LMFDB - Embedded newform 48.2.j.a.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,2,Mod(13,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("48.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	48.j (of order $4$, 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:	$0.383281929702$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.18939904.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 $ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.2
Root			$0.500000 - 1.44392i$ of defining polynomial
Character	$\chi$	$=$	48.13
Dual form			48.2.j.a.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.167452 - 1.40426i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-1.94392 + 0.470294i) q^{4} +(1.74912 - 1.74912i) q^{5} +(-0.874559 + 1.11137i) q^{6} +2.55765i q^{7} +(0.985930 + 2.65103i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.167452 - 1.40426i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-1.94392 + 0.470294i) q^{4} +(1.74912 - 1.74912i) q^{5} +(-0.874559 + 1.11137i) q^{6} +2.55765i q^{7} +(0.985930 + 2.65103i) q^{8} +1.00000i q^{9} +(-2.74912 - 2.16333i) q^{10} +(0.473626 - 0.473626i) q^{11} +(1.70711 + 1.04201i) q^{12} +(2.88784 + 2.88784i) q^{13} +(3.59161 - 0.428283i) q^{14} -2.47363 q^{15} +(3.55765 - 1.82843i) q^{16} -6.44549 q^{17} +(1.40426 - 0.167452i) q^{18} +(-4.55765 - 4.55765i) q^{19} +(-2.57754 + 4.22274i) q^{20} +(1.80853 - 1.80853i) q^{21} +(-0.744406 - 0.585786i) q^{22} +2.82843i q^{23} +(1.17740 - 2.57172i) q^{24} -1.11882i q^{25} +(3.57172 - 4.53887i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.20285 - 4.97186i) q^{28} +(-3.07931 - 3.07931i) q^{29} +(0.414214 + 3.47363i) q^{30} +6.55765 q^{31} +(-3.16333 - 4.68971i) q^{32} -0.669808 q^{33} +(1.07931 + 9.05117i) q^{34} +(4.47363 + 4.47363i) q^{35} +(-0.470294 - 1.94392i) q^{36} +(-2.72922 + 2.72922i) q^{37} +(-5.63696 + 7.16333i) q^{38} -4.08402i q^{39} +(6.36147 + 2.91245i) q^{40} +0.788632i q^{41} +(-2.84250 - 2.23681i) q^{42} +(-0.389604 + 0.389604i) q^{43} +(-0.697947 + 1.14343i) q^{44} +(1.74912 + 1.74912i) q^{45} +(3.97186 - 0.473626i) q^{46} +2.82843 q^{47} +(-3.80853 - 1.22274i) q^{48} +0.458440 q^{49} +(-1.57113 + 0.187349i) q^{50} +(4.55765 + 4.55765i) q^{51} +(-6.97186 - 4.25559i) q^{52} +(-2.57754 + 2.57754i) q^{53} +(-1.11137 - 0.874559i) q^{54} -1.65685i q^{55} +(-6.78039 + 2.52166i) q^{56} +6.44549i q^{57} +(-3.80853 + 4.83980i) q^{58} +(4.00000 - 4.00000i) q^{59} +(4.80853 - 1.16333i) q^{60} +(-4.38607 - 4.38607i) q^{61} +(-1.09809 - 9.20867i) q^{62} -2.55765 q^{63} +(-6.05588 + 5.22746i) q^{64} +10.1023 q^{65} +(0.112161 + 0.940588i) q^{66} +(-2.11882 - 2.11882i) q^{67} +(12.5295 - 3.03127i) q^{68} +(2.00000 - 2.00000i) q^{69} +(5.53304 - 7.03127i) q^{70} -5.11529i q^{71} +(-2.65103 + 0.985930i) q^{72} -14.7721i q^{73} +(4.28956 + 3.37553i) q^{74} +(-0.791128 + 0.791128i) q^{75} +(11.0031 + 6.71627i) q^{76} +(1.21137 + 1.21137i) q^{77} +(-5.73505 + 0.683878i) q^{78} -6.32000 q^{79} +(3.02461 - 9.42088i) q^{80} -1.00000 q^{81} +(1.10745 - 0.132058i) q^{82} +(0.641669 + 0.641669i) q^{83} +(-2.66510 + 4.36618i) q^{84} +(-11.2739 + 11.2739i) q^{85} +(0.612348 + 0.481868i) q^{86} +4.35480i q^{87} +(1.72256 + 0.788632i) q^{88} +6.31724i q^{89} +(2.16333 - 2.74912i) q^{90} +(-7.38607 + 7.38607i) q^{91} +(-1.33019 - 5.49824i) q^{92} +(-4.63696 - 4.63696i) q^{93} +(-0.473626 - 3.97186i) q^{94} -15.9437 q^{95} +(-1.07931 + 5.55294i) q^{96} +12.6533 q^{97} +(-0.0767667 - 0.643772i) q^{98} +(0.473626 + 0.473626i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4} - 12 q^{8}+O(q^{10}) $ 8 * q - 4 * q^4 - 12 * q^8	$ 8 q - 4 q^{4} - 12 q^{8} - 8 q^{10} - 8 q^{11} + 8 q^{12} + 12 q^{14} - 8 q^{15} + 4 q^{18} - 8 q^{19} + 16 q^{20} + 4 q^{24} + 20 q^{26} + 8 q^{28} - 16 q^{29} - 8 q^{30} + 24 q^{31} + 24 q^{35} - 4 q^{36} - 16 q^{37} - 8 q^{38} + 16 q^{40} - 20 q^{42} - 8 q^{43} - 40 q^{44} - 8 q^{46} - 16 q^{48} - 8 q^{49} - 36 q^{50} + 8 q^{51} - 16 q^{52} + 16 q^{53} + 4 q^{54} - 16 q^{58} + 32 q^{59} + 24 q^{60} + 16 q^{61} - 12 q^{62} + 8 q^{63} + 8 q^{64} - 16 q^{65} + 24 q^{66} - 16 q^{67} + 32 q^{68} + 16 q^{69} + 32 q^{70} - 4 q^{72} + 52 q^{74} + 16 q^{75} + 8 q^{76} + 16 q^{77} - 12 q^{78} - 24 q^{79} + 8 q^{80} - 8 q^{81} + 40 q^{82} - 40 q^{83} - 24 q^{84} - 16 q^{85} - 16 q^{86} + 32 q^{88} - 8 q^{90} - 8 q^{91} - 16 q^{92} + 8 q^{94} - 48 q^{95} - 40 q^{98} - 8 q^{99}+O(q^{100}) $ 8 * q - 4 * q^4 - 12 * q^8 - 8 * q^10 - 8 * q^11 + 8 * q^12 + 12 * q^14 - 8 * q^15 + 4 * q^18 - 8 * q^19 + 16 * q^20 + 4 * q^24 + 20 * q^26 + 8 * q^28 - 16 * q^29 - 8 * q^30 + 24 * q^31 + 24 * q^35 - 4 * q^36 - 16 * q^37 - 8 * q^38 + 16 * q^40 - 20 * q^42 - 8 * q^43 - 40 * q^44 - 8 * q^46 - 16 * q^48 - 8 * q^49 - 36 * q^50 + 8 * q^51 - 16 * q^52 + 16 * q^53 + 4 * q^54 - 16 * q^58 + 32 * q^59 + 24 * q^60 + 16 * q^61 - 12 * q^62 + 8 * q^63 + 8 * q^64 - 16 * q^65 + 24 * q^66 - 16 * q^67 + 32 * q^68 + 16 * q^69 + 32 * q^70 - 4 * q^72 + 52 * q^74 + 16 * q^75 + 8 * q^76 + 16 * q^77 - 12 * q^78 - 24 * q^79 + 8 * q^80 - 8 * q^81 + 40 * q^82 - 40 * q^83 - 24 * q^84 - 16 * q^85 - 16 * q^86 + 32 * q^88 - 8 * q^90 - 8 * q^91 - 16 * q^92 + 8 * q^94 - 48 * q^95 - 40 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.167452	−	1.40426i	−0.118406	−	0.992965i
$2$	−0.167452	−	1.40426i	−0.118406	−	0.992965i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	−1.94392	+	0.470294i	−0.971960	+	0.235147i
$5$	1.74912	−	1.74912i	0.782229	−	0.782229i	−0.197977	−	0.980207i	$-0.563437\pi$
$5$	1.74912	−	1.74912i	0.782229	−	0.782229i	0.980207	+	0.197977i	$0.0634373\pi$
$6$	−0.874559	+	1.11137i	−0.357037	+	0.453716i
$7$			2.55765i			0.966700i	0.875427	+	0.483350i	$0.160580\pi$
$7$			2.55765i			0.966700i	−0.875427	+	0.483350i	$0.839420\pi$
$8$	0.985930	+	2.65103i	0.348579	+	0.937279i
$9$			1.00000i			0.333333i
$10$	−2.74912	−	2.16333i	−0.869347	−	0.684105i
$11$	0.473626	−	0.473626i	0.142804	−	0.142804i	−0.632091	−	0.774894i	$-0.717803\pi$
$11$	0.473626	−	0.473626i	0.142804	−	0.142804i	0.774894	+	0.632091i	$0.217803\pi$
$12$	1.70711	+	1.04201i	0.492799	+	0.300803i
$13$	2.88784	+	2.88784i	0.800943	+	0.800943i	0.983243	−	0.182300i	$-0.0583543\pi$
$13$	2.88784	+	2.88784i	0.800943	+	0.800943i	−0.182300	+	0.983243i	$0.558354\pi$
$14$	3.59161	−	0.428283i	0.959899	−	0.114463i
$15$	−2.47363			−0.638687
$16$	3.55765	−	1.82843i	0.889412	−	0.457107i
$17$	−6.44549			−1.56326			−0.781630	−	0.623742i	$-0.785611\pi$
$17$	−6.44549			−1.56326			−0.781630	+	0.623742i	$0.785611\pi$
$18$	1.40426	−	0.167452i	0.330988	−	0.0394688i
$19$	−4.55765	−	4.55765i	−1.04560	−	1.04560i	−0.998910	−	0.0466864i	$-0.985134\pi$
$19$	−4.55765	−	4.55765i	−1.04560	−	1.04560i	−0.0466864	−	0.998910i	$-0.514866\pi$
$20$	−2.57754	+	4.22274i	−0.576357	+	0.944234i
$21$	1.80853	−	1.80853i	0.394654	−	0.394654i
$22$	−0.744406	−	0.585786i	−0.158708	−	0.124890i
$23$			2.82843i			0.589768i	0.955533	+	0.294884i	$0.0952810\pi$
$23$			2.82843i			0.589768i	−0.955533	+	0.294884i	$0.904719\pi$
$24$	1.17740	−	2.57172i	0.240336	−	0.524950i
$25$		−	1.11882i		−	0.223765i
$26$	3.57172	−	4.53887i	0.700471	−	0.890145i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−1.20285	−	4.97186i	−0.227317	−	0.939593i
