LMFDB - Embedded newform 430.2.q.c.111.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (of order $21$, degree $12$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			111.1
Character	$\chi$	$=$	430.111
Dual form			430.2.q.c.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.900969 + 0.433884i) q^{2} +(-2.07183 - 1.41255i) q^{3} +(0.623490 + 0.781831i) q^{4} +(-0.733052 + 0.680173i) q^{5} +(-1.25377 - 2.17160i) q^{6} +(-0.525199 + 0.909671i) q^{7} +(0.222521 + 0.974928i) q^{8} +(1.20117 + 3.06053i) q^{9} +O(q^{10})$	\(q+(0.900969 + 0.433884i) q^{2} +(-2.07183 - 1.41255i) q^{3} +(0.623490 + 0.781831i) q^{4} +(-0.733052 + 0.680173i) q^{5} +(-1.25377 - 2.17160i) q^{6} +(-0.525199 + 0.909671i) q^{7} +(0.222521 + 0.974928i) q^{8} +(1.20117 + 3.06053i) q^{9} +(-0.955573 + 0.294755i) q^{10} +(-1.70818 + 2.14199i) q^{11} +(-0.187389 - 2.50054i) q^{12} +(-3.45045 - 1.06432i) q^{13} +(-0.867879 + 0.591710i) q^{14} +(2.47954 - 0.373731i) q^{15} +(-0.222521 + 0.974928i) q^{16} +(4.89786 + 4.54455i) q^{17} +(-0.245698 + 3.27861i) q^{18} +(-2.58033 + 6.57457i) q^{19} +(-0.988831 - 0.149042i) q^{20} +(2.37308 - 1.14282i) q^{21} +(-2.46839 + 1.18872i) q^{22} +(-6.00762 - 0.905502i) q^{23} +(0.916110 - 2.33421i) q^{24} +(0.0747301 - 0.997204i) q^{25} +(-2.64696 - 2.45602i) q^{26} +(0.160587 - 0.703576i) q^{27} +(-1.03867 + 0.156554i) q^{28} +(3.75396 - 2.55940i) q^{29} +(2.39615 + 0.739113i) q^{30} +(0.765334 + 10.2127i) q^{31} +(-0.623490 + 0.781831i) q^{32} +(6.56474 - 2.02495i) q^{33} +(2.44101 + 6.21960i) q^{34} +(-0.233735 - 1.02406i) q^{35} +(-1.64390 + 2.84732i) q^{36} +(-2.03556 - 3.52569i) q^{37} +(-5.17739 + 4.80392i) q^{38} +(5.64535 + 7.07904i) q^{39} +(-0.826239 - 0.563320i) q^{40} +(-4.34304 - 2.09150i) q^{41} +2.63392 q^{42} +(3.71223 - 5.40549i) q^{43} -2.73971 q^{44} +(-2.96220 - 1.42652i) q^{45} +(-5.01979 - 3.42244i) q^{46} +(-6.32377 - 7.92976i) q^{47} +(1.83816 - 1.70557i) q^{48} +(2.94833 + 5.10666i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-3.72813 - 16.3340i) q^{51} +(-1.31920 - 3.36126i) q^{52} +(-2.77789 + 0.856866i) q^{53} +(0.449954 - 0.564224i) q^{54} +(-0.204739 - 2.73205i) q^{55} +(-1.00373 - 0.309610i) q^{56} +(14.6329 - 9.97656i) q^{57} +(4.49268 - 0.677163i) q^{58} +(-0.712596 + 3.12209i) q^{59} +(1.83816 + 1.70557i) q^{60} +(0.421528 - 5.62489i) q^{61} +(-3.74157 + 9.53336i) q^{62} +(-3.41492 - 0.514717i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(3.25328 - 1.56670i) q^{65} +(6.79322 + 1.02391i) q^{66} +(3.20497 - 8.16612i) q^{67} +(-0.499306 + 6.66278i) q^{68} +(11.1677 + 10.3621i) q^{69} +(0.233735 - 1.02406i) q^{70} +(-0.0787975 + 0.0118768i) q^{71} +(-2.71651 + 1.85208i) q^{72} +(7.69834 + 2.37462i) q^{73} +(-0.304235 - 4.05973i) q^{74} +(-1.56343 + 1.96048i) q^{75} +(-6.74901 + 2.08179i) q^{76} +(-1.05137 - 2.67885i) q^{77} +(2.01480 + 8.82742i) q^{78} +(2.18548 - 3.78537i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(5.90384 - 5.47796i) q^{81} +(-3.00547 - 3.76874i) q^{82} +(-8.81559 - 6.01037i) q^{83} +(2.37308 + 1.14282i) q^{84} -6.68146 q^{85} +(5.68996 - 3.25951i) q^{86} -11.3929 q^{87} +(-2.46839 - 1.18872i) q^{88} +(5.33963 + 3.64050i) q^{89} +(-2.04991 - 2.57050i) q^{90} +(2.78035 - 2.57979i) q^{91} +(-3.03774 - 5.26151i) q^{92} +(12.8403 - 22.2400i) q^{93} +(-2.25693 - 9.88825i) q^{94} +(-2.58033 - 6.57457i) q^{95} +(2.39615 - 0.739113i) q^{96} +(-8.81384 + 11.0522i) q^{97} +(0.440658 + 5.88018i) q^{98} +(-8.60743 - 2.65504i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9}+O(q^{10}) $ 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9} - 4 q^{10} + q^{11} + 14 q^{12} - 23 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{17} - 20 q^{18} - 3 q^{19} + 4 q^{20} - 8 q^{21} - q^{22} + 7 q^{23} + 4 q^{25} - 19 q^{26} + 32 q^{27} + 4 q^{28} + 30 q^{29} + 9 q^{31} + 8 q^{32} + 39 q^{33} - 8 q^{34} - 22 q^{35} - 29 q^{36} - 37 q^{37} - 11 q^{38} - 52 q^{39} - 4 q^{40} - 28 q^{41} - 6 q^{42} + 41 q^{43} + 8 q^{44} + 2 q^{45} - 28 q^{46} + 3 q^{47} - 41 q^{49} + 24 q^{50} - 30 q^{51} - 9 q^{52} - 69 q^{53} + 3 q^{54} + 10 q^{55} - 11 q^{56} + 116 q^{57} + 5 q^{58} + 10 q^{59} - 19 q^{61} - 93 q^{62} + 34 q^{63} - 8 q^{64} - 3 q^{65} - 18 q^{66} + 3 q^{67} + 8 q^{68} + 42 q^{69} + 22 q^{70} - 36 q^{71} + 22 q^{72} - 56 q^{73} + 9 q^{74} - 10 q^{76} + 3 q^{77} + 45 q^{78} + 16 q^{79} - 24 q^{80} - 19 q^{81} + 14 q^{82} + 64 q^{83} - 8 q^{84} - 30 q^{85} + 36 q^{86} + 78 q^{87} - q^{88} - 75 q^{89} + 5 q^{90} + 5 q^{91} + 14 q^{92} - 10 q^{93} - 45 q^{94} - 3 q^{95} + 33 q^{97} - q^{98} - 11 q^{99}+O(q^{100}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9 - 4 * q^10 + q^11 + 14 * q^12 - 23 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^17 - 20 * q^18 - 3 * q^19 + 4 * q^20 - 8 * q^21 - q^22 + 7 * q^23 + 4 * q^25 - 19 * q^26 + 32 * q^27 + 4 * q^28 + 30 * q^29 + 9 * q^31 + 8 * q^32 + 39 * q^33 - 8 * q^34 - 22 * q^35 - 29 * q^36 - 37 * q^37 - 11 * q^38 - 52 * q^39 - 4 * q^40 - 28 * q^41 - 6 * q^42 + 41 * q^43 + 8 * q^44 + 2 * q^45 - 28 * q^46 + 3 * q^47 - 41 * q^49 + 24 * q^50 - 30 * q^51 - 9 * q^52 - 69 * q^53 + 3 * q^54 + 10 * q^55 - 11 * q^56 + 116 * q^57 + 5 * q^58 + 10 * q^59 - 19 * q^61 - 93 * q^62 + 34 * q^63 - 8 * q^64 - 3 * q^65 - 18 * q^66 + 3 * q^67 + 8 * q^68 + 42 * q^69 + 22 * q^70 - 36 * q^71 + 22 * q^72 - 56 * q^73 + 9 * q^74 - 10 * q^76 + 3 * q^77 + 45 * q^78 + 16 * q^79 - 24 * q^80 - 19 * q^81 + 14 * q^82 + 64 * q^83 - 8 * q^84 - 30 * q^85 + 36 * q^86 + 78 * q^87 - q^88 - 75 * q^89 + 5 * q^90 + 5 * q^91 + 14 * q^92 - 10 * q^93 - 45 * q^94 - 3 * q^95 + 33 * q^97 - q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{4}{21}\right)$

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 $

$2$	0.900969	+	0.433884i	0.637081	+	0.306802i
$2$	0.900969	+	0.433884i	0.637081	+	0.306802i
$3$	−2.07183	−	1.41255i	−1.19617	−	0.815537i	−0.209430	−	0.977824i	$-0.567161\pi$
$3$	−2.07183	−	1.41255i	−1.19617	−	0.815537i	−0.986744	+	0.162286i	$0.948113\pi$
$4$	0.623490	+	0.781831i	0.311745	+	0.390916i
$5$	−0.733052	+	0.680173i	−0.327831	+	0.304182i
$5$	−0.733052	+	0.680173i	−0.327831	+	0.304182i
$6$	−1.25377	−	2.17160i	−0.511851	−	0.886552i
$7$	−0.525199	+	0.909671i	−0.198506	+	0.343823i	−0.948044	−	0.318138i	$-0.896942\pi$
$7$	−0.525199	+	0.909671i	−0.198506	+	0.343823i	0.749538	+	0.661961i	$0.230276\pi$
$8$	0.222521	+	0.974928i	0.0786730	+	0.344689i
$9$	1.20117	+	3.06053i	0.400389	+	1.02018i
$10$	−0.955573	+	0.294755i	−0.302179	+	0.0932098i
$11$	−1.70818	+	2.14199i	−0.515036	+	0.645834i	−0.969547	−	0.244907i	$-0.921243\pi$
$11$	−1.70818	+	2.14199i	−0.515036	+	0.645834i	0.454511	+	0.890741i	$0.349814\pi$
$12$	−0.187389	−	2.50054i	−0.0540946	−	0.721843i
$13$	−3.45045	−	1.06432i	−0.956983	−	0.295190i	−0.223351	−	0.974738i	$-0.571700\pi$
$13$	−3.45045	−	1.06432i	−0.956983	−	0.295190i	−0.733631	+	0.679548i	$0.762176\pi$
$14$	−0.867879	+	0.591710i	−0.231950	+	0.158141i
$15$	2.47954	−	0.373731i	0.640215	−	0.0964968i
$16$	−0.222521	+	0.974928i	−0.0556302	+	0.243732i
$17$	4.89786	+	4.54455i	1.18790	+	1.10221i	0.992595	+	0.121473i	$0.0387618\pi$
$17$	4.89786	+	4.54455i	1.18790	+	1.10221i	0.195310	+	0.980742i	$0.437429\pi$
$18$	−0.245698	+	3.27861i	−0.0579115	+	0.772775i
$19$	−2.58033	+	6.57457i	−0.591968	+	1.50831i	0.249706	+	0.968322i	$0.419666\pi$
$19$	−2.58033	+	6.57457i	−0.591968	+	1.50831i	−0.841673	+	0.539987i	$0.818429\pi$
$20$	−0.988831	−	0.149042i	−0.221109	−	0.0333269i
$21$	2.37308	−	1.14282i	0.517849	−	0.249383i
$22$	−2.46839	+	1.18872i	−0.526263	+	0.253435i
$23$	−6.00762	−	0.905502i	−1.25267	−	0.188810i	−0.511006	−	0.859577i	$-0.670727\pi$
$23$	−6.00762	−	0.905502i	−1.25267	−	0.188810i	−0.741668	+	0.670767i	$0.765965\pi$
$24$	0.916110	−	2.33421i	0.187000	−	0.476469i
$25$	0.0747301	−	0.997204i	0.0149460	−	0.199441i
$26$	−2.64696	−	2.45602i	−0.519111	−	0.481664i
$27$	0.160587	−	0.703576i	0.0309049	−	0.135403i
$28$	−1.03867	+	0.156554i	−0.196289	+	0.0295858i
$29$	3.75396	−	2.55940i	0.697092	−	0.475269i	−0.162198	−	0.986758i	$-0.551858\pi$
$29$	3.75396	−	2.55940i	0.697092	−	0.475269i	0.859290	+	0.511489i	$0.170906\pi$
$30$	2.39615	+	0.739113i	0.437474	+	0.134943i
$31$	0.765334	+	10.2127i	0.137458	+	1.83425i	0.460261	+	0.887784i	$0.347756\pi$
$31$	0.765334	+	10.2127i	0.137458	+	1.83425i	−0.322803	+	0.946466i	$0.604625\pi$
$32$	−0.623490	+	0.781831i	−0.110218	+	0.138210i
$33$	6.56474	−	2.02495i	1.14277	−	0.352499i
$34$	2.44101	+	6.21960i	0.418630	+	1.06665i
$35$	−0.233735	−	1.02406i	−0.0395085	−	0.173098i
$36$	−1.64390	+	2.84732i	−0.273983	+	0.474553i
$37$	−2.03556	−	3.52569i	−0.334644	−	0.579620i	0.648773	−	0.760982i	$-0.275283\pi$
$37$	−2.03556	−	3.52569i	−0.334644	−	0.579620i	−0.983416	+	0.181362i	$0.941949\pi$
$38$	−5.17739	+	4.80392i	−0.839884	+	0.779298i
$39$	5.64535	+	7.07904i	0.903979	+	1.13355i
$40$	−0.826239	−	0.563320i	−0.130640	−	0.0890687i
$41$	−4.34304	−	2.09150i	−0.678268	−	0.326637i	0.0628388	−	0.998024i	$-0.479985\pi$
$41$	−4.34304	−	2.09150i	−0.678268	−	0.326637i	−0.741107	+	0.671387i	$0.765699\pi$
$42$	2.63392			0.406423
$43$	3.71223	−	5.40549i	0.566109	−	0.824330i
$43$	3.71223	−	5.40549i	0.566109	−	0.824330i
$44$	−2.73971			−0.413027
$45$	−2.96220	−	1.42652i	−0.441579	−	0.212653i
$46$	−5.01979	−	3.42244i	−0.740128	−	0.504611i
$47$	−6.32377	−	7.92976i	−0.922417	−	1.15667i	−0.987314	−	0.158782i	$-0.949243\pi$
$47$	−6.32377	−	7.92976i	−0.922417	−	1.15667i	0.0648966	−	0.997892i	$-0.479328\pi$
$48$	1.83816	−	1.70557i	0.265316	−	0.246177i
$49$	2.94833	+	5.10666i	0.421190	+	0.729523i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−3.72813	−	16.3340i	−0.522043	−	2.28722i
$52$	−1.31920	−	3.36126i	−0.182940	−	0.466124i
$53$	−2.77789	+	0.856866i	−0.381573	+	0.117700i	−0.479607	−	0.877483i	$-0.659221\pi$
