LMFDB - Embedded newform 245.2.e.g.116.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,2,Mod(116,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("245.116");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	245.e (of order $3$, 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:	$1.95633484952$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			116.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	245.116
Dual form			245.2.e.g.226.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 1.22474i) q^{2} +(-0.207107 + 0.358719i) q^{3} +(0.500000 + 0.866025i) q^{5} -0.585786 q^{6} +2.82843 q^{8} +(1.41421 + 2.44949i) q^{9} +O(q^{10})$	\(q+(0.707107 + 1.22474i) q^{2} +(-0.207107 + 0.358719i) q^{3} +(0.500000 + 0.866025i) q^{5} -0.585786 q^{6} +2.82843 q^{8} +(1.41421 + 2.44949i) q^{9} +(-0.707107 + 1.22474i) q^{10} +(0.0857864 - 0.148586i) q^{11} -4.41421 q^{13} -0.414214 q^{15} +(2.00000 + 3.46410i) q^{16} +(1.62132 - 2.80821i) q^{17} +(-2.00000 + 3.46410i) q^{18} +(3.00000 + 5.19615i) q^{19} +0.242641 q^{22} +(-3.70711 - 6.42090i) q^{23} +(-0.585786 + 1.01461i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-3.12132 - 5.40629i) q^{26} -2.41421 q^{27} -8.65685 q^{29} +(-0.292893 - 0.507306i) q^{30} +(5.12132 - 8.87039i) q^{31} +(0.0355339 + 0.0615465i) q^{33} +4.58579 q^{34} +(-1.12132 - 1.94218i) q^{37} +(-4.24264 + 7.34847i) q^{38} +(0.914214 - 1.58346i) q^{39} +(1.41421 + 2.44949i) q^{40} +6.24264 q^{41} +2.00000 q^{43} +(-1.41421 + 2.44949i) q^{45} +(5.24264 - 9.08052i) q^{46} +(-3.62132 - 6.27231i) q^{47} -1.65685 q^{48} -1.41421 q^{50} +(0.671573 + 1.16320i) q^{51} +(-2.12132 + 3.67423i) q^{53} +(-1.70711 - 2.95680i) q^{54} +0.171573 q^{55} -2.48528 q^{57} +(-6.12132 - 10.6024i) q^{58} +(-1.12132 + 1.94218i) q^{59} +(-1.41421 - 2.44949i) q^{61} +14.4853 q^{62} +8.00000 q^{64} +(-2.20711 - 3.82282i) q^{65} +(-0.0502525 + 0.0870399i) q^{66} +(4.12132 - 7.13834i) q^{67} +3.07107 q^{69} -3.17157 q^{71} +(4.00000 + 6.92820i) q^{72} +(-4.24264 + 7.34847i) q^{73} +(1.58579 - 2.74666i) q^{74} +(-0.207107 - 0.358719i) q^{75} +2.58579 q^{78} +(-0.742641 - 1.28629i) q^{79} +(-2.00000 + 3.46410i) q^{80} +(-3.74264 + 6.48244i) q^{81} +(4.41421 + 7.64564i) q^{82} +3.24264 q^{85} +(1.41421 + 2.44949i) q^{86} +(1.79289 - 3.10538i) q^{87} +(0.242641 - 0.420266i) q^{88} +(-4.00000 - 6.92820i) q^{89} -4.00000 q^{90} +(2.12132 + 3.67423i) q^{93} +(5.12132 - 8.87039i) q^{94} +(-3.00000 + 5.19615i) q^{95} -13.2426 q^{97} +0.485281 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{5} - 8 q^{6}+O(q^{10}) $ 4 * q + 2 * q^3 + 2 * q^5 - 8 * q^6	$ 4 q + 2 q^{3} + 2 q^{5} - 8 q^{6} + 6 q^{11} - 12 q^{13} + 4 q^{15} + 8 q^{16} - 2 q^{17} - 8 q^{18} + 12 q^{19} - 16 q^{22} - 12 q^{23} - 8 q^{24} - 2 q^{25} - 4 q^{26} - 4 q^{27} - 12 q^{29} - 4 q^{30} + 12 q^{31} - 14 q^{33} + 24 q^{34} + 4 q^{37} - 2 q^{39} + 8 q^{41} + 8 q^{43} + 4 q^{46} - 6 q^{47} + 16 q^{48} + 14 q^{51} - 4 q^{54} + 12 q^{55} + 24 q^{57} - 16 q^{58} + 4 q^{59} + 24 q^{62} + 32 q^{64} - 6 q^{65} - 20 q^{66} + 8 q^{67} - 16 q^{69} - 24 q^{71} + 16 q^{72} + 12 q^{74} + 2 q^{75} + 16 q^{78} + 14 q^{79} - 8 q^{80} + 2 q^{81} + 12 q^{82} - 4 q^{85} + 10 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} + 12 q^{94} - 12 q^{95} - 36 q^{97} - 32 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^5 - 8 * q^6 + 6 * q^11 - 12 * q^13 + 4 * q^15 + 8 * q^16 - 2 * q^17 - 8 * q^18 + 12 * q^19 - 16 * q^22 - 12 * q^23 - 8 * q^24 - 2 * q^25 - 4 * q^26 - 4 * q^27 - 12 * q^29 - 4 * q^30 + 12 * q^31 - 14 * q^33 + 24 * q^34 + 4 * q^37 - 2 * q^39 + 8 * q^41 + 8 * q^43 + 4 * q^46 - 6 * q^47 + 16 * q^48 + 14 * q^51 - 4 * q^54 + 12 * q^55 + 24 * q^57 - 16 * q^58 + 4 * q^59 + 24 * q^62 + 32 * q^64 - 6 * q^65 - 20 * q^66 + 8 * q^67 - 16 * q^69 - 24 * q^71 + 16 * q^72 + 12 * q^74 + 2 * q^75 + 16 * q^78 + 14 * q^79 - 8 * q^80 + 2 * q^81 + 12 * q^82 - 4 * q^85 + 10 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 + 12 * q^94 - 12 * q^95 - 36 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.707107	+	1.22474i	0.500000	+	0.866025i	1.00000			$0$
$2$	0.707107	+	1.22474i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$3$	−0.207107	+	0.358719i	−0.119573	+	0.207107i	−0.919599	−	0.392859i	$-0.871486\pi$
$3$	−0.207107	+	0.358719i	−0.119573	+	0.207107i	0.800025	+	0.599966i	$0.204819\pi$
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−0.585786			−0.239146
$7$		0			0
$7$		0			0
$8$	2.82843			1.00000
$9$	1.41421	+	2.44949i	0.471405	+	0.816497i
$10$	−0.707107	+	1.22474i	−0.223607	+	0.387298i
$11$	0.0857864	−	0.148586i	0.0258656	−	0.0448005i	−0.852803	−	0.522233i	$-0.825099\pi$
$11$	0.0857864	−	0.148586i	0.0258656	−	0.0448005i	0.878668	+	0.477432i	$0.158432\pi$
$12$		0			0
$13$	−4.41421			−1.22428			−0.612141	−	0.790748i	$-0.709692\pi$
$13$	−4.41421			−1.22428			−0.612141	+	0.790748i	$0.709692\pi$
$14$		0			0
$15$	−0.414214			−0.106949
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	1.62132	−	2.80821i	0.393228	−	0.681091i	−0.599645	−	0.800266i	$-0.704692\pi$
$17$	1.62132	−	2.80821i	0.393228	−	0.681091i	0.992873	+	0.119175i	$0.0380250\pi$
$18$	−2.00000	+	3.46410i	−0.471405	+	0.816497i
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	0.972404	+	0.233301i	$0.0749529\pi$
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	−0.284157	+	0.958778i	$0.591714\pi$
$20$		0			0
$21$		0			0
$22$	0.242641			0.0517312
$23$	−3.70711	−	6.42090i	−0.772985	−	1.33885i	−0.935920	−	0.352213i	$-0.885429\pi$
$23$	−3.70711	−	6.42090i	−0.772985	−	1.33885i	0.162935	−	0.986637i	$-0.447904\pi$
$24$	−0.585786	+	1.01461i	−0.119573	+	0.207107i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−3.12132	−	5.40629i	−0.612141	−	1.06026i
$27$	−2.41421			−0.464616
$28$		0			0
$29$	−8.65685			−1.60754			−0.803769	−	0.594942i	$-0.797175\pi$
$29$	−8.65685			−1.60754			−0.803769	+	0.594942i	$0.797175\pi$
$30$	−0.292893	−	0.507306i	−0.0534747	−	0.0926210i
$31$	5.12132	−	8.87039i	0.919816	−	1.59317i	0.120124	−	0.992759i	$-0.461671\pi$
$31$	5.12132	−	8.87039i	0.919816	−	1.59317i	0.799693	−	0.600410i	$-0.204996\pi$
$32$		0			0
$33$	0.0355339	+	0.0615465i	0.00618566	+	0.0107139i
$34$	4.58579			0.786456
$35$		0			0
$36$		0			0
$37$	−1.12132	−	1.94218i	−0.184344	−	0.319293i	0.759011	−	0.651077i	$-0.225683\pi$
$37$	−1.12132	−	1.94218i	−0.184344	−	0.319293i	−0.943355	+	0.331784i	$0.892349\pi$
$38$	−4.24264	+	7.34847i	−0.688247	+	1.19208i
$39$	0.914214	−	1.58346i	0.146391	−	0.253557i
$40$	1.41421	+	2.44949i	0.223607	+	0.387298i
$41$	6.24264			0.974937			0.487468	−	0.873141i	$-0.337920\pi$
$41$	6.24264			0.974937			0.487468	+	0.873141i	$0.337920\pi$
$42$		0			0
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$		0			0
$45$	−1.41421	+	2.44949i	−0.210819	+	0.365148i
$46$	5.24264	−	9.08052i	0.772985	−	1.33885i
$47$	−3.62132	−	6.27231i	−0.528224	−	0.914911i	−0.999459	−	0.0329027i	$-0.989525\pi$
$47$	−3.62132	−	6.27231i	−0.528224	−	0.914911i	0.471235	−	0.882008i	$-0.343808\pi$
$48$	−1.65685			−0.239146
$49$		0			0
$50$	−1.41421			−0.200000
$51$	0.671573	+	1.16320i	0.0940390	+	0.162880i
$52$		0			0
$53$	−2.12132	+	3.67423i	−0.291386	+	0.504695i	−0.974138	−	0.225955i	$-0.927450\pi$
$53$	−2.12132	+	3.67423i	−0.291386	+	0.504695i	0.682752	+	0.730650i	$0.260783\pi$
$54$	−1.70711	−	2.95680i	−0.232308	−	0.402369i
$55$	0.171573			0.0231349
$56$		0			0
$57$	−2.48528			−0.329184
$58$	−6.12132	−	10.6024i	−0.803769	−	1.39217i
$59$	−1.12132	+	1.94218i	−0.145983	+	0.252851i	−0.929739	−	0.368218i	$-0.879968\pi$
$59$	−1.12132	+	1.94218i	−0.145983	+	0.252851i	0.783756	+	0.621069i	$0.213301\pi$
