LMFDB - Embedded newform 1950.2.y.j.199.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(49,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("1950.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.y (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.17284886784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 30x^{5} + 185x^{4} + 36x^{3} + 8x^{2} + 208x + 2704 $ x^8 - 2x^7 + 2x^6 + 30x^5 + 185x^4 + 36x^3 + 8x^2 + 208*x + 2704
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.4
Root			$-1.70006 - 1.70006i$ of defining polynomial
Character	$\chi$	$=$	1950.199
Dual form			1950.2.y.j.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(2.32233 + 4.02239i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(2.32233 + 4.02239i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(3.81062 + 2.20006i) q^{11} -1.00000i q^{12} +(-1.32233 + 3.35432i) q^{13} -4.64466 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.46410 + 2.00000i) q^{17} -1.00000 q^{18} +(6.96699 - 4.02239i) q^{19} +4.64466i q^{21} +(-3.81062 + 2.20006i) q^{22} +(0.845746 + 0.488292i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-2.24376 - 2.82233i) q^{26} +1.00000i q^{27} +(2.32233 - 4.02239i) q^{28} +(-2.15637 + 3.73494i) q^{29} -6.44069i q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.20006 + 3.81062i) q^{33} -4.00000i q^{34} +(0.500000 - 0.866025i) q^{36} +(-1.89801 + 3.28745i) q^{37} +8.04479i q^{38} +(-2.82233 + 2.24376i) q^{39} +(-6.31274 - 3.64466i) q^{41} +(-4.02239 - 2.32233i) q^{42} +(0.620469 - 0.358228i) q^{43} -4.40013i q^{44} +(-0.845746 + 0.488292i) q^{46} +9.75342 q^{47} +(-0.866025 + 0.500000i) q^{48} +(-7.28643 + 12.6205i) q^{49} -4.00000 q^{51} +(3.56609 - 0.531987i) q^{52} -13.5089i q^{53} +(-0.866025 - 0.500000i) q^{54} +(2.32233 + 4.02239i) q^{56} +8.04479 q^{57} +(-2.15637 - 3.73494i) q^{58} +(1.88842 - 1.09028i) q^{59} +(-3.73205 - 6.46410i) q^{61} +(5.57780 + 3.22034i) q^{62} +(-2.32233 + 4.02239i) q^{63} +1.00000 q^{64} -4.40013 q^{66} +(0.912609 - 1.58068i) q^{67} +(3.46410 + 2.00000i) q^{68} +(0.488292 + 0.845746i) q^{69} +(-6.88764 + 3.97658i) q^{71} +(0.500000 + 0.866025i) q^{72} +4.36112 q^{73} +(-1.89801 - 3.28745i) q^{74} +(-6.96699 - 4.02239i) q^{76} +20.4371i q^{77} +(-0.531987 - 3.56609i) q^{78} +14.9340 q^{79} +(-0.500000 + 0.866025i) q^{81} +(6.31274 - 3.64466i) q^{82} -3.51093 q^{83} +(4.02239 - 2.32233i) q^{84} +0.716456i q^{86} +(-3.73494 + 2.15637i) q^{87} +(3.81062 + 2.20006i) q^{88} +(-7.07780 - 4.08637i) q^{89} +(-16.5633 + 2.47090i) q^{91} -0.976584i q^{92} +(3.22034 - 5.57780i) q^{93} +(-4.87671 + 8.44671i) q^{94} -1.00000i q^{96} +(6.91261 + 11.9730i) q^{97} +(-7.28643 - 12.6205i) q^{98} +4.40013i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{4} + 2 q^{7} + 8 q^{8} + 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 4 * q^4 + 2 * q^7 + 8 * q^8 + 4 * q^9	$ 8 q - 4 q^{2} - 4 q^{4} + 2 q^{7} + 8 q^{8} + 4 q^{9} + 6 q^{11} + 6 q^{13} - 4 q^{14} - 4 q^{16} - 8 q^{18} + 6 q^{19} - 6 q^{22} + 6 q^{23} - 12 q^{26} + 2 q^{28} + 8 q^{29} - 4 q^{32} + 2 q^{33} + 4 q^{36} - 10 q^{37} - 6 q^{39} - 48 q^{43} - 6 q^{46} - 16 q^{47} - 14 q^{49} - 32 q^{51} + 6 q^{52} + 2 q^{56} + 8 q^{58} - 24 q^{59} - 16 q^{61} + 30 q^{62} - 2 q^{63} + 8 q^{64} - 4 q^{66} - 12 q^{67} - 4 q^{69} - 12 q^{71} + 4 q^{72} + 24 q^{73} - 10 q^{74} - 6 q^{76} - 6 q^{78} + 20 q^{79} - 4 q^{81} - 32 q^{83} + 6 q^{87} + 6 q^{88} - 42 q^{89} - 10 q^{91} + 4 q^{93} + 8 q^{94} + 36 q^{97} - 14 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 + 2 * q^7 + 8 * q^8 + 4 * q^9 + 6 * q^11 + 6 * q^13 - 4 * q^14 - 4 * q^16 - 8 * q^18 + 6 * q^19 - 6 * q^22 + 6 * q^23 - 12 * q^26 + 2 * q^28 + 8 * q^29 - 4 * q^32 + 2 * q^33 + 4 * q^36 - 10 * q^37 - 6 * q^39 - 48 * q^43 - 6 * q^46 - 16 * q^47 - 14 * q^49 - 32 * q^51 + 6 * q^52 + 2 * q^56 + 8 * q^58 - 24 * q^59 - 16 * q^61 + 30 * q^62 - 2 * q^63 + 8 * q^64 - 4 * q^66 - 12 * q^67 - 4 * q^69 - 12 * q^71 + 4 * q^72 + 24 * q^73 - 10 * q^74 - 6 * q^76 - 6 * q^78 + 20 * q^79 - 4 * q^81 - 32 * q^83 + 6 * q^87 + 6 * q^88 - 42 * q^89 - 10 * q^91 + 4 * q^93 + 8 * q^94 + 36 * q^97 - 14 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	2.32233	+	4.02239i	0.877758	+	1.52032i	0.853795	+	0.520609i	$0.174295\pi$
$7$	2.32233	+	4.02239i	0.877758	+	1.52032i	0.0239629	+	0.999713i	$0.492372\pi$
$8$	1.00000			0.353553
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	3.81062	+	2.20006i	1.14895	+	0.663344i	0.948630	−	0.316387i	$-0.102470\pi$
$11$	3.81062	+	2.20006i	1.14895	+	0.663344i	0.200316	+	0.979731i	$0.435803\pi$
$12$		−	1.00000i		−	0.288675i
$13$	−1.32233	+	3.35432i	−0.366748	+	0.930320i
$13$	−1.32233	+	3.35432i	−0.366748	+	0.930320i
$14$	−4.64466			−1.24134
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.46410	+	2.00000i	−0.840168	+	0.485071i	−0.857321	−	0.514782i	$-0.827873\pi$
$17$	−3.46410	+	2.00000i	−0.840168	+	0.485071i	0.0171533	+	0.999853i	$0.494540\pi$
$18$	−1.00000			−0.235702
$19$	6.96699	−	4.02239i	1.59834	−	0.922800i	0.606529	−	0.795061i	$-0.292561\pi$
$19$	6.96699	−	4.02239i	1.59834	−	0.922800i	0.991808	−	0.127739i	$-0.0407720\pi$
$20$		0			0
$21$			4.64466i			1.01355i
$22$	−3.81062	+	2.20006i	−0.812427	+	0.469055i
$23$	0.845746	+	0.488292i	0.176350	+	0.101816i	0.585577	−	0.810617i	$-0.300868\pi$
$23$	0.845746	+	0.488292i	0.176350	+	0.101816i	−0.409226	+	0.912433i	$0.634201\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$		0			0
$26$	−2.24376	−	2.82233i	−0.440037	−	0.553504i
$27$			1.00000i			0.192450i
$28$	2.32233	−	4.02239i	0.438879	−	0.760161i
$29$	−2.15637	+	3.73494i	−0.400427	+	0.693561i	−0.993777	−	0.111384i	$-0.964472\pi$
$29$	−2.15637	+	3.73494i	−0.400427	+	0.693561i	0.593350	+	0.804945i	$0.297805\pi$
$30$		0			0
$31$		−	6.44069i		−	1.15678i	−0.815760	−	0.578391i	$-0.803681\pi$
$31$		−	6.44069i		−	1.15678i	0.815760	−	0.578391i	$-0.196319\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	2.20006	+	3.81062i	0.382982	+	0.663344i
$34$		−	4.00000i		−	0.685994i
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−1.89801	+	3.28745i	−0.312031	+	0.540454i	−0.978802	−	0.204809i	$-0.934343\pi$
$37$	−1.89801	+	3.28745i	−0.312031	+	0.540454i	0.666771	+	0.745263i	$0.267676\pi$
$38$			8.04479i			1.30504i
$39$	−2.82233	+	2.24376i	−0.451934	+	0.359289i
$40$		0			0
$41$	−6.31274	−	3.64466i	−0.985884	−	0.569200i	−0.0818424	−	0.996645i	$-0.526080\pi$
$41$	−6.31274	−	3.64466i	−0.985884	−	0.569200i	−0.904041	+	0.427445i	$0.859414\pi$
$42$	−4.02239	−	2.32233i	−0.620669	−	0.358343i
$43$	0.620469	−	0.358228i	0.0946207	−	0.0546293i	−0.451943	−	0.892047i	$-0.649269\pi$
$43$	0.620469	−	0.358228i	0.0946207	−	0.0546293i	0.546564	+	0.837418i	$0.315936\pi$
$44$		−	4.40013i		−	0.663344i
$45$		0			0
$46$	−0.845746	+	0.488292i	−0.124698	+	0.0719947i
$47$	9.75342			1.42268			0.711341	−	0.702847i	$-0.248088\pi$
$47$	9.75342			1.42268			0.711341	+	0.702847i	$0.248088\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	−7.28643	+	12.6205i	−1.04092	+	1.80292i
$50$		0			0
$51$	−4.00000			−0.560112
$52$	3.56609	−	0.531987i	0.494528	−	0.0737734i
$53$		−	13.5089i		−	1.85559i	−0.373092	−	0.927794i	$-0.621703\pi$
$53$		−	13.5089i		−	1.85559i	0.373092	−	0.927794i	$-0.378297\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$		0			0
$56$	2.32233	+	4.02239i	0.310334	+	0.537515i
$57$	8.04479			1.06556
$58$	−2.15637	−	3.73494i	−0.283145	−	0.490421i
$59$	1.88842	−	1.09028i	0.245851	−	0.141942i	−0.372012	−	0.928228i	$-0.621332\pi$
$59$	1.88842	−	1.09028i	0.245851	−	0.141942i	0.617863	+	0.786286i	$0.287999\pi$
$60$		0			0
$61$	−3.73205	−	6.46410i	−0.477840	−	0.827643i	0.521837	−	0.853045i	$-0.325247\pi$
$61$	−3.73205	−	6.46410i	−0.477840	−	0.827643i	−0.999677	+	0.0254017i	$0.991914\pi$
$62$	5.57780	+	3.22034i	0.708381	+	0.408984i
$63$	−2.32233	+	4.02239i	−0.292586	+	0.506774i
$64$	1.00000			0.125000
$65$		0			0
$66$	−4.40013			−0.541618
$67$	0.912609	−	1.58068i	0.111493	−	0.193111i	−0.804879	−	0.593438i	$-0.797770\pi$
