42505i	0.796697	−	0.140479i
$299$	26.6969	+	22.4014i	1.54392	+	1.29550i
$300$	0.411244	+	0.730131i	0.0237432	+	0.0421541i
$301$	31.7941	+	6.08511i	1.83258	+	0.350740i
$302$	−9.53638	+	11.3650i	−0.548757	+	0.653983i
$303$	2.33803	+	0.437961i	0.134316	+	0.0251602i
$304$	1.29333	+	4.16261i	0.0741775	+	0.238742i
$305$	−2.40386	+	1.38787i	−0.137645	+	0.0794693i
$306$	17.3831	+	10.5357i	0.993727	+	0.602283i
$307$	−4.24523	−	11.6637i	−0.242288	−	0.665681i	−0.999916	−	0.0129941i	$-0.995864\pi$
$307$	−4.24523	−	11.6637i	−0.242288	−	0.665681i	0.757627	−	0.652687i	$-0.226358\pi$
$308$	−8.25731	+	6.72614i	−0.470504	+	0.383257i
$309$	3.37877	−	0.558762i	0.192211	−	0.0317869i
$310$	−4.21509	+	3.53688i	−0.239401	+	0.200881i
$311$	−5.82371	−	3.36232i	−0.330232	−	0.190660i	0.325712	−	0.945469i	$-0.394396\pi$
$311$	−5.82371	−	3.36232i	−0.330232	−	0.190660i	−0.655944	+	0.754809i	$0.727729\pi$
$312$	−3.43304	−	9.75393i	−0.194358	−	0.552207i
$313$	1.65447	+	9.38295i	0.0935160	+	0.530355i	0.995192	+	0.0979432i	$0.0312264\pi$
$313$	1.65447	+	9.38295i	0.0935160	+	0.530355i	−0.901676	+	0.432412i	$0.857663\pi$
$314$	6.05410	−	5.08000i	0.341653	−	0.286681i
$315$	2.33170	+	16.7058i	0.131376	+	0.941264i
$316$	−8.05986	+	4.65336i	−0.453403	+	0.261772i
$317$	−6.64229	+	5.57354i	−0.373068	+	0.313041i	−0.809974	−	0.586466i	$-0.800519\pi$
$317$	−6.64229	+	5.57354i	−0.373068	+	0.313041i	0.436906	+	0.899507i	$0.356074\pi$
$318$	−0.248904	+	0.204381i	−0.0139578	+	0.0114611i
$319$	8.21893	+	9.79494i	0.460172	+	0.548411i
$320$	−2.09285	−	0.369026i	−0.116994	−	0.0206292i
$321$	4.72410	+	1.77659i	0.263673	+	0.0991594i
$322$	−15.4430	−	0.225039i	−0.860604	−	0.0125409i
$323$	28.2040	−	8.76301i	1.56931	−	0.487587i
$324$	6.64198	+	6.07323i	0.368999	+	0.337402i
$325$	−2.84449	−	0.501560i	−0.157784	−	0.0278215i
$326$	−12.2454	−	10.2751i	−0.678209	−	0.569085i
$327$	0.125265	−	11.7707i	0.00692714	−	0.650921i
$328$	−0.394140	+	2.23528i	−0.0217627	+	0.123423i
$329$	1.13870	+	7.05773i	0.0627783	+	0.389105i
$330$	−11.2482	−	9.64421i	−0.619195	−	0.530896i
$331$	−20.1545	+	11.6362i	−1.10779	+	0.639582i	−0.938256	−	0.345942i	$-0.887559\pi$
$331$	−20.1545	+	11.6362i	−1.10779	+	0.639582i	−0.169533	+	0.985524i	$0.554226\pi$
$332$	2.10154	−	5.77393i	0.115337	−	0.316886i
$333$	9.00363	+	26.4775i	0.493396	+	1.45096i
$334$	−9.07136	−	15.7121i	−0.496363	−	0.859725i
$335$	−12.5739	−	21.7786i	−0.686985	−	1.18989i
$336$	3.90960	+	2.39061i	0.213286	+	0.130418i
$337$	7.55254	+	1.33172i	0.411413	+	0.0725432i	0.375524	−	0.926813i	$-0.377463\pi$
$337$	7.55254	+	1.33172i	0.411413	+	0.0725432i	0.0358888	+	0.999356i	$0.488574\pi$
$338$	21.2762	+	7.74389i	1.15727	+	0.421212i
$339$	25.7723	+	9.69215i	1.39976	+	0.526406i
$340$	−2.50035	+	14.1802i	−0.135601	+	0.769029i
$341$	−5.21123	+	9.02612i	−0.282204	+	0.488792i
$342$	13.0041	−	1.37611i	0.703181	−	0.0744117i
$343$	0.809329	−	18.5026i	0.0436996	−	0.999045i
$344$	9.37268	+	7.86461i	0.505341	+	0.424031i
$345$	−3.50578	−	21.1990i	−0.188745	−	1.14132i
$346$	−2.78527	+	2.33712i	−0.149737	+	0.125644i
$347$	−4.45095	−	12.2289i	−0.238939	−	0.656480i	−0.999970	−	0.00776437i	$-0.997529\pi$
$347$	−4.45095	−	12.2289i	−0.238939	−	0.656480i	0.761031	−	0.648716i	$-0.224694\pi$
$348$	2.80145	−	4.73515i	0.150173	−	0.253831i
$349$	0.251987	+	0.436453i	0.0134885	+	0.0233628i	0.872691	−	0.488273i	$-0.162373\pi$
$349$	0.251987	+	0.436453i	0.0134885	+	0.0233628i	−0.859202	+	0.511636i	$0.829040\pi$
$350$	1.11775	−	0.623799i	0.0597464	−	0.0333434i
$351$	−30.7064	+	4.40891i	−1.63899	+	0.235330i
$352$	−3.96420	+	0.698995i	−0.211292	+	0.0372565i
$353$		−	0.969519i		−	0.0516023i	−0.999667	−	0.0258012i	$-0.991786\pi$
$353$		−	0.969519i		−	0.0516023i	0.999667	−	0.0258012i	$-0.00821367\pi$
$354$	−2.11391	+	11.2850i	−0.112353	+	0.599790i
$355$	−5.03160	−	5.99643i	−0.267049	−	0.318257i
$356$	0.236473	−	1.34111i	0.0125331	−	0.0710786i
$357$	16.1977	−	26.4897i	0.857273	−	1.40198i
$358$	−6.93931	+	2.52570i	−0.366754	+	0.133487i
$359$	−3.80720	−	10.4602i	−0.200936	−	0.552068i	0.797767	−	0.602965i	$-0.206014\pi$
$359$	−3.80720	−	10.4602i	−0.200936	−	0.552068i	−0.998704	+	0.0508969i	$0.983792\pi$
$360$	−2.30752	+	5.94315i	−0.121617	+	0.313232i
$361$	11.0279	−	15.4721i	0.580416	−	0.814320i
$362$	0.611287	+	0.352927i	0.0321285	+	0.0185494i
$363$	−8.43582	−	3.17245i	−0.442766	−	0.166510i
$364$	−14.9199	+	5.18547i	−0.782013	+	0.271792i
$365$	28.6165	−	5.04586i	1.49785	−	0.264112i
$366$	2.11753	+	0.796337i	0.110685	+	0.0416252i
$367$	3.22904	+	18.3128i	0.168555	+	0.955921i	0.945323	+	0.326135i	$0.105746\pi$
$367$	3.22904	+	18.3128i	0.168555	+	0.955921i	−0.776769	+	0.629786i	$0.783143\pi$
$368$	−5.05544	−	2.91876i	−0.263533	−	0.152151i
$369$	6.34762	+	2.46456i	0.330444	+	0.128300i
$370$	−15.1759	+	12.7341i	−0.788960	+	0.662016i
$371$	0.310701	+	0.381430i	0.0161308	+	0.0198029i
$372$	4.40797	+	0.825703i	0.228543	+	0.0428107i
$373$			17.9729i			0.930602i	0.885152	+	0.465301i	$0.154054\pi$
$373$			17.9729i			0.930602i	−0.885152	+	0.465301i	$0.845946\pi$
$374$	4.73607	+	26.8596i	0.244897	+	1.38888i
$375$	12.8094	+	15.5998i	0.661474	+	0.805571i
$376$	−0.924161	+	2.53911i	−0.0476600	+	0.130945i
$377$	6.48596	+	17.8200i	0.334044	+	0.917778i
$378$	9.31681	−	10.1093i	0.479205	−	0.519964i
$379$		−	10.5738i		−	0.543138i	−0.962419	−	0.271569i	$-0.912457\pi$
$379$		−	10.5738i		−	0.543138i	0.962419	−	0.271569i	$-0.0875426\pi$
$380$	4.24285	+	8.23443i	0.217653	+	0.422417i
$381$	−17.8117	+	20.7742i	−0.912522	+	1.06429i
$382$	24.0197	+	4.23532i	1.22895	+	0.216698i
$383$	−2.89897	+	16.4409i	−0.148130	+	0.840089i	0.816670	+	0.577105i	$0.195818\pi$
$383$	−2.89897	+	16.4409i	−0.148130	+	0.840089i	−0.964800	+	0.262984i	$0.915293\pi$
$384$	0.850014	+	1.50913i	0.0433771	+	0.0770125i
$385$	−14.7992	+	17.1239i	−0.754236	+	0.872717i
$386$	−6.07692	+	16.6962i	−0.309307	+	0.849815i
$387$	28.6138	−	22.9901i	1.45452	−	1.16865i
$388$			4.93701i			0.250639i
$389$	−1.11745	+	3.07017i	−0.0566570	+	0.155664i	−0.964792	−	0.263013i	$-0.915284\pi$
$389$	−1.11745	+	3.07017i	−0.0566570	+	0.155664i	0.908135	+	0.418677i	$0.137506\pi$
$390$	−10.7843	−	19.1466i	−0.546083	−	0.969526i
$391$	−19.7762	+	34.2534i	−1.00013	+	1.73227i
$392$	3.67516	−	5.95762i	0.185623	−	0.300905i
$393$	0.0389305	−	3.65818i	0.00196379	−	0.184531i
