LMFDB - Embedded newform 805.2.u.d.36.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [805,2,Mod(36,805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(805, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("805.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 805 = 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	805.u (of order $11$, degree $10$, 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:	$6.42795736271$
Analytic rank:	$0$
Dimension:	$130$
Relative dimension:	$13$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			36.10
Character	$\chi$	$=$	805.36
Dual form			805.2.u.d.246.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13848 + 1.31387i) q^{2} +(-2.68348 - 1.72457i) q^{3} +(-0.145502 + 1.01199i) q^{4} +(0.415415 - 0.909632i) q^{5} +(-0.789218 - 5.48913i) q^{6} +(0.959493 + 0.281733i) q^{7} +(1.42977 - 0.918859i) q^{8} +(2.98068 + 6.52678i) q^{9} +O(q^{10})$	\(q+(1.13848 + 1.31387i) q^{2} +(-2.68348 - 1.72457i) q^{3} +(-0.145502 + 1.01199i) q^{4} +(0.415415 - 0.909632i) q^{5} +(-0.789218 - 5.48913i) q^{6} +(0.959493 + 0.281733i) q^{7} +(1.42977 - 0.918859i) q^{8} +(2.98068 + 6.52678i) q^{9} +(1.66808 - 0.489793i) q^{10} +(1.34335 - 1.55030i) q^{11} +(2.13569 - 2.46472i) q^{12} +(-4.46763 + 1.31182i) q^{13} +(0.722200 + 1.58140i) q^{14} +(-2.68348 + 1.72457i) q^{15} +(4.79698 + 1.40852i) q^{16} +(-0.977880 - 6.80130i) q^{17} +(-5.18192 + 11.3468i) q^{18} +(-0.382742 + 2.66203i) q^{19} +(0.860092 + 0.552747i) q^{20} +(-2.08891 - 2.41073i) q^{21} +3.56627 q^{22} +(1.87122 - 4.41571i) q^{23} -5.42139 q^{24} +(-0.654861 - 0.755750i) q^{25} +(-6.80986 - 4.37643i) q^{26} +(1.89538 - 13.1827i) q^{27} +(-0.424717 + 0.930001i) q^{28} +(-1.03373 - 7.18972i) q^{29} +(-5.32094 - 1.56237i) q^{30} +(-4.33310 + 2.78471i) q^{31} +(2.19858 + 4.81423i) q^{32} +(-6.27844 + 1.84352i) q^{33} +(7.82275 - 9.02794i) q^{34} +(0.654861 - 0.755750i) q^{35} +(-7.03870 + 2.06675i) q^{36} +(-1.40538 - 3.07734i) q^{37} +(-3.93331 + 2.52778i) q^{38} +(14.2511 + 4.18450i) q^{39} +(-0.241874 - 1.68227i) q^{40} +(3.81956 - 8.36367i) q^{41} +(0.789218 - 5.48913i) q^{42} +(-3.88345 - 2.49574i) q^{43} +(1.37343 + 1.58502i) q^{44} +7.17518 q^{45} +(7.93203 - 2.56865i) q^{46} +6.24880 q^{47} +(-10.4435 - 12.0525i) q^{48} +(0.841254 + 0.540641i) q^{49} +(0.247415 - 1.72081i) q^{50} +(-9.10518 + 19.9376i) q^{51} +(-0.677491 - 4.71205i) q^{52} +(-3.36097 - 0.986869i) q^{53} +(19.4782 - 12.5179i) q^{54} +(-0.852160 - 1.86597i) q^{55} +(1.63073 - 0.478825i) q^{56} +(5.61792 - 6.48343i) q^{57} +(8.26950 - 9.54351i) q^{58} +(-3.60588 + 1.05878i) q^{59} +(-1.35479 - 2.96657i) q^{60} +(-5.77643 + 3.71228i) q^{61} +(-8.59189 - 2.52281i) q^{62} +(1.02113 + 7.10215i) q^{63} +(0.331490 - 0.725862i) q^{64} +(-0.662653 + 4.60885i) q^{65} +(-9.57001 - 6.15027i) q^{66} +(3.52619 + 4.06944i) q^{67} +7.02511 q^{68} +(-12.6366 + 8.62243i) q^{69} +1.73850 q^{70} +(-0.718707 - 0.829432i) q^{71} +(10.2589 + 6.59298i) q^{72} +(1.94014 - 13.4940i) q^{73} +(2.44325 - 5.34997i) q^{74} +(0.453964 + 3.15739i) q^{75} +(-2.63824 - 0.774659i) q^{76} +(1.72570 - 1.10904i) q^{77} +(10.7267 + 23.4881i) q^{78} +(-5.26451 + 1.54580i) q^{79} +(3.27398 - 3.77837i) q^{80} +(-13.7244 + 15.8388i) q^{81} +(15.3373 - 4.50343i) q^{82} +(5.21486 + 11.4190i) q^{83} +(2.74357 - 1.76318i) q^{84} +(-6.59291 - 1.93585i) q^{85} +(-1.14213 - 7.94371i) q^{86} +(-9.62517 + 21.0762i) q^{87} +(0.496168 - 3.45093i) q^{88} +(11.1535 + 7.16790i) q^{89} +(8.16878 + 9.42728i) q^{90} -4.65624 q^{91} +(4.19638 + 2.53614i) q^{92} +16.4302 q^{93} +(7.11412 + 8.21013i) q^{94} +(2.26247 + 1.45400i) q^{95} +(2.40260 - 16.7105i) q^{96} +(4.41352 - 9.66427i) q^{97} +(0.247415 + 1.72081i) q^{98} +(14.1226 + 4.14676i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9}+O(q^{10}) $ 130 * q + 2 * q^2 + 2 * q^3 - 16 * q^4 - 13 * q^5 + 5 * q^6 + 13 * q^7 - 7 * q^8 - 39 * q^9	\( 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9} + 2 q^{10} + 2 q^{11} - 5 q^{12} + 13 q^{13} - 2 q^{14} + 2 q^{15} - 6 q^{16} - 51 q^{17} + q^{18} - 9 q^{19} - 16 q^{20} - 2 q^{21} + 34 q^{22} - 10 q^{23} - 76 q^{24} - 13 q^{25} - 31 q^{26} + 14 q^{27} + 27 q^{28} + 3 q^{29} + 5 q^{30} + 6 q^{31} + 22 q^{32} - 58 q^{33} + q^{34} + 13 q^{35} + 193 q^{36} - 36 q^{37} + 4 q^{38} - 2 q^{39} - 29 q^{40} - 34 q^{41} - 5 q^{42} - 22 q^{43} + 8 q^{44} + 170 q^{45} - 198 q^{46} - 14 q^{47} - 120 q^{48} - 13 q^{49} + 2 q^{50} - 6 q^{51} + 33 q^{52} - 18 q^{53} + 188 q^{54} - 31 q^{55} - 15 q^{56} - 9 q^{57} + 114 q^{58} + 46 q^{59} - 16 q^{60} - 56 q^{61} - 146 q^{62} + 17 q^{63} - 109 q^{64} + 2 q^{65} - 14 q^{66} - 10 q^{67} + 86 q^{68} - 6 q^{69} - 2 q^{70} - 25 q^{72} + 64 q^{73} + 79 q^{74} + 2 q^{75} + 32 q^{76} - 13 q^{77} - 64 q^{78} - 118 q^{79} - 17 q^{80} + 23 q^{81} + 129 q^{82} - 117 q^{83} - 72 q^{84} - 7 q^{85} + 74 q^{86} - 51 q^{87} - 40 q^{88} - 35 q^{89} + 100 q^{90} + 42 q^{91} + 76 q^{92} - 90 q^{93} - 7 q^{94} + 2 q^{95} + 393 q^{96} - 4 q^{97} + 2 q^{98} - 40 q^{99}+O(q^{100}) \) 130 * q + 2 * q^2 + 2 * q^3 - 16 * q^4 - 13 * q^5 + 5 * q^6 + 13 * q^7 - 7 * q^8 - 39 * q^9 + 2 * q^10 + 2 * q^11 - 5 * q^12 + 13 * q^13 - 2 * q^14 + 2 * q^15 - 6 * q^16 - 51 * q^17 + q^18 - 9 * q^19 - 16 * q^20 - 2 * q^21 + 34 * q^22 - 10 * q^23 - 76 * q^24 - 13 * q^25 - 31 * q^26 + 14 * q^27 + 27 * q^28 + 3 * q^29 + 5 * q^30 + 6 * q^31 + 22 * q^32 - 58 * q^33 + q^34 + 13 * q^35 + 193 * q^36 - 36 * q^37 + 4 * q^38 - 2 * q^39 - 29 * q^40 - 34 * q^41 - 5 * q^42 - 22 * q^43 + 8 * q^44 + 170 * q^45 - 198 * q^46 - 14 * q^47 - 120 * q^48 - 13 * q^49 + 2 * q^50 - 6 * q^51 + 33 * q^52 - 18 * q^53 + 188 * q^54 - 31 * q^55 - 15 * q^56 - 9 * q^57 + 114 * q^58 + 46 * q^59 - 16 * q^60 - 56 * q^61 - 146 * q^62 + 17 * q^63 - 109 * q^64 + 2 * q^65 - 14 * q^66 - 10 * q^67 + 86 * q^68 - 6 * q^69 - 2 * q^70 - 25 * q^72 + 64 * q^73 + 79 * q^74 + 2 * q^75 + 32 * q^76 - 13 * q^77 - 64 * q^78 - 118 * q^79 - 17 * q^80 + 23 * q^81 + 129 * q^82 - 117 * q^83 - 72 * q^84 - 7 * q^85 + 74 * q^86 - 51 * q^87 - 40 * q^88 - 35 * q^89 + 100 * q^90 + 42 * q^91 + 76 * q^92 - 90 * q^93 - 7 * q^94 + 2 * q^95 + 393 * q^96 - 4 * q^97 + 2 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/805\mathbb{Z}\right)^\times$.

$n$	$162$	$281$	$346$
$\chi(n)$	$1$	$e\left(\frac{7}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	1.13848	+	1.31387i	0.805025	+	0.929048i	0.998646	−	0.0520280i	$-0.0165685\pi$
$2$	1.13848	+	1.31387i	0.805025	+	0.929048i	−0.193621	+	0.981076i	$0.562023\pi$
$3$	−2.68348	−	1.72457i	−1.54931	−	0.995679i	−0.985481	−	0.169785i	$-0.945693\pi$
$3$	−2.68348	−	1.72457i	−1.54931	−	0.995679i	−0.563826	−	0.825894i	$-0.690671\pi$
$4$	−0.145502	+	1.01199i	−0.0727508	+	0.505993i
$5$	0.415415	−	0.909632i	0.185779	−	0.406800i
$5$	0.415415	−	0.909632i	0.185779	−	0.406800i
$6$	−0.789218	−	5.48913i	−0.322197	−	2.24093i
$7$	0.959493	+	0.281733i	0.362654	+	0.106485i
$7$	0.959493	+	0.281733i	0.362654	+	0.106485i
$8$	1.42977	−	0.918859i	0.505501	−	0.324866i
$9$	2.98068	+	6.52678i	0.993560	+	2.17559i
$10$	1.66808	−	0.489793i	0.527494	−	0.154886i
$11$	1.34335	−	1.55030i	0.405034	−	0.467434i	−0.516186	−	0.856477i	$-0.672649\pi$
$11$	1.34335	−	1.55030i	0.405034	−	0.467434i	0.921220	+	0.389042i	$0.127194\pi$
$12$	2.13569	−	2.46472i	0.616520	−	0.711502i
$13$	−4.46763	+	1.31182i	−1.23910	+	0.363832i	−0.834677	−	0.550740i	$-0.814345\pi$
$13$	−4.46763	+	1.31182i	−1.23910	+	0.363832i	−0.404422	+	0.914573i	$0.632527\pi$
$14$	0.722200	+	1.58140i	0.193016	+	0.422646i
$15$	−2.68348	+	1.72457i	−0.692871	+	0.445281i
$16$	4.79698	+	1.40852i	1.19925	+	0.352130i
$17$	−0.977880	−	6.80130i	−0.237171	−	1.64956i	−0.665838	−	0.746096i	$-0.731926\pi$
$17$	−0.977880	−	6.80130i	−0.237171	−	1.64956i	0.428668	−	0.903462i	$-0.358983\pi$
$18$	−5.18192	+	11.3468i	−1.22139	+	2.67447i
$19$	−0.382742	+	2.66203i	−0.0878069	+	0.610711i	0.897640	+	0.440729i	$0.145280\pi$
$19$	−0.382742	+	2.66203i	−0.0878069	+	0.610711i	−0.985447	+	0.169982i	$0.945629\pi$
$20$	0.860092	+	0.552747i	0.192322	+	0.123598i
$21$	−2.08891	−	2.41073i	−0.455838	−	0.526065i
$22$	3.56627			0.760332
$23$	1.87122	−	4.41571i	0.390176	−	0.920740i
$23$	1.87122	−	4.41571i	0.390176	−	0.920740i
$24$	−5.42139			−1.10664
$25$	−0.654861	−	0.755750i	−0.130972	−	0.151150i
$26$	−6.80986	−	4.37643i	−1.33552	−	0.858288i
$27$	1.89538	−	13.1827i	0.364766	−	2.53701i
$28$	−0.424717	+	0.930001i	−0.0802640	+	0.175754i
$29$	−1.03373	−	7.18972i	−0.191958	−	1.33510i	−0.826818	−	0.562470i	$-0.809851\pi$
$29$	−1.03373	−	7.18972i	−0.191958	−	1.33510i	0.634860	−	0.772627i	$-0.281058\pi$
$30$	−5.32094	−	1.56237i	−0.971466	−	0.285248i
$31$	−4.33310	+	2.78471i	−0.778247	+	0.500149i	−0.868452	−	0.495774i	$-0.834884\pi$
$31$	−4.33310	+	2.78471i	−0.778247	+	0.500149i	0.0902041	+	0.995923i	$0.471248\pi$
$32$	2.19858	+	4.81423i	0.388658	+	0.851043i
$33$	−6.27844	+	1.84352i	−1.09294	+	0.320915i
$34$	7.82275	−	9.02794i	1.34159	−	1.54828i
$35$	0.654861	−	0.755750i	0.110692	−	0.127745i
$36$	−7.03870	+	2.06675i	−1.17312	+	0.344458i
$37$	−1.40538	−	3.07734i	−0.231042	−	0.505912i	0.758231	−	0.651985i	$-0.226064\pi$
$37$	−1.40538	−	3.07734i	−0.231042	−	0.505912i	−0.989274	+	0.146073i	$0.953336\pi$
$38$	−3.93331	+	2.52778i	−0.638067	+	0.410061i
$39$	14.2511	+	4.18450i	2.28200	+	0.670057i
$40$	−0.241874	−	1.68227i	−0.0382437	−	0.265991i
$41$	3.81956	−	8.36367i	0.596515	−	1.30619i	−0.334910	−	0.942250i	$-0.608706\pi$
$41$	3.81956	−	8.36367i	0.596515	−	1.30619i	0.931424	−	0.363935i	$-0.118567\pi$
$42$	0.789218	−	5.48913i	0.121779	−	0.846991i
$43$	−3.88345	−	2.49574i	−0.592221	−	0.380597i	0.209932	−	0.977716i	$-0.432676\pi$
$43$	−3.88345	−	2.49574i	−0.592221	−	0.380597i	−0.802153	+	0.597119i	$0.796312\pi$
