LMFDB - Embedded newform 275.2.h.b.26.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,2,Mod(26,275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(275, 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("275.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.h (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:	$2.19588605559$
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			26.1
Root			$0.453245 - 1.39494i$ of defining polynomial
Character	$\chi$	$=$	275.26
Dual form			275.2.h.b.201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0756511 + 0.0549637i) q^{2} +(-0.453245 + 1.39494i) q^{3} +(-0.615332 - 1.89380i) q^{4} +(-0.110960 + 0.0806171i) q^{6} +(-1.39815 - 4.30308i) q^{7} +(0.115332 - 0.354955i) q^{8} +(0.686611 + 0.498852i) q^{9} +O(q^{10})$	\(q+(0.0756511 + 0.0549637i) q^{2} +(-0.453245 + 1.39494i) q^{3} +(-0.615332 - 1.89380i) q^{4} +(-0.110960 + 0.0806171i) q^{6} +(-1.39815 - 4.30308i) q^{7} +(0.115332 - 0.354955i) q^{8} +(0.686611 + 0.498852i) q^{9} +(-2.39815 - 2.29104i) q^{11} +2.92064 q^{12} +(-0.924349 - 0.671579i) q^{13} +(0.130741 - 0.402380i) q^{14} +(-3.19369 + 2.32035i) q^{16} +(2.72899 - 1.98273i) q^{17} +(0.0245241 + 0.0754774i) q^{18} +(1.88030 - 5.78696i) q^{19} +6.63626 q^{21} +(-0.0554990 - 0.305131i) q^{22} +5.45258 q^{23} +(0.442869 + 0.321763i) q^{24} +(-0.0330155 - 0.101611i) q^{26} +(-4.56691 + 3.31805i) q^{27} +(-7.28883 + 5.29564i) q^{28} +(1.02619 + 3.15830i) q^{29} +(-1.44887 - 1.05267i) q^{31} -1.11558 q^{32} +(4.28282 - 2.30689i) q^{33} +0.315430 q^{34} +(0.522231 - 1.60726i) q^{36} +(-0.460067 - 1.41594i) q^{37} +(0.460319 - 0.334441i) q^{38} +(1.35577 - 0.985026i) q^{39} +(-0.539933 + 1.66174i) q^{41} +(0.502041 + 0.364754i) q^{42} +0.263041 q^{43} +(-2.86310 + 5.95137i) q^{44} +(0.412494 + 0.299694i) q^{46} +(-2.13986 + 6.58580i) q^{47} +(-1.78924 - 5.50670i) q^{48} +(-10.8985 + 7.91824i) q^{49} +(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} +(-2.02452 + 1.47090i) q^{61} +(-0.0517503 - 0.159271i) q^{62} +(1.18661 - 3.65201i) q^{63} +(6.30297 + 4.57938i) q^{64} +(0.450796 + 0.0608810i) q^{66} +0.516598 q^{67} +(-5.43413 - 3.94812i) q^{68} +(-2.47136 + 7.60605i) q^{69} +(8.68098 - 6.30710i) q^{71} +(0.256258 - 0.186183i) q^{72} +(1.75560 + 5.40317i) q^{73} +(0.0430208 - 0.132404i) q^{74} -12.1163 q^{76} +(-6.50552 + 13.5227i) q^{77} +0.156706 q^{78} +(9.14460 + 6.64394i) q^{79} +(-1.77179 - 5.45300i) q^{81} +(-0.132182 + 0.0960360i) q^{82} +(3.62511 - 2.63380i) q^{83} +(-4.08350 - 12.5677i) q^{84} +(0.0198994 + 0.0144577i) q^{86} -4.87077 q^{87} +(-1.08980 + 0.587008i) q^{88} +13.2676 q^{89} +(-1.59747 + 4.91652i) q^{91} +(-3.35515 - 10.3261i) q^{92} +(2.12511 - 1.54398i) q^{93} +(-0.523863 + 0.380608i) q^{94} +(0.505633 - 1.55618i) q^{96} +(-2.71551 - 1.97293i) q^{97} -1.25970 q^{98} +(-0.503711 - 2.76938i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - q^{3} - 6 q^{4} + 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 + 13 * q^6 + 3 * q^7 + 2 * q^8 - 5 * q^9	$ 8 q + 4 q^{2} - q^{3} - 6 q^{4} + 13 q^{6} + 3 q^{7} + 2 q^{8} - 5 q^{9} - 5 q^{11} + 28 q^{12} - 4 q^{13} + 16 q^{14} - 20 q^{16} - q^{17} - 14 q^{18} - q^{19} - 12 q^{21} - 33 q^{22} + 18 q^{23} + 25 q^{24} - 14 q^{26} - 10 q^{27} - 4 q^{28} + 19 q^{29} + 6 q^{31} - 12 q^{32} + 19 q^{33} - 20 q^{34} + 21 q^{36} - 4 q^{37} + 6 q^{38} + 9 q^{39} - 4 q^{41} - 29 q^{42} - 42 q^{43} - 28 q^{44} - 41 q^{46} - 4 q^{47} + 19 q^{48} - 15 q^{49} + 13 q^{51} + 26 q^{52} - 3 q^{53} - 40 q^{54} + 30 q^{56} + 5 q^{57} + 6 q^{58} - 19 q^{59} - 2 q^{61} + 38 q^{62} - q^{63} + 6 q^{64} + 13 q^{66} + 2 q^{67} - 35 q^{68} - 21 q^{69} + 40 q^{71} + 34 q^{72} + 23 q^{73} + 48 q^{74} + 16 q^{76} + 28 q^{77} - 12 q^{78} + 17 q^{79} - 2 q^{82} + 25 q^{83} - 4 q^{84} - 31 q^{86} - 30 q^{87} - 22 q^{88} - 12 q^{91} - 81 q^{92} + 13 q^{93} + 33 q^{94} + 23 q^{96} - 12 q^{97} + 84 q^{98} + 4 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 - q^3 - 6 * q^4 + 13 * q^6 + 3 * q^7 + 2 * q^8 - 5 * q^9 - 5 * q^11 + 28 * q^12 - 4 * q^13 + 16 * q^14 - 20 * q^16 - q^17 - 14 * q^18 - q^19 - 12 * q^21 - 33 * q^22 + 18 * q^23 + 25 * q^24 - 14 * q^26 - 10 * q^27 - 4 * q^28 + 19 * q^29 + 6 * q^31 - 12 * q^32 + 19 * q^33 - 20 * q^34 + 21 * q^36 - 4 * q^37 + 6 * q^38 + 9 * q^39 - 4 * q^41 - 29 * q^42 - 42 * q^43 - 28 * q^44 - 41 * q^46 - 4 * q^47 + 19 * q^48 - 15 * q^49 + 13 * q^51 + 26 * q^52 - 3 * q^53 - 40 * q^54 + 30 * q^56 + 5 * q^57 + 6 * q^58 - 19 * q^59 - 2 * q^61 + 38 * q^62 - q^63 + 6 * q^64 + 13 * q^66 + 2 * q^67 - 35 * q^68 - 21 * q^69 + 40 * q^71 + 34 * q^72 + 23 * q^73 + 48 * q^74 + 16 * q^76 + 28 * q^77 - 12 * q^78 + 17 * q^79 - 2 * q^82 + 25 * q^83 - 4 * q^84 - 31 * q^86 - 30 * q^87 - 22 * q^88 - 12 * q^91 - 81 * q^92 + 13 * q^93 + 33 * q^94 + 23 * q^96 - 12 * q^97 + 84 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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 $

$2$	0.0756511	+	0.0549637i	0.0534934	+	0.0388652i	0.614211	−	0.789142i	$-0.289475\pi$
$2$	0.0756511	+	0.0549637i	0.0534934	+	0.0388652i	−0.560717	+	0.828007i	$0.689475\pi$
$3$	−0.453245	+	1.39494i	−0.261681	+	0.805372i	0.730758	+	0.682636i	$0.239167\pi$
$3$	−0.453245	+	1.39494i	−0.261681	+	0.805372i	−0.992439	+	0.122735i	$0.960833\pi$
$4$	−0.615332	−	1.89380i	−0.307666	−	0.946898i
$5$		0			0
$5$		0			0
$6$	−0.110960	+	0.0806171i	−0.0452992	+	0.0329118i
$7$	−1.39815	−	4.30308i	−0.528453	−	1.62641i	−0.757385	−	0.652968i	$-0.773523\pi$
$7$	−1.39815	−	4.30308i	−0.528453	−	1.62641i	0.228932	−	0.973442i	$-0.426477\pi$
$8$	0.115332	−	0.354955i	0.0407760	−	0.125496i
$9$	0.686611	+	0.498852i	0.228870	+	0.166284i
$10$		0			0
$11$	−2.39815	−	2.29104i	−0.723071	−	0.690774i
$11$	−2.39815	−	2.29104i	−0.723071	−	0.690774i
$12$	2.92064			0.843116
$13$	−0.924349	−	0.671579i	−0.256368	−	0.186262i	0.452176	−	0.891929i	$-0.350648\pi$
$13$	−0.924349	−	0.671579i	−0.256368	−	0.186262i	−0.708544	+	0.705666i	$0.750648\pi$
$14$	0.130741	−	0.402380i	0.0349421	−	0.107541i
$15$		0			0
$16$	−3.19369	+	2.32035i	−0.798421	+	0.580087i
$17$	2.72899	−	1.98273i	0.661878	−	0.480883i	−0.205418	−	0.978674i	$-0.565856\pi$
$17$	2.72899	−	1.98273i	0.661878	−	0.480883i	0.867297	+	0.497792i	$0.165856\pi$
$18$	0.0245241	+	0.0754774i	0.00578038	+	0.0177902i
$19$	1.88030	−	5.78696i	0.431369	−	1.32762i	−0.465392	−	0.885105i	$-0.654087\pi$
$19$	1.88030	−	5.78696i	0.431369	−	1.32762i	0.896762	−	0.442514i	$-0.145913\pi$
$20$		0			0
$21$	6.63626			1.44815
$22$	−0.0554990	−	0.305131i	−0.0118324	−	0.0650542i
$23$	5.45258			1.13694			0.568471	−	0.822703i	$-0.307535\pi$
$23$	5.45258			1.13694			0.568471	+	0.822703i	$0.307535\pi$
$24$	0.442869	+	0.321763i	0.0904003	+	0.0656797i
$25$		0			0
$26$	−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	$-0.000229343\pi$
$29$	1.02619	+	3.15830i	0.190559	+	0.586482i	−0.809440	+	0.587202i	$0.800229\pi$
$30$		0			0
$31$	−1.44887	−	1.05267i	−0.260225	−	0.189065i	0.450021	−	0.893018i	$-0.351416\pi$
$31$	−1.44887	−	1.05267i	−0.260225	−	0.189065i	−0.710246	+	0.703953i	$0.751416\pi$
