LMFDB - Embedded newform 605.2.g.n.366.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(81,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("605.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.g (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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			366.1
Root			$0.453245 + 1.39494i$ of defining polynomial
Character	$\chi$	$=$	605.366
Dual form			605.2.g.n.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0756511 - 0.0549637i) q^{2} +(0.453245 + 1.39494i) q^{3} +(-0.615332 + 1.89380i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.110960 + 0.0806171i) q^{6} +(-1.39815 + 4.30308i) q^{7} +(0.115332 + 0.354955i) q^{8} +(0.686611 - 0.498852i) q^{9} +O(q^{10})$	\(q+(0.0756511 - 0.0549637i) q^{2} +(0.453245 + 1.39494i) q^{3} +(-0.615332 + 1.89380i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.110960 + 0.0806171i) q^{6} +(-1.39815 + 4.30308i) q^{7} +(0.115332 + 0.354955i) q^{8} +(0.686611 - 0.498852i) q^{9} -0.0935099 q^{10} -2.92064 q^{12} +(-0.924349 + 0.671579i) q^{13} +(0.130741 + 0.402380i) q^{14} +(0.453245 - 1.39494i) q^{15} +(-3.19369 - 2.32035i) q^{16} +(2.72899 + 1.98273i) q^{17} +(0.0245241 - 0.0754774i) q^{18} +(-1.88030 - 5.78696i) q^{19} +(1.61096 - 1.17043i) q^{20} -6.63626 q^{21} -5.45258 q^{23} +(-0.442869 + 0.321763i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-0.0330155 + 0.101611i) q^{26} +(4.56691 + 3.31805i) q^{27} +(-7.28883 - 5.29564i) q^{28} +(-1.02619 + 3.15830i) q^{29} +(-0.0423829 - 0.130441i) q^{30} +(-1.44887 + 1.05267i) q^{31} -1.11558 q^{32} +0.315430 q^{34} +(3.66042 - 2.65945i) q^{35} +(0.522231 + 1.60726i) q^{36} +(0.460067 - 1.41594i) q^{37} +(-0.460319 - 0.334441i) q^{38} +(-1.35577 - 0.985026i) q^{39} +(0.115332 - 0.354955i) q^{40} +(0.539933 + 1.66174i) q^{41} +(-0.502041 + 0.364754i) q^{42} +0.263041 q^{43} -0.848698 q^{45} +(-0.412494 + 0.299694i) q^{46} +(2.13986 + 6.58580i) q^{47} +(1.78924 - 5.50670i) q^{48} +(-10.8985 - 7.91824i) q^{49} +(0.0756511 + 0.0549637i) q^{50} +(-1.52890 + 4.70546i) q^{51} +(-0.703052 - 2.16377i) q^{52} +(1.16479 - 0.846269i) q^{53} +0.527864 q^{54} -1.68865 q^{56} +(7.22025 - 5.24582i) q^{57} +(0.0959593 + 0.295332i) q^{58} +(-2.18416 + 6.72216i) q^{59} +(2.36285 + 1.71671i) q^{60} +(2.02452 + 1.47090i) q^{61} +(-0.0517503 + 0.159271i) q^{62} +(1.18661 + 3.65201i) q^{63} +(6.30297 - 4.57938i) q^{64} +1.14256 q^{65} -0.516598 q^{67} +(-5.43413 + 3.94812i) q^{68} +(-2.47136 - 7.60605i) q^{69} +(0.130741 - 0.402380i) q^{70} +(8.68098 + 6.30710i) q^{71} +(0.256258 + 0.186183i) q^{72} +(1.75560 - 5.40317i) q^{73} +(-0.0430208 - 0.132404i) q^{74} +(-1.18661 + 0.862123i) q^{75} +12.1163 q^{76} -0.156706 q^{78} +(-9.14460 + 6.64394i) q^{79} +(1.21988 + 3.75440i) q^{80} +(-1.77179 + 5.45300i) q^{81} +(0.132182 + 0.0960360i) q^{82} +(3.62511 + 2.63380i) q^{83} +(4.08350 - 12.5677i) q^{84} +(-1.04238 - 3.20812i) q^{85} +(0.0198994 - 0.0144577i) q^{86} -4.87077 q^{87} +13.2676 q^{89} +(-0.0642049 + 0.0466476i) q^{90} +(-1.59747 - 4.91652i) q^{91} +(3.35515 - 10.3261i) q^{92} +(-2.12511 - 1.54398i) q^{93} +(0.523863 + 0.380608i) q^{94} +(-1.88030 + 5.78696i) q^{95} +(-0.505633 - 1.55618i) q^{96} +(2.71551 - 1.97293i) q^{97} -1.25970 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + q^{3} - 6 q^{4} - 2 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 5 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 + q^3 - 6 * q^4 - 2 * q^5 - 13 * q^6 + 3 * q^7 + 2 * q^8 - 5 * q^9	$ 8 q + 4 q^{2} + q^{3} - 6 q^{4} - 2 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 5 q^{9} - 6 q^{10} - 28 q^{12} - 4 q^{13} + 16 q^{14} + q^{15} - 20 q^{16} - q^{17} - 14 q^{18} + q^{19} - q^{20} + 12 q^{21} - 18 q^{23} - 25 q^{24} - 2 q^{25} - 14 q^{26} + 10 q^{27} - 4 q^{28} - 19 q^{29} + 12 q^{30} + 6 q^{31} - 12 q^{32} - 20 q^{34} + 8 q^{35} + 21 q^{36} + 4 q^{37} - 6 q^{38} - 9 q^{39} + 2 q^{40} + 4 q^{41} + 29 q^{42} - 42 q^{43} + 41 q^{46} + 4 q^{47} - 19 q^{48} - 15 q^{49} + 4 q^{50} - 13 q^{51} + 26 q^{52} + 3 q^{53} + 40 q^{54} + 30 q^{56} + 5 q^{57} - 6 q^{58} - 19 q^{59} + 22 q^{60} + 2 q^{61} + 38 q^{62} - q^{63} + 6 q^{64} - 14 q^{65} - 2 q^{67} - 35 q^{68} - 21 q^{69} + 16 q^{70} + 40 q^{71} + 34 q^{72} + 23 q^{73} - 48 q^{74} + q^{75} - 16 q^{76} + 12 q^{78} - 17 q^{79} + 15 q^{80} + 2 q^{82} + 25 q^{83} + 4 q^{84} + 4 q^{85} - 31 q^{86} - 30 q^{87} + 16 q^{90} - 12 q^{91} + 81 q^{92} - 13 q^{93} - 33 q^{94} + q^{95} - 23 q^{96} + 12 q^{97} + 84 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 + q^3 - 6 * q^4 - 2 * q^5 - 13 * q^6 + 3 * q^7 + 2 * q^8 - 5 * q^9 - 6 * q^10 - 28 * q^12 - 4 * q^13 + 16 * q^14 + q^15 - 20 * q^16 - q^17 - 14 * q^18 + q^19 - q^20 + 12 * q^21 - 18 * q^23 - 25 * q^24 - 2 * q^25 - 14 * q^26 + 10 * q^27 - 4 * q^28 - 19 * q^29 + 12 * q^30 + 6 * q^31 - 12 * q^32 - 20 * q^34 + 8 * q^35 + 21 * q^36 + 4 * q^37 - 6 * q^38 - 9 * q^39 + 2 * q^40 + 4 * q^41 + 29 * q^42 - 42 * q^43 + 41 * q^46 + 4 * q^47 - 19 * q^48 - 15 * q^49 + 4 * q^50 - 13 * q^51 + 26 * q^52 + 3 * q^53 + 40 * q^54 + 30 * q^56 + 5 * q^57 - 6 * q^58 - 19 * q^59 + 22 * q^60 + 2 * q^61 + 38 * q^62 - q^63 + 6 * q^64 - 14 * q^65 - 2 * q^67 - 35 * q^68 - 21 * q^69 + 16 * q^70 + 40 * q^71 + 34 * q^72 + 23 * q^73 - 48 * q^74 + q^75 - 16 * q^76 + 12 * q^78 - 17 * q^79 + 15 * q^80 + 2 * q^82 + 25 * q^83 + 4 * q^84 + 4 * q^85 - 31 * q^86 - 30 * q^87 + 16 * q^90 - 12 * q^91 + 81 * q^92 - 13 * q^93 - 33 * q^94 + q^95 - 23 * q^96 + 12 * q^97 + 84 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.0756511	−	0.0549637i	0.0534934	−	0.0388652i	−0.560717	−	0.828007i	$-0.689475\pi$
$2$	0.0756511	−	0.0549637i	0.0534934	−	0.0388652i	0.614211	+	0.789142i	$0.289475\pi$
$3$	0.453245	+	1.39494i	0.261681	+	0.805372i	0.992439	+	0.122735i	$0.0391667\pi$
$3$	0.453245	+	1.39494i	0.261681	+	0.805372i	−0.730758	+	0.682636i	$0.760833\pi$
$4$	−0.615332	+	1.89380i	−0.307666	+	0.946898i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$	0.110960	+	0.0806171i	0.0452992	+	0.0329118i
$7$	−1.39815	+	4.30308i	−0.528453	+	1.62641i	0.228932	+	0.973442i	$0.426477\pi$
$7$	−1.39815	+	4.30308i	−0.528453	+	1.62641i	−0.757385	+	0.652968i	$0.773523\pi$
$8$	0.115332	+	0.354955i	0.0407760	+	0.125496i
$9$	0.686611	−	0.498852i	0.228870	−	0.166284i
$10$	−0.0935099			−0.0295704
$11$		0			0
$11$		0			0
$12$	−2.92064			−0.843116
$13$	−0.924349	+	0.671579i	−0.256368	+	0.186262i	−0.708544	−	0.705666i	$-0.750648\pi$
$13$	−0.924349	+	0.671579i	−0.256368	+	0.186262i	0.452176	+	0.891929i	$0.350648\pi$
$14$	0.130741	+	0.402380i	0.0349421	+	0.107541i
$15$	0.453245	−	1.39494i	0.117027	−	0.360173i
$16$	−3.19369	−	2.32035i	−0.798421	−	0.580087i
$17$	2.72899	+	1.98273i	0.661878	+	0.480883i	0.867297	−	0.497792i	$-0.165856\pi$
$17$	2.72899	+	1.98273i	0.661878	+	0.480883i	−0.205418	+	0.978674i	$0.565856\pi$
$18$	0.0245241	−	0.0754774i	0.00578038	−	0.0177902i
$19$	−1.88030	−	5.78696i	−0.431369	−	1.32762i	−0.896762	−	0.442514i	$-0.854087\pi$
$19$	−1.88030	−	5.78696i	−0.431369	−	1.32762i	0.465392	−	0.885105i	$-0.345913\pi$
$20$	1.61096	−	1.17043i	0.360222	−	0.261716i
$21$	−6.63626			−1.44815
$22$		0			0
$23$	−5.45258			−1.13694			−0.568471	−	0.822703i	$-0.692465\pi$
$23$	−5.45258			−1.13694			−0.568471	+	0.822703i	$0.692465\pi$
$24$	−0.442869	+	0.321763i	−0.0904003	+	0.0656797i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	−0.0330155	+	0.101611i	−0.00647488	+	0.0199276i
$27$	4.56691	+	3.31805i	0.878902	+	0.638559i
$28$	−7.28883	−	5.29564i	−1.37746	−	1.00078i
$29$	−1.02619	+	3.15830i	−0.190559	+	0.586482i	−1.00000		0.000720503i	$-0.999771\pi$
$29$	−1.02619	+	3.15830i	−0.190559	+	0.586482i	0.809440	+	0.587202i	$0.199771\pi$
$30$	−0.0423829	−	0.130441i	−0.00773802	−	0.0238152i
$31$	−1.44887	+	1.05267i	−0.260225	+	0.189065i	−0.710246	−	0.703953i	$-0.751416\pi$
$31$	−1.44887	+	1.05267i	−0.260225	+	0.189065i	0.450021	+	0.893018i	$0.351416\pi$
$32$	−1.11558			−0.197209
$33$		0			0
$34$	0.315430			0.0540957
$35$	3.66042	−	2.65945i	0.618723	−	0.449529i
$36$	0.522231	+	1.60726i	0.0870385	+	0.267877i
$37$	0.460067	−	1.41594i	0.0756345	−	0.232779i	−0.906091	−	0.423084i	$-0.860948\pi$
$37$	0.460067	−	1.41594i	0.0756345	−	0.232779i	0.981725	+	0.190305i	$0.0609476\pi$
$38$	−0.460319	−	0.334441i	−0.0746736	−	0.0542536i
$39$	−1.35577	−	0.985026i	−0.217097	−	0.157730i
$40$	0.115332	−	0.354955i	0.0182356	−	0.0561233i
$41$	0.539933	+	1.66174i	0.0843234	+	0.259521i	0.984325	−	0.176367i	$-0.0564345\pi$
$41$	0.539933	+	1.66174i	0.0843234	+	0.259521i	−0.900001	+	0.435888i	$0.856434\pi$
$42$	−0.502041	+	0.364754i	−0.0774665	+	0.0562827i
$43$	0.263041			0.0401134			0.0200567	−	0.999799i	$-0.493615\pi$
$43$	0.263041			0.0401134			0.0200567	+	0.999799i	$0.493615\pi$
$44$		0			0
$45$	−0.848698			−0.126516
$46$	−0.412494	+	0.299694i	−0.0608189	+	0.0441875i
$47$	2.13986	+	6.58580i	0.312130	+	0.960638i	0.976920	+	0.213607i	$0.0685212\pi$
$47$	2.13986	+	6.58580i	0.312130	+	0.960638i	−0.664790	+	0.747031i	$0.731479\pi$
$48$	1.78924	−	5.50670i	0.258254	−	0.794824i
$49$	−10.8985	−	7.91824i	−1.55693	−	1.13118i
$50$	0.0756511	+	0.0549637i	0.0106987	+	0.00777305i
$51$	−1.52890	+	4.70546i	−0.214088	+	0.658896i
