LMFDB - Embedded newform 441.2.i.d.68.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(68,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 5]))

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

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

chi := DirichletCharacter("441.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			68.3
Character	$\chi$	$=$	441.68
Dual form			441.2.i.d.227.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.37274i q^{2} +(-1.65098 - 0.523694i) q^{3} -3.62990 q^{4} +(1.71774 + 2.97522i) q^{5} +(-1.24259 + 3.91735i) q^{6} +3.86732i q^{8} +(2.45149 + 1.72922i) q^{9} +O(q^{10})$	\(q-2.37274i q^{2} +(-1.65098 - 0.523694i) q^{3} -3.62990 q^{4} +(1.71774 + 2.97522i) q^{5} +(-1.24259 + 3.91735i) q^{6} +3.86732i q^{8} +(2.45149 + 1.72922i) q^{9} +(7.05942 - 4.07576i) q^{10} +(-0.271895 - 0.156979i) q^{11} +(5.99290 + 1.90095i) q^{12} +(5.09882 + 2.94381i) q^{13} +(-1.27786 - 5.81160i) q^{15} +1.91636 q^{16} +(0.476712 + 0.825689i) q^{17} +(4.10299 - 5.81675i) q^{18} +(-1.09214 - 0.630546i) q^{19} +(-6.23523 - 10.7997i) q^{20} +(-0.372470 + 0.645137i) q^{22} +(5.91336 - 3.41408i) q^{23} +(2.02529 - 6.38488i) q^{24} +(-3.40128 + 5.89118i) q^{25} +(6.98489 - 12.0982i) q^{26} +(-3.14179 - 4.13874i) q^{27} +(3.43518 - 1.98330i) q^{29} +(-13.7894 + 3.03203i) q^{30} +5.23527i q^{31} +3.18763i q^{32} +(0.366686 + 0.401559i) q^{33} +(1.95915 - 1.13111i) q^{34} +(-8.89866 - 6.27688i) q^{36} +(-2.68802 + 4.65579i) q^{37} +(-1.49612 + 2.59136i) q^{38} +(-6.87642 - 7.53040i) q^{39} +(-11.5061 + 6.64306i) q^{40} +(-0.0699627 + 0.121179i) q^{41} +(1.44078 + 2.49550i) q^{43} +(0.986951 + 0.569817i) q^{44} +(-0.933772 + 10.2641i) q^{45} +(-8.10072 - 14.0309i) q^{46} -2.01390 q^{47} +(-3.16387 - 1.00358i) q^{48} +(13.9783 + 8.07035i) q^{50} +(-0.354635 - 1.61285i) q^{51} +(-18.5082 - 10.6857i) q^{52} +(10.3749 - 5.98997i) q^{53} +(-9.82016 + 7.45465i) q^{54} -1.07860i q^{55} +(1.47289 + 1.61297i) q^{57} +(-4.70586 - 8.15079i) q^{58} +1.64892 q^{59} +(4.63850 + 21.0955i) q^{60} -2.97247i q^{61} +12.4219 q^{62} +11.3961 q^{64} +20.2268i q^{65} +(0.952795 - 0.870049i) q^{66} -1.86812 q^{67} +(-1.73041 - 2.99717i) q^{68} +(-11.5508 + 2.53980i) q^{69} -10.9981i q^{71} +(-6.68744 + 9.48070i) q^{72} +(-0.354655 + 0.204760i) q^{73} +(11.0470 + 6.37798i) q^{74} +(8.70063 - 7.94502i) q^{75} +(3.96435 + 2.28882i) q^{76} +(-17.8677 + 16.3160i) q^{78} +10.4665 q^{79} +(3.29181 + 5.70158i) q^{80} +(3.01961 + 8.47832i) q^{81} +(0.287526 + 0.166003i) q^{82} +(4.00094 + 6.92984i) q^{83} +(-1.63774 + 2.83664i) q^{85} +(5.92117 - 3.41859i) q^{86} +(-6.71007 + 1.47542i) q^{87} +(0.607087 - 1.05151i) q^{88} +(-1.05931 + 1.83478i) q^{89} +(24.3540 + 2.21560i) q^{90} +(-21.4649 + 12.3927i) q^{92} +(2.74168 - 8.64335i) q^{93} +4.77847i q^{94} -4.33246i q^{95} +(1.66934 - 5.26272i) q^{96} +(-10.5054 + 6.06531i) q^{97} +(-0.395098 - 0.854998i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4} - 8 q^{9}+O(q^{10}) $ 48 * q - 48 * q^4 - 8 * q^9	$ 48 q - 48 q^{4} - 8 q^{9} + 24 q^{11} - 40 q^{15} + 48 q^{16} - 16 q^{18} + 48 q^{23} - 24 q^{25} - 24 q^{30} - 8 q^{36} - 56 q^{39} - 96 q^{44} + 48 q^{50} - 24 q^{51} - 48 q^{53} + 80 q^{57} + 168 q^{60} - 48 q^{64} - 88 q^{72} + 168 q^{74} - 88 q^{78} + 48 q^{79} - 24 q^{81} - 24 q^{85} - 24 q^{86} - 144 q^{92} + 16 q^{93} - 72 q^{99}+O(q^{100}) $ 48 * q - 48 * q^4 - 8 * q^9 + 24 * q^11 - 40 * q^15 + 48 * q^16 - 16 * q^18 + 48 * q^23 - 24 * q^25 - 24 * q^30 - 8 * q^36 - 56 * q^39 - 96 * q^44 + 48 * q^50 - 24 * q^51 - 48 * q^53 + 80 * q^57 + 168 * q^60 - 48 * q^64 - 88 * q^72 + 168 * q^74 - 88 * q^78 + 48 * q^79 - 24 * q^81 - 24 * q^85 - 24 * q^86 - 144 * q^92 + 16 * q^93 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		−	2.37274i		−	1.67778i	−0.544300	−	0.838890i	$-0.683205\pi$
$2$		−	2.37274i		−	1.67778i	0.544300	−	0.838890i	$-0.316795\pi$
$3$	−1.65098	−	0.523694i	−0.953196	−	0.302355i
$3$	−1.65098	−	0.523694i	−0.953196	−	0.302355i
$4$	−3.62990			−1.81495
$5$	1.71774	+	2.97522i	0.768198	+	1.33056i	0.938539	+	0.345172i	$0.112180\pi$
$5$	1.71774	+	2.97522i	0.768198	+	1.33056i	−0.170342	+	0.985385i	$0.554487\pi$
$6$	−1.24259	+	3.91735i	−0.507285	+	1.59925i
$7$		0			0
$7$		0			0
$8$			3.86732i			1.36730i
$9$	2.45149	+	1.72922i	0.817163	+	0.576406i
$10$	7.05942	−	4.07576i	2.23238	−	1.28887i
$11$	−0.271895	−	0.156979i	−0.0819795	−	0.0473309i	0.458450	−	0.888720i	$-0.348405\pi$
$11$	−0.271895	−	0.156979i	−0.0819795	−	0.0473309i	−0.540429	+	0.841389i	$0.681738\pi$
$12$	5.99290	+	1.90095i	1.73000	+	0.548758i
$13$	5.09882	+	2.94381i	1.41416	+	0.816465i	0.995777	−	0.0918054i	$-0.0292638\pi$
$13$	5.09882	+	2.94381i	1.41416	+	0.816465i	0.418383	+	0.908271i	$0.362597\pi$
$14$		0			0
$15$	−1.27786	−	5.81160i	−0.329942	−	1.50055i
$16$	1.91636			0.479089
$17$	0.476712	+	0.825689i	0.115620	+	0.200259i	0.918027	−	0.396517i	$-0.129781\pi$
$17$	0.476712	+	0.825689i	0.115620	+	0.200259i	−0.802408	+	0.596776i	$0.796448\pi$
$18$	4.10299	−	5.81675i	0.967083	−	1.37102i
$19$	−1.09214	−	0.630546i	−0.250553	−	0.144657i	0.369464	−	0.929245i	$-0.379541\pi$
$19$	−1.09214	−	0.630546i	−0.250553	−	0.144657i	−0.620018	+	0.784588i	$0.712875\pi$
$20$	−6.23523	−	10.7997i	−1.39424	−	2.41489i
$21$		0			0
$22$	−0.372470	+	0.645137i	−0.0794108	+	0.137544i
$23$	5.91336	−	3.41408i	1.23302	−	0.711884i	0.265362	−	0.964149i	$-0.414509\pi$
$23$	5.91336	−	3.41408i	1.23302	−	0.711884i	0.967658	+	0.252265i	$0.0811754\pi$
$24$	2.02529	−	6.38488i	0.413411	−	1.30331i
$25$	−3.40128	+	5.89118i	−0.680255	+	1.17824i
$26$	6.98489	−	12.0982i	1.36985	−	2.37265i
$27$	−3.14179	−	4.13874i	−0.604637	−	0.796501i
$28$		0			0
$29$	3.43518	−	1.98330i	0.637897	−	0.368290i	−0.145907	−	0.989298i	$-0.546610\pi$
$29$	3.43518	−	1.98330i	0.637897	−	0.368290i	0.783804	+	0.621008i	$0.213277\pi$
$30$	−13.7894	+	3.03203i	−2.51759	+	0.553571i
$31$			5.23527i			0.940283i	0.882591	+	0.470141i	$0.155797\pi$
$31$			5.23527i			0.940283i	−0.882591	+	0.470141i	$0.844203\pi$
$32$			3.18763i			0.563498i
$33$	0.366686	+	0.401559i	0.0638318	+	0.0699024i
$34$	1.95915	−	1.13111i	0.335991	−	0.193984i
$35$		0			0
$36$	−8.89866	−	6.27688i	−1.48311	−	1.04615i
$37$	−2.68802	+	4.65579i	−0.441908	+	0.765407i	−0.997831	−	0.0658264i	$-0.979032\pi$
$37$	−2.68802	+	4.65579i	−0.441908	+	0.765407i	0.555923	+	0.831234i	$0.312365\pi$
$38$	−1.49612	+	2.59136i	−0.242703	+	0.420374i
$39$	−6.87642	−	7.53040i	−1.10111	−	1.20583i
$40$	−11.5061	+	6.64306i	−1.81928	+	1.05036i
$41$	−0.0699627	+	0.121179i	−0.0109263	+	0.0189250i	−0.871437	−	0.490508i	$-0.836811\pi$
$41$	−0.0699627	+	0.121179i	−0.0109263	+	0.0189250i	0.860511	+	0.509433i	$0.170145\pi$
$42$		0			0
$43$	1.44078	+	2.49550i	0.219716	+	0.380560i	0.954721	−	0.297502i	$-0.0961535\pi$
$43$	1.44078	+	2.49550i	0.219716	+	0.380560i	−0.735005	+	0.678062i	$0.762820\pi$
$44$	0.986951	+	0.569817i	0.148788	+	0.0859031i
$45$	−0.933772	+	10.2641i	−0.139198	+	1.53008i
$46$	−8.10072	−	14.0309i	−1.19439	−	2.06874i
$47$	−2.01390			−0.293758			−0.146879	−	0.989154i	$-0.546923\pi$
$47$	−2.01390			−0.293758			−0.146879	+	0.989154i	$0.546923\pi$
$48$	−3.16387	−	1.00358i	−0.456666	−	0.144855i
$49$		0			0
$50$	13.9783	+	8.07035i	1.97682	+	1.14132i
$51$	−0.354635	−	1.61285i	−0.0496588	−	0.225844i
$52$	−18.5082	−	10.6857i	−2.56663	−	1.48184i
$53$	10.3749	−	5.98997i	1.42511	−	0.822786i	0.428378	−	0.903599i	$-0.359085\pi$
$53$	10.3749	−	5.98997i	1.42511	−	0.822786i	0.996729	+	0.0808132i	$0.0257517\pi$
$54$	−9.82016	+	7.45465i	−1.33635	+	1.01445i
$55$		−	1.07860i		−	0.145438i
$56$		0			0
$57$	1.47289	+	1.61297i	0.195089	+	0.213643i
$58$	−4.70586	−	8.15079i	−0.617910	−	1.07025i
$59$	1.64892			0.214671			0.107335	−	0.994223i	$-0.465768\pi$
$59$	1.64892			0.214671			0.107335	+	0.994223i	$0.465768\pi$
$60$	4.63850	+	21.0955i	0.598828	+	2.72342i
$61$		−	2.97247i		−	0.380585i	−0.981727	−	0.190293i	$-0.939056\pi$
$61$		−	2.97247i		−	0.380585i	0.981727	−	0.190293i	$-0.0609437\pi$
$62$	12.4219			1.57759
$63$		0			0
$64$	11.3961			1.42452
$65$			20.2268i			2.50883i
$66$	0.952795	−	0.870049i	0.117281	−	0.107096i
$67$	−1.86812			−0.228227			−0.114113	−	0.993468i	$-0.536403\pi$
$67$	−1.86812			−0.228227			−0.114113	+	0.993468i	$0.536403\pi$
$68$	−1.73041	−	2.99717i	−0.209844	−	0.363460i
$69$	−11.5508	+	2.53980i	−1.39055	+	0.305756i
$70$		0			0
