LMFDB - Embedded newform 1950.2.y.k.49.4

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			49.4
Root			$-1.80668 - 1.80668i$ of defining polynomial
Character	$\chi$	$=$	1950.49
Dual form			1950.2.y.k.199.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(0.661290 - 1.14539i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(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} +(0.661290 - 1.14539i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-3.99528 + 2.30668i) q^{11} +1.00000i q^{12} +(-1.66129 + 3.20002i) q^{13} +1.32258 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.46410 - 2.00000i) q^{17} +1.00000 q^{18} +(-1.98387 - 1.14539i) q^{19} -1.32258i q^{21} +(-3.99528 - 2.30668i) q^{22} +(-7.50670 + 4.33399i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-3.60194 + 0.161290i) q^{26} -1.00000i q^{27} +(0.661290 + 1.14539i) q^{28} +(-1.01141 - 1.75182i) q^{29} +10.1321i q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.30668 + 3.99528i) q^{33} -4.00000i q^{34} +(0.500000 + 0.866025i) q^{36} +(-3.40475 - 5.89721i) q^{37} -2.29078i q^{38} +(0.161290 + 3.60194i) q^{39} +(-4.02283 + 2.32258i) q^{41} +(1.14539 - 0.661290i) q^{42} +(7.45269 + 4.30281i) q^{43} -4.61335i q^{44} +(-7.50670 - 4.33399i) q^{46} +9.10926 q^{47} +(-0.866025 - 0.500000i) q^{48} +(2.62539 + 4.54731i) q^{49} -4.00000 q^{51} +(-1.94065 - 3.03873i) q^{52} +0.826674i q^{53} +(0.866025 - 0.500000i) q^{54} +(-0.661290 + 1.14539i) q^{56} -2.29078 q^{57} +(1.01141 - 1.75182i) q^{58} +(-2.72064 - 1.57076i) q^{59} +(-0.267949 + 0.464102i) q^{61} +(-8.77464 + 5.06604i) q^{62} +(-0.661290 - 1.14539i) q^{63} +1.00000 q^{64} -4.61335 q^{66} +(1.59053 + 2.75488i) q^{67} +(3.46410 - 2.00000i) q^{68} +(-4.33399 + 7.50670i) q^{69} +(-9.81724 - 5.66799i) q^{71} +(-0.500000 + 0.866025i) q^{72} -6.28304 q^{73} +(3.40475 - 5.89721i) q^{74} +(1.98387 - 1.14539i) q^{76} +6.10153i q^{77} +(-3.03873 + 1.94065i) q^{78} -2.96774 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-4.02283 - 2.32258i) q^{82} +15.8719 q^{83} +(1.14539 + 0.661290i) q^{84} +8.60562i q^{86} +(-1.75182 - 1.01141i) q^{87} +(3.99528 - 2.30668i) q^{88} +(-10.2746 + 5.93207i) q^{89} +(2.56667 + 4.01896i) q^{91} -8.66799i q^{92} +(5.06604 + 8.77464i) q^{93} +(4.55463 + 7.88885i) q^{94} -1.00000i q^{96} +(-4.40947 + 7.63743i) q^{97} +(-2.62539 + 4.54731i) q^{98} +4.61335i 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 $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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
$7$	0.661290	−	1.14539i	0.249944	−	0.432916i	−0.713566	−	0.700588i	$-0.752921\pi$
$7$	0.661290	−	1.14539i	0.249944	−	0.432916i	0.963510	+	0.267672i	$0.0862544\pi$
$8$	−1.00000			−0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−3.99528	+	2.30668i	−1.20462	+	0.695489i	−0.961580	−	0.274526i	$-0.911479\pi$
$11$	−3.99528	+	2.30668i	−1.20462	+	0.695489i	−0.243043	+	0.970015i	$0.578146\pi$
$12$			1.00000i			0.288675i
$13$	−1.66129	+	3.20002i	−0.460759	+	0.887525i
$13$	−1.66129	+	3.20002i	−0.460759	+	0.887525i
$14$	1.32258			0.353474
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.46410	−	2.00000i	−0.840168	−	0.485071i	0.0171533	−	0.999853i	$-0.494540\pi$
$17$	−3.46410	−	2.00000i	−0.840168	−	0.485071i	−0.857321	+	0.514782i	$0.827873\pi$
$18$	1.00000			0.235702
$19$	−1.98387	−	1.14539i	−0.455131	−	0.262770i	0.254864	−	0.966977i	$-0.417969\pi$
$19$	−1.98387	−	1.14539i	−0.455131	−	0.262770i	−0.709995	+	0.704207i	$0.751303\pi$
$20$		0			0
$21$		−	1.32258i		−	0.288611i
$22$	−3.99528	−	2.30668i	−0.851797	−	0.491785i
$23$	−7.50670	+	4.33399i	−1.56525	+	0.903700i	−0.568544	+	0.822653i	$0.692493\pi$
$23$	−7.50670	+	4.33399i	−1.56525	+	0.903700i	−0.996710	+	0.0810471i	$0.974174\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$		0			0
$26$	−3.60194	+	0.161290i	−0.706399	+	0.0316315i
$27$		−	1.00000i		−	0.192450i
$28$	0.661290	+	1.14539i	0.124972	+	0.216458i
$29$	−1.01141	−	1.75182i	−0.187815	−	0.325305i	0.756707	−	0.653755i	$-0.226807\pi$
$29$	−1.01141	−	1.75182i	−0.187815	−	0.325305i	−0.944521	+	0.328450i	$0.893474\pi$
$30$		0			0
$31$			10.1321i			1.81978i	0.414853	+	0.909888i	$0.363833\pi$
$31$			10.1321i			1.81978i	−0.414853	+	0.909888i	$0.636167\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−2.30668	+	3.99528i	−0.401541	+	0.695489i
$34$		−	4.00000i		−	0.685994i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−3.40475	−	5.89721i	−0.559738	−	0.969495i	−0.997518	−	0.0704126i	$-0.977568\pi$
$37$	−3.40475	−	5.89721i	−0.559738	−	0.969495i	0.437780	−	0.899082i	$-0.355765\pi$
$38$		−	2.29078i		−	0.371613i
$39$	0.161290	+	3.60194i	0.0258270	+	0.576772i
$40$		0			0
$41$	−4.02283	+	2.32258i	−0.628260	+	0.362726i	−0.780078	−	0.625682i	$-0.784821\pi$
$41$	−4.02283	+	2.32258i	−0.628260	+	0.362726i	0.151818	+	0.988408i	$0.451487\pi$
$42$	1.14539	−	0.661290i	0.176737	−	0.102039i
$43$	7.45269	+	4.30281i	1.13652	+	0.656173i	0.945568	−	0.325426i	$-0.105508\pi$
$43$	7.45269	+	4.30281i	1.13652	+	0.656173i	0.190957	+	0.981598i	$0.438841\pi$
$44$		−	4.61335i		−	0.695489i
$45$		0			0
$46$	−7.50670	−	4.33399i	−1.10680	−	0.639012i
$47$	9.10926			1.32872			0.664361	−	0.747412i	$-0.268704\pi$
$47$	9.10926			1.32872			0.664361	+	0.747412i	$0.268704\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	2.62539	+	4.54731i	0.375056	+	0.649616i
$50$		0			0
$51$	−4.00000			−0.560112
$52$	−1.94065	−	3.03873i	−0.269120	−	0.421396i
$53$			0.826674i			0.113552i	0.998387	+	0.0567762i	$0.0180821\pi$
$53$			0.826674i			0.113552i	−0.998387	+	0.0567762i	$0.981918\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$		0			0
$56$	−0.661290	+	1.14539i	−0.0883686	+	0.153059i
$57$	−2.29078			−0.303421
$58$	1.01141	−	1.75182i	0.132805	−	0.230025i
$59$	−2.72064	−	1.57076i	−0.354197	−	0.204496i	0.312335	−	0.949972i	$-0.398889\pi$
$59$	−2.72064	−	1.57076i	−0.354197	−	0.204496i	−0.666532	+	0.745476i	$0.732222\pi$
$60$		0			0
$61$	−0.267949	+	0.464102i	−0.0343074	+	0.0594221i	−0.882669	−	0.469995i	$-0.844256\pi$
$61$	−0.267949	+	0.464102i	−0.0343074	+	0.0594221i	0.848362	+	0.529417i	$0.177589\pi$
$62$	−8.77464	+	5.06604i	−1.11438	+	0.643388i
$63$	−0.661290	−	1.14539i	−0.0833147	−	0.144305i
$64$	1.00000			0.125000
$65$		0			0
$66$	−4.61335			−0.567865
$67$	1.59053	+	2.75488i	0.194314	+	0.336562i	0.946675	−	0.322189i	$-0.104419\pi$
$67$	1.59053	+	2.75488i	0.194314	+	0.336562i	−0.752361	+	0.658751i	$0.771085\pi$
$68$	3.46410	−	2.00000i	0.420084	−	0.242536i
$69$	−4.33399	+	7.50670i	−0.521751	+	0.903700i
$70$		0			0
$71$	−9.81724	−	5.66799i	−1.16509	−	0.672666i	−0.212573	−	0.977145i	$-0.568184\pi$
$71$	−9.81724	−	5.66799i	−1.16509	−	0.672666i	−0.952519	+	0.304479i	$0.901518\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−6.28304			−0.735375			−0.367687	−	0.929949i	$-0.619850\pi$
$73$	−6.28304			−0.735375			−0.367687	+	0.929949i	$0.619850\pi$
$74$	3.40475	−	5.89721i	0.395795	−	0.685536i
$75$		0			0
$76$	1.98387	−	1.14539i	0.227565	−	0.131385i
$77$			6.10153i			0.695334i
$78$	−3.03873	+	1.94065i	−0.344068	+	0.219736i
$79$	−2.96774			−0.333897			−0.166948	−	0.985966i	$-0.553391\pi$
$79$	−2.96774			−0.333897			−0.166948	+	0.985966i	$0.553391\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−4.02283	−	2.32258i	−0.444247	−	0.256486i
$83$	15.8719			1.74216			0.871082	−	0.491138i	$-0.163419\pi$
$83$	15.8719			1.74216			0.871082	+	0.491138i	$0.163419\pi$
$84$	1.14539	+	0.661290i	0.124972	+	0.0721526i
$85$		0			0
$86$			8.60562i			0.927968i
$87$	−1.75182	−	1.01141i	−0.187815	−	0.108435i
$88$	3.99528	−	2.30668i	0.425899	−	0.245893i
