LMFDB - Embedded newform 125.2.h.a.109.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,2,Mod(4,125)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("125.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.h (of order $50$, degree $20$, 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:	$0.998130025266$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			109.5
Character	$\chi$	$=$	125.109
Dual form			125.2.h.a.39.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.103450 + 0.818889i) q^{2} +(2.60539 - 2.15537i) q^{3} +(1.27729 + 0.327952i) q^{4} +(-1.92641 + 1.13531i) q^{5} +(1.49548 + 2.35650i) q^{6} +(-2.37759 + 0.772526i) q^{7} +(-1.00839 + 2.54690i) q^{8} +(1.58032 - 8.28430i) q^{9} +O(q^{10})$	\(q+(-0.103450 + 0.818889i) q^{2} +(2.60539 - 2.15537i) q^{3} +(1.27729 + 0.327952i) q^{4} +(-1.92641 + 1.13531i) q^{5} +(1.49548 + 2.35650i) q^{6} +(-2.37759 + 0.772526i) q^{7} +(-1.00839 + 2.54690i) q^{8} +(1.58032 - 8.28430i) q^{9} +(-0.730408 - 1.69497i) q^{10} +(-2.77013 - 0.349948i) q^{11} +(4.03470 - 1.89858i) q^{12} +(-1.41963 - 0.270809i) q^{13} +(-0.386652 - 2.02690i) q^{14} +(-2.57204 + 7.11007i) q^{15} +(0.329893 + 0.181360i) q^{16} +(1.12367 + 4.37641i) q^{17} +(6.62044 + 2.15111i) q^{18} +(1.27961 - 1.54678i) q^{19} +(-2.83291 + 0.818352i) q^{20} +(-4.52948 + 7.13732i) q^{21} +(0.573138 - 2.23222i) q^{22} +(-0.249735 + 0.265940i) q^{23} +(2.86226 + 8.80913i) q^{24} +(2.42213 - 4.37416i) q^{25} +(0.368623 - 1.13451i) q^{26} +(-8.85142 - 16.1007i) q^{27} +(-3.29022 + 0.207003i) q^{28} +(-0.0132545 - 0.210674i) q^{29} +(-5.55628 - 2.84175i) q^{30} +(8.91669 - 2.28942i) q^{31} +(-3.40284 + 4.68360i) q^{32} +(-7.97154 + 5.05889i) q^{33} +(-3.70004 + 0.467424i) q^{34} +(3.70316 - 4.18751i) q^{35} +(4.73537 - 10.0632i) q^{36} +(-2.56621 + 4.66791i) q^{37} +(1.13426 + 1.20787i) q^{38} +(-4.28240 + 2.35427i) q^{39} +(-0.948956 - 6.05122i) q^{40} +(-0.00261804 + 0.00245850i) q^{41} +(-5.37610 - 4.44749i) q^{42} +(-2.43143 - 3.34658i) q^{43} +(-3.42349 - 1.35545i) q^{44} +(6.36094 + 17.7531i) q^{45} +(-0.191941 - 0.232016i) q^{46} +(-1.74465 - 4.40648i) q^{47} +(1.25040 - 0.238526i) q^{48} +(-0.606978 + 0.440995i) q^{49} +(3.33138 + 2.43596i) q^{50} +(12.3604 + 8.98035i) q^{51} +(-1.72447 - 0.811474i) q^{52} +(-0.196133 - 0.124470i) q^{53} +(14.1003 - 5.58272i) q^{54} +(5.73371 - 2.47082i) q^{55} +(0.429990 - 6.83450i) q^{56} -6.78799i q^{57} +(0.173890 + 0.0109402i) q^{58} +(1.27732 + 2.71444i) q^{59} +(-5.61700 + 8.23810i) q^{60} +(3.05737 + 2.87107i) q^{61} +(0.952349 + 7.53862i) q^{62} +(2.64250 + 20.9175i) q^{63} +(-2.93448 - 2.75566i) q^{64} +(3.04225 - 1.09004i) q^{65} +(-3.31802 - 7.05114i) q^{66} +(5.55888 + 0.349735i) q^{67} +5.95846i q^{68} +(-0.0774573 + 1.23115i) q^{69} +(3.04602 + 3.46567i) q^{70} +(1.10628 - 0.438005i) q^{71} +(19.5057 + 12.3787i) q^{72} +(2.26608 + 1.06634i) q^{73} +(-3.55703 - 2.58433i) q^{74} +(-3.11733 - 16.6170i) q^{75} +(2.14170 - 1.55603i) q^{76} +(6.85657 - 1.30796i) q^{77} +(-1.48487 - 3.75035i) q^{78} +(2.29397 + 2.77294i) q^{79} +(-0.841411 + 0.0251572i) q^{80} +(-34.2400 - 13.5566i) q^{81} +(-0.00174240 - 0.00239821i) q^{82} +(-7.53443 - 6.23303i) q^{83} +(-8.12615 + 7.63097i) q^{84} +(-7.13325 - 7.15506i) q^{85} +(2.99200 - 1.64487i) q^{86} +(-0.488613 - 0.520320i) q^{87} +(3.68465 - 6.70235i) q^{88} +(4.40291 - 9.35667i) q^{89} +(-15.1959 + 3.37234i) q^{90} +(3.58451 - 0.452829i) q^{91} +(-0.406199 + 0.257782i) q^{92} +(18.2970 - 25.1836i) q^{93} +(3.78890 - 0.972824i) q^{94} +(-0.708972 + 4.43249i) q^{95} +(1.22916 + 19.5370i) q^{96} +(-0.984685 + 0.0619511i) q^{97} +(-0.298334 - 0.542668i) q^{98} +(-7.27675 + 22.3955i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9}+O(q^{10}) $ 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18} - 10 q^{19} - 10 q^{20} - 35 q^{21} - 25 q^{22} + 70 q^{23} + 15 q^{24} + 35 q^{25} - 45 q^{26} - 20 q^{27} - 10 q^{28} - 10 q^{29} - 40 q^{30} - 30 q^{31} - 25 q^{32} - 35 q^{33} - 20 q^{34} - 40 q^{35} + 170 q^{36} - 55 q^{37} - 40 q^{38} - 35 q^{40} - 35 q^{41} - 10 q^{42} - 25 q^{43} + 15 q^{44} + 140 q^{45} - 40 q^{46} + 100 q^{47} + 5 q^{48} + 35 q^{49} - 10 q^{50} - 55 q^{51} - 15 q^{52} - 15 q^{53} + 30 q^{54} - 15 q^{55} + 65 q^{56} + 255 q^{58} + 5 q^{59} + 135 q^{60} - 40 q^{61} + 5 q^{62} - 35 q^{63} + 25 q^{64} - 30 q^{65} - 95 q^{66} + 105 q^{67} - 10 q^{69} - 55 q^{70} + 45 q^{71} - 30 q^{72} - 40 q^{73} + 35 q^{74} - 15 q^{75} - 65 q^{76} - 35 q^{77} + 100 q^{78} + 430 q^{80} - 95 q^{81} + 175 q^{82} + 20 q^{83} + 45 q^{84} - 10 q^{85} - 80 q^{86} - 5 q^{87} - 5 q^{88} + 30 q^{89} + 65 q^{91} - 55 q^{92} + 275 q^{93} + 60 q^{94} + 10 q^{95} - 135 q^{96} + 35 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9 - 20 * q^10 - 25 * q^11 + 60 * q^12 - 20 * q^13 - 30 * q^14 - 40 * q^15 - 40 * q^16 - 15 * q^17 - 25 * q^18 - 10 * q^19 - 10 * q^20 - 35 * q^21 - 25 * q^22 + 70 * q^23 + 15 * q^24 + 35 * q^25 - 45 * q^26 - 20 * q^27 - 10 * q^28 - 10 * q^29 - 40 * q^30 - 30 * q^31 - 25 * q^32 - 35 * q^33 - 20 * q^34 - 40 * q^35 + 170 * q^36 - 55 * q^37 - 40 * q^38 - 35 * q^40 - 35 * q^41 - 10 * q^42 - 25 * q^43 + 15 * q^44 + 140 * q^45 - 40 * q^46 + 100 * q^47 + 5 * q^48 + 35 * q^49 - 10 * q^50 - 55 * q^51 - 15 * q^52 - 15 * q^53 + 30 * q^54 - 15 * q^55 + 65 * q^56 + 255 * q^58 + 5 * q^59 + 135 * q^60 - 40 * q^61 + 5 * q^62 - 35 * q^63 + 25 * q^64 - 30 * q^65 - 95 * q^66 + 105 * q^67 - 10 * q^69 - 55 * q^70 + 45 * q^71 - 30 * q^72 - 40 * q^73 + 35 * q^74 - 15 * q^75 - 65 * q^76 - 35 * q^77 + 100 * q^78 + 430 * q^80 - 95 * q^81 + 175 * q^82 + 20 * q^83 + 45 * q^84 - 10 * q^85 - 80 * q^86 - 5 * q^87 - 5 * q^88 + 30 * q^89 + 65 * q^91 - 55 * q^92 + 275 * q^93 + 60 * q^94 + 10 * q^95 - 135 * q^96 + 35 * q^97 - 15 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{27}{50}\right)$

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 $

$2$	−0.103450	+	0.818889i	−0.0731500	+	0.579042i	0.912356	+	0.409399i	$0.134262\pi$
$2$	−0.103450	+	0.818889i	−0.0731500	+	0.579042i	−0.985506	+	0.169643i	$0.945738\pi$
$3$	2.60539	−	2.15537i	1.50422	−	1.24440i	0.613639	−	0.789587i	$-0.289705\pi$
$3$	2.60539	−	2.15537i	1.50422	−	1.24440i	0.890585	−	0.454816i	$-0.150295\pi$
$4$	1.27729	+	0.327952i	0.638645	+	0.163976i
$5$	−1.92641	+	1.13531i	−0.861518	+	0.507727i
$5$	−1.92641	+	1.13531i	−0.861518	+	0.507727i
$6$	1.49548	+	2.35650i	0.610527	+	0.962037i
$7$	−2.37759	+	0.772526i	−0.898645	+	0.291987i	−0.721678	−	0.692229i	$-0.756629\pi$
$7$	−2.37759	+	0.772526i	−0.898645	+	0.291987i	−0.176967	+	0.984217i	$0.556629\pi$
$8$	−1.00839	+	2.54690i	−0.356520	+	0.900466i
$9$	1.58032	−	8.28430i	0.526772	−	2.76143i
$10$	−0.730408	−	1.69497i	−0.230975	−	0.535995i
$11$	−2.77013	−	0.349948i	−0.835224	−	0.105513i	−0.303923	−	0.952696i	$-0.598297\pi$
$11$	−2.77013	−	0.349948i	−0.835224	−	0.105513i	−0.531301	+	0.847183i	$0.678297\pi$
$12$	4.03470	−	1.89858i	1.16472	−	0.548074i
$13$	−1.41963	−	0.270809i	−0.393735	−	0.0751090i	−0.0132882	−	0.999912i	$-0.504230\pi$
$13$	−1.41963	−	0.270809i	−0.393735	−	0.0751090i	−0.380447	+	0.924803i	$0.624230\pi$
$14$	−0.386652	−	2.02690i	−0.103337	−	0.541712i
$15$	−2.57204	+	7.11007i	−0.664099	+	1.83581i
$16$	0.329893	+	0.181360i	0.0824732	+	0.0453401i
$17$	1.12367	+	4.37641i	0.272530	+	1.06144i	0.946507	+	0.322683i	$0.104585\pi$
$17$	1.12367	+	4.37641i	0.272530	+	1.06144i	−0.673977	+	0.738753i	$0.735415\pi$
$18$	6.62044	+	2.15111i	1.56045	+	0.507022i
$19$	1.27961	−	1.54678i	0.293562	−	0.354855i	−0.603026	−	0.797722i	$-0.706038\pi$
$19$	1.27961	−	1.54678i	0.293562	−	0.354855i	0.896588	+	0.442866i	$0.146038\pi$
$20$	−2.83291	+	0.818352i	−0.633459	+	0.182989i
$21$	−4.52948	+	7.13732i	−0.988414	+	1.55749i
$22$	0.573138	−	2.23222i	0.122193	−	0.475912i
$23$	−0.249735	+	0.265940i	−0.0520733	+	0.0554524i	−0.754478	−	0.656326i	$-0.772110\pi$
$23$	−0.249735	+	0.265940i	−0.0520733	+	0.0554524i	0.702405	+	0.711778i	$0.252110\pi$
$24$	2.86226	+	8.80913i	0.584256	+	1.79816i
$25$	2.42213	−	4.37416i	0.484426	−	0.874832i
$26$	0.368623	−	1.13451i	0.0722930	−	0.222495i
$27$	−8.85142	−	16.1007i	−1.70346	−	3.09858i
$28$	−3.29022	+	0.207003i	−0.621794	+	0.0391199i
$29$	−0.0132545	−	0.210674i	−0.00246129	−	0.0391212i	0.996604	−	0.0823390i	$-0.0262390\pi$
$29$	−0.0132545	−	0.210674i	−0.00246129	−	0.0391212i	−0.999066	+	0.0432179i	$0.986239\pi$
$30$	−5.55628	−	2.84175i	−1.01443	−	0.518831i
$31$	8.91669	−	2.28942i	1.60149	−	0.411192i	0.660825	−	0.750540i	$-0.270207\pi$
$31$	8.91669	−	2.28942i	1.60149	−	0.411192i	0.940661	+	0.339348i	$0.110207\pi$
$32$	−3.40284	+	4.68360i	−0.601542	+	0.827952i
$33$	−7.97154	+	5.05889i	−1.38767	+	0.880640i
$34$	−3.70004	+	0.467424i	−0.634552	+	0.0801625i
$35$	3.70316	−	4.18751i	0.625949	−	0.707819i
$36$	4.73537	−	10.0632i	0.789229	−	1.67720i
$37$	−2.56621	+	4.66791i	−0.421882	+	0.767400i	−0.998778	−	0.0494171i	$-0.984264\pi$
$37$	−2.56621	+	4.66791i	−0.421882	+	0.767400i	0.576896	+	0.816817i	$0.304264\pi$
$38$	1.13426	+	1.20787i	0.184002	+	0.195942i
$39$	−4.28240	+	2.35427i	−0.685732	+	0.376984i
$40$	−0.948956	−	6.05122i	−0.150043	−	0.956782i
$41$	−0.00261804	+	0.00245850i	−0.000408869	+	0.000383953i	−0.684752	−	0.728777i	$-0.740089\pi$
$41$	−0.00261804	+	0.00245850i	−0.000408869	+	0.000383953i	0.684343	+	0.729161i	$0.260089\pi$
$42$	−5.37610	−	4.44749i	−0.829550	−	0.686263i
$43$	−2.43143	−	3.34658i	−0.370790	−	0.510348i	0.582326	−	0.812956i	$-0.302143\pi$
$43$	−2.43143	−	3.34658i	−0.370790	−	0.510348i	−0.953115	+	0.302608i	$0.902143\pi$
$44$	−3.42349	−	1.35545i	−0.516110	−	0.204342i
$45$	6.36094	+	17.7531i	0.948233	+	2.64648i
$46$	−0.191941	−	0.232016i	−0.0283001	−	0.0342089i
$47$	−1.74465	−	4.40648i	−0.254483	−	0.642751i	0.745227	−	0.666810i	$-0.232341\pi$
$47$	−1.74465	−	4.40648i	−0.254483	−	0.642751i	−0.999711	+	0.0240593i	$0.992341\pi$
$48$	1.25040	−	0.238526i	0.180480	−	0.0344283i
$49$	−0.606978	+	0.440995i	−0.0867111	+	0.0629993i
$50$	3.33138	+	2.43596i	0.471129	+	0.344497i