$71$		−	10.9981i		−	1.30524i	−0.757686	−	0.652619i	$-0.773670\pi$
$71$		−	10.9981i		−	1.30524i	0.757686	−	0.652619i	$-0.226330\pi$
$72$	−6.68744	+	9.48070i	−0.788123	+	1.11731i
$73$	−0.354655	+	0.204760i	−0.0415092	+	0.0239653i	−0.520611	−	0.853794i	$-0.674296\pi$
$73$	−0.354655	+	0.204760i	−0.0415092	+	0.0239653i	0.479102	+	0.877759i	$0.340962\pi$
$74$	11.0470	+	6.37798i	1.28419	+	0.741425i
$75$	8.70063	−	7.94502i	1.00466	−	0.917412i
$76$	3.96435	+	2.28882i	0.454742	+	0.262545i
$77$		0			0
$78$	−17.8677	+	16.3160i	−2.02312	+	1.84742i
$79$	10.4665			1.17757			0.588787	−	0.808288i	$-0.299606\pi$
$79$	10.4665			1.17757			0.588787	+	0.808288i	$0.299606\pi$
$80$	3.29181	+	5.70158i	0.368035	+	0.637456i
$81$	3.01961	+	8.47832i	0.335512	+	0.942036i
$82$	0.287526	+	0.166003i	0.0317519	+	0.0183320i
$83$	4.00094	+	6.92984i	0.439161	+	0.760649i	0.997625	−	0.0688800i	$-0.0219426\pi$
$83$	4.00094	+	6.92984i	0.439161	+	0.760649i	−0.558464	+	0.829529i	$0.688609\pi$
$84$		0			0
$85$	−1.63774	+	2.83664i	−0.177637	+	0.307677i
$86$	5.92117	−	3.41859i	0.638496	−	0.368636i
$87$	−6.71007	+	1.47542i	−0.719395	+	0.158181i
$88$	0.607087	−	1.05151i	0.0647157	−	0.112091i
$89$	−1.05931	+	1.83478i	−0.112287	+	0.194487i	−0.916692	−	0.399595i	$-0.869151\pi$
$89$	−1.05931	+	1.83478i	−0.112287	+	0.194487i	0.804405	+	0.594081i	$0.202484\pi$
$90$	24.3540	+	2.21560i	2.56713	+	0.233545i
$91$		0			0
$92$	−21.4649	+	12.3927i	−2.23787	+	1.29203i
$93$	2.74168	−	8.64335i	0.284299	−	0.896273i
$94$			4.77847i			0.492862i
$95$		−	4.33246i		−	0.444501i
$96$	1.66934	−	5.26272i	0.170376	−	0.537124i
$97$	−10.5054	+	6.06531i	−1.06666	+	0.615839i	−0.927268	−	0.374398i	$-0.877850\pi$
$97$	−10.5054	+	6.06531i	−1.06666	+	0.615839i	−0.139396	+	0.990237i	$0.544516\pi$
$98$		0			0
$99$	−0.395098	−	0.854998i	−0.0397088	−	0.0859305i
$100$	12.3463	−	21.3844i	1.23463	−	2.13844i
$101$	6.26039	−	10.8433i	0.622932	−	1.07895i	−0.366005	−	0.930613i	$-0.619275\pi$
$101$	6.26039	−	10.8433i	0.622932	−	1.07895i	0.988937	−	0.148337i	$-0.0473920\pi$
$102$	−3.82687	+	0.841457i	−0.378917	+	0.0833166i
$103$	−15.6040	+	9.00897i	−1.53751	+	0.887680i	−0.538523	+	0.842611i	$0.681017\pi$
$103$	−15.6040	+	9.00897i	−1.53751	+	0.887680i	−0.998984	+	0.0450689i	$0.985649\pi$
$104$	−11.3847	+	19.7188i	−1.11636	+	1.93359i
$105$		0			0
$106$	−14.2127	−	24.6170i	−1.38046	−	2.39102i
$107$	3.11610	+	1.79908i	0.301245	+	0.173924i	0.643002	−	0.765864i	$-0.277689\pi$
$107$	3.11610	+	1.79908i	0.301245	+	0.173924i	−0.341757	+	0.939788i	$0.611022\pi$
$108$	11.4044	+	15.0232i	1.09739	+	1.44561i
$109$	3.28109	+	5.68302i	0.314271	+	0.544334i	0.979282	−	0.202499i	$-0.0649064\pi$
$109$	3.28109	+	5.68302i	0.314271	+	0.544334i	−0.665011	+	0.746834i	$0.731573\pi$
$110$	−2.55923			−0.244013
$111$	6.87609	−	6.27893i	0.652649	−	0.595970i
$112$		0			0
$113$	−1.87912	−	1.08491i	−0.176773	−	0.102060i	0.409003	−	0.912533i	$-0.365877\pi$
$113$	−1.87912	−	1.08491i	−0.176773	−	0.102060i	−0.585775	+	0.810473i	$0.699210\pi$
$114$	3.82715	−	3.49478i	0.358445	−	0.327316i
$115$	20.3152	+	11.7290i	1.89441	+	1.09374i
$116$	−12.4694	+	7.19918i	−1.15775	+	0.668427i
$117$	7.40923	+	16.0337i	0.684984	+	1.48232i
$118$		−	3.91246i		−	0.360171i
$119$		0			0
$120$	22.4753	−	4.94190i	2.05171	−	0.451132i
$121$	−5.45072	−	9.44092i	−0.495520	−	0.858265i
$122$	−7.05289			−0.638539
$123$	0.178968	−	0.163425i	0.0161370	−	0.0147356i
$124$		−	19.0035i		−	1.70656i
$125$	−6.19265			−0.553887
$126$		0			0
$127$	2.34967			0.208499			0.104250	−	0.994551i	$-0.466756\pi$
$127$	2.34967			0.208499			0.104250	+	0.994551i	$0.466756\pi$
$128$		−	20.6648i		−	1.82653i
$129$	−1.07182	−	4.87455i	−0.0943686	−	0.429180i
$130$	47.9930			4.20926
$131$	−4.74594	−	8.22021i	−0.414655	−	0.718203i	0.580737	−	0.814091i	$-0.302764\pi$
$131$	−4.74594	−	8.22021i	−0.414655	−	0.718203i	−0.995392	+	0.0958879i	$0.969431\pi$
$132$	−1.33103	−	1.45762i	−0.115851	−	0.126869i
$133$		0			0
$134$			4.43256i			0.382915i
$135$	6.91687	−	16.4568i	0.595309	−	1.41637i
$136$	−3.19320	+	1.84360i	−0.273815	+	0.158087i
$137$	−8.85456	−	5.11218i	−0.756496	−	0.436763i	0.0715401	−	0.997438i	$-0.477209\pi$
$137$	−8.85456	−	5.11218i	−0.756496	−	0.436763i	−0.828036	+	0.560674i	$0.810542\pi$
$138$	6.02628	+	27.4070i	0.512991	+	2.33304i
$139$	−4.56556	−	2.63593i	−0.387246	−	0.223577i	0.293720	−	0.955891i	$-0.405107\pi$
$139$	−4.56556	−	2.63593i	−0.387246	−	0.223577i	−0.680966	+	0.732315i	$0.738440\pi$
$140$		0			0
$141$	3.32492	+	1.05467i	0.280009	+	0.0888192i
$142$	−26.0957			−2.18990
$143$	−0.924230	−	1.60081i	−0.0772880	−	0.133867i
$144$	4.69793	+	3.31380i	0.391494	+	0.276150i
$145$	11.8015	+	6.81361i	0.980062	+	0.565839i
$146$	0.485842	+	0.841504i	0.0402086	+	0.0696433i
$147$		0			0
$148$	9.75724	−	16.9000i	0.802040	−	1.38917i
$149$	−15.8151	+	9.13086i	−1.29562	+	0.748029i	−0.979645	−	0.200737i	$-0.935666\pi$
$149$	−15.8151	+	9.13086i	−1.29562	+	0.748029i	−0.315979	+	0.948766i	$0.602333\pi$
$150$	−18.8515	−	20.6443i	−1.53922	−	1.68560i
$151$	−11.5551	+	20.0140i	−0.940340	+	1.62872i	−0.175517	+	0.984476i	$0.556160\pi$
$151$	−11.5551	+	20.0140i	−0.940340	+	1.62872i	−0.764823	+	0.644240i	$0.777174\pi$
$152$	2.43852	−	4.22365i	0.197790	−	0.342583i
$153$	−0.259142	+	2.84851i	−0.0209504	+	0.230288i
$154$		0			0
$155$	−15.5761	+	8.99285i	−1.25110	+	0.722323i
$156$	24.9607	+	27.3346i	1.99846	+	2.18852i
$157$		−	6.52936i		−	0.521100i	−0.965460	−	0.260550i	$-0.916096\pi$
$157$		−	6.52936i		−	0.521100i	0.965460	−	0.260550i	$-0.0839038\pi$
$158$		−	24.8343i		−	1.97571i
$159$	−20.2658	+	4.45606i	−1.60718	+	0.353388i
$160$	−9.48388	+	5.47552i	−0.749767	+	0.432878i
$161$		0			0
$162$	20.1169	−	7.16474i	1.58053	−	0.562915i
$163$	−12.2623	+	21.2389i	−0.960457	+	1.66356i	−0.239103	+	0.970994i	$0.576853\pi$
$163$	−12.2623	+	21.2389i	−0.960457	+	1.66356i	−0.721354	+	0.692566i	$0.756480\pi$
$164$	0.253957	−	0.439867i	0.0198307	−	0.0343478i
$165$	−0.564854	+	1.78074i	−0.0439738	+	0.138631i
$166$	16.4427	−	9.49320i	1.27620	−	0.736815i
$167$	−6.99871	+	12.1221i	−0.541576	+	0.938037i	0.457238	+	0.889345i	$0.348839\pi$
$167$	−6.99871	+	12.1221i	−0.541576	+	0.938037i	−0.998814	+	0.0486928i	$0.984494\pi$
$168$		0			0
$169$	10.8320	+	18.7616i	0.833232	+	1.44320i
$170$	6.73061	+	3.88592i	0.516214	+	0.298037i
$171$	−1.58701	−	3.43432i	−0.121362	−	0.262629i
$172$	−5.22987	−	9.05840i	−0.398774	−	0.690697i
$173$	−10.8995			−0.828672			−0.414336	−	0.910124i	$-0.635986\pi$
$173$	−10.8995			−0.828672			−0.414336	+	0.910124i	$0.635986\pi$
$174$	3.50078	+	15.9212i	0.265394	+	1.20699i
$175$		0			0
$176$	−0.521048	−	0.300827i	−0.0392755	−	0.0226757i
$177$	−2.72234	−	0.863528i	−0.204623	−	0.0649068i
$178$	4.35346	+	2.51347i	0.326306	+	0.188393i
$179$	1.38517	−	0.799726i	0.103532	−	0.0597743i	−0.447340	−	0.894364i	$-0.647629\pi$
$179$	1.38517	−	0.799726i	0.103532	−	0.0597743i	0.550872	+	0.834590i	$0.314295\pi$
$180$	3.38949	−	37.2575i	0.252638	−	2.77701i
$181$		−	17.5088i		−	1.30142i	−0.759326	−	0.650710i	$-0.774471\pi$
$181$		−	17.5088i		−	1.30142i	0.759326	−	0.650710i	$-0.225529\pi$
$182$		0			0
$183$	−1.55666	+	4.90749i	−0.115072	+	0.362772i
$184$	13.2033	+	22.8688i	0.973363	+	1.68591i
$185$	−18.4693			−1.35789
$186$	−20.5084	−	6.50529i	−1.50375	−	0.476991i
$187$		−	0.299334i		−	0.0218895i
$188$	7.31027			0.533156
$189$		0			0
$190$	−10.2798			−0.745775
$191$		−	16.0628i		−	1.16226i	−0.813811	−	0.581130i	$-0.802611\pi$
$191$		−	16.0628i		−	1.16226i	0.813811	−	0.581130i	$-0.197389\pi$
$192$	−18.8148	−	5.96808i	−1.35784	−	0.430709i
$193$	−10.8839			−0.783441			−0.391721	−	0.920084i	$-0.628120\pi$
$193$	−10.8839			−0.783441			−0.391721	+	0.920084i	$0.628120\pi$
$194$	14.3914	+	24.9267i	1.03324	+	1.78963i
$195$	10.5927	−	33.3941i	0.758556	−	2.39140i
$196$		0			0
$197$			6.50777i			0.463660i	0.972756	+	0.231830i	$0.0744712\pi$
$197$			6.50777i			0.463660i	−0.972756	+	0.231830i	$0.925529\pi$
$198$	−2.02869	+	0.937464i	−0.144173	+	0.0666227i
$199$	15.4217	−	8.90372i	1.09321	−	0.631168i	0.158784	−	0.987313i	$-0.449243\pi$
$199$	15.4217	−	8.90372i	1.09321	−	0.631168i	0.934431	+	0.356145i	$0.115909\pi$
$200$	−22.7831	−	13.1538i	−1.61101	−	0.930116i
$201$	3.08423	+	0.978321i	0.217545	+	0.0690054i
$202$	−25.7284	−	14.8543i	−1.81024	−	1.04514i
$203$		0			0
$204$	1.28729	+	5.85448i	0.0901282	+	0.409895i
$205$	−0.480711			−0.0335743