$89$	−10.2746	+	5.93207i	−1.08911	+	0.628798i	−0.933339	−	0.358995i	$-0.883119\pi$
$89$	−10.2746	+	5.93207i	−1.08911	+	0.628798i	−0.155771	+	0.987793i	$0.549786\pi$
$90$		0			0
$91$	2.56667	+	4.01896i	0.269060	+	0.421302i
$92$		−	8.66799i		−	0.903700i
$93$	5.06604	+	8.77464i	0.525324	+	0.909888i
$94$	4.55463	+	7.88885i	0.469774	+	0.813673i
$95$		0			0
$96$		−	1.00000i		−	0.102062i
$97$	−4.40947	+	7.63743i	−0.447714	+	0.775463i	−0.998237	−	0.0593568i	$-0.981095\pi$
$97$	−4.40947	+	7.63743i	−0.447714	+	0.775463i	0.550523	+	0.834820i	$0.314428\pi$
$98$	−2.62539	+	4.54731i	−0.265205	+	0.459348i
$99$			4.61335i			0.463660i
$100$		0			0
$101$	−3.61335	−	6.25851i	−0.359542	−	0.622745i	0.628342	−	0.777937i	$-0.283734\pi$
$101$	−3.61335	−	6.25851i	−0.359542	−	0.622745i	−0.987884	+	0.155192i	$0.950400\pi$
$102$	−2.00000	−	3.46410i	−0.198030	−	0.342997i
$103$		−	18.4000i		−	1.81301i	−0.422196	−	0.906505i	$-0.638740\pi$
$103$		−	18.4000i		−	1.81301i	0.422196	−	0.906505i	$-0.361260\pi$
$104$	1.66129	−	3.20002i	0.162903	−	0.313788i
$105$		0			0
$106$	−0.715920	+	0.413337i	−0.0695363	+	0.0401468i
$107$	−2.66025	+	1.53590i	−0.257176	+	0.148481i	−0.623046	−	0.782185i	$-0.714105\pi$
$107$	−2.66025	+	1.53590i	−0.257176	+	0.148481i	0.365869	+	0.930666i	$0.380772\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$			13.2267i			1.26689i	0.773788	+	0.633445i	$0.218360\pi$
$109$			13.2267i			1.26689i	−0.773788	+	0.633445i	$0.781640\pi$
$110$		0			0
$111$	−5.89721	−	3.40475i	−0.559738	−	0.323165i
$112$	−1.32258			−0.124972
$113$	7.00306	+	4.04322i	0.658792	+	0.380354i	0.791817	−	0.610759i	$-0.209136\pi$
$113$	7.00306	+	4.04322i	0.658792	+	0.380354i	−0.133024	+	0.991113i	$0.542469\pi$
$114$	−1.14539	−	1.98387i	−0.107275	−	0.185806i
$115$		0			0
$116$	2.02283			0.187815
$117$	1.94065	+	3.03873i	0.179413	+	0.280931i
$118$		−	3.14152i		−	0.289201i
$119$	−4.58155	+	2.64516i	−0.419990	+	0.242481i
$120$		0			0
$121$	5.14152	−	8.90538i	0.467411	−	0.809580i
$122$	−0.535898			−0.0485180
$123$	−2.32258	+	4.02283i	−0.209420	+	0.362726i
$124$	−8.77464	−	5.06604i	−0.787986	−	0.454944i
$125$		0			0
$126$	0.661290	−	1.14539i	0.0589124	−	0.102039i
$127$	9.93490	−	5.73592i	0.881580	−	0.508980i	0.0104008	−	0.999946i	$-0.496689\pi$
$127$	9.93490	−	5.73592i	0.881580	−	0.508980i	0.871179	+	0.490966i	$0.163356\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	8.60562			0.757683
$130$		0			0
$131$	−15.9906			−1.39710			−0.698551	−	0.715560i	$-0.746172\pi$
$131$	−15.9906			−1.39710			−0.698551	+	0.715560i	$0.746172\pi$
$132$	−2.30668	−	3.99528i	−0.200771	−	0.347745i
$133$	−2.62383	+	1.51487i	−0.227515	+	0.131356i
$134$	−1.59053	+	2.75488i	−0.137401	+	0.237985i
$135$		0			0
$136$	3.46410	+	2.00000i	0.297044	+	0.171499i
$137$	8.03486	−	13.9168i	0.686465	−	1.18899i	−0.286509	−	0.958077i	$-0.592495\pi$
$137$	8.03486	−	13.9168i	0.686465	−	1.18899i	0.972974	−	0.230914i	$-0.0741717\pi$
$138$	−8.66799			−0.737868
$139$	4.66129	−	8.07359i	0.395365	−	0.684793i	−0.597782	−	0.801658i	$-0.703951\pi$
$139$	4.66129	−	8.07359i	0.395365	−	0.684793i	0.993148	+	0.116865i	$0.0372846\pi$
$140$		0			0
$141$	7.88885	−	4.55463i	0.664361	−	0.383569i
$142$		−	11.3360i		−	0.951294i
$143$	−0.744087	−	16.6170i	−0.0622237	−	1.38959i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	−3.14152	−	5.44128i	−0.259994	−	0.450323i
$147$	4.54731	+	2.62539i	0.375056	+	0.216539i
$148$	6.80951			0.559738
$149$	−3.53788	−	2.04259i	−0.289834	−	0.167336i	0.348033	−	0.937482i	$-0.386850\pi$
$149$	−3.53788	−	2.04259i	−0.289834	−	0.167336i	−0.637867	+	0.770146i	$0.720183\pi$
$150$		0			0
$151$			19.9811i			1.62604i	0.582235	+	0.813021i	$0.302178\pi$
$151$			19.9811i			1.62604i	−0.582235	+	0.813021i	$0.697822\pi$
$152$	1.98387	+	1.14539i	0.160913	+	0.0929032i
$153$	−3.46410	+	2.00000i	−0.280056	+	0.161690i
$154$	−5.28408	+	3.05076i	−0.425803	+	0.245838i
$155$		0			0
$156$	−3.20002	−	1.66129i	−0.256206	−	0.133010i
$157$		−	7.13379i		−	0.569338i	−0.958626	−	0.284669i	$-0.908116\pi$
$157$		−	7.13379i		−	0.569338i	0.958626	−	0.284669i	$-0.0918838\pi$
$158$	−1.48387	−	2.57014i	−0.118050	−	0.204469i
$159$	0.413337	+	0.715920i	0.0327797	+	0.0567762i
$160$		0			0
$161$			11.4641i			0.903498i
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	4.94735	−	8.56906i	0.387506	−	0.671180i	−0.604607	−	0.796524i	$-0.706670\pi$
$163$	4.94735	−	8.56906i	0.387506	−	0.671180i	0.992113	+	0.125343i	$0.0400032\pi$
$164$		−	4.64516i		−	0.362726i
$165$		0			0
$166$	7.93593	+	13.7454i	0.615948	+	1.06685i
$167$	−12.0187	−	20.8171i	−0.930037	−	1.61087i	−0.783253	−	0.621704i	$-0.786441\pi$
$167$	−12.0187	−	20.8171i	−0.930037	−	1.61087i	−0.146785	−	0.989168i	$-0.546892\pi$
$168$			1.32258i			0.102039i
$169$	−7.48023	−	10.6323i	−0.575402	−	0.817870i
$170$		0			0
$171$	−1.98387	+	1.14539i	−0.151710	+	0.0875900i
$172$	−7.45269	+	4.30281i	−0.568262	+	0.328086i
$173$	2.18946	+	1.26408i	0.166461	+	0.0961065i	0.580916	−	0.813963i	$-0.302694\pi$
$173$	2.18946	+	1.26408i	0.166461	+	0.0961065i	−0.414455	+	0.910070i	$0.636028\pi$
$174$		−	2.02283i		−	0.153350i
$175$		0			0
$176$	3.99528	+	2.30668i	0.301156	+	0.173872i
$177$	−3.14152			−0.236131
$178$	−10.2746	−	5.93207i	−0.770117	−	0.444627i
$179$	3.13784	+	5.43490i	0.234533	+	0.406223i	0.959137	−	0.282942i	$-0.0913105\pi$
$179$	3.13784	+	5.43490i	0.234533	+	0.406223i	−0.724604	+	0.689166i	$0.757977\pi$
$180$		0			0
$181$	−12.2830			−0.912991			−0.456496	−	0.889726i	$-0.650896\pi$
$181$	−12.2830			−0.912991			−0.456496	+	0.889726i	$0.650896\pi$
$182$	−2.19719	+	4.23228i	−0.162866	+	0.313717i
$183$			0.535898i			0.0396147i
$184$	7.50670	−	4.33399i	0.553401	−	0.319506i
$185$		0			0
$186$	−5.06604	+	8.77464i	−0.371460	+	0.643388i
$187$	18.4534			1.34945
$188$	−4.55463	+	7.88885i	−0.332181	+	0.575354i
$189$	−1.14539	−	0.661290i	−0.0833147	−	0.0481018i
$190$		0			0
$191$	4.87357	−	8.44128i	0.352639	−	0.610789i	−0.634072	−	0.773274i	$-0.718618\pi$
$191$	4.87357	−	8.44128i	0.352639	−	0.610789i	0.986711	+	0.162485i	$0.0519509\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	−6.88130	−	11.9188i	−0.495327	−	0.857932i	0.504658	−	0.863319i	$-0.331618\pi$
$193$	−6.88130	−	11.9188i	−0.495327	−	0.857932i	−0.999985	+	0.00538741i	$0.998285\pi$
$194$	−8.81894			−0.633163
$195$		0			0
$196$	−5.25078			−0.375056
$197$	5.07076	+	8.78282i	0.361277	+	0.625750i	0.988171	−	0.153354i	$-0.0490076\pi$
$197$	5.07076	+	8.78282i	0.361277	+	0.625750i	−0.626894	+	0.779104i	$0.715674\pi$
$198$	−3.99528	+	2.30668i	−0.283932	+	0.163928i
$199$	−4.78668	+	8.29078i	−0.339319	+	0.587717i	−0.984305	−	0.176477i	$-0.943530\pi$
$199$	−4.78668	+	8.29078i	−0.339319	+	0.587717i	0.644986	+	0.764194i	$0.276863\pi$
$200$		0			0
$201$	2.75488	+	1.59053i	0.194314	+	0.112187i
$202$	3.61335	−	6.25851i	0.254235	−	0.440348i
$203$	−2.67535			−0.187773
$204$	2.00000	−	3.46410i	0.140028	−	0.242536i
$205$		0			0
$206$	15.9349	−	9.20002i	1.11024	−	0.640996i
$207$			8.66799i			0.602467i
$208$	3.60194	−	0.161290i	0.249750	−	0.0111834i
$209$	10.5682			0.731015
$210$		0			0
$211$	0.542594	+	0.939800i	0.0373537	+	0.0646985i	0.884098	−	0.467302i	$-0.154774\pi$
$211$	0.542594	+	0.939800i	0.0373537	+	0.0646985i	−0.846744	+	0.532000i	$0.821441\pi$
$212$	−0.715920	−	0.413337i	−0.0491696	−	0.0283881i
$213$	−11.3360			−0.776728
$214$	−2.66025	−	1.53590i	−0.181851	−	0.104992i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	11.6052	+	6.70025i	0.787810	+	0.454842i
$218$	−11.4547	+	6.61335i	−0.775808	+	0.447913i
$219$	−5.44128	+	3.14152i	−0.367687	+	0.212284i
$220$		0			0