$32$	−1.11558			−0.197209
$33$	4.28282	−	2.30689i	0.745544	−	0.401578i
$34$	0.315430			0.0540957
$35$		0			0
$36$	0.522231	−	1.60726i	0.0870385	−	0.267877i
$37$	−0.460067	−	1.41594i	−0.0756345	−	0.232779i	0.906091	−	0.423084i	$-0.139052\pi$
$37$	−0.460067	−	1.41594i	−0.0756345	−	0.232779i	−0.981725	+	0.190305i	$0.939052\pi$
$38$	0.460319	−	0.334441i	0.0746736	−	0.0542536i
$39$	1.35577	−	0.985026i	0.217097	−	0.157730i
$40$		0			0
$41$	−0.539933	+	1.66174i	−0.0843234	+	0.259521i	−0.984325	−	0.176367i	$-0.943566\pi$
$41$	−0.539933	+	1.66174i	−0.0843234	+	0.259521i	0.900001	+	0.435888i	$0.143566\pi$
$42$	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	$0.493615\pi$
$44$	−2.86310	+	5.95137i	−0.431628	+	0.897202i
$45$		0			0
$46$	0.412494	+	0.299694i	0.0608189	+	0.0441875i
$47$	−2.13986	+	6.58580i	−0.312130	+	0.960638i	0.664790	+	0.747031i	$0.268521\pi$
$47$	−2.13986	+	6.58580i	−0.312130	+	0.960638i	−0.976920	+	0.213607i	$0.931479\pi$
$48$	−1.78924	−	5.50670i	−0.258254	−	0.794824i
$49$	−10.8985	+	7.91824i	−1.55693	+	1.13118i
$50$		0			0
$51$	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	$-0.331527\pi$
$53$	−1.16479	−	0.846269i	−0.159996	−	0.116244i	−0.664903	+	0.746930i	$0.731527\pi$
$54$	−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	−0.986592	−	0.163208i	$-0.947816\pi$
$59$	−2.18416	−	6.72216i	−0.284354	−	0.875150i	0.702238	−	0.711942i	$-0.252184\pi$
$60$		0			0
$61$	−2.02452	+	1.47090i	−0.259214	+	0.188330i	−0.709800	−	0.704403i	$-0.751215\pi$
$61$	−2.02452	+	1.47090i	−0.259214	+	0.188330i	0.450587	+	0.892733i	$0.351215\pi$
$62$	−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
$65$		0			0
$66$	0.450796	+	0.0608810i	0.0554891	+	0.00749394i
$67$	0.516598			0.0631124			0.0315562	−	0.999502i	$-0.489954\pi$
$67$	0.516598			0.0631124			0.0315562	+	0.999502i	$0.489954\pi$
$68$	−5.43413	−	3.94812i	−0.658984	−	0.478780i
$69$	−2.47136	+	7.60605i	−0.297516	+	0.915661i
$70$		0			0
$71$	8.68098	−	6.30710i	1.03024	−	0.748515i	0.0618853	−	0.998083i	$-0.480289\pi$
$71$	8.68098	−	6.30710i	1.03024	−	0.748515i	0.968357	+	0.249568i	$0.0802887\pi$
$72$	0.256258	−	0.186183i	0.0302003	−	0.0219418i
$73$	1.75560	+	5.40317i	0.205477	+	0.632393i	0.999693	+	0.0247584i	$0.00788163\pi$
$73$	1.75560	+	5.40317i	0.205477	+	0.632393i	−0.794216	+	0.607635i	$0.792118\pi$
$74$	0.0430208	−	0.132404i	0.00500106	−	0.0153917i
$75$		0			0
$76$	−12.1163			−1.38984
$77$	−6.50552	+	13.5227i	−0.741373	+	1.54105i
$78$	0.156706			0.0177435
$79$	9.14460	+	6.64394i	1.02885	+	0.747502i	0.968078	−	0.250650i	$-0.0806444\pi$
$79$	9.14460	+	6.64394i	1.02885	+	0.747502i	0.0607700	+	0.998152i	$0.480644\pi$
$80$		0			0
$81$	−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	−0.370781	−	0.928720i	$-0.620910\pi$
$83$	3.62511	−	2.63380i	0.397907	−	0.289097i	0.768688	+	0.639624i	$0.220910\pi$
$84$	−4.08350	−	12.5677i	−0.445547	−	1.37125i
$85$		0			0
$86$	0.0198994	+	0.0144577i	0.00214580	+	0.00155902i
$87$	−4.87077			−0.522202
$88$	−1.08980	+	0.587008i	−0.116173	+	0.0625752i
$89$	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			0
$91$	−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
$95$		0			0
$96$	0.505633	−	1.55618i	0.0516060	−	0.158827i
$97$	−2.71551	−	1.97293i	−0.275718	−	0.200321i	0.441330	−	0.897345i	$-0.354507\pi$
$97$	−2.71551	−	1.97293i	−0.275718	−	0.200321i	−0.717048	+	0.697024i	$0.754507\pi$
$98$	−1.25970			−0.127249
$99$	−0.503711	−	2.76938i	−0.0506248	−	0.278333i
$100$		0			0
$101$	7.55216	+	5.48696i	0.751468	+	0.545973i	0.896282	−	0.443486i	$-0.146258\pi$
$101$	7.55216	+	5.48696i	0.751468	+	0.545973i	−0.144814	+	0.989459i	$0.546258\pi$
$102$	−0.142967	+	0.440007i	−0.0141558	+	0.0435672i
$103$	4.30027	+	13.2349i	0.423718	+	1.30407i	0.904216	+	0.427075i	$0.140456\pi$
$103$	4.30027	+	13.2349i	0.423718	+	1.30407i	−0.480498	+	0.876996i	$0.659544\pi$
$104$	−0.344987	+	0.250648i	−0.0338288	+	0.0245781i
$105$		0			0
$106$	−0.0416035	−	0.128042i	−0.00404089	−	0.0124366i
$107$	5.18787	−	15.9666i	0.501531	−	1.54355i	−0.304996	−	0.952354i	$-0.598655\pi$
$107$	5.18787	−	15.9666i	0.501531	−	1.54355i	0.806526	−	0.591198i	$-0.201345\pi$
$108$	9.09388	+	6.60709i	0.875059	+	0.635768i
$109$	−3.65293			−0.349888			−0.174944	−	0.984578i	$-0.555974\pi$
$109$	−3.65293			−0.349888			−0.174944	+	0.984578i	$0.555974\pi$
$110$		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	−0.615047	−	0.788490i	$-0.710863\pi$
$113$	3.67802	−	11.3198i	0.345999	−	1.06488i	0.961047	−	0.276386i	$-0.0891369\pi$
$114$	0.257890	+	0.793704i	0.0241536	+	0.0743372i
$115$		0			0
$116$	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			0
$121$	0.502293	+	10.9885i	0.0456630	+	0.998957i
$122$	−0.234004			−0.0211857
$123$	−2.07332	−	1.50635i	−0.186945	−	0.135823i
$124$	−1.10200	+	3.39161i	−0.0989626	+	0.304576i
$125$		0			0
$126$	0.290497	−	0.211058i	0.0258795	−	0.0188026i
$127$	15.9883	−	11.6162i	1.41873	−	1.03077i	0.426756	−	0.904367i	$-0.359656\pi$
$127$	15.9883	−	11.6162i	1.41873	−	1.03077i	0.991979	−	0.126404i	$-0.0403435\pi$
$128$	0.914596	+	2.81484i	0.0808397	+	0.248799i
$129$	−0.119222	+	0.366928i	−0.0104969	+	0.0323062i
$130$		0			0
$131$	−1.93479			−0.169043			−0.0845215	−	0.996422i	$-0.526936\pi$
$131$	−1.93479			−0.169043			−0.0845215	+	0.996422i	$0.526936\pi$
$132$	−7.00414	−	6.69129i	−0.609632	−	0.582402i
$133$	−27.5307			−2.38721
$134$	0.0390812	+	0.0283941i	0.00337610	+	0.00245288i
$135$		0			0
$136$	−0.389040	−	1.19734i	−0.0333599	−	0.102671i
$137$	−10.1413	+	7.36808i	−0.866429	+	0.629498i	−0.929626	−	0.368503i	$-0.879870\pi$
$137$	−10.1413	+	7.36808i	−0.866429	+	0.629498i	0.0631970	+	0.998001i	$0.479870\pi$
$138$	−0.605018	+	0.439571i	−0.0515025	+	0.0374188i
$139$	−3.47491	−	10.6947i	−0.294738	−	0.907111i	−0.983309	−	0.181942i	$-0.941762\pi$
$139$	−3.47491	−	10.6947i	−0.294738	−	0.907111i	0.688571	−	0.725169i	$-0.258238\pi$
$140$		0			0
$141$	−8.21695	−	5.96996i	−0.691992	−	0.502762i
$142$	1.00339			0.0842024
$143$	0.678120	+	3.72827i	0.0567072	+	0.311773i
$144$	−3.35033			−0.279194
$145$		0			0
$146$	−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	$-0.448688\pi$
$149$	14.0232	−	10.1885i	1.14883	−	0.834672i	0.988325	+	0.152363i	$0.0486884\pi$
$150$		0			0
$151$	−0.00166997	+	0.00513965i	−0.000135901	+	0.000418259i	−0.951124	−	0.308808i	$-0.900070\pi$
$151$	−0.00166997	+	0.00513965i	−0.000135901	+	0.000418259i	0.950989	+	0.309226i	$0.100070\pi$
$152$	−1.83725	−	1.33484i	−0.149021	−	0.108270i
$153$	2.86285			0.231447
$154$	−1.23541	+	0.665437i	−0.0995519	+	0.0536225i
$155$		0			0
$156$	−2.69969	−	1.96144i	−0.216148	−	0.157041i
$157$	−0.171454	+	0.527682i	−0.0136835	+	0.0421136i	−0.957665	−	0.287884i	$-0.907048\pi$
$157$	−0.171454	+	0.527682i	−0.0136835	+	0.0421136i	0.943982	+	0.329998i	$0.107048\pi$
$158$	0.326623	+	1.00524i	0.0259847	+	0.0799728i
$159$	1.70843	−	1.24125i	0.135488	−	0.0984375i
$160$		0			0
$161$	−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	$-0.400967\pi$
$163$	−6.44324	−	4.68129i	−0.504673	−	0.366667i	−0.810799	+	0.585324i	$0.800967\pi$
$164$	3.47924			0.271683
