LMFDB - Embedded newform 6534.2.a.bx.1.1

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:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 594)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} -4.23607 q^{5} +1.00000 q^{7} +1.00000 q^{8} +O(q^{10})$	$q+1.00000 q^{2} +1.00000 q^{4} -4.23607 q^{5} +1.00000 q^{7} +1.00000 q^{8} -4.23607 q^{10} -1.38197 q^{13} +1.00000 q^{14} +1.00000 q^{16} +1.61803 q^{17} +3.85410 q^{19} -4.23607 q^{20} -6.23607 q^{23} +12.9443 q^{25} -1.38197 q^{26} +1.00000 q^{28} +0.381966 q^{29} +8.70820 q^{31} +1.00000 q^{32} +1.61803 q^{34} -4.23607 q^{35} -4.85410 q^{37} +3.85410 q^{38} -4.23607 q^{40} -10.4721 q^{41} -10.8541 q^{43} -6.23607 q^{46} -0.527864 q^{47} -6.00000 q^{49} +12.9443 q^{50} -1.38197 q^{52} +10.7984 q^{53} +1.00000 q^{56} +0.381966 q^{58} +2.61803 q^{59} +7.61803 q^{61} +8.70820 q^{62} +1.00000 q^{64} +5.85410 q^{65} +7.76393 q^{67} +1.61803 q^{68} -4.23607 q^{70} -5.61803 q^{71} -10.2361 q^{73} -4.85410 q^{74} +3.85410 q^{76} +6.00000 q^{79} -4.23607 q^{80} -10.4721 q^{82} +5.23607 q^{83} -6.85410 q^{85} -10.8541 q^{86} -12.1803 q^{89} -1.38197 q^{91} -6.23607 q^{92} -0.527864 q^{94} -16.3262 q^{95} +7.14590 q^{97} -6.00000 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{4} - 4 q^{5} + 2 q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^4 - 4 * q^5 + 2 * q^7 + 2 * q^8	$ 2 q + 2 q^{2} + 2 q^{4} - 4 q^{5} + 2 q^{7} + 2 q^{8} - 4 q^{10} - 5 q^{13} + 2 q^{14} + 2 q^{16} + q^{17} + q^{19} - 4 q^{20} - 8 q^{23} + 8 q^{25} - 5 q^{26} + 2 q^{28} + 3 q^{29} + 4 q^{31} + 2 q^{32} + q^{34} - 4 q^{35} - 3 q^{37} + q^{38} - 4 q^{40} - 12 q^{41} - 15 q^{43} - 8 q^{46} - 10 q^{47} - 12 q^{49} + 8 q^{50} - 5 q^{52} - 3 q^{53} + 2 q^{56} + 3 q^{58} + 3 q^{59} + 13 q^{61} + 4 q^{62} + 2 q^{64} + 5 q^{65} + 20 q^{67} + q^{68} - 4 q^{70} - 9 q^{71} - 16 q^{73} - 3 q^{74} + q^{76} + 12 q^{79} - 4 q^{80} - 12 q^{82} + 6 q^{83} - 7 q^{85} - 15 q^{86} - 2 q^{89} - 5 q^{91} - 8 q^{92} - 10 q^{94} - 17 q^{95} + 21 q^{97} - 12 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^4 - 4 * q^5 + 2 * q^7 + 2 * q^8 - 4 * q^10 - 5 * q^13 + 2 * q^14 + 2 * q^16 + q^17 + q^19 - 4 * q^20 - 8 * q^23 + 8 * q^25 - 5 * q^26 + 2 * q^28 + 3 * q^29 + 4 * q^31 + 2 * q^32 + q^34 - 4 * q^35 - 3 * q^37 + q^38 - 4 * q^40 - 12 * q^41 - 15 * q^43 - 8 * q^46 - 10 * q^47 - 12 * q^49 + 8 * q^50 - 5 * q^52 - 3 * q^53 + 2 * q^56 + 3 * q^58 + 3 * q^59 + 13 * q^61 + 4 * q^62 + 2 * q^64 + 5 * q^65 + 20 * q^67 + q^68 - 4 * q^70 - 9 * q^71 - 16 * q^73 - 3 * q^74 + q^76 + 12 * q^79 - 4 * q^80 - 12 * q^82 + 6 * q^83 - 7 * q^85 - 15 * q^86 - 2 * q^89 - 5 * q^91 - 8 * q^92 - 10 * q^94 - 17 * q^95 + 21 * 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
$5$	−4.23607	−1.89443	−0.947214	−	0.320603i	$-0.896114\pi$
$5$	−4.23607	−1.89443	−0.947214	+	0.320603i	$0.896114\pi$
$6$	0	0
$7$	1.00000	0.377964	0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000	0.377964	0.188982	+	0.981981i	$0.439481\pi$
