LMFDB - Embedded newform 990.2.t.a.131.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(131,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.131"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.t (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.1
Character	$\chi$	$=$	990.131
Dual form			990.2.t.a.461.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.72761 + 0.123910i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +(0.971116 + 1.43420i) q^{6} +(4.54797 - 2.62577i) q^{7} +1.00000 q^{8} +(2.96929 - 0.428137i) q^{9} -1.00000i q^{10} +(-2.48417 - 2.19748i) q^{11} +(0.756497 - 1.55811i) q^{12} +(5.39031 + 3.11210i) q^{13} +(-4.54797 - 2.62577i) q^{14} +(-1.55811 - 0.756497i) q^{15} +(-0.500000 - 0.866025i) q^{16} -4.35881 q^{17} +(-1.85542 - 2.35741i) q^{18} +0.748972i q^{19} +(-0.866025 + 0.500000i) q^{20} +(-7.53177 + 5.09986i) q^{21} +(-0.660985 + 3.25009i) q^{22} +(2.87695 + 1.66101i) q^{23} +(-1.72761 + 0.123910i) q^{24} +(0.500000 + 0.866025i) q^{25} -6.22419i q^{26} +(-5.07674 + 1.10758i) q^{27} +5.25154i q^{28} +(5.20486 + 9.01507i) q^{29} +(0.123910 + 1.72761i) q^{30} +(2.83113 - 4.90367i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(4.56397 + 3.48857i) q^{33} +(2.17940 + 3.77484i) q^{34} +5.25154 q^{35} +(-1.11387 + 2.78555i) q^{36} -7.09847 q^{37} +(0.648629 - 0.374486i) q^{38} +(-9.69798 - 4.70858i) q^{39} +(0.866025 + 0.500000i) q^{40} +(2.75133 - 4.76544i) q^{41} +(8.18249 + 3.97278i) q^{42} +(1.41561 - 0.817304i) q^{43} +(3.14515 - 1.05262i) q^{44} +(2.78555 + 1.11387i) q^{45} -3.32202i q^{46} +(0.640537 - 0.369814i) q^{47} +(0.971116 + 1.43420i) q^{48} +(10.2894 - 17.8217i) q^{49} +(0.500000 - 0.866025i) q^{50} +(7.53033 - 0.540100i) q^{51} +(-5.39031 + 3.11210i) q^{52} -2.46463i q^{53} +(3.49756 + 3.84279i) q^{54} +(-1.05262 - 3.14515i) q^{55} +(4.54797 - 2.62577i) q^{56} +(-0.0928052 - 1.29393i) q^{57} +(5.20486 - 9.01507i) q^{58} +(-0.877216 - 0.506461i) q^{59} +(1.43420 - 0.971116i) q^{60} +(0.800939 - 0.462422i) q^{61} -5.66227 q^{62} +(12.3801 - 9.74384i) q^{63} +1.00000 q^{64} +(3.11210 + 5.39031i) q^{65} +(0.739208 - 5.69680i) q^{66} +(-0.821341 + 1.42261i) q^{67} +(2.17940 - 3.77484i) q^{68} +(-5.17607 - 2.51310i) q^{69} +(-2.62577 - 4.54797i) q^{70} -6.56094i q^{71} +(2.96929 - 0.428137i) q^{72} +9.67062i q^{73} +(3.54924 + 6.14746i) q^{74} +(-0.971116 - 1.43420i) q^{75} +(-0.648629 - 0.374486i) q^{76} +(-17.0680 - 3.47119i) q^{77} +(0.771240 + 10.7530i) q^{78} +(10.6885 - 6.17100i) q^{79} -1.00000i q^{80} +(8.63340 - 2.54253i) q^{81} -5.50266 q^{82} +(2.86275 + 4.95842i) q^{83} +(-0.650719 - 9.07263i) q^{84} +(-3.77484 - 2.17940i) q^{85} +(-1.41561 - 0.817304i) q^{86} +(-10.1090 - 14.9296i) q^{87} +(-2.48417 - 2.19748i) q^{88} -8.41930i q^{89} +(-0.428137 - 2.96929i) q^{90} +32.6866 q^{91} +(-2.87695 + 1.66101i) q^{92} +(-4.28349 + 8.82245i) q^{93} +(-0.640537 - 0.369814i) q^{94} +(-0.374486 + 0.648629i) q^{95} +(0.756497 - 1.55811i) q^{96} +(8.16763 + 14.1467i) q^{97} -20.5787 q^{98} +(-8.31705 - 5.46138i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{6} + 48 q^{8} + 10 q^{9} - 6 q^{11} + 4 q^{12} + 24 q^{13} - 4 q^{15} - 24 q^{16} - 12 q^{17} - 8 q^{18} - 16 q^{21} + 12 q^{22} + 36 q^{23} - 2 q^{24} + 24 q^{25}+ \cdots - 48 q^{99}+O(q^{100}) $ 48 * q - 24 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^6 + 48 * q^8 + 10 * q^9 - 6 * q^11 + 4 * q^12 + 24 * q^13 - 4 * q^15 - 24 * q^16 - 12 * q^17 - 8 * q^18 - 16 * q^21 + 12 * q^22 + 36 * q^23 - 2 * q^24 + 24 * q^25 - 8 * q^27 + 8 * q^30 - 24 * q^32 + 2 * q^33 + 6 * q^34 - 2 * q^36 - 6 * q^38 - 40 * q^39 - 6 * q^41 + 8 * q^42 + 30 * q^43 - 6 * q^44 - 2 * q^48 + 24 * q^49 + 24 * q^50 + 22 * q^51 - 24 * q^52 + 22 * q^54 + 40 * q^57 - 54 * q^59 - 4 * q^60 - 38 * q^63 + 48 * q^64 + 8 * q^66 - 6 * q^67 + 6 * q^68 + 76 * q^69 + 10 * q^72 + 2 * q^75 + 6 * q^76 + 6 * q^77 + 32 * q^78 + 10 * q^81 + 12 * q^82 + 36 * q^83 + 8 * q^84 - 30 * q^86 - 44 * q^87 - 6 * q^88 + 24 * q^91 - 36 * q^92 - 68 * q^93 + 4 * q^96 + 6 * q^97 - 48 * q^98 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.72761	+	0.123910i	−0.997438	+	0.0715395i
$3$	−1.72761	+	0.123910i	−0.997438	+	0.0715395i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	0.971116	+	1.43420i	0.396456	+	0.585510i
$7$	4.54797	−	2.62577i	1.71897	−	0.992448i	0.798154	−	0.602453i	$-0.205810\pi$
$7$	4.54797	−	2.62577i	1.71897	−	0.992448i	0.920817	−	0.389995i	$-0.127523\pi$
$8$	1.00000			0.353553
$9$	2.96929	−	0.428137i	0.989764	−	0.142712i
$10$		−	1.00000i		−	0.316228i
$11$	−2.48417	−	2.19748i	−0.749005	−	0.662564i
$11$	−2.48417	−	2.19748i	−0.749005	−	0.662564i
$12$	0.756497	−	1.55811i	0.218382	−	0.449788i
$13$	5.39031	+	3.11210i	1.49500	+	0.863140i	0.999984	−	0.00574230i	$-0.00182784\pi$
$13$	5.39031	+	3.11210i	1.49500	+	0.863140i	0.495019	+	0.868882i	$0.335161\pi$
$14$	−4.54797	−	2.62577i	−1.21550	−	0.701767i
$15$	−1.55811	−	0.756497i	−0.402303	−	0.195327i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−4.35881			−1.05717			−0.528583	−	0.848881i	$-0.677277\pi$
$17$	−4.35881			−1.05717			−0.528583	+	0.848881i	$0.677277\pi$
$18$	−1.85542	−	2.35741i	−0.437328	−	0.555648i
$19$			0.748972i			0.171826i	0.996303	+	0.0859130i	$0.0273807\pi$
$19$			0.748972i			0.171826i	−0.996303	+	0.0859130i	$0.972619\pi$
$20$	−0.866025	+	0.500000i	−0.193649	+	0.111803i
$21$	−7.53177	+	5.09986i	−1.64357	+	1.11288i
$22$	−0.660985	+	3.25009i	−0.140923	+	0.692922i
$23$	2.87695	+	1.66101i	0.599886	+	0.346344i	0.768997	−	0.639253i	$-0.220756\pi$
$23$	2.87695	+	1.66101i	0.599886	+	0.346344i	−0.169111	+	0.985597i	$0.554090\pi$
$24$	−1.72761	+	0.123910i	−0.352648	+	0.0252930i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$		−	6.22419i		−	1.22066i
$27$	−5.07674	+	1.10758i	−0.977019	+	0.213154i
$28$			5.25154i			0.992448i
$29$	5.20486	+	9.01507i	0.966517	+	1.67406i	0.705482	+	0.708728i	$0.250731\pi$
$29$	5.20486	+	9.01507i	0.966517	+	1.67406i	0.261036	+	0.965329i	$0.415936\pi$
$30$	0.123910	+	1.72761i	0.0226228	+	0.315418i
$31$	2.83113	−	4.90367i	0.508487	−	0.880725i	−0.491465	−	0.870897i	$-0.663538\pi$
$31$	2.83113	−	4.90367i	0.508487	−	0.880725i	0.999952	−	0.00982755i	$-0.00312826\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	4.56397	+	3.48857i	0.794486	+	0.607283i
$34$	2.17940	+	3.77484i	0.373765	+	0.647380i
$35$	5.25154			0.887673
$36$	−1.11387	+	2.78555i	−0.185645	+	0.464259i
$37$	−7.09847			−1.16698			−0.583491	−	0.812120i	$-0.698314\pi$
$37$	−7.09847			−1.16698			−0.583491	+	0.812120i	$0.698314\pi$
$38$	0.648629	−	0.374486i	0.105222	−	0.0607497i
$39$	−9.69798	−	4.70858i	−1.55292	−	0.753977i
$40$	0.866025	+	0.500000i	0.136931	+	0.0790569i
$41$	2.75133	−	4.76544i	0.429686	−	0.744237i	−0.567160	−	0.823608i	$-0.691958\pi$
$41$	2.75133	−	4.76544i	0.429686	−	0.744237i	0.996845	+	0.0793706i	$0.0252910\pi$
$42$	8.18249	+	3.97278i	1.26259	+	0.613013i
$43$	1.41561	−	0.817304i	0.215879	−	0.124638i	−0.388162	−	0.921591i	$-0.626890\pi$
$43$	1.41561	−	0.817304i	0.215879	−	0.124638i	0.604041	+	0.796954i	$0.293556\pi$
$44$	3.14515	−	1.05262i	0.474150	−	0.158688i
$45$	2.78555	+	1.11387i	0.415245	+	0.166046i
$46$		−	3.32202i		−	0.489805i
$47$	0.640537	−	0.369814i	0.0934319	−	0.0539429i	−0.452556	−	0.891736i	$-0.649488\pi$
$47$	0.640537	−	0.369814i	0.0934319	−	0.0539429i	0.545988	+	0.837793i	$0.316154\pi$
$48$	0.971116	+	1.43420i	0.140168	+	0.207009i
$49$	10.2894	−	17.8217i	1.46991	−	2.54595i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	7.53033	−	0.540100i	1.05446	−	0.0756292i
$52$	−5.39031	+	3.11210i	−0.747501	+	0.431570i
$53$		−	2.46463i		−	0.338542i	−0.985570	−	0.169271i	$-0.945859\pi$
$53$		−	2.46463i		−	0.338542i	0.985570	−	0.169271i	$-0.0541414\pi$
$54$	3.49756	+	3.84279i	0.475958	+	0.522938i
$55$	−1.05262	−	3.14515i	−0.141935	−	0.424093i
$56$	4.54797	−	2.62577i	0.607748	−	0.350884i
$57$	−0.0928052	−	1.29393i	−0.0122924	−	0.171386i
$58$	5.20486	−	9.01507i	0.683431	−	1.18374i
$59$	−0.877216	−	0.506461i	−0.114204	−	0.0659356i	0.441810	−	0.897109i	$-0.354337\pi$
$59$	−0.877216	−	0.506461i	−0.114204	−	0.0659356i	−0.556014	+	0.831173i	$0.687670\pi$
$60$	1.43420	−	0.971116i	0.185155	−	0.125371i
$61$	0.800939	−	0.462422i	0.102550	−	0.0592071i	−0.447848	−	0.894110i	$-0.647809\pi$
$61$	0.800939	−	0.462422i	0.102550	−	0.0592071i	0.550398	+	0.834903i	$0.314476\pi$
$62$	−5.66227			−0.719109
$63$	12.3801	−	9.74384i	1.55974	−	1.22761i
$64$	1.00000			0.125000
$65$	3.11210	+	5.39031i	0.386008	+	0.668585i
$66$	0.739208	−	5.69680i	0.0909902	−	0.701228i
$67$	−0.821341	+	1.42261i	−0.100343	+	0.173799i	−0.911826	−	0.410577i	$-0.865327\pi$
$67$	−0.821341	+	1.42261i	−0.100343	+	0.173799i	0.811483	+	0.584376i	$0.198661\pi$
$68$	2.17940	−	3.77484i	0.264292	−	0.457766i
$69$	−5.17607	−	2.51310i	−0.623126	−	0.302541i
$70$	−2.62577	−	4.54797i	−0.313840	−	0.543586i
$71$		−	6.56094i		−	0.778640i	−0.921103	−	0.389320i	$-0.872710\pi$