$165$		0			0
$166$	0.419007			0.0325212
$167$	2.77204	+	2.01400i	0.214507	+	0.155848i	0.689850	−	0.723952i	$-0.257676\pi$
$167$	2.77204	+	2.01400i	0.214507	+	0.155848i	−0.475344	+	0.879800i	$0.657676\pi$
$168$	0.765373	−	2.35558i	0.0590498	−	0.181737i
$169$	−3.61382	−	11.1222i	−0.277986	−	0.855553i
$170$		0			0
$171$	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	0.351368	+	0.936237i	$0.385717\pi$
$173$	−6.35552	+	19.5603i	−0.483201	+	1.48714i	−0.834569	+	0.550903i	$0.814283\pi$
$174$	−0.368479	−	0.267716i	−0.0279343	−	0.0202955i
$175$		0			0
$176$	12.9750	+	1.75230i	0.978024	+	0.132084i
$177$	10.3670			0.779231
$178$	1.00371	+	0.729238i	0.0752313	+	0.0546587i
$179$	−0.792419	+	2.43882i	−0.0592282	+	0.182286i	−0.976293	−	0.216452i	$-0.930552\pi$
$179$	−0.792419	+	2.43882i	−0.0592282	+	0.182286i	0.917065	+	0.398738i	$0.130552\pi$
$180$		0			0
$181$	−10.8545	+	7.88624i	−0.806807	+	0.586179i	−0.912903	−	0.408177i	$-0.866165\pi$
$181$	−10.8545	+	7.88624i	−0.806807	+	0.586179i	0.106096	+	0.994356i	$0.466165\pi$
$182$	−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
$185$		0			0
$186$	0.245630			0.0180104
$187$	−11.0871	−	1.49733i	−0.810766	−	0.109496i
$188$	13.7889			1.00566
$189$	20.6631	+	15.0126i	1.50302	+	1.09201i
$190$		0			0
$191$	5.62097	+	17.2996i	0.406719	+	1.25175i	0.919452	+	0.393203i	$0.128633\pi$
$191$	5.62097	+	17.2996i	0.406719	+	1.25175i	−0.512733	+	0.858548i	$0.671367\pi$
$192$	−9.24477	+	6.71672i	−0.667184	+	0.484738i
$193$	12.6924	−	9.22156i	0.913618	−	0.663782i	−0.0283094	−	0.999599i	$-0.509012\pi$
$193$	12.6924	−	9.22156i	0.913618	−	0.663782i	0.941927	+	0.335817i	$0.109012\pi$
$194$	−0.0969914	−	0.298509i	−0.00696358	−	0.0214317i
$195$		0			0
$196$	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	$0.216070\pi$
$198$	0.114109	−	0.237192i	0.00810937	−	0.0168565i
$199$	−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			0
$201$	−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			0
$206$	−0.402118	+	1.23759i	−0.0280169	+	0.0862271i
$207$	3.74380	+	2.72003i	0.260212	+	0.189055i
$208$	4.51038			0.312738
$209$	−17.7674	+	9.57019i	−1.22900	+	0.661984i
$210$		0			0
$211$	−15.3393	−	11.1447i	−1.05600	−	0.767230i	−0.0826575	−	0.996578i	$-0.526341\pi$
$211$	−15.3393	−	11.1447i	−1.05600	−	0.767230i	−0.973345	+	0.229348i	$0.926341\pi$
$212$	−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			0
$216$	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	$-0.952239\pi$
$223$	−1.50785	+	4.64070i	−0.100973	+	0.310764i	0.887791	+	0.460247i	$0.152239\pi$
$224$	1.55976	+	4.80045i	0.104216	+	0.320743i
$225$		0			0
$226$	0.900424	−	0.654197i	0.0598953	−	0.0435165i
$227$	−5.04404	−	15.5240i	−0.334785	−	1.03036i	−0.966828	−	0.255428i	$-0.917784\pi$
$227$	−5.04404	−	15.5240i	−0.334785	−	1.03036i	0.632043	−	0.774933i	$-0.282216\pi$
$228$	5.49166	−	16.9016i	0.363694	−	1.11934i
$229$	3.90890	+	2.83998i	0.258307	+	0.187671i	0.709401	−	0.704806i	$-0.248966\pi$
$229$	3.90890	+	2.83998i	0.258307	+	0.187671i	−0.451093	+	0.892477i	$0.648966\pi$
$230$		0			0
$231$	−15.9148	−	15.2039i	−1.04712	−	1.00035i
$232$	1.23941			0.0813711
$233$	−6.81172	−	4.94900i	−0.446251	−	0.324220i	0.341863	−	0.939750i	$-0.388942\pi$
$233$	−6.81172	−	4.94900i	−0.446251	−	0.324220i	−0.788114	+	0.615530i	$0.788942\pi$
$234$	0.0280202	−	0.0862373i	0.00183174	−	0.00563751i
$235$		0			0
$236$	−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	0.419175	+	0.907905i	$0.362319\pi$
$239$	−7.01245	+	21.5821i	−0.453598	+	1.39603i	−0.872773	+	0.488126i	$0.837681\pi$
$240$		0			0
$241$	11.6065			0.747638			0.373819	−	0.927502i	$-0.378048\pi$
$241$	11.6065			0.747638			0.373819	+	0.927502i	$0.378048\pi$
$242$	−0.565971	+	0.858902i	−0.0363820	+	0.0552123i
$243$	−8.52534			−0.546901
$244$	4.03135	+	2.92894i	0.258080	+	0.187506i
$245$		0			0
$246$	−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			0
$251$	−2.68032	−	1.94736i	−0.169180	−	0.122917i	0.499973	−	0.866041i	$-0.333343\pi$
$251$	−2.68032	−	1.94736i	−0.169180	−	0.122917i	−0.669153	+	0.743124i	$0.733343\pi$
$252$	−7.64633			−0.481674
$253$	−13.0761	−	12.4921i	−0.822090	−	0.785370i
$254$	1.84800			0.115954
$255$		0			0
$256$	4.72952	−	14.5560i	0.295595	−	0.909748i
$257$	8.29606	+	25.5326i	0.517494	+	1.59268i	0.778698	+	0.627399i	$0.215880\pi$
$257$	8.29606	+	25.5326i	0.517494	+	1.59268i	−0.261204	+	0.965284i	$0.584120\pi$
$258$	−0.0291870	+	0.0212056i	−0.00181711	+	0.00132020i
$259$	−5.44965	+	3.95940i	−0.338625	+	0.246025i
$260$		0			0
$261$	−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	$0.622413\pi$
$264$	−0.324897	−	1.78627i	−0.0199960	−	0.109937i
$265$		0			0
$266$	−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	−0.534954	−	0.844881i	$-0.679671\pi$
$269$	1.69369	−	1.23053i	0.103266	−	0.0750270i	0.638220	+	0.769854i	$0.279671\pi$
$270$		0			0
$271$	4.67938	+	14.4017i	0.284252	+	0.874838i	0.986622	+	0.163026i	$0.0521254\pi$
$271$	4.67938	+	14.4017i	0.284252	+	0.874838i	−0.702370	+	0.711812i	$0.747875\pi$
$272$	−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	0.770367	−	0.637601i	$-0.220073\pi$
$277$	6.69110	+	4.86137i	0.402029	+	0.292091i	−0.368338	+	0.929692i	$0.620073\pi$
$278$	0.324939	−	1.00006i	0.0194885	−	0.0599795i
$279$	−0.469687	−	1.44555i	−0.0281194	−	0.0865426i
$280$		0			0
$281$	−1.97985	+	1.43844i	−0.118108	+	0.0858104i	−0.645271	−	0.763954i	$-0.723256\pi$
$281$	−1.97985	+	1.43844i	−0.118108	+	0.0858104i	0.527163	+	0.849764i	$0.323256\pi$
$282$	−0.293490	−	0.903268i	−0.0174771	−	0.0537888i
$283$	−8.06372	+	24.8176i	−0.479339	+	1.47525i	0.360677	+	0.932691i	$0.382546\pi$
$283$	−8.06372	+	24.8176i	−0.479339	+	1.47525i	−0.840016	+	0.542562i	$0.817454\pi$
$284$	−17.2860	−	12.5590i	−1.02574	−	0.745242i
$285$		0			0
$286$	−0.153619	+	0.319320i	−0.00908369	+	0.0188818i
$287$	7.90553			0.466648
$288$	−0.765973	−	0.556512i	−0.0451354	−	0.0327928i
$289$	−1.73710	+	5.34624i	−0.102182	+	0.314485i
$290$		0			0
$291$	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	−0.995980	−	0.0895739i	$-0.971449\pi$
$293$	−4.15719	−	12.7945i	−0.242866	−	0.747463i	0.753115	−	0.657889i	$-0.228551\pi$
$294$	0.570953	−	1.75721i	0.0332987	−	0.102483i
$295$		0			0
$296$	−0.555655			−0.0322968
$297$	18.5539	+	2.50575i	1.07661	+	0.145399i
$298$	1.62087			0.0938944
$299$	−5.04009	−	3.66184i	−0.291476	−	0.211770i
$300$		0			0
$301$	−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			0
$306$	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	$0.782627\pi$
$308$	29.6123	+	3.99921i	1.68731	+	0.227876i
$309$	−20.4110			−1.16114
$310$		0			0
$311$	−4.07872	+	12.5530i	−0.231283	+	0.711817i	0.766310	+	0.642472i	$0.222091\pi$
$311$	−4.07872	+	12.5530i	−0.231283	+	0.711817i	−0.997593	+	0.0693450i	$0.977909\pi$
$312$	−0.193276	−	0.594843i	−0.0109421	−	0.0336764i
$313$	13.0833	−	9.50561i	0.739515	−	0.537289i	−0.153044	−	0.988219i	$-0.548908\pi$
$313$	13.0833	−	9.50561i	0.739515	−	0.537289i	0.892559	+	0.450931i	$0.148908\pi$
$314$	−0.0419741	+	0.0304959i	−0.00236873	+	0.00172099i
$315$		0			0
$316$	6.95531	−	21.4062i	0.391267	−	1.20420i
