LMFDB - Embedded newform 836.2.i.b.353.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [836,2,Mod(45,836)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(836, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("836.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 836 = 2^{2} \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	836.i (of order $3$, 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:	$6.67549360898$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			353.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	836.353
Dual form			836.2.i.b.45.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 2.59808i) q^{3} +(0.500000 - 0.866025i) q^{5} -4.00000 q^{7} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 2.59808i) q^{3} +(0.500000 - 0.866025i) q^{5} -4.00000 q^{7} +(-3.00000 - 5.19615i) q^{9} +1.00000 q^{11} +(-0.500000 - 0.866025i) q^{13} +(1.50000 + 2.59808i) q^{15} +(1.50000 - 2.59808i) q^{17} +(4.00000 - 1.73205i) q^{19} +(6.00000 - 10.3923i) q^{21} +(-0.500000 - 0.866025i) q^{23} +(2.00000 + 3.46410i) q^{25} +9.00000 q^{27} +(-4.50000 - 7.79423i) q^{29} +(-1.50000 + 2.59808i) q^{33} +(-2.00000 + 3.46410i) q^{35} +2.00000 q^{37} +3.00000 q^{39} +(1.50000 - 2.59808i) q^{41} +(-0.500000 + 0.866025i) q^{43} -6.00000 q^{45} +(5.50000 + 9.52628i) q^{47} +9.00000 q^{49} +(4.50000 + 7.79423i) q^{51} +(-1.50000 - 2.59808i) q^{53} +(0.500000 - 0.866025i) q^{55} +(-1.50000 + 12.9904i) q^{57} +(4.50000 - 7.79423i) q^{59} +(-0.500000 - 0.866025i) q^{61} +(12.0000 + 20.7846i) q^{63} -1.00000 q^{65} +(-0.500000 - 0.866025i) q^{67} +3.00000 q^{69} +(4.50000 - 7.79423i) q^{71} +(5.50000 - 9.52628i) q^{73} -12.0000 q^{75} -4.00000 q^{77} +(1.50000 - 2.59808i) q^{79} +(-4.50000 + 7.79423i) q^{81} -12.0000 q^{83} +(-1.50000 - 2.59808i) q^{85} +27.0000 q^{87} +(-5.50000 - 9.52628i) q^{89} +(2.00000 + 3.46410i) q^{91} +(0.500000 - 4.33013i) q^{95} +(8.50000 - 14.7224i) q^{97} +(-3.00000 - 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{3} + q^{5} - 8 q^{7} - 6 q^{9}+O(q^{10}) $ 2 * q - 3 * q^3 + q^5 - 8 * q^7 - 6 * q^9	$ 2 q - 3 q^{3} + q^{5} - 8 q^{7} - 6 q^{9} + 2 q^{11} - q^{13} + 3 q^{15} + 3 q^{17} + 8 q^{19} + 12 q^{21} - q^{23} + 4 q^{25} + 18 q^{27} - 9 q^{29} - 3 q^{33} - 4 q^{35} + 4 q^{37} + 6 q^{39} + 3 q^{41} - q^{43} - 12 q^{45} + 11 q^{47} + 18 q^{49} + 9 q^{51} - 3 q^{53} + q^{55} - 3 q^{57} + 9 q^{59} - q^{61} + 24 q^{63} - 2 q^{65} - q^{67} + 6 q^{69} + 9 q^{71} + 11 q^{73} - 24 q^{75} - 8 q^{77} + 3 q^{79} - 9 q^{81} - 24 q^{83} - 3 q^{85} + 54 q^{87} - 11 q^{89} + 4 q^{91} + q^{95} + 17 q^{97} - 6 q^{99}+O(q^{100}) $ 2 * q - 3 * q^3 + q^5 - 8 * q^7 - 6 * q^9 + 2 * q^11 - q^13 + 3 * q^15 + 3 * q^17 + 8 * q^19 + 12 * q^21 - q^23 + 4 * q^25 + 18 * q^27 - 9 * q^29 - 3 * q^33 - 4 * q^35 + 4 * q^37 + 6 * q^39 + 3 * q^41 - q^43 - 12 * q^45 + 11 * q^47 + 18 * q^49 + 9 * q^51 - 3 * q^53 + q^55 - 3 * q^57 + 9 * q^59 - q^61 + 24 * q^63 - 2 * q^65 - q^67 + 6 * q^69 + 9 * q^71 + 11 * q^73 - 24 * q^75 - 8 * q^77 + 3 * q^79 - 9 * q^81 - 24 * q^83 - 3 * q^85 + 54 * q^87 - 11 * q^89 + 4 * q^91 + q^95 + 17 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/836\mathbb{Z}\right)^\times$.

$n$	$419$	$705$	$761$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.50000	+	2.59808i	−0.866025	+	1.50000i			1.00000i	$0.5\pi$
$3$	−1.50000	+	2.59808i	−0.866025	+	1.50000i	−0.866025	+	0.500000i	$0.833333\pi$
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	−0.732294	−	0.680989i	$-0.761550\pi$
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	0.955901	+	0.293691i	$0.0948835\pi$
$6$		0			0
$7$	−4.00000			−1.51186			−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−4.00000			−1.51186			−0.755929	+	0.654654i	$0.772814\pi$
$8$		0			0
$9$	−3.00000	−	5.19615i	−1.00000	−	1.73205i
$10$		0			0
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$		0			0
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	0.788320	−	0.615265i	$-0.210951\pi$
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	−0.926995	+	0.375073i	$0.877618\pi$
$14$		0			0
$15$	1.50000	+	2.59808i	0.387298	+	0.670820i
$16$		0			0
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$		0			0
$19$	4.00000	−	1.73205i	0.917663	−	0.397360i
$19$	4.00000	−	1.73205i	0.917663	−	0.397360i
$20$		0			0
$21$	6.00000	−	10.3923i	1.30931	−	2.26779i
$22$		0			0
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i	0.809177	−	0.587565i	$-0.199913\pi$
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i	−0.913434	+	0.406986i	$0.866580\pi$
$24$		0			0
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$		0			0
$27$	9.00000			1.73205
$28$		0			0
$29$	−4.50000	−	7.79423i	−0.835629	−	1.44735i	−0.893517	−	0.449029i	$-0.851770\pi$
$29$	−4.50000	−	7.79423i	−0.835629	−	1.44735i	0.0578882	−	0.998323i	$-0.481563\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$		0			0
$33$	−1.50000	+	2.59808i	−0.261116	+	0.452267i
$34$		0			0
$35$	−2.00000	+	3.46410i	−0.338062	+	0.585540i
$36$		0			0
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$		0			0
$39$	3.00000			0.480384
$40$		0			0
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	−0.724797	−	0.688963i	$-0.758066\pi$
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	0.959058	+	0.283211i	$0.0913998\pi$
$42$		0			0
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	−0.901629	−	0.432511i	$-0.857628\pi$
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	0.825380	+	0.564578i	$0.190961\pi$
$44$		0			0
$45$	−6.00000			−0.894427
$46$		0			0
$47$	5.50000	+	9.52628i	0.802257	+	1.38955i	0.918127	+	0.396286i	$0.129701\pi$
$47$	5.50000	+	9.52628i	0.802257	+	1.38955i	−0.115870	+	0.993264i	$0.536965\pi$
$48$		0			0
$49$	9.00000			1.28571
$50$		0			0
$51$	4.50000	+	7.79423i	0.630126	+	1.09141i
$52$		0			0
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	0.744423	−	0.667708i	$-0.232725\pi$
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	−0.950464	+	0.310835i	$0.899391\pi$
$54$		0			0
$55$	0.500000	−	0.866025i	0.0674200	−	0.116775i
$56$		0			0
$57$	−1.50000	+	12.9904i	−0.198680	+	1.72062i
$58$		0			0
$59$	4.50000	−	7.79423i	0.585850	−	1.01472i	−0.408919	−	0.912571i	$-0.634094\pi$
$59$	4.50000	−	7.79423i	0.585850	−	1.01472i	0.994769	−	0.102151i	$-0.0325726\pi$
$60$		0			0
