LMFDB - Embedded newform 441.2.o.e.146.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(146,441)]

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([1, 3]))

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

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

chi := DirichletCharacter("441.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
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			146.3
Character	$\chi$	$=$	441.146
Dual form			441.2.o.e.293.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.05485 - 1.18637i) q^{2} +(-1.27902 - 1.16795i) q^{3} +(1.81495 + 3.14358i) q^{4} +(-1.71774 - 2.97522i) q^{5} +(1.24259 + 3.91735i) q^{6} -3.86732i q^{8} +(0.271802 + 2.98766i) q^{9} +O(q^{10})$	\(q+(-2.05485 - 1.18637i) q^{2} +(-1.27902 - 1.16795i) q^{3} +(1.81495 + 3.14358i) q^{4} +(-1.71774 - 2.97522i) q^{5} +(1.24259 + 3.91735i) q^{6} -3.86732i q^{8} +(0.271802 + 2.98766i) q^{9} +8.15151i q^{10} +(0.271895 + 0.156979i) q^{11} +(1.35017 - 6.14048i) q^{12} +(-5.09882 + 2.94381i) q^{13} +(-1.27786 + 5.81160i) q^{15} +(-0.958178 + 1.65961i) q^{16} +0.953423 q^{17} +(2.98596 - 6.46167i) q^{18} +1.26109i q^{19} +(6.23523 - 10.7997i) q^{20} +(-0.372470 - 0.645137i) q^{22} +(-5.91336 + 3.41408i) q^{23} +(-4.51682 + 4.94639i) q^{24} +(-3.40128 + 5.89118i) q^{25} +13.9698 q^{26} +(3.14179 - 4.13874i) q^{27} +(3.43518 + 1.98330i) q^{29} +(9.52053 - 10.4260i) q^{30} +(4.53388 - 2.61764i) q^{31} +(-2.76057 + 1.59381i) q^{32} +(-0.164418 - 0.518338i) q^{33} +(-1.95915 - 1.13111i) q^{34} +(-8.89866 + 6.27688i) q^{36} +5.37604 q^{37} +(1.49612 - 2.59136i) q^{38} +(9.95973 + 2.18996i) q^{39} +(-11.5061 + 6.64306i) q^{40} +(0.0699627 + 0.121179i) q^{41} +(1.44078 - 2.49550i) q^{43} +1.13963i q^{44} +(8.42206 - 5.94070i) q^{45} +16.2014 q^{46} +(-1.00695 + 1.74409i) q^{47} +(3.16387 - 1.00358i) q^{48} +(13.9783 - 8.07035i) q^{50} +(-1.21945 - 1.11355i) q^{51} +(-18.5082 - 10.6857i) q^{52} -11.9799i q^{53} +(-11.3660 + 4.77718i) q^{54} -1.07860i q^{55} +(1.47289 - 1.61297i) q^{57} +(-4.70586 - 8.15079i) q^{58} +(0.824459 + 1.42801i) q^{59} +(-20.5885 + 6.53070i) q^{60} +(2.57423 + 1.48623i) q^{61} -12.4219 q^{62} +11.3961 q^{64} +(17.5169 + 10.1134i) q^{65} +(-0.277087 + 1.26017i) q^{66} +(0.934059 + 1.61784i) q^{67} +(1.73041 + 2.99717i) q^{68} +(11.5508 + 2.53980i) q^{69} +10.9981i q^{71} +(11.5542 - 1.05115i) q^{72} -0.409520i q^{73} +(-11.0470 - 6.37798i) q^{74} +(11.2309 - 3.56245i) q^{75} +(-3.96435 + 2.28882i) q^{76} +(-17.8677 - 16.3160i) q^{78} +(-5.23325 + 9.06426i) q^{79} +6.58361 q^{80} +(-8.85225 + 1.62411i) q^{81} -0.332007i q^{82} +(-4.00094 + 6.92984i) q^{83} +(-1.63774 - 2.83664i) q^{85} +(-5.92117 + 3.41859i) q^{86} +(-2.07729 - 6.54880i) q^{87} +(0.607087 - 1.05151i) q^{88} -2.11862 q^{89} +(-24.3540 + 2.21560i) q^{90} +(-21.4649 - 12.3927i) q^{92} +(-8.85620 - 1.94731i) q^{93} +(4.13828 - 2.38924i) q^{94} +(3.75202 - 2.16623i) q^{95} +(5.39232 + 1.18567i) q^{96} +(10.5054 + 6.06531i) q^{97} +(-0.395098 + 0.854998i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4} + 16 q^{9}+O(q^{10}) $ 48 * q + 24 * q^4 + 16 * q^9	$ 48 q + 24 q^{4} + 16 q^{9} - 24 q^{11} - 40 q^{15} - 24 q^{16} - 16 q^{18} - 48 q^{23} - 24 q^{25} - 24 q^{30} + 120 q^{32} - 8 q^{36} + 88 q^{39} + 48 q^{50} + 24 q^{51} + 80 q^{57} - 96 q^{60} - 48 q^{64} + 120 q^{65} + 56 q^{72} - 168 q^{74} - 88 q^{78} - 24 q^{79} - 96 q^{81} - 24 q^{85} + 24 q^{86} - 144 q^{92} - 32 q^{93} + 96 q^{95} - 72 q^{99}+O(q^{100}) $ 48 * q + 24 * q^4 + 16 * q^9 - 24 * q^11 - 40 * q^15 - 24 * q^16 - 16 * q^18 - 48 * q^23 - 24 * q^25 - 24 * q^30 + 120 * q^32 - 8 * q^36 + 88 * q^39 + 48 * q^50 + 24 * q^51 + 80 * q^57 - 96 * q^60 - 48 * q^64 + 120 * q^65 + 56 * q^72 - 168 * q^74 - 88 * q^78 - 24 * q^79 - 96 * q^81 - 24 * q^85 + 24 * q^86 - 144 * q^92 - 32 * q^93 + 96 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−2.05485	−	1.18637i	−1.45300	−	0.838890i	−0.454350	−	0.890823i	$-0.650129\pi$
$2$	−2.05485	−	1.18637i	−1.45300	−	0.838890i	−0.998651	+	0.0519328i	$0.983462\pi$
$3$	−1.27902	−	1.16795i	−0.738445	−	0.674314i
$3$	−1.27902	−	1.16795i	−0.738445	−	0.674314i
$4$	1.81495	+	3.14358i	0.907474	+	1.57179i
$5$	−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
$9$	0.271802	+	2.98766i	0.0906007	+	0.995887i
$10$			8.15151i			2.57773i
$11$	0.271895	+	0.156979i	0.0819795	+	0.0473309i	0.540429	−	0.841389i	$-0.318262\pi$
$11$	0.271895	+	0.156979i	0.0819795	+	0.0473309i	−0.458450	+	0.888720i	$0.651595\pi$
$12$	1.35017	−	6.14048i	0.389762	−	1.77260i
$13$	−5.09882	+	2.94381i	−1.41416	+	0.816465i	−0.995777	−	0.0918054i	$-0.970736\pi$
$13$	−5.09882	+	2.94381i	−1.41416	+	0.816465i	−0.418383	+	0.908271i	$0.637403\pi$
$14$		0			0
$15$	−1.27786	+	5.81160i	−0.329942	+	1.50055i
$16$	−0.958178	+	1.65961i	−0.239545	+	0.414903i
$17$	0.953423			0.231239			0.115620	−	0.993294i	$-0.463115\pi$
$17$	0.953423			0.231239			0.115620	+	0.993294i	$0.463115\pi$
$18$	2.98596	−	6.46167i	0.703797	−	1.52303i
$19$			1.26109i			0.289314i	0.989482	+	0.144657i	$0.0462079\pi$
$19$			1.26109i			0.289314i	−0.989482	+	0.144657i	$0.953792\pi$
$20$	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	−0.967658	−	0.252265i	$-0.918825\pi$
$23$	−5.91336	+	3.41408i	−1.23302	+	0.711884i	−0.265362	+	0.964149i	$0.585491\pi$
$24$	−4.51682	+	4.94639i	−0.921993	+	1.00968i
$25$	−3.40128	+	5.89118i	−0.680255	+	1.17824i
$26$	13.9698			2.73970
$27$	3.14179	−	4.13874i	0.604637	−	0.796501i
$28$		0			0
$29$	3.43518	+	1.98330i	0.637897	+	0.368290i	0.783804	−	0.621008i	$-0.213277\pi$
$29$	3.43518	+	1.98330i	0.637897	+	0.368290i	−0.145907	+	0.989298i	$0.546610\pi$
$30$	9.52053	−	10.4260i	1.73820	−	1.90351i
$31$	4.53388	−	2.61764i	0.814309	−	0.470141i	−0.0341412	−	0.999417i	$-0.510870\pi$
$31$	4.53388	−	2.61764i	0.814309	−	0.470141i	0.848450	+	0.529276i	$0.177536\pi$
$32$	−2.76057	+	1.59381i	−0.488004	+	0.281749i
$33$	−0.164418	−	0.518338i	−0.0286214	−	0.0902311i
$34$	−1.95915	−	1.13111i	−0.335991	−	0.193984i
$35$		0			0
$36$	−8.89866	+	6.27688i	−1.48311	+	1.04615i
$37$	5.37604			0.883816			0.441908	−	0.897060i	$-0.354302\pi$
$37$	5.37604			0.883816			0.441908	+	0.897060i	$0.354302\pi$
$38$	1.49612	−	2.59136i	0.242703	−	0.420374i
$39$	9.95973	+	2.18996i	1.59483	+	0.350673i
$40$	−11.5061	+	6.64306i	−1.81928	+	1.05036i
$41$	0.0699627	+	0.121179i	0.0109263	+	0.0189250i	0.871437	−	0.490508i	$-0.163189\pi$
$41$	0.0699627	+	0.121179i	0.0109263	+	0.0189250i	−0.860511	+	0.509433i	$0.829855\pi$
$42$		0			0
$43$	1.44078	−	2.49550i	0.219716	−	0.380560i	−0.735005	−	0.678062i	$-0.762820\pi$
$43$	1.44078	−	2.49550i	0.219716	−	0.380560i	0.954721	+	0.297502i	$0.0961535\pi$
$44$			1.13963i			0.171806i
$45$	8.42206	−	5.94070i	1.25549	−	0.885588i
$46$	16.2014			2.38877
$47$	−1.00695	+	1.74409i	−0.146879	+	0.254402i	−0.930072	−	0.367376i	$-0.880256\pi$
$47$	−1.00695	+	1.74409i	−0.146879	+	0.254402i	0.783193	+	0.621778i	$0.213589\pi$
$48$	3.16387	−	1.00358i	0.456666	−	0.144855i
$49$		0			0
$50$	13.9783	−	8.07035i	1.97682	−	1.14132i
$51$	−1.21945	−	1.11355i	−0.170757	−	0.155928i
$52$	−18.5082	−	10.6857i	−2.56663	−	1.48184i
$53$		−	11.9799i		−	1.64557i	−0.568351	−	0.822786i	$-0.692418\pi$
$53$		−	11.9799i		−	1.64557i	0.568351	−	0.822786i	$-0.307582\pi$
$54$	−11.3660	+	4.77718i	−1.54672	+	0.650092i