$52$	−0.703052	−	2.16377i	−0.0974958	−	0.300061i
$53$	1.16479	−	0.846269i	0.159996	−	0.116244i	−0.504907	−	0.863174i	$-0.668473\pi$
$53$	1.16479	−	0.846269i	0.159996	−	0.116244i	0.664903	+	0.746930i	$0.268473\pi$
$54$	0.527864			0.0718332
$55$		0			0
$56$	−1.68865			−0.225656
$57$	7.22025	−	5.24582i	0.956345	−	0.694826i
$58$	0.0959593	+	0.295332i	0.0126001	+	0.0387790i
$59$	−2.18416	+	6.72216i	−0.284354	+	0.875150i	0.702238	+	0.711942i	$0.252184\pi$
$59$	−2.18416	+	6.72216i	−0.284354	+	0.875150i	−0.986592	+	0.163208i	$0.947816\pi$
$60$	2.36285	+	1.71671i	0.305042	+	0.221626i
$61$	2.02452	+	1.47090i	0.259214	+	0.188330i	0.709800	−	0.704403i	$-0.248785\pi$
$61$	2.02452	+	1.47090i	0.259214	+	0.188330i	−0.450587	+	0.892733i	$0.648785\pi$
$62$	−0.0517503	+	0.159271i	−0.00657229	+	0.0202274i
$63$	1.18661	+	3.65201i	0.149499	+	0.460110i
$64$	6.30297	−	4.57938i	0.787872	−	0.572422i
$65$	1.14256			0.141717
$66$		0			0
$67$	−0.516598			−0.0631124			−0.0315562	−	0.999502i	$-0.510046\pi$
$67$	−0.516598			−0.0631124			−0.0315562	+	0.999502i	$0.510046\pi$
$68$	−5.43413	+	3.94812i	−0.658984	+	0.478780i
$69$	−2.47136	−	7.60605i	−0.297516	−	0.915661i
$70$	0.130741	−	0.402380i	0.0156266	−	0.0480937i
$71$	8.68098	+	6.30710i	1.03024	+	0.748515i	0.968357	−	0.249568i	$-0.0802887\pi$
$71$	8.68098	+	6.30710i	1.03024	+	0.748515i	0.0618853	+	0.998083i	$0.480289\pi$
$72$	0.256258	+	0.186183i	0.0302003	+	0.0219418i
$73$	1.75560	−	5.40317i	0.205477	−	0.632393i	−0.794216	−	0.607635i	$-0.792118\pi$
$73$	1.75560	−	5.40317i	0.205477	−	0.632393i	0.999693	−	0.0247584i	$-0.00788163\pi$
$74$	−0.0430208	−	0.132404i	−0.00500106	−	0.0153917i
$75$	−1.18661	+	0.862123i	−0.137018	+	0.0995494i
$76$	12.1163			1.38984
$77$		0			0
$78$	−0.156706			−0.0177435
$79$	−9.14460	+	6.64394i	−1.02885	+	0.747502i	−0.968078	−	0.250650i	$-0.919356\pi$
$79$	−9.14460	+	6.64394i	−1.02885	+	0.747502i	−0.0607700	+	0.998152i	$0.519356\pi$
$80$	1.21988	+	3.75440i	0.136387	+	0.419755i
$81$	−1.77179	+	5.45300i	−0.196865	+	0.605888i
$82$	0.132182	+	0.0960360i	0.0145971	+	0.0106054i
$83$	3.62511	+	2.63380i	0.397907	+	0.289097i	0.768688	−	0.639624i	$-0.220910\pi$
$83$	3.62511	+	2.63380i	0.397907	+	0.289097i	−0.370781	+	0.928720i	$0.620910\pi$
$84$	4.08350	−	12.5677i	0.445547	−	1.37125i
$85$	−1.04238	−	3.20812i	−0.113062	−	0.347970i
$86$	0.0198994	−	0.0144577i	0.00214580	−	0.00155902i
$87$	−4.87077			−0.522202
$88$		0			0
$89$	13.2676			1.40637			0.703183	−	0.711009i	$-0.251762\pi$
$89$	13.2676			1.40637			0.703183	+	0.711009i	$0.251762\pi$
$90$	−0.0642049	+	0.0466476i	−0.00676779	+	0.00491709i
$91$	−1.59747	−	4.91652i	−0.167461	−	0.515391i
$92$	3.35515	−	10.3261i	0.349798	−	1.07657i
$93$	−2.12511	−	1.54398i	−0.220363	−	0.160103i
$94$	0.523863	+	0.380608i	0.0540323	+	0.0392568i
$95$	−1.88030	+	5.78696i	−0.192914	+	0.593729i
$96$	−0.505633	−	1.55618i	−0.0516060	−	0.158827i
$97$	2.71551	−	1.97293i	0.275718	−	0.200321i	−0.441330	−	0.897345i	$-0.645493\pi$
$97$	2.71551	−	1.97293i	0.275718	−	0.200321i	0.717048	+	0.697024i	$0.245493\pi$
$98$	−1.25970			−0.127249
$99$		0			0
$100$	−1.99126			−0.199126
$101$	−7.55216	+	5.48696i	−0.751468	+	0.545973i	−0.896282	−	0.443486i	$-0.853742\pi$
$101$	−7.55216	+	5.48696i	−0.751468	+	0.545973i	0.144814	+	0.989459i	$0.453742\pi$
$102$	0.142967	+	0.440007i	0.0141558	+	0.0435672i
$103$	−4.30027	+	13.2349i	−0.423718	+	1.30407i	0.480498	+	0.876996i	$0.340456\pi$
$103$	−4.30027	+	13.2349i	−0.423718	+	1.30407i	−0.904216	+	0.427075i	$0.859544\pi$
$104$	−0.344987	−	0.250648i	−0.0338288	−	0.0245781i
$105$	5.36885	+	3.90070i	0.523946	+	0.380669i
$106$	0.0416035	−	0.128042i	0.00404089	−	0.0124366i
$107$	5.18787	+	15.9666i	0.501531	+	1.54355i	0.806526	+	0.591198i	$0.201345\pi$
$107$	5.18787	+	15.9666i	0.501531	+	1.54355i	−0.304996	+	0.952354i	$0.598655\pi$
$108$	−9.09388	+	6.60709i	−0.875059	+	0.635768i
$109$	3.65293			0.349888			0.174944	−	0.984578i	$-0.444026\pi$
$109$	3.65293			0.349888			0.174944	+	0.984578i	$0.444026\pi$
$110$		0			0
$111$	2.18368			0.207266
$112$	14.4499	−	10.4985i	1.36539	−	0.992012i
$113$	−3.67802	−	11.3198i	−0.345999	−	1.06488i	−0.961047	−	0.276386i	$-0.910863\pi$
$113$	−3.67802	−	11.3198i	−0.345999	−	1.06488i	0.615047	−	0.788490i	$-0.289137\pi$
$114$	0.257890	−	0.793704i	0.0241536	−	0.0743372i
$115$	4.41123	+	3.20495i	0.411350	+	0.298863i
$116$	−5.34973	−	3.88681i	−0.496710	−	0.360881i
$117$	−0.299650	+	0.922227i	−0.0277026	+	0.0852599i
$118$	0.204241	+	0.628588i	0.0188019	+	0.0578662i
$119$	−12.3474	+	8.97091i	−1.13188	+	0.822362i
$120$	0.547416			0.0499721
$121$		0			0
$122$	0.234004			0.0211857
$123$	−2.07332	+	1.50635i	−0.186945	+	0.135823i
$124$	−1.10200	−	3.39161i	−0.0989626	−	0.304576i
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$	0.290497	+	0.211058i	0.0258795	+	0.0188026i
$127$	15.9883	+	11.6162i	1.41873	+	1.03077i	0.991979	+	0.126404i	$0.0403435\pi$
$127$	15.9883	+	11.6162i	1.41873	+	1.03077i	0.426756	+	0.904367i	$0.359656\pi$
$128$	0.914596	−	2.81484i	0.0808397	−	0.248799i
$129$	0.119222	+	0.366928i	0.0104969	+	0.0323062i
$130$	0.0864358	−	0.0627993i	0.00758092	−	0.00550786i
$131$	1.93479			0.169043			0.0845215	−	0.996422i	$-0.473064\pi$
$131$	1.93479			0.169043			0.0845215	+	0.996422i	$0.473064\pi$
$132$		0			0
$133$	27.5307			2.38721
$134$	−0.0390812	+	0.0283941i	−0.00337610	+	0.00245288i
$135$	−1.74440	−	5.36872i	−0.150134	−	0.462066i
$136$	−0.389040	+	1.19734i	−0.0333599	+	0.102671i
$137$	10.1413	+	7.36808i	0.866429	+	0.629498i	0.929626	−	0.368503i	$-0.120130\pi$
$137$	10.1413	+	7.36808i	0.866429	+	0.629498i	−0.0631970	+	0.998001i	$0.520130\pi$
$138$	−0.605018	−	0.439571i	−0.0515025	−	0.0374188i
$139$	3.47491	−	10.6947i	0.294738	−	0.907111i	−0.688571	−	0.725169i	$-0.741762\pi$
$139$	3.47491	−	10.6947i	0.294738	−	0.907111i	0.983309	−	0.181942i	$-0.0582383\pi$
$140$	2.78408	+	8.56853i	0.235298	+	0.724173i
$141$	−8.21695	+	5.96996i	−0.691992	+	0.502762i
$142$	1.00339			0.0842024
$143$		0			0
$144$	−3.35033			−0.279194
$145$	2.68661	−	1.95194i	0.223111	−	0.162100i
$146$	−0.164166	−	0.505250i	−0.0135864	−	0.0418148i
$147$	6.10581	−	18.7917i	0.503599	−	1.54992i
$148$	2.39841	+	1.74255i	0.197148	+	0.143236i
$149$	−14.0232	−	10.1885i	−1.14883	−	0.834672i	−0.160503	−	0.987035i	$-0.551312\pi$
$149$	−14.0232	−	10.1885i	−1.14883	−	0.834672i	−0.988325	+	0.152363i	$0.951312\pi$
$150$	−0.0423829	+	0.130441i	−0.00346055	+	0.0106505i
$151$	0.00166997	+	0.00513965i	0.000135901	+	0.000418259i	0.951124	−	0.308808i	$-0.0999300\pi$
$151$	0.00166997	+	0.00513965i	0.000135901	+	0.000418259i	−0.950989	+	0.309226i	$0.899930\pi$
$152$	1.83725	−	1.33484i	0.149021	−	0.108270i
$153$	2.86285			0.231447
$154$		0			0
$155$	1.79091			0.143849
$156$	2.69969	−	1.96144i	0.216148	−	0.157041i
$157$	0.171454	+	0.527682i	0.0136835	+	0.0421136i	0.957665	−	0.287884i	$-0.0929519\pi$
$157$	0.171454	+	0.527682i	0.0136835	+	0.0421136i	−0.943982	+	0.329998i	$0.892952\pi$
$158$	−0.326623	+	1.00524i	−0.0259847	+	0.0799728i
$159$	1.70843	+	1.24125i	0.135488	+	0.0984375i
$160$	0.902527	+	0.655724i	0.0713510	+	0.0518395i
$161$	7.62356	−	23.4629i	0.600820	−	1.84914i
$162$	0.165679	+	0.509909i	0.0130170	+	0.0400622i
$163$	6.44324	−	4.68129i	0.504673	−	0.366667i	−0.306126	−	0.951991i	$-0.599033\pi$
$163$	6.44324	−	4.68129i	0.504673	−	0.366667i	0.810799	+	0.585324i	$0.199033\pi$
$164$	−3.47924			−0.271683
$165$		0			0
$166$	0.419007			0.0325212
$167$	2.77204	−	2.01400i	0.214507	−	0.155848i	−0.475344	−	0.879800i	$-0.657676\pi$
$167$	2.77204	−	2.01400i	0.214507	−	0.155848i	0.689850	+	0.723952i	$0.257676\pi$
$168$	−0.765373	−	2.35558i	−0.0590498	−	0.181737i
$169$	−3.61382	+	11.1222i	−0.277986	+	0.855553i
$170$	−0.255188	−	0.185405i	−0.0195720	−	0.0142199i
$171$	−4.17787	−	3.03540i	−0.319489	−	0.232123i
$172$	−0.161858	+	0.498147i	−0.0123415	+	0.0379834i
$173$	−6.35552	−	19.5603i	−0.483201	−	1.48714i	−0.834569	−	0.550903i	$-0.814283\pi$
$173$	−6.35552	−	19.5603i	−0.483201	−	1.48714i	0.351368	−	0.936237i	$-0.385717\pi$
$174$	−0.368479	+	0.267716i	−0.0279343	+	0.0202955i
$175$	−4.52452			−0.342022
$176$		0			0
$177$	−10.3670			−0.779231
$178$	1.00371	−	0.729238i	0.0752313	−	0.0546587i
$179$	−0.792419	−	2.43882i	−0.0592282	−	0.182286i	0.917065	−	0.398738i	$-0.130552\pi$
$179$	−0.792419	−	2.43882i	−0.0592282	−	0.182286i	−0.976293	+	0.216452i	$0.930552\pi$
$180$	0.522231	−	1.60726i	0.0389248	−	0.119798i
$181$	−10.8545	−	7.88624i	−0.806807	−	0.586179i	0.106096	−	0.994356i	$-0.466165\pi$
$181$	−10.8545	−	7.88624i	−0.806807	−	0.586179i	−0.912903	+	0.408177i	$0.866165\pi$
$182$	−0.391081	−	0.284137i	−0.0289888	−	0.0210616i
$183$	−1.13422	+	3.49078i	−0.0838442	+	0.258046i
$184$	−0.628857	−	1.93542i	−0.0463599	−	0.142681i
$185$	−1.20447	+	0.875099i	−0.0885544	+	0.0643385i
$186$	−0.245630			−0.0180104
$187$		0			0
$188$	−13.7889			−1.00566
$189$	−20.6631	+	15.0126i	−1.50302	+	1.09201i
$190$	0.175826	+	0.541138i	0.0127558	+	0.0392583i
$191$	5.62097	−	17.2996i	0.406719	−	1.25175i	−0.512733	−	0.858548i	$-0.671367\pi$
$191$	5.62097	−	17.2996i	0.406719	−	1.25175i	0.919452	−	0.393203i	$-0.128633\pi$
$192$	9.24477	+	6.71672i	0.667184	+	0.484738i
$193$	12.6924	+	9.22156i	0.913618	+	0.663782i	0.941927	−	0.335817i	$-0.109012\pi$