$67$	0.912609	−	1.58068i	0.111493	−	0.193111i	0.916372	+	0.400327i	$0.131103\pi$
$68$	3.46410	+	2.00000i	0.420084	+	0.242536i
$69$	0.488292	+	0.845746i	0.0587834	+	0.101816i
$70$		0			0
$71$	−6.88764	+	3.97658i	−0.817413	+	0.471934i	−0.849524	−	0.527551i	$-0.823110\pi$
$71$	−6.88764	+	3.97658i	−0.817413	+	0.471934i	0.0321105	+	0.999484i	$0.489777\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	4.36112			0.510430			0.255215	−	0.966884i	$-0.417854\pi$
$73$	4.36112			0.510430			0.255215	+	0.966884i	$0.417854\pi$
$74$	−1.89801	−	3.28745i	−0.220640	−	0.382159i
$75$		0			0
$76$	−6.96699	−	4.02239i	−0.799168	−	0.461400i
$77$			20.4371i			2.32902i
$78$	−0.531987	−	3.56609i	−0.0602357	−	0.403780i
$79$	14.9340			1.68020			0.840102	−	0.542429i	$-0.182495\pi$
$79$	14.9340			1.68020			0.840102	+	0.542429i	$0.182495\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	6.31274	−	3.64466i	0.697125	−	0.402485i
$83$	−3.51093			−0.385375			−0.192688	−	0.981260i	$-0.561720\pi$
$83$	−3.51093			−0.385375			−0.192688	+	0.981260i	$0.561720\pi$
$84$	4.02239	−	2.32233i	0.438879	−	0.253387i
$85$		0			0
$86$			0.716456i			0.0772575i
$87$	−3.73494	+	2.15637i	−0.400427	+	0.231187i
$88$	3.81062	+	2.20006i	0.406214	+	0.234528i
$89$	−7.07780	−	4.08637i	−0.750245	−	0.433154i	0.0755374	−	0.997143i	$-0.475933\pi$
$89$	−7.07780	−	4.08637i	−0.750245	−	0.433154i	−0.825782	+	0.563989i	$0.809266\pi$
$90$		0			0
$91$	−16.5633	+	2.47090i	−1.73630	+	0.259021i
$92$		−	0.976584i		−	0.101816i
$93$	3.22034	−	5.57780i	0.333934	−	0.578391i
$94$	−4.87671	+	8.44671i	−0.502994	+	0.871212i
$95$		0			0
$96$		−	1.00000i		−	0.102062i
$97$	6.91261	+	11.9730i	0.701869	+	1.21567i	0.967810	+	0.251683i	$0.0809842\pi$
$97$	6.91261	+	11.9730i	0.701869	+	1.21567i	−0.265941	+	0.963989i	$0.585682\pi$
$98$	−7.28643	−	12.6205i	−0.736041	−	1.27486i
$99$			4.40013i			0.442229i
$100$		0			0
$101$	−3.40013	+	5.88919i	−0.338325	+	0.585997i	−0.984118	−	0.177516i	$-0.943194\pi$
$101$	−3.40013	+	5.88919i	−0.338325	+	0.585997i	0.645793	+	0.763513i	$0.276527\pi$
$102$	2.00000	−	3.46410i	0.198030	−	0.342997i
$103$			5.29137i			0.521374i	0.965423	+	0.260687i	$0.0839490\pi$
$103$			5.29137i			0.521374i	−0.965423	+	0.260687i	$0.916051\pi$
$104$	−1.32233	+	3.35432i	−0.129665	+	0.328918i
$105$		0			0
$106$	11.6990	+	6.75444i	1.13631	+	0.656050i
$107$	−14.6603	−	8.46410i	−1.41726	−	0.818256i	−0.421203	−	0.906966i	$-0.638392\pi$
$107$	−14.6603	−	8.46410i	−1.41726	−	0.818256i	−0.996057	+	0.0887109i	$0.971725\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$			12.8003i			1.22604i	0.790067	+	0.613021i	$0.210046\pi$
$109$			12.8003i			1.22604i	−0.790067	+	0.613021i	$0.789954\pi$
$110$		0			0
$111$	−3.28745	+	1.89801i	−0.312031	+	0.180151i
$112$	−4.64466			−0.438879
$113$	−11.3156	+	6.53308i	−1.06448	+	0.614580i	−0.926669	−	0.375878i	$-0.877341\pi$
$113$	−11.3156	+	6.53308i	−1.06448	+	0.614580i	−0.137815	+	0.990458i	$0.544008\pi$
$114$	−4.02239	+	6.96699i	−0.376732	+	0.652518i
$115$		0			0
$116$	4.31274			0.400427
$117$	−3.56609	+	0.531987i	−0.329685	+	0.0491823i
$118$			2.18056i			0.200737i
$119$	−16.0896	−	9.28932i	−1.47493	−	0.851550i
$120$		0			0
$121$	4.18056	+	7.24094i	0.380051	+	0.658267i
$122$	7.46410			0.675768
$123$	−3.64466	−	6.31274i	−0.328628	−	0.569200i
$124$	−5.57780	+	3.22034i	−0.500901	+	0.289195i
$125$		0			0
$126$	−2.32233	−	4.02239i	−0.206890	−	0.358343i
$127$	10.5825	+	6.10978i	0.939041	+	0.542156i	0.889660	−	0.456624i	$-0.150942\pi$
$127$	10.5825	+	6.10978i	0.939041	+	0.542156i	0.0493816	+	0.998780i	$0.484275\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	0.716456			0.0630805
$130$		0			0
$131$	−0.378757			−0.0330921			−0.0165461	−	0.999863i	$-0.505267\pi$
$131$	−0.378757			−0.0330921			−0.0165461	+	0.999863i	$0.505267\pi$
$132$	2.20006	−	3.81062i	0.191491	−	0.331672i
$133$	32.3593	+	18.6826i	2.80591	+	1.61999i
$134$	0.912609	+	1.58068i	0.0788374	+	0.136550i
$135$		0			0
$136$	−3.46410	+	2.00000i	−0.297044	+	0.171499i
$137$	−0.626177	−	1.08457i	−0.0534979	−	0.0926612i	0.838036	−	0.545615i	$-0.183704\pi$
$137$	−0.626177	−	1.08457i	−0.0534979	−	0.0926612i	−0.891534	+	0.452953i	$0.850370\pi$
$138$	−0.976584			−0.0831323
$139$	1.67767	+	2.90581i	0.142298	+	0.246468i	0.928362	−	0.371678i	$-0.121217\pi$
$139$	1.67767	+	2.90581i	0.142298	+	0.246468i	−0.786064	+	0.618146i	$0.787884\pi$
$140$		0			0
$141$	8.44671	+	4.87671i	0.711341	+	0.410693i
$142$		−	7.95317i		−	0.667415i
$143$	−12.4186	+	9.87282i	−1.03850	+	0.825607i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	−2.18056	+	3.77684i	−0.180464	+	0.312573i
$147$	−12.6205	+	7.28643i	−1.04092	+	0.600975i
$148$	3.79603			0.312031
$149$	4.00077	−	2.30985i	0.327756	−	0.189230i	−0.327088	−	0.944994i	$-0.606067\pi$
$149$	4.00077	−	2.30985i	0.327756	−	0.189230i	0.654844	+	0.755764i	$0.272734\pi$
$150$		0			0
$151$		−	11.2425i		−	0.914901i	−0.889235	−	0.457450i	$-0.848763\pi$
$151$		−	11.2425i		−	0.914901i	0.889235	−	0.457450i	$-0.151237\pi$
$152$	6.96699	−	4.02239i	0.565097	−	0.326259i
$153$	−3.46410	−	2.00000i	−0.280056	−	0.161690i
$154$	−17.6990	−	10.2185i	−1.42623	−	0.823434i
$155$		0			0
$156$	3.35432	+	1.32233i	0.268560	+	0.105871i
$157$		−	1.50311i		−	0.119961i	−0.998200	−	0.0599807i	$-0.980896\pi$
$157$		−	1.50311i		−	0.119961i	0.998200	−	0.0599807i	$-0.0191039\pi$
$158$	−7.46699	+	12.9332i	−0.594042	+	1.02891i
$159$	6.75444	−	11.6990i	0.535662	−	0.927794i
$160$		0			0
$161$			4.53590i			0.357479i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	0.0881650	+	0.152706i	0.00690561	+	0.0119609i	0.869458	−	0.494008i	$-0.164469\pi$
$163$	0.0881650	+	0.152706i	0.00690561	+	0.0119609i	−0.862552	+	0.505969i	$0.831135\pi$
$164$			7.28932i			0.569200i
$165$		0			0
$166$	1.75547	−	3.04056i	0.136251	−	0.235993i
$167$	−4.34081	+	7.51851i	−0.335902	+	0.581800i	−0.983658	−	0.180049i	$-0.942374\pi$
$167$	−4.34081	+	7.51851i	−0.335902	+	0.581800i	0.647756	+	0.761848i	$0.275708\pi$
$168$			4.64466i			0.358343i
$169$	−9.50289	−	8.87103i	−0.730991	−	0.682387i
$170$		0			0
$171$	6.96699	+	4.02239i	0.532779	+	0.307600i
$172$	−0.620469	−	0.358228i	−0.0473103	−	0.0273146i
$173$	1.54190	−	0.890216i	0.117228	−	0.0676818i	−0.440239	−	0.897880i	$-0.645106\pi$
$173$	1.54190	−	0.890216i	0.117228	−	0.0676818i	0.557468	+	0.830199i	$0.311773\pi$
$174$		−	4.31274i		−	0.326948i
$175$		0			0
$176$	−3.81062	+	2.20006i	−0.287236	+	0.165836i
$177$	2.18056			0.163901
$178$	7.07780	−	4.08637i	0.530503	−	0.306286i
$179$	8.70786	−	15.0825i	0.650856	−	1.12732i	−0.332059	−	0.943258i	$-0.607743\pi$
$179$	8.70786	−	15.0825i	0.650856	−	1.12732i	0.982916	−	0.184057i	$-0.0589232\pi$
$180$		0			0
$181$	−10.3611			−0.770136			−0.385068	−	0.922888i	$-0.625822\pi$
$181$	−10.3611			−0.770136			−0.385068	+	0.922888i	$0.625822\pi$
$182$	6.14177	−	15.5797i	0.455258	−	1.15484i
$183$		−	7.46410i		−	0.551762i
$184$	0.845746	+	0.488292i	0.0623492	+	0.0359973i
$185$		0			0
$186$	3.22034	+	5.57780i	0.236127	+	0.408984i
$187$	−17.6005			−1.28708
$188$	−4.87671	−	8.44671i	−0.355671	−	0.616040i
$189$	−4.02239	+	2.32233i	−0.292586	+	0.168925i
$190$		0			0
$191$	0.448507	+	0.776837i	0.0324528	+	0.0562100i	0.881796	−	0.471632i	$-0.156335\pi$
$191$	0.448507	+	0.776837i	0.0324528	+	0.0562100i	−0.849343	+	0.527842i	$0.823001\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	10.1322	−	17.5494i	0.729330	−	1.26324i	−0.227837	−	0.973699i	$-0.573165\pi$
$193$	10.1322	−	17.5494i	0.729330	−	1.26324i	0.957167	−	0.289537i	$-0.0935015\pi$
$194$	−13.8252			−0.992593
$195$		0			0
$196$	14.5729			1.04092
$197$	−4.59028	+	7.95060i	−0.327044	+	0.566457i	−0.981924	−	0.189276i	$-0.939386\pi$
$197$	−4.59028	+	7.95060i	−0.327044	+	0.566457i	0.654880	+	0.755733i	$0.272719\pi$
$198$	−3.81062	−	2.20006i	−0.270809	−	0.156352i
$199$	8.10876	+	14.0448i	0.574815	+	0.995609i	0.996062	+	0.0886625i	$0.0282593\pi$
$199$	8.10876	+	14.0448i	0.574815	+	0.995609i	−0.421247	+	0.906946i	$0.638407\pi$