$206$	21.3759	+	37.0242i	1.48933	+	2.57960i
$207$	20.4002	+	1.85591i	1.41791	+	0.128994i
$208$	9.77117	+	5.64139i	0.677508	+	0.391160i
$209$	0.197965	+	0.342885i	0.0136935	+	0.0237178i
$210$		0			0
$211$	−0.282402	+	0.489135i	−0.0194414	+	0.0336735i	−0.875582	−	0.483069i	$-0.839522\pi$
$211$	−0.282402	+	0.489135i	−0.0194414	+	0.0336735i	0.856141	+	0.516742i	$0.172855\pi$
$212$	−37.6600	+	21.7430i	−2.58650	+	1.49331i
$213$	−5.75965	+	18.1577i	−0.394645	+	1.24415i
$214$	4.26875	−	7.39370i	0.291806	−	0.505423i
$215$	−4.94977	+	8.57325i	−0.337571	+	0.584691i
$216$	16.0058	−	12.1503i	1.08906	−	0.826723i
$217$		0			0
$218$	13.4843	−	7.78518i	0.913273	−	0.527279i
$219$	0.692761	−	0.152325i	0.0468124	−	0.0102932i
$220$			3.91519i			0.263962i
$221$			5.61339i			0.377598i
$222$	−14.8983	−	16.3152i	−0.999907	−	1.09500i
$223$	7.61261	−	4.39514i	0.509778	−	0.294321i	−0.222964	−	0.974827i	$-0.571573\pi$
$223$	7.61261	−	4.39514i	0.509778	−	0.294321i	0.732742	+	0.680506i	$0.238240\pi$
$224$		0			0
$225$	−18.5253	+	8.56063i	−1.23502	+	0.570709i
$226$	−2.57421	+	4.45866i	−0.171234	+	0.296586i
$227$	8.45329	−	14.6415i	0.561065	−	0.971793i	−0.436339	−	0.899782i	$-0.643725\pi$
$227$	8.45329	−	14.6415i	0.561065	−	0.971793i	0.997404	−	0.0720104i	$-0.0229415\pi$
$228$	−5.34643	−	5.85490i	−0.354076	−	0.387750i
$229$	16.9410	−	9.78088i	1.11949	−	0.646339i	0.178221	−	0.983991i	$-0.442966\pi$
$229$	16.9410	−	9.78088i	1.11949	−	0.646339i	0.941271	+	0.337652i	$0.109633\pi$
$230$	27.8299	−	48.2028i	1.83505	−	3.17840i
$231$		0			0
$232$	7.67007	+	13.2849i	0.503565	+	0.872200i
$233$	17.0926	+	9.86840i	1.11977	+	0.646500i	0.941342	−	0.337453i	$-0.109565\pi$
$233$	17.0926	+	9.86840i	1.11977	+	0.646500i	0.178428	+	0.983953i	$0.442899\pi$
$234$	38.0438	−	17.5802i	2.48700	−	1.14925i
$235$	−3.45937	−	5.99180i	−0.225664	−	0.390862i
$236$	−5.98541			−0.389617
$237$	−17.2800	−	5.48124i	−1.12246	−	0.356045i
$238$		0			0
$239$	−16.9761	−	9.80118i	−1.09809	−	0.633985i	−0.162375	−	0.986729i	$-0.551915\pi$
$239$	−16.9761	−	9.80118i	−1.09809	−	0.633985i	−0.935720	+	0.352744i	$0.885249\pi$
$240$	−2.44884	−	11.1371i	−0.158072	−	0.718897i
$241$	−13.8166	−	7.97702i	−0.890006	−	0.513845i	−0.0160617	−	0.999871i	$-0.505113\pi$
$241$	−13.8166	−	7.97702i	−0.890006	−	0.513845i	−0.873945	+	0.486026i	$0.838446\pi$
$242$	−22.4008	+	12.9331i	−1.43998	+	0.831373i
$243$	−0.545277	−	15.5789i	−0.0349795	−	0.999388i
$244$			10.7897i			0.690743i
$245$		0			0
$246$	−0.387766	−	0.424644i	−0.0247230	−	0.0270743i
$247$	−3.71241	−	6.43008i	−0.236215	−	0.409136i
$248$	−20.2465			−1.28565
$249$	−2.97638	−	13.5363i	−0.188620	−	0.857829i
$250$			14.6935i			0.929301i
$251$	−0.976065			−0.0616087			−0.0308044	−	0.999525i	$-0.509807\pi$
$251$	−0.976065			−0.0616087			−0.0308044	+	0.999525i	$0.509807\pi$
$252$		0			0
$253$	−2.14375			−0.134776
$254$		−	5.57515i		−	0.349816i
$255$	4.18940	−	3.82558i	0.262351	−	0.239567i
$256$	−26.2399			−1.64000
$257$	−6.11947	−	10.5992i	−0.381722	−	0.661162i	0.609587	−	0.792720i	$-0.291335\pi$
$257$	−6.11947	−	10.5992i	−0.381722	−	0.661162i	−0.991309	+	0.131558i	$0.958002\pi$
$258$	−11.5660	+	2.54315i	−0.720071	+	0.158330i
$259$		0			0
$260$		−	73.4212i		−	4.55339i
$261$	11.8509	+	1.07813i	0.733551	+	0.0667347i
$262$	−19.5044	+	11.2609i	−1.20499	+	0.695700i
$263$	3.64436	+	2.10407i	0.224721	+	0.129743i	0.608134	−	0.793834i	$-0.291918\pi$
$263$	3.64436	+	2.10407i	0.224721	+	0.129743i	−0.383413	+	0.923577i	$0.625252\pi$
$264$	−1.55296	+	1.41809i	−0.0955779	+	0.0872775i
$265$	35.6429	+	20.5785i	2.18953	+	1.26413i
$266$		0			0
$267$	2.70977	−	2.47444i	0.165835	−	0.151433i
$268$	6.78107			0.414220
$269$	−10.8299	−	18.7579i	−0.660309	−	1.14369i	−0.980534	−	0.196348i	$-0.937092\pi$
$269$	−10.8299	−	18.7579i	−0.660309	−	1.14369i	0.320225	−	0.947341i	$-0.396241\pi$
$270$	−39.0477	−	16.4119i	−2.37637	−	0.998798i
$271$	−17.8987	−	10.3338i	−1.08727	−	0.627736i	−0.154423	−	0.988005i	$-0.549352\pi$
$271$	−17.8987	−	10.3338i	−1.08727	−	0.627736i	−0.932849	+	0.360268i	$0.882685\pi$
$272$	0.913549	+	1.58231i	0.0553921	+	0.0959419i
$273$		0			0
$274$	−12.1299	+	21.0096i	−0.732793	+	1.26923i
$275$	1.84958	−	1.06786i	0.111534	−	0.0643942i
$276$	41.9281	−	9.21920i	2.52378	−	0.554931i
$277$	13.9448	−	24.1532i	0.837864	−	1.45122i	−0.0538127	−	0.998551i	$-0.517137\pi$
$277$	13.9448	−	24.1532i	0.837864	−	1.45122i	0.891677	−	0.452672i	$-0.149529\pi$
$278$	−6.25437	+	10.8329i	−0.375112	+	0.649714i
$279$	−9.05293	+	12.8342i	−0.541985	+	0.768365i
$280$		0			0
$281$	16.7176	−	9.65190i	0.997287	−	0.575784i	0.0898425	−	0.995956i	$-0.471364\pi$
$281$	16.7176	−	9.65190i	0.997287	−	0.575784i	0.907444	+	0.420172i	$0.138030\pi$
$282$	2.50246	−	7.88918i	0.149019	−	0.469794i
$283$		−	17.6326i		−	1.04815i	−0.851672	−	0.524075i	$-0.824411\pi$
$283$		−	17.6326i		−	1.04815i	0.851672	−	0.524075i	$-0.175589\pi$
$284$			39.9221i			2.36894i
$285$	−2.26888	+	7.15282i	−0.134397	+	0.423696i
$286$	−3.79832	+	2.19296i	−0.224599	+	0.129672i
$287$		0			0
$288$	−5.51210	+	7.81444i	−0.324804	+	0.460470i
$289$	8.04549	−	13.9352i	0.473264	−	0.819718i
$290$	16.1669	−	28.0019i	0.949354	−	1.64433i
$291$	20.5206	−	4.51210i	1.20294	−	0.264504i
$292$	1.28736	−	0.743258i	0.0753371	−	0.0434959i
$293$	−14.1138	+	24.4458i	−0.824536	+	1.42814i	0.0777369	+	0.996974i	$0.475231\pi$
$293$	−14.1138	+	24.4458i	−0.824536	+	1.42814i	−0.902273	+	0.431165i	$0.858103\pi$
$294$		0			0
$295$	2.83242	+	4.90589i	0.164910	+	0.285632i
$296$	−18.0054	−	10.3954i	−1.04655	−	0.604223i
$297$	0.204543	+	1.61850i	0.0118688	+	0.0939147i
$298$	21.6651	+	37.5251i	1.25503	+	2.17377i
$299$	40.2015			2.32492
$300$	−31.5824	+	28.8396i	−1.82341	+	1.66505i
$301$		0			0
$302$	47.4880	+	27.4172i	2.73263	+	1.57768i
$303$	−16.0144	+	14.6236i	−0.920001	+	0.840104i
$304$	−2.09292	−	1.20835i	−0.120037	−	0.0693036i
$305$	8.84374	−	5.10593i	0.506391	−	0.292365i
$306$	6.75877	+	0.614878i	0.386373	+	0.0351502i
$307$		−	8.56651i		−	0.488917i	−0.969660	−	0.244458i	$-0.921390\pi$
$307$		−	8.56651i		−	0.488917i	0.969660	−	0.244458i	$-0.0786102\pi$
$308$		0			0
$309$	30.4799	−	6.70194i	1.73394	−	0.381260i
$310$	21.3377	+	36.9580i	1.21190	+	2.09907i
$311$	19.3583			1.09771			0.548854	−	0.835918i	$-0.315064\pi$
$311$	19.3583			1.09771			0.548854	+	0.835918i	$0.315064\pi$
$312$	29.1225	−	26.5933i	1.64874	−	1.50555i
$313$			26.5012i			1.49793i	0.662608	+	0.748967i	$0.269450\pi$
$313$			26.5012i			1.49793i	−0.662608	+	0.748967i	$0.730550\pi$
$314$	−15.4925			−0.874291
$315$		0			0
$316$	−37.9923			−2.13724
$317$		−	8.66555i		−	0.486706i	−0.969938	−	0.243353i	$-0.921753\pi$
$317$		−	8.66555i		−	0.486706i	0.969938	−	0.243353i	$-0.0782473\pi$
$318$	10.5731	+	48.0854i	0.592908	+	2.69649i
$319$	−1.24535			−0.0697260
$320$	19.5756	+	33.9059i	1.09431	+	1.89540i
$321$	−4.20246	−	4.60214i	−0.234559	−	0.256866i
$322$		0			0
$323$		−	1.20235i		−	0.0669008i
$324$	−10.9609	−	30.7754i	−0.608937	−	1.70975i
$325$	−34.6850	+	20.0254i	−1.92398	+	1.11081i
$326$	50.3944	+	29.0952i	2.79109	+	1.61144i
$327$	−2.44087	−	11.1008i	−0.134980	−	0.613878i
$328$	−0.468638	−	0.270568i	−0.0258762	−	0.0149396i
$329$		0			0
$330$	4.22524	+	1.34025i	0.232592	+	0.0737784i
$331$	19.3382			1.06293			0.531463	−	0.847081i	$-0.321642\pi$
$331$	19.3382			1.06293			0.531463	+	0.847081i	$0.321642\pi$
$332$	−14.5230	−	25.1546i	−0.797054	−	1.38054i
$333$	−14.6405	+	6.76545i	−0.802297	+	0.370744i
$334$	28.7626	+	16.6061i	1.57382	+	0.908646i
$335$	−3.20894	−	5.55805i	−0.175323	−	0.303669i
$336$		0			0
$337$	−12.4451	+	21.5556i	−0.677930	+	1.17421i	0.297673	+	0.954668i	$0.403790\pi$
$337$	−12.4451	+	21.5556i	−0.677930	+	1.17421i	−0.975603	+	0.219542i	$0.929544\pi$
$338$	44.5164	−	25.7015i	2.42137	−	1.39798i
$339$	2.53423	+	2.77525i	0.137641	+	0.150731i
$340$	5.94481	−	10.2967i	0.322403	−	0.558418i
$341$	0.821826	−	1.42345i	0.0445044	−	0.0770839i
$342$	−8.14875	+	3.76557i	−0.440634	+	0.203619i
$343$		0			0
$344$	−9.65090	+	5.57195i	−0.520341	+	0.300419i
$345$	−27.3977	−	30.0034i	−1.47504	−	1.61533i
$346$			25.8616i			1.39033i
$347$		−	5.79346i		−	0.311009i	−0.987835	−	0.155505i	$-0.950300\pi$
$347$		−	5.79346i		−	0.311009i	0.987835	−	0.155505i	$-0.0497003\pi$
$348$	24.3569	−	5.35561i	1.30566	−	0.287091i
$349$	13.3430	−	7.70360i	0.714236	−	0.412364i	−0.0983918	−	0.995148i	$-0.531370\pi$
$349$	13.3430	−	7.70360i	0.714236	−	0.412364i	0.812627	+	0.582784i	$0.198037\pi$