$221$	12.1549	−	7.76261i	0.817628	−	0.522170i
$222$		−	6.80951i		−	0.457024i
$223$	12.4708	+	21.6001i	0.835106	+	1.44645i	0.893944	+	0.448179i	$0.147927\pi$
$223$	12.4708	+	21.6001i	0.835106	+	1.44645i	−0.0588375	+	0.998268i	$0.518739\pi$
$224$	−0.661290	−	1.14539i	−0.0441843	−	0.0765294i
$225$		0			0
$226$			8.08643i			0.537902i
$227$	−9.66025	+	16.7321i	−0.641174	+	1.11055i	0.343998	+	0.938971i	$0.388219\pi$
$227$	−9.66025	+	16.7321i	−0.641174	+	1.11055i	−0.985171	+	0.171575i	$0.945115\pi$
$228$	1.14539	−	1.98387i	0.0758551	−	0.131385i
$229$			4.15491i			0.274564i	0.990532	+	0.137282i	$0.0438367\pi$
$229$			4.15491i			0.274564i	−0.990532	+	0.137282i	$0.956163\pi$
$230$		0			0
$231$	3.05076	+	5.28408i	0.200726	+	0.347667i
$232$	1.01141	+	1.75182i	0.0664025	+	0.115013i
$233$			16.9665i			1.11151i	0.831346	+	0.555756i	$0.187571\pi$
$233$			16.9665i			1.11151i	−0.831346	+	0.555756i	$0.812429\pi$
$234$	−1.66129	+	3.20002i	−0.108602	+	0.209192i
$235$		0			0
$236$	2.72064	−	1.57076i	0.177098	−	0.102248i
$237$	−2.57014	+	1.48387i	−0.166948	+	0.0963877i
$238$	−4.58155	−	2.64516i	−0.296978	−	0.171460i
$239$		−	6.34416i		−	0.410370i	−0.978723	−	0.205185i	$-0.934220\pi$
$239$		−	6.34416i		−	0.410370i	0.978723	−	0.205185i	$-0.0657795\pi$
$240$		0			0
$241$	20.9452	+	12.0927i	1.34920	+	0.778962i	0.988136	−	0.153579i	$-0.0490800\pi$
$241$	20.9452	+	12.0927i	1.34920	+	0.778962i	0.361065	+	0.932541i	$0.382413\pi$
$242$	10.2830			0.661019
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−0.267949	−	0.464102i	−0.0171537	−	0.0297111i
$245$		0			0
$246$	−4.64516			−0.296165
$247$	6.96104	−	4.44560i	0.442921	−	0.282867i
$248$		−	10.1321i		−	0.643388i
$249$	13.7454	−	7.93593i	0.871082	−	0.502919i
$250$		0			0
$251$	4.41249	−	7.64265i	0.278514	−	0.482400i	−0.692502	−	0.721416i	$-0.743492\pi$
$251$	4.41249	−	7.64265i	0.278514	−	0.482400i	0.971016	+	0.239016i	$0.0768249\pi$
$252$	1.32258			0.0833147
$253$	19.9942	−	34.6311i	1.25703	−	2.17724i
$254$	9.93490	+	5.73592i	0.623371	+	0.359903i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.26157	−	4.19247i	0.452964	−	0.261519i	−0.256117	−	0.966646i	$-0.582443\pi$
$257$	7.26157	−	4.19247i	0.452964	−	0.261519i	0.709081	+	0.705127i	$0.249110\pi$
$258$	4.30281	+	7.45269i	0.267881	+	0.463984i
$259$	−9.00612			−0.559613
$260$		0			0
$261$	−2.02283			−0.125210
$262$	−7.99528	−	13.8482i	−0.493950	−	0.855547i
$263$	1.66389	−	0.960648i	0.102600	−	0.0592361i	−0.447822	−	0.894123i	$-0.647800\pi$
$263$	1.66389	−	0.960648i	0.102600	−	0.0592361i	0.550422	+	0.834887i	$0.314467\pi$
$264$	2.30668	−	3.99528i	0.141966	−	0.245893i
$265$		0			0
$266$	−2.62383	−	1.51487i	−0.160877	−	0.0928824i
$267$	−5.93207	+	10.2746i	−0.363037	+	0.628798i
$268$	−3.18106			−0.194314
$269$	−16.1549	+	27.9811i	−0.984982	+	1.70604i	−0.342968	+	0.939347i	$0.611432\pi$
$269$	−16.1549	+	27.9811i	−0.984982	+	1.70604i	−0.642014	+	0.766693i	$0.721901\pi$
$270$		0			0
$271$	20.3105	−	11.7263i	1.23378	−	0.712322i	0.265962	−	0.963983i	$-0.414310\pi$
$271$	20.3105	−	11.7263i	1.23378	−	0.712322i	0.967815	+	0.251662i	$0.0809770\pi$
$272$			4.00000i			0.242536i
$273$	4.23228	+	2.19719i	0.256149	+	0.132980i
$274$	16.0697			0.970808
$275$		0			0
$276$	−4.33399	−	7.50670i	−0.260876	−	0.451850i
$277$	7.79913	+	4.50283i	0.468604	+	0.270549i	0.715655	−	0.698454i	$-0.246128\pi$
$277$	7.79913	+	4.50283i	0.468604	+	0.270549i	−0.247051	+	0.969002i	$0.579462\pi$
$278$	9.32258			0.559131
$279$	8.77464	+	5.06604i	0.525324	+	0.303296i
$280$		0			0
$281$		−	1.71696i		−	0.102425i	−0.998688	−	0.0512125i	$-0.983691\pi$
$281$		−	1.71696i		−	0.102425i	0.998688	−	0.0512125i	$-0.0163086\pi$
$282$	7.88885	+	4.55463i	0.469774	+	0.271224i
$283$	1.34172	−	0.774645i	0.0797572	−	0.0460479i	−0.459591	−	0.888131i	$-0.652004\pi$
$283$	1.34172	−	0.774645i	0.0797572	−	0.0460479i	0.539348	+	0.842083i	$0.318671\pi$
$284$	9.81724	−	5.66799i	0.582546	−	0.336333i
$285$		0			0
$286$	14.0187	−	8.95292i	0.828945	−	0.529397i
$287$			6.14359i			0.362645i
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$		0			0
$291$			8.81894i			0.516976i
$292$	3.14152	−	5.44128i	0.183844	−	0.318427i
$293$	−15.2028	+	26.3321i	−0.888160	+	1.53834i	−0.0461113	+	0.998936i	$0.514683\pi$
$293$	−15.2028	+	26.3321i	−0.888160	+	1.53834i	−0.842049	+	0.539402i	$0.818650\pi$
$294$			5.25078i			0.306232i
$295$		0			0
$296$	3.40475	+	5.89721i	0.197897	+	0.342768i
$297$	2.30668	+	3.99528i	0.133847	+	0.231830i
$298$		−	4.08519i		−	0.236649i
$299$	−1.39806	−	31.2216i	−0.0808518	−	1.80559i
$300$		0			0
$301$	9.85677	−	5.69081i	0.568135	−	0.328013i
$302$	−17.3042	+	9.99057i	−0.995743	+	0.574892i
$303$	−6.25851	−	3.61335i	−0.359542	−	0.207582i
$304$			2.29078i			0.131385i
$305$		0			0
$306$	−3.46410	−	2.00000i	−0.198030	−	0.114332i
$307$	−9.82622			−0.560812			−0.280406	−	0.959882i	$-0.590469\pi$
$307$	−9.82622			−0.560812			−0.280406	+	0.959882i	$0.590469\pi$
$308$	−5.28408	−	3.05076i	−0.301088	−	0.173833i
$309$	−9.20002	−	15.9349i	−0.523371	−	0.906505i
$310$		0			0
$311$	−3.40049			−0.192824			−0.0964121	−	0.995342i	$-0.530737\pi$
$311$	−3.40049			−0.192824			−0.0964121	+	0.995342i	$0.530737\pi$
$312$	−0.161290	−	3.60194i	−0.00913124	−	0.203920i
$313$		−	16.2340i		−	0.917599i	−0.888540	−	0.458800i	$-0.848280\pi$
$313$		−	16.2340i		−	0.917599i	0.888540	−	0.458800i	$-0.151720\pi$
$314$	6.17804	−	3.56690i	0.348647	−	0.201292i
$315$		0			0
$316$	1.48387	−	2.57014i	0.0834742	−	0.144582i
$317$	−23.5231			−1.32119			−0.660596	−	0.750742i	$-0.729696\pi$
$317$	−23.5231			−1.32119			−0.660596	+	0.750742i	$0.729696\pi$
$318$	−0.413337	+	0.715920i	−0.0231788	+	0.0401468i
$319$	8.08176	+	4.66601i	0.452492	+	0.261246i
$320$		0			0
$321$	−1.53590	+	2.66025i	−0.0857255	+	0.148481i
$322$	−9.92820	+	5.73205i	−0.553277	+	0.319435i
$323$	4.58155	+	7.93548i	0.254924	+	0.441542i
$324$	1.00000			0.0555556
$325$		0			0
$326$	9.89470			0.548016
$327$	6.61335	+	11.4547i	0.365719	+	0.633445i
$328$	4.02283	−	2.32258i	0.222123	−	0.128243i
$329$	6.02386	−	10.4336i	0.332106	−	0.575225i
$330$		0			0
$331$	15.6667	+	9.04520i	0.861122	+	0.497169i	0.864388	−	0.502826i	$-0.167706\pi$
$331$	15.6667	+	9.04520i	0.861122	+	0.497169i	−0.00326597	+	0.999995i	$0.501040\pi$
$332$	−7.93593	+	13.7454i	−0.435541	+	0.754379i
$333$	−6.80951			−0.373159
$334$	12.0187	−	20.8171i	0.657636	−	1.13906i
$335$		0			0
$336$	−1.14539	+	0.661290i	−0.0624860	+	0.0360763i
$337$			5.69900i			0.310444i	0.987880	+	0.155222i	$0.0496093\pi$
$337$			5.69900i			0.310444i	−0.987880	+	0.155222i	$0.950391\pi$
$338$	5.46774	−	11.7942i	0.297406	−	0.641521i
$339$	8.08643			0.439195
$340$		0			0
$341$	−23.3715	−	40.4806i	−1.26564	−	2.19214i
$342$	−1.98387	−	1.14539i	−0.107275	−	0.0619355i
$343$	16.2026			0.874860
$344$	−7.45269	−	4.30281i	−0.401822	−	0.231992i
$345$		0			0
$346$			2.52817i			0.135915i
$347$	−13.6374	−	7.87357i	−0.732095	−	0.422676i	0.0870928	−	0.996200i	$-0.472242\pi$
$347$	−13.6374	−	7.87357i	−0.732095	−	0.422676i	−0.819188	+	0.573525i	$0.805576\pi$
$348$	1.75182	−	1.01141i	0.0939073	−	0.0542174i
$349$	−13.2679	+	7.66025i	−0.710217	+	0.410044i	−0.811141	−	0.584850i	$-0.801153\pi$
$349$	−13.2679	+	7.66025i	−0.710217	+	0.410044i	0.100924	+	0.994894i	$0.467820\pi$
$350$		0			0
$351$	3.20002	+	1.66129i	0.170804	+	0.0886731i
$352$			4.61335i			0.245893i
$353$	0.599964	+	1.03917i	0.0319328	+	0.0553093i	0.881550	−	0.472090i	$-0.156500\pi$
$353$	0.599964	+	1.03917i	0.0319328	+	0.0553093i	−0.849617	+	0.527400i	$0.823167\pi$
$354$	−1.57076	−	2.72064i	−0.0834850	−	0.144600i
$355$		0			0
$356$		−	11.8641i		−	0.628798i
