LMFDB - Embedded newform 1950.2.y.j.49.1

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			49.1
Root			$-1.80668 - 1.80668i$ of defining polynomial
Character	$\chi$	$=$	1950.49
Dual form			1950.2.y.j.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-0.661290 + 1.14539i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(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	−0.963510	−	0.267672i	$-0.913746\pi$
$7$	−0.661290	+	1.14539i	−0.249944	+	0.432916i	0.713566	+	0.700588i	$0.247079\pi$
$8$	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	0.857321	−	0.514782i	$-0.172127\pi$
$17$	3.46410	+	2.00000i	0.840168	+	0.485071i	−0.0171533	+	0.999853i	$0.505460\pi$
$18$	−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	$-0.307507\pi$
$23$	7.50670	−	4.33399i	1.56525	−	0.903700i	0.996710	−	0.0810471i	$-0.0258264\pi$
$24$	−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	$0.0224316\pi$
$37$	3.40475	+	5.89721i	0.559738	+	0.969495i	−0.437780	+	0.899082i	$0.644235\pi$
$38$			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	−0.190957	−	0.981598i	$-0.561159\pi$
$43$	−7.45269	−	4.30281i	−1.13652	−	0.656173i	−0.945568	+	0.325426i	$0.894492\pi$
$44$		−	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	$-0.731296\pi$
$47$	−9.10926			−1.32872			−0.664361	+	0.747412i	$0.731296\pi$
$48$	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	$-0.981918\pi$
$53$		−	0.826674i		−	0.113552i	0.998387	−	0.0567762i	$-0.0180821\pi$
$54$	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	0.752361	−	0.658751i	$-0.228915\pi$
$67$	−1.59053	−	2.75488i	−0.194314	−	0.336562i	−0.946675	+	0.322189i	$0.895581\pi$
$68$	−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	$-0.380150\pi$
$73$	6.28304			0.735375			0.367687	+	0.929949i	$0.380150\pi$
$74$	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	$-0.836581\pi$
$83$	−15.8719			−1.74216			−0.871082	+	0.491138i	$0.836581\pi$
$84$	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	−0.550523	−	0.834820i	$-0.685572\pi$
$97$	4.40947	−	7.63743i	0.447714	−	0.775463i	0.998237	+	0.0593568i	$0.0189050\pi$
$98$	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	$0.361260\pi$
$103$			18.4000i			1.81301i	−0.422196	+	0.906505i	$0.638740\pi$
$104$	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	−0.365869	−	0.930666i	$-0.619228\pi$
$107$	2.66025	−	1.53590i	0.257176	−	0.148481i	0.623046	+	0.782185i	$0.285895\pi$
$108$	−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	0.133024	−	0.991113i	$-0.457531\pi$
$113$	−7.00306	−	4.04322i	−0.658792	−	0.380354i	−0.791817	+	0.610759i	$0.790864\pi$
$114$	−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	−0.871179	−	0.490966i	$-0.836644\pi$
$127$	−9.93490	+	5.73592i	−0.881580	+	0.508980i	−0.0104008	+	0.999946i	$0.503311\pi$
$128$	−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	$0.407505\pi$
$137$	−8.03486	+	13.9168i	−0.686465	+	1.18899i	−0.972974	+	0.230914i	$0.925828\pi$
$138$	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	$0.0918838\pi$
$157$			7.13379i			0.569338i	−0.958626	+	0.284669i	$0.908116\pi$
$158$	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	−0.992113	−	0.125343i	$-0.959997\pi$
$163$	−4.94735	+	8.56906i	−0.387506	+	0.671180i	0.604607	+	0.796524i	$0.293330\pi$
$164$		−	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	$0.213559\pi$
$167$	12.0187	+	20.8171i	0.930037	+	1.61087i	0.146785	+	0.989168i	$0.453108\pi$
$168$		−	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	0.414455	−	0.910070i	$-0.363972\pi$
$173$	−2.18946	−	1.26408i	−0.166461	−	0.0961065i	−0.580916	+	0.813963i	$0.697306\pi$
$174$		−	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	0.999985	−	0.00538741i	$-0.00171487\pi$
$193$	6.88130	+	11.9188i	0.495327	+	0.857932i	−0.504658	+	0.863319i	$0.668382\pi$
$194$	−8.81894			−0.633163
$195$		0			0
$196$	−5.25078			−0.375056
$197$	−5.07076	−	8.78282i	−0.361277	−	0.625750i	0.626894	−	0.779104i	$-0.284326\pi$
