LMFDB - Embedded newform 490.2.g.c.293.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(97,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("490.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 $ x^16 + 10x^14 + 61x^12 + 266x^10 + 852x^8 + 1438x^6 + 1933x^4 + 3038*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			293.6
Root			$-1.01089 + 0.750919i$ of defining polynomial
Character	$\chi$	$=$	490.293
Dual form			490.2.g.c.97.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-0.204875 + 0.204875i) q^{3} -1.00000i q^{4} +(-1.42962 + 1.71936i) q^{5} +0.289737i q^{6} +(-0.707107 - 0.707107i) q^{8} +2.91605i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.204875 + 0.204875i) q^{3} -1.00000i q^{4} +(-1.42962 + 1.71936i) q^{5} +0.289737i q^{6} +(-0.707107 - 0.707107i) q^{8} +2.91605i q^{9} +(0.204875 + 2.22666i) q^{10} +5.62576 q^{11} +(0.204875 + 0.204875i) q^{12} +(-1.42962 + 1.42962i) q^{13} +(-0.0593598 - 0.645146i) q^{15} -1.00000 q^{16} +(3.75384 + 3.75384i) q^{17} +(2.06196 + 2.06196i) q^{18} +3.89180 q^{19} +(1.71936 + 1.42962i) q^{20} +(3.97801 - 3.97801i) q^{22} +(-0.794732 - 0.794732i) q^{23} +0.289737 q^{24} +(-0.912375 - 4.91605i) q^{25} +2.02179i q^{26} +(-1.21205 - 1.21205i) q^{27} +3.15502i q^{29} +(-0.498161 - 0.414214i) q^{30} +3.84846i q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.15258 + 1.15258i) q^{33} +5.30873 q^{34} +2.91605 q^{36} +(-3.56380 + 3.56380i) q^{37} +(2.75192 - 2.75192i) q^{38} -0.585786i q^{39} +(2.22666 - 0.204875i) q^{40} -7.21050i q^{41} +(1.85669 + 1.85669i) q^{43} -5.62576i q^{44} +(-5.01373 - 4.16885i) q^{45} -1.12392 q^{46} +(-4.16885 - 4.16885i) q^{47} +(0.204875 - 0.204875i) q^{48} +(-4.12132 - 2.83103i) q^{50} -1.53813 q^{51} +(1.42962 + 1.42962i) q^{52} +(-0.978013 - 0.978013i) q^{53} -1.71410 q^{54} +(-8.04270 + 9.67269i) q^{55} +(-0.797333 + 0.797333i) q^{57} +(2.23093 + 2.23093i) q^{58} -5.47845 q^{59} +(-0.645146 + 0.0593598i) q^{60} -4.60924i q^{61} +(2.72127 + 2.72127i) q^{62} +1.00000i q^{64} +(-0.414214 - 4.50184i) q^{65} +1.62999i q^{66} +(0.597494 - 0.597494i) q^{67} +(3.75384 - 3.75384i) q^{68} +0.325641 q^{69} +4.77710 q^{71} +(2.06196 - 2.06196i) q^{72} +(3.96848 - 3.96848i) q^{73} +5.03997i q^{74} +(1.19410 + 0.820253i) q^{75} -3.89180i q^{76} +(-0.414214 - 0.414214i) q^{78} +6.24784i q^{79} +(1.42962 - 1.71936i) q^{80} -8.25152 q^{81} +(-5.09860 - 5.09860i) q^{82} +(5.67281 - 5.67281i) q^{83} +(-11.8207 + 1.08763i) q^{85} +2.62576 q^{86} +(-0.646383 - 0.646383i) q^{87} +(-3.97801 - 3.97801i) q^{88} +11.9218 q^{89} +(-6.49307 + 0.597426i) q^{90} +(-0.794732 + 0.794732i) q^{92} +(-0.788454 - 0.788454i) q^{93} -5.89564 q^{94} +(-5.56380 + 6.69140i) q^{95} -0.289737i q^{96} +(-6.63103 - 6.63103i) q^{97} +16.4050i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 24 q^{11} + 16 q^{15} - 16 q^{16} + 16 q^{18} - 8 q^{22} + 8 q^{23} - 24 q^{25} - 40 q^{30} - 8 q^{36} - 8 q^{37} - 8 q^{43} + 16 q^{46} - 32 q^{50} + 32 q^{51} + 56 q^{53} + 8 q^{57} + 64 q^{58} - 16 q^{60} + 16 q^{65} - 64 q^{67} + 16 q^{71} + 16 q^{72} + 16 q^{78} + 24 q^{85} - 24 q^{86} + 8 q^{88} + 8 q^{92} - 56 q^{93} - 40 q^{95}+O(q^{100}) $ 16 * q + 24 * q^11 + 16 * q^15 - 16 * q^16 + 16 * q^18 - 8 * q^22 + 8 * q^23 - 24 * q^25 - 40 * q^30 - 8 * q^36 - 8 * q^37 - 8 * q^43 + 16 * q^46 - 32 * q^50 + 32 * q^51 + 56 * q^53 + 8 * q^57 + 64 * q^58 - 16 * q^60 + 16 * q^65 - 64 * q^67 + 16 * q^71 + 16 * q^72 + 16 * q^78 + 24 * q^85 - 24 * q^86 + 8 * q^88 + 8 * q^92 - 56 * q^93 - 40 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−0.204875	+	0.204875i	−0.118285	+	0.118285i	−0.763771	−	0.645487i	$-0.776655\pi$
$3$	−0.204875	+	0.204875i	−0.118285	+	0.118285i	0.645487	+	0.763771i	$0.276655\pi$
$4$		−	1.00000i		−	0.500000i
$5$	−1.42962	+	1.71936i	−0.639345	+	0.768920i
$5$	−1.42962	+	1.71936i	−0.639345	+	0.768920i
$6$			0.289737i			0.118285i
$7$		0			0
$7$		0			0
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$			2.91605i			0.972018i
$10$	0.204875	+	2.22666i	0.0647871	+	0.704133i
$11$	5.62576			1.69623			0.848115	−	0.529812i	$-0.177737\pi$
$11$	5.62576			1.69623			0.848115	+	0.529812i	$0.177737\pi$
$12$	0.204875	+	0.204875i	0.0591423	+	0.0591423i
$13$	−1.42962	+	1.42962i	−0.396505	+	0.396505i	−0.876998	−	0.480493i	$-0.840458\pi$
$13$	−1.42962	+	1.42962i	−0.396505	+	0.396505i	0.480493	+	0.876998i	$0.340458\pi$
$14$		0			0
$15$	−0.0593598	−	0.645146i	−0.0153266	−	0.166576i
$16$	−1.00000			−0.250000
$17$	3.75384	+	3.75384i	0.910440	+	0.910440i	0.996307	−	0.0858670i	$-0.0273660\pi$
$17$	3.75384	+	3.75384i	0.910440	+	0.910440i	−0.0858670	+	0.996307i	$0.527366\pi$
$18$	2.06196	+	2.06196i	0.486009	+	0.486009i
$19$	3.89180			0.892841			0.446420	−	0.894823i	$-0.352699\pi$
$19$	3.89180			0.892841			0.446420	+	0.894823i	$0.352699\pi$
$20$	1.71936	+	1.42962i	0.384460	+	0.319673i
$21$		0			0
$22$	3.97801	−	3.97801i	0.848115	−	0.848115i
$23$	−0.794732	−	0.794732i	−0.165713	−	0.165713i	0.619379	−	0.785092i	$-0.287384\pi$
$23$	−0.794732	−	0.794732i	−0.165713	−	0.165713i	−0.785092	+	0.619379i	$0.787384\pi$
$24$	0.289737			0.0591423
$25$	−0.912375	−	4.91605i	−0.182475	−	0.983211i
$26$			2.02179i			0.396505i
$27$	−1.21205	−	1.21205i	−0.233259	−	0.233259i
$28$		0			0
$29$			3.15502i			0.585872i	0.956132	+	0.292936i	$0.0946322\pi$
$29$			3.15502i			0.585872i	−0.956132	+	0.292936i	$0.905368\pi$
$30$	−0.498161	−	0.414214i	−0.0909513	−	0.0756247i
$31$			3.84846i			0.691204i	0.938381	+	0.345602i	$0.112325\pi$
$31$			3.84846i			0.691204i	−0.938381	+	0.345602i	$0.887675\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−1.15258	+	1.15258i	−0.200638	+	0.200638i
$34$	5.30873			0.910440
$35$		0			0
$36$	2.91605			0.486009
$37$	−3.56380	+	3.56380i	−0.585885	+	0.585885i	−0.936514	−	0.350629i	$-0.885968\pi$
$37$	−3.56380	+	3.56380i	−0.585885	+	0.585885i	0.350629	+	0.936514i	$0.385968\pi$
$38$	2.75192	−	2.75192i	0.446420	−	0.446420i
$39$		−	0.585786i		−	0.0938009i
$40$	2.22666	−	0.204875i	0.352066	−	0.0323936i
$41$		−	7.21050i		−	1.12609i	−0.826426	−	0.563046i	$-0.809629\pi$
$41$		−	7.21050i		−	1.12609i	0.826426	−	0.563046i	$-0.190371\pi$
$42$		0			0
$43$	1.85669	+	1.85669i	0.283143	+	0.283143i	0.834361	−	0.551218i	$-0.185837\pi$
$43$	1.85669	+	1.85669i	0.283143	+	0.283143i	−0.551218	+	0.834361i	$0.685837\pi$
$44$		−	5.62576i		−	0.848115i
$45$	−5.01373	−	4.16885i	−0.747403	−	0.621455i
$46$	−1.12392			−0.165713
$47$	−4.16885	−	4.16885i	−0.608089	−	0.608089i	0.334358	−	0.942446i	$-0.391481\pi$
$47$	−4.16885	−	4.16885i	−0.608089	−	0.608089i	−0.942446	+	0.334358i	$0.891481\pi$
$48$	0.204875	−	0.204875i	0.0295711	−	0.0295711i
$49$		0			0
$50$	−4.12132	−	2.83103i	−0.582843	−	0.400368i
$51$	−1.53813			−0.215382
$52$	1.42962	+	1.42962i	0.198253	+	0.198253i
$53$	−0.978013	−	0.978013i	−0.134340	−	0.134340i	0.636739	−	0.771079i	$-0.280283\pi$
$53$	−0.978013	−	0.978013i	−0.134340	−	0.134340i	−0.771079	+	0.636739i	$0.780283\pi$
$54$	−1.71410			−0.233259
$55$	−8.04270	+	9.67269i	−1.08448	+	1.30426i
$56$		0			0
$57$	−0.797333	+	0.797333i	−0.105609	+	0.105609i
$58$	2.23093	+	2.23093i	0.292936	+	0.292936i
$59$	−5.47845			−0.713234			−0.356617	−	0.934251i	$-0.616070\pi$
$59$	−5.47845			−0.713234			−0.356617	+	0.934251i	$0.616070\pi$
$60$	−0.645146	+	0.0593598i	−0.0832880	+	0.00766332i
$61$		−	4.60924i		−	0.590153i	−0.955474	−	0.295077i	$-0.904655\pi$
$61$		−	4.60924i		−	0.590153i	0.955474	−	0.295077i	$-0.0953451\pi$
$62$	2.72127	+	2.72127i	0.345602	+	0.345602i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−0.414214	−	4.50184i	−0.0513769	−	0.558384i
$66$			1.62999i			0.200638i
$67$	0.597494	−	0.597494i	0.0729956	−	0.0729956i	−0.669666	−	0.742662i	$-0.733563\pi$
$67$	0.597494	−	0.597494i	0.0729956	−	0.0729956i	0.742662	+	0.669666i	$0.233563\pi$
$68$	3.75384	−	3.75384i	0.455220	−	0.455220i
$69$	0.325641			0.0392026
$70$		0			0
$71$	4.77710			0.566937			0.283469	−	0.958982i	$-0.408515\pi$