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	0.832240	−	0.554416i	$-0.187058\pi$
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	−0.896258	+	0.443533i	$0.853725\pi$
$62$		0			0
$63$	12.0000	+	20.7846i	1.51186	+	2.61861i
$64$		0			0
$65$	−1.00000			−0.124035
$66$		0			0
$67$	−0.500000	−	0.866025i	−0.0610847	−	0.105802i	0.833866	−	0.551967i	$-0.186123\pi$
$67$	−0.500000	−	0.866025i	−0.0610847	−	0.105802i	−0.894951	+	0.446165i	$0.852789\pi$
$68$		0			0
$69$	3.00000			0.361158
$70$		0			0
$71$	4.50000	−	7.79423i	0.534052	−	0.925005i	−0.465157	−	0.885228i	$-0.654002\pi$
$71$	4.50000	−	7.79423i	0.534052	−	0.925005i	0.999209	−	0.0397765i	$-0.0126646\pi$
$72$		0			0
$73$	5.50000	−	9.52628i	0.643726	−	1.11497i	−0.340868	−	0.940111i	$-0.610721\pi$
$73$	5.50000	−	9.52628i	0.643726	−	1.11497i	0.984594	−	0.174855i	$-0.0559458\pi$
$74$		0			0
$75$	−12.0000			−1.38564
$76$		0			0
$77$	−4.00000			−0.455842
$78$		0			0
$79$	1.50000	−	2.59808i	0.168763	−	0.292306i	−0.769222	−	0.638982i	$-0.779356\pi$
$79$	1.50000	−	2.59808i	0.168763	−	0.292306i	0.937985	+	0.346675i	$0.112689\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$		0			0
$85$	−1.50000	−	2.59808i	−0.162698	−	0.281801i
$86$		0			0
$87$	27.0000			2.89470
$88$		0			0
$89$	−5.50000	−	9.52628i	−0.582999	−	1.00978i	−0.995122	−	0.0986553i	$-0.968546\pi$
$89$	−5.50000	−	9.52628i	−0.582999	−	1.00978i	0.412123	−	0.911128i	$-0.364787\pi$
$90$		0			0
$91$	2.00000	+	3.46410i	0.209657	+	0.363137i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.500000	−	4.33013i	0.0512989	−	0.444262i
$96$		0			0
$97$	8.50000	−	14.7224i	0.863044	−	1.49484i	−0.00593185	−	0.999982i	$-0.501888\pi$
$97$	8.50000	−	14.7224i	0.863044	−	1.49484i	0.868976	−	0.494854i	$-0.164778\pi$
$98$		0			0
$99$	−3.00000	−	5.19615i	−0.301511	−	0.522233i
$100$		0			0
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	0.930953	−	0.365140i	$-0.118979\pi$
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	−0.781697	+	0.623658i	$0.785646\pi$
$102$		0			0
$103$	−16.0000			−1.57653			−0.788263	−	0.615338i	$-0.789020\pi$
$103$	−16.0000			−1.57653			−0.788263	+	0.615338i	$0.789020\pi$
$104$		0			0
$105$	−6.00000	−	10.3923i	−0.585540	−	1.01419i
$106$		0			0
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$		0			0
$109$	−6.50000	+	11.2583i	−0.622587	+	1.07835i	0.366415	+	0.930451i	$0.380585\pi$
$109$	−6.50000	+	11.2583i	−0.622587	+	1.07835i	−0.989002	+	0.147901i	$0.952748\pi$
$110$		0			0
$111$	−3.00000	+	5.19615i	−0.284747	+	0.493197i
$112$		0			0
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$		0			0
$115$	−1.00000			−0.0932505
$116$		0			0
$117$	−3.00000	+	5.19615i	−0.277350	+	0.480384i
$118$		0			0
$119$	−6.00000	+	10.3923i	−0.550019	+	0.952661i
$120$		0			0
$121$	1.00000			0.0909091
$122$		0			0
$123$	4.50000	+	7.79423i	0.405751	+	0.702782i
$124$		0			0
$125$	9.00000			0.804984
$126$		0			0
$127$	−9.50000	−	16.4545i	−0.842989	−	1.46010i	−0.887357	−	0.461084i	$-0.847461\pi$
$127$	−9.50000	−	16.4545i	−0.842989	−	1.46010i	0.0443678	−	0.999015i	$-0.485873\pi$
$128$		0			0
$129$	−1.50000	−	2.59808i	−0.132068	−	0.228748i
$130$		0			0
$131$	−0.500000	+	0.866025i	−0.0436852	+	0.0756650i	−0.887041	−	0.461690i	$-0.847243\pi$
$131$	−0.500000	+	0.866025i	−0.0436852	+	0.0756650i	0.843356	+	0.537355i	$0.180577\pi$
$132$		0			0
$133$	−16.0000	+	6.92820i	−1.38738	+	0.600751i
$134$		0			0
$135$	4.50000	−	7.79423i	0.387298	−	0.670820i
$136$		0			0
$137$	8.50000	+	14.7224i	0.726204	+	1.25782i	0.958477	+	0.285171i	$0.0920506\pi$
$137$	8.50000	+	14.7224i	0.726204	+	1.25782i	−0.232273	+	0.972651i	$0.574616\pi$
$138$		0			0
$139$	−3.50000	−	6.06218i	−0.296866	−	0.514187i	0.678551	−	0.734553i	$-0.262608\pi$
$139$	−3.50000	−	6.06218i	−0.296866	−	0.514187i	−0.975417	+	0.220366i	$0.929275\pi$
$140$		0			0
$141$	−33.0000			−2.77910
$142$		0			0
$143$	−0.500000	−	0.866025i	−0.0418121	−	0.0724207i
$144$		0			0
$145$	−9.00000			−0.747409
$146$		0			0
$147$	−13.5000	+	23.3827i	−1.11346	+	1.92857i
$148$		0			0
$149$	7.50000	−	12.9904i	0.614424	−	1.06421i	−0.376061	−	0.926595i	$-0.622722\pi$
$149$	7.50000	−	12.9904i	0.614424	−	1.06421i	0.990485	−	0.137619i	$-0.0439449\pi$
$150$		0			0
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$		0			0
$153$	−18.0000			−1.45521
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	−0.971219	−	0.238190i	$-0.923446\pi$
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	0.691888	+	0.722005i	$0.256779\pi$
$158$		0			0
$159$	9.00000			0.713746
$160$		0			0
$161$	2.00000	+	3.46410i	0.157622	+	0.273009i
$162$		0			0
$163$	−24.0000			−1.87983			−0.939913	−	0.341415i	$-0.889094\pi$
$163$	−24.0000			−1.87983			−0.939913	+	0.341415i	$0.889094\pi$
$164$		0			0
$165$	1.50000	+	2.59808i	0.116775	+	0.202260i
$166$		0			0
$167$	−11.5000	−	19.9186i	−0.889897	−	1.54135i	−0.839996	−	0.542592i	$-0.817443\pi$
$167$	−11.5000	−	19.9186i	−0.889897	−	1.54135i	−0.0499004	−	0.998754i	$-0.515890\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$		0			0
$171$	−21.0000	−	15.5885i	−1.60591	−	1.19208i
$172$		0			0
$173$	−2.50000	+	4.33013i	−0.190071	+	0.329213i	−0.945274	−	0.326278i	$-0.894205\pi$
$173$	−2.50000	+	4.33013i	−0.190071	+	0.329213i	0.755202	+	0.655492i	$0.227539\pi$
$174$		0			0
$175$	−8.00000	−	13.8564i	−0.604743	−	1.04745i
$176$		0			0
$177$	13.5000	+	23.3827i	1.01472	+	1.75755i
$178$		0			0
$179$	−4.00000			−0.298974			−0.149487	−	0.988764i	$-0.547762\pi$
$179$	−4.00000			−0.298974			−0.149487	+	0.988764i	$0.547762\pi$
$180$		0			0
$181$	−11.5000	−	19.9186i	−0.854788	−	1.48054i	−0.876841	−	0.480780i	$-0.840354\pi$
$181$	−11.5000	−	19.9186i	−0.854788	−	1.48054i	0.0220530	−	0.999757i	$-0.492980\pi$
$182$		0			0
$183$	3.00000			0.221766
$184$		0			0
$185$	1.00000	−	1.73205i	0.0735215	−	0.127343i
$186$		0			0
$187$	1.50000	−	2.59808i	0.109691	−	0.189990i
$188$		0			0
$189$	−36.0000			−2.61861
$190$		0			0
$191$	−12.0000			−0.868290			−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000			−0.868290			−0.434145	+	0.900843i	$0.642949\pi$
$192$		0			0
$193$	−10.5000	+	18.1865i	−0.755807	+	1.30910i	0.189166	+	0.981945i	$0.439422\pi$
$193$	−10.5000	+	18.1865i	−0.755807	+	1.30910i	−0.944972	+	0.327150i	$0.893912\pi$
$194$		0			0
$195$	1.50000	−	2.59808i	0.107417	−	0.186052i
$196$		0			0
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$		0			0
