LMFDB - Embedded newform 6032.2.a.bc.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6032,2,Mod(1,6032)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6032, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6032.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6032 = 2^{4} \cdot 13 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6032.a (trivial)

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:	yes
Analytic conductor:	$48.1657624992$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 5x^{10} - 9x^{9} + 65x^{8} + 19x^{7} - 298x^{6} + 17x^{5} + 541x^{4} - 60x^{3} - 287x^{2} + 16x + 16 $ x^11 - 5x^10 - 9x^9 + 65x^8 + 19x^7 - 298x^6 + 17x^5 + 541x^4 - 60x^3 - 287x^2 + 16x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 3016)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.59661$ of defining polynomial
Character	$\chi$	$=$	6032.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.59661 q^{3} -0.374330 q^{5} +3.78268 q^{7} -0.450834 q^{9} +O(q^{10})$	$q-1.59661 q^{3} -0.374330 q^{5} +3.78268 q^{7} -0.450834 q^{9} -1.97735 q^{11} +1.00000 q^{13} +0.597659 q^{15} -2.38796 q^{17} -2.09435 q^{19} -6.03947 q^{21} -8.30935 q^{23} -4.85988 q^{25} +5.50964 q^{27} -1.00000 q^{29} +1.33210 q^{31} +3.15707 q^{33} -1.41597 q^{35} +6.92327 q^{37} -1.59661 q^{39} -7.04435 q^{41} +12.4188 q^{43} +0.168760 q^{45} +10.0174 q^{47} +7.30865 q^{49} +3.81264 q^{51} -0.963766 q^{53} +0.740182 q^{55} +3.34387 q^{57} +4.25675 q^{59} -5.88047 q^{61} -1.70536 q^{63} -0.374330 q^{65} -0.790177 q^{67} +13.2668 q^{69} +9.34260 q^{71} -4.16337 q^{73} +7.75933 q^{75} -7.47970 q^{77} +14.8175 q^{79} -7.44425 q^{81} -8.66686 q^{83} +0.893883 q^{85} +1.59661 q^{87} +5.24301 q^{89} +3.78268 q^{91} -2.12685 q^{93} +0.783978 q^{95} -12.7896 q^{97} +0.891458 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 6 q^{3} - 2 q^{5} + 3 q^{7} + 11 q^{9}+O(q^{10}) $ 11 * q + 6 * q^3 - 2 * q^5 + 3 * q^7 + 11 * q^9	$ 11 q + 6 q^{3} - 2 q^{5} + 3 q^{7} + 11 q^{9} + 13 q^{11} + 11 q^{13} + 8 q^{15} - 6 q^{17} + 12 q^{19} + q^{21} + 13 q^{23} + 11 q^{25} + 24 q^{27} - 11 q^{29} + 11 q^{31} + 17 q^{33} + 4 q^{35} + 11 q^{37} + 6 q^{39} - 9 q^{41} + 30 q^{43} - 16 q^{45} + q^{47} - 4 q^{49} + 13 q^{51} - 9 q^{53} + q^{55} + 2 q^{57} + 9 q^{59} - 5 q^{61} + 6 q^{63} - 2 q^{65} + 25 q^{67} + 26 q^{71} + 10 q^{73} + 41 q^{75} - 8 q^{77} + 14 q^{79} + 3 q^{81} + 6 q^{83} + 19 q^{85} - 6 q^{87} - 11 q^{89} + 3 q^{91} - 3 q^{93} + 31 q^{95} + 12 q^{97} + 35 q^{99}+O(q^{100}) $ 11 * q + 6 * q^3 - 2 * q^5 + 3 * q^7 + 11 * q^9 + 13 * q^11 + 11 * q^13 + 8 * q^15 - 6 * q^17 + 12 * q^19 + q^21 + 13 * q^23 + 11 * q^25 + 24 * q^27 - 11 * q^29 + 11 * q^31 + 17 * q^33 + 4 * q^35 + 11 * q^37 + 6 * q^39 - 9 * q^41 + 30 * q^43 - 16 * q^45 + q^47 - 4 * q^49 + 13 * q^51 - 9 * q^53 + q^55 + 2 * q^57 + 9 * q^59 - 5 * q^61 + 6 * q^63 - 2 * q^65 + 25 * q^67 + 26 * q^71 + 10 * q^73 + 41 * q^75 - 8 * q^77 + 14 * q^79 + 3 * q^81 + 6 * q^83 + 19 * q^85 - 6 * q^87 - 11 * q^89 + 3 * q^91 - 3 * q^93 + 31 * q^95 + 12 * q^97 + 35 * q^99

Display 100 coefficients 10 coefficients

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	0
$2$	0	0
$3$	−1.59661	−0.921804	−0.460902	−	0.887451i	$-0.652474\pi$
$3$	−1.59661	−0.921804	−0.460902	+	0.887451i	$0.652474\pi$
$4$	0	0
$5$	−0.374330	−0.167405	−0.0837026	−	0.996491i	$-0.526675\pi$
$5$	−0.374330	−0.167405	−0.0837026	+	0.996491i	$0.526675\pi$
$6$	0	0
$7$	3.78268	1.42972	0.714859	−	0.699269i	$-0.246491\pi$
$7$	3.78268	1.42972	0.714859	+	0.699269i	$0.246491\pi$
$8$	0	0
$9$	−0.450834	−0.150278
$10$	0	0
$11$	−1.97735	−0.596195	−0.298097	−	0.954535i	$-0.596352\pi$
$11$	−1.97735	−0.596195	−0.298097	+	0.954535i	$0.596352\pi$
$12$	0	0
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	0.597659	0.154315
$16$	0	0
$17$	−2.38796	−0.579165	−0.289582	−	0.957153i	$-0.593516\pi$
$17$	−2.38796	−0.579165	−0.289582	+	0.957153i	$0.593516\pi$
$18$	0	0
$19$	−2.09435	−0.480477	−0.240239	−	0.970714i	$-0.577226\pi$
$19$	−2.09435	−0.480477	−0.240239	+	0.970714i	$0.577226\pi$
$20$	0	0
$21$	−6.03947	−1.31792
$22$	0	0
$23$	−8.30935	−1.73262	−0.866309	−	0.499508i	$-0.833514\pi$
$23$	−8.30935	−1.73262	−0.866309	+	0.499508i	$0.833514\pi$
$24$	0	0
$25$	−4.85988	−0.971975
$26$	0	0
$27$	5.50964	1.06033
$28$	0	0
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0	0
$31$	1.33210	0.239252	0.119626	−	0.992819i	$-0.461830\pi$
$31$	1.33210	0.239252	0.119626	+	0.992819i	$0.461830\pi$
$32$	0	0
$33$	3.15707	0.549575
$34$	0	0
$35$	−1.41597	−0.239342
$36$	0	0
$37$	6.92327	1.13818	0.569090	−	0.822276i	$-0.307296\pi$
$37$	6.92327	1.13818	0.569090	+	0.822276i	$0.307296\pi$
$38$	0	0
$39$	−1.59661	−0.255662
$40$	0	0
$41$	−7.04435	−1.10014	−0.550071	−	0.835118i	$-0.685399\pi$
$41$	−7.04435	−1.10014	−0.550071	+	0.835118i	$0.685399\pi$
$42$	0	0
