LMFDB - Embedded newform 847.2.f.z.372.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			372.1
Character	$\chi$	$=$	847.372
Dual form			847.2.f.z.148.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.835334 + 2.57089i) q^{2} +(2.27106 - 1.65003i) q^{3} +(-4.29367 - 3.11953i) q^{4} +(-0.137535 - 0.423289i) q^{5} +(2.34494 + 7.21698i) q^{6} +(0.809017 + 0.587785i) q^{7} +(7.23277 - 5.25492i) q^{8} +(1.50810 - 4.64146i) q^{9} +O(q^{10})$	\(q+(-0.835334 + 2.57089i) q^{2} +(2.27106 - 1.65003i) q^{3} +(-4.29367 - 3.11953i) q^{4} +(-0.137535 - 0.423289i) q^{5} +(2.34494 + 7.21698i) q^{6} +(0.809017 + 0.587785i) q^{7} +(7.23277 - 5.25492i) q^{8} +(1.50810 - 4.64146i) q^{9} +1.20312 q^{10} -14.8985 q^{12} +(-0.139346 + 0.428863i) q^{13} +(-2.18693 + 1.58890i) q^{14} +(-1.01079 - 0.734380i) q^{15} +(4.18797 + 12.8893i) q^{16} +(-1.49291 - 4.59472i) q^{17} +(10.6729 + 7.75433i) q^{18} +(-0.878946 + 0.638592i) q^{19} +(-0.729935 + 2.24651i) q^{20} +2.80719 q^{21} +4.57222 q^{23} +(7.75535 - 23.8685i) q^{24} +(3.88483 - 2.82249i) q^{25} +(-0.986160 - 0.716487i) q^{26} +(-1.63112 - 5.02007i) q^{27} +(-1.64004 - 5.04751i) q^{28} +(-1.60534 - 1.16635i) q^{29} +(2.73236 - 1.98517i) q^{30} +(2.55205 - 7.85440i) q^{31} -18.7549 q^{32} +13.0596 q^{34} +(0.137535 - 0.423289i) q^{35} +(-20.9545 + 15.2243i) q^{36} +(-5.91978 - 4.30097i) q^{37} +(-0.907538 - 2.79311i) q^{38} +(0.391171 + 1.20390i) q^{39} +(-3.21911 - 2.33882i) q^{40} +(1.43255 - 1.04081i) q^{41} +(-2.34494 + 7.21698i) q^{42} +11.4084 q^{43} -2.17209 q^{45} +(-3.81933 + 11.7547i) q^{46} +(-0.827289 + 0.601061i) q^{47} +(30.7788 + 22.3621i) q^{48} +(0.309017 + 0.951057i) q^{49} +(4.01120 + 12.3452i) q^{50} +(-10.9719 - 7.97156i) q^{51} +(1.93616 - 1.40670i) q^{52} +(-1.10388 + 3.39738i) q^{53} +14.2686 q^{54} +8.94020 q^{56} +(-0.942452 + 2.90057i) q^{57} +(4.33956 - 3.15287i) q^{58} +(11.6495 + 8.46386i) q^{59} +(2.04907 + 6.30638i) q^{60} +(-1.52335 - 4.68837i) q^{61} +(18.0610 + 13.1221i) q^{62} +(3.94826 - 2.86858i) q^{63} +(7.29061 - 22.4382i) q^{64} +0.200698 q^{65} -6.18858 q^{67} +(-7.92330 + 24.3854i) q^{68} +(10.3838 - 7.54427i) q^{69} +(0.973343 + 0.707175i) q^{70} +(-1.82989 - 5.63182i) q^{71} +(-13.4827 - 41.4956i) q^{72} +(-1.34116 - 0.974409i) q^{73} +(16.0023 - 11.6264i) q^{74} +(4.16551 - 12.8201i) q^{75} +5.76602 q^{76} -3.42186 q^{78} +(1.11504 - 3.43173i) q^{79} +(4.87989 - 3.54545i) q^{80} +(-0.142838 - 0.103778i) q^{81} +(1.47915 + 4.55236i) q^{82} +(3.33888 + 10.2760i) q^{83} +(-12.0532 - 8.75713i) q^{84} +(-1.73957 + 1.26387i) q^{85} +(-9.52984 + 29.3298i) q^{86} -5.57035 q^{87} -5.21170 q^{89} +(1.81442 - 5.58422i) q^{90} +(-0.364813 + 0.265052i) q^{91} +(-19.6316 - 14.2632i) q^{92} +(-7.16409 - 22.0488i) q^{93} +(-0.854200 - 2.62896i) q^{94} +(0.391195 + 0.284220i) q^{95} +(-42.5935 + 30.9460i) q^{96} +(-1.64083 + 5.04996i) q^{97} -2.70320 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} - 6 q^{6} + 6 q^{7} + 12 q^{8} - 8 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 - 6 * q^6 + 6 * q^7 + 12 * q^8 - 8 * q^9	\( 24 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} - 6 q^{6} + 6 q^{7} + 12 q^{8} - 8 q^{9} + 32 q^{10} - 56 q^{12} + 4 q^{13} - 4 q^{14} - 2 q^{15} - 8 q^{16} + 22 q^{17} + 24 q^{18} + 6 q^{19} - 2 q^{20} + 8 q^{21} + 8 q^{23} - 20 q^{24} - 4 q^{25} - 6 q^{26} + 2 q^{27} + 4 q^{28} + 12 q^{29} + 20 q^{30} + 2 q^{31} - 32 q^{32} + 96 q^{34} - 4 q^{35} - 18 q^{36} - 14 q^{37} + 22 q^{38} + 20 q^{39} + 18 q^{40} + 26 q^{41} + 6 q^{42} + 16 q^{43} - 144 q^{45} + 12 q^{46} + 16 q^{47} + 24 q^{48} - 6 q^{49} - 4 q^{50} - 4 q^{51} + 12 q^{52} - 4 q^{53} + 128 q^{54} + 48 q^{56} + 20 q^{57} + 2 q^{58} + 4 q^{59} - 24 q^{60} - 8 q^{61} + 20 q^{62} + 8 q^{63} - 26 q^{64} - 96 q^{65} + 24 q^{67} + 12 q^{68} + 14 q^{69} + 8 q^{70} - 22 q^{71} + 16 q^{72} + 14 q^{73} + 44 q^{74} + 20 q^{75} + 120 q^{76} + 128 q^{78} - 28 q^{79} + 4 q^{80} + 6 q^{81} + 4 q^{82} + 22 q^{83} - 14 q^{84} - 24 q^{85} + 30 q^{86} - 88 q^{87} - 22 q^{90} - 4 q^{91} - 10 q^{92} + 50 q^{93} - 38 q^{94} - 24 q^{95} - 62 q^{96} + 4 q^{97} - 16 q^{98}+O(q^{100}) \) 24 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 - 6 * q^6 + 6 * q^7 + 12 * q^8 - 8 * q^9 + 32 * q^10 - 56 * q^12 + 4 * q^13 - 4 * q^14 - 2 * q^15 - 8 * q^16 + 22 * q^17 + 24 * q^18 + 6 * q^19 - 2 * q^20 + 8 * q^21 + 8 * q^23 - 20 * q^24 - 4 * q^25 - 6 * q^26 + 2 * q^27 + 4 * q^28 + 12 * q^29 + 20 * q^30 + 2 * q^31 - 32 * q^32 + 96 * q^34 - 4 * q^35 - 18 * q^36 - 14 * q^37 + 22 * q^38 + 20 * q^39 + 18 * q^40 + 26 * q^41 + 6 * q^42 + 16 * q^43 - 144 * q^45 + 12 * q^46 + 16 * q^47 + 24 * q^48 - 6 * q^49 - 4 * q^50 - 4 * q^51 + 12 * q^52 - 4 * q^53 + 128 * q^54 + 48 * q^56 + 20 * q^57 + 2 * q^58 + 4 * q^59 - 24 * q^60 - 8 * q^61 + 20 * q^62 + 8 * q^63 - 26 * q^64 - 96 * q^65 + 24 * q^67 + 12 * q^68 + 14 * q^69 + 8 * q^70 - 22 * q^71 + 16 * q^72 + 14 * q^73 + 44 * q^74 + 20 * q^75 + 120 * q^76 + 128 * q^78 - 28 * q^79 + 4 * q^80 + 6 * q^81 + 4 * q^82 + 22 * q^83 - 14 * q^84 - 24 * q^85 + 30 * q^86 - 88 * q^87 - 22 * q^90 - 4 * q^91 - 10 * q^92 + 50 * q^93 - 38 * q^94 - 24 * q^95 - 62 * q^96 + 4 * q^97 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−0.835334	+	2.57089i	−0.590670	+	1.81790i	−0.0154732	+	0.999880i	$0.504925\pi$
$2$	−0.835334	+	2.57089i	−0.590670	+	1.81790i	−0.575197	+	0.818015i	$0.695075\pi$
$3$	2.27106	−	1.65003i	1.31120	−	0.952643i	0.311203	−	0.950344i	$-0.399268\pi$
$3$	2.27106	−	1.65003i	1.31120	−	0.952643i	0.999997	−	0.00229892i	$-0.000731771\pi$
$4$	−4.29367	−	3.11953i	−2.14684	−	1.55977i
$5$	−0.137535	−	0.423289i	−0.0615075	−	0.189301i	0.915581	−	0.402133i	$-0.131731\pi$
$5$	−0.137535	−	0.423289i	−0.0615075	−	0.189301i	−0.977089	+	0.212833i	$0.931731\pi$
$6$	2.34494	+	7.21698i	0.957318	+	2.94632i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$8$	7.23277	−	5.25492i	2.55717	−	1.85789i
$9$	1.50810	−	4.64146i	0.502701	−	1.54715i
$10$	1.20312			0.380459
$11$		0			0
$11$		0			0
$12$	−14.8985			−4.30083
$13$	−0.139346	+	0.428863i	−0.0386476	+	0.118945i	−0.968519	−	0.248940i	$-0.919918\pi$
$13$	−0.139346	+	0.428863i	−0.0386476	+	0.118945i	0.929871	+	0.367885i	$0.119918\pi$
$14$	−2.18693	+	1.58890i	−0.584482	+	0.424651i
$15$	−1.01079	−	0.734380i	−0.260984	−	0.189616i
$16$	4.18797	+	12.8893i	1.04699	+	3.22231i
$17$	−1.49291	−	4.59472i	−0.362085	−	1.11438i	−0.951786	−	0.306762i	$-0.900755\pi$
$17$	−1.49291	−	4.59472i	−0.362085	−	1.11438i	0.589701	−	0.807621i	$-0.299245\pi$
$18$	10.6729	+	7.75433i	2.51563	+	1.82771i
$19$	−0.878946	+	0.638592i	−0.201644	+	0.146503i	−0.684025	−	0.729459i	$-0.739772\pi$
$19$	−0.878946	+	0.638592i	−0.201644	+	0.146503i	0.482381	+	0.875962i	$0.339772\pi$
$20$	−0.729935	+	2.24651i	−0.163218	+	0.502334i
$21$	2.80719			0.612579
$22$		0			0
$23$	4.57222			0.953373			0.476687	−	0.879073i	$-0.341838\pi$
$23$	4.57222			0.953373			0.476687	+	0.879073i	$0.341838\pi$
$24$	7.75535	−	23.8685i	1.58305	−	4.87214i
$25$	3.88483	−	2.82249i	0.776965	−	0.564498i
$26$	−0.986160	−	0.716487i	−0.193402	−	0.140515i
$27$	−1.63112	−	5.02007i	−0.313909	−	0.966113i
$28$	−1.64004	−	5.04751i	−0.309938	−	0.953890i
$29$	−1.60534	−	1.16635i	−0.298105	−	0.216586i	0.428671	−	0.903461i	$-0.358982\pi$
$29$	−1.60534	−	1.16635i	−0.298105	−	0.216586i	−0.726776	+	0.686875i	$0.758982\pi$
$30$	2.73236	−	1.98517i	0.498858	−	0.362442i
$31$	2.55205	−	7.85440i	0.458362	−	1.41069i	−0.408781	−	0.912632i	$-0.634046\pi$
$31$	2.55205	−	7.85440i	0.458362	−	1.41069i	0.867143	−	0.498060i	$-0.165954\pi$
$32$	−18.7549			−3.31542
$33$		0			0
$34$	13.0596			2.23970
$35$	0.137535	−	0.423289i	0.0232476	−	0.0715489i
$36$	−20.9545	+	15.2243i	−3.49241	+	2.53739i
$37$	−5.91978	−	4.30097i	−0.973206	−	0.707076i	−0.0170260	−	0.999855i	$-0.505420\pi$
$37$	−5.91978	−	4.30097i	−0.973206	−	0.707076i	−0.956180	+	0.292780i	$0.905420\pi$
$38$	−0.907538	−	2.79311i	−0.147222	−	0.453103i
$39$	0.391171	+	1.20390i	0.0626375	+	0.192778i
$40$	−3.21911	−	2.33882i	−0.508985	−	0.369799i
$41$	1.43255	−	1.04081i	0.223727	−	0.162547i	−0.470276	−	0.882520i	$-0.655846\pi$
$41$	1.43255	−	1.04081i	0.223727	−	0.162547i	0.694003	+	0.719972i	$0.255846\pi$
$42$	−2.34494	+	7.21698i	−0.361832	+	1.11360i
$43$	11.4084			1.73977			0.869884	−	0.493257i	$-0.164194\pi$
$43$	11.4084			1.73977			0.869884	+	0.493257i	$0.164194\pi$
$44$		0			0
$45$	−2.17209			−0.323797
$46$	−3.81933	+	11.7547i	−0.563129	+	1.73313i
$47$	−0.827289	+	0.601061i	−0.120672	+	0.0876737i	−0.646485	−	0.762927i	$-0.723762\pi$
$47$	−0.827289	+	0.601061i	−0.120672	+	0.0876737i	0.525812	+	0.850601i	$0.323762\pi$
$48$	30.7788	+	22.3621i	4.44253	+	3.22769i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	4.01120	+	12.3452i	0.567269	+	1.74587i
$51$	−10.9719	−	7.97156i	−1.53637	−	1.11624i
$52$	1.93616	−	1.40670i	0.268497	−	0.195074i
$53$	−1.10388	+	3.39738i	−0.151629	+	0.466666i	−0.997804	−	0.0662394i	$-0.978900\pi$