$71$		−	6.56094i		−	0.778640i	0.921103	−	0.389320i	$-0.127290\pi$
$72$	2.96929	−	0.428137i	0.349934	−	0.0504565i
$73$			9.67062i			1.13186i	0.824453	+	0.565930i	$0.191483\pi$
$73$			9.67062i			1.13186i	−0.824453	+	0.565930i	$0.808517\pi$
$74$	3.54924	+	6.14746i	0.412590	+	0.714627i
$75$	−0.971116	−	1.43420i	−0.112135	−	0.165607i
$76$	−0.648629	−	0.374486i	−0.0744028	−	0.0429565i
$77$	−17.0680	−	3.47119i	−1.94508	−	0.395579i
$78$	0.771240	+	10.7530i	0.0873257	+	1.21754i
$79$	10.6885	−	6.17100i	1.20255	−	0.694292i	0.241427	−	0.970419i	$-0.422384\pi$
$79$	10.6885	−	6.17100i	1.20255	−	0.694292i	0.961121	+	0.276127i	$0.0890511\pi$
$80$		−	1.00000i		−	0.111803i
$81$	8.63340	−	2.54253i	0.959266	−	0.282503i
$82$	−5.50266			−0.607667
$83$	2.86275	+	4.95842i	0.314227	+	0.544258i	0.979273	−	0.202545i	$-0.0649213\pi$
$83$	2.86275	+	4.95842i	0.314227	+	0.544258i	−0.665046	+	0.746803i	$0.731588\pi$
$84$	−0.650719	−	9.07263i	−0.0709993	−	0.989906i
$85$	−3.77484	−	2.17940i	−0.409439	−	0.236390i
$86$	−1.41561	−	0.817304i	−0.152649	−	0.0881321i
$87$	−10.1090	−	14.9296i	−1.08380	−	1.60062i
$88$	−2.48417	−	2.19748i	−0.264813	−	0.234252i
$89$		−	8.41930i		−	0.892444i	−0.894922	−	0.446222i	$-0.852769\pi$
$89$		−	8.41930i		−	0.892444i	0.894922	−	0.446222i	$-0.147231\pi$
$90$	−0.428137	−	2.96929i	−0.0451296	−	0.312991i
$91$	32.6866			3.42649
$92$	−2.87695	+	1.66101i	−0.299943	+	0.173172i
$93$	−4.28349	+	8.82245i	−0.444177	+	0.914845i
$94$	−0.640537	−	0.369814i	−0.0660663	−	0.0381434i
$95$	−0.374486	+	0.648629i	−0.0384215	+	0.0665479i
$96$	0.756497	−	1.55811i	0.0772097	−	0.159024i
$97$	8.16763	+	14.1467i	0.829297	+	1.43638i	0.898590	+	0.438788i	$0.144592\pi$
$97$	8.16763	+	14.1467i	0.829297	+	1.43638i	−0.0692933	+	0.997596i	$0.522074\pi$
$98$	−20.5787			−2.07876
$99$	−8.31705	−	5.46138i	−0.835895	−	0.548890i
$100$	−1.00000			−0.100000
$101$	−3.41322	−	5.91188i	−0.339628	−	0.588254i	0.644734	−	0.764407i	$-0.276968\pi$
$101$	−3.41322	−	5.91188i	−0.339628	−	0.588254i	−0.984363	+	0.176153i	$0.943635\pi$
$102$	−4.23291	−	6.25141i	−0.419120	−	0.618982i
$103$	0.536621	−	0.929456i	0.0528749	−	0.0915820i	−0.838377	−	0.545092i	$-0.816495\pi$
$103$	0.536621	−	0.929456i	0.0528749	−	0.0915820i	0.891251	+	0.453510i	$0.149828\pi$
$104$	5.39031	+	3.11210i	0.528563	+	0.305166i
$105$	−9.07263	+	0.650719i	−0.885398	+	0.0635037i
$106$	−2.13443	+	1.23231i	−0.207314	+	0.119693i
$107$	13.1135			1.26773			0.633863	−	0.773445i	$-0.281468\pi$
$107$	13.1135			1.26773			0.633863	+	0.773445i	$0.281468\pi$
$108$	1.57918	−	4.95037i	0.151956	−	0.476350i
$109$		−	12.7274i		−	1.21906i	−0.792762	−	0.609531i	$-0.791358\pi$
$109$		−	12.7274i		−	1.21906i	0.792762	−	0.609531i	$-0.208642\pi$
$110$	−2.19748	+	2.48417i	−0.209521	+	0.236856i
$111$	12.2634	−	0.879572i	1.16399	−	0.0834853i
$112$	−4.54797	−	2.62577i	−0.429743	−	0.248112i
$113$	−6.01231	−	3.47121i	−0.565591	−	0.326544i	0.189796	−	0.981824i	$-0.439217\pi$
$113$	−6.01231	−	3.47121i	−0.565591	−	0.326544i	−0.755386	+	0.655280i	$0.772551\pi$
$114$	−1.07418	+	0.727339i	−0.100606	+	0.0681215i
$115$	1.66101	+	2.87695i	0.154890	+	0.268277i
$116$	−10.4097			−0.966517
$117$	17.3378	+	6.93293i	1.60288	+	0.640950i
$118$			1.01292i			0.0932470i
$119$	−19.8237	+	11.4452i	−1.81724	+	1.04918i
$120$	−1.55811	−	0.756497i	−0.142235	−	0.0690584i
$121$	1.34220	+	10.9178i	0.122018	+	0.992528i
$122$	−0.800939	−	0.462422i	−0.0725136	−	0.0418657i
$123$	−4.16275	+	8.57376i	−0.375342	+	0.773070i
$124$	2.83113	+	4.90367i	0.254243	+	0.440362i
$125$			1.00000i			0.0894427i
$126$	−14.6284	−	5.84953i	−1.30321	−	0.521117i
$127$			2.60810i			0.231432i	0.993282	+	0.115716i	$0.0369162\pi$
$127$			2.60810i			0.231432i	−0.993282	+	0.115716i	$0.963084\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−2.34436	+	1.58739i	−0.206409	+	0.139762i
$130$	3.11210	−	5.39031i	0.272949	−	0.472761i
$131$	−0.604819	+	1.04758i	−0.0528433	+	0.0915273i	−0.891237	−	0.453538i	$-0.850162\pi$
$131$	−0.604819	+	1.04758i	−0.0528433	+	0.0915273i	0.838394	+	0.545065i	$0.183495\pi$
$132$	−5.30318	+	2.20823i	−0.461583	+	0.192202i
$133$	1.96663	+	3.40630i	0.170528	+	0.295364i
$134$	1.64268			0.141906
$135$	−4.95037	−	1.57918i	−0.426060	−	0.135914i
$136$	−4.35881			−0.373765
$137$	−14.8740	+	8.58754i	−1.27078	+	0.733683i	−0.975134	−	0.221616i	$-0.928867\pi$
$137$	−14.8740	+	8.58754i	−1.27078	+	0.733683i	−0.295642	+	0.955299i	$0.595533\pi$
$138$	0.411631	+	5.73916i	0.0350404	+	0.488550i
$139$	−10.5934	−	6.11608i	−0.898517	−	0.518759i	−0.0217983	−	0.999762i	$-0.506939\pi$
$139$	−10.5934	−	6.11608i	−0.898517	−	0.518759i	−0.876719	+	0.481003i	$0.840272\pi$
$140$	−2.62577	+	4.54797i	−0.221918	+	0.384374i
$141$	−1.06078	+	0.718264i	−0.0893334	+	0.0604888i
$142$	−5.68194	+	3.28047i	−0.476818	+	0.275291i
$143$	−6.55168	−	19.5760i	−0.547879	−	1.63703i
$144$	−1.85542	−	2.35741i	−0.154619	−	0.196451i
$145$			10.4097i			0.864479i
$146$	8.37500	−	4.83531i	0.693120	−	0.400173i
$147$	−15.5677	+	32.0639i	−1.28401	+	2.64459i
$148$	3.54924	−	6.14746i	0.291745	−	0.505318i
$149$	2.09557	−	3.62963i	0.171676	−	0.297351i	−0.767330	−	0.641252i	$-0.778415\pi$
$149$	2.09557	−	3.62963i	0.171676	−	0.297351i	0.939006	+	0.343901i	$0.111749\pi$
$150$	−0.756497	+	1.55811i	−0.0617677	+	0.127219i
$151$	9.01876	−	5.20698i	0.733936	−	0.423738i	−0.0859241	−	0.996302i	$-0.527384\pi$
$151$	9.01876	−	5.20698i	0.733936	−	0.423738i	0.819860	+	0.572563i	$0.194051\pi$
$152$			0.748972i			0.0607497i
$153$	−12.9426	+	1.86617i	−1.04635	+	0.150871i
$154$	5.52786	+	16.5169i	0.445447	+	1.33097i
$155$	4.90367	−	2.83113i	0.393872	−	0.227402i
$156$	8.92674	−	6.04441i	0.714712	−	0.483940i
$157$	5.55695	−	9.62492i	0.443493	−	0.768152i	−0.554453	−	0.832215i	$-0.687072\pi$
$157$	5.55695	−	9.62492i	0.443493	−	0.768152i	0.997946	+	0.0640627i	$0.0204058\pi$
$158$	−10.6885	−	6.17100i	−0.850330	−	0.490938i
$159$	0.305392	+	4.25792i	0.0242192	+	0.337675i
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	17.4457			1.37491
$162$	−6.51859	−	6.20548i	−0.512149	−	0.487548i
$163$	−2.63238			−0.206184			−0.103092	−	0.994672i	$-0.532874\pi$
$163$	−2.63238			−0.206184			−0.103092	+	0.994672i	$0.532874\pi$
$164$	2.75133	+	4.76544i	0.214843	+	0.372119i
$165$	2.20823	+	5.30318i	0.171910	+	0.412852i
$166$	2.86275	−	4.95842i	0.222192	−	0.384848i
$167$	2.05504	−	3.55943i	0.159024	−	0.275437i	−0.775493	−	0.631356i	$-0.782499\pi$
$167$	2.05504	−	3.55943i	0.159024	−	0.275437i	0.934517	+	0.355919i	$0.115832\pi$
$168$	−7.53177	+	5.09986i	−0.581089	+	0.393462i
$169$	12.8703	+	22.2920i	0.990021	+	1.71477i
$170$			4.35881i			0.334305i
$171$	0.320663	+	2.22392i	0.0245217	+	0.170067i
$172$			1.63461i			0.124638i
$173$	2.40803	+	4.17083i	0.183079	+	0.317102i	0.942928	−	0.332998i	$-0.108060\pi$
$173$	2.40803	+	4.17083i	0.183079	+	0.317102i	−0.759849	+	0.650100i	$0.774727\pi$
$174$	−7.87492	+	16.2195i	−0.596996	+	1.22960i
$175$	4.54797	+	2.62577i	0.343794	+	0.198490i
$176$	−0.660985	+	3.25009i	−0.0498236	+	0.244985i
$177$	1.57824	+	0.766272i	0.118628	+	0.0575965i
$178$	−7.29133	+	4.20965i	−0.546508	+	0.315527i
$179$			11.7239i			0.876288i	0.898905	+	0.438144i	$0.144364\pi$
$179$			11.7239i			0.876288i	−0.898905	+	0.438144i	$0.855636\pi$
$180$	−2.35741	+	1.85542i	−0.175711	+	0.138295i
$181$	−11.5905			−0.861515			−0.430757	−	0.902468i	$-0.641754\pi$
$181$	−11.5905			−0.861515			−0.430757	+	0.902468i	$0.641754\pi$
$182$	−16.3433	−	28.3074i	−1.21145	−	2.09829i
$183$	−1.32641	+	0.898131i	−0.0980513	+	0.0663917i
$184$	2.87695	+	1.66101i	0.212092	+	0.122451i
$185$	−6.14746	−	3.54924i	−0.451970	−	0.260945i
$186$	9.78221	−	0.701612i	0.717266	−	0.0514447i
$187$	10.8280	+	9.57838i	0.791823	+	0.700440i
$188$			0.739628i			0.0539429i
$189$	−20.1806	+	18.3676i	−1.46792	+	1.33605i
$190$	0.748972			0.0543362
$191$	−5.16248	+	2.98056i	−0.373544	+	0.215666i	−0.675005	−	0.737813i	$-0.735859\pi$
$191$	−5.16248	+	2.98056i	−0.373544	+	0.215666i	0.301462	+	0.953478i	$0.402525\pi$
$192$	−1.72761	+	0.123910i	−0.124680	+	0.00894244i
$193$	−8.79421	−	5.07734i	−0.633021	−	0.365475i	0.148900	−	0.988852i	$-0.452427\pi$
$193$	−8.79421	−	5.07734i	−0.633021	−	0.365475i	−0.781921	+	0.623377i	$0.785760\pi$
$194$	8.16763	−	14.1467i	0.586402	−	1.01568i
$195$	−6.04441	−	8.92674i	−0.432849	−	0.639257i
$196$	10.2894	+	17.8217i	0.734954	+	1.27298i
$197$	25.8739			1.84344			0.921721	−	0.387854i	$-0.126784\pi$
$197$	25.8739			1.84344			0.921721	+	0.387854i	$0.126784\pi$
$198$	−0.571173	+	9.93347i	−0.0405915	+	0.705941i
$199$	−19.0396			−1.34968			−0.674842	−	0.737962i	$-0.735788\pi$
$199$	−19.0396			−1.34968			−0.674842	+	0.737962i	$0.735788\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	1.24268	−	2.55948i	0.0876522	−	0.180532i
$202$	−3.41322	+	5.91188i	−0.240154	+	0.415958i
$203$	47.3431	+	27.3335i	3.32283	+	1.91844i
$204$	−3.29743	+	6.79151i	−0.230866	+	0.475501i
$205$	4.76544	−	2.75133i	0.332833	−	0.192161i