$55$		−	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
$59$	0.824459	+	1.42801i	0.107335	+	0.185910i	0.914690	−	0.404156i	$-0.132435\pi$
$59$	0.824459	+	1.42801i	0.107335	+	0.185910i	−0.807355	+	0.590067i	$0.799101\pi$
$60$	−20.5885	+	6.53070i	−2.65796	+	0.843109i
$61$	2.57423	+	1.48623i	0.329597	+	0.190293i	0.655662	−	0.755055i	$-0.272390\pi$
$61$	2.57423	+	1.48623i	0.329597	+	0.190293i	−0.326065	+	0.945347i	$0.605723\pi$
$62$	−12.4219			−1.57759
$63$		0			0
$64$	11.3961			1.42452
$65$	17.5169	+	10.1134i	2.17271	+	1.25441i
$66$	−0.277087	+	1.26017i	−0.0341071	+	0.155116i
$67$	0.934059	+	1.61784i	0.114113	+	0.197650i	0.917425	−	0.397909i	$-0.130264\pi$
$67$	0.934059	+	1.61784i	0.114113	+	0.197650i	−0.803312	+	0.595559i	$0.796931\pi$
$68$	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	$0.226330\pi$
$71$			10.9981i			1.30524i	−0.757686	+	0.652619i	$0.773670\pi$
$72$	11.5542	−	1.05115i	1.36168	−	0.123879i
$73$		−	0.409520i		−	0.0479307i	−0.999713	−	0.0239653i	$-0.992371\pi$
$73$		−	0.409520i		−	0.0479307i	0.999713	−	0.0239653i	$-0.00762914\pi$
$74$	−11.0470	−	6.37798i	−1.28419	−	0.741425i
$75$	11.2309	−	3.56245i	1.29683	−	0.411357i
$76$	−3.96435	+	2.28882i	−0.454742	+	0.262545i
$77$		0			0
$78$	−17.8677	−	16.3160i	−2.02312	−	1.84742i
$79$	−5.23325	+	9.06426i	−0.588787	+	1.01981i	0.405605	+	0.914049i	$0.367061\pi$
$79$	−5.23325	+	9.06426i	−0.588787	+	1.01981i	−0.994392	+	0.105760i	$0.966272\pi$
$80$	6.58361			0.736070
$81$	−8.85225	+	1.62411i	−0.983583	+	0.180456i
$82$		−	0.332007i		−	0.0366640i
$83$	−4.00094	+	6.92984i	−0.439161	+	0.760649i	−0.997625	−	0.0688800i	$-0.978057\pi$
$83$	−4.00094	+	6.92984i	−0.439161	+	0.760649i	0.558464	+	0.829529i	$0.311391\pi$
$84$		0			0
$85$	−1.63774	−	2.83664i	−0.177637	−	0.307677i
$86$	−5.92117	+	3.41859i	−0.638496	+	0.368636i
$87$	−2.07729	−	6.54880i	−0.222708	−	0.702105i
$88$	0.607087	−	1.05151i	0.0647157	−	0.112091i
$89$	−2.11862			−0.224574			−0.112287	−	0.993676i	$-0.535818\pi$
$89$	−2.11862			−0.224574			−0.112287	+	0.993676i	$0.535818\pi$
$90$	−24.3540	+	2.21560i	−2.56713	+	0.233545i
$91$		0			0
$92$	−21.4649	−	12.3927i	−2.23787	−	1.29203i
$93$	−8.85620	−	1.94731i	−0.918345	−	0.201927i
$94$	4.13828	−	2.38924i	0.426831	−	0.246431i
$95$	3.75202	−	2.16623i	0.384949	−	0.222251i
$96$	5.39232	+	1.18567i	0.550351	+	0.121012i
$97$	10.5054	+	6.06531i	1.06666	+	0.615839i	0.927268	−	0.374398i	$-0.122150\pi$
$97$	10.5054	+	6.06531i	1.06666	+	0.615839i	0.139396	+	0.990237i	$0.455484\pi$
$98$		0			0
$99$	−0.395098	+	0.854998i	−0.0397088	+	0.0859305i
$100$	−24.6926			−2.46926
$101$	−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	$0.952608\pi$
$102$	1.18471	+	3.73490i	0.117304	+	0.369810i
$103$	−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
$107$			3.59816i			0.347848i	0.984759	+	0.173924i	$0.0556447\pi$
$107$			3.59816i			0.347848i	−0.984759	+	0.173924i	$0.944355\pi$
$108$	18.7127	+	2.36487i	1.80063	+	0.227560i
$109$	−6.56218			−0.628543			−0.314271	−	0.949333i	$-0.601760\pi$
$109$	−6.56218			−0.628543			−0.314271	+	0.949333i	$0.601760\pi$
$110$	−1.27961	+	2.21636i	−0.122006	+	0.211321i
$111$	−6.87609	−	6.27893i	−0.652649	−	0.595970i
$112$		0			0
$113$	−1.87912	+	1.08491i	−0.176773	+	0.102060i	−0.585775	−	0.810473i	$-0.699210\pi$
$113$	−1.87912	+	1.08491i	−0.176773	+	0.102060i	0.409003	+	0.912533i	$0.365877\pi$
$114$	−4.94014	+	1.56702i	−0.462687	+	0.146765i
$115$	20.3152	+	11.7290i	1.89441	+	1.09374i
$116$			14.3984i			1.33685i
$117$	−10.1810	−	14.4334i	−0.941231	−	1.33437i
$118$		−	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
$122$	−3.52645	−	6.10798i	−0.319269	−	0.552991i
$123$	0.0520466	−	0.236703i	0.00469288	−	0.0213428i
$124$	16.4575	+	9.50175i	1.47793	+	0.853282i
$125$	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	$0.466756\pi$
$128$	−17.8962	−	10.3324i	−1.58182	−	0.913263i
$129$	−4.75740	+	1.50905i	−0.418865	+	0.132865i
$130$	−23.9965	−	41.5631i	−2.10463	−	3.64533i
$131$	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
$135$	−17.7104	−	2.23821i	−1.52427	−	0.192635i
$136$		−	3.68719i		−	0.316174i
$137$	8.85456	+	5.11218i	0.756496	+	0.436763i	0.828036	−	0.560674i	$-0.189458\pi$
$137$	8.85456	+	5.11218i	0.756496	+	0.436763i	−0.0715401	+	0.997438i	$0.522791\pi$
$138$	−20.7220	−	18.9224i	−1.76398	−	1.61078i
$139$	4.56556	−	2.63593i	0.387246	−	0.223577i	−0.293720	−	0.955891i	$-0.594893\pi$
$139$	4.56556	−	2.63593i	0.387246	−	0.223577i	0.680966	+	0.732315i	$0.261560\pi$
$140$		0			0
$141$	3.32492	−	1.05467i	0.280009	−	0.0888192i
$142$	13.0479	−	22.5996i	1.09495	−	1.89651i
$143$	−1.84846			−0.154576
$144$	−5.21880	−	2.41163i	−0.434900	−	0.200969i
$145$		−	13.6272i		−	1.13168i
$146$	−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	0.315979	−	0.948766i	$-0.397667\pi$
$149$	15.8151	−	9.13086i	1.29562	−	0.748029i	0.979645	+	0.200737i	$0.0643338\pi$
$150$	−27.3042	−	6.00369i	−2.22938	−	0.490199i
$151$	−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	$0.777174\pi$
$152$	4.87705			0.395581
$153$	0.259142	+	2.84851i	0.0209504	+	0.230288i
$154$		0			0
$155$	−15.5761	−	8.99285i	−1.25110	−	0.722323i
$156$	11.1921	+	35.2839i	0.896084	+	2.82497i
$157$	−5.65459	+	3.26468i	−0.451286	+	0.260550i	−0.708373	−	0.705838i	$-0.750570\pi$
$157$	−5.65459	+	3.26468i	−0.451286	+	0.260550i	0.257087	+	0.966388i	$0.417237\pi$
$158$	21.5071	−	12.4172i	1.71102	−	0.987855i
$159$	−13.9919	+	15.3226i	−1.10963	+	1.21516i
$160$	9.48388	+	5.47552i	0.749767	+	0.432878i
$161$		0			0
$162$	20.1169	+	7.16474i	1.58053	+	0.562915i
$163$	24.5246			1.92091			0.960457	−	0.278428i	$-0.0898133\pi$
$163$	24.5246			1.92091			0.960457	+	0.278428i	$0.0898133\pi$
$164$	−0.253957	+	0.439867i	−0.0198307	+	0.0343478i
$165$	−1.25974	+	1.37955i	−0.0980708	+	0.107398i
$166$	16.4427	−	9.49320i	1.27620	−	0.736815i
$167$	6.99871	+	12.1221i	0.541576	+	0.938037i	0.998814	+	0.0486928i	$0.0155055\pi$
$167$	6.99871	+	12.1221i	0.541576	+	0.938037i	−0.457238	+	0.889345i	$0.651161\pi$
$168$		0			0
$169$	10.8320	−	18.7616i	0.833232	−	1.44320i
$170$			7.77184i			0.596073i
$171$	−3.76772	+	0.342767i	−0.288124	+	0.0262121i
$172$	10.4597			0.797548
$173$	−5.44974	+	9.43923i	−0.414336	+	0.717651i	−0.995359	−	0.0962363i	$-0.969320\pi$
$173$	−5.44974	+	9.43923i	−0.414336	+	0.717651i	0.581022	+	0.813888i	$0.302653\pi$
$174$	−3.50078	+	15.9212i	−0.265394	+	1.20699i
$175$		0			0
$176$	−0.521048	+	0.300827i	−0.0392755	+	0.0226757i
$177$	0.613331	−	2.78938i	0.0461008	−	0.209662i
$178$	4.35346	+	2.51347i	0.326306	+	0.188393i
$179$		−	1.59945i		−	0.119549i	−0.998212	−	0.0597743i	$-0.980962\pi$
$179$		−	1.59945i		−	0.119549i	0.998212	−	0.0597743i	$-0.0190381\pi$
$180$	33.9607	+	15.6934i	2.53128	+	1.16971i
$181$		−	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
$185$	−9.23466	−	15.9949i	−0.678946	−	1.17597i
$186$	15.8880	+	14.5082i	1.16496	+	1.06379i
$187$	0.259231	+	0.149667i	0.0189569	+	0.0109447i
$188$	−7.31027			−0.533156
$189$		0			0
$190$	−10.2798			−0.745775
$191$	−13.9107	−	8.03138i	−1.00655	−	0.581130i	−0.0963679	−	0.995346i	$-0.530723\pi$
$191$	−13.9107	−	8.03138i	−1.00655	−	0.581130i	−0.910179	+	0.414216i	$0.864056\pi$
$192$	−14.5759	−	13.3101i	−1.05193	−	0.960571i
$193$	5.44196	+	9.42575i	0.391721	+	0.678480i	0.992677	−	0.120802i	$-0.0385467\pi$
