LMFDB - Embedded newform 210.2.d.b.209.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(209,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("210.209");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.d (of order $2$, degree $1$, 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:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.10070523904.11
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 10x^{4} + 81 $ x^8 - 10*x^4 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			209.5
Root			$0.420861 - 1.68014i$ of defining polynomial
Character	$\chi$	$=$	210.209
Dual form			210.2.d.b.209.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(0.420861 - 1.68014i) q^{3} +1.00000 q^{4} +(1.95522 - 1.08495i) q^{5} +(0.420861 - 1.68014i) q^{6} +(-2.37608 + 1.16372i) q^{7} +1.00000 q^{8} +(-2.64575 - 1.41421i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(0.420861 - 1.68014i) q^{3} +1.00000 q^{4} +(1.95522 - 1.08495i) q^{5} +(0.420861 - 1.68014i) q^{6} +(-2.37608 + 1.16372i) q^{7} +1.00000 q^{8} +(-2.64575 - 1.41421i) q^{9} +(1.95522 - 1.08495i) q^{10} +2.82843i q^{11} +(0.420861 - 1.68014i) q^{12} -0.841723 q^{13} +(-2.37608 + 1.16372i) q^{14} +(-1.00000 - 3.74166i) q^{15} +1.00000 q^{16} -1.19038i q^{17} +(-2.64575 - 1.41421i) q^{18} +4.55066i q^{19} +(1.95522 - 1.08495i) q^{20} +(0.955218 + 4.48191i) q^{21} +2.82843i q^{22} +3.29150 q^{23} +(0.420861 - 1.68014i) q^{24} +(2.64575 - 4.24264i) q^{25} -0.841723 q^{26} +(-3.48957 + 3.85005i) q^{27} +(-2.37608 + 1.16372i) q^{28} -7.98430i q^{29} +(-1.00000 - 3.74166i) q^{30} +5.53019i q^{31} +1.00000 q^{32} +(4.75216 + 1.19038i) q^{33} -1.19038i q^{34} +(-3.38317 + 4.85326i) q^{35} +(-2.64575 - 1.41421i) q^{36} +10.8127i q^{37} +4.55066i q^{38} +(-0.354249 + 1.41421i) q^{39} +(1.95522 - 1.08495i) q^{40} -7.82087 q^{41} +(0.955218 + 4.48191i) q^{42} -4.65489i q^{43} +2.82843i q^{44} +(-6.70738 + 0.105422i) q^{45} +3.29150 q^{46} +4.33981i q^{47} +(0.420861 - 1.68014i) q^{48} +(4.29150 - 5.53019i) q^{49} +(2.64575 - 4.24264i) q^{50} +(-2.00000 - 0.500983i) q^{51} -0.841723 q^{52} -12.5830 q^{53} +(-3.48957 + 3.85005i) q^{54} +(3.06871 + 5.53019i) q^{55} +(-2.37608 + 1.16372i) q^{56} +(7.64575 + 1.91520i) q^{57} -7.98430i q^{58} +3.91044 q^{59} +(-1.00000 - 3.74166i) q^{60} -10.0808i q^{61} +5.53019i q^{62} +(7.93227 + 0.281364i) q^{63} +1.00000 q^{64} +(-1.64575 + 0.913230i) q^{65} +(4.75216 + 1.19038i) q^{66} +4.65489i q^{67} -1.19038i q^{68} +(1.38527 - 5.53019i) q^{69} +(-3.38317 + 4.85326i) q^{70} -12.6392i q^{71} +(-2.64575 - 1.41421i) q^{72} +3.06871 q^{73} +10.8127i q^{74} +(-6.01474 - 6.23080i) q^{75} +4.55066i q^{76} +(-3.29150 - 6.72057i) q^{77} +(-0.354249 + 1.41421i) q^{78} -7.29150 q^{79} +(1.95522 - 1.08495i) q^{80} +(5.00000 + 7.48331i) q^{81} -7.82087 q^{82} -7.70010i q^{83} +(0.955218 + 4.48191i) q^{84} +(-1.29150 - 2.32744i) q^{85} -4.65489i q^{86} +(-13.4148 - 3.36028i) q^{87} +2.82843i q^{88} +12.8712 q^{89} +(-6.70738 + 0.105422i) q^{90} +(2.00000 - 0.979531i) q^{91} +3.29150 q^{92} +(9.29150 + 2.32744i) q^{93} +4.33981i q^{94} +(4.93725 + 8.89753i) q^{95} +(0.420861 - 1.68014i) q^{96} +8.11905 q^{97} +(4.29150 - 5.53019i) q^{98} +(4.00000 - 7.48331i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^4 + 8 * q^8	$ 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8} - 8 q^{15} + 8 q^{16} - 8 q^{21} - 16 q^{23} - 8 q^{30} + 8 q^{32} - 16 q^{35} - 24 q^{39} - 8 q^{42} - 16 q^{46} - 8 q^{49} - 16 q^{51} - 16 q^{53} + 40 q^{57} - 8 q^{60} - 8 q^{63} + 8 q^{64} + 8 q^{65} - 16 q^{70} + 16 q^{77} - 24 q^{78} - 16 q^{79} + 40 q^{81} - 8 q^{84} + 32 q^{85} + 16 q^{91} - 16 q^{92} + 32 q^{93} - 24 q^{95} - 8 q^{98} + 32 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^4 + 8 * q^8 - 8 * q^15 + 8 * q^16 - 8 * q^21 - 16 * q^23 - 8 * q^30 + 8 * q^32 - 16 * q^35 - 24 * q^39 - 8 * q^42 - 16 * q^46 - 8 * q^49 - 16 * q^51 - 16 * q^53 + 40 * q^57 - 8 * q^60 - 8 * q^63 + 8 * q^64 + 8 * q^65 - 16 * q^70 + 16 * q^77 - 24 * q^78 - 16 * q^79 + 40 * q^81 - 8 * q^84 + 32 * q^85 + 16 * q^91 - 16 * q^92 + 32 * q^93 - 24 * q^95 - 8 * q^98 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	0.420861	−	1.68014i	0.242984	−	0.970030i
$3$	0.420861	−	1.68014i	0.242984	−	0.970030i
$4$	1.00000			0.500000
$5$	1.95522	−	1.08495i	0.874400	−	0.485206i
$5$	1.95522	−	1.08495i	0.874400	−	0.485206i
$6$	0.420861	−	1.68014i	0.171816	−	0.685915i
$7$	−2.37608	+	1.16372i	−0.898073	+	0.439846i
$7$	−2.37608	+	1.16372i	−0.898073	+	0.439846i
$8$	1.00000			0.353553
$9$	−2.64575	−	1.41421i	−0.881917	−	0.471405i
$10$	1.95522	−	1.08495i	0.618294	−	0.343092i
$11$			2.82843i			0.852803i	0.904534	+	0.426401i	$0.140219\pi$
$11$			2.82843i			0.852803i	−0.904534	+	0.426401i	$0.859781\pi$
$12$	0.420861	−	1.68014i	0.121492	−	0.485015i
$13$	−0.841723			−0.233452			−0.116726	−	0.993164i	$-0.537240\pi$
$13$	−0.841723			−0.233452			−0.116726	+	0.993164i	$0.537240\pi$
$14$	−2.37608	+	1.16372i	−0.635034	+	0.311018i
$15$	−1.00000	−	3.74166i	−0.258199	−	0.966092i
$16$	1.00000			0.250000
$17$		−	1.19038i		−	0.288709i	−0.989526	−	0.144354i	$-0.953890\pi$
$17$		−	1.19038i		−	0.288709i	0.989526	−	0.144354i	$-0.0461105\pi$
$18$	−2.64575	−	1.41421i	−0.623610	−	0.333333i
$19$			4.55066i			1.04399i	0.852948	+	0.521996i	$0.174813\pi$
$19$			4.55066i			1.04399i	−0.852948	+	0.521996i	$0.825187\pi$
$20$	1.95522	−	1.08495i	0.437200	−	0.242603i
$21$	0.955218	+	4.48191i	0.208446	+	0.978034i
$22$			2.82843i			0.603023i
$23$	3.29150			0.686326			0.343163	−	0.939276i	$-0.388502\pi$
$23$	3.29150			0.686326			0.343163	+	0.939276i	$0.388502\pi$
$24$	0.420861	−	1.68014i	0.0859080	−	0.342957i
$25$	2.64575	−	4.24264i	0.529150	−	0.848528i
$26$	−0.841723			−0.165075
$27$	−3.48957	+	3.85005i	−0.671569	+	0.740942i
$28$	−2.37608	+	1.16372i	−0.449037	+	0.219923i
$29$		−	7.98430i		−	1.48265i	−0.671148	−	0.741323i	$-0.734198\pi$
$29$		−	7.98430i		−	1.48265i	0.671148	−	0.741323i	$-0.265802\pi$
$30$	−1.00000	−	3.74166i	−0.182574	−	0.683130i
$31$			5.53019i			0.993252i	0.867965	+	0.496626i	$0.165428\pi$
$31$			5.53019i			0.993252i	−0.867965	+	0.496626i	$0.834572\pi$
$32$	1.00000			0.176777
$33$	4.75216	+	1.19038i	0.827245	+	0.207218i
$34$		−	1.19038i		−	0.204148i
$35$	−3.38317	+	4.85326i	−0.571860	+	0.820352i
$36$	−2.64575	−	1.41421i	−0.440959	−	0.235702i
$37$			10.8127i			1.77760i	0.458294	+	0.888801i	$0.348461\pi$
$37$			10.8127i			1.77760i	−0.458294	+	0.888801i	$0.651539\pi$
$38$			4.55066i			0.738214i
$39$	−0.354249	+	1.41421i	−0.0567252	+	0.226455i
$40$	1.95522	−	1.08495i	0.309147	−	0.171546i
$41$	−7.82087			−1.22141			−0.610707	−	0.791856i	$-0.709115\pi$
$41$	−7.82087			−1.22141			−0.610707	+	0.791856i	$0.709115\pi$
$42$	0.955218	+	4.48191i	0.147393	+	0.691574i
$43$		−	4.65489i		−	0.709864i	−0.934892	−	0.354932i	$-0.884504\pi$
$43$		−	4.65489i		−	0.709864i	0.934892	−	0.354932i	$-0.115496\pi$
$44$			2.82843i			0.426401i
$45$	−6.70738	+	0.105422i	−0.999877	+	0.0157154i
$46$	3.29150			0.485306
$47$			4.33981i			0.633027i	0.948588	+	0.316513i	$0.102512\pi$
$47$			4.33981i			0.633027i	−0.948588	+	0.316513i	$0.897488\pi$
$48$	0.420861	−	1.68014i	0.0607461	−	0.242508i
$49$	4.29150	−	5.53019i	0.613072	−	0.790027i
$50$	2.64575	−	4.24264i	0.374166	−	0.600000i
$51$	−2.00000	−	0.500983i	−0.280056	−	0.0701517i
$52$	−0.841723			−0.116726
$53$	−12.5830			−1.72841			−0.864204	−	0.503141i	$-0.832178\pi$
$53$	−12.5830			−1.72841			−0.864204	+	0.503141i	$0.832178\pi$
$54$	−3.48957	+	3.85005i	−0.474871	+	0.523925i
$55$	3.06871	+	5.53019i	0.413785	+	0.745691i
$56$	−2.37608	+	1.16372i	−0.317517	+	0.155509i
$57$	7.64575	+	1.91520i	1.01270	+	0.253674i
$58$		−	7.98430i		−	1.04839i
$59$	3.91044			0.509095			0.254548	−	0.967060i	$-0.418073\pi$
$59$	3.91044			0.509095			0.254548	+	0.967060i	$0.418073\pi$
$60$	−1.00000	−	3.74166i	−0.129099	−	0.483046i
$61$		−	10.0808i		−	1.29072i	−0.763878	−	0.645360i	$-0.776707\pi$
$61$		−	10.0808i		−	1.29072i	0.763878	−	0.645360i	$-0.223293\pi$
$62$			5.53019i			0.702335i