$60$		0			0
$61$	−1.41421	−	2.44949i	−0.181071	−	0.313625i	0.761174	−	0.648547i	$-0.224623\pi$
$61$	−1.41421	−	2.44949i	−0.181071	−	0.313625i	−0.942246	+	0.334922i	$0.891290\pi$
$62$	14.4853			1.83963
$63$		0			0
$64$	8.00000			1.00000
$65$	−2.20711	−	3.82282i	−0.273758	−	0.474163i
$66$	−0.0502525	+	0.0870399i	−0.00618566	+	0.0107139i
$67$	4.12132	−	7.13834i	0.503499	−	0.872087i	−0.496492	−	0.868041i	$-0.665379\pi$
$67$	4.12132	−	7.13834i	0.503499	−	0.872087i	0.999992	−	0.00404550i	$-0.00128773\pi$
$68$		0			0
$69$	3.07107			0.369713
$70$		0			0
$71$	−3.17157			−0.376396			−0.188198	−	0.982131i	$-0.560265\pi$
$71$	−3.17157			−0.376396			−0.188198	+	0.982131i	$0.560265\pi$
$72$	4.00000	+	6.92820i	0.471405	+	0.816497i
$73$	−4.24264	+	7.34847i	−0.496564	+	0.860073i	−0.999992	−	0.00396356i	$-0.998738\pi$
$73$	−4.24264	+	7.34847i	−0.496564	+	0.860073i	0.503429	+	0.864037i	$0.332072\pi$
$74$	1.58579	−	2.74666i	0.184344	−	0.319293i
$75$	−0.207107	−	0.358719i	−0.0239146	−	0.0414214i
$76$		0			0
$77$		0			0
$78$	2.58579			0.292783
$79$	−0.742641	−	1.28629i	−0.0835536	−	0.144719i	0.821220	−	0.570611i	$-0.193294\pi$
$79$	−0.742641	−	1.28629i	−0.0835536	−	0.144719i	−0.904774	+	0.425892i	$0.859960\pi$
$80$	−2.00000	+	3.46410i	−0.223607	+	0.387298i
$81$	−3.74264	+	6.48244i	−0.415849	+	0.720272i
$82$	4.41421	+	7.64564i	0.487468	+	0.844320i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	3.24264			0.351714
$86$	1.41421	+	2.44949i	0.152499	+	0.264135i
$87$	1.79289	−	3.10538i	0.192218	−	0.332932i
$88$	0.242641	−	0.420266i	0.0258656	−	0.0448005i
$89$	−4.00000	−	6.92820i	−0.423999	−	0.734388i	0.572327	−	0.820025i	$-0.306041\pi$
$89$	−4.00000	−	6.92820i	−0.423999	−	0.734388i	−0.996326	+	0.0856373i	$0.972707\pi$
$90$	−4.00000			−0.421637
$91$		0			0
$92$		0			0
$93$	2.12132	+	3.67423i	0.219971	+	0.381000i
$94$	5.12132	−	8.87039i	0.528224	−	0.914911i
$95$	−3.00000	+	5.19615i	−0.307794	+	0.533114i
$96$		0			0
$97$	−13.2426			−1.34459			−0.672293	−	0.740285i	$-0.734691\pi$
$97$	−13.2426			−1.34459			−0.672293	+	0.740285i	$0.734691\pi$
$98$		0			0
$99$	0.485281			0.0487726
$100$		0			0
$101$	1.24264	−	2.15232i	0.123647	−	0.214164i	−0.797556	−	0.603245i	$-0.793874\pi$
$101$	1.24264	−	2.15232i	0.123647	−	0.214164i	0.921203	+	0.389081i	$0.127208\pi$
$102$	−0.949747	+	1.64501i	−0.0940390	+	0.162880i
$103$	9.62132	+	16.6646i	0.948017	+	1.64201i	0.749595	+	0.661897i	$0.230248\pi$
$103$	9.62132	+	16.6646i	0.948017	+	1.64201i	0.198422	+	0.980117i	$0.436418\pi$
$104$	−12.4853			−1.22428
$105$		0			0
$106$	−6.00000			−0.582772
$107$	1.24264	+	2.15232i	0.120131	+	0.208072i	0.919819	−	0.392343i	$-0.128335\pi$
$107$	1.24264	+	2.15232i	0.120131	+	0.208072i	−0.799688	+	0.600415i	$0.795002\pi$
$108$		0			0
$109$	−2.50000	+	4.33013i	−0.239457	+	0.414751i	−0.960558	−	0.278078i	$-0.910303\pi$
$109$	−2.50000	+	4.33013i	−0.239457	+	0.414751i	0.721102	+	0.692829i	$0.243636\pi$
$110$	0.121320	+	0.210133i	0.0115674	+	0.0200354i
$111$	0.928932			0.0881703
$112$		0			0
$113$	−13.0711			−1.22962			−0.614811	−	0.788674i	$-0.710768\pi$
$113$	−13.0711			−1.22962			−0.614811	+	0.788674i	$0.710768\pi$
$114$	−1.75736	−	3.04384i	−0.164592	−	0.285081i
$115$	3.70711	−	6.42090i	0.345689	−	0.598752i
$116$		0			0
$117$	−6.24264	−	10.8126i	−0.577132	−	0.999623i
$118$	−3.17157			−0.291967
$119$		0			0
$120$	−1.17157			−0.106949
$121$	5.48528	+	9.50079i	0.498662	+	0.863708i
$122$	2.00000	−	3.46410i	0.181071	−	0.313625i
$123$	−1.29289	+	2.23936i	−0.116576	+	0.201916i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	8.24264			0.731416			0.365708	−	0.930730i	$-0.380827\pi$
$127$	8.24264			0.731416			0.365708	+	0.930730i	$0.380827\pi$
$128$	5.65685	+	9.79796i	0.500000	+	0.866025i
$129$	−0.414214	+	0.717439i	−0.0364695	+	0.0631670i
$130$	3.12132	−	5.40629i	0.273758	−	0.474163i
$131$	6.12132	+	10.6024i	0.534822	+	0.926339i	0.999172	+	0.0406873i	$0.0129548\pi$
$131$	6.12132	+	10.6024i	0.534822	+	0.926339i	−0.464350	+	0.885652i	$0.653712\pi$
$132$		0			0
$133$		0			0
$134$	11.6569			1.00700
$135$	−1.20711	−	2.09077i	−0.103891	−	0.179945i
$136$	4.58579	−	7.94282i	0.393228	−	0.681091i
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	0.487278	+	0.873247i	$0.337990\pi$
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	−0.999893	+	0.0146279i	$0.995344\pi$
$138$	2.17157	+	3.76127i	0.184857	+	0.320181i
$139$	−7.75736			−0.657971			−0.328985	−	0.944335i	$-0.606707\pi$
$139$	−7.75736			−0.657971			−0.328985	+	0.944335i	$0.606707\pi$
$140$		0			0
$141$	3.00000			0.252646
$142$	−2.24264	−	3.88437i	−0.188198	−	0.325969i
$143$	−0.378680	+	0.655892i	−0.0316668	+	0.0548485i
$144$	−5.65685	+	9.79796i	−0.471405	+	0.816497i
$145$	−4.32843	−	7.49706i	−0.359456	−	0.622597i
$146$	−12.0000			−0.993127
$147$		0			0
$148$		0			0
$149$	4.58579	+	7.94282i	0.375682	+	0.650701i	0.990429	−	0.138024i	$-0.0440751\pi$
$149$	4.58579	+	7.94282i	0.375682	+	0.650701i	−0.614747	+	0.788725i	$0.710742\pi$
$150$	0.292893	−	0.507306i	0.0239146	−	0.0414214i
$151$	3.74264	−	6.48244i	0.304572	−	0.527534i	−0.672594	−	0.740012i	$-0.734820\pi$
$151$	3.74264	−	6.48244i	0.304572	−	0.527534i	0.977166	+	0.212478i	$0.0681533\pi$
$152$	8.48528	+	14.6969i	0.688247	+	1.19208i
$153$	9.17157			0.741478
$154$		0			0
$155$	10.2426			0.822709
$156$		0			0
$157$	−7.58579	+	13.1390i	−0.605412	+	1.04860i	0.386575	+	0.922258i	$0.373658\pi$
$157$	−7.58579	+	13.1390i	−0.605412	+	1.04860i	−0.991986	+	0.126346i	$0.959675\pi$
$158$	1.05025	−	1.81909i	0.0835536	−	0.144719i
$159$	−0.878680	−	1.52192i	−0.0696838	−	0.120696i
$160$		0			0
$161$		0			0
$162$	−10.5858			−0.831698
$163$	5.12132	+	8.87039i	0.401133	+	0.694782i	0.993863	−	0.110619i	$-0.0352833\pi$
$163$	5.12132	+	8.87039i	0.401133	+	0.694782i	−0.592730	+	0.805401i	$0.701950\pi$
$164$		0			0
$165$	−0.0355339	+	0.0615465i	−0.00276631	+	0.00479139i
$166$		0			0
$167$	−0.757359			−0.0586062			−0.0293031	−	0.999571i	$-0.509329\pi$
$167$	−0.757359			−0.0586062			−0.0293031	+	0.999571i	$0.509329\pi$
$168$		0			0
$169$	6.48528			0.498868
$170$	2.29289	+	3.97141i	0.175857	+	0.304593i
$171$	−8.48528	+	14.6969i	−0.648886	+	1.12390i
$172$		0			0
$173$	−3.62132	−	6.27231i	−0.275324	−	0.476875i	0.694893	−	0.719113i	$-0.255452\pi$
$173$	−3.62132	−	6.27231i	−0.275324	−	0.476875i	−0.970217	+	0.242238i	$0.922118\pi$
$174$	5.07107			0.384437
$175$		0			0
$176$	0.686292			0.0517312
$177$	−0.464466	−	0.804479i	−0.0349114	−	0.0604683i
$178$	5.65685	−	9.79796i	0.423999	−	0.734388i
$179$	7.24264	−	12.5446i	0.541340	−	0.937629i	−0.457487	−	0.889216i	$-0.651250\pi$
$179$	7.24264	−	12.5446i	0.541340	−	0.937629i	0.998827	−	0.0484128i	$-0.0154163\pi$
$180$		0			0
$181$	18.7279			1.39204			0.696018	−	0.718025i	$-0.254953\pi$
$181$	18.7279			1.39204			0.696018	+	0.718025i	$0.254953\pi$
$182$		0			0
$183$	1.17157			0.0866052
$184$	−10.4853	−	18.1610i	−0.772985	−	1.33885i
$185$	1.12132	−	1.94218i	0.0824411	−	0.142792i
$186$	−3.00000	+	5.19615i	−0.219971	+	0.381000i
$187$	−0.278175	−	0.481813i	−0.0203421	−	0.0352336i
$188$		0			0
$189$		0			0
$190$	−8.48528			−0.615587
$191$	−6.98528	−	12.0989i	−0.505437	−	0.875443i	−0.999980	−	0.00628978i	$-0.997998\pi$
$191$	−6.98528	−	12.0989i	−0.505437	−	0.875443i	0.494543	−	0.869153i	$-0.335335\pi$
$192$	−1.65685	+	2.86976i	−0.119573	+	0.207107i
$193$	8.00000	−	13.8564i	0.575853	−	0.997406i	−0.420096	−	0.907480i	$-0.638004\pi$
$193$	8.00000	−	13.8564i	0.575853	−	0.997406i	0.995948	−	0.0899262i	$-0.0286631\pi$
$194$	−9.36396	−	16.2189i	−0.672293	−	1.16445i
$195$	1.82843			0.130936
$196$		0			0
$197$	13.4142			0.955723			0.477862	−	0.878435i	$-0.341412\pi$