$51$	12.3604	+	8.98035i	1.73080	+	1.25750i
$52$	−1.72447	−	0.811474i	−0.239141	−	0.112531i
$53$	−0.196133	−	0.124470i	−0.0269409	−	0.0170972i	0.522288	−	0.852769i	$-0.325079\pi$
$53$	−0.196133	−	0.124470i	−0.0269409	−	0.0170972i	−0.549229	+	0.835672i	$0.685079\pi$
$54$	14.1003	−	5.58272i	1.91881	−	0.759712i
$55$	5.73371	−	2.47082i	0.773133	−	0.333165i
$56$	0.429990	−	6.83450i	0.0574598	−	0.913298i
$57$		−	6.78799i		−	0.899091i
$58$	0.173890	+	0.0109402i	0.0228328	+	0.00143652i
$59$	1.27732	+	2.71444i	0.166293	+	0.353390i	0.970553	−	0.240887i	$-0.0774384\pi$
$59$	1.27732	+	2.71444i	0.166293	+	0.353390i	−0.804261	+	0.594277i	$0.797438\pi$
$60$	−5.61700	+	8.23810i	−0.725152	+	1.06353i
$61$	3.05737	+	2.87107i	0.391457	+	0.367602i	0.855139	−	0.518399i	$-0.173472\pi$
$61$	3.05737	+	2.87107i	0.391457	+	0.367602i	−0.463682	+	0.886002i	$0.653472\pi$
$62$	0.952349	+	7.53862i	0.120949	+	0.957406i
$63$	2.64250	+	20.9175i	0.332923	+	2.63536i
$64$	−2.93448	−	2.75566i	−0.366809	−	0.344457i
$65$	3.04225	−	1.09004i	0.377345	−	0.135202i
$66$	−3.31802	−	7.05114i	−0.408420	−	0.867936i
$67$	5.55888	+	0.349735i	0.679125	+	0.0427269i	0.398607	−	0.917122i	$-0.369494\pi$
$67$	5.55888	+	0.349735i	0.679125	+	0.0427269i	0.280518	+	0.959849i	$0.409494\pi$
$68$			5.95846i			0.722569i
$69$	−0.0774573	+	1.23115i	−0.00932477	+	0.148213i
$70$	3.04602	+	3.46567i	0.364069	+	0.414227i
$71$	1.10628	−	0.438005i	0.131291	−	0.0519817i	−0.301561	−	0.953447i	$-0.597508\pi$
$71$	1.10628	−	0.438005i	0.131291	−	0.0519817i	0.432851	+	0.901465i	$0.357508\pi$
$72$	19.5057	+	12.3787i	2.29877	+	1.45885i
$73$	2.26608	+	1.06634i	0.265224	+	0.124805i	0.553794	−	0.832654i	$-0.313180\pi$
$73$	2.26608	+	1.06634i	0.265224	+	0.124805i	−0.288569	+	0.957459i	$0.593180\pi$
$74$	−3.55703	−	2.58433i	−0.413496	−	0.300423i
$75$	−3.11733	−	16.6170i	−0.359958	−	1.91876i
$76$	2.14170	−	1.55603i	0.245669	−	0.178489i
$77$	6.85657	−	1.30796i	0.781379	−	0.149056i
$78$	−1.48487	−	3.75035i	−0.168128	−	0.424644i
$79$	2.29397	+	2.77294i	0.258092	+	0.311980i	0.883604	−	0.468235i	$-0.155110\pi$
$79$	2.29397	+	2.77294i	0.258092	+	0.311980i	−0.625512	+	0.780215i	$0.715110\pi$
$80$	−0.841411	+	0.0251572i	−0.0940726	+	0.00281266i
$81$	−34.2400	−	13.5566i	−3.80444	−	1.50628i
$82$	−0.00174240	−	0.00239821i	−0.000192416	−	0.000264838i
$83$	−7.53443	−	6.23303i	−0.827012	−	0.684163i	0.124351	−	0.992238i	$-0.460315\pi$
$83$	−7.53443	−	6.23303i	−0.827012	−	0.684163i	−0.951362	+	0.308075i	$0.900315\pi$
$84$	−8.12615	+	7.63097i	−0.886636	+	0.832607i
$85$	−7.13325	−	7.15506i	−0.773710	−	0.776075i
$86$	2.99200	−	1.64487i	0.322636	−	0.177371i
$87$	−0.488613	−	0.520320i	−0.0523848	−	0.0557842i
$88$	3.68465	−	6.70235i	0.392785	−	0.714473i
$89$	4.40291	−	9.35667i	0.466708	−	0.991805i	−0.523477	−	0.852040i	$-0.675365\pi$
$89$	4.40291	−	9.35667i	0.466708	−	0.991805i	0.990185	−	0.139765i	$-0.0446347\pi$
$90$	−15.1959	+	3.37234i	−1.60179	+	0.355476i
$91$	3.58451	−	0.452829i	0.375759	−	0.0474694i
$92$	−0.406199	+	0.257782i	−0.0423492	+	0.0268756i
$93$	18.2970	−	25.1836i	1.89731	−	2.61142i
$94$	3.78890	−	0.972824i	0.390795	−	0.100339i
$95$	−0.708972	+	4.43249i	−0.0727390	+	0.454764i
$96$	1.22916	+	19.5370i	0.125451	+	1.99399i
$97$	−0.984685	+	0.0619511i	−0.0999796	+	0.00629018i	−0.112702	−	0.993629i	$-0.535950\pi$
$97$	−0.984685	+	0.0619511i	−0.0999796	+	0.00629018i	0.0127219	+	0.999919i	$0.495950\pi$
$98$	−0.298334	−	0.542668i	−0.0301363	−	0.0548178i
$99$	−7.27675	+	22.3955i	−0.731341	+	2.25084i
$100$	4.52828	−	4.79273i	0.452828	−	0.479273i
$101$	1.19088	+	3.66516i	0.118497	+	0.364697i	0.992660	−	0.120936i	$-0.0385894\pi$
$101$	1.19088	+	3.66516i	0.118497	+	0.364697i	−0.874163	+	0.485632i	$0.838589\pi$
$102$	−8.63259	+	9.19277i	−0.854753	+	0.910220i
$103$	−2.00476	+	7.80803i	−0.197535	+	0.769348i	0.790153	+	0.612910i	$0.210001\pi$
$103$	−2.00476	+	7.80803i	−0.197535	+	0.769348i	−0.987688	+	0.156438i	$0.949999\pi$
$104$	2.12127	−	3.34258i	0.208007	−	0.327767i
$105$	0.622557	−	18.8918i	0.0607554	−	1.84365i
$106$	0.122217	−	0.147734i	0.0118707	−	0.0143492i
$107$	16.8992	+	5.49088i	1.63371	+	0.530823i	0.975119	−	0.221682i	$-0.0711546\pi$
$107$	16.8992	+	5.49088i	1.63371	+	0.530823i	0.658587	+	0.752505i	$0.271155\pi$
$108$	−6.02557	−	23.4681i	−0.579811	−	2.25821i
$109$	−10.9765	−	6.03437i	−1.05136	−	0.577988i	−0.140232	−	0.990119i	$-0.544785\pi$
$109$	−10.9765	−	6.03437i	−1.05136	−	0.577988i	−0.911125	+	0.412131i	$0.864785\pi$
$110$	1.43017	+	4.95087i	0.136362	+	0.472047i
$111$	3.37510	+	17.6929i	0.320350	+	1.67933i
$112$	−0.924456	−	0.176349i	−0.0873529	−	0.0166635i
$113$	−0.0440382	+	0.0207228i	−0.00414276	+	0.00194944i	−0.427850	−	0.903850i	$-0.640729\pi$
$113$	−0.0440382	+	0.0207228i	−0.00414276	+	0.00194944i	0.423707	+	0.905799i	$0.360729\pi$
$114$	5.55861	+	0.702216i	0.520612	+	0.0657685i
$115$	0.179166	−	0.795838i	0.0167073	−	0.0742122i
$116$	0.0521611	−	0.273438i	0.00484304	−	0.0253881i
$117$	−4.48694	+	11.3327i	−0.414817	+	1.04771i
$118$	−2.35496	+	0.765173i	−0.216792	+	0.0704399i
$119$	−6.05252	−	9.53725i	−0.554834	−	0.874279i
$120$	−15.5150	−	13.7205i	−1.41632	−	1.25250i
$121$	−3.10328	−	0.796787i	−0.282116	−	0.0724352i
$122$	−2.66737	+	2.20664i	−0.241492	+	0.199780i
$123$	−0.00152204	+	0.0120482i	−0.000137238	+	0.00108635i
$124$	12.1400			1.09021
$125$	0.300022	+	11.1763i	0.0268347	+	0.999640i
$126$	−17.4025			−1.55034
$127$	0.893402	−	7.07200i	0.0792766	−	0.627539i	−0.901553	−	0.432670i	$-0.857572\pi$
$127$	0.893402	−	7.07200i	0.0792766	−	0.627539i	0.980829	−	0.194869i	$-0.0624283\pi$
$128$	−6.36124	+	5.26248i	−0.562260	+	0.465142i
$129$	−13.5479	−	3.47852i	−1.19283	−	0.306266i
$130$	0.577899	+	2.60403i	0.0506851	+	0.228389i
$131$	7.52225	+	11.8532i	0.657222	+	1.03562i	0.995518	+	0.0945767i	$0.0301498\pi$
$131$	7.52225	+	11.8532i	0.657222	+	1.03562i	−0.338295	+	0.941040i	$0.609850\pi$
$132$	−11.8410	+	3.84738i	−1.03063	+	0.334872i
$133$	−1.84745	+	4.66614i	−0.160195	+	0.404605i
$134$	−0.861458	+	4.51592i	−0.0744187	+	0.390116i
$135$	35.3308	+	20.9674i	3.04079	+	1.80459i
$136$	−12.2794	−	1.55125i	−1.05295	−	0.133018i
$137$	10.6652	−	5.01866i	0.911188	−	0.428773i	0.0877266	−	0.996145i	$-0.472040\pi$
$137$	10.6652	−	5.01866i	0.911188	−	0.428773i	0.823462	+	0.567372i	$0.192040\pi$
$138$	−1.00016	−	0.190791i	−0.0851394	−	0.0162412i
$139$	2.45973	+	12.8944i	0.208632	+	1.09369i	0.920313	+	0.391183i	$0.127934\pi$
$139$	2.45973	+	12.8944i	0.208632	+	1.09369i	−0.711681	+	0.702502i	$0.752066\pi$
$140$	6.10331	−	4.13421i	0.515824	−	0.349404i
$141$	−14.0431	−	7.72025i	−1.18264	−	0.650162i
$142$	0.244234	+	0.951228i	0.0204956	+	0.0798253i
$143$	3.83779	+	1.24697i	0.320932	+	0.104277i
$144$	2.02378	−	2.44633i	0.168648	−	0.203861i
$145$	0.264714	+	0.390797i	0.0219833	+	0.0324539i
$146$	−1.10764	+	1.74535i	−0.0916686	+	0.144447i
$147$	−0.630909	+	2.45723i	−0.0520365	+	0.202669i
$148$	−4.80864	+	5.12068i	−0.395268	+	0.420917i
$149$	−5.24655	−	16.1472i	−0.429814	−	1.32283i	−0.898309	−	0.439365i	$-0.855203\pi$
$149$	−5.24655	−	16.1472i	−0.429814	−	1.32283i	0.468495	−	0.883466i	$-0.344797\pi$
$150$	13.9300	−	0.833725i	1.13738	−	0.0680733i
$151$	5.74156	−	17.6707i	0.467241	−	1.43802i	−0.388901	−	0.921280i	$-0.627145\pi$
$151$	5.74156	−	17.6707i	0.467241	−	1.43802i	0.856142	−	0.516741i	$-0.172855\pi$
$152$	2.64915	+	4.81879i	0.214875	+	0.390855i
$153$	38.0313	−	2.39273i	3.07465	−	0.193440i
$154$	0.361764	+	5.75008i	0.0291518	+	0.463354i
$155$	−14.5780	+	14.5336i	−1.17094	+	1.16737i
$156$	−6.24194	+	1.60266i	−0.499756	+	0.128315i
$157$	−9.47423	+	13.0402i	−0.756126	+	1.04072i	0.241401	+	0.970426i	$0.422393\pi$
$157$	−9.47423	+	13.0402i	−0.756126	+	1.04072i	−0.997526	+	0.0702924i	$0.977607\pi$
$158$	−2.50804	+	1.59165i	−0.199529	+	0.126625i
$159$	−0.779280	+	0.0984460i	−0.0618009	+	0.00780728i
$160$	1.23791	−	12.8858i	0.0978656	−	1.01871i
$161$	0.388321	−	0.825224i	0.0306040	−	0.0650367i
$162$	14.6434	−	26.6363i	1.15050	−	2.09275i
$163$	−7.63540	−	8.13088i	−0.598051	−	0.636860i	0.356717	−	0.934213i	$-0.383896\pi$
$163$	−7.63540	−	8.13088i	−0.598051	−	0.636860i	−0.954768	+	0.297353i	$0.903896\pi$
$164$	−0.00415026	+	0.00228163i	−0.000324081	+	0.000178165i
$165$	9.61304	−	18.7957i	0.748374	−	1.46324i
$166$	5.88359	−	5.52506i	0.456655	−	0.428828i
$167$	−0.637087	−	0.527044i	−0.0492992	−	0.0407839i	0.612448	−	0.790511i	$-0.290185\pi$
$167$	−0.637087	−	0.527044i	−0.0492992	−	0.0407839i	−0.661747	+	0.749727i	$0.730185\pi$
$168$	−13.6106	−	18.7333i	−1.05008	−	1.44531i
$169$	−10.1451	−	4.01672i	−0.780390	−	0.308978i
$170$	6.59713	−	5.10115i	0.505977	−	0.391241i
$171$	−10.7918	−	13.0450i	−0.825270	−	0.997580i
$172$	−2.00812	−	5.07194i	−0.153118	−	0.386732i
$173$	−20.6190	+	3.93328i	−1.56763	+	0.299042i	−0.896755	−	0.442528i	$-0.854082\pi$
$173$	−20.6190	+	3.93328i	−1.56763	+	0.299042i	−0.670876	+	0.741569i	$0.734082\pi$
$174$	0.476631	−	0.346293i	0.0361333	−	0.0262524i
$175$	−2.37968	+	12.2711i	−0.179887	+	0.927610i
$176$	−0.850378	−	0.617836i	−0.0640997	−	0.0465712i
$177$	9.17853	+	4.31909i	0.689900	+	0.324642i
$178$	7.20659	+	4.57344i	0.540157	+	0.342794i
$179$	−7.59801	+	3.00826i	−0.567902	+	0.224848i	−0.634488	−	0.772932i	$-0.718789\pi$
$179$	−7.59801	+	3.00826i	−0.567902	+	0.224848i	0.0665866	+	0.997781i	$0.478789\pi$
$180$	2.30258	+	24.7620i	0.171624	+	1.84565i
$181$	−1.13439	+	18.0306i	−0.0843183	+	1.34020i	0.697451	+	0.716633i	$0.254318\pi$
$181$	−1.13439	+	18.0306i	−0.0843183	+	1.34020i	−0.781769	+	0.623568i	$0.785682\pi$
$182$			2.98216i			0.221053i
$183$	14.1539	+	0.890486i	1.04628	+	0.0658266i
$184$	−0.425494	−	0.904221i	−0.0313678	−	0.0666600i
$185$	−0.355969	−	11.9058i	−0.0261714	−	0.875330i
$186$	18.7298	+	17.5884i	1.37333	+	1.28964i
$187$	−1.58119	−	12.5164i	−0.115628	−	0.915293i
$188$	−0.783307	−	6.20051i	−0.0571285	−	0.452219i
$189$	33.4832	+	31.4428i	2.43555	+	2.28713i
$190$	−3.55637	−	1.03911i	−0.258006	−	0.0753849i
$191$	−8.24962	−	17.5313i	−0.596921	−	1.26852i	−0.943770	−	0.330602i	$-0.892748\pi$