$53$	−1.10388	+	3.39738i	−0.151629	+	0.466666i	0.846175	+	0.532906i	$0.178900\pi$
$54$	14.2686			1.94171
$55$		0			0
$56$	8.94020			1.19468
$57$	−0.942452	+	2.90057i	−0.124831	+	0.384190i
$58$	4.33956	−	3.15287i	0.569812	−	0.413993i
$59$	11.6495	+	8.46386i	1.51664	+	1.10190i	0.963123	+	0.269061i	$0.0867133\pi$
$59$	11.6495	+	8.46386i	1.51664	+	1.10190i	0.553514	+	0.832840i	$0.313287\pi$
$60$	2.04907	+	6.30638i	0.264533	+	0.814150i
$61$	−1.52335	−	4.68837i	−0.195044	−	0.600285i	−0.999976	−	0.00691741i	$-0.997798\pi$
$61$	−1.52335	−	4.68837i	−0.195044	−	0.600285i	0.804932	−	0.593367i	$-0.202202\pi$
$62$	18.0610	+	13.1221i	2.29375	+	1.66651i
$63$	3.94826	−	2.86858i	0.497434	−	0.361407i
$64$	7.29061	−	22.4382i	0.911326	−	2.80477i
$65$	0.200698			0.0248935
$66$		0			0
$67$	−6.18858			−0.756055			−0.378028	−	0.925794i	$-0.623398\pi$
$67$	−6.18858			−0.756055			−0.378028	+	0.925794i	$0.623398\pi$
$68$	−7.92330	+	24.3854i	−0.960841	+	2.95717i
$69$	10.3838	−	7.54427i	1.25006	−	0.908224i
$70$	0.973343	+	0.707175i	0.116337	+	0.0845236i
$71$	−1.82989	−	5.63182i	−0.217168	−	0.668375i	−0.998993	−	0.0448760i	$-0.985711\pi$
$71$	−1.82989	−	5.63182i	−0.217168	−	0.668375i	0.781825	−	0.623499i	$-0.214289\pi$
$72$	−13.4827	−	41.4956i	−1.58895	−	4.89030i
$73$	−1.34116	−	0.974409i	−0.156971	−	0.114046i	0.506527	−	0.862224i	$-0.330929\pi$
$73$	−1.34116	−	0.974409i	−0.156971	−	0.114046i	−0.663498	+	0.748178i	$0.730929\pi$
$74$	16.0023	−	11.6264i	1.86023	−	1.35154i
$75$	4.16551	−	12.8201i	0.480992	−	1.48034i
$76$	5.76602			0.661407
$77$		0			0
$78$	−3.42186			−0.387449
$79$	1.11504	−	3.43173i	0.125451	−	0.386099i	−0.868532	−	0.495634i	$-0.834936\pi$
$79$	1.11504	−	3.43173i	0.125451	−	0.386099i	0.993983	+	0.109534i	$0.0349359\pi$
$80$	4.87989	−	3.54545i	0.545588	−	0.396393i
$81$	−0.142838	−	0.103778i	−0.0158709	−	0.0115309i
$82$	1.47915	+	4.55236i	0.163345	+	0.502724i
$83$	3.33888	+	10.2760i	0.366489	+	1.12794i	0.949043	+	0.315146i	$0.102053\pi$
$83$	3.33888	+	10.2760i	0.366489	+	1.12794i	−0.582554	+	0.812792i	$0.697947\pi$
$84$	−12.0532	−	8.75713i	−1.31511	−	0.955481i
$85$	−1.73957	+	1.26387i	−0.188682	+	0.137086i
$86$	−9.52984	+	29.3298i	−1.02763	+	3.16272i
$87$	−5.57035			−0.597204
$88$		0			0
$89$	−5.21170			−0.552439			−0.276220	−	0.961095i	$-0.589082\pi$
$89$	−5.21170			−0.552439			−0.276220	+	0.961095i	$0.589082\pi$
$90$	1.81442	−	5.58422i	0.191257	−	0.588629i
$91$	−0.364813	+	0.265052i	−0.0382428	+	0.0277850i
$92$	−19.6316	−	14.2632i	−2.04674	−	1.48704i
$93$	−7.16409	−	22.0488i	−0.742882	−	2.28635i
$94$	−0.854200	−	2.62896i	−0.0881040	−	0.271156i
$95$	0.391195	+	0.284220i	0.0401357	+	0.0291603i
$96$	−42.5935	+	30.9460i	−4.34718	+	3.15841i
$97$	−1.64083	+	5.04996i	−0.166601	+	0.512746i	−0.999151	−	0.0412047i	$-0.986880\pi$
$97$	−1.64083	+	5.04996i	−0.166601	+	0.512746i	0.832549	+	0.553951i	$0.186880\pi$
$98$	−2.70320			−0.273064
$99$		0			0
$100$	−25.4850			−2.54850
$101$	−4.80842	+	14.7988i	−0.478456	+	1.47254i	0.362783	+	0.931873i	$0.381826\pi$
$101$	−4.80842	+	14.7988i	−0.478456	+	1.47254i	−0.841239	+	0.540663i	$0.818174\pi$
$102$	29.6592	−	21.5487i	2.93670	−	2.13364i
$103$	11.4649	+	8.32970i	1.12967	+	0.820750i	0.985646	−	0.168825i	$-0.0539972\pi$
$103$	11.4649	+	8.32970i	1.12967	+	0.820750i	0.144019	+	0.989575i	$0.453997\pi$
$104$	1.24578	+	3.83412i	0.122159	+	0.375966i
$105$	−0.386087	−	1.18825i	−0.0376782	−	0.115962i
$106$	−7.81220	−	5.67589i	−0.758787	−	0.551291i
$107$	−9.51009	+	6.90949i	−0.919375	+	0.667965i	−0.943368	−	0.331747i	$-0.892362\pi$
$107$	−9.51009	+	6.90949i	−0.919375	+	0.667965i	0.0239932	+	0.999712i	$0.492362\pi$
$108$	−8.65679	+	26.6429i	−0.833000	+	2.56371i
$109$	−15.7800			−1.51145			−0.755723	−	0.654891i	$-0.772714\pi$
$109$	−15.7800			−1.51145			−0.755723	+	0.654891i	$0.772714\pi$
$110$		0			0
$111$	−20.5409			−1.94966
$112$	−4.18797	+	12.8893i	−0.395726	+	1.21792i
$113$	4.79219	−	3.48173i	0.450811	−	0.327534i	−0.339105	−	0.940749i	$-0.610124\pi$
$113$	4.79219	−	3.48173i	0.450811	−	0.327534i	0.789916	+	0.613215i	$0.210124\pi$
$114$	−6.66979	−	4.84588i	−0.624683	−	0.453859i
$115$	−0.628839	−	1.93537i	−0.0586396	−	0.180474i
$116$	3.25435	+	10.0158i	0.302158	+	0.929948i
$117$	1.78040	+	1.29354i	0.164598	+	0.119588i
$118$	−31.4909	+	22.8795i	−2.89897	+	2.10623i
$119$	1.49291	−	4.59472i	0.136855	−	0.421197i
$120$	−11.1699			−1.01967
$121$		0			0
$122$	13.3258			1.20646
$123$	1.53606	−	4.72749i	0.138501	−	0.426264i
$124$	−35.4597	+	25.7630i	−3.18438	+	2.31359i
$125$	−3.52938	−	2.56425i	−0.315678	−	0.229353i
$126$	4.07669	+	12.5468i	0.363181	+	1.11776i
$127$	−3.13149	−	9.63774i	−0.277875	−	0.855211i	−0.988444	−	0.151584i	$-0.951563\pi$
$127$	−3.13149	−	9.63774i	−0.277875	−	0.855211i	0.710569	−	0.703627i	$-0.248437\pi$
$128$	21.2501	+	15.4391i	1.87826	+	1.36464i
$129$	25.9093	−	18.8242i	2.28118	−	1.65738i
$130$	−0.167650	+	0.515973i	−0.0147038	+	0.0452538i
$131$	6.83340			0.597037			0.298519	−	0.954404i	$-0.403508\pi$
$131$	6.83340			0.597037			0.298519	+	0.954404i	$0.403508\pi$
$132$		0			0
$133$	−1.08644			−0.0942061
$134$	5.16953	−	15.9102i	0.446579	−	1.37443i
$135$	−1.90060	+	1.38087i	−0.163578	+	0.118846i
$136$	−34.9428	−	25.3874i	−2.99632	−	2.17695i
$137$	4.47064	+	13.7592i	0.381952	+	1.17553i	0.938667	+	0.344825i	$0.112062\pi$
$137$	4.47064	+	13.7592i	0.381952	+	1.17553i	−0.556715	+	0.830704i	$0.687938\pi$
$138$	10.7216	+	32.9976i	0.912681	+	2.80894i
$139$	−11.8890	−	8.63790i	−1.00842	−	0.732657i	−0.0445393	−	0.999008i	$-0.514182\pi$
$139$	−11.8890	−	8.63790i	−1.00842	−	0.732657i	−0.963876	+	0.266351i	$0.914182\pi$
$140$	−1.91099	+	1.38842i	−0.161508	+	0.117343i
$141$	−0.887062	+	2.73010i	−0.0747041	+	0.229915i
$142$	16.0074			1.34331
$143$		0			0
$144$	66.1409			5.51174
$145$	−0.272912	+	0.839938i	−0.0226641	+	0.0697531i
$146$	3.62542	−	2.63402i	0.300042	−	0.217993i
$147$	2.27106	+	1.65003i	0.187314	+	0.136092i
$148$	12.0006	+	36.9339i	0.986440	+	3.03595i
$149$	−0.309449	−	0.952386i	−0.0253510	−	0.0780225i	0.937581	−	0.347768i	$-0.113060\pi$
$149$	−0.309449	−	0.952386i	−0.0253510	−	0.0780225i	−0.962932	+	0.269746i	$0.913060\pi$
$150$	29.4796	+	21.4182i	2.40700	+	1.74879i
$151$	1.11271	−	0.808431i	0.0905511	−	0.0657892i	−0.541589	−	0.840644i	$-0.682177\pi$
$151$	1.11271	−	0.808431i	0.0905511	−	0.0657892i	0.632140	+	0.774855i	$0.282177\pi$
$152$	−3.00147	+	9.23758i	−0.243451	+	0.749267i
$153$	−23.5777			−1.90614
$154$		0			0
$155$	−3.67568			−0.295237
$156$	2.07605	−	6.38942i	0.166217	−	0.511563i
$157$	−4.34983	+	3.16034i	−0.347154	+	0.252222i	−0.747674	−	0.664066i	$-0.768829\pi$
$157$	−4.34983	+	3.16034i	−0.347154	+	0.252222i	0.400520	+	0.916288i	$0.368829\pi$
$158$	7.89117	+	5.73327i	0.627788	+	0.456115i
$159$	3.09879	+	9.53710i	0.245750	+	0.756341i
$160$	2.57945	+	7.93872i	0.203923	+	0.627611i
$161$	3.69900	+	2.68748i	0.291522	+	0.211803i
$162$	0.386120	−	0.280532i	0.0303364	−	0.0220407i
$163$	−2.91252	+	8.96383i	−0.228127	+	0.702101i	0.769833	+	0.638246i	$0.220340\pi$
$163$	−2.91252	+	8.96383i	−0.228127	+	0.702101i	−0.997959	+	0.0638555i	$0.979660\pi$
$164$	−9.39775			−0.733841
$165$		0			0
$166$	−29.2076			−2.26695
$167$	−6.18400	+	19.0324i	−0.478532	+	1.47277i	0.362602	+	0.931944i	$0.381888\pi$
$167$	−6.18400	+	19.0324i	−0.478532	+	1.47277i	−0.841134	+	0.540826i	$0.818112\pi$
$168$	20.3038	−	14.7516i	1.56647	−	1.13811i
$169$	10.3527	+	7.52169i	0.796363	+	0.578591i
$170$	−1.79615	−	5.52799i	−0.137759	−	0.423977i
$171$	1.63846	+	5.04266i	0.125296	+	0.385622i
$172$	−48.9840	−	35.5890i	−3.73499	−	2.71363i
$173$	8.77504	−	6.37544i	0.667154	−	0.484716i	−0.201917	−	0.979403i	$-0.564717\pi$
$173$	8.77504	−	6.37544i	0.667154	−	0.484716i	0.869071	+	0.494687i	$0.164717\pi$
$174$	4.65310	−	14.3208i	0.352750	−	1.08565i
$175$	4.80191			0.362990
$176$		0			0
$177$	40.4224			3.03833
$178$	4.35351	−	13.3987i	0.326309	−	1.00428i
$179$	−13.6306	+	9.90324i	−1.01880	+	0.740203i	−0.966037	−	0.258404i	$-0.916803\pi$
$179$	−13.6306	+	9.90324i	−1.01880	+	0.740203i	−0.0527648	+	0.998607i	$0.516803\pi$
$180$	9.32626	+	6.77592i	0.695138	+	0.505048i
$181$	−6.27432	−	19.3104i	−0.466367	−	1.43533i	−0.857256	−	0.514891i	$-0.827832\pi$
$181$	−6.27432	−	19.3104i	−0.466367	−	1.43533i	0.390889	−	0.920438i	$-0.372168\pi$
$182$	−0.376680	−	1.15930i	−0.0279214	−	0.0859331i
$183$	−11.1956	−	8.13405i	−0.827599	−	0.601286i
$184$	33.0698	−	24.0266i	2.43794	−	1.77127i
$185$	−1.00638	+	3.09731i	−0.0739903	+	0.227719i
$186$	62.6695			4.59515
$187$		0			0
$188$	5.42714			0.395815
$189$	1.63112	−	5.02007i	0.118647	−	0.365156i
$190$	−1.05748	+	0.768301i	−0.0767174	+	0.0557384i
$191$	−2.05842	−	1.49553i	−0.148942	−	0.108213i	0.510819	−	0.859689i	$-0.329342\pi$
$191$	−2.05842	−	1.49553i	−0.148942	−	0.108213i	−0.659761	+	0.751476i	$0.729342\pi$
$192$	−20.4661	−	62.9883i	−1.47702	−	4.54579i