$357$	−2.64516	+	4.58155i	−0.139997	+	0.242481i
$358$	−3.13784	+	5.43490i	−0.165840	+	0.287243i
$359$			16.2830i			0.859386i	0.902975	+	0.429693i	$0.141378\pi$
$359$			16.2830i			0.859386i	−0.902975	+	0.429693i	$0.858622\pi$
$360$		0			0
$361$	−6.87617	−	11.9099i	−0.361904	−	0.626836i
$362$	−6.14152	−	10.6374i	−0.322791	−	0.559091i
$363$		−	10.2830i		−	0.539720i
$364$	−4.76386	+	0.213319i	−0.249694	+	0.0111809i
$365$		0			0
$366$	−0.464102	+	0.267949i	−0.0242590	+	0.0140059i
$367$	17.0040	−	9.81724i	0.887599	−	0.512456i	0.0144428	−	0.999896i	$-0.495403\pi$
$367$	17.0040	−	9.81724i	0.887599	−	0.512456i	0.873156	+	0.487440i	$0.162069\pi$
$368$	7.50670	+	4.33399i	0.391314	+	0.225925i
$369$			4.64516i			0.241817i
$370$		0			0
$371$	0.946862	+	0.546671i	0.0491586	+	0.0283817i
$372$	−10.1321			−0.525324
$373$	2.21484	+	1.27874i	0.114680	+	0.0662106i	0.556243	−	0.831020i	$-0.312242\pi$
$373$	2.21484	+	1.27874i	0.114680	+	0.0662106i	−0.441563	+	0.897230i	$0.645576\pi$
$374$	9.22671	+	15.9811i	0.477102	+	0.826365i
$375$		0			0
$376$	−9.10926			−0.469774
$377$	7.28610	−	0.326261i	0.375253	−	0.0168033i
$378$		−	1.32258i		−	0.0680262i
$379$	13.0846	−	7.55440i	0.672111	−	0.388044i	−0.124765	−	0.992186i	$-0.539818\pi$
$379$	13.0846	−	7.55440i	0.672111	−	0.388044i	0.796876	+	0.604143i	$0.206484\pi$
$380$		0			0
$381$	5.73592	−	9.93490i	0.293860	−	0.508980i
$382$	9.74715			0.498707
$383$	9.36517	−	16.2210i	0.478538	−	0.828852i	−0.521159	−	0.853459i	$-0.674500\pi$
$383$	9.36517	−	16.2210i	0.478538	−	0.828852i	0.999697	+	0.0246073i	$0.00783355\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$		0			0
$386$	6.88130	−	11.9188i	0.350249	−	0.606649i
$387$	7.45269	−	4.30281i	0.378841	−	0.218724i
$388$	−4.40947	−	7.63743i	−0.223857	−	0.387732i
$389$	−6.96899			−0.353342			−0.176671	−	0.984270i	$-0.556533\pi$
$389$	−6.96899			−0.353342			−0.176671	+	0.984270i	$0.556533\pi$
$390$		0			0
$391$	34.6719			1.75344
$392$	−2.62539	−	4.54731i	−0.132602	−	0.229674i
$393$	−13.8482	+	7.99528i	−0.698551	+	0.403309i
$394$	−5.07076	+	8.78282i	−0.255461	+	0.442472i
$395$		0			0
$396$	−3.99528	−	2.30668i	−0.200771	−	0.115915i
$397$	−9.28606	+	16.0839i	−0.466054	+	0.807229i	−0.999248	−	0.0387637i	$-0.987658\pi$
$397$	−9.28606	+	16.0839i	−0.466054	+	0.807229i	0.533195	+	0.845993i	$0.320991\pi$
$398$	−9.57336			−0.479869
$399$	−1.51487	+	2.62383i	−0.0758382	+	0.131356i
$400$		0			0
$401$	−25.7126	+	14.8452i	−1.28403	+	0.741333i	−0.977582	−	0.210556i	$-0.932473\pi$
$401$	−25.7126	+	14.8452i	−1.28403	+	0.741333i	−0.306444	+	0.951889i	$0.599139\pi$
$402$			3.18106i			0.158657i
$403$	−32.4229	−	16.8323i	−1.61510	−	0.838478i
$404$	7.22671			0.359542
$405$		0			0
$406$	−1.33767	−	2.31692i	−0.0663877	−	0.114987i
$407$	27.2059	+	15.7073i	1.34855	+	0.778584i
$408$	4.00000			0.198030
$409$	21.0752	+	12.1678i	1.04210	+	0.601657i	0.920427	−	0.390913i	$-0.127841\pi$
$409$	21.0752	+	12.1678i	1.04210	+	0.601657i	0.121673	+	0.992570i	$0.461174\pi$
$410$		0			0
$411$		−	16.0697i		−	0.792661i
$412$	15.9349	+	9.20002i	0.785056	+	0.453252i
$413$	−3.59826	+	2.07746i	−0.177059	+	0.102225i
$414$	−7.50670	+	4.33399i	−0.368934	+	0.213004i
$415$		0			0
$416$	1.94065	+	3.03873i	0.0951483	+	0.148986i
$417$		−	9.32258i		−	0.456529i
$418$	5.28408	+	9.15229i	0.258453	+	0.447653i
$419$	−1.44128	−	2.49636i	−0.0704109	−	0.121955i	0.828671	−	0.559737i	$-0.189098\pi$
$419$	−1.44128	−	2.49636i	−0.0704109	−	0.121955i	−0.899081	+	0.437781i	$0.855764\pi$
$420$		0			0
$421$			4.94707i			0.241106i	0.992707	+	0.120553i	$0.0384667\pi$
$421$			4.94707i			0.241106i	−0.992707	+	0.120553i	$0.961533\pi$
$422$	−0.542594	+	0.939800i	−0.0264131	+	0.0457488i
$423$	4.55463	−	7.88885i	0.221454	−	0.383569i
$424$		−	0.826674i		−	0.0401468i
$425$		0			0
$426$	−5.66799	−	9.81724i	−0.274615	−	0.475647i
$427$	0.354384	+	0.613811i	0.0171499	+	0.0297044i
$428$		−	3.07180i		−	0.148481i
$429$	−8.95292	−	14.0187i	−0.432251	−	0.676831i
$430$		0			0
$431$	−15.3829	+	8.88130i	−0.740967	+	0.427797i	−0.822421	−	0.568880i	$-0.807377\pi$
$431$	−15.3829	+	8.88130i	−0.740967	+	0.427797i	0.0814539	+	0.996677i	$0.474044\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	31.0362	+	17.9188i	1.49151	+	0.861121i	0.999953	−	0.00972676i	$-0.00309617\pi$
$433$	31.0362	+	17.9188i	1.49151	+	0.861121i	0.491553	+	0.870848i	$0.336430\pi$
$434$			13.4005i			0.643244i
$435$		0			0
$436$	−11.4547	−	6.61335i	−0.548579	−	0.316722i
$437$	19.8564			0.949861
$438$	−5.44128	−	3.14152i	−0.259994	−	0.150108i
$439$	−5.04520	−	8.73854i	−0.240794	−	0.417068i	0.720147	−	0.693822i	$-0.244075\pi$
$439$	−5.04520	−	8.73854i	−0.240794	−	0.417068i	−0.960941	+	0.276754i	$0.910741\pi$
$440$		0			0
$441$	5.25078			0.250037
$442$	12.8001	+	6.64516i	0.608837	+	0.316078i
$443$			13.6981i			0.650816i	0.945574	+	0.325408i	$0.105502\pi$
$443$			13.6981i			0.650816i	−0.945574	+	0.325408i	$0.894498\pi$
$444$	5.89721	−	3.40475i	0.279869	−	0.161582i
$445$		0			0
$446$	−12.4708	+	21.6001i	−0.590509	+	1.02279i
$447$	−4.08519			−0.193223
$448$	0.661290	−	1.14539i	0.0312430	−	0.0541145i
$449$	−13.2613	−	7.65639i	−0.625837	−	0.361327i	0.153301	−	0.988180i	$-0.451010\pi$
$449$	−13.2613	−	7.65639i	−0.625837	−	0.361327i	−0.779138	+	0.626852i	$0.784343\pi$
$450$		0			0
$451$	10.7149	−	18.5587i	0.504544	−	0.873896i
$452$	−7.00306	+	4.04322i	−0.329396	+	0.190177i
$453$	9.99057	+	17.3042i	0.469398	+	0.813021i
$454$	−19.3205			−0.906756
$455$		0			0
$456$	2.29078			0.107275
$457$	7.77770	+	13.4714i	0.363826	+	0.630164i	0.988587	−	0.150651i	$-0.0481371\pi$
$457$	7.77770	+	13.4714i	0.363826	+	0.630164i	−0.624761	+	0.780816i	$0.714804\pi$
$458$	−3.59826	+	2.07746i	−0.168136	+	0.0970732i
$459$	−2.00000	+	3.46410i	−0.0933520	+	0.161690i
$460$		0			0
$461$	13.5473	+	7.82154i	0.630961	+	0.364286i	0.781124	−	0.624376i	$-0.214647\pi$
$461$	13.5473	+	7.82154i	0.630961	+	0.364286i	−0.150163	+	0.988661i	$0.547980\pi$
$462$	−3.05076	+	5.28408i	−0.141934	+	0.245838i
$463$	13.7170			0.637481			0.318741	−	0.947842i	$-0.396740\pi$
$463$	13.7170			0.637481			0.318741	+	0.947842i	$0.396740\pi$
$464$	−1.01141	+	1.75182i	−0.0469537	+	0.0813261i
$465$		0			0
$466$	−14.6934	+	8.48325i	−0.680659	+	0.392979i
$467$			0.943666i			0.0436677i	0.999762	+	0.0218338i	$0.00695048\pi$
$467$			0.943666i			0.0436677i	−0.999762	+	0.0218338i	$0.993050\pi$
$468$	−3.60194	+	0.161290i	−0.166500	+	0.00745563i
$469$	4.20720			0.194271
$470$		0			0
$471$	−3.56690	−	6.17804i	−0.164354	−	0.284669i
$472$	2.72064	+	1.57076i	0.125228	+	0.0723001i
$473$	−39.7008			−1.82544
$474$	−2.57014	−	1.48387i	−0.118050	−	0.0681564i
$475$		0			0
$476$		−	5.29032i		−	0.242481i
$477$	0.715920	+	0.413337i	0.0327797	+	0.0189254i
$478$	5.49420	−	3.17208i	0.251299	−	0.145088i
$479$	9.61460	−	5.55099i	0.439302	−	0.253631i	−0.263999	−	0.964523i	$-0.585042\pi$
$479$	9.61460	−	5.55099i	0.439302	−	0.253631i	0.703302	+	0.710892i	$0.251708\pi$
$480$		0			0
$481$	24.5275	−	1.09830i	1.11836	−	0.0500784i
$482$			24.1855i			1.10162i
$483$	5.73205	+	9.92820i	0.260817	+	0.451749i
$484$	5.14152	+	8.90538i	0.233706	+	0.404790i
$485$		0			0
$486$		−	1.00000i		−	0.0453609i
$487$	−16.4708	+	28.5283i	−0.746363	+	1.29274i	0.203192	+	0.979139i	$0.434868\pi$
$487$	−16.4708	+	28.5283i	−0.746363	+	1.29274i	−0.949555	+	0.313600i	$0.898465\pi$
$488$	0.267949	−	0.464102i	0.0121295	−	0.0210089i
$489$		−	9.89470i		−	0.447454i
$490$		0			0
$491$	14.2257	+	24.6396i	0.641996	+	1.11197i	0.984987	+	0.172630i	$0.0552266\pi$
$491$	14.2257	+	24.6396i	0.641996	+	1.11197i	−0.342991	+	0.939339i	$0.611440\pi$
$492$	−2.32258	−	4.02283i	−0.104710	−	0.181363i