$200$		0			0
$201$	1.58068	−	0.912609i	0.111493	−	0.0643705i
$202$	−3.40013	−	5.88919i	−0.239232	−	0.414362i
$203$	−20.0312			−1.40591
$204$	2.00000	+	3.46410i	0.140028	+	0.242536i
$205$		0			0
$206$	−4.58246	−	2.64568i	−0.319275	−	0.184333i
$207$			0.976584i			0.0678773i
$208$	−2.24376	−	2.82233i	−0.155577	−	0.195693i
$209$	35.3981			2.44854
$210$		0			0
$211$	0.809848	−	1.40270i	0.0557522	−	0.0965657i	−0.836802	−	0.547505i	$-0.815578\pi$
$211$	0.809848	−	1.40270i	0.0557522	−	0.0965657i	0.892555	+	0.450939i	$0.148911\pi$
$212$	−11.6990	+	6.75444i	−0.803493	+	0.463897i
$213$	−7.95317			−0.544942
$214$	14.6603	−	8.46410i	1.00215	−	0.578594i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	25.9070	−	14.9574i	1.75868	−	1.01537i
$218$	−11.0853	−	6.40013i	−0.750794	−	0.433471i
$219$	3.77684	+	2.18056i	0.255215	+	0.147348i
$220$		0			0
$221$	−2.12795	−	14.2644i	−0.143141	−	0.959524i
$222$		−	3.79603i		−	0.254773i
$223$	1.11836	−	1.93705i	0.0748906	−	0.129714i	−0.826148	−	0.563453i	$-0.809473\pi$
$223$	1.11836	−	1.93705i	0.0748906	−	0.129714i	0.901039	+	0.433739i	$0.142806\pi$
$224$	2.32233	−	4.02239i	0.155167	−	0.268757i
$225$		0			0
$226$		−	13.0662i		−	0.869148i
$227$	−7.66025	−	13.2679i	−0.508429	−	0.880625i	−0.999952	−	0.00976038i	$-0.996893\pi$
$227$	−7.66025	−	13.2679i	−0.508429	−	0.880625i	0.491523	−	0.870864i	$-0.336440\pi$
$228$	−4.02239	−	6.96699i	−0.266389	−	0.461400i
$229$		−	10.1279i		−	0.669274i	−0.942347	−	0.334637i	$-0.891386\pi$
$229$		−	10.1279i		−	0.669274i	0.942347	−	0.334637i	$-0.108614\pi$
$230$		0			0
$231$	−10.2185	+	17.6990i	−0.672331	+	1.16451i
$232$	−2.15637	+	3.73494i	−0.141572	+	0.245211i
$233$		−	20.7519i		−	1.35950i	−0.733444	−	0.679750i	$-0.762088\pi$
$233$		−	20.7519i		−	1.35950i	0.733444	−	0.679750i	$-0.237912\pi$
$234$	1.32233	−	3.35432i	0.0864434	−	0.219279i
$235$		0			0
$236$	−1.88842	−	1.09028i	−0.122926	−	0.0709711i
$237$	12.9332	+	7.46699i	0.840102	+	0.485033i
$238$	16.0896	−	9.28932i	1.04293	−	0.602137i
$239$		−	24.3539i		−	1.57532i	−0.616107	−	0.787662i	$-0.711291\pi$
$239$		−	24.3539i		−	1.57532i	0.616107	−	0.787662i	$-0.288709\pi$
$240$		0			0
$241$	−17.2066	+	9.93423i	−1.10837	+	0.639920i	−0.938408	−	0.345530i	$-0.887699\pi$
$241$	−17.2066	+	9.93423i	−1.10837	+	0.639920i	−0.169966	+	0.985450i	$0.554366\pi$
$242$	−8.36112			−0.537473
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−3.73205	+	6.46410i	−0.238920	+	0.413822i
$245$		0			0
$246$	7.28932			0.464750
$247$	4.27973	+	28.6884i	0.272312	+	1.82540i
$248$		−	6.44069i		−	0.408984i
$249$	−3.04056	−	1.75547i	−0.192688	−	0.111248i
$250$		0			0
$251$	6.78566	+	11.7531i	0.428307	+	0.741849i	0.996723	−	0.0808920i	$-0.0257769\pi$
$251$	6.78566	+	11.7531i	0.428307	+	0.741849i	−0.568416	+	0.822741i	$0.692444\pi$
$252$	4.64466			0.292586
$253$	2.14855	+	3.72139i	0.135078	+	0.233962i
$254$	−10.5825	+	6.10978i	−0.664002	+	0.383362i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.573569	+	0.331150i	0.0357783	+	0.0206566i	0.517782	−	0.855512i	$-0.326758\pi$
$257$	0.573569	+	0.331150i	0.0357783	+	0.0206566i	−0.482004	+	0.876169i	$0.660091\pi$
$258$	−0.358228	+	0.620469i	−0.0223023	+	0.0386287i
$259$	−17.6312			−1.09555
$260$		0			0
$261$	−4.31274			−0.266952
$262$	0.189378	−	0.328013i	0.0116998	−	0.0202647i
$263$	26.6301	+	15.3749i	1.64208	+	0.948058i	0.980091	+	0.198548i	$0.0636225\pi$
$263$	26.6301	+	15.3749i	1.64208	+	0.948058i	0.661993	+	0.749510i	$0.269711\pi$
$264$	2.20006	+	3.81062i	0.135405	+	0.234528i
$265$		0			0
$266$	−32.3593	+	18.6826i	−1.98408	+	1.14551i
$267$	−4.08637	−	7.07780i	−0.250082	−	0.433154i
$268$	−1.82522			−0.111493
$269$	−1.87205	−	3.24249i	−0.114141	−	0.197698i	0.803295	−	0.595581i	$-0.203078\pi$
$269$	−1.87205	−	3.24249i	−0.114141	−	0.197698i	−0.917436	+	0.397883i	$0.869745\pi$
$270$		0			0
$271$	24.0419	+	13.8806i	1.46044	+	0.843186i	0.999031	−	0.0440009i	$-0.0140104\pi$
$271$	24.0419	+	13.8806i	1.46044	+	0.843186i	0.461410	+	0.887187i	$0.347344\pi$
$272$		−	4.00000i		−	0.242536i
$273$	−15.5797	−	6.14177i	−0.942924	−	0.371717i
$274$	1.25235			0.0756575
$275$		0			0
$276$	0.488292	−	0.845746i	0.0293917	−	0.0509079i
$277$	−10.3855	+	5.99609i	−0.624006	+	0.360270i	−0.778427	−	0.627735i	$-0.783982\pi$
$277$	−10.3855	+	5.99609i	−0.624006	+	0.360270i	0.154421	+	0.988005i	$0.450649\pi$
$278$	−3.35534			−0.201240
$279$	5.57780	−	3.22034i	0.333934	−	0.192797i
$280$		0			0
$281$		−	3.63888i		−	0.217078i	−0.994092	−	0.108539i	$-0.965383\pi$
$281$		−	3.63888i		−	0.217078i	0.994092	−	0.108539i	$-0.0346172\pi$
$282$	−8.44671	+	4.87671i	−0.502994	+	0.290404i
$283$	−4.19538	−	2.42220i	−0.249389	−	0.143985i	0.370095	−	0.928994i	$-0.379325\pi$
$283$	−4.19538	−	2.42220i	−0.249389	−	0.143985i	−0.619485	+	0.785009i	$0.712658\pi$
$284$	6.88764	+	3.97658i	0.408707	+	0.235967i
$285$		0			0
$286$	−2.34081	−	15.6912i	−0.138415	−	0.927843i
$287$		−	33.8564i		−	1.99848i
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$		0			0
$291$			13.8252i			0.810449i
$292$	−2.18056	−	3.77684i	−0.127608	−	0.221023i
$293$	−1.85041	−	3.20500i	−0.108102	−	0.187238i	0.806899	−	0.590689i	$-0.201144\pi$
$293$	−1.85041	−	3.20500i	−0.108102	−	0.187238i	−0.915001	+	0.403451i	$0.867811\pi$
$294$		−	14.5729i		−	0.849907i
$295$		0			0
$296$	−1.89801	+	3.28745i	−0.110320	+	0.191079i
$297$	−2.20006	+	3.81062i	−0.127661	+	0.221115i
$298$			4.61970i			0.267612i
$299$	−2.75624	+	2.19122i	−0.159398	+	0.126721i
$300$		0			0
$301$	2.88187	+	1.66385i	0.166108	+	0.0959026i
$302$	9.73628	+	5.62124i	0.560260	+	0.323466i
$303$	−5.88919	+	3.40013i	−0.338325	+	0.195332i
$304$			8.04479i			0.461400i
$305$		0			0
$306$	3.46410	−	2.00000i	0.198030	−	0.114332i
$307$	−7.11454			−0.406048			−0.203024	−	0.979174i	$-0.565077\pi$
$307$	−7.11454			−0.406048			−0.203024	+	0.979174i	$0.565077\pi$
$308$	17.6990	−	10.2185i	1.00850	−	0.582256i
$309$	−2.64568	+	4.58246i	−0.150508	+	0.260687i
$310$		0			0
$311$	−19.9148			−1.12926			−0.564632	−	0.825343i	$-0.690982\pi$
$311$	−19.9148			−1.12926			−0.564632	+	0.825343i	$0.690982\pi$
$312$	−2.82233	+	2.24376i	−0.159783	+	0.127028i
$313$		−	6.13950i		−	0.347025i	−0.984832	−	0.173513i	$-0.944488\pi$
$313$		−	6.13950i		−	0.347025i	0.984832	−	0.173513i	$-0.0555117\pi$
$314$	1.30173	+	0.751556i	0.0734611	+	0.0424128i
$315$		0			0
$316$	−7.46699	−	12.9332i	−0.420051	−	0.727550i
$317$	7.85286			0.441061			0.220530	−	0.975380i	$-0.429221\pi$
$317$	7.85286			0.441061			0.220530	+	0.975380i	$0.429221\pi$
$318$	6.75444	+	11.6990i	0.378770	+	0.656050i
$319$	−16.4342	+	9.48829i	−0.920139	+	0.531242i
$320$		0			0
$321$	−8.46410	−	14.6603i	−0.472420	−	0.818256i
$322$	−3.92820	−	2.26795i	−0.218910	−	0.126388i
$323$	−16.0896	+	27.8680i	−0.895248	+	1.55061i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−0.176330			−0.00976601
$327$	−6.40013	+	11.0853i	−0.353928	+	0.613021i
$328$	−6.31274	−	3.64466i	−0.348563	−	0.201243i
$329$	22.6507	+	39.2321i	1.24877	+	2.16294i
$330$		0			0
$331$	27.7093	−	15.9980i	1.52304	−	0.879327i	0.523410	−	0.852081i	$-0.324659\pi$
$331$	27.7093	−	15.9980i	1.52304	−	0.879327i	0.999629	−	0.0272463i	$-0.00867385\pi$
$332$	1.75547	+	3.04056i	0.0963438	+	0.166872i
$333$	−3.79603			−0.208021
$334$	−4.34081	−	7.51851i	−0.237519	−	0.411394i
$335$		0			0
$336$	−4.02239	−	2.32233i	−0.219440	−	0.126693i
$337$		−	35.6432i		−	1.94161i	−0.239867	−	0.970806i	$-0.577104\pi$
$337$		−	35.6432i		−	1.94161i	0.239867	−	0.970806i	$-0.422896\pi$
$338$	12.4340	−	3.79423i	0.676319	−	0.206379i
$339$	−13.0662			−0.709656
$340$		0			0
$341$	14.1699	−	24.5430i	0.767344	−	1.32908i
$342$	−6.96699	+	4.02239i	−0.376732	+	0.217506i
$343$	−35.1734			−1.89918
$344$	0.620469	−	0.358228i	0.0334535	−	0.0193144i
$345$		0			0
$346$			1.78043i			0.0957166i
$347$	−5.97299	+	3.44851i	−0.320647	+	0.185126i	−0.651681	−	0.758493i	$-0.725936\pi$
$347$	−5.97299	+	3.44851i	−0.320647	+	0.185126i	0.331034	+	0.943619i	$0.392603\pi$