$394$	6.71123	−	7.99813i	0.338107	−	0.402940i
$395$	−15.1509	+	12.7131i	−0.762322	+	0.639664i
$396$	−0.256999	+	12.0733i	−0.0129147	+	0.606707i
$397$	−30.6003	+	11.1376i	−1.53579	+	0.558981i	−0.965030	−	0.262138i	$-0.915572\pi$
$397$	−30.6003	+	11.1376i	−1.53579	+	0.558981i	−0.570757	+	0.821119i	$0.693350\pi$
$398$	3.36102			0.168473
$399$	−2.02398	−	19.8722i	−0.101325	−	0.994853i
$400$	0.483809			0.0241904
$401$	21.7640	−	7.92146i	1.08684	−	0.395579i	0.264393	−	0.964415i	$-0.414829\pi$
$401$	21.7640	−	7.92146i	1.08684	−	0.395579i	0.822451	+	0.568836i	$0.192606\pi$
$402$	−7.21469	+	19.1845i	−0.359836	+	0.956835i
$403$	−11.8413	+	9.93603i	−0.589857	+	0.494949i
$404$	0.882767	−	1.05204i	0.0439193	−	0.0523410i
$405$	16.1418	+	10.2593i	0.802094	+	0.509788i
$406$	−7.21619	−	4.30767i	−0.358134	−	0.213786i
$407$	−18.7624	+	32.4975i	−0.930020	+	1.61084i
$408$	10.2252	−	5.75931i	0.506222	−	0.285128i
$409$	−1.24765	+	3.42790i	−0.0616925	+	0.169499i	−0.966709	−	0.255877i	$-0.917636\pi$
$409$	−1.24765	+	3.42790i	−0.0616925	+	0.169499i	0.905017	+	0.425376i	$0.139858\pi$
$410$			4.82355i			0.238218i
$411$	0.127968	+	0.363580i	0.00631217	+	0.0179341i
$412$	0.676251	−	1.85799i	0.0333165	−	0.0915364i
$413$	17.2253	+	3.29676i	0.847601	+	0.162223i
$414$	−11.5398	+	13.1728i	−0.567151	+	0.647408i
$415$	2.26747	−	12.8595i	0.111306	−	0.631247i
$416$	−5.87936	−	1.03669i	−0.288259	−	0.0508279i
$417$	15.9769	+	13.6986i	0.782394	+	0.670823i
$418$	12.8866	+	11.9080i	0.630304	+	0.582441i
$419$			7.90283i			0.386078i	0.981191	+	0.193039i	$0.0618344\pi$
$419$			7.90283i			0.386078i	−0.981191	+	0.193039i	$0.938166\pi$
$420$	9.06440	+	3.56044i	0.442297	+	0.173732i
$421$	−0.813545	−	2.23520i	−0.0396498	−	0.108937i	0.918288	−	0.395914i	$-0.129572\pi$
$421$	−0.813545	−	2.23520i	−0.0396498	−	0.108937i	−0.957938	+	0.286977i	$0.907350\pi$
$422$	−7.56080	+	20.7731i	−0.368054	+	1.01122i
$423$	6.93233	+	4.20158i	0.337061	+	0.204288i
$424$	0.0322887	+	0.183118i	0.00156808	+	0.00889301i
$425$		−	3.27807i		−	0.159010i
$426$	−1.17465	+	6.27082i	−0.0569121	+	0.303822i
$427$	1.22913	−	3.22978i	0.0594816	−	0.156300i
$428$	2.23222	−	1.87305i	0.107898	−	0.0905374i
$429$	−31.5992	−	27.0931i	−1.52563	−	1.30807i
$430$	22.5178	+	13.0007i	1.08591	+	0.626948i
$431$	−3.34421	−	18.9660i	−0.161085	−	0.913558i	−0.953010	−	0.302940i	$-0.902032\pi$
$431$	−3.34421	−	18.9660i	−0.161085	−	0.913558i	0.791925	−	0.610619i	$-0.209079\pi$
$432$	4.93703	−	1.62043i	0.237533	−	0.0779628i
$433$	27.6771	−	4.88022i	1.33008	−	0.234528i	0.536964	−	0.843605i	$-0.319571\pi$
$433$	27.6771	−	4.88022i	1.33008	−	0.234528i	0.793111	+	0.609077i	$0.208460\pi$
$434$	1.28773	−	6.72828i	0.0618131	−	0.322968i
$435$	4.11561	−	10.9438i	0.197328	−	0.524713i
$436$	−5.88568	−	3.39810i	−0.281873	−	0.162739i
$437$	3.21560	+	25.2412i	0.153823	+	1.20745i
$438$	−17.9793	−	15.4154i	−0.859085	−	0.736577i
$439$	−4.20632	−	11.5568i	−0.200757	−	0.551575i	0.797933	−	0.602746i	$-0.205927\pi$
$439$	−4.20632	−	11.5568i	−0.200757	−	0.551575i	−0.998690	+	0.0511712i	$0.983705\pi$
$440$	−8.03851	+	2.92578i	−0.383221	+	0.139481i
$441$	−15.3861	−	14.2922i	−0.732671	−	0.680583i
$442$	−7.02414	+	39.8359i	−0.334104	+	1.89480i
$443$	−14.7626	−	17.5934i	−0.701394	−	0.835889i	0.291289	−	0.956635i	$-0.405916\pi$
$443$	−14.7626	−	17.5934i	−0.701394	−	0.835889i	−0.992683	+	0.120746i	$0.961471\pi$
$444$	15.8704	+	2.97285i	0.753175	+	0.141085i
$445$		−	2.89400i		−	0.137189i
$446$	−9.56900	+	1.68727i	−0.453105	+	0.0798947i
$447$	−20.8180	−	12.3165i	−0.984659	−	0.582552i
$448$	2.31032	−	1.28935i	0.109152	−	0.0609160i
$449$	6.95776	+	12.0512i	0.328357	+	0.568731i	0.982186	−	0.187911i	$-0.0601718\pi$
$449$	6.95776	+	12.0512i	0.328357	+	0.568731i	−0.653829	+	0.756642i	$0.726838\pi$
$450$	0.282400	−	1.42369i	0.0133125	−	0.0671133i
$451$	3.12490	+	8.58558i	0.147146	+	0.404279i
$452$	12.1778	−	10.2184i	0.572798	−	0.480634i
$453$	25.3523	−	4.19263i	1.19116	−	0.196987i
$454$	−10.5804	−	8.87803i	−0.496564	−	0.416667i
$455$	−29.3114	+	16.3582i	−1.37414	+	0.766884i
$456$	2.99231	−	6.93153i	0.140128	−	0.324599i
$457$	3.75219	−	6.49899i	0.175520	−	0.304010i	−0.764821	−	0.644243i	$-0.777173\pi$
$457$	3.75219	−	6.49899i	0.175520	−	0.304010i	0.940341	+	0.340233i	$0.110506\pi$
$458$	−1.12956	+	6.40605i	−0.0527808	+	0.299335i
$459$	−10.9793	−	33.4511i	−0.512469	−	1.56136i
$460$	−11.6574	−	4.24294i	−0.543528	−	0.197828i
$461$	−19.5269	−	3.44312i	−0.909460	−	0.160362i	−0.300702	−	0.953718i	$-0.597221\pi$
$461$	−19.5269	−	3.44312i	−0.909460	−	0.160362i	−0.608758	+	0.793356i	$0.708332\pi$
$462$	18.4406	+	0.465039i	0.857935	+	0.0216356i
$463$	−6.24074	−	10.8093i	−0.290032	−	0.502350i	0.683785	−	0.729683i	$-0.260333\pi$
$463$	−6.24074	−	10.8093i	−0.290032	−	0.502350i	−0.973817	+	0.227334i	$0.926999\pi$
$464$	−1.58823	−	2.75090i	−0.0737318	−	0.127707i
$465$	9.52992	+	0.101418i	0.441939	+	0.00470315i
$466$	7.71621	−	21.2001i	0.357446	−	0.982076i
$467$	−36.2451	+	20.9261i	−1.67723	+	0.968346i	−0.713807	+	0.700342i	$0.753031\pi$
$467$	−36.2451	+	20.9261i	−1.67723	+	0.968346i	−0.963418	+	0.268004i	$0.913636\pi$
$468$	−6.48243	+	16.6959i	−0.299650	+	0.771768i
$469$	29.2612	+	11.1357i	1.35116	+	0.514198i
$470$	−0.997131	+	5.65501i	−0.0459942	+	0.260846i
$471$	−13.6877	−	0.145666i	−0.630698	−	0.00671193i
$472$	5.07789	+	4.26085i	0.233729	+	0.196122i
$473$	48.5026	+	8.55232i	2.23015	+	0.393236i
$474$	15.8441	+	2.96793i	0.727746	+	0.136322i
$475$	−1.27678	−	1.67844i	−0.0585829	−	0.0770122i
$476$	−8.73605	−	15.6537i	−0.400416	−	0.717486i
$477$	0.557703	+	0.0118716i	0.0255355	+	0.000543562i
$478$	24.1300	+	4.25477i	1.10368	+	0.194609i
$479$	−15.1360	−	18.0384i	−0.691583	−	0.824197i	0.299963	−	0.953951i	$-0.403026\pi$
$479$	−15.1360	−	18.0384i	−0.691583	−	0.824197i	−0.991546	+	0.129754i	$0.958581\pi$
$480$	2.33586	+	2.84470i	0.106617	+	0.129842i
$481$	−42.6332	+	35.7735i	−1.94391	+	1.63113i
$482$	−0.889122	+	0.513335i	−0.0404984	+	0.0233818i
$483$	20.0524	+	17.7063i	0.912414	+	0.805664i
$484$	−3.98607	+	3.34471i	−0.181185	+	0.152032i
$485$	1.82188	+	10.3324i	0.0827274	+	0.469170i
$486$	−1.88663	−	15.4739i	−0.0855791	−	0.701909i
$487$	−0.0106207	−	0.00613184i	−0.000481268	−	0.000277860i	0.499759	−	0.866164i	$-0.333422\pi$
$487$	−0.0106207	−	0.00613184i	−0.000481268	−	0.000277860i	−0.500241	+	0.865886i	$0.666755\pi$