$350$		0			0
$351$	−3.83577	−	30.3515i	−0.204738	−	1.62004i
$352$	0.500390	−	0.866700i	0.0266709	−	0.0461953i
$353$	−8.87263	+	15.3679i	−0.472243	+	0.817948i	−0.999496	−	0.0317602i	$-0.989889\pi$
$353$	−8.87263	+	15.3679i	−0.472243	+	0.817948i	0.527253	+	0.849708i	$0.323222\pi$
$354$	−2.04893	+	6.45940i	−0.108899	+	0.343313i
$355$	32.7218	−	18.8920i	1.73669	−	1.00268i
$356$	3.84519	−	6.66007i	0.203795	−	0.352983i
$357$		0			0
$358$	−1.89754	−	3.28664i	−0.100288	−	0.173704i
$359$	−19.8490	−	11.4599i	−1.04759	−	0.604828i	−0.125618	−	0.992079i	$-0.540091\pi$
$359$	−19.8490	−	11.4599i	−1.04759	−	0.604828i	−0.921974	+	0.387251i	$0.873425\pi$
$360$	−39.6944	−	3.61120i	−2.09208	−	0.190327i
$361$	−8.70482	−	15.0772i	−0.458149	−	0.793537i
$362$	−41.5439			−2.18350
$363$	4.05489	+	18.4413i	0.212827	+	0.967917i
$364$		0			0
$365$	−1.21841	−	0.703450i	−0.0637745	−	0.0368203i
$366$	11.6442	+	3.69355i	0.608652	+	0.193065i
$367$	4.33253	+	2.50139i	0.226156	+	0.130571i	0.608797	−	0.793326i	$-0.291652\pi$
$367$	4.33253	+	2.50139i	0.226156	+	0.130571i	−0.382641	+	0.923897i	$0.624986\pi$
$368$	11.3321	−	6.54259i	0.590726	−	0.341056i
$369$	−0.381058	+	0.176088i	−0.0198371	+	0.00916678i
$370$			43.8229i			2.27824i
$371$		0			0
$372$	−9.95201	+	31.3745i	−0.515988	+	1.62669i
$373$	−4.76280	−	8.24941i	−0.246608	−	0.427138i	0.715974	−	0.698127i	$-0.245983\pi$
$373$	−4.76280	−	8.24941i	−0.246608	−	0.427138i	−0.962583	+	0.270988i	$0.912649\pi$
$374$	−0.710243			−0.0367258
$375$	10.2240	+	3.24305i	0.527963	+	0.167470i
$376$		−	7.78842i		−	0.401657i
$377$	23.3538			1.20278
$378$		0			0
$379$	−13.8369			−0.710756			−0.355378	−	0.934723i	$-0.615648\pi$
$379$	−13.8369			−0.710756			−0.355378	+	0.934723i	$0.615648\pi$
$380$			15.7264i			0.806746i
$381$	−3.87926	−	1.23051i	−0.198741	−	0.0630407i
$382$	−38.1127			−1.95002
$383$	−10.6160	−	18.3874i	−0.542452	−	0.939554i	−0.998763	−	0.0497336i	$-0.984163\pi$
$383$	−10.6160	−	18.3874i	−0.542452	−	0.939554i	0.456311	−	0.889821i	$-0.349171\pi$
$384$	−10.8220	+	34.1172i	−0.552259	+	1.74104i
$385$		0			0
$386$			25.8247i			1.31444i
$387$	−0.783212	+	8.60911i	−0.0398129	+	0.437626i
$388$	38.1336	−	22.0165i	1.93594	−	1.11772i
$389$	3.91419	+	2.25986i	0.198457	+	0.114579i	0.595936	−	0.803032i	$-0.296781\pi$
$389$	3.91419	+	2.25986i	0.198457	+	0.114579i	−0.397478	+	0.917612i	$0.630115\pi$
$390$	−79.2356	−	25.1336i	−4.01225	−	1.27269i
$391$	5.63793	+	3.25506i	0.285122	+	0.164616i
$392$		0			0
$393$	3.53060	+	16.0568i	0.178095	+	0.809961i
$394$	15.4413			0.777919
$395$	17.9788	+	31.1401i	0.904610	+	1.56683i
$396$	1.43416	+	3.10355i	0.0720694	+	0.155959i
$397$	−13.5830	−	7.84214i	−0.681710	−	0.393586i	0.118789	−	0.992920i	$-0.462099\pi$
$397$	−13.5830	−	7.84214i	−0.681710	−	0.393586i	−0.800499	+	0.599334i	$0.795432\pi$
$398$	−21.1262	−	36.5917i	−1.05896	−	1.83417i
$399$		0			0
$400$	−6.51806	+	11.2896i	−0.325903	+	0.564480i
$401$	−9.34292	+	5.39414i	−0.466563	+	0.269370i	−0.714800	−	0.699329i	$-0.753482\pi$
$401$	−9.34292	+	5.39414i	−0.466563	+	0.269370i	0.248237	+	0.968699i	$0.420149\pi$
$402$	2.32130	−	7.31808i	0.115776	−	0.364993i
$403$	−15.4116	+	26.6937i	−0.767708	+	1.32971i
$404$	−22.7246	+	39.3601i	−1.13059	+	1.95824i
$405$	−20.0379	+	23.5476i	−0.995693	+	1.17009i
$406$		0			0
$407$	1.46172	−	0.843925i	0.0724548	−	0.0418318i
$408$	6.23741	−	1.37149i	0.308798	−	0.0678987i
$409$		−	19.6138i		−	0.969839i	−0.874559	−	0.484920i	$-0.838849\pi$
$409$		−	19.6138i		−	0.969839i	0.874559	−	0.484920i	$-0.161151\pi$
$410$			1.14060i			0.0563304i
$411$	11.9415	+	13.0772i	0.589031	+	0.645051i
$412$	56.6409	−	32.7016i	2.79050	−	1.61109i
$413$		0			0
$414$	4.40358	−	48.4044i	0.216424	−	2.37895i
$415$	−13.7452	+	23.8074i	−0.674724	+	1.16866i
$416$	−9.38376	+	16.2532i	−0.460077	+	0.796876i
$417$	6.15725	+	6.74283i	0.301522	+	0.330198i
$418$	0.813576	−	0.469718i	0.0397933	−	0.0229747i
$419$	8.83829	−	15.3084i	0.431779	−	0.747862i	−0.565248	−	0.824921i	$-0.691220\pi$
$419$	8.83829	−	15.3084i	0.431779	−	0.747862i	0.997027	+	0.0770586i	$0.0245528\pi$
$420$		0			0
$421$	−16.9507	−	29.3594i	−0.826124	−	1.43089i	−0.901057	−	0.433701i	$-0.857208\pi$
$421$	−16.9507	−	29.3594i	−0.826124	−	1.43089i	0.0749327	−	0.997189i	$-0.476126\pi$
$422$	1.16059	+	0.670068i	0.0564967	+	0.0326184i
$423$	−4.93707	−	3.48248i	−0.240048	−	0.169324i
$424$	23.1652	+	40.1232i	1.12500	+	1.94856i
$425$	−6.48571			−0.314603
$426$	43.0836	+	13.6662i	2.08741	+	0.662128i
$427$		0			0
$428$	−11.3111	−	6.53048i	−0.546744	−	0.315663i
$429$	0.687553	+	3.12693i	0.0331954	+	0.150970i
$430$	20.3421	+	11.7445i	0.980983	+	0.566371i
$431$	−12.2317	+	7.06195i	−0.589178	+	0.340162i	−0.764772	−	0.644300i	$-0.777149\pi$
$431$	−12.2317	+	7.06195i	−0.589178	+	0.340162i	0.175594	+	0.984463i	$0.443815\pi$
$432$	−6.02079	−	7.93130i	−0.289675	−	0.381595i
$433$			9.10088i			0.437360i	0.975797	+	0.218680i	$0.0701752\pi$
$433$			9.10088i			0.437360i	−0.975797	+	0.218680i	$0.929825\pi$
$434$		0			0
$435$	−15.9159	−	17.4295i	−0.763107	−	0.835682i
$436$	−11.9100	−	20.6288i	−0.570387	−	0.987938i
$437$	−8.61093			−0.411917
$438$	−0.361427	−	1.64374i	−0.0172697	−	0.0785410i
$439$			11.7225i			0.559486i	0.960075	+	0.279743i	$0.0902492\pi$
$439$			11.7225i			0.559486i	−0.960075	+	0.279743i	$0.909751\pi$
$440$	4.17128			0.198858
$441$		0			0
$442$	13.3191			0.633526
$443$		−	7.13370i		−	0.338932i	−0.985536	−	0.169466i	$-0.945796\pi$
$443$		−	7.13370i		−	0.338932i	0.985536	−	0.169466i	$-0.0542043\pi$
$444$	−24.9595	+	22.7919i	−1.18452	+	1.08165i
$445$	−7.27850			−0.345034
$446$	−10.4285	−	18.0628i	−0.493805	−	0.855296i
$447$	30.8922	−	6.79262i	1.46115	−	0.321280i
$448$		0			0
$449$		−	3.17445i		−	0.149811i	−0.997191	−	0.0749057i	$-0.976134\pi$
$449$		−	3.17445i		−	0.149811i	0.997191	−	0.0749057i	$-0.0238656\pi$
$450$	20.3122	+	43.9558i	0.957524	+	2.07210i
$451$	0.0380450	−	0.0219653i	0.00179147	−	0.00103431i
$452$	6.82100	+	3.93811i	0.320833	+	0.185233i
$453$	29.5585	−	26.9915i	1.38878	−	1.26817i
$454$	−34.7406	−	20.0575i	−1.63045	−	0.941344i
$455$		0			0
$456$	−6.23786	+	5.69613i	−0.292114	+	0.266746i
$457$	24.1490			1.12964			0.564821	−	0.825213i	$-0.308945\pi$
$457$	24.1490			1.12964			0.564821	+	0.825213i	$0.308945\pi$
$458$	−23.2075	−	40.1966i	−1.08442	−	1.87826i
$459$	1.91958	−	4.56712i	0.0895985	−	0.213175i
$460$	−73.7422	−	42.5751i	−3.43825	−	1.98507i
$461$	−6.87281	−	11.9041i	−0.320099	−	0.554427i	0.660409	−	0.750906i	$-0.270383\pi$
$461$	−6.87281	−	11.9041i	−0.320099	−	0.554427i	−0.980508	+	0.196478i	$0.937049\pi$
$462$		0			0
$463$	10.3157	−	17.8673i	0.479411	−	0.830364i	−0.520310	−	0.853977i	$-0.674184\pi$
$463$	10.3157	−	17.8673i	0.479411	−	0.830364i	0.999721	+	0.0236135i	$0.00751711\pi$
$464$	6.58303	−	3.80071i	0.305610	−	0.176444i
$465$	30.4253	−	6.68995i	1.41094	−	0.310239i
$466$	23.4151	−	40.5562i	1.08469	−	1.87873i
$467$	−0.465894	+	0.806952i	−0.0215590	+	0.0373413i	−0.876604	−	0.481213i	$-0.840196\pi$
$467$	−0.465894	+	0.806952i	−0.0215590	+	0.0373413i	0.855045	+	0.518554i	$0.173530\pi$
$468$	−26.8947	−	58.2007i	−1.24321	−	2.69033i
$469$		0			0
$470$	−14.2170	+	8.20819i	−0.655781	+	0.378615i
$471$	−3.41938	+	10.7799i	−0.157557	+	0.496710i
$472$			6.37690i			0.293521i
$473$		−	0.904685i		−	0.0415975i
$474$	−13.0056	+	41.0010i	−0.597365	+	1.88324i
$475$	7.42932	−	4.28932i	0.340881	−	0.196808i
$476$		0			0
$477$	35.7920	+	3.25617i	1.63880	+	0.149090i
$478$	−23.2556	+	40.2800i	−1.06369	+	1.84236i
$479$	−16.2031	+	28.0647i	−0.740340	+	1.28231i	0.212000	+	0.977270i	$0.432002\pi$
$479$	−16.2031	+	28.0647i	−0.740340	+	1.28231i	−0.952340	+	0.305037i	$0.901331\pi$
$480$	18.5252	−	4.07335i	0.845557	−	0.185922i
$481$	−27.4115	+	15.8260i	−1.24986	+	0.721605i
$482$	−18.9274	+	32.7832i	−0.862120	+	1.49324i
$483$		0			0
$484$	19.7855	+	34.2695i	0.899342	+	1.55771i
$485$	−36.0912	−	20.8373i	−1.63882	−	0.946172i
$486$	−36.9647	+	1.29380i	−1.67675	+	0.0586880i
$487$	17.1867	+	29.7682i	0.778802	+	1.34892i	0.932633	+	0.360828i	$0.117506\pi$
$487$	17.1867	+	29.7682i	0.778802	+	1.34892i	−0.153830	+	0.988097i	$0.549161\pi$
$488$	11.4955			0.520376
$489$	31.3675	−	28.6434i	1.41849	−	1.29530i
$490$		0			0
$491$	−7.31048	−	4.22071i	−0.329917	−	0.190478i	0.325887	−	0.945409i	$-0.394337\pi$
$491$	−7.31048	−	4.22071i	−0.329917	−	0.190478i	−0.655804	+	0.754931i	$0.727670\pi$