$44$	1.37343	+	1.58502i	0.207052	+	0.238951i
$45$	7.17518			1.06961
$46$	7.93203	−	2.56865i	1.16951	−	0.378726i
$47$	6.24880			0.911481			0.455741	−	0.890113i	$-0.349374\pi$
$47$	6.24880			0.911481			0.455741	+	0.890113i	$0.349374\pi$
$48$	−10.4435	−	12.0525i	−1.50739	−	1.73962i
$49$	0.841254	+	0.540641i	0.120179	+	0.0772344i
$50$	0.247415	−	1.72081i	0.0349897	−	0.243359i
$51$	−9.10518	+	19.9376i	−1.27498	+	2.79182i
$52$	−0.677491	−	4.71205i	−0.0939511	−	0.653444i
$53$	−3.36097	−	0.986869i	−0.461664	−	0.135557i	0.0426258	−	0.999091i	$-0.486428\pi$
$53$	−3.36097	−	0.986869i	−0.461664	−	0.135557i	−0.504290	+	0.863534i	$0.668246\pi$
$54$	19.4782	−	12.5179i	2.65065	−	1.70347i
$55$	−0.852160	−	1.86597i	−0.114905	−	0.251607i
$56$	1.63073	−	0.478825i	0.217915	−	0.0639857i
$57$	5.61792	−	6.48343i	0.744112	−	0.858751i
$58$	8.26950	−	9.54351i	1.08584	−	1.25312i
$59$	−3.60588	+	1.05878i	−0.469446	+	0.137842i	−0.507895	−	0.861419i	$-0.669576\pi$
$59$	−3.60588	+	1.05878i	−0.469446	+	0.137842i	0.0384493	+	0.999261i	$0.487758\pi$
$60$	−1.35479	−	2.96657i	−0.174902	−	0.382983i
$61$	−5.77643	+	3.71228i	−0.739595	+	0.475309i	−0.855403	−	0.517962i	$-0.826691\pi$
$61$	−5.77643	+	3.71228i	−0.739595	+	0.475309i	0.115808	+	0.993272i	$0.463054\pi$
$62$	−8.59189	−	2.52281i	−1.09117	−	0.320397i
$63$	1.02113	+	7.10215i	0.128651	+	0.894787i
$64$	0.331490	−	0.725862i	0.0414363	−	0.0907328i
$65$	−0.662653	+	4.60885i	−0.0821919	+	0.571657i
$66$	−9.57001	−	6.15027i	−1.17799	−	0.757046i
$67$	3.52619	+	4.06944i	0.430792	+	0.497161i	0.929094	−	0.369843i	$-0.120588\pi$
$67$	3.52619	+	4.06944i	0.430792	+	0.497161i	−0.498302	+	0.867003i	$0.666043\pi$
$68$	7.02511			0.851920
$69$	−12.6366	+	8.62243i	−1.52126	+	1.03802i
$70$	1.73850			0.207791
$71$	−0.718707	−	0.829432i	−0.0852948	−	0.0984355i	0.711498	−	0.702688i	$-0.248017\pi$
$71$	−0.718707	−	0.829432i	−0.0852948	−	0.0984355i	−0.796793	+	0.604253i	$0.793472\pi$
$72$	10.2589	+	6.59298i	1.20902	+	0.776990i
$73$	1.94014	−	13.4940i	0.227076	−	1.57935i	−0.483252	−	0.875481i	$-0.660545\pi$
$73$	1.94014	−	13.4940i	0.227076	−	1.57935i	0.710329	−	0.703870i	$-0.248546\pi$
$74$	2.44325	−	5.34997i	0.284022	−	0.621921i
$75$	0.453964	+	3.15739i	0.0524192	+	0.364584i
$76$	−2.63824	−	0.774659i	−0.302627	−	0.0888594i
$77$	1.72570	−	1.10904i	0.196662	−	0.126387i
$78$	10.7267	+	23.4881i	1.21455	+	2.65950i
$79$	−5.26451	+	1.54580i	−0.592303	+	0.173916i	−0.564128	−	0.825687i	$-0.690788\pi$
$79$	−5.26451	+	1.54580i	−0.592303	+	0.173916i	−0.0281749	+	0.999603i	$0.508970\pi$
$80$	3.27398	−	3.77837i	0.366042	−	0.422434i
$81$	−13.7244	+	15.8388i	−1.52493	+	1.75986i
$82$	15.3373	−	4.50343i	1.69372	−	0.497321i
$83$	5.21486	+	11.4190i	0.572405	+	1.25339i	0.945507	+	0.325602i	$0.105567\pi$
$83$	5.21486	+	11.4190i	0.572405	+	1.25339i	−0.373101	+	0.927791i	$0.621706\pi$
$84$	2.74357	−	1.76318i	0.299348	−	0.192379i
$85$	−6.59291	−	1.93585i	−0.715101	−	0.209973i
$86$	−1.14213	−	7.94371i	−0.123159	−	0.856593i
$87$	−9.62517	+	21.0762i	−1.03193	+	2.25960i
$88$	0.496168	−	3.45093i	0.0528917	−	0.367870i
$89$	11.1535	+	7.16790i	1.18227	+	0.759796i	0.975802	−	0.218658i	$-0.0701679\pi$
$89$	11.1535	+	7.16790i	1.18227	+	0.759796i	0.206464	+	0.978454i	$0.433804\pi$
$90$	8.16878	+	9.42728i	0.861065	+	0.993722i
$91$	−4.65624			−0.488107
$92$	4.19638	+	2.53614i	0.437503	+	0.264411i
$93$	16.4302			1.70373
$94$	7.11412	+	8.21013i	0.733765	+	0.846810i
$95$	2.26247	+	1.45400i	0.232124	+	0.149177i
$96$	2.40260	−	16.7105i	0.245215	−	1.70551i
$97$	4.41352	−	9.66427i	0.448125	−	0.981258i	−0.541910	−	0.840437i	$-0.682299\pi$
$97$	4.41352	−	9.66427i	0.448125	−	0.981258i	0.990035	−	0.140821i	$-0.0449742\pi$
$98$	0.247415	+	1.72081i	0.0249927	+	0.173828i
$99$	14.1226	+	4.14676i	1.41937	+	0.416765i
$100$	0.860092	−	0.552747i	0.0860092	−	0.0552747i
$101$	4.38197	+	9.59518i	0.436023	+	0.954756i	0.992311	+	0.123767i	$0.0394976\pi$
$101$	4.38197	+	9.59518i	0.436023	+	0.954756i	−0.556289	+	0.830989i	$0.687775\pi$
$102$	−36.5615	+	10.7354i	−3.62012	+	1.06296i
$103$	5.74144	−	6.62597i	0.565721	−	0.652876i	−0.398752	−	0.917059i	$-0.630557\pi$
$103$	5.74144	−	6.62597i	0.565721	−	0.652876i	0.964473	+	0.264182i	$0.0851021\pi$
$104$	−5.18232	+	5.98072i	−0.508169	+	0.586458i
$105$	−3.06064	+	0.898686i	−0.298688	+	0.0877028i
$106$	−2.52977	−	5.53941i	−0.245713	−	0.538035i
$107$	−11.8089	+	7.58915i	−1.14161	+	0.733671i	−0.967952	−	0.251135i	$-0.919196\pi$
$107$	−11.8089	+	7.58915i	−1.14161	+	0.733671i	−0.173662	+	0.984805i	$0.555560\pi$
$108$	13.0649	+	3.83620i	1.25717	+	0.369139i
$109$	0.190936	+	1.32799i	0.0182884	+	0.127199i	0.996920	−	0.0784215i	$-0.0249880\pi$
$109$	0.190936	+	1.32799i	0.0182884	+	0.127199i	−0.978632	+	0.205620i	$0.934079\pi$
$110$	1.48148	−	3.24399i	0.141254	−	0.309303i
$111$	−1.53579	+	10.6816i	−0.145771	+	1.01386i
$112$	4.20585	+	2.70293i	0.397415	+	0.255403i
$113$	−10.1229	−	11.6824i	−0.952280	−	1.09899i	−0.994997	−	0.0999022i	$-0.968147\pi$
$113$	−10.1229	−	11.6824i	−0.952280	−	1.09899i	0.0427175	−	0.999087i	$-0.486398\pi$
$114$	14.9143			1.39685
$115$	−3.23934	−	3.53648i	−0.302070	−	0.329778i
$116$	7.42631			0.689515
$117$	−21.8785	−	25.2491i	−2.02267	−	2.33428i
$118$	−5.49632	−	3.53227i	−0.505978	−	0.325172i
$119$	0.977880	−	6.80130i	0.0896421	−	0.623474i
$120$	−2.25213	+	4.93147i	−0.205590	+	0.450180i
$121$	0.966600	+	6.72285i	0.0878727	+	0.611168i
$122$	−11.4538	−	3.36314i	−1.03698	−	0.304484i
$123$	−24.6734	+	15.8566i	−2.22473	+	1.42974i
$124$	−2.18762	−	4.79022i	−0.196454	−	0.430174i
$125$	−0.959493	+	0.281733i	−0.0858197	+	0.0251989i
$126$	−8.16878	+	9.42728i	−0.727733	+	0.839849i
$127$	−9.71520	+	11.2119i	−0.862084	+	0.994899i	0.137906	+	0.990445i	$0.455963\pi$
$127$	−9.71520	+	11.2119i	−0.862084	+	0.994899i	−0.999990	+	0.00445316i	$0.998583\pi$
$128$	11.4873	−	3.37298i	1.01534	−	0.298132i
$129$	6.11709	+	13.3946i	0.538579	+	1.17932i
$130$	−6.80986	+	4.37643i	−0.597264	+	0.383838i
$131$	0.361378	+	0.106110i	0.0315738	+	0.00927089i	0.297481	−	0.954728i	$-0.403853\pi$
$131$	0.361378	+	0.106110i	0.0315738	+	0.00927089i	−0.265908	+	0.963999i	$0.585672\pi$
$132$	−0.952090	−	6.62193i	−0.0828688	−	0.576365i
$133$	−1.11722	+	2.44636i	−0.0968750	+	0.212127i
$134$	−1.33224	+	9.26592i	−0.115088	+	0.800454i
$135$	−11.2040	−	7.20038i	−0.964288	−	0.619710i
$136$	−7.64758	−	8.82578i	−0.655775	−	0.756804i
$137$	15.1156			1.29142			0.645708	−	0.763584i	$-0.276562\pi$
$137$	15.1156			1.29142			0.645708	+	0.763584i	$0.276562\pi$
$138$	−25.7152	−	6.78640i	−2.18903	−	0.577697i
$139$	13.1739			1.11740			0.558699	−	0.829371i	$-0.311301\pi$
$139$	13.1739			1.11740			0.558699	+	0.829371i	$0.311301\pi$
$140$	0.669525	+	0.772673i	0.0565852	+	0.0653028i
$141$	−16.7685	−	10.7765i	−1.41216	−	0.907543i
$142$	0.271537	−	1.88858i	0.0227869	−	0.158486i
$143$	−3.96786	+	8.68841i	−0.331809	+	0.726561i
$144$	5.10516	+	35.5072i	0.425430	+	2.95893i
$145$	−6.96942	−	2.04641i	−0.578779	−	0.169945i
$146$	19.9382	−	12.8135i	1.65010	−	1.06045i
$147$	−1.32511	−	2.90160i	−0.109294	−	0.239320i
$148$	3.31871	−	0.974462i	0.272797	−	0.0801003i
$149$	−2.30295	+	2.65775i	−0.188665	+	0.217731i	−0.842200	−	0.539165i	$-0.818740\pi$
$149$	−2.30295	+	2.65775i	−0.188665	+	0.217731i	0.653535	+	0.756896i	$0.273285\pi$
$150$	−3.63158	+	4.19107i	−0.296517	+	0.342199i
$151$	12.2830	−	3.60662i	0.999578	−	0.293502i	0.259295	−	0.965798i	$-0.416510\pi$
$151$	12.2830	−	3.60662i	0.999578	−	0.293502i	0.740283	+	0.672296i	$0.234692\pi$
$152$	1.89879	+	4.15778i	0.154012	+	0.337240i
$153$	41.4758	−	26.6549i	3.35312	−	2.15492i
$154$	3.42181	+	1.00473i	0.275737	+	0.0809638i
$155$	0.733030	+	5.09834i	0.0588784	+	0.409508i
$156$	−6.30822	+	13.8131i	−0.505062	+	1.10593i
$157$	−0.580618	+	4.03828i	−0.0463383	+	0.322290i	0.953447	+	0.301561i	$0.0975078\pi$
$157$	−0.580618	+	4.03828i	−0.0463383	+	0.322290i	−0.999785	+	0.0207289i	$0.993401\pi$
$158$	−8.02451	−	5.15704i	−0.638395	−	0.410272i
$159$	7.31716	+	8.44445i	0.580289	+	0.669689i
$160$	5.29250			0.418409
$161$	3.03947	−	3.70966i	0.239544	−	0.292362i
$162$	−36.4350			−2.86261
$163$	−2.10836	−	2.43318i	−0.165140	−	0.190581i	0.667148	−	0.744925i	$-0.267515\pi$
$163$	−2.10836	−	2.43318i	−0.165140	−	0.190581i	−0.832288	+	0.554344i	$0.812969\pi$
$164$	7.90816	+	5.08227i	0.617524	+	0.396858i
$165$	−0.931237	+	6.47690i	−0.0724967	+	0.504226i
$166$	−9.06605	+	19.8519i	−0.703662	+	1.54081i
$167$	2.25236	+	15.6655i	0.174293	+	1.21223i	0.869686	+	0.493605i	$0.164321\pi$
$167$	2.25236	+	15.6655i	0.174293	+	1.21223i	−0.695394	+	0.718629i	$0.744770\pi$
$168$	−5.20179	−	1.52738i	−0.401327	−	0.117840i
$169$	7.30259	−	4.69309i	0.561737	−	0.361007i
$170$	−4.96241	−	10.8662i	−0.380600	−	0.833397i
$171$	−18.5153	+	5.43658i	−1.41590	+	0.415745i
$172$	3.09071	−	3.56687i	0.235664	−	0.271971i
$173$	−0.880519	+	1.01617i	−0.0669446	+	0.0772582i	−0.788234	−	0.615376i	$-0.789004\pi$
$173$	−0.880519	+	1.01617i	−0.0669446	+	0.0772582i	0.721289	+	0.692634i	$0.243550\pi$
$174$	−38.6495	+	11.3485i	−2.93001	+	0.860328i
$175$	−0.415415	−	0.909632i	−0.0314024	−	0.0687617i
$176$	8.62764	−	5.54465i	0.650333	−	0.417944i
$177$	11.5023	+	3.37737i	0.864562	+	0.253858i
$178$	3.28026	+	22.8147i	0.245866	+	1.71004i
$179$	5.39521	−	11.8139i	0.403257	−	0.883009i	−0.593673	−	0.804706i	$-0.702323\pi$
$179$	5.39521	−	11.8139i	0.403257	−	0.883009i	0.996930	−	0.0783024i	$-0.0249500\pi$
$180$	−1.04400	+	7.26119i	−0.0778153	+	0.541217i
$181$	15.8414	+	10.1806i	1.17748	+	0.756721i	0.974922	−	0.222549i	$-0.0714376\pi$
$181$	15.8414	+	10.1806i	1.17748	+	0.756721i	0.202560	+	0.979270i	$0.435074\pi$
$182$	−5.30103	−	6.11771i	−0.392938	−	0.453475i
$183$	21.9030			1.61912
$184$	−1.38200	−	8.03285i	−0.101882	−	0.592190i
$185$	−3.38306			−0.248728
