LMFDB - Embedded newform 637.2.f.l.295.6

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:	16.0.468066644398978174550016.2
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			295.6
Root			$0.141226 + 0.244611i$ of defining polynomial
Character	$\chi$	$=$	637.295
Dual form			637.2.f.l.393.6

$q$-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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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	−0.461354	−	0.887216i	$-0.652636\pi$
$2$	0.760387	−	1.31703i	0.537675	−	0.931280i	0.999029	−	0.0440636i	$-0.0140304\pi$
$3$	1.06311	−	1.84135i	0.613784	−	1.06311i	−0.376812	−	0.926290i	$-0.622980\pi$
$3$	1.06311	−	1.84135i	0.613784	−	1.06311i	0.990596	−	0.136816i	$-0.0436869\pi$
$4$	−0.156376	−	0.270851i	−0.0781880	−	0.135426i
$5$	0.589391			0.263584			0.131792	−	0.991277i	$-0.457927\pi$
$5$	0.589391			0.263584			0.131792	+	0.991277i	$0.457927\pi$
$6$	−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	−0.957591	−	0.288132i	$-0.906966\pi$
$11$	−0.760387	+	1.31703i	−0.229265	+	0.397099i	0.728325	+	0.685232i	$0.240299\pi$
$12$	−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	−0.995307	−	0.0967643i	$-0.969151\pi$
$17$	−2.39740	−	4.15241i	−0.581454	−	1.00711i	0.413853	−	0.910344i	$-0.364183\pi$
$18$	−2.31275			−0.545121
$19$	−0.841957	−	1.45831i	−0.193158	−	0.334560i	0.753137	−	0.657864i	$-0.228540\pi$
$19$	−0.841957	−	1.45831i	−0.193158	−	0.334560i	−0.946295	+	0.323304i	$0.895206\pi$
$20$	−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	−0.943558	−	0.331206i	$-0.892544\pi$
$23$	−0.886972	+	1.53628i	−0.184946	+	0.320337i	0.758612	+	0.651543i	$0.225878\pi$
$24$	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	0.345489	+	0.938423i	$0.387713\pi$
$29$	−3.44625	+	5.96909i	−0.639953	+	1.10843i	−0.985443	+	0.170009i	$0.945620\pi$
$30$	−0.952894	−	1.65046i	−0.173974	−	0.301332i
$31$	−6.08640			−1.09315			−0.546575	−	0.837410i	$-0.684069\pi$
$31$	−6.08640			−1.09315			−0.546575	+	0.837410i	$0.684069\pi$
$32$	−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	−0.918111	−	0.396323i	$-0.870286\pi$
$37$	−0.704563	+	1.22034i	−0.115830	+	0.200623i	0.802282	+	0.596946i	$0.203619\pi$
$38$	−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	$-0.867088\pi$
$41$	−0.677729	+	1.17386i	−0.105843	+	0.183326i	0.808239	+	0.588855i	$0.200421\pi$
$42$		0			0
$43$	5.77978	+	10.0109i	0.881408	+	1.52664i	0.849776	+	0.527144i	$0.176737\pi$
$43$	5.77978	+	10.0109i	0.881408	+	1.52664i	0.0316319	+	0.999500i	$0.489930\pi$
$44$	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	$-0.510793\pi$
$47$	−0.464832			−0.0678027			−0.0339013	+	0.999425i	$0.510793\pi$
$48$	−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	0.935890	+	0.352291i	$0.114597\pi$
$59$	5.93782	+	10.2846i	0.773038	+	1.33894i	−0.162852	+	0.986651i	$0.552069\pi$
$60$	−0.391931			−0.0505981
$61$	−1.24009	−	2.14789i	−0.158777	−	0.275009i	0.775651	−	0.631162i	$-0.217422\pi$
$61$	−1.24009	−	2.14789i	−0.158777	−	0.275009i	−0.934428	+	0.356153i	$0.884088\pi$
$62$	−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	−0.536504	−	0.843898i	$-0.680255\pi$
$67$	3.78642	−	6.55827i	0.462585	−	0.801220i	0.999089	+	0.0426774i	$0.0135888\pi$
$68$	−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	0.600785	−	0.799411i	$-0.294855\pi$
$71$	−3.30235	−	5.71984i	−0.391917	−	0.678821i	−0.992702	+	0.120590i	$0.961521\pi$
$72$	−1.95109	−	3.37939i	−0.229939	−	0.398265i