$53$	−2.77789	+	0.856866i	−0.381573	+	0.117700i	0.0980343	+	0.995183i	$0.468745\pi$
$54$	0.449954	−	0.564224i	0.0612309	−	0.0767811i
$55$	−0.204739	−	2.73205i	−0.0276070	−	0.368389i
$56$	−1.00373	−	0.309610i	−0.134129	−	0.0413734i
$57$	14.6329	−	9.97656i	1.93818	−	1.32143i
$58$	4.49268	−	0.677163i	0.589918	−	0.0889158i
$59$	−0.712596	+	3.12209i	−0.0927720	+	0.406461i	−0.999896	−	0.0144020i	$-0.995416\pi$
$59$	−0.712596	+	3.12209i	−0.0927720	+	0.406461i	0.907124	+	0.420863i	$0.138273\pi$
$60$	1.83816	+	1.70557i	0.237306	+	0.220188i
$61$	0.421528	−	5.62489i	0.0539711	−	0.720194i	−0.902931	−	0.429785i	$-0.858590\pi$
$61$	0.421528	−	5.62489i	0.0539711	−	0.720194i	0.956903	−	0.290409i	$-0.0937914\pi$
$62$	−3.74157	+	9.53336i	−0.475180	+	1.21074i
$63$	−3.41492	−	0.514717i	−0.430240	−	0.0648482i
$64$	−0.900969	+	0.433884i	−0.112621	+	0.0542355i
$65$	3.25328	−	1.56670i	0.403520	−	0.194325i
$66$	6.79322	+	1.02391i	0.836188	+	0.126035i
$67$	3.20497	−	8.16612i	0.391549	−	0.997650i	−0.590164	−	0.807283i	$-0.700937\pi$
$67$	3.20497	−	8.16612i	0.391549	−	0.997650i	0.981713	−	0.190367i	$-0.0609677\pi$
$68$	−0.499306	+	6.66278i	−0.0605498	+	0.807980i
$69$	11.1677	+	10.3621i	1.34443	+	1.24745i
$70$	0.233735	−	1.02406i	0.0279367	−	0.122399i
$71$	−0.0787975	+	0.0118768i	−0.00935154	+	0.00140952i	−0.153716	−	0.988115i	$-0.549124\pi$
$71$	−0.0787975	+	0.0118768i	−0.00935154	+	0.00140952i	0.144365	+	0.989525i	$0.453886\pi$
$72$	−2.71651	+	1.85208i	−0.320143	+	0.218270i
$73$	7.69834	+	2.37462i	0.901023	+	0.277929i	0.710453	−	0.703745i	$-0.248490\pi$
$73$	7.69834	+	2.37462i	0.901023	+	0.277929i	0.190570	+	0.981674i	$0.438966\pi$
$74$	−0.304235	−	4.05973i	−0.0353666	−	0.471935i
$75$	−1.56343	+	1.96048i	−0.180529	+	0.226377i
$76$	−6.74901	+	2.08179i	−0.774165	+	0.238798i
$77$	−1.05137	−	2.67885i	−0.119815	−	0.305283i
$78$	2.01480	+	8.82742i	0.228131	+	0.999508i
$79$	2.18548	−	3.78537i	0.245886	−	0.425887i	−0.716494	−	0.697593i	$-0.754254\pi$
$79$	2.18548	−	3.78537i	0.245886	−	0.425887i	0.962380	+	0.271706i	$0.0875877\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	5.90384	−	5.47796i	0.655982	−	0.608662i
$82$	−3.00547	−	3.76874i	−0.331899	−	0.416188i
$83$	−8.81559	−	6.01037i	−0.967637	−	0.659724i	−0.0271780	−	0.999631i	$-0.508652\pi$
$83$	−8.81559	−	6.01037i	−0.967637	−	0.659724i	−0.940459	+	0.339907i	$0.889604\pi$
$84$	2.37308	+	1.14282i	0.258924	+	0.124691i
$85$	−6.68146			−0.724706
$86$	5.68996	−	3.25951i	0.613564	−	0.351482i
$87$	−11.3929			−1.22144
$88$	−2.46839	−	1.18872i	−0.263132	−	0.126717i
$89$	5.33963	+	3.64050i	0.566000	+	0.385892i	0.812246	−	0.583315i	$-0.198245\pi$
$89$	5.33963	+	3.64050i	0.566000	+	0.385892i	−0.246246	+	0.969207i	$0.579197\pi$
$90$	−2.04991	−	2.57050i	−0.216079	−	0.270955i
$91$	2.78035	−	2.57979i	0.291460	−	0.270436i
$92$	−3.03774	−	5.26151i	−0.316706	−	0.548551i
$93$	12.8403	−	22.2400i	1.33148	−	2.30618i
$94$	−2.25693	−	9.88825i	−0.232784	−	1.01989i
$95$	−2.58033	−	6.57457i	−0.264736	−	0.674536i
$96$	2.39615	−	0.739113i	0.244556	−	0.0754354i
$97$	−8.81384	+	11.0522i	−0.894910	+	1.12218i	0.0970057	+	0.995284i	$0.469074\pi$
$97$	−8.81384	+	11.0522i	−0.894910	+	1.12218i	−0.991916	+	0.126898i	$0.959498\pi$
$98$	0.440658	+	5.88018i	0.0445132	+	0.593988i
$99$	−8.60743	−	2.65504i	−0.865079	−	0.266842i
$100$	0.826239	−	0.563320i	0.0826239	−	0.0563320i
$101$	−1.28384	+	0.193507i	−0.127747	+	0.0192547i	−0.212604	−	0.977138i	$-0.568195\pi$
$101$	−1.28384	+	0.193507i	−0.127747	+	0.0192547i	0.0848577	+	0.996393i	$0.472956\pi$
$102$	3.72813	−	16.3340i	0.369140	−	1.61731i
$103$	9.44023	+	8.75926i	0.930174	+	0.863075i	0.990834	−	0.135083i	$-0.0431302\pi$
$103$	9.44023	+	8.75926i	0.930174	+	0.863075i	−0.0606605	+	0.998158i	$0.519321\pi$
$104$	0.269841	−	3.60077i	0.0264601	−	0.353085i
$105$	−0.962280	+	2.45185i	−0.0939089	+	0.239276i
$106$	−2.87457	−	0.433272i	−0.279203	−	0.0420831i
$107$	−11.2064	+	5.39673i	−1.08337	+	0.521721i	−0.888391	−	0.459087i	$-0.848177\pi$
$107$	−11.2064	+	5.39673i	−1.08337	+	0.521721i	−0.194974	+	0.980808i	$0.562462\pi$
$108$	0.650202	−	0.313121i	0.0625657	−	0.0301300i
$109$	4.12821	+	0.622228i	0.395411	+	0.0595986i	0.343738	−	0.939065i	$-0.388307\pi$
$109$	4.12821	+	0.622228i	0.395411	+	0.0595986i	0.0516727	+	0.998664i	$0.483545\pi$
$110$	1.00093	−	2.55032i	0.0954347	−	0.243164i
$111$	−0.762884	+	10.1800i	−0.0724097	+	0.966241i
$112$	−0.769996	−	0.714451i	−0.0727577	−	0.0675093i
$113$	−0.326192	+	1.42914i	−0.0306855	+	0.134442i	−0.987950	−	0.154770i	$-0.950536\pi$
$113$	−0.326192	+	1.42914i	−0.0306855	+	0.134442i	0.957265	+	0.289212i	$0.0933934\pi$
$114$	17.5125	−	2.63958i	1.64019	−	0.247219i
$115$	5.01979	−	3.42244i	0.468098	−	0.319144i
$116$	4.34157	+	1.33920i	0.403105	+	0.124341i
$117$	−0.887182	−	11.8386i	−0.0820200	−	1.09448i
$118$	−1.99665	+	2.50372i	−0.183806	+	0.230486i
$119$	−6.70639	+	2.06865i	−0.614774	+	0.189633i
$120$	0.916110	+	2.33421i	0.0836290	+	0.213083i
$121$	0.777487	+	3.40639i	0.0706807	+	0.309672i
$122$	2.82033	−	4.88496i	0.255341	−	0.442264i
$123$	6.04370	+	10.4680i	0.544942	+	0.943867i
$124$	−7.50741	+	6.96586i	−0.674185	+	0.625553i
$125$	0.623490	+	0.781831i	0.0557666	+	0.0699291i
$126$	−2.85341	−	1.94542i	−0.254202	−	0.173312i
$127$	11.8856	+	5.72382i	1.05468	+	0.507907i	0.879139	−	0.476565i	$-0.158118\pi$
$127$	11.8856	+	5.72382i	1.05468	+	0.507907i	0.175541	+	0.984472i	$0.443833\pi$
$128$	−1.00000			−0.0883883
$129$	−15.3267	+	5.95557i	−1.34944	+	0.524358i
$130$	3.61087			0.316694
$131$	6.86817	+	3.30754i	0.600075	+	0.288981i	0.709156	−	0.705052i	$-0.249076\pi$
$131$	6.86817	+	3.30754i	0.600075	+	0.288981i	−0.109081	+	0.994033i	$0.534791\pi$
$132$	5.67622	+	3.86998i	0.494052	+	0.336839i
$133$	−4.62551	−	5.80020i	−0.401082	−	0.502941i
$134$	6.43072	−	5.96684i	0.555530	−	0.515456i
$135$	0.360835	+	0.624984i	0.0310557	+	0.0537901i
$136$	−3.34073	+	5.78631i	−0.286465	+	0.496172i
$137$	2.58981	+	11.3467i	0.221262	+	0.969414i	0.956529	+	0.291636i	$0.0941997\pi$
$137$	2.58981	+	11.3467i	0.221262	+	0.969414i	−0.735267	+	0.677778i	$0.762943\pi$
$138$	5.56580	+	14.1814i	0.473793	+	1.20720i
$139$	−22.3436	+	6.89210i	−1.89516	+	0.584580i	−0.909542	+	0.415612i	$0.863567\pi$
$139$	−22.3436	+	6.89210i	−1.89516	+	0.584580i	−0.985622	+	0.168968i	$0.945956\pi$
$140$	0.654912	−	0.821234i	0.0553502	−	0.0694069i
$141$	1.90060	+	25.3618i	0.160060	+	2.13585i
$142$	−0.0761472	−	0.0234883i	−0.00639013	−	0.00197109i
$143$	8.17376	−	5.57278i	0.683524	−	0.466019i
$144$	−3.25108	+	0.490021i	−0.270923	+	0.0408351i
$145$	−1.01101	+	4.42951i	−0.0839596	+	0.367851i
$146$	5.90566	+	5.47965i	0.488756	+	0.453499i
$147$	1.10497	−	14.7448i	0.0911366	−	1.21613i
$148$	1.48735	−	3.78970i	0.122259	−	0.311511i
$149$	−4.09658	−	0.617460i	−0.335605	−	0.0505843i	−0.0209219	−	0.999781i	$-0.506660\pi$
$149$	−4.09658	−	0.617460i	−0.335605	−	0.0505843i	−0.314683	+	0.949197i	$0.601898\pi$
$150$	−2.25922	+	1.08798i	−0.184465	+	0.0888336i
$151$	12.5906	−	6.06330i	1.02461	−	0.493425i	0.155389	−	0.987853i	$-0.450337\pi$
$151$	12.5906	−	6.06330i	1.02461	−	0.493425i	0.869218	+	0.494429i	$0.164623\pi$
$152$	−6.98390	−	1.05265i	−0.566469	−	0.0853815i
$153$	−8.02555	+	20.4488i	−0.648828	+	1.65319i
$154$	0.215057	−	2.86974i	0.0173298	−	0.231250i
$155$	−7.50741	−	6.96586i	−0.603010	−	0.559511i
$156$	−2.01480	+	8.82742i	−0.161313	+	0.706759i
$157$	12.1626	−	1.83322i	0.970682	−	0.146307i	0.355487	−	0.934681i	$-0.384315\pi$
$157$	12.1626	−	1.83322i	0.970682	−	0.146307i	0.615196	+	0.788375i	$0.289077\pi$
$158$	3.61146	−	2.46225i	0.287313	−	0.195886i
$159$	6.96569	+	2.14863i	0.552415	+	0.170398i
$160$	−0.0747301	−	0.997204i	−0.00590793	−	0.0788359i
$161$	3.97890	−	4.98938i	0.313581	−	0.393218i
$162$	7.69597	−	2.37389i	0.604652	−	0.186511i
$163$	5.95269	+	15.1672i	0.466250	+	1.18799i	0.949852	+	0.312698i	$0.101233\pi$
$163$	5.95269	+	15.1672i	0.466250	+	1.18799i	−0.483602	+	0.875288i	$0.660672\pi$
$164$	−1.07264	−	4.69955i	−0.0837592	−	0.366973i
$165$	−3.43498	+	5.94955i	−0.267413	+	0.463172i
$166$	−5.33477	−	9.24010i	−0.414059	−	0.717171i
$167$	6.00398	−	5.57087i	0.464602	−	0.431087i	−0.412816	−	0.910814i	$-0.635455\pi$
$167$	6.00398	−	5.57087i	0.464602	−	0.431087i	0.877418	+	0.479727i	$0.159264\pi$
$168$	1.64222	+	2.05928i	0.126700	+	0.158877i
$169$	0.0317156	+	0.0216233i	0.00243966	+	0.00166333i
$170$	−6.01979	−	2.89898i	−0.461697	−	0.222341i
$171$	−23.2210			−1.77576
$172$	6.54072	−	0.467933i	0.498725	−	0.0356796i
$173$	−11.3978			−0.866555			−0.433277	−	0.901261i	$-0.642643\pi$
$173$	−11.3978			−0.866555			−0.433277	+	0.901261i	$0.642643\pi$
$174$	−10.2646	−	4.94318i	−0.778158	−	0.374741i
$175$	0.867879	+	0.591710i	0.0656055	+	0.0447291i
$176$	−1.70818	−	2.14199i	−0.128759	−	0.161459i
$177$	5.88649	−	5.46186i	0.442456	−	0.410539i
$178$	3.23129	+	5.59675i	0.242195	+	0.419494i
$179$	−3.35669	+	5.81396i	−0.250891	+	0.434555i	−0.963771	−	0.266730i	$-0.914057\pi$
$179$	−3.35669	+	5.81396i	−0.250891	+	0.434555i	0.712881	+	0.701285i	$0.247390\pi$
$180$	−0.731604	−	3.20537i	−0.0545305	−	0.238914i
$181$	4.69249	+	11.9563i	0.348790	+	0.888703i	0.992367	+	0.123321i	$0.0393546\pi$
$181$	4.69249	+	11.9563i	0.348790	+	0.888703i	−0.643576	+	0.765382i	$0.722550\pi$
$182$	3.62434	−	1.11796i	0.268654	−	0.0828688i
$183$	−8.81879	+	11.0584i	−0.651904	+	0.817462i
$184$	−0.454021	−	6.05849i	−0.0334709	−	0.446637i
$185$	3.89025	+	1.19998i	0.286017	+	0.0882245i
$186$	21.2183	−	14.4664i	1.55580	−	1.06073i
$187$	−18.1008	+	2.72826i	−1.32366	+	0.199510i
$188$	2.25693	−	9.88825i	0.164603	−	0.721175i
$189$	0.555682	+	0.515598i	0.0404199	+	0.0375042i
$190$	0.527803	−	7.04304i	0.0382909	−	0.510956i
$191$	3.83366	−	9.76800i	0.277394	−	0.706788i	−0.722488	−	0.691384i	$-0.757001\pi$
$191$	3.83366	−	9.76800i	0.277394	−	0.706788i	0.999881	−	0.0154040i	$-0.00490342\pi$