$348$	3.73494	+	2.15637i	0.200214	+	0.115593i
$349$	−16.7321	−	9.66025i	−0.895646	−	0.517102i	−0.0198610	−	0.999803i	$-0.506322\pi$
$349$	−16.7321	−	9.66025i	−0.895646	−	0.517102i	−0.875785	+	0.482701i	$0.839656\pi$
$350$		0			0
$351$	−3.35432	−	1.32233i	−0.179040	−	0.0705807i
$352$		−	4.40013i		−	0.234528i
$353$	−13.7086	+	23.7441i	−0.729637	+	1.26377i	0.227400	+	0.973802i	$0.426978\pi$
$353$	−13.7086	+	23.7441i	−0.729637	+	1.26377i	−0.957037	+	0.289967i	$0.906356\pi$
$354$	−1.09028	+	1.88842i	−0.0579477	+	0.100368i
$355$		0			0
$356$			8.17274i			0.433154i
$357$	−9.28932	−	16.0896i	−0.491643	−	0.851550i
$358$	8.70786	+	15.0825i	0.460225	+	0.797133i
$359$			14.3611i			0.757951i	0.925407	+	0.378975i	$0.123723\pi$
$359$			14.3611i			0.757951i	−0.925407	+	0.378975i	$0.876277\pi$
$360$		0			0
$361$	22.8593	−	39.5935i	1.20312	−	2.08387i
$362$	5.18056	−	8.97299i	0.272284	−	0.471610i
$363$			8.36112i			0.438845i
$364$	10.4215	+	13.1088i	0.546235	+	0.687086i
$365$		0			0
$366$	6.46410	+	3.73205i	0.337884	+	0.195077i
$367$	11.9298	+	6.88764i	0.622728	+	0.359532i	0.777930	−	0.628351i	$-0.216270\pi$
$367$	11.9298	+	6.88764i	0.622728	+	0.359532i	−0.155202	+	0.987883i	$0.549603\pi$
$368$	−0.845746	+	0.488292i	−0.0440876	+	0.0254540i
$369$		−	7.28932i		−	0.379467i
$370$		0			0
$371$	54.3381	−	31.3721i	2.82109	−	1.62876i
$372$	−6.44069			−0.333934
$373$	28.9795	−	16.7313i	1.50050	−	0.866316i	0.500504	−	0.865734i	$-0.333148\pi$
$373$	28.9795	−	16.7313i	1.50050	−	0.866316i	1.00000		0.000581860i	$-0.000185212\pi$
$374$	8.80025	−	15.2425i	0.455050	−	0.788170i
$375$		0			0
$376$	9.75342			0.502994
$377$	−9.67674	−	12.1720i	−0.498377	−	0.626888i
$378$		−	4.64466i		−	0.238896i
$379$	28.9052	+	16.6884i	1.48476	+	0.857227i	0.999850	−	0.0173371i	$-0.00551884\pi$
$379$	28.9052	+	16.6884i	1.48476	+	0.857227i	0.484910	+	0.874564i	$0.338852\pi$
$380$		0			0
$381$	6.10978	+	10.5825i	0.313014	+	0.542156i
$382$	−0.897014			−0.0458952
$383$	−3.66519	−	6.34829i	−0.187282	−	0.324383i	0.757061	−	0.653344i	$-0.226635\pi$
$383$	−3.66519	−	6.34829i	−0.187282	−	0.324383i	−0.944343	+	0.328962i	$0.893301\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$		0			0
$386$	10.1322	+	17.5494i	0.515714	+	0.893243i
$387$	0.620469	+	0.358228i	0.0315402	+	0.0182098i
$388$	6.91261	−	11.9730i	0.350935	−	0.607836i
$389$	32.6198			1.65389			0.826946	−	0.562282i	$-0.190076\pi$
$389$	32.6198			1.65389			0.826946	+	0.562282i	$0.190076\pi$
$390$		0			0
$391$	−3.90633			−0.197552
$392$	−7.28643	+	12.6205i	−0.368020	+	0.637430i
$393$	−0.328013	−	0.189378i	−0.0165461	−	0.00955288i
$394$	−4.59028	−	7.95060i	−0.231255	−	0.400545i
$395$		0			0
$396$	3.81062	−	2.20006i	0.191491	−	0.110557i
$397$	7.23416	+	12.5299i	0.363072	+	0.628860i	0.988465	−	0.151451i	$-0.0483945\pi$
$397$	7.23416	+	12.5299i	0.363072	+	0.628860i	−0.625392	+	0.780310i	$0.715061\pi$
$398$	−16.2175			−0.812911
$399$	18.6826	+	32.3593i	0.935302	+	1.61999i
$400$		0			0
$401$	−6.31096	−	3.64364i	−0.315154	−	0.181955i	0.334076	−	0.942546i	$-0.391576\pi$
$401$	−6.31096	−	3.64364i	−0.315154	−	0.181955i	−0.649231	+	0.760592i	$0.724909\pi$
$402$			1.82522i			0.0910336i
$403$	21.6041	+	8.51671i	1.07618	+	0.424248i
$404$	6.80025			0.338325
$405$		0			0
$406$	10.0156	−	17.3475i	0.497066	−	0.860943i
$407$	−14.4652	+	8.35150i	−0.717014	+	0.413968i
$408$	−4.00000			−0.198030
$409$	21.2840	−	12.2883i	1.05242	−	0.607617i	0.129097	−	0.991632i	$-0.458792\pi$
$409$	21.2840	−	12.2883i	1.05242	−	0.607617i	0.923327	+	0.384015i	$0.125459\pi$
$410$		0			0
$411$		−	1.25235i		−	0.0617741i
$412$	4.58246	−	2.64568i	0.225761	−	0.130343i
$413$	8.77106	+	5.06397i	0.431596	+	0.249182i
$414$	−0.845746	−	0.488292i	−0.0415662	−	0.0239982i
$415$		0			0
$416$	3.56609	−	0.531987i	0.174842	−	0.0260828i
$417$			3.35534i			0.164312i
$418$	−17.6990	+	30.6556i	−0.865688	+	1.49942i
$419$	7.77684	−	13.4699i	0.379923	−	0.658047i	−0.611127	−	0.791532i	$-0.709284\pi$
$419$	7.77684	−	13.4699i	0.379923	−	0.658047i	0.991051	+	0.133486i	$0.0426170\pi$
$420$		0			0
$421$			22.3143i			1.08753i	0.839237	+	0.543766i	$0.183002\pi$
$421$			22.3143i			1.08753i	−0.839237	+	0.543766i	$0.816998\pi$
$422$	0.809848	+	1.40270i	0.0394228	+	0.0682822i
$423$	4.87671	+	8.44671i	0.237114	+	0.410693i
$424$		−	13.5089i		−	0.656050i
$425$		0			0
$426$	3.97658	−	6.88764i	0.192666	−	0.333707i
$427$	17.3341	−	30.0236i	0.838856	−	1.45294i
$428$			16.9282i			0.818256i
$429$	−15.6912	+	2.34081i	−0.757580	+	0.113015i
$430$		0			0
$431$	21.0135	+	12.1322i	1.01219	+	0.584386i	0.911831	−	0.410565i	$-0.134669\pi$
$431$	21.0135	+	12.1322i	1.01219	+	0.584386i	0.100356	+	0.994952i	$0.468002\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$	−20.0042	+	11.5494i	−0.961342	+	0.555031i	−0.896586	−	0.442870i	$-0.853960\pi$
$433$	−20.0042	+	11.5494i	−0.961342	+	0.555031i	−0.0647561	+	0.997901i	$0.520627\pi$
$434$			29.9148i			1.43596i
$435$		0			0
$436$	11.0853	−	6.40013i	0.530892	−	0.306510i
$437$	7.85641			0.375823
$438$	−3.77684	+	2.18056i	−0.180464	+	0.104191i
$439$	19.9980	−	34.6375i	0.954450	−	1.65316i	0.218829	−	0.975763i	$-0.429776\pi$
$439$	19.9980	−	34.6375i	0.954450	−	1.65316i	0.735621	−	0.677393i	$-0.236890\pi$
$440$		0			0
$441$	−14.5729			−0.693946
$442$	13.4173	+	5.28932i	0.638194	+	0.251587i
$443$			15.6036i			0.741350i	0.928763	+	0.370675i	$0.120874\pi$
$443$			15.6036i			0.741350i	−0.928763	+	0.370675i	$0.879126\pi$
$444$	3.28745	+	1.89801i	0.156016	+	0.0900757i
$445$		0			0
$446$	1.11836	+	1.93705i	0.0529557	+	0.0917219i
$447$	4.61970			0.218504
$448$	2.32233	+	4.02239i	0.109720	+	0.190040i
$449$	−23.3863	+	13.5021i	−1.10367	+	0.637203i	−0.937182	−	0.348841i	$-0.886575\pi$
$449$	−23.3863	+	13.5021i	−1.10367	+	0.637203i	−0.166486	+	0.986044i	$0.553242\pi$
$450$		0			0
$451$	−16.0370	−	27.7768i	−0.755151	−	1.30796i
$452$	11.3156	+	6.53308i	0.532242	+	0.307290i
$453$	5.62124	−	9.73628i	0.264109	−	0.457450i
$454$	15.3205			0.719027
$455$		0			0
$456$	8.04479			0.376732
$457$	−8.89342	+	15.4039i	−0.416017	+	0.720562i	−0.995535	−	0.0943975i	$-0.969908\pi$
$457$	−8.89342	+	15.4039i	−0.416017	+	0.720562i	0.579518	+	0.814959i	$0.303241\pi$
$458$	8.77106	+	5.06397i	0.409845	+	0.236624i
$459$	−2.00000	−	3.46410i	−0.0933520	−	0.161690i
$460$		0			0
$461$	21.6205	−	12.4826i	1.00697	−	0.581372i	0.0966638	−	0.995317i	$-0.469183\pi$
$461$	21.6205	−	12.4826i	1.00697	−	0.581372i	0.910302	+	0.413945i	$0.135849\pi$
$462$	−10.2185	−	17.6990i	−0.475410	−	0.823434i
$463$	−15.6389			−0.726801			−0.363400	−	0.931633i	$-0.618384\pi$
$463$	−15.6389			−0.726801			−0.363400	+	0.931633i	$0.618384\pi$
$464$	−2.15637	−	3.73494i	−0.100107	−	0.173390i
$465$		0			0
$466$	17.9716	+	10.3759i	0.832521	+	0.480656i
$467$		−	2.43914i		−	0.112870i	−0.998406	−	0.0564349i	$-0.982027\pi$
$467$		−	2.43914i		−	0.112870i	0.998406	−	0.0564349i	$-0.0179733\pi$
$468$	2.24376	+	2.82233i	0.103718	+	0.130462i
$469$	8.47751			0.391455
$470$		0			0
$471$	0.751556	−	1.30173i	0.0346299	−	0.0599807i
$472$	1.88842	−	1.09028i	0.0869215	−	0.0501842i
$473$	3.15250			0.144952
$474$	−12.9332	+	7.46699i	−0.594042	+	0.342970i
$475$		0			0
$476$			18.5786i			0.851550i
$477$	11.6990	−	6.75444i	0.535662	−	0.309265i
$478$	21.0911	+	12.1770i	0.964685	+	0.556961i
$479$	−12.2857	−	7.09317i	−0.561349	−	0.324095i	0.192338	−	0.981329i	$-0.438393\pi$
$479$	−12.2857	−	7.09317i	−0.561349	−	0.324095i	−0.753687	+	0.657234i	$0.771726\pi$
$480$		0			0
$481$	−8.51737	−	10.7136i	−0.388358	−	0.488500i
$482$		−	19.8685i		−	0.904983i
$483$	−2.26795	+	3.92820i	−0.103195	+	0.178739i
$484$	4.18056	−	7.24094i	0.190025	−	0.329134i
$485$		0			0
$486$		−	1.00000i		−	0.0453609i
$487$	2.88164	+	4.99115i	0.130580	+	0.226171i	0.923900	−	0.382633i	$-0.124983\pi$
$487$	2.88164	+	4.99115i	0.130580	+	0.226171i	−0.793320	+	0.608804i	$0.791649\pi$
$488$	−3.73205	−	6.46410i	−0.168942	−	0.292616i
$489$			0.176330i			0.00797392i
$490$		0			0
$491$	−0.537671	+	0.931273i	−0.0242647	+	0.0420278i	−0.877903	−	0.478839i	$-0.841058\pi$