$43$	12.4188	1.89385	0.946926	−	0.321453i	$-0.104171\pi$
$43$	12.4188	1.89385	0.946926	+	0.321453i	$0.104171\pi$
$44$	0	0
$45$	0.168760	0.0251573
$46$	0	0
$47$	10.0174	1.46119	0.730597	−	0.682809i	$-0.239242\pi$
$47$	10.0174	1.46119	0.730597	+	0.682809i	$0.239242\pi$
$48$	0	0
$49$	7.30865	1.04409
$50$	0	0
$51$	3.81264	0.533876
$52$	0	0
$53$	−0.963766	−0.132383	−0.0661917	−	0.997807i	$-0.521085\pi$
$53$	−0.963766	−0.132383	−0.0661917	+	0.997807i	$0.521085\pi$
$54$	0	0
$55$	0.740182	0.0998062
$56$	0	0
$57$	3.34387	0.442906
$58$	0	0
$59$	4.25675	0.554182	0.277091	−	0.960844i	$-0.410630\pi$
$59$	4.25675	0.554182	0.277091	+	0.960844i	$0.410630\pi$
$60$	0	0
$61$	−5.88047	−0.752917	−0.376459	−	0.926433i	$-0.622858\pi$
$61$	−5.88047	−0.752917	−0.376459	+	0.926433i	$0.622858\pi$
$62$	0	0
$63$	−1.70536	−0.214855
$64$	0	0
$65$	−0.374330	−0.0464299
$66$	0	0
$67$	−0.790177	−0.0965354	−0.0482677	−	0.998834i	$-0.515370\pi$
$67$	−0.790177	−0.0965354	−0.0482677	+	0.998834i	$0.515370\pi$
$68$	0	0
$69$	13.2668	1.59713
$70$	0	0
$71$	9.34260	1.10876	0.554381	−	0.832263i	$-0.312955\pi$
$71$	9.34260	1.10876	0.554381	+	0.832263i	$0.312955\pi$
$72$	0	0
$73$	−4.16337	−0.487285	−0.243643	−	0.969865i	$-0.578342\pi$
$73$	−4.16337	−0.487285	−0.243643	+	0.969865i	$0.578342\pi$
$74$	0	0
$75$	7.75933	0.895971
$76$	0	0
$77$	−7.47970	−0.852390
$78$	0	0
$79$	14.8175	1.66710	0.833551	−	0.552442i	$-0.186304\pi$
$79$	14.8175	1.66710	0.833551	+	0.552442i	$0.186304\pi$
$80$	0	0
$81$	−7.44425	−0.827139
$82$	0	0
$83$	−8.66686	−0.951311	−0.475656	−	0.879632i	$-0.657789\pi$
$83$	−8.66686	−0.951311	−0.475656	+	0.879632i	$0.657789\pi$
$84$	0	0
$85$	0.893883	0.0969552
$86$	0	0
$87$	1.59661	0.171175
$88$	0	0
$89$	5.24301	0.555757	0.277879	−	0.960616i	$-0.410369\pi$
$89$	5.24301	0.555757	0.277879	+	0.960616i	$0.410369\pi$
$90$	0	0
$91$	3.78268	0.396532
$92$	0	0
$93$	−2.12685	−0.220544
$94$	0	0
$95$	0.783978	0.0804344
$96$	0	0
$97$	−12.7896	−1.29858	−0.649291	−	0.760540i	$-0.724934\pi$
$97$	−12.7896	−1.29858	−0.649291	+	0.760540i	$0.724934\pi$
$98$	0	0
$99$	0.891458	0.0895949
$100$	0	0
$101$	0.445244	0.0443035	0.0221517	−	0.999755i	$-0.492948\pi$
$101$	0.445244	0.0443035	0.0221517	+	0.999755i	$0.492948\pi$
$102$	0	0
$103$	11.4999	1.13312	0.566560	−	0.824021i	$-0.308274\pi$
$103$	11.4999	1.13312	0.566560	+	0.824021i	$0.308274\pi$
$104$	0	0
$105$	2.26075	0.220627
$106$	0	0
$107$	−7.91548	−0.765218	−0.382609	−	0.923910i	$-0.624974\pi$
$107$	−7.91548	−0.765218	−0.382609	+	0.923910i	$0.624974\pi$
$108$	0	0
$109$	8.80103	0.842986	0.421493	−	0.906832i	$-0.361506\pi$
$109$	8.80103	0.842986	0.421493	+	0.906832i	$0.361506\pi$
$110$	0	0
$111$	−11.0538	−1.04918
$112$	0	0
$113$	−14.5838	−1.37193	−0.685965	−	0.727635i	$-0.740620\pi$
$113$	−14.5838	−1.37193	−0.685965	+	0.727635i	$0.740620\pi$
$114$	0	0
$115$	3.11043	0.290049
$116$	0	0
$117$	−0.450834	−0.0416796
$118$	0	0
$119$	−9.03287	−0.828042
$120$	0	0
$121$	−7.09007	−0.644552
$122$	0	0
$123$	11.2471	1.01412
$124$	0	0
$125$	3.69084	0.330119
$126$	0	0
$127$	−0.235234	−0.0208736	−0.0104368	−	0.999946i	$-0.503322\pi$
$127$	−0.235234	−0.0208736	−0.0104368	+	0.999946i	$0.503322\pi$
$128$	0	0
$129$	−19.8280	−1.74576
$130$	0	0
$131$	6.05280	0.528835	0.264418	−	0.964408i	$-0.414820\pi$
$131$	6.05280	0.528835	0.264418	+	0.964408i	$0.414820\pi$
$132$	0	0
$133$	−7.92226	−0.686947
$134$	0	0
$135$	−2.06242	−0.177505
$136$	0	0
$137$	−9.65148	−0.824581	−0.412291	−	0.911052i	$-0.635271\pi$
$137$	−9.65148	−0.824581	−0.412291	+	0.911052i	$0.635271\pi$
$138$	0	0
$139$	9.73580	0.825780	0.412890	−	0.910781i	$-0.364519\pi$
$139$	9.73580	0.825780	0.412890	+	0.910781i	$0.364519\pi$
$140$	0	0
$141$	−15.9940	−1.34693
$142$	0	0
$143$	−1.97735	−0.165355
$144$	0	0
$145$	0.374330	0.0310864
$146$	0	0
$147$	−11.6691	−0.962449
$148$	0	0
$149$	19.6747	1.61181	0.805907	−	0.592042i	$-0.201678\pi$
$149$	19.6747	1.61181	0.805907	+	0.592042i	$0.201678\pi$
$150$	0	0
$151$	5.92923	0.482514	0.241257	−	0.970461i	$-0.422440\pi$
$151$	5.92923	0.482514	0.241257	+	0.970461i	$0.422440\pi$
$152$	0	0
$153$	1.07657	0.0870356
$154$	0	0
$155$	−0.498645	−0.0400521
$156$	0	0
$157$	3.63690	0.290256	0.145128	−	0.989413i	$-0.453641\pi$
$157$	3.63690	0.290256	0.145128	+	0.989413i	$0.453641\pi$
$158$	0	0
$159$	1.53876	0.122032
$160$	0	0
$161$	−31.4316	−2.47716
$162$	0	0
$163$	5.21102	0.408158	0.204079	−	0.978954i	$-0.434580\pi$
$163$	5.21102	0.408158	0.204079	+	0.978954i	$0.434580\pi$
$164$	0	0
$165$	−1.18178	−0.0920017
$166$	0	0
$167$	−22.7288	−1.75881	−0.879405	−	0.476074i	$-0.842060\pi$
$167$	−22.7288	−1.75881	−0.879405	+	0.476074i	$0.842060\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	0	0
$171$	0.944204	0.0722051
$172$	0	0
$173$	18.4291	1.40114	0.700570	−	0.713584i	$-0.252929\pi$
$173$	18.4291	1.40114	0.700570	+	0.713584i	$0.252929\pi$
$174$	0	0
$175$	−18.3834	−1.38965
$176$	0	0
$177$	−6.79638	−0.510847
