LMFDB - Embedded newform 441.2.i.b.68.5

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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			68.5
Root			$1.07065 - 1.85442i$ of defining polynomial
Character	$\chi$	$=$	441.68
Dual form			441.2.i.b.227.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.59354i q^{2} +(-1.34151 + 1.09561i) q^{3} -4.72645 q^{4} +(-0.626493 - 1.08512i) q^{5} +(-2.84151 - 3.47925i) q^{6} -7.07116i q^{8} +(0.599280 - 2.93953i) q^{9} +O(q^{10})$	\(q+2.59354i q^{2} +(-1.34151 + 1.09561i) q^{3} -4.72645 q^{4} +(-0.626493 - 1.08512i) q^{5} +(-2.84151 - 3.47925i) q^{6} -7.07116i q^{8} +(0.599280 - 2.93953i) q^{9} +(2.81429 - 1.62483i) q^{10} +(-0.534126 - 0.308378i) q^{11} +(6.34056 - 5.17834i) q^{12} +(-1.06343 - 0.613974i) q^{13} +(2.02931 + 0.769301i) q^{15} +8.88643 q^{16} +(-2.21501 - 3.83652i) q^{17} +(7.62380 + 1.55426i) q^{18} +(1.64679 + 0.950775i) q^{19} +(2.96109 + 5.12875i) q^{20} +(0.799790 - 1.38528i) q^{22} +(-4.11267 + 2.37445i) q^{23} +(7.74722 + 9.48600i) q^{24} +(1.71501 - 2.97049i) q^{25} +(1.59237 - 2.75806i) q^{26} +(2.41664 + 4.59998i) q^{27} +(-5.07629 + 2.93080i) q^{29} +(-1.99521 + 5.26309i) q^{30} -2.48089i q^{31} +8.90499i q^{32} +(1.05440 - 0.171503i) q^{33} +(9.95016 - 5.74473i) q^{34} +(-2.83247 + 13.8936i) q^{36} +(1.33217 - 2.30738i) q^{37} +(-2.46587 + 4.27102i) q^{38} +(2.09928 - 0.341458i) q^{39} +(-7.67303 + 4.43003i) q^{40} +(2.09966 - 3.63671i) q^{41} +(-2.24637 - 3.89083i) q^{43} +(2.52452 + 1.45753i) q^{44} +(-3.56518 + 1.19131i) q^{45} +(-6.15823 - 10.6664i) q^{46} -7.61476 q^{47} +(-11.9212 + 9.73605i) q^{48} +(7.70409 + 4.44796i) q^{50} +(7.17478 + 2.71992i) q^{51} +(5.02627 + 2.90192i) q^{52} +(-2.67782 + 1.54604i) q^{53} +(-11.9302 + 6.26766i) q^{54} +0.772786i q^{55} +(-3.25086 + 0.528768i) q^{57} +(-7.60114 - 13.1656i) q^{58} -3.56459 q^{59} +(-9.59142 - 3.63606i) q^{60} -14.4495i q^{61} +6.43428 q^{62} -5.32259 q^{64} +1.53860i q^{65} +(0.444799 + 2.73462i) q^{66} +13.6129 q^{67} +(10.4692 + 18.1331i) q^{68} +(2.91570 - 7.69121i) q^{69} -10.4095i q^{71} +(-20.7859 - 4.23760i) q^{72} +(-9.95016 + 5.74473i) q^{73} +(5.98429 + 3.45503i) q^{74} +(0.953796 + 5.86392i) q^{75} +(-7.78348 - 4.49379i) q^{76} +(0.885586 + 5.44457i) q^{78} -4.03185 q^{79} +(-5.56728 - 9.64281i) q^{80} +(-8.28173 - 3.52321i) q^{81} +(9.43196 + 5.44554i) q^{82} +(4.36775 + 7.56516i) q^{83} +(-2.77538 + 4.80710i) q^{85} +(10.0910 - 5.82605i) q^{86} +(3.59887 - 9.49331i) q^{87} +(-2.18059 + 3.77689i) q^{88} +(-0.811226 + 1.40508i) q^{89} +(-3.08970 - 9.24645i) q^{90} +(19.4383 - 11.2227i) q^{92} +(2.71808 + 3.32813i) q^{93} -19.7492i q^{94} -2.38261i q^{95} +(-9.75639 - 11.9461i) q^{96} +(-8.76527 + 5.06063i) q^{97} +(-1.22658 + 1.38528i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{3} - 8 q^{4} - 12 q^{6} + 3 q^{9}+O(q^{10}) $ 10 * q + 3 * q^3 - 8 * q^4 - 12 * q^6 + 3 * q^9	$ 10 q + 3 q^{3} - 8 q^{4} - 12 q^{6} + 3 q^{9} + 15 q^{10} - 12 q^{11} + 12 q^{12} + 6 q^{13} - 3 q^{15} + 12 q^{16} - 12 q^{17} + 24 q^{18} - 3 q^{19} - 3 q^{20} + 5 q^{22} - 15 q^{23} + 7 q^{25} + 3 q^{26} + 27 q^{27} - 15 q^{29} + 6 q^{30} + 3 q^{34} - 18 q^{36} + 6 q^{37} - 18 q^{38} + 18 q^{39} - 15 q^{40} - 9 q^{41} + 3 q^{43} - 24 q^{44} - 30 q^{45} - 13 q^{46} - 30 q^{47} - 15 q^{48} + 3 q^{50} + 21 q^{51} + 12 q^{52} + 9 q^{53} - 9 q^{54} - 36 q^{57} + 8 q^{58} + 36 q^{59} - 48 q^{60} + 12 q^{62} + 6 q^{64} + 39 q^{66} + 20 q^{67} + 27 q^{68} - 3 q^{69} - 30 q^{72} - 3 q^{73} - 30 q^{74} - 6 q^{75} + 9 q^{76} + 24 q^{78} - 40 q^{79} - 30 q^{80} + 15 q^{81} - 9 q^{82} - 15 q^{83} + 18 q^{85} + 54 q^{86} - 6 q^{87} - 8 q^{88} + 24 q^{89} + 24 q^{90} + 39 q^{92} + 36 q^{93} - 33 q^{96} + 6 q^{97} + 21 q^{99}+O(q^{100}) $ 10 * q + 3 * q^3 - 8 * q^4 - 12 * q^6 + 3 * q^9 + 15 * q^10 - 12 * q^11 + 12 * q^12 + 6 * q^13 - 3 * q^15 + 12 * q^16 - 12 * q^17 + 24 * q^18 - 3 * q^19 - 3 * q^20 + 5 * q^22 - 15 * q^23 + 7 * q^25 + 3 * q^26 + 27 * q^27 - 15 * q^29 + 6 * q^30 + 3 * q^34 - 18 * q^36 + 6 * q^37 - 18 * q^38 + 18 * q^39 - 15 * q^40 - 9 * q^41 + 3 * q^43 - 24 * q^44 - 30 * q^45 - 13 * q^46 - 30 * q^47 - 15 * q^48 + 3 * q^50 + 21 * q^51 + 12 * q^52 + 9 * q^53 - 9 * q^54 - 36 * q^57 + 8 * q^58 + 36 * q^59 - 48 * q^60 + 12 * q^62 + 6 * q^64 + 39 * q^66 + 20 * q^67 + 27 * q^68 - 3 * q^69 - 30 * q^72 - 3 * q^73 - 30 * q^74 - 6 * q^75 + 9 * q^76 + 24 * q^78 - 40 * q^79 - 30 * q^80 + 15 * q^81 - 9 * q^82 - 15 * q^83 + 18 * q^85 + 54 * q^86 - 6 * q^87 - 8 * q^88 + 24 * q^89 + 24 * q^90 + 39 * q^92 + 36 * q^93 - 33 * q^96 + 6 * q^97 + 21 * 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 $

$2$			2.59354i			1.83391i	0.398991	+	0.916955i	$0.369360\pi$
$2$			2.59354i			1.83391i	−0.398991	+	0.916955i	$0.630640\pi$
$3$	−1.34151	+	1.09561i	−0.774519	+	0.632550i
$3$	−1.34151	+	1.09561i	−0.774519	+	0.632550i
$4$	−4.72645			−2.36322
$5$	−0.626493	−	1.08512i	−0.280176	−	0.485279i	0.691252	−	0.722614i	$-0.257059\pi$
$5$	−0.626493	−	1.08512i	−0.280176	−	0.485279i	−0.971428	+	0.237335i	$0.923726\pi$
$6$	−2.84151	−	3.47925i	−1.16004	−	1.42040i
$7$		0			0
$7$		0			0
$8$		−	7.07116i		−	2.50003i
$9$	0.599280	−	2.93953i	0.199760	−	0.979845i
$10$	2.81429	−	1.62483i	0.889958	−	0.513817i
$11$	−0.534126	−	0.308378i	−0.161045	−	0.0929794i	0.417311	−	0.908764i	$-0.362972\pi$
$11$	−0.534126	−	0.308378i	−0.161045	−	0.0929794i	−0.578357	+	0.815784i	$0.696306\pi$
$12$	6.34056	−	5.17834i	1.83036	−	1.49486i
$13$	−1.06343	−	0.613974i	−0.294944	−	0.170286i	0.345226	−	0.938520i	$-0.387802\pi$
$13$	−1.06343	−	0.613974i	−0.294944	−	0.170286i	−0.640169	+	0.768234i	$0.721136\pi$
$14$		0			0
$15$	2.02931	+	0.769301i	0.523965	+	0.198633i
$16$	8.88643			2.22161
$17$	−2.21501	−	3.83652i	−0.537220	−	0.930492i	−0.999052	−	0.0435249i	$-0.986141\pi$
$17$	−2.21501	−	3.83652i	−0.537220	−	0.930492i	0.461833	−	0.886967i	$-0.347192\pi$
$18$	7.62380	+	1.55426i	1.79695	+	0.366342i
$19$	1.64679	+	0.950775i	0.377800	+	0.218123i	0.676861	−	0.736111i	$-0.263340\pi$
$19$	1.64679	+	0.950775i	0.377800	+	0.218123i	−0.299061	+	0.954234i	$0.596673\pi$
$20$	2.96109	+	5.12875i	0.662119	+	1.14682i
$21$		0			0
$22$	0.799790	−	1.38528i	0.170516	−	0.295342i
$23$	−4.11267	+	2.37445i	−0.857550	+	0.495107i	−0.863191	−	0.504877i	$-0.831538\pi$
$23$	−4.11267	+	2.37445i	−0.857550	+	0.495107i	0.00564111	+	0.999984i	$0.498204\pi$
$24$	7.74722	+	9.48600i	1.58140	+	1.93632i
$25$	1.71501	−	2.97049i	0.343003	−	0.594098i
$26$	1.59237	−	2.75806i	0.312289	−	0.540900i
$27$	2.41664	+	4.59998i	0.465083	+	0.885267i
$28$		0			0
$29$	−5.07629	+	2.93080i	−0.942643	+	0.544235i	−0.890788	−	0.454419i	$-0.849847\pi$
$29$	−5.07629	+	2.93080i	−0.942643	+	0.544235i	−0.0518553	+	0.998655i	$0.516513\pi$
$30$	−1.99521	+	5.26309i	−0.364274	+	0.960905i
$31$		−	2.48089i		−	0.445580i	−0.974866	−	0.222790i	$-0.928484\pi$
$31$		−	2.48089i		−	0.445580i	0.974866	−	0.222790i	$-0.0715165\pi$
$32$			8.90499i			1.57419i
$33$	1.05440	−	0.171503i	0.183547	−	0.0298548i
$34$	9.95016	−	5.74473i	1.70644	−	0.985213i
$35$		0			0
$36$	−2.83247	+	13.8936i	−0.472078	+	2.31559i
$37$	1.33217	−	2.30738i	0.219007	−	0.379331i	−0.735498	−	0.677527i	$-0.763052\pi$
$37$	1.33217	−	2.30738i	0.219007	−	0.379331i	0.954505	+	0.298196i	$0.0963849\pi$
$38$	−2.46587	+	4.27102i	−0.400018	+	0.692851i
$39$	2.09928	−	0.341458i	0.336154	−	0.0546771i
$40$	−7.67303	+	4.43003i	−1.21321	+	0.700449i
$41$	2.09966	−	3.63671i	0.327911	−	0.567959i	−0.654186	−	0.756334i	$-0.726989\pi$
$41$	2.09966	−	3.63671i	0.327911	−	0.567959i	0.982097	+	0.188375i	$0.0603220\pi$
$42$		0			0
$43$	−2.24637	−	3.89083i	−0.342568	−	0.593346i	0.642340	−	0.766419i	$-0.277964\pi$
$43$	−2.24637	−	3.89083i	−0.342568	−	0.593346i	−0.984909	+	0.173073i	$0.944630\pi$
$44$	2.52452	+	1.45753i	0.380586	+	0.219731i
$45$	−3.56518	+	1.19131i	−0.531466	+	0.177590i
$46$	−6.15823	−	10.6664i	−0.907981	−	1.57267i
$47$	−7.61476			−1.11073			−0.555364	−	0.831608i	$-0.687421\pi$
$47$	−7.61476			−1.11073			−0.555364	+	0.831608i	$0.687421\pi$
$48$	−11.9212	+	9.73605i	−1.72068	+	1.40528i
$49$		0			0
$50$	7.70409	+	4.44796i	1.08952	+	0.629036i
$51$	7.17478	+	2.71992i	1.00467	+	0.380865i
$52$	5.02627	+	2.90192i	0.697018	+	0.402424i
$53$	−2.67782	+	1.54604i	−0.367827	+	0.212365i	−0.672509	−	0.740089i	$-0.734783\pi$
$53$	−2.67782	+	1.54604i	−0.367827	+	0.212365i	0.304682	+	0.952454i	$0.401450\pi$
$54$	−11.9302	+	6.26766i	−1.62350	+	0.852921i
$55$			0.772786i			0.104202i
$56$		0			0
$57$	−3.25086	+	0.528768i	−0.430587	+	0.0700371i
$58$	−7.60114	−	13.1656i	−0.998078	−	1.72872i
$59$	−3.56459			−0.464070			−0.232035	−	0.972707i	$-0.574538\pi$
$59$	−3.56459			−0.464070			−0.232035	+	0.972707i	$0.574538\pi$