$191$	−8.24962	−	17.5313i	−0.596921	−	1.26852i	0.346849	−	0.937921i	$-0.387252\pi$
$192$	−13.5849	−	0.854691i	−0.980407	−	0.0616820i
$193$			11.8885i			0.855754i	0.903837	+	0.427877i	$0.140738\pi$
$193$			11.8885i			0.855754i	−0.903837	+	0.427877i	$0.859262\pi$
$194$	0.0511343	−	0.812756i	0.00367123	−	0.0583525i
$195$	5.57683	−	9.39715i	0.399365	−	0.672944i
$196$	−0.919912	+	0.364219i	−0.0657080	+	0.0260156i
$197$	−7.32101	−	4.64606i	−0.521601	−	0.331018i	0.248824	−	0.968549i	$-0.419956\pi$
$197$	−7.32101	−	4.64606i	−0.521601	−	0.331018i	−0.770425	+	0.637531i	$0.779956\pi$
$198$	−17.5867	−	8.27566i	−1.24983	−	0.588126i
$199$	9.47974	+	6.88743i	0.672001	+	0.488237i	0.870694	−	0.491825i	$-0.163670\pi$
$199$	9.47974	+	6.88743i	0.672001	+	0.488237i	−0.198694	+	0.980062i	$0.563670\pi$
$200$	8.69811	+	10.5798i	0.615049	+	0.748104i
$201$	15.2369	−	11.0702i	1.07473	−	0.780834i
$202$	−3.12455	+	0.596040i	−0.219843	+	0.0419372i
$203$	0.194265	+	0.490657i	0.0136347	+	0.0344374i
$204$	12.8427	+	15.5241i	0.899167	+	1.08691i
$205$	0.00225225	−	0.00770838i	0.000157304	−	0.000538377i
$206$	−6.18652	−	2.44942i	−0.431035	−	0.170659i
$207$	1.80847	+	2.48915i	0.125697	+	0.173008i
$208$	−0.419213	−	0.346803i	−0.0290672	−	0.0240465i
$209$	−4.08596	+	3.83698i	−0.282632	+	0.265409i
$210$	15.4059	+	2.46416i	1.06311	+	0.170043i
$211$	−7.01056	+	3.85409i	−0.482627	+	0.265326i	−0.704441	−	0.709763i	$-0.748802\pi$
$211$	−7.01056	+	3.85409i	−0.482627	+	0.265326i	0.221814	+	0.975089i	$0.428802\pi$
$212$	−0.209698	−	0.223306i	−0.0144021	−	0.0153367i
$213$	1.93822	−	3.52561i	0.132805	−	0.241571i
$214$	−6.24464	+	13.2705i	−0.426874	+	0.907154i
$215$	8.48335	+	3.68645i	0.578559	+	0.251414i
$216$	49.9325	−	6.30794i	3.39748	−	0.429201i
$217$	−19.4316	+	12.3317i	−1.31910	+	0.837129i
$218$	6.07700	−	8.36427i	0.411586	−	0.566500i
$219$	8.20237	−	2.10601i	0.554265	−	0.142311i
$220$	8.13391	−	1.27556i	0.548388	−	0.0859985i
$221$	−0.410027	−	6.51720i	−0.0275814	−	0.438394i
$222$	−14.8376	+	0.933506i	−0.995838	+	0.0626528i
$223$	8.98546	+	16.3445i	0.601711	+	1.09451i	0.985272	+	0.170993i	$0.0546976\pi$
$223$	8.98546	+	16.3445i	0.601711	+	1.09451i	−0.383561	+	0.923516i	$0.625302\pi$
$224$	4.47235	−	13.7645i	0.298821	−	0.919677i
$225$	−32.4092	−	26.9782i	−2.16061	−	1.79855i
$226$	−0.0124139	−	0.0382061i	−0.000825762	−	0.00254143i
$227$	18.6055	−	19.8129i	1.23489	−	1.31503i	0.302691	−	0.953089i	$-0.402115\pi$
$227$	18.6055	−	19.8129i	1.23489	−	1.31503i	0.932202	−	0.361938i	$-0.117885\pi$
$228$	2.22614	−	8.67023i	0.147429	−	0.574200i
$229$	−10.6662	+	16.8072i	−0.704842	+	1.11065i	0.283584	+	0.958947i	$0.408477\pi$
$229$	−10.6662	+	16.8072i	−0.704842	+	1.11065i	−0.988426	+	0.151706i	$0.951523\pi$
$230$	0.633168	+	0.229046i	0.0417499	+	0.0151029i
$231$	15.0449	−	18.1862i	0.989883	−	1.19656i
$232$	0.549931	+	0.178684i	0.0361048	+	0.0117311i
$233$	0.149644	+	0.582827i	0.00980354	+	0.0381823i	0.973297	−	0.229550i	$-0.0737256\pi$
$233$	0.149644	+	0.582827i	0.00980354	+	0.0381823i	−0.963493	+	0.267733i	$0.913726\pi$
$234$	−8.81605	−	4.84667i	−0.576323	−	0.316837i
$235$	8.36365	+	6.50798i	0.545584	+	0.424533i
$236$	0.741298	+	3.88602i	0.0482544	+	0.252958i
$237$	11.9534	+	2.28023i	0.776457	+	0.148117i
$238$	8.43608	−	3.96972i	0.546830	−	0.257319i
$239$	8.53977	+	1.07882i	0.552392	+	0.0697833i	0.396574	−	0.918003i	$-0.370199\pi$
$239$	8.53977	+	1.07882i	0.552392	+	0.0697833i	0.155817	+	0.987786i	$0.450199\pi$
$240$	−2.13798	+	1.87909i	−0.138006	+	0.121295i
$241$	−5.39662	+	28.2901i	−0.347627	+	1.82232i	0.193164	+	0.981166i	$0.438125\pi$
$241$	−5.39662	+	28.2901i	−0.347627	+	1.82232i	−0.540791	+	0.841157i	$0.681875\pi$
$242$	0.973513	−	2.45881i	0.0625798	−	0.158059i
$243$	−66.0057	+	21.4466i	−4.23427	+	1.37580i
$244$	2.96358	+	4.66985i	0.189724	+	0.298957i
$245$	0.668622	−	1.53865i	0.0427167	−	0.0983007i
$246$	−0.00970868	−	0.00249277i	−0.000619003	−	0.000158933i
$247$	−2.23545	+	1.84933i	−0.142239	+	0.117670i
$248$	−3.16058	+	25.0186i	−0.200697	+	1.58868i
$249$	−33.0646			−2.09539
$250$	−9.18320	−	0.910502i	−0.580796	−	0.0575852i
$251$	−28.4383			−1.79501			−0.897506	−	0.441003i	$-0.854623\pi$
$251$	−28.4383			−1.79501			−0.897506	+	0.441003i	$0.854623\pi$
$252$	−3.48471	+	27.5843i	−0.219516	+	1.73765i
$253$	0.784862	−	0.649294i	0.0493438	−	0.0408208i
$254$	5.69876	+	1.46319i	0.357572	+	0.0918089i
$255$	−34.0067	−	3.26695i	−2.12958	−	0.204584i
$256$	−7.96528	−	12.5513i	−0.497830	−	0.784454i
$257$	28.8808	−	9.38395i	1.80154	−	0.585355i	0.801614	−	0.597842i	$-0.203975\pi$
$257$	28.8808	−	9.38395i	1.80154	−	0.585355i	0.999922	+	0.0124874i	$0.00397497\pi$
$258$	4.25005	−	10.7344i	0.264597	−	0.668295i
$259$	2.49531	−	13.0808i	0.155051	−	0.812804i
$260$	4.24331	−	0.394579i	0.263159	−	0.0244708i
$261$	−1.76623	−	0.223127i	−0.109327	−	0.0138112i
$262$	−10.4846	+	4.93368i	−0.647741	+	0.304804i
$263$	−19.7482	−	3.76717i	−1.21773	−	0.232293i	−0.461819	−	0.886974i	$-0.652803\pi$
$263$	−19.7482	−	3.76717i	−1.21773	−	0.232293i	−0.755906	+	0.654680i	$0.772803\pi$
$264$	−4.84608	−	25.4040i	−0.298256	−	1.56351i
$265$	0.519144	+	0.0171078i	0.0318908	+	0.00105092i
$266$	−3.62993	−	1.99557i	−0.222565	−	0.122356i
$267$	−8.69575	−	33.8677i	−0.532171	−	2.07267i
$268$	6.98560	+	2.26976i	0.426713	+	0.138648i
$269$	12.5898	−	15.2185i	0.767614	−	0.927886i	−0.231374	−	0.972865i	$-0.574322\pi$
$269$	12.5898	−	15.2185i	0.767614	−	0.927886i	0.998988	+	0.0449793i	$0.0143222\pi$
$270$	−20.8249	+	26.7629i	−1.26736	+	1.62874i
$271$	−0.436679	+	0.688096i	−0.0265263	+	0.0417988i	−0.857332	−	0.514763i	$-0.827880\pi$
$271$	−0.436679	+	0.688096i	−0.0265263	+	0.0417988i	0.830806	+	0.556562i	$0.187880\pi$
$272$	−0.423016	+	1.64754i	−0.0256491	+	0.0998966i
$273$	8.36305	−	8.90575i	0.506155	−	0.539000i
$274$	3.00641	+	9.25278i	0.181624	+	0.558981i
$275$	−8.24033	+	11.2694i	−0.496911	+	0.679568i
$276$	−0.502693	+	1.54713i	−0.0302586	+	0.0931263i
$277$	−8.97114	−	16.3184i	−0.539024	−	0.980480i	−0.995857	−	0.0909282i	$-0.971017\pi$
$277$	−8.97114	−	16.3184i	−0.539024	−	0.980480i	0.456834	−	0.889552i	$-0.348983\pi$
$278$	−10.8135	+	0.680328i	−0.648551	+	0.0408034i
$279$	−4.87504	−	77.4866i	−0.291861	−	4.63900i
$280$	6.93095	+	13.6542i	0.414204	+	0.815996i
$281$	−15.0220	+	3.85698i	−0.896135	+	0.230088i	−0.668548	−	0.743669i	$-0.733084\pi$
$281$	−15.0220	+	3.85698i	−0.896135	+	0.230088i	−0.227587	+	0.973758i	$0.573084\pi$
$282$	7.77478	−	10.7011i	0.462981	−	0.637239i
$283$	10.3500	−	6.56832i	0.615244	−	0.390446i	−0.191375	−	0.981517i	$-0.561295\pi$
$283$	10.3500	−	6.56832i	0.615244	−	0.390446i	0.806619	+	0.591071i	$0.201295\pi$
$284$	1.55668	−	0.196654i	0.0923718	−	0.0116693i
$285$	7.70649	+	13.0765i	0.456493	+	0.774583i
$286$	−1.41815	+	3.01373i	−0.0838571	+	0.178205i
$287$	0.00432537	−	0.00786781i	0.000255318	−	0.000464422i
$288$	33.4228	+	35.5917i	1.96946	+	2.09726i
$289$	−2.99314	+	1.64549i	−0.176067	+	0.0967936i
$290$	−0.347404	+	0.176344i	−0.0204003	+	0.0103553i
$291$	−2.43196	+	2.28377i	−0.142564	+	0.133877i
$292$	2.54473	+	2.10518i	0.148919	+	0.123197i
$293$	3.03877	+	4.18251i	0.177527	+	0.244345i	0.888502	−	0.458872i	$-0.151746\pi$
$293$	3.03877	+	4.18251i	0.177527	+	0.244345i	−0.710975	+	0.703217i	$0.751746\pi$
$294$	−1.94693	−	0.770844i	−0.113547	−	0.0449565i
$295$	−5.54238	−	3.77897i	−0.322690	−	0.220020i
$296$	−9.30098	−	11.2430i	−0.540608	−	0.653483i
$297$	18.8851	+	47.6984i	1.09583	+	2.76774i
$298$	13.7655	−	2.62592i	0.797416	−	0.152115i
$299$	0.426551	−	0.309907i	0.0246681	−	0.0179224i
$300$	1.46784	−	22.2470i	0.0847460	−	1.28443i
$301$	8.36626	+	6.07845i	0.482223	+	0.350356i
$302$	13.8764	+	6.52972i	0.798495	+	0.375743i
$303$	11.0025	+	6.98238i	0.632076	+	0.401128i
$304$	0.702657	−	0.278202i	0.0403002	−	0.0159560i
$305$	−9.14932	−	2.05978i	−0.523889	−	0.117943i
$306$	−1.97495	+	31.3909i	−0.112900	+	1.79450i
$307$			34.8043i			1.98638i	0.116491	+	0.993192i	$0.462835\pi$
$307$			34.8043i			1.98638i	−0.116491	+	0.993192i	$0.537165\pi$
$308$	9.18677	+	0.577983i	0.523465	+	0.0329336i
$309$	11.6060	+	24.6640i	0.660242	+	1.40309i
$310$	−10.3933	−	13.4413i	−0.590300	−	0.763413i
$311$	15.1739	+	14.2493i	0.860434	+	0.808001i	0.982836	−	0.184479i	$-0.0590598\pi$
$311$	15.1739	+	14.2493i	0.860434	+	0.808001i	−0.122402	+	0.992481i	$0.539060\pi$
$312$	−1.67776	−	13.2809i	−0.0949846	−	0.751881i
$313$	0.234892	+	1.85936i	0.0132769	+	0.105097i	0.997361	−	0.0726086i	$-0.0231324\pi$
$313$	0.234892	+	1.85936i	0.0132769	+	0.105097i	−0.984084	+	0.177706i	$0.943132\pi$
$314$	−9.69833	−	9.10734i	−0.547309	−	0.513957i
$315$	−28.8385	−	37.2957i	−1.62486	−	2.10137i
$316$	2.02068	+	4.29416i	0.113672	+	0.241565i
$317$	−24.4424	−	1.53778i	−1.37282	−	0.0863706i	−0.640829	−	0.767683i	$-0.721409\pi$
$317$	−24.4424	−	1.53778i	−1.37282	−	0.0863706i	−0.731992	+	0.681313i	$0.761409\pi$
$318$		−	0.648328i		−	0.0363564i
$319$	−0.0370084	+	0.588232i	−0.00207207	+	0.0329346i
$320$	8.78154	+	1.97698i	0.490903	+	0.110517i
$321$	55.8639	−	22.1181i	3.11802	−	1.23451i
$322$	0.635595	+	0.403361i	0.0354203	+	0.0224784i
$323$	8.20720	+	3.86202i	0.456661	+	0.214888i
$324$	−39.2884	−	28.5447i	−2.18269	−	1.58582i
$325$	−4.62310	+	5.55377i	−0.256443	+	0.308068i
$326$	7.44817	−	5.41141i	0.412516	−	0.299710i
$327$	−41.6044	+	7.93645i	−2.30073	+	0.438887i
$328$	−0.00362156	−	0.00914701i	−0.000199967	−	0.000505059i
$329$	7.55218	+	9.12902i	0.416365	+	0.503299i
$330$	14.3971	+	9.81642i	0.792535	+	0.540376i
$331$	23.3410	+	9.24138i	1.28294	+	0.507952i	0.907951	−	0.419077i	$-0.137646\pi$
$331$	23.3410	+	9.24138i	1.28294	+	0.507952i	0.374989	+	0.927029i	$0.377646\pi$
$332$	−7.57952	−	10.4323i	−0.415980	−	0.572547i
$333$	34.6150	+	28.6360i	1.89689	+	1.56924i
$334$	0.497497	−	0.467181i	0.0272218	−	0.0255630i
$335$	−11.1057	+	5.63733i	−0.606772	+	0.308000i
$336$	−2.78867	+	1.53308i	−0.152134	+	0.0836366i
$337$	3.95691	+	4.21368i	0.215546	+	0.229534i	0.827651	−	0.561243i	$-0.189677\pi$