$492$	−0.649635	+	0.593217i	−0.0292878	+	0.0267443i
$493$	3.27518	+	1.89093i	0.147507	+	0.0851631i
$494$	−15.2569	+	8.80859i	−0.686441	+	0.396317i
$495$	1.86513	−	2.64417i	0.0838313	−	0.118846i
$496$			10.0326i			0.450479i
$497$		0			0
$498$	−32.1182	+	7.06217i	−1.43925	+	0.316464i
$499$	5.70400	+	9.87961i	0.255346	+	0.442272i	0.964989	−	0.262289i	$-0.0844773\pi$
$499$	5.70400	+	9.87961i	0.255346	+	0.442272i	−0.709643	+	0.704561i	$0.751144\pi$
$500$	22.4787			1.00528
$501$	17.9030	−	16.3482i	0.799848	−	0.730385i
$502$			2.31595i			0.103366i
$503$	32.8028			1.46261			0.731303	−	0.682053i	$-0.238913\pi$
$503$	32.8028			1.46261			0.731303	+	0.682053i	$0.238913\pi$
$504$		0			0
$505$	43.0149			1.91414
$506$			5.08656i			0.226125i
$507$	−8.05814	−	36.6477i	−0.357875	−	1.62758i
$508$	−8.52905			−0.378415
$509$	9.75828	+	16.9018i	0.432528	+	0.749160i	0.997090	−	0.0762300i	$-0.0242883\pi$
$509$	9.75828	+	16.9018i	0.432528	+	0.749160i	−0.564562	+	0.825390i	$0.690955\pi$
$510$	−9.07710	−	9.94037i	−0.401941	−	0.440167i
$511$		0			0
$512$			20.9310i			0.925027i
$513$	0.821599	+	6.50111i	0.0362745	+	0.287031i
$514$	−25.1492	+	14.5199i	−1.10928	+	0.640446i
$515$	−53.6073	−	30.9502i	−2.36222	−	1.36383i
$516$	3.89060	+	17.6941i	0.171274	+	0.778940i
$517$	0.547571	+	0.316140i	0.0240821	+	0.0139038i
$518$		0			0
$519$	17.9949	+	5.70799i	0.789887	+	0.250553i
$520$	−78.2236			−3.43033
$521$	9.93108	+	17.2011i	0.435088	+	0.753595i	0.997303	−	0.0733964i	$-0.0233838\pi$
$521$	9.93108	+	17.2011i	0.435088	+	0.753595i	−0.562215	+	0.826991i	$0.690050\pi$
$522$	2.55813	−	28.1190i	0.111966	−	1.23074i
$523$	−6.71478	−	3.87678i	−0.293617	−	0.169520i	0.345955	−	0.938251i	$-0.387555\pi$
$523$	−6.71478	−	3.87678i	−0.293617	−	0.169520i	−0.639572	+	0.768731i	$0.720888\pi$
$524$	17.2273	+	29.8385i	0.752577	+	1.30350i
$525$		0			0
$526$	4.99242	−	8.64713i	0.217680	−	0.377033i
$527$	−4.32271	+	2.49572i	−0.188300	+	0.108715i
$528$	0.702700	+	0.769530i	0.0305811	+	0.0334895i
$529$	11.8118	−	20.4587i	0.513559	−	0.889509i
$530$	48.8274	−	84.5715i	2.12092	−	3.67355i
$531$	4.04231	+	2.85134i	0.175421	+	0.123738i
$532$		0			0
$533$	−0.713455	+	0.411913i	−0.0309032	+	0.0178419i
$534$	−5.87120	−	6.42958i	−0.254072	−	0.278235i
$535$			12.3614i			0.534432i
$536$		−	7.22461i		−	0.312056i
$537$	−2.70570	+	0.594932i	−0.116759	+	0.0256732i
$538$	−44.5076	+	25.6965i	−1.91886	+	1.10785i
$539$		0			0
$540$	−25.1075	+	59.7364i	−1.08046	+	2.57065i
$541$	9.04616	−	15.6684i	0.388925	−	0.673638i	−0.603380	−	0.797454i	$-0.706180\pi$
$541$	9.04616	−	15.6684i	0.388925	−	0.673638i	0.992305	+	0.123816i	$0.0395133\pi$
$542$	−24.5195	+	42.4691i	−1.05320	+	1.82420i
$543$	−9.16925	+	28.9068i	−0.393490	+	1.24051i
$544$	−2.63199	+	1.51958i	−0.112846	+	0.0651514i
$545$	−11.2721	+	19.5239i	−0.482845	+	0.836313i
$546$		0			0
$547$	3.46839	+	6.00743i	0.148298	+	0.256859i	0.930598	−	0.366042i	$-0.119287\pi$
$547$	3.46839	+	6.00743i	0.148298	+	0.256859i	−0.782301	+	0.622901i	$0.785954\pi$
$548$	32.1411	+	18.5567i	1.37300	+	0.792703i
$549$	5.14005	−	7.28697i	0.219372	−	0.311000i
$550$	−2.53375	−	4.38858i	−0.108039	−	0.187130i
$551$	−5.00225			−0.213103
$552$	−9.82221	−	44.6706i	−0.418061	−	1.90131i
$553$		0			0
$554$	−57.3092	−	33.0875i	−2.43483	−	1.40575i
$555$	30.4925	+	9.67226i	1.29434	+	0.410565i
$556$	16.5725	+	9.56815i	0.702831	+	0.405780i
$557$	13.6993	−	7.90931i	0.580459	−	0.335128i	−0.180857	−	0.983509i	$-0.557887\pi$
$557$	13.6993	−	7.90931i	0.580459	−	0.335128i	0.761316	+	0.648381i	$0.224554\pi$
$558$	30.4523	+	21.4803i	1.28915	+	0.909332i
$559$			16.9655i			0.717563i
$560$		0			0
$561$	−0.156759	+	0.494196i	−0.00661839	+	0.0208650i
$562$	−22.9014	−	39.6665i	−0.966039	−	1.67323i
$563$	−32.1123			−1.35337			−0.676686	−	0.736272i	$-0.736584\pi$
$563$	−32.1123			−1.35337			−0.676686	+	0.736272i	$0.736584\pi$
$564$	−12.0691	−	3.82834i	−0.508202	−	0.161202i
$565$		−	7.45438i		−	0.313608i
$566$	−41.8376			−1.75857
$567$		0			0
$568$	42.5333			1.78466
$569$			36.1545i			1.51567i	0.652444	+	0.757837i	$0.273744\pi$
$569$			36.1545i			1.51567i	−0.652444	+	0.757837i	$0.726256\pi$
$570$	16.9718	+	5.38347i	0.710870	+	0.225489i
$571$	28.3583			1.18676			0.593380	−	0.804923i	$-0.297793\pi$
$571$	28.3583			1.18676			0.593380	+	0.804923i	$0.297793\pi$
$572$	3.35486	+	5.81079i	0.140274	+	0.242961i
$573$	−8.41196	+	26.5193i	−0.351415	+	1.10786i
$574$		0			0
$575$			46.4489i			1.93705i
$576$	27.9375	+	19.7064i	1.16406	+	0.821099i
$577$	−36.3589	+	20.9918i	−1.51364	+	0.873901i	−0.513768	+	0.857929i	$0.671751\pi$
$577$	−36.3589	+	20.9918i	−1.51364	+	0.873901i	−0.999872	+	0.0159713i	$0.994916\pi$
$578$	−33.0646	−	19.0899i	−1.37531	−	0.794034i
$579$	17.9692	+	5.69984i	0.746773	+	0.236877i
$580$	−42.8383	−	24.7327i	−1.77876	−	1.02697i
$581$		0			0
$582$	−10.7060	−	48.6902i	−0.443780	−	2.01827i
$583$	−3.76119			−0.155773
$584$	−0.791873	−	1.37156i	−0.0327679	−	0.0567557i
$585$	−34.9766	+	49.5858i	−1.44610	+	2.05012i
$586$	58.0035	+	33.4884i	2.39610	+	1.38339i
$587$	−9.79227	−	16.9607i	−0.404170	−	0.700043i	0.590054	−	0.807364i	$-0.299106\pi$
$587$	−9.79227	−	16.9607i	−0.404170	−	0.700043i	−0.994225	+	0.107320i	$0.965773\pi$
$588$		0			0
$589$	3.30108	−	5.71764i	0.136019	−	0.235591i
$590$	11.6404	−	6.72059i	0.479228	−	0.276682i
$591$	3.40808	−	10.7442i	0.140190	−	0.441958i
$592$	−5.15121	+	8.92216i	−0.211713	+	0.366698i
$593$	9.96374	−	17.2577i	0.409162	−	0.708689i	−0.585634	−	0.810575i	$-0.699154\pi$
$593$	9.96374	−	17.2577i	0.409162	−	0.708689i	0.994796	+	0.101886i	$0.0324878\pi$
$594$	3.84027	−	0.485327i	0.157568	−	0.0199132i
$595$		0			0
$596$	57.4072	−	33.1441i	2.35149	−	1.35763i
$597$	−30.1238	+	6.62365i	−1.23288	+	0.271088i
$598$		−	95.3878i		−	3.90070i
$599$		−	0.0309043i		−	0.00126271i	−1.00000		0.000631357i	$-0.999799\pi$
$599$		−	0.0309043i		−	0.00126271i	1.00000		0.000631357i	$-0.000200967\pi$
$600$	30.7259	+	33.6481i	1.25438	+	1.37368i
$601$	−25.8633	+	14.9322i	−1.05499	+	0.609097i	−0.924041	−	0.382293i	$-0.875135\pi$
$601$	−25.8633	+	14.9322i	−1.05499	+	0.609097i	−0.130945	+	0.991390i	$0.541801\pi$
$602$		0			0
$603$	−4.57967	−	3.23038i	−0.186499	−	0.131551i
$604$	41.9438	−	72.6488i	1.70667	−	2.95604i
$605$	18.7258	−	32.4341i	0.761314	−	1.31863i
$606$	34.6980	+	37.9979i	1.40951	+	1.54356i
$607$	27.1898	−	15.6980i	1.10360	−	0.637163i	0.166435	−	0.986052i	$-0.446774\pi$
$607$	27.1898	−	15.6980i	1.10360	−	0.637163i	0.937164	+	0.348889i	$0.113441\pi$
$608$	2.00994	−	3.48133i	0.0815140	−	0.141186i
$609$		0			0
$610$	−12.1151	−	20.9839i	−0.490524	−	0.849613i
$611$	−10.2685	−	5.92855i	−0.415421	−	0.239843i
$612$	0.940660	−	10.3398i	0.0380239	−	0.417961i
$613$	2.23146	+	3.86500i	0.0901278	+	0.156106i	0.907565	−	0.419912i	$-0.137939\pi$
$613$	2.23146	+	3.86500i	0.0901278	+	0.156106i	−0.817437	+	0.576018i	$0.804606\pi$
$614$	−20.3261			−0.820295
$615$	0.793646	+	0.251745i	0.0320029	+	0.0101514i
$616$		0			0
$617$	26.9685	+	15.5703i	1.08571	+	0.626835i	0.932431	−	0.361348i	$-0.117683\pi$
$617$	26.9685	+	15.5703i	1.08571	+	0.626835i	0.153279	+	0.988183i	$0.451017\pi$
$618$	−15.9020	−	72.3208i	−0.639671	−	2.90917i
$619$	1.13493	+	0.655252i	0.0456167	+	0.0263368i	0.522635	−	0.852557i	$-0.324949\pi$
$619$	1.13493	+	0.655252i	0.0456167	+	0.0263368i	−0.477018	+	0.878893i	$0.658282\pi$
$620$	56.5395	−	32.6431i	2.27068	−	1.31098i
$621$	−32.7085	−	13.7475i	−1.31255	−	0.551669i
$622$		−	45.9322i		−	1.84171i
$623$		0			0
$624$	−13.1777	−	14.4309i	−0.527529	−	0.577699i
$625$	6.36901	+	11.0315i	0.254761	+	0.441258i
$626$	62.8803			2.51320
$627$	−0.147270	−	0.669769i	−0.00588138	−	0.0267480i
$628$			23.7009i			0.945769i
$629$	−5.12565			−0.204373
$630$		0			0
$631$	−28.8892			−1.15006			−0.575030	−	0.818132i	$-0.695010\pi$
$631$	−28.8892			−1.15006			−0.575030	+	0.818132i	$0.695010\pi$
$632$			40.4773i			1.61010i
$633$	0.722399	−	0.659662i	0.0287128	−	0.0262192i
$634$	−20.5611			−0.816585
$635$	4.03612	+	6.99077i	0.160169	+	0.277420i
$636$	73.5626	−	16.1750i	2.91695	−	0.641382i
$637$		0			0
$638$			2.95488i			0.116985i
$639$	19.0182	−	26.9618i	0.752347	−	1.06659i
$640$	61.4822	−	35.4968i	2.43030	−	1.40313i
$641$	−2.41325	−	1.39329i	−0.0953176	−	0.0550316i	0.451584	−	0.892229i	$-0.350859\pi$
$641$	−2.41325	−	1.39329i	−0.0953176	−	0.0550316i	−0.546901	+	0.837197i	$0.684193\pi$
$642$	−10.9197	+	9.97135i	−0.430965	+	0.393538i