$8$	1.00000	0.353553
$9$	0	0
$10$	−4.23607	−1.33956
$11$	0	0
$11$	0	0
$12$	0	0
$13$	−1.38197	−0.383288	−0.191644	−	0.981464i	$-0.561382\pi$
$13$	−1.38197	−0.383288	−0.191644	+	0.981464i	$0.561382\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	1.61803	0.392431	0.196215	−	0.980561i	$-0.437135\pi$
$17$	1.61803	0.392431	0.196215	+	0.980561i	$0.437135\pi$
$18$	0	0
$19$	3.85410	0.884192	0.442096	−	0.896968i	$-0.354235\pi$
$19$	3.85410	0.884192	0.442096	+	0.896968i	$0.354235\pi$
$20$	−4.23607	−0.947214
$21$	0	0
$22$	0	0
$23$	−6.23607	−1.30031	−0.650155	−	0.759802i	$-0.725296\pi$
$23$	−6.23607	−1.30031	−0.650155	+	0.759802i	$0.725296\pi$
$24$	0	0
$25$	12.9443	2.58885
$26$	−1.38197	−0.271026
$27$	0	0
$28$	1.00000	0.188982
$29$	0.381966	0.0709293	0.0354647	−	0.999371i	$-0.488709\pi$
$29$	0.381966	0.0709293	0.0354647	+	0.999371i	$0.488709\pi$
$30$	0	0
$31$	8.70820	1.56404	0.782020	−	0.623254i	$-0.214190\pi$
$31$	8.70820	1.56404	0.782020	+	0.623254i	$0.214190\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	1.61803	0.277491
$35$	−4.23607	−0.716026
$36$	0	0
$37$	−4.85410	−0.798009	−0.399005	−	0.916949i	$-0.630644\pi$
$37$	−4.85410	−0.798009	−0.399005	+	0.916949i	$0.630644\pi$
$38$	3.85410	0.625218
$39$	0	0
$40$	−4.23607	−0.669781
$41$	−10.4721	−1.63547	−0.817736	−	0.575593i	$-0.804771\pi$
$41$	−10.4721	−1.63547	−0.817736	+	0.575593i	$0.804771\pi$
$42$	0	0
$43$	−10.8541	−1.65524	−0.827618	−	0.561292i	$-0.810304\pi$
$43$	−10.8541	−1.65524	−0.827618	+	0.561292i	$0.810304\pi$
$44$	0	0
$45$	0	0
$46$	−6.23607	−0.919458
$47$	−0.527864	−0.0769969	−0.0384984	−	0.999259i	$-0.512257\pi$
$47$	−0.527864	−0.0769969	−0.0384984	+	0.999259i	$0.512257\pi$
$48$	0	0
$49$	−6.00000	−0.857143
$50$	12.9443	1.83060
$51$	0	0
$52$	−1.38197	−0.191644
$53$	10.7984	1.48327	0.741635	−	0.670803i	$-0.234050\pi$
$53$	10.7984	1.48327	0.741635	+	0.670803i	$0.234050\pi$
$54$	0	0
$55$	0	0
$56$	1.00000	0.133631
$57$	0	0
$58$	0.381966	0.0501546
$59$	2.61803	0.340839	0.170419	−	0.985372i	$-0.445488\pi$
$59$	2.61803	0.340839	0.170419	+	0.985372i	$0.445488\pi$
$60$	0	0
$61$	7.61803	0.975389	0.487695	−	0.873014i	$-0.337838\pi$
$61$	7.61803	0.975389	0.487695	+	0.873014i	$0.337838\pi$
$62$	8.70820	1.10594
$63$	0	0
$64$	1.00000	0.125000
$65$	5.85410	0.726112
$66$	0	0
$67$	7.76393	0.948515	0.474258	−	0.880386i	$-0.342717\pi$
$67$	7.76393	0.948515	0.474258	+	0.880386i	$0.342717\pi$
$68$	1.61803	0.196215
$69$	0	0
$70$	−4.23607	−0.506307
$71$	−5.61803	−0.666738	−0.333369	−	0.942796i	$-0.608185\pi$
$71$	−5.61803	−0.666738	−0.333369	+	0.942796i	$0.608185\pi$
$72$	0	0
$73$	−10.2361	−1.19804	−0.599021	−	0.800734i	$-0.704443\pi$
$73$	−10.2361	−1.19804	−0.599021	+	0.800734i	$0.704443\pi$
$74$	−4.85410	−0.564278
$75$	0	0
$76$	3.85410	0.442096
$77$	0	0
$78$	0	0
$79$	6.00000	0.675053	0.337526	−	0.941316i	$-0.390410\pi$
$79$	6.00000	0.675053	0.337526	+	0.941316i	$0.390410\pi$
$80$	−4.23607	−0.473607
$81$	0	0
$82$	−10.4721	−1.15645
$83$	5.23607	0.574733	0.287367	−	0.957821i	$-0.407220\pi$