$178$	0	0
$179$	2.35816	0.176257	0.0881285	−	0.996109i	$-0.471911\pi$
$179$	2.35816	0.176257	0.0881285	+	0.996109i	$0.471911\pi$
$180$	0	0
$181$	23.4701	1.74452	0.872258	−	0.489046i	$-0.162655\pi$
$181$	23.4701	1.74452	0.872258	+	0.489046i	$0.162655\pi$
$182$	0	0
$183$	9.38883	0.694042
$184$	0	0
$185$	−2.59159	−0.190537
$186$	0	0
$187$	4.72184	0.345295
$188$	0	0
$189$	20.8412	1.51597
$190$	0	0
$191$	7.99984	0.578848	0.289424	−	0.957201i	$-0.406536\pi$
$191$	7.99984	0.578848	0.289424	+	0.957201i	$0.406536\pi$
$192$	0	0
$193$	−0.527214	−0.0379497	−0.0189749	−	0.999820i	$-0.506040\pi$
$193$	−0.527214	−0.0379497	−0.0189749	+	0.999820i	$0.506040\pi$
$194$	0	0
$195$	0.597659	0.0427992
$196$	0	0
$197$	10.7783	0.767923	0.383962	−	0.923349i	$-0.374559\pi$
$197$	10.7783	0.767923	0.383962	+	0.923349i	$0.374559\pi$
$198$	0	0
$199$	−17.7396	−1.25753	−0.628765	−	0.777595i	$-0.716439\pi$
$199$	−17.7396	−1.25753	−0.628765	+	0.777595i	$0.716439\pi$
$200$	0	0
$201$	1.26160	0.0889867
$202$	0	0
$203$	−3.78268	−0.265492
$204$	0	0
$205$	2.63691	0.184170
$206$	0	0
$207$	3.74613	0.260374
$208$	0	0
$209$	4.14128	0.286458
$210$	0	0
$211$	−10.1569	−0.699228	−0.349614	−	0.936894i	$-0.613687\pi$
$211$	−10.1569	−0.699228	−0.349614	+	0.936894i	$0.613687\pi$
$212$	0	0
$213$	−14.9165	−1.02206
$214$	0	0
$215$	−4.64873	−0.317041
$216$	0	0
$217$	5.03891	0.342063
$218$	0	0
$219$	6.64728	0.449181
$220$	0	0
$221$	−2.38796	−0.160631
$222$	0	0
$223$	19.6394	1.31515	0.657576	−	0.753389i	$-0.271582\pi$
$223$	19.6394	1.31515	0.657576	+	0.753389i	$0.271582\pi$
$224$	0	0
$225$	2.19100	0.146066
$226$	0	0
$227$	−7.08384	−0.470171	−0.235086	−	0.971975i	$-0.575537\pi$
$227$	−7.08384	−0.470171	−0.235086	+	0.971975i	$0.575537\pi$
$228$	0	0
$229$	22.6135	1.49434	0.747170	−	0.664633i	$-0.231412\pi$
$229$	22.6135	1.49434	0.747170	+	0.664633i	$0.231412\pi$
$230$	0	0
$231$	11.9422	0.785737
$232$	0	0
$233$	16.3382	1.07035	0.535177	−	0.844740i	$-0.320245\pi$
$233$	16.3382	1.07035	0.535177	+	0.844740i	$0.320245\pi$
$234$	0	0
$235$	−3.74982	−0.244612
$236$	0	0
$237$	−23.6578	−1.53674
$238$	0	0
$239$	−0.543809	−0.0351761	−0.0175880	−	0.999845i	$-0.505599\pi$
$239$	−0.543809	−0.0351761	−0.0175880	+	0.999845i	$0.505599\pi$
$240$	0	0
$241$	14.8689	0.957793	0.478896	−	0.877871i	$-0.341037\pi$
$241$	14.8689	0.957793	0.478896	+	0.877871i	$0.341037\pi$
$242$	0	0
$243$	−4.64335	−0.297871
$244$	0	0
$245$	−2.73585	−0.174787
$246$	0	0
$247$	−2.09435	−0.133260
$248$	0	0
$249$	13.8376	0.876922
$250$	0	0
$251$	22.2678	1.40553	0.702766	−	0.711421i	$-0.251948\pi$
$251$	22.2678	1.40553	0.702766	+	0.711421i	$0.251948\pi$
$252$	0	0
$253$	16.4305	1.03298
$254$	0	0
$255$	−1.42718	−0.0893737
$256$	0	0
$257$	7.35376	0.458715	0.229357	−	0.973342i	$-0.426338\pi$
$257$	7.35376	0.458715	0.229357	+	0.973342i	$0.426338\pi$
$258$	0	0
$259$	26.1885	1.62728
$260$	0	0
$261$	0.450834	0.0279059
$262$	0	0
$263$	16.1420	0.995360	0.497680	−	0.867361i	$-0.334185\pi$
$263$	16.1420	0.995360	0.497680	+	0.867361i	$0.334185\pi$
$264$	0	0
$265$	0.360766	0.0221617
$266$	0	0
$267$	−8.37104	−0.512299
$268$	0	0
$269$	−10.3975	−0.633945	−0.316972	−	0.948435i	$-0.602666\pi$
$269$	−10.3975	−0.633945	−0.316972	+	0.948435i	$0.602666\pi$
$270$	0	0
$271$	−13.2071	−0.802275	−0.401138	−	0.916018i	$-0.631385\pi$
$271$	−13.2071	−0.802275	−0.401138	+	0.916018i	$0.631385\pi$
$272$	0	0
$273$	−6.03947	−0.365525
$274$	0	0
$275$	9.60970	0.579487
$276$	0	0
$277$	19.1467	1.15041	0.575207	−	0.818008i	$-0.304921\pi$
$277$	19.1467	1.15041	0.575207	+	0.818008i	$0.304921\pi$
$278$	0	0
$279$	−0.600556	−0.0359543
$280$	0	0
$281$	−9.88460	−0.589666	−0.294833	−	0.955549i	$-0.595264\pi$
$281$	−9.88460	−0.589666	−0.294833	+	0.955549i	$0.595264\pi$
$282$	0	0
$283$	0.715711	0.0425446	0.0212723	−	0.999774i	$-0.493228\pi$
$283$	0.715711	0.0425446	0.0212723	+	0.999774i	$0.493228\pi$
$284$	0	0
$285$	−1.25171	−0.0741448
$286$	0	0
$287$	−26.6465	−1.57289
$288$	0	0
$289$	−11.2977	−0.664568
$290$	0	0
$291$	20.4199	1.19704
$292$	0	0
$293$	0.923804	0.0539692	0.0269846	−	0.999636i	$-0.491409\pi$
$293$	0.923804	0.0539692	0.0269846	+	0.999636i	$0.491409\pi$
$294$	0	0
$295$	−1.59343	−0.0927730
$296$	0	0
$297$	−10.8945	−0.632164
$298$	0	0
$299$	−8.30935	−0.480542
$300$	0	0
$301$	46.9764	2.70767
$302$	0	0
$303$	−0.710882	−0.0408391
$304$	0	0
$305$	2.20123	0.126042
$306$	0	0
$307$	−14.6480	−0.836005	−0.418002	−	0.908446i	$-0.637270\pi$
$307$	−14.6480	−0.836005	−0.418002	+	0.908446i	$0.637270\pi$
$308$	0	0
$309$	−18.3609	−1.04451
$310$	0	0
$311$	14.2370	0.807309	0.403654	−	0.914912i	$-0.367740\pi$
$311$	14.2370	0.807309	0.403654	+	0.914912i	$0.367740\pi$
$312$	0	0
$313$	24.4970	1.38465	0.692325	−	0.721585i	$-0.256586\pi$
$313$	24.4970	1.38465	0.692325	+	0.721585i	$0.256586\pi$
$314$	0	0
$315$	0.638366	0.0359679
$316$	0	0
$317$	9.89315	0.555655	0.277827	−	0.960631i	$-0.410386\pi$