$29$	−3.07931	−	3.07931i	−0.571813	−	0.571813i	0.360821	−	0.932635i	$-0.382496\pi$
$29$	−3.07931	−	3.07931i	−0.571813	−	0.571813i	−0.932635	+	0.360821i	$0.882496\pi$
$30$	0.414214	+	3.47363i	0.0756247	+	0.634194i
$31$	6.55765			1.17779			0.588894	−	0.808210i	$-0.299563\pi$
$31$	6.55765			1.17779			0.588894	+	0.808210i	$0.299563\pi$
$32$	−3.16333	−	4.68971i	−0.559203	−	0.829031i
$33$	−0.669808			−0.116599
$34$	1.07931	+	9.05117i	0.185100	+	1.55226i
$35$	4.47363	+	4.47363i	0.756181	+	0.756181i
$36$	−0.470294	−	1.94392i	−0.0783823	−	0.323987i
$37$	−2.72922	+	2.72922i	−0.448681	+	0.448681i	−0.894916	−	0.446235i	$-0.852765\pi$
$37$	−2.72922	+	2.72922i	−0.448681	+	0.448681i	0.446235	+	0.894916i	$0.352765\pi$
$38$	−5.63696	+	7.16333i	−0.914435	+	1.16205i
$39$		−	4.08402i		−	0.653967i
$40$	6.36147	+	2.91245i	1.00584	+	0.460499i
$41$			0.788632i			0.123164i	0.998102	+	0.0615818i	$0.0196145\pi$
$41$			0.788632i			0.123164i	−0.998102	+	0.0615818i	$0.980385\pi$
$42$	−2.84250	−	2.23681i	−0.438607	−	0.345148i
$43$	−0.389604	+	0.389604i	−0.0594141	+	0.0594141i	−0.736190	−	0.676775i	$-0.763377\pi$
$43$	−0.389604	+	0.389604i	−0.0594141	+	0.0594141i	0.676775	+	0.736190i	$0.263377\pi$
$44$	−0.697947	+	1.14343i	−0.105219	+	0.172379i
$45$	1.74912	+	1.74912i	0.260743	+	0.260743i
$46$	3.97186	−	0.473626i	0.585619	−	0.0698323i
$47$	2.82843			0.412568			0.206284	−	0.978492i	$-0.433863\pi$
$47$	2.82843			0.412568			0.206284	+	0.978492i	$0.433863\pi$
$48$	−3.80853	−	1.22274i	−0.549714	−	0.176488i
$49$	0.458440			0.0654915
$50$	−1.57113	+	0.187349i	−0.222191	+	0.0264952i
$51$	4.55765	+	4.55765i	0.638198	+	0.638198i
$52$	−6.97186	−	4.25559i	−0.966823	−	0.590145i
$53$	−2.57754	+	2.57754i	−0.354053	+	0.354053i	−0.861615	−	0.507562i	$-0.830547\pi$
$53$	−2.57754	+	2.57754i	−0.354053	+	0.354053i	0.507562	+	0.861615i	$0.330547\pi$
$54$	−1.11137	−	0.874559i	−0.151239	−	0.119012i
$55$		−	1.65685i		−	0.223410i
$56$	−6.78039	+	2.52166i	−0.906068	+	0.336971i
$57$			6.44549i			0.853726i
$58$	−3.80853	+	4.83980i	−0.500084	+	0.635497i
$59$	4.00000	−	4.00000i	0.520756	−	0.520756i	−0.397044	−	0.917800i	$-0.629964\pi$
$59$	4.00000	−	4.00000i	0.520756	−	0.520756i	0.917800	+	0.397044i	$0.129964\pi$
$60$	4.80853	−	1.16333i	0.620779	−	0.150185i
$61$	−4.38607	−	4.38607i	−0.561579	−	0.561579i	0.368177	−	0.929756i	$-0.379982\pi$
$61$	−4.38607	−	4.38607i	−0.561579	−	0.561579i	−0.929756	+	0.368177i	$0.879982\pi$
$62$	−1.09809	−	9.20867i	−0.139458	−	1.16950i
$63$	−2.55765			−0.322233
$64$	−6.05588	+	5.22746i	−0.756985	+	0.653432i
$65$	10.1023			1.25304
$66$	0.112161	+	0.940588i	0.0138060	+	0.115778i
$67$	−2.11882	−	2.11882i	−0.258856	−	0.258856i	0.565733	−	0.824589i	$-0.308593\pi$
$67$	−2.11882	−	2.11882i	−0.258856	−	0.258856i	−0.824589	+	0.565733i	$0.808593\pi$
$68$	12.5295	−	3.03127i	1.51943	−	0.367596i
$69$	2.00000	−	2.00000i	0.240772	−	0.240772i
$70$	5.53304	−	7.03127i	0.661325	−	0.840398i
$71$		−	5.11529i		−	0.607074i	−0.952820	−	0.303537i	$-0.901832\pi$
$71$		−	5.11529i		−	0.607074i	0.952820	−	0.303537i	$-0.0981676\pi$
$72$	−2.65103	+	0.985930i	−0.312426	+	0.116193i
$73$		−	14.7721i		−	1.72895i	−0.502676	−	0.864475i	$-0.667651\pi$
$73$		−	14.7721i		−	1.72895i	0.502676	−	0.864475i	$-0.332349\pi$
$74$	4.28956	+	3.37553i	0.498651	+	0.392398i
$75$	−0.791128	+	0.791128i	−0.0913516	+	0.0913516i
$76$	11.0031	+	6.71627i	1.26215	+	0.770409i
$77$	1.21137	+	1.21137i	0.138048	+	0.138048i
$78$	−5.73505	+	0.683878i	−0.649366	+	0.0774339i
$79$	−6.32000			−0.711055			−0.355528	−	0.934666i	$-0.615699\pi$
$79$	−6.32000			−0.711055			−0.355528	+	0.934666i	$0.615699\pi$
$80$	3.02461	−	9.42088i	0.338162	−	1.05329i
$81$	−1.00000			−0.111111
$82$	1.10745	−	0.132058i	0.122297	−	0.0145834i
$83$	0.641669	+	0.641669i	0.0704323	+	0.0704323i	0.741445	−	0.671013i	$-0.234141\pi$
$83$	0.641669	+	0.641669i	0.0704323	+	0.0704323i	−0.671013	+	0.741445i	$0.734141\pi$
$84$	−2.66510	+	4.36618i	−0.290786	+	0.476389i
$85$	−11.2739	+	11.2739i	−1.22283	+	1.22283i
$86$	0.612348	+	0.481868i	0.0660311	+	0.0519611i
$87$			4.35480i			0.466884i
$88$	1.72256	+	0.788632i	0.183625	+	0.0840685i
$89$			6.31724i			0.669626i	0.942285	+	0.334813i	$0.108673\pi$
$89$			6.31724i			0.669626i	−0.942285	+	0.334813i	$0.891327\pi$
$90$	2.16333	−	2.74912i	0.228035	−	0.289782i
$91$	−7.38607	+	7.38607i	−0.774271	+	0.774271i
$92$	−1.33019	−	5.49824i	−0.138682	−	0.573231i
$93$	−4.63696	−	4.63696i	−0.480830	−	0.480830i
$94$	−0.473626	−	3.97186i	−0.0488508	−	0.409666i
$95$	−15.9437			−1.63579
$96$	−1.07931	+	5.55294i	−0.110157	+	0.566744i
$97$	12.6533			1.28475			0.642375	−	0.766390i	$-0.277949\pi$
$97$	12.6533			1.28475			0.642375	+	0.766390i	$0.277949\pi$
$98$	−0.0767667	−	0.643772i	−0.00775461	−	0.0650308i
$99$	0.473626	+	0.473626i	0.0476012	+	0.0476012i
$100$	0.526176	+	2.17490i	0.0526176	+	0.217490i
$101$	7.52480	−	7.52480i	0.748745	−	0.748745i	−0.225498	−	0.974244i	$-0.572401\pi$
$101$	7.52480	−	7.52480i	0.748745	−	0.748745i	0.974244	+	0.225498i	$0.0724010\pi$
$102$	5.63696	−	7.16333i	0.558142	−	0.709275i
$103$		−	3.33686i		−	0.328790i	−0.986395	−	0.164395i	$-0.947433\pi$
$103$		−	3.33686i		−	0.328790i	0.986395	−	0.164395i	$-0.0525672\pi$
$104$	−4.80853	+	10.5029i	−0.471515	+	1.02990i
$105$		−	6.32666i		−	0.617419i
$106$	4.05117	+	3.18794i	0.393484	+	0.309640i
$107$	−14.0625	+	14.0625i	−1.35948	+	1.35948i	−0.484918	+	0.874560i	$0.661151\pi$
$107$	−14.0625	+	14.0625i	−1.35948	+	1.35948i	−0.874560	+	0.484918i	$0.838849\pi$
$108$	−1.04201	+	1.70711i	−0.100268	+	0.164266i
$109$	2.76901	+	2.76901i	0.265224	+	0.265224i	0.827172	−	0.561949i	$-0.189948\pi$
$109$	2.76901	+	2.76901i	0.265224	+	0.265224i	−0.561949	+	0.827172i	$0.689948\pi$
$110$	−2.32666	+	0.277444i	−0.221839	+	0.0264532i
$111$	3.85970			0.366347
$112$	4.67647	+	9.09921i	0.441885	+	0.859794i
$113$	2.23765			0.210500			0.105250	−	0.994446i	$-0.466436\pi$
$113$	2.23765			0.210500			0.105250	+	0.994446i	$0.466436\pi$
$114$	9.05117	−	1.07931i	0.847720	−	0.101087i
$115$	4.94725	+	4.94725i	0.461334	+	0.461334i
$116$	7.43411	+	4.53775i	0.690240	+	0.421320i
$117$	−2.88784	+	2.88784i	−0.266981	+	0.266981i
$118$	−6.28687	−	4.94725i	−0.578753	−	0.455431i
$119$		−	16.4853i		−	1.51120i
$120$	−2.43882	−	6.55765i	−0.222633	−	0.598629i
$121$			10.5514i			0.959214i
$122$	−5.42475	+	6.89367i	−0.491134	+	0.624123i
$123$	0.557647	−	0.557647i	0.0502814	−	0.0502814i
$124$	−12.7475	+	3.08402i	−1.14476	+	0.276953i
$125$	6.78863	+	6.78863i	0.607194	+	0.607194i
$126$	0.428283	+	3.59161i	0.0381545	+	0.319966i
$127$	12.2145			1.08386			0.541931	−	0.840423i	$-0.317693\pi$
$127$	12.2145			1.08386			0.541931	+	0.840423i	$0.317693\pi$
$128$	8.35480	+	7.62872i	0.738467	+	0.674290i
$129$	0.550984			0.0485114
$130$	−1.69166	−	14.1864i	−0.148368	−	1.24423i
$131$	−3.77568	−	3.77568i	−0.329883	−	0.329883i	0.522659	−	0.852542i	$-0.324940\pi$
$131$	−3.77568	−	3.77568i	−0.329883	−	0.329883i	−0.852542	+	0.522659i	$0.824940\pi$
$132$	1.30205	−	0.315007i	0.113329	−	0.0274178i
$133$	11.6569	−	11.6569i	1.01078	−	1.01078i
$134$	−2.62059	+	3.33019i	−0.226384	+	0.287685i
$135$		−	2.47363i		−	0.212896i
$136$	−6.35480	−	17.0872i	−0.544920	−	1.46521i
$137$		−	5.10587i		−	0.436224i	−0.975924	−	0.218112i	$-0.930010\pi$