$643$	0.324584	+	0.187399i	0.0128004	+	0.00739029i	0.506387	−	0.862307i	$-0.330981\pi$
$643$	0.324584	+	0.187399i	0.0128004	+	0.00739029i	−0.493586	+	0.869697i	$0.664314\pi$
$644$		0			0
$645$	12.6617	−	11.5621i	0.498555	−	0.455258i
$646$	−2.85287			−0.112245
$647$	25.1608	+	43.5798i	0.989172	+	1.71330i	0.621682	+	0.783270i	$0.286450\pi$
$647$	25.1608	+	43.5798i	0.989172	+	1.71330i	0.367490	+	0.930027i	$0.380217\pi$
$648$	−32.7884	+	11.6778i	−1.28805	+	0.458747i
$649$	−0.448333	−	0.258845i	−0.0175986	−	0.0101606i
$650$	47.5151	+	82.2986i	1.86370	+	3.22802i
$651$		0			0
$652$	44.5109	−	77.0951i	1.74318	−	3.01928i
$653$	25.0515	−	14.4635i	0.980342	−	0.566000i	0.0779684	−	0.996956i	$-0.475157\pi$
$653$	25.0515	−	14.4635i	0.980342	−	0.566000i	0.902373	+	0.430955i	$0.141823\pi$
$654$	−26.3394	+	5.79154i	−1.02995	+	0.226467i
$655$	16.3046	−	28.2404i	0.637074	−	1.10344i
$656$	−0.134073	+	0.232222i	−0.00523469	+	0.00906674i
$657$	−1.22351	−	0.111308i	−0.0477336	−	0.00434255i
$658$		0			0
$659$	−22.8449	+	13.1895i	−0.889910	+	0.513790i	−0.873913	−	0.486082i	$-0.838426\pi$
$659$	−22.8449	+	13.1895i	−0.889910	+	0.513790i	−0.0159971	+	0.999872i	$0.505092\pi$
$660$	2.05036	−	6.46392i	0.0798102	−	0.251608i
$661$			11.6086i			0.451521i	0.974183	+	0.225760i	$0.0724866\pi$
$661$			11.6086i			0.451521i	−0.974183	+	0.225760i	$0.927513\pi$
$662$		−	45.8846i		−	1.78336i
$663$	2.93970	−	9.26761i	0.114168	−	0.359924i
$664$	−26.7999	+	15.4729i	−1.04004	+	0.600466i
$665$		0			0
$666$	16.0527	+	34.7382i	0.622028	+	1.34608i
$667$	13.5423	−	23.4559i	0.524360	−	0.908218i
$668$	25.4046	−	44.0020i	0.982933	−	1.70249i
$669$	−14.8700	+	3.26963i	−0.574907	+	0.126411i
$670$	−13.1878	+	7.61399i	−0.509490	+	0.294154i
$671$	−0.466614	+	0.808199i	−0.0180134	+	0.0312002i
$672$		0			0
$673$	−13.7692	−	23.8490i	−0.530764	−	0.919310i	−0.999356	−	0.0358949i	$-0.988572\pi$
$673$	−13.7692	−	23.8490i	−0.530764	−	0.919310i	0.468592	−	0.883415i	$-0.344761\pi$
$674$	51.1459	+	29.5291i	1.97007	+	1.13742i
$675$	35.0682	−	4.43185i	1.34977	−	0.170582i
$676$	−39.3191	−	68.1026i	−1.51227	−	2.61933i
$677$	4.63127			0.177994			0.0889970	−	0.996032i	$-0.471634\pi$
$677$	4.63127			0.177994			0.0889970	+	0.996032i	$0.471634\pi$
$678$	6.58495	−	6.01307i	0.252893	−	0.230931i
$679$		0			0
$680$	−10.9702	−	6.33365i	−0.420688	−	0.242884i
$681$	−21.6239	+	19.7460i	−0.828630	+	0.756668i
$682$	−3.37747	−	1.94998i	−0.129330	−	0.0746686i
$683$	12.0197	−	6.93959i	0.459922	−	0.265536i	−0.252089	−	0.967704i	$-0.581118\pi$
$683$	12.0197	−	6.93959i	0.459922	−	0.265536i	0.712012	+	0.702168i	$0.247784\pi$
$684$	5.76069	+	12.4662i	0.220266	+	0.476658i
$685$		−	35.1257i		−	1.34208i
$686$		0			0
$687$	−33.0915	+	7.27619i	−1.26252	+	0.277604i
$688$	2.76104	+	4.78227i	0.105264	+	0.182322i
$689$	70.5333			2.68711
$690$	−71.1902	+	65.0077i	−2.71016	+	2.47480i
$691$			22.6515i			0.861704i	0.902423	+	0.430852i	$0.141787\pi$
$691$			22.6515i			0.861704i	−0.902423	+	0.430852i	$0.858213\pi$
$692$	39.5640			1.50400
$693$		0			0
$694$	−13.7464			−0.521805
$695$		−	18.1114i		−	0.687004i
$696$	−5.70591	−	25.9500i	−0.216282	−	0.983632i
$697$	−0.133408			−0.00505319
$698$	−18.2786	−	31.6595i	−0.691856	−	1.19833i
$699$	−23.0515	−	25.2438i	−0.871888	−	0.954809i
$700$		0			0
$701$			16.3485i			0.617474i	0.951147	+	0.308737i	$0.0999063\pi$
$701$			16.3485i			0.617474i	−0.951147	+	0.308737i	$0.900094\pi$
$702$	−72.0163	+	9.10129i	−2.71808	+	0.343506i
$703$	5.87138	−	3.38984i	0.221443	−	0.127850i
$704$	−3.09855	−	1.78895i	−0.116781	−	0.0674236i
$705$	2.57349	+	11.7040i	0.0969233	+	0.440799i
$706$	36.4639	+	21.0525i	1.37234	+	0.792320i
$707$		0			0
$708$	9.88180	+	3.13452i	0.371381	+	0.117802i
$709$	15.3071			0.574871			0.287435	−	0.957800i	$-0.407197\pi$
$709$	15.3071			0.574871			0.287435	+	0.957800i	$0.407197\pi$
$710$	−44.8257	−	77.6404i	−1.68228	−	2.91379i
$711$	25.6585	+	18.0989i	0.962270	+	0.678761i
$712$	−7.09569	−	4.09670i	−0.265922	−	0.153530i
$713$	17.8736	+	30.9580i	0.669372	+	1.15939i
$714$		0			0
$715$	3.17518	−	5.49957i	0.118745	−	0.205672i
$716$	−5.02801	+	2.90292i	−0.187906	+	0.108487i
$717$	22.8945	+	25.0719i	0.855011	+	0.936326i
$718$	−27.1913	+	47.0966i	−1.01477	+	1.75763i
$719$	−7.46359	+	12.9273i	−0.278345	+	0.482108i	−0.970974	−	0.239187i	$-0.923119\pi$
$719$	−7.46359	+	12.9273i	−0.278345	+	0.482108i	0.692629	+	0.721294i	$0.256453\pi$
$720$	−1.78944	+	19.6696i	−0.0666885	+	0.733043i
$721$		0			0
$722$	−35.7743	+	20.6543i	−1.33138	+	0.768673i
$723$	18.6335	+	20.4056i	0.692986	+	0.758893i
$724$			63.5552i			2.36201i
$725$			26.9830i			1.00213i
$726$	43.7564	−	9.62121i	1.62395	−	0.357076i
$727$	4.62968	−	2.67295i	0.171705	−	0.0991341i	−0.411684	−	0.911326i	$-0.635059\pi$
$727$	4.62968	−	2.67295i	0.171705	−	0.0991341i	0.583390	+	0.812192i	$0.301726\pi$
$728$		0			0
$729$	−7.25834	+	26.0061i	−0.268827	+	0.963188i
$730$	−1.66910	+	2.89097i	−0.0617763	+	0.107000i
$731$	−1.37367	+	2.37927i	−0.0508070	+	0.0880004i
$732$	5.65052	−	17.8137i	0.208849	−	0.658413i
$733$	16.4099	−	9.47428i	0.606115	−	0.349941i	−0.165328	−	0.986239i	$-0.552868\pi$
$733$	16.4099	−	9.47428i	0.606115	−	0.349941i	0.771443	+	0.636298i	$0.219535\pi$
$734$	5.93514	−	10.2800i	0.219070	−	0.379440i
$735$		0			0
$736$	10.8828	+	18.8496i	0.401145	+	0.694804i
$737$	0.507932	+	0.293255i	0.0187099	+	0.0108022i
$738$	0.417811	+	0.904151i	0.0153799	+	0.0332822i
$739$	−22.8430	−	39.5653i	−0.840295	−	1.45543i	−0.889646	−	0.456651i	$-0.849049\pi$
$739$	−22.8430	−	39.5653i	−0.840295	−	1.45543i	0.0493510	−	0.998781i	$-0.484285\pi$
$740$	67.0417			2.46450
$741$	2.76173	+	12.5601i	0.101455	+	0.461408i
$742$		0			0
$743$	−25.0448	−	14.4596i	−0.918804	−	0.530472i	−0.0355508	−	0.999368i	$-0.511319\pi$
$743$	−25.0448	−	14.4596i	−0.918804	−	0.530472i	−0.883253	+	0.468896i	$0.844652\pi$
$744$	33.4266	+	10.6030i	1.22548	+	0.388723i
$745$	−54.3326	−	31.3689i	−1.99059	−	1.14927i
$746$	−19.5737	+	11.3009i	−0.716644	+	0.413755i
$747$	−2.17493	+	23.9069i	−0.0795765	+	0.874709i
$748$			1.08655i			0.0397283i
$749$		0			0
$750$	7.69491	−	24.2588i	0.280979	−	0.885806i
$751$	−22.1007	−	38.2795i	−0.806465	−	1.39684i	−0.915297	−	0.402779i	$-0.868044\pi$
$751$	−22.1007	−	38.2795i	−0.806465	−	1.39684i	0.108832	−	0.994060i	$-0.465289\pi$
$752$	−3.85936			−0.140736
$753$	1.61147	+	0.511159i	0.0587251	+	0.0186277i
$754$		−	55.4126i		−	2.01801i
$755$	−79.3947			−2.88947
$756$		0			0
$757$	−27.5029			−0.999611			−0.499805	−	0.866138i	$-0.666595\pi$
$757$	−27.5029			−0.999611			−0.499805	+	0.866138i	$0.666595\pi$
$758$			32.8315i			1.19249i
$759$	3.53929	+	1.12267i	0.128468	+	0.0407503i
$760$	16.7550			0.607768
$761$	−2.54651	−	4.41069i	−0.0923109	−	0.159887i	0.816172	−	0.577809i	$-0.196092\pi$
$761$	−2.54651	−	4.41069i	−0.0923109	−	0.159887i	−0.908483	+	0.417921i	$0.862759\pi$
$762$	−2.91967	+	9.20448i	−0.105769	+	0.333443i
$763$		0			0
$764$			58.3061i			2.10944i
$765$	−8.92006	+	4.12200i	−0.322506	+	0.149031i
$766$	−43.6286	+	25.1890i	−1.57637	+	0.910115i
$767$	8.40755	+	4.85410i	0.303579	+	0.175271i
$768$	43.3217	+	13.7417i	1.56324	+	0.495860i
$769$	−33.4505	−	19.3126i	−1.20626	−	0.696432i	−0.244316	−	0.969696i	$-0.578564\pi$
$769$	−33.4505	−	19.3126i	−1.20626	−	0.696432i	−0.961939	+	0.273264i	$0.911897\pi$
$770$		0			0
$771$	4.55239	+	20.7039i	0.163950	+	0.745632i
$772$	39.5075			1.42191
$773$	−17.1754	−	29.7486i	−0.617754	−	1.06998i	−0.989895	−	0.141806i	$-0.954709\pi$
$773$	−17.1754	−	29.7486i	−0.617754	−	1.06998i	0.372140	−	0.928177i	$-0.378624\pi$
$774$	20.4272	+	1.85836i	0.734240	+	0.0667973i
$775$	−30.8420	−	17.8066i	−1.10788	−	0.639632i
$776$	−23.4565	−	40.6279i	−0.842040	−	1.45846i
$777$		0			0
$778$	5.36206	−	9.28736i	0.192239	−	0.332968i
$779$	0.152818	−	0.0882293i	0.00547526	−	0.00316114i
$780$	−38.4502	+	121.217i	−1.37674	+	4.34027i
$781$	−1.72647	+	2.99034i	−0.0617781	+	0.107003i
$782$	7.72341	−	13.3773i	0.276189	−	0.478373i
$783$	−19.0010	−	7.98620i	−0.679040	−	0.285404i
$784$		0			0
$785$	19.4263	−	11.2158i	0.693353	−	0.400308i
$786$	38.0987	−	8.37719i	1.35894	−	0.298804i
$787$		−	23.4800i		−	0.836972i	−0.908223	−	0.418486i	$-0.862561\pi$
$787$		−	23.4800i		−	0.836972i	0.908223	−	0.418486i	$-0.137439\pi$
$788$		−	23.6225i		−	0.841518i
$789$	−4.91489	−	5.38232i	−0.174975	−	0.191616i
$790$	73.8874	−	42.6589i	2.62880	−	1.51774i
$791$		0			0
