LMFDB - Embedded newform 429.2.n.c.196.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(157,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 0]))

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

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

chi := DirichletCharacter("429.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			196.3
Character	$\chi$	$=$	429.196
Dual form			429.2.n.c.313.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0279051 - 0.0858830i) q^{2} +(0.809017 - 0.587785i) q^{3} +(1.61144 + 1.17078i) q^{4} +(0.964032 + 2.96698i) q^{5} +(-0.0279051 - 0.0858830i) q^{6} +(-2.21929 - 1.61241i) q^{7} +(0.291630 - 0.211882i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.0279051 - 0.0858830i) q^{2} +(0.809017 - 0.587785i) q^{3} +(1.61144 + 1.17078i) q^{4} +(0.964032 + 2.96698i) q^{5} +(-0.0279051 - 0.0858830i) q^{6} +(-2.21929 - 1.61241i) q^{7} +(0.291630 - 0.211882i) q^{8} +(0.309017 - 0.951057i) q^{9} +0.281715 q^{10} +(3.27445 - 0.527223i) q^{11} +1.99185 q^{12} +(0.309017 - 0.951057i) q^{13} +(-0.200408 + 0.145605i) q^{14} +(2.52387 + 1.83370i) q^{15} +(1.22097 + 3.75776i) q^{16} +(0.167284 + 0.514849i) q^{17} +(-0.0730564 - 0.0530786i) q^{18} +(-3.41670 + 2.48238i) q^{19} +(-1.92020 + 5.90977i) q^{20} -2.74320 q^{21} +(0.0460943 - 0.295932i) q^{22} +5.16998 q^{23} +(0.111393 - 0.342832i) q^{24} +(-3.82856 + 2.78161i) q^{25} +(-0.0730564 - 0.0530786i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(-1.68848 - 5.19659i) q^{28} +(-3.17880 - 2.30953i) q^{29} +(0.227912 - 0.165588i) q^{30} +(-2.23138 + 6.86748i) q^{31} +1.07775 q^{32} +(2.33919 - 2.35121i) q^{33} +0.0488848 q^{34} +(2.64453 - 8.13902i) q^{35} +(1.61144 - 1.17078i) q^{36} +(-7.09010 - 5.15126i) q^{37} +(0.117851 + 0.362708i) q^{38} +(-0.309017 - 0.951057i) q^{39} +(0.909790 + 0.661001i) q^{40} +(2.64829 - 1.92410i) q^{41} +(-0.0765491 + 0.235594i) q^{42} +1.39234 q^{43} +(5.89383 + 2.98407i) q^{44} +3.11967 q^{45} +(0.144269 - 0.444013i) q^{46} +(2.17550 - 1.58060i) q^{47} +(3.19654 + 2.32242i) q^{48} +(0.162271 + 0.499418i) q^{49} +(0.132057 + 0.406429i) q^{50} +(0.437956 + 0.318194i) q^{51} +(1.61144 - 1.17078i) q^{52} +(2.91795 - 8.98052i) q^{53} -0.0903027 q^{54} +(4.72094 + 9.20699i) q^{55} -0.988852 q^{56} +(-1.30506 + 4.01657i) q^{57} +(-0.287054 + 0.208557i) q^{58} +(-2.83276 - 2.05812i) q^{59} +(1.92020 + 5.90977i) q^{60} +(-3.67386 - 11.3070i) q^{61} +(0.527533 + 0.383275i) q^{62} +(-2.21929 + 1.61241i) q^{63} +(-2.41186 + 7.42295i) q^{64} +3.11967 q^{65} +(-0.136653 - 0.266508i) q^{66} +4.08390 q^{67} +(-0.333205 + 1.02550i) q^{68} +(4.18260 - 3.03884i) q^{69} +(-0.625208 - 0.454240i) q^{70} +(-2.06353 - 6.35089i) q^{71} +(-0.111393 - 0.342832i) q^{72} +(-8.11596 - 5.89659i) q^{73} +(-0.640256 + 0.465173i) q^{74} +(-1.46238 + 4.50074i) q^{75} -8.41211 q^{76} +(-8.11706 - 4.10970i) q^{77} -0.0903027 q^{78} +(0.429184 - 1.32089i) q^{79} +(-9.97215 + 7.24519i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.0913464 - 0.281135i) q^{82} +(4.92910 + 15.1702i) q^{83} +(-4.42049 - 3.21167i) q^{84} +(-1.36628 + 0.992661i) q^{85} +(0.0388535 - 0.119579i) q^{86} -3.92921 q^{87} +(0.843220 - 0.847550i) q^{88} -17.2008 q^{89} +(0.0870547 - 0.267927i) q^{90} +(-2.21929 + 1.61241i) q^{91} +(8.33110 + 6.05290i) q^{92} +(2.23138 + 6.86748i) q^{93} +(-0.0750387 - 0.230945i) q^{94} +(-10.6590 - 7.74421i) q^{95} +(0.871916 - 0.633484i) q^{96} +(4.53940 - 13.9708i) q^{97} +0.0474197 q^{98} +(0.510442 - 3.27711i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9}+O(q^{10}) $ 28 * q + q^2 + 7 * q^3 - 5 * q^4 - 4 * q^5 - q^6 + q^7 - 7 * q^8 - 7 * q^9	\( 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9} - 2 q^{10} + 14 q^{11} - 30 q^{12} - 7 q^{13} - 9 q^{14} + 4 q^{15} + q^{16} - 12 q^{17} - 4 q^{18} + 10 q^{19} - 41 q^{20} - 6 q^{21} + 5 q^{22} + 30 q^{23} + 2 q^{24} + 3 q^{25} - 4 q^{26} + 7 q^{27} - 12 q^{28} - 4 q^{29} + 7 q^{30} - 4 q^{31} + 22 q^{32} + q^{33} - 24 q^{34} - 6 q^{35} - 5 q^{36} - 8 q^{37} + 73 q^{38} + 7 q^{39} - 28 q^{40} + 10 q^{41} + 9 q^{42} - 12 q^{43} - 22 q^{44} + 16 q^{45} + 35 q^{46} + 12 q^{47} + 14 q^{48} + 16 q^{49} - 57 q^{50} - 13 q^{51} - 5 q^{52} + q^{53} - 6 q^{54} - 28 q^{55} + 48 q^{56} - 30 q^{58} - 15 q^{59} + 41 q^{60} - 22 q^{61} - 40 q^{62} + q^{63} - 19 q^{64} + 16 q^{65} + 20 q^{66} - 88 q^{67} + 39 q^{68} + 14 q^{70} + 34 q^{71} - 2 q^{72} - 59 q^{73} + 79 q^{74} + 27 q^{75} - 124 q^{76} - 42 q^{77} - 6 q^{78} - 3 q^{79} + 37 q^{80} - 7 q^{81} + 82 q^{82} - 8 q^{83} - 8 q^{84} + 70 q^{85} - 35 q^{86} - 36 q^{87} + 59 q^{88} + 126 q^{89} + 8 q^{90} + q^{91} - 82 q^{92} + 4 q^{93} + 23 q^{94} - 77 q^{95} + 73 q^{96} - 18 q^{97} - 66 q^{98} - 6 q^{99}+O(q^{100}) \) 28 * q + q^2 + 7 * q^3 - 5 * q^4 - 4 * q^5 - q^6 + q^7 - 7 * q^8 - 7 * q^9 - 2 * q^10 + 14 * q^11 - 30 * q^12 - 7 * q^13 - 9 * q^14 + 4 * q^15 + q^16 - 12 * q^17 - 4 * q^18 + 10 * q^19 - 41 * q^20 - 6 * q^21 + 5 * q^22 + 30 * q^23 + 2 * q^24 + 3 * q^25 - 4 * q^26 + 7 * q^27 - 12 * q^28 - 4 * q^29 + 7 * q^30 - 4 * q^31 + 22 * q^32 + q^33 - 24 * q^34 - 6 * q^35 - 5 * q^36 - 8 * q^37 + 73 * q^38 + 7 * q^39 - 28 * q^40 + 10 * q^41 + 9 * q^42 - 12 * q^43 - 22 * q^44 + 16 * q^45 + 35 * q^46 + 12 * q^47 + 14 * q^48 + 16 * q^49 - 57 * q^50 - 13 * q^51 - 5 * q^52 + q^53 - 6 * q^54 - 28 * q^55 + 48 * q^56 - 30 * q^58 - 15 * q^59 + 41 * q^60 - 22 * q^61 - 40 * q^62 + q^63 - 19 * q^64 + 16 * q^65 + 20 * q^66 - 88 * q^67 + 39 * q^68 + 14 * q^70 + 34 * q^71 - 2 * q^72 - 59 * q^73 + 79 * q^74 + 27 * q^75 - 124 * q^76 - 42 * q^77 - 6 * q^78 - 3 * q^79 + 37 * q^80 - 7 * q^81 + 82 * q^82 - 8 * q^83 - 8 * q^84 + 70 * q^85 - 35 * q^86 - 36 * q^87 + 59 * q^88 + 126 * q^89 + 8 * q^90 + q^91 - 82 * q^92 + 4 * q^93 + 23 * q^94 - 77 * q^95 + 73 * q^96 - 18 * q^97 - 66 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.0279051	−	0.0858830i	0.0197319	−	0.0607285i	−0.940706	−	0.339224i	$-0.889836\pi$
$2$	0.0279051	−	0.0858830i	0.0197319	−	0.0607285i	0.960438	+	0.278495i	$0.0898356\pi$
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	1.61144	+	1.17078i	0.805718	+	0.585389i
$5$	0.964032	+	2.96698i	0.431128	+	1.32688i	0.897003	+	0.442025i	$0.145740\pi$
$5$	0.964032	+	2.96698i	0.431128	+	1.32688i	−0.465875	+	0.884851i	$0.654260\pi$
$6$	−0.0279051	−	0.0858830i	−0.0113922	−	0.0350616i
$7$	−2.21929	−	1.61241i	−0.838813	−	0.609434i	0.0832256	−	0.996531i	$-0.473478\pi$
$7$	−2.21929	−	1.61241i	−0.838813	−	0.609434i	−0.922039	+	0.387097i	$0.873478\pi$
$8$	0.291630	−	0.211882i	0.103107	−	0.0749115i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	0.281715			0.0890861
$11$	3.27445	−	0.527223i	0.987284	−	0.158964i
$11$	3.27445	−	0.527223i	0.987284	−	0.158964i
$12$	1.99185			0.574996
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i
$14$	−0.200408	+	0.145605i	−0.0535613	+	0.0389146i
$15$	2.52387	+	1.83370i	0.651660	+	0.473459i
$16$	1.22097	+	3.75776i	0.305242	+	0.939439i
$17$	0.167284	+	0.514849i	0.0405724	+	0.124869i	0.969291	−	0.245916i	$-0.0790887\pi$
$17$	0.167284	+	0.514849i	0.0405724	+	0.124869i	−0.928719	+	0.370785i	$0.879089\pi$
$18$	−0.0730564	−	0.0530786i	−0.0172196	−	0.0125107i
$19$	−3.41670	+	2.48238i	−0.783845	+	0.569497i	−0.906131	−	0.422998i	$-0.860978\pi$
$19$	−3.41670	+	2.48238i	−0.783845	+	0.569497i	0.122285	+	0.992495i	$0.460978\pi$
$20$	−1.92020	+	5.90977i	−0.429370	+	1.32147i
$21$	−2.74320			−0.598614
$22$	0.0460943	−	0.295932i	0.00982734	−	0.0630929i
$23$	5.16998			1.07802			0.539008	−	0.842301i	$-0.318799\pi$
$23$	5.16998			1.07802			0.539008	+	0.842301i	$0.318799\pi$
$24$	0.111393	−	0.342832i	0.0227380	−	0.0699802i
$25$	−3.82856	+	2.78161i	−0.765711	+	0.556322i
$26$	−0.0730564	−	0.0530786i	−0.0143275	−	0.0104096i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	−1.68848	−	5.19659i	−0.319092	−	0.982064i
$29$	−3.17880	−	2.30953i	−0.590288	−	0.428869i	0.252131	−	0.967693i	$-0.418869\pi$
$29$	−3.17880	−	2.30953i	−0.590288	−	0.428869i	−0.842418	+	0.538824i	$0.818869\pi$
$30$	0.227912	−	0.165588i	0.0416109	−	0.0302321i
$31$	−2.23138	+	6.86748i	−0.400768	+	1.23344i	0.523610	+	0.851958i	$0.324585\pi$
$31$	−2.23138	+	6.86748i	−0.400768	+	1.23344i	−0.924378	+	0.381478i	$0.875415\pi$
$32$	1.07775			0.190521
$33$	2.33919	−	2.35121i	0.407201	−	0.409293i
$34$	0.0488848			0.00838368
$35$	2.64453	−	8.13902i	0.447007	−	1.37575i
$36$	1.61144	−	1.17078i	0.268573	−	0.195130i
$37$	−7.09010	−	5.15126i	−1.16561	−	0.846862i	−0.175129	−	0.984545i	$-0.556034\pi$
$37$	−7.09010	−	5.15126i	−1.16561	−	0.846862i	−0.990476	+	0.137683i	$0.956034\pi$
$38$	0.117851	+	0.362708i	0.0191179	+	0.0588389i
$39$	−0.309017	−	0.951057i	−0.0494823	−	0.152291i
$40$	0.909790	+	0.661001i	0.143850	+	0.104513i
$41$	2.64829	−	1.92410i	0.413594	−	0.300493i	−0.361461	−	0.932387i	$-0.617722\pi$
$41$	2.64829	−	1.92410i	0.413594	−	0.300493i	0.775055	+	0.631894i	$0.217722\pi$
$42$	−0.0765491	+	0.235594i	−0.0118118	+	0.0363529i
$43$	1.39234			0.212330			0.106165	−	0.994349i	$-0.466143\pi$
$43$	1.39234			0.212330			0.106165	+	0.994349i	$0.466143\pi$
$44$	5.89383	+	2.98407i	0.888529	+	0.449865i
$45$	3.11967			0.465053
$46$	0.144269	−	0.444013i	0.0212713	−	0.0654662i
$47$	2.17550	−	1.58060i	0.317330	−	0.230554i	−0.417705	−	0.908583i	$-0.637166\pi$
$47$	2.17550	−	1.58060i	0.317330	−	0.230554i	0.735035	+	0.678029i	$0.237166\pi$
$48$	3.19654	+	2.32242i	0.461381	+	0.335213i
$49$	0.162271	+	0.499418i	0.0231815	+	0.0713454i
$50$	0.132057	+	0.406429i	0.0186756	+	0.0574777i
