LMFDB - Embedded newform 847.2.f.y.323.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			323.2
Character	$\chi$	$=$	847.323
Dual form			847.2.f.y.729.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70653 - 1.23987i) q^{2} +(0.524869 - 1.61538i) q^{3} +(0.756943 + 2.32963i) q^{4} +(-0.398353 + 0.289420i) q^{5} +(-2.89857 + 2.10593i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.293014 - 0.901803i) q^{8} +(0.0930802 + 0.0676268i) q^{9} +O(q^{10})$	\(q+(-1.70653 - 1.23987i) q^{2} +(0.524869 - 1.61538i) q^{3} +(0.756943 + 2.32963i) q^{4} +(-0.398353 + 0.289420i) q^{5} +(-2.89857 + 2.10593i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.293014 - 0.901803i) q^{8} +(0.0930802 + 0.0676268i) q^{9} +1.03864 q^{10} +4.16054 q^{12} +(-4.28803 - 3.11543i) q^{13} +(0.651837 - 2.00615i) q^{14} +(0.258441 + 0.795400i) q^{15} +(2.34525 - 1.70393i) q^{16} +(-2.45715 + 1.78523i) q^{17} +(-0.0749961 - 0.230814i) q^{18} +(-1.44194 + 4.43784i) q^{19} +(-0.975773 - 0.708941i) q^{20} +1.69851 q^{21} -5.63835 q^{23} +(-1.30296 - 0.946657i) q^{24} +(-1.47016 + 4.52470i) q^{25} +(3.45493 + 10.6332i) q^{26} +(4.28048 - 3.10995i) q^{27} +(-1.98170 + 1.43979i) q^{28} +(2.13931 + 6.58412i) q^{29} +(0.545153 - 1.67781i) q^{30} +(1.02393 + 0.743930i) q^{31} -8.01131 q^{32} +6.40665 q^{34} +(-0.398353 - 0.289420i) q^{35} +(-0.0870890 + 0.268032i) q^{36} +(3.36082 + 10.3436i) q^{37} +(7.96305 - 5.78550i) q^{38} +(-7.28327 + 5.29160i) q^{39} +(0.144277 + 0.444040i) q^{40} +(-0.445979 + 1.37258i) q^{41} +(-2.89857 - 2.10593i) q^{42} +2.88224 q^{43} -0.0566513 q^{45} +(9.62202 + 6.99081i) q^{46} +(-2.70551 + 8.32671i) q^{47} +(-1.52154 - 4.68282i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(8.11891 - 5.89873i) q^{50} +(1.59414 + 4.90625i) q^{51} +(4.01202 - 12.3477i) q^{52} +(-5.37054 - 3.90192i) q^{53} -11.1607 q^{54} +0.948212 q^{56} +(6.41198 + 4.65857i) q^{57} +(4.51264 - 13.8885i) q^{58} +(-2.58256 - 7.94830i) q^{59} +(-1.65736 + 1.20414i) q^{60} +(11.2415 - 8.16744i) q^{61} +(-0.824997 - 2.53908i) q^{62} +(-0.0355535 + 0.109422i) q^{63} +(8.98105 + 6.52511i) q^{64} +2.60982 q^{65} -9.70431 q^{67} +(-6.01884 - 4.37294i) q^{68} +(-2.95940 + 9.10809i) q^{69} +(0.320959 + 0.987809i) q^{70} +(-4.81163 + 3.49586i) q^{71} +(0.0882598 - 0.0641245i) q^{72} +(-1.16629 - 3.58948i) q^{73} +(7.08928 - 21.8186i) q^{74} +(6.53747 + 4.74975i) q^{75} -11.4300 q^{76} +18.9900 q^{78} +(7.12245 + 5.17476i) q^{79} +(-0.441088 + 1.35753i) q^{80} +(-2.67040 - 8.21865i) q^{81} +(2.46290 - 1.78940i) q^{82} +(-8.97183 + 6.51842i) q^{83} +(1.28568 + 3.95691i) q^{84} +(0.462133 - 1.42230i) q^{85} +(-4.91863 - 3.57359i) q^{86} +11.7587 q^{87} +3.10324 q^{89} +(0.0966773 + 0.0702401i) q^{90} +(1.63788 - 5.04088i) q^{91} +(-4.26791 - 13.1353i) q^{92} +(1.73916 - 1.26357i) q^{93} +(14.9411 - 10.8553i) q^{94} +(-0.710000 - 2.18515i) q^{95} +(-4.20489 + 12.9413i) q^{96} +(5.11036 + 3.71290i) q^{97} +2.10939 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) $ 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9	\( 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9} - 32 q^{10} - 56 q^{12} - 4 q^{13} - 4 q^{14} - 2 q^{15} - 8 q^{16} - 22 q^{17} - 24 q^{18} - 6 q^{19} - 2 q^{20} - 8 q^{21} + 8 q^{23} + 20 q^{24} - 4 q^{25} - 6 q^{26} + 2 q^{27} - 4 q^{28} - 12 q^{29} - 20 q^{30} + 2 q^{31} + 32 q^{32} + 96 q^{34} + 4 q^{35} - 18 q^{36} - 14 q^{37} + 22 q^{38} - 20 q^{39} - 18 q^{40} - 26 q^{41} + 6 q^{42} - 16 q^{43} - 144 q^{45} - 12 q^{46} + 16 q^{47} + 24 q^{48} - 6 q^{49} + 4 q^{50} + 4 q^{51} - 12 q^{52} - 4 q^{53} - 128 q^{54} + 48 q^{56} - 20 q^{57} + 2 q^{58} + 4 q^{59} - 24 q^{60} + 8 q^{61} - 20 q^{62} - 8 q^{63} - 26 q^{64} + 96 q^{65} + 24 q^{67} - 12 q^{68} + 14 q^{69} + 8 q^{70} - 22 q^{71} - 16 q^{72} - 14 q^{73} - 44 q^{74} + 20 q^{75} - 120 q^{76} + 128 q^{78} + 28 q^{79} + 4 q^{80} + 6 q^{81} + 4 q^{82} - 22 q^{83} + 14 q^{84} + 24 q^{85} + 30 q^{86} + 88 q^{87} + 22 q^{90} - 4 q^{91} - 10 q^{92} + 50 q^{93} + 38 q^{94} + 24 q^{95} + 62 q^{96} + 4 q^{97} + 16 q^{98}+O(q^{100}) \) 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9 - 32 * q^10 - 56 * q^12 - 4 * q^13 - 4 * q^14 - 2 * q^15 - 8 * q^16 - 22 * q^17 - 24 * q^18 - 6 * q^19 - 2 * q^20 - 8 * q^21 + 8 * q^23 + 20 * q^24 - 4 * q^25 - 6 * q^26 + 2 * q^27 - 4 * q^28 - 12 * q^29 - 20 * q^30 + 2 * q^31 + 32 * q^32 + 96 * q^34 + 4 * q^35 - 18 * q^36 - 14 * q^37 + 22 * q^38 - 20 * q^39 - 18 * q^40 - 26 * q^41 + 6 * q^42 - 16 * q^43 - 144 * q^45 - 12 * q^46 + 16 * q^47 + 24 * q^48 - 6 * q^49 + 4 * q^50 + 4 * q^51 - 12 * q^52 - 4 * q^53 - 128 * q^54 + 48 * q^56 - 20 * q^57 + 2 * q^58 + 4 * q^59 - 24 * q^60 + 8 * q^61 - 20 * q^62 - 8 * q^63 - 26 * q^64 + 96 * q^65 + 24 * q^67 - 12 * q^68 + 14 * q^69 + 8 * q^70 - 22 * q^71 - 16 * q^72 - 14 * q^73 - 44 * q^74 + 20 * q^75 - 120 * q^76 + 128 * q^78 + 28 * q^79 + 4 * q^80 + 6 * q^81 + 4 * q^82 - 22 * q^83 + 14 * q^84 + 24 * q^85 + 30 * q^86 + 88 * q^87 + 22 * q^90 - 4 * q^91 - 10 * q^92 + 50 * q^93 + 38 * q^94 + 24 * q^95 + 62 * q^96 + 4 * q^97 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.70653	−	1.23987i	−1.20670	−	0.876719i	−0.211773	−	0.977319i	$-0.567924\pi$
$2$	−1.70653	−	1.23987i	−1.20670	−	0.876719i	−0.994927	+	0.100600i	$0.967924\pi$
$3$	0.524869	−	1.61538i	0.303033	−	0.932641i	−0.677370	−	0.735642i	$-0.736880\pi$
$3$	0.524869	−	1.61538i	0.303033	−	0.932641i	0.980404	−	0.196999i	$-0.0631195\pi$
$4$	0.756943	+	2.32963i	0.378472	+	1.16482i
$5$	−0.398353	+	0.289420i	−0.178149	+	0.129433i	−0.673286	−	0.739382i	$-0.735118\pi$
$5$	−0.398353	+	0.289420i	−0.178149	+	0.129433i	0.495137	+	0.868815i	$0.335118\pi$
$6$	−2.89857	+	2.10593i	−1.18333	+	0.859743i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$8$	0.293014	−	0.901803i	0.103596	−	0.318835i
$9$	0.0930802	+	0.0676268i	0.0310267	+	0.0225423i
$10$	1.03864			0.328448
$11$		0			0
$11$		0			0
$12$	4.16054			1.20104
$13$	−4.28803	−	3.11543i	−1.18928	−	0.864066i	−0.196096	−	0.980585i	$-0.562826\pi$
$13$	−4.28803	−	3.11543i	−1.18928	−	0.864066i	−0.993188	+	0.116519i	$0.962826\pi$
$14$	0.651837	−	2.00615i	0.174211	−	0.536166i
$15$	0.258441	+	0.795400i	0.0667292	+	0.205371i
$16$	2.34525	−	1.70393i	0.586313	−	0.425982i
$17$	−2.45715	+	1.78523i	−0.595947	+	0.432981i	−0.844438	−	0.535653i	$-0.820065\pi$
$17$	−2.45715	+	1.78523i	−0.595947	+	0.432981i	0.248491	+	0.968634i	$0.420065\pi$
$18$	−0.0749961	−	0.230814i	−0.0176768	−	0.0544035i
$19$	−1.44194	+	4.43784i	−0.330804	+	1.01811i	0.637948	+	0.770080i	$0.279784\pi$
$19$	−1.44194	+	4.43784i	−0.330804	+	1.01811i	−0.968752	+	0.248031i	$0.920216\pi$
$20$	−0.975773	−	0.708941i	−0.218189	−	0.158524i
$21$	1.69851			0.370646
$22$		0			0
$23$	−5.63835			−1.17568			−0.587839	−	0.808978i	$-0.700021\pi$
$23$	−5.63835			−1.17568			−0.587839	+	0.808978i	$0.700021\pi$
$24$	−1.30296	−	0.946657i	−0.265966	−	0.193236i
$25$	−1.47016	+	4.52470i	−0.294033	+	0.904940i
$26$	3.45493	+	10.6332i	0.677567	+	2.08534i
$27$	4.28048	−	3.10995i	0.823778	−	0.598510i
$28$	−1.98170	+	1.43979i	−0.374507	+	0.272095i
$29$	2.13931	+	6.58412i	0.397260	+	1.22264i	0.927187	+	0.374598i	$0.122219\pi$
$29$	2.13931	+	6.58412i	0.397260	+	1.22264i	−0.529927	+	0.848043i	$0.677781\pi$
$30$	0.545153	−	1.67781i	0.0995308	−	0.306324i
$31$	1.02393	+	0.743930i	0.183904	+	0.133614i	0.675928	−	0.736968i	$-0.263743\pi$
$31$	1.02393	+	0.743930i	0.183904	+	0.133614i	−0.492025	+	0.870581i	$0.663743\pi$
$32$	−8.01131			−1.41621
$33$		0			0
$34$	6.40665			1.09873
$35$	−0.398353	−	0.289420i	−0.0673339	−	0.0489210i
$36$	−0.0870890	+	0.268032i	−0.0145148	+	0.0446721i
$37$	3.36082	+	10.3436i	0.552516	+	1.70047i	0.702414	+	0.711768i	$0.252105\pi$
$37$	3.36082	+	10.3436i	0.552516	+	1.70047i	−0.149898	+	0.988701i	$0.547895\pi$
$38$	7.96305	−	5.78550i	1.29178	−	0.938532i
$39$	−7.28327	+	5.29160i	−1.16626	+	0.847335i
$40$	0.144277	+	0.444040i	0.0228122	+	0.0702089i
$41$	−0.445979	+	1.37258i	−0.0696502	+	0.214361i	−0.979823	−	0.199868i	$-0.935949\pi$
$41$	−0.445979	+	1.37258i	−0.0696502	+	0.214361i	0.910173	+	0.414229i	$0.135949\pi$
$42$	−2.89857	−	2.10593i	−0.447258	−	0.324952i
$43$	2.88224			0.439537			0.219769	−	0.975552i	$-0.429470\pi$
$43$	2.88224			0.439537			0.219769	+	0.975552i	$0.429470\pi$
$44$		0			0
$45$	−0.0566513			−0.00844508
$46$	9.62202	+	6.99081i	1.41869	+	1.03074i
$47$	−2.70551	+	8.32671i	−0.394639	+	1.21458i	0.534603	+	0.845104i	$0.320461\pi$
$47$	−2.70551	+	8.32671i	−0.394639	+	1.21458i	−0.929242	+	0.369472i	$0.879539\pi$
$48$	−1.52154	−	4.68282i	−0.219615	−	0.675907i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	8.11891	−	5.89873i	1.14819	−	0.834207i
$51$	1.59414	+	4.90625i	0.223224	+	0.687012i
$52$	4.01202	−	12.3477i	0.556367	−	1.71232i
$53$	−5.37054	−	3.90192i	−0.737700	−	0.535971i	0.154290	−	0.988026i	$-0.450691\pi$
$53$	−5.37054	−	3.90192i	−0.737700	−	0.535971i	−0.891990	+	0.452055i	$0.850691\pi$