$193$	−5.41045	−	16.6517i	−0.389453	−	1.19861i	−0.933198	−	0.359363i	$-0.882994\pi$
$193$	−5.41045	−	16.6517i	−0.389453	−	1.19861i	0.543745	−	0.839250i	$-0.317006\pi$
$194$	−11.6123	−	8.43681i	−0.833712	−	0.605727i
$195$	0.455798	−	0.331157i	0.0326404	−	0.0237146i
$196$	1.64004	−	5.04751i	0.117145	−	0.360537i
$197$	2.16558			0.154291			0.0771457	−	0.997020i	$-0.475419\pi$
$197$	2.16558			0.154291			0.0771457	+	0.997020i	$0.475419\pi$
$198$		0			0
$199$	−14.5756			−1.03324			−0.516620	−	0.856215i	$-0.672810\pi$
$199$	−14.5756			−1.03324			−0.516620	+	0.856215i	$0.672810\pi$
$200$	13.2661	−	40.8289i	0.938055	−	2.88704i
$201$	−14.0547	+	10.2113i	−0.991339	+	0.720250i
$202$	−34.0295	−	24.7239i	−2.39431	−	1.73957i
$203$	−0.613187	−	1.88719i	−0.0430373	−	0.132455i
$204$	22.2422	+	68.4545i	1.55727	+	4.79277i
$205$	−0.637589	−	0.463235i	−0.0445311	−	0.0323538i
$206$	−30.9917	+	22.5168i	−2.15930	+	1.56882i
$207$	6.89537	−	21.2218i	0.479261	−	1.47501i
$208$	−6.11130			−0.423743
$209$		0			0
$210$	3.37738			0.233061
$211$	1.12184	−	3.45266i	0.0772304	−	0.237691i	−0.904987	−	0.425440i	$-0.860119\pi$
$211$	1.12184	−	3.45266i	0.0772304	−	0.237691i	0.982217	+	0.187749i	$0.0601193\pi$
$212$	15.3379	−	11.1437i	1.05341	−	0.765349i
$213$	−13.4485	−	9.77087i	−0.921473	−	0.669489i
$214$	−9.81945	−	30.2211i	−0.671243	−	2.06587i
$215$	−1.56906	−	4.82906i	−0.107009	−	0.329339i
$216$	−38.1776	−	27.7376i	−2.59765	−	1.88731i
$217$	6.68135	−	4.85429i	0.453560	−	0.329530i
$218$	13.1815	−	40.5686i	0.892766	−	2.74765i
$219$	−4.65366			−0.314465
$220$		0			0
$221$	2.17854			0.146544
$222$	17.1585	−	52.8085i	1.15160	−	3.54427i
$223$	3.91614	−	2.84524i	0.262244	−	0.190532i	−0.448892	−	0.893586i	$-0.648181\pi$
$223$	3.91614	−	2.84524i	0.262244	−	0.190532i	0.711136	+	0.703055i	$0.248181\pi$
$224$	−15.1730	−	11.0238i	−1.01379	−	0.736560i
$225$	−7.24177	−	22.2879i	−0.482785	−	1.48586i
$226$	4.94808	+	15.2286i	0.329141	+	1.01299i
$227$	18.3895	+	13.3607i	1.22055	+	0.886782i	0.996146	−	0.0877139i	$-0.0279561\pi$
$227$	18.3895	+	13.3607i	1.22055	+	0.886782i	0.224405	+	0.974496i	$0.427956\pi$
$228$	13.0950	−	9.51407i	0.867237	−	0.630085i
$229$	−7.00639	+	21.5635i	−0.462995	+	1.42495i	0.398491	+	0.917172i	$0.369534\pi$
$229$	−7.00639	+	21.5635i	−0.462995	+	1.42495i	−0.861486	+	0.507781i	$0.830466\pi$
$230$	5.50092			0.362720
$231$		0			0
$232$	−17.7402			−1.16470
$233$	0.181480	−	0.558539i	0.0118892	−	0.0365911i	−0.944936	−	0.327255i	$-0.893876\pi$
$233$	0.181480	−	0.558539i	0.0118892	−	0.0365911i	0.956825	+	0.290664i	$0.0938763\pi$
$234$	−4.81278	+	3.49669i	−0.314621	+	0.228586i
$235$	0.368203	+	0.267515i	0.0240189	+	0.0174508i
$236$	−23.6158	−	72.6821i	−1.53726	−	4.73120i
$237$	−3.13012	−	9.63351i	−0.203323	−	0.625764i
$238$	10.5654	+	7.67625i	0.684856	+	0.497577i
$239$	−12.1127	+	8.80039i	−0.783505	+	0.569250i	−0.906029	−	0.423216i	$-0.860901\pi$
$239$	−12.1127	+	8.80039i	−0.783505	+	0.569250i	0.122524	+	0.992466i	$0.460901\pi$
$240$	5.23247	−	16.1039i	0.337754	−	1.03950i
$241$	18.2746			1.17717			0.588586	−	0.808435i	$-0.299685\pi$
$241$	18.2746			1.17717			0.588586	+	0.808435i	$0.299685\pi$
$242$		0			0
$243$	15.3396			0.984037
$244$	−8.08480	+	24.8825i	−0.517577	+	1.59294i
$245$	0.360071	−	0.261607i	0.0230041	−	0.0167135i
$246$	10.8708	+	7.89807i	0.693094	+	0.503562i
$247$	−0.151391	−	0.465933i	−0.00963276	−	0.0296466i
$248$	−22.8158	−	70.2199i	−1.44881	−	4.45897i
$249$	24.5385	+	17.8282i	1.55506	+	1.12982i
$250$	9.54062	−	6.93166i	0.603402	−	0.438397i
$251$	3.26473	−	10.0478i	0.206068	−	0.634212i	−0.793600	−	0.608440i	$-0.791796\pi$
$251$	3.26473	−	10.0478i	0.206068	−	0.634212i	0.999668	−	0.0257719i	$-0.00820435\pi$
$252$	−25.9012			−1.63162
$253$		0			0
$254$	27.3934			1.71882
$255$	−1.86525	+	5.74065i	−0.116807	+	0.359494i
$256$	−19.2690	+	13.9998i	−1.20431	+	0.874986i
$257$	15.7499	+	11.4430i	0.982453	+	0.713794i	0.958255	−	0.285913i	$-0.0922969\pi$
$257$	15.7499	+	11.4430i	0.982453	+	0.713794i	0.0241975	+	0.999707i	$0.492297\pi$
$258$	26.7521	+	82.3344i	1.66551	+	5.12592i
$259$	−2.26116	−	6.95912i	−0.140501	−	0.432419i
$260$	−0.861731	−	0.626084i	−0.0534423	−	0.0388281i
$261$	−7.83459	+	5.69216i	−0.484949	+	0.352336i
$262$	−5.70817	+	17.5679i	−0.352652	+	1.08535i
$263$	−21.1885			−1.30654			−0.653269	−	0.757126i	$-0.726603\pi$
$263$	−21.1885			−1.30654			−0.653269	+	0.757126i	$0.726603\pi$
$264$		0			0
$265$	1.58989			0.0976665
$266$	0.907538	−	2.79311i	0.0556447	−	0.171257i
$267$	−11.8361	+	8.59944i	−0.724358	+	0.526277i
$268$	26.5717	+	19.3055i	1.62313	+	1.17927i
$269$	7.15572	+	22.0230i	0.436292	+	1.34277i	0.891757	+	0.452515i	$0.149473\pi$
$269$	7.15572	+	22.0230i	0.436292	+	1.34277i	−0.455465	+	0.890254i	$0.650527\pi$
$270$	−1.96243	−	6.03974i	−0.119430	−	0.367567i
$271$	21.7004	+	15.7663i	1.31821	+	0.957733i	0.999953	+	0.00972711i	$0.00309628\pi$
$271$	21.7004	+	15.7663i	1.31821	+	0.957733i	0.318253	+	0.948006i	$0.396904\pi$
$272$	52.9702	−	38.4851i	3.21179	−	2.33350i
$273$	−0.391171	+	1.20390i	−0.0236747	+	0.0728633i
$274$	−39.1079			−2.36260
$275$		0			0
$276$	−68.1193			−4.10030
$277$	4.34193	−	13.3631i	0.260881	−	0.802910i	−0.731732	−	0.681592i	$-0.761288\pi$
$277$	4.34193	−	13.3631i	0.260881	−	0.802910i	0.992614	−	0.121318i	$-0.0387121\pi$
$278$	32.1384	−	23.3499i	1.92753	−	1.40044i
$279$	−32.6071	−	23.6905i	−1.95214	−	1.41831i
$280$	−1.22959	−	3.78429i	−0.0734820	−	0.226154i
$281$	0.539351	+	1.65995i	0.0321750	+	0.0990244i	0.965854	−	0.259086i	$-0.0834212\pi$
$281$	0.539351	+	1.65995i	0.0321750	+	0.0990244i	−0.933679	+	0.358110i	$0.883421\pi$
$282$	−6.27779	−	4.56108i	−0.373837	−	0.271608i
$283$	−3.77431	+	2.74220i	−0.224360	+	0.163007i	−0.694287	−	0.719698i	$-0.744280\pi$
$283$	−3.77431	+	2.74220i	−0.224360	+	0.163007i	0.469927	+	0.882705i	$0.344280\pi$
$284$	−9.71172	+	29.8896i	−0.576285	+	1.77362i
$285$	1.35740			0.0804053
$286$		0			0
$287$	1.77073			0.104523
$288$	−28.2842	+	87.0499i	−1.66666	+	5.12946i
$289$	−5.12936	+	3.72670i	−0.301727	+	0.219218i
$290$	−1.93142	−	1.40326i	−0.113417	−	0.0824021i
$291$	4.60613	+	14.1762i	0.270016	+	0.831024i
$292$	2.71879	+	8.36758i	0.159105	+	0.489676i
$293$	11.7382	+	8.52830i	0.685753	+	0.498229i	0.875261	−	0.483650i	$-0.160689\pi$
$293$	11.7382	+	8.52830i	0.685753	+	0.498229i	−0.189508	+	0.981879i	$0.560689\pi$
$294$	−6.13913	+	4.46034i	−0.358042	+	0.260132i
$295$	1.98045	−	6.09518i	0.115306	−	0.354875i
$296$	−65.4177			−3.80232
$297$		0			0
$298$	2.70698			0.156811
$299$	−0.637120	+	1.96085i	−0.0368456	+	0.113399i
$300$	−57.8782	+	42.0509i	−3.34160	+	2.42781i
$301$	9.22961	+	6.70570i	0.531986	+	0.386510i
$302$	1.14891	+	3.53597i	0.0661121	+	0.203472i
$303$	13.4982	+	41.5431i	0.775449	+	2.38659i
$304$	−11.9120	−	8.65456i	−0.683199	−	0.496373i
$305$	−1.77502	+	1.28963i	−0.101638	+	0.0738440i
$306$	19.6952	−	60.6157i	1.12590	−	3.46517i
$307$	−2.35679			−0.134509			−0.0672547	−	0.997736i	$-0.521424\pi$
$307$	−2.35679			−0.134509			−0.0672547	+	0.997736i	$0.521424\pi$
$308$		0			0
$309$	39.7816			2.26310
$310$	3.07042	−	9.44977i	0.174388	−	0.536711i
$311$	16.1844	−	11.7586i	0.917732	−	0.666772i	−0.0252262	−	0.999682i	$-0.508031\pi$
$311$	16.1844	−	11.7586i	0.917732	−	0.666772i	0.942959	+	0.332910i	$0.108031\pi$
$312$	9.15564	+	6.65196i	0.518336	+	0.376593i
$313$	5.79501	+	17.8352i	0.327553	+	1.00811i	0.970275	+	0.242005i	$0.0778052\pi$
$313$	5.79501	+	17.8352i	0.327553	+	1.00811i	−0.642722	+	0.766100i	$0.722195\pi$
$314$	−4.49133	−	13.8229i	−0.253460	−	0.780070i
$315$	−1.75726	−	1.27673i	−0.0990105	−	0.0719353i
$316$	−15.4930	+	11.2563i	−0.871549	+	0.633217i
$317$	1.29850	−	3.99637i	0.0729309	−	0.224458i	−0.907946	−	0.419087i	$-0.862350\pi$
$317$	1.29850	−	3.99637i	0.0729309	−	0.224458i	0.980877	+	0.194629i	$0.0623502\pi$
$318$	−27.1074			−1.52011
$319$		0			0
$320$	−10.5005			−0.586999
$321$	−10.1972	+	31.3838i	−0.569153	+	1.75167i
$322$	−9.99913	+	7.26479i	−0.557230	+	0.404851i
$323$	4.24634	+	3.08515i	0.236273	+	0.171662i
$324$	0.289561	+	0.891177i	0.0160867	+	0.0495098i
$325$	0.669127	+	2.05936i	0.0371165	+	0.114233i
$326$	−20.6121	−	14.9756i	−1.14160	−	0.829420i
$327$	−35.8373	+	26.0373i	−1.98181	+	1.43987i
$328$	4.89195	−	15.0559i	0.270113	−	0.831322i
$329$	−1.02259			−0.0563770
$330$		0			0
$331$	−0.0682694			−0.00375242			−0.00187621	−	0.999998i	$-0.500597\pi$
$331$	−0.0682694			−0.00375242			−0.00187621	+	0.999998i	$0.500597\pi$
$332$	17.7203	−	54.5375i	0.972529	−	2.99314i
$333$	−28.8904	+	20.9901i	−1.58319	+	1.15025i
$334$	−43.7645	−	31.7968i	−2.39469	−	1.73984i
$335$	0.851145	+	2.61956i	0.0465030	+	0.143122i
$336$	11.7564	+	36.1826i	0.641366	+	1.97392i
$337$	17.5930	+	12.7821i	0.958351	+	0.696283i	0.952767	−	0.303702i	$-0.0982226\pi$
$337$	17.5930	+	12.7821i	0.958351	+	0.696283i	0.00558394	+	0.999984i	$0.498223\pi$
$338$	−27.9854	+	20.3326i	−1.52221	+	1.10595i
$339$	5.13843	−	15.8145i	0.279081	−	0.858924i
$340$	11.4118			0.618892