$317$	9.89315	0.555655	0.277827	+	0.960631i	$0.410386\pi$
$318$	0	0
$319$	1.97735	0.110711
$320$	0	0
$321$	12.6379	0.705381
$322$	0	0
$323$	5.00122	0.278275
$324$	0	0
$325$	−4.85988	−0.269577
$326$	0	0
$327$	−14.0518	−0.777068
$328$	0	0
$329$	37.8927	2.08909
$330$	0	0
$331$	1.20093	0.0660089	0.0330045	−	0.999455i	$-0.489492\pi$
$331$	1.20093	0.0660089	0.0330045	+	0.999455i	$0.489492\pi$
$332$	0	0
$333$	−3.12124	−0.171043
$334$	0	0
$335$	0.295786	0.0161605
$336$	0	0
$337$	−3.90109	−0.212506	−0.106253	−	0.994339i	$-0.533885\pi$
$337$	−3.90109	−0.212506	−0.106253	+	0.994339i	$0.533885\pi$
$338$	0	0
$339$	23.2847	1.26465
$340$	0	0
$341$	−2.63404	−0.142641
$342$	0	0
$343$	1.16754	0.0630411
$344$	0	0
$345$	−4.96615	−0.267369
$346$	0	0
$347$	19.9813	1.07265	0.536326	−	0.844011i	$-0.319812\pi$
$347$	19.9813	1.07265	0.536326	+	0.844011i	$0.319812\pi$
$348$	0	0
$349$	10.7734	0.576689	0.288344	−	0.957527i	$-0.406895\pi$
$349$	10.7734	0.576689	0.288344	+	0.957527i	$0.406895\pi$
$350$	0	0
$351$	5.50964	0.294083
$352$	0	0
$353$	−18.2864	−0.973289	−0.486645	−	0.873600i	$-0.661779\pi$
$353$	−18.2864	−0.973289	−0.486645	+	0.873600i	$0.661779\pi$
$354$	0	0
$355$	−3.49721	−0.185613
$356$	0	0
$357$	14.4220	0.763292
$358$	0	0
$359$	−16.6894	−0.880831	−0.440415	−	0.897794i	$-0.645169\pi$
$359$	−16.6894	−0.880831	−0.440415	+	0.897794i	$0.645169\pi$
$360$	0	0
$361$	−14.6137	−0.769142
$362$	0	0
$363$	11.3201	0.594150
$364$	0	0
$365$	1.55847	0.0815741
$366$	0	0
$367$	22.7975	1.19002	0.595010	−	0.803719i	$-0.297148\pi$
$367$	22.7975	1.19002	0.595010	+	0.803719i	$0.297148\pi$
$368$	0	0
$369$	3.17583	0.165327
$370$	0	0
$371$	−3.64562	−0.189271
$372$	0	0
$373$	−36.2478	−1.87684	−0.938420	−	0.345496i	$-0.887711\pi$
$373$	−36.2478	−1.87684	−0.938420	+	0.345496i	$0.887711\pi$
$374$	0	0
$375$	−5.89284	−0.304305
$376$	0	0
$377$	−1.00000	−0.0515026
$378$	0	0
$379$	−12.8710	−0.661137	−0.330568	−	0.943782i	$-0.607240\pi$
$379$	−12.8710	−0.661137	−0.330568	+	0.943782i	$0.607240\pi$
$380$	0	0
$381$	0.375577	0.0192414
$382$	0	0
$383$	24.1743	1.23525	0.617624	−	0.786473i	$-0.288095\pi$
$383$	24.1743	1.23525	0.617624	+	0.786473i	$0.288095\pi$
$384$	0	0
$385$	2.79987	0.142695
$386$	0	0
$387$	−5.59882	−0.284604
$388$	0	0
$389$	−22.0103	−1.11597	−0.557983	−	0.829852i	$-0.688425\pi$
$389$	−22.0103	−1.11597	−0.557983	+	0.829852i	$0.688425\pi$
$390$	0	0
$391$	19.8424	1.00347
$392$	0	0
$393$	−9.66396	−0.487483
$394$	0	0
$395$	−5.54664	−0.279082
$396$	0	0
$397$	24.9383	1.25162	0.625810	−	0.779976i	$-0.284769\pi$
$397$	24.9383	1.25162	0.625810	+	0.779976i	$0.284769\pi$
$398$	0	0
$399$	12.6488	0.633230
$400$	0	0
$401$	1.79545	0.0896604	0.0448302	−	0.998995i	$-0.485725\pi$
$401$	1.79545	0.0896604	0.0448302	+	0.998995i	$0.485725\pi$
$402$	0	0
$403$	1.33210	0.0663567
$404$	0	0
$405$	2.78660	0.138467
$406$	0	0
$407$	−13.6898	−0.678576
$408$	0	0
$409$	10.3691	0.512718	0.256359	−	0.966582i	$-0.417477\pi$
$409$	10.3691	0.512718	0.256359	+	0.966582i	$0.417477\pi$
$410$	0	0
$411$	15.4097	0.760102
$412$	0	0
$413$	16.1019	0.792324
$414$	0	0
$415$	3.24426	0.159255
$416$	0	0
$417$	−15.5443	−0.761207
$418$	0	0
$419$	20.8152	1.01689	0.508445	−	0.861095i	$-0.330221\pi$
$419$	20.8152	1.01689	0.508445	+	0.861095i	$0.330221\pi$
$420$	0	0
$421$	−31.1356	−1.51746	−0.758728	−	0.651407i	$-0.774179\pi$
$421$	−31.1356	−1.51746	−0.758728	+	0.651407i	$0.774179\pi$
$422$	0	0
$423$	−4.51620	−0.219585
$424$	0	0
$425$	11.6052	0.562934
$426$	0	0
$427$	−22.2439	−1.07646
$428$	0	0
$429$	3.15707	0.152425
$430$	0	0
$431$	33.1140	1.59505	0.797524	−	0.603288i	$-0.206143\pi$
$431$	33.1140	1.59505	0.797524	+	0.603288i	$0.206143\pi$
$432$	0	0
$433$	13.4094	0.644413	0.322207	−	0.946669i	$-0.395575\pi$
$433$	13.4094	0.644413	0.322207	+	0.946669i	$0.395575\pi$
$434$	0	0
$435$	−0.597659	−0.0286555
$436$	0	0
$437$	17.4027	0.832484
$438$	0	0
$439$	38.1546	1.82102	0.910510	−	0.413487i	$-0.135689\pi$
$439$	38.1546	1.82102	0.910510	+	0.413487i	$0.135689\pi$
$440$	0	0
$441$	−3.29499	−0.156904
$442$	0	0
$443$	30.3967	1.44419	0.722095	−	0.691794i	$-0.243179\pi$
$443$	30.3967	1.44419	0.722095	+	0.691794i	$0.243179\pi$
$444$	0	0
$445$	−1.96261	−0.0930367
$446$	0	0
$447$	−31.4128	−1.48578
$448$	0	0
$449$	−0.467432	−0.0220595	−0.0110297	−	0.999939i	$-0.503511\pi$
$449$	−0.467432	−0.0220595	−0.0110297	+	0.999939i	$0.503511\pi$
$450$	0	0
$451$	13.9292	0.655899
$452$	0	0
$453$	−9.46667	−0.444783
$454$	0	0
$455$	−1.41597	−0.0663816
$456$	0	0
$457$	−4.97186	−0.232574	−0.116287	−	0.993216i	$-0.537099\pi$
$457$	−4.97186	−0.232574	−0.116287	+	0.993216i	$0.537099\pi$
$458$	0	0
$459$	−13.1568	−0.614106
$460$	0	0
$461$	−26.2804	−1.22400	−0.612001	−	0.790857i	$-0.709635\pi$
$461$	−26.2804	−1.22400	−0.612001	+	0.790857i	$0.709635\pi$
$462$	0	0
$463$	−5.81628	−0.270305	−0.135153	−	0.990825i	$-0.543153\pi$