$488$	1.00057	−	0.839577i	0.0452936	−	0.0380059i
$489$	4.51740	+	27.3162i	0.204284	+	1.23528i
$490$	5.49303	−	13.8246i	0.248150	−	0.624533i
$491$	−7.23268	−	19.8716i	−0.326406	−	0.896793i	−0.989013	−	0.147826i	$-0.952772\pi$
$491$	−7.23268	−	19.8716i	−0.326406	−	0.896793i	0.662607	−	0.748967i	$-0.269450\pi$
$492$	3.03830	−	2.49483i	0.136977	−	0.112476i
$493$	−18.6389	+	10.7611i	−0.839452	+	0.484658i
$494$	11.9193	+	23.1327i	0.536274	+	1.04079i
$495$	3.91750	+	25.3624i	0.176079	+	1.13996i
$496$	1.66431	−	1.98345i	0.0747297	−	0.0890594i
$497$	9.57170	+	1.83194i	0.429350	+	0.0821736i
$498$	−9.27283	+	5.22290i	−0.415526	+	0.234044i
$499$	13.2651	+	11.1307i	0.593827	+	0.498280i	0.889455	−	0.457023i	$-0.151084\pi$
$499$	13.2651	+	11.1307i	0.593827	+	0.498280i	−0.295628	+	0.955303i	$0.595529\pi$
$500$	11.4768	−	2.02367i	0.513257	−	0.0905011i
$501$	−5.78575	+	30.8869i	−0.258488	+	1.37992i
$502$	25.1293	−	14.5084i	1.12158	−	0.647543i
$503$	15.2396	+	18.1618i	0.679500	+	0.809796i	0.990043	−	0.140763i	$-0.0449555\pi$
$503$	15.2396	+	18.1618i	0.679500	+	0.809796i	−0.310543	+	0.950559i	$0.600511\pi$
$504$	−2.44559	−	7.55110i	−0.108935	−	0.336353i
$505$	1.45927	−	2.52752i	0.0649365	−	0.112473i
$506$	−23.4981			−1.04462
$507$	−19.2457	−	34.1691i	−0.854731	−	1.51751i
$508$	5.40357	+	14.8462i	0.239745	+	0.658693i
$509$	−23.9936	−	8.73294i	−1.06350	−	0.387081i	−0.249755	−	0.968309i	$-0.580350\pi$
$509$	−23.9936	−	8.73294i	−1.06350	−	0.387081i	−0.813741	+	0.581228i	$0.802572\pi$
$510$	19.2744	−	15.8267i	0.853486	−	0.700819i
$511$	−23.6552	+	27.3711i	−1.04644	+	1.21083i
$512$	1.00000			0.0441942
$513$	−18.6506	−	12.8513i	−0.823443	−	0.567399i
$514$	−4.06211	−	7.03579i	−0.179172	−	0.310335i
$515$	0.729647	−	4.13804i	0.0321521	−	0.182344i
$516$	−3.45764	−	20.9080i	−0.152214	−	0.920421i
$517$	1.88873	+	10.7115i	0.0830662	+	0.471092i
$518$	4.63633	−	24.2244i	0.203709	−	1.06436i
$519$	6.29723	+	0.0670155i	0.276418	+	0.00294165i
$520$	−12.6872			−0.556369
$521$	−30.6383			−1.34229			−0.671145	−	0.741326i	$-0.734197\pi$
$521$	−30.6383			−1.34229			−0.671145	+	0.741326i	$0.734197\pi$
$522$	−9.02203	+	3.06793i	−0.394884	+	0.134280i
$523$	−33.4042	+	5.89006i	−1.46066	+	0.257554i	−0.846822	−	0.531876i	$-0.821487\pi$
$523$	−33.4042	+	5.89006i	−1.46066	+	0.257554i	−0.613840	+	0.789430i	$0.710376\pi$
$524$	−1.82919	−	1.05608i	−0.0799086	−	0.0461353i
$525$	−2.17301	−	0.439915i	−0.0948378	−	0.0191995i
$526$	0.569398	−	1.56441i	0.0248269	−	0.0682114i
$527$	−13.4390	−	11.2766i	−0.585410	−	0.491217i
$528$	6.00059	+	3.55011i	0.261142	+	0.154499i
$529$	−8.48522	−	7.11994i	−0.368923	−	0.309563i
$530$	0.135151	+	0.371323i	0.00587057	+	0.0161293i
$531$	15.5023	−	12.4555i	0.672740	−	0.540521i
$532$	−10.5700	−	4.61240i	−0.458269	−	0.199973i
$533$			13.5506i			0.586942i
$534$	−1.82290	+	1.49683i	−0.0788846	+	0.0647742i
$535$	3.98049	−	4.74376i	0.172091	−	0.205091i
$536$	7.60643	+	9.06499i	0.328548	+	0.391548i
$537$	11.9720	+	4.50230i	0.516630	+	0.194288i
$538$	−14.1501	−	5.15022i	−0.610055	−	0.222042i
$539$	0.821041	−	28.1655i	0.0353648	−	1.21317i
$540$	9.73446	−	5.21319i	0.418905	−	0.224340i
$541$	6.22347	+	35.2950i	0.267568	+	1.51745i	0.761622	+	0.648021i	$0.224403\pi$
$541$	6.22347	+	35.2950i	0.267568	+	1.51745i	−0.494055	+	0.869431i	$0.664486\pi$
$542$	−3.13443	−	1.14084i	−0.134635	−	0.0490033i
$543$	−0.405896	−	1.15323i	−0.0174187	−	0.0494898i
$544$		−	6.77555i		−	0.290499i
$545$	−13.5718	−	4.93974i	−0.581353	−	0.211595i
$546$	25.4643	+	10.0022i	1.08977	+	0.428055i
$547$	19.2012	−	3.38568i	0.820982	−	0.144761i	0.252647	−	0.967558i	$-0.418699\pi$
$547$	19.2012	−	3.38568i	0.820982	−	0.144761i	0.568335	+	0.822797i	$0.307588\pi$
$548$	0.219155	+	0.0386429i	0.00936183	+	0.00165074i
$549$	−1.88656	−	3.43440i	−0.0805165	−	0.146577i
$550$	1.68658	−	0.973750i	0.0719162	−	0.0415208i
$551$	−5.35211	+	12.7696i	−0.228007	+	0.544005i
$552$	3.35682	+	9.53739i	0.142876	+	0.405938i
$553$	4.62866	−	24.1843i	0.196831	−	1.02842i
$554$	8.87958	−	3.23190i	0.377257	−	0.137310i
$555$	34.3114	+	0.365144i	1.45644	+	0.0154995i
$556$	11.4179	−	4.15576i	0.484225	−	0.176244i
$557$	−7.50752	+	1.32378i	−0.318104	+	0.0560903i	−0.330420	−	0.943834i	$-0.607191\pi$
$557$	−7.50752	+	1.32378i	−0.318104	+	0.0560903i	0.0123166	+	0.999924i	$0.496079\pi$
$558$	−4.86517	−	6.05525i	−0.205959	−	0.256339i
$559$	63.2585	+	36.5223i	2.67555	+	1.54473i
$560$	4.35934	−	3.55098i	0.184216	−	0.150056i
$561$	24.0540	−	40.6573i	1.01556	−	1.71655i
$562$	12.0618	+	20.8917i	0.508797	+	0.881262i
$563$	4.70699	−	8.15274i	0.198376	−	0.343597i	−0.749626	−	0.661862i	$-0.769767\pi$
$563$	4.70699	−	8.15274i	0.198376	−	0.343597i	0.948002	+	0.318264i	$0.103100\pi$
$564$	4.07777	−	2.29679i	0.171705	−	0.0967125i
$565$	21.7155	−	25.8795i	0.913579	−	1.08876i
$566$	5.30044	+	30.0603i	0.222794	+	1.26353i
$567$	−23.6479	+	2.78897i	−0.993117	+	0.117126i
$568$	2.82167	+	2.36766i	0.118395	+	0.0993449i
$569$	9.09323	−	15.7499i	0.381208	−	0.660272i	−0.610027	−	0.792381i	$-0.708841\pi$
$569$	9.09323	−	15.7499i	0.381208	−	0.660272i	0.991235	+	0.132109i	$0.0421748\pi$
$570$	3.70453	−	15.6109i	0.155166	−	0.653867i
$571$	−1.94938	−	3.37643i	−0.0815791	−	0.141299i	0.822349	−	0.568983i	$-0.192663\pi$
$571$	−1.94938	−	3.37643i	−0.0815791	−	0.141299i	−0.903928	+	0.427684i	$0.859330\pi$
$572$	−22.5823	+	8.21928i	−0.944213	+	0.343666i
$573$	−26.8087	−	32.6488i	−1.11995	−	1.36392i
$574$	−3.79265	−	4.65603i	−0.158302	−	0.194339i
$575$	2.78134	+	0.490425i	0.115990	+	0.0204521i
$576$	0.583702	−	2.94267i	0.0243209	−	0.122611i
$577$	13.4734	−	23.3366i	0.560905	−	0.971516i	−0.436513	−	0.899698i	$-0.643787\pi$
$577$	13.4734	−	23.3366i	0.560905	−	0.971516i	0.997418	−	0.0718176i	$-0.0228800\pi$
$578$	−28.9081			−1.20242
$579$	26.8138	−	15.1028i	1.11435	−	0.627652i
$580$	−4.33908	−	5.17111i	−0.180170	−	0.214719i
$581$	7.92239	+	14.1957i	0.328676	+	0.588938i
$582$	5.56597	−	6.49170i	0.230717	−	0.269090i
$583$	0.481118	+	0.573374i	0.0199259	+	0.0237467i
$584$	−12.8489	+	4.67660i	−0.531689	+	0.193519i
$585$	−7.40552	+	37.3341i	−0.306181	+	1.54358i
$586$	0.388906	−	2.20559i	0.0160655	−	0.0911122i
$587$	4.92940	−	5.87463i	0.203458	−	0.242472i	−0.654661	−	0.755923i	$-0.727189\pi$