$341$		0			0
$342$	−14.3328			−0.775028
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$	82.5145	−	59.9503i	4.44888	−	3.23230i
$345$	−4.62154	−	3.35775i	−0.248815	−	0.180775i
$346$	9.06048	+	27.8853i	0.487094	+	1.49912i
$347$	−7.39635	−	22.7636i	−0.397057	−	1.22202i	−0.927348	−	0.374200i	$-0.877917\pi$
$347$	−7.39635	−	22.7636i	−0.397057	−	1.22202i	0.530291	−	0.847816i	$-0.322083\pi$
$348$	23.9172	+	17.3769i	1.28210	+	0.931499i
$349$	−21.3702	+	15.5264i	−1.14392	+	0.831108i	−0.987661	−	0.156607i	$-0.949944\pi$
$349$	−21.3702	+	15.5264i	−1.14392	+	0.831108i	−0.156262	+	0.987716i	$0.549944\pi$
$350$	−4.01120	+	12.3452i	−0.214407	+	0.659878i
$351$	2.38021			0.127046
$352$		0			0
$353$	−4.44182			−0.236414			−0.118207	−	0.992989i	$-0.537715\pi$
$353$	−4.44182			−0.236414			−0.118207	+	0.992989i	$0.537715\pi$
$354$	−33.7662	+	103.922i	−1.79465	+	5.52337i
$355$	−2.13221	+	1.54914i	−0.113166	+	0.0822201i
$356$	22.3773	+	16.2581i	1.18600	+	0.861677i
$357$	−4.19090	−	12.8983i	−0.221806	−	0.682648i
$358$	−14.0740	−	43.3154i	−0.743836	−	2.28929i
$359$	−11.7571	−	8.54200i	−0.620514	−	0.450830i	0.232587	−	0.972576i	$-0.425281\pi$
$359$	−11.7571	−	8.54200i	−0.620514	−	0.450830i	−0.853101	+	0.521746i	$0.825281\pi$
$360$	−15.7103	+	11.4142i	−0.828004	+	0.601580i
$361$	−5.50658	+	16.9475i	−0.289820	+	0.891974i
$362$	54.8860			2.88475
$363$		0			0
$364$	2.39322			0.125439
$365$	−0.228000	+	0.701713i	−0.0119341	+	0.0367293i
$366$	30.2638	−	21.9879i	1.58191	−	1.14933i
$367$	−4.03019	−	2.92810i	−0.210374	−	0.152846i	0.477609	−	0.878573i	$-0.341504\pi$
$367$	−4.03019	−	2.92810i	−0.210374	−	0.152846i	−0.687983	+	0.725727i	$0.741504\pi$
$368$	19.1483	+	58.9325i	0.998175	+	3.07207i
$369$	−2.67044	−	8.21878i	−0.139018	−	0.427852i
$370$	−7.12219	−	5.17458i	−0.370265	−	0.269013i
$371$	−2.88998	+	2.09970i	−0.150041	+	0.109011i
$372$	−38.0218	+	117.019i	−1.97134	+	6.06715i
$373$	13.6638			0.707485			0.353743	−	0.935343i	$-0.384909\pi$
$373$	13.6638			0.707485			0.353743	+	0.935343i	$0.384909\pi$
$374$		0			0
$375$	−12.2465			−0.632408
$376$	−2.82507	+	8.69467i	−0.145692	+	0.448393i
$377$	0.723903	−	0.525946i	0.0372829	−	0.0270876i
$378$	11.5435	+	8.38687i	0.593735	+	0.431374i
$379$	−2.58410	−	7.95304i	−0.132736	−	0.408520i	0.862495	−	0.506066i	$-0.168901\pi$
$379$	−2.58410	−	7.95304i	−0.132736	−	0.408520i	−0.995231	+	0.0975457i	$0.968901\pi$
$380$	−0.793028	−	2.44069i	−0.0406815	−	0.125205i
$381$	−23.0143	−	16.7209i	−1.17906	−	0.856637i
$382$	5.56431	−	4.04271i	0.284695	−	0.206843i
$383$	−0.613952	+	1.88955i	−0.0313715	+	0.0965514i	−0.965516	−	0.260343i	$-0.916164\pi$
$383$	−0.613952	+	1.88955i	−0.0313715	+	0.0965514i	0.934145	+	0.356894i	$0.116164\pi$
$384$	73.7352			3.76278
$385$		0			0
$386$	47.3292			2.40899
$387$	17.2051	−	52.9517i	0.874582	−	2.69169i
$388$	22.7987	−	16.5642i	1.15743	−	0.840922i
$389$	−11.9998	−	8.71834i	−0.608412	−	0.442037i	0.240443	−	0.970663i	$-0.422707\pi$
$389$	−11.9998	−	8.71834i	−0.608412	−	0.442037i	−0.848855	+	0.528626i	$0.822707\pi$
$390$	0.470625	+	1.44843i	0.0238310	+	0.0733443i
$391$	−6.82593	−	21.0081i	−0.345202	−	1.06242i
$392$	7.23277	+	5.25492i	0.365310	+	0.265413i
$393$	15.5191	−	11.2753i	0.782835	−	0.568763i
$394$	−1.80898	+	5.56748i	−0.0911353	+	0.280486i
$395$	−1.60597			−0.0808050
$396$		0			0
$397$	11.4630			0.575314			0.287657	−	0.957734i	$-0.407124\pi$
$397$	11.4630			0.575314			0.287657	+	0.957734i	$0.407124\pi$
$398$	12.1755	−	37.4724i	0.610304	−	1.87832i
$399$	−2.46737	+	1.79265i	−0.123523	+	0.0897447i
$400$	52.6494	+	38.2520i	2.63247	+	1.91260i
$401$	1.33195	+	4.09934i	0.0665146	+	0.204711i	0.978790	−	0.204867i	$-0.0656761\pi$
$401$	1.33195	+	4.09934i	0.0665146	+	0.204711i	−0.912275	+	0.409578i	$0.865676\pi$
$402$	−14.5118	−	44.6629i	−0.723785	−	2.22758i
$403$	3.01284	+	2.18896i	0.150080	+	0.109040i
$404$	66.8112	−	48.5412i	3.32398	−	2.41501i
$405$	−0.0242828	+	0.0747349i	−0.00120662	+	0.00371361i
$406$	5.36399			0.266210
$407$		0			0
$408$	−121.247			−6.00263
$409$	2.87757	−	8.85626i	0.142287	−	0.437914i	−0.854365	−	0.519673i	$-0.826054\pi$
$409$	2.87757	−	8.85626i	0.142287	−	0.437914i	0.996652	+	0.0817591i	$0.0260538\pi$
$410$	1.72353	−	1.25222i	0.0851190	−	0.0618426i
$411$	32.8562	+	23.8714i	1.62067	+	1.17749i
$412$	−23.2415	−	71.5300i	−1.14503	−	3.52403i
$413$	4.44972	+	13.6948i	0.218956	+	0.673878i
$414$	48.7989	+	35.4545i	2.39834	+	1.74249i
$415$	3.89051	−	2.82662i	0.190977	−	0.138753i
$416$	2.61341	−	8.04326i	0.128133	−	0.394353i
$417$	−41.2535			−2.02019
$418$		0			0
$419$	−26.3424			−1.28691			−0.643454	−	0.765485i	$-0.722499\pi$
$419$	−26.3424			−1.28691			−0.643454	+	0.765485i	$0.722499\pi$
$420$	−2.04907	+	6.30638i	−0.0999842	+	0.307720i
$421$	−11.4712	+	8.33434i	−0.559074	+	0.406191i	−0.831120	−	0.556093i	$-0.812300\pi$
$421$	−11.4712	+	8.33434i	−0.559074	+	0.406191i	0.272046	+	0.962284i	$0.412300\pi$
$422$	7.93930	+	5.76824i	0.386479	+	0.280794i
$423$	1.54216	+	4.74629i	0.0749825	+	0.230772i
$424$	9.86887	+	30.3733i	0.479275	+	1.47506i
$425$	−18.7683	−	13.6360i	−0.910395	−	0.661441i
$426$	36.3538	−	26.4126i	1.76135	−	1.27969i
$427$	1.52335	−	4.68837i	0.0737198	−	0.226886i
$428$	62.3876			3.01562
$429$		0			0
$430$	13.7257			0.661911
$431$	−2.34708	+	7.22357i	−0.113055	+	0.347947i	−0.991536	−	0.129829i	$-0.958557\pi$
$431$	−2.34708	+	7.22357i	−0.113055	+	0.347947i	0.878482	+	0.477776i	$0.158557\pi$
$432$	57.8739	−	42.0478i	2.78446	−	2.02303i
$433$	−18.1227	−	13.1669i	−0.870920	−	0.632760i	0.0599138	−	0.998204i	$-0.480917\pi$
$433$	−18.1227	−	13.1669i	−0.870920	−	0.632760i	−0.930834	+	0.365443i	$0.880917\pi$
$434$	6.89869	+	21.2320i	0.331148	+	1.01917i
$435$	0.766117	+	2.35787i	0.0367325	+	0.113051i
$436$	67.7540	+	49.2261i	3.24483	+	2.35750i
$437$	−4.01873	+	2.91978i	−0.192242	+	0.139672i
$438$	3.88736	−	11.9641i	0.185745	−	0.571665i
$439$	−15.4051			−0.735244			−0.367622	−	0.929975i	$-0.619828\pi$
$439$	−15.4051			−0.735244			−0.367622	+	0.929975i	$0.619828\pi$
$440$		0			0
$441$	4.88032			0.232396
$442$	−1.81980	+	5.60078i	−0.0865593	+	0.266402i
$443$	−17.1592	+	12.4669i	−0.815258	+	0.592319i	−0.915350	−	0.402659i	$-0.868086\pi$
$443$	−17.1592	+	12.4669i	−0.815258	+	0.592319i	0.100092	+	0.994978i	$0.468086\pi$
$444$	88.1959	+	64.0781i	4.18559	+	3.04101i
$445$	0.716791	+	2.20606i	0.0339791	+	0.104577i
$446$	4.04353	+	12.4447i	0.191467	+	0.589274i
$447$	−2.27424	−	1.65233i	−0.107568	−	0.0781526i
$448$	19.0871	−	13.8676i	0.901779	−	0.655181i
$449$	−3.59438	+	11.0623i	−0.169629	+	0.522065i	−0.999348	−	0.0361175i	$-0.988501\pi$
$449$	−3.59438	+	11.0623i	−0.169629	+	0.522065i	0.829718	+	0.558182i	$0.188501\pi$
$450$	63.3490			2.98630
$451$		0			0
$452$	−31.4375			−1.47869
$453$	1.19311	−	3.67200i	0.0560570	−	0.172526i
$454$	−49.7103	+	36.1166i	−2.33302	+	1.69504i
$455$	0.162368	+	0.117967i	0.00761193	+	0.00553039i
$456$	8.42570	+	25.9316i	0.394570	+	1.21436i
$457$	−9.76419	−	30.0511i	−0.456750	−	1.40573i	−0.869069	−	0.494692i	$-0.835281\pi$
$457$	−9.76419	−	30.0511i	−0.456750	−	1.40573i	0.412319	−	0.911040i	$-0.364719\pi$
$458$	−49.5846	−	36.0253i	−2.31694	−	1.68335i
$459$	−20.6307	+	14.9891i	−0.962958	+	0.699630i
$460$	−3.33742	+	10.2715i	−0.155608	+	0.478912i
$461$	8.86324			0.412802			0.206401	−	0.978467i	$-0.433825\pi$
$461$	8.86324			0.412802			0.206401	+	0.978467i	$0.433825\pi$
$462$		0			0
$463$	−25.6132			−1.19035			−0.595173	−	0.803597i	$-0.702917\pi$
$463$	−25.6132			−1.19035			−0.595173	+	0.803597i	$0.702917\pi$
$464$	8.31025	−	25.5763i	0.385794	−	1.18735i
$465$	−8.34770	+	6.06496i	−0.387115	+	0.281256i
$466$	1.28435	+	0.933132i	0.0594962	+	0.0432265i
$467$	6.34726	+	19.5349i	0.293716	+	0.903966i	0.983650	+	0.180093i	$0.0576399\pi$
$467$	6.34726	+	19.5349i	0.293716	+	0.903966i	−0.689933	+	0.723873i	$0.742360\pi$
$468$	−3.60922	−	11.1081i	−0.166836	−	0.513470i
$469$	−5.00666	−	3.63755i	−0.231186	−	0.167967i
$470$	−0.995326	+	0.723147i	−0.0459110	+	0.0333563i
$471$	−4.66411	+	14.3547i	−0.214911	+	0.661428i
$472$	128.735			5.92551
$473$		0			0
$474$	27.3814			1.25767
$475$	−1.61213	+	4.96164i	−0.0739698	+	0.227656i
$476$	−20.7435	+	15.0710i	−0.950775	+	0.690779i
$477$	14.1040	+	10.2472i	0.645780	+	0.469187i
$478$	−12.5067	−	38.4917i	−0.572043	−	1.76057i
$479$	8.51303	+	26.2004i	0.388970	+	1.19713i	0.933559	+	0.358424i	$0.116686\pi$
$479$	8.51303	+	26.2004i	0.388970	+	1.19713i	−0.544588	+	0.838703i	$0.683314\pi$
$480$	18.9572	+	13.7732i	0.865273	+	0.628658i
$481$	2.66943	−	1.93945i	0.121715	−	0.0884314i
$482$	−15.2654	+	46.9821i	−0.695320	+	2.13998i
$483$	12.8351			0.584017
$484$		0			0
$485$	2.36327			0.107310
$486$	−12.8137	+	39.4365i	−0.581241	+	1.78888i
$487$	9.79018	−	7.11299i	0.443636	−	0.322320i	−0.343442	−	0.939174i	$-0.611593\pi$
$487$	9.79018	−	7.11299i	0.443636	−	0.322320i	0.787078	+	0.616854i	$0.211593\pi$
$488$	−35.6550	−	25.9049i	−1.61403	−	1.17266i
$489$	8.17601	+	25.1632i	0.369732	+	1.13792i
