LMFDB - Embedded newform 637.2.f.l.393.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(295,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("637.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.f (of order $3$, degree $2$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 8x^{14} + 45x^{12} + 124x^{10} + 248x^{8} + 250x^{6} + 177x^{4} + 14x^{2} + 1 $ x^16 + 8x^14 + 45x^12 + 124x^10 + 248x^8 + 250x^6 + 177x^4 + 14*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			393.5
Root			$-0.141226 + 0.244611i$ of defining polynomial
Character	$\chi$	$=$	637.393
Dual form			637.2.f.l.295.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.760387 + 1.31703i) q^{2} +(-1.06311 - 1.84135i) q^{3} +(-0.156376 + 0.270851i) q^{4} -0.589391 q^{5} +(1.61674 - 2.80028i) q^{6} +2.56592 q^{8} +(-0.760387 + 1.31703i) q^{9} +O(q^{10})$	\(q+(0.760387 + 1.31703i) q^{2} +(-1.06311 - 1.84135i) q^{3} +(-0.156376 + 0.270851i) q^{4} -0.589391 q^{5} +(1.61674 - 2.80028i) q^{6} +2.56592 q^{8} +(-0.760387 + 1.31703i) q^{9} +(-0.448165 - 0.776245i) q^{10} +(-0.760387 - 1.31703i) q^{11} +0.664976 q^{12} +(-3.32565 - 1.39285i) q^{13} +(0.626585 + 1.08528i) q^{15} +(2.26384 + 3.92109i) q^{16} +(2.39740 - 4.15241i) q^{17} -2.31275 q^{18} +(0.841957 - 1.45831i) q^{19} +(0.0921666 - 0.159637i) q^{20} +(1.15638 - 2.00290i) q^{22} +(-0.886972 - 1.53628i) q^{23} +(-2.72785 - 4.72477i) q^{24} -4.65262 q^{25} +(-0.694354 - 5.43908i) q^{26} -3.14515 q^{27} +(-3.44625 - 5.96909i) q^{29} +(-0.952894 + 1.65046i) q^{30} +6.08640 q^{31} +(-0.876873 + 1.51879i) q^{32} +(-1.61674 + 2.80028i) q^{33} +7.29179 q^{34} +(-0.237812 - 0.411903i) q^{36} +(-0.704563 - 1.22034i) q^{37} +2.56085 q^{38} +(0.970785 + 7.60445i) q^{39} -1.51233 q^{40} +(0.677729 + 1.17386i) q^{41} +(5.77978 - 10.0109i) q^{43} +0.475625 q^{44} +(0.448165 - 0.776245i) q^{45} +(1.34888 - 2.33633i) q^{46} +0.464832 q^{47} +(4.81341 - 8.33707i) q^{48} +(-3.53779 - 6.12763i) q^{50} -10.1947 q^{51} +(0.897307 - 0.682948i) q^{52} +8.24681 q^{53} +(-2.39153 - 4.14225i) q^{54} +(0.448165 + 0.776245i) q^{55} -3.58035 q^{57} +(5.24097 - 9.07763i) q^{58} +(-5.93782 + 10.2846i) q^{59} -0.391931 q^{60} +(1.24009 - 2.14789i) q^{61} +(4.62802 + 8.01596i) q^{62} +6.38833 q^{64} +(1.96011 + 0.820936i) q^{65} -4.91740 q^{66} +(3.78642 + 6.55827i) q^{67} +(0.749790 + 1.29867i) q^{68} +(-1.88589 + 3.26646i) q^{69} +(-3.30235 + 5.71984i) q^{71} +(-1.95109 + 3.37939i) q^{72} +16.3712 q^{73} +(1.07148 - 1.85586i) q^{74} +(4.94622 + 8.56711i) q^{75} +(0.263323 + 0.456090i) q^{76} +(-9.27710 + 7.06087i) q^{78} -14.9623 q^{79} +(-1.33429 - 2.31106i) q^{80} +(5.62478 + 9.74241i) q^{81} +(-1.03067 + 1.78518i) q^{82} -10.1222 q^{83} +(-1.41300 + 2.44740i) q^{85} +17.5795 q^{86} +(-7.32746 + 12.6915i) q^{87} +(-1.95109 - 3.37939i) q^{88} +(8.24250 + 14.2764i) q^{89} +1.36312 q^{90} +0.554804 q^{92} +(-6.47049 - 11.2072i) q^{93} +(0.353452 + 0.612196i) q^{94} +(-0.496242 + 0.859516i) q^{95} +3.72883 q^{96} +(-0.486935 + 0.843396i) q^{97} +2.31275 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} - 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 - 4 * q^9	$ 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} - 4 q^{9} - 4 q^{11} - 8 q^{15} - 4 q^{16} - 56 q^{18} + 28 q^{22} + 12 q^{23} - 24 q^{25} + 8 q^{29} + 28 q^{30} + 4 q^{36} - 8 q^{37} - 4 q^{39} + 32 q^{43} - 8 q^{44} - 4 q^{46} + 36 q^{50} - 88 q^{51} - 8 q^{53} - 96 q^{57} - 48 q^{58} + 128 q^{60} - 64 q^{64} + 16 q^{65} + 20 q^{67} + 8 q^{71} + 28 q^{72} + 76 q^{74} + 28 q^{78} - 8 q^{79} + 56 q^{81} + 36 q^{85} + 8 q^{86} + 28 q^{88} - 160 q^{92} + 8 q^{93} + 52 q^{95} + 56 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 - 4 * q^9 - 4 * q^11 - 8 * q^15 - 4 * q^16 - 56 * q^18 + 28 * q^22 + 12 * q^23 - 24 * q^25 + 8 * q^29 + 28 * q^30 + 4 * q^36 - 8 * q^37 - 4 * q^39 + 32 * q^43 - 8 * q^44 - 4 * q^46 + 36 * q^50 - 88 * q^51 - 8 * q^53 - 96 * q^57 - 48 * q^58 + 128 * q^60 - 64 * q^64 + 16 * q^65 + 20 * q^67 + 8 * q^71 + 28 * q^72 + 76 * q^74 + 28 * q^78 - 8 * q^79 + 56 * q^81 + 36 * q^85 + 8 * q^86 + 28 * q^88 - 160 * q^92 + 8 * q^93 + 52 * q^95 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.760387	+	1.31703i	0.537675	+	0.931280i	0.999029	+	0.0440636i	$0.0140304\pi$
$2$	0.760387	+	1.31703i	0.537675	+	0.931280i	−0.461354	+	0.887216i	$0.652636\pi$
$3$	−1.06311	−	1.84135i	−0.613784	−	1.06311i	−0.990596	−	0.136816i	$-0.956313\pi$
$3$	−1.06311	−	1.84135i	−0.613784	−	1.06311i	0.376812	−	0.926290i	$-0.377020\pi$
$4$	−0.156376	+	0.270851i	−0.0781880	+	0.135426i
$5$	−0.589391			−0.263584			−0.131792	−	0.991277i	$-0.542073\pi$
$5$	−0.589391			−0.263584			−0.131792	+	0.991277i	$0.542073\pi$
$6$	1.61674	−	2.80028i	0.660032	−	1.14321i
$7$		0			0
$7$		0			0
$8$	2.56592			0.907190
$9$	−0.760387	+	1.31703i	−0.253462	+	0.439009i
$10$	−0.448165	−	0.776245i	−0.141722	−	0.245470i
$11$	−0.760387	−	1.31703i	−0.229265	−	0.397099i	0.728325	−	0.685232i	$-0.240299\pi$
$11$	−0.760387	−	1.31703i	−0.229265	−	0.397099i	−0.957591	+	0.288132i	$0.906966\pi$
$12$	0.664976			0.191962
$13$	−3.32565	−	1.39285i	−0.922370	−	0.386308i
$13$	−3.32565	−	1.39285i	−0.922370	−	0.386308i
$14$		0			0
$15$	0.626585	+	1.08528i	0.161784	+	0.280217i
$16$	2.26384	+	3.92109i	0.565961	+	0.980274i
$17$	2.39740	−	4.15241i	0.581454	−	1.00711i	−0.413853	−	0.910344i	$-0.635817\pi$
$17$	2.39740	−	4.15241i	0.581454	−	1.00711i	0.995307	−	0.0967643i	$-0.0308493\pi$
$18$	−2.31275			−0.545121
$19$	0.841957	−	1.45831i	0.193158	−	0.334560i	−0.753137	−	0.657864i	$-0.771460\pi$
$19$	0.841957	−	1.45831i	0.193158	−	0.334560i	0.946295	+	0.323304i	$0.104794\pi$
$20$	0.0921666	−	0.159637i	0.0206091	−	0.0356960i
$21$		0			0
$22$	1.15638	−	2.00290i	0.246540	−	0.427020i
$23$	−0.886972	−	1.53628i	−0.184946	−	0.320337i	0.758612	−	0.651543i	$-0.225878\pi$
$23$	−0.886972	−	1.53628i	−0.184946	−	0.320337i	−0.943558	+	0.331206i	$0.892544\pi$
$24$	−2.72785	−	4.72477i	−0.556819	−	0.964439i
$25$	−4.65262			−0.930524
$26$	−0.694354	−	5.43908i	−0.136174	−	1.06669i
$27$	−3.14515			−0.605284
$28$		0			0
$29$	−3.44625	−	5.96909i	−0.639953	−	1.10843i	−0.985443	−	0.170009i	$-0.945620\pi$
$29$	−3.44625	−	5.96909i	−0.639953	−	1.10843i	0.345489	−	0.938423i	$-0.387713\pi$
$30$	−0.952894	+	1.65046i	−0.173974	+	0.301332i
$31$	6.08640			1.09315			0.546575	−	0.837410i	$-0.315931\pi$
$31$	6.08640			1.09315			0.546575	+	0.837410i	$0.315931\pi$
$32$	−0.876873	+	1.51879i	−0.155011	+	0.268486i
$33$	−1.61674	+	2.80028i	−0.281439	+	0.487466i
$34$	7.29179			1.25053
$35$		0			0
$36$	−0.237812	−	0.411903i	−0.0396354	−	0.0686505i
$37$	−0.704563	−	1.22034i	−0.115830	−	0.200623i	0.802282	−	0.596946i	$-0.203619\pi$
$37$	−0.704563	−	1.22034i	−0.115830	−	0.200623i	−0.918111	+	0.396323i	$0.870286\pi$
$38$	2.56085			0.415425
$39$	0.970785	+	7.60445i	0.155450	+	1.21769i
$40$	−1.51233			−0.239121
$41$	0.677729	+	1.17386i	0.105843	+	0.183326i	0.914082	−	0.405528i	$-0.132912\pi$
$41$	0.677729	+	1.17386i	0.105843	+	0.183326i	−0.808239	+	0.588855i	$0.799579\pi$
$42$		0			0
$43$	5.77978	−	10.0109i	0.881408	−	1.52664i	0.0316319	−	0.999500i	$-0.489930\pi$
$43$	5.77978	−	10.0109i	0.881408	−	1.52664i	0.849776	−	0.527144i	$-0.176737\pi$
$44$	0.475625			0.0717031
$45$	0.448165	−	0.776245i	0.0668085	−	0.115716i
$46$	1.34888	−	2.33633i	0.198882	−	0.344474i
$47$	0.464832			0.0678027			0.0339013	−	0.999425i	$-0.489207\pi$
$47$	0.464832			0.0678027			0.0339013	+	0.999425i	$0.489207\pi$
$48$	4.81341	−	8.33707i	0.694756	−	1.20335i
$49$		0			0
$50$	−3.53779	−	6.12763i	−0.500319	−	0.866578i
$51$	−10.1947			−1.42755
$52$	0.897307	−	0.682948i	0.124434	−	0.0947078i
$53$	8.24681			1.13279			0.566393	−	0.824135i	$-0.308338\pi$
$53$	8.24681			1.13279			0.566393	+	0.824135i	$0.308338\pi$
$54$	−2.39153	−	4.14225i	−0.325446	−	0.563689i
$55$	0.448165	+	0.776245i	0.0604306	+	0.104669i
$56$		0			0
$57$	−3.58035			−0.474230
$58$	5.24097	−	9.07763i	0.688173	−	1.19195i
$59$	−5.93782	+	10.2846i	−0.773038	+	1.33894i	0.162852	+	0.986651i	$0.447931\pi$
$59$	−5.93782	+	10.2846i	−0.773038	+	1.33894i	−0.935890	+	0.352291i	$0.885403\pi$
$60$	−0.391931			−0.0505981