$463$	−5.81628	−0.270305	−0.135153	+	0.990825i	$0.543153\pi$
$464$	0	0
$465$	0.796142	0.0369202
$466$	0	0
$467$	5.55651	0.257124	0.128562	−	0.991701i	$-0.458964\pi$
$467$	5.55651	0.257124	0.128562	+	0.991701i	$0.458964\pi$
$468$	0	0
$469$	−2.98898	−0.138018
$470$	0	0
$471$	−5.80672	−0.267559
$472$	0	0
$473$	−24.5564	−1.12910
$474$	0	0
$475$	10.1783	0.467012
$476$	0	0
$477$	0.434498	0.0198943
$478$	0	0
$479$	5.59107	0.255462	0.127731	−	0.991809i	$-0.459231\pi$
$479$	5.59107	0.255462	0.127731	+	0.991809i	$0.459231\pi$
$480$	0	0
$481$	6.92327	0.315674
$482$	0	0
$483$	50.1840	2.28345
$484$	0	0
$485$	4.78751	0.217390
$486$	0	0
$487$	−25.4415	−1.15287	−0.576433	−	0.817145i	$-0.695556\pi$
$487$	−25.4415	−1.15287	−0.576433	+	0.817145i	$0.695556\pi$
$488$	0	0
$489$	−8.31996	−0.376242
$490$	0	0
$491$	−32.4771	−1.46567	−0.732835	−	0.680407i	$-0.761803\pi$
$491$	−32.4771	−1.46567	−0.732835	+	0.680407i	$0.761803\pi$
$492$	0	0
$493$	2.38796	0.107548
$494$	0	0
$495$	−0.333699	−0.0149987
$496$	0	0
$497$	35.3400	1.58522
$498$	0	0
$499$	22.9970	1.02949	0.514744	−	0.857344i	$-0.327887\pi$
$499$	22.9970	1.02949	0.514744	+	0.857344i	$0.327887\pi$
$500$	0	0
$501$	36.2891	1.62128
$502$	0	0
$503$	−38.3196	−1.70859	−0.854293	−	0.519791i	$-0.826010\pi$
$503$	−38.3196	−1.70859	−0.854293	+	0.519791i	$0.826010\pi$
$504$	0	0
$505$	−0.166668	−0.00741663
$506$	0	0
$507$	−1.59661	−0.0709080
$508$	0	0
$509$	−5.84165	−0.258927	−0.129463	−	0.991584i	$-0.541325\pi$
$509$	−5.84165	−0.258927	−0.129463	+	0.991584i	$0.541325\pi$
$510$	0	0
$511$	−15.7487	−0.696681
$512$	0	0
$513$	−11.5391	−0.509465
$514$	0	0
$515$	−4.30475	−0.189690
$516$	0	0
$517$	−19.8080	−0.871156
$518$	0	0
$519$	−29.4241	−1.29158
$520$	0	0
$521$	15.6507	0.685667	0.342834	−	0.939396i	$-0.388613\pi$
$521$	15.6507	0.685667	0.342834	+	0.939396i	$0.388613\pi$
$522$	0	0
$523$	−38.1900	−1.66993	−0.834967	−	0.550300i	$-0.814513\pi$
$523$	−38.1900	−1.66993	−0.834967	+	0.550300i	$0.814513\pi$
$524$	0	0
$525$	29.3511	1.28099
$526$	0	0
$527$	−3.18100	−0.138566
$528$	0	0
$529$	46.0452	2.00197
$530$	0	0
$531$	−1.91909	−0.0832813
$532$	0	0
$533$	−7.04435	−0.305125
$534$	0	0
$535$	2.96300	0.128102
$536$	0	0
$537$	−3.76506	−0.162474
$538$	0	0
$539$	−14.4518	−0.622483
$540$	0	0
$541$	30.3129	1.30325	0.651627	−	0.758539i	$-0.274087\pi$
$541$	30.3129	1.30325	0.651627	+	0.758539i	$0.274087\pi$
$542$	0	0
$543$	−37.4726	−1.60810
$544$	0	0
$545$	−3.29449	−0.141120
$546$	0	0
$547$	33.6951	1.44070	0.720349	−	0.693612i	$-0.243982\pi$
$547$	33.6951	1.44070	0.720349	+	0.693612i	$0.243982\pi$
$548$	0	0
$549$	2.65111	0.113147
$550$	0	0
$551$	2.09435	0.0892224
$552$	0	0
$553$	56.0500	2.38349
$554$	0	0
$555$	4.13775	0.175638
$556$	0	0
$557$	24.7000	1.04657	0.523286	−	0.852157i	$-0.324706\pi$
$557$	24.7000	1.04657	0.523286	+	0.852157i	$0.324706\pi$
$558$	0	0
$559$	12.4188	0.525260
$560$	0	0
$561$	−7.53894	−0.318294
$562$	0	0
$563$	35.3358	1.48923	0.744613	−	0.667496i	$-0.232634\pi$
$563$	35.3358	1.48923	0.744613	+	0.667496i	$0.232634\pi$
$564$	0	0
$565$	5.45915	0.229668
$566$	0	0
$567$	−28.1592	−1.18258
$568$	0	0
$569$	31.7813	1.33234	0.666171	−	0.745799i	$-0.267932\pi$
$569$	31.7813	1.33234	0.666171	+	0.745799i	$0.267932\pi$
$570$	0	0
$571$	40.8188	1.70821	0.854107	−	0.520098i	$-0.174105\pi$
$571$	40.8188	1.70821	0.854107	+	0.520098i	$0.174105\pi$
$572$	0	0
$573$	−12.7726	−0.533585
$574$	0	0
$575$	40.3824	1.68406
$576$	0	0
$577$	−21.9603	−0.914219	−0.457109	−	0.889410i	$-0.651115\pi$
$577$	−21.9603	−0.914219	−0.457109	+	0.889410i	$0.651115\pi$
$578$	0	0
$579$	0.841756	0.0349822
$580$	0	0
$581$	−32.7839	−1.36011
$582$	0	0
$583$	1.90571	0.0789263
$584$	0	0
$585$	0.168760	0.00697738
$586$	0	0
$587$	−12.1905	−0.503156	−0.251578	−	0.967837i	$-0.580949\pi$
$587$	−12.1905	−0.503156	−0.251578	+	0.967837i	$0.580949\pi$
$588$	0	0
$589$	−2.78989	−0.114955
$590$	0	0
$591$	−17.2088	−0.707875
$592$	0	0
$593$	45.6453	1.87443	0.937214	−	0.348756i	$-0.113396\pi$
$593$	45.6453	1.87443	0.937214	+	0.348756i	$0.113396\pi$
$594$	0	0
$595$	3.38127	0.138619
$596$	0	0
$597$	28.3233	1.15920
$598$	0	0
$599$	−3.11753	−0.127379	−0.0636895	−	0.997970i	$-0.520287\pi$
$599$	−3.11753	−0.127379	−0.0636895	+	0.997970i	$0.520287\pi$
$600$	0	0
$601$	−9.71050	−0.396099	−0.198050	−	0.980192i	$-0.563461\pi$
$601$	−9.71050	−0.396099	−0.198050	+	0.980192i	$0.563461\pi$
$602$	0	0
$603$	0.356238	0.0145071
$604$	0	0
$605$	2.65402	0.107901
$606$	0	0
$607$	15.7606	0.639702	0.319851	−	0.947468i	$-0.396367\pi$
$607$	15.7606	0.639702	0.319851	+	0.947468i	$0.396367\pi$
$608$	0	0
$609$	6.03947	0.244731
$610$	0	0
$611$	10.0174	0.405262
$612$	0	0
$613$	27.6892	1.11836	0.559179	−	0.829047i	$-0.311117\pi$
$613$	27.6892	1.11836	0.559179	+	0.829047i	$0.311117\pi$
$614$	0	0
$615$	−4.21012	−0.169768
$616$	0	0
$617$	−20.2749	−0.816237	−0.408119	−	0.912929i	$-0.633815\pi$