$197$	13.4142			0.955723			0.477862	+	0.878435i	$0.341412\pi$
$198$	0.343146	+	0.594346i	0.0243863	+	0.0422383i
$199$	−3.70711	+	6.42090i	−0.262790	+	0.455165i	−0.966982	−	0.254844i	$-0.917976\pi$
$199$	−3.70711	+	6.42090i	−0.262790	+	0.455165i	0.704192	+	0.710009i	$0.251309\pi$
$200$	−1.41421	+	2.44949i	−0.100000	+	0.173205i
$201$	1.70711	+	2.95680i	0.120410	+	0.208556i
$202$	3.51472			0.247295
$203$		0			0
$204$		0			0
$205$	3.12132	+	5.40629i	0.218002	+	0.377591i
$206$	−13.6066	+	23.5673i	−0.948017	+	1.64201i
$207$	10.4853	−	18.1610i	0.728777	−	1.26228i
$208$	−8.82843	−	15.2913i	−0.612141	−	1.06026i
$209$	1.02944			0.0712077
$210$		0			0
$211$	9.00000			0.619586			0.309793	−	0.950804i	$-0.399740\pi$
$211$	9.00000			0.619586			0.309793	+	0.950804i	$0.399740\pi$
$212$		0			0
$213$	0.656854	−	1.13770i	0.0450069	−	0.0779543i
$214$	−1.75736	+	3.04384i	−0.120131	+	0.208072i
$215$	1.00000	+	1.73205i	0.0681994	+	0.118125i
$216$	−6.82843			−0.464616
$217$		0			0
$218$	−7.07107			−0.478913
$219$	−1.75736	−	3.04384i	−0.118751	−	0.205683i
$220$		0			0
$221$	−7.15685	+	12.3960i	−0.481422	+	0.833848i
$222$	0.656854	+	1.13770i	0.0440852	+	0.0763578i
$223$	24.2132			1.62144			0.810718	−	0.585437i	$-0.199077\pi$
$223$	24.2132			1.62144			0.810718	+	0.585437i	$0.199077\pi$
$224$		0			0
$225$	−2.82843			−0.188562
$226$	−9.24264	−	16.0087i	−0.614811	−	1.06488i
$227$	7.86396	−	13.6208i	0.521949	−	0.904043i	−0.477725	−	0.878510i	$-0.658538\pi$
$227$	7.86396	−	13.6208i	0.521949	−	0.904043i	0.999674	−	0.0255332i	$-0.00812837\pi$
$228$		0			0
$229$	9.02082	+	15.6245i	0.596112	+	1.03250i	0.993389	+	0.114798i	$0.0366220\pi$
$229$	9.02082	+	15.6245i	0.596112	+	1.03250i	−0.397277	+	0.917699i	$0.630045\pi$
$230$	10.4853			0.691379
$231$		0			0
$232$	−24.4853			−1.60754
$233$	4.58579	+	7.94282i	0.300425	+	0.520351i	0.976232	−	0.216727i	$-0.0695382\pi$
$233$	4.58579	+	7.94282i	0.300425	+	0.520351i	−0.675807	+	0.737078i	$0.736205\pi$
$234$	8.82843	−	15.2913i	0.577132	−	0.999623i
$235$	3.62132	−	6.27231i	0.236229	−	0.409160i
$236$		0			0
$237$	0.615224			0.0399631
$238$		0			0
$239$	−17.4853			−1.13103			−0.565514	−	0.824738i	$-0.691322\pi$
$239$	−17.4853			−1.13103			−0.565514	+	0.824738i	$0.691322\pi$
$240$	−0.828427	−	1.43488i	−0.0534747	−	0.0926210i
$241$	−0.363961	+	0.630399i	−0.0234448	+	0.0406076i	−0.877510	−	0.479559i	$-0.840797\pi$
$241$	−0.363961	+	0.630399i	−0.0234448	+	0.0406076i	0.854065	+	0.520166i	$0.174130\pi$
$242$	−7.75736	+	13.4361i	−0.498662	+	0.863708i
$243$	−5.17157	−	8.95743i	−0.331757	−	0.574619i
$244$		0			0
$245$		0			0
$246$	−3.65685			−0.233153
$247$	−13.2426	−	22.9369i	−0.842609	−	1.45944i
$248$	14.4853	−	25.0892i	0.919816	−	1.59317i
$249$		0			0
$250$	−0.707107	−	1.22474i	−0.0447214	−	0.0774597i
$251$	−17.2132			−1.08649			−0.543244	−	0.839575i	$-0.682804\pi$
$251$	−17.2132			−1.08649			−0.543244	+	0.839575i	$0.682804\pi$
$252$		0			0
$253$	−1.27208			−0.0799749
$254$	5.82843	+	10.0951i	0.365708	+	0.633425i
$255$	−0.671573	+	1.16320i	−0.0420555	+	0.0728423i
$256$		0			0
$257$	−4.75736	−	8.23999i	−0.296756	−	0.513996i	0.678636	−	0.734475i	$-0.262571\pi$
$257$	−4.75736	−	8.23999i	−0.296756	−	0.513996i	−0.975392	+	0.220479i	$0.929238\pi$
$258$	−1.17157			−0.0729389
$259$		0			0
$260$		0			0
$261$	−12.2426	−	21.2049i	−0.757800	−	1.31255i
$262$	−8.65685	+	14.9941i	−0.534822	+	0.926339i
$263$	8.31371	−	14.3998i	0.512645	−	0.887928i	−0.487247	−	0.873264i	$-0.661999\pi$
$263$	8.31371	−	14.3998i	0.512645	−	0.887928i	0.999892	−	0.0146635i	$-0.00466771\pi$
$264$	0.100505	+	0.174080i	0.00618566	+	0.0107139i
$265$	−4.24264			−0.260623
$266$		0			0
$267$	3.31371			0.202796
$268$		0			0
$269$	−8.12132	+	14.0665i	−0.495166	+	0.857652i	−0.999984	−	0.00557327i	$-0.998226\pi$
$269$	−8.12132	+	14.0665i	−0.495166	+	0.857652i	0.504819	+	0.863225i	$0.331559\pi$
$270$	1.70711	−	2.95680i	0.103891	−	0.179945i
$271$	−0.343146	−	0.594346i	−0.0208446	−	0.0361039i	0.855415	−	0.517943i	$-0.173302\pi$
$271$	−0.343146	−	0.594346i	−0.0208446	−	0.0361039i	−0.876260	+	0.481839i	$0.839969\pi$
$272$	12.9706			0.786456
$273$		0			0
$274$	−16.9706			−1.02523
$275$	0.0857864	+	0.148586i	0.00517312	+	0.00896010i
$276$		0			0
$277$	−7.60660	+	13.1750i	−0.457036	+	0.791610i	−0.998803	−	0.0489189i	$-0.984422\pi$
$277$	−7.60660	+	13.1750i	−0.457036	+	0.791610i	0.541766	+	0.840529i	$0.317756\pi$
$278$	−5.48528	−	9.50079i	−0.328985	−	0.569819i
$279$	28.9706			1.73442
$280$		0			0
$281$	2.31371			0.138024			0.0690121	−	0.997616i	$-0.478015\pi$
$281$	2.31371			0.138024			0.0690121	+	0.997616i	$0.478015\pi$
$282$	2.12132	+	3.67423i	0.126323	+	0.218797i
$283$	12.2782	−	21.2664i	0.729862	−	1.26416i	−0.227080	−	0.973876i	$-0.572918\pi$
$283$	12.2782	−	21.2664i	0.729862	−	1.26416i	0.956941	−	0.290281i	$-0.0937489\pi$
$284$		0			0
$285$	−1.24264	−	2.15232i	−0.0736077	−	0.127492i
$286$	−1.07107			−0.0633336
$287$		0			0
$288$		0			0
$289$	3.24264	+	5.61642i	0.190744	+	0.330378i
$290$	6.12132	−	10.6024i	0.359456	−	0.622597i
$291$	2.74264	−	4.75039i	0.160776	−	0.278473i
$292$		0			0
$293$	−25.7279			−1.50304			−0.751521	−	0.659710i	$-0.770679\pi$
$293$	−25.7279			−1.50304			−0.751521	+	0.659710i	$0.770679\pi$
$294$		0			0
$295$	−2.24264			−0.130572
$296$	−3.17157	−	5.49333i	−0.184344	−	0.319293i
$297$	−0.207107	+	0.358719i	−0.0120176	+	0.0208150i
$298$	−6.48528	+	11.2328i	−0.375682	+	0.650701i
$299$	16.3640	+	28.3432i	0.946352	+	1.63913i
$300$		0			0
$301$		0			0
$302$	10.5858			0.609144
$303$	0.514719	+	0.891519i	0.0295698	+	0.0512164i
$304$	−12.0000	+	20.7846i	−0.688247	+	1.19208i
$305$	1.41421	−	2.44949i	0.0809776	−	0.140257i
$306$	6.48528	+	11.2328i	0.370739	+	0.642139i
$307$	−30.8995			−1.76353			−0.881764	−	0.471691i	$-0.843644\pi$
$307$	−30.8995			−1.76353			−0.881764	+	0.471691i	$0.843644\pi$
$308$		0			0
$309$	−7.97056			−0.453429
$310$	7.24264	+	12.5446i	0.411354	+	0.712487i
$311$	−5.00000	+	8.66025i	−0.283524	+	0.491078i	−0.972250	−	0.233944i	$-0.924837\pi$
$311$	−5.00000	+	8.66025i	−0.283524	+	0.491078i	0.688726	+	0.725022i	$0.258170\pi$
$312$	2.58579	−	4.47871i	0.146391	−	0.253557i
$313$	−9.10660	−	15.7731i	−0.514736	−	0.891548i	−0.999854	−	0.0170996i	$-0.994557\pi$
$313$	−9.10660	−	15.7731i	−0.514736	−	0.891548i	0.485118	−	0.874449i	$-0.338777\pi$
$314$	−21.4558			−1.21082
$315$		0			0
$316$		0			0
$317$	0.171573	+	0.297173i	0.00963649	+	0.0166909i	0.870803	−	0.491631i	$-0.163599\pi$
$317$	0.171573	+	0.297173i	0.00963649	+	0.0166909i	−0.861167	+	0.508322i	$0.830266\pi$
$318$	1.24264	−	2.15232i	0.0696838	−	0.120696i
$319$	−0.742641	+	1.28629i	−0.0415799	+	0.0720185i
$320$	4.00000	+	6.92820i	0.223607	+	0.387298i
$321$	−1.02944			−0.0574576
$322$		0			0
$323$	19.4558			1.08255
$324$		0			0
$325$	2.20711	−	3.82282i	0.122428	−	0.212052i
$326$	−7.24264	+	12.5446i	−0.401133	+	0.694782i
$327$	−1.03553	−	1.79360i	−0.0572652	−	0.0991862i
$328$	17.6569			0.974937
$329$		0			0
$330$	−0.100505			−0.00553262
$331$	13.7279	+	23.7775i	0.754555	+	1.30693i	0.945595	+	0.325345i	$0.105480\pi$
$331$	13.7279	+	23.7775i	0.754555	+	1.30693i	−0.191040	+	0.981582i	$0.561186\pi$
$332$		0			0
$333$	3.17157	−	5.49333i	0.173801	−	0.301032i
$334$	−0.535534	−	0.927572i	−0.0293031	−	0.0507545i
$335$	8.24264			0.450344
$336$		0			0
$337$	22.2426			1.21163			0.605817	−	0.795604i	$-0.292846\pi$
$337$	22.2426			1.21163			0.605817	+	0.795604i	$0.292846\pi$
$338$	4.58579	+	7.94282i	0.249434	+	0.432032i
$339$	2.70711	−	4.68885i	0.147030	−	0.254663i
$340$		0			0
$341$	−0.878680	−	1.52192i	−0.0475832	−	0.0824165i
$342$	−24.0000			−1.29777