$337$	3.95691	+	4.21368i	0.215546	+	0.229534i	−0.612104	+	0.790777i	$0.709677\pi$
$338$	4.33875	−	7.89216i	0.235997	−	0.429277i
$339$	−0.0700715	+	0.148909i	−0.00380576	+	0.00808765i
$340$	−6.76471	−	11.4784i	−0.366868	−	0.622506i
$341$	−25.5015	+	3.22159i	−1.38099	+	0.174459i
$342$	11.7989	−	7.48778i	0.638009	−	0.404893i
$343$	11.3885	−	15.6749i	0.614921	−	0.846366i
$344$	10.9752	−	2.81796i	0.591745	−	0.151934i
$345$	−1.24852	−	2.45964i	−0.0672183	−	0.132423i
$346$	−1.08789	−	17.2915i	−0.0584854	−	0.929599i
$347$	18.6056	−	1.17056i	0.998801	−	0.0628392i	0.445036	−	0.895513i	$-0.353191\pi$
$347$	18.6056	−	1.17056i	0.998801	−	0.0628392i	0.553765	+	0.832673i	$0.313191\pi$
$348$	−0.453460	−	0.824841i	−0.0243080	−	0.0442161i
$349$	6.21295	−	19.1215i	0.332572	−	1.02355i	−0.635334	−	0.772237i	$-0.719138\pi$
$349$	6.21295	−	19.1215i	0.332572	−	1.02355i	0.967906	−	0.251313i	$-0.0808623\pi$
$350$	−9.80251	−	3.21814i	−0.523966	−	0.172017i
$351$	8.20555	+	25.2541i	0.437980	+	1.34796i
$352$	11.0653	−	11.7834i	0.589783	−	0.628055i
$353$	1.61151	−	6.27640i	0.0857718	−	0.334059i	−0.911187	−	0.411994i	$-0.864833\pi$
$353$	1.61151	−	6.27640i	0.0857718	−	0.334059i	0.996958	+	0.0779346i	$0.0248325\pi$
$354$	−4.48637	+	7.06939i	−0.238448	+	0.375734i
$355$	−1.63387	+	2.09975i	−0.0867168	+	0.111443i
$356$	8.69233	−	10.5072i	0.460693	−	0.556882i
$357$	−36.3255	−	11.8029i	−1.92255	−	0.624674i
$358$	−1.67742	−	6.53313i	−0.0886545	−	0.345287i
$359$	20.2487	+	11.1318i	1.06868	+	0.587514i	0.916171	−	0.400788i	$-0.131264\pi$
$359$	20.2487	+	11.1318i	1.06868	+	0.587514i	0.152513	+	0.988302i	$0.451264\pi$
$360$	−51.6298	−	1.70140i	−2.72113	−	0.0896716i
$361$	2.80511	+	14.7049i	0.147638	+	0.773943i
$362$	−14.6477	−	2.79419i	−0.769865	−	0.146860i
$363$	−9.80263	+	4.61277i	−0.514505	+	0.242108i
$364$	4.72697	+	0.597155i	0.247760	+	0.0312994i
$365$	−5.57603	+	0.518506i	−0.291863	+	0.0271398i
$366$	−2.19342	+	11.4983i	−0.114652	+	0.601027i
$367$	11.2995	−	28.5394i	0.589831	−	1.48974i	−0.261548	−	0.965191i	$-0.584233\pi$
$367$	11.2995	−	28.5394i	0.589831	−	1.48974i	0.851379	−	0.524552i	$-0.175767\pi$
$368$	−0.130617	+	0.0424399i	−0.00680886	+	0.00221233i
$369$	0.0162296	+	0.0255738i	0.000844882	+	0.00133132i
$370$	9.78633	+	0.940150i	0.508767	+	0.0488761i
$371$	0.562479	+	0.144420i	0.0292025	+	0.00749792i
$372$	31.6295	−	26.1662i	1.63991	−	1.35665i
$373$	3.78729	−	29.9795i	0.196098	−	1.55228i	−0.519930	−	0.854209i	$-0.674042\pi$
$373$	3.78729	−	29.9795i	0.196098	−	1.55228i	0.716029	−	0.698071i	$-0.245958\pi$
$374$	10.4132			0.538451
$375$	24.8708	+	28.4720i	1.28432	+	1.47029i
$376$	12.9822			0.669504
$377$	−0.0382360	+	0.302669i	−0.00196925	+	0.0155882i
$378$	−29.2120	+	24.1663i	−1.50250	+	1.24298i
$379$	5.46248	+	1.40253i	0.280589	+	0.0720430i	0.386362	−	0.922347i	$-0.373732\pi$
$379$	5.46248	+	1.40253i	0.280589	+	0.0720430i	−0.105773	+	0.994390i	$0.533732\pi$
$380$	−2.35921	+	5.42906i	−0.121025	+	0.278505i
$381$	−12.9151	−	20.3510i	−0.661661	−	1.04261i
$382$	15.2096	−	4.94191i	0.778193	−	0.252850i
$383$	−1.78480	+	4.50790i	−0.0911992	+	0.230343i	−0.968215	−	0.250118i	$-0.919531\pi$
$383$	−1.78480	+	4.50790i	−0.0911992	+	0.230343i	0.877016	+	0.480461i	$0.159531\pi$
$384$	−5.23096	+	27.4217i	−0.266941	+	1.39936i
$385$	−11.7236	+	10.3040i	−0.597492	+	0.525142i
$386$	−9.73537	−	1.22986i	−0.495517	−	0.0625984i
$387$	−31.5665	+	14.8541i	−1.60461	+	0.755074i
$388$	−1.27804	−	0.243800i	−0.0648829	−	0.0123771i
$389$	0.423246	+	2.21873i	0.0214594	+	0.112494i	0.991405	−	0.130827i	$-0.0417632\pi$
$389$	0.423246	+	2.21873i	0.0214594	+	0.112494i	−0.969946	+	0.243321i	$0.921763\pi$
$390$	7.11830	+	5.53894i	0.360449	+	0.280475i
$391$	−1.44448	−	0.794112i	−0.0730507	−	0.0401600i
$392$	−0.511101	−	1.99061i	−0.0258145	−	0.100541i
$393$	45.1464	+	14.6690i	2.27733	+	0.739951i
$394$	4.56196	−	5.51446i	0.229828	−	0.277815i
$395$	−7.56729	−	2.73744i	−0.380752	−	0.137736i
$396$	−16.6392	+	26.2191i	−0.836150	+	1.31756i
$397$	1.22385	−	4.76659i	0.0614234	−	0.239228i	−0.930457	−	0.366400i	$-0.880590\pi$
$397$	1.22385	−	4.76659i	0.0614234	−	0.239228i	0.991881	+	0.127172i	$0.0405901\pi$
$398$	−6.62072	+	7.05035i	−0.331867	+	0.353402i
$399$	5.24390	+	16.1391i	0.262523	+	0.807964i
$400$	1.59234	−	1.00373i	0.0796171	−	0.0501864i
$401$	5.72001	−	17.6044i	0.285643	−	0.879120i	−0.700562	−	0.713592i	$-0.747067\pi$
$401$	5.72001	−	17.6044i	0.285643	−	0.879120i	0.986205	−	0.165528i	$-0.0529329\pi$
$402$	7.48904	+	13.6225i	0.373519	+	0.679429i
$403$	−13.2784	+	0.835408i	−0.661446	+	0.0416146i
$404$	0.319104	+	5.07202i	0.0158760	+	0.252342i
$405$	81.3512	−	12.7575i	4.04238	−	0.633928i
$406$	−0.421890	+	0.108323i	−0.0209381	+	0.00537598i
$407$	8.74224	−	12.0327i	0.433337	−	0.596437i
$408$	−35.3362	+	22.4250i	−1.74940	+	1.11020i
$409$	−22.0852	+	2.79001i	−1.09204	+	0.137957i	−0.650665	−	0.759365i	$-0.725510\pi$
$409$	−22.0852	+	2.79001i	−1.09204	+	0.137957i	−0.441377	+	0.897322i	$0.645510\pi$
$410$	0.00607931	+	0.00264177i	0.000300236	+	0.000130468i
$411$	16.9699	−	36.0630i	0.837066	−	1.77886i
$412$	−5.12132	+	9.31565i	−0.252309	+	0.458949i
$413$	−5.13391	−	5.46706i	−0.252623	−	0.269016i
$414$	−2.22542	+	1.22344i	−0.109373	+	0.0601286i
$415$	21.5909	+	3.45344i	1.05985	+	0.169523i
$416$	6.09914	−	5.72748i	0.299035	−	0.280813i
$417$	34.2007	+	28.2933i	1.67481	+	1.38553i
$418$	−2.71937	−	3.74288i	−0.133008	−	0.183070i
$419$	2.81114	+	1.11301i	0.137333	+	0.0543740i	0.435786	−	0.900050i	$-0.356471\pi$
$419$	2.81114	+	1.11301i	0.137333	+	0.0543740i	−0.298453	+	0.954424i	$0.596471\pi$
$420$	6.99079	−	23.9261i	0.341116	−	1.16747i
$421$	−12.1274	−	14.6595i	−0.591055	−	0.714462i	0.387171	−	0.922008i	$-0.373452\pi$
$421$	−12.1274	−	14.6595i	−0.591055	−	0.714462i	−0.978225	+	0.207546i	$0.933452\pi$
$422$	−2.43083	−	6.13957i	−0.118331	−	0.298870i
$423$	−39.2617	+	7.48957i	−1.90897	+	0.364155i
$424$	0.514790	−	0.374017i	0.0250004	−	0.0181639i
$425$	21.8648	+	5.68512i	1.06060	+	0.275769i
$426$	2.68657	+	1.95191i	0.130165	+	0.0945703i
$427$	−9.48716	−	4.46432i	−0.459116	−	0.216043i
$428$	19.7844	+	12.5556i	0.956315	+	0.606896i
$429$	12.6866	−	5.02300i	0.612517	−	0.242513i
$430$	−3.89639	+	6.56556i	−0.187901	+	0.316619i
$431$	−0.911376	+	14.4859i	−0.0438994	+	0.697762i	0.913112	+	0.407710i	$0.133673\pi$
$431$	−0.911376	+	14.4859i	−0.0438994	+	0.697762i	−0.957011	+	0.290052i	$0.906327\pi$
$432$		−	6.91679i		−	0.332784i
$433$	−36.6590	−	2.30639i	−1.76172	−	0.110838i	−0.851340	−	0.524614i	$-0.824210\pi$
$433$	−36.6590	−	2.30639i	−1.76172	−	0.110838i	−0.910379	+	0.413776i	$0.864210\pi$
$434$	−8.08808	−	17.1880i	−0.388240	−	0.825052i
$435$	1.53200	+	0.447622i	0.0734536	+	0.0214618i
$436$	−12.0412	−	11.3074i	−0.576667	−	0.541526i
$437$	0.0917888	+	0.726583i	0.00439085	+	0.0347572i
$438$	0.876056	+	6.93470i	0.0418596	+	0.331353i
$439$	−14.7014	−	13.8055i	−0.701660	−	0.658902i	0.249226	−	0.968445i	$-0.419824\pi$
$439$	−14.7014	−	13.8055i	−0.701660	−	0.658902i	−0.950885	+	0.309543i	$0.899824\pi$
$440$	0.511113	+	17.0947i	0.0243663	+	0.814959i
$441$	2.69412	+	5.72530i	0.128292	+	0.272633i
$442$	5.37928	+	0.338436i	0.255866	+	0.0160977i
$443$		−	11.7882i		−	0.560073i	−0.959989	−	0.280036i	$-0.909653\pi$
$443$		−	11.7882i		−	0.560073i	0.959989	−	0.280036i	$-0.0903465\pi$
$444$	−1.49144	+	23.7058i	−0.0707807	+	1.12503i
$445$	2.14092	+	23.0235i	0.101489	+	1.09142i
$446$	−14.3139	+	5.66726i	−0.677782	+	0.268353i
$447$	−48.4725	−	30.7616i	−2.29267	−	1.45497i
$448$	9.10580	+	4.28486i	0.430208	+	0.202441i
$449$	29.3050	+	21.2913i	1.38299	+	1.00480i	0.996594	+	0.0824653i	$0.0262794\pi$
$449$	29.3050	+	21.2913i	1.38299	+	1.00480i	0.386394	+	0.922334i	$0.373721\pi$
$450$	25.4449	−	23.7486i	1.19948	−	1.11952i
$451$	0.00811264	−	0.00589418i	0.000382009	−	0.000277546i
$452$	−0.0630456	+	0.0120266i	−0.00296541	+	0.000565683i
$453$	−23.1278	−	58.4143i	−1.08664	−	2.74454i
$454$	14.2998	+	17.2855i	0.671123	+	0.811249i
$455$	−6.39115	+	4.94188i	−0.299622	+	0.231679i
$456$	17.2883	+	6.84494i	0.809601	+	0.320544i
$457$	6.04435	+	8.31934i	0.282743	+	0.389162i	0.926640	−	0.375950i	$-0.122683\pi$
$457$	6.04435	+	8.31934i	0.282743	+	0.389162i	−0.643897	+	0.765112i	$0.722683\pi$
$458$	−12.6598	−	10.4731i	−0.591556	−	0.489377i
$459$	60.5171	−	56.8293i	2.82470	−	2.65257i
$460$	0.489844	−	0.957757i	0.0228391	−	0.0446556i
$461$	−12.5816	+	6.91682i	−0.585986	+	0.322148i	−0.747021	−	0.664800i	$-0.768517\pi$
$461$	−12.5816	+	6.91682i	−0.585986	+	0.322148i	0.161035	+	0.986949i	$0.448517\pi$
$462$	13.3361	+	14.2015i	0.620450	+	0.660712i
$463$	6.14774	−	11.1827i	0.285710	−	0.519704i	−0.694038	−	0.719938i	$-0.744170\pi$
$463$	6.14774	−	11.1827i	0.285710	−	0.519704i	0.979748	+	0.200234i	$0.0641702\pi$
$464$	0.0338353	−	0.0719037i	0.00157076	−	0.00333804i
$465$	−6.65622	+	69.2868i	−0.308675	+	3.21310i
$466$	−0.492751	+	0.0622489i	−0.0228263	+	0.00288363i
$467$	−5.25776	+	3.33668i	−0.243300	+	0.154403i	−0.651886	−	0.758317i	$-0.726022\pi$
$467$	−5.25776	+	3.33668i	−0.243300	+	0.154403i	0.408586	+	0.912720i	$0.366022\pi$
$468$	−9.44770	+	13.0036i	−0.436720	+	0.601093i
$469$	−13.4869	+	3.46285i	−0.622768	+	0.159900i
$470$	−6.19453	+	6.17565i	−0.285732	+	0.284861i
$471$	3.42226	+	54.3952i	0.157689	+	2.50640i
$472$	−8.20144	+	0.515991i	−0.377502	+	0.0237504i
$473$	5.56424	+	10.1213i	0.255844	+	0.465378i
$474$	−3.10384	+	9.55262i	−0.142564	+	0.438767i
$475$	−3.66649	−	9.34370i	−0.168230	−	0.428719i
$476$	−4.60306	−	14.1668i	−0.210981	−	0.649333i
$477$	−1.34109	+	1.42812i	−0.0614045	+	0.0653892i
$478$	−1.76687	+	6.88152i	−0.0808149	+	0.314753i
$479$	−0.277246	+	0.436870i	−0.0126677	+	0.0199611i	−0.850603	−	0.525809i	$-0.823763\pi$
$479$	−0.277246	+	0.436870i	−0.0126677	+	0.0199611i	0.837935	+	0.545770i	$0.183763\pi$
$480$	−24.5485	−	36.2408i	−1.12048	−	1.65416i
$481$	4.90719	−	5.93177i	0.223748	−	0.270465i
$482$	−22.6081	−	7.34583i	−1.02977	−	0.334593i
$483$	−0.766933	−	2.98701i	−0.0348967	−	0.135913i
$484$	−3.70248	−	2.03545i	−0.168294	−	0.0925207i