$197$	−5.07076	−	8.78282i	−0.361277	−	0.625750i	−0.988171	+	0.153354i	$0.950992\pi$
$198$	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	$-0.852073\pi$
$223$	−12.4708	−	21.6001i	−0.835106	−	1.44645i	0.0588375	−	0.998268i	$-0.481261\pi$
$224$	−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	$-0.611781\pi$
$227$	9.66025	−	16.7321i	0.641174	−	1.11055i	0.985171	−	0.171575i	$-0.0548855\pi$
$228$	−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	$-0.812429\pi$
$233$		−	16.9665i		−	1.11151i	0.831346	−	0.555756i	$-0.187571\pi$
$234$	−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	−0.709081	−	0.705127i	$-0.750890\pi$
$257$	−7.26157	+	4.19247i	−0.452964	+	0.261519i	0.256117	+	0.966646i	$0.417557\pi$
$258$	−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	−0.550422	−	0.834887i	$-0.685533\pi$
$263$	−1.66389	+	0.960648i	−0.102600	+	0.0592361i	0.447822	+	0.894123i	$0.352200\pi$
$264$	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	0.247051	−	0.969002i	$-0.420538\pi$
$277$	−7.79913	−	4.50283i	−0.468604	−	0.270549i	−0.715655	+	0.698454i	$0.753872\pi$
$278$	−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	−0.539348	−	0.842083i	$-0.681329\pi$
$283$	−1.34172	+	0.774645i	−0.0797572	+	0.0460479i	0.459591	+	0.888131i	$0.347996\pi$
$284$	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	$-0.485317\pi$
$293$	15.2028	−	26.3321i	0.888160	−	1.53834i	0.842049	−	0.539402i	$-0.181350\pi$
$294$			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	$-0.409531\pi$
$307$	9.82622			0.560812			0.280406	+	0.959882i	$0.409531\pi$
$308$	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	$0.151720\pi$
$313$			16.2340i			0.917599i	−0.888540	+	0.458800i	$0.848280\pi$
$314$	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	$-0.270304\pi$
$317$	23.5231			1.32119			0.660596	+	0.750742i	$0.270304\pi$
$318$	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	$-0.950391\pi$
$337$		−	5.69900i		−	0.310444i	0.987880	−	0.155222i	$-0.0496093\pi$
$338$	−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	0.819188	−	0.573525i	$-0.194424\pi$
$347$	13.6374	+	7.87357i	0.732095	+	0.422676i	−0.0870928	+	0.996200i	$0.527758\pi$
$348$	−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	0.849617	−	0.527400i	$-0.176833\pi$
$353$	−0.599964	−	1.03917i	−0.0319328	−	0.0553093i	−0.881550	+	0.472090i	$0.843500\pi$
$354$	−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	−0.873156	−	0.487440i	$-0.837931\pi$
$367$	−17.0040	+	9.81724i	−0.887599	+	0.512456i	−0.0144428	+	0.999896i	$0.504597\pi$
$368$	−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	0.441563	−	0.897230i	$-0.354424\pi$
$373$	−2.21484	−	1.27874i	−0.114680	−	0.0662106i	−0.556243	+	0.831020i	$0.687758\pi$
$374$	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	−0.999697	−	0.0246073i	$-0.992166\pi$
$383$	−9.36517	+	16.2210i	−0.478538	+	0.828852i	0.521159	+	0.853459i	$0.325500\pi$
$384$	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	−0.533195	−	0.845993i	$-0.679009\pi$
$397$	9.28606	−	16.0839i	0.466054	−	0.807229i	0.999248	+	0.0387637i	$0.0123420\pi$
$398$	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	−0.491553	−	0.870848i	$-0.663570\pi$
$433$	−31.0362	−	17.9188i	−1.49151	−	0.861121i	−0.999953	+	0.00972676i	$0.996904\pi$
$434$			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	$-0.894498\pi$
$443$		−	13.6981i		−	0.650816i	0.945574	−	0.325408i	$-0.105502\pi$
$444$	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	0.624761	−	0.780816i	$-0.285196\pi$
$457$	−7.77770	−	13.4714i	−0.363826	−	0.630164i	−0.988587	+	0.150651i	$0.951863\pi$
$458$	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	$-0.603260\pi$
$463$	−13.7170			−0.637481			−0.318741	+	0.947842i	$0.603260\pi$
$464$	−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	$-0.993050\pi$
$467$		−	0.943666i		−	0.0436677i	0.999762	−	0.0218338i	$-0.00695048\pi$