$199$	7.50000	+	12.9904i	0.531661	+	0.920864i	0.999317	+	0.0369532i	$0.0117652\pi$
$199$	7.50000	+	12.9904i	0.531661	+	0.920864i	−0.467656	+	0.883911i	$0.654901\pi$
$200$		0			0
$201$	3.00000			0.211604
$202$		0			0
$203$	18.0000	+	31.1769i	1.26335	+	2.18819i
$204$		0			0
$205$	−1.50000	−	2.59808i	−0.104765	−	0.181458i
$206$		0			0
$207$	−3.00000	+	5.19615i	−0.208514	+	0.361158i
$208$		0			0
$209$	4.00000	−	1.73205i	0.276686	−	0.119808i
$210$		0			0
$211$	13.5000	−	23.3827i	0.929378	−	1.60973i	0.145014	−	0.989430i	$-0.453677\pi$
$211$	13.5000	−	23.3827i	0.929378	−	1.60973i	0.784364	−	0.620301i	$-0.212990\pi$
$212$		0			0
$213$	13.5000	+	23.3827i	0.925005	+	1.60216i
$214$		0			0
$215$	0.500000	+	0.866025i	0.0340997	+	0.0590624i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	16.5000	+	28.5788i	1.11497	+	1.93118i
$220$		0			0
$221$	−3.00000			−0.201802
$222$		0			0
$223$	0.500000	−	0.866025i	0.0334825	−	0.0579934i	−0.848799	−	0.528716i	$-0.822674\pi$
$223$	0.500000	−	0.866025i	0.0334825	−	0.0579934i	0.882281	+	0.470723i	$0.156007\pi$
$224$		0			0
$225$	12.0000	−	20.7846i	0.800000	−	1.38564i
$226$		0			0
$227$	8.00000			0.530979			0.265489	−	0.964114i	$-0.414466\pi$
$227$	8.00000			0.530979			0.265489	+	0.964114i	$0.414466\pi$
$228$		0			0
$229$	−22.0000			−1.45380			−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000			−1.45380			−0.726900	+	0.686743i	$0.759040\pi$
$230$		0			0
$231$	6.00000	−	10.3923i	0.394771	−	0.683763i
$232$		0			0
$233$	7.50000	−	12.9904i	0.491341	−	0.851028i	−0.508609	−	0.860998i	$-0.669840\pi$
$233$	7.50000	−	12.9904i	0.491341	−	0.851028i	0.999950	+	0.00996947i	$0.00317343\pi$
$234$		0			0
$235$	11.0000			0.717561
$236$		0			0
$237$	4.50000	+	7.79423i	0.292306	+	0.506290i
$238$		0			0
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	−2.50000	−	4.33013i	−0.161039	−	0.278928i	0.774202	−	0.632938i	$-0.218151\pi$
$241$	−2.50000	−	4.33013i	−0.161039	−	0.278928i	−0.935242	+	0.354010i	$0.884818\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	4.50000	−	7.79423i	0.287494	−	0.497955i
$246$		0			0
$247$	−3.50000	−	2.59808i	−0.222700	−	0.165312i
$248$		0			0
$249$	18.0000	−	31.1769i	1.14070	−	1.97576i
$250$		0			0
$251$	7.50000	+	12.9904i	0.473396	+	0.819946i	0.999536	−	0.0304521i	$-0.00969471\pi$
$251$	7.50000	+	12.9904i	0.473396	+	0.819946i	−0.526140	+	0.850398i	$0.676361\pi$
$252$		0			0
$253$	−0.500000	−	0.866025i	−0.0314347	−	0.0544466i
$254$		0			0
$255$	9.00000			0.563602
$256$		0			0
$257$	6.50000	+	11.2583i	0.405459	+	0.702275i	0.994375	−	0.105919i	$-0.0337784\pi$
$257$	6.50000	+	11.2583i	0.405459	+	0.702275i	−0.588916	+	0.808194i	$0.700445\pi$
$258$		0			0
$259$	−8.00000			−0.497096
$260$		0			0
$261$	−27.0000	+	46.7654i	−1.67126	+	2.89470i
$262$		0			0
$263$	−10.5000	+	18.1865i	−0.647458	+	1.12143i	0.336270	+	0.941766i	$0.390834\pi$
$263$	−10.5000	+	18.1865i	−0.647458	+	1.12143i	−0.983728	+	0.179664i	$0.942499\pi$
$264$		0			0
$265$	−3.00000			−0.184289
$266$		0			0
$267$	33.0000			2.01957
$268$		0			0
$269$	−5.50000	+	9.52628i	−0.335341	+	0.580828i	−0.983550	−	0.180635i	$-0.942185\pi$
$269$	−5.50000	+	9.52628i	−0.335341	+	0.580828i	0.648209	+	0.761462i	$0.275518\pi$
$270$		0			0
$271$	7.50000	−	12.9904i	0.455593	−	0.789109i	−0.543130	−	0.839649i	$-0.682761\pi$
$271$	7.50000	−	12.9904i	0.455593	−	0.789109i	0.998722	+	0.0505395i	$0.0160941\pi$
$272$		0			0
$273$	−12.0000			−0.726273
$274$		0			0
$275$	2.00000	+	3.46410i	0.120605	+	0.208893i
$276$		0			0
$277$	−10.0000			−0.600842			−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000			−0.600842			−0.300421	+	0.953807i	$0.597127\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	9.50000	+	16.4545i	0.566722	+	0.981592i	0.996887	+	0.0788417i	$0.0251222\pi$
$281$	9.50000	+	16.4545i	0.566722	+	0.981592i	−0.430165	+	0.902750i	$0.641545\pi$
$282$		0			0
$283$	11.5000	−	19.9186i	0.683604	−	1.18404i	−0.290269	−	0.956945i	$-0.593745\pi$
$283$	11.5000	−	19.9186i	0.683604	−	1.18404i	0.973873	−	0.227092i	$-0.0729218\pi$
$284$		0			0
$285$	10.5000	+	7.79423i	0.621966	+	0.461690i
$286$		0			0
$287$	−6.00000	+	10.3923i	−0.354169	+	0.613438i
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	25.5000	+	44.1673i	1.49484	+	2.58913i
$292$		0			0
$293$	−2.00000			−0.116841			−0.0584206	−	0.998292i	$-0.518606\pi$
$293$	−2.00000			−0.116841			−0.0584206	+	0.998292i	$0.518606\pi$
$294$		0			0
$295$	−4.50000	−	7.79423i	−0.262000	−	0.453798i
$296$		0			0
$297$	9.00000			0.522233
$298$		0			0
$299$	−0.500000	+	0.866025i	−0.0289157	+	0.0500835i
$300$		0			0
$301$	2.00000	−	3.46410i	0.115278	−	0.199667i
$302$		0			0
$303$	−9.00000			−0.517036
$304$		0			0
$305$	−1.00000			−0.0572598
$306$		0			0
$307$	−0.500000	+	0.866025i	−0.0285365	+	0.0494267i	−0.879941	−	0.475083i	$-0.842418\pi$
$307$	−0.500000	+	0.866025i	−0.0285365	+	0.0494267i	0.851404	+	0.524510i	$0.175751\pi$
$308$		0			0
$309$	24.0000	−	41.5692i	1.36531	−	2.36479i
$310$		0			0
$311$	8.00000			0.453638			0.226819	−	0.973937i	$-0.427167\pi$
$311$	8.00000			0.453638			0.226819	+	0.973937i	$0.427167\pi$
$312$		0			0
$313$	10.5000	+	18.1865i	0.593495	+	1.02796i	0.993757	+	0.111563i	$0.0355857\pi$
$313$	10.5000	+	18.1865i	0.593495	+	1.02796i	−0.400262	+	0.916401i	$0.631081\pi$
$314$		0			0
$315$	24.0000			1.35225
$316$		0			0
$317$	16.5000	+	28.5788i	0.926732	+	1.60515i	0.788751	+	0.614713i	$0.210728\pi$
$317$	16.5000	+	28.5788i	0.926732	+	1.60515i	0.137981	+	0.990435i	$0.455939\pi$
$318$		0			0
$319$	−4.50000	−	7.79423i	−0.251952	−	0.436393i
$320$		0			0
$321$	−18.0000	+	31.1769i	−1.00466	+	1.74013i
$322$		0			0
$323$	1.50000	−	12.9904i	0.0834622	−	0.722804i
$324$		0			0
$325$	2.00000	−	3.46410i	0.110940	−	0.192154i
$326$		0			0
$327$	−19.5000	−	33.7750i	−1.07835	−	1.86776i
$328$		0			0
$329$	−22.0000	−	38.1051i	−1.21290	−	2.10080i
$330$		0			0
$331$		0			0			−	1.00000i	$-0.5\pi$
$331$		0			0				1.00000i	$0.5\pi$
$332$		0			0
$333$	−6.00000	−	10.3923i	−0.328798	−	0.569495i
$334$		0			0
$335$	−1.00000			−0.0546358
$336$		0			0
$337$	−6.50000	+	11.2583i	−0.354078	+	0.613280i	−0.986960	−	0.160968i	$-0.948538\pi$
$337$	−6.50000	+	11.2583i	−0.354078	+	0.613280i	0.632882	+	0.774248i	$0.281872\pi$
$338$		0			0
$339$	−9.00000	+	15.5885i	−0.488813	+	0.846649i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−8.00000			−0.431959
