LMFDB - Embedded newform 441.2.i.d.68.4

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			68.4
Character	$\chi$	$=$	441.68
Dual form			441.2.i.d.227.22

$q$-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	$-0.887820\pi$
$5$	−1.71774	−	2.97522i	−0.768198	−	1.33056i	0.170342	−	0.985385i	$-0.445513\pi$
$6$	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	−0.418383	−	0.908271i	$-0.637403\pi$
$13$	−5.09882	−	2.94381i	−1.41416	−	0.816465i	−0.995777	+	0.0918054i	$0.970736\pi$
$14$		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	0.802408	−	0.596776i	$-0.203552\pi$
$17$	−0.476712	−	0.825689i	−0.115620	−	0.200259i	−0.918027	+	0.396517i	$0.870219\pi$
$18$	4.10299	−	5.81675i	0.967083	−	1.37102i
$19$	1.09214	+	0.630546i	0.250553	+	0.144657i	0.620018	−	0.784588i	$-0.287125\pi$
$19$	1.09214	+	0.630546i	0.250553	+	0.144657i	−0.369464	+	0.929245i	$0.620459\pi$
$20$	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	$-0.844203\pi$
$31$		−	5.23527i		−	0.940283i	0.882591	−	0.470141i	$-0.155797\pi$
$32$			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	−0.860511	−	0.509433i	$-0.829855\pi$
$41$	0.0699627	−	0.121179i	0.0109263	−	0.0189250i	0.871437	+	0.490508i	$0.163189\pi$
$42$		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	$-0.453077\pi$
$47$	2.01390			0.293758			0.146879	+	0.989154i	$0.453077\pi$
$48$	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	$-0.534232\pi$
$59$	−1.64892			−0.214671			−0.107335	+	0.994223i	$0.534232\pi$
$60$	4.63850	+	21.0955i	0.598828	+	2.72342i
$61$			2.97247i			0.380585i	0.981727	+	0.190293i	$0.0609437\pi$
$61$			2.97247i			0.380585i	−0.981727	+	0.190293i	$0.939056\pi$
$62$	−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	−0.479102	−	0.877759i	$-0.659038\pi$
$73$	0.354655	−	0.204760i	0.0415092	−	0.0239653i	0.520611	+	0.853794i	$0.325704\pi$
$74$	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	0.558464	−	0.829529i	$-0.311391\pi$
$83$	−4.00094	−	6.92984i	−0.439161	−	0.760649i	−0.997625	+	0.0688800i	$0.978057\pi$
$84$		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	−0.804405	−	0.594081i	$-0.797516\pi$
$89$	1.05931	−	1.83478i	0.112287	−	0.194487i	0.916692	+	0.399595i	$0.130849\pi$
$90$	−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	0.139396	−	0.990237i	$-0.455484\pi$
$97$	10.5054	−	6.06531i	1.06666	−	0.615839i	0.927268	+	0.374398i	$0.122150\pi$
$98$		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	$0.380725\pi$
$101$	−6.26039	+	10.8433i	−0.622932	+	1.07895i	−0.988937	+	0.148337i	$0.952608\pi$
$102$	−3.82687	+	0.841457i	−0.378917	+	0.0833166i
$103$	15.6040	−	9.00897i	1.53751	−	0.887680i	0.538523	−	0.842611i	$-0.318983\pi$
$103$	15.6040	−	9.00897i	1.53751	−	0.887680i	0.998984	−	0.0450689i	$-0.0143507\pi$
$104$	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	0.995392	−	0.0958879i	$-0.0305690\pi$
$131$	4.74594	+	8.22021i	0.414655	+	0.718203i	−0.580737	+	0.814091i	$0.697236\pi$
$132$	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	0.680966	−	0.732315i	$-0.261560\pi$
$139$	4.56556	+	2.63593i	0.387246	+	0.223577i	−0.293720	+	0.955891i	$0.594893\pi$
$140$		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	$0.0839038\pi$
$157$			6.52936i			0.521100i	−0.965460	+	0.260550i	$0.916096\pi$
$158$		−	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	$-0.651161\pi$
$167$	6.99871	−	12.1221i	0.541576	−	0.938037i	0.998814	−	0.0486928i	$-0.0155055\pi$
$168$		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	$-0.364014\pi$
$173$	10.8995			0.828672			0.414336	+	0.910124i	$0.364014\pi$
$174$	−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	$0.225529\pi$
$181$			17.5088i			1.30142i	−0.759326	+	0.650710i	$0.774471\pi$
$182$		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	−0.934431	−	0.356145i	$-0.884091\pi$
$199$	−15.4217	+	8.90372i	−1.09321	+	0.631168i	−0.158784	+	0.987313i	$0.550757\pi$