$617$	−20.2749	−0.816237	−0.408119	+	0.912929i	$0.633815\pi$
$618$	0	0
$619$	9.39878	0.377769	0.188884	−	0.981999i	$-0.439513\pi$
$619$	9.39878	0.377769	0.188884	+	0.981999i	$0.439513\pi$
$620$	0	0
$621$	−45.7815	−1.83715
$622$	0	0
$623$	19.8326	0.794576
$624$	0	0
$625$	22.9178	0.916712
$626$	0	0
$627$	−6.61201	−0.264058
$628$	0	0
$629$	−16.5325	−0.659193
$630$	0	0
$631$	34.7327	1.38269	0.691343	−	0.722527i	$-0.257020\pi$
$631$	34.7327	1.38269	0.691343	+	0.722527i	$0.257020\pi$
$632$	0	0
$633$	16.2166	0.644551
$634$	0	0
$635$	0.0880550	0.00349435
$636$	0	0
$637$	7.30865	0.289579
$638$	0	0
$639$	−4.21196	−0.166622
$640$	0	0
$641$	8.80741	0.347872	0.173936	−	0.984757i	$-0.444351\pi$
$641$	8.80741	0.347872	0.173936	+	0.984757i	$0.444351\pi$
$642$	0	0
$643$	3.20098	0.126235	0.0631173	−	0.998006i	$-0.479896\pi$
$643$	3.20098	0.126235	0.0631173	+	0.998006i	$0.479896\pi$
$644$	0	0
$645$	7.42221	0.292249
$646$	0	0
$647$	11.4369	0.449632	0.224816	−	0.974401i	$-0.427822\pi$
$647$	11.4369	0.449632	0.224816	+	0.974401i	$0.427822\pi$
$648$	0	0
$649$	−8.41711	−0.330400
$650$	0	0
$651$	−8.04518	−0.315315
$652$	0	0
$653$	−35.5212	−1.39005	−0.695026	−	0.718985i	$-0.744607\pi$
$653$	−35.5212	−1.39005	−0.695026	+	0.718985i	$0.744607\pi$
$654$	0	0
$655$	−2.26574	−0.0885298
$656$	0	0
$657$	1.87699	0.0732282
$658$	0	0
$659$	−6.47851	−0.252367	−0.126183	−	0.992007i	$-0.540273\pi$
$659$	−6.47851	−0.252367	−0.126183	+	0.992007i	$0.540273\pi$
$660$	0	0
$661$	31.5049	1.22540	0.612699	−	0.790316i	$-0.290084\pi$
$661$	31.5049	1.22540	0.612699	+	0.790316i	$0.290084\pi$
$662$	0	0
$663$	3.81264	0.148071
$664$	0	0
$665$	2.96554	0.114999
$666$	0	0
$667$	8.30935	0.321739
$668$	0	0
$669$	−31.3565	−1.21231
$670$	0	0
$671$	11.6278	0.448885
$672$	0	0
$673$	−3.16302	−0.121926	−0.0609628	−	0.998140i	$-0.519417\pi$
$673$	−3.16302	−0.121926	−0.0609628	+	0.998140i	$0.519417\pi$
$674$	0	0
$675$	−26.7762	−1.03062
$676$	0	0
$677$	−5.62778	−0.216293	−0.108147	−	0.994135i	$-0.534492\pi$
$677$	−5.62778	−0.216293	−0.108147	+	0.994135i	$0.534492\pi$
$678$	0	0
$679$	−48.3788	−1.85661
$680$	0	0
$681$	11.3101	0.433405
$682$	0	0
$683$	13.9002	0.531878	0.265939	−	0.963990i	$-0.414318\pi$
$683$	13.9002	0.531878	0.265939	+	0.963990i	$0.414318\pi$
$684$	0	0
$685$	3.61283	0.138039
$686$	0	0
$687$	−36.1049	−1.37749
$688$	0	0
$689$	−0.963766	−0.0367166
$690$	0	0
$691$	−10.6617	−0.405590	−0.202795	−	0.979221i	$-0.565003\pi$
$691$	−10.6617	−0.405590	−0.202795	+	0.979221i	$0.565003\pi$
$692$	0	0
$693$	3.37210	0.128095
$694$	0	0
$695$	−3.64440	−0.138240
$696$	0	0
$697$	16.8216	0.637163
$698$	0	0
$699$	−26.0858	−0.986656
$700$	0	0
$701$	−8.08298	−0.305290	−0.152645	−	0.988281i	$-0.548779\pi$
$701$	−8.08298	−0.305290	−0.152645	+	0.988281i	$0.548779\pi$
$702$	0	0
$703$	−14.4998	−0.546869
$704$	0	0
$705$	5.98701	0.225484
$706$	0	0
$707$	1.68422	0.0633415
$708$	0	0
$709$	−5.55484	−0.208617	−0.104308	−	0.994545i	$-0.533263\pi$
$709$	−5.55484	−0.208617	−0.104308	+	0.994545i	$0.533263\pi$
$710$	0	0
$711$	−6.68024	−0.250529
$712$	0	0
$713$	−11.0689	−0.414533
$714$	0	0
$715$	0.740182	0.0276812
$716$	0	0
$717$	0.868251	0.0324254
$718$	0	0
$719$	6.41254	0.239147	0.119574	−	0.992825i	$-0.461847\pi$
$719$	6.41254	0.239147	0.119574	+	0.992825i	$0.461847\pi$
$720$	0	0
$721$	43.5004	1.62004
$722$	0	0
$723$	−23.7399	−0.882897
$724$	0	0
$725$	4.85988	0.180491
$726$	0	0
$727$	−48.6527	−1.80443	−0.902214	−	0.431289i	$-0.858059\pi$
$727$	−48.6527	−1.80443	−0.902214	+	0.431289i	$0.858059\pi$
$728$	0	0
$729$	29.7464	1.10172
$730$	0	0
$731$	−29.6556	−1.09685
$732$	0	0
$733$	31.0843	1.14812	0.574062	−	0.818812i	$-0.305367\pi$
$733$	31.0843	1.14812	0.574062	+	0.818812i	$0.305367\pi$
$734$	0	0
$735$	4.36808	0.161119
$736$	0	0
$737$	1.56246	0.0575539
$738$	0	0
$739$	20.8553	0.767176	0.383588	−	0.923504i	$-0.374688\pi$
$739$	20.8553	0.767176	0.383588	+	0.923504i	$0.374688\pi$
$740$	0	0
$741$	3.34387	0.122840
$742$	0	0
$743$	−28.5743	−1.04829	−0.524145	−	0.851629i	$-0.675615\pi$
$743$	−28.5743	−1.04829	−0.524145	+	0.851629i	$0.675615\pi$
$744$	0	0
$745$	−7.36482	−0.269826
$746$	0	0
$747$	3.90731	0.142961
$748$	0	0
$749$	−29.9417	−1.09405
$750$	0	0
$751$	−37.9755	−1.38575	−0.692873	−	0.721060i	$-0.743655\pi$
$751$	−37.9755	−1.38575	−0.692873	+	0.721060i	$0.743655\pi$
$752$	0	0
$753$	−35.5531	−1.29563
$754$	0	0
$755$	−2.21949	−0.0807754
$756$	0	0
$757$	12.8228	0.466054	0.233027	−	0.972470i	$-0.425137\pi$
$757$	12.8228	0.466054	0.233027	+	0.972470i	$0.425137\pi$
$758$	0	0
$759$	−26.2332	−0.952203
$760$	0	0
$761$	−39.1917	−1.42070	−0.710348	−	0.703850i	$-0.751463\pi$
$761$	−39.1917	−1.42070	−0.710348	+	0.703850i	$0.751463\pi$
$762$	0	0
$763$	33.2915	1.20523
$764$	0	0
$765$	−0.402992	−0.0145702
$766$	0	0
$767$	4.25675	0.153702
$768$	0	0
$769$	−37.0777	−1.33706	−0.668528	−	0.743687i	$-0.733075\pi$
$769$	−37.0777	−1.33706	−0.668528	+	0.743687i	$0.733075\pi$