$71$	4.77710			0.566937			0.283469	+	0.958982i	$0.408515\pi$
$72$	2.06196	−	2.06196i	0.243004	−	0.243004i
$73$	3.96848	−	3.96848i	0.464475	−	0.464475i	−0.435644	−	0.900119i	$-0.643479\pi$
$73$	3.96848	−	3.96848i	0.464475	−	0.464475i	0.900119	+	0.435644i	$0.143479\pi$
$74$			5.03997i			0.585885i
$75$	1.19410	+	0.820253i	0.137883	+	0.0947147i
$76$		−	3.89180i		−	0.446420i
$77$		0			0
$78$	−0.414214	−	0.414214i	−0.0469005	−	0.0469005i
$79$			6.24784i			0.702937i	0.936200	+	0.351469i	$0.114318\pi$
$79$			6.24784i			0.702937i	−0.936200	+	0.351469i	$0.885682\pi$
$80$	1.42962	−	1.71936i	0.159836	−	0.192230i
$81$	−8.25152			−0.916836
$82$	−5.09860	−	5.09860i	−0.563046	−	0.563046i
$83$	5.67281	−	5.67281i	0.622672	−	0.622672i	−0.323542	−	0.946214i	$-0.604874\pi$
$83$	5.67281	−	5.67281i	0.622672	−	0.622672i	0.946214	+	0.323542i	$0.104874\pi$
$84$		0			0
$85$	−11.8207	+	1.08763i	−1.28214	+	0.117970i
$86$	2.62576			0.283143
$87$	−0.646383	−	0.646383i	−0.0692996	−	0.0692996i
$88$	−3.97801	−	3.97801i	−0.424058	−	0.424058i
$89$	11.9218			1.26371			0.631855	−	0.775087i	$-0.282294\pi$
$89$	11.9218			1.26371			0.631855	+	0.775087i	$0.282294\pi$
$90$	−6.49307	+	0.597426i	−0.684429	+	0.0629742i
$91$		0			0
$92$	−0.794732	+	0.794732i	−0.0828566	+	0.0828566i
$93$	−0.788454	−	0.788454i	−0.0817588	−	0.0817588i
$94$	−5.89564			−0.608089
$95$	−5.56380	+	6.69140i	−0.570834	+	0.686523i
$96$		−	0.289737i		−	0.0295711i
$97$	−6.63103	−	6.63103i	−0.673279	−	0.673279i	0.285191	−	0.958471i	$-0.407943\pi$
$97$	−6.63103	−	6.63103i	−0.673279	−	0.673279i	−0.958471	+	0.285191i	$0.907943\pi$
$98$		0			0
$99$			16.4050i			1.64877i
$100$	−4.91605	+	0.912375i	−0.491605	+	0.0912375i
$101$		−	16.0992i		−	1.60193i	−0.598711	−	0.800965i	$-0.704320\pi$
$101$		−	16.0992i		−	1.60193i	0.598711	−	0.800965i	$-0.295680\pi$
$102$	−1.08763	+	1.08763i	−0.107691	+	0.107691i
$103$	−13.9084	+	13.9084i	−1.37044	+	1.37044i	−0.510653	+	0.859787i	$0.670596\pi$
$103$	−13.9084	+	13.9084i	−1.37044	+	1.37044i	−0.859787	+	0.510653i	$0.829404\pi$
$104$	2.02179			0.198253
$105$		0			0
$106$	−1.38312			−0.134340
$107$	1.98061	−	1.98061i	0.191473	−	0.191473i	−0.604859	−	0.796332i	$-0.706771\pi$
$107$	1.98061	−	1.98061i	0.191473	−	0.191473i	0.796332	+	0.604859i	$0.206771\pi$
$108$	−1.21205	+	1.21205i	−0.116630	+	0.116630i
$109$			5.91085i			0.566157i	0.959097	+	0.283078i	$0.0913557\pi$
$109$			5.91085i			0.566157i	−0.959097	+	0.283078i	$0.908644\pi$
$110$	1.15258	+	12.5267i	0.109894	+	1.19437i
$111$		−	1.46027i		−	0.138602i
$112$		0			0
$113$	−13.5818	−	13.5818i	−1.27767	−	1.27767i	−0.941970	−	0.335697i	$-0.891028\pi$
$113$	−13.5818	−	13.5818i	−1.27767	−	1.27767i	−0.335697	−	0.941970i	$-0.608972\pi$
$114$			1.12760i			0.105609i
$115$	2.50259	−	0.230263i	0.233368	−	0.0214722i
$116$	3.15502			0.292936
$117$	−4.16885	−	4.16885i	−0.385410	−	0.385410i
$118$	−3.87385	+	3.87385i	−0.356617	+	0.356617i
$119$		0			0
$120$	−0.414214	+	0.498161i	−0.0378124	+	0.0454757i
$121$	20.6492			1.87720
$122$	−3.25923	−	3.25923i	−0.295077	−	0.295077i
$123$	1.47725	+	1.47725i	0.133199	+	0.133199i
$124$	3.84846			0.345602
$125$	9.75680	+	5.45939i	0.872674	+	0.488303i
$126$		0			0
$127$	4.63487	−	4.63487i	0.411278	−	0.411278i	−0.470906	−	0.882184i	$-0.656073\pi$
$127$	4.63487	−	4.63487i	0.411278	−	0.411278i	0.882184	+	0.470906i	$0.156073\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−0.760780			−0.0669829
$130$	−3.47617	−	2.89039i	−0.304881	−	0.253504i
$131$		−	7.69535i		−	0.672346i	−0.941800	−	0.336173i	$-0.890867\pi$
$131$		−	7.69535i		−	0.672346i	0.941800	−	0.336173i	$-0.109133\pi$
$132$	1.15258	+	1.15258i	0.100319	+	0.100319i
$133$		0			0
$134$		−	0.844985i		−	0.0729956i
$135$	3.81672	−	0.351176i	0.328491	−	0.0302244i
$136$		−	5.30873i		−	0.455220i
$137$	−6.24784	+	6.24784i	−0.533789	+	0.533789i	−0.921698	−	0.387909i	$-0.873198\pi$
$137$	−6.24784	+	6.24784i	−0.533789	+	0.533789i	0.387909	+	0.921698i	$0.373198\pi$
$138$	0.230263	−	0.230263i	0.0196013	−	0.0196013i
$139$	11.0631			0.938361			0.469180	−	0.883102i	$-0.344549\pi$
$139$	11.0631			0.938361			0.469180	+	0.883102i	$0.344549\pi$
$140$		0			0
$141$	1.70818			0.143855
$142$	3.37792	−	3.37792i	0.283469	−	0.283469i
$143$	−8.04270	+	8.04270i	−0.672564	+	0.672564i
$144$		−	2.91605i		−	0.243004i
$145$	−5.42460	−	4.51047i	−0.450488	−	0.374574i
$146$		−	5.61227i		−	0.464475i
$147$		0			0
$148$	3.56380	+	3.56380i	0.292943	+	0.292943i
$149$		−	5.04885i		−	0.413618i	−0.978381	−	0.206809i	$-0.933692\pi$
$149$		−	5.04885i		−	0.413618i	0.978381	−	0.206809i	$-0.0663079\pi$
$150$	1.42436	−	0.264349i	0.116299	−	0.0215840i
$151$	13.4428			1.09396			0.546981	−	0.837145i	$-0.315777\pi$
$151$	13.4428			1.09396			0.546981	+	0.837145i	$0.315777\pi$
$152$	−2.75192	−	2.75192i	−0.223210	−	0.223210i
$153$	−10.9464	+	10.9464i	−0.884963	+	0.884963i
$154$		0			0
$155$	−6.61688	−	5.50184i	−0.531481	−	0.441918i
$156$	−0.585786			−0.0469005
$157$	0.779844	+	0.779844i	0.0622383	+	0.0622383i	0.737541	−	0.675303i	$-0.235987\pi$
$157$	0.779844	+	0.779844i	0.0622383	+	0.0622383i	−0.675303	+	0.737541i	$0.735987\pi$
$158$	4.41789	+	4.41789i	0.351469	+	0.351469i
$159$	0.400741			0.0317808
$160$	−0.204875	−	2.22666i	−0.0161968	−	0.176033i
$161$		0			0
$162$	−5.83471	+	5.83471i	−0.458418	+	0.458418i
$163$	−9.36288	−	9.36288i	−0.733358	−	0.733358i	0.237926	−	0.971283i	$-0.423533\pi$
$163$	−9.36288	−	9.36288i	−0.733358	−	0.733358i	−0.971283	+	0.237926i	$0.923533\pi$
$164$	−7.21050			−0.563046
$165$	−0.333944	−	3.62944i	−0.0259975	−	0.282551i
$166$		−	8.02257i		−	0.622672i
$167$	−4.70680	−	4.70680i	−0.364223	−	0.364223i	0.501142	−	0.865365i	$-0.332913\pi$
$167$	−4.70680	−	4.70680i	−0.364223	−	0.364223i	−0.865365	+	0.501142i	$0.832913\pi$
$168$		0			0
$169$			8.91237i			0.685567i
$170$	−7.58946	+	9.12760i	−0.582085	+	0.700055i
$171$			11.3487i			0.867857i
$172$	1.85669	−	1.85669i	0.141571	−	0.141571i
$173$	4.98835	−	4.98835i	0.379257	−	0.379257i	−0.491577	−	0.870834i	$-0.663579\pi$
$173$	4.98835	−	4.98835i	0.379257	−	0.379257i	0.870834	+	0.491577i	$0.163579\pi$
$174$	−0.914124			−0.0692996
$175$		0			0
$176$	−5.62576			−0.424058
$177$	1.12240	−	1.12240i	0.0843646	−	0.0843646i
$178$	8.42999	−	8.42999i	0.631855	−	0.631855i
$179$		−	2.20635i		−	0.164910i	−0.996595	−	0.0824550i	$-0.973724\pi$
$179$		−	2.20635i		−	0.164910i	0.996595	−	0.0824550i	$-0.0262761\pi$
$180$	−4.16885	+	5.01373i	−0.310727	+	0.373702i
$181$			4.11867i			0.306139i	0.988215	+	0.153069i	$0.0489158\pi$
$181$			4.11867i			0.306139i	−0.988215	+	0.153069i	$0.951084\pi$
$182$		0			0
$183$	0.944318	+	0.944318i	0.0698060	+	0.0698060i
$184$			1.12392i			0.0828566i
$185$	−1.03256	−	11.2223i	−0.0759156	−	0.825081i
$186$	−1.11504			−0.0817588
$187$	21.1182	+	21.1182i	1.54432	+	1.54432i
$188$	−4.16885	+	4.16885i	−0.304044	+	0.304044i
$189$		0			0
$190$	0.797333	+	8.66573i	0.0578446	+	0.628678i
$191$	−17.2023			−1.24472			−0.622359	−	0.782732i	$-0.713826\pi$
$191$	−17.2023			−1.24472			−0.622359	+	0.782732i	$0.713826\pi$
$192$	−0.204875	−	0.204875i	−0.0147856	−	0.0147856i
$193$	−8.53293	−	8.53293i	−0.614214	−	0.614214i	0.329827	−	0.944041i	$-0.393009\pi$
$193$	−8.53293	−	8.53293i	−0.614214	−	0.614214i	−0.944041	+	0.329827i	$0.893009\pi$
$194$	−9.37769			−0.673279
$195$	1.00718	+	0.837452i	0.0721254	+	0.0599712i
$196$		0			0
$197$	14.3135	−	14.3135i	1.01979	−	1.01979i	0.0199932	−	0.999800i	$-0.493636\pi$
$197$	14.3135	−	14.3135i	1.01979	−	1.01979i	0.999800	−	0.0199932i	$-0.00636444\pi$
$198$	11.6001	+	11.6001i	0.824383	+	0.824383i
$199$	7.53307			0.534005			0.267002	−	0.963696i	$-0.413967\pi$
$199$	7.53307			0.534005			0.267002	+	0.963696i	$0.413967\pi$
$200$	−2.83103	+	4.12132i	−0.200184	+	0.291421i
$201$			0.244823i			0.0172685i
$202$	−11.3839	−	11.3839i	−0.800965	−	0.800965i
$203$		0			0
$204$			1.53813i			0.107691i
$205$	12.3974	+	10.3083i	0.865874	+	0.719961i
$206$			19.6695i			1.37044i