$490$	0.371784	+	1.14423i	0.0167955	+	0.0516912i
$491$	−31.8645	−	23.1509i	−1.43803	−	1.04479i	−0.988450	−	0.151546i	$-0.951575\pi$
$491$	−31.8645	−	23.1509i	−1.43803	−	1.04479i	−0.449576	−	0.893242i	$-0.648425\pi$
$492$	−21.3429	+	15.5065i	−0.962212	+	0.699088i
$493$	−2.96241	+	9.11736i	−0.133420	+	0.410625i
$494$	1.32432			0.0595842
$495$		0			0
$496$	111.925			5.02560
$497$	1.82989	−	5.63182i	0.0820818	−	0.252622i
$498$	−66.3323	+	48.1932i	−2.97242	+	2.15959i
$499$	28.1402	+	20.4451i	1.25973	+	0.915246i	0.998744	−	0.0500968i	$-0.0159530\pi$
$499$	28.1402	+	20.4451i	1.25973	+	0.915246i	0.260984	+	0.965343i	$0.415953\pi$
$500$	7.15475	+	22.0201i	0.319970	+	0.984768i
$501$	17.3597	+	53.4275i	0.775573	+	2.38697i
$502$	23.1047	+	16.7865i	1.03121	+	0.749220i
$503$	2.61494	−	1.89986i	0.116594	−	0.0847107i	−0.527960	−	0.849269i	$-0.677043\pi$
$503$	2.61494	−	1.89986i	0.116594	−	0.0847107i	0.644554	+	0.764558i	$0.277043\pi$
$504$	13.4827	−	41.4956i	0.600568	−	1.84836i
$505$	6.92550			0.308181
$506$		0			0
$507$	35.9227			1.59538
$508$	−16.6197	+	51.1501i	−0.737378	+	2.26942i
$509$	10.6966	−	7.77152i	0.474118	−	0.344467i	−0.324926	−	0.945739i	$-0.605339\pi$
$509$	10.6966	−	7.77152i	0.474118	−	0.344467i	0.799044	+	0.601273i	$0.205339\pi$
$510$	−13.2005	−	9.59072i	−0.584528	−	0.424684i
$511$	−0.512277	−	1.57663i	−0.0226618	−	0.0697459i
$512$	−3.66221	−	11.2711i	−0.161848	−	0.498118i
$513$	4.63944	+	3.37075i	0.204836	+	0.148822i
$514$	−42.5751	+	30.9326i	−1.87791	+	1.36438i
$515$	1.94905	−	5.99857i	0.0858856	−	0.264329i
$516$	−169.969			−7.48245
$517$		0			0
$518$	19.7800			0.869082
$519$	9.40905	−	28.9581i	0.413011	−	1.27112i
$520$	1.45160	−	1.05465i	0.0636569	−	0.0462495i
$521$	−5.90776	−	4.29224i	−0.258824	−	0.188046i	0.450805	−	0.892623i	$-0.351137\pi$
$521$	−5.90776	−	4.29224i	−0.258824	−	0.188046i	−0.709628	+	0.704576i	$0.751137\pi$
$522$	−8.08944	−	24.8967i	−0.354065	−	1.08970i
$523$	−2.58958	−	7.96992i	−0.113235	−	0.348500i	0.878340	−	0.478036i	$-0.158651\pi$
$523$	−2.58958	−	7.96992i	−0.113235	−	0.348500i	−0.991575	+	0.129536i	$0.958651\pi$
$524$	−29.3404	−	21.3170i	−1.28174	−	0.931239i
$525$	10.9055	−	7.92327i	0.475953	−	0.345800i
$526$	17.6995	−	54.4733i	0.771733	−	2.37515i
$527$	−39.8988			−1.73802
$528$		0			0
$529$	−2.09483			−0.0910794
$530$	−1.32809	+	4.08745i	−0.0576887	+	0.177547i
$531$	56.8533	−	41.3064i	2.46722	−	1.79254i
$532$	4.66481	+	3.38918i	0.202245	+	0.146940i
$533$	0.246744	+	0.759401i	0.0106877	+	0.0328933i
$534$	−12.2211	−	37.6128i	−0.528860	−	1.62766i
$535$	4.23268	+	3.07522i	0.182995	+	0.132953i
$536$	−44.7606	+	32.5205i	−1.93336	+	1.40467i
$537$	−14.6155	+	44.9818i	−0.630704	+	1.94111i
$538$	−62.5963			−2.69872
$539$		0			0
$540$	12.4682			0.536548
$541$	1.17355	−	3.61181i	0.0504547	−	0.155284i	−0.922655	−	0.385627i	$-0.873985\pi$
$541$	1.17355	−	3.61181i	0.0504547	−	0.155284i	0.973109	+	0.230344i	$0.0739850\pi$
$542$	−58.6605	+	42.6193i	−2.51968	+	1.83066i
$543$	−46.1120	−	33.5023i	−1.97886	−	1.43772i
$544$	27.9994	+	86.1733i	1.20046	+	3.69465i
$545$	2.17030	+	6.67948i	0.0929653	+	0.286118i
$546$	−2.76834	−	2.01132i	−0.118474	−	0.0860764i
$547$	7.35384	−	5.34288i	0.314428	−	0.228445i	−0.419366	−	0.907817i	$-0.637748\pi$
$547$	7.35384	−	5.34288i	0.314428	−	0.228445i	0.733794	+	0.679372i	$0.237748\pi$
$548$	23.7269	−	73.0238i	1.01356	−	3.11942i
$549$	−24.0583			−1.02678
$550$		0			0
$551$	2.15583			0.0918416
$552$	35.4591	−	109.132i	1.50924	−	4.64497i
$553$	2.91920	−	2.12092i	0.124137	−	0.0901909i
$554$	30.7281	+	22.3253i	1.30551	+	0.948510i
$555$	2.82509	+	8.69474i	0.119919	+	0.369071i
$556$	24.1014	+	74.1766i	1.02213	+	3.14579i
$557$	14.7542	+	10.7196i	0.625156	+	0.454203i	0.854719	−	0.519091i	$-0.173730\pi$
$557$	14.7542	+	10.7196i	0.625156	+	0.454203i	−0.229563	+	0.973294i	$0.573730\pi$
$558$	88.1435	−	64.0400i	3.73141	−	2.71103i
$559$	−1.58972	+	4.89265i	−0.0672379	+	0.206937i
$560$	6.03187			0.254893
$561$		0			0
$562$	−4.71809			−0.199021
$563$	4.81276	−	14.8122i	0.202834	−	0.624258i	−0.796962	−	0.604030i	$-0.793561\pi$
$563$	4.81276	−	14.8122i	0.202834	−	0.624258i	0.999795	−	0.0202283i	$-0.00643930\pi$
$564$	12.3254	−	8.95491i	0.518992	−	0.377070i
$565$	−2.13287	−	1.54962i	−0.0897306	−	0.0651931i
$566$	−3.89709	−	11.9940i	−0.163807	−	0.504145i
$567$	−0.0545593	−	0.167916i	−0.00229128	−	0.00705182i
$568$	−42.8299	−	31.1178i	−1.79710	−	1.30567i
$569$	19.7606	−	14.3569i	0.828407	−	0.601873i	−0.0907010	−	0.995878i	$-0.528911\pi$
$569$	19.7606	−	14.3569i	0.828407	−	0.601873i	0.919108	+	0.394005i	$0.128911\pi$
$570$	−1.13388	+	3.48972i	−0.0474930	+	0.146168i
$571$	14.9541			0.625808			0.312904	−	0.949785i	$-0.398698\pi$
$571$	14.9541			0.625808			0.312904	+	0.949785i	$0.398698\pi$
$572$		0			0
$573$	−7.14247			−0.298381
$574$	−1.47915	+	4.55236i	−0.0617386	+	0.190012i
$575$	17.7623	−	12.9050i	0.740738	−	0.538178i
$576$	−93.1510	−	67.6781i	−3.88129	−	2.81992i
$577$	−6.63405	−	20.4175i	−0.276179	−	0.849991i	−0.988905	−	0.148549i	$-0.952540\pi$
$577$	−6.63405	−	20.4175i	−0.276179	−	0.849991i	0.712726	−	0.701442i	$-0.247460\pi$
$578$	−5.29622	−	16.3001i	−0.220294	−	0.677994i
$579$	−39.7632	−	28.8896i	−1.65250	−	1.20061i
$580$	3.79201	−	2.75506i	0.157455	−	0.114398i
$581$	−3.33888	+	10.2760i	−0.138520	+	0.426320i
$582$	−40.2932			−1.67021
$583$		0			0
$584$	−14.8207			−0.613286
$585$	0.302673	−	0.931531i	0.0125140	−	0.0385141i
$586$	−31.7307	+	23.0537i	−1.31078	+	0.952338i
$587$	16.7273	+	12.1531i	0.690408	+	0.501611i	0.876794	−	0.480866i	$-0.159678\pi$
$587$	16.7273	+	12.1531i	0.690408	+	0.501611i	−0.186386	+	0.982477i	$0.559678\pi$
$588$	−4.60389	−	14.1693i	−0.189861	−	0.584333i
$589$	2.77264	+	8.53332i	0.114245	+	0.351609i
$590$	14.0157	+	10.1830i	0.577018	+	0.419228i
$591$	4.91818	−	3.57327i	0.202307	−	0.146985i
$592$	30.6445	−	94.3139i	1.25948	−	3.87628i
$593$	−3.30237			−0.135612			−0.0678060	−	0.997699i	$-0.521600\pi$
$593$	−3.30237			−0.135612			−0.0678060	+	0.997699i	$0.521600\pi$
$594$		0			0
$595$	−2.15022			−0.0881505
$596$	−1.64233	+	5.05457i	−0.0672724	+	0.207043i
$597$	−33.1022	+	24.0502i	−1.35478	+	0.984308i
$598$	−4.50894	−	3.27594i	−0.184384	−	0.133963i
$599$	12.0273	+	37.0163i	0.491423	+	1.51245i	0.822457	+	0.568827i	$0.192602\pi$
$599$	12.0273	+	37.0163i	0.491423	+	1.51245i	−0.331034	+	0.943619i	$0.607398\pi$
$600$	−37.2405	−	114.614i	−1.52034	−	4.67912i
$601$	35.9028	+	26.0849i	1.46451	+	1.06403i	0.982160	+	0.188045i	$0.0602151\pi$
$601$	35.9028	+	26.0849i	1.46451	+	1.06403i	0.482346	+	0.875981i	$0.339785\pi$
$602$	−24.9494	+	18.1268i	−1.01686	+	0.738794i
$603$	−9.33300	+	28.7240i	−0.380069	+	1.16973i
$604$	−7.29954			−0.297014
$605$		0			0
$606$	−118.078			−4.79660
$607$	5.84223	−	17.9805i	0.237129	−	0.729808i	−0.759703	−	0.650270i	$-0.774656\pi$
$607$	5.84223	−	17.9805i	0.237129	−	0.729808i	0.996832	−	0.0795376i	$-0.0253444\pi$
$608$	16.4845	−	11.9767i	0.668535	−	0.485719i
$609$	−4.50651	−	3.27417i	−0.182613	−	0.132676i
$610$	−1.83276	−	5.64067i	−0.0742064	−	0.228384i
$611$	−0.142493	−	0.438549i	−0.00576466	−	0.0177418i
$612$	101.235	+	73.5514i	4.09217	+	2.97314i
$613$	−7.83222	+	5.69044i	−0.316341	+	0.229835i	−0.734612	−	0.678487i	$-0.762636\pi$
$613$	−7.83222	+	5.69044i	−0.316341	+	0.229835i	0.418272	+	0.908322i	$0.362636\pi$
$614$	1.96871	−	6.05906i	0.0794506	−	0.244524i
$615$	−2.21236			−0.0892108
$616$		0			0
$617$	−26.2775			−1.05789			−0.528947	−	0.848655i	$-0.677413\pi$
$617$	−26.2775			−1.05789			−0.528947	+	0.848655i	$0.677413\pi$
$618$	−33.2309	+	102.274i	−1.33674	+	4.11408i
$619$	20.0599	−	14.5744i	0.806275	−	0.585793i	−0.106474	−	0.994316i	$-0.533956\pi$
$619$	20.0599	−	14.5744i	0.806275	−	0.585793i	0.912748	+	0.408523i	$0.133956\pi$
$620$	15.7821	+	11.4664i	0.633826	+	0.460502i
$621$	−7.45783	−	22.9529i	−0.299273	−	0.921066i
$622$	16.7108	+	51.4307i	0.670044	+	2.06218i
$623$	−4.21636	−	3.06336i	−0.168925	−	0.122731i
$624$	−13.8792	+	10.0838i	−0.555611	+	0.403675i
$625$	6.81936	−	20.9878i	0.272774	−	0.839513i
$626$	−50.6931			−2.02611
$627$		0			0
$628$	28.5355			1.13869
$629$	−10.9240	+	33.6207i	−0.435570	+	1.34055i
$630$	4.75022	−	3.45124i	0.189253	−	0.137501i
$631$	9.55509	+	6.94218i	0.380382	+	0.276364i	0.761503	−	0.648161i	$-0.224462\pi$
$631$	9.55509	+	6.94218i	0.380382	+	0.276364i	−0.381121	+	0.924525i	$0.624462\pi$
$632$	−9.96864	−	30.6803i	−0.396531	−	1.22040i
$633$	−3.14921	−	9.69227i	−0.125170	−	0.385233i
$634$	9.18955	+	6.67660i	0.364964	+	0.265162i
$635$	−3.64886	+	2.65105i	−0.144801	+	0.105204i
$636$	16.4461	−	50.6159i	0.652131	−	2.00705i
$637$	−0.450933			−0.0178666
$638$		0			0
$639$	−28.8995			−1.14325
$640$	3.61257	−	11.1183i	0.142799	−	0.439491i
$641$	18.2176	−	13.2359i	0.719553	−	0.522786i	−0.166688	−	0.986010i	$-0.553307\pi$
$641$	18.2176	−	13.2359i	0.719553	−	0.522786i	0.886241	+	0.463224i	$0.153307\pi$
$642$	−72.1662	−	52.4318i	−2.84817	−	2.06932i