$186$	18.7054	+	21.5872i	1.37155	+	1.58285i
$187$	−11.8577	−	7.62049i	−0.867122	−	0.557266i
$188$	−0.909211	+	6.32370i	−0.0663110	+	0.461203i
$189$	5.53259	−	12.1147i	0.402437	−	0.881214i
$190$	0.665397	+	4.62794i	0.0482730	+	0.335746i
$191$	−0.204097	−	0.0599284i	−0.0147680	−	0.00433627i	0.274340	−	0.961633i	$-0.411541\pi$
$191$	−0.204097	−	0.0599284i	−0.0147680	−	0.00433627i	−0.289108	+	0.957296i	$0.593359\pi$
$192$	−2.14134	+	1.37616i	−0.154538	+	0.0993157i
$193$	−3.84816	−	8.42629i	−0.276997	−	0.606538i	0.719090	−	0.694917i	$-0.244559\pi$
$193$	−3.84816	−	8.42629i	−0.276997	−	0.606538i	−0.996087	+	0.0883787i	$0.971831\pi$
$194$	17.7223	−	5.20374i	1.27239	−	0.373607i
$195$	9.72648	−	11.2250i	0.696528	−	0.803836i
$196$	−0.669525	+	0.772673i	−0.0478232	+	0.0551909i
$197$	16.1960	−	4.75558i	1.15392	−	0.338821i	0.351851	−	0.936056i	$-0.385552\pi$
$197$	16.1960	−	4.75558i	1.15392	−	0.338821i	0.802066	+	0.597235i	$0.203734\pi$
$198$	10.6299	+	23.2763i	0.755435	+	1.65417i
$199$	23.3062	−	14.9780i	1.65213	−	1.06176i	0.723794	−	0.690016i	$-0.242396\pi$
$199$	23.3062	−	14.9780i	1.65213	−	1.06176i	0.928335	−	0.371744i	$-0.121240\pi$
$200$	−1.63073	−	0.478825i	−0.115310	−	0.0338580i
$201$	−2.44443	−	17.0014i	−0.172417	−	1.19918i
$202$	−7.61807	+	16.6813i	−0.536006	+	1.17369i
$203$	1.03373	−	7.18972i	0.0725533	−	0.504619i
$204$	−18.8517	−	12.1153i	−1.31988	−	0.848238i
$205$	−6.02116	−	6.94878i	−0.420536	−	0.485324i
$206$	15.2422			1.06197
$207$	34.3979	−	0.948799i	2.39082	−	0.0659461i
$208$	−23.2789			−1.61410
$209$	3.61280	+	4.16939i	0.249902	+	0.288403i
$210$	−4.66523	−	2.99816i	−0.321932	−	0.206893i
$211$	−3.86678	+	26.8941i	−0.266200	+	1.85146i	0.217281	+	0.976109i	$0.430281\pi$
$211$	−3.86678	+	26.8941i	−0.266200	+	1.85146i	−0.483481	+	0.875355i	$0.660628\pi$
$212$	1.48772	−	3.25766i	0.102177	−	0.223737i
$213$	0.498223	+	3.46522i	0.0341377	+	0.237433i
$214$	−23.4154	−	6.87538i	−1.60064	−	0.469991i
$215$	−3.88345	+	2.49574i	−0.264849	+	0.170208i
$216$	−9.40305	−	20.5898i	−0.639796	−	1.40096i
$217$	−4.94212	+	1.45114i	−0.335493	+	0.0985097i
$218$	−1.52744	+	1.76275i	−0.103451	+	0.119389i
$219$	−28.4776	+	32.8649i	−1.92434	+	2.22080i
$220$	2.01233	−	0.590872i	0.135671	−	0.0398366i
$221$	13.2909	+	29.1029i	0.894040	+	1.95767i
$222$	−15.7828	+	10.1430i	−1.05927	+	0.680752i
$223$	19.9164	+	5.84797i	1.33370	+	0.391609i	0.869417	−	0.494079i	$-0.164495\pi$
$223$	19.9164	+	5.84797i	1.33370	+	0.391609i	0.464281	+	0.885688i	$0.346313\pi$
$224$	0.753201	+	5.23863i	0.0503254	+	0.350021i
$225$	2.98068	−	6.52678i	0.198712	−	0.435118i
$226$	3.82455	−	26.6003i	0.254405	−	1.76943i
$227$	9.71091	+	6.24082i	0.644536	+	0.414218i	0.821666	−	0.569969i	$-0.193045\pi$
$227$	9.71091	+	6.24082i	0.644536	+	0.414218i	−0.177130	+	0.984187i	$0.556681\pi$
$228$	5.74372	+	6.62861i	0.380387	+	0.438990i
$229$	11.1099			0.734160			0.367080	−	0.930189i	$-0.380357\pi$
$229$	11.1099			0.734160			0.367080	+	0.930189i	$0.380357\pi$
$230$	0.958560	−	8.28228i	0.0632056	−	0.546118i
$231$	−6.54350			−0.430531
$232$	−8.08432	−	9.32981i	−0.530762	−	0.612532i
$233$	−16.6973	−	10.7307i	−1.09388	−	0.702991i	−0.136154	−	0.990688i	$-0.543474\pi$
$233$	−16.6973	−	10.7307i	−1.09388	−	0.702991i	−0.957722	+	0.287696i	$0.907111\pi$
$234$	8.26598	−	57.4911i	0.540364	−	3.75831i
$235$	2.59585	−	5.68411i	0.169334	−	0.370790i
$236$	−0.546812	−	3.80316i	−0.0355944	−	0.247565i
$237$	16.7930	+	4.93088i	1.09082	+	0.320295i
$238$	10.0493	−	6.45832i	0.651402	−	0.418631i
$239$	9.10682	+	19.9412i	0.589071	+	1.28989i	0.936002	+	0.351995i	$0.114497\pi$
$239$	9.10682	+	19.9412i	0.589071	+	1.28989i	−0.346930	+	0.937891i	$0.612776\pi$
$240$	−15.3017	+	4.49298i	−0.987720	+	0.290021i
$241$	4.27448	−	4.93302i	0.275344	−	0.317764i	−0.601188	−	0.799108i	$-0.705306\pi$
$241$	4.27448	−	4.93302i	0.275344	−	0.317764i	0.876532	+	0.481344i	$0.159851\pi$
$242$	−7.73252	+	8.92380i	−0.497065	+	0.573644i
$243$	25.8078	−	7.57786i	1.65557	−	0.486120i
$244$	−2.91630	−	6.38581i	−0.186697	−	0.408809i
$245$	0.841254	−	0.540641i	0.0537457	−	0.0345403i
$246$	−48.9237	−	14.3653i	−3.11926	−	0.915898i
$247$	−1.78214	−	12.3950i	−0.113395	−	0.788678i
$248$	−3.63658	+	7.96301i	−0.230923	+	0.505652i
$249$	5.69878	−	39.6359i	0.361146	−	2.51182i
$250$	−1.46252	−	0.939906i	−0.0924980	−	0.0594449i
$251$	−8.27498	−	9.54984i	−0.522312	−	0.602780i	0.431896	−	0.901923i	$-0.357845\pi$
$251$	−8.27498	−	9.54984i	−0.522312	−	0.602780i	−0.954208	+	0.299143i	$0.903299\pi$
$252$	−7.33586			−0.462115
$253$	−4.33201	−	8.83279i	−0.272351	−	0.555313i
$254$	−25.7916			−1.61831
$255$	14.3534	+	16.5647i	0.898846	+	1.03732i
$256$	16.1671	+	10.3900i	1.01044	+	0.649373i
$257$	−0.571005	+	3.97142i	−0.0356183	+	0.247731i	−0.999850	−	0.0173308i	$-0.994483\pi$
$257$	−0.571005	+	3.97142i	−0.0356183	+	0.247731i	0.964232	+	0.265061i	$0.0853922\pi$
$258$	−10.6346	+	23.2865i	−0.662080	+	1.44975i
$259$	−0.481460	−	3.34863i	−0.0299165	−	0.208074i
$260$	−4.56768	−	1.34119i	−0.283275	−	0.0831771i
$261$	43.8445	−	28.1771i	2.71390	−	1.74412i
$262$	0.272006	+	0.595609i	0.0168046	+	0.0367969i
$263$	−15.2300	+	4.47194i	−0.939125	+	0.275752i	−0.715252	−	0.698867i	$-0.753688\pi$
$263$	−15.2300	+	4.47194i	−0.939125	+	0.275752i	−0.223873	+	0.974618i	$0.571870\pi$
$264$	−7.28281	+	8.40481i	−0.448226	+	0.517280i
$265$	−2.29388	+	2.64728i	−0.140912	+	0.162621i
$266$	−4.48614	+	1.31725i	−0.275063	+	0.0807657i
$267$	−17.5686	−	38.4698i	−1.07518	−	2.35431i
$268$	−4.63128	+	2.97634i	−0.282900	+	0.181809i
$269$	−30.0074	−	8.81096i	−1.82958	−	0.537214i	−0.829800	−	0.558061i	$-0.811546\pi$
$269$	−30.0074	−	8.81096i	−1.82958	−	0.537214i	−0.999783	+	0.0208468i	$0.993364\pi$
$270$	−3.29513	−	22.9181i	−0.200535	−	1.39475i
$271$	6.63318	−	14.5246i	0.402937	−	0.882309i	−0.594027	−	0.804445i	$-0.702463\pi$
$271$	6.63318	−	14.5246i	0.402937	−	0.882309i	0.996964	−	0.0778636i	$-0.0248099\pi$
$272$	4.88891	−	34.0031i	0.296434	−	2.06174i
$273$	12.4949	+	8.03000i	0.756227	+	0.485998i
$274$	17.2088	+	19.8600i	1.03962	+	1.19979i
$275$	−2.05135			−0.123701
$276$	−6.88714	−	14.0426i	−0.414557	−	0.845266i
$277$	−0.0997974			−0.00599625			−0.00299812	−	0.999996i	$-0.500954\pi$
$277$	−0.0997974			−0.00599625			−0.00299812	+	0.999996i	$0.500954\pi$
$278$	14.9982	+	17.3089i	0.899533	+	1.03812i
$279$	−31.0908	−	19.9808i	−1.86136	−	1.19622i
$280$	0.241874	−	1.68227i	0.0144548	−	0.100535i
$281$	−4.86948	+	10.6627i	−0.290489	+	0.636082i	−0.997465	−	0.0711554i	$-0.977331\pi$
$281$	−4.86948	+	10.6627i	−0.290489	+	0.636082i	0.706976	+	0.707237i	$0.250059\pi$
$282$	−4.93166	−	34.3005i	−0.293676	−	2.04256i
$283$	−17.1778	−	5.04387i	−1.02112	−	0.299827i	−0.272022	−	0.962291i	$-0.587692\pi$
$283$	−17.1778	−	5.04387i	−1.02112	−	0.299827i	−0.749094	+	0.662464i	$0.769511\pi$
$284$	0.943947	−	0.606638i	0.0560129	−	0.0359973i
$285$	−3.56376	−	7.80355i	−0.211099	−	0.462243i
$286$	−15.9328	+	4.67829i	−0.942126	+	0.276633i
$287$	6.02116	−	6.94878i	0.355418	−	0.410174i
$288$	−24.8681	+	28.6993i	−1.46537	+	1.69112i
$289$	−28.9901	+	8.51226i	−1.70530	+	0.500721i
$290$	−5.24581	−	11.4867i	−0.308045	−	0.674524i
$291$	−28.5103	+	18.3224i	−1.67130	+	1.07408i
$292$	13.3734	+	3.92679i	0.782621	+	0.229798i
$293$	2.65564	+	18.4704i	0.155144	+	1.07905i	0.907427	+	0.420211i	$0.138044\pi$
$293$	2.65564	+	18.4704i	0.155144	+	1.07905i	−0.752282	+	0.658841i	$0.771047\pi$
$294$	2.30372	−	5.04443i	0.134355	−	0.294197i
$295$	−0.534835	+	3.71986i	−0.0311393	+	0.216579i
$296$	−4.83701	−	3.10856i	−0.281145	−	0.180681i
$297$	−17.8910	−	20.6473i	−1.03814	−	1.19808i
$298$	−6.11380			−0.354163
$299$	−2.56732	+	22.1825i	−0.148472	+	1.28285i
$300$	−3.26129			−0.188290
$301$	−3.02301	−	3.48874i	−0.174244	−	0.201088i
$302$	18.7226	+	12.0323i	1.07736	+	0.692379i
$303$	4.78860	−	33.3055i	0.275098	−	1.91335i
$304$	−5.58553	+	12.2306i	−0.320352	+	0.701473i
$305$	0.977198	+	6.79656i	0.0559542	+	0.389170i
$306$	82.2404	+	24.1480i	4.70137	+	1.38045i
$307$	3.72207	−	2.39203i	0.212430	−	0.136520i	−0.430100	−	0.902781i	$-0.641522\pi$
$307$	3.72207	−	2.39203i	0.212430	−	0.136520i	0.642529	+	0.766261i	$0.277885\pi$
$308$	0.871242	+	1.90775i	0.0496436	+	0.108704i
$309$	−26.8340	+	7.87916i	−1.52653	+	0.448230i
$310$	−5.86403	+	6.76745i	−0.333054	+	0.384365i
$311$	−3.98162	+	4.59504i	−0.225777	+	0.260561i	−0.857324	−	0.514777i	$-0.827875\pi$
$311$	−3.98162	+	4.59504i	−0.225777	+	0.260561i	0.631547	+	0.775338i	$0.282420\pi$
$312$	24.2208	−	7.11187i	1.37123	−	0.402630i
$313$	−1.28636	−	2.81673i	−0.0727092	−	0.159211i	0.869787	−	0.493427i	$-0.164256\pi$
$313$	−1.28636	−	2.81673i	−0.0727092	−	0.159211i	−0.942497	+	0.334216i	$0.891529\pi$
$314$	−5.96681	+	3.83464i	−0.336727	+	0.216401i
$315$	6.88454	+	2.02148i	0.387900	+	0.113898i
$316$	−0.798333	−	5.55253i	−0.0449097	−	0.312354i
$317$	1.47895	−	3.23844i	0.0830660	−	0.181889i	−0.863541	−	0.504278i	$-0.831759\pi$
$317$	1.47895	−	3.23844i	0.0830660	−	0.181889i	0.946607	+	0.322389i	$0.104486\pi$
$318$	−2.76452	+	19.2276i	−0.155026	+	1.07823i
$319$	−12.5349	−	8.05569i	−0.701820	−	0.451032i
$320$	−0.522562	−	0.603068i	−0.0292121	−	0.0337125i
$321$	44.7770			2.49921
$322$	8.33440	−	0.229888i	0.464458	−	0.0128112i
$323$	18.4795			1.02823
$324$	−14.0317	−	16.1934i	−0.779539	−	0.899636i
$325$	3.91708	+	2.51736i	0.217281	+	0.139638i
$326$	0.796566	−	5.54024i	0.0441177	−	0.306845i
$327$	1.77784	−	3.89292i	0.0983146	−	0.215279i
$328$	−2.22393	−	15.4678i	−0.122796	−	0.854065i
$329$	5.99568	+	1.76049i	0.330553	+	0.0970590i
$330$	−9.57001	+	6.15027i	−0.526812	+	0.338561i
$331$	−3.90287	−	8.54609i	−0.214521	−	0.469736i	0.771527	−	0.636197i	$-0.219493\pi$
$331$	−3.90287	−	8.54609i	−0.214521	−	0.469736i	−0.986048	+	0.166461i	$0.946766\pi$