$207$	2.31748	−	2.31748i	0.161076	−	0.161076i
$208$	1.42962	−	1.42962i	0.0991263	−	0.0991263i
$209$	21.8944			1.51446
$210$		0			0
$211$	19.5766			1.34771			0.673854	−	0.738865i	$-0.264638\pi$
$211$	19.5766			1.34771			0.673854	+	0.738865i	$0.264638\pi$
$212$	−0.978013	+	0.978013i	−0.0671702	+	0.0671702i
$213$	−0.978707	+	0.978707i	−0.0670599	+	0.0670599i
$214$		−	2.80101i		−	0.191473i
$215$	−5.84668	+	0.537952i	−0.398740	+	0.0366880i
$216$			1.71410i			0.116630i
$217$		0			0
$218$	4.17960	+	4.17960i	0.283078	+	0.283078i
$219$			1.62608i			0.109880i
$220$	9.67269	+	8.04270i	0.652132	+	0.542239i
$221$	−10.7331			−0.721988
$222$	−1.03256	−	1.03256i	−0.0693012	−	0.0693012i
$223$	1.46027	−	1.46027i	0.0977867	−	0.0977867i	−0.656521	−	0.754308i	$-0.727973\pi$
$223$	1.46027	−	1.46027i	0.0977867	−	0.0977867i	0.754308	+	0.656521i	$0.227973\pi$
$224$		0			0
$225$	14.3355	−	2.66053i	0.955698	−	0.177369i
$226$	−19.2075			−1.27767
$227$	13.1828	+	13.1828i	0.874974	+	0.874974i	0.993009	−	0.118035i	$-0.0376596\pi$
$227$	13.1828	+	13.1828i	0.874974	+	0.874974i	−0.118035	+	0.993009i	$0.537660\pi$
$228$	0.797333	+	0.797333i	0.0528047	+	0.0528047i
$229$	4.00767			0.264834			0.132417	−	0.991194i	$-0.457726\pi$
$229$	4.00767			0.264834			0.132417	+	0.991194i	$0.457726\pi$
$230$	1.60678	−	1.93242i	0.105948	−	0.127420i
$231$		0			0
$232$	2.23093	−	2.23093i	0.146468	−	0.146468i
$233$	−9.70971	−	9.70971i	−0.636104	−	0.636104i	0.313488	−	0.949592i	$-0.398502\pi$
$233$	−9.70971	−	9.70971i	−0.636104	−	0.636104i	−0.949592	+	0.313488i	$0.898502\pi$
$234$	−5.89564			−0.385410
$235$	13.1276	−	1.20787i	0.856350	−	0.0787927i
$236$			5.47845i			0.356617i
$237$	−1.28003	−	1.28003i	−0.0831466	−	0.0831466i
$238$		0			0
$239$		−	19.6621i		−	1.27183i	−0.771758	−	0.635916i	$-0.780622\pi$
$239$		−	19.6621i		−	1.27183i	0.771758	−	0.635916i	$-0.219378\pi$
$240$	0.0593598	+	0.645146i	0.00383166	+	0.0416440i
$241$			5.88512i			0.379094i	0.981872	+	0.189547i	$0.0607020\pi$
$241$			5.88512i			0.379094i	−0.981872	+	0.189547i	$0.939298\pi$
$242$	14.6012	−	14.6012i	0.938599	−	0.938599i
$243$	5.32668	−	5.32668i	0.341707	−	0.341707i
$244$	−4.60924			−0.295077
$245$		0			0
$246$	2.08915			0.133199
$247$	−5.56380	+	5.56380i	−0.354016	+	0.354016i
$248$	2.72127	−	2.72127i	0.172801	−	0.172801i
$249$			2.32443i			0.147305i
$250$	10.7595	−	3.03873i	0.680488	−	0.192186i
$251$			7.09950i			0.448116i	0.974576	+	0.224058i	$0.0719306\pi$
$251$			7.09950i			0.448116i	−0.974576	+	0.224058i	$0.928069\pi$
$252$		0			0
$253$	−4.47097	−	4.47097i	−0.281088	−	0.281088i
$254$		−	6.55469i		−	0.411278i
$255$	2.19895	−	2.64460i	0.137703	−	0.165611i
$256$	1.00000			0.0625000
$257$	−6.99107	−	6.99107i	−0.436091	−	0.436091i	0.454603	−	0.890694i	$-0.349781\pi$
$257$	−6.99107	−	6.99107i	−0.436091	−	0.436091i	−0.890694	+	0.454603i	$0.849781\pi$
$258$	−0.537952	+	0.537952i	−0.0334915	+	0.0334915i
$259$		0			0
$260$	−4.50184	+	0.414214i	−0.279192	+	0.0256884i
$261$	−9.20019			−0.569477
$262$	−5.44144	−	5.44144i	−0.336173	−	0.336173i
$263$	9.72142	+	9.72142i	0.599448	+	0.599448i	0.940166	−	0.340718i	$-0.110670\pi$
$263$	9.72142	+	9.72142i	0.599448	+	0.599448i	−0.340718	+	0.940166i	$0.610670\pi$
$264$	1.62999			0.100319
$265$	3.07974	−	0.283366i	0.189187	−	0.0174071i
$266$		0			0
$267$	−2.44248	+	2.44248i	−0.149477	+	0.149477i
$268$	−0.597494	−	0.597494i	−0.0364978	−	0.0364978i
$269$	26.5020			1.61586			0.807928	−	0.589281i	$-0.200589\pi$
$269$	26.5020			1.61586			0.807928	+	0.589281i	$0.200589\pi$
$270$	2.45051	−	2.94715i	0.149133	−	0.179358i
$271$		−	12.7969i		−	0.777355i	−0.921374	−	0.388678i	$-0.872932\pi$
$271$		−	12.7969i		−	0.777355i	0.921374	−	0.388678i	$-0.127068\pi$
$272$	−3.75384	−	3.75384i	−0.227610	−	0.227610i
$273$		0			0
$274$			8.83578i			0.533789i
$275$	−5.13280	−	27.6565i	−0.309520	−	1.66775i
$276$		−	0.325641i		−	0.0196013i
$277$	14.2152	−	14.2152i	0.854110	−	0.854110i	−0.136526	−	0.990636i	$-0.543594\pi$
$277$	14.2152	−	14.2152i	0.854110	−	0.854110i	0.990636	+	0.136526i	$0.0435938\pi$
$278$	7.82280	−	7.82280i	0.469180	−	0.469180i
$279$	−11.2223			−0.671863
$280$		0			0
$281$	−14.1498			−0.844107			−0.422054	−	0.906571i	$-0.638691\pi$
$281$	−14.1498			−0.844107			−0.422054	+	0.906571i	$0.638691\pi$
$282$	1.20787	−	1.20787i	0.0719275	−	0.0719275i
$283$	−19.1397	+	19.1397i	−1.13774	+	1.13774i	−0.148885	+	0.988854i	$0.547569\pi$
$283$	−19.1397	+	19.1397i	−1.13774	+	1.13774i	−0.988854	+	0.148885i	$0.952431\pi$
$284$		−	4.77710i		−	0.283469i
$285$	−0.231017	−	2.51078i	−0.0136843	−	0.148726i
$286$			11.3741i			0.672564i
$287$		0			0
$288$	−2.06196	−	2.06196i	−0.121502	−	0.121502i
$289$			11.1826i			0.657800i
$290$	−7.02515	+	0.646383i	−0.412531	+	0.0379569i
$291$	2.71706			0.159277
$292$	−3.96848	−	3.96848i	−0.232237	−	0.232237i
$293$	17.1191	−	17.1191i	1.00011	−	1.00011i	0.000106876	−	1.00000i	$-0.499966\pi$
$293$	17.1191	−	17.1191i	1.00011	−	1.00011i	1.00000		0.000106876i	$-3.40197e-5\pi$
$294$		0			0
$295$	7.83211	−	9.41941i	0.456003	−	0.548420i
$296$	5.03997			0.292943
$297$	−6.81871	−	6.81871i	−0.395661	−	0.395661i
$298$	−3.57008	−	3.57008i	−0.206809	−	0.206809i
$299$	2.27233			0.131412
$300$	0.820253	−	1.19410i	0.0473573	−	0.0689413i
$301$		0			0
$302$	9.50552	−	9.50552i	0.546981	−	0.546981i
$303$	3.29832	+	3.29832i	0.189484	+	0.189484i
$304$	−3.89180			−0.223210
$305$	7.92493	+	6.58946i	0.453780	+	0.377312i
$306$			15.4805i			0.884963i
$307$	17.2974	+	17.2974i	0.987217	+	0.987217i	0.999919	−	0.0127019i	$-0.00404326\pi$
$307$	17.2974	+	17.2974i	0.987217	+	0.987217i	−0.0127019	+	0.999919i	$0.504043\pi$
$308$		0			0
$309$		−	5.69898i		−	0.324204i
$310$	−8.56923	+	0.788454i	−0.486699	+	0.0447812i
$311$			10.9823i			0.622749i	0.950287	+	0.311374i	$0.100789\pi$
$311$			10.9823i			0.622749i	−0.950287	+	0.311374i	$0.899211\pi$
$312$	−0.414214	+	0.414214i	−0.0234502	+	0.0234502i
$313$	−20.7967	+	20.7967i	−1.17550	+	1.17550i	−0.194620	+	0.980879i	$0.562347\pi$
$313$	−20.7967	+	20.7967i	−1.17550	+	1.17550i	−0.980879	+	0.194620i	$0.937653\pi$
$314$	1.10287			0.0622383
$315$		0			0
$316$	6.24784			0.351469
$317$	3.03630	−	3.03630i	0.170535	−	0.170535i	−0.616679	−	0.787215i	$-0.711522\pi$
$317$	3.03630	−	3.03630i	0.170535	−	0.170535i	0.787215	+	0.616679i	$0.211522\pi$
$318$	0.283366	−	0.283366i	0.0158904	−	0.0158904i
$319$			17.7494i			0.993773i
$320$	−1.71936	−	1.42962i	−0.0961150	−	0.0799182i
$321$			0.811556i			0.0452966i
$322$		0			0
$323$	14.6092	+	14.6092i	0.812878	+	0.812878i
$324$			8.25152i			0.458418i
$325$	8.33243	+	5.72374i	0.462200	+	0.317496i
$326$	−13.2411			−0.733358
$327$	−1.21099	−	1.21099i	−0.0669676	−	0.0669676i
$328$	−5.09860	+	5.09860i	−0.281523	+	0.281523i
$329$		0			0
$330$	−2.80253	−	2.33027i	−0.154274	−	0.128277i
$331$	35.4499			1.94850			0.974250	−	0.225469i	$-0.0723914\pi$
$331$	35.4499			1.94850			0.974250	+	0.225469i	$0.0723914\pi$
$332$	−5.67281	−	5.67281i	−0.311336	−	0.311336i
$333$	−10.3922	−	10.3922i	−0.569491	−	0.569491i
$334$	−6.65642			−0.364223
$335$	0.173116	+	1.88150i	0.00945835	+	0.102797i
$336$		0			0
$337$	−12.1473	+	12.1473i	−0.661708	+	0.661708i	−0.955782	−	0.294075i	$-0.904989\pi$
$337$	−12.1473	+	12.1473i	−0.661708	+	0.661708i	0.294075	+	0.955782i	$0.404989\pi$
$338$	6.30200	+	6.30200i	0.342784	+	0.342784i
$339$	5.56513			0.302257
$340$	1.08763	+	11.8207i	0.0589848	+	0.641070i
$341$			21.6505i			1.17244i
$342$	8.02475	+	8.02475i	0.433929	+	0.433929i
$343$		0			0
$344$		−	2.62576i		−	0.141571i
$345$	−0.465543	+	0.559894i	−0.0250640	+	0.0301437i
$346$		−	7.05459i		−	0.379257i
$347$	6.34718	−	6.34718i	0.340734	−	0.340734i	−0.515909	−	0.856643i	$-0.672546\pi$
$347$	6.34718	−	6.34718i	0.340734	−	0.340734i	0.856643	+	0.515909i	$0.172546\pi$
$348$	−0.646383	+	0.646383i	−0.0346498	+	0.0346498i
$349$	−26.0251			−1.39309			−0.696546	−	0.717512i	$-0.745281\pi$
$349$	−26.0251			−1.39309			−0.696546	+	0.717512i	$0.745281\pi$
$350$		0			0