$587$	4.92940	−	5.87463i	0.203458	−	0.242472i	0.858119	+	0.513451i	$0.171633\pi$
$588$	−11.5491	+	3.69035i	−0.476276	+	0.152187i
$589$	−11.2732	−	0.539500i	−0.464504	−	0.0222297i
$590$	12.1996	+	7.04345i	0.502250	+	0.289974i
$591$	−17.8417	+	2.95056i	−0.733909	+	0.121370i
$592$	5.99216	−	7.14117i	0.246276	−	0.293500i
$593$	15.1473	−	41.6170i	0.622026	−	1.70900i	−0.0799455	−	0.996799i	$-0.525475\pi$
$593$	15.1473	−	41.6170i	0.622026	−	1.70900i	0.701972	−	0.712205i	$-0.252303\pi$
$594$	13.9494	−	15.5855i	0.572349	−	0.639482i
$595$	−24.0598	−	29.5370i	−0.986357	−	1.21090i
$596$	−12.0943	+	6.98264i	−0.495401	+	0.286020i
$597$	−4.41942	−	3.78920i	−0.180875	−	0.155082i
$598$	−32.7486	−	11.9195i	−1.33919	−	0.487426i
$599$	14.7035	+	5.35162i	0.600767	+	0.218661i	0.624459	−	0.781058i	$-0.285320\pi$
$599$	14.7035	+	5.35162i	0.600767	+	0.218661i	−0.0236912	+	0.999719i	$0.507542\pi$
$600$	−0.636163	−	0.545444i	−0.0259712	−	0.0222677i
$601$	−32.0421	+	18.4995i	−1.30703	+	0.754612i	−0.981599	−	0.190955i	$-0.938842\pi$
$601$	−32.0421	+	18.4995i	−1.30703	+	0.754612i	−0.325428	+	0.945567i	$0.605508\pi$
$602$	−31.9579	+	5.15610i	−1.30251	+	0.210147i
$603$	31.1152	−	17.0920i	1.26711	−	0.696038i
$604$	5.07420	−	13.9413i	0.206466	−	0.567262i
$605$	−7.10795	+	8.47093i	−0.288979	+	0.344392i
$606$	−2.34682	+	0.388105i	−0.0953331	+	0.0157657i
$607$	4.85391	+	2.80241i	0.197014	+	0.113746i	0.595262	−	0.803532i	$-0.297048\pi$
$607$	4.85391	+	2.80241i	0.197014	+	0.113746i	−0.398248	+	0.917278i	$0.630382\pi$
$608$	−2.63903	−	3.46923i	−0.107027	−	0.140696i
$609$	4.63216	+	13.7997i	0.187704	+	0.559192i
$610$	1.78421	−	2.12634i	0.0722407	−	0.0860931i
$611$	−2.80120	+	15.8864i	−0.113325	+	0.642696i
$612$	−19.9382	−	3.95490i	−0.805954	−	0.159867i
$613$	−8.46307	+	3.08031i	−0.341820	+	0.124412i	−0.507226	−	0.861813i	$-0.669329\pi$
$613$	−8.46307	+	3.08031i	−0.341820	+	0.124412i	0.165405	+	0.986226i	$0.447107\pi$
$614$	7.97843	+	9.50832i	0.321983	+	0.383725i
$615$	5.43805	−	6.34251i	0.219283	−	0.255755i
$616$	5.45886	−	9.14467i	0.219944	−	0.368449i
$617$	−15.4083	−	18.3629i	−0.620317	−	0.739265i	0.360808	−	0.932640i	$-0.382501\pi$
$617$	−15.4083	−	18.3629i	−0.620317	−	0.739265i	−0.981125	+	0.193376i	$0.938056\pi$
$618$	−2.98389	+	1.68067i	−0.120030	+	0.0676065i
$619$	−18.3637			−0.738099			−0.369050	−	0.929410i	$-0.620317\pi$
$619$	−18.3637			−0.738099			−0.369050	+	0.929410i	$0.620317\pi$
$620$	2.75121	−	4.76523i	0.110491	−	0.191376i
$621$	30.0247	−	4.31103i	1.20485	−	0.172996i
$622$	6.62248	+	1.16772i	0.265537	+	0.0468214i
$623$	2.27549	+	2.79349i	0.0911654	+	0.111919i
$624$	6.56204	+	7.99152i	0.262692	+	0.319917i
$625$	20.9992	−	7.64309i	0.839968	−	0.305723i
$626$	−4.76385	−	8.25122i	−0.190402	−	0.329785i
$627$	−3.51956	−	30.1862i	−0.140558	−	1.20552i
$628$	−3.95154	+	6.84426i	−0.157683	+	0.273116i
$629$	−48.3854	−	40.6002i	−1.92925	−	1.61883i
$630$	−7.90479	−	14.9008i	−0.314935	−	0.593663i
$631$	−5.26155	−	29.8398i	−0.209459	−	1.18790i	−0.890267	−	0.455440i	$-0.849482\pi$
$631$	−5.26155	−	29.8398i	−0.209459	−	1.18790i	0.680808	−	0.732462i	$-0.261629\pi$
$632$	5.98225	−	7.12937i	0.237961	−	0.283591i
$633$	33.3613	−	18.7907i	1.32599	−	0.746862i
$634$	4.33544	−	7.50921i	0.172182	−	0.298229i
$635$	16.7875	+	29.0767i	0.666190	+	1.15388i
$636$	0.163990	−	0.277185i	0.00650265	−	0.0109911i
$637$	15.4314	−	38.8370i	0.611413	−	1.53878i
$638$	−11.0733	−	6.39319i	−0.438397	−	0.253109i
$639$	8.61426	−	6.92123i	0.340775	−	0.273800i
$640$	2.09285	−	0.369026i	0.0827271	−	0.0145870i
$641$	−23.9675	+	8.72347i	−0.946660	+	0.344556i	−0.768793	−	0.639498i	$-0.779142\pi$
$641$	−23.9675	+	8.72347i	−0.946660	+	0.344556i	−0.177868	+	0.984054i	$0.556920\pi$
$642$	−5.04683	−	0.0537087i	−0.199182	−	0.00211971i
$643$	−1.00942	+	0.367400i	−0.0398077	+	0.0144888i	−0.361847	−	0.932237i	$-0.617854\pi$
$643$	−1.00942	+	0.367400i	−0.0398077	+	0.0144888i	0.322040	+	0.946726i	$0.395632\pi$
$644$	14.5886	−	5.07035i	0.574873	−	0.199800i
$645$	−14.9519	−	42.4812i	−0.588730	−	1.67270i
$646$	−23.5059	+	17.8809i	−0.924828	+	0.703513i
$647$	37.9377	−	21.9033i	1.49148	−	0.861108i	0.491531	−	0.870860i	$-0.336437\pi$
$647$	37.9377	−	21.9033i	1.49148	−	0.861108i	0.999952	+	0.00975161i	$0.00310408\pi$
$648$	−8.31858	−	3.43528i	−0.326785	−	0.134951i
$649$	26.2775	+	4.63344i	1.03148	+	0.181878i
$650$	2.84449	−	0.501560i	0.111570	−	0.0196728i
$651$	−9.27869	+	7.39526i	−0.363660	+	0.289843i
$652$	15.0212	+	5.46726i	0.588275	+	0.214115i
$653$			43.1851i			1.68997i	0.534794	+	0.844983i	$0.320389\pi$
$653$			43.1851i			1.68997i	−0.534794	+	0.844983i	$0.679611\pi$
$654$	3.90811	+	11.1037i	0.152819	+	0.434188i
$655$	−4.21794	−	1.53521i	−0.164809	−	0.0599854i
$656$	−0.394140	−	2.23528i	−0.0153886	−	0.0872730i
$657$	6.26178	+	40.5396i	0.244295	+	1.58160i
$658$	−3.48391	−	6.24264i	−0.135817	−	0.243363i
$659$	35.4707	+	12.9103i	1.38174	+	0.502913i	0.922706	−	0.385504i	$-0.125973\pi$
$659$	35.4707	+	12.9103i	1.38174	+	0.502913i	0.459036	+	0.888417i	$0.348195\pi$
$660$	13.8684	+	5.21547i	0.539827	+	0.203012i
$661$	−6.47649	−	7.71838i	−0.251906	−	0.300210i	0.625241	−	0.780432i	$-0.285001\pi$
$661$	−6.47649	−	7.71838i	−0.251906	−	0.300210i	−0.877147	+	0.480222i	$0.840556\pi$
$662$	14.9592	−	17.8277i	0.581405	−	0.692892i
$663$	54.1470	−	44.4614i	2.10289	−	1.72674i
$664$			6.14449i			0.238452i
$665$	−23.8236	−	5.75243i	−0.923839	−	0.223070i
$666$	−17.5165	−	21.8012i	−0.678749	−	0.844781i
$667$	−6.34197	−	17.4244i	−0.245562	−	0.674676i
$668$	13.8981	+	11.6619i	0.537735	+	0.451213i
$669$	14.4845	+	8.56946i	0.560005	+	0.331314i
$670$	19.2643	+	16.1647i	0.744246	+	0.624496i
$671$	1.79824	−	4.94063i	0.0694204	−	0.190731i
$672$	−4.49146	−	0.909275i	−0.173262	−	0.0350761i
$673$	33.5453	+	19.3674i	1.29308	+	0.746559i	0.979199	−	0.202904i	$-0.0650379\pi$
$673$	33.5453	+	19.3674i	1.29308	+	0.746559i	0.313879	+	0.949463i	$0.398371\pi$
$674$	−7.55254	+	1.33172i	−0.290913	+	0.0512958i
$675$	−1.97639	+	1.55364i	−0.0760713	+	0.0597995i
$676$	−22.6416			−0.870831
$677$	−0.209539			−0.00805324			−0.00402662	−	0.999992i	$-0.501282\pi$
$677$	−0.209539			−0.00805324			−0.00402662	+	0.999992i	$0.501282\pi$
$678$	−27.5329	−	0.293007i	−1.05740	−	0.0112529i
$679$	−9.88275	−	8.54106i	−0.379265	−	0.327776i
$680$	−2.50035	−	14.1802i	−0.0958841	−	0.543786i