$317$	−4.35344	−	3.16296i	−0.244514	−	0.177650i	0.458778	−	0.888551i	$-0.348287\pi$
$317$	−4.35344	−	3.16296i	−0.244514	−	0.177650i	−0.703292	+	0.710901i	$0.748287\pi$
$318$	0.197469			0.0110735
$319$	4.77481	−	9.92514i	0.267338	−	0.555701i
$320$		0			0
$321$	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			0
$326$	−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			0
$336$	−21.1941	+	15.3984i	−1.15623	+	0.840054i
$337$	−2.78305	−	8.56535i	−0.151603	−	0.466585i	0.846198	−	0.532868i	$-0.178886\pi$
$337$	−2.78305	−	8.56535i	−0.151603	−	0.466585i	−0.997801	+	0.0662836i	$0.978886\pi$
$338$	0.337928	−	1.04003i	0.0183808	−	0.0565704i
$339$	14.1234	+	10.2613i	0.767080	+	0.557316i
$340$		0			0
$341$	1.06292	+	5.84388i	0.0575604	+	0.316464i
$342$	0.482897			0.0261121
$343$	23.6877	+	17.2101i	1.27902	+	0.929260i
$344$	0.0303371	−	0.0933679i	0.00163567	−	0.00503406i
$345$		0			0
$346$	−1.55591	+	1.13043i	−0.0836461	+	0.0607725i
$347$	8.30939	−	6.03712i	0.446071	−	0.324090i	−0.341971	−	0.939710i	$-0.611095\pi$
$347$	8.30939	−	6.03712i	0.446071	−	0.324090i	0.788043	+	0.615621i	$0.211095\pi$
$348$	2.99714	+	9.22425i	0.160664	+	0.494472i
$349$	5.33402	−	16.4164i	0.285524	−	0.878752i	−0.700718	−	0.713439i	$-0.747137\pi$
$349$	5.33402	−	16.4164i	0.285524	−	0.878752i	0.986241	−	0.165313i	$-0.0528633\pi$
$350$		0			0
$351$	6.44975			0.344262
$352$	2.67534	+	2.55585i	0.142596	+	0.136227i
$353$	22.8096			1.21403			0.607017	−	0.794689i	$-0.292366\pi$
$353$	22.8096			1.21403			0.607017	+	0.794689i	$0.292366\pi$
$354$	0.784275	+	0.569809i	0.0416837	+	0.0302850i
$355$		0			0
$356$	−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	−0.992333	−	0.123597i	$-0.960557\pi$
$359$	−4.96736	−	15.2879i	−0.262167	−	0.806867i	0.730166	−	0.683270i	$-0.239443\pi$
$360$		0			0
$361$	−14.5820	−	10.5945i	−0.767475	−	0.557603i
$362$	−1.25461			−0.0659408
$363$	−15.5560	−	4.27982i	−0.816481	−	0.224632i
$364$	10.2939			0.539545
$365$		0			0
$366$	0.106061	−	0.326422i	0.00554390	−	0.0170624i
$367$	−6.79759	−	20.9208i	−0.354832	−	1.09206i	−0.956107	−	0.293017i	$-0.905341\pi$
$367$	−6.79759	−	20.9208i	−0.354832	−	1.09206i	0.601276	−	0.799042i	$-0.294659\pi$
$368$	−17.4138	+	12.6519i	−0.907759	+	0.659525i
$369$	−1.19969	+	0.871625i	−0.0624533	+	0.0453750i
$370$		0			0
$371$	−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	$0.324244\pi$
$374$	−0.756449	−	0.722661i	−0.0391151	−	0.0373679i
$375$		0			0
$376$	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	−0.507630	−	0.861575i	$-0.669478\pi$
$379$	3.01578	−	2.19109i	0.154910	−	0.112549i	0.662540	+	0.749026i	$0.269478\pi$
$380$		0			0
$381$	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	$-0.390656\pi$
$383$	−8.89708	−	6.46411i	−0.454620	−	0.330301i	−0.791417	+	0.611277i	$0.790656\pi$
$384$	−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	0.997263	−	0.0739418i	$-0.0235579\pi$
$389$	2.89926	+	8.92300i	0.146998	+	0.452414i	−0.850264	+	0.526356i	$0.823558\pi$
$390$		0			0
$391$	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
$395$		0			0
$396$	−4.93469	+	2.65801i	−0.247977	+	0.133570i
$397$	−22.3136			−1.11989			−0.559945	−	0.828530i	$-0.689178\pi$
$397$	−22.3136			−1.11989			−0.559945	+	0.828530i	$0.689178\pi$
$398$	−0.344364	−	0.250195i	−0.0172614	−	0.0125411i
$399$	12.4781	−	38.4038i	0.624688	−	1.92259i
$400$		0			0
$401$	19.9683	−	14.5078i	0.997171	−	0.724487i	0.0356909	−	0.999363i	$-0.488637\pi$
$401$	19.9683	−	14.5078i	0.997171	−	0.724487i	0.961480	+	0.274876i	$0.0886368\pi$
$402$	−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
$405$		0			0
$406$	1.40500			0.0697292
$407$	−2.14066	+	4.44967i	−0.106109	+	0.220562i
$408$	1.84656			0.0914182
$409$	−23.8705	−	17.3429i	−1.18032	−	0.857553i	−0.188113	−	0.982147i	$-0.560237\pi$
$409$	−23.8705	−	17.3429i	−1.18032	−	0.857553i	−0.992208	+	0.124594i	$0.960237\pi$
$410$		0			0
$411$	−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
$415$		0			0
$416$	1.03119	+	0.749203i	0.0505582	+	0.0367327i
$417$	16.4935			0.807689
$418$	−1.87013	−	0.252566i	−0.0914713	−	0.0123534i
$419$	9.03564			0.441420			0.220710	−	0.975339i	$-0.429163\pi$
$419$	9.03564			0.441420			0.220710	+	0.975339i	$0.429163\pi$
$420$		0			0
$421$	4.39426	−	13.5242i	0.214163	−	0.659127i	−0.785049	−	0.619434i	$-0.787362\pi$
$421$	4.39426	−	13.5242i	0.214163	−	0.659127i	0.999212	−	0.0396928i	$-0.0126379\pi$
$422$	−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
$425$		0			0
$426$	−0.454780	+	1.39967i	−0.0220342	+	0.0678142i
$427$	9.16001	+	6.65514i	0.443284	+	0.322065i
$428$	−33.4298			−1.61589
$429$	−5.50808	−	0.743880i	−0.265933	−	0.0359149i
$430$		0			0
$431$	1.40086	+	1.01778i	0.0674769	+	0.0490248i	0.621012	−	0.783801i	$-0.286722\pi$
$431$	1.40086	+	1.01778i	0.0674769	+	0.0490248i	−0.553535	+	0.832826i	$0.686722\pi$
$432$	6.88623	−	21.1936i	0.331314	−	1.01968i
$433$	−5.70062	−	17.5447i	−0.273955	−	0.843145i	−0.989494	−	0.144573i	$-0.953819\pi$
$433$	−5.70062	−	17.5447i	−0.273955	−	0.843145i	0.715540	−	0.698572i	$-0.246181\pi$
$434$	−0.613000	+	0.445371i	−0.0294250	+	0.0213785i
$435$		0			0
$436$	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	$-0.634384\pi$
$439$	−17.1704			−0.819499			−0.409750	+	0.912198i	$0.634384\pi$
$440$		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	0.201185	+	0.979553i	$0.435521\pi$
$443$	−11.3098	+	34.8079i	−0.537344	+	1.65377i	−0.738529	+	0.674221i	$0.764479\pi$
$444$	−1.34369	−	4.13545i	−0.0637686	−	0.196260i
$445$		0			0
$446$	−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	0.857748	−	0.514070i	$-0.171863\pi$
$449$	13.4320	+	9.75895i	0.633897	+	0.460553i	−0.223851	+	0.974623i	$0.571863\pi$
$450$		0			0
$451$	5.10196	−	2.74811i	0.240242	−	0.129404i
$452$	−23.7006			−1.11478
$453$	−0.00641262	−	0.00465904i	−0.000301291	−	0.000218901i
$454$	0.471667	−	1.45164i	0.0221365	−	0.0681290i
$455$		0			0
$456$	2.69476	−	1.95785i	0.126193	−	0.0916849i
$457$	−25.6178	+	18.6124i	−1.19835	+	0.870651i	−0.994121	−	0.108272i	$-0.965468\pi$
$457$	−25.6178	+	18.6124i	−1.19835	+	0.870651i	−0.204227	+	0.978923i	$0.565468\pi$
$458$	0.139617	+	0.429696i	0.00652385	+	0.0200784i
$459$	−5.88426	+	18.1099i	−0.274654	+	0.845297i
$460$		0			0
$461$	−25.4351			−1.18463			−0.592315	−	0.805706i	$-0.701786\pi$
$461$	−25.4351			−1.18463			−0.592315	+	0.805706i	$0.701786\pi$
$462$	−0.368306	−	2.02493i	−0.0171352	−	0.0942083i
$463$	16.3319			0.759007			0.379503	−	0.925190i	$-0.376095\pi$
$463$	16.3319			0.759007			0.379503	+	0.925190i	$0.376095\pi$
$464$	−10.6057	−	7.70549i	−0.492357	−	0.357718i
$465$		0			0
$466$	−0.243298	−	0.748795i	−0.0112706	−	0.0346873i
$467$	6.90020	−	5.01329i	0.319303	−	0.231987i	−0.416575	−	0.909101i	$-0.636770\pi$
$467$	6.90020	−	5.01329i	0.319303	−	0.231987i	0.735878	+	0.677114i	$0.236770\pi$
$468$	−1.56213	+	1.13495i	−0.0722093	+	0.0524631i
$469$	−0.722284	−	2.22296i	−0.0333520	−	0.102647i
$470$		0			0
$471$	−0.658376	−	0.478338i	−0.0303364	−	0.0220407i
$472$	−2.63797			−0.121422
$473$	−0.630814	−	0.602638i	−0.0290049	−	0.0277093i