$468$	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	$-0.565132\pi$
$487$	16.4708	−	28.5283i	0.746363	−	1.29274i	0.949555	−	0.313600i	$-0.101535\pi$
$488$	−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	0.606641	−	0.794976i	$-0.292517\pi$
$503$	4.96753	+	2.86800i	0.221491	+	0.127878i	−0.385149	+	0.922854i	$0.625850\pi$
$504$	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	−0.302472	−	0.953158i	$-0.597812\pi$
$523$	8.50166	−	4.90844i	0.371752	−	0.214631i	0.674223	+	0.738527i	$0.264478\pi$
$524$	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	$0.428005\pi$
$547$			45.5847i			1.94906i	−0.224257	+	0.974530i	$0.571995\pi$
$548$	−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	$-0.881435\pi$
$557$	−18.4296	−	31.9209i	−0.780885	−	1.35253i	0.150541	−	0.988604i	$-0.451898\pi$
$558$		−	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	−0.265109	−	0.964218i	$-0.585408\pi$
$563$	−29.2491	−	16.8870i	−1.23270	−	0.711701i	−0.967592	+	0.252518i	$0.918741\pi$
$564$			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	$-0.563864\pi$
$577$	−9.57428			−0.398582			−0.199291	+	0.979940i	$0.563864\pi$
$578$	−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	0.880115	−	0.474761i	$-0.157466\pi$
$587$	0.700246	+	1.21286i	0.0289023	+	0.0500602i	−0.851212	+	0.524821i	$0.824132\pi$
$588$	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	$-0.429289\pi$
$593$	10.7303			0.440643			0.220321	+	0.975427i	$0.429289\pi$
$594$	−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	0.615897	−	0.787826i	$-0.288794\pi$
$607$	5.95161	+	3.43616i	0.241568	+	0.139470i	−0.374329	+	0.927296i	$0.622127\pi$
$608$	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	0.873611	−	0.486625i	$-0.161772\pi$
$613$	0.380681	+	0.659358i	0.0153755	+	0.0266312i	−0.858235	+	0.513257i	$0.828439\pi$
$614$	−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	−0.999985	−	0.00550613i	$-0.998247\pi$
$617$	−12.3011	+	21.3061i	−0.495224	+	0.857753i	0.504761	+	0.863259i	$0.331581\pi$
$618$	−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	−0.999499	−	0.0316570i	$-0.989922\pi$
$643$	−11.9772	+	20.7451i	−0.472334	+	0.818106i	0.527165	+	0.849763i	$0.323255\pi$
$644$	−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	−0.776878	−	0.629652i	$-0.783198\pi$
$647$	−15.7710	+	9.10540i	−0.620022	+	0.357970i	0.156855	+	0.987622i	$0.449864\pi$
$648$	−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	$-0.275331\pi$
$653$	41.7065	−	24.0793i	1.63210	−	0.942294i	0.983444	−	0.181213i	$-0.0580024\pi$
$654$	−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	−0.0482556	−	0.998835i	$-0.515366\pi$
$673$	20.5627	−	11.8719i	0.792633	−	0.457627i	0.840889	+	0.541208i	$0.182033\pi$
$674$	−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	$0.00713033\pi$
$677$			1.16559i			0.0447975i	−0.999749	+	0.0223987i	$0.992870\pi$
$678$	−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	−0.702271	−	0.711910i	$-0.747831\pi$
$683$	6.93593	−	12.0134i	0.265396	−	0.459680i	0.967667	+	0.252230i	$0.0811639\pi$
$684$		−	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	$0.201084\pi$
$727$			31.8453i			1.18108i	−0.807010	+	0.590538i	$0.798916\pi$
$728$	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	$-0.464847\pi$
$733$	5.96774			0.220423			0.110212	+	0.993908i	$0.464847\pi$
$734$	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	0.624516	−	0.781012i	$-0.285296\pi$
$743$	−9.92515	−	17.1909i	−0.364118	−	0.630671i	−0.988634	+	0.150341i	$0.951963\pi$
$744$	−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	0.425137	−	0.905129i	$-0.360226\pi$
$757$	39.1125	−	22.5816i	1.42157	−	0.820744i	0.996433	+	0.0843855i	$0.0268927\pi$
$758$	−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	$-0.653567\pi$
$773$	14.8803	−	25.7734i	0.535206	−	0.927004i	0.999153	−	0.0411413i	$-0.0130994\pi$
$774$	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	$-0.572133\pi$