$332$	−12.3146	+	3.61589i	−0.675851	+	0.198448i
$333$	15.8962	−	18.3451i	0.871104	−	1.00531i
$334$	−18.0182	+	20.7941i	−0.985914	+	1.13780i
$335$	5.16652	−	1.51703i	0.282277	−	0.0828840i
$336$	−6.62491	−	14.5065i	−0.361418	−	0.791396i
$337$	−9.26918	+	5.95694i	−0.504924	+	0.324495i	−0.768183	−	0.640230i	$-0.778839\pi$
$337$	−9.26918	+	5.95694i	−0.504924	+	0.324495i	0.263259	+	0.964725i	$0.415203\pi$
$338$	14.4800	+	4.25170i	0.787605	+	0.231262i
$339$	7.01740	+	48.8071i	0.381133	+	2.65084i
$340$	2.91834	−	6.39026i	0.158269	−	0.346561i
$341$	−1.50370	+	10.4585i	−0.0814298	+	0.566357i
$342$	−28.2222	−	18.1373i	−1.52608	−	0.980753i
$343$	0.654861	+	0.755750i	0.0353592	+	0.0408066i
$344$	−7.84569			−0.423011
$345$	2.59382	+	15.0765i	0.139647	+	0.811692i
$346$	−2.33757			−0.125669
$347$	17.0503	+	19.6770i	0.915306	+	1.05632i	0.998213	+	0.0597618i	$0.0190341\pi$
$347$	17.0503	+	19.6770i	0.915306	+	1.05632i	−0.0829070	+	0.996557i	$0.526420\pi$
$348$	−19.9283	−	12.8072i	−1.06827	−	0.686536i
$349$	1.24802	−	8.68017i	0.0668050	−	0.464639i	−0.928769	−	0.370659i	$-0.879132\pi$
$349$	1.24802	−	8.68017i	0.0668050	−	0.464639i	0.995574	−	0.0939801i	$-0.0299590\pi$
$350$	0.722200	−	1.58140i	0.0386032	−	0.0845293i
$351$	8.82536	+	61.3817i	0.471063	+	3.27631i
$352$	10.4170	+	3.05870i	0.555226	+	0.163029i
$353$	21.4427	−	13.7804i	1.14128	−	0.733456i	0.173396	−	0.984852i	$-0.444526\pi$
$353$	21.4427	−	13.7804i	1.14128	−	0.733456i	0.967884	+	0.251396i	$0.0808896\pi$
$354$	8.65762	+	18.9575i	0.460147	+	1.00758i
$355$	−1.05304	+	0.309200i	−0.0558895	+	0.0164106i
$356$	−8.87667	+	10.2442i	−0.470463	+	0.542943i
$357$	−14.3534	+	16.5647i	−0.759663	+	0.876698i
$358$	21.6642	−	6.36119i	1.14499	−	0.336199i
$359$	−0.786409	−	1.72200i	−0.0415051	−	0.0908834i	0.887744	−	0.460338i	$-0.152272\pi$
$359$	−0.786409	−	1.72200i	−0.0415051	−	0.0908834i	−0.929249	+	0.369455i	$0.879545\pi$
$360$	10.2589	−	6.59298i	0.540690	−	0.347480i
$361$	11.2905	+	3.31518i	0.594235	+	0.174483i
$362$	4.65899	+	32.4040i	0.244871	+	1.70312i
$363$	9.00015	−	19.7076i	0.472385	−	1.03438i
$364$	0.677491	−	4.71205i	0.0355102	−	0.246979i
$365$	−11.4686	−	7.37042i	−0.600294	−	0.385785i
$366$	24.9361	+	28.7777i	1.30343	+	1.50424i
$367$	−25.4187			−1.32684			−0.663422	−	0.748245i	$-0.730897\pi$
$367$	−25.4187			−1.32684			−0.663422	+	0.748245i	$0.730897\pi$
$368$	15.1958	−	18.5465i	0.792138	−	0.966801i
$369$	65.9726			3.43440
$370$	−3.85154	−	4.44492i	−0.200232	−	0.231080i
$371$	−2.94679	−	1.89379i	−0.152990	−	0.0983206i
$372$	−2.39062	+	16.6271i	−0.123948	+	0.862077i
$373$	14.5107	−	31.7739i	0.751333	−	1.64519i	−0.0126215	−	0.999920i	$-0.504018\pi$
$373$	14.5107	−	31.7739i	0.751333	−	1.64519i	0.763955	−	0.645270i	$-0.223255\pi$
$374$	−3.48738	−	24.2553i	−0.180328	−	1.25421i
$375$	3.06064	+	0.898686i	0.158051	+	0.0464080i
$376$	8.93436	−	5.74176i	0.460754	−	0.296109i
$377$	14.0499	+	30.7650i	0.723606	+	1.58448i
$378$	22.2159	−	6.52318i	1.14266	−	0.335516i
$379$	−15.2977	+	17.6545i	−0.785789	+	0.906849i	−0.997513	−	0.0704806i	$-0.977547\pi$
$379$	−15.2977	+	17.6545i	−0.785789	+	0.906849i	0.211724	+	0.977329i	$0.432092\pi$
$380$	−1.80062	+	2.07803i	−0.0923699	+	0.106601i
$381$	45.4063	−	13.3325i	2.32623	−	0.683044i
$382$	−0.153622	−	0.336385i	−0.00785999	−	0.0172110i
$383$	−21.1869	+	13.6160i	−1.08260	+	0.695744i	−0.955156	−	0.296102i	$-0.904313\pi$
$383$	−21.1869	+	13.6160i	−1.08260	+	0.695744i	−0.127442	+	0.991846i	$0.540677\pi$
$384$	−36.6429	−	10.7593i	−1.86992	−	0.549059i
$385$	−0.291937	−	2.03047i	−0.0148785	−	0.103482i
$386$	6.69004	−	14.6491i	0.340514	−	0.745621i
$387$	4.71384	−	32.7854i	0.239618	−	1.66658i
$388$	9.13793	+	5.87259i	0.463908	+	0.298136i
$389$	2.30027	+	2.65465i	0.116628	+	0.134596i	0.811061	−	0.584961i	$-0.198890\pi$
$389$	2.30027	+	2.65465i	0.116628	+	0.134596i	−0.694433	+	0.719557i	$0.744345\pi$
$390$	25.8215			1.30752
$391$	−31.8624	−	8.40869i	−1.61135	−	0.425246i
$392$	1.69957			0.0858414
$393$	−0.786756	−	0.907965i	−0.0396866	−	0.0458008i
$394$	24.6870	+	15.8654i	1.24371	+	0.799286i
$395$	−0.780847	+	5.43091i	−0.0392887	+	0.273259i
$396$	−6.25132	+	13.6885i	−0.314141	+	0.687872i
$397$	4.18730	+	29.1233i	0.210155	+	1.46166i	0.772636	+	0.634849i	$0.218938\pi$
$397$	4.18730	+	29.1233i	0.210155	+	1.46166i	−0.562482	+	0.826810i	$0.690153\pi$
$398$	46.2127	+	13.5693i	2.31643	+	0.680166i
$399$	7.21695	−	4.63805i	0.361299	−	0.232193i
$400$	−2.07687	−	4.54770i	−0.103843	−	0.227385i
$401$	32.8019	−	9.63151i	1.63805	−	0.480975i	0.672263	−	0.740312i	$-0.265322\pi$
$401$	32.8019	−	9.63151i	1.63805	−	0.480975i	0.965787	+	0.259338i	$0.0835042\pi$
$402$	19.5547	−	22.5674i	0.975301	−	1.12556i
$403$	15.7057	−	18.1253i	0.782355	−	0.902886i
$404$	−10.3478	+	3.03838i	−0.514821	+	0.151165i
$405$	8.70614	+	19.0638i	0.432612	+	0.947288i
$406$	10.6232	−	6.82715i	0.527223	−	0.338826i
$407$	−6.65872	−	1.95518i	−0.330061	−	0.0969145i
$408$	5.30147	+	36.8725i	0.262462	+	1.82546i
$409$	−12.9121	+	28.2736i	−0.638464	+	1.39804i	0.262835	+	0.964841i	$0.415343\pi$
$409$	−12.9121	+	28.2736i	−0.638464	+	1.39804i	−0.901298	+	0.433199i	$0.857385\pi$
$410$	2.27487	−	15.8221i	0.112348	−	0.781396i
$411$	−40.5625	−	26.0679i	−2.00080	−	1.28584i
$412$	5.87001	+	6.77435i	0.289194	+	0.333748i
$413$	−3.75811			−0.184925
$414$	40.4078	+	44.1143i	1.98594	+	2.16810i
$415$	12.5534			0.616221
$416$	−16.1378	−	18.6241i	−0.791222	−	0.913119i
$417$	−35.3519	−	22.7193i	−1.73119	−	1.11257i
$418$	−1.36496	+	9.49351i	−0.0667624	+	0.464343i
$419$	6.69279	−	14.6552i	0.326964	−	0.715952i	−0.672750	−	0.739870i	$-0.734887\pi$
$419$	6.69279	−	14.6552i	0.326964	−	0.715952i	0.999714	+	0.0239182i	$0.00761412\pi$
$420$	−0.464129	−	3.22809i	−0.0226472	−	0.157515i
$421$	−9.09997	−	2.67199i	−0.443506	−	0.130225i	0.0523523	−	0.998629i	$-0.483328\pi$
$421$	−9.09997	−	2.67199i	−0.443506	−	0.130225i	−0.495858	+	0.868404i	$0.665146\pi$
$422$	−39.7376	+	25.5378i	−1.93440	+	1.24316i
$423$	18.6257	+	40.7845i	0.905611	+	1.98301i
$424$	−5.71221	+	1.67726i	−0.277409	+	0.0814548i
$425$	−4.49971	+	5.19294i	−0.218268	+	0.251894i
$426$	−3.98564	+	4.59968i	−0.193105	+	0.222855i
$427$	−6.58831	+	1.93450i	−0.318831	+	0.0936171i
$428$	−5.96189	−	13.0547i	−0.288179	−	0.631024i
$429$	25.6314	−	16.4723i	1.23750	−	0.795291i
$430$	−7.70032	−	2.26102i	−0.371342	−	0.109036i
$431$	3.35583	+	23.3403i	0.161645	+	1.12426i	0.895533	+	0.444994i	$0.146794\pi$
$431$	3.35583	+	23.3403i	0.161645	+	1.12426i	−0.733889	+	0.679270i	$0.762297\pi$
$432$	27.6602	−	60.5674i	1.33080	−	2.91405i
$433$	−1.68575	+	11.7247i	−0.0810120	+	0.563451i	0.908376	+	0.418154i	$0.137323\pi$
$433$	−1.68575	+	11.7247i	−0.0810120	+	0.563451i	−0.989388	+	0.145297i	$0.953586\pi$
$434$	−7.53310	−	4.84123i	−0.361601	−	0.232387i
$435$	15.1731	+	17.5107i	0.727496	+	0.839575i
$436$	−1.37169			−0.0656921
$437$	11.0386	+	6.67131i	0.528046	+	0.319132i
$438$	−75.6014			−3.61237
$439$	−3.97225	−	4.58422i	−0.189585	−	0.218793i	0.652997	−	0.757360i	$-0.273511\pi$
$439$	−3.97225	−	4.58422i	−0.189585	−	0.218793i	−0.842582	+	0.538567i	$0.818966\pi$
$440$	−2.93296	−	1.88490i	−0.139823	−	0.0898589i
$441$	−1.02113	+	7.10215i	−0.0486255	+	0.338198i
$442$	−23.1062	+	50.5955i	−1.09905	+	2.40658i
$443$	0.926674	+	6.44516i	0.0440276	+	0.306219i	0.999922	+	0.0125075i	$0.00398136\pi$
$443$	0.926674	+	6.44516i	0.0440276	+	0.306219i	−0.955894	+	0.293711i	$0.905110\pi$
$444$	−10.5862	−	3.10839i	−0.502400	−	0.147518i
$445$	11.1535	−	7.16790i	0.528725	−	0.339791i
$446$	14.9908	+	32.8253i	0.709836	+	1.55433i
$447$	10.7634	−	3.16041i	0.509090	−	0.149482i
$448$	0.522562	−	0.603068i	0.0246887	−	0.0284923i
$449$	2.73488	−	3.15622i	0.129067	−	0.148951i	−0.687537	−	0.726149i	$-0.741308\pi$
$449$	2.73488	−	3.15622i	0.129067	−	0.148951i	0.816605	+	0.577198i	$0.195854\pi$
$450$	11.9688	−	3.51435i	0.564214	−	0.165668i
$451$	−7.83523	−	17.1568i	−0.368947	−	0.807881i
$452$	13.2953	−	8.54440i	0.625360	−	0.401895i
$453$	−39.1811	−	11.5046i	−1.84089	−	0.540533i
$454$	2.85600	+	19.8639i	0.134039	+	0.932261i
$455$	−1.93427	+	4.23547i	−0.0906801	+	0.198562i
$456$	2.07499	−	14.4319i	0.0971704	−	0.675835i
$457$	4.08611	+	2.62598i	0.191140	+	0.122838i	0.632711	−	0.774388i	$-0.281942\pi$
$457$	4.08611	+	2.62598i	0.191140	+	0.122838i	−0.441571	+	0.897226i	$0.645579\pi$
$458$	12.6483	+	14.5969i	0.591017	+	0.682070i
$459$	−91.5128			−4.27145
$460$	4.05019	−	2.76361i	0.188841	−	0.128854i
$461$	−34.9871			−1.62951			−0.814757	−	0.579803i	$-0.803129\pi$
$461$	−34.9871			−1.62951			−0.814757	+	0.579803i	$0.803129\pi$
$462$	−7.44963	−	8.59733i	−0.346588	−	0.399984i
$463$	7.65901	+	4.92215i	0.355944	+	0.228752i	0.706376	−	0.707837i	$-0.250329\pi$
$463$	7.65901	+	4.92215i	0.355944	+	0.228752i	−0.350432	+	0.936588i	$0.613965\pi$
$464$	5.16811	−	35.9450i	0.239923	−	1.66870i
$465$	6.82535	−	14.9454i	0.316518	−	0.693078i
$466$	−4.91071	−	34.1548i	−0.227484	−	1.58219i
$467$	−30.2520	−	8.88280i	−1.39990	−	0.411047i	−0.507249	−	0.861800i	$-0.669338\pi$
$467$	−30.2520	−	8.88280i	−1.39990	−	0.411047i	−0.892649	+	0.450753i	$0.851156\pi$
$468$	28.7351	−	18.4670i	1.32828	−	0.853635i
$469$	2.23686	+	4.89804i	0.103289	+	0.226170i
$470$	10.4235	−	3.06062i	0.480801	−	0.141176i
$471$	8.52236	−	9.83533i	0.392690	−	0.453188i
$472$	−4.18272	+	4.82711i	−0.192525	+	0.222186i
$473$	−9.08599	+	2.66789i	−0.417774	+	0.122670i
$474$	12.6399	+	27.6776i	0.580571	+	1.27127i
$475$	2.26247	−	1.45400i	0.103809	−	0.0667141i
$476$	6.74054	+	1.97920i	0.308952	+	0.0907166i
$477$	−3.57689	−	24.8778i	−0.163775	−	1.13908i
$478$	−15.8322	+	34.6678i	−0.724150	+	1.58567i
$479$	3.63037	−	25.2498i	0.165876	−	1.15369i	−0.721422	−	0.692496i	$-0.756511\pi$
$479$	3.63037	−	25.2498i	0.165876	−	1.15369i	0.887298	−	0.461197i	$-0.152580\pi$