$193$	5.44196	+	9.42575i	0.391721	+	0.678480i	−0.600956	+	0.799282i	$0.705213\pi$
$194$	−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	$-0.925529\pi$
$197$		−	6.50777i		−	0.463660i	0.972756	−	0.231830i	$-0.0744712\pi$
$198$	1.82621	−	1.28816i	0.129783	−	0.0915458i
$199$			17.8074i			1.26234i	0.775646	+	0.631168i	$0.217424\pi$
$199$			17.8074i			1.26234i	−0.775646	+	0.631168i	$0.782576\pi$
$200$	22.7831	+	13.1538i	1.61101	+	0.930116i
$201$	0.694864	−	3.16018i	0.0490119	−	0.222902i
$202$	25.7284	−	14.8543i	1.81024	−	1.04514i
$203$		0			0
$204$	1.28729	−	5.85448i	0.0901282	−	0.409895i
$205$	0.240356	−	0.416308i	0.0167872	−	0.0290762i
$206$	42.7519			2.97866
$207$	−11.8074	−	16.7392i	−0.820669	−	1.16345i
$208$		−	11.2828i		−	0.782319i
$209$	−0.197965	+	0.342885i	−0.0136935	+	0.0237178i
$210$		0			0
$211$	−0.282402	−	0.489135i	−0.0194414	−	0.0336735i	0.856141	−	0.516742i	$-0.172855\pi$
$211$	−0.282402	−	0.489135i	−0.0194414	−	0.0336735i	−0.875582	+	0.483069i	$0.839522\pi$
$212$	37.6600	−	21.7430i	2.58650	−	1.49331i
$213$	12.8452	−	14.0669i	0.880141	−	0.963846i
$214$	4.26875	−	7.39370i	0.291806	−	0.505423i
$215$	−9.89953			−0.675143
$216$	−16.0058	−	12.1503i	−1.08906	−	0.826723i
$217$		0			0
$218$	13.4843	+	7.78518i	0.913273	+	0.527279i
$219$	−0.478298	+	0.523786i	−0.0323204	+	0.0353942i
$220$	3.39066	−	1.95760i	0.228598	−	0.131981i
$221$	−4.86134	+	2.80670i	−0.327009	+	0.188799i
$222$	6.68021	+	21.0599i	0.448347	+	1.41345i
$223$	−7.61261	−	4.39514i	−0.509778	−	0.294321i	0.222964	−	0.974827i	$-0.428427\pi$
$223$	−7.61261	−	4.39514i	−0.509778	−	0.294321i	−0.732742	+	0.680506i	$0.761760\pi$
$224$		0			0
$225$	−18.5253	−	8.56063i	−1.23502	−	0.570709i
$226$	5.14842			0.342468
$227$	−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	$0.977059\pi$
$228$	7.74371	+	1.70269i	0.512839	+	0.112764i
$229$	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
$233$			19.7368i			1.29300i	0.762914	+	0.646500i	$0.223768\pi$
$233$			19.7368i			1.29300i	−0.762914	+	0.646500i	$0.776232\pi$
$234$	3.79702	+	41.7370i	0.248219	+	2.72843i
$235$	6.91874			0.451329
$236$	−2.99270	+	5.18351i	−0.194808	+	0.337418i
$237$	17.2800	−	5.48124i	1.12246	−	0.356045i
$238$		0			0
$239$	−16.9761	+	9.80118i	−1.09809	+	0.633985i	−0.935720	−	0.352744i	$-0.885249\pi$
$239$	−16.9761	+	9.80118i	−1.09809	+	0.633985i	−0.162375	+	0.986729i	$0.551915\pi$
$240$	−8.42060	−	7.68931i	−0.543547	−	0.496343i
$241$	−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	$0.838446\pi$
$242$			25.8663i			1.66275i
$243$	13.2191	+	8.26168i	0.848006	+	0.529987i
$244$			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
$248$	−10.1232	−	17.5340i	−0.642826	−	1.11341i
$249$	13.2110	−	4.19054i	0.837212	−	0.265565i
$250$	−12.7250	−	7.34677i	−0.804798	−	0.464651i
$251$	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
$254$	−4.82822	−	2.78758i	−0.302950	−	0.174908i
$255$	−1.21834	+	5.54092i	−0.0762956	+	0.346986i
$256$	13.1200	+	22.7244i	0.819998	+	1.42028i
$257$	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
$261$	−4.99175	+	10.8022i	−0.308981	+	0.668641i
$262$		−	22.5218i		−	1.39140i
$263$	−3.64436	−	2.10407i	−0.224721	−	0.129743i	0.383413	−	0.923577i	$-0.374748\pi$
$263$	−3.64436	−	2.10407i	−0.224721	−	0.129743i	−0.608134	+	0.793834i	$0.708082\pi$
$264$	−2.00458	+	0.635855i	−0.123373	+	0.0391342i
$265$	−35.6429	+	20.5785i	−2.18953	+	1.26413i
$266$		0			0
$267$	2.70977	+	2.47444i	0.165835	+	0.151433i
$268$	−3.39054	+	5.87258i	−0.207110	+	0.358725i
$269$	−21.6597			−1.32062			−0.660309	−	0.750994i	$-0.729575\pi$
$269$	−21.6597			−1.32062			−0.660309	+	0.750994i	$0.729575\pi$
$270$	33.7370	+	25.6103i	2.05317	+	1.55859i
$271$			20.6677i			1.25547i	0.778426	+	0.627736i	$0.216018\pi$
$271$			20.6677i			1.25547i	−0.778426	+	0.627736i	$0.783982\pi$
$272$	−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
$276$	12.9800	+	40.9204i	0.781304	+	2.46312i
$277$	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	$-0.149529\pi$
$278$	−12.5087			−0.750225
$279$	9.05293	+	12.8342i	0.541985	+	0.768365i
$280$		0			0
$281$	16.7176	+	9.65190i	0.997287	+	0.575784i	0.907444	−	0.420172i	$-0.138030\pi$
$281$	16.7176	+	9.65190i	0.997287	+	0.575784i	0.0898425	+	0.995956i	$0.471364\pi$
$282$	−8.08346	−	1.77740i	−0.481363	−	0.105843i
$283$	−15.2703	+	8.81631i	−0.907725	+	0.524075i	−0.879698	−	0.475532i	$-0.842256\pi$
$283$	−15.2703	+	8.81631i	−0.907725	+	0.524075i	−0.0280263	+	0.999607i	$0.508922\pi$
$284$	−34.5735	+	19.9610i	−2.05156	+	1.18447i
$285$	−7.32896	−	1.61150i	−0.434130	−	0.0954570i
$286$	3.79832	+	2.19296i	0.224599	+	0.129672i
$287$		0			0
$288$	−5.51210	−	7.81444i	−0.324804	−	0.460470i
$289$	−16.0910			−0.946528
$290$	−16.1669	+	28.0019i	−0.949354	+	1.64433i
$291$	−6.35273	−	20.0275i	−0.372404	−	1.17403i
$292$	1.28736	−	0.743258i	0.0753371	−	0.0434959i
$293$	14.1138	+	24.4458i	0.824536	+	1.42814i	0.902273	+	0.431165i	$0.141897\pi$
$293$	14.1138	+	24.4458i	0.824536	+	1.42814i	−0.0777369	+	0.996974i	$0.524769\pi$
$294$		0			0
$295$	2.83242	−	4.90589i	0.164910	−	0.285632i
$296$		−	20.7909i		−	1.20845i
$297$	1.50393	−	0.632109i	0.0872669	−	0.0366787i
$298$	−43.3303			−2.51006
$299$	20.1008	−	34.8156i	1.16246	−	2.01344i
$300$	31.5824	+	28.8396i	1.82341	+	1.66505i
$301$		0			0
$302$	47.4880	−	27.4172i	2.73263	−	1.57768i
$303$	20.6716	−	6.55705i	1.18755	−	0.376693i
$304$	−2.09292	−	1.20835i	−0.120037	−	0.0693036i
$305$		−	10.2119i		−	0.584730i
$306$	2.84688	−	6.16070i	0.162746	−	0.352184i
$307$		−	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
$311$	9.67914	+	16.7648i	0.548854	+	0.950642i	0.998353	+	0.0573619i	$0.0182689\pi$
$311$	9.67914	+	16.7648i	0.548854	+	0.950642i	−0.449500	+	0.893280i	$0.648398\pi$
$312$	8.46926	−	38.5175i	0.479477	−	2.18062i
$313$	−22.9507	−	13.2506i	−1.29725	−	0.748967i	−0.317321	−	0.948318i	$-0.602783\pi$
$313$	−22.9507	−	13.2506i	−1.29725	−	0.748967i	−0.979928	+	0.199352i	$0.936116\pi$
$314$	15.4925			0.874291
$315$		0			0
$316$	−37.9923			−2.13724
$317$	−7.50458	−	4.33277i	−0.421499	−	0.243353i	0.274219	−	0.961667i	$-0.411581\pi$
$317$	−7.50458	−	4.33277i	−0.421499	−	0.243353i	−0.695719	+	0.718314i	$0.744914\pi$
$318$	46.9297	−	14.8862i	2.63169	−	0.834774i
$319$	0.622673	+	1.07850i	0.0348630	+	0.0603844i
$320$	−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
$324$	−21.1719	−	24.8801i	−1.17622	−	1.38223i
$325$		−	40.0508i		−	2.22162i
$326$	−50.3944	−	29.0952i	−2.79109	−	1.61144i
$327$	8.39318	+	7.66428i	0.464144	+	0.423835i
$328$	0.468638	−	0.270568i	0.0258762	−	0.0149396i
$329$		0			0
$330$	4.22524	−	1.34025i	0.232592	−	0.0737784i
$331$	−9.66912	+	16.7474i	−0.531463	+	0.920521i	0.467863	+	0.883801i	$0.345024\pi$
$331$	−9.66912	+	16.7474i	−0.531463	+	0.920521i	−0.999326	+	0.0367197i	$0.988309\pi$
$332$	−29.0460			−1.59411
$333$	1.46122	+	16.0618i	0.0800744	+	0.880181i
$334$		−	33.2122i		−	1.81729i
$335$	3.20894	−	5.55805i	0.175323	−	0.303669i
$336$		0			0
$337$	−12.4451	−	21.5556i	−0.677930	−	1.17421i	−0.975603	−	0.219542i	$-0.929544\pi$
$337$	−12.4451	−	21.5556i	−0.677930	−	1.17421i	0.297673	−	0.954668i	$-0.403790\pi$
$338$	−44.5164	+	25.7015i	−2.42137	+	1.39798i
$339$	3.67055	+	0.807085i	0.199357	+	0.0438348i
$340$	5.94481	−	10.2967i	0.322403	−	0.558418i
$341$	1.64365			0.0890088