$60$	−9.59142	−	3.63606i	−1.23825	−	0.469413i
$61$		−	14.4495i		−	1.85006i	−0.379890	−	0.925032i	$-0.624038\pi$
$61$		−	14.4495i		−	1.85006i	0.379890	−	0.925032i	$-0.375962\pi$
$62$	6.43428			0.817154
$63$		0			0
$64$	−5.32259			−0.665324
$65$			1.53860i			0.190840i
$66$	0.444799	+	2.73462i	0.0547510	+	0.336608i
$67$	13.6129			1.66308			0.831539	−	0.555467i	$-0.187460\pi$
$67$	13.6129			1.66308			0.831539	+	0.555467i	$0.187460\pi$
$68$	10.4692	+	18.1331i	1.26957	+	2.19896i
$69$	2.91570	−	7.69121i	0.351009	−	0.925913i
$70$		0			0
$71$		−	10.4095i		−	1.23538i	−0.786420	−	0.617692i	$-0.788068\pi$
$71$		−	10.4095i		−	1.23538i	0.786420	−	0.617692i	$-0.211932\pi$
$72$	−20.7859	−	4.23760i	−2.44964	−	0.499406i
$73$	−9.95016	+	5.74473i	−1.16458	+	0.672369i	−0.952397	−	0.304861i	$-0.901390\pi$
$73$	−9.95016	+	5.74473i	−1.16458	+	0.672369i	−0.212181	+	0.977230i	$0.568057\pi$
$74$	5.98429	+	3.45503i	0.695659	+	0.401639i
$75$	0.953796	+	5.86392i	0.110135	+	0.677107i
$76$	−7.78348	−	4.49379i	−0.892826	−	0.515473i
$77$		0			0
$78$	0.885586	+	5.44457i	0.100273	+	0.616476i
$79$	−4.03185			−0.453618			−0.226809	−	0.973939i	$-0.572829\pi$
$79$	−4.03185			−0.453618			−0.226809	+	0.973939i	$0.572829\pi$
$80$	−5.56728	−	9.64281i	−0.622441	−	1.07810i
$81$	−8.28173	−	3.52321i	−0.920192	−	0.391468i
$82$	9.43196	+	5.44554i	1.04159	+	0.601360i
$83$	4.36775	+	7.56516i	0.479422	+	0.830384i	0.999721	−	0.0236001i	$-0.00751285\pi$
$83$	4.36775	+	7.56516i	0.479422	+	0.830384i	−0.520299	+	0.853984i	$0.674180\pi$
$84$		0			0
$85$	−2.77538	+	4.80710i	−0.301032	+	0.521403i
$86$	10.0910	−	5.82605i	1.08814	−	0.628240i
$87$	3.59887	−	9.49331i	0.385839	−	1.01779i
$88$	−2.18059	+	3.77689i	−0.232451	+	0.402618i
$89$	−0.811226	+	1.40508i	−0.0859897	+	0.148939i	−0.905813	−	0.423679i	$-0.860739\pi$
$89$	−0.811226	+	1.40508i	−0.0859897	+	0.148939i	0.819823	+	0.572617i	$0.194072\pi$
$90$	−3.08970	−	9.24645i	−0.325683	−	0.974661i
$91$		0			0
$92$	19.4383	−	11.2227i	2.02658	−	1.17005i
$93$	2.71808	+	3.32813i	0.281852	+	0.345111i
$94$		−	19.7492i		−	2.03697i
$95$		−	2.38261i		−	0.244451i
$96$	−9.75639	−	11.9461i	−0.995757	−	1.21924i
$97$	−8.76527	+	5.06063i	−0.889979	+	0.513829i	−0.873936	−	0.486042i	$-0.838440\pi$
$97$	−8.76527	+	5.06063i	−0.889979	+	0.513829i	−0.0160431	+	0.999871i	$0.505107\pi$
$98$		0			0
$99$	−1.22658	+	1.38528i	−0.123276	+	0.139226i
$100$	−8.10593	+	14.0399i	−0.810593	+	1.40399i
$101$	0.856611	−	1.48369i	0.0852360	−	0.147633i	−0.820256	−	0.571997i	$-0.806169\pi$
$101$	0.856611	−	1.48369i	0.0852360	−	0.147633i	0.905492	+	0.424364i	$0.139502\pi$
$102$	−7.05423	+	18.6081i	−0.698473	+	1.84247i
$103$	6.41315	−	3.70263i	0.631906	−	0.364831i	−0.149584	−	0.988749i	$-0.547793\pi$
$103$	6.41315	−	3.70263i	0.631906	−	0.364831i	0.781490	+	0.623918i	$0.214460\pi$
$104$	−4.34151	+	7.51971i	−0.425720	+	0.737368i
$105$		0			0
$106$	−4.00972	−	6.94503i	−0.389458	−	0.674561i
$107$	0.131657	+	0.0760123i	0.0127278	+	0.00734839i	0.506350	−	0.862328i	$-0.330994\pi$
$107$	0.131657	+	0.0760123i	0.0127278	+	0.00734839i	−0.493623	+	0.869676i	$0.664328\pi$
$108$	−11.4221	−	21.7416i	−1.09910	−	2.09208i
$109$	2.70051	+	4.67742i	0.258662	+	0.448016i	0.965884	−	0.258976i	$-0.0833851\pi$
$109$	2.70051	+	4.67742i	0.258662	+	0.448016i	−0.707222	+	0.706992i	$0.750052\pi$
$110$	−2.00425			−0.191098
$111$	0.740877	+	4.55490i	0.0703210	+	0.432332i
$112$		0			0
$113$	−5.60391	−	3.23542i	−0.527171	−	0.304362i	0.212693	−	0.977119i	$-0.431777\pi$
$113$	−5.60391	−	3.23542i	−0.527171	−	0.304362i	−0.739864	+	0.672757i	$0.765110\pi$
$114$	−1.37138	−	8.43123i	−0.128442	−	0.789657i
$115$	5.15311	+	2.97515i	0.480530	+	0.277434i
$116$	23.9928	−	13.8523i	2.22768	−	1.28615i
$117$	−2.44209	+	2.75806i	−0.225772	+	0.254983i
$118$		−	9.24490i		−	0.851062i
$119$		0			0
$120$	5.43984	−	14.3496i	0.496588	−	1.30993i
$121$	−5.30981	−	9.19685i	−0.482710	−	0.836078i
$122$	37.4752			3.39285
$123$	1.16771	+	7.17908i	0.105289	+	0.647316i
$124$			11.7258i			1.05301i
$125$	−10.5627			−0.944757
$126$		0			0
$127$	−2.93175			−0.260151			−0.130075	−	0.991504i	$-0.541522\pi$
$127$	−2.93175			−0.260151			−0.130075	+	0.991504i	$0.541522\pi$
$128$			4.00562i			0.354050i
$129$	7.27635	+	2.75843i	0.640647	+	0.242866i
$130$	−3.99042			−0.349983
$131$	−8.11382	−	14.0535i	−0.708908	−	1.22786i	−0.965263	−	0.261281i	$-0.915855\pi$
$131$	−8.11382	−	14.0535i	−0.708908	−	1.22786i	0.256355	−	0.966583i	$-0.417478\pi$
$132$	−4.98355	+	0.810598i	−0.433762	+	0.0705535i
$133$		0			0
$134$			35.3055i			3.04993i
$135$	3.47751	−	5.50420i	0.299296	−	0.473726i
$136$	−27.1286	+	15.6627i	−2.32626	+	1.34307i
$137$	−15.0711	−	8.70129i	−1.28761	−	0.743402i	−0.309382	−	0.950938i	$-0.600122\pi$
$137$	−15.0711	−	8.70129i	−1.28761	−	0.743402i	−0.978227	+	0.207536i	$0.933456\pi$
$138$	19.9475	+	7.56198i	1.69804	+	0.643719i
$139$	5.45273	+	3.14813i	0.462494	+	0.267021i	0.713092	−	0.701070i	$-0.247294\pi$
$139$	5.45273	+	3.14813i	0.462494	+	0.267021i	−0.250598	+	0.968091i	$0.580627\pi$
$140$		0			0
$141$	10.2153	−	8.34280i	0.860279	−	0.702591i
$142$	26.9975			2.26558
$143$	0.378672	+	0.655879i	0.0316661	+	0.0548474i
$144$	5.32546	−	26.1220i	0.443788	−	2.17683i
$145$	6.36052	+	3.67225i	0.528212	+	0.304963i
$146$	−14.8992	−	25.8061i	−1.23306	−	2.13573i
$147$		0			0
$148$	−6.29642	+	10.9057i	−0.517563	+	0.896445i
$149$	−9.20319	+	5.31346i	−0.753954	+	0.435296i	−0.827121	−	0.562024i	$-0.810023\pi$
$149$	−9.20319	+	5.31346i	−0.753954	+	0.435296i	0.0731665	+	0.997320i	$0.476690\pi$
$150$	−15.2083	+	2.47371i	−1.24175	+	0.201977i
$151$	−4.74465	+	8.21798i	−0.386114	+	0.668770i	−0.991923	−	0.126841i	$-0.959516\pi$
$151$	−4.74465	+	8.21798i	−0.386114	+	0.668770i	0.605809	+	0.795610i	$0.292850\pi$
$152$	6.72308	−	11.6447i	0.545314	−	0.944511i
$153$	−12.6050	+	4.21196i	−1.01905	+	0.340517i
$154$		0			0
$155$	−2.69205	+	1.55426i	−0.216231	+	0.124841i
$156$	−9.92214	+	1.61389i	−0.794407	+	0.129214i
$157$			23.8116i			1.90037i	0.311688	+	0.950185i	$0.399106\pi$
$157$			23.8116i			1.90037i	−0.311688	+	0.950185i	$0.600894\pi$
$158$		−	10.4568i		−	0.831895i
$159$	1.89846	−	5.00787i	0.150557	−	0.397150i
$160$	9.66295	−	5.57891i	0.763924	−	0.441051i
$161$		0			0
$162$	9.13759	−	21.4790i	0.717916	−	1.68755i
$163$	−4.41101	+	7.64009i	−0.345497	+	0.598418i	−0.985444	−	0.170001i	$-0.945623\pi$
$163$	−4.41101	+	7.64009i	−0.345497	+	0.598418i	0.639947	+	0.768419i	$0.278956\pi$
$164$	−9.92392	+	17.1887i	−0.774928	+	1.34221i
$165$	−0.846671	−	1.03670i	−0.0659133	−	0.0807068i
$166$	−19.6205	+	11.3279i	−1.52285	+	0.879217i
$167$	−11.0335	+	19.1106i	−0.853800	+	1.47883i	0.0239535	+	0.999713i	$0.492375\pi$
$167$	−11.0335	+	19.1106i	−0.853800	+	1.47883i	−0.877754	+	0.479112i	$0.840959\pi$
$168$		0			0
$169$	−5.74607	−	9.95249i	−0.442005	−	0.765576i
$170$	−12.4674	−	7.19806i	−0.956206	−	0.552066i
$171$	3.78173	−	4.27102i	0.289196	−	0.326613i
$172$	10.6174	+	18.3898i	0.809566	+	1.40221i
$173$	−4.06750			−0.309246			−0.154623	−	0.987974i	$-0.549416\pi$
$173$	−4.06750			−0.309246			−0.154623	+	0.987974i	$0.549416\pi$
$174$	24.6213	+	9.33381i	1.86653	+	0.707594i
$175$		0			0
$176$	−4.74647	−	2.74038i	−0.357779	−	0.206564i
$177$	4.78192	−	3.90539i	0.359431	−	0.293547i
$178$	−3.64414	−	2.10395i	−0.273140	−	0.157697i
$179$	−7.20787	+	4.16146i	−0.538741	+	0.311042i	−0.744569	−	0.667546i	$-0.767345\pi$
$179$	−7.20787	+	4.16146i	−0.538741	+	0.311042i	0.205827	+	0.978588i	$0.434011\pi$
$180$	16.8507	−	5.63065i	1.25597	−	0.419684i
$181$		−	12.6701i		−	0.941763i	−0.882196	−	0.470881i	$-0.843936\pi$
$181$		−	12.6701i		−	0.941763i	0.882196	−	0.470881i	$-0.156064\pi$
$182$		0			0
$183$	15.8310	+	19.3840i	1.17026	+	1.43291i
$184$	16.7901	+	29.0813i	1.23778	+	2.14390i
$185$	−3.33837			−0.245442
$186$	−8.63163	+	7.04946i	−0.632902	+	0.516891i
$187$			2.73225i			0.199802i
$188$	35.9908			2.62490
$189$		0			0
$190$	6.17941			0.448301
$191$			3.80050i			0.274995i	0.990502	+	0.137497i	$0.0439059\pi$
$191$			3.80050i			0.274995i	−0.990502	+	0.137497i	$0.956094\pi$
$192$	7.14029	−	5.83148i	0.515306	−	0.420851i
$193$	6.78897			0.488680			0.244340	−	0.969690i	$-0.421429\pi$
$193$	6.78897			0.488680			0.244340	+	0.969690i	$0.421429\pi$
$194$	−13.1250	−	22.7331i	−0.942317	−	1.63214i
$195$	−1.68571	−	2.06404i	−0.120716	−	0.147809i
$196$		0			0
$197$			6.41453i			0.457017i	0.973542	+	0.228508i	$0.0733848\pi$
$197$			6.41453i			0.457017i	−0.973542	+	0.228508i	$0.926615\pi$
$198$	−3.59277	−	3.18118i	−0.255327	−	0.226077i
$199$	13.8921	−	8.02063i	0.984788	−	0.568568i	0.0810756	−	0.996708i	$-0.474164\pi$
$199$	13.8921	−	8.02063i	0.984788	−	0.568568i	0.903712	+	0.428140i	$0.140831\pi$
$200$	−21.0048	−	12.1271i	−1.48526	−	0.857518i