$206$	−1.07324			−0.0747764
$207$	9.25365	+	3.70029i	0.643173	+	0.257188i
$208$		−	6.22419i		−	0.431570i
$209$	1.64585	−	1.86057i	0.113846	−	0.128699i
$210$	5.09986	+	7.53177i	0.351924	+	0.519742i
$211$	14.2014	+	8.19916i	0.977662	+	0.564454i	0.901564	−	0.432647i	$-0.142420\pi$
$211$	14.2014	+	8.19916i	0.977662	+	0.564454i	0.0760987	+	0.997100i	$0.475754\pi$
$212$	2.13443	+	1.23231i	0.146593	+	0.0846356i
$213$	0.812966	+	11.3348i	0.0557035	+	0.776645i
$214$	−6.55673	−	11.3566i	−0.448209	−	0.776320i
$215$	1.63461			0.111479
$216$	−5.07674	+	1.10758i	−0.345428	+	0.0753613i
$217$		−	29.7357i		−	2.01859i
$218$	−11.0222	+	6.36369i	−0.746520	+	0.431004i
$219$	−1.19829	−	16.7071i	−0.0809728	−	1.12896i
$220$	3.25009	+	0.660985i	0.219121	+	0.0445636i
$221$	−23.4953	−	13.5650i	−1.58047	−	0.912483i
$222$	−6.89344	−	10.1806i	−0.462657	−	0.683280i
$223$	−10.9519	−	18.9692i	−0.733393	−	1.27027i	−0.955425	−	0.295235i	$-0.904602\pi$
$223$	−10.9519	−	18.9692i	−0.733393	−	1.27027i	0.222032	−	0.975039i	$-0.428731\pi$
$224$			5.25154i			0.350884i
$225$	1.85542	+	2.35741i	0.123695	+	0.157161i
$226$			6.94242i			0.461803i
$227$	−8.93371	−	15.4736i	−0.592951	−	1.02702i	−0.993832	−	0.110892i	$-0.964629\pi$
$227$	−8.93371	−	15.4736i	−0.592951	−	1.02702i	0.400881	−	0.916130i	$-0.368704\pi$
$228$	1.16698	+	0.566595i	0.0772853	+	0.0375237i
$229$	−4.31866	+	7.48013i	−0.285385	+	0.494301i	−0.972702	−	0.232056i	$-0.925455\pi$
$229$	−4.31866	+	7.48013i	−0.285385	+	0.494301i	0.687318	+	0.726357i	$0.258788\pi$
$230$	1.66101	−	2.87695i	0.109524	−	0.189700i
$231$	29.9170	+	3.88198i	1.96839	+	0.255416i
$232$	5.20486	+	9.01507i	0.341715	+	0.591869i
$233$	−16.6152			−1.08850			−0.544250	−	0.838923i	$-0.683186\pi$
$233$	−16.6152			−1.08850			−0.544250	+	0.838923i	$0.683186\pi$
$234$	−2.66481	−	18.4814i	−0.174204	−	1.20817i
$235$	0.739628			0.0482480
$236$	0.877216	−	0.506461i	0.0571019	−	0.0329678i
$237$	−17.7009	+	11.9855i	−1.14980	+	0.778542i
$238$	19.8237	+	11.4452i	1.28498	+	0.741885i
$239$	6.12388	−	10.6069i	0.396121	−	0.686102i	−0.597123	−	0.802150i	$-0.703689\pi$
$239$	6.12388	−	10.6069i	0.396121	−	0.686102i	0.993244	+	0.116048i	$0.0370228\pi$
$240$	0.123910	+	1.72761i	0.00799836	+	0.111517i
$241$	−13.4650	+	7.77403i	−0.867358	+	0.500770i	−0.866469	−	0.499230i	$-0.833616\pi$
$241$	−13.4650	+	7.77403i	−0.867358	+	0.500770i	−0.000888829		1.00000i	$0.500283\pi$
$242$	8.78400	−	6.62128i	0.564657	−	0.425632i
$243$	−14.6001	+	5.46227i	−0.936598	+	0.350405i
$244$			0.924844i			0.0592071i
$245$	17.8217	−	10.2894i	1.13859	−	0.657363i
$246$	9.50647	−	0.681835i	0.606110	−	0.0434722i
$247$	−2.33087	+	4.03719i	−0.148310	+	0.256880i
$248$	2.83113	−	4.90367i	0.179777	−	0.311383i
$249$	−5.56012	−	8.21151i	−0.352358	−	0.520383i
$250$	0.866025	−	0.500000i	0.0547723	−	0.0316228i
$251$		−	6.72650i		−	0.424573i	−0.977207	−	0.212286i	$-0.931909\pi$
$251$		−	6.72650i		−	0.424573i	0.977207	−	0.212286i	$-0.0680910\pi$
$252$	2.24838	+	15.5934i	0.141635	+	0.982290i
$253$	−3.49681	−	10.4483i	−0.219842	−	0.656876i
$254$	2.25868	−	1.30405i	0.141722	−	0.0818234i
$255$	6.79151	+	3.29743i	0.425301	+	0.206493i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−9.78608	−	5.64999i	−0.610439	−	0.352437i	0.162698	−	0.986676i	$-0.447980\pi$
$257$	−9.78608	−	5.64999i	−0.610439	−	0.352437i	−0.773137	+	0.634239i	$0.781314\pi$
$258$	2.54690	+	1.23658i	0.158563	+	0.0769859i
$259$	−32.2836	+	18.6390i	−2.00601	+	1.15817i
$260$	−6.22419			−0.386008
$261$	19.3144	+	24.5400i	1.19553	+	1.51899i
$262$	1.20964			0.0747317
$263$	2.98399	+	5.16843i	0.184001	+	0.318699i	0.943239	−	0.332114i	$-0.107762\pi$
$263$	2.98399	+	5.16843i	0.184001	+	0.318699i	−0.759239	+	0.650812i	$0.774428\pi$
$264$	4.56397	+	3.48857i	0.280893	+	0.214707i
$265$	1.23231	−	2.13443i	0.0757004	−	0.131117i
$266$	1.96663	−	3.40630i	0.120582	−	0.208854i
$267$	1.04324	+	14.5453i	0.0638450	+	0.890157i
$268$	−0.821341	−	1.42261i	−0.0501714	−	0.0868994i
$269$			26.2484i			1.60039i	0.599738	+	0.800197i	$0.295272\pi$
$269$			26.2484i			1.60039i	−0.599738	+	0.800197i	$0.704728\pi$
$270$	1.10758	+	5.07674i	0.0674052	+	0.308960i
$271$			7.60818i			0.462164i	0.972934	+	0.231082i	$0.0742266\pi$
$271$			7.60818i			0.462164i	−0.972934	+	0.231082i	$0.925773\pi$
$272$	2.17940	+	3.77484i	0.132146	+	0.228883i
$273$	−56.4698	+	4.05020i	−3.41771	+	0.245129i
$274$	14.8740	+	8.58754i	0.898574	+	0.518792i
$275$	0.660985	−	3.25009i	0.0398589	−	0.195988i
$276$	4.76444	−	3.22606i	0.286786	−	0.194186i
$277$	−8.68513	+	5.01436i	−0.521839	+	0.301284i	−0.737687	−	0.675143i	$-0.764082\pi$
$277$	−8.68513	+	5.01436i	−0.521839	+	0.301284i	0.215848	+	0.976427i	$0.430748\pi$
$278$			12.2322i			0.733636i
$279$	6.30702	−	15.7725i	0.377592	−	0.944277i
$280$	5.25154			0.313840
$281$	−0.989858	−	1.71448i	−0.0590500	−	0.102278i	0.834989	−	0.550266i	$-0.185474\pi$
$281$	−0.989858	−	1.71448i	−0.0590500	−	0.102278i	−0.894039	+	0.447989i	$0.852140\pi$
$282$	1.15242	+	0.559527i	0.0686258	+	0.0333193i
$283$	19.9164	+	11.4987i	1.18391	+	0.683530i	0.956915	−	0.290367i	$-0.0937773\pi$
$283$	19.9164	+	11.4987i	1.18391	+	0.683530i	0.226993	+	0.973896i	$0.427111\pi$
$284$	5.68194	+	3.28047i	0.337161	+	0.194660i
$285$	0.566595	−	1.16698i	0.0335622	−	0.0691261i
$286$	−13.6775	+	15.4619i	−0.808768	+	0.914284i
$287$		−	28.8975i		−	1.70576i
$288$	−1.11387	+	2.78555i	−0.0656353	+	0.164140i
$289$	1.99921			0.117601
$290$	9.01507	−	5.20486i	0.529383	−	0.305640i
$291$	−15.8634	−	23.4281i	−0.929931	−	1.37338i
$292$	−8.37500	−	4.83531i	−0.490110	−	0.282965i
$293$	−4.62455	+	8.00995i	−0.270169	+	0.467946i	−0.968905	−	0.247433i	$-0.920413\pi$
$293$	−4.62455	+	8.00995i	−0.270169	+	0.467946i	0.698736	+	0.715380i	$0.253746\pi$
$294$	35.5520	−	2.54991i	2.07344	−	0.148714i
$295$	−0.506461	−	0.877216i	−0.0294873	−	0.0510735i
$296$	−7.09847			−0.412590
$297$	15.0454	+	8.40459i	0.873020	+	0.487684i
$298$	−4.19114			−0.242786
$299$	10.3384	+	17.9067i	0.597887	+	1.03557i
$300$	1.72761	−	0.123910i	0.0997438	−	0.00715395i
$301$	4.29211	−	7.43415i	0.247393	−	0.428497i
$302$	−9.01876	−	5.20698i	−0.518971	−	0.299628i
$303$	6.62927	+	9.79050i	0.380842	+	0.562450i
$304$	0.648629	−	0.374486i	0.0372014	−	0.0214783i
$305$	0.924844			0.0529564
$306$	8.08744	+	10.2755i	0.462328	+	0.587412i
$307$			4.44897i			0.253916i	0.991908	+	0.126958i	$0.0405214\pi$
$307$			4.44897i			0.253916i	−0.991908	+	0.126958i	$0.959479\pi$
$308$	11.5401	−	13.0457i	0.657561	−	0.743349i
$309$	−0.811905	+	1.67223i	−0.0461877	+	0.0951300i
$310$	−4.90367	−	2.83113i	−0.278510	−	0.160798i
$311$	−16.4416	−	9.49258i	−0.932319	−	0.538275i	−0.0447747	−	0.998997i	$-0.514257\pi$
$311$	−16.4416	−	9.49258i	−0.932319	−	0.538275i	−0.887544	+	0.460723i	$0.847590\pi$
$312$	−9.69798	−	4.70858i	−0.549040	−	0.266571i
$313$	11.2352	+	19.4599i	0.635049	+	1.09994i	0.986505	+	0.163733i	$0.0523535\pi$
$313$	11.2352	+	19.4599i	0.635049	+	1.09994i	−0.351456	+	0.936205i	$0.614313\pi$
$314$	−11.1139			−0.627194
$315$	15.5934	−	2.24838i	0.878587	−	0.126682i
$316$			12.3420i			0.694292i
$317$	−7.53086	+	4.34795i	−0.422975	+	0.244205i	−0.696350	−	0.717703i	$-0.745194\pi$
$317$	−7.53086	+	4.34795i	−0.422975	+	0.244205i	0.273374	+	0.961908i	$0.411860\pi$
$318$	3.53477	−	2.39344i	0.198220	−	0.134217i
$319$	6.88067	−	33.8325i	0.385243	−	1.89426i
$320$	0.866025	+	0.500000i	0.0484123	+	0.0279508i
$321$	−22.6550	+	1.62489i	−1.26448	+	0.0906925i
$322$	−8.72286	−	15.1084i	−0.486106	−	0.841960i
$323$		−	3.26463i		−	0.181649i
$324$	−2.11480	+	8.74801i	−0.117489	+	0.486000i
$325$			6.22419i			0.345256i
$326$	1.31619	+	2.27971i	0.0728971	+	0.126261i
$327$	1.57705	+	21.9880i	0.0872112	+	1.21594i
$328$	2.75133	−	4.76544i	0.151917	−	0.263128i
$329$	1.94209	−	3.36381i	0.107071	−	0.185453i
$330$	3.48857	−	4.56397i	0.192040	−	0.251238i
$331$	−11.0808	−	19.1925i	−0.609054	−	1.05491i	−0.991397	−	0.130892i	$-0.958216\pi$
$331$	−11.0808	−	19.1925i	−0.609054	−	1.05491i	0.382343	−	0.924021i	$-0.375117\pi$
$332$	−5.72549			−0.314227
$333$	−21.0774	+	3.03912i	−1.15504	+	0.166543i
$334$	−4.11008			−0.224893
$335$	−1.42261	+	0.821341i	−0.0777252	+	0.0448747i
$336$	8.18249	+	3.97278i	0.446391	+	0.216733i
$337$	8.20371	+	4.73641i	0.446884	+	0.258009i	0.706513	−	0.707700i	$-0.250267\pi$
$337$	8.20371	+	4.73641i	0.446884	+	0.258009i	−0.259629	+	0.965708i	$0.583600\pi$
$338$	12.8703	−	22.2920i	0.700051	−	1.21252i
$339$	10.8171	+	5.25192i	0.587502	+	0.285245i
$340$	3.77484	−	2.17940i	0.204719	−	0.118195i
$341$	−17.8087	+	5.96019i	−0.964396	+	0.322763i
$342$	1.76564	−	1.38966i	0.0954747	−	0.0751443i
$343$		−	71.3092i		−	3.85033i
$344$	1.41561	−	0.817304i	0.0763247	−	0.0440661i
$345$	−3.22606	−	4.76444i	−0.173685	−	0.256509i
$346$	2.40803	−	4.17083i	0.129456	−	0.224225i
$347$	−14.1436	+	24.4975i	−0.759269	+	1.31509i	0.183955	+	0.982935i	$0.441110\pi$
$347$	−14.1436	+	24.4975i	−0.759269	+	1.31509i	−0.943224	+	0.332158i	$0.892223\pi$