$342$	8.14875	+	3.76557i	0.440634	+	0.203619i
$343$		0			0
$344$	−9.65090	−	5.57195i	−0.520341	−	0.300419i
$345$	−12.2848	−	38.7288i	−0.661392	−	2.08509i
$346$	22.3968	−	12.9308i	1.20406	−	0.695165i
$347$	5.01728	−	2.89673i	0.269342	−	0.155505i	−0.359247	−	0.933243i	$-0.616966\pi$
$347$	5.01728	−	2.89673i	0.269342	−	0.155505i	0.628588	+	0.777738i	$0.283633\pi$
$348$	16.8165	−	18.4158i	0.901460	−	0.987193i
$349$	−13.3430	−	7.70360i	−0.714236	−	0.412364i	0.0983918	−	0.995148i	$-0.468630\pi$
$349$	−13.3430	−	7.70360i	−0.714236	−	0.412364i	−0.812627	+	0.582784i	$0.801963\pi$
$350$		0			0
$351$	−3.83577	+	30.3515i	−0.204738	+	1.62004i
$352$	−1.00078			−0.0533417
$353$	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	$0.0101113\pi$
$354$	−4.56954	+	5.00412i	−0.242868	+	0.265966i
$355$	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
$359$		−	22.9197i		−	1.20966i	−0.796356	−	0.604828i	$-0.793242\pi$
$359$		−	22.9197i		−	1.20966i	0.796356	−	0.604828i	$-0.206758\pi$
$360$	−22.9746	−	32.5708i	−1.21087	−	1.71663i
$361$	17.4096			0.916297
$362$	−20.7719	+	35.9781i	−1.09175	+	1.89096i
$363$	−4.05489	+	18.4413i	−0.212827	+	0.967917i
$364$		0			0
$365$	−1.21841	+	0.703450i	−0.0637745	+	0.0368203i
$366$	−2.62339	+	11.9310i	−0.137127	+	0.623641i
$367$	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	$0.624986\pi$
$368$		−	13.0852i		−	0.682112i
$369$	−0.343026	+	0.241961i	−0.0178572	+	0.0125960i
$370$			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	$0.912649\pi$
$374$	−0.355121	−	0.615088i	−0.0183629	−	0.0318055i
$375$	−7.92054	−	7.23268i	−0.409015	−	0.373494i
$376$	6.74497	+	3.89421i	0.347845	+	0.200828i
$377$	−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	$0.615648\pi$
$380$	13.6194	+	7.86319i	0.698663	+	0.403373i
$381$	−3.00528	−	2.74429i	−0.153965	−	0.140594i
$382$	19.0564	+	33.0066i	0.975009	+	1.68876i
$383$	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
$387$	7.84731	+	3.62627i	0.398901	+	0.184334i
$388$			44.0329i			2.23543i
$389$	−3.91419	−	2.25986i	−0.198457	−	0.114579i	0.397478	−	0.917612i	$-0.369885\pi$
$389$	−3.91419	−	2.25986i	−0.198457	−	0.114579i	−0.595936	+	0.803032i	$0.703219\pi$
$390$	−17.8514	+	81.1868i	−0.903943	+	4.11106i
$391$	−5.63793	+	3.25506i	−0.285122	+	0.164616i
$392$		0			0
$393$	3.53060	−	16.0568i	0.178095	−	0.809961i
$394$	−7.72063	+	13.3725i	−0.388960	+	0.673698i
$395$	35.9575			1.80922
$396$	−3.40484	+	0.309755i	−0.171100	+	0.0155658i
$397$			15.6843i			0.787171i	0.919288	+	0.393586i	$0.128765\pi$
$397$			15.6843i			0.787171i	−0.919288	+	0.393586i	$0.871235\pi$
$398$	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	−0.248237	−	0.968699i	$-0.579851\pi$
$401$	9.34292	−	5.39414i	0.466563	−	0.269370i	0.714800	+	0.699329i	$0.246518\pi$
$402$	−5.17699	+	5.66934i	−0.258205	+	0.282761i
$403$	−15.4116	+	26.6937i	−0.767708	+	1.32971i
$404$	−45.4491			−2.26118
$405$	20.0379	+	23.5476i	0.995693	+	1.17009i
$406$		0			0
$407$	1.46172	+	0.843925i	0.0724548	+	0.0418318i
$408$	−4.30645	+	4.71601i	−0.213201	+	0.233477i
$409$	−16.9860	+	9.80689i	−0.839906	+	0.484920i	−0.857232	−	0.514930i	$-0.827818\pi$
$409$	−16.9860	+	9.80689i	−0.839906	+	0.484920i	0.0173265	+	0.999850i	$0.494485\pi$
$410$	−0.987791	+	0.570302i	−0.0487835	+	0.0281652i
$411$	−5.35444	−	16.8803i	−0.264115	−	0.832642i
$412$	−56.6409	−	32.7016i	−2.79050	−	1.61109i
$413$		0			0
$414$	4.40358	+	48.4044i	0.216424	+	2.37895i
$415$	27.4904			1.34945
$416$	9.38376	−	16.2532i	0.460077	−	0.796876i
$417$	−8.91808	−	1.96092i	−0.436720	−	0.0960266i
$418$	0.813576	−	0.469718i	0.0397933	−	0.0229747i
$419$	−8.83829	−	15.3084i	−0.431779	−	0.747862i	0.565248	−	0.824921i	$-0.308780\pi$
$419$	−8.83829	−	15.3084i	−0.431779	−	0.747862i	−0.997027	+	0.0770586i	$0.975447\pi$
$420$		0			0
$421$	−16.9507	+	29.3594i	−0.826124	+	1.43089i	0.0749327	+	0.997189i	$0.476126\pi$
$421$	−16.9507	+	29.3594i	−0.826124	+	1.43089i	−0.901057	+	0.433701i	$0.857208\pi$
$422$			1.34014i			0.0652368i
$423$	−5.48445	−	2.53439i	−0.266663	−	0.123226i
$424$	−46.3303			−2.25000
$425$	−3.24286	+	5.61679i	−0.157302	+	0.272454i
$426$	−43.0836	+	13.6662i	−2.08741	+	0.662128i
$427$		0			0
$428$	−11.3111	+	6.53048i	−0.546744	+	0.315663i
$429$	2.36422	+	2.15890i	0.114146	+	0.104233i
$430$	20.3421	+	11.7445i	0.980983	+	0.566371i
$431$			14.1239i			0.680324i	0.940367	+	0.340162i	$0.110482\pi$
$431$			14.1239i			0.680324i	−0.940367	+	0.340162i	$0.889518\pi$
$432$	3.85832	+	9.17980i	0.185633	+	0.441664i
$433$			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
$437$	−4.30546	−	7.45728i	−0.205958	−	0.356730i
$438$	1.60424	−	0.508865i	0.0766533	−	0.0243145i
$439$	−10.1520	−	5.86126i	−0.484529	−	0.279743i	0.237773	−	0.971321i	$-0.423583\pi$
$439$	−10.1520	−	5.86126i	−0.484529	−	0.279743i	−0.722302	+	0.691578i	$0.756916\pi$
$440$	−4.17128			−0.198858
$441$		0			0
$442$	13.3191			0.633526
$443$	−6.17796	−	3.56685i	−0.293524	−	0.169466i	0.346006	−	0.938232i	$-0.387538\pi$
$443$	−6.17796	−	3.56685i	−0.293524	−	0.169466i	−0.639530	+	0.768766i	$0.720871\pi$
$444$	7.25860	−	33.0115i	0.344478	−	1.56666i
$445$	3.63925	+	6.30337i	0.172517	+	0.298808i
$446$	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	$0.0238656\pi$
$449$			3.17445i			0.149811i	−0.997191	+	0.0749057i	$0.976134\pi$
$450$	27.9108	+	39.5688i	1.31573	+	1.86529i
$451$			0.0439306i			0.00206861i
$452$	−6.82100	−	3.93811i	−0.320833	−	0.185233i
$453$	38.1545	−	12.1027i	1.79266	−	0.568632i
$454$	34.7406	−	20.0575i	1.63045	−	0.941344i
$455$		0			0
$456$	−6.23786	−	5.69613i	−0.292114	−	0.266746i
$457$	−12.0745	+	20.9137i	−0.564821	+	0.978299i	0.432245	+	0.901756i	$0.357722\pi$
$457$	−12.0745	+	20.9137i	−0.564821	+	0.978299i	−0.997066	+	0.0765431i	$0.975612\pi$
$458$	−46.4150			−2.16883
$459$	2.99545	−	3.94597i	0.139816	−	0.184182i
$460$			85.1502i			3.97015i
$461$	6.87281	−	11.9041i	0.320099	−	0.554427i	−0.660409	−	0.750906i	$-0.729617\pi$
$461$	6.87281	−	11.9041i	0.320099	−	0.554427i	0.980508	+	0.196478i	$0.0629505\pi$
$462$		0			0
$463$	10.3157	+	17.8673i	0.479411	+	0.830364i	0.999721	−	0.0236135i	$-0.00751711\pi$
$463$	10.3157	+	17.8673i	0.479411	+	0.830364i	−0.520310	+	0.853977i	$0.674184\pi$
$464$	−6.58303	+	3.80071i	−0.305610	+	0.176444i
$465$	9.41899	+	29.6941i	0.436795	+	1.37703i
$466$	23.4151	−	40.5562i	1.08469	−	1.87873i
$467$	−0.931788			−0.0431180			−0.0215590	−	0.999768i	$-0.506863\pi$
$467$	−0.931788			−0.0431180			−0.0215590	+	0.999768i	$0.506863\pi$
$468$	26.8947	−	58.2007i	1.24321	−	2.69033i
$469$		0			0
$470$	−14.2170	−	8.20819i	−0.655781	−	0.378615i
$471$	11.0453	+	2.42866i	0.508942	+	0.111907i
$472$	5.52256	−	3.18845i	0.254196	−	0.146760i
$473$	0.783481	−	0.452343i	0.0360245	−	0.0207987i
$474$	−42.0107	−	9.23736i	−1.92962	−	0.424286i
$475$	−7.42932	−	4.28932i	−0.340881	−	0.196808i
$476$		0			0
$477$	35.7920	−	3.25617i	1.63880	−	0.149090i
$478$	46.5113			2.12738
$479$	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	$-0.0986690\pi$
$480$	−5.73499	−	18.0800i	−0.261765	−	0.825235i
$481$	−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
$485$		−	41.6746i		−	1.89234i
$486$	−17.3619	−	32.6593i	−0.787552	−	1.48146i
$487$	−34.3733			−1.55760			−0.778802	−	0.627270i	$-0.784172\pi$
$487$	−34.3733			−1.55760			−0.778802	+	0.627270i	$0.784172\pi$