$343$		0			0
$344$	5.65685			0.304997
$345$	1.53553	+	2.65962i	0.0826704	+	0.143189i
$346$	5.12132	−	8.87039i	0.275324	−	0.476875i
$347$	−6.53553	+	11.3199i	−0.350846	+	0.607683i	−0.986398	−	0.164375i	$-0.947439\pi$
$347$	−6.53553	+	11.3199i	−0.350846	+	0.607683i	0.635552	+	0.772058i	$0.280773\pi$
$348$		0			0
$349$	10.9706			0.587241			0.293620	−	0.955922i	$-0.405140\pi$
$349$	10.9706			0.587241			0.293620	+	0.955922i	$0.405140\pi$
$350$		0			0
$351$	10.6569			0.568821
$352$		0			0
$353$	−3.10660	+	5.38079i	−0.165348	+	0.286391i	−0.936779	−	0.349922i	$-0.886208\pi$
$353$	−3.10660	+	5.38079i	−0.165348	+	0.286391i	0.771431	+	0.636313i	$0.219541\pi$
$354$	0.656854	−	1.13770i	0.0349114	−	0.0604683i
$355$	−1.58579	−	2.74666i	−0.0841648	−	0.145778i
$356$		0			0
$357$		0			0
$358$	20.4853			1.08268
$359$	5.65685	+	9.79796i	0.298557	+	0.517116i	0.975806	−	0.218638i	$-0.0701613\pi$
$359$	5.65685	+	9.79796i	0.298557	+	0.517116i	−0.677249	+	0.735754i	$0.736828\pi$
$360$	−4.00000	+	6.92820i	−0.210819	+	0.365148i
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$	13.2426	+	22.9369i	0.696018	+	1.20554i
$363$	−4.54416			−0.238506
$364$		0			0
$365$	−8.48528			−0.444140
$366$	0.828427	+	1.43488i	0.0433026	+	0.0750023i
$367$	−11.9350	+	20.6721i	−0.623003	+	1.07907i	0.365920	+	0.930646i	$0.380754\pi$
$367$	−11.9350	+	20.6721i	−0.623003	+	1.07907i	−0.988923	+	0.148427i	$0.952579\pi$
$368$	14.8284	−	25.6836i	0.772985	−	1.33885i
$369$	8.82843	+	15.2913i	0.459590	+	0.796032i
$370$	3.17157			0.164882
$371$		0			0
$372$		0			0
$373$	8.24264	+	14.2767i	0.426788	+	0.739218i	0.996586	−	0.0825669i	$-0.0263118\pi$
$373$	8.24264	+	14.2767i	0.426788	+	0.739218i	−0.569798	+	0.821785i	$0.692978\pi$
$374$	0.393398	−	0.681386i	0.0203421	−	0.0352336i
$375$	0.207107	−	0.358719i	0.0106949	−	0.0185242i
$376$	−10.2426	−	17.7408i	−0.528224	−	0.914911i
$377$	38.2132			1.96808
$378$		0			0
$379$	2.00000			0.102733			0.0513665	−	0.998680i	$-0.483642\pi$
$379$	2.00000			0.102733			0.0513665	+	0.998680i	$0.483642\pi$
$380$		0			0
$381$	−1.70711	+	2.95680i	−0.0874577	+	0.151481i
$382$	9.87868	−	17.1104i	0.505437	−	0.875443i
$383$	2.24264	+	3.88437i	0.114594	+	0.198482i	0.917617	−	0.397465i	$-0.130110\pi$
$383$	2.24264	+	3.88437i	0.114594	+	0.198482i	−0.803024	+	0.595947i	$0.796777\pi$
$384$	−4.68629			−0.239146
$385$		0			0
$386$	22.6274			1.15171
$387$	2.82843	+	4.89898i	0.143777	+	0.249029i
$388$		0			0
$389$	3.42893	−	5.93908i	0.173854	−	0.301124i	−0.765910	−	0.642948i	$-0.777711\pi$
$389$	3.42893	−	5.93908i	0.173854	−	0.301124i	0.939764	+	0.341824i	$0.111045\pi$
$390$	1.29289	+	2.23936i	0.0654682	+	0.113394i
$391$	−24.0416			−1.21584
$392$		0			0
$393$	−5.07107			−0.255802
$394$	9.48528	+	16.4290i	0.477862	+	0.827681i
$395$	0.742641	−	1.28629i	0.0373663	−	0.0647203i
$396$		0			0
$397$	0.792893	+	1.37333i	0.0397942	+	0.0689255i	0.885237	−	0.465141i	$-0.153996\pi$
$397$	0.792893	+	1.37333i	0.0397942	+	0.0689255i	−0.845442	+	0.534067i	$0.820663\pi$
$398$	−10.4853			−0.525580
$399$		0			0
$400$	−4.00000			−0.200000
$401$	−5.91421	−	10.2437i	−0.295342	−	0.511547i	0.679723	−	0.733469i	$-0.262100\pi$
$401$	−5.91421	−	10.2437i	−0.295342	−	0.511547i	−0.975064	+	0.221922i	$0.928767\pi$
$402$	−2.41421	+	4.18154i	−0.120410	+	0.208556i
$403$	−22.6066	+	39.1558i	−1.12612	+	1.95049i
$404$		0			0
$405$	−7.48528			−0.371947
$406$		0			0
$407$	−0.384776			−0.0190727
$408$	1.89949	+	3.29002i	0.0940390	+	0.162880i
$409$	1.24264	−	2.15232i	0.0614446	−	0.106425i	−0.833667	−	0.552268i	$-0.813763\pi$
$409$	1.24264	−	2.15232i	0.0614446	−	0.106425i	0.895111	+	0.445843i	$0.147096\pi$
$410$	−4.41421	+	7.64564i	−0.218002	+	0.377591i
$411$	−2.48528	−	4.30463i	−0.122590	−	0.212332i
$412$		0			0
$413$		0			0
$414$	29.6569			1.45755
$415$		0			0
$416$		0			0
$417$	1.60660	−	2.78272i	0.0786756	−	0.136270i
$418$	0.727922	+	1.26080i	0.0356038	+	0.0616676i
$419$	−18.7279			−0.914919			−0.457459	−	0.889230i	$-0.651241\pi$
$419$	−18.7279			−0.914919			−0.457459	+	0.889230i	$0.651241\pi$
$420$		0			0
$421$	−19.0000			−0.926003			−0.463002	−	0.886357i	$-0.653228\pi$
$421$	−19.0000			−0.926003			−0.463002	+	0.886357i	$0.653228\pi$
$422$	6.36396	+	11.0227i	0.309793	+	0.536577i
$423$	10.2426	−	17.7408i	0.498014	−	0.862586i
$424$	−6.00000	+	10.3923i	−0.291386	+	0.504695i
$425$	1.62132	+	2.80821i	0.0786456	+	0.136218i
$426$	1.85786			0.0900138
$427$		0			0
$428$		0			0
$429$	−0.156854	−	0.271680i	−0.00757299	−	0.0131168i
$430$	−1.41421	+	2.44949i	−0.0681994	+	0.118125i
$431$	14.3995	−	24.9407i	0.693599	−	1.20135i	−0.277051	−	0.960855i	$-0.589357\pi$
$431$	14.3995	−	24.9407i	0.693599	−	1.20135i	0.970651	−	0.240494i	$-0.0773095\pi$
$432$	−4.82843	−	8.36308i	−0.232308	−	0.402369i
$433$	−10.9706			−0.527212			−0.263606	−	0.964630i	$-0.584912\pi$
$433$	−10.9706			−0.527212			−0.263606	+	0.964630i	$0.584912\pi$
$434$		0			0
$435$	3.58579			0.171925
$436$		0			0
$437$	22.2426	−	38.5254i	1.06401	−	1.84292i
$438$	2.48528	−	4.30463i	0.118751	−	0.205683i
$439$	−15.1924	−	26.3140i	−0.725093	−	1.25590i	−0.958936	−	0.283624i	$-0.908463\pi$
$439$	−15.1924	−	26.3140i	−0.725093	−	1.25590i	0.233843	−	0.972274i	$-0.424870\pi$
$440$	0.485281			0.0231349
$441$		0			0
$442$	−20.2426			−0.962844
$443$	−7.58579	−	13.1390i	−0.360412	−	0.624251i	0.627617	−	0.778522i	$-0.284030\pi$
$443$	−7.58579	−	13.1390i	−0.360412	−	0.624251i	−0.988029	+	0.154271i	$0.950697\pi$
$444$		0			0
$445$	4.00000	−	6.92820i	0.189618	−	0.328428i
$446$	17.1213	+	29.6550i	0.810718	+	1.40420i
$447$	−3.79899			−0.179686
$448$		0			0
$449$	−24.1716			−1.14073			−0.570364	−	0.821392i	$-0.693198\pi$
$449$	−24.1716			−1.14073			−0.570364	+	0.821392i	$0.693198\pi$
$450$	−2.00000	−	3.46410i	−0.0942809	−	0.163299i
$451$	0.535534	−	0.927572i	0.0252173	−	0.0436777i
$452$		0			0
$453$	1.55025	+	2.68512i	0.0728372	+	0.126158i
$454$	22.2426			1.04390
$455$		0			0
$456$	−7.02944			−0.329184
$457$	5.87868	+	10.1822i	0.274993	+	0.476302i	0.970133	−	0.242572i	$-0.0779911\pi$
$457$	5.87868	+	10.1822i	0.274993	+	0.476302i	−0.695140	+	0.718874i	$0.744658\pi$
$458$	−12.7574	+	22.0964i	−0.596112	+	1.03250i
$459$	−3.91421	+	6.77962i	−0.182700	+	0.316445i
$460$		0			0
$461$	−3.02944			−0.141095			−0.0705475	−	0.997508i	$-0.522475\pi$
$461$	−3.02944			−0.141095			−0.0705475	+	0.997508i	$0.522475\pi$
$462$		0			0
$463$	−21.4558			−0.997138			−0.498569	−	0.866850i	$-0.666141\pi$
$463$	−21.4558			−0.997138			−0.498569	+	0.866850i	$0.666141\pi$
$464$	−17.3137	−	29.9882i	−0.803769	−	1.39217i
$465$	−2.12132	+	3.67423i	−0.0983739	+	0.170389i
$466$	−6.48528	+	11.2328i	−0.300425	+	0.520351i
$467$	−2.86396	−	4.96053i	−0.132528	−	0.229546i	0.792122	−	0.610362i	$-0.208976\pi$
$467$	−2.86396	−	4.96053i	−0.132528	−	0.229546i	−0.924651	+	0.380817i	$0.875643\pi$
$468$		0			0
$469$		0			0
$470$	10.2426			0.472458
$471$	−3.14214	−	5.44234i	−0.144782	−	0.250770i
$472$	−3.17157	+	5.49333i	−0.145983	+	0.252851i
$473$	0.171573	−	0.297173i	0.00788893	−	0.0136640i
$474$	0.435029	+	0.753492i	0.0199815	+	0.0346090i
$475$	−6.00000			−0.275299
$476$		0			0
$477$	−12.0000			−0.549442
$478$	−12.3640	−	21.4150i	−0.565514	−	0.979500i
$479$	5.87868	−	10.1822i	0.268604	−	0.465235i	−0.699898	−	0.714243i	$-0.746771\pi$
$479$	5.87868	−	10.1822i	0.268604	−	0.465235i	0.968501	+	0.249008i	$0.0801045\pi$
$480$		0			0
$481$	4.94975	+	8.57321i	0.225689	+	0.390905i
$482$	−1.02944			−0.0468896
$483$		0			0
$484$		0			0
$485$	−6.62132	−	11.4685i	−0.300659	−	0.520756i
$486$	7.31371	−	12.6677i	0.331757	−	0.574619i
$487$	−13.8492	+	23.9876i	−0.627569	+	1.08698i	0.360469	+	0.932771i	$0.382617\pi$