$474$	−1.55030			−0.0712076
$475$		0			0
$476$	−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	$-0.939838\pi$
$479$	−24.2283	+	17.6029i	−1.10702	+	0.804296i	−0.124827	+	0.992178i	$0.539838\pi$
$480$		0			0
$481$	−0.525653	+	1.61779i	−0.0239677	+	0.0737650i
$482$	0.878041	+	0.637934i	0.0399937	+	0.0290571i
$483$	36.1848			1.64646
$484$	20.5010	−	7.71283i	0.931862	−	0.350583i
$485$		0			0
$486$	−0.644951	−	0.468585i	−0.0292556	−	0.0212554i
$487$	6.05768	−	18.6436i	0.274500	−	0.844823i	−0.714852	−	0.699276i	$-0.753506\pi$
$487$	6.05768	−	18.6436i	0.274500	−	0.844823i	0.989351	−	0.145547i	$-0.0464942\pi$
$488$	0.288612	+	0.888257i	0.0130649	+	0.0402095i
$489$	9.45050	−	6.86619i	0.427367	−	0.310500i
$490$		0			0
$491$	−4.87911	−	15.0163i	−0.220191	−	0.677678i	−0.998744	−	0.0500997i	$-0.984046\pi$
$491$	−4.87911	−	15.0163i	−0.220191	−	0.677678i	0.778553	−	0.627579i	$-0.215954\pi$
$492$	−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	0.998166	−	0.0605408i	$-0.0192825\pi$
$499$	3.46350	+	10.6596i	0.155048	+	0.477188i	−0.843118	+	0.537729i	$0.819283\pi$
$500$		0			0
$501$	−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	−0.948666	−	0.316279i	$-0.897567\pi$
$503$	0.105965	−	0.326125i	0.00472473	−	0.0145412i	0.953391	+	0.301737i	$0.0975666\pi$
$504$	−1.15945	−	0.842387i	−0.0516459	−	0.0375229i
$505$		0			0
$506$	−0.302613	−	1.66375i	−0.0134528	−	0.0739628i
$507$	17.1528			0.761782
$508$	−31.8368	−	23.1308i	−1.41253	−	1.02626i
$509$	−6.04518	+	18.6052i	−0.267948	+	0.824659i	0.723052	+	0.690794i	$0.242739\pi$
$509$	−6.04518	+	18.6052i	−0.267948	+	0.824659i	−0.991000	+	0.133865i	$0.957261\pi$
$510$		0			0
$511$	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
$515$		0			0
$516$	0.768249			0.0338203
$517$	20.2200	−	10.8913i	0.889275	−	0.478998i
$518$	−0.629896			−0.0276760
$519$	−24.4049	−	17.7312i	−1.07126	−	0.778313i
$520$		0			0
$521$	12.9869	+	39.9695i	0.568966	+	1.75110i	0.655864	+	0.754879i	$0.272305\pi$
$521$	12.9869	+	39.9695i	0.568966	+	1.75110i	−0.0868981	+	0.996217i	$0.527695\pi$
$522$	−0.213214	+	0.154909i	−0.00933212	+	0.00678018i
$523$	24.2790	−	17.6398i	1.06165	−	0.771333i	0.0872555	−	0.996186i	$-0.472190\pi$
$523$	24.2790	−	17.6398i	1.06165	−	0.771333i	0.974393	+	0.224853i	$0.0721903\pi$
$524$	1.19054	+	3.66409i	0.0520088	+	0.160067i
$525$		0			0
$526$	−0.920538	−	0.668810i	−0.0401374	−	0.0291615i
$527$	−6.04112			−0.263155
$528$	−8.32519	+	17.3051i	−0.362308	+	0.753109i
$529$	6.73067			0.292638
$530$		0			0
$531$	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
$535$		0			0
$536$	0.0595802	−	0.183369i	0.00257347	−	0.00792033i
$537$	−3.04285	−	2.21076i	−0.131309	−	0.0954014i
$538$	0.195764			0.00843998
$539$	44.2773	+	5.97976i	1.90716	+	0.257567i
$540$		0			0
$541$	8.35196	+	6.06806i	0.359079	+	0.260886i	0.752668	−	0.658400i	$-0.228767\pi$
$541$	8.35196	+	6.06806i	0.359079	+	0.260886i	−0.393589	+	0.919287i	$0.628767\pi$
$542$	−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
$545$		0			0
$546$	−0.219100	−	0.674320i	−0.00937660	−	0.0288582i
$547$	−12.9221	+	39.7702i	−0.552510	+	1.70045i	0.149921	+	0.988698i	$0.452098\pi$
$547$	−12.9221	+	39.7702i	−0.552510	+	1.70045i	−0.702431	+	0.711752i	$0.747902\pi$
$548$	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
$555$		0			0
$556$	−18.1153	+	13.1616i	−0.768261	+	0.558174i
$557$	11.8918	+	36.5993i	0.503874	+	1.55076i	0.802656	+	0.596442i	$0.203420\pi$
$557$	11.8918	+	36.5993i	0.503874	+	1.55076i	−0.298782	+	0.954321i	$0.596580\pi$
$558$	0.0439203	−	0.135173i	0.00185930	−	0.00572233i
$559$	−0.243142	−	0.176653i	−0.0102838	−	0.00747163i
$560$		0			0
$561$	7.11385	−	14.7872i	0.300347	−	0.624315i
$562$	−0.228840			−0.00965303
$563$	24.8258	+	18.0370i	1.04628	+	0.760170i	0.971502	−	0.237030i	$-0.0761740\pi$
$563$	24.8258	+	18.0370i	1.04628	+	0.760170i	0.0747817	+	0.997200i	$0.476174\pi$
$564$	−6.24975	+	19.2347i	−0.263162	+	0.809929i
$565$		0			0
$566$	−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	$-0.811815\pi$
$569$	4.03220	−	12.4098i	0.169039	−	0.520247i	0.999311	+	0.0371104i	$0.0118153\pi$
$570$		0			0
$571$	16.1300			0.675018			0.337509	−	0.941322i	$-0.390416\pi$
$571$	16.1300			0.675018			0.337509	+	0.941322i	$0.390416\pi$
$572$	6.64331	−	3.57834i	0.277771	−	0.149618i
$573$	−26.6796			−1.11456
$574$	0.598062	+	0.434517i	0.0249626	+	0.0181364i
$575$		0			0
$576$	2.04326	+	6.28850i	0.0851358	+	0.262021i
$577$	−11.7885	+	8.56487i	−0.490763	+	0.356560i	−0.805478	−	0.592626i	$-0.798091\pi$
$577$	−11.7885	+	8.56487i	−0.490763	+	0.356560i	0.314715	+	0.949186i	$0.398091\pi$
$578$	−0.425263	+	0.308972i	−0.0176886	+	0.0128515i
$579$	7.11080	+	21.8848i	0.295515	+	0.909501i
$580$		0			0
$581$	−16.4019	−	11.9167i	−0.680465	−	0.494387i
$582$	0.460364			0.0190827
$583$	0.854511	+	4.69806i	0.0353902	+	0.194574i
$584$	2.12036			0.0877411
$585$		0			0
$586$	0.388738	−	1.19641i	0.0160586	−	0.0494234i
$587$	8.61360	+	26.5099i	0.355521	+	1.09418i	0.955707	+	0.294321i	$0.0950936\pi$
$587$	8.61360	+	26.5099i	0.355521	+	1.09418i	−0.600185	+	0.799861i	$0.704906\pi$
$588$	−31.8307	+	23.1263i	−1.31267	+	0.953713i
$589$	−8.81605	+	6.40524i	−0.363259	+	0.263923i
$590$		0			0
$591$	−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	$0.600369\pi$
$594$	1.26590	+	1.20936i	0.0519405	+	0.0496205i
$595$		0			0
$596$	−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	−0.0712774	−	0.997457i	$-0.522708\pi$
$599$	20.9339	−	15.2093i	0.855334	−	0.621437i	0.926612	+	0.376020i	$0.122708\pi$
$600$		0			0
$601$	−14.5321	−	44.7252i	−0.592776	−	1.82438i	−0.565498	−	0.824750i	$-0.691316\pi$
$601$	−14.5321	−	44.7252i	−0.592776	−	1.82438i	−0.0272781	−	0.999628i	$-0.508684\pi$
$602$	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	−0.167297	−	0.985907i	$-0.553504\pi$
$607$	−28.4967	−	20.7041i	−1.15665	−	0.840353i	−0.989350	+	0.145553i	$0.953504\pi$
$608$	−2.09763	+	6.45584i	−0.0850701	+	0.261819i
$609$	6.81009	+	20.9593i	0.275959	+	0.849314i
$610$		0			0
$611$	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	−0.691943	−	0.721952i	$-0.743245\pi$
$613$	7.23461	−	22.2658i	0.292203	−	0.899309i	0.984147	−	0.177357i	$-0.0567548\pi$
$614$	−2.05653	−	1.49416i	−0.0829948	−	0.0602993i
$615$		0			0
$616$	4.04965	+	3.86876i	0.163165	+	0.155877i
$617$	−22.8910			−0.921557			−0.460778	−	0.887515i	$-0.652430\pi$
$617$	−22.8910			−0.921557			−0.460778	+	0.887515i	$0.652430\pi$
$618$	−1.54411	−	1.12187i	−0.0621134	−	0.0451280i
$619$	0.657441	−	2.02339i	0.0264248	−	0.0813271i	−0.936974	−	0.349398i	$-0.886386\pi$
$619$	0.657441	−	2.02339i	0.0264248	−	0.0813271i	0.963399	+	0.268071i	$0.0863861\pi$
$620$		0			0
$621$	−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			0
$626$	1.51223			0.0604410
$627$	−5.29691	−	29.1221i	−0.211538	−	1.16303i
$628$	1.10482			0.0440873
$629$	−4.06294	−	2.95190i	−0.162000	−	0.117700i
$630$		0			0
$631$	4.77702	+	14.7022i	0.190170	+	0.585284i	0.999999	−	0.00138227i	$-0.000439991\pi$
$631$	4.77702	+	14.7022i	0.190170	+	0.585284i	−0.809829	+	0.586666i	$0.800440\pi$
$632$	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