$787$	20.5224	−	35.5459i	0.731545	−	1.26707i	0.956223	−	0.292640i	$-0.0945338\pi$
$788$	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	0.993110	−	0.117188i	$-0.0373880\pi$
$797$	39.1899	+	22.6263i	1.38818	+	0.801464i	0.395067	+	0.918652i	$0.370721\pi$
$798$	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	0.463059	−	0.886328i	$-0.346752\pi$
$823$	−2.09404	−	1.20900i	−0.0729938	−	0.0421430i	−0.536053	+	0.844185i	$0.680085\pi$
$824$			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	$-0.476356\pi$
$827$	4.26832			0.148424			0.0742120	+	0.997242i	$0.476356\pi$
$828$	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	$-0.616134\pi$
$853$	−20.8418			−0.713609			−0.356804	+	0.934179i	$0.616134\pi$
$854$	−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	$0.215820\pi$
$857$			36.7250i			1.25450i	−0.778818	+	0.627250i	$0.784180\pi$
$858$	−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	$-0.693854\pi$
$863$	−33.6104			−1.14411			−0.572056	+	0.820215i	$0.693854\pi$
$864$	−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	−0.584323	−	0.811521i	$-0.698640\pi$
$877$	12.1607	−	21.0629i	0.410637	−	0.711243i	0.994959	+	0.100278i	$0.0319732\pi$
$878$	−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	$0.265120\pi$
$883$			43.9718i			1.47977i	−0.672734	+	0.739884i	$0.734880\pi$
$884$	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	0.470797	−	0.882242i	$-0.343966\pi$
$887$	43.7875	−	25.2807i	1.47024	−	0.848843i	0.999442	+	0.0333988i	$0.0106332\pi$
$888$	−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	−0.690611	−	0.723226i	$-0.742658\pi$
$907$	−12.3352	+	7.12175i	−0.409585	+	0.236474i	0.281026	+	0.959700i	$0.409325\pi$
$908$	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	$0.216672\pi$
$937$			38.5283i			1.25867i	−0.777136	+	0.629333i	$0.783328\pi$
$938$	−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	$0.128477\pi$
$947$	24.6173	+	42.6384i	0.799955	+	1.38556i	−0.119689	+	0.992811i	$0.538190\pi$
$948$			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	0.823407	−	0.567451i	$-0.192070\pi$
$953$	22.9580	+	13.2548i	0.743684	+	0.429366i	−0.0797233	+	0.996817i	$0.525404\pi$
$954$			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	$-0.181179\pi$
$967$	52.3877			1.68468			0.842338	+	0.538950i	$0.181179\pi$
$968$	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	$0.0580009\pi$
$977$	20.2750	+	35.1173i	0.648654	+	1.12350i	−0.334791	+	0.942292i	$0.608666\pi$
$978$	−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	$-0.616364\pi$
$983$	−22.4160			−0.714958			−0.357479	+	0.933921i	$0.616364\pi$
$984$	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	0.891056	−	0.453894i	$-0.149965\pi$
$997$	29.7913	+	17.2000i	0.943500	+	0.544730i	0.0524443	+	0.998624i	$0.483299\pi$
$998$	−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.j.49.1		8
5.2	odd	4		1950.2.bc.g.751.3		8
5.3	odd	4		390.2.bb.c.361.2	yes	8
5.4	even	2		1950.2.y.k.49.4		8
13.4	even	6		1950.2.y.k.199.4		8
15.8	even	4		1170.2.bs.f.361.4		8
65.3	odd	12		5070.2.b.ba.1351.2		8
65.4	even	6	inner	1950.2.y.j.199.1		8
65.17	odd	12		1950.2.bc.g.901.3		8
65.23	odd	12		5070.2.b.ba.1351.7		8
65.28	even	12		5070.2.a.bz.1.3		4
65.43	odd	12		390.2.bb.c.121.2	✓	8
65.63	even	12		5070.2.a.ca.1.2		4
195.173	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	65.43	odd	12
390.2.bb.c.361.2	yes	8	5.3	odd	4
1170.2.bs.f.361.4		8	15.8	even	4
1170.2.bs.f.901.4		8	195.173	even	12
1950.2.y.j.49.1		8	1.1	even	1	trivial
1950.2.y.j.199.1		8	65.4	even	6	inner
1950.2.y.k.49.4		8	5.4	even	2
1950.2.y.k.199.4		8	13.4	even	6
1950.2.bc.g.751.3		8	5.2	odd	4
1950.2.bc.g.901.3		8	65.17	odd	12
5070.2.a.bz.1.3		4	65.28	even	12
5070.2.a.ca.1.2		4	65.63	even	12
5070.2.b.ba.1351.2		8	65.3	odd	12
5070.2.b.ba.1351.7		8	65.23	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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