LMFDB - Embedded newform 6534.2.a.cc.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6534,2,Mod(1,6534)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6534, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6534.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6534 = 2 \cdot 3^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6534.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:	$52.1742526807$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{37}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 9 $ x^2 - x - 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.54138$ of defining polynomial
Character	$\chi$	$=$	6534.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +2.54138 q^{5} -1.00000 q^{7} +1.00000 q^{8} +O(q^{10})$	$q+1.00000 q^{2} +1.00000 q^{4} +2.54138 q^{5} -1.00000 q^{7} +1.00000 q^{8} +2.54138 q^{10} -6.54138 q^{13} -1.00000 q^{14} +1.00000 q^{16} -5.08276 q^{17} +1.54138 q^{19} +2.54138 q^{20} -5.54138 q^{23} +1.45862 q^{25} -6.54138 q^{26} -1.00000 q^{28} +3.00000 q^{29} -3.54138 q^{31} +1.00000 q^{32} -5.08276 q^{34} -2.54138 q^{35} +10.0828 q^{37} +1.54138 q^{38} +2.54138 q^{40} -9.00000 q^{41} -6.08276 q^{43} -5.54138 q^{46} +7.62414 q^{47} -6.00000 q^{49} +1.45862 q^{50} -6.54138 q^{52} -2.08276 q^{53} -1.00000 q^{56} +3.00000 q^{58} -10.6241 q^{59} -6.08276 q^{61} -3.54138 q^{62} +1.00000 q^{64} -16.6241 q^{65} +9.16553 q^{67} -5.08276 q^{68} -2.54138 q^{70} -6.00000 q^{71} +2.45862 q^{73} +10.0828 q^{74} +1.54138 q^{76} +3.62414 q^{79} +2.54138 q^{80} -9.00000 q^{82} -11.5414 q^{83} -12.9172 q^{85} -6.08276 q^{86} +0.458619 q^{89} +6.54138 q^{91} -5.54138 q^{92} +7.62414 q^{94} +3.91724 q^{95} +6.16553 q^{97} -6.00000 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{4} - q^{5} - 2 q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^4 - q^5 - 2 * q^7 + 2 * q^8	$ 2 q + 2 q^{2} + 2 q^{4} - q^{5} - 2 q^{7} + 2 q^{8} - q^{10} - 7 q^{13} - 2 q^{14} + 2 q^{16} + 2 q^{17} - 3 q^{19} - q^{20} - 5 q^{23} + 9 q^{25} - 7 q^{26} - 2 q^{28} + 6 q^{29} - q^{31} + 2 q^{32} + 2 q^{34} + q^{35} + 8 q^{37} - 3 q^{38} - q^{40} - 18 q^{41} - 5 q^{46} - 3 q^{47} - 12 q^{49} + 9 q^{50} - 7 q^{52} + 8 q^{53} - 2 q^{56} + 6 q^{58} - 3 q^{59} - q^{62} + 2 q^{64} - 15 q^{65} - 6 q^{67} + 2 q^{68} + q^{70} - 12 q^{71} + 11 q^{73} + 8 q^{74} - 3 q^{76} - 11 q^{79} - q^{80} - 18 q^{82} - 17 q^{83} - 38 q^{85} + 7 q^{89} + 7 q^{91} - 5 q^{92} - 3 q^{94} + 20 q^{95} - 12 q^{97} - 12 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^4 - q^5 - 2 * q^7 + 2 * q^8 - q^10 - 7 * q^13 - 2 * q^14 + 2 * q^16 + 2 * q^17 - 3 * q^19 - q^20 - 5 * q^23 + 9 * q^25 - 7 * q^26 - 2 * q^28 + 6 * q^29 - q^31 + 2 * q^32 + 2 * q^34 + q^35 + 8 * q^37 - 3 * q^38 - q^40 - 18 * q^41 - 5 * q^46 - 3 * q^47 - 12 * q^49 + 9 * q^50 - 7 * q^52 + 8 * q^53 - 2 * q^56 + 6 * q^58 - 3 * q^59 - q^62 + 2 * q^64 - 15 * q^65 - 6 * q^67 + 2 * q^68 + q^70 - 12 * q^71 + 11 * q^73 + 8 * q^74 - 3 * q^76 - 11 * q^79 - q^80 - 18 * q^82 - 17 * q^83 - 38 * q^85 + 7 * q^89 + 7 * q^91 - 5 * q^92 - 3 * q^94 + 20 * q^95 - 12 * q^97 - 12 * q^98

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	2.54138	1.13654	0.568270	−	0.822842i	$-0.307613\pi$
$5$	2.54138	1.13654	0.568270	+	0.822842i	$0.307613\pi$
$6$	0	0
$7$	−1.00000	−0.377964	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000	−0.377964	−0.188982	+	0.981981i	$0.560519\pi$
$8$	1.00000	0.353553
$9$	0	0
$10$	2.54138	0.803655
$11$	0	0
$11$	0	0
$12$	0	0
$13$	−6.54138	−1.81425	−0.907126	−	0.420858i	$-0.861729\pi$
$13$	−6.54138	−1.81425	−0.907126	+	0.420858i	$0.861729\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	−5.08276	−1.23275	−0.616375	−	0.787452i	$-0.711400\pi$
$17$	−5.08276	−1.23275	−0.616375	+	0.787452i	$0.711400\pi$
$18$	0	0
$19$	1.54138	0.353617	0.176809	−	0.984245i	$-0.443423\pi$
$19$	1.54138	0.353617	0.176809	+	0.984245i	$0.443423\pi$
$20$	2.54138	0.568270
$21$	0	0
$22$	0	0
$23$	−5.54138	−1.15546	−0.577729	−	0.816229i	$-0.696061\pi$
$23$	−5.54138	−1.15546	−0.577729	+	0.816229i	$0.696061\pi$
$24$	0	0
$25$	1.45862	0.291724
$26$	−6.54138	−1.28287
$27$	0	0
$28$	−1.00000	−0.188982
$29$	3.00000	0.557086	0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000	0.557086	0.278543	+	0.960424i	$0.410149\pi$
$30$	0	0
$31$	−3.54138	−0.636051	−0.318025	−	0.948082i	$-0.603020\pi$
$31$	−3.54138	−0.636051	−0.318025	+	0.948082i	$0.603020\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−5.08276	−0.871687
$35$	−2.54138	−0.429572
$36$	0	0
$37$	10.0828	1.65760	0.828798	−	0.559548i	$-0.189025\pi$
$37$	10.0828	1.65760	0.828798	+	0.559548i	$0.189025\pi$
$38$	1.54138	0.250045
$39$	0	0
$40$	2.54138	0.401828
$41$	−9.00000	−1.40556	−0.702782	−	0.711405i	$-0.748059\pi$
$41$	−9.00000	−1.40556	−0.702782	+	0.711405i	$0.748059\pi$
$42$	0	0
$43$	−6.08276	−0.927613	−0.463806	−	0.885937i	$-0.653517\pi$
$43$	−6.08276	−0.927613	−0.463806	+	0.885937i	$0.653517\pi$
$44$	0	0
$45$	0	0
$46$	−5.54138	−0.817032
$47$	7.62414	1.11210	0.556048	−	0.831150i	$-0.312317\pi$
$47$	7.62414	1.11210	0.556048	+	0.831150i	$0.312317\pi$