$681$	3.90319	+	23.6021i	0.149571	+	0.904435i
$682$	1.80984	−	10.2641i	0.0693024	−	0.393034i
$683$	−22.7187	−	39.3499i	−0.869306	−	1.50568i	−0.862707	−	0.505704i	$-0.831233\pi$
$683$	−22.7187	−	39.3499i	−0.869306	−	1.50568i	−0.00659954	−	0.999978i	$-0.502101\pi$
$684$	−11.7492	+	5.74078i	−0.449241	+	0.219504i
$685$	0.472918			0.0180693
$686$	5.56773	+	17.6635i	0.212577	+	0.674397i
$687$	8.70743	−	7.14989i	0.332209	−	0.272785i
$688$	−11.4973	−	4.18467i	−0.438330	−	0.159539i
$689$	0.379674	+	1.04315i	0.0144644	+	0.0397407i
$690$	10.5449	+	18.7215i	0.401436	+	0.712717i
$691$	−30.2437			−1.15052			−0.575262	−	0.817969i	$-0.695100\pi$
$691$	−30.2437			−1.15052			−0.575262	+	0.817969i	$0.695100\pi$
$692$	1.81796	−	3.14879i	0.0691083	−	0.119699i
$693$	−23.7234	−	21.4014i	−0.901176	−	0.812971i
$694$	8.36504	+	9.96907i	0.317533	+	0.378421i
$695$	22.3623	−	12.9109i	0.848249	−	0.489737i
$696$	−1.01298	+	5.40774i	−0.0383969	+	0.204980i
$697$	−15.1452	+	2.67052i	−0.573667	+	0.101153i
$698$	−0.386066	−	0.323948i	−0.0146128	−	0.0122616i
$699$	−34.0470	+	19.1769i	−1.28778	+	0.725337i
$700$	−0.836992	+	0.968473i	−0.0316353	+	0.0366048i
$701$	−4.39883	+	5.24232i	−0.166142	+	0.198000i	−0.842691	−	0.538397i	$-0.819030\pi$
$701$	−4.39883	+	5.24232i	−0.166142	+	0.198000i	0.676550	+	0.736397i	$0.263474\pi$
$702$	27.3467	−	14.6452i	1.03213	−	0.552749i
$703$	−40.5878	−	1.94241i	−1.53080	−	0.0732592i
$704$	3.48606	−	2.01268i	0.131386	−	0.0758555i
$705$	7.68658	−	6.31164i	0.289493	−	0.237710i
$706$	0.331595	+	0.911050i	0.0124797	+	0.0342878i
$707$	0.578749	+	3.58713i	0.0217661	+	0.134908i
$708$	−1.87327	−	11.3274i	−0.0704017	−	0.425710i
$709$	16.6109	−	13.9382i	0.623836	−	0.523461i	−0.275170	−	0.961395i	$-0.588734\pi$
$709$	16.6109	−	13.9382i	0.623836	−	0.523461i	0.899007	+	0.437935i	$0.144290\pi$
$710$	6.77905	+	3.91389i	0.254413	+	0.146886i
$711$	−17.4875	−	21.7652i	−0.655833	−	0.816259i
$712$	0.236473	+	1.34111i	0.00886222	+	0.0502601i
$713$	11.5784	−	9.71545i	0.433615	−	0.363846i
$714$	−6.16084	+	30.4321i	−0.230564	+	1.13889i
$715$	−44.2282	+	25.5352i	−1.65404	+	0.954961i
$716$	5.65697	−	4.74677i	0.211411	−	0.177395i
$717$	−26.9318	−	32.7987i	−1.00579	−	1.22489i
$718$	7.15520	+	8.52723i	0.267030	+	0.318234i
$719$	47.5028	+	8.37602i	1.77156	+	0.312373i	0.961669	−	0.274213i	$-0.0884175\pi$
$719$	47.5028	+	8.37602i	1.77156	+	0.312373i	0.809887	+	0.586586i	$0.199529\pi$
$720$	0.135679	−	6.37396i	0.00505648	−	0.237543i
$721$	2.54934	+	4.56803i	0.0949423	+	0.170122i
$722$	−5.07108	+	18.3108i	−0.188726	+	0.681456i
$723$	1.74784	+	0.327407i	0.0650030	+	0.0121764i
$724$	−0.695130	−	0.122570i	−0.0258343	−	0.00455528i
$725$	1.17726	+	0.987837i	0.0437223	+	0.0366873i
$726$	9.01212	+	0.0959076i	0.334471	+	0.00355946i
$727$	−0.103017	+	0.584238i	−0.00382069	+	0.0216682i	−0.986658	−	0.162804i	$-0.947946\pi$
$727$	−0.103017	+	0.584238i	−0.00382069	+	0.0216682i	0.982838	+	0.184472i	$0.0590574\pi$
$728$	12.2465	−	9.97564i	0.453887	−	0.369722i
$729$	−14.9645	+	22.4736i	−0.554239	+	0.832357i
$730$	−25.1649	+	14.5290i	−0.931395	+	0.537741i
$731$	−28.3535	+	77.9005i	−1.04869	+	2.88125i
$732$	−2.26219	−	0.0240744i	−0.0836130	−	0.000889815i
$733$	12.3358	+	21.3663i	0.455634	+	0.789181i	0.998724	−	0.0504932i	$-0.0160793\pi$
$733$	12.3358	+	21.3663i	0.455634	+	0.789181i	−0.543091	+	0.839674i	$0.682746\pi$
$734$	−9.29765	−	16.1040i	−0.343183	−	0.594410i
$735$	−22.8086	+	11.9852i	−0.841309	+	0.442082i
$736$	5.74884	+	1.01368i	0.211905	+	0.0373646i
$737$	44.7613	+	16.2918i	1.64880	+	0.600116i
$738$	−6.80774	−	0.144913i	−0.250597	−	0.00533433i
$739$	−4.63393	+	26.2803i	−0.170462	+	0.966738i	0.772790	+	0.634661i	$0.218860\pi$
$739$	−4.63393	+	26.2803i	−0.170462	+	0.966738i	−0.943252	+	0.332077i	$0.892251\pi$
$740$	9.90540	−	17.1566i	0.364130	−	0.630691i
$741$	10.4070	−	43.8551i	0.382311	−	1.61106i
$742$	−0.422420	−	0.252161i	−0.0155075	−	0.00925714i
$743$	35.8701	+	30.0986i	1.31595	+	1.10421i	0.987148	+	0.159809i	$0.0510879\pi$
$743$	35.8701	+	30.0986i	1.31595	+	1.10421i	0.328798	+	0.944400i	$0.393357\pi$
$744$	−4.42454	+	0.731707i	−0.162212	+	0.0268257i
$745$	−22.7347	+	19.0767i	−0.832936	+	0.698917i
$746$	−6.14710	−	16.8890i	−0.225061	−	0.618351i
$747$	18.0812	+	3.58655i	0.661556	+	0.131225i
$748$	−13.6370	−	23.6199i	−0.498617	−	0.863631i
$749$	−0.112334	+	7.70878i	−0.00410459	+	0.281673i
$750$	−17.3723	−	10.2780i	−0.634348	−	0.375298i
$751$	−24.5793	+	4.33399i	−0.896911	+	0.158150i	−0.603055	−	0.797700i	$-0.706050\pi$
$751$	−24.5793	+	4.33399i	−0.896911	+	0.158150i	−0.293856	+	0.955850i	$0.594939\pi$
$752$		−	2.70207i		−	0.0985342i
$753$	−49.3995	−	9.25353i	−1.80022	−	0.337217i
$754$	−12.1896	−	14.5270i	−0.443920	−	0.529043i
$755$	5.47486	−	31.0494i	0.199250	−	1.13001i
$756$	−5.29737	+	12.6861i	−0.192663	+	0.461390i
$757$	42.4170	−	15.4385i	1.54167	−	0.561123i	0.575227	−	0.817994i	$-0.304914\pi$
$757$	42.4170	−	15.4385i	1.54167	−	0.561123i	0.966446	+	0.256870i	$0.0826914\pi$
$758$	3.61644	+	9.93610i	0.131355	+	0.360895i
$759$	30.8977	+	26.4917i	1.12152	+	0.961586i
$760$	−6.80331	−	6.28670i	−0.246782	−	0.228042i
$761$	11.1636	+	6.44533i	0.404682	+	0.233643i	0.688502	−	0.725234i	$-0.258269\pi$
$761$	11.1636	+	6.44533i	0.404682	+	0.233643i	−0.283820	+	0.958877i	$0.591602\pi$
$762$	9.63236	−	25.6133i	0.348944	−	0.927872i
$763$	16.9845	−	5.90303i	0.614879	−	0.213704i
$764$	−24.0197	+	4.23532i	−0.869002	+	0.153229i
$765$	−43.1871	−	0.919303i	−1.56143	−	0.0332375i
$766$	−2.89897	−	16.4409i	−0.104744	−	0.594033i
$767$	34.2719	+	19.7869i	1.23749	+	0.714464i
$768$	−1.31491	−	1.12740i	−0.0474476	−	0.0406814i
$769$	17.8252	−	14.9571i	0.642794	−	0.539368i	−0.262081	−	0.965046i	$-0.584409\pi$
$769$	17.8252	−	14.9571i	0.642794	−	0.539368i	0.904875	+	0.425677i	$0.139964\pi$
$770$	8.04995	−	21.1529i	0.290100	−	0.762296i
$771$	−2.59083	+	13.8310i	−0.0933065	+	0.498112i
$772$		−	17.7677i		−	0.639475i
$773$	−0.980244	−	5.55924i	−0.0352569	−	0.199952i	0.962091	−	0.272727i	$-0.0879256\pi$
$773$	−0.980244	−	5.55924i	−0.0352569	−	0.199952i	−0.997348	+	0.0727751i	$0.976814\pi$
$774$	−19.0251	+	31.3901i	−0.683843	+	1.12829i
$775$	−0.428442	+	1.17714i	−0.0153901	+	0.0422839i
$776$	−1.68856	−	4.63927i	−0.0606156	−	0.166540i
$777$	−33.4068	+	26.6258i	−1.19846	+	0.955195i
$778$		−	3.26721i		−	0.117135i
