LMFDB - Embedded newform 1950.2.bc.g.901.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(751,1950)]

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, 0, 5]))

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

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

chi := DirichletCharacter("1950.751");

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.bc (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.5708283941$
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			901.3
Root			$3.17270 - 3.17270i$ of defining polynomial
Character	$\chi$	$=$	1950.901
Dual form			1950.2.bc.g.751.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(-1.14539 + 0.661290i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(-1.14539 + 0.661290i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-3.99528 - 2.30668i) q^{11} +1.00000 q^{12} +(-3.20002 + 1.66129i) q^{13} -1.32258 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} -1.00000i q^{18} +(1.98387 - 1.14539i) q^{19} +1.32258i q^{21} +(-2.30668 - 3.99528i) q^{22} +(-4.33399 + 7.50670i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-3.60194 - 0.161290i) q^{26} -1.00000 q^{27} +(-1.14539 - 0.661290i) q^{28} +(1.01141 - 1.75182i) q^{29} -10.1321i q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.99528 + 2.30668i) q^{33} -4.00000i q^{34} +(0.500000 - 0.866025i) q^{36} +(-5.89721 - 3.40475i) q^{37} +2.29078 q^{38} +(-0.161290 + 3.60194i) q^{39} +(-4.02283 - 2.32258i) q^{41} +(-0.661290 + 1.14539i) q^{42} +(-4.30281 - 7.45269i) q^{43} -4.61335i q^{44} +(-7.50670 + 4.33399i) q^{46} +9.10926i q^{47} +(0.500000 + 0.866025i) q^{48} +(-2.62539 + 4.54731i) q^{49} -4.00000 q^{51} +(-3.03873 - 1.94065i) q^{52} -0.826674 q^{53} +(-0.866025 - 0.500000i) q^{54} +(-0.661290 - 1.14539i) q^{56} -2.29078i q^{57} +(1.75182 - 1.01141i) q^{58} +(2.72064 - 1.57076i) q^{59} +(-0.267949 - 0.464102i) q^{61} +(5.06604 - 8.77464i) q^{62} +(1.14539 + 0.661290i) q^{63} -1.00000 q^{64} -4.61335 q^{66} +(2.75488 + 1.59053i) q^{67} +(2.00000 - 3.46410i) q^{68} +(4.33399 + 7.50670i) q^{69} +(-9.81724 + 5.66799i) q^{71} +(0.866025 - 0.500000i) q^{72} +6.28304i q^{73} +(-3.40475 - 5.89721i) q^{74} +(1.98387 + 1.14539i) q^{76} +6.10153 q^{77} +(-1.94065 + 3.03873i) q^{78} +2.96774 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-2.32258 - 4.02283i) q^{82} -15.8719i q^{83} +(-1.14539 + 0.661290i) q^{84} -8.60562i q^{86} +(-1.01141 - 1.75182i) q^{87} +(2.30668 - 3.99528i) q^{88} +(10.2746 + 5.93207i) q^{89} +(2.56667 - 4.01896i) q^{91} -8.66799 q^{92} +(-8.77464 - 5.06604i) q^{93} +(-4.55463 + 7.88885i) q^{94} +1.00000i q^{96} +(7.63743 - 4.40947i) q^{97} +(-4.54731 + 2.62539i) q^{98} +4.61335i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9	$ 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9} + 6 q^{11} + 8 q^{12} + 12 q^{13} + 4 q^{14} - 4 q^{16} - 16 q^{17} - 6 q^{19} - 2 q^{22} - 4 q^{23} - 12 q^{26} - 8 q^{27} - 8 q^{29} + 6 q^{33} + 4 q^{36} - 30 q^{37} + 6 q^{39} + 2 q^{42} - 14 q^{43} - 6 q^{46} + 4 q^{48} + 14 q^{49} - 32 q^{51} + 6 q^{52} - 16 q^{53} + 2 q^{56} + 6 q^{58} + 24 q^{59} - 16 q^{61} - 4 q^{62} - 8 q^{64} - 4 q^{66} - 24 q^{67} + 16 q^{68} + 4 q^{69} - 12 q^{71} + 10 q^{74} - 6 q^{76} - 16 q^{77} - 6 q^{78} - 20 q^{79} - 4 q^{81} - 4 q^{82} + 8 q^{87} + 2 q^{88} + 42 q^{89} - 10 q^{91} - 8 q^{92} - 30 q^{93} - 8 q^{94} + 24 q^{97} - 48 q^{98}+O(q^{100}) $ 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9 + 6 * q^11 + 8 * q^12 + 12 * q^13 + 4 * q^14 - 4 * q^16 - 16 * q^17 - 6 * q^19 - 2 * q^22 - 4 * q^23 - 12 * q^26 - 8 * q^27 - 8 * q^29 + 6 * q^33 + 4 * q^36 - 30 * q^37 + 6 * q^39 + 2 * q^42 - 14 * q^43 - 6 * q^46 + 4 * q^48 + 14 * q^49 - 32 * q^51 + 6 * q^52 - 16 * q^53 + 2 * q^56 + 6 * q^58 + 24 * q^59 - 16 * q^61 - 4 * q^62 - 8 * q^64 - 4 * q^66 - 24 * q^67 + 16 * q^68 + 4 * q^69 - 12 * q^71 + 10 * q^74 - 6 * q^76 - 16 * q^77 - 6 * q^78 - 20 * q^79 - 4 * q^81 - 4 * q^82 + 8 * q^87 + 2 * q^88 + 42 * q^89 - 10 * q^91 - 8 * q^92 - 30 * q^93 - 8 * q^94 + 24 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	−1.14539	+	0.661290i	−0.432916	+	0.249944i	−0.700588	−	0.713566i	$-0.747079\pi$
$7$	−1.14539	+	0.661290i	−0.432916	+	0.249944i	0.267672	+	0.963510i	$0.413746\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−3.99528	−	2.30668i	−1.20462	−	0.695489i	−0.243043	−	0.970015i	$-0.578146\pi$
$11$	−3.99528	−	2.30668i	−1.20462	−	0.695489i	−0.961580	+	0.274526i	$0.911479\pi$
$12$	1.00000			0.288675
$13$	−3.20002	+	1.66129i	−0.887525	+	0.460759i
$13$	−3.20002	+	1.66129i	−0.887525	+	0.460759i
$14$	−1.32258			−0.353474
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	0.514782	−	0.857321i	$-0.327873\pi$
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	−0.999853	+	0.0171533i	$0.994540\pi$
$18$		−	1.00000i		−	0.235702i
$19$	1.98387	−	1.14539i	0.455131	−	0.262770i	−0.254864	−	0.966977i	$-0.582031\pi$
$19$	1.98387	−	1.14539i	0.455131	−	0.262770i	0.709995	+	0.704207i	$0.248697\pi$
$20$		0			0
$21$			1.32258i			0.288611i
$22$	−2.30668	−	3.99528i	−0.491785	−	0.851797i
$23$	−4.33399	+	7.50670i	−0.903700	+	1.56525i	−0.0810471	+	0.996710i	$0.525826\pi$
$23$	−4.33399	+	7.50670i	−0.903700	+	1.56525i	−0.822653	+	0.568544i	$0.807507\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$		0			0
$26$	−3.60194	−	0.161290i	−0.706399	−	0.0316315i
$27$	−1.00000			−0.192450
$28$	−1.14539	−	0.661290i	−0.216458	−	0.124972i
$29$	1.01141	−	1.75182i	0.187815	−	0.325305i	−0.756707	−	0.653755i	$-0.773193\pi$
$29$	1.01141	−	1.75182i	0.187815	−	0.325305i	0.944521	+	0.328450i	$0.106526\pi$
$30$		0			0
$31$		−	10.1321i		−	1.81978i	−0.414853	−	0.909888i	$-0.636167\pi$
$31$		−	10.1321i		−	1.81978i	0.414853	−	0.909888i	$-0.363833\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−3.99528	+	2.30668i	−0.695489	+	0.401541i
$34$		−	4.00000i		−	0.685994i
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−5.89721	−	3.40475i	−0.969495	−	0.559738i	−0.0704126	−	0.997518i	$-0.522432\pi$
$37$	−5.89721	−	3.40475i	−0.969495	−	0.559738i	−0.899082	+	0.437780i	$0.855765\pi$
$38$	2.29078			0.371613
$39$	−0.161290	+	3.60194i	−0.0258270	+	0.576772i
$40$		0			0
$41$	−4.02283	−	2.32258i	−0.628260	−	0.362726i	0.151818	−	0.988408i	$-0.451487\pi$
$41$	−4.02283	−	2.32258i	−0.628260	−	0.362726i	−0.780078	+	0.625682i	$0.784821\pi$
$42$	−0.661290	+	1.14539i	−0.102039	+	0.176737i
$43$	−4.30281	−	7.45269i	−0.656173	−	1.13652i	−0.981598	−	0.190957i	$-0.938841\pi$
$43$	−4.30281	−	7.45269i	−0.656173	−	1.13652i	0.325426	−	0.945568i	$-0.394492\pi$
$44$		−	4.61335i		−	0.695489i
$45$		0			0
$46$	−7.50670	+	4.33399i	−1.10680	+	0.639012i
$47$			9.10926i			1.32872i	0.747412	+	0.664361i	$0.231296\pi$
$47$			9.10926i			1.32872i	−0.747412	+	0.664361i	$0.768704\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−2.62539	+	4.54731i	−0.375056	+	0.649616i
$50$		0			0
$51$	−4.00000			−0.560112
$52$	−3.03873	−	1.94065i	−0.421396	−	0.269120i
$53$	−0.826674			−0.113552			−0.0567762	−	0.998387i	$-0.518082\pi$
$53$	−0.826674			−0.113552			−0.0567762	+	0.998387i	$0.518082\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$		0			0
$56$	−0.661290	−	1.14539i	−0.0883686	−	0.153059i
$57$		−	2.29078i		−	0.303421i
$58$	1.75182	−	1.01141i	0.230025	−	0.132805i
$59$	2.72064	−	1.57076i	0.354197	−	0.204496i	−0.312335	−	0.949972i	$-0.601111\pi$
$59$	2.72064	−	1.57076i	0.354197	−	0.204496i	0.666532	+	0.745476i	$0.267778\pi$
$60$		0			0
$61$	−0.267949	−	0.464102i	−0.0343074	−	0.0594221i	0.848362	−	0.529417i	$-0.177589\pi$
$61$	−0.267949	−	0.464102i	−0.0343074	−	0.0594221i	−0.882669	+	0.469995i	$0.844256\pi$
$62$	5.06604	−	8.77464i	0.643388	−	1.11438i
$63$	1.14539	+	0.661290i	0.144305	+	0.0833147i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−4.61335			−0.567865