$344$		0			0
$345$	1.50000	−	2.59808i	0.0807573	−	0.139876i
$346$		0			0
$347$	7.50000	−	12.9904i	0.402621	−	0.697360i	−0.591420	−	0.806363i	$-0.701433\pi$
$347$	7.50000	−	12.9904i	0.402621	−	0.697360i	0.994041	+	0.109003i	$0.0347659\pi$
$348$		0			0
$349$	−26.0000			−1.39175			−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000			−1.39175			−0.695874	+	0.718164i	$0.744983\pi$
$350$		0			0
$351$	−4.50000	−	7.79423i	−0.240192	−	0.416025i
$352$		0			0
$353$	−14.0000			−0.745145			−0.372572	−	0.928003i	$-0.621524\pi$
$353$	−14.0000			−0.745145			−0.372572	+	0.928003i	$0.621524\pi$
$354$		0			0
$355$	−4.50000	−	7.79423i	−0.238835	−	0.413675i
$356$		0			0
$357$	−18.0000	−	31.1769i	−0.952661	−	1.65006i
$358$		0			0
$359$	17.5000	−	30.3109i	0.923615	−	1.59975i	0.129841	−	0.991535i	$-0.458553\pi$
$359$	17.5000	−	30.3109i	0.923615	−	1.59975i	0.793774	−	0.608213i	$-0.208113\pi$
$360$		0			0
$361$	13.0000	−	13.8564i	0.684211	−	0.729285i
$362$		0			0
$363$	−1.50000	+	2.59808i	−0.0787296	+	0.136364i
$364$		0			0
$365$	−5.50000	−	9.52628i	−0.287883	−	0.498628i
$366$		0			0
$367$	−14.5000	−	25.1147i	−0.756894	−	1.31098i	−0.944427	−	0.328720i	$-0.893383\pi$
$367$	−14.5000	−	25.1147i	−0.756894	−	1.31098i	0.187533	−	0.982258i	$-0.439951\pi$
$368$		0			0
$369$	−18.0000			−0.937043
$370$		0			0
$371$	6.00000	+	10.3923i	0.311504	+	0.539542i
$372$		0			0
$373$	38.0000			1.96757			0.983783	−	0.179364i	$-0.0574041\pi$
$373$	38.0000			1.96757			0.983783	+	0.179364i	$0.0574041\pi$
$374$		0			0
$375$	−13.5000	+	23.3827i	−0.697137	+	1.20748i
$376$		0			0
$377$	−4.50000	+	7.79423i	−0.231762	+	0.401423i
$378$		0			0
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$		0			0
$381$	57.0000			2.92020
$382$		0			0
$383$	−7.50000	+	12.9904i	−0.383232	+	0.663777i	−0.991522	−	0.129937i	$-0.958522\pi$
$383$	−7.50000	+	12.9904i	−0.383232	+	0.663777i	0.608290	+	0.793715i	$0.291856\pi$
$384$		0			0
$385$	−2.00000	+	3.46410i	−0.101929	+	0.176547i
$386$		0			0
$387$	6.00000			0.304997
$388$		0			0
$389$	−1.50000	−	2.59808i	−0.0760530	−	0.131728i	0.825491	−	0.564416i	$-0.190898\pi$
$389$	−1.50000	−	2.59808i	−0.0760530	−	0.131728i	−0.901544	+	0.432688i	$0.857565\pi$
$390$		0			0
$391$	−3.00000			−0.151717
$392$		0			0
$393$	−1.50000	−	2.59808i	−0.0756650	−	0.131056i
$394$		0			0
$395$	−1.50000	−	2.59808i	−0.0754732	−	0.130723i
$396$		0			0
$397$	−5.50000	+	9.52628i	−0.276037	+	0.478110i	−0.970396	−	0.241518i	$-0.922355\pi$
$397$	−5.50000	+	9.52628i	−0.276037	+	0.478110i	0.694359	+	0.719629i	$0.255688\pi$
$398$		0			0
$399$	6.00000	−	51.9615i	0.300376	−	2.60133i
$400$		0			0
$401$	18.5000	−	32.0429i	0.923846	−	1.60015i	0.130439	−	0.991456i	$-0.458361\pi$
$401$	18.5000	−	32.0429i	0.923846	−	1.60015i	0.793407	−	0.608692i	$-0.208305\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	4.50000	+	7.79423i	0.223607	+	0.387298i
$406$		0			0
$407$	2.00000			0.0991363
$408$		0			0
$409$	3.50000	+	6.06218i	0.173064	+	0.299755i	0.939490	−	0.342578i	$-0.111300\pi$
$409$	3.50000	+	6.06218i	0.173064	+	0.299755i	−0.766426	+	0.642333i	$0.777967\pi$
$410$		0			0
$411$	−51.0000			−2.51564
$412$		0			0
$413$	−18.0000	+	31.1769i	−0.885722	+	1.53412i
$414$		0			0
$415$	−6.00000	+	10.3923i	−0.294528	+	0.510138i
$416$		0			0
$417$	21.0000			1.02837
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	−17.5000	+	30.3109i	−0.852898	+	1.47726i	0.0256838	+	0.999670i	$0.491824\pi$
$421$	−17.5000	+	30.3109i	−0.852898	+	1.47726i	−0.878582	+	0.477592i	$0.841510\pi$
$422$		0			0
$423$	33.0000	−	57.1577i	1.60451	−	2.77910i
$424$		0			0
$425$	12.0000			0.582086
$426$		0			0
$427$	2.00000	+	3.46410i	0.0967868	+	0.167640i
$428$		0			0
$429$	3.00000			0.144841
$430$		0			0
$431$	14.5000	+	25.1147i	0.698440	+	1.20973i	0.969007	+	0.247033i	$0.0794556\pi$
$431$	14.5000	+	25.1147i	0.698440	+	1.20973i	−0.270567	+	0.962701i	$0.587211\pi$
$432$		0			0
$433$	−9.50000	−	16.4545i	−0.456541	−	0.790752i	0.542234	−	0.840227i	$-0.317578\pi$
$433$	−9.50000	−	16.4545i	−0.456541	−	0.790752i	−0.998775	+	0.0494752i	$0.984245\pi$
$434$		0			0
$435$	13.5000	−	23.3827i	0.647275	−	1.12111i
$436$		0			0
$437$	−3.50000	−	2.59808i	−0.167428	−	0.124283i
$438$		0			0
$439$	13.5000	−	23.3827i	0.644320	−	1.11599i	−0.340138	−	0.940375i	$-0.610474\pi$
$439$	13.5000	−	23.3827i	0.644320	−	1.11599i	0.984458	−	0.175619i	$-0.0561928\pi$
$440$		0			0
$441$	−27.0000	−	46.7654i	−1.28571	−	2.22692i
$442$		0			0
$443$	19.5000	+	33.7750i	0.926473	+	1.60470i	0.789175	+	0.614168i	$0.210508\pi$
$443$	19.5000	+	33.7750i	0.926473	+	1.60470i	0.137298	+	0.990530i	$0.456158\pi$
$444$		0			0
$445$	−11.0000			−0.521450
$446$		0			0
$447$	22.5000	+	38.9711i	1.06421	+	1.84327i
$448$		0			0
$449$	18.0000			0.849473			0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000			0.849473			0.424736	+	0.905317i	$0.360367\pi$
$450$		0			0
$451$	1.50000	−	2.59808i	0.0706322	−	0.122339i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	4.00000			0.187523
$456$		0			0
$457$	22.0000			1.02912			0.514558	−	0.857455i	$-0.327956\pi$
$457$	22.0000			1.02912			0.514558	+	0.857455i	$0.327956\pi$
$458$		0			0
$459$	13.5000	−	23.3827i	0.630126	−	1.09141i
$460$		0			0
$461$	3.50000	−	6.06218i	0.163011	−	0.282344i	−0.772936	−	0.634484i	$-0.781213\pi$
$461$	3.50000	−	6.06218i	0.163011	−	0.282344i	0.935947	+	0.352140i	$0.114546\pi$
$462$		0			0
$463$	8.00000			0.371792			0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000			0.371792			0.185896	+	0.982569i	$0.440481\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−28.0000			−1.29569			−0.647843	−	0.761774i	$-0.724329\pi$
$467$	−28.0000			−1.29569			−0.647843	+	0.761774i	$0.724329\pi$
$468$		0			0
$469$	2.00000	+	3.46410i	0.0923514	+	0.159957i
$470$		0			0
$471$	−10.5000	−	18.1865i	−0.483814	−	0.837991i
$472$		0			0
$473$	−0.500000	+	0.866025i	−0.0229900	+	0.0398199i
$474$		0			0
$475$	14.0000	+	10.3923i	0.642364	+	0.476832i
$476$		0			0
$477$	−9.00000	+	15.5885i	−0.412082	+	0.713746i
$478$		0			0
$479$	12.5000	+	21.6506i	0.571140	+	0.989243i	0.996449	+	0.0841949i	$0.0268318\pi$
$479$	12.5000	+	21.6506i	0.571140	+	0.989243i	−0.425310	+	0.905048i	$0.639835\pi$
$480$		0			0
$481$	−1.00000	−	1.73205i	−0.0455961	−	0.0789747i
$482$		0			0
$483$	−12.0000			−0.546019
$484$		0			0