$137$		−	5.10587i		−	0.436224i	0.975924	−	0.218112i	$-0.0699898\pi$
$138$	−3.14343	−	2.47363i	−0.267587	−	0.210569i
$139$	11.7757	−	11.7757i	0.998800	−	0.998800i	−0.00119925	−	0.999999i	$-0.500382\pi$
$139$	11.7757	−	11.7757i	0.998800	−	0.998800i	0.999999	+	0.00119925i	$0.000381735\pi$
$140$	−10.8003	−	6.59245i	−0.912791	−	0.557164i
$141$	−2.00000	−	2.00000i	−0.168430	−	0.168430i
$142$	−7.18323	+	0.856566i	−0.602803	+	0.0718814i
$143$	2.73551			0.228755
$144$	1.82843	+	3.55765i	0.152369	+	0.296471i
$145$	−10.7721			−0.894578
$146$	−20.7440	+	2.47363i	−1.71679	+	0.204719i
$147$	−0.324166	−	0.324166i	−0.0267368	−	0.0267368i
$148$	4.02185	−	6.58892i	0.330594	−	0.541606i
$149$	−7.90774	+	7.90774i	−0.647827	+	0.647827i	−0.952467	−	0.304640i	$-0.901464\pi$
$149$	−7.90774	+	7.90774i	−0.647827	+	0.647827i	0.304640	+	0.952467i	$0.401464\pi$
$150$	1.24343	+	0.978478i	0.101526	+	0.0798924i
$151$			14.6506i			1.19225i	0.802893	+	0.596123i	$0.203293\pi$
$151$			14.6506i			1.19225i	−0.802893	+	0.596123i	$0.796707\pi$
$152$	7.58892	−	16.5760i	0.615543	−	1.34449i
$153$		−	6.44549i		−	0.521087i
$154$	1.49824	−	1.90393i	0.120731	−	0.153423i
$155$	11.4701	−	11.4701i	0.921300	−	0.921300i
$156$	1.92069	+	7.93901i	0.153778	+	0.635629i
$157$	−3.15196	−	3.15196i	−0.251553	−	0.251553i	0.570054	−	0.821607i	$-0.306922\pi$
$157$	−3.15196	−	3.15196i	−0.251553	−	0.251553i	−0.821607	+	0.570054i	$0.806922\pi$
$158$	1.05830	+	8.87495i	0.0841935	+	0.706053i
$159$	3.64520			0.289083
$160$	−13.7359	−	2.66981i	−1.08592	−	0.211067i
$161$	−7.23412			−0.570128
$162$	0.167452	+	1.40426i	0.0131563	+	0.110329i
$163$	5.50490	+	5.50490i	0.431177	+	0.431177i	0.889029	−	0.457852i	$-0.151381\pi$
$163$	5.50490	+	5.50490i	0.431177	+	0.431177i	−0.457852	+	0.889029i	$0.651381\pi$
$164$	−0.370889	−	1.53304i	−0.0289616	−	0.119710i
$165$	−1.17157	+	1.17157i	−0.0912068	+	0.0912068i
$166$	0.793624	−	1.00852i	0.0615972	−	0.0782765i
$167$			20.1814i			1.56168i	0.624730	+	0.780841i	$0.285209\pi$
$167$			20.1814i			1.56168i	−0.624730	+	0.780841i	$0.714791\pi$
$168$	6.57754	+	3.01138i	0.507469	+	0.232333i
$169$			3.67923i			0.283018i
$170$	17.7194	+	13.9437i	1.35902	+	1.06943i
$171$	4.55765	−	4.55765i	0.348532	−	0.348532i
$172$	0.574131	−	0.940588i	0.0437771	−	0.0717191i
$173$	4.35322	+	4.35322i	0.330969	+	0.330969i	0.852955	−	0.521985i	$-0.174808\pi$
$173$	4.35322	+	4.35322i	0.330969	+	0.330969i	−0.521985	+	0.852955i	$0.674808\pi$
$174$	6.11529	−	0.729220i	0.463599	−	0.0552820i
$175$	2.86156			0.216313
$176$	0.819003	−	2.55098i	0.0617347	−	0.192288i
$177$	−5.65685			−0.425195
$178$	8.87108	−	1.05783i	0.664915	−	0.0792880i
$179$	−13.2833	−	13.2833i	−0.992843	−	0.992843i	0.00713130	−	0.999975i	$-0.497730\pi$
$179$	−13.2833	−	13.2833i	−0.992843	−	0.992843i	−0.999975	+	0.00713130i	$0.997730\pi$
$180$	−4.22274	−	2.57754i	−0.314745	−	0.192119i
$181$	6.34628	−	6.34628i	0.471715	−	0.471715i	−0.430754	−	0.902469i	$-0.641752\pi$
$181$	6.34628	−	6.34628i	0.471715	−	0.471715i	0.902469	+	0.430754i	$0.141752\pi$
$182$	11.6088	+	9.13519i	0.860503	+	0.677145i
$183$			6.20285i			0.458528i
$184$	−7.49824	+	2.78863i	−0.552777	+	0.205581i
$185$			9.54745i			0.701943i
$186$	−5.73505	+	7.28798i	−0.420514	+	0.534381i
$187$	−3.05275	+	3.05275i	−0.223239	+	0.223239i
$188$	−5.49824	+	1.33019i	−0.401000	+	0.0970142i
$189$	1.80853	+	1.80853i	0.131551	+	0.131551i
$190$	2.66981	+	22.3892i	0.193688	+	1.62428i
$191$	5.60058			0.405243			0.202622	−	0.979257i	$-0.435054\pi$
$191$	5.60058			0.405243			0.202622	+	0.979257i	$0.435054\pi$
$192$	7.97852	+	0.585786i	0.575800	+	0.0422755i
$193$	−19.4514			−1.40014			−0.700071	−	0.714074i	$-0.746848\pi$
$193$	−19.4514			−1.40014			−0.700071	+	0.714074i	$0.746848\pi$
$194$	−2.11882	−	17.7686i	−0.152123	−	1.27571i
$195$	−7.14343	−	7.14343i	−0.511552	−	0.511552i
$196$	−0.891171	+	0.215602i	−0.0636551	+	0.0154001i
$197$	1.23793	−	1.23793i	0.0881988	−	0.0881988i	−0.661631	−	0.749830i	$-0.730135\pi$
$197$	1.23793	−	1.23793i	0.0881988	−	0.0881988i	0.749830	+	0.661631i	$0.230135\pi$
$198$	0.585786	−	0.744406i	0.0416300	−	0.0529026i
$199$			0.993710i			0.0704422i	0.999380	+	0.0352211i	$0.0112135\pi$
$199$			0.993710i			0.0704422i	−0.999380	+	0.0352211i	$0.988786\pi$
$200$	2.96603	−	1.10308i	0.209730	−	0.0779997i
$201$			2.99647i			0.211355i
$202$	−11.8268	−	9.30676i	−0.832134	−	0.654822i
$203$	7.87579	−	7.87579i	0.552772	−	0.552772i
$204$	−11.0031	−	6.71627i	−0.770373	−	0.470233i
$205$	1.37941	+	1.37941i	0.0963422	+	0.0963422i
$206$	−4.68583	+	0.558763i	−0.326477	+	0.0389309i
$207$	−2.82843			−0.196589
$208$	15.5541	+	4.99371i	1.07848	+	0.346251i
$209$	−4.31724			−0.298630
$210$	−8.88431	+	1.05941i	−0.613076	+	0.0731064i
$211$	4.22432	+	4.22432i	0.290814	+	0.290814i	0.837402	−	0.546588i	$-0.184073\pi$
$211$	4.22432	+	4.22432i	0.290814	+	0.290814i	−0.546588	+	0.837402i	$0.684073\pi$
$212$	3.79834	−	6.22274i	0.260871	−	0.427380i
$213$	−3.61706	+	3.61706i	−0.247837	+	0.247837i
$214$	22.1023	+	17.3927i	1.51088	+	1.18894i
$215$			1.36293i			0.0929509i
$216$	2.57172	+	1.17740i	0.174983	+	0.0801120i
$217$			16.7721i			1.13857i
$218$	3.42475	−	4.35211i	0.231954	−	0.294762i
$219$	−10.4455	+	10.4455i	−0.705841	+	0.705841i
$220$	0.779208	+	3.22079i	0.0525342	+	0.217146i
$221$	−18.6135	−	18.6135i	−1.25208	−	1.25208i
$222$	−0.646314	−	5.42004i	−0.0433778	−	0.363769i
$223$	−23.7659			−1.59148			−0.795740	−	0.605639i	$-0.792918\pi$
$223$	−23.7659			−1.59148			−0.795740	+	0.605639i	$0.792918\pi$
$224$	11.9946	−	8.09069i	0.801424	−	0.540582i
$225$	1.11882			0.0745883
$226$	−0.374699	−	3.14225i	−0.0249246	−	0.209019i
$227$	−0.641669	−	0.641669i	−0.0425891	−	0.0425891i	0.685492	−	0.728081i	$-0.259587\pi$
$227$	−0.641669	−	0.641669i	−0.0425891	−	0.0425891i	−0.728081	+	0.685492i	$0.759587\pi$
$228$	−3.03127	−	12.5295i	−0.200751	−	0.829787i
$229$	5.34275	−	5.34275i	0.353059	−	0.353059i	−0.508188	−	0.861246i	$-0.669684\pi$
$229$	5.34275	−	5.34275i	0.353059	−	0.353059i	0.861246	+	0.508188i	$0.169684\pi$
$230$	6.11882	−	7.77568i	0.403463	−	0.512713i
$231$		−	1.71313i		−	0.112716i
$232$	5.12735	−	11.1993i	0.336627	−	0.735271i
$233$		−	23.2271i		−	1.52166i	−0.648954	−	0.760828i	$-0.724793\pi$
$233$		−	23.2271i		−	1.52166i	0.648954	−	0.760828i	$-0.275207\pi$
$234$	4.53887	+	3.57172i	0.296715	+	0.233490i
$235$	4.94725	−	4.94725i	0.322723	−	0.322723i
$236$	−5.89450	+	9.65685i	−0.383699	+	0.628608i
$237$	4.46891	+	4.46891i	0.290287	+	0.290287i
$238$	−23.1497	+	2.76049i	−1.50057	+	0.178936i
$239$	26.9213			1.74140			0.870698	−	0.491817i	$-0.163667\pi$
$239$	26.9213			1.74140			0.870698	+	0.491817i	$0.163667\pi$
$240$	−8.80029	+	4.52284i	−0.568056	+	0.291948i
$241$	−10.3494			−0.666664			−0.333332	−	0.942809i	$-0.608173\pi$
$241$	−10.3494			−0.666664			−0.333332	+	0.942809i	$0.608173\pi$
$242$	14.8169	−	1.76685i	0.952466	−	0.113577i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	10.5889	+	6.46343i	0.677886	+	0.413779i
$245$	0.801866	−	0.801866i	0.0512293	−	0.0512293i
$246$	−0.876464	−	0.689705i	−0.0558813	−	0.0439740i
$247$		−	26.3235i		−	1.67492i
$248$	6.46538	+	17.3845i	0.410552	+	1.10392i
$249$		−	0.907457i		−	0.0575077i
$250$	8.39627	−	10.6698i	0.531027	−	0.674818i
$251$	−9.75696	+	9.75696i	−0.615854	+	0.615854i	−0.944465	−	0.328611i	$-0.893419\pi$