$67$	2.75488	+	1.59053i	0.336562	+	0.194314i	0.658751	−	0.752361i	$-0.271085\pi$
$67$	2.75488	+	1.59053i	0.336562	+	0.194314i	−0.322189	+	0.946675i	$0.604419\pi$
$68$	2.00000	−	3.46410i	0.242536	−	0.420084i
$69$	4.33399	+	7.50670i	0.521751	+	0.903700i
$70$		0			0
$71$	−9.81724	+	5.66799i	−1.16509	+	0.672666i	−0.952519	−	0.304479i	$-0.901518\pi$
$71$	−9.81724	+	5.66799i	−1.16509	+	0.672666i	−0.212573	+	0.977145i	$0.568184\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$			6.28304i			0.735375i	0.929949	+	0.367687i	$0.119850\pi$
$73$			6.28304i			0.735375i	−0.929949	+	0.367687i	$0.880150\pi$
$74$	−3.40475	−	5.89721i	−0.395795	−	0.685536i
$75$		0			0
$76$	1.98387	+	1.14539i	0.227565	+	0.131385i
$77$	6.10153			0.695334
$78$	−1.94065	+	3.03873i	−0.219736	+	0.344068i
$79$	2.96774			0.333897			0.166948	−	0.985966i	$-0.446609\pi$
$79$	2.96774			0.333897			0.166948	+	0.985966i	$0.446609\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.32258	−	4.02283i	−0.256486	−	0.444247i
$83$		−	15.8719i		−	1.74216i	−0.491138	−	0.871082i	$-0.663419\pi$
$83$		−	15.8719i		−	1.74216i	0.491138	−	0.871082i	$-0.336581\pi$
$84$	−1.14539	+	0.661290i	−0.124972	+	0.0721526i
$85$		0			0
$86$		−	8.60562i		−	0.927968i
$87$	−1.01141	−	1.75182i	−0.108435	−	0.187815i
$88$	2.30668	−	3.99528i	0.245893	−	0.425899i
$89$	10.2746	+	5.93207i	1.08911	+	0.628798i	0.933339	−	0.358995i	$-0.116881\pi$
$89$	10.2746	+	5.93207i	1.08911	+	0.628798i	0.155771	+	0.987793i	$0.450214\pi$
$90$		0			0
$91$	2.56667	−	4.01896i	0.269060	−	0.421302i
$92$	−8.66799			−0.903700
$93$	−8.77464	−	5.06604i	−0.909888	−	0.525324i
$94$	−4.55463	+	7.88885i	−0.469774	+	0.813673i
$95$		0			0
$96$			1.00000i			0.102062i
$97$	7.63743	−	4.40947i	0.775463	−	0.447714i	−0.0593568	−	0.998237i	$-0.518905\pi$
$97$	7.63743	−	4.40947i	0.775463	−	0.447714i	0.834820	+	0.550523i	$0.185572\pi$
$98$	−4.54731	+	2.62539i	−0.459348	+	0.265205i
$99$			4.61335i			0.463660i
$100$		0			0
$101$	−3.61335	+	6.25851i	−0.359542	+	0.622745i	−0.987884	−	0.155192i	$-0.950400\pi$
$101$	−3.61335	+	6.25851i	−0.359542	+	0.622745i	0.628342	+	0.777937i	$0.283734\pi$
$102$	−3.46410	−	2.00000i	−0.342997	−	0.198030i
$103$	18.4000			1.81301			0.906505	−	0.422196i	$-0.138740\pi$
$103$	18.4000			1.81301			0.906505	+	0.422196i	$0.138740\pi$
$104$	−1.66129	−	3.20002i	−0.162903	−	0.313788i
$105$		0			0
$106$	−0.715920	−	0.413337i	−0.0695363	−	0.0401468i
$107$	1.53590	−	2.66025i	0.148481	−	0.257176i	−0.782185	−	0.623046i	$-0.785895\pi$
$107$	1.53590	−	2.66025i	0.148481	−	0.257176i	0.930666	+	0.365869i	$0.119228\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$			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
$112$		−	1.32258i		−	0.124972i
$113$	−4.04322	−	7.00306i	−0.380354	−	0.658792i	0.610759	−	0.791817i	$-0.290864\pi$
$113$	−4.04322	−	7.00306i	−0.380354	−	0.658792i	−0.991113	+	0.133024i	$0.957531\pi$
$114$	1.14539	−	1.98387i	0.107275	−	0.185806i
$115$		0			0
$116$	2.02283			0.187815
$117$	3.03873	+	1.94065i	0.280931	+	0.179413i
$118$	3.14152			0.289201
$119$	4.58155	+	2.64516i	0.419990	+	0.242481i
$120$		0			0
$121$	5.14152	+	8.90538i	0.467411	+	0.809580i
$122$		−	0.535898i		−	0.0485180i
$123$	−4.02283	+	2.32258i	−0.362726	+	0.209420i
$124$	8.77464	−	5.06604i	0.787986	−	0.454944i
$125$		0			0
$126$	0.661290	+	1.14539i	0.0589124	+	0.102039i
$127$	−5.73592	+	9.93490i	−0.508980	+	0.881580i	0.490966	+	0.871179i	$0.336644\pi$
$127$	−5.73592	+	9.93490i	−0.508980	+	0.881580i	−0.999946	+	0.0104008i	$0.996689\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−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	$0.746172\pi$
$132$	−3.99528	−	2.30668i	−0.347745	−	0.200771i
$133$	−1.51487	+	2.62383i	−0.131356	+	0.227515i
$134$	1.59053	+	2.75488i	0.137401	+	0.237985i
$135$		0			0
$136$	3.46410	−	2.00000i	0.297044	−	0.171499i
$137$	−13.9168	+	8.03486i	−1.18899	+	0.686465i	−0.958077	−	0.286509i	$-0.907505\pi$
$137$	−13.9168	+	8.03486i	−1.18899	+	0.686465i	−0.230914	+	0.972974i	$0.574172\pi$
$138$			8.66799i			0.737868i
$139$	−4.66129	−	8.07359i	−0.395365	−	0.684793i	0.597782	−	0.801658i	$-0.296049\pi$
$139$	−4.66129	−	8.07359i	−0.395365	−	0.684793i	−0.993148	+	0.116865i	$0.962715\pi$
$140$		0			0
$141$	7.88885	+	4.55463i	0.664361	+	0.383569i
$142$	−11.3360			−0.951294
$143$	16.6170	+	0.744087i	1.38959	+	0.0622237i
$144$	1.00000			0.0833333
$145$		0			0
$146$	−3.14152	+	5.44128i	−0.259994	+	0.450323i
$147$	2.62539	+	4.54731i	0.216539	+	0.375056i
$148$		−	6.80951i		−	0.559738i
$149$	3.53788	−	2.04259i	0.289834	−	0.167336i	−0.348033	−	0.937482i	$-0.613150\pi$
$149$	3.53788	−	2.04259i	0.289834	−	0.167336i	0.637867	+	0.770146i	$0.279817\pi$
$150$		0			0
$151$		−	19.9811i		−	1.62604i	−0.582235	−	0.813021i	$-0.697822\pi$
$151$		−	19.9811i		−	1.62604i	0.582235	−	0.813021i	$-0.302178\pi$
$152$	1.14539	+	1.98387i	0.0929032	+	0.160913i
$153$	−2.00000	+	3.46410i	−0.161690	+	0.280056i
$154$	5.28408	+	3.05076i	0.425803	+	0.245838i
$155$		0			0
$156$	−3.20002	+	1.66129i	−0.256206	+	0.133010i
$157$	−7.13379			−0.569338			−0.284669	−	0.958626i	$-0.591884\pi$
$157$	−7.13379			−0.569338			−0.284669	+	0.958626i	$0.591884\pi$
$158$	2.57014	+	1.48387i	0.204469	+	0.118050i
$159$	−0.413337	+	0.715920i	−0.0327797	+	0.0567762i
$160$		0			0
$161$		−	11.4641i		−	0.903498i
$162$	−0.866025	+	0.500000i	−0.0680414	+	0.0392837i
$163$	8.56906	−	4.94735i	0.671180	−	0.387506i	−0.125343	−	0.992113i	$-0.540003\pi$
$163$	8.56906	−	4.94735i	0.671180	−	0.387506i	0.796524	+	0.604607i	$0.206670\pi$
$164$		−	4.64516i		−	0.362726i
$165$		0			0
$166$	7.93593	−	13.7454i	0.615948	−	1.06685i
$167$	−20.8171	−	12.0187i	−1.61087	−	0.930037i	−0.989168	−	0.146785i	$-0.953108\pi$
$167$	−20.8171	−	12.0187i	−1.61087	−	0.930037i	−0.621704	−	0.783253i	$-0.713559\pi$
$168$	−1.32258			−0.102039
$169$	7.48023	−	10.6323i	0.575402	−	0.817870i
$170$		0			0
$171$	−1.98387	−	1.14539i	−0.151710	−	0.0875900i
$172$	4.30281	−	7.45269i	0.328086	−	0.568262i
$173$	−1.26408	−	2.18946i	−0.0961065	−	0.166461i	0.813963	−	0.580916i	$-0.197306\pi$
$173$	−1.26408	−	2.18946i	−0.0961065	−	0.166461i	−0.910070	+	0.414455i	$0.863972\pi$
$174$		−	2.02283i		−	0.153350i
$175$		0			0
$176$	3.99528	−	2.30668i	0.301156	−	0.173872i
$177$		−	3.14152i		−	0.236131i
$178$	5.93207	+	10.2746i	0.444627	+	0.770117i
$179$	−3.13784	+	5.43490i	−0.234533	+	0.406223i	−0.959137	−	0.282942i	$-0.908689\pi$
$179$	−3.13784	+	5.43490i	−0.234533	+	0.406223i	0.724604	+	0.689166i	$0.242023\pi$
$180$		0			0
$181$	−12.2830			−0.912991			−0.456496	−	0.889726i	$-0.650896\pi$
$181$	−12.2830			−0.912991			−0.456496	+	0.889726i	$0.650896\pi$
$182$	4.23228	−	2.19719i	0.313717	−	0.162866i
$183$	−0.535898			−0.0396147
$184$	−7.50670	−	4.33399i	−0.553401	−	0.319506i
$185$		0			0
$186$	−5.06604	−	8.77464i	−0.371460	−	0.643388i
$187$			18.4534i			1.34945i
$188$	−7.88885	+	4.55463i	−0.575354	+	0.332181i
$189$	1.14539	−	0.661290i	0.0833147	−	0.0481018i
$190$		0			0
$191$	4.87357	+	8.44128i	0.352639	+	0.610789i	0.986711	−	0.162485i	$-0.0519509\pi$
$191$	4.87357	+	8.44128i	0.352639	+	0.610789i	−0.634072	+	0.773274i	$0.718618\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	11.9188	+	6.88130i	0.857932	+	0.495327i	0.863319	−	0.504658i	$-0.168382\pi$
$193$	11.9188	+	6.88130i	0.857932	+	0.495327i	−0.00538741	+	0.999985i	$0.501715\pi$
$194$	8.81894			0.633163
$195$		0			0
$196$	−5.25078			−0.375056
$197$	8.78282	+	5.07076i	0.625750	+	0.361277i	0.779104	−	0.626894i	$-0.215674\pi$
$197$	8.78282	+	5.07076i	0.625750	+	0.361277i	−0.153354	+	0.988171i	$0.549008\pi$
$198$	−2.30668	+	3.99528i	−0.163928	+	0.283932i
$199$	4.78668	+	8.29078i	0.339319	+	0.587717i	0.984305	−	0.176477i	$-0.0564701\pi$