$487$	−13.8492	+	23.9876i	−0.627569	+	1.08698i	−0.988038	+	0.154210i	$0.950717\pi$
$488$	−4.00000	−	6.92820i	−0.181071	−	0.313625i
$489$	−4.24264			−0.191859
$490$		0			0
$491$	−37.2843			−1.68262			−0.841308	−	0.540556i	$-0.818214\pi$
$491$	−37.2843			−1.68262			−0.841308	+	0.540556i	$0.818214\pi$
$492$		0			0
$493$	−14.0355	+	24.3103i	−0.632129	+	1.09488i
$494$	18.7279	−	32.4377i	0.842609	−	1.45944i
$495$	0.242641	+	0.420266i	0.0109059	+	0.0188896i
$496$	40.9706			1.83963
$497$		0			0
$498$		0			0
$499$	−1.50000	−	2.59808i	−0.0671492	−	0.116306i	0.830496	−	0.557024i	$-0.188057\pi$
$499$	−1.50000	−	2.59808i	−0.0671492	−	0.116306i	−0.897645	+	0.440719i	$0.854724\pi$
$500$		0			0
$501$	0.156854	−	0.271680i	0.00700773	−	0.0121377i
$502$	−12.1716	−	21.0818i	−0.543244	−	0.940926i
$503$	41.2426			1.83892			0.919459	−	0.393185i	$-0.128627\pi$
$503$	41.2426			1.83892			0.919459	+	0.393185i	$0.128627\pi$
$504$		0			0
$505$	2.48528			0.110594
$506$	−0.899495	−	1.55797i	−0.0399874	−	0.0692603i
$507$	−1.34315	+	2.32640i	−0.0596512	+	0.103319i
$508$		0			0
$509$	−12.6066	−	21.8353i	−0.558778	−	0.967832i	−0.997599	−	0.0692571i	$-0.977937\pi$
$509$	−12.6066	−	21.8353i	−0.558778	−	0.967832i	0.438821	−	0.898574i	$-0.355396\pi$
$510$	−1.89949			−0.0841110
$511$		0			0
$512$	22.6274			1.00000
$513$	−7.24264	−	12.5446i	−0.319770	−	0.553859i
$514$	6.72792	−	11.6531i	0.296756	−	0.513996i
$515$	−9.62132	+	16.6646i	−0.423966	+	0.734331i
$516$		0			0
$517$	−1.24264			−0.0546513
$518$		0			0
$519$	3.00000			0.131685
$520$	−6.24264	−	10.8126i	−0.273758	−	0.474163i
$521$	7.48528	−	12.9649i	0.327936	−	0.568002i	−0.654166	−	0.756351i	$-0.726980\pi$
$521$	7.48528	−	12.9649i	0.327936	−	0.568002i	0.982102	+	0.188349i	$0.0603136\pi$
$522$	17.3137	−	29.9882i	0.757800	−	1.31255i
$523$	16.2426	+	28.1331i	0.710241	+	1.23017i	0.964767	+	0.263108i	$0.0847474\pi$
$523$	16.2426	+	28.1331i	0.710241	+	1.23017i	−0.254525	+	0.967066i	$0.581919\pi$
$524$		0			0
$525$		0			0
$526$	23.5147			1.02529
$527$	−16.6066	−	28.7635i	−0.723395	−	1.25296i
$528$	−0.142136	+	0.246186i	−0.00618566	+	0.0107139i
$529$	−15.9853	+	27.6873i	−0.695012	+	1.20380i
$530$	−3.00000	−	5.19615i	−0.130312	−	0.225706i
$531$	−6.34315			−0.275269
$532$		0			0
$533$	−27.5563			−1.19360
$534$	2.34315	+	4.05845i	0.101398	+	0.175626i
$535$	−1.24264	+	2.15232i	−0.0537240	+	0.0930528i
$536$	11.6569	−	20.1903i	0.503499	−	0.872087i
$537$	3.00000	+	5.19615i	0.129460	+	0.224231i
$538$	−22.9706			−0.990331
$539$		0			0
$540$		0			0
$541$	10.9853	+	19.0271i	0.472294	+	0.818037i	0.999497	−	0.0317018i	$-0.0100927\pi$
$541$	10.9853	+	19.0271i	0.472294	+	0.818037i	−0.527203	+	0.849739i	$0.676759\pi$
$542$	0.485281	−	0.840532i	0.0208446	−	0.0361039i
$543$	−3.87868	+	6.71807i	−0.166450	+	0.288300i
$544$		0			0
$545$	−5.00000			−0.214176
$546$		0			0
$547$	−24.4853			−1.04692			−0.523458	−	0.852052i	$-0.675358\pi$
$547$	−24.4853			−1.04692			−0.523458	+	0.852052i	$0.675358\pi$
$548$		0			0
$549$	4.00000	−	6.92820i	0.170716	−	0.295689i
$550$	−0.121320	+	0.210133i	−0.00517312	+	0.00896010i
$551$	−25.9706	−	44.9823i	−1.10638	−	1.91631i
$552$	8.68629			0.369713
$553$		0			0
$554$	−21.5147			−0.914073
$555$	0.464466	+	0.804479i	0.0197155	+	0.0341482i
$556$		0			0
$557$	3.89949	−	6.75412i	0.165227	−	0.286181i	−0.771509	−	0.636218i	$-0.780498\pi$
$557$	3.89949	−	6.75412i	0.165227	−	0.286181i	0.936736	+	0.350037i	$0.113831\pi$
$558$	20.4853	+	35.4815i	0.867211	+	1.50205i
$559$	−8.82843			−0.373403
$560$		0			0
$561$	0.230447			0.00972950
$562$	1.63604	+	2.83370i	0.0690121	+	0.119533i
$563$	−15.9706	+	27.6618i	−0.673079	+	1.16581i	0.303947	+	0.952689i	$0.401695\pi$
$563$	−15.9706	+	27.6618i	−0.673079	+	1.16581i	−0.977026	+	0.213118i	$0.931638\pi$
$564$		0			0
$565$	−6.53553	−	11.3199i	−0.274952	−	0.476231i
$566$	34.7279			1.45972
$567$		0			0
$568$	−8.97056			−0.376396
$569$	−13.0711	−	22.6398i	−0.547968	−	0.949108i	−0.998414	−	0.0563042i	$-0.982068\pi$
$569$	−13.0711	−	22.6398i	−0.547968	−	0.949108i	0.450446	−	0.892804i	$-0.351265\pi$
$570$	1.75736	−	3.04384i	0.0736077	−	0.127492i
$571$	8.75736	−	15.1682i	0.366484	−	0.634769i	−0.622529	−	0.782597i	$-0.713895\pi$
$571$	8.75736	−	15.1682i	0.366484	−	0.634769i	0.989013	+	0.147828i	$0.0472281\pi$
$572$		0			0
$573$	5.78680			0.241747
$574$		0			0
$575$	7.41421			0.309194
$576$	11.3137	+	19.5959i	0.471405	+	0.816497i
$577$	7.86396	−	13.6208i	0.327381	−	0.567040i	−0.654610	−	0.755966i	$-0.727167\pi$
$577$	7.86396	−	13.6208i	0.327381	−	0.567040i	0.981991	+	0.188926i	$0.0605006\pi$
$578$	−4.58579	+	7.94282i	−0.190744	+	0.330378i
$579$	3.31371	+	5.73951i	0.137713	+	0.238526i
$580$		0			0
$581$		0			0
$582$	7.75736			0.321553
$583$	0.363961	+	0.630399i	0.0150737	+	0.0261085i
$584$	−12.0000	+	20.7846i	−0.496564	+	0.860073i
$585$	6.24264	−	10.8126i	0.258101	−	0.447045i
$586$	−18.1924	−	31.5101i	−0.751521	−	1.30167i
$587$	37.4558			1.54597			0.772984	−	0.634425i	$-0.218763\pi$
$587$	37.4558			1.54597			0.772984	+	0.634425i	$0.218763\pi$
$588$		0			0
$589$	61.4558			2.53224
$590$	−1.58579	−	2.74666i	−0.0652858	−	0.113078i
$591$	−2.77817	+	4.81194i	−0.114279	+	0.197937i
$592$	4.48528	−	7.76874i	0.184344	−	0.319293i
$593$	9.62132	+	16.6646i	0.395100	+	0.684334i	0.993114	−	0.117152i	$-0.0373765\pi$
$593$	9.62132	+	16.6646i	0.395100	+	0.684334i	−0.598014	+	0.801486i	$0.704043\pi$
$594$	−0.585786			−0.0240351
$595$		0			0
$596$		0			0
$597$	−1.53553	−	2.65962i	−0.0628452	−	0.108851i
$598$	−23.1421	+	40.0834i	−0.946352	+	1.63913i
$599$	8.91421	−	15.4399i	0.364225	−	0.630856i	−0.624427	−	0.781084i	$-0.714667\pi$
$599$	8.91421	−	15.4399i	0.364225	−	0.630856i	0.988651	+	0.150228i	$0.0480006\pi$
$600$	−0.585786	−	1.01461i	−0.0239146	−	0.0414214i
$601$	10.9706			0.447499			0.223749	−	0.974647i	$-0.428170\pi$
$601$	10.9706			0.447499			0.223749	+	0.974647i	$0.428170\pi$
$602$		0			0
$603$	23.3137			0.949408
$604$		0			0
$605$	−5.48528	+	9.50079i	−0.223008	+	0.386262i
$606$	−0.727922	+	1.26080i	−0.0295698	+	0.0512164i
$607$	−2.55025	−	4.41717i	−0.103512	−	0.179287i	0.809618	−	0.586958i	$-0.199675\pi$
$607$	−2.55025	−	4.41717i	−0.103512	−	0.179287i	−0.913129	+	0.407670i	$0.866341\pi$
$608$		0			0
$609$		0			0
$610$	4.00000			0.161955
$611$	15.9853	+	27.6873i	0.646695	+	1.12011i
$612$		0			0
$613$	11.9706	−	20.7336i	0.483486	−	0.837423i	−0.516334	−	0.856387i	$-0.672704\pi$
$613$	11.9706	−	20.7336i	0.483486	−	0.837423i	0.999820	+	0.0189643i	$0.00603690\pi$
$614$	−21.8492	−	37.8440i	−0.881764	−	1.52726i
$615$	−2.58579			−0.104269
$616$		0			0
$617$	4.58579			0.184617			0.0923084	−	0.995730i	$-0.470575\pi$
$617$	4.58579			0.184617			0.0923084	+	0.995730i	$0.470575\pi$
$618$	−5.63604	−	9.76191i	−0.226715	−	0.392681i
$619$	8.46447	−	14.6609i	0.340216	−	0.589271i	−0.644257	−	0.764809i	$-0.722833\pi$
$619$	8.46447	−	14.6609i	0.340216	−	0.589271i	0.984473	+	0.175538i	$0.0561666\pi$
$620$		0			0
$621$	8.94975	+	15.5014i	0.359141	+	0.622050i
$622$	−14.1421			−0.567048
$623$		0			0
$624$	7.31371			0.292783
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	12.8787	−	22.3065i	0.514736	−	0.891548i
$627$	−0.213203	+	0.369279i	−0.00851453	+	0.0147476i
$628$		0			0
$629$	−7.27208			−0.289957
$630$		0			0
$631$	−42.4558			−1.69014			−0.845070	−	0.534655i	$-0.820441\pi$
$631$	−42.4558			−1.69014			−0.845070	+	0.534655i	$0.820441\pi$
$632$	−2.10051	−	3.63818i	−0.0835536	−	0.144719i
$633$	−1.86396	+	3.22848i	−0.0740858	+	0.128320i
$634$	−0.242641	+	0.420266i	−0.00963649	+	0.0166909i
$635$	4.12132	+	7.13834i	0.163550	+	0.283276i
$636$		0			0
$637$		0			0