$61$	1.24009	−	2.14789i	0.158777	−	0.275009i	−0.775651	−	0.631162i	$-0.782578\pi$
$61$	1.24009	−	2.14789i	0.158777	−	0.275009i	0.934428	+	0.356153i	$0.115912\pi$
$62$	4.62802	+	8.01596i	0.587759	+	1.01803i
$63$		0			0
$64$	6.38833			0.798541
$65$	1.96011	+	0.820936i	0.243122	+	0.101825i
$66$	−4.91740			−0.605290
$67$	3.78642	+	6.55827i	0.462585	+	0.801220i	0.999089	−	0.0426774i	$-0.0135888\pi$
$67$	3.78642	+	6.55827i	0.462585	+	0.801220i	−0.536504	+	0.843898i	$0.680255\pi$
$68$	0.749790	+	1.29867i	0.0909254	+	0.157487i
$69$	−1.88589	+	3.26646i	−0.227034	+	0.393235i
$70$		0			0
$71$	−3.30235	+	5.71984i	−0.391917	+	0.678821i	−0.992702	−	0.120590i	$-0.961521\pi$
$71$	−3.30235	+	5.71984i	−0.391917	+	0.678821i	0.600785	+	0.799411i	$0.294855\pi$
$72$	−1.95109	+	3.37939i	−0.229939	+	0.398265i
$73$	16.3712			1.91610			0.958049	−	0.286604i	$-0.0925263\pi$
$73$	16.3712			1.91610			0.958049	+	0.286604i	$0.0925263\pi$
$74$	1.07148	−	1.85586i	0.124557	−	0.215739i
$75$	4.94622	+	8.56711i	0.571141	+	0.989245i
$76$	0.263323	+	0.456090i	0.0302053	+	0.0523171i
$77$		0			0
$78$	−9.27710	+	7.06087i	−1.05042	+	0.799486i
$79$	−14.9623			−1.68339			−0.841696	−	0.539951i	$-0.818443\pi$
$79$	−14.9623			−1.68339			−0.841696	+	0.539951i	$0.818443\pi$
$80$	−1.33429	−	2.31106i	−0.149178	−	0.258384i
$81$	5.62478	+	9.74241i	0.624976	+	1.08249i
$82$	−1.03067	+	1.78518i	−0.113819	+	0.197140i
$83$	−10.1222			−1.11105			−0.555526	−	0.831499i	$-0.687483\pi$
$83$	−10.1222			−1.11105			−0.555526	+	0.831499i	$0.687483\pi$
$84$		0			0
$85$	−1.41300	+	2.44740i	−0.153262	+	0.265457i
$86$	17.5795			1.89564
$87$	−7.32746	+	12.6915i	−0.785586	+	1.36068i
$88$	−1.95109	−	3.37939i	−0.207987	−	0.360244i
$89$	8.24250	+	14.2764i	0.873703	+	1.51330i	0.858138	+	0.513419i	$0.171621\pi$
$89$	8.24250	+	14.2764i	0.873703	+	1.51330i	0.0155650	+	0.999879i	$0.495045\pi$
$90$	1.36312			0.143685
$91$		0			0
$92$	0.554804			0.0578423
$93$	−6.47049	−	11.2072i	−0.670958	−	1.16213i
$94$	0.353452	+	0.612196i	0.0364558	+	0.0631432i
$95$	−0.496242	+	0.859516i	−0.0509133	+	0.0881845i
$96$	3.72883			0.380573
$97$	−0.486935	+	0.843396i	−0.0494407	+	0.0856338i	−0.889687	−	0.456572i	$-0.849077\pi$
$97$	−0.486935	+	0.843396i	−0.0494407	+	0.0856338i	0.840246	+	0.542205i	$0.182411\pi$
$98$		0			0
$99$	2.31275			0.232440
$100$	0.727557	−	1.26017i	0.0727557	−	0.126017i
$101$	−1.47012	−	2.54632i	−0.146282	−	0.253368i	0.783568	−	0.621305i	$-0.213397\pi$
$101$	−1.47012	−	2.54632i	−0.146282	−	0.253368i	−0.929851	+	0.367937i	$0.880064\pi$
$102$	−7.75195	−	13.4268i	−0.767557	−	1.32945i
$103$	−0.528682			−0.0520926			−0.0260463	−	0.999661i	$-0.508292\pi$
$103$	−0.528682			−0.0520926			−0.0260463	+	0.999661i	$0.508292\pi$
$104$	−8.53336	−	3.57395i	−0.836765	−	0.350455i
$105$		0			0
$106$	6.27076	+	10.8613i	0.609070	+	1.05494i
$107$	9.66119	+	16.7337i	0.933983	+	1.61771i	0.776438	+	0.630194i	$0.217024\pi$
$107$	9.66119	+	16.7337i	0.933983	+	1.61771i	0.157545	+	0.987512i	$0.449642\pi$
$108$	0.491825	−	0.851866i	0.0473259	−	0.0819709i
$109$	−5.73240			−0.549064			−0.274532	−	0.961578i	$-0.588523\pi$
$109$	−5.73240			−0.549064			−0.274532	+	0.961578i	$0.588523\pi$
$110$	−0.681558	+	1.18049i	−0.0649840	+	0.112556i
$111$	−1.49805	+	2.59470i	−0.142189	+	0.246278i
$112$		0			0
$113$	−2.57480	+	4.45968i	−0.242216	+	0.419531i	−0.961345	−	0.275346i	$-0.911208\pi$
$113$	−2.57480	+	4.45968i	−0.242216	+	0.419531i	0.719129	+	0.694877i	$0.244541\pi$
$114$	−2.72245	−	4.71543i	−0.254981	−	0.441640i
$115$	0.522774	+	0.905470i	0.0487489	+	0.0844355i
$116$	2.15564			0.200147
$117$	4.36321	−	3.32087i	0.403379	−	0.307015i
$118$	−18.0602			−1.66257
$119$		0			0
$120$	1.60777	+	2.78474i	0.146769	+	0.254211i
$121$	4.34362	−	7.52338i	0.394875	−	0.683943i
$122$	3.77178			0.341481
$123$	1.44099	−	2.49588i	0.129930	−	0.225045i
$124$	−0.951766	+	1.64851i	−0.0854711	+	0.148040i
$125$	5.68917			0.508855
$126$		0			0
$127$	4.50166	+	7.79710i	0.399457	+	0.691881i	0.993659	−	0.112436i	$-0.0358652\pi$
$127$	4.50166	+	7.79710i	0.399457	+	0.691881i	−0.594202	+	0.804316i	$0.702532\pi$
$128$	6.61135	+	11.4512i	0.584366	+	1.01215i
$129$	−24.5781			−2.16398
$130$	0.409246	+	3.20575i	0.0358933	+	0.281163i
$131$	−6.79840			−0.593979			−0.296989	−	0.954881i	$-0.595983\pi$
$131$	−6.79840			−0.593979			−0.296989	+	0.954881i	$0.595983\pi$
$132$	−0.505639	−	0.875793i	−0.0440102	−	0.0762280i
$133$		0			0
$134$	−5.75829	+	9.97364i	−0.497440	+	0.861592i
$135$	1.85372			0.159543
$136$	6.15153	−	10.6548i	0.527490	−	0.913639i
$137$	7.03779	−	12.1898i	0.601279	−	1.04145i	−0.391349	−	0.920242i	$-0.627991\pi$
$137$	7.03779	−	12.1898i	0.601279	−	1.04145i	0.992628	−	0.121203i	$-0.0386753\pi$
$138$	−5.73602			−0.488283
$139$	8.64313	−	14.9703i	0.733101	−	1.26977i	−0.222451	−	0.974944i	$-0.571406\pi$
$139$	8.64313	−	14.9703i	0.733101	−	1.26977i	0.955552	−	0.294824i	$-0.0952611\pi$
$140$		0			0
$141$	−0.494165	−	0.855919i	−0.0416162	−	0.0720814i
$142$	−10.0443			−0.842896
$143$	0.694354	+	5.43908i	0.0580648	+	0.454839i
$144$	−6.88559			−0.573799
$145$	2.03119	+	3.51813i	0.168681	+	0.292165i
$146$	12.4484	+	21.5613i	1.03024	+	1.78442i
$147$		0			0
$148$	0.440707			0.0362259
$149$	8.56260	−	14.8309i	0.701475	−	1.21499i	−0.266473	−	0.963842i	$-0.585858\pi$
$149$	8.56260	−	14.8309i	0.701475	−	1.21499i	0.967949	−	0.251148i	$-0.0808082\pi$
$150$	−7.52209	+	13.0286i	−0.614176	+	1.06378i
$151$	15.7975			1.28558			0.642789	−	0.766043i	$-0.277777\pi$
$151$	15.7975			1.28558			0.642789	+	0.766043i	$0.277777\pi$
$152$	2.16040	−	3.74191i	0.175231	−	0.303509i
$153$	3.64590	+	6.31488i	0.294753	+	0.510528i
$154$		0			0
$155$	−3.58727			−0.288137
$156$	−2.21148	−	0.926214i	−0.177060	−	0.0741565i
$157$	3.78351			0.301957			0.150979	−	0.988537i	$-0.451758\pi$
$157$	3.78351			0.301957			0.150979	+	0.988537i	$0.451758\pi$
$158$	−11.3771	−	19.7058i	−0.905117	−	1.56771i
$159$	−8.76722	−	15.1853i	−0.695286	−	1.20427i
$160$	0.516821	−	0.895161i	0.0408583	−	0.0707687i
$161$		0			0
$162$	−8.55402	+	14.8160i	−0.672067	+	1.16406i
$163$	−0.857757	+	1.48568i	−0.0671847	+	0.116367i	−0.897661	−	0.440687i	$-0.854735\pi$
$163$	−0.857757	+	1.48568i	−0.0671847	+	0.116367i	0.830476	+	0.557054i	$0.188068\pi$
$164$	−0.423922			−0.0331027
$165$	0.952894	−	1.65046i	0.0741827	−	0.128488i
$166$	−7.69677	−	13.3312i	−0.597385	−	1.03470i
$167$	6.32605	+	10.9570i	0.489524	+	0.847881i	0.999927	−	0.0120542i	$-0.00383706\pi$
$167$	6.32605	+	10.9570i	0.489524	+	0.847881i	−0.510403	+	0.859935i	$0.670504\pi$
$168$		0			0
$169$	9.11992	+	9.26429i	0.701532	+	0.712638i
$170$	−4.29772			−0.329620
$171$	1.28043	+	2.21776i	0.0979166	+	0.169596i
$172$	1.80764	+	3.13092i	0.137831	+	0.238730i
$173$	−5.74371	+	9.94839i	−0.436686	+	0.756362i	−0.997432	−	0.0716259i	$-0.977181\pi$
$173$	−5.74371	+	9.94839i	−0.436686	+	0.756362i	0.560746	+	0.827988i	$0.310515\pi$
$174$	−22.2868			−1.68956
$175$		0			0
$176$	3.44280	−	5.96310i	0.259510	−	0.449485i
$177$	25.2501			1.89792
$178$	−12.5350	+	21.7112i	−0.939536	+	1.62732i
$179$	1.09225	+	1.89184i	0.0816389	+	0.141403i	0.903954	−	0.427630i	$-0.140651\pi$
$179$	1.09225	+	1.89184i	0.0816389	+	0.141403i	−0.822315	+	0.569032i	$0.807318\pi$
$180$	0.140165	+	0.242772i	0.0104472	+	0.0180952i
$181$	11.5981			0.862081			0.431041	−	0.902333i	$-0.358147\pi$
$181$	11.5981			0.862081			0.431041	+	0.902333i	$0.358147\pi$
$182$		0			0
$183$	−5.27337			−0.389819
$184$	−2.27590	−	3.94198i	−0.167782	−	0.290606i
$185$	0.415264	+	0.719258i	0.0305308	+	0.0528809i
$186$	9.84014	−	17.0436i	0.721514	−	1.24970i
$187$	−7.29179			−0.533229
$188$	−0.0726885	+	0.125900i	−0.00530135	+	0.00918221i
$189$		0			0
$190$	−1.50934			−0.109499
$191$	−8.87961	+	15.3799i	−0.642506	+	1.11285i	0.342365	+	0.939567i	$0.388772\pi$
$191$	−8.87961	+	15.3799i	−0.642506	+	1.11285i	−0.984871	+	0.173286i	$0.944561\pi$
$192$	−6.79147	−	11.7632i	−0.490132	−	0.848934i
$193$	−11.3189	−	19.6050i	−0.814756	−	1.41120i	−0.909503	−	0.415697i	$-0.863538\pi$
$193$	−11.3189	−	19.6050i	−0.814756	−	1.41120i	0.0947474	−	0.995501i	$-0.469796\pi$
$194$	−1.48103			−0.106332
$195$	−0.572172	−	4.48200i	−0.0409741	−	0.320962i
$196$		0			0
$197$	−10.0032	−	17.3260i	−0.712696	−	1.23442i	−0.963842	−	0.266476i	$-0.914141\pi$