$83$	5.23607	0.574733	0.287367	+	0.957821i	$0.407220\pi$
$84$	0	0
$85$	−6.85410	−0.743432
$86$	−10.8541	−1.17043
$87$	0	0
$88$	0	0
$89$	−12.1803	−1.29111	−0.645557	−	0.763712i	$-0.723375\pi$
$89$	−12.1803	−1.29111	−0.645557	+	0.763712i	$0.723375\pi$
$90$	0	0
$91$	−1.38197	−0.144869
$92$	−6.23607	−0.650155
$93$	0	0
$94$	−0.527864	−0.0544450
$95$	−16.3262	−1.67504
$96$	0	0
$97$	7.14590	0.725556	0.362778	−	0.931876i	$-0.381828\pi$
$97$	7.14590	0.725556	0.362778	+	0.931876i	$0.381828\pi$
$98$	−6.00000	−0.606092
$99$	0	0
$100$	12.9443	1.29443
$101$	1.76393	0.175518	0.0877589	−	0.996142i	$-0.472029\pi$
$101$	1.76393	0.175518	0.0877589	+	0.996142i	$0.472029\pi$
$102$	0	0
$103$	−9.00000	−0.886796	−0.443398	−	0.896325i	$-0.646227\pi$
$103$	−9.00000	−0.886796	−0.443398	+	0.896325i	$0.646227\pi$
$104$	−1.38197	−0.135513
$105$	0	0
$106$	10.7984	1.04883
$107$	3.70820	0.358486	0.179243	−	0.983805i	$-0.442635\pi$
$107$	3.70820	0.358486	0.179243	+	0.983805i	$0.442635\pi$
$108$	0	0
$109$	10.3262	0.989074	0.494537	−	0.869157i	$-0.335338\pi$
$109$	10.3262	0.989074	0.494537	+	0.869157i	$0.335338\pi$
$110$	0	0
$111$	0	0
$112$	1.00000	0.0944911
$113$	0.708204	0.0666222	0.0333111	−	0.999445i	$-0.489395\pi$
$113$	0.708204	0.0666222	0.0333111	+	0.999445i	$0.489395\pi$
$114$	0	0
$115$	26.4164	2.46334
$116$	0.381966	0.0354647
$117$	0	0
$118$	2.61803	0.241010
$119$	1.61803	0.148325
$120$	0	0
$121$	0	0
$122$	7.61803	0.689704
$123$	0	0
$124$	8.70820	0.782020
$125$	−33.6525	−3.00997
$126$	0	0
$127$	−11.3262	−1.00504	−0.502521	−	0.864565i	$-0.667594\pi$
$127$	−11.3262	−1.00504	−0.502521	+	0.864565i	$0.667594\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	5.85410	0.513439
$131$	−21.2361	−1.85540	−0.927702	−	0.373322i	$-0.878219\pi$
$131$	−21.2361	−1.85540	−0.927702	+	0.373322i	$0.878219\pi$
$132$	0	0
$133$	3.85410	0.334193
$134$	7.76393	0.670702
$135$	0	0
$136$	1.61803	0.138745
$137$	−15.3820	−1.31417	−0.657085	−	0.753816i	$-0.728211\pi$
$137$	−15.3820	−1.31417	−0.657085	+	0.753816i	$0.728211\pi$
$138$	0	0
$139$	−9.00000	−0.763370	−0.381685	−	0.924292i	$-0.624656\pi$
$139$	−9.00000	−0.763370	−0.381685	+	0.924292i	$0.624656\pi$
$140$	−4.23607	−0.358013
$141$	0	0
$142$	−5.61803	−0.471455
$143$	0	0
$144$	0	0
$145$	−1.61803	−0.134370
$146$	−10.2361	−0.847143
$147$	0	0
$148$	−4.85410	−0.399005
$149$	−21.2361	−1.73973	−0.869863	−	0.493293i	$-0.835793\pi$
$149$	−21.2361	−1.73973	−0.869863	+	0.493293i	$0.835793\pi$
$150$	0	0
$151$	−21.4164	−1.74284	−0.871421	−	0.490535i	$-0.836801\pi$
$151$	−21.4164	−1.74284	−0.871421	+	0.490535i	$0.836801\pi$
$152$	3.85410	0.312609
$153$	0	0
$154$	0	0
$155$	−36.8885	−2.96296
$156$	0	0
$157$	3.00000	0.239426	0.119713	−	0.992809i	$-0.461803\pi$
$157$	3.00000	0.239426	0.119713	+	0.992809i	$0.461803\pi$
$158$	6.00000	0.477334
$159$	0	0
$160$	−4.23607	−0.334891
$161$	−6.23607	−0.491471
$162$	0	0
$163$	−15.8885	−1.24449	−0.622243	−	0.782824i	$-0.713779\pi$
$163$	−15.8885	−1.24449	−0.622243	+	0.782824i	$0.713779\pi$