$480$	−14.2023	−	9.12726i	−0.648243	−	0.416601i
$481$	10.3156	+	11.9048i	0.470351	+	0.542814i
$482$	11.3478			0.516876
$483$	−14.5539	+	4.71303i	−0.662226	+	0.214450i
$484$	−6.94407			−0.315640
$485$	−6.95748	−	8.02936i	−0.315923	−	0.364595i
$486$	39.3380	+	25.2810i	1.78441	+	1.14677i
$487$	−1.49666	+	10.4095i	−0.0678200	+	0.471698i	0.927403	+	0.374065i	$0.122036\pi$
$487$	−1.49666	+	10.4095i	−0.0678200	+	0.471698i	−0.995222	+	0.0976332i	$0.968873\pi$
$488$	−4.84791	+	10.6154i	−0.219454	+	0.480538i
$489$	1.46156	+	10.1654i	0.0660941	+	0.459695i
$490$	1.66808	+	0.489793i	0.0753562	+	0.0221266i
$491$	27.6182	−	17.7491i	1.24639	−	0.801006i	0.260029	−	0.965601i	$-0.416268\pi$
$491$	27.6182	−	17.7491i	1.24639	−	0.801006i	0.986361	+	0.164595i	$0.0526316\pi$
$492$	−12.4567	−	27.2763i	−0.561590	−	1.22971i
$493$	−47.8886	+	14.0614i	−2.15679	+	0.633292i
$494$	14.2566	−	16.4530i	0.641434	−	0.740254i
$495$	9.63875	−	11.1237i	0.433230	−	0.499974i
$496$	−24.7081	+	7.25496i	−1.10943	+	0.325757i
$497$	−0.455916	−	0.998317i	−0.0204506	−	0.0447807i
$498$	58.5644	−	37.6371i	2.62434	−	1.68656i
$499$	33.2790	+	9.77159i	1.48977	+	0.437437i	0.922469	−	0.386072i	$-0.126168\pi$
$499$	33.2790	+	9.77159i	1.48977	+	0.437437i	0.567303	+	0.823509i	$0.307987\pi$
$500$	−0.145502	−	1.01199i	−0.00650703	−	0.0452574i
$501$	20.9721	−	45.9224i	0.936962	−	2.05166i
$502$	3.12639	−	21.7445i	0.139538	−	0.970507i
$503$	10.2218	+	6.56916i	0.455768	+	0.292904i	0.748311	−	0.663348i	$-0.230865\pi$
$503$	10.2218	+	6.56916i	0.455768	+	0.292904i	−0.292543	+	0.956252i	$0.594501\pi$
$504$	7.98586	+	9.21617i	0.355719	+	0.410521i
$505$	10.5484			0.469399
$506$	6.67328	−	15.7476i	0.296663	−	0.700068i
$507$	−27.6899			−1.22975
$508$	−9.93275	−	11.4630i	−0.440695	−	0.508589i
$509$	−22.2595	−	14.3053i	−0.986635	−	0.634072i	−0.0553899	−	0.998465i	$-0.517640\pi$
$509$	−22.2595	−	14.3053i	−0.986635	−	0.634072i	−0.931245	+	0.364393i	$0.881277\pi$
$510$	−5.42290	+	37.7171i	−0.240130	+	1.67014i
$511$	5.66325	−	12.4008i	0.250527	−	0.548578i
$512$	1.34713	+	9.36946i	0.0595351	+	0.414076i
$513$	34.3672	+	10.0911i	1.51735	+	0.445534i
$514$	−5.86802	+	3.77115i	−0.258827	+	0.166338i
$515$	−3.64212	−	7.97512i	−0.160491	−	0.351426i
$516$	−14.4451	+	4.24148i	−0.635912	+	0.186721i
$517$	8.39430	−	9.68754i	0.369181	−	0.426057i
$518$	3.85154	−	4.44492i	0.169227	−	0.195298i
$519$	4.11531	−	1.20836i	0.180642	−	0.0530413i
$520$	3.28744	+	7.19849i	0.144164	+	0.315675i
$521$	−0.538212	+	0.345888i	−0.0235795	+	0.0151536i	−0.552377	−	0.833594i	$-0.686279\pi$
$521$	−0.538212	+	0.345888i	−0.0235795	+	0.0151536i	0.528798	+	0.848748i	$0.322643\pi$
$522$	86.9371	+	25.5270i	3.80513	+	1.11729i
$523$	−3.09028	−	21.4933i	−0.135128	−	0.939838i	−0.938726	−	0.344665i	$-0.887993\pi$
$523$	−3.09028	−	21.4933i	−0.135128	−	0.939838i	0.803598	−	0.595173i	$-0.202917\pi$
$524$	−0.159963	+	0.350271i	−0.00698803	+	0.0153016i
$525$	−0.453964	+	3.15739i	−0.0198126	+	0.137800i
$526$	−23.2146	−	14.9191i	−1.01221	−	0.650505i
$527$	23.1769	+	26.7476i	1.00960	+	1.16514i
$528$	−32.7142			−1.42370
$529$	−15.9971	−	16.5255i	−0.695525	−	0.718502i
$530$	−6.08973			−0.264521
$531$	−17.6584	−	20.3789i	−0.766310	−	0.884369i
$532$	−2.31313	−	1.48656i	−0.100287	−	0.0644505i
$533$	−6.09280	+	42.3763i	−0.263908	+	1.83552i
$534$	30.5430	−	66.8799i	1.32173	−	2.89418i
$535$	1.99772	+	13.8944i	0.0863689	+	0.600709i
$536$	8.78088	+	2.57830i	0.379276	+	0.111366i
$537$	−34.8517	+	22.3978i	−1.50396	+	0.966537i
$538$	−22.5862	−	49.4570i	−0.973762	−	2.13224i
$539$	1.96825	−	0.577931i	0.0847786	−	0.0248932i
$540$	8.91689	−	10.2906i	0.383722	−	0.442839i
$541$	7.53941	−	8.70095i	0.324145	−	0.374083i	−0.570166	−	0.821530i	$-0.693121\pi$
$541$	7.53941	−	8.70095i	0.324145	−	0.374083i	0.894311	+	0.447447i	$0.147667\pi$
$542$	26.6352	−	7.82081i	1.14408	−	0.335933i
$543$	−24.9528	−	54.6391i	−1.07083	−	2.34479i
$544$	30.5931	−	19.6610i	1.31167	−	0.842957i
$545$	1.28730	+	0.377986i	0.0551419	+	0.0161911i
$546$	3.67479	+	25.5587i	0.157266	+	1.09381i
$547$	−2.31643	+	5.07228i	−0.0990435	+	0.216875i	−0.952667	−	0.304015i	$-0.901673\pi$
$547$	−2.31643	+	5.07228i	−0.0990435	+	0.216875i	0.853624	+	0.520890i	$0.174400\pi$
$548$	−2.19935	+	15.2968i	−0.0939516	+	0.653448i
$549$	−41.4469	−	26.6363i	−1.76891	−	1.13681i
$550$	−2.33541	−	2.69521i	−0.0995823	−	0.114924i
$551$	19.5349			0.832213
$552$	−10.1446	+	23.9393i	−0.431784	+	1.01893i
$553$	−5.48676			−0.233321
$554$	−0.113617	−	0.131121i	−0.00482713	−	0.00557080i
$555$	9.07838	+	5.83432i	0.385356	+	0.247653i
$556$	−1.91683	+	13.3318i	−0.0812916	+	0.565395i
$557$	16.4910	−	36.1103i	0.698746	−	1.53004i	−0.142739	−	0.989760i	$-0.545591\pi$
$557$	16.4910	−	36.1103i	0.698746	−	1.53004i	0.841485	−	0.540281i	$-0.181682\pi$
$558$	−9.14387	−	63.5970i	−0.387091	−	2.69228i
$559$	20.6238	+	6.05570i	0.872294	+	0.256129i
$560$	4.20585	−	2.70293i	0.177729	−	0.114220i
$561$	18.6779	+	40.8988i	0.788580	+	1.72675i
$562$	−19.5532	+	5.74133i	−0.824801	+	0.242184i
$563$	20.8583	−	24.0718i	0.879072	−	1.01450i	−0.120690	−	0.992690i	$-0.538511\pi$
$563$	20.8583	−	24.0718i	0.879072	−	1.01450i	0.999762	−	0.0218132i	$-0.00694390\pi$
$564$	13.3455	−	15.4015i	0.561947	−	0.648521i
$565$	−14.8319	+	4.35504i	−0.623982	+	0.183218i
$566$	−12.9296	−	28.3118i	−0.543470	−	1.19003i
$567$	−17.6307	+	11.3306i	−0.740421	+	0.475840i
$568$	−1.78972	−	0.525508i	−0.0750949	−	0.0220498i
$569$	−2.36538	−	16.4516i	−0.0991619	−	0.689686i	−0.977390	−	0.211444i	$-0.932183\pi$
$569$	−2.36538	−	16.4516i	−0.0991619	−	0.689686i	0.878228	−	0.478242i	$-0.158726\pi$
$570$	6.19561	−	13.5665i	0.259506	−	0.568238i
$571$	−0.848125	+	5.89884i	−0.0354929	+	0.246859i	−0.999842	−	0.0177746i	$-0.994342\pi$
$571$	−0.848125	+	5.89884i	−0.0354929	+	0.246859i	0.964349	+	0.264633i	$0.0852509\pi$
$572$	−8.21522	−	5.27960i	−0.343496	−	0.220751i
$573$	0.444340	+	0.512796i	0.0185626	+	0.0214224i
$574$	15.9848			0.667191
$575$	−4.56256	+	1.47751i	−0.190272	+	0.0616162i
$576$	5.72561			0.238567
$577$	15.1234	+	17.4534i	0.629596	+	0.726593i	0.977500	−	0.210937i	$-0.0676516\pi$
$577$	15.1234	+	17.4534i	0.629596	+	0.726593i	−0.347903	+	0.937530i	$0.613106\pi$
$578$	−44.1886	−	28.3983i	−1.83800	−	1.18121i
$579$	−4.20525	+	29.2482i	−0.174764	+	1.21551i
$580$	3.08500	−	6.75520i	0.128098	−	0.280495i
$581$	1.78653	+	12.4256i	0.0741178	+	0.515501i
$582$	−56.5316	−	16.5992i	−2.34331	−	0.688058i
$583$	−6.04489	+	3.88481i	−0.250354	+	0.160893i
$584$	−9.62510	−	21.0760i	−0.398290	−	0.872132i
$585$	−32.0561	+	9.41251i	−1.32536	+	0.389160i
$586$	−21.2444	+	24.5173i	−0.877596	+	1.01280i
$587$	0.532714	−	0.614784i	0.0219875	−	0.0253749i	−0.744649	−	0.667456i	$-0.767383\pi$
$587$	0.532714	−	0.614784i	0.0219875	−	0.0253749i	0.766637	+	0.642081i	$0.221929\pi$
$588$	3.12918	−	0.918811i	0.129045	−	0.0378911i
$589$	−5.75452	−	12.6006i	−0.237111	−	0.519201i
$590$	−5.49632	+	3.53227i	−0.226280	+	0.145421i
$591$	−51.6629	−	15.1696i	−2.12513	−	0.623994i
$592$	−2.40706	−	16.7415i	−0.0989295	−	0.688070i
$593$	−17.8689	+	39.1275i	−0.733789	+	1.60677i	0.0597199	+	0.998215i	$0.480979\pi$
$593$	−17.8689	+	39.1275i	−0.733789	+	1.60677i	−0.793509	+	0.608559i	$0.791748\pi$
$594$	6.75945	−	47.0130i	0.277343	−	1.92897i
$595$	−5.78046	−	3.71487i	−0.236976	−	0.152295i
$596$	−2.35452	−	2.71726i	−0.0964449	−	0.111303i
$597$	−88.3720			−3.61683
$598$	−32.0678	+	21.8811i	−1.31135	+	0.894786i
$599$	8.71078			0.355913			0.177956	−	0.984038i	$-0.443051\pi$
$599$	8.71078			0.355913			0.177956	+	0.984038i	$0.443051\pi$
$600$	3.55026	+	4.09722i	0.144939	+	0.167268i
$601$	−24.1758	−	15.5368i	−0.986150	−	0.633760i	−0.0550341	−	0.998484i	$-0.517527\pi$
$601$	−24.1758	−	15.5368i	−0.986150	−	0.633760i	−0.931115	+	0.364725i	$0.881163\pi$
$602$	1.14213	−	7.94371i	0.0465499	−	0.323762i
$603$	−16.0499	+	35.1443i	−0.653601	+	1.43119i
$604$	1.86265	+	12.9550i	0.0757901	+	0.527132i
$605$	6.51686	+	1.91352i	0.264948	+	0.0777957i
$606$	49.2109	−	31.6259i	1.99905	−	1.28471i
$607$	1.82335	+	3.99258i	0.0740076	+	0.162054i	0.943020	−	0.332737i	$-0.107972\pi$
$607$	1.82335	+	3.99258i	0.0740076	+	0.162054i	−0.869012	+	0.494791i	$0.835245\pi$
$608$	−13.6571	+	4.01008i	−0.553868	+	0.162630i
$609$	−15.1731	+	17.5107i	−0.614846	+	0.709570i
$610$	−7.81730	+	9.02164i	−0.316513	+	0.365276i
$611$	−27.9173	+	8.19727i	−1.12941	+	0.331626i
$612$	20.9396	+	45.8513i	0.846433	+	1.85343i
$613$	−21.6544	+	13.9164i	−0.874612	+	0.562079i	−0.899160	−	0.437620i	$-0.855822\pi$
$613$	−21.6544	+	13.9164i	−0.874612	+	0.562079i	0.0245484	+	0.999699i	$0.492185\pi$
$614$	7.38031	+	2.16705i	0.297845	+	0.0874552i
$615$	4.17400	+	29.0308i	0.168312	+	1.17063i
$616$	1.44831	−	3.17135i	0.0583540	−	0.127777i
$617$	3.30498	−	22.9866i	0.133053	−	0.925407i	−0.808489	−	0.588512i	$-0.799714\pi$
$617$	3.30498	−	22.9866i	0.133053	−	0.925407i	0.941542	−	0.336895i	$-0.109377\pi$
$618$	−40.9021	−	26.2862i	−1.64532	−	1.05738i
$619$	1.46010	+	1.68505i	0.0586866	+	0.0677279i	0.784334	−	0.620339i	$-0.213005\pi$
$619$	1.46010	+	1.68505i	0.0586866	+	0.0677279i	−0.725647	+	0.688067i	$0.758460\pi$
$620$	−5.26610			−0.211492
$621$	−54.6642	−	33.0371i	−2.19360	−	1.32573i
$622$	−10.5703			−0.423830
$623$	8.68225	+	10.0198i	0.347847	+	0.401437i
$624$	62.4684	+	40.1460i	2.50074	+	1.60713i
$625$	−0.142315	+	0.989821i	−0.00569259	+	0.0395929i
$626$	2.23633	−	4.89689i	0.0893819	−	0.195719i
$627$	−2.50447	−	17.4190i	−0.100019	−	0.695646i
$628$	−4.00221	−	1.17515i	−0.159705	−	0.0468938i
$629$	−19.5556	+	12.5677i	−0.779735	+	0.501105i
$630$	5.18192	+	11.3468i	0.206453	+	0.452068i
$631$	−5.04020	+	1.47994i	−0.200647	+	0.0589153i	−0.380512	−	0.924776i	$-0.624252\pi$
$631$	−5.04020	+	1.47994i	−0.200647	+	0.0589153i	0.179865	+	0.983691i	$0.442434\pi$