$51$	0.437956	+	0.318194i	0.0613262	+	0.0445561i
$52$	1.61144	−	1.17078i	0.223466	−	0.162358i
$53$	2.91795	−	8.98052i	0.400811	−	1.23357i	−0.523532	−	0.852006i	$-0.675386\pi$
$53$	2.91795	−	8.98052i	0.400811	−	1.23357i	0.924343	−	0.381563i	$-0.124614\pi$
$54$	−0.0903027			−0.0122886
$55$	4.72094	+	9.20699i	0.636571	+	1.24147i
$56$	−0.988852			−0.132141
$57$	−1.30506	+	4.01657i	−0.172860	+	0.532008i
$58$	−0.287054	+	0.208557i	−0.0376920	+	0.0273849i
$59$	−2.83276	−	2.05812i	−0.368794	−	0.267945i	0.387917	−	0.921694i	$-0.373195\pi$
$59$	−2.83276	−	2.05812i	−0.368794	−	0.267945i	−0.756711	+	0.653750i	$0.773195\pi$
$60$	1.92020	+	5.90977i	0.247897	+	0.762949i
$61$	−3.67386	−	11.3070i	−0.470390	−	1.44771i	−0.852075	−	0.523420i	$-0.824656\pi$
$61$	−3.67386	−	11.3070i	−0.470390	−	1.44771i	0.381685	−	0.924293i	$-0.375344\pi$
$62$	0.527533	+	0.383275i	0.0669968	+	0.0486760i
$63$	−2.21929	+	1.61241i	−0.279604	+	0.203145i
$64$	−2.41186	+	7.42295i	−0.301483	+	0.927869i
$65$	3.11967			0.386948
$66$	−0.136653	−	0.266508i	−0.0168209	−	0.0328048i
$67$	4.08390			0.498928			0.249464	−	0.968384i	$-0.419746\pi$
$67$	4.08390			0.498928			0.249464	+	0.968384i	$0.419746\pi$
$68$	−0.333205	+	1.02550i	−0.0404070	+	0.124360i
$69$	4.18260	−	3.03884i	0.503526	−	0.365833i
$70$	−0.625208	−	0.454240i	−0.0747266	−	0.0542920i
$71$	−2.06353	−	6.35089i	−0.244896	−	0.753712i	−0.995654	−	0.0931346i	$-0.970311\pi$
$71$	−2.06353	−	6.35089i	−0.244896	−	0.753712i	0.750758	−	0.660578i	$-0.229689\pi$
$72$	−0.111393	−	0.342832i	−0.0131278	−	0.0404031i
$73$	−8.11596	−	5.89659i	−0.949901	−	0.690144i	0.000882358	−	1.00000i	$-0.499719\pi$
$73$	−8.11596	−	5.89659i	−0.949901	−	0.690144i	−0.950783	+	0.309856i	$0.899719\pi$
$74$	−0.640256	+	0.465173i	−0.0744282	+	0.0540752i
$75$	−1.46238	+	4.50074i	−0.168861	+	0.519700i
$76$	−8.41211			−0.964935
$77$	−8.11706	−	4.10970i	−0.925025	−	0.468343i
$78$	−0.0903027			−0.0102248
$79$	0.429184	−	1.32089i	0.0482870	−	0.148612i	−0.924006	−	0.382378i	$-0.875105\pi$
$79$	0.429184	−	1.32089i	0.0482870	−	0.148612i	0.972293	+	0.233766i	$0.0751051\pi$
$80$	−9.97215	+	7.24519i	−1.11492	+	0.810037i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−0.0913464	−	0.281135i	−0.0100875	−	0.0310462i
$83$	4.92910	+	15.1702i	0.541038	+	1.66515i	0.730227	+	0.683204i	$0.239414\pi$
$83$	4.92910	+	15.1702i	0.541038	+	1.66515i	−0.189189	+	0.981941i	$0.560586\pi$
$84$	−4.42049	−	3.21167i	−0.482314	−	0.350422i
$85$	−1.36628	+	0.992661i	−0.148194	+	0.107669i
$86$	0.0388535	−	0.119579i	0.00418968	−	0.0128945i
$87$	−3.92921			−0.421255
$88$	0.843220	−	0.847550i	0.0898875	−	0.0903492i
$89$	−17.2008			−1.82328			−0.911642	−	0.410986i	$-0.865185\pi$
$89$	−17.2008			−1.82328			−0.911642	+	0.410986i	$0.865185\pi$
$90$	0.0870547	−	0.267927i	0.00917637	−	0.0282420i
$91$	−2.21929	+	1.61241i	−0.232645	+	0.169026i
$92$	8.33110	+	6.05290i	0.868577	+	0.631058i
$93$	2.23138	+	6.86748i	0.231383	+	0.712125i
$94$	−0.0750387	−	0.230945i	−0.00773966	−	0.0238202i
$95$	−10.6590	−	7.74421i	−1.09359	−	0.794539i
$96$	0.871916	−	0.633484i	0.0889896	−	0.0646547i
$97$	4.53940	−	13.9708i	0.460906	−	1.41852i	−0.403153	−	0.915133i	$-0.632086\pi$
$97$	4.53940	−	13.9708i	0.460906	−	1.41852i	0.864059	−	0.503391i	$-0.167914\pi$
$98$	0.0474197			0.00479011
$99$	0.510442	−	3.27711i	0.0513014	−	0.329362i
$100$	−9.42612			−0.942612
$101$	−3.34150	+	10.2841i	−0.332492	+	1.02331i	0.635452	+	0.772140i	$0.280814\pi$
$101$	−3.34150	+	10.2841i	−0.332492	+	1.02331i	−0.967944	+	0.251165i	$0.919186\pi$
$102$	0.0395487	−	0.0287338i	0.00391590	−	0.00284507i
$103$	1.14895	+	0.834760i	0.113209	+	0.0822514i	0.642949	−	0.765909i	$-0.277711\pi$
$103$	1.14895	+	0.834760i	0.113209	+	0.0822514i	−0.529740	+	0.848160i	$0.677711\pi$
$104$	−0.111393	−	0.342832i	−0.0109230	−	0.0336174i
$105$	−2.64453	−	8.13902i	−0.258079	−	0.794287i
$106$	−0.689848	−	0.501204i	−0.0670040	−	0.0486813i
$107$	7.72394	−	5.61177i	0.746701	−	0.542510i	−0.148101	−	0.988972i	$-0.547316\pi$
$107$	7.72394	−	5.61177i	0.746701	−	0.542510i	0.894803	+	0.446462i	$0.147316\pi$
$108$	0.615514	−	1.89436i	0.0592279	−	0.182285i
$109$	−19.6195			−1.87921			−0.939603	−	0.342265i	$-0.888806\pi$
$109$	−19.6195			−1.87921			−0.939603	+	0.342265i	$0.888806\pi$
$110$	0.922462	−	0.148527i	0.0879533	−	0.0141615i
$111$	−8.76385			−0.831828
$112$	3.34936	−	10.3083i	0.316484	−	0.974039i
$113$	3.80758	−	2.76637i	0.358187	−	0.260238i	−0.394109	−	0.919064i	$-0.628947\pi$
$113$	3.80758	−	2.76637i	0.358187	−	0.260238i	0.752295	+	0.658826i	$0.228947\pi$
$114$	0.308537	+	0.224166i	0.0288972	+	0.0209950i
$115$	4.98403	+	15.3393i	0.464763	+	1.43039i
$116$	−2.41848	−	7.44332i	−0.224550	−	0.691095i
$117$	−0.809017	−	0.587785i	−0.0747936	−	0.0543408i
$118$	−0.255806	+	0.185854i	−0.0235489	+	0.0171092i
$119$	0.458894	−	1.41233i	0.0420667	−	0.129468i
$120$	1.12456			0.102658
$121$	10.4441	−	3.45274i	0.949461	−	0.313885i
$122$	−1.07360			−0.0971990
$123$	1.01156	−	3.11325i	0.0912091	−	0.280713i
$124$	−11.6360	+	8.45406i	−1.04495	+	0.759197i
$125$	0.675501	+	0.490780i	0.0604187	+	0.0438967i
$126$	0.0765491	+	0.235594i	0.00681953	+	0.0209884i
$127$	−4.34530	−	13.3735i	−0.385583	−	1.18670i	−0.936056	−	0.351850i	$-0.885553\pi$
$127$	−4.34530	−	13.3735i	−0.385583	−	1.18670i	0.550473	−	0.834853i	$-0.314447\pi$
$128$	2.31403	+	1.68124i	0.204534	+	0.148602i
$129$	1.12643	−	0.818399i	0.0991766	−	0.0720560i
$130$	0.0870547	−	0.267927i	0.00763520	−	0.0234987i
$131$	11.9439			1.04354			0.521771	−	0.853086i	$-0.325272\pi$
$131$	11.9439			1.04354			0.521771	+	0.853086i	$0.325272\pi$
$132$	6.52220	−	1.05015i	0.567685	−	0.0914036i
$133$	11.5853			1.00457
$134$	0.113962	−	0.350737i	0.00984478	−	0.0302991i
$135$	2.52387	−	1.83370i	0.217220	−	0.157820i
$136$	0.157872	+	0.114701i	0.0135374	+	0.00983551i
$137$	1.67456	+	5.15378i	0.143068	+	0.440317i	0.996757	−	0.0804649i	$-0.0256405\pi$
$137$	1.67456	+	5.15378i	0.143068	+	0.440317i	−0.853690	+	0.520782i	$0.825640\pi$
$138$	−0.144269	−	0.444013i	−0.0122810	−	0.0377969i
$139$	12.2706	+	8.91512i	1.04078	+	0.756170i	0.970438	−	0.241352i	$-0.0775910\pi$
$139$	12.2706	+	8.91512i	1.04078	+	0.756170i	0.0703418	+	0.997523i	$0.477591\pi$
$140$	13.7905	−	10.0194i	1.16551	−	0.846790i
$141$	0.830969	−	2.55746i	0.0699802	−	0.215377i
$142$	−0.603017			−0.0506040
$143$	0.510442	−	3.27711i	0.0426853	−	0.274046i
$144$	3.95114			0.329262
$145$	3.78788	−	11.6579i	0.314566	−	0.968136i
$146$	−0.732893	+	0.532478i	−0.0606547	+	0.0440682i
$147$	0.424830	+	0.308657i	0.0350394	+	0.0254576i
$148$	−5.39427	−	16.6019i	−0.443406	−	1.36466i
$149$	3.88480	+	11.9562i	0.318255	+	0.979488i	0.974394	+	0.224848i	$0.0721885\pi$
$149$	3.88480	+	11.9562i	0.318255	+	0.979488i	−0.656139	+	0.754640i	$0.727811\pi$
$150$	0.345729	+	0.251187i	0.0282287	+	0.0205093i
$151$	−4.05967	+	2.94952i	−0.330371	+	0.240029i	−0.740588	−	0.671959i	$-0.765453\pi$
$151$	−4.05967	+	2.94952i	−0.330371	+	0.240029i	0.410217	+	0.911988i	$0.365453\pi$
$152$	−0.470442	+	1.44787i	−0.0381579	+	0.117438i
$153$	0.541344			0.0437651
$154$	−0.579460	+	0.582436i	−0.0466942	+	0.0469341i
$155$	−22.5268			−1.80940
$156$	0.615514	−	1.89436i	0.0492806	−	0.151670i
$157$	−14.6663	+	10.6557i	−1.17050	+	0.850419i	−0.991069	−	0.133351i	$-0.957426\pi$
$157$	−14.6663	+	10.6557i	−1.17050	+	0.850419i	−0.179433	+	0.983770i	$0.557426\pi$
$158$	−0.101466	−	0.0737192i	−0.00807218	−	0.00586478i
$159$	−2.91795	−	8.98052i	−0.231408	−	0.712201i
$160$	1.03898	+	3.19766i	0.0821388	+	0.252797i
$161$	−11.4737	−	8.33613i	−0.904254	−	0.656979i
$162$	−0.0730564	+	0.0530786i	−0.00573986	+	0.00417025i
$163$	0.478711	−	1.47332i	0.0374956	−	0.115399i	−0.930557	−	0.366147i	$-0.880677\pi$
$163$	0.478711	−	1.47332i	0.0374956	−	0.115399i	0.968052	+	0.250748i	$0.0806766\pi$
$164$	6.52025			0.509146
$165$	9.23105	+	4.67371i	0.718636	+	0.363848i
$166$	1.44041			0.111797
$167$	−5.57577	+	17.1605i	−0.431466	+	1.32792i	0.465198	+	0.885207i	$0.345983\pi$
$167$	−5.57577	+	17.1605i	−0.431466	+	1.32792i	−0.896665	+	0.442710i	$0.854017\pi$
$168$	−0.799998	+	0.581233i	−0.0617212	+	0.0448431i
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$	0.0471265	+	0.145041i	0.00361444	+	0.0111241i
$171$	1.30506	+	4.01657i	0.0998007	+	0.307155i
$172$	2.24367	+	1.63012i	0.171079	+	0.124296i
$173$	5.45426	−	3.96275i	0.414680	−	0.301282i	−0.360814	−	0.932638i	$-0.617501\pi$
$173$	5.45426	−	3.96275i	0.414680	−	0.301282i	0.775494	+	0.631355i	$0.217501\pi$
$174$	−0.109645	+	0.337452i	−0.00831215	+	0.0255822i
$175$	12.9818			0.981330
$176$	5.97918	+	11.6609i	0.450698	+	0.878971i
$177$	−3.50149			−0.263188
$178$	−0.479990	+	1.47726i	−0.0359768	+	0.110725i
$179$	−10.5689	+	7.67875i	−0.789956	+	0.573936i	−0.907950	−	0.419078i	$-0.862353\pi$
$179$	−10.5689	+	7.67875i	−0.789956	+	0.573936i	0.117995	+	0.993014i	$0.462353\pi$
$180$	5.02715	+	3.65244i	0.374702	+	0.272237i
$181$	5.84203	+	17.9799i	0.434235	+	1.33644i	0.893869	+	0.448329i	$0.147981\pi$
$181$	5.84203	+	17.9799i	0.434235	+	1.33644i	−0.459634	+	0.888108i	$0.652019\pi$
$182$	0.0765491	+	0.235594i	0.00567419	+	0.0174634i
$183$	−9.61830	−	6.98811i	−0.711005	−	0.516576i
$184$	1.50772	−	1.09542i	0.111151	−	0.0807557i
$185$	8.44863	−	26.0022i	0.621155	−	1.91172i
$186$	0.652067			0.0478119
$187$	0.819205	+	1.59765i	0.0599062	+	0.116832i
$188$	5.35621			0.390642
$189$	−0.847694	+	2.60893i	−0.0616607	+	0.189772i
$190$	−0.962536	+	0.699323i	−0.0698297	+	0.0507342i
$191$	7.48469	+	5.43794i	0.541573	+	0.393476i	0.824669	−	0.565616i	$-0.191361\pi$