$54$	−11.1607			−1.51878
$55$		0			0
$56$	0.948212			0.126710
$57$	6.41198	+	4.65857i	0.849287	+	0.617043i
$58$	4.51264	−	13.8885i	0.592538	−	1.82365i
$59$	−2.58256	−	7.94830i	−0.336220	−	1.03478i	−0.966118	−	0.258102i	$-0.916903\pi$
$59$	−2.58256	−	7.94830i	−0.336220	−	1.03478i	0.629897	−	0.776678i	$-0.283097\pi$
$60$	−1.65736	+	1.20414i	−0.213965	+	0.155454i
$61$	11.2415	−	8.16744i	1.43933	−	1.04573i	0.451147	−	0.892450i	$-0.351015\pi$
$61$	11.2415	−	8.16744i	1.43933	−	1.04573i	0.988182	−	0.153284i	$-0.0489851\pi$
$62$	−0.824997	−	2.53908i	−0.104775	−	0.322463i
$63$	−0.0355535	+	0.109422i	−0.00447932	+	0.0137859i
$64$	8.98105	+	6.52511i	1.12263	+	0.815639i
$65$	2.60982			0.323708
$66$		0			0
$67$	−9.70431			−1.18557			−0.592785	−	0.805361i	$-0.701972\pi$
$67$	−9.70431			−1.18557			−0.592785	+	0.805361i	$0.701972\pi$
$68$	−6.01884	−	4.37294i	−0.729892	−	0.530297i
$69$	−2.95940	+	9.10809i	−0.356270	+	1.09649i
$70$	0.320959	+	0.987809i	0.0383619	+	0.118066i
$71$	−4.81163	+	3.49586i	−0.571036	+	0.414882i	−0.835481	−	0.549519i	$-0.814811\pi$
$71$	−4.81163	+	3.49586i	−0.571036	+	0.414882i	0.264445	+	0.964401i	$0.414811\pi$
$72$	0.0882598	−	0.0641245i	0.0104015	−	0.00755714i
$73$	−1.16629	−	3.58948i	−0.136504	−	0.420117i	0.859317	−	0.511444i	$-0.170889\pi$
$73$	−1.16629	−	3.58948i	−0.136504	−	0.420117i	−0.995821	+	0.0913267i	$0.970889\pi$
$74$	7.08928	−	21.8186i	0.824113	−	2.53636i
$75$	6.53747	+	4.74975i	0.754882	+	0.548454i
$76$	−11.4300			−1.31111
$77$		0			0
$78$	18.9900			2.15020
$79$	7.12245	+	5.17476i	0.801338	+	0.582206i	0.911306	−	0.411729i	$-0.135075\pi$
$79$	7.12245	+	5.17476i	0.801338	+	0.582206i	−0.109968	+	0.993935i	$0.535075\pi$
$80$	−0.441088	+	1.35753i	−0.0493151	+	0.151776i
$81$	−2.67040	−	8.21865i	−0.296711	−	0.913184i
$82$	2.46290	−	1.78940i	0.271982	−	0.197606i
$83$	−8.97183	+	6.51842i	−0.984787	+	0.715489i	−0.958773	−	0.284172i	$-0.908281\pi$
$83$	−8.97183	+	6.51842i	−0.984787	+	0.715489i	−0.0260135	+	0.999662i	$0.508281\pi$
$84$	1.28568	+	3.95691i	0.140279	+	0.431734i
$85$	0.462133	−	1.42230i	0.0501254	−	0.154270i
$86$	−4.91863	−	3.57359i	−0.530389	−	0.385350i
$87$	11.7587			1.26067
$88$		0			0
$89$	3.10324			0.328943			0.164472	−	0.986382i	$-0.447408\pi$
$89$	3.10324			0.328943			0.164472	+	0.986382i	$0.447408\pi$
$90$	0.0966773	+	0.0702401i	0.0101907	+	0.00740396i
$91$	1.63788	−	5.04088i	0.171697	−	0.528428i
$92$	−4.26791	−	13.1353i	−0.444960	−	1.36945i
$93$	1.73916	−	1.26357i	0.180343	−	0.131027i
$94$	14.9411	−	10.8553i	1.54105	−	1.11964i
$95$	−0.710000	−	2.18515i	−0.0728444	−	0.224192i
$96$	−4.20489	+	12.9413i	−0.429160	+	1.32082i
$97$	5.11036	+	3.71290i	0.518879	+	0.376988i	0.816181	−	0.577796i	$-0.196087\pi$
$97$	5.11036	+	3.71290i	0.518879	+	0.376988i	−0.297302	+	0.954783i	$0.596087\pi$
$98$	2.10939			0.213080
$99$		0			0
$100$	−11.6537			−1.16537
$101$	−9.54511	−	6.93493i	−0.949774	−	0.690051i	0.000979100	−	1.00000i	$-0.499688\pi$
$101$	−9.54511	−	6.93493i	−0.949774	−	0.690051i	−0.950754	+	0.309948i	$0.899688\pi$
$102$	3.36265	−	10.3492i	0.332952	−	1.02472i
$103$	2.16486	+	6.66277i	0.213310	+	0.656502i	0.999269	+	0.0382232i	$0.0121698\pi$
$103$	2.16486	+	6.66277i	0.213310	+	0.656502i	−0.785959	+	0.618279i	$0.787830\pi$
$104$	−4.06596	+	2.95409i	−0.398700	+	0.289672i
$105$	−0.676607	+	0.491584i	−0.0660301	+	0.0479737i
$106$	4.32712	+	13.3175i	0.420287	+	1.29351i
$107$	3.50879	−	10.7990i	0.339208	−	1.04397i	−0.625404	−	0.780301i	$-0.715066\pi$
$107$	3.50879	−	10.7990i	0.339208	−	1.04397i	0.964612	−	0.263674i	$-0.0849342\pi$
$108$	10.4851	+	7.61788i	1.00893	+	0.733031i
$109$	18.9414			1.81426			0.907129	−	0.420853i	$-0.138269\pi$
$109$	18.9414			1.81426			0.907129	+	0.420853i	$0.138269\pi$
$110$		0			0
$111$	18.4728			1.75336
$112$	2.34525	+	1.70393i	0.221606	+	0.161006i
$113$	−4.17053	+	12.8356i	−0.392330	+	1.20747i	0.538691	+	0.842503i	$0.318919\pi$
$113$	−4.17053	+	12.8356i	−0.392330	+	1.20747i	−0.931021	+	0.364965i	$0.881081\pi$
$114$	−5.16622	−	15.9000i	−0.483861	−	1.48917i
$115$	2.24605	−	1.63185i	0.209445	−	0.152171i
$116$	−13.7192	+	9.96761i	−1.27380	+	0.925470i
$117$	−0.188444	−	0.579971i	−0.0174216	−	0.0536183i
$118$	−5.44762	+	16.7660i	−0.501494	+	1.54344i
$119$	−2.45715	−	1.78523i	−0.225247	−	0.163651i
$120$	0.793021			0.0723925
$121$		0			0
$122$	−29.3106			−2.65365
$123$	1.98316	+	1.44085i	0.178816	+	0.129917i
$124$	−0.958024	+	2.94850i	−0.0860331	+	0.264783i
$125$	−1.48468	−	4.56938i	−0.132794	−	0.408698i
$126$	0.196342	−	0.142651i	0.0174916	−	0.0127084i
$127$	3.77054	−	2.73945i	0.334581	−	0.243087i	−0.407791	−	0.913075i	$-0.633701\pi$
$127$	3.77054	−	2.73945i	0.334581	−	0.243087i	0.742372	+	0.669988i	$0.233701\pi$
$128$	−2.28490	−	7.03220i	−0.201958	−	0.621564i
$129$	1.51280	−	4.65591i	0.133194	−	0.409930i
$130$	−4.45373	−	3.23583i	−0.390618	−	0.283801i
$131$	9.03676			0.789545			0.394773	−	0.918779i	$-0.370823\pi$
$131$	9.03676			0.789545			0.394773	+	0.918779i	$0.370823\pi$
$132$		0			0
$133$	−4.66622			−0.404613
$134$	16.5607	+	12.0321i	1.43063	+	1.03941i
$135$	−0.805058	+	2.47771i	−0.0692883	+	0.213248i
$136$	0.889943	+	2.73896i	0.0763119	+	0.234864i
$137$	1.32495	−	0.962629i	0.113198	−	0.0822429i	−0.529746	−	0.848156i	$-0.677713\pi$
$137$	1.32495	−	0.962629i	0.113198	−	0.0822429i	0.642944	+	0.765913i	$0.277713\pi$
$138$	16.3431	−	11.8740i	1.39122	−	1.01078i
$139$	−0.474255	−	1.45961i	−0.0402257	−	0.123802i	0.928927	−	0.370263i	$-0.120732\pi$
$139$	−0.474255	−	1.45961i	−0.0402257	−	0.123802i	−0.969153	+	0.246461i	$0.920732\pi$
$140$	0.372712	−	1.14709i	0.0314999	−	0.0969468i
$141$	12.0308	+	8.74087i	1.01317	+	0.736114i
$142$	12.5456			1.05280
$143$		0			0
$144$	0.333528			0.0277940
$145$	−2.75778	−	2.00364i	−0.229021	−	0.166394i
$146$	−2.46017	+	7.57162i	−0.203605	+	0.626631i
$147$	0.524869	+	1.61538i	0.0432905	+	0.133234i
$148$	−21.5527	+	15.6590i	−1.77162	+	1.28716i
$149$	−10.9144	+	7.92977i	−0.894142	+	0.649632i	−0.936955	−	0.349451i	$-0.886368\pi$
$149$	−10.9144	+	7.92977i	−0.894142	+	0.649632i	0.0428125	+	0.999083i	$0.486368\pi$
$150$	−5.26734	−	16.2112i	−0.430076	−	1.32364i
$151$	−3.78145	+	11.6381i	−0.307730	+	0.947095i	0.670915	+	0.741535i	$0.265902\pi$
$151$	−3.78145	+	11.6381i	−0.307730	+	0.947095i	−0.978644	+	0.205560i	$0.934098\pi$
$152$	3.57955	+	2.60070i	0.290340	+	0.210944i
$153$	−0.349441			−0.0282507
$154$		0			0
$155$	−0.623194			−0.0500562
$156$	−17.8405	−	12.9619i	−1.42838	−	1.03778i
$157$	0.778853	−	2.39706i	0.0621592	−	0.191306i	−0.915154	−	0.403103i	$-0.867932\pi$
$157$	0.778853	−	2.39706i	0.0621592	−	0.191306i	0.977314	+	0.211797i	$0.0679315\pi$
$158$	−5.73866	−	17.6618i	−0.456543	−	1.40510i
$159$	−9.12193	+	6.62747i	−0.723416	+	0.525593i
$160$	3.19133	−	2.31864i	0.252297	−	0.183304i
$161$	−1.74235	−	5.36239i	−0.137316	−	0.422616i
$162$	−5.63292	+	17.3363i	−0.442564	+	1.36207i
$163$	−6.37428	−	4.63119i	−0.499272	−	0.362743i	0.309467	−	0.950910i	$-0.399849\pi$
$163$	−6.37428	−	4.63119i	−0.499272	−	0.362743i	−0.808739	+	0.588168i	$0.799849\pi$
$164$	−3.53519			−0.276052
$165$		0			0
$166$	23.3927			1.81562
$167$	1.66241	+	1.20781i	0.128641	+	0.0934634i	0.650245	−	0.759724i	$-0.274666\pi$
$167$	1.66241	+	1.20781i	0.128641	+	0.0934634i	−0.521604	+	0.853188i	$0.674666\pi$
$168$	0.497687	−	1.53172i	0.0383974	−	0.118175i
$169$	4.66403	+	14.3544i	0.358771	+	1.10418i
$170$	−2.55211	+	1.85421i	−0.195738	+	0.142212i
$171$	−0.434333	+	0.315562i	−0.0332143	+	0.0241316i
$172$	2.18169	+	6.71455i	0.166352	+	0.511980i
$173$	−7.19103	+	22.1317i	−0.546724	+	1.68264i	0.170133	+	0.985421i	$0.445580\pi$
$173$	−7.19103	+	22.1317i	−0.546724	+	1.68264i	−0.716856	+	0.697221i	$0.754420\pi$
$174$	−20.0666	−	14.5793i	−1.52125	−	1.10525i
$175$	−4.75755			−0.359637
$176$		0			0
$177$	−14.1950			−1.06696
$178$	−5.29578	−	3.84761i	−0.396936	−	0.288391i
$179$	5.45711	−	16.7953i	0.407883	−	1.25534i	−0.510580	−	0.859830i	$-0.670569\pi$
$179$	5.45711	−	16.7953i	0.407883	−	1.25534i	0.918463	−	0.395506i	$-0.129431\pi$
$180$	−0.0428818	−	0.131977i	−0.00319622	−	0.00983697i
$181$	−12.5156	+	9.09309i	−0.930274	+	0.675884i	−0.946060	−	0.323992i	$-0.894975\pi$
$181$	−12.5156	+	9.09309i	−0.930274	+	0.675884i	0.0157857	+	0.999875i	$0.494975\pi$
$182$	−9.04511	+	6.57166i	−0.670468	+	0.487124i
$183$	−7.29321	−	22.4462i	−0.539130	−	1.65927i
$184$	−1.65211	+	5.08468i	−0.121795	+	0.374848i
$185$	−4.33243	−	3.14769i	−0.318526	−	0.231423i
$186$	−4.53460			−0.332493
$187$		0			0
$188$	−21.4461			−1.56412
$189$	4.28048	+	3.10995i	0.311359	+	0.226215i
$190$	−1.49766	+	4.60934i	−0.108652	+	0.334397i
$191$	4.92527	+	15.1584i	0.356380	+	1.09682i	0.955205	+	0.295945i	$0.0956344\pi$
$191$	4.92527	+	15.1584i	0.356380	+	1.09682i	−0.598825	+	0.800880i	$0.704366\pi$
$192$	15.2544	−	11.0830i	1.10089	−	0.799846i
$193$	−6.83932	+	4.96906i	−0.492305	+	0.357680i	−0.806070	−	0.591820i	$-0.798410\pi$
$193$	−6.83932	+	4.96906i	−0.492305	+	0.357680i	0.313765	+	0.949501i	$0.398410\pi$