$197$	−10.0032	−	17.3260i	−0.712696	−	1.23442i	0.251146	−	0.967949i	$-0.419193\pi$
$198$	1.75859	+	3.04596i	0.124977	+	0.216467i
$199$	−0.924426	+	1.60115i	−0.0655309	+	0.113503i	−0.896929	−	0.442174i	$-0.854207\pi$
$199$	−0.924426	+	1.60115i	−0.0655309	+	0.113503i	0.831398	+	0.555677i	$0.187541\pi$
$200$	−11.9383			−0.844162
$201$	8.05073	−	13.9443i	0.567854	−	0.983553i
$202$	2.23572	−	3.87237i	0.157304	−	0.272459i
$203$		0			0
$204$	1.59421	−	2.76126i	0.111617	−	0.193327i
$205$	−0.399447	−	0.691863i	−0.0278986	−	0.0483218i
$206$	−0.402003	−	0.696289i	−0.0280088	−	0.0485127i
$207$	2.69777			0.187508
$208$	−2.06725	−	16.1934i	−0.143338	−	1.12281i
$209$	−2.56085			−0.177138
$210$		0			0
$211$	8.08474	+	14.0032i	0.556576	+	0.964019i	0.997779	+	0.0666110i	$0.0212187\pi$
$211$	8.08474	+	14.0032i	0.556576	+	0.964019i	−0.441203	+	0.897407i	$0.645448\pi$
$212$	−1.28960	+	2.23366i	−0.0885702	+	0.153408i
$213$	14.0430			0.962210
$214$	−14.6925	+	25.4481i	−1.00436	+	1.73960i
$215$	−3.40655	+	5.90032i	−0.232325	+	0.402399i
$216$	−8.07020			−0.549108
$217$		0			0
$218$	−4.35884	−	7.54973i	−0.295218	−	0.511332i
$219$	−17.4043	−	30.1451i	−1.17607	−	2.03701i
$220$	−0.280329			−0.0188998
$221$	−13.7566	+	10.4703i	−0.925369	+	0.704306i
$222$	−4.55639			−0.305805
$223$	−6.21589	−	10.7662i	−0.416247	−	0.720961i	0.579312	−	0.815106i	$-0.303321\pi$
$223$	−6.21589	−	10.7662i	−0.416247	−	0.720961i	−0.995558	+	0.0941455i	$0.969988\pi$
$224$		0			0
$225$	3.53779	−	6.12763i	0.235853	−	0.408509i
$226$	−7.83136			−0.520934
$227$	0.617487	−	1.06952i	0.0409841	−	0.0709865i	−0.844806	−	0.535073i	$-0.820284\pi$
$227$	0.617487	−	1.06952i	0.0409841	−	0.0709865i	0.885790	+	0.464087i	$0.153617\pi$
$228$	0.559881	−	0.969743i	0.0370790	−	0.0642228i
$229$	−6.55514			−0.433176			−0.216588	−	0.976263i	$-0.569493\pi$
$229$	−6.55514			−0.433176			−0.216588	+	0.976263i	$0.569493\pi$
$230$	−0.795020	+	1.37702i	−0.0524221	+	0.0907977i
$231$		0			0
$232$	−8.84282	−	15.3162i	−0.580559	−	1.00556i
$233$	6.29887			0.412653			0.206326	−	0.978483i	$-0.433849\pi$
$233$	6.29887			0.412653			0.206326	+	0.978483i	$0.433849\pi$
$234$	7.69141	+	3.22132i	0.502803	+	0.210585i
$235$	−0.273968			−0.0178717
$236$	−1.85706	−	3.21653i	−0.120885	−	0.209378i
$237$	15.9065	+	27.5509i	1.03324	+	1.78962i
$238$		0			0
$239$	−18.9193			−1.22379			−0.611895	−	0.790939i	$-0.709592\pi$
$239$	−18.9193			−1.22379			−0.611895	+	0.790939i	$0.709592\pi$
$240$	−2.83698	+	4.91380i	−0.183126	+	0.317184i
$241$	11.1484	−	19.3096i	0.718131	−	1.24384i	−0.243609	−	0.969874i	$-0.578331\pi$
$241$	11.1484	−	19.3096i	0.718131	−	1.24384i	0.961740	−	0.273965i	$-0.0883353\pi$
$242$	13.2113			0.849257
$243$	7.24176	−	12.5431i	0.464559	−	0.804640i
$244$	0.387839	+	0.671757i	0.0248289	+	0.0430048i
$245$		0			0
$246$	4.38285			0.279440
$247$	−4.83127	+	3.67711i	−0.307406	+	0.233969i
$248$	15.6172			0.991695
$249$	10.7609	+	18.6385i	0.681947	+	1.18117i
$250$	4.32597	+	7.49280i	0.273598	+	0.473886i
$251$	−3.47657	+	6.02160i	−0.219439	+	0.380080i	−0.954637	−	0.297773i	$-0.903756\pi$
$251$	−3.47657	+	6.02160i	−0.219439	+	0.380080i	0.735197	+	0.677853i	$0.237090\pi$
$252$		0			0
$253$	−1.34888	+	2.33633i	−0.0848036	+	0.146884i
$254$	−6.84600	+	11.8576i	−0.429556	+	0.744013i
$255$	6.00869			0.376279
$256$	−3.66603	+	6.34975i	−0.229127	+	0.396860i
$257$	10.5776	+	18.3209i	0.659811	+	1.14283i	0.980664	+	0.195697i	$0.0626970\pi$
$257$	10.5776	+	18.3209i	0.659811	+	1.14283i	−0.320853	+	0.947129i	$0.603970\pi$
$258$	−18.6888	−	32.3700i	−1.16352	−	2.01527i
$259$		0			0
$260$	−0.528865	+	0.402523i	−0.0327988	+	0.0249634i
$261$	10.4819			0.648816
$262$	−5.16941	−	8.95368i	−0.319367	−	0.553160i
$263$	4.21496	+	7.30053i	0.259906	+	0.450170i	0.966216	−	0.257732i	$-0.0829752\pi$
$263$	4.21496	+	7.30053i	0.259906	+	0.450170i	−0.706311	+	0.707902i	$0.749642\pi$
$264$	−4.14844	+	7.18530i	−0.255319	+	0.442225i
$265$	−4.86060			−0.298584
$266$		0			0
$267$	17.5253	−	30.3547i	1.07253	−	1.85768i
$268$	−2.36842			−0.144674
$269$	−2.91519	+	5.04926i	−0.177743	+	0.307859i	−0.941107	−	0.338109i	$-0.890213\pi$
$269$	−2.91519	+	5.04926i	−0.177743	+	0.307859i	0.763364	+	0.645968i	$0.223546\pi$
$270$	1.40955	+	2.44141i	0.0857823	+	0.148579i
$271$	9.21497	+	15.9608i	0.559769	+	0.969549i	0.997515	+	0.0704502i	$0.0224436\pi$
$271$	9.21497	+	15.9608i	0.559769	+	0.969549i	−0.437746	+	0.899099i	$0.644223\pi$
$272$	21.7093			1.31632
$273$		0			0
$274$	21.4058			1.29317
$275$	3.53779	+	6.12763i	0.213337	+	0.369510i
$276$	−0.589815	−	1.02159i	−0.0355027	−	0.0614925i
$277$	3.09154	−	5.35470i	0.185752	−	0.321733i	−0.758077	−	0.652165i	$-0.773861\pi$
$277$	3.09154	−	5.35470i	0.185752	−	0.321733i	0.943830	+	0.330432i	$0.107194\pi$
$278$	26.2885			1.57668
$279$	−4.62802	+	8.01596i	−0.277072	+	0.479903i
$280$		0			0
$281$	−5.64049			−0.336483			−0.168242	−	0.985746i	$-0.553809\pi$
$281$	−5.64049			−0.336483			−0.168242	+	0.985746i	$0.553809\pi$
$282$	0.751513	−	1.30166i	0.0447520	−	0.0775127i
$283$	−8.22771	−	14.2508i	−0.489086	−	0.847123i	0.510835	−	0.859679i	$-0.329336\pi$
$283$	−8.22771	−	14.2508i	−0.489086	−	0.847123i	−0.999921	+	0.0125564i	$0.996003\pi$
$284$	−1.03282	−	1.78889i	−0.0612864	−	0.106151i
$285$	2.11023			0.124999
$286$	−6.63545	+	5.05029i	−0.392362	+	0.298630i
$287$		0			0
$288$	−1.33353	−	2.30973i	−0.0785787	−	0.136102i
$289$	−2.99502	−	5.18752i	−0.176177	−	0.305148i
$290$	−3.08898	+	5.35028i	−0.181391	+	0.314179i
$291$	2.07065			0.121384
$292$	−2.56005	+	4.43414i	−0.149816	+	0.259489i
$293$	15.3086	−	26.5152i	0.894335	−	1.54903i	0.0597104	−	0.998216i	$-0.480982\pi$
$293$	15.3086	−	26.5152i	0.894335	−	1.54903i	0.834625	−	0.550819i	$-0.185684\pi$
$294$		0			0
$295$	3.49970	−	6.06166i	0.203760	−	0.352923i
$296$	−1.80785	−	3.13130i	−0.105079	−	0.182003i
$297$	2.39153	+	4.14225i	0.138771	+	0.240358i
$298$	26.0435			1.50866
$299$	0.809947	+	6.34456i	0.0468404	+	0.366915i
$300$	−3.09388			−0.178625
$301$		0			0
$302$	12.0122	+	20.8057i	0.691223	+	1.19723i
$303$	−3.12578	+	5.41401i	−0.179571	+	0.311027i
$304$	7.62424			0.437280
$305$	−0.730896	+	1.26595i	−0.0418510	+	0.0724880i
$306$	−5.54458	+	9.60350i	−0.316963	+	0.548995i
$307$	9.96020			0.568459			0.284229	−	0.958756i	$-0.408262\pi$
$307$	9.96020			0.568459			0.284229	+	0.958756i	$0.408262\pi$
$308$		0			0
$309$	0.562044	+	0.973489i	0.0319736	+	0.0553799i
$310$	−2.72771	−	4.72454i	−0.154924	−	0.268336i
$311$	−27.7468			−1.57337			−0.786687	−	0.617352i	$-0.788205\pi$
$311$	−27.7468			−1.57337			−0.786687	+	0.617352i	$0.788205\pi$
$312$	2.49096	+	19.5124i	0.141023	+	1.10467i
$313$	16.5227			0.933920			0.466960	−	0.884278i	$-0.345349\pi$
$313$	16.5227			0.933920			0.466960	+	0.884278i	$0.345349\pi$
$314$	2.87693	+	4.98300i	0.162355	+	0.281207i
$315$		0			0
$316$	2.33975	−	4.05256i	0.131621	−	0.227974i
$317$	23.6793			1.32996			0.664980	−	0.746861i	$-0.268440\pi$
$317$	23.6793			1.32996			0.664980	+	0.746861i	$0.268440\pi$
$318$	13.3330	−	23.0934i	0.747675	−	1.29501i
$319$	−5.24097	+	9.07763i	−0.293438	+	0.508250i
$320$	−3.76523			−0.210483
$321$	20.5417	−	35.5793i	1.14653	−	1.98584i
$322$		0			0
$323$	−4.03701	−	6.99230i	−0.224625	−	0.389062i
$324$	−3.51832			−0.195462
$325$	15.4730	+	6.48041i	0.858287	+	0.359469i
$326$	−2.60891			−0.144494
$327$	6.09414	+	10.5554i	0.337007	+	0.583713i
$328$	1.73900	+	3.01203i	0.0960202	+	0.166312i
$329$		0			0
$330$	2.89827			0.159545
$331$	−3.97604	+	6.88671i	−0.218543	+	0.378528i	−0.954363	−	0.298650i	$-0.903464\pi$
$331$	−3.97604	+	6.88671i	−0.218543	+	0.378528i	0.735820	+	0.677178i	$0.236797\pi$
$332$	1.58286	−	2.74160i	0.0868710	−	0.150465i
$333$	2.14296			0.117434
$334$	−9.62049	+	16.6632i	−0.526410	+	0.911768i
$335$	−2.23168	−	3.86539i	−0.121930	−	0.211189i
$336$		0			0
$337$	−7.91326			−0.431063			−0.215531	−	0.976497i	$-0.569148\pi$
$337$	−7.91326			−0.431063			−0.215531	+	0.976497i	$0.569148\pi$
$338$	−5.26667	+	19.0556i	−0.286469	+	1.03649i
$339$	10.9491			0.594674
$340$	−0.441920	−	0.765427i	−0.0239665	−	0.0415111i
$341$	−4.62802	−	8.01596i	−0.250621	−	0.434089i
$342$	−1.94724	+	3.37271i	−0.105294	+	0.182375i
$343$		0			0