$193$	12.6924	+	9.22156i	0.913618	+	0.663782i	−0.0283094	+	0.999599i	$0.509012\pi$
$194$	0.0969914	−	0.298509i	0.00696358	−	0.0214317i
$195$	0.517859	+	1.59381i	0.0370846	+	0.114135i
$196$	21.7018	−	15.7672i	1.55013	−	1.12623i
$197$	21.8486			1.55665			0.778325	−	0.627862i	$-0.216070\pi$
$197$	21.8486			1.55665			0.778325	+	0.627862i	$0.216070\pi$
$198$		0			0
$199$	−4.55200			−0.322683			−0.161341	−	0.986899i	$-0.551582\pi$
$199$	−4.55200			−0.322683			−0.161341	+	0.986899i	$0.551582\pi$
$200$	−0.301943	+	0.219374i	−0.0213506	+	0.0155121i
$201$	−0.234145	−	0.720625i	−0.0165153	−	0.0508290i
$202$	−0.269745	+	0.830190i	−0.0189792	+	0.0584119i
$203$	−12.1556	−	8.83159i	−0.853158	−	0.619856i
$204$	−7.97040	−	5.79084i	−0.558040	−	0.405440i
$205$	0.539933	−	1.66174i	0.0377106	−	0.116061i
$206$	0.402118	+	1.23759i	0.0280169	+	0.0862271i
$207$	−3.74380	+	2.72003i	−0.260212	+	0.189055i
$208$	4.51038			0.312738
$209$		0			0
$210$	0.620556			0.0428225
$211$	15.3393	−	11.1447i	1.05600	−	0.767230i	0.0826575	−	0.996578i	$-0.473659\pi$
$211$	15.3393	−	11.1447i	1.05600	−	0.767230i	0.973345	+	0.229348i	$0.0736593\pi$
$212$	0.885929	+	2.72661i	0.0608459	+	0.187264i
$213$	−4.86345	+	14.9681i	−0.333238	+	1.02560i
$214$	1.27005	+	0.922748i	0.0868191	+	0.0630778i
$215$	−0.212805	−	0.154612i	−0.0145132	−	0.0105444i
$216$	−0.651050	+	2.00372i	−0.0442983	+	0.136336i
$217$	−2.50396	−	7.70641i	−0.169980	−	0.523145i
$218$	0.276348	−	0.200779i	0.0187167	−	0.0135985i
$219$	8.33284			0.563081
$220$		0			0
$221$	−3.85410			−0.259255
$222$	0.165198	−	0.120023i	0.0110873	−	0.00805543i
$223$	1.50785	+	4.64070i	0.100973	+	0.310764i	0.988764	−	0.149483i	$-0.0477609\pi$
$223$	1.50785	+	4.64070i	0.100973	+	0.310764i	−0.887791	+	0.460247i	$0.847761\pi$
$224$	1.55976	−	4.80045i	0.104216	−	0.320743i
$225$	0.686611	+	0.498852i	0.0457741	+	0.0332568i
$226$	−0.900424	−	0.654197i	−0.0598953	−	0.0435165i
$227$	−5.04404	+	15.5240i	−0.334785	+	1.03036i	0.632043	+	0.774933i	$0.282216\pi$
$227$	−5.04404	+	15.5240i	−0.334785	+	1.03036i	−0.966828	+	0.255428i	$0.917784\pi$
$228$	5.49166	+	16.9016i	0.363694	+	1.11934i
$229$	3.90890	−	2.83998i	0.258307	−	0.187671i	−0.451093	−	0.892477i	$-0.648966\pi$
$229$	3.90890	−	2.83998i	0.258307	−	0.187671i	0.709401	+	0.704806i	$0.248966\pi$
$230$	0.509871			0.0336199
$231$		0			0
$232$	−1.23941			−0.0813711
$233$	−6.81172	+	4.94900i	−0.446251	+	0.324220i	−0.788114	−	0.615530i	$-0.788942\pi$
$233$	−6.81172	+	4.94900i	−0.446251	+	0.324220i	0.341863	+	0.939750i	$0.388942\pi$
$234$	0.0280202	+	0.0862373i	0.00183174	+	0.00563751i
$235$	2.13986	−	6.58580i	0.139589	−	0.429610i
$236$	−11.3864	−	8.27272i	−0.741193	−	0.538508i
$237$	−13.4127	−	9.74488i	−0.871247	−	0.632998i
$238$	−0.441019	+	1.35732i	−0.0285870	+	0.0879819i
$239$	7.01245	+	21.5821i	0.453598	+	1.39603i	0.872773	+	0.488126i	$0.162319\pi$
$239$	7.01245	+	21.5821i	0.453598	+	1.39603i	−0.419175	+	0.907905i	$0.637681\pi$
$240$	−4.68428	+	3.40333i	−0.302369	+	0.219684i
$241$	−11.6065			−0.747638			−0.373819	−	0.927502i	$-0.621952\pi$
$241$	−11.6065			−0.747638			−0.373819	+	0.927502i	$0.621952\pi$
$242$		0			0
$243$	8.52534			0.546901
$244$	−4.03135	+	2.92894i	−0.258080	+	0.187506i
$245$	4.16287	+	12.8120i	0.265956	+	0.818528i
$246$	−0.0740540	+	0.227915i	−0.00472151	+	0.0145313i
$247$	5.62445	+	4.08640i	0.357875	+	0.260011i
$248$	−0.540751	−	0.392879i	−0.0343377	−	0.0249478i
$249$	−2.03094	+	6.25058i	−0.128705	+	0.396114i
$250$	−0.0288961	−	0.0889332i	−0.00182755	−	0.00562463i
$251$	−2.68032	+	1.94736i	−0.169180	+	0.122917i	−0.669153	−	0.743124i	$-0.733343\pi$
$251$	−2.68032	+	1.94736i	−0.169180	+	0.122917i	0.499973	+	0.866041i	$0.333343\pi$
$252$	−7.64633			−0.481674
$253$		0			0
$254$	1.84800			0.115954
$255$	4.00270	−	2.90813i	0.250659	−	0.182114i
$256$	4.72952	+	14.5560i	0.295595	+	0.909748i
$257$	−8.29606	+	25.5326i	−0.517494	+	1.59268i	0.261204	+	0.965284i	$0.415880\pi$
$257$	−8.29606	+	25.5326i	−0.517494	+	1.59268i	−0.778698	+	0.627399i	$0.784120\pi$
$258$	0.0291870	+	0.0212056i	0.00181711	+	0.00132020i
$259$	5.44965	+	3.95940i	0.338625	+	0.246025i
$260$	−0.703052	+	2.16377i	−0.0436015	+	0.134192i
$261$	0.870929	+	2.68044i	0.0539091	+	0.165915i
$262$	0.146369	−	0.106343i	0.00904269	−	0.00656990i
$263$	−12.1682			−0.750324			−0.375162	−	0.926959i	$-0.622413\pi$
$263$	−12.1682			−0.750324			−0.375162	+	0.926959i	$0.622413\pi$
$264$		0			0
$265$	−1.43976			−0.0884436
$266$	2.08273	−	1.51319i	0.127700	−	0.0927795i
$267$	6.01349	+	18.5076i	0.368019	+	1.13265i
$268$	0.317879	−	0.978331i	0.0194176	−	0.0597611i
$269$	1.69369	+	1.23053i	0.103266	+	0.0750270i	0.638220	−	0.769854i	$-0.279671\pi$
$269$	1.69369	+	1.23053i	0.103266	+	0.0750270i	−0.534954	+	0.844881i	$0.679671\pi$
$270$	−0.427051	−	0.310271i	−0.0259895	−	0.0188825i
$271$	−4.67938	+	14.4017i	−0.284252	+	0.874838i	0.702370	+	0.711812i	$0.252125\pi$
$271$	−4.67938	+	14.4017i	−0.284252	+	0.874838i	−0.986622	+	0.163026i	$0.947875\pi$
$272$	−4.11492	−	12.6644i	−0.249504	−	0.767894i
$273$	6.13422	−	4.45677i	0.371260	−	0.269736i
$274$	1.17218			0.0708138
$275$		0			0
$276$	15.9250			0.958574
$277$	6.69110	−	4.86137i	0.402029	−	0.292091i	−0.368338	−	0.929692i	$-0.620073\pi$
$277$	6.69110	−	4.86137i	0.402029	−	0.292091i	0.770367	+	0.637601i	$0.220073\pi$
$278$	−0.324939	−	1.00006i	−0.0194885	−	0.0599795i
$279$	−0.469687	+	1.44555i	−0.0281194	+	0.0865426i
$280$	1.36615	+	0.992564i	0.0816429	+	0.0593171i
$281$	1.97985	+	1.43844i	0.118108	+	0.0858104i	0.645271	−	0.763954i	$-0.276744\pi$
$281$	1.97985	+	1.43844i	0.118108	+	0.0858104i	−0.527163	+	0.849764i	$0.676744\pi$
$282$	−0.293490	+	0.903268i	−0.0174771	+	0.0537888i
$283$	−8.06372	−	24.8176i	−0.479339	−	1.47525i	−0.840016	−	0.542562i	$-0.817454\pi$
$283$	−8.06372	−	24.8176i	−0.479339	−	1.47525i	0.360677	−	0.932691i	$-0.382546\pi$
$284$	−17.2860	+	12.5590i	−1.02574	+	0.745242i
$285$	−8.92472			−0.528655
$286$		0			0
$287$	−7.90553			−0.466648
$288$	−0.765973	+	0.556512i	−0.0451354	+	0.0327928i
$289$	−1.73710	−	5.34624i	−0.102182	−	0.314485i
$290$	0.0959593	−	0.295332i	0.00563492	−	0.0173425i
$291$	3.98292	+	2.89376i	0.233483	+	0.169635i
$292$	9.15223	+	6.64949i	0.535594	+	0.389132i
$293$	−4.15719	+	12.7945i	−0.242866	+	0.747463i	0.753115	+	0.657889i	$0.228551\pi$
$293$	−4.15719	+	12.7945i	−0.242866	+	0.747463i	−0.995980	+	0.0895739i	$0.971449\pi$
$294$	−0.570953	−	1.75721i	−0.0332987	−	0.102483i
$295$	5.71821	−	4.15452i	0.332927	−	0.241886i
$296$	0.555655			0.0322968
$297$		0			0
$298$	−1.62087			−0.0938944
$299$	5.04009	−	3.66184i	0.291476	−	0.211770i
$300$	−0.902527	−	2.77769i	−0.0521074	−	0.160370i
$301$	−0.367773	+	1.13189i	−0.0211981	+	0.0652409i
$302$	0.000408830	0	0.000297032i	2.35255e−5	0	1.70923e-5i
$303$	−11.0770	−	8.04791i	−0.636357	−	0.462340i
$304$	−7.42268	+	22.8447i	−0.425720	+	1.31023i
$305$	−0.773299	−	2.37997i	−0.0442790	−	0.136277i
$306$	0.216577	−	0.157353i	0.0123809	−	0.00899526i
$307$	−27.1844			−1.55150			−0.775748	−	0.631042i	$-0.782627\pi$
$307$	−27.1844			−1.55150			−0.775748	+	0.631042i	$0.782627\pi$
$308$		0			0
$309$	−20.4110			−1.16114
$310$	0.135484	−	0.0984349i	0.00769497	−	0.00559072i
$311$	−4.07872	−	12.5530i	−0.231283	−	0.711817i	−0.997593	−	0.0693450i	$-0.977909\pi$
$311$	−4.07872	−	12.5530i	−0.231283	−	0.711817i	0.766310	−	0.642472i	$-0.222091\pi$
$312$	0.193276	−	0.594843i	0.0109421	−	0.0336764i
$313$	−13.0833	−	9.50561i	−0.739515	−	0.537289i	0.153044	−	0.988219i	$-0.451092\pi$
$313$	−13.0833	−	9.50561i	−0.739515	−	0.537289i	−0.892559	+	0.450931i	$0.851092\pi$
$314$	0.0419741	+	0.0304959i	0.00236873	+	0.00172099i
$315$	1.18661	−	3.65201i	0.0668580	−	0.205768i
$316$	−6.95531	−	21.4062i	−0.391267	−	1.20420i
$317$	4.35344	−	3.16296i	0.244514	−	0.177650i	−0.458778	−	0.888551i	$-0.651713\pi$
$317$	4.35344	−	3.16296i	0.244514	−	0.177650i	0.703292	+	0.710901i	$0.251713\pi$
$318$	0.197469			0.0110735
$319$		0			0
$320$	−7.79091			−0.435525
$321$	−19.9212	+	14.4736i	−1.11189	+	0.807837i
$322$	−0.712878	−	2.19401i	−0.0397271	−	0.122268i
$323$	6.34266	−	19.5207i	0.352915	−	1.08616i
$324$	−9.23663	−	6.71080i	−0.513146	−	0.372822i
$325$	−0.924349	−	0.671579i	−0.0512737	−	0.0372525i
$326$	0.230137	−	0.708289i	0.0127461	−	0.0392285i
$327$	1.65567	+	5.09564i	0.0915590	+	0.281790i
$328$	−0.527573	+	0.383304i	−0.0291304	+	0.0211644i
$329$	−31.3311			−1.72734
$330$		0			0
$331$	−18.5702			−1.02071			−0.510356	−	0.859963i	$-0.670486\pi$
$331$	−18.5702			−1.02071			−0.510356	+	0.859963i	$0.670486\pi$
$332$	−7.21852	+	5.24456i	−0.396168	+	0.287833i
$333$	−0.390457	−	1.20170i	−0.0213969	−	0.0658530i
$334$	0.0990106	−	0.304723i	0.00541762	−	0.0166737i
$335$	0.417936	+	0.303648i	0.0228343	+	0.0165901i
$336$	21.1941	+	15.3984i	1.15623	+	0.840054i
$337$	−2.78305	+	8.56535i	−0.151603	+	0.466585i	−0.997801	−	0.0662836i	$-0.978886\pi$
$337$	−2.78305	+	8.56535i	−0.151603	+	0.466585i	0.846198	+	0.532868i	$0.178886\pi$
$338$	0.337928	+	1.04003i	0.0183808	+	0.0565704i
$339$	14.1234	−	10.2613i	0.767080	−	0.557316i
$340$	6.71695			0.364278
$341$		0			0
$342$	−0.482897			−0.0261121
$343$	23.6877	−	17.2101i	1.27902	−	0.929260i
$344$	0.0303371	+	0.0933679i	0.00163567	+	0.00503406i