$191$	7.48469	+	5.43794i	0.541573	+	0.393476i	−0.283096	+	0.959092i	$0.591361\pi$
$192$	2.41186	+	7.42295i	0.174061	+	0.535705i
$193$	6.71279	+	20.6599i	0.483198	+	1.48713i	0.834575	+	0.550895i	$0.185714\pi$
$193$	6.71279	+	20.6599i	0.483198	+	1.48713i	−0.351377	+	0.936234i	$0.614286\pi$
$194$	−1.07319	−	0.779715i	−0.0770502	−	0.0559803i
$195$	2.52387	−	1.83370i	0.180738	−	0.131314i
$196$	−0.323218	+	0.994763i	−0.0230870	+	0.0710545i
$197$	−7.02637			−0.500608			−0.250304	−	0.968167i	$-0.580531\pi$
$197$	−7.02637			−0.500608			−0.250304	+	0.968167i	$0.580531\pi$
$198$	−0.267204	−	0.135286i	−0.0189894	−	0.00961438i
$199$	−9.43953			−0.669150			−0.334575	−	0.942369i	$-0.608593\pi$
$199$	−9.43953			−0.669150			−0.334575	+	0.942369i	$0.608593\pi$
$200$	−0.527150	+	1.62240i	−0.0372751	+	0.114721i
$201$	3.30394	−	2.40046i	0.233042	−	0.169315i
$202$	0.789984	+	0.573957i	0.0555831	+	0.0403834i
$203$	3.33077	+	10.2510i	0.233774	+	0.719482i
$204$	0.333205	+	1.02550i	0.0233290	+	0.0717993i
$205$	8.26180	+	6.00255i	0.577029	+	0.419236i
$206$	0.103753	−	0.0753811i	0.00722883	−	0.00525205i
$207$	1.59761	−	4.91694i	0.111042	−	0.341751i
$208$	3.95114			0.273962
$209$	−9.87906	+	9.92980i	−0.683349	+	0.686858i
$210$	−0.772799			−0.0533282
$211$	−1.24775	+	3.84019i	−0.0858989	+	0.264370i	−0.984775	−	0.173833i	$-0.944385\pi$
$211$	−1.24775	+	3.84019i	−0.0858989	+	0.264370i	0.898876	+	0.438203i	$0.144385\pi$
$212$	15.2163	−	11.0553i	1.04506	−	0.759279i
$213$	−5.40239	−	3.92507i	−0.370166	−	0.268941i
$214$	−0.266418	−	0.819952i	−0.0182120	−	0.0560507i
$215$	1.34226	+	4.13106i	0.0915416	+	0.281736i
$216$	−0.291630	−	0.211882i	−0.0198429	−	0.0144167i
$217$	16.0253	−	11.6430i	1.08787	−	0.790381i
$218$	−0.547484	+	1.68498i	−0.0370803	+	0.114121i
$219$	−10.0319			−0.677891
$220$	−3.17184	+	20.3636i	−0.213845	+	1.37292i
$221$	0.541344			0.0364147
$222$	−0.244556	+	0.752666i	−0.0164135	+	0.0505156i
$223$	−1.43857	+	1.04518i	−0.0963335	+	0.0699904i	−0.634909	−	0.772587i	$-0.718963\pi$
$223$	−1.43857	+	1.04518i	−0.0963335	+	0.0699904i	0.538576	+	0.842577i	$0.318963\pi$
$224$	−2.39184	−	1.73777i	−0.159811	−	0.116110i
$225$	1.46238	+	4.50074i	0.0974919	+	0.300049i
$226$	−0.131333	−	0.404202i	−0.00873616	−	0.0268871i
$227$	−2.50882	−	1.82276i	−0.166516	−	0.120981i	0.501406	−	0.865212i	$-0.332816\pi$
$227$	−2.50882	−	1.82276i	−0.166516	−	0.120981i	−0.667922	+	0.744231i	$0.732816\pi$
$228$	−6.80554	+	4.94452i	−0.450708	+	0.327459i
$229$	4.87461	−	15.0025i	0.322123	−	0.991393i	−0.650599	−	0.759421i	$-0.725482\pi$
$229$	4.87461	−	15.0025i	0.322123	−	0.991393i	0.972722	−	0.231972i	$-0.0745178\pi$
$230$	1.45646			0.0960362
$231$	−8.98246	+	1.44628i	−0.591002	+	0.0951580i
$232$	−1.41638			−0.0929899
$233$	−0.778663	+	2.39648i	−0.0510119	+	0.156998i	−0.973317	−	0.229463i	$-0.926303\pi$
$233$	−0.778663	+	2.39648i	−0.0510119	+	0.156998i	0.922305	+	0.386462i	$0.126303\pi$
$234$	−0.0730564	+	0.0530786i	−0.00477585	+	0.00346986i
$235$	6.78686	+	4.93094i	0.442726	+	0.321659i
$236$	−2.15521	−	6.63307i	−0.140292	−	0.431776i
$237$	−0.429184	−	1.32089i	−0.0278785	−	0.0858012i
$238$	−0.108490	−	0.0788224i	−0.00703234	−	0.00510930i
$239$	24.0937	−	17.5051i	1.55849	−	1.13231i	0.621263	−	0.783602i	$-0.286620\pi$
$239$	24.0937	−	17.5051i	1.55849	−	1.13231i	0.937231	−	0.348710i	$-0.113380\pi$
$240$	−3.80902	+	11.7230i	−0.245871	+	0.756714i
$241$	8.43145			0.543118			0.271559	−	0.962422i	$-0.412461\pi$
$241$	8.43145			0.543118			0.271559	+	0.962422i	$0.412461\pi$
$242$	−0.00508864	−	0.993317i	−0.000327110	−	0.0638528i
$243$	−1.00000			−0.0641500
$244$	7.31777	−	22.5218i	0.468472	−	1.44181i
$245$	−1.32533	+	0.962909i	−0.0846723	+	0.0615180i
$246$	−0.239148	−	0.173751i	−0.0152475	−	0.0110780i
$247$	1.30506	+	4.01657i	0.0830392	+	0.255568i
$248$	0.804356	+	2.47555i	0.0510766	+	0.157198i
$249$	12.9045	+	9.37570i	0.817792	+	0.594161i
$250$	0.0609996	−	0.0443188i	0.00385795	−	0.00280297i
$251$	6.54553	−	20.1451i	0.413150	−	1.27155i	−0.500745	−	0.865595i	$-0.666941\pi$
$251$	6.54553	−	20.1451i	0.413150	−	1.27155i	0.913895	−	0.405950i	$-0.133059\pi$
$252$	−5.46402			−0.344201
$253$	16.9289	−	2.72573i	1.06431	−	0.171365i
$254$	−1.26981			−0.0796749
$255$	−0.521873	+	1.60616i	−0.0326809	+	0.100582i
$256$	−12.4197	+	9.02345i	−0.776232	+	0.563966i
$257$	−20.9573	−	15.2264i	−1.30728	−	0.949796i	−0.307284	−	0.951618i	$-0.599420\pi$
$257$	−20.9573	−	15.2264i	−1.30728	−	0.949796i	−0.999998	+	0.00182149i	$0.999420\pi$
$258$	−0.0388535	−	0.119579i	−0.00241891	−	0.00744464i
$259$	7.42906	+	22.8643i	0.461619	+	1.42072i
$260$	5.02715	+	3.65244i	0.311771	+	0.226515i
$261$	−3.17880	+	2.30953i	−0.196763	+	0.142956i
$262$	0.333295	−	1.02578i	0.0205910	−	0.0633726i
$263$	−11.3339			−0.698876			−0.349438	−	0.936960i	$-0.613627\pi$
$263$	−11.3339			−0.698876			−0.349438	+	0.936960i	$0.613627\pi$
$264$	0.184001	−	1.18131i	0.0113245	−	0.0727049i
$265$	29.4581			1.80959
$266$	0.323288	−	0.994978i	0.0198220	−	0.0610060i
$267$	−13.9158	+	10.1104i	−0.851630	+	0.618746i
$268$	6.58094	+	4.78134i	0.401995	+	0.292067i
$269$	6.82328	+	20.9999i	0.416023	+	1.28039i	0.911333	+	0.411670i	$0.135054\pi$
$269$	6.82328	+	20.9999i	0.416023	+	1.28039i	−0.495310	+	0.868716i	$0.664946\pi$
$270$	−0.0870547	−	0.267927i	−0.00529798	−	0.0163055i
$271$	−0.0534586	−	0.0388400i	−0.00324738	−	0.00235936i	0.586160	−	0.810195i	$-0.300639\pi$
$271$	−0.0534586	−	0.0388400i	−0.00324738	−	0.00235936i	−0.589408	+	0.807836i	$0.700639\pi$
$272$	−1.73043	+	1.25723i	−0.104923	+	0.0762307i
$273$	−0.847694	+	2.60893i	−0.0513048	+	0.157900i
$274$	0.489351			0.0295628
$275$	−11.0699	+	11.1267i	−0.667540	+	0.670968i
$276$	10.2978			0.619855
$277$	4.58767	−	14.1194i	0.275647	−	0.848353i	−0.713401	−	0.700756i	$-0.752846\pi$
$277$	4.58767	−	14.1194i	0.275647	−	0.848353i	0.989048	−	0.147597i	$-0.0471538\pi$
$278$	1.10807	−	0.805060i	0.0664576	−	0.0482843i
$279$	5.84183	+	4.24434i	0.349741	+	0.254102i
$280$	−0.953285	−	2.93391i	−0.0569697	−	0.175335i
$281$	8.63738	+	26.5831i	0.515263	+	1.58582i	0.782803	+	0.622270i	$0.213789\pi$
$281$	8.63738	+	26.5831i	0.515263	+	1.58582i	−0.267540	+	0.963547i	$0.586211\pi$
$282$	−0.196454	−	0.142732i	−0.0116987	−	0.00849958i
$283$	18.0470	−	13.1119i	1.07279	−	0.779424i	0.0963743	−	0.995345i	$-0.469275\pi$
$283$	18.0470	−	13.1119i	1.07279	−	0.779424i	0.976411	+	0.215921i	$0.0692754\pi$
$284$	4.11023	−	12.6500i	0.243898	−	0.750639i
$285$	−13.1752			−0.780434
$286$	−0.267204	−	0.135286i	−0.0158001	−	0.00799965i
$287$	−8.97977			−0.530059
$288$	0.333042	−	1.02500i	0.0196247	−	0.0603986i
$289$	13.5162	−	9.82010i	0.795071	−	0.577653i
$290$	−0.895514	−	0.650629i	−0.0525864	−	0.0382063i
$291$	−4.53940	−	13.9708i	−0.266104	−	0.818985i
$292$	−6.17476	−	19.0040i	−0.361351	−	1.11212i
$293$	−8.41356	−	6.11281i	−0.491525	−	0.357114i	0.314245	−	0.949342i	$-0.398249\pi$
$293$	−8.41356	−	6.11281i	−0.491525	−	0.357114i	−0.805771	+	0.592228i	$0.798249\pi$
$294$	0.0383633	−	0.0278726i	0.00223739	−	0.00162556i
$295$	3.37554	−	10.3889i	0.196532	−	0.604863i
$296$	−3.15914			−0.183622
$297$	−1.51328	−	2.95127i	−0.0878094	−	0.171250i
$298$	1.13524			0.0657626
$299$	1.59761	−	4.91694i	0.0923923	−	0.284354i
$300$	−7.62589	+	5.54053i	−0.440281	+	0.319883i
$301$	−3.09002	−	2.24503i	−0.178106	−	0.129401i
$302$	0.140028	+	0.430963i	0.00805772	+	0.0247991i
$303$	3.34150	+	10.2841i	0.191964	+	0.590806i
$304$	−13.4999	−	9.80822i	−0.774270	−	0.562540i
$305$	30.0060	−	21.8006i	1.71814	−	1.24830i
$306$	0.0151062	−	0.0464922i	0.000863566	−	0.00265778i
$307$	15.1134			0.862569			0.431284	−	0.902216i	$-0.358061\pi$
$307$	15.1134			0.862569			0.431284	+	0.902216i	$0.358061\pi$
$308$	−8.26860	−	16.1258i	−0.471147	−	0.918852i
$309$	1.42018			0.0807912
$310$	−0.628613	+	1.93467i	−0.0357028	+	0.109882i
$311$	−23.1151	+	16.7941i	−1.31073	+	0.952305i	−0.310736	+	0.950496i	$0.600576\pi$
$311$	−23.1151	+	16.7941i	−1.31073	+	0.952305i	−0.999998	+	0.00180838i	$0.999424\pi$
$312$	−0.291630	−	0.211882i	−0.0165103	−	0.0119954i
$313$	3.73489	+	11.4948i	0.211109	+	0.649726i	0.999407	+	0.0344325i	$0.0109624\pi$
$313$	3.73489	+	11.4948i	0.211109	+	0.649726i	−0.788298	+	0.615293i	$0.789038\pi$
$314$	0.505880	+	1.55694i	0.0285485	+	0.0878631i
$315$	−6.92346	−	5.03019i	−0.390093	−	0.283419i
$316$	2.23807	−	1.62606i	0.125901	−	0.0914728i
$317$	−2.87956	+	8.86238i	−0.161732	+	0.497761i	−0.998781	−	0.0493681i	$-0.984279\pi$
$317$	−2.87956	+	8.86238i	−0.161732	+	0.497761i	0.837048	+	0.547129i	$0.184279\pi$
$318$	−0.852699			−0.0478170
$319$	−11.6265	−	5.88651i	−0.650956	−	0.329581i
$320$	−24.3489			−1.36114
$321$	2.95028	−	9.08003i	0.164669	−	0.506798i
$322$	−1.03611	+	0.752775i	−0.0577399	+	0.0419505i
$323$	−1.84961	−	1.34382i	−0.102915	−	0.0747722i
$324$	−0.615514	−	1.89436i	−0.0341952	−	0.105242i
$325$	1.46238	+	4.50074i	0.0811181	+	0.249656i
$326$	−0.113175	−	0.0822263i	−0.00626817	−	0.00455409i
$327$	−15.8725	+	11.5320i	−0.877752	+	0.637724i
$328$	0.364641	−	1.12225i	0.0201339	−	0.0619658i
$329$	−7.37665			−0.406688
$330$	0.658986	−	0.662370i	0.0362760	−	0.0364623i
$331$	0.522300			0.0287082			0.0143541	−	0.999897i	$-0.495431\pi$
$331$	0.522300			0.0287082			0.0143541	+	0.999897i	$0.495431\pi$
$332$	−9.81800	+	30.2167i	−0.538833	+	1.65836i
$333$	−7.09010	+	5.15126i	−0.388535	+	0.282287i
$334$	1.31820	+	0.957729i	0.0721287	+	0.0524046i
$335$	3.93701	+	12.1169i	0.215102	+	0.662015i
$336$	−3.34936	−	10.3083i	−0.182722	−	0.562362i