$351$	3.46554			0.184977
$352$	−3.97801	+	3.97801i	−0.212029	+	0.212029i
$353$	7.04715	−	7.04715i	0.375082	−	0.375082i	−0.494242	−	0.869324i	$-0.664554\pi$
$353$	7.04715	−	7.04715i	0.375082	−	0.375082i	0.869324	+	0.494242i	$0.164554\pi$
$354$		−	1.58731i		−	0.0843646i
$355$	−6.82943	+	8.21353i	−0.362469	+	0.435929i
$356$		−	11.9218i		−	0.631855i
$357$		0			0
$358$	−1.56012	−	1.56012i	−0.0824550	−	0.0824550i
$359$			11.5741i			0.610858i	0.952215	+	0.305429i	$0.0987999\pi$
$359$			11.5741i			0.610858i	−0.952215	+	0.305429i	$0.901200\pi$
$360$	0.597426	+	6.49307i	0.0314871	+	0.342215i
$361$	−3.85386			−0.202835
$362$	2.91234	+	2.91234i	0.153069	+	0.153069i
$363$	−4.23050	+	4.23050i	−0.222044	+	0.222044i
$364$		0			0
$365$	1.14981	+	12.4966i	0.0601840	+	0.654104i
$366$	1.33547			0.0698060
$367$	−11.8047	−	11.8047i	−0.616202	−	0.616202i	0.328353	−	0.944555i	$-0.393506\pi$
$367$	−11.8047	−	11.8047i	−0.616202	−	0.616202i	−0.944555	+	0.328353i	$0.893506\pi$
$368$	0.794732	+	0.794732i	0.0414283	+	0.0414283i
$369$	21.0262			1.09458
$370$	−8.66551	−	7.20525i	−0.450499	−	0.374583i
$371$		0			0
$372$	−0.788454	+	0.788454i	−0.0408794	+	0.0408794i
$373$	2.24784	+	2.24784i	0.116389	+	0.116389i	0.762902	−	0.646514i	$-0.223774\pi$
$373$	2.24784	+	2.24784i	0.116389	+	0.116389i	−0.646514	+	0.762902i	$0.723774\pi$
$374$	29.8656			1.54432
$375$	−3.11741	+	0.880431i	−0.160983	+	0.0454653i
$376$			5.89564i			0.304044i
$377$	−4.51047	−	4.51047i	−0.232301	−	0.232301i
$378$		0			0
$379$		−	7.15349i		−	0.367450i	−0.982978	−	0.183725i	$-0.941184\pi$
$379$		−	7.15349i		−	0.367450i	0.982978	−	0.183725i	$-0.0588156\pi$
$380$	6.69140	+	5.56380i	0.343262	+	0.285417i
$381$			1.89914i			0.0972957i
$382$	−12.1639	+	12.1639i	−0.622359	+	0.622359i
$383$	10.3191	−	10.3191i	0.527280	−	0.527280i	−0.392480	−	0.919760i	$-0.628383\pi$
$383$	10.3191	−	10.3191i	0.527280	−	0.527280i	0.919760	+	0.392480i	$0.128383\pi$
$384$	−0.289737			−0.0147856
$385$		0			0
$386$	−12.0674			−0.614214
$387$	−5.41421	+	5.41421i	−0.275220	+	0.275220i
$388$	−6.63103	+	6.63103i	−0.336640	+	0.336640i
$389$		−	6.19651i		−	0.314176i	−0.987585	−	0.157088i	$-0.949789\pi$
$389$		−	6.19651i		−	0.314176i	0.987585	−	0.157088i	$-0.0502106\pi$
$390$	1.30435	−	0.120013i	0.0660483	−	0.00607709i
$391$		−	5.96659i		−	0.301744i
$392$		0			0
$393$	1.57658	+	1.57658i	0.0795282	+	0.0795282i
$394$		−	20.2423i		−	1.01979i
$395$	−10.7423	−	8.93204i	−0.540502	−	0.449420i
$396$	16.4050			0.824383
$397$	2.06184	+	2.06184i	0.103481	+	0.103481i	0.756952	−	0.653471i	$-0.226688\pi$
$397$	2.06184	+	2.06184i	0.103481	+	0.103481i	−0.653471	+	0.756952i	$0.726688\pi$
$398$	5.32668	−	5.32668i	0.267002	−	0.267002i
$399$		0			0
$400$	0.912375	+	4.91605i	0.0456187	+	0.245803i
$401$	−19.9706			−0.997282			−0.498641	−	0.866809i	$-0.666167\pi$
$401$	−19.9706			−0.997282			−0.498641	+	0.866809i	$0.666167\pi$
$402$	0.173116	+	0.173116i	0.00863425	+	0.00863425i
$403$	−5.50184	−	5.50184i	−0.274066	−	0.274066i
$404$	−16.0992			−0.800965
$405$	11.7965	−	14.1873i	0.586175	−	0.704973i
$406$		0			0
$407$	−20.0491	+	20.0491i	−0.993796	+	0.993796i
$408$	1.08763	+	1.08763i	0.0538455	+	0.0538455i
$409$	−34.3582			−1.69890			−0.849451	−	0.527668i	$-0.823067\pi$
$409$	−34.3582			−1.69890			−0.849451	+	0.527668i	$0.823067\pi$
$410$	16.0554	−	1.47725i	0.792918	−	0.0729562i
$411$		−	2.56005i		−	0.126278i
$412$	13.9084	+	13.9084i	0.685220	+	0.685220i
$413$		0			0
$414$		−	3.27741i		−	0.161076i
$415$	1.64362	+	17.8636i	0.0806823	+	0.876887i
$416$		−	2.02179i		−	0.0991263i
$417$	−2.26655	+	2.26655i	−0.110994	+	0.110994i
$418$	15.4816	−	15.4816i	0.757232	−	0.757232i
$419$	−31.1360			−1.52109			−0.760547	−	0.649283i	$-0.775069\pi$
$419$	−31.1360			−1.52109			−0.760547	+	0.649283i	$0.775069\pi$
$420$		0			0
$421$	−33.6728			−1.64111			−0.820555	−	0.571567i	$-0.806336\pi$
$421$	−33.6728			−1.64111			−0.820555	+	0.571567i	$0.806336\pi$
$422$	13.8427	−	13.8427i	0.673854	−	0.673854i
$423$	12.1566	−	12.1566i	0.591073	−	0.591073i
$424$			1.38312i			0.0671702i
$425$	15.0292	−	21.8790i	0.729021	−	1.06129i
$426$			1.38410i			0.0670599i
$427$		0			0
$428$	−1.98061	−	1.98061i	−0.0957366	−	0.0957366i
$429$		−	3.29549i		−	0.159108i
$430$	−3.75384	+	4.51462i	−0.181026	+	0.217714i
$431$	−14.7457			−0.710274			−0.355137	−	0.934814i	$-0.615566\pi$
$431$	−14.7457			−0.710274			−0.355137	+	0.934814i	$0.615566\pi$
$432$	1.21205	+	1.21205i	0.0583148	+	0.0583148i
$433$	−9.98256	+	9.98256i	−0.479731	+	0.479731i	−0.905046	−	0.425315i	$-0.860163\pi$
$433$	−9.98256	+	9.98256i	−0.479731	+	0.479731i	0.425315	+	0.905046i	$0.360163\pi$
$434$		0			0
$435$	2.03545	−	0.187281i	0.0975922	−	0.00897944i
$436$	5.91085			0.283078
$437$	−3.09294	−	3.09294i	−0.147955	−	0.147955i
$438$	1.14981	+	1.14981i	0.0549402	+	0.0549402i
$439$	−38.4285			−1.83409			−0.917046	−	0.398782i	$-0.869433\pi$
$439$	−38.4285			−1.83409			−0.917046	+	0.398782i	$0.869433\pi$
$440$	12.5267	−	1.15258i	0.597186	−	0.0549470i
$441$		0			0
$442$	−7.58946	+	7.58946i	−0.360994	+	0.360994i
$443$	4.05568	+	4.05568i	0.192691	+	0.192691i	0.796858	−	0.604167i	$-0.206494\pi$
$443$	4.05568	+	4.05568i	0.192691	+	0.192691i	−0.604167	+	0.796858i	$0.706494\pi$
$444$	−1.46027			−0.0693012
$445$	−17.0437	+	20.4978i	−0.807947	+	0.971691i
$446$		−	2.06513i		−	0.0977867i
$447$	1.03438	+	1.03438i	0.0489247	+	0.0489247i
$448$		0			0
$449$		−	7.30267i		−	0.344635i	−0.985042	−	0.172317i	$-0.944875\pi$
$449$		−	7.30267i		−	0.344635i	0.985042	−	0.172317i	$-0.0551254\pi$
$450$	8.25543	−	12.0180i	0.389165	−	0.566533i
$451$		−	40.5646i		−	1.91011i
$452$	−13.5818	+	13.5818i	−0.638833	+	0.638833i
$453$	−2.75410	+	2.75410i	−0.129399	+	0.129399i
$454$	18.6433			0.874974
$455$		0			0
$456$	1.12760			0.0528047
$457$	3.63864	−	3.63864i	0.170208	−	0.170208i	−0.616863	−	0.787071i	$-0.711597\pi$
$457$	3.63864	−	3.63864i	0.170208	−	0.170208i	0.787071	+	0.616863i	$0.211597\pi$
$458$	2.83385	−	2.83385i	0.132417	−	0.132417i
$459$		−	9.09969i		−	0.424737i
$460$	−0.230263	−	2.50259i	−0.0107361	−	0.116684i
$461$			29.4110i			1.36981i	0.728634	+	0.684903i	$0.240155\pi$
$461$			29.4110i			1.36981i	−0.728634	+	0.684903i	$0.759845\pi$
$462$		0			0
$463$	−4.04625	−	4.04625i	−0.188045	−	0.188045i	0.606805	−	0.794851i	$-0.292451\pi$
$463$	−4.04625	−	4.04625i	−0.188045	−	0.188045i	−0.794851	+	0.606805i	$0.792451\pi$
$464$		−	3.15502i		−	0.146468i
$465$	2.48282	−	0.228444i	0.115138	−	0.0105938i
$466$	−13.7316			−0.636104
$467$	11.7682	+	11.7682i	0.544568	+	0.544568i	0.924865	−	0.380297i	$-0.124178\pi$
$467$	11.7682	+	11.7682i	0.544568	+	0.544568i	−0.380297	+	0.924865i	$0.624178\pi$
$468$	−4.16885	+	4.16885i	−0.192705	+	0.192705i
$469$		0			0
$470$	8.42852	−	10.1367i	0.388779	−	0.467571i
$471$	−0.319541			−0.0147237
$472$	3.87385	+	3.87385i	0.178308	+	0.178308i
$473$	10.4453	+	10.4453i	0.480276	+	0.480276i
$474$	−1.81023			−0.0831466
$475$	−3.55078	−	19.1323i	−0.162921	−	0.877851i
$476$		0			0
$477$	2.85194	−	2.85194i	0.130581	−	0.130581i
$478$	−13.9032	−	13.9032i	−0.635916	−	0.635916i
$479$	−15.3892			−0.703150			−0.351575	−	0.936160i	$-0.614354\pi$
$479$	−15.3892			−0.703150			−0.351575	+	0.936160i	$0.614354\pi$
$480$	0.498161	+	0.414214i	0.0227378	+	0.0189062i
$481$		−	10.1898i		−	0.464613i
$482$	4.16141	+	4.16141i	0.189547	+	0.189547i
$483$		0			0
$484$		−	20.6492i		−	0.938599i
$485$	20.8810	−	1.92125i	0.948155	−	0.0872396i
$486$		−	7.53307i		−	0.341707i
$487$	−25.4502	+	25.4502i	−1.15326	+	1.15326i	−0.167363	+	0.985895i	$0.553525\pi$
$487$	−25.4502	+	25.4502i	−1.15326	+	1.15326i	−0.985895	+	0.167363i	$0.946475\pi$
$488$	−3.25923	+	3.25923i	−0.147538	+	0.147538i
$489$	3.83644			0.173490
$490$		0			0
$491$	−15.2823			−0.689680			−0.344840	−	0.938661i	$-0.612067\pi$
$491$	−15.2823			−0.689680			−0.344840	+	0.938661i	$0.612067\pi$
$492$	1.47725	−	1.47725i	0.0665996	−	0.0665996i
$493$	−11.8434	+	11.8434i	−0.533401	+	0.533401i