$348$	17.9840	−	1.28987i	0.964041	−	0.0691442i
$349$	−21.0255	+	12.1391i	−1.12547	+	0.649790i	−0.942792	−	0.333382i	$-0.891810\pi$
$349$	−21.0255	+	12.1391i	−1.12547	+	0.649790i	−0.182678	+	0.983173i	$0.558477\pi$
$350$		−	5.25154i		−	0.280707i
$351$	−30.8121	−	9.82909i	−1.64463	−	0.524638i
$352$	3.14515	−	1.05262i	0.167637	−	0.0561046i
$353$	−10.3031	+	5.94847i	−0.548377	+	0.316605i	−0.748467	−	0.663172i	$-0.769210\pi$
$353$	−10.3031	+	5.94847i	−0.548377	+	0.316605i	0.200090	+	0.979777i	$0.435876\pi$
$354$	−0.125511	−	1.74994i	−0.00667084	−	0.0930080i
$355$	3.28047	−	5.68194i	0.174109	−	0.301566i
$356$	7.29133	+	4.20965i	0.386439	+	0.223111i
$357$	32.8296	−	22.2293i	1.73752	−	1.17650i
$358$	10.1532	−	5.86196i	0.536614	−	0.309814i
$359$	−14.4825			−0.764359			−0.382180	−	0.924088i	$-0.624826\pi$
$359$	−14.4825			−0.764359			−0.382180	+	0.924088i	$0.624826\pi$
$360$	2.78555	+	1.11387i	0.146811	+	0.0587060i
$361$	18.4390			0.970476
$362$	5.79525	+	10.0377i	0.304591	+	0.527568i
$363$	−3.67162	−	18.6954i	−0.192710	−	0.981256i
$364$	−16.3433	+	28.3074i	−0.856622	+	1.48371i
$365$	−4.83531	+	8.37500i	−0.253092	+	0.438368i
$366$	1.44101	+	0.699642i	0.0753228	+	0.0365709i
$367$	4.14790	+	7.18437i	0.216519	+	0.375021i	0.953741	−	0.300629i	$-0.0971965\pi$
$367$	4.14790	+	7.18437i	0.216519	+	0.375021i	−0.737223	+	0.675650i	$0.763863\pi$
$368$		−	3.32202i		−	0.173172i
$369$	6.12924	−	15.3279i	0.319076	−	0.797941i
$370$			7.09847i			0.369032i
$371$	−6.47155	−	11.2090i	−0.335986	−	0.581945i
$372$	−5.49872	−	8.12084i	−0.285095	−	0.421046i
$373$	−10.5518	−	6.09206i	−0.546349	−	0.315435i	0.201299	−	0.979530i	$-0.435484\pi$
$373$	−10.5518	−	6.09206i	−0.546349	−	0.315435i	−0.747648	+	0.664095i	$0.768817\pi$
$374$	2.88111	−	14.1665i	0.148979	−	0.732534i
$375$	−0.123910	−	1.72761i	−0.00639869	−	0.0892135i
$376$	0.640537	−	0.369814i	0.0330332	−	0.0190717i
$377$			64.7920i			3.33696i
$378$	25.9971	+	8.29311i	1.33715	+	0.426551i
$379$	−22.9047			−1.17653			−0.588267	−	0.808666i	$-0.700190\pi$
$379$	−22.9047			−1.17653			−0.588267	+	0.808666i	$0.700190\pi$
$380$	−0.374486	−	0.648629i	−0.0192107	−	0.0332740i
$381$	−0.323170	−	4.50579i	−0.0165565	−	0.230839i
$382$	5.16248	+	2.98056i	0.264135	+	0.152499i
$383$	16.5551	+	9.55806i	0.845924	+	0.488394i	0.859273	−	0.511517i	$-0.170916\pi$
$383$	16.5551	+	9.55806i	0.845924	+	0.488394i	−0.0133497	+	0.999911i	$0.504249\pi$
$384$	0.971116	+	1.43420i	0.0495570	+	0.0731888i
$385$	−13.0457	−	11.5401i	−0.664872	−	0.588140i
$386$			10.1547i			0.516859i
$387$	3.85345	−	3.03289i	0.195882	−	0.154171i
$388$	−16.3353			−0.829297
$389$	26.6198	−	15.3689i	1.34968	−	0.779235i	0.361472	−	0.932383i	$-0.382274\pi$
$389$	26.6198	−	15.3689i	1.34968	−	0.779235i	0.988203	+	0.153148i	$0.0489411\pi$
$390$	−4.70858	+	9.69798i	−0.238428	+	0.491077i
$391$	−12.5401	−	7.24002i	−0.634179	−	0.366143i
$392$	10.2894	−	17.8217i	0.519691	−	0.900131i
$393$	0.915088	−	1.88475i	0.0461601	−	0.0950732i
$394$	−12.9370	−	22.4075i	−0.651755	−	1.12887i
$395$	12.3420			0.620993
$396$	8.88822	−	4.47208i	0.446650	−	0.224731i
$397$	−19.1437			−0.960796			−0.480398	−	0.877051i	$-0.659508\pi$
$397$	−19.1437			−0.960796			−0.480398	+	0.877051i	$0.659508\pi$
$398$	9.51981	+	16.4888i	0.477185	+	0.826509i
$399$	−3.81965	−	5.64109i	−0.191222	−	0.282408i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	−1.63962	−	0.946638i	−0.0818789	−	0.0472728i	0.458502	−	0.888694i	$-0.348386\pi$
$401$	−1.63962	−	0.946638i	−0.0818789	−	0.0472728i	−0.540380	+	0.841421i	$0.681720\pi$
$402$	−2.83792	+	0.203545i	−0.141543	+	0.0101519i
$403$	30.5214	−	17.6215i	1.52038	−	0.877790i
$404$	6.82645			0.339628
$405$	8.74801	+	2.11480i	0.434692	+	0.105085i
$406$		−	54.6670i		−	2.71308i
$407$	17.6338	+	15.5987i	0.874075	+	0.773200i
$408$	7.53033	−	0.540100i	0.372807	−	0.0267390i
$409$	3.27154	+	1.88883i	0.161767	+	0.0933965i	0.578698	−	0.815542i	$-0.303561\pi$
$409$	3.27154	+	1.88883i	0.161767	+	0.0933965i	−0.416931	+	0.908938i	$0.636894\pi$
$410$	−4.76544	−	2.75133i	−0.235349	−	0.135879i
$411$	24.6325	−	16.6790i	1.21503	−	0.822714i
$412$	0.536621	+	0.929456i	0.0264374	+	0.0457910i
$413$	−5.31940			−0.261751
$414$	−1.42228	−	9.86404i	−0.0699012	−	0.484791i
$415$			5.72549i			0.281053i
$416$	−5.39031	+	3.11210i	−0.264282	+	0.152583i
$417$	19.0591	+	9.25359i	0.933327	+	0.453150i
$418$	−2.43423	−	0.495060i	−0.119062	−	0.0242142i
$419$	−16.4092	−	9.47385i	−0.801641	−	0.462828i	0.0424036	−	0.999101i	$-0.486498\pi$
$419$	−16.4092	−	9.47385i	−0.801641	−	0.462828i	−0.844045	+	0.536273i	$0.819832\pi$
$420$	3.97278	−	8.18249i	0.193852	−	0.399265i
$421$	4.89817	+	8.48389i	0.238722	+	0.413479i	0.960348	−	0.278804i	$-0.0899381\pi$
$421$	4.89817	+	8.48389i	0.238722	+	0.413479i	−0.721626	+	0.692284i	$0.756605\pi$
$422$		−	16.3983i		−	0.798258i
$423$	1.74361	−	1.37232i	0.0847772	−	0.0667247i
$424$		−	2.46463i		−	0.119693i
$425$	−2.17940	−	3.77484i	−0.105717	−	0.183107i
$426$	9.40971	−	6.37143i	0.455902	−	0.308697i
$427$	2.42843	−	4.20616i	0.117520	−	0.203551i
$428$	−6.55673	+	11.3566i	−0.316931	+	0.548941i
$429$	13.7444	+	33.0080i	0.663588	+	1.59364i
$430$	−0.817304	−	1.41561i	−0.0394139	−	0.0682669i
$431$	20.6446			0.994417			0.497209	−	0.867631i	$-0.334358\pi$
$431$	20.6446			0.994417			0.497209	+	0.867631i	$0.334358\pi$
$432$	3.49756	+	3.84279i	0.168277	+	0.184886i
$433$	19.8184			0.952411			0.476206	−	0.879334i	$-0.342012\pi$
$433$	19.8184			0.952411			0.476206	+	0.879334i	$0.342012\pi$
$434$	−25.7518	+	14.8678i	−1.23613	+	0.713678i
$435$	−1.28987	−	17.9840i	−0.0618444	−	0.862264i
$436$	11.0222	+	6.36369i	0.527870	+	0.304766i
$437$	−1.24405	+	2.15476i	−0.0595109	+	0.103076i
$438$	−13.8696	+	9.39129i	−0.662716	+	0.448733i
$439$	−16.5483	+	9.55418i	−0.789809	+	0.455996i	−0.839895	−	0.542749i	$-0.817384\pi$
$439$	−16.5483	+	9.55418i	−0.789809	+	0.455996i	0.0500866	+	0.998745i	$0.484050\pi$
$440$	−1.05262	−	3.14515i	−0.0501815	−	0.149939i
$441$	22.9220	−	57.3231i	1.09152	−	2.72967i
$442$			27.1301i			1.29045i
$443$	−0.733684	+	0.423593i	−0.0348584	+	0.0201255i	−0.517328	−	0.855787i	$-0.673073\pi$
$443$	−0.733684	+	0.423593i	−0.0348584	+	0.0201255i	0.482470	+	0.875913i	$0.339740\pi$
$444$	−5.36997	+	11.0602i	−0.254848	+	0.524894i
$445$	4.20965	−	7.29133i	0.199556	−	0.345642i
$446$	−10.9519	+	18.9692i	−0.518587	+	0.898219i
$447$	−3.17058	+	6.53026i	−0.149963	+	0.308871i
$448$	4.54797	−	2.62577i	0.214871	−	0.124056i
$449$		−	30.6594i		−	1.44690i	−0.690374	−	0.723452i	$-0.742554\pi$
$449$		−	30.6594i		−	1.44690i	0.690374	−	0.723452i	$-0.257446\pi$
$450$	1.11387	−	2.78555i	0.0525083	−	0.131312i
$451$	−17.3067	+	5.79219i	−0.814942	+	0.272744i
$452$	6.01231	−	3.47121i	0.282795	−	0.163272i
$453$	−14.9357	+	10.1132i	−0.701742	+	0.475158i
$454$	−8.93371	+	15.4736i	−0.419280	+	0.726214i
$455$	28.3074	+	16.3433i	1.32707	+	0.766186i
$456$	−0.0928052	−	1.29393i	−0.00434600	−	0.0605940i
$457$	−34.5586	+	19.9524i	−1.61658	+	0.933333i	−0.628785	+	0.777579i	$0.716447\pi$
$457$	−34.5586	+	19.9524i	−1.61658	+	0.933333i	−0.987796	+	0.155754i	$0.950219\pi$
$458$	8.63731			0.403595
$459$	22.1285	−	4.82773i	1.03287	−	0.225339i
$460$	−3.32202			−0.154890
$461$	20.0031	+	34.6465i	0.931639	+	1.61365i	0.780520	+	0.625131i	$0.214955\pi$
$461$	20.0031	+	34.6465i	0.931639	+	1.61365i	0.151120	+	0.988515i	$0.451712\pi$
$462$	−11.5966	−	27.8499i	−0.539523	−	1.29569i
$463$	0.670343	−	1.16107i	0.0311535	−	0.0539594i	−0.850028	−	0.526737i	$-0.823415\pi$
$463$	0.670343	−	1.16107i	0.0311535	−	0.0539594i	0.881182	+	0.472778i	$0.156749\pi$
$464$	5.20486	−	9.01507i	0.241629	−	0.418514i
$465$	−8.12084	+	5.49872i	−0.376595	+	0.254997i
$466$	8.30762	+	14.3892i	0.384843	+	0.666567i
$467$			4.43805i			0.205369i	0.994714	+	0.102684i	$0.0327431\pi$
$467$			4.43805i			0.205369i	−0.994714	+	0.102684i	$0.967257\pi$
$468$	−14.6730	+	11.5485i	−0.678259	+	0.533830i
$469$			8.62662i			0.398340i
$470$	−0.369814	−	0.640537i	−0.0170583	−	0.0295458i
$471$	−8.40764	+	17.3167i	−0.387403	+	0.797911i
$472$	−0.877216	−	0.506461i	−0.0403771	−	0.0233117i
$473$	−5.31263	−	1.08045i	−0.244275	−	0.0496792i
$474$	19.2302	+	9.33669i	0.883273	+	0.428848i
$475$	−0.648629	+	0.374486i	−0.0297611	+	0.0171826i
$476$		−	22.8905i		−	1.04918i
$477$	−1.05520	−	7.31820i	−0.0483142	−	0.335077i
$478$	−12.2478			−0.560200
$479$	−10.8806	−	18.8457i	−0.497145	−	0.861080i	0.502850	−	0.864374i	$-0.332285\pi$
$479$	−10.8806	−	18.8457i	−0.497145	−	0.861080i	−0.999995	+	0.00329348i	$0.998952\pi$
$480$	1.43420	−	0.971116i	0.0654620	−	0.0443252i
$481$	−38.2629	−	22.0911i	−1.74464	−	1.00727i
$482$	13.4650	+	7.77403i	0.613315	+	0.354098i
$483$	−30.1394	+	2.16170i	−1.37139	+	0.0983607i
$484$	−10.1262	−	4.29653i	−0.460282	−	0.195297i
$485$			16.3353i			0.741746i
$486$	12.0305	+	9.91294i	0.545716	+	0.449660i
$487$	−2.19251			−0.0993520			−0.0496760	−	0.998765i	$-0.515819\pi$
$487$	−2.19251			−0.0993520			−0.0496760	+	0.998765i	$0.515819\pi$