$192$	2.47954	+	0.373731i	0.178945	+	0.0269717i
$193$	12.3861	−	5.96483i	0.891571	−	0.429358i	0.0687339	−	0.997635i	$-0.478104\pi$
$193$	12.3861	−	5.96483i	0.891571	−	0.429358i	0.822837	+	0.568277i	$0.192390\pi$
$194$	−12.7364	+	6.13351i	−0.914418	+	0.440361i
$195$	−8.95330	−	1.34949i	−0.641159	−	0.0966392i
$196$	−2.15429	+	5.48905i	−0.153878	+	0.392075i
$197$	−0.654604	+	8.73508i	−0.0466386	+	0.622349i	0.924091	+	0.382173i	$0.124824\pi$
$197$	−0.654604	+	8.73508i	−0.0466386	+	0.622349i	−0.970729	+	0.240176i	$0.922795\pi$
$198$	−6.60305	−	6.12673i	−0.469258	−	0.435408i
$199$	−0.662244	+	2.90148i	−0.0469452	+	0.205680i	−0.992961	−	0.118439i	$-0.962211\pi$
$199$	−0.662244	+	2.90148i	−0.0469452	+	0.205680i	0.946016	+	0.324120i	$0.105068\pi$
$200$	0.988831	−	0.149042i	0.0699209	−	0.0105389i
$201$	−18.1752	+	12.3917i	−1.28198	+	0.874040i
$202$	−1.24066	−	0.382692i	−0.0872924	−	0.0269261i
$203$	0.356642	+	4.75906i	0.0250314	+	0.334020i
$204$	10.4460	−	13.0989i	0.731366	−	0.917104i
$205$	4.60625	−	1.42084i	0.321714	−	0.0992357i
$206$	4.70486	+	11.9878i	0.327803	+	0.835228i
$207$	−4.44484	−	19.4741i	−0.308938	−	1.35354i
$208$	1.80544	−	3.12711i	0.125184	−	0.216826i
$209$	−9.67499	−	16.7576i	−0.669233	−	1.15915i
$210$	−1.93080	+	1.79152i	−0.133238	+	0.123627i
$211$	−5.42163	−	6.79850i	−0.373240	−	0.468028i	0.559368	−	0.828920i	$-0.311044\pi$
$211$	−5.42163	−	6.79850i	−0.373240	−	0.468028i	−0.932608	+	0.360891i	$0.882473\pi$
$212$	−2.40191	−	1.63759i	−0.164964	−	0.112470i
$213$	0.180032	+	0.0866988i	0.0123356	+	0.00594050i
$214$	−12.4382			−0.850257
$215$	0.955414	+	6.48746i	0.0651587	+	0.442441i
$216$	0.721669			0.0491034
$217$	−9.69212	−	4.66748i	−0.657944	−	0.316849i
$218$	3.44942	+	2.35177i	0.233624	+	0.159282i
$219$	−12.5954	−	15.7941i	−0.851119	−	1.06727i
$220$	2.00835	−	1.86348i	0.135403	−	0.125635i
$221$	−12.0629	−	20.8936i	−0.811441	−	1.40546i
$222$	−5.10426	+	8.84084i	−0.342576	+	0.593358i
$223$	−1.66584	−	7.29854i	−0.111553	−	0.488746i	−0.999581	−	0.0289561i	$-0.990782\pi$
$223$	−1.66584	−	7.29854i	−0.111553	−	0.488746i	0.888028	−	0.459790i	$-0.152075\pi$
$224$	−0.383753	−	0.977787i	−0.0256406	−	0.0653311i
$225$	3.14173	−	0.969096i	0.209449	−	0.0646064i
$226$	−0.913969	+	1.14608i	−0.0607963	+	0.0762362i
$227$	0.971195	+	12.9597i	0.0644605	+	0.860166i	0.931921	+	0.362660i	$0.118131\pi$
$227$	0.971195	+	12.9597i	0.0644605	+	0.860166i	−0.867461	+	0.497505i	$0.834250\pi$
$228$	16.9235	+	5.22020i	1.12078	+	0.345716i
$229$	11.3137	−	7.71357i	0.747632	−	0.509727i	−0.128552	−	0.991703i	$-0.541033\pi$
$229$	11.3137	−	7.71357i	0.747632	−	0.509727i	0.876185	+	0.481976i	$0.160081\pi$
$230$	6.00762	−	0.905502i	0.396130	−	0.0597071i
$231$	−1.60575	+	7.03525i	−0.105651	+	0.462886i
$232$	3.33057	+	3.09031i	0.218662	+	0.202889i
$233$	1.15247	−	15.3786i	0.0755006	−	1.00749i	−0.822865	−	0.568237i	$-0.807626\pi$
$233$	1.15247	−	15.3786i	0.0755006	−	1.00749i	0.898366	−	0.439249i	$-0.144755\pi$
$234$	4.33726	−	11.0512i	0.283536	−	0.722437i
$235$	10.0293	+	1.51167i	0.654237	+	0.0986103i
$236$	−2.88524	+	1.38946i	−0.187813	+	0.0904461i
$237$	−9.87499	+	4.75555i	−0.641450	+	0.308906i
$238$	−6.93980	−	1.04601i	−0.449840	−	0.0678025i
$239$	−7.20978	+	18.3702i	−0.466362	+	1.18827i	0.483429	+	0.875384i	$0.339391\pi$
$239$	−7.20978	+	18.3702i	−0.466362	+	1.18827i	−0.949791	+	0.312886i	$0.898704\pi$
$240$	−0.187389	+	2.50054i	−0.0120959	+	0.161409i
$241$	7.37147	+	6.83972i	0.474838	+	0.440585i	0.880930	−	0.473247i	$-0.156918\pi$
$241$	7.37147	+	6.83972i	0.474838	+	0.440585i	−0.406092	+	0.913832i	$0.633109\pi$
$242$	−0.777487	+	3.40639i	−0.0499788	+	0.218971i
$243$	−22.1105	+	3.33262i	−1.41839	+	0.213788i
$244$	4.66054	−	3.17750i	0.298360	−	0.203419i
$245$	−5.63469	−	1.73807i	−0.359987	−	0.111041i
$246$	0.903293	+	12.0536i	0.0575918	+	0.768510i
$247$	15.9007	−	19.9389i	1.01174	−	1.26868i
$248$	−9.78632	+	3.01868i	−0.621432	+	0.191686i
$249$	9.77448	+	24.9050i	0.619433	+	1.57829i
$250$	0.222521	+	0.974928i	0.0140735	+	0.0616599i
$251$	0.526981	−	0.912758i	0.0332627	−	0.0576127i	−0.848915	−	0.528530i	$-0.822744\pi$
$251$	0.526981	−	0.912758i	0.0332627	−	0.0576127i	0.882178	+	0.470917i	$0.156077\pi$
$252$	−1.72675	−	2.99081i	−0.108775	−	0.188404i
$253$	12.2017	−	11.3215i	0.767112	−	0.711776i
$254$	8.22512	+	10.3140i	0.516090	+	0.647156i
$255$	13.8429	+	9.43791i	0.866874	+	0.591025i
$256$	−0.900969	−	0.433884i	−0.0563106	−	0.0271177i
$257$	−22.6154			−1.41071			−0.705356	−	0.708854i	$-0.749213\pi$
$257$	−22.6154			−1.41071			−0.705356	+	0.708854i	$0.749213\pi$
$258$	−16.3929	−	1.28421i	−1.02058	−	0.0799513i
$259$	4.27629			0.265716
$260$	3.25328	+	1.56670i	0.201760	+	0.0971625i
$261$	12.3422	+	8.41480i	0.763966	+	0.520863i
$262$	4.75292	+	5.95998i	0.293637	+	0.368209i
$263$	15.7837	−	14.6451i	0.973264	−	0.903057i	−0.0220495	−	0.999757i	$-0.507019\pi$
$263$	15.7837	−	14.6451i	0.973264	−	0.903057i	0.995314	+	0.0966997i	$0.0308287\pi$
$264$	3.43498	+	5.94955i	0.211408	+	0.366170i
$265$	1.45352	−	2.51757i	0.0892891	−	0.154653i
$266$	−1.65082	−	7.23273i	−0.101218	−	0.443467i
$267$	−5.92043	−	15.0850i	−0.362325	−	0.923188i
$268$	8.38279	−	2.58575i	0.512060	−	0.157950i
$269$	13.5108	−	16.9421i	0.823770	−	1.03298i	−0.175057	−	0.984558i	$-0.556011\pi$
$269$	13.5108	−	16.9421i	0.823770	−	1.03298i	0.998827	−	0.0484169i	$-0.0154176\pi$
$270$	0.0539304	+	0.719651i	0.00328210	+	0.0437966i
$271$	1.48651	+	0.458527i	0.0902989	+	0.0278535i	0.339575	−	0.940579i	$-0.389717\pi$
$271$	1.48651	+	0.458527i	0.0902989	+	0.0278535i	−0.249277	+	0.968432i	$0.580193\pi$
$272$	−5.52048	+	3.76380i	−0.334728	+	0.228214i
$273$	−9.40452	+	1.41750i	−0.569188	+	0.0857912i
$274$	−2.58981	+	11.3467i	−0.156456	+	0.685479i
$275$	2.00835	+	1.86348i	0.121108	+	0.112372i
$276$	−1.13848	+	15.1919i	−0.0685284	+	0.914448i
$277$	−11.5118	+	29.3316i	−0.691678	+	1.76237i	−0.0457680	+	0.998952i	$0.514573\pi$
$277$	−11.5118	+	29.3316i	−0.691678	+	1.76237i	−0.645910	+	0.763414i	$0.723522\pi$
$278$	−23.1213	−	3.48498i	−1.38672	−	0.209015i
$279$	−30.3368	+	14.6095i	−1.81622	+	0.874645i
$280$	0.946375	−	0.455750i	0.0565567	−	0.0272363i
$281$	−16.0007	−	2.41172i	−0.954524	−	0.143871i	−0.346729	−	0.937965i	$-0.612708\pi$
$281$	−16.0007	−	2.41172i	−0.954524	−	0.143871i	−0.607795	+	0.794094i	$0.707946\pi$
$282$	−9.29169	+	23.6748i	−0.553312	+	1.40982i
$283$	0.596037	−	7.95357i	0.0354307	−	0.472790i	−0.951064	−	0.308995i	$-0.900007\pi$
$283$	0.596037	−	7.95357i	0.0354307	−	0.472790i	0.986494	−	0.163795i	$-0.0523736\pi$
$284$	−0.0584151	−	0.0542013i	−0.00346630	−	0.00321625i
$285$	−3.94091	+	17.2663i	−0.233439	+	1.02276i
$286$	9.78224	−	1.47444i	0.578436	−	0.0871852i
$287$	4.18353	−	2.85228i	0.246946	−	0.168365i
$288$	−3.14173	−	0.969096i	−0.185128	−	0.0571045i
$289$	2.06568	+	27.5646i	0.121511	+	1.62145i
$290$	−2.83278	+	3.55219i	−0.166347	+	0.208592i
$291$	33.8726	−	10.4483i	1.98565	−	0.612492i
$292$	2.94328	+	7.49936i	0.172243	+	0.438867i
$293$	6.09725	+	26.7138i	0.356205	+	1.56064i	0.762558	+	0.646920i	$0.223943\pi$
$293$	6.09725	+	26.7138i	0.356205	+	1.56064i	−0.406353	+	0.913716i	$0.633200\pi$
$294$	7.39309	−	12.8052i	0.431174	−	0.746815i
$295$	−1.60119	−	2.77334i	−0.0932248	−	0.161470i
$296$	2.98434	−	2.76906i	0.173461	−	0.160949i
$297$	1.23274	+	1.54581i	0.0715309	+	0.0896969i
$298$	−3.42299	−	2.33375i	−0.198288	−	0.135191i
$299$	19.7652	+	9.51843i	1.14305	+	0.550465i
$300$	−2.50755			−0.144773
$301$	2.96756	+	6.21586i	0.171047	+	0.358276i
$302$	13.9745			0.804141
$303$	2.93324	+	1.41257i	0.168510	+	0.0811502i
$304$	−5.83555	−	3.97861i	−0.334692	−	0.228189i
$305$	3.51690	+	4.41005i	0.201377	+	0.252519i
$306$	−16.1032	+	14.9416i	−0.920557	+	0.854152i
$307$	−2.33244	−	4.03990i	−0.133119	−	0.230569i	0.791758	−	0.610835i	$-0.209166\pi$
$307$	−2.33244	−	4.03990i	−0.133119	−	0.230569i	−0.924877	+	0.380265i	$0.875833\pi$
$308$	1.43889	−	2.49223i	0.0819884	−	0.142008i
$309$	−7.18568	−	31.4825i	−0.408779	−	1.79098i
$310$	−3.74157	−	9.53336i	−0.212507	−	0.541459i
$311$	8.51371	−	2.62613i	0.482768	−	0.148914i	−0.0438118	−	0.999040i	$-0.513950\pi$
$311$	8.51371	−	2.62613i	0.482768	−	0.148914i	0.526580	+	0.850126i	$0.323474\pi$
$312$	−5.64535	+	7.07904i	−0.319605	+	0.400772i
$313$	−0.412342	−	5.50232i	−0.0233070	−	0.311010i	−0.996658	−	0.0816890i	$-0.973969\pi$
$313$	−0.412342	−	5.50232i	−0.0233070	−	0.311010i	0.973351	−	0.229321i	$-0.0736505\pi$
$314$	11.7535	+	3.62549i	0.663291	+	0.204598i
$315$	2.85341	−	1.94542i	0.160771	−	0.109612i
$316$	4.32215	−	0.651459i	0.243140	−	0.0366474i
$317$	2.82749	−	12.3880i	0.158808	−	0.695782i	−0.831341	−	0.555763i	$-0.812426\pi$
$317$	2.82749	−	12.3880i	0.158808	−	0.695782i	0.990149	−	0.140019i	$-0.0447165\pi$
$318$	5.34362	+	4.95815i	0.299655	+	0.278039i
$319$	−0.930215	+	12.4129i	−0.0520821	+	0.694987i
$320$	0.365341	−	0.930874i	0.0204232	−	0.0520374i
$321$	30.8410	+	4.64853i	1.72138	+	0.259456i
$322$	5.74968	−	2.76890i	0.320417	−	0.154305i
$323$	−42.5165	+	20.4749i	−2.36568	+	1.13925i
$324$	7.96382	+	1.20035i	0.442435	+	0.0666863i
$325$	−1.31920	+	3.36126i	−0.0731760	+	0.186449i
$326$	−1.21762	+	16.2479i	−0.0674375	+	0.899890i
$327$	−7.67404	−	7.12047i	−0.424376	−	0.393763i
$328$	1.07264	−	4.69955i	0.0592267	−	0.259489i
$329$	10.5347	−	1.58785i	0.580797	−	0.0875411i
$330$	−5.67622	+	3.86998i	−0.312466	+	0.213035i
$331$	28.4975	+	8.79032i	1.56637	+	0.483160i	0.952061	−	0.305909i	$-0.0989605\pi$
$331$	28.4975	+	8.79032i	1.56637	+	0.483160i	0.614304	+	0.789069i	$0.289437\pi$
$332$	−0.797336	−	10.6397i	−0.0437595	−	0.583930i
$333$	8.34542	−	10.4648i	0.457326	−	0.573469i
$334$	7.82651	−	2.41416i	0.428247	−	0.132097i
$335$	3.20497	+	8.16612i	0.175106	+	0.446163i
$336$	0.586103	+	2.56788i	0.0319745	+	0.140090i
$337$	−17.1628	+	29.7268i	−0.934915	+	1.61932i	−0.160131	+	0.987096i	$0.551192\pi$