$200$	−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	−0.732742	−	0.680506i	$-0.761760\pi$
$223$	−7.61261	+	4.39514i	−0.509778	+	0.294321i	0.222964	+	0.974827i	$0.428427\pi$
$224$		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	$0.356275\pi$
$227$	−8.45329	+	14.6415i	−0.561065	+	0.971793i	−0.997404	+	0.0720104i	$0.977059\pi$
$228$	−5.34643	−	5.85490i	−0.354076	−	0.387750i
$229$	−16.9410	+	9.78088i	−1.11949	+	0.646339i	−0.941271	−	0.337652i	$-0.890367\pi$
$229$	−16.9410	+	9.78088i	−1.11949	+	0.646339i	−0.178221	+	0.983991i	$0.557034\pi$
$230$	−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	0.873945	−	0.486026i	$-0.161554\pi$
$241$	13.8166	+	7.97702i	0.890006	+	0.513845i	0.0160617	+	0.999871i	$0.494887\pi$
$242$	−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	$-0.490193\pi$
$251$	0.976065			0.0616087			0.0308044	+	0.999525i	$0.490193\pi$
$252$		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	0.991309	−	0.131558i	$-0.0419979\pi$
$257$	6.11947	+	10.5992i	0.381722	+	0.661162i	−0.609587	+	0.792720i	$0.708665\pi$
$258$	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	$0.0629081\pi$
$269$	10.8299	+	18.7579i	0.660309	+	1.14369i	−0.320225	+	0.947341i	$0.603759\pi$
$270$	−39.0477	−	16.4119i	−2.37637	−	0.998798i
$271$	17.8987	+	10.3338i	1.08727	+	0.627736i	0.932849	−	0.360268i	$-0.117315\pi$
$271$	17.8987	+	10.3338i	1.08727	+	0.627736i	0.154423	+	0.988005i	$0.450648\pi$
$272$	−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	$0.175589\pi$
$283$			17.6326i			1.04815i	−0.851672	+	0.524075i	$0.824411\pi$
$284$			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	$-0.524769\pi$
$293$	14.1138	−	24.4458i	0.824536	−	1.42814i	0.902273	−	0.431165i	$-0.141897\pi$
$294$		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	$0.0786102\pi$
$307$			8.56651i			0.488917i	−0.969660	+	0.244458i	$0.921390\pi$
$308$		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	$-0.684936\pi$
$311$	−19.3583			−1.09771			−0.548854	+	0.835918i	$0.684936\pi$
$312$	29.1225	−	26.5933i	1.64874	−	1.50555i
$313$		−	26.5012i		−	1.49793i	−0.662608	−	0.748967i	$-0.730550\pi$
$313$		−	26.5012i		−	1.49793i	0.662608	−	0.748967i	$-0.269450\pi$
$314$	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	−0.812627	−	0.582784i	$-0.801963\pi$
$349$	−13.3430	+	7.70360i	−0.714236	+	0.412364i	0.0983918	+	0.995148i	$0.468630\pi$
$350$		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	−0.527253	−	0.849708i	$-0.676778\pi$
$353$	8.87263	−	15.3679i	0.472243	−	0.817948i	0.999496	+	0.0317602i	$0.0101113\pi$
$354$	−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	0.382641	−	0.923897i	$-0.375014\pi$
$367$	−4.33253	−	2.50139i	−0.226156	−	0.130571i	−0.608797	+	0.793326i	$0.708348\pi$
$368$	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	$0.0158372\pi$
$383$	10.6160	+	18.3874i	0.542452	+	0.939554i	−0.456311	+	0.889821i	$0.650829\pi$
$384$	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	0.800499	−	0.599334i	$-0.204568\pi$
$397$	13.5830	+	7.84214i	0.681710	+	0.393586i	−0.118789	+	0.992920i	$0.537901\pi$
$398$	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	$0.161151\pi$
$409$			19.6138i			0.969839i	−0.874559	+	0.484920i	$0.838849\pi$
$410$			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	−0.997027	−	0.0770586i	$-0.975447\pi$
$419$	−8.83829	+	15.3084i	−0.431779	+	0.747862i	0.565248	+	0.824921i	$0.308780\pi$
$420$		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	$-0.929825\pi$
$433$		−	9.10088i		−	0.437360i	0.975797	−	0.218680i	$-0.0701752\pi$
$434$		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	$-0.909751\pi$
$439$		−	11.7225i		−	0.559486i	0.960075	−	0.279743i	$-0.0902492\pi$
$440$	−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	0.980508	−	0.196478i	$-0.0629505\pi$
$461$	6.87281	+	11.9041i	0.320099	+	0.554427i	−0.660409	+	0.750906i	$0.729617\pi$