$164$	−10.4721	−0.817736
$165$	0	0
$166$	5.23607	0.406398
$167$	7.05573	0.545989	0.272994	−	0.962016i	$-0.411986\pi$
$167$	7.05573	0.545989	0.272994	+	0.962016i	$0.411986\pi$
$168$	0	0
$169$	−11.0902	−0.853090
$170$	−6.85410	−0.525686
$171$	0	0
$172$	−10.8541	−0.827618
$173$	−18.0344	−1.37113	−0.685567	−	0.728010i	$-0.740445\pi$
$173$	−18.0344	−1.37113	−0.685567	+	0.728010i	$0.740445\pi$
$174$	0	0
$175$	12.9443	0.978495
$176$	0	0
$177$	0	0
$178$	−12.1803	−0.912955
$179$	−4.52786	−0.338428	−0.169214	−	0.985579i	$-0.554123\pi$
$179$	−4.52786	−0.338428	−0.169214	+	0.985579i	$0.554123\pi$
$180$	0	0
$181$	−8.38197	−0.623027	−0.311513	−	0.950242i	$-0.600836\pi$
$181$	−8.38197	−0.623027	−0.311513	+	0.950242i	$0.600836\pi$
$182$	−1.38197	−0.102438
$183$	0	0
$184$	−6.23607	−0.459729
$185$	20.5623	1.51177
$186$	0	0
$187$	0	0
$188$	−0.527864	−0.0384984
$189$	0	0
$190$	−16.3262	−1.18443
$191$	2.09017	0.151239	0.0756197	−	0.997137i	$-0.475907\pi$
$191$	2.09017	0.151239	0.0756197	+	0.997137i	$0.475907\pi$
$192$	0	0
$193$	−22.1246	−1.59256	−0.796282	−	0.604925i	$-0.793203\pi$
$193$	−22.1246	−1.59256	−0.796282	+	0.604925i	$0.793203\pi$
$194$	7.14590	0.513046
$195$	0	0
$196$	−6.00000	−0.428571
$197$	4.52786	0.322597	0.161298	−	0.986906i	$-0.448432\pi$
$197$	4.52786	0.322597	0.161298	+	0.986906i	$0.448432\pi$
$198$	0	0
$199$	−3.18034	−0.225448	−0.112724	−	0.993626i	$-0.535958\pi$
$199$	−3.18034	−0.225448	−0.112724	+	0.993626i	$0.535958\pi$
$200$	12.9443	0.915298
$201$	0	0
$202$	1.76393	0.124110
$203$	0.381966	0.0268088
$204$	0	0
$205$	44.3607	3.09828
$206$	−9.00000	−0.627060
$207$	0	0
$208$	−1.38197	−0.0958221
$209$	0	0
$210$	0	0
$211$	−5.76393	−0.396805	−0.198403	−	0.980121i	$-0.563575\pi$
$211$	−5.76393	−0.396805	−0.198403	+	0.980121i	$0.563575\pi$
$212$	10.7984	0.741635
$213$	0	0
$214$	3.70820	0.253488
$215$	45.9787	3.13572
$216$	0	0
$217$	8.70820	0.591151
$218$	10.3262	0.699381
$219$	0	0
$220$	0	0
$221$	−2.23607	−0.150414
$222$	0	0
$223$	6.56231	0.439445	0.219722	−	0.975562i	$-0.429485\pi$
$223$	6.56231	0.439445	0.219722	+	0.975562i	$0.429485\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	0.708204	0.0471090
$227$	−7.79837	−0.517596	−0.258798	−	0.965931i	$-0.583326\pi$
$227$	−7.79837	−0.517596	−0.258798	+	0.965931i	$0.583326\pi$
$228$	0	0
$229$	−20.7082	−1.36844	−0.684218	−	0.729277i	$-0.739856\pi$
$229$	−20.7082	−1.36844	−0.684218	+	0.729277i	$0.739856\pi$
$230$	26.4164	1.74185
$231$	0	0
$232$	0.381966	0.0250773
$233$	−19.6525	−1.28748	−0.643738	−	0.765246i	$-0.722617\pi$
$233$	−19.6525	−1.28748	−0.643738	+	0.765246i	$0.722617\pi$
$234$	0	0
$235$	2.23607	0.145865
$236$	2.61803	0.170419
$237$	0	0
$238$	1.61803	0.104882
$239$	8.29180	0.536352	0.268176	−	0.963370i	$-0.413579\pi$
$239$	8.29180	0.536352	0.268176	+	0.963370i	$0.413579\pi$
$240$	0	0
$241$	18.5279	1.19348	0.596742	−	0.802433i	$-0.296461\pi$
$241$	18.5279	1.19348	0.596742	+	0.802433i	$0.296461\pi$
$242$	0	0
$243$	0	0
$244$	7.61803	0.487695
$245$	25.4164	1.62379
$246$	0	0