$251$	−9.75696	+	9.75696i	−0.615854	+	0.615854i	0.328611	+	0.944465i	$0.393419\pi$
$252$	4.97186	−	1.20285i	0.313198	−	0.0757722i
$253$	1.33962	+	1.33962i	0.0842209	+	0.0842209i
$254$	−2.04534	−	17.1524i	−0.128336	−	1.07624i
$255$	15.9437			0.998435
$256$	9.31371	−	13.0098i	0.582107	−	0.813112i
$257$	16.9965			1.06021			0.530105	−	0.847932i	$-0.322152\pi$
$257$	16.9965			1.06021			0.530105	+	0.847932i	$0.322152\pi$
$258$	−0.0922633	−	0.773727i	−0.00574406	−	0.0481701i
$259$	−6.98038	−	6.98038i	−0.433740	−	0.433740i
$260$	−19.6381	+	4.75107i	−1.21791	+	0.294649i
$261$	3.07931	−	3.07931i	0.190604	−	0.190604i
$262$	−4.66981	+	5.93430i	−0.288502	+	0.366622i
$263$			29.9929i			1.84944i	0.380643	+	0.924722i	$0.375703\pi$
$263$			29.9929i			1.84944i	−0.380643	+	0.924722i	$0.624297\pi$
$264$	−0.660384	−	1.77568i	−0.0406438	−	0.109285i
$265$			9.01686i			0.553901i
$266$	−18.3213	−	14.4173i	−1.12335	−	0.883984i
$267$	4.46696	−	4.46696i	0.273374	−	0.273374i
$268$	5.11529	+	3.12235i	0.312466	+	0.190728i
$269$	20.6003	+	20.6003i	1.25602	+	1.25602i	0.952976	+	0.303046i	$0.0980037\pi$
$269$	20.6003	+	20.6003i	1.25602	+	1.25602i	0.303046	+	0.952976i	$0.401996\pi$
$270$	−3.47363	+	0.414214i	−0.211398	+	0.0252082i
$271$	−26.6506			−1.61891			−0.809453	−	0.587184i	$-0.800236\pi$
$271$	−26.6506			−1.61891			−0.809453	+	0.587184i	$0.800236\pi$
$272$	−22.9308	+	11.7851i	−1.39038	+	0.714577i
$273$	10.4455			0.632190
$274$	−7.16999	+	0.854988i	−0.433155	+	0.0516517i
$275$	−0.529904	−	0.529904i	−0.0319544	−	0.0319544i
$276$	−2.94725	+	4.82843i	−0.177404	+	0.290637i
$277$	12.1220	−	12.1220i	0.728338	−	0.728338i	−0.241951	−	0.970289i	$-0.577787\pi$
$277$	12.1220	−	12.1220i	0.728338	−	0.728338i	0.970289	+	0.241951i	$0.0777872\pi$
$278$	−18.5080	−	14.5643i	−1.11004	−	0.873509i
$279$			6.55765i			0.392596i
$280$	−7.44902	+	16.2704i	−0.445164	+	0.972341i
$281$		−	2.76588i		−	0.164999i	−0.996591	−	0.0824993i	$-0.973710\pi$
$281$		−	2.76588i		−	0.164999i	0.996591	−	0.0824993i	$-0.0262902\pi$
$282$	−2.47363	+	3.14343i	−0.147302	+	0.187189i
$283$	4.48528	−	4.48528i	0.266622	−	0.266622i	−0.561115	−	0.827738i	$-0.689628\pi$
$283$	4.48528	−	4.48528i	0.266622	−	0.266622i	0.827738	+	0.561115i	$0.189628\pi$
$284$	2.40569	+	9.94372i	0.142752	+	0.590051i
$285$	11.2739	+	11.2739i	0.667809	+	0.667809i
$286$	−0.458067	−	3.84138i	−0.0270860	−	0.227146i
$287$	−2.01704			−0.119062
$288$	4.68971	−	3.16333i	0.276344	−	0.186401i
$289$	24.5443			1.44378
$290$	1.80382	+	15.1270i	0.105924	+	0.888285i
$291$	−8.94725	−	8.94725i	−0.524497	−	0.524497i
$292$	6.94725	+	28.7159i	0.406557	+	1.68047i
$293$	−8.20793	+	8.20793i	−0.479512	+	0.479512i	−0.904976	−	0.425463i	$-0.860111\pi$
$293$	−8.20793	+	8.20793i	−0.479512	+	0.479512i	0.425463	+	0.904976i	$0.360111\pi$
$294$	−0.400933	+	0.509498i	−0.0233829	+	0.0297145i
$295$		−	13.9929i		−	0.814700i
$296$	−9.92606	−	4.54441i	−0.576940	−	0.264139i
$297$		−	0.669808i		−	0.0388662i
$298$	12.4287	+	9.78039i	0.719977	+	0.566563i
$299$	−8.16804	+	8.16804i	−0.472370	+	0.472370i
$300$	1.16583	−	1.90995i	0.0673091	−	0.110271i
$301$	−0.996470	−	0.996470i	−0.0574356	−	0.0574356i
$302$	20.5733	−	2.45327i	1.18386	−	0.141170i
$303$	−10.6417			−0.611348
$304$	−24.5478	−	7.88118i	−1.40791	−	0.452016i
$305$	−15.3435			−0.878567
$306$	−9.05117	+	1.07931i	−0.517421	+	0.0617000i
$307$	10.4549	+	10.4549i	0.596693	+	0.596693i	0.939431	−	0.342738i	$-0.111354\pi$
$307$	10.4549	+	10.4549i	0.596693	+	0.596693i	−0.342738	+	0.939431i	$0.611354\pi$
$308$	−2.92450	−	1.78510i	−0.166639	−	0.101716i
$309$	−2.35951	+	2.35951i	−0.134228	+	0.134228i
$310$	−18.0277	−	14.1864i	−1.02391	−	0.805731i
$311$		−	15.0761i		−	0.854885i	−0.904043	−	0.427442i	$-0.859415\pi$
$311$		−	15.0761i		−	0.854885i	0.904043	−	0.427442i	$-0.140585\pi$
$312$	10.8268	−	4.02656i	0.612950	−	0.227959i
$313$		−	23.0027i		−	1.30019i	−0.759852	−	0.650096i	$-0.774729\pi$
$313$		−	23.0027i		−	1.30019i	0.759852	−	0.650096i	$-0.225271\pi$
$314$	−3.89838	+	4.95398i	−0.219998	+	0.279569i
$315$	−4.47363	+	4.47363i	−0.252060	+	0.252060i
$316$	12.2856	−	2.97226i	0.691117	−	0.167203i
$317$	−6.75892	−	6.75892i	−0.379618	−	0.379618i	0.491346	−	0.870964i	$-0.336505\pi$
$317$	−6.75892	−	6.75892i	−0.379618	−	0.379618i	−0.870964	+	0.491346i	$0.836505\pi$
$318$	−0.610396	−	5.11882i	−0.0342293	−	0.287049i
$319$	−2.91688			−0.163314
$320$	−1.44902	+	19.7359i	−0.0810025	+	1.10327i
$321$	19.8874			1.11001
$322$	1.21137	+	10.1586i	0.0675069	+	0.566118i
$323$	29.3763	+	29.3763i	1.63454	+	1.63454i
$324$	1.94392	−	0.470294i	0.107996	−	0.0261274i
$325$	3.23099	−	3.23099i	0.179223	−	0.179223i
$326$	6.80853	−	8.65214i	0.377090	−	0.479198i
$327$		−	3.91598i		−	0.216554i
$328$	−2.09069	+	0.777537i	−0.115439	+	0.0429323i
$329$			7.23412i			0.398830i
$330$	1.84138	+	1.44902i	0.101365	+	0.0797657i
$331$	−19.6631	+	19.6631i	−1.08078	+	1.08078i	−0.0843464	+	0.996436i	$0.526880\pi$
$331$	−19.6631	+	19.6631i	−1.08078	+	1.08078i	−0.996436	+	0.0843464i	$0.973120\pi$
$332$	−1.54913	−	0.945580i	−0.0850193	−	0.0518954i
$333$	−2.72922	−	2.72922i	−0.149560	−	0.149560i
$334$	28.3400	−	3.37941i	1.55070	−	0.184913i
$335$	−7.41215			−0.404969
$336$	3.12735	−	9.74088i	0.170611	−	0.531408i
$337$	3.00980			0.163954			0.0819771	−	0.996634i	$-0.473877\pi$
$337$	3.00980			0.163954			0.0819771	+	0.996634i	$0.473877\pi$
$338$	5.16662	−	0.616095i	0.281027	−	0.0335111i
$339$	−1.58226	−	1.58226i	−0.0859364	−	0.0859364i
$340$	16.6135	−	27.2176i	0.900995	−	1.47608i
$341$	3.10587	−	3.10587i	0.168192	−	0.168192i
$342$	−7.16333	−	5.63696i	−0.387349	−	0.304812i
$343$			19.0761i			1.03001i
$344$	−1.41697	−	0.648728i	−0.0763981	−	0.0349771i
$345$		−	6.99647i		−	0.376677i
$346$	5.38412	−	6.84203i	0.289452	−	0.367830i
$347$	6.27521	−	6.27521i	0.336871	−	0.336871i	−0.518317	−	0.855188i	$-0.673441\pi$
$347$	6.27521	−	6.27521i	0.336871	−	0.336871i	0.855188	+	0.518317i	$0.173441\pi$
$348$	−2.04804	−	8.46538i	−0.109786	−	0.453792i
$349$	−4.74255	−	4.74255i	−0.253863	−	0.253863i	0.568690	−	0.822552i	$-0.307451\pi$
$349$	−4.74255	−	4.74255i	−0.253863	−	0.253863i	−0.822552	+	0.568690i	$0.807451\pi$
$350$	−0.479174	−	4.01839i	−0.0256129	−	0.214792i
$351$	4.08402			0.217989
$352$	−3.71940	−	0.722930i	−0.198245	−	0.0385323i
$353$	−8.75882			−0.466185			−0.233093	−	0.972455i	$-0.574884\pi$
$353$	−8.75882			−0.466185			−0.233093	+	0.972455i	$0.574884\pi$
$354$	0.947252	+	7.94372i	0.0503459	+	0.422204i
$355$	−8.94725	−	8.94725i	−0.474871	−	0.474871i
$356$	−2.97096	−	12.2802i	−0.157460	−	0.650849i
$357$	−11.6569	+	11.6569i	−0.616946	+	0.616946i
$358$	−16.4290	+	20.8776i	−0.868300	+	1.10342i
$359$		−	32.7917i		−	1.73068i	−0.501184	−	0.865341i	$-0.667102\pi$
$359$		−	32.7917i		−	1.73068i	0.501184	−	0.865341i	$-0.332898\pi$
$360$	−2.91245	+	6.36147i	−0.153500	+	0.335279i
$361$			22.5443i			1.18654i
$362$	−9.97455	−	7.84916i	−0.524251	−	0.412543i
$363$	7.46094	−	7.46094i	0.391598	−	0.391598i
$364$	10.8843	−	17.8316i	0.570493	−	0.934628i
$365$	−25.8382	−	25.8382i	−1.35243	−	1.35243i
$366$	8.71044	−	1.03868i	0.455302	−	0.0542926i
$367$	20.6435			1.07758			0.538791	−	0.842439i	$-0.318881\pi$
$367$	20.6435			1.07758			0.538791	+	0.842439i	$0.318881\pi$
$368$	5.17157	+	10.0625i	0.269587	+	0.524546i
