LMFDB - Embedded newform 144.2.k.b.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,2,Mod(37,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("144.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	144.k (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:	$1.14984578911$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.3
Root			$0.500000 + 1.44392i$ of defining polynomial
Character	$\chi$	$=$	144.37
Dual form			144.2.k.b.109.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.167452 - 1.40426i) q^{2} +(-1.94392 - 0.470294i) q^{4} +(-1.74912 - 1.74912i) q^{5} -2.55765i q^{7} +(-0.985930 + 2.65103i) q^{8} +O(q^{10})$	\(q+(0.167452 - 1.40426i) q^{2} +(-1.94392 - 0.470294i) q^{4} +(-1.74912 - 1.74912i) q^{5} -2.55765i q^{7} +(-0.985930 + 2.65103i) q^{8} +(-2.74912 + 2.16333i) q^{10} +(-0.473626 - 0.473626i) q^{11} +(2.88784 - 2.88784i) q^{13} +(-3.59161 - 0.428283i) q^{14} +(3.55765 + 1.82843i) q^{16} +6.44549 q^{17} +(-4.55765 + 4.55765i) q^{19} +(2.57754 + 4.22274i) q^{20} +(-0.744406 + 0.585786i) q^{22} +2.82843i q^{23} +1.11882i q^{25} +(-3.57172 - 4.53887i) q^{26} +(-1.20285 + 4.97186i) q^{28} +(3.07931 - 3.07931i) q^{29} +6.55765 q^{31} +(3.16333 - 4.68971i) q^{32} +(1.07931 - 9.05117i) q^{34} +(-4.47363 + 4.47363i) q^{35} +(-2.72922 - 2.72922i) q^{37} +(5.63696 + 7.16333i) q^{38} +(6.36147 - 2.91245i) q^{40} +0.788632i q^{41} +(-0.389604 - 0.389604i) q^{43} +(0.697947 + 1.14343i) q^{44} +(3.97186 + 0.473626i) q^{46} -2.82843 q^{47} +0.458440 q^{49} +(1.57113 + 0.187349i) q^{50} +(-6.97186 + 4.25559i) q^{52} +(2.57754 + 2.57754i) q^{53} +1.65685i q^{55} +(6.78039 + 2.52166i) q^{56} +(-3.80853 - 4.83980i) q^{58} +(-4.00000 - 4.00000i) q^{59} +(-4.38607 + 4.38607i) q^{61} +(1.09809 - 9.20867i) q^{62} +(-6.05588 - 5.22746i) q^{64} -10.1023 q^{65} +(-2.11882 + 2.11882i) q^{67} +(-12.5295 - 3.03127i) q^{68} +(5.53304 + 7.03127i) q^{70} -5.11529i q^{71} +14.7721i q^{73} +(-4.28956 + 3.37553i) q^{74} +(11.0031 - 6.71627i) q^{76} +(-1.21137 + 1.21137i) q^{77} -6.32000 q^{79} +(-3.02461 - 9.42088i) q^{80} +(1.10745 + 0.132058i) q^{82} +(-0.641669 + 0.641669i) q^{83} +(-11.2739 - 11.2739i) q^{85} +(-0.612348 + 0.481868i) q^{86} +(1.72256 - 0.788632i) q^{88} +6.31724i q^{89} +(-7.38607 - 7.38607i) q^{91} +(1.33019 - 5.49824i) q^{92} +(-0.473626 + 3.97186i) q^{94} +15.9437 q^{95} +12.6533 q^{97} +(0.0767667 - 0.643772i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 12 q^{14} - 8 q^{19} - 16 q^{20} - 20 q^{26} + 8 q^{28} + 16 q^{29} + 24 q^{31} - 24 q^{35} - 16 q^{37} + 8 q^{38} + 16 q^{40} - 8 q^{43} + 40 q^{44} - 8 q^{46} - 8 q^{49} + 36 q^{50} - 16 q^{52} - 16 q^{53} - 16 q^{58} - 32 q^{59} + 16 q^{61} + 12 q^{62} + 8 q^{64} + 16 q^{65} - 16 q^{67} - 32 q^{68} + 32 q^{70} - 52 q^{74} + 8 q^{76} - 16 q^{77} - 24 q^{79} - 8 q^{80} + 40 q^{82} + 40 q^{83} - 16 q^{85} + 16 q^{86} + 32 q^{88} - 8 q^{91} + 16 q^{92} + 8 q^{94} + 48 q^{95} + 40 q^{98}+O(q^{100}) $ 8 * q - 4 * q^4 + 12 * q^8 - 8 * q^10 + 8 * q^11 - 12 * q^14 - 8 * q^19 - 16 * q^20 - 20 * q^26 + 8 * q^28 + 16 * q^29 + 24 * q^31 - 24 * q^35 - 16 * q^37 + 8 * q^38 + 16 * q^40 - 8 * q^43 + 40 * q^44 - 8 * q^46 - 8 * q^49 + 36 * q^50 - 16 * q^52 - 16 * q^53 - 16 * q^58 - 32 * q^59 + 16 * q^61 + 12 * q^62 + 8 * q^64 + 16 * q^65 - 16 * q^67 - 32 * q^68 + 32 * q^70 - 52 * q^74 + 8 * q^76 - 16 * q^77 - 24 * q^79 - 8 * q^80 + 40 * q^82 + 40 * q^83 - 16 * q^85 + 16 * q^86 + 32 * q^88 - 8 * q^91 + 16 * q^92 + 8 * q^94 + 48 * q^95 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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 $

$2$	0.167452	−	1.40426i	0.118406	−	0.992965i
$2$	0.167452	−	1.40426i	0.118406	−	0.992965i
$3$		0			0
$3$		0			0
$4$	−1.94392	−	0.470294i	−0.971960	−	0.235147i
$5$	−1.74912	−	1.74912i	−0.782229	−	0.782229i	0.197977	−	0.980207i	$-0.436563\pi$
$5$	−1.74912	−	1.74912i	−0.782229	−	0.782229i	−0.980207	+	0.197977i	$0.936563\pi$
$6$		0			0
$7$		−	2.55765i		−	0.966700i	−0.875427	−	0.483350i	$-0.839420\pi$
$7$		−	2.55765i		−	0.966700i	0.875427	−	0.483350i	$-0.160580\pi$
$8$	−0.985930	+	2.65103i	−0.348579	+	0.937279i
$9$		0			0
$10$	−2.74912	+	2.16333i	−0.869347	+	0.684105i
$11$	−0.473626	−	0.473626i	−0.142804	−	0.142804i	0.632091	−	0.774894i	$-0.282197\pi$
$11$	−0.473626	−	0.473626i	−0.142804	−	0.142804i	−0.774894	+	0.632091i	$0.782197\pi$
$12$		0			0
$13$	2.88784	−	2.88784i	0.800943	−	0.800943i	−0.182300	−	0.983243i	$-0.558354\pi$
$13$	2.88784	−	2.88784i	0.800943	−	0.800943i	0.983243	+	0.182300i	$0.0583543\pi$
$14$	−3.59161	−	0.428283i	−0.959899	−	0.114463i
$15$		0			0
$16$	3.55765	+	1.82843i	0.889412	+	0.457107i
$17$	6.44549			1.56326			0.781630	−	0.623742i	$-0.214389\pi$
$17$	6.44549			1.56326			0.781630	+	0.623742i	$0.214389\pi$
$18$		0			0
$19$	−4.55765	+	4.55765i	−1.04560	+	1.04560i	−0.0466864	+	0.998910i	$0.514866\pi$
$19$	−4.55765	+	4.55765i	−1.04560	+	1.04560i	−0.998910	+	0.0466864i	$0.985134\pi$
$20$	2.57754	+	4.22274i	0.576357	+	0.944234i
$21$		0			0
$22$	−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	$0.904719\pi$
$24$		0			0
$25$			1.11882i			0.223765i
$26$	−3.57172	−	4.53887i	−0.700471	−	0.890145i
$27$		0			0
$28$	−1.20285	+	4.97186i	−0.227317	+	0.939593i
$29$	3.07931	−	3.07931i	0.571813	−	0.571813i	−0.360821	−	0.932635i	$-0.617504\pi$
$29$	3.07931	−	3.07931i	0.571813	−	0.571813i	0.932635	+	0.360821i	$0.117504\pi$
$30$		0			0
$31$	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			0
$34$	1.07931	−	9.05117i	0.185100	−	1.55226i
$35$	−4.47363	+	4.47363i	−0.756181	+	0.756181i
$36$		0			0
$37$	−2.72922	−	2.72922i	−0.448681	−	0.448681i	0.446235	−	0.894916i	$-0.352765\pi$
$37$	−2.72922	−	2.72922i	−0.448681	−	0.448681i	−0.894916	+	0.446235i	$0.852765\pi$
$38$	5.63696	+	7.16333i	0.914435	+	1.16205i
$39$		0			0
$40$	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	$0.980385\pi$
$42$		0			0
$43$	−0.389604	−	0.389604i	−0.0594141	−	0.0594141i	0.676775	−	0.736190i	$-0.263377\pi$
$43$	−0.389604	−	0.389604i	−0.0594141	−	0.0594141i	−0.736190	+	0.676775i	$0.763377\pi$
$44$	0.697947	+	1.14343i	0.105219	+	0.172379i
$45$		0			0
$46$	3.97186	+	0.473626i	0.585619	+	0.0698323i
$47$	−2.82843			−0.412568			−0.206284	−	0.978492i	$-0.566137\pi$
$47$	−2.82843			−0.412568			−0.206284	+	0.978492i	$0.566137\pi$
$48$		0			0
$49$	0.458440			0.0654915
$50$	1.57113	+	0.187349i	0.222191	+	0.0264952i
$51$		0			0
$52$	−6.97186	+	4.25559i	−0.966823	+	0.590145i
$53$	2.57754	+	2.57754i	0.354053	+	0.354053i	0.861615	−	0.507562i	$-0.169453\pi$
$53$	2.57754	+	2.57754i	0.354053	+	0.354053i	−0.507562	+	0.861615i	$0.669453\pi$
$54$		0			0
$55$			1.65685i			0.223410i
$56$	6.78039	+	2.52166i	0.906068	+	0.336971i
$57$		0			0
$58$	−3.80853	−	4.83980i	−0.500084	−	0.635497i
$59$	−4.00000	−	4.00000i	−0.520756	−	0.520756i	0.397044	−	0.917800i	$-0.370036\pi$
$59$	−4.00000	−	4.00000i	−0.520756	−	0.520756i	−0.917800	+	0.397044i	$0.870036\pi$
$60$		0			0
$61$	−4.38607	+	4.38607i	−0.561579	+	0.561579i	−0.929756	−	0.368177i	$-0.879982\pi$