$201$	−18.2618	+	14.9144i	−1.28809	+	1.05198i
$202$	3.84802	+	2.22166i	0.270746	+	0.156315i
$203$		0			0
$204$	−33.9112	−	12.8556i	−2.37426	−	0.900070i
$205$	−5.26168			−0.367491
$206$	9.60292	+	16.6327i	0.669067	+	1.15886i
$207$	4.51513	+	13.5123i	0.313824	+	0.939168i
$208$	−9.45013	−	5.45604i	−0.655249	−	0.378308i
$209$	−0.586396	−	1.01567i	−0.0405619	−	0.0702552i
$210$		0			0
$211$	−4.06070	+	7.03333i	−0.279550	+	0.484194i	−0.971273	−	0.237968i	$-0.923519\pi$
$211$	−4.06070	+	7.03333i	−0.279550	+	0.484194i	0.691723	+	0.722163i	$0.256852\pi$
$212$	12.6566	−	7.30728i	0.869257	−	0.501866i
$213$	11.4048	+	13.9644i	0.781442	+	0.956828i
$214$	−0.197141	+	0.341458i	−0.0134763	+	0.0233416i
$215$	−2.81467	+	4.87515i	−0.191959	+	0.332483i
$216$	32.5272	−	17.0885i	2.21319	−	1.16272i
$217$		0			0
$218$	−12.1311	+	7.00388i	−0.821620	+	0.474363i
$219$	7.05423	−	18.6081i	0.476681	−	1.25742i
$220$		−	3.65253i		−	0.246254i
$221$			5.43985i			0.365924i
$222$	−11.8133	+	1.92150i	−0.792858	+	0.128962i
$223$	−6.96205	+	4.01954i	−0.466213	+	0.269168i	−0.714653	−	0.699479i	$-0.753415\pi$
$223$	−6.96205	+	4.01954i	−0.466213	+	0.269168i	0.248440	+	0.968647i	$0.420082\pi$
$224$		0			0
$225$	−7.70409	−	6.82150i	−0.513606	−	0.454767i
$226$	8.39118	−	14.5340i	0.558173	−	0.966784i
$227$	10.4117	−	18.0336i	0.691048	−	1.19693i	−0.280447	−	0.959870i	$-0.590483\pi$
$227$	10.4117	−	18.0336i	0.691048	−	1.19693i	0.971495	−	0.237061i	$-0.0761840\pi$
$228$	15.3650	−	2.49920i	1.01757	−	0.165513i
$229$	−5.21276	+	3.00959i	−0.344469	+	0.198879i	−0.662247	−	0.749286i	$-0.730397\pi$
$229$	−5.21276	+	3.00959i	−0.344469	+	0.198879i	0.317777	+	0.948165i	$0.397064\pi$
$230$	−7.71617	+	13.3648i	−0.508789	+	0.881248i
$231$		0			0
$232$	20.7241	+	35.8952i	1.36061	+	2.35664i
$233$	18.2156	+	10.5168i	1.19335	+	0.688978i	0.959064	−	0.283191i	$-0.0913929\pi$
$233$	18.2156	+	10.5168i	1.19335	+	0.688978i	0.234282	+	0.972169i	$0.424726\pi$
$234$	−7.15314	−	6.33367i	−0.467615	−	0.414045i
$235$	4.77059	+	8.26291i	0.311199	+	0.539013i
$236$	16.8478			1.09670
$237$	5.40875	−	4.41733i	0.351336	−	0.286936i
$238$		0			0
$239$	−7.51079	−	4.33636i	−0.485832	−	0.280496i	0.237011	−	0.971507i	$-0.423832\pi$
$239$	−7.51079	−	4.33636i	−0.485832	−	0.280496i	−0.722844	+	0.691011i	$0.757165\pi$
$240$	18.0333	+	6.83633i	1.16404	+	0.441283i
$241$	−7.33797	−	4.23658i	−0.472680	−	0.272902i	0.244681	−	0.969604i	$-0.421317\pi$
$241$	−7.33797	−	4.23658i	−0.472680	−	0.272902i	−0.717361	+	0.696702i	$0.754650\pi$
$242$	23.8524	−	13.7712i	1.53329	−	0.885246i
$243$	14.9701	−	4.34713i	0.960329	−	0.278868i
$244$			68.2946i			4.37211i
$245$		0			0
$246$	−18.6192	+	3.02851i	−1.18712	+	0.193091i
$247$	−1.16750	−	2.02217i	−0.0742864	−	0.128668i
$248$	−17.5427			−1.11396
$249$	−14.1478	−	5.36337i	−0.896582	−	0.339890i
$250$		−	27.3948i		−	1.73260i
$251$	23.4435			1.47974			0.739871	−	0.672749i	$-0.234887\pi$
$251$	23.4435			1.47974			0.739871	+	0.672749i	$0.234887\pi$
$252$		0			0
$253$	2.92891			0.184139
$254$		−	7.60361i		−	0.477093i
$255$	−1.54351	−	9.48949i	−0.0966585	−	0.594255i
$256$	−21.0339			−1.31462
$257$	12.2585	+	21.2324i	0.764665	+	1.32444i	0.940423	+	0.340005i	$0.110429\pi$
$257$	12.2585	+	21.2324i	0.764665	+	1.32444i	−0.175758	+	0.984433i	$0.556238\pi$
$258$	−7.15409	+	18.8715i	−0.445394	+	1.17489i
$259$		0			0
$260$		−	7.27212i		−	0.450998i
$261$	5.57306	+	16.6783i	0.344964	+	1.03236i
$262$	36.4484	−	21.0435i	2.25179	−	1.30007i
$263$	9.14036	+	5.27719i	0.563619	+	0.325406i	0.754597	−	0.656189i	$-0.227833\pi$
$263$	9.14036	+	5.27719i	0.563619	+	0.325406i	−0.190978	+	0.981594i	$0.561166\pi$
$264$	−1.21272	−	7.45579i	−0.0746379	−	0.458872i
$265$	3.35527	+	1.93716i	0.206112	+	0.118999i
$266$		0			0
$267$	−0.451159	−	2.77372i	−0.0276105	−	0.169749i
$268$	−64.3406			−3.93023
$269$	1.14451	+	1.98235i	0.0697821	+	0.120866i	0.898805	−	0.438348i	$-0.144436\pi$
$269$	1.14451	+	1.98235i	0.0697821	+	0.120866i	−0.829023	+	0.559214i	$0.811103\pi$
$270$	14.2754	+	9.01906i	0.868770	+	0.548883i
$271$	20.9239	+	12.0804i	1.27103	+	0.733831i	0.975182	−	0.221403i	$-0.0710635\pi$
$271$	20.9239	+	12.0804i	1.27103	+	0.733831i	0.295851	+	0.955234i	$0.404397\pi$
$272$	−19.6836	−	34.0929i	−1.19349	−	2.06719i
$273$		0			0
$274$	22.5672	−	39.0875i	1.36333	−	2.36136i
$275$	−1.83207	+	1.05774i	−0.110478	+	0.0637844i
$276$	−13.7809	+	36.3521i	−0.829513	+	2.18814i
$277$	5.68551	−	9.84760i	0.341609	−	0.591685i	−0.643122	−	0.765763i	$-0.722361\pi$
$277$	5.68551	−	9.84760i	0.341609	−	0.591685i	0.984732	+	0.174079i	$0.0556947\pi$
$278$	−8.16481	+	14.1419i	−0.489693	+	0.848173i
$279$	−7.29265	−	1.48675i	−0.436600	−	0.0890092i
$280$		0			0
$281$	17.6382	−	10.1834i	1.05221	−	0.607492i	0.128941	−	0.991652i	$-0.458842\pi$
$281$	17.6382	−	10.1834i	1.05221	−	0.607492i	0.923267	+	0.384160i	$0.125509\pi$
$282$	21.6374	+	26.4937i	1.28849	+	1.57767i
$283$			12.1611i			0.722903i	0.932391	+	0.361451i	$0.117719\pi$
$283$			12.1611i			0.722903i	−0.932391	+	0.361451i	$0.882281\pi$
$284$			49.2001i			2.91949i
$285$	2.61042	+	3.19629i	0.154628	+	0.189332i
$286$	−1.70105	+	0.982101i	−0.100585	+	0.0580729i
$287$		0			0
$288$	26.1765	+	5.33658i	1.54247	+	0.314461i
$289$	−1.31257	+	2.27345i	−0.0772103	+	0.133732i
$290$	−9.52411	+	16.4962i	−0.559275	+	0.968693i
$291$	6.21420	−	16.3922i	0.364283	−	0.960927i
$292$	47.0289	−	27.1522i	2.75216	−	1.58896i
$293$	13.4674	−	23.3262i	0.786773	−	1.36273i	−0.141161	−	0.989987i	$-0.545083\pi$
$293$	13.4674	−	23.3262i	0.786773	−	1.36273i	0.927934	−	0.372745i	$-0.121583\pi$
$294$		0			0
$295$	2.23319	+	3.86799i	0.130021	+	0.225203i
$296$	−16.3159	−	9.41996i	−0.948340	−	0.547524i
$297$	0.127740	−	3.20221i	0.00741225	−	0.185811i
$298$	−13.7807	−	23.8688i	−0.798293	−	1.38268i
$299$	5.83140			0.337239
$300$	−4.50807	−	27.7155i	−0.260273	−	1.60016i
$301$		0			0
$302$	−21.3137	−	12.3054i	−1.22646	−	0.708099i
$303$	0.476400	+	2.92890i	0.0273684	+	0.168261i
$304$	14.6341	+	8.44899i	0.839322	+	0.484583i
$305$	−15.6793	+	9.05248i	−0.897797	+	0.518343i
$306$	−10.9239	−	32.6915i	−0.624477	−	1.86885i
$307$		−	21.3700i		−	1.21965i	−0.792536	−	0.609825i	$-0.791240\pi$
$307$		−	21.3700i		−	1.21965i	0.792536	−	0.609825i	$-0.208760\pi$
$308$		0			0
$309$	−4.54664	+	11.9934i	−0.258649	+	0.682281i
$310$	−4.03103	−	6.98195i	−0.228947	−	0.396548i
$311$	−16.2312			−0.920385			−0.460192	−	0.887819i	$-0.652220\pi$
$311$	−16.2312			−0.920385			−0.460192	+	0.887819i	$0.652220\pi$
$312$	−2.41450	−	14.8443i	−0.136694	−	0.840395i
$313$		−	14.0805i		−	0.795880i	−0.917412	−	0.397940i	$-0.869725\pi$
$313$		−	14.0805i		−	0.795880i	0.917412	−	0.397940i	$-0.130275\pi$
$314$	−61.7562			−3.48511
$315$		0			0
$316$	19.0563			1.07200
$317$		−	20.2968i		−	1.13998i	−0.821651	−	0.569991i	$-0.806947\pi$
$317$		−	20.2968i		−	1.13998i	0.821651	−	0.569991i	$-0.193053\pi$
$318$	12.9881	+	4.92372i	0.728337	+	0.276109i
$319$	3.61517			0.202411
$320$	3.33456	+	5.77563i	0.186408	+	0.322868i
$321$	−0.259899	+	0.0422738i	−0.0145061	+	0.00235950i
$322$		0			0
$323$		−	8.42392i		−	0.468720i
$324$	39.1432	+	16.6523i	2.17462	+	0.925126i
$325$	−3.64761	+	2.10595i	−0.202333	+	0.116817i
$326$	−19.8149	−	11.4401i	−1.09744	−	0.633610i
$327$	−8.74738	−	3.31609i	−0.483731	−	0.183380i
$328$	−25.7158	−	14.8470i	−1.41991	−	0.819788i
$329$		0			0
$330$	2.68872	−	2.19588i	0.148009	−	0.120879i
$331$	26.4682			1.45482			0.727411	−	0.686202i	$-0.240723\pi$
$331$	26.4682			1.45482			0.727411	+	0.686202i	$0.240723\pi$
$332$	−20.6439	−	35.7563i	−1.13298	−	1.96238i
$333$	−5.98429	−	5.29872i	−0.327937	−	0.290368i
$334$	−49.5642	−	28.6159i	−2.71203	−	1.56579i
$335$	−8.52836	−	14.7716i	−0.465954	−	0.807057i
$336$		0			0
$337$	−1.73659	+	3.00785i	−0.0945979	+	0.163848i	−0.909441	−	0.415834i	$-0.863490\pi$
$337$	−1.73659	+	3.00785i	−0.0945979	+	0.163848i	0.814843	+	0.579682i	$0.196823\pi$
$338$	25.8122	−	14.9027i	1.40400	−	0.810598i
$339$	11.0624	−	1.79936i	0.600829	−	0.0977278i
$340$	13.1177	−	22.7205i	0.711407	−	1.23219i
$341$	−0.765051	+	1.32511i	−0.0414298	+	0.0717585i
$342$	11.0771	+	9.80806i	0.598979	+	0.530359i
$343$		0			0
$344$	−27.5127	+	15.8844i	−1.48338	+	0.856432i
$345$	−10.1725	+	1.65461i	−0.547671	+	0.0890813i
$346$		−	10.5492i		−	0.567130i
$347$			9.40810i			0.505053i	0.967590	+	0.252527i	$0.0812615\pi$
$347$			9.40810i			0.505053i	−0.967590	+	0.252527i	$0.918738\pi$
$348$	−17.0099	+	44.8697i	−0.911824	+	2.40527i
$349$	−12.3253	+	7.11603i	−0.659759	+	0.380912i	−0.792185	−	0.610281i	$-0.791057\pi$
$349$	−12.3253	+	7.11603i	−0.659759	+	0.380912i	0.132426	+	0.991193i	$0.457723\pi$
$350$		0			0
$351$	0.254329	−	6.37554i	0.0135751	−	0.340301i
$352$	2.74610	−	4.75639i	0.146368	−	0.253516i