$73$	−16.3712			−1.91610			−0.958049	−	0.286604i	$-0.907474\pi$
$73$	−16.3712			−1.91610			−0.958049	+	0.286604i	$0.907474\pi$
$74$	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	$-0.312517\pi$
$83$	10.1222			1.11105			0.555526	+	0.831499i	$0.312517\pi$
$84$		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	−0.0155650	+	0.999879i	$0.504955\pi$
$89$	−8.24250	+	14.2764i	−0.873703	+	1.51330i	−0.858138	+	0.513419i	$0.828379\pi$
$90$	−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	$-0.150923\pi$
$97$	0.486935	+	0.843396i	0.0494407	+	0.0856338i	−0.840246	+	0.542205i	$0.817589\pi$
$98$		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	$-0.786603\pi$
$101$	1.47012	−	2.54632i	0.146282	−	0.253368i	0.929851	+	0.367937i	$0.119936\pi$
$102$	−7.75195	+	13.4268i	−0.767557	+	1.32945i
$103$	0.528682			0.0520926			0.0260463	−	0.999661i	$-0.491708\pi$
$103$	0.528682			0.0520926			0.0260463	+	0.999661i	$0.491708\pi$
$104$	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	0.157545	−	0.987512i	$-0.449642\pi$
$107$	9.66119	−	16.7337i	0.933983	−	1.61771i	0.776438	−	0.630194i	$-0.217024\pi$
$108$	−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	0.719129	−	0.694877i	$-0.244541\pi$
$113$	−2.57480	−	4.45968i	−0.242216	−	0.419531i	−0.961345	+	0.275346i	$0.911208\pi$
$114$	−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	−0.594202	−	0.804316i	$-0.702532\pi$
$127$	4.50166	−	7.79710i	0.399457	−	0.691881i	0.993659	+	0.112436i	$0.0358652\pi$
$128$	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	$-0.404017\pi$
$131$	6.79840			0.593979			0.296989	+	0.954881i	$0.404017\pi$
$132$	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	0.992628	+	0.121203i	$0.0386753\pi$
$137$	7.03779	+	12.1898i	0.601279	+	1.04145i	−0.391349	+	0.920242i	$0.627991\pi$
$138$	5.73602			0.488283
$139$	−8.64313	−	14.9703i	−0.733101	−	1.26977i	−0.955552	−	0.294824i	$-0.904739\pi$
$139$	−8.64313	−	14.9703i	−0.733101	−	1.26977i	0.222451	−	0.974944i	$-0.428594\pi$
$140$		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	0.967949	+	0.251148i	$0.0808082\pi$
$149$	8.56260	+	14.8309i	0.701475	+	1.21499i	−0.266473	+	0.963842i	$0.585858\pi$
$150$	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	$-0.548242\pi$
$157$	−3.78351			−0.301957			−0.150979	+	0.988537i	$0.548242\pi$
$158$	−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	0.830476	−	0.557054i	$-0.188068\pi$
$163$	−0.857757	−	1.48568i	−0.0671847	−	0.116367i	−0.897661	+	0.440687i	$0.854735\pi$
$164$	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	$-0.996163\pi$
$167$	−6.32605	+	10.9570i	−0.489524	+	0.847881i	0.510403	+	0.859935i	$0.329496\pi$
$168$		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	$-0.0228188\pi$
$173$	5.74371	+	9.94839i	0.436686	+	0.756362i	−0.560746	+	0.827988i	$0.689485\pi$
$174$	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	−0.822315	−	0.569032i	$-0.807318\pi$
$179$	1.09225	−	1.89184i	0.0816389	−	0.141403i	0.903954	+	0.427630i	$0.140651\pi$
$180$	−0.140165	+	0.242772i	−0.0104472	+	0.0180952i
$181$	−11.5981			−0.862081			−0.431041	−	0.902333i	$-0.641853\pi$
$181$	−11.5981			−0.862081			−0.431041	+	0.902333i	$0.641853\pi$
$182$		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	−0.984871	−	0.173286i	$-0.944561\pi$
$191$	−8.87961	−	15.3799i	−0.642506	−	1.11285i	0.342365	−	0.939567i	$-0.388772\pi$
$192$	6.79147	−	11.7632i	0.490132	−	0.848934i