$61$	−4.38607	+	4.38607i	−0.561579	+	0.561579i	0.368177	+	0.929756i	$0.379982\pi$
$62$	1.09809	−	9.20867i	0.139458	−	1.16950i
$63$		0			0
$64$	−6.05588	−	5.22746i	−0.756985	−	0.653432i
$65$	−10.1023			−1.25304
$66$		0			0
$67$	−2.11882	+	2.11882i	−0.258856	+	0.258856i	−0.824589	−	0.565733i	$-0.808593\pi$
$67$	−2.11882	+	2.11882i	−0.258856	+	0.258856i	0.565733	+	0.824589i	$0.308593\pi$
$68$	−12.5295	−	3.03127i	−1.51943	−	0.367596i
$69$		0			0
$70$	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	$-0.0981676\pi$
$72$		0			0
$73$			14.7721i			1.72895i	0.502676	+	0.864475i	$0.332349\pi$
$73$			14.7721i			1.72895i	−0.502676	+	0.864475i	$0.667651\pi$
$74$	−4.28956	+	3.37553i	−0.498651	+	0.392398i
$75$		0			0
$76$	11.0031	−	6.71627i	1.26215	−	0.770409i
$77$	−1.21137	+	1.21137i	−0.138048	+	0.138048i
$78$		0			0
$79$	−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
$81$		0			0
$82$	1.10745	+	0.132058i	0.122297	+	0.0145834i
$83$	−0.641669	+	0.641669i	−0.0704323	+	0.0704323i	−0.741445	−	0.671013i	$-0.765859\pi$
$83$	−0.641669	+	0.641669i	−0.0704323	+	0.0704323i	0.671013	+	0.741445i	$0.265859\pi$
$84$		0			0
$85$	−11.2739	−	11.2739i	−1.22283	−	1.22283i
$86$	−0.612348	+	0.481868i	−0.0660311	+	0.0519611i
$87$		0			0
$88$	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	$0.891327\pi$
$90$		0			0
$91$	−7.38607	−	7.38607i	−0.774271	−	0.774271i
$92$	1.33019	−	5.49824i	0.138682	−	0.573231i
$93$		0			0
$94$	−0.473626	+	3.97186i	−0.0488508	+	0.409666i
$95$	15.9437			1.63579
$96$		0			0
$97$	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			0
$100$	0.526176	−	2.17490i	0.0526176	−	0.217490i
$101$	−7.52480	−	7.52480i	−0.748745	−	0.748745i	0.225498	−	0.974244i	$-0.427599\pi$
$101$	−7.52480	−	7.52480i	−0.748745	−	0.748745i	−0.974244	+	0.225498i	$0.927599\pi$
$102$		0			0
$103$			3.33686i			0.328790i	0.986395	+	0.164395i	$0.0525672\pi$
$103$			3.33686i			0.328790i	−0.986395	+	0.164395i	$0.947433\pi$
$104$	4.80853	+	10.5029i	0.471515	+	1.02990i
$105$		0			0
$106$	4.05117	−	3.18794i	0.393484	−	0.309640i
$107$	14.0625	+	14.0625i	1.35948	+	1.35948i	0.874560	+	0.484918i	$0.161151\pi$
$107$	14.0625	+	14.0625i	1.35948	+	1.35948i	0.484918	+	0.874560i	$0.338849\pi$
$108$		0			0
$109$	2.76901	−	2.76901i	0.265224	−	0.265224i	−0.561949	−	0.827172i	$-0.689948\pi$
$109$	2.76901	−	2.76901i	0.265224	−	0.265224i	0.827172	+	0.561949i	$0.189948\pi$
$110$	2.32666	+	0.277444i	0.221839	+	0.0264532i
$111$		0			0
$112$	4.67647	−	9.09921i	0.441885	−	0.859794i
$113$	−2.23765			−0.210500			−0.105250	−	0.994446i	$-0.533564\pi$
$113$	−2.23765			−0.210500			−0.105250	+	0.994446i	$0.533564\pi$
$114$		0			0
$115$	4.94725	−	4.94725i	0.461334	−	0.461334i
$116$	−7.43411	+	4.53775i	−0.690240	+	0.421320i
$117$		0			0
$118$	−6.28687	+	4.94725i	−0.578753	+	0.455431i
$119$		−	16.4853i		−	1.51120i
$120$		0			0
$121$		−	10.5514i		−	0.959214i
$122$	5.42475	+	6.89367i	0.491134	+	0.624123i
$123$		0			0
$124$	−12.7475	−	3.08402i	−1.14476	−	0.276953i
$125$	−6.78863	+	6.78863i	−0.607194	+	0.607194i
$126$		0			0
$127$	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			0
$130$	−1.69166	+	14.1864i	−0.148368	+	1.24423i
$131$	3.77568	−	3.77568i	0.329883	−	0.329883i	−0.522659	−	0.852542i	$-0.675060\pi$
$131$	3.77568	−	3.77568i	0.329883	−	0.329883i	0.852542	+	0.522659i	$0.175060\pi$
$132$		0			0
$133$	11.6569	+	11.6569i	1.01078	+	1.01078i
$134$	2.62059	+	3.33019i	0.226384	+	0.287685i
$135$		0			0
$136$	−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	$-0.0699898\pi$
$138$		0			0
$139$	11.7757	+	11.7757i	0.998800	+	0.998800i	0.999999	−	0.00119925i	$-0.000381735\pi$
$139$	11.7757	+	11.7757i	0.998800	+	0.998800i	−0.00119925	+	0.999999i	$0.500382\pi$
$140$	10.8003	−	6.59245i	0.912791	−	0.557164i
$141$		0			0
$142$	−7.18323	−	0.856566i	−0.602803	−	0.0718814i
$143$	−2.73551			−0.228755
$144$		0			0
$145$	−10.7721			−0.894578
$146$	20.7440	+	2.47363i	1.71679	+	0.204719i
$147$		0			0
$148$	4.02185	+	6.58892i	0.330594	+	0.541606i
$149$	7.90774	+	7.90774i	0.647827	+	0.647827i	0.952467	−	0.304640i	$-0.0985363\pi$
$149$	7.90774	+	7.90774i	0.647827	+	0.647827i	−0.304640	+	0.952467i	$0.598536\pi$
$150$		0			0
$151$		−	14.6506i		−	1.19225i	−0.802893	−	0.596123i	$-0.796707\pi$
$151$		−	14.6506i		−	1.19225i	0.802893	−	0.596123i	$-0.203293\pi$
$152$	−7.58892	−	16.5760i	−0.615543	−	1.34449i
$153$		0			0
$154$	1.49824	+	1.90393i	0.120731	+	0.153423i
$155$	−11.4701	−	11.4701i	−0.921300	−	0.921300i
$156$		0			0
$157$	−3.15196	+	3.15196i	−0.251553	+	0.251553i	−0.821607	−	0.570054i	$-0.806922\pi$
$157$	−3.15196	+	3.15196i	−0.251553	+	0.251553i	0.570054	+	0.821607i	$0.306922\pi$
$158$	−1.05830	+	8.87495i	−0.0841935	+	0.706053i
$159$		0			0
$160$	−13.7359	+	2.66981i	−1.08592	+	0.211067i
$161$	7.23412			0.570128
$162$		0			0
$163$	5.50490	−	5.50490i	0.431177	−	0.431177i	−0.457852	−	0.889029i	$-0.651381\pi$
$163$	5.50490	−	5.50490i	0.431177	−	0.431177i	0.889029	+	0.457852i	$0.151381\pi$
$164$	0.370889	−	1.53304i	0.0289616	−	0.119710i
$165$		0			0
$166$	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	$0.714791\pi$
$168$		0			0
$169$		−	3.67923i		−	0.283018i
$170$	−17.7194	+	13.9437i	−1.35902	+	1.06943i
$171$		0			0
$172$	0.574131	+	0.940588i	0.0437771	+	0.0717191i
$173$	−4.35322	+	4.35322i	−0.330969	+	0.330969i	−0.852955	−	0.521985i	$-0.825192\pi$
$173$	−4.35322	+	4.35322i	−0.330969	+	0.330969i	0.521985	+	0.852955i	$0.325192\pi$
$174$		0			0
$175$	2.86156			0.216313
$176$	−0.819003	−	2.55098i	−0.0617347	−	0.192288i
$177$		0			0
$178$	8.87108	+	1.05783i	0.664915	+	0.0792880i
$179$	13.2833	−	13.2833i	0.992843	−	0.992843i	−0.00713130	−	0.999975i	$-0.502270\pi$
$179$	13.2833	−	13.2833i	0.992843	−	0.992843i	0.999975	+	0.00713130i	$0.00226998\pi$
$180$		0			0
$181$	6.34628	+	6.34628i	0.471715	+	0.471715i	0.902469	−	0.430754i	$-0.141752\pi$
$181$	6.34628	+	6.34628i	0.471715	+	0.471715i	−0.430754	+	0.902469i	$0.641752\pi$
$182$	−11.6088	+	9.13519i	−0.860503	+	0.677145i
$183$		0			0
$184$	−7.49824	−	2.78863i	−0.552777	−	0.205581i
$185$			9.54745i			0.701943i
$186$		0			0
$187$	−3.05275	−	3.05275i	−0.223239	−	0.223239i
$188$	5.49824	+	1.33019i	0.401000	+	0.0970142i
$189$		0			0
$190$	2.66981	−	22.3892i	0.193688	−	1.62428i
$191$	−5.60058			−0.405243			−0.202622	−	0.979257i	$-0.564946\pi$
$191$	−5.60058			−0.405243			−0.202622	+	0.979257i	$0.564946\pi$
$192$		0			0
$193$	−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
$195$		0			0
$196$	−0.891171	−	0.215602i	−0.0636551	−	0.0154001i
$197$	−1.23793	−	1.23793i	−0.0881988	−	0.0881988i	0.661631	−	0.749830i	$-0.269865\pi$
$197$	−1.23793	−	1.23793i	−0.0881988	−	0.0881988i	−0.749830	+	0.661631i	$0.769865\pi$
$198$		0			0
$199$		−	0.993710i		−	0.0704422i	−0.999380	−	0.0352211i	$-0.988786\pi$
$199$		−	0.993710i		−	0.0704422i	0.999380	−	0.0352211i	$-0.0112135\pi$
$200$	−2.96603	−	1.10308i	−0.209730	−	0.0779997i
$201$		0			0
$202$	−11.8268	+	9.30676i	−0.832134	+	0.654822i
$203$	−7.87579	−	7.87579i	−0.552772	−	0.552772i
$204$		0			0
$205$	1.37941	−	1.37941i	0.0963422	−	0.0963422i