$345$	−2.47136	+	7.60605i	−0.133053	+	0.409496i
$346$	−1.55591	−	1.13043i	−0.0836461	−	0.0607725i
$347$	8.30939	+	6.03712i	0.446071	+	0.324090i	0.788043	−	0.615621i	$-0.211095\pi$
$347$	8.30939	+	6.03712i	0.446071	+	0.324090i	−0.341971	+	0.939710i	$0.611095\pi$
$348$	2.99714	−	9.22425i	0.160664	−	0.494472i
$349$	−5.33402	−	16.4164i	−0.285524	−	0.878752i	−0.986241	−	0.165313i	$-0.947137\pi$
$349$	−5.33402	−	16.4164i	−0.285524	−	0.878752i	0.700718	−	0.713439i	$-0.252863\pi$
$350$	−0.342285	+	0.248685i	−0.0182959	+	0.0132928i
$351$	−6.44975			−0.344262
$352$		0			0
$353$	−22.8096			−1.21403			−0.607017	−	0.794689i	$-0.707634\pi$
$353$	−22.8096			−1.21403			−0.607017	+	0.794689i	$0.707634\pi$
$354$	−0.784275	+	0.569809i	−0.0416837	+	0.0302850i
$355$	−3.31584	−	10.2051i	−0.175986	−	0.541631i
$356$	−8.16399	+	25.1262i	−0.432691	+	1.33169i
$357$	−18.1103	−	13.1579i	−0.958500	−	0.696391i
$358$	−0.193994	−	0.140945i	−0.0102529	−	0.00744916i
$359$	4.96736	−	15.2879i	0.262167	−	0.806867i	−0.730166	−	0.683270i	$-0.760557\pi$
$359$	4.96736	−	15.2879i	0.262167	−	0.806867i	0.992333	−	0.123597i	$-0.0394429\pi$
$360$	−0.0978819	−	0.301250i	−0.00515883	−	0.0158773i
$361$	−14.5820	+	10.5945i	−0.767475	+	0.557603i
$362$	−1.25461			−0.0659408
$363$		0			0
$364$	10.2939			0.539545
$365$	−4.59621	+	3.33934i	−0.240577	+	0.174789i
$366$	0.106061	+	0.326422i	0.00554390	+	0.0170624i
$367$	6.79759	−	20.9208i	0.354832	−	1.09206i	−0.601276	−	0.799042i	$-0.705341\pi$
$367$	6.79759	−	20.9208i	0.354832	−	1.09206i	0.956107	−	0.293017i	$-0.0946594\pi$
$368$	17.4138	+	12.6519i	0.907759	+	0.659525i
$369$	1.19969	+	0.871625i	0.0624533	+	0.0453750i
$370$	−0.0430208	+	0.132404i	−0.00223654	+	0.00688337i
$371$	2.01301	+	6.19539i	0.104510	+	0.321649i
$372$	4.23163	−	3.07446i	0.219400	−	0.159403i
$373$	20.2604			1.04905			0.524523	−	0.851396i	$-0.324244\pi$
$373$	20.2604			1.04905			0.524523	+	0.851396i	$0.324244\pi$
$374$		0			0
$375$	1.46673			0.0757417
$376$	−2.09087	+	1.51911i	−0.107828	+	0.0783419i
$377$	−1.17249	−	3.60854i	−0.0603861	−	0.185849i
$378$	−0.738036	+	2.27144i	−0.0379605	+	0.116830i
$379$	3.01578	+	2.19109i	0.154910	+	0.112549i	0.662540	−	0.749026i	$-0.269478\pi$
$379$	3.01578	+	2.19109i	0.154910	+	0.112549i	−0.507630	+	0.861575i	$0.669478\pi$
$380$	−9.80231	−	7.12180i	−0.502848	−	0.365341i
$381$	−8.95733	+	27.5678i	−0.458898	+	1.41234i
$382$	−0.525616	−	1.61768i	−0.0268928	−	0.0827677i
$383$	8.89708	−	6.46411i	0.454620	−	0.330301i	−0.336797	−	0.941577i	$-0.609344\pi$
$383$	8.89708	−	6.46411i	0.454620	−	0.330301i	0.791417	+	0.611277i	$0.209344\pi$
$384$	4.34108			0.221530
$385$		0			0
$386$	1.46704			0.0746706
$387$	0.180607	−	0.131219i	0.00918078	−	0.00667023i
$388$	2.06539	+	6.35663i	0.104854	+	0.322709i
$389$	2.89926	−	8.92300i	0.146998	−	0.452414i	−0.850264	−	0.526356i	$-0.823558\pi$
$389$	2.89926	−	8.92300i	0.146998	−	0.452414i	0.997263	+	0.0739418i	$0.0235579\pi$
$390$	0.126778	+	0.0921097i	0.00641966	+	0.00466415i
$391$	−14.8801	−	10.8110i	−0.752517	−	0.546736i
$392$	1.55367	−	4.78171i	0.0784723	−	0.241513i
$393$	0.876932	+	2.69892i	0.0442354	+	0.136143i
$394$	1.65287	−	1.20088i	0.0832705	−	0.0604996i
$395$	11.3033			0.568733
$396$		0			0
$397$	22.3136			1.11989			0.559945	−	0.828530i	$-0.310822\pi$
$397$	22.3136			1.11989			0.559945	+	0.828530i	$0.310822\pi$
$398$	−0.344364	+	0.250195i	−0.0172614	+	0.0125411i
$399$	12.4781	+	38.4038i	0.624688	+	1.92259i
$400$	1.21988	−	3.75440i	0.0609940	−	0.187720i
$401$	19.9683	+	14.5078i	0.997171	+	0.724487i	0.961480	−	0.274876i	$-0.0886368\pi$
$401$	19.9683	+	14.5078i	0.997171	+	0.724487i	0.0356909	+	0.999363i	$0.488637\pi$
$402$	−0.0573216	−	0.0416466i	−0.00285894	−	0.00207714i
$403$	0.632315	−	1.94606i	0.0314978	−	0.0969404i
$404$	−5.74411	−	17.6786i	−0.285780	−	0.879541i
$405$	4.63859	−	3.37014i	0.230494	−	0.167463i
$406$	−1.40500			−0.0697292
$407$		0			0
$408$	−1.84656			−0.0914182
$409$	23.8705	−	17.3429i	1.18032	−	0.857553i	0.188113	−	0.982147i	$-0.439763\pi$
$409$	23.8705	−	17.3429i	1.18032	−	0.857553i	0.992208	+	0.124594i	$0.0397630\pi$
$410$	−0.0504891	−	0.155390i	−0.00249348	−	0.00767414i
$411$	−5.68158	+	17.4861i	−0.280252	+	0.862526i
$412$	−22.4181	−	16.2877i	−1.10446	−	0.802437i
$413$	−25.8722	−	18.7972i	−1.27309	−	0.924951i
$414$	−0.133720	+	0.411547i	−0.00657196	+	0.0202264i
$415$	−1.38467	−	4.26157i	−0.0679707	−	0.209192i
$416$	1.03119	−	0.749203i	0.0505582	−	0.0367327i
$417$	16.4935			0.807689
$418$		0			0
$419$	9.03564			0.441420			0.220710	−	0.975339i	$-0.429163\pi$
$419$	9.03564			0.441420			0.220710	+	0.975339i	$0.429163\pi$
$420$	−10.6908	+	7.76729i	−0.521655	+	0.379005i
$421$	4.39426	+	13.5242i	0.214163	+	0.659127i	0.999212	+	0.0396928i	$0.0126379\pi$
$421$	4.39426	+	13.5242i	0.214163	+	0.659127i	−0.785049	+	0.619434i	$0.787362\pi$
$422$	0.547884	−	1.68621i	0.0266706	−	0.0820835i
$423$	4.75459	+	3.45441i	0.231176	+	0.167959i
$424$	0.434725	+	0.315846i	0.0211121	+	0.0153388i
$425$	−1.04238	+	3.20812i	−0.0505630	+	0.155617i
$426$	0.454780	+	1.39967i	0.0220342	+	0.0678142i
$427$	−9.16001	+	6.65514i	−0.443284	+	0.322065i
$428$	−33.4298			−1.61589
$429$		0			0
$430$	−0.0245970			−0.00118617
$431$	−1.40086	+	1.01778i	−0.0674769	+	0.0490248i	−0.621012	−	0.783801i	$-0.713278\pi$
$431$	−1.40086	+	1.01778i	−0.0674769	+	0.0490248i	0.553535	+	0.832826i	$0.313278\pi$
$432$	−6.88623	−	21.1936i	−0.331314	−	1.01968i
$433$	5.70062	−	17.5447i	0.273955	−	0.843145i	−0.715540	−	0.698572i	$-0.753819\pi$
$433$	5.70062	−	17.5447i	0.273955	−	0.843145i	0.989494	−	0.144573i	$-0.0461809\pi$
$434$	−0.613000	−	0.445371i	−0.0294250	−	0.0213785i
$435$	3.94054	+	2.86297i	0.188934	+	0.137269i
$436$	−2.24777	+	6.91791i	−0.107649	+	0.331308i
$437$	10.2525	+	31.5539i	0.490442	+	1.50943i
$438$	0.630389	−	0.458004i	0.0301211	−	0.0218843i
$439$	17.1704			0.819499			0.409750	−	0.912198i	$-0.365616\pi$
$439$	17.1704			0.819499			0.409750	+	0.912198i	$0.365616\pi$
$440$		0			0
$441$	−11.4331			−0.544432
$442$	−0.291567	+	0.211836i	−0.0138684	+	0.0100760i
$443$	11.3098	+	34.8079i	0.537344	+	1.65377i	0.738529	+	0.674221i	$0.235521\pi$
$443$	11.3098	+	34.8079i	0.537344	+	1.65377i	−0.201185	+	0.979553i	$0.564479\pi$
$444$	−1.34369	+	4.13545i	−0.0637686	+	0.196260i
$445$	−10.7337	−	7.79852i	−0.508828	−	0.369685i
$446$	0.369141	+	0.268196i	0.0174793	+	0.0126995i
$447$	7.85640	−	24.1795i	0.371595	−	1.14365i
$448$	10.8929	+	33.5249i	0.514641	+	1.58390i
$449$	13.4320	−	9.75895i	0.633897	−	0.460553i	−0.223851	−	0.974623i	$-0.571863\pi$
$449$	13.4320	−	9.75895i	0.633897	−	0.460553i	0.857748	+	0.514070i	$0.171863\pi$
$450$	0.0793616			0.00374114
$451$		0			0
$452$	23.7006			1.11478
$453$	−0.00641262	+	0.00465904i	−0.000301291	+	0.000218901i
$454$	0.471667	+	1.45164i	0.0221365	+	0.0681290i
$455$	−1.59747	+	4.91652i	−0.0748907	+	0.230490i
$456$	2.69476	+	1.95785i	0.126193	+	0.0916849i
$457$	−25.6178	−	18.6124i	−1.19835	−	0.870651i	−0.204227	−	0.978923i	$-0.565468\pi$
$457$	−25.6178	−	18.6124i	−1.19835	−	0.870651i	−0.994121	+	0.108272i	$0.965468\pi$
$458$	0.139617	−	0.429696i	0.00652385	−	0.0200784i
$459$	5.88426	+	18.1099i	0.274654	+	0.845297i
$460$	−8.78389	+	6.38187i	−0.409551	+	0.297556i
$461$	25.4351			1.18463			0.592315	−	0.805706i	$-0.298214\pi$
$461$	25.4351			1.18463			0.592315	+	0.805706i	$0.298214\pi$
$462$		0			0
$463$	−16.3319			−0.759007			−0.379503	−	0.925190i	$-0.623905\pi$
$463$	−16.3319			−0.759007			−0.379503	+	0.925190i	$0.623905\pi$
$464$	10.6057	−	7.70549i	0.492357	−	0.357718i
$465$	0.811719	+	2.49821i	0.0376426	+	0.115852i
$466$	−0.243298	+	0.748795i	−0.0112706	+	0.0346873i
$467$	−6.90020	−	5.01329i	−0.319303	−	0.231987i	0.416575	−	0.909101i	$-0.363230\pi$
$467$	−6.90020	−	5.01329i	−0.319303	−	0.231987i	−0.735878	+	0.677114i	$0.763230\pi$
$468$	−1.56213	−	1.13495i	−0.0722093	−	0.0524631i
$469$	0.722284	−	2.22296i	0.0333520	−	0.102647i
$470$	−0.200098	−	0.615837i	−0.00922982	−	0.0284065i
$471$	−0.658376	+	0.478338i	−0.0303364	+	0.0220407i
$472$	−2.63797			−0.121422
$473$		0			0
$474$	−1.55030			−0.0712076
$475$	4.92268	−	3.57654i	0.225868	−	0.164103i
$476$	−9.39133	−	28.9036i	−0.430451	−	1.32479i
$477$	0.377594	−	1.16211i	0.0172888	−	0.0532096i
$478$	1.71673	+	1.24728i	0.0785216	+	0.0570493i
$479$	24.2283	+	17.6029i	1.10702	+	0.804296i	0.982192	−	0.187882i	$-0.0601623\pi$
$479$	24.2283	+	17.6029i	1.10702	+	0.804296i	0.124827	+	0.992178i	$0.460162\pi$
$480$	−0.505633	+	1.55618i	−0.0230789	+	0.0710295i
$481$	0.525653	+	1.61779i	0.0239677	+	0.0737650i
$482$	−0.878041	+	0.637934i	−0.0399937	+	0.0290571i
$483$	36.1848			1.64646
$484$		0			0
$485$	−3.35655			−0.152413
$486$	0.644951	−	0.468585i	0.0292556	−	0.0212554i
$487$	−6.05768	−	18.6436i	−0.274500	−	0.844823i	−0.989351	−	0.145547i	$-0.953506\pi$
$487$	−6.05768	−	18.6436i	−0.274500	−	0.844823i	0.714852	−	0.699276i	$-0.246494\pi$
$488$	−0.288612	+	0.888257i	−0.0130649	+	0.0402095i
$489$	9.45050	+	6.86619i	0.427367	+	0.310500i
$490$	1.01912	+	0.740434i	0.0460391	+	0.0334494i
$491$	4.87911	−	15.0163i	0.220191	−	0.677678i	−0.778553	−	0.627579i	$-0.784046\pi$
$491$	4.87911	−	15.0163i	0.220191	−	0.677678i	0.998744	−	0.0500997i	$-0.0159539\pi$
$492$	−1.57695	−	4.85335i	−0.0710944	−	0.218806i