$491$	−0.537671	+	0.931273i	−0.0242647	+	0.0420278i	0.853638	+	0.520867i	$0.174391\pi$
$492$	−3.64466	+	6.31274i	−0.164314	+	0.284600i
$493$		−	17.2509i		−	0.776943i
$494$	−26.9848	−	10.6379i	−1.21410	−	0.478620i
$495$		0			0
$496$	5.57780	+	3.22034i	0.250450	+	0.144598i
$497$	−31.9908	−	18.4699i	−1.43498	−	0.828487i
$498$	3.04056	−	1.75547i	0.136251	−	0.0786644i
$499$			14.7534i			0.660454i	0.943902	+	0.330227i	$0.107125\pi$
$499$			14.7534i			0.660454i	−0.943902	+	0.330227i	$0.892875\pi$
$500$		0			0
$501$	−7.51851	+	4.34081i	−0.335902	+	0.193933i
$502$	−13.5713			−0.605717
$503$	23.0898	−	13.3309i	1.02952	−	0.594395i	0.112675	−	0.993632i	$-0.464058\pi$
$503$	23.0898	−	13.3309i	1.02952	−	0.594395i	0.916848	+	0.399236i	$0.130725\pi$
$504$	−2.32233	+	4.02239i	−0.103445	+	0.179172i
$505$		0			0
$506$	−4.29709			−0.191029
$507$	−3.79423	−	12.4340i	−0.168508	−	0.552212i
$508$		−	12.2196i		−	0.542156i
$509$	−12.2807	−	7.09028i	−0.544333	−	0.314271i	0.202500	−	0.979282i	$-0.435093\pi$
$509$	−12.2807	−	7.09028i	−0.544333	−	0.314271i	−0.746833	+	0.665011i	$0.768427\pi$
$510$		0			0
$511$	10.1279	+	17.5421i	0.448034	+	0.776018i
$512$	1.00000			0.0441942
$513$	4.02239	+	6.96699i	0.177593	+	0.307600i
$514$	−0.573569	+	0.331150i	−0.0252990	+	0.0146064i
$515$		0			0
$516$	−0.358228	−	0.620469i	−0.0157701	−	0.0273146i
$517$	37.1666	+	21.4581i	1.63459	+	0.943728i
$518$	8.81562	−	15.2691i	0.387336	−	0.670886i
$519$	1.78043			0.0781523
$520$		0			0
$521$	23.7476			1.04040			0.520202	−	0.854043i	$-0.325857\pi$
$521$	23.7476			1.04040			0.520202	+	0.854043i	$0.325857\pi$
$522$	2.15637	−	3.73494i	0.0943817	−	0.163474i
$523$	11.9950	+	6.92532i	0.524505	+	0.302823i	0.738776	−	0.673951i	$-0.235404\pi$
$523$	11.9950	+	6.92532i	0.524505	+	0.302823i	−0.214271	+	0.976774i	$0.568738\pi$
$524$	0.189378	+	0.328013i	0.00827303	+	0.0143293i
$525$		0			0
$526$	−26.6301	+	15.3749i	−1.16113	+	0.670378i
$527$	12.8814	+	22.3112i	0.561121	+	0.971891i
$528$	−4.40013			−0.191491
$529$	−11.0231	−	19.0926i	−0.479267	−	0.830115i
$530$		0			0
$531$	1.88842	+	1.09028i	0.0819504	+	0.0473141i
$532$		−	37.3653i		−	1.61999i
$533$	20.5729	−	16.3555i	0.891110	−	0.708434i
$534$	8.17274			0.353669
$535$		0			0
$536$	0.912609	−	1.58068i	0.0394187	−	0.0682752i
$537$	15.0825	−	8.70786i	0.650856	−	0.375772i
$538$	3.74410			0.161420
$539$	−55.5317	+	32.0612i	−2.39192	+	1.38097i
$540$		0			0
$541$		−	14.8898i		−	0.640164i	−0.947390	−	0.320082i	$-0.896290\pi$
$541$		−	14.8898i		−	0.640164i	0.947390	−	0.320082i	$-0.103710\pi$
$542$	−24.0419	+	13.8806i	−1.03269	+	0.596223i
$543$	−8.97299	−	5.18056i	−0.385068	−	0.222319i
$544$	3.46410	+	2.00000i	0.148522	+	0.0857493i
$545$		0			0
$546$	13.1088	−	10.4215i	0.561003	−	0.445999i
$547$		−	22.2019i		−	0.949284i	−0.880179	−	0.474642i	$-0.842578\pi$
$547$		−	22.2019i		−	0.949284i	0.880179	−	0.474642i	$-0.157422\pi$
$548$	−0.626177	+	1.08457i	−0.0267490	+	0.0463306i
$549$	3.73205	−	6.46410i	0.159280	−	0.275881i
$550$		0			0
$551$			34.6950i			1.47806i
$552$	0.488292	+	0.845746i	0.0207831	+	0.0359973i
$553$	34.6816	+	60.0703i	1.47481	+	2.55445i
$554$		−	11.9922i		−	0.509499i
$555$		0			0
$556$	1.67767	−	2.90581i	0.0711491	−	0.123234i
$557$	−0.949847	+	1.64518i	−0.0402463	+	0.0697087i	−0.885447	−	0.464741i	$-0.846148\pi$
$557$	−0.949847	+	1.64518i	−0.0402463	+	0.0697087i	0.845201	+	0.534449i	$0.179481\pi$
$558$			6.44069i			0.272656i
$559$	0.381146	+	2.55495i	0.0161207	+	0.108063i
$560$		0			0
$561$	−15.2425	−	8.80025i	−0.643538	−	0.371547i
$562$	3.15137	+	1.81944i	0.132932	+	0.0767485i
$563$	−1.48956	+	0.860000i	−0.0627777	+	0.0362447i	−0.531060	−	0.847334i	$-0.678206\pi$
$563$	−1.48956	+	0.860000i	−0.0627777	+	0.0362447i	0.468283	+	0.883579i	$0.344873\pi$
$564$		−	9.75342i		−	0.410693i
$565$		0			0
$566$	4.19538	−	2.42220i	0.176345	−	0.101813i
$567$	−4.64466			−0.195057
$568$	−6.88764	+	3.97658i	−0.288999	+	0.166854i
$569$	0.300960	−	0.521278i	0.0126169	−	0.0218531i	−0.859648	−	0.510887i	$-0.829317\pi$
$569$	0.300960	−	0.521278i	0.0126169	−	0.0218531i	0.872265	+	0.489034i	$0.162650\pi$
$570$		0			0
$571$	11.9808			0.501381			0.250691	−	0.968067i	$-0.419342\pi$
$571$	11.9808			0.501381			0.250691	+	0.968067i	$0.419342\pi$
$572$	14.7594	+	5.81842i	0.617122	+	0.243280i
$573$			0.897014i			0.0374733i
$574$	29.3205	+	16.9282i	1.22381	+	0.706570i
$575$		0			0
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−43.0293			−1.79133			−0.895667	−	0.444725i	$-0.853301\pi$
$577$	−43.0293			−1.79133			−0.895667	+	0.444725i	$0.853301\pi$
$578$	−0.500000	−	0.866025i	−0.0207973	−	0.0360219i
$579$	17.5494	−	10.1322i	0.729330	−	0.421079i
$580$		0			0
$581$	−8.15355	−	14.1224i	−0.338266	−	0.585894i
$582$	−11.9730	−	6.91261i	−0.496296	−	0.286537i
$583$	29.7204	−	51.4773i	1.23089	−	2.13197i
$584$	4.36112			0.180464
$585$		0			0
$586$	3.70081			0.152879
$587$	8.95740	−	15.5147i	0.369711	−	0.640359i	−0.619809	−	0.784753i	$-0.712790\pi$
$587$	8.95740	−	15.5147i	0.369711	−	0.640359i	0.989520	+	0.144394i	$0.0461233\pi$
$588$	12.6205	+	7.28643i	0.520459	+	0.300487i
$589$	−25.9070	−	44.8722i	−1.06748	−	1.84893i
$590$		0			0
$591$	−7.95060	+	4.59028i	−0.327044	+	0.188819i
$592$	−1.89801	−	3.28745i	−0.0780078	−	0.135114i
$593$	−0.669624			−0.0274981			−0.0137491	−	0.999905i	$-0.504377\pi$
$593$	−0.669624			−0.0274981			−0.0137491	+	0.999905i	$0.504377\pi$
$594$	−2.20006	−	3.81062i	−0.0902697	−	0.156352i
$595$		0			0
$596$	−4.00077	−	2.30985i	−0.163878	−	0.0946151i
$597$			16.2175i			0.663739i
$598$	−0.519530	−	3.48258i	−0.0212452	−	0.142413i
$599$	−1.29241			−0.0528066			−0.0264033	−	0.999651i	$-0.508405\pi$
$599$	−1.29241			−0.0528066			−0.0264033	+	0.999651i	$0.508405\pi$
$600$		0			0
$601$	5.73671	−	9.93627i	0.234005	−	0.405309i	−0.724978	−	0.688772i	$-0.758150\pi$
$601$	5.73671	−	9.93627i	0.234005	−	0.405309i	0.958983	+	0.283463i	$0.0914834\pi$
$602$	−2.88187	+	1.66385i	−0.117456	+	0.0678134i
$603$	1.82522			0.0743286
$604$	−9.73628	+	5.62124i	−0.396164	+	0.228725i
$605$		0			0
$606$		−	6.80025i		−	0.276241i
$607$	−20.9010	+	12.0672i	−0.848344	+	0.489792i	−0.860092	−	0.510139i	$-0.829594\pi$
$607$	−20.9010	+	12.0672i	−0.848344	+	0.489792i	0.0117477	+	0.999931i	$0.496261\pi$
$608$	−6.96699	−	4.02239i	−0.282549	−	0.163130i
$609$	−17.3475	−	10.0156i	−0.702957	−	0.405852i
$610$		0			0
$611$	−12.8972	+	32.7161i	−0.521766	+	1.32355i
$612$			4.00000i			0.161690i
$613$	14.4751	−	25.0716i	0.584644	−	1.01263i	−0.410276	−	0.911961i	$-0.634568\pi$
$613$	14.4751	−	25.0716i	0.584644	−	1.01263i	0.994920	−	0.100671i	$-0.0320991\pi$
$614$	3.55727	−	6.16137i	0.143560	−	0.248653i
$615$		0			0
$616$			20.4371i			0.823434i
$617$	−0.420655	−	0.728597i	−0.0169349	−	0.0293322i	0.857434	−	0.514594i	$-0.172057\pi$
$617$	−0.420655	−	0.728597i	−0.0169349	−	0.0293322i	−0.874369	+	0.485262i	$0.838724\pi$
$618$	−2.64568	−	4.58246i	−0.106425	−	0.184333i
$619$		−	6.25076i		−	0.251239i	−0.992078	−	0.125620i	$-0.959908\pi$
$619$		−	6.25076i		−	0.251239i	0.992078	−	0.125620i	$-0.0400919\pi$
$620$		0			0
$621$	−0.488292	+	0.845746i	−0.0195945	+	0.0339386i
$622$	9.95740	−	17.2467i	0.399255	−	0.691530i
$623$		−	37.9596i		−	1.52082i
$624$	−0.531987	−	3.56609i	−0.0212965	−	0.142758i
$625$		0			0
$626$	5.31696	+	3.06975i	0.212509	+	0.122692i
$627$	30.6556	+	17.6990i	1.22427	+	0.706832i
$628$	−1.30173	+	0.751556i	−0.0519448	+	0.0299904i
$629$		−	15.1841i		−	0.605430i
$630$		0			0
$631$	2.61970	−	1.51248i	0.104288	−	0.0602110i	−0.446949	−	0.894560i	$-0.647489\pi$
$631$	2.61970	−	1.51248i	0.104288	−	0.0602110i	0.551237	+	0.834349i	$0.314156\pi$
$632$	14.9340			0.594042
$633$	1.40270	−	0.809848i	0.0557522	−	0.0321886i
$634$	−3.92643	+	6.80078i	−0.155938	+	0.270093i
$635$		0			0
$636$	−13.5089			−0.535662
$637$	−32.6980	−	41.1294i	−1.29554	−	1.62961i
$638$		−	18.9766i		−	0.751290i
$639$	−6.88764	−	3.97658i	−0.272471	−	0.157311i
$640$		0			0