$194$	−4.11750	−	12.6723i	−0.295619	−	0.909822i
$195$	1.36981	−	4.21585i	0.0980944	−	0.301903i
$196$	−1.98170	−	1.43979i	−0.141550	−	0.102842i
$197$	−14.3384			−1.02157			−0.510785	−	0.859708i	$-0.670645\pi$
$197$	−14.3384			−1.02157			−0.510785	+	0.859708i	$0.670645\pi$
$198$		0			0
$199$	−22.1343			−1.56906			−0.784528	−	0.620094i	$-0.787095\pi$
$199$	−22.1343			−1.56906			−0.784528	+	0.620094i	$0.787095\pi$
$200$	3.64961	+	2.65160i	0.258066	+	0.187496i
$201$	−5.09349	+	15.6762i	−0.359267	+	1.10571i
$202$	7.69064	+	23.6694i	0.541111	+	1.66537i
$203$	−5.60079	+	4.06921i	−0.393098	+	0.285603i
$204$	−10.2231	+	7.42750i	−0.715759	+	0.520029i
$205$	−0.219596	−	0.675848i	−0.0153373	−	0.0472032i
$206$	4.56654	−	14.0544i	0.318166	−	0.979214i
$207$	−0.524819	−	0.381303i	−0.0364774	−	0.0265024i
$208$	−15.3650			−1.06537
$209$		0			0
$210$	1.76415			0.121738
$211$	−1.76610	−	1.28315i	−0.121584	−	0.0883356i	0.525332	−	0.850898i	$-0.323941\pi$
$211$	−1.76610	−	1.28315i	−0.121584	−	0.0883356i	−0.646915	+	0.762562i	$0.723941\pi$
$212$	5.02485	−	15.4649i	0.345108	−	1.06213i
$213$	3.12166	+	9.60749i	0.213893	+	0.658295i
$214$	−19.3771	+	14.0783i	−1.32459	+	0.962374i
$215$	−1.14815	+	0.834178i	−0.0783030	+	0.0568905i
$216$	−1.55032	−	4.77140i	−0.105486	−	0.324653i
$217$	−0.391107	+	1.20370i	−0.0265501	+	0.0817127i
$218$	−32.3241	−	23.4848i	−2.18926	−	1.59059i
$219$	−6.41054			−0.433184
$220$		0			0
$221$	16.0981			1.08287
$222$	−31.5244	−	22.9038i	−2.11578	−	1.53720i
$223$	8.42391	−	25.9261i	0.564107	−	1.73614i	−0.106485	−	0.994314i	$-0.533960\pi$
$223$	8.42391	−	25.9261i	0.564107	−	1.73614i	0.670591	−	0.741827i	$-0.266040\pi$
$224$	−2.47563	−	7.61921i	−0.165410	−	0.509080i
$225$	−0.442834	+	0.321738i	−0.0295223	+	0.0214492i
$226$	23.0315	−	16.7334i	1.53204	−	1.11309i
$227$	−4.19929	−	12.9241i	−0.278716	−	0.857801i	−0.988212	−	0.153091i	$-0.951077\pi$
$227$	−4.19929	−	12.9241i	−0.278716	−	0.857801i	0.709496	−	0.704710i	$-0.248923\pi$
$228$	−5.99926	+	18.4638i	−0.397311	+	1.22280i
$229$	6.71599	+	4.87945i	0.443805	+	0.322443i	0.787145	−	0.616768i	$-0.211558\pi$
$229$	6.71599	+	4.87945i	0.443805	+	0.322443i	−0.343340	+	0.939211i	$0.611558\pi$
$230$	−5.85624			−0.386149
$231$		0			0
$232$	6.56443			0.430976
$233$	−10.4749	−	7.61044i	−0.686231	−	0.498576i	0.189188	−	0.981941i	$-0.439415\pi$
$233$	−10.4749	−	7.61044i	−0.686231	−	0.498576i	−0.875419	+	0.483365i	$0.839415\pi$
$234$	−0.397501	+	1.22338i	−0.0259855	+	0.0799751i
$235$	−1.33217	−	4.10000i	−0.0869012	−	0.267454i
$236$	16.5618	−	12.0328i	1.07808	−	0.783270i
$237$	12.0976	−	8.78940i	0.785822	−	0.570933i
$238$	1.97976	+	6.09308i	0.128329	+	0.394956i
$239$	0.585098	−	1.80075i	0.0378469	−	0.116481i	−0.930348	−	0.366677i	$-0.880495\pi$
$239$	0.585098	−	1.80075i	0.0378469	−	0.116481i	0.968195	+	0.250197i	$0.0804953\pi$
$240$	1.96141	+	1.42505i	0.126609	+	0.0919866i
$241$	−11.6983			−0.753557			−0.376778	−	0.926303i	$-0.622968\pi$
$241$	−11.6983			−0.753557			−0.376778	+	0.926303i	$0.622968\pi$
$242$		0			0
$243$	1.19500			0.0766595
$244$	27.5363	+	20.0063i	1.76283	+	1.28077i
$245$	0.152157	−	0.468292i	0.00972097	−	0.0299181i
$246$	−1.59786	−	4.91772i	−0.101876	−	0.313543i
$247$	20.0089	−	14.5373i	1.27314	−	0.924987i
$248$	0.970904	−	0.705403i	0.0616524	−	0.0447931i
$249$	5.82069	+	17.9143i	0.368872	+	1.13527i
$250$	−3.13177	+	9.63860i	−0.198071	+	0.609599i
$251$	10.6677	+	7.75052i	0.673338	+	0.489208i	0.871141	−	0.491033i	$-0.163381\pi$
$251$	10.6677	+	7.75052i	0.673338	+	0.489208i	−0.197803	+	0.980242i	$0.563381\pi$
$252$	−0.281826			−0.0177534
$253$		0			0
$254$	−9.83110			−0.616858
$255$	−2.05500	−	1.49304i	−0.128689	−	0.0934979i
$256$	2.04117	−	6.28208i	0.127573	−	0.392630i
$257$	−4.74172	−	14.5935i	−0.295780	−	0.910318i	−0.982958	−	0.183829i	$-0.941151\pi$
$257$	−4.74172	−	14.5935i	−0.295780	−	0.910318i	0.687178	−	0.726489i	$-0.258849\pi$
$258$	−8.35435	+	6.06979i	−0.520119	+	0.377889i
$259$	−8.79875	+	6.39267i	−0.546728	+	0.397221i
$260$	1.97548	+	6.07991i	0.122514	+	0.377060i
$261$	−0.246135	+	0.757526i	−0.0152354	+	0.0468897i
$262$	−15.4215	−	11.2044i	−0.952744	−	0.692209i
$263$	10.4197			0.642507			0.321254	−	0.946993i	$-0.395896\pi$
$263$	10.4197			0.642507			0.321254	+	0.946993i	$0.395896\pi$
$264$		0			0
$265$	3.26867			0.200792
$266$	7.96305	+	5.78550i	0.488246	+	0.354732i
$267$	1.62880	−	5.01293i	0.0996808	−	0.306786i
$268$	−7.34561	−	22.6075i	−0.448705	−	1.38097i
$269$	−13.1637	+	9.56399i	−0.802605	+	0.583127i	−0.911677	−	0.410907i	$-0.865212\pi$
$269$	−13.1637	+	9.56399i	−0.802605	+	0.583127i	0.109072	+	0.994034i	$0.465212\pi$
$270$	4.44589	−	3.23013i	0.270568	−	0.196579i
$271$	−1.80442	−	5.55343i	−0.109611	−	0.337347i	0.881174	−	0.472792i	$-0.156754\pi$
$271$	−1.80442	−	5.55343i	−0.109611	−	0.337347i	−0.990785	+	0.135445i	$0.956754\pi$
$272$	−2.72075	+	8.37361i	−0.164970	+	0.507725i
$273$	−7.28327	−	5.29160i	−0.440804	−	0.320263i
$274$	−3.45459			−0.208700
$275$		0			0
$276$	−23.4586			−1.41204
$277$	−12.8840	−	9.36075i	−0.774123	−	0.562433i	0.129087	−	0.991633i	$-0.458795\pi$
$277$	−12.8840	−	9.36075i	−0.774123	−	0.562433i	−0.903209	+	0.429200i	$0.858795\pi$
$278$	−1.00039	+	3.07888i	−0.0599992	+	0.184659i
$279$	0.0449982	+	0.138490i	0.00269397	+	0.00829120i
$280$	−0.377723	+	0.274432i	−0.0225733	+	0.0164004i
$281$	−8.25228	+	5.99563i	−0.492290	+	0.357669i	−0.806064	−	0.591828i	$-0.798406\pi$
$281$	−8.25228	+	5.99563i	−0.492290	+	0.357669i	0.313774	+	0.949498i	$0.398406\pi$
$282$	−9.69337	−	29.8331i	−0.577232	−	1.77654i
$283$	−4.99475	+	15.3723i	−0.296907	+	0.913786i	0.685667	+	0.727915i	$0.259511\pi$
$283$	−4.99475	+	15.3723i	−0.296907	+	0.913786i	−0.982574	+	0.185871i	$0.940489\pi$
$284$	−11.7862	−	8.56317i	−0.699382	−	0.508131i
$285$	−3.90252			−0.231165
$286$		0			0
$287$	−1.44322			−0.0851905
$288$	−0.745695	−	0.541779i	−0.0439405	−	0.0319246i
$289$	−2.40272	+	7.39482i	−0.141337	+	0.434990i
$290$	2.22198	+	6.83856i	0.130479	+	0.401574i
$291$	8.68002	−	6.30640i	0.508832	−	0.369688i
$292$	7.47936	−	5.43407i	0.437696	−	0.318005i
$293$	8.35943	+	25.7277i	0.488363	+	1.50303i	0.827050	+	0.562128i	$0.190017\pi$
$293$	8.35943	+	25.7277i	0.488363	+	1.50303i	−0.338687	+	0.940899i	$0.609983\pi$
$294$	1.10715	−	3.40747i	0.0645705	−	0.198728i
$295$	3.32917	+	2.41878i	0.193832	+	0.140827i
$296$	10.3126			0.599408
$297$		0			0
$298$	28.4576			1.64851
$299$	24.1774	+	17.5659i	1.39821	+	1.01586i
$300$	−6.11668	+	18.8252i	−0.353147	+	1.08687i
$301$	0.890660	+	2.74117i	0.0513368	+	0.157998i
$302$	20.8829	−	15.1723i	1.20167	−	0.873067i
$303$	−16.2125	+	11.7791i	−0.931384	+	0.676690i
$304$	4.18004	+	12.8648i	0.239741	+	0.737848i
$305$	−2.11427	+	6.50705i	−0.121063	+	0.372593i
$306$	0.596332	+	0.433261i	0.0340901	+	0.0247679i
$307$	29.7251			1.69650			0.848250	−	0.529596i	$-0.177657\pi$
$307$	29.7251			1.69650			0.848250	+	0.529596i	$0.177657\pi$
$308$		0			0
$309$	11.8992			0.676921
$310$	1.06350	+	0.772678i	0.0604028	+	0.0438852i
$311$	6.92288	−	21.3064i	0.392560	−	1.20818i	−0.538285	−	0.842763i	$-0.680928\pi$
$311$	6.92288	−	21.3064i	0.392560	−	1.20818i	0.930845	−	0.365414i	$-0.119072\pi$
$312$	2.63789	+	8.11858i	0.149341	+	0.459624i
$313$	−8.04837	+	5.84748i	−0.454921	+	0.330519i	−0.791536	−	0.611123i	$-0.790718\pi$
$313$	−8.04837	+	5.84748i	−0.454921	+	0.330519i	0.336615	+	0.941642i	$0.390718\pi$
$314$	−4.30118	+	3.12499i	−0.242729	+	0.176353i
$315$	−0.0175062	−	0.0538786i	−0.000986364	−	0.00303572i
$316$	−6.66400	+	20.5097i	−0.374879	+	1.15376i
$317$	9.01405	+	6.54909i	0.506280	+	0.367834i	0.811410	−	0.584477i	$-0.198700\pi$
$317$	9.01405	+	6.54909i	0.506280	+	0.367834i	−0.305131	+	0.952310i	$0.598700\pi$
$318$	23.7840			1.33374
$319$		0			0
$320$	−5.46613			−0.305566
$321$	−15.6028	−	11.3361i	−0.870862	−	0.632719i
$322$	−3.67528	+	11.3114i	−0.204816	+	0.630358i
$323$	−4.37948	−	13.4786i	−0.243681	−	0.749972i
$324$	17.1251	−	12.4421i	0.951394	−	0.691228i
$325$	20.4005	−	14.8218i	1.13162	−	0.822167i
$326$	5.13585	+	15.8065i	0.284449	+	0.875443i
$327$	9.94176	−	30.5976i	0.549781	−	1.69205i
$328$	1.10712	+	0.804371i	0.0611305	+	0.0444139i
$329$	−8.75522			−0.482691
$330$		0			0
$331$	14.5950			0.802214			0.401107	−	0.916031i	$-0.368626\pi$
$331$	14.5950			0.802214			0.401107	+	0.916031i	$0.368626\pi$
$332$	−21.9767	−	15.9670i	−1.20613	−	0.876303i
$333$	−0.386675	+	1.19006i	−0.0211896	+	0.0652150i
$334$	−1.33943	−	4.12234i	−0.0732903	−	0.225564i
$335$	3.86574	−	2.80862i	0.211208	−	0.153452i
$336$	3.98344	−	2.89414i	0.217315	−	0.157888i
$337$	3.89544	+	11.9889i	0.212198	+	0.653079i	0.999341	+	0.0363079i	$0.0115597\pi$
$337$	3.89544	+	11.9889i	0.212198	+	0.653079i	−0.787142	+	0.616771i	$0.788440\pi$
$338$	9.83824	−	30.2790i	0.535130	−	1.64696i
$339$	18.5454	+	13.4740i	1.00725	+	0.731807i
$340$	3.66324			0.198667
$341$		0			0
$342$	1.13246			0.0612363
$343$	−0.809017	−	0.587785i	−0.0436828	−	0.0317374i