$494$			7.86840i			0.354016i
$495$	−28.2061	−	23.4529i	−1.26777	−	1.05413i
$496$		−	3.84846i		−	0.172801i
$497$		0			0
$498$	1.64362	+	1.64362i	0.0736525	+	0.0736525i
$499$		−	31.5850i		−	1.41394i	−0.707245	−	0.706969i	$-0.750062\pi$
$499$		−	31.5850i		−	1.41394i	0.707245	−	0.706969i	$-0.249938\pi$
$500$	5.45939	−	9.75680i	0.244151	−	0.436337i
$501$	1.92861			0.0861639
$502$	5.02010	+	5.02010i	0.224058	+	0.224058i
$503$	16.9777	−	16.9777i	0.756997	−	0.756997i	−0.218778	−	0.975775i	$-0.570207\pi$
$503$	16.9777	−	16.9777i	0.756997	−	0.756997i	0.975775	+	0.218778i	$0.0702070\pi$
$504$		0			0
$505$	27.6803	+	23.0157i	1.23176	+	1.02419i
$506$	−6.32291			−0.281088
$507$	−1.82592	−	1.82592i	−0.0810920	−	0.0810920i
$508$	−4.63487	−	4.63487i	−0.205639	−	0.205639i
$509$	−21.5141			−0.953597			−0.476799	−	0.879013i	$-0.658203\pi$
$509$	−21.5141			−0.953597			−0.476799	+	0.879013i	$0.658203\pi$
$510$	−0.315125	−	3.42491i	−0.0139540	−	0.151657i
$511$		0			0
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−4.71706	−	4.71706i	−0.208263	−	0.208263i
$514$	−9.88686			−0.436091
$515$	−4.02979	−	43.7974i	−0.177574	−	1.92994i
$516$			0.760780i			0.0334915i
$517$	−23.4529	−	23.4529i	−1.03146	−	1.03146i
$518$		0			0
$519$			2.04397i			0.0897205i
$520$	−2.89039	+	3.47617i	−0.126752	+	0.152440i
$521$		−	13.2395i		−	0.580031i	−0.957022	−	0.290016i	$-0.906340\pi$
$521$		−	13.2395i		−	0.580031i	0.957022	−	0.290016i	$-0.0936605\pi$
$522$	−6.50552	+	6.50552i	−0.284739	+	0.284739i
$523$	19.0426	−	19.0426i	0.832673	−	0.832673i	−0.155209	−	0.987882i	$-0.549605\pi$
$523$	19.0426	−	19.0426i	0.832673	−	0.832673i	0.987882	+	0.155209i	$0.0496051\pi$
$524$	−7.69535			−0.336173
$525$		0			0
$526$	13.7482			0.599448
$527$	−14.4465	+	14.4465i	−0.629300	+	0.629300i
$528$	1.15258	−	1.15258i	0.0501595	−	0.0501595i
$529$		−	21.7368i		−	0.945078i
$530$	1.97733	−	2.37808i	0.0858899	−	0.103297i
$531$		−	15.9755i		−	0.693276i
$532$		0			0
$533$	10.3083	+	10.3083i	0.446501	+	0.446501i
$534$			3.45419i			0.149477i
$535$	0.573857	+	6.23691i	0.0248100	+	0.269645i
$536$	−0.844985			−0.0364978
$537$	0.452025	+	0.452025i	0.0195063	+	0.0195063i
$538$	18.7398	−	18.7398i	0.807928	−	0.807928i
$539$		0			0
$540$	−0.351176	−	3.81672i	−0.0151122	−	0.164245i
$541$	−11.3298			−0.487107			−0.243553	−	0.969888i	$-0.578313\pi$
$541$	−11.3298			−0.487107			−0.243553	+	0.969888i	$0.578313\pi$
$542$	−9.04876	−	9.04876i	−0.388678	−	0.388678i
$543$	−0.843813	−	0.843813i	−0.0362115	−	0.0362115i
$544$	−5.30873			−0.227610
$545$	−10.1629	−	8.45027i	−0.435329	−	0.361970i
$546$		0			0
$547$	−30.9149	+	30.9149i	−1.32182	+	1.32182i	−0.409527	+	0.912298i	$0.634306\pi$
$547$	−30.9149	+	30.9149i	−1.32182	+	1.32182i	−0.912298	+	0.409527i	$0.865694\pi$
$548$	6.24784	+	6.24784i	0.266895	+	0.266895i
$549$	13.4408			0.573639
$550$	−23.1856	−	15.9267i	−0.988636	−	0.679116i
$551$			12.2787i			0.523090i
$552$	−0.230263	−	0.230263i	−0.00980065	−	0.00980065i
$553$		0			0
$554$		−	20.1034i		−	0.854110i
$555$	2.51072	+	2.08763i	0.106574	+	0.0886148i
$556$		−	11.0631i		−	0.469180i
$557$	−18.6675	+	18.6675i	−0.790967	+	0.790967i	−0.981651	−	0.190685i	$-0.938929\pi$
$557$	−18.6675	+	18.6675i	−0.790967	+	0.790967i	0.190685	+	0.981651i	$0.438929\pi$
$558$	−7.93538	+	7.93538i	−0.335931	+	0.335931i
$559$	−5.30873			−0.224535
$560$		0			0
$561$	−8.65318			−0.365337
$562$	−10.0054	+	10.0054i	−0.422054	+	0.422054i
$563$	14.2790	−	14.2790i	0.601788	−	0.601788i	−0.338999	−	0.940787i	$-0.610088\pi$
$563$	14.2790	−	14.2790i	0.601788	−	0.601788i	0.940787	+	0.338999i	$0.110088\pi$
$564$		−	1.70818i		−	0.0719275i
$565$	42.7687	−	3.93514i	1.79929	−	0.165553i
$566$			27.0677i			1.13774i
$567$		0			0
$568$	−3.37792	−	3.37792i	−0.141734	−	0.141734i
$569$			24.8134i			1.04023i	0.854096	+	0.520116i	$0.174111\pi$
$569$			24.8134i			1.04023i	−0.854096	+	0.520116i	$0.825889\pi$
$570$	−1.93874	−	1.61204i	−0.0812051	−	0.0675208i
$571$	4.58059			0.191692			0.0958458	−	0.995396i	$-0.469444\pi$
$571$	4.58059			0.191692			0.0958458	+	0.995396i	$0.469444\pi$
$572$	8.04270	+	8.04270i	0.336282	+	0.336282i
$573$	3.52433	−	3.52433i	0.147231	−	0.147231i
$574$		0			0
$575$	−3.18185	+	4.63204i	−0.132692	+	0.193169i
$576$	−2.91605			−0.121502
$577$	13.9869	+	13.9869i	0.582284	+	0.582284i	0.935530	−	0.353247i	$-0.114922\pi$
$577$	13.9869	+	13.9869i	0.582284	+	0.582284i	−0.353247	+	0.935530i	$0.614922\pi$
$578$	7.90730	+	7.90730i	0.328900	+	0.328900i
$579$	3.49637			0.145304
$580$	−4.51047	+	5.42460i	−0.187287	+	0.225244i
$581$		0			0
$582$	1.92125	−	1.92125i	0.0796385	−	0.0796385i
$583$	−5.50207	−	5.50207i	−0.227872	−	0.227872i
$584$	−5.61227			−0.232237
$585$	13.1276	−	1.20787i	0.542759	−	0.0499392i
$586$		−	24.2100i		−	1.00011i
$587$	19.3782	+	19.3782i	0.799824	+	0.799824i	0.983068	−	0.183244i	$-0.0586597\pi$
$587$	19.3782	+	19.3782i	0.799824	+	0.799824i	−0.183244	+	0.983068i	$0.558660\pi$
$588$		0			0
$589$			14.9775i			0.617136i
$590$	−1.12240	−	12.1987i	−0.0462084	−	0.502211i
$591$			5.86495i			0.241252i
$592$	3.56380	−	3.56380i	0.146471	−	0.146471i
$593$	−2.28943	+	2.28943i	−0.0940155	+	0.0940155i	−0.752550	−	0.658535i	$-0.771177\pi$
$593$	−2.28943	+	2.28943i	−0.0940155	+	0.0940155i	0.658535	+	0.752550i	$0.271177\pi$
$594$	−9.64311			−0.395661
$595$		0			0
$596$	−5.04885			−0.206809
$597$	−1.54334	+	1.54334i	−0.0631645	+	0.0631645i
$598$	1.60678	−	1.60678i	0.0657061	−	0.0657061i
$599$		−	7.80349i		−	0.318842i	−0.987211	−	0.159421i	$-0.949037\pi$
$599$		−	7.80349i		−	0.318842i	0.987211	−	0.159421i	$-0.0509627\pi$
$600$	−0.264349	−	1.42436i	−0.0107920	−	0.0581493i
$601$			31.7170i			1.29377i	0.762590	+	0.646883i	$0.223928\pi$
$601$			31.7170i			1.29377i	−0.762590	+	0.646883i	$0.776072\pi$
$602$		0			0
$603$	1.74233	+	1.74233i	0.0709530	+	0.0709530i
$604$		−	13.4428i		−	0.546981i
$605$	−29.5205	+	35.5033i	−1.20018	+	1.44341i
$606$	4.66453			0.189484
$607$	0.544276	+	0.544276i	0.0220915	+	0.0220915i	0.718066	−	0.695975i	$-0.245027\pi$
$607$	0.544276	+	0.544276i	0.0220915	+	0.0220915i	−0.695975	+	0.718066i	$0.745027\pi$
$608$	−2.75192	+	2.75192i	−0.111605	+	0.111605i
$609$		0			0
$610$	10.2632	−	0.944318i	0.415546	−	0.0382343i
$611$	11.9197			0.482221
$612$	10.9464	+	10.9464i	0.442482	+	0.442482i
$613$	24.7496	+	24.7496i	0.999626	+	0.999626i	1.00000		0.000373538i	$-0.000118901\pi$
$613$	24.7496	+	24.7496i	0.999626	+	0.999626i	−0.000373538		1.00000i	$0.500119\pi$
$614$	24.4623			0.987217
$615$	−4.65183	+	0.428014i	−0.187580	+	0.0172592i
$616$		0			0
$617$	21.5403	−	21.5403i	0.867179	−	0.867179i	−0.124980	−	0.992159i	$-0.539887\pi$
$617$	21.5403	−	21.5403i	0.867179	−	0.867179i	0.992159	+	0.124980i	$0.0398866\pi$
$618$	−4.02979	−	4.02979i	−0.162102	−	0.162102i
$619$	43.3415			1.74204			0.871021	−	0.491247i	$-0.163459\pi$
$619$	43.3415			1.74204			0.871021	+	0.491247i	$0.163459\pi$
$620$	−5.50184	+	6.61688i	−0.220959	+	0.265740i
$621$			1.92651i			0.0773082i
$622$	7.76566	+	7.76566i	0.311374	+	0.311374i
$623$		0			0
$624$			0.585786i			0.0234502i
$625$	−23.3351	+	8.97056i	−0.933406	+	0.358823i
$626$			29.4110i			1.17550i
$627$	−4.48560	+	4.48560i	−0.179138	+	0.179138i
$628$	0.779844	−	0.779844i	0.0311192	−	0.0311192i
$629$	−26.7559			−1.06683
$630$		0			0
$631$	7.53463			0.299949			0.149974	−	0.988690i	$-0.452081\pi$
$631$	7.53463			0.299949			0.149974	+	0.988690i	$0.452081\pi$
$632$	4.41789	−	4.41789i	0.175734	−	0.175734i
$633$	−4.01075	+	4.01075i	−0.159413	+	0.159413i
$634$		−	4.29397i		−	0.170535i
$635$	1.34289	+	14.5951i	0.0532910	+	0.579188i
$636$		−	0.400741i		−	0.0158904i
$637$		0			0
$638$	12.5507	+	12.5507i	0.496887	+	0.496887i
$639$			13.9303i			0.551073i
$640$	−2.22666	+	0.204875i	−0.0880166	+	0.00809839i
$641$	24.3315			0.961035			0.480518	−	0.876985i	$-0.340449\pi$
$641$	24.3315			0.961035			0.480518	+	0.876985i	$0.340449\pi$
$642$	0.573857	+	0.573857i	0.0226483	+	0.0226483i