$779$	−6.71455	+	7.26632i	−0.240574	+	0.260343i
$780$	16.6824	+	14.3035i	0.597327	+	0.512147i
$781$	14.6018	+	2.57470i	0.522495	+	0.0921299i
$782$	6.86821	−	38.9515i	0.245607	−	1.39290i
$783$	15.3219	+	6.13737i	0.547560	+	0.219332i
$784$	−1.41589	+	6.85531i	−0.0505675	+	0.244832i
$785$	−5.74426	+	15.7822i	−0.205021	+	0.563291i
$786$	1.21459	+	3.45088i	0.0433229	+	0.123089i
$787$		−	30.2580i		−	1.07858i	−0.842120	−	0.539290i	$-0.818693\pi$
$787$		−	30.2580i		−	1.07858i	0.842120	−	0.539290i	$-0.181307\pi$
$788$	−3.57097	+	9.81116i	−0.127211	+	0.349508i
$789$	−2.51241	+	1.41511i	−0.0894443	+	0.0503793i
$790$	9.88902	−	17.1283i	0.351835	−	0.609397i
$791$	−0.612837	+	42.0552i	−0.0217900	+	1.49531i
$792$	−3.88782	−	11.4331i	−0.138148	−	0.406258i
$793$	5.01233	−	5.97346i	0.177993	−	0.212124i
$794$	24.9456	−	20.9319i	0.885287	−	0.742844i
$795$	0.240919	−	0.640624i	0.00854450	−	0.0227206i
$796$	−3.15833	+	1.14954i	−0.111944	+	0.0407442i
$797$	25.2933			0.895934			0.447967	−	0.894050i	$-0.352148\pi$
$797$	25.2933			0.895934			0.447967	+	0.894050i	$0.352148\pi$
$798$	8.69860	+	17.9815i	0.307927	+	0.636538i
$799$	−18.3080			−0.647690
$800$	−0.454631	+	0.165472i	−0.0160736	+	0.00585033i
$801$	4.08446	+	0.0869441i	0.144317	+	0.00307202i
$802$	−17.7422	+	14.8875i	−0.626499	+	0.525695i
$803$	−35.3793	+	42.1635i	−1.24851	+	1.48792i
$804$	0.218110	−	20.4951i	0.00769215	−	0.722806i
$805$	28.6607	−	15.9950i	1.01016	−	0.563751i
$806$	7.72886	−	13.3868i	0.272238	−	0.471529i
$807$	12.7997	+	22.7248i	0.450571	+	0.799952i
$808$	−0.469710	+	1.29052i	−0.0165244	+	0.0454003i
$809$		−	36.3209i		−	1.27697i	−0.769633	−	0.638487i	$-0.779561\pi$
$809$		−	36.3209i		−	1.27697i	0.769633	−	0.638487i	$-0.220439\pi$
$810$	−18.6772	−	4.11975i	−0.656251	−	0.144753i
$811$	11.7876	−	32.3862i	0.413920	−	1.13723i	−0.541169	−	0.840914i	$-0.682018\pi$
$811$	11.7876	−	32.3862i	0.413920	−	1.13723i	0.955088	−	0.296321i	$-0.0957598\pi$
$812$	8.25431	+	1.57980i	0.289670	+	0.0554402i
$813$	2.83530	+	5.03385i	0.0994384	+	0.176545i
$814$	6.51613	−	36.9548i	0.228390	−	1.29526i
$815$	33.4546	+	5.89895i	1.17186	+	0.206631i
$816$	−7.63874	+	8.90921i	−0.267409	+	0.311885i
$817$	15.8241	+	50.9302i	0.553615	+	1.78182i
$818$		−	3.64790i		−	0.127546i
$819$	−22.2067	−	41.8603i	−0.775963	−	1.46272i
$820$	−1.64975	−	4.53265i	−0.0576118	−	0.158287i
$821$	−8.57359	+	23.5557i	−0.299220	+	0.822101i	0.695410	+	0.718613i	$0.255223\pi$
$821$	−8.57359	+	23.5557i	−0.299220	+	0.822101i	−0.994631	+	0.103488i	$0.967000\pi$
$822$	−0.244602	−	0.297886i	−0.00853147	−	0.0103900i
$823$	−3.06861	−	17.4030i	−0.106965	−	0.606629i	−0.990417	−	0.138108i	$-0.955898\pi$
$823$	−3.06861	−	17.4030i	−0.106965	−	0.606629i	0.883452	−	0.468522i	$-0.155213\pi$
$824$			1.97723i			0.0688800i
$825$	−3.31550	−	0.621061i	−0.115431	−	0.0216226i
$826$	−17.3140	+	2.79345i	−0.602432	+	0.0971965i
$827$	−28.0856	+	23.5666i	−0.976631	+	0.819490i	−0.983578	−	0.180485i	$-0.942233\pi$
$827$	−28.0856	+	23.5666i	−0.976631	+	0.819490i	0.00694693	+	0.999976i	$0.497789\pi$
$828$	6.33852	−	16.3252i	0.220279	−	0.567341i
$829$	18.5066	+	10.6848i	0.642762	+	0.371099i	0.785678	−	0.618636i	$-0.212314\pi$
$829$	18.5066	+	10.6848i	0.642762	+	0.371099i	−0.142915	+	0.989735i	$0.545648\pi$
$830$	2.26747	+	12.8595i	0.0787051	+	0.446359i
$831$	−15.3195	−	5.76117i	−0.531426	−	0.199853i
$832$	5.87936	−	1.03669i	0.203830	−	0.0359408i
$833$	46.4485	+	9.59343i	1.60934	+	0.332393i
$834$	−19.6986	−	7.40803i	−0.682107	−	0.256519i
$835$	33.3902	+	19.2778i	1.15552	+	0.667137i
$836$	−16.1822	−	6.78242i	−0.559674	−	0.234575i
$837$	−0.429443	+	13.4471i	−0.0148437	+	0.464798i
$838$	−2.70293	−	7.42623i	−0.0933710	−	0.256535i
$839$	11.5879	−	4.21765i	0.400058	−	0.145609i	−0.134152	−	0.990961i	$-0.542831\pi$
$839$	11.5879	−	4.21765i	0.400058	−	0.145609i	0.534211	+	0.845351i	$0.320609\pi$
$840$	−9.73549	−	0.245511i	−0.335906	−	0.00847095i
$841$	−3.28370	+	18.6228i	−0.113231	+	0.642165i
$842$	1.52897	+	1.82215i	0.0526916	+	0.0627954i
$843$	7.69307	−	41.0690i	0.264963	−	1.41449i
$844$		−	22.1063i		−	0.760930i
$845$	−47.3854	+	8.35533i	−1.63011	+	0.287432i
$846$	−7.95128	−	1.57720i	−0.273371	−	0.0542253i
$847$	0.200595	−	13.7656i	0.00689251	−	0.472990i
$848$	−0.0929716	−	0.161032i	−0.00319266	−	0.00552985i
$849$	26.9203	−	45.5021i	0.923902	−	1.56163i
$850$	1.12117	+	3.08038i	0.0384557	+	0.105656i
$851$	41.6868	−	34.9793i	1.42900	−	1.19908i
$852$	−1.04093	−	6.29439i	−0.0356618	−	0.215642i
$853$	−40.7170	−	34.1656i	−1.39412	−	1.16981i	−0.963639	−	0.267209i	$-0.913899\pi$
$853$	−40.7170	−	34.1656i	−1.39412	−	1.16981i	−0.430484	−	0.902598i	$-0.641657\pi$
$854$	−0.0503526	+	3.45538i	−0.00172303	+	0.118241i
$855$	−22.4708	+	16.3503i	−0.768484	+	0.559170i
$856$	−1.45698	+	2.52356i	−0.0497984	+	0.0862534i
$857$	−8.53413	+	48.3995i	−0.291520	+	1.65329i	0.389497	+	0.921028i	$0.372649\pi$
$857$	−8.53413	+	48.3995i	−0.291520	+	1.65329i	−0.681018	+	0.732267i	$0.738462\pi$
$858$	38.9600	+	14.6516i	1.33007	+	0.500199i
$859$	9.94599	+	3.62005i	0.339353	+	0.123514i	0.506075	−	0.862490i	$-0.331096\pi$
$859$	9.94599	+	3.62005i	0.339353	+	0.123514i	−0.166722	+	0.986004i	$0.553318\pi$
$860$	−25.6063	−	4.51509i	−0.873169	−	0.153963i
$861$	−0.262220	+	10.3981i	−0.00893644	+	0.354365i
$862$	9.62927	+	16.6784i	0.327974	+	0.568068i
$863$	−11.9861	−	20.7605i	−0.408011	−	0.706695i	0.586656	−	0.809836i	$-0.300444\pi$
$863$	−11.9861	−	20.7605i	−0.408011	−	0.706695i	−0.994667	+	0.103141i	$0.967111\pi$
$864$	−4.08507	+	3.21127i	−0.138977	+	0.109249i
$865$	2.64272	−	7.26081i	0.0898552	−	0.246875i
$866$	−24.3388	+	14.0520i	−0.827067	+	0.477507i
$867$	38.0114	+	32.5909i	1.29093	+	1.10684i
$868$	1.09113	+	6.76294i	0.0370355	+	0.229549i
$869$	6.50535	−	36.8937i	0.220679	−	1.25153i
$870$	−0.124421	+	11.6914i	−0.00421825	+	0.396375i
$871$	54.1185	+	45.4109i	1.83374	+	1.53869i
$872$	6.69295	+	1.18015i	0.226652	+	0.0399648i
$873$	−14.6374	+	2.26091i	−0.495402	+	0.0765202i
$874$	−11.6547	−	22.6191i	−0.394225	−	0.765104i
$875$	−15.8040	+	26.4748i	−0.534272	+	0.895012i
$876$	22.1674	+	8.33647i	0.748967	+	0.281663i
$877$	25.1467	+	4.43404i	0.849142	+	0.149727i	0.581253	−	0.813723i	$-0.302563\pi$
$877$	25.1467	+	4.43404i	0.849142	+	0.149727i	0.267889	+	0.963450i	$0.413674\pi$
$878$	7.90530	+	9.42117i	0.266791	+	0.317949i