$462$		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	−0.855045	−	0.518554i	$-0.826470\pi$
$467$	0.465894	−	0.806952i	0.0215590	−	0.0373413i	0.876604	+	0.481213i	$0.159804\pi$
$468$	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	$-0.567998\pi$
$479$	16.2031	−	28.0647i	0.740340	−	1.28231i	0.952340	−	0.305037i	$-0.0986690\pi$
$480$	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	$-0.761087\pi$
$503$	−32.8028			−1.46261			−0.731303	+	0.682053i	$0.761087\pi$
$504$		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	0.564562	−	0.825390i	$-0.309045\pi$
$509$	−9.75828	−	16.9018i	−0.432528	−	0.749160i	−0.997090	+	0.0762300i	$0.975712\pi$
$510$	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	0.562215	−	0.826991i	$-0.309950\pi$
$521$	−9.93108	−	17.2011i	−0.435088	−	0.753595i	−0.997303	+	0.0733964i	$0.976616\pi$
$522$	2.55813	−	28.1190i	0.111966	−	1.23074i
$523$	6.71478	+	3.87678i	0.293617	+	0.169520i	0.639572	−	0.768731i	$-0.279112\pi$
$523$	6.71478	+	3.87678i	0.293617	+	0.169520i	−0.345955	+	0.938251i	$0.612445\pi$
$524$	−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	$-0.263416\pi$
$563$	32.1123			1.35337			0.676686	+	0.736272i	$0.263416\pi$
$564$	−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	$-0.328249\pi$
$577$	36.3589	−	20.9918i	1.51364	−	0.873901i	0.999872	−	0.0159713i	$-0.00508404\pi$
$578$	−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	0.994225	−	0.107320i	$-0.0342270\pi$
$587$	9.79227	+	16.9607i	0.404170	+	0.700043i	−0.590054	+	0.807364i	$0.700894\pi$
$588$		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	−0.994796	−	0.101886i	$-0.967512\pi$
$593$	−9.96374	+	17.2577i	−0.409162	+	0.708689i	0.585634	+	0.810575i	$0.300846\pi$
$594$	−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	0.130945	−	0.991390i	$-0.458199\pi$
$601$	25.8633	−	14.9322i	1.05499	−	0.609097i	0.924041	+	0.382293i	$0.124865\pi$
$602$		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	−0.937164	−	0.348889i	$-0.886559\pi$
$607$	−27.1898	+	15.6980i	−1.10360	+	0.637163i	−0.166435	+	0.986052i	$0.553226\pi$
$608$	−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	0.477018	−	0.878893i	$-0.341718\pi$
$619$	−1.13493	−	0.655252i	−0.0456167	−	0.0263368i	−0.522635	+	0.852557i	$0.675051\pi$
$620$	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	0.493586	−	0.869697i	$-0.335686\pi$
$643$	−0.324584	−	0.187399i	−0.0128004	−	0.00739029i	−0.506387	+	0.862307i	$0.669019\pi$
$644$		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	$-0.713550\pi$
$647$	−25.1608	−	43.5798i	−0.989172	−	1.71330i	−0.367490	−	0.930027i	$-0.619783\pi$
$648$	−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	$-0.927513\pi$
$661$		−	11.6086i		−	0.451521i	0.974183	−	0.225760i	$-0.0724866\pi$
$662$		−	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	$-0.528366\pi$
$677$	−4.63127			−0.177994			−0.0889970	+	0.996032i	$0.528366\pi$
$678$	−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	$-0.858213\pi$
$691$		−	22.6515i		−	0.861704i	0.902423	−	0.430852i	$-0.141787\pi$
$692$	−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	−0.692629	−	0.721294i	$-0.743547\pi$
$719$	7.46359	−	12.9273i	0.278345	−	0.482108i	0.970974	+	0.239187i	$0.0768808\pi$
$720$	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	−0.583390	−	0.812192i	$-0.698274\pi$
$727$	−4.62968	+	2.67295i	−0.171705	+	0.0991341i	0.411684	+	0.911326i	$0.364941\pi$
$728$		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	−0.771443	−	0.636298i	$-0.780465\pi$
$733$	−16.4099	+	9.47428i	−0.606115	+	0.349941i	0.165328	+	0.986239i	$0.447132\pi$
$734$	−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	0.908483	−	0.417921i	$-0.137241\pi$
$761$	2.54651	+	4.41069i	0.0923109	+	0.159887i	−0.816172	+	0.577809i	$0.803908\pi$
$762$	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	0.961939	−	0.273264i	$-0.0881031\pi$