$63$	7.93227	+	0.281364i	0.999372	+	0.0354486i
$64$	1.00000			0.125000
$65$	−1.64575	+	0.913230i	−0.204130	+	0.113272i
$66$	4.75216	+	1.19038i	0.584950	+	0.146525i
$67$			4.65489i			0.568685i	0.958723	+	0.284343i	$0.0917753\pi$
$67$			4.65489i			0.568685i	−0.958723	+	0.284343i	$0.908225\pi$
$68$		−	1.19038i		−	0.144354i
$69$	1.38527	−	5.53019i	0.166766	−	0.665757i
$70$	−3.38317	+	4.85326i	−0.404366	+	0.580076i
$71$		−	12.6392i		−	1.50000i	−0.661440	−	0.749998i	$-0.730055\pi$
$71$		−	12.6392i		−	1.50000i	0.661440	−	0.749998i	$-0.269945\pi$
$72$	−2.64575	−	1.41421i	−0.311805	−	0.166667i
$73$	3.06871			0.359166			0.179583	−	0.983743i	$-0.442525\pi$
$73$	3.06871			0.359166			0.179583	+	0.983743i	$0.442525\pi$
$74$			10.8127i			1.25695i
$75$	−6.01474	−	6.23080i	−0.694523	−	0.719471i
$76$			4.55066i			0.521996i
$77$	−3.29150	−	6.72057i	−0.375102	−	0.765880i
$78$	−0.354249	+	1.41421i	−0.0401108	+	0.160128i
$79$	−7.29150			−0.820358			−0.410179	−	0.912005i	$-0.634534\pi$
$79$	−7.29150			−0.820358			−0.410179	+	0.912005i	$0.634534\pi$
$80$	1.95522	−	1.08495i	0.218600	−	0.121302i
$81$	5.00000	+	7.48331i	0.555556	+	0.831479i
$82$	−7.82087			−0.863671
$83$		−	7.70010i		−	0.845196i	−0.906317	−	0.422598i	$-0.861118\pi$
$83$		−	7.70010i		−	0.845196i	0.906317	−	0.422598i	$-0.138882\pi$
$84$	0.955218	+	4.48191i	0.104223	+	0.489017i
$85$	−1.29150	−	2.32744i	−0.140083	−	0.252447i
$86$		−	4.65489i		−	0.501949i
$87$	−13.4148	−	3.36028i	−1.43821	−	0.360260i
$88$			2.82843i			0.301511i
$89$	12.8712			1.36435			0.682173	−	0.731191i	$-0.261035\pi$
$89$	12.8712			1.36435			0.682173	+	0.731191i	$0.261035\pi$
$90$	−6.70738	+	0.105422i	−0.707019	+	0.0111125i
$91$	2.00000	−	0.979531i	0.209657	−	0.102683i
$92$	3.29150			0.343163
$93$	9.29150	+	2.32744i	0.963484	+	0.241345i
$94$			4.33981i			0.447618i
$95$	4.93725	+	8.89753i	0.506552	+	0.912867i
$96$	0.420861	−	1.68014i	0.0429540	−	0.171479i
$97$	8.11905			0.824365			0.412182	−	0.911101i	$-0.364767\pi$
$97$	8.11905			0.824365			0.412182	+	0.911101i	$0.364767\pi$
$98$	4.29150	−	5.53019i	0.433507	−	0.558634i
$99$	4.00000	−	7.48331i	0.402015	−	0.752101i
$100$	2.64575	−	4.24264i	0.264575	−	0.424264i
$101$	−3.91044			−0.389103			−0.194551	−	0.980892i	$-0.562325\pi$
$101$	−3.91044			−0.389103			−0.194551	+	0.980892i	$0.562325\pi$
$102$	−2.00000	−	0.500983i	−0.198030	−	0.0496047i
$103$	−12.5730			−1.23886			−0.619429	−	0.785053i	$-0.712636\pi$
$103$	−12.5730			−1.23886			−0.619429	+	0.785053i	$0.712636\pi$
$104$	−0.841723			−0.0825377
$105$	6.73033	+	7.72675i	0.656813	+	0.754054i
$106$	−12.5830			−1.22217
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$	−3.48957	+	3.85005i	−0.335784	+	0.370471i
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$	3.06871	+	5.53019i	0.292590	+	0.527283i
$111$	18.1669	+	4.55066i	1.72433	+	0.431929i
$112$	−2.37608	+	1.16372i	−0.224518	+	0.109961i
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$	7.64575	+	1.91520i	0.716090	+	0.179375i
$115$	6.43560	−	3.57113i	0.600123	−	0.333009i
$116$		−	7.98430i		−	0.741323i
$117$	2.22699	+	1.19038i	0.205885	+	0.110050i
$118$	3.91044			0.359985
$119$	1.38527	+	2.82843i	0.126987	+	0.259281i
$120$	−1.00000	−	3.74166i	−0.0912871	−	0.341565i
$121$	3.00000			0.272727
$122$		−	10.0808i		−	0.912677i
$123$	−3.29150	+	13.1402i	−0.296785	+	1.18481i
$124$			5.53019i			0.496626i
$125$	0.569951	−	11.1658i	0.0509780	−	0.998700i
$126$	7.93227	+	0.281364i	0.706662	+	0.0250659i
$127$		−	10.8127i		−	0.959474i	−0.877412	−	0.479737i	$-0.840732\pi$
$127$		−	10.8127i		−	0.959474i	0.877412	−	0.479737i	$-0.159268\pi$
$128$	1.00000			0.0883883
$129$	−7.82087	−	1.95906i	−0.688589	−	0.172486i
$130$	−1.64575	+	0.913230i	−0.144342	+	0.0800956i
$131$	−8.96077			−0.782906			−0.391453	−	0.920198i	$-0.628027\pi$
$131$	−8.96077			−0.782906			−0.391453	+	0.920198i	$0.628027\pi$
$132$	4.75216	+	1.19038i	0.413622	+	0.103609i
$133$	−5.29570	−	10.8127i	−0.459196	−	0.937582i
$134$			4.65489i			0.402121i
$135$	−2.64575	+	11.3137i	−0.227710	+	0.973729i
$136$		−	1.19038i		−	0.102074i
$137$	9.29150			0.793827			0.396913	−	0.917856i	$-0.370081\pi$
$137$	9.29150			0.793827			0.396913	+	0.917856i	$0.370081\pi$
$138$	1.38527	−	5.53019i	0.117922	−	0.470761i
$139$		−	15.6110i		−	1.32411i	−0.749455	−	0.662056i	$-0.769684\pi$
$139$		−	15.6110i		−	1.32411i	0.749455	−	0.662056i	$-0.230316\pi$
$140$	−3.38317	+	4.85326i	−0.285930	+	0.410176i
$141$	7.29150	+	1.82646i	0.614055	+	0.153816i
$142$		−	12.6392i		−	1.06066i
$143$		−	2.38075i		−	0.199088i
$144$	−2.64575	−	1.41421i	−0.220479	−	0.117851i
$145$	−8.66259	−	15.6110i	−0.719389	−	1.29643i
$146$	3.06871			0.253968
$147$	−7.48537	−	9.53778i	−0.617383	−	0.786662i
$148$			10.8127i			0.888801i
$149$		−	3.32941i		−	0.272756i	−0.990657	−	0.136378i	$-0.956454\pi$
$149$		−	3.32941i		−	0.272756i	0.990657	−	0.136378i	$-0.0435462\pi$
$150$	−6.01474	−	6.23080i	−0.491102	−	0.508743i
$151$	−22.5830			−1.83778			−0.918889	−	0.394515i	$-0.870913\pi$
$151$	−22.5830			−1.83778			−0.918889	+	0.394515i	$0.870913\pi$
$152$			4.55066i			0.369107i
$153$	−1.68345	+	3.14944i	−0.136099	+	0.254617i
$154$	−3.29150	−	6.72057i	−0.265237	−	0.541559i
$155$	6.00000	+	10.8127i	0.481932	+	0.868499i
$156$	−0.354249	+	1.41421i	−0.0283626	+	0.113228i
$157$	22.6209			1.80534			0.902672	−	0.430330i	$-0.141603\pi$
$157$	22.6209			1.80534			0.902672	+	0.430330i	$0.141603\pi$
$158$	−7.29150			−0.580081
$159$	−5.29570	+	21.1412i	−0.419976	+	1.67661i
$160$	1.95522	−	1.08495i	0.154574	−	0.0857731i
$161$	−7.82087	+	3.83039i	−0.616371	+	0.301877i
$162$	5.00000	+	7.48331i	0.392837	+	0.587945i
$163$		0			0		1.00000			$0$
$163$		0			0		−1.00000			$\pi$
$164$	−7.82087			−0.610707
$165$	10.5830	−	2.82843i	0.823886	−	0.220193i
$166$		−	7.70010i		−	0.597643i
$167$			11.4821i			0.888509i	0.895901	+	0.444255i	$0.146531\pi$
$167$			11.4821i			0.888509i	−0.895901	+	0.444255i	$0.853469\pi$
$168$	0.955218	+	4.48191i	0.0736966	+	0.345787i
$169$	−12.2915			−0.945500
$170$	−1.29150	−	2.32744i	−0.0990537	−	0.178507i
$171$	6.43560	−	12.0399i	0.492143	−	0.920715i
$172$		−	4.65489i		−	0.354932i
$173$			8.89047i			0.675930i	0.941159	+	0.337965i	$0.109739\pi$
$173$			8.89047i			0.675930i	−0.941159	+	0.337965i	$0.890261\pi$
$174$	−13.4148	−	3.36028i	−1.01697	−	0.254742i
$175$	−1.34926	+	13.1598i	−0.101994	+	0.994785i
$176$			2.82843i			0.213201i
$177$	1.64575	−	6.57008i	0.123702	−	0.493838i
$178$	12.8712			0.964738
$179$		−	9.48725i		−	0.709110i	−0.935035	−	0.354555i	$-0.884632\pi$
$179$		−	9.48725i		−	0.709110i	0.935035	−	0.354555i	$-0.115368\pi$
$180$	−6.70738	+	0.105422i	−0.499938	+	0.00785771i
$181$			12.0399i			0.894920i	0.894304	+	0.447460i	$0.147671\pi$
$181$			12.0399i			0.894920i	−0.894304	+	0.447460i	$0.852329\pi$
$182$	2.00000	−	0.979531i	0.148250	−	0.0726077i
$183$	−16.9373	−	4.24264i	−1.25204	−	0.313625i
$184$	3.29150			0.242653
$185$	11.7313	+	21.1412i	0.862503	+	1.55433i
$186$	9.29150	+	2.32744i	0.681286	+	0.170656i
$187$	3.36689			0.246211
$188$			4.33981i			0.316513i
$189$	3.81112	−	13.2089i	0.277218	−	0.960807i
$190$	4.93725	+	8.89753i	0.358186	+	0.645495i
$191$		−	7.98430i		−	0.577724i	−0.957371	−	0.288862i	$-0.906723\pi$
$191$		−	7.98430i		−	0.577724i	0.957371	−	0.288862i	$-0.0932768\pi$
$192$	0.420861	−	1.68014i	0.0303731	−	0.121254i
$193$			8.48528i			0.610784i	0.952227	+	0.305392i	$0.0987875\pi$
$193$			8.48528i			0.610784i	−0.952227	+	0.305392i	$0.901213\pi$
$194$	8.11905			0.582914
$195$	0.841723	+	3.14944i	0.0602770	+	0.225536i
$196$	4.29150	−	5.53019i	0.306536	−	0.395014i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$	4.00000	−	7.48331i	0.284268	−	0.531816i
$199$			16.5906i			1.17607i	0.808834	+	0.588037i	$0.200099\pi$
$199$			16.5906i			1.17607i	−0.808834	+	0.588037i	$0.799901\pi$
$200$	2.64575	−	4.24264i	0.187083	−	0.300000i
$201$	7.82087	+	1.95906i	0.551642	+	0.138182i
$202$	−3.91044			−0.275137
$203$	9.29150	+	18.9713i	0.652136	+	1.33153i
$204$	−2.00000	−	0.500983i	−0.140028	−	0.0350758i
$205$	−15.2915	+	8.48528i	−1.06800	+	0.592638i
$206$	−12.5730			−0.876004