$485$	−8.50000	−	14.7224i	−0.385965	−	0.668511i
$486$		0			0
$487$	−12.0000			−0.543772			−0.271886	−	0.962329i	$-0.587647\pi$
$487$	−12.0000			−0.543772			−0.271886	+	0.962329i	$0.587647\pi$
$488$		0			0
$489$	36.0000	−	62.3538i	1.62798	−	2.81974i
$490$		0			0
$491$	−12.5000	+	21.6506i	−0.564117	+	0.977079i	0.433014	+	0.901387i	$0.357450\pi$
$491$	−12.5000	+	21.6506i	−0.564117	+	0.977079i	−0.997131	+	0.0756923i	$0.975883\pi$
$492$		0			0
$493$	−27.0000			−1.21602
$494$		0			0
$495$	−6.00000			−0.269680
$496$		0			0
$497$	−18.0000	+	31.1769i	−0.807410	+	1.39848i
$498$		0			0
$499$	−19.5000	+	33.7750i	−0.872940	+	1.51198i	−0.0139987	+	0.999902i	$0.504456\pi$
$499$	−19.5000	+	33.7750i	−0.872940	+	1.51198i	−0.858941	+	0.512074i	$0.828877\pi$
$500$		0			0
$501$	69.0000			3.08269
$502$		0			0
$503$	−9.50000	−	16.4545i	−0.423584	−	0.733669i	0.572703	−	0.819763i	$-0.305895\pi$
$503$	−9.50000	−	16.4545i	−0.423584	−	0.733669i	−0.996287	+	0.0860938i	$0.972562\pi$
$504$		0			0
$505$	3.00000			0.133498
$506$		0			0
$507$	18.0000	+	31.1769i	0.799408	+	1.38462i
$508$		0			0
$509$	−1.50000	−	2.59808i	−0.0664863	−	0.115158i	0.830866	−	0.556473i	$-0.187846\pi$
$509$	−1.50000	−	2.59808i	−0.0664863	−	0.115158i	−0.897352	+	0.441315i	$0.854512\pi$
$510$		0			0
$511$	−22.0000	+	38.1051i	−0.973223	+	1.68567i
$512$		0			0
$513$	36.0000	−	15.5885i	1.58944	−	0.688247i
$514$		0			0
$515$	−8.00000	+	13.8564i	−0.352522	+	0.610586i
$516$		0			0
$517$	5.50000	+	9.52628i	0.241890	+	0.418965i
$518$		0			0
$519$	−7.50000	−	12.9904i	−0.329213	−	0.570214i
$520$		0			0
$521$	−10.0000			−0.438108			−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000			−0.438108			−0.219054	+	0.975713i	$0.570297\pi$
$522$		0			0
$523$	2.50000	+	4.33013i	0.109317	+	0.189343i	0.915494	−	0.402332i	$-0.131800\pi$
$523$	2.50000	+	4.33013i	0.109317	+	0.189343i	−0.806177	+	0.591675i	$0.798467\pi$
$524$		0			0
$525$	48.0000			2.09489
$526$		0			0
$527$		0			0
$528$		0			0
$529$	11.0000	−	19.0526i	0.478261	−	0.828372i
$530$		0			0
$531$	−54.0000			−2.34340
$532$		0			0
$533$	−3.00000			−0.129944
$534$		0			0
$535$	6.00000	−	10.3923i	0.259403	−	0.449299i
$536$		0			0
$537$	6.00000	−	10.3923i	0.258919	−	0.448461i
$538$		0			0
$539$	9.00000			0.387657
$540$		0			0
$541$	17.5000	+	30.3109i	0.752384	+	1.30317i	0.946664	+	0.322221i	$0.104429\pi$
$541$	17.5000	+	30.3109i	0.752384	+	1.30317i	−0.194281	+	0.980946i	$0.562237\pi$
$542$		0			0
$543$	69.0000			2.96107
$544$		0			0
$545$	6.50000	+	11.2583i	0.278429	+	0.482254i
$546$		0			0
$547$	−3.50000	−	6.06218i	−0.149649	−	0.259200i	0.781449	−	0.623970i	$-0.214481\pi$
$547$	−3.50000	−	6.06218i	−0.149649	−	0.259200i	−0.931098	+	0.364770i	$0.881148\pi$
$548$		0			0
$549$	−3.00000	+	5.19615i	−0.128037	+	0.221766i
$550$		0			0
$551$	−31.5000	−	23.3827i	−1.34195	−	0.996136i
$552$		0			0
$553$	−6.00000	+	10.3923i	−0.255146	+	0.441926i
$554$		0			0
$555$	3.00000	+	5.19615i	0.127343	+	0.220564i
$556$		0			0
$557$	5.50000	+	9.52628i	0.233042	+	0.403641i	0.958702	−	0.284413i	$-0.0917985\pi$
$557$	5.50000	+	9.52628i	0.233042	+	0.403641i	−0.725660	+	0.688054i	$0.758465\pi$
$558$		0			0
$559$	1.00000			0.0422955
$560$		0			0
$561$	4.50000	+	7.79423i	0.189990	+	0.329073i
$562$		0			0
$563$	−44.0000			−1.85438			−0.927189	−	0.374593i	$-0.877783\pi$
$563$	−44.0000			−1.85438			−0.927189	+	0.374593i	$0.877783\pi$
$564$		0			0
$565$	3.00000	−	5.19615i	0.126211	−	0.218604i
$566$		0			0
$567$	18.0000	−	31.1769i	0.755929	−	1.30931i
$568$		0			0
$569$	26.0000			1.08998			0.544988	−	0.838444i	$-0.316534\pi$
$569$	26.0000			1.08998			0.544988	+	0.838444i	$0.316534\pi$
$570$		0			0
$571$	12.0000			0.502184			0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000			0.502184			0.251092	+	0.967963i	$0.419210\pi$
$572$		0			0
$573$	18.0000	−	31.1769i	0.751961	−	1.30243i
$574$		0			0
$575$	2.00000	−	3.46410i	0.0834058	−	0.144463i
$576$		0			0
$577$	46.0000			1.91501			0.957503	−	0.288425i	$-0.0931316\pi$
$577$	46.0000			1.91501			0.957503	+	0.288425i	$0.0931316\pi$
$578$		0			0
$579$	−31.5000	−	54.5596i	−1.30910	−	2.26742i
$580$		0			0
$581$	48.0000			1.99138
$582$		0			0
$583$	−1.50000	−	2.59808i	−0.0621237	−	0.107601i
$584$		0			0
$585$	3.00000	+	5.19615i	0.124035	+	0.214834i
$586$		0			0
$587$	−9.50000	+	16.4545i	−0.392107	+	0.679149i	−0.992727	−	0.120385i	$-0.961587\pi$
$587$	−9.50000	+	16.4545i	−0.392107	+	0.679149i	0.600620	+	0.799534i	$0.294920\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	−9.00000	+	15.5885i	−0.370211	+	0.641223i
$592$		0			0
$593$	−22.5000	−	38.9711i	−0.923964	−	1.60035i	−0.793219	−	0.608937i	$-0.791596\pi$
$593$	−22.5000	−	38.9711i	−0.923964	−	1.60035i	−0.130746	−	0.991416i	$-0.541737\pi$
$594$		0			0
$595$	6.00000	+	10.3923i	0.245976	+	0.426043i
$596$		0			0
$597$	−45.0000			−1.84173
$598$		0			0
$599$	7.50000	+	12.9904i	0.306442	+	0.530773i	0.977581	−	0.210558i	$-0.0675282\pi$
$599$	7.50000	+	12.9904i	0.306442	+	0.530773i	−0.671140	+	0.741331i	$0.734195\pi$
$600$		0			0
$601$	−10.0000			−0.407909			−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000			−0.407909			−0.203954	+	0.978980i	$0.565379\pi$
$602$		0			0
$603$	−3.00000	+	5.19615i	−0.122169	+	0.211604i
$604$		0			0
$605$	0.500000	−	0.866025i	0.0203279	−	0.0352089i
$606$		0			0
$607$	−8.00000			−0.324710			−0.162355	−	0.986732i	$-0.551909\pi$
$607$	−8.00000			−0.324710			−0.162355	+	0.986732i	$0.551909\pi$
$608$		0			0
$609$	−108.000			−4.37638
$610$		0			0
$611$	5.50000	−	9.52628i	0.222506	−	0.385392i
$612$		0			0
$613$	5.50000	−	9.52628i	0.222143	−	0.384763i	−0.733316	−	0.679888i	$-0.762028\pi$
$613$	5.50000	−	9.52628i	0.222143	−	0.384763i	0.955458	+	0.295126i	$0.0953615\pi$
$614$		0			0
$615$	9.00000			0.362915
$616$		0			0
$617$	16.5000	+	28.5788i	0.664265	+	1.15054i	0.979484	+	0.201522i	$0.0645887\pi$
$617$	16.5000	+	28.5788i	0.664265	+	1.15054i	−0.315219	+	0.949019i	$0.602078\pi$
$618$		0			0
$619$	−4.00000			−0.160774			−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000			−0.160774			−0.0803868	+	0.996764i	$0.525616\pi$
$620$		0			0
$621$	−4.50000	−	7.79423i	−0.180579	−	0.312772i
$622$		0			0
$623$	22.0000	+	38.1051i	0.881411	+	1.52665i
$624$		0			0
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$		0			0
$627$	−1.50000	+	12.9904i	−0.0599042	+	0.518786i
$628$		0			0