$485$	1.82658	−	1.23727i	0.0829405	−	0.0561815i
$486$	−10.7341	−	56.2700i	−0.486908	−	2.55246i
$487$	−28.3307	−	5.40437i	−1.28379	−	0.244895i	−0.500054	−	0.865994i	$-0.666686\pi$
$487$	−28.3307	−	5.40437i	−1.28379	−	0.244895i	−0.783732	+	0.621099i	$0.786686\pi$
$488$	−10.3953	+	4.89168i	−0.470575	+	0.221436i
$489$	−37.4183	−	4.72703i	−1.69211	−	0.213764i
$490$	1.19081	+	0.706700i	0.0537955	+	0.0319255i
$491$	2.98358	−	15.6405i	0.134647	−	0.705845i	−0.849374	−	0.527792i	$-0.823020\pi$
$491$	2.98358	−	15.6405i	0.134647	−	0.705845i	0.984021	−	0.178053i	$-0.0569799\pi$
$492$	−0.00589532	+	0.0148899i	−0.000265782	+	0.000671287i
$493$	0.907102	−	0.294735i	0.0408538	−	0.0132742i
$494$	−1.28314	−	2.02190i	−0.0577311	−	0.0909696i
$495$	−11.4079	−	51.4044i	−0.512748	−	2.31046i
$496$	3.35676	+	0.861871i	0.150723	+	0.0386991i
$497$	−2.29190	+	1.89602i	−0.102806	+	0.0850483i
$498$	3.42053	−	27.0763i	0.153277	−	1.21332i
$499$	19.9262			0.892020			0.446010	−	0.895028i	$-0.352845\pi$
$499$	19.9262			0.892020			0.446010	+	0.895028i	$0.352845\pi$
$500$	−3.28208	+	14.3738i	−0.146779	+	0.642815i
$501$	−2.79583			−0.124909
$502$	2.94194	−	23.2878i	0.131305	−	1.03939i
$503$	16.8474	−	13.9374i	0.751188	−	0.621437i	−0.180970	−	0.983489i	$-0.557924\pi$
$503$	16.8474	−	13.9374i	0.751188	−	0.621437i	0.932158	+	0.362052i	$0.117924\pi$
$504$	−55.9395	−	14.3628i	−2.49174	−	0.639771i
$505$	−6.45523	−	5.70858i	−0.287254	−	0.254028i
$506$	0.450506	+	0.709884i	0.0200274	+	0.0315582i
$507$	−35.0894	+	11.4012i	−1.55838	+	0.506347i
$508$	3.46041	−	8.74000i	0.153531	−	0.387775i
$509$	−2.06765	+	10.8390i	−0.0916469	+	0.480430i	0.906639	+	0.421907i	$0.138639\pi$
$509$	−2.06765	+	10.8390i	−0.0916469	+	0.480430i	−0.998286	+	0.0585229i	$0.981361\pi$
$510$	6.19325	−	27.5098i	0.274242	−	1.21815i
$511$	−6.21158	−	0.784705i	−0.274784	−	0.0347133i
$512$	−3.83814	+	1.80609i	−0.169623	+	0.0798187i
$513$	−36.2305	−	6.91134i	−1.59962	−	0.305143i
$514$	4.69670	+	24.6209i	0.207162	+	1.08598i
$515$	−5.00256	−	17.3175i	−0.220439	−	0.763101i
$516$	−16.1638	−	8.88615i	−0.711574	−	0.391191i
$517$	3.29086	+	12.8170i	0.144732	+	0.563693i
$518$	10.4536	+	3.39659i	0.459306	+	0.149238i
$519$	−45.2428	+	54.6892i	−1.98594	+	2.40059i
$520$	−0.291559	+	8.84750i	−0.0127857	+	0.387988i
$521$	−0.423157	+	0.666788i	−0.0185388	+	0.0292125i	−0.853471	−	0.521140i	$-0.825507\pi$
$521$	−0.423157	+	0.666788i	−0.0185388	+	0.0292125i	0.834932	+	0.550353i	$0.185507\pi$
$522$	0.365433	−	1.42327i	0.0159945	−	0.0622947i
$523$	28.6393	−	30.4978i	1.25231	−	1.33357i	0.331552	−	0.943437i	$-0.392428\pi$
$523$	28.6393	−	30.4978i	1.25231	−	1.33357i	0.920757	−	0.390137i	$-0.127572\pi$
$524$	5.72082	+	17.6069i	0.249915	+	0.769160i
$525$	20.2488	+	37.1002i	0.883730	+	1.61918i
$526$	5.12784	−	15.7819i	0.223584	−	0.688122i
$527$	20.0389	+	36.4506i	0.872907	+	1.58781i
$528$	−3.54723	+	0.223173i	−0.154374	+	0.00971236i
$529$	1.43583	+	22.8218i	0.0624272	+	0.992252i
$530$	−0.0677147	+	0.423352i	−0.00294134	+	0.0183892i
$531$	24.5058	−	6.29202i	1.06346	−	0.273050i
$532$	−3.89000	+	5.35413i	−0.168653	+	0.232131i
$533$	0.00438244	−	0.00278118i	0.000189824	−	0.000120466i
$534$	28.6335	−	3.61725i	1.23909	−	0.156534i
$535$	−38.7887	+	8.60817i	−1.67698	+	0.372163i
$536$	−6.49625	+	13.8052i	−0.280595	+	0.596296i
$537$	−13.3119	+	24.2142i	−0.574450	+	1.04492i
$538$	11.1598	+	11.8840i	0.481134	+	0.512355i
$539$	1.83573	−	1.00920i	0.0790705	−	0.0434694i
$540$	38.2513	+	38.3682i	1.64607	+	1.65111i
$541$	3.00020	−	2.81737i	0.128989	−	0.121128i	−0.617368	−	0.786674i	$-0.711801\pi$
$541$	3.00020	−	2.81737i	0.128989	−	0.121128i	0.746357	+	0.665546i	$0.231801\pi$
$542$	−0.518300	−	0.428775i	−0.0222629	−	0.0184175i
$543$	35.9070	+	49.4217i	1.54092	+	2.12089i
$544$	−24.3211	−	9.62939i	−1.04276	−	0.412857i
$545$	27.9961	−	0.837052i	1.19922	−	0.0358554i
$546$	6.42766	+	7.76971i	0.275078	+	0.332513i
$547$	−7.80955	−	19.7247i	−0.333912	−	0.843367i	−0.995610	−	0.0935960i	$-0.970164\pi$
$547$	−7.80955	−	19.7247i	−0.333912	−	0.843367i	0.661698	−	0.749771i	$-0.269836\pi$
$548$	15.2684	−	2.91260i	0.652234	−	0.124420i
$549$	28.6164	−	20.7910i	1.22132	−	0.887339i
$550$	−8.37589	−	7.91373i	−0.357149	−	0.337443i
$551$	−0.342826	−	0.249078i	−0.0146049	−	0.0106111i
$552$	−3.05751	−	1.43875i	−0.130136	−	0.0612374i
$553$	−7.59630	−	4.82076i	−0.323027	−	0.204999i
$554$	14.2911	−	5.65823i	0.607169	−	0.240395i
$555$	−26.5888	−	30.2520i	−1.12863	−	1.28412i
$556$	−1.08695	+	17.2765i	−0.0460968	+	0.732687i
$557$		−	4.37756i		−	0.185483i	−0.995690	−	0.0927415i	$-0.970437\pi$
$557$		−	4.37756i		−	0.185483i	0.995690	−	0.0927415i	$-0.0295630\pi$
$558$	63.9572	+	4.02385i	2.70753	+	0.170343i
$559$	2.54545	+	5.40936i	0.107661	+	0.228792i
$560$	1.98110	−	0.709825i	0.0837166	−	0.0299956i
$561$	−31.0972	−	29.2022i	−1.31292	−	1.23292i
$562$	−1.60442	−	12.7003i	−0.0676785	−	0.535731i
$563$	−1.95535	−	15.4782i	−0.0824081	−	0.652328i	−0.978172	−	0.207797i	$-0.933371\pi$
$563$	−1.95535	−	15.4782i	−0.0824081	−	0.652328i	0.895764	−	0.444530i	$-0.146629\pi$
$564$	−15.4052	−	14.4665i	−0.648676	−	0.609148i
$565$	0.0613088	−	0.0899177i	0.00257928	−	0.00378287i
$566$	4.30802	+	9.15500i	0.181079	+	0.384813i
$567$	91.8814	+	5.78069i	3.85866	+	0.242766i
$568$			3.25925i			0.136755i
$569$	0.0501859	−	0.797682i	0.00210390	−	0.0334406i	−0.996835	−	0.0795020i	$-0.974667\pi$
$569$	0.0501859	−	0.797682i	0.00210390	−	0.0334406i	0.998939	+	0.0460614i	$0.0146670\pi$
$570$	−11.5054	+	4.95800i	−0.481909	+	0.207668i
$571$	−29.7757	+	11.7890i	−1.24607	+	0.493356i	−0.896287	−	0.443474i	$-0.853746\pi$
$571$	−29.7757	+	11.7890i	−1.24607	+	0.493356i	−0.349787	+	0.936829i	$0.613746\pi$
$572$	4.49302	+	2.85136i	0.187863	+	0.119221i
$573$	−59.2800	−	27.8950i	−2.47646	−	1.16533i
$574$	0.00599541	+	0.00435592i	0.000250243	+	0.000181812i
$575$	0.558376	+	1.73652i	0.0232859	+	0.0724179i
$576$	−27.4661	+	19.9553i	−1.14442	+	0.831470i
$577$	33.6370	−	6.41661i	1.40033	−	0.267127i	0.568739	−	0.822518i	$-0.307431\pi$
$577$	33.6370	−	6.41661i	1.40033	−	0.267127i	0.831589	+	0.555391i	$0.187431\pi$
$578$	−1.03784	−	2.62127i	−0.0431683	−	0.109031i
$579$	25.6241	+	30.9743i	1.06490	+	1.28725i
$580$	0.209954	+	0.585974i	0.00871787	+	0.0243313i
$581$	22.7290	+	8.99904i	0.942957	+	0.373343i
$582$	−1.61856	−	2.22776i	−0.0670917	−	0.0923437i
$583$	0.499754	+	0.413433i	0.0206977	+	0.0171226i
$584$	−5.00094	+	4.69620i	−0.206940	+	0.194330i
$585$	−4.22248	−	26.9255i	−0.174578	−	1.11323i
$586$	−3.73937	+	2.05574i	−0.154472	+	0.0849218i
$587$	13.2096	+	14.0668i	0.545218	+	0.580598i	0.941281	−	0.337626i	$-0.109624\pi$
$587$	13.2096	+	14.0668i	0.545218	+	0.580598i	−0.396063	+	0.918223i	$0.629624\pi$
$588$	−1.61171	+	2.93168i	−0.0664656	+	0.120901i
$589$	7.86864	−	16.7217i	0.324222	−	0.689006i
$590$	3.66791	−	4.14766i	0.151006	−	0.170756i
$591$	−29.0881	+	3.67468i	−1.19652	+	0.151156i
$592$	−1.69315	+	1.07450i	−0.0695879	+	0.0441618i
$593$	−4.97557	+	6.84828i	−0.204322	+	0.281225i	−0.898865	−	0.438226i	$-0.855607\pi$
$593$	−4.97557	+	6.84828i	−0.204322	+	0.281225i	0.694543	+	0.719452i	$0.255607\pi$
$594$	−41.0134	+	10.5304i	−1.68280	+	0.432069i
$595$	22.4874	+	11.5012i	0.921895	+	0.471502i
$596$	−1.40585	−	22.3453i	−0.0575857	−	0.915298i
$597$	39.5434	−	2.48786i	1.61840	−	0.101821i
$598$	0.209653	+	0.381357i	0.00857335	+	0.0155949i
$599$	−2.57156	+	7.91446i	−0.105071	+	0.323376i	−0.989747	−	0.142831i	$-0.954380\pi$
$599$	−2.57156	+	7.91446i	−0.105071	+	0.323376i	0.884676	+	0.466206i	$0.154380\pi$
$600$	45.4653	+	8.81687i	1.85611	+	0.359947i
$601$	5.63166	+	17.3325i	0.229720	+	0.707006i	0.997778	+	0.0666258i	$0.0212234\pi$
$601$	5.63166	+	17.3325i	0.229720	+	0.707006i	−0.768058	+	0.640381i	$0.778777\pi$
$602$	−5.84306	+	6.22223i	−0.238145	+	0.253599i
$603$	11.6821	−	45.4987i	0.475731	−	1.85285i
$604$	13.1288	−	20.6876i	0.534202	−	0.841768i
$605$	6.88280	−	1.98825i	0.279826	−	0.0808340i
$606$	−6.85600	+	8.28748i	−0.278506	+	0.336656i
$607$	30.9241	+	10.0478i	1.25517	+	0.407829i	0.859771	−	0.510680i	$-0.170606\pi$
$607$	30.9241	+	10.0478i	1.25517	+	0.407829i	0.395399	+	0.918510i	$0.370606\pi$
$608$	2.89021	+	11.2566i	0.117213	+	0.456516i
$609$	1.56368	+	0.859642i	0.0633636	+	0.0348344i
$610$	2.63323	−	7.27919i	0.106616	−	0.294726i
$611$	1.28344	+	6.72805i	0.0519226	+	0.272188i
$612$	49.3617	+	9.41624i	1.99533	+	0.380629i
$613$	26.5052	−	12.4724i	1.07053	−	0.503755i	0.191981	−	0.981399i	$-0.438509\pi$
$613$	26.5052	−	12.4724i	1.07053	−	0.503755i	0.878554	+	0.477643i	$0.158509\pi$
$614$	−28.5008	−	3.60049i	−1.15020	−	0.145304i
$615$	−0.0107464	−	0.0249378i	−0.000433336	−	0.00100559i
$616$	−3.58285	+	18.7819i	−0.144357	+	0.756746i
$617$	−1.36279	+	3.44201i	−0.0548638	+	0.138570i	−0.954623	−	0.297816i	$-0.903742\pi$
$617$	−1.36279	+	3.44201i	−0.0548638	+	0.138570i	0.899760	+	0.436386i	$0.143742\pi$
$618$	−21.3977	+	6.95254i	−0.860742	+	0.279672i
$619$	−5.30204	−	8.35468i	−0.213107	−	0.335803i	0.720912	−	0.693027i	$-0.243723\pi$
$619$	−5.30204	−	8.35468i	−0.213107	−	0.335803i	−0.934019	+	0.357224i	$0.883723\pi$
$620$	−23.3867	+	13.7827i	−0.939232	+	0.553527i
$621$	6.49232	+	1.66694i	0.260528	+	0.0668922i
$622$	−13.2383	+	10.9517i	−0.530807	+	0.439122i
$623$	−3.24006	+	25.6477i	−0.129810	+	1.02755i
$624$	−1.83970			−0.0736470
$625$	−13.2666	−	21.1896i	−0.530663	−	0.847583i
$626$	−1.54691			−0.0618270
$627$	−2.37545	+	18.8036i	−0.0948662	+	0.750943i
$628$	−16.3779	+	13.5490i	−0.653549	+	0.540662i
$629$	−23.3123	−	5.98558i	−0.929522	−	0.238661i
$630$	33.5244	−	19.7573i	1.33564	−	0.787148i
$631$	1.54394	+	2.43285i	0.0614631	+	0.0968504i	0.873670	−	0.486520i	$-0.161734\pi$
$631$	1.54394	+	2.43285i	0.0614631	+	0.0968504i	−0.812207	+	0.583370i	$0.801734\pi$
$632$	−9.37562	+	3.04632i	−0.372942	+	0.121176i
$633$	−9.95828	+	25.1517i	−0.395806	+	0.999692i
$634$	3.78783	−	19.8565i	0.150434	−	0.788603i
$635$	6.30788	+	14.6379i	0.250320	+	0.580887i
$636$	−1.02765	−	0.129823i	−0.0407490	−	0.00514780i
$637$	0.981112	−	0.461676i	0.0388731	−	0.0182923i