$199$	4.78668	+	8.29078i	0.339319	+	0.587717i	−0.644986	+	0.764194i	$0.723137\pi$
$200$		0			0
$201$	2.75488	−	1.59053i	0.194314	−	0.112187i
$202$	−6.25851	+	3.61335i	−0.440348	+	0.254235i
$203$			2.67535i			0.187773i
$204$	−2.00000	−	3.46410i	−0.140028	−	0.242536i
$205$		0			0
$206$	15.9349	+	9.20002i	1.11024	+	0.640996i
$207$	8.66799			0.602467
$208$	0.161290	−	3.60194i	0.0111834	−	0.249750i
$209$	−10.5682			−0.731015
$210$		0			0
$211$	0.542594	−	0.939800i	0.0373537	−	0.0646985i	−0.846744	−	0.532000i	$-0.821441\pi$
$211$	0.542594	−	0.939800i	0.0373537	−	0.0646985i	0.884098	+	0.467302i	$0.154774\pi$
$212$	−0.413337	−	0.715920i	−0.0283881	−	0.0491696i
$213$			11.3360i			0.776728i
$214$	2.66025	−	1.53590i	0.181851	−	0.104992i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	6.70025	+	11.6052i	0.454842	+	0.787810i
$218$	−6.61335	+	11.4547i	−0.447913	+	0.775808i
$219$	5.44128	+	3.14152i	0.367687	+	0.212284i
$220$		0			0
$221$	12.1549	+	7.76261i	0.817628	+	0.522170i
$222$	−6.80951			−0.457024
$223$	−21.6001	−	12.4708i	−1.44645	−	0.835106i	−0.448179	−	0.893944i	$-0.647927\pi$
$223$	−21.6001	−	12.4708i	−1.44645	−	0.835106i	−0.998268	+	0.0588375i	$0.981261\pi$
$224$	0.661290	−	1.14539i	0.0441843	−	0.0765294i
$225$		0			0
$226$		−	8.08643i		−	0.537902i
$227$	16.7321	−	9.66025i	1.11055	−	0.641174i	0.171575	−	0.985171i	$-0.445115\pi$
$227$	16.7321	−	9.66025i	1.11055	−	0.641174i	0.938971	+	0.343998i	$0.111781\pi$
$228$	1.98387	−	1.14539i	0.131385	−	0.0758551i
$229$			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
$232$	1.75182	+	1.01141i	0.115013	+	0.0664025i
$233$	−16.9665			−1.11151			−0.555756	−	0.831346i	$-0.687571\pi$
$233$	−16.9665			−1.11151			−0.555756	+	0.831346i	$0.687571\pi$
$234$	1.66129	+	3.20002i	0.108602	+	0.209192i
$235$		0			0
$236$	2.72064	+	1.57076i	0.177098	+	0.102248i
$237$	1.48387	−	2.57014i	0.0963877	−	0.166948i
$238$	2.64516	+	4.58155i	0.171460	+	0.296978i
$239$		−	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	0.361065	−	0.932541i	$-0.382413\pi$
$241$	20.9452	−	12.0927i	1.34920	−	0.778962i	0.988136	+	0.153579i	$0.0490800\pi$
$242$			10.2830i			0.661019i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	0.267949	−	0.464102i	0.0171537	−	0.0297111i
$245$		0			0
$246$	−4.64516			−0.296165
$247$	−4.44560	+	6.96104i	−0.282867	+	0.442921i
$248$	10.1321			0.643388
$249$	−13.7454	−	7.93593i	−0.871082	−	0.502919i
$250$		0			0
$251$	4.41249	+	7.64265i	0.278514	+	0.482400i	0.971016	−	0.239016i	$-0.0768249\pi$
$251$	4.41249	+	7.64265i	0.278514	+	0.482400i	−0.692502	+	0.721416i	$0.743492\pi$
$252$			1.32258i			0.0833147i
$253$	34.6311	−	19.9942i	2.17724	−	1.25703i
$254$	−9.93490	+	5.73592i	−0.623371	+	0.359903i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.19247	+	7.26157i	−0.261519	+	0.452964i	−0.966646	−	0.256117i	$-0.917557\pi$
$257$	−4.19247	+	7.26157i	−0.261519	+	0.452964i	0.705127	+	0.709081i	$0.250890\pi$
$258$	−7.45269	−	4.30281i	−0.463984	−	0.267881i
$259$	9.00612			0.559613
$260$		0			0
$261$	−2.02283			−0.125210
$262$	−13.8482	−	7.99528i	−0.855547	−	0.493950i
$263$	0.960648	−	1.66389i	0.0592361	−	0.102600i	−0.834887	−	0.550422i	$-0.814467\pi$
$263$	0.960648	−	1.66389i	0.0592361	−	0.102600i	0.894123	+	0.447822i	$0.147800\pi$
$264$	−2.30668	−	3.99528i	−0.141966	−	0.245893i
$265$		0			0
$266$	−2.62383	+	1.51487i	−0.160877	+	0.0928824i
$267$	10.2746	−	5.93207i	0.628798	−	0.363037i
$268$			3.18106i			0.194314i
$269$	16.1549	+	27.9811i	0.984982	+	1.70604i	0.642014	+	0.766693i	$0.278099\pi$
$269$	16.1549	+	27.9811i	0.984982	+	1.70604i	0.342968	+	0.939347i	$0.388568\pi$
$270$		0			0
$271$	20.3105	+	11.7263i	1.23378	+	0.712322i	0.967815	−	0.251662i	$-0.0809770\pi$
$271$	20.3105	+	11.7263i	1.23378	+	0.712322i	0.265962	+	0.963983i	$0.414310\pi$
$272$	4.00000			0.242536
$273$	−2.19719	−	4.23228i	−0.132980	−	0.256149i
$274$	−16.0697			−0.970808
$275$		0			0
$276$	−4.33399	+	7.50670i	−0.260876	+	0.451850i
$277$	4.50283	+	7.79913i	0.270549	+	0.468604i	0.969002	−	0.247051i	$-0.0794615\pi$
$277$	4.50283	+	7.79913i	0.270549	+	0.468604i	−0.698454	+	0.715655i	$0.746128\pi$
$278$		−	9.32258i		−	0.559131i
$279$	−8.77464	+	5.06604i	−0.525324	+	0.303296i
$280$		0			0
$281$			1.71696i			0.102425i	0.998688	+	0.0512125i	$0.0163086\pi$
$281$			1.71696i			0.102425i	−0.998688	+	0.0512125i	$0.983691\pi$
$282$	4.55463	+	7.88885i	0.271224	+	0.469774i
$283$	0.774645	−	1.34172i	0.0460479	−	0.0797572i	−0.842083	−	0.539348i	$-0.818671\pi$
$283$	0.774645	−	1.34172i	0.0460479	−	0.0797572i	0.888131	+	0.459591i	$0.152004\pi$
$284$	−9.81724	−	5.66799i	−0.582546	−	0.336333i
$285$		0			0
$286$	14.0187	+	8.95292i	0.828945	+	0.529397i
$287$	6.14359			0.362645
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$		0			0
$291$		−	8.81894i		−	0.516976i
$292$	−5.44128	+	3.14152i	−0.318427	+	0.183844i
$293$	−26.3321	+	15.2028i	−1.53834	+	0.888160i	−0.539402	+	0.842049i	$0.681350\pi$
$293$	−26.3321	+	15.2028i	−1.53834	+	0.888160i	−0.998936	+	0.0461113i	$0.985317\pi$
$294$			5.25078i			0.306232i
$295$		0			0
$296$	3.40475	−	5.89721i	0.197897	−	0.342768i
$297$	3.99528	+	2.30668i	0.231830	+	0.133847i
$298$	4.08519			0.236649
$299$	1.39806	−	31.2216i	0.0808518	−	1.80559i
$300$		0			0
$301$	9.85677	+	5.69081i	0.568135	+	0.328013i
$302$	9.99057	−	17.3042i	0.574892	−	0.995743i
$303$	3.61335	+	6.25851i	0.207582	+	0.359542i
$304$			2.29078i			0.131385i
$305$		0			0
$306$	−3.46410	+	2.00000i	−0.198030	+	0.114332i
$307$		−	9.82622i		−	0.560812i	−0.959882	−	0.280406i	$-0.909531\pi$
$307$		−	9.82622i		−	0.560812i	0.959882	−	0.280406i	$-0.0904691\pi$
$308$	3.05076	+	5.28408i	0.173833	+	0.301088i
$309$	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	$0.530737\pi$
$312$	−3.60194	−	0.161290i	−0.203920	−	0.00913124i
$313$	16.2340			0.917599			0.458800	−	0.888540i	$-0.348280\pi$
$313$	16.2340			0.917599			0.458800	+	0.888540i	$0.348280\pi$
$314$	−6.17804	−	3.56690i	−0.348647	−	0.201292i
$315$		0			0
$316$	1.48387	+	2.57014i	0.0834742	+	0.144582i
$317$		−	23.5231i		−	1.32119i	−0.750742	−	0.660596i	$-0.770304\pi$
$317$		−	23.5231i		−	1.32119i	0.750742	−	0.660596i	$-0.229696\pi$
$318$	−0.715920	+	0.413337i	−0.0401468	+	0.0231788i
$319$	−8.08176	+	4.66601i	−0.452492	+	0.261246i
$320$		0			0
$321$	−1.53590	−	2.66025i	−0.0857255	−	0.148481i
$322$	5.73205	−	9.92820i	0.319435	−	0.553277i
$323$	−7.93548	−	4.58155i	−0.441542	−	0.254924i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	9.89470			0.548016
$327$	11.4547	+	6.61335i	0.633445	+	0.365719i
$328$	2.32258	−	4.02283i	0.128243	−	0.222123i
$329$	−6.02386	−	10.4336i	−0.332106	−	0.575225i
$330$		0			0
$331$	15.6667	−	9.04520i	0.861122	−	0.497169i	−0.00326597	−	0.999995i	$-0.501040\pi$
$331$	15.6667	−	9.04520i	0.861122	−	0.497169i	0.864388	+	0.502826i	$0.167706\pi$
$332$	13.7454	−	7.93593i	0.754379	−	0.435541i
$333$			6.80951i			0.373159i
$334$	−12.0187	−	20.8171i	−0.657636	−	1.13906i
$335$		0			0
$336$	−1.14539	−	0.661290i	−0.0624860	−	0.0360763i
$337$	5.69900			0.310444			0.155222	−	0.987880i	$-0.450391\pi$
$337$	5.69900			0.310444			0.155222	+	0.987880i	$0.450391\pi$
$338$	11.7942	−	5.46774i	0.641521	−	0.297406i
$339$	−8.08643			−0.439195
$340$		0			0
$341$	−23.3715	+	40.4806i	−1.26564	+	2.19214i
$342$	−1.14539	−	1.98387i	−0.0619355	−	0.107275i
$343$		−	16.2026i		−	0.874860i
$344$	7.45269	−	4.30281i	0.401822	−	0.231992i
$345$		0			0
$346$		−	2.52817i		−	0.135915i
$347$	−7.87357	−	13.6374i	−0.422676	−	0.732095i	0.573525	−	0.819188i	$-0.305576\pi$
$347$	−7.87357	−	13.6374i	−0.422676	−	0.732095i	−0.996200	+	0.0870928i	$0.972242\pi$
$348$	1.01141	−	1.75182i	0.0542174	−	0.0939073i
$349$	13.2679	+	7.66025i	0.710217	+	0.410044i	0.811141	−	0.584850i	$-0.198847\pi$
$349$	13.2679	+	7.66025i	0.710217	+	0.410044i	−0.100924	+	0.994894i	$0.532180\pi$