$369$	−0.788632			−0.0410546
$370$	13.4072	−	1.59874i	0.697005	−	0.0831145i
$371$	−6.59245	−	6.59245i	−0.342263	−	0.342263i
$372$	11.1946	+	6.83314i	0.580413	+	0.354282i
$373$	−16.6167	+	16.6167i	−0.860378	+	0.860378i	−0.991382	−	0.131004i	$-0.958180\pi$
$373$	−16.6167	+	16.6167i	−0.860378	+	0.860378i	0.131004	+	0.991382i	$0.458180\pi$
$374$	4.79806	+	3.77568i	0.248102	+	0.195236i
$375$		−	9.60058i		−	0.495772i
$376$	2.78863	+	7.49824i	0.143813	+	0.386692i
$377$		−	17.7851i		−	0.915979i
$378$	2.23681	−	2.84250i	0.115049	−	0.146202i
$379$	7.77844	−	7.77844i	0.399552	−	0.399552i	−0.478523	−	0.878075i	$-0.658828\pi$
$379$	7.77844	−	7.77844i	0.399552	−	0.399552i	0.878075	+	0.478523i	$0.158828\pi$
$380$	30.9933	−	7.49824i	1.58992	−	0.384651i
$381$	−8.63696	−	8.63696i	−0.442485	−	0.442485i
$382$	−0.937828	−	7.86469i	−0.0479834	−	0.402393i
$383$	−17.2037			−0.879070			−0.439535	−	0.898225i	$-0.644857\pi$
$383$	−17.2037			−0.879070			−0.439535	+	0.898225i	$0.644857\pi$
$384$	−0.513421	−	11.3021i	−0.0262004	−	0.576755i
$385$	4.23765			0.215971
$386$	3.25717	+	27.3149i	0.165786	+	1.39029i
$387$	−0.389604	−	0.389604i	−0.0198047	−	0.0198047i
$388$	−24.5970	+	5.95078i	−1.24873	+	0.302105i
$389$	−23.8515	+	23.8515i	−1.20932	+	1.20932i	−0.238069	+	0.971248i	$0.576514\pi$
$389$	−23.8515	+	23.8515i	−1.20932	+	1.20932i	−0.971248	+	0.238069i	$0.923486\pi$
$390$	−8.83509	+	11.2275i	−0.447382	+	0.568524i
$391$		−	18.2306i		−	0.921961i
$392$	0.451990	+	1.21534i	0.0228290	+	0.0613838i
$393$			5.33962i			0.269348i
$394$	−1.94567	−	1.53109i	−0.0980216	−	0.0771350i
$395$	−11.0544	+	11.0544i	−0.556208	+	0.556208i
$396$	−1.14343	−	0.697947i	−0.0574597	−	0.0350732i
$397$	−10.2673	−	10.2673i	−0.515299	−	0.515299i	0.400847	−	0.916145i	$-0.368716\pi$
$397$	−10.2673	−	10.2673i	−0.515299	−	0.515299i	−0.916145	+	0.400847i	$0.868716\pi$
$398$	1.39543	−	0.166399i	0.0699467	−	0.00834081i
$399$	−16.4853			−0.825296
$400$	−2.04569	−	3.98038i	−0.102284	−	0.199019i
$401$	32.2274			1.60936			0.804681	−	0.593708i	$-0.202337\pi$
$401$	32.2274			1.60936			0.804681	+	0.593708i	$0.202337\pi$
$402$	4.20784	−	0.501765i	0.209868	−	0.0250258i
$403$	18.9374	+	18.9374i	0.943341	+	0.943341i
$404$	−11.0887	+	18.1665i	−0.551685	+	0.903815i
$405$	−1.74912	+	1.74912i	−0.0869143	+	0.0869143i
$406$	−12.3785	−	9.74088i	−0.614335	−	0.483432i
$407$			2.58526i			0.128146i
$408$	−7.58892	+	16.5760i	−0.375708	+	0.820633i
$409$			11.5702i			0.572110i	0.958213	+	0.286055i	$0.0923440\pi$
$409$			11.5702i			0.572110i	−0.958213	+	0.286055i	$0.907656\pi$
$410$	1.70607	−	2.16804i	0.0842569	−	0.107072i
$411$	−3.61040	+	3.61040i	−0.178088	+	0.178088i
$412$	1.56930	+	6.48658i	0.0773140	+	0.319571i
$413$	10.2306	+	10.2306i	0.503414	+	0.503414i
$414$	0.473626	+	3.97186i	0.0232774	+	0.195206i
$415$	2.24471			0.110188
$416$	4.40792	−	22.6783i	0.216116	−	1.11190i
$417$	−16.6533			−0.815517
$418$	0.722930	+	6.06255i	0.0353597	+	0.296529i
$419$	6.74717	+	6.74717i	0.329621	+	0.329621i	0.852442	−	0.522822i	$-0.175121\pi$
$419$	6.74717	+	6.74717i	0.329621	+	0.329621i	−0.522822	+	0.852442i	$0.675121\pi$
$420$	2.97539	+	12.2985i	0.145184	+	0.600106i
$421$	−17.2239	+	17.2239i	−0.839443	+	0.839443i	−0.988785	−	0.149343i	$-0.952284\pi$
$421$	−17.2239	+	17.2239i	−0.839443	+	0.839443i	0.149343	+	0.988785i	$0.452284\pi$
$422$	5.22470	−	6.63944i	0.254334	−	0.323203i
$423$			2.82843i			0.137523i
$424$	−9.37442	−	4.29186i	−0.455262	−	0.208431i
$425$			7.21137i			0.349803i
$426$	5.68499	+	4.47363i	0.275439	+	0.216748i
$427$	11.2180	−	11.2180i	0.542879	−	0.542879i
$428$	20.7229	−	33.9500i	1.00168	−	1.64103i
$429$	−1.93430	−	1.93430i	−0.0933888	−	0.0933888i
$430$	1.91391	−	0.228225i	0.0922970	−	0.0110060i
$431$	40.7088			1.96087			0.980437	−	0.196832i	$-0.0630654\pi$
$431$	40.7088			1.96087			0.980437	+	0.196832i	$0.0630654\pi$
$432$	1.22274	−	3.80853i	0.0588293	−	0.183238i
$433$	7.31371			0.351474			0.175737	−	0.984437i	$-0.443769\pi$
$433$	7.31371			0.351474			0.175737	+	0.984437i	$0.443769\pi$
$434$	23.5525	−	2.80853i	1.13056	−	0.134814i
$435$	7.61706	+	7.61706i	0.365210	+	0.365210i
$436$	−6.68499	−	4.08049i	−0.320153	−	0.195420i
$437$	12.8910	−	12.8910i	0.616659	−	0.616659i
$438$	16.4173	+	12.9191i	0.784451	+	0.617299i
$439$			17.7122i			0.845356i	0.906280	+	0.422678i	$0.138910\pi$
$439$			17.7122i			0.845356i	−0.906280	+	0.422678i	$0.861090\pi$
$440$	4.39236	−	1.63354i	0.209398	−	0.0778761i
$441$			0.458440i			0.0218305i
$442$	−23.0215	+	29.2552i	−1.09502	+	1.39153i
$443$	15.6944	−	15.6944i	0.745664	−	0.745664i	−0.227997	−	0.973662i	$-0.573218\pi$
$443$	15.6944	−	15.6944i	0.745664	−	0.745664i	0.973662	+	0.227997i	$0.0732178\pi$
$444$	−7.50295	+	1.81519i	−0.356074	+	0.0861453i
$445$	11.0496	+	11.0496i	0.523801	+	0.523801i
$446$	3.97964	+	33.3736i	0.188441	+	1.58028i
$447$	11.1832			0.528949
$448$	−13.3700	−	15.4888i	−0.631673	−	0.731778i
$449$	−28.3400			−1.33745			−0.668723	−	0.743511i	$-0.733159\pi$
$449$	−28.3400			−1.33745			−0.668723	+	0.743511i	$0.733159\pi$
$450$	−0.187349	−	1.57113i	−0.00883173	−	0.0740636i
$451$	0.373517	+	0.373517i	0.0175882	+	0.0175882i
$452$	−4.34981	+	1.05235i	−0.204598	+	0.0494985i
$453$	10.3595	−	10.3595i	0.486732	−	0.486732i
$454$	−0.793624	+	1.00852i	−0.0372466	+	0.0473323i
$455$			25.8382i			1.21131i
$456$	−17.0872	+	6.35480i	−0.800179	+	0.297591i
$457$		−	17.3396i		−	0.811113i	−0.914070	−	0.405557i	$-0.867078\pi$
$457$		−	17.3396i		−	0.811113i	0.914070	−	0.405557i	$-0.132922\pi$
$458$	−8.39729	−	6.60798i	−0.392380	−	0.308771i
$459$	−4.55765	+	4.55765i	−0.212733	+	0.212733i
$460$	−11.9437	−	7.29040i	−0.556879	−	0.339917i
$461$	−1.69284	−	1.69284i	−0.0788434	−	0.0788434i	0.666585	−	0.745429i	$-0.267755\pi$
$461$	−1.69284	−	1.69284i	−0.0788434	−	0.0788434i	−0.745429	+	0.666585i	$0.767755\pi$
$462$	−2.40569	+	0.286867i	−0.111923	+	0.0133463i
$463$	2.70238			0.125590			0.0627951	−	0.998026i	$-0.479999\pi$
$463$	2.70238			0.125590			0.0627951	+	0.998026i	$0.479999\pi$
$464$	−16.5854	−	5.32480i	−0.769957	−	0.247198i
$465$	−16.2212			−0.752239
$466$	−32.6169	+	3.88942i	−1.51095	+	0.180174i
$467$	−17.1136	−	17.1136i	−0.791924	−	0.791924i	0.189883	−	0.981807i	$-0.439189\pi$
$467$	−17.1136	−	17.1136i	−0.791924	−	0.791924i	−0.981807	+	0.189883i	$0.939189\pi$
$468$	4.25559	−	6.97186i	0.196715	−	0.322274i
$469$	5.41921	−	5.41921i	0.250236	−	0.250236i
$470$	−7.77568	−	6.11882i	−0.358665	−	0.282240i
$471$			4.45754i			0.205393i
$472$	14.5478	+	6.66038i	0.669618	+	0.306569i
$473$			0.369053i			0.0169691i
$474$	5.52721	−	7.02387i	0.253873	−	0.322617i
$475$	−5.09921	+	5.09921i	−0.233968	+	0.233968i
$476$	7.75293	+	32.0461i	0.355355	+	1.46883i
$477$	−2.57754	−	2.57754i	−0.118018	−	0.118018i
$478$	−4.50803	−	37.8047i	−0.206193	−	1.72915i
$479$	−22.2251			−1.01549			−0.507745	−	0.861508i	$-0.669521\pi$
$479$	−22.2251			−1.01549			−0.507745	+	0.861508i	$0.669521\pi$
$480$	7.82490	+	11.6006i	0.357156	+	0.529491i
$481$	−15.7631			−0.718735
$482$	1.73303	+	14.5333i	0.0789373	+	0.661974i
$483$	5.11529	+	5.11529i	0.232754	+	0.232754i
$484$	−4.96224	−	20.5110i	−0.225556	−	0.932318i
$485$	22.1322	−	22.1322i	1.00497	−	1.00497i
$486$	0.874559	−	1.11137i	0.0396708	−	0.0504128i
$487$		−	13.9839i		−	0.633672i	−0.948480	−	0.316836i	$-0.897380\pi$