$337$	−11.5749	−	8.40966i	−0.630526	−	0.458104i	0.226057	−	0.974114i	$-0.427417\pi$
$337$	−11.5749	−	8.40966i	−0.630526	−	0.458104i	−0.856582	+	0.516011i	$0.827417\pi$
$338$	−0.0730564	+	0.0530786i	−0.00397375	+	0.00288710i
$339$	1.45437	−	4.47608i	0.0789903	−	0.243107i
$340$	−3.36386			−0.182431
$341$	−3.68585	+	23.6637i	−0.199600	+	1.28146i
$342$	0.381373			0.0206223
$343$	−5.48872	+	16.8925i	−0.296363	+	0.912111i
$344$	0.406049	−	0.295012i	0.0218927	−	0.0159060i
$345$	13.0483	+	9.48018i	0.702499	+	0.510396i
$346$	−0.188131	−	0.579009i	−0.0101140	−	0.0311277i
$347$	1.80421	+	5.55279i	0.0968551	+	0.298089i	0.987733	−	0.156154i	$-0.0499096\pi$
$347$	1.80421	+	5.55279i	0.0968551	+	0.298089i	−0.890878	+	0.454243i	$0.849910\pi$
$348$	−6.33167	−	4.60023i	−0.339413	−	0.246598i
$349$	4.95487	−	3.59992i	0.265228	−	0.192700i	−0.447221	−	0.894424i	$-0.647586\pi$
$349$	4.95487	−	3.59992i	0.265228	−	0.192700i	0.712449	+	0.701724i	$0.247586\pi$
$350$	0.362257	−	1.11491i	0.0193635	−	0.0595946i
$351$	−1.00000			−0.0533761
$352$	3.52903	−	0.568214i	0.188098	−	0.0302859i
$353$	7.19595			0.383002			0.191501	−	0.981492i	$-0.438664\pi$
$353$	7.19595			0.383002			0.191501	+	0.981492i	$0.438664\pi$
$354$	−0.0977092	+	0.300718i	−0.00519319	+	0.0159830i
$355$	16.8537	−	12.2449i	0.894501	−	0.649893i
$356$	−27.7180	−	20.1383i	−1.46905	−	1.06733i
$357$	−0.458894	−	1.41233i	−0.0242872	−	0.0747484i
$358$	0.364548	+	1.12196i	0.0192670	+	0.0592976i
$359$	2.41295	+	1.75311i	0.127351	+	0.0925256i	0.649637	−	0.760244i	$-0.274921\pi$
$359$	2.41295	+	1.75311i	0.127351	+	0.0925256i	−0.522287	+	0.852770i	$0.674921\pi$
$360$	0.909790	−	0.661001i	0.0479501	−	0.0348378i
$361$	−0.359679	+	1.10698i	−0.0189305	+	0.0582620i
$362$	1.70719			0.0897280
$363$	6.41996	−	8.93219i	0.336961	−	0.468819i
$364$	−5.46402			−0.286392
$365$	9.67105	−	29.7644i	0.506206	−	1.55794i
$366$	−0.868559	+	0.631045i	−0.0454003	+	0.0329853i
$367$	−9.16961	−	6.66211i	−0.478650	−	0.347759i	0.322153	−	0.946688i	$-0.395593\pi$
$367$	−9.16961	−	6.66211i	−0.478650	−	0.347759i	−0.800803	+	0.598928i	$0.795593\pi$
$368$	6.31239	+	19.4275i	0.329056	+	1.01273i
$369$	−1.01156	−	3.11325i	−0.0526596	−	0.162070i
$370$	−1.99739	−	1.45119i	−0.103839	−	0.0754436i
$371$	−20.9560	+	15.2255i	−1.08798	+	0.790467i
$372$	−4.44456	+	13.6790i	−0.230440	+	0.709221i
$373$	−5.88048			−0.304480			−0.152240	−	0.988344i	$-0.548649\pi$
$373$	−5.88048			−0.304480			−0.152240	+	0.988344i	$0.548649\pi$
$374$	0.160071	−	0.0257732i	0.00827708	−	0.00133270i
$375$	0.834965			0.0431174
$376$	0.299543	−	0.921899i	0.0154478	−	0.0475433i
$377$	−3.17880	+	2.30953i	−0.163716	+	0.118947i
$378$	0.200408	+	0.145605i	0.0103079	+	0.00748911i
$379$	5.26434	+	16.2020i	0.270411	+	0.832239i	0.990397	+	0.138251i	$0.0441481\pi$
$379$	5.26434	+	16.2020i	0.270411	+	0.832239i	−0.719986	+	0.693988i	$0.755852\pi$
$380$	−8.10954	−	24.9586i	−0.416011	−	1.28035i
$381$	−11.3762	−	8.26526i	−0.582818	−	0.423442i
$382$	0.675888	−	0.491061i	0.0345814	−	0.0251249i
$383$	7.15524	−	22.0216i	0.365616	−	1.12525i	−0.583979	−	0.811769i	$-0.698505\pi$
$383$	7.15524	−	22.0216i	0.365616	−	1.12525i	0.949595	−	0.313480i	$-0.101495\pi$
$384$	2.86030			0.145964
$385$	4.36830	−	28.0451i	0.222629	−	1.42931i
$386$	1.96165			0.0998454
$387$	0.430258	−	1.32420i	0.0218712	−	0.0673128i
$388$	23.6717	−	17.1985i	1.20175	−	0.873121i
$389$	2.00407	+	1.45604i	0.101610	+	0.0738243i	0.637430	−	0.770508i	$-0.279997\pi$
$389$	2.00407	+	1.45604i	0.101610	+	0.0738243i	−0.535820	+	0.844332i	$0.679997\pi$
$390$	−0.0870547	−	0.267927i	−0.00440819	−	0.0135670i
$391$	0.864857	+	2.66176i	0.0437377	+	0.134611i
$392$	0.153140	+	0.111263i	0.00773476	+	0.00561963i
$393$	9.66280	−	7.02043i	0.487424	−	0.354134i
$394$	−0.196071	+	0.603445i	−0.00987793	+	0.0304011i
$395$	4.33281			0.218007
$396$	4.65931	−	4.68324i	0.234139	−	0.235342i
$397$	11.9289			0.598695			0.299347	−	0.954144i	$-0.403231\pi$
$397$	11.9289			0.598695			0.299347	+	0.954144i	$0.403231\pi$
$398$	−0.263411	+	0.810695i	−0.0132036	+	0.0406365i
$399$	9.37268	−	6.80965i	0.469221	−	0.340909i
$400$	−15.1272	−	10.9905i	−0.756358	−	0.549526i
$401$	−1.04960	−	3.23033i	−0.0524144	−	0.161315i	0.921423	−	0.388561i	$-0.127028\pi$
$401$	−1.04960	−	3.23033i	−0.0524144	−	0.161315i	−0.973837	+	0.227246i	$0.927028\pi$
$402$	−0.113962	−	0.350737i	−0.00568388	−	0.0174932i
$403$	5.84183	+	4.24434i	0.291002	+	0.211425i
$404$	−17.4250	+	12.6600i	−0.866926	+	0.629859i
$405$	0.964032	−	2.96698i	0.0479031	−	0.147431i
$406$	0.973335			0.0483058
$407$	−25.9321	−	13.1295i	−1.28540	−	0.650804i
$408$	0.195141			0.00966090
$409$	−12.0901	+	37.2095i	−0.597816	+	1.83989i	−0.0576413	+	0.998337i	$0.518358\pi$
$409$	−12.0901	+	37.2095i	−0.597816	+	1.83989i	−0.540175	+	0.841553i	$0.681642\pi$
$410$	0.746064	−	0.542047i	0.0368455	−	0.0267698i
$411$	4.38407	+	3.18521i	0.216250	+	0.157115i
$412$	0.874140	+	2.69033i	0.0430658	+	0.132543i
$413$	2.96819	+	9.13514i	0.146055	+	0.449511i
$414$	−0.377700	−	0.274415i	−0.0185630	−	0.0134868i
$415$	−40.2579	+	29.2491i	−1.97618	+	1.43578i
$416$	0.333042	−	1.02500i	0.0163287	−	0.0502547i
$417$	15.1673			0.742746
$418$	0.577125	+	1.12553i	0.0282281	+	0.0550517i
$419$	25.8021			1.26052			0.630258	−	0.776386i	$-0.282949\pi$
$419$	25.8021			1.26052			0.630258	+	0.776386i	$0.282949\pi$
$420$	5.26749	−	16.2117i	0.257027	−	0.791048i
$421$	−28.5110	+	20.7144i	−1.38954	+	1.00956i	−0.393623	+	0.919272i	$0.628778\pi$
$421$	−28.5110	+	20.7144i	−1.38954	+	1.00956i	−0.995916	+	0.0902870i	$0.971222\pi$
$422$	0.294988	+	0.214322i	0.0143598	+	0.0104330i
$423$	−0.830969	−	2.55746i	−0.0404031	−	0.124348i
$424$	−1.05185	−	3.23725i	−0.0510821	−	0.157215i
$425$	−2.07256	−	1.50581i	−0.100534	−	0.0730423i
$426$	−0.487851	+	0.354444i	−0.0236365	+	0.0171729i
$427$	−10.0781	+	31.0173i	−0.487715	+	1.50103i
$428$	19.0168			0.919210
$429$	−1.51328	−	2.95127i	−0.0730619	−	0.142489i
$430$	0.392244			0.0189157
$431$	−0.580383	+	1.78624i	−0.0279561	+	0.0860399i	−0.964061	−	0.265681i	$-0.914403\pi$
$431$	−0.580383	+	1.78624i	−0.0279561	+	0.0860399i	0.936105	+	0.351721i	$0.114403\pi$
$432$	3.19654	−	2.32242i	0.153794	−	0.111738i
$433$	26.3963	+	19.1781i	1.26853	+	0.921639i	0.999143	−	0.0413940i	$-0.0131799\pi$
$433$	26.3963	+	19.1781i	1.26853	+	0.921639i	0.269384	+	0.963033i	$0.413180\pi$
$434$	−0.552753	−	1.70120i	−0.0265330	−	0.0816602i
$435$	−3.78788	−	11.6579i	−0.181615	−	0.558953i
$436$	−31.6156	−	22.9701i	−1.51411	−	1.10007i
$437$	−17.6643	+	12.8339i	−0.844997	+	0.613926i
$438$	−0.279940	+	0.861568i	−0.0133761	+	0.0411673i
$439$	−24.2522			−1.15750			−0.578748	−	0.815507i	$-0.696458\pi$
$439$	−24.2522			−1.15750			−0.578748	+	0.815507i	$0.696458\pi$
$440$	3.32756	+	1.68475i	0.158635	+	0.0803175i
$441$	0.525119			0.0250057
$442$	0.0151062	−	0.0464922i	0.000718531	−	0.00221141i
$443$	4.37795	−	3.18076i	0.208002	−	0.151123i	−0.478907	−	0.877866i	$-0.658967\pi$
$443$	4.37795	−	3.18076i	0.208002	−	0.151123i	0.686909	+	0.726743i	$0.258967\pi$
$444$	−14.1224	−	10.2605i	−0.670219	−	0.486942i
$445$	−16.5821	−	51.0346i	−0.786069	−	2.41927i
$446$	0.0496198	+	0.152714i	0.00234957	+	0.00723122i
$447$	10.1705	+	7.38932i	0.481050	+	0.349503i
$448$	17.3215	−	12.5848i	0.818362	−	0.594575i
$449$	6.65619	−	20.4856i	0.314125	−	0.966777i	−0.661988	−	0.749514i	$-0.730287\pi$
$449$	6.65619	−	20.4856i	0.314125	−	0.966777i	0.976113	−	0.217263i	$-0.0697129\pi$
$450$	0.427345			0.0201452
$451$	7.65728	−	7.69661i	0.360567	−	0.362419i
$452$	9.37447			0.440938
$453$	−1.55065	+	4.77242i	−0.0728561	+	0.224228i
$454$	−0.226553	+	0.164600i	−0.0106327	+	0.00772507i
$455$	−6.92346	−	5.03019i	−0.324577	−	0.235819i
$456$	0.470442	+	1.44787i	0.0220305	+	0.0678028i
$457$	−11.3316	−	34.8751i	−0.530070	−	1.63139i	−0.754067	−	0.656798i	$-0.771911\pi$
$457$	−11.3316	−	34.8751i	−0.530070	−	1.63139i	0.223997	−	0.974590i	$-0.428089\pi$
$458$	−1.15243	−	0.837292i	−0.0538497	−	0.0391241i
$459$	0.437956	−	0.318194i	0.0204421	−	0.0148520i
$460$	−9.92741	+	30.5534i	−0.462868	+	1.42456i
$461$	−32.4998			−1.51367			−0.756834	−	0.653607i	$-0.773255\pi$
$461$	−32.4998			−1.51367			−0.756834	+	0.653607i	$0.773255\pi$
$462$	−0.126446	+	0.811799i	−0.00588279	+	0.0377683i
$463$	−9.71565			−0.451525			−0.225762	−	0.974182i	$-0.572487\pi$
$463$	−9.71565			−0.451525			−0.225762	+	0.974182i	$0.572487\pi$
$464$	4.79744	−	14.7650i	0.222716	−	0.685448i
$465$	−18.2246	+	13.2409i	−0.845145	+	0.614034i
$466$	0.184088	+	0.133748i	0.00852771	+	0.00619575i
$467$	9.62994	+	29.6379i	0.445621	+	1.37148i	0.881802	+	0.471620i	$0.156331\pi$
$467$	9.62994	+	29.6379i	0.445621	+	1.37148i	−0.436181	+	0.899859i	$0.643669\pi$
$468$	−0.615514	−	1.89436i	−0.0284521	−	0.0875667i
$469$	−9.06336	−	6.58492i	−0.418507	−	0.304063i
$470$	0.612872	−	0.445278i	0.0282697	−	0.0205391i
$471$	−5.60204	+	17.2413i	−0.258129	+	0.794438i
$472$	−1.26220			−0.0580973
$473$	4.55916	−	0.734076i	0.209631	−	0.0337529i
$474$	−0.125419			−0.00576067
$475$	6.17602	−	19.0079i	0.283375	−	0.872140i
$476$	2.39300	−	1.73862i	0.109683	−	0.0796894i
$477$	−7.63929	−	5.55027i	−0.349779	−	0.254129i
$478$	−0.831055	−	2.55772i	−0.0380116	−	0.116988i
$479$	−3.91829	−	12.0592i	−0.179031	−	0.551001i	0.820763	−	0.571268i	$-0.193548\pi$
$479$	−3.91829	−	12.0592i	−0.179031	−	0.551001i	−0.999795	+	0.0202670i	$0.993548\pi$
$480$	2.72009	+	1.97626i	0.124155	+	0.0902037i
$481$	−7.09010	+	5.15126i	−0.323281	+	0.234877i
$482$	0.235280	−	0.724118i	0.0107167	−	0.0329827i
$483$	−14.1823			−0.645315