$206$	4.68583	+	0.558763i	0.326477	+	0.0389309i
$207$		0			0
$208$	15.5541	−	4.99371i	1.07848	−	0.346251i
$209$	4.31724			0.298630
$210$		0			0
$211$	4.22432	−	4.22432i	0.290814	−	0.290814i	−0.546588	−	0.837402i	$-0.684073\pi$
$211$	4.22432	−	4.22432i	0.290814	−	0.290814i	0.837402	+	0.546588i	$0.184073\pi$
$212$	−3.79834	−	6.22274i	−0.260871	−	0.427380i
$213$		0			0
$214$	22.1023	−	17.3927i	1.51088	−	1.18894i
$215$			1.36293i			0.0929509i
$216$		0			0
$217$		−	16.7721i		−	1.13857i
$218$	−3.42475	−	4.35211i	−0.231954	−	0.294762i
$219$		0			0
$220$	0.779208	−	3.22079i	0.0525342	−	0.217146i
$221$	18.6135	−	18.6135i	1.25208	−	1.25208i
$222$		0			0
$223$	−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
$225$		0			0
$226$	−0.374699	+	3.14225i	−0.0249246	+	0.209019i
$227$	0.641669	−	0.641669i	0.0425891	−	0.0425891i	−0.685492	−	0.728081i	$-0.740413\pi$
$227$	0.641669	−	0.641669i	0.0425891	−	0.0425891i	0.728081	+	0.685492i	$0.240413\pi$
$228$		0			0
$229$	5.34275	+	5.34275i	0.353059	+	0.353059i	0.861246	−	0.508188i	$-0.169684\pi$
$229$	5.34275	+	5.34275i	0.353059	+	0.353059i	−0.508188	+	0.861246i	$0.669684\pi$
$230$	−6.11882	−	7.77568i	−0.403463	−	0.512713i
$231$		0			0
$232$	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	$-0.275207\pi$
$234$		0			0
$235$	4.94725	+	4.94725i	0.322723	+	0.322723i
$236$	5.89450	+	9.65685i	0.383699	+	0.628608i
$237$		0			0
$238$	−23.1497	−	2.76049i	−1.50057	−	0.178936i
$239$	−26.9213			−1.74140			−0.870698	−	0.491817i	$-0.836333\pi$
$239$	−26.9213			−1.74140			−0.870698	+	0.491817i	$0.836333\pi$
$240$		0			0
$241$	−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			0
$244$	10.5889	−	6.46343i	0.677886	−	0.413779i
$245$	−0.801866	−	0.801866i	−0.0512293	−	0.0512293i
$246$		0			0
$247$			26.3235i			1.67492i
$248$	−6.46538	+	17.3845i	−0.410552	+	1.10392i
$249$		0			0
$250$	8.39627	+	10.6698i	0.531027	+	0.674818i
$251$	9.75696	+	9.75696i	0.615854	+	0.615854i	0.944465	−	0.328611i	$-0.106581\pi$
$251$	9.75696	+	9.75696i	0.615854	+	0.615854i	−0.328611	+	0.944465i	$0.606581\pi$
$252$		0			0
$253$	1.33962	−	1.33962i	0.0842209	−	0.0842209i
$254$	2.04534	−	17.1524i	0.128336	−	1.07624i
$255$		0			0
$256$	9.31371	+	13.0098i	0.582107	+	0.813112i
$257$	−16.9965			−1.06021			−0.530105	−	0.847932i	$-0.677848\pi$
$257$	−16.9965			−1.06021			−0.530105	+	0.847932i	$0.677848\pi$
$258$		0			0
$259$	−6.98038	+	6.98038i	−0.433740	+	0.433740i
$260$	19.6381	+	4.75107i	1.21791	+	0.294649i
$261$		0			0
$262$	−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			0
$265$		−	9.01686i		−	0.553901i
$266$	18.3213	−	14.4173i	1.12335	−	0.883984i
$267$		0			0
$268$	5.11529	−	3.12235i	0.312466	−	0.190728i
$269$	−20.6003	+	20.6003i	−1.25602	+	1.25602i	−0.303046	+	0.952976i	$0.598004\pi$
$269$	−20.6003	+	20.6003i	−1.25602	+	1.25602i	−0.952976	+	0.303046i	$0.901996\pi$
$270$		0			0
$271$	−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
$273$		0			0
$274$	−7.16999	−	0.854988i	−0.433155	−	0.0516517i
$275$	0.529904	−	0.529904i	0.0319544	−	0.0319544i
$276$		0			0
$277$	12.1220	+	12.1220i	0.728338	+	0.728338i	0.970289	−	0.241951i	$-0.0777872\pi$
$277$	12.1220	+	12.1220i	0.728338	+	0.728338i	−0.241951	+	0.970289i	$0.577787\pi$
$278$	18.5080	−	14.5643i	1.11004	−	0.873509i
$279$		0			0
$280$	−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	$-0.0262902\pi$
$282$		0			0
$283$	4.48528	+	4.48528i	0.266622	+	0.266622i	0.827738	−	0.561115i	$-0.189628\pi$
$283$	4.48528	+	4.48528i	0.266622	+	0.266622i	−0.561115	+	0.827738i	$0.689628\pi$
$284$	−2.40569	+	9.94372i	−0.142752	+	0.590051i
$285$		0			0
$286$	−0.458067	+	3.84138i	−0.0270860	+	0.227146i
$287$	2.01704			0.119062
$288$		0			0
$289$	24.5443			1.44378
$290$	−1.80382	+	15.1270i	−0.105924	+	0.888285i
$291$		0			0
$292$	6.94725	−	28.7159i	0.406557	−	1.68047i
$293$	8.20793	+	8.20793i	0.479512	+	0.479512i	0.904976	−	0.425463i	$-0.139889\pi$
$293$	8.20793	+	8.20793i	0.479512	+	0.479512i	−0.425463	+	0.904976i	$0.639889\pi$
$294$		0			0
$295$			13.9929i			0.814700i
$296$	9.92606	−	4.54441i	0.576940	−	0.264139i
$297$		0			0
$298$	12.4287	−	9.78039i	0.719977	−	0.566563i
$299$	8.16804	+	8.16804i	0.472370	+	0.472370i
$300$		0			0
$301$	−0.996470	+	0.996470i	−0.0574356	+	0.0574356i
$302$	−20.5733	−	2.45327i	−1.18386	−	0.141170i
$303$		0			0
$304$	−24.5478	+	7.88118i	−1.40791	+	0.452016i
$305$	15.3435			0.878567
$306$		0			0
$307$	10.4549	−	10.4549i	0.596693	−	0.596693i	−0.342738	−	0.939431i	$-0.611354\pi$
$307$	10.4549	−	10.4549i	0.596693	−	0.596693i	0.939431	+	0.342738i	$0.111354\pi$
$308$	2.92450	−	1.78510i	0.166639	−	0.101716i
$309$		0			0
$310$	−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	$-0.140585\pi$
$312$		0			0
$313$			23.0027i			1.30019i	0.759852	+	0.650096i	$0.225271\pi$
$313$			23.0027i			1.30019i	−0.759852	+	0.650096i	$0.774729\pi$
$314$	3.89838	+	4.95398i	0.219998	+	0.279569i
$315$		0			0
$316$	12.2856	+	2.97226i	0.691117	+	0.167203i
$317$	6.75892	−	6.75892i	0.379618	−	0.379618i	−0.491346	−	0.870964i	$-0.663495\pi$
$317$	6.75892	−	6.75892i	0.379618	−	0.379618i	0.870964	+	0.491346i	$0.163495\pi$
$318$		0			0
$319$	−2.91688			−0.163314
$320$	1.44902	+	19.7359i	0.0810025	+	1.10327i
$321$		0			0
$322$	1.21137	−	10.1586i	0.0675069	−	0.566118i
$323$	−29.3763	+	29.3763i	−1.63454	+	1.63454i
$324$		0			0
$325$	3.23099	+	3.23099i	0.179223	+	0.179223i
$326$	−6.80853	−	8.65214i	−0.377090	−	0.479198i
$327$		0			0
$328$	−2.09069	−	0.777537i	−0.115439	−	0.0429323i
$329$			7.23412i			0.398830i
$330$		0			0
$331$	−19.6631	−	19.6631i	−1.08078	−	1.08078i	−0.996436	−	0.0843464i	$-0.973120\pi$
$331$	−19.6631	−	19.6631i	−1.08078	−	1.08078i	−0.0843464	−	0.996436i	$-0.526880\pi$
$332$	1.54913	−	0.945580i	0.0850193	−	0.0518954i
$333$		0			0
$334$	28.3400	+	3.37941i	1.55070	+	0.184913i
$335$	7.41215			0.404969
$336$		0			0
$337$	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
$339$		0			0
$340$	16.6135	+	27.2176i	0.900995	+	1.47608i
$341$	−3.10587	−	3.10587i	−0.168192	−	0.168192i
$342$		0			0
$343$		−	19.0761i		−	1.03001i
$344$	1.41697	−	0.648728i	0.0763981	−	0.0349771i
$345$		0			0
$346$	5.38412	+	6.84203i	0.289452	+	0.367830i
$347$	−6.27521	−	6.27521i	−0.336871	−	0.336871i	0.518317	−	0.855188i	$-0.326559\pi$
$347$	−6.27521	−	6.27521i	−0.336871	−	0.336871i	−0.855188	+	0.518317i	$0.826559\pi$
$348$		0			0
$349$	−4.74255	+	4.74255i	−0.253863	+	0.253863i	−0.822552	−	0.568690i	$-0.807451\pi$
$349$	−4.74255	+	4.74255i	−0.253863	+	0.253863i	0.568690	+	0.822552i	$0.307451\pi$
$350$	0.479174	−	4.01839i	0.0256129	−	0.214792i
$351$		0			0
$352$	−3.71940	+	0.722930i	−0.198245	+	0.0385323i
$353$	8.75882			0.466185			0.233093	−	0.972455i	$-0.425116\pi$
$353$	8.75882			0.466185			0.233093	+	0.972455i	$0.425116\pi$
$354$		0			0
$355$	−8.94725	+	8.94725i	−0.474871	+	0.474871i
$356$	2.97096	−	12.2802i	0.157460	−	0.650849i
$357$		0			0
$358$	−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	$-0.332898\pi$
$360$		0			0
$361$		−	22.5443i		−	1.18654i
$362$	9.97455	−	7.84916i	0.524251	−	0.412543i
$363$		0			0