$638$	−2.10051			−0.0831598
$639$	−4.48528	−	7.76874i	−0.177435	−	0.307326i
$640$	−5.65685	+	9.79796i	−0.223607	+	0.387298i
$641$	11.6569	−	20.1903i	0.460418	−	0.797467i	−0.538564	−	0.842585i	$-0.681033\pi$
$641$	11.6569	−	20.1903i	0.460418	−	0.797467i	0.998982	+	0.0451174i	$0.0143662\pi$
$642$	−0.727922	−	1.26080i	−0.0287288	−	0.0497597i
$643$	−2.27208			−0.0896020			−0.0448010	−	0.998996i	$-0.514265\pi$
$643$	−2.27208			−0.0896020			−0.0448010	+	0.998996i	$0.514265\pi$
$644$		0			0
$645$	−0.828427			−0.0326193
$646$	13.7574	+	23.8284i	0.541276	+	0.937518i
$647$	−5.75736	+	9.97204i	−0.226345	+	0.392041i	−0.956722	−	0.291003i	$-0.906011\pi$
$647$	−5.75736	+	9.97204i	−0.226345	+	0.392041i	0.730377	+	0.683044i	$0.239344\pi$
$648$	−10.5858	+	18.3351i	−0.415849	+	0.720272i
$649$	0.192388	+	0.333226i	0.00755190	+	0.0130803i
$650$	6.24264			0.244857
$651$		0			0
$652$		0			0
$653$	−17.4853	−	30.2854i	−0.684252	−	1.18516i	−0.973671	−	0.227957i	$-0.926796\pi$
$653$	−17.4853	−	30.2854i	−0.684252	−	1.18516i	0.289419	−	0.957202i	$-0.406538\pi$
$654$	1.46447	−	2.53653i	0.0572652	−	0.0991862i
$655$	−6.12132	+	10.6024i	−0.239180	+	0.414272i
$656$	12.4853	+	21.6251i	0.487468	+	0.844320i
$657$	−24.0000			−0.936329
$658$		0			0
$659$	19.9706			0.777943			0.388971	−	0.921250i	$-0.372831\pi$
$659$	19.9706			0.777943			0.388971	+	0.921250i	$0.372831\pi$
$660$		0			0
$661$	6.72792	−	11.6531i	0.261686	−	0.453253i	−0.705004	−	0.709203i	$-0.749055\pi$
$661$	6.72792	−	11.6531i	0.261686	−	0.453253i	0.966690	+	0.255950i	$0.0823882\pi$
$662$	−19.4142	+	33.6264i	−0.754555	+	1.30693i
$663$	−2.96447	−	5.13461i	−0.115130	−	0.199412i
$664$		0			0
$665$		0			0
$666$	8.97056			0.347602
$667$	32.0919	+	55.5848i	1.24260	+	2.15225i
$668$		0			0
$669$	−5.01472	+	8.68575i	−0.193880	+	0.335810i
$670$	5.82843	+	10.0951i	0.225172	+	0.390009i
$671$	−0.485281			−0.0187341
$672$		0			0
$673$	3.51472			0.135482			0.0677412	−	0.997703i	$-0.478421\pi$
$673$	3.51472			0.135482			0.0677412	+	0.997703i	$0.478421\pi$
$674$	15.7279	+	27.2416i	0.605817	+	1.04931i
$675$	1.20711	−	2.09077i	0.0464616	−	0.0804738i
$676$		0			0
$677$	22.1066	+	38.2898i	0.849626	+	1.47159i	0.881543	+	0.472104i	$0.156505\pi$
$677$	22.1066	+	38.2898i	0.849626	+	1.47159i	−0.0319169	+	0.999491i	$0.510161\pi$
$678$	7.65685			0.294060
$679$		0			0
$680$	9.17157			0.351714
$681$	3.25736	+	5.64191i	0.124822	+	0.216199i
$682$	1.24264	−	2.15232i	0.0475832	−	0.0824165i
$683$	−15.8995	+	27.5387i	−0.608377	+	1.05374i	0.383131	+	0.923694i	$0.374846\pi$
$683$	−15.8995	+	27.5387i	−0.608377	+	1.05374i	−0.991508	+	0.130046i	$0.958487\pi$
$684$		0			0
$685$	−12.0000			−0.458496
$686$		0			0
$687$	−7.47309			−0.285116
$688$	4.00000	+	6.92820i	0.152499	+	0.264135i
$689$	9.36396	−	16.2189i	0.356739	−	0.617889i
$690$	−2.17157	+	3.76127i	−0.0826704	+	0.143189i
$691$	7.41421	+	12.8418i	0.282050	+	0.488525i	0.971890	−	0.235437i	$-0.0756523\pi$
$691$	7.41421	+	12.8418i	0.282050	+	0.488525i	−0.689840	+	0.723962i	$0.742319\pi$
$692$		0			0
$693$		0			0
$694$	−18.4853			−0.701692
$695$	−3.87868	−	6.71807i	−0.147127	−	0.254831i
$696$	5.07107	−	8.78335i	0.192218	−	0.332932i
$697$	10.1213	−	17.5306i	0.383372	−	0.664020i
$698$	7.75736	+	13.4361i	0.293620	+	0.508565i
$699$	−3.79899			−0.143691
$700$		0			0
$701$	46.4558			1.75461			0.877307	−	0.479931i	$-0.159338\pi$
$701$	46.4558			1.75461			0.877307	+	0.479931i	$0.159338\pi$
$702$	7.53553	+	13.0519i	0.284410	+	0.492613i
$703$	6.72792	−	11.6531i	0.253748	−	0.439505i
$704$	0.686292	−	1.18869i	0.0258656	−	0.0448005i
$705$	1.50000	+	2.59808i	0.0564933	+	0.0978492i
$706$	−8.78680			−0.330695
$707$		0			0
$708$		0			0
$709$	−8.50000	−	14.7224i	−0.319224	−	0.552913i	0.661102	−	0.750296i	$-0.270089\pi$
$709$	−8.50000	−	14.7224i	−0.319224	−	0.552913i	−0.980326	+	0.197383i	$0.936756\pi$
$710$	2.24264	−	3.88437i	0.0841648	−	0.145778i
$711$	2.10051	−	3.63818i	0.0787751	−	0.136442i
$712$	−11.3137	−	19.5959i	−0.423999	−	0.734388i
$713$	−75.9411			−2.84402
$714$		0			0
$715$	−0.757359			−0.0283236
$716$		0			0
$717$	3.62132	−	6.27231i	0.135241	−	0.234244i
$718$	−8.00000	+	13.8564i	−0.298557	+	0.517116i
$719$	−12.6066	−	21.8353i	−0.470147	−	0.814318i	0.529270	−	0.848453i	$-0.322466\pi$
$719$	−12.6066	−	21.8353i	−0.470147	−	0.814318i	−0.999417	+	0.0341349i	$0.989132\pi$
$720$	−11.3137			−0.421637
$721$		0			0
$722$	−24.0416			−0.894737
$723$	−0.150758	−	0.261120i	−0.00560674	−	0.00971115i
$724$		0			0
$725$	4.32843	−	7.49706i	0.160754	−	0.278434i
$726$	−3.21320	−	5.56543i	−0.119253	−	0.206553i
$727$	6.68629			0.247981			0.123990	−	0.992283i	$-0.460431\pi$
$727$	6.68629			0.247981			0.123990	+	0.992283i	$0.460431\pi$
$728$		0			0
$729$	−18.1716			−0.673021
$730$	−6.00000	−	10.3923i	−0.222070	−	0.384636i
$731$	3.24264	−	5.61642i	0.119933	−	0.207731i
$732$		0			0
$733$	7.34924	+	12.7293i	0.271450	+	0.470166i	0.969233	−	0.246143i	$-0.0791634\pi$
$733$	7.34924	+	12.7293i	0.271450	+	0.470166i	−0.697783	+	0.716309i	$0.745830\pi$
$734$	−33.7574			−1.24601
$735$		0			0
$736$		0			0
$737$	−0.707107	−	1.22474i	−0.0260466	−	0.0451141i
$738$	−12.4853	+	21.6251i	−0.459590	+	0.796032i
$739$	−14.9853	+	25.9553i	−0.551242	+	0.954780i	0.446943	+	0.894563i	$0.352513\pi$
$739$	−14.9853	+	25.9553i	−0.551242	+	0.954780i	−0.998185	+	0.0602175i	$0.980821\pi$
$740$		0			0
$741$	10.9706			0.403014
$742$		0			0
$743$	11.2721			0.413532			0.206766	−	0.978390i	$-0.433706\pi$
$743$	11.2721			0.413532			0.206766	+	0.978390i	$0.433706\pi$
$744$	6.00000	+	10.3923i	0.219971	+	0.381000i
$745$	−4.58579	+	7.94282i	−0.168010	+	0.291002i
$746$	−11.6569	+	20.1903i	−0.426788	+	0.739218i
$747$		0			0
$748$		0			0
$749$		0			0
$750$	0.585786			0.0213899
$751$	−14.7426	−	25.5350i	−0.537967	−	0.931785i	−0.999013	−	0.0444097i	$-0.985859\pi$
$751$	−14.7426	−	25.5350i	−0.537967	−	0.931785i	0.461047	−	0.887376i	$-0.347474\pi$
$752$	14.4853	−	25.0892i	0.528224	−	0.914911i
$753$	3.56497	−	6.17471i	0.129915	−	0.225019i
$754$	27.0208	+	46.8014i	0.984040	+	1.70441i
$755$	7.48528			0.272417
$756$		0			0
$757$	0.485281			0.0176379			0.00881893	−	0.999961i	$-0.497193\pi$
$757$	0.485281			0.0176379			0.00881893	+	0.999961i	$0.497193\pi$
$758$	1.41421	+	2.44949i	0.0513665	+	0.0889695i
$759$	0.263456	−	0.456319i	0.00956285	−	0.0165633i
$760$	−8.48528	+	14.6969i	−0.307794	+	0.533114i
$761$	−6.36396	−	11.0227i	−0.230693	−	0.399573i	0.727319	−	0.686300i	$-0.240766\pi$
$761$	−6.36396	−	11.0227i	−0.230693	−	0.399573i	−0.958012	+	0.286727i	$0.907433\pi$
$762$	−4.82843			−0.174915
$763$		0			0
$764$		0			0
$765$	4.58579	+	7.94282i	0.165799	+	0.287173i
$766$	−3.17157	+	5.49333i	−0.114594	+	0.198482i
$767$	4.94975	−	8.57321i	0.178725	−	0.309561i
$768$		0			0
$769$	8.82843			0.318361			0.159181	−	0.987249i	$-0.449115\pi$
$769$	8.82843			0.318361			0.159181	+	0.987249i	$0.449115\pi$
$770$		0			0
$771$	3.94113			0.141936
$772$		0			0
$773$	−3.10660	+	5.38079i	−0.111737	+	0.193534i	−0.916471	−	0.400102i	$-0.868975\pi$
$773$	−3.10660	+	5.38079i	−0.111737	+	0.193534i	0.804734	+	0.593636i	$0.202308\pi$
$774$	−4.00000	+	6.92820i	−0.143777	+	0.249029i
$775$	5.12132	+	8.87039i	0.183963	+	0.318634i
$776$	−37.4558			−1.34459
$777$		0			0
$778$	9.69848			0.347708
$779$	18.7279	+	32.4377i	0.670997	+	1.16220i
$780$		0			0
$781$	−0.272078	+	0.471253i	−0.00973571	+	0.0168628i
$782$	−17.0000	−	29.4449i	−0.607919	−	1.05295i
$783$	20.8995			0.746887
$784$		0			0
$785$	−15.1716			−0.541497
$786$	−3.58579	−	6.21076i	−0.127901	−	0.221531i
$787$	10.1360	−	17.5561i	0.361311	−	0.625809i	−0.626866	−	0.779127i	$-0.715663\pi$