$484$	20.8723	+	6.66382i	0.948743	+	0.302901i
$485$	45.8274			2.08091
$486$	−0.0279051	+	0.0858830i	−0.00126580	+	0.00389573i
$487$	3.58680	−	2.60596i	0.162533	−	0.118087i	−0.503546	−	0.863969i	$-0.667971\pi$
$487$	3.58680	−	2.60596i	0.162533	−	0.118087i	0.666079	+	0.745881i	$0.267971\pi$
$488$	−3.46715	−	2.51903i	−0.156951	−	0.114031i
$489$	−0.478711	−	1.47332i	−0.0216481	−	0.0666259i
$490$	0.0457141	+	0.140693i	0.00206515	+	0.00635588i
$491$	10.9139	+	7.92945i	0.492540	+	0.357851i	0.806160	−	0.591697i	$-0.201542\pi$
$491$	10.9139	+	7.92945i	0.492540	+	0.357851i	−0.313621	+	0.949548i	$0.601542\pi$
$492$	5.27499	−	3.83250i	0.237815	−	0.172783i
$493$	0.657295	−	2.02295i	0.0296031	−	0.0911089i
$494$	0.381373			0.0171588
$495$	10.2152	−	1.64476i	0.459140	−	0.0739266i
$496$	−28.5308			−1.28107
$497$	−5.66067	+	17.4217i	−0.253916	+	0.781472i
$498$	1.16532	−	0.846651i	0.0522190	−	0.0379393i
$499$	21.6245	+	15.7111i	0.968047	+	0.703328i	0.955006	−	0.296587i	$-0.0958486\pi$
$499$	21.6245	+	15.7111i	0.968047	+	0.703328i	0.0130417	+	0.999915i	$0.495849\pi$
$500$	0.513933	+	1.58172i	0.0229838	+	0.0707368i
$501$	5.57577	+	17.1605i	0.249107	+	0.766673i
$502$	−1.54746	−	1.12430i	−0.0690667	−	0.0501799i
$503$	−12.0367	+	8.74515i	−0.536688	+	0.389927i	−0.822854	−	0.568253i	$-0.807619\pi$
$503$	−12.0367	+	8.74515i	−0.536688	+	0.389927i	0.286165	+	0.958180i	$0.407619\pi$
$504$	−0.305572	+	0.940454i	−0.0136113	+	0.0418912i
$505$	−33.7341			−1.50115
$506$	0.238307	−	1.52996i	0.0105940	−	0.0680151i
$507$	−1.00000			−0.0444116
$508$	8.65517	−	26.6379i	0.384011	−	1.18186i
$509$	26.6694	−	19.3765i	1.18210	−	0.858847i	0.189694	−	0.981843i	$-0.439250\pi$
$509$	26.6694	−	19.3765i	1.18210	−	0.858847i	0.992407	+	0.122997i	$0.0392505\pi$
$510$	0.123379	+	0.0896400i	0.00546331	+	0.00396932i
$511$	8.50396	+	26.1725i	0.376193	+	1.15780i
$512$	2.19615	+	6.75906i	0.0970572	+	0.298711i
$513$	3.41670	+	2.48238i	0.150851	+	0.109600i
$514$	−1.89250	+	1.37498i	−0.0834748	+	0.0606480i
$515$	−1.36910	+	4.21365i	−0.0603297	+	0.185676i
$516$	2.77333			0.122089
$517$	6.29026	−	6.32256i	0.276645	−	0.278066i
$518$	2.17096			0.0953866
$519$	2.08334	−	6.41186i	0.0914485	−	0.281450i
$520$	0.909790	−	0.661001i	0.0398969	−	0.0289868i
$521$	−21.9390	−	15.9396i	−0.961164	−	0.698327i	−0.00774348	−	0.999970i	$-0.502465\pi$
$521$	−21.9390	−	15.9396i	−0.961164	−	0.698327i	−0.953421	+	0.301643i	$0.902465\pi$
$522$	0.109645	+	0.337452i	0.00479902	+	0.0147699i
$523$	4.95798	+	15.2591i	0.216797	+	0.667234i	0.999021	+	0.0442363i	$0.0140854\pi$
$523$	4.95798	+	15.2591i	0.216797	+	0.667234i	−0.782224	+	0.622998i	$0.785915\pi$
$524$	19.2468	+	13.9836i	0.840800	+	0.610877i
$525$	10.5025	−	7.63049i	0.458366	−	0.333022i
$526$	−0.316272	+	0.973386i	−0.0137901	+	0.0424416i
$527$	−3.90899			−0.170278
$528$	11.6913	+	5.91937i	0.508801	+	0.257607i
$529$	3.72870			0.162117
$530$	0.822029	−	2.52995i	0.0357067	−	0.109894i
$531$	−2.83276	+	2.05812i	−0.122931	+	0.0893149i
$532$	18.6689	+	13.5638i	0.809401	+	0.588064i
$533$	−1.01156	−	3.11325i	−0.0438154	−	0.134850i
$534$	0.479990	+	1.47726i	0.0207712	+	0.0639272i
$535$	24.0962	+	17.5069i	1.04177	+	0.756888i
$536$	1.19099	−	0.865303i	0.0514428	−	0.0373754i
$537$	−4.03696	+	12.4245i	−0.174208	+	0.536156i
$538$	1.99394			0.0859648
$539$	0.794652	+	1.54977i	0.0342281	+	0.0667532i
$540$	6.21390			0.267404
$541$	−0.347650	+	1.06996i	−0.0149466	+	0.0460011i	−0.958252	−	0.285926i	$-0.907699\pi$
$541$	−0.347650	+	1.06996i	−0.0149466	+	0.0460011i	0.943305	+	0.331927i	$0.107699\pi$
$542$	−0.00482746	+	0.00350735i	−0.000207357	+	0.000150654i
$543$	15.2946	+	11.1122i	0.656356	+	0.476870i
$544$	0.180290	+	0.554877i	0.00772989	+	0.0237902i
$545$	−18.9138	−	58.2107i	−0.810179	−	2.49347i
$546$	0.200408	+	0.145605i	0.00857667	+	0.00623132i
$547$	−35.9393	+	26.1114i	−1.53665	+	1.11644i	−0.584259	+	0.811567i	$0.698615\pi$
$547$	−35.9393	+	26.1114i	−1.53665	+	1.11644i	−0.952392	+	0.304876i	$0.901385\pi$
$548$	−3.33547	+	10.2655i	−0.142484	+	0.438522i
$549$	−11.8889			−0.507405
$550$	0.646692	+	1.26121i	0.0275750	+	0.0537781i
$551$	16.5941			0.706933
$552$	0.575898	−	1.77243i	0.0245119	−	0.0754398i
$553$	−3.08230	+	2.23942i	−0.131073	+	0.0952300i
$554$	−1.08460	−	0.788006i	−0.0460801	−	0.0334792i
$555$	−8.44863	−	26.0022i	−0.358624	−	1.10373i
$556$	9.33569	+	28.7323i	0.395921	+	1.21852i
$557$	−16.8811	−	12.2648i	−0.715276	−	0.519678i	0.169596	−	0.985514i	$-0.445754\pi$
$557$	−16.8811	−	12.2648i	−0.715276	−	0.519678i	−0.884871	+	0.465836i	$0.845754\pi$
$558$	0.527533	−	0.383275i	0.0223323	−	0.0162253i
$559$	0.430258	−	1.32420i	0.0181980	−	0.0560076i
$560$	33.8133			1.42887
$561$	1.60183	+	0.811010i	0.0676292	+	0.0342409i
$562$	2.52407			0.106471
$563$	−2.53254	+	7.79436i	−0.106734	+	0.328493i	−0.990133	−	0.140127i	$-0.955249\pi$
$563$	−2.53254	+	7.79436i	−0.106734	+	0.328493i	0.883400	+	0.468620i	$0.155249\pi$
$564$	4.33327	−	3.14830i	0.182464	−	0.132567i
$565$	11.8784	+	8.63016i	0.499728	+	0.363074i
$566$	−0.622489	−	1.91582i	−0.0261652	−	0.0805281i
$567$	0.847694	+	2.60893i	0.0355998	+	0.109565i
$568$	−1.94743	−	1.41489i	−0.0817121	−	0.0593674i
$569$	−7.34828	+	5.33884i	−0.308056	+	0.223816i	−0.731062	−	0.682311i	$-0.760975\pi$
$569$	−7.34828	+	5.33884i	−0.308056	+	0.223816i	0.423006	+	0.906127i	$0.360975\pi$
$570$	−0.367656	+	1.13153i	−0.0153994	+	0.0473945i
$571$	−31.2375			−1.30725			−0.653624	−	0.756820i	$-0.726752\pi$
$571$	−31.2375			−1.30725			−0.653624	+	0.756820i	$0.726752\pi$
$572$	4.65931	−	4.68324i	0.194816	−	0.195816i
$573$	9.25158			0.386490
$574$	−0.250581	+	0.771209i	−0.0104591	+	0.0321897i
$575$	−19.7936	+	14.3809i	−0.825448	+	0.599723i
$576$	6.31434	+	4.58764i	0.263098	+	0.191152i
$577$	6.44252	+	19.8280i	0.268206	+	0.825452i	0.990937	+	0.134324i	$0.0428862\pi$
$577$	6.44252	+	19.8280i	0.268206	+	0.825452i	−0.722732	+	0.691129i	$0.757114\pi$
$578$	−0.466209	−	1.43484i	−0.0193917	−	0.0596816i
$579$	17.5743	+	12.7685i	0.730364	+	0.530640i
$580$	19.7527	−	14.3512i	0.820188	−	0.595901i
$581$	13.5215	−	41.6148i	0.560965	−	1.72647i
$582$	−1.32653			−0.0549864
$583$	4.81994	−	30.9447i	0.199621	−	1.28160i
$584$	−3.61624			−0.149641
$585$	0.964032	−	2.96698i	0.0398578	−	0.122670i
$586$	−0.759767	+	0.552003i	−0.0313857	+	0.0228030i
$587$	−16.4994	−	11.9875i	−0.681003	−	0.494778i	0.192687	−	0.981260i	$-0.438280\pi$
$587$	−16.4994	−	11.9875i	−0.681003	−	0.494778i	−0.873690	+	0.486483i	$0.838280\pi$
$588$	0.323218	+	0.994763i	0.0133293	+	0.0410233i
$589$	−9.42373	−	29.0033i	−0.388298	−	1.19506i
$590$	−0.798031	−	0.579804i	−0.0328544	−	0.0238701i
$591$	−5.68445	+	4.12999i	−0.233827	+	0.169885i
$592$	10.7004	−	32.9324i	0.439783	−	1.35351i
$593$	47.1384			1.93574			0.967872	−	0.251444i	$-0.0809053\pi$
$593$	47.1384			1.93574			0.967872	+	0.251444i	$0.0809053\pi$
$594$	−0.295692	+	0.0476097i	−0.0121324	+	0.00195345i
$595$	4.63275			0.189924
$596$	−7.73791	+	23.8149i	−0.316957	+	0.975494i
$597$	−7.63674	+	5.54841i	−0.312551	+	0.227081i
$598$	−0.377700	−	0.274415i	−0.0154453	−	0.0112217i
$599$	−0.502091	−	1.54528i	−0.0205149	−	0.0631384i	0.940275	−	0.340416i	$-0.110568\pi$
$599$	−0.502091	−	1.54528i	−0.0205149	−	0.0631384i	−0.960790	+	0.277278i	$0.910568\pi$
$600$	0.527150	+	1.62240i	0.0215208	+	0.0662342i
$601$	−7.49525	−	5.44562i	−0.305738	−	0.222131i	0.424328	−	0.905509i	$-0.360510\pi$
$601$	−7.49525	−	5.44562i	−0.305738	−	0.222131i	−0.730065	+	0.683377i	$0.760510\pi$
$602$	−0.279037	+	0.202732i	−0.0113727	+	0.00826275i
$603$	1.26199	−	3.88402i	0.0513924	−	0.158169i
$604$	−9.99513			−0.406696
$605$	20.3126	+	27.6589i	0.825826	+	1.12449i
$606$	0.976473			0.0396665
$607$	−14.4389	+	44.4382i	−0.586055	+	1.80369i	0.00893700	+	0.999960i	$0.497155\pi$
$607$	−14.4389	+	44.4382i	−0.586055	+	1.80369i	−0.594992	+	0.803732i	$0.702845\pi$
$608$	−3.68234	+	2.67538i	−0.149339	+	0.108501i
$609$	8.72006	+	6.33549i	0.353355	+	0.256727i
$610$	−1.03498	−	3.18535i	−0.0419052	−	0.128971i
$611$	−0.830969	−	2.55746i	−0.0336174	−	0.103464i
$612$	0.872341	+	0.633793i	0.0352623	+	0.0256196i
$613$	20.9581	−	15.2270i	0.846490	−	0.615011i	−0.0776861	−	0.996978i	$-0.524753\pi$
$613$	20.9581	−	15.2270i	0.846490	−	0.615011i	0.924176	+	0.381967i	$0.124753\pi$
$614$	0.421741	−	1.29799i	0.0170201	−	0.0523825i
$615$	10.2122			0.411794
$616$	−3.23795	+	0.521346i	−0.130461	+	0.0210056i
$617$	8.08502			0.325491			0.162745	−	0.986668i	$-0.447965\pi$
$617$	8.08502			0.325491			0.162745	+	0.986668i	$0.447965\pi$
$618$	0.0396302	−	0.121969i	0.00159416	−	0.00490632i
$619$	5.60692	−	4.07367i	0.225361	−	0.163735i	−0.469375	−	0.882999i	$-0.655521\pi$
$619$	5.60692	−	4.07367i	0.225361	−	0.163735i	0.694737	+	0.719264i	$0.255521\pi$
$620$	−36.3006	−	26.3739i	−1.45787	−	1.05920i
$621$	−1.59761	−	4.91694i	−0.0641100	−	0.197310i
$622$	0.797298	+	2.45383i	0.0319687	+	0.0983896i
$623$	38.1736	+	27.7348i	1.52939	+	1.11117i
$624$	3.19654	−	2.32242i	0.127964	−	0.0929713i
$625$	−8.11682	+	24.9810i	−0.324673	+	0.999241i
$626$	1.09143			0.0436224
$627$	−2.15574	+	13.8401i	−0.0860919	+	0.552722i
$628$	−36.1094			−1.44092
$629$	1.46606	−	4.51205i	0.0584555	−	0.179907i
$630$	−0.625208	+	0.454240i	−0.0249089	+	0.0180973i
$631$	17.6122	+	12.7960i	0.701131	+	0.509401i	0.880300	−	0.474417i	$-0.157341\pi$
$631$	17.6122	+	12.7960i	0.701131	+	0.509401i	−0.179169	+	0.983818i	$0.557341\pi$
$632$	−0.154710	−	0.476148i	−0.00615403	−	0.0189401i
$633$	1.24775	+	3.84019i	0.0495937	+	0.152634i
$634$	0.680773	+	0.494611i	0.0270370	+	0.0196435i