$48$	0	0
$49$	−6.00000	−0.857143
$50$	1.45862	0.206280
$51$	0	0
$52$	−6.54138	−0.907126
$53$	−2.08276	−0.286089	−0.143045	−	0.989716i	$-0.545689\pi$
$53$	−2.08276	−0.286089	−0.143045	+	0.989716i	$0.545689\pi$
$54$	0	0
$55$	0	0
$56$	−1.00000	−0.133631
$57$	0	0
$58$	3.00000	0.393919
$59$	−10.6241	−1.38315	−0.691573	−	0.722307i	$-0.743082\pi$
$59$	−10.6241	−1.38315	−0.691573	+	0.722307i	$0.743082\pi$
$60$	0	0
$61$	−6.08276	−0.778818	−0.389409	−	0.921065i	$-0.627321\pi$
$61$	−6.08276	−0.778818	−0.389409	+	0.921065i	$0.627321\pi$
$62$	−3.54138	−0.449756
$63$	0	0
$64$	1.00000	0.125000
$65$	−16.6241	−2.06197
$66$	0	0
$67$	9.16553	1.11975	0.559874	−	0.828578i	$-0.310850\pi$
$67$	9.16553	1.11975	0.559874	+	0.828578i	$0.310850\pi$
$68$	−5.08276	−0.616375
$69$	0	0
$70$	−2.54138	−0.303753
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	0	0
$73$	2.45862	0.287760	0.143880	−	0.989595i	$-0.454042\pi$
$73$	2.45862	0.287760	0.143880	+	0.989595i	$0.454042\pi$
$74$	10.0828	1.17210
$75$	0	0
$76$	1.54138	0.176809
$77$	0	0
$78$	0	0
$79$	3.62414	0.407748	0.203874	−	0.978997i	$-0.434647\pi$
$79$	3.62414	0.407748	0.203874	+	0.978997i	$0.434647\pi$
$80$	2.54138	0.284135
$81$	0	0
$82$	−9.00000	−0.993884
$83$	−11.5414	−1.26683	−0.633416	−	0.773812i	$-0.718348\pi$
$83$	−11.5414	−1.26683	−0.633416	+	0.773812i	$0.718348\pi$
$84$	0	0
$85$	−12.9172	−1.40107
$86$	−6.08276	−0.655921
$87$	0	0
$88$	0	0
$89$	0.458619	0.0486135	0.0243067	−	0.999705i	$-0.492262\pi$
$89$	0.458619	0.0486135	0.0243067	+	0.999705i	$0.492262\pi$
$90$	0	0
$91$	6.54138	0.685723
$92$	−5.54138	−0.577729
$93$	0	0
$94$	7.62414	0.786370
$95$	3.91724	0.401900
$96$	0	0
$97$	6.16553	0.626014	0.313007	−	0.949751i	$-0.398664\pi$
$97$	6.16553	0.626014	0.313007	+	0.949751i	$0.398664\pi$
$98$	−6.00000	−0.606092
$99$	0	0
$100$	1.45862	0.145862
$101$	6.91724	0.688291	0.344145	−	0.938916i	$-0.388169\pi$
$101$	6.91724	0.688291	0.344145	+	0.938916i	$0.388169\pi$
$102$	0	0
$103$	−11.1655	−1.10017	−0.550086	−	0.835108i	$-0.685405\pi$
$103$	−11.1655	−1.10017	−0.550086	+	0.835108i	$0.685405\pi$
$104$	−6.54138	−0.641435
$105$	0	0
$106$	−2.08276	−0.202296
$107$	−0.917237	−0.0886727	−0.0443363	−	0.999017i	$-0.514117\pi$
$107$	−0.917237	−0.0886727	−0.0443363	+	0.999017i	$0.514117\pi$
$108$	0	0
$109$	−15.5414	−1.48859	−0.744297	−	0.667849i	$-0.767215\pi$
$109$	−15.5414	−1.48859	−0.744297	+	0.667849i	$0.767215\pi$
$110$	0	0
$111$	0	0
$112$	−1.00000	−0.0944911
$113$	−9.45862	−0.889792	−0.444896	−	0.895582i	$-0.646759\pi$
$113$	−9.45862	−0.889792	−0.444896	+	0.895582i	$0.646759\pi$
$114$	0	0
$115$	−14.0828	−1.31322
$116$	3.00000	0.278543
$117$	0	0
$118$	−10.6241	−0.978032
$119$	5.08276	0.465936
$120$	0	0
$121$	0	0
$122$	−6.08276	−0.550707
$123$	0	0
$124$	−3.54138	−0.318025
$125$	−9.00000	−0.804984
$126$	0	0
$127$	−15.5414	−1.37907	−0.689537	−	0.724250i	$-0.742186\pi$
$127$	−15.5414	−1.37907	−0.689537	+	0.724250i	$0.742186\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	−16.6241	−1.45803
$131$	8.08276	0.706194	0.353097	−	0.935587i	$-0.385129\pi$
$131$	8.08276	0.706194	0.353097	+	0.935587i	$0.385129\pi$
$132$	0	0
$133$	−1.54138	−0.133655
$134$	9.16553	0.791781
$135$	0	0
$136$	−5.08276	−0.435843
$137$	17.5414	1.49866	0.749331	−	0.662196i	$-0.230375\pi$
$137$	17.5414	1.49866	0.749331	+	0.662196i	$0.230375\pi$
$138$	0	0
$139$	20.2483	1.71744	0.858719	−	0.512447i	$-0.171261\pi$
$139$	20.2483	1.71744	0.858719	+	0.512447i	$0.171261\pi$
$140$	−2.54138	−0.214786
$141$	0	0
$142$	−6.00000	−0.503509
$143$	0	0
$144$	0	0
$145$	7.62414	0.633151
$146$	2.45862	0.203477
$147$	0	0
$148$	10.0828	0.828798
$149$	5.54138	0.453968	0.226984	−	0.973899i	$-0.427114\pi$
$149$	5.54138	0.453968	0.226984	+	0.973899i	$0.427114\pi$
$150$	0	0
$151$	−24.0828	−1.95983	−0.979914	−	0.199422i	$-0.936094\pi$
$151$	−24.0828	−1.95983	−0.979914	+	0.199422i	$0.936094\pi$
$152$	1.54138	0.125023
$153$	0	0
$154$	0	0
$155$	−9.00000	−0.722897
$156$	0	0
$157$	20.2483	1.61599	0.807995	−	0.589190i	$-0.200553\pi$
$157$	20.2483	1.61599	0.807995	+	0.589190i	$0.200553\pi$
$158$	3.62414	0.288321
$159$	0	0
$160$	2.54138	0.200914
$161$	5.54138	0.436722
$162$	0	0
$163$	−13.4586	−1.05416	−0.527080	−	0.849816i	$-0.676713\pi$
$163$	−13.4586	−1.05416	−0.527080	+	0.849816i	$0.676713\pi$
$164$	−9.00000	−0.702782
$165$	0	0
$166$	−11.5414	−0.895785
$167$	19.6241	1.51856	0.759281	−	0.650763i	$-0.225551\pi$
$167$	19.6241	1.51856	0.759281	+	0.650763i	$0.225551\pi$
$168$	0	0
$169$	29.7897	2.29151
$170$	−12.9172	−0.990707
$171$	0	0
$172$	−6.08276	−0.463806
$173$	−2.08276	−0.158350	−0.0791748	−	0.996861i	$-0.525229\pi$
$173$	−2.08276	−0.158350	−0.0791748	+	0.996861i	$0.525229\pi$
$174$	0	0
$175$	−1.45862	−0.110261
$176$	0	0
$177$	0	0
$178$	0.458619	0.0343749
$179$	−15.7069	−1.17399	−0.586995	−	0.809591i	$-0.699689\pi$
$179$	−15.7069	−1.17399	−0.586995	+	0.809591i	$0.699689\pi$
$180$	0	0
$181$	−4.45862	−0.331407	−0.165703	−	0.986176i	$-0.552989\pi$
$181$	−4.45862	−0.331407	−0.165703	+	0.986176i	$0.552989\pi$
$182$	6.54138	0.484879
$183$	0	0
$184$	−5.54138	−0.408516
$185$	25.6241	1.88392
$186$	0	0