$488$	0.800939	−	0.462422i	0.0362568	−	0.0209329i
$489$	4.54774	−	0.326179i	0.205656	−	0.0147503i
$490$	−17.8217	−	10.2894i	−0.805102	−	0.464826i
$491$	16.6168	−	28.7811i	0.749904	−	1.29887i	−0.197964	−	0.980209i	$-0.563433\pi$
$491$	16.6168	−	28.7811i	0.749904	−	1.29887i	0.947868	−	0.318663i	$-0.103234\pi$
$492$	−5.34372	−	7.89193i	−0.240914	−	0.355795i
$493$	−22.6870	−	39.2950i	−1.02177	−	1.76976i
$494$	4.66175			0.209742
$495$	−4.47208	−	8.88822i	−0.201005	−	0.399496i
$496$	−5.66227			−0.254243
$497$	−17.2275	−	29.8389i	−0.772760	−	1.33846i
$498$	−4.33132	+	8.92096i	−0.194091	+	0.399758i
$499$	−11.7512	+	20.3537i	−0.526057	+	0.911157i	0.473482	+	0.880803i	$0.342997\pi$
$499$	−11.7512	+	20.3537i	−0.526057	+	0.911157i	−0.999539	+	0.0303538i	$0.990337\pi$
$500$	−0.866025	−	0.500000i	−0.0387298	−	0.0223607i
$501$	−3.10926	+	6.40396i	−0.138912	+	0.286108i
$502$	−5.82532	+	3.36325i	−0.259997	+	0.150109i
$503$	−1.96441			−0.0875886			−0.0437943	−	0.999041i	$-0.513945\pi$
$503$	−1.96441			−0.0875886			−0.0437943	+	0.999041i	$0.513945\pi$
$504$	12.3801	−	9.74384i	0.551452	−	0.434025i
$505$		−	6.82645i		−	0.303773i
$506$	−7.30005	+	8.25245i	−0.324527	+	0.366866i
$507$	−24.9971	−	36.9171i	−1.11016	−	1.63955i
$508$	−2.25868	−	1.30405i	−0.100213	−	0.0578579i
$509$	0.489274	+	0.282483i	0.0216867	+	0.0125208i	0.510804	−	0.859697i	$-0.329348\pi$
$509$	0.489274	+	0.282483i	0.0216867	+	0.0125208i	−0.489117	+	0.872218i	$0.662681\pi$
$510$	−0.540100	−	7.53033i	−0.0239160	−	0.333449i
$511$	25.3928	+	43.9817i	1.12331	+	1.94564i
$512$	1.00000			0.0441942
$513$	−0.829547	−	3.80234i	−0.0366254	−	0.167877i
$514$			11.3000i			0.498421i
$515$	0.929456	−	0.536621i	0.0409567	−	0.0236464i
$516$	−0.202544	−	2.82397i	−0.00891652	−	0.124318i
$517$	−2.40386	−	0.488883i	−0.105722	−	0.0215011i
$518$	32.2836	+	18.6390i	1.41846	+	0.818949i
$519$	−4.67695	−	6.90719i	−0.205295	−	0.303192i
$520$	3.11210	+	5.39031i	0.136474	+	0.236381i
$521$			7.99680i			0.350346i	0.984538	+	0.175173i	$0.0560485\pi$
$521$			7.99680i			0.350346i	−0.984538	+	0.175173i	$0.943951\pi$
$522$	11.5950	−	28.9968i	0.507501	−	1.26915i
$523$			23.4207i			1.02411i	0.858951	+	0.512057i	$0.171116\pi$
$523$			23.4207i			1.02411i	−0.858951	+	0.512057i	$0.828884\pi$
$524$	−0.604819	−	1.04758i	−0.0264217	−	0.0457636i
$525$	−8.18249	−	3.97278i	−0.357113	−	0.173386i
$526$	2.98399	−	5.16843i	0.130108	−	0.225354i
$527$	−12.3404	+	21.3742i	−0.537555	+	0.931073i
$528$	0.739208	−	5.69680i	0.0321699	−	0.247922i
$529$	−5.98210	−	10.3613i	−0.260092	−	0.450492i
$530$	−2.46463			−0.107057
$531$	−2.82154	−	1.12826i	−0.122445	−	0.0489624i
$532$	−3.93326			−0.170528
$533$	29.6610	−	17.1248i	1.28476	−	0.741758i
$534$	12.0750	−	8.17611i	0.522535	−	0.353815i
$535$	11.3566	+	6.55673i	0.490988	+	0.283472i
$536$	−0.821341	+	1.42261i	−0.0354765	+	0.0614472i
$537$	−1.45271	−	20.2544i	−0.0626892	−	0.874042i
$538$	22.7318	−	13.1242i	0.980037	−	0.565825i
$539$	−64.7232	+	21.6615i	−2.78783	+	0.933026i
$540$	3.84279	−	3.49756i	0.165367	−	0.150511i
$541$			3.02049i			0.129861i	0.997890	+	0.0649304i	$0.0206825\pi$
$541$			3.02049i			0.129861i	−0.997890	+	0.0649304i	$0.979317\pi$
$542$	6.58888	−	3.80409i	0.283017	−	0.163400i
$543$	20.0239	−	1.43618i	0.859307	−	0.0616323i
$544$	2.17940	−	3.77484i	0.0934412	−	0.161845i
$545$	6.36369	−	11.0222i	0.272591	−	0.472141i
$546$	31.7425	+	46.8792i	1.35845	+	2.00624i
$547$	21.5408	−	12.4366i	0.921017	−	0.531750i	0.0370579	−	0.999313i	$-0.488201\pi$
$547$	21.5408	−	12.4366i	0.921017	−	0.531750i	0.883959	+	0.467563i	$0.154868\pi$
$548$		−	17.1751i		−	0.733683i
$549$	2.18024	−	1.71598i	0.0930504	−	0.0732362i
$550$	−3.14515	+	1.05262i	−0.134110	+	0.0448837i
$551$	−6.75204	+	3.89829i	−0.287647	+	0.166073i
$552$	−5.17607	−	2.51310i	−0.220308	−	0.106964i
$553$	32.4073	−	56.1310i	1.37810	−	2.38693i
$554$	8.68513	+	5.01436i	0.368996	+	0.213040i
$555$	11.0602	+	5.36997i	0.469480	+	0.227943i
$556$	10.5934	−	6.11608i	0.449259	−	0.259380i
$557$	3.70445			0.156963			0.0784814	−	0.996916i	$-0.474993\pi$
$557$	3.70445			0.156963			0.0784814	+	0.996916i	$0.474993\pi$
$558$	−16.8129	+	2.42423i	−0.711748	+	0.102626i
$559$	10.1741			0.430319
$560$	−2.62577	−	4.54797i	−0.110959	−	0.192187i
$561$	−19.8935	−	15.2060i	−0.839904	−	0.641999i
$562$	−0.989858	+	1.71448i	−0.0417546	+	0.0723211i
$563$	−13.9825	+	24.2185i	−0.589294	+	1.02069i	0.405031	+	0.914303i	$0.367261\pi$
$563$	−13.9825	+	24.2185i	−0.589294	+	1.02069i	−0.994325	+	0.106384i	$0.966073\pi$
$564$	−0.0916474	−	1.27779i	−0.00385905	−	0.0538047i
$565$	−3.47121	−	6.01231i	−0.146035	−	0.252940i
$566$		−	22.9975i		−	0.966657i
$567$	32.5883	−	34.2327i	1.36858	−	1.43764i
$568$		−	6.56094i		−	0.275291i
$569$	5.20091	+	9.00824i	0.218034	+	0.377645i	0.954207	−	0.299148i	$-0.0967024\pi$
$569$	5.20091	+	9.00824i	0.218034	+	0.377645i	−0.736173	+	0.676793i	$0.763369\pi$
$570$	−1.29393	+	0.0928052i	−0.0541969	+	0.00388718i
$571$	25.5328	+	14.7414i	1.06852	+	0.616908i	0.927775	−	0.373139i	$-0.121719\pi$
$571$	25.5328	+	14.7414i	1.06852	+	0.616908i	0.140740	+	0.990047i	$0.455052\pi$
$572$	20.2292	+	4.11410i	0.845825	+	0.172019i
$573$	8.54944	−	5.78893i	0.357158	−	0.241836i
$574$	−25.0259	+	14.4487i	−1.04456	+	0.603078i
$575$			3.32202i			0.138538i
$576$	2.96929	−	0.428137i	0.123721	−	0.0178391i
$577$	−11.3733			−0.473475			−0.236738	−	0.971574i	$-0.576078\pi$
$577$	−11.3733			−0.473475			−0.236738	+	0.971574i	$0.576078\pi$
$578$	−0.999607	−	1.73137i	−0.0415782	−	0.0720155i
$579$	15.8221	+	7.68198i	0.657545	+	0.319252i
$580$	−9.01507	−	5.20486i	−0.374331	−	0.216120i
$581$	26.0394	+	15.0338i	1.08030	+	0.623709i
$582$	−12.3576	+	25.4522i	−0.512238	+	1.05503i
$583$	−5.41596	+	6.12255i	−0.224306	+	0.253570i
$584$			9.67062i			0.400173i
$585$	11.5485	+	14.6730i	0.477472	+	0.606654i
$586$	9.24909			0.382076
$587$	−18.1289	+	10.4667i	−0.748259	+	0.432007i	−0.825064	−	0.565039i	$-0.808861\pi$
$587$	−18.1289	+	10.4667i	−0.748259	+	0.432007i	0.0768057	+	0.997046i	$0.475528\pi$
$588$	−19.9843	−	29.5140i	−0.824139	−	1.21714i
$589$	3.67271	+	2.12044i	0.151331	+	0.0873712i
$590$	−0.506461	+	0.877216i	−0.0208507	+	0.0361144i
$591$	−44.7001	+	3.20604i	−1.83872	+	0.131879i
$592$	3.54924	+	6.14746i	0.145873	+	0.252659i
$593$	39.7650			1.63295			0.816476	−	0.577380i	$-0.195925\pi$
$593$	39.7650			1.63295			0.816476	+	0.577380i	$0.195925\pi$
$594$	−0.244091	−	17.2320i	−0.0100152	−	0.707036i
$595$	−22.8905			−0.938418
$596$	2.09557	+	3.62963i	0.0858378	+	0.148675i
$597$	32.8931	−	2.35920i	1.34623	−	0.0965557i
$598$	10.3384	−	17.9067i	0.422770	−	0.732259i
$599$	−30.0865	−	17.3704i	−1.22930	−	0.709737i	−0.262416	−	0.964955i	$-0.584519\pi$
$599$	−30.0865	−	17.3704i	−1.22930	−	0.709737i	−0.966883	+	0.255218i	$0.917853\pi$
$600$	−0.971116	−	1.43420i	−0.0396456	−	0.0585510i
$601$	22.3427	−	12.8995i	0.911376	−	0.526183i	0.0305024	−	0.999535i	$-0.490289\pi$
$601$	22.3427	−	12.8995i	0.911376	−	0.526183i	0.880874	+	0.473352i	$0.156956\pi$
$602$	−8.58421			−0.349866
$603$	−1.82973	+	4.57578i	−0.0745125	+	0.186340i
$604$			10.4140i			0.423738i
$605$	−4.29653	+	10.1262i	−0.174679	+	0.411688i
$606$	5.16419	−	10.6364i	0.209781	−	0.432073i
$607$	−29.9048	−	17.2656i	−1.21380	−	0.700788i	−0.250215	−	0.968190i	$-0.580501\pi$
$607$	−29.9048	−	17.2656i	−1.21380	−	0.700788i	−0.963585	+	0.267403i	$0.913835\pi$
$608$	−0.648629	−	0.374486i	−0.0263054	−	0.0151874i
$609$	−85.1774	−	41.3555i	−3.45156	−	1.67581i
$610$	−0.462422	−	0.800939i	−0.0187229	−	0.0324291i
$611$	4.60359			0.186241
$612$	4.85514	−	12.1417i	0.196257	−	0.490799i
$613$		−	6.59175i		−	0.266238i	−0.991100	−	0.133119i	$-0.957501\pi$
$613$		−	6.59175i		−	0.266238i	0.991100	−	0.133119i	$-0.0424993\pi$
$614$	3.85292	−	2.22448i	0.155491	−	0.0897729i
$615$	−7.89193	+	5.34372i	−0.318233	+	0.215480i
$616$	−17.0680	−	3.47119i	−0.687689	−	0.139858i
$617$	22.5798	+	13.0364i	0.909027	+	0.524827i	0.880118	−	0.474755i	$-0.157463\pi$
$617$	22.5798	+	13.0364i	0.909027	+	0.524827i	0.0289089	+	0.999582i	$0.490797\pi$
$618$	1.85415	−	0.132986i	0.0745848	−	0.00534947i
$619$	8.53992	+	14.7916i	0.343248	+	0.594524i	0.985034	−	0.172361i	$-0.0551394\pi$
$619$	8.53992	+	14.7916i	0.343248	+	0.594524i	−0.641786	+	0.766884i	$0.721806\pi$
$620$			5.66227i			0.227402i
$621$	−16.4452	−	5.24605i	−0.659924	−	0.210517i
$622$			18.9852i			0.761235i
$623$	−22.1072	−	38.2907i	−0.885704	−	1.53408i
$624$	0.771240	+	10.7530i	0.0308743	+	0.430464i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	11.2352	−	19.4599i	0.449048	−	0.777773i
$627$	−2.61285	+	3.41829i	−0.104347	+	0.136513i
$628$	5.55695	+	9.62492i	0.221746	+	0.384076i
$629$	30.9409			1.23369
$630$	−9.74384	−	12.3801i	−0.388204	−	0.493233i
$631$	−40.0533			−1.59450			−0.797248	−	0.603651i	$-0.793712\pi$
$631$	−40.0533			−1.59450			−0.797248	+	0.603651i	$0.793712\pi$
$632$	10.6885	−	6.17100i	0.425165	−	0.245469i