$337$	−17.1628	+	29.7268i	−0.934915	+	1.61932i	−0.774785	+	0.632225i	$0.782142\pi$
$338$	0.0191927	+	0.0332428i	0.00104395	+	0.00180817i
$339$	2.69455	−	2.50018i	0.146348	−	0.135791i
$340$	−4.16582	−	5.22378i	−0.225923	−	0.283299i
$341$	−23.1828	−	15.8057i	−1.25542	−	0.855929i
$342$	−20.9214	−	10.0752i	−1.13130	−	0.544806i
$343$	−13.5466			−0.731449
$344$	6.09602	+	2.41632i	0.328675	+	0.130279i
$345$	−15.2345			−0.820200
$346$	−10.2690	−	4.94530i	−0.552066	−	0.265861i
$347$	15.7870	+	10.7634i	0.847490	+	0.577809i	0.907340	−	0.420399i	$-0.138110\pi$
$347$	15.7870	+	10.7634i	0.847490	+	0.577809i	−0.0598496	+	0.998207i	$0.519062\pi$
$348$	−7.10333	−	8.90730i	−0.380779	−	0.477481i
$349$	12.8780	−	11.9491i	0.689346	−	0.639619i	−0.255624	−	0.966776i	$-0.582281\pi$
$349$	12.8780	−	11.9491i	0.689346	−	0.639619i	0.944970	+	0.327157i	$0.106091\pi$
$350$	0.525199	+	0.909671i	0.0280730	+	0.0486239i
$351$	−1.30293	+	2.25674i	−0.0695451	+	0.120456i
$352$	−0.609643	−	2.67102i	−0.0324941	−	0.142366i
$353$	0.776509	+	1.97851i	0.0413294	+	0.105306i	0.950048	−	0.312103i	$-0.101034\pi$
$353$	0.776509	+	1.97851i	0.0413294	+	0.105306i	−0.908719	+	0.417409i	$0.862938\pi$
$354$	7.67336	−	2.36692i	0.407834	−	0.125800i
$355$	0.0496844	−	0.0623022i	0.00263697	−	0.00330666i
$356$	0.482949	+	6.44450i	0.0255962	+	0.341558i
$357$	16.8166	+	5.18723i	0.890028	+	0.274537i
$358$	−5.54685	+	3.78178i	−0.293160	+	0.199873i
$359$	3.66577	−	0.552525i	0.193472	−	0.0291612i	−0.0515915	−	0.998668i	$-0.516429\pi$
$359$	3.66577	−	0.552525i	0.193472	−	0.0291612i	0.245063	+	0.969507i	$0.421191\pi$
$360$	0.731604	−	3.20537i	0.0385589	−	0.168938i
$361$	−22.6388	−	21.0058i	−1.19152	−	1.10557i
$362$	−0.959844	+	12.8082i	−0.0504483	+	0.673186i
$363$	3.20089	−	8.15572i	0.168003	−	0.428064i
$364$	3.75048	+	0.565295i	0.196579	+	0.0296295i
$365$	−7.25844	+	3.49548i	−0.379924	+	0.182962i
$366$	−12.7435	+	6.13696i	−0.666115	+	0.320784i
$367$	8.67293	+	1.30723i	0.452723	+	0.0682370i	0.371446	−	0.928455i	$-0.378862\pi$
$367$	8.67293	+	1.30723i	0.452723	+	0.0682370i	0.0812770	+	0.996692i	$0.474100\pi$
$368$	2.21962	−	5.65550i	0.115706	−	0.294813i
$369$	1.18436	−	15.8042i	0.0616554	−	0.822734i
$370$	2.98434	+	2.76906i	0.155148	+	0.143957i
$371$	0.679478	−	2.97699i	0.0352768	−	0.154558i
$372$	25.3937	−	3.82749i	1.31660	−	0.198446i
$373$	17.4855	−	11.9214i	0.905364	−	0.617267i	−0.0185659	−	0.999828i	$-0.505910\pi$
$373$	17.4855	−	11.9214i	0.905364	−	0.617267i	0.923930	+	0.382561i	$0.124958\pi$
$374$	−17.4920	−	5.39557i	−0.904490	−	0.278998i
$375$	−0.187389	−	2.50054i	−0.00967674	−	0.129127i
$376$	6.32377	−	7.92976i	0.326124	−	0.408946i
$377$	−15.6769	+	4.83567i	−0.807400	+	0.249050i
$378$	0.276943	+	0.705639i	0.0142444	+	0.0362942i
$379$	1.30920	+	5.73597i	0.0672490	+	0.294637i	0.997358	−	0.0726473i	$-0.0231447\pi$
$379$	1.30920	+	5.73597i	0.0672490	+	0.294637i	−0.930109	+	0.367284i	$0.880288\pi$
$380$	3.53140	−	6.11656i	0.181157	−	0.313773i
$381$	−16.5399	−	28.6479i	−0.847363	−	1.46768i
$382$	7.69218	−	7.13730i	0.393566	−	0.365176i
$383$	20.3829	+	25.5594i	1.04152	+	1.30602i	0.950685	+	0.310159i	$0.100382\pi$
$383$	20.3829	+	25.5594i	1.04152	+	1.30602i	0.0908350	+	0.995866i	$0.471046\pi$
$384$	2.07183	+	1.41255i	0.105728	+	0.0720840i
$385$	2.59279	+	1.24862i	0.132141	+	0.0636357i
$386$	13.7475			0.699731
$387$	21.0027	+	4.86846i	1.06763	+	0.247478i
$388$	−14.1363			−0.717662
$389$	−27.6397	−	13.3106i	−1.40139	−	0.674874i	−0.427947	−	0.903804i	$-0.640763\pi$
$389$	−27.6397	−	13.3106i	−1.40139	−	0.674874i	−0.973443	+	0.228930i	$0.926477\pi$
$390$	−7.48112	−	5.10054i	−0.378821	−	0.258276i
$391$	−25.3093	−	31.7369i	−1.27995	−	1.60500i
$392$	−4.32256	+	4.01075i	−0.218322	+	0.202574i
$393$	−9.55764	−	16.5543i	−0.482119	−	0.835055i
$394$	−4.37979	+	7.58601i	−0.220650	+	0.382178i
$395$	0.972632	+	4.26138i	0.0489384	+	0.214413i
$396$	−3.29085	−	8.38495i	−0.165371	−	0.421360i
$397$	−17.5196	+	5.40408i	−0.879283	+	0.271223i	−0.701348	−	0.712819i	$-0.747418\pi$
$397$	−17.5196	+	5.40408i	−0.879283	+	0.271223i	−0.177935	+	0.984042i	$0.556942\pi$
$398$	−1.85557	+	2.32681i	−0.0930111	+	0.116632i
$399$	1.39019	+	18.5508i	0.0695966	+	0.928703i
$400$	0.955573	+	0.294755i	0.0477786	+	0.0147378i
$401$	1.47332	−	1.00449i	0.0735740	−	0.0501619i	−0.525974	−	0.850500i	$-0.676299\pi$
$401$	1.47332	−	1.00449i	0.0735740	−	0.0501619i	0.599548	+	0.800338i	$0.295347\pi$
$402$	−21.7518	+	3.27856i	−1.08488	+	0.163520i
$403$	8.22883	−	36.0529i	0.409907	−	1.79592i
$404$	−0.951750	−	0.883095i	−0.0473513	−	0.0439356i
$405$	−0.601859	+	8.03126i	−0.0299066	+	0.399076i
$406$	−1.74355	+	4.44250i	−0.0865311	+	0.220478i
$407$	11.0291	+	1.66237i	0.546692	+	0.0824006i
$408$	15.0949	−	7.26932i	0.747309	−	0.359885i
$409$	35.4480	−	17.0709i	1.75279	−	0.844100i	0.775753	−	0.631037i	$-0.217370\pi$
$409$	35.4480	−	17.0709i	1.75279	−	0.844100i	0.977038	−	0.213063i	$-0.0683440\pi$
$410$	4.76657	+	0.718444i	0.235404	+	0.0354814i
$411$	10.6622	−	27.1667i	0.525925	−	1.34004i
$412$	−0.962373	+	12.8420i	−0.0474127	+	0.632679i
$413$	−2.46581	−	2.28794i	−0.121335	−	0.112582i
$414$	4.44484	−	19.4741i	0.218452	−	0.957101i
$415$	10.5504	−	1.59021i	0.517898	−	0.0780605i
$416$	2.98344	−	2.03408i	0.146275	−	0.0997288i
$417$	56.0278	+	17.2823i	2.74369	+	0.846317i
$418$	−1.44603	−	19.2959i	−0.0707275	−	0.943792i
$419$	21.0886	−	26.4443i	1.03025	−	1.29189i	0.0746502	−	0.997210i	$-0.476216\pi$
$419$	21.0886	−	26.4443i	1.03025	−	1.29189i	0.955596	−	0.294679i	$-0.0952126\pi$
$420$	−2.51690	+	0.776362i	−0.122812	+	0.0378826i
$421$	5.16973	+	13.1722i	0.251957	+	0.641976i	0.999759	−	0.0219456i	$-0.00698605\pi$
$421$	5.16973	+	13.1722i	0.251957	+	0.641976i	−0.747802	+	0.663922i	$0.768891\pi$
$422$	−1.93496	−	8.47760i	−0.0941922	−	0.412683i
$423$	16.6733	−	28.8790i	0.810685	−	1.40415i
$424$	−1.45352	−	2.51757i	−0.0705892	−	0.122264i
$425$	4.89786	−	4.54455i	0.237581	−	0.220443i
$426$	0.124586	+	0.156226i	0.00603621	+	0.00756916i
$427$	4.89541	+	3.33764i	0.236906	+	0.161520i
$428$	−11.2064	−	5.39673i	−0.541683	−	0.260861i
$429$	−24.8065			−1.19767
$430$	−1.95401	+	6.25954i	−0.0942306	+	0.301862i
$431$	−15.8621			−0.764052			−0.382026	−	0.924152i	$-0.624774\pi$
$431$	−15.8621			−0.764052			−0.382026	+	0.924152i	$0.624774\pi$
$432$	0.650202	+	0.313121i	0.0312828	+	0.0150650i
$433$	5.20204	+	3.54669i	0.249994	+	0.170443i	0.681834	−	0.731507i	$-0.261183\pi$
$433$	5.20204	+	3.54669i	0.249994	+	0.170443i	−0.431839	+	0.901951i	$0.642135\pi$
$434$	−6.70715	−	8.41051i	−0.321954	−	0.403717i
$435$	8.35156	−	7.74911i	0.400427	−	0.371542i
$436$	2.08742	+	3.61552i	0.0999694	+	0.173152i
$437$	21.4549	−	37.1610i	1.02633	−	1.77765i
$438$	−4.49525	−	19.6950i	−0.214791	−	0.941062i
$439$	13.2188	+	33.6809i	0.630899	+	1.60750i	0.785033	+	0.619454i	$0.212646\pi$
$439$	13.2188	+	33.6809i	0.630899	+	1.60750i	−0.154135	+	0.988050i	$0.549259\pi$
$440$	2.61799	−	0.807543i	0.124808	−	0.0384981i
$441$	−12.0876	+	15.1574i	−0.575601	+	0.721781i
$442$	−1.80293	−	24.0584i	−0.0857566	−	1.14434i
$443$	−30.3751	−	9.36948i	−1.44316	−	0.445157i	−0.528348	−	0.849028i	$-0.677188\pi$
$443$	−30.3751	−	9.36948i	−1.44316	−	0.445157i	−0.914816	+	0.403870i	$0.867665\pi$
$444$	−8.43468	+	5.75067i	−0.400292	+	0.272915i
$445$	−6.39039	+	0.963197i	−0.302934	+	0.0456599i
$446$	1.66584	−	7.29854i	0.0788800	−	0.345596i
$447$	7.61524	+	7.06591i	0.360188	+	0.334206i
$448$	0.0784963	−	1.04746i	0.00370860	−	0.0494878i
$449$	−0.476007	+	1.21285i	−0.0224642	+	0.0572378i	−0.941666	−	0.336549i	$-0.890740\pi$
$449$	−0.476007	+	1.21285i	−0.0224642	+	0.0572378i	0.919202	+	0.393787i	$0.128835\pi$
$450$	3.25108	+	0.490021i	0.153257	+	0.0230998i
$451$	11.8987	−	5.73009i	0.560286	−	0.269819i
$452$	−1.32072	+	0.636027i	−0.0621216	+	0.0299162i
$453$	−34.6503	−	5.22269i	−1.62801	−	0.245384i
$454$	−4.74799	+	12.0977i	−0.222834	+	0.567772i
$455$	−0.283440	+	3.78224i	−0.0132879	+	0.177314i
$456$	12.9826	+	12.0461i	0.607964	+	0.564108i
$457$	4.28600	−	18.7782i	0.200491	−	0.878407i	−0.770148	−	0.637865i	$-0.779818\pi$
$457$	4.28600	−	18.7782i	0.200491	−	0.878407i	0.970639	−	0.240542i	$-0.0773252\pi$
$458$	13.5401	−	2.04084i	0.632688	−	0.0953623i
$459$	3.98396	−	2.71622i	0.185955	−	0.126782i
$460$	5.80556	+	1.79078i	0.270686	+	0.0834954i
$461$	−1.29269	−	17.2498i	−0.0602067	−	0.803403i	−0.942820	−	0.333303i	$-0.891837\pi$
$461$	−1.29269	−	17.2498i	−0.0602067	−	0.803403i	0.882613	−	0.470100i	$-0.155782\pi$
$462$	−4.49921	+	5.64183i	−0.209322	+	0.262482i
$463$	39.4303	−	12.1627i	1.83248	−	0.565246i	0.832547	−	0.553954i	$-0.186882\pi$
$463$	39.4303	−	12.1627i	1.83248	−	0.565246i	0.999936	−	0.0112923i	$-0.00359453\pi$
$464$	1.65990	+	4.22936i	0.0770589	+	0.196343i
$465$	5.71447	+	25.0367i	0.265002	+	1.16105i
$466$	7.71086	−	13.3556i	0.357199	−	0.618686i
$467$	−4.68530	−	8.11518i	−0.216810	−	0.375526i	0.737021	−	0.675870i	$-0.236232\pi$
$467$	−4.68530	−	8.11518i	−0.216810	−	0.375526i	−0.953831	+	0.300344i	$0.902899\pi$
$468$	8.70266	−	8.07489i	0.402280	−	0.373262i
$469$	5.74523	+	7.20430i	0.265290	+	0.332663i
$470$	8.38016	+	5.71350i	0.386548	+	0.263544i
$471$	−27.7884	−	13.3822i	−1.28042	−	0.616619i
$472$	−3.20238			−0.147401
$473$	5.23736	+	17.1851i	0.240814	+	0.790173i
$474$	−10.9604			−0.503429
$475$	6.36335	+	3.06443i	0.291971	+	0.140606i
$476$	−5.79870	−	3.95348i	−0.265783	−	0.181208i
$477$	−5.95917	−	7.47256i	−0.272852	−	0.342145i
$478$	−14.4663	+	13.4228i	−0.661674	+	0.613944i
$479$	−19.8148	−	34.3202i	−0.905359	−	1.56813i	−0.820434	−	0.571741i	$-0.806268\pi$
$479$	−19.8148	−	34.3202i	−0.905359	−	1.56813i	−0.0849246	−	0.996387i	$-0.527065\pi$
$480$	−1.25377	+	2.17160i	−0.0572267	+	0.0991196i
$481$	3.27112	+	14.3317i	0.149150	+	0.653470i
$482$	3.67382	+	9.36073i	0.167338	+	0.426370i