$207$	−8.70850	−	4.65489i	−0.605282	−	0.323537i
$208$	−0.841723			−0.0583630
$209$	−12.8712			−0.890320
$210$	6.73033	+	7.72675i	0.464437	+	0.533197i
$211$	21.1660			1.45713			0.728564	−	0.684978i	$-0.240188\pi$
$211$	21.1660			1.45713			0.728564	+	0.684978i	$0.240188\pi$
$212$	−12.5830			−0.864204
$213$	−21.2356	−	5.31935i	−1.45504	−	0.364476i
$214$		0			0
$215$	−5.05034	−	9.10132i	−0.344430	−	0.620705i
$216$	−3.48957	+	3.85005i	−0.237435	+	0.261963i
$217$	−6.43560	−	13.1402i	−0.436877	−	0.892013i
$218$	2.00000			0.135457
$219$	1.29150	−	5.15587i	0.0872717	−	0.348401i
$220$	3.06871	+	5.53019i	0.206893	+	0.372845i
$221$			1.00197i			0.0673996i
$222$	18.1669	+	4.55066i	1.21928	+	0.305420i
$223$	−4.75216			−0.318228			−0.159114	−	0.987260i	$-0.550864\pi$
$223$	−4.75216			−0.318228			−0.159114	+	0.987260i	$0.550864\pi$
$224$	−2.37608	+	1.16372i	−0.158758	+	0.0777544i
$225$	−13.0000	+	7.48331i	−0.866667	+	0.498888i
$226$	6.00000			0.399114
$227$			1.40122i			0.0930023i	0.998918	+	0.0465011i	$0.0148071\pi$
$227$			1.40122i			0.0930023i	−0.998918	+	0.0465011i	$0.985193\pi$
$228$	7.64575	+	1.91520i	0.506352	+	0.126837i
$229$			28.2835i			1.86903i	0.355930	+	0.934513i	$0.384164\pi$
$229$			28.2835i			1.86903i	−0.355930	+	0.934513i	$0.615836\pi$
$230$	6.43560	−	3.57113i	0.424351	−	0.235473i
$231$	−12.6768	+	2.70176i	−0.834070	+	0.177763i
$232$		−	7.98430i		−	0.524195i
$233$	−2.70850			−0.177440			−0.0887198	−	0.996057i	$-0.528278\pi$
$233$	−2.70850			−0.177440			−0.0887198	+	0.996057i	$0.528278\pi$
$234$	2.22699	+	1.19038i	0.145583	+	0.0778173i
$235$	4.70850	+	8.48528i	0.307149	+	0.553519i
$236$	3.91044			0.254548
$237$	−3.06871	+	12.2508i	−0.199334	+	0.795772i
$238$	1.38527	+	2.82843i	0.0897935	+	0.183340i
$239$			22.1264i			1.43124i	0.698490	+	0.715620i	$0.253856\pi$
$239$			22.1264i			1.43124i	−0.698490	+	0.715620i	$0.746144\pi$
$240$	−1.00000	−	3.74166i	−0.0645497	−	0.241523i
$241$			1.95906i			0.126194i	0.998007	+	0.0630972i	$0.0200978\pi$
$241$			1.95906i			0.126194i	−0.998007	+	0.0630972i	$0.979902\pi$
$242$	3.00000			0.192847
$243$	14.6773	−	5.25127i	0.941551	−	0.336869i
$244$		−	10.0808i		−	0.645360i
$245$	2.39082	−	15.4688i	0.152744	−	0.988266i
$246$	−3.29150	+	13.1402i	−0.209859	+	0.837787i
$247$		−	3.83039i		−	0.243722i
$248$			5.53019i			0.351167i
$249$	−12.9373	−	3.24067i	−0.819865	−	0.205369i
$250$	0.569951	−	11.1658i	0.0360469	−	0.706187i
$251$	−11.7313			−0.740473			−0.370237	−	0.928937i	$-0.620723\pi$
$251$	−11.7313			−0.740473			−0.370237	+	0.928937i	$0.620723\pi$
$252$	7.93227	+	0.281364i	0.499686	+	0.0177243i
$253$			9.30978i			0.585301i
$254$		−	10.8127i		−	0.678451i
$255$	−4.45398	+	1.19038i	−0.278919	+	0.0745442i
$256$	1.00000			0.0625000
$257$		−	14.2098i		−	0.886384i	−0.896427	−	0.443192i	$-0.853846\pi$
$257$		−	14.2098i		−	0.886384i	0.896427	−	0.443192i	$-0.146154\pi$
$258$	−7.82087	−	1.95906i	−0.486906	−	0.121966i
$259$	−12.5830	−	25.6919i	−0.781870	−	1.59642i
$260$	−1.64575	+	0.913230i	−0.102065	+	0.0566361i
$261$	−11.2915	+	21.1245i	−0.698926	+	1.30757i
$262$	−8.96077			−0.553598
$263$	6.58301			0.405925			0.202963	−	0.979186i	$-0.434943\pi$
$263$	6.58301			0.405925			0.202963	+	0.979186i	$0.434943\pi$
$264$	4.75216	+	1.19038i	0.292475	+	0.0732626i
$265$	−24.6025	+	13.6520i	−1.51132	+	0.838634i
$266$	−5.29570	−	10.8127i	−0.324700	−	0.662971i
$267$	5.41699	−	21.6255i	0.331515	−	1.32346i
$268$			4.65489i			0.284343i
$269$	24.6025			1.50004			0.750021	−	0.661414i	$-0.230043\pi$
$269$	24.6025			1.50004			0.750021	+	0.661414i	$0.230043\pi$
$270$	−2.64575	+	11.3137i	−0.161015	+	0.688530i
$271$		−	7.48925i		−	0.454940i	−0.973785	−	0.227470i	$-0.926955\pi$
$271$		−	7.48925i		−	0.454940i	0.973785	−	0.227470i	$-0.0730453\pi$
$272$		−	1.19038i		−	0.0721771i
$273$	−0.804028	−	3.77253i	−0.0486620	−	0.228324i
$274$	9.29150			0.561320
$275$	12.0000	+	7.48331i	0.723627	+	0.451261i
$276$	1.38527	−	5.53019i	0.0833832	−	0.332878i
$277$		−	15.4676i		−	0.929359i	−0.885479	−	0.464679i	$-0.846170\pi$
$277$		−	15.4676i		−	0.929359i	0.885479	−	0.464679i	$-0.153830\pi$
$278$		−	15.6110i		−	0.936288i
$279$	7.82087	−	14.6315i	0.468223	−	0.875965i
$280$	−3.38317	+	4.85326i	−0.202183	+	0.290038i
$281$			20.6235i			1.23029i	0.788412	+	0.615147i	$0.210903\pi$
$281$			20.6235i			1.23029i	−0.788412	+	0.615147i	$0.789097\pi$
$282$	7.29150	+	1.82646i	0.434203	+	0.108764i
$283$	9.74968			0.579558			0.289779	−	0.957094i	$-0.406418\pi$
$283$	9.74968			0.579558			0.289779	+	0.957094i	$0.406418\pi$
$284$		−	12.6392i		−	0.749998i
$285$	17.0270	−	4.55066i	1.00859	−	0.269558i
$286$		−	2.38075i		−	0.140777i
$287$	18.5830	−	9.10132i	1.09692	−	0.537234i
$288$	−2.64575	−	1.41421i	−0.155902	−	0.0833333i
$289$	15.5830			0.916647
$290$	−8.66259	−	15.6110i	−0.508685	−	0.916712i
$291$	3.41699	−	13.6412i	0.200308	−	0.799659i
$292$	3.06871			0.179583
$293$		−	11.2712i		−	0.658472i	−0.944248	−	0.329236i	$-0.893209\pi$
$293$		−	11.2712i		−	0.658472i	0.944248	−	0.329236i	$-0.106791\pi$
$294$	−7.48537	−	9.53778i	−0.436556	−	0.556254i
$295$	7.64575	−	4.24264i	0.445153	−	0.247016i
$296$			10.8127i			0.628477i
$297$	−10.8896	−	9.87000i	−0.631878	−	0.572716i
$298$		−	3.32941i		−	0.192868i
$299$	−2.77053			−0.160224
$300$	−6.01474	−	6.23080i	−0.347261	−	0.359735i
$301$	5.41699	+	11.0604i	0.312230	+	0.637510i
$302$	−22.5830			−1.29951
$303$	−1.64575	+	6.57008i	−0.0945459	+	0.377441i
$304$			4.55066i			0.260998i
$305$	−10.9373	−	19.7103i	−0.626265	−	1.12861i
$306$	−1.68345	+	3.14944i	−0.0962362	+	0.180041i
$307$	14.8000			0.844682			0.422341	−	0.906437i	$-0.361209\pi$
$307$	14.8000			0.844682			0.422341	+	0.906437i	$0.361209\pi$
$308$	−3.29150	−	6.72057i	−0.187551	−	0.382940i
$309$	−5.29150	+	21.1245i	−0.301023	+	1.20173i
$310$	6.00000	+	10.8127i	0.340777	+	0.614122i
$311$	2.77053			0.157103			0.0785513	−	0.996910i	$-0.474971\pi$
$311$	2.77053			0.157103			0.0785513	+	0.996910i	$0.474971\pi$
$312$	−0.354249	+	1.41421i	−0.0200554	+	0.0800641i
$313$	8.11905			0.458916			0.229458	−	0.973319i	$-0.426305\pi$
$313$	8.11905			0.458916			0.229458	+	0.973319i	$0.426305\pi$
$314$	22.6209			1.27657
$315$	15.8146	−	8.05601i	0.891050	−	0.453905i
$316$	−7.29150			−0.410179
$317$	−6.00000			−0.336994			−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000			−0.336994			−0.168497	+	0.985702i	$0.553891\pi$
$318$	−5.29570	+	21.1412i	−0.296968	+	1.18554i
$319$	22.5830			1.26441
$320$	1.95522	−	1.08495i	0.109300	−	0.0606508i
$321$		0			0
$322$	−7.82087	+	3.83039i	−0.435840	+	0.213459i
$323$	5.41699			0.301410
$324$	5.00000	+	7.48331i	0.277778	+	0.415740i
$325$	−2.22699	+	3.57113i	−0.123531	+	0.198091i
$326$		0			0
$327$	0.841723	−	3.36028i	0.0465474	−	0.185824i
$328$	−7.82087			−0.431835
$329$	−5.05034	−	10.3117i	−0.278434	−	0.568505i
$330$	10.5830	−	2.82843i	0.582575	−	0.155700i
$331$	8.00000			0.439720			0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000			0.439720			0.219860	+	0.975531i	$0.429440\pi$
$332$		−	7.70010i		−	0.422598i
$333$	15.2915	−	28.6078i	0.837969	−	1.56770i
$334$			11.4821i			0.628271i
$335$	5.05034	+	9.10132i	0.275929	+	0.497258i
$336$	0.955218	+	4.48191i	0.0521114	+	0.244508i
$337$			22.4499i			1.22293i	0.791273	+	0.611463i	$0.209419\pi$
$337$			22.4499i			1.22293i	−0.791273	+	0.611463i	$0.790581\pi$
$338$	−12.2915			−0.668570
$339$	2.52517	−	10.0808i	0.137148	−	0.547517i
$340$	−1.29150	−	2.32744i	−0.0700416	−	0.126223i
$341$	−15.6417			−0.847048
$342$	6.43560	−	12.0399i	0.347998	−	0.651044i
$343$	−3.76135	+	18.1343i	−0.203094	+	0.979159i
$344$		−	4.65489i		−	0.250975i
$345$	−3.29150	−	12.3157i	−0.177209	−	0.663054i
$346$			8.89047i			0.477955i
$347$	24.0000			1.28839			0.644194	−	0.764862i	$-0.277193\pi$
$347$	24.0000			1.28839			0.644194	+	0.764862i	$0.277193\pi$
$348$	−13.4148	−	3.36028i	−0.719106	−	0.180130i
$349$		−	19.1822i		−	1.02680i	−0.858150	−	0.513399i	$-0.828386\pi$
$349$		−	19.1822i		−	1.02680i	0.858150	−	0.513399i	$-0.171614\pi$
$350$	−1.34926	+	13.1598i	−0.0721210	+	0.703419i
$351$	2.93725	−	3.24067i	0.156779	−	0.172974i