$344$	0.844534	−	2.59921i	0.0455342	−	0.140140i
$345$	−1.45718	−	4.48474i	−0.0784520	−	0.241450i
$346$	39.7121	−	28.8525i	2.13494	−	1.55112i
$347$	−0.332291	+	0.241424i	−0.0178383	+	0.0129603i	−0.596669	−	0.802488i	$-0.703509\pi$
$347$	−0.332291	+	0.241424i	−0.0178383	+	0.0129603i	0.578830	+	0.815448i	$0.303509\pi$
$348$	8.90069	+	27.3935i	0.477127	+	1.46845i
$349$	4.14162	−	12.7466i	0.221696	−	0.682309i	−0.776915	−	0.629606i	$-0.783216\pi$
$349$	4.14162	−	12.7466i	0.221696	−	0.682309i	0.998610	−	0.0527030i	$-0.0167836\pi$
$350$	8.11891	+	5.89873i	0.433974	+	0.315301i
$351$	−28.0436			−1.49686
$352$		0			0
$353$	12.3419			0.656892			0.328446	−	0.944523i	$-0.393475\pi$
$353$	12.3419			0.656892			0.328446	+	0.944523i	$0.393475\pi$
$354$	24.2243	+	17.6000i	1.28751	+	0.935428i
$355$	0.904956	−	2.78517i	0.0480301	−	0.147821i
$356$	2.34898	+	7.22942i	0.124496	+	0.383158i
$357$	−4.17350	+	3.03223i	−0.220885	+	0.160483i
$358$	−30.1366	+	21.8955i	−1.59277	+	1.15721i
$359$	−7.72842	−	23.7856i	−0.407890	−	1.25536i	−0.918458	−	0.395520i	$-0.870565\pi$
$359$	−7.72842	−	23.7856i	−0.407890	−	1.25536i	0.510567	−	0.859838i	$-0.329435\pi$
$360$	−0.0165996	+	0.0510883i	−0.000874876	+	0.00269259i
$361$	−2.24392	−	1.63030i	−0.118101	−	0.0858054i
$362$	32.6324			1.71512
$363$		0			0
$364$	12.9832			0.680503
$365$	1.50347	+	1.09233i	0.0786950	+	0.0571753i
$366$	−15.3842	+	47.3477i	−0.804146	+	2.47491i
$367$	−0.639402	−	1.96788i	−0.0333765	−	0.102722i	0.932980	−	0.359927i	$-0.117198\pi$
$367$	−0.639402	−	1.96788i	−0.0333765	−	0.102722i	−0.966357	+	0.257205i	$0.917198\pi$
$368$	−13.2234	+	9.60733i	−0.689315	+	0.500817i
$369$	−0.134335	+	0.0976002i	−0.00699321	+	0.00508086i
$370$	3.49070	+	10.7433i	0.181473	+	0.558516i
$371$	2.05136	−	6.31345i	0.106501	−	0.327778i
$372$	4.26011	+	3.09515i	0.220876	+	0.160476i
$373$	−14.7623			−0.764365			−0.382183	−	0.924087i	$-0.624828\pi$
$373$	−14.7623			−0.764365			−0.382183	+	0.924087i	$0.624828\pi$
$374$		0			0
$375$	−8.16056			−0.421410
$376$	6.71630	+	4.87968i	0.346367	+	0.251650i
$377$	11.3390	−	34.8978i	0.583987	−	1.79733i
$378$	−3.44884	−	10.6144i	−0.177389	−	0.545948i
$379$	−22.4508	+	16.3115i	−1.15322	+	0.837865i	−0.988906	−	0.148543i	$-0.952542\pi$
$379$	−22.4508	+	16.3115i	−1.15322	+	0.837865i	−0.164316	+	0.986408i	$0.552542\pi$
$380$	4.55317	−	3.30808i	0.233573	−	0.169701i
$381$	−2.44623	−	7.52871i	−0.125324	−	0.385708i
$382$	10.3893	−	31.9750i	0.531563	−	1.63598i
$383$	14.5893	+	10.5998i	0.745480	+	0.541623i	0.894423	−	0.447223i	$-0.147587\pi$
$383$	14.5893	+	10.5998i	0.745480	+	0.541623i	−0.148942	+	0.988846i	$0.547587\pi$
$384$	−12.5590			−0.640897
$385$		0			0
$386$	17.8325			0.907649
$387$	0.268279	+	0.194916i	0.0136374	+	0.00990816i
$388$	−4.78143	+	14.7157i	−0.242740	+	0.747077i
$389$	4.18445	+	12.8784i	0.212160	+	0.652961i	0.999343	+	0.0362419i	$0.0115387\pi$
$389$	4.18445	+	12.8784i	0.212160	+	0.652961i	−0.787183	+	0.616719i	$0.788461\pi$
$390$	−7.56473	+	5.49610i	−0.383055	+	0.278306i
$391$	13.8543	−	10.0657i	0.700641	−	0.509046i
$392$	0.293014	+	0.901803i	0.0147994	+	0.0455479i
$393$	4.74312	−	14.5978i	0.239259	−	0.736363i
$394$	24.4690	+	17.7778i	1.23273	+	0.895630i
$395$	−4.33493			−0.218114
$396$		0			0
$397$	−24.6525			−1.23727			−0.618637	−	0.785677i	$-0.712315\pi$
$397$	−24.6525			−1.23727			−0.618637	+	0.785677i	$0.712315\pi$
$398$	37.7728	+	27.4435i	1.89338	+	1.37562i
$399$	−2.44916	+	7.53773i	−0.122611	+	0.377359i
$400$	4.26185	+	13.1166i	0.213092	+	0.655831i
$401$	−15.1601	+	11.0145i	−0.757060	+	0.550036i	−0.898007	−	0.439981i	$-0.854985\pi$
$401$	−15.1601	+	11.0145i	−0.757060	+	0.550036i	0.140947	+	0.990017i	$0.454985\pi$
$402$	28.1286	−	20.4366i	1.40293	−	1.01929i
$403$	−2.07298	−	6.37998i	−0.103263	−	0.317809i
$404$	8.93073	−	27.4860i	0.444320	−	1.36748i
$405$	3.44241	+	2.50105i	0.171055	+	0.124278i
$406$	14.6032			0.724745
$407$		0			0
$408$	4.89157			0.242169
$409$	−12.7095	−	9.23401i	−0.628445	−	0.456592i	0.227416	−	0.973798i	$-0.426972\pi$
$409$	−12.7095	−	9.23401i	−0.628445	−	0.456592i	−0.855861	+	0.517205i	$0.826972\pi$
$410$	−0.463214	+	1.42563i	−0.0228765	+	0.0704066i
$411$	−0.859590	−	2.64555i	−0.0424005	−	0.130495i
$412$	−13.8831	+	10.0867i	−0.683972	+	0.496935i
$413$	6.76123	−	4.91232i	0.332698	−	0.241719i
$414$	0.422854	+	1.30141i	0.0207822	+	0.0639609i
$415$	1.68739	−	5.19326i	0.0828309	−	0.254927i
$416$	34.3527	+	24.9587i	1.68428	+	1.22370i
$417$	−2.60674			−0.127653
$418$		0			0
$419$	22.6034			1.10425			0.552125	−	0.833761i	$-0.313817\pi$
$419$	22.6034			1.10425			0.552125	+	0.833761i	$0.313817\pi$
$420$	−1.65736	−	1.20414i	−0.0808710	−	0.0587563i
$421$	−7.20970	+	22.1892i	−0.351379	+	1.08143i	0.606700	+	0.794931i	$0.292493\pi$
$421$	−7.20970	+	22.1892i	−0.351379	+	1.08143i	−0.958079	+	0.286504i	$0.907507\pi$
$422$	1.42298	+	4.37947i	0.0692694	+	0.213189i
$423$	−0.814938	+	0.592087i	−0.0396236	+	0.0287883i
$424$	−5.09241	+	3.69985i	−0.247309	+	0.179681i
$425$	−4.46519	−	13.7424i	−0.216594	−	0.666607i
$426$	6.58480	−	20.2659i	0.319035	−	0.981888i
$427$	11.2415	+	8.16744i	0.544015	+	0.395250i
$428$	27.8136			1.34442
$429$		0			0
$430$	2.99362			0.144365
$431$	7.71719	+	5.60687i	0.371724	+	0.270073i	0.757926	−	0.652341i	$-0.226213\pi$
$431$	7.71719	+	5.60687i	0.371724	+	0.270073i	−0.386201	+	0.922415i	$0.626213\pi$
$432$	4.73968	−	14.5872i	0.228038	−	0.701828i
$433$	−7.11064	−	21.8843i	−0.341716	−	1.05169i	−0.963319	−	0.268360i	$-0.913518\pi$
$433$	−7.11064	−	21.8843i	−0.341716	−	1.05169i	0.621603	−	0.783332i	$-0.286482\pi$
$434$	2.15987	−	1.56924i	0.103677	−	0.0753258i
$435$	−4.68412	+	3.40321i	−0.224587	+	0.163172i
$436$	14.3376	+	44.1265i	0.686645	+	2.11328i
$437$	8.13018	−	25.0221i	0.388919	−	1.19697i
$438$	10.9398	+	7.94822i	0.522723	+	0.379781i
$439$	−27.6434			−1.31935			−0.659673	−	0.751553i	$-0.729305\pi$
$439$	−27.6434			−1.31935			−0.659673	+	0.751553i	$0.729305\pi$
$440$		0			0
$441$	−0.115054			−0.00547874
$442$	−27.4719	−	19.9595i	−1.30670	−	0.949376i
$443$	4.56459	−	14.0484i	0.216870	−	0.667458i	−0.782145	−	0.623096i	$-0.785875\pi$
$443$	4.56459	−	14.0484i	0.216870	−	0.667458i	0.999016	−	0.0443620i	$-0.0141255\pi$
$444$	13.9828	+	43.0348i	0.663597	+	2.04234i
$445$	−1.23619	+	0.898142i	−0.0586009	+	0.0425760i
$446$	−46.5206	+	33.7992i	−2.20281	+	1.60044i
$447$	7.08098	+	21.7930i	0.334919	+	1.03077i
$448$	−3.43046	+	10.5579i	−0.162074	+	0.498812i
$449$	−24.4864	−	17.7904i	−1.15559	−	0.839583i	−0.166373	−	0.986063i	$-0.553205\pi$
$449$	−24.4864	−	17.7904i	−1.15559	−	0.839583i	−0.989214	+	0.146480i	$0.953205\pi$
$450$	1.15462			0.0544294
$451$		0			0
$452$	−33.0590			−1.55496
$453$	16.8152	+	12.2170i	0.790047	+	0.574003i
$454$	−8.85792	+	27.2619i	−0.415723	+	1.27946i
$455$	0.806478	+	2.48208i	0.0378083	+	0.116362i
$456$	6.07991	−	4.41731i	0.284718	−	0.206860i
$457$	16.3878	−	11.9065i	0.766591	−	0.556961i	−0.134334	−	0.990936i	$-0.542889\pi$
$457$	16.3878	−	11.9065i	0.766591	−	0.556961i	0.900925	+	0.433975i	$0.142889\pi$
$458$	−5.41117	−	16.6539i	−0.252847	−	0.778184i
$459$	−4.96582	+	15.2832i	−0.231785	+	0.713360i
$460$	5.50175	+	3.99726i	0.256520	+	0.186373i
$461$	8.51184			0.396436			0.198218	−	0.980158i	$-0.436485\pi$
$461$	8.51184			0.396436			0.198218	+	0.980158i	$0.436485\pi$
$462$		0			0
$463$	−0.591469			−0.0274879			−0.0137440	−	0.999906i	$-0.504375\pi$
$463$	−0.591469			−0.0274879			−0.0137440	+	0.999906i	$0.504375\pi$
$464$	16.2361	+	11.7962i	0.753741	+	0.547625i
$465$	−0.327096	+	1.00670i	−0.0151687	+	0.0466844i
$466$	8.43975	+	25.9749i	0.390964	+	1.20326i
$467$	33.1978	−	24.1196i	1.53621	−	1.11612i	0.583553	−	0.812075i	$-0.301662\pi$
$467$	33.1978	−	24.1196i	1.53621	−	1.11612i	0.952657	−	0.304046i	$-0.0983378\pi$
$468$	1.20848	−	0.878010i	0.0558619	−	0.0405860i
$469$	−2.99880	−	9.22935i	−0.138472	−	0.426172i
$470$	−2.81006	+	8.64849i	−0.129619	+	0.398925i
$471$	−3.46338	−	2.51629i	−0.159584	−	0.115945i
$472$	−7.92452			−0.364756
$473$		0			0
$474$	−31.5426			−1.44880
$475$	−17.9600	−	13.0487i	−0.824062	−	0.598716i
$476$	2.29899	−	7.07557i	0.105374	−	0.324308i
$477$	−0.236017	−	0.726384i	−0.0108065	−	0.0332588i
$478$	−3.23118	+	2.34759i	−0.147791	+	0.107376i
$479$	−16.4584	+	11.9577i	−0.752003	+	0.546362i	−0.896447	−	0.443151i	$-0.853861\pi$
$479$	−16.4584	+	11.9577i	−0.752003	+	0.546362i	0.144444	+	0.989513i	$0.453861\pi$
$480$	−2.07045	−	6.37220i	−0.0945028	−	0.290850i
$481$	17.8134	−	54.8239i	0.812219	−	2.49975i
$482$	19.9636	+	14.5044i	0.909317	+	0.660657i
$483$	−9.57681			−0.435760
$484$		0			0
$485$	−3.11032			−0.141232
$486$	−2.03931	−	1.48165i	−0.0925050	−	0.0672088i
$487$	−8.90478	+	27.4061i	−0.403514	+	1.24189i	0.518615	+	0.855008i	$0.326448\pi$
$487$	−8.90478	+	27.4061i	−0.403514	+	1.24189i	−0.922129	+	0.386881i	$0.873552\pi$
$488$	−4.07151	−	12.5308i	−0.184308	−	0.567243i
$489$	−10.8268	+	7.86613i	−0.489605	+	0.355719i