$483$	−15.2914	+	4.71677i	−0.695782	+	0.214620i
$484$	−2.17847	+	2.73172i	−0.0990214	+	0.124169i
$485$	−1.05641	−	14.0968i	−0.0479690	−	0.640102i
$486$	−21.3668	−	6.59080i	−0.969219	−	0.298965i
$487$	−33.2756	+	22.6869i	−1.50786	+	1.02804i	−0.523469	+	0.852045i	$0.675363\pi$
$487$	−33.2756	+	22.6869i	−1.50786	+	1.02804i	−0.984391	+	0.175997i	$0.943685\pi$
$488$	5.57766	−	0.840698i	0.252489	−	0.0380566i
$489$	9.09148	−	39.8324i	0.411131	−	1.80128i
$490$	−4.32256	−	4.01075i	−0.195273	−	0.181187i
$491$	−0.673814	+	8.99143i	−0.0304088	+	0.405777i	0.961142	+	0.276056i	$0.0890274\pi$
$491$	−0.673814	+	8.99143i	−0.0304088	+	0.405777i	−0.991550	+	0.129722i	$0.958592\pi$
$492$	−4.41602	+	11.2518i	−0.199090	+	0.507272i
$493$	30.0177	+	4.52443i	1.35193	+	0.203770i
$494$	22.9772	−	11.0653i	1.03380	−	0.497850i
$495$	8.11558	−	3.90826i	0.364768	−	0.175663i
$496$	−10.1269	−	1.52639i	−0.454712	−	0.0685368i
$497$	0.0305803	−	0.0779174i	0.00137172	−	0.00349507i
$498$	−1.99936	+	26.6796i	−0.0895934	+	1.19554i
$499$	0.268430	+	0.249066i	0.0120166	+	0.0111497i	0.686158	−	0.727452i	$-0.259296\pi$
$499$	0.268430	+	0.249066i	0.0120166	+	0.0111497i	−0.674142	+	0.738602i	$0.735486\pi$
$500$	−0.222521	+	0.974928i	−0.00995144	+	0.0436001i
$501$	−20.3084	+	3.06100i	−0.907312	+	0.136755i
$502$	0.870824	−	0.593718i	0.0388668	−	0.0264989i
$503$	−15.6906	−	4.83992i	−0.699610	−	0.215801i	−0.0755095	−	0.997145i	$-0.524058\pi$
$503$	−15.6906	−	4.83992i	−0.699610	−	0.215801i	−0.624101	+	0.781344i	$0.714535\pi$
$504$	−0.258080	−	3.44384i	−0.0114958	−	0.153401i
$505$	0.809501	−	1.01508i	0.0360223	−	0.0451706i
$506$	15.9055	−	4.90621i	0.707087	−	0.218108i
$507$	−0.0351653	−	0.0895998i	−0.00156175	−	0.00397927i
$508$	2.93551	+	12.8613i	0.130242	+	0.570629i
$509$	3.76310	−	6.51788i	0.166797	−	0.288900i	−0.770495	−	0.637446i	$-0.779991\pi$
$509$	3.76310	−	6.51788i	0.166797	−	0.288900i	0.937292	+	0.348546i	$0.113324\pi$
$510$	8.37704	+	14.5095i	0.370942	+	0.642490i
$511$	−6.20329	+	5.75581i	−0.274417	+	0.254622i
$512$	−0.623490	−	0.781831i	−0.0275546	−	0.0345524i
$513$	4.21134	+	2.87124i	0.185935	+	0.126768i
$514$	−20.3758	−	9.81246i	−0.898738	−	0.432809i
$515$	−12.8780			−0.567472
$516$	−14.2123	−	8.26963i	−0.625660	−	0.364050i
$517$	27.7876			1.22210
$518$	3.85280	+	1.85541i	0.169283	+	0.0815222i
$519$	23.6142	+	16.0999i	1.03655	+	0.706708i
$520$	2.25134	+	2.82309i	0.0987278	+	0.123801i
$521$	−9.91284	+	9.19777i	−0.434289	+	0.402962i	−0.866791	−	0.498671i	$-0.833821\pi$
$521$	−9.91284	+	9.19777i	−0.434289	+	0.402962i	0.432502	+	0.901633i	$0.357631\pi$
$522$	7.46894	+	12.9366i	0.326906	+	0.566219i
$523$	−5.50724	+	9.53882i	−0.240815	+	0.417103i	−0.960947	−	0.276734i	$-0.910748\pi$
$523$	−5.50724	+	9.53882i	−0.240815	+	0.417103i	0.720132	+	0.693837i	$0.244081\pi$
$524$	1.69630	+	7.43197i	0.0741032	+	0.324667i
$525$	−0.962280	−	2.45185i	−0.0419973	−	0.107007i
$526$	20.5749	−	6.34652i	0.897108	−	0.276721i
$527$	−42.6635	+	53.4983i	−1.85845	+	2.33042i
$528$	0.513392	+	6.85074i	0.0223425	+	0.298140i
$529$	13.2933	+	4.10045i	0.577971	+	0.178280i
$530$	2.40191	−	1.63759i	0.104332	−	0.0711326i
$531$	−10.4112	+	1.56923i	−0.451806	+	0.0680988i
$532$	1.65082	−	7.23273i	0.0715723	−	0.313579i
$533$	12.7594	+	11.8390i	0.552671	+	0.512804i
$534$	1.21102	−	16.1599i	0.0524059	−	0.699308i
$535$	4.54418	−	11.5784i	0.196462	−	0.500577i
$536$	8.67455	+	1.30748i	0.374683	+	0.0564744i
$537$	15.1670	−	7.30405i	0.654505	−	0.315193i
$538$	19.5237	−	9.40213i	0.841728	−	0.405355i
$539$	−15.9747	−	2.40780i	−0.688079	−	0.103711i
$540$	−0.263655	+	0.671783i	−0.0113459	+	0.0289089i
$541$	0.832403	−	11.1076i	0.0357878	−	0.477555i	−0.950301	−	0.311334i	$-0.899224\pi$
$541$	0.832403	−	11.1076i	0.0357878	−	0.477555i	0.986088	−	0.166221i	$-0.0531566\pi$
$542$	1.14035	+	1.05809i	0.0489822	+	0.0454489i
$543$	7.16680	−	31.3998i	0.307557	−	1.34749i
$544$	−6.60683	+	0.995820i	−0.283266	+	0.0426954i
$545$	−3.44942	+	2.35177i	−0.147757	+	0.100739i
$546$	−9.08821	−	2.80334i	−0.388940	−	0.119972i
$547$	3.02665	+	40.3879i	0.129410	+	1.72686i	0.563607	+	0.826043i	$0.309413\pi$
$547$	3.02665	+	40.3879i	0.129410	+	1.72686i	−0.434197	+	0.900818i	$0.642968\pi$
$548$	−7.25649	+	9.09935i	−0.309982	+	0.388705i
$549$	17.7215	−	5.46635i	0.756333	−	0.233298i
$550$	1.00093	+	2.55032i	0.0426797	+	0.108746i
$551$	7.14053	+	31.2847i	0.304197	+	1.33277i
$552$	−7.61727	+	13.1935i	−0.324213	+	0.561553i
$553$	2.29563	+	3.97614i	0.0976200	+	0.169083i
$554$	−23.0983	+	21.4321i	−0.981352	+	0.910562i
$555$	−6.36491	−	7.98135i	−0.270175	−	0.338789i
$556$	−19.3195	−	13.1718i	−0.819329	−	0.558609i
$557$	13.3704	+	6.43885i	0.566523	+	0.272823i	0.695144	−	0.718871i	$-0.255341\pi$
$557$	13.3704	+	6.43885i	0.566523	+	0.272823i	−0.128621	+	0.991694i	$0.541055\pi$
$558$	−33.6714			−1.42542
$559$	−18.5620	+	14.7004i	−0.785091	+	0.621760i
$560$	1.05040			0.0443874
$561$	41.3557	+	19.9158i	1.74604	+	0.840847i
$562$	−13.3698	−	9.11535i	−0.563969	−	0.384508i
$563$	6.45527	+	8.09465i	0.272057	+	0.341149i	0.899026	−	0.437896i	$-0.144276\pi$
$563$	6.45527	+	8.09465i	0.272057	+	0.341149i	−0.626969	+	0.779044i	$0.715705\pi$
$564$	−18.6436	+	17.2988i	−0.785039	+	0.728410i
$565$	−0.732946	−	1.26950i	−0.0308353	−	0.0534083i
$566$	3.98793	−	6.90730i	0.167625	−	0.290336i
$567$	1.88245	+	8.24756i	0.0790556	+	0.346365i
$568$	−0.0291131	−	0.0741790i	−0.00122156	−	0.00311248i
$569$	−9.26377	+	2.85750i	−0.388358	+	0.119792i	−0.482784	−	0.875739i	$-0.660374\pi$
$569$	−9.26377	+	2.85750i	−0.388358	+	0.119792i	0.0944266	+	0.995532i	$0.469898\pi$
$570$	−11.0422	+	13.8465i	−0.462506	+	0.579964i
$571$	−2.72199	−	36.3224i	−0.113912	−	1.52004i	−0.702542	−	0.711642i	$-0.747952\pi$
$571$	−2.72199	−	36.3224i	−0.113912	−	1.52004i	0.588630	−	0.808402i	$-0.299667\pi$
$572$	9.45323	+	2.91593i	0.395259	+	0.121921i
$573$	−21.7405	+	14.8224i	−0.908223	+	0.619216i
$574$	5.00679	−	0.754652i	0.208979	−	0.0314986i
$575$	−1.35192	+	5.92315i	−0.0563790	+	0.247012i
$576$	−2.41013	−	2.23627i	−0.100422	−	0.0931780i
$577$	−3.26003	+	43.5021i	−0.135717	+	1.81102i	0.349838	+	0.936810i	$0.386237\pi$
$577$	−3.26003	+	43.5021i	−0.135717	+	1.81102i	−0.485555	+	0.874206i	$0.661382\pi$
$578$	−10.0987	+	25.7311i	−0.420051	+	1.07027i
$579$	−34.0876	−	5.13788i	−1.41663	−	0.213523i
$580$	−4.09349	+	1.97132i	−0.169973	+	0.0818546i
$581$	10.0974	−	4.86265i	0.418910	−	0.201737i
$582$	35.0516	+	5.28317i	1.45293	+	0.218994i
$583$	2.90974	−	7.41390i	0.120509	−	0.307052i
$584$	−0.602045	+	8.03373i	−0.0249128	+	0.332438i
$585$	8.70266	+	8.07489i	0.359811	+	0.333855i
$586$	−6.09725	+	26.7138i	−0.251875	+	1.10354i
$587$	8.15759	−	1.22956i	0.336700	−	0.0507493i	0.0214835	−	0.999769i	$-0.493161\pi$
$587$	8.15759	−	1.22956i	0.336700	−	0.0507493i	0.315216	+	0.949020i	$0.397923\pi$
$588$	12.2169	−	8.32935i	0.503817	−	0.343497i
$589$	−69.1187	−	21.3203i	−2.84799	−	0.878487i
$590$	−0.239314	−	3.19342i	−0.00985239	−	0.131471i
$591$	13.6950	−	17.1730i	0.563337	−	0.706402i
$592$	3.89025	−	1.19998i	0.159888	−	0.0493190i
$593$	3.27137	+	8.33532i	0.134339	+	0.342290i	0.982175	−	0.187968i	$-0.0601901\pi$
$593$	3.27137	+	8.33532i	0.134339	+	0.342290i	−0.847836	+	0.530258i	$0.822095\pi$
$594$	0.439960	+	1.92759i	0.0180518	+	0.0790901i
$595$	3.50909	−	6.07793i	0.143859	−	0.249171i
$596$	−2.07143	−	3.58782i	−0.0848489	−	0.146963i
$597$	5.47055	−	5.07593i	0.223895	−	0.207744i
$598$	13.6780	+	17.1516i	0.559333	+	0.701382i
$599$	24.2795	+	16.5535i	0.992034	+	0.676357i	0.946533	−	0.322607i	$-0.104559\pi$
$599$	24.2795	+	16.5535i	0.992034	+	0.676357i	0.0455007	+	0.998964i	$0.485512\pi$
$600$	−2.25922	−	1.08798i	−0.0922324	−	0.0444168i
$601$	−36.7619			−1.49955			−0.749775	−	0.661693i	$-0.769838\pi$
$601$	−36.7619			−1.49955			−0.749775	+	0.661693i	$0.769838\pi$
$602$	−0.0232809	+	6.88787i	−0.000948859	+	0.280729i
$603$	28.8423			1.17455
$604$	12.5906	+	6.06330i	0.512303	+	0.246712i
$605$	−2.88687	−	1.96824i	−0.117368	−	0.0800203i
$606$	2.02986	+	2.54537i	0.0824576	+	0.103399i
$607$	14.4339	−	13.3927i	0.585856	−	0.543595i	−0.330579	−	0.943778i	$-0.607244\pi$
$607$	14.4339	−	13.3927i	0.585856	−	0.543595i	0.916435	+	0.400184i	$0.131054\pi$
$608$	−3.53140	−	6.11656i	−0.143217	−	0.248059i
$609$	5.98351	−	10.3638i	0.242464	−	0.419960i
$610$	1.25517	+	5.49924i	0.0508202	+	0.222658i
$611$	13.3800	+	34.0918i	0.541298	+	1.37921i
$612$	−20.9914	+	6.47497i	−0.848525	+	0.261735i
$613$	5.29852	−	6.64414i	0.214005	−	0.268354i	−0.663229	−	0.748416i	$-0.730814\pi$
$613$	5.29852	−	6.64414i	0.214005	−	0.268354i	0.877234	+	0.480062i	$0.159386\pi$
$614$	−0.348607	−	4.65183i	−0.0140686	−	0.187733i
$615$	−11.5504	−	3.56282i	−0.465757	−	0.143667i
$616$	2.37774	−	1.62111i	0.0958017	−	0.0653165i
$617$	4.37453	−	0.659355i	0.176112	−	0.0265446i	−0.0603941	−	0.998175i	$-0.519236\pi$
$617$	4.37453	−	0.659355i	0.176112	−	0.0265446i	0.236506	+	0.971630i	$0.423998\pi$
$618$	7.18568	−	31.4825i	0.289051	−	1.26641i
$619$	−18.7653	−	17.4116i	−0.754240	−	0.699832i	0.206141	−	0.978522i	$-0.433909\pi$
$619$	−18.7653	−	17.4116i	−0.754240	−	0.699832i	−0.960381	+	0.278690i	$0.910100\pi$
$620$	0.765334	−	10.2127i	0.0307365	−	0.410151i
$621$	−1.60183	+	4.08140i	−0.0642793	+	0.163781i
$622$	8.81003	+	1.32790i	0.353250	+	0.0532438i
$623$	−6.11602	+	2.94532i	−0.245033	+	0.118002i
$624$	−8.15776	+	3.92857i	−0.326572	+	0.157269i
$625$	−0.988831	−	0.149042i	−0.0395532	−	0.00596169i
$626$	2.01586	−	5.13633i	0.0805700	−	0.205289i
$627$	−3.62598	+	48.3854i	−0.144808	+	1.93233i
$628$	9.01653	+	8.36612i	0.359799	+	0.333845i
$629$	6.05279	−	26.5190i	0.241341	−	1.05738i
$630$	3.41492	−	0.514717i	0.136054	−	0.0205068i
$631$	1.61182	−	1.09892i	0.0641656	−	0.0437474i	−0.530812	−	0.847489i	$-0.678113\pi$
$631$	1.61182	−	1.09892i	0.0641656	−	0.0437474i	0.594978	+	0.803742i	$0.297161\pi$