$635$	35.4899	−	25.7849i	1.40837	−	1.02324i
$636$	5.81210	−	17.8878i	0.230465	−	0.709298i
$637$	0.525119			0.0208060
$638$	−0.829988	+	0.834251i	−0.0328595	+	0.0330283i
$639$	−6.67773			−0.264167
$640$	−2.75742	+	8.48648i	−0.108997	+	0.335458i
$641$	−3.13720	+	2.27931i	−0.123912	+	0.0900273i	−0.648015	−	0.761628i	$-0.724401\pi$
$641$	−3.13720	+	2.27931i	−0.123912	+	0.0900273i	0.524103	+	0.851655i	$0.324401\pi$
$642$	−0.697493	−	0.506758i	−0.0275278	−	0.0200001i
$643$	−12.5291	−	38.5605i	−0.494099	−	1.52068i	−0.818357	−	0.574711i	$-0.805115\pi$
$643$	−12.5291	−	38.5605i	−0.494099	−	1.52068i	0.324258	−	0.945969i	$-0.394885\pi$
$644$	−8.72938	−	26.8663i	−0.343986	−	1.05868i
$645$	3.51409	+	2.55314i	0.138367	+	0.100530i
$646$	−0.167025	+	0.121351i	−0.00657151	+	0.00477448i
$647$	−10.0303	+	30.8702i	−0.394333	+	1.21363i	0.535147	+	0.844759i	$0.320256\pi$
$647$	−10.0303	+	30.8702i	−0.394333	+	1.21363i	−0.929480	+	0.368873i	$0.879744\pi$
$648$	−0.360475			−0.0141608
$649$	−10.3608	−	5.24572i	−0.406698	−	0.205913i
$650$	0.427345			0.0167618
$651$	6.12111	−	18.8388i	0.239905	−	0.738352i
$652$	2.49634	−	1.81370i	0.0977644	−	0.0710300i
$653$	28.2535	+	20.5274i	1.10565	+	0.803298i	0.981972	−	0.189025i	$-0.0605327\pi$
$653$	28.2535	+	20.5274i	1.10565	+	0.803298i	0.123673	+	0.992323i	$0.460533\pi$
$654$	0.547484	+	1.68498i	0.0214083	+	0.0658880i
$655$	11.5143	+	35.4373i	0.449900	+	1.38465i
$656$	10.4638	+	7.60238i	0.408542	+	0.296823i
$657$	−8.11596	+	5.89659i	−0.316634	+	0.230048i
$658$	−0.205846	+	0.633529i	−0.00802471	+	0.0246975i
$659$	22.1005			0.860915			0.430457	−	0.902611i	$-0.358352\pi$
$659$	22.1005			0.860915			0.430457	+	0.902611i	$0.358352\pi$
$660$	9.40338	+	18.3389i	0.366026	+	0.713841i
$661$	−8.25578			−0.321113			−0.160556	−	0.987027i	$-0.551329\pi$
$661$	−8.25578			−0.321113			−0.160556	+	0.987027i	$0.551329\pi$
$662$	0.0145748	−	0.0448567i	0.000566466	−	0.00174340i
$663$	0.437956	−	0.318194i	0.0170088	−	0.0123576i
$664$	4.65176	+	3.37970i	0.180523	+	0.131158i
$665$	11.1686	+	34.3733i	0.433098	+	1.33294i
$666$	0.244556	+	0.752666i	0.00947635	+	0.0291652i
$667$	−16.4343	−	11.9402i	−0.636339	−	0.462327i
$668$	−29.0761	+	21.1250i	−1.12499	+	0.817352i
$669$	−0.549483	+	1.69113i	−0.0212442	+	0.0653831i
$670$	1.15050			0.0444475
$671$	−17.9912	−	35.0873i	−0.694543	−	1.35453i
$672$	−2.95647			−0.114048
$673$	14.8144	−	45.5939i	0.571052	−	1.75752i	−0.0781931	−	0.996938i	$-0.524915\pi$
$673$	14.8144	−	45.5939i	0.571052	−	1.75752i	0.649245	−	0.760579i	$-0.275085\pi$
$674$	−1.04525	+	0.759416i	−0.0402614	+	0.0292516i
$675$	3.82856	+	2.78161i	0.147361	+	0.107064i
$676$	−0.615514	−	1.89436i	−0.0236736	−	0.0728599i
$677$	6.28872	+	19.3547i	0.241695	+	0.743862i	0.996162	+	0.0875238i	$0.0278954\pi$
$677$	6.28872	+	19.3547i	0.241695	+	0.743862i	−0.754467	+	0.656338i	$0.772105\pi$
$678$	−0.343835	−	0.249811i	−0.0132049	−	0.00959392i
$679$	−32.6010	+	23.6860i	−1.25111	+	0.908985i
$680$	−0.188122	+	0.578979i	−0.00721414	+	0.0222028i
$681$	−3.10107			−0.118833
$682$	1.92945	+	0.976889i	0.0738826	+	0.0374070i
$683$	−9.86547			−0.377492			−0.188746	−	0.982026i	$-0.560442\pi$
$683$	−9.86547			−0.377492			−0.188746	+	0.982026i	$0.560442\pi$
$684$	−2.59949	+	8.00039i	−0.0993938	+	0.305903i
$685$	−13.6768	+	9.93681i	−0.522565	+	0.379666i
$686$	1.29762	+	0.942775i	0.0495433	+	0.0359953i
$687$	−4.87461	−	15.0025i	−0.185978	−	0.572381i
$688$	1.70001	+	5.23209i	0.0648122	+	0.199472i
$689$	−7.63929	−	5.55027i	−0.291034	−	0.211448i
$690$	1.17830	−	0.856086i	0.0448572	−	0.0325906i
$691$	−1.23199	+	3.79167i	−0.0468671	+	0.144242i	−0.971752	−	0.236006i	$-0.924161\pi$
$691$	−1.23199	+	3.79167i	−0.0468671	+	0.144242i	0.924884	+	0.380248i	$0.124161\pi$
$692$	13.4287			0.510482
$693$	−6.41686	+	6.44982i	−0.243756	+	0.245008i
$694$	0.527237			0.0200136
$695$	−14.6218	+	45.0012i	−0.554635	+	1.70699i
$696$	−1.14587	+	0.832527i	−0.0434343	+	0.0315568i
$697$	1.43364	+	1.04160i	0.0543029	+	0.0394533i
$698$	−0.170906	−	0.525995i	−0.00646890	−	0.0199092i
$699$	0.778663	+	2.39648i	0.0294517	+	0.0906431i
$700$	20.9193	+	15.1988i	0.790675	+	0.574459i
$701$	33.3771	−	24.2499i	1.26064	−	0.915905i	0.261846	−	0.965110i	$-0.415669\pi$
$701$	33.3771	−	24.2499i	1.26064	−	0.915905i	0.998789	+	0.0492045i	$0.0156686\pi$
$702$	−0.0279051	+	0.0858830i	−0.00105321	+	0.00324145i
$703$	37.0121			1.39594
$704$	−3.98398	+	25.5777i	−0.150152	+	0.963996i
$705$	8.38902			0.315949
$706$	0.200804	−	0.618010i	0.00755734	−	0.0232591i
$707$	23.9979	−	17.4355i	0.902535	−	0.655730i
$708$	−5.64242	−	4.09946i	−0.212055	−	0.154067i
$709$	−14.7811	−	45.4915i	−0.555115	−	1.70847i	−0.695639	−	0.718392i	$-0.744879\pi$
$709$	−14.7811	−	45.4915i	−0.555115	−	1.70847i	0.140524	−	0.990077i	$-0.455121\pi$
$710$	−0.581327	−	1.78914i	−0.0218168	−	0.0671453i
$711$	−1.12362	−	0.816356i	−0.0421390	−	0.0306157i
$712$	−5.01628	+	3.64454i	−0.187993	+	0.136585i
$713$	−11.5362	+	35.5047i	−0.432034	+	1.32966i
$714$	−0.134101			−0.00501859
$715$	10.2152	−	1.64476i	0.382027	−	0.0615107i
$716$	−26.0212			−0.972458
$717$	9.20299	−	28.3239i	0.343692	−	1.05777i
$718$	0.217896	−	0.158311i	0.00813180	−	0.00590810i
$719$	39.6664	+	28.8193i	1.47931	+	1.07478i	0.977779	+	0.209638i	$0.0672285\pi$
$719$	39.6664	+	28.8193i	1.47931	+	1.07478i	0.501528	+	0.865141i	$0.332771\pi$
$720$	3.80902	+	11.7230i	0.141954	+	0.436889i
$721$	−1.20388	−	3.70515i	−0.0448347	−	0.137987i
$722$	0.0850338	+	0.0617807i	0.00316463	+	0.00229924i
$723$	6.82119	−	4.95588i	0.253683	−	0.184311i
$724$	−11.6364	+	35.8132i	−0.432464	+	1.33099i
$725$	18.5944			0.690579
$726$	−0.587974	−	0.800619i	−0.0218218	−	0.0297138i
$727$	−12.5887			−0.466888			−0.233444	−	0.972370i	$-0.575000\pi$
$727$	−12.5887			−0.466888			−0.233444	+	0.972370i	$0.575000\pi$
$728$	−0.305572	+	0.940454i	−0.0113253	+	0.0348555i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−2.28639	−	1.66116i	−0.0846230	−	0.0614822i
$731$	0.232918	+	0.716846i	0.00861477	+	0.0265135i
$732$	−7.31777	−	22.5218i	−0.270473	−	0.832429i
$733$	9.20909	+	6.69080i	0.340146	+	0.247130i	0.744723	−	0.667373i	$-0.232581\pi$
$733$	9.20909	+	6.69080i	0.340146	+	0.247130i	−0.404578	+	0.914504i	$0.632581\pi$
$734$	−0.828041	+	0.601607i	−0.0305635	+	0.0222057i
$735$	−0.506231	+	1.55802i	−0.0186726	+	0.0574684i
$736$	5.57193			0.205384
$737$	13.3725	−	2.15313i	0.492583	−	0.0793114i
$738$	−0.295603			−0.0108813
$739$	−1.36118	+	4.18929i	−0.0500720	+	0.154106i	−0.972966	−	0.230948i	$-0.925817\pi$
$739$	−1.36118	+	4.18929i	−0.0500720	+	0.154106i	0.922894	+	0.385054i	$0.125817\pi$
$740$	44.0572	−	32.0094i	1.61958	−	1.17669i
$741$	3.41670	+	2.48238i	0.125516	+	0.0911925i
$742$	0.722828	+	2.22464i	0.0265359	+	0.0816690i
$743$	−0.880995	−	2.71142i	−0.0323206	−	0.0994725i	0.933595	−	0.358330i	$-0.116654\pi$
$743$	−0.880995	−	2.71142i	−0.0323206	−	0.0994725i	−0.965915	+	0.258858i	$0.916654\pi$
$744$	2.10583	+	1.52998i	0.0772035	+	0.0560916i
$745$	−31.7287	+	23.0523i	−1.16245	+	0.844570i
$746$	−0.164095	+	0.505034i	−0.00600796	+	0.0184906i
$747$	15.9509			0.583612
$748$	−0.550396	+	3.53362i	−0.0201245	+	0.129202i
$749$	−26.1901			−0.956967
$750$	0.0232998	−	0.0717093i	0.000850787	−	0.00261845i
$751$	35.4532	−	25.7582i	1.29370	−	0.939931i	0.293831	−	0.955857i	$-0.405070\pi$
$751$	35.4532	−	25.7582i	1.29370	−	0.939931i	0.999873	+	0.0159263i	$0.00506971\pi$
$752$	8.59572	+	6.24516i	0.313454	+	0.227737i
$753$	−6.54553	−	20.1451i	−0.238532	−	0.734127i
$754$	0.109645	+	0.337452i	0.00399303	+	0.0122893i
$755$	−12.6648	−	9.20153i	−0.460920	−	0.334878i
$756$	−4.42049	+	3.21167i	−0.160771	+	0.116807i
$757$	3.81364	−	11.7372i	0.138609	−	0.426595i	−0.857525	−	0.514443i	$-0.827999\pi$
$757$	3.81364	−	11.7372i	0.138609	−	0.426595i	0.996134	+	0.0878474i	$0.0279988\pi$
$758$	1.53838			0.0558763
$759$	12.0936	−	12.1557i	0.438969	−	0.441224i
$760$	−4.74934			−0.172277
$761$	−8.14990	+	25.0828i	−0.295434	+	0.909251i	0.687642	+	0.726050i	$0.258646\pi$
$761$	−8.14990	+	25.0828i	−0.295434	+	0.909251i	−0.983075	+	0.183201i	$0.941354\pi$
$762$	−1.02730	+	0.746375i	−0.0372151	+	0.0270383i
$763$	43.5414	+	31.6347i	1.57630	+	1.14525i
$764$	5.69448	+	17.5258i	0.206019	+	0.634061i
$765$	0.521873	+	1.60616i	0.0188683	+	0.0580708i
$766$	−1.69161	−	1.22903i	−0.0611203	−	0.0444065i
$767$	−2.83276	+	2.05812i	−0.102285	+	0.0743145i
$768$	−4.74391	+	14.6003i	−0.171181	+	0.526841i
$769$	−32.7367			−1.18051			−0.590257	−	0.807215i	$-0.700974\pi$
$769$	−32.7367			−1.18051			−0.590257	+	0.807215i	$0.700974\pi$
$770$	−2.28670	−	1.15776i	−0.0824069	−	0.0417229i
$771$	−25.9047			−0.932935
$772$	−13.3708	+	41.1512i	−0.481227	+	1.48107i
$773$	−8.18005	+	5.94315i	−0.294216	+	0.213760i	−0.725094	−	0.688650i	$-0.758204\pi$
$773$	−8.18005	+	5.94315i	−0.294216	+	0.213760i	0.430878	+	0.902410i	$0.358204\pi$
$774$	−0.101720	−	0.0739037i	−0.00365624	−	0.00265641i
$775$	−10.5597	−	32.4994i	−0.379315	−	1.16741i
$776$	−1.63634	−	5.03613i	−0.0587411	−	0.180787i
$777$	19.4495	+	14.1309i	0.697748	+	0.506944i
$778$	0.180973	−	0.131485i	0.00648820	−	0.00471395i
$779$	−4.27209	+	13.1481i	−0.153063	+	0.471081i
$780$	6.21390			0.222493
$781$	−10.1053	−	19.7078i	−0.361595	−	0.705199i
$782$	0.252734			0.00903774
$783$	−1.21419	+	3.73690i	−0.0433917	+	0.133546i
$784$	−1.67856	+	1.21955i	−0.0599487	+	0.0435553i
$785$	−45.7542	−	33.2424i	−1.63304	−	1.18647i
$786$	−0.333295	−	1.02578i	−0.0118882	−	0.0365882i
$787$	1.21924	+	3.75245i	0.0434613	+	0.133760i	0.970433	−	0.241372i	$-0.0775973\pi$