$353$	−8.58262	+	14.8655i	−0.456807	+	0.791213i	−0.998790	−	0.0491765i	$-0.984340\pi$
$353$	−8.58262	+	14.8655i	−0.456807	+	0.791213i	0.541983	+	0.840389i	$0.317674\pi$
$354$	10.1288	+	12.4021i	0.538340	+	0.659164i
$355$	−11.2956	+	6.52149i	−0.599506	+	0.346125i
$356$	3.83422	−	6.64106i	0.203213	−	0.351975i
$357$		0			0
$358$	−10.7929	−	18.6939i	−0.570424	−	0.988003i
$359$	−24.4705	−	14.1281i	−1.29150	−	0.745650i	−0.312583	−	0.949890i	$-0.601194\pi$
$359$	−24.4705	−	14.1281i	−1.29150	−	0.745650i	−0.978921	+	0.204241i	$0.934528\pi$
$360$	8.42392	+	25.2100i	0.443980	+	1.32868i
$361$	−7.69205	−	13.3230i	−0.404845	−	0.701212i
$362$	32.8605			1.72711
$363$	17.1993	+	6.52017i	0.902729	+	0.342220i
$364$		0			0
$365$	12.4674	+	7.19806i	0.652574	+	0.376764i
$366$	−50.2733	+	41.0582i	−2.62783	+	2.14615i
$367$	−19.9796	−	11.5352i	−1.04293	−	0.602133i	−0.122265	−	0.992498i	$-0.539016\pi$
$367$	−19.9796	−	11.5352i	−1.04293	−	0.602133i	−0.920661	+	0.390364i	$0.872349\pi$
$368$	−36.5469	+	21.1004i	−1.90514	+	1.09993i
$369$	−9.43196	−	8.35142i	−0.491008	−	0.434758i
$370$		−	8.65820i		−	0.450118i
$371$		0			0
$372$	−12.8469	−	15.7302i	−0.666080	−	0.815574i
$373$	6.93635	+	12.0141i	0.359150	+	0.622067i	0.987819	−	0.155607i	$-0.0497332\pi$
$373$	6.93635	+	12.0141i	0.359150	+	0.622067i	−0.628669	+	0.777673i	$0.716400\pi$
$374$	−7.08619			−0.366418
$375$	14.1699	−	11.5726i	0.731732	−	0.597606i
$376$			53.8452i			2.77685i
$377$	7.19773			0.370702
$378$		0			0
$379$	22.7814			1.17020			0.585101	−	0.810961i	$-0.301055\pi$
$379$	22.7814			1.17020			0.585101	+	0.810961i	$0.301055\pi$
$380$			11.2613i			0.577693i
$381$	3.93296	−	3.21205i	0.201492	−	0.164558i
$382$	−9.85676			−0.504316
$383$	7.61598	+	13.1913i	0.389158	+	0.674042i	0.992337	−	0.123564i	$-0.0394325\pi$
$383$	7.61598	+	13.1913i	0.389158	+	0.674042i	−0.603178	+	0.797606i	$0.706099\pi$
$384$	−4.38860	−	5.37357i	−0.223955	−	0.274219i
$385$		0			0
$386$			17.6075i			0.896196i
$387$	−12.7834	+	4.27159i	−0.649819	+	0.217137i
$388$	41.4286	−	23.9188i	2.10322	−	1.21429i
$389$	12.2525	+	7.07396i	0.621224	+	0.358664i	0.777346	−	0.629074i	$-0.216566\pi$
$389$	12.2525	+	7.07396i	0.621224	+	0.358664i	−0.156121	+	0.987738i	$0.549899\pi$
$390$	5.35318	−	4.37195i	0.271069	−	0.221382i
$391$	18.2192	+	10.5189i	0.921386	+	0.531962i
$392$		0			0
$393$	26.2819	+	9.96335i	1.32575	+	0.502584i
$394$	−16.6363			−0.838127
$395$	2.52592	+	4.37503i	0.127093	+	0.220131i
$396$	5.79736	−	6.54744i	0.291328	−	0.329021i
$397$	−8.40688	−	4.85371i	−0.421929	−	0.243601i	0.273973	−	0.961737i	$-0.411662\pi$
$397$	−8.40688	−	4.85371i	−0.421929	−	0.243601i	−0.695902	+	0.718136i	$0.744995\pi$
$398$	20.8018	+	36.0298i	1.04270	+	1.80601i
$399$		0			0
$400$	15.2403	−	26.3970i	0.762017	−	1.31985i
$401$	−7.56156	+	4.36567i	−0.377606	+	0.218011i	−0.676776	−	0.736189i	$-0.736624\pi$
$401$	−7.56156	+	4.36567i	−0.377606	+	0.218011i	0.299170	+	0.954200i	$0.403290\pi$
$402$	−38.6811	−	47.3626i	−1.92924	−	2.36223i
$403$	−1.52320	+	2.63826i	−0.0758760	+	0.131421i
$404$	−4.04873	+	7.01261i	−0.201432	+	0.348890i
$405$	1.36535	+	11.1939i	0.0678446	+	0.556230i
$406$		0			0
$407$	−1.42309	+	0.821622i	−0.0705400	+	0.0407263i
$408$	19.2330	−	50.7340i	0.952175	−	2.51171i
$409$		−	14.8918i		−	0.736353i	−0.929756	−	0.368176i	$-0.879982\pi$
$409$		−	14.8918i		−	0.736353i	0.929756	−	0.368176i	$-0.120018\pi$
$410$		−	13.6464i		−	0.673946i
$411$	29.7512	−	4.83918i	1.46752	−	0.238699i
$412$	−30.3114	+	17.5003i	−1.49334	+	0.862178i
$413$		0			0
$414$	−35.0446	+	11.7102i	−1.72235	+	0.575524i
$415$	5.47272	−	9.47903i	0.268645	−	0.465307i
$416$	5.46743	−	9.46987i	0.268063	−	0.464299i
$417$	−10.7640	+	1.75082i	−0.527115	+	0.0857379i
$418$	2.63418	−	1.52084i	0.128842	−	0.0743868i
$419$	−2.13859	+	3.70414i	−0.104477	+	0.180959i	−0.913524	−	0.406784i	$-0.866650\pi$
$419$	−2.13859	+	3.70414i	−0.104477	+	0.180959i	0.809048	+	0.587743i	$0.199983\pi$
$420$		0			0
$421$	5.76681	+	9.98841i	0.281057	+	0.486805i	0.971645	−	0.236443i	$-0.0759816\pi$
$421$	5.76681	+	9.98841i	0.281057	+	0.486805i	−0.690588	+	0.723248i	$0.742648\pi$
$422$	−18.2412	−	10.5316i	−0.887969	−	0.512669i
$423$	−4.56338	+	22.3839i	−0.221879	+	1.08834i
$424$	10.9323	+	18.9353i	0.530919	+	0.919578i
$425$	−15.1951			−0.737072
$426$	−36.2174	+	29.5787i	−1.75474	+	1.43309i
$427$		0			0
$428$	−0.622271	−	0.359268i	−0.0300786	−	0.0173659i
$429$	−1.22658	−	0.464990i	−0.0592198	−	0.0224499i
$430$	−12.6439	−	7.29996i	−0.609743	−	0.352035i
$431$	14.4497	−	8.34254i	0.696018	−	0.401846i	−0.109845	−	0.993949i	$-0.535035\pi$
$431$	14.4497	−	8.34254i	0.696018	−	0.401846i	0.805863	+	0.592103i	$0.201702\pi$
$432$	21.4753	+	40.8774i	1.03323	+	1.96671i
$433$		−	12.3503i		−	0.593516i	−0.954953	−	0.296758i	$-0.904094\pi$
$433$		−	12.3503i		−	0.593516i	0.954953	−	0.296758i	$-0.0959055\pi$
$434$		0			0
$435$	−12.5560	+	2.04230i	−0.602015	+	0.0979207i
$436$	−12.7638	−	22.1076i	−0.611276	−	1.05876i
$437$	−9.03027			−0.431976
$438$	48.2608	+	18.2954i	2.30599	+	0.874189i
$439$			22.1346i			1.05643i	0.849112	+	0.528213i	$0.177138\pi$
$439$			22.1346i			1.05643i	−0.849112	+	0.528213i	$0.822862\pi$
$440$	5.46449			0.260509
$441$		0			0
$442$	−14.1085			−0.671071
$443$			4.88329i			0.232012i	0.993248	+	0.116006i	$0.0370092\pi$
$443$			4.88329i			0.232012i	−0.993248	+	0.116006i	$0.962991\pi$
$444$	−3.50172	−	21.5285i	−0.166184	−	1.02170i
$445$	2.03291			0.0963690
$446$	−10.4248	−	18.0563i	−0.493630	−	0.854993i
$447$	6.52466	−	17.2111i	0.308606	−	0.814059i
$448$		0			0
$449$		−	12.4409i		−	0.587121i	−0.955941	−	0.293560i	$-0.905160\pi$
$449$		−	12.4409i		−	0.587121i	0.955941	−	0.293560i	$-0.0948401\pi$
$450$	17.6918	−	19.9809i	0.834001	−	0.941907i
$451$	−2.24296	+	1.29498i	−0.105617	+	0.0609780i
$452$	26.4866	+	15.2920i	1.24582	+	0.719277i
$453$	−2.63871	−	16.2228i	−0.123977	−	0.762212i
$454$	46.7708	+	27.0031i	2.19506	+	1.26732i
$455$		0			0
$456$	3.73900	+	22.9873i	0.175095	+	1.07648i
$457$	−10.7755			−0.504056			−0.252028	−	0.967720i	$-0.581098\pi$
$457$	−10.7755			−0.504056			−0.252028	+	0.967720i	$0.581098\pi$
$458$	−7.80549	−	13.5195i	−0.364727	−	0.631725i
$459$	12.2950	−	19.4605i	0.573882	−	0.908339i
$460$	−24.3559	−	14.0619i	−1.13560	−	0.655639i
$461$	−0.333303	−	0.577297i	−0.0155235	−	0.0268874i	0.858159	−	0.513383i	$-0.171608\pi$
$461$	−0.333303	−	0.577297i	−0.0155235	−	0.0268874i	−0.873683	+	0.486496i	$0.838275\pi$
$462$		0			0
$463$	−20.7892	+	36.0079i	−0.966155	+	1.67343i	−0.259677	+	0.965696i	$0.583616\pi$
$463$	−20.7892	+	36.0079i	−0.966155	+	1.67343i	−0.706479	+	0.707734i	$0.749717\pi$
$464$	−45.1101	+	26.0443i	−2.09418	+	1.20908i
$465$	1.90855	−	5.03448i	0.0885068	−	0.233469i
$466$	−27.2757	+	47.2429i	−1.26352	+	2.18849i
$467$	19.6568	−	34.0465i	0.909606	−	1.57548i	0.0949943	−	0.995478i	$-0.469717\pi$
$467$	19.6568	−	34.0465i	0.909606	−	1.57548i	0.814612	−	0.580006i	$-0.196950\pi$
$468$	11.5424	−	13.0358i	0.533549	−	0.602581i
$469$		0			0
$470$	−21.4302	+	12.3727i	−0.988500	+	0.570711i
$471$	−26.0882	−	31.9434i	−1.20208	−	1.47187i
$472$			25.2057i			1.16019i
$473$			2.77093i			0.127407i
$474$	11.4565	+	14.0278i	0.526215	+	0.644319i
$475$	5.64854	−	3.26119i	0.259173	−	0.149633i
$476$		0			0
$477$	2.93987	+	8.79805i	0.134608	+	0.402835i
$478$	11.2465	−	19.4795i	0.514403	−	0.890973i
$479$	19.0577	−	33.0088i	0.870767	−	1.50821i	0.00956182	−	0.999954i	$-0.496956\pi$
$479$	19.0577	−	33.0088i	0.870767	−	1.50821i	0.861205	−	0.508258i	$-0.169710\pi$
$480$	−6.85061	+	18.0710i	−0.312686	+	0.824823i
$481$	−2.83335	+	1.63583i	−0.129189	+	0.0745875i
$482$	10.9877	−	19.0313i	0.500477	−	0.866852i
$483$		0			0
$484$	25.0965	+	43.4685i	1.14075	+	1.97584i
$485$	10.9828	+	6.34090i	0.498701	+	0.287925i
$486$	11.2744	+	38.8254i	0.511419	+	1.76116i
$487$	−3.80277	−	6.58659i	−0.172320	−	0.298467i	0.766911	−	0.641754i	$-0.221793\pi$
$487$	−3.80277	−	6.58659i	−0.172320	−	0.298467i	−0.939231	+	0.343287i	$0.888460\pi$
$488$	−102.174			−4.62521
$489$	−2.45316	−	15.0820i	−0.110936	−	0.682030i
$490$		0			0
$491$	3.33297	+	1.92429i	0.150415	+	0.0868420i	0.573318	−	0.819333i	$-0.305656\pi$
$491$	3.33297	+	1.92429i	0.150415	+	0.0868420i	−0.422904	+	0.906175i	$0.638989\pi$
$492$	−5.51913	−	33.9315i	−0.248822	−	1.52975i
$493$	22.4881	+	12.9835i	1.01281	+	0.584748i
$494$	5.24459	−	3.02797i	0.235965	−	0.136235i
$495$	2.27163	+	0.463115i	0.102102	+	0.0208155i
$496$		−	22.0462i		−	0.989904i
$497$		0			0
$498$	13.9101	−	36.6929i	0.623327	−	1.64425i
$499$	16.0794	+	27.8503i	0.719812	+	1.24675i	0.961074	+	0.276291i	$0.0891053\pi$
$499$	16.0794	+	27.8503i	0.719812	+	1.24675i	−0.241262	+	0.970460i	$0.577561\pi$
$500$	49.9241			2.23267
$501$	−6.13624	−	37.7255i	−0.274147	−	1.68545i