$629$	3.00000	−	5.19615i	0.119618	−	0.207184i
$630$		0			0
$631$	11.5000	+	19.9186i	0.457808	+	0.792946i	0.998845	−	0.0480524i	$-0.0153015\pi$
$631$	11.5000	+	19.9186i	0.457808	+	0.792946i	−0.541037	+	0.840999i	$0.681968\pi$
$632$		0			0
$633$	40.5000	+	70.1481i	1.60973	+	2.78813i
$634$		0			0
$635$	−19.0000			−0.753992
$636$		0			0
$637$	−4.50000	−	7.79423i	−0.178296	−	0.308819i
$638$		0			0
$639$	−54.0000			−2.13621
$640$		0			0
$641$	−1.50000	+	2.59808i	−0.0592464	+	0.102618i	−0.894127	−	0.447813i	$-0.852203\pi$
$641$	−1.50000	+	2.59808i	−0.0592464	+	0.102618i	0.834881	+	0.550431i	$0.185536\pi$
$642$		0			0
$643$	4.50000	−	7.79423i	0.177463	−	0.307374i	−0.763548	−	0.645751i	$-0.776544\pi$
$643$	4.50000	−	7.79423i	0.177463	−	0.307374i	0.941011	+	0.338377i	$0.109878\pi$
$644$		0			0
$645$	−3.00000			−0.118125
$646$		0			0
$647$	28.0000			1.10079			0.550397	−	0.834903i	$-0.314476\pi$
$647$	28.0000			1.10079			0.550397	+	0.834903i	$0.314476\pi$
$648$		0			0
$649$	4.50000	−	7.79423i	0.176640	−	0.305950i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	18.0000			0.704394			0.352197	−	0.935926i	$-0.385435\pi$
$653$	18.0000			0.704394			0.352197	+	0.935926i	$0.385435\pi$
$654$		0			0
$655$	0.500000	+	0.866025i	0.0195366	+	0.0338384i
$656$		0			0
$657$	−66.0000			−2.57491
$658$		0			0
$659$	0.500000	+	0.866025i	0.0194772	+	0.0337356i	0.875600	−	0.483037i	$-0.160466\pi$
$659$	0.500000	+	0.866025i	0.0194772	+	0.0337356i	−0.856123	+	0.516773i	$0.827133\pi$
$660$		0			0
$661$	6.50000	+	11.2583i	0.252821	+	0.437898i	0.964301	−	0.264807i	$-0.0853084\pi$
$661$	6.50000	+	11.2583i	0.252821	+	0.437898i	−0.711481	+	0.702706i	$0.751975\pi$
$662$		0			0
$663$	4.50000	−	7.79423i	0.174766	−	0.302703i
$664$		0			0
$665$	−2.00000	+	17.3205i	−0.0775567	+	0.671660i
$666$		0			0
$667$	−4.50000	+	7.79423i	−0.174241	+	0.301794i
$668$		0			0
$669$	1.50000	+	2.59808i	0.0579934	+	0.100447i
$670$		0			0
$671$	−0.500000	−	0.866025i	−0.0193023	−	0.0334325i
$672$		0			0
$673$	14.0000			0.539660			0.269830	−	0.962908i	$-0.413032\pi$
$673$	14.0000			0.539660			0.269830	+	0.962908i	$0.413032\pi$
$674$		0			0
$675$	18.0000	+	31.1769i	0.692820	+	1.20000i
$676$		0			0
$677$	−6.00000			−0.230599			−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000			−0.230599			−0.115299	+	0.993331i	$0.536783\pi$
$678$		0			0
$679$	−34.0000	+	58.8897i	−1.30480	+	2.25998i
$680$		0			0
$681$	−12.0000	+	20.7846i	−0.459841	+	0.796468i
$682$		0			0
$683$	4.00000			0.153056			0.0765279	−	0.997067i	$-0.475617\pi$
$683$	4.00000			0.153056			0.0765279	+	0.997067i	$0.475617\pi$
$684$		0			0
$685$	17.0000			0.649537
$686$		0			0
$687$	33.0000	−	57.1577i	1.25903	−	2.18070i
$688$		0			0
$689$	−1.50000	+	2.59808i	−0.0571454	+	0.0989788i
$690$		0			0
$691$	−28.0000			−1.06517			−0.532585	−	0.846376i	$-0.678779\pi$
$691$	−28.0000			−1.06517			−0.532585	+	0.846376i	$0.678779\pi$
$692$		0			0
$693$	12.0000	+	20.7846i	0.455842	+	0.789542i
$694$		0			0
$695$	−7.00000			−0.265525
$696$		0			0
$697$	−4.50000	−	7.79423i	−0.170450	−	0.295227i
$698$		0			0
$699$	22.5000	+	38.9711i	0.851028	+	1.47402i
$700$		0			0
$701$	11.5000	−	19.9186i	0.434349	−	0.752315i	−0.562893	−	0.826530i	$-0.690312\pi$
$701$	11.5000	−	19.9186i	0.434349	−	0.752315i	0.997242	+	0.0742151i	$0.0236451\pi$
$702$		0			0
$703$	8.00000	−	3.46410i	0.301726	−	0.130651i
$704$		0			0
$705$	−16.5000	+	28.5788i	−0.621426	+	1.07634i
$706$		0			0
$707$	−6.00000	−	10.3923i	−0.225653	−	0.390843i
$708$		0			0
$709$	−17.5000	−	30.3109i	−0.657226	−	1.13835i	−0.981331	−	0.192328i	$-0.938396\pi$
$709$	−17.5000	−	30.3109i	−0.657226	−	1.13835i	0.324104	−	0.946021i	$-0.394937\pi$
$710$		0			0
$711$	−18.0000			−0.675053
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−1.00000			−0.0373979
$716$		0			0
$717$		0			0
$718$		0			0
$719$	20.5000	−	35.5070i	0.764521	−	1.32419i	−0.175978	−	0.984394i	$-0.556309\pi$
$719$	20.5000	−	35.5070i	0.764521	−	1.32419i	0.940499	−	0.339795i	$-0.110358\pi$
$720$		0			0
$721$	64.0000			2.38348
$722$		0			0
$723$	15.0000			0.557856
$724$		0			0
$725$	18.0000	−	31.1769i	0.668503	−	1.15788i
$726$		0			0
$727$	−11.5000	+	19.9186i	−0.426511	+	0.738739i	−0.996560	−	0.0828714i	$-0.973591\pi$
$727$	−11.5000	+	19.9186i	−0.426511	+	0.738739i	0.570049	+	0.821611i	$0.306924\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	1.50000	+	2.59808i	0.0554795	+	0.0960933i
$732$		0			0
$733$	−30.0000			−1.10808			−0.554038	−	0.832492i	$-0.686914\pi$
$733$	−30.0000			−1.10808			−0.554038	+	0.832492i	$0.686914\pi$
$734$		0			0
$735$	13.5000	+	23.3827i	0.497955	+	0.862483i
$736$		0			0
$737$	−0.500000	−	0.866025i	−0.0184177	−	0.0319005i
$738$		0			0
$739$	−12.5000	+	21.6506i	−0.459820	+	0.796431i	−0.998951	−	0.0457903i	$-0.985419\pi$
$739$	−12.5000	+	21.6506i	−0.459820	+	0.796431i	0.539131	+	0.842222i	$0.318753\pi$
$740$		0			0
$741$	12.0000	−	5.19615i	0.440831	−	0.190885i
$742$		0			0
$743$	−10.5000	+	18.1865i	−0.385208	+	0.667199i	−0.991798	−	0.127815i	$-0.959204\pi$
$743$	−10.5000	+	18.1865i	−0.385208	+	0.667199i	0.606590	+	0.795015i	$0.292537\pi$
$744$		0			0
$745$	−7.50000	−	12.9904i	−0.274779	−	0.475931i
$746$		0			0
$747$	36.0000	+	62.3538i	1.31717	+	2.28141i
$748$		0			0
$749$	−48.0000			−1.75388
$750$		0			0
$751$	−22.5000	−	38.9711i	−0.821037	−	1.42208i	−0.904911	−	0.425601i	$-0.860063\pi$
$751$	−22.5000	−	38.9711i	−0.821037	−	1.42208i	0.0838743	−	0.996476i	$-0.473271\pi$
$752$		0			0
$753$	−45.0000			−1.63989
$754$		0			0
$755$		0			0
$756$		0			0
$757$	4.50000	−	7.79423i	0.163555	−	0.283286i	−0.772586	−	0.634910i	$-0.781037\pi$
$757$	4.50000	−	7.79423i	0.163555	−	0.283286i	0.936141	+	0.351624i	$0.114370\pi$
$758$		0			0
$759$	3.00000			0.108893
$760$		0			0
$761$	−14.0000			−0.507500			−0.253750	−	0.967270i	$-0.581664\pi$
$761$	−14.0000			−0.507500			−0.253750	+	0.967270i	$0.581664\pi$
$762$		0			0
$763$	26.0000	−	45.0333i	0.941263	−	1.63032i
$764$		0			0
$765$	−9.00000	+	15.5885i	−0.325396	+	0.563602i
$766$		0			0
$767$	−9.00000			−0.324971
$768$		0			0
$769$	−10.5000	−	18.1865i	−0.378640	−	0.655823i	0.612225	−	0.790684i	$-0.290275\pi$
$769$	−10.5000	−	18.1865i	−0.378640	−	0.655823i	−0.990865	+	0.134860i	$0.956941\pi$
$770$		0			0
$771$	−39.0000			−1.40455
$772$		0			0
$773$	−15.5000	−	26.8468i	−0.557496	−	0.965612i	−0.997705	−	0.0677162i	$-0.978429\pi$