$344$	14.8305	−	25.6871i	0.799605	−	1.38496i
$345$	1.11153	−	1.92522i	0.0598426	−	0.103650i
$346$	−17.4698			−0.939180
$347$	−3.56786	+	6.17971i	−0.191533	+	0.331744i	−0.945758	−	0.324871i	$-0.894679\pi$
$347$	−3.56786	+	6.17971i	−0.191533	+	0.331744i	0.754226	+	0.656615i	$0.228012\pi$
$348$	−2.29168	−	3.96930i	−0.122847	−	0.212777i
$349$	−0.688402	−	1.19235i	−0.0368493	−	0.0638249i	0.847013	−	0.531573i	$-0.178399\pi$
$349$	−0.688402	−	1.19235i	−0.0368493	−	0.0638249i	−0.883862	+	0.467748i	$0.845065\pi$
$350$		0			0
$351$	10.4597	+	4.38073i	0.558296	+	0.233826i
$352$	2.66705			0.142154
$353$	−0.346608	−	0.600342i	−0.0184481	−	0.0319530i	0.856654	−	0.515891i	$-0.172539\pi$
$353$	−0.346608	−	0.600342i	−0.0184481	−	0.0319530i	−0.875102	+	0.483938i	$0.839206\pi$
$354$	19.1999	+	33.2551i	1.02046	+	1.76749i
$355$	1.94638	−	3.37123i	0.103303	−	0.178926i
$356$	−5.15571			−0.273252
$357$		0			0
$358$	−1.66107	+	2.87706i	−0.0877904	+	0.152057i
$359$	−5.80365			−0.306305			−0.153152	−	0.988203i	$-0.548943\pi$
$359$	−5.80365			−0.306305			−0.153152	+	0.988203i	$0.548943\pi$
$360$	1.14996	−	1.99178i	0.0606081	−	0.104976i
$361$	8.08222	+	13.9988i	0.425380	+	0.736780i
$362$	8.81905	+	15.2750i	0.463519	+	0.802839i
$363$	−18.4709			−0.969472
$364$		0			0
$365$	−9.64902			−0.505053
$366$	−4.00980	−	6.94518i	−0.209596	−	0.363030i
$367$	−3.67578	−	6.36664i	−0.191874	−	0.332336i	0.753997	−	0.656878i	$-0.228123\pi$
$367$	−3.67578	−	6.36664i	−0.191874	−	0.332336i	−0.945871	+	0.324542i	$0.894790\pi$
$368$	4.01593	−	6.95580i	0.209345	−	0.362596i
$369$	−2.06134			−0.107309
$370$	−0.631522	+	1.09383i	−0.0328313	+	0.0568654i
$371$		0			0
$372$	4.04731			0.209843
$373$	−9.19942	+	15.9339i	−0.476328	+	0.825024i	−0.999632	−	0.0271216i	$-0.991366\pi$
$373$	−9.19942	+	15.9339i	−0.476328	+	0.825024i	0.523304	+	0.852146i	$0.324699\pi$
$374$	−5.54458	−	9.60350i	−0.286704	−	0.496585i
$375$	−6.04819	−	10.4758i	−0.312327	−	0.540966i
$376$	1.19272			0.0615099
$377$	3.14698	+	24.6512i	0.162078	+	1.26960i
$378$		0			0
$379$	2.42550	+	4.20110i	0.124590	+	0.215796i	0.921573	−	0.388206i	$-0.126905\pi$
$379$	2.42550	+	4.20110i	0.124590	+	0.215796i	−0.796983	+	0.604002i	$0.793572\pi$
$380$	−0.155201	−	0.268815i	−0.00796162	−	0.0137899i
$381$	9.57147	−	16.5783i	0.490361	−	0.849331i
$382$	−27.0078			−1.38184
$383$	11.4103	−	19.7631i	0.583037	−	1.00985i	−0.412080	−	0.911148i	$-0.635198\pi$
$383$	11.4103	−	19.7631i	0.583037	−	1.00985i	0.995117	−	0.0987019i	$-0.0314690\pi$
$384$	14.0571	−	24.3476i	0.717349	−	1.24249i
$385$		0			0
$386$	17.2136	−	29.8148i	0.876147	−	1.51753i
$387$	8.78973	+	15.2243i	0.446807	+	0.773893i
$388$	−0.152290	−	0.263773i	−0.00773134	−	0.0133911i
$389$	−20.3122			−1.02987			−0.514933	−	0.857230i	$-0.672183\pi$
$389$	−20.3122			−1.02987			−0.514933	+	0.857230i	$0.672183\pi$
$390$	5.46784	−	4.16162i	0.276875	−	0.210732i
$391$	−8.50569			−0.430151
$392$		0			0
$393$	7.22741	+	12.5182i	0.364575	+	0.631462i
$394$	15.2125	−	26.3489i	0.766397	−	1.32744i
$395$	8.81866			0.443715
$396$	−0.361659	+	0.626411i	−0.0181740	+	0.0314783i
$397$	17.0689	−	29.5641i	0.856662	−	1.48378i	−0.0184326	−	0.999830i	$-0.505868\pi$
$397$	17.0689	−	29.5641i	0.856662	−	1.48378i	0.875095	−	0.483952i	$-0.160799\pi$
$398$	−2.81169			−0.140937
$399$		0			0
$400$	−10.5328	−	18.2434i	−0.526640	−	0.912168i
$401$	1.51298	+	2.62056i	0.0755547	+	0.130865i	0.901327	−	0.433139i	$-0.142594\pi$
$401$	1.51298	+	2.62056i	0.0755547	+	0.130865i	−0.825773	+	0.564003i	$0.809261\pi$
$402$	24.4867			1.22128
$403$	−20.2412	−	8.47746i	−1.00829	−	0.422292i
$404$	0.919564			0.0457500
$405$	−3.31520	−	5.74209i	−0.164734	−	0.285327i
$406$		0			0
$407$	−1.07148	+	1.85586i	−0.0531114	+	0.0919916i
$408$	−26.1589			−1.29506
$409$	−2.69162	+	4.66203i	−0.133092	+	0.230523i	−0.924867	−	0.380291i	$-0.875824\pi$
$409$	−2.69162	+	4.66203i	−0.133092	+	0.230523i	0.791775	+	0.610813i	$0.209157\pi$
$410$	0.607469	−	1.05217i	0.0300008	−	0.0519628i
$411$	−29.9276			−1.47622
$412$	0.0826731	−	0.143194i	0.00407301	−	0.00705466i
$413$		0			0
$414$	2.05135	+	3.55304i	0.100818	+	0.174622i
$415$	5.96592			0.292856
$416$	5.03162	−	3.82961i	0.246696	−	0.187762i
$417$	−36.7543			−1.79986
$418$	−1.94724	−	3.37271i	−0.0952425	−	0.164965i
$419$	−2.94117	−	5.09426i	−0.143686	−	0.248871i	0.785196	−	0.619247i	$-0.212562\pi$
$419$	−2.94117	−	5.09426i	−0.143686	−	0.248871i	−0.928882	+	0.370376i	$0.879229\pi$
$420$		0			0
$421$	−28.7614			−1.40174			−0.700872	−	0.713287i	$-0.747206\pi$
$421$	−28.7614			−1.40174			−0.700872	+	0.713287i	$0.747206\pi$
$422$	−12.2951	+	21.2957i	−0.598514	+	1.03666i
$423$	−0.353452	+	0.612196i	−0.0171854	+	0.0297660i
$424$	21.1607			1.02765
$425$	−11.1542	+	19.3196i	−0.541057	+	0.937138i
$426$	10.6781	+	18.4950i	0.517356	+	0.896087i
$427$		0			0
$428$	−6.04311			−0.292105
$429$	9.27710	−	7.06087i	0.447903	−	0.340902i
$430$	−10.3612			−0.499661
$431$	−4.19294	−	7.26238i	−0.201967	−	0.349817i	0.747195	−	0.664605i	$-0.231400\pi$
$431$	−4.19294	−	7.26238i	−0.201967	−	0.349817i	−0.949162	+	0.314788i	$0.898067\pi$
$432$	−7.12013	−	12.3324i	−0.342567	−	0.593344i
$433$	13.7996	−	23.9017i	0.663168	−	1.14864i	−0.316611	−	0.948556i	$-0.602545\pi$
$433$	13.7996	−	23.9017i	0.663168	−	1.14864i	0.979779	−	0.200085i	$-0.0641218\pi$
$434$		0			0
$435$	4.31874	−	7.48028i	0.207068	−	0.358652i
$436$	0.896409	−	1.55263i	0.0429302	−	0.0743573i
$437$	−2.98717			−0.142896
$438$	26.4679	−	45.8438i	1.26469	−	2.19050i
$439$	−15.5869	−	26.9973i	−0.743921	−	1.28851i	−0.950697	−	0.310121i	$-0.899631\pi$
$439$	−15.5869	−	26.9973i	−0.743921	−	1.28851i	0.206776	−	0.978388i	$-0.433703\pi$
$440$	1.14996	+	1.99178i	0.0548221	+	0.0949546i
$441$		0			0
$442$	−24.2500	−	10.1564i	−1.15345	−	0.483090i
$443$	−23.5883			−1.12071			−0.560357	−	0.828251i	$-0.689336\pi$
$443$	−23.5883			−1.12071			−0.560357	+	0.828251i	$0.689336\pi$
$444$	−0.468518	−	0.811497i	−0.0222349	−	0.0385119i
$445$	−4.85806	−	8.41440i	−0.230294	−	0.398881i
$446$	9.45296	−	16.3730i	0.447611	−	0.775284i
$447$	−36.4118			−1.72222
$448$		0			0
$449$	−1.41328	+	2.44787i	−0.0666968	+	0.115522i	−0.897445	−	0.441125i	$-0.854579\pi$
$449$	−1.41328	+	2.44787i	−0.0666968	+	0.115522i	0.830749	+	0.556648i	$0.187913\pi$
$450$	10.7604			0.507248
$451$	1.03067	−	1.78518i	0.0485324	−	0.0840607i
$452$	−0.805272	−	1.39477i	−0.0378768	−	0.0656046i
$453$	−16.7944	−	29.0887i	−0.789068	−	1.36671i
$454$	1.87812			0.0881444
$455$		0			0
$456$	−9.18691			−0.430217
$457$	18.8716	+	32.6866i	0.882776	+	1.52901i	0.848242	+	0.529609i	$0.177661\pi$
$457$	18.8716	+	32.6866i	0.882776	+	1.52901i	0.0345338	+	0.999404i	$0.489005\pi$
$458$	−4.98444	−	8.63330i	−0.232908	−	0.403408i
$459$	−7.54017	+	13.0599i	−0.351945	+	0.609586i
$460$	−0.326997			−0.0152463
$461$	−17.3293	+	30.0152i	−0.807106	+	1.39795i	0.107754	+	0.994178i	$0.465634\pi$
$461$	−17.3293	+	30.0152i	−0.807106	+	1.39795i	−0.914860	+	0.403771i	$0.867699\pi$
$462$		0			0
$463$	18.5114			0.860296			0.430148	−	0.902758i	$-0.358461\pi$
$463$	18.5114			0.860296			0.430148	+	0.902758i	$0.358461\pi$
$464$	15.6036	−	27.0262i	0.724377	−	1.25466i
$465$	3.81365	+	6.60543i	0.176854	+	0.306320i
$466$	4.78958	+	8.29579i	0.221873	+	0.384295i
$467$	6.62783			0.306700			0.153350	−	0.988172i	$-0.450994\pi$
$467$	6.62783			0.306700			0.153350	+	0.988172i	$0.450994\pi$
$468$	0.217161	+	1.70108i	0.0100383	+	0.0786326i
$469$		0			0
$470$	−0.208321	−	0.360823i	−0.00960915	−	0.0166435i
$471$	−4.02227	−	6.96678i	−0.185337	−	0.321012i
$472$	−15.2360	+	26.3895i	−0.701293	+	1.21468i
$473$	−17.5795			−0.808305
$474$	−24.1902	+	41.8987i	−1.11109	+	1.92447i
$475$	−3.91730	+	6.78497i	−0.179738	+	0.311316i
$476$		0			0
$477$	−6.27076	+	10.8613i	−0.287118	+	0.497304i
$478$	−14.3860	−	24.9173i	−0.658001	−	1.13969i
$479$	8.72630	+	15.1144i	0.398715	+	0.690594i	0.993568	−	0.113240i	$-0.0361230\pi$
$479$	8.72630	+	15.1144i	0.398715	+	0.690594i	−0.594853	+	0.803835i	$0.702790\pi$
$480$	−2.19774			−0.100313
$481$	0.643379	+	5.03978i	0.0293355	+	0.229794i
$482$	33.9083			1.54448
$483$		0			0
$484$	1.35848	+	2.35295i	0.0617489	+	0.106952i
$485$	0.286995	−	0.497090i	0.0130318	−	0.0225717i