$635$		0			0
$636$	−3.40193	−	2.47164i	−0.134895	−	0.0980071i
$637$	15.3918			0.609844
$638$	0.906743	−	0.488406i	0.0358983	−	0.0193362i
$639$	9.10676			0.360258
$640$		0			0
$641$	4.38201	−	13.4864i	0.173079	−	0.532682i	−0.826461	−	0.562993i	$-0.809650\pi$
$641$	4.38201	−	13.4864i	0.173079	−	0.532682i	0.999541	+	0.0303108i	$0.00964970\pi$
$642$	0.711537	+	2.18989i	0.0280821	+	0.0864279i
$643$	−10.0270	+	7.28504i	−0.395426	+	0.287294i	−0.767675	−	0.640839i	$-0.778587\pi$
$643$	−10.0270	+	7.28504i	−0.395426	+	0.287294i	0.372249	+	0.928133i	$0.378587\pi$
$644$	−39.7429	+	28.8749i	−1.56609	+	1.13783i
$645$		0			0
$646$	0.593101	−	1.82538i	0.0233352	−	0.0718185i
$647$	26.8970	+	19.5418i	1.05743	+	0.768267i	0.973611	−	0.228214i	$-0.0732885\pi$
$647$	26.8970	+	19.5418i	1.05743	+	0.768267i	0.0838181	+	0.996481i	$0.473289\pi$
$648$	−2.13991			−0.0840637
$649$	−10.1628	+	21.1248i	−0.398923	+	0.829220i
$650$		0			0
$651$	−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	0.906858	+	0.421435i	$0.138474\pi$
$653$	10.7558	+	33.1030i	0.420908	+	1.29542i	−0.485951	+	0.873986i	$0.661526\pi$
$654$	0.405329	−	0.294489i	0.0158496	−	0.0115154i
$655$		0			0
$656$	−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	$-0.734510\pi$
$659$	−34.4953			−1.34375			−0.671873	+	0.740666i	$0.734510\pi$
$660$		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
$665$		0			0
$666$	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			0
$671$	8.22502	+	1.11081i	0.317523	+	0.0428823i
$672$	−7.40331			−0.285589
$673$	15.6111	+	11.3422i	0.601765	+	0.437208i	0.846505	−	0.532381i	$-0.178703\pi$
$673$	15.6111	+	11.3422i	0.601765	+	0.437208i	−0.244740	+	0.969589i	$0.578703\pi$
$674$	0.260243	−	0.800945i	0.0100242	−	0.0308513i
$675$		0			0
$676$	−18.8395	+	13.6877i	−0.724595	+	0.526449i
$677$	−13.6805	+	9.93949i	−0.525786	+	0.382006i	−0.818779	−	0.574109i	$-0.805349\pi$
$677$	−13.6805	+	9.93949i	−0.525786	+	0.382006i	0.292993	+	0.956114i	$0.405349\pi$
$678$	0.504455	+	1.55255i	0.0193735	+	0.0596255i
$679$	−4.69298	+	14.4435i	−0.180100	+	0.554291i
$680$		0			0
$681$	23.9412			0.917430
$682$	−0.240791	+	0.500518i	−0.00922035	+	0.0191658i
$683$	−4.14018			−0.158420			−0.0792098	−	0.996858i	$-0.525240\pi$
$683$	−4.14018			−0.158420			−0.0792098	+	0.996858i	$0.525240\pi$
$684$	−8.31920	−	6.04425i	−0.318093	−	0.231108i
$685$		0			0
$686$	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			0
$691$	37.4996	+	27.2450i	1.42655	+	1.03645i	0.990646	+	0.136457i	$0.0435714\pi$
$691$	37.4996	+	27.2450i	1.42655	+	1.03645i	0.435904	+	0.899993i	$0.356429\pi$
$692$	40.9539			1.55684
$693$	−11.2126	+	6.03952i	−0.425931	+	0.229422i
$694$	0.960437			0.0364577
$695$		0			0
$696$	−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
$700$		0			0
$701$	−14.0465	+	43.2306i	−0.530528	+	1.63280i	0.222591	+	0.974912i	$0.428548\pi$
$701$	−14.0465	+	43.2306i	−0.530528	+	1.63280i	−0.753119	+	0.657884i	$0.771452\pi$
$702$	0.487931	+	0.354502i	0.0184158	+	0.0133798i
$703$	−9.05904			−0.341668
$704$	−4.62398	−	25.4224i	−0.174273	−	0.958143i
$705$		0			0
$706$	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	−0.353988	−	0.935250i	$-0.615175\pi$
$709$	11.3458	−	8.24318i	0.426099	−	0.309579i	0.780087	+	0.625671i	$0.215175\pi$
$710$		0			0
$711$	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	0.997780	−	0.0666007i	$-0.0212154\pi$
$719$	4.05999	+	12.4954i	0.151412	+	0.465998i	−0.846368	+	0.532599i	$0.821215\pi$
$720$		0			0
$721$	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
$725$		0			0
$726$	−0.941597	−	1.17879i	−0.0349459	−	0.0437491i
$727$	18.3635			0.681063			0.340532	−	0.940233i	$-0.389393\pi$
$727$	18.3635			0.681063			0.340532	+	0.940233i	$0.389393\pi$
$728$	1.56090	+	1.13406i	0.0578509	+	0.0420312i
$729$	9.17943	−	28.2514i	0.339979	−	1.04635i
$730$		0			0
$731$	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	0.905571	+	0.424195i	$0.139443\pi$
$733$	11.4329	+	35.1869i	0.422284	+	1.29966i	−0.483287	+	0.875462i	$0.660557\pi$
$734$	0.635642	−	1.95631i	0.0234620	−	0.0722086i
$735$		0			0
$736$	−6.08282			−0.224216
$737$	−1.23888	−	1.18354i	−0.0456348	−	0.0435964i
$738$	−0.138666			−0.00510435
$739$	−7.96909	−	5.78988i	−0.293148	−	0.212984i	0.431484	−	0.902121i	$-0.357990\pi$
$739$	−7.96909	−	5.78988i	−0.293148	−	0.212984i	−0.724632	+	0.689136i	$0.757990\pi$
$740$		0			0
$741$	−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	−0.100540	−	0.994933i	$-0.532057\pi$
$743$	22.2052	−	16.1330i	0.814629	−	0.591862i	0.915169	+	0.403071i	$0.132057\pi$
$744$	−0.302951	−	0.932388i	−0.0111067	−	0.0341830i
$745$		0			0
$746$	1.53272	+	1.11359i	0.0561170	+	0.0407714i
$747$	3.80291			0.139141
$748$	3.98658	+	21.9180i	0.145764	+	0.801401i
$749$	−75.9591			−2.77549
$750$		0			0
$751$	4.24232	−	13.0565i	0.154804	−	0.476439i	−0.843337	−	0.537385i	$-0.819412\pi$
$751$	4.24232	−	13.0565i	0.154804	−	0.476439i	0.998141	+	0.0609469i	$0.0194120\pi$
$752$	−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			0
$756$	15.7162	−	48.3694i	0.571592	−	1.75918i
$757$	−18.5507	−	13.4779i	−0.674236	−	0.489861i	0.197205	−	0.980362i	$-0.436814\pi$
$757$	−18.5507	−	13.4779i	−0.674236	−	0.489861i	−0.871440	+	0.490501i	$0.836814\pi$
$758$	0.348578			0.0126609
$759$	23.3524	−	12.5785i	0.847640	−	0.456571i
$760$		0			0
$761$	16.7319	+	12.1565i	0.606533	+	0.440672i	0.848192	−	0.529689i	$-0.177692\pi$
$761$	16.7319	+	12.1565i	0.606533	+	0.440672i	−0.241659	+	0.970361i	$0.577692\pi$
$762$	−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
$765$		0			0
$766$	−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	$-0.256323\pi$
$769$	38.4306			1.38584			0.692922	+	0.721013i	$0.256323\pi$
$770$		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	0.140693	+	0.990053i	$0.455067\pi$
$773$	−15.4325	+	47.4964i	−0.555069	+	1.70833i	−0.695762	+	0.718272i	$0.744933\pi$
$774$	0.00645085	+	0.0198537i	0.000231871	+	0.000713626i
$775$		0			0
$776$	−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
$780$		0			0
$781$	−35.2681	−	4.76305i	−1.26199	−	0.170435i
$782$	1.71991			0.0615037
$783$	−15.1659	−	11.0187i	−0.541986	−	0.393776i
$784$	16.4334	−	50.5767i	0.586906	−	1.80631i
$785$		0			0
$786$	0.214684	−	0.155977i	0.00765751	−	0.00556351i
$787$	−12.5834	+	9.14241i	−0.448551	+	0.325892i	−0.789024	−	0.614363i	$-0.789413\pi$
$787$	−12.5834	+	9.14241i	−0.448551	+	0.325892i	0.340472	+	0.940255i	$0.389413\pi$
$788$	−13.4442	−	41.3769i	−0.478928	−	1.47399i
$789$	5.51518	−	16.9740i	0.196346	−	0.604290i
$790$		0			0
$791$	−53.8524			−1.91477
$792$	−1.04110	−	0.140603i	−0.0369938	−	0.00499610i
$793$	2.85919			0.101533
$794$	−1.68805	−	1.22644i	−0.0599067	−	0.0435248i
$795$		0			0
$796$	2.80099	+	8.62057i	0.0992786	+	0.305548i
$797$	37.3012	−	27.1009i	1.32127	−	0.959962i	0.321359	−	0.946957i	$-0.395860\pi$
$797$	37.3012	−	27.1009i	1.32127	−	0.959962i	0.999915	−	0.0130049i	$-0.00413972\pi$
$798$	3.05480	−	2.21944i	0.108139	−	0.0785674i
$799$	7.21821	+	22.2154i	0.255362	+	0.785923i
$800$		0			0
$801$	9.10970	+	6.61858i	0.321875	+	0.233856i