$187$	0	0
$188$	7.62414	0.556048
$189$	0	0
$190$	3.91724	0.284186
$191$	1.62414	0.117519	0.0587595	−	0.998272i	$-0.481286\pi$
$191$	1.62414	0.117519	0.0587595	+	0.998272i	$0.481286\pi$
$192$	0	0
$193$	−1.45862	−0.104994	−0.0524968	−	0.998621i	$-0.516718\pi$
$193$	−1.45862	−0.104994	−0.0524968	+	0.998621i	$0.516718\pi$
$194$	6.16553	0.442659
$195$	0	0
$196$	−6.00000	−0.428571
$197$	−0.917237	−0.0653505	−0.0326752	−	0.999466i	$-0.510403\pi$
$197$	−0.917237	−0.0653505	−0.0326752	+	0.999466i	$0.510403\pi$
$198$	0	0
$199$	8.00000	0.567105	0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000	0.567105	0.283552	+	0.958957i	$0.408487\pi$
$200$	1.45862	0.103140
$201$	0	0
$202$	6.91724	0.486695
$203$	−3.00000	−0.210559
$204$	0	0
$205$	−22.8724	−1.59748
$206$	−11.1655	−0.777939
$207$	0	0
$208$	−6.54138	−0.453563
$209$	0	0
$210$	0	0
$211$	−7.00000	−0.481900	−0.240950	−	0.970538i	$-0.577459\pi$
$211$	−7.00000	−0.481900	−0.240950	+	0.970538i	$0.577459\pi$
$212$	−2.08276	−0.143045
$213$	0	0
$214$	−0.917237	−0.0627011
$215$	−15.4586	−1.05427
$216$	0	0
$217$	3.54138	0.240405
$218$	−15.5414	−1.05260
$219$	0	0
$220$	0	0
$221$	33.2483	2.23652
$222$	0	0
$223$	17.4586	1.16912	0.584558	−	0.811352i	$-0.301268\pi$
$223$	17.4586	1.16912	0.584558	+	0.811352i	$0.301268\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	−9.45862	−0.629178
$227$	25.6241	1.70073	0.850367	−	0.526190i	$-0.176380\pi$
$227$	25.6241	1.70073	0.850367	+	0.526190i	$0.176380\pi$
$228$	0	0
$229$	−29.6241	−1.95762	−0.978809	−	0.204774i	$-0.934354\pi$
$229$	−29.6241	−1.95762	−0.978809	+	0.204774i	$0.934354\pi$
$230$	−14.0828	−0.928590
$231$	0	0
$232$	3.00000	0.196960
$233$	−17.5414	−1.14917	−0.574587	−	0.818443i	$-0.694837\pi$
$233$	−17.5414	−1.14917	−0.574587	+	0.818443i	$0.694837\pi$
$234$	0	0
$235$	19.3759	1.26394
$236$	−10.6241	−0.691573
$237$	0	0
$238$	5.08276	0.329467
$239$	−8.08276	−0.522830	−0.261415	−	0.965226i	$-0.584189\pi$
$239$	−8.08276	−0.522830	−0.261415	+	0.965226i	$0.584189\pi$
$240$	0	0
$241$	18.1655	1.17014	0.585072	−	0.810981i	$-0.301066\pi$
$241$	18.1655	1.17014	0.585072	+	0.810981i	$0.301066\pi$
$242$	0	0
$243$	0	0
$244$	−6.08276	−0.389409
$245$	−15.2483	−0.974177
$246$	0	0
$247$	−10.0828	−0.641551
$248$	−3.54138	−0.224878
$249$	0	0
$250$	−9.00000	−0.569210
$251$	20.5414	1.29656	0.648280	−	0.761402i	$-0.275489\pi$
$251$	20.5414	1.29656	0.648280	+	0.761402i	$0.275489\pi$
$252$	0	0
$253$	0	0
$254$	−15.5414	−0.975153
$255$	0	0
$256$	1.00000	0.0625000
$257$	19.1655	1.19551	0.597756	−	0.801678i	$-0.296059\pi$
$257$	19.1655	1.19551	0.597756	+	0.801678i	$0.296059\pi$
$258$	0	0
$259$	−10.0828	−0.626512
$260$	−16.6241	−1.03099
$261$	0	0
$262$	8.08276	0.499355
$263$	21.2483	1.31023	0.655113	−	0.755531i	$-0.272621\pi$
$263$	21.2483	1.31023	0.655113	+	0.755531i	$0.272621\pi$
$264$	0	0
$265$	−5.29309	−0.325152
$266$	−1.54138	−0.0945081
$267$	0	0
$268$	9.16553	0.559874
$269$	−15.7069	−0.957667	−0.478833	−	0.877906i	$-0.658940\pi$
$269$	−15.7069	−0.957667	−0.478833	+	0.877906i	$0.658940\pi$
$270$	0	0
$271$	9.62414	0.584625	0.292313	−	0.956323i	$-0.405575\pi$
$271$	9.62414	0.584625	0.292313	+	0.956323i	$0.405575\pi$
$272$	−5.08276	−0.308188
$273$	0	0
$274$	17.5414	1.05971
$275$	0	0
$276$	0	0
$277$	−22.2483	−1.33677	−0.668385	−	0.743815i	$-0.733014\pi$
$277$	−22.2483	−1.33677	−0.668385	+	0.743815i	$0.733014\pi$
$278$	20.2483	1.21441
$279$	0	0
$280$	−2.54138	−0.151877
$281$	26.7897	1.59814	0.799069	−	0.601240i	$-0.205326\pi$
$281$	26.7897	1.59814	0.799069	+	0.601240i	$0.205326\pi$
$282$	0	0
$283$	−8.83447	−0.525155	−0.262578	−	0.964911i	$-0.584573\pi$
$283$	−8.83447	−0.525155	−0.262578	+	0.964911i	$0.584573\pi$
$284$	−6.00000	−0.356034
$285$	0	0
$286$	0	0
$287$	9.00000	0.531253
$288$	0	0
$289$	8.83447	0.519675
$290$	7.62414	0.447705
$291$	0	0
$292$	2.45862	0.143880
$293$	12.4586	0.727840	0.363920	−	0.931430i	$-0.381438\pi$
$293$	12.4586	0.727840	0.363920	+	0.931430i	$0.381438\pi$
$294$	0	0
$295$	−27.0000	−1.57200
$296$	10.0828	0.586049
$297$	0	0
$298$	5.54138	0.321004
$299$	36.2483	2.09629
$300$	0	0
$301$	6.08276	0.350605
$302$	−24.0828	−1.38581
$303$	0	0
$304$	1.54138	0.0884043
$305$	−15.4586	−0.885158
$306$	0	0
$307$	−31.7069	−1.80961	−0.904804	−	0.425828i	$-0.859983\pi$
$307$	−31.7069	−1.80961	−0.904804	+	0.425828i	$0.859983\pi$
$308$	0	0
$309$	0	0
$310$	−9.00000	−0.511166
$311$	2.08276	0.118103	0.0590513	−	0.998255i	$-0.481192\pi$
$311$	2.08276	0.118103	0.0590513	+	0.998255i	$0.481192\pi$
$312$	0	0
$313$	15.6241	0.883129	0.441564	−	0.897230i	$-0.354424\pi$
$313$	15.6241	0.883129	0.441564	+	0.897230i	$0.354424\pi$
$314$	20.2483	1.14268
$315$	0	0
$316$	3.62414	0.203874
$317$	−27.2483	−1.53042	−0.765208	−	0.643783i	$-0.777364\pi$
$317$	−27.2483	−1.53042	−0.765208	+	0.643783i	$0.777364\pi$
$318$	0	0
$319$	0	0
$320$	2.54138	0.142068
$321$	0	0
$322$	5.54138	0.308809
$323$	−7.83447	−0.435922
$324$	0	0
$325$	−9.54138	−0.529261
$326$	−13.4586	−0.745404
$327$	0	0
$328$	−9.00000	−0.496942
$329$	−7.62414	−0.420333
$330$	0	0
$331$	−28.2483	−1.55267	−0.776333	−	0.630323i	$-0.782923\pi$