$486$	22.0261			0.999126
$487$	17.7569	−	30.7558i	0.804641	−	1.39368i	−0.111892	−	0.993720i	$-0.535691\pi$
$487$	17.7569	−	30.7558i	0.804641	−	1.39368i	0.916533	−	0.399959i	$-0.130976\pi$
$488$	3.18196	−	5.51132i	0.144041	−	0.249486i
$489$	3.64754			0.164948
$490$		0			0
$491$	14.9059	+	25.8178i	0.672695	+	1.16514i	0.977137	+	0.212611i	$0.0681966\pi$
$491$	14.9059	+	25.8178i	0.672695	+	1.16514i	−0.304442	+	0.952531i	$0.598470\pi$
$492$	0.450674	+	0.780590i	0.0203179	+	0.0351917i
$493$	−33.0481			−1.48841
$494$	−8.51650	−	3.56689i	−0.383175	−	0.160482i
$495$	−1.36312			−0.0612675
$496$	13.7787	+	23.8653i	0.618680	+	1.07159i
$497$		0			0
$498$	−16.3649	+	28.3449i	−0.733331	+	1.27017i
$499$	−7.50966			−0.336178			−0.168089	−	0.985772i	$-0.553760\pi$
$499$	−7.50966			−0.336178			−0.168089	+	0.985772i	$0.553760\pi$
$500$	−0.889649	+	1.54092i	−0.0397863	+	0.0689119i
$501$	13.4505	−	23.2970i	0.600925	−	1.04083i
$502$	−10.5742			−0.471948
$503$	−0.492171	+	0.852466i	−0.0219448	+	0.0380096i	−0.876789	−	0.480875i	$-0.840319\pi$
$503$	−0.492171	+	0.852466i	−0.0219448	+	0.0380096i	0.854844	+	0.518884i	$0.173652\pi$
$504$		0			0
$505$	0.866474	+	1.50078i	0.0385576	+	0.0667837i
$506$	−4.10269			−0.182387
$507$	7.36339	−	26.6419i	0.327019	−	1.18321i
$508$	−2.81580			−0.124931
$509$	−6.48958	−	11.2403i	−0.287646	−	0.498217i	0.685602	−	0.727977i	$-0.259539\pi$
$509$	−6.48958	−	11.2403i	−0.287646	−	0.498217i	−0.973247	+	0.229760i	$0.926206\pi$
$510$	4.56893	+	7.91362i	0.202316	+	0.350421i
$511$		0			0
$512$	15.2950			0.675949
$513$	−2.64808	+	4.58661i	−0.116916	+	0.202504i
$514$	−16.0861	+	27.8619i	−0.709527	+	1.22894i
$515$	0.311600			0.0137308
$516$	3.84342	−	6.65699i	0.169197	−	0.293058i
$517$	−0.353452	−	0.612196i	−0.0155448	−	0.0269244i
$518$		0			0
$519$	24.4247			1.07212
$520$	5.02949	+	2.10646i	0.220558	+	0.0923742i
$521$	−19.4146			−0.850569			−0.425285	−	0.905060i	$-0.639826\pi$
$521$	−19.4146			−0.850569			−0.425285	+	0.905060i	$0.639826\pi$
$522$	7.97033	+	13.8050i	0.348852	+	0.604229i
$523$	−13.6360	−	23.6182i	−0.596259	−	1.03275i	−0.993368	−	0.114979i	$-0.963320\pi$
$523$	−13.6360	−	23.6182i	−0.596259	−	1.03275i	0.397109	−	0.917771i	$-0.370013\pi$
$524$	1.06311	−	1.84135i	0.0464420	−	0.0804399i
$525$		0			0
$526$	−6.41000	+	11.1024i	−0.279489	+	0.484090i
$527$	14.5915	−	25.2732i	0.635616	−	1.10092i
$528$	−14.6402			−0.637134
$529$	9.92656	−	17.1933i	0.431590	−	0.747535i
$530$	−3.69593	−	6.40154i	−0.160541	−	0.278065i
$531$	−9.03008	−	15.6406i	−0.391872	−	0.678742i
$532$		0			0
$533$	−0.618874	−	4.84783i	−0.0268064	−	0.209983i
$534$	53.3040			2.30669
$535$	−5.69422	−	9.86268i	−0.246183	−	0.426401i
$536$	9.71566	+	16.8280i	0.419652	+	0.726859i
$537$	2.32236	−	4.02245i	0.100217	−	0.173582i
$538$	−8.86670			−0.382271
$539$		0			0
$540$	−0.289878	+	0.502083i	−0.0124743	+	0.0216062i
$541$	−30.0990			−1.29406			−0.647029	−	0.762465i	$-0.723989\pi$
$541$	−30.0990			−1.29406			−0.647029	+	0.762465i	$0.723989\pi$
$542$	−14.0139	+	24.2727i	−0.601947	+	1.04260i
$543$	−12.3300	−	21.3562i	−0.529132	−	0.916483i
$544$	4.20442	+	7.28228i	0.180263	+	0.312225i
$545$	3.37863			0.144724
$546$		0			0
$547$	−26.1451			−1.11788			−0.558942	−	0.829207i	$-0.688793\pi$
$547$	−26.1451			−1.11788			−0.558942	+	0.829207i	$0.688793\pi$
$548$	2.20108	+	3.81238i	0.0940255	+	0.162857i
$549$	1.88589	+	3.26646i	0.0804878	+	0.139409i
$550$	−5.38018	+	9.31874i	−0.229411	+	0.397352i
$551$	−11.6064			−0.494449
$552$	−4.83905	+	8.38147i	−0.205963	+	0.356739i
$553$		0			0
$554$	9.40305			0.399497
$555$	0.882938	−	1.52929i	0.0374786	−	0.0649149i
$556$	2.70316	+	4.68200i	0.114639	+	0.198561i
$557$	−8.95317	−	15.5073i	−0.379358	−	0.657067i	0.611611	−	0.791159i	$-0.290522\pi$
$557$	−8.95317	−	15.5073i	−0.379358	−	0.657067i	−0.990969	+	0.134091i	$0.957188\pi$
$558$	−14.0763			−0.595899
$559$	−33.1652	+	25.2423i	−1.40274	+	1.06764i
$560$		0			0
$561$	7.75195	+	13.4268i	0.327287	+	0.566878i
$562$	−4.28895	−	7.42868i	−0.180919	−	0.313360i
$563$	15.8275	−	27.4140i	0.667048	−	1.15536i	−0.311678	−	0.950188i	$-0.600891\pi$
$563$	15.8275	−	27.4140i	0.667048	−	1.15536i	0.978726	−	0.205173i	$-0.0657756\pi$
$564$	0.309102			0.0130155
$565$	1.51756	−	2.62850i	0.0638443	−	0.110582i
$566$	12.5125	−	21.6722i	0.525939	−	0.910953i
$567$		0			0
$568$	−8.47358	+	14.6767i	−0.355544	+	0.615820i
$569$	13.0555	+	22.6129i	0.547317	+	0.947981i	0.998457	+	0.0555278i	$0.0176841\pi$
$569$	13.0555	+	22.6129i	0.547317	+	0.947981i	−0.451140	+	0.892453i	$0.648983\pi$
$570$	1.60459	+	2.77923i	0.0672089	+	0.116409i
$571$	13.3041			0.556760			0.278380	−	0.960471i	$-0.410203\pi$
$571$	13.3041			0.556760			0.278380	+	0.960471i	$0.410203\pi$
$572$	−1.58176	−	0.662475i	−0.0661368	−	0.0276995i
$573$	37.7599			1.57744
$574$		0			0
$575$	4.12674	+	7.14773i	0.172097	+	0.298081i
$576$	−4.85760	+	8.41361i	−0.202400	+	0.350567i
$577$	−16.7713			−0.698198			−0.349099	−	0.937086i	$-0.613512\pi$
$577$	−16.7713			−0.698198			−0.349099	+	0.937086i	$0.613512\pi$
$578$	4.55474	−	7.88904i	0.189452	−	0.328141i
$579$	−24.0665	+	41.6844i	−1.00017	+	1.73234i
$580$	−1.27052			−0.0527554
$581$		0			0
$582$	1.57450	+	2.72711i	0.0652650	+	0.113042i
$583$	−6.27076	−	10.8613i	−0.259708	−	0.449828i
$584$	42.0071			1.73827
$585$	−2.57164	+	1.95729i	−0.106324	+	0.0809241i
$586$	46.5617			1.92345
$587$	5.03261	+	8.71673i	0.207718	+	0.359778i	0.950995	−	0.309205i	$-0.100063\pi$
$587$	5.03261	+	8.71673i	0.207718	+	0.359778i	−0.743277	+	0.668983i	$0.766730\pi$
$588$		0			0
$589$	5.12448	−	8.87587i	0.211151	−	0.365724i
$590$	10.6445			0.438227
$591$	−21.2688	+	36.8387i	−0.874883	+	1.51534i
$592$	3.19004	−	5.52532i	0.131110	−	0.227089i
$593$	39.4322			1.61929			0.809643	−	0.586923i	$-0.199661\pi$
$593$	39.4322			1.61929			0.809643	+	0.586923i	$0.199661\pi$
$594$	−3.63697	+	6.29942i	−0.149227	+	0.258468i
$595$		0			0
$596$	2.67797	+	4.63838i	0.109694	+	0.189995i
$597$	3.93105			0.160887
$598$	−7.74009	+	5.89104i	−0.316516	+	0.240902i
$599$	13.7720			0.562709			0.281355	−	0.959604i	$-0.409216\pi$
$599$	13.7720			0.562709			0.281355	+	0.959604i	$0.409216\pi$
$600$	12.6916	+	21.9825i	0.518133	+	0.897433i
$601$	−16.6312	−	28.8060i	−0.678399	−	1.17502i	−0.975463	−	0.220164i	$-0.929341\pi$
$601$	−16.6312	−	28.8060i	−0.678399	−	1.17502i	0.297064	−	0.954858i	$-0.403993\pi$
$602$		0			0
$603$	−11.5166			−0.468991
$604$	−2.47034	+	4.27876i	−0.100517	+	0.174100i
$605$	−2.56009	+	4.43421i	−0.104083	+	0.180276i
$606$	−9.50720			−0.386204
$607$	−21.9824	+	38.0747i	−0.892240	+	1.54540i	−0.0550554	+	0.998483i	$0.517534\pi$
$607$	−21.9824	+	38.0747i	−0.892240	+	1.54540i	−0.837184	+	0.546921i	$0.815800\pi$
$608$	1.47658	+	2.55751i	0.0598831	+	0.103721i
$609$		0			0
$610$	−2.22305			−0.0900088
$611$	−1.54587	−	0.647442i	−0.0625391	−	0.0261927i
$612$	−2.28052			−0.0921846
$613$	−1.35045	−	2.33906i	−0.0545443	−	0.0944736i	0.837464	−	0.546492i	$-0.184037\pi$
$613$	−1.35045	−	2.33906i	−0.0545443	−	0.0944736i	−0.892008	+	0.452019i	$0.850704\pi$
$614$	7.57361	+	13.1179i	0.305646	+	0.529394i
$615$	−0.849310	+	1.47105i	−0.0342475	+	0.0593184i
$616$		0			0
$617$	−3.00208	+	5.19975i	−0.120859	+	0.209334i	−0.920107	−	0.391668i	$-0.871898\pi$
$617$	−3.00208	+	5.19975i	−0.120859	+	0.209334i	0.799248	+	0.601002i	$0.205232\pi$
$618$	−0.854742	+	1.48046i	−0.0343828	+	0.0595527i
$619$	−13.3641			−0.537148			−0.268574	−	0.963259i	$-0.586552\pi$
$619$	−13.3641			−0.537148			−0.268574	+	0.963259i	$0.586552\pi$
$620$	0.560963	−	0.971616i	0.0225288	−	0.0390210i
$621$	2.78966	+	4.83183i	0.111945	+	0.193895i
$622$	−21.0983	−	36.5433i	−0.845963	−	1.46525i
$623$		0			0
$624$	−27.6201	+	21.0218i	−1.10569	+	0.841547i
$625$	19.9099			0.796398
$626$	12.5637	+	21.7609i	0.502145	+	0.869741i
$627$	2.72245	+	4.71543i	0.108724	+	0.188316i
$628$	−0.591650	+	1.02477i	−0.0236094	+	0.0408927i
$629$	−6.75647			−0.269398
$630$		0			0
$631$	−20.2228	+	35.0270i	−0.805059	+	1.39440i	0.111192	+	0.993799i	$0.464533\pi$
$631$	−20.2228	+	35.0270i	−0.805059	+	1.39440i	−0.916251	+	0.400604i	$0.868800\pi$
$632$	−38.3921			−1.52716
$633$	17.1899	−	29.7737i	0.683236	−	1.18340i
$634$	18.0054	+	31.1863i	0.715086	+	1.23857i