$352$			2.82843i			0.150756i
$353$		−	21.3521i		−	1.13646i	−0.822871	−	0.568228i	$-0.807629\pi$
$353$		−	21.3521i		−	1.13646i	0.822871	−	0.568228i	$-0.192371\pi$
$354$	1.64575	−	6.57008i	0.0874707	−	0.349196i
$355$	−13.7129	−	24.7124i	−0.727807	−	1.31160i
$356$	12.8712			0.682173
$357$	5.33516	−	1.13707i	0.282367	−	0.0601800i
$358$		−	9.48725i		−	0.501417i
$359$			26.7813i			1.41346i	0.707481	+	0.706732i	$0.249831\pi$
$359$			26.7813i			1.41346i	−0.707481	+	0.706732i	$0.750169\pi$
$360$	−6.70738	+	0.105422i	−0.353510	+	0.00555624i
$361$	−1.70850			−0.0899209
$362$			12.0399i			0.632804i
$363$	1.26258	−	5.04042i	0.0662685	−	0.264554i
$364$	2.00000	−	0.979531i	0.104828	−	0.0513414i
$365$	6.00000	−	3.32941i	0.314054	−	0.174269i
$366$	−16.9373	−	4.24264i	−0.885324	−	0.221766i
$367$	8.11905			0.423811			0.211905	−	0.977290i	$-0.432033\pi$
$367$	8.11905			0.423811			0.211905	+	0.977290i	$0.432033\pi$
$368$	3.29150			0.171581
$369$	20.6921	+	11.0604i	1.07719	+	0.575780i
$370$	11.7313	+	21.1412i	0.609882	+	1.09908i
$371$	29.8982	−	14.6431i	1.55224	−	0.760233i
$372$	9.29150	+	2.32744i	0.481742	+	0.120672i
$373$			15.4676i			0.800883i	0.916322	+	0.400441i	$0.131143\pi$
$373$			15.4676i			0.800883i	−0.916322	+	0.400441i	$0.868857\pi$
$374$	3.36689			0.174098
$375$	−18.5203	−	5.65685i	−0.956382	−	0.292119i
$376$			4.33981i			0.223809i
$377$			6.72057i			0.346127i
$378$	3.81112	−	13.2089i	0.196023	−	0.679393i
$379$	14.5830			0.749079			0.374539	−	0.927211i	$-0.377801\pi$
$379$	14.5830			0.749079			0.374539	+	0.927211i	$0.377801\pi$
$380$	4.93725	+	8.89753i	0.253276	+	0.456434i
$381$	−18.1669	−	4.55066i	−0.930719	−	0.233137i
$382$		−	7.98430i		−	0.408512i
$383$			11.4821i			0.586706i	0.956004	+	0.293353i	$0.0947712\pi$
$383$			11.4821i			0.586706i	−0.956004	+	0.293353i	$0.905229\pi$
$384$	0.420861	−	1.68014i	0.0214770	−	0.0857394i
$385$	−13.7271	−	9.56904i	−0.699598	−	0.487684i
$386$			8.48528i			0.431889i
$387$	−6.58301	+	12.3157i	−0.334633	+	0.626041i
$388$	8.11905			0.412182
$389$		−	0.323511i		−	0.0164026i	−0.999966	−	0.00820132i	$-0.997389\pi$
$389$		−	0.323511i		−	0.0164026i	0.999966	−	0.00820132i	$-0.00261059\pi$
$390$	0.841723	+	3.14944i	0.0426223	+	0.159478i
$391$		−	3.91813i		−	0.198148i
$392$	4.29150	−	5.53019i	0.216754	−	0.279317i
$393$	−3.77124	+	15.0554i	−0.190234	+	0.759443i
$394$	−18.0000			−0.906827
$395$	−14.2565	+	7.91094i	−0.717321	+	0.398043i
$396$	4.00000	−	7.48331i	0.201008	−	0.376051i
$397$	−21.5338			−1.08075			−0.540375	−	0.841424i	$-0.681718\pi$
$397$	−21.5338			−1.08075			−0.540375	+	0.841424i	$0.681718\pi$
$398$			16.5906i			0.831610i
$399$	−20.3957	+	4.34687i	−1.02106	+	0.217616i
$400$	2.64575	−	4.24264i	0.132288	−	0.212132i
$401$			7.48331i			0.373699i	0.982389	+	0.186849i	$0.0598277\pi$
$401$			7.48331i			0.373699i	−0.982389	+	0.186849i	$0.940172\pi$
$402$	7.82087	+	1.95906i	0.390070	+	0.0977092i
$403$		−	4.65489i		−	0.231876i
$404$	−3.91044			−0.194551
$405$	17.8951	+	9.20674i	0.889217	+	0.457487i
$406$	9.29150	+	18.9713i	0.461130	+	0.941531i
$407$	−30.5830			−1.51594
$408$	−2.00000	−	0.500983i	−0.0990148	−	0.0248024i
$409$			13.0194i			0.643770i	0.946779	+	0.321885i	$0.104316\pi$
$409$			13.0194i			0.643770i	−0.946779	+	0.321885i	$0.895684\pi$
$410$	−15.2915	+	8.48528i	−0.755193	+	0.419058i
$411$	3.91044	−	15.6110i	0.192888	−	0.770036i
$412$	−12.5730			−0.619429
$413$	−9.29150	+	4.55066i	−0.457205	+	0.223923i
$414$	−8.70850	−	4.65489i	−0.427999	−	0.228775i
$415$	−8.35425	−	15.0554i	−0.410094	−	0.739039i
$416$	−0.841723			−0.0412689
$417$	−26.2288	−	6.57008i	−1.28443	−	0.321738i
$418$	−12.8712			−0.629551
$419$	−21.8320			−1.06656			−0.533281	−	0.845938i	$-0.679041\pi$
$419$	−21.8320			−1.06656			−0.533281	+	0.845938i	$0.679041\pi$
$420$	6.73033	+	7.72675i	0.328406	+	0.377027i
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	21.1660			1.03035
$423$	6.13742	−	11.4821i	0.298412	−	0.558277i
$424$	−12.5830			−0.611085
$425$	−5.05034	−	3.14944i	−0.244977	−	0.152770i
$426$	−21.2356	−	5.31935i	−1.02887	−	0.257723i
$427$	11.7313	+	23.9529i	0.567718	+	1.15916i
$428$		0			0
$429$	−4.00000	−	1.00197i	−0.193122	−	0.0483754i
$430$	−5.05034	−	9.10132i	−0.243549	−	0.438905i
$431$		−	16.4696i		−	0.793312i	−0.917967	−	0.396656i	$-0.870171\pi$
$431$		−	16.4696i		−	0.793312i	0.917967	−	0.396656i	$-0.129829\pi$
$432$	−3.48957	+	3.85005i	−0.167892	+	0.185236i
$433$	26.5313			1.27501			0.637507	−	0.770445i	$-0.279966\pi$
$433$	26.5313			1.27501			0.637507	+	0.770445i	$0.279966\pi$
$434$	−6.43560	−	13.1402i	−0.308919	−	0.630748i
$435$	−29.8745	+	7.98430i	−1.43237	+	0.382818i
$436$	2.00000			0.0957826
$437$			14.9785i			0.716519i
$438$	1.29150	−	5.15587i	0.0617104	−	0.246357i
$439$			18.5496i			0.885326i	0.896688	+	0.442663i	$0.145966\pi$
$439$			18.5496i			0.885326i	−0.896688	+	0.442663i	$0.854034\pi$
$440$	3.06871	+	5.53019i	0.146295	+	0.263641i
$441$	−19.1751	+	8.56241i	−0.913101	+	0.407734i
$442$			1.00197i			0.0476587i
$443$	−13.1660			−0.625536			−0.312768	−	0.949830i	$-0.601256\pi$
$443$	−13.1660			−0.625536			−0.312768	+	0.949830i	$0.601256\pi$
$444$	18.1669	+	4.55066i	0.862163	+	0.215965i
$445$	25.1660	−	13.9647i	1.19298	−	0.661989i
$446$	−4.75216			−0.225021
$447$	−5.59388	−	1.40122i	−0.264581	−	0.0662755i
$448$	−2.37608	+	1.16372i	−0.112259	+	0.0549807i
$449$			8.30781i			0.392070i	0.980597	+	0.196035i	$0.0628066\pi$
$449$			8.30781i			0.392070i	−0.980597	+	0.196035i	$0.937193\pi$
$450$	−13.0000	+	7.48331i	−0.612826	+	0.352767i
$451$		−	22.1208i		−	1.04163i
$452$	6.00000			0.282216
$453$	−9.50432	+	37.9426i	−0.446552	+	1.78270i
$454$			1.40122i			0.0657625i
$455$	2.84769	−	4.08510i	0.133502	−	0.191513i
$456$	7.64575	+	1.91520i	0.358045	+	0.0896873i
$457$		−	8.48528i		−	0.396925i	−0.980109	−	0.198462i	$-0.936405\pi$
$457$		−	8.48528i		−	0.396925i	0.980109	−	0.198462i	$-0.0635948\pi$
$458$			28.2835i			1.32160i
$459$	4.58301	+	4.15390i	0.213916	+	0.193888i
$460$	6.43560	−	3.57113i	0.300062	−	0.166505i
$461$	8.96077			0.417345			0.208672	−	0.977986i	$-0.433086\pi$
$461$	8.96077			0.417345			0.208672	+	0.977986i	$0.433086\pi$
$462$	−12.6768	+	2.70176i	−0.589777	+	0.125697i
$463$		−	23.9529i		−	1.11319i	−0.830786	−	0.556593i	$-0.812108\pi$
$463$		−	23.9529i		−	1.11319i	0.830786	−	0.556593i	$-0.187892\pi$
$464$		−	7.98430i		−	0.370662i
$465$	20.6921	−	5.53019i	0.959572	−	0.256456i
$466$	−2.70850			−0.125469
$467$			3.36028i			0.155495i	0.996973	+	0.0777477i	$0.0247729\pi$
$467$			3.36028i			0.155495i	−0.996973	+	0.0777477i	$0.975227\pi$
$468$	2.22699	+	1.19038i	0.102943	+	0.0550251i
$469$	−5.41699	−	11.0604i	−0.250134	−	0.510721i
$470$	4.70850	+	8.48528i	0.217187	+	0.391397i
$471$	9.52026	−	38.0063i	0.438670	−	1.75124i
$472$	3.91044			0.179992
$473$	13.1660			0.605374
$474$	−3.06871	+	12.2508i	−0.140951	+	0.562696i
$475$	19.3068	+	12.0399i	0.885857	+	0.552429i
$476$	1.38527	+	2.82843i	0.0634936	+	0.129641i
$477$	33.2915	+	17.7951i	1.52431	+	0.814780i
$478$			22.1264i			1.01204i
$479$	−39.1044			−1.78672			−0.893362	−	0.449338i	$-0.851660\pi$
$479$	−39.1044			−1.78672			−0.893362	+	0.449338i	$0.851660\pi$
$480$	−1.00000	−	3.74166i	−0.0456435	−	0.170783i
$481$		−	9.10132i		−	0.414984i
$482$			1.95906i			0.0892329i
$483$	3.14410	+	14.7522i	0.143062	+	0.671250i
$484$	3.00000			0.136364
$485$	15.8745	−	8.80879i	0.720824	−	0.399987i
$486$	14.6773	−	5.25127i	0.665777	−	0.238202i
$487$			32.4382i			1.46991i	0.678114	+	0.734957i	$0.262798\pi$
$487$			32.4382i			1.46991i	−0.678114	+	0.734957i	$0.737202\pi$
$488$		−	10.0808i		−	0.456339i
$489$		0			0
$490$	2.39082	−	15.4688i	0.108006	−	0.698809i
$491$		−	14.1421i		−	0.638226i	−0.947717	−	0.319113i	$-0.896615\pi$
$491$		−	14.1421i		−	0.638226i	0.947717	−	0.319113i	$-0.103385\pi$
$492$	−3.29150	+	13.1402i	−0.148392	+	0.592405i
$493$	−9.50432			−0.428053
$494$		−	3.83039i		−	0.172338i
$495$	−0.298179	−	18.9713i	−0.0134022	−	0.852698i
$496$			5.53019i			0.248313i
$497$	14.7085	+	30.0317i	0.659766	+	1.34711i
$498$	−12.9373	−	3.24067i	−0.579732	−	0.145218i