$502$			60.8017i			2.71371i
$503$	−0.425693			−0.0189807			−0.00949035	−	0.999955i	$-0.503021\pi$
$503$	−0.425693			−0.0189807			−0.00949035	+	0.999955i	$0.503021\pi$
$504$		0			0
$505$	−2.14664			−0.0955243
$506$			7.59624i			0.337694i
$507$	18.6124	+	7.05588i	0.826607	+	0.313363i
$508$	13.8568			0.614794
$509$	12.8963	+	22.3370i	0.571617	+	0.990071i	0.996400	+	0.0847751i	$0.0270172\pi$
$509$	12.8963	+	22.3370i	0.571617	+	0.990071i	−0.424783	+	0.905295i	$0.639649\pi$
$510$	24.6114	−	4.00316i	1.08981	−	0.177263i
$511$		0			0
$512$		−	46.5411i		−	2.05684i
$513$	−0.393843	+	9.87290i	−0.0173886	+	0.435899i
$514$	−55.0670	+	31.7929i	−2.42890	+	1.40233i
$515$	−8.03558	−	4.63934i	−0.354090	−	0.204434i
$516$	−34.3913	−	13.0376i	−1.51399	−	0.573947i
$517$	4.06724	+	2.34822i	0.178877	+	0.103275i
$518$		0			0
$519$	5.45658	−	4.45639i	0.239517	−	0.195614i
$520$	10.8797			0.477106
$521$	−9.07174	−	15.7127i	−0.397440	−	0.688386i	0.595969	−	0.803007i	$-0.296768\pi$
$521$	−9.07174	−	15.7127i	−0.397440	−	0.688386i	−0.993409	+	0.114621i	$0.963435\pi$
$522$	−43.2558	+	14.4540i	−1.89326	+	0.632632i
$523$	−12.0723	−	6.96997i	−0.527887	−	0.304776i	0.212269	−	0.977211i	$-0.431915\pi$
$523$	−12.0723	−	6.96997i	−0.527887	−	0.304776i	−0.740155	+	0.672436i	$0.765248\pi$
$524$	38.3495	+	66.4234i	1.67531	+	2.90172i
$525$		0			0
$526$	−13.6866	+	23.7059i	−0.596764	+	1.03363i
$527$	−9.51796	+	5.49520i	−0.414609	+	0.239375i
$528$	9.36981	−	1.52405i	0.407768	−	0.0663256i
$529$	−0.223990	+	0.387962i	−0.00973870	+	0.0168679i
$530$	−5.02411	+	8.70202i	−0.218234	+	0.377992i
$531$	−2.13619	+	10.4782i	−0.0927026	+	0.454716i
$532$		0			0
$533$	−4.46569	+	2.57827i	−0.193431	+	0.111677i
$534$	7.19374	−	1.17010i	0.311304	−	0.0506351i
$535$		−	0.190485i		−	0.00823537i
$536$		−	96.2587i		−	4.15774i
$537$	5.11006	−	13.4796i	0.220515	−	0.581689i
$538$	−5.14131	+	2.96834i	−0.221658	+	0.127974i
$539$		0			0
$540$	−16.4363	+	26.0153i	−0.707305	+	1.11952i
$541$	−14.8576	+	25.7341i	−0.638779	+	1.10640i	0.346922	+	0.937894i	$0.387227\pi$
$541$	−14.8576	+	25.7341i	−0.638779	+	1.10640i	−0.985701	+	0.168503i	$0.946107\pi$
$542$	−31.3310	+	54.2668i	−1.34578	+	2.33096i
$543$	13.8815	+	16.9971i	0.595713	+	0.729414i
$544$	34.1641	−	19.7247i	1.46478	−	0.845688i
$545$	3.38370	−	5.86074i	0.144942	−	0.251046i
$546$		0			0
$547$	−9.13516	−	15.8226i	−0.390591	−	0.676524i	0.601937	−	0.798544i	$-0.294396\pi$
$547$	−9.13516	−	15.8226i	−0.390591	−	0.676524i	−0.992528	+	0.122020i	$0.961063\pi$
$548$	71.2327	+	41.1262i	3.04291	+	1.75683i
$549$	−42.4747	−	8.65927i	−1.81277	−	0.369569i
$550$	−2.74330	−	4.75154i	−0.116975	−	0.202606i
$551$	−11.1461			−0.474841
$552$	−54.3858	−	20.6174i	−2.31481	−	0.877533i
$553$		0			0
$554$	25.5401	+	14.7456i	1.08510	+	0.626481i
$555$	4.47845	−	3.65755i	0.190100	−	0.155254i
$556$	−25.7720	−	14.8795i	−1.09298	−	0.631031i
$557$	0.359456	−	0.207532i	0.0152307	−	0.00879343i	−0.492365	−	0.870389i	$-0.663868\pi$
$557$	0.359456	−	0.207532i	0.0152307	−	0.00879343i	0.507596	+	0.861595i	$0.330534\pi$
$558$	3.85594	−	18.9138i	0.163235	−	0.800684i
$559$			5.51686i			0.233338i
$560$		0			0
$561$	−2.99347	−	3.66532i	−0.126385	−	0.154750i
$562$	26.4111	+	45.7454i	1.11409	+	1.92965i
$563$	−3.65925			−0.154219			−0.0771095	−	0.997023i	$-0.524569\pi$
$563$	−3.65925			−0.154219			−0.0771095	+	0.997023i	$0.524569\pi$
$564$	−48.2819	+	39.4318i	−2.03303	+	1.66038i
$565$			8.10786i			0.341100i
$566$	−31.5403			−1.32574
$567$		0			0
$568$	−73.6074			−3.08850
$569$		−	35.1828i		−	1.47494i	−0.675380	−	0.737470i	$-0.736020\pi$
$569$		−	35.1828i		−	1.47494i	0.675380	−	0.737470i	$-0.263980\pi$
$570$	−8.28972	+	6.77022i	−0.347218	+	0.283573i
$571$	−10.0536			−0.420730			−0.210365	−	0.977623i	$-0.567465\pi$
$571$	−10.0536			−0.420730			−0.210365	+	0.977623i	$0.567465\pi$
$572$	−1.78977	−	3.09998i	−0.0748342	−	0.129617i
$573$	−4.16387	−	5.09840i	−0.173948	−	0.212989i
$574$		0			0
$575$			16.2888i			0.679292i
$576$	−3.18972	+	15.6459i	−0.132905	+	0.651914i
$577$	−0.0597672	+	0.0345066i	−0.00248814	+	0.00143653i	−0.501244	−	0.865306i	$-0.667124\pi$
$577$	−0.0597672	+	0.0345066i	−0.00248814	+	0.00143653i	0.498755	+	0.866743i	$0.333791\pi$
$578$	−5.89627	−	3.40421i	−0.245253	−	0.141597i
$579$	−9.10744	+	7.43805i	−0.378492	+	0.309115i
$580$	−30.0627	−	17.3567i	−1.24828	−	0.720697i
$581$		0			0
$582$	42.5138	+	16.1168i	1.76225	+	0.668061i
$583$	1.90706			0.0789823
$584$	40.6219	+	70.3591i	1.68094	+	2.91148i
$585$	4.52277	+	0.922053i	0.186994	+	0.0381222i
$586$	60.4974	+	34.9282i	2.49913	+	1.44287i
$587$	−11.4799	−	19.8838i	−0.473827	−	0.820693i	0.525724	−	0.850655i	$-0.323795\pi$
$587$	−11.4799	−	19.8838i	−0.473827	−	0.820693i	−0.999551	+	0.0299626i	$0.990461\pi$
$588$		0			0
$589$	2.35877	−	4.08550i	0.0971913	−	0.168340i
$590$	−10.0318	+	5.79186i	−0.413003	+	0.238447i
$591$	−7.02782	−	8.60514i	−0.289086	−	0.353968i
$592$	11.8382	−	20.5044i	0.486547	−	0.842725i
$593$	14.3970	−	24.9363i	0.591213	−	1.02401i	−0.402856	−	0.915263i	$-0.631982\pi$
$593$	14.3970	−	24.9363i	0.591213	−	1.02401i	0.994069	−	0.108748i	$-0.0346843\pi$
$594$	8.30506	+	0.331300i	0.340761	+	0.0135934i
$595$		0			0
$596$	43.4984	−	25.1138i	1.78176	−	1.02870i
$597$	−9.84892	+	25.9801i	−0.403090	+	1.06329i
$598$			15.1240i			0.618465i
$599$		−	38.2885i		−	1.56442i	−0.623012	−	0.782212i	$-0.714091\pi$
$599$		−	38.2885i		−	1.56442i	0.623012	−	0.782212i	$-0.285909\pi$
$600$	41.4647	−	6.74444i	1.69279	−	0.275340i
$601$	26.7618	−	15.4509i	1.09164	−	0.630257i	0.157625	−	0.987499i	$-0.449616\pi$
$601$	26.7618	−	15.4509i	1.09164	−	0.630257i	0.934012	+	0.357242i	$0.116283\pi$
$602$		0			0
$603$	8.15793	−	40.0155i	0.332216	−	1.62956i
$604$	22.4254	−	38.8419i	0.912475	−	1.58045i
$605$	−6.65311	+	11.5235i	−0.270487	+	0.468498i
$606$	−7.59621	+	1.23556i	−0.308575	+	0.0501913i
$607$	−28.7339	+	16.5895i	−1.16627	+	0.673349i	−0.952800	−	0.303600i	$-0.901811\pi$
$607$	−28.7339	+	16.5895i	−1.16627	+	0.673349i	−0.213475	+	0.976949i	$0.568478\pi$
$608$	−8.46664	+	14.6647i	−0.343368	+	0.594730i
$609$		0			0
$610$	−23.4780	−	40.6650i	−0.950595	−	1.64648i
$611$	8.09780	+	4.67527i	0.327602	+	0.189141i
$612$	59.5768	−	19.9076i	2.40825	−	0.804718i
$613$	−2.01164	−	3.48426i	−0.0812492	−	0.140728i	0.822538	−	0.568711i	$-0.192558\pi$
$613$	−2.01164	−	3.48426i	−0.0812492	−	0.140728i	−0.903787	+	0.427983i	$0.859224\pi$
$614$	55.4239			2.23673
$615$	7.05857	−	5.76474i	0.284629	−	0.232457i
$616$		0			0
$617$	27.1191	+	15.6572i	1.09177	+	0.630336i	0.934048	−	0.357147i	$-0.116251\pi$
$617$	27.1191	+	15.6572i	1.09177	+	0.630336i	0.157726	+	0.987483i	$0.449584\pi$
$618$	−31.1054	−	11.7919i	−1.25124	−	0.474339i
$619$	−12.0646	−	6.96550i	−0.484917	−	0.279967i	0.237546	−	0.971376i	$-0.423657\pi$
$619$	−12.0646	−	6.96550i	−0.484917	−	0.279967i	−0.722463	+	0.691409i	$0.756990\pi$
$620$	12.7238	−	7.34612i	0.511002	−	0.295027i
$621$	−20.8613	−	13.1800i	−0.837134	−	0.528895i
$622$		−	42.0962i		−	1.68790i
$623$		0			0
$624$	18.6551	−	3.03434i	0.746802	−	0.121471i
$625$	−1.95762	−	3.39069i	−0.0783047	−	0.135628i
$626$	36.5185			1.45957
$627$	1.89943	+	0.720064i	0.0758559	+	0.0287566i
$628$		−	112.544i		−	4.49100i
$629$	−11.8031			−0.470620
$630$		0			0
$631$	−4.61815			−0.183846			−0.0919229	−	0.995766i	$-0.529301\pi$
$631$	−4.61815			−0.183846			−0.0919229	+	0.995766i	$0.529301\pi$
$632$			28.5098i			1.13406i
$633$	−2.25833	−	13.8842i	−0.0897607	−	0.551847i
$634$	52.6406			2.09063
$635$	1.83672	+	3.18129i	0.0728879	+	0.126246i
$636$	−8.97296	+	23.6694i	−0.355801	+	0.938554i
$637$		0			0
$638$			9.37609i			0.371203i
$639$	−30.5992	−	6.23822i	−1.21048	−	0.246780i
$640$	4.34657	−	2.50949i	0.171813	−	0.0991964i
$641$	36.7821	+	21.2362i	1.45281	+	0.838779i	0.998640	−	0.0521380i	$-0.0166036\pi$
$641$	36.7821	+	21.2362i	1.45281	+	0.838779i	0.454167	+	0.890917i	$0.349937\pi$
$642$	−0.109639	−	0.674058i	−0.00432710	−	0.0266030i
$643$	−3.13514	−	1.81008i	−0.123638	−	0.0713825i	0.436905	−	0.899507i	$-0.356074\pi$
$643$	−3.13514	−	1.81008i	−0.123638	−	0.0713825i	−0.560544	+	0.828125i	$0.689408\pi$
$644$		0			0
$645$	−1.56536	−	9.62383i	−0.0616361	−	0.378938i
$646$	21.8478			0.859589
$647$	6.00617	+	10.4030i	0.236127	+	0.408984i	0.959600	−	0.281369i	$-0.0907886\pi$
$647$	6.00617	+	10.4030i	0.236127	+	0.408984i	−0.723473	+	0.690353i	$0.757455\pi$
$648$	−24.9132	+	58.5614i	−0.978681	+	2.30051i
$649$	1.90394	+	1.09924i	0.0747361	+	0.0431489i
$650$	−5.46186	−	9.46022i	−0.214232	−	0.371060i
$651$		0			0
$652$	20.8484	−	36.1105i	0.816486	−	1.41420i
$653$	39.9950	−	23.0911i	1.56512	−	0.903625i	0.568400	−	0.822752i	$-0.307563\pi$
$653$	39.9950	−	23.0911i	1.56512	−	0.903625i	0.996724	−	0.0808728i	$-0.0257707\pi$