$635$	−2.65324	−	4.59554i	−0.105291	−	0.182369i
$636$	5.48393			0.217452
$637$		0			0
$638$	−15.9407			−0.631097
$639$	−5.02213	−	8.69859i	−0.198672	−	0.344111i
$640$	−3.89667	−	6.74923i	−0.154029	−	0.266787i
$641$	−5.10991	+	8.85062i	−0.201829	+	0.349578i	−0.949118	−	0.314921i	$-0.898022\pi$
$641$	−5.10991	+	8.85062i	−0.201829	+	0.349578i	0.747289	+	0.664500i	$0.231355\pi$
$642$	62.4786			2.46584
$643$	−15.9014	+	27.5420i	−0.627088	+	1.08615i	0.361045	+	0.932548i	$0.382420\pi$
$643$	−15.9014	+	27.5420i	−0.627088	+	1.08615i	−0.988133	+	0.153600i	$0.950913\pi$
$644$		0			0
$645$	14.4861			0.570389
$646$	6.13937	−	10.6337i	0.241550	−	0.418378i
$647$	17.2617	+	29.8981i	0.678626	+	1.17541i	0.975395	+	0.220465i	$0.0707575\pi$
$647$	17.2617	+	29.8981i	0.678626	+	1.17541i	−0.296769	+	0.954949i	$0.595909\pi$
$648$	14.4328	+	24.9983i	0.566972	+	0.982025i
$649$	18.0602			0.708923
$650$	3.23057	+	25.3060i	0.126713	+	0.992582i
$651$		0			0
$652$	−0.268265	−	0.464649i	−0.0105061	−	0.0181970i
$653$	−5.05899	−	8.76244i	−0.197974	−	0.342901i	0.749898	−	0.661554i	$-0.230103\pi$
$653$	−5.05899	−	8.76244i	−0.197974	−	0.342901i	−0.947871	+	0.318653i	$0.896769\pi$
$654$	−9.26781	+	16.0523i	−0.362400	+	0.627695i
$655$	4.00692			0.156563
$656$	−3.06855	+	5.31488i	−0.119807	+	0.207511i
$657$	−12.4484	+	21.5613i	−0.485659	+	0.841185i
$658$		0			0
$659$	17.3841	−	30.1101i	0.677187	−	1.17292i	−0.298637	−	0.954367i	$-0.596532\pi$
$659$	17.3841	−	30.1101i	0.677187	−	1.17292i	0.975824	−	0.218556i	$-0.0701345\pi$
$660$	0.298019	+	0.516185i	0.0116004	+	0.0200925i
$661$	8.28076	+	14.3427i	0.322084	+	0.557866i	0.980918	−	0.194422i	$-0.0622833\pi$
$661$	8.28076	+	14.3427i	0.322084	+	0.557866i	−0.658834	+	0.752289i	$0.728950\pi$
$662$	−12.0933			−0.470020
$663$	33.9042	+	14.1998i	1.31673	+	0.551474i
$664$	−25.9727			−1.00794
$665$		0			0
$666$	1.62948	+	2.82234i	0.0631411	+	0.109364i
$667$	−6.11346	+	10.5888i	−0.236714	+	0.410001i
$668$	−3.95697			−0.153100
$669$	−13.2163	+	22.8913i	−0.510972	+	0.885029i
$670$	3.39388	−	5.87838i	0.131117	−	0.227102i
$671$	−3.77178			−0.145608
$672$		0			0
$673$	20.9437	+	36.2756i	0.807321	+	1.39832i	0.914713	+	0.404104i	$0.132417\pi$
$673$	20.9437	+	36.2756i	0.807321	+	1.39832i	−0.107393	+	0.994217i	$0.534250\pi$
$674$	−6.01714	−	10.4220i	−0.231771	−	0.401440i
$675$	14.6332			0.563231
$676$	−3.93538	+	1.02143i	−0.151361	+	0.0392857i
$677$	−31.5715			−1.21339			−0.606696	−	0.794934i	$-0.707505\pi$
$677$	−31.5715			−1.21339			−0.606696	+	0.794934i	$0.707505\pi$
$678$	8.32556	+	14.4203i	0.319741	+	0.553808i
$679$		0			0
$680$	−3.62566	+	6.27983i	−0.139038	+	0.240820i
$681$	−2.62582			−0.100621
$682$	7.03817	−	12.1905i	0.269505	−	0.466797i
$683$	13.1338	−	22.7484i	0.502551	−	0.870444i	−0.497445	−	0.867496i	$-0.665728\pi$
$683$	13.1338	−	22.7484i	0.502551	−	0.870444i	0.999996	−	0.00294809i	$-0.000938408\pi$
$684$	−0.800911			−0.0306236
$685$	−4.14801	+	7.18457i	−0.158487	+	0.274508i
$686$		0			0
$687$	6.96880	+	12.0703i	0.265876	+	0.460512i
$688$	52.3381			1.99537
$689$	−27.4260	−	11.4866i	−1.04485	−	0.437604i
$690$	3.38076			0.128703
$691$	−3.05047	−	5.28358i	−0.116046	−	0.200997i	0.802152	−	0.597120i	$-0.203689\pi$
$691$	−3.05047	−	5.28358i	−0.116046	−	0.200997i	−0.918197	+	0.396124i	$0.870355\pi$
$692$	−1.79635	−	3.11138i	−0.0682872	−	0.118277i
$693$		0			0
$694$	−10.8518			−0.411929
$695$	−5.09419	+	8.82339i	−0.193234	+	0.334690i
$696$	−18.8017	+	32.5655i	−0.712677	+	1.23439i
$697$	6.49914			0.246172
$698$	1.04690	−	1.81329i	0.0396259	−	0.0686341i
$699$	−6.69636	−	11.5984i	−0.253280	−	0.438693i
$700$		0			0
$701$	−20.5701			−0.776921			−0.388461	−	0.921465i	$-0.626993\pi$
$701$	−20.5701			−0.776921			−0.388461	+	0.921465i	$0.626993\pi$
$702$	2.18385	+	17.1067i	0.0824240	+	0.645652i
$703$	−2.37285			−0.0894936
$704$	−4.85760	−	8.41361i	−0.183078	−	0.317100i
$705$	0.291257	+	0.504471i	0.0109694	+	0.0189995i
$706$	0.527111	−	0.912984i	0.0198381	−	0.0343606i
$707$		0			0
$708$	−3.94851	+	6.83902i	−0.148394	+	0.257026i
$709$	21.5764	−	37.3715i	0.810320	−	1.40352i	−0.102320	−	0.994751i	$-0.532627\pi$
$709$	21.5764	−	37.3715i	0.810320	−	1.40352i	0.912640	−	0.408764i	$-0.134040\pi$
$710$	5.92000			0.222174
$711$	11.3771	−	19.7058i	0.426676	−	0.739025i
$712$	21.1496	+	36.6322i	0.792615	+	1.37285i
$713$	−5.39847	−	9.35042i	−0.202174	−	0.350176i
$714$		0			0
$715$	−0.409246	−	3.20575i	−0.0153050	−	0.119888i
$716$	−0.683209			−0.0255327
$717$	20.1132	+	34.8372i	0.751143	+	1.30102i
$718$	−4.41302	−	7.64357i	−0.164692	−	0.285255i
$719$	−14.1042	+	24.4292i	−0.525999	+	0.911057i	0.473542	+	0.880771i	$0.342975\pi$
$719$	−14.1042	+	24.4292i	−0.525999	+	0.911057i	−0.999541	+	0.0302857i	$0.990358\pi$
$720$	4.05831			0.151244
$721$		0			0
$722$	−12.2912	+	21.2890i	−0.457432	+	0.792295i
$723$	−47.4076			−1.76311
$724$	−1.81367	+	3.14136i	−0.0674044	+	0.116748i
$725$	16.0341	+	27.7719i	0.595492	+	1.03142i
$726$	−14.0450	−	24.3267i	−0.521260	−	0.902850i
$727$	19.5116			0.723646			0.361823	−	0.932247i	$-0.382155\pi$
$727$	19.5116			0.723646			0.361823	+	0.932247i	$0.382155\pi$
$728$		0			0
$729$	2.95370			0.109396
$730$	−7.33698	−	12.7080i	−0.271554	−	0.470345i
$731$	−27.7128	−	48.0000i	−1.02500	−	1.77535i
$732$	0.824628	−	1.42830i	0.0304791	−	0.0527914i
$733$	−20.3666			−0.752259			−0.376129	−	0.926567i	$-0.622745\pi$
$733$	−20.3666			−0.752259			−0.376129	+	0.926567i	$0.622745\pi$
$734$	5.59003	−	9.68222i	0.206332	−	0.357377i
$735$		0			0
$736$	3.11105			0.114675
$737$	5.75829	−	9.97364i	0.212109	−	0.367384i
$738$	−1.56742	−	2.71485i	−0.0576975	−	0.0999349i
$739$	5.20995	+	9.02391i	0.191651	+	0.331950i	0.945798	−	0.324757i	$-0.105282\pi$
$739$	5.20995	+	9.02391i	0.191651	+	0.331950i	−0.754146	+	0.656706i	$0.771949\pi$
$740$	−0.259749			−0.00954856
$741$	11.9070	+	4.98691i	0.437415	+	0.183199i
$742$		0			0
$743$	8.70470	+	15.0770i	0.319344	+	0.553121i	0.980351	−	0.197259i	$-0.0632040\pi$
$743$	8.70470	+	15.0770i	0.319344	+	0.553121i	−0.661007	+	0.750380i	$0.729871\pi$
$744$	−16.6028	−	28.7568i	−0.608687	−	1.05428i
$745$	−5.04672	+	8.74118i	−0.184898	+	0.320252i
$746$	−27.9805			−1.02444
$747$	7.69677	−	13.3312i	0.281610	−	0.487763i
$748$	1.14026	−	1.97499i	0.0416921	−	0.0722128i
$749$		0			0
$750$	9.19792	−	15.9313i	0.335861	−	0.581728i
$751$	0.907626	+	1.57205i	0.0331197	+	0.0573651i	0.882110	−	0.471043i	$-0.156122\pi$
$751$	0.907626	+	1.57205i	0.0331197	+	0.0573651i	−0.848990	+	0.528408i	$0.822789\pi$
$752$	1.05231	+	1.82265i	0.0383737	+	0.0664652i
$753$	14.7839			0.538754
$754$	−30.0734	+	22.8891i	−1.09521	+	0.833573i
$755$	−9.31088			−0.338858
$756$		0			0
$757$	−26.7814	−	46.3867i	−0.973385	−	1.68595i	−0.685165	−	0.728388i	$-0.740270\pi$
$757$	−26.7814	−	46.3867i	−0.973385	−	1.68595i	−0.288220	−	0.957564i	$-0.593063\pi$
$758$	−3.68864	+	6.38892i	−0.133978	+	0.232056i
$759$	5.73602			0.208204
$760$	−1.27332	+	2.20545i	−0.0461881	+	0.0800001i
$761$	1.84083	−	3.18841i	0.0667300	−	0.115580i	−0.830730	−	0.556675i	$-0.812077\pi$
$761$	1.84083	−	3.18841i	0.0667300	−	0.115580i	0.897460	+	0.441096i	$0.145410\pi$
$762$	29.1121			1.05462
$763$		0			0
$764$	−2.77711	−	4.81010i	−0.100472	−	0.174023i
$765$	−2.14886	−	3.72193i	−0.0776922	−	0.134567i
$766$	34.7048			1.25394
$767$	34.0721	−	25.9325i	1.23027	−	0.936369i
$768$	15.5895			0.562538
$769$	2.61897	+	4.53619i	0.0944424	+	0.163579i	0.909376	−	0.415976i	$-0.136560\pi$
$769$	2.61897	+	4.53619i	0.0944424	+	0.163579i	−0.814933	+	0.579555i	$0.803227\pi$
$770$		0			0
$771$	22.4902	−	38.9541i	0.809963	−	1.40290i
$772$	7.08004			0.254816
$773$	−20.3069	+	35.1726i	−0.730388	+	1.26507i	0.226329	+	0.974051i	$0.427328\pi$
$773$	−20.3069	+	35.1726i	−0.730388	+	1.26507i	−0.956717	+	0.291019i	$0.906006\pi$
$774$	−13.3672	+	23.1527i	−0.480474	+	0.832205i
$775$	−28.3177			−1.01720
$776$	−1.24944	+	2.16409i	−0.0448522	+	0.0776862i
$777$		0			0
$778$	−15.4451	−	26.7517i	−0.553733	−	0.959094i
$779$	2.28247			0.0817781
$780$	1.30343	+	0.545903i	0.0466702	+	0.0195465i
$781$	10.0443			0.359412
$782$	−6.46762	−	11.2022i	−0.231281	−	0.400591i
$783$	10.8390	+	18.7737i	0.387353	+	0.670916i
$784$		0			0
$785$	−2.22997			−0.0795911