$632$	4.17678	+	1.28837i	0.166143	+	0.0512484i
$633$	1.62947	+	21.7437i	0.0647654	+	0.864235i
$634$	7.92245	−	9.93444i	0.314641	−	0.394547i
$635$	−12.6060	+	3.88843i	−0.500253	+	0.154308i
$636$	2.66317	+	6.78565i	0.105602	+	0.269068i
$637$	−4.73794	−	20.7583i	−0.187724	−	0.822472i
$638$	−6.22383	+	10.7800i	−0.246404	+	0.426784i
$639$	−0.130998	−	0.226896i	−0.00518221	−	0.00897585i
$640$	0.733052	−	0.680173i	0.0289764	−	0.0268862i
$641$	−14.0162	−	17.5758i	−0.553608	−	0.694202i	0.423754	−	0.905777i	$-0.360712\pi$
$641$	−14.0162	−	17.5758i	−0.553608	−	0.694202i	−0.977362	+	0.211575i	$0.932141\pi$
$642$	25.7698	+	17.5696i	1.01705	+	0.693416i
$643$	−17.2659	−	8.31481i	−0.680900	−	0.327904i	0.0612647	−	0.998122i	$-0.480487\pi$
$643$	−17.2659	−	8.31481i	−0.680900	−	0.327904i	−0.742165	+	0.670217i	$0.766201\pi$
$644$	6.38166			0.251473
$645$	7.18442	−	14.7905i	0.282886	−	0.582376i
$646$	−47.1898			−1.85666
$647$	7.68142	+	3.69918i	0.301988	+	0.145430i	0.578741	−	0.815511i	$-0.303544\pi$
$647$	7.68142	+	3.69918i	0.301988	+	0.145430i	−0.276753	+	0.960941i	$0.589259\pi$
$648$	6.65434	+	4.53685i	0.261407	+	0.178224i
$649$	−5.47024	−	6.85946i	−0.214726	−	0.269257i
$650$	−2.64696	+	2.45602i	−0.103822	+	0.0963329i
$651$	13.4874	+	23.3609i	0.528613	+	0.915584i
$652$	−8.14675	+	14.1106i	−0.319051	+	0.552613i
$653$	3.99817	+	17.5171i	0.156460	+	0.685498i	0.990923	+	0.134433i	$0.0429213\pi$
$653$	3.99817	+	17.5171i	0.156460	+	0.685498i	−0.834462	+	0.551065i	$0.814222\pi$
$654$	−3.82462	−	9.74497i	−0.149554	−	0.381058i
$655$	−7.28442	+	2.24695i	−0.284626	+	0.0877955i
$656$	3.00547	−	3.76874i	0.117344	−	0.147145i
$657$	1.97940	+	26.4133i	0.0772239	+	1.03048i
$658$	10.1804	+	3.14023i	0.396873	+	0.122419i
$659$	38.1043	−	25.9790i	1.48433	−	1.01200i	0.494591	−	0.869126i	$-0.335318\pi$
$659$	38.1043	−	25.9790i	1.48433	−	1.01200i	0.989741	−	0.142874i	$-0.0456344\pi$
$660$	−6.79322	+	1.02391i	−0.264426	+	0.0398558i
$661$	−7.58644	+	33.2384i	−0.295078	+	1.29282i	0.582281	+	0.812988i	$0.302160\pi$
$661$	−7.58644	+	33.2384i	−0.295078	+	1.29282i	−0.877359	+	0.479834i	$0.840697\pi$
$662$	21.8614	+	20.2844i	0.849667	+	0.788376i
$663$	−4.52093	+	60.3277i	−0.175579	+	2.34293i
$664$	3.89802	−	9.93200i	0.151273	−	0.385436i
$665$	7.33587	+	1.10571i	0.284473	+	0.0428774i
$666$	12.0595	−	5.80754i	0.467295	−	0.225038i
$667$	−24.8699	+	11.9767i	−0.962965	+	0.463740i
$668$	8.09890	+	1.22071i	0.313356	+	0.0472308i
$669$	−6.85822	+	17.4745i	−0.265154	+	0.675601i
$670$	−0.655572	+	8.74800i	−0.0253270	+	0.337965i
$671$	11.3284	+	10.5112i	0.437329	+	0.405782i
$672$	−0.586103	+	2.56788i	−0.0226094	+	0.0990583i
$673$	−23.1613	+	3.49101i	−0.892804	+	0.134569i	−0.579392	−	0.815049i	$-0.696710\pi$
$673$	−23.1613	+	3.49101i	−0.892804	+	0.134569i	−0.313412	+	0.949617i	$0.601472\pi$
$674$	−28.3611	+	19.3363i	−1.09243	+	0.744805i
$675$	−0.689608	−	0.212716i	−0.0265430	−	0.00818743i
$676$	0.00286855	+	0.0382781i	0.000110329	+	0.00147224i
$677$	−11.6760	+	14.6413i	−0.448746	+	0.562709i	−0.953825	−	0.300364i	$-0.902892\pi$
$677$	−11.6760	+	14.6413i	−0.448746	+	0.562709i	0.505079	+	0.863073i	$0.331463\pi$
$678$	3.51249	−	1.08346i	0.134896	−	0.0416100i
$679$	−5.42485	−	13.8223i	−0.208187	−	0.530451i
$680$	−1.48676	−	6.51394i	−0.0570148	−	0.249798i
$681$	16.2941	−	28.2222i	0.624391	−	1.08148i
$682$	−14.0291	−	24.2991i	−0.537202	−	0.930461i
$683$	−29.5228	+	27.3932i	−1.12966	+	1.04817i	−0.131275	+	0.991346i	$0.541907\pi$
$683$	−29.5228	+	27.3932i	−1.12966	+	1.04817i	−0.998384	+	0.0568241i	$0.981903\pi$
$684$	−14.4781	−	18.1549i	−0.553583	−	0.694171i
$685$	−9.61618	−	6.55620i	−0.367416	−	0.250500i
$686$	−12.2051	−	5.87766i	−0.465992	−	0.224410i
$687$	−34.3360			−1.31000
$688$	4.44392	+	4.82199i	0.169423	+	0.183837i
$689$	10.4970			0.399902
$690$	−13.7258	−	6.61002i	−0.522534	−	0.251639i
$691$	19.1612	+	13.0639i	0.728925	+	0.496972i	0.870016	−	0.493024i	$-0.164109\pi$
$691$	19.1612	+	13.0639i	0.728925	+	0.496972i	−0.141091	+	0.989997i	$0.545061\pi$
$692$	−7.10638	−	8.91112i	−0.270144	−	0.338750i
$693$	6.93582	−	6.43550i	0.263470	−	0.244464i
$694$	9.55353	+	16.5472i	0.362647	+	0.628123i
$695$	11.6912	−	20.2498i	0.443474	−	0.768119i
$696$	−2.53515	−	11.1072i	−0.0960946	−	0.421018i
$697$	−11.7667	−	29.9810i	−0.445694	−	1.13561i
$698$	16.7872	−	5.17817i	0.635406	−	0.195997i
$699$	−24.1108	+	30.2340i	−0.911954	+	1.14355i
$700$	0.0784963	+	1.04746i	0.00296688	+	0.0395903i
$701$	−15.1694	−	4.67915i	−0.572941	−	0.176729i	−0.00527245	−	0.999986i	$-0.501678\pi$
$701$	−15.1694	−	4.67915i	−0.572941	−	0.176729i	−0.567669	+	0.823257i	$0.692154\pi$
$702$	−2.15306	+	1.46793i	−0.0812619	+	0.0554035i
$703$	28.4323	−	4.28548i	1.07234	−	0.161630i
$704$	0.609643	−	2.67102i	0.0229768	−	0.100668i
$705$	−18.6436	−	17.2988i	−0.702160	−	0.651510i
$706$	−0.158834	+	2.11949i	−0.00597779	+	0.0797681i
$707$	0.498242	−	1.26950i	0.0187383	−	0.0477444i
$708$	7.94042	+	1.19683i	0.298419	+	0.0449795i
$709$	27.6697	−	13.3250i	1.03916	−	0.500431i	0.165110	−	0.986275i	$-0.447202\pi$
$709$	27.6697	−	13.3250i	1.03916	−	0.500431i	0.874046	+	0.485844i	$0.161488\pi$
$710$	0.0717960	−	0.0345751i	0.00269445	−	0.00129758i
$711$	14.2104	+	2.14187i	0.532930	+	0.0803263i
$712$	−2.36104	+	6.01584i	−0.0884839	+	0.225453i
$713$	4.64977	−	62.0468i	0.174135	−	2.32367i
$714$	12.9006	+	11.9700i	0.482792	+	0.447965i
$715$	−2.20134	+	9.64470i	−0.0823255	+	0.360691i
$716$	−6.63840	+	1.00058i	−0.248088	+	0.0373933i
$717$	40.8863	−	27.8758i	1.52693	−	1.04104i
$718$	3.54247	+	1.09271i	0.132204	+	0.0407795i
$719$	−2.68235	−	35.7935i	−0.100035	−	1.33487i	−0.790926	−	0.611912i	$-0.790401\pi$
$719$	−2.68235	−	35.7935i	−0.100035	−	1.33487i	0.690891	−	0.722959i	$-0.257218\pi$
$720$	2.04991	−	2.57050i	0.0763956	−	0.0957971i
$721$	−12.9260	+	3.98715i	−0.481391	+	0.148489i
$722$	−11.2828	−	28.7482i	−0.419903	−	1.06990i
$723$	−5.61099	−	24.5833i	−0.208675	−	0.914264i
$724$	−6.42207	+	11.1234i	−0.238674	+	0.413396i
$725$	−2.27171	−	3.93472i	−0.0843693	−	0.146132i
$726$	6.42253	−	5.95924i	0.238363	−	0.221168i
$727$	−4.43538	−	5.56179i	−0.164499	−	0.206275i	0.692749	−	0.721179i	$-0.256399\pi$
$727$	−4.43538	−	5.56179i	−0.164499	−	0.206275i	−0.857248	+	0.514903i	$0.827828\pi$
$728$	3.13380	+	2.13659i	0.116146	+	0.0791872i
$729$	28.7482	+	13.8444i	1.06475	+	0.512755i
$730$	−8.05626			−0.298176
$731$	42.7475	−	9.60494i	1.58107	−	0.355251i
$732$	−14.1442			−0.522786
$733$	−25.4997	−	12.2800i	−0.941853	−	0.453573i	−0.101031	−	0.994883i	$-0.532214\pi$
$733$	−25.4997	−	12.2800i	−0.941853	−	0.453573i	−0.840823	+	0.541311i	$0.817928\pi$
$734$	7.24685	+	4.94082i	0.267486	+	0.182369i
$735$	9.21903	+	11.5603i	0.340049	+	0.426408i
$736$	4.45364	−	4.13237i	0.164163	−	0.152321i
$737$	12.0171	+	20.8142i	0.442655	+	0.766701i
$738$	7.92426	−	13.7252i	0.291696	−	0.505232i
$739$	−0.810310	−	3.55020i	−0.0298077	−	0.130596i	0.957835	−	0.287319i	$-0.0927641\pi$
$739$	−0.810310	−	3.55020i	−0.0298077	−	0.130596i	−0.987643	+	0.156723i	$0.949907\pi$
$740$	1.48735	+	3.78970i	0.0546759	+	0.139312i
$741$	−61.1085	+	18.8495i	−2.24488	+	0.692452i
$742$	1.90386	−	2.38736i	0.0698928	−	0.0876427i
$743$	1.56452	+	20.8771i	0.0573967	+	0.765905i	0.949439	+	0.313953i	$0.101653\pi$
$743$	1.56452	+	20.8771i	0.0573967	+	0.765905i	−0.892042	+	0.451953i	$0.850728\pi$
$744$	24.5397	+	7.56948i	0.899668	+	0.277511i
$745$	3.42299	−	2.33375i	0.125408	−	0.0855021i
$746$	20.9264	−	3.15415i	0.766170	−	0.115481i
$747$	7.80588	−	34.1998i	0.285602	−	1.25131i
$748$	−13.4187	−	12.4507i	−0.490636	−	0.455244i
$749$	0.976351	−	13.0285i	0.0356751	−	0.476051i
$750$	0.916110	−	2.33421i	0.0334516	−	0.0852333i
$751$	−28.8695	−	4.35137i	−1.05346	−	0.158784i	−0.400594	−	0.916256i	$-0.631196\pi$
$751$	−28.8695	−	4.35137i	−1.05346	−	0.158784i	−0.652868	+	0.757472i	$0.726434\pi$
$752$	9.13812	−	4.40068i	0.333233	−	0.160476i
$753$	−2.38113	+	1.14669i	−0.0867734	+	0.0417879i
$754$	−16.2225	−	2.44515i	−0.590788	−	0.0890470i
$755$	−5.10545	+	13.0085i	−0.185806	+	0.473427i
$756$	−0.0566484	+	0.755920i	−0.00206028	+	0.0274925i
$757$	−15.1351	−	14.0433i	−0.550095	−	0.510414i	0.355432	−	0.934702i	$-0.384334\pi$
$757$	−15.1351	−	14.0433i	−0.550095	−	0.510414i	−0.905527	+	0.424288i	$0.860524\pi$
$758$	−1.30920	+	5.73597i	−0.0475522	+	0.208340i
$759$	−41.2720	+	6.22076i	−1.49808	+	0.225799i
$760$	5.83555	−	3.97861i	0.211678	−	0.144319i
$761$	11.8973	+	3.66984i	0.431278	+	0.133032i	0.502791	−	0.864408i	$-0.332307\pi$
$761$	11.8973	+	3.66984i	0.431278	+	0.133032i	−0.0715129	+	0.997440i	$0.522783\pi$
$762$	−2.47205	−	32.9872i	−0.0895530	−	1.19500i
$763$	−2.73415	+	3.42852i	−0.0989830	+	0.124121i
$764$	10.0272	−	3.09298i	0.362771	−	0.111900i
$765$	−8.02555	−	20.4488i	−0.290165	−	0.739327i
$766$	7.27459	+	31.8721i	0.262842	+	1.15158i
$767$	5.78168	−	10.0142i	0.208764	−	0.361591i
$768$	1.25377	+	2.17160i	0.0452417	+	0.0783609i
$769$	−38.3646	+	35.5972i	−1.38346	+	1.28367i	−0.466600	+	0.884469i	$0.654521\pi$
$769$	−38.3646	+	35.5972i	−1.38346	+	1.28367i	−0.916864	+	0.399199i	$0.869288\pi$
$770$	1.79427	+	2.24994i	0.0646609	+	0.0810822i
$771$	46.8554	+	31.9455i	1.68746	+	1.15049i
$772$	12.3861	+	5.96483i	0.445786	+	0.214679i
$773$	−11.0771			−0.398416			−0.199208	−	0.979957i	$-0.563837\pi$
$773$	−11.0771			−0.398416			−0.199208	+	0.979957i	$0.563837\pi$
$774$	16.8104	+	13.4990i	0.604237	+	0.485213i
$775$	10.2413			0.367879
$776$	−12.7364	−	6.13351i	−0.457209	−	0.220180i
$777$	−8.85976	−	6.04048i	−0.317842	−	0.216701i
$778$	−19.1273	−	23.9849i	−0.685747	−	0.859899i
$779$	24.9571	−	23.1568i	0.894182	−	0.829680i
$780$	−4.52722	−	7.84137i	−0.162100	−	0.280766i
$781$	0.109160	−	0.189071i	0.00390606	−	0.00676550i
$782$	−9.03280	−	39.5753i	−0.323012	−	1.41521i
$783$	−1.19790	−	3.05220i	−0.0428094	−	0.109077i