$638$	−0.477868	−	0.0911582i	−0.0189190	−	0.00360899i
$639$	−1.88031	−	9.85691i	−0.0743837	−	0.389933i
$640$	6.27982	−	17.3597i	0.248232	−	0.686203i
$641$	−0.0741811	−	0.0407814i	−0.00292998	−	0.00161077i	0.480288	−	0.877111i	$-0.340532\pi$
$641$	−0.0741811	−	0.0407814i	−0.00292998	−	0.00161077i	−0.483218	+	0.875500i	$0.660532\pi$
$642$	12.3331	+	48.0344i	0.486750	+	1.89577i
$643$	4.39935	+	1.42944i	0.173493	+	0.0563714i	0.394476	−	0.918906i	$-0.370926\pi$
$643$	4.39935	+	1.42944i	0.173493	+	0.0563714i	−0.220982	+	0.975278i	$0.570926\pi$
$644$	0.766632	−	0.926699i	0.0302095	−	0.0365170i
$645$	30.0481	−	8.68008i	1.18314	−	0.341778i
$646$	−4.01159	+	6.32126i	−0.157834	+	0.248707i
$647$	4.28356	−	16.6834i	0.168404	−	0.655891i	−0.827173	−	0.561947i	$-0.810052\pi$
$647$	4.28356	−	16.6834i	0.168404	−	0.655891i	0.995577	−	0.0939441i	$-0.0299475\pi$
$648$	69.0545	−	73.5355i	2.71272	−	2.88875i
$649$	−2.58842	−	7.96633i	−0.101604	−	0.312706i
$650$	−4.06966	−	4.36034i	−0.159625	−	0.171027i
$651$	−24.0477	+	74.0112i	−0.942503	+	2.90073i
$652$	−7.08608	−	12.8895i	−0.277512	−	0.504793i
$653$	−26.8568	+	1.68969i	−1.05099	+	0.0661227i	−0.578876	−	0.815415i	$-0.696509\pi$
$653$	−26.8568	+	1.68969i	−1.05099	+	0.0661227i	−0.472113	+	0.881538i	$0.656509\pi$
$654$	−2.19512	−	34.8904i	−0.0858358	−	1.36432i
$655$	−27.9480	−	14.2940i	−1.09202	−	0.558513i
$656$	−0.00130955		0.000336234i	−5.11292e−5		1.31277e-5i
$657$	12.4150	−	17.0877i	0.484354	−	0.666656i
$658$	−8.25692	+	5.24000i	−0.321888	+	0.204277i
$659$	−44.9264	+	5.67552i	−1.75008	+	0.221087i	−0.934106	−	0.356996i	$-0.883801\pi$
$659$	−44.9264	+	5.67552i	−1.75008	+	0.221087i	−0.815978	+	0.578083i	$0.803801\pi$
$660$	18.4427	−	20.8549i	0.717882	−	0.811777i
$661$	8.82399	−	18.7519i	0.343213	−	0.729366i	−0.656474	−	0.754348i	$-0.727953\pi$
$661$	8.82399	−	18.7519i	0.343213	−	0.729366i	0.999688	+	0.0249825i	$0.00795301\pi$
$662$	−9.98228	+	18.1577i	−0.387973	+	0.705719i
$663$	−15.1153	−	16.0961i	−0.587028	−	0.625121i
$664$	23.4725	−	12.9041i	0.910911	−	0.500778i
$665$	−1.73857	−	11.0863i	−0.0674187	−	0.429910i
$666$	−27.0306	+	25.3834i	−1.04742	+	0.983589i
$667$	0.0593368	+	0.0490877i	0.00229753	+	0.00190068i
$668$	−0.640899	−	0.882121i	−0.0247971	−	0.0341303i
$669$	58.6391	+	23.2169i	2.26712	+	0.897616i
$670$	−3.46746	−	9.67755i	−0.133960	−	0.373876i
$671$	−7.46459	−	9.02314i	−0.288167	−	0.348334i
$672$	−18.0153	−	45.5014i	−0.694955	−	1.75526i
$673$	11.6277	−	2.21810i	0.448214	−	0.0855013i	0.0416675	−	0.999132i	$-0.486733\pi$
$673$	11.6277	−	2.21810i	0.448214	−	0.0855013i	0.406546	+	0.913630i	$0.366733\pi$
$674$	−3.85987	+	2.80436i	−0.148677	+	0.108020i
$675$	−91.8662	−	0.280374i	−3.53593	−	0.0107916i
$676$	−11.6409	−	8.45761i	−0.447727	−	0.325293i
$677$	−1.81844	−	0.855692i	−0.0698882	−	0.0328869i	0.390518	−	0.920595i	$-0.372296\pi$
$677$	−1.81844	−	0.855692i	−0.0698882	−	0.0328869i	−0.460406	+	0.887709i	$0.652296\pi$
$678$	−0.114691	−	0.0727854i	−0.00440470	−	0.00279531i
$679$	2.29332	−	0.907989i	0.0880095	−	0.0348454i
$680$	25.4163	−	10.9526i	0.974672	−	0.420013i
$681$	5.77067	−	91.7221i	0.221132	−	3.51480i
$682$		−	21.2162i		−	0.812411i
$683$	−7.90979	−	0.497642i	−0.302660	−	0.0190417i	−0.0892653	−	0.996008i	$-0.528452\pi$
$683$	−7.90979	−	0.497642i	−0.302660	−	0.0190417i	−0.213394	+	0.976966i	$0.568452\pi$
$684$	−9.50610	−	20.2015i	−0.363475	−	0.772423i
$685$	−14.8478	+	21.7763i	−0.567305	+	0.832031i
$686$	11.6579	+	10.9475i	0.445100	+	0.417976i
$687$	8.43615	+	66.7790i	0.321859	+	2.54778i
$688$	−0.195176	−	1.54498i	−0.00744101	−	0.0589017i
$689$	0.244729	+	0.229816i	0.00932342	+	0.00875528i
$690$	2.14333	−	0.767954i	0.0815952	−	0.0292355i
$691$	2.04659	+	4.34923i	0.0778561	+	0.165453i	0.939965	−	0.341270i	$-0.110857\pi$
$691$	2.04659	+	4.34923i	0.0778561	+	0.165453i	−0.862109	+	0.506722i	$0.830857\pi$
$692$	−27.6263	−	1.73810i	−1.05019	−	0.0660726i
$693$		−	58.8689i		−	2.23624i
$694$	−0.966181	+	15.3570i	−0.0366757	+	0.582944i
$695$	−19.3776	−	22.0473i	−0.735034	−	0.836301i
$696$	1.81792	−	0.719764i	0.0689079	−	0.0272826i
$697$	−0.0137012	−	0.00869507i	−0.000518971	−	0.000329349i
$698$	15.0156	+	7.06583i	0.568351	+	0.267446i
$699$	1.64609	+	1.19595i	0.0622608	+	0.0452351i
$700$	−7.06388	+	14.8934i	−0.266990	+	0.562916i
$701$	−9.88007	+	7.17829i	−0.373165	+	0.271120i	−0.758522	−	0.651647i	$-0.774078\pi$
$701$	−9.88007	+	7.17829i	−0.373165	+	0.271120i	0.385357	+	0.922768i	$0.374078\pi$
$702$	−21.5292	+	4.10691i	−0.812565	+	0.155005i
$703$	3.93649	+	9.94245i	0.148468	+	0.374986i
$704$	7.16453	+	8.66043i	0.270023	+	0.326402i
$705$	35.8177	−	1.07091i	1.34897	−	0.0403327i
$706$	4.97297	+	1.96894i	0.187160	+	0.0741019i
$707$	−5.66286	−	7.79425i	−0.212974	−	0.293133i
$708$	10.3072	+	8.52684i	0.387367	+	0.320458i
$709$	9.41694	−	8.84310i	0.353661	−	0.332110i	−0.487271	−	0.873251i	$-0.662008\pi$
$709$	9.41694	−	8.84310i	0.353661	−	0.332110i	0.840932	+	0.541141i	$0.182008\pi$
$710$	−1.55044	−	1.55518i	−0.0581868	−	0.0583647i
$711$	26.5971	−	14.6219i	0.997468	−	0.548363i
$712$	19.3907	+	20.6490i	0.726696	+	0.773852i
$713$	−1.61796	+	2.94306i	−0.0605930	+	0.110218i
$714$	13.4231	−	28.5255i	0.502347	−	1.06754i
$715$	−8.80888	+	1.95491i	−0.329433	+	0.0731094i
$716$	−10.6914	+	1.35064i	−0.399557	+	0.0504758i
$717$	24.5747	−	15.5956i	0.917760	−	0.582428i
$718$	−11.2104	+	15.4298i	−0.418369	+	0.575836i
$719$	27.6292	−	7.09397i	1.03039	−	0.264560i	0.304606	−	0.952478i	$-0.401475\pi$
$719$	27.6292	−	7.09397i	1.03039	−	0.264560i	0.725788	+	0.687918i	$0.241475\pi$
$720$	−1.12128	+	7.01026i	−0.0417878	+	0.261257i
$721$	−1.26541	−	20.1130i	−0.0471262	−	0.749049i
$722$	−12.3319	+	0.775856i	−0.458945	+	0.0288744i
$723$	46.9152	+	85.3384i	1.74480	+	3.17377i
$724$	−7.36210	+	22.6582i	−0.273610	+	0.842086i
$725$	−0.953626	−	0.452302i	−0.0354168	−	0.0167981i
$726$	−2.76327	−	8.50446i	−0.102554	−	0.315630i
$727$	4.03868	−	4.30076i	0.149786	−	0.159506i	−0.649700	−	0.760191i	$-0.725105\pi$
$727$	4.03868	−	4.30076i	0.149786	−	0.159506i	0.799486	+	0.600685i	$0.205105\pi$
$728$	−2.46127	+	9.58603i	−0.0912209	+	0.355282i
$729$	−66.5486	+	104.864i	−2.46476	+	3.88384i
$730$	0.152240	−	4.61979i	0.00563464	−	0.170986i
$731$	11.9139	−	14.4014i	0.440650	−	0.532655i
$732$	17.7865	+	5.77920i	0.657410	+	0.213605i
$733$	−7.50818	−	29.2424i	−0.277321	−	1.08009i	−0.942714	−	0.333601i	$-0.891736\pi$
$733$	−7.50818	−	29.2424i	−0.277321	−	1.08009i	0.665394	−	0.746493i	$-0.268264\pi$
$734$	22.2016	+	12.2054i	0.819477	+	0.450511i
$735$	−1.57433	−	5.44991i	−0.0580701	−	0.201023i
$736$	−0.395753	−	2.07461i	−0.0145876	−	0.0764711i
$737$	−15.2764	−	2.91413i	−0.562713	−	0.107343i
$738$	−0.0226211	+	0.0106447i	−0.000832693	+	0.000391836i
$739$	−35.7097	−	4.51118i	−1.31360	−	0.165947i	−0.562866	−	0.826548i	$-0.690301\pi$
$739$	−35.7097	−	4.51118i	−1.31360	−	0.165947i	−0.750736	+	0.660602i	$0.770301\pi$
$740$	3.44985	−	15.3239i	0.126819	−	0.563316i
$741$	−1.83825	+	9.63645i	−0.0675299	+	0.354004i
$742$	−0.176452	+	0.445668i	−0.00647777	+	0.0163610i
$743$	3.21786	−	1.04555i	0.118052	−	0.0383573i	−0.249395	−	0.968402i	$-0.580232\pi$
$743$	3.21786	−	1.04555i	0.118052	−	0.0383573i	0.367447	+	0.930044i	$0.380232\pi$
$744$	45.6897	+	71.9954i	1.67507	+	2.63948i
$745$	28.4392	+	25.1497i	1.04193	+	0.921415i
$746$	24.1581	+	6.20274i	0.884490	+	0.227098i
$747$	−63.5431	+	52.5674i	−2.32492	+	1.92334i
$748$	2.08515	−	16.5057i	0.0762407	−	0.603507i
$749$	−44.4212			−1.62312
$750$	−25.8883	+	17.4210i	−0.945307	+	0.636123i
$751$	31.6421			1.15464			0.577318	−	0.816519i	$-0.304099\pi$
$751$	31.6421			1.15464			0.577318	+	0.816519i	$0.304099\pi$
$752$	0.223613	−	1.77008i	0.00815432	−	0.0645481i
$753$	−74.0930	+	61.2951i	−2.70010	+	2.23372i
$754$	−0.243897	−	0.0626220i	−0.00888220	−	0.00228056i
$755$	9.00116	+	40.5595i	0.327586	+	1.47611i
$756$	32.4560	+	51.1425i	1.18041	+	1.86003i
$757$	13.3808	−	4.34770i	0.486335	−	0.158020i	−0.0555783	−	0.998454i	$-0.517700\pi$
$757$	13.3808	−	4.34770i	0.486335	−	0.158020i	0.541913	+	0.840435i	$0.317700\pi$
$758$	−1.71361	+	4.32808i	−0.0622410	+	0.157203i
$759$	0.645405	−	3.38333i	0.0234267	−	0.122807i
$760$	−10.5742	−	6.27536i	−0.383566	−	0.227631i
$761$	29.0797	+	3.67362i	1.05414	+	0.133169i	0.633253	−	0.773945i	$-0.281719\pi$
$761$	29.0797	+	3.67362i	1.05414	+	0.133169i	0.420886	+	0.907114i	$0.361719\pi$
$762$	18.0012	−	8.47074i	0.652116	−	0.306863i
$763$	30.7593	+	5.86765i	1.11356	+	0.212423i
$764$	−4.78771	−	25.0981i	−0.173213	−	0.908016i
$765$	−70.5475	+	47.7868i	−2.55065	+	1.72773i
$766$	−3.50683	−	1.92790i	−0.126707	−	0.0696578i
$767$	−1.07823	−	4.19941i	−0.0389325	−	0.151632i
$768$	−47.8053	−	15.5329i	−1.72502	−	0.560494i
$769$	24.0616	−	29.0854i	0.867682	−	1.04885i	−0.130668	−	0.991426i	$-0.541712\pi$
$769$	24.0616	−	29.0854i	0.867682	−	1.04885i	0.998350	−	0.0574212i	$-0.0182878\pi$
$770$	−7.22504	−	10.6663i	−0.260373	−	0.384387i
$771$	55.0200	−	86.6977i	1.98150	−	3.12234i
$772$	−3.89886	+	15.1851i	−0.140323	+	0.546523i
$773$	18.3457	−	19.5361i	0.659848	−	0.702666i	−0.308794	−	0.951129i	$-0.599925\pi$
$773$	18.3457	−	19.5361i	0.659848	−	0.702666i	0.968641	+	0.248463i	$0.0799253\pi$
$774$	−8.89828	−	27.3861i	−0.319842	−	0.984373i
$775$	11.5831	−	44.5483i	0.416077	−	1.60022i
$776$	0.835163	−	2.57037i	0.0299806	−	0.0922708i
$777$	−21.6928	−	39.4591i	−0.778225	−	1.41559i
$778$	−1.86068	+	0.117064i	−0.0667086	+	0.00419695i
$779$	0.000452699		0.00719544i	1.62196e−5		0.000257803i
$780$	10.2050	−	10.1739i	0.365399	−	0.364286i
$781$	−3.21780	+	0.826191i	−0.115142	+	0.0295634i
$782$	0.799721	−	1.10072i	0.0285980	−	0.0393617i
$783$	−3.27467	+	2.07817i	−0.117027	+	0.0742677i
$784$	−0.280217	+	0.0353996i	−0.0100077	+	0.00126427i
$785$	3.44661	−	35.8769i	0.123015	−	1.28050i
$786$	−16.6826	+	35.4524i	−0.595049	+	1.26454i
$787$	5.61962	−	10.2220i	0.200318	−	0.364377i	−0.757000	−	0.653415i	$-0.773336\pi$
$787$	5.61962	−	10.2220i	0.200318	−	0.364377i	0.957317	+	0.289039i	$0.0933356\pi$