$654$	8.60040	−	22.6867i	0.336302	−	0.887119i
$655$	−10.1665	+	17.6089i	−0.397238	+	0.688036i
$656$	18.6584	−	32.3174i	0.728490	−	1.26178i
$657$	10.9239	+	32.6915i	0.426182	+	1.27542i
$658$		0			0
$659$	−16.3479	+	9.43847i	−0.636824	+	0.367671i	−0.783390	−	0.621530i	$-0.786511\pi$
$659$	−16.3479	+	9.43847i	−0.636824	+	0.367671i	0.146566	+	0.989201i	$0.453178\pi$
$660$	4.00175	+	4.89990i	0.155768	+	0.190728i
$661$			3.32787i			0.129439i	0.997903	+	0.0647195i	$0.0206153\pi$
$661$			3.32787i			0.129439i	−0.997903	+	0.0647195i	$0.979385\pi$
$662$			68.6463i			2.66801i
$663$	−5.95995	−	7.29759i	−0.231465	−	0.283415i
$664$	53.4944	−	30.8850i	2.07599	−	1.19857i
$665$		0			0
$666$	13.7424	−	15.5205i	0.532509	−	0.601407i
$667$	13.9181	−	24.1068i	0.538909	−	0.933418i
$668$	52.1494	−	90.3254i	2.01772	−	3.49480i
$669$	4.93579	−	13.0199i	0.190829	−	0.503379i
$670$	38.3106	−	22.1187i	1.48007	−	0.854518i
$671$	−4.45589	+	7.71783i	−0.172018	+	0.297944i
$672$		0			0
$673$	−16.3678	−	28.3499i	−0.630934	−	1.09281i	−0.987361	−	0.158487i	$-0.949339\pi$
$673$	−16.3678	−	28.3499i	−0.630934	−	1.09281i	0.356427	−	0.934323i	$-0.383995\pi$
$674$	−7.80099	−	4.50390i	−0.300483	−	0.173484i
$675$	17.8088	+	0.710416i	0.685460	+	0.0273439i
$676$	27.1585	+	47.0399i	1.04456	+	1.80923i
$677$	33.8456			1.30079			0.650396	−	0.759596i	$-0.274603\pi$
$677$	33.8456			1.30079			0.650396	+	0.759596i	$0.274603\pi$
$678$	4.66671	+	28.6909i	0.179224	+	1.10187i
$679$		0			0
$680$	33.9917	+	19.6251i	1.30352	+	0.752590i
$681$	5.79040	+	35.5993i	0.221889	+	1.36417i
$682$	−3.43672	−	1.98419i	−0.131599	−	0.0759785i
$683$	−4.79617	+	2.76907i	−0.183520	+	0.105956i	−0.588946	−	0.808173i	$-0.700457\pi$
$683$	−4.79617	+	2.76907i	−0.183520	+	0.105956i	0.405425	+	0.914128i	$0.367123\pi$
$684$	−17.8741	+	20.1868i	−0.683435	+	0.771860i
$685$			21.8052i			0.833133i
$686$		0			0
$687$	3.69562	−	9.74854i	0.140997	−	0.371930i
$688$	−19.9622	−	34.5756i	−0.761052	−	1.31818i
$689$	3.79691			0.144651
$690$	−4.29130	−	26.3829i	−0.163367	−	1.00438i
$691$		−	14.2510i		−	0.542134i	−0.962561	−	0.271067i	$-0.912624\pi$
$691$		−	14.2510i		−	0.542134i	0.962561	−	0.271067i	$-0.0873764\pi$
$692$	19.2248			0.730818
$693$		0			0
$694$	−24.4003			−0.926222
$695$		−	7.88913i		−	0.299252i
$696$	−67.1287	−	25.4481i	−2.54451	−	0.964610i
$697$	−18.6031			−0.704642
$698$	−18.4557	−	31.9662i	−0.698559	−	1.20994i
$699$	−35.9587	+	5.84886i	−1.36008	+	0.221224i
$700$		0			0
$701$		−	18.6105i		−	0.702908i	−0.936205	−	0.351454i	$-0.885687\pi$
$701$		−	18.6105i		−	0.702908i	0.936205	−	0.351454i	$-0.114313\pi$
$702$	16.5352	+	0.659611i	0.624081	+	0.0248954i
$703$	4.38760	−	2.53318i	0.165482	−	0.0955408i
$704$	2.84293	+	1.64137i	0.107147	+	0.0618614i
$705$	−15.4527	−	5.85804i	−0.581982	−	0.220627i
$706$	−38.5544	−	22.2594i	−1.45101	−	0.837743i
$707$		0			0
$708$	−22.6015	+	18.4587i	−0.849416	+	0.693719i
$709$	−13.4947			−0.506803			−0.253401	−	0.967361i	$-0.581549\pi$
$709$	−13.4947			−0.506803			−0.253401	+	0.967361i	$0.581549\pi$
$710$	−16.9137	−	29.2955i	−0.634762	−	1.09944i
$711$	−2.41621	+	11.8518i	−0.0906148	+	0.444475i
$712$	9.93557	+	5.73630i	0.372351	+	0.214977i
$713$	5.89074	+	10.2031i	0.220610	+	0.382107i
$714$		0			0
$715$	0.474470	−	0.821807i	0.0177442	−	0.0307338i
$716$	34.0676	−	19.6689i	1.27317	−	0.735063i
$717$	14.8267	−	2.41164i	0.553714	−	0.0900643i
$718$	36.6417	−	63.4652i	1.36745	−	2.36850i
$719$	−18.8692	+	32.6824i	−0.703702	+	1.21885i	0.263456	+	0.964671i	$0.415137\pi$
$719$	−18.8692	+	32.6824i	−0.703702	+	1.21885i	−0.967158	+	0.254176i	$0.918196\pi$
$720$	−31.6817	+	10.5865i	−1.18071	+	0.394534i
$721$		0			0
$722$	34.5538	−	19.9496i	1.28596	−	0.742449i
$723$	14.4856	−	2.35615i	0.538724	−	0.0876261i
$724$			59.8847i			2.22560i
$725$			20.1054i			0.746697i
$726$	−16.9103	+	44.6071i	−0.627601	+	1.65552i
$727$	1.98480	−	1.14592i	0.0736121	−	0.0424999i	−0.462742	−	0.886493i	$-0.653134\pi$
$727$	1.98480	−	1.14592i	0.0736121	−	0.0424999i	0.536354	+	0.843993i	$0.319801\pi$
$728$		0			0
$729$	−15.3197	+	22.2330i	−0.567395	+	0.823446i
$730$	−18.6685	+	32.3347i	−0.690950	+	1.19676i
$731$	−9.95149	+	17.2365i	−0.368069	+	0.637514i
$732$	−74.8242	−	91.6177i	−2.76558	−	3.38629i
$733$	21.4678	−	12.3944i	0.792930	−	0.457798i	−0.0480633	−	0.998844i	$-0.515305\pi$
$733$	21.4678	−	12.3944i	0.792930	−	0.457798i	0.840993	+	0.541046i	$0.181972\pi$
$734$	29.9170	−	51.8178i	1.10426	−	1.91263i
$735$		0			0
$736$	−21.1444	−	36.6232i	−0.779394	−	1.34995i
$737$	−7.27099	−	4.19791i	−0.267830	−	0.154632i
$738$	21.6597	−	24.4622i	0.797306	−	0.900464i
$739$	8.10081	+	14.0310i	0.297993	+	0.516139i	0.975677	−	0.219214i	$-0.0703494\pi$
$739$	8.10081	+	14.0310i	0.297993	+	0.516139i	−0.677684	+	0.735354i	$0.737016\pi$
$740$	15.7786			0.580035
$741$	3.78173	+	1.43363i	0.138925	+	0.0526658i
$742$		0			0
$743$	−18.8312	−	10.8722i	−0.690848	−	0.398862i	0.113081	−	0.993586i	$-0.463928\pi$
$743$	−18.8312	−	10.8722i	−0.690848	−	0.398862i	−0.803930	+	0.594724i	$0.797261\pi$
$744$	23.5337	−	19.2200i	0.862787	−	0.704639i
$745$	11.5315	+	6.65769i	0.422480	+	0.243919i
$746$	−31.1591	+	17.9897i	−1.14081	+	0.658649i
$747$	24.8555	−	8.30549i	0.909417	−	0.303882i
$748$		−	12.9138i		−	0.472176i
$749$		0			0
$750$	30.0140	+	36.7503i	1.09596	+	1.34193i
$751$	3.78997	+	6.56443i	0.138298	+	0.239539i	0.926853	−	0.375426i	$-0.122503\pi$
$751$	3.78997	+	6.56443i	0.138298	+	0.239539i	−0.788554	+	0.614965i	$0.789170\pi$
$752$	−67.6680			−2.46760
$753$	−31.4496	+	25.6849i	−1.14609	+	0.936011i
$754$			18.6676i			0.679834i
$755$	11.8900			0.432720
$756$		0			0
$757$	10.3436			0.375944			0.187972	−	0.982174i	$-0.439809\pi$
$757$	10.3436			0.375944			0.187972	+	0.982174i	$0.439809\pi$
$758$			59.0844i			2.14604i
$759$	−3.92915	+	3.20894i	−0.142619	+	0.116477i
$760$	−16.8478			−0.611135
$761$	17.2169	+	29.8206i	0.624114	+	1.08100i	0.988711	+	0.149832i	$0.0478732\pi$
$761$	17.2169	+	29.8206i	0.624114	+	1.08100i	−0.364598	+	0.931165i	$0.618793\pi$
$762$	8.33058	+	10.2003i	0.301785	+	0.369517i
$763$		0			0
$764$		−	17.9629i		−	0.649874i
$765$	12.4674	+	11.0391i	0.450760	+	0.399120i
$766$	−34.2121	+	19.7523i	−1.23613	+	0.713681i
$767$	3.79070	+	2.18856i	0.136874	+	0.0790245i
$768$	28.2172	−	23.0450i	1.01820	−	0.831564i
$769$	−12.9344	−	7.46765i	−0.466425	−	0.269290i	0.248317	−	0.968679i	$-0.420123\pi$
$769$	−12.9344	−	7.46765i	−0.466425	−	0.269290i	−0.714742	+	0.699388i	$0.753456\pi$
$770$		0			0
$771$	−39.7073	−	15.0528i	−1.43002	−	0.542114i
$772$	−32.0877			−1.15486
$773$	19.9924	+	34.6278i	0.719076	+	1.24548i	0.961366	+	0.275272i	$0.0887680\pi$
$773$	19.9924	+	34.6278i	0.719076	+	1.24548i	−0.242290	+	0.970204i	$0.577899\pi$
$774$	−11.0785	−	33.1544i	−0.398210	−	1.19171i
$775$	−7.36945	−	4.25476i	−0.264719	−	0.152835i
$776$	35.7845	+	61.9806i	1.28459	+	2.22497i
$777$		0			0
$778$	−18.3466	+	31.7772i	−0.657758	+	1.13927i
$779$	6.91539	−	3.99260i	0.247770	−	0.143050i
$780$	7.96740	+	9.75560i	0.285279	+	0.349306i
$781$	−3.21007	+	5.56000i	−0.114865	+	0.198952i
$782$	−27.2811	+	47.2523i	−0.975571	+	1.68974i
$783$	−25.7492	−	16.2681i	−0.920201	−	0.581376i
$784$		0			0
$785$	25.8383	−	14.9178i	0.922209	−	0.532438i
$786$	−25.8403	+	68.1632i	−0.921695	+	2.43130i
$787$		−	2.24117i		−	0.0798892i	−0.999202	−	0.0399446i	$-0.987282\pi$
$787$		−	2.24117i		−	0.0798892i	0.999202	−	0.0399446i	$-0.0127181\pi$
$788$		−	30.3180i		−	1.08003i
$789$	−18.0436	+	2.93488i	−0.642369	+	0.104485i
$790$	−11.3468	+	6.55108i	−0.403701	+	0.233077i
$791$		0			0
$792$	9.79551	+	8.67333i	0.348068	+	0.308193i
$793$	−8.87159	+	15.3660i	−0.315039	+	0.545664i
$794$	12.5883	−	21.8036i	0.446742	−	0.773780i
$795$	−6.62349	+	1.07734i	−0.234911	+	0.0382094i
$796$	−65.6605	+	37.9091i	−2.32727	+	1.34365i
$797$	−22.1077	+	38.2916i	−0.783094	+	1.35636i	0.147037	+	0.989131i	$0.453026\pi$
$797$	−22.1077	+	38.2916i	−0.783094	+	1.35636i	−0.930131	+	0.367227i	$0.880307\pi$
$798$		0			0
$799$	16.8668	+	29.2142i	0.596705	+	1.03352i
$800$	26.4522	+	15.2722i	0.935226	+	0.539953i
$801$	3.64414	+	3.22666i	0.128759	+	0.114009i
$802$	−11.3225	−	19.6112i	−0.399812	−	0.692495i
$803$	7.08619			0.250066
$804$	86.3133	−	70.4921i	3.04404	−	2.48607i
$805$		0			0
$806$	−6.84243	−	3.95048i	−0.241014	−	0.139150i
$807$	−3.70725	−	1.40540i	−0.130502	−	0.0494725i
$808$	−10.4914	−	6.05723i	−0.369087	−	0.213093i
$809$	−4.31478	+	2.49114i	−0.151699	+	0.0875837i	−0.573928	−	0.818906i	$-0.694581\pi$
$809$	−4.31478	+	2.49114i	−0.151699	+	0.0875837i	0.422229	+	0.906489i	$0.361248\pi$
$810$	−29.0318	+	3.54108i	−1.02008	+	0.124421i
$811$			36.5749i			1.28432i	0.766571	+	0.642160i	$0.221961\pi$
$811$			36.5749i			1.28432i	−0.766571	+	0.642160i	$0.778039\pi$