$499$	1.41699			0.0634334			0.0317167	−	0.999497i	$-0.489903\pi$
$499$	1.41699			0.0634334			0.0317167	+	0.999497i	$0.489903\pi$
$500$	0.569951	−	11.1658i	0.0254890	−	0.499350i
$501$	19.2915	+	4.83236i	0.861881	+	0.215894i
$502$	−11.7313			−0.523594
$503$		−	8.67963i		−	0.387006i	−0.981100	−	0.193503i	$-0.938015\pi$
$503$		−	8.67963i		−	0.387006i	0.981100	−	0.193503i	$-0.0619848\pi$
$504$	7.93227	+	0.281364i	0.353331	+	0.0125330i
$505$	−7.64575	+	4.24264i	−0.340231	+	0.188795i
$506$			9.30978i			0.413870i
$507$	−5.17302	+	20.6515i	−0.229742	+	0.917164i
$508$		−	10.8127i		−	0.479737i
$509$	−30.1436			−1.33609			−0.668045	−	0.744121i	$-0.732869\pi$
$509$	−30.1436			−1.33609			−0.668045	+	0.744121i	$0.732869\pi$
$510$	−4.45398	+	1.19038i	−0.197225	+	0.0527107i
$511$	−7.29150	+	3.57113i	−0.322557	+	0.157977i
$512$	1.00000			0.0441942
$513$	−17.5203	−	15.8799i	−0.773538	−	0.701113i
$514$		−	14.2098i		−	0.626768i
$515$	−24.5830	+	13.6412i	−1.08326	+	0.601101i
$516$	−7.82087	−	1.95906i	−0.344295	−	0.0862429i
$517$	−12.2748			−0.539847
$518$	−12.5830	−	25.6919i	−0.552866	−	1.12884i
$519$	14.9373	+	3.74166i	0.655673	+	0.164241i
$520$	−1.64575	+	0.913230i	−0.0721710	+	0.0400478i
$521$	23.4626			1.02792			0.513958	−	0.857815i	$-0.328179\pi$
$521$	23.4626			1.02792			0.513958	+	0.857815i	$0.328179\pi$
$522$	−11.2915	+	21.1245i	−0.494216	+	0.924593i
$523$	4.20861			0.184030			0.0920149	−	0.995758i	$-0.470669\pi$
$523$	4.20861			0.184030			0.0920149	+	0.995758i	$0.470669\pi$
$524$	−8.96077			−0.391453
$525$	21.5424	+	7.80539i	0.940188	+	0.340655i
$526$	6.58301			0.287033
$527$	6.58301			0.286760
$528$	4.75216	+	1.19038i	0.206811	+	0.0518045i
$529$	−12.1660			−0.528957
$530$	−24.6025	+	13.6520i	−1.06866	+	0.593004i
$531$	−10.3460	−	5.53019i	−0.448980	−	0.239990i
$532$	−5.29570	−	10.8127i	−0.229598	−	0.468791i
$533$	6.58301			0.285142
$534$	5.41699	−	21.6255i	0.234416	−	0.935825i
$535$		0			0
$536$			4.65489i			0.201061i
$537$	−15.9399	−	3.99282i	−0.687858	−	0.172303i
$538$	24.6025			1.06069
$539$	15.6417	+	12.1382i	0.673737	+	0.522829i
$540$	−2.64575	+	11.3137i	−0.113855	+	0.486864i
$541$	2.00000			0.0859867			0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000			0.0859867			0.0429934	+	0.999075i	$0.486311\pi$
$542$		−	7.48925i		−	0.321691i
$543$	20.2288	+	5.06713i	0.868099	+	0.217452i
$544$		−	1.19038i		−	0.0510369i
$545$	3.91044	−	2.16991i	0.167505	−	0.0929486i
$546$	−0.804028	−	3.77253i	−0.0344092	−	0.161449i
$547$			16.9706i			0.725609i	0.931865	+	0.362804i	$0.118181\pi$
$547$			16.9706i			0.725609i	−0.931865	+	0.362804i	$0.881819\pi$
$548$	9.29150			0.396913
$549$	−14.2565	+	26.6714i	−0.608451	+	1.13831i
$550$	12.0000	+	7.48331i	0.511682	+	0.319090i
$551$	36.3338			1.54787
$552$	1.38527	−	5.53019i	0.0589609	−	0.235381i
$553$	17.3252	−	8.48528i	0.736742	−	0.360831i
$554$		−	15.4676i		−	0.657156i
$555$	40.4575	−	10.8127i	1.71733	−	0.458975i
$556$		−	15.6110i		−	0.662056i
$557$	−7.16601			−0.303634			−0.151817	−	0.988409i	$-0.548512\pi$
$557$	−7.16601			−0.303634			−0.151817	+	0.988409i	$0.548512\pi$
$558$	7.82087	−	14.6315i	0.331084	−	0.619401i
$559$			3.91813i			0.165719i
$560$	−3.38317	+	4.85326i	−0.142965	+	0.205088i
$561$	1.41699	−	5.65685i	0.0598256	−	0.238833i
$562$			20.6235i			0.869949i
$563$		−	18.7605i		−	0.790660i	−0.918539	−	0.395330i	$-0.870630\pi$
$563$		−	18.7605i		−	0.790660i	0.918539	−	0.395330i	$-0.129370\pi$
$564$	7.29150	+	1.82646i	0.307028	+	0.0769079i
$565$	11.7313	−	6.50972i	0.493540	−	0.273866i
$566$	9.74968			0.409810
$567$	−20.5889	−	11.9623i	−0.864652	−	0.502371i
$568$		−	12.6392i		−	0.530328i
$569$		−	11.1362i		−	0.466855i	−0.972374	−	0.233428i	$-0.925006\pi$
$569$		−	11.1362i		−	0.466855i	0.972374	−	0.233428i	$-0.0749942\pi$
$570$	17.0270	−	4.55066i	0.713183	−	0.190606i
$571$	−34.5830			−1.44725			−0.723627	−	0.690191i	$-0.757526\pi$
$571$	−34.5830			−1.44725			−0.723627	+	0.690191i	$0.757526\pi$
$572$		−	2.38075i		−	0.0995442i
$573$	−13.4148	−	3.36028i	−0.560409	−	0.140378i
$574$	18.5830	−	9.10132i	0.775640	−	0.379882i
$575$	8.70850	−	13.9647i	0.363169	−	0.582367i
$576$	−2.64575	−	1.41421i	−0.110240	−	0.0589256i
$577$	−30.9853			−1.28993			−0.644967	−	0.764210i	$-0.723129\pi$
$577$	−30.9853			−1.28993			−0.644967	+	0.764210i	$0.723129\pi$
$578$	15.5830			0.648168
$579$	14.2565	+	3.57113i	0.592479	+	0.148411i
$580$	−8.66259	−	15.6110i	−0.359695	−	0.648213i
$581$	8.96077	+	18.2960i	0.371755	+	0.759048i
$582$	3.41699	−	13.6412i	0.141639	−	0.565444i
$583$		−	35.5901i		−	1.47399i
$584$	3.06871			0.126984
$585$	5.64575	−	0.0887363i	0.233423	−	0.00366880i
$586$		−	11.2712i		−	0.465610i
$587$		−	44.1054i		−	1.82042i	−0.414143	−	0.910212i	$-0.635919\pi$
$587$		−	44.1054i		−	1.82042i	0.414143	−	0.910212i	$-0.364081\pi$
$588$	−7.48537	−	9.53778i	−0.308692	−	0.393331i
$589$	−25.1660			−1.03695
$590$	7.64575	−	4.24264i	0.314771	−	0.174667i
$591$	−7.57551	+	30.2425i	−0.311615	+	1.24401i
$592$			10.8127i			0.444400i
$593$			7.91094i			0.324863i	0.986720	+	0.162432i	$0.0519337\pi$
$593$			7.91094i			0.324863i	−0.986720	+	0.162432i	$0.948066\pi$
$594$	−10.8896	−	9.87000i	−0.446805	−	0.404971i
$595$	5.77721	+	4.02724i	0.236843	+	0.165101i
$596$		−	3.32941i		−	0.136378i
$597$	27.8745	+	6.98233i	1.14083	+	0.285768i
$598$	−2.77053			−0.113296
$599$			18.2960i			0.747556i	0.927518	+	0.373778i	$0.121938\pi$
$599$			18.2960i			0.747556i	−0.927518	+	0.373778i	$0.878062\pi$
$600$	−6.01474	−	6.23080i	−0.245551	−	0.254371i
$601$			11.0604i			0.451162i	0.974224	+	0.225581i	$0.0724281\pi$
$601$			11.0604i			0.451162i	−0.974224	+	0.225581i	$0.927572\pi$
$602$	5.41699	+	11.0604i	0.220780	+	0.450787i
$603$	6.58301	−	12.3157i	0.268081	−	0.501533i
$604$	−22.5830			−0.918889
$605$	5.86565	−	3.25486i	0.238473	−	0.132329i
$606$	−1.64575	+	6.57008i	−0.0668541	+	0.266891i
$607$	23.7608			0.964421			0.482210	−	0.876055i	$-0.339834\pi$
$607$	23.7608			0.964421			0.482210	+	0.876055i	$0.339834\pi$
$608$			4.55066i			0.184554i
$609$	35.7849	−	7.62674i	1.45008	−	0.309051i
$610$	−10.9373	−	19.7103i	−0.442836	−	0.798045i
$611$		−	3.65292i		−	0.147781i
$612$	−1.68345	+	3.14944i	−0.0680493	+	0.127309i
$613$		−	40.0990i		−	1.61958i	−0.586719	−	0.809791i	$-0.699581\pi$
$613$		−	40.0990i		−	1.61958i	0.586719	−	0.809791i	$-0.300419\pi$
$614$	14.8000			0.597280
$615$	7.82087	+	29.2630i	0.315368	+	1.18000i
$616$	−3.29150	−	6.72057i	−0.132618	−	0.270779i
$617$	−4.83399			−0.194609			−0.0973045	−	0.995255i	$-0.531022\pi$
$617$	−4.83399			−0.194609			−0.0973045	+	0.995255i	$0.531022\pi$
$618$	−5.29150	+	21.1245i	−0.212855	+	0.849751i
$619$			0.632534i			0.0254237i	0.999919	+	0.0127118i	$0.00404641\pi$
$619$			0.632534i			0.0254237i	−0.999919	+	0.0127118i	$0.995954\pi$
$620$	6.00000	+	10.8127i	0.240966	+	0.434249i
$621$	−11.4859	+	12.6724i	−0.460915	+	0.508528i
$622$	2.77053			0.111088
$623$	−30.5830	+	14.9785i	−1.22528	+	0.600101i
$624$	−0.354249	+	1.41421i	−0.0141813	+	0.0566139i
$625$	−11.0000	−	22.4499i	−0.440000	−	0.897998i
$626$	8.11905			0.324502
$627$	−5.41699	+	21.6255i	−0.216334	+	0.863637i
$628$	22.6209			0.902672
$629$	12.8712			0.513209
$630$	15.8146	−	8.05601i	0.630068	−	0.320959i
$631$	−20.4575			−0.814401			−0.407200	−	0.913339i	$-0.633495\pi$
$631$	−20.4575			−0.814401			−0.407200	+	0.913339i	$0.633495\pi$
$632$	−7.29150			−0.290040
$633$	8.90796	−	35.5619i	0.354060	−	1.41346i
$634$	−6.00000			−0.238290
$635$	−11.7313	−	21.1412i	−0.465543	−	0.838964i
$636$	−5.29570	+	21.1412i	−0.209988	+	0.838304i
$637$	−3.61226	+	4.65489i	−0.143123	+	0.184433i
$638$	22.5830			0.894070
$639$	−17.8745	+	33.4401i	−0.707105	+	1.32287i
$640$	1.95522	−	1.08495i	0.0772868	−	0.0428866i
$641$			16.7931i			0.663287i	0.943405	+	0.331644i	$0.107603\pi$
$641$			16.7931i			0.663287i	−0.943405	+	0.331644i	$0.892397\pi$
$642$		0			0
$643$	−47.7669			−1.88374			−0.941872	−	0.335971i	$-0.890935\pi$
$643$	−47.7669			−1.88374			−0.941872	+	0.335971i	$0.890935\pi$
$644$	−7.82087	+	3.83039i	−0.308185	+	0.150939i
$645$	−17.4170	+	4.65489i	−0.685793	+	0.183286i