$364$	10.8843	+	17.8316i	0.570493	+	0.934628i
$365$	25.8382	−	25.8382i	1.35243	−	1.35243i
$366$		0			0
$367$	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			0
$370$	13.4072	+	1.59874i	0.697005	+	0.0831145i
$371$	6.59245	−	6.59245i	0.342263	−	0.342263i
$372$		0			0
$373$	−16.6167	−	16.6167i	−0.860378	−	0.860378i	0.131004	−	0.991382i	$-0.458180\pi$
$373$	−16.6167	−	16.6167i	−0.860378	−	0.860378i	−0.991382	+	0.131004i	$0.958180\pi$
$374$	−4.79806	+	3.77568i	−0.248102	+	0.195236i
$375$		0			0
$376$	2.78863	−	7.49824i	0.143813	−	0.386692i
$377$		−	17.7851i		−	0.915979i
$378$		0			0
$379$	7.77844	+	7.77844i	0.399552	+	0.399552i	0.878075	−	0.478523i	$-0.158828\pi$
$379$	7.77844	+	7.77844i	0.399552	+	0.399552i	−0.478523	+	0.878075i	$0.658828\pi$
$380$	−30.9933	−	7.49824i	−1.58992	−	0.384651i
$381$		0			0
$382$	−0.937828	+	7.86469i	−0.0479834	+	0.402393i
$383$	17.2037			0.879070			0.439535	−	0.898225i	$-0.355143\pi$
$383$	17.2037			0.879070			0.439535	+	0.898225i	$0.355143\pi$
$384$		0			0
$385$	4.23765			0.215971
$386$	−3.25717	+	27.3149i	−0.165786	+	1.39029i
$387$		0			0
$388$	−24.5970	−	5.95078i	−1.24873	−	0.302105i
$389$	23.8515	+	23.8515i	1.20932	+	1.20932i	0.971248	+	0.238069i	$0.0765143\pi$
$389$	23.8515	+	23.8515i	1.20932	+	1.20932i	0.238069	+	0.971248i	$0.423486\pi$
$390$		0			0
$391$			18.2306i			0.921961i
$392$	−0.451990	+	1.21534i	−0.0228290	+	0.0613838i
$393$		0			0
$394$	−1.94567	+	1.53109i	−0.0980216	+	0.0771350i
$395$	11.0544	+	11.0544i	0.556208	+	0.556208i
$396$		0			0
$397$	−10.2673	+	10.2673i	−0.515299	+	0.515299i	−0.916145	−	0.400847i	$-0.868716\pi$
$397$	−10.2673	+	10.2673i	−0.515299	+	0.515299i	0.400847	+	0.916145i	$0.368716\pi$
$398$	−1.39543	−	0.166399i	−0.0699467	−	0.00834081i
$399$		0			0
$400$	−2.04569	+	3.98038i	−0.102284	+	0.199019i
$401$	−32.2274			−1.60936			−0.804681	−	0.593708i	$-0.797663\pi$
$401$	−32.2274			−1.60936			−0.804681	+	0.593708i	$0.797663\pi$
$402$		0			0
$403$	18.9374	−	18.9374i	0.943341	−	0.943341i
$404$	11.0887	+	18.1665i	0.551685	+	0.903815i
$405$		0			0
$406$	−12.3785	+	9.74088i	−0.614335	+	0.483432i
$407$			2.58526i			0.128146i
$408$		0			0
$409$		−	11.5702i		−	0.572110i	−0.958213	−	0.286055i	$-0.907656\pi$
$409$		−	11.5702i		−	0.572110i	0.958213	−	0.286055i	$-0.0923440\pi$
$410$	−1.70607	−	2.16804i	−0.0842569	−	0.107072i
$411$		0			0
$412$	1.56930	−	6.48658i	0.0773140	−	0.319571i
$413$	−10.2306	+	10.2306i	−0.503414	+	0.503414i
$414$		0			0
$415$	2.24471			0.110188
$416$	−4.40792	−	22.6783i	−0.216116	−	1.11190i
$417$		0			0
$418$	0.722930	−	6.06255i	0.0353597	−	0.296529i
$419$	−6.74717	+	6.74717i	−0.329621	+	0.329621i	−0.852442	−	0.522822i	$-0.824879\pi$
$419$	−6.74717	+	6.74717i	−0.329621	+	0.329621i	0.522822	+	0.852442i	$0.324879\pi$
$420$		0			0
$421$	−17.2239	−	17.2239i	−0.839443	−	0.839443i	0.149343	−	0.988785i	$-0.452284\pi$
$421$	−17.2239	−	17.2239i	−0.839443	−	0.839443i	−0.988785	+	0.149343i	$0.952284\pi$
$422$	−5.22470	−	6.63944i	−0.254334	−	0.323203i
$423$		0			0
$424$	−9.37442	+	4.29186i	−0.455262	+	0.208431i
$425$			7.21137i			0.349803i
$426$		0			0
$427$	11.2180	+	11.2180i	0.542879	+	0.542879i
$428$	−20.7229	−	33.9500i	−1.00168	−	1.64103i
$429$		0			0
$430$	1.91391	+	0.228225i	0.0922970	+	0.0110060i
$431$	−40.7088			−1.96087			−0.980437	−	0.196832i	$-0.936935\pi$
$431$	−40.7088			−1.96087			−0.980437	+	0.196832i	$0.936935\pi$
$432$		0			0
$433$	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
$435$		0			0
$436$	−6.68499	+	4.08049i	−0.320153	+	0.195420i
$437$	−12.8910	−	12.8910i	−0.616659	−	0.616659i
$438$		0			0
$439$		−	17.7122i		−	0.845356i	−0.906280	−	0.422678i	$-0.861090\pi$
$439$		−	17.7122i		−	0.845356i	0.906280	−	0.422678i	$-0.138910\pi$
$440$	−4.39236	−	1.63354i	−0.209398	−	0.0778761i
$441$		0			0
$442$	−23.0215	−	29.2552i	−1.09502	−	1.39153i
$443$	−15.6944	−	15.6944i	−0.745664	−	0.745664i	0.227997	−	0.973662i	$-0.426782\pi$
$443$	−15.6944	−	15.6944i	−0.745664	−	0.745664i	−0.973662	+	0.227997i	$0.926782\pi$
$444$		0			0
$445$	11.0496	−	11.0496i	0.523801	−	0.523801i
$446$	−3.97964	+	33.3736i	−0.188441	+	1.58028i
$447$		0			0
$448$	−13.3700	+	15.4888i	−0.631673	+	0.731778i
$449$	28.3400			1.33745			0.668723	−	0.743511i	$-0.266841\pi$
$449$	28.3400			1.33745			0.668723	+	0.743511i	$0.266841\pi$
$450$		0			0
$451$	0.373517	−	0.373517i	0.0175882	−	0.0175882i
$452$	4.34981	+	1.05235i	0.204598	+	0.0494985i
$453$		0			0
$454$	−0.793624	−	1.00852i	−0.0372466	−	0.0473323i
$455$			25.8382i			1.21131i
$456$		0			0
$457$			17.3396i			0.811113i	0.914070	+	0.405557i	$0.132922\pi$
$457$			17.3396i			0.811113i	−0.914070	+	0.405557i	$0.867078\pi$
$458$	8.39729	−	6.60798i	0.392380	−	0.308771i
$459$		0			0
$460$	−11.9437	+	7.29040i	−0.556879	+	0.339917i
$461$	1.69284	−	1.69284i	0.0788434	−	0.0788434i	−0.666585	−	0.745429i	$-0.732245\pi$
$461$	1.69284	−	1.69284i	0.0788434	−	0.0788434i	0.745429	+	0.666585i	$0.232245\pi$
$462$		0			0
$463$	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
$465$		0			0
$466$	−32.6169	−	3.88942i	−1.51095	−	0.180174i
$467$	17.1136	−	17.1136i	0.791924	−	0.791924i	−0.189883	−	0.981807i	$-0.560811\pi$
$467$	17.1136	−	17.1136i	0.791924	−	0.791924i	0.981807	+	0.189883i	$0.0608108\pi$
$468$		0			0
$469$	5.41921	+	5.41921i	0.250236	+	0.250236i
$470$	7.77568	−	6.11882i	0.358665	−	0.282240i
$471$		0			0
$472$	14.5478	−	6.66038i	0.669618	−	0.306569i
$473$			0.369053i			0.0169691i
$474$		0			0
$475$	−5.09921	−	5.09921i	−0.233968	−	0.233968i
$476$	−7.75293	+	32.0461i	−0.355355	+	1.46883i
$477$		0			0
$478$	−4.50803	+	37.8047i	−0.206193	+	1.72915i
$479$	22.2251			1.01549			0.507745	−	0.861508i	$-0.330479\pi$
$479$	22.2251			1.01549			0.507745	+	0.861508i	$0.330479\pi$
$480$		0			0
$481$	−15.7631			−0.718735
$482$	−1.73303	+	14.5333i	−0.0789373	+	0.661974i
$483$		0			0
$484$	−4.96224	+	20.5110i	−0.225556	+	0.932318i
$485$	−22.1322	−	22.1322i	−1.00497	−	1.00497i
$486$		0			0
$487$			13.9839i			0.633672i	0.948480	+	0.316836i	$0.102620\pi$
$487$			13.9839i			0.633672i	−0.948480	+	0.316836i	$0.897380\pi$
$488$	−7.30324	−	15.9520i	−0.330602	−	0.722111i
$489$		0			0
$490$	−1.26031	+	0.991758i	−0.0569348	+	0.0448031i
$491$	−7.23412	−	7.23412i	−0.326471	−	0.326471i	0.524772	−	0.851243i	$-0.324151\pi$
$491$	−7.23412	−	7.23412i	−0.326471	−	0.326471i	−0.851243	+	0.524772i	$0.824151\pi$
$492$		0			0
$493$	19.8476	−	19.8476i	0.893893	−	0.893893i
$494$	36.9652	+	4.40792i	1.66314	+	0.198322i
$495$		0			0
$496$	23.3298	+	11.9902i	1.04754	+	0.538375i
$497$	−13.0831			−0.586858
$498$		0			0
$499$	2.59078	−	2.59078i	0.115979	−	0.115979i	−0.646735	−	0.762715i	$-0.723866\pi$
$499$	2.59078	−	2.59078i	0.115979	−	0.115979i	0.762715	+	0.646735i	$0.223866\pi$
$500$	16.3892	−	10.0039i	0.732948	−	0.447388i
$501$		0			0
$502$	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	$-0.345041\pi$
$504$		0			0
$505$			26.3235i			1.17138i
$506$	−1.65685	−	2.10550i	−0.0736562	−	0.0936008i
$507$		0			0
$508$	−23.7440	−	5.74441i	−1.05347	−	0.254867i