$792$	3.30655	−	1.52797i	0.117493	−	0.0542940i
$793$	8.75037	−	15.1561i	0.310735	−	0.538209i
$794$	−18.6074	+	32.2289i	−0.660350	+	1.14376i
$795$	−48.0691	−	52.6407i	−1.70483	−	1.86697i
$796$	−55.9791	+	32.3196i	−1.98413	+	1.14554i
$797$	5.82399	−	10.0875i	0.206296	−	0.357316i	−0.744249	−	0.667903i	$-0.767192\pi$
$797$	5.82399	−	10.0875i	0.206296	−	0.357316i	0.950545	+	0.310587i	$0.100526\pi$
$798$		0			0
$799$	−0.960052	−	1.66286i	−0.0339642	−	0.0588277i
$800$	−18.7789	−	10.8420i	−0.663934	−	0.383323i
$801$	−5.76963	+	2.66617i	−0.203860	+	0.0942045i
$802$	12.7989	+	22.1683i	0.451945	+	0.782791i
$803$	0.128572			0.00453720
$804$	−11.1954	−	3.55120i	−0.394833	−	0.125241i
$805$		0			0
$806$	63.3373	+	36.5678i	2.23096	+	1.28805i
$807$	8.05655	+	36.6405i	0.283604	+	1.28981i
$808$	41.9346	+	24.2109i	1.47525	+	0.851738i
$809$	−13.7723	+	7.95147i	−0.484210	+	0.279559i	−0.722169	−	0.691716i	$-0.756855\pi$
$809$	−13.7723	+	7.95147i	−0.484210	+	0.279559i	0.237959	+	0.971275i	$0.423521\pi$
$810$	55.8722	+	47.5448i	1.96315	+	1.67056i
$811$			3.56109i			0.125047i	0.998044	+	0.0625233i	$0.0199148\pi$
$811$			3.56109i			0.125047i	−0.998044	+	0.0625233i	$0.980085\pi$
$812$		0			0
$813$	24.1388	+	26.4345i	0.846583	+	0.927097i
$814$	−2.00241	−	3.46828i	−0.0701846	−	0.121563i
$815$	−84.2539			−2.95128
$816$	−0.679607	−	3.09079i	−0.0237910	−	0.108199i
$817$		−	3.63390i		−	0.127134i
$818$	−46.5384			−1.62718
$819$		0			0
$820$	1.74493			0.0609357
$821$		−	0.130990i		−	0.00457157i	−0.999997	−	0.00228579i	$-0.999272\pi$
$821$		−	0.130990i		−	0.00457157i	0.999997	−	0.00228579i	$-0.000727589\pi$
$822$	31.0288	−	28.3341i	1.08225	−	0.988266i
$823$	46.0287			1.60446			0.802231	−	0.597014i	$-0.203646\pi$
$823$	46.0287			1.60446			0.802231	+	0.597014i	$0.203646\pi$
$824$	−34.8406	−	60.3456i	−1.21373	−	2.10224i
$825$	−3.61286	+	0.794399i	−0.125784	+	0.0276574i
$826$		0			0
$827$		−	40.5836i		−	1.41123i	−0.708595	−	0.705615i	$-0.750671\pi$
$827$		−	40.5836i		−	1.41123i	0.708595	−	0.705615i	$-0.249329\pi$
$828$	−74.0507	−	6.73675i	−2.57344	−	0.234118i
$829$	26.0930	−	15.0648i	0.906248	−	0.523223i	0.0270260	−	0.999635i	$-0.491396\pi$
$829$	26.0930	−	15.0648i	0.906248	−	0.523223i	0.879222	+	0.476412i	$0.158063\pi$
$830$	56.4887	+	32.6137i	1.96075	+	1.13204i
$831$	−35.6716	+	32.5737i	−1.23743	+	1.12997i
$832$	58.1068	+	33.5480i	2.01449	+	1.16307i
$833$		0			0
$834$	15.9990	−	14.6095i	0.553999	−	0.505887i
$835$	−48.0879			−1.66415
$836$	−0.718591	−	1.24464i	−0.0248530	−	0.0430466i
$837$	21.6674	−	16.4481i	0.748936	−	0.568530i
$838$	−36.3228	−	20.9710i	−1.25475	−	0.724430i
$839$	−5.81551	−	10.0728i	−0.200774	−	0.347750i	0.748004	−	0.663694i	$-0.231012\pi$
$839$	−5.81551	−	10.0728i	−0.200774	−	0.347750i	−0.948778	+	0.315944i	$0.897679\pi$
$840$		0			0
$841$	−6.63302	+	11.4887i	−0.228725	+	0.396163i
$842$	−69.6622	+	40.2195i	−2.40072	+	1.38606i
$843$	−32.6551	+	7.18023i	−1.12470	+	0.247300i
$844$	1.02509	−	1.77551i	0.0352851	−	0.0611156i
$845$	−37.2132	+	64.4552i	−1.28017	+	2.21732i
$846$	−8.26302	+	11.7144i	−0.284089	+	0.402749i
$847$		0			0
$848$	19.8821	−	11.4789i	0.682754	−	0.394188i
$849$	−9.23409	+	29.1111i	−0.316913	+	0.999092i
$850$			15.3889i			0.527835i
$851$			36.7085i			1.25835i
$852$	20.9069	−	65.9107i	0.716260	−	2.25806i
$853$	−20.6854	+	11.9427i	−0.708254	+	0.408911i	−0.810414	−	0.585857i	$-0.800758\pi$
$853$	−20.6854	+	11.9427i	−0.708254	+	0.408911i	0.102160	+	0.994768i	$0.467425\pi$
$854$		0			0
$855$	7.49177	−	10.6210i	0.256213	−	0.363230i
$856$	−6.95763	+	12.0510i	−0.237807	+	0.411894i
$857$	17.3362	−	30.0271i	0.592193	−	1.02571i	−0.401744	−	0.915752i	$-0.631596\pi$
$857$	17.3362	−	30.0271i	0.592193	−	1.02571i	0.993936	−	0.109956i	$-0.0350709\pi$
$858$	7.41939	−	1.63138i	0.253294	−	0.0556945i
$859$	−26.3932	+	15.2381i	−0.900525	+	0.519918i	−0.877371	−	0.479813i	$-0.840704\pi$
$859$	−26.3932	+	15.2381i	−0.900525	+	0.519918i	−0.0231546	+	0.999732i	$0.507371\pi$
$860$	17.9671	−	31.1200i	0.612674	−	1.06118i
$861$		0			0
$862$	16.7562	+	29.0225i	0.570717	+	0.988512i
$863$	28.9298	+	16.7026i	0.984781	+	0.568564i	0.903710	−	0.428145i	$-0.140833\pi$
$863$	28.9298	+	16.7026i	0.984781	+	0.568564i	0.0810708	+	0.996708i	$0.474166\pi$
$864$	13.1928	−	10.0148i	0.448827	−	0.340712i
$865$	−18.7225	−	32.4283i	−0.636584	−	1.10260i
$866$	21.5940			0.733795
$867$	−20.5807	+	18.7934i	−0.698959	+	0.638258i
$868$		0			0
$869$	−2.84579	−	1.64302i	−0.0965369	−	0.0557356i
$870$	−41.3557	+	37.7642i	−1.40209	+	1.28033i
$871$	−9.52520	−	5.49938i	−0.322749	−	0.186339i
$872$	−21.9780	+	12.6890i	−0.744271	+	0.429705i
$873$	−36.2422	−	3.29713i	−1.22661	−	0.111591i
$874$			20.4315i			0.691106i
$875$		0			0
$876$	−2.51465	+	0.552924i	−0.0849621	+	0.0186816i
$877$	27.7600	+	48.0817i	0.937389	+	1.62360i	0.770318	+	0.637660i	$0.220097\pi$
$877$	27.7600	+	48.0817i	0.937389	+	1.62360i	0.167070	+	0.985945i	$0.446569\pi$
$878$	27.8145			0.938694
$879$	36.1037	−	32.9683i	1.21775	−	1.11199i
$880$		−	2.06697i		−	0.0696777i
$881$	19.9850			0.673313			0.336656	−	0.941628i	$-0.390704\pi$
$881$	19.9850			0.673313			0.336656	+	0.941628i	$0.390704\pi$
$882$		0			0
$883$	35.5837			1.19749			0.598743	−	0.800941i	$-0.295667\pi$
$883$	35.5837			1.19749			0.598743	+	0.800941i	$0.295667\pi$
$884$		−	20.3760i		−	0.685320i
$885$	−2.10709	−	9.58286i	−0.0708290	−	0.322124i
$886$	−16.9264			−0.568654
$887$	−17.8317	−	30.8853i	−0.598729	−	1.03703i	−0.993009	−	0.118038i	$-0.962339\pi$
$887$	−17.8317	−	30.8853i	−0.598729	−	1.03703i	0.394280	−	0.918990i	$-0.370994\pi$
$888$	24.2827	+	26.5920i	0.814872	+	0.892370i
$889$		0			0
$890$			17.2700i			0.578892i
$891$	0.509900	−	2.77923i	0.0170823	−	0.0931077i
$892$	−27.6330	+	15.9539i	−0.925221	+	0.534177i
$893$	2.19946	+	1.26986i	0.0736021	+	0.0424942i
$894$	−16.1171	−	73.2993i	−0.539037	−	2.45149i
$895$	4.75872	+	2.74745i	0.159066	+	0.0918370i
$896$		0			0
$897$	−66.3721	−	21.0533i	−2.21610	−	0.702949i
$898$	−7.53214			−0.251351
$899$	10.3831	+	17.9841i	0.346297	+	0.599804i
$900$	67.2451	−	31.0742i	2.24150	−	1.03581i
$901$	9.89171	+	5.71098i	0.329541	+	0.190260i
$902$	−0.0521180	−	0.0902710i	−0.00173534	−	0.00300569i
$903$		0			0
$904$	4.19569	−	7.26715i	0.139547	−	0.241702i
$905$	52.0925	−	30.0756i	1.73161	−	0.999748i
$906$	−64.0437	−	70.1346i	−2.12771	−	2.33007i
$907$	−18.6215	+	32.2533i	−0.618315	+	1.07095i	0.371478	+	0.928442i	$0.378851\pi$
$907$	−18.6215	+	32.2533i	−0.618315	+	1.07095i	−0.989793	+	0.142512i	$0.954482\pi$
$908$	−30.6846	+	53.1472i	−1.01830	+	1.76375i
$909$	34.0977	−	15.7567i	1.13095	−	0.522616i
$910$		0			0
$911$	−18.8068	+	10.8581i	−0.623098	+	0.359746i	−0.778074	−	0.628172i	$-0.783803\pi$
$911$	−18.8068	+	10.8581i	−0.623098	+	0.359746i	0.154976	+	0.987918i	$0.450470\pi$
$912$	2.82258	+	3.09102i	0.0934649	+	0.102354i
$913$		−	2.51225i		−	0.0831434i
$914$		−	57.2993i		−	1.89529i
$915$	−17.2748	+	3.79840i	−0.571087	+	0.125571i
$916$	−61.4940	+	35.5036i	−2.03182	+	1.17307i
$917$		0			0
$918$	−10.8366	−	4.55468i	−0.357661	−	0.150327i
$919$	−17.1023	+	29.6220i	−0.564153	+	0.977141i	0.432975	+	0.901406i	$0.357464\pi$
$919$	−17.1023	+	29.6220i	−0.564153	+	0.977141i	−0.997128	+	0.0757353i	$0.975870\pi$
$920$	−45.3598	+	78.5656i	−1.49547	+	2.59023i
$921$	−4.48623	+	14.1432i	−0.147826	+	0.466033i
$922$	−28.2452	+	16.3074i	−0.930208	+	0.537056i
$923$	32.3764	−	56.0776i	1.06568	−	1.84582i
$924$		0			0
$925$	−18.2854	−	31.6713i	−0.601221	−	1.04135i
$926$	−42.3945	−	24.4764i	−1.39317	−	0.804346i
$927$	−53.8315	−	4.89731i	−1.76806	−	0.160849i
$928$	6.32203	+	10.9501i	0.207531	+	0.359454i
$929$	46.9514			1.54043			0.770213	−	0.637786i	$-0.220150\pi$
$929$	46.9514			1.54043			0.770213	+	0.637786i	$0.220150\pi$
$930$	−15.8735	−	72.1914i	−0.520513	−	2.36725i
$931$		0			0
$932$	−62.0442	−	35.8213i	−2.03233	−	1.17336i
$933$	−31.9602	−	10.1378i	−1.04633	−	0.331897i
$934$	1.91469	+	1.10545i	0.0626505	+	0.0361713i
$935$	0.890585	−	0.514179i	0.0291252	−	0.0168155i
$936$	−62.0075	+	28.6539i	−2.02678	+	0.936581i
$937$		−	28.8826i		−	0.943555i	−0.881718	−	0.471777i	$-0.843613\pi$
$937$		−	28.8826i		−	0.943555i	0.881718	−	0.471777i	$-0.156387\pi$
$938$		0			0
$939$	13.8785	−	43.7530i	0.452907	−	1.42782i
$940$	12.5572	+	21.7496i	0.409569	+	0.709395i
$941$	1.45409			0.0474019			0.0237009	−	0.999719i	$-0.492455\pi$
$941$	1.45409			0.0474019			0.0237009	+	0.999719i	$0.492455\pi$