$493$	−9.06253	+	6.58432i	−0.408156	+	0.296543i
$494$	0.650099			0.0292494
$495$		0			0
$496$	7.06980			0.317443
$497$	−39.2773	+	28.5366i	−1.76183	+	1.28004i
$498$	0.189913	+	0.584491i	0.00851019	+	0.0261917i
$499$	3.46350	−	10.6596i	0.155048	−	0.477188i	−0.843118	−	0.537729i	$-0.819283\pi$
$499$	3.46350	−	10.6596i	0.155048	−	0.477188i	0.998166	+	0.0605408i	$0.0192825\pi$
$500$	1.61096	+	1.17043i	0.0720443	+	0.0523433i
$501$	4.06584	+	2.95400i	0.181648	+	0.131975i
$502$	−0.0957345	+	0.294640i	−0.00427284	+	0.0131504i
$503$	0.105965	+	0.326125i	0.00472473	+	0.0145412i	0.953391	−	0.301737i	$-0.0975666\pi$
$503$	0.105965	+	0.326125i	0.00472473	+	0.0145412i	−0.948666	+	0.316279i	$0.897567\pi$
$504$	−1.15945	+	0.842387i	−0.0516459	+	0.0375229i
$505$	9.33498			0.415401
$506$		0			0
$507$	−17.1528			−0.761782
$508$	−31.8368	+	23.1308i	−1.41253	+	1.02626i
$509$	−6.04518	−	18.6052i	−0.267948	−	0.824659i	−0.991000	−	0.133865i	$-0.957261\pi$
$509$	−6.04518	−	18.6052i	−0.267948	−	0.824659i	0.723052	−	0.690794i	$-0.242739\pi$
$510$	0.142967	−	0.440007i	0.00633068	−	0.0194838i
$511$	20.7957	+	15.1089i	0.919946	+	0.668380i
$512$	5.94673	+	4.32055i	0.262811	+	0.190943i
$513$	10.6143	−	32.6674i	0.468632	−	1.44230i
$514$	0.775763	+	2.38755i	0.0342175	+	0.105311i
$515$	11.2583	−	8.17961i	0.496098	−	0.360436i
$516$	−0.768249			−0.0338203
$517$		0			0
$518$	0.629896			0.0276760
$519$	24.4049	−	17.7312i	1.07126	−	0.778313i
$520$	0.131773	+	0.405557i	0.00577865	+	0.0177848i
$521$	12.9869	−	39.9695i	0.568966	−	1.75110i	−0.0868981	−	0.996217i	$-0.527695\pi$
$521$	12.9869	−	39.9695i	0.568966	−	1.75110i	0.655864	−	0.754879i	$-0.272305\pi$
$522$	0.213214	+	0.154909i	0.00933212	+	0.00678018i
$523$	24.2790	+	17.6398i	1.06165	+	0.771333i	0.974393	−	0.224853i	$-0.0721903\pi$
$523$	24.2790	+	17.6398i	1.06165	+	0.771333i	0.0872555	+	0.996186i	$0.472190\pi$
$524$	−1.19054	+	3.66409i	−0.0520088	+	0.160067i
$525$	−2.05072	−	6.31146i	−0.0895007	−	0.275455i
$526$	−0.920538	+	0.668810i	−0.0401374	+	0.0291615i
$527$	−6.04112			−0.263155
$528$		0			0
$529$	6.73067			0.292638
$530$	−0.108919	+	0.0791345i	−0.00473115	+	0.00343738i
$531$	1.85369	+	5.70508i	0.0804434	+	0.247579i
$532$	−16.9405	+	52.1375i	−0.734464	+	2.26045i
$533$	−1.61508	−	1.17342i	−0.0699568	−	0.0508266i
$534$	1.47217	+	1.06960i	0.0637072	+	0.0462860i
$535$	5.18787	−	15.9666i	0.224291	−	0.690298i
$536$	−0.0595802	−	0.183369i	−0.00257347	−	0.00792033i
$537$	3.04285	−	2.21076i	0.131309	−	0.0954014i
$538$	0.195764			0.00843998
$539$		0			0
$540$	11.2407			0.483721
$541$	−8.35196	+	6.06806i	−0.359079	+	0.260886i	−0.752668	−	0.658400i	$-0.771233\pi$
$541$	−8.35196	+	6.06806i	−0.359079	+	0.260886i	0.393589	+	0.919287i	$0.371233\pi$
$542$	0.437568	+	1.34670i	0.0187952	+	0.0578456i
$543$	6.08113	−	18.7158i	0.260966	−	0.803171i
$544$	−3.04442	−	2.21190i	−0.130529	−	0.0948346i
$545$	−2.95529	−	2.14714i	−0.126591	−	0.0919734i
$546$	0.219100	−	0.674320i	0.00937660	−	0.0288582i
$547$	−12.9221	−	39.7702i	−0.552510	−	1.70045i	−0.702431	−	0.711752i	$-0.747902\pi$
$547$	−12.9221	−	39.7702i	−0.552510	−	1.70045i	0.149921	−	0.988698i	$-0.452098\pi$
$548$	−20.1939	+	14.6717i	−0.862641	+	0.626746i
$549$	2.12382			0.0906426
$550$		0			0
$551$	20.2065			0.860826
$552$	2.41478	−	1.75444i	0.102780	−	0.0746740i
$553$	−15.8038	−	48.6392i	−0.672047	−	2.06835i
$554$	0.238990	−	0.735536i	0.0101537	−	0.0312499i
$555$	−1.76663	−	1.28353i	−0.0749894	−	0.0544830i
$556$	18.1153	+	13.1616i	0.768261	+	0.558174i
$557$	11.8918	−	36.5993i	0.503874	−	1.55076i	−0.298782	−	0.954321i	$-0.596580\pi$
$557$	11.8918	−	36.5993i	0.503874	−	1.55076i	0.802656	−	0.596442i	$-0.203420\pi$
$558$	0.0439203	+	0.135173i	0.00185930	+	0.00572233i
$559$	−0.243142	+	0.176653i	−0.0102838	+	0.00747163i
$560$	−17.8611			−0.754768
$561$		0			0
$562$	0.228840			0.00965303
$563$	24.8258	−	18.0370i	1.04628	−	0.760170i	0.0747817	−	0.997200i	$-0.476174\pi$
$563$	24.8258	−	18.0370i	1.04628	−	0.760170i	0.971502	+	0.237030i	$0.0761740\pi$
$564$	−6.24975	−	19.2347i	−0.263162	−	0.809929i
$565$	−3.67802	+	11.3198i	−0.154736	+	0.476227i
$566$	−1.97410	−	1.43427i	−0.0829775	−	0.0602867i
$567$	−20.9874	−	15.2483i	−0.881389	−	0.640367i
$568$	−1.23754	+	3.80877i	−0.0519262	+	0.159812i
$569$	−4.03220	−	12.4098i	−0.169039	−	0.520247i	0.830273	−	0.557357i	$-0.188185\pi$
$569$	−4.03220	−	12.4098i	−0.169039	−	0.520247i	−0.999311	+	0.0371104i	$0.988185\pi$
$570$	−0.675165	+	0.490536i	−0.0282795	+	0.0205463i
$571$	−16.1300			−0.675018			−0.337509	−	0.941322i	$-0.609584\pi$
$571$	−16.1300			−0.675018			−0.337509	+	0.941322i	$0.609584\pi$
$572$		0			0
$573$	26.6796			1.11456
$574$	−0.598062	+	0.434517i	−0.0249626	+	0.0181364i
$575$	−1.68494	−	5.18572i	−0.0702669	−	0.216259i
$576$	2.04326	−	6.28850i	0.0851358	−	0.262021i
$577$	11.7885	+	8.56487i	0.490763	+	0.356560i	0.805478	−	0.592626i	$-0.201909\pi$
$577$	11.7885	+	8.56487i	0.490763	+	0.356560i	−0.314715	+	0.949186i	$0.601909\pi$
$578$	−0.425263	−	0.308972i	−0.0176886	−	0.0128515i
$579$	−7.11080	+	21.8848i	−0.295515	+	0.909501i
$580$	2.04341	+	6.28898i	0.0848482	+	0.261136i
$581$	−16.4019	+	11.9167i	−0.680465	+	0.494387i
$582$	0.460364			0.0190827
$583$		0			0
$584$	2.12036			0.0877411
$585$	0.784493	−	0.569967i	0.0324348	−	0.0235653i
$586$	0.388738	+	1.19641i	0.0160586	+	0.0494234i
$587$	−8.61360	+	26.5099i	−0.355521	+	1.09418i	0.600185	+	0.799861i	$0.295094\pi$
$587$	−8.61360	+	26.5099i	−0.355521	+	1.09418i	−0.955707	+	0.294321i	$0.904906\pi$
$588$	31.8307	+	23.1263i	1.31267	+	0.953713i
$589$	8.81605	+	6.40524i	0.363259	+	0.263923i
$590$	0.204241	−	0.628588i	0.00840846	−	0.0258786i
$591$	9.90278	+	30.4776i	0.407346	+	1.25368i
$592$	−4.75478	+	3.45455i	−0.195420	+	0.141981i
$593$	−15.1037			−0.620236			−0.310118	−	0.950698i	$-0.600369\pi$
$593$	−15.1037			−0.620236			−0.310118	+	0.950698i	$0.600369\pi$
$594$		0			0
$595$	15.2622			0.625690
$596$	27.9238	−	20.2878i	1.14380	−	0.831023i
$597$	−2.06317	−	6.34979i	−0.0844400	−	0.259880i
$598$	0.180020	−	0.554044i	0.00736156	−	0.0226566i
$599$	20.9339	+	15.2093i	0.855334	+	0.621437i	0.926612	−	0.376020i	$-0.122708\pi$
$599$	20.9339	+	15.2093i	0.855334	+	0.621437i	−0.0712774	+	0.997457i	$0.522708\pi$
$600$	−0.442869	−	0.321763i	−0.0180801	−	0.0131359i
$601$	14.5321	−	44.7252i	0.592776	−	1.82438i	0.0272781	−	0.999628i	$-0.491316\pi$
$601$	14.5321	−	44.7252i	0.592776	−	1.82438i	0.565498	−	0.824750i	$-0.308684\pi$
$602$	0.0343904	+	0.105843i	0.00140165	+	0.00431383i
$603$	−0.354702	+	0.257706i	−0.0144446	+	0.0104946i
$604$	−0.0107610			−0.000437861
$605$		0			0
$606$	−1.28033			−0.0520098
$607$	−28.4967	+	20.7041i	−1.15665	+	0.840353i	−0.989350	−	0.145553i	$-0.953504\pi$
$607$	−28.4967	+	20.7041i	−1.15665	+	0.840353i	−0.167297	+	0.985907i	$0.553504\pi$
$608$	2.09763	+	6.45584i	0.0850701	+	0.261819i
$609$	6.81009	−	20.9593i	0.275959	−	0.849314i
$610$	−0.189313	−	0.137544i	−0.00766506	−	0.00556899i
$611$	−6.40086	−	4.65049i	−0.258951	−	0.188139i
$612$	−1.76160	+	5.42165i	−0.0712085	+	0.219157i
$613$	7.23461	+	22.2658i	0.292203	+	0.899309i	0.984147	+	0.177357i	$0.0567548\pi$
$613$	7.23461	+	22.2658i	0.292203	+	0.899309i	−0.691943	+	0.721952i	$0.743245\pi$
$614$	−2.05653	+	1.49416i	−0.0829948	+	0.0602993i
$615$	2.56276			0.103341
$616$		0			0
$617$	22.8910			0.921557			0.460778	−	0.887515i	$-0.347570\pi$
$617$	22.8910			0.921557			0.460778	+	0.887515i	$0.347570\pi$
$618$	−1.54411	+	1.12187i	−0.0621134	+	0.0451280i
$619$	0.657441	+	2.02339i	0.0264248	+	0.0813271i	0.963399	−	0.268071i	$-0.0863861\pi$
$619$	0.657441	+	2.02339i	0.0264248	+	0.0813271i	−0.936974	+	0.349398i	$0.886386\pi$
$620$	−1.10200	+	3.39161i	−0.0442574	+	0.136210i
$621$	−24.9014	−	18.0920i	−0.999260	−	0.726005i
$622$	−0.998521	−	0.725468i	−0.0400370	−	0.0290886i
$623$	−18.5502	+	57.0916i	−0.743198	+	2.28733i
$624$	2.04431	+	6.29173i	0.0818377	+	0.251871i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	−1.51223			−0.0604410
$627$		0			0
$628$	−1.10482			−0.0440873
$629$	4.06294	−	2.95190i	0.162000	−	0.117700i
$630$	−0.110960	−	0.341499i	−0.00442075	−	0.0136057i
$631$	4.77702	−	14.7022i	0.190170	−	0.585284i	−0.809829	−	0.586666i	$-0.800440\pi$
$631$	4.77702	−	14.7022i	0.190170	−	0.585284i	0.999999	+	0.00138227i	$0.000439991\pi$
$632$	−3.41296	−	2.47966i	−0.135760	−	0.0986357i
$633$	22.4987	+	16.3462i	0.894242	+	0.649705i
$634$	0.155494	−	0.478563i	0.00617547	−	0.0190062i
$635$	−6.10700	−	18.7954i	−0.242349	−	0.745873i
$636$	−3.40193	+	2.47164i	−0.134895	+	0.0980071i
$637$	15.3918			0.609844
$638$		0			0
$639$	9.10676			0.360258
$640$	−2.39444	+	1.73967i	−0.0946487	+	0.0687663i
$641$	4.38201	+	13.4864i	0.173079	+	0.532682i	0.999541	−	0.0303108i	$-0.00964970\pi$
$641$	4.38201	+	13.4864i	0.173079	+	0.532682i	−0.826461	+	0.562993i	$0.809650\pi$
$642$	−0.711537	+	2.18989i	−0.0280821	+	0.0864279i
$643$	10.0270	+	7.28504i	0.395426	+	0.287294i	0.767675	−	0.640839i	$-0.221413\pi$
$643$	10.0270	+	7.28504i	0.395426	+	0.287294i	−0.372249	+	0.928133i	$0.621413\pi$
$644$	39.7429	+	28.8749i	1.56609	+	1.13783i
$645$	0.119222	−	0.366928i	0.00469437	−	0.0144478i
$646$	−0.593101	−	1.82538i	−0.0233352	−	0.0718185i
$647$	−26.8970	+	19.5418i	−1.05743	+	0.768267i	−0.973611	−	0.228214i	$-0.926711\pi$