$879$	−2.99795	+	2.46170i	−0.101118	+	0.0830309i
$880$	6.55305	−	5.49867i	0.220903	−	0.185360i
$881$	−26.1261	+	15.0839i	−0.880212	+	0.508190i	−0.870728	−	0.491765i	$-0.836352\pi$
$881$	−26.1261	+	15.0839i	−0.880212	+	0.508190i	−0.00948336	+	0.999955i	$0.503019\pi$
$882$	19.3464	+	8.16795i	0.651428	+	0.275029i
$883$	−5.87608	+	4.93062i	−0.197746	+	0.165929i	−0.736284	−	0.676673i	$-0.763421\pi$
$883$	−5.87608	+	4.93062i	−0.197746	+	0.165929i	0.538538	+	0.842601i	$0.318977\pi$
$884$	−7.02414	−	39.8359i	−0.236248	−	1.33983i
$885$	−8.10057	−	23.0153i	−0.272298	−	0.773650i
$886$	19.8897	+	11.4833i	0.668206	+	0.385789i
$887$	−10.4815	+	8.79505i	−0.351935	+	0.295309i	−0.801567	−	0.597905i	$-0.796000\pi$
$887$	−10.4815	+	8.79505i	−0.351935	+	0.295309i	0.449631	+	0.893214i	$0.351555\pi$
$888$	−15.9301	+	2.63443i	−0.534578	+	0.0884056i
$889$	−39.0668	−	14.8673i	−1.31026	−	0.498634i
$890$	0.989806	+	2.71947i	0.0331784	+	0.0911568i
$891$	−35.9132	+	4.76703i	−1.20314	+	0.159701i
$892$	8.41483	−	4.85831i	0.281749	−	0.162668i
$893$	−9.37408	+	7.13082i	−0.313692	+	0.238624i
$894$	23.7751	+	4.45356i	0.795157	+	0.148949i
$895$	10.0875	−	12.0218i	0.337188	−	0.401845i
$896$	−1.73001	+	2.00177i	−0.0577955	+	0.0668744i
$897$	29.6233	+	52.5937i	0.989093	+	1.75605i
$898$	−10.6599	−	8.94472i	−0.355726	−	0.298489i
$899$	8.09958	−	1.42817i	0.270136	−	0.0476323i
$900$	0.221561	+	1.43442i	0.00738536	+	0.0478139i
$901$	−1.09108	+	0.629934i	−0.0363491	+	0.0209861i
$902$	−5.87289	−	6.99903i	−0.195546	−	0.233042i
$903$	47.8346	+	29.2495i	1.59184	+	0.973362i
$904$	−7.94852	+	13.7672i	−0.264364	+	0.457892i
$905$	−1.50003			−0.0498628
$906$	−22.3894	+	12.6108i	−0.743839	+	0.418966i
$907$	−1.20240	−	3.30356i	−0.0399250	−	0.109693i	0.918128	−	0.396284i	$-0.129700\pi$
$907$	−1.20240	−	3.30356i	−0.0399250	−	0.109693i	−0.958053	+	0.286591i	$0.907478\pi$
$908$	12.9788	+	4.72390i	0.430717	+	0.156768i
$909$	3.52340	+	2.13548i	0.116864	+	0.0708294i
$910$	21.9489	−	25.3968i	0.727599	−	0.841895i
$911$	−32.1835			−1.06629			−0.533143	−	0.846025i	$-0.678989\pi$
$911$	−32.1835			−1.06629			−0.533143	+	0.846025i	$0.678989\pi$
$912$	−0.441127	+	7.53694i	−0.0146072	+	0.249573i
$913$	12.3669	+	21.4200i	0.409283	+	0.708899i
$914$	−1.30312	+	7.39038i	−0.0431035	+	0.244452i
$915$	−4.74330	+	0.784422i	−0.156809	+	0.0259322i
$916$	−1.12956	−	6.40605i	−0.0373217	−	0.211662i
$917$	5.27855	−	1.83458i	0.174313	−	0.0605833i
$918$	21.7581	+	27.6786i	0.718124	+	0.913529i
$919$	−55.8691			−1.84295			−0.921476	−	0.388436i	$-0.873015\pi$
$919$	−55.8691			−1.84295			−0.921476	+	0.388436i	$0.873015\pi$
$920$	12.4055			0.408998
$921$	0.228777	−	21.4974i	0.00753845	−	0.708363i
$922$	19.5269	−	3.44312i	0.643085	−	0.113393i
$923$	19.0441	+	10.9951i	0.626846	+	0.361910i
$924$	−17.4876	+	5.87007i	−0.575298	+	0.193111i
$925$	−1.54256	+	4.23814i	−0.0507189	+	0.139349i
$926$	9.56137	+	8.02294i	0.314206	+	0.263650i
$927$	5.81832	+	1.15411i	0.191099	+	0.0379060i
$928$	2.43331	+	2.04179i	0.0798774	+	0.0670251i
$929$	5.97870	+	16.4264i	0.196155	+	0.538931i	0.998305	−	0.0581907i	$-0.0185331\pi$
$929$	5.97870	+	16.4264i	0.196155	+	0.538931i	−0.802151	+	0.597122i	$0.796311\pi$
$930$	−8.98988	+	3.16412i	−0.294790	+	0.103756i
$931$	27.5192	−	13.1793i	0.901905	−	0.431934i
$932$			22.5607i			0.739000i
$933$	−7.39145	−	9.00161i	−0.241985	−	0.294700i
$934$	26.9021	−	32.0607i	0.880265	−	1.04906i
$935$	−37.2565	−	44.4005i	−1.21842	−	1.45205i
$936$	0.381159	−	17.9061i	0.0124586	−	0.585280i
$937$	6.60919	+	2.40555i	0.215913	+	0.0785859i	0.447712	−	0.894178i	$-0.352239\pi$
$937$	6.60919	+	2.40555i	0.215913	+	0.0785859i	−0.231799	+	0.972764i	$0.574461\pi$
$938$	−31.3052	−	0.456186i	−1.02215	−	0.0148950i
$939$	−3.03840	+	16.2203i	−0.0991544	+	0.529330i
$940$	−0.997131	−	5.65501i	−0.0325228	−	0.184446i
$941$	20.2003	+	7.35231i	0.658511	+	0.239678i	0.649593	−	0.760282i	$-0.274939\pi$
$941$	20.2003	+	7.35231i	0.658511	+	0.239678i	0.00891768	+	0.999960i	$0.497161\pi$
$942$	12.9121	−	4.54460i	0.420699	−	0.148071i
$943$		−	13.2498i		−	0.431472i
$944$	−6.22895	−	2.26715i	−0.202735	−	0.0737896i
$945$	−6.40508	+	28.5050i	−0.208357	+	0.927268i
$946$	−48.5026	+	8.55232i	−1.57696	+	0.278060i
$947$	30.5175	+	5.38106i	0.991686	+	0.174861i	0.645875	−	0.763443i	$-0.276493\pi$
$947$	30.5175	+	5.38106i	0.991686	+	0.174861i	0.345811	+	0.938304i	$0.387604\pi$
$948$	−15.9037	+	2.63007i	−0.516529	+	0.0854207i
$949$	−70.6949	+	40.8157i	−2.29485	+	1.32493i
$950$	1.77385	+	1.14053i	0.0575511	+	0.0370038i
$951$	−14.1666	+	4.98613i	−0.459382	+	0.161686i
$952$	13.5631	+	11.7217i	0.439582	+	0.379904i
$953$	43.0588	−	15.6721i	1.39481	−	0.507670i	0.468177	−	0.883635i	$-0.344911\pi$
$953$	43.0588	−	15.6721i	1.39481	−	0.507670i	0.926634	+	0.375965i	$0.122689\pi$
$954$	−0.528130	+	0.179590i	−0.0170988	+	0.00581445i
$955$	−48.7066	+	17.7278i	−1.57611	+	0.573657i
$956$	−24.1300	+	4.25477i	−0.780420	+	0.137609i
$957$	7.35272	+	20.8905i	0.237680	+	0.675293i
$958$	20.3927	+	11.7737i	0.658859	+	0.380392i
$959$	−0.456494	+	0.371845i	−0.0147409	+	0.0120075i
$960$	−3.16793	−	1.87424i	−0.102245	−	0.0604907i
$961$	−12.1480	−	21.0410i	−0.391871	−	0.678741i
$962$	27.8269	−	48.1975i	0.897174	−	1.55395i
$963$	6.57555	+	5.76040i	0.211894	+	0.185626i
$964$	0.659930	−	0.786475i	0.0212549	−	0.0253306i
$965$	−6.55675	−	37.1852i	−0.211069	−	1.19703i
$966$	−24.8990	−	9.78016i	−0.801111	−	0.314671i
$967$	0.810496	+	0.680087i	0.0260638	+	0.0218701i	0.655726	−	0.754999i	$-0.272362\pi$
$967$	0.810496	+	0.680087i	0.0260638	+	0.0218701i	−0.629663	+	0.776869i	$0.716807\pi$
$968$	2.60172	−	4.50631i	0.0836225	−	0.144838i
$969$	51.0669	+	2.98888i	1.64050	+	0.0960167i
$970$	−5.24590	−	9.08617i	−0.168436	−	0.291739i
$971$	9.27123	−	3.37445i	0.297528	−	0.108291i	−0.188943	−	0.981988i	$-0.560506\pi$
$971$	9.27123	−	3.37445i	0.297528	−	0.108291i	0.486471	+	0.873697i	$0.338284\pi$
$972$	7.06522	+	13.8954i	0.226617	+	0.445696i
$973$	−11.4341	+	30.0454i	−0.366561	+	0.963211i
$974$	0.0120774	+	0.00212956i	0.000386984	+	6.82357e-5i
$975$	−4.30569	−	2.54736i	−0.137892	−	0.0815809i
$976$	−0.653075	+	1.13116i	−0.0209044	+	0.0362075i
$977$	3.90212			0.124840			0.0624200	−	0.998050i	$-0.480118\pi$
$977$	3.90212			0.124840			0.0624200	+	0.998050i	$0.480118\pi$