$788$	−7.82737	−	8.33530i	−0.278838	−	0.296933i
$789$	−59.5714	+	32.7497i	−2.12080	+	1.16592i
$790$	3.02450	−	5.91358i	0.107607	−	0.210396i
$791$	0.0886958	−	0.0832909i	0.00315366	−	0.00296148i
$792$	−49.7014	−	41.1166i	−1.76606	−	1.46101i
$793$	−3.56284	−	4.90382i	−0.126520	−	0.174140i
$794$	3.77670	+	1.49530i	0.134030	+	0.0530663i
$795$	1.38945	−	1.07437i	0.0492787	−	0.0381041i
$796$	9.84962	+	11.9061i	0.349110	+	0.422002i
$797$	11.2096	+	28.3123i	0.397066	+	1.00287i	0.981505	+	0.191437i	$0.0613146\pi$
$797$	11.2096	+	28.3123i	0.397066	+	1.00287i	−0.584439	+	0.811438i	$0.698685\pi$
$798$	−13.7586	+	2.62459i	−0.487048	+	0.0929095i
$799$	17.3242	−	12.5867i	0.612885	−	0.445287i
$800$	12.2447	+	26.2289i	0.432916	+	0.927330i
$801$	−70.5555	−	51.2616i	−2.49296	−	1.81124i
$802$	13.8243	+	6.50522i	0.488153	+	0.229707i
$803$	−5.90416	−	3.74689i	−0.208353	−	0.132225i
$804$	23.0924	−	9.14292i	0.814406	−	0.322446i
$805$	0.188821	+	2.03059i	0.00665507	+	0.0715688i
$806$	0.689544	−	10.9600i	0.0242881	−	0.386049i
$807$		−	66.7857i		−	2.35097i
$808$	−10.5357	−	0.662848i	−0.370643	−	0.0233189i
$809$	16.4934	+	35.0502i	0.579876	+	1.23230i	0.952563	+	0.304342i	$0.0984365\pi$
$809$	16.4934	+	35.0502i	0.579876	+	1.23230i	−0.372687	+	0.927957i	$0.621564\pi$
$810$	2.03125	+	67.9374i	0.0713708	+	2.38708i
$811$	−32.3484	−	30.3772i	−1.13591	−	1.06669i	−0.997079	−	0.0763709i	$-0.975667\pi$
$811$	−32.3484	−	30.3772i	−1.13591	−	1.06669i	−0.138827	−	0.990317i	$-0.544333\pi$
$812$	0.0872204	+	0.690420i	0.00306083	+	0.0242290i
$813$	0.345380	+	2.73396i	0.0121130	+	0.0958843i
$814$	8.94904	+	8.40370i	0.313664	+	0.294550i
$815$	23.9400	+	6.99485i	0.838583	+	0.245019i
$816$	2.44893	+	5.20424i	0.0857296	+	0.182185i
$817$	−8.28769	−	0.521417i	−0.289949	−	0.0182421i
$818$		−	18.3739i		−	0.642429i
$819$	1.91329	−	30.4108i	0.0668556	−	1.06264i
$820$	0.00540476	−	0.00910720i	0.000188742	−	0.000318037i
$821$	24.2653	−	9.60733i	0.846866	−	0.335298i	0.0956994	−	0.995410i	$-0.469491\pi$
$821$	24.2653	−	9.60733i	0.846866	−	0.335298i	0.751167	+	0.660112i	$0.229491\pi$
$822$	27.7760	+	17.6272i	0.968800	+	0.614819i
$823$	1.39516	+	0.656510i	0.0486321	+	0.0228845i	0.449942	−	0.893058i	$-0.351445\pi$
$823$	1.39516	+	0.656510i	0.0486321	+	0.0228845i	−0.401309	+	0.915943i	$0.631445\pi$
$824$	−17.8647	−	12.9795i	−0.622347	−	0.452161i
$825$	2.82031	+	47.1221i	0.0981907	+	1.64058i
$826$	5.00802	−	3.63854i	0.174251	−	0.126601i
$827$	−25.0907	+	4.78632i	−0.872491	+	0.166436i	−0.604134	−	0.796883i	$-0.706481\pi$
$827$	−25.0907	+	4.78632i	−0.872491	+	0.166436i	−0.268357	+	0.963320i	$0.586481\pi$
$828$	1.49362	+	3.77245i	0.0519069	+	0.131102i
$829$	−11.2012	−	13.5399i	−0.389033	−	0.470260i	0.539244	−	0.842150i	$-0.318710\pi$
$829$	−11.2012	−	13.5399i	−0.389033	−	0.470260i	−0.928277	+	0.371889i	$0.878710\pi$
$830$	−5.06155	+	17.3233i	−0.175689	+	0.601299i
$831$	−58.5456	−	23.1798i	−2.03092	−	0.804100i
$832$	3.41962	+	4.70670i	0.118554	+	0.163176i
$833$	−2.61202	−	2.16085i	−0.0905012	−	0.0748691i
$834$	−26.7071	+	25.0796i	−0.924791	+	0.868436i
$835$	1.82565	+	0.292011i	0.0631793	+	0.0101055i
$836$	−6.47730	+	3.56093i	−0.224022	+	0.123157i
$837$	−115.787	−	123.300i	−4.00217	−	4.26188i
$838$	−1.20224	+	2.18687i	−0.0415308	+	0.0755442i
$839$	11.8908	−	25.2693i	0.410517	−	0.872392i	−0.587487	−	0.809234i	$-0.699883\pi$
$839$	11.8908	−	25.2693i	0.410517	−	0.872392i	0.998004	−	0.0631585i	$-0.0201174\pi$
$840$	47.4878	+	20.6359i	1.63848	+	0.712006i
$841$	28.7271	−	3.62908i	0.990590	−	0.125141i
$842$	13.2591	−	8.41449i	0.456939	−	0.289982i
$843$	−30.8249	+	42.4268i	−1.06167	+	1.46126i
$844$	−10.2185	+	2.62366i	−0.351734	+	0.0903100i
$845$	24.1038	−	3.77998i	0.829197	−	0.130035i
$846$	−2.07151	−	32.9258i	−0.0712201	−	1.13201i
$847$	7.99387	−	0.502932i	0.274673	−	0.0172809i
$848$	−0.0421290	−	0.0766323i	−0.00144671	−	0.00263156i
$849$	12.8087	−	39.4211i	0.439594	−	1.35293i
$850$	−6.91739	+	17.3167i	−0.237264	+	0.593959i
$851$	−0.600516	−	1.84820i	−0.0205854	−	0.0633554i
$852$	3.63190	−	3.86758i	0.124427	−	0.132501i
$853$	−9.41580	+	36.6721i	−0.322391	+	1.25563i	0.576369	+	0.817189i	$0.304469\pi$
$853$	−9.41580	+	36.6721i	−0.322391	+	1.25563i	−0.898760	+	0.438440i	$0.855531\pi$
$854$	4.63722	−	7.30710i	0.158683	−	0.250044i
$855$	35.5997	+	12.8781i	1.21748	+	0.440421i
$856$	−31.0257	+	37.5036i	−1.06044	+	1.28185i
$857$	1.39039	+	0.451765i	0.0474948	+	0.0154320i	0.332668	−	0.943044i	$-0.392051\pi$
$857$	1.39039	+	0.451765i	0.0474948	+	0.0154320i	−0.285173	+	0.958476i	$0.592051\pi$
$858$	2.80085	+	10.9086i	0.0956194	+	0.372413i
$859$	2.03588	+	1.11924i	0.0694634	+	0.0381878i	0.516107	−	0.856524i	$-0.327381\pi$
$859$	2.03588	+	1.11924i	0.0694634	+	0.0381878i	−0.446643	+	0.894712i	$0.647381\pi$
$860$	9.62671	+	7.49080i	0.328268	+	0.255434i
$861$	−0.00568876	−	0.0298215i	−0.000193872	−	0.00101631i
$862$	−11.7681	−	2.24488i	−0.400822	−	0.0764609i
$863$	−21.4527	+	10.0949i	−0.730257	+	0.343633i	−0.754702	−	0.656068i	$-0.772218\pi$
$863$	−21.4527	+	10.0949i	−0.730257	+	0.343633i	0.0244443	+	0.999701i	$0.492218\pi$
$864$	105.529	+	13.3314i	3.59017	+	0.453544i
$865$	35.2551	−	30.9861i	1.19871	−	1.05356i
$866$	5.68104	−	29.7811i	0.193050	−	1.01200i
$867$	−4.25166	+	10.7385i	−0.144394	+	0.364697i
$868$	−28.8640	+	9.37848i	−0.979708	+	0.318326i
$869$	−5.38421	−	8.48416i	−0.182647	−	0.287805i
$870$	−0.525037	+	1.20823i	−0.0178004	+	0.0409628i
$871$	−7.79685	−	2.00189i	−0.264186	−	0.0678315i
$872$	26.4375	−	21.8710i	0.895288	−	0.740646i
$873$	−1.04289	+	8.25533i	−0.0352965	+	0.279401i
$874$	−0.604486			−0.0204471
$875$	−9.34732	−	26.3409i	−0.315997	−	0.890486i
$876$	11.1675			0.377314
$877$	−6.10777	+	48.3480i	−0.206245	+	1.63260i	0.460747	+	0.887531i	$0.347581\pi$
$877$	−6.10777	+	48.3480i	−0.206245	+	1.63260i	−0.666992	+	0.745065i	$0.732419\pi$
$878$	12.8261	−	10.6106i	0.432858	−	0.358092i
$879$	16.9321	+	4.34741i	0.571104	+	0.146635i
$880$	2.33962	+	0.224762i	0.0788685	+	0.00757671i
$881$	2.95911	+	4.66282i	0.0996951	+	0.157094i	0.890514	−	0.454956i	$-0.150345\pi$
$881$	2.95911	+	4.66282i	0.0996951	+	0.157094i	−0.790819	+	0.612050i	$0.790345\pi$
$882$	−4.96709	+	1.61391i	−0.167251	+	0.0543430i
$883$	0.736547	−	1.86031i	0.0247868	−	0.0626043i	−0.916856	−	0.399218i	$-0.869282\pi$
$883$	0.736547	−	1.86031i	0.0247868	−	0.0626043i	0.941643	+	0.336614i	$0.109282\pi$
$884$	1.61361	−	8.45882i	0.0542714	−	0.284501i
$885$	−22.5851	+	2.10016i	−0.759191	+	0.0705960i
$886$	9.65320	+	1.21948i	0.324306	+	0.0409693i
$887$	45.2628	−	21.2991i	1.51978	−	0.715152i	0.528745	−	0.848781i	$-0.322663\pi$
$887$	45.2628	−	21.2991i	1.51978	−	0.715152i	0.991031	+	0.133629i	$0.0426629\pi$
$888$	−48.4654	−	9.24527i	−1.62639	−	0.310251i
$889$	3.33916	+	17.5045i	0.111992	+	0.587082i
$890$	−19.0752	−	0.628600i	−0.639401	−	0.0210707i
$891$	90.1049	+	49.5356i	3.01863	+	1.65951i
$892$	6.11682	+	23.8235i	0.204806	+	0.797668i
$893$	−9.04831	−	2.93998i	−0.302790	−	0.0983825i
$894$	30.2048	−	36.5113i	1.01020	−	1.22112i
$895$	11.2216	−	14.4213i	0.375096	−	0.482050i
$896$	11.0590	−	17.4262i	0.369456	−	0.582170i
$897$	0.443368	−	1.72680i	0.0148036	−	0.0576563i
$898$	−20.4668	+	21.7949i	−0.682986	+	0.727307i
$899$	−0.600507	−	1.84817i	−0.0200280	−	0.0616399i
$900$	−32.5483	−	45.0876i	−1.08494	−	1.50292i
$901$	0.324341	−	0.998220i	0.0108054	−	0.0332555i
$902$	0.00398743	+	0.00725310i	0.000132767	+	0.000241502i
$903$	34.8987	−	2.19564i	1.16136	−	0.0730663i
$904$	−0.00837127	−	0.133058i	−0.000278424	−	0.00442543i
$905$	−18.2850	−	36.0222i	−0.607815	−	1.19742i
$906$	50.2274	−	12.8962i	1.66869	−	0.428447i
$907$	−7.07905	+	9.74348i	−0.235056	+	0.323527i	−0.910208	−	0.414152i	$-0.864078\pi$
$907$	−7.07905	+	9.74348i	−0.235056	+	0.323527i	0.675152	+	0.737679i	$0.264078\pi$
$908$	30.2623	−	19.2051i	1.00429	−	0.637342i
$909$	32.2452	−	4.07352i	1.06951	−	0.135110i
$910$	−3.38569	−	5.74488i	−0.112234	−	0.190441i
$911$	−18.6364	+	39.6045i	−0.617453	+	1.31215i	0.314391	+	0.949294i	$0.398200\pi$
$911$	−18.6364	+	39.6045i	−0.617453	+	1.31215i	−0.931843	+	0.362860i	$0.881800\pi$
$912$	1.23107	−	2.23931i	0.0407648	−	0.0741510i
$913$	18.6901	+	19.9029i	0.618552	+	0.658691i
$914$	−7.43790	+	4.08902i	−0.246024	+	0.135253i
$915$	−28.2772	+	14.3536i	−0.934814	+	0.474516i
$916$	−19.1358	+	17.9697i	−0.632264	+	0.593735i
$917$	−27.0417	−	22.3709i	−0.892997	−	0.738751i
$918$	40.2764	+	55.4357i	1.32932	+	1.82965i
$919$	−38.1637	−	15.1101i	−1.25890	−	0.498436i	−0.358517	−	0.933523i	$-0.616717\pi$
$919$	−38.1637	−	15.1101i	−1.25890	−	0.498436i	−0.900388	+	0.435088i	$0.856717\pi$
$920$	1.84625	+	1.25883i	0.0608691	+	0.0415025i
$921$	75.0160	+	90.6788i	2.47186	+	2.98797i
$922$	−4.36254	−	11.0185i	−0.143673	−	0.362875i
$923$	−1.68912	+	0.322217i	−0.0555981	+	0.0106059i
$924$	25.1809	−	18.2950i	0.828391	−	0.601862i
$925$	14.2025	+	22.5313i	0.466976	+	0.740824i
$926$	8.52140	+	6.19116i	0.280031	+	0.203454i
$927$	61.5160	+	28.9472i	2.02045	+	0.950751i
$928$	1.03182	+	0.654810i	0.0338710	+	0.0214952i
$929$	−30.4441	+	12.0537i	−0.998839	+	0.395468i	−0.809930	−	0.586526i	$-0.800495\pi$
$929$	−30.4441	+	12.0537i	−0.998839	+	0.395468i	−0.188909	+	0.981995i	$0.560495\pi$
$930$	−56.0496	−	12.6184i	−1.83794	−	0.413774i
$931$	−0.0945709	+	1.50316i	−0.00309944	+	0.0492641i
$932$			0.793515i			0.0259924i
$933$	70.2464	+	4.41953i	2.29976	+	0.144689i
$934$	−2.18845	−	4.65070i	−0.0716084	−	0.152176i
$935$	17.2561	+	22.3167i	0.564335	+	0.729833i
$936$	−24.3387	−	22.8556i	−0.795535	−	0.747057i
$937$	−1.79667	−	14.2221i	−0.0586945	−	0.464615i	−0.993881	−	0.110459i	$-0.964768\pi$
$937$	−1.79667	−	14.2221i	−0.0586945	−	0.464615i	0.935186	−	0.354156i	$-0.115232\pi$
$938$	−1.44047	−	11.4025i	−0.0470331	−	0.372305i
$939$	4.61960	+	4.33809i	0.150755	+	0.141568i
$940$	8.54849	+	11.0554i	0.278821	+	0.360589i
$941$	21.1400	+	44.9248i	0.689145	+	1.46451i	0.876095	+	0.482138i	$0.160140\pi$
$941$	21.1400	+	44.9248i	0.689145	+	1.46451i	−0.186951	+	0.982369i	$0.559860\pi$