$647$	−26.8970	+	19.5418i	−1.05743	+	0.768267i	−0.0838181	+	0.996481i	$0.526711\pi$
$648$	−2.13991			−0.0840637
$649$		0			0
$650$	−0.106840			−0.00419063
$651$	9.61510	−	6.98578i	0.376846	−	0.273794i
$652$	4.90068	+	15.0827i	0.191925	+	0.590685i
$653$	−10.7558	+	33.1030i	−0.420908	+	1.29542i	0.485951	+	0.873986i	$0.338474\pi$
$653$	−10.7558	+	33.1030i	−0.420908	+	1.29542i	−0.906858	+	0.421435i	$0.861526\pi$
$654$	0.405329	+	0.294489i	0.0158496	+	0.0115154i
$655$	−1.56528	−	1.13724i	−0.0611604	−	0.0444356i
$656$	2.13145	−	6.55992i	0.0832191	−	0.256122i
$657$	−1.48997	−	4.58566i	−0.0581293	−	0.178904i
$658$	−2.37023	+	1.72207i	−0.0924011	+	0.0671334i
$659$	34.4953			1.34375			0.671873	−	0.740666i	$-0.265490\pi$
$659$	34.4953			1.34375			0.671873	+	0.740666i	$0.265490\pi$
$660$		0			0
$661$	1.77827			0.0691668			0.0345834	−	0.999402i	$-0.488990\pi$
$661$	1.77827			0.0691668			0.0345834	+	0.999402i	$0.488990\pi$
$662$	−1.40486	+	1.02069i	−0.0546014	+	0.0396702i
$663$	−1.74685	−	5.37626i	−0.0678421	−	0.208797i
$664$	−0.516788	+	1.59051i	−0.0200553	+	0.0617238i
$665$	−22.2728	−	16.1821i	−0.863701	−	0.627516i
$666$	−0.0955887	−	0.0694493i	−0.00370399	−	0.00269110i
$667$	5.59541	−	17.2209i	0.216655	−	0.666796i
$668$	2.10839	+	6.48896i	0.0815761	+	0.251065i
$669$	−5.79009	+	4.20675i	−0.223858	+	0.162642i
$670$	0.0483070			0.00186626
$671$		0			0
$672$	7.40331			0.285589
$673$	15.6111	−	11.3422i	0.601765	−	0.437208i	−0.244740	−	0.969589i	$-0.578703\pi$
$673$	15.6111	−	11.3422i	0.601765	−	0.437208i	0.846505	+	0.532381i	$0.178703\pi$
$674$	0.260243	+	0.800945i	0.0100242	+	0.0308513i
$675$	−1.74440	+	5.36872i	−0.0671421	+	0.206642i
$676$	−18.8395	−	13.6877i	−0.724595	−	0.526449i
$677$	−13.6805	−	9.93949i	−0.525786	−	0.382006i	0.292993	−	0.956114i	$-0.405349\pi$
$677$	−13.6805	−	9.93949i	−0.525786	−	0.382006i	−0.818779	+	0.574109i	$0.805349\pi$
$678$	0.504455	−	1.55255i	0.0193735	−	0.0596255i
$679$	4.69298	+	14.4435i	0.180100	+	0.554291i
$680$	1.01852	−	0.739998i	0.0390585	−	0.0283776i
$681$	−23.9412			−0.917430
$682$		0			0
$683$	4.14018			0.158420			0.0792098	−	0.996858i	$-0.474760\pi$
$683$	4.14018			0.158420			0.0792098	+	0.996858i	$0.474760\pi$
$684$	8.31920	−	6.04425i	0.318093	−	0.231108i
$685$	−3.87363	−	11.9218i	−0.148004	−	0.455509i
$686$	0.846069	−	2.60393i	0.0323031	−	0.0994186i
$687$	5.73331	+	4.16549i	0.218739	+	0.158923i
$688$	−0.840072	−	0.610348i	−0.0320274	−	0.0232693i
$689$	−0.508335	+	1.56450i	−0.0193660	+	0.0596025i
$690$	0.231096	+	0.711241i	0.00879769	+	0.0270765i
$691$	37.4996	−	27.2450i	1.42655	−	1.03645i	0.435904	−	0.899993i	$-0.356429\pi$
$691$	37.4996	−	27.2450i	1.42655	−	1.03645i	0.990646	−	0.136457i	$-0.0435714\pi$
$692$	40.9539			1.55684
$693$		0			0
$694$	0.960437			0.0364577
$695$	−9.09743	+	6.60967i	−0.345085	+	0.250719i
$696$	−0.561756	−	1.72891i	−0.0212933	−	0.0655340i
$697$	−1.82132	+	5.60543i	−0.0689872	+	0.212321i
$698$	−1.30583	−	0.948743i	−0.0494265	−	0.0359105i
$699$	−9.99096	−	7.25886i	−0.377893	−	0.274555i
$700$	2.78408	−	8.56853i	0.105228	−	0.323860i
$701$	14.0465	+	43.2306i	0.530528	+	1.63280i	0.753119	+	0.657884i	$0.228548\pi$
$701$	14.0465	+	43.2306i	0.530528	+	1.63280i	−0.222591	+	0.974912i	$0.571452\pi$
$702$	−0.487931	+	0.354502i	−0.0184158	+	0.0133798i
$703$	−9.05904			−0.341668
$704$		0			0
$705$	10.1567			0.382524
$706$	−1.72557	+	1.25370i	−0.0649428	+	0.0471837i
$707$	−13.0518	−	40.1692i	−0.490862	−	1.51072i
$708$	6.37915	−	19.6330i	0.239743	−	0.737853i
$709$	11.3458	+	8.24318i	0.426099	+	0.309579i	0.780087	−	0.625671i	$-0.215175\pi$
$709$	11.3458	+	8.24318i	0.426099	+	0.309579i	−0.353988	+	0.935250i	$0.615175\pi$
$710$	−0.811757	−	0.589776i	−0.0304647	−	0.0221339i
$711$	−2.96444	+	9.12360i	−0.111175	+	0.342162i
$712$	1.53018	+	4.70941i	0.0573460	+	0.176493i
$713$	7.90010	−	5.73976i	0.295861	−	0.214956i
$714$	−2.09327			−0.0783388
$715$		0			0
$716$	5.10622			0.190829
$717$	−26.9275	+	19.5640i	−1.00563	+	0.730630i
$718$	−0.464497	−	1.42957i	−0.0173349	−	0.0533512i
$719$	4.05999	−	12.4954i	0.151412	−	0.465998i	−0.846368	−	0.532599i	$-0.821215\pi$
$719$	4.05999	−	12.4954i	0.151412	−	0.465998i	0.997780	+	0.0666007i	$0.0212154\pi$
$720$	2.71047	+	1.96927i	0.101013	+	0.0733905i
$721$	−50.9383	−	37.0088i	−1.89704	−	1.37828i
$722$	−0.520835	+	1.60297i	−0.0193835	+	0.0596562i
$723$	−5.26057	−	16.1904i	−0.195643	−	0.602126i
$724$	21.6140	−	15.7035i	0.803279	−	0.583616i
$725$	−3.32083			−0.123333
$726$		0			0
$727$	−18.3635			−0.681063			−0.340532	−	0.940233i	$-0.610607\pi$
$727$	−18.3635			−0.681063			−0.340532	+	0.940233i	$0.610607\pi$
$728$	1.56090	−	1.13406i	0.0578509	−	0.0420312i
$729$	9.17943	+	28.2514i	0.339979	+	1.04635i
$730$	−0.164166	+	0.505250i	−0.00607604	+	0.0187001i
$731$	0.717839	+	0.521540i	0.0265502	+	0.0192899i
$732$	−5.91290	−	4.29598i	−0.218547	−	0.158784i
$733$	11.4329	−	35.1869i	0.422284	−	1.29966i	−0.483287	−	0.875462i	$-0.660557\pi$
$733$	11.4329	−	35.1869i	0.422284	−	1.29966i	0.905571	−	0.424195i	$-0.139443\pi$
$734$	−0.635642	−	1.95631i	−0.0234620	−	0.0722086i
$735$	−15.9852	+	11.6139i	−0.589623	+	0.428387i
$736$	6.08282			0.224216
$737$		0			0
$738$	0.138666			0.00510435
$739$	7.96909	−	5.78988i	0.293148	−	0.212984i	−0.431484	−	0.902121i	$-0.642010\pi$
$739$	7.96909	−	5.78988i	0.293148	−	0.212984i	0.724632	+	0.689136i	$0.242010\pi$
$740$	−0.916110	−	2.81950i	−0.0336769	−	0.103647i
$741$	−3.15105	+	9.69793i	−0.115757	+	0.356262i
$742$	0.492808	+	0.358046i	0.0180915	+	0.0131443i
$743$	22.2052	+	16.1330i	0.814629	+	0.591862i	0.915169	−	0.403071i	$-0.132057\pi$
$743$	22.2052	+	16.1330i	0.814629	+	0.591862i	−0.100540	+	0.994933i	$0.532057\pi$
$744$	0.302951	−	0.932388i	0.0111067	−	0.0341830i
$745$	5.35640	+	16.4853i	0.196243	+	0.603974i
$746$	1.53272	−	1.11359i	0.0561170	−	0.0407714i
$747$	3.80291			0.139141
$748$		0			0
$749$	−75.9591			−2.77549
$750$	0.110960	−	0.0806171i	0.00405168	−	0.00294372i
$751$	4.24232	+	13.0565i	0.154804	+	0.476439i	0.998141	−	0.0609469i	$-0.0194120\pi$
$751$	4.24232	+	13.0565i	0.154804	+	0.476439i	−0.843337	+	0.537385i	$0.819412\pi$
$752$	8.44732	−	25.9982i	0.308042	−	0.948056i
$753$	−3.93131	−	2.85626i	−0.143265	−	0.104088i
$754$	−0.287039	−	0.208546i	−0.0104533	−	0.00759479i
$755$	0.00166997	−	0.00513965i	6.07766e−5	−	0.000187051i
$756$	−15.7162	−	48.3694i	−0.571592	−	1.75918i
$757$	18.5507	−	13.4779i	0.674236	−	0.489861i	−0.197205	−	0.980362i	$-0.563186\pi$
$757$	18.5507	−	13.4779i	0.674236	−	0.489861i	0.871440	+	0.490501i	$0.163186\pi$
$758$	0.348578			0.0126609
$759$		0			0
$760$	−2.27097			−0.0823767
$761$	−16.7319	+	12.1565i	−0.606533	+	0.440672i	−0.848192	−	0.529689i	$-0.822308\pi$
$761$	−16.7319	+	12.1565i	−0.606533	+	0.440672i	0.241659	+	0.970361i	$0.422308\pi$
$762$	0.837599	+	2.57786i	0.0303430	+	0.0933861i
$763$	−5.10737	+	15.7189i	−0.184899	+	0.569061i
$764$	29.3031	+	21.2899i	1.06015	+	0.770243i
$765$	−2.31609	−	1.68274i	−0.0837385	−	0.0608395i
$766$	0.317783	−	0.978034i	0.0114819	−	0.0353378i
$767$	−2.49553	−	7.68046i	−0.0901084	−	0.277325i
$768$	−18.1611	+	13.1948i	−0.655334	+	0.476128i
$769$	−38.4306			−1.38584			−0.692922	−	0.721013i	$-0.743677\pi$
$769$	−38.4306			−1.38584			−0.692922	+	0.721013i	$0.743677\pi$
$770$		0			0
$771$	−39.3768			−1.41812
$772$	−25.2738	+	18.3625i	−0.909624	+	0.660880i
$773$	15.4325	+	47.4964i	0.555069	+	1.70833i	0.695762	+	0.718272i	$0.255067\pi$
$773$	15.4325	+	47.4964i	0.555069	+	1.70833i	−0.140693	+	0.990053i	$0.544933\pi$
$774$	0.00645085	−	0.0198537i	0.000231871	−	0.000713626i
$775$	−1.44887	−	1.05267i	−0.0520451	−	0.0378129i
$776$	1.01349	+	0.736341i	0.0363821	+	0.0264331i
$777$	−3.05312	+	9.39654i	−0.109530	+	0.337099i
$778$	−0.271109	−	0.834389i	−0.00971975	−	0.0299143i
$779$	8.60121	−	6.24914i	0.308170	−	0.223899i
$780$	−3.33700			−0.119484
$781$		0			0
$782$	−1.71991			−0.0615037
$783$	−15.1659	+	11.0187i	−0.541986	+	0.393776i
$784$	16.4334	+	50.5767i	0.586906	+	1.80631i
$785$	0.171454	−	0.527682i	0.00611946	−	0.0188338i
$786$	0.214684	+	0.155977i	0.00765751	+	0.00556351i
$787$	−12.5834	−	9.14241i	−0.448551	−	0.325892i	0.340472	−	0.940255i	$-0.389413\pi$
$787$	−12.5834	−	9.14241i	−0.448551	−	0.325892i	−0.789024	+	0.614363i	$0.789413\pi$
$788$	−13.4442	+	41.3769i	−0.478928	+	1.47399i
$789$	−5.51518	−	16.9740i	−0.196346	−	0.604290i
$790$	0.855110	−	0.621274i	0.0304235	−	0.0221039i
$791$	53.8524			1.91477
$792$		0			0
$793$	−2.85919			−0.101533
$794$	1.68805	−	1.22644i	0.0599067	−	0.0435248i
$795$	−0.652563	−	2.00838i	−0.0231440	−	0.0712300i
$796$	2.80099	−	8.62057i	0.0992786	−	0.305548i
$797$	−37.3012	−	27.1009i	−1.32127	−	0.959962i	−0.999915	−	0.0130049i	$-0.995860\pi$
$797$	−37.3012	−	27.1009i	−1.32127	−	0.959962i	−0.321359	−	0.946957i	$-0.604140\pi$
$798$	3.05480	+	2.21944i	0.108139	+	0.0785674i
$799$	−7.21821	+	22.2154i	−0.255362	+	0.785923i
$800$	−0.344735	−	1.06098i	−0.0121882	−	0.0375114i
$801$	9.10970	−	6.61858i	0.321875	−	0.233856i
$802$	2.30803			0.0814994
$803$		0			0
$804$	1.50879			0.0532111
$805$	−19.9587	+	14.5009i	−0.703453	+	0.511088i
$806$	−0.0591277	−	0.181976i	−0.00208268	−	0.00640984i
$807$	−0.948873	+	2.92033i	−0.0334019	+	0.102801i