$641$	0.386305	+	0.669099i	0.0152581	+	0.0264278i	0.873554	−	0.486728i	$-0.161810\pi$
$641$	0.386305	+	0.669099i	0.0152581	+	0.0264278i	−0.858296	+	0.513156i	$0.828476\pi$
$642$	16.9282			0.668103
$643$	−9.68726	−	16.7788i	−0.382028	−	0.661693i	0.609324	−	0.792922i	$-0.291441\pi$
$643$	−9.68726	−	16.7788i	−0.382028	−	0.661693i	−0.991352	+	0.131229i	$0.958108\pi$
$644$	3.92820	−	2.26795i	0.154793	−	0.0893697i
$645$		0			0
$646$	−16.0896	−	27.8680i	−0.633036	−	1.09645i
$647$	−23.5477	−	13.5953i	−0.925755	−	0.534485i	−0.0402882	−	0.999188i	$-0.512828\pi$
$647$	−23.5477	−	13.5953i	−0.925755	−	0.534485i	−0.885466	+	0.464703i	$0.846161\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	9.59473			0.376626
$650$		0			0
$651$	29.9148			1.17245
$652$	0.0881650	−	0.152706i	0.00345281	−	0.00598044i
$653$	13.6797	+	7.89799i	0.535329	+	0.309072i	0.743184	−	0.669088i	$-0.233315\pi$
$653$	13.6797	+	7.89799i	0.535329	+	0.309072i	−0.207855	+	0.978160i	$0.566648\pi$
$654$	−6.40013	−	11.0853i	−0.250265	−	0.433471i
$655$		0			0
$656$	6.31274	−	3.64466i	0.246471	−	0.142300i
$657$	2.18056	+	3.77684i	0.0850717	+	0.147348i
$658$	−45.3013			−1.76603
$659$	15.2381	+	26.3932i	0.593593	+	1.02813i	0.993744	+	0.111684i	$0.0356243\pi$
$659$	15.2381	+	26.3932i	0.593593	+	1.02813i	−0.400151	+	0.916449i	$0.631042\pi$
$660$		0			0
$661$	−24.1514	−	13.9438i	−0.939379	−	0.542351i	−0.0496136	−	0.998768i	$-0.515799\pi$
$661$	−24.1514	−	13.9438i	−0.939379	−	0.542351i	−0.889766	+	0.456418i	$0.849132\pi$
$662$			31.9959i			1.24356i
$663$	5.28932	−	13.4173i	0.205420	−	0.521084i
$664$	−3.51093			−0.136251
$665$		0			0
$666$	1.89801	−	3.28745i	0.0735465	−	0.127386i
$667$	−3.64748	+	2.10587i	−0.141231	+	0.0815397i
$668$	8.68162			0.335902
$669$	1.93705	−	1.11836i	0.0748906	−	0.0432381i
$670$		0			0
$671$		−	32.8430i		−	1.26789i
$672$	4.02239	−	2.32233i	0.155167	−	0.0895858i
$673$	0.847086	+	0.489066i	0.0326528	+	0.0188521i	0.516238	−	0.856445i	$-0.327332\pi$
$673$	0.847086	+	0.489066i	0.0326528	+	0.0188521i	−0.483585	+	0.875298i	$0.660666\pi$
$674$	30.8680	+	17.8216i	1.18899	+	0.686463i
$675$		0			0
$676$	−2.93109	+	12.6653i	−0.112734	+	0.487125i
$677$		−	19.1926i		−	0.737630i	−0.929503	−	0.368815i	$-0.879764\pi$
$677$		−	19.1926i		−	0.737630i	0.929503	−	0.368815i	$-0.120236\pi$
$678$	6.53308	−	11.3156i	0.250901	−	0.434574i
$679$	−32.1067	+	55.6105i	−1.23214	+	2.13413i
$680$		0			0
$681$		−	15.3205i		−	0.587083i
$682$	14.1699	+	24.5430i	0.542594	+	0.939801i
$683$	0.755467	+	1.30851i	0.0289071	+	0.0500687i	0.880117	−	0.474757i	$-0.157464\pi$
$683$	0.755467	+	1.30851i	0.0289071	+	0.0500687i	−0.851210	+	0.524825i	$0.824131\pi$
$684$		−	8.04479i		−	0.307600i
$685$		0			0
$686$	17.5867	−	30.4610i	0.671463	−	1.16301i
$687$	5.06397	−	8.77106i	0.193203	−	0.334637i
$688$			0.716456i			0.0273146i
$689$	45.3131	+	17.8632i	1.72629	+	0.680534i
$690$		0			0
$691$	28.6798	+	16.5583i	1.09103	+	0.629907i	0.933851	−	0.357663i	$-0.116426\pi$
$691$	28.6798	+	16.5583i	1.09103	+	0.629907i	0.157180	+	0.987570i	$0.449760\pi$
$692$	−1.54190	−	0.890216i	−0.0586142	−	0.0338409i
$693$	−17.6990	+	10.2185i	−0.672331	+	0.388170i
$694$		−	6.89701i		−	0.261807i
$695$		0			0
$696$	−3.73494	+	2.15637i	−0.141572	+	0.0817369i
$697$	29.1573			1.10441
$698$	16.7321	−	9.66025i	0.633317	−	0.365646i
$699$	10.3759	−	17.9716i	0.392454	−	0.679750i
$700$		0			0
$701$	27.8695			1.05262			0.526308	−	0.850294i	$-0.323576\pi$
$701$	27.8695			1.05262			0.526308	+	0.850294i	$0.323576\pi$
$702$	2.82233	−	2.24376i	0.106522	−	0.0846852i
$703$			30.5382i			1.15177i
$704$	3.81062	+	2.20006i	0.143618	+	0.0829180i
$705$		0			0
$706$	−13.7086	−	23.7441i	−0.515931	−	0.893619i
$707$	−31.5849			−1.18787
$708$	−1.09028	−	1.88842i	−0.0409752	−	0.0709711i
$709$	9.57491	−	5.52808i	0.359593	−	0.207611i	−0.309309	−	0.950962i	$-0.600098\pi$
$709$	9.57491	−	5.52808i	0.359593	−	0.207611i	0.668902	+	0.743350i	$0.266764\pi$
$710$		0			0
$711$	7.46699	+	12.9332i	0.280034	+	0.485033i
$712$	−7.07780	−	4.08637i	−0.265252	−	0.153143i
$713$	3.14493	−	5.44719i	0.117779	−	0.203999i
$714$	18.5786			0.695288
$715$		0			0
$716$	−17.4157			−0.650856
$717$	12.1770	−	21.0911i	0.454757	−	0.787662i
$718$	−12.4371	−	7.18056i	−0.464148	−	0.267976i
$719$	−5.85641	−	10.1436i	−0.218407	−	0.378292i	0.735914	−	0.677075i	$-0.236753\pi$
$719$	−5.85641	−	10.1436i	−0.218407	−	0.378292i	−0.954321	+	0.298783i	$0.903419\pi$
$720$		0			0
$721$	−21.2840	+	12.2883i	−0.792656	+	0.457640i
$722$	22.8593	+	39.5935i	0.850735	+	1.47352i
$723$	−19.8685			−0.738916
$724$	5.18056	+	8.97299i	0.192534	+	0.333479i
$725$		0			0
$726$	−7.24094	−	4.18056i	−0.268736	−	0.155155i
$727$		−	19.4152i		−	0.720071i	−0.932939	−	0.360035i	$-0.882765\pi$
$727$		−	19.4152i		−	0.720071i	0.932939	−	0.360035i	$-0.117235\pi$
$728$	−16.5633	+	2.47090i	−0.613876	+	0.0915777i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−1.43291	+	2.48188i	−0.0529982	+	0.0917956i
$732$	−6.46410	+	3.73205i	−0.238920	+	0.137941i
$733$	−11.9340			−0.440792			−0.220396	−	0.975411i	$-0.570735\pi$
$733$	−11.9340			−0.440792			−0.220396	+	0.975411i	$0.570735\pi$
$734$	−11.9298	+	6.88764i	−0.440335	+	0.254228i
$735$		0			0
$736$		−	0.976584i		−	0.0359973i
$737$	6.95521	−	4.01559i	0.256199	−	0.147916i
$738$	6.31274	+	3.64466i	0.232375	+	0.134162i
$739$	−17.2017	−	9.93141i	−0.632775	−	0.365333i	0.149051	−	0.988830i	$-0.452378\pi$
$739$	−17.2017	−	9.93141i	−0.632775	−	0.365333i	−0.781826	+	0.623497i	$0.785711\pi$
$740$		0			0
$741$	−10.6379	+	26.9848i	−0.390792	+	0.991310i
$742$			62.7442i			2.30341i
$743$	8.24383	−	14.2787i	0.302437	−	0.523836i	−0.674251	−	0.738503i	$-0.735533\pi$
$743$	8.24383	−	14.2787i	0.302437	−	0.523836i	0.976687	+	0.214667i	$0.0688666\pi$
$744$	3.22034	−	5.57780i	0.118063	−	0.204492i
$745$		0			0
$746$			33.4627i			1.22516i
$747$	−1.75547	−	3.04056i	−0.0642292	−	0.111248i
$748$	8.80025	+	15.2425i	0.321769	+	0.557320i
$749$		−	78.6257i		−	2.87292i
$750$		0			0
$751$	−23.3312	+	40.4109i	−0.851368	+	1.47461i	0.0286056	+	0.999591i	$0.490893\pi$
$751$	−23.3312	+	40.4109i	−0.851368	+	1.47461i	−0.879974	+	0.475022i	$0.842440\pi$
$752$	−4.87671	+	8.44671i	−0.177835	+	0.308020i
$753$			13.5713i			0.494566i
$754$	15.3796	−	2.29432i	0.560092	−	0.0835542i
$755$		0			0
$756$	4.02239	+	2.32233i	0.146293	+	0.0844623i
$757$	−2.28282	−	1.31799i	−0.0829705	−	0.0479030i	0.457941	−	0.888983i	$-0.348587\pi$
$757$	−2.28282	−	1.31799i	−0.0829705	−	0.0479030i	−0.540911	+	0.841080i	$0.681921\pi$
$758$	−28.9052	+	16.6884i	−1.04988	+	0.606151i
$759$			4.29709i			0.155975i
$760$		0			0
$761$	0.0693410	−	0.0400340i	0.00251361	−	0.00145123i	−0.498743	−	0.866750i	$-0.666205\pi$
$761$	0.0693410	−	0.0400340i	0.00251361	−	0.00145123i	0.501256	+	0.865299i	$0.332871\pi$
$762$	−12.2196			−0.442668
$763$	−51.4877	+	29.7264i	−1.86398	+	1.07617i
$764$	0.448507	−	0.776837i	0.0162264	−	0.0281050i
$765$		0			0
$766$	7.33038			0.264857
$767$	1.16003	+	7.77606i	0.0418862	+	0.280777i
$768$		−	1.00000i		−	0.0360844i
$769$	−4.92177	−	2.84159i	−0.177484	−	0.102470i	0.408626	−	0.912702i	$-0.366008\pi$
$769$	−4.92177	−	2.84159i	−0.177484	−	0.102470i	−0.586110	+	0.810232i	$0.699341\pi$
$770$		0			0
$771$	0.331150	+	0.573569i	0.0119261	+	0.0206566i
$772$	−20.2644			−0.729330
$773$	3.79425	+	6.57184i	0.136470	+	0.236373i	0.926158	−	0.377136i	$-0.123091\pi$
$773$	3.79425	+	6.57184i	0.136470	+	0.236373i	−0.789688	+	0.613508i	$0.789758\pi$
$774$	−0.620469	+	0.358228i	−0.0223023	+	0.0128762i
$775$		0			0
$776$	6.91261	+	11.9730i	0.248148	+	0.429805i
$777$	−15.2691	−	8.81562i	−0.547776	−	0.316259i
$778$	−16.3099	+	28.2496i	−0.584739	+	1.01280i
$779$	−58.6410			−2.10103
$780$		0			0
$781$	−34.9949			−1.25222
$782$	1.95317	−	3.38298i	0.0698451	−	0.120975i
$783$	−3.73494	−	2.15637i	−0.133476	−	0.0770623i
$784$	−7.28643	−	12.6205i	−0.260230	−	0.450731i
$785$		0			0
$786$	0.328013	−	0.189378i	0.0116998	−	0.00675490i
$787$	−2.36811	−	4.10169i	−0.0844142	−	0.146210i	0.820727	−	0.571320i	$-0.193569\pi$