$331$	−28.2483	−1.55267	−0.776333	+	0.630323i	$0.782923\pi$
$332$	−11.5414	−0.633416
$333$	0	0
$334$	19.6241	1.07379
$335$	23.2931	1.27264
$336$	0	0
$337$	13.0828	0.712663	0.356332	−	0.934360i	$-0.384027\pi$
$337$	13.0828	0.712663	0.356332	+	0.934360i	$0.384027\pi$
$338$	29.7897	1.62034
$339$	0	0
$340$	−12.9172	−0.700536
$341$	0	0
$342$	0	0
$343$	13.0000	0.701934
$344$	−6.08276	−0.327961
$345$	0	0
$346$	−2.08276	−0.111970
$347$	5.78967	0.310806	0.155403	−	0.987851i	$-0.450332\pi$
$347$	5.78967	0.310806	0.155403	+	0.987851i	$0.450332\pi$
$348$	0	0
$349$	5.70691	0.305484	0.152742	−	0.988266i	$-0.451190\pi$
$349$	5.70691	0.305484	0.152742	+	0.988266i	$0.451190\pi$
$350$	−1.45862	−0.0779665
$351$	0	0
$352$	0	0
$353$	−30.0000	−1.59674	−0.798369	−	0.602168i	$-0.794304\pi$
$353$	−30.0000	−1.59674	−0.798369	+	0.602168i	$0.794304\pi$
$354$	0	0
$355$	−15.2483	−0.809295
$356$	0.458619	0.0243067
$357$	0	0
$358$	−15.7069	−0.830136
$359$	12.2483	0.646440	0.323220	−	0.946324i	$-0.395235\pi$
$359$	12.2483	0.646440	0.323220	+	0.946324i	$0.395235\pi$
$360$	0	0
$361$	−16.6241	−0.874955
$362$	−4.45862	−0.234340
$363$	0	0
$364$	6.54138	0.342862
$365$	6.24829	0.327050
$366$	0	0
$367$	18.3759	0.959212	0.479606	−	0.877484i	$-0.340780\pi$
$367$	18.3759	0.959212	0.479606	+	0.877484i	$0.340780\pi$
$368$	−5.54138	−0.288864
$369$	0	0
$370$	25.6241	1.33214
$371$	2.08276	0.108132
$372$	0	0
$373$	−13.4586	−0.696861	−0.348430	−	0.937335i	$-0.613285\pi$
$373$	−13.4586	−0.696861	−0.348430	+	0.937335i	$0.613285\pi$
$374$	0	0
$375$	0	0
$376$	7.62414	0.393185
$377$	−19.6241	−1.01069
$378$	0	0
$379$	−14.6241	−0.751192	−0.375596	−	0.926784i	$-0.622562\pi$
$379$	−14.6241	−0.751192	−0.375596	+	0.926784i	$0.622562\pi$
$380$	3.91724	0.200950
$381$	0	0
$382$	1.62414	0.0830984
$383$	−14.0828	−0.719596	−0.359798	−	0.933030i	$-0.617154\pi$
$383$	−14.0828	−0.719596	−0.359798	+	0.933030i	$0.617154\pi$
$384$	0	0
$385$	0	0
$386$	−1.45862	−0.0742417
$387$	0	0
$388$	6.16553	0.313007
$389$	−0.248288	−0.0125887	−0.00629434	−	0.999980i	$-0.502004\pi$
$389$	−0.248288	−0.0125887	−0.00629434	+	0.999980i	$0.502004\pi$
$390$	0	0
$391$	28.1655	1.42439
$392$	−6.00000	−0.303046
$393$	0	0
$394$	−0.917237	−0.0462098
$395$	9.21033	0.463422
$396$	0	0
$397$	14.9172	0.748675	0.374337	−	0.927293i	$-0.377870\pi$
$397$	14.9172	0.748675	0.374337	+	0.927293i	$0.377870\pi$
$398$	8.00000	0.401004
$399$	0	0
$400$	1.45862	0.0729309
$401$	3.45862	0.172715	0.0863576	−	0.996264i	$-0.472477\pi$
$401$	3.45862	0.172715	0.0863576	+	0.996264i	$0.472477\pi$
$402$	0	0
$403$	23.1655	1.15396
$404$	6.91724	0.344145
$405$	0	0
$406$	−3.00000	−0.148888
$407$	0	0
$408$	0	0
$409$	−4.70691	−0.232742	−0.116371	−	0.993206i	$-0.537126\pi$
$409$	−4.70691	−0.232742	−0.116371	+	0.993206i	$0.537126\pi$
$410$	−22.8724	−1.12959
$411$	0	0
$412$	−11.1655	−0.550086
$413$	10.6241	0.522780
$414$	0	0
$415$	−29.3311	−1.43980
$416$	−6.54138	−0.320718
$417$	0	0
$418$	0	0
$419$	21.0000	1.02592	0.512959	−	0.858413i	$-0.328549\pi$
$419$	21.0000	1.02592	0.512959	+	0.858413i	$0.328549\pi$
$420$	0	0
$421$	−1.00000	−0.0487370	−0.0243685	−	0.999703i	$-0.507758\pi$
$421$	−1.00000	−0.0487370	−0.0243685	+	0.999703i	$0.507758\pi$
$422$	−7.00000	−0.340755
$423$	0	0
$424$	−2.08276	−0.101148
$425$	−7.41381	−0.359623
$426$	0	0
$427$	6.08276	0.294366
$428$	−0.917237	−0.0443363
$429$	0	0
$430$	−15.4586	−0.745481
$431$	−33.2483	−1.60151	−0.800757	−	0.598990i	$-0.795569\pi$
$431$	−33.2483	−1.60151	−0.800757	+	0.598990i	$0.795569\pi$
$432$	0	0
$433$	18.6241	0.895019	0.447510	−	0.894279i	$-0.352311\pi$
$433$	18.6241	0.895019	0.447510	+	0.894279i	$0.352311\pi$
$434$	3.54138	0.169992
$435$	0	0
$436$	−15.5414	−0.744297
$437$	−8.54138	−0.408590
$438$	0	0
$439$	−33.3311	−1.59080	−0.795402	−	0.606082i	$-0.792740\pi$
$439$	−33.3311	−1.59080	−0.795402	+	0.606082i	$0.792740\pi$
$440$	0	0
$441$	0	0
$442$	33.2483	1.58146
$443$	11.0828	0.526558	0.263279	−	0.964720i	$-0.415196\pi$
$443$	11.0828	0.526558	0.263279	+	0.964720i	$0.415196\pi$
$444$	0	0
$445$	1.16553	0.0552512
$446$	17.4586	0.826690
$447$	0	0
$448$	−1.00000	−0.0472456
$449$	37.1655	1.75395	0.876975	−	0.480536i	$-0.159558\pi$
$449$	37.1655	1.75395	0.876975	+	0.480536i	$0.159558\pi$
$450$	0	0
$451$	0	0
$452$	−9.45862	−0.444896
$453$	0	0
$454$	25.6241	1.20260
$455$	16.6241	0.779352
$456$	0	0
$457$	0.165525	0.00774294	0.00387147	−	0.999993i	$-0.498768\pi$
$457$	0.165525	0.00774294	0.00387147	+	0.999993i	$0.498768\pi$
$458$	−29.6241	−1.38425
$459$	0	0
$460$	−14.0828	−0.656612
$461$	7.16553	0.333732	0.166866	−	0.985980i	$-0.446635\pi$
$461$	7.16553	0.333732	0.166866	+	0.985980i	$0.446635\pi$
$462$	0	0
$463$	−39.7897	−1.84918	−0.924591	−	0.380960i	$-0.875593\pi$
$463$	−39.7897	−1.84918	−0.924591	+	0.380960i	$0.875593\pi$
$464$	3.00000	0.139272
$465$	0	0
$466$	−17.5414	−0.812589
$467$	7.62414	0.352803	0.176402	−	0.984318i	$-0.443554\pi$
$467$	7.62414	0.352803	0.176402	+	0.984318i	$0.443554\pi$
$468$	0	0
$469$	−9.16553	−0.423225
$470$	19.3759	0.893742
$471$	0	0
$472$	−10.6241	−0.489016
$473$	0	0
$474$	0	0
$475$	2.24829	0.103159
$476$	5.08276	0.232968