$488$	5.74774	−	9.95538i	0.260188	−	0.450659i
$489$	−31.3675	−	28.6434i	−1.41849	−	1.29530i
$490$		0			0
$491$	−7.31048	+	4.22071i	−0.329917	+	0.190478i	−0.655804	−	0.754931i	$-0.727670\pi$
$491$	−7.31048	+	4.22071i	−0.329917	+	0.190478i	0.325887	+	0.945409i	$0.394337\pi$
$492$	0.838558	−	0.265992i	0.0378051	−	0.0119918i
$493$	3.27518	+	1.89093i	0.147507	+	0.0851631i
$494$			17.6172i			0.792634i
$495$	3.22248	−	0.293165i	0.144840	−	0.0131768i
$496$			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	$0.751144\pi$
$500$	11.2393	+	19.4671i	0.502638	+	0.870595i
$501$	5.20647	−	23.6786i	0.232608	−	1.05788i
$502$	−2.00567	−	1.15797i	−0.0895175	−	0.0516830i
$503$	−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
$506$	4.40509	+	2.54328i	0.195830	+	0.113063i
$507$	−35.7669	+	11.3453i	−1.58847	+	0.503863i
$508$	4.26453	+	7.38638i	0.189208	+	0.327717i
$509$	−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
$513$	5.21933	+	3.96208i	0.230439	+	0.174930i
$514$		−	29.0398i		−	1.28089i
$515$	53.6073	+	30.9502i	2.36222	+	1.36383i
$516$	−13.3783	−	12.2164i	−0.588945	−	0.537798i
$517$	−0.547571	+	0.316140i	−0.0240821	+	0.0139038i
$518$		0			0
$519$	17.9949	−	5.70799i	0.789887	−	0.250553i
$520$	39.1118	−	67.7436i	1.71517	−	2.97075i
$521$	19.8622			0.870177			0.435088	−	0.900388i	$-0.356717\pi$
$521$	19.8622			0.870177			0.435088	+	0.900388i	$0.356717\pi$
$522$	23.0727	−	16.2749i	1.00987	−	0.712334i
$523$			7.75356i			0.339039i	0.985527	+	0.169520i	$0.0542216\pi$
$523$			7.75356i			0.339039i	−0.985527	+	0.169520i	$0.945778\pi$
$524$	−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
$528$	1.01778	+	0.223791i	0.0442933	+	0.00973926i
$529$	11.8118	−	20.4587i	0.513559	−	0.889509i
$530$	97.6547			4.24185
$531$	−4.04231	+	2.85134i	−0.175421	+	0.123738i
$532$		0			0
$533$	−0.713455	−	0.411913i	−0.0309032	−	0.0178419i
$534$	−2.63258	−	8.29940i	−0.113923	−	0.359150i
$535$	10.7053	−	6.18072i	0.462831	−	0.267216i
$536$	6.25670	−	3.61231i	0.270248	−	0.156028i
$537$	−1.86807	+	2.04574i	−0.0806134	+	0.0882801i
$538$	44.5076	+	25.6965i	1.91886	+	1.10785i
$539$		0			0
$540$	−25.1075	−	59.7364i	−1.08046	−	2.57065i
$541$	−18.0923			−0.777850			−0.388925	−	0.921269i	$-0.627153\pi$
$541$	−18.0923			−0.777850			−0.388925	+	0.921269i	$0.627153\pi$
$542$	24.5195	−	42.4691i	1.05320	−	1.82420i
$543$	−20.4494	+	22.3942i	−0.877566	+	0.961027i
$544$	−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	−0.782301	−	0.622901i	$-0.785954\pi$
$547$	3.46839	−	6.00743i	0.148298	−	0.256859i	0.930598	+	0.366042i	$0.119287\pi$
$548$			37.1134i			1.58541i
$549$	−3.74068	+	8.09490i	−0.159648	+	0.345482i
$550$	5.06749			0.216079
$551$	−2.50113	+	4.33208i	−0.106552	+	0.184553i
$552$	9.82221	−	44.6706i	0.418061	−	1.90131i
$553$		0			0
$554$	−57.3092	+	33.0875i	−2.43483	+	1.40575i
$555$	−6.86984	+	31.2434i	−0.291608	+	1.32621i
$556$	16.5725	+	9.56815i	0.702831	+	0.405780i
$557$		−	15.8186i		−	0.670257i	−0.942172	−	0.335128i	$-0.891220\pi$
$557$		−	15.8186i		−	0.670257i	0.942172	−	0.335128i	$-0.108780\pi$
$558$	−3.37631	−	37.1126i	−0.142931	−	1.57110i
$559$			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
$563$	−16.0561	−	27.8101i	−0.676686	−	1.17205i	−0.975973	−	0.217891i	$-0.930082\pi$
$563$	−16.0561	−	27.8101i	−0.676686	−	1.17205i	0.299287	−	0.954163i	$-0.403251\pi$
$564$	9.35000	+	8.53800i	0.393706	+	0.359515i
$565$	6.45568	+	3.72719i	0.271593	+	0.156804i
$566$	41.8376			1.75857
$567$		0			0
$568$	42.5333			1.78466
$569$	31.3107	+	18.0772i	1.31261	+	0.757837i	0.982528	−	0.186114i	$-0.0595894\pi$
$569$	31.3107	+	18.0772i	1.31261	+	0.757837i	0.330084	+	0.943951i	$0.392923\pi$
$570$	13.1481	+	12.0063i	0.550714	+	0.502887i
$571$	−14.1792	−	24.5590i	−0.593380	−	1.02776i	−0.993773	−	0.111421i	$-0.964460\pi$
$571$	−14.1792	−	24.5590i	−0.593380	−	1.02776i	0.400393	−	0.916343i	$-0.368873\pi$
$572$	−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
$576$	3.09749	+	34.0478i	0.129062	+	1.41866i
$577$		−	41.9836i		−	1.74780i	−0.486105	−	0.873901i	$-0.661583\pi$
$577$		−	41.9836i		−	1.74780i	0.486105	−	0.873901i	$-0.338417\pi$
$578$	33.0646	+	19.0899i	1.37531	+	0.794034i
$579$	4.04838	−	18.4117i	0.168245	−	0.765163i
$580$	42.8383	−	24.7327i	1.77876	−	1.02697i
$581$		0			0
$582$	−10.7060	+	48.6902i	−0.443780	+	2.01827i
$583$	1.88060	−	3.25729i	0.0778864	−	0.134903i
$584$	−1.58375			−0.0655359
$585$	−25.4543	+	55.0835i	−1.05241	+	2.27742i
$586$		−	66.9767i		−	2.76678i
$587$	9.79227	−	16.9607i	0.404170	−	0.700043i	−0.590054	−	0.807364i	$-0.700894\pi$
$587$	9.79227	−	16.9607i	0.404170	−	0.700043i	0.994225	+	0.107320i	$0.0342270\pi$
$588$		0			0
$589$	3.30108	+	5.71764i	0.136019	+	0.235591i
$590$	−11.6404	+	6.72059i	−0.479228	+	0.276682i
$591$	−7.60073	+	8.32359i	−0.312652	+	0.342387i
$592$	−5.15121	+	8.92216i	−0.211713	+	0.366698i
$593$	19.9275			0.818324			0.409162	−	0.912462i	$-0.365821\pi$
$593$	19.9275			0.818324			0.409162	+	0.912462i	$0.365821\pi$
$594$	−3.84027	−	0.485327i	−0.157568	−	0.0199132i
$595$		0			0
$596$	57.4072	+	33.1441i	2.35149	+	1.35763i
$597$	20.7981	−	22.7761i	0.851211	−	0.932165i
$598$	−82.6083	+	47.6939i	−3.37810	+	1.95035i
$599$	0.0267639	−	0.0154521i	0.00109354	−	0.000631357i	−0.499453	−	0.866341i	$-0.666466\pi$
$599$	0.0267639	−	0.0154521i	0.00109354	−	0.000631357i	0.500547	+	0.865710i	$0.333132\pi$
$600$	−13.7772	−	43.4335i	−0.562450	−	1.77317i
$601$	25.8633	+	14.9322i	1.05499	+	0.609097i	0.924041	−	0.382293i	$-0.124865\pi$
$601$	25.8633	+	14.9322i	1.05499	+	0.609097i	0.130945	+	0.991390i	$0.458199\pi$
$602$		0			0
$603$	−4.57967	+	3.23038i	−0.186499	+	0.131551i
$604$	−83.8876			−3.41334
$605$	−18.7258	+	32.4341i	−0.761314	+	1.31863i
$606$	−50.2562	−	11.0504i	−2.04152	−	0.448891i
$607$	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
$611$		−	11.8571i		−	0.479687i
$612$	−8.48419	+	5.98453i	−0.342953	+	0.241910i
$613$	−4.46292			−0.180256			−0.0901278	−	0.995930i	$-0.528728\pi$
$613$	−4.46292			−0.180256			−0.0901278	+	0.995930i	$0.528728\pi$
$614$	−10.1631	+	17.6029i	−0.410148	+	0.710396i
$615$	−0.793646	+	0.251745i	−0.0320029	+	0.0101514i
$616$		0			0
$617$	26.9685	−	15.5703i	1.08571	−	0.626835i	0.153279	−	0.988183i	$-0.451017\pi$
$617$	26.9685	−	15.5703i	1.08571	−	0.626835i	0.932431	+	0.361348i	$0.117683\pi$
$618$	−54.6807	−	49.9319i	−2.19958	−	2.00856i
$619$	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	$0.658282\pi$
$620$		−	65.2862i		−	2.62196i
$621$	−4.44853	+	35.2001i	−0.178513	+	1.41253i
$622$		−	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
$626$	31.4402	+	54.4560i	1.25660	+	2.17650i
$627$	0.653672	−	0.207346i	0.0261052	−	0.00828058i
$628$	−20.5256	−	11.8505i	−0.819060	−	0.472884i
$629$	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	$0.695010\pi$
$632$	35.0544	+	20.2387i	1.39439	+	0.805051i
$633$	−0.210085	+	0.955447i	−0.00835011	+	0.0379756i
$634$	10.2805	+	17.8064i	0.408293	+	0.707183i
$635$	−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
$639$	−32.8587	+	2.98932i	−1.29987	+	0.118255i
$640$			70.9936i			2.80627i
$641$	2.41325	+	1.39329i	0.0953176	+	0.0550316i	0.546901	−	0.837197i	$-0.315807\pi$
$641$	2.41325	+	1.39329i	0.0953176	+	0.0550316i	−0.451584	+	0.892229i	$0.649141\pi$
$642$	−14.0953	+	4.47104i	−0.556296	+	0.176458i