$493$			8.09130i			0.364414i
$494$	7.33052	+	3.80564i	0.329816	+	0.171224i
$495$		0			0
$496$	8.77464	−	5.06604i	0.393993	−	0.227472i
$497$	−12.9841	+	7.49636i	−0.582416	+	0.336258i
$498$	13.7454	+	7.93593i	0.615948	+	0.355618i
$499$		−	4.10926i		−	0.183956i	−0.995761	−	0.0919779i	$-0.970681\pi$
$499$		−	4.10926i		−	0.183956i	0.995761	−	0.0919779i	$-0.0293189\pi$
$500$		0			0
$501$	−20.8171	−	12.0187i	−0.930037	−	0.536957i
$502$	8.82497			0.393878
$503$	−4.96753	−	2.86800i	−0.221491	−	0.127878i	0.385149	−	0.922854i	$-0.374150\pi$
$503$	−4.96753	−	2.86800i	−0.221491	−	0.127878i	−0.606641	+	0.794976i	$0.707483\pi$
$504$	0.661290	+	1.14539i	0.0294562	+	0.0510196i
$505$		0			0
$506$	39.9885			1.77771
$507$	−11.7942	−	5.46774i	−0.523800	−	0.242831i
$508$			11.4718i			0.508980i
$509$	13.1129	−	7.57076i	0.581221	−	0.335568i	−0.180397	−	0.983594i	$-0.557738\pi$
$509$	13.1129	−	7.57076i	0.581221	−	0.335568i	0.761618	+	0.648026i	$0.224405\pi$
$510$		0			0
$511$	−4.15491	+	7.19652i	−0.183803	+	0.318355i
$512$	−1.00000			−0.0441942
$513$	−1.14539	+	1.98387i	−0.0505701	+	0.0875900i
$514$	7.26157	+	4.19247i	0.320294	+	0.184922i
$515$		0			0
$516$	−4.30281	+	7.45269i	−0.189421	+	0.328086i
$517$	−36.3941	+	21.0121i	−1.60061	+	0.924112i
$518$	−4.50306	−	7.79953i	−0.197853	−	0.342691i
$519$	2.52817			0.110974
$520$		0			0
$521$	8.93027			0.391242			0.195621	−	0.980680i	$-0.437328\pi$
$521$	8.93027			0.391242			0.195621	+	0.980680i	$0.437328\pi$
$522$	−1.01141	−	1.75182i	−0.0442683	−	0.0766750i
$523$	−8.50166	+	4.90844i	−0.371752	+	0.214631i	−0.674223	−	0.738527i	$-0.735522\pi$
$523$	−8.50166	+	4.90844i	−0.371752	+	0.214631i	0.302472	+	0.953158i	$0.402188\pi$
$524$	7.99528	−	13.8482i	0.349276	−	0.604963i
$525$		0			0
$526$	1.66389	+	0.960648i	0.0725491	+	0.0418863i
$527$	20.2642	−	35.0986i	0.882721	−	1.52892i
$528$	4.61335			0.200771
$529$	26.0670	−	45.1493i	1.13335	−	1.96301i
$530$		0			0
$531$	−2.72064	+	1.57076i	−0.118066	+	0.0681652i
$532$		−	3.02973i		−	0.131356i
$533$	−0.749217	−	16.7316i	−0.0324522	−	0.724726i
$534$	−11.8641			−0.513411
$535$		0			0
$536$	−1.59053	−	2.75488i	−0.0687004	−	0.118993i
$537$	5.43490	+	3.13784i	0.234533	+	0.135408i
$538$	−32.3098			−1.39298
$539$	−20.9784	−	12.1119i	−0.903602	−	0.521695i
$540$		0			0
$541$		−	3.80826i		−	0.163730i	−0.996643	−	0.0818650i	$-0.973912\pi$
$541$		−	3.80826i		−	0.163730i	0.996643	−	0.0818650i	$-0.0260876\pi$
$542$	20.3105	+	11.7263i	0.872413	+	0.503688i
$543$	−10.6374	+	6.14152i	−0.456496	+	0.263558i
$544$	−3.46410	+	2.00000i	−0.148522	+	0.0857493i
$545$		0			0
$546$	0.213319	+	4.76386i	0.00912920	+	0.203874i
$547$		−	45.5847i		−	1.94906i	−0.224257	−	0.974530i	$-0.571995\pi$
$547$		−	45.5847i		−	1.94906i	0.224257	−	0.974530i	$-0.428005\pi$
$548$	8.03486	+	13.9168i	0.343232	+	0.594496i
$549$	0.267949	+	0.464102i	0.0114358	+	0.0198074i
$550$		0			0
$551$			4.63384i			0.197408i
$552$	4.33399	−	7.50670i	0.184467	−	0.319506i
$553$	−1.96254	+	3.39921i	−0.0834555	+	0.144549i
$554$			9.00566i			0.382614i
$555$		0			0
$556$	4.66129	+	8.07359i	0.197683	+	0.342397i
$557$	18.4296	+	31.9209i	0.780885	+	1.35253i	0.931427	+	0.363929i	$0.118565\pi$
$557$	18.4296	+	31.9209i	0.780885	+	1.35253i	−0.150541	+	0.988604i	$0.548102\pi$
$558$			10.1321i			0.428925i
$559$	−26.1502	+	16.7005i	−1.10603	+	0.706357i
$560$		0			0
$561$	15.9811	−	9.22671i	0.674724	−	0.389552i
$562$	1.48693	−	0.858478i	0.0627223	−	0.0362127i
$563$	29.2491	+	16.8870i	1.23270	+	0.711701i	0.967592	−	0.252518i	$-0.0812586\pi$
$563$	29.2491	+	16.8870i	1.23270	+	0.711701i	0.265109	+	0.964218i	$0.414592\pi$
$564$			9.10926i			0.383569i
$565$		0			0
$566$	1.34172	+	0.774645i	0.0563969	+	0.0325607i
$567$	−1.32258			−0.0555431
$568$	9.81724	+	5.66799i	0.411922	+	0.237823i
$569$	12.7159	+	22.0246i	0.533079	+	0.923320i	0.999254	+	0.0386274i	$0.0122985\pi$
$569$	12.7159	+	22.0246i	0.533079	+	0.923320i	−0.466175	+	0.884693i	$0.654368\pi$
$570$		0			0
$571$	13.3682			0.559443			0.279722	−	0.960081i	$-0.409758\pi$
$571$	13.3682			0.559443			0.279722	+	0.960081i	$0.409758\pi$
$572$	14.7628	+	7.66412i	0.617264	+	0.320453i
$573$		−	9.74715i		−	0.407193i
$574$	−5.32051	+	3.07180i	−0.222074	+	0.128214i
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	9.57428			0.398582			0.199291	−	0.979940i	$-0.436136\pi$
$577$	9.57428			0.398582			0.199291	+	0.979940i	$0.436136\pi$
$578$	0.500000	−	0.866025i	0.0207973	−	0.0360219i
$579$	−11.9188	−	6.88130i	−0.495327	−	0.285977i
$580$		0			0
$581$	10.4959	−	18.1794i	0.435444	−	0.754210i
$582$	−7.63743	+	4.40947i	−0.316582	+	0.182778i
$583$	−1.90687	−	3.30279i	−0.0789745	−	0.136788i
$584$	6.28304			0.259994
$585$		0			0
$586$	−30.4057			−1.25605
$587$	−0.700246	−	1.21286i	−0.0289023	−	0.0500602i	0.851212	−	0.524821i	$-0.175868\pi$
$587$	−0.700246	−	1.21286i	−0.0289023	−	0.0500602i	−0.880115	+	0.474761i	$0.842534\pi$
$588$	−4.54731	+	2.62539i	−0.187528	+	0.108269i
$589$	11.6052	−	20.1007i	0.478183	−	0.828237i
$590$		0			0
$591$	8.78282	+	5.07076i	0.361277	+	0.208583i
$592$	−3.40475	+	5.89721i	−0.139935	+	0.242374i
$593$	−10.7303			−0.440643			−0.220321	−	0.975427i	$-0.570711\pi$
$593$	−10.7303			−0.440643			−0.220321	+	0.975427i	$0.570711\pi$
$594$	−2.30668	+	3.99528i	−0.0946441	+	0.163928i
$595$		0			0
$596$	3.53788	−	2.04259i	0.144917	−	0.0836679i
$597$			9.57336i			0.391812i
$598$	26.3397	−	16.8215i	1.07711	−	0.687884i
$599$	40.7967			1.66691			0.833453	−	0.552590i	$-0.186360\pi$
$599$	40.7967			1.66691			0.833453	+	0.552590i	$0.186360\pi$
$600$		0			0
$601$	−21.4416	−	37.1379i	−0.874621	−	1.51489i	−0.857166	−	0.515040i	$-0.827777\pi$
$601$	−21.4416	−	37.1379i	−0.874621	−	1.51489i	−0.0174548	−	0.999848i	$-0.505556\pi$
$602$	9.85677	+	5.69081i	0.401732	+	0.231940i
$603$	3.18106			0.129543
$604$	−17.3042	−	9.99057i	−0.704097	−	0.406510i
$605$		0			0
$606$		−	7.22671i		−	0.293565i
$607$	−5.95161	−	3.43616i	−0.241568	−	0.139470i	0.374329	−	0.927296i	$-0.377873\pi$
$607$	−5.95161	−	3.43616i	−0.241568	−	0.139470i	−0.615897	+	0.787826i	$0.711206\pi$
$608$	−1.98387	+	1.14539i	−0.0804565	+	0.0464516i
$609$	−2.31692	+	1.33767i	−0.0938863	+	0.0542053i
$610$		0			0
$611$	−15.1331	+	29.1498i	−0.612221	+	1.17927i
$612$		−	4.00000i		−	0.161690i
$613$	−0.380681	−	0.659358i	−0.0153755	−	0.0266312i	0.858235	−	0.513257i	$-0.171561\pi$
$613$	−0.380681	−	0.659358i	−0.0153755	−	0.0266312i	−0.873611	+	0.486625i	$0.838228\pi$
$614$	−4.91311	−	8.50975i	−0.198277	−	0.343426i
$615$		0			0
$616$		−	6.10153i		−	0.245838i
$617$	12.3011	−	21.3061i	0.495224	−	0.857753i	−0.504761	−	0.863259i	$-0.668419\pi$
$617$	12.3011	−	21.3061i	0.495224	−	0.857753i	0.999985	+	0.00550613i	$0.00175266\pi$
$618$	9.20002	−	15.9349i	0.370079	−	0.640996i
$619$			17.2035i			0.691468i	0.938333	+	0.345734i	$0.112370\pi$
$619$			17.2035i			0.691468i	−0.938333	+	0.345734i	$0.887630\pi$
$620$		0			0
$621$	4.33399	+	7.50670i	0.173917	+	0.301233i
$622$	−1.70025	−	2.94491i	−0.0681737	−	0.118080i
$623$			15.6913i			0.628657i
$624$	3.03873	−	1.94065i	0.121646	−	0.0776883i
$625$		0			0
$626$	14.0590	−	8.11699i	0.561912	−	0.324420i
$627$	9.15229	−	5.28408i	0.365507	−	0.211026i
$628$	6.17804	+	3.56690i	0.246531	+	0.142335i
$629$			27.2380i			1.08605i
$630$		0			0
$631$	2.08519	+	1.20388i	0.0830100	+	0.0479259i	0.540930	−	0.841067i	$-0.318072\pi$
$631$	2.08519	+	1.20388i	0.0830100	+	0.0479259i	−0.457920	+	0.888993i	$0.651406\pi$
$632$	2.96774			0.118050
$633$	0.939800	+	0.542594i	0.0373537	+	0.0215662i
$634$	−11.7616	−	20.3716i	−0.467112	−	0.809061i
$635$		0			0
$636$	−0.826674			−0.0327797