$808$	−2.81863	−	2.04786i	−0.0991591	−	0.0720433i
$809$	−30.3700	−	22.0651i	−1.06775	−	0.775767i	−0.0922454	−	0.995736i	$-0.529404\pi$
$809$	−30.3700	−	22.0651i	−1.06775	−	0.775767i	−0.975507	+	0.219969i	$0.929404\pi$
$810$	0.165679	−	0.509909i	0.00582138	−	0.0179164i
$811$	−2.22661	−	6.85281i	−0.0781870	−	0.240635i	0.904322	−	0.426852i	$-0.140377\pi$
$811$	−2.22661	−	6.85281i	−0.0781870	−	0.240635i	−0.982509	+	0.186217i	$0.940377\pi$
$812$	24.2050	−	17.5859i	0.849428	−	0.617146i
$813$	−22.2104			−0.778953
$814$		0			0
$815$	−7.96428			−0.278977
$816$	15.8011	−	11.4802i	0.553150	−	0.401887i
$817$	−0.494596	−	1.52221i	−0.0173037	−	0.0532554i
$818$	0.852597	−	2.62402i	0.0298104	−	0.0917469i
$819$	−3.54946	−	2.57883i	−0.124028	−	0.0901117i
$820$	2.81477	+	2.04505i	0.0982960	+	0.0714162i
$821$	2.66807	−	8.21147i	0.0931163	−	0.286582i	−0.893642	−	0.448781i	$-0.851858\pi$
$821$	2.66807	−	8.21147i	0.0931163	−	0.286582i	0.986758	+	0.162198i	$0.0518584\pi$
$822$	0.531284	+	1.63512i	0.0185306	+	0.0570315i
$823$	20.2352	−	14.7017i	0.705354	−	0.512470i	−0.176318	−	0.984333i	$-0.556419\pi$
$823$	20.2352	−	14.7017i	0.705354	−	0.512470i	0.881672	+	0.471864i	$0.156419\pi$
$824$	−5.19375			−0.180933
$825$		0			0
$826$	−2.99042			−0.104050
$827$	39.5387	−	28.7265i	1.37489	−	0.998919i	0.377558	−	0.925986i	$-0.376764\pi$
$827$	39.5387	−	28.7265i	1.37489	−	0.998919i	0.997337	−	0.0729332i	$-0.0232360\pi$
$828$	−2.84751	−	8.76373i	−0.0989577	−	0.304561i
$829$	1.63522	−	5.03270i	0.0567937	−	0.174793i	−0.918636	−	0.395106i	$-0.870708\pi$
$829$	1.63522	−	5.03270i	0.0567937	−	0.174793i	0.975429	+	0.220313i	$0.0707079\pi$
$830$	−0.338983	−	0.246286i	−0.0117663	−	0.00854871i
$831$	9.81405	+	7.13033i	0.340446	+	0.247348i
$832$	−2.75073	+	8.46589i	−0.0953645	+	0.293502i
$833$	−14.0423	−	43.2177i	−0.486536	−	1.49740i
$834$	1.24775	−	0.906543i	0.0432060	−	0.0313910i
$835$	−3.42643			−0.118576
$836$		0			0
$837$	−10.1097			−0.349441
$838$	0.683556	−	0.496633i	0.0236131	−	0.0171559i
$839$	−4.09196	−	12.5938i	−0.141270	−	0.434785i	0.855242	−	0.518228i	$-0.173408\pi$
$839$	−4.09196	−	12.5938i	−0.141270	−	0.434785i	−0.996513	+	0.0834435i	$0.973408\pi$
$840$	−0.765373	+	2.35558i	−0.0264079	+	0.0812751i
$841$	14.5397	+	10.5637i	0.501369	+	0.364266i
$842$	1.07577	+	0.781592i	0.0370734	+	0.0269354i
$843$	−1.10919	+	3.41375i	−0.0382026	+	0.117576i
$844$	11.6670	+	35.9072i	0.401593	+	1.23598i
$845$	9.46110	−	6.87389i	0.325472	−	0.236469i
$846$	0.549557			0.0188942
$847$		0			0
$848$	−5.68361			−0.195176
$849$	30.9643	−	22.4969i	1.06269	−	0.772092i
$850$	0.0974731	+	0.299991i	0.00334330	+	0.0102896i
$851$	−2.50855	+	7.72053i	−0.0859920	+	0.264656i
$852$	−25.3540	−	18.4208i	−0.868614	−	0.631085i
$853$	1.79509	+	1.30421i	0.0614626	+	0.0446552i	0.618092	−	0.786106i	$-0.287906\pi$
$853$	1.79509	+	1.30421i	0.0614626	+	0.0446552i	−0.556630	+	0.830761i	$0.687906\pi$
$854$	−0.327174	+	1.00694i	−0.0111956	+	0.0344567i
$855$	1.59580	+	4.91138i	0.0545753	+	0.167966i
$856$	−5.06911	+	3.68292i	−0.173259	+	0.125880i
$857$	−31.4625			−1.07474			−0.537368	−	0.843348i	$-0.680582\pi$
$857$	−31.4625			−1.07474			−0.537368	+	0.843348i	$0.680582\pi$
$858$		0			0
$859$	9.07676			0.309695			0.154848	−	0.987938i	$-0.450511\pi$
$859$	9.07676			0.309695			0.154848	+	0.987938i	$0.450511\pi$
$860$	0.423749	−	0.307872i	0.0144497	−	0.0104983i
$861$	−3.58314	−	11.0278i	−0.122113	−	0.375826i
$862$	−0.0500352	+	0.153993i	−0.00170421	+	0.00524501i
$863$	−34.3704	−	24.9716i	−1.16998	−	0.850042i	−0.178976	−	0.983853i	$-0.557279\pi$
$863$	−34.3704	−	24.9716i	−1.16998	−	0.850042i	−0.991007	+	0.133811i	$0.957279\pi$
$864$	−5.09477	−	3.70157i	−0.173328	−	0.125930i
$865$	−6.35552	+	19.5603i	−0.216094	+	0.665069i
$866$	−0.533065	−	1.64060i	−0.0181143	−	0.0557500i
$867$	6.67038	−	4.84632i	0.226538	−	0.164590i
$868$	16.1351			0.547662
$869$		0			0
$870$	0.455465			0.0154417
$871$	0.477516	−	0.346936i	0.0161800	−	0.0117555i
$872$	0.421300	+	1.29663i	0.0142670	+	0.0439094i
$873$	0.880296	−	2.70927i	0.0297935	−	0.0916950i
$874$	2.50993	+	1.82357i	0.0848996	+	0.0616832i
$875$	3.66042	+	2.65945i	0.123745	+	0.0899058i
$876$	−5.12746	+	15.7807i	−0.173241	+	0.533181i
$877$	9.67537	+	29.7777i	0.326714	+	1.00552i	0.970661	+	0.240452i	$0.0772957\pi$
$877$	9.67537	+	29.7777i	0.326714	+	1.00552i	−0.643947	+	0.765070i	$0.722704\pi$
$878$	1.29896	−	0.943750i	0.0438378	−	0.0318500i
$879$	−19.7319			−0.665539
$880$		0			0
$881$	21.5189			0.724990			0.362495	−	0.931986i	$-0.381925\pi$
$881$	21.5189			0.724990			0.362495	+	0.931986i	$0.381925\pi$
$882$	−0.864925	+	0.628405i	−0.0291235	+	0.0211595i
$883$	−0.201650	−	0.620614i	−0.00678605	−	0.0208853i	0.947606	−	0.319441i	$-0.103495\pi$
$883$	−0.201650	−	0.620614i	−0.00678605	−	0.0208853i	−0.954392	+	0.298556i	$0.903495\pi$
$884$	2.37155	−	7.29889i	0.0797639	−	0.245488i
$885$	8.38708	+	6.09357i	0.281929	+	0.204833i
$886$	2.76877	+	2.01163i	0.0930187	+	0.0675820i
$887$	4.52593	−	13.9294i	0.151966	−	0.467702i	−0.845875	−	0.533381i	$-0.820921\pi$
$887$	4.52593	−	13.9294i	0.151966	−	0.467702i	0.997841	+	0.0656786i	$0.0209212\pi$
$888$	0.251848	+	0.775108i	0.00845146	+	0.0260109i
$889$	−72.3396	+	52.5578i	−2.42619	+	1.76273i
$890$	−1.24065			−0.0415868
$891$		0			0
$892$	−9.71637			−0.325328
$893$	34.0882	−	24.7665i	1.14072	−	0.828780i
$894$	−0.734651	−	2.26102i	−0.0245704	−	0.0756199i
$895$	−0.792419	+	2.43882i	−0.0264877	+	0.0815206i
$896$	10.8337	+	7.87116i	0.361929	+	0.262957i
$897$	7.39246	+	5.37094i	0.246827	+	0.179330i
$898$	0.479760	−	1.47655i	0.0160098	−	0.0492731i
$899$	−1.83782	−	5.65622i	−0.0612946	−	0.188645i
$900$	−1.36722	+	0.993342i	−0.0455739	+	0.0331114i
$901$	4.85662			0.161798
$902$		0			0
$903$	−1.74561			−0.0580903
$904$	3.59382	−	2.61107i	0.119529	−	0.0868428i
$905$	4.14604	+	12.7602i	0.137819	+	0.424163i
$906$	−0.000229044	0	0.000704924i	−7.60946e−6	0	2.34195e-5i
$907$	−23.2552	−	16.8959i	−0.772175	−	0.561018i	0.130445	−	0.991456i	$-0.458359\pi$
$907$	−23.2552	−	16.8959i	−0.772175	−	0.561018i	−0.902620	+	0.430437i	$0.858359\pi$
$908$	−26.2955	−	19.1048i	−0.872645	−	0.634014i
$909$	−2.44821	+	7.53482i	−0.0812020	+	0.249914i
$910$	0.149380	+	0.459743i	0.00495188	+	0.0152403i
$911$	−13.9813	+	10.1580i	−0.463222	+	0.336550i	−0.794794	−	0.606880i	$-0.792421\pi$
$911$	−13.9813	+	10.1580i	−0.463222	+	0.336550i	0.331572	+	0.943430i	$0.392421\pi$
$912$	−35.2313			−1.16663
$913$		0			0
$914$	−2.96102			−0.0979418
$915$	2.96943	−	2.15742i	0.0981665	−	0.0713221i
$916$	2.97308	+	9.15020i	0.0982333	+	0.302331i
$917$	−2.70513	+	8.32554i	−0.0893313	+	0.274933i
$918$	1.44054	+	1.04661i	0.0475448	+	0.0345433i
$919$	−1.77859	−	1.29222i	−0.0586701	−	0.0426263i	0.558064	−	0.829798i	$-0.311544\pi$
$919$	−1.77859	−	1.29222i	−0.0586701	−	0.0426263i	−0.616734	+	0.787172i	$0.711544\pi$
$920$	−0.628857	+	1.93542i	−0.0207328	+	0.0638090i
$921$	−12.3212	−	37.9208i	−0.405997	−	1.24953i
$922$	1.92419	−	1.39801i	0.0633699	−	0.0460409i
$923$	−12.2600			−0.403542
$924$		0			0
$925$	1.48881			0.0489517
$926$	−1.23552	+	0.897661i	−0.0406019	+	0.0294990i
$927$	3.64963	+	11.2324i	0.119870	+	0.368921i
$928$	1.14481	−	3.52335i	0.0375801	−	0.115660i
$929$	−19.5866	−	14.2305i	−0.642616	−	0.466888i	0.218132	−	0.975919i	$-0.430004\pi$
$929$	−19.5866	−	14.2305i	−0.642616	−	0.466888i	−0.860748	+	0.509031i	$0.830004\pi$
$930$	0.198719	+	0.144378i	0.00651624	+	0.00473433i
$931$	−25.3301	+	77.9579i	−0.830159	+	2.55497i
$932$	−5.18094	−	15.9453i	−0.169707	−	0.522305i
$933$	15.6621	−	11.3792i	0.512754	−	0.372538i
$934$	−0.797556			−0.0260968
$935$		0			0
$936$	−0.361908			−0.0118293
$937$	−16.8459	+	12.2393i	−0.550333	+	0.399840i	−0.827908	−	0.560864i	$-0.810469\pi$
$937$	−16.8459	+	12.2393i	−0.550333	+	0.399840i	0.277575	+	0.960704i	$0.410469\pi$
$938$	−0.0675407	−	0.207869i	−0.00220528	−	0.00678716i
$939$	7.32984	−	22.5589i	0.239200	−	0.736183i
$940$	11.1554	+	8.10491i	0.363851	+	0.264353i
$941$	27.6787	+	20.1098i	0.902301	+	0.655560i	0.939056	−	0.343764i	$-0.111702\pi$
$941$	27.6787	+	20.1098i	0.902301	+	0.655560i	−0.0367552	+	0.999324i	$0.511702\pi$
$942$	−0.0235156	+	0.0723736i	−0.000766180	+	0.00235806i
$943$	−2.94403	−	9.06080i	−0.0958709	−	0.295060i
$944$	22.5733	−	16.4004i	0.734697	−	0.533789i
$945$	25.5410			0.830848
$946$		0			0
$947$	33.8128			1.09877			0.549383	−	0.835570i	$-0.314863\pi$
$947$	33.8128			1.09877			0.549383	+	0.835570i	$0.314863\pi$
$948$	26.7081	−	19.4045i	0.867438	−	0.630230i
$949$	2.00587	+	6.17344i	0.0651133	+	0.200398i
$950$	0.175826	−	0.541138i	0.00570456	−	0.0175568i
$951$	6.38533	+	4.63921i	0.207058	+	0.150437i
$952$	−4.60832	−	3.34814i	−0.149356	−	0.108514i
$953$	−7.91027	+	24.3453i	−0.256239	+	0.788622i	0.737344	+	0.675517i	$0.236080\pi$
$953$	−7.91027	+	24.3453i	−0.256239	+	0.788622i	−0.993583	+	0.113105i	$0.963920\pi$
$954$	−0.0353088	−	0.108669i	−0.00114316	−	0.00351830i
$955$	−14.7159	+	10.6917i	−0.476195	+	0.345976i
$956$	−45.1871			−1.46146
$957$		0			0
$958$	2.80042			0.0904774
$959$	−45.8845	+	33.3371i	−1.48169	+	1.07651i
$960$	−3.53119	−	10.8679i	−0.113969	−	0.350759i
$961$	−8.58840	+	26.4324i	−0.277045	+	0.852658i
$962$	0.128686	+	0.0934959i	0.00414901	+	0.00301443i
$963$	11.5270	+	8.37488i	0.371454	+	0.269877i