$477$	0	0
$478$	−8.08276	−0.369697
$479$	−34.8724	−1.59336	−0.796681	−	0.604400i	$-0.793413\pi$
$479$	−34.8724	−1.59336	−0.796681	+	0.604400i	$0.793413\pi$
$480$	0	0
$481$	−65.9552	−3.00730
$482$	18.1655	0.827417
$483$	0	0
$484$	0	0
$485$	15.6689	0.711490
$486$	0	0
$487$	11.0000	0.498458	0.249229	−	0.968445i	$-0.419823\pi$
$487$	11.0000	0.498458	0.249229	+	0.968445i	$0.419823\pi$
$488$	−6.08276	−0.275354
$489$	0	0
$490$	−15.2483	−0.688847
$491$	−20.0828	−0.906322	−0.453161	−	0.891429i	$-0.649704\pi$
$491$	−20.0828	−0.906322	−0.453161	+	0.891429i	$0.649704\pi$
$492$	0	0
$493$	−15.2483	−0.686748
$494$	−10.0828	−0.453645
$495$	0	0
$496$	−3.54138	−0.159013
$497$	6.00000	0.269137
$498$	0	0
$499$	−40.2483	−1.80176	−0.900880	−	0.434067i	$-0.857078\pi$
$499$	−40.2483	−1.80176	−0.900880	+	0.434067i	$0.857078\pi$
$500$	−9.00000	−0.402492
$501$	0	0
$502$	20.5414	0.916807
$503$	−24.4586	−1.09056	−0.545278	−	0.838255i	$-0.683576\pi$
$503$	−24.4586	−1.09056	−0.545278	+	0.838255i	$0.683576\pi$
$504$	0	0
$505$	17.5793	0.782270
$506$	0	0
$507$	0	0
$508$	−15.5414	−0.689537
$509$	40.4138	1.79131	0.895655	−	0.444749i	$-0.146707\pi$
$509$	40.4138	1.79131	0.895655	+	0.444749i	$0.146707\pi$
$510$	0	0
$511$	−2.45862	−0.108763
$512$	1.00000	0.0441942
$513$	0	0
$514$	19.1655	0.845355
$515$	−28.3759	−1.25039
$516$	0	0
$517$	0	0
$518$	−10.0828	−0.443011
$519$	0	0
$520$	−16.6241	−0.729017
$521$	25.6241	1.12261	0.561307	−	0.827608i	$-0.310299\pi$
$521$	25.6241	1.12261	0.561307	+	0.827608i	$0.310299\pi$
$522$	0	0
$523$	−8.37586	−0.366251	−0.183125	−	0.983090i	$-0.558621\pi$
$523$	−8.37586	−0.366251	−0.183125	+	0.983090i	$0.558621\pi$
$524$	8.08276	0.353097
$525$	0	0
$526$	21.2483	0.926469
$527$	18.0000	0.784092
$528$	0	0
$529$	7.70691	0.335083
$530$	−5.29309	−0.229917
$531$	0	0
$532$	−1.54138	−0.0668274
$533$	58.8724	2.55005
$534$	0	0
$535$	−2.33105	−0.100780
$536$	9.16553	0.395890
$537$	0	0
$538$	−15.7069	−0.677173
$539$	0	0
$540$	0	0
$541$	−27.3311	−1.17505	−0.587527	−	0.809205i	$-0.699898\pi$
$541$	−27.3311	−1.17505	−0.587527	+	0.809205i	$0.699898\pi$
$542$	9.62414	0.413392
$543$	0	0
$544$	−5.08276	−0.217922
$545$	−39.4966	−1.69185
$546$	0	0
$547$	−14.8724	−0.635899	−0.317950	−	0.948108i	$-0.602994\pi$
$547$	−14.8724	−0.635899	−0.317950	+	0.948108i	$0.602994\pi$
$548$	17.5414	0.749331
$549$	0	0
$550$	0	0
$551$	4.62414	0.196995
$552$	0	0
$553$	−3.62414	−0.154114
$554$	−22.2483	−0.945239
$555$	0	0
$556$	20.2483	0.858719
$557$	40.8724	1.73182	0.865910	−	0.500199i	$-0.166740\pi$
$557$	40.8724	1.73182	0.865910	+	0.500199i	$0.166740\pi$
$558$	0	0
$559$	39.7897	1.68292
$560$	−2.54138	−0.107393
$561$	0	0
$562$	26.7897	1.13005
$563$	−43.4138	−1.82967	−0.914837	−	0.403823i	$-0.867681\pi$
$563$	−43.4138	−1.82967	−0.914837	+	0.403823i	$0.867681\pi$
$564$	0	0
$565$	−24.0380	−1.01128
$566$	−8.83447	−0.371341
$567$	0	0
$568$	−6.00000	−0.251754
$569$	4.83447	0.202672	0.101336	−	0.994852i	$-0.467688\pi$
$569$	4.83447	0.202672	0.101336	+	0.994852i	$0.467688\pi$
$570$	0	0
$571$	−0.0827625	−0.00346350	−0.00173175	−	0.999999i	$-0.500551\pi$
$571$	−0.0827625	−0.00346350	−0.00173175	+	0.999999i	$0.500551\pi$
$572$	0	0
$573$	0	0
$574$	9.00000	0.375653
$575$	−8.08276	−0.337074
$576$	0	0
$577$	−0.751712	−0.0312942	−0.0156471	−	0.999878i	$-0.504981\pi$
$577$	−0.751712	−0.0312942	−0.0156471	+	0.999878i	$0.504981\pi$
$578$	8.83447	0.367466
$579$	0	0
$580$	7.62414	0.316575
$581$	11.5414	0.478817
$582$	0	0
$583$	0	0
$584$	2.45862	0.101738
$585$	0	0
$586$	12.4586	0.514661
$587$	28.3759	1.17120	0.585598	−	0.810601i	$-0.300860\pi$
$587$	28.3759	1.17120	0.585598	+	0.810601i	$0.300860\pi$
$588$	0	0
$589$	−5.45862	−0.224918
$590$	−27.0000	−1.11157
$591$	0	0
$592$	10.0828	0.414399
$593$	31.6241	1.29865	0.649324	−	0.760512i	$-0.275052\pi$
$593$	31.6241	1.29865	0.649324	+	0.760512i	$0.275052\pi$
$594$	0	0
$595$	12.9172	0.529555
$596$	5.54138	0.226984
$597$	0	0
$598$	36.2483	1.48230
$599$	13.6241	0.556667	0.278334	−	0.960484i	$-0.410218\pi$
$599$	13.6241	0.556667	0.278334	+	0.960484i	$0.410218\pi$
$600$	0	0
$601$	24.4138	0.995860	0.497930	−	0.867217i	$-0.334094\pi$
$601$	24.4138	0.995860	0.497930	+	0.867217i	$0.334094\pi$
$602$	6.08276	0.247915
$603$	0	0
$604$	−24.0828	−0.979914
$605$	0	0
$606$	0	0
$607$	30.4138	1.23446	0.617229	−	0.786783i	$-0.288255\pi$
$607$	30.4138	1.23446	0.617229	+	0.786783i	$0.288255\pi$
$608$	1.54138	0.0625113
$609$	0	0
$610$	−15.4586	−0.625901
$611$	−49.8724	−2.01762
$612$	0	0
$613$	34.3311	1.38662	0.693309	−	0.720640i	$-0.256152\pi$
$613$	34.3311	1.38662	0.693309	+	0.720640i	$0.256152\pi$
$614$	−31.7069	−1.27959
$615$	0	0
$616$	0	0
$617$	−24.4586	−0.984667	−0.492333	−	0.870407i	$-0.663856\pi$
$617$	−24.4586	−0.984667	−0.492333	+	0.870407i	$0.663856\pi$
$618$	0	0
$619$	15.6241	0.627987	0.313994	−	0.949425i	$-0.398333\pi$
$619$	15.6241	0.627987	0.313994	+	0.949425i	$0.398333\pi$
$620$	−9.00000	−0.361449
$621$	0	0
$622$	2.08276	0.0835112
$623$	−0.458619	−0.0183742
$624$	0	0
$625$	−30.1655	−1.20662
$626$	15.6241	0.624466
$627$	0	0
$628$	20.2483	0.807995
$629$	−51.2483	−2.04340
$630$	0	0