$509$	−20.2875	+	20.2875i	−0.899229	+	0.899229i	−0.995368	−	0.0961393i	$-0.969351\pi$
$509$	−20.2875	+	20.2875i	−0.899229	+	0.899229i	0.0961393	+	0.995368i	$0.469351\pi$
$510$		0			0
$511$	37.7819			1.67137
$512$	19.8288	−	10.9004i	0.876317	−	0.481734i
$513$		0			0
$514$	−2.84609	+	23.8675i	−0.125536	+	1.05275i
$515$	5.83655	−	5.83655i	0.257189	−	0.257189i
$516$		0			0
$517$	1.33962	+	1.33962i	0.0589162	+	0.0589162i
$518$	8.63343	+	10.9712i	0.379331	+	0.482046i
$519$		0			0
$520$	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	$0.830484\pi$
$522$		0			0
$523$	−5.78550	−	5.78550i	−0.252982	−	0.252982i	0.569210	−	0.822192i	$-0.307249\pi$
$523$	−5.78550	−	5.78550i	−0.252982	−	0.252982i	−0.822192	+	0.569210i	$0.807249\pi$
$524$	−9.11529	+	5.56394i	−0.398203	+	0.243062i
$525$		0			0
$526$	42.1180	+	5.02238i	1.83643	+	0.218986i
$527$	42.2672			1.84119
$528$		0			0
$529$	15.0000			0.652174
$530$	−12.6621	−	1.50989i	−0.550005	−	0.0655855i
$531$		0			0
$532$	−17.1778	−	28.1421i	−0.744754	−	1.22012i
$533$	2.27744	+	2.27744i	0.0986470	+	0.0986470i
$534$		0			0
$535$		−	49.1941i		−	2.12685i
$536$	−3.52805	−	7.70607i	−0.152388	−	0.332852i
$537$		0			0
$538$	25.4787	+	32.3778i	1.09847	+	1.39591i
$539$	−0.217129	−	0.217129i	−0.00935241	−	0.00935241i
$540$		0			0
$541$	4.55175	−	4.55175i	0.195695	−	0.195695i	−0.602457	−	0.798152i	$-0.705811\pi$
$541$	4.55175	−	4.55175i	0.195695	−	0.195695i	0.798152	+	0.602457i	$0.205811\pi$
$542$	−4.46269	+	37.4245i	−0.191689	+	1.60752i
$543$		0			0
$544$	20.3892	−	30.2274i	0.874180	−	1.29599i
$545$	−9.68667			−0.414931
$546$		0			0
$547$	−27.7355	+	27.7355i	−1.18588	+	1.18588i	−0.207689	+	0.978195i	$0.566594\pi$
$547$	−27.7355	+	27.7355i	−1.18588	+	1.18588i	−0.978195	+	0.207689i	$0.933406\pi$
$548$	−2.40126	+	9.92540i	−0.102577	+	0.423992i
$549$		0			0
$550$	−0.655392	−	0.832859i	−0.0279460	−	0.0355132i
$551$			28.0688i			1.19577i
$552$		0			0
$553$			16.1643i			0.687377i
$554$	19.0523	−	14.9926i	0.809454	−	0.636974i
$555$		0			0
$556$	−17.3529	−	28.4290i	−0.735929	−	1.20566i
$557$	1.17538	−	1.17538i	0.0498026	−	0.0498026i	−0.681767	−	0.731569i	$-0.738788\pi$
$557$	1.17538	−	1.17538i	0.0498026	−	0.0498026i	0.731569	+	0.681767i	$0.238788\pi$
$558$		0			0
$559$	−2.25023			−0.0951745
$560$	−24.0953	+	7.73588i	−1.01821	+	0.326901i
$561$		0			0
$562$	−3.88403	−	0.463152i	−0.163838	−	0.0195369i
$563$	28.7346	−	28.7346i	1.21102	−	1.21102i	0.240326	−	0.970692i	$-0.422746\pi$
$563$	28.7346	−	28.7346i	1.21102	−	1.21102i	0.970692	−	0.240326i	$-0.0772544\pi$
$564$		0			0
$565$	3.91391	+	3.91391i	0.164659	+	0.164659i
$566$	7.04959	−	5.54745i	0.296316	−	0.233177i
$567$		0			0
$568$	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	$0.808507\pi$
$570$		0			0
$571$	−14.8284	−	14.8284i	−0.620550	−	0.620550i	0.325122	−	0.945672i	$-0.394595\pi$
$571$	−14.8284	−	14.8284i	−0.620550	−	0.620550i	−0.945672	+	0.325122i	$0.894595\pi$
$572$	5.31761	+	1.28649i	0.222341	+	0.0537910i
$573$		0			0
$574$	0.337758	−	2.83246i	0.0140977	−	0.118225i
$575$	−3.16451			−0.131969
$576$		0			0
$577$	−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
$579$		0			0
$580$	20.9402	+	5.06608i	0.869494	+	0.210357i
$581$	1.64116	+	1.64116i	0.0680869	+	0.0680869i
$582$		0			0
$583$		−	2.44158i		−	0.101120i
$584$	−39.1614	−	14.5643i	−1.62051	−	0.602675i
$585$		0			0
$586$	12.9005	−	10.1517i	0.532917	−	0.419362i
$587$	31.2574	+	31.2574i	1.29013	+	1.29013i	0.934703	+	0.355429i	$0.115665\pi$
$587$	31.2574	+	31.2574i	1.29013	+	1.29013i	0.355429	+	0.934703i	$0.384335\pi$
$588$		0			0
$589$	−29.8874	+	29.8874i	−1.23149	+	1.23149i
$590$	19.6498	+	2.34315i	0.808969	+	0.0964658i
$591$		0			0
$592$	−4.71942	−	14.6998i	−0.193967	−	0.604157i
$593$	3.59611			0.147675			0.0738373	−	0.997270i	$-0.476475\pi$
$593$	3.59611			0.147675			0.0738373	+	0.997270i	$0.476475\pi$
$594$		0			0
$595$	−28.8347	+	28.8347i	−1.18211	+	1.18211i
$596$	−11.6530	−	19.0910i	−0.477327	−	0.781996i
$597$		0			0
$598$	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	$0.851405\pi$
$600$		0			0
$601$			10.7721i			0.439405i	0.975567	+	0.219703i	$0.0705087\pi$
$601$			10.7721i			0.439405i	−0.975567	+	0.219703i	$0.929491\pi$
$602$	1.23245	+	1.56617i	0.0502308	+	0.0638323i
$603$		0			0
$604$	−6.89007	+	28.4795i	−0.280353	+	1.15882i
$605$	−18.4556	+	18.4556i	−0.750325	+	0.750325i
$606$		0			0
$607$	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
$609$		0			0
$610$	2.56930	−	21.5464i	0.104028	−	0.872387i
$611$	−8.16804	+	8.16804i	−0.330444	+	0.330444i
$612$		0			0
$613$	−10.5049	−	10.5049i	−0.424289	−	0.424289i	0.462389	−	0.886677i	$-0.346993\pi$
$613$	−10.5049	−	10.5049i	−0.424289	−	0.424289i	−0.886677	+	0.462389i	$0.846993\pi$
$614$	−12.9308	−	16.4322i	−0.521843	−	0.663148i
$615$		0			0
$616$	−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	$0.852370\pi$
$618$		0			0
$619$	11.6398	+	11.6398i	0.467843	+	0.467843i	0.901215	−	0.433372i	$-0.142676\pi$
$619$	11.6398	+	11.6398i	0.467843	+	0.467843i	−0.433372	+	0.901215i	$0.642676\pi$
$620$	16.9026	+	27.6913i	0.678826	+	1.11211i
$621$		0			0
$622$	−21.1708	−	2.52452i	−0.848871	−	0.101224i
$623$	16.1573			0.647327
$624$		0			0
$625$	29.3424			1.17369
$626$	32.3019	+	3.85185i	1.29105	+	0.153951i
$627$		0			0
$628$	7.60949	−	4.64480i	0.303652	−	0.185348i
$629$	−17.5912	−	17.5912i	−0.701405	−	0.701405i
$630$		0			0
$631$			4.06977i			0.162015i	0.996713	+	0.0810075i	$0.0258138\pi$
$631$			4.06977i			0.162015i	−0.996713	+	0.0810075i	$0.974186\pi$
$632$	6.23108	−	16.7545i	0.247859	−	0.666458i
$633$		0			0
$634$	−8.35951	−	10.6231i	−0.331999	−	0.421897i
$635$	−21.3646	−	21.3646i	−0.847828	−	0.847828i
$636$		0			0
$637$	1.32390	−	1.32390i	0.0524549	−	0.0524549i
$638$	−0.488437	+	4.09607i	−0.0193374	+	0.162165i
$639$		0			0
$640$	27.9570	+	1.27001i	1.10510	+	0.0502016i
$641$	8.41958			0.332553			0.166277	−	0.986079i	$-0.446826\pi$
$641$	8.41958			0.332553			0.166277	+	0.986079i	$0.446826\pi$
$642$		0			0
$643$	−7.37275	+	7.37275i	−0.290753	+	0.290753i	−0.837378	−	0.546625i	$-0.815912\pi$
$643$	−7.37275	+	7.37275i	−0.290753	+	0.290753i	0.546625	+	0.837378i	$0.315912\pi$
$644$	−14.0625	−	3.40216i	−0.554142	−	0.134064i
$645$		0			0
$646$	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			0
$649$			3.78901i			0.148731i
$650$	5.07819	−	3.99612i	0.199183	−	0.156741i
$651$		0			0
$652$	−13.2900	+	8.11216i	−0.520477	+	0.317697i
$653$	1.93049	−	1.93049i	0.0755458	−	0.0755458i	−0.668324	−	0.743870i	$-0.732988\pi$
$653$	1.93049	−	1.93049i	0.0755458	−	0.0755458i	0.743870	+	0.668324i	$0.232988\pi$
$654$		0			0
$655$	−13.2082			−0.516088
$656$	−1.44196	+	2.80568i	−0.0562990	+	0.109543i
$657$		0			0
$658$	10.1586	+	1.21137i	0.396024	+	0.0472240i
$659$	−22.3102	+	22.3102i	−0.869081	+	0.869081i	−0.992371	−	0.123290i	$-0.960656\pi$
$659$	−22.3102	+	22.3102i	−0.869081	+	0.869081i	0.123290	+	0.992371i	$0.460656\pi$
$660$		0			0
$661$	10.7033	+	10.7033i	0.416311	+	0.416311i	0.883930	−	0.467619i	$-0.154888\pi$
$661$	10.7033	+	10.7033i	0.416311	+	0.416311i	−0.467619	+	0.883930i	$0.654888\pi$