$633$	−25.5504	−	12.4053i	−1.01554	−	0.493066i
$634$	7.53086	+	4.34795i	0.299089	+	0.172679i
$635$	−1.30405	+	2.25868i	−0.0517497	+	0.0896331i
$636$	−3.84016	−	1.86448i	−0.152272	−	0.0739316i
$637$	110.926	−	64.0429i	4.39503	−	2.53747i
$638$	−32.7402	+	10.9574i	−1.29620	+	0.433809i
$639$	−2.80898	−	19.4813i	−0.111122	−	0.770670i
$640$		−	1.00000i		−	0.0395285i
$641$	22.5994	−	13.0478i	0.892623	−	0.515356i	0.0178236	−	0.999841i	$-0.494326\pi$
$641$	22.5994	−	13.0478i	0.892623	−	0.515356i	0.874800	+	0.484485i	$0.160993\pi$
$642$	12.7347	+	18.8073i	0.502598	+	0.742267i
$643$	−13.5959	+	23.5487i	−0.536168	+	0.928671i	0.462938	+	0.886391i	$0.346795\pi$
$643$	−13.5959	+	23.5487i	−0.536168	+	0.928671i	−0.999106	+	0.0422797i	$0.986538\pi$
$644$	−8.72286	+	15.1084i	−0.343729	+	0.595356i
$645$	−2.82397	+	0.202544i	−0.111194	+	0.00797518i
$646$	−2.82725	+	1.63231i	−0.111237	+	0.0642225i
$647$		−	49.6172i		−	1.95065i	−0.220766	−	0.975327i	$-0.570856\pi$
$647$		−	49.6172i		−	1.95065i	0.220766	−	0.975327i	$-0.429144\pi$
$648$	8.63340	−	2.54253i	0.339152	−	0.0998800i
$649$	1.06622	+	3.18579i	0.0418527	+	0.125053i
$650$	5.39031	−	3.11210i	0.211425	−	0.122066i
$651$	3.68455	+	51.3717i	0.144409	+	2.01342i
$652$	1.31619	−	2.27971i	0.0515460	−	0.0892803i
$653$	11.5265	+	6.65480i	0.451065	+	0.260422i	0.708280	−	0.705932i	$-0.249472\pi$
$653$	11.5265	+	6.65480i	0.451065	+	0.260422i	−0.257215	+	0.966354i	$0.582805\pi$
$654$	18.2536	−	12.3598i	0.713774	−	0.483305i
$655$	−1.04758	+	0.604819i	−0.0409322	+	0.0236322i
$656$	−5.50266			−0.214843
$657$	4.14035	+	28.7149i	0.161531	+	1.12028i
$658$	−3.88419			−0.151421
$659$	0.890304	+	1.54205i	0.0346813	+	0.0600698i	0.882845	−	0.469664i	$-0.155625\pi$
$659$	0.890304	+	1.54205i	0.0346813	+	0.0600698i	−0.848164	+	0.529734i	$0.822292\pi$
$660$	−5.69680	−	0.739208i	−0.221748	−	0.0287736i
$661$	−1.07164	+	1.85613i	−0.0416818	+	0.0721950i	−0.886114	−	0.463468i	$-0.846605\pi$
$661$	−1.07164	+	1.85613i	−0.0416818	+	0.0721950i	0.844432	+	0.535663i	$0.179938\pi$
$662$	−11.0808	+	19.1925i	−0.430666	+	0.745936i
$663$	42.2717	+	20.5238i	1.64170	+	0.797079i
$664$	2.86275	+	4.95842i	0.111096	+	0.192424i
$665$			3.93326i			0.152525i
$666$	13.1707	+	16.7340i	0.510353	+	0.648431i
$667$			34.5812i			1.33899i
$668$	2.05504	+	3.55943i	0.0795119	+	0.137719i
$669$	21.2711	+	31.4144i	0.822389	+	1.21455i
$670$	1.42261	+	0.821341i	0.0549600	+	0.0317312i
$671$	−3.00583	−	0.611309i	−0.116039	−	0.0235993i
$672$	−0.650719	−	9.07263i	−0.0251020	−	0.349984i
$673$	0.768862	−	0.443903i	0.0296375	−	0.0171112i	−0.485108	−	0.874454i	$-0.661220\pi$
$673$	0.768862	−	0.443903i	0.0296375	−	0.0171112i	0.514746	+	0.857343i	$0.327886\pi$
$674$		−	9.47283i		−	0.364880i
$675$	−3.49756	−	3.84279i	−0.134621	−	0.147909i
$676$	−25.7406			−0.990021
$677$	0.0859441	+	0.148859i	0.00330310	+	0.00572114i	0.867672	−	0.497137i	$-0.165615\pi$
$677$	0.0859441	+	0.148859i	0.00330310	+	0.00572114i	−0.864369	+	0.502858i	$0.832282\pi$
$678$	−0.860236	−	11.9938i	−0.0330372	−	0.460620i
$679$	74.2923	+	42.8927i	2.85108	+	1.64607i
$680$	−3.77484	−	2.17940i	−0.144758	−	0.0835763i
$681$	17.3513	+	25.6255i	0.664905	+	0.981971i
$682$	14.0660	+	12.4427i	0.538616	+	0.476456i
$683$			37.6674i			1.44130i	0.693297	+	0.720652i	$0.256157\pi$
$683$			37.6674i			1.44130i	−0.693297	+	0.720652i	$0.743843\pi$
$684$	−2.08630	−	0.834256i	−0.0797717	−	0.0318986i
$685$	−17.1751			−0.656226
$686$	−61.7556	+	35.6546i	−2.35784	+	1.36130i
$687$	6.53410	−	13.4579i	0.249292	−	0.513451i
$688$	−1.41561	−	0.817304i	−0.0539697	−	0.0311594i
$689$	7.67015	−	13.2851i	0.292210	−	0.506122i
$690$	−2.51310	+	5.17607i	−0.0956719	+	0.197050i
$691$	22.4912	+	38.9559i	0.855606	+	1.48195i	0.876081	+	0.482163i	$0.160149\pi$
$691$	22.4912	+	38.9559i	0.855606	+	1.48195i	−0.0204751	+	0.999790i	$0.506518\pi$
$692$	−4.81606			−0.183079
$693$	−52.1660	−	2.99954i	−1.98162	−	0.113943i
$694$	28.2872			1.07377
$695$	−6.11608	−	10.5934i	−0.231996	−	0.401829i
$696$	−10.1090	−	14.9296i	−0.383182	−	0.565906i
$697$	−11.9925	+	20.7717i	−0.454249	+	0.786783i
$698$	21.0255	+	12.1391i	0.795827	+	0.459471i
$699$	28.7047	−	2.05880i	1.08571	−	0.0778708i
$700$	−4.54797	+	2.62577i	−0.171897	+	0.0992448i
$701$	18.7504			0.708191			0.354095	−	0.935209i	$-0.384789\pi$
$701$	18.7504			0.708191			0.354095	+	0.935209i	$0.384789\pi$
$702$	6.89380	+	31.5986i	0.260190	+	1.19261i
$703$		−	5.31656i		−	0.200518i
$704$	−2.48417	−	2.19748i	−0.0936257	−	0.0828205i
$705$	−1.27779	+	0.0916474i	−0.0481244	+	0.00345164i
$706$	10.3031	+	5.94847i	0.387761	+	0.223874i
$707$	−31.0465	−	17.9247i	−1.16762	−	0.674127i
$708$	−1.45273	+	0.983664i	−0.0545971	+	0.0369683i
$709$	−0.424093	−	0.734550i	−0.0159271	−	0.0275866i	0.857952	−	0.513730i	$-0.171737\pi$
$709$	−0.424093	−	0.734550i	−0.0159271	−	0.0275866i	−0.873879	+	0.486143i	$0.838403\pi$
$710$	−6.56094			−0.246228
$711$	29.0952	−	22.8996i	1.09116	−	0.858804i
$712$		−	8.41930i		−	0.315527i
$713$	16.2901	−	9.40507i	0.610068	−	0.352223i
$714$	−35.6659	−	17.3166i	−1.33476	−	0.648057i
$715$	4.11410	−	20.2292i	0.153859	−	0.756529i
$716$	−10.1532	−	5.86196i	−0.379444	−	0.219072i
$717$	−9.26540	+	19.0834i	−0.346023	+	0.712682i
$718$	7.24127	+	12.5422i	0.270242	+	0.468072i
$719$			11.8199i			0.440809i	0.975409	+	0.220405i	$0.0707378\pi$
$719$			11.8199i			0.440809i	−0.975409	+	0.220405i	$0.929262\pi$
$720$	−0.428137	−	2.96929i	−0.0159557	−	0.110659i
$721$		−	5.63618i		−	0.209902i
$722$	−9.21952	−	15.9687i	−0.343115	−	0.594293i
$723$	22.2991	−	15.0990i	0.829311	−	0.561537i
$724$	5.79525	−	10.0377i	0.215379	−	0.373047i
$725$	−5.20486	+	9.01507i	−0.193303	+	0.334811i
$726$	−14.3549	+	12.5274i	−0.532761	+	0.464937i
$727$	18.9116	+	32.7559i	0.701394	+	1.21485i	0.967977	+	0.251038i	$0.0807720\pi$
$727$	18.9116	+	32.7559i	0.701394	+	1.21485i	−0.266583	+	0.963812i	$0.585895\pi$
$728$	32.6866			1.21145
$729$	24.5465	−	11.2458i	0.909131	−	0.416511i
$730$	9.67062			0.357926
$731$	−6.17038	+	3.56247i	−0.228220	+	0.131763i
$732$	−0.114598	−	1.59777i	−0.00423565	−	0.0590554i
$733$	−6.67442	−	3.85348i	−0.246525	−	0.142332i	0.371647	−	0.928374i	$-0.378793\pi$
$733$	−6.67442	−	3.85348i	−0.246525	−	0.142332i	−0.618172	+	0.786043i	$0.712127\pi$
$734$	4.14790	−	7.18437i	0.153102	−	0.265180i
$735$	−29.5140	+	19.9843i	−1.08864	+	0.737132i
$736$	−2.87695	+	1.66101i	−0.106046	+	0.0612256i
$737$	5.16649	−	1.72911i	0.190310	−	0.0636927i
$738$	−16.3390	+	2.35589i	−0.601447	+	0.0867217i
$739$		−	38.3377i		−	1.41027i	−0.709071	−	0.705137i	$-0.750885\pi$
$739$		−	38.3377i		−	1.41027i	0.709071	−	0.705137i	$-0.249115\pi$
$740$	6.14746	−	3.54924i	0.225985	−	0.130472i
$741$	3.52660	−	7.26352i	0.129553	−	0.266832i
$742$	−6.47155	+	11.2090i	−0.237578	+	0.411497i
$743$	−8.40585	+	14.5594i	−0.308381	+	0.534131i	−0.978008	−	0.208566i	$-0.933120\pi$
$743$	−8.40585	+	14.5594i	−0.308381	+	0.534131i	0.669628	+	0.742697i	$0.266454\pi$
$744$	−4.28349	+	8.82245i	−0.157040	+	0.323447i
$745$	3.62963	−	2.09557i	0.132979	−	0.0767757i
$746$			12.1841i			0.446092i
$747$	10.6232	+	13.4974i	0.388683	+	0.493843i
$748$	−13.7091	+	4.58815i	−0.501255	+	0.167759i
$749$	59.6396	−	34.4330i	2.17918	−	1.25815i
$750$	−1.43420	+	0.971116i	−0.0523696	+	0.0354601i
$751$	−18.0406	+	31.2472i	−0.658310	+	1.14023i	0.322743	+	0.946487i	$0.395395\pi$
$751$	−18.0406	+	31.2472i	−0.658310	+	1.14023i	−0.981053	+	0.193740i	$0.937938\pi$
$752$	−0.640537	−	0.369814i	−0.0233580	−	0.0134857i
$753$	0.833481	+	11.6208i	0.0303737	+	0.423485i
$754$	56.1115	−	32.3960i	2.04346	−	1.17979i
$755$	10.4140			0.379003
$756$	−5.81651	−	26.6607i	−0.211544	−	0.969641i
$757$	−26.6674			−0.969242			−0.484621	−	0.874724i	$-0.661042\pi$
$757$	−26.6674			−0.969242			−0.484621	+	0.874724i	$0.661042\pi$
$758$	11.4523	+	19.8360i	0.415968	+	0.720478i
$759$	7.33577	+	17.6173i	0.266272	+	0.639466i
$760$	−0.374486	+	0.648629i	−0.0135840	+	0.0235282i
$761$	−5.58743	+	9.67771i	−0.202544	+	0.350817i	−0.949348	−	0.314228i	$-0.898254\pi$
$761$	−5.58743	+	9.67771i	−0.202544	+	0.350817i	0.746803	+	0.665045i	$0.231588\pi$
$762$	−3.74054	+	2.53277i	−0.135506	+	0.0917525i
$763$	−33.4192	−	57.8838i	−1.20986	−	2.09553i
$764$		−	5.96111i		−	0.215666i
$765$	−12.1417	−	4.85514i	−0.438984	−	0.175538i
$766$		−	19.1161i		−	0.690694i
$767$	−3.15231	−	5.45996i	−0.113823	−	0.197148i
$768$	0.756497	−	1.55811i	0.0272977	−	0.0562235i
$769$	−40.0727	−	23.1360i	−1.44506	−	0.834304i	−0.446877	−	0.894596i	$-0.647464\pi$
$769$	−40.0727	−	23.1360i	−1.44506	−	0.834304i	−0.998181	+	0.0602912i	$0.980797\pi$
$770$	−3.47119	+	17.0680i	−0.125093	+	0.615088i
$771$	17.6066	+	8.54841i	0.634088	+	0.307863i
$772$	8.79421	−	5.07734i	0.316510	−	0.182737i
$773$			3.86173i			0.138897i	0.997586	+	0.0694483i	$0.0221239\pi$
$773$			3.86173i			0.138897i	−0.997586	+	0.0694483i	$0.977876\pi$
$774$	−4.55328	−	1.82074i	−0.163664	−	0.0654451i
$775$	5.66227			0.203395
$776$	8.16763	+	14.1467i	0.293201	+	0.507839i