$787$	10.1360	−	17.5561i	0.361311	−	0.625809i	0.988177	+	0.153318i	$0.0489960\pi$
$788$		0			0
$789$	3.44365	+	5.96458i	0.122597	+	0.212345i
$790$	2.10051			0.0747326
$791$		0			0
$792$	1.37258			0.0487726
$793$	6.24264	+	10.8126i	0.221683	+	0.383966i
$794$	−1.12132	+	1.94218i	−0.0397942	+	0.0689255i
$795$	0.878680	−	1.52192i	0.0311636	−	0.0539769i
$796$		0			0
$797$	21.1838			0.750367			0.375184	−	0.926950i	$-0.377580\pi$
$797$	21.1838			0.750367			0.375184	+	0.926950i	$0.377580\pi$
$798$		0			0
$799$	−23.4853			−0.830850
$800$		0			0
$801$	11.3137	−	19.5959i	0.399750	−	0.692388i
$802$	8.36396	−	14.4868i	0.295342	−	0.511547i
$803$	0.727922	+	1.26080i	0.0256878	+	0.0444926i
$804$		0			0
$805$		0			0
$806$	−63.9411			−2.25223
$807$	−3.36396	−	5.82655i	−0.118417	−	0.205104i
$808$	3.51472	−	6.08767i	0.123647	−	0.214164i
$809$	24.2990	−	42.0871i	0.854307	−	1.47970i	−0.0229795	−	0.999736i	$-0.507315\pi$
$809$	24.2990	−	42.0871i	0.854307	−	1.47970i	0.877286	−	0.479967i	$-0.159351\pi$
$810$	−5.29289	−	9.16756i	−0.185973	−	0.322115i
$811$	−47.3553			−1.66287			−0.831435	−	0.555621i	$-0.812480\pi$
$811$	−47.3553			−1.66287			−0.831435	+	0.555621i	$0.812480\pi$
$812$		0			0
$813$	0.284271			0.00996983
$814$	−0.272078	−	0.471253i	−0.00953633	−	0.0165174i
$815$	−5.12132	+	8.87039i	−0.179392	+	0.310716i
$816$	−2.68629	+	4.65279i	−0.0940390	+	0.162880i
$817$	6.00000	+	10.3923i	0.209913	+	0.363581i
$818$	3.51472			0.122889
$819$		0			0
$820$		0			0
$821$	11.7426	+	20.3389i	0.409821	+	0.709831i	0.994869	−	0.101168i	$-0.0322578\pi$
$821$	11.7426	+	20.3389i	0.409821	+	0.709831i	−0.585048	+	0.810998i	$0.698925\pi$
$822$	3.51472	−	6.08767i	0.122590	−	0.212332i
$823$	−8.36396	+	14.4868i	−0.291549	+	0.504978i	−0.974176	−	0.225789i	$-0.927504\pi$
$823$	−8.36396	+	14.4868i	−0.291549	+	0.504978i	0.682627	+	0.730767i	$0.260837\pi$
$824$	27.2132	+	47.1347i	0.948017	+	1.64201i
$825$	−0.0710678			−0.00247426
$826$		0			0
$827$	42.0416			1.46193			0.730965	−	0.682415i	$-0.239070\pi$
$827$	42.0416			1.46193			0.730965	+	0.682415i	$0.239070\pi$
$828$		0			0
$829$	2.97918	−	5.16010i	0.103471	−	0.179218i	−0.809641	−	0.586925i	$-0.800338\pi$
$829$	2.97918	−	5.16010i	0.103471	−	0.179218i	0.913113	+	0.407707i	$0.133672\pi$
$830$		0			0
$831$	−3.15076	−	5.45727i	−0.109299	−	0.189311i
$832$	−35.3137			−1.22428
$833$		0			0
$834$	4.54416			0.157351
$835$	−0.378680	−	0.655892i	−0.0131047	−	0.0226981i
$836$		0			0
$837$	−12.3640	+	21.4150i	−0.427361	+	0.740211i
$838$	−13.2426	−	22.9369i	−0.457459	−	0.792343i
$839$	23.2721			0.803441			0.401721	−	0.915762i	$-0.368412\pi$
$839$	23.2721			0.803441			0.401721	+	0.915762i	$0.368412\pi$
$840$		0			0
$841$	45.9411			1.58418
$842$	−13.4350	−	23.2702i	−0.463002	−	0.801942i
$843$	−0.479185	+	0.829972i	−0.0165040	+	0.0285858i
$844$		0			0
$845$	3.24264	+	5.61642i	0.111550	+	0.193211i
$846$	28.9706			0.996028
$847$		0			0
$848$	−16.9706			−0.582772
$849$	5.08579	+	8.80884i	0.174544	+	0.302319i
$850$	−2.29289	+	3.97141i	−0.0786456	+	0.136218i
$851$	−8.31371	+	14.3998i	−0.284990	+	0.493618i
$852$		0			0
$853$	−10.9706			−0.375625			−0.187812	−	0.982205i	$-0.560140\pi$
$853$	−10.9706			−0.375625			−0.187812	+	0.982205i	$0.560140\pi$
$854$		0			0
$855$	−16.9706			−0.580381
$856$	3.51472	+	6.08767i	0.120131	+	0.208072i
$857$	−11.2426	+	19.4728i	−0.384041	+	0.665179i	−0.991636	−	0.129068i	$-0.958801\pi$
$857$	−11.2426	+	19.4728i	−0.384041	+	0.665179i	0.607594	+	0.794247i	$0.292135\pi$
$858$	0.221825	−	0.384213i	0.00757299	−	0.0131168i
$859$	−12.3848	−	21.4511i	−0.422563	−	0.731901i	0.573626	−	0.819117i	$-0.305536\pi$
$859$	−12.3848	−	21.4511i	−0.422563	−	0.731901i	−0.996189	+	0.0872164i	$0.972203\pi$
$860$		0			0
$861$		0			0
$862$	40.7279			1.38720
$863$	−9.19239	−	15.9217i	−0.312913	−	0.541980i	0.666079	−	0.745881i	$-0.267971\pi$
$863$	−9.19239	−	15.9217i	−0.312913	−	0.541980i	−0.978992	+	0.203901i	$0.934638\pi$
$864$		0			0
$865$	3.62132	−	6.27231i	0.123129	−	0.213265i
$866$	−7.75736	−	13.4361i	−0.263606	−	0.456579i
$867$	−2.68629			−0.0912312
$868$		0			0
$869$	−0.254834			−0.00864465
$870$	2.53553	+	4.39167i	0.0859627	+	0.148892i
$871$	−18.1924	+	31.5101i	−0.616426	+	1.06768i
$872$	−7.07107	+	12.2474i	−0.239457	+	0.414751i
$873$	−18.7279	−	32.4377i	−0.633844	−	1.09785i
$874$	62.9117			2.12802
$875$		0			0
$876$		0			0
$877$	−6.51472	−	11.2838i	−0.219986	−	0.381028i	0.734817	−	0.678265i	$-0.237268\pi$
$877$	−6.51472	−	11.2838i	−0.219986	−	0.381028i	−0.954804	+	0.297238i	$0.903935\pi$
$878$	21.4853	−	37.2136i	0.725093	−	1.25590i
$879$	5.32843	−	9.22911i	0.179723	−	0.311290i
$880$	0.343146	+	0.594346i	0.0115674	+	0.0200354i
$881$	52.9706			1.78462			0.892312	−	0.451420i	$-0.149082\pi$
$881$	52.9706			1.78462			0.892312	+	0.451420i	$0.149082\pi$
$882$		0			0
$883$	31.5147			1.06055			0.530277	−	0.847824i	$-0.322088\pi$
$883$	31.5147			1.06055			0.530277	+	0.847824i	$0.322088\pi$
$884$		0			0
$885$	0.464466	−	0.804479i	0.0156129	−	0.0270423i
$886$	10.7279	−	18.5813i	0.360412	−	0.624251i
$887$	1.48528	+	2.57258i	0.0498709	+	0.0863789i	0.889883	−	0.456188i	$-0.150786\pi$
$887$	1.48528	+	2.57258i	0.0498709	+	0.0863789i	−0.840012	+	0.542567i	$0.817452\pi$
$888$	2.62742			0.0881703
$889$		0			0
$890$	11.3137			0.379236
$891$	0.642136	+	1.11221i	0.0215124	+	0.0372605i
$892$		0			0
$893$	21.7279	−	37.6339i	0.727097	−	1.25937i
$894$	−2.68629	−	4.65279i	−0.0898430	−	0.155613i
$895$	14.4853			0.484190
$896$		0			0
$897$	−13.5563			−0.452633
$898$	−17.0919	−	29.6040i	−0.570364	−	0.987899i
$899$	−44.3345	+	76.7896i	−1.47864	+	2.56108i
$900$		0			0
$901$	6.87868	+	11.9142i	0.229162	+	0.396920i
$902$	1.51472			0.0504346
$903$		0			0
$904$	−36.9706			−1.22962
$905$	9.36396	+	16.2189i	0.311269	+	0.539133i
$906$	−2.19239	+	3.79733i	−0.0728372	+	0.126158i
$907$	22.0919	−	38.2643i	0.733549	−	1.27054i	−0.221808	−	0.975090i	$-0.571196\pi$
$907$	22.0919	−	38.2643i	0.733549	−	1.27054i	0.955357	−	0.295454i	$-0.0954708\pi$
$908$		0			0
$909$	7.02944			0.233152
$910$		0			0
$911$	5.65685			0.187420			0.0937100	−	0.995600i	$-0.470127\pi$
$911$	5.65685			0.187420			0.0937100	+	0.995600i	$0.470127\pi$
$912$	−4.97056	−	8.60927i	−0.164592	−	0.285081i
$913$		0			0
$914$	−8.31371	+	14.3998i	−0.274993	+	0.476302i
$915$	0.585786	+	1.01461i	0.0193655	+	0.0335420i
$916$		0			0
$917$		0			0
$918$	−11.0711			−0.365400
$919$	−6.22792	−	10.7871i	−0.205440	−	0.355833i	0.744833	−	0.667251i	$-0.232529\pi$
$919$	−6.22792	−	10.7871i	−0.205440	−	0.355833i	−0.950273	+	0.311418i	$0.899196\pi$
$920$	10.4853	−	18.1610i	0.345689	−	0.598752i
$921$	6.39949	−	11.0843i	0.210871	−	0.365238i
$922$	−2.14214	−	3.71029i	−0.0705475	−	0.122192i
$923$	14.0000			0.460816
$924$		0			0
$925$	2.24264			0.0737376
$926$	−15.1716	−	26.2779i	−0.498569	−	0.863547i
$927$	−27.2132	+	47.1347i	−0.893799	+	1.54811i
$928$		0			0
$929$	14.6360	+	25.3504i	0.480193	+	0.831718i	0.999742	−	0.0227223i	$-0.00723334\pi$
$929$	14.6360	+	25.3504i	0.480193	+	0.831718i	−0.519549	+	0.854441i	$0.673900\pi$
$930$	−6.00000			−0.196748
$931$		0			0
$932$		0			0
$933$	−2.07107	−	3.58719i	−0.0678037	−	0.117439i
$934$	4.05025	−	7.01524i	0.132528	−	0.229546i
$935$	0.278175	−	0.481813i	0.00909728	−	0.0157570i
$936$	−17.6569	−	30.5826i	−0.577132	−	0.999623i
$937$	48.5563			1.58627			0.793133	−	0.609048i	$-0.208448\pi$
$937$	48.5563			1.58627			0.793133	+	0.609048i	$0.208448\pi$
$938$		0			0
$939$	7.54416			0.246194
$940$		0			0
$941$	14.4853	−	25.0892i	0.472207	−	0.817886i	−0.527288	−	0.849687i	$-0.676791\pi$
$941$	14.4853	−	25.0892i	0.472207	−	0.817886i	0.999494	+	0.0318010i	$0.0101243\pi$