$643$	−6.21713	+	6.21713i	−0.245180	+	0.245180i	−0.818989	−	0.573809i	$-0.805465\pi$
$643$	−6.21713	+	6.21713i	−0.245180	+	0.245180i	0.573809	+	0.818989i	$0.305465\pi$
$644$		0			0
$645$	1.08763	−	1.30805i	0.0428252	−	0.0515045i
$646$	20.6605			0.812878
$647$	−14.5856	−	14.5856i	−0.573418	−	0.573418i	0.359664	−	0.933082i	$-0.382891\pi$
$647$	−14.5856	−	14.5856i	−0.573418	−	0.573418i	−0.933082	+	0.359664i	$0.882891\pi$
$648$	5.83471	+	5.83471i	0.229209	+	0.229209i
$649$	−30.8205			−1.20981
$650$	9.93921	−	1.84463i	0.389848	−	0.0723523i
$651$		0			0
$652$	−9.36288	+	9.36288i	−0.366679	+	0.366679i
$653$	18.4835	+	18.4835i	0.723316	+	0.723316i	0.969279	−	0.245963i	$-0.0791041\pi$
$653$	18.4835	+	18.4835i	0.723316	+	0.723316i	−0.245963	+	0.969279i	$0.579104\pi$
$654$	−1.71259			−0.0669676
$655$	13.2311	+	11.0014i	0.516980	+	0.429861i
$656$			7.21050i			0.281523i
$657$	11.5723	+	11.5723i	0.451478	+	0.451478i
$658$		0			0
$659$		−	24.2448i		−	0.944443i	−0.881480	−	0.472222i	$-0.843452\pi$
$659$		−	24.2448i		−	0.944443i	0.881480	−	0.472222i	$-0.156548\pi$
$660$	−3.62944	+	0.333944i	−0.141276	+	0.0129988i
$661$		−	17.9326i		−	0.697497i	−0.937216	−	0.348749i	$-0.886607\pi$
$661$		−	17.9326i		−	0.697497i	0.937216	−	0.348749i	$-0.113393\pi$
$662$	25.0668	−	25.0668i	0.974250	−	0.974250i
$663$	2.19895	−	2.19895i	0.0854001	−	0.0854001i
$664$	−8.02257			−0.311336
$665$		0			0
$666$	−14.6968			−0.569491
$667$	2.50739	−	2.50739i	0.0970866	−	0.0970866i
$668$	−4.70680	+	4.70680i	−0.182112	+	0.182112i
$669$			0.598344i			0.0231333i
$670$	1.45283	+	1.20801i	0.0561277	+	0.0466694i
$671$		−	25.9305i		−	1.00104i
$672$		0			0
$673$	−4.85386	−	4.85386i	−0.187103	−	0.187103i	0.607340	−	0.794442i	$-0.292237\pi$
$673$	−4.85386	−	4.85386i	−0.187103	−	0.187103i	−0.794442	+	0.607340i	$0.792237\pi$
$674$			17.1789i			0.661708i
$675$	−4.85266	+	7.06435i	−0.186779	+	0.271907i
$676$	8.91237			0.342784
$677$	−13.0676	−	13.0676i	−0.502227	−	0.502227i	0.409902	−	0.912129i	$-0.365563\pi$
$677$	−13.0676	−	13.0676i	−0.502227	−	0.502227i	−0.912129	+	0.409902i	$0.865563\pi$
$678$	3.93514	−	3.93514i	0.151128	−	0.151128i
$679$		0			0
$680$	9.12760	+	7.58946i	0.350027	+	0.291043i
$681$	−5.40166			−0.206992
$682$	15.3092	+	15.3092i	0.586221	+	0.586221i
$683$	−18.9512	−	18.9512i	−0.725147	−	0.725147i	0.244502	−	0.969649i	$-0.421375\pi$
$683$	−18.9512	−	18.9512i	−0.725147	−	0.725147i	−0.969649	+	0.244502i	$0.921375\pi$
$684$	11.3487			0.433929
$685$	−1.81023	−	19.6743i	−0.0691653	−	0.751717i
$686$		0			0
$687$	−0.821071	+	0.821071i	−0.0313258	+	0.0313258i
$688$	−1.85669	−	1.85669i	−0.0707857	−	0.0707857i
$689$	2.79637			0.106533
$690$	0.0667157	+	0.725093i	0.00253983	+	0.0276038i
$691$			29.0722i			1.10596i	0.833194	+	0.552980i	$0.186509\pi$
$691$			29.0722i			1.10596i	−0.833194	+	0.552980i	$0.813491\pi$
$692$	−4.98835	−	4.98835i	−0.189628	−	0.189628i
$693$		0			0
$694$		−	8.97626i		−	0.340734i
$695$	−15.8160	+	19.0214i	−0.599937	+	0.721524i
$696$			0.914124i			0.0346498i
$697$	27.0671	−	27.0671i	1.02524	−	1.02524i
$698$	−18.4025	+	18.4025i	−0.696546	+	0.696546i
$699$	3.97855			0.150483
$700$		0			0
$701$	25.4462			0.961089			0.480545	−	0.876970i	$-0.340439\pi$
$701$	25.4462			0.961089			0.480545	+	0.876970i	$0.340439\pi$
$702$	2.45051	−	2.45051i	0.0924885	−	0.0924885i
$703$	−13.8696	+	13.8696i	−0.523102	+	0.523102i
$704$			5.62576i			0.212029i
$705$	−2.44205	+	2.93698i	−0.0919731	+	0.110613i
$706$		−	9.96618i		−	0.375082i
$707$		0			0
$708$	−1.12240	−	1.12240i	−0.0421823	−	0.0421823i
$709$		−	31.4072i		−	1.17952i	−0.807578	−	0.589760i	$-0.799222\pi$
$709$		−	31.4072i		−	1.17952i	0.807578	−	0.589760i	$-0.200778\pi$
$710$	0.978707	+	10.6370i	0.0367302	+	0.399199i
$711$	−18.2190			−0.683267
$712$	−8.42999	−	8.42999i	−0.315927	−	0.315927i
$713$	3.05850	−	3.05850i	0.114542	−	0.114542i
$714$		0			0
$715$	−2.33027	−	25.3263i	−0.0871470	−	0.947149i
$716$	−2.20635			−0.0824550
$717$	4.02826	+	4.02826i	0.150438	+	0.150438i
$718$	8.18413	+	8.18413i	0.305429	+	0.305429i
$719$	10.8043			0.402932			0.201466	−	0.979496i	$-0.435430\pi$
$719$	10.8043			0.402932			0.201466	+	0.979496i	$0.435430\pi$
$720$	5.01373	+	4.16885i	0.186851	+	0.155364i
$721$		0			0
$722$	−2.72509	+	2.72509i	−0.101417	+	0.101417i
$723$	−1.20571	−	1.20571i	−0.0448410	−	0.0448410i
$724$	4.11867			0.153069
$725$	15.5102	−	2.87856i	0.576035	−	0.106907i
$726$			5.98283i			0.222044i
$727$	33.6108	+	33.6108i	1.24656	+	1.24656i	0.957231	+	0.289326i	$0.0934311\pi$
$727$	33.6108	+	33.6108i	1.24656	+	1.24656i	0.289326	+	0.957231i	$0.406569\pi$
$728$		0			0
$729$		−	22.5720i		−	0.835998i
$730$	9.64950	+	8.02342i	0.357144	+	0.296960i
$731$			13.9394i			0.515569i
$732$	0.944318	−	0.944318i	0.0349030	−	0.0349030i
$733$	−18.2134	+	18.2134i	−0.672729	+	0.672729i	−0.958344	−	0.285616i	$-0.907802\pi$
$733$	−18.2134	+	18.2134i	−0.672729	+	0.672729i	0.285616	+	0.958344i	$0.407802\pi$
$734$	−16.6944			−0.616202
$735$		0			0
$736$	1.12392			0.0414283
$737$	3.36136	−	3.36136i	0.123817	−	0.123817i
$738$	14.8678	−	14.8678i	0.547290	−	0.547290i
$739$		−	12.1184i		−	0.445782i	−0.974843	−	0.222891i	$-0.928451\pi$
$739$		−	12.1184i		−	0.445782i	0.974843	−	0.222891i	$-0.0715495\pi$
$740$	−11.2223	+	1.03256i	−0.412541	+	0.0379578i
$741$		−	2.27977i		−	0.0837493i
$742$		0			0
$743$	23.2618	+	23.2618i	0.853393	+	0.853393i	0.990549	−	0.137157i	$-0.0437964\pi$
$743$	23.2618	+	23.2618i	0.853393	+	0.853393i	−0.137157	+	0.990549i	$0.543796\pi$
$744$			1.11504i			0.0408794i
$745$	8.68078	+	7.21794i	0.318039	+	0.264445i
$746$	3.17893			0.116389
$747$	16.5422	+	16.5422i	0.605248	+	0.605248i
$748$	21.1182	−	21.1182i	0.772158	−	0.772158i
$749$		0			0
$750$	−1.58179	+	2.82690i	−0.0577587	+	0.103224i
$751$	13.9777			0.510055			0.255028	−	0.966934i	$-0.417915\pi$
$751$	13.9777			0.510055			0.255028	+	0.966934i	$0.417915\pi$
$752$	4.16885	+	4.16885i	0.152022	+	0.152022i
$753$	−1.45451	−	1.45451i	−0.0530053	−	0.0530053i
$754$	−6.37877			−0.232301
$755$	−19.2181	+	23.1130i	−0.699420	+	0.841169i
$756$		0			0
$757$	17.5547	−	17.5547i	0.638036	−	0.638036i	−0.312035	−	0.950071i	$-0.601010\pi$
$757$	17.5547	−	17.5547i	0.638036	−	0.638036i	0.950071	+	0.312035i	$0.101010\pi$
$758$	−5.05828	−	5.05828i	−0.183725	−	0.183725i
$759$	1.83198			0.0664967
$760$	8.66573	−	0.797333i	0.314339	−	0.0289223i
$761$			21.8667i			0.792669i	0.918106	+	0.396334i	$0.129718\pi$
$761$			21.8667i			0.792669i	−0.918106	+	0.396334i	$0.870282\pi$
$762$	1.34289	+	1.34289i	0.0486478	+	0.0486478i
$763$		0			0
$764$			17.2023i			0.622359i
$765$	−3.17157	−	34.4699i	−0.114668	−	1.24626i
$766$		−	14.5934i		−	0.527280i
$767$	7.83211	−	7.83211i	0.282801	−	0.282801i
$768$	−0.204875	+	0.204875i	−0.00739279	+	0.00739279i
$769$	31.0506			1.11971			0.559857	−	0.828589i	$-0.310856\pi$
$769$	31.0506			1.11971			0.559857	+	0.828589i	$0.310856\pi$
$770$		0			0
$771$	2.86459			0.103166
$772$	−8.53293	+	8.53293i	−0.307107	+	0.307107i
$773$	−4.29108	+	4.29108i	−0.154340	+	0.154340i	−0.780053	−	0.625713i	$-0.784808\pi$
$773$	−4.29108	+	4.29108i	−0.154340	+	0.154340i	0.625713	+	0.780053i	$0.284808\pi$
$774$			7.65685i			0.275220i
$775$	18.9192	−	3.51124i	0.679599	−	0.126127i
$776$			9.37769i			0.336640i
$777$		0			0
$778$	−4.38160	−	4.38160i	−0.157088	−	0.157088i
$779$		−	28.0619i		−	1.00542i
$780$	0.837452	−	1.00718i	0.0299856	−	0.0360627i
$781$	26.8748			0.961656
$782$	−4.21902	−	4.21902i	−0.150872	−	0.150872i
$783$	3.82404	−	3.82404i	0.136660	−	0.136660i
$784$		0			0
$785$	−2.45571	+	0.225950i	−0.0876481	+	0.00806449i
$786$	2.22963			0.0795282
$787$	15.8118	+	15.8118i	0.563630	+	0.563630i	0.930336	−	0.366707i	$-0.119515\pi$
$787$	15.8118	+	15.8118i	0.563630	+	0.563630i	−0.366707	+	0.930336i	$0.619515\pi$
$788$	−14.3135	−	14.3135i	−0.509897	−	0.509897i
$789$	−3.98335			−0.141811
$790$	−13.9118	+	1.28003i	−0.494961	+	0.0455413i
$791$		0			0
$792$	11.6001	−	11.6001i	0.412191	−	0.412191i