$662$	−30.9049	+	24.3196i	−1.20115	+	0.945208i
$663$		0			0
$664$	−1.06844	−	2.33372i	−0.0414635	−	0.0905660i
$665$		−	40.7784i		−	1.58132i
$666$		0			0
$667$	8.70960	+	8.70960i	0.337237	+	0.337237i
$668$	9.49118	−	39.2310i	0.367225	−	1.51789i
$669$		0			0
$670$	1.24118	−	10.4086i	0.0479509	−	0.402120i
$671$	4.15472			0.160391
$672$		0			0
$673$	−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			0
$676$	−1.73032	+	7.15213i	−0.0665508	+	0.275082i
$677$	−26.8246	−	26.8246i	−1.03095	−	1.03095i	−0.999505	−	0.0314484i	$-0.989988\pi$
$677$	−26.8246	−	26.8246i	−1.03095	−	1.03095i	−0.0314484	−	0.999505i	$-0.510012\pi$
$678$		0			0
$679$		−	32.3627i		−	1.24197i
$680$	41.0027	−	18.7721i	1.57238	−	0.719879i
$681$		0			0
$682$	−4.88155	+	3.84138i	−0.186924	+	0.147094i
$683$	−12.9026	−	12.9026i	−0.493705	−	0.493705i	0.415766	−	0.909472i	$-0.363513\pi$
$683$	−12.9026	−	12.9026i	−0.493705	−	0.493705i	−0.909472	+	0.415766i	$0.863513\pi$
$684$		0			0
$685$	−8.93077	+	8.93077i	−0.341227	+	0.341227i
$686$	−26.7878	−	3.19432i	−1.02276	−	0.121960i
$687$		0			0
$688$	−0.673711	−	2.09844i	−0.0256850	−	0.0800022i
$689$	14.8871			0.567152
$690$		0			0
$691$	−21.3923	+	21.3923i	−0.813803	+	0.813803i	−0.985202	−	0.171399i	$-0.945171\pi$
$691$	−21.3923	+	21.3923i	−0.813803	+	0.813803i	0.171399	+	0.985202i	$0.445171\pi$
$692$	10.5096	−	6.41502i	0.399515	−	0.243863i
$693$		0			0
$694$	−9.86286	+	7.76126i	−0.374389	+	0.294614i
$695$		−	41.1941i		−	1.56258i
$696$		0			0
$697$			5.08312i			0.192537i
$698$	5.86564	+	7.45394i	0.222018	+	0.282136i
$699$		0			0
$700$	−5.56264	−	1.34577i	−0.210248	−	0.0508655i
$701$	−14.2040	+	14.2040i	−0.536479	+	0.536479i	−0.922493	−	0.386014i	$-0.873852\pi$
$701$	−14.2040	+	14.2040i	−0.536479	+	0.536479i	0.386014	+	0.922493i	$0.373852\pi$
$702$		0			0
$703$	24.8776			0.938278
$704$	0.392364	+	5.34408i	0.0147878	+	0.201413i
$705$		0			0
$706$	1.46668	−	12.2997i	0.0551993	−	0.462906i
$707$	−19.2458	+	19.2458i	−0.723812	+	0.723812i
$708$		0			0
$709$	−29.5474	−	29.5474i	−1.10968	−	1.10968i	−0.993192	−	0.116485i	$-0.962837\pi$
$709$	−29.5474	−	29.5474i	−1.10968	−	1.10968i	−0.116485	−	0.993192i	$-0.537163\pi$
$710$	11.0661	+	14.0625i	0.415302	+	0.527758i
$711$		0			0
$712$	−16.7472	−	6.22836i	−0.627627	−	0.233418i
$713$			18.5478i			0.694622i
$714$		0			0
$715$	4.78473	+	4.78473i	0.178939	+	0.178939i
$716$	−32.0688	+	19.5747i	−1.19847	+	0.731540i
$717$		0			0
$718$	−46.0483	−	5.49104i	−1.71851	−	0.204924i
$719$	−28.3683			−1.05796			−0.528979	−	0.848635i	$-0.677425\pi$
$719$	−28.3683			−1.05796			−0.528979	+	0.848635i	$0.677425\pi$
$720$		0			0
$721$	8.53450			0.317841
$722$	−31.6582	−	3.77509i	−1.17819	−	0.140494i
$723$		0			0
$724$	−9.35204	−	15.3213i	−0.347566	−	0.569411i
$725$	3.44521	+	3.44521i	0.127952	+	0.127952i
$726$		0			0
$727$			20.4843i			0.759722i	0.925044	+	0.379861i	$0.124028\pi$
$727$			20.4843i			0.759722i	−0.925044	+	0.379861i	$0.875972\pi$
$728$	26.8628	−	12.2985i	0.995603	−	0.455814i
$729$		0			0
$730$	−31.9570	−	40.6104i	−1.18278	−	1.50306i
$731$	−2.51119	−	2.51119i	−0.0928797	−	0.0928797i
$732$		0			0
$733$	33.9961	−	33.9961i	1.25567	−	1.25567i	0.302536	−	0.953138i	$-0.402167\pi$
$733$	33.9961	−	33.9961i	1.25567	−	1.25567i	0.953138	−	0.302536i	$-0.0978331\pi$
$734$	3.45680	−	28.9889i	0.127593	−	1.07000i
$735$		0			0
$736$	13.2645	+	8.94725i	0.488936	+	0.329800i
$737$	2.00706			0.0739310
$738$		0			0
$739$	15.1645	−	15.1645i	0.557836	−	0.557836i	−0.370855	−	0.928691i	$-0.620935\pi$
$739$	15.1645	−	15.1645i	0.557836	−	0.557836i	0.928691	+	0.370855i	$0.120935\pi$
$740$	4.49011	−	18.5595i	0.165060	−	0.682260i
$741$		0			0
$742$	−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	$-0.0126988\pi$
$744$		0			0
$745$		−	27.6631i		−	1.01350i
$746$	−26.1167	+	20.5517i	−0.956200	+	0.752451i
$747$		0			0
$748$	4.49861	+	7.36999i	0.164485	+	0.269473i
$749$	35.9670	−	35.9670i	1.31421	−	1.31421i
$750$		0			0
$751$	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
$753$		0			0
$754$	−24.9750	−	2.97815i	−0.909536	−	0.108458i
$755$	−25.6256	+	25.6256i	−0.932610	+	0.932610i
$756$		0			0
$757$	−15.3294	−	15.3294i	−0.557157	−	0.557157i	0.371340	−	0.928497i	$-0.378899\pi$
$757$	−15.3294	−	15.3294i	−0.557157	−	0.557157i	−0.928497	+	0.371340i	$0.878899\pi$
$758$	12.2255	−	9.62047i	0.444050	−	0.349431i
$759$		0			0
$760$	−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	$-0.0248015\pi$
$762$		0			0
$763$	−7.08216	−	7.08216i	−0.256392	−	0.256392i
$764$	10.8871	+	2.63392i	0.393880	+	0.0952918i
$765$		0			0
$766$	2.88080	−	24.1586i	0.104088	−	0.872886i
$767$	−23.1027			−0.834191
$768$		0			0
$769$	33.8819			1.22181			0.610907	−	0.791703i	$-0.290805\pi$
$769$	33.8819			1.22181			0.610907	+	0.791703i	$0.290805\pi$
$770$	0.709603	−	5.95078i	0.0255723	−	0.214451i
$771$		0			0
$772$	37.8119	+	9.14787i	1.36088	+	0.329239i
$773$	35.0230	+	35.0230i	1.25969	+	1.25969i	0.951240	+	0.308450i	$0.0998104\pi$
$773$	35.0230	+	35.0230i	1.25969	+	1.25969i	0.308450	+	0.951240i	$0.400190\pi$
$774$		0			0
$775$			7.33686i			0.263548i
$776$	−12.4753	+	33.5443i	−0.447837	+	1.20417i
$777$		0			0
$778$	37.4877	−	29.4998i	1.34400	−	1.05762i
$779$	−3.59431	−	3.59431i	−0.128779	−	0.128779i
$780$		0			0
$781$	−2.42274	+	2.42274i	−0.0866923	+	0.0866923i
$782$	25.6006	+	3.05275i	0.915475	+	0.109166i
$783$		0			0
$784$	1.63097	+	0.838225i	0.0582489	+	0.0299366i
$785$	11.0263			0.393545
$786$		0			0
$787$	24.1090	−	24.1090i	0.859393	−	0.859393i	−0.131873	−	0.991267i	$-0.542099\pi$
$787$	24.1090	−	24.1090i	0.859393	−	0.859393i	0.991267	+	0.131873i	$0.0420992\pi$
$788$	1.82424	+	2.98862i	0.0649860	+	0.106465i
$789$		0			0
$790$	17.3744	−	13.6722i	0.618154	−	0.486437i
$791$			5.72312i			0.203491i
$792$		0			0
$793$			25.3326i			0.899585i
$794$	12.6987	+	16.1372i	0.450659	+	0.572688i
$795$		0			0
$796$	−0.467336	+	1.93169i	−0.0165643	+	0.0684670i
$797$	28.7722	−	28.7722i	1.01917	−	1.01917i	0.0193524	−	0.999813i	$-0.493840\pi$
$797$	28.7722	−	28.7722i	1.01917	−	1.01917i	0.999813	−	0.0193524i	$-0.00616044\pi$
$798$		0			0
$799$	−18.2306			−0.644952
$800$	5.24696	+	3.53921i	0.185508	+	0.125130i
$801$		0			0
$802$	−5.39655	+	45.2559i	−0.190559	+	1.59804i
$803$	6.99647	−	6.99647i	0.246900	−	0.246900i
$804$		0			0
$805$	−12.6533	−	12.6533i	−0.445971	−	0.445971i
$806$	−23.4221	−	29.7643i	−0.825007	−	1.04840i
$807$		0			0
$808$	27.3674	−	12.5295i	0.962780	−	0.440787i
$809$		−	10.9926i		−	0.386478i	−0.981152	−	0.193239i	$-0.938101\pi$
$809$		−	10.9926i		−	0.386478i	0.981152	−	0.193239i	$-0.0618993\pi$
$810$		0			0
$811$	−15.0259	−	15.0259i	−0.527630	−	0.527630i	0.392235	−	0.919865i	$-0.371702\pi$
$811$	−15.0259	−	15.0259i	−0.527630	−	0.527630i	−0.919865	+	0.392235i	$0.871702\pi$
$812$	11.6060	+	19.0138i	0.407289	+	0.667255i
$813$		0			0
$814$	3.63039	+	0.432907i	0.127245	+	0.0151734i
$815$	−19.2574			−0.674558
$816$		0			0
$817$	3.55136			0.124246
$818$	−16.2476	−	1.93745i	−0.568085	−	0.0677415i
$819$		0			0
$820$	−3.33019	+	2.03274i	−0.116295	+	0.0709862i