$637$	−18.9130	+	0.846898i	−0.749361	+	0.0335553i
$638$			9.33201i			0.369458i
$639$	−9.81724	+	5.66799i	−0.388364	+	0.224222i
$640$		0			0
$641$	−9.73875	+	16.8680i	−0.384657	+	0.666246i	−0.991722	−	0.128407i	$-0.959014\pi$
$641$	−9.73875	+	16.8680i	−0.384657	+	0.666246i	0.607064	+	0.794653i	$0.292347\pi$
$642$	−3.07180			−0.121234
$643$	11.9772	−	20.7451i	0.472334	−	0.818106i	−0.527165	−	0.849763i	$-0.676745\pi$
$643$	11.9772	−	20.7451i	0.472334	−	0.818106i	0.999499	+	0.0316570i	$0.0100784\pi$
$644$	−9.92820	−	5.73205i	−0.391226	−	0.225874i
$645$		0			0
$646$	−4.58155	+	7.93548i	−0.180259	+	0.312217i
$647$	15.7710	−	9.10540i	0.620022	−	0.357970i	−0.156855	−	0.987622i	$-0.550136\pi$
$647$	15.7710	−	9.10540i	0.620022	−	0.357970i	0.776878	+	0.629652i	$0.216802\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	14.4930			0.568898
$650$		0			0
$651$	13.4005			0.525207
$652$	4.94735	+	8.56906i	0.193753	+	0.335590i
$653$	−41.7065	+	24.0793i	−1.63210	+	0.942294i	−0.648657	+	0.761081i	$0.724669\pi$
$653$	−41.7065	+	24.0793i	−1.63210	+	0.942294i	−0.983444	+	0.181213i	$0.941998\pi$
$654$	−6.61335	+	11.4547i	−0.258603	+	0.447913i
$655$		0			0
$656$	4.02283	+	2.32258i	0.157065	+	0.0906815i
$657$	−3.14152	+	5.44128i	−0.122562	+	0.212284i
$658$	12.0477			0.469669
$659$	−18.4127	+	31.8917i	−0.717257	+	1.24233i	0.244826	+	0.969567i	$0.421269\pi$
$659$	−18.4127	+	31.8917i	−0.717257	+	1.24233i	−0.962083	+	0.272758i	$0.912064\pi$
$660$		0			0
$661$	−19.5131	+	11.2659i	−0.758971	+	0.438192i	−0.828926	−	0.559358i	$-0.811048\pi$
$661$	−19.5131	+	11.2659i	−0.758971	+	0.438192i	0.0699555	+	0.997550i	$0.477714\pi$
$662$			18.0904i			0.703103i
$663$	6.64516	−	12.8001i	0.258077	−	0.497114i
$664$	−15.8719			−0.615948
$665$		0			0
$666$	−3.40475	−	5.89721i	−0.131932	−	0.228512i
$667$	15.1847	+	8.76691i	0.587955	+	0.339456i
$668$	24.0375			0.930037
$669$	21.6001	+	12.4708i	0.835106	+	0.482149i
$670$		0			0
$671$		−	2.47229i		−	0.0954417i
$672$	−1.14539	−	0.661290i	−0.0441843	−	0.0255098i
$673$	−20.5627	+	11.8719i	−0.792633	+	0.457627i	−0.840889	−	0.541208i	$-0.817967\pi$
$673$	−20.5627	+	11.8719i	−0.792633	+	0.457627i	0.0482556	+	0.998835i	$0.484634\pi$
$674$	−4.93548	+	2.84950i	−0.190108	+	0.109759i
$675$		0			0
$676$	12.9480	−	1.16191i	0.497999	−	0.0446890i
$677$		−	1.16559i		−	0.0447975i	−0.999749	−	0.0223987i	$-0.992870\pi$
$677$		−	1.16559i		−	0.0447975i	0.999749	−	0.0223987i	$-0.00713033\pi$
$678$	4.04322	+	7.00306i	0.155279	+	0.268951i
$679$	5.83188	+	10.1011i	0.223807	+	0.387645i
$680$		0			0
$681$			19.3205i			0.740363i
$682$	23.3715	−	40.4806i	0.894939	−	1.55008i
$683$	−6.93593	+	12.0134i	−0.265396	+	0.459680i	−0.967667	−	0.252230i	$-0.918836\pi$
$683$	−6.93593	+	12.0134i	−0.265396	+	0.459680i	0.702271	+	0.711910i	$0.252169\pi$
$684$		−	2.29078i		−	0.0875900i
$685$		0			0
$686$	8.10132	+	14.0319i	0.309310	+	0.535740i
$687$	2.07746	+	3.59826i	0.0792599	+	0.137282i
$688$		−	8.60562i		−	0.328086i
$689$	−2.64537	−	1.37334i	−0.100781	−	0.0523203i
$690$		0			0
$691$	−35.6967	+	20.6095i	−1.35797	+	0.784022i	−0.989349	−	0.145560i	$-0.953502\pi$
$691$	−35.6967	+	20.6095i	−1.35797	+	0.784022i	−0.368616	+	0.929582i	$0.620168\pi$
$692$	−2.18946	+	1.26408i	−0.0832307	+	0.0480532i
$693$	5.28408	+	3.05076i	0.200726	+	0.115889i
$694$		−	15.7471i		−	0.597753i
$695$		0			0
$696$	1.75182	+	1.01141i	0.0664025	+	0.0383375i
$697$	18.5806			0.703792
$698$	−13.2679	−	7.66025i	−0.502199	−	0.289945i
$699$	8.48325	+	14.6934i	0.320866	+	0.555756i
$700$		0			0
$701$	−23.0112			−0.869122			−0.434561	−	0.900642i	$-0.643096\pi$
$701$	−23.0112			−0.869122			−0.434561	+	0.900642i	$0.643096\pi$
$702$	0.161290	+	3.60194i	0.00608749	+	0.135947i
$703$			15.5991i			0.588329i
$704$	−3.99528	+	2.30668i	−0.150578	+	0.0869362i
$705$		0			0
$706$	−0.599964	+	1.03917i	−0.0225799	+	0.0391096i
$707$	−9.55790			−0.359462
$708$	1.57076	−	2.72064i	0.0590328	−	0.102248i
$709$	14.7944	+	8.54156i	0.555616	+	0.320785i	0.751384	−	0.659865i	$-0.229387\pi$
$709$	14.7944	+	8.54156i	0.555616	+	0.320785i	−0.195768	+	0.980650i	$0.562720\pi$
$710$		0			0
$711$	−1.48387	+	2.57014i	−0.0556495	+	0.0963877i
$712$	10.2746	−	5.93207i	0.385059	−	0.222314i
$713$	−43.9124	−	76.0585i	−1.64453	−	2.84841i
$714$	−5.29032			−0.197985
$715$		0			0
$716$	−6.27568			−0.234533
$717$	−3.17208	−	5.49420i	−0.118463	−	0.205185i
$718$	−14.1015	+	8.14152i	−0.526264	+	0.303839i
$719$	21.8564	−	37.8564i	0.815106	−	1.41181i	−0.0941451	−	0.995558i	$-0.530012\pi$
$719$	21.8564	−	37.8564i	0.815106	−	1.41181i	0.909251	−	0.416247i	$-0.136655\pi$
$720$		0			0
$721$	−21.0752	−	12.1678i	−0.784880	−	0.453151i
$722$	6.87617	−	11.9099i	0.255905	−	0.443240i
$723$	24.1855			0.899467
$724$	6.14152	−	10.6374i	0.228248	−	0.395337i
$725$		0			0
$726$	8.90538	−	5.14152i	0.330510	−	0.190820i
$727$		−	31.8453i		−	1.18108i	−0.807010	−	0.590538i	$-0.798916\pi$
$727$		−	31.8453i		−	1.18108i	0.807010	−	0.590538i	$-0.201084\pi$
$728$	−2.56667	−	4.01896i	−0.0951270	−	0.148953i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−17.2112	−	29.8108i	−0.636581	−	1.10259i
$732$	−0.464102	−	0.267949i	−0.0171537	−	0.00990369i
$733$	−5.96774			−0.220423			−0.110212	−	0.993908i	$-0.535153\pi$
$733$	−5.96774			−0.220423			−0.110212	+	0.993908i	$0.535153\pi$
$734$	17.0040	+	9.81724i	0.627627	+	0.362361i
$735$		0			0
$736$			8.66799i			0.319506i
$737$	−12.7092	−	7.33767i	−0.468150	−	0.270287i
$738$	−4.02283	+	2.32258i	−0.148082	+	0.0854953i
$739$	−9.37833	+	5.41458i	−0.344988	+	0.199179i	−0.662475	−	0.749084i	$-0.730494\pi$
$739$	−9.37833	+	5.41458i	−0.344988	+	0.199179i	0.317488	+	0.948262i	$0.397161\pi$
$740$		0			0
$741$	3.80564	−	7.33052i	0.139804	−	0.269293i
$742$			1.09334i			0.0401378i
$743$	9.92515	+	17.1909i	0.364118	+	0.630671i	0.988634	−	0.150341i	$-0.0480371\pi$
$743$	9.92515	+	17.1909i	0.364118	+	0.630671i	−0.624516	+	0.781012i	$0.714704\pi$
$744$	−5.06604	−	8.77464i	−0.185730	−	0.321694i
$745$		0			0
$746$			2.55748i			0.0936359i
$747$	7.93593	−	13.7454i	0.290361	−	0.502919i
$748$	−9.22671	+	15.9811i	−0.337362	+	0.584328i
$749$			4.06270i			0.148448i
$750$		0			0
$751$	−7.66538	−	13.2768i	−0.279714	−	0.484479i	0.691600	−	0.722281i	$-0.256906\pi$
$751$	−7.66538	−	13.2768i	−0.279714	−	0.484479i	−0.971314	+	0.237802i	$0.923573\pi$
$752$	−4.55463	−	7.88885i	−0.166090	−	0.287677i
$753$		−	8.82497i		−	0.321600i
$754$	3.92560	+	6.14682i	0.142962	+	0.223854i
$755$		0			0
$756$	1.14539	−	0.661290i	0.0416573	−	0.0240509i
$757$	−39.1125	+	22.5816i	−1.42157	+	0.820744i	−0.996433	−	0.0843855i	$-0.973107\pi$
$757$	−39.1125	+	22.5816i	−1.42157	+	0.820744i	−0.425137	+	0.905129i	$0.639774\pi$
$758$	13.0846	+	7.55440i	0.475254	+	0.274388i
$759$		−	39.9885i		−	1.45149i
$760$		0			0
$761$	−18.7978	−	10.8529i	−0.681419	−	0.393418i	0.118970	−	0.992898i	$-0.462041\pi$
$761$	−18.7978	−	10.8529i	−0.681419	−	0.393418i	−0.800390	+	0.599480i	$0.795374\pi$
$762$	11.4718			0.415581
$763$	15.1497	+	8.74669i	0.548456	+	0.316651i
$764$	4.87357	+	8.44128i	0.176320	+	0.305395i
$765$		0			0
$766$	18.7303			0.676755
$767$	9.54623	−	6.09660i	0.344694	−	0.220136i
$768$			1.00000i			0.0360844i
$769$	−36.4711	+	21.0566i	−1.31518	+	0.759321i	−0.982949	−	0.183877i	$-0.941135\pi$
$769$	−36.4711	+	21.0566i	−1.31518	+	0.759321i	−0.332233	+	0.943197i	$0.607802\pi$
$770$		0			0
$771$	4.19247	−	7.26157i	0.150988	−	0.261519i
$772$	13.7626			0.495327
$773$	−14.8803	+	25.7734i	−0.535206	+	0.927004i	0.463947	+	0.885863i	$0.346433\pi$
$773$	−14.8803	+	25.7734i	−0.535206	+	0.927004i	−0.999153	+	0.0411413i	$0.986901\pi$