$632$	−6.10667	+	7.04748i	−0.242910	+	0.280334i
$633$	56.7570	−	65.5011i	2.25589	−	2.60344i
$634$	5.93865	−	1.74375i	0.235854	−	0.0692530i
$635$	6.16290	+	13.4949i	0.244567	+	0.535527i
$636$	−9.61033	+	6.17619i	−0.381074	+	0.244902i
$637$	−4.46763	−	1.31182i	−0.177014	−	0.0519760i
$638$	−3.68654	−	25.6405i	−0.145952	−	1.01512i
$639$	3.27128	−	7.16311i	0.129410	−	0.283368i
$640$	1.70383	−	11.8504i	0.0673499	−	0.468429i
$641$	−13.7662	−	8.84698i	−0.543731	−	0.349435i	0.239766	−	0.970831i	$-0.422929\pi$
$641$	−13.7662	−	8.84698i	−0.543731	−	0.349435i	−0.783497	+	0.621396i	$0.786566\pi$
$642$	50.9776	+	58.8313i	2.01193	+	2.32189i
$643$	−14.3140			−0.564489			−0.282244	−	0.959343i	$-0.591079\pi$
$643$	−14.3140			−0.564489			−0.282244	+	0.959343i	$0.591079\pi$
$644$	3.31188	+	3.61567i	0.130506	+	0.142477i
$645$	14.7252			0.579806
$646$	21.0385	+	24.2797i	0.827749	+	0.955274i
$647$	23.2870	+	14.9657i	0.915508	+	0.588361i	0.911351	−	0.411630i	$-0.135040\pi$
$647$	23.2870	+	14.9657i	0.915508	+	0.588361i	0.00415678	+	0.999991i	$0.498677\pi$
$648$	−5.06913	+	35.2566i	−0.199134	+	1.38501i
$649$	−3.20251	+	7.01253i	−0.125710	+	0.275266i
$650$	1.15202	+	8.01250i	0.0451861	+	0.314276i
$651$	15.7647	+	4.62892i	0.617866	+	0.181422i
$652$	2.76911	−	1.77960i	0.108447	−	0.0696946i
$653$	12.5020	+	27.3756i	0.489242	+	1.07129i	0.979818	+	0.199892i	$0.0640591\pi$
$653$	12.5020	+	27.3756i	0.489242	+	1.07129i	−0.490576	+	0.871398i	$0.663214\pi$
$654$	7.13883	−	2.09615i	0.279150	−	0.0819659i
$655$	0.246643	−	0.284641i	0.00963715	−	0.0111219i
$656$	30.1028	−	34.7404i	1.17532	−	1.35639i
$657$	93.8551	−	27.5584i	3.66164	−	1.07515i
$658$	4.51289	+	9.88184i	0.175931	+	0.385234i
$659$	31.8131	−	20.4450i	1.23926	−	0.796425i	0.253954	−	0.967216i	$-0.418269\pi$
$659$	31.8131	−	20.4450i	1.23926	−	0.796425i	0.985307	+	0.170792i	$0.0546326\pi$
$660$	−6.41903	−	1.88480i	−0.249861	−	0.0733657i
$661$	−0.742576	−	5.16473i	−0.0288829	−	0.200885i	0.970271	−	0.242023i	$-0.0778108\pi$
$661$	−0.742576	−	5.16473i	−0.0288829	−	0.200885i	−0.999153	+	0.0411379i	$0.986902\pi$
$662$	6.78515	−	14.8574i	0.263712	−	0.577450i
$663$	14.5242	−	101.018i	0.564073	−	3.92321i
$664$	17.9485	+	11.5348i	0.696536	+	0.447636i
$665$	1.76118	+	2.03251i	0.0682957	+	0.0788175i
$666$	42.2006			1.63524
$667$	−33.6821	−	8.88890i	−1.30417	−	0.344180i
$668$	−16.1810			−0.626062
$669$	−43.3599	−	50.0400i	−1.67639	−	1.93466i
$670$	7.87515	+	5.06105i	0.304243	+	0.195525i
$671$	−2.00457	+	13.9421i	−0.0773856	+	0.538229i
$672$	7.01316	−	15.3567i	0.270539	−	0.592397i
$673$	0.475138	+	3.30466i	0.0183152	+	0.127385i	0.996928	−	0.0783273i	$-0.0249579\pi$
$673$	0.475138	+	3.30466i	0.0183152	+	0.127385i	−0.978612	+	0.205712i	$0.934049\pi$
$674$	−18.3794	−	5.39668i	−0.707949	−	0.207872i
$675$	−11.2040	+	7.20038i	−0.431243	+	0.277143i
$676$	3.68680	+	8.07297i	0.141800	+	0.310499i
$677$	−25.1004	+	7.37014i	−0.964686	+	0.283257i	−0.725889	−	0.687812i	$-0.758571\pi$
$677$	−25.1004	+	7.37014i	−0.964686	+	0.283257i	−0.238797	+	0.971069i	$0.576753\pi$
$678$	−56.1371	+	64.7857i	−2.15593	+	2.48808i
$679$	6.95748	−	8.02936i	0.267004	−	0.308139i
$680$	−11.2051	+	3.29012i	−0.429697	+	0.126170i
$681$	−15.2963	−	33.4942i	−0.586155	−	1.28350i
$682$	−15.4530	+	9.93104i	−0.591726	+	0.380279i
$683$	46.4931	+	13.6516i	1.77901	+	0.522364i	0.995132	−	0.0985540i	$-0.0314217\pi$
$683$	46.4931	+	13.6516i	1.77901	+	0.522364i	0.783876	+	0.620918i	$0.213240\pi$
$684$	−2.80774	−	19.5282i	−0.107357	−	0.746681i
$685$	6.27926	−	13.7497i	0.239918	−	0.525348i
$686$	−0.247415	+	1.72081i	−0.00944634	+	0.0657007i
$687$	−29.8131	−	19.1597i	−1.13744	−	0.730988i
$688$	−15.1136	−	17.4420i	−0.576199	−	0.664969i
$689$	16.3102			0.621368
$690$	−16.8556	+	20.5722i	−0.641683	+	0.783171i
$691$	33.4589			1.27284			0.636419	−	0.771344i	$-0.280415\pi$
$691$	33.4589			1.27284			0.636419	+	0.771344i	$0.280415\pi$
$692$	−0.900237	−	1.03893i	−0.0342219	−	0.0394941i
$693$	12.3822	+	7.95757i	0.470362	+	0.302283i
$694$	−6.44181	+	44.8037i	−0.244528	+	1.70073i
$695$	5.47264	−	11.9834i	0.207589	−	0.454557i
$696$	5.60423	+	38.9783i	0.212428	+	1.47747i
$697$	−60.6189	−	17.7993i	−2.29610	−	0.674197i
$698$	12.8255	−	8.24244i	0.485452	−	0.311981i
$699$	26.3010	+	57.5912i	0.994795	+	2.17830i
$700$	0.980979	−	0.288041i	0.0370775	−	0.0108869i
$701$	9.78545	−	11.2930i	0.369591	−	0.426531i	−0.540239	−	0.841512i	$-0.681666\pi$
$701$	9.78545	−	11.2930i	0.369591	−	0.426531i	0.909830	+	0.414980i	$0.136212\pi$
$702$	−70.6003	+	81.4771i	−2.66464	+	3.07516i
$703$	8.72986	−	2.56332i	0.329253	−	0.0966774i
$704$	−0.680001	−	1.48899i	−0.0256285	−	0.0561186i
$705$	−16.7685	+	10.7765i	−0.631539	+	0.405865i
$706$	42.5177	+	12.4843i	1.60018	+	0.469854i
$707$	1.50120	+	10.4411i	0.0564583	+	0.392676i
$708$	−5.09144	+	11.1487i	−0.191348	+	0.418994i
$709$	−0.182384	+	1.26851i	−0.00684959	+	0.0476399i	−0.992960	−	0.118454i	$-0.962206\pi$
$709$	−0.182384	+	1.26851i	−0.00684959	+	0.0476399i	0.986110	+	0.166094i	$0.0531154\pi$
$710$	−1.60511	−	1.03154i	−0.0602388	−	0.0387131i
$711$	−25.7809	−	29.7527i	−0.966859	−	1.11581i
$712$	22.5332			0.844468
$713$	4.18832	+	24.3445i	0.156854	+	0.911710i
$714$	−38.1050			−1.42604
$715$	6.25495	+	7.21859i	0.233922	+	0.269960i
$716$	11.1704	+	7.17881i	0.417459	+	0.268285i
$717$	9.95190	−	69.2170i	0.371660	−	2.58496i
$718$	1.36717	−	2.99369i	0.0510225	−	0.111724i
$719$	−0.382320	−	2.65910i	−0.0142581	−	0.0991675i	0.981450	−	0.191720i	$-0.0614065\pi$
$719$	−0.382320	−	2.65910i	−0.0142581	−	0.0991675i	−0.995708	+	0.0925524i	$0.970497\pi$
$720$	34.4192	+	10.1064i	1.28273	+	0.376643i
$721$	7.37562	−	4.74002i	0.274682	−	0.176528i
$722$	8.49822	+	18.6085i	0.316271	+	0.692537i
$723$	−19.9778	+	5.86601i	−0.742982	+	0.218159i
$724$	−12.6076	+	14.5500i	−0.468559	+	0.540745i
$725$	−4.75668	+	5.48950i	−0.176659	+	0.203875i
$726$	36.1397	−	10.6116i	1.34127	−	0.393833i
$727$	17.4396	+	38.1875i	0.646800	+	1.41629i	0.894327	+	0.447414i	$0.147655\pi$
$727$	17.4396	+	38.1875i	0.646800	+	1.41629i	−0.247527	+	0.968881i	$0.579618\pi$
$728$	−6.65737	+	4.27843i	−0.246738	+	0.158569i
$729$	−21.9969	−	6.45888i	−0.814701	−	0.239218i
$730$	−3.37294	−	23.4593i	−0.124838	−	0.868269i
$731$	−13.1768	+	28.8531i	−0.487360	+	1.06717i
$732$	−3.18692	+	22.1655i	−0.117792	+	0.819261i
$733$	−25.0389	−	16.0915i	−0.924834	−	0.594355i	−0.0107778	−	0.999942i	$-0.503431\pi$
$733$	−25.0389	−	16.0915i	−0.924834	−	0.594355i	−0.914056	+	0.405587i	$0.867067\pi$
$734$	−28.9386	−	33.3969i	−1.06814	−	1.23270i
$735$	−3.18986			−0.117660
$736$	25.3723	−	0.699845i	0.935235	−	0.0257966i
$737$	11.0457			0.406875
$738$	75.1084	+	86.6797i	2.76478	+	3.19072i
$739$	31.4117	+	20.1871i	1.15550	+	0.742594i	0.970727	−	0.240187i	$-0.0772087\pi$
$739$	31.4117	+	20.1871i	1.15550	+	0.742594i	0.184773	+	0.982781i	$0.440845\pi$
$740$	0.492241	−	3.42361i	0.0180952	−	0.125855i
$741$	−16.5937	+	36.3352i	−0.609586	+	1.33481i
$742$	−0.866659	−	6.02775i	−0.0318161	−	0.221286i
$743$	6.70891	+	1.96992i	0.246126	+	0.0722692i	0.402469	−	0.915434i	$-0.368152\pi$
$743$	6.70891	+	1.96992i	0.246126	+	0.0722692i	−0.156343	+	0.987703i	$0.549970\pi$
$744$	23.4914	−	15.0970i	0.861238	−	0.553484i
$745$	1.46089	+	3.19890i	0.0535229	+	0.117199i
$746$	58.2669	−	17.1087i	2.13330	−	0.626394i
$747$	−58.9851	+	68.0725i	−2.15815	+	2.49064i
$748$	9.43715	−	10.8911i	0.345056	−	0.398216i
$749$	−13.4687	+	3.95477i	−0.492136	+	0.144504i
$750$	2.30372	+	5.04443i	0.0841198	+	0.184197i
$751$	−19.6507	+	12.6287i	−0.717064	+	0.460829i	−0.847614	−	0.530613i	$-0.821962\pi$
$751$	−19.6507	+	12.6287i	−0.717064	+	0.460829i	0.130551	+	0.991442i	$0.458325\pi$
$752$	29.9754	+	8.80157i	1.09309	+	0.320960i
$753$	5.73640	+	39.8975i	0.209046	+	1.45395i
$754$	−24.4258	+	53.4850i	−0.889534	+	1.94781i
$755$	1.82185	−	12.6713i	0.0663040	−	0.461155i
$756$	11.4549	+	7.36162i	0.416611	+	0.267739i
$757$	7.78169	+	8.98055i	0.282830	+	0.326404i	0.879333	−	0.476208i	$-0.157989\pi$
$757$	7.78169	+	8.98055i	0.282830	+	0.326404i	−0.596503	+	0.802611i	$0.703443\pi$
$758$	−40.6118			−1.47509
$759$	−3.60790	+	31.1734i	−0.130958	+	1.13152i
$760$	4.57083			0.165802
$761$	−24.2786	−	28.0190i	−0.880097	−	1.01569i	−0.999738	−	0.0228690i	$-0.992720\pi$
$761$	−24.2786	−	28.0190i	−0.880097	−	1.01569i	0.119641	−	0.992817i	$-0.461826\pi$
$762$	69.2112	+	44.4793i	2.50726	+	1.61132i
$763$	−0.190936	+	1.32799i	−0.00691236	+	0.0480765i
$764$	0.0903433	−	0.197824i	0.00326851	−	0.00715703i
$765$	−7.01647	−	48.8006i	−0.253681	−	1.76439i
$766$	−42.0104	−	12.3354i	−1.51790	−	0.445695i
$767$	14.7208	−	9.46051i	0.531539	−	0.341599i
$768$	−25.4659	−	55.7625i	−0.918921	−	2.01216i
$769$	48.6298	−	14.2790i	1.75364	−	0.514914i	0.762411	−	0.647093i	$-0.224015\pi$
$769$	48.6298	−	14.2790i	1.75364	−	0.514914i	0.991226	+	0.132179i	$0.0421972\pi$
$770$	2.33541	−	2.69521i	0.0841624	−	0.0971286i
$771$	8.38126	−	9.67249i	0.301844	−	0.348346i
$772$	9.08721	−	2.66825i	0.327056	−	0.0960322i
$773$	−14.8053	−	32.4192i	−0.532511	−	1.16604i	−0.964482	−	0.264149i	$-0.914909\pi$
$773$	−14.8053	−	32.4192i	−0.532511	−	1.16604i	0.431971	−	0.901888i	$-0.357818\pi$
$774$	48.4425	−	31.1321i	1.74123	−	1.11902i
$775$	4.94212	+	1.45114i	0.177526	+	0.0521264i
$776$	−2.56976	−	17.8731i	−0.0922491	−	0.641607i
$777$	−4.48295	+	9.81628i	−0.160825	+	0.352157i
$778$	−0.869071	+	6.04452i	−0.0311577	+	0.216707i
$779$	20.8024	+	13.3689i	0.745323	+	0.478990i
$780$	9.94428	+	11.4763i	0.356063	+	0.410918i
$781$	−2.25134			−0.0805594
$782$	−25.2267	−	51.4363i	−0.902106	−	1.83936i
$783$	−96.7390			−3.45717
$784$	3.27398	+	3.77837i	0.116928	+	0.134942i
$785$	3.43216	+	2.20571i	0.122499	+	0.0787252i
$786$	0.297247	−	2.06740i	0.0106024	−	0.0737416i