$942$	−44.8977	−	2.82472i	−1.46284	−	0.0920344i
$943$		−	0.00131021i		−	4.26665e-5i
$944$	−0.0709129	+	1.12713i	−0.00230802	+	0.0366849i
$945$	−100.200	−	22.5579i	−3.25951	−	0.733810i
$946$	−8.86385	+	3.50945i	−0.288189	+	0.114102i
$947$	−5.99630	−	3.80537i	−0.194854	−	0.123658i	0.434821	−	0.900517i	$-0.356812\pi$
$947$	−5.99630	−	3.80537i	−0.194854	−	0.123658i	−0.629674	+	0.776859i	$0.716812\pi$
$948$	14.5202	+	6.83266i	0.471593	+	0.221915i
$949$	−2.92823	−	2.12748i	−0.0950542	−	0.0690609i
$950$	8.03075	−	2.03584i	0.260552	−	0.0660514i
$951$	−66.9965	+	48.6758i	−2.17251	+	1.57842i
$952$	30.3937	−	5.79792i	0.985067	−	0.187912i
$953$	6.76739	+	17.0925i	0.219217	+	0.553679i	0.997214	−	0.0745883i	$-0.0237642\pi$
$953$	6.76739	+	17.0925i	0.219217	+	0.553679i	−0.777997	+	0.628268i	$0.783764\pi$
$954$	−1.03074	−	1.24595i	−0.0333713	−	0.0403390i
$955$	35.7957	+	24.4067i	1.15832	+	0.789781i
$956$	10.5540	+	4.17861i	0.341339	+	0.135146i
$957$	1.17143	+	1.61234i	0.0378671	+	0.0521196i
$958$	−0.329067	−	0.272228i	−0.0106317	−	0.00879528i
$959$	−21.4804	+	20.1714i	−0.693638	+	0.651370i
$960$	27.1405	−	13.7766i	0.875956	−	0.444639i
$961$	47.1005	−	25.8937i	1.51937	−	0.835281i
$962$	4.34981	+	4.63208i	0.140244	+	0.149344i
$963$	72.1941	−	131.321i	2.32642	−	4.23175i
$964$	−16.1708	+	34.3648i	−0.520827	+	1.10681i
$965$	−13.4972	−	22.9022i	−0.434490	−	0.737247i
$966$	2.52537	−	0.319028i	0.0812523	−	0.0102646i
$967$	26.8156	−	17.0177i	0.862331	−	0.547252i	−0.0295285	−	0.999564i	$-0.509401\pi$
$967$	26.8156	−	17.0177i	0.862331	−	0.547252i	0.891860	+	0.452312i	$0.149401\pi$
$968$	5.15865	−	7.10028i	0.165805	−	0.228212i
$969$	29.7070	−	7.62747i	0.954328	−	0.245030i
$970$	0.824227	+	1.62376i	0.0264643	+	0.0521357i
$971$	−2.19333	−	34.8620i	−0.0703874	−	1.11878i	−0.861718	−	0.507387i	$-0.830611\pi$
$971$	−2.19333	−	34.8620i	−0.0703874	−	1.11878i	0.791331	−	0.611388i	$-0.209389\pi$
$972$	−91.3419	+	5.74674i	−2.92979	+	0.184327i
$973$	−15.8095	−	28.7573i	−0.506828	−	0.921917i
$974$	7.35638	−	22.6406i	0.235714	−	0.725452i
$975$	−0.0745728	+	24.4342i	−0.00238824	+	0.782522i
$976$	0.487909	+	1.50163i	0.0156176	+	0.0480660i
$977$	−19.2159	+	20.4628i	−0.614770	+	0.654664i	−0.958729	−	0.284321i	$-0.908232\pi$
$977$	−19.2159	+	20.4628i	−0.614770	+	0.654664i	0.343959	+	0.938985i	$0.388232\pi$
$978$	7.74182	−	30.1524i	0.247556	−	0.964167i
$979$	−15.4710	+	24.3784i	−0.494455	+	0.779136i
$980$	1.35863	−	1.74602i	0.0433997	−	0.0557747i
$981$	−67.3369	+	81.3963i	−2.14990	+	2.59878i
$982$	12.4992	+	4.06122i	0.398864	+	0.129599i
$983$	−1.05948	−	4.12642i	−0.0337923	−	0.131612i	0.949449	−	0.313921i	$-0.101643\pi$
$983$	−1.05948	−	4.12642i	−0.0337923	−	0.131612i	−0.983241	+	0.182309i	$0.941643\pi$
$984$	−0.0291508	−	0.0160258i	−0.000929292	−	0.000510883i
$985$	19.3780	+	0.638580i	0.617435	+	0.0203469i
$986$	0.147516	+	0.773306i	0.00469787	+	0.0246271i
$987$	39.3528	+	7.50695i	1.25261	+	0.238949i
$988$	−3.46181	+	1.62901i	−0.110135	+	0.0518256i
$989$	1.49720	+	0.189141i	0.0476082	+	0.00601432i
$990$	43.2747	−	4.02404i	1.37536	−	0.127892i
$991$	4.35637	−	22.8369i	0.138385	−	0.725438i	−0.843673	−	0.536858i	$-0.819611\pi$
$991$	4.35637	−	22.8369i	0.138385	−	0.725438i	0.982058	−	0.188581i	$-0.0603887\pi$
$992$	−19.6193	+	49.5528i	−0.622914	+	1.57330i
$993$	80.7312	−	26.2312i	2.56193	−	0.832420i
$994$	−1.31554	−	2.07295i	−0.0417263	−	0.0657501i
$995$	−26.0813	−	2.50557i	−0.826832	−	0.0794318i
$996$	−42.2331	−	10.8436i	−1.33821	−	0.343593i
$997$	−25.6731	+	21.2386i	−0.813075	+	0.672634i	−0.948017	−	0.318220i	$-0.896915\pi$
$997$	−25.6731	+	21.2386i	−0.813075	+	0.672634i	0.134942	+	0.990853i	$0.456915\pi$
$998$	−2.06136	+	16.3174i	−0.0652513	+	0.516517i
$999$	97.8711			3.09650

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.h.a.109.5	yes	240
5.2	odd	4		625.2.g.b.451.10		480
5.3	odd	4		625.2.g.b.451.15		480
5.4	even	2		625.2.h.a.174.8		240
125.27	odd	100		625.2.g.b.176.10		480
125.39	even	50	inner	125.2.h.a.39.5	✓	240
125.86	even	25		625.2.h.a.449.8		240
125.98	odd	100		625.2.g.b.176.15		480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.h.a.39.5	✓	240	125.39	even	50	inner
125.2.h.a.109.5	yes	240	1.1	even	1	trivial
625.2.g.b.176.10		480	125.27	odd	100
625.2.g.b.176.15		480	125.98	odd	100
625.2.g.b.451.10		480	5.2	odd	4
625.2.g.b.451.15		480	5.3	odd	4
625.2.h.a.174.8		240	5.4	even	2
625.2.h.a.449.8		240	125.86	even	25

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:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.h (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.103450 + 0.818889i) q^{2} +(2.60539 - 2.15537i) q^{3} +(1.27729 + 0.327952i) q^{4} +(-1.92641 + 1.13531i) q^{5} +(1.49548 + 2.35650i) q^{6} +(-2.37759 + 0.772526i) q^{7} +(-1.00839 + 2.54690i) q^{8} +(1.58032 - 8.28430i) q^{9} +O(q^{10})\)	\(q+(-0.103450 + 0.818889i) q^{2} +(2.60539 - 2.15537i) q^{3} +(1.27729 + 0.327952i) q^{4} +(-1.92641 + 1.13531i) q^{5} +(1.49548 + 2.35650i) q^{6} +(-2.37759 + 0.772526i) q^{7} +(-1.00839 + 2.54690i) q^{8} +(1.58032 - 8.28430i) q^{9} +(-0.730408 - 1.69497i) q^{10} +(-2.77013 - 0.349948i) q^{11} +(4.03470 - 1.89858i) q^{12} +(-1.41963 - 0.270809i) q^{13} +(-0.386652 - 2.02690i) q^{14} +(-2.57204 + 7.11007i) q^{15} +(0.329893 + 0.181360i) q^{16} +(1.12367 + 4.37641i) q^{17} +(6.62044 + 2.15111i) q^{18} +(1.27961 - 1.54678i) q^{19} +(-2.83291 + 0.818352i) q^{20} +(-4.52948 + 7.13732i) q^{21} +(0.573138 - 2.23222i) q^{22} +(-0.249735 + 0.265940i) q^{23} +(2.86226 + 8.80913i) q^{24} +(2.42213 - 4.37416i) q^{25} +(0.368623 - 1.13451i) q^{26} +(-8.85142 - 16.1007i) q^{27} +(-3.29022 + 0.207003i) q^{28} +(-0.0132545 - 0.210674i) q^{29} +(-5.55628 - 2.84175i) q^{30} +(8.91669 - 2.28942i) q^{31} +(-3.40284 + 4.68360i) q^{32} +(-7.97154 + 5.05889i) q^{33} +(-3.70004 + 0.467424i) q^{34} +(3.70316 - 4.18751i) q^{35} +(4.73537 - 10.0632i) q^{36} +(-2.56621 + 4.66791i) q^{37} +(1.13426 + 1.20787i) q^{38} +(-4.28240 + 2.35427i) q^{39} +(-0.948956 - 6.05122i) q^{40} +(-0.00261804 + 0.00245850i) q^{41} +(-5.37610 - 4.44749i) q^{42} +(-2.43143 - 3.34658i) q^{43} +(-3.42349 - 1.35545i) q^{44} +(6.36094 + 17.7531i) q^{45} +(-0.191941 - 0.232016i) q^{46} +(-1.74465 - 4.40648i) q^{47} +(1.25040 - 0.238526i) q^{48} +(-0.606978 + 0.440995i) q^{49} +(3.33138 + 2.43596i) q^{50} +(12.3604 + 8.98035i) q^{51} +(-1.72447 - 0.811474i) q^{52} +(-0.196133 - 0.124470i) q^{53} +(14.1003 - 5.58272i) q^{54} +(5.73371 - 2.47082i) q^{55} +(0.429990 - 6.83450i) q^{56} -6.78799i q^{57} +(0.173890 + 0.0109402i) q^{58} +(1.27732 + 2.71444i) q^{59} +(-5.61700 + 8.23810i) q^{60} +(3.05737 + 2.87107i) q^{61} +(0.952349 + 7.53862i) q^{62} +(2.64250 + 20.9175i) q^{63} +(-2.93448 - 2.75566i) q^{64} +(3.04225 - 1.09004i) q^{65} +(-3.31802 - 7.05114i) q^{66} +(5.55888 + 0.349735i) q^{67} +5.95846i q^{68} +(-0.0774573 + 1.23115i) q^{69} +(3.04602 + 3.46567i) q^{70} +(1.10628 - 0.438005i) q^{71} +(19.5057 + 12.3787i) q^{72} +(2.26608 + 1.06634i) q^{73} +(-3.55703 - 2.58433i) q^{74} +(-3.11733 - 16.6170i) q^{75} +(2.14170 - 1.55603i) q^{76} +(6.85657 - 1.30796i) q^{77} +(-1.48487 - 3.75035i) q^{78} +(2.29397 + 2.77294i) q^{79} +(-0.841411 + 0.0251572i) q^{80} +(-34.2400 - 13.5566i) q^{81} +(-0.00174240 - 0.00239821i) q^{82} +(-7.53443 - 6.23303i) q^{83} +(-8.12615 + 7.63097i) q^{84} +(-7.13325 - 7.15506i) q^{85} +(2.99200 - 1.64487i) q^{86} +(-0.488613 - 0.520320i) q^{87} +(3.68465 - 6.70235i) q^{88} +(4.40291 - 9.35667i) q^{89} +(-15.1959 + 3.37234i) q^{90} +(3.58451 - 0.452829i) q^{91} +(-0.406199 + 0.257782i) q^{92} +(18.2970 - 25.1836i) q^{93} +(3.78890 - 0.972824i) q^{94} +(-0.708972 + 4.43249i) q^{95} +(1.22916 + 19.5370i) q^{96} +(-0.984685 + 0.0619511i) q^{97} +(-0.298334 - 0.542668i) q^{98} +(-7.27675 + 22.3955i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9}+O(q^{10}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18} - 10 q^{19} - 10 q^{20} - 35 q^{21} - 25 q^{22} + 70 q^{23} + 15 q^{24} + 35 q^{25} - 45 q^{26} - 20 q^{27} - 10 q^{28} - 10 q^{29} - 40 q^{30} - 30 q^{31} - 25 q^{32} - 35 q^{33} - 20 q^{34} - 40 q^{35} + 170 q^{36} - 55 q^{37} - 40 q^{38} - 35 q^{40} - 35 q^{41} - 10 q^{42} - 25 q^{43} + 15 q^{44} + 140 q^{45} - 40 q^{46} + 100 q^{47} + 5 q^{48} + 35 q^{49} - 10 q^{50} - 55 q^{51} - 15 q^{52} - 15 q^{53} + 30 q^{54} - 15 q^{55} + 65 q^{56} + 255 q^{58} + 5 q^{59} + 135 q^{60} - 40 q^{61} + 5 q^{62} - 35 q^{63} + 25 q^{64} - 30 q^{65} - 95 q^{66} + 105 q^{67} - 10 q^{69} - 55 q^{70} + 45 q^{71} - 30 q^{72} - 40 q^{73} + 35 q^{74} - 15 q^{75} - 65 q^{76} - 35 q^{77} + 100 q^{78} + 430 q^{80} - 95 q^{81} + 175 q^{82} + 20 q^{83} + 45 q^{84} - 10 q^{85} - 80 q^{86} - 5 q^{87} - 5 q^{88} + 30 q^{89} + 65 q^{91} - 55 q^{92} + 275 q^{93} + 60 q^{94} + 10 q^{95} - 135 q^{96} + 35 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9 - 20 * q^10 - 25 * q^11 + 60 * q^12 - 20 * q^13 - 30 * q^14 - 40 * q^15 - 40 * q^16 - 15 * q^17 - 25 * q^18 - 10 * q^19 - 10 * q^20 - 35 * q^21 - 25 * q^22 + 70 * q^23 + 15 * q^24 + 35 * q^25 - 45 * q^26 - 20 * q^27 - 10 * q^28 - 10 * q^29 - 40 * q^30 - 30 * q^31 - 25 * q^32 - 35 * q^33 - 20 * q^34 - 40 * q^35 + 170 * q^36 - 55 * q^37 - 40 * q^38 - 35 * q^40 - 35 * q^41 - 10 * q^42 - 25 * q^43 + 15 * q^44 + 140 * q^45 - 40 * q^46 + 100 * q^47 + 5 * q^48 + 35 * q^49 - 10 * q^50 - 55 * q^51 - 15 * q^52 - 15 * q^53 + 30 * q^54 - 15 * q^55 + 65 * q^56 + 255 * q^58 + 5 * q^59 + 135 * q^60 - 40 * q^61 + 5 * q^62 - 35 * q^63 + 25 * q^64 - 30 * q^65 - 95 * q^66 + 105 * q^67 - 10 * q^69 - 55 * q^70 + 45 * q^71 - 30 * q^72 - 40 * q^73 + 35 * q^74 - 15 * q^75 - 65 * q^76 - 35 * q^77 + 100 * q^78 + 430 * q^80 - 95 * q^81 + 175 * q^82 + 20 * q^83 + 45 * q^84 - 10 * q^85 - 80 * q^86 - 5 * q^87 - 5 * q^88 + 30 * q^89 + 65 * q^91 - 55 * q^92 + 275 * q^93 + 60 * q^94 + 10 * q^95 - 135 * q^96 + 35 * q^97 - 15 * q^98 + 45 * q^99

Introduction

L-functions

Modular forms

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