$487$		−	13.9839i		−	0.633672i	0.948480	−	0.316836i	$-0.102620\pi$
$488$	7.30324	−	15.9520i	0.330602	−	0.722111i
$489$		−	7.78510i		−	0.352055i
$490$	−1.26031	−	0.991758i	−0.0569348	−	0.0448031i
$491$	7.23412	−	7.23412i	0.326471	−	0.326471i	−0.524772	−	0.851243i	$-0.675849\pi$
$491$	7.23412	−	7.23412i	0.326471	−	0.326471i	0.851243	+	0.524772i	$0.175849\pi$
$492$	−0.821763	+	1.34628i	−0.0370480	+	0.0606950i
$493$	19.8476	+	19.8476i	0.893893	+	0.893893i
$494$	−36.9652	+	4.40792i	−1.66314	+	0.198322i
$495$	1.65685			0.0744701
$496$	23.3298	−	11.9902i	1.04754	−	0.538375i
$497$	13.0831			0.586858
$498$	−1.27431	+	0.151955i	−0.0571032	+	0.00680929i
$499$	2.59078	+	2.59078i	0.115979	+	0.115979i	0.762715	−	0.646735i	$-0.223866\pi$
$499$	2.59078	+	2.59078i	0.115979	+	0.115979i	−0.646735	+	0.762715i	$0.723866\pi$
$500$	−16.3892	−	10.0039i	−0.732948	−	0.447388i
$501$	14.2704	−	14.2704i	0.637554	−	0.637554i
$502$	15.3352	+	12.0675i	0.684443	+	0.538601i
$503$		−	39.6443i		−	1.76765i	−0.467817	−	0.883825i	$-0.654959\pi$
$503$		−	39.6443i		−	1.76765i	0.467817	−	0.883825i	$-0.345041\pi$
$504$	−2.52166	−	6.78039i	−0.112324	−	0.302023i
$505$		−	26.3235i		−	1.17138i
$506$	1.65685	−	2.10550i	0.0736562	−	0.0936008i
$507$	2.60161	−	2.60161i	0.115542	−	0.115542i
$508$	−23.7440	+	5.74441i	−1.05347	+	0.254867i
$509$	20.2875	+	20.2875i	0.899229	+	0.899229i	0.995368	−	0.0961393i	$-0.0306494\pi$
$509$	20.2875	+	20.2875i	0.899229	+	0.899229i	−0.0961393	+	0.995368i	$0.530649\pi$
$510$	−2.66981	−	22.3892i	−0.118221	−	0.991411i
$511$	37.7819			1.67137
$512$	−19.8288	−	10.9004i	−0.876317	−	0.481734i
$513$	−6.44549			−0.284575
$514$	−2.84609	−	23.8675i	−0.125536	−	1.05275i
$515$	−5.83655	−	5.83655i	−0.257189	−	0.257189i
$516$	−1.07107	+	0.259124i	−0.0471511	+	0.0114073i
$517$	1.33962	−	1.33962i	0.0589162	−	0.0589162i
$518$	−8.63343	+	10.9712i	−0.379331	+	0.482046i
$519$		−	6.15639i		−	0.270235i
$520$	9.96021	+	26.7816i	0.436784	+	1.17445i
$521$			23.1784i			1.01546i	0.861515	+	0.507732i	$0.169516\pi$
$521$			23.1784i			1.01546i	−0.861515	+	0.507732i	$0.830484\pi$
$522$	−4.83980	−	3.80853i	−0.211832	−	0.166695i
$523$	−5.78550	+	5.78550i	−0.252982	+	0.252982i	−0.822192	−	0.569210i	$-0.807249\pi$
$523$	−5.78550	+	5.78550i	−0.252982	+	0.252982i	0.569210	+	0.822192i	$0.307249\pi$
$524$	9.11529	+	5.56394i	0.398203	+	0.243062i
$525$	−2.02343	−	2.02343i	−0.0883096	−	0.0883096i
$526$	42.1180	−	5.02238i	1.83643	−	0.218986i
$527$	−42.2672			−1.84119
$528$	−2.38294	+	1.22470i	−0.103704	+	0.0532980i
$529$	15.0000			0.652174
$530$	12.6621	−	1.50989i	0.550005	−	0.0655855i
$531$	4.00000	+	4.00000i	0.173585	+	0.173585i
$532$	−17.1778	+	28.1421i	−0.744754	+	1.22012i
$533$	−2.27744	+	2.27744i	−0.0986470	+	0.0986470i
$534$	−7.02080	−	5.52480i	−0.303820	−	0.239081i
$535$			49.1941i			2.12685i
$536$	3.52805	−	7.70607i	0.152388	−	0.332852i
$537$			18.7855i			0.810653i
$538$	25.4787	−	32.3778i	1.09847	−	1.39591i
$539$	0.217129	−	0.217129i	0.00935241	−	0.00935241i
$540$	1.16333	+	4.80853i	0.0500618	+	0.206926i
$541$	4.55175	+	4.55175i	0.195695	+	0.195695i	0.798152	−	0.602457i	$-0.205811\pi$
$541$	4.55175	+	4.55175i	0.195695	+	0.195695i	−0.602457	+	0.798152i	$0.705811\pi$
$542$	4.46269	+	37.4245i	0.191689	+	1.60752i
$543$	−8.97499			−0.385154
$544$	20.3892	+	30.2274i	0.874180	+	1.29599i
$545$	9.68667			0.414931
$546$	−1.74912	−	14.6682i	−0.0748553	−	0.627742i
$547$	−27.7355	−	27.7355i	−1.18588	−	1.18588i	−0.978195	−	0.207689i	$-0.933406\pi$
$547$	−27.7355	−	27.7355i	−1.18588	−	1.18588i	−0.207689	−	0.978195i	$-0.566594\pi$
$548$	2.40126	+	9.92540i	0.102577	+	0.423992i
$549$	4.38607	−	4.38607i	0.187193	−	0.187193i
$550$	−0.655392	+	0.832859i	−0.0279460	+	0.0355132i
$551$			28.0688i			1.19577i
$552$	7.27391	+	3.33019i	0.309598	+	0.141742i
$553$		−	16.1643i		−	0.687377i
$554$	−19.0523	−	14.9926i	−0.809454	−	0.636974i
$555$	6.75107	−	6.75107i	0.286567	−	0.286567i
$556$	−17.3529	+	28.4290i	−0.735929	+	1.20566i
$557$	−1.17538	−	1.17538i	−0.0498026	−	0.0498026i	0.681767	−	0.731569i	$-0.261212\pi$
$557$	−1.17538	−	1.17538i	−0.0498026	−	0.0498026i	−0.731569	+	0.681767i	$0.761212\pi$
$558$	9.20867	−	1.09809i	0.389834	−	0.0464859i
$559$	−2.25023			−0.0951745
$560$	24.0953	+	7.73588i	1.01821	+	0.326901i
$561$	4.31724			0.182274
$562$	−3.88403	+	0.463152i	−0.163838	+	0.0195369i
$563$	−28.7346	−	28.7346i	−1.21102	−	1.21102i	−0.970692	−	0.240326i	$-0.922746\pi$
$563$	−28.7346	−	28.7346i	−1.21102	−	1.21102i	−0.240326	−	0.970692i	$-0.577254\pi$
$564$	4.82843	+	2.94725i	0.203313	+	0.124102i
$565$	3.91391	−	3.91391i	0.164659	−	0.164659i
$566$	−7.04959	−	5.54745i	−0.296316	−	0.233177i
$567$		−	2.55765i		−	0.107411i
$568$	13.5608	−	5.04332i	0.568998	−	0.211613i
$569$			27.0004i			1.13191i	0.824435	+	0.565957i	$0.191493\pi$
$569$			27.0004i			1.13191i	−0.824435	+	0.565957i	$0.808507\pi$
$570$	13.9437	−	17.7194i	0.584038	−	0.742184i
$571$	−14.8284	+	14.8284i	−0.620550	+	0.620550i	−0.945672	−	0.325122i	$-0.894595\pi$
$571$	−14.8284	+	14.8284i	−0.620550	+	0.620550i	0.325122	+	0.945672i	$0.394595\pi$
$572$	−5.31761	+	1.28649i	−0.222341	+	0.0537910i
$573$	−3.96021	−	3.96021i	−0.165440	−	0.165440i
$574$	0.337758	+	2.83246i	0.0140977	+	0.118225i
$575$	3.16451			0.131969
$576$	−5.22746	−	6.05588i	−0.217811	−	0.252328i
$577$	−37.6372			−1.56686			−0.783429	−	0.621481i	$-0.786531\pi$
$577$	−37.6372			−1.56686			−0.783429	+	0.621481i	$0.786531\pi$
$578$	−4.10999	−	34.4667i	−0.170953	−	1.43363i
$579$	13.7542	+	13.7542i	0.571605	+	0.571605i
$580$	20.9402	−	5.06608i	0.869494	−	0.210357i
$581$	−1.64116	+	1.64116i	−0.0680869	+	0.0680869i
$582$	−11.0661	+	14.0625i	−0.458704	+	0.582911i
$583$			2.44158i			0.101120i
$584$	39.1614	−	14.5643i	1.62051	−	0.602675i
$585$			10.1023i			0.417680i
$586$	12.9005	+	10.1517i	0.532917	+	0.419362i
$587$	−31.2574	+	31.2574i	−1.29013	+	1.29013i	−0.355429	+	0.934703i	$0.615665\pi$
$587$	−31.2574	+	31.2574i	−1.29013	+	1.29013i	−0.934703	+	0.355429i	$0.884335\pi$
$588$	0.782607	+	0.477700i	0.0322742	+	0.0197000i
$589$	−29.8874	−	29.8874i	−1.23149	−	1.23149i
$590$	−19.6498	+	2.34315i	−0.808969	+	0.0964658i
$591$	−1.75070			−0.0720140
$592$	−4.71942	+	14.6998i	−0.193967	+	0.604157i
$593$	−3.59611			−0.147675			−0.0738373	−	0.997270i	$-0.523525\pi$
$593$	−3.59611			−0.147675			−0.0738373	+	0.997270i	$0.523525\pi$
$594$	−0.940588	+	0.112161i	−0.0385928	+	0.00460201i
$595$	−28.8347	−	28.8347i	−1.18211	−	1.18211i
$596$	11.6530	−	19.0910i	0.477327	−	0.781996i
$597$	0.702659	−	0.702659i	0.0287579	−	0.0287579i
$598$	12.8379	+	10.1023i	0.524979	+	0.413115i
$599$			22.0296i			0.900104i	0.893002	+	0.450052i	$0.148595\pi$
$599$			22.0296i			0.900104i	−0.893002	+	0.450052i	$0.851405\pi$
$600$	−2.87730	−	1.31730i	−0.117465	−	0.0537787i
$601$		−	10.7721i		−	0.439405i	−0.975567	−	0.219703i	$-0.929491\pi$
$601$		−	10.7721i		−	0.439405i	0.975567	−	0.219703i	$-0.0705087\pi$
$602$	−1.23245	+	1.56617i	−0.0502308	+	0.0638323i
$603$	2.11882	−	2.11882i	0.0862852	−	0.0862852i
$604$	−6.89007	−	28.4795i	−0.280353	−	1.15882i
$605$	18.4556	+	18.4556i	0.750325	+	0.750325i
$606$	1.78197	+	14.9437i	0.0723875	+	0.607047i
$607$	5.47453			0.222204			0.111102	−	0.993809i	$-0.464562\pi$