$770$	0	0
$771$	−11.7411	−0.422845
$772$	0	0
$773$	−25.4090	−0.913897	−0.456949	−	0.889493i	$-0.651058\pi$
$773$	−25.4090	−0.913897	−0.456949	+	0.889493i	$0.651058\pi$
$774$	0	0
$775$	−6.47385	−0.232547
$776$	0	0
$777$	−41.8129	−1.50003
$778$	0	0
$779$	14.7533	0.528593
$780$	0	0
$781$	−18.4736	−0.661038
$782$	0	0
$783$	−5.50964	−0.196898
$784$	0	0
$785$	−1.36140	−0.0485904
$786$	0	0
$787$	−17.7111	−0.631332	−0.315666	−	0.948870i	$-0.602228\pi$
$787$	−17.7111	−0.631332	−0.315666	+	0.948870i	$0.602228\pi$
$788$	0	0
$789$	−25.7725	−0.917527
$790$	0	0
$791$	−55.1659	−1.96147
$792$	0	0
$793$	−5.88047	−0.208822
$794$	0	0
$795$	−0.576003	−0.0204287
$796$	0	0
$797$	−10.0961	−0.357621	−0.178810	−	0.983884i	$-0.557225\pi$
$797$	−10.0961	−0.357621	−0.178810	+	0.983884i	$0.557225\pi$
$798$	0	0
$799$	−23.9212	−0.846271
$800$	0	0
$801$	−2.36372	−0.0835181
$802$	0	0
$803$	8.23245	0.290517
$804$	0	0
$805$	11.7658	0.414689
$806$	0	0
$807$	16.6007	0.584373
$808$	0	0
$809$	−26.0668	−0.916459	−0.458229	−	0.888834i	$-0.651516\pi$
$809$	−26.0668	−0.916459	−0.458229	+	0.888834i	$0.651516\pi$
$810$	0	0
$811$	−1.06555	−0.0374167	−0.0187083	−	0.999825i	$-0.505955\pi$
$811$	−1.06555	−0.0374167	−0.0187083	+	0.999825i	$0.505955\pi$
$812$	0	0
$813$	21.0866	0.739540
$814$	0	0
$815$	−1.95064	−0.0683278
$816$	0	0
$817$	−26.0094	−0.909952
$818$	0	0
$819$	−1.70536	−0.0595900
$820$	0	0
$821$	−9.12811	−0.318573	−0.159287	−	0.987232i	$-0.550919\pi$
$821$	−9.12811	−0.318573	−0.159287	+	0.987232i	$0.550919\pi$
$822$	0	0
$823$	−14.0378	−0.489325	−0.244663	−	0.969608i	$-0.578677\pi$
$823$	−14.0378	−0.489325	−0.244663	+	0.969608i	$0.578677\pi$
$824$	0	0
$825$	−15.3430	−0.534173
$826$	0	0
$827$	−35.5668	−1.23678	−0.618389	−	0.785872i	$-0.712214\pi$
$827$	−35.5668	−1.23678	−0.618389	+	0.785872i	$0.712214\pi$
$828$	0	0
$829$	8.25882	0.286841	0.143420	−	0.989662i	$-0.454190\pi$
$829$	8.25882	0.286841	0.143420	+	0.989662i	$0.454190\pi$
$830$	0	0
$831$	−30.5699	−1.06046
$832$	0	0
$833$	−17.4527	−0.604702
$834$	0	0
$835$	8.50808	0.294434
$836$	0	0
$837$	7.33939	0.253687
$838$	0	0
$839$	2.59845	0.0897084	0.0448542	−	0.998994i	$-0.485718\pi$
$839$	2.59845	0.0897084	0.0448542	+	0.998994i	$0.485718\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	0	0
$843$	15.7819	0.543556
$844$	0	0
$845$	−0.374330	−0.0128773
$846$	0	0
$847$	−26.8194	−0.921527
$848$	0	0
$849$	−1.14271	−0.0392177
$850$	0	0
$851$	−57.5279	−1.97203
$852$	0	0
$853$	40.9303	1.40143	0.700714	−	0.713442i	$-0.252865\pi$
$853$	40.9303	1.40143	0.700714	+	0.713442i	$0.252865\pi$
$854$	0	0
$855$	−0.353444	−0.0120875
$856$	0	0
$857$	25.8928	0.884480	0.442240	−	0.896897i	$-0.354184\pi$
$857$	25.8928	0.884480	0.442240	+	0.896897i	$0.354184\pi$
$858$	0	0
$859$	−46.0563	−1.57142	−0.785711	−	0.618594i	$-0.787703\pi$
$859$	−46.0563	−1.57142	−0.785711	+	0.618594i	$0.787703\pi$
$860$	0	0
$861$	42.5441	1.44990
$862$	0	0
$863$	29.0968	0.990466	0.495233	−	0.868760i	$-0.335083\pi$
$863$	29.0968	0.990466	0.495233	+	0.868760i	$0.335083\pi$
$864$	0	0
$865$	−6.89856	−0.234558
$866$	0	0
$867$	18.0380	0.612602
$868$	0	0
$869$	−29.2995	−0.993918
$870$	0	0
$871$	−0.790177	−0.0267741
$872$	0	0
$873$	5.76596	0.195148
$874$	0	0
$875$	13.9613	0.471977
$876$	0	0
$877$	−7.25600	−0.245018	−0.122509	−	0.992467i	$-0.539094\pi$
$877$	−7.25600	−0.245018	−0.122509	+	0.992467i	$0.539094\pi$
$878$	0	0
$879$	−1.47496	−0.0497490
$880$	0	0
$881$	−17.6891	−0.595962	−0.297981	−	0.954572i	$-0.596313\pi$
$881$	−17.6891	−0.595962	−0.297981	+	0.954572i	$0.596313\pi$
$882$	0	0
$883$	−10.1093	−0.340205	−0.170103	−	0.985426i	$-0.554410\pi$
$883$	−10.1093	−0.340205	−0.170103	+	0.985426i	$0.554410\pi$
$884$	0	0
$885$	2.54408	0.0855185
$886$	0	0
$887$	54.0779	1.81576	0.907880	−	0.419230i	$-0.137700\pi$
$887$	54.0779	1.81576	0.907880	+	0.419230i	$0.137700\pi$
$888$	0	0
$889$	−0.889814	−0.0298434
$890$	0	0
$891$	14.7199	0.493136
$892$	0	0
$893$	−20.9800	−0.702070
$894$	0	0
$895$	−0.882728	−0.0295063
$896$	0	0
$897$	13.2668	0.442965
$898$	0	0
$899$	−1.33210	−0.0444281
$900$	0	0
$901$	2.30143	0.0766718
$902$	0	0
$903$	−75.0030	−2.49594
$904$	0	0
$905$	−8.78554	−0.292041
$906$	0	0
$907$	4.26137	0.141497	0.0707483	−	0.997494i	$-0.477461\pi$
$907$	4.26137	0.141497	0.0707483	+	0.997494i	$0.477461\pi$
$908$	0	0
$909$	−0.200731	−0.00665783
$910$	0	0
$911$	52.6816	1.74542	0.872709	−	0.488240i	$-0.162361\pi$
$911$	52.6816	1.74542	0.872709	+	0.488240i	$0.162361\pi$
$912$	0	0
$913$	17.1375	0.567167
$914$	0	0
$915$	−3.51452	−0.116186
$916$	0	0
$917$	22.8958	0.756086
$918$	0	0
$919$	46.0919	1.52043	0.760216	−	0.649671i	$-0.225093\pi$
$919$	46.0919	1.52043	0.760216	+	0.649671i	$0.225093\pi$
$920$	0	0
$921$	23.3871	0.770632
$922$	0	0
$923$	9.34260	0.307515
$924$	0	0
$925$	−33.6463	−1.10628
$926$	0	0
$927$	−5.18454	−0.170283
$928$	0	0