$247$	−5.32624	−0.338900
$248$	8.70820	0.552972
$249$	0	0
$250$	−33.6525	−2.12837
$251$	−3.81966	−0.241095	−0.120547	−	0.992708i	$-0.538465\pi$
$251$	−3.81966	−0.241095	−0.120547	+	0.992708i	$0.538465\pi$
$252$	0	0
$253$	0	0
$254$	−11.3262	−0.710671
$255$	0	0
$256$	1.00000	0.0625000
$257$	−1.09017	−0.0680029	−0.0340015	−	0.999422i	$-0.510825\pi$
$257$	−1.09017	−0.0680029	−0.0340015	+	0.999422i	$0.510825\pi$
$258$	0	0
$259$	−4.85410	−0.301619
$260$	5.85410	0.363056
$261$	0	0
$262$	−21.2361	−1.31197
$263$	22.3607	1.37882	0.689409	−	0.724372i	$-0.257870\pi$
$263$	22.3607	1.37882	0.689409	+	0.724372i	$0.257870\pi$
$264$	0	0
$265$	−45.7426	−2.80995
$266$	3.85410	0.236310
$267$	0	0
$268$	7.76393	0.474258
$269$	−8.05573	−0.491166	−0.245583	−	0.969376i	$-0.578979\pi$
$269$	−8.05573	−0.491166	−0.245583	+	0.969376i	$0.578979\pi$
$270$	0	0
$271$	−1.00000	−0.0607457	−0.0303728	−	0.999539i	$-0.509669\pi$
$271$	−1.00000	−0.0607457	−0.0303728	+	0.999539i	$0.509669\pi$
$272$	1.61803	0.0981077
$273$	0	0
$274$	−15.3820	−0.929259
$275$	0	0
$276$	0	0
$277$	27.1246	1.62976	0.814880	−	0.579630i	$-0.196803\pi$
$277$	27.1246	1.62976	0.814880	+	0.579630i	$0.196803\pi$
$278$	−9.00000	−0.539784
$279$	0	0
$280$	−4.23607	−0.253153
$281$	8.50658	0.507460	0.253730	−	0.967275i	$-0.418343\pi$
$281$	8.50658	0.507460	0.253730	+	0.967275i	$0.418343\pi$
$282$	0	0
$283$	24.9787	1.48483	0.742415	−	0.669940i	$-0.233680\pi$
$283$	24.9787	1.48483	0.742415	+	0.669940i	$0.233680\pi$
$284$	−5.61803	−0.333369
$285$	0	0
$286$	0	0
$287$	−10.4721	−0.618151
$288$	0	0
$289$	−14.3820	−0.845998
$290$	−1.61803	−0.0950142
$291$	0	0
$292$	−10.2361	−0.599021
$293$	−19.7426	−1.15338	−0.576689	−	0.816964i	$-0.695655\pi$
$293$	−19.7426	−1.15338	−0.576689	+	0.816964i	$0.695655\pi$
$294$	0	0
$295$	−11.0902	−0.645695
$296$	−4.85410	−0.282139
$297$	0	0
$298$	−21.2361	−1.23017
$299$	8.61803	0.498394
$300$	0	0
$301$	−10.8541	−0.625620
$302$	−21.4164	−1.23238
$303$	0	0
$304$	3.85410	0.221048
$305$	−32.2705	−1.84780
$306$	0	0
$307$	21.4721	1.22548	0.612740	−	0.790285i	$-0.290067\pi$
$307$	21.4721	1.22548	0.612740	+	0.790285i	$0.290067\pi$
$308$	0	0
$309$	0	0
$310$	−36.8885	−2.09513
$311$	6.32624	0.358728	0.179364	−	0.983783i	$-0.442596\pi$
$311$	6.32624	0.358728	0.179364	+	0.983783i	$0.442596\pi$
$312$	0	0
$313$	15.9443	0.901224	0.450612	−	0.892720i	$-0.351206\pi$
$313$	15.9443	0.901224	0.450612	+	0.892720i	$0.351206\pi$
$314$	3.00000	0.169300
$315$	0	0
$316$	6.00000	0.337526
$317$	−31.4164	−1.76452	−0.882261	−	0.470761i	$-0.843979\pi$
$317$	−31.4164	−1.76452	−0.882261	+	0.470761i	$0.843979\pi$
$318$	0	0
$319$	0	0
$320$	−4.23607	−0.236803
$321$	0	0
$322$	−6.23607	−0.347522
$323$	6.23607	0.346984
$324$	0	0
$325$	−17.8885	−0.992278
$326$	−15.8885	−0.879985
$327$	0	0
$328$	−10.4721	−0.578227
$329$	−0.527864	−0.0291021
$330$	0	0
$331$	−20.1246	−1.10615	−0.553074	−	0.833132i	$-0.686545\pi$
$331$	−20.1246	−1.10615	−0.553074	+	0.833132i	$0.686545\pi$
$332$	5.23607	0.287367
$333$	0	0