$643$	−0.324584	+	0.187399i	−0.0128004	+	0.00739029i	−0.506387	−	0.862307i	$-0.669019\pi$
$643$	−0.324584	+	0.187399i	−0.0128004	+	0.00739029i	0.493586	+	0.869697i	$0.335686\pi$
$644$		0			0
$645$	12.6617	+	11.5621i	0.498555	+	0.455258i
$646$	1.42644	−	2.47066i	0.0561224	−	0.0972069i
$647$	50.3216			1.97834			0.989172	−	0.146758i	$-0.0468837\pi$
$647$	50.3216			1.97834			0.989172	+	0.146758i	$0.0468837\pi$
$648$	6.28094	+	34.2345i	0.246738	+	1.34486i
$649$			0.517690i			0.0203211i
$650$	−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	−0.902373	−	0.430955i	$-0.858177\pi$
$653$	−25.0515	+	14.4635i	−0.980342	+	0.566000i	−0.0779684	+	0.996956i	$0.524843\pi$
$654$	−8.15409	−	25.7064i	−0.318850	−	1.00520i
$655$	16.3046	−	28.2404i	0.637074	−	1.10344i
$656$	−0.268147			−0.0104694
$657$	1.22351	−	0.111308i	0.0477336	−	0.00434255i
$658$		0			0
$659$	−22.8449	−	13.1895i	−0.889910	−	0.513790i	−0.0159971	−	0.999872i	$-0.505092\pi$
$659$	−22.8449	−	13.1895i	−0.889910	−	0.513790i	−0.873913	+	0.486082i	$0.838426\pi$
$660$	−6.62310	−	1.45629i	−0.257804	−	0.0566861i
$661$	10.0533	−	5.80428i	0.391028	−	0.225760i	−0.291577	−	0.956547i	$-0.594180\pi$
$661$	10.0533	−	5.80428i	0.391028	−	0.225760i	0.682606	+	0.730787i	$0.260847\pi$
$662$	39.7373	−	22.9423i	1.54443	−	0.891678i
$663$	9.49584	+	2.08795i	0.368788	+	0.0810894i
$664$	26.7999	+	15.4729i	1.04004	+	0.600466i
$665$		0			0
$666$	16.0527	−	34.7382i	0.622028	−	1.34608i
$667$	−27.0846			−1.04872
$668$	−25.4046	+	44.0020i	−0.982933	+	1.70249i
$669$	4.60342	+	14.5126i	0.177978	+	0.561090i
$670$	−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	0.468592	+	0.883415i	$0.344761\pi$
$673$	−13.7692	+	23.8490i	−0.530764	+	0.919310i	−0.999356	+	0.0358949i	$0.988572\pi$
$674$			59.0582i			2.27484i
$675$	13.6960	+	32.5859i	0.527159	+	1.25423i
$676$	78.6382			3.02454
$677$	2.31563	−	4.01080i	0.0889970	−	0.154147i	−0.818090	−	0.575090i	$-0.804967\pi$
$677$	2.31563	−	4.01080i	0.0889970	−	0.154147i	0.907087	+	0.420942i	$0.138300\pi$
$678$	−6.58495	−	6.01307i	−0.252893	−	0.230931i
$679$		0			0
$680$	−10.9702	+	6.33365i	−0.420688	+	0.242884i
$681$	27.9125	−	8.85387i	1.06961	−	0.339281i
$682$	−3.37747	−	1.94998i	−0.129330	−	0.0746686i
$683$		−	13.8792i		−	0.531072i	−0.964101	−	0.265536i	$-0.914451\pi$
$683$		−	13.8792i		−	0.531072i	0.964101	−	0.265536i	$-0.0855490\pi$
$684$	−7.91573	−	11.2220i	−0.302665	−	0.429085i
$685$		−	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
$689$	35.2667	+	61.0837i	1.34355	+	2.32710i
$690$	−20.7032	+	94.1563i	−0.788157	+	3.58447i
$691$	−19.6168	−	11.3258i	−0.746258	−	0.430852i	0.0780825	−	0.996947i	$-0.475120\pi$
$691$	−19.6168	−	11.3258i	−0.746258	−	0.430852i	−0.824340	+	0.566095i	$0.808454\pi$
$692$	−39.5640			−1.50400
$693$		0			0
$694$	−13.7464			−0.521805
$695$	−15.6849	−	9.05569i	−0.594963	−	0.343502i
$696$	−25.3263	+	8.03353i	−0.959991	+	0.304510i
$697$	0.0667040	+	0.115535i	0.00252660	+	0.00437619i
$698$	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	$-0.900094\pi$
$701$		−	16.3485i		−	0.617474i	0.951147	−	0.308737i	$-0.0999063\pi$
$702$	43.8901	−	57.8173i	1.65653	−	2.18217i
$703$			6.77968i			0.255701i
$704$	3.09855	+	1.78895i	0.116781	+	0.0674236i
$705$	−8.84923	−	8.08072i	−0.333281	−	0.304337i
$706$	−36.4639	+	21.0525i	−1.37234	+	0.792320i
$707$		0			0
$708$	9.88180	−	3.13452i	0.371381	−	0.117802i
$709$	−7.65356	+	13.2564i	−0.287435	+	0.497853i	−0.973197	−	0.229974i	$-0.926136\pi$
$709$	−7.65356	+	13.2564i	−0.287435	+	0.497853i	0.685761	+	0.727826i	$0.259469\pi$
$710$	−89.6514			−3.36456
$711$	−28.5034	−	13.1715i	−1.06896	−	0.493970i
$712$			8.19340i			0.307061i
$713$	−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
$717$	33.1601	+	7.29128i	1.23839	+	0.272298i
$718$	−27.1913	+	47.0966i	−1.01477	+	1.75763i
$719$	−14.9272			−0.556690			−0.278345	−	0.960481i	$-0.589786\pi$
$719$	−14.9272			−0.556690			−0.278345	+	0.960481i	$0.589786\pi$
$720$	1.78944	+	19.6696i	0.0666885	+	0.733043i
$721$		0			0
$722$	−35.7743	−	20.6543i	−1.33138	−	0.768673i
$723$	8.35503	+	26.3399i	0.310727	+	0.979590i
$724$	55.0404	−	31.7776i	2.04556	−	1.18101i
$725$	−23.3680	+	13.4915i	−0.867866	+	0.501063i
$726$	30.2104	−	33.0836i	1.12121	−	1.22785i
$727$	−4.62968	−	2.67295i	−0.171705	−	0.0991341i	0.411684	−	0.911326i	$-0.364941\pi$
$727$	−4.62968	−	2.67295i	−0.171705	−	0.0991341i	−0.583390	+	0.812192i	$0.698274\pi$
$728$		0			0
$729$	−7.25834	−	26.0061i	−0.268827	−	0.963188i
$730$	3.33821			0.123553
$731$	1.37367	−	2.37927i	0.0508070	−	0.0880004i
$732$	12.6018	−	13.8003i	0.465778	−	0.510075i
$733$	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
$737$			0.586509i			0.0216044i
$738$	0.991923	−	0.0902400i	0.0365132	−	0.00332178i
$739$	45.6861			1.68059			0.840295	−	0.542130i	$-0.182382\pi$
$739$	45.6861			1.68059			0.840295	+	0.542130i	$0.182382\pi$
$740$	33.5209	−	58.0598i	1.23225	−	2.13432i
$741$	−2.76173	+	12.5601i	−0.101455	+	0.461408i
$742$		0			0
$743$	−25.0448	+	14.4596i	−0.918804	+	0.530472i	−0.883253	−	0.468896i	$-0.844652\pi$
$743$	−25.0448	+	14.4596i	−0.918804	+	0.530472i	−0.0355508	+	0.999368i	$0.511319\pi$
$744$	−7.53087	+	34.2498i	−0.276095	+	1.25566i
$745$	−54.3326	−	31.3689i	−1.99059	−	1.14927i
$746$			22.6018i			0.827510i
$747$	−21.7915	−	10.0699i	−0.797309	−	0.368439i
$748$			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	$-0.465289\pi$
$752$	−1.92968	−	3.34230i	−0.0703682	−	0.121881i
$753$	−1.24841	−	1.13999i	−0.0454946	−	0.0415436i
$754$	47.9887	+	27.7063i	1.74765	+	1.00900i
$755$	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	$0.666595\pi$
$758$	28.4329	+	16.4157i	1.03273	+	0.596246i
$759$	2.74191	+	2.50379i	0.0995249	+	0.0908816i
$760$	−8.37751	−	14.5103i	−0.303884	−	0.526343i
$761$	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
$765$	8.02979	−	5.66401i	0.290317	−	0.204783i
$766$		−	50.3780i		−	1.82023i
$767$	−8.40755	−	4.85410i	−0.303579	−	0.175271i
$768$	9.76019	−	44.3885i	0.352191	−	1.60173i
$769$	33.4505	−	19.3126i	1.20626	−	0.696432i	0.244316	−	0.969696i	$-0.421436\pi$
$769$	33.4505	−	19.3126i	1.20626	−	0.696432i	0.961939	+	0.273264i	$0.0881031\pi$
$770$		0			0
$771$	4.55239	−	20.7039i	0.163950	−	0.745632i
$772$	−19.7537	+	34.2145i	−0.710953	+	1.23141i
$773$	−34.3507			−1.23551			−0.617754	−	0.786371i	$-0.711957\pi$
$773$	−34.3507			−1.23551			−0.617754	+	0.786371i	$0.711957\pi$
$774$	−11.8230	−	16.7613i	−0.424968	−	0.602472i
$775$			35.6132i			1.27926i
$776$	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
$780$	85.7521	−	93.9075i	3.07042	−	3.36243i
$781$	−1.72647	+	2.99034i	−0.0617781	+	0.107003i
$782$	15.4468			0.552377
$783$	19.0010	−	7.98620i	0.679040	−	0.285404i
$784$		0			0
$785$	19.4263	+	11.2158i	0.693353	+	0.400308i
$786$	−26.3042	+	28.8059i	−0.938240	+	1.02747i
$787$	−20.3343	+	11.7400i	−0.724839	+	0.418486i	−0.816531	−	0.577301i	$-0.804106\pi$
$787$	−20.3343	+	11.7400i	−0.724839	+	0.418486i	0.0916921	+	0.995787i	$0.470772\pi$
$788$	20.4577	−	11.8113i	0.728776	−	0.420759i
$789$	2.20378	+	6.94758i	0.0784567	+	0.247340i
$790$	−73.8874	−	42.6589i	−2.62880	−	1.51774i
$791$		0			0
$792$	3.30655	+	1.52797i	0.117493	+	0.0542940i
$793$	−17.5007			−0.621470
$794$	18.6074	−	32.2289i	0.660350	−	1.14376i
$795$	69.6227	+	15.3087i	2.46926	+	0.542944i
$796$	−55.9791	+	32.3196i	−1.98413	+	1.14554i