$193$	−11.3189	+	19.6050i	−0.814756	+	1.41120i	0.0947474	+	0.995501i	$0.469796\pi$
$193$	−11.3189	+	19.6050i	−0.814756	+	1.41120i	−0.909503	+	0.415697i	$0.863538\pi$
$194$	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	0.251146	+	0.967949i	$0.419193\pi$
$197$	−10.0032	+	17.3260i	−0.712696	+	1.23442i	−0.963842	+	0.266476i	$0.914141\pi$
$198$	1.75859	−	3.04596i	0.124977	−	0.216467i
$199$	0.924426	+	1.60115i	0.0655309	+	0.113503i	0.896929	−	0.442174i	$-0.145793\pi$
$199$	0.924426	+	1.60115i	0.0655309	+	0.113503i	−0.831398	+	0.555677i	$0.812459\pi$
$200$	−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	−0.441203	−	0.897407i	$-0.645448\pi$
$211$	8.08474	−	14.0032i	0.556576	−	0.964019i	0.997779	−	0.0666110i	$-0.0212187\pi$
$212$	−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	$-0.696679\pi$
$223$	6.21589	−	10.7662i	0.416247	−	0.720961i	0.995558	+	0.0941455i	$0.0300119\pi$
$224$		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	$-0.179716\pi$
$227$	−0.617487	−	1.06952i	−0.0409841	−	0.0709865i	−0.885790	+	0.464087i	$0.846383\pi$
$228$	0.559881	+	0.969743i	0.0370790	+	0.0642228i
$229$	6.55514			0.433176			0.216588	−	0.976263i	$-0.430507\pi$
$229$	6.55514			0.433176			0.216588	+	0.976263i	$0.430507\pi$
$230$	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	−0.961740	−	0.273965i	$-0.911665\pi$
$241$	−11.1484	−	19.3096i	−0.718131	−	1.24384i	0.243609	−	0.969874i	$-0.421669\pi$
$242$	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	$-0.0962438\pi$
$251$	3.47657	+	6.02160i	0.219439	+	0.380080i	−0.735197	+	0.677853i	$0.762910\pi$
$252$		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	0.320853	+	0.947129i	$0.396030\pi$
$257$	−10.5776	+	18.3209i	−0.659811	+	1.14283i	−0.980664	+	0.195697i	$0.937303\pi$
$258$	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	−0.706311	−	0.707902i	$-0.749642\pi$
$263$	4.21496	−	7.30053i	0.259906	−	0.450170i	0.966216	+	0.257732i	$0.0829752\pi$
$264$	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	$-0.109787\pi$
$269$	2.91519	+	5.04926i	0.177743	+	0.307859i	−0.763364	+	0.645968i	$0.776454\pi$
$270$	1.40955	−	2.44141i	0.0857823	−	0.148579i
$271$	−9.21497	+	15.9608i	−0.559769	+	0.969549i	0.437746	+	0.899099i	$0.355777\pi$
$271$	−9.21497	+	15.9608i	−0.559769	+	0.969549i	−0.997515	+	0.0704502i	$0.977556\pi$
$272$	−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	0.943830	−	0.330432i	$-0.107194\pi$
$277$	3.09154	+	5.35470i	0.185752	+	0.321733i	−0.758077	+	0.652165i	$0.773861\pi$
$278$	−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	$-0.670664\pi$
$283$	8.22771	−	14.2508i	0.489086	−	0.847123i	0.999921	+	0.0125564i	$0.00399694\pi$
$284$	−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	−0.834625	−	0.550819i	$-0.814316\pi$
$293$	−15.3086	−	26.5152i	−0.894335	−	1.54903i	−0.0597104	−	0.998216i	$-0.519018\pi$
$294$		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	$-0.591738\pi$
$307$	−9.96020			−0.568459			−0.284229	+	0.958756i	$0.591738\pi$
$308$		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	$-0.211795\pi$
$311$	27.7468			1.57337			0.786687	+	0.617352i	$0.211795\pi$
$312$	2.49096	−	19.5124i	0.141023	−	1.10467i
$313$	−16.5227			−0.933920			−0.466960	−	0.884278i	$-0.654651\pi$
$313$	−16.5227			−0.933920			−0.466960	+	0.884278i	$0.654651\pi$
$314$	−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	0.735820	−	0.677178i	$-0.236797\pi$
$331$	−3.97604	−	6.88671i	−0.218543	−	0.378528i	−0.954363	+	0.298650i	$0.903464\pi$