$812$		0			0
$813$	−41.3049	+	6.71844i	−1.44863	+	0.235626i
$814$	−2.13091	−	3.69084i	−0.0746883	−	0.129364i
$815$	11.0539			0.387200
$816$	63.7581	+	24.1704i	2.23198	+	0.846133i
$817$		−	8.54318i		−	0.298888i
$818$	38.6225			1.35040
$819$		0			0
$820$	24.8690			0.868465
$821$		−	40.2294i		−	1.40402i	−0.712169	−	0.702008i	$-0.752287\pi$
$821$		−	40.2294i		−	1.40402i	0.712169	−	0.702008i	$-0.247713\pi$
$822$	12.5506	+	77.1609i	0.437752	+	2.69129i
$823$	−35.8032			−1.24802			−0.624011	−	0.781416i	$-0.714498\pi$
$823$	−35.8032			−1.24802			−0.624011	+	0.781416i	$0.714498\pi$
$824$	−26.1819	−	45.3483i	−0.912089	−	1.57978i
$825$	1.29886	−	3.42620i	0.0452204	−	0.119285i
$826$		0			0
$827$			32.0733i			1.11530i	0.830077	+	0.557648i	$0.188296\pi$
$827$			32.0733i			1.11530i	−0.830077	+	0.557648i	$0.811704\pi$
$828$	−21.3406	−	63.8651i	−0.741635	−	2.21947i
$829$	14.0640	−	8.11986i	0.488463	−	0.282014i	−0.235474	−	0.971881i	$-0.575664\pi$
$829$	14.0640	−	8.11986i	0.488463	−	0.282014i	0.723937	+	0.689866i	$0.242331\pi$
$830$	24.5842	+	14.1937i	0.853332	+	0.492671i
$831$	3.16197	+	19.4397i	0.109687	+	0.674357i
$832$	5.66023	+	3.26793i	0.196233	+	0.113295i
$833$		0			0
$834$	−4.54081	−	27.9169i	−0.157236	−	0.966682i
$835$	27.6497			0.956857
$836$	2.77157	+	4.80050i	0.0958568	+	0.166029i
$837$	11.4120	−	5.99542i	0.394458	−	0.207232i
$838$	−9.60684	−	5.54651i	−0.331863	−	0.191601i
$839$	−1.35145	−	2.34077i	−0.0466571	−	0.0808125i	0.841754	−	0.539862i	$-0.181523\pi$
$839$	−1.35145	−	2.34077i	−0.0466571	−	0.0808125i	−0.888411	+	0.459049i	$0.848190\pi$
$840$		0			0
$841$	2.67914	−	4.64041i	0.0923842	−	0.160014i
$842$	−25.9053	+	14.9565i	−0.892757	+	0.515434i
$843$	−12.5047	+	32.9857i	−0.430686	+	1.13609i
$844$	19.1927	−	33.2427i	0.660639	−	1.14426i
$845$	−7.19974	+	12.4703i	−0.247679	+	0.428992i
$846$	−58.0534	−	11.8353i	−1.99592	−	0.406906i
$847$		0			0
$848$	−23.7962	+	13.7388i	−0.817166	+	0.471791i
$849$	−13.3238	−	16.3142i	−0.457272	−	0.559902i
$850$		−	39.4092i		−	1.35172i
$851$			12.6526i			0.433727i
$852$	−53.9041	−	66.0023i	−1.84672	−	2.26120i
$853$	−41.3187	+	23.8554i	−1.41473	+	0.816793i	−0.995829	−	0.0912411i	$-0.970917\pi$
$853$	−41.3187	+	23.8554i	−1.41473	+	0.816793i	−0.418897	+	0.908034i	$0.637583\pi$
$854$		0			0
$855$	−7.00378	−	1.42785i	−0.239524	−	0.0488316i
$856$	0.537495	−	0.930969i	0.0183712	−	0.0318199i
$857$	−8.93973	+	15.4841i	−0.305375	+	0.528926i	−0.977345	−	0.211653i	$-0.932115\pi$
$857$	−8.93973	+	15.4841i	−0.305375	+	0.528926i	0.671969	+	0.740579i	$0.265449\pi$
$858$	1.20597	−	3.18118i	0.0411711	−	0.108604i
$859$	−29.1901	+	16.8529i	−0.995953	+	0.575014i	−0.907048	−	0.421026i	$-0.861670\pi$
$859$	−29.1901	+	16.8529i	−0.995953	+	0.575014i	−0.0889047	+	0.996040i	$0.528337\pi$
$860$	13.3034	−	23.0422i	0.453642	−	0.785731i
$861$		0			0
$862$	21.6367	+	37.4759i	0.736950	+	1.27643i
$863$	16.4318	+	9.48693i	0.559347	+	0.322939i	0.752883	−	0.658154i	$-0.228662\pi$
$863$	16.4318	+	9.48693i	0.559347	+	0.322939i	−0.193537	+	0.981093i	$0.561996\pi$
$864$	−40.9628	+	21.5202i	−1.39358	+	0.732131i
$865$	2.54826	+	4.41371i	0.0866434	+	0.150071i
$866$	32.0309			1.08846
$867$	−0.729981	−	4.48791i	−0.0247915	−	0.152417i
$868$		0			0
$869$	2.15351	+	1.24333i	0.0730530	+	0.0421772i
$870$	−5.29678	−	32.5645i	−0.179578	−	1.10404i
$871$	−14.4764	−	8.35795i	−0.490514	−	0.283198i
$872$	33.0748	−	19.0957i	1.12005	−	0.646663i
$873$	9.62305	+	28.7986i	0.325691	+	0.974684i
$874$		−	23.4204i		−	0.792206i
$875$		0			0
$876$	−33.3415	+	87.9501i	−1.12650	+	2.97156i
$877$	−18.6188	−	32.2487i	−0.628712	−	1.08896i	−0.987810	−	0.155662i	$-0.950249\pi$
$877$	−18.6188	−	32.2487i	−0.628712	−	1.08896i	0.359098	−	0.933300i	$-0.383084\pi$
$878$	−57.4070			−1.93739
$879$	7.48981	+	46.0473i	0.252625	+	1.55314i
$880$			6.86730i			0.231497i
$881$	−4.71527			−0.158862			−0.0794308	−	0.996840i	$-0.525310\pi$
$881$	−4.71527			−0.158862			−0.0794308	+	0.996840i	$0.525310\pi$
$882$		0			0
$883$	30.1766			1.01552			0.507762	−	0.861497i	$-0.330473\pi$
$883$	30.1766			1.01552			0.507762	+	0.861497i	$0.330473\pi$
$884$		−	25.7112i		−	0.864760i
$885$	−7.23365	−	2.74224i	−0.243156	−	0.0921793i
$886$	−12.6650			−0.425490
$887$	−19.2217	−	33.2930i	−0.645402	−	1.11787i	−0.984208	−	0.177013i	$-0.943356\pi$
$887$	−19.2217	−	33.2930i	−0.645402	−	1.11787i	0.338806	−	0.940856i	$-0.389977\pi$
$888$	32.2084	−	5.23886i	1.08084	−	0.175805i
$889$		0			0
$890$			5.27243i			0.176732i
$891$	3.33701	+	4.43574i	0.111794	+	0.148603i
$892$	32.9058	−	18.9981i	1.10177	−	0.636105i
$893$	−12.5399	−	7.23993i	−0.419632	−	0.242275i
$894$	44.6378	+	16.9220i	1.49291	+	0.565955i
$895$	9.03135	+	5.21425i	0.301885	+	0.174293i
$896$		0			0
$897$	−7.82286	+	6.38894i	−0.261198	+	0.213320i
$898$	32.2659			1.07673
$899$	7.27098	+	12.5937i	0.242501	+	0.420023i
$900$	36.4130	+	32.2415i	1.21377	+	1.07472i
$901$	11.8628	+	6.84900i	0.395208	+	0.228173i
$902$	−3.35857	−	5.81721i	−0.111828	−	0.193692i
$903$		0			0
$904$	−22.8781	+	39.6261i	−0.760916	+	1.31794i
$905$	−13.7486	+	7.93774i	−0.457018	+	0.263859i
$906$	42.0744	−	6.84360i	1.39783	−	0.227364i
$907$	−21.7951	+	37.7503i	−0.723695	+	1.25348i	0.235814	+	0.971798i	$0.424224\pi$
$907$	−21.7951	+	37.7503i	−0.723695	+	1.25348i	−0.959509	+	0.281678i	$0.909109\pi$
$908$	−49.2103	+	85.2348i	−1.63310	+	2.82862i
$909$	−3.84802	−	3.40719i	−0.127631	−	0.113009i
$910$		0			0
$911$	−1.67736	+	0.968423i	−0.0555734	+	0.0320853i	−0.527529	−	0.849537i	$-0.676881\pi$
$911$	−1.67736	+	0.968423i	−0.0555734	+	0.0320853i	0.471956	+	0.881622i	$0.343548\pi$
$912$	−28.8885	+	4.69886i	−0.956595	+	0.155595i
$913$		−	5.38766i		−	0.178306i
$914$		−	27.9467i		−	0.924393i
$915$	11.1160	−	29.3224i	0.367483	−	0.969369i
$916$	24.6379	−	14.2247i	0.814058	−	0.469997i
$917$		0			0
$918$	50.4716	+	31.8876i	1.66581	+	1.05245i
$919$	4.61421	−	7.99205i	0.152209	−	0.263634i	−0.779830	−	0.625991i	$-0.784695\pi$
$919$	4.61421	−	7.99205i	0.152209	−	0.263634i	0.932039	+	0.362357i	$0.118028\pi$
$920$	21.0377	−	36.4384i	0.693594	−	1.20134i
$921$	23.4132	+	28.6680i	0.771490	+	0.944642i
$922$	1.49724	−	0.864434i	0.0493091	−	0.0284686i
$923$	−6.39118	+	11.0698i	−0.210368	+	0.364368i
$924$		0			0
$925$	−4.56937	−	7.91438i	−0.150240	−	0.260223i
$926$	−93.3880	−	53.9176i	−3.06892	−	1.77184i
$927$	−7.04074	−	21.0706i	−0.231248	−	0.692048i
$928$	−26.0987	−	45.2043i	−0.856732	−	1.48390i
$929$	−53.3699			−1.75101			−0.875504	−	0.483211i	$-0.839471\pi$
$929$	−53.3699			−1.75101			−0.875504	+	0.483211i	$0.839471\pi$
$930$	13.0571	+	4.94989i	0.428160	+	0.162313i
$931$		0			0
$932$	−86.0952	−	49.7071i	−2.82014	−	1.62821i
$933$	21.7742	−	17.7830i	0.712856	−	0.582190i
$934$	88.3010	+	50.9806i	2.88930	+	1.66814i
$935$	2.96481	−	1.71173i	0.0969595	−	0.0559796i
$936$	19.5027	+	17.2684i	0.637465	+	0.564436i
$937$		−	28.6378i		−	0.935555i	−0.883846	−	0.467778i	$-0.845055\pi$
$937$		−	28.6378i		−	0.935555i	0.883846	−	0.467778i	$-0.154945\pi$
$938$		0			0
$939$	15.4268	+	18.8891i	0.503434	+	0.616424i
$940$	−22.5480	−	39.0542i	−0.735433	−	1.27381i
$941$	1.37662			0.0448764			0.0224382	−	0.999748i	$-0.492857\pi$
$941$	1.37662			0.0448764			0.0224382	+	0.999748i	$0.492857\pi$
$942$	82.8464	−	67.6607i	2.69928	−	2.20450i
$943$			19.9421i			0.649404i
$944$	−31.6764			−1.03098
$945$		0			0
$946$	−7.18651			−0.233653
$947$			54.2801i			1.76387i	0.471374	+	0.881933i	$0.343758\pi$
$947$			54.2801i			1.76387i	−0.471374	+	0.881933i	$0.656242\pi$
$948$	−25.5642	+	20.8783i	−0.830286	+	0.678095i
$949$	14.1085			0.457980
$950$	8.45802	+	14.6497i	0.274414	+	0.475300i
$951$	22.2374	+	27.2283i	0.721097	+	0.882939i
$952$		0			0
$953$		−	11.2998i		−	0.366036i	−0.983110	−	0.183018i	$-0.941413\pi$
$953$		−	11.2998i		−	0.366036i	0.983110	−	0.183018i	$-0.0585867\pi$
$954$	−22.8181	+	7.62468i	−0.738763	+	0.246858i
$955$	4.12399	−	2.38099i	0.133449	−	0.0770469i
$956$	35.4994	+	20.4956i	1.14813	+	0.662874i
$957$	−4.84978	+	3.96082i	−0.156771	+	0.128035i
$958$	85.6097	+	49.4268i	2.76592	+	1.59691i
$959$		0			0
$960$	−10.8012	−	4.09467i	−0.348607	−	0.132155i
$961$	24.8452			0.801458
$962$	−4.24260	−	7.34839i	−0.136787	−	0.236922i
$963$	0.302340	−	0.341458i	0.00974279	−	0.0110033i
$964$	34.6825	+	20.0240i	1.11705	+	0.644928i
$965$	−4.25324	−	7.36682i	−0.136917	−	0.237146i
$966$		0			0
$967$	5.93412	−	10.2782i	0.190829	−	0.330525i	−0.754696	−	0.656074i	$-0.772216\pi$
$967$	5.93412	−	10.2782i	0.190829	−	0.330525i	0.945525	+	0.325549i	$0.105549\pi$
$968$	−65.0324	+	37.5465i	−2.09022	+	1.20679i
$969$	9.22933	+	11.3007i	0.296489	+	0.363032i
$970$	−16.4454	+	28.4842i	−0.528029	+	0.914573i
$971$	28.0837	−	48.6424i	0.901249	−	1.56101i	0.0753736	−	0.997155i	$-0.475985\pi$