$787$	−17.7068	+	38.7726i	−0.631180	+	1.38209i	0.275921	+	0.961180i	$0.411017\pi$
$787$	−17.7068	+	38.7726i	−0.631180	+	1.38209i	−0.907102	+	0.420912i	$0.861710\pi$
$788$	2.45603	+	17.0821i	0.0874926	+	0.608524i
$789$	48.5816	+	14.2649i	1.72955	+	0.507842i
$790$	−8.02451	+	5.15704i	−0.285499	+	0.183479i
$791$	−6.42151	−	14.0611i	−0.228323	−	0.499957i
$792$	24.0023	−	7.04772i	0.852886	−	0.250430i
$793$	20.9371	−	24.1627i	0.743499	−	0.858043i
$794$	−33.4972	+	38.6578i	−1.18877	+	1.37192i
$795$	10.7210	−	3.14797i	0.380235	−	0.111647i
$796$	11.7664	+	25.7648i	0.417049	+	0.913210i
$797$	−7.25599	+	4.66314i	−0.257020	+	0.165177i	−0.662806	−	0.748792i	$-0.730634\pi$
$797$	−7.25599	+	4.66314i	−0.257020	+	0.165177i	0.405785	+	0.913968i	$0.366998\pi$
$798$	14.3101	+	4.20184i	0.506573	+	0.148743i
$799$	−6.11058	−	42.5000i	−0.216177	−	1.50354i
$800$	2.19858	−	4.81423i	0.0777316	−	0.170209i
$801$	−13.5384	+	94.1614i	−0.478355	+	3.32703i
$802$	49.9988	+	32.1323i	1.76552	+	1.13463i
$803$	−18.3135	−	21.1349i	−0.646269	−	0.745834i
$804$	17.5608			0.619323
$805$	−2.11179	−	4.30585i	−0.0744307	−	0.151761i
$806$	41.6949			1.46864
$807$	65.3291	+	75.3938i	2.29969	+	2.65399i
$808$	15.0818	+	9.69251i	0.530577	+	0.340981i
$809$	0.647763	−	4.50529i	0.0227741	−	0.158397i	−0.975261	−	0.221057i	$-0.929049\pi$
$809$	0.647763	−	4.50529i	0.0227741	−	0.158397i	0.998035	+	0.0626598i	$0.0199583\pi$
$810$	−15.1357	+	33.1425i	−0.531813	+	1.16451i
$811$	−3.98688	−	27.7294i	−0.139998	−	0.973710i	−0.931811	−	0.362945i	$-0.881771\pi$
$811$	−3.98688	−	27.7294i	−0.139998	−	0.973710i	0.791812	−	0.610765i	$-0.209138\pi$
$812$	7.12549	+	2.09223i	0.250056	+	0.0734229i
$813$	−42.8487	+	27.5372i	−1.50277	+	0.965771i
$814$	−5.01195	−	10.9746i	−0.175669	−	0.384661i
$815$	−3.08914	+	0.907054i	−0.108208	+	0.0317727i
$816$	−71.7599	+	82.8153i	−2.51210	+	2.89912i
$817$	8.13010	−	9.38263i	0.284436	−	0.328257i
$818$	−51.8481	+	15.2240i	−1.81283	+	0.532294i
$819$	−13.8788	−	30.3903i	−0.484963	−	1.06192i
$820$	7.90816	−	5.08227i	0.276165	−	0.177481i
$821$	−21.3745	−	6.27613i	−0.745976	−	0.219038i	−0.113414	−	0.993548i	$-0.536179\pi$
$821$	−21.3745	−	6.27613i	−0.745976	−	0.219038i	−0.632562	+	0.774509i	$0.717997\pi$
$822$	−11.9295	−	82.9717i	−0.416090	−	2.89397i
$823$	−11.5478	+	25.2862i	−0.402531	+	0.881420i	0.594476	+	0.804113i	$0.297359\pi$
$823$	−11.5478	+	25.2862i	−0.402531	+	0.881420i	−0.997007	+	0.0773070i	$0.975368\pi$
$824$	2.12061	−	14.7492i	0.0738751	−	0.513813i
$825$	5.50474	+	3.53768i	0.191650	+	0.123166i
$826$	−4.27853	−	4.93768i	−0.148869	−	0.171804i
$827$	−28.2811			−0.983432			−0.491716	−	0.870756i	$-0.663630\pi$
$827$	−28.2811			−0.983432			−0.491716	+	0.870756i	$0.663630\pi$
$828$	−4.04478	+	34.9482i	−0.140566	+	1.21454i
$829$	−33.7548			−1.17235			−0.586177	−	0.810183i	$-0.699368\pi$
$829$	−33.7548			−1.17235			−0.586177	+	0.810183i	$0.699368\pi$
$830$	14.2917	+	16.4935i	0.496073	+	0.572499i
$831$	0.267804	+	0.172107i	0.00929002	+	0.00597034i
$832$	−0.528779	+	3.67774i	−0.0183321	+	0.127503i
$833$	2.85442	−	6.25030i	0.0988997	−	0.216560i
$834$	−10.3971	−	72.3133i	−0.360022	−	2.50401i
$835$	15.1855	+	4.45887i	0.525516	+	0.154306i
$836$	−4.74503	+	3.04945i	−0.164110	+	0.105467i
$837$	28.4971	+	62.3999i	0.985003	+	2.15686i
$838$	26.8746	−	7.89110i	0.928369	−	0.272594i
$839$	25.6535	−	29.6057i	0.885656	−	1.02210i	−0.113934	−	0.993488i	$-0.536345\pi$
$839$	25.6535	−	29.6057i	0.885656	−	1.02210i	0.999591	−	0.0286134i	$-0.00910916\pi$
$840$	−3.55026	+	4.09722i	−0.122496	+	0.141367i
$841$	−22.7982	+	6.69414i	−0.786143	+	0.230833i
$842$	−6.84945	−	14.9982i	−0.236048	−	0.516873i
$843$	31.4556	−	20.2153i	1.08339	−	0.696252i
$844$	−26.6538	−	7.82626i	−0.917462	−	0.269391i
$845$	−1.23538	−	8.59225i	−0.0424983	−	0.295582i
$846$	−32.3808	+	70.9040i	−1.11327	+	2.43773i
$847$	−0.966600	+	6.72285i	−0.0332128	+	0.231000i
$848$	−14.7325	−	9.46799i	−0.505916	−	0.325132i
$849$	37.3978	+	43.1594i	1.28349	+	1.48123i
$850$	−11.9457			−0.409733
$851$	−16.2184	+	0.447354i	−0.555961	+	0.0153351i
$852$	−3.57925			−0.122623
$853$	20.3804	+	23.5203i	0.697813	+	0.805319i	0.988455	−	0.151513i	$-0.0484146\pi$
$853$	20.3804	+	23.5203i	0.697813	+	0.805319i	−0.290643	+	0.956832i	$0.593869\pi$
$854$	−10.0423	−	6.45382i	−0.343642	−	0.220845i
$855$	−2.74624	+	19.1005i	−0.0939195	+	0.653224i
$856$	−9.91074	+	21.7015i	−0.338742	+	0.741742i
$857$	4.12240	+	28.6719i	0.140818	+	0.979413i	0.930603	+	0.366029i	$0.119283\pi$
$857$	4.12240	+	28.6719i	0.140818	+	0.979413i	−0.789785	+	0.613384i	$0.789808\pi$
$858$	50.8233	+	14.9231i	1.73508	+	0.509465i
$859$	−24.8798	+	15.9893i	−0.848888	+	0.545547i	−0.891228	−	0.453556i	$-0.850155\pi$
$859$	−24.8798	+	15.9893i	−0.848888	+	0.545547i	0.0423396	+	0.999103i	$0.486519\pi$
$860$	−1.96061	−	4.29314i	−0.0668563	−	0.146395i
$861$	−28.1413	+	8.26303i	−0.959052	+	0.281603i
$862$	−26.8457	+	30.9816i	−0.914368	+	1.05524i
$863$	−9.90079	+	11.4261i	−0.337027	+	0.388950i	−0.898813	−	0.438333i	$-0.855569\pi$
$863$	−9.90079	+	11.4261i	−0.337027	+	0.388950i	0.561786	+	0.827283i	$0.310115\pi$
$864$	67.6315	−	19.8584i	2.30087	−	0.675597i
$865$	0.558563	+	1.22308i	0.0189917	+	0.0415860i
$866$	−17.3239	+	11.1334i	−0.588690	+	0.378328i
$867$	92.4742	+	27.1529i	3.14059	+	0.922160i
$868$	−0.749445	−	5.21250i	−0.0254378	−	0.176924i
$869$	−4.67560	+	10.2381i	−0.158609	+	0.347305i
$870$	−5.73260	+	39.8711i	−0.194353	+	1.35176i
$871$	−21.0921	−	13.5550i	−0.714677	−	0.459295i
$872$	1.49323	+	1.72328i	0.0505672	+	0.0583577i
$873$	76.2318			2.58006
$874$	3.80189	+	22.0984i	0.128601	+	0.747489i
$875$	−1.00000			−0.0338062
$876$	−29.1153	−	33.6008i	−0.983715	−	1.13527i
$877$	−13.2170	−	8.49407i	−0.446307	−	0.286824i	0.298119	−	0.954529i	$-0.403641\pi$
$877$	−13.2170	−	8.49407i	−0.446307	−	0.286824i	−0.744427	+	0.667704i	$0.767277\pi$
$878$	1.50077	−	10.4381i	0.0506484	−	0.352267i
$879$	24.7271	−	54.1447i	0.834023	−	1.82626i
$880$	−1.45954	−	10.1513i	−0.0492010	−	0.342201i
$881$	−23.9439	−	7.03056i	−0.806690	−	0.236865i	−0.147714	−	0.989030i	$-0.547192\pi$
$881$	−23.9439	−	7.03056i	−0.806690	−	0.236865i	−0.658975	+	0.752165i	$0.729010\pi$
$882$	−10.4939	+	6.74400i	−0.353347	+	0.227082i
$883$	5.84851	+	12.8065i	0.196818	+	0.430972i	0.982149	−	0.188105i	$-0.0602344\pi$
$883$	5.84851	+	12.8065i	0.196818	+	0.430972i	−0.785331	+	0.619076i	$0.787507\pi$
$884$	−31.3856	+	9.21565i	−1.05561	+	0.309956i
$885$	7.85037	−	9.05981i	0.263887	−	0.304542i
$886$	−7.41312	+	8.55520i	−0.249049	+	0.287418i
$887$	−6.11604	+	1.79583i	−0.205357	+	0.0602981i	−0.382793	−	0.923834i	$-0.625038\pi$
$887$	−6.11604	+	1.79583i	−0.205357	+	0.0602981i	0.177436	+	0.984132i	$0.443220\pi$
$888$	7.61909	+	16.6835i	0.255680	+	0.559861i
$889$	−12.4804	+	8.02069i	−0.418580	+	0.269005i
$890$	22.1157	+	6.49375i	0.741320	+	0.217671i
$891$	6.11833	+	42.5539i	0.204972	+	1.42561i
$892$	−8.81593	+	19.3042i	−0.295179	+	0.646352i
$893$	−2.39168	+	16.6345i	−0.0800344	+	0.556651i
$894$	16.4062	+	10.5436i	0.548707	+	0.352632i
$895$	−8.50501	−	9.81530i	−0.284291	−	0.328089i
$896$	11.9723			0.399966
$897$	45.1445	−	55.0987i	1.50733	−	1.83969i
$898$	7.26047			0.242285
$899$	24.5005	+	28.2751i	0.817139	+	0.943028i
$900$	6.17131	+	3.96606i	0.205710	+	0.132202i
$901$	−3.42537	+	23.8240i	−0.114116	+	0.793693i
$902$	13.6216	−	29.8271i	0.453549	−	0.993134i
$903$	2.09562	+	14.5754i	0.0697379	+	0.485038i
$904$	−25.2079	−	7.40170i	−0.838402	−	0.246177i
$905$	15.8414	−	10.1806i	0.526586	−	0.338416i
$906$	−29.4912	−	64.5767i	−0.979778	−	2.14542i
$907$	16.8654	−	4.95212i	0.560006	−	0.164432i	0.0105334	−	0.999945i	$-0.496647\pi$
$907$	16.8654	−	4.95212i	0.560006	−	0.164432i	0.549472	+	0.835512i	$0.314829\pi$
$908$	−7.72858	+	8.91926i	−0.256482	+	0.295996i
$909$	−49.5643	+	57.2003i	−1.64395	+	1.89721i
$910$	−7.76699	+	2.28059i	−0.257473	+	0.0756010i
$911$	−21.1478	−	46.3072i	−0.700657	−	1.53423i	−0.839173	−	0.543865i	$-0.816960\pi$
$911$	−21.1478	−	46.3072i	−0.700657	−	1.53423i	0.138515	−	0.990360i	$-0.455767\pi$
$912$	36.0811	−	23.1879i	1.19477	−	0.767829i
$913$	24.7082	+	7.25499i	0.817722	+	0.240105i
$914$	1.20174	+	8.35826i	0.0397499	+	0.276467i
$915$	9.09883	−	19.9237i	0.300798	−	0.658656i
$916$	−1.61650	+	11.2430i	−0.0534108	+	0.371480i
$917$	0.316845	+	0.203624i	0.0104632	+	0.00672426i
$918$	−104.185	−	120.236i	−3.43863	−	3.96839i
$919$	28.4342			0.937957			0.468979	−	0.883210i	$-0.344622\pi$
$919$	28.4342			0.937957			0.468979	+	0.883210i	$0.344622\pi$
$920$	−7.88104	−	2.07985i	−0.259830	−	0.0685708i
$921$	−14.1133			−0.465049
$922$	−39.8321	−	45.9686i	−1.31180	−	1.51390i
$923$	4.29898	+	2.76279i	0.141503	+	0.0909382i
$924$	0.952090	−	6.62193i	0.0313215	−	0.217846i
$925$	−1.40538	+	3.07734i	−0.0462085	+	0.101182i
$926$	2.25253	+	15.6667i	0.0740229	+	0.514840i
$927$	60.3596	+	17.7232i	1.98247	+	0.582106i
$928$	32.3402	−	20.7838i	1.06162	−	0.682261i
$929$	−3.91676	−	8.57651i	−0.128505	−	0.281386i	0.834433	−	0.551109i	$-0.185795\pi$
$929$	−3.91676	−	8.57651i	−0.128505	−	0.281386i	−0.962938	+	0.269723i	$0.913068\pi$
$930$	27.4069	−	8.04739i	0.898708	−	0.263884i
$931$	−1.76118	+	2.03251i	−0.0577204	+	0.0666129i
$932$	13.2888	−	15.3361i	0.435289	−	0.502351i
$933$	18.6090	−	5.46411i	0.609233	−	0.178887i
$934$	−22.7704	−	49.8602i	−0.745070	−	1.63148i
$935$	−11.8577	+	7.62049i	−0.387789	+	0.249217i
$936$	−54.4816	−	15.9973i	−1.78079	−	0.522887i
$937$	−4.88439	−	33.9717i	−0.159566	−	1.10981i	−0.899435	−	0.437055i	$-0.856022\pi$
$937$	−4.88439	−	33.9717i	−0.159566	−	1.10981i	0.739869	−	0.672751i	$-0.234888\pi$
$938$	−3.88878	+	8.51525i	−0.126973	+	0.278033i
$939$	−1.40573	+	9.77704i	−0.0458741	+	0.319061i
$940$	5.37454	+	3.45401i	0.175298	+	0.112657i
$941$	12.4006	+	14.3111i	0.404248	+	0.466527i	0.920974	−	0.389624i	$-0.127395\pi$