$773$	−15.5000	−	26.8468i	−0.557496	−	0.965612i	0.440208	−	0.897896i	$-0.354905\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	12.0000	−	20.7846i	0.430498	−	0.745644i
$778$		0			0
$779$	1.50000	−	12.9904i	0.0537431	−	0.465429i
$780$		0			0
$781$	4.50000	−	7.79423i	0.161023	−	0.278899i
$782$		0			0
$783$	−40.5000	−	70.1481i	−1.44735	−	2.50689i
$784$		0			0
$785$	3.50000	+	6.06218i	0.124920	+	0.216368i
$786$		0			0
$787$	8.00000			0.285169			0.142585	−	0.989783i	$-0.454459\pi$
$787$	8.00000			0.285169			0.142585	+	0.989783i	$0.454459\pi$
$788$		0			0
$789$	−31.5000	−	54.5596i	−1.12143	−	1.94237i
$790$		0			0
$791$	−24.0000			−0.853342
$792$		0			0
$793$	−0.500000	+	0.866025i	−0.0177555	+	0.0307535i
$794$		0			0
$795$	4.50000	−	7.79423i	0.159599	−	0.276433i
$796$		0			0
$797$	−2.00000			−0.0708436			−0.0354218	−	0.999372i	$-0.511277\pi$
$797$	−2.00000			−0.0708436			−0.0354218	+	0.999372i	$0.511277\pi$
$798$		0			0
$799$	33.0000			1.16746
$800$		0			0
$801$	−33.0000	+	57.1577i	−1.16600	+	2.01957i
$802$		0			0
$803$	5.50000	−	9.52628i	0.194091	−	0.336175i
$804$		0			0
$805$	4.00000			0.140981
$806$		0			0
$807$	−16.5000	−	28.5788i	−0.580828	−	1.00602i
$808$		0			0
$809$	−6.00000			−0.210949			−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000			−0.210949			−0.105474	+	0.994422i	$0.533636\pi$
$810$		0			0
$811$	−5.50000	−	9.52628i	−0.193131	−	0.334513i	0.753155	−	0.657843i	$-0.228531\pi$
$811$	−5.50000	−	9.52628i	−0.193131	−	0.334513i	−0.946286	+	0.323330i	$0.895198\pi$
$812$		0			0
$813$	22.5000	+	38.9711i	0.789109	+	1.36678i
$814$		0			0
$815$	−12.0000	+	20.7846i	−0.420342	+	0.728053i
$816$		0			0
$817$	−0.500000	+	4.33013i	−0.0174928	+	0.151492i
$818$		0			0
$819$	12.0000	−	20.7846i	0.419314	−	0.726273i
$820$		0			0
$821$	15.5000	+	26.8468i	0.540954	+	0.936959i	0.998850	+	0.0479535i	$0.0152699\pi$
$821$	15.5000	+	26.8468i	0.540954	+	0.936959i	−0.457896	+	0.889006i	$0.651397\pi$
$822$		0			0
$823$	−6.50000	−	11.2583i	−0.226576	−	0.392441i	0.730215	−	0.683217i	$-0.239420\pi$
$823$	−6.50000	−	11.2583i	−0.226576	−	0.392441i	−0.956791	+	0.290776i	$0.906086\pi$
$824$		0			0
$825$	−12.0000			−0.417786
$826$		0			0
$827$	−13.5000	−	23.3827i	−0.469441	−	0.813096i	0.529949	−	0.848030i	$-0.322211\pi$
$827$	−13.5000	−	23.3827i	−0.469441	−	0.813096i	−0.999390	+	0.0349341i	$0.988878\pi$
$828$		0			0
$829$	−38.0000			−1.31979			−0.659897	−	0.751356i	$-0.729400\pi$
$829$	−38.0000			−1.31979			−0.659897	+	0.751356i	$0.729400\pi$
$830$		0			0
$831$	15.0000	−	25.9808i	0.520344	−	0.901263i
$832$		0			0
$833$	13.5000	−	23.3827i	0.467747	−	0.810162i
$834$		0			0
$835$	−23.0000			−0.795948
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−1.50000	+	2.59808i	−0.0517858	+	0.0896956i	−0.890756	−	0.454481i	$-0.849825\pi$
$839$	−1.50000	+	2.59808i	−0.0517858	+	0.0896956i	0.838971	+	0.544177i	$0.183158\pi$
$840$		0			0
$841$	−26.0000	+	45.0333i	−0.896552	+	1.55287i
$842$		0			0
$843$	−57.0000			−1.96318
$844$		0			0
$845$	−6.00000	−	10.3923i	−0.206406	−	0.357506i
$846$		0			0
$847$	−4.00000			−0.137442
$848$		0			0
$849$	34.5000	+	59.7558i	1.18404	+	2.05081i
$850$		0			0
$851$	−1.00000	−	1.73205i	−0.0342796	−	0.0593739i
$852$		0			0
$853$	3.50000	−	6.06218i	0.119838	−	0.207565i	−0.799866	−	0.600179i	$-0.795096\pi$
$853$	3.50000	−	6.06218i	0.119838	−	0.207565i	0.919703	+	0.392614i	$0.128429\pi$
$854$		0			0
$855$	−24.0000	+	10.3923i	−0.820783	+	0.355409i
$856$		0			0
$857$	23.5000	−	40.7032i	0.802745	−	1.39039i	−0.115058	−	0.993359i	$-0.536706\pi$
$857$	23.5000	−	40.7032i	0.802745	−	1.39039i	0.917803	−	0.397036i	$-0.129961\pi$
$858$		0			0
$859$	17.5000	+	30.3109i	0.597092	+	1.03419i	0.993248	+	0.116011i	$0.0370107\pi$
$859$	17.5000	+	30.3109i	0.597092	+	1.03419i	−0.396156	+	0.918183i	$0.629656\pi$
$860$		0			0
$861$	−18.0000	−	31.1769i	−0.613438	−	1.06251i
$862$		0			0
$863$	24.0000			0.816970			0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000			0.816970			0.408485	+	0.912765i	$0.366057\pi$
$864$		0			0
$865$	2.50000	+	4.33013i	0.0850026	+	0.147229i
$866$		0			0
$867$	−24.0000			−0.815083
$868$		0			0
$869$	1.50000	−	2.59808i	0.0508840	−	0.0881337i
$870$		0			0
$871$	−0.500000	+	0.866025i	−0.0169419	+	0.0293442i
$872$		0			0
$873$	−102.000			−3.45218
$874$		0			0
$875$	−36.0000			−1.21702
$876$		0			0
$877$	−0.500000	+	0.866025i	−0.0168838	+	0.0292436i	−0.874344	−	0.485307i	$-0.838708\pi$
$877$	−0.500000	+	0.866025i	−0.0168838	+	0.0292436i	0.857460	+	0.514551i	$0.172041\pi$
$878$		0			0
$879$	3.00000	−	5.19615i	0.101187	−	0.175262i
$880$		0			0
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$		0			0
$883$	−28.5000	−	49.3634i	−0.959101	−	1.66121i	−0.724690	−	0.689075i	$-0.758017\pi$
$883$	−28.5000	−	49.3634i	−0.959101	−	1.66121i	−0.234411	−	0.972138i	$-0.575316\pi$
$884$		0			0
$885$	27.0000			0.907595
$886$		0			0
$887$	−7.50000	−	12.9904i	−0.251825	−	0.436174i	0.712203	−	0.701974i	$-0.247698\pi$
$887$	−7.50000	−	12.9904i	−0.251825	−	0.436174i	−0.964028	+	0.265799i	$0.914364\pi$
$888$		0			0
$889$	38.0000	+	65.8179i	1.27448	+	2.20746i
$890$		0			0
$891$	−4.50000	+	7.79423i	−0.150756	+	0.261116i
$892$		0			0
$893$	38.5000	+	28.5788i	1.28835	+	0.956354i
$894$		0			0
$895$	−2.00000	+	3.46410i	−0.0668526	+	0.115792i
$896$		0			0
$897$	−1.50000	−	2.59808i	−0.0500835	−	0.0867472i
$898$		0			0
$899$		0			0
$900$		0			0
$901$	−9.00000			−0.299833
$902$		0			0
$903$	6.00000	+	10.3923i	0.199667	+	0.345834i
$904$		0			0
$905$	−23.0000			−0.764546
$906$		0			0
$907$	−3.50000	+	6.06218i	−0.116216	+	0.201291i	−0.918265	−	0.395966i	$-0.870410\pi$
$907$	−3.50000	+	6.06218i	−0.116216	+	0.201291i	0.802049	+	0.597258i	$0.203743\pi$
$908$		0			0
$909$	9.00000	−	15.5885i	0.298511	−	0.517036i
$910$		0			0
$911$	40.0000			1.32526			0.662630	−	0.748947i	$-0.269440\pi$
$911$	40.0000			1.32526			0.662630	+	0.748947i	$0.269440\pi$
$912$		0			0
$913$	−12.0000			−0.397142
$914$		0			0
$915$	1.50000	−	2.59808i	0.0495885	−	0.0858898i
$916$		0			0
$917$	2.00000	−	3.46410i	0.0660458	−	0.114395i
$918$		0			0
$919$	−16.0000			−0.527791			−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000			−0.527791			−0.263896	+	0.964551i	$0.585007\pi$
$920$		0			0
$921$	−1.50000	−	2.59808i	−0.0494267	−	0.0856095i
$922$		0			0
$923$	−9.00000			−0.296239
$924$		0			0