$797$	−5.82399	−	10.0875i	−0.206296	−	0.357316i	0.744249	−	0.667903i	$-0.232808\pi$
$797$	−5.82399	−	10.0875i	−0.206296	−	0.357316i	−0.950545	+	0.310587i	$0.899474\pi$
$798$		0			0
$799$	−0.960052	+	1.66286i	−0.0339642	+	0.0588277i
$800$		−	21.6840i		−	0.766645i
$801$	−0.575846	−	6.32973i	−0.0203465	−	0.223650i
$802$	−25.5978			−0.903889
$803$	0.0642859	−	0.111347i	0.00226860	−	0.00392933i
$804$	11.1954	−	3.55120i	0.394833	−	0.125241i
$805$		0			0
$806$	63.3373	−	36.5678i	2.23096	−	1.28805i
$807$	27.7033	+	25.2974i	0.975203	+	0.890512i
$808$	41.9346	+	24.2109i	1.47525	+	0.851738i
$809$			15.9029i			0.559117i	0.960129	+	0.279559i	$0.0901881\pi$
$809$			15.9029i			0.559117i	−0.960129	+	0.279559i	$0.909812\pi$
$810$	−13.2389	−	72.1592i	−0.465168	−	2.53542i
$811$			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
$815$	−42.1269	−	72.9660i	−1.47564	−	2.55589i
$816$	3.01651	−	0.956840i	0.105599	−	0.0334961i
$817$	3.14705	+	1.81695i	0.110101	+	0.0635671i
$818$	46.5384			1.62718
$819$		0			0
$820$	1.74493			0.0609357
$821$	−0.113440	−	0.0654949i	−0.00395910	−	0.00228579i	0.498019	−	0.867166i	$-0.334061\pi$
$821$	−0.113440	−	0.0654949i	−0.00395910	−	0.00228579i	−0.501978	+	0.864880i	$0.667394\pi$
$822$	−9.02365	+	41.0388i	−0.314736	+	1.43139i
$823$	−23.0144	−	39.8621i	−0.802231	−	1.38950i	−0.918145	−	0.396245i	$-0.870313\pi$
$823$	−23.0144	−	39.8621i	−0.802231	−	1.38950i	0.115914	−	0.993259i	$-0.463020\pi$
$824$	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	$0.249329\pi$
$827$			40.5836i			1.41123i	−0.708595	+	0.705615i	$0.750671\pi$
$828$	31.1911	−	67.4981i	1.08397	−	2.34572i
$829$			30.1296i			1.04645i	0.852196	+	0.523223i	$0.175270\pi$
$829$			30.1296i			1.04645i	−0.852196	+	0.523223i	$0.824730\pi$
$830$	−56.4887	−	32.6137i	−1.96075	−	1.13204i
$831$	−46.0454	+	14.6056i	−1.59730	+	0.506664i
$832$	−58.1068	+	33.5480i	−2.01449	+	1.16307i
$833$		0			0
$834$	15.9990	+	14.6095i	0.553999	+	0.505887i
$835$	24.0439	−	41.6453i	0.832075	−	1.44120i
$836$	−1.43718			−0.0497060
$837$	3.41077	−	26.9886i	0.117893	−	0.932863i
$838$			41.9419i			1.44886i
$839$	5.81551	−	10.0728i	0.200774	−	0.347750i	−0.748004	−	0.663694i	$-0.768988\pi$
$839$	5.81551	−	10.0728i	0.200774	−	0.347750i	0.948778	+	0.315944i	$0.102321\pi$
$840$		0			0
$841$	−6.63302	−	11.4887i	−0.228725	−	0.396163i
$842$	69.6622	−	40.2195i	2.40072	−	1.38606i
$843$	−10.1093	−	31.8702i	−0.348182	−	1.09767i
$844$	1.02509	−	1.77551i	0.0352851	−	0.0611156i
$845$	−74.4264			−2.56035
$846$	8.26302	+	11.7144i	0.284089	+	0.402749i
$847$		0			0
$848$	19.8821	+	11.4789i	0.682754	+	0.394188i
$849$	29.8280	+	6.55862i	1.02370	+	0.225091i
$850$	13.3272	−	7.69446i	0.457119	−	0.263918i
$851$	−31.7905	+	18.3542i	−1.08976	+	0.629175i
$852$	67.5338	+	14.8494i	2.31367	+	0.508732i
$853$	20.6854	+	11.9427i	0.708254	+	0.408911i	0.810414	−	0.585857i	$-0.199242\pi$
$853$	20.6854	+	11.9427i	0.708254	+	0.408911i	−0.102160	+	0.994768i	$0.532575\pi$
$854$		0			0
$855$	7.49177	+	10.6210i	0.256213	+	0.363230i
$856$	13.9153			0.475614
$857$	−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	$0.964929\pi$
$858$	−2.29688	−	7.24108i	−0.0784141	−	0.247206i
$859$	−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
$863$			33.4052i			1.13713i	0.822639	+	0.568564i	$0.192501\pi$
$863$			33.4052i			1.13713i	−0.822639	+	0.568564i	$0.807499\pi$
$864$	−2.07673	+	16.4327i	−0.0706519	+	0.559051i
$865$	37.4450			1.27317
$866$	10.7970	−	18.7010i	0.366898	−	0.635485i
$867$	20.5807	+	18.7934i	0.698959	+	0.638258i
$868$		0			0
$869$	−2.84579	+	1.64302i	−0.0965369	+	0.0557356i
$870$	53.3826	−	16.9330i	1.80984	−	0.574083i
$871$	−9.52520	−	5.49938i	−0.322749	−	0.186339i
$872$			25.3781i			0.859410i
$873$	−15.2657	+	33.0352i	−0.516666	+	1.11807i
$874$			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	$0.446569\pi$
$878$	13.9073	+	24.0881i	0.469347	+	0.812933i
$879$	10.4995	−	47.7509i	0.354140	−	1.61060i
$880$	1.79005	+	1.03349i	0.0603426	+	0.0348388i
$881$	−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	$0.295667\pi$
$884$	−17.6462	−	10.1880i	−0.593504	−	0.342660i
$885$	−9.35255	+	2.96664i	−0.314382	+	0.0997224i
$886$	8.46321	+	14.6587i	0.284327	+	0.492469i
$887$	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
$891$	−2.66183	−	0.948028i	−0.0891748	−	0.0317601i
$892$		−	31.9078i		−	1.06835i
$893$	−2.19946	−	1.26986i	−0.0736021	−	0.0424942i
$894$	55.4205	+	50.6075i	1.85354	+	1.69257i
$895$	−4.75872	+	2.74745i	−0.159066	+	0.0918370i
$896$		0			0
$897$	−66.3721	+	21.0533i	−2.21610	+	0.702949i
$898$	3.76607	−	6.52302i	0.125675	−	0.217676i
$899$	20.7663			0.692594
$900$	−6.71149	−	73.7730i	−0.223716	−	2.45910i
$901$		−	11.4220i		−	0.380521i
$902$	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
$906$	−92.7602	−	20.3962i	−3.08175	−	0.677619i
$907$	−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	$0.954482\pi$
$908$	−61.3692			−2.03661
$909$	−34.0977	−	15.7567i	−1.13095	−	0.522616i
$910$		0			0
$911$	−18.8068	−	10.8581i	−0.623098	−	0.359746i	0.154976	−	0.987918i	$-0.450470\pi$
$911$	−18.8068	−	10.8581i	−0.623098	−	0.359746i	−0.778074	+	0.628172i	$0.783803\pi$
$912$	1.26561	+	3.98993i	0.0419086	+	0.132120i
$913$	−2.17567	+	1.25613i	−0.0720043	+	0.0415717i
$914$	49.6227	−	28.6497i	1.64137	−	0.947647i
$915$	−11.9269	+	13.0612i	−0.394292	+	0.431790i
$916$	61.4940	+	35.5036i	2.03182	+	1.17307i
$917$		0			0
$918$	−10.8366	+	4.55468i	−0.357661	+	0.150327i
$919$	34.2046			1.12831			0.564153	−	0.825671i	$-0.309203\pi$
$919$	34.2046			1.12831			0.564153	+	0.825671i	$0.309203\pi$
$920$	45.3598	−	78.5656i	1.49547	−	2.59023i
$921$	−10.0052	+	10.9568i	−0.329684	+	0.361038i
$922$	−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
$926$		−	48.9529i		−	1.60869i
$927$	−31.1569	−	44.1708i	−1.02333	−	1.45076i
$928$	−12.6441			−0.415062
$929$	23.4757	−	40.6611i	0.770213	−	1.33405i	−0.167233	−	0.985917i	$-0.553483\pi$
$929$	23.4757	−	40.6611i	0.770213	−	1.33405i	0.937446	−	0.348131i	$-0.113184\pi$
$930$	15.8735	−	72.1914i	0.520513	−	2.36725i
$931$		0			0
$932$	−62.0442	+	35.8213i	−2.03233	+	1.17336i
$933$	7.20050	−	32.7472i	0.235734	−	1.07210i
$934$	1.91469	+	1.10545i	0.0626505	+	0.0361713i
$935$		−	1.02836i		−	0.0336309i
$936$	−55.8187	+	39.3731i	−1.82449	+	1.28695i
$937$		−	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
$941$	0.727044	+	1.25928i	0.0237009	+	0.0410512i	0.877633	−	0.479334i	$-0.159122\pi$
$941$	0.727044	+	1.25928i	0.0237009	+	0.0410512i	−0.853932	+	0.520385i	$0.825788\pi$
$942$	−19.8152	−	18.0944i	−0.645615	−	0.589547i
$943$	−0.827428	−	0.477716i	−0.0269448	−	0.0155566i
$944$	−3.15992			−0.102847
$945$		0			0
$946$	−2.14658			−0.0697914
$947$	−36.9596	−	21.3386i	−1.20102	−	0.693412i	−0.240241	−	0.970713i	$-0.577227\pi$
$947$	−36.9596	−	21.3386i	−1.20102	−	0.693412i	−0.960783	+	0.277301i	$0.910560\pi$
$948$	48.5931	+	44.3730i	1.57823	+	1.44117i
$949$	1.20555	+	2.08807i	0.0391338	+	0.0677817i
$950$	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	$0.0560574\pi$
$953$			10.8171i			0.350401i	−0.984533	+	0.175200i	$0.943943\pi$
$954$	−77.4104	−	35.7716i	−2.50625	−	1.15815i
$955$			55.1833i			1.78569i
$956$	−61.6216	−	35.5773i	−1.99299	−	1.15065i
$957$	0.463218	−	2.10668i	0.0149737	−	0.0680992i
$958$	−66.5902	+	38.4458i	−2.15143	+	1.24213i
$959$		0			0