$821$	21.2536	+	21.2536i	0.741756	+	0.741756i	0.972916	−	0.231159i	$-0.0742519\pi$
$821$	21.2536	+	21.2536i	0.741756	+	0.741756i	−0.231159	+	0.972916i	$0.574252\pi$
$822$		0			0
$823$			55.0851i			1.92015i	0.279751	+	0.960073i	$0.409748\pi$
$823$			55.0851i			1.92015i	−0.279751	+	0.960073i	$0.590252\pi$
$824$	−8.84609	−	3.28991i	−0.308168	−	0.114609i
$825$		0			0
$826$	12.6533	+	16.0796i	0.440265	+	0.559480i
$827$	24.4290	+	24.4290i	0.849480	+	0.849480i	0.990068	−	0.140588i	$-0.0448994\pi$
$827$	24.4290	+	24.4290i	0.849480	+	0.849480i	−0.140588	+	0.990068i	$0.544899\pi$
$828$		0			0
$829$	−21.9235	+	21.9235i	−0.761436	+	0.761436i	−0.976582	−	0.215146i	$-0.930977\pi$
$829$	−21.9235	+	21.9235i	−0.761436	+	0.761436i	0.215146	+	0.976582i	$0.430977\pi$
$830$	0.375881	−	3.15217i	0.0130470	−	0.109413i
$831$		0			0
$832$	−32.5845	+	2.39236i	−1.12966	+	0.0829403i
$833$	2.95487			0.102380
$834$		0			0
$835$	35.2996	−	35.2996i	1.22159	−	1.22159i
$836$	−8.39236	−	2.03037i	−0.290256	−	0.0702218i
$837$		0			0
$838$	8.34498	+	10.6046i	0.288273	+	0.366331i
$839$		−	5.14195i		−	0.177520i	−0.996053	−	0.0887599i	$-0.971710\pi$
$839$		−	5.14195i		−	0.177520i	0.996053	−	0.0887599i	$-0.0282904\pi$
$840$		0			0
$841$			10.0357i			0.346059i
$842$	−27.0711	+	21.3028i	−0.932933	+	0.734142i
$843$		0			0
$844$	−10.1984	+	6.22507i	−0.351044	+	0.214276i
$845$	−6.43541	+	6.43541i	−0.221385	+	0.221385i
$846$		0			0
$847$	−26.9867			−0.927272
$848$	4.45714	+	13.8828i	0.153059	+	0.476739i
$849$		0			0
$850$	10.1267	+	1.20756i	0.347342	+	0.0414189i
$851$	7.71940	−	7.71940i	0.264618	−	0.264618i
$852$		0			0
$853$	13.0857	+	13.0857i	0.448046	+	0.448046i	0.894704	−	0.446659i	$-0.147386\pi$
$853$	13.0857	+	13.0857i	0.448046	+	0.448046i	−0.446659	+	0.894704i	$0.647386\pi$
$854$	17.6316	−	13.8746i	0.603340	−	0.474779i
$855$		0			0
$856$	−51.1449	+	23.4155i	−1.74810	+	0.800325i
$857$		−	22.8878i		−	0.781833i	−0.920426	−	0.390916i	$-0.872158\pi$
$857$		−	22.8878i		−	0.781833i	0.920426	−	0.390916i	$-0.127842\pi$
$858$		0			0
$859$	−25.1225	−	25.1225i	−0.857169	−	0.857169i	0.133834	−	0.991004i	$-0.457271\pi$
$859$	−25.1225	−	25.1225i	−0.857169	−	0.857169i	−0.991004	+	0.133834i	$0.957271\pi$
$860$	0.640976	−	2.64942i	0.0218571	−	0.0903445i
$861$		0			0
$862$	−6.81677	+	57.1660i	−0.232180	+	1.94708i
$863$	43.9296			1.49538			0.747691	−	0.664047i	$-0.231163\pi$
$863$	43.9296			1.49538			0.747691	+	0.664047i	$0.231163\pi$
$864$		0			0
$865$	15.2286			0.517788
$866$	1.22470	−	10.2704i	0.0416168	−	0.349002i
$867$		0			0
$868$	−7.88784	+	32.6037i	−0.267731	+	1.10664i
$869$	2.99331	+	2.99331i	0.101541	+	0.101541i
$870$		0			0
$871$			12.2376i			0.414657i
$872$	4.61068	+	10.0708i	0.156137	+	0.341040i
$873$		0			0
$874$	−20.2610	+	15.9437i	−0.685337	+	0.539304i
$875$	17.3629	+	17.3629i	0.586974	+	0.586974i
$876$		0			0
$877$	15.2575	−	15.2575i	0.515208	−	0.515208i	−0.400910	−	0.916117i	$-0.631306\pi$
$877$	15.2575	−	15.2575i	0.515208	−	0.515208i	0.916117	+	0.400910i	$0.131306\pi$
$878$	−24.8726	−	2.96594i	−0.839409	−	0.100096i
$879$		0			0
$880$	−3.02944	+	5.89450i	−0.102122	+	0.198704i
$881$	−21.6686			−0.730035			−0.365018	−	0.931001i	$-0.618937\pi$
$881$	−21.6686			−0.730035			−0.365018	+	0.931001i	$0.618937\pi$
$882$		0			0
$883$	−0.0590385	+	0.0590385i	−0.00198680	+	0.00198680i	−0.708099	−	0.706113i	$-0.750447\pi$
$883$	−0.0590385	+	0.0590385i	−0.00198680	+	0.00198680i	0.706113	+	0.708099i	$0.250447\pi$
$884$	−44.9370	+	27.4294i	−1.51140	+	0.922550i
$885$		0			0
$886$	−24.6672	+	19.4111i	−0.828710	+	0.652127i
$887$			30.8043i			1.03431i	0.855892	+	0.517154i	$0.173009\pi$
$887$			30.8043i			1.03431i	−0.855892	+	0.517154i	$0.826991\pi$
$888$		0			0
$889$		−	31.2404i		−	1.04777i
$890$	−13.6663	−	17.3668i	−0.458095	−	0.582137i
$891$		0			0
$892$	46.1989	+	11.1769i	1.54685	+	0.374232i
$893$	12.8910	−	12.8910i	0.431380	−	0.431380i
$894$		0			0
$895$	−46.4682			−1.55326
$896$	19.5116	+	21.3686i	0.651836	+	0.713876i
$897$		0			0
$898$	4.74559	−	39.7969i	0.158362	−	1.32804i
$899$	20.1930	−	20.1930i	0.673475	−	0.673475i
$900$		0			0
$901$	16.6135	+	16.6135i	0.553477	+	0.553477i
$902$	−0.461970	−	0.587062i	−0.0153819	−	0.0195470i
$903$		0			0
$904$	2.20617	−	5.93207i	0.0733760	−	0.197298i
$905$		−	22.2008i		−	0.737979i
$906$		0			0
$907$	35.0170	+	35.0170i	1.16272	+	1.16272i	0.983878	+	0.178844i	$0.0572356\pi$
$907$	35.0170	+	35.0170i	1.16272	+	1.16272i	0.178844	+	0.983878i	$0.442764\pi$
$908$	−1.54913	+	0.945580i	−0.0514095	+	0.0313802i
$909$		0			0
$910$	36.2837	+	4.32666i	1.20279	+	0.143427i
$911$	−0.0829331			−0.00274770			−0.00137385	−	0.999999i	$-0.500437\pi$
$911$	−0.0829331			−0.00274770			−0.00137385	+	0.999999i	$0.500437\pi$
$912$		0			0
$913$	0.607822			0.0201160
$914$	24.3494	+	2.90355i	0.805407	+	0.0960410i
$915$		0			0
$916$	−7.87321	−	12.8985i	−0.260138	−	0.426180i
$917$	−9.65685	−	9.65685i	−0.318897	−	0.318897i
$918$		0			0
$919$		−	20.1161i		−	0.663568i	−0.943355	−	0.331784i	$-0.892350\pi$
$919$		−	20.1161i		−	0.663568i	0.943355	−	0.331784i	$-0.107650\pi$
$920$	8.23765	+	17.9929i	0.271587	+	0.593210i
$921$		0			0
$922$	−2.09373	−	2.66066i	−0.0689532	−	0.0876243i
$923$	−14.7721	−	14.7721i	−0.486231	−	0.486231i
$924$		0			0
$925$	3.05352	−	3.05352i	0.100399	−	0.100399i
$926$	0.452519	−	3.79486i	0.0148707	−	0.124707i
$927$		0			0
$928$	−4.70018	−	24.1819i	−0.154291	−	0.793811i
$929$	−8.55098			−0.280549			−0.140274	−	0.990113i	$-0.544798\pi$
$929$	−8.55098			−0.280549			−0.140274	+	0.990113i	$0.544798\pi$
$930$		0			0
$931$	−2.08941	+	2.08941i	−0.0684776	+	0.0684776i
$932$	−10.9235	+	45.1515i	−0.357813	+	1.47899i
$933$		0			0
$934$	−21.1663	−	26.8978i	−0.692584	−	0.880122i
$935$			10.6792i			0.349248i
$936$		0			0
$937$		−	33.5780i		−	1.09695i	−0.836168	−	0.548473i	$-0.815209\pi$
$937$		−	33.5780i		−	1.09695i	0.836168	−	0.548473i	$-0.184791\pi$
$938$	8.51746	−	6.70254i	0.278105	−	0.218846i
$939$		0			0
$940$	−7.29040	−	11.9437i	−0.237787	−	0.389561i
$941$	8.48463	−	8.48463i	0.276591	−	0.276591i	−0.555156	−	0.831747i	$-0.687341\pi$
$941$	8.48463	−	8.48463i	0.276591	−	0.276591i	0.831747	+	0.555156i	$0.187341\pi$
$942$		0			0
$943$	−2.23059			−0.0726380
$944$	−6.91688	−	21.5443i	−0.225125	−	0.701207i
$945$		0			0
$946$	0.518248	+	0.0617987i	0.0168497	+	0.00200925i
$947$	−17.8571	+	17.8571i	−0.580277	+	0.580277i	−0.934979	−	0.354702i	$-0.884582\pi$
$947$	−17.8571	+	17.8571i	−0.580277	+	0.580277i	0.354702	+	0.934979i	$0.384582\pi$
$948$		0			0
$949$	42.6596	+	42.6596i	1.38479	+	1.38479i
$950$	−8.01451	+	6.30676i	−0.260025	+	0.204618i
$951$		0			0
$952$	43.7029	+	16.2533i	1.41642	+	0.526774i
$953$		−	3.86469i		−	0.125190i	−0.998039	−	0.0625948i	$-0.980062\pi$
$953$		−	3.86469i		−	0.125190i	0.998039	−	0.0625948i	$-0.0199376\pi$
$954$		0			0
$955$	9.79607	+	9.79607i	0.316993	+	0.316993i
$956$	52.3329	+	12.6609i	1.69257	+	0.409484i
$957$		0			0
$958$	3.72163	−	31.2099i	0.120240	−	1.00835i
$959$	−13.0590			−0.421698
$960$		0			0
$961$	12.0027			0.387185
$962$	−2.63956	+	22.1356i	−0.0851029	+	0.713679i