$490$	−0.840281	+	0.610500i	−0.0379600	+	0.0275796i
$491$	0.828304	+	2.54926i	0.0373808	+	0.115046i	0.968006	−	0.250928i	$-0.0807358\pi$
$491$	0.828304	+	2.54926i	0.0373808	+	0.115046i	−0.930625	+	0.365974i	$0.880736\pi$
$492$	−1.85551	+	5.71069i	−0.0836531	+	0.257458i
$493$	−17.0108	−	12.3590i	−0.766126	−	0.556623i
$494$	−52.1701			−2.34725
$495$		0			0
$496$	3.66898			0.164742
$497$	−4.81163	−	3.49586i	−0.215831	−	0.156811i
$498$	12.2781	−	37.7881i	0.550195	−	1.69333i
$499$	6.90423	+	21.2490i	0.309076	+	0.951237i	0.978125	+	0.208019i	$0.0667015\pi$
$499$	6.90423	+	21.2490i	0.309076	+	0.951237i	−0.669049	+	0.743218i	$0.733298\pi$
$500$	9.52116	−	6.91752i	0.425799	−	0.309361i
$501$	2.82363	−	2.05149i	0.126150	−	0.0916536i
$502$	−8.59510	−	26.4530i	−0.383618	−	1.18066i
$503$	−1.38316	+	4.25692i	−0.0616719	+	0.189807i	−0.977146	−	0.212571i	$-0.931816\pi$
$503$	−1.38316	+	4.25692i	−0.0616719	+	0.189807i	0.915474	+	0.402378i	$0.131816\pi$
$504$	0.0882598	+	0.0641245i	0.00393140	+	0.00285633i
$505$	5.80943			0.258516
$506$		0			0
$507$	25.6358			1.13853
$508$	9.23600	+	6.71035i	0.409781	+	0.297724i
$509$	−5.30109	+	16.3151i	−0.234967	+	0.723153i	0.762159	+	0.647390i	$0.224139\pi$
$509$	−5.30109	+	16.3151i	−0.234967	+	0.723153i	−0.997126	+	0.0757632i	$0.975861\pi$
$510$	1.65574	+	5.09585i	0.0733174	+	0.225648i
$511$	3.05340	−	2.21842i	0.135074	−	0.0981373i
$512$	−23.2362	+	16.8821i	−1.02690	+	0.746088i
$513$	7.62926	+	23.4804i	0.336840	+	1.03669i
$514$	−10.0021	+	30.7834i	−0.441175	+	1.35780i
$515$	−2.79072	−	2.02758i	−0.122974	−	0.0893457i
$516$	11.9917			0.527904
$517$		0			0
$518$	22.9414			1.00799
$519$	31.9768	+	23.2325i	1.40363	+	1.01979i
$520$	0.764712	−	2.35354i	0.0335348	−	0.103210i
$521$	0.311974	+	0.960156i	0.0136678	+	0.0420652i	0.957658	−	0.287909i	$-0.0929600\pi$
$521$	0.311974	+	0.960156i	0.0136678	+	0.0420652i	−0.943990	+	0.329974i	$0.892960\pi$
$522$	1.35927	−	0.987567i	0.0594936	−	0.0432246i
$523$	11.0376	−	8.01931i	0.482642	−	0.350660i	−0.319706	−	0.947517i	$-0.603584\pi$
$523$	11.0376	−	8.01931i	0.482642	−	0.350660i	0.802348	+	0.596857i	$0.203584\pi$
$524$	6.84031	+	21.0523i	0.298821	+	0.919675i
$525$	−2.49709	+	7.68526i	−0.108982	+	0.335412i
$526$	−17.7816	−	12.9191i	−0.775314	−	0.563298i
$527$	−3.84404			−0.167449
$528$		0			0
$529$	8.79099			0.382217
$530$	−5.57808	−	4.05271i	−0.242296	−	0.176039i
$531$	0.297132	−	0.914479i	0.0128944	−	0.0396850i
$532$	−3.53207	−	10.8706i	−0.153134	−	0.471299i
$533$	6.18856	−	4.49625i	0.268056	−	0.194754i
$534$	−8.99496	+	6.53522i	−0.389250	+	0.282807i
$535$	1.72770	+	5.31731i	0.0746950	+	0.229887i
$536$	−2.84349	+	8.75137i	−0.122820	+	0.378002i
$537$	−24.2665	−	17.6306i	−1.04718	−	0.760818i
$538$	34.3223			1.47974
$539$		0			0
$540$	−6.38154			−0.274618
$541$	2.23559	+	1.62425i	0.0961157	+	0.0698322i	0.634805	−	0.772672i	$-0.281080\pi$
$541$	2.23559	+	1.62425i	0.0961157	+	0.0698322i	−0.538689	+	0.842504i	$0.681080\pi$
$542$	−3.80622	+	11.7143i	−0.163491	+	0.503174i
$543$	8.11977	+	24.9901i	0.348453	+	1.07243i
$544$	19.6850	−	14.3020i	0.843988	−	0.613193i
$545$	−7.54536	+	5.48203i	−0.323208	+	0.234824i
$546$	5.86824	+	18.0606i	0.251137	+	0.772921i
$547$	4.70993	−	14.4957i	0.201382	−	0.619791i	−0.798460	−	0.602047i	$-0.794352\pi$
$547$	4.70993	−	14.4957i	0.201382	−	0.619791i	0.999843	−	0.0177434i	$-0.00564821\pi$
$548$	3.24548	+	2.35798i	0.138640	+	0.100728i
$549$	1.59870			0.0682309
$550$		0			0
$551$	−32.3041			−1.37620
$552$	7.34656	+	5.33759i	0.312690	+	0.227183i
$553$	−2.72053	+	8.37294i	−0.115689	+	0.356054i
$554$	10.3808	+	31.9488i	0.441038	+	1.35738i
$555$	−7.35869	+	5.34640i	−0.312359	+	0.226942i
$556$	3.04136	−	2.20968i	0.128982	−	0.0937112i
$557$	1.10236	+	3.39271i	0.0467084	+	0.143754i	0.971691	−	0.236256i	$-0.0759205\pi$
$557$	1.10236	+	3.39271i	0.0467084	+	0.143754i	−0.924982	+	0.380010i	$0.875921\pi$
$558$	0.0949188	−	0.292130i	0.00401823	−	0.0123668i
$559$	−12.3591	−	8.97942i	−0.522735	−	0.379789i
$560$	−1.42739			−0.0603182
$561$		0			0
$562$	21.5166			0.907621
$563$	−29.7314	−	21.6011i	−1.25303	−	0.910379i	−0.254635	−	0.967037i	$-0.581955\pi$
$563$	−29.7314	−	21.6011i	−1.25303	−	0.910379i	−0.998394	+	0.0566587i	$0.981955\pi$
$564$	−11.2564	+	34.6436i	−0.473980	+	1.45876i
$565$	−2.05353	−	6.32012i	−0.0863927	−	0.265889i
$566$	27.5833	−	20.0404i	1.15941	−	0.842361i
$567$	6.99120	−	5.07941i	0.293603	−	0.213315i
$568$	1.74270	+	5.36348i	0.0731221	+	0.225047i
$569$	−10.5314	+	32.4122i	−0.441498	+	1.35879i	0.444781	+	0.895639i	$0.353282\pi$
$569$	−10.5314	+	32.4122i	−0.441498	+	1.35879i	−0.886279	+	0.463152i	$0.846718\pi$
$570$	6.65976	+	4.83860i	0.278947	+	0.202667i
$571$	−5.79312			−0.242434			−0.121217	−	0.992626i	$-0.538680\pi$
$571$	−5.79312			−0.242434			−0.121217	+	0.992626i	$0.538680\pi$
$572$		0			0
$573$	27.0718			1.13094
$574$	2.46290	+	1.78940i	0.102799	+	0.0746881i
$575$	8.28930	−	25.5118i	0.345688	−	1.06392i
$576$	0.394686	+	1.21472i	0.0164452	+	0.0506133i
$577$	25.1791	−	18.2937i	1.04822	−	0.761578i	0.0763482	−	0.997081i	$-0.475674\pi$
$577$	25.1791	−	18.2937i	1.04822	−	0.761578i	0.971873	+	0.235504i	$0.0756739\pi$
$578$	13.2689	−	9.64044i	0.551914	−	0.400989i
$579$	4.43717	+	13.6562i	0.184403	+	0.567533i
$580$	2.58027	−	7.94125i	0.107140	−	0.329743i
$581$	−8.97183	−	6.51842i	−0.372214	−	0.270430i
$582$	−22.6318			−0.938120
$583$		0			0
$584$	−3.57875			−0.148090
$585$	0.242922	+	0.176493i	0.0100436	+	0.00729711i
$586$	17.6333	−	54.2697i	0.728424	−	2.24186i
$587$	−14.7384	−	45.3602i	−0.608320	−	1.87222i	−0.472118	−	0.881536i	$-0.656510\pi$
$587$	−14.7384	−	45.3602i	−0.608320	−	1.87222i	−0.136202	−	0.990681i	$-0.543490\pi$
$588$	−3.36595	+	2.44550i	−0.138809	+	0.100851i
$589$	−4.77789	+	3.47134i	−0.196870	+	0.143034i
$590$	−2.68236	−	8.25545i	−0.110431	−	0.339872i
$591$	−7.52580	+	23.1620i	−0.309570	+	0.952759i
$592$	25.5066	+	18.5317i	1.04832	+	0.761646i
$593$	44.5859			1.83092			0.915462	−	0.402404i	$-0.131825\pi$
$593$	44.5859			1.83092			0.915462	+	0.402404i	$0.131825\pi$
$594$		0			0
$595$	1.49549			0.0613093
$596$	−26.7350	−	19.4241i	−1.09511	−	0.795644i
$597$	−11.6176	+	35.7553i	−0.475476	+	1.46337i
$598$	−19.4801	−	59.9535i	−0.796600	−	2.45168i
$599$	6.52826	−	4.74306i	0.266738	−	0.193796i	−0.446375	−	0.894846i	$-0.647285\pi$
$599$	6.52826	−	4.74306i	0.266738	−	0.193796i	0.713112	+	0.701050i	$0.247285\pi$
$600$	6.19891	−	4.50377i	0.253069	−	0.183866i
$601$	−8.93324	−	27.4937i	−0.364394	−	1.12149i	−0.950359	−	0.311154i	$-0.899284\pi$
$601$	−8.93324	−	27.4937i	−0.364394	−	1.12149i	0.585965	−	0.810336i	$-0.300716\pi$
$602$	1.87875	−	5.78219i	0.0765721	−	0.235665i
$603$	−0.903279	−	0.656271i	−0.0367844	−	0.0267254i
$604$	−29.9748			−1.21966
$605$		0			0
$606$	42.2716			1.71717
$607$	7.97132	+	5.79151i	0.323546	+	0.235070i	0.737687	−	0.675143i	$-0.235918\pi$
$607$	7.97132	+	5.79151i	0.323546	+	0.235070i	−0.414141	+	0.910213i	$0.635918\pi$
$608$	11.5519	−	35.5529i	0.468489	−	1.44186i
$609$	3.63365	+	11.1832i	0.147243	+	0.453167i
$610$	11.6759	−	8.48307i	0.472745	−	0.343469i
$611$	37.5426	−	27.2763i	1.51881	−	1.10348i
$612$	−0.264507	−	0.814069i	−0.0106921	−	0.0329068i
$613$	−11.0730	+	34.0791i	−0.447233	+	1.37644i	0.432784	+	0.901498i	$0.357531\pi$
$613$	−11.0730	+	34.0791i	−0.447233	+	1.37644i	−0.880017	+	0.474943i	$0.842469\pi$
$614$	−50.7268	−	36.8551i	−2.04717	−	1.48735i
$615$	−1.20701			−0.0486714
$616$		0			0
$617$	−38.4398			−1.54753			−0.773764	−	0.633474i	$-0.781628\pi$
$617$	−38.4398			−1.54753			−0.773764	+	0.633474i	$0.781628\pi$
$618$	−20.3063	−	14.7534i	−0.816840	−	0.593469i
$619$	1.29649	−	3.99018i	0.0521103	−	0.160379i	−0.921615	−	0.388106i	$-0.873129\pi$
$619$	1.29649	−	3.99018i	0.0521103	−	0.160379i	0.973725	+	0.227727i	$0.0731294\pi$
$620$	−0.471723	−	1.45181i	−0.0189448	−	0.0583062i
$621$	−24.1348	+	17.5350i	−0.968497	+	0.703654i
$622$	−38.2313	+	27.7766i	−1.53293	+	1.11374i
$623$	0.958955	+	2.95136i	0.0384197	+	0.118244i
$624$	−8.06461	+	24.8203i	−0.322843	+	0.993608i
$625$	−17.3308	−	12.5916i	−0.693232	−	0.503662i
$626$	20.9849			0.838725
$627$		0			0
$628$	6.17382			0.246362
$629$	−26.7236	−	19.4159i	−1.06554	−	0.774161i
$630$	−0.0369274	+	0.113651i	−0.00147122	+	0.00452796i
$631$	−1.08712	−	3.34580i	−0.0432774	−	0.133194i	0.927083	−	0.374855i	$-0.122308\pi$
$631$	−1.08712	−	3.34580i	−0.0432774	−	0.133194i	−0.970361	+	0.241661i	$0.922308\pi$
$632$	6.75359	−	4.90677i	0.268643	−	0.195181i
$633$	−2.99975	+	2.17945i	−0.119229	+	0.0866252i
$634$	−7.26276	−	22.3525i	−0.288441	−	0.887730i
$635$	−0.709150	+	2.18254i	−0.0281418	+	0.0866114i
$636$	−22.3443	−	16.2341i	−0.886011	−	0.643725i
$637$	5.30029			0.210005
$638$		0			0
$639$	−0.684281			−0.0270698
$640$	2.94546	+	2.14000i	0.116429	+	0.0845909i
$641$	4.97370	−	15.3075i	0.196449	−	0.604609i	−0.803507	−	0.595295i	$-0.797035\pi$
$641$	4.97370	−	15.3075i	0.196449	−	0.604609i	0.999957	−	0.00931390i	$-0.00296475\pi$