$334$	7.05573	0.386072
$335$	−32.8885	−1.79689
$336$	0	0
$337$	−20.7426	−1.12992	−0.564962	−	0.825117i	$-0.691109\pi$
$337$	−20.7426	−1.12992	−0.564962	+	0.825117i	$0.691109\pi$
$338$	−11.0902	−0.603226
$339$	0	0
$340$	−6.85410	−0.371716
$341$	0	0
$342$	0	0
$343$	−13.0000	−0.701934
$344$	−10.8541	−0.585214
$345$	0	0
$346$	−18.0344	−0.969538
$347$	31.0689	1.66787	0.833933	−	0.551866i	$-0.186084\pi$
$347$	31.0689	1.66787	0.833933	+	0.551866i	$0.186084\pi$
$348$	0	0
$349$	21.4721	1.14938	0.574689	−	0.818372i	$-0.305123\pi$
$349$	21.4721	1.14938	0.574689	+	0.818372i	$0.305123\pi$
$350$	12.9443	0.691900
$351$	0	0
$352$	0	0
$353$	26.9443	1.43410	0.717049	−	0.697022i	$-0.245492\pi$
$353$	26.9443	1.43410	0.717049	+	0.697022i	$0.245492\pi$
$354$	0	0
$355$	23.7984	1.26309
$356$	−12.1803	−0.645557
$357$	0	0
$358$	−4.52786	−0.239305
$359$	20.1246	1.06214	0.531068	−	0.847329i	$-0.321791\pi$
$359$	20.1246	1.06214	0.531068	+	0.847329i	$0.321791\pi$
$360$	0	0
$361$	−4.14590	−0.218205
$362$	−8.38197	−0.440546
$363$	0	0
$364$	−1.38197	−0.0724347
$365$	43.3607	2.26960
$366$	0	0
$367$	23.4164	1.22233	0.611163	−	0.791505i	$-0.290702\pi$
$367$	23.4164	1.22233	0.611163	+	0.791505i	$0.290702\pi$
$368$	−6.23607	−0.325078
$369$	0	0
$370$	20.5623	1.06898
$371$	10.7984	0.560624
$372$	0	0
$373$	6.12461	0.317120	0.158560	−	0.987349i	$-0.449315\pi$
$373$	6.12461	0.317120	0.158560	+	0.987349i	$0.449315\pi$
$374$	0	0
$375$	0	0
$376$	−0.527864	−0.0272225
$377$	−0.527864	−0.0271864
$378$	0	0
$379$	−7.70820	−0.395944	−0.197972	−	0.980208i	$-0.563435\pi$
$379$	−7.70820	−0.395944	−0.197972	+	0.980208i	$0.563435\pi$
$380$	−16.3262	−0.837518
$381$	0	0
$382$	2.09017	0.106942
$383$	−2.88854	−0.147598	−0.0737988	−	0.997273i	$-0.523512\pi$
$383$	−2.88854	−0.147598	−0.0737988	+	0.997273i	$0.523512\pi$
$384$	0	0
$385$	0	0
$386$	−22.1246	−1.12611
$387$	0	0
$388$	7.14590	0.362778
$389$	−12.6180	−0.639760	−0.319880	−	0.947458i	$-0.603643\pi$
$389$	−12.6180	−0.639760	−0.319880	+	0.947458i	$0.603643\pi$
$390$	0	0
$391$	−10.0902	−0.510282
$392$	−6.00000	−0.303046
$393$	0	0
$394$	4.52786	0.228110
$395$	−25.4164	−1.27884
$396$	0	0
$397$	10.1459	0.509208	0.254604	−	0.967045i	$-0.418055\pi$
$397$	10.1459	0.509208	0.254604	+	0.967045i	$0.418055\pi$
$398$	−3.18034	−0.159416
$399$	0	0
$400$	12.9443	0.647214
$401$	−18.8885	−0.943249	−0.471624	−	0.881800i	$-0.656332\pi$
$401$	−18.8885	−0.943249	−0.471624	+	0.881800i	$0.656332\pi$
$402$	0	0
$403$	−12.0344	−0.599478
$404$	1.76393	0.0877589
$405$	0	0
$406$	0.381966	0.0189567
$407$	0	0
$408$	0	0
$409$	−3.70820	−0.183359	−0.0916794	−	0.995789i	$-0.529224\pi$
$409$	−3.70820	−0.183359	−0.0916794	+	0.995789i	$0.529224\pi$
$410$	44.3607	2.19082
$411$	0	0
$412$	−9.00000	−0.443398
$413$	2.61803	0.128825
$414$	0	0
$415$	−22.1803	−1.08879
$416$	−1.38197	−0.0677565
$417$	0	0
$418$	0	0
$419$	−13.4164	−0.655434	−0.327717	−	0.944776i	$-0.606279\pi$
$419$	−13.4164	−0.655434	−0.327717	+	0.944776i	$0.606279\pi$
$420$	0	0
$421$	−30.9787	−1.50981	−0.754905	−	0.655834i	$-0.772317\pi$