$643$	4.29229	+	13.2103i	0.169271	+	0.520964i	0.999326	−	0.0367187i	$-0.0116906\pi$
$643$	4.29229	+	13.2103i	0.169271	+	0.520964i	−0.830054	+	0.557683i	$0.811691\pi$
$644$	−7.49860	−	23.0783i	−0.295486	−	0.909413i
$645$	−11.5315	−	8.37812i	−0.454052	−	0.329888i
$646$	−11.4787	+	8.33976i	−0.451623	+	0.328124i
$647$	15.7016	−	48.3247i	0.617295	−	1.89984i	0.262161	−	0.965024i	$-0.415565\pi$
$647$	15.7016	−	48.3247i	0.617295	−	1.89984i	0.355134	−	0.934815i	$-0.384435\pi$
$648$	−1.57846			−0.0620078
$649$		0			0
$650$	−5.85334			−0.229587
$651$	7.16409	−	22.0488i	0.280783	−	0.864161i
$652$	40.4684	−	29.4020i	1.58486	−	1.15147i
$653$	3.89470	+	2.82966i	0.152411	+	0.110733i	0.661377	−	0.750053i	$-0.269972\pi$
$653$	3.89470	+	2.82966i	0.152411	+	0.110733i	−0.508966	+	0.860787i	$0.669972\pi$
$654$	−37.0031	−	113.884i	−1.44693	−	4.45321i
$655$	−0.939831	−	2.89250i	−0.0367222	−	0.113019i
$656$	19.4147	+	14.1056i	0.758019	+	0.550733i
$657$	−6.54528	+	4.75543i	−0.255356	+	0.185527i
$658$	0.854200	−	2.62896i	0.0333002	−	0.102487i
$659$	28.0409			1.09232			0.546159	−	0.837681i	$-0.316089\pi$
$659$	28.0409			1.09232			0.546159	+	0.837681i	$0.316089\pi$
$660$		0			0
$661$	−41.7390			−1.62346			−0.811730	−	0.584033i	$-0.801474\pi$
$661$	−41.7390			−1.62346			−0.811730	+	0.584033i	$0.801474\pi$
$662$	0.0570277	−	0.175513i	0.00221644	−	0.00682151i
$663$	4.94760	−	3.59464i	0.192149	−	0.139604i
$664$	78.1489	+	56.7785i	3.03276	+	2.20343i
$665$	0.149423	+	0.459877i	0.00579438	+	0.0178333i
$666$	−29.8302	−	91.8079i	−1.15590	−	3.55748i
$667$	−7.33998	−	5.33281i	−0.284205	−	0.206487i
$668$	85.9243	−	62.4276i	3.32451	−	2.41540i
$669$	4.19909	−	12.9235i	0.162346	−	0.499650i
$670$	−7.44559			−0.287648
$671$		0			0
$672$	−52.6484			−2.03096
$673$	8.89187	−	27.3664i	0.342757	−	1.05490i	−0.620017	−	0.784588i	$-0.712874\pi$
$673$	8.89187	−	27.3664i	0.342757	−	1.05490i	0.962774	−	0.270308i	$-0.0871256\pi$
$674$	−47.5573	+	34.5524i	−1.83184	+	1.33091i
$675$	−20.5057	−	14.8983i	−0.789266	−	0.573435i
$676$	−20.9870	−	64.5913i	−0.807192	−	2.48428i
$677$	3.79663	+	11.6848i	0.145916	+	0.449085i	0.997128	−	0.0757386i	$-0.0241315\pi$
$677$	3.79663	+	11.6848i	0.145916	+	0.449085i	−0.851211	+	0.524823i	$0.824131\pi$
$678$	36.3650	+	26.4207i	1.39659	+	1.01468i
$679$	−4.29576	+	3.12105i	−0.164856	+	0.119775i
$680$	−5.94036	+	18.2825i	−0.227802	+	0.701104i
$681$	63.8092			2.44517
$682$		0			0
$683$	30.5940			1.17065			0.585323	−	0.810800i	$-0.300968\pi$
$683$	30.5940			1.17065			0.585323	+	0.810800i	$0.300968\pi$
$684$	8.69574	−	26.7627i	0.332490	−	1.02330i
$685$	5.20925	−	3.78474i	0.199035	−	0.144608i
$686$	−2.18693	−	1.58890i	−0.0834974	−	0.0606644i
$687$	19.6683	+	60.5327i	0.750391	+	2.30947i
$688$	47.7782	+	147.046i	1.82153	+	5.60608i
$689$	−1.30319	−	0.946823i	−0.0496476	−	0.0360711i
$690$	12.4929	−	9.07665i	0.475598	−	0.345542i
$691$	−5.28794	+	16.2746i	−0.201163	+	0.619115i	0.798687	+	0.601747i	$0.205529\pi$
$691$	−5.28794	+	16.2746i	−0.201163	+	0.619115i	−0.999849	+	0.0173677i	$0.994471\pi$
$692$	−57.5655			−2.18831
$693$		0			0
$694$	64.7013			2.45603
$695$	−2.02117	+	6.22051i	−0.0766672	+	0.235957i
$696$	−40.2890	+	29.2717i	−1.52715	+	1.10954i
$697$	−6.92090	−	5.02833i	−0.262148	−	0.190462i
$698$	−22.0654	−	67.9103i	−0.835187	−	2.57044i
$699$	−0.509450	−	1.56792i	−0.0192692	−	0.0593044i
$700$	−20.6178	−	14.9797i	−0.779280	−	0.566180i
$701$	10.9975	−	7.99012i	0.415368	−	0.301783i	−0.360403	−	0.932797i	$-0.617361\pi$
$701$	10.9975	−	7.99012i	0.415368	−	0.301783i	0.775771	+	0.631014i	$0.217361\pi$
$702$	−1.98827	+	6.11927i	−0.0750425	+	0.230957i
$703$	7.94974			0.299830
$704$		0			0
$705$	1.27762			0.0481180
$706$	3.71040	−	11.4194i	0.139643	−	0.429776i
$707$	−12.5886	+	9.14616i	−0.473444	+	0.343977i
$708$	−173.560	−	126.099i	−6.52280	−	4.73909i
$709$	9.14675	+	28.1508i	0.343513	+	1.05723i	0.962375	+	0.271725i	$0.0875942\pi$
$709$	9.14675	+	28.1508i	0.343513	+	1.05723i	−0.618861	+	0.785500i	$0.712406\pi$
$710$	−2.20157	−	6.77575i	−0.0826236	−	0.254289i
$711$	−14.2466	−	10.3508i	−0.534291	−	0.388185i
$712$	−37.6950	+	27.3871i	−1.41268	+	1.02637i
$713$	11.6685	−	35.9120i	0.436990	−	1.34492i
$714$	36.6608			1.37200
$715$		0			0
$716$	89.4190			3.34174
$717$	−12.9879	+	39.9725i	−0.485040	+	1.49280i
$718$	31.7816	−	23.0907i	1.18608	−	0.861737i
$719$	−36.8432	−	26.7681i	−1.37402	−	0.998283i	−0.997411	−	0.0719100i	$-0.977091\pi$
$719$	−36.8432	−	26.7681i	−1.37402	−	0.998283i	−0.376608	−	0.926373i	$-0.622909\pi$
$720$	−9.09668	−	27.9967i	−0.339013	−	1.04337i
$721$	4.37918	+	13.4777i	0.163089	+	0.501937i
$722$	−38.9704	−	28.3136i	−1.45033	−	1.05372i
$723$	41.5029	−	30.1536i	1.54351	−	1.12142i
$724$	−33.2995	+	102.485i	−1.23757	+	3.80884i
$725$	−9.52850			−0.353880
$726$		0			0
$727$	−43.8796			−1.62740			−0.813702	−	0.581283i	$-0.802551\pi$
$727$	−43.8796			−1.62740			−0.813702	+	0.581283i	$0.802551\pi$
$728$	−1.24578	+	3.83412i	−0.0461717	+	0.142102i
$729$	35.2658	−	25.6221i	1.30614	−	0.948966i
$730$	−1.61357	−	1.17233i	−0.0597210	−	0.0433898i
$731$	−17.0318	−	52.4185i	−0.629944	−	1.93877i
$732$	22.6956	+	69.8498i	0.838853	+	2.58172i
$733$	11.3973	+	8.28060i	0.420968	+	0.305851i	0.778027	−	0.628231i	$-0.216221\pi$
$733$	11.3973	+	8.28060i	0.420968	+	0.305851i	−0.357059	+	0.934082i	$0.616221\pi$
$734$	10.8944	−	7.91523i	0.402119	−	0.292157i
$735$	0.386087	−	1.18825i	0.0142410	−	0.0438294i
$736$	−85.7513			−3.16083
$737$		0			0
$738$	23.3603			0.859904
$739$	12.2054	−	37.5644i	0.448983	−	1.38183i	−0.429073	−	0.903270i	$-0.641160\pi$
$739$	12.2054	−	37.5644i	0.448983	−	1.38183i	0.878056	−	0.478558i	$-0.158840\pi$
$740$	13.9832	−	10.1594i	0.514033	−	0.373467i
$741$	−1.11262	−	0.808365i	−0.0408731	−	0.0296960i
$742$	−2.98399	−	9.18379i	−0.109546	−	0.337147i
$743$	−5.75272	−	17.7051i	−0.211047	−	0.649535i	−0.999411	−	0.0343261i	$-0.989072\pi$
$743$	−5.75272	−	17.7051i	−0.211047	−	0.649535i	0.788364	−	0.615209i	$-0.210928\pi$
$744$	−167.681	−	121.827i	−6.14748	−	4.46640i
$745$	−0.360574	+	0.261973i	−0.0132104	+	0.00959794i
$746$	−11.4138	+	35.1282i	−0.417890	+	1.28613i
$747$	52.7310			1.92933
$748$		0			0
$749$	−11.7551			−0.429523
$750$	10.2299	−	31.4845i	0.373545	−	1.14965i
$751$	12.7873	−	9.29052i	0.466615	−	0.339016i	−0.329505	−	0.944154i	$-0.606882\pi$
$751$	12.7873	−	9.29052i	0.466615	−	0.339016i	0.796121	+	0.605138i	$0.206882\pi$
$752$	−11.2119	−	8.14591i	−0.408855	−	0.297051i
$753$	−9.16472	−	28.2061i	−0.333981	−	1.02789i
$754$	0.747451	+	2.30042i	0.0272205	+	0.0837762i
$755$	−0.495237	−	0.359810i	−0.0180235	−	0.0130948i
$756$	−22.6638	+	16.4662i	−0.824273	+	0.598870i
$757$	−1.11590	+	3.43438i	−0.0405579	+	0.124825i	−0.969285	−	0.245939i	$-0.920904\pi$
$757$	−1.11590	+	3.43438i	−0.0405579	+	0.124825i	0.928727	+	0.370763i	$0.120904\pi$
$758$	22.6050			0.821051
$759$		0			0
$760$	4.32297			0.156811
$761$	−12.2315	+	37.6446i	−0.443391	+	1.36462i	0.440848	+	0.897582i	$0.354678\pi$
$761$	−12.2315	+	37.6446i	−0.443391	+	1.36462i	−0.884239	+	0.467035i	$0.845322\pi$
$762$	62.2123	−	45.1998i	2.25371	−	1.63742i
$763$	−12.7663	−	9.27523i	−0.462170	−	0.335786i
$764$	4.17282	+	12.8426i	0.150967	+	0.464630i
$765$	3.24275	+	9.98017i	0.117242	+	0.360834i
$766$	−4.34497	−	3.15681i	−0.156990	−	0.114060i
$767$	−5.25315	+	3.81664i	−0.189680	+	0.137811i
$768$	−20.6612	+	63.5888i	−0.745548	+	2.29456i
$769$	10.5472			0.380341			0.190171	−	0.981751i	$-0.439096\pi$
$769$	10.5472			0.380341			0.190171	+	0.981751i	$0.439096\pi$
$770$		0			0
$771$	54.6503			1.96818
$772$	−28.7147	+	88.3749i	−1.03347	+	3.18068i
$773$	−33.6253	+	24.4302i	−1.20942	+	0.878694i	−0.995178	−	0.0980867i	$-0.968728\pi$
$773$	−33.6253	+	24.4302i	−1.20942	+	0.878694i	−0.214241	+	0.976781i	$0.568728\pi$
$774$	121.761	+	88.4647i	4.37662	+	3.17980i
$775$	−12.2547	−	37.7161i	−0.440202	−	1.35480i
$776$	14.6694	+	45.1477i	0.526600	+	1.62071i
$777$	−16.6180	−	12.0736i	−0.596166	−	0.433140i
$778$	32.4377	−	23.5674i	1.16295	−	0.844932i
$779$	−0.594483	+	1.82963i	−0.0212996	+	0.0655534i
$780$	−2.99010			−0.107063
$781$		0			0
$782$	59.7114			2.13527
$783$	−3.23665	+	9.96139i	−0.115669	+	0.355991i
$784$	−10.9643	+	7.96600i	−0.391581	+	0.284500i
$785$	1.93599	+	1.40658i	0.0690984	+	0.0502029i
$786$	16.0239	+	49.3165i	0.571554	+	1.75906i
$787$	−3.56834	−	10.9822i	−0.127198	−	0.391474i	0.867097	−	0.498139i	$-0.165983\pi$
$787$	−3.56834	−	10.9822i	−0.127198	−	0.391474i	−0.994295	+	0.106665i	$0.965983\pi$
$788$	−9.29830	−	6.75561i	−0.331238	−	0.240659i
$789$	−48.1204	+	34.9616i	−1.71313	+	1.24466i
$790$	1.34152	−	4.12877i	0.0477291	−	0.146895i
$791$	5.92347			0.210614
$792$		0			0
$793$	2.22294			0.0789390
$794$	−9.57547	+	29.4703i	−0.339821	+	1.04586i
$795$	3.61075	−	2.62337i	0.128060	−	0.0930412i
$796$	62.5830	+	45.4692i	2.21820	+	1.61161i
$797$	13.0762	+	40.2445i	0.463183	+	1.42553i	0.861253	+	0.508177i	$0.169680\pi$