$963$		0			0
$964$	20.1184	+	4.86727i	0.647971	+	0.156764i
$965$	34.0228	+	34.0228i	1.09523	+	1.09523i
$966$		0			0
$967$		−	37.8714i		−	1.21786i	−0.793224	−	0.608930i	$-0.791599\pi$
$967$		−	37.8714i		−	1.21786i	0.793224	−	0.608930i	$-0.208401\pi$
$968$	27.9719	+	10.4029i	0.899052	+	0.334362i
$969$		0			0
$970$	−34.7855	+	27.3733i	−1.11689	+	0.878905i
$971$	−2.64873	−	2.64873i	−0.0850017	−	0.0850017i	0.663327	−	0.748329i	$-0.269144\pi$
$971$	−2.64873	−	2.64873i	−0.0850017	−	0.0850017i	−0.748329	+	0.663327i	$0.769144\pi$
$972$		0			0
$973$	30.1180	−	30.1180i	0.965540	−	0.965540i
$974$	19.6371	+	2.34163i	0.629214	+	0.0750308i
$975$		0			0
$976$	−23.6237	+	7.58449i	−0.756177	+	0.242774i
$977$	−17.6530			−0.564768			−0.282384	−	0.959301i	$-0.591125\pi$
$977$	−17.6530			−0.564768			−0.282384	+	0.959301i	$0.591125\pi$
$978$		0			0
$979$	2.99201	−	2.99201i	0.0956250	−	0.0956250i
$980$	1.18165	+	1.93588i	0.0377464	+	0.0618393i
$981$		0			0
$982$	−11.3700	+	8.94725i	−0.362831	+	0.285518i
$983$			22.3557i			0.713035i	0.934289	+	0.356518i	$0.116036\pi$
$983$			22.3557i			0.713035i	−0.934289	+	0.356518i	$0.883964\pi$
$984$		0			0
$985$			4.33057i			0.137983i
$986$	−24.5478	−	31.1949i	−0.781762	−	0.993447i
$987$		0			0
$988$	12.3798	−	51.1708i	0.393853	−	1.62796i
$989$	1.10197	−	1.10197i	0.0350405	−	0.0350405i
$990$		0			0
$991$	17.8769			0.567878			0.283939	−	0.958842i	$-0.408359\pi$
$991$	17.8769			0.567878			0.283939	+	0.958842i	$0.408359\pi$
$992$	20.7440	−	30.7534i	0.658623	−	0.976422i
$993$		0			0
$994$	−2.19079	+	18.3722i	−0.0694878	+	0.582730i
$995$	−1.73812	+	1.73812i	−0.0551020	+	0.0551020i
$996$		0			0
$997$	4.28610	+	4.28610i	0.135742	+	0.135742i	0.771713	−	0.635971i	$-0.219400\pi$
$997$	4.28610	+	4.28610i	0.135742	+	0.135742i	−0.635971	+	0.771713i	$0.719400\pi$
$998$	−3.20431	−	4.07197i	−0.101431	−	0.128896i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.2.k.b.37.3		8
3.2	odd	2		48.2.j.a.37.2	yes	8
4.3	odd	2		576.2.k.b.433.1		8
8.3	odd	2		1152.2.k.f.865.4		8
8.5	even	2		1152.2.k.c.865.4		8
12.11	even	2		192.2.j.a.49.4		8
16.3	odd	4		576.2.k.b.145.1		8
16.5	even	4		1152.2.k.c.289.4		8
16.11	odd	4		1152.2.k.f.289.4		8
16.13	even	4	inner	144.2.k.b.109.3		8
24.5	odd	2		384.2.j.b.97.3		8
24.11	even	2		384.2.j.a.97.1		8
32.3	odd	8		9216.2.a.bn.1.3		4
32.13	even	8		9216.2.a.y.1.2		4
32.19	odd	8		9216.2.a.x.1.2		4
32.29	even	8		9216.2.a.bo.1.3		4
48.5	odd	4		384.2.j.b.289.3		8
48.11	even	4		384.2.j.a.289.1		8
48.29	odd	4		48.2.j.a.13.2	✓	8
48.35	even	4		192.2.j.a.145.4		8
96.5	odd	8		3072.2.d.f.1537.3		8
96.11	even	8		3072.2.d.i.1537.2		8
96.29	odd	8		3072.2.a.i.1.2		4
96.35	even	8		3072.2.a.o.1.2		4
96.53	odd	8		3072.2.d.f.1537.6		8
96.59	even	8		3072.2.d.i.1537.7		8
96.77	odd	8		3072.2.a.t.1.3		4
96.83	even	8		3072.2.a.n.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.2.j.a.13.2	✓	8	48.29	odd	4
48.2.j.a.37.2	yes	8	3.2	odd	2
144.2.k.b.37.3		8	1.1	even	1	trivial
144.2.k.b.109.3		8	16.13	even	4	inner
192.2.j.a.49.4		8	12.11	even	2
192.2.j.a.145.4		8	48.35	even	4
384.2.j.a.97.1		8	24.11	even	2
384.2.j.a.289.1		8	48.11	even	4
384.2.j.b.97.3		8	24.5	odd	2
384.2.j.b.289.3		8	48.5	odd	4
576.2.k.b.145.1		8	16.3	odd	4
576.2.k.b.433.1		8	4.3	odd	2
1152.2.k.c.289.4		8	16.5	even	4
1152.2.k.c.865.4		8	8.5	even	2
1152.2.k.f.289.4		8	16.11	odd	4
1152.2.k.f.865.4		8	8.3	odd	2
3072.2.a.i.1.2		4	96.29	odd	8
3072.2.a.n.1.3		4	96.83	even	8
3072.2.a.o.1.2		4	96.35	even	8
3072.2.a.t.1.3		4	96.77	odd	8
3072.2.d.f.1537.3		8	96.5	odd	8
3072.2.d.f.1537.6		8	96.53	odd	8
3072.2.d.i.1537.2		8	96.11	even	8
3072.2.d.i.1537.7		8	96.59	even	8
9216.2.a.x.1.2		4	32.19	odd	8
9216.2.a.y.1.2		4	32.13	even	8
9216.2.a.bn.1.3		4	32.3	odd	8
9216.2.a.bo.1.3		4	32.29	even	8

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	144.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.167452 - 1.40426i) q^{2} +(-1.94392 - 0.470294i) q^{4} +(-1.74912 - 1.74912i) q^{5} -2.55765i q^{7} +(-0.985930 + 2.65103i) q^{8} +O(q^{10})\)	\(q+(0.167452 - 1.40426i) q^{2} +(-1.94392 - 0.470294i) q^{4} +(-1.74912 - 1.74912i) q^{5} -2.55765i q^{7} +(-0.985930 + 2.65103i) q^{8} +(-2.74912 + 2.16333i) q^{10} +(-0.473626 - 0.473626i) q^{11} +(2.88784 - 2.88784i) q^{13} +(-3.59161 - 0.428283i) q^{14} +(3.55765 + 1.82843i) q^{16} +6.44549 q^{17} +(-4.55765 + 4.55765i) q^{19} +(2.57754 + 4.22274i) q^{20} +(-0.744406 + 0.585786i) q^{22} +2.82843i q^{23} +1.11882i q^{25} +(-3.57172 - 4.53887i) q^{26} +(-1.20285 + 4.97186i) q^{28} +(3.07931 - 3.07931i) q^{29} +6.55765 q^{31} +(3.16333 - 4.68971i) q^{32} +(1.07931 - 9.05117i) q^{34} +(-4.47363 + 4.47363i) q^{35} +(-2.72922 - 2.72922i) q^{37} +(5.63696 + 7.16333i) q^{38} +(6.36147 - 2.91245i) q^{40} +0.788632i q^{41} +(-0.389604 - 0.389604i) q^{43} +(0.697947 + 1.14343i) q^{44} +(3.97186 + 0.473626i) q^{46} -2.82843 q^{47} +0.458440 q^{49} +(1.57113 + 0.187349i) q^{50} +(-6.97186 + 4.25559i) q^{52} +(2.57754 + 2.57754i) q^{53} +1.65685i q^{55} +(6.78039 + 2.52166i) q^{56} +(-3.80853 - 4.83980i) q^{58} +(-4.00000 - 4.00000i) q^{59} +(-4.38607 + 4.38607i) q^{61} +(1.09809 - 9.20867i) q^{62} +(-6.05588 - 5.22746i) q^{64} -10.1023 q^{65} +(-2.11882 + 2.11882i) q^{67} +(-12.5295 - 3.03127i) q^{68} +(5.53304 + 7.03127i) q^{70} -5.11529i q^{71} +14.7721i q^{73} +(-4.28956 + 3.37553i) q^{74} +(11.0031 - 6.71627i) q^{76} +(-1.21137 + 1.21137i) q^{77} -6.32000 q^{79} +(-3.02461 - 9.42088i) q^{80} +(1.10745 + 0.132058i) q^{82} +(-0.641669 + 0.641669i) q^{83} +(-11.2739 - 11.2739i) q^{85} +(-0.612348 + 0.481868i) q^{86} +(1.72256 - 0.788632i) q^{88} +6.31724i q^{89} +(-7.38607 - 7.38607i) q^{91} +(1.33019 - 5.49824i) q^{92} +(-0.473626 + 3.97186i) q^{94} +15.9437 q^{95} +12.6533 q^{97} +(0.0767667 - 0.643772i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4} + 12 q^{8}+O(q^{10}) \) 8 * q - 4 * q^4 + 12 * q^8	\( 8 q - 4 q^{4} + 12 q^{8} - 8 q^{10} + 8 q^{11} - 12 q^{14} - 8 q^{19} - 16 q^{20} - 20 q^{26} + 8 q^{28} + 16 q^{29} + 24 q^{31} - 24 q^{35} - 16 q^{37} + 8 q^{38} + 16 q^{40} - 8 q^{43} + 40 q^{44} - 8 q^{46} - 8 q^{49} + 36 q^{50} - 16 q^{52} - 16 q^{53} - 16 q^{58} - 32 q^{59} + 16 q^{61} + 12 q^{62} + 8 q^{64} + 16 q^{65} - 16 q^{67} - 32 q^{68} + 32 q^{70} - 52 q^{74} + 8 q^{76} - 16 q^{77} - 24 q^{79} - 8 q^{80} + 40 q^{82} + 40 q^{83} - 16 q^{85} + 16 q^{86} + 32 q^{88} - 8 q^{91} + 16 q^{92} + 8 q^{94} + 48 q^{95} + 40 q^{98}+O(q^{100}) \) 8 * q - 4 * q^4 + 12 * q^8 - 8 * q^10 + 8 * q^11 - 12 * q^14 - 8 * q^19 - 16 * q^20 - 20 * q^26 + 8 * q^28 + 16 * q^29 + 24 * q^31 - 24 * q^35 - 16 * q^37 + 8 * q^38 + 16 * q^40 - 8 * q^43 + 40 * q^44 - 8 * q^46 - 8 * q^49 + 36 * q^50 - 16 * q^52 - 16 * q^53 - 16 * q^58 - 32 * q^59 + 16 * q^61 + 12 * q^62 + 8 * q^64 + 16 * q^65 - 16 * q^67 - 32 * q^68 + 32 * q^70 - 52 * q^74 + 8 * q^76 - 16 * q^77 - 24 * q^79 - 8 * q^80 + 40 * q^82 + 40 * q^83 - 16 * q^85 + 16 * q^86 + 32 * q^88 - 8 * q^91 + 16 * q^92 + 8 * q^94 + 48 * q^95 + 40 * q^98

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