$784$	−5.63469	+	1.73807i	−0.201239	+	0.0620740i
$785$	−7.66892	+	9.61652i	−0.273716	+	0.343228i
$786$	−1.42849	−	19.0618i	−0.0509524	−	0.679913i
$787$	−23.4103	−	7.22111i	−0.834485	−	0.257405i	−0.152070	−	0.988370i	$-0.548594\pi$
$787$	−23.4103	−	7.22111i	−0.834485	−	0.257405i	−0.682415	+	0.730965i	$0.739070\pi$
$788$	−7.23750	+	4.93444i	−0.257825	+	0.175782i
$789$	−53.3882	+	8.04697i	−1.90067	+	0.286480i
$790$	−0.972632	+	4.26138i	−0.0346047	+	0.151613i
$791$	−1.12873	−	1.04731i	−0.0401330	−	0.0372380i
$792$	0.673140	−	8.98242i	0.0239190	−	0.319177i
$793$	−7.44116	+	18.9598i	−0.264243	+	0.673281i
$794$	−18.1293	−	2.73256i	−0.643386	−	0.0969749i
$795$	−6.56766	+	3.16282i	−0.232931	+	0.112174i
$796$	−2.68137	+	1.29128i	−0.0950387	+	0.0457682i
$797$	−13.0963	−	1.97394i	−0.463893	−	0.0699206i	−0.0870626	−	0.996203i	$-0.527748\pi$
$797$	−13.0963	−	1.97394i	−0.463893	−	0.0699206i	−0.376831	+	0.926282i	$0.622986\pi$
$798$	−6.79638	+	17.3169i	−0.240589	+	0.613011i
$799$	5.06423	−	67.5775i	0.179160	−	2.39072i
$800$	0.733052	+	0.680173i	0.0259173	+	0.0240477i
$801$	−4.72805	+	20.7149i	−0.167057	+	0.731926i
$802$	1.76325	−	0.265767i	0.0622624	−	0.00938455i
$803$	−18.2366	+	12.4335i	−0.643555	+	0.438768i
$804$	−21.0203	−	6.48389i	−0.741327	−	0.228669i
$805$	0.476902	+	6.36382i	0.0168086	+	0.224295i
$806$	23.0567	−	28.9122i	0.812137	−	1.01839i
$807$	−51.9237	+	16.0164i	−1.82780	+	0.563802i
$808$	−0.474337	−	1.20859i	−0.0166871	−	0.0425180i
$809$	2.94924	+	12.9215i	0.103690	+	0.454294i	0.999942	+	0.0107500i	$0.00342189\pi$
$809$	2.94924	+	12.9215i	0.103690	+	0.454294i	−0.896253	+	0.443544i	$0.853721\pi$
$810$	−4.02689	+	6.97477i	−0.141490	+	0.245069i
$811$	14.9260	+	25.8526i	0.524122	+	0.907806i	0.999606	+	0.0280813i	$0.00893973\pi$
$811$	14.9260	+	25.8526i	0.524122	+	0.907806i	−0.475484	+	0.879725i	$0.657727\pi$
$812$	−3.49842	+	3.24606i	−0.122770	+	0.113914i
$813$	−2.43210	−	3.04976i	−0.0852976	−	0.106960i
$814$	9.21560	+	6.28309i	0.323007	+	0.220222i
$815$	−14.6799	−	7.06949i	−0.514216	−	0.247633i
$816$	16.7541			0.586510
$817$	25.9600	+	38.3542i	0.908226	+	1.34184i
$818$	39.3443			1.37564
$819$	11.2352	+	5.41058i	0.392589	+	0.189061i
$820$	3.98281	+	2.71543i	0.139086	+	0.0948270i
$821$	24.6599	+	30.9225i	0.860635	+	1.07920i	0.996084	+	0.0884174i	$0.0281809\pi$
$821$	24.6599	+	30.9225i	0.860635	+	1.07920i	−0.135449	+	0.990784i	$0.543248\pi$
$822$	21.3935	−	19.8502i	0.746183	−	0.692357i
$823$	−16.4199	−	28.4401i	−0.572361	−	0.991359i	−0.996323	−	0.0856785i	$-0.972694\pi$
$823$	−16.4199	−	28.4401i	−0.572361	−	0.991359i	0.423962	−	0.905680i	$-0.360639\pi$
$824$	−6.43899	+	11.1527i	−0.224313	+	0.388521i
$825$	−1.52871	−	6.69771i	−0.0532228	−	0.233184i
$826$	−1.22892	−	3.13124i	−0.0427597	−	0.108950i
$827$	15.8564	−	4.89106i	0.551382	−	0.170079i	−0.00653021	−	0.999979i	$-0.502079\pi$
$827$	15.8564	−	4.89106i	0.551382	−	0.170079i	0.557913	+	0.829900i	$0.311602\pi$
$828$	12.4542	−	15.6170i	0.432812	−	0.542729i
$829$	4.05006	+	54.0443i	0.140664	+	1.87704i	0.407376	+	0.913261i	$0.366444\pi$
$829$	4.05006	+	54.0443i	0.140664	+	1.87704i	−0.266711	+	0.963777i	$0.585937\pi$
$830$	10.1955	+	3.14490i	0.353892	+	0.109161i
$831$	65.2830	−	44.5092i	2.26464	−	1.54401i
$832$	3.57054	−	0.538172i	0.123786	−	0.0186578i
$833$	−8.76695	+	38.4105i	−0.303757	+	1.33085i
$834$	42.9808	+	39.8803i	1.48830	+	1.38094i
$835$	−0.612068	+	8.16748i	−0.0211815	+	0.282647i
$836$	7.06934	−	18.0124i	0.244498	−	0.622972i
$837$	7.30829	+	1.10155i	0.252611	+	0.0380750i
$838$	30.4739	−	14.6755i	1.05270	−	0.506956i
$839$	−13.7332	+	6.61355i	−0.474122	+	0.228325i	−0.655656	−	0.755060i	$-0.727608\pi$
$839$	−13.7332	+	6.61355i	−0.474122	+	0.228325i	0.181534	+	0.983385i	$0.441894\pi$
$840$	−2.60450	−	0.392566i	−0.0898639	−	0.0135448i
$841$	−3.05326	+	7.77957i	−0.105285	+	0.268261i
$842$	−1.05746	+	14.1108i	−0.0364425	+	0.486292i
$843$	29.7442	+	27.5986i	1.02444	+	0.950545i
$844$	1.93496	−	8.47760i	0.0666039	−	0.291811i
$845$	−0.0379567	+	0.00572106i	−0.00130575	+	0.000196810i
$846$	27.5523	−	18.7848i	0.947267	−	0.645836i
$847$	−3.50703	−	1.08178i	−0.120503	−	0.0371703i
$848$	−0.217244	−	2.89891i	−0.00746017	−	0.0995491i
$849$	−12.4697	+	15.6365i	−0.427960	+	0.536644i
$850$	6.38462	−	1.96939i	0.218991	−	0.0675497i
$851$	9.03633	+	23.0242i	0.309762	+	0.789260i
$852$	0.0444642	+	0.194810i	0.00152332	+	0.00667409i
$853$	−16.3602	+	28.3367i	−0.560162	+	0.970228i	0.437320	+	0.899306i	$0.355928\pi$
$853$	−16.3602	+	28.3367i	−0.560162	+	0.970228i	−0.997482	+	0.0709226i	$0.977406\pi$
$854$	2.96247	+	5.13115i	0.101374	+	0.175584i
$855$	17.0222	−	15.7943i	0.582148	−	0.540154i
$856$	−7.75508	−	9.72456i	−0.265063	−	0.332379i
$857$	−1.91152	−	1.30325i	−0.0652964	−	0.0445183i	0.530232	−	0.847853i	$-0.322105\pi$
$857$	−1.91152	−	1.30325i	−0.0652964	−	0.0445183i	−0.595528	+	0.803334i	$0.703057\pi$
$858$	−22.3499	−	10.7631i	−0.763013	−	0.367448i
$859$	8.87489			0.302807			0.151404	−	0.988472i	$-0.451621\pi$
$859$	8.87489			0.302807			0.151404	+	0.988472i	$0.451621\pi$
$860$	−4.47641	+	4.79184i	−0.152644	+	0.163400i
$861$	−12.6966			−0.432698
$862$	−14.2913	−	6.88232i	−0.486763	−	0.234413i
$863$	16.0825	+	10.9649i	0.547456	+	0.373249i	0.805236	−	0.592954i	$-0.202039\pi$
$863$	16.0825	+	10.9649i	0.547456	+	0.373249i	−0.257780	+	0.966204i	$0.582991\pi$
$864$	0.449954	+	0.564224i	0.0153077	+	0.0191953i
$865$	8.35514	−	7.75244i	0.284083	−	0.263591i
$866$	3.14803	+	5.45254i	0.106974	+	0.185285i
$867$	34.6567	−	60.0272i	1.17700	−	2.03863i
$868$	−2.39376	−	10.4877i	−0.0812494	−	0.355977i
$869$	4.37502	+	11.1474i	0.148413	+	0.378149i
$870$	10.8867	−	3.35810i	0.369094	−	0.113850i
$871$	−19.7500	+	24.7657i	−0.669202	+	0.839152i
$872$	0.311986	+	4.16317i	0.0105652	+	0.140983i
$873$	−44.4125	−	13.6994i	−1.50313	−	0.463656i
$874$	35.4537	−	24.1719i	1.19924	−	0.817628i
$875$	−1.03867	+	0.156554i	−0.0351133	+	0.00529248i
$876$	4.49525	−	19.6950i	0.151880	−	0.665431i
$877$	−0.161343	−	0.149705i	−0.00544818	−	0.00505517i	0.677444	−	0.735574i	$-0.263088\pi$
$877$	−0.161343	−	0.149705i	−0.00544818	−	0.00505517i	−0.682892	+	0.730519i	$0.739278\pi$
$878$	−2.70389	+	36.0809i	−0.0912519	+	1.21767i
$879$	25.1021	−	63.9592i	0.846674	−	2.15729i
$880$	2.70911	+	0.408332i	0.0913240	+	0.0137649i
$881$	13.1505	−	6.33293i	0.443050	−	0.213362i	−0.199039	−	0.979992i	$-0.563782\pi$
$881$	13.1505	−	6.33293i	0.443050	−	0.213362i	0.642089	+	0.766630i	$0.278068\pi$
$882$	−17.4671	+	8.41173i	−0.588149	+	0.283238i
$883$	31.5614	+	4.75711i	1.06212	+	0.160090i	0.656786	−	0.754077i	$-0.271915\pi$
$883$	31.5614	+	4.75711i	1.06212	+	0.160090i	0.405339	+	0.914167i	$0.367154\pi$
$884$	8.81418	−	22.4582i	0.296453	−	0.755349i
$885$	−0.600091	+	8.00766i	−0.0201718	+	0.269174i
$886$	−23.3018	−	21.6209i	−0.782838	−	0.726367i
$887$	−5.17593	+	22.6773i	−0.173791	+	0.761428i	0.810624	+	0.585567i	$0.199128\pi$
$887$	−5.17593	+	22.6773i	−0.173791	+	0.761428i	−0.984415	+	0.175861i	$0.943729\pi$
$888$	−10.0945	+	1.52150i	−0.338749	+	0.0510583i
$889$	−11.4491	+	7.80587i	−0.383991	+	0.261801i
$890$	−6.17546	−	1.90488i	−0.207002	−	0.0638516i
$891$	1.64892	+	22.0033i	0.0552409	+	0.737138i
$892$	4.66759	−	5.85297i	0.156283	−	0.195972i
$893$	68.4521	−	21.1147i	2.29066	−	0.706576i
$894$	3.79531	+	9.67029i	0.126934	+	0.323423i
$895$	−1.49387	−	6.54506i	−0.0499345	−	0.218777i
$896$	0.525199	−	0.909671i	0.0175457	−	0.0303900i
$897$	−27.5050	−	47.6400i	−0.918365	−	1.59065i
$898$	−0.955102	+	0.886205i	−0.0318722	+	0.0295730i
$899$	29.0114	+	36.3791i	0.967583	+	1.21331i
$900$	2.71651	+	1.85208i	0.0905502	+	0.0617361i
$901$	−17.4998	−	8.42745i	−0.583002	−	0.280759i
$902$	13.2065			0.439729
$903$	2.63194	−	17.0701i	0.0875854	−	0.568056i
$904$	−1.46589			−0.0487549
$905$	−11.5722	−	5.57287i	−0.384672	−	0.185248i
$906$	−28.9528	−	19.7397i	−0.961893	−	0.655807i
$907$	26.2313	+	32.8930i	0.870996	+	1.09219i	0.994996	+	0.0999123i	$0.0318562\pi$
$907$	26.2313	+	32.8930i	0.870996	+	1.09219i	−0.124000	+	0.992282i	$0.539572\pi$
$908$	−9.52677	+	8.83955i	−0.316157	+	0.293351i
$909$	−2.13434	−	3.69678i	−0.0707916	−	0.122615i
$910$	−1.89642	+	3.28470i	−0.0628658	+	0.108887i
$911$	−7.79918	−	34.1704i	−0.258398	−	1.13212i	−0.922964	−	0.384887i	$-0.874240\pi$
$911$	−7.79918	−	34.1704i	−0.258398	−	1.13212i	0.664565	−	0.747230i	$-0.268617\pi$
$912$	6.47030	+	16.4860i	0.214253	+	0.545907i
$913$	27.9328	−	8.61612i	0.924440	−	0.285152i
$914$	12.0091	−	15.0589i	0.397226	−	0.498106i
$915$	−1.05700	−	14.1047i	−0.0349434	−	0.466287i
$916$	13.0847	+	4.03610i	0.432331	+	0.133356i
$917$	−6.61592	+	4.51066i	−0.218477	+	0.148955i
$918$	4.76795	−	0.718653i	0.157366	−	0.0237191i
$919$	−0.260531	+	1.14146i	−0.00859411	+	0.0376533i	−0.979043	−	0.203653i	$-0.934719\pi$
$919$	−0.260531	+	1.14146i	−0.00859411	+	0.0376533i	0.970449	+	0.241306i	$0.0775758\pi$
$920$	4.45364	+	4.13237i	0.146832	+	0.136240i
$921$	−0.874148	+	11.6647i	−0.0288042	+	0.384365i
$922$	6.31973	−	16.1024i	0.208129	−	0.530304i
$923$	0.284527	+	0.0428856i	0.00936534	+	0.00141160i
$924$	−6.50155	+	3.13098i	−0.213885	+	0.103002i
$925$	−3.66795	+	1.76639i	−0.120601	+	0.0580786i
$926$	40.8027	+	6.15002i	1.34086	+	0.202102i
$927$	−15.4686	+	39.4134i	−0.508056	+	1.29451i
$928$	−0.339531	+	4.53072i	−0.0111456	+	0.148728i
$929$	4.55513	+	4.22655i	0.149449	+	0.138668i	0.751354	−	0.659899i	$-0.229401\pi$
$929$	4.55513	+	4.22655i	0.149449	+	0.138668i	−0.601905	+	0.798568i	$0.705591\pi$
$930$	−5.71447	+	25.0367i	−0.187385	+	0.820986i
$931$	−41.1818	+	6.20715i	−1.34968	+	0.203431i
$932$	12.7420	−	8.68736i	0.417379	−	0.284564i
$933$	−21.3485	−	6.58515i	−0.698920	−	0.215588i
$934$	−0.700266	−	9.34440i	−0.0229134	−	0.305758i
$935$	11.4131	−	14.3116i	0.373250	−	0.468040i
$936$	11.3444	−	3.49928i	0.370803	−	0.114378i
$937$	−19.3227	−	49.2333i	−0.631244	−	1.60838i	−0.784453	−	0.620189i	$-0.787056\pi$