$787$	−2.36811	−	4.10169i	−0.0844142	−	0.146210i	−0.905141	+	0.425111i	$0.860235\pi$
$788$	9.18056			0.327044
$789$	15.3749	+	26.6301i	0.547361	+	0.948058i
$790$		0			0
$791$	−52.5572	−	30.3439i	−1.86872	−	1.07891i
$792$			4.40013i			0.156352i
$793$	26.6176	−	3.97081i	0.945220	−	0.141008i
$794$	−14.4683			−0.513462
$795$		0			0
$796$	8.10876	−	14.0448i	0.287407	−	0.497804i
$797$	35.5621	−	20.5318i	1.25968	−	0.727274i	0.286664	−	0.958031i	$-0.407454\pi$
$797$	35.5621	−	20.5318i	1.25968	−	0.727274i	0.973011	+	0.230757i	$0.0741203\pi$
$798$	−37.3653			−1.32272
$799$	−33.7868	+	19.5068i	−1.19529	+	0.690102i
$800$		0			0
$801$		−	8.17274i		−	0.288769i
$802$	6.31096	−	3.64364i	0.222848	−	0.128661i
$803$	16.6186	+	9.59473i	0.586456	+	0.338591i
$804$	−1.58068	−	0.912609i	−0.0557465	−	0.0321852i
$805$		0			0
$806$	−18.1777	+	14.4513i	−0.640284	+	0.509027i
$807$		−	3.74410i		−	0.131799i
$808$	−3.40013	+	5.88919i	−0.119616	+	0.207181i
$809$	−13.8003	+	23.9027i	−0.485191	+	0.840376i	−0.999855	−	0.0170163i	$-0.994583\pi$
$809$	−13.8003	+	23.9027i	−0.485191	+	0.840376i	0.514664	+	0.857392i	$0.327917\pi$
$810$		0			0
$811$		−	10.6930i		−	0.375482i	−0.982219	−	0.187741i	$-0.939883\pi$
$811$		−	10.6930i		−	0.375482i	0.982219	−	0.187741i	$-0.0601165\pi$
$812$	10.0156	+	17.3475i	0.351478	+	0.608779i
$813$	13.8806	+	24.0419i	0.486814	+	0.843186i
$814$		−	16.7030i		−	0.585440i
$815$		0			0
$816$	2.00000	−	3.46410i	0.0700140	−	0.121268i
$817$	2.88187	−	4.99154i	0.100824	−	0.174632i
$818$			24.5766i			0.859300i
$819$	−10.4215	−	13.1088i	−0.364157	−	0.458057i
$820$		0			0
$821$	15.2105	+	8.78177i	0.530849	+	0.306486i	0.741362	−	0.671105i	$-0.234180\pi$
$821$	15.2105	+	8.78177i	0.530849	+	0.306486i	−0.210513	+	0.977591i	$0.567513\pi$
$822$	1.08457	+	0.626177i	0.0378288	+	0.0218404i
$823$	−33.5264	+	19.3565i	−1.16866	+	0.674725i	−0.953364	−	0.301824i	$-0.902404\pi$
$823$	−33.5264	+	19.3565i	−1.16866	+	0.674725i	−0.215295	+	0.976549i	$0.569071\pi$
$824$			5.29137i			0.184333i
$825$		0			0
$826$	−8.77106	+	5.06397i	−0.305184	+	0.176198i
$827$	28.4703			0.990010			0.495005	−	0.868890i	$-0.335166\pi$
$827$	28.4703			0.990010			0.495005	+	0.868890i	$0.335166\pi$
$828$	0.845746	−	0.488292i	0.0293917	−	0.0169693i
$829$	−4.14354	+	7.17683i	−0.143911	+	0.249262i	−0.928966	−	0.370165i	$-0.879301\pi$
$829$	−4.14354	+	7.17683i	−0.143911	+	0.249262i	0.785055	+	0.619426i	$0.212635\pi$
$830$		0			0
$831$	−11.9922			−0.416004
$832$	−1.32233	+	3.35432i	−0.0458435	+	0.116290i
$833$		−	58.2915i		−	2.01968i
$834$	−2.90581	−	1.67767i	−0.100620	−	0.0580930i
$835$		0			0
$836$	−17.6990	−	30.6556i	−0.612134	−	1.06025i
$837$	6.44069			0.222623
$838$	7.77684	+	13.4699i	0.268646	+	0.465309i
$839$	36.8606	−	21.2815i	1.27257	−	0.734719i	0.297099	−	0.954847i	$-0.403981\pi$
$839$	36.8606	−	21.2815i	1.27257	−	0.734719i	0.975471	+	0.220128i	$0.0706474\pi$
$840$		0			0
$841$	5.20016	+	9.00693i	0.179316	+	0.310584i
$842$	−19.3247	−	11.1571i	−0.665974	−	0.384500i
$843$	1.81944	−	3.15137i	0.0626649	−	0.108539i
$844$	−1.61970			−0.0557522
$845$		0			0
$846$	−9.75342			−0.335330
$847$	−19.4173	+	33.6317i	−0.667185	+	1.15560i
$848$	11.6990	+	6.75444i	0.401747	+	0.231949i
$849$	−2.42220	−	4.19538i	−0.0831298	−	0.143985i
$850$		0			0
$851$	−3.21047	+	1.85357i	−0.110054	+	0.0635395i
$852$	3.97658	+	6.88764i	0.136236	+	0.235967i
$853$	−28.1380			−0.963425			−0.481713	−	0.876329i	$-0.659985\pi$
$853$	−28.1380			−0.963425			−0.481713	+	0.876329i	$0.659985\pi$
$854$	17.3341	+	30.0236i	0.593161	+	1.02738i
$855$		0			0
$856$	−14.6603	−	8.46410i	−0.501077	−	0.289297i
$857$		−	10.3355i		−	0.353053i	−0.984296	−	0.176526i	$-0.943514\pi$
$857$		−	10.3355i		−	0.353053i	0.984296	−	0.176526i	$-0.0564861\pi$
$858$	5.81842	−	14.7594i	0.198638	−	0.503878i
$859$	−0.380304			−0.0129758			−0.00648791	−	0.999979i	$-0.502065\pi$
$859$	−0.380304			−0.0129758			−0.00648791	+	0.999979i	$0.502065\pi$
$860$		0			0
$861$	16.9282	−	29.3205i	0.576912	−	0.999240i
$862$	−21.0135	+	12.1322i	−0.715724	+	0.413224i
$863$	−47.1484			−1.60495			−0.802475	−	0.596685i	$-0.796484\pi$
$863$	−47.1484			−1.60495			−0.802475	+	0.596685i	$0.796484\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$		0			0
$866$		−	23.0989i		−	0.784932i
$867$	−0.866025	+	0.500000i	−0.0294118	+	0.0169809i
$868$	−25.9070	−	14.9574i	−0.879340	−	0.507687i
$869$	56.9077	+	32.8557i	1.93046	+	1.11455i
$870$		0			0
$871$	4.09535	+	5.15137i	0.138766	+	0.174547i
$872$			12.8003i			0.433471i
$873$	−6.91261	+	11.9730i	−0.233956	+	0.405224i
$874$	−3.92820	+	6.80385i	−0.132873	+	0.230144i
$875$		0			0
$876$		−	4.36112i		−	0.147348i
$877$	20.0206	+	34.6767i	0.676047	+	1.17095i	0.976162	+	0.217045i	$0.0696419\pi$
$877$	20.0206	+	34.6767i	0.676047	+	1.17095i	−0.300114	+	0.953903i	$0.597025\pi$
$878$	19.9980	+	34.6375i	0.674898	+	1.16896i
$879$		−	3.70081i		−	0.124825i
$880$		0			0
$881$	−7.72246	+	13.3757i	−0.260176	+	0.450638i	−0.966289	−	0.257461i	$-0.917114\pi$
$881$	−7.72246	+	13.3757i	−0.260176	+	0.450638i	0.706112	+	0.708100i	$0.250447\pi$
$882$	7.28643	−	12.6205i	0.245347	−	0.424953i
$883$			6.02142i			0.202637i	0.994854	+	0.101318i	$0.0323061\pi$
$883$			6.02142i			0.202637i	−0.994854	+	0.101318i	$0.967694\pi$
$884$	−11.2893	+	8.97504i	−0.379701	+	0.301863i
$885$		0			0
$886$	−13.5131	−	7.80180i	−0.453982	−	0.262107i
$887$	42.5548	+	24.5690i	1.42885	+	0.824947i	0.997030	−	0.0770129i	$-0.0245383\pi$
$887$	42.5548	+	24.5690i	1.42885	+	0.824947i	0.431820	+	0.901960i	$0.357872\pi$
$888$	−3.28745	+	1.89801i	−0.110320	+	0.0636931i
$889$			56.7557i			1.90353i
$890$		0			0
$891$	−3.81062	+	2.20006i	−0.127661	+	0.0737049i
$892$	−2.23671			−0.0748906
$893$	67.9520	−	39.2321i	2.27393	−	1.31285i
$894$	−2.30985	+	4.00077i	−0.0772529	+	0.133806i
$895$		0			0
$896$	−4.64466			−0.155167
$897$	−3.48258	+	0.519530i	−0.116280	+	0.0173466i
$898$		−	27.0042i		−	0.901141i
$899$	24.0556	+	13.8885i	0.802298	+	0.463207i
$900$		0			0
$901$	27.0178	+	46.7962i	0.900093	+	1.55901i
$902$	32.0739			1.06795
$903$	1.66385	+	2.88187i	0.0553694	+	0.0959026i
$904$	−11.3156	+	6.53308i	−0.376352	+	0.217287i
$905$		0			0
$906$	5.62124	+	9.73628i	0.186753	+	0.323466i
$907$	14.1741	+	8.18345i	0.470645	+	0.271727i	0.716510	−	0.697577i	$-0.245739\pi$
$907$	14.1741	+	8.18345i	0.470645	+	0.271727i	−0.245865	+	0.969304i	$0.579072\pi$
$908$	−7.66025	+	13.2679i	−0.254214	+	0.440312i
$909$	−6.80025			−0.225550
$910$		0			0
$911$	−10.4819			−0.347280			−0.173640	−	0.984809i	$-0.555553\pi$
$911$	−10.4819			−0.347280			−0.173640	+	0.984809i	$0.555553\pi$
$912$	−4.02239	+	6.96699i	−0.133195	+	0.230700i
$913$	−13.3788	−	7.72428i	−0.442775	−	0.255636i
$914$	−8.89342	−	15.4039i	−0.294168	−	0.509514i
$915$		0			0
$916$	−8.77106	+	5.06397i	−0.289804	+	0.167318i
$917$	−0.879598	−	1.52351i	−0.0290469	−	0.0503107i
$918$	4.00000			0.132020
$919$	1.60565	+	2.78107i	0.0529655	+	0.0917389i	0.891293	−	0.453429i	$-0.149799\pi$
$919$	1.60565	+	2.78107i	0.0529655	+	0.0917389i	−0.838327	+	0.545168i	$0.816466\pi$
$920$		0			0
$921$	−6.16137	−	3.55727i	−0.203024	−	0.117216i
$922$			24.9652i			0.822184i
$923$	−4.23098	−	28.3617i	−0.139265	−	0.933537i
$924$	20.4371			0.672331
$925$		0			0
$926$	7.81944	−	13.5437i	0.256963	−	0.445073i
$927$	−4.58246	+	2.64568i	−0.150508	+	0.0868956i
$928$	4.31274			0.141572
$929$	−40.2518	+	23.2394i	−1.32062	+	0.762460i	−0.983827	−	0.179120i	$-0.942675\pi$
$929$	−40.2518	+	23.2394i	−1.32062	+	0.762460i	−0.336792	+	0.941579i	$0.609342\pi$
$930$		0			0
$931$			117.236i			3.84224i
$932$	−17.9716	+	10.3759i	−0.588681	+	0.339875i
$933$	−17.2467	−	9.95740i	−0.564632	−	0.325990i
$934$	2.11236	+	1.21957i	0.0691184	+	0.0399055i
$935$		0			0
$936$	−3.56609	+	0.531987i	−0.116561	+	0.0173886i
$937$		−	27.7627i		−	0.906969i	−0.891264	−	0.453485i	$-0.850181\pi$
$937$		−	27.7627i		−	0.906969i	0.891264	−	0.453485i	$-0.149819\pi$
$938$	−4.23876	+	7.34174i	−0.138400	+	0.239716i
$939$	3.06975	−	5.31696i	0.100178	−	0.173513i