$942$	25.5778	+	8.11331i	0.833370	+	0.264346i
$943$			0.955432i			0.0311131i
$944$	3.15992			0.102847
$945$		0			0
$946$	−2.14658			−0.0697914
$947$		−	42.6772i		−	1.38682i	−0.720542	−	0.693412i	$-0.756107\pi$
$947$		−	42.6772i		−	1.38682i	0.720542	−	0.693412i	$-0.243893\pi$
$948$	62.7247	+	19.8963i	2.03720	+	0.646203i
$949$	−2.41110			−0.0782675
$950$	−10.1774	−	17.6279i	−0.330200	−	0.571923i
$951$	−4.53809	+	14.3067i	−0.147158	+	0.463926i
$952$		0			0
$953$		−	10.8171i		−	0.350401i	−0.984533	−	0.175200i	$-0.943943\pi$
$953$		−	10.8171i		−	0.350401i	0.984533	−	0.175200i	$-0.0560574\pi$
$954$	7.72606	−	84.9252i	0.250140	−	2.74956i
$955$	47.7902	−	27.5917i	1.54645	−	0.892845i
$956$	61.6216	+	35.5773i	1.99299	+	1.15065i
$957$	2.05604	+	0.652179i	0.0664625	+	0.0210820i
$958$	66.5902	+	38.4458i	2.15143	+	1.24213i
$959$		0			0
$960$	−14.5627	−	66.2298i	−0.470008	−	2.13756i
$961$	3.59192			0.115868
$962$	37.5511	+	65.0404i	1.21070	+	2.09699i
$963$	4.52809	+	9.79885i	0.145916	+	0.315764i
$964$	50.1529	+	28.9558i	1.61532	+	0.932603i
$965$	−18.6958	−	32.3820i	−0.601838	−	1.04241i
$966$		0			0
$967$	−22.4942	+	38.9611i	−0.723365	+	1.25290i	0.236279	+	0.971685i	$0.424072\pi$
$967$	−22.4942	+	38.9611i	−0.723365	+	1.25290i	−0.959643	+	0.281219i	$0.909261\pi$
$968$	36.5111	−	21.0797i	1.17351	−	0.677526i
$969$	−0.629665	+	1.98507i	−0.0202278	+	0.0637695i
$970$	−49.4415	+	85.6351i	−1.58747	+	2.74958i
$971$	3.40171	−	5.89194i	0.109166	−	0.189081i	−0.806267	−	0.591552i	$-0.798515\pi$
$971$	3.40171	−	5.89194i	0.109166	−	0.189081i	0.915433	+	0.402471i	$0.131849\pi$
$972$	1.97930	+	56.5499i	0.0634860	+	1.81384i
$973$		0			0
$974$	70.6321	−	40.7795i	2.26320	−	1.30666i
$975$	67.7516	−	14.8973i	2.16979	−	0.477095i
$976$		−	5.69631i		−	0.182334i
$977$			33.7917i			1.08109i	0.841314	+	0.540546i	$0.181782\pi$
$977$			33.7917i			1.08109i	−0.841314	+	0.540546i	$0.818218\pi$
$978$	−67.9634	−	74.4270i	−2.17323	−	2.37991i
$979$	0.576044	−	0.332579i	0.0184104	−	0.0106293i
$980$		0			0
$981$	−1.78361	+	19.6056i	−0.0569464	+	0.625958i
$982$	−10.0146	+	17.3459i	−0.319580	+	0.553529i
$983$	−23.4913	+	40.6881i	−0.749256	+	1.29775i	0.198923	+	0.980015i	$0.436256\pi$
$983$	−23.4913	+	40.6881i	−0.749256	+	1.29775i	−0.948180	+	0.317735i	$0.897078\pi$
$984$	0.632018	+	0.692126i	0.0201480	+	0.0220642i
$985$	−19.3620	+	11.1787i	−0.616926	+	0.356182i
$986$	4.48668	−	7.77116i	0.142885	−	0.247484i
$987$		0			0
$988$	13.4757	+	23.3405i	0.428718	+	0.742562i
$989$	17.0397	+	9.83785i	0.541829	+	0.312825i
$990$	−6.27392	−	4.42546i	−0.199398	−	0.140650i
$991$	−0.300449	−	0.520392i	−0.00954406	−	0.0165308i	0.861214	−	0.508243i	$-0.169705\pi$
$991$	−0.300449	−	0.520392i	−0.00954406	−	0.0165308i	−0.870758	+	0.491712i	$0.836371\pi$
$992$	−16.6881			−0.529848
$993$	−31.9271	−	10.1273i	−1.01318	−	0.321381i
$994$		0			0
$995$	52.9810	+	30.5886i	1.67961	+	0.969723i
$996$	10.8039	+	49.1354i	0.342336	+	1.55692i
$997$	41.9387	+	24.2133i	1.32821	+	0.766844i	0.985023	−	0.172423i	$-0.0551594\pi$
$997$	41.9387	+	24.2133i	1.32821	+	0.766844i	0.343189	+	0.939266i	$0.388493\pi$
$998$	23.4418	−	13.5341i	0.742036	−	0.428415i
$999$	27.7143	−	3.50248i	0.876842	−	0.110814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.i.d.68.3		48
3.2	odd	2		1323.2.i.d.1097.4		48
7.2	even	3		441.2.o.e.293.4	yes	48
7.3	odd	6		441.2.s.d.374.21		48
7.4	even	3		441.2.s.d.374.22		48
7.5	odd	6		441.2.o.e.293.3	yes	48
7.6	odd	2	inner	441.2.i.d.68.4		48
9.2	odd	6		441.2.s.d.362.21		48
9.7	even	3		1323.2.s.d.656.3		48
21.2	odd	6		1323.2.o.e.881.22		48
21.5	even	6		1323.2.o.e.881.21		48
21.11	odd	6		1323.2.s.d.962.4		48
21.17	even	6		1323.2.s.d.962.3		48
21.20	even	2		1323.2.i.d.1097.24		48
63.2	odd	6		441.2.o.e.146.3	✓	48
63.11	odd	6	inner	441.2.i.d.227.22		48
63.16	even	3		1323.2.o.e.440.21		48
63.20	even	6		441.2.s.d.362.22		48
63.25	even	3		1323.2.i.d.521.24		48
63.34	odd	6		1323.2.s.d.656.4		48
63.38	even	6	inner	441.2.i.d.227.21		48
63.47	even	6		441.2.o.e.146.4	yes	48
63.52	odd	6		1323.2.i.d.521.4		48
63.61	odd	6		1323.2.o.e.440.22		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.3		48	1.1	even	1	trivial
441.2.i.d.68.4		48	7.6	odd	2	inner
441.2.i.d.227.21		48	63.38	even	6	inner
441.2.i.d.227.22		48	63.11	odd	6	inner
441.2.o.e.146.3	✓	48	63.2	odd	6
441.2.o.e.146.4	yes	48	63.47	even	6
441.2.o.e.293.3	yes	48	7.5	odd	6
441.2.o.e.293.4	yes	48	7.2	even	3
441.2.s.d.362.21		48	9.2	odd	6
441.2.s.d.362.22		48	63.20	even	6
441.2.s.d.374.21		48	7.3	odd	6
441.2.s.d.374.22		48	7.4	even	3
1323.2.i.d.521.4		48	63.52	odd	6
1323.2.i.d.521.24		48	63.25	even	3
1323.2.i.d.1097.4		48	3.2	odd	2
1323.2.i.d.1097.24		48	21.20	even	2
1323.2.o.e.440.21		48	63.16	even	3
1323.2.o.e.440.22		48	63.61	odd	6
1323.2.o.e.881.21		48	21.5	even	6
1323.2.o.e.881.22		48	21.2	odd	6
1323.2.s.d.656.3		48	9.7	even	3
1323.2.s.d.656.4		48	63.34	odd	6
1323.2.s.d.962.3		48	21.17	even	6
1323.2.s.d.962.4		48	21.11	odd	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.37274i q^{2} +(-1.65098 - 0.523694i) q^{3} -3.62990 q^{4} +(1.71774 + 2.97522i) q^{5} +(-1.24259 + 3.91735i) q^{6} +3.86732i q^{8} +(2.45149 + 1.72922i) q^{9} +O(q^{10})\)	\(q-2.37274i q^{2} +(-1.65098 - 0.523694i) q^{3} -3.62990 q^{4} +(1.71774 + 2.97522i) q^{5} +(-1.24259 + 3.91735i) q^{6} +3.86732i q^{8} +(2.45149 + 1.72922i) q^{9} +(7.05942 - 4.07576i) q^{10} +(-0.271895 - 0.156979i) q^{11} +(5.99290 + 1.90095i) q^{12} +(5.09882 + 2.94381i) q^{13} +(-1.27786 - 5.81160i) q^{15} +1.91636 q^{16} +(0.476712 + 0.825689i) q^{17} +(4.10299 - 5.81675i) q^{18} +(-1.09214 - 0.630546i) q^{19} +(-6.23523 - 10.7997i) q^{20} +(-0.372470 + 0.645137i) q^{22} +(5.91336 - 3.41408i) q^{23} +(2.02529 - 6.38488i) q^{24} +(-3.40128 + 5.89118i) q^{25} +(6.98489 - 12.0982i) q^{26} +(-3.14179 - 4.13874i) q^{27} +(3.43518 - 1.98330i) q^{29} +(-13.7894 + 3.03203i) q^{30} +5.23527i q^{31} +3.18763i q^{32} +(0.366686 + 0.401559i) q^{33} +(1.95915 - 1.13111i) q^{34} +(-8.89866 - 6.27688i) q^{36} +(-2.68802 + 4.65579i) q^{37} +(-1.49612 + 2.59136i) q^{38} +(-6.87642 - 7.53040i) q^{39} +(-11.5061 + 6.64306i) q^{40} +(-0.0699627 + 0.121179i) q^{41} +(1.44078 + 2.49550i) q^{43} +(0.986951 + 0.569817i) q^{44} +(-0.933772 + 10.2641i) q^{45} +(-8.10072 - 14.0309i) q^{46} -2.01390 q^{47} +(-3.16387 - 1.00358i) q^{48} +(13.9783 + 8.07035i) q^{50} +(-0.354635 - 1.61285i) q^{51} +(-18.5082 - 10.6857i) q^{52} +(10.3749 - 5.98997i) q^{53} +(-9.82016 + 7.45465i) q^{54} -1.07860i q^{55} +(1.47289 + 1.61297i) q^{57} +(-4.70586 - 8.15079i) q^{58} +1.64892 q^{59} +(4.63850 + 21.0955i) q^{60} -2.97247i q^{61} +12.4219 q^{62} +11.3961 q^{64} +20.2268i q^{65} +(0.952795 - 0.870049i) q^{66} -1.86812 q^{67} +(-1.73041 - 2.99717i) q^{68} +(-11.5508 + 2.53980i) q^{69} -10.9981i q^{71} +(-6.68744 + 9.48070i) q^{72} +(-0.354655 + 0.204760i) q^{73} +(11.0470 + 6.37798i) q^{74} +(8.70063 - 7.94502i) q^{75} +(3.96435 + 2.28882i) q^{76} +(-17.8677 + 16.3160i) q^{78} +10.4665 q^{79} +(3.29181 + 5.70158i) q^{80} +(3.01961 + 8.47832i) q^{81} +(0.287526 + 0.166003i) q^{82} +(4.00094 + 6.92984i) q^{83} +(-1.63774 + 2.83664i) q^{85} +(5.92117 - 3.41859i) q^{86} +(-6.71007 + 1.47542i) q^{87} +(0.607087 - 1.05151i) q^{88} +(-1.05931 + 1.83478i) q^{89} +(24.3540 + 2.21560i) q^{90} +(-21.4649 + 12.3927i) q^{92} +(2.74168 - 8.64335i) q^{93} +4.77847i q^{94} -4.33246i q^{95} +(1.66934 - 5.26272i) q^{96} +(-10.5054 + 6.06531i) q^{97} +(-0.395098 - 0.854998i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} - 8 q^{9}+O(q^{10}) \) 48 * q - 48 * q^4 - 8 * q^9	\( 48 q - 48 q^{4} - 8 q^{9} + 24 q^{11} - 40 q^{15} + 48 q^{16} - 16 q^{18} + 48 q^{23} - 24 q^{25} - 24 q^{30} - 8 q^{36} - 56 q^{39} - 96 q^{44} + 48 q^{50} - 24 q^{51} - 48 q^{53} + 80 q^{57} + 168 q^{60} - 48 q^{64} - 88 q^{72} + 168 q^{74} - 88 q^{78} + 48 q^{79} - 24 q^{81} - 24 q^{85} - 24 q^{86} - 144 q^{92} + 16 q^{93} - 72 q^{99}+O(q^{100}) \) 48 * q - 48 * q^4 - 8 * q^9 + 24 * q^11 - 40 * q^15 + 48 * q^16 - 16 * q^18 + 48 * q^23 - 24 * q^25 - 24 * q^30 - 8 * q^36 - 56 * q^39 - 96 * q^44 + 48 * q^50 - 24 * q^51 - 48 * q^53 + 80 * q^57 + 168 * q^60 - 48 * q^64 - 88 * q^72 + 168 * q^74 - 88 * q^78 + 48 * q^79 - 24 * q^81 - 24 * q^85 - 24 * q^86 - 144 * q^92 + 16 * q^93 - 72 * q^99

Introduction

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