$421$	−30.9787	−1.50981	−0.754905	+	0.655834i	$0.772317\pi$
$422$	−5.76393	−0.280584
$423$	0	0
$424$	10.7984	0.524415
$425$	20.9443	1.01595
$426$	0	0
$427$	7.61803	0.368663
$428$	3.70820	0.179243
$429$	0	0
$430$	45.9787	2.21729
$431$	9.67376	0.465969	0.232984	−	0.972480i	$-0.425151\pi$
$431$	9.67376	0.465969	0.232984	+	0.972480i	$0.425151\pi$
$432$	0	0
$433$	−8.90983	−0.428179	−0.214090	−	0.976814i	$-0.568678\pi$
$433$	−8.90983	−0.428179	−0.214090	+	0.976814i	$0.568678\pi$
$434$	8.70820	0.418007
$435$	0	0
$436$	10.3262	0.494537
$437$	−24.0344	−1.14972
$438$	0	0
$439$	6.72949	0.321181	0.160591	−	0.987021i	$-0.448660\pi$
$439$	6.72949	0.321181	0.160591	+	0.987021i	$0.448660\pi$
$440$	0	0
$441$	0	0
$442$	−2.23607	−0.106359
$443$	9.97871	0.474103	0.237051	−	0.971497i	$-0.423819\pi$
$443$	9.97871	0.474103	0.237051	+	0.971497i	$0.423819\pi$
$444$	0	0
$445$	51.5967	2.44592
$446$	6.56231	0.310734
$447$	0	0
$448$	1.00000	0.0472456
$449$	−19.1459	−0.903551	−0.451775	−	0.892132i	$-0.649209\pi$
$449$	−19.1459	−0.903551	−0.451775	+	0.892132i	$0.649209\pi$
$450$	0	0
$451$	0	0
$452$	0.708204	0.0333111
$453$	0	0
$454$	−7.79837	−0.365996
$455$	5.85410	0.274445
$456$	0	0
$457$	−4.85410	−0.227065	−0.113533	−	0.993534i	$-0.536217\pi$
$457$	−4.85410	−0.227065	−0.113533	+	0.993534i	$0.536217\pi$
$458$	−20.7082	−0.967631
$459$	0	0
$460$	26.4164	1.23167
$461$	13.5066	0.629064	0.314532	−	0.949247i	$-0.398152\pi$
$461$	13.5066	0.629064	0.314532	+	0.949247i	$0.398152\pi$
$462$	0	0
$463$	−28.8541	−1.34096	−0.670482	−	0.741926i	$-0.733913\pi$
$463$	−28.8541	−1.34096	−0.670482	+	0.741926i	$0.733913\pi$
$464$	0.381966	0.0177323
$465$	0	0
$466$	−19.6525	−0.910383
$467$	14.0344	0.649437	0.324718	−	0.945811i	$-0.394731\pi$
$467$	14.0344	0.649437	0.324718	+	0.945811i	$0.394731\pi$
$468$	0	0
$469$	7.76393	0.358505
$470$	2.23607	0.103142
$471$	0	0
$472$	2.61803	0.120505
$473$	0	0
$474$	0	0
$475$	49.8885	2.28904
$476$	1.61803	0.0741625
$477$	0	0
$478$	8.29180	0.379258
$479$	15.3262	0.700274	0.350137	−	0.936699i	$-0.386135\pi$
$479$	15.3262	0.700274	0.350137	+	0.936699i	$0.386135\pi$
$480$	0	0
$481$	6.70820	0.305868
$482$	18.5279	0.843921
$483$	0	0
$484$	0	0
$485$	−30.2705	−1.37451
$486$	0	0
$487$	8.47214	0.383909	0.191955	−	0.981404i	$-0.438517\pi$
$487$	8.47214	0.383909	0.191955	+	0.981404i	$0.438517\pi$
$488$	7.61803	0.344852
$489$	0	0
$490$	25.4164	1.14820
$491$	−10.4164	−0.470086	−0.235043	−	0.971985i	$-0.575523\pi$
$491$	−10.4164	−0.470086	−0.235043	+	0.971985i	$0.575523\pi$
$492$	0	0
$493$	0.618034	0.0278349
$494$	−5.32624	−0.239639
$495$	0	0
$496$	8.70820	0.391010
$497$	−5.61803	−0.252003
$498$	0	0
$499$	12.1246	0.542772	0.271386	−	0.962471i	$-0.412518\pi$
$499$	12.1246	0.542772	0.271386	+	0.962471i	$0.412518\pi$
$500$	−33.6525	−1.50498
$501$	0	0
$502$	−3.81966	−0.170480
$503$	−17.4721	−0.779044	−0.389522	−	0.921017i	$-0.627360\pi$
$503$	−17.4721	−0.779044	−0.389522	+	0.921017i	$0.627360\pi$
$504$	0	0
$505$	−7.47214	−0.332506