$350$		0			0
$351$	3.20002	−	1.66129i	0.170804	−	0.0886731i
$352$	4.61335			0.245893
$353$	−1.03917	−	0.599964i	−0.0553093	−	0.0319328i	0.472090	−	0.881550i	$-0.343500\pi$
$353$	−1.03917	−	0.599964i	−0.0553093	−	0.0319328i	−0.527400	+	0.849617i	$0.676833\pi$
$354$	1.57076	−	2.72064i	0.0834850	−	0.144600i
$355$		0			0
$356$			11.8641i			0.628798i
$357$	4.58155	−	2.64516i	0.242481	−	0.139997i
$358$	−5.43490	+	3.13784i	−0.287243	+	0.165840i
$359$			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
$362$	−10.6374	−	6.14152i	−0.559091	−	0.322791i
$363$	10.2830			0.539720
$364$	4.76386	+	0.213319i	0.249694	+	0.0111809i
$365$		0			0
$366$	−0.464102	−	0.267949i	−0.0242590	−	0.0140059i
$367$	−9.81724	+	17.0040i	−0.512456	+	0.887599i	0.487440	+	0.873156i	$0.337931\pi$
$367$	−9.81724	+	17.0040i	−0.512456	+	0.887599i	−0.999896	+	0.0144428i	$0.995403\pi$
$368$	−4.33399	−	7.50670i	−0.225925	−	0.391314i
$369$			4.64516i			0.241817i
$370$		0			0
$371$	0.946862	−	0.546671i	0.0491586	−	0.0283817i
$372$		−	10.1321i		−	0.525324i
$373$	−1.27874	−	2.21484i	−0.0662106	−	0.114680i	0.831020	−	0.556243i	$-0.187758\pi$
$373$	−1.27874	−	2.21484i	−0.0662106	−	0.114680i	−0.897230	+	0.441563i	$0.854424\pi$
$374$	−9.22671	+	15.9811i	−0.477102	+	0.826365i
$375$		0			0
$376$	−9.10926			−0.469774
$377$	−0.326261	+	7.28610i	−0.0168033	+	0.375253i
$378$	1.32258			0.0680262
$379$	−13.0846	−	7.55440i	−0.672111	−	0.388044i	0.124765	−	0.992186i	$-0.460182\pi$
$379$	−13.0846	−	7.55440i	−0.672111	−	0.388044i	−0.796876	+	0.604143i	$0.793516\pi$
$380$		0			0
$381$	5.73592	+	9.93490i	0.293860	+	0.508980i
$382$			9.74715i			0.498707i
$383$	16.2210	−	9.36517i	0.828852	−	0.478538i	−0.0246073	−	0.999697i	$-0.507834\pi$
$383$	16.2210	−	9.36517i	0.828852	−	0.478538i	0.853459	+	0.521159i	$0.174500\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$		0			0
$386$	6.88130	+	11.9188i	0.350249	+	0.606649i
$387$	−4.30281	+	7.45269i	−0.218724	+	0.378841i
$388$	7.63743	+	4.40947i	0.387732	+	0.223857i
$389$	6.96899			0.353342			0.176671	−	0.984270i	$-0.443467\pi$
$389$	6.96899			0.353342			0.176671	+	0.984270i	$0.443467\pi$
$390$		0			0
$391$	34.6719			1.75344
$392$	−4.54731	−	2.62539i	−0.229674	−	0.132602i
$393$	−7.99528	+	13.8482i	−0.403309	+	0.698551i
$394$	5.07076	+	8.78282i	0.255461	+	0.442472i
$395$		0			0
$396$	−3.99528	+	2.30668i	−0.200771	+	0.115915i
$397$	16.0839	−	9.28606i	0.807229	−	0.466054i	−0.0387637	−	0.999248i	$-0.512342\pi$
$397$	16.0839	−	9.28606i	0.807229	−	0.466054i	0.845993	+	0.533195i	$0.179009\pi$
$398$			9.57336i			0.479869i
$399$	1.51487	+	2.62383i	0.0758382	+	0.131356i
$400$		0			0
$401$	−25.7126	−	14.8452i	−1.28403	−	0.741333i	−0.306444	−	0.951889i	$-0.599139\pi$
$401$	−25.7126	−	14.8452i	−1.28403	−	0.741333i	−0.977582	+	0.210556i	$0.932473\pi$
$402$	3.18106			0.158657
$403$	16.8323	+	32.4229i	0.838478	+	1.61510i
$404$	−7.22671			−0.359542
$405$		0			0
$406$	−1.33767	+	2.31692i	−0.0663877	+	0.114987i
$407$	15.7073	+	27.2059i	0.778584	+	1.34855i
$408$		−	4.00000i		−	0.198030i
$409$	−21.0752	+	12.1678i	−1.04210	+	0.601657i	−0.920427	−	0.390913i	$-0.872159\pi$
$409$	−21.0752	+	12.1678i	−1.04210	+	0.601657i	−0.121673	+	0.992570i	$0.538826\pi$
$410$		0			0
$411$			16.0697i			0.792661i
$412$	9.20002	+	15.9349i	0.453252	+	0.785056i
$413$	−2.07746	+	3.59826i	−0.102225	+	0.177059i
$414$	7.50670	+	4.33399i	0.368934	+	0.213004i
$415$		0			0
$416$	1.94065	−	3.03873i	0.0951483	−	0.148986i
$417$	−9.32258			−0.456529
$418$	−9.15229	−	5.28408i	−0.447653	−	0.258453i
$419$	1.44128	−	2.49636i	0.0704109	−	0.121955i	−0.828671	−	0.559737i	$-0.810902\pi$
$419$	1.44128	−	2.49636i	0.0704109	−	0.121955i	0.899081	+	0.437781i	$0.144236\pi$
$420$		0			0
$421$		−	4.94707i		−	0.241106i	−0.992707	−	0.120553i	$-0.961533\pi$
$421$		−	4.94707i		−	0.241106i	0.992707	−	0.120553i	$-0.0384667\pi$
$422$	0.939800	−	0.542594i	0.0457488	−	0.0264131i
$423$	7.88885	−	4.55463i	0.383569	−	0.221454i
$424$		−	0.826674i		−	0.0401468i
$425$		0			0
$426$	−5.66799	+	9.81724i	−0.274615	+	0.475647i
$427$	0.613811	+	0.354384i	0.0297044	+	0.0171499i
$428$	3.07180			0.148481
$429$	8.95292	−	14.0187i	0.432251	−	0.676831i
$430$		0			0
$431$	−15.3829	−	8.88130i	−0.740967	−	0.427797i	0.0814539	−	0.996677i	$-0.474044\pi$
$431$	−15.3829	−	8.88130i	−0.740967	−	0.427797i	−0.822421	+	0.568880i	$0.807377\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−17.9188	−	31.0362i	−0.861121	−	1.49151i	−0.870848	−	0.491553i	$-0.836430\pi$
$433$	−17.9188	−	31.0362i	−0.861121	−	1.49151i	0.00972676	−	0.999953i	$-0.496904\pi$
$434$			13.4005i			0.643244i
$435$		0			0
$436$	−11.4547	+	6.61335i	−0.548579	+	0.316722i
$437$			19.8564i			0.949861i
$438$	3.14152	+	5.44128i	0.150108	+	0.259994i
$439$	5.04520	−	8.73854i	0.240794	−	0.417068i	−0.720147	−	0.693822i	$-0.755925\pi$
$439$	5.04520	−	8.73854i	0.240794	−	0.417068i	0.960941	+	0.276754i	$0.0892588\pi$
$440$		0			0
$441$	5.25078			0.250037
$442$	6.64516	+	12.8001i	0.316078	+	0.608837i
$443$	−13.6981			−0.650816			−0.325408	−	0.945574i	$-0.605502\pi$
$443$	−13.6981			−0.650816			−0.325408	+	0.945574i	$0.605502\pi$
$444$	−5.89721	−	3.40475i	−0.279869	−	0.161582i
$445$		0			0
$446$	−12.4708	−	21.6001i	−0.590509	−	1.02279i
$447$		−	4.08519i		−	0.193223i
$448$	1.14539	−	0.661290i	0.0541145	−	0.0312430i
$449$	13.2613	−	7.65639i	0.625837	−	0.361327i	−0.153301	−	0.988180i	$-0.548990\pi$
$449$	13.2613	−	7.65639i	0.625837	−	0.361327i	0.779138	+	0.626852i	$0.215657\pi$
$450$		0			0
$451$	10.7149	+	18.5587i	0.504544	+	0.873896i
$452$	4.04322	−	7.00306i	0.190177	−	0.329396i
$453$	−17.3042	−	9.99057i	−0.813021	−	0.469398i
$454$	19.3205			0.906756
$455$		0			0
$456$	2.29078			0.107275
$457$	13.4714	+	7.77770i	0.630164	+	0.363826i	0.780816	−	0.624761i	$-0.214804\pi$
$457$	13.4714	+	7.77770i	0.630164	+	0.363826i	−0.150651	+	0.988587i	$0.548137\pi$
$458$	−2.07746	+	3.59826i	−0.0970732	+	0.168136i
$459$	2.00000	+	3.46410i	0.0933520	+	0.161690i
$460$		0			0
$461$	13.5473	−	7.82154i	0.630961	−	0.364286i	−0.150163	−	0.988661i	$-0.547980\pi$
$461$	13.5473	−	7.82154i	0.630961	−	0.364286i	0.781124	+	0.624376i	$0.214647\pi$
$462$	5.28408	−	3.05076i	0.245838	−	0.141934i
$463$		−	13.7170i		−	0.637481i	−0.947842	−	0.318741i	$-0.896740\pi$
$463$		−	13.7170i		−	0.637481i	0.947842	−	0.318741i	$-0.103260\pi$
$464$	1.01141	+	1.75182i	0.0469537	+	0.0813261i
$465$		0			0
$466$	−14.6934	−	8.48325i	−0.680659	−	0.392979i
$467$	0.943666			0.0436677			0.0218338	−	0.999762i	$-0.493050\pi$
$467$	0.943666			0.0436677			0.0218338	+	0.999762i	$0.493050\pi$
$468$	−0.161290	+	3.60194i	−0.00745563	+	0.166500i
$469$	−4.20720			−0.194271
$470$		0			0
$471$	−3.56690	+	6.17804i	−0.164354	+	0.284669i
$472$	1.57076	+	2.72064i	0.0723001	+	0.125228i
$473$			39.7008i			1.82544i
$474$	2.57014	−	1.48387i	0.118050	−	0.0681564i
$475$		0			0
$476$			5.29032i			0.242481i
$477$	0.413337	+	0.715920i	0.0189254	+	0.0327797i
$478$	3.17208	−	5.49420i	0.145088	−	0.251299i
$479$	−9.61460	−	5.55099i	−0.439302	−	0.253631i	0.263999	−	0.964523i	$-0.414958\pi$
$479$	−9.61460	−	5.55099i	−0.439302	−	0.253631i	−0.703302	+	0.710892i	$0.748292\pi$
$480$		0			0
$481$	24.5275	+	1.09830i	1.11836	+	0.0500784i
$482$	24.1855			1.10162
$483$	−9.92820	−	5.73205i	−0.451749	−	0.260817i
$484$	−5.14152	+	8.90538i	−0.233706	+	0.404790i
$485$		0			0
$486$			1.00000i			0.0453609i
$487$	28.5283	−	16.4708i	1.29274	−	0.746363i	0.313600	−	0.949555i	$-0.398465\pi$
$487$	28.5283	−	16.4708i	1.29274	−	0.746363i	0.979139	+	0.203192i	$0.0651316\pi$
$488$	0.464102	−	0.267949i	0.0210089	−	0.0121295i
$489$		−	9.89470i		−	0.447454i
$490$		0			0
$491$	14.2257	−	24.6396i	0.641996	−	1.11197i	−0.342991	−	0.939339i	$-0.611440\pi$