$769$	33.4505	+	19.3126i	1.20626	+	0.696432i	0.244316	+	0.969696i	$0.421436\pi$
$770$		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	$0.0452908\pi$
$773$	17.1754	+	29.7486i	0.617754	+	1.06998i	−0.372140	+	0.928177i	$0.621376\pi$
$774$	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	$0.137439\pi$
$787$			23.4800i			0.836972i	−0.908223	+	0.418486i	$0.862561\pi$
$788$		−	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	−0.950545	−	0.310587i	$-0.899474\pi$
$797$	−5.82399	+	10.0875i	−0.206296	+	0.357316i	0.744249	+	0.667903i	$0.232808\pi$
$798$		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	$-0.980085\pi$
$811$		−	3.56109i		−	0.125047i	0.998044	−	0.0625233i	$-0.0199148\pi$
$812$		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	−0.879222	−	0.476412i	$-0.841937\pi$
$829$	−26.0930	+	15.0648i	−0.906248	+	0.523223i	−0.0270260	+	0.999635i	$0.508604\pi$
$830$	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	0.948778	−	0.315944i	$-0.102321\pi$
$839$	5.81551	+	10.0728i	0.200774	+	0.347750i	−0.748004	+	0.663694i	$0.768988\pi$
$840$		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	−0.102160	−	0.994768i	$-0.532575\pi$
$853$	20.6854	−	11.9427i	0.708254	−	0.408911i	0.810414	+	0.585857i	$0.199242\pi$
$854$		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	$0.368404\pi$
$857$	−17.3362	+	30.0271i	−0.592193	+	1.02571i	−0.993936	+	0.109956i	$0.964929\pi$
$858$	7.41939	−	1.63138i	0.253294	−	0.0556945i
$859$	26.3932	−	15.2381i	0.900525	−	0.519918i	0.0231546	−	0.999732i	$-0.492629\pi$
$859$	26.3932	−	15.2381i	0.900525	−	0.519918i	0.877371	+	0.479813i	$0.159296\pi$
$860$	−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	$-0.609296\pi$
$881$	−19.9850			−0.673313			−0.336656	+	0.941628i	$0.609296\pi$
$882$		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	$0.0376606\pi$
$887$	17.8317	+	30.8853i	0.598729	+	1.03703i	−0.394280	+	0.918990i	$0.629006\pi$
$888$	−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	$-0.779850\pi$
$929$	−46.9514			−1.54043			−0.770213	+	0.637786i	$0.779850\pi$
$930$	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	$0.156387\pi$
$937$			28.8826i			0.943555i	−0.881718	+	0.471777i	$0.843613\pi$
$938$		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	$-0.507545\pi$
$941$	−1.45409			−0.0474019			−0.0237009	+	0.999719i	$0.507545\pi$
$942$	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	−0.915433	−	0.402471i	$-0.868151\pi$
$971$	−3.40171	+	5.89194i	−0.109166	+	0.189081i	0.806267	+	0.591552i	$0.201485\pi$
$972$	−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	$-0.563744\pi$
$983$	23.4913	−	40.6881i	0.749256	−	1.29775i	0.948180	−	0.317735i	$-0.102922\pi$
$984$	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	−0.343189	−	0.939266i	$-0.611507\pi$
$997$	−41.9387	−	24.2133i	−1.32821	−	0.766844i	−0.985023	+	0.172423i	$0.944841\pi$
$998$	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.68.4		48
3.2	odd	2		1323.2.i.d.1097.24		48
7.2	even	3		441.2.o.e.293.3	yes	48
7.3	odd	6		441.2.s.d.374.22		48
7.4	even	3		441.2.s.d.374.21		48
7.5	odd	6		441.2.o.e.293.4	yes	48
7.6	odd	2	inner	441.2.i.d.68.3		48
9.2	odd	6		441.2.s.d.362.22		48
9.7	even	3		1323.2.s.d.656.4		48
21.2	odd	6		1323.2.o.e.881.21		48
21.5	even	6		1323.2.o.e.881.22		48
21.11	odd	6		1323.2.s.d.962.3		48
21.17	even	6		1323.2.s.d.962.4		48
21.20	even	2		1323.2.i.d.1097.4		48
63.2	odd	6		441.2.o.e.146.4	yes	48
63.11	odd	6	inner	441.2.i.d.227.21		48
63.16	even	3		1323.2.o.e.440.22		48
63.20	even	6		441.2.s.d.362.21		48
63.25	even	3		1323.2.i.d.521.4		48
63.34	odd	6		1323.2.s.d.656.3		48
63.38	even	6	inner	441.2.i.d.227.22		48
63.47	even	6		441.2.o.e.146.3	✓	48
63.52	odd	6		1323.2.i.d.521.24		48
63.61	odd	6		1323.2.o.e.440.21		48

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
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

L-functions

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