$971$	28.0837	−	48.6424i	0.901249	−	1.56101i	0.825875	−	0.563853i	$-0.190682\pi$
$972$	−70.7552	+	20.5465i	−2.26947	+	0.659029i
$973$		0			0
$974$	17.0826	−	9.86263i	0.547361	−	0.316019i
$975$	2.58600	−	6.82150i	0.0828182	−	0.218463i
$976$		−	128.404i		−	4.11011i
$977$			21.6651i			0.693129i	0.938026	+	0.346565i	$0.112652\pi$
$977$			21.6651i			0.693129i	−0.938026	+	0.346565i	$0.887348\pi$
$978$	39.1157	−	6.36236i	1.25078	−	0.203446i
$979$	0.866594	−	0.500328i	0.0276964	−	0.0159906i
$980$		0			0
$981$	15.3678	−	5.13516i	0.490656	−	0.163953i
$982$	−4.99072	+	8.64419i	−0.159260	+	0.275847i
$983$	9.70006	−	16.8010i	0.309384	−	0.535869i	−0.668844	−	0.743403i	$-0.733211\pi$
$983$	9.70006	−	16.8010i	0.309384	−	0.535869i	0.978228	+	0.207534i	$0.0665438\pi$
$984$	50.7644	−	8.25707i	1.61831	−	0.263226i
$985$	6.96052	−	4.01866i	0.221781	−	0.128045i
$986$	−33.6733	+	58.3238i	−1.07238	+	1.85741i
$987$		0			0
$988$	5.51814	+	9.55771i	0.175556	+	0.304071i
$989$	18.4771	+	10.6678i	0.587539	+	0.339216i
$990$	−1.20111	+	5.89156i	−0.0381737	+	0.187246i
$991$	−12.6630	−	21.9330i	−0.402254	−	0.696725i	0.591743	−	0.806126i	$-0.298440\pi$
$991$	−12.6630	−	21.9330i	−0.402254	−	0.696725i	−0.993998	+	0.109402i	$0.965107\pi$
$992$	22.0923			0.701430
$993$	−35.5072	+	28.9988i	−1.12679	+	0.920248i
$994$		0			0
$995$	−17.4066	−	10.0497i	−0.551828	−	0.318598i
$996$	66.8690	+	25.3497i	2.11882	+	0.803235i
$997$	−4.82016	−	2.78292i	−0.152656	−	0.0881360i	0.421726	−	0.906723i	$-0.361424\pi$
$997$	−4.82016	−	2.78292i	−0.152656	−	0.0881360i	−0.574382	+	0.818587i	$0.694758\pi$
$998$	−72.2309	+	41.7025i	−2.28643	+	1.32007i
$999$	13.8333	+	0.551828i	0.437666	+	0.0174591i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.i.b.68.5		10
3.2	odd	2		1323.2.i.b.1097.1		10
7.2	even	3		441.2.o.c.293.5		10
7.3	odd	6		441.2.s.b.374.1		10
7.4	even	3		63.2.s.b.59.1	yes	10
7.5	odd	6		441.2.o.d.293.5		10
7.6	odd	2		63.2.i.b.5.5	✓	10
9.2	odd	6		441.2.s.b.362.1		10
9.7	even	3		1323.2.s.b.656.5		10
21.2	odd	6		1323.2.o.d.881.1		10
21.5	even	6		1323.2.o.c.881.1		10
21.11	odd	6		189.2.s.b.17.5		10
21.17	even	6		1323.2.s.b.962.5		10
21.20	even	2		189.2.i.b.152.1		10
28.11	odd	6		1008.2.df.b.689.1		10
28.27	even	2		1008.2.ca.b.257.1		10
63.2	odd	6		441.2.o.d.146.5		10
63.4	even	3		567.2.p.c.80.5		10
63.11	odd	6		63.2.i.b.38.1	yes	10
63.13	odd	6		567.2.p.d.404.1		10
63.16	even	3		1323.2.o.c.440.1		10
63.20	even	6		63.2.s.b.47.1	yes	10
63.25	even	3		189.2.i.b.143.5		10
63.32	odd	6		567.2.p.d.80.1		10
63.34	odd	6		189.2.s.b.89.5		10
63.38	even	6	inner	441.2.i.b.227.1		10
63.41	even	6		567.2.p.c.404.5		10
63.47	even	6		441.2.o.c.146.5		10
63.52	odd	6		1323.2.i.b.521.5		10
63.61	odd	6		1323.2.o.d.440.1		10
84.11	even	6		3024.2.df.b.17.2		10
84.83	odd	2		3024.2.ca.b.2609.2		10
252.11	even	6		1008.2.ca.b.353.1		10
252.83	odd	6		1008.2.df.b.929.1		10
252.151	odd	6		3024.2.ca.b.2033.2		10
252.223	even	6		3024.2.df.b.1601.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.5	✓	10	7.6	odd	2
63.2.i.b.38.1	yes	10	63.11	odd	6
63.2.s.b.47.1	yes	10	63.20	even	6
63.2.s.b.59.1	yes	10	7.4	even	3
189.2.i.b.143.5		10	63.25	even	3
189.2.i.b.152.1		10	21.20	even	2
189.2.s.b.17.5		10	21.11	odd	6
189.2.s.b.89.5		10	63.34	odd	6
441.2.i.b.68.5		10	1.1	even	1	trivial
441.2.i.b.227.1		10	63.38	even	6	inner
441.2.o.c.146.5		10	63.47	even	6
441.2.o.c.293.5		10	7.2	even	3
441.2.o.d.146.5		10	63.2	odd	6
441.2.o.d.293.5		10	7.5	odd	6
441.2.s.b.362.1		10	9.2	odd	6
441.2.s.b.374.1		10	7.3	odd	6
567.2.p.c.80.5		10	63.4	even	3
567.2.p.c.404.5		10	63.41	even	6
567.2.p.d.80.1		10	63.32	odd	6
567.2.p.d.404.1		10	63.13	odd	6
1008.2.ca.b.257.1		10	28.27	even	2
1008.2.ca.b.353.1		10	252.11	even	6
1008.2.df.b.689.1		10	28.11	odd	6
1008.2.df.b.929.1		10	252.83	odd	6
1323.2.i.b.521.5		10	63.52	odd	6
1323.2.i.b.1097.1		10	3.2	odd	2
1323.2.o.c.440.1		10	63.16	even	3
1323.2.o.c.881.1		10	21.5	even	6
1323.2.o.d.440.1		10	63.61	odd	6
1323.2.o.d.881.1		10	21.2	odd	6
1323.2.s.b.656.5		10	9.7	even	3
1323.2.s.b.962.5		10	21.17	even	6
3024.2.ca.b.2033.2		10	252.151	odd	6
3024.2.ca.b.2609.2		10	84.83	odd	2
3024.2.df.b.17.2		10	84.11	even	6
3024.2.df.b.1601.2		10	252.223	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)

\(f(q)\)	\(=\)	\(q+2.59354i q^{2} +(-1.34151 + 1.09561i) q^{3} -4.72645 q^{4} +(-0.626493 - 1.08512i) q^{5} +(-2.84151 - 3.47925i) q^{6} -7.07116i q^{8} +(0.599280 - 2.93953i) q^{9} +O(q^{10})\)	\(q+2.59354i q^{2} +(-1.34151 + 1.09561i) q^{3} -4.72645 q^{4} +(-0.626493 - 1.08512i) q^{5} +(-2.84151 - 3.47925i) q^{6} -7.07116i q^{8} +(0.599280 - 2.93953i) q^{9} +(2.81429 - 1.62483i) q^{10} +(-0.534126 - 0.308378i) q^{11} +(6.34056 - 5.17834i) q^{12} +(-1.06343 - 0.613974i) q^{13} +(2.02931 + 0.769301i) q^{15} +8.88643 q^{16} +(-2.21501 - 3.83652i) q^{17} +(7.62380 + 1.55426i) q^{18} +(1.64679 + 0.950775i) q^{19} +(2.96109 + 5.12875i) q^{20} +(0.799790 - 1.38528i) q^{22} +(-4.11267 + 2.37445i) q^{23} +(7.74722 + 9.48600i) q^{24} +(1.71501 - 2.97049i) q^{25} +(1.59237 - 2.75806i) q^{26} +(2.41664 + 4.59998i) q^{27} +(-5.07629 + 2.93080i) q^{29} +(-1.99521 + 5.26309i) q^{30} -2.48089i q^{31} +8.90499i q^{32} +(1.05440 - 0.171503i) q^{33} +(9.95016 - 5.74473i) q^{34} +(-2.83247 + 13.8936i) q^{36} +(1.33217 - 2.30738i) q^{37} +(-2.46587 + 4.27102i) q^{38} +(2.09928 - 0.341458i) q^{39} +(-7.67303 + 4.43003i) q^{40} +(2.09966 - 3.63671i) q^{41} +(-2.24637 - 3.89083i) q^{43} +(2.52452 + 1.45753i) q^{44} +(-3.56518 + 1.19131i) q^{45} +(-6.15823 - 10.6664i) q^{46} -7.61476 q^{47} +(-11.9212 + 9.73605i) q^{48} +(7.70409 + 4.44796i) q^{50} +(7.17478 + 2.71992i) q^{51} +(5.02627 + 2.90192i) q^{52} +(-2.67782 + 1.54604i) q^{53} +(-11.9302 + 6.26766i) q^{54} +0.772786i q^{55} +(-3.25086 + 0.528768i) q^{57} +(-7.60114 - 13.1656i) q^{58} -3.56459 q^{59} +(-9.59142 - 3.63606i) q^{60} -14.4495i q^{61} +6.43428 q^{62} -5.32259 q^{64} +1.53860i q^{65} +(0.444799 + 2.73462i) q^{66} +13.6129 q^{67} +(10.4692 + 18.1331i) q^{68} +(2.91570 - 7.69121i) q^{69} -10.4095i q^{71} +(-20.7859 - 4.23760i) q^{72} +(-9.95016 + 5.74473i) q^{73} +(5.98429 + 3.45503i) q^{74} +(0.953796 + 5.86392i) q^{75} +(-7.78348 - 4.49379i) q^{76} +(0.885586 + 5.44457i) q^{78} -4.03185 q^{79} +(-5.56728 - 9.64281i) q^{80} +(-8.28173 - 3.52321i) q^{81} +(9.43196 + 5.44554i) q^{82} +(4.36775 + 7.56516i) q^{83} +(-2.77538 + 4.80710i) q^{85} +(10.0910 - 5.82605i) q^{86} +(3.59887 - 9.49331i) q^{87} +(-2.18059 + 3.77689i) q^{88} +(-0.811226 + 1.40508i) q^{89} +(-3.08970 - 9.24645i) q^{90} +(19.4383 - 11.2227i) q^{92} +(2.71808 + 3.32813i) q^{93} -19.7492i q^{94} -2.38261i q^{95} +(-9.75639 - 11.9461i) q^{96} +(-8.76527 + 5.06063i) q^{97} +(-1.22658 + 1.38528i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{3} - 8 q^{4} - 12 q^{6} + 3 q^{9}+O(q^{10}) \) 10 * q + 3 * q^3 - 8 * q^4 - 12 * q^6 + 3 * q^9	\( 10 q + 3 q^{3} - 8 q^{4} - 12 q^{6} + 3 q^{9} + 15 q^{10} - 12 q^{11} + 12 q^{12} + 6 q^{13} - 3 q^{15} + 12 q^{16} - 12 q^{17} + 24 q^{18} - 3 q^{19} - 3 q^{20} + 5 q^{22} - 15 q^{23} + 7 q^{25} + 3 q^{26} + 27 q^{27} - 15 q^{29} + 6 q^{30} + 3 q^{34} - 18 q^{36} + 6 q^{37} - 18 q^{38} + 18 q^{39} - 15 q^{40} - 9 q^{41} + 3 q^{43} - 24 q^{44} - 30 q^{45} - 13 q^{46} - 30 q^{47} - 15 q^{48} + 3 q^{50} + 21 q^{51} + 12 q^{52} + 9 q^{53} - 9 q^{54} - 36 q^{57} + 8 q^{58} + 36 q^{59} - 48 q^{60} + 12 q^{62} + 6 q^{64} + 39 q^{66} + 20 q^{67} + 27 q^{68} - 3 q^{69} - 30 q^{72} - 3 q^{73} - 30 q^{74} - 6 q^{75} + 9 q^{76} + 24 q^{78} - 40 q^{79} - 30 q^{80} + 15 q^{81} - 9 q^{82} - 15 q^{83} + 18 q^{85} + 54 q^{86} - 6 q^{87} - 8 q^{88} + 24 q^{89} + 24 q^{90} + 39 q^{92} + 36 q^{93} - 33 q^{96} + 6 q^{97} + 21 q^{99}+O(q^{100}) \) 10 * q + 3 * q^3 - 8 * q^4 - 12 * q^6 + 3 * q^9 + 15 * q^10 - 12 * q^11 + 12 * q^12 + 6 * q^13 - 3 * q^15 + 12 * q^16 - 12 * q^17 + 24 * q^18 - 3 * q^19 - 3 * q^20 + 5 * q^22 - 15 * q^23 + 7 * q^25 + 3 * q^26 + 27 * q^27 - 15 * q^29 + 6 * q^30 + 3 * q^34 - 18 * q^36 + 6 * q^37 - 18 * q^38 + 18 * q^39 - 15 * q^40 - 9 * q^41 + 3 * q^43 - 24 * q^44 - 30 * q^45 - 13 * q^46 - 30 * q^47 - 15 * q^48 + 3 * q^50 + 21 * q^51 + 12 * q^52 + 9 * q^53 - 9 * q^54 - 36 * q^57 + 8 * q^58 + 36 * q^59 - 48 * q^60 + 12 * q^62 + 6 * q^64 + 39 * q^66 + 20 * q^67 + 27 * q^68 - 3 * q^69 - 30 * q^72 - 3 * q^73 - 30 * q^74 - 6 * q^75 + 9 * q^76 + 24 * q^78 - 40 * q^79 - 30 * q^80 + 15 * q^81 - 9 * q^82 - 15 * q^83 + 18 * q^85 + 54 * q^86 - 6 * q^87 - 8 * q^88 + 24 * q^89 + 24 * q^90 + 39 * q^92 + 36 * q^93 - 33 * q^96 + 6 * q^97 + 21 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

Properties

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