$491$	14.2257	−	24.6396i	0.641996	−	1.11197i	0.984987	−	0.172630i	$-0.0552266\pi$
$492$	−4.02283	−	2.32258i	−0.181363	−	0.104710i
$493$	−8.09130			−0.364414
$494$	−7.33052	+	3.80564i	−0.329816	+	0.171224i
$495$		0			0
$496$	8.77464	+	5.06604i	0.393993	+	0.227472i
$497$	7.49636	−	12.9841i	0.336258	−	0.582416i
$498$	−7.93593	−	13.7454i	−0.355618	−	0.615948i
$499$		−	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
$502$			8.82497i			0.393878i
$503$	2.86800	+	4.96753i	0.127878	+	0.221491i	0.922854	−	0.385149i	$-0.125850\pi$
$503$	2.86800	+	4.96753i	0.127878	+	0.221491i	−0.794976	+	0.606641i	$0.792517\pi$
$504$	−0.661290	+	1.14539i	−0.0294562	+	0.0510196i
$505$		0			0
$506$	39.9885			1.77771
$507$	−5.46774	−	11.7942i	−0.242831	−	0.523800i
$508$	−11.4718			−0.508980
$509$	−13.1129	−	7.57076i	−0.581221	−	0.335568i	0.180397	−	0.983594i	$-0.442262\pi$
$509$	−13.1129	−	7.57076i	−0.581221	−	0.335568i	−0.761618	+	0.648026i	$0.775595\pi$
$510$		0			0
$511$	−4.15491	−	7.19652i	−0.183803	−	0.318355i
$512$		−	1.00000i		−	0.0441942i
$513$	−1.98387	+	1.14539i	−0.0875900	+	0.0505701i
$514$	−7.26157	+	4.19247i	−0.320294	+	0.184922i
$515$		0			0
$516$	−4.30281	−	7.45269i	−0.189421	−	0.328086i
$517$	21.0121	−	36.3941i	0.924112	−	1.60061i
$518$	7.79953	+	4.50306i	0.342691	+	0.197853i
$519$	−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	$0.437328\pi$
$522$	−1.75182	−	1.01141i	−0.0766750	−	0.0442683i
$523$	−4.90844	+	8.50166i	−0.214631	+	0.371752i	−0.953158	−	0.302472i	$-0.902188\pi$
$523$	−4.90844	+	8.50166i	−0.214631	+	0.371752i	0.738527	+	0.674223i	$0.235522\pi$
$524$	−7.99528	−	13.8482i	−0.349276	−	0.604963i
$525$		0			0
$526$	1.66389	−	0.960648i	0.0725491	−	0.0418863i
$527$	−35.0986	+	20.2642i	−1.52892	+	0.882721i
$528$		−	4.61335i		−	0.200771i
$529$	−26.0670	−	45.1493i	−1.13335	−	1.96301i
$530$		0			0
$531$	−2.72064	−	1.57076i	−0.118066	−	0.0681652i
$532$	−3.02973			−0.131356
$533$	16.7316	+	0.749217i	0.724726	+	0.0324522i
$534$	11.8641			0.513411
$535$		0			0
$536$	−1.59053	+	2.75488i	−0.0687004	+	0.118993i
$537$	3.13784	+	5.43490i	0.135408	+	0.234533i
$538$			32.3098i			1.39298i
$539$	20.9784	−	12.1119i	0.903602	−	0.521695i
$540$		0			0
$541$			3.80826i			0.163730i	0.996643	+	0.0818650i	$0.0260876\pi$
$541$			3.80826i			0.163730i	−0.996643	+	0.0818650i	$0.973912\pi$
$542$	11.7263	+	20.3105i	0.503688	+	0.872413i
$543$	−6.14152	+	10.6374i	−0.263558	+	0.456496i
$544$	3.46410	+	2.00000i	0.148522	+	0.0857493i
$545$		0			0
$546$	0.213319	−	4.76386i	0.00912920	−	0.203874i
$547$	−45.5847			−1.94906			−0.974530	−	0.224257i	$-0.928005\pi$
$547$	−45.5847			−1.94906			−0.974530	+	0.224257i	$0.928005\pi$
$548$	−13.9168	−	8.03486i	−0.594496	−	0.343232i
$549$	−0.267949	+	0.464102i	−0.0114358	+	0.0198074i
$550$		0			0
$551$		−	4.63384i		−	0.197408i
$552$	−7.50670	+	4.33399i	−0.319506	+	0.184467i
$553$	−3.39921	+	1.96254i	−0.144549	+	0.0834555i
$554$			9.00566i			0.382614i
$555$		0			0
$556$	4.66129	−	8.07359i	0.197683	−	0.342397i
$557$	31.9209	+	18.4296i	1.35253	+	0.780885i	0.988604	−	0.150541i	$-0.0481016\pi$
$557$	31.9209	+	18.4296i	1.35253	+	0.780885i	0.363929	+	0.931427i	$0.381435\pi$
$558$	−10.1321			−0.428925
$559$	26.1502	+	16.7005i	1.10603	+	0.706357i
$560$		0			0
$561$	15.9811	+	9.22671i	0.674724	+	0.389552i
$562$	−0.858478	+	1.48693i	−0.0362127	+	0.0627223i
$563$	−16.8870	−	29.2491i	−0.711701	−	1.23270i	−0.964218	−	0.265109i	$-0.914592\pi$
$563$	−16.8870	−	29.2491i	−0.711701	−	1.23270i	0.252518	−	0.967592i	$-0.418741\pi$
$564$			9.10926i			0.383569i
$565$		0			0
$566$	1.34172	−	0.774645i	0.0563969	−	0.0325607i
$567$		−	1.32258i		−	0.0555431i
$568$	−5.66799	−	9.81724i	−0.237823	−	0.411922i
$569$	−12.7159	+	22.0246i	−0.533079	+	0.923320i	0.466175	+	0.884693i	$0.345632\pi$
$569$	−12.7159	+	22.0246i	−0.533079	+	0.923320i	−0.999254	+	0.0386274i	$0.987701\pi$
$570$		0			0
$571$	13.3682			0.559443			0.279722	−	0.960081i	$-0.409758\pi$
$571$	13.3682			0.559443			0.279722	+	0.960081i	$0.409758\pi$
$572$	7.66412	+	14.7628i	0.320453	+	0.617264i
$573$	9.74715			0.407193
$574$	5.32051	+	3.07180i	0.222074	+	0.128214i
$575$		0			0
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$			9.57428i			0.398582i	0.979940	+	0.199291i	$0.0638639\pi$
$577$			9.57428i			0.398582i	−0.979940	+	0.199291i	$0.936136\pi$
$578$	0.866025	−	0.500000i	0.0360219	−	0.0207973i
$579$	11.9188	−	6.88130i	0.495327	−	0.285977i
$580$		0			0
$581$	10.4959	+	18.1794i	0.435444	+	0.754210i
$582$	4.40947	−	7.63743i	0.182778	−	0.316582i
$583$	3.30279	+	1.90687i	0.136788	+	0.0789745i
$584$	−6.28304			−0.259994
$585$		0			0
$586$	−30.4057			−1.25605
$587$	−1.21286	−	0.700246i	−0.0500602	−	0.0289023i	0.474761	−	0.880115i	$-0.342534\pi$
$587$	−1.21286	−	0.700246i	−0.0500602	−	0.0289023i	−0.524821	+	0.851212i	$0.675868\pi$
$588$	−2.62539	+	4.54731i	−0.108269	+	0.187528i
$589$	−11.6052	−	20.1007i	−0.478183	−	0.828237i
$590$		0			0
$591$	8.78282	−	5.07076i	0.361277	−	0.208583i
$592$	5.89721	−	3.40475i	0.242374	−	0.139935i
$593$			10.7303i			0.440643i	0.975427	+	0.220321i	$0.0707106\pi$
$593$			10.7303i			0.440643i	−0.975427	+	0.220321i	$0.929289\pi$
$594$	2.30668	+	3.99528i	0.0946441	+	0.163928i
$595$		0			0
$596$	3.53788	+	2.04259i	0.144917	+	0.0836679i
$597$	9.57336			0.391812
$598$	16.8215	−	26.3397i	0.687884	−	1.07711i
$599$	−40.7967			−1.66691			−0.833453	−	0.552590i	$-0.813640\pi$
$599$	−40.7967			−1.66691			−0.833453	+	0.552590i	$0.813640\pi$
$600$		0			0
$601$	−21.4416	+	37.1379i	−0.874621	+	1.51489i	−0.0174548	+	0.999848i	$0.505556\pi$
$601$	−21.4416	+	37.1379i	−0.874621	+	1.51489i	−0.857166	+	0.515040i	$0.827777\pi$
$602$	5.69081	+	9.85677i	0.231940	+	0.401732i
$603$		−	3.18106i		−	0.129543i
$604$	17.3042	−	9.99057i	0.704097	−	0.406510i
$605$		0			0
$606$			7.22671i			0.293565i
$607$	−3.43616	−	5.95161i	−0.139470	−	0.241568i	0.787826	−	0.615897i	$-0.211206\pi$
$607$	−3.43616	−	5.95161i	−0.139470	−	0.241568i	−0.927296	+	0.374329i	$0.877873\pi$
$608$	−1.14539	+	1.98387i	−0.0464516	+	0.0804565i
$609$	2.31692	+	1.33767i	0.0938863	+	0.0542053i
$610$		0			0
$611$	−15.1331	−	29.1498i	−0.612221	−	1.17927i
$612$	−4.00000			−0.161690
$613$	0.659358	+	0.380681i	0.0266312	+	0.0153755i	0.513257	−	0.858235i	$-0.328439\pi$
$613$	0.659358	+	0.380681i	0.0266312	+	0.0153755i	−0.486625	+	0.873611i	$0.661772\pi$
$614$	4.91311	−	8.50975i	0.198277	−	0.343426i
$615$		0			0
$616$			6.10153i			0.245838i
$617$	−21.3061	+	12.3011i	−0.857753	+	0.495224i	−0.863259	−	0.504761i	$-0.831581\pi$
$617$	−21.3061	+	12.3011i	−0.857753	+	0.495224i	0.00550613	+	0.999985i	$0.498247\pi$
$618$	15.9349	−	9.20002i	0.640996	−	0.370079i
$619$			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
$622$	−2.94491	−	1.70025i	−0.118080	−	0.0681737i
$623$	−15.6913			−0.628657
$624$	−3.03873	−	1.94065i	−0.121646	−	0.0776883i
$625$		0			0
$626$	14.0590	+	8.11699i	0.561912	+	0.324420i
$627$	−5.28408	+	9.15229i	−0.211026	+	0.365507i
$628$	−3.56690	−	6.17804i	−0.142335	−	0.246531i
$629$			27.2380i			1.08605i
$630$		0			0
$631$	2.08519	−	1.20388i	0.0830100	−	0.0479259i	−0.457920	−	0.888993i	$-0.651406\pi$
$631$	2.08519	−	1.20388i	0.0830100	−	0.0479259i	0.540930	+	0.841067i	$0.318072\pi$
$632$			2.96774i			0.118050i
$633$	−0.542594	−	0.939800i	−0.0215662	−	0.0373537i
$634$	11.7616	−	20.3716i	0.467112	−	0.809061i
$635$		0			0
$636$	−0.826674			−0.0327797
$637$	0.846898	−	18.9130i	0.0335553	−	0.749361i
$638$	−9.33201			−0.369458
$639$	9.81724	+	5.66799i	0.388364	+	0.224222i
$640$		0			0
$641$	−9.73875	−	16.8680i	−0.384657	−	0.666246i	0.607064	−	0.794653i	$-0.292347\pi$
$641$	−9.73875	−	16.8680i	−0.384657	−	0.666246i	−0.991722	+	0.128407i	$0.959014\pi$
$642$		−	3.07180i		−	0.121234i
$643$	20.7451	−	11.9772i	0.818106	−	0.472334i	−0.0316570	−	0.999499i	$-0.510078\pi$