$607$	5.47453			0.222204			0.111102	+	0.993809i	$0.464562\pi$
$608$	−6.95668	+	35.7914i	−0.282130	+	1.45153i
$609$	−11.1380			−0.451336
$610$	2.56930	+	21.5464i	0.104028	+	0.872387i
$611$	8.16804	+	8.16804i	0.330444	+	0.330444i
$612$	3.03127	+	12.5295i	0.122532	+	0.506475i
$613$	−10.5049	+	10.5049i	−0.424289	+	0.424289i	−0.886677	−	0.462389i	$-0.846993\pi$
$613$	−10.5049	+	10.5049i	−0.424289	+	0.424289i	0.462389	+	0.886677i	$0.346993\pi$
$614$	12.9308	−	16.4322i	0.521843	−	0.663148i
$615$		−	1.95078i		−	0.0786631i
$616$	−2.01704	+	4.40569i	−0.0812690	+	0.177510i
$617$			22.2235i			0.894686i	0.894363	+	0.447343i	$0.147630\pi$
$617$			22.2235i			0.894686i	−0.894363	+	0.447343i	$0.852370\pi$
$618$	3.70849	+	2.91828i	0.149177	+	0.117390i
$619$	11.6398	−	11.6398i	0.467843	−	0.467843i	−0.433372	−	0.901215i	$-0.642676\pi$
$619$	11.6398	−	11.6398i	0.467843	−	0.467843i	0.901215	+	0.433372i	$0.142676\pi$
$620$	−16.9026	+	27.6913i	−0.678826	+	1.11211i
$621$	2.00000	+	2.00000i	0.0802572	+	0.0802572i
$622$	−21.1708	+	2.52452i	−0.848871	+	0.101224i
$623$	−16.1573			−0.647327
$624$	−7.46734	−	14.5295i	−0.298933	−	0.581646i
$625$	29.3424			1.17369
$626$	−32.3019	+	3.85185i	−1.29105	+	0.153951i
$627$	3.05275	+	3.05275i	0.121915	+	0.121915i
$628$	7.60949	+	4.64480i	0.303652	+	0.185348i
$629$	17.5912	−	17.5912i	0.701405	−	0.701405i
$630$	7.03127	+	5.53304i	0.280133	+	0.220442i
$631$		−	4.06977i		−	0.162015i	−0.996713	−	0.0810075i	$-0.974186\pi$
$631$		−	4.06977i		−	0.162015i	0.996713	−	0.0810075i	$-0.0258138\pi$
$632$	−6.23108	−	16.7545i	−0.247859	−	0.666458i
$633$		−	5.97409i		−	0.237449i
$634$	−8.35951	+	10.6231i	−0.331999	+	0.421897i
$635$	21.3646	−	21.3646i	0.847828	−	0.847828i
$636$	−7.08597	+	1.71431i	−0.280977	+	0.0679770i
$637$	1.32390	+	1.32390i	0.0524549	+	0.0524549i
$638$	0.488437	+	4.09607i	0.0193374	+	0.162165i
$639$	5.11529			0.202358
$640$	27.9570	−	1.27001i	1.10510	−	0.0502016i
$641$	−8.41958			−0.332553			−0.166277	−	0.986079i	$-0.553174\pi$
$641$	−8.41958			−0.332553			−0.166277	+	0.986079i	$0.553174\pi$
$642$	−3.33019	−	27.9272i	−0.131432	−	1.10220i
$643$	−7.37275	−	7.37275i	−0.290753	−	0.290753i	0.546625	−	0.837378i	$-0.315912\pi$
$643$	−7.37275	−	7.37275i	−0.290753	−	0.290753i	−0.837378	+	0.546625i	$0.815912\pi$
$644$	14.0625	−	3.40216i	0.554142	−	0.134064i
$645$	0.963735	−	0.963735i	0.0379470	−	0.0379470i
$646$	36.3329	−	46.1712i	1.42950	−	1.81658i
$647$		−	11.6132i		−	0.456560i	−0.973595	−	0.228280i	$-0.926690\pi$
$647$		−	11.6132i		−	0.456560i	0.973595	−	0.228280i	$-0.0733102\pi$
$648$	−0.985930	−	2.65103i	−0.0387310	−	0.104142i
$649$		−	3.78901i		−	0.148731i
$650$	−5.07819	−	3.99612i	−0.199183	−	0.156741i
$651$	11.8597	−	11.8597i	0.464818	−	0.464818i
$652$	−13.2900	−	8.11216i	−0.520477	−	0.317697i
$653$	−1.93049	−	1.93049i	−0.0755458	−	0.0755458i	0.668324	−	0.743870i	$-0.267012\pi$
$653$	−1.93049	−	1.93049i	−0.0755458	−	0.0755458i	−0.743870	+	0.668324i	$0.767012\pi$
$654$	−5.49907	+	0.655738i	−0.215031	+	0.0256414i
$655$	−13.2082			−0.516088
$656$	1.44196	+	2.80568i	0.0562990	+	0.109543i
$657$	14.7721			0.576316
$658$	10.1586	−	1.21137i	0.396024	−	0.0472240i
$659$	22.3102	+	22.3102i	0.869081	+	0.869081i	0.992371	−	0.123290i	$-0.0393444\pi$
$659$	22.3102	+	22.3102i	0.869081	+	0.869081i	−0.123290	+	0.992371i	$0.539344\pi$
$660$	1.72646	−	2.82843i	0.0672024	−	0.110096i
$661$	10.7033	−	10.7033i	0.416311	−	0.416311i	−0.467619	−	0.883930i	$-0.654888\pi$
$661$	10.7033	−	10.7033i	0.416311	−	0.416311i	0.883930	+	0.467619i	$0.154888\pi$
$662$	30.9049	+	24.3196i	1.20115	+	0.945208i
$663$			26.3235i			1.02232i
$664$	−1.06844	+	2.33372i	−0.0414635	+	0.0905660i
$665$		−	40.7784i		−	1.58132i
$666$	−3.37553	+	4.28956i	−0.130799	+	0.166217i
$667$	8.70960	−	8.70960i	0.337237	−	0.337237i
$668$	−9.49118	−	39.2310i	−0.367225	−	1.51789i
$669$	16.8050	+	16.8050i	0.649719	+	0.649719i
$670$	1.24118	+	10.4086i	0.0479509	+	0.402120i
$671$	−4.15472			−0.160391
$672$	−14.2025	−	2.76049i	−0.547871	−	0.106488i
$673$	−20.6345			−0.795401			−0.397700	−	0.917515i	$-0.630192\pi$
$673$	−20.6345			−0.795401			−0.397700	+	0.917515i	$0.630192\pi$
$674$	−0.503997	−	4.22655i	−0.0194132	−	0.162801i
$675$	−0.791128	−	0.791128i	−0.0304505	−	0.0304505i
$676$	−1.73032	−	7.15213i	−0.0665508	−	0.275082i
$677$	26.8246	−	26.8246i	1.03095	−	1.03095i	0.0314484	−	0.999505i	$-0.489988\pi$
$677$	26.8246	−	26.8246i	1.03095	−	1.03095i	0.999505	−	0.0314484i	$-0.0100120\pi$
$678$	−1.95696	+	2.48686i	−0.0751564	+	0.0955073i
$679$			32.3627i			1.24197i
$680$	−41.0027	−	18.7721i	−1.57238	−	0.719879i
$681$			0.907457i			0.0347738i
$682$	−4.88155	−	3.84138i	−0.186924	−	0.147094i
$683$	12.9026	−	12.9026i	0.493705	−	0.493705i	−0.415766	−	0.909472i	$-0.636487\pi$
$683$	12.9026	−	12.9026i	0.493705	−	0.493705i	0.909472	+	0.415766i	$0.136487\pi$
$684$	−6.71627	+	11.0031i	−0.256803	+	0.420715i
$685$	−8.93077	−	8.93077i	−0.341227	−	0.341227i
$686$	26.7878	−	3.19432i	1.02276	−	0.121960i
$687$	−7.55579			−0.288271
$688$	−0.673711	+	2.09844i	−0.0256850	+	0.0800022i
$689$	−14.8871			−0.567152
$690$	−9.82490	+	1.17157i	−0.374027	+	0.0446010i
$691$	−21.3923	−	21.3923i	−0.813803	−	0.813803i	0.171399	−	0.985202i	$-0.445171\pi$
$691$	−21.3923	−	21.3923i	−0.813803	−	0.813803i	−0.985202	+	0.171399i	$0.945171\pi$
$692$	−10.5096	−	6.41502i	−0.399515	−	0.243863i
$693$	−1.21137	+	1.21137i	−0.0460161	+	0.0460161i
$694$	−9.86286	−	7.76126i	−0.374389	−	0.294614i
$695$		−	41.1941i		−	1.56258i
$696$	−11.5447	+	4.29353i	−0.437600	+	0.162746i
$697$		−	5.08312i		−	0.192537i
$698$	−5.86564	+	7.45394i	−0.222018	+	0.282136i
$699$	−16.4240	+	16.4240i	−0.621213	+	0.621213i
$700$	−5.56264	+	1.34577i	−0.210248	+	0.0508655i
$701$	14.2040	+	14.2040i	0.536479	+	0.536479i	0.922493	−	0.386014i	$-0.126148\pi$
$701$	14.2040	+	14.2040i	0.536479	+	0.536479i	−0.386014	+	0.922493i	$0.626148\pi$
$702$	−0.683878	−	5.73505i	−0.0258113	−	0.216455i
$703$	24.8776			0.938278
$704$	−0.392364	+	5.34408i	−0.0147878	+	0.201413i
$705$	−6.99647			−0.263502
$706$	1.46668	+	12.2997i	0.0551993	+	0.462906i
$707$	19.2458	+	19.2458i	0.723812	+	0.723812i
$708$	10.9965	−	2.66038i	0.413273	−	0.0999834i
$709$	−29.5474	+	29.5474i	−1.10968	+	1.10968i	−0.116485	+	0.993192i	$0.537163\pi$
$709$	−29.5474	+	29.5474i	−1.10968	+	1.10968i	−0.993192	+	0.116485i	$0.962837\pi$
$710$	−11.0661	+	14.0625i	−0.415302	+	0.527758i
$711$		−	6.32000i		−	0.237018i
$712$	−16.7472	+	6.22836i	−0.627627	+	0.233418i
$713$			18.5478i			0.694622i
$714$	18.3213	+	14.4173i	0.685656	+	0.539556i
$715$	4.78473	−	4.78473i	0.178939	−	0.178939i
$716$	32.0688	+	19.5747i	1.19847	+	0.731540i
$717$	−19.0363	−	19.0363i	−0.710922	−	0.710922i
$718$	−46.0483	+	5.49104i	−1.71851	+	0.204924i
$719$	28.3683			1.05796			0.528979	−	0.848635i	$-0.322575\pi$
$719$	28.3683			1.05796			0.528979	+	0.848635i	$0.322575\pi$
$720$	9.42088	+	3.02461i	0.351095	+	0.112721i
$721$	8.53450			0.317841
$722$	31.6582	−	3.77509i	1.17819	−	0.140494i
$723$	7.31814	+	7.31814i	0.272165	+	0.272165i
$724$	−9.35204	+	15.3213i	−0.347566	+	0.569411i
$725$	−3.44521	+	3.44521i	−0.127952	+	0.127952i
$726$	−11.7265	−	9.22778i	−0.435210	−	0.342475i
$727$		−	20.4843i		−	0.759722i	−0.925044	−	0.379861i	$-0.875972\pi$
$727$		−	20.4843i		−	0.759722i	0.925044	−	0.379861i	$-0.124028\pi$