$793$	6.58946	+	6.58946i	0.233999	+	0.233999i
$794$	2.91588			0.103481
$795$	−0.572907	+	0.689016i	−0.0203189	+	0.0244369i
$796$		−	7.53307i		−	0.267002i
$797$	16.5528	+	16.5528i	0.586330	+	0.586330i	0.936636	−	0.350305i	$-0.113922\pi$
$797$	16.5528	+	16.5528i	0.586330	+	0.586330i	−0.350305	+	0.936636i	$0.613922\pi$
$798$		0			0
$799$		−	31.2984i		−	1.10726i
$800$	4.12132	+	2.83103i	0.145711	+	0.100092i
$801$			34.7646i			1.22835i
$802$	−14.1213	+	14.1213i	−0.498641	+	0.498641i
$803$	22.3257	−	22.3257i	0.787857	−	0.787857i
$804$	0.244823			0.00863425
$805$		0			0
$806$	−7.78078			−0.274066
$807$	−5.42960	+	5.42960i	−0.191131	+	0.191131i
$808$	−11.3839	+	11.3839i	−0.400483	+	0.400483i
$809$		−	3.28096i		−	0.115352i	−0.998335	−	0.0576762i	$-0.981631\pi$
$809$		−	3.28096i		−	0.115352i	0.998335	−	0.0576762i	$-0.0183691\pi$
$810$	−1.69053	−	18.3734i	−0.0593991	−	0.645574i
$811$		−	17.8693i		−	0.627476i	−0.949510	−	0.313738i	$-0.898419\pi$
$811$		−	17.8693i		−	0.627476i	0.949510	−	0.313738i	$-0.101581\pi$
$812$		0			0
$813$	2.62176	+	2.62176i	0.0919491	+	0.0919491i
$814$			28.3537i			0.993796i
$815$	29.4835	−	2.71277i	1.03276	−	0.0950243i
$816$	1.53813			0.0538455
$817$	7.22588	+	7.22588i	0.252802	+	0.252802i
$818$	−24.2949	+	24.2949i	−0.849451	+	0.849451i
$819$		0			0
$820$	10.3083	−	12.3974i	0.359981	−	0.432937i
$821$	−11.8167			−0.412407			−0.206204	−	0.978509i	$-0.566111\pi$
$821$	−11.8167			−0.412407			−0.206204	+	0.978509i	$0.566111\pi$
$822$	−1.81023	−	1.81023i	−0.0631390	−	0.0631390i
$823$	24.9625	+	24.9625i	0.870139	+	0.870139i	0.992487	−	0.122348i	$-0.0390424\pi$
$823$	24.9625	+	24.9625i	0.870139	+	0.870139i	−0.122348	+	0.992487i	$0.539042\pi$
$824$	19.6695			0.685220
$825$	6.71771	+	4.61455i	0.233881	+	0.160658i
$826$		0			0
$827$	−17.2835	+	17.2835i	−0.601005	+	0.601005i	−0.940579	−	0.339574i	$-0.889717\pi$
$827$	−17.2835	+	17.2835i	−0.601005	+	0.601005i	0.339574	+	0.940579i	$0.389717\pi$
$828$	−2.31748	−	2.31748i	−0.0805380	−	0.0805380i
$829$	−34.5754			−1.20085			−0.600426	−	0.799680i	$-0.705002\pi$
$829$	−34.5754			−1.20085			−0.600426	+	0.799680i	$0.705002\pi$
$830$	13.7937	+	11.4692i	0.478785	+	0.398102i
$831$			5.82469i			0.202056i
$832$	−1.42962	−	1.42962i	−0.0495631	−	0.0495631i
$833$		0			0
$834$			3.20539i			0.110994i
$835$	14.8216	−	1.36373i	0.512923	−	0.0471939i
$836$		−	21.8944i		−	0.757232i
$837$	4.66453	−	4.66453i	0.161230	−	0.161230i
$838$	−22.0165	+	22.0165i	−0.760547	+	0.760547i
$839$	−50.1328			−1.73078			−0.865388	−	0.501102i	$-0.832928\pi$
$839$	−50.1328			−1.73078			−0.865388	+	0.501102i	$0.832928\pi$
$840$		0			0
$841$	19.0459			0.656754
$842$	−23.8102	+	23.8102i	−0.820555	+	0.820555i
$843$	2.89894	−	2.89894i	0.0998449	−	0.0998449i
$844$		−	19.5766i		−	0.673854i
$845$	−15.3236	−	12.7413i	−0.527146	−	0.438314i
$846$		−	17.1920i		−	0.591073i
$847$		0			0
$848$	0.978013	+	0.978013i	0.0335851	+	0.0335851i
$849$		−	7.84251i		−	0.269154i
$850$	−4.84355	−	26.0980i	−0.166132	−	0.895154i
$851$	5.66453			0.194178
$852$	0.978707	+	0.978707i	0.0335300	+	0.0335300i
$853$	−2.37500	+	2.37500i	−0.0813183	+	0.0813183i	−0.746596	−	0.665278i	$-0.768313\pi$
$853$	−2.37500	+	2.37500i	−0.0813183	+	0.0813183i	0.665278	+	0.746596i	$0.268313\pi$
$854$		0			0
$855$	−19.5125	−	16.2243i	−0.667312	−	0.554860i
$856$	−2.80101			−0.0957366
$857$	29.6551	+	29.6551i	1.01300	+	1.01300i	0.999914	+	0.0130861i	$0.00416555\pi$
$857$	29.6551	+	29.6551i	1.01300	+	1.01300i	0.0130861	+	0.999914i	$0.495834\pi$
$858$	−2.33027	−	2.33027i	−0.0795540	−	0.0795540i
$859$	2.35695			0.0804179			0.0402090	−	0.999191i	$-0.487198\pi$
$859$	2.35695			0.0804179			0.0402090	+	0.999191i	$0.487198\pi$
$860$	0.537952	+	5.84668i	0.0183440	+	0.199370i
$861$		0			0
$862$	−10.4268	+	10.4268i	−0.355137	+	0.355137i
$863$	34.1884	+	34.1884i	1.16379	+	1.16379i	0.983640	+	0.180146i	$0.0576572\pi$
$863$	34.1884	+	34.1884i	1.16379	+	1.16379i	0.180146	+	0.983640i	$0.442343\pi$
$864$	1.71410			0.0583148
$865$	1.44531	+	15.7082i	0.0491419	+	0.534094i
$866$			14.1175i			0.479731i
$867$	−2.29104	−	2.29104i	−0.0778076	−	0.0778076i
$868$		0			0
$869$			35.1489i			1.19234i
$870$	1.30685	−	1.57171i	0.0443064	−	0.0532858i
$871$			1.70838i			0.0578862i
$872$	4.17960	−	4.17960i	0.141539	−	0.141539i
$873$	19.3364	−	19.3364i	0.654439	−	0.654439i
$874$	−4.37408			−0.147955
$875$		0			0
$876$	1.62608			0.0549402
$877$	−9.74471	+	9.74471i	−0.329055	+	0.329055i	−0.852227	−	0.523172i	$-0.824749\pi$
$877$	−9.74471	+	9.74471i	−0.329055	+	0.329055i	0.523172	+	0.852227i	$0.324749\pi$
$878$	−27.1730	+	27.1730i	−0.917046	+	0.917046i
$879$			7.01454i			0.236594i
$880$	8.04270	−	9.67269i	0.271119	−	0.326066i
$881$		−	3.32542i		−	0.112036i	−0.998430	−	0.0560181i	$-0.982160\pi$
$881$		−	3.32542i		−	0.112036i	0.998430	−	0.0560181i	$-0.0178405\pi$
$882$		0			0
$883$	−36.8930	−	36.8930i	−1.24155	−	1.24155i	−0.959358	−	0.282191i	$-0.908939\pi$
$883$	−36.8930	−	36.8930i	−1.24155	−	1.24155i	−0.282191	−	0.959358i	$-0.591061\pi$
$884$			10.7331i			0.360994i
$885$	0.325200	+	3.53440i	0.0109315	+	0.118808i
$886$	5.73560			0.192691
$887$	−25.3290	−	25.3290i	−0.850465	−	0.850465i	0.139725	−	0.990190i	$-0.455378\pi$
$887$	−25.3290	−	25.3290i	−0.850465	−	0.850465i	−0.990190	+	0.139725i	$0.955378\pi$
$888$	−1.03256	+	1.03256i	−0.0346506	+	0.0346506i
$889$		0			0
$890$	2.44248	+	26.5458i	0.0818721	+	0.889819i
$891$	−46.4211			−1.55516
$892$	−1.46027	−	1.46027i	−0.0488933	−	0.0488933i
$893$	−16.2243	−	16.2243i	−0.542927	−	0.542927i
$894$	1.46284			0.0489247
$895$	3.79349	+	3.15423i	0.126803	+	0.105434i
$896$		0			0
$897$	−0.465543	+	0.465543i	−0.0155440	+	0.0155440i
$898$	−5.16377	−	5.16377i	−0.172317	−	0.172317i
$899$	−12.1420			−0.404957
$900$	−2.66053	−	14.3355i	−0.0886844	−	0.477849i
$901$		−	7.34261i		−	0.244618i
$902$	−28.6835	−	28.6835i	−0.955055	−	0.955055i
$903$		0			0
$904$			19.2075i			0.638833i
$905$	−7.08147	−	5.88814i	−0.235396	−	0.195728i
$906$			3.89488i			0.129399i
$907$	−12.2030	+	12.2030i	−0.405195	+	0.405195i	−0.880059	−	0.474864i	$-0.842497\pi$
$907$	−12.2030	+	12.2030i	−0.405195	+	0.405195i	0.474864	+	0.880059i	$0.342497\pi$
$908$	13.1828	−	13.1828i	0.437487	−	0.437487i
$909$	46.9461			1.55710
$910$		0			0
$911$	5.56820			0.184483			0.0922414	−	0.995737i	$-0.470597\pi$
$911$	5.56820			0.184483			0.0922414	+	0.995737i	$0.470597\pi$
$912$	0.797333	−	0.797333i	0.0264023	−	0.0264023i
$913$	31.9139	−	31.9139i	1.05620	−	1.05620i
$914$		−	5.14581i		−	0.170208i
$915$	−2.97364	+	0.273604i	−0.0983054	+	0.00904506i
$916$		−	4.00767i		−	0.132417i
$917$		0			0
$918$	−6.43445	−	6.43445i	−0.212368	−	0.212368i
$919$			6.21187i			0.204911i	0.994738	+	0.102455i	$0.0326699\pi$
$919$			6.21187i			0.204911i	−0.994738	+	0.102455i	$0.967330\pi$
$920$	−1.93242	−	1.60678i	−0.0637100	−	0.0529740i
$921$	−7.08763			−0.233545
$922$	20.7967	+	20.7967i	0.684903	+	0.684903i
$923$	−6.82943	+	6.82943i	−0.224794	+	0.224794i
$924$		0			0
$925$	20.7713	+	14.2683i	0.682958	+	0.469139i
$926$	−5.72226			−0.188045
$927$	−40.5578	−	40.5578i	−1.33209	−	1.33209i
$928$	−2.23093	−	2.23093i	−0.0732340	−	0.0732340i
$929$	−0.189459			−0.00621596			−0.00310798	−	0.999995i	$-0.500989\pi$
$929$	−0.189459			−0.00621596			−0.00310798	+	0.999995i	$0.500989\pi$
$930$	1.59409	−	1.91715i	0.0522721	−	0.0628660i
$931$		0			0
$932$	−9.70971	+	9.70971i	−0.318052	+	0.318052i
$933$	−2.25000	−	2.25000i	−0.0736616	−	0.0736616i
$934$	16.6428			0.544568
$935$	−66.5007	+	6.11872i	−2.17481	+	0.200104i
$936$			5.89564i			0.192705i
$937$	−34.2022	−	34.2022i	−1.11734	−	1.11734i	−0.992131	−	0.125208i	$-0.960040\pi$
$937$	−34.2022	−	34.2022i	−1.11734	−	1.11734i	−0.125208	−	0.992131i	$-0.539960\pi$
$938$		0			0
$939$		−	8.52144i		−	0.278087i
$940$	−1.20787	−	13.1276i	−0.0393963	−	0.428175i
$941$			18.9170i			0.616677i	0.951277	+	0.308339i	$0.0997730\pi$
$941$			18.9170i			0.616677i	−0.951277	+	0.308339i	$0.900227\pi$