$942$	4.44365	−	7.69663i	0.144782	−	0.250770i
$943$	−23.1421	−	40.0834i	−0.753612	−	1.30529i
$944$	−8.97056			−0.291967
$945$		0			0
$946$	0.485281			0.0157779
$947$	26.1213	+	45.2435i	0.848829	+	1.47021i	0.882254	+	0.470773i	$0.156025\pi$
$947$	26.1213	+	45.2435i	0.848829	+	1.47021i	−0.0334253	+	0.999441i	$0.510642\pi$
$948$		0			0
$949$	18.7279	−	32.4377i	0.607934	−	1.05297i
$950$	−4.24264	−	7.34847i	−0.137649	−	0.238416i
$951$	−0.142136			−0.00460906
$952$		0			0
$953$	53.0122			1.71723			0.858617	−	0.512618i	$-0.171324\pi$
$953$	53.0122			1.71723			0.858617	+	0.512618i	$0.171324\pi$
$954$	−8.48528	−	14.6969i	−0.274721	−	0.475831i
$955$	6.98528	−	12.0989i	0.226038	−	0.391510i
$956$		0			0
$957$	−0.307612	−	0.532799i	−0.00994368	−	0.0172230i
$958$	16.6274			0.537207
$959$		0			0
$960$	−3.31371			−0.106949
$961$	−36.9558	−	64.0094i	−1.19212	−	2.06482i
$962$	−7.00000	+	12.1244i	−0.225689	+	0.390905i
$963$	−3.51472	+	6.08767i	−0.113260	+	0.196172i
$964$		0			0
$965$	16.0000			0.515058
$966$		0			0
$967$	−60.4264			−1.94318			−0.971591	−	0.236666i	$-0.923945\pi$
$967$	−60.4264			−1.94318			−0.971591	+	0.236666i	$0.923945\pi$
$968$	15.5147	+	26.8723i	0.498662	+	0.863708i
$969$	−4.02944	+	6.97919i	−0.129444	+	0.224204i
$970$	9.36396	−	16.2189i	0.300659	−	0.520756i
$971$	−8.63604	−	14.9581i	−0.277144	−	0.480027i	0.693530	−	0.720428i	$-0.256054\pi$
$971$	−8.63604	−	14.9581i	−0.277144	−	0.480027i	−0.970674	+	0.240401i	$0.922721\pi$
$972$		0			0
$973$		0			0
$974$	−39.1716			−1.25514
$975$	0.914214	+	1.58346i	0.0292783	+	0.0507114i
$976$	5.65685	−	9.79796i	0.181071	−	0.313625i
$977$	−21.3848	+	37.0395i	−0.684160	+	1.18500i	0.289541	+	0.957166i	$0.406498\pi$
$977$	−21.3848	+	37.0395i	−0.684160	+	1.18500i	−0.973700	+	0.227833i	$0.926836\pi$
$978$	−3.00000	−	5.19615i	−0.0959294	−	0.166155i
$979$	−1.37258			−0.0438679
$980$		0			0
$981$	−14.1421			−0.451524
$982$	−26.3640	−	45.6637i	−0.841308	−	1.45719i
$983$	0.106602	−	0.184640i	0.00340007	−	0.00588909i	−0.864320	−	0.502942i	$-0.832251\pi$
$983$	0.106602	−	0.184640i	0.00340007	−	0.00588909i	0.867720	+	0.497053i	$0.165584\pi$
$984$	−3.65685	+	6.33386i	−0.116576	+	0.201916i
$985$	6.70711	+	11.6170i	0.213706	+	0.370150i
$986$	−39.6985			−1.26426
$987$		0			0
$988$		0			0
$989$	−7.41421	−	12.8418i	−0.235758	−	0.408345i
$990$	−0.343146	+	0.594346i	−0.0109059	+	0.0188896i
$991$	−9.97056	+	17.2695i	−0.316725	+	0.548584i	−0.979803	−	0.199966i	$-0.935917\pi$
$991$	−9.97056	+	17.2695i	−0.316725	+	0.548584i	0.663077	+	0.748551i	$0.269250\pi$
$992$		0			0
$993$	−11.3726			−0.360898
$994$		0			0
$995$	−7.41421			−0.235046
$996$		0			0
$997$	−10.8640	+	18.8169i	−0.344065	+	0.595938i	−0.985183	−	0.171504i	$-0.945137\pi$
$997$	−10.8640	+	18.8169i	−0.344065	+	0.595938i	0.641118	+	0.767442i	$0.278471\pi$
$998$	2.12132	−	3.67423i	0.0671492	−	0.116306i
$999$	2.70711	+	4.68885i	0.0856491	+	0.148349i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.2.e.g.116.2		4
7.2	even	3	inner	245.2.e.g.226.2		4
7.3	odd	6		245.2.a.f.1.1	yes	2
7.4	even	3		245.2.a.e.1.1	✓	2
7.5	odd	6		245.2.e.f.226.2		4
7.6	odd	2		245.2.e.f.116.2		4
21.11	odd	6		2205.2.a.v.1.2		2
21.17	even	6		2205.2.a.t.1.2		2
28.3	even	6		3920.2.a.br.1.2		2
28.11	odd	6		3920.2.a.bw.1.1		2
35.3	even	12		1225.2.b.j.99.4		4
35.4	even	6		1225.2.a.r.1.2		2
35.17	even	12		1225.2.b.j.99.1		4
35.18	odd	12		1225.2.b.i.99.3		4
35.24	odd	6		1225.2.a.p.1.2		2
35.32	odd	12		1225.2.b.i.99.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.2.a.e.1.1	✓	2	7.4	even	3
245.2.a.f.1.1	yes	2	7.3	odd	6
245.2.e.f.116.2		4	7.6	odd	2
245.2.e.f.226.2		4	7.5	odd	6
245.2.e.g.116.2		4	1.1	even	1	trivial
245.2.e.g.226.2		4	7.2	even	3	inner
1225.2.a.p.1.2		2	35.24	odd	6
1225.2.a.r.1.2		2	35.4	even	6
1225.2.b.i.99.2		4	35.32	odd	12
1225.2.b.i.99.3		4	35.18	odd	12
1225.2.b.j.99.1		4	35.17	even	12
1225.2.b.j.99.4		4	35.3	even	12
2205.2.a.t.1.2		2	21.17	even	6
2205.2.a.v.1.2		2	21.11	odd	6
3920.2.a.br.1.2		2	28.3	even	6
3920.2.a.bw.1.1		2	28.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(-0.207107 + 0.358719i) q^{3} +(0.500000 + 0.866025i) q^{5} -0.585786 q^{6} +2.82843 q^{8} +(1.41421 + 2.44949i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 1.22474i) q^{2} +(-0.207107 + 0.358719i) q^{3} +(0.500000 + 0.866025i) q^{5} -0.585786 q^{6} +2.82843 q^{8} +(1.41421 + 2.44949i) q^{9} +(-0.707107 + 1.22474i) q^{10} +(0.0857864 - 0.148586i) q^{11} -4.41421 q^{13} -0.414214 q^{15} +(2.00000 + 3.46410i) q^{16} +(1.62132 - 2.80821i) q^{17} +(-2.00000 + 3.46410i) q^{18} +(3.00000 + 5.19615i) q^{19} +0.242641 q^{22} +(-3.70711 - 6.42090i) q^{23} +(-0.585786 + 1.01461i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-3.12132 - 5.40629i) q^{26} -2.41421 q^{27} -8.65685 q^{29} +(-0.292893 - 0.507306i) q^{30} +(5.12132 - 8.87039i) q^{31} +(0.0355339 + 0.0615465i) q^{33} +4.58579 q^{34} +(-1.12132 - 1.94218i) q^{37} +(-4.24264 + 7.34847i) q^{38} +(0.914214 - 1.58346i) q^{39} +(1.41421 + 2.44949i) q^{40} +6.24264 q^{41} +2.00000 q^{43} +(-1.41421 + 2.44949i) q^{45} +(5.24264 - 9.08052i) q^{46} +(-3.62132 - 6.27231i) q^{47} -1.65685 q^{48} -1.41421 q^{50} +(0.671573 + 1.16320i) q^{51} +(-2.12132 + 3.67423i) q^{53} +(-1.70711 - 2.95680i) q^{54} +0.171573 q^{55} -2.48528 q^{57} +(-6.12132 - 10.6024i) q^{58} +(-1.12132 + 1.94218i) q^{59} +(-1.41421 - 2.44949i) q^{61} +14.4853 q^{62} +8.00000 q^{64} +(-2.20711 - 3.82282i) q^{65} +(-0.0502525 + 0.0870399i) q^{66} +(4.12132 - 7.13834i) q^{67} +3.07107 q^{69} -3.17157 q^{71} +(4.00000 + 6.92820i) q^{72} +(-4.24264 + 7.34847i) q^{73} +(1.58579 - 2.74666i) q^{74} +(-0.207107 - 0.358719i) q^{75} +2.58579 q^{78} +(-0.742641 - 1.28629i) q^{79} +(-2.00000 + 3.46410i) q^{80} +(-3.74264 + 6.48244i) q^{81} +(4.41421 + 7.64564i) q^{82} +3.24264 q^{85} +(1.41421 + 2.44949i) q^{86} +(1.79289 - 3.10538i) q^{87} +(0.242641 - 0.420266i) q^{88} +(-4.00000 - 6.92820i) q^{89} -4.00000 q^{90} +(2.12132 + 3.67423i) q^{93} +(5.12132 - 8.87039i) q^{94} +(-3.00000 + 5.19615i) q^{95} -13.2426 q^{97} +0.485281 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{5} - 8 q^{6}+O(q^{10}) \) 4 * q + 2 * q^3 + 2 * q^5 - 8 * q^6	\( 4 q + 2 q^{3} + 2 q^{5} - 8 q^{6} + 6 q^{11} - 12 q^{13} + 4 q^{15} + 8 q^{16} - 2 q^{17} - 8 q^{18} + 12 q^{19} - 16 q^{22} - 12 q^{23} - 8 q^{24} - 2 q^{25} - 4 q^{26} - 4 q^{27} - 12 q^{29} - 4 q^{30} + 12 q^{31} - 14 q^{33} + 24 q^{34} + 4 q^{37} - 2 q^{39} + 8 q^{41} + 8 q^{43} + 4 q^{46} - 6 q^{47} + 16 q^{48} + 14 q^{51} - 4 q^{54} + 12 q^{55} + 24 q^{57} - 16 q^{58} + 4 q^{59} + 24 q^{62} + 32 q^{64} - 6 q^{65} - 20 q^{66} + 8 q^{67} - 16 q^{69} - 24 q^{71} + 16 q^{72} + 12 q^{74} + 2 q^{75} + 16 q^{78} + 14 q^{79} - 8 q^{80} + 2 q^{81} + 12 q^{82} - 4 q^{85} + 10 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} + 12 q^{94} - 12 q^{95} - 36 q^{97} - 32 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^5 - 8 * q^6 + 6 * q^11 - 12 * q^13 + 4 * q^15 + 8 * q^16 - 2 * q^17 - 8 * q^18 + 12 * q^19 - 16 * q^22 - 12 * q^23 - 8 * q^24 - 2 * q^25 - 4 * q^26 - 4 * q^27 - 12 * q^29 - 4 * q^30 + 12 * q^31 - 14 * q^33 + 24 * q^34 + 4 * q^37 - 2 * q^39 + 8 * q^41 + 8 * q^43 + 4 * q^46 - 6 * q^47 + 16 * q^48 + 14 * q^51 - 4 * q^54 + 12 * q^55 + 24 * q^57 - 16 * q^58 + 4 * q^59 + 24 * q^62 + 32 * q^64 - 6 * q^65 - 20 * q^66 + 8 * q^67 - 16 * q^69 - 24 * q^71 + 16 * q^72 + 12 * q^74 + 2 * q^75 + 16 * q^78 + 14 * q^79 - 8 * q^80 + 2 * q^81 + 12 * q^82 - 4 * q^85 + 10 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 + 12 * q^94 - 12 * q^95 - 36 * q^97 - 32 * q^99

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