$631$	−3.08276	−0.122723	−0.0613614	−	0.998116i	$-0.519544\pi$
$631$	−3.08276	−0.122723	−0.0613614	+	0.998116i	$0.519544\pi$
$632$	3.62414	0.144161
$633$	0	0
$634$	−27.2483	−1.08217
$635$	−39.4966	−1.56737
$636$	0	0
$637$	39.2483	1.55507
$638$	0	0
$639$	0	0
$640$	2.54138	0.100457
$641$	13.6241	0.538121	0.269061	−	0.963123i	$-0.413287\pi$
$641$	13.6241	0.538121	0.269061	+	0.963123i	$0.413287\pi$
$642$	0	0
$643$	20.0000	0.788723	0.394362	−	0.918955i	$-0.370966\pi$
$643$	20.0000	0.788723	0.394362	+	0.918955i	$0.370966\pi$
$644$	5.54138	0.218361
$645$	0	0
$646$	−7.83447	−0.308243
$647$	−29.3311	−1.15312	−0.576561	−	0.817054i	$-0.695606\pi$
$647$	−29.3311	−1.15312	−0.576561	+	0.817054i	$0.695606\pi$
$648$	0	0
$649$	0	0
$650$	−9.54138	−0.374244
$651$	0	0
$652$	−13.4586	−0.527080
$653$	−9.24829	−0.361913	−0.180957	−	0.983491i	$-0.557919\pi$
$653$	−9.24829	−0.361913	−0.180957	+	0.983491i	$0.557919\pi$
$654$	0	0
$655$	20.5414	0.802618
$656$	−9.00000	−0.351391
$657$	0	0
$658$	−7.62414	−0.297220
$659$	−22.8724	−0.890983	−0.445492	−	0.895286i	$-0.646971\pi$
$659$	−22.8724	−0.890983	−0.445492	+	0.895286i	$0.646971\pi$
$660$	0	0
$661$	−44.4138	−1.72750	−0.863749	−	0.503923i	$-0.831890\pi$
$661$	−44.4138	−1.72750	−0.863749	+	0.503923i	$0.831890\pi$
$662$	−28.2483	−1.09790
$663$	0	0
$664$	−11.5414	−0.447892
$665$	−3.91724	−0.151904
$666$	0	0
$667$	−16.6241	−0.643689
$668$	19.6241	0.759281
$669$	0	0
$670$	23.2931	0.899891
$671$	0	0
$672$	0	0
$673$	−4.00000	−0.154189	−0.0770943	−	0.997024i	$-0.524564\pi$
$673$	−4.00000	−0.154189	−0.0770943	+	0.997024i	$0.524564\pi$
$674$	13.0828	0.503929
$675$	0	0
$676$	29.7897	1.14576
$677$	9.45862	0.363524	0.181762	−	0.983343i	$-0.441820\pi$
$677$	9.45862	0.363524	0.181762	+	0.983343i	$0.441820\pi$
$678$	0	0
$679$	−6.16553	−0.236611
$680$	−12.9172	−0.495353
$681$	0	0
$682$	0	0
$683$	40.6241	1.55444	0.777220	−	0.629229i	$-0.216629\pi$
$683$	40.6241	1.55444	0.777220	+	0.629229i	$0.216629\pi$
$684$	0	0
$685$	44.5793	1.70329
$686$	13.0000	0.496342
$687$	0	0
$688$	−6.08276	−0.231903
$689$	13.6241	0.519039
$690$	0	0
$691$	−9.54138	−0.362971	−0.181486	−	0.983394i	$-0.558091\pi$
$691$	−9.54138	−0.362971	−0.181486	+	0.983394i	$0.558091\pi$
$692$	−2.08276	−0.0791748
$693$	0	0
$694$	5.78967	0.219773
$695$	51.4586	1.95194
$696$	0	0
$697$	45.7449	1.73271
$698$	5.70691	0.216010
$699$	0	0
$700$	−1.45862	−0.0551306
$701$	7.87243	0.297338	0.148669	−	0.988887i	$-0.452501\pi$
$701$	7.87243	0.297338	0.148669	+	0.988887i	$0.452501\pi$
$702$	0	0
$703$	15.5414	0.586154
$704$	0	0
$705$	0	0
$706$	−30.0000	−1.12906
$707$	−6.91724	−0.260149
$708$	0	0
$709$	6.83447	0.256674	0.128337	−	0.991731i	$-0.459036\pi$
$709$	6.83447	0.256674	0.128337	+	0.991731i	$0.459036\pi$
$710$	−15.2483	−0.572258
$711$	0	0
$712$	0.458619	0.0171875
$713$	19.6241	0.734930
$714$	0	0
$715$	0	0
$716$	−15.7069	−0.586995
$717$	0	0
$718$	12.2483	0.457102
$719$	−27.4966	−1.02545	−0.512725	−	0.858553i	$-0.671364\pi$
$719$	−27.4966	−1.02545	−0.512725	+	0.858553i	$0.671364\pi$
$720$	0	0
$721$	11.1655	0.415826
$722$	−16.6241	−0.618687
$723$	0	0
$724$	−4.45862	−0.165703
$725$	4.37586	0.162515
$726$	0	0
$727$	31.0828	1.15280	0.576398	−	0.817169i	$-0.304458\pi$
$727$	31.0828	1.15280	0.576398	+	0.817169i	$0.304458\pi$
$728$	6.54138	0.242440
$729$	0	0
$730$	6.24829	0.231259
$731$	30.9172	1.14352
$732$	0	0
$733$	−17.8724	−0.660133	−0.330067	−	0.943958i	$-0.607071\pi$
$733$	−17.8724	−0.660133	−0.330067	+	0.943958i	$0.607071\pi$
$734$	18.3759	0.678265
$735$	0	0
$736$	−5.54138	−0.204258
$737$	0	0
$738$	0	0
$739$	−23.6241	−0.869028	−0.434514	−	0.900665i	$-0.643080\pi$
$739$	−23.6241	−0.869028	−0.434514	+	0.900665i	$0.643080\pi$
$740$	25.6241	0.941962
$741$	0	0
$742$	2.08276	0.0764606
$743$	9.70691	0.356112	0.178056	−	0.984020i	$-0.443019\pi$
$743$	9.70691	0.356112	0.178056	+	0.984020i	$0.443019\pi$
$744$	0	0
$745$	14.0828	0.515952
$746$	−13.4586	−0.492755
$747$	0	0
$748$	0	0
$749$	0.917237	0.0335151
$750$	0	0
$751$	−22.0000	−0.802791	−0.401396	−	0.915905i	$-0.631475\pi$
$751$	−22.0000	−0.802791	−0.401396	+	0.915905i	$0.631475\pi$
$752$	7.62414	0.278024
$753$	0	0
$754$	−19.6241	−0.714669
$755$	−61.2035	−2.22742
$756$	0	0
$757$	−10.2483	−0.372480	−0.186240	−	0.982504i	$-0.559630\pi$
$757$	−10.2483	−0.372480	−0.186240	+	0.982504i	$0.559630\pi$
$758$	−14.6241	−0.531173
$759$	0	0
$760$	3.91724	0.142093
$761$	0.248288	0.00900042	0.00450021	−	0.999990i	$-0.498568\pi$
$761$	0.248288	0.00900042	0.00450021	+	0.999990i	$0.498568\pi$
$762$	0	0
$763$	15.5414	0.562636
$764$	1.62414	0.0587595
$765$	0	0
$766$	−14.0828	−0.508831
$767$	69.4966	2.50938
$768$	0	0
$769$	1.78967	0.0645371	0.0322686	−	0.999479i	$-0.489727\pi$
$769$	1.78967	0.0645371	0.0322686	+	0.999479i	$0.489727\pi$
$770$	0	0
$771$	0	0
$772$	−1.45862	−0.0524968
$773$	48.2483	1.73537	0.867685	−	0.497114i	$-0.165607\pi$
$773$	48.2483	1.73537	0.867685	+	0.497114i	$0.165607\pi$
$774$	0	0
$775$	−5.16553	−0.185551
$776$	6.16553	0.221329
$777$	0	0
$778$	−0.248288	−0.00890154
$779$	−13.8724	−0.497031
$780$	0	0
$781$	0	0
$782$	28.1655	1.00720
$783$	0	0