$646$	5.41699			0.213129
$647$			15.4002i			0.605444i	0.953079	+	0.302722i	$0.0978954\pi$
$647$			15.4002i			0.605444i	−0.953079	+	0.302722i	$0.902105\pi$
$648$	5.00000	+	7.48331i	0.196419	+	0.293972i
$649$			11.0604i			0.434158i
$650$	−2.22699	+	3.57113i	−0.0873497	+	0.140071i
$651$	−24.7858	+	5.28253i	−0.971434	+	0.207039i
$652$		0			0
$653$	−19.1660			−0.750024			−0.375012	−	0.927020i	$-0.622361\pi$
$653$	−19.1660			−0.750024			−0.375012	+	0.927020i	$0.622361\pi$
$654$	0.841723	−	3.36028i	0.0329140	−	0.131397i
$655$	−17.5203	+	9.72202i	−0.684573	+	0.379871i
$656$	−7.82087			−0.305354
$657$	−8.11905	−	4.33981i	−0.316754	−	0.169312i
$658$	−5.05034	−	10.3117i	−0.196883	−	0.401994i
$659$		−	32.7617i		−	1.27621i	−0.769948	−	0.638107i	$-0.779718\pi$
$659$		−	32.7617i		−	1.27621i	0.769948	−	0.638107i	$-0.220282\pi$
$660$	10.5830	−	2.82843i	0.411943	−	0.110096i
$661$			0.979531i			0.0380994i	0.999819	+	0.0190497i	$0.00606407\pi$
$661$			0.979531i			0.0380994i	−0.999819	+	0.0190497i	$0.993936\pi$
$662$	8.00000			0.310929
$663$	1.68345	+	0.421689i	0.0653796	+	0.0163770i
$664$		−	7.70010i		−	0.298822i
$665$	−22.0856	−	15.3956i	−0.856441	−	0.597017i
$666$	15.2915	−	28.6078i	0.592534	−	1.10853i
$667$		−	26.2803i		−	1.01758i
$668$			11.4821i			0.444255i
$669$	−2.00000	+	7.98430i	−0.0773245	+	0.308691i
$670$	5.05034	+	9.10132i	0.195112	+	0.351615i
$671$	28.5129			1.10073
$672$	0.955218	+	4.48191i	0.0368483	+	0.172894i
$673$			38.5960i			1.48777i	0.668309	+	0.743883i	$0.267018\pi$
$673$			38.5960i			1.48777i	−0.668309	+	0.743883i	$0.732982\pi$
$674$			22.4499i			0.864740i
$675$	7.10183	+	24.9913i	0.273350	+	0.961915i
$676$	−12.2915			−0.472750
$677$		−	42.4933i		−	1.63315i	−0.577239	−	0.816575i	$-0.695870\pi$
$677$		−	42.4933i		−	1.63315i	0.577239	−	0.816575i	$-0.304130\pi$
$678$	2.52517	−	10.0808i	0.0969785	−	0.387153i
$679$	−19.2915	+	9.44832i	−0.740340	+	0.362593i
$680$	−1.29150	−	2.32744i	−0.0495269	−	0.0892534i
$681$	2.35425	+	0.589720i	0.0902150	+	0.0225981i
$682$	−15.6417			−0.598953
$683$	−5.41699			−0.207276			−0.103638	−	0.994615i	$-0.533048\pi$
$683$	−5.41699			−0.207276			−0.103638	+	0.994615i	$0.533048\pi$
$684$	6.43560	−	12.0399i	0.246071	−	0.460358i
$685$	18.1669	−	10.0808i	0.694122	−	0.385169i
$686$	−3.76135	+	18.1343i	−0.143609	+	0.692370i
$687$	47.5203	+	11.9034i	1.81301	+	0.454144i
$688$		−	4.65489i		−	0.177466i
$689$	10.5914			0.403500
$690$	−3.29150	−	12.3157i	−0.125305	−	0.468850i
$691$			6.50972i			0.247641i	0.992305	+	0.123821i	$0.0395148\pi$
$691$			6.50972i			0.247641i	−0.992305	+	0.123821i	$0.960485\pi$
$692$			8.89047i			0.337965i
$693$	−0.795819	+	22.4358i	−0.0302306	+	0.852267i
$694$	24.0000			0.911028
$695$	−16.9373	−	30.5230i	−0.642467	−	1.15780i
$696$	−13.4148	−	3.36028i	−0.508485	−	0.127371i
$697$			9.30978i			0.352633i
$698$		−	19.1822i		−	0.726056i
$699$	−1.13990	+	4.55066i	−0.0431151	+	0.172122i
$700$	−1.34926	+	13.1598i	−0.0509972	+	0.497392i
$701$			1.32548i			0.0500626i	0.999687	+	0.0250313i	$0.00796854\pi$
$701$			1.32548i			0.0500626i	−0.999687	+	0.0250313i	$0.992031\pi$
$702$	2.93725	−	3.24067i	0.110860	−	0.122311i
$703$	−49.2050			−1.85580
$704$			2.82843i			0.106600i
$705$	16.2381	−	4.33981i	0.611562	−	0.163447i
$706$		−	21.3521i		−	0.803596i
$707$	9.29150	−	4.55066i	0.349443	−	0.171145i
$708$	1.64575	−	6.57008i	0.0618511	−	0.246919i
$709$	20.5830			0.773011			0.386505	−	0.922287i	$-0.373682\pi$
$709$	20.5830			0.773011			0.386505	+	0.922287i	$0.373682\pi$
$710$	−13.7129	−	24.7124i	−0.514637	−	0.927438i
$711$	19.2915	+	10.3117i	0.723488	+	0.386721i
$712$	12.8712			0.482369
$713$			18.2026i			0.681694i
$714$	5.33516	−	1.13707i	0.199663	−	0.0425537i
$715$	−2.58301	−	4.65489i	−0.0965989	−	0.174083i
$716$		−	9.48725i		−	0.354555i
$717$	37.1755	+	9.31216i	1.38835	+	0.347769i
$718$			26.7813i			0.999470i
$719$	36.3338			1.35502			0.677511	−	0.735512i	$-0.263058\pi$
$719$	36.3338			1.35502			0.677511	+	0.735512i	$0.263058\pi$
$720$	−6.70738	+	0.105422i	−0.249969	+	0.00392886i
$721$	29.8745	−	14.6315i	1.11258	−	0.544906i
$722$	−1.70850			−0.0635837
$723$	3.29150	+	0.824494i	0.122412	+	0.0306633i
$724$			12.0399i			0.447460i
$725$	−33.8745	−	21.1245i	−1.25807	−	0.784543i
$726$	1.26258	−	5.04042i	0.0468589	−	0.187068i
$727$	−7.03196			−0.260801			−0.130401	−	0.991461i	$-0.541626\pi$
$727$	−7.03196			−0.260801			−0.130401	+	0.991461i	$0.541626\pi$
$728$	2.00000	−	0.979531i	0.0741249	−	0.0363038i
$729$	−2.64575	−	26.8701i	−0.0979908	−	0.995187i
$730$	6.00000	−	3.32941i	0.222070	−	0.123227i
$731$	−5.54107			−0.204944
$732$	−16.9373	−	4.24264i	−0.626019	−	0.156813i
$733$	24.9007			0.919728			0.459864	−	0.887989i	$-0.347898\pi$
$733$	24.9007			0.919728			0.459864	+	0.887989i	$0.347898\pi$
$734$	8.11905			0.299680
$735$	−24.9836	−	10.5271i	−0.921533	−	0.388299i
$736$	3.29150			0.121326
$737$	−13.1660			−0.484976
$738$	20.6921	+	11.0604i	0.761686	+	0.407138i
$739$	9.16601			0.337177			0.168589	−	0.985687i	$-0.446079\pi$
$739$	9.16601			0.337177			0.168589	+	0.985687i	$0.446079\pi$
$740$	11.7313	+	21.1412i	0.431251	+	0.777167i
$741$	−6.43560	−	1.61206i	−0.236418	−	0.0592207i
$742$	29.8982	−	14.6431i	1.09760	−	0.537566i
$743$	33.8745			1.24274			0.621368	−	0.783519i	$-0.286577\pi$
$743$	33.8745			1.24274			0.621368	+	0.783519i	$0.286577\pi$
$744$	9.29150	+	2.32744i	0.340643	+	0.0853282i
$745$	−3.61226	−	6.50972i	−0.132343	−	0.238498i
$746$			15.4676i			0.566310i
$747$	−10.8896	+	20.3725i	−0.398429	+	0.745392i
$748$	3.36689			0.123106
$749$		0			0
$750$	−18.5203	−	5.65685i	−0.676264	−	0.206559i
$751$	21.1660			0.772359			0.386179	−	0.922424i	$-0.373795\pi$
$751$	21.1660			0.772359			0.386179	+	0.922424i	$0.373795\pi$
$752$			4.33981i			0.158257i
$753$	−4.93725	+	19.7103i	−0.179924	+	0.718282i
$754$			6.72057i			0.244749i
$755$	−44.1547	+	24.5015i	−1.60695	+	0.891701i
$756$	3.81112	−	13.2089i	0.138609	−	0.480404i
$757$		−	3.15194i		−	0.114559i	−0.998358	−	0.0572796i	$-0.981757\pi$
$757$		−	3.15194i		−	0.114559i	0.998358	−	0.0572796i	$-0.0182426\pi$
$758$	14.5830			0.529679
$759$	15.6417	+	3.91813i	0.567759	+	0.142219i
$760$	4.93725	+	8.89753i	0.179093	+	0.322747i
$761$	−20.6921			−0.750087			−0.375044	−	0.927007i	$-0.622372\pi$
$761$	−20.6921			−0.750087			−0.375044	+	0.927007i	$0.622372\pi$
$762$	−18.1669	−	4.55066i	−0.658118	−	0.164853i
$763$	−4.75216	+	2.32744i	−0.172040	+	0.0842591i
$764$		−	7.98430i		−	0.288862i
$765$	0.125492	+	7.98430i	0.00453718	+	0.288673i
$766$			11.4821i			0.414864i
$767$	−3.29150			−0.118849
$768$	0.420861	−	1.68014i	0.0151865	−	0.0606269i
$769$		−	35.1402i		−	1.26719i	−0.773666	−	0.633594i	$-0.781579\pi$
$769$		−	35.1402i		−	1.26719i	0.773666	−	0.633594i	$-0.218421\pi$
$770$	−13.7271	−	9.56904i	−0.494691	−	0.344844i
$771$	−23.8745	−	5.98036i	−0.859819	−	0.215378i
$772$			8.48528i			0.305392i
$773$		−	7.35310i		−	0.264473i	−0.991218	−	0.132236i	$-0.957784\pi$
$773$		−	7.35310i		−	0.264473i	0.991218	−	0.132236i	$-0.0422158\pi$
$774$	−6.58301	+	12.3157i	−0.236621	+	0.442678i
$775$	23.4626	+	14.6315i	0.842802	+	0.525579i
$776$	8.11905			0.291457
$777$	−48.4617	+	10.3285i	−1.73855	+	0.370533i
$778$		−	0.323511i		−	0.0115984i
$779$		−	35.5901i		−	1.27515i
$780$	0.841723	+	3.14944i	0.0301385	+	0.112768i
$781$	35.7490			1.27920
$782$		−	3.91813i		−	0.140112i
$783$	30.7399	+	27.8618i	1.09856	+	0.995699i
$784$	4.29150	−	5.53019i	0.153268	−	0.197507i
$785$	44.2288	−	24.5426i	1.57859	−	0.875963i
$786$	−3.77124	+	15.0554i	−0.134516	+	0.537007i
$787$	24.9007			0.887614			0.443807	−	0.896122i	$-0.353628\pi$
$787$	24.9007			0.887614			0.443807	+	0.896122i	$0.353628\pi$
$788$	−18.0000			−0.641223
$789$	2.77053	−	11.0604i	0.0986336	−	0.393760i
$790$	−14.2565	+	7.91094i	−0.507223	+	0.281459i
$791$	−14.2565	+	6.98233i	−0.506902	+	0.248263i
$792$	4.00000	−	7.48331i	0.142134	−	0.265908i
$793$			8.48528i			0.301321i
$794$	−21.5338			−0.764206
$795$	12.5830	+	47.0813i	0.446273	+	1.66980i
$796$			16.5906i			0.588037i
$797$			6.93141i			0.245523i	0.992436	+	0.122762i	$0.0391750\pi$