$797$	13.0762	+	40.2445i	0.463183	+	1.42553i	−0.398069	+	0.917355i	$0.630320\pi$
$798$	−2.54763	−	7.84080i	−0.0901852	−	0.277561i
$799$	3.99678	+	2.90383i	0.141396	+	0.102730i
$800$	−72.8594	+	52.9354i	−2.57597	+	1.87155i
$801$	−7.85978	+	24.1899i	−0.277712	+	0.854708i
$802$	−11.6516			−0.411431
$803$		0			0
$804$	92.2006			3.25167
$805$	0.628839	−	1.93537i	0.0221637	−	0.0682128i
$806$	−8.14431	+	5.91719i	−0.286871	+	0.208424i
$807$	52.5897	+	38.2086i	1.85124	+	1.34501i
$808$	42.9883	+	132.304i	1.51232	+	4.65445i
$809$	5.55657	+	17.1014i	0.195359	+	0.601252i	0.999972	+	0.00745333i	$0.00237249\pi$
$809$	5.55657	+	17.1014i	0.195359	+	0.601252i	−0.804614	+	0.593799i	$0.797628\pi$
$810$	−0.171851	−	0.124857i	−0.00603823	−	0.00438703i
$811$	25.1766	−	18.2919i	0.884071	−	0.642315i	−0.0502542	−	0.998736i	$-0.516003\pi$
$811$	25.1766	−	18.2919i	0.884071	−	0.642315i	0.934325	+	0.356421i	$0.116003\pi$
$812$	−3.25435	+	10.0158i	−0.114205	+	0.351487i
$813$	75.2978			2.64081
$814$		0			0
$815$	4.19486			0.146940
$816$	56.7974	−	174.804i	1.98831	−	6.11938i
$817$	−10.0274	+	7.28533i	−0.350814	+	0.254881i
$818$	20.3648	+	14.7959i	0.712037	+	0.517325i
$819$	0.680053	+	2.09299i	0.0237630	+	0.0731349i
$820$	1.29252	+	3.97796i	0.0451367	+	0.138916i
$821$	39.5346	+	28.7236i	1.37977	+	1.00246i	0.996902	+	0.0786568i	$0.0250631\pi$
$821$	39.5346	+	28.7236i	1.37977	+	1.00246i	0.382867	+	0.923804i	$0.374937\pi$
$822$	−88.8166	+	64.5291i	−3.09784	+	2.25071i
$823$	9.14138	−	28.1343i	0.318649	−	0.980700i	−0.655578	−	0.755128i	$-0.727575\pi$
$823$	9.14138	−	28.1343i	0.318649	−	0.980700i	0.974226	−	0.225572i	$-0.0724251\pi$
$824$	126.695			4.41361
$825$		0			0
$826$	−38.9249			−1.35437
$827$	−7.84669	+	24.1496i	−0.272856	+	0.839764i	0.716923	+	0.697153i	$0.245550\pi$
$827$	−7.84669	+	24.1496i	−0.272856	+	0.839764i	−0.989779	+	0.142612i	$0.954450\pi$
$828$	−95.8085	+	69.6089i	−3.32957	+	2.41908i
$829$	−5.74063	−	4.17081i	−0.199380	−	0.144858i	0.483616	−	0.875281i	$-0.339323\pi$
$829$	−5.74063	−	4.17081i	−0.199380	−	0.144858i	−0.682996	+	0.730422i	$0.739323\pi$
$830$	4.01706	+	12.3632i	0.139434	+	0.429134i
$831$	−12.1886	−	37.5127i	−0.422819	−	1.30130i
$832$	8.60699	+	6.25334i	0.298394	+	0.216796i
$833$	3.90850	−	2.83969i	0.135422	−	0.0983895i
$834$	34.4605	−	106.058i	1.19327	−	3.67250i
$835$	8.90671			0.308230
$836$		0			0
$837$	−43.5923			−1.50677
$838$	22.0047	−	67.7234i	0.760138	−	2.33946i
$839$	19.1967	−	13.9472i	0.662745	−	0.481512i	−0.204844	−	0.978795i	$-0.565669\pi$
$839$	19.1967	−	13.9472i	0.662745	−	0.481512i	0.867589	+	0.497283i	$0.165669\pi$
$840$	−9.03664	−	6.56551i	−0.311794	−	0.226531i
$841$	−7.74474	−	23.8359i	−0.267060	−	0.821926i
$842$	−11.8444	−	36.4532i	−0.408184	−	1.25626i
$843$	3.96386	+	2.87991i	0.136523	+	0.0991895i
$844$	−15.5875	+	11.3250i	−0.536543	+	0.389821i
$845$	1.75999	−	5.41668i	0.0605454	−	0.186340i
$846$	−13.4904			−0.463810
$847$		0			0
$848$	−48.4127			−1.66250
$849$	−4.04701	+	12.4554i	−0.138893	+	0.427469i
$850$	50.7343	−	36.8606i	1.74017	−	1.26431i
$851$	−27.0665	−	19.6650i	−0.927829	−	0.674107i
$852$	27.2627	+	83.9058i	0.934003	+	2.87457i
$853$	11.9448	+	36.7624i	0.408983	+	1.25872i	0.917524	+	0.397681i	$0.130185\pi$
$853$	11.9448	+	36.7624i	0.408983	+	1.25872i	−0.508541	+	0.861038i	$0.669815\pi$
$854$	10.7808	+	7.83271i	0.368912	+	0.268030i
$855$	1.90915	−	1.38708i	0.0652917	−	0.0474372i
$856$	−32.4755	+	99.9495i	−1.10999	+	3.41620i
$857$	−34.0838			−1.16428			−0.582139	−	0.813089i	$-0.697784\pi$
$857$	−34.0838			−1.16428			−0.582139	+	0.813089i	$0.697784\pi$
$858$		0			0
$859$	56.7283			1.93555			0.967773	−	0.251825i	$-0.0810308\pi$
$859$	56.7283			1.93555			0.967773	+	0.251825i	$0.0810308\pi$
$860$	−8.32740	+	25.6291i	−0.283962	+	0.873945i
$861$	4.02144	−	2.92175i	0.137050	−	0.0995730i
$862$	−16.6104	−	12.0682i	−0.565753	−	0.411044i
$863$	7.53784	+	23.1991i	0.256591	+	0.789706i	0.993512	+	0.113727i	$0.0362790\pi$
$863$	7.53784	+	23.1991i	0.256591	+	0.789706i	−0.736921	+	0.675979i	$0.763721\pi$
$864$	30.5914	+	94.1507i	1.04074	+	3.20307i
$865$	−3.90553	−	2.83753i	−0.132792	−	0.0964789i
$866$	48.9891	−	35.5927i	1.66472	−	1.20949i
$867$	−5.49997	+	16.9272i	−0.186789	+	0.574876i
$868$	−43.8306			−1.48771
$869$		0			0
$870$	−6.70178			−0.227212
$871$	0.862354	−	2.65405i	0.0292197	−	0.0899291i
$872$	−114.133	+	82.9224i	−3.86503	+	2.80811i
$873$	20.9647	+	15.2317i	0.709546	+	0.515515i
$874$	−4.14946	−	12.7707i	−0.140358	−	0.431976i
$875$	−1.34810	−	4.14904i	−0.0455743	−	0.140263i
$876$	19.9813	+	14.5172i	0.675105	+	0.490492i
$877$	24.6710	−	17.9245i	0.833080	−	0.605268i	−0.0873493	−	0.996178i	$-0.527840\pi$
$877$	24.6710	−	17.9245i	0.833080	−	0.605268i	0.920429	+	0.390910i	$0.127840\pi$
$878$	12.8684	−	39.6048i	0.434286	−	1.33660i
$879$	40.7301			1.37379
$880$		0			0
$881$	2.10056			0.0707697			0.0353848	−	0.999374i	$-0.488734\pi$
$881$	2.10056			0.0707697			0.0353848	+	0.999374i	$0.488734\pi$
$882$	−4.07669	+	12.5468i	−0.137269	+	0.422472i
$883$	−36.5639	+	26.5653i	−1.23047	+	0.893992i	−0.996926	−	0.0783529i	$-0.975034\pi$
$883$	−36.5639	+	26.5653i	−1.23047	+	0.893992i	−0.233549	+	0.972345i	$0.575034\pi$
$884$	−9.35392	−	6.79602i	−0.314606	−	0.228575i
$885$	−5.55949	−	17.1103i	−0.186880	−	0.575158i
$886$	−17.7174	−	54.5284i	−0.595226	−	1.83192i
$887$	4.19684	+	3.04919i	0.140916	+	0.102382i	0.656010	−	0.754752i	$-0.272243\pi$
$887$	4.19684	+	3.04919i	0.140916	+	0.102382i	−0.515094	+	0.857134i	$0.672243\pi$
$888$	−148.568	+	107.941i	−4.98561	+	3.62226i
$889$	3.13149	−	9.63774i	0.105027	−	0.323239i
$890$	−6.27029			−0.210181
$891$		0			0
$892$	−25.6905			−0.860181
$893$	0.343310	−	1.05660i	0.0114884	−	0.0353578i
$894$	6.14772	−	4.46658i	0.205610	−	0.149385i
$895$	6.06662	+	4.40766i	0.202785	+	0.147332i
$896$	8.11681	+	24.9810i	0.271164	+	0.834556i
$897$	1.78852	+	5.50449i	0.0597169	+	0.183790i
$898$	−25.4376	−	18.4815i	−0.848864	−	0.616736i
$899$	−13.2579	+	9.63243i	−0.442176	+	0.321259i
$900$	−38.4340	+	118.288i	−1.28113	+	3.94292i
$901$	17.2580			0.574947
$902$		0			0
$903$	32.0256			1.06575
$904$	16.3646	−	50.3651i	0.544279	−	1.67512i
$905$	−7.31093	+	5.31170i	−0.243024	+	0.176567i
$906$	8.44368	+	6.13469i	0.280522	+	0.203811i
$907$	−11.9427	−	36.7558i	−0.396550	−	1.22045i	−0.927748	−	0.373207i	$-0.878258\pi$
$907$	−11.9427	−	36.7558i	−0.396550	−	1.22045i	0.531198	−	0.847248i	$-0.321742\pi$
$908$	−37.2790	−	114.733i	−1.23715	−	3.80755i
$909$	61.4365	+	44.6362i	2.03772	+	1.48049i
$910$	−0.438912	+	0.318889i	−0.0145498	+	0.0105711i
$911$	−5.68560	+	17.4985i	−0.188372	+	0.579750i	−0.999990	−	0.00443848i	$-0.998587\pi$
$911$	−5.68560	+	17.4985i	−0.188372	+	0.579750i	0.811618	+	0.584189i	$0.198587\pi$
$912$	−41.3331			−1.36868
$913$		0			0
$914$	85.4145			2.82526
$915$	−1.90327	+	5.85767i	−0.0629202	+	0.193649i
$916$	97.3511	−	70.7297i	3.21657	−	2.33697i
$917$	5.52834	+	4.01657i	0.182562	+	0.132639i
$918$	−21.3018	−	65.5602i	−0.703064	−	2.16381i
$919$	−5.45518	−	16.7893i	−0.179950	−	0.553829i	0.819875	−	0.572543i	$-0.194043\pi$
$919$	−5.45518	−	16.7893i	−0.179950	−	0.553829i	−0.999825	+	0.0187137i	$0.994043\pi$
$920$	−14.7185	−	10.6936i	−0.485253	−	0.352557i
$921$	−5.35243	+	3.88877i	−0.176369	+	0.128139i
$922$	−7.40376	+	22.7864i	−0.243830	+	0.750431i
$923$	2.67027			0.0878930
$924$		0			0
$925$	−35.1368			−1.15529
$926$	21.3956	−	65.8488i	0.703102	−	2.16393i
$927$	55.9521	−	40.6516i	1.83771	−	1.33517i
$928$	30.1080	+	21.8747i	0.988343	+	0.718073i
$929$	−4.15577	−	12.7901i	−0.136346	−	0.419631i	0.859451	−	0.511219i	$-0.170806\pi$
$929$	−4.15577	−	12.7901i	−0.136346	−	0.419631i	−0.995797	+	0.0915876i	$0.970806\pi$
$930$	−8.61924	−	26.5273i	−0.282636	−	0.869865i
$931$	−0.878946	−	0.638592i	−0.0288063	−	0.0209290i
$932$	−2.52160	+	1.83205i	−0.0825977	+	0.0600107i
$933$	17.3537	−	53.4093i	0.568136	−	1.74854i
$934$	−55.5241			−1.81680
$935$		0			0
$936$	19.6747			0.643087
$937$	2.65625	−	8.17510i	0.0867759	−	0.267069i	−0.898247	−	0.439490i	$-0.855159\pi$
$937$	2.65625	−	8.17510i	0.0867759	−	0.267069i	0.985023	+	0.172421i	$0.0551591\pi$
$938$	13.5340	−	9.83302i	0.441901	−	0.321060i
$939$	42.5894	+	30.9430i	1.38985	+	1.00979i
$940$	−0.746421	−	2.29725i	−0.0243456	−	0.0749279i
$941$	10.4131	+	32.0483i	0.339458	+	1.04474i	0.964484	+	0.264140i	$0.0850881\pi$
$941$	10.4131	+	32.0483i	0.339458	+	1.04474i	−0.625027	+	0.780603i	$0.714912\pi$
$942$	−33.0082	−	23.9819i	−1.07546	−	0.781371i
$943$	6.54994	−	4.75881i	0.213295	−	0.154968i
$944$	−60.3051	+	185.600i	−1.96276	+	6.04076i
$945$	−2.34928			−0.0764220
$946$		0			0
$947$	−15.3289			−0.498121			−0.249061	−	0.968488i	$-0.580122\pi$
$947$	−15.3289			−0.498121			−0.249061	+	0.968488i	$0.580122\pi$
$948$	−16.6124	+	51.1276i	−0.539545	+	1.66055i
$949$	0.604773	−	0.439393i	0.0196318	−	0.0142633i
$950$	−11.4092	−	8.28925i	−0.370162	−	0.268939i
$951$	−3.64513	−	11.2186i	−0.118202	−	0.363787i