$728$	−26.8628	−	12.2985i	−0.995603	−	0.455814i
$729$		−	1.00000i		−	0.0370370i
$730$	−31.9570	+	40.6104i	−1.18278	+	1.50306i
$731$	2.51119	−	2.51119i	0.0928797	−	0.0928797i
$732$	−2.91716	−	12.0578i	−0.107821	−	0.445670i
$733$	33.9961	+	33.9961i	1.25567	+	1.25567i	0.953138	+	0.302536i	$0.0978331\pi$
$733$	33.9961	+	33.9961i	1.25567	+	1.25567i	0.302536	+	0.953138i	$0.402167\pi$
$734$	−3.45680	−	28.9889i	−0.127593	−	1.07000i
$735$	−1.13401			−0.0418286
$736$	13.2645	−	8.94725i	0.488936	−	0.329800i
$737$	−2.00706			−0.0739310
$738$	0.132058	+	1.10745i	0.00486112	+	0.0407658i
$739$	15.1645	+	15.1645i	0.557836	+	0.557836i	0.928691	−	0.370855i	$-0.120935\pi$
$739$	15.1645	+	15.1645i	0.557836	+	0.557836i	−0.370855	+	0.928691i	$0.620935\pi$
$740$	−4.49011	−	18.5595i	−0.165060	−	0.682260i
$741$	−18.6135	+	18.6135i	−0.683785	+	0.683785i
$742$	−8.15363	+	10.3615i	−0.299329	+	0.380381i
$743$		−	2.17431i		−	0.0797677i	−0.999204	−	0.0398839i	$-0.987301\pi$
$743$		−	2.17431i		−	0.0797677i	0.999204	−	0.0398839i	$-0.0126988\pi$
$744$	7.72098	−	16.8644i	0.283065	−	0.618279i
$745$			27.6631i			1.01350i
$746$	26.1167	+	20.5517i	0.956200	+	0.752451i
$747$	−0.641669	+	0.641669i	−0.0234774	+	0.0234774i
$748$	4.49861	−	7.36999i	0.164485	−	0.269473i
$749$	−35.9670	−	35.9670i	−1.31421	−	1.31421i
$750$	−13.4818	+	1.60764i	−0.492284	+	0.0587026i
$751$	29.8980			1.09099			0.545497	−	0.838113i	$-0.316341\pi$
$751$	29.8980			1.09099			0.545497	+	0.838113i	$0.316341\pi$
$752$	10.0625	−	5.17157i	0.366943	−	0.188588i
$753$	13.7984			0.502843
$754$	−24.9750	+	2.97815i	−0.909536	+	0.108458i
$755$	25.6256	+	25.6256i	0.932610	+	0.932610i
$756$	−4.36618	−	2.66510i	−0.158796	−	0.0969286i
$757$	−15.3294	+	15.3294i	−0.557157	+	0.557157i	−0.928497	−	0.371340i	$-0.878899\pi$
$757$	−15.3294	+	15.3294i	−0.557157	+	0.557157i	0.371340	+	0.928497i	$0.378899\pi$
$758$	−12.2255	−	9.62047i	−0.444050	−	0.349431i
$759$		−	1.89450i		−	0.0687661i
$760$	−15.7194	−	42.2672i	−0.570203	−	1.53319i
$761$		−	4.29449i		−	0.155675i	−0.996966	−	0.0778375i	$-0.975198\pi$
$761$		−	4.29449i		−	0.155675i	0.996966	−	0.0778375i	$-0.0248015\pi$
$762$	−10.6823	+	13.5749i	−0.386979	+	0.491765i
$763$	−7.08216	+	7.08216i	−0.256392	+	0.256392i
$764$	−10.8871	+	2.63392i	−0.393880	+	0.0952918i
$765$	−11.2739	−	11.2739i	−0.407609	−	0.407609i
$766$	2.88080	+	24.1586i	0.104088	+	0.872886i
$767$	23.1027			0.834191
$768$	−15.7851	+	2.61353i	−0.569596	+

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	48.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.167452 - 1.40426i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-1.94392 + 0.470294i) q^{4} +(1.74912 - 1.74912i) q^{5} +(-0.874559 + 1.11137i) q^{6} +2.55765i q^{7} +(0.985930 + 2.65103i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.167452 - 1.40426i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-1.94392 + 0.470294i) q^{4} +(1.74912 - 1.74912i) q^{5} +(-0.874559 + 1.11137i) q^{6} +2.55765i q^{7} +(0.985930 + 2.65103i) q^{8} +1.00000i q^{9} +(-2.74912 - 2.16333i) q^{10} +(0.473626 - 0.473626i) q^{11} +(1.70711 + 1.04201i) q^{12} +(2.88784 + 2.88784i) q^{13} +(3.59161 - 0.428283i) q^{14} -2.47363 q^{15} +(3.55765 - 1.82843i) q^{16} -6.44549 q^{17} +(1.40426 - 0.167452i) q^{18} +(-4.55765 - 4.55765i) q^{19} +(-2.57754 + 4.22274i) q^{20} +(1.80853 - 1.80853i) q^{21} +(-0.744406 - 0.585786i) q^{22} +2.82843i q^{23} +(1.17740 - 2.57172i) q^{24} -1.11882i q^{25} +(3.57172 - 4.53887i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.20285 - 4.97186i) q^{28} +(-3.07931 - 3.07931i) q^{29} +(0.414214 + 3.47363i) q^{30} +6.55765 q^{31} +(-3.16333 - 4.68971i) q^{32} -0.669808 q^{33} +(1.07931 + 9.05117i) q^{34} +(4.47363 + 4.47363i) q^{35} +(-0.470294 - 1.94392i) q^{36} +(-2.72922 + 2.72922i) q^{37} +(-5.63696 + 7.16333i) q^{38} -4.08402i q^{39} +(6.36147 + 2.91245i) q^{40} +0.788632i q^{41} +(-2.84250 - 2.23681i) q^{42} +(-0.389604 + 0.389604i) q^{43} +(-0.697947 + 1.14343i) q^{44} +(1.74912 + 1.74912i) q^{45} +(3.97186 - 0.473626i) q^{46} +2.82843 q^{47} +(-3.80853 - 1.22274i) q^{48} +0.458440 q^{49} +(-1.57113 + 0.187349i) q^{50} +(4.55765 + 4.55765i) q^{51} +(-6.97186 - 4.25559i) q^{52} +(-2.57754 + 2.57754i) q^{53} +(-1.11137 - 0.874559i) q^{54} -1.65685i q^{55} +(-6.78039 + 2.52166i) q^{56} +6.44549i q^{57} +(-3.80853 + 4.83980i) q^{58} +(4.00000 - 4.00000i) q^{59} +(4.80853 - 1.16333i) q^{60} +(-4.38607 - 4.38607i) q^{61} +(-1.09809 - 9.20867i) q^{62} -2.55765 q^{63} +(-6.05588 + 5.22746i) q^{64} +10.1023 q^{65} +(0.112161 + 0.940588i) q^{66} +(-2.11882 - 2.11882i) q^{67} +(12.5295 - 3.03127i) q^{68} +(2.00000 - 2.00000i) q^{69} +(5.53304 - 7.03127i) q^{70} -5.11529i q^{71} +(-2.65103 + 0.985930i) q^{72} -14.7721i q^{73} +(4.28956 + 3.37553i) q^{74} +(-0.791128 + 0.791128i) q^{75} +(11.0031 + 6.71627i) q^{76} +(1.21137 + 1.21137i) q^{77} +(-5.73505 + 0.683878i) q^{78} -6.32000 q^{79} +(3.02461 - 9.42088i) q^{80} -1.00000 q^{81} +(1.10745 - 0.132058i) q^{82} +(0.641669 + 0.641669i) q^{83} +(-2.66510 + 4.36618i) q^{84} +(-11.2739 + 11.2739i) q^{85} +(0.612348 + 0.481868i) q^{86} +4.35480i q^{87} +(1.72256 + 0.788632i) q^{88} +6.31724i q^{89} +(2.16333 - 2.74912i) q^{90} +(-7.38607 + 7.38607i) q^{91} +(-1.33019 - 5.49824i) q^{92} +(-4.63696 - 4.63696i) q^{93} +(-0.473626 - 3.97186i) q^{94} -15.9437 q^{95} +(-1.07931 + 5.55294i) q^{96} +12.6533 q^{97} +(-0.0767667 - 0.643772i) q^{98} +(0.473626 + 0.473626i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4} - 12 q^{8}+O(q^{10}) \) 8 * q - 4 * q^4 - 12 * q^8	\( 8 q - 4 q^{4} - 12 q^{8} - 8 q^{10} - 8 q^{11} + 8 q^{12} + 12 q^{14} - 8 q^{15} + 4 q^{18} - 8 q^{19} + 16 q^{20} + 4 q^{24} + 20 q^{26} + 8 q^{28} - 16 q^{29} - 8 q^{30} + 24 q^{31} + 24 q^{35} - 4 q^{36} - 16 q^{37} - 8 q^{38} + 16 q^{40} - 20 q^{42} - 8 q^{43} - 40 q^{44} - 8 q^{46} - 16 q^{48} - 8 q^{49} - 36 q^{50} + 8 q^{51} - 16 q^{52} + 16 q^{53} + 4 q^{54} - 16 q^{58} + 32 q^{59} + 24 q^{60} + 16 q^{61} - 12 q^{62} + 8 q^{63} + 8 q^{64} - 16 q^{65} + 24 q^{66} - 16 q^{67} + 32 q^{68} + 16 q^{69} + 32 q^{70} - 4 q^{72} + 52 q^{74} + 16 q^{75} + 8 q^{76} + 16 q^{77} - 12 q^{78} - 24 q^{79} + 8 q^{80} - 8 q^{81} + 40 q^{82} - 40 q^{83} - 24 q^{84} - 16 q^{85} - 16 q^{86} + 32 q^{88} - 8 q^{90} - 8 q^{91} - 16 q^{92} + 8 q^{94} - 48 q^{95} - 40 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 4 * q^4 - 12 * q^8 - 8 * q^10 - 8 * q^11 + 8 * q^12 + 12 * q^14 - 8 * q^15 + 4 * q^18 - 8 * q^19 + 16 * q^20 + 4 * q^24 + 20 * q^26 + 8 * q^28 - 16 * q^29 - 8 * q^30 + 24 * q^31 + 24 * q^35 - 4 * q^36 - 16 * q^37 - 8 * q^38 + 16 * q^40 - 20 * q^42 - 8 * q^43 - 40 * q^44 - 8 * q^46 - 16 * q^48 - 8 * q^49 - 36 * q^50 + 8 * q^51 - 16 * q^52 + 16 * q^53 + 4 * q^54 - 16 * q^58 + 32 * q^59 + 24 * q^60 + 16 * q^61 - 12 * q^62 + 8 * q^63 + 8 * q^64 - 16 * q^65 + 24 * q^66 - 16 * q^67 + 32 * q^68 + 16 * q^69 + 32 * q^70 - 4 * q^72 + 52 * q^74 + 16 * q^75 + 8 * q^76 + 16 * q^77 - 12 * q^78 - 24 * q^79 + 8 * q^80 - 8 * q^81 + 40 * q^82 - 40 * q^83 - 24 * q^84 - 16 * q^85 - 16 * q^86 + 32 * q^88 - 8 * q^90 - 8 * q^91 - 16 * q^92 + 8 * q^94 - 48 * q^95 - 40 * q^98 - 8 * q^99

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