$940$		0			0
$941$			20.7962i			0.677935i	0.940798	+	0.338968i	$0.110078\pi$
$941$			20.7962i			0.677935i	−0.940798	+	0.338968i	$0.889922\pi$
$942$	0.751556	+	1.30173i	0.0244870	+	0.0424128i
$943$	−3.55931	−	6.16491i	−0.115907	−	0.200757i
$944$			2.18056i			0.0709711i
$945$		0			0
$946$	−1.57625	+	2.73014i	−0.0512483	+	0.0887646i
$947$	−4.52962	+	7.84554i	−0.147193	+	0.254946i	−0.930189	−	0.367081i	$-0.880357\pi$
$947$	−4.52962	+	7.84554i	−0.147193	+	0.254946i	0.782996	+	0.622027i	$0.213691\pi$
$948$		−	14.9340i		−	0.485033i
$949$	−5.76683	+	14.6286i	−0.187199	+	0.474863i
$950$		0			0
$951$	6.80078	+	3.92643i	0.220530	+	0.127323i
$952$	−16.0896	−	9.28932i	−0.521466	−	0.301069i
$953$	−13.2296	+	7.63811i	−0.428549	+	0.247423i	−0.698728	−	0.715387i	$-0.746250\pi$
$953$	−13.2296	+	7.63811i	−0.428549	+	0.247423i	0.270180	+	0.962810i	$0.412917\pi$
$954$			13.5089i			0.437366i
$955$		0			0
$956$	−21.0911	+	12.1770i	−0.682136	+	0.393831i
$957$	−18.9766			−0.613426
$958$	12.2857	−	7.09317i	0.396934	−	0.229170i
$959$	2.90838	−	5.03746i	0.0939165	−	0.162668i
$960$		0			0
$961$	−10.4824			−0.338143
$962$	13.5370	−	2.01944i	0.436449	−	0.0651093i
$963$		−	16.9282i		−	0.545504i
$964$	17.2066	+	9.93423i	0.554187	+	0.319960i
$965$		0			0
$966$	−2.26795	−	3.92820i	−0.0729701	−	0.126388i
$967$	46.3036			1.48902			0.744511	−	0.667610i	$-0.232683\pi$
$967$	46.3036			1.48902			0.744511	+	0.667610i	$0.232683\pi$
$968$	4.18056	+	7.24094i	0.134368	+	0.232733i
$969$	−27.8680	+	16.0896i	−0.895248	+	0.516872i
$970$		0			0
$971$	−5.98258	−	10.3621i	−0.191990	−	0.332537i	0.753919	−	0.656967i	$-0.228161\pi$
$971$	−5.98258	−	10.3621i	−0.191990	−	0.332537i	−0.945910	+	0.324430i	$0.894828\pi$
$972$	0.866025	+	0.500000i	0.0277778	+	0.0160375i
$973$	−7.79221	+	13.4965i	−0.249807	+	0.432678i
$974$	−5.76329			−0.184668
$975$		0			0
$976$	7.46410			0.238920
$977$	−0.882077	+	1.52780i	−0.0282201	+	0.0488787i	−0.879791	−	0.475362i	$-0.842317\pi$
$977$	−0.882077	+	1.52780i	−0.0282201	+	0.0488787i	0.851570	+	0.524240i	$0.175651\pi$
$978$	−0.152706	−	0.0881650i	−0.00488301	−	0.00281921i
$979$	−17.9805	−	31.1432i	−0.574660	−	0.995341i
$980$		0			0
$981$	−11.0853	+	6.40013i	−0.353928	+	0.204340i
$982$	−0.537671	−	0.931273i	−0.0171578	−	0.0297181i
$983$	−54.2821			−1.73133			−0.865666	−	0.500623i	$-0.833104\pi$
$983$	−54.2821			−1.73133			−0.865666	+	0.500623i	$0.833104\pi$
$984$	−3.64466	−	6.31274i	−0.116188	−	0.201243i
$985$		0			0
$986$	14.9398	+	8.62547i	0.475779	+	0.274691i
$987$			45.3013i			1.44196i
$988$	22.7050	−	18.0506i	0.722344	−	0.574265i
$989$	0.699680			0.0222485
$990$		0			0
$991$	8.73917	−	15.1367i	0.277609	−	0.480833i	−0.693181	−	0.720763i	$-0.743791\pi$
$991$	8.73917	−	15.1367i	0.277609	−	0.480833i	0.970790	+	0.239931i	$0.0771248\pi$
$992$	−5.57780	+	3.22034i	−0.177095	+	0.102246i
$993$	31.9959			1.01536
$994$	31.9908	−	18.4699i	1.01469	−	0.585829i
$995$		0			0
$996$			3.51093i			0.111248i
$997$	−18.4389	+	10.6457i	−0.583965	+	0.337152i	−0.762707	−	0.646744i	$-0.776130\pi$
$997$	−18.4389	+	10.6457i	−0.583965	+	0.337152i	0.178743	+	0.983896i	$0.442797\pi$
$998$	−12.7768	−	7.37671i	−0.404444	−	0.233506i
$999$	−3.28745	−	1.89801i	−0.104010	−	0.0600505i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.y.j.199.4		8
5.2	odd	4		1950.2.bc.g.901.1		8
5.3	odd	4		390.2.bb.c.121.4	✓	8
5.4	even	2		1950.2.y.k.199.1		8
13.10	even	6		1950.2.y.k.49.1		8
15.8	even	4		1170.2.bs.f.901.2		8
65.23	odd	12		390.2.bb.c.361.4	yes	8
65.33	even	12		5070.2.a.ca.1.4		4
65.43	odd	12		5070.2.b.ba.1351.5		8
65.48	odd	12		5070.2.b.ba.1351.4		8
65.49	even	6	inner	1950.2.y.j.49.4		8
65.58	even	12		5070.2.a.bz.1.1		4
65.62	odd	12		1950.2.bc.g.751.1		8
195.23	even	12		1170.2.bs.f.361.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bb.c.121.4	✓	8	5.3	odd	4
390.2.bb.c.361.4	yes	8	65.23	odd	12
1170.2.bs.f.361.2		8	195.23	even	12
1170.2.bs.f.901.2		8	15.8	even	4
1950.2.y.j.49.4		8	65.49	even	6	inner
1950.2.y.j.199.4		8	1.1	even	1	trivial
1950.2.y.k.49.1		8	13.10	even	6
1950.2.y.k.199.1		8	5.4	even	2
1950.2.bc.g.751.1		8	65.62	odd	12
1950.2.bc.g.901.1		8	5.2	odd	4
5070.2.a.bz.1.1		4	65.58	even	12
5070.2.a.ca.1.4		4	65.33	even	12
5070.2.b.ba.1351.4		8	65.48	odd	12
5070.2.b.ba.1351.5		8	65.43	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.y (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(2.32233 + 4.02239i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(2.32233 + 4.02239i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(3.81062 + 2.20006i) q^{11} -1.00000i q^{12} +(-1.32233 + 3.35432i) q^{13} -4.64466 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.46410 + 2.00000i) q^{17} -1.00000 q^{18} +(6.96699 - 4.02239i) q^{19} +4.64466i q^{21} +(-3.81062 + 2.20006i) q^{22} +(0.845746 + 0.488292i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-2.24376 - 2.82233i) q^{26} +1.00000i q^{27} +(2.32233 - 4.02239i) q^{28} +(-2.15637 + 3.73494i) q^{29} -6.44069i q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.20006 + 3.81062i) q^{33} -4.00000i q^{34} +(0.500000 - 0.866025i) q^{36} +(-1.89801 + 3.28745i) q^{37} +8.04479i q^{38} +(-2.82233 + 2.24376i) q^{39} +(-6.31274 - 3.64466i) q^{41} +(-4.02239 - 2.32233i) q^{42} +(0.620469 - 0.358228i) q^{43} -4.40013i q^{44} +(-0.845746 + 0.488292i) q^{46} +9.75342 q^{47} +(-0.866025 + 0.500000i) q^{48} +(-7.28643 + 12.6205i) q^{49} -4.00000 q^{51} +(3.56609 - 0.531987i) q^{52} -13.5089i q^{53} +(-0.866025 - 0.500000i) q^{54} +(2.32233 + 4.02239i) q^{56} +8.04479 q^{57} +(-2.15637 - 3.73494i) q^{58} +(1.88842 - 1.09028i) q^{59} +(-3.73205 - 6.46410i) q^{61} +(5.57780 + 3.22034i) q^{62} +(-2.32233 + 4.02239i) q^{63} +1.00000 q^{64} -4.40013 q^{66} +(0.912609 - 1.58068i) q^{67} +(3.46410 + 2.00000i) q^{68} +(0.488292 + 0.845746i) q^{69} +(-6.88764 + 3.97658i) q^{71} +(0.500000 + 0.866025i) q^{72} +4.36112 q^{73} +(-1.89801 - 3.28745i) q^{74} +(-6.96699 - 4.02239i) q^{76} +20.4371i q^{77} +(-0.531987 - 3.56609i) q^{78} +14.9340 q^{79} +(-0.500000 + 0.866025i) q^{81} +(6.31274 - 3.64466i) q^{82} -3.51093 q^{83} +(4.02239 - 2.32233i) q^{84} +0.716456i q^{86} +(-3.73494 + 2.15637i) q^{87} +(3.81062 + 2.20006i) q^{88} +(-7.07780 - 4.08637i) q^{89} +(-16.5633 + 2.47090i) q^{91} -0.976584i q^{92} +(3.22034 - 5.57780i) q^{93} +(-4.87671 + 8.44671i) q^{94} -1.00000i q^{96} +(6.91261 + 11.9730i) q^{97} +(-7.28643 - 12.6205i) q^{98} +4.40013i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} + 2 q^{7} + 8 q^{8} + 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 4 * q^4 + 2 * q^7 + 8 * q^8 + 4 * q^9	\( 8 q - 4 q^{2} - 4 q^{4} + 2 q^{7} + 8 q^{8} + 4 q^{9} + 6 q^{11} + 6 q^{13} - 4 q^{14} - 4 q^{16} - 8 q^{18} + 6 q^{19} - 6 q^{22} + 6 q^{23} - 12 q^{26} + 2 q^{28} + 8 q^{29} - 4 q^{32} + 2 q^{33} + 4 q^{36} - 10 q^{37} - 6 q^{39} - 48 q^{43} - 6 q^{46} - 16 q^{47} - 14 q^{49} - 32 q^{51} + 6 q^{52} + 2 q^{56} + 8 q^{58} - 24 q^{59} - 16 q^{61} + 30 q^{62} - 2 q^{63} + 8 q^{64} - 4 q^{66} - 12 q^{67} - 4 q^{69} - 12 q^{71} + 4 q^{72} + 24 q^{73} - 10 q^{74} - 6 q^{76} - 6 q^{78} + 20 q^{79} - 4 q^{81} - 32 q^{83} + 6 q^{87} + 6 q^{88} - 42 q^{89} - 10 q^{91} + 4 q^{93} + 8 q^{94} + 36 q^{97} - 14 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 + 2 * q^7 + 8 * q^8 + 4 * q^9 + 6 * q^11 + 6 * q^13 - 4 * q^14 - 4 * q^16 - 8 * q^18 + 6 * q^19 - 6 * q^22 + 6 * q^23 - 12 * q^26 + 2 * q^28 + 8 * q^29 - 4 * q^32 + 2 * q^33 + 4 * q^36 - 10 * q^37 - 6 * q^39 - 48 * q^43 - 6 * q^46 - 16 * q^47 - 14 * q^49 - 32 * q^51 + 6 * q^52 + 2 * q^56 + 8 * q^58 - 24 * q^59 - 16 * q^61 + 30 * q^62 - 2 * q^63 + 8 * q^64 - 4 * q^66 - 12 * q^67 - 4 * q^69 - 12 * q^71 + 4 * q^72 + 24 * q^73 - 10 * q^74 - 6 * q^76 - 6 * q^78 + 20 * q^79 - 4 * q^81 - 32 * q^83 + 6 * q^87 + 6 * q^88 - 42 * q^89 - 10 * q^91 + 4 * q^93 + 8 * q^94 + 36 * q^97 - 14 * q^98

Introduction

L-functions

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