$937$	−19.3227	−	49.2333i	−0.631244	−	1.60838i	0.153209	−	0.988194i	$-0.451039\pi$
$938$	2.05045	+	8.98361i	0.0669496	+	0.293325i
$939$	−6.91801	+	11.9824i	−0.225761	+	0.391029i
$940$	5.07127	+	8.78370i	0.165407	+	0.286493i
$941$	−17.0988	+	15.8654i	−0.557405	+	0.517197i	−0.907799	−	0.419406i	$-0.862238\pi$
$941$	−17.0988	+	15.8654i	−0.557405	+	0.517197i	0.350393	+	0.936603i	$0.386048\pi$
$942$	−19.2302	−	24.1139i	−0.626553	−	0.785673i
$943$	24.1974	+	16.4975i	0.787977	+	0.537233i
$944$	−2.88524	−	1.38946i	−0.0939066	−	0.0452230i
$945$	−0.758039			−0.0246590
$946$	−2.73764	+	17.7557i	−0.0890085	+	0.577286i
$947$	44.6099			1.44963			0.724813	−	0.688946i	$-0.241926\pi$
$947$	44.6099			1.44963			0.724813	+	0.688946i	$0.241926\pi$
$948$	−9.87499	−	4.75555i	−0.320725	−	0.154453i
$949$	−24.0354	−	16.3870i	−0.780222	−	0.531946i
$950$	4.40358	+	5.52191i	0.142871	+	0.179154i
$951$	−23.3569	+	21.6720i	−0.757398	+	0.702763i
$952$	−3.50909	−	6.07793i	−0.113730	−	0.196987i
$953$	−5.06575	+	8.77414i	−0.164096	+	0.284222i	−0.936334	−	0.351111i	$-0.885804\pi$
$953$	−5.06575	+	8.77414i	−0.164096	+	0.284222i	0.772238	+	0.635333i	$0.219137\pi$
$954$	−2.12680	−	9.31814i	−0.0688578	−	0.301686i
$955$	3.83366	+	9.76800i	0.124054	+	0.316085i
$956$	−18.8576	+	5.81681i	−0.609899	+	0.188129i
$957$	19.4611	−	24.4034i	0.629087	−	0.788850i
$958$	−2.96152	−	39.5187i	−0.0956823	−	1.27679i
$959$	−11.6819	−	3.60340i	−0.377229	−	0.116360i
$960$	−2.07183	+	1.41255i	−0.0668681	+	0.0455899i
$961$	−73.0592	+	11.0119i	−2.35675	+	0.355222i
$962$	−3.27112	+	14.3317i	−0.105465	+	0.462073i
$963$	−29.9776	−	27.8152i	−0.966015	−	0.896331i
$964$	−0.751475	+	10.0277i	−0.0242034	+	0.322972i
$965$	−5.02254	+	12.7972i	−0.161681	+	0.411957i
$966$	−15.8236	−	2.38502i	−0.509116	−	0.0767368i
$967$	−32.8579	+	15.8236i	−1.05664	+	0.508851i	−0.879778	−	0.475385i	$-0.842309\pi$
$967$	−32.8579	+	15.8236i	−1.05664	+	0.508851i	−0.176862	+	0.984236i	$0.556595\pi$
$968$	−3.14798	+	1.51599i	−0.101180	+	0.0487257i
$969$	117.009	+	17.6363i	3.75887	+	0.566558i
$970$	5.16457	−	13.1591i	0.165824	−	0.422514i
$971$	4.57532	−	61.0534i	0.146829	−	1.95930i	−0.112873	−	0.993609i	$-0.536005\pi$
$971$	4.57532	−	61.0534i	0.146829	−	1.95930i	0.259702	−	0.965689i	$-0.416376\pi$
$972$	−16.3912	−	15.2088i	−0.525748	−	0.487823i
$973$	5.46531	−	23.9451i	0.175210	−	0.767644i
$974$	−39.8237	+	6.00246i	−1.27603	+	0.192331i
$975$	7.48112	−	5.10054i	0.239588	−	0.163348i
$976$	5.39007	+	1.66262i	0.172532	+	0.0532190i
$977$	−4.53766	−	60.5509i	−0.145173	−	1.93719i	−0.309725	−	0.950826i	$-0.600237\pi$
$977$	−4.53766	−	60.5509i	−0.145173	−	1.93719i	0.164552	−	0.986368i	$-0.447382\pi$
$978$	25.4738	−	31.9431i	0.814561	−	1.02143i
$979$	−16.9190	+	5.21881i	−0.540732	+	0.166794i
$980$	−2.15429	−	5.48905i	−0.0688164	−	0.175341i
$981$	3.05433	+	13.3819i	0.0975173	+	0.427251i
$982$	−4.50832	+	7.80864i	−0.143866	+	0.249184i
$983$	−11.3905	−	19.7289i	−0.363301	−	0.629256i	0.625201	−	0.780464i	$-0.285017\pi$
$983$	−11.3905	−	19.7289i	−0.363301	−	0.629256i	−0.988502	+	0.151208i	$0.951684\pi$
$984$	−8.86069	+	8.22152i	−0.282469	+	0.262092i
$985$	−5.46150	−	6.84851i	−0.174018	−	0.218212i
$986$	25.0819	+	17.1006i	0.798770	+	0.544592i
$987$	−24.0691	−	11.5911i	−0.766127	−	0.368947i
$988$	25.5028			0.811353
$989$	−27.1963	+	29.1127i	−0.864793	+	0.925730i
$990$	9.00761			0.286281
$991$	2.86702	+	1.38068i	0.0910739	+	0.0438589i	0.478866	−	0.877888i	$-0.341048\pi$
$991$	2.86702	+	1.38068i	0.0910739	+	0.0438589i	−0.387792	+	0.921747i	$0.626762\pi$
$992$	−8.46177	−	5.76913i	−0.268661	−	0.183170i
$993$	−46.6253	−	58.4663i	−1.47961	−	1.85537i
$994$	0.0613590	−	0.0569329i	0.00194619	−	0.00180580i
$995$	−1.48805	−	2.57738i	−0.0471743	−	0.0817083i
$996$	−13.3772	+	23.1700i	−0.423873	+	0.734169i
$997$	1.28347	+	5.62324i	0.0406479	+	0.178090i	0.991177	−	0.132546i	$-0.0423152\pi$
$997$	1.28347	+	5.62324i	0.0406479	+	0.178090i	−0.950529	+	0.310636i	$0.899458\pi$
$998$	0.133781	+	0.340868i	0.00423476	+	0.0107900i
$999$	−2.80747	+	0.865991i	−0.0888246	+	0.0273987i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.c.111.1	yes	48
43.31	even	21	inner	430.2.q.c.31.1	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.c.31.1	✓	48	43.31	even	21	inner
430.2.q.c.111.1	yes	48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.900969 + 0.433884i) q^{2} +(-2.07183 - 1.41255i) q^{3} +(0.623490 + 0.781831i) q^{4} +(-0.733052 + 0.680173i) q^{5} +(-1.25377 - 2.17160i) q^{6} +(-0.525199 + 0.909671i) q^{7} +(0.222521 + 0.974928i) q^{8} +(1.20117 + 3.06053i) q^{9} +O(q^{10})\)	\(q+(0.900969 + 0.433884i) q^{2} +(-2.07183 - 1.41255i) q^{3} +(0.623490 + 0.781831i) q^{4} +(-0.733052 + 0.680173i) q^{5} +(-1.25377 - 2.17160i) q^{6} +(-0.525199 + 0.909671i) q^{7} +(0.222521 + 0.974928i) q^{8} +(1.20117 + 3.06053i) q^{9} +(-0.955573 + 0.294755i) q^{10} +(-1.70818 + 2.14199i) q^{11} +(-0.187389 - 2.50054i) q^{12} +(-3.45045 - 1.06432i) q^{13} +(-0.867879 + 0.591710i) q^{14} +(2.47954 - 0.373731i) q^{15} +(-0.222521 + 0.974928i) q^{16} +(4.89786 + 4.54455i) q^{17} +(-0.245698 + 3.27861i) q^{18} +(-2.58033 + 6.57457i) q^{19} +(-0.988831 - 0.149042i) q^{20} +(2.37308 - 1.14282i) q^{21} +(-2.46839 + 1.18872i) q^{22} +(-6.00762 - 0.905502i) q^{23} +(0.916110 - 2.33421i) q^{24} +(0.0747301 - 0.997204i) q^{25} +(-2.64696 - 2.45602i) q^{26} +(0.160587 - 0.703576i) q^{27} +(-1.03867 + 0.156554i) q^{28} +(3.75396 - 2.55940i) q^{29} +(2.39615 + 0.739113i) q^{30} +(0.765334 + 10.2127i) q^{31} +(-0.623490 + 0.781831i) q^{32} +(6.56474 - 2.02495i) q^{33} +(2.44101 + 6.21960i) q^{34} +(-0.233735 - 1.02406i) q^{35} +(-1.64390 + 2.84732i) q^{36} +(-2.03556 - 3.52569i) q^{37} +(-5.17739 + 4.80392i) q^{38} +(5.64535 + 7.07904i) q^{39} +(-0.826239 - 0.563320i) q^{40} +(-4.34304 - 2.09150i) q^{41} +2.63392 q^{42} +(3.71223 - 5.40549i) q^{43} -2.73971 q^{44} +(-2.96220 - 1.42652i) q^{45} +(-5.01979 - 3.42244i) q^{46} +(-6.32377 - 7.92976i) q^{47} +(1.83816 - 1.70557i) q^{48} +(2.94833 + 5.10666i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-3.72813 - 16.3340i) q^{51} +(-1.31920 - 3.36126i) q^{52} +(-2.77789 + 0.856866i) q^{53} +(0.449954 - 0.564224i) q^{54} +(-0.204739 - 2.73205i) q^{55} +(-1.00373 - 0.309610i) q^{56} +(14.6329 - 9.97656i) q^{57} +(4.49268 - 0.677163i) q^{58} +(-0.712596 + 3.12209i) q^{59} +(1.83816 + 1.70557i) q^{60} +(0.421528 - 5.62489i) q^{61} +(-3.74157 + 9.53336i) q^{62} +(-3.41492 - 0.514717i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(3.25328 - 1.56670i) q^{65} +(6.79322 + 1.02391i) q^{66} +(3.20497 - 8.16612i) q^{67} +(-0.499306 + 6.66278i) q^{68} +(11.1677 + 10.3621i) q^{69} +(0.233735 - 1.02406i) q^{70} +(-0.0787975 + 0.0118768i) q^{71} +(-2.71651 + 1.85208i) q^{72} +(7.69834 + 2.37462i) q^{73} +(-0.304235 - 4.05973i) q^{74} +(-1.56343 + 1.96048i) q^{75} +(-6.74901 + 2.08179i) q^{76} +(-1.05137 - 2.67885i) q^{77} +(2.01480 + 8.82742i) q^{78} +(2.18548 - 3.78537i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(5.90384 - 5.47796i) q^{81} +(-3.00547 - 3.76874i) q^{82} +(-8.81559 - 6.01037i) q^{83} +(2.37308 + 1.14282i) q^{84} -6.68146 q^{85} +(5.68996 - 3.25951i) q^{86} -11.3929 q^{87} +(-2.46839 - 1.18872i) q^{88} +(5.33963 + 3.64050i) q^{89} +(-2.04991 - 2.57050i) q^{90} +(2.78035 - 2.57979i) q^{91} +(-3.03774 - 5.26151i) q^{92} +(12.8403 - 22.2400i) q^{93} +(-2.25693 - 9.88825i) q^{94} +(-2.58033 - 6.57457i) q^{95} +(2.39615 - 0.739113i) q^{96} +(-8.81384 + 11.0522i) q^{97} +(0.440658 + 5.88018i) q^{98} +(-8.60743 - 2.65504i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9}+O(q^{10}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9} - 4 q^{10} + q^{11} + 14 q^{12} - 23 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{17} - 20 q^{18} - 3 q^{19} + 4 q^{20} - 8 q^{21} - q^{22} + 7 q^{23} + 4 q^{25} - 19 q^{26} + 32 q^{27} + 4 q^{28} + 30 q^{29} + 9 q^{31} + 8 q^{32} + 39 q^{33} - 8 q^{34} - 22 q^{35} - 29 q^{36} - 37 q^{37} - 11 q^{38} - 52 q^{39} - 4 q^{40} - 28 q^{41} - 6 q^{42} + 41 q^{43} + 8 q^{44} + 2 q^{45} - 28 q^{46} + 3 q^{47} - 41 q^{49} + 24 q^{50} - 30 q^{51} - 9 q^{52} - 69 q^{53} + 3 q^{54} + 10 q^{55} - 11 q^{56} + 116 q^{57} + 5 q^{58} + 10 q^{59} - 19 q^{61} - 93 q^{62} + 34 q^{63} - 8 q^{64} - 3 q^{65} - 18 q^{66} + 3 q^{67} + 8 q^{68} + 42 q^{69} + 22 q^{70} - 36 q^{71} + 22 q^{72} - 56 q^{73} + 9 q^{74} - 10 q^{76} + 3 q^{77} + 45 q^{78} + 16 q^{79} - 24 q^{80} - 19 q^{81} + 14 q^{82} + 64 q^{83} - 8 q^{84} - 30 q^{85} + 36 q^{86} + 78 q^{87} - q^{88} - 75 q^{89} + 5 q^{90} + 5 q^{91} + 14 q^{92} - 10 q^{93} - 45 q^{94} - 3 q^{95} + 33 q^{97} - q^{98} - 11 q^{99}+O(q^{100}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9 - 4 * q^10 + q^11 + 14 * q^12 - 23 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^17 - 20 * q^18 - 3 * q^19 + 4 * q^20 - 8 * q^21 - q^22 + 7 * q^23 + 4 * q^25 - 19 * q^26 + 32 * q^27 + 4 * q^28 + 30 * q^29 + 9 * q^31 + 8 * q^32 + 39 * q^33 - 8 * q^34 - 22 * q^35 - 29 * q^36 - 37 * q^37 - 11 * q^38 - 52 * q^39 - 4 * q^40 - 28 * q^41 - 6 * q^42 + 41 * q^43 + 8 * q^44 + 2 * q^45 - 28 * q^46 + 3 * q^47 - 41 * q^49 + 24 * q^50 - 30 * q^51 - 9 * q^52 - 69 * q^53 + 3 * q^54 + 10 * q^55 - 11 * q^56 + 116 * q^57 + 5 * q^58 + 10 * q^59 - 19 * q^61 - 93 * q^62 + 34 * q^63 - 8 * q^64 - 3 * q^65 - 18 * q^66 + 3 * q^67 + 8 * q^68 + 42 * q^69 + 22 * q^70 - 36 * q^71 + 22 * q^72 - 56 * q^73 + 9 * q^74 - 10 * q^76 + 3 * q^77 + 45 * q^78 + 16 * q^79 - 24 * q^80 - 19 * q^81 + 14 * q^82 + 64 * q^83 - 8 * q^84 - 30 * q^85 + 36 * q^86 + 78 * q^87 - q^88 - 75 * q^89 + 5 * q^90 + 5 * q^91 + 14 * q^92 - 10 * q^93 - 45 * q^94 - 3 * q^95 + 33 * q^97 - q^98 - 11 * q^99

Introduction

L-functions

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