$942$	−0.225950	+	0.225950i	−0.00736184	+	0.00736184i
$943$	−5.73042	+	5.73042i	−0.186608	+	0.186608i
$944$	5.47845			0.178308
$945$		0			0
$946$	14.7719			0.480276
$947$	33.3401	−	33.3401i	1.08341	−	1.08341i	0.0872195	−	0.996189i	$-0.472202\pi$
$947$	33.3401	−	33.3401i	1.08341	−	1.08341i	0.996189	−	0.0872195i	$-0.0277981\pi$
$948$	−1.28003	+	1.28003i	−0.0415733	+	0.0415733i
$949$			11.3468i			0.368333i
$950$	−16.0394	−	11.0178i	−0.520386	−	0.357465i
$951$			1.24412i			0.0403434i
$952$		0			0
$953$	18.8431	+	18.8431i	0.610389	+	0.610389i	0.943047	−	0.332658i	$-0.107946\pi$
$953$	18.8431	+	18.8431i	0.610389	+	0.610389i	−0.332658	+	0.943047i	$0.607946\pi$
$954$		−	4.03325i		−	0.130581i
$955$	24.5928	−	29.5770i	0.795805	−	0.957088i
$956$	−19.6621			−0.635916
$957$	−3.63640	−	3.63640i	−0.117548	−	0.117548i
$958$	−10.8818	+	10.8818i	−0.351575	+	0.351575i
$959$		0			0
$960$	0.645146	−	0.0593598i	0.0208220	−	0.00191583i
$961$	16.1893			0.522237
$962$	−7.20525	−	7.20525i	−0.232306	−	0.232306i
$963$	5.77557	+	5.77557i	0.186115	+	0.186115i
$964$	5.88512			0.189547
$965$	26.8700	−	2.47231i	0.864976	−	0.0795863i
$966$		0			0
$967$	27.3703	−	27.3703i	0.880169	−	0.880169i	−0.113383	−	0.993551i	$-0.536169\pi$
$967$	27.3703	−	27.3703i	0.880169	−	0.880169i	0.993551	+	0.113383i	$0.0361687\pi$
$968$	−14.6012	−	14.6012i	−0.469299	−	0.469299i
$969$	−5.98612			−0.192302
$970$	13.4065	−	16.1236i	0.430458	−	0.517698i
$971$		−	32.1872i		−	1.03294i	−0.856306	−	0.516469i	$-0.827246\pi$
$971$		−	32.1872i		−	1.03294i	0.856306	−	0.516469i	$-0.172754\pi$
$972$	−5.32668	−	5.32668i	−0.170853	−	0.170853i
$973$		0			0
$974$			35.9920i			1.15326i
$975$	−2.87976	+	0.534457i	−0.0922260	+	0.0171163i
$976$			4.60924i			0.147538i
$977$	−16.4600	+	16.4600i	−0.526603	+	0.526603i	−0.919558	−	0.392955i	$-0.871453\pi$
$977$	−16.4600	+	16.4600i	−0.526603	+	0.526603i	0.392955	+	0.919558i	$0.371453\pi$
$978$	2.71277	−	2.71277i	0.0867449	−	0.0867449i
$979$	67.0692			2.14354
$980$		0			0
$981$	−17.2364			−0.550314
$982$	−10.8062	+	10.8062i	−0.344840	+	0.344840i
$983$	40.3334	−	40.3334i	1.28644	−	1.28644i	0.349499	−	0.936937i	$-0.386352\pi$
$983$	40.3334	−	40.3334i	1.28644	−	1.28644i	0.936937	−	0.349499i	$-0.113648\pi$
$984$		−	2.08915i		−	0.0665996i
$985$	4.14714	+	45.0728i	0.132139	+	1.43614i
$986$			16.7491i			0.533401i
$987$		0			0
$988$	5.56380	+	5.56380i	0.177008	+	0.177008i
$989$		−	2.95115i		−	0.0938410i
$990$	−36.5284	+	3.36098i	−1.16095	+	0.106819i
$991$	−57.5405			−1.82784			−0.913918	−	0.405900i	$-0.866958\pi$
$991$	−57.5405			−1.82784			−0.913918	+	0.405900i	$0.866958\pi$
$992$	−2.72127	−	2.72127i	−0.0864005	−	0.0864005i
$993$	−7.26279	+	7.26279i	−0.230478	+	0.230478i
$994$		0			0
$995$	−10.7694	+	12.9520i	−0.341414	+	0.410607i
$996$	2.32443			0.0736525
$997$	−17.1508	−	17.1508i	−0.543171	−	0.543171i	0.381286	−	0.924457i	$-0.375481\pi$
$997$	−17.1508	−	17.1508i	−0.543171	−	0.543171i	−0.924457	+	0.381286i	$0.875481\pi$
$998$	−22.3339	−	22.3339i	−0.706969	−	0.706969i
$999$	8.63901			0.273326

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.g.c.293.6		16
5.2	odd	4	inner	490.2.g.c.97.7		16
7.2	even	3		70.2.k.a.3.1	✓	16
7.3	odd	6		70.2.k.a.33.3	yes	16
7.4	even	3		490.2.l.c.313.4		16
7.5	odd	6		490.2.l.c.423.2		16
7.6	odd	2	inner	490.2.g.c.293.7		16
21.2	odd	6		630.2.bv.c.73.3		16
21.17	even	6		630.2.bv.c.523.1		16
28.3	even	6		560.2.ci.c.33.3		16
28.23	odd	6		560.2.ci.c.353.3		16
35.2	odd	12		70.2.k.a.17.3	yes	16
35.3	even	12		350.2.o.c.257.4		16
35.9	even	6		350.2.o.c.143.4		16
35.12	even	12		490.2.l.c.227.4		16
35.17	even	12		70.2.k.a.47.1	yes	16
35.23	odd	12		350.2.o.c.157.2		16
35.24	odd	6		350.2.o.c.243.2		16
35.27	even	4	inner	490.2.g.c.97.6		16
35.32	odd	12		490.2.l.c.117.2		16
105.2	even	12		630.2.bv.c.577.1		16
105.17	odd	12		630.2.bv.c.397.3		16
140.87	odd	12		560.2.ci.c.257.3		16
140.107	even	12		560.2.ci.c.17.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.1	✓	16	7.2	even	3
70.2.k.a.17.3	yes	16	35.2	odd	12
70.2.k.a.33.3	yes	16	7.3	odd	6
70.2.k.a.47.1	yes	16	35.17	even	12
350.2.o.c.143.4		16	35.9	even	6
350.2.o.c.157.2		16	35.23	odd	12
350.2.o.c.243.2		16	35.24	odd	6
350.2.o.c.257.4		16	35.3	even	12
490.2.g.c.97.6		16	35.27	even	4	inner
490.2.g.c.97.7		16	5.2	odd	4	inner
490.2.g.c.293.6		16	1.1	even	1	trivial
490.2.g.c.293.7		16	7.6	odd	2	inner
490.2.l.c.117.2		16	35.32	odd	12
490.2.l.c.227.4		16	35.12	even	12
490.2.l.c.313.4		16	7.4	even	3
490.2.l.c.423.2		16	7.5	odd	6
560.2.ci.c.17.3		16	140.107	even	12
560.2.ci.c.33.3		16	28.3	even	6
560.2.ci.c.257.3		16	140.87	odd	12
560.2.ci.c.353.3		16	28.23	odd	6
630.2.bv.c.73.3		16	21.2	odd	6
630.2.bv.c.397.3		16	105.17	odd	12
630.2.bv.c.523.1		16	21.17	even	6
630.2.bv.c.577.1		16	105.2	even	12

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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.204875 + 0.204875i) q^{3} -1.00000i q^{4} +(-1.42962 + 1.71936i) q^{5} +0.289737i q^{6} +(-0.707107 - 0.707107i) q^{8} +2.91605i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.204875 + 0.204875i) q^{3} -1.00000i q^{4} +(-1.42962 + 1.71936i) q^{5} +0.289737i q^{6} +(-0.707107 - 0.707107i) q^{8} +2.91605i q^{9} +(0.204875 + 2.22666i) q^{10} +5.62576 q^{11} +(0.204875 + 0.204875i) q^{12} +(-1.42962 + 1.42962i) q^{13} +(-0.0593598 - 0.645146i) q^{15} -1.00000 q^{16} +(3.75384 + 3.75384i) q^{17} +(2.06196 + 2.06196i) q^{18} +3.89180 q^{19} +(1.71936 + 1.42962i) q^{20} +(3.97801 - 3.97801i) q^{22} +(-0.794732 - 0.794732i) q^{23} +0.289737 q^{24} +(-0.912375 - 4.91605i) q^{25} +2.02179i q^{26} +(-1.21205 - 1.21205i) q^{27} +3.15502i q^{29} +(-0.498161 - 0.414214i) q^{30} +3.84846i q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.15258 + 1.15258i) q^{33} +5.30873 q^{34} +2.91605 q^{36} +(-3.56380 + 3.56380i) q^{37} +(2.75192 - 2.75192i) q^{38} -0.585786i q^{39} +(2.22666 - 0.204875i) q^{40} -7.21050i q^{41} +(1.85669 + 1.85669i) q^{43} -5.62576i q^{44} +(-5.01373 - 4.16885i) q^{45} -1.12392 q^{46} +(-4.16885 - 4.16885i) q^{47} +(0.204875 - 0.204875i) q^{48} +(-4.12132 - 2.83103i) q^{50} -1.53813 q^{51} +(1.42962 + 1.42962i) q^{52} +(-0.978013 - 0.978013i) q^{53} -1.71410 q^{54} +(-8.04270 + 9.67269i) q^{55} +(-0.797333 + 0.797333i) q^{57} +(2.23093 + 2.23093i) q^{58} -5.47845 q^{59} +(-0.645146 + 0.0593598i) q^{60} -4.60924i q^{61} +(2.72127 + 2.72127i) q^{62} +1.00000i q^{64} +(-0.414214 - 4.50184i) q^{65} +1.62999i q^{66} +(0.597494 - 0.597494i) q^{67} +(3.75384 - 3.75384i) q^{68} +0.325641 q^{69} +4.77710 q^{71} +(2.06196 - 2.06196i) q^{72} +(3.96848 - 3.96848i) q^{73} +5.03997i q^{74} +(1.19410 + 0.820253i) q^{75} -3.89180i q^{76} +(-0.414214 - 0.414214i) q^{78} +6.24784i q^{79} +(1.42962 - 1.71936i) q^{80} -8.25152 q^{81} +(-5.09860 - 5.09860i) q^{82} +(5.67281 - 5.67281i) q^{83} +(-11.8207 + 1.08763i) q^{85} +2.62576 q^{86} +(-0.646383 - 0.646383i) q^{87} +(-3.97801 - 3.97801i) q^{88} +11.9218 q^{89} +(-6.49307 + 0.597426i) q^{90} +(-0.794732 + 0.794732i) q^{92} +(-0.788454 - 0.788454i) q^{93} -5.89564 q^{94} +(-5.56380 + 6.69140i) q^{95} -0.289737i q^{96} +(-6.63103 - 6.63103i) q^{97} +16.4050i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 24 q^{11} + 16 q^{15} - 16 q^{16} + 16 q^{18} - 8 q^{22} + 8 q^{23} - 24 q^{25} - 40 q^{30} - 8 q^{36} - 8 q^{37} - 8 q^{43} + 16 q^{46} - 32 q^{50} + 32 q^{51} + 56 q^{53} + 8 q^{57} + 64 q^{58} - 16 q^{60} + 16 q^{65} - 64 q^{67} + 16 q^{71} + 16 q^{72} + 16 q^{78} + 24 q^{85} - 24 q^{86} + 8 q^{88} + 8 q^{92} - 56 q^{93} - 40 q^{95}+O(q^{100}) \) 16 * q + 24 * q^11 + 16 * q^15 - 16 * q^16 + 16 * q^18 - 8 * q^22 + 8 * q^23 - 24 * q^25 - 40 * q^30 - 8 * q^36 - 8 * q^37 - 8 * q^43 + 16 * q^46 - 32 * q^50 + 32 * q^51 + 56 * q^53 + 8 * q^57 + 64 * q^58 - 16 * q^60 + 16 * q^65 - 64 * q^67 + 16 * q^71 + 16 * q^72 + 16 * q^78 + 24 * q^85 - 24 * q^86 + 8 * q^88 + 8 * q^92 - 56 * q^93 - 40 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more