$952$	−13.3470	−	41.0777i	−0.432577	−	1.33134i
$953$	36.3553	+	26.4136i	1.17766	+	0.855622i	0.991906	−	0.126974i	$-0.0405265\pi$
$953$	36.3553	+	26.4136i	1.17766	+	0.855622i	0.185756	+	0.982596i	$0.440527\pi$
$954$	−38.1260	+	27.7002i	−1.23438	+	0.896826i
$955$	−0.349937	+	1.07699i	−0.0113237	+	0.0348507i
$956$	79.4610			2.56995
$957$		0			0
$958$	−74.4697			−2.40601
$959$	−4.47064	+	13.7592i	−0.144364	+	0.444308i
$960$	−23.8474	+	17.3262i	−0.769672	+	0.559200i
$961$	−30.0991	−	21.8683i	−0.970940	−	0.705429i
$962$	2.75626	+	8.48289i	0.0888654	+	0.273499i
$963$	17.7279	+	54.5609i	0.571274	+	1.75820i
$964$	−78.4652	−	57.0083i	−2.52719	−	1.83611i
$965$	−6.30434	+	4.58037i	−0.202944	+	0.147447i
$966$	−10.7216	+	32.9976i	−0.344961	+	1.06168i
$967$	−33.9453			−1.09161			−0.545804	−	0.837913i	$-0.683776\pi$
$967$	−33.9453			−1.09161			−0.545804	+	0.837913i	$0.683776\pi$
$968$		0			0
$969$	14.7343			0.473334
$970$	−1.97411	+	6.07570i	−0.0633850	+	0.195079i
$971$	44.8681	−	32.5986i	1.43989	−	1.04614i	0.451820	−	0.892109i	$-0.350775\pi$
$971$	44.8681	−	32.5986i	1.43989	−	1.04614i	0.988066	−	0.154029i	$-0.0492250\pi$
$972$	−65.8632	−	47.8524i	−2.11256	−	1.53487i
$973$	−4.54121	−	13.9764i	−0.145585	−	0.448063i
$974$	10.1086	+	31.1112i	0.323902	+	0.996868i
$975$	4.91763	+	3.57287i	0.157490	+	0.114423i
$976$	54.0499	−	39.2696i	1.73010	−	1.25699i
$977$	−11.7200	+	36.0706i	−0.374957	+	1.15400i	0.568550	+	0.822649i	$0.307505\pi$
$977$	−11.7200	+	36.0706i	−0.374957	+	1.15400i	−0.943507	+	0.331351i	$0.892495\pi$
$978$	−71.5215			−2.28701
$979$		0			0
$980$	−2.36212			−0.0754551
$981$	−23.7978	+	73.2421i	−0.759805	+	2.33844i
$982$	86.1361	−	62.5815i	2.74871	−	1.99706i
$983$	−25.5113	−	18.5350i	−0.813683	−	0.591176i	0.101213	−	0.994865i	$-0.467728\pi$
$983$	−25.5113	−	18.5350i	−0.813683	−	0.591176i	−0.914896	+	0.403689i	$0.867728\pi$
$984$	−13.7326	−	42.2647i	−0.437780	−	1.34735i
$985$	−0.297843	−	0.916668i	−0.00949008	−	0.0292075i
$986$	−20.9652	−	15.2321i	−0.667667	−	0.485088i
$987$	−2.32236	+	1.68729i	−0.0739215	+	0.0537071i
$988$	−0.803471	+	2.47283i	−0.0255618	+	0.0786712i
$989$	52.1618			1.65865
$990$		0			0
$991$	39.8173			1.26484			0.632419	−	0.774627i	$-0.282062\pi$
$991$	39.8173			1.26484			0.632419	+	0.774627i	$0.282062\pi$
$992$	−47.8633	+	147.308i	−1.51966	+	4.67704i
$993$	−0.155044	+	0.112646i	−0.00492018	+	0.00357472i
$994$	12.9502	+	9.40890i	0.410757	+	0.298432i
$995$	2.00466	+	6.16971i	0.0635520	+	0.195593i
$996$	−49.7443	−	153.097i	−1.57621	−	4.85107i
$997$	−15.1440	−	11.0027i	−0.479614	−	0.348460i	0.321562	−	0.946889i	$-0.395792\pi$
$997$	−15.1440	−	11.0027i	−0.479614	−	0.348460i	−0.801176	+	0.598428i	$0.795792\pi$
$998$	−76.0685	+	55.2670i	−2.40791	+	1.74945i
$999$	−11.9353	+	36.7331i	−0.377617	+	1.16218i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.z.372.1		24
11.2	odd	10		847.2.f.y.729.1		24
11.3	even	5	inner	847.2.f.z.323.6		24
11.4	even	5		847.2.a.m.1.1	✓	6
11.5	even	5	inner	847.2.f.z.148.1		24
11.6	odd	10		847.2.f.y.148.6		24
11.7	odd	10		847.2.a.n.1.6	yes	6
11.8	odd	10		847.2.f.y.323.1		24
11.9	even	5	inner	847.2.f.z.729.6		24
11.10	odd	2		847.2.f.y.372.6		24
33.26	odd	10		7623.2.a.cs.1.6		6
33.29	even	10		7623.2.a.cp.1.1		6
77.48	odd	10		5929.2.a.bj.1.1		6
77.62	even	10		5929.2.a.bm.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.m.1.1	✓	6	11.4	even	5
847.2.a.n.1.6	yes	6	11.7	odd	10
847.2.f.y.148.6		24	11.6	odd	10
847.2.f.y.323.1		24	11.8	odd	10
847.2.f.y.372.6		24	11.10	odd	2
847.2.f.y.729.1		24	11.2	odd	10
847.2.f.z.148.1		24	11.5	even	5	inner
847.2.f.z.323.6		24	11.3	even	5	inner
847.2.f.z.372.1		24	1.1	even	1	trivial
847.2.f.z.729.6		24	11.9	even	5	inner
5929.2.a.bj.1.1		6	77.48	odd	10
5929.2.a.bm.1.6		6	77.62	even	10
7623.2.a.cp.1.1		6	33.29	even	10
7623.2.a.cs.1.6		6	33.26	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.835334 + 2.57089i) q^{2} +(2.27106 - 1.65003i) q^{3} +(-4.29367 - 3.11953i) q^{4} +(-0.137535 - 0.423289i) q^{5} +(2.34494 + 7.21698i) q^{6} +(0.809017 + 0.587785i) q^{7} +(7.23277 - 5.25492i) q^{8} +(1.50810 - 4.64146i) q^{9} +O(q^{10})\)	\(q+(-0.835334 + 2.57089i) q^{2} +(2.27106 - 1.65003i) q^{3} +(-4.29367 - 3.11953i) q^{4} +(-0.137535 - 0.423289i) q^{5} +(2.34494 + 7.21698i) q^{6} +(0.809017 + 0.587785i) q^{7} +(7.23277 - 5.25492i) q^{8} +(1.50810 - 4.64146i) q^{9} +1.20312 q^{10} -14.8985 q^{12} +(-0.139346 + 0.428863i) q^{13} +(-2.18693 + 1.58890i) q^{14} +(-1.01079 - 0.734380i) q^{15} +(4.18797 + 12.8893i) q^{16} +(-1.49291 - 4.59472i) q^{17} +(10.6729 + 7.75433i) q^{18} +(-0.878946 + 0.638592i) q^{19} +(-0.729935 + 2.24651i) q^{20} +2.80719 q^{21} +4.57222 q^{23} +(7.75535 - 23.8685i) q^{24} +(3.88483 - 2.82249i) q^{25} +(-0.986160 - 0.716487i) q^{26} +(-1.63112 - 5.02007i) q^{27} +(-1.64004 - 5.04751i) q^{28} +(-1.60534 - 1.16635i) q^{29} +(2.73236 - 1.98517i) q^{30} +(2.55205 - 7.85440i) q^{31} -18.7549 q^{32} +13.0596 q^{34} +(0.137535 - 0.423289i) q^{35} +(-20.9545 + 15.2243i) q^{36} +(-5.91978 - 4.30097i) q^{37} +(-0.907538 - 2.79311i) q^{38} +(0.391171 + 1.20390i) q^{39} +(-3.21911 - 2.33882i) q^{40} +(1.43255 - 1.04081i) q^{41} +(-2.34494 + 7.21698i) q^{42} +11.4084 q^{43} -2.17209 q^{45} +(-3.81933 + 11.7547i) q^{46} +(-0.827289 + 0.601061i) q^{47} +(30.7788 + 22.3621i) q^{48} +(0.309017 + 0.951057i) q^{49} +(4.01120 + 12.3452i) q^{50} +(-10.9719 - 7.97156i) q^{51} +(1.93616 - 1.40670i) q^{52} +(-1.10388 + 3.39738i) q^{53} +14.2686 q^{54} +8.94020 q^{56} +(-0.942452 + 2.90057i) q^{57} +(4.33956 - 3.15287i) q^{58} +(11.6495 + 8.46386i) q^{59} +(2.04907 + 6.30638i) q^{60} +(-1.52335 - 4.68837i) q^{61} +(18.0610 + 13.1221i) q^{62} +(3.94826 - 2.86858i) q^{63} +(7.29061 - 22.4382i) q^{64} +0.200698 q^{65} -6.18858 q^{67} +(-7.92330 + 24.3854i) q^{68} +(10.3838 - 7.54427i) q^{69} +(0.973343 + 0.707175i) q^{70} +(-1.82989 - 5.63182i) q^{71} +(-13.4827 - 41.4956i) q^{72} +(-1.34116 - 0.974409i) q^{73} +(16.0023 - 11.6264i) q^{74} +(4.16551 - 12.8201i) q^{75} +5.76602 q^{76} -3.42186 q^{78} +(1.11504 - 3.43173i) q^{79} +(4.87989 - 3.54545i) q^{80} +(-0.142838 - 0.103778i) q^{81} +(1.47915 + 4.55236i) q^{82} +(3.33888 + 10.2760i) q^{83} +(-12.0532 - 8.75713i) q^{84} +(-1.73957 + 1.26387i) q^{85} +(-9.52984 + 29.3298i) q^{86} -5.57035 q^{87} -5.21170 q^{89} +(1.81442 - 5.58422i) q^{90} +(-0.364813 + 0.265052i) q^{91} +(-19.6316 - 14.2632i) q^{92} +(-7.16409 - 22.0488i) q^{93} +(-0.854200 - 2.62896i) q^{94} +(0.391195 + 0.284220i) q^{95} +(-42.5935 + 30.9460i) q^{96} +(-1.64083 + 5.04996i) q^{97} -2.70320 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} - 6 q^{6} + 6 q^{7} + 12 q^{8} - 8 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 - 6 * q^6 + 6 * q^7 + 12 * q^8 - 8 * q^9	\( 24 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} - 6 q^{6} + 6 q^{7} + 12 q^{8} - 8 q^{9} + 32 q^{10} - 56 q^{12} + 4 q^{13} - 4 q^{14} - 2 q^{15} - 8 q^{16} + 22 q^{17} + 24 q^{18} + 6 q^{19} - 2 q^{20} + 8 q^{21} + 8 q^{23} - 20 q^{24} - 4 q^{25} - 6 q^{26} + 2 q^{27} + 4 q^{28} + 12 q^{29} + 20 q^{30} + 2 q^{31} - 32 q^{32} + 96 q^{34} - 4 q^{35} - 18 q^{36} - 14 q^{37} + 22 q^{38} + 20 q^{39} + 18 q^{40} + 26 q^{41} + 6 q^{42} + 16 q^{43} - 144 q^{45} + 12 q^{46} + 16 q^{47} + 24 q^{48} - 6 q^{49} - 4 q^{50} - 4 q^{51} + 12 q^{52} - 4 q^{53} + 128 q^{54} + 48 q^{56} + 20 q^{57} + 2 q^{58} + 4 q^{59} - 24 q^{60} - 8 q^{61} + 20 q^{62} + 8 q^{63} - 26 q^{64} - 96 q^{65} + 24 q^{67} + 12 q^{68} + 14 q^{69} + 8 q^{70} - 22 q^{71} + 16 q^{72} + 14 q^{73} + 44 q^{74} + 20 q^{75} + 120 q^{76} + 128 q^{78} - 28 q^{79} + 4 q^{80} + 6 q^{81} + 4 q^{82} + 22 q^{83} - 14 q^{84} - 24 q^{85} + 30 q^{86} - 88 q^{87} - 22 q^{90} - 4 q^{91} - 10 q^{92} + 50 q^{93} - 38 q^{94} - 24 q^{95} - 62 q^{96} + 4 q^{97} - 16 q^{98}+O(q^{100}) \) 24 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 - 6 * q^6 + 6 * q^7 + 12 * q^8 - 8 * q^9 + 32 * q^10 - 56 * q^12 + 4 * q^13 - 4 * q^14 - 2 * q^15 - 8 * q^16 + 22 * q^17 + 24 * q^18 + 6 * q^19 - 2 * q^20 + 8 * q^21 + 8 * q^23 - 20 * q^24 - 4 * q^25 - 6 * q^26 + 2 * q^27 + 4 * q^28 + 12 * q^29 + 20 * q^30 + 2 * q^31 - 32 * q^32 + 96 * q^34 - 4 * q^35 - 18 * q^36 - 14 * q^37 + 22 * q^38 + 20 * q^39 + 18 * q^40 + 26 * q^41 + 6 * q^42 + 16 * q^43 - 144 * q^45 + 12 * q^46 + 16 * q^47 + 24 * q^48 - 6 * q^49 - 4 * q^50 - 4 * q^51 + 12 * q^52 - 4 * q^53 + 128 * q^54 + 48 * q^56 + 20 * q^57 + 2 * q^58 + 4 * q^59 - 24 * q^60 - 8 * q^61 + 20 * q^62 + 8 * q^63 - 26 * q^64 - 96 * q^65 + 24 * q^67 + 12 * q^68 + 14 * q^69 + 8 * q^70 - 22 * q^71 + 16 * q^72 + 14 * q^73 + 44 * q^74 + 20 * q^75 + 120 * q^76 + 128 * q^78 - 28 * q^79 + 4 * q^80 + 6 * q^81 + 4 * q^82 + 22 * q^83 - 14 * q^84 - 24 * q^85 + 30 * q^86 - 88 * q^87 - 22 * q^90 - 4 * q^91 - 10 * q^92 + 50 * q^93 - 38 * q^94 - 24 * q^95 - 62 * q^96 + 4 * q^97 - 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more