$332$	−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	0.754226	−	0.656615i	$-0.228012\pi$
$347$	−3.56786	−	6.17971i	−0.191533	−	0.331744i	−0.945758	+	0.324871i	$0.894679\pi$
$348$	2.29168	−	3.96930i	0.122847	−	0.212777i
$349$	0.688402	−	1.19235i	0.0368493	−	0.0638249i	−0.847013	−	0.531573i	$-0.821601\pi$
$349$	0.688402	−	1.19235i	0.0368493	−	0.0638249i	0.883862	+	0.467748i	$0.154935\pi$
$350$		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	$-0.827461\pi$
$353$	0.346608	−	0.600342i	0.0184481	−	0.0319530i	0.875102	+	0.483938i	$0.160794\pi$
$354$	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	$-0.771877\pi$
$367$	3.67578	−	6.36664i	0.191874	−	0.332336i	0.945871	+	0.324542i	$0.105210\pi$
$368$	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	0.523304	−	0.852146i	$-0.324699\pi$
$373$	−9.19942	−	15.9339i	−0.476328	−	0.825024i	−0.999632	+	0.0271216i	$0.991366\pi$
$374$	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	−0.796983	−	0.604002i	$-0.793572\pi$
$379$	2.42550	−	4.20110i	0.124590	−	0.215796i	0.921573	+	0.388206i	$0.126905\pi$
$380$	−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	−0.995117	−	0.0987019i	$-0.968531\pi$
$383$	−11.4103	−	19.7631i	−0.583037	−	1.00985i	0.412080	−	0.911148i	$-0.364802\pi$
$384$	−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	−0.875095	−	0.483952i	$-0.839201\pi$
$397$	−17.0689	−	29.5641i	−0.856662	−	1.48378i	0.0184326	−	0.999830i	$-0.494132\pi$
$398$	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	−0.825773	−	0.564003i	$-0.809261\pi$
$401$	1.51298	−	2.62056i	0.0755547	−	0.130865i	0.901327	+	0.433139i	$0.142594\pi$
$402$	−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	$-0.124176\pi$
$409$	2.69162	+	4.66203i	0.133092	+	0.230523i	−0.791775	+	0.610813i	$0.790843\pi$
$410$	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	$-0.787438\pi$
$419$	2.94117	−	5.09426i	0.143686	−	0.248871i	0.928882	+	0.370376i	$0.120771\pi$
$420$		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	−0.949162	−	0.314788i	$-0.898067\pi$
$431$	−4.19294	+	7.26238i	−0.201967	+	0.349817i	0.747195	+	0.664605i	$0.231400\pi$
$432$	7.12013	−	12.3324i	0.342567	−	0.593344i
$433$	−13.7996	−	23.9017i	−0.663168	−	1.14864i	−0.979779	−	0.200085i	$-0.935878\pi$
$433$	−13.7996	−	23.9017i	−0.663168	−	1.14864i	0.316611	−	0.948556i	$-0.397455\pi$
$434$		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	−0.206776	−	0.978388i	$-0.566297\pi$
$439$	15.5869	−	26.9973i	0.743921	−	1.28851i	0.950697	−	0.310121i	$-0.100369\pi$
$440$	−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	0.830749	−	0.556648i	$-0.187913\pi$
$449$	−1.41328	−	2.44787i	−0.0666968	−	0.115522i	−0.897445	+	0.441125i	$0.854579\pi$
$450$	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	0.0345338	−	0.999404i	$-0.489005\pi$
$457$	18.8716	−	32.6866i	0.882776	−	1.52901i	0.848242	−	0.529609i	$-0.177661\pi$
$458$	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	0.914860	+	0.403771i	$0.132301\pi$
$461$	17.3293	+	30.0152i	0.807106	+	1.39795i	−0.107754	+	0.994178i	$0.534366\pi$
$462$		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	$-0.549006\pi$
$467$	−6.62783			−0.306700			−0.153350	+	0.988172i	$0.549006\pi$
$468$	−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	$-0.963877\pi$
$479$	−8.72630	+	15.1144i	−0.398715	+	0.690594i	0.594853	+	0.803835i	$0.297210\pi$
$480$	−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	0.916533	+	0.399959i	$0.130976\pi$