$784$	−6.00000	−0.214286
$785$	51.4586	1.83664
$786$	0	0
$787$	−15.3311	−0.546493	−0.273246	−	0.961944i	$-0.588097\pi$
$787$	−15.3311	−0.546493	−0.273246	+	0.961944i	$0.588097\pi$
$788$	−0.917237	−0.0326752
$789$	0	0
$790$	9.21033	0.327689
$791$	9.45862	0.336310
$792$	0	0
$793$	39.7897	1.41297
$794$	14.9172	0.529393
$795$	0	0
$796$	8.00000	0.283552
$797$	30.0000	1.06265	0.531327	−	0.847167i	$-0.321693\pi$
$797$	30.0000	1.06265	0.531327	+	0.847167i	$0.321693\pi$
$798$	0	0
$799$	−38.7517	−1.37094
$800$	1.45862	0.0515700
$801$	0	0
$802$	3.45862	0.122128
$803$	0	0
$804$	0	0
$805$	14.0828	0.496352
$806$	23.1655	0.815971
$807$	0	0
$808$	6.91724	0.243348
$809$	−31.1655	−1.09572	−0.547861	−	0.836570i	$-0.684558\pi$
$809$	−31.1655	−1.09572	−0.547861	+	0.836570i	$0.684558\pi$
$810$	0	0
$811$	−5.62414	−0.197490	−0.0987452	−	0.995113i	$-0.531483\pi$
$811$	−5.62414	−0.197490	−0.0987452	+	0.995113i	$0.531483\pi$
$812$	−3.00000	−0.105279
$813$	0	0
$814$	0	0
$815$	−34.2035	−1.19810
$816$	0	0
$817$	−9.37586	−0.328020
$818$	−4.70691	−0.164573
$819$	0	0
$820$	−22.8724	−0.798740
$821$	48.7069	1.69988	0.849941	−	0.526877i	$-0.176637\pi$
$821$	48.7069	1.69988	0.849941	+	0.526877i	$0.176637\pi$
$822$	0	0
$823$	49.1207	1.71224	0.856120	−	0.516777i	$-0.172868\pi$
$823$	49.1207	1.71224	0.856120	+	0.516777i	$0.172868\pi$
$824$	−11.1655	−0.388969
$825$	0	0
$826$	10.6241	0.369661
$827$	−19.8345	−0.689712	−0.344856	−	0.938656i	$-0.612072\pi$
$827$	−19.8345	−0.689712	−0.344856	+	0.938656i	$0.612072\pi$
$828$	0	0
$829$	−22.7069	−0.788643	−0.394322	−	0.918972i	$-0.629020\pi$
$829$	−22.7069	−0.788643	−0.394322	+	0.918972i	$0.629020\pi$
$830$	−29.3311	−1.01810
$831$	0	0
$832$	−6.54138	−0.226782
$833$	30.4966	1.05664
$834$	0	0
$835$	49.8724	1.72591
$836$	0	0
$837$	0	0
$838$	21.0000	0.725433
$839$	−25.3759	−0.876072	−0.438036	−	0.898957i	$-0.644326\pi$
$839$	−25.3759	−0.876072	−0.438036	+	0.898957i	$0.644326\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	−1.00000	−0.0344623
$843$	0	0
$844$	−7.00000	−0.240950
$845$	75.7069	2.60440
$846$	0	0
$847$	0	0
$848$	−2.08276	−0.0715224
$849$	0	0
$850$	−7.41381	−0.254292
$851$	−55.8724	−1.91528
$852$	0	0
$853$	31.3311	1.07275	0.536377	−	0.843978i	$-0.319792\pi$
$853$	31.3311	1.07275	0.536377	+	0.843978i	$0.319792\pi$
$854$	6.08276	0.208148
$855$	0	0
$856$	−0.917237	−0.0313505
$857$	−3.45862	−0.118144	−0.0590721	−	0.998254i	$-0.518814\pi$
$857$	−3.45862	−0.118144	−0.0590721	+	0.998254i	$0.518814\pi$
$858$	0	0
$859$	−36.5793	−1.24807	−0.624035	−	0.781396i	$-0.714508\pi$
$859$	−36.5793	−1.24807	−0.624035	+	0.781396i	$0.714508\pi$
$860$	−15.4586	−0.527135
$861$	0	0
$862$	−33.2483	−1.13244
$863$	−5.08276	−0.173019	−0.0865096	−	0.996251i	$-0.527571\pi$
$863$	−5.08276	−0.173019	−0.0865096	+	0.996251i	$0.527571\pi$
$864$	0	0
$865$	−5.29309	−0.179971
$866$	18.6241	0.632874
$867$	0	0
$868$	3.54138	0.120202
$869$	0	0
$870$	0	0
$871$	−59.9552	−2.03150
$872$	−15.5414	−0.526298
$873$	0	0
$874$	−8.54138	−0.288917
$875$	9.00000	0.304256
$876$	0	0
$877$	34.5793	1.16766	0.583831	−	0.811875i	$-0.301553\pi$
$877$	34.5793	1.16766	0.583831	+	0.811875i	$0.301553\pi$
$878$	−33.3311	−1.12487
$879$	0	0
$880$	0	0
$881$	−5.54138	−0.186694	−0.0933469	−	0.995634i	$-0.529757\pi$
$881$	−5.54138	−0.186694	−0.0933469	+	0.995634i	$0.529757\pi$
$882$	0	0
$883$	−54.5793	−1.83674	−0.918370	−	0.395722i	$-0.870494\pi$
$883$	−54.5793	−1.83674	−0.918370	+	0.395722i	$0.870494\pi$
$884$	33.2483	1.11826
$885$	0	0
$886$	11.0828	0.372333
$887$	−36.2483	−1.21710	−0.608549	−	0.793516i	$-0.708248\pi$
$887$	−36.2483	−1.21710	−0.608549	+	0.793516i	$0.708248\pi$
$888$	0	0
$889$	15.5414	0.521241
$890$	1.16553	0.0390685
$891$	0	0
$892$	17.4586	0.584558
$893$	11.7517	0.393256
$894$	0	0
$895$	−39.9172	−1.33429
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	37.1655	1.24023
$899$	−10.6241	−0.354335
$900$	0	0
$901$	10.5862	0.352677
$902$	0	0
$903$	0	0
$904$	−9.45862	−0.314589
$905$	−11.3311	−0.376657
$906$	0	0
$907$	−19.4586	−0.646113	−0.323056	−	0.946380i	$-0.604710\pi$
$907$	−19.4586	−0.646113	−0.323056	+	0.946380i	$0.604710\pi$
$908$	25.6241	0.850367
$909$	0	0
$910$	16.6241	0.551085
$911$	−17.7517	−0.588140	−0.294070	−	0.955784i	$-0.595010\pi$
$911$	−17.7517	−0.588140	−0.294070	+	0.955784i	$0.595010\pi$
$912$	0	0
$913$	0	0
$914$	0.165525	0.00547508
$915$	0	0
$916$	−29.6241	−0.978809
$917$	−8.08276	−0.266916
$918$	0	0
$919$	−35.6241	−1.17513	−0.587566	−	0.809176i	$-0.699914\pi$
$919$	−35.6241	−1.17513	−0.587566	+	0.809176i	$0.699914\pi$
$920$	−14.0828	−0.464295
$921$	0	0
$922$	7.16553	0.235984
$923$	39.2483	1.29187
$924$	0	0
$925$	14.7069	0.483560
$926$	−39.7897	−1.30757
$927$	0	0
$928$	3.00000	0.0984798
$929$	10.3759	0.340421	0.170210	−	0.985408i	$-0.445555\pi$
$929$	10.3759	0.340421	0.170210	+	0.985408i	$0.445555\pi$
$930$	0	0
$931$	−9.24829	−0.303100
$932$	−17.5414	−0.574587
$933$	0	0
$934$	7.62414	0.249470
$935$	0	0
$936$	0	0
$937$	−12.0828	−0.394727	−0.197363	−	0.980330i	$-0.563238\pi$
$937$	−12.0828	−0.394727	−0.197363	+	0.980330i	$0.563238\pi$
$938$	−9.16553	−0.299265
$939$	0	0