$941$	12.4006	+	14.3111i	0.404248	+	0.466527i	−0.516726	+	0.856151i	$0.672849\pi$
$942$	22.6249			0.737159
$943$	−29.7843	−	32.5163i	−0.969911	−	1.05888i
$944$	−18.7887			−0.611520
$945$	−8.72159	−	10.0652i	−0.283713	−	0.327423i
$946$	−13.8495	−	8.90050i	−0.450285	−	0.289380i
$947$	3.20602	−	22.2984i	0.104182	−	0.724600i	−0.869042	−	0.494739i	$-0.835264\pi$
$947$	3.20602	−	22.2984i	0.104182	−	0.724600i	0.973223	−	0.229861i	$-0.0738273\pi$
$948$	−7.43339	+	16.2769i	−0.241425	+	0.528648i
$949$	9.03377	+	62.8313i	0.293249	+	2.03959i
$950$	4.48614	+	1.31725i	0.145550	+	0.0427372i
$951$	−9.55363	+	6.13975i	−0.309798	+	0.199095i
$952$	−4.85129	−	10.6228i	−0.157231	−	0.344288i
$953$	24.6105	−	7.22631i	0.797214	−	0.234083i	0.142336	−	0.989818i	$-0.454539\pi$
$953$	24.6105	−	7.22631i	0.797214	−	0.234083i	0.654877	+	0.755735i	$0.272720\pi$
$954$	28.6141	−	33.0224i	0.926415	−	1.06914i
$955$	−0.139298	+	0.160758i	−0.00450758	+	0.00520202i
$956$	−21.5052	+	6.31451i	−0.695529	+	0.204226i
$957$	19.7445	+	43.2345i	0.638251	+	1.39757i
$958$	37.3081	−	23.9765i	1.20537	−	0.774645i
$959$	14.5033	+	4.25857i	0.468337	+	0.137516i
$960$	0.362251	+	2.51951i	0.0116916	+	0.0813169i
$961$	−1.85675	+	4.06572i	−0.0598952	+	0.131152i
$962$	−3.89737	+	27.1068i	−0.125656	+	0.873958i
$963$	−84.7313	−	54.4535i	−2.73043	−	1.75474i
$964$	4.37020	+	5.04348i	0.140755	+	0.162440i
$965$	−9.26341			−0.298200
$966$	−22.7616	−	13.7563i	−0.732343	−	0.442602i
$967$	−2.19987			−0.0707431			−0.0353716	−	0.999374i	$-0.511261\pi$
$967$	−2.19987			−0.0707431			−0.0353716	+	0.999374i	$0.511261\pi$
$968$	7.55936	+	8.72397i	0.242967	+	0.280399i
$969$	−49.5894	−	31.8692i	−1.59304	−	1.02379i
$970$	2.62863	−	18.2825i	0.0844001	−	0.587016i
$971$	−4.50691	+	9.86875i	−0.144634	+	0.316703i	−0.968060	−	0.250720i	$-0.919333\pi$
$971$	−4.50691	+	9.86875i	−0.144634	+	0.316703i	0.823426	+	0.567424i	$0.192060\pi$
$972$	3.91361	+	27.2198i	0.125529	+	0.873074i
$973$	12.6403	+	3.71152i	0.405229	+	0.118986i
$974$	−15.3806	+	9.88453i	−0.492827	+	0.316721i
$975$	−6.17005	−	13.5105i	−0.197600	−	0.432683i
$976$	−32.9382	+	9.67154i	−1.05433	+	0.309579i
$977$	−10.3083	+	11.8964i	−0.329793	+	0.380601i	−0.896294	−	0.443460i	$-0.853751\pi$
$977$	−10.3083	+	11.8964i	−0.329793	+	0.380601i	0.566502	+	0.824061i	$0.308296\pi$
$978$	−11.6921	+	13.4934i	−0.373871	+	0.431470i
$979$	26.0954	−	7.66230i	0.834013	−	0.244888i
$980$	0.424717	+	0.930001i	0.0135671	+	0.0297078i
$981$	−8.09838	+	5.20451i	−0.258561	+	0.166167i
$982$	54.7627	+	16.0798i	1.74755	+	0.513127i
$983$	2.58595	+	17.9857i	0.0824790	+	0.573654i	0.988592	+	0.150618i	$0.0481265\pi$
$983$	2.58595	+	17.9857i	0.0824790	+	0.573654i	−0.906113	+	0.423036i	$0.860964\pi$
$984$	−20.7073	+	45.3427i	−0.660125	+	1.44547i
$985$	2.40224	−	16.7079i	0.0765417	−	0.532359i
$986$	−72.9949	−	46.9110i	−2.32463	−	1.49395i
$987$	−13.0532	−	15.0642i	−0.415488	−	0.479498i
$988$	12.8029			0.407315
$989$	−18.2873	+	12.4781i	−0.581502	+	0.396782i
$990$	25.5886			0.813261
$991$	−9.03605	−	10.4282i	−0.287040	−	0.331261i	0.593857	−	0.804571i	$-0.297605\pi$
$991$	−9.03605	−	10.4282i	−0.287040	−	0.331261i	−0.880896	+	0.473310i	$0.843059\pi$
$992$	−22.9329	−	14.7381i	−0.728121	−	0.467935i
$993$	−4.26504	+	29.6640i	−0.135347	+	0.941359i
$994$	0.792612	−	1.73558i	0.0251401	−	0.0550492i
$995$	−3.94270	−	27.4221i	−0.124992	−	0.869339i
$996$	39.2818	+	11.5342i	1.24469	+	0.365474i
$997$	−39.0385	+	25.0885i	−1.23636	+	0.794561i	−0.984869	−	0.173299i	$-0.944557\pi$
$997$	−39.0385	+	25.0885i	−1.23636	+	0.794561i	−0.251491	+	0.967860i	$0.580921\pi$
$998$	25.0487	+	54.8491i	0.792904	+	1.73622i
$999$	−43.2313	+	12.6939i	−1.36778	+	0.401616i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	805.2.u.d.36.10	✓	130
23.16	even	11	inner	805.2.u.d.246.10	yes	130

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.u.d.36.10	✓	130	1.1	even	1	trivial
805.2.u.d.246.10	yes	130	23.16	even	11	inner

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:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.u (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.13848 + 1.31387i) q^{2} +(-2.68348 - 1.72457i) q^{3} +(-0.145502 + 1.01199i) q^{4} +(0.415415 - 0.909632i) q^{5} +(-0.789218 - 5.48913i) q^{6} +(0.959493 + 0.281733i) q^{7} +(1.42977 - 0.918859i) q^{8} +(2.98068 + 6.52678i) q^{9} +O(q^{10})\)	\(q+(1.13848 + 1.31387i) q^{2} +(-2.68348 - 1.72457i) q^{3} +(-0.145502 + 1.01199i) q^{4} +(0.415415 - 0.909632i) q^{5} +(-0.789218 - 5.48913i) q^{6} +(0.959493 + 0.281733i) q^{7} +(1.42977 - 0.918859i) q^{8} +(2.98068 + 6.52678i) q^{9} +(1.66808 - 0.489793i) q^{10} +(1.34335 - 1.55030i) q^{11} +(2.13569 - 2.46472i) q^{12} +(-4.46763 + 1.31182i) q^{13} +(0.722200 + 1.58140i) q^{14} +(-2.68348 + 1.72457i) q^{15} +(4.79698 + 1.40852i) q^{16} +(-0.977880 - 6.80130i) q^{17} +(-5.18192 + 11.3468i) q^{18} +(-0.382742 + 2.66203i) q^{19} +(0.860092 + 0.552747i) q^{20} +(-2.08891 - 2.41073i) q^{21} +3.56627 q^{22} +(1.87122 - 4.41571i) q^{23} -5.42139 q^{24} +(-0.654861 - 0.755750i) q^{25} +(-6.80986 - 4.37643i) q^{26} +(1.89538 - 13.1827i) q^{27} +(-0.424717 + 0.930001i) q^{28} +(-1.03373 - 7.18972i) q^{29} +(-5.32094 - 1.56237i) q^{30} +(-4.33310 + 2.78471i) q^{31} +(2.19858 + 4.81423i) q^{32} +(-6.27844 + 1.84352i) q^{33} +(7.82275 - 9.02794i) q^{34} +(0.654861 - 0.755750i) q^{35} +(-7.03870 + 2.06675i) q^{36} +(-1.40538 - 3.07734i) q^{37} +(-3.93331 + 2.52778i) q^{38} +(14.2511 + 4.18450i) q^{39} +(-0.241874 - 1.68227i) q^{40} +(3.81956 - 8.36367i) q^{41} +(0.789218 - 5.48913i) q^{42} +(-3.88345 - 2.49574i) q^{43} +(1.37343 + 1.58502i) q^{44} +7.17518 q^{45} +(7.93203 - 2.56865i) q^{46} +6.24880 q^{47} +(-10.4435 - 12.0525i) q^{48} +(0.841254 + 0.540641i) q^{49} +(0.247415 - 1.72081i) q^{50} +(-9.10518 + 19.9376i) q^{51} +(-0.677491 - 4.71205i) q^{52} +(-3.36097 - 0.986869i) q^{53} +(19.4782 - 12.5179i) q^{54} +(-0.852160 - 1.86597i) q^{55} +(1.63073 - 0.478825i) q^{56} +(5.61792 - 6.48343i) q^{57} +(8.26950 - 9.54351i) q^{58} +(-3.60588 + 1.05878i) q^{59} +(-1.35479 - 2.96657i) q^{60} +(-5.77643 + 3.71228i) q^{61} +(-8.59189 - 2.52281i) q^{62} +(1.02113 + 7.10215i) q^{63} +(0.331490 - 0.725862i) q^{64} +(-0.662653 + 4.60885i) q^{65} +(-9.57001 - 6.15027i) q^{66} +(3.52619 + 4.06944i) q^{67} +7.02511 q^{68} +(-12.6366 + 8.62243i) q^{69} +1.73850 q^{70} +(-0.718707 - 0.829432i) q^{71} +(10.2589 + 6.59298i) q^{72} +(1.94014 - 13.4940i) q^{73} +(2.44325 - 5.34997i) q^{74} +(0.453964 + 3.15739i) q^{75} +(-2.63824 - 0.774659i) q^{76} +(1.72570 - 1.10904i) q^{77} +(10.7267 + 23.4881i) q^{78} +(-5.26451 + 1.54580i) q^{79} +(3.27398 - 3.77837i) q^{80} +(-13.7244 + 15.8388i) q^{81} +(15.3373 - 4.50343i) q^{82} +(5.21486 + 11.4190i) q^{83} +(2.74357 - 1.76318i) q^{84} +(-6.59291 - 1.93585i) q^{85} +(-1.14213 - 7.94371i) q^{86} +(-9.62517 + 21.0762i) q^{87} +(0.496168 - 3.45093i) q^{88} +(11.1535 + 7.16790i) q^{89} +(8.16878 + 9.42728i) q^{90} -4.65624 q^{91} +(4.19638 + 2.53614i) q^{92} +16.4302 q^{93} +(7.11412 + 8.21013i) q^{94} +(2.26247 + 1.45400i) q^{95} +(2.40260 - 16.7105i) q^{96} +(4.41352 - 9.66427i) q^{97} +(0.247415 + 1.72081i) q^{98} +(14.1226 + 4.14676i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9}+O(q^{10}) \) 130 * q + 2 * q^2 + 2 * q^3 - 16 * q^4 - 13 * q^5 + 5 * q^6 + 13 * q^7 - 7 * q^8 - 39 * q^9	\( 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9} + 2 q^{10} + 2 q^{11} - 5 q^{12} + 13 q^{13} - 2 q^{14} + 2 q^{15} - 6 q^{16} - 51 q^{17} + q^{18} - 9 q^{19} - 16 q^{20} - 2 q^{21} + 34 q^{22} - 10 q^{23} - 76 q^{24} - 13 q^{25} - 31 q^{26} + 14 q^{27} + 27 q^{28} + 3 q^{29} + 5 q^{30} + 6 q^{31} + 22 q^{32} - 58 q^{33} + q^{34} + 13 q^{35} + 193 q^{36} - 36 q^{37} + 4 q^{38} - 2 q^{39} - 29 q^{40} - 34 q^{41} - 5 q^{42} - 22 q^{43} + 8 q^{44} + 170 q^{45} - 198 q^{46} - 14 q^{47} - 120 q^{48} - 13 q^{49} + 2 q^{50} - 6 q^{51} + 33 q^{52} - 18 q^{53} + 188 q^{54} - 31 q^{55} - 15 q^{56} - 9 q^{57} + 114 q^{58} + 46 q^{59} - 16 q^{60} - 56 q^{61} - 146 q^{62} + 17 q^{63} - 109 q^{64} + 2 q^{65} - 14 q^{66} - 10 q^{67} + 86 q^{68} - 6 q^{69} - 2 q^{70} - 25 q^{72} + 64 q^{73} + 79 q^{74} + 2 q^{75} + 32 q^{76} - 13 q^{77} - 64 q^{78} - 118 q^{79} - 17 q^{80} + 23 q^{81} + 129 q^{82} - 117 q^{83} - 72 q^{84} - 7 q^{85} + 74 q^{86} - 51 q^{87} - 40 q^{88} - 35 q^{89} + 100 q^{90} + 42 q^{91} + 76 q^{92} - 90 q^{93} - 7 q^{94} + 2 q^{95} + 393 q^{96} - 4 q^{97} + 2 q^{98} - 40 q^{99}+O(q^{100}) \) 130 * q + 2 * q^2 + 2 * q^3 - 16 * q^4 - 13 * q^5 + 5 * q^6 + 13 * q^7 - 7 * q^8 - 39 * q^9 + 2 * q^10 + 2 * q^11 - 5 * q^12 + 13 * q^13 - 2 * q^14 + 2 * q^15 - 6 * q^16 - 51 * q^17 + q^18 - 9 * q^19 - 16 * q^20 - 2 * q^21 + 34 * q^22 - 10 * q^23 - 76 * q^24 - 13 * q^25 - 31 * q^26 + 14 * q^27 + 27 * q^28 + 3 * q^29 + 5 * q^30 + 6 * q^31 + 22 * q^32 - 58 * q^33 + q^34 + 13 * q^35 + 193 * q^36 - 36 * q^37 + 4 * q^38 - 2 * q^39 - 29 * q^40 - 34 * q^41 - 5 * q^42 - 22 * q^43 + 8 * q^44 + 170 * q^45 - 198 * q^46 - 14 * q^47 - 120 * q^48 - 13 * q^49 + 2 * q^50 - 6 * q^51 + 33 * q^52 - 18 * q^53 + 188 * q^54 - 31 * q^55 - 15 * q^56 - 9 * q^57 + 114 * q^58 + 46 * q^59 - 16 * q^60 - 56 * q^61 - 146 * q^62 + 17 * q^63 - 109 * q^64 + 2 * q^65 - 14 * q^66 - 10 * q^67 + 86 * q^68 - 6 * q^69 - 2 * q^70 - 25 * q^72 + 64 * q^73 + 79 * q^74 + 2 * q^75 + 32 * q^76 - 13 * q^77 - 64 * q^78 - 118 * q^79 - 17 * q^80 + 23 * q^81 + 129 * q^82 - 117 * q^83 - 72 * q^84 - 7 * q^85 + 74 * q^86 - 51 * q^87 - 40 * q^88 - 35 * q^89 + 100 * q^90 + 42 * q^91 + 76 * q^92 - 90 * q^93 - 7 * q^94 + 2 * q^95 + 393 * q^96 - 4 * q^97 + 2 * q^98 - 40 * q^99

Introduction

L-functions

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