$787$	1.21924	+	3.75245i	0.0434613	+	0.133760i	−0.926971	+	0.375132i	$0.877597\pi$
$788$	−11.3225	−	8.22631i	−0.403349	−	0.293050i
$789$	−9.16928	+	6.66188i	−0.326435	+	0.237169i
$790$	0.120907	−	0.372115i	0.00430170	−	0.0132393i
$791$	−12.9106			−0.459050
$792$	−0.545499	−	1.06386i	−0.0193835	−	0.0378025i
$793$	−11.8889			−0.422186
$794$	0.332877	−	1.02449i	0.0118134	−	0.0363578i
$795$	23.8321	−	17.3150i	0.845236	−	0.614100i
$796$	−15.2112	−	11.0516i	−0.539147	−	0.391713i
$797$	−1.70415	−	5.24483i	−0.0603640	−	0.185781i	0.916327	−	0.400430i	$-0.131139\pi$
$797$	−1.70415	−	5.24483i	−0.0603640	−	0.185781i	−0.976691	+	0.214649i	$0.931139\pi$
$798$	−0.323288	−	0.994978i	−0.0114443	−	0.0352218i
$799$	1.17770	+	0.855646i	0.0416639	+	0.0302706i
$800$	−4.12622	+	2.99787i	−0.145884	+	0.105991i
$801$	−5.31535	+	16.3590i	−0.187809	+	0.578015i
$802$	−0.306719			−0.0108306
$803$	−29.6841	−	15.0292i	−1.04753	−	0.530368i
$804$	8.13449			0.286882
$805$	13.6722	−	42.0786i	0.481880	−	1.48307i
$806$	0.527533	−	0.383275i	0.0185816	−	0.0135003i
$807$	17.8636	+	12.9786i	0.628828	+	0.456870i
$808$	1.20453	+	3.70715i	0.0423751	+	0.130417i
$809$	7.38898	+	22.7409i	0.259783	+	0.799529i	0.992850	+	0.119372i	$0.0380882\pi$
$809$	7.38898	+	22.7409i	0.259783	+	0.799529i	−0.733067	+	0.680157i	$0.761912\pi$
$810$	−0.227912	−	0.165588i	−0.00800802	−	0.00581817i
$811$	40.4921	−	29.4192i	1.42187	−	1.03305i	0.430409	−	0.902634i	$-0.358369\pi$
$811$	40.4921	−	29.4192i	1.42187	−	1.03305i	0.991460	−	0.130414i	$-0.0416307\pi$
$812$	−6.63437	+	20.4185i	−0.232821	+	0.716548i
$813$	−0.0660785			−0.00231747
$814$	−1.85124	+	1.86074i	−0.0648858	+	0.0652190i
$815$	4.83282			0.169286
$816$	−0.660964	+	2.03424i	−0.0231384	+	0.0712126i
$817$	−4.75722	+	3.45633i	−0.166434	+	0.120922i
$818$	2.85829	+	2.07667i	0.0999376	+	0.0726089i
$819$	0.847694	+	2.60893i	0.0296208	+	0.0911635i
$820$	6.28572	+	19.3455i	0.219507	+	0.675573i
$821$	39.4361	+	28.6520i	1.37633	+	0.999962i	0.997213	+	0.0746135i	$0.0237723\pi$
$821$	39.4361	+	28.6520i	1.37633	+	0.999962i	0.379117	+	0.925349i	$0.376228\pi$
$822$	0.395893	−	0.287633i	0.0138084	−	0.0100324i
$823$	4.23830	−	13.0441i	0.147738	−	0.454690i	−0.849615	−	0.527403i	$-0.823166\pi$
$823$	4.23830	−	13.0441i	0.147738	−	0.454690i	0.997353	+	0.0727132i	$0.0231658\pi$
$824$	0.511938			0.0178342
$825$	−2.41559	+	15.5084i	−0.0841002	+	0.539935i
$826$	0.867381			0.0301800
$827$	13.0236	−	40.0824i	0.452873	−	1.39380i	−0.420740	−	0.907181i	$-0.638230\pi$
$827$	13.0236	−	40.0824i	0.452873	−	1.39380i	0.873614	−	0.486620i	$-0.161770\pi$
$828$	8.33110	−	6.05290i	0.289526	−	0.210353i
$829$	−17.2555	−	12.5369i	−0.599308	−	0.435423i	0.246325	−	0.969187i	$-0.420777\pi$
$829$	−17.2555	−	12.5369i	−0.599308	−	0.435423i	−0.845633	+	0.533764i	$0.820777\pi$
$830$	1.38860	+	4.27367i	0.0481990	+	0.148341i
$831$	−4.58767	−	14.1194i	−0.159145	−	0.489797i
$832$	6.31434	+	4.58764i	0.218910	+	0.159048i
$833$	−0.229979	+	0.167090i	−0.00796830	+	0.00578931i
$834$	0.423245	−	1.30261i	0.0146558	−	0.0451058i
$835$	−56.2901			−1.94800
$836$	−27.5451	+	4.43506i	−0.952666	+	0.153390i
$837$	7.22090			0.249591
$838$	0.720010	−	2.21596i	0.0248723	−	0.0765492i
$839$	14.6052	−	10.6113i	0.504228	−	0.366343i	−0.306401	−	0.951902i	$-0.599125\pi$
$839$	14.6052	−	10.6113i	0.504228	−	0.366343i	0.810630	+	0.585559i	$0.199125\pi$
$840$	−2.49573	−	1.81326i	−0.0861109	−	0.0625632i
$841$	−4.19068	−	12.8976i	−0.144506	−	0.444745i
$842$	0.983416	+	3.02664i	0.0338908	+	0.104305i
$843$	22.6130	+	16.4293i	0.778832	+	0.565854i
$844$	−6.50668	+	4.72738i	−0.223969	+	0.162723i
$845$	0.964032	−	2.96698i	0.0331637	−	0.102067i
$846$	−0.242830			−0.00834868
$847$	−28.7457	−	9.17749i	−0.987713	−	0.315342i
$848$	37.3093			1.28121
$849$	6.89336	−	21.2156i	0.236579	−	0.728116i
$850$	−0.187158	+	0.135978i	−0.00641948	+	0.00466402i
$851$	−36.6557	−	26.6319i	−1.25654	−	0.912930i
$852$	−4.11023	−	12.6500i	−0.140814	−	0.433382i
$853$	−8.73190	−	26.8740i	−0.298974	−	0.920149i	−0.981857	−	0.189621i	$-0.939274\pi$
$853$	−8.73190	−	26.8740i	−0.298974	−	0.920149i	0.682883	−	0.730528i	$-0.260726\pi$
$854$	2.38263	+	1.73108i	0.0815318	+	0.0592363i
$855$	−10.6590	+	7.74421i	−0.364530	+	0.264846i
$856$	1.06350	−	3.27312i	0.0363497	−	0.111873i
$857$	18.0406			0.616256			0.308128	−	0.951345i	$-0.400298\pi$
$857$	18.0406			0.616256			0.308128	+	0.951345i	$0.400298\pi$
$858$	−0.295692	+	0.0476097i	−0.0100948	+	0.00162537i
$859$	−4.27894			−0.145995			−0.0729977	−	0.997332i	$-0.523257\pi$
$859$	−4.27894			−0.145995			−0.0729977	+	0.997332i	$0.523257\pi$
$860$	−2.67358	+	8.22844i	−0.0911684	+	0.280587i
$861$	−7.26478	+	5.27817i	−0.247583	+	0.179880i
$862$	0.137212	+	0.0996901i	0.00467345	+	0.00339546i
$863$	−16.3637	−	50.3621i	−0.557025	−	1.71435i	−0.690534	−	0.723300i	$-0.742625\pi$
$863$	−16.3637	−	50.3621i	−0.557025	−	1.71435i	0.133509	−	0.991048i	$-0.457375\pi$
$864$	−0.333042	−	1.02500i	−0.0113303	−	0.0348712i
$865$	17.0155	+	12.3625i	0.578544	+	0.420337i
$866$	2.38366	−	1.73183i	0.0810001	−	0.0588500i
$867$	5.16273	−	15.8893i	0.175336	−	0.539627i
$868$	39.4551			1.33919
$869$	0.708937	−	4.55147i	0.0240490	−	0.154398i
$870$	−1.10692			−0.0375280
$871$	1.26199	−	3.88402i	0.0427610	−	0.131605i
$872$	−5.72163	+	4.15701i	−0.193759	+	0.140774i
$873$	−11.8843	−	8.63445i	−0.402223	−	0.292232i
$874$	0.609287	+	1.87519i	0.0206094	+	0.0634293i
$875$	−0.707795	−	2.17837i	−0.0239278	−	0.0736423i
$876$	−16.1657	−	11.7451i	−0.546190	−	0.396830i
$877$	−39.3511	+	28.5902i	−1.32879	+	0.965423i	−0.329013	+	0.944325i	$0.606716\pi$
$877$	−39.3511	+	28.5902i	−1.32879	+	0.965423i	−0.999777	+	0.0210976i	$0.993284\pi$
$878$	−0.676760	+	2.08285i	−0.0228396	+	0.0702929i
$879$	−10.3997			−0.350774
$880$	−28.8335	+	28.9816i	−0.971977	+	0.976969i
$881$	−15.2202			−0.512780			−0.256390	−	0.966573i	$-0.582533\pi$
$881$	−15.2202			−0.512780			−0.256390	+	0.966573i	$0.582533\pi$
$882$	0.0146535	−	0.0450988i	0.000493408	−	0.00151856i
$883$	38.5832	−	28.0324i	1.29843	−	0.943364i	0.298490	−	0.954413i	$-0.403517\pi$
$883$	38.5832	−	28.0324i	1.29843	−	0.943364i	0.999939	+	0.0110490i	$0.00351707\pi$
$884$	0.872341	+	0.633793i	0.0293400	+	0.0213168i
$885$	−3.37554	−	10.3889i	−0.113468	−	0.349218i
$886$	−0.151007	−	0.464751i	−0.00507317	−	0.0156136i
$887$	−14.6001	−	10.6076i	−0.490224	−	0.356168i	0.315047	−	0.949076i	$-0.397980\pi$
$887$	−14.6001	−	10.6076i	−0.490224	−	0.356168i	−0.805270	+	0.592908i	$0.797980\pi$
$888$	−2.55580	+	1.85690i	−0.0857671	+	0.0623134i
$889$	−11.9200	+	36.6860i	−0.399784	+	1.23041i
$890$	−4.84573			−0.162429
$891$	−2.95898	−	1.49814i	−0.0991296	−	0.0501896i
$892$	−3.54183			−0.118589
$893$	−3.50941	+	10.8009i	−0.117438	+	0.361437i
$894$	0.918427	−	0.667276i	0.0307168	−	0.0223170i
$895$	−32.9715	−	23.9552i	−1.10211	−	0.800733i
$896$	−2.42466	−	7.46234i	−0.0810023	−	0.249299i
$897$	−1.59761	−	4.91694i	−0.0533427	−	0.164172i
$898$	−1.57363	−	1.14331i	−0.0525126	−	0.0381526i
$899$	22.9538	−	16.6769i	0.765551	−	0.556205i
$900$	−2.91283	+	8.96477i	−0.0970944	+	0.298826i
$901$	5.11173			0.170297
$902$	−0.447331	−	0.872404i	−0.0148945	−	0.0290479i
$903$	−3.81947			−0.127104
$904$	0.524262	−	1.61351i	0.0174367	−	0.0536646i
$905$	−47.7143	+	34.6664i	−1.58608	+	1.15235i
$906$	0.366599	+	0.266350i	0.0121794	+	0.00884888i
$907$	−14.8370	−	45.6637i	−0.492655	−	1.51624i	−0.820579	−	0.571533i	$-0.806349\pi$
$907$	−14.8370	−	45.6637i	−0.492655	−	1.51624i	0.327924	−	0.944704i	$-0.393651\pi$
$908$	−1.90875	−	5.87453i	−0.0633441	−	0.194953i
$909$	8.74817	+	6.35592i	0.290158	+	0.210812i
$910$	−0.625208	+	0.454240i	−0.0207254	+	0.0150579i
$911$	6.42809	−	19.7836i	0.212972	−	0.655461i	−0.786319	−	0.617821i	$-0.788016\pi$
$911$	6.42809	−	19.7836i	0.212972	−	0.655461i	0.999291	−	0.0376405i	$-0.0119842\pi$
$912$	−16.6867			−0.552553
$913$	24.1382	+	47.0753i	0.798857	+	1.55797i
$914$	−3.31139			−0.109531
$915$	11.4613	−	35.2741i	0.378897	−	1.16613i
$916$	25.4197	−	18.4685i	0.839891	−	0.610216i
$917$	−26.5069	−	19.2584i	−0.875336	−	0.635969i
$918$	−0.0151062	−	0.0464922i	−0.000498580	−	0.00153447i
$919$	−7.08655	−	21.8102i	−0.233764	−	0.719451i	−0.997283	−	0.0736656i	$-0.976530\pi$
$919$	−7.08655	−	21.8102i	−0.233764	−	0.719451i	0.763519	−	0.645785i	$-0.223470\pi$
$920$	4.70360	+	3.41736i	0.155073	+	0.112667i
$921$	12.2270	−	8.88345i	0.402894	−	0.292720i
$922$	−0.906911	+	2.79118i	−0.0298675	+	0.0919228i
$923$	−6.67773			−0.219800
$924$	−16.1679	−	8.18588i	−0.531886	−	0.269296i
$925$	41.4736			1.36364
$926$	−0.271116	+	0.834409i	−0.00890942	+	0.0274204i
$927$	1.14895	−	0.834760i	0.0377364	−	0.0274171i
$928$	−3.42594	−	2.48909i	−0.112462	−	0.0817084i
$929$	−11.2510	−	34.6270i	−0.369133	−	1.13607i	−0.947352	−	0.320193i	$-0.896252\pi$
$929$	−11.2510	−	34.6270i	−0.369133	−	1.13607i	0.578220	−	0.815881i	$-0.303748\pi$
$930$	0.628613	+	1.93467i	0.0206130	+	0.0634404i
$931$	−1.79417	−	1.30354i	−0.0588017	−	0.0427219i
$932$	−4.06051	+	2.95013i	−0.133006	+	0.0966347i
$933$	−8.82917	+	27.1734i	−0.289054	+	0.889617i
$934$	2.81412			0.0920807
$935$	−3.95047	+	3.97075i	−0.129194	+	0.129858i
$936$	−0.360475			−0.0117825
$937$	−8.66049	+	26.6543i	−0.282926	+	0.870756i	0.704087	+	0.710114i	$0.251357\pi$
$937$	−8.66049	+	26.6543i	−0.282926	+	0.870756i	−0.987013	+	0.160642i	$0.948643\pi$
$938$	−0.818446	+	0.594636i	−0.0267232	+	0.0194156i
$939$	9.77808	+	7.10419i	0.319096	+	0.231836i
$940$	5.16356	+	15.8918i	0.168417	+	0.518333i
$941$	3.70416	+	11.4002i	0.120752	+	0.371637i	0.993103	−	0.117243i	$-0.0374055\pi$