$940$	19.3759	0.631971
$941$	18.0000	0.586783	0.293392	−	0.955992i	$-0.405216\pi$
$941$	18.0000	0.586783	0.293392	+	0.955992i	$0.405216\pi$
$942$	0	0
$943$	49.8724	1.62407
$944$	−10.6241	−0.345786
$945$	0	0
$946$	0	0
$947$	6.24829	0.203042	0.101521	−	0.994833i	$-0.467629\pi$
$947$	6.24829	0.203042	0.101521	+	0.994833i	$0.467629\pi$
$948$	0	0
$949$	−16.0828	−0.522069
$950$	2.24829	0.0729441
$951$	0	0
$952$	5.08276	0.164733
$953$	−42.2483	−1.36856	−0.684278	−	0.729221i	$-0.739883\pi$
$953$	−42.2483	−1.36856	−0.684278	+	0.729221i	$0.739883\pi$
$954$	0	0
$955$	4.12757	0.133565
$956$	−8.08276	−0.261415
$957$	0	0
$958$	−34.8724	−1.12668
$959$	−17.5414	−0.566441
$960$	0	0
$961$	−18.4586	−0.595439
$962$	−65.9552	−2.12648
$963$	0	0
$964$	18.1655	0.585072
$965$	−3.70691	−0.119330
$966$	0	0
$967$	−31.9552	−1.02761	−0.513805	−	0.857907i	$-0.671764\pi$
$967$	−31.9552	−1.02761	−0.513805	+	0.857907i	$0.671764\pi$
$968$	0	0
$969$	0	0
$970$	15.6689	0.503100
$971$	−42.0000	−1.34784	−0.673922	−	0.738802i	$-0.735392\pi$
$971$	−42.0000	−1.34784	−0.673922	+	0.738802i	$0.735392\pi$
$972$	0	0
$973$	−20.2483	−0.649130
$974$	11.0000	0.352463
$975$	0	0
$976$	−6.08276	−0.194704
$977$	22.1655	0.709138	0.354569	−	0.935030i	$-0.384628\pi$
$977$	22.1655	0.709138	0.354569	+	0.935030i	$0.384628\pi$
$978$	0	0
$979$	0	0
$980$	−15.2483	−0.487089
$981$	0	0
$982$	−20.0828	−0.640867
$983$	39.4966	1.25975	0.629873	−	0.776699i	$-0.283107\pi$
$983$	39.4966	1.25975	0.629873	+	0.776699i	$0.283107\pi$
$984$	0	0
$985$	−2.33105	−0.0742734
$986$	−15.2483	−0.485604
$987$	0	0
$988$	−10.0828	−0.320775
$989$	33.7069	1.07182
$990$	0	0
$991$	−7.00000	−0.222362	−0.111181	−	0.993800i	$-0.535463\pi$
$991$	−7.00000	−0.222362	−0.111181	+	0.993800i	$0.535463\pi$
$992$	−3.54138	−0.112439
$993$	0	0
$994$	6.00000	0.190308
$995$	20.3311	0.644538
$996$	0	0
$997$	−1.45862	−0.0461949	−0.0230975	−	0.999733i	$-0.507353\pi$
$997$	−1.45862	−0.0461949	−0.0230975	+	0.999733i	$0.507353\pi$
$998$	−40.2483	−1.27404
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6534.2.a.cc.1.2	yes	2
3.2	odd	2		6534.2.a.bp.1.1	yes	2
11.10	odd	2		6534.2.a.bk.1.2	✓	2
33.32	even	2		6534.2.a.cl.1.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6534.2.a.bk.1.2	✓	2	11.10	odd	2
6534.2.a.bp.1.1	yes	2	3.2	odd	2
6534.2.a.cc.1.2	yes	2	1.1	even	1	trivial
6534.2.a.cl.1.1	yes	2	33.32	even	2

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:	\( N \)	\(=\)	\( 6534 = 2 \cdot 3^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6534.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +2.54138 q^{5} -1.00000 q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +2.54138 q^{5} -1.00000 q^{7} +1.00000 q^{8} +2.54138 q^{10} -6.54138 q^{13} -1.00000 q^{14} +1.00000 q^{16} -5.08276 q^{17} +1.54138 q^{19} +2.54138 q^{20} -5.54138 q^{23} +1.45862 q^{25} -6.54138 q^{26} -1.00000 q^{28} +3.00000 q^{29} -3.54138 q^{31} +1.00000 q^{32} -5.08276 q^{34} -2.54138 q^{35} +10.0828 q^{37} +1.54138 q^{38} +2.54138 q^{40} -9.00000 q^{41} -6.08276 q^{43} -5.54138 q^{46} +7.62414 q^{47} -6.00000 q^{49} +1.45862 q^{50} -6.54138 q^{52} -2.08276 q^{53} -1.00000 q^{56} +3.00000 q^{58} -10.6241 q^{59} -6.08276 q^{61} -3.54138 q^{62} +1.00000 q^{64} -16.6241 q^{65} +9.16553 q^{67} -5.08276 q^{68} -2.54138 q^{70} -6.00000 q^{71} +2.45862 q^{73} +10.0828 q^{74} +1.54138 q^{76} +3.62414 q^{79} +2.54138 q^{80} -9.00000 q^{82} -11.5414 q^{83} -12.9172 q^{85} -6.08276 q^{86} +0.458619 q^{89} +6.54138 q^{91} -5.54138 q^{92} +7.62414 q^{94} +3.91724 q^{95} +6.16553 q^{97} -6.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{4} - q^{5} - 2 q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^4 - q^5 - 2 * q^7 + 2 * q^8	\( 2 q + 2 q^{2} + 2 q^{4} - q^{5} - 2 q^{7} + 2 q^{8} - q^{10} - 7 q^{13} - 2 q^{14} + 2 q^{16} + 2 q^{17} - 3 q^{19} - q^{20} - 5 q^{23} + 9 q^{25} - 7 q^{26} - 2 q^{28} + 6 q^{29} - q^{31} + 2 q^{32} + 2 q^{34} + q^{35} + 8 q^{37} - 3 q^{38} - q^{40} - 18 q^{41} - 5 q^{46} - 3 q^{47} - 12 q^{49} + 9 q^{50} - 7 q^{52} + 8 q^{53} - 2 q^{56} + 6 q^{58} - 3 q^{59} - q^{62} + 2 q^{64} - 15 q^{65} - 6 q^{67} + 2 q^{68} + q^{70} - 12 q^{71} + 11 q^{73} + 8 q^{74} - 3 q^{76} - 11 q^{79} - q^{80} - 18 q^{82} - 17 q^{83} - 38 q^{85} + 7 q^{89} + 7 q^{91} - 5 q^{92} - 3 q^{94} + 20 q^{95} - 12 q^{97} - 12 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^4 - q^5 - 2 * q^7 + 2 * q^8 - q^10 - 7 * q^13 - 2 * q^14 + 2 * q^16 + 2 * q^17 - 3 * q^19 - q^20 - 5 * q^23 + 9 * q^25 - 7 * q^26 - 2 * q^28 + 6 * q^29 - q^31 + 2 * q^32 + 2 * q^34 + q^35 + 8 * q^37 - 3 * q^38 - q^40 - 18 * q^41 - 5 * q^46 - 3 * q^47 - 12 * q^49 + 9 * q^50 - 7 * q^52 + 8 * q^53 - 2 * q^56 + 6 * q^58 - 3 * q^59 - q^62 + 2 * q^64 - 15 * q^65 - 6 * q^67 + 2 * q^68 + q^70 - 12 * q^71 + 11 * q^73 + 8 * q^74 - 3 * q^76 - 11 * q^79 - q^80 - 18 * q^82 - 17 * q^83 - 38 * q^85 + 7 * q^89 + 7 * q^91 - 5 * q^92 - 3 * q^94 + 20 * q^95 - 12 * q^97 - 12 * q^98

Introduction

L-functions

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Database

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