$774$	7.45269	+	4.30281i	0.267881	+	0.154661i
$775$		0			0
$776$	4.40947	−	7.63743i	0.158291	−	0.274168i
$777$	−7.79953	+	4.50306i	−0.279806	+	0.161546i
$778$	−3.48449	−	6.03532i	−0.124925	−	0.216377i
$779$	10.6410			0.381254
$780$		0			0
$781$	52.2969			1.87133
$782$	17.3360	+	30.0268i	0.619933	+	1.07376i
$783$	−1.75182	+	1.01141i	−0.0626049	+	0.0361450i
$784$	2.62539	−	4.54731i	0.0937640	−	0.162404i
$785$		0			0
$786$	−13.8482	−	7.99528i	−0.493950	−	0.285182i
$787$	−20.5224	+	35.5459i	−0.731545	+	1.26707i	0.224678	+	0.974433i	$0.427867\pi$
$787$	−20.5224	+	35.5459i	−0.731545	+	1.26707i	−0.956223	+	0.292640i	$0.905466\pi$
$788$	−10.1415			−0.361277
$789$	0.960648	−	1.66389i	0.0342000	−	0.0592361i
$790$		0			0
$791$	9.26210	−	5.34748i	0.329322	−	0.190134i
$792$		−	4.61335i		−	0.163928i
$793$	−1.03999	−	1.62845i	−0.0369312	−	0.0578279i
$794$	−18.5721			−0.659100
$795$		0			0
$796$	−4.78668	−	8.29078i	−0.169659	−	0.293859i
$797$	−39.1899	−	22.6263i	−1.38818	−	0.801464i	−0.395067	−	0.918652i	$-0.629279\pi$
$797$	−39.1899	−	22.6263i	−1.38818	−	0.801464i	−0.993110	+	0.117188i	$0.962612\pi$
$798$	−3.02973			−0.107251
$799$	−31.5554	−	18.2185i	−1.11635	−	0.644525i
$800$		0			0
$801$			11.8641i			0.419199i
$802$	−25.7126	−	14.8452i	−0.907944	−	0.524201i
$803$	25.1025	−	14.4930i	0.885849	−	0.511445i
$804$	−2.75488	+	1.59053i	−0.0971570	+	0.0560936i
$805$		0			0
$806$	−1.63420	−	36.4952i	−0.0575623	−	1.28549i
$807$			32.3098i			1.13736i
$808$	3.61335	+	6.25851i	0.127117	+	0.220174i
$809$	−14.2267	−	24.6414i	−0.500184	−	0.866345i	−1.00000		0.000213036i	$-0.999932\pi$
$809$	−14.2267	−	24.6414i	−0.500184	−	0.866345i	0.499815	−	0.866132i	$-0.333401\pi$
$810$		0			0
$811$			44.4114i			1.55949i	0.626095	+	0.779747i	$0.284652\pi$
$811$			44.4114i			1.55949i	−0.626095	+	0.779747i	$0.715348\pi$
$812$	1.33767	−	2.31692i	0.0469432	−	0.0813079i
$813$	11.7263	−	20.3105i	0.411259	−	0.712322i
$814$			31.4147i			1.10108i
$815$		0			0
$816$	2.00000	+	3.46410i	0.0700140	+	0.121268i
$817$	−9.85677	−	17.0724i	−0.344845	−	0.597289i
$818$			24.3355i			0.850871i
$819$	4.76386	−	0.213319i	0.166463	−	0.00745396i
$820$		0			0
$821$	−39.1169	+	22.5842i	−1.36519	+	0.788192i	−0.990309	−	0.138881i	$-0.955649\pi$
$821$	−39.1169	+	22.5842i	−1.36519	+	0.788192i	−0.374880	+	0.927073i	$0.622316\pi$
$822$	13.9168	−	8.03486i	0.485404	−	0.280248i
$823$	2.09404	+	1.20900i	0.0729938	+	0.0421430i	0.536053	−	0.844185i	$-0.319915\pi$
$823$	2.09404	+	1.20900i	0.0729938	+	0.0421430i	−0.463059	+	0.886328i	$0.653248\pi$
$824$			18.4000i			0.640996i
$825$		0			0
$826$	−3.59826	−	2.07746i	−0.125199	−	0.0722840i
$827$	−4.26832			−0.148424			−0.0742120	−	0.997242i	$-0.523644\pi$
$827$	−4.26832			−0.148424			−0.0742120	+	0.997242i	$0.523644\pi$
$828$	−7.50670	−	4.33399i	−0.260876	−	0.150617i
$829$	21.4926	+	37.2263i	0.746468	+	1.29292i	0.949506	+	0.313750i	$0.101585\pi$
$829$	21.4926	+	37.2263i	0.746468	+	1.29292i	−0.203037	+	0.979171i	$0.565081\pi$
$830$		0			0
$831$	9.00566			0.312403
$832$	−1.66129	+	3.20002i	−0.0575949	+	0.110941i
$833$		−	21.0031i		−	0.727715i
$834$	8.07359	−	4.66129i	0.279566	−	0.161407i
$835$		0			0
$836$	−5.28408	+	9.15229i	−0.182754	+	0.316539i
$837$	10.1321			0.350216
$838$	1.44128	−	2.49636i	0.0497880	−	0.0862354i
$839$	20.1798	+	11.6508i	0.696684	+	0.402231i	0.806111	−	0.591764i	$-0.201568\pi$
$839$	20.1798	+	11.6508i	0.696684	+	0.402231i	−0.109427	+	0.993995i	$0.534902\pi$
$840$		0			0
$841$	12.4541	−	21.5711i	0.429451	−	0.743831i
$842$	−4.28429	+	2.47354i	−0.147646	+	0.0852437i
$843$	−0.858478	−	1.48693i	−0.0295676	−	0.0512125i
$844$	−1.08519			−0.0373537
$845$		0			0
$846$	9.10926			0.313183
$847$	−6.80007	−	11.7781i	−0.233653	−	0.404699i
$848$	0.715920	−	0.413337i	0.0245848	−	0.0141940i
$849$	0.774645	−	1.34172i	0.0265857	−	0.0460479i
$850$		0			0
$851$	51.1169	+	29.5124i	1.75226	+	1.01167i
$852$	5.66799	−	9.81724i	0.194182	−	0.336333i
$853$	20.8418			0.713609			0.356804	−	0.934179i	$-0.383866\pi$
$853$	20.8418			0.713609			0.356804	+	0.934179i	$0.383866\pi$
$854$	−0.354384	+	0.613811i	−0.0121268	+	0.0210042i
$855$		0			0
$856$	2.66025	−	1.53590i	0.0909256	−	0.0524959i
$857$		−	36.7250i		−	1.25450i	−0.778818	−	0.627250i	$-0.784180\pi$
$857$		−	36.7250i		−	1.25450i	0.778818	−	0.627250i	$-0.215820\pi$
$858$	7.66412	−	14.7628i	0.261649	−	0.503994i
$859$	−0.914812			−0.0312130			−0.0156065	−	0.999878i	$-0.504968\pi$
$859$	−0.914812			−0.0312130			−0.0156065	+	0.999878i	$0.504968\pi$
$860$		0			0
$861$	3.07180	+	5.32051i	0.104687	+	0.181322i
$862$	−15.3829	−	8.88130i	−0.523943	−	0.302498i
$863$	33.6104			1.14411			0.572056	−	0.820215i	$-0.306146\pi$
$863$	33.6104			1.14411			0.572056	+	0.820215i	$0.306146\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$		0			0
$866$			35.8375i			1.21781i
$867$	−0.866025	−	0.500000i	−0.0294118	−	0.0169809i
$868$	−11.6052	+	6.70025i	−0.393905	+	0.227421i
$869$	11.8570	−	6.84562i	0.402220	−	0.232222i
$870$		0			0
$871$	−11.4580	+	0.513072i	−0.388239	+	0.0173848i
$872$		−	13.2267i		−	0.447913i
$873$	4.40947	+	7.63743i	0.149238	+	0.258488i
$874$	9.92820	+	17.1962i	0.335826	+	0.581669i
$875$		0			0
$876$		−	6.28304i		−	0.212284i
$877$	−12.1607	+	21.0629i	−0.410637	+	0.711243i	−0.994959	−	0.100278i	$-0.968027\pi$
$877$	−12.1607	+	21.0629i	−0.410637	+	0.711243i	0.584323	+	0.811521i	$0.301360\pi$
$878$	5.04520	−	8.73854i	0.170267	−	0.294911i
$879$			30.4057i			1.02556i
$880$		0			0
$881$	−4.95207	−	8.57723i	−0.166839	−	0.288974i	0.770468	−	0.637479i	$-0.220023\pi$
$881$	−4.95207	−	8.57723i	−0.166839	−	0.288974i	−0.937307	+	0.348505i	$0.886689\pi$
$882$	2.62539	+	4.54731i	0.0884015	+	0.153116i
$883$		−	43.9718i		−	1.47977i	−0.672734	−	0.739884i	$-0.734880\pi$
$883$		−	43.9718i		−	1.47977i	0.672734	−	0.739884i	$-0.265120\pi$
$884$	0.645159	+	14.4078i	0.0216991	+	0.484586i
$885$		0			0
$886$	−11.8629	+	6.84904i	−0.398542	+	0.230098i
$887$	−43.7875	+	25.2807i	−1.47024	+	0.848843i	−0.999442	−	0.0333988i	$-0.989367\pi$
$887$	−43.7875	+	25.2807i	−1.47024	+	0.848843i	−0.470797	+	0.882242i	$0.656034\pi$
$888$	5.89721	+	3.40475i	0.197897	+	0.114256i
$889$		−	15.1724i		−	0.508866i
$890$		0			0
$891$	3.99528	+	2.30668i	0.133847	+	0.0772766i
$892$	−24.9416			−0.835106
$893$	−18.0716	−	10.4336i	−0.604743	−	0.349148i
$894$	−2.04259	−	3.53788i	−0.0683146	−	0.118324i
$895$		0			0
$896$	1.32258			0.0441843
$897$	−16.8215	−	26.3397i	−0.561655	−	0.879455i
$898$		−	15.3128i		−	0.510994i
$899$	17.7496	−	10.2477i	0.591982	−	0.341781i
$900$		0			0
$901$	1.65335	−	2.86368i	0.0550810	−	0.0954031i
$902$	21.4298			0.713533
$903$	5.69081	−	9.85677i	0.189378	−	0.328013i
$904$	−7.00306	−	4.04322i	−0.232918	−	0.134475i
$905$		0			0
$906$	−9.99057	+	17.3042i	−0.331914	+	0.574892i
$907$	12.3352	−	7.12175i	0.409585	−	0.236474i	−0.281026	−	0.959700i	$-0.590675\pi$
$907$	12.3352	−	7.12175i	0.409585	−	0.236474i	0.690611	+	0.723226i	$0.257342\pi$
$908$	−9.66025	−	16.7321i	−0.320587	−	0.555273i
$909$	−7.22671			−0.239695
$910$		0			0
$911$	21.8108			0.722623			0.361311	−	0.932445i	$-0.382329\pi$
$911$	21.8108			0.722623			0.361311	+	0.932445i	$0.382329\pi$
$912$	1.14539	+	1.98387i	0.0379276	+	0.0656925i
$913$	−63.4126	+	36.6113i	−2.09865	+	1.21166i
$914$	−7.77770	+	13.4714i	−0.257264	+	0.445594i
$915$		0			0
$916$	−3.59826	−	2.07746i	−0.118890	−	0.0686411i
$917$	−10.5744	+	18.3154i	−0.349197	+	0.604828i
$918$	−4.00000			−0.132020
$919$	−2.65289	+	4.59494i	−0.0875108	+	0.151573i	−0.906458	−	0.422295i	$-0.861225\pi$
$919$	−2.65289	+	4.59494i	−0.0875108	+	0.151573i	0.818948	+	0.573868i	$0.194558\pi$
$920$		0			0