$802$	2.30803			0.0814994
$803$	8.16868	−	16.9798i	0.288266	−	0.599203i
$804$	1.50879			0.0532111
$805$		0			0
$806$	−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	$-0.470596\pi$
$809$	30.3700	−	22.0651i	1.06775	−	0.775767i	0.975507	+	0.219969i	$0.0705956\pi$
$810$		0			0
$811$	2.22661	−	6.85281i	0.0781870	−	0.240635i	−0.904322	−	0.426852i	$-0.859623\pi$
$811$	2.22661	−	6.85281i	0.0781870	−	0.240635i	0.982509	+	0.186217i	$0.0596227\pi$
$812$	−24.2050	−	17.5859i	−0.849428	−	0.617146i
$813$	−22.2104			−0.778953
$814$	−0.406514	+	0.218964i	−0.0142483	+	0.00767468i
$815$		0			0
$816$	−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
$820$		0			0
$821$	−2.66807	−	8.21147i	−0.0931163	−	0.286582i	0.893642	−	0.448781i	$-0.148142\pi$
$821$	−2.66807	−	8.21147i	−0.0931163	−	0.286582i	−0.986758	+	0.162198i	$0.948142\pi$
$822$	0.531284	−	1.63512i	0.0185306	−	0.0570315i
$823$	−20.2352	−	14.7017i	−0.705354	−	0.512470i	0.176318	−	0.984333i	$-0.443581\pi$
$823$	−20.2352	−	14.7017i	−0.705354	−	0.512470i	−0.881672	+	0.471864i	$0.843581\pi$
$824$	5.19375			0.180933
$825$		0			0
$826$	−2.99042			−0.104050
$827$	39.5387	+	28.7265i	1.37489	+	0.998919i	0.997337	+	0.0729332i	$0.0232360\pi$
$827$	39.5387	+	28.7265i	1.37489	+	0.998919i	0.377558	+	0.925986i	$0.376764\pi$
$828$	2.84751	−	8.76373i	0.0989577	−	0.304561i
$829$	1.63522	+	5.03270i	0.0567937	+	0.174793i	0.975429	−	0.220313i	$-0.0707079\pi$
$829$	1.63522	+	5.03270i	0.0567937	+	0.174793i	−0.918636	+	0.395106i	$0.870708\pi$
$830$		0			0
$831$	−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
$835$		0			0
$836$	29.0568	+	27.7590i	1.00495	+	0.960064i
$837$	10.1097			0.349441
$838$	0.683556	+	0.496633i	0.0236131	+	0.0171559i
$839$	−4.09196	+	12.5938i	−0.141270	+	0.434785i	−0.996513	−	0.0834435i	$-0.973408\pi$
$839$	−4.09196	+	12.5938i	−0.141270	+	0.434785i	0.855242	+	0.518228i	$0.173408\pi$
$840$		0			0
$841$	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
$845$		0			0
$846$	−0.549557			−0.0188942
$847$	46.5822	−	17.5251i	1.60058	−	0.602168i
$848$	5.68361			0.195176
$849$	−30.9643	−	22.4969i	−1.06269	−	0.772092i
$850$		0			0
$851$	−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	−0.556630	−	0.830761i	$-0.687906\pi$
$853$	1.79509	−	1.30421i	0.0614626	−	0.0446552i	0.618092	+	0.786106i	$0.287906\pi$
$854$	0.327174	+	1.00694i	0.0111956	+	0.0344567i
$855$		0			0
$856$	−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	$0.680582\pi$
$858$	−0.375806	−	0.359020i	−0.0128298	−	0.0122567i
$859$	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			0
$861$	−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	$-0.442721\pi$
$863$	34.3704	−	24.9716i	1.16998	−	0.850042i	0.991007	+	0.133811i	$0.0427215\pi$
$864$	5.09477	−	3.70157i	0.173328	−	0.125930i
$865$		0			0
$866$	0.533065	−	1.64060i	0.0181143	−	0.0557500i
$867$	−6.67038	−	4.84632i	−0.226538	−	0.164590i
$868$	16.1351			0.547662
$869$	−6.70865	−	36.8838i	−0.227575	−	1.25120i
$870$		0			0
$871$	−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
$875$		0			0
$876$	5.12746	+	15.7807i	0.173241	+	0.533181i
$877$	9.67537	−	29.7777i	0.326714	−	1.00552i	−0.643947	−	0.765070i	$-0.722704\pi$
$877$	9.67537	−	29.7777i	0.326714	−	1.00552i	0.970661	−	0.240452i	$-0.0772957\pi$
$878$	−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	$-0.896505\pi$
$883$	0.201650	−	0.620614i	0.00678605	−	0.0208853i	0.954392	+	0.298556i	$0.0965049\pi$
$884$	2.37155	+	7.29889i	0.0797639	+	0.245488i
$885$		0			0
$886$	−2.76877	+	2.01163i	−0.0930187	+	0.0675820i
$887$	4.52593	+	13.9294i	0.151966	+	0.467702i	0.997841	−	0.0656786i	$-0.0209212\pi$
$887$	4.52593	+	13.9294i	0.151966	+	0.467702i	−0.845875	+	0.533381i	$0.820921\pi$
$888$	0.251848	−	0.775108i	0.00845146	−	0.0260109i
$889$	−72.3396	−	52.5578i	−2.42619	−	1.76273i
$890$		0			0
$891$	−8.24400	+	17.1364i	−0.276184	+	0.574089i
$892$	9.71637			0.325328
$893$	34.0882	+	24.7665i	1.14072	+	0.828780i
$894$	−0.734651	+	2.26102i	−0.0245704	+	0.0756199i
$895$		0			0
$896$	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
$900$		0			0
$901$	−4.85662			−0.161798
$902$	0.537016	+	0.0725252i	0.0178807	+	0.00241483i
$903$	1.74561			0.0580903
$904$	−3.59382	−	2.61107i	−0.119529	−	0.0868428i
$905$		0			0
$906$	−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	$-0.541641\pi$
$907$	23.2552	−	16.8959i	0.772175	−	0.561018i	0.902620	+	0.430437i	$0.141641\pi$
$908$	−26.2955	+	19.1048i	−0.872645	+	0.634014i
$909$	2.44821	+	7.53482i	0.0812020	+	0.249914i
$910$		0			0
$911$	−13.9813	−	10.1580i	−0.463222	−	0.336550i	0.331572	−	0.943430i	$-0.392421\pi$
$911$	−13.9813	−	10.1580i	−0.463222	−	0.336550i	−0.794794	+	0.606880i	$0.792421\pi$
$912$	−35.2313			−1.16663
$913$	−14.7277	−	1.98901i	−0.487416	−	0.0658266i
$914$	−2.96102			−0.0979418
$915$		0			0
$916$	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	$-0.688456\pi$
$919$	1.77859	−	1.29222i	0.0586701	−	0.0426263i	0.616734	+	0.787172i	$0.288456\pi$
$920$		0			0
$921$	12.3212	−	37.9208i	0.405997	−	1.24953i
$922$	−1.92419	−	1.39801i	−0.0633699	−	0.0460409i
$923$	−12.2600			−0.403542
$924$	−19.0003	+	39.4948i	−0.625063	+	1.29928i
$925$		0			0
$926$	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	−0.860748	−	0.509031i	$-0.830004\pi$
$929$	−19.5866	+	14.2305i	−0.642616	+	0.466888i	0.218132	+	0.975919i	$0.430004\pi$
$930$		0			0
$931$	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	0.277575	−	0.960704i	$-0.410469\pi$
$937$	−16.8459	−	12.2393i	−0.550333	−	0.399840i	−0.827908	+	0.560864i	$0.810469\pi$
$938$	0.0675407	−	0.207869i	0.00220528	−	0.00678716i
$939$	7.32984	+	22.5589i	0.239200	+	0.736183i
$940$		0			0
$941$	−27.6787	+	20.1098i	−0.902301	+	0.655560i	−0.939056	−	0.343764i	$-0.888298\pi$
$941$	−27.6787	+	20.1098i	−0.902301	+	0.655560i	0.0367552	+	0.999324i	$0.488298\pi$
$942$	−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
$945$		0			0
$946$	−0.0145986	−	0.0802621i	−0.000474640	−	0.00260955i
$947$	−33.8128			−1.09877			−0.549383	−	0.835570i	$-0.685137\pi$
$947$	−33.8128			−1.09877			−0.549383	+	0.835570i	$0.685137\pi$
$948$	26.7081	+	19.4045i	0.867438	+	0.630230i
$949$	2.00587	−	6.17344i	0.0651133	−	0.200398i
$950$		0			0
$951$	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	−0.993583	−	0.113105i	$-0.963920\pi$
$953$	−7.91027	−	24.3453i	−0.256239	−	0.788622i	0.737344	−	0.675517i	$-0.236080\pi$
$954$	0.0353088	−	0.108669i	0.00114316	−	0.00351830i
$955$		0			0
$956$	45.1871			1.46146
$957$	11.6809	+	11.1591i	0.377589	+	0.360723i
$958$	−2.80042			−0.0904774
$959$	45.8845	+	33.3371i	1.48169	+	1.07651i
$960$		0			0
$961$	−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
$965$		0			0
$966$	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	$0.749400\pi$
$968$	3.95836	+	1.08904i	0.127227	+	0.0350029i
$969$	30.1051			0.967114
$970$		0			0
$971$	11.2392	−	34.5906i	0.360682	−	1.11006i	−0.591959	−	0.805968i	$-0.701645\pi$
$971$	11.2392	−	34.5906i	0.360682	−	1.11006i	0.952641	−	0.304097i	$-0.0983547\pi$
$972$	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			0