$797$			6.93141i			0.245523i	−0.992436	+	0.122762i	$0.960825\pi$
$798$	−20.3957	+	4.34687i	−0.721999	+	0.153878i
$799$	5.16601			0.182760
$800$	2.64575	−	4.24264i	0.0935414	−	0.150000i
$801$	−34.0540	−	18.2026i	−1.20324	−	0.643159i
$802$			7.48331i			0.264245i
$803$			8.67963i			0.306297i
$804$	7.82087	+	1.95906i	0.275821	+	0.0690908i
$805$	−11.1357	+	15.9745i	−0.392482	+	0.563028i
$806$		−	4.65489i		−	0.163961i
$807$	10.3542	−	41.3357i	0.364487	−	1.45509i
$808$	−3.91044			−0.137569
$809$			33.7637i			1.18707i	0.804809	+	0.593533i	$0.202268\pi$
$809$			33.7637i			1.18707i	−0.804809	+	0.593533i	$0.797732\pi$
$810$	17.8951	+	9.20674i	0.628771	+	0.323492i
$811$			28.6305i			1.00535i	0.864475	+	0.502676i	$0.167651\pi$
$811$			28.6305i			1.00535i	−0.864475	+	0.502676i	$0.832349\pi$
$812$	9.29150	+	18.9713i	0.326068	+	0.665763i
$813$	−12.5830	−	3.15194i	−0.441305	−	0.110543i
$814$	−30.5830			−1.07193
$815$		0			0
$816$	−2.00000	−	0.500983i	−0.0700140	−	0.0175379i
$817$	21.1828			0.741093
$818$			13.0194i			0.455214i
$819$	−6.67677	−	0.236831i	−0.233305	−	0.00827554i
$820$	−15.2915	+	8.48528i	−0.534002	+	0.296319i
$821$			5.98036i			0.208716i	0.994540	+	0.104358i	$0.0332788\pi$
$821$			5.98036i			0.208716i	−0.994540	+	0.104358i	$0.966721\pi$
$822$	3.91044	−	15.6110i	0.136392	−	0.544498i
$823$			19.2980i			0.672686i	0.941740	+	0.336343i	$0.109190\pi$
$823$			19.2980i			0.672686i	−0.941740	+	0.336343i	$0.890810\pi$
$824$	−12.5730			−0.438002
$825$	17.6234	−	17.0123i	0.613567	−	0.592291i
$826$	−9.29150	+	4.55066i	−0.323293	+	0.158338i
$827$	−36.0000			−1.25184			−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000			−1.25184			−0.625921	+	0.779886i	$0.715277\pi$
$828$	−8.70850	−	4.65489i	−0.302641	−	0.161769i
$829$		−	45.2211i		−	1.57059i	−0.619120	−	0.785296i	$-0.712511\pi$
$829$		−	45.2211i		−	1.57059i	0.619120	−	0.785296i	$-0.287489\pi$
$830$	−8.35425	−	15.0554i	−0.289980	−	0.522579i
$831$	−25.9878	−	6.50972i	−0.901506	−	0.225820i
$832$	−0.841723			−0.0291815
$833$	−6.58301	−	5.10850i	−0.228088	−	0.176999i
$834$	−26.2288	−	6.57008i	−0.908228	−	0.227503i
$835$	12.4575	+	22.4499i	0.431110	+	0.776912i
$836$	−12.8712			−0.445160
$837$	−21.2915	−	19.2980i	−0.735942	−	0.667037i
$838$	−21.8320			−0.754173
$839$	−26.2331			−0.905669			−0.452834	−	0.891595i	$-0.649587\pi$
$839$	−26.2331			−0.905669			−0.452834	+	0.891595i	$0.649587\pi$
$840$	6.73033	+	7.72675i	0.232218	+	0.266598i
$841$	−34.7490			−1.19824
$842$	−10.0000			−0.344623
$843$	34.6504	+	8.67963i	1.19342	+	0.298942i
$844$	21.1660			0.728564
$845$	−24.0326	+	13.3357i	−0.826745	+	0.458762i
$846$	6.13742	−	11.4821i	0.211009	−	0.394762i
$847$	−7.12824	+	3.49117i	−0.244929	+	0.119958i
$848$	−12.5830			−0.432102
$849$	4.10326	−	16.3808i	0.140824	−	0.562189i
$850$	−5.05034	−	3.14944i	−0.173225	−	0.108025i
$851$			35.5901i			1.22001i
$852$	−21.2356	−	5.31935i	−0.727520	−	0.182238i
$853$	−5.89206			−0.201740			−0.100870	−	0.994900i	$-0.532163\pi$
$853$	−5.89206			−0.201740			−0.100870	+	0.994900i	$0.532163\pi$
$854$	11.7313	+	23.9529i	0.401437	+	0.819651i
$855$	−0.479741	−	30.5230i	−0.0164068	−	1.04386i
$856$		0			0
$857$			24.1545i			0.825103i	0.910934	+	0.412551i	$0.135362\pi$
$857$			24.1545i			0.825103i	−0.910934	+	0.412551i	$0.864638\pi$
$858$	−4.00000	−	1.00197i	−0.136558	−	0.0342066i
$859$			2.59160i			0.0884241i	0.999022	+	0.0442121i	$0.0140777\pi$
$859$			2.59160i			0.0884241i	−0.999022	+	0.0442121i	$0.985922\pi$
$860$	−5.05034	−	9.10132i	−0.172215	−	0.310352i
$861$	−7.47063	−	35.0525i	−0.254598	−	1.19459i
$862$		−	16.4696i		−	0.560956i
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$	−3.48957	+	3.85005i	−0.118718	+	0.130981i
$865$	9.64575	+	17.3828i	0.327965	+	0.591033i
$866$	26.5313			0.901571
$867$	6.55829	−	26.1817i	0.222731	−	0.889176i
$868$	−6.43560	−	13.1402i	−0.218439	−	0.446006i
$869$		−	20.6235i		−	0.699604i
$870$	−29.8745	+	7.98430i	−1.01284	+	0.270693i
$871$		−	3.91813i		−	0.132761i
$872$	2.00000			0.0677285
$873$	−21.4810	−	11.4821i	−0.727021	−	0.388609i
$874$			14.9785i			0.506656i
$875$	11.6396	+	27.1941i	0.393492	+	0.919328i
$876$	1.29150	−	5.15587i	0.0436358	−	0.174201i
$877$			1.50295i			0.0507510i	0.999678	+	0.0253755i	$0.00807814\pi$
$877$			1.50295i			0.0507510i	−0.999678	+	0.0253755i	$0.991922\pi$
$878$			18.5496i			0.626020i
$879$	−18.9373	−	4.74362i	−0.638738	−	0.159998i
$880$	3.06871	+	5.53019i	0.103446	+	0.186423i
$881$	−12.8712			−0.433642			−0.216821	−	0.976211i	$-0.569569\pi$
$881$	−12.8712			−0.433642			−0.216821	+	0.976211i	$0.569569\pi$
$882$	−19.1751	+	8.56241i	−0.645660	+	0.288311i
$883$		−	13.9647i		−	0.469948i	−0.972002	−	0.234974i	$-0.924499\pi$
$883$		−	13.9647i		−	0.469948i	0.972002	−	0.234974i	$-0.0755006\pi$
$884$			1.00197i			0.0336998i
$885$	−3.91044	−	14.6315i	−0.131448	−	0.491833i
$886$	−13.1660			−0.442321
$887$			44.6632i			1.49964i	0.661640	+	0.749822i	$0.269861\pi$
$887$			44.6632i			1.49964i	−0.661640	+	0.749822i	$0.730139\pi$
$888$	18.1669	+	4.55066i	0.609642	+	0.152710i
$889$	12.5830	+	25.6919i	0.422020	+	0.861678i
$890$	25.1660	−	13.9647i	0.843567	−	0.468097i
$891$	−21.1660	+	14.1421i	−0.709088	+	0.473779i
$892$	−4.75216			−0.159114
$893$	−19.7490			−0.660876
$894$	−5.59388	−	1.40122i	−0.187087	−	0.0468638i
$895$	−10.2932	−	18.5496i	−0.344065	−	0.620046i
$896$	−2.37608	+	1.16372i	−0.0793792	+	0.0388772i
$897$	−1.16601	+	4.65489i	−0.0389320	+	0.155422i
$898$			8.30781i			0.277235i
$899$	44.1547			1.47264
$900$	−13.0000	+	7.48331i	−0.433333	+	0.249444i
$901$			14.9785i			0.499006i
$902$		−	22.1208i		−	0.736541i
$903$	20.8628	−	4.44643i	0.694271	−	0.147968i
$904$	6.00000			0.199557
$905$	13.0627	+	23.5406i	0.434220	+	0.782518i
$906$	−9.50432	+	37.9426i	−0.315760	+	1.26056i
$907$		−	33.9411i		−	1.12700i	−0.826117	−	0.563498i	$-0.809455\pi$
$907$		−	33.9411i		−	1.12700i	0.826117	−	0.563498i	$-0.190545\pi$
$908$			1.40122i			0.0465011i
$909$	10.3460	+	5.53019i	0.343156	+	0.183425i
$910$	2.84769	−	4.08510i	0.0944000	−	0.135420i
$911$		−	4.15390i		−	0.137625i	−0.997630	−	0.0688125i	$-0.978079\pi$
$911$		−	4.15390i		−	0.137625i	0.997630	−	0.0688125i	$-0.0219210\pi$
$912$	7.64575	+	1.91520i	0.253176	+	0.0634185i
$913$	21.7792			0.720785
$914$		−	8.48528i		−	0.280668i
$915$	−37.7191	+	10.0808i	−1.24695	+	0.333263i
$916$			28.2835i			0.934513i
$917$	21.2915	−	10.4278i	0.703107	−	0.344358i
$918$	4.58301	+	4.15390i	0.151262	+	0.137099i
$919$	10.1255			0.334009			0.167005	−	0.985956i	$-0.446591\pi$
$919$	10.1255			0.334009			0.167005	+	0.985956i	$0.446591\pi$
$920$	6.43560	−	3.57113i	0.212176	−	0.117737i
$921$	6.22876	−	24.8661i	0.205245	−	0.819367i
$922$	8.96077			0.295107
$923$			10.6387i			0.350177i
$924$	−12.6768	+	2.70176i	−0.417035	+	0.0888815i
$925$	45.8745	+	28.6078i	1.50834	+	0.940618i
$926$		−	23.9529i		−	0.787141i
$927$	33.2651	+	17.7809i	1.09257	+	0.584003i
$928$		−	7.98430i		−	0.262097i
$929$	−30.7928			−1.01028			−0.505139	−	0.863038i	$-0.668559\pi$
$929$	−30.7928			−1.01028			−0.505139	+	0.863038i	$0.668559\pi$
$930$	20.6921	−	5.53019i	0.678520	−	0.181342i
$931$	25.1660	+	19.5292i	0.824783	+	0.640043i
$932$	−2.70850			−0.0887198
$933$	1.16601	−	4.65489i	0.0381735	−	0.152394i
$934$			3.36028i			0.109952i
$935$	6.58301	−	3.65292i	0.215287	−	0.119463i
$936$	2.22699	+	1.19038i	0.0727914	+	0.0389087i
$937$	3.06871			0.100250			0.0501252	−	0.998743i	$-0.484038\pi$
$937$	3.06871			0.100250			0.0501252	+	0.998743i	$0.484038\pi$
$938$	−5.41699	−	11.0604i	−0.176871	−	0.361134i
$939$	3.41699	−	13.6412i	0.111509	−	0.445162i
$940$	4.70850	+	8.48528i	0.153574	+	0.276759i
$941$	40.2443			1.31193			0.655963	−	0.754793i	$-0.272263\pi$
$941$	40.2443			1.31193			0.655963	+	0.754793i	$0.272263\pi$
$942$	9.52026	−	38.0063i	0.310187	−	1.23831i
$943$	−25.7424			−0.838288
$944$	3.91044			0.127274
$945$	−6.87950	−	29.9612i	−0.223790	−	0.974637i
$946$	13.1660			0.428064
$947$	−24.0000			−0.779895			−0.389948	−	0.920837i	$-0.627507\pi$
$947$	−24.0000			−0.779895			−0.389948	+	0.920837i	$0.627507\pi$