$643$	20.7451	−	11.9772i	0.818106	−	0.472334i	0.849763	+	0.527165i	$0.176745\pi$
$644$	9.92820	−	5.73205i	0.391226	−	0.225874i
$645$		0			0
$646$	−4.58155	−	7.93548i	−0.180259	−	0.312217i
$647$	−9.10540	+	15.7710i	−0.357970	+	0.620022i	−0.987622	−	0.156855i	$-0.949864\pi$
$647$	−9.10540	+	15.7710i	−0.357970	+	0.620022i	0.629652	+	0.776878i	$0.283198\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−14.4930			−0.568898
$650$		0			0
$651$	13.4005			0.525207
$652$	8.56906	+	4.94735i	0.335590	+	0.193753i
$653$	−24.0793	+	41.7065i	−0.942294	+	1.63210i	−0.181213	+	0.983444i	$0.558002\pi$
$653$	−24.0793	+	41.7065i	−0.942294	+	1.63210i	−0.761081	+	0.648657i	$0.775331\pi$
$654$	6.61335	+	11.4547i	0.258603	+	0.447913i
$655$		0			0
$656$	4.02283	−	2.32258i	0.157065	−	0.0906815i
$657$	5.44128	−	3.14152i	0.212284	−	0.122562i
$658$		−	12.0477i		−	0.469669i
$659$	18.4127	+	31.8917i	0.717257	+	1.24233i	0.962083	+	0.272758i	$0.0879359\pi$
$659$	18.4127	+	31.8917i	0.717257	+	1.24233i	−0.244826	+	0.969567i	$0.578731\pi$
$660$		0			0
$661$	−19.5131	−	11.2659i	−0.758971	−	0.438192i	0.0699555	−	0.997550i	$-0.477714\pi$
$661$	−19.5131	−	11.2659i	−0.758971	−	0.438192i	−0.828926	+	0.559358i	$0.811048\pi$
$662$	18.0904			0.703103
$663$	12.8001	−	6.64516i	0.497114	−	0.258077i
$664$	15.8719			0.615948
$665$		0			0
$666$	−3.40475	+	5.89721i	−0.131932	+	0.228512i
$667$	8.76691	+	15.1847i	0.339456	+	0.587955i
$668$		−	24.0375i		−	0.930037i
$669$	−21.6001	+	12.4708i	−0.835106	+	0.482149i
$670$		0			0
$671$			2.47229i			0.0954417i
$672$	−0.661290	−	1.14539i	−0.0255098	−	0.0441843i
$673$	−11.8719	+	20.5627i	−0.457627	+	0.792633i	−0.998835	−	0.0482556i	$-0.984634\pi$
$673$	−11.8719	+	20.5627i	−0.457627	+	0.792633i	0.541208	+	0.840889i	$0.317967\pi$
$674$	4.93548	+	2.84950i	0.190108	+	0.109759i
$675$		0			0
$676$	12.9480	+	1.16191i	0.497999	+	0.0446890i
$677$	−1.16559			−0.0447975			−0.0223987	−	0.999749i	$-0.507130\pi$
$677$	−1.16559			−0.0447975			−0.0223987	+	0.999749i	$0.507130\pi$
$678$	−7.00306	−	4.04322i	−0.268951	−	0.155279i
$679$	−5.83188	+	10.1011i	−0.223807	+	0.387645i
$680$		0			0
$681$		−	19.3205i		−	0.740363i
$682$	−40.4806	+	23.3715i	−1.55008	+	0.894939i
$683$	−12.0134	+	6.93593i	−0.459680	+	0.265396i	−0.711910	−	0.702271i	$-0.752169\pi$
$683$	−12.0134	+	6.93593i	−0.459680	+	0.265396i	0.252230	+	0.967667i	$0.418836\pi$
$684$		−	2.29078i		−	0.0875900i
$685$		0			0
$686$	8.10132	−	14.0319i	0.309310	−	0.535740i
$687$	3.59826	+	2.07746i	0.137282	+	0.0792599i
$688$	8.60562			0.328086
$689$	2.64537	−	1.37334i	0.100781	−	0.0523203i
$690$		0			0
$691$	−35.6967	−	20.6095i	−1.35797	−	0.784022i	−0.368616	−	0.929582i	$-0.620168\pi$
$691$	−35.6967	−	20.6095i	−1.35797	−	0.784022i	−0.989349	+	0.145560i	$0.953502\pi$
$692$	1.26408	−	2.18946i	0.0480532	−	0.0832307i
$693$	−3.05076	−	5.28408i	−0.115889	−	0.200726i
$694$		−	15.7471i		−	0.597753i
$695$		0			0
$696$	1.75182	−	1.01141i	0.0664025	−	0.0383375i
$697$			18.5806i			0.703792i
$698$	7.66025	+	13.2679i	0.289945	+	0.502199i
$699$	−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	$0.643096\pi$
$702$	3.60194	+	0.161290i	0.135947	+	0.00608749i
$703$	−15.5991			−0.588329
$704$	3.99528	+	2.30668i	0.150578	+	0.0869362i
$705$		0			0
$706$	−0.599964	−	1.03917i	−0.0225799	−	0.0391096i
$707$		−	9.55790i		−	0.359462i
$708$	2.72064	−	1.57076i	0.102248	−	0.0590328i
$709$	−14.7944	+	8.54156i	−0.555616	+	0.320785i	−0.751384	−	0.659865i	$-0.770613\pi$
$709$	−14.7944	+	8.54156i	−0.555616	+	0.320785i	0.195768	+	0.980650i	$0.437280\pi$
$710$		0			0
$711$	−1.48387	−	2.57014i	−0.0556495	−	0.0963877i
$712$	−5.93207	+	10.2746i	−0.222314	+	0.385059i
$713$	76.0585	+	43.9124i	2.84841	+	1.64453i
$714$	5.29032			0.197985
$715$		0			0
$716$	−6.27568			−0.234533
$717$	−5.49420	−	3.17208i	−0.205185	−	0.118463i
$718$	−8.14152	+	14.1015i	−0.303839	+	0.526264i
$719$	−21.8564	−	37.8564i	−0.815106	−	1.41181i	−0.909251	−	0.416247i	$-0.863345\pi$
$719$	−21.8564	−	37.8564i	−0.815106	−	1.41181i	0.0941451	−	0.995558i	$-0.469988\pi$
$720$		0			0
$721$	−21.0752	+	12.1678i	−0.784880	+	0.453151i
$722$	−11.9099	+	6.87617i	−0.443240	+	0.255905i
$723$		−	24.1855i		−	0.899467i
$724$	−6.14152	−	10.6374i	−0.228248	−	0.395337i
$725$		0			0
$726$	8.90538	+	5.14152i	0.330510	+	0.190820i
$727$	−31.8453			−1.18108			−0.590538	−	0.807010i	$-0.701084\pi$
$727$	−31.8453			−1.18108			−0.590538	+	0.807010i	$0.701084\pi$
$728$	4.01896	+	2.56667i	0.148953	+	0.0951270i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−17.2112	+	29.8108i	−0.636581	+	1.10259i
$732$	−0.267949	−	0.464102i	−0.00990369	−	0.0171537i
$733$			5.96774i			0.220423i	0.993908	+	0.110212i	$0.0351529\pi$
$733$			5.96774i			0.220423i	−0.993908	+	0.110212i	$0.964847\pi$
$734$	−17.0040	+	9.81724i	−0.627627	+	0.362361i
$735$		0			0
$736$		−	8.66799i		−	0.319506i
$737$	−7.33767	−	12.7092i	−0.270287	−	0.468150i
$738$	−2.32258	+	4.02283i	−0.0854953	+	0.148082i
$739$	9.37833	+	5.41458i	0.344988	+	0.199179i	0.662475	−	0.749084i	$-0.269506\pi$
$739$	9.37833	+	5.41458i	0.344988	+	0.199179i	−0.317488	+	0.948262i	$0.602839\pi$
$740$		0			0
$741$	3.80564	+	7.33052i	0.139804	+	0.269293i
$742$	1.09334			0.0401378
$743$	−17.1909	−	9.92515i	−0.630671	−	0.364118i	0.150341	−	0.988634i	$-0.451963\pi$
$743$	−17.1909	−	9.92515i	−0.630671	−	0.364118i	−0.781012	+	0.624516i	$0.785296\pi$
$744$	5.06604	−	8.77464i	0.185730	−	0.321694i
$745$		0			0
$746$		−	2.55748i		−	0.0936359i
$747$	−13.7454	+	7.93593i	−0.502919	+	0.290361i
$748$	−15.9811	+	9.22671i	−0.584328	+	0.337362i
$749$			4.06270i			0.148448i
$750$		0			0
$751$	−7.66538	+	13.2768i	−0.279714	+	0.484479i	−0.971314	−	0.237802i	$-0.923573\pi$
$751$	−7.66538	+	13.2768i	−0.279714	+	0.484479i	0.691600	+	0.722281i	$0.256906\pi$
$752$	−7.88885	−	4.55463i	−0.287677	−	0.166090i
$753$	8.82497			0.321600
$754$	−3.92560	+	6.14682i	−0.142962	+	0.223854i
$755$		0			0
$756$	1.14539	+	0.661290i	0.0416573	+	0.0240509i
$757$	22.5816	−	39.1125i	0.820744	−	1.42157i	−0.0843855	−	0.996433i	$-0.526893\pi$
$757$	22.5816	−	39.1125i	0.820744	−	1.42157i	0.905129	−	0.425137i	$-0.139774\pi$
$758$	−7.55440	−	13.0846i	−0.274388	−	0.475254i
$759$		−	39.9885i		−	1.45149i
$760$		0			0
$761$	−18.7978	+	10.8529i	−0.681419	+	0.393418i	−0.800390	−	0.599480i	$-0.795374\pi$
$761$	−18.7978	+	10.8529i	−0.681419	+	0.393418i	0.118970	+	0.992898i	$0.462041\pi$
$762$			11.4718i			0.415581i
$763$	−8.74669	−	15.1497i	−0.316651	−	0.548456i
$764$	−4.87357	+	8.44128i	−0.176320	+	0.305395i
$765$		0			0
$766$	18.7303			0.676755
$767$	−6.09660	+	9.54623i	−0.220136	+	0.344694i
$768$	−1.00000			−0.0360844
$769$	36.4711	+	21.0566i	1.31518	+	0.759321i	0.982949	−	0.183877i	$-0.0588647\pi$
$769$	36.4711	+	21.0566i	1.31518	+	0.759321i	0.332233	+	0.943197i	$0.392198\pi$
$770$		0			0
$771$	4.19247	+	7.26157i	0.150988	+	0.261519i
$772$			13.7626i			0.495327i
$773$	−25.7734	+	14.8803i	−0.927004	+	0.535206i	−0.885863	−	0.463947i	$-0.846433\pi$
$773$	−25.7734	+	14.8803i	−0.927004	+	0.535206i	−0.0411413	+	0.999153i	$0.513099\pi$
$774$	−7.45269	+	4.30281i	−0.267881	+	0.154661i
$775$		0			0
$776$	4.40947	+	7.63743i	0.158291	+	0.274168i
$777$	4.50306	−	7.79953i	0.161546	−	0.279806i
$778$	6.03532	+	3.48449i	0.216377	+	0.124925i
$779$	−10.6410			−0.381254
$780$		0			0
$781$	52.2969			1.87133
$782$	30.0268	+	17.3360i	1.07376	+	0.619933i
$783$	−1.01141	+	1.75182i	−0.0361450	+	0.0626049i
$784$	−2.62539	−	4.54731i	−0.0937640	−	0.162404i
$785$		0			0
$786$	−13.8482	+	7.99528i	−0.493950	+	0.285182i
$787$	35.5459	−	20.5224i	1.26707	−	0.731545i	0.292640	−	0.956223i	$-0.405466\pi$
$787$	35.5459	−	20.5224i	1.26707	−	0.731545i	0.974433	+	0.224678i	$0.0721329\pi$
$788$			10.1415i			0.361277i
$789$	−0.960648	−	1.66389i	−0.0342000	−	0.0592361i