$487$	17.7569	+	30.7558i	0.804641	+	1.39368i	−0.111892	+	0.993720i	$0.535691\pi$
$488$	−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	−0.304442	−	0.952531i	$-0.598470\pi$
$491$	14.9059	−	25.8178i	0.672695	−	1.16514i	0.977137	−	0.212611i	$-0.0681966\pi$
$492$	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	$-0.159681\pi$
$503$	0.492171	+	0.852466i	0.0219448	+	0.0380096i	−0.854844	+	0.518884i	$0.826348\pi$
$504$		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	$-0.740461\pi$
$509$	6.48958	−	11.2403i	0.287646	−	0.498217i	0.973247	+	0.229760i	$0.0737941\pi$
$510$	−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	$-0.360174\pi$
$521$	19.4146			0.850569			0.425285	+	0.905060i	$0.360174\pi$
$522$	7.97033	−	13.8050i	0.348852	−	0.604229i
$523$	13.6360	−	23.6182i	0.596259	−	1.03275i	−0.397109	−	0.917771i	$-0.629987\pi$
$523$	13.6360	−	23.6182i	0.596259	−	1.03275i	0.993368	−	0.114979i	$-0.0366801\pi$
$524$	−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	−0.990969	−	0.134091i	$-0.957188\pi$
$557$	−8.95317	+	15.5073i	−0.379358	+	0.657067i	0.611611	+	0.791159i	$0.290522\pi$
$558$	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	−0.978726	−	0.205173i	$-0.934224\pi$
$563$	−15.8275	−	27.4140i	−0.667048	−	1.15536i	0.311678	−	0.950188i	$-0.399109\pi$
$564$	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	−0.451140	−	0.892453i	$-0.648983\pi$
$569$	13.0555	−	22.6129i	0.547317	−	0.947981i	0.998457	−	0.0555278i	$-0.0176841\pi$
$570$	−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	$-0.386488\pi$
$577$	16.7713			0.698198			0.349099	+	0.937086i	$0.386488\pi$
$578$	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	$-0.899937\pi$
$587$	−5.03261	+	8.71673i	−0.207718	+	0.359778i	0.743277	+	0.668983i	$0.233270\pi$
$588$		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	$-0.800339\pi$
$593$	−39.4322			−1.61929			−0.809643	+	0.586923i	$0.800339\pi$
$594$	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	−0.297064	−	0.954858i	$-0.596007\pi$
$601$	16.6312	−	28.8060i	0.678399	−	1.17502i	0.975463	−	0.220164i	$-0.0706592\pi$
$602$		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	0.837184	+	0.546921i	$0.184200\pi$
$607$	21.9824	+	38.0747i	0.892240	+	1.54540i	0.0550554	+	0.998483i	$0.482466\pi$
$608$	−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	−0.892008	−	0.452019i	$-0.850704\pi$
$613$	−1.35045	+	2.33906i	−0.0545443	+	0.0944736i	0.837464	+	0.546492i	$0.184037\pi$
$614$	−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	0.799248	−	0.601002i	$-0.205232\pi$
$617$	−3.00208	−	5.19975i	−0.120859	−	0.209334i	−0.920107	+	0.391668i	$0.871898\pi$
$618$	−0.854742	−	1.48046i	−0.0343828	−	0.0595527i
$619$	13.3641			0.537148			0.268574	−	0.963259i	$-0.413448\pi$
$619$	13.3641			0.537148			0.268574	+	0.963259i	$0.413448\pi$
$620$	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	−0.916251	−	0.400604i	$-0.868800\pi$
$631$	−20.2228	−	35.0270i	−0.805059	−	1.39440i	0.111192	−	0.993799i	$-0.464533\pi$
$632$	−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	0.747289	−	0.664500i	$-0.231355\pi$
$641$	−5.10991	−	8.85062i	−0.201829	−	0.349578i	−0.949118	+	0.314921i	$0.898022\pi$
$642$	−62.4786			−2.46584
$643$	15.9014	+	27.5420i	0.627088	+	1.08615i	0.988133	+	0.153600i	$0.0490868\pi$
$643$	15.9014	+	27.5420i	0.627088	+	1.08615i	−0.361045	+	0.932548i	$0.617580\pi$
$644$		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	0.296769	+	0.954949i	$0.404091\pi$