$948$	−3.06871	+	12.2508i	−0.0996671	+	0.397886i
$949$	−2.58301			−0.0838479
$950$	19.3068	+	12.0399i	0.626396	+	0.390626i
$951$	−2.52517	+	10.0808i	−0.0818842	+	0.326894i
$952$	1.38527	+	2.82843i	0.0448967	+	0.0916698i
$953$	27.8745			0.902944			0.451472	−	0.892285i	$-0.350899\pi$
$953$	27.8745			0.902944			0.451472	+	0.892285i	$0.350899\pi$
$954$	33.2915	+	17.7951i	1.07785	+	0.576136i
$955$	−8.66259	−	15.6110i	−0.280315	−	0.505161i
$956$			22.1264i			0.715620i
$957$	9.50432	−	37.9426i	0.307231	−	1.22651i
$958$	−39.1044			−1.26340
$959$	−22.0773	+	10.8127i	−0.712915	+	0.349161i
$960$	−1.00000	−	3.74166i	−0.0322749	−	0.120761i
$961$	0.416995			0.0134514
$962$		−	9.10132i		−	0.293438i
$963$		0			0
$964$			1.95906i			0.0630972i
$965$	9.20614	+	16.5906i	0.296356	+	0.534069i
$966$	3.14410	+	14.7522i	0.101160	+	0.474645i
$967$		−	49.4087i		−	1.58888i	−0.607344	−	0.794439i	$-0.707765\pi$
$967$		−	49.4087i		−	1.58888i	0.607344	−	0.794439i	$-0.292235\pi$
$968$	3.00000			0.0964237
$969$	2.27980	−	9.10132i	0.0732379	−	0.292376i
$970$	15.8745	−	8.80879i	0.509700	−	0.282833i
$971$	24.6025			0.789532			0.394766	−	0.918782i	$-0.370826\pi$
$971$	24.6025			0.789532			0.394766	+	0.918782i	$0.370826\pi$
$972$	14.6773	−	5.25127i	0.470776	−	0.168435i
$973$	18.1669	+	37.0931i	0.582404	+	1.18915i
$974$			32.4382i			1.03939i
$975$	5.06275	+	5.24461i	0.162138	+	0.167962i
$976$		−	10.0808i		−	0.322680i
$977$	51.8745			1.65961			0.829806	−	0.558052i	$-0.188451\pi$
$977$	51.8745			1.65961			0.829806	+	0.558052i	$0.188451\pi$
$978$		0			0
$979$			36.4053i			1.16352i
$980$	2.39082	−	15.4688i	0.0763720	−	0.494133i
$981$	−5.29150	−	2.82843i	−0.168945	−	0.0903047i
$982$		−	14.1421i		−	0.451294i
$983$		−	62.0225i		−	1.97821i	−0.147213	−	0.989105i	$-0.547030\pi$
$983$		−	62.0225i		−	1.97821i	0.147213	−	0.989105i	$-0.452970\pi$
$984$	−3.29150	+	13.1402i	−0.104929	+	0.418893i
$985$	−35.1939	+	19.5292i	−1.12137	+	0.622251i
$986$	−9.50432			−0.302679
$987$	−19.4507	+	4.14547i	−0.619122	+	0.131952i
$988$		−	3.83039i		−	0.121861i
$989$		−	15.3216i		−	0.487198i
$990$	−0.298179	−	18.9713i	−0.00947676	−	0.602948i
$991$	−0.708497			−0.0225062			−0.0112531	−	0.999937i	$-0.503582\pi$
$991$	−0.708497			−0.0225062			−0.0112531	+	0.999937i	$0.503582\pi$
$992$			5.53019i			0.175584i
$993$	3.36689	−	13.4411i	0.106845	−	0.426541i
$994$	14.7085	+	30.0317i	0.466525	+	0.952548i
$995$	18.0000	+	32.4382i	0.570638	+	1.02836i
$996$	−12.9373	−	3.24067i	−0.409933	−	0.102685i
$997$	−42.2259			−1.33731			−0.668653	−	0.743574i	$-0.733129\pi$
$997$	−42.2259			−1.33731			−0.668653	+	0.743574i	$0.733129\pi$
$998$	1.41699			0.0448542
$999$	−41.6295	−	37.7318i	−1.31710	−	1.19378i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.d.b.209.5	yes	8
3.2	odd	2		210.2.d.a.209.6	yes	8
4.3	odd	2		1680.2.k.f.209.4		8
5.2	odd	4		1050.2.b.f.251.9		16
5.3	odd	4		1050.2.b.f.251.8		16
5.4	even	2		210.2.d.a.209.4	yes	8
7.6	odd	2	inner	210.2.d.b.209.4	yes	8
12.11	even	2		1680.2.k.e.209.3		8
15.2	even	4		1050.2.b.f.251.7		16
15.8	even	4		1050.2.b.f.251.10		16
15.14	odd	2	inner	210.2.d.b.209.3	yes	8
20.19	odd	2		1680.2.k.e.209.5		8
21.20	even	2		210.2.d.a.209.3	✓	8
28.27	even	2		1680.2.k.f.209.5		8
35.13	even	4		1050.2.b.f.251.1		16
35.27	even	4		1050.2.b.f.251.16		16
35.34	odd	2		210.2.d.a.209.5	yes	8
60.59	even	2		1680.2.k.f.209.6		8
84.83	odd	2		1680.2.k.e.209.6		8
105.62	odd	4		1050.2.b.f.251.2		16
105.83	odd	4		1050.2.b.f.251.15		16
105.104	even	2	inner	210.2.d.b.209.6	yes	8
140.139	even	2		1680.2.k.e.209.4		8
420.419	odd	2		1680.2.k.f.209.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.d.a.209.3	✓	8	21.20	even	2
210.2.d.a.209.4	yes	8	5.4	even	2
210.2.d.a.209.5	yes	8	35.34	odd	2
210.2.d.a.209.6	yes	8	3.2	odd	2
210.2.d.b.209.3	yes	8	15.14	odd	2	inner
210.2.d.b.209.4	yes	8	7.6	odd	2	inner
210.2.d.b.209.5	yes	8	1.1	even	1	trivial
210.2.d.b.209.6	yes	8	105.104	even	2	inner
1050.2.b.f.251.1		16	35.13	even	4
1050.2.b.f.251.2		16	105.62	odd	4
1050.2.b.f.251.7		16	15.2	even	4
1050.2.b.f.251.8		16	5.3	odd	4
1050.2.b.f.251.9		16	5.2	odd	4
1050.2.b.f.251.10		16	15.8	even	4
1050.2.b.f.251.15		16	105.83	odd	4
1050.2.b.f.251.16		16	35.27	even	4
1680.2.k.e.209.3		8	12.11	even	2
1680.2.k.e.209.4		8	140.139	even	2
1680.2.k.e.209.5		8	20.19	odd	2
1680.2.k.e.209.6		8	84.83	odd	2
1680.2.k.f.209.3		8	420.419	odd	2
1680.2.k.f.209.4		8	4.3	odd	2
1680.2.k.f.209.5		8	28.27	even	2
1680.2.k.f.209.6		8	60.59	even	2

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.420861 - 1.68014i) q^{3} +1.00000 q^{4} +(1.95522 - 1.08495i) q^{5} +(0.420861 - 1.68014i) q^{6} +(-2.37608 + 1.16372i) q^{7} +1.00000 q^{8} +(-2.64575 - 1.41421i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(0.420861 - 1.68014i) q^{3} +1.00000 q^{4} +(1.95522 - 1.08495i) q^{5} +(0.420861 - 1.68014i) q^{6} +(-2.37608 + 1.16372i) q^{7} +1.00000 q^{8} +(-2.64575 - 1.41421i) q^{9} +(1.95522 - 1.08495i) q^{10} +2.82843i q^{11} +(0.420861 - 1.68014i) q^{12} -0.841723 q^{13} +(-2.37608 + 1.16372i) q^{14} +(-1.00000 - 3.74166i) q^{15} +1.00000 q^{16} -1.19038i q^{17} +(-2.64575 - 1.41421i) q^{18} +4.55066i q^{19} +(1.95522 - 1.08495i) q^{20} +(0.955218 + 4.48191i) q^{21} +2.82843i q^{22} +3.29150 q^{23} +(0.420861 - 1.68014i) q^{24} +(2.64575 - 4.24264i) q^{25} -0.841723 q^{26} +(-3.48957 + 3.85005i) q^{27} +(-2.37608 + 1.16372i) q^{28} -7.98430i q^{29} +(-1.00000 - 3.74166i) q^{30} +5.53019i q^{31} +1.00000 q^{32} +(4.75216 + 1.19038i) q^{33} -1.19038i q^{34} +(-3.38317 + 4.85326i) q^{35} +(-2.64575 - 1.41421i) q^{36} +10.8127i q^{37} +4.55066i q^{38} +(-0.354249 + 1.41421i) q^{39} +(1.95522 - 1.08495i) q^{40} -7.82087 q^{41} +(0.955218 + 4.48191i) q^{42} -4.65489i q^{43} +2.82843i q^{44} +(-6.70738 + 0.105422i) q^{45} +3.29150 q^{46} +4.33981i q^{47} +(0.420861 - 1.68014i) q^{48} +(4.29150 - 5.53019i) q^{49} +(2.64575 - 4.24264i) q^{50} +(-2.00000 - 0.500983i) q^{51} -0.841723 q^{52} -12.5830 q^{53} +(-3.48957 + 3.85005i) q^{54} +(3.06871 + 5.53019i) q^{55} +(-2.37608 + 1.16372i) q^{56} +(7.64575 + 1.91520i) q^{57} -7.98430i q^{58} +3.91044 q^{59} +(-1.00000 - 3.74166i) q^{60} -10.0808i q^{61} +5.53019i q^{62} +(7.93227 + 0.281364i) q^{63} +1.00000 q^{64} +(-1.64575 + 0.913230i) q^{65} +(4.75216 + 1.19038i) q^{66} +4.65489i q^{67} -1.19038i q^{68} +(1.38527 - 5.53019i) q^{69} +(-3.38317 + 4.85326i) q^{70} -12.6392i q^{71} +(-2.64575 - 1.41421i) q^{72} +3.06871 q^{73} +10.8127i q^{74} +(-6.01474 - 6.23080i) q^{75} +4.55066i q^{76} +(-3.29150 - 6.72057i) q^{77} +(-0.354249 + 1.41421i) q^{78} -7.29150 q^{79} +(1.95522 - 1.08495i) q^{80} +(5.00000 + 7.48331i) q^{81} -7.82087 q^{82} -7.70010i q^{83} +(0.955218 + 4.48191i) q^{84} +(-1.29150 - 2.32744i) q^{85} -4.65489i q^{86} +(-13.4148 - 3.36028i) q^{87} +2.82843i q^{88} +12.8712 q^{89} +(-6.70738 + 0.105422i) q^{90} +(2.00000 - 0.979531i) q^{91} +3.29150 q^{92} +(9.29150 + 2.32744i) q^{93} +4.33981i q^{94} +(4.93725 + 8.89753i) q^{95} +(0.420861 - 1.68014i) q^{96} +8.11905 q^{97} +(4.29150 - 5.53019i) q^{98} +(4.00000 - 7.48331i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^4 + 8 * q^8	\( 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8} - 8 q^{15} + 8 q^{16} - 8 q^{21} - 16 q^{23} - 8 q^{30} + 8 q^{32} - 16 q^{35} - 24 q^{39} - 8 q^{42} - 16 q^{46} - 8 q^{49} - 16 q^{51} - 16 q^{53} + 40 q^{57} - 8 q^{60} - 8 q^{63} + 8 q^{64} + 8 q^{65} - 16 q^{70} + 16 q^{77} - 24 q^{78} - 16 q^{79} + 40 q^{81} - 8 q^{84} + 32 q^{85} + 16 q^{91} - 16 q^{92} + 32 q^{93} - 24 q^{95} - 8 q^{98} + 32 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^4 + 8 * q^8 - 8 * q^15 + 8 * q^16 - 8 * q^21 - 16 * q^23 - 8 * q^30 + 8 * q^32 - 16 * q^35 - 24 * q^39 - 8 * q^42 - 16 * q^46 - 8 * q^49 - 16 * q^51 - 16 * q^53 + 40 * q^57 - 8 * q^60 - 8 * q^63 + 8 * q^64 + 8 * q^65 - 16 * q^70 + 16 * q^77 - 24 * q^78 - 16 * q^79 + 40 * q^81 - 8 * q^84 + 32 * q^85 + 16 * q^91 - 16 * q^92 + 32 * q^93 - 24 * q^95 - 8 * q^98 + 32 * q^99

Introduction

L-functions

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