$790$		0			0
$791$	9.26210	+	5.34748i	0.329322	+	0.190134i
$792$	−4.61335			−0.163928
$793$	1.62845	+	1.03999i	0.0578279	+	0.0369312i
$794$	18.5721			0.659100
$795$		0			0
$796$	−4.78668	+	8.29078i	−0.169659	+	0.293859i
$797$	−22.6263	−	39.1899i	−0.801464	−	1.38818i	−0.918652	−	0.395067i	$-0.870721\pi$
$797$	−22.6263	−	39.1899i	−0.801464	−	1.38818i	0.117188	−	0.993110i	$-0.462612\pi$
$798$			3.02973i			0.107251i
$799$	31.5554	−	18.2185i	1.11635	−	0.644525i
$800$		0			0
$801$		−	11.8641i		−	0.419199i
$802$	−14.8452	−	25.7126i	−0.524201	−	0.907944i
$803$	14.4930	−	25.1025i	0.511445	−	0.885849i
$804$	2.75488	+	1.59053i	0.0971570	+	0.0560936i
$805$		0			0
$806$	−1.63420	+	36.4952i	−0.0575623	+	1.28549i
$807$	32.3098			1.13736
$808$	−6.25851	−	3.61335i	−0.220174	−	0.127117i
$809$	14.2267	−	24.6414i	0.500184	−	0.866345i	−0.499815	−	0.866132i	$-0.666599\pi$
$809$	14.2267	−	24.6414i	0.500184	−	0.866345i	1.00000		0.000213036i	$-6.78113e-5\pi$
$810$		0			0
$811$		−	44.4114i		−	1.55949i	−0.626095	−	0.779747i	$-0.715348\pi$
$811$		−	44.4114i		−	1.55949i	0.626095	−	0.779747i	$-0.284652\pi$
$812$	−2.31692	+	1.33767i	−0.0813079	+	0.0469432i
$813$	20.3105	−	11.7263i	0.712322	−	0.411259i
$814$			31.4147i			1.10108i
$815$		0			0
$816$	2.00000	−	3.46410i	0.0700140	−	0.121268i
$817$	−17.0724	−	9.85677i	−0.597289	−	0.344845i
$818$	−24.3355			−0.850871
$819$	−4.76386	−	0.213319i	−0.166463	−	0.00745396i
$820$		0			0
$821$	−39.1169	−	22.5842i	−1.36519	−	0.788192i	−0.374880	−	0.927073i	$-0.622316\pi$
$821$	−39.1169	−	22.5842i	−1.36519	−	0.788192i	−0.990309	+	0.138881i	$0.955649\pi$
$822$	−8.03486	+	13.9168i	−0.280248	+	0.485404i
$823$	−1.20900	−	2.09404i	−0.0421430	−	0.0729938i	0.844185	−	0.536053i	$-0.180085\pi$
$823$	−1.20900	−	2.09404i	−0.0421430	−	0.0729938i	−0.886328	+	0.463059i	$0.846752\pi$
$824$			18.4000i			0.640996i
$825$		0			0
$826$	−3.59826	+	2.07746i	−0.125199	+	0.0722840i
$827$		−	4.26832i		−	0.148424i	−0.997242	−	0.0742120i	$-0.976356\pi$
$827$		−	4.26832i		−	0.148424i	0.997242	−	0.0742120i	$-0.0236441\pi$
$828$	4.33399	+	7.50670i	0.150617	+	0.260876i
$829$	−21.4926	+	37.2263i	−0.746468	+	1.29292i	0.203037	+	0.979171i	$0.434919\pi$
$829$	−21.4926	+	37.2263i	−0.746468	+	1.29292i	−0.949506	+	0.313750i	$0.898415\pi$
$830$		0			0
$831$	9.00566			0.312403
$832$	3.20002	−	1.66129i	0.110941	−	0.0575949i
$833$	21.0031			0.727715
$834$	−8.07359	−	4.66129i	−0.279566	−	0.161407i
$835$		0			0
$836$	−5.28408	−	9.15229i	−0.182754	−	0.316539i
$837$			10.1321i			0.350216i
$838$	2.49636	−	1.44128i	0.0862354	−	0.0497880i
$839$	−20.1798	+	11.6508i	−0.696684	+	0.402231i	−0.806111	−	0.591764i	$-0.798432\pi$
$839$	−20.1798	+	11.6508i	−0.696684	+	0.402231i	0.109427	+	0.993995i	$0.465098\pi$
$840$		0			0
$841$	12.4541	+	21.5711i	0.429451	+	0.743831i
$842$	2.47354	−	4.28429i	0.0852437	−	0.147646i
$843$	1.48693	+	0.858478i	0.0512125	+	0.0295676i
$844$	1.08519			0.0373537
$845$		0			0
$846$	9.10926			0.313183
$847$	−11.7781	−	6.80007i	−0.404699	−	0.233653i
$848$	0.413337	−	0.715920i	0.0141940	−	0.0245848i
$849$	−0.774645	−	1.34172i	−0.0265857	−	0.0460479i
$850$		0			0
$851$	51.1169	−	29.5124i	1.75226	−	1.01167i
$852$	−9.81724	+	5.66799i	−0.336333	+	0.194182i
$853$		−	20.8418i		−	0.713609i	−0.934179	−	0.356804i	$-0.883866\pi$
$853$		−	20.8418i		−	0.713609i	0.934179	−	0.356804i	$-0.116134\pi$
$854$	0.354384	+	0.613811i	0.0121268	+	0.0210042i
$855$		0			0
$856$	2.66025	+	1.53590i	0.0909256	+	0.0524959i
$857$	−36.7250			−1.25450			−0.627250	−	0.778818i	$-0.715820\pi$
$857$	−36.7250			−1.25450			−0.627250	+	0.778818i	$0.715820\pi$
$858$	14.7628	−	7.66412i	0.503994	−	0.261649i
$859$	0.914812			0.0312130			0.0156065	−	0.999878i	$-0.495032\pi$
$859$	0.914812			0.0312130			0.0156065	+	0.999878i	$0.495032\pi$
$860$		0			0
$861$	3.07180	−	5.32051i	0.104687	−	0.181322i
$862$	−8.88130	−	15.3829i	−0.302498	−	0.523943i
$863$		−	33.6104i		−	1.14411i	−0.820215	−	0.572056i	$-0.806146\pi$
$863$		−	33.6104i		−	1.14411i	0.820215	−	0.572056i	$-0.193854\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$		0			0
$866$		−	35.8375i		−	1.21781i
$867$	−0.500000	−	0.866025i	−0.0169809	−	0.0294118i
$868$	−6.70025	+	11.6052i	−0.227421	+	0.393905i
$869$	−11.8570	−	6.84562i	−0.402220	−	0.232222i
$870$		0			0
$871$	−11.4580	−	0.513072i	−0.388239	−	0.0173848i
$872$	−13.2267			−0.447913
$873$	−7.63743	−	4.40947i	−0.258488	−	0.149238i
$874$	−9.92820	+	17.1962i	−0.335826	+	0.581669i
$875$		0			0
$876$			6.28304i			0.212284i
$877$	21.0629	−	12.1607i	0.711243	−	0.410637i	−0.100278	−	0.994959i	$-0.531973\pi$
$877$	21.0629	−	12.1607i	0.711243	−	0.410637i	0.811521	+	0.584323i	$0.198640\pi$
$878$	8.73854	−	5.04520i	0.294911	−	0.170267i
$879$			30.4057i			1.02556i
$880$		0			0
$881$	−4.95207	+	8.57723i	−0.166839	+	0.288974i	−0.937307	−	0.348505i	$-0.886689\pi$
$881$	−4.95207	+	8.57723i	−0.166839	+	0.288974i	0.770468	+	0.637479i	$0.220023\pi$
$882$	4.54731	+	2.62539i	0.153116	+	0.0884015i
$883$	43.9718			1.47977			0.739884	−	0.672734i	$-0.234880\pi$
$883$	43.9718			1.47977			0.739884	+	0.672734i	$0.234880\pi$
$884$	−0.645159	+	14.4078i	−0.0216991	+	0.484586i
$885$		0			0
$886$	−11.8629	−	6.84904i	−0.398542	−	0.230098i
$887$	25.2807	−	43.7875i	0.848843	−	1.47024i	−0.0333988	−	0.999442i	$-0.510633\pi$
$887$	25.2807	−	43.7875i	0.848843	−	1.47024i	0.882242	−	0.470797i	$-0.156034\pi$
$888$	−3.40475	−	5.89721i	−0.114256	−	0.197897i
$889$		−	15.1724i		−	0.508866i
$890$		0			0
$891$	3.99528	−	2.30668i	0.133847	−	0.0772766i
$892$		−	24.9416i		−	0.835106i
$893$	10.4336	+	18.0716i	0.349148	+	0.604743i
$894$	2.04259	−	3.53788i	0.0683146	−	0.118324i
$895$		0			0
$896$	1.32258			0.0441843
$897$	−26.3397	−	16.8215i	−0.879455	−	0.561655i
$898$	15.3128			0.510994
$899$	−17.7496	−	10.2477i	−0.591982	−	0.341781i
$900$		0			0
$901$	1.65335	+	2.86368i	0.0550810	+	0.0954031i
$902$			21.4298i			0.713533i
$903$	9.85677	−	5.69081i	0.328013	−	0.189378i
$904$	7.00306	−	4.04322i	0.232918	−	0.134475i
$905$		0			0
$906$	−9.99057	−	17.3042i	−0.331914	−	0.574892i
$907$	−7.12175	+	12.3352i	−0.236474	+	0.409585i	−0.959700	−	0.281026i	$-0.909325\pi$
$907$	−7.12175	+	12.3352i	−0.236474	+	0.409585i	0.723226	+	0.690611i	$0.242658\pi$
$908$	16.7321	+	9.66025i	0.555273	+	0.320587i
$909$	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	$0.382329\pi$
$912$	1.98387	+	1.14539i	0.0656925	+	0.0379276i
$913$	−36.6113	+	63.4126i	−1.21166	+	2.09865i
$914$	7.77770	+	13.4714i	0.257264	+	0.445594i
$915$		0			0
$916$	−3.59826	+	2.07746i	−0.118890	+	0.0686411i
$917$	18.3154	−	10.5744i	0.604828	−	0.349197i
$918$			4.00000i			0.132020i
$919$	2.65289	+	4.59494i	0.0875108	+	0.151573i	0.906458	−	0.422295i	$-0.138775\pi$
$919$	2.65289	+	4.59494i	0.0875108	+	0.151573i	−0.818948	+	0.573868i	$0.805442\pi$
$920$		0			0
$921$	−8.50975	−	4.91311i	−0.280406	−	0.161892i
$922$	15.6431			0.515178
$923$	21.9992	−	34.4469i	0.724112	−	1.13383i
$924$	6.10153			0.200726
$925$		0			0
$926$	6.85848	−	11.8792i	0.225384	−	0.390376i
$927$	−9.20002	−	15.9349i	−0.302168	−	0.523371i
$928$			2.02283i			0.0664025i
$929$	−38.4002	+	22.1704i	−1.25987	+	0.727386i	−0.973049	−	0.230598i	$-0.925932\pi$
$929$	−38.4002	+	22.1704i	−1.25987	+	0.727386i	−0.286821	+	0.957984i	$0.592599\pi$
$930$		0			0
$931$			12.0284i			0.394214i
$932$	−8.48325	−	14.6934i	−0.277878	−	0.481299i
$933$	−1.70025	+	2.94491i	−0.0556636	+	0.0964121i
$934$	0.817239	+	0.471833i	0.0267409	+	0.0154388i
$935$		0			0
$936$	−1.94065	+	3.03873i	−0.0634322	+	0.0993239i
$937$	−38.5283			−1.25867			−0.629333	−	0.777136i	$-0.716672\pi$
$937$	−38.5283			−1.25867			−0.629333	+	0.777136i	$0.716672\pi$
$938$	−3.64354	−	2.10360i	−0.118966	−	0.0686850i
$939$	8.11699	−	14.0590i	0.264888	−	0.458800i
$940$		0			0