$941$	3.70416	+	11.4002i	0.120752	+	0.371637i	−0.872351	+	0.488880i	$0.837406\pi$
$942$	1.32441	+	0.962241i	0.0431516	+	0.0313515i
$943$	13.6916	−	9.94754i	0.445861	−	0.323937i
$944$	4.27521	−	13.1577i	0.139146	−	0.428248i
$945$	−8.55787			−0.278388
$946$	0.0641791	−	0.412039i	0.00208664	−	0.0133965i
$947$	11.6646			0.379048			0.189524	−	0.981876i	$-0.439305\pi$
$947$	11.6646			0.379048			0.189524	+	0.981876i	$0.439305\pi$
$948$	0.854868	−	2.63101i	0.0277648	−	0.0854513i
$949$	−8.11596	+	5.89659i	−0.263455	+	0.191411i
$950$	−1.46011	−	1.06083i	−0.0473722	−	0.0344179i
$951$	2.87956	+	8.86238i	0.0933762	+	0.287382i
$952$	−0.165420	−	0.509109i	−0.00536128	−	0.0165003i
$953$	−35.8579	−	26.0523i	−1.16155	−	0.843917i	−0.171579	−	0.985170i	$-0.554887\pi$
$953$	−35.8579	−	26.0523i	−1.16155	−	0.843917i	−0.989974	+	0.141253i	$0.954887\pi$
$954$	−0.689848	+	0.501204i	−0.0223347	+	0.0162271i
$955$	−8.91882	+	27.4493i	−0.288606	+	0.888239i
$956$	59.3201			1.91855
$957$	−12.8660	+	2.07157i	−0.415899	+	0.0669643i
$958$	−1.14502			−0.0369941
$959$	4.59366	−	14.1378i	0.148337	−	0.456534i
$960$	−19.6987	+	14.3119i	−0.635772	+	0.461915i
$961$	−17.1037	−	12.4266i	−0.551733	−	0.400857i
$962$	0.244556	+	0.752666i	0.00788480	+	0.0242669i
$963$	−2.95028	−	9.08003i	−0.0950715	−	0.292600i
$964$	13.5868	+	9.87135i	0.437600	+	0.317935i
$965$	−54.8261	+	39.8335i	−1.76492	+	1.28229i
$966$	−0.395757	+	1.21802i	−0.0127333	+	0.0391890i
$967$	28.7174			0.923489			0.461744	−	0.887013i	$-0.347224\pi$
$967$	28.7174			0.923489			0.461744	+	0.887013i	$0.347224\pi$
$968$	2.31423	−	3.21983i	0.0743823	−	0.103489i
$969$	−2.28624			−0.0734447
$970$	1.27882	−	3.93579i	0.0410603	−	0.126371i
$971$	−8.51231	+	6.18456i	−0.273173	+	0.198472i	−0.715934	−	0.698168i	$-0.753999\pi$
$971$	−8.51231	+	6.18456i	−0.273173	+	0.198472i	0.442761	+	0.896640i	$0.353999\pi$
$972$	−1.61144	−	1.17078i	−0.0516869	−	0.0375527i
$973$	−12.8572	−	39.5705i	−0.412184	−	1.26857i
$974$	−0.123718	−	0.380764i	−0.00396418	−	0.0122005i
$975$	3.82856	+	2.78161i	0.122612	+	0.0890828i
$976$	38.0033	−	27.6110i	1.21645	−	0.883806i
$977$	16.1322	−	49.6498i	0.516115	−	1.58844i	−0.265130	−	0.964213i	$-0.585415\pi$
$977$	16.1322	−	49.6498i	0.516115	−	1.58844i	0.781245	−	0.624225i	$-0.214585\pi$
$978$	−0.139892			−0.00447325
$979$	−56.3233	+	9.06867i	−1.80010	+	0.289836i
$980$	−3.26304			−0.104234
$981$	−6.06276	+	18.6592i	−0.193569	+	0.595744i
$982$	0.985559	−	0.716051i	0.0314505	−	0.0228501i
$983$	10.0910	+	7.33153i	0.321852	+	0.233840i	0.736966	−	0.675930i	$-0.236258\pi$
$983$	10.0910	+	7.33153i	0.321852	+	0.233840i	−0.415113	+	0.909770i	$0.636258\pi$
$984$	−0.364641	−	1.12225i	−0.0116243	−	0.0357760i
$985$	−6.77364	−	20.8471i	−0.215826	−	0.664244i
$986$	−0.155395	−	0.112901i	−0.00494878	−	0.00359550i
$987$	−5.96783	+	4.33588i	−0.189958	+	0.138013i
$988$	−2.59949	+	8.00039i	−0.0827006	+	0.254526i
$989$	7.19839			0.228896
$990$	0.143799	−	0.923211i	0.00457024	−	0.0293416i
$991$	−45.9904			−1.46093			−0.730466	−	0.682949i	$-0.760697\pi$
$991$	−45.9904			−1.46093			−0.730466	+	0.682949i	$0.760697\pi$
$992$	−2.40486	+	7.40141i	−0.0763545	+	0.234995i
$993$	0.422549	−	0.307000i	0.0134092	−	0.00974235i
$994$	1.33827	+	0.972310i	0.0424473	+	0.0308398i
$995$	−9.10000	−	28.0069i	−0.288489	−	0.887879i
$996$	9.81800	+	30.2167i	0.311095	+	0.957452i
$997$	14.7286	+	10.7010i	0.466460	+	0.338903i	0.796060	−	0.605218i	$-0.206914\pi$
$997$	14.7286	+	10.7010i	0.466460	+	0.338903i	−0.329600	+	0.944121i	$0.606914\pi$
$998$	1.95276	−	1.41876i	0.0618134	−	0.0449101i
$999$	−2.70818	+	8.33491i	−0.0856830	+	0.263705i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.n.c.196.3	✓	28
11.4	even	5		4719.2.a.bp.1.7		14
11.5	even	5	inner	429.2.n.c.313.3	yes	28
11.7	odd	10		4719.2.a.bo.1.8		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.c.196.3	✓	28	1.1	even	1	trivial
429.2.n.c.313.3	yes	28	11.5	even	5	inner
4719.2.a.bo.1.8		14	11.7	odd	10
4719.2.a.bp.1.7		14	11.4	even	5

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0279051 - 0.0858830i) q^{2} +(0.809017 - 0.587785i) q^{3} +(1.61144 + 1.17078i) q^{4} +(0.964032 + 2.96698i) q^{5} +(-0.0279051 - 0.0858830i) q^{6} +(-2.21929 - 1.61241i) q^{7} +(0.291630 - 0.211882i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.0279051 - 0.0858830i) q^{2} +(0.809017 - 0.587785i) q^{3} +(1.61144 + 1.17078i) q^{4} +(0.964032 + 2.96698i) q^{5} +(-0.0279051 - 0.0858830i) q^{6} +(-2.21929 - 1.61241i) q^{7} +(0.291630 - 0.211882i) q^{8} +(0.309017 - 0.951057i) q^{9} +0.281715 q^{10} +(3.27445 - 0.527223i) q^{11} +1.99185 q^{12} +(0.309017 - 0.951057i) q^{13} +(-0.200408 + 0.145605i) q^{14} +(2.52387 + 1.83370i) q^{15} +(1.22097 + 3.75776i) q^{16} +(0.167284 + 0.514849i) q^{17} +(-0.0730564 - 0.0530786i) q^{18} +(-3.41670 + 2.48238i) q^{19} +(-1.92020 + 5.90977i) q^{20} -2.74320 q^{21} +(0.0460943 - 0.295932i) q^{22} +5.16998 q^{23} +(0.111393 - 0.342832i) q^{24} +(-3.82856 + 2.78161i) q^{25} +(-0.0730564 - 0.0530786i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(-1.68848 - 5.19659i) q^{28} +(-3.17880 - 2.30953i) q^{29} +(0.227912 - 0.165588i) q^{30} +(-2.23138 + 6.86748i) q^{31} +1.07775 q^{32} +(2.33919 - 2.35121i) q^{33} +0.0488848 q^{34} +(2.64453 - 8.13902i) q^{35} +(1.61144 - 1.17078i) q^{36} +(-7.09010 - 5.15126i) q^{37} +(0.117851 + 0.362708i) q^{38} +(-0.309017 - 0.951057i) q^{39} +(0.909790 + 0.661001i) q^{40} +(2.64829 - 1.92410i) q^{41} +(-0.0765491 + 0.235594i) q^{42} +1.39234 q^{43} +(5.89383 + 2.98407i) q^{44} +3.11967 q^{45} +(0.144269 - 0.444013i) q^{46} +(2.17550 - 1.58060i) q^{47} +(3.19654 + 2.32242i) q^{48} +(0.162271 + 0.499418i) q^{49} +(0.132057 + 0.406429i) q^{50} +(0.437956 + 0.318194i) q^{51} +(1.61144 - 1.17078i) q^{52} +(2.91795 - 8.98052i) q^{53} -0.0903027 q^{54} +(4.72094 + 9.20699i) q^{55} -0.988852 q^{56} +(-1.30506 + 4.01657i) q^{57} +(-0.287054 + 0.208557i) q^{58} +(-2.83276 - 2.05812i) q^{59} +(1.92020 + 5.90977i) q^{60} +(-3.67386 - 11.3070i) q^{61} +(0.527533 + 0.383275i) q^{62} +(-2.21929 + 1.61241i) q^{63} +(-2.41186 + 7.42295i) q^{64} +3.11967 q^{65} +(-0.136653 - 0.266508i) q^{66} +4.08390 q^{67} +(-0.333205 + 1.02550i) q^{68} +(4.18260 - 3.03884i) q^{69} +(-0.625208 - 0.454240i) q^{70} +(-2.06353 - 6.35089i) q^{71} +(-0.111393 - 0.342832i) q^{72} +(-8.11596 - 5.89659i) q^{73} +(-0.640256 + 0.465173i) q^{74} +(-1.46238 + 4.50074i) q^{75} -8.41211 q^{76} +(-8.11706 - 4.10970i) q^{77} -0.0903027 q^{78} +(0.429184 - 1.32089i) q^{79} +(-9.97215 + 7.24519i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.0913464 - 0.281135i) q^{82} +(4.92910 + 15.1702i) q^{83} +(-4.42049 - 3.21167i) q^{84} +(-1.36628 + 0.992661i) q^{85} +(0.0388535 - 0.119579i) q^{86} -3.92921 q^{87} +(0.843220 - 0.847550i) q^{88} -17.2008 q^{89} +(0.0870547 - 0.267927i) q^{90} +(-2.21929 + 1.61241i) q^{91} +(8.33110 + 6.05290i) q^{92} +(2.23138 + 6.86748i) q^{93} +(-0.0750387 - 0.230945i) q^{94} +(-10.6590 - 7.74421i) q^{95} +(0.871916 - 0.633484i) q^{96} +(4.53940 - 13.9708i) q^{97} +0.0474197 q^{98} +(0.510442 - 3.27711i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9}+O(q^{10}) \) 28 * q + q^2 + 7 * q^3 - 5 * q^4 - 4 * q^5 - q^6 + q^7 - 7 * q^8 - 7 * q^9	\( 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9} - 2 q^{10} + 14 q^{11} - 30 q^{12} - 7 q^{13} - 9 q^{14} + 4 q^{15} + q^{16} - 12 q^{17} - 4 q^{18} + 10 q^{19} - 41 q^{20} - 6 q^{21} + 5 q^{22} + 30 q^{23} + 2 q^{24} + 3 q^{25} - 4 q^{26} + 7 q^{27} - 12 q^{28} - 4 q^{29} + 7 q^{30} - 4 q^{31} + 22 q^{32} + q^{33} - 24 q^{34} - 6 q^{35} - 5 q^{36} - 8 q^{37} + 73 q^{38} + 7 q^{39} - 28 q^{40} + 10 q^{41} + 9 q^{42} - 12 q^{43} - 22 q^{44} + 16 q^{45} + 35 q^{46} + 12 q^{47} + 14 q^{48} + 16 q^{49} - 57 q^{50} - 13 q^{51} - 5 q^{52} + q^{53} - 6 q^{54} - 28 q^{55} + 48 q^{56} - 30 q^{58} - 15 q^{59} + 41 q^{60} - 22 q^{61} - 40 q^{62} + q^{63} - 19 q^{64} + 16 q^{65} + 20 q^{66} - 88 q^{67} + 39 q^{68} + 14 q^{70} + 34 q^{71} - 2 q^{72} - 59 q^{73} + 79 q^{74} + 27 q^{75} - 124 q^{76} - 42 q^{77} - 6 q^{78} - 3 q^{79} + 37 q^{80} - 7 q^{81} + 82 q^{82} - 8 q^{83} - 8 q^{84} + 70 q^{85} - 35 q^{86} - 36 q^{87} + 59 q^{88} + 126 q^{89} + 8 q^{90} + q^{91} - 82 q^{92} + 4 q^{93} + 23 q^{94} - 77 q^{95} + 73 q^{96} - 18 q^{97} - 66 q^{98} - 6 q^{99}+O(q^{100}) \) 28 * q + q^2 + 7 * q^3 - 5 * q^4 - 4 * q^5 - q^6 + q^7 - 7 * q^8 - 7 * q^9 - 2 * q^10 + 14 * q^11 - 30 * q^12 - 7 * q^13 - 9 * q^14 + 4 * q^15 + q^16 - 12 * q^17 - 4 * q^18 + 10 * q^19 - 41 * q^20 - 6 * q^21 + 5 * q^22 + 30 * q^23 + 2 * q^24 + 3 * q^25 - 4 * q^26 + 7 * q^27 - 12 * q^28 - 4 * q^29 + 7 * q^30 - 4 * q^31 + 22 * q^32 + q^33 - 24 * q^34 - 6 * q^35 - 5 * q^36 - 8 * q^37 + 73 * q^38 + 7 * q^39 - 28 * q^40 + 10 * q^41 + 9 * q^42 - 12 * q^43 - 22 * q^44 + 16 * q^45 + 35 * q^46 + 12 * q^47 + 14 * q^48 + 16 * q^49 - 57 * q^50 - 13 * q^51 - 5 * q^52 + q^53 - 6 * q^54 - 28 * q^55 + 48 * q^56 - 30 * q^58 - 15 * q^59 + 41 * q^60 - 22 * q^61 - 40 * q^62 + q^63 - 19 * q^64 + 16 * q^65 + 20 * q^66 - 88 * q^67 + 39 * q^68 + 14 * q^70 + 34 * q^71 - 2 * q^72 - 59 * q^73 + 79 * q^74 + 27 * q^75 - 124 * q^76 - 42 * q^77 - 6 * q^78 - 3 * q^79 + 37 * q^80 - 7 * q^81 + 82 * q^82 - 8 * q^83 - 8 * q^84 + 70 * q^85 - 35 * q^86 - 36 * q^87 + 59 * q^88 + 126 * q^89 + 8 * q^90 + q^91 - 82 * q^92 + 4 * q^93 + 23 * q^94 - 77 * q^95 + 73 * q^96 - 18 * q^97 - 66 * q^98 - 6 * q^99

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