$642$	12.5714	+	38.6908i	0.496153	+	1.52700i
$643$	28.1749	−	20.4703i	1.11111	−	0.807268i	0.128272	−	0.991739i	$-0.459057\pi$
$643$	28.1749	−	20.4703i	1.11111	−	0.807268i	0.982838	+	0.184471i	$0.0590570\pi$
$644$	11.1735	−	8.11805i	0.440299	−	0.319896i
$645$	0.744888	+	2.29253i	0.0293300	+	0.0902683i
$646$	−9.23802	+	28.4317i	−0.363465	+	1.11863i
$647$	−13.6765	−	9.93656i	−0.537679	−	0.390646i	0.285543	−	0.958366i	$-0.407826\pi$
$647$	−13.6765	−	9.93656i	−0.537679	−	0.390646i	−0.823222	+	0.567719i	$0.807826\pi$
$648$	−8.19407			−0.321893
$649$		0			0
$650$	−53.1912			−2.08633
$651$	1.73916	+	1.26357i	0.0681631	+	0.0495234i
$652$	5.96399	−	18.3553i	0.233568	−	0.718848i
$653$	1.09021	+	3.35532i	0.0426631	+	0.131304i	0.970119	−	0.242628i	$-0.0780094\pi$
$653$	1.09021	+	3.35532i	0.0426631	+	0.131304i	−0.927456	+	0.373932i	$0.878009\pi$
$654$	−54.9029	+	39.8893i	−2.14687	+	1.55979i
$655$	−3.59982	+	2.61542i	−0.140657	+	0.102193i
$656$	1.29285	+	3.97897i	0.0504771	+	0.155353i
$657$	0.134186	−	0.412983i	0.00523510	−	0.0161120i
$658$	14.9411	+	10.8553i	0.582463	+	0.423184i
$659$	29.4409			1.14686			0.573428	−	0.819256i	$-0.305613\pi$
$659$	29.4409			1.14686			0.573428	+	0.819256i	$0.305613\pi$
$660$		0			0
$661$	15.2989			0.595059			0.297529	−	0.954713i	$-0.403837\pi$
$661$	15.2989			0.595059			0.297529	+	0.954713i	$0.403837\pi$
$662$	−24.9068	−	18.0959i	−0.968032	−	0.703316i
$663$	8.44939	−	26.0046i	0.328147	−	1.00993i
$664$	3.24946	+	10.0008i	0.126104	+	0.388107i
$665$	1.85880	−	1.35050i	0.0720813	−	0.0523701i
$666$	2.13539	−	1.55145i	0.0827447	−	0.0601176i
$667$	−12.0622	−	37.1236i	−0.467050	−	1.43743i
$668$	−1.55541	+	4.78705i	−0.0601805	+	0.185217i
$669$	−37.4591	−	27.2157i	−1.44825	−	1.05222i
$670$	−10.0793			−0.389398
$671$		0			0
$672$	−13.6073			−0.524914
$673$	−9.84189	−	7.15055i	−0.379377	−	0.275634i	0.381712	−	0.924282i	$-0.375335\pi$
$673$	−9.84189	−	7.15055i	−0.379377	−	0.275634i	−0.761089	+	0.648648i	$0.775335\pi$
$674$	8.21700	−	25.2893i	0.316507	−	0.974109i
$675$	7.77858	+	23.9400i	0.299398	+	0.921451i
$676$	−29.9100	+	21.7309i	−1.15039	+	0.835805i
$677$	0.253723	−	0.184340i	0.00975136	−	0.00708478i	−0.582899	−	0.812545i	$-0.698082\pi$
$677$	0.253723	−	0.184340i	0.00975136	−	0.00708478i	0.592650	+	0.805460i	$0.298082\pi$
$678$	−14.9423	−	45.9876i	−0.573854	−	1.76614i
$679$	−1.95199	+	6.00759i	−0.0749103	+	0.230550i
$680$	−1.14722	−	0.833506i	−0.0439940	−	0.0319635i
$681$	−23.0814			−0.884481
$682$		0			0
$683$	38.2419			1.46328			0.731642	−	0.681689i	$-0.238754\pi$
$683$	38.2419			1.46328			0.731642	+	0.681689i	$0.238754\pi$
$684$	−1.06391	−	0.772974i	−0.0406795	−	0.0295554i
$685$	−0.249191	+	0.766932i	−0.00952111	+	0.0293030i
$686$	0.651837	+	2.00615i	0.0248872	+	0.0765951i
$687$	11.4072	−	8.28781i	0.435211	−	0.316200i
$688$	6.75958	−	4.91112i	0.257706	−	0.187235i
$689$	10.8728	+	33.4631i	0.414222	+	1.27484i
$690$	−3.07376	+	9.46006i	−0.117016	+	0.360138i
$691$	8.31299	+	6.03974i	0.316241	+	0.229763i	0.734570	−	0.678533i	$-0.237384\pi$
$691$	8.31299	+	6.03974i	0.316241	+	0.229763i	−0.418329	+	0.908296i	$0.637384\pi$
$692$	−57.0019			−2.16689
$693$		0			0
$694$	0.866398			0.0328880
$695$	0.611360	+	0.444179i	0.0231902	+	0.0168487i
$696$	3.44547	−	10.6041i	0.130600	−	0.401946i
$697$	−1.35453	−	4.16882i	−0.0513065	−	0.157905i
$698$	−22.8719	+	16.6174i	−0.865713	+	0.628977i
$699$	−17.7917	+	12.9264i	−0.672944	+	0.488922i
$700$	−3.60120	−	11.0833i	−0.136112	−	0.418911i
$701$	5.84622	−	17.9928i	0.220809	−	0.679579i	−0.777882	−	0.628411i	$-0.783706\pi$
$701$	5.84622	−	17.9928i	0.220809	−	0.679579i	0.998690	−	0.0511679i	$-0.0162944\pi$
$702$	47.8573	+	34.7704i	1.80626	+	1.31232i
$703$	−50.7492			−1.91404
$704$		0			0
$705$	−7.32228			−0.275773
$706$	−21.0618	−	15.3023i	−0.792671	−	0.575909i
$707$	3.64591	−	11.2210i	0.137119	−	0.422007i
$708$	−10.7448	−	33.0692i	−0.403816	−	1.24282i
$709$	11.4475	−	8.31707i	0.429919	−	0.312354i	−0.351698	−	0.936114i	$-0.614395\pi$
$709$	11.4475	−	8.31707i	0.429919	−	0.312354i	0.781616	+	0.623759i	$0.214395\pi$
$710$	−4.99758	+	3.63095i	−0.187556	+	0.136267i
$711$	0.313007	+	0.963336i	0.0117387	+	0.0361279i
$712$	0.909293	−	2.79852i	0.0340772	−	0.104879i
$713$	−5.77328	−	4.19454i	−0.216211	−	0.157087i
$714$	10.8818			0.407240
$715$		0			0
$716$	43.2575			1.61661
$717$	−2.60179	−	1.89031i	−0.0971658	−	0.0705951i
$718$	−16.3022	+	50.1731i	−0.608394	+	1.87244i
$719$	−4.92357	−	15.1532i	−0.183618	−	0.565119i	0.816304	−	0.577623i	$-0.196020\pi$
$719$	−4.92357	−	15.1532i	−0.183618	−	0.565119i	−0.999922	+	0.0125042i	$0.996020\pi$
$720$	−0.132862	+	0.0965297i	−0.00495146	+	0.00359745i
$721$	−5.66769	+	4.11782i	−0.211076	+	0.153356i
$722$	1.80796	+	5.56433i	0.0672853	+	0.207083i
$723$	−6.14010	+	18.8973i	−0.228353	+	0.702798i
$724$	−30.6571	−	22.2737i	−1.13936	−	0.827795i
$725$	−32.9363			−1.22322
$726$		0			0
$727$	−4.20455			−0.155938			−0.0779691	−	0.996956i	$-0.524844\pi$
$727$	−4.20455			−0.155938			−0.0779691	+	0.996956i	$0.524844\pi$
$728$	−4.06596	−	2.95409i	−0.150694	−	0.109486i
$729$	8.63843	−	26.5863i	0.319942	−	0.984679i
$730$	−1.21136	−	3.72820i	−0.0448346	−	0.137987i
$731$	−7.08209	+	5.14544i	−0.261941	+	0.190311i
$732$	46.7708	−	33.9810i	1.72870	−	1.25597i
$733$	10.5306	+	32.4098i	0.388956	+	1.19708i	0.933569	+	0.358397i	$0.116677\pi$
$733$	10.5306	+	32.4098i	0.388956	+	1.19708i	−0.544613	+	0.838688i	$0.683323\pi$
$734$	−1.34875	+	4.15102i	−0.0497832	+	0.153217i
$735$	−0.676607	−	0.491584i	−0.0249570	−	0.0181324i
$736$	45.1706			1.66501
$737$		0			0
$738$	0.350258			0.0128932
$739$	−21.1401	−	15.3592i	−0.777652	−	0.564997i	0.126622	−	0.991951i	$-0.459587\pi$
$739$	−21.1401	−	15.3592i	−0.777652	−	0.564997i	−0.904273	+	0.426954i	$0.859587\pi$
$740$	4.05356	−	12.4756i	0.149012	−	0.458612i
$741$	−12.9813	−	39.9522i	−0.476878	−	1.46768i
$742$	−11.3286	+	8.23067i	−0.415884	+	0.302158i
$743$	19.1141	−	13.8872i	0.701228	−	0.509472i	−0.179104	−	0.983830i	$-0.557320\pi$
$743$	19.1141	−	13.8872i	0.701228	−	0.509472i	0.880332	+	0.474358i	$0.157320\pi$
$744$	−0.629897	−	1.93862i	−0.0230932	−	0.0710734i
$745$	2.05274	−	6.31770i	0.0752067	−	0.231462i
$746$	25.1924	+	18.3034i	0.922360	+	0.670133i
$747$	−1.27592			−0.0466835
$748$		0			0
$749$	11.3547			0.414892
$750$	13.9262	+	10.1180i	0.508515	+	0.369458i
$751$	−0.718028	+	2.20986i	−0.0262012	+	0.0806391i	−0.963302	−	0.268420i	$-0.913499\pi$
$751$	−0.718028	+	2.20986i	−0.0262012	+	0.0806391i	0.937101	+	0.349059i	$0.113499\pi$
$752$	7.84299	+	24.1382i	0.286004	+	0.880231i
$753$	18.1192	−	13.1644i	0.660300	−	0.479736i
$754$	−62.6189	+	45.4953i	−2.28045	+	1.65684i
$755$	−1.86195	−	5.73050i	−0.0677633	−	0.208554i
$756$	−4.00496	+	12.3260i	−0.145659	+	0.448292i
$757$	11.9452	+	8.67872i	0.434157	+	0.315433i	0.783309	−	0.621633i	$-0.213530\pi$
$757$	11.9452	+	8.67872i	0.434157	+	0.315433i	−0.349152	+	0.937066i	$0.613530\pi$
$758$	58.5371			2.12616
$759$		0			0
$760$	−2.17862			−0.0790268
$761$	38.1756	+	27.7362i	1.38386	+	1.00544i	0.996507	+	0.0835050i	$0.0266115\pi$
$761$	38.1756	+	27.7362i	1.38386	+	1.00544i	0.387356	+	0.921930i	$0.373389\pi$
$762$	−5.16004	+	15.8810i	−0.186929	+	0.575307i
$763$	5.85322	+	18.0143i	0.211901	+	0.652163i
$764$	−31.5854	+	22.9481i	−1.14272	+	0.830234i
$765$	0.139201	−	0.101135i	0.00503282	−	0.00365656i
$766$	−11.7548	−	36.1777i	−0.424720	−	1.30715i
$767$	−13.6883	+	42.1283i	−0.494256	+	1.52116i
$768$	−9.07661	−	6.59454i	−0.327524	−	0.237960i
$769$	−12.4418			−0.448662			−0.224331	−	0.974513i	$-0.572020\pi$
$769$	−12.4418			−0.448662			−0.224331	+	0.974513i	$0.572020\pi$
$770$		0			0
$771$	−26.0629			−0.938631
$772$	−16.7530	−	12.1718i	−0.602955	−	0.438073i
$773$	−10.8990	+	33.5436i	−0.392009	+	1.20648i	0.539258	+	0.842141i	$0.318705\pi$
$773$	−10.8990	+	33.5436i	−0.392009	+	1.20648i	−0.931267	+	0.364338i	$0.881295\pi$
$774$	−0.216157	−	0.665262i	−0.00776959	−	0.0239123i
$775$	−4.87141	+	3.53928i	−0.174986	+	0.127135i
$776$	4.84571	−	3.52061i	0.173951	−	0.126383i
$777$	5.70840	+	17.5687i	0.204788	+	0.630272i
$778$	8.82663	−	27.1656i	0.316450	−	0.973933i
$779$	−5.44823	−	3.95837i	−0.195203	−	0.141823i
$780$	10.8583			0.388788
$781$		0			0
$782$	−36.1229			−1.29175
$783$	29.6335	+	21.5300i	1.05902	+	0.769420i
$784$	−0.895807	+	2.75701i	−0.0319931	+	0.0984647i
$785$	0.383500	+	1.18029i	0.0136877	+	0.0421265i
$786$	−26.1936	+	19.0308i	−0.934296	+	0.678806i
$787$	13.2179	−	9.60340i	0.471169	−	0.342324i	−0.326728	−	0.945118i	$-0.605946\pi$
$787$	13.2179	−	9.60340i	0.471169	−	0.342324i	0.797897	+	0.602794i	$0.205946\pi$
$788$	−10.8534	−	33.4033i	−0.386636	−	1.18994i
$789$	5.46899	−	16.8318i	0.194701	−	0.599229i
$790$	7.39769	+	5.37474i	0.263198	+	0.191225i
$791$	−13.4961			−0.479867
$792$		0			0
$793$	−73.6491			−2.61536
$794$	42.0703	+	30.5659i	1.49302	+	1.08474i
$795$	1.71562	−	5.28014i	0.0608469	−	0.187267i
$796$	−16.7544	−	51.5647i	−0.593843	−	1.82766i