$777$	53.4641	−	36.2012i	1.91801	−	1.29871i
$778$	−26.6198	−	15.3689i	−0.954364	−	0.551003i
$779$	3.56919	+	2.06067i	0.127879	+	0.0738312i
$780$	10.7530	−	0.771240i	0.385019	−	0.0276148i
$781$	−14.4175	+	16.2985i	−0.515899	+	0.583206i
$782$			14.4800i			0.517805i
$783$	−36.4086	−	40.0024i	−1.30114	−	1.42957i
$784$	−20.5787			−0.734954
$785$	9.62492	−	5.55695i	0.343528	−	0.198336i
$786$	−2.08979	+	0.149886i	−0.0745402	+	0.00534627i
$787$	−16.4345	−	9.48845i	−0.585826	−	0.338227i	0.177619	−	0.984099i	$-0.443160\pi$
$787$	−16.4345	−	9.48845i	−0.585826	−	0.338227i	−0.763445	+	0.645872i	$0.776494\pi$
$788$	−12.9370	+	22.4075i	−0.460860	+	0.798234i
$789$	−5.79560	−	8.55929i	−0.206329	−	0.304719i
$790$	−6.17100	−	10.6885i	−0.219554	−	0.380279i
$791$	−36.4584			−1.29631
$792$	−8.31705	−	5.46138i	−0.295533	−	0.194062i
$793$	5.75641			0.204416
$794$	9.57186	+	16.5789i	0.339693	+	0.588365i
$795$	−1.86448	+	3.84016i	−0.0661264	+	0.136197i
$796$	9.51981	−	16.4888i	0.337421	−	0.584430i
$797$	22.5593	+	13.0246i	0.799091	+	0.461355i	0.843153	−	0.537673i	$-0.180697\pi$
$797$	22.5593	+	13.0246i	0.799091	+	0.461355i	−0.0440623	+	0.999029i	$0.514030\pi$
$798$	−2.97550	+	6.12846i	−0.105332	+	0.216945i
$799$	−2.79198	+	1.61195i	−0.0987731	+	0.0570266i
$800$	−1.00000			−0.0353553
$801$	−3.60462	−	24.9994i	−0.127363	−	0.883309i
$802$			1.89328i			0.0668539i
$803$	21.2510	−	24.0235i	0.749930	−	0.847770i
$804$	1.59524	+	2.35594i	0.0562596	+	0.0830875i
$805$	15.1084	+	8.72286i	0.532502	+	0.307440i
$806$	−30.5214	−	17.6215i	−1.07507	−	0.620692i
$807$	−3.25244	−	45.3471i	−0.114491	−	1.59629i
$808$	−3.41322	−	5.91188i	−0.120077	−	0.207979i
$809$	19.6768			0.691800			0.345900	−	0.938271i	$-0.387574\pi$
$809$	19.6768			0.691800			0.345900	+	0.938271i	$0.387574\pi$
$810$	−2.54253	−	8.63340i	−0.0893354	−	0.303347i
$811$			21.6225i			0.759270i	0.925136	+	0.379635i	$0.123950\pi$
$811$			21.6225i			0.759270i	−0.925136	+	0.379635i	$0.876050\pi$
$812$	−47.3431	+	27.3335i	−1.66142	+	0.959219i
$813$	−0.942731	−	13.1440i	−0.0330630	−	0.460980i
$814$	4.69199	−	23.0707i	0.164454	−	0.808627i
$815$	−2.27971	−	1.31619i	−0.0798547	−	0.0461042i
$816$	−4.23291	−	6.25141i	−0.148181	−	0.218843i
$817$	0.612138	+	1.06025i	0.0214160	+	0.0370936i
$818$		−	3.77765i		−	0.132083i
$819$	97.0561	−	13.9944i	3.39141	−	0.489002i
$820$			5.50266i			0.192161i
$821$	0.412392	+	0.714283i	0.0143926	+	0.0249287i	0.873132	−	0.487484i	$-0.162085\pi$
$821$	0.412392	+	0.714283i	0.0143926	+	0.0249287i	−0.858739	+	0.512413i	$0.828752\pi$
$822$	−26.7607	−	12.9929i	−0.933386	−	0.453179i
$823$	−18.7187	+	32.4217i	−0.652492	+	1.13015i	0.330025	+	0.943972i	$0.392943\pi$
$823$	−18.7187	+	32.4217i	−0.652492	+	1.13015i	−0.982516	+	0.186176i	$0.940390\pi$
$824$	0.536621	−	0.929456i	0.0186941	−	0.0323791i
$825$	−0.739208	+	5.69680i	−0.0257359	+	0.198337i
$826$	2.65970	+	4.60674i	0.0925428	+	0.160289i
$827$	−37.1032			−1.29020			−0.645102	−	0.764096i	$-0.723185\pi$
$827$	−37.1032			−1.29020			−0.645102	+	0.764096i	$0.723185\pi$
$828$	−7.83137	+	6.16375i	−0.272159	+	0.214205i
$829$	−36.7868			−1.27766			−0.638829	−	0.769349i	$-0.720581\pi$
$829$	−36.7868			−1.27766			−0.638829	+	0.769349i	$0.720581\pi$
$830$	4.95842	−	2.86275i	0.172109	−	0.0993674i
$831$	14.3832	−	9.73905i	0.498948	−	0.337844i
$832$	5.39031	+	3.11210i	0.186875	+	0.107892i
$833$	−44.8493	+	77.6813i	−1.55394	+	2.69150i
$834$	−1.51569	−	21.1324i	−0.0524840	−	0.731756i
$835$	3.55943	−	2.05504i	0.123179	−	0.0711176i
$836$	0.788380	+	2.35563i	0.0272667	+	0.0814713i
$837$	−8.94172	+	28.0303i	−0.309071	+	0.968871i
$838$			18.9477i			0.654537i
$839$	13.0381	−	7.52757i	0.450126	−	0.259880i	−0.257757	−	0.966210i	$-0.582984\pi$
$839$	13.0381	−	7.52757i	0.450126	−	0.259880i	0.707883	+	0.706329i	$0.249650\pi$
$840$	−9.07263	+	0.650719i	−0.313036	+	0.0224519i
$841$	−39.6810	+	68.7296i	−1.36831	+	2.36999i
$842$	4.89817	−	8.48389i	0.168802	−	0.292374i
$843$	1.92253	+	2.83931i	0.0662156	+	0.0977911i
$844$	−14.2014	+	8.19916i	−0.488831	+	0.282227i
$845$			25.7406i			0.885502i
$846$	−2.06027	−	0.823848i	−0.0708336	−	0.0283245i
$847$	34.7719	+	46.1296i	1.19478	+	1.58503i
$848$	−2.13443	+	1.23231i	−0.0732966	+	0.0423178i
$849$	−35.8327	−	17.3975i	−1.22977	−	0.597082i
$850$	−2.17940	+	3.77484i	−0.0747530	+	0.129476i
$851$	−20.4219	−	11.7906i	−0.700055	−	0.404177i
$852$	−10.2227	−	4.96333i	−0.350223	−	0.170041i
$853$	−22.8609	+	13.1987i	−0.782742	+	0.451916i	−0.837401	−	0.546589i	$-0.815926\pi$
$853$	−22.8609	+	13.1987i	−0.782742	+	0.451916i	0.0546593	+	0.998505i	$0.482593\pi$
$854$	−4.85686			−0.166198
$855$	−0.834256	+	2.08630i	−0.0285310	+	0.0713500i
$856$	13.1135			0.448209
$857$	27.1443	+	47.0154i	0.927233	+	1.60601i	0.787930	+	0.615764i	$0.211153\pi$
$857$	27.1443	+	47.0154i	0.927233	+	1.60601i	0.139302	+	0.990250i	$0.455514\pi$
$858$	21.7136	−	28.4070i	0.741288	−	0.969800i
$859$	7.15517	−	12.3931i	0.244131	−	0.422847i	−0.717756	−	0.696295i	$-0.754831\pi$
$859$	7.15517	−	12.3931i	0.244131	−	0.422847i	0.961887	+	0.273447i	$0.0881639\pi$
$860$	−0.817304	+	1.41561i	−0.0278698	+	0.0482720i
$861$	3.58069	+	49.9236i	0.122030	+	1.70139i
$862$	−10.3223	−	17.8788i	−0.351580	−	0.608954i
$863$		−	9.34374i		−	0.318064i	−0.987273	−	0.159032i	$-0.949163\pi$
$863$		−	9.34374i		−	0.318064i	0.987273	−	0.159032i	$-0.0508374\pi$
$864$	1.57918	−	4.95037i	0.0537246	−	0.168415i
$865$			4.81606i			0.163751i
$866$	−9.90919	−	17.1632i	−0.336728	−	0.583230i
$867$	−3.45387	+	0.247723i	−0.117300	+	0.00841311i
$868$	25.7518	+	14.8678i	0.874074	+	0.504647i
$869$	−40.1126	−	8.15788i	−1.36073	−	0.276737i
$870$	−14.9296	+	10.1090i	−0.506162	+	0.342728i
$871$	−8.85457	+	5.11219i	−0.300026	+	0.173220i
$872$		−	12.7274i		−	0.431004i
$873$	30.3088	+	38.5090i	1.02580	+	1.30333i
$874$	2.48810			0.0841612
$875$	2.62577	+	4.54797i	0.0887673	+	0.153749i
$876$	15.0679	+	7.31580i	0.509098	+	0.247178i
$877$	−26.9922	−	15.5840i	−0.911462	−	0.526233i	−0.0305610	−	0.999533i	$-0.509729\pi$
$877$	−26.9922	−	15.5840i	−0.911462	−	0.526233i	−0.880901	+	0.473300i	$0.843063\pi$
$878$	16.5483	+	9.55418i	0.558479	+	0.322438i
$879$	6.99691	−	14.4111i	0.236000	−	0.486075i
$880$	−2.19748	+	2.48417i	−0.0740769	+	0.0837413i
$881$			55.9686i			1.88563i	0.333318	+	0.942814i	$0.391832\pi$
$881$			55.9686i			1.88563i	−0.333318	+	0.942814i	$0.608168\pi$
$882$	−61.1042	+	8.81051i	−2.05749	+	0.296665i
$883$	−16.4039			−0.552034			−0.276017	−	0.961153i	$-0.589015\pi$
$883$	−16.4039			−0.552034			−0.276017	+	0.961153i	$0.589015\pi$
$884$	23.4953	−	13.5650i	0.790233	−	0.456241i
$885$	0.983664	+	1.45273i	0.0330655	+	0.0488331i
$886$	0.733684	+	0.423593i	0.0246486	+	0.0142309i
$887$	−23.6084	+	40.8910i	−0.792693	+	1.37298i	0.131601	+	0.991303i	$0.457988\pi$
$887$	−23.6084	+	40.8910i	−0.792693	+	1.37298i	−0.924294	+	0.381682i	$0.875345\pi$
$888$	12.2634	−	0.879572i	0.411533	−	0.0295165i
$889$	6.84828	+	11.8616i	0.229684	+	0.397824i
$890$	−8.41930			−0.282215
$891$	−27.0340	−	12.6556i	−0.905672	−	0.423979i
$892$	21.9038			0.733393
$893$	0.276980	+	0.479744i	0.00926880	+	0.0160540i
$894$	7.24066	−	0.519324i	0.242164	−	0.0173688i
$895$	−5.86196	+	10.1532i	−0.195944	+	0.339385i
$896$	−4.54797	−	2.62577i	−0.151937	−	0.0877209i
$897$	−20.0796	−	29.6548i	−0.670439	−	0.990145i
$898$	−26.5518	+	15.3297i	−0.886044	+	0.511558i
$899$	58.9426			1.96585
$900$	−2.96929	+	0.428137i	−0.0989764	+	0.0142712i
$901$			10.7428i			0.357896i
$902$	13.6695	+	12.0920i	0.455146	+	0.402618i
$903$	−6.49393	+	13.3752i	−0.216105	+	0.445098i
$904$	−6.01231	−	3.47121i	−0.199967	−	0.115451i
$905$	−10.0377	−	5.79525i	−0.333663	−	0.192641i
$906$	16.2261	+	7.87814i	0.539077	+	0.261734i
$907$	−12.7126	−	22.0189i	−0.422115	−	0.731125i	0.574031	−	0.818833i	$-0.305379\pi$
$907$	−12.7126	−	22.0189i	−0.422115	−	0.731125i	−0.996146	+	0.0877088i	$0.972045\pi$
$908$	17.8674			0.592951
$909$	−12.6660	−	16.0928i	−0.420103	−	0.533763i
$910$		−	32.6866i		−	1.08355i
$911$	2.74924	−	1.58727i	0.0910864	−	0.0525887i	−0.453765	−	0.891121i	$-0.649919\pi$
$911$	2.74924	−	1.58727i	0.0910864	−	0.0525887i	0.544851	+	0.838533i	$0.316586\pi$
$912$	−1.07418	+	0.727339i	−0.0355696	+	0.0240846i
$913$	3.78447	−	18.6084i	0.125248	−	0.615848i
$914$	34.5586	+	19.9524i	1.14310	+	0.659966i
$915$	−1.59777	+	0.114598i	−0.0528207	+	0.00378848i
$916$	−4.31866	−	7.48013i	−0.142692	−	0.247151i
$917$			6.35247i			0.209777i
$918$	−15.2452	−	16.7500i	−0.503167	−	0.552832i
$919$		−	13.8687i		−	0.457485i	−0.973487	−	0.228743i	$-0.926539\pi$
$919$		−	13.8687i		−	0.457485i	0.973487	−	0.228743i	$-0.0734615\pi$
$920$	1.66101	+	2.87695i	0.0547618	+	0.0948502i
$921$	−0.551272	−	7.68610i	−0.0181650	−	0.253265i
$922$	20.0031	−	34.6465i	0.658769	−	1.14102i
$923$	20.4183	−	35.3655i	0.672075	−	1.16407i
$924$	−18.3204	+	23.9679i	−0.602697	+	0.788486i
$925$	−3.54924	−	6.14746i	−0.116698	−	0.202127i
$926$	−1.34069			−0.0440577