$960$	−14.5627	+	66.2298i	−0.470008	+	2.13756i
$961$	−1.79596	+	3.11070i	−0.0579342	+	0.100345i
$962$	75.1022			2.42139
$963$	−10.7501	+	0.977988i	−0.346417	+	0.0315152i
$964$		−	57.9115i		−	1.86521i
$965$	18.6958	−	32.3820i	0.601838	−	1.04241i
$966$		0			0
$967$	−22.4942	−	38.9611i	−0.723365	−	1.25290i	−0.959643	−	0.281219i	$-0.909261\pi$
$967$	−22.4942	−	38.9611i	−0.723365	−	1.25290i	0.236279	−	0.971685i	$-0.424072\pi$
$968$	−36.5111	+	21.0797i	−1.17351	+	0.677526i
$969$	1.40429	−	1.53784i	0.0451121	−	0.0494025i
$970$	−49.4415	+	85.6351i	−1.58747	+	2.74958i
$971$	6.80343			0.218332			0.109166	−	0.994024i	$-0.465182\pi$
$971$	6.80343			0.218332			0.109166	+	0.994024i	$0.465182\pi$
$972$	−1.97930	+	56.5499i	−0.0634860	+	1.81384i
$973$		0			0
$974$	70.6321	+	40.7795i	2.26320	+	1.30666i
$975$	−46.7772	+	51.2259i	−1.49807	+	1.64054i
$976$	−4.93315	+	2.84815i	−0.157906	+	0.0911672i
$977$	−29.2645	+	16.8959i	−0.936254	+	0.540546i	−0.888784	−	0.458326i	$-0.848449\pi$
$977$	−29.2645	+	16.8959i	−0.936254	+	0.540546i	−0.0474698	+	0.998873i	$0.515116\pi$
$978$	30.4740	+	96.0715i	0.974451	+	3.07203i
$979$	−0.576044	−	0.332579i	−0.0184104	−	0.0106293i
$980$		0			0
$981$	−1.78361	−	19.6056i	−0.0569464	−	0.625958i
$982$	20.0293			0.639160
$983$	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	$-0.102922\pi$
$984$	−0.915408	−	0.201281i	−0.0291821	−	0.00641660i
$985$	−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
$989$			19.6757i			0.625651i
$990$	−6.96953	−	3.22064i	−0.221506	−	0.102359i
$991$	0.600897			0.0190881			0.00954406	−	0.999954i	$-0.496962\pi$
$991$	0.600897			0.0190881			0.00954406	+	0.999954i	$0.496962\pi$
$992$	−8.34405	+	14.4523i	−0.264924	+	0.458861i
$993$	31.9271	−	10.1273i	1.01318	−	0.321381i
$994$		0			0
$995$	52.9810	−	30.5886i	1.67961	−	0.969723i
$996$	37.1505	+	33.9242i	1.17716	+	1.07493i
$997$	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	$0.388493\pi$
$998$		−	27.0682i		−	0.856829i
$999$	16.8904	−	22.2501i	0.534388	−	0.703960i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.o.e.146.3	✓	48
3.2	odd	2		1323.2.o.e.440.21		48
7.2	even	3		441.2.i.d.227.22		48
7.3	odd	6		441.2.s.d.362.22		48
7.4	even	3		441.2.s.d.362.21		48
7.5	odd	6		441.2.i.d.227.21		48
7.6	odd	2	inner	441.2.o.e.146.4	yes	48
9.4	even	3		1323.2.o.e.881.22		48
9.5	odd	6	inner	441.2.o.e.293.4	yes	48
21.2	odd	6		1323.2.i.d.521.24		48
21.5	even	6		1323.2.i.d.521.4		48
21.11	odd	6		1323.2.s.d.656.3		48
21.17	even	6		1323.2.s.d.656.4		48
21.20	even	2		1323.2.o.e.440.22		48
63.4	even	3		1323.2.i.d.1097.4		48
63.5	even	6		441.2.s.d.374.21		48
63.13	odd	6		1323.2.o.e.881.21		48
63.23	odd	6		441.2.s.d.374.22		48
63.31	odd	6		1323.2.i.d.1097.24		48
63.32	odd	6		441.2.i.d.68.3		48
63.40	odd	6		1323.2.s.d.962.3		48
63.41	even	6	inner	441.2.o.e.293.3	yes	48
63.58	even	3		1323.2.s.d.962.4		48
63.59	even	6		441.2.i.d.68.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.3		48	63.32	odd	6
441.2.i.d.68.4		48	63.59	even	6
441.2.i.d.227.21		48	7.5	odd	6
441.2.i.d.227.22		48	7.2	even	3
441.2.o.e.146.3	✓	48	1.1	even	1	trivial
441.2.o.e.146.4	yes	48	7.6	odd	2	inner
441.2.o.e.293.3	yes	48	63.41	even	6	inner
441.2.o.e.293.4	yes	48	9.5	odd	6	inner
441.2.s.d.362.21		48	7.4	even	3
441.2.s.d.362.22		48	7.3	odd	6
441.2.s.d.374.21		48	63.5	even	6
441.2.s.d.374.22		48	63.23	odd	6
1323.2.i.d.521.4		48	21.5	even	6
1323.2.i.d.521.24		48	21.2	odd	6
1323.2.i.d.1097.4		48	63.4	even	3
1323.2.i.d.1097.24		48	63.31	odd	6
1323.2.o.e.440.21		48	3.2	odd	2
1323.2.o.e.440.22		48	21.20	even	2
1323.2.o.e.881.21		48	63.13	odd	6
1323.2.o.e.881.22		48	9.4	even	3
1323.2.s.d.656.3		48	21.11	odd	6
1323.2.s.d.656.4		48	21.17	even	6
1323.2.s.d.962.3		48	63.40	odd	6
1323.2.s.d.962.4		48	63.58	even	3

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.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.05485 - 1.18637i) q^{2} +(-1.27902 - 1.16795i) q^{3} +(1.81495 + 3.14358i) q^{4} +(-1.71774 - 2.97522i) q^{5} +(1.24259 + 3.91735i) q^{6} -3.86732i q^{8} +(0.271802 + 2.98766i) q^{9} +O(q^{10})\)	\(q+(-2.05485 - 1.18637i) q^{2} +(-1.27902 - 1.16795i) q^{3} +(1.81495 + 3.14358i) q^{4} +(-1.71774 - 2.97522i) q^{5} +(1.24259 + 3.91735i) q^{6} -3.86732i q^{8} +(0.271802 + 2.98766i) q^{9} +8.15151i q^{10} +(0.271895 + 0.156979i) q^{11} +(1.35017 - 6.14048i) q^{12} +(-5.09882 + 2.94381i) q^{13} +(-1.27786 + 5.81160i) q^{15} +(-0.958178 + 1.65961i) q^{16} +0.953423 q^{17} +(2.98596 - 6.46167i) q^{18} +1.26109i q^{19} +(6.23523 - 10.7997i) q^{20} +(-0.372470 - 0.645137i) q^{22} +(-5.91336 + 3.41408i) q^{23} +(-4.51682 + 4.94639i) q^{24} +(-3.40128 + 5.89118i) q^{25} +13.9698 q^{26} +(3.14179 - 4.13874i) q^{27} +(3.43518 + 1.98330i) q^{29} +(9.52053 - 10.4260i) q^{30} +(4.53388 - 2.61764i) q^{31} +(-2.76057 + 1.59381i) q^{32} +(-0.164418 - 0.518338i) q^{33} +(-1.95915 - 1.13111i) q^{34} +(-8.89866 + 6.27688i) q^{36} +5.37604 q^{37} +(1.49612 - 2.59136i) q^{38} +(9.95973 + 2.18996i) q^{39} +(-11.5061 + 6.64306i) q^{40} +(0.0699627 + 0.121179i) q^{41} +(1.44078 - 2.49550i) q^{43} +1.13963i q^{44} +(8.42206 - 5.94070i) q^{45} +16.2014 q^{46} +(-1.00695 + 1.74409i) q^{47} +(3.16387 - 1.00358i) q^{48} +(13.9783 - 8.07035i) q^{50} +(-1.21945 - 1.11355i) q^{51} +(-18.5082 - 10.6857i) q^{52} -11.9799i q^{53} +(-11.3660 + 4.77718i) q^{54} -1.07860i q^{55} +(1.47289 - 1.61297i) q^{57} +(-4.70586 - 8.15079i) q^{58} +(0.824459 + 1.42801i) q^{59} +(-20.5885 + 6.53070i) q^{60} +(2.57423 + 1.48623i) q^{61} -12.4219 q^{62} +11.3961 q^{64} +(17.5169 + 10.1134i) q^{65} +(-0.277087 + 1.26017i) q^{66} +(0.934059 + 1.61784i) q^{67} +(1.73041 + 2.99717i) q^{68} +(11.5508 + 2.53980i) q^{69} +10.9981i q^{71} +(11.5542 - 1.05115i) q^{72} -0.409520i q^{73} +(-11.0470 - 6.37798i) q^{74} +(11.2309 - 3.56245i) q^{75} +(-3.96435 + 2.28882i) q^{76} +(-17.8677 - 16.3160i) q^{78} +(-5.23325 + 9.06426i) q^{79} +6.58361 q^{80} +(-8.85225 + 1.62411i) q^{81} -0.332007i q^{82} +(-4.00094 + 6.92984i) q^{83} +(-1.63774 - 2.83664i) q^{85} +(-5.92117 + 3.41859i) q^{86} +(-2.07729 - 6.54880i) q^{87} +(0.607087 - 1.05151i) q^{88} -2.11862 q^{89} +(-24.3540 + 2.21560i) q^{90} +(-21.4649 - 12.3927i) q^{92} +(-8.85620 - 1.94731i) q^{93} +(4.13828 - 2.38924i) q^{94} +(3.75202 - 2.16623i) q^{95} +(5.39232 + 1.18567i) q^{96} +(10.5054 + 6.06531i) q^{97} +(-0.395098 + 0.854998i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4} + 16 q^{9}+O(q^{10}) \) 48 * q + 24 * q^4 + 16 * q^9	\( 48 q + 24 q^{4} + 16 q^{9} - 24 q^{11} - 40 q^{15} - 24 q^{16} - 16 q^{18} - 48 q^{23} - 24 q^{25} - 24 q^{30} + 120 q^{32} - 8 q^{36} + 88 q^{39} + 48 q^{50} + 24 q^{51} + 80 q^{57} - 96 q^{60} - 48 q^{64} + 120 q^{65} + 56 q^{72} - 168 q^{74} - 88 q^{78} - 24 q^{79} - 96 q^{81} - 24 q^{85} + 24 q^{86} - 144 q^{92} - 32 q^{93} + 96 q^{95} - 72 q^{99}+O(q^{100}) \) 48 * q + 24 * q^4 + 16 * q^9 - 24 * q^11 - 40 * q^15 - 24 * q^16 - 16 * q^18 - 48 * q^23 - 24 * q^25 - 24 * q^30 + 120 * q^32 - 8 * q^36 + 88 * q^39 + 48 * q^50 + 24 * q^51 + 80 * q^57 - 96 * q^60 - 48 * q^64 + 120 * q^65 + 56 * q^72 - 168 * q^74 - 88 * q^78 - 24 * q^79 - 96 * q^81 - 24 * q^85 + 24 * q^86 - 144 * q^92 - 32 * q^93 + 96 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

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