$647$	−17.2617	+	29.8981i	−0.678626	+	1.17541i	−0.975395	+	0.220465i	$0.929243\pi$
$648$	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	−0.947871	−	0.318653i	$-0.896769\pi$
$653$	−5.05899	+	8.76244i	−0.197974	+	0.342901i	0.749898	+	0.661554i	$0.230103\pi$
$654$	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	0.975824	+	0.218556i	$0.0701345\pi$
$659$	17.3841	+	30.1101i	0.677187	+	1.17292i	−0.298637	+	0.954367i	$0.596532\pi$
$660$	0.298019	−	0.516185i	0.0116004	−	0.0200925i
$661$	−8.28076	+	14.3427i	−0.322084	+	0.557866i	−0.980918	−	0.194422i	$-0.937717\pi$
$661$	−8.28076	+	14.3427i	−0.322084	+	0.557866i	0.658834	+	0.752289i	$0.271050\pi$
$662$	−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	−0.107393	−	0.994217i	$-0.534250\pi$
$673$	20.9437	−	36.2756i	0.807321	−	1.39832i	0.914713	−	0.404104i	$-0.132417\pi$
$674$	−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	$-0.292495\pi$
$677$	31.5715			1.21339			0.606696	+	0.794934i	$0.292495\pi$
$678$	−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	0.999996	+	0.00294809i	$0.000938408\pi$
$683$	13.1338	+	22.7484i	0.502551	+	0.870444i	−0.497445	+	0.867496i	$0.665728\pi$
$684$	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	$-0.796311\pi$
$691$	3.05047	−	5.28358i	0.116046	−	0.200997i	0.918197	+	0.396124i	$0.129645\pi$
$692$	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	0.912640	+	0.408764i	$0.134040\pi$
$709$	21.5764	+	37.3715i	0.810320	+	1.40352i	−0.102320	+	0.994751i	$0.532627\pi$
$710$	−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	0.999541	+	0.0302857i	$0.00964171\pi$
$719$	14.1042	+	24.4292i	0.525999	+	0.911057i	−0.473542	+	0.880771i	$0.657025\pi$
$720$	−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	$-0.617845\pi$
$727$	−19.5116			−0.723646			−0.361823	+	0.932247i	$0.617845\pi$
$728$		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	$-0.377255\pi$
$733$	20.3666			0.752259			0.376129	+	0.926567i	$0.377255\pi$
$734$	−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	−0.754146	−	0.656706i	$-0.771949\pi$
$739$	5.20995	−	9.02391i	0.191651	−	0.331950i	0.945798	+	0.324757i	$0.105282\pi$
$740$	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	−0.661007	−	0.750380i	$-0.729871\pi$
$743$	8.70470	−	15.0770i	0.319344	−	0.553121i	0.980351	+	0.197259i	$0.0632040\pi$
$744$	−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	−0.848990	−	0.528408i	$-0.822789\pi$
$751$	0.907626	−	1.57205i	0.0331197	−	0.0573651i	0.882110	+	0.471043i	$0.156122\pi$
$752$	−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	−0.288220	+	0.957564i	$0.593063\pi$
$757$	−26.7814	+	46.3867i	−0.973385	+	1.68595i	−0.685165	+	0.728388i	$0.740270\pi$
$758$	−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	$-0.187923\pi$
$761$	−1.84083	−	3.18841i	−0.0667300	−	0.115580i	−0.897460	+	0.441096i	$0.854590\pi$
$762$	−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	$-0.863440\pi$
$769$	−2.61897	+	4.53619i	−0.0944424	+	0.163579i	0.814933	+	0.579555i	$0.196773\pi$
$770$		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	0.956717	+	0.291019i	$0.0939942\pi$
$773$	20.3069	+	35.1726i	0.730388	+	1.26507i	−0.226329	+	0.974051i	$0.572672\pi$
$774$	−13.3672	−	23.1527i	−0.480474	−	0.832205i
$775$	28.3177			1.01720
$776$	1.24944	+	2.16409i	0.0448522	+	0.0776862i

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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more