$797$	0.236962	−	0.172163i	0.00839364	−	0.00609834i	−0.583581	−	0.812055i	$-0.698349\pi$
$797$	0.236962	−	0.172163i	0.00839364	−	0.00609834i	0.591974	+	0.805957i	$0.298349\pi$
$798$	13.5254	−	9.82674i	0.478792	−	0.347863i
$799$	−8.21720	−	25.2899i	−0.290703	−	0.894693i
$800$	11.7779	−	36.2488i	0.416413	−	1.28159i
$801$	0.288851	+	0.209862i	0.0102060	+	0.00741512i
$802$	39.5277			1.39577
$803$		0			0
$804$	−40.3752			−1.42392
$805$	2.24605	+	1.63185i	0.0791630	+	0.0575153i
$806$	−4.37272	+	13.4579i	−0.154023	+	0.474033i
$807$	8.54027	+	26.2842i	0.300632	+	0.925249i
$808$	−9.05079	+	6.57578i	−0.318406	+	0.231335i
$809$	8.92935	−	6.48755i	0.313939	−	0.228090i	−0.419646	−	0.907688i	$-0.637846\pi$
$809$	8.92935	−	6.48755i	0.313939	−	0.228090i	0.733585	+	0.679598i	$0.237846\pi$
$810$	−2.77360	−	8.53626i	−0.0974543	−	0.299933i
$811$	−1.61234	+	4.96226i	−0.0566167	+	0.174248i	−0.975366	−	0.220593i	$-0.929201\pi$
$811$	−1.61234	+	4.96226i	−0.0566167	+	0.174248i	0.918749	+	0.394842i	$0.129201\pi$
$812$	−13.7192	−	9.96761i	−0.481451	−	0.349795i
$813$	−9.91799			−0.347839
$814$		0			0
$815$	3.87957			0.135896
$816$	12.0985	+	8.79010i	0.423534	+	0.307715i
$817$	−4.15602	+	12.7909i	−0.145401	+	0.447497i
$818$	10.2402	+	31.5162i	0.358042	+	1.10194i
$819$	0.493353	−	0.358442i	0.0172391	−	0.0125250i
$820$	1.40825	−	1.02316i	0.0491784	−	0.0357302i
$821$	8.17252	+	25.1524i	0.285223	+	0.877825i	0.986332	+	0.164771i	$0.0526886\pi$
$821$	8.17252	+	25.1524i	0.285223	+	0.877825i	−0.701109	+	0.713054i	$0.747311\pi$
$822$	−1.81321	+	5.58049i	−0.0632430	+	0.194642i
$823$	39.7951	+	28.9128i	1.38717	+	1.00784i	0.996169	+	0.0874486i	$0.0278714\pi$
$823$	39.7951	+	28.9128i	1.38717	+	1.00784i	0.391002	+	0.920390i	$0.372129\pi$
$824$	6.64284			0.231414
$825$		0			0
$826$	−17.6289			−0.613387
$827$	33.8174	+	24.5698i	1.17595	+	0.854375i	0.991709	−	0.128507i	$-0.0410185\pi$
$827$	33.8174	+	24.5698i	1.17595	+	0.854375i	0.184237	+	0.982882i	$0.441019\pi$
$828$	0.491038	−	1.51126i	0.0170648	−	0.0525199i
$829$	−7.69415	−	23.6802i	−0.267229	−	0.822446i	−0.991172	−	0.132586i	$-0.957672\pi$
$829$	−7.69415	−	23.6802i	−0.267229	−	0.822446i	0.723943	−	0.689860i	$-0.242328\pi$
$830$	−9.31854	+	6.77032i	−0.323451	+	0.235001i
$831$	−21.8836	+	15.8994i	−0.759133	+	0.551543i
$832$	−18.1824	−	55.9597i	−0.630362	−	1.94005i
$833$	0.938548	−	2.88855i	0.0325188	−	0.100082i
$834$	4.44849	+	3.23201i	0.154038	+	0.111916i
$835$	−1.01179			−0.0350145
$836$		0			0
$837$	6.69650			0.231465
$838$	−38.5735	−	28.0253i	−1.33250	−	0.968116i
$839$	−16.4679	+	50.6829i	−0.568534	+	1.74977i	0.0886751	+	0.996061i	$0.471737\pi$
$839$	−16.4679	+	50.6829i	−0.568534	+	1.74977i	−0.657209	+	0.753708i	$0.728263\pi$
$840$	0.245057	+	0.754207i	0.00845526	+	0.0260226i
$841$	−15.3125	+	11.1252i	−0.528018	+	0.383627i
$842$	39.8152	−	28.9275i	1.37212	−	0.996906i
$843$	5.35387	+	16.4775i	0.184397	+	0.567516i
$844$	1.65243	−	5.08564i	0.0568788	−	0.175055i
$845$	−6.01238	−	4.36825i	−0.206832	−	0.150272i
$846$	2.12483			0.0730530
$847$		0			0
$848$	−19.2439			−0.660837
$849$	22.2105	+	16.1369i	0.762262	+	0.553816i
$850$	−9.41882	+	28.9882i	−0.323063	+	0.994286i
$851$	−18.9495	−	58.3206i	−0.649581	−	1.99920i
$852$	−20.0190	+	14.5447i	−0.685840	+	0.498292i
$853$	−10.8170	+	7.85903i	−0.370368	+	0.269088i	−0.757363	−	0.652994i	$-0.773513\pi$
$853$	−10.8170	+	7.85903i	−0.370368	+	0.269088i	0.386996	+	0.922082i	$0.373513\pi$
$854$	−9.05746	−	27.8760i	−0.309940	−	0.953897i
$855$	0.0816879	−	0.251410i	0.00279367	−	0.00859803i
$856$	−8.71041	−	6.32848i	−0.297716	−	0.216303i
$857$	43.4419			1.48395			0.741974	−	0.670429i	$-0.233890\pi$
$857$	43.4419			1.48395			0.741974	+	0.670429i	$0.233890\pi$
$858$		0			0
$859$	−7.96898			−0.271898			−0.135949	−	0.990716i	$-0.543408\pi$
$859$	−7.96898			−0.271898			−0.135949	+	0.990716i	$0.543408\pi$
$860$	−2.81241	−	2.04334i	−0.0959024	−	0.0696771i
$861$	−0.757501	+	2.33135i	−0.0258156	+	0.0794522i
$862$	−6.21786	−	19.1366i	−0.211781	−	0.651795i
$863$	−40.7317	+	29.5933i	−1.38652	+	1.00737i	−0.390286	+	0.920694i	$0.627624\pi$
$863$	−40.7317	+	29.5933i	−1.38652	+	1.00737i	−0.996237	+	0.0866744i	$0.972376\pi$
$864$	−34.2922	+	24.9148i	−1.16665	+	0.847618i
$865$	−3.54080	−	10.8975i	−0.120391	−	0.370525i
$866$	−14.9991	+	46.1625i	−0.509690	+	1.56867i
$867$	10.6843	+	7.76263i	0.362859	+	0.263633i
$868$	−3.10023			−0.105229
$869$		0			0
$870$	12.2131			0.414064
$871$	41.6123	+	30.2331i	1.40998	+	1.02441i
$872$	5.55009	−	17.0814i	0.187950	−	0.578450i
$873$	0.224583	+	0.691195i	0.00760098	+	0.0233934i
$874$	−44.8985	+	32.6207i	−1.51871	+	1.10341i
$875$	3.88695	−	2.82403i	0.131403	−	0.0954697i
$876$	−4.85241	−	14.9342i	−0.163948	−	0.504580i
$877$	−17.0516	+	52.4794i	−0.575791	+	1.77210i	0.0576796	+	0.998335i	$0.481630\pi$
$877$	−17.0516	+	52.4794i	−0.575791	+	1.77210i	−0.633470	+	0.773767i	$0.718370\pi$
$878$	47.1743	+	34.2741i	1.59205	+	1.15670i
$879$	45.9476			1.54978
$880$		0			0
$881$	−22.6475			−0.763014			−0.381507	−	0.924366i	$-0.624595\pi$
$881$	−22.6475			−0.763014			−0.381507	+	0.924366i	$0.624595\pi$
$882$	0.196342	+	0.142651i	0.00661119	+	0.00480331i
$883$	−3.92606	+	12.0832i	−0.132122	+	0.406631i	−0.995131	−	0.0985577i	$-0.968577\pi$
$883$	−3.92606	+	12.0832i	−0.132122	+	0.406631i	0.863009	+	0.505189i	$0.168577\pi$
$884$	12.1853	+	37.5026i	0.409837	+	1.26135i
$885$	5.65463	−	4.10833i	0.190078	−	0.138100i
$886$	−25.2077	+	18.3145i	−0.846870	+	0.615287i
$887$	2.07042	+	6.37211i	0.0695181	+	0.213955i	0.979780	−	0.200079i	$-0.0641197\pi$
$887$	2.07042	+	6.37211i	0.0695181	+	0.213955i	−0.910262	+	0.414033i	$0.864120\pi$
$888$	5.41278	−	16.6588i	0.181641	−	0.559033i
$889$	3.77054	+	2.73945i	0.126460	+	0.0918784i
$890$	3.22317			0.108041
$891$		0			0
$892$	66.7747			2.23578
$893$	−33.0514	−	24.0133i	−1.10602	−	0.803573i
$894$	14.9365	−	45.9699i	0.499553	−	1.53746i
$895$	2.68703	+	8.26983i	0.0898176	+	0.276430i
$896$	5.98194	−	4.34614i	0.199843	−	0.145194i
$897$	41.0656	−	29.8359i	1.37114	−	0.996192i
$898$	19.7291	+	60.7199i	0.658368	+	2.02625i
$899$	−2.70762	+	8.33319i	−0.0903041	+	0.277927i
$900$	−1.08473	−	0.788103i	−0.0361577	−	0.0262701i
$901$	20.1620			0.671695
$902$		0			0
$903$	4.89552			0.162913
$904$	10.3531	+	7.52199i	0.344340	+	0.250178i
$905$	2.35389	−	7.24451i	0.0782458	−	0.240816i
$906$	−13.5483	−	41.6973i	−0.450111	−	1.38530i
$907$	46.6952	−	33.9260i	1.55049	−	1.12650i	0.607185	−	0.794560i	$-0.292299\pi$
$907$	46.6952	−	33.9260i	1.55049	−	1.12650i	0.943302	−	0.331935i	$-0.107701\pi$
$908$	26.9297	−	19.5656i	0.893694	−	0.649306i
$909$	−0.419475	−	1.29101i	−0.0139131	−	0.0428201i
$910$	1.70118	−	5.23568i	0.0563934	−	0.173561i
$911$	2.30054	+	1.67144i	0.0762203	+	0.0553773i	0.625243	−	0.780430i	$-0.285000\pi$
$911$	2.30054	+	1.67144i	0.0762203	+	0.0553773i	−0.549023	+	0.835808i	$0.685000\pi$
$912$	22.9756			0.760798
$913$		0			0
$914$	−42.7288			−1.41334
$915$	9.40165	+	6.83070i	0.310809	+	0.225816i
$916$	−6.28370	+	19.3392i	−0.207619	+	0.638986i
$917$	2.79251	+	8.59447i	0.0922169	+	0.283814i
$918$	27.4235	−	19.9243i	0.905110	−	0.657601i
$919$	7.57906	−	5.50651i	0.250010	−	0.181643i	−0.455721	−	0.890123i	$-0.650619\pi$
$919$	7.57906	−	5.50651i	0.250010	−	0.181643i	0.705731	+	0.708480i	$0.250619\pi$
$920$	−0.813486	−	2.50365i	−0.0268198	−	0.0825430i
$921$	15.6018	−	48.0173i	0.514096	−	1.58223i
$922$	−14.5257	−	10.5535i	−0.478379	−	0.347563i
$923$	31.5235			1.03761
$924$		0			0
$925$	−51.7424			−1.70128
$926$	1.00936	+	0.733344i	0.0331697	+	0.0240992i
$927$	−0.249075	+	0.766575i	−0.00818071	+	0.0251776i
$928$	−17.1387	−	52.7475i	−0.562605	−	1.73152i
$929$	35.4703	−	25.7707i	1.16374	−	0.845509i	0.173496	−	0.984835i	$-0.444494\pi$
$929$	35.4703	−	25.7707i	1.16374	−	0.845509i	0.990247	+	0.139326i	$0.0444936\pi$
$930$	1.80637	−	1.31240i	0.0592332	−	0.0430354i
$931$	−1.44194	−	4.43784i	−0.0472577	−	0.145444i
$932$	9.80063	−	30.1633i	0.321030	−	0.988030i
$933$	−30.7844	−	22.3662i	−1.00784	−	0.732236i
$934$	−86.5581			−2.83227
$935$		0			0
$936$	−0.578236			−0.0189002
$937$	−2.59634	−	1.88635i	−0.0848186	−	0.0616243i	0.544568	−	0.838717i	$-0.316694\pi$
$937$	−2.59634	−	1.88635i	−0.0848186	−	0.0616243i	−0.629386	+	0.777092i	$0.716694\pi$
$938$	−6.32563	+	19.4683i	−0.206539	+	0.635662i
$939$	5.22158	+	16.0704i	0.170400	+	0.524436i
$940$	8.54311	−	6.20693i	0.278645	−	0.202448i
$941$	−9.00597	+	6.54322i	−0.293586	+	0.213303i	−0.724822	−	0.688937i	$-0.758078\pi$
$941$	−9.00597	+	6.54322i	−0.293586	+	0.213303i	0.431235	+	0.902239i	$0.358078\pi$
$942$	2.79049	+	8.58825i	0.0909192	+	0.279820i
$943$	2.51459	−	7.73910i	0.0818862	−	0.252020i
$944$	−19.6001	−	14.2403i	−0.637928	−	0.463482i
$945$	−2.60522			−0.0847479
$946$		0			0
$947$	51.6934			1.67981			0.839905	−	0.542733i	$-0.182610\pi$
$947$	51.6934			1.67981			0.839905	+	0.542733i	$0.182610\pi$
$948$	29.6332	+	21.5298i	0.962443	+	0.699256i
$949$	−6.18170	+	19.0253i	−0.200666	+	0.617588i