$978$	−13.5877	−	24.1238i	−0.434485	−	0.771393i
$979$	3.52357	+	4.19923i	0.112614	+	0.134208i
$980$	−0.433459	+	14.8696i	−0.0138463	+	0.474992i
$981$	7.37947	−	19.0063i	0.235608	−	0.606824i
$982$	13.5930	+	16.1995i	0.433770	+	0.516946i
$983$	−24.8607	+	9.04855i	−0.792933	+	0.288604i	−0.706555	−	0.707658i	$-0.749752\pi$
$983$	−24.8607	+	9.04855i	−0.792933	+	0.288604i	−0.0863782	+	0.996262i	$0.527529\pi$
$984$	−2.00179	+	3.38353i	−0.0638148	+	0.107863i
$985$	−3.85293	+	21.8510i	−0.122764	+	0.696232i
$986$	13.8343	−	16.4870i	0.440573	−	0.525054i
$987$	−2.45692	+	12.1362i	−0.0782047	+	0.386300i
$988$	−19.1123	−	17.6610i	−0.608043	−	0.561871i
$989$	−61.8542	−	35.7115i	−1.96685	−	1.13556i
$990$	−12.3557	−	22.4930i	−0.392690	−	0.714876i
$991$	−27.3230	+	32.5623i	−0.867944	+	1.03438i	0.131130	+	0.991365i	$0.458139\pi$
$991$	−27.3230	+	32.5623i	−0.867944	+	1.03438i	−0.999075	+	0.0430106i	$0.986305\pi$
$992$	−0.885561	+	2.43306i	−0.0281166	+	0.0772497i
$993$	−39.7688	+	6.57674i	−1.26202	+	0.208707i
$994$	−9.62102	+	1.55226i	−0.305160	+	0.0492346i
$995$	−6.18569	+	3.57131i	−0.196099	+	0.113218i
$996$	6.92728	−	8.07942i	0.219499	−	0.256006i
$997$	−29.5164	−	10.7431i	−0.934794	−	0.340237i	−0.170686	−	0.985325i	$-0.554598\pi$
$997$	−29.5164	−	10.7431i	−0.934794	−	0.340237i	−0.764108	+	0.645088i	$0.776821\pi$
$998$	−16.2720	−	5.92254i	−0.515083	−	0.187475i
$999$	−1.54616	+	48.4146i	−0.0489184	+	1.53177i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bu.a.611.24	yes	162
3.2	odd	2		798.2.bu.b.611.10	yes	162
7.4	even	3		798.2.cc.a.725.13	yes	162
19.13	odd	18		798.2.cc.b.317.9	yes	162
21.11	odd	6		798.2.cc.b.725.9	yes	162
57.32	even	18		798.2.cc.a.317.13	yes	162
133.32	odd	18		798.2.bu.b.431.10	yes	162
399.32	even	18	inner	798.2.bu.a.431.24	✓	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bu.a.431.24	✓	162	399.32	even	18	inner
798.2.bu.a.611.24	yes	162	1.1	even	1	trivial
798.2.bu.b.431.10	yes	162	133.32	odd	18
798.2.bu.b.611.10	yes	162	3.2	odd	2
798.2.cc.a.317.13	yes	162	57.32	even	18
798.2.cc.a.725.13	yes	162	7.4	even	3
798.2.cc.b.317.9	yes	162	19.13	odd	18
798.2.cc.b.725.9	yes	162	21.11	odd	6

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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bu (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(1.62120 + 0.609683i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.36601 - 1.62795i) q^{5} +(-1.73195 - 0.0184316i) q^{6} +(-0.0385504 + 2.64547i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.25657 + 1.97683i) q^{9} +(-0.726838 + 1.99697i) q^{10} +4.02535i q^{11} +(1.63381 - 0.575043i) q^{12} +(-2.04188 + 5.61002i) q^{13} +(-0.868579 - 2.49911i) q^{14} +(3.20710 - 1.80639i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-6.67261 - 1.17656i) q^{17} +(-2.79660 - 1.08582i) q^{18} +(-3.87478 + 1.99651i) q^{19} -2.12513i q^{20} +(-1.67540 + 4.26533i) q^{21} +(-1.37675 - 3.78259i) q^{22} +(1.99655 - 5.48548i) q^{23} +(-1.33860 + 1.09916i) q^{24} +(0.0840125 + 0.476459i) q^{25} -5.97006i q^{26} +(2.45311 + 4.58064i) q^{27} +(1.67094 + 2.05133i) q^{28} +(2.43331 - 2.04179i) q^{29} +(-2.39587 + 2.79435i) q^{30} +(2.24232 + 1.29460i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-2.45419 + 6.52589i) q^{33} +(6.67261 - 1.17656i) q^{34} +(4.25402 + 3.67650i) q^{35} +(2.99932 + 0.0638452i) q^{36} +(8.07321 + 4.66107i) q^{37} +(2.95826 - 3.20136i) q^{38} +(-6.73063 + 7.85006i) q^{39} +(0.726838 + 1.99697i) q^{40} +(2.13288 - 0.776304i) q^{41} +(0.115528 - 4.58112i) q^{42} +(2.12461 - 12.0493i) q^{43} +(2.58745 + 3.08360i) q^{44} +(6.30068 - 0.973208i) q^{45} +5.83752i q^{46} +(2.66102 - 0.469209i) q^{47} +(0.881939 - 1.49070i) q^{48} +(-6.99703 - 0.203968i) q^{49} +(-0.241904 - 0.418991i) q^{50} +(-10.1003 - 5.97562i) q^{51} +(2.04188 + 5.61002i) q^{52} +(0.142441 - 0.119522i) q^{53} +(-3.87184 - 3.46538i) q^{54} +(6.55305 + 5.49867i) q^{55} +(-2.27177 - 1.35612i) q^{56} +(-7.49903 + 0.874349i) q^{57} +(-1.58823 + 2.75090i) q^{58} +(1.15106 - 6.52801i) q^{59} +(1.29566 - 3.44526i) q^{60} +(-1.22738 - 0.446730i) q^{61} +(-2.54987 - 0.449611i) q^{62} +(-5.31665 + 5.89349i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(6.34359 + 10.9874i) q^{65} +(0.0741935 - 6.97172i) q^{66} +(4.04730 - 11.1199i) q^{67} +(-5.86780 + 3.38777i) q^{68} +(6.58121 - 7.67579i) q^{69} +(-5.25491 - 1.99981i) q^{70} +(0.639621 - 3.62747i) q^{71} +(-2.84028 + 0.965833i) q^{72} +(10.4745 + 8.78913i) q^{73} +(-9.18052 - 1.61877i) q^{74} +(-0.154288 + 0.823655i) q^{75} +(-1.68493 + 4.02008i) q^{76} +(-10.6489 - 0.155179i) q^{77} +(3.63984 - 9.67866i) q^{78} +(-9.16534 - 1.61610i) q^{79} +(-1.36601 - 1.62795i) q^{80} +(1.18425 + 8.92175i) q^{81} +(-1.73874 + 1.45898i) q^{82} +(5.32128 - 3.07224i) q^{83} +(1.45827 + 4.34436i) q^{84} +(-11.0302 + 9.25546i) q^{85} +(2.12461 + 12.0493i) q^{86} +(5.18973 - 1.82660i) q^{87} +(-3.48606 - 2.01268i) q^{88} +(1.04320 - 0.875346i) q^{89} +(-5.58785 + 3.06948i) q^{90} +(-14.7624 - 5.61800i) q^{91} +(-1.99655 - 5.48548i) q^{92} +(2.84595 + 3.46591i) q^{93} +(-2.34006 + 1.35103i) q^{94} +(-2.04278 + 9.03519i) q^{95} +(-0.318902 + 1.70244i) q^{96} +(-3.17345 + 3.78197i) q^{97} +(6.64482 - 2.20146i) q^{98} +(-7.95745 + 9.08350i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q - 81 q^{8} + 15 q^{13} + 6 q^{14} + 27 q^{15} - 6 q^{17} - 18 q^{18} + 9 q^{19} - 6 q^{22} - 6 q^{25} - 9 q^{27} + 9 q^{28} + 6 q^{29} - 24 q^{33} + 6 q^{34} + 24 q^{35} + 18 q^{37} - 9 q^{39} - 9 q^{43}+ \cdots - 57 q^{99}+O(q^{100}) \) 162 * q - 81 * q^8 + 15 * q^13 + 6 * q^14 + 27 * q^15 - 6 * q^17 - 18 * q^18 + 9 * q^19 - 6 * q^22 - 6 * q^25 - 9 * q^27 + 9 * q^28 + 6 * q^29 - 24 * q^33 + 6 * q^34 + 24 * q^35 + 18 * q^37 - 9 * q^39 - 9 * q^43 - 12 * q^44 - 63 * q^45 + 12 * q^47 - 48 * q^49 + 87 * q^50 - 24 * q^51 - 15 * q^52 - 18 * q^54 - 18 * q^57 - 48 * q^59 + 6 * q^60 + 45 * q^61 + 36 * q^62 - 15 * q^63 - 81 * q^64 + 36 * q^65 + 12 * q^66 + 9 * q^67 + 9 * q^69 - 24 * q^70 + 12 * q^71 + 102 * q^73 + 39 * q^74 - 6 * q^78 - 42 * q^79 + 84 * q^81 - 3 * q^84 - 6 * q^85 - 9 * q^86 + 60 * q^87 + 54 * q^89 + 36 * q^90 - 18 * q^91 - 21 * q^93 - 72 * q^94 - 12 * q^97 - 27 * q^98 - 57 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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