$921$	−8.50975	+	4.91311i	−0.280406	+	0.161892i
$922$			15.6431i			0.515178i
$923$	34.4469	−	21.9992i	1.13383	−	0.724112i
$924$	−6.10153			−0.200726
$925$		0			0
$926$	6.85848	+	11.8792i	0.225384	+	0.390376i
$927$	−15.9349	−	9.20002i	−0.523371	−	0.302168i
$928$	−2.02283			−0.0664025
$929$	38.4002	+	22.1704i	1.25987	+	0.727386i	0.973049	−	0.230598i	$-0.0740681\pi$
$929$	38.4002	+	22.1704i	1.25987	+	0.727386i	0.286821	+	0.957984i	$0.407401\pi$
$930$		0			0
$931$		−	12.0284i		−	0.394214i
$932$	−14.6934	−	8.48325i	−0.481299	−	0.277878i
$933$	−2.94491	+	1.70025i	−0.0964121	+	0.0556636i
$934$	−0.817239	+	0.471833i	−0.0267409	+	0.0154388i
$935$		0			0
$936$	−1.94065	−	3.03873i	−0.0634322	−	0.0993239i
$937$		−	38.5283i		−	1.25867i	−0.777136	−	0.629333i	$-0.783328\pi$
$937$		−	38.5283i		−	1.25867i	0.777136	−	0.629333i	$-0.216672\pi$
$938$	2.10360	+	3.64354i	0.0686850	+	0.118966i
$939$	−8.11699	−	14.0590i	−0.264888	−	0.458800i
$940$		0			0
$941$		−	28.8637i		−	0.940929i	−0.882419	−	0.470465i	$-0.844086\pi$
$941$		−	28.8637i		−	0.940929i	0.882419	−	0.470465i	$-0.155914\pi$
$942$	3.56690	−	6.17804i	0.116216	−	0.201292i
$943$	20.1321	−	34.8698i	0.655591	−	1.13552i
$944$			3.14152i			0.102248i
$945$		0			0
$946$	−19.8504	−	34.3819i	−0.645392	−	1.11785i
$947$	−24.6173	−	42.6384i	−0.799955	−	1.38556i	−0.919645	−	0.392752i	$-0.871523\pi$
$947$	−24.6173	−	42.6384i	−0.799955	−	1.38556i	0.119689	−	0.992811i	$-0.461810\pi$
$948$		−	2.96774i		−	0.0963877i
$949$	10.4380	−	20.1059i	0.338830	−	0.652664i
$950$		0			0
$951$	−20.3716	+	11.7616i	−0.660596	+	0.381395i
$952$	4.58155	−	2.64516i	0.148489	−	0.0857301i
$953$	−22.9580	−	13.2548i	−0.743684	−	0.429366i	0.0797233	−	0.996817i	$-0.474596\pi$
$953$	−22.9580	−	13.2548i	−0.743684	−	0.429366i	−0.823407	+	0.567451i	$0.807930\pi$
$954$			0.826674i			0.0267645i
$955$		0			0
$956$	5.49420	+	3.17208i	0.177695	+	0.102592i
$957$	9.33201			0.301661
$958$	9.61460	+	5.55099i	0.310634	+	0.179344i
$959$	−10.6267	−	18.4061i	−0.343156	−	0.594363i
$960$		0			0
$961$	−71.6592			−2.31159
$962$	13.2149	+	20.6922i	0.426065	+	0.667145i
$963$			3.07180i			0.0989873i
$964$	−20.9452	+	12.0927i	−0.674600	+	0.389481i
$965$		0			0
$966$	−5.73205	+	9.92820i	−0.184426	+	0.319435i
$967$	−52.3877			−1.68468			−0.842338	−	0.538950i	$-0.818821\pi$
$967$	−52.3877			−1.68468			−0.842338	+	0.538950i	$0.818821\pi$
$968$	−5.14152	+	8.90538i	−0.165255	+	0.286230i
$969$	7.93548	+	4.58155i	0.254924	+	0.147181i
$970$		0			0
$971$	14.3215	−	24.8056i	0.459600	−	0.796051i	−0.539339	−	0.842088i	$-0.681326\pi$
$971$	14.3215	−	24.8056i	0.459600	−	0.796051i	0.998940	+	0.0460375i	$0.0146594\pi$
$972$	0.866025	−	0.500000i	0.0277778	−	0.0160375i
$973$	−6.16493	−	10.6780i	−0.197638	−	0.342320i
$974$	−32.9416			−1.05552
$975$		0			0
$976$	0.535898			0.0171537
$977$	−20.2750	−	35.1173i	−0.648654	−	1.12350i	−0.983445	−	0.181209i	$-0.941999\pi$
$977$	−20.2750	−	35.1173i	−0.648654	−	1.12350i	0.334791	−	0.942292i	$-0.391334\pi$
$978$	8.56906	−	4.94735i	0.274008	−	0.158199i
$979$	27.3667	−	47.4006i	0.874645	−	1.51493i
$980$		0			0
$981$	11.4547	+	6.61335i	0.365719	+	0.211148i
$982$	−14.2257	+	24.6396i	−0.453960	+	0.786281i
$983$	22.4160			0.714958			0.357479	−	0.933921i	$-0.383636\pi$
$983$	22.4160			0.714958			0.357479	+	0.933921i	$0.383636\pi$
$984$	2.32258	−	4.02283i	0.0740411	−	0.128243i
$985$		0			0
$986$	−7.00727	+	4.04565i	−0.223157	+	0.128840i
$987$		−	12.0477i		−	0.383483i
$988$	0.369479	+	8.25124i	0.0117547	+	0.262507i
$989$	−74.5934			−2.37193
$990$		0			0
$991$	14.2844	+	24.7413i	0.453759	+	0.785933i	0.998616	−	0.0525955i	$-0.0167494\pi$
$991$	14.2844	+	24.7413i	0.453759	+	0.785933i	−0.544857	+	0.838529i	$0.683416\pi$
$992$	8.77464	+	5.06604i	0.278595	+	0.160847i
$993$	18.0904			0.574081
$994$	−12.9841	−	7.49636i	−0.411830	−	0.237770i
$995$		0			0
$996$			15.8719i			0.502919i
$997$	−29.7913	−	17.2000i	−0.943500	−	0.544730i	−0.0524443	−	0.998624i	$-0.516701\pi$
$997$	−29.7913	−	17.2000i	−0.943500	−	0.544730i	−0.891056	+	0.453894i	$0.850035\pi$
$998$	3.55872	−	2.05463i	0.112649	−	0.0650382i
$999$	−5.89721	+	3.40475i	−0.186579	+	0.107722i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.y.k.49.4		8
5.2	odd	4		390.2.bb.c.361.2	yes	8
5.3	odd	4		1950.2.bc.g.751.3		8
5.4	even	2		1950.2.y.j.49.1		8
13.4	even	6		1950.2.y.j.199.1		8
15.2	even	4		1170.2.bs.f.361.4		8
65.2	even	12		5070.2.a.bz.1.3		4
65.4	even	6	inner	1950.2.y.k.199.4		8
65.17	odd	12		390.2.bb.c.121.2	✓	8
65.37	even	12		5070.2.a.ca.1.2		4
65.42	odd	12		5070.2.b.ba.1351.2		8
65.43	odd	12		1950.2.bc.g.901.3		8
65.62	odd	12		5070.2.b.ba.1351.7		8
195.17	even	12		1170.2.bs.f.901.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bb.c.121.2	✓	8	65.17	odd	12
390.2.bb.c.361.2	yes	8	5.2	odd	4
1170.2.bs.f.361.4		8	15.2	even	4
1170.2.bs.f.901.4		8	195.17	even	12
1950.2.y.j.49.1		8	5.4	even	2
1950.2.y.j.199.1		8	13.4	even	6
1950.2.y.k.49.4		8	1.1	even	1	trivial
1950.2.y.k.199.4		8	65.4	even	6	inner
1950.2.bc.g.751.3		8	5.3	odd	4
1950.2.bc.g.901.3		8	65.43	odd	12
5070.2.a.bz.1.3		4	65.2	even	12
5070.2.a.ca.1.2		4	65.37	even	12
5070.2.b.ba.1351.2		8	65.42	odd	12
5070.2.b.ba.1351.7		8	65.62	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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(0.661290 - 1.14539i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(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} +(0.661290 - 1.14539i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-3.99528 + 2.30668i) q^{11} +1.00000i q^{12} +(-1.66129 + 3.20002i) q^{13} +1.32258 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.46410 - 2.00000i) q^{17} +1.00000 q^{18} +(-1.98387 - 1.14539i) q^{19} -1.32258i q^{21} +(-3.99528 - 2.30668i) q^{22} +(-7.50670 + 4.33399i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-3.60194 + 0.161290i) q^{26} -1.00000i q^{27} +(0.661290 + 1.14539i) q^{28} +(-1.01141 - 1.75182i) q^{29} +10.1321i q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.30668 + 3.99528i) q^{33} -4.00000i q^{34} +(0.500000 + 0.866025i) q^{36} +(-3.40475 - 5.89721i) q^{37} -2.29078i q^{38} +(0.161290 + 3.60194i) q^{39} +(-4.02283 + 2.32258i) q^{41} +(1.14539 - 0.661290i) q^{42} +(7.45269 + 4.30281i) q^{43} -4.61335i q^{44} +(-7.50670 - 4.33399i) q^{46} +9.10926 q^{47} +(-0.866025 - 0.500000i) q^{48} +(2.62539 + 4.54731i) q^{49} -4.00000 q^{51} +(-1.94065 - 3.03873i) q^{52} +0.826674i q^{53} +(0.866025 - 0.500000i) q^{54} +(-0.661290 + 1.14539i) q^{56} -2.29078 q^{57} +(1.01141 - 1.75182i) q^{58} +(-2.72064 - 1.57076i) q^{59} +(-0.267949 + 0.464102i) q^{61} +(-8.77464 + 5.06604i) q^{62} +(-0.661290 - 1.14539i) q^{63} +1.00000 q^{64} -4.61335 q^{66} +(1.59053 + 2.75488i) q^{67} +(3.46410 - 2.00000i) q^{68} +(-4.33399 + 7.50670i) q^{69} +(-9.81724 - 5.66799i) q^{71} +(-0.500000 + 0.866025i) q^{72} -6.28304 q^{73} +(3.40475 - 5.89721i) q^{74} +(1.98387 - 1.14539i) q^{76} +6.10153i q^{77} +(-3.03873 + 1.94065i) q^{78} -2.96774 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-4.02283 - 2.32258i) q^{82} +15.8719 q^{83} +(1.14539 + 0.661290i) q^{84} +8.60562i q^{86} +(-1.75182 - 1.01141i) q^{87} +(3.99528 - 2.30668i) q^{88} +(-10.2746 + 5.93207i) q^{89} +(2.56667 + 4.01896i) q^{91} -8.66799i q^{92} +(5.06604 + 8.77464i) q^{93} +(4.55463 + 7.88885i) q^{94} -1.00000i q^{96} +(-4.40947 + 7.63743i) q^{97} +(-2.62539 + 4.54731i) q^{98} +4.61335i 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

Modular forms

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Database

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