$927$	1.19545	−	2.98957i	0.0392638	−	0.0981905i
$928$	−10.4097			−0.341715
$929$	−27.8096	+	16.0559i	−0.912405	+	0.526777i	−0.881204	−	0.472736i	$-0.843266\pi$
$929$	−27.8096	+	16.0559i	−0.912405	+	0.526777i	−0.0312007	+	0.999513i	$0.509933\pi$
$930$	8.82245	+	4.28349i	0.289299	+	0.140461i
$931$	13.3479	+	7.70644i	0.437461	+	0.252568i
$932$	8.30762	−	14.3892i	0.272125	−	0.471334i
$933$	29.5810	+	14.3622i	0.968438	+	0.470198i
$934$	3.84347	−	2.21903i	0.125762	−	0.0726088i
$935$	4.58815	+	13.7091i	0.150049	+	0.448336i
$936$	17.3378	+	6.93293i	0.566704	+	0.226610i
$937$		−	22.7790i		−	0.744158i	−0.928201	−	0.372079i	$-0.878645\pi$
$937$		−	22.7790i		−	0.744158i	0.928201	−	0.372079i	$-0.121355\pi$
$938$	7.47087	−	4.31331i	0.243933	−	0.140835i
$939$	−21.8213	−	32.2270i	−0.712111	−	1.05169i
$940$	−0.369814	+	0.640537i	−0.0120620	+	0.0208920i
$941$	12.1465	−	21.0384i	0.395965	−	0.685832i	−0.597259	−	0.802049i	$-0.703743\pi$
$941$	12.1465	−	21.0384i	0.395965	−	0.685832i	0.993224	+	0.116217i	$0.0370767\pi$
$942$	19.2005	−	1.37712i	0.625587	−	0.0448691i
$943$	15.8309	−	9.13996i	0.515524	−	0.297638i
$944$			1.01292i			0.0329678i
$945$	−26.6607	+	5.81651i	−0.867273	+	0.189211i
$946$	1.72061	+	5.14109i	0.0559420	+	0.167151i
$947$	−32.6946	+	18.8763i	−1.06243	+	0.613396i	−0.926104	−	0.377268i	$-0.876864\pi$
$947$	−32.6946	+	18.8763i	−1.06243	+	0.613396i	−0.136329	+	0.990664i	$0.543530\pi$
$948$	−1.52930	−	21.3222i	−0.0496693	−	0.692513i
$949$	−30.0959	+	52.1276i	−0.976954	+	1.69213i
$950$	0.648629	+	0.374486i	0.0210443	+	0.0121499i
$951$	12.4717	−	8.44472i	0.404421	−	0.273839i
$952$	−19.8237	+	11.4452i	−0.642491	+	0.370942i
$953$	32.1754			1.04226			0.521132	−	0.853476i	$-0.325510\pi$
$953$	32.1754			1.04226			0.521132	+	0.853476i	$0.325510\pi$
$954$	−5.81015	+	4.57293i	−0.188110	+	0.148054i
$955$	−5.96111			−0.192897
$956$	6.12388	+	10.6069i	0.198060	+	0.343051i
$957$	−7.69494	+	59.3021i	−0.248742	+	1.91696i
$958$	−10.8806	+	18.8457i	−0.351535	+	0.608876i
$959$	−45.0978	+	78.1117i	−1.45628	+	2.52236i
$960$	−1.55811	−	0.756497i	−0.0502878	−	0.0244158i
$961$	−0.530645	−	0.919104i	−0.0171176	−	0.0296485i
$962$			44.1822i			1.42449i
$963$	38.9377	−	5.61436i	1.25475	−	0.180920i
$964$		−	15.5481i		−	0.500770i
$965$	−5.07734	−	8.79421i	−0.163445	−	0.283096i
$966$	16.9418	+	25.0207i	0.545094	+	0.805027i
$967$	−24.6705	−	14.2435i	−0.793351	−	0.458042i	0.0477898	−	0.998857i	$-0.484782\pi$
$967$	−24.6705	−	14.2435i	−0.793351	−	0.458042i	−0.841141	+	0.540816i	$0.818116\pi$
$968$	1.34220	+	10.9178i	0.0431398	+	0.350912i
$969$	0.404520	+	5.64001i	0.0129951	+	0.181183i
$970$	14.1467	−	8.16763i	0.454225	−	0.262247i
$971$		−	7.25145i		−	0.232710i	−0.993208	−	0.116355i	$-0.962879\pi$
$971$		−	7.25145i		−	0.232710i	0.993208	−	0.116355i	$-0.0371211\pi$
$972$	2.56959	−	15.3752i	0.0824198	−	0.493160i
$973$	−64.2377			−2.05937
$974$	1.09625	+	1.89877i	0.0351263	+	0.0608405i
$975$	−0.771240	−	10.7530i	−0.0246995	−	0.344371i
$976$	−0.800939	−	0.462422i	−0.0256374	−	0.0148018i
$977$	9.85390	+	5.68915i	0.315254	+	0.182012i	0.649275	−	0.760554i	$-0.275072\pi$
$977$	9.85390	+	5.68915i	0.315254	+	0.182012i	−0.334021	+	0.942566i	$0.608406\pi$
$978$	−2.55635	−	3.77537i	−0.0817430	−	0.120723i
$979$	−18.5012	+	20.9150i	−0.591301	+	0.668445i
$980$			20.5787i			0.657363i
$981$	−5.44907	−	37.7913i	−0.173975	−	1.20658i
$982$	−33.2335			−1.06052
$983$	−37.4974	+	21.6492i	−1.19598	+	0.690501i	−0.959657	−	0.281173i	$-0.909276\pi$
$983$	−37.4974	+	21.6492i	−1.19598	+	0.690501i	−0.236325	+	0.971674i	$0.575943\pi$
$984$	−4.16275	+	8.57376i	−0.132704	+	0.273322i
$985$	22.4075	+	12.9370i	0.713962	+	0.412206i
$986$	−22.6870	+	39.2950i	−0.722500	+	1.25141i
$987$	−2.93838	+	6.05200i	−0.0935296	+	0.192637i
$988$	−2.33087	−	4.03719i	−0.0741549	−	0.128440i
$989$	5.43019			0.172670
$990$	−5.46138	+	8.31705i	−0.173574	+	0.264333i
$991$	−20.6875			−0.657161			−0.328581	−	0.944476i	$-0.606570\pi$
$991$	−20.6875			−0.657161			−0.328581	+	0.944476i	$0.606570\pi$
$992$	2.83113	+	4.90367i	0.0898886	+	0.155692i
$993$	21.5214	+	31.7841i	0.682961	+	1.00864i
$994$	−17.2275	+	29.8389i	−0.546424	+	0.946434i
$995$	−16.4888	−	9.51981i	−0.522730	−	0.301798i
$996$	9.89144	−	0.709446i	0.313422	−	0.0224797i
$997$	−35.9742	+	20.7697i	−1.13932	+	0.657784i	−0.946261	−	0.323404i	$-0.895173\pi$
$997$	−35.9742	+	20.7697i	−1.13932	+	0.657784i	−0.193055	+	0.981188i	$0.561839\pi$
$998$	23.5024			0.743957
$999$	36.0371	−	7.86213i	1.14016	−	0.248747i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.t.a.131.1	✓	48
3.2	odd	2		2970.2.t.b.2771.1		48
9.2	odd	6		990.2.t.b.461.1	yes	48
9.7	even	3		2970.2.t.a.791.1		48
11.10	odd	2		990.2.t.b.131.1	yes	48
33.32	even	2		2970.2.t.a.2771.1		48
99.43	odd	6		2970.2.t.b.791.1		48
99.65	even	6	inner	990.2.t.a.461.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.t.a.131.1	✓	48	1.1	even	1	trivial
990.2.t.a.461.1	yes	48	99.65	even	6	inner
990.2.t.b.131.1	yes	48	11.10	odd	2
990.2.t.b.461.1	yes	48	9.2	odd	6
2970.2.t.a.791.1		48	9.7	even	3
2970.2.t.a.2771.1		48	33.32	even	2
2970.2.t.b.791.1		48	99.43	odd	6
2970.2.t.b.2771.1		48	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.72761 + 0.123910i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +(0.971116 + 1.43420i) q^{6} +(4.54797 - 2.62577i) q^{7} +1.00000 q^{8} +(2.96929 - 0.428137i) q^{9} -1.00000i q^{10} +(-2.48417 - 2.19748i) q^{11} +(0.756497 - 1.55811i) q^{12} +(5.39031 + 3.11210i) q^{13} +(-4.54797 - 2.62577i) q^{14} +(-1.55811 - 0.756497i) q^{15} +(-0.500000 - 0.866025i) q^{16} -4.35881 q^{17} +(-1.85542 - 2.35741i) q^{18} +0.748972i q^{19} +(-0.866025 + 0.500000i) q^{20} +(-7.53177 + 5.09986i) q^{21} +(-0.660985 + 3.25009i) q^{22} +(2.87695 + 1.66101i) q^{23} +(-1.72761 + 0.123910i) q^{24} +(0.500000 + 0.866025i) q^{25} -6.22419i q^{26} +(-5.07674 + 1.10758i) q^{27} +5.25154i q^{28} +(5.20486 + 9.01507i) q^{29} +(0.123910 + 1.72761i) q^{30} +(2.83113 - 4.90367i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(4.56397 + 3.48857i) q^{33} +(2.17940 + 3.77484i) q^{34} +5.25154 q^{35} +(-1.11387 + 2.78555i) q^{36} -7.09847 q^{37} +(0.648629 - 0.374486i) q^{38} +(-9.69798 - 4.70858i) q^{39} +(0.866025 + 0.500000i) q^{40} +(2.75133 - 4.76544i) q^{41} +(8.18249 + 3.97278i) q^{42} +(1.41561 - 0.817304i) q^{43} +(3.14515 - 1.05262i) q^{44} +(2.78555 + 1.11387i) q^{45} -3.32202i q^{46} +(0.640537 - 0.369814i) q^{47} +(0.971116 + 1.43420i) q^{48} +(10.2894 - 17.8217i) q^{49} +(0.500000 - 0.866025i) q^{50} +(7.53033 - 0.540100i) q^{51} +(-5.39031 + 3.11210i) q^{52} -2.46463i q^{53} +(3.49756 + 3.84279i) q^{54} +(-1.05262 - 3.14515i) q^{55} +(4.54797 - 2.62577i) q^{56} +(-0.0928052 - 1.29393i) q^{57} +(5.20486 - 9.01507i) q^{58} +(-0.877216 - 0.506461i) q^{59} +(1.43420 - 0.971116i) q^{60} +(0.800939 - 0.462422i) q^{61} -5.66227 q^{62} +(12.3801 - 9.74384i) q^{63} +1.00000 q^{64} +(3.11210 + 5.39031i) q^{65} +(0.739208 - 5.69680i) q^{66} +(-0.821341 + 1.42261i) q^{67} +(2.17940 - 3.77484i) q^{68} +(-5.17607 - 2.51310i) q^{69} +(-2.62577 - 4.54797i) q^{70} -6.56094i q^{71} +(2.96929 - 0.428137i) q^{72} +9.67062i q^{73} +(3.54924 + 6.14746i) q^{74} +(-0.971116 - 1.43420i) q^{75} +(-0.648629 - 0.374486i) q^{76} +(-17.0680 - 3.47119i) q^{77} +(0.771240 + 10.7530i) q^{78} +(10.6885 - 6.17100i) q^{79} -1.00000i q^{80} +(8.63340 - 2.54253i) q^{81} -5.50266 q^{82} +(2.86275 + 4.95842i) q^{83} +(-0.650719 - 9.07263i) q^{84} +(-3.77484 - 2.17940i) q^{85} +(-1.41561 - 0.817304i) q^{86} +(-10.1090 - 14.9296i) q^{87} +(-2.48417 - 2.19748i) q^{88} -8.41930i q^{89} +(-0.428137 - 2.96929i) q^{90} +32.6866 q^{91} +(-2.87695 + 1.66101i) q^{92} +(-4.28349 + 8.82245i) q^{93} +(-0.640537 - 0.369814i) q^{94} +(-0.374486 + 0.648629i) q^{95} +(0.756497 - 1.55811i) q^{96} +(8.16763 + 14.1467i) q^{97} -20.5787 q^{98} +(-8.31705 - 5.46138i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{6} + 48 q^{8} + 10 q^{9} - 6 q^{11} + 4 q^{12} + 24 q^{13} - 4 q^{15} - 24 q^{16} - 12 q^{17} - 8 q^{18} - 16 q^{21} + 12 q^{22} + 36 q^{23} - 2 q^{24} + 24 q^{25}+ \cdots - 48 q^{99}+O(q^{100}) \) 48 * q - 24 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^6 + 48 * q^8 + 10 * q^9 - 6 * q^11 + 4 * q^12 + 24 * q^13 - 4 * q^15 - 24 * q^16 - 12 * q^17 - 8 * q^18 - 16 * q^21 + 12 * q^22 + 36 * q^23 - 2 * q^24 + 24 * q^25 - 8 * q^27 + 8 * q^30 - 24 * q^32 + 2 * q^33 + 6 * q^34 - 2 * q^36 - 6 * q^38 - 40 * q^39 - 6 * q^41 + 8 * q^42 + 30 * q^43 - 6 * q^44 - 2 * q^48 + 24 * q^49 + 24 * q^50 + 22 * q^51 - 24 * q^52 + 22 * q^54 + 40 * q^57 - 54 * q^59 - 4 * q^60 - 38 * q^63 + 48 * q^64 + 8 * q^66 - 6 * q^67 + 6 * q^68 + 76 * q^69 + 10 * q^72 + 2 * q^75 + 6 * q^76 + 6 * q^77 + 32 * q^78 + 10 * q^81 + 12 * q^82 + 36 * q^83 + 8 * q^84 - 30 * q^86 - 44 * q^87 - 6 * q^88 + 24 * q^91 - 36 * q^92 - 68 * q^93 + 4 * q^96 + 6 * q^97 - 48 * q^98 - 48 * q^99

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