$976$	3.05269	−	9.39520i	0.0977141	−	0.300733i
$977$	8.37462	+	6.08452i	0.267928	+	0.194661i	0.713635	−	0.700518i	$-0.247048\pi$
$977$	8.37462	+	6.08452i	0.267928	+	0.194661i	−0.445707	+	0.895179i	$0.647048\pi$
$978$	1.09233			0.0349289
$979$	−31.8178	−	30.3966i	−1.01690	−	0.971481i
$980$		0			0
$981$	−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	0.998929	+	0.0462712i	$0.0147338\pi$
$983$	6.83416	+	21.0334i	0.217976	+	0.670861i	−0.780953	+	0.624590i	$0.785266\pi$
$984$	−0.773808	+	0.562205i	−0.0246681	+	0.0179224i
$985$		0			0
$986$	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
$995$		0			0
$996$	10.5876	−	7.69236i	0.335482	−	0.243742i
$997$	−3.33465	−	10.2630i	−0.105609	−	0.325032i	0.884264	−	0.466988i	$-0.154661\pi$
$997$	−3.33465	−	10.2630i	−0.105609	−	0.325032i	−0.989873	+	0.141956i	$0.954661\pi$
$998$	−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	275.2.h.b.26.1		8
5.2	odd	4		275.2.z.b.224.2		16
5.3	odd	4		275.2.z.b.224.3		16
5.4	even	2		55.2.g.a.26.2	✓	8
11.3	even	5	inner	275.2.h.b.201.1		8
11.5	even	5		3025.2.a.v.1.3		4
11.6	odd	10		3025.2.a.be.1.2		4
15.14	odd	2		495.2.n.f.136.1		8
20.19	odd	2		880.2.bo.e.81.1		8
55.3	odd	20		275.2.z.b.124.2		16
55.4	even	10		605.2.g.j.251.1		8
55.9	even	10		605.2.g.j.511.1		8
55.14	even	10		55.2.g.a.36.2	yes	8
55.19	odd	10		605.2.g.n.366.1		8
55.24	odd	10		605.2.g.g.511.2		8
55.29	odd	10		605.2.g.g.251.2		8
55.39	odd	10		605.2.a.i.1.3		4
55.47	odd	20		275.2.z.b.124.3		16
55.49	even	10		605.2.a.l.1.2		4
55.54	odd	2		605.2.g.n.81.1		8
165.14	odd	10		495.2.n.f.91.1		8
165.104	odd	10		5445.2.a.bg.1.3		4
165.149	even	10		5445.2.a.bu.1.2		4
220.39	even	10		9680.2.a.cv.1.1		4
220.159	odd	10		9680.2.a.cs.1.1		4
220.179	odd	10		880.2.bo.e.641.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.a.26.2	✓	8	5.4	even	2
55.2.g.a.36.2	yes	8	55.14	even	10
275.2.h.b.26.1		8	1.1	even	1	trivial
275.2.h.b.201.1		8	11.3	even	5	inner
275.2.z.b.124.2		16	55.3	odd	20
275.2.z.b.124.3		16	55.47	odd	20
275.2.z.b.224.2		16	5.2	odd	4
275.2.z.b.224.3		16	5.3	odd	4
495.2.n.f.91.1		8	165.14	odd	10
495.2.n.f.136.1		8	15.14	odd	2
605.2.a.i.1.3		4	55.39	odd	10
605.2.a.l.1.2		4	55.49	even	10
605.2.g.g.251.2		8	55.29	odd	10
605.2.g.g.511.2		8	55.24	odd	10
605.2.g.j.251.1		8	55.4	even	10
605.2.g.j.511.1		8	55.9	even	10
605.2.g.n.81.1		8	55.54	odd	2
605.2.g.n.366.1		8	55.19	odd	10
880.2.bo.e.81.1		8	20.19	odd	2
880.2.bo.e.641.1		8	220.179	odd	10
3025.2.a.v.1.3		4	11.5	even	5
3025.2.a.be.1.2		4	11.6	odd	10
5445.2.a.bg.1.3		4	165.104	odd	10
5445.2.a.bu.1.2		4	165.149	even	10
9680.2.a.cs.1.1		4	220.159	odd	10
9680.2.a.cv.1.1		4	220.39	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0756511 + 0.0549637i) q^{2} +(-0.453245 + 1.39494i) q^{3} +(-0.615332 - 1.89380i) q^{4} +(-0.110960 + 0.0806171i) q^{6} +(-1.39815 - 4.30308i) q^{7} +(0.115332 - 0.354955i) q^{8} +(0.686611 + 0.498852i) q^{9} +O(q^{10})\)	\(q+(0.0756511 + 0.0549637i) q^{2} +(-0.453245 + 1.39494i) q^{3} +(-0.615332 - 1.89380i) q^{4} +(-0.110960 + 0.0806171i) q^{6} +(-1.39815 - 4.30308i) q^{7} +(0.115332 - 0.354955i) q^{8} +(0.686611 + 0.498852i) q^{9} +(-2.39815 - 2.29104i) q^{11} +2.92064 q^{12} +(-0.924349 - 0.671579i) q^{13} +(0.130741 - 0.402380i) q^{14} +(-3.19369 + 2.32035i) q^{16} +(2.72899 - 1.98273i) q^{17} +(0.0245241 + 0.0754774i) q^{18} +(1.88030 - 5.78696i) q^{19} +6.63626 q^{21} +(-0.0554990 - 0.305131i) q^{22} +5.45258 q^{23} +(0.442869 + 0.321763i) q^{24} +(-0.0330155 - 0.101611i) q^{26} +(-4.56691 + 3.31805i) q^{27} +(-7.28883 + 5.29564i) q^{28} +(1.02619 + 3.15830i) q^{29} +(-1.44887 - 1.05267i) q^{31} -1.11558 q^{32} +(4.28282 - 2.30689i) q^{33} +0.315430 q^{34} +(0.522231 - 1.60726i) q^{36} +(-0.460067 - 1.41594i) q^{37} +(0.460319 - 0.334441i) q^{38} +(1.35577 - 0.985026i) q^{39} +(-0.539933 + 1.66174i) q^{41} +(0.502041 + 0.364754i) q^{42} +0.263041 q^{43} +(-2.86310 + 5.95137i) q^{44} +(0.412494 + 0.299694i) q^{46} +(-2.13986 + 6.58580i) q^{47} +(-1.78924 - 5.50670i) q^{48} +(-10.8985 + 7.91824i) q^{49} +(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} +(-2.02452 + 1.47090i) q^{61} +(-0.0517503 - 0.159271i) q^{62} +(1.18661 - 3.65201i) q^{63} +(6.30297 + 4.57938i) q^{64} +(0.450796 + 0.0608810i) q^{66} +0.516598 q^{67} +(-5.43413 - 3.94812i) q^{68} +(-2.47136 + 7.60605i) q^{69} +(8.68098 - 6.30710i) q^{71} +(0.256258 - 0.186183i) q^{72} +(1.75560 + 5.40317i) q^{73} +(0.0430208 - 0.132404i) q^{74} -12.1163 q^{76} +(-6.50552 + 13.5227i) q^{77} +0.156706 q^{78} +(9.14460 + 6.64394i) q^{79} +(-1.77179 - 5.45300i) q^{81} +(-0.132182 + 0.0960360i) q^{82} +(3.62511 - 2.63380i) q^{83} +(-4.08350 - 12.5677i) q^{84} +(0.0198994 + 0.0144577i) q^{86} -4.87077 q^{87} +(-1.08980 + 0.587008i) q^{88} +13.2676 q^{89} +(-1.59747 + 4.91652i) q^{91} +(-3.35515 - 10.3261i) q^{92} +(2.12511 - 1.54398i) q^{93} +(-0.523863 + 0.380608i) q^{94} +(0.505633 - 1.55618i) q^{96} +(-2.71551 - 1.97293i) q^{97} -1.25970 q^{98} +(-0.503711 - 2.76938i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - q^{3} - 6 q^{4} + 13 q^{6} + 3 q^{7} + 2 q^{8} - 5 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 - q^3 - 6 * q^4 + 13 * q^6 + 3 * q^7 + 2 * q^8 - 5 * q^9	\( 8 q + 4 q^{2} - q^{3} - 6 q^{4} + 13 q^{6} + 3 q^{7} + 2 q^{8} - 5 q^{9} - 5 q^{11} + 28 q^{12} - 4 q^{13} + 16 q^{14} - 20 q^{16} - q^{17} - 14 q^{18} - q^{19} - 12 q^{21} - 33 q^{22} + 18 q^{23} + 25 q^{24} - 14 q^{26} - 10 q^{27} - 4 q^{28} + 19 q^{29} + 6 q^{31} - 12 q^{32} + 19 q^{33} - 20 q^{34} + 21 q^{36} - 4 q^{37} + 6 q^{38} + 9 q^{39} - 4 q^{41} - 29 q^{42} - 42 q^{43} - 28 q^{44} - 41 q^{46} - 4 q^{47} + 19 q^{48} - 15 q^{49} + 13 q^{51} + 26 q^{52} - 3 q^{53} - 40 q^{54} + 30 q^{56} + 5 q^{57} + 6 q^{58} - 19 q^{59} - 2 q^{61} + 38 q^{62} - q^{63} + 6 q^{64} + 13 q^{66} + 2 q^{67} - 35 q^{68} - 21 q^{69} + 40 q^{71} + 34 q^{72} + 23 q^{73} + 48 q^{74} + 16 q^{76} + 28 q^{77} - 12 q^{78} + 17 q^{79} - 2 q^{82} + 25 q^{83} - 4 q^{84} - 31 q^{86} - 30 q^{87} - 22 q^{88} - 12 q^{91} - 81 q^{92} + 13 q^{93} + 33 q^{94} + 23 q^{96} - 12 q^{97} + 84 q^{98} + 4 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - q^3 - 6 * q^4 + 13 * q^6 + 3 * q^7 + 2 * q^8 - 5 * q^9 - 5 * q^11 + 28 * q^12 - 4 * q^13 + 16 * q^14 - 20 * q^16 - q^17 - 14 * q^18 - q^19 - 12 * q^21 - 33 * q^22 + 18 * q^23 + 25 * q^24 - 14 * q^26 - 10 * q^27 - 4 * q^28 + 19 * q^29 + 6 * q^31 - 12 * q^32 + 19 * q^33 - 20 * q^34 + 21 * q^36 - 4 * q^37 + 6 * q^38 + 9 * q^39 - 4 * q^41 - 29 * q^42 - 42 * q^43 - 28 * q^44 - 41 * q^46 - 4 * q^47 + 19 * q^48 - 15 * q^49 + 13 * q^51 + 26 * q^52 - 3 * q^53 - 40 * q^54 + 30 * q^56 + 5 * q^57 + 6 * q^58 - 19 * q^59 - 2 * q^61 + 38 * q^62 - q^63 + 6 * q^64 + 13 * q^66 + 2 * q^67 - 35 * q^68 - 21 * q^69 + 40 * q^71 + 34 * q^72 + 23 * q^73 + 48 * q^74 + 16 * q^76 + 28 * q^77 - 12 * q^78 + 17 * q^79 - 2 * q^82 + 25 * q^83 - 4 * q^84 - 31 * q^86 - 30 * q^87 - 22 * q^88 - 12 * q^91 - 81 * q^92 + 13 * q^93 + 33 * q^94 + 23 * q^96 - 12 * q^97 + 84 * q^98 + 4 * q^99

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