$941$			28.8637i			0.940929i	0.882419	+	0.470465i	$0.155914\pi$
$941$			28.8637i			0.940929i	−0.882419	+	0.470465i	$0.844086\pi$
$942$	−6.17804	+	3.56690i	−0.201292	+	0.116216i
$943$	34.8698	−	20.1321i	1.13552	−	0.655591i
$944$			3.14152i			0.102248i
$945$		0			0
$946$	−19.8504	+	34.3819i	−0.645392	+	1.11785i
$947$	−42.6384	−	24.6173i	−1.38556	−	0.799955i	−0.392752	−	0.919645i	$-0.628477\pi$
$947$	−42.6384	−	24.6173i	−1.38556	−	0.799955i	−0.992811	+	0.119689i	$0.961810\pi$
$948$	2.96774			0.0963877
$949$	−10.4380	−	20.1059i	−0.338830	−	0.652664i
$950$		0			0
$951$	−20.3716	−	11.7616i	−0.660596	−	0.381395i
$952$	−2.64516	+	4.58155i	−0.0857301	+	0.148489i
$953$	13.2548	+	22.9580i	0.429366	+	0.743684i	0.996817	−	0.0797233i	$-0.0254037\pi$
$953$	13.2548	+	22.9580i	0.429366	+	0.743684i	−0.567451	+	0.823407i	$0.692070\pi$
$954$			0.826674i			0.0267645i
$955$		0			0
$956$	5.49420	−	3.17208i	0.177695	−	0.102592i
$957$			9.33201i			0.301661i
$958$	−5.55099	−	9.61460i	−0.179344	−	0.310634i
$959$	10.6267	−	18.4061i	0.343156	−	0.594363i
$960$		0			0
$961$	−71.6592			−2.31159
$962$	20.6922	+	13.2149i	0.667145	+	0.426065i
$963$	−3.07180			−0.0989873
$964$	20.9452	+	12.0927i	0.674600	+	0.389481i
$965$		0			0
$966$	−5.73205	−	9.92820i	−0.184426	−	0.319435i
$967$		−	52.3877i		−	1.68468i	−0.538950	−	0.842338i	$-0.681179\pi$
$967$		−	52.3877i		−	1.68468i	0.538950	−	0.842338i	$-0.318821\pi$
$968$	−8.90538	+	5.14152i	−0.286230	+	0.165255i
$969$	−7.93548	+	4.58155i	−0.254924	+	0.147181i
$970$		0			0
$971$	14.3215	+	24.8056i	0.459600	+	0.796051i	0.998940	−	0.0460375i	$-0.0146594\pi$
$971$	14.3215	+	24.8056i	0.459600	+	0.796051i	−0.539339	+	0.842088i	$0.681326\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	10.6780	+	6.16493i	0.342320	+	0.197638i
$974$	32.9416			1.05552
$975$		0			0
$976$	0.535898			0.0171537
$977$	−35.1173	−	20.2750i	−1.12350	−	0.648654i	−0.181209	−	0.983445i	$-0.558001\pi$
$977$	−35.1173	−	20.2750i	−1.12350	−	0.648654i	−0.942292	+	0.334791i	$0.891334\pi$
$978$	4.94735	−	8.56906i	0.158199	−	0.274008i
$979$	−27.3667	−	47.4006i	−0.874645	−	1.51493i
$980$		0			0
$981$	11.4547	−	6.61335i	0.365719	−	0.211148i
$982$	24.6396	−	14.2257i	0.786281	−	0.453960i
$983$		−	22.4160i		−	0.714958i	−0.933921	−	0.357479i	$-0.883636\pi$
$983$		−	22.4160i		−	0.714958i	0.933921	−	0.357479i	$-0.116364\pi$
$984$	−2.32258	−	4.02283i	−0.0740411	−	0.128243i
$985$		0			0
$986$	−7.00727	−	4.04565i	−0.223157	−	0.128840i
$987$	−12.0477			−0.383483
$988$	−8.25124	−	0.369479i	−0.262507	−	0.0117547i
$989$	74.5934			2.37193
$990$		0			0
$991$	14.2844	−	24.7413i	0.453759	−	0.785933i	−0.544857	−	0.838529i	$-0.683416\pi$
$991$	14.2844	−	24.7413i	0.453759	−	0.785933i	0.998616	+	0.0525955i	$0.0167494\pi$
$992$	5.06604	+	8.77464i	0.160847	+	0.278595i
$993$		−	18.0904i		−	0.574081i
$994$	12.9841	−	7.49636i	0.411830	−	0.237770i
$995$		0			0
$996$		−	15.8719i		−	0.502919i
$997$	−17.2000	−	29.7913i	−0.544730	−	0.943500i	−0.998624	−	0.0524443i	$-0.983299\pi$
$997$	−17.2000	−	29.7913i	−0.544730	−	0.943500i	0.453894	−	0.891056i	$-0.350035\pi$
$998$	2.05463	−	3.55872i	0.0650382	−	0.112649i
$999$	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.bc.g.901.3		8
5.2	odd	4		1950.2.y.j.199.1		8
5.3	odd	4		1950.2.y.k.199.4		8
5.4	even	2		390.2.bb.c.121.2	✓	8
13.10	even	6	inner	1950.2.bc.g.751.3		8
15.14	odd	2		1170.2.bs.f.901.4		8
65.4	even	6		5070.2.b.ba.1351.2		8
65.9	even	6		5070.2.b.ba.1351.7		8
65.19	odd	12		5070.2.a.ca.1.2		4
65.23	odd	12		1950.2.y.j.49.1		8
65.49	even	6		390.2.bb.c.361.2	yes	8
65.59	odd	12		5070.2.a.bz.1.3		4
65.62	odd	12		1950.2.y.k.49.4		8
195.179	odd	6		1170.2.bs.f.361.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bb.c.121.2	✓	8	5.4	even	2
390.2.bb.c.361.2	yes	8	65.49	even	6
1170.2.bs.f.361.4		8	195.179	odd	6
1170.2.bs.f.901.4		8	15.14	odd	2
1950.2.y.j.49.1		8	65.23	odd	12
1950.2.y.j.199.1		8	5.2	odd	4
1950.2.y.k.49.4		8	65.62	odd	12
1950.2.y.k.199.4		8	5.3	odd	4
1950.2.bc.g.751.3		8	13.10	even	6	inner
1950.2.bc.g.901.3		8	1.1	even	1	trivial
5070.2.a.bz.1.3		4	65.59	odd	12
5070.2.a.ca.1.2		4	65.19	odd	12
5070.2.b.ba.1351.2		8	65.4	even	6
5070.2.b.ba.1351.7		8	65.9	even	6

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.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(-1.14539 + 0.661290i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(-1.14539 + 0.661290i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-3.99528 - 2.30668i) q^{11} +1.00000 q^{12} +(-3.20002 + 1.66129i) q^{13} -1.32258 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} -1.00000i q^{18} +(1.98387 - 1.14539i) q^{19} +1.32258i q^{21} +(-2.30668 - 3.99528i) q^{22} +(-4.33399 + 7.50670i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-3.60194 - 0.161290i) q^{26} -1.00000 q^{27} +(-1.14539 - 0.661290i) q^{28} +(1.01141 - 1.75182i) q^{29} -10.1321i q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.99528 + 2.30668i) q^{33} -4.00000i q^{34} +(0.500000 - 0.866025i) q^{36} +(-5.89721 - 3.40475i) q^{37} +2.29078 q^{38} +(-0.161290 + 3.60194i) q^{39} +(-4.02283 - 2.32258i) q^{41} +(-0.661290 + 1.14539i) q^{42} +(-4.30281 - 7.45269i) q^{43} -4.61335i q^{44} +(-7.50670 + 4.33399i) q^{46} +9.10926i q^{47} +(0.500000 + 0.866025i) q^{48} +(-2.62539 + 4.54731i) q^{49} -4.00000 q^{51} +(-3.03873 - 1.94065i) q^{52} -0.826674 q^{53} +(-0.866025 - 0.500000i) q^{54} +(-0.661290 - 1.14539i) q^{56} -2.29078i q^{57} +(1.75182 - 1.01141i) q^{58} +(2.72064 - 1.57076i) q^{59} +(-0.267949 - 0.464102i) q^{61} +(5.06604 - 8.77464i) q^{62} +(1.14539 + 0.661290i) q^{63} -1.00000 q^{64} -4.61335 q^{66} +(2.75488 + 1.59053i) q^{67} +(2.00000 - 3.46410i) q^{68} +(4.33399 + 7.50670i) q^{69} +(-9.81724 + 5.66799i) q^{71} +(0.866025 - 0.500000i) q^{72} +6.28304i q^{73} +(-3.40475 - 5.89721i) q^{74} +(1.98387 + 1.14539i) q^{76} +6.10153 q^{77} +(-1.94065 + 3.03873i) q^{78} +2.96774 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-2.32258 - 4.02283i) q^{82} -15.8719i q^{83} +(-1.14539 + 0.661290i) q^{84} -8.60562i q^{86} +(-1.01141 - 1.75182i) q^{87} +(2.30668 - 3.99528i) q^{88} +(10.2746 + 5.93207i) q^{89} +(2.56667 - 4.01896i) q^{91} -8.66799 q^{92} +(-8.77464 - 5.06604i) q^{93} +(-4.55463 + 7.88885i) q^{94} +1.00000i q^{96} +(7.63743 - 4.40947i) q^{97} +(-4.54731 + 2.62539i) q^{98} +4.61335i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9	\( 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9} + 6 q^{11} + 8 q^{12} + 12 q^{13} + 4 q^{14} - 4 q^{16} - 16 q^{17} - 6 q^{19} - 2 q^{22} - 4 q^{23} - 12 q^{26} - 8 q^{27} - 8 q^{29} + 6 q^{33} + 4 q^{36} - 30 q^{37} + 6 q^{39} + 2 q^{42} - 14 q^{43} - 6 q^{46} + 4 q^{48} + 14 q^{49} - 32 q^{51} + 6 q^{52} - 16 q^{53} + 2 q^{56} + 6 q^{58} + 24 q^{59} - 16 q^{61} - 4 q^{62} - 8 q^{64} - 4 q^{66} - 24 q^{67} + 16 q^{68} + 4 q^{69} - 12 q^{71} + 10 q^{74} - 6 q^{76} - 16 q^{77} - 6 q^{78} - 20 q^{79} - 4 q^{81} - 4 q^{82} + 8 q^{87} + 2 q^{88} + 42 q^{89} - 10 q^{91} - 8 q^{92} - 30 q^{93} - 8 q^{94} + 24 q^{97} - 48 q^{98}+O(q^{100}) \) 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9 + 6 * q^11 + 8 * q^12 + 12 * q^13 + 4 * q^14 - 4 * q^16 - 16 * q^17 - 6 * q^19 - 2 * q^22 - 4 * q^23 - 12 * q^26 - 8 * q^27 - 8 * q^29 + 6 * q^33 + 4 * q^36 - 30 * q^37 + 6 * q^39 + 2 * q^42 - 14 * q^43 - 6 * q^46 + 4 * q^48 + 14 * q^49 - 32 * q^51 + 6 * q^52 - 16 * q^53 + 2 * q^56 + 6 * q^58 + 24 * q^59 - 16 * q^61 - 4 * q^62 - 8 * q^64 - 4 * q^66 - 24 * q^67 + 16 * q^68 + 4 * q^69 - 12 * q^71 + 10 * q^74 - 6 * q^76 - 16 * q^77 - 6 * q^78 - 20 * q^79 - 4 * q^81 - 4 * q^82 + 8 * q^87 + 2 * q^88 + 42 * q^89 - 10 * q^91 - 8 * q^92 - 30 * q^93 - 8 * q^94 + 24 * q^97 - 48 * q^98

Introduction

L-functions

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