$786$	−10.9913	+	19.0374i	−0.392045	+	0.679042i
$787$	17.1000	−	29.6181i	0.609550	−	1.05577i	−0.381765	−	0.924259i	$-0.624684\pi$
$787$	17.1000	−	29.6181i	0.609550	−	1.05577i	0.991315	−	0.131512i	$-0.0419830\pi$
$788$	6.25701			0.222897
$789$	8.96190	−	15.5225i	0.319052	−	0.552614i
$790$	6.70559	+	11.6144i	0.238574	+	0.413223i
$791$		0			0
$792$	5.93434			0.210868
$793$	−7.11579	+	5.41588i	−0.252689	+	0.192324i
$794$	51.9158			1.84242
$795$	5.16733	+	8.95007i	0.183266	+	0.317426i
$796$	−0.289116	−	0.500764i	−0.0102474	−	0.0177491i
$797$	15.6903	−	27.1763i	0.555778	−	0.962635i	−0.442065	−	0.896983i	$-0.645754\pi$
$797$	15.6903	−	27.1763i	0.555778	−	0.962635i	0.997843	−	0.0656522i	$-0.0209128\pi$
$798$		0			0
$799$	1.11439	−	1.93017i	0.0394241	−	0.0682846i
$800$	4.07976	−	7.06634i	0.144241	−	0.249833i
$801$	−25.0699			−0.885803
$802$	−2.30090	+	3.98528i	−0.0812477	+	0.140725i
$803$	−12.4484	−	21.5613i	−0.439295	−	0.760881i
$804$	2.51788	+	4.36109i	0.0887988	+	0.153804i
$805$		0			0
$806$	−4.22612	−	33.1044i	−0.148859	−	1.16605i
$807$	12.3966			0.436382
$808$	−3.77221	−	6.53365i	−0.132706	−	0.229853i
$809$	18.9709	+	32.8585i	0.666981	+	1.15524i	0.978744	+	0.205085i	$0.0657470\pi$
$809$	18.9709	+	32.8585i	0.666981	+	1.15524i	−0.311764	+	0.950160i	$0.600920\pi$
$810$	5.04167	−	8.73242i	0.177146	−	0.306826i
$811$	32.1023			1.12726			0.563632	−	0.826026i	$-0.309403\pi$
$811$	32.1023			1.12726			0.563632	+	0.826026i	$0.309403\pi$
$812$		0			0
$813$	19.5930	−	33.9360i	0.687155	−	1.19019i
$814$	−3.25896			−0.114227
$815$	0.505555	−	0.875646i	0.0177088	−	0.0306725i
$816$	−23.0793	−	39.9745i	−0.807938	−	1.39939i
$817$	−9.73265	−	16.8574i	−0.340502	−	0.589767i
$818$	−8.18670			−0.286241
$819$		0			0
$820$	0.249856			0.00872534
$821$	8.46117	+	14.6552i	0.295297	+	0.511469i	0.975054	−	0.221968i	$-0.0712481\pi$
$821$	8.46117	+	14.6552i	0.295297	+	0.511469i	−0.679757	+	0.733437i	$0.737915\pi$
$822$	−22.7566	−	39.4156i	−0.793727	−	1.37478i
$823$	7.23666	−	12.5343i	0.252254	−	0.436917i	−0.711892	−	0.702289i	$-0.752161\pi$
$823$	7.23666	−	12.5343i	0.252254	−	0.436917i	0.964146	+	0.265372i	$0.0854948\pi$
$824$	−1.35656			−0.0472579
$825$	7.52209	−	13.0286i	0.261885	−	0.453599i
$826$		0			0
$827$	27.5792			0.959021			0.479511	−	0.877536i	$-0.340814\pi$
$827$	27.5792			0.959021			0.479511	+	0.877536i	$0.340814\pi$
$828$	−0.421866	+	0.730693i	−0.0146608	+	0.0253933i
$829$	10.5465	+	18.2671i	0.366296	+	0.634443i	0.988983	−	0.148028i	$-0.0472925\pi$
$829$	10.5465	+	18.2671i	0.366296	+	0.634443i	−0.622687	+	0.782471i	$0.713959\pi$
$830$	4.53641	+	7.85729i	0.157461	+	0.272730i
$831$	−13.1465			−0.456047
$832$	−21.2454	−	8.89800i	−0.736550	−	0.308483i
$833$		0			0
$834$	−27.9474	−	48.4064i	−0.967741	−	1.67618i
$835$	−3.72852	−	6.45798i	−0.129031	−	0.223488i
$836$	0.400455	−	0.693609i	0.0138500	−	0.0239890i
$837$	−19.1426			−0.661666
$838$	4.47286	−	7.74722i	0.154512	−	0.267623i
$839$	−6.35488	+	11.0070i	−0.219395	+	0.380003i	−0.954623	−	0.297817i	$-0.903742\pi$
$839$	−6.35488	+	11.0070i	−0.219395	+	0.380003i	0.735228	+	0.677819i	$0.237075\pi$
$840$		0			0
$841$	−9.25333	+	16.0272i	−0.319080	+	0.552663i
$842$	−21.8698	−	37.8796i	−0.753682	−	1.30542i
$843$	5.99643	+	10.3861i	0.206528	+	0.357717i
$844$	−5.05703			−0.174070
$845$	−5.37520	−	5.46029i	−0.184913	−	0.187840i
$846$	−1.07504			−0.0369606
$847$		0			0
$848$	18.6695	+	32.3365i	0.641113	+	1.11044i
$849$	−17.4938	+	30.3002i	−0.600387	+	1.03990i
$850$	−33.9259			−1.16365
$851$	−1.24986	+	2.16481i	−0.0428445	+	0.0742089i
$852$	−2.19599	+	3.80356i	−0.0752333	+	0.130308i
$853$	35.0471			1.19999			0.599996	−	0.800003i	$-0.295169\pi$
$853$	35.0471			1.19999			0.599996	+	0.800003i	$0.295169\pi$
$854$		0			0
$855$	−0.754672	−	1.30713i	−0.0258092	−	0.0447029i
$856$	24.7899	+	42.9373i	0.847300	+	1.46757i
$857$	25.5940			0.874275			0.437138	−	0.899395i	$-0.355992\pi$
$857$	25.5940			0.874275			0.437138	+	0.899395i	$0.355992\pi$
$858$	16.3536	+	6.84921i	0.558301	+	0.233828i
$859$	−0.745486			−0.0254357			−0.0127178	−	0.999919i	$-0.504048\pi$
$859$	−0.745486			−0.0254357			−0.0127178	+	0.999919i	$0.504048\pi$
$860$	−1.06541	−	1.84534i	−0.0363300	−	0.0629254i
$861$		0			0
$862$	6.37651	−	11.0444i	0.217185	−	0.376175i
$863$	−21.9816			−0.748263			−0.374132	−	0.927376i	$-0.622059\pi$
$863$	−21.9816			−0.748263			−0.374132	+	0.927376i	$0.622059\pi$
$864$	2.75790	−	4.77682i	0.0938255	−	0.162511i
$865$	3.38529	−	5.86350i	0.115103	−	0.199365i
$866$	41.9722			1.42627
$867$	−6.36804	+	11.0298i	−0.216270	+	0.374590i
$868$		0			0
$869$	11.3771	+	19.7058i	0.385943	+	0.668473i
$870$	13.1357			0.445341
$871$	−3.45761	−	27.0845i	−0.117156	−	0.917722i
$872$	−14.7089			−0.498106
$873$	−0.740517	−	1.28261i	−0.0250627	−	0.0434099i
$874$	−2.27140	−	3.93418i	−0.0768313	−	0.133076i
$875$		0			0
$876$	10.8864			0.367818
$877$	−14.7095	+	25.4776i	−0.496705	+	0.860319i	−0.999993	−	0.00380023i	$-0.998790\pi$
$877$	−14.7095	+	25.4776i	−0.496705	+	0.860319i	0.503287	+	0.864119i	$0.332124\pi$
$878$	23.7041	−	41.0567i	0.799975	−	1.38560i
$879$	−65.0984			−2.19572
$880$	−2.02915	+	3.51460i	−0.0684028	+	0.118477i
$881$	−24.1414	−	41.8142i	−0.813345	−	1.40876i	−0.910510	−	0.413487i	$-0.864311\pi$
$881$	−24.1414	−	41.8142i	−0.813345	−	1.40876i	0.0971649	−	0.995268i	$-0.469023\pi$
$882$		0			0
$883$	16.4465			0.553469			0.276735	−	0.960946i	$-0.410748\pi$
$883$	16.4465			0.553469			0.276735	+	0.960946i	$0.410748\pi$
$884$	−0.684678	−	5.36329i	−0.0230282	−	0.180387i
$885$	−14.8822			−0.500260
$886$	−17.9362	−	31.0664i	−0.602579	−	1.04370i
$887$	−14.5827	−	25.2579i	−0.489638	−	0.848078i	0.510291	−	0.860002i	$-0.329538\pi$
$887$	−14.5827	−	25.2579i	−0.489638	−	0.848078i	−0.999929	+	0.0119239i	$0.996204\pi$
$888$	−3.84388	+	6.65780i	−0.128992	+	0.223421i
$889$		0			0
$890$	7.38800	−	12.7964i	0.247646	−	0.428936i
$891$	8.55402	−	14.8160i	0.286571	−	0.496355i
$892$	3.88806			0.130182
$893$	0.391368	−	0.677869i	0.0130966	−	0.0226840i
$894$	−27.6870	−	47.9553i	−0.925993	−	1.60387i
$895$	−0.643765	−	1.11503i	−0.0215187	−	0.0372715i
$896$		0			0
$897$	10.8215	−	8.23633i	0.361320	−	0.275003i
$898$	−4.29856			−0.143445
$899$	−20.9753	−	36.3302i	−0.699565	−	1.21168i
$900$	1.10645	+	1.91643i	0.0368817	+	0.0638809i
$901$	19.7709	−	34.2441i	0.658663	−	1.14084i
$902$	3.13484			0.104379
$903$		0			0
$904$	−6.60673	+	11.4432i	−0.219736	+	0.380595i
$905$	−6.83583			−0.227231
$906$	25.5404	−	44.2373i	0.848524	−	1.46969i
$907$	17.6607	+	30.5893i	0.586416	+	1.01570i	0.994697	+	0.102846i	$0.0327947\pi$
$907$	17.6607	+	30.5893i	0.586416	+	1.01570i	−0.408282	+	0.912856i	$0.633872\pi$
$908$	0.193120	+	0.334494i	0.00640892	+	0.0111006i
$909$	4.47143			0.148308
$910$		0			0
$911$	−43.6496			−1.44617			−0.723087	−	0.690757i	$-0.757278\pi$
$911$	−43.6496			−1.44617			−0.723087	+	0.690757i	$0.757278\pi$
$912$	−8.10537	−	14.0389i	−0.268396	−	0.464875i
$913$	7.69677	+	13.3312i	0.254726	+	0.441198i
$914$	−28.6994	+	49.7088i	−0.949292	+	1.64422i
$915$	3.10808			0.102750
$916$	1.02507	−	1.77547i	0.0338691	−	0.0586630i
$917$		0			0
$918$	−22.9338			−0.756927
$919$	8.89389	−	15.4047i	0.293382	−	0.508153i	−0.681225	−	0.732074i	$-0.738552\pi$
$919$	8.89389	−	15.4047i	0.293382	−	0.508153i	0.974607	+	0.223921i	$0.0718858\pi$
$920$	1.34140	+	2.32337i	0.0442245	+	0.0765991i
$921$	−10.5887	−	18.3403i	−0.348911	−	0.604332i
$922$	−52.7079			−1.73584
$923$	18.9494	−	14.4225i	0.623726	−	0.474723i
$924$		0			0
$925$	3.27806	+	5.67777i	0.107782	+	0.186684i
$926$	14.0758	+	24.3800i	0.462559	+	0.801176i
$927$	0.402003	−	0.696289i	0.0132035	−	0.0228691i
$928$	12.0877			0.396798
$929$	−1.95710	+	3.38980i	−0.0642103	+	0.111216i	−0.896343	−	0.443360i	$-0.853786\pi$
$929$	−1.95710	+	3.38980i	−0.0642103	+	0.111216i	0.832133	+	0.554576i	$0.187120\pi$
$930$	−5.79969	+	10.0454i	−0.190179	+	0.329401i
$931$		0			0
$932$	−0.984992	+	1.70606i	−0.0322645	+	0.0558837i
$933$	29.4977	+	51.0916i	0.965712	+	1.67266i
$934$	5.03972	+	8.72905i	0.164905	+	0.285623i
$935$	4.29772			0.140550
$936$	11.1957	−	8.52110i	0.365941	−	0.278521i
$937$	−0.207362			−0.00677421			−0.00338710	−	0.999994i	$-0.501078\pi$