$950$	14.4706	+	44.5361i	0.469490	+	1.44494i
$951$	15.3105	−	11.1237i	0.496477	−	0.360711i
$952$	−2.32990	+	1.69277i	−0.0755125	+	0.0548630i
$953$	8.66189	+	26.6586i	0.280586	+	0.863555i	0.987687	+	0.156443i	$0.0500027\pi$
$953$	8.66189	+	26.6586i	0.280586	+	0.863555i	−0.707101	+	0.707113i	$0.749997\pi$
$954$	−0.497851	+	1.53223i	−0.0161185	+	0.0496077i
$955$	−6.34915	−	4.61293i	−0.205454	−	0.149271i
$956$	4.63796			0.150002
$957$		0			0
$958$	42.9127			1.38645
$959$	1.32495	+	0.962629i	0.0427847	+	0.0310849i
$960$	−2.86900	+	8.82988i	−0.0925967	+	0.284983i
$961$	−9.08452	−	27.9593i	−0.293049	−	0.901912i
$962$	−98.3734	+	71.4724i	−3.17168	+	2.30436i
$963$	1.05690	−	0.767881i	0.0340581	−	0.0247446i
$964$	−8.85498	−	27.2528i	−0.285200	−	0.877755i
$965$	1.28632	−	3.95887i	0.0414080	−	0.127441i
$966$	16.3431	+	11.8740i	0.525831	+	0.382039i
$967$	−25.5912			−0.822957			−0.411479	−	0.911419i	$-0.634988\pi$
$967$	−25.5912			−0.822957			−0.411479	+	0.911419i	$0.634988\pi$
$968$		0			0
$969$	−24.0718			−0.773298
$970$	5.30785	+	3.85638i	0.170425	+	0.123821i
$971$	3.88547	−	11.9583i	0.124691	−	0.383759i	−0.869154	−	0.494542i	$-0.835336\pi$
$971$	3.88547	−	11.9583i	0.124691	−	0.383759i	0.993845	+	0.110783i	$0.0353359\pi$
$972$	0.904549	+	2.78392i	0.0290134	+	0.0892942i
$973$	1.24161	−	0.902086i	0.0398043	−	0.0289195i
$974$	49.1762	−	35.7286i	1.57571	−	1.14482i
$975$	−13.2353	−	40.7341i	−0.423870	−	1.30454i
$976$	12.4475	−	38.3095i	0.398435	−	1.22626i
$977$	11.7440	+	8.53251i	0.375724	+	0.272979i	0.759580	−	0.650413i	$-0.225404\pi$
$977$	11.7440	+	8.53251i	0.375724	+	0.272979i	−0.383857	+	0.923393i	$0.625404\pi$
$978$	28.2292			0.902671
$979$		0			0
$980$	1.20612			0.0385281
$981$	1.76307	+	1.28095i	0.0562905	+	0.0408975i
$982$	1.74721	−	5.37737i	0.0557558	−	0.171599i
$983$	−4.01362	−	12.3526i	−0.128015	−	0.393988i	0.866424	−	0.499309i	$-0.166413\pi$
$983$	−4.01362	−	12.3526i	−0.128015	−	0.393988i	−0.994438	+	0.105321i	$0.966413\pi$
$984$	1.88046	−	1.36623i	0.0599469	−	0.0435539i
$985$	5.71175	−	4.14983i	0.181992	−	0.132225i
$986$	13.7058	+	42.1821i	0.436482	+	1.34335i
$987$	−4.59535	+	14.1430i	−0.146271	+	0.450177i
$988$	49.0122	+	35.6094i	1.55928	+	1.13289i
$989$	−16.2511			−0.516754
$990$		0			0
$991$	7.01006			0.222682			0.111341	−	0.993782i	$-0.464485\pi$
$991$	7.01006			0.222682			0.111341	+	0.993782i	$0.464485\pi$
$992$	−8.20304	−	5.95985i	−0.260447	−	0.189226i
$993$	7.66047	−	23.5765i	0.243098	−	0.748178i
$994$	3.87680	+	11.9316i	0.122965	+	0.378447i
$995$	8.81724	−	6.40610i	0.279525	−	0.203087i
$996$	−37.3277	+	27.1202i	−1.18277	+	0.859335i
$997$	−9.85112	−	30.3186i	−0.311988	−	0.960200i	−0.976977	−	0.213347i	$-0.931564\pi$
$997$	−9.85112	−	30.3186i	−0.311988	−	0.960200i	0.664989	−	0.746854i	$-0.268436\pi$
$998$	14.5637	−	44.8224i	0.461006	−	1.41883i
$999$	46.5538	+	33.8233i	1.47290	+	1.07012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.y.323.2		24
11.2	odd	10		847.2.f.z.148.2		24
11.3	even	5	inner	847.2.f.y.729.2		24
11.4	even	5	inner	847.2.f.y.372.5		24
11.5	even	5		847.2.a.n.1.5	yes	6
11.6	odd	10		847.2.a.m.1.2	✓	6
11.7	odd	10		847.2.f.z.372.2		24
11.8	odd	10		847.2.f.z.729.5		24
11.9	even	5	inner	847.2.f.y.148.5		24
11.10	odd	2		847.2.f.z.323.5		24
33.5	odd	10		7623.2.a.cp.1.2		6
33.17	even	10		7623.2.a.cs.1.5		6
77.6	even	10		5929.2.a.bj.1.2		6
77.27	odd	10		5929.2.a.bm.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.m.1.2	✓	6	11.6	odd	10
847.2.a.n.1.5	yes	6	11.5	even	5
847.2.f.y.148.5		24	11.9	even	5	inner
847.2.f.y.323.2		24	1.1	even	1	trivial
847.2.f.y.372.5		24	11.4	even	5	inner
847.2.f.y.729.2		24	11.3	even	5	inner
847.2.f.z.148.2		24	11.2	odd	10
847.2.f.z.323.5		24	11.10	odd	2
847.2.f.z.372.2		24	11.7	odd	10
847.2.f.z.729.5		24	11.8	odd	10
5929.2.a.bj.1.2		6	77.6	even	10
5929.2.a.bm.1.5		6	77.27	odd	10
7623.2.a.cp.1.2		6	33.5	odd	10
7623.2.a.cs.1.5		6	33.17	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.70653 - 1.23987i) q^{2} +(0.524869 - 1.61538i) q^{3} +(0.756943 + 2.32963i) q^{4} +(-0.398353 + 0.289420i) q^{5} +(-2.89857 + 2.10593i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.293014 - 0.901803i) q^{8} +(0.0930802 + 0.0676268i) q^{9} +O(q^{10})\)	\(q+(-1.70653 - 1.23987i) q^{2} +(0.524869 - 1.61538i) q^{3} +(0.756943 + 2.32963i) q^{4} +(-0.398353 + 0.289420i) q^{5} +(-2.89857 + 2.10593i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.293014 - 0.901803i) q^{8} +(0.0930802 + 0.0676268i) q^{9} +1.03864 q^{10} +4.16054 q^{12} +(-4.28803 - 3.11543i) q^{13} +(0.651837 - 2.00615i) q^{14} +(0.258441 + 0.795400i) q^{15} +(2.34525 - 1.70393i) q^{16} +(-2.45715 + 1.78523i) q^{17} +(-0.0749961 - 0.230814i) q^{18} +(-1.44194 + 4.43784i) q^{19} +(-0.975773 - 0.708941i) q^{20} +1.69851 q^{21} -5.63835 q^{23} +(-1.30296 - 0.946657i) q^{24} +(-1.47016 + 4.52470i) q^{25} +(3.45493 + 10.6332i) q^{26} +(4.28048 - 3.10995i) q^{27} +(-1.98170 + 1.43979i) q^{28} +(2.13931 + 6.58412i) q^{29} +(0.545153 - 1.67781i) q^{30} +(1.02393 + 0.743930i) q^{31} -8.01131 q^{32} +6.40665 q^{34} +(-0.398353 - 0.289420i) q^{35} +(-0.0870890 + 0.268032i) q^{36} +(3.36082 + 10.3436i) q^{37} +(7.96305 - 5.78550i) q^{38} +(-7.28327 + 5.29160i) q^{39} +(0.144277 + 0.444040i) q^{40} +(-0.445979 + 1.37258i) q^{41} +(-2.89857 - 2.10593i) q^{42} +2.88224 q^{43} -0.0566513 q^{45} +(9.62202 + 6.99081i) q^{46} +(-2.70551 + 8.32671i) q^{47} +(-1.52154 - 4.68282i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(8.11891 - 5.89873i) q^{50} +(1.59414 + 4.90625i) q^{51} +(4.01202 - 12.3477i) q^{52} +(-5.37054 - 3.90192i) q^{53} -11.1607 q^{54} +0.948212 q^{56} +(6.41198 + 4.65857i) q^{57} +(4.51264 - 13.8885i) q^{58} +(-2.58256 - 7.94830i) q^{59} +(-1.65736 + 1.20414i) q^{60} +(11.2415 - 8.16744i) q^{61} +(-0.824997 - 2.53908i) q^{62} +(-0.0355535 + 0.109422i) q^{63} +(8.98105 + 6.52511i) q^{64} +2.60982 q^{65} -9.70431 q^{67} +(-6.01884 - 4.37294i) q^{68} +(-2.95940 + 9.10809i) q^{69} +(0.320959 + 0.987809i) q^{70} +(-4.81163 + 3.49586i) q^{71} +(0.0882598 - 0.0641245i) q^{72} +(-1.16629 - 3.58948i) q^{73} +(7.08928 - 21.8186i) q^{74} +(6.53747 + 4.74975i) q^{75} -11.4300 q^{76} +18.9900 q^{78} +(7.12245 + 5.17476i) q^{79} +(-0.441088 + 1.35753i) q^{80} +(-2.67040 - 8.21865i) q^{81} +(2.46290 - 1.78940i) q^{82} +(-8.97183 + 6.51842i) q^{83} +(1.28568 + 3.95691i) q^{84} +(0.462133 - 1.42230i) q^{85} +(-4.91863 - 3.57359i) q^{86} +11.7587 q^{87} +3.10324 q^{89} +(0.0966773 + 0.0702401i) q^{90} +(1.63788 - 5.04088i) q^{91} +(-4.26791 - 13.1353i) q^{92} +(1.73916 - 1.26357i) q^{93} +(14.9411 - 10.8553i) q^{94} +(-0.710000 - 2.18515i) q^{95} +(-4.20489 + 12.9413i) q^{96} +(5.11036 + 3.71290i) q^{97} +2.10939 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) \) 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9	\( 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9} - 32 q^{10} - 56 q^{12} - 4 q^{13} - 4 q^{14} - 2 q^{15} - 8 q^{16} - 22 q^{17} - 24 q^{18} - 6 q^{19} - 2 q^{20} - 8 q^{21} + 8 q^{23} + 20 q^{24} - 4 q^{25} - 6 q^{26} + 2 q^{27} - 4 q^{28} - 12 q^{29} - 20 q^{30} + 2 q^{31} + 32 q^{32} + 96 q^{34} + 4 q^{35} - 18 q^{36} - 14 q^{37} + 22 q^{38} - 20 q^{39} - 18 q^{40} - 26 q^{41} + 6 q^{42} - 16 q^{43} - 144 q^{45} - 12 q^{46} + 16 q^{47} + 24 q^{48} - 6 q^{49} + 4 q^{50} + 4 q^{51} - 12 q^{52} - 4 q^{53} - 128 q^{54} + 48 q^{56} - 20 q^{57} + 2 q^{58} + 4 q^{59} - 24 q^{60} + 8 q^{61} - 20 q^{62} - 8 q^{63} - 26 q^{64} + 96 q^{65} + 24 q^{67} - 12 q^{68} + 14 q^{69} + 8 q^{70} - 22 q^{71} - 16 q^{72} - 14 q^{73} - 44 q^{74} + 20 q^{75} - 120 q^{76} + 128 q^{78} + 28 q^{79} + 4 q^{80} + 6 q^{81} + 4 q^{82} - 22 q^{83} + 14 q^{84} + 24 q^{85} + 30 q^{86} + 88 q^{87} + 22 q^{90} - 4 q^{91} - 10 q^{92} + 50 q^{93} + 38 q^{94} + 24 q^{95} + 62 q^{96} + 4 q^{97} + 16 q^{98}+O(q^{100}) \) 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9 - 32 * q^10 - 56 * q^12 - 4 * q^13 - 4 * q^14 - 2 * q^15 - 8 * q^16 - 22 * q^17 - 24 * q^18 - 6 * q^19 - 2 * q^20 - 8 * q^21 + 8 * q^23 + 20 * q^24 - 4 * q^25 - 6 * q^26 + 2 * q^27 - 4 * q^28 - 12 * q^29 - 20 * q^30 + 2 * q^31 + 32 * q^32 + 96 * q^34 + 4 * q^35 - 18 * q^36 - 14 * q^37 + 22 * q^38 - 20 * q^39 - 18 * q^40 - 26 * q^41 + 6 * q^42 - 16 * q^43 - 144 * q^45 - 12 * q^46 + 16 * q^47 + 24 * q^48 - 6 * q^49 + 4 * q^50 + 4 * q^51 - 12 * q^52 - 4 * q^53 - 128 * q^54 + 48 * q^56 - 20 * q^57 + 2 * q^58 + 4 * q^59 - 24 * q^60 + 8 * q^61 - 20 * q^62 - 8 * q^63 - 26 * q^64 + 96 * q^65 + 24 * q^67 - 12 * q^68 + 14 * q^69 + 8 * q^70 - 22 * q^71 - 16 * q^72 - 14 * q^73 - 44 * q^74 + 20 * q^75 - 120 * q^76 + 128 * q^78 + 28 * q^79 + 4 * q^80 + 6 * q^81 + 4 * q^82 - 22 * q^83 + 14 * q^84 + 24 * q^85 + 30 * q^86 + 88 * q^87 + 22 * q^90 - 4 * q^91 - 10 * q^92 + 50 * q^93 + 38 * q^94 + 24 * q^95 + 62 * q^96 + 4 * q^97 + 16 * q^98

Introduction

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