$964$	7.14182	−	21.9803i	0.230023	−	0.707937i
$965$	−4.84806	−	14.9208i	−0.156065	−	0.480317i
$966$	2.73742	−	1.98885i	0.0880750	−	0.0639902i
$967$	−43.8942			−1.41154			−0.705772	−	0.708439i	$-0.749400\pi$
$967$	−43.8942			−1.41154			−0.705772	+	0.708439i	$0.749400\pi$
$968$		0			0
$969$	30.1051			0.967114
$970$	−0.253927	+	0.184489i	−0.00815310	+	0.00592357i
$971$	11.2392	+	34.5906i	0.360682	+	1.11006i	0.952641	+	0.304097i	$0.0983547\pi$
$971$	11.2392	+	34.5906i	0.360682	+	1.11006i	−0.591959	+	0.805968i	$0.701645\pi$
$972$	−5.24591	+	16.1453i	−0.168263	+	0.517860i
$973$	41.1616	+	29.9056i	1.31958	+	0.958730i
$974$	−1.48299	−	1.07746i	−0.0475182	−	0.0345240i
$975$	0.517859	−	1.59381i	0.0165848	−	0.0510426i
$976$	−3.05269	−	9.39520i	−0.0977141	−	0.300733i
$977$	−8.37462	+	6.08452i	−0.267928	+	0.194661i	−0.713635	−	0.700518i	$-0.752952\pi$
$977$	−8.37462	+	6.08452i	−0.267928	+	0.194661i	0.445707	+	0.895179i	$0.352952\pi$
$978$	1.09233			0.0349289
$979$		0			0
$980$	−26.8248			−0.856888
$981$	2.50814	−	1.82227i	0.0800789	−	0.0581807i
$982$	−0.456245	−	1.40418i	−0.0145594	−	0.0448091i
$983$	−6.83416	+	21.0334i	−0.217976	+	0.670861i	0.780953	+	0.624590i	$0.214734\pi$
$983$	−6.83416	+	21.0334i	−0.217976	+	0.670861i	−0.998929	+	0.0462712i	$0.985266\pi$
$984$	−0.773808	−	0.562205i	−0.0246681	−	0.0179224i
$985$	−17.6759	−	12.8423i	−0.563201	−	0.409190i
$986$	−0.323692	+	0.996222i	−0.0103085	+	0.0317262i
$987$	−14.2006	−	43.7051i	−0.452012	−	1.39115i
$988$	−11.1997	+	8.13707i	−0.356310	+	0.258875i
$989$	−1.43426			−0.0456067
$990$		0			0
$991$	−55.5911			−1.76591			−0.882955	−	0.469457i	$-0.844450\pi$
$991$	−55.5911			−1.76591			−0.882955	+	0.469457i	$0.844450\pi$
$992$	1.61634	−	1.17434i	0.0513189	−	0.0372853i
$993$	−8.41687	−	25.9044i	−0.267101	−	0.822053i
$994$	−1.40289	+	4.31765i	−0.0444970	+	0.136948i
$995$	3.68265	+	2.67560i	0.116748	+	0.0848222i
$996$	−10.5876	−	7.69236i	−0.335482	−	0.243742i
$997$	−3.33465	+	10.2630i	−0.105609	+	0.325032i	−0.989873	−	0.141956i	$-0.954661\pi$
$997$	−3.33465	+	10.2630i	−0.105609	+	0.325032i	0.884264	+	0.466988i	$0.154661\pi$
$998$	−0.323872	−	0.996775i	−0.0102520	−	0.0315524i
$999$	6.79924	−	4.93994i	0.215118	−	0.156293i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.n.366.1		8
11.2	odd	10		605.2.a.l.1.2		4
11.3	even	5		605.2.g.g.511.2		8
11.4	even	5	inner	605.2.g.n.81.1		8
11.5	even	5		605.2.g.g.251.2		8
11.6	odd	10		605.2.g.j.251.1		8
11.7	odd	10		55.2.g.a.26.2	✓	8
11.8	odd	10		605.2.g.j.511.1		8
11.9	even	5		605.2.a.i.1.3		4
11.10	odd	2		55.2.g.a.36.2	yes	8
33.2	even	10		5445.2.a.bg.1.3		4
33.20	odd	10		5445.2.a.bu.1.2		4
33.29	even	10		495.2.n.f.136.1		8
33.32	even	2		495.2.n.f.91.1		8
44.7	even	10		880.2.bo.e.81.1		8
44.31	odd	10		9680.2.a.cv.1.1		4
44.35	even	10		9680.2.a.cs.1.1		4
44.43	even	2		880.2.bo.e.641.1		8
55.7	even	20		275.2.z.b.224.3		16
55.9	even	10		3025.2.a.be.1.2		4
55.18	even	20		275.2.z.b.224.2		16
55.24	odd	10		3025.2.a.v.1.3		4
55.29	odd	10		275.2.h.b.26.1		8
55.32	even	4		275.2.z.b.124.2		16
55.43	even	4		275.2.z.b.124.3		16
55.54	odd	2		275.2.h.b.201.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.a.26.2	✓	8	11.7	odd	10
55.2.g.a.36.2	yes	8	11.10	odd	2
275.2.h.b.26.1		8	55.29	odd	10
275.2.h.b.201.1		8	55.54	odd	2
275.2.z.b.124.2		16	55.32	even	4
275.2.z.b.124.3		16	55.43	even	4
275.2.z.b.224.2		16	55.18	even	20
275.2.z.b.224.3		16	55.7	even	20
495.2.n.f.91.1		8	33.32	even	2
495.2.n.f.136.1		8	33.29	even	10
605.2.a.i.1.3		4	11.9	even	5
605.2.a.l.1.2		4	11.2	odd	10
605.2.g.g.251.2		8	11.5	even	5
605.2.g.g.511.2		8	11.3	even	5
605.2.g.j.251.1		8	11.6	odd	10
605.2.g.j.511.1		8	11.8	odd	10
605.2.g.n.81.1		8	11.4	even	5	inner
605.2.g.n.366.1		8	1.1	even	1	trivial
880.2.bo.e.81.1		8	44.7	even	10
880.2.bo.e.641.1		8	44.43	even	2
3025.2.a.v.1.3		4	55.24	odd	10
3025.2.a.be.1.2		4	55.9	even	10
5445.2.a.bg.1.3		4	33.2	even	10
5445.2.a.bu.1.2		4	33.20	odd	10
9680.2.a.cs.1.1		4	44.35	even	10
9680.2.a.cv.1.1		4	44.31	odd	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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0756511 - 0.0549637i) q^{2} +(0.453245 + 1.39494i) q^{3} +(-0.615332 + 1.89380i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.110960 + 0.0806171i) q^{6} +(-1.39815 + 4.30308i) q^{7} +(0.115332 + 0.354955i) q^{8} +(0.686611 - 0.498852i) q^{9} +O(q^{10})\)	\(q+(0.0756511 - 0.0549637i) q^{2} +(0.453245 + 1.39494i) q^{3} +(-0.615332 + 1.89380i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.110960 + 0.0806171i) q^{6} +(-1.39815 + 4.30308i) q^{7} +(0.115332 + 0.354955i) q^{8} +(0.686611 - 0.498852i) q^{9} -0.0935099 q^{10} -2.92064 q^{12} +(-0.924349 + 0.671579i) q^{13} +(0.130741 + 0.402380i) q^{14} +(0.453245 - 1.39494i) q^{15} +(-3.19369 - 2.32035i) q^{16} +(2.72899 + 1.98273i) q^{17} +(0.0245241 - 0.0754774i) q^{18} +(-1.88030 - 5.78696i) q^{19} +(1.61096 - 1.17043i) q^{20} -6.63626 q^{21} -5.45258 q^{23} +(-0.442869 + 0.321763i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-0.0330155 + 0.101611i) q^{26} +(4.56691 + 3.31805i) q^{27} +(-7.28883 - 5.29564i) q^{28} +(-1.02619 + 3.15830i) q^{29} +(-0.0423829 - 0.130441i) q^{30} +(-1.44887 + 1.05267i) q^{31} -1.11558 q^{32} +0.315430 q^{34} +(3.66042 - 2.65945i) q^{35} +(0.522231 + 1.60726i) q^{36} +(0.460067 - 1.41594i) q^{37} +(-0.460319 - 0.334441i) q^{38} +(-1.35577 - 0.985026i) q^{39} +(0.115332 - 0.354955i) q^{40} +(0.539933 + 1.66174i) q^{41} +(-0.502041 + 0.364754i) q^{42} +0.263041 q^{43} -0.848698 q^{45} +(-0.412494 + 0.299694i) q^{46} +(2.13986 + 6.58580i) q^{47} +(1.78924 - 5.50670i) q^{48} +(-10.8985 - 7.91824i) q^{49} +(0.0756511 + 0.0549637i) q^{50} +(-1.52890 + 4.70546i) q^{51} +(-0.703052 - 2.16377i) q^{52} +(1.16479 - 0.846269i) q^{53} +0.527864 q^{54} -1.68865 q^{56} +(7.22025 - 5.24582i) q^{57} +(0.0959593 + 0.295332i) q^{58} +(-2.18416 + 6.72216i) q^{59} +(2.36285 + 1.71671i) q^{60} +(2.02452 + 1.47090i) q^{61} +(-0.0517503 + 0.159271i) q^{62} +(1.18661 + 3.65201i) q^{63} +(6.30297 - 4.57938i) q^{64} +1.14256 q^{65} -0.516598 q^{67} +(-5.43413 + 3.94812i) q^{68} +(-2.47136 - 7.60605i) q^{69} +(0.130741 - 0.402380i) q^{70} +(8.68098 + 6.30710i) q^{71} +(0.256258 + 0.186183i) q^{72} +(1.75560 - 5.40317i) q^{73} +(-0.0430208 - 0.132404i) q^{74} +(-1.18661 + 0.862123i) q^{75} +12.1163 q^{76} -0.156706 q^{78} +(-9.14460 + 6.64394i) q^{79} +(1.21988 + 3.75440i) q^{80} +(-1.77179 + 5.45300i) q^{81} +(0.132182 + 0.0960360i) q^{82} +(3.62511 + 2.63380i) q^{83} +(4.08350 - 12.5677i) q^{84} +(-1.04238 - 3.20812i) q^{85} +(0.0198994 - 0.0144577i) q^{86} -4.87077 q^{87} +13.2676 q^{89} +(-0.0642049 + 0.0466476i) q^{90} +(-1.59747 - 4.91652i) q^{91} +(3.35515 - 10.3261i) q^{92} +(-2.12511 - 1.54398i) q^{93} +(0.523863 + 0.380608i) q^{94} +(-1.88030 + 5.78696i) q^{95} +(-0.505633 - 1.55618i) q^{96} +(2.71551 - 1.97293i) q^{97} -1.25970 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + q^{3} - 6 q^{4} - 2 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 5 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 + q^3 - 6 * q^4 - 2 * q^5 - 13 * q^6 + 3 * q^7 + 2 * q^8 - 5 * q^9	\( 8 q + 4 q^{2} + q^{3} - 6 q^{4} - 2 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 5 q^{9} - 6 q^{10} - 28 q^{12} - 4 q^{13} + 16 q^{14} + q^{15} - 20 q^{16} - q^{17} - 14 q^{18} + q^{19} - q^{20} + 12 q^{21} - 18 q^{23} - 25 q^{24} - 2 q^{25} - 14 q^{26} + 10 q^{27} - 4 q^{28} - 19 q^{29} + 12 q^{30} + 6 q^{31} - 12 q^{32} - 20 q^{34} + 8 q^{35} + 21 q^{36} + 4 q^{37} - 6 q^{38} - 9 q^{39} + 2 q^{40} + 4 q^{41} + 29 q^{42} - 42 q^{43} + 41 q^{46} + 4 q^{47} - 19 q^{48} - 15 q^{49} + 4 q^{50} - 13 q^{51} + 26 q^{52} + 3 q^{53} + 40 q^{54} + 30 q^{56} + 5 q^{57} - 6 q^{58} - 19 q^{59} + 22 q^{60} + 2 q^{61} + 38 q^{62} - q^{63} + 6 q^{64} - 14 q^{65} - 2 q^{67} - 35 q^{68} - 21 q^{69} + 16 q^{70} + 40 q^{71} + 34 q^{72} + 23 q^{73} - 48 q^{74} + q^{75} - 16 q^{76} + 12 q^{78} - 17 q^{79} + 15 q^{80} + 2 q^{82} + 25 q^{83} + 4 q^{84} + 4 q^{85} - 31 q^{86} - 30 q^{87} + 16 q^{90} - 12 q^{91} + 81 q^{92} - 13 q^{93} - 33 q^{94} + q^{95} - 23 q^{96} + 12 q^{97} + 84 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 + q^3 - 6 * q^4 - 2 * q^5 - 13 * q^6 + 3 * q^7 + 2 * q^8 - 5 * q^9 - 6 * q^10 - 28 * q^12 - 4 * q^13 + 16 * q^14 + q^15 - 20 * q^16 - q^17 - 14 * q^18 + q^19 - q^20 + 12 * q^21 - 18 * q^23 - 25 * q^24 - 2 * q^25 - 14 * q^26 + 10 * q^27 - 4 * q^28 - 19 * q^29 + 12 * q^30 + 6 * q^31 - 12 * q^32 - 20 * q^34 + 8 * q^35 + 21 * q^36 + 4 * q^37 - 6 * q^38 - 9 * q^39 + 2 * q^40 + 4 * q^41 + 29 * q^42 - 42 * q^43 + 41 * q^46 + 4 * q^47 - 19 * q^48 - 15 * q^49 + 4 * q^50 - 13 * q^51 + 26 * q^52 + 3 * q^53 + 40 * q^54 + 30 * q^56 + 5 * q^57 - 6 * q^58 - 19 * q^59 + 22 * q^60 + 2 * q^61 + 38 * q^62 - q^63 + 6 * q^64 - 14 * q^65 - 2 * q^67 - 35 * q^68 - 21 * q^69 + 16 * q^70 + 40 * q^71 + 34 * q^72 + 23 * q^73 - 48 * q^74 + q^75 - 16 * q^76 + 12 * q^78 - 17 * q^79 + 15 * q^80 + 2 * q^82 + 25 * q^83 + 4 * q^84 + 4 * q^85 - 31 * q^86 - 30 * q^87 + 16 * q^90 - 12 * q^91 + 81 * q^92 - 13 * q^93 - 33 * q^94 + q^95 - 23 * q^96 + 12 * q^97 + 84 * q^98

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