$925$	4.00000	+	6.92820i	0.131519	+	0.227798i
$926$		0			0
$927$	48.0000	+	83.1384i	1.57653	+	2.73062i
$928$		0			0
$929$	−17.5000	+	30.3109i	−0.574156	+	0.994468i	0.421976	+	0.906607i	$0.361337\pi$
$929$	−17.5000	+	30.3109i	−0.574156	+	0.994468i	−0.996133	+	0.0878612i	$0.971997\pi$
$930$		0			0
$931$	36.0000	−	15.5885i	1.17985	−	0.510891i
$932$		0			0
$933$	−12.0000	+	20.7846i	−0.392862	+	0.680458i
$934$		0			0
$935$	−1.50000	−	2.59808i	−0.0490552	−	0.0849662i
$936$		0			0
$937$	1.50000	+	2.59808i	0.0490029	+	0.0848755i	0.889486	−	0.456962i	$-0.151062\pi$
$937$	1.50000	+	2.59808i	0.0490029	+	0.0848755i	−0.840484	+	0.541837i	$0.817729\pi$
$938$		0			0
$939$	−63.0000			−2.05593
$940$		0			0
$941$	−8.50000	−	14.7224i	−0.277092	−	0.479938i	0.693569	−	0.720390i	$-0.256037\pi$
$941$	−8.50000	−	14.7224i	−0.277092	−	0.479938i	−0.970661	+	0.240453i	$0.922704\pi$
$942$		0			0
$943$	−3.00000			−0.0976934
$944$		0			0
$945$	−18.0000	+	31.1769i	−0.585540	+	1.01419i
$946$		0			0
$947$	−13.5000	+	23.3827i	−0.438691	+	0.759835i	−0.997589	−	0.0694014i	$-0.977891\pi$
$947$	−13.5000	+	23.3827i	−0.438691	+	0.759835i	0.558898	+	0.829237i	$0.311224\pi$
$948$		0			0
$949$	−11.0000			−0.357075
$950$		0			0
$951$	−99.0000			−3.21029
$952$		0			0
$953$	−26.5000	+	45.8993i	−0.858419	+	1.48683i	0.0150171	+	0.999887i	$0.495220\pi$
$953$	−26.5000	+	45.8993i	−0.858419	+	1.48683i	−0.873436	+	0.486938i	$0.838114\pi$
$954$		0			0
$955$	−6.00000	+	10.3923i	−0.194155	+	0.336287i
$956$		0			0
$957$	27.0000			0.872786
$958$		0			0
$959$	−34.0000	−	58.8897i	−1.09792	−	1.90165i
$960$		0			0
$961$	−31.0000			−1.00000
$962$		0			0
$963$	−36.0000	−	62.3538i	−1.16008	−	2.00932i
$964$		0			0
$965$	10.5000	+	18.1865i	0.338007	+	0.585445i
$966$		0			0
$967$	−6.50000	+	11.2583i	−0.209026	+	0.362043i	−0.951408	−	0.307933i	$-0.900363\pi$
$967$	−6.50000	+	11.2583i	−0.209026	+	0.362043i	0.742382	+	0.669977i	$0.233696\pi$
$968$		0			0
$969$	31.5000	+	23.3827i	1.01193	+	0.751160i
$970$		0			0
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	−0.960910	−	0.276861i	$-0.910706\pi$
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	0.720224	+	0.693742i	$0.244039\pi$
$972$		0			0
$973$	14.0000	+	24.2487i	0.448819	+	0.777378i
$974$		0			0
$975$	6.00000	+	10.3923i	0.192154	+	0.332820i
$976$		0			0
$977$	2.00000			0.0639857			0.0319928	−	0.999488i	$-0.489815\pi$
$977$	2.00000			0.0639857			0.0319928	+	0.999488i	$0.489815\pi$
$978$		0			0
$979$	−5.50000	−	9.52628i	−0.175781	−	0.304461i
$980$		0			0
$981$	78.0000			2.49035
$982$		0			0
$983$	14.5000	−	25.1147i	0.462478	−	0.801036i	−0.536606	−	0.843833i	$-0.680294\pi$
$983$	14.5000	−	25.1147i	0.462478	−	0.801036i	0.999084	+	0.0427975i	$0.0136270\pi$
$984$		0			0
$985$	3.00000	−	5.19615i	0.0955879	−	0.165563i
$986$		0			0
$987$	132.000			4.20161
$988$		0			0
$989$	1.00000			0.0317982
$990$		0			0
$991$	14.5000	−	25.1147i	0.460608	−	0.797796i	−0.538384	−	0.842700i	$-0.680965\pi$
$991$	14.5000	−	25.1147i	0.460608	−	0.797796i	0.998991	+	0.0449040i	$0.0142982\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	15.0000			0.475532
$996$		0			0
$997$	7.50000	+	12.9904i	0.237527	+	0.411409i	0.960004	−	0.279986i	$-0.0903297\pi$
$997$	7.50000	+	12.9904i	0.237527	+	0.411409i	−0.722477	+	0.691395i	$0.756996\pi$
$998$		0			0
$999$	18.0000			0.569495

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	836.2.i.b.353.1	yes	2
19.7	even	3	inner	836.2.i.b.45.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
836.2.i.b.45.1	✓	2	19.7	even	3	inner
836.2.i.b.353.1	yes	2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 836 = 2^{2} \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	836.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 2.59808i) q^{3} +(0.500000 - 0.866025i) q^{5} -4.00000 q^{7} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 2.59808i) q^{3} +(0.500000 - 0.866025i) q^{5} -4.00000 q^{7} +(-3.00000 - 5.19615i) q^{9} +1.00000 q^{11} +(-0.500000 - 0.866025i) q^{13} +(1.50000 + 2.59808i) q^{15} +(1.50000 - 2.59808i) q^{17} +(4.00000 - 1.73205i) q^{19} +(6.00000 - 10.3923i) q^{21} +(-0.500000 - 0.866025i) q^{23} +(2.00000 + 3.46410i) q^{25} +9.00000 q^{27} +(-4.50000 - 7.79423i) q^{29} +(-1.50000 + 2.59808i) q^{33} +(-2.00000 + 3.46410i) q^{35} +2.00000 q^{37} +3.00000 q^{39} +(1.50000 - 2.59808i) q^{41} +(-0.500000 + 0.866025i) q^{43} -6.00000 q^{45} +(5.50000 + 9.52628i) q^{47} +9.00000 q^{49} +(4.50000 + 7.79423i) q^{51} +(-1.50000 - 2.59808i) q^{53} +(0.500000 - 0.866025i) q^{55} +(-1.50000 + 12.9904i) q^{57} +(4.50000 - 7.79423i) q^{59} +(-0.500000 - 0.866025i) q^{61} +(12.0000 + 20.7846i) q^{63} -1.00000 q^{65} +(-0.500000 - 0.866025i) q^{67} +3.00000 q^{69} +(4.50000 - 7.79423i) q^{71} +(5.50000 - 9.52628i) q^{73} -12.0000 q^{75} -4.00000 q^{77} +(1.50000 - 2.59808i) q^{79} +(-4.50000 + 7.79423i) q^{81} -12.0000 q^{83} +(-1.50000 - 2.59808i) q^{85} +27.0000 q^{87} +(-5.50000 - 9.52628i) q^{89} +(2.00000 + 3.46410i) q^{91} +(0.500000 - 4.33013i) q^{95} +(8.50000 - 14.7224i) q^{97} +(-3.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{3} + q^{5} - 8 q^{7} - 6 q^{9}+O(q^{10}) \) 2 * q - 3 * q^3 + q^5 - 8 * q^7 - 6 * q^9	\( 2 q - 3 q^{3} + q^{5} - 8 q^{7} - 6 q^{9} + 2 q^{11} - q^{13} + 3 q^{15} + 3 q^{17} + 8 q^{19} + 12 q^{21} - q^{23} + 4 q^{25} + 18 q^{27} - 9 q^{29} - 3 q^{33} - 4 q^{35} + 4 q^{37} + 6 q^{39} + 3 q^{41} - q^{43} - 12 q^{45} + 11 q^{47} + 18 q^{49} + 9 q^{51} - 3 q^{53} + q^{55} - 3 q^{57} + 9 q^{59} - q^{61} + 24 q^{63} - 2 q^{65} - q^{67} + 6 q^{69} + 9 q^{71} + 11 q^{73} - 24 q^{75} - 8 q^{77} + 3 q^{79} - 9 q^{81} - 24 q^{83} - 3 q^{85} + 54 q^{87} - 11 q^{89} + 4 q^{91} + q^{95} + 17 q^{97} - 6 q^{99}+O(q^{100}) \) 2 * q - 3 * q^3 + q^5 - 8 * q^7 - 6 * q^9 + 2 * q^11 - q^13 + 3 * q^15 + 3 * q^17 + 8 * q^19 + 12 * q^21 - q^23 + 4 * q^25 + 18 * q^27 - 9 * q^29 - 3 * q^33 - 4 * q^35 + 4 * q^37 + 6 * q^39 + 3 * q^41 - q^43 - 12 * q^45 + 11 * q^47 + 18 * q^49 + 9 * q^51 - 3 * q^53 + q^55 - 3 * q^57 + 9 * q^59 - q^61 + 24 * q^63 - 2 * q^65 - q^67 + 6 * q^69 + 9 * q^71 + 11 * q^73 - 24 * q^75 - 8 * q^77 + 3 * q^79 - 9 * q^81 - 24 * q^83 - 3 * q^85 + 54 * q^87 - 11 * q^89 + 4 * q^91 + q^95 + 17 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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