$929$	4.94987	0.162400	0.0811999	−	0.996698i	$-0.474125\pi$
$929$	4.94987	0.162400	0.0811999	+	0.996698i	$0.474125\pi$
$930$	0	0
$931$	−15.3069	−0.501663
$932$	0	0
$933$	−22.7310	−0.744180
$934$	0	0
$935$	−1.76752	−0.0578042
$936$	0	0
$937$	−12.3735	−0.404226	−0.202113	−	0.979362i	$-0.564781\pi$
$937$	−12.3735	−0.404226	−0.202113	+	0.979362i	$0.564781\pi$
$938$	0	0
$939$	−39.1121	−1.27638
$940$	0	0
$941$	−41.8508	−1.36430	−0.682148	−	0.731214i	$-0.738954\pi$
$941$	−41.8508	−1.36430	−0.682148	+	0.731214i	$0.738954\pi$
$942$	0	0
$943$	58.5339	1.90613
$944$	0	0
$945$	−7.80147	−0.253782
$946$	0	0
$947$	15.2634	0.495995	0.247997	−	0.968761i	$-0.420228\pi$
$947$	15.2634	0.495995	0.247997	+	0.968761i	$0.420228\pi$
$948$	0	0
$949$	−4.16337	−0.135149
$950$	0	0
$951$	−15.7955	−0.512205
$952$	0	0
$953$	32.2925	1.04606	0.523028	−	0.852315i	$-0.324802\pi$
$953$	32.2925	1.04606	0.523028	+	0.852315i	$0.324802\pi$
$954$	0	0
$955$	−2.99458	−0.0969023
$956$	0	0
$957$	−3.15707	−0.102053
$958$	0	0
$959$	−36.5084	−1.17892
$960$	0	0
$961$	−29.2255	−0.942758
$962$	0	0
$963$	3.56856	0.114995
$964$	0	0
$965$	0.197352	0.00635298
$966$	0	0
$967$	−15.6719	−0.503973	−0.251986	−	0.967731i	$-0.581084\pi$
$967$	−15.6719	−0.503973	−0.251986	+	0.967731i	$0.581084\pi$
$968$	0	0
$969$	−7.98500	−0.256515
$970$	0	0
$971$	−25.3511	−0.813554	−0.406777	−	0.913528i	$-0.633347\pi$
$971$	−25.3511	−0.813554	−0.406777	+	0.913528i	$0.633347\pi$
$972$	0	0
$973$	36.8274	1.18063
$974$	0	0
$975$	7.75933	0.248498
$976$	0	0
$977$	−18.2845	−0.584973	−0.292487	−	0.956270i	$-0.594483\pi$
$977$	−18.2845	−0.584973	−0.292487	+	0.956270i	$0.594483\pi$
$978$	0	0
$979$	−10.3673	−0.331340
$980$	0	0
$981$	−3.96780	−0.126682
$982$	0	0
$983$	−52.7162	−1.68139	−0.840693	−	0.541512i	$-0.817852\pi$
$983$	−52.7162	−1.68139	−0.840693	+	0.541512i	$0.817852\pi$
$984$	0	0
$985$	−4.03464	−0.128554
$986$	0	0
$987$	−60.5000	−1.92574
$988$	0	0
$989$	−103.192	−3.28132
$990$	0	0
$991$	−47.6656	−1.51415	−0.757074	−	0.653329i	$-0.773372\pi$
$991$	−47.6656	−1.51415	−0.757074	+	0.653329i	$0.773372\pi$
$992$	0	0
$993$	−1.91741	−0.0608473
$994$	0	0
$995$	6.64048	0.210517
$996$	0	0
$997$	53.2495	1.68643	0.843215	−	0.537577i	$-0.180660\pi$
$997$	53.2495	1.68643	0.843215	+	0.537577i	$0.180660\pi$
$998$	0	0
$999$	38.1447	1.20685

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6032.2.a.bc.1.3		11
4.3	odd	2		3016.2.a.i.1.9	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3016.2.a.i.1.9	✓	11	4.3	odd	2
6032.2.a.bc.1.3		11	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6032 = 2^{4} \cdot 13 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6032.a (trivial)

\(f(q)\)	\(=\)	\(q-1.59661 q^{3} -0.374330 q^{5} +3.78268 q^{7} -0.450834 q^{9} +O(q^{10})\)	\(q-1.59661 q^{3} -0.374330 q^{5} +3.78268 q^{7} -0.450834 q^{9} -1.97735 q^{11} +1.00000 q^{13} +0.597659 q^{15} -2.38796 q^{17} -2.09435 q^{19} -6.03947 q^{21} -8.30935 q^{23} -4.85988 q^{25} +5.50964 q^{27} -1.00000 q^{29} +1.33210 q^{31} +3.15707 q^{33} -1.41597 q^{35} +6.92327 q^{37} -1.59661 q^{39} -7.04435 q^{41} +12.4188 q^{43} +0.168760 q^{45} +10.0174 q^{47} +7.30865 q^{49} +3.81264 q^{51} -0.963766 q^{53} +0.740182 q^{55} +3.34387 q^{57} +4.25675 q^{59} -5.88047 q^{61} -1.70536 q^{63} -0.374330 q^{65} -0.790177 q^{67} +13.2668 q^{69} +9.34260 q^{71} -4.16337 q^{73} +7.75933 q^{75} -7.47970 q^{77} +14.8175 q^{79} -7.44425 q^{81} -8.66686 q^{83} +0.893883 q^{85} +1.59661 q^{87} +5.24301 q^{89} +3.78268 q^{91} -2.12685 q^{93} +0.783978 q^{95} -12.7896 q^{97} +0.891458 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 6 q^{3} - 2 q^{5} + 3 q^{7} + 11 q^{9}+O(q^{10}) \) 11 * q + 6 * q^3 - 2 * q^5 + 3 * q^7 + 11 * q^9	\( 11 q + 6 q^{3} - 2 q^{5} + 3 q^{7} + 11 q^{9} + 13 q^{11} + 11 q^{13} + 8 q^{15} - 6 q^{17} + 12 q^{19} + q^{21} + 13 q^{23} + 11 q^{25} + 24 q^{27} - 11 q^{29} + 11 q^{31} + 17 q^{33} + 4 q^{35} + 11 q^{37} + 6 q^{39} - 9 q^{41} + 30 q^{43} - 16 q^{45} + q^{47} - 4 q^{49} + 13 q^{51} - 9 q^{53} + q^{55} + 2 q^{57} + 9 q^{59} - 5 q^{61} + 6 q^{63} - 2 q^{65} + 25 q^{67} + 26 q^{71} + 10 q^{73} + 41 q^{75} - 8 q^{77} + 14 q^{79} + 3 q^{81} + 6 q^{83} + 19 q^{85} - 6 q^{87} - 11 q^{89} + 3 q^{91} - 3 q^{93} + 31 q^{95} + 12 q^{97} + 35 q^{99}+O(q^{100}) \) 11 * q + 6 * q^3 - 2 * q^5 + 3 * q^7 + 11 * q^9 + 13 * q^11 + 11 * q^13 + 8 * q^15 - 6 * q^17 + 12 * q^19 + q^21 + 13 * q^23 + 11 * q^25 + 24 * q^27 - 11 * q^29 + 11 * q^31 + 17 * q^33 + 4 * q^35 + 11 * q^37 + 6 * q^39 - 9 * q^41 + 30 * q^43 - 16 * q^45 + q^47 - 4 * q^49 + 13 * q^51 - 9 * q^53 + q^55 + 2 * q^57 + 9 * q^59 - 5 * q^61 + 6 * q^63 - 2 * q^65 + 25 * q^67 + 26 * q^71 + 10 * q^73 + 41 * q^75 - 8 * q^77 + 14 * q^79 + 3 * q^81 + 6 * q^83 + 19 * q^85 - 6 * q^87 - 11 * q^89 + 3 * q^91 - 3 * q^93 + 31 * q^95 + 12 * q^97 + 35 * q^99

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