$937$	−0.207362			−0.00677421			−0.00338710	+	0.999994i	$0.501078\pi$
$938$		0			0
$939$	−17.5654	−	30.4242i	−0.573225	−	0.992855i
$940$	0.0428420	−	0.0742044i	0.00139735	−	0.00242028i
$941$	27.4656			0.895355			0.447677	−	0.894195i	$-0.352251\pi$
$941$	27.4656			0.895355			0.447677	+	0.894195i	$0.352251\pi$
$942$	6.11697	−	10.5949i	0.199302	−	0.345200i
$943$	1.20225	−	2.08236i	0.0391507	−	0.0678111i
$944$	−53.7692			−1.75004
$945$		0			0
$946$	−13.3672	−	23.1527i	−0.434605	−	0.752758i
$947$	11.5182	+	19.9501i	0.374290	+	0.648290i	0.990221	−	0.139511i	$-0.0445531\pi$
$947$	11.5182	+	19.9501i	0.374290	+	0.648290i	−0.615930	+	0.787801i	$0.711220\pi$
$948$	−9.94959			−0.323148
$949$	−54.4448	−	22.8026i	−1.76735	−	0.740204i
$950$	−11.9147			−0.386563
$951$	−25.1736	−	43.6019i	−0.816309	−	1.41389i
$952$		0			0
$953$	−7.22808	+	12.5194i	−0.234140	+	0.405543i	−0.959022	−	0.283330i	$-0.908561\pi$
$953$	−7.22808	+	12.5194i	−0.234140	+	0.405543i	0.724882	+	0.688873i	$0.241894\pi$
$954$	−19.0728			−0.617505
$955$	5.23357	−	9.06480i	0.169354	−	0.293330i
$956$	2.95853	−	5.12432i	0.0956856	−	0.165732i
$957$	22.2868			0.720431
$958$	−13.2707	+	22.9856i	−0.428758	+	0.742630i
$959$		0			0
$960$	4.00283	+	6.93311i	0.129191	+	0.223765i
$961$	6.04426			0.194976
$962$	−6.14831	+	4.67953i	−0.198230	+	0.150874i
$963$	−29.3850			−0.946917
$964$	3.48668	+	6.03910i	0.112298	+	0.194506i
$965$	6.67129	+	11.5550i	0.214756	+	0.371969i
$966$		0			0
$967$	32.3357			1.03984			0.519922	−	0.854213i	$-0.325961\pi$
$967$	32.3357			1.03984			0.519922	+	0.854213i	$0.325961\pi$
$968$	11.1454	−	19.3044i	0.358227	−	0.620467i
$969$	−8.58353	+	14.8671i	−0.275743	+	0.477600i
$970$	0.872909			0.0280274
$971$	−12.3118	+	21.3246i	−0.395103	+	0.684338i	−0.993114	−	0.117149i	$-0.962624\pi$
$971$	−12.3118	+	21.3246i	−0.395103	+	0.684338i	0.598011	+	0.801488i	$0.295958\pi$
$972$	2.26487	+	3.92287i	0.0726458	+	0.125826i
$973$		0			0
$974$	54.0084			1.73054
$975$	−4.51669	−	35.3806i	−0.144650	−	1.13309i
$976$	11.2294			0.359446
$977$	−3.00496	−	5.20474i	−0.0961372	−	0.166514i	0.813945	−	0.580941i	$-0.197315\pi$
$977$	−3.00496	−	5.20474i	−0.0961372	−	0.166514i	−0.910083	+	0.414427i	$0.863982\pi$
$978$	2.77354	+	4.80392i	0.0886882	+	0.153612i
$979$	12.5350	−	21.7112i	0.400619	−	0.693893i
$980$		0			0
$981$	4.35884	−	7.54973i	0.139167	−	0.241044i
$982$	−22.6685	+	39.2630i	−0.723382	+	1.25293i
$983$	−35.9093			−1.14533			−0.572664	−	0.819790i	$-0.694090\pi$
$983$	−35.9093			−1.14533			−0.572664	+	0.819790i	$0.694090\pi$
$984$	3.69748	−	6.40422i	0.117871	−	0.204159i
$985$	5.89578	+	10.2118i	0.187855	+	0.325374i
$986$	−25.1294	−	43.5253i	−0.800282	−	1.38613i
$987$		0			0
$988$	−0.240456	−	1.88357i	−0.00764994	−	0.0599242i
$989$	−20.5060			−0.652053
$990$	−1.03650	−	1.79526i	−0.0329420	−	0.0570572i
$991$	−14.0000	−	24.2487i	−0.444724	−	0.770285i	0.553309	−	0.832976i	$-0.313365\pi$
$991$	−14.0000	−	24.2487i	−0.444724	−	0.770285i	−0.998033	+	0.0626912i	$0.980032\pi$
$992$	−5.33700	+	9.24396i	−0.169450	+	0.293496i
$993$	16.9078			0.536553
$994$		0			0
$995$	0.544849	−	0.943706i	0.0172729	−	0.0299175i
$996$	−6.73101			−0.213280
$997$	16.5040	−	28.5858i	0.522688	−	0.905323i	−0.476963	−	0.878923i	$-0.658263\pi$
$997$	16.5040	−	28.5858i	0.522688	−	0.905323i	0.999651	−	0.0263994i	$-0.00840416\pi$
$998$	−5.71024	−	9.89043i	−0.180755	−	0.313076i
$999$	2.21596	+	3.83815i	0.0701097	+	0.121434i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.f.l.393.5	yes	16
7.2	even	3		637.2.g.m.263.6		16
7.3	odd	6		637.2.h.m.471.4		16
7.4	even	3		637.2.h.m.471.3		16
7.5	odd	6		637.2.g.m.263.5		16
7.6	odd	2	inner	637.2.f.l.393.6	yes	16
13.3	even	3		8281.2.a.ci.1.4		8
13.9	even	3	inner	637.2.f.l.295.5	✓	16
13.10	even	6		8281.2.a.cl.1.6		8
91.9	even	3		637.2.h.m.165.3		16
91.48	odd	6	inner	637.2.f.l.295.6	yes	16
91.55	odd	6		8281.2.a.ci.1.3		8
91.61	odd	6		637.2.h.m.165.4		16
91.62	odd	6		8281.2.a.cl.1.5		8
91.74	even	3		637.2.g.m.373.6		16
91.87	odd	6		637.2.g.m.373.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.f.l.295.5	✓	16	13.9	even	3	inner
637.2.f.l.295.6	yes	16	91.48	odd	6	inner
637.2.f.l.393.5	yes	16	1.1	even	1	trivial
637.2.f.l.393.6	yes	16	7.6	odd	2	inner
637.2.g.m.263.5		16	7.5	odd	6
637.2.g.m.263.6		16	7.2	even	3
637.2.g.m.373.5		16	91.87	odd	6
637.2.g.m.373.6		16	91.74	even	3
637.2.h.m.165.3		16	91.9	even	3
637.2.h.m.165.4		16	91.61	odd	6
637.2.h.m.471.3		16	7.4	even	3
637.2.h.m.471.4		16	7.3	odd	6
8281.2.a.ci.1.3		8	91.55	odd	6
8281.2.a.ci.1.4		8	13.3	even	3
8281.2.a.cl.1.5		8	91.62	odd	6
8281.2.a.cl.1.6		8	13.10	even	6

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.760387 + 1.31703i) q^{2} +(-1.06311 - 1.84135i) q^{3} +(-0.156376 + 0.270851i) q^{4} -0.589391 q^{5} +(1.61674 - 2.80028i) q^{6} +2.56592 q^{8} +(-0.760387 + 1.31703i) q^{9} +O(q^{10})\)	\(q+(0.760387 + 1.31703i) q^{2} +(-1.06311 - 1.84135i) q^{3} +(-0.156376 + 0.270851i) q^{4} -0.589391 q^{5} +(1.61674 - 2.80028i) q^{6} +2.56592 q^{8} +(-0.760387 + 1.31703i) q^{9} +(-0.448165 - 0.776245i) q^{10} +(-0.760387 - 1.31703i) q^{11} +0.664976 q^{12} +(-3.32565 - 1.39285i) q^{13} +(0.626585 + 1.08528i) q^{15} +(2.26384 + 3.92109i) q^{16} +(2.39740 - 4.15241i) q^{17} -2.31275 q^{18} +(0.841957 - 1.45831i) q^{19} +(0.0921666 - 0.159637i) q^{20} +(1.15638 - 2.00290i) q^{22} +(-0.886972 - 1.53628i) q^{23} +(-2.72785 - 4.72477i) q^{24} -4.65262 q^{25} +(-0.694354 - 5.43908i) q^{26} -3.14515 q^{27} +(-3.44625 - 5.96909i) q^{29} +(-0.952894 + 1.65046i) q^{30} +6.08640 q^{31} +(-0.876873 + 1.51879i) q^{32} +(-1.61674 + 2.80028i) q^{33} +7.29179 q^{34} +(-0.237812 - 0.411903i) q^{36} +(-0.704563 - 1.22034i) q^{37} +2.56085 q^{38} +(0.970785 + 7.60445i) q^{39} -1.51233 q^{40} +(0.677729 + 1.17386i) q^{41} +(5.77978 - 10.0109i) q^{43} +0.475625 q^{44} +(0.448165 - 0.776245i) q^{45} +(1.34888 - 2.33633i) q^{46} +0.464832 q^{47} +(4.81341 - 8.33707i) q^{48} +(-3.53779 - 6.12763i) q^{50} -10.1947 q^{51} +(0.897307 - 0.682948i) q^{52} +8.24681 q^{53} +(-2.39153 - 4.14225i) q^{54} +(0.448165 + 0.776245i) q^{55} -3.58035 q^{57} +(5.24097 - 9.07763i) q^{58} +(-5.93782 + 10.2846i) q^{59} -0.391931 q^{60} +(1.24009 - 2.14789i) q^{61} +(4.62802 + 8.01596i) q^{62} +6.38833 q^{64} +(1.96011 + 0.820936i) q^{65} -4.91740 q^{66} +(3.78642 + 6.55827i) q^{67} +(0.749790 + 1.29867i) q^{68} +(-1.88589 + 3.26646i) q^{69} +(-3.30235 + 5.71984i) q^{71} +(-1.95109 + 3.37939i) q^{72} +16.3712 q^{73} +(1.07148 - 1.85586i) q^{74} +(4.94622 + 8.56711i) q^{75} +(0.263323 + 0.456090i) q^{76} +(-9.27710 + 7.06087i) q^{78} -14.9623 q^{79} +(-1.33429 - 2.31106i) q^{80} +(5.62478 + 9.74241i) q^{81} +(-1.03067 + 1.78518i) q^{82} -10.1222 q^{83} +(-1.41300 + 2.44740i) q^{85} +17.5795 q^{86} +(-7.32746 + 12.6915i) q^{87} +(-1.95109 - 3.37939i) q^{88} +(8.24250 + 14.2764i) q^{89} +1.36312 q^{90} +0.554804 q^{92} +(-6.47049 - 11.2072i) q^{93} +(0.353452 + 0.612196i) q^{94} +(-0.496242 + 0.859516i) q^{95} +3.72883 q^{96} +(-0.486935 + 0.843396i) q^{97} +2.31275 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 - 4 * q^9	\( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} - 4 q^{9} - 4 q^{11} - 8 q^{15} - 4 q^{16} - 56 q^{18} + 28 q^{22} + 12 q^{23} - 24 q^{25} + 8 q^{29} + 28 q^{30} + 4 q^{36} - 8 q^{37} - 4 q^{39} + 32 q^{43} - 8 q^{44} - 4 q^{46} + 36 q^{50} - 88 q^{51} - 8 q^{53} - 96 q^{57} - 48 q^{58} + 128 q^{60} - 64 q^{64} + 16 q^{65} + 20 q^{67} + 8 q^{71} + 28 q^{72} + 76 q^{74} + 28 q^{78} - 8 q^{79} + 56 q^{81} + 36 q^{85} + 8 q^{86} + 28 q^{88} - 160 q^{92} + 8 q^{93} + 52 q^{95} + 56 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 - 4 * q^9 - 4 * q^11 - 8 * q^15 - 4 * q^16 - 56 * q^18 + 28 * q^22 + 12 * q^23 - 24 * q^25 + 8 * q^29 + 28 * q^30 + 4 * q^36 - 8 * q^37 - 4 * q^39 + 32 * q^43 - 8 * q^44 - 4 * q^46 + 36 * q^50 - 88 * q^51 - 8 * q^53 - 96 * q^57 - 48 * q^58 + 128 * q^60 - 64 * q^64 + 16 * q^65 + 20 * q^67 + 8 * q^71 + 28 * q^72 + 76 * q^74 + 28 * q^78 - 8 * q^79 + 56 * q^81 + 36 * q^85 + 8 * q^86 + 28 * q^88 - 160 * q^92 + 8 * q^93 + 52 * q^95 + 56 * q^99

Introduction

L-functions

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