$506$	0	0
$507$	0	0
$508$	−11.3262	−0.502521
$509$	12.9787	0.575271	0.287636	−	0.957740i	$-0.407131\pi$
$509$	12.9787	0.575271	0.287636	+	0.957740i	$0.407131\pi$
$510$	0	0
$511$	−10.2361	−0.452817
$512$	1.00000	0.0441942
$513$	0	0
$514$	−1.09017	−0.0480853
$515$	38.1246	1.67997
$516$	0	0
$517$	0	0
$518$	−4.85410	−0.213277
$519$	0	0
$520$	5.85410	0.256719
$521$	−14.5279	−0.636477	−0.318239	−	0.948011i	$-0.603091\pi$
$521$	−14.5279	−0.636477	−0.318239	+	0.948011i	$0.603091\pi$
$522$	0	0
$523$	41.6525	1.82134	0.910668	−	0.413139i	$-0.135568\pi$
$523$	41.6525	1.82134	0.910668	+	0.413139i	$0.135568\pi$
$524$	−21.2361	−0.927702
$525$	0	0
$526$	22.3607	0.974972
$527$	14.0902	0.613777
$528$	0	0
$529$	15.8885	0.690806
$530$	−45.7426	−1.98693
$531$	0	0
$532$	3.85410	0.167097
$533$	14.4721	0.626858
$534$	0	0
$535$	−15.7082	−0.679125
$536$	7.76393	0.335351
$537$	0	0
$538$	−8.05573	−0.347307
$539$	0	0
$540$	0	0
$541$	22.2918	0.958399	0.479200	−	0.877706i	$-0.340927\pi$
$541$	22.2918	0.958399	0.479200	+	0.877706i	$0.340927\pi$
$542$	−1.00000	−0.0429537
$543$	0	0
$544$	1.61803	0.0693726
$545$	−43.7426	−1.87373
$546$	0	0
$547$	0.965558	0.0412843	0.0206421	−	0.999787i	$-0.493429\pi$
$547$	0.965558	0.0412843	0.0206421	+	0.999787i	$0.493429\pi$
$548$	−15.3820	−0.657085
$549$	0	0
$550$	0	0
$551$	1.47214	0.0627151
$552$	0	0
$553$	6.00000	0.255146
$554$	27.1246	1.15241
$555$	0	0
$556$	−9.00000	−0.381685
$557$	7.03444	0.298059	0.149029	−	0.988833i	$-0.452385\pi$
$557$	7.03444	0.298059	0.149029	+	0.988833i	$0.452385\pi$
$558$	0	0
$559$	15.0000	0.634432
$560$	−4.23607	−0.179007
$561$	0	0
$562$	8.50658	0.358828
$563$	40.3050	1.69865	0.849326	−	0.527869i	$-0.177009\pi$
$563$	40.3050	1.69865	0.849326	+	0.527869i	$0.177009\pi$
$564$	0	0
$565$	−3.00000	−0.126211
$566$	24.9787	1.04993
$567$	0	0
$568$	−5.61803	−0.235727
$569$	−45.0689	−1.88939	−0.944693	−	0.327956i	$-0.893640\pi$
$569$	−45.0689	−1.88939	−0.944693	+	0.327956i	$0.893640\pi$
$570$	0	0
$571$	−9.23607	−0.386517	−0.193259	−	0.981148i	$-0.561906\pi$
$571$	−9.23607	−0.386517	−0.193259	+	0.981148i	$0.561906\pi$
$572$	0	0
$573$	0	0
$574$	−10.4721	−0.437099
$575$	−80.7214	−3.36631
$576$	0	0
$577$	7.65248	0.318577	0.159288	−	0.987232i	$-0.449080\pi$
$577$	7.65248	0.318577	0.159288	+	0.987232i	$0.449080\pi$
$578$	−14.3820	−0.598211
$579$	0	0
$580$	−1.61803	−0.0671852
$581$	5.23607	0.217229
$582$	0	0
$583$	0	0
$584$	−10.2361	−0.423572
$585$	0	0
$586$	−19.7426	−0.815561
$587$	24.4377	1.00865	0.504326	−	0.863513i	$-0.331741\pi$
$587$	24.4377	1.00865	0.504326	+	0.863513i	$0.331741\pi$
$588$	0	0
$589$	33.5623	1.38291
$590$	−11.0902	−0.456575
$591$	0	0
$592$	−4.85410	−0.199502
$593$	−26.5623	−1.09078	−0.545392	−	0.838181i	$-0.683619\pi$
$593$	−26.5623	−1.09078	−0.545392	+	0.838181i	$0.683619\pi$
$594$	0	0
$595$	−6.85410	−0.280991
$596$	−21.2361	−0.869863
$597$	0	0
$598$	8.61803	0.352418
$599$	27.2705	1.11424	0.557121	−	0.830431i	$-0.311906\pi$
$599$	27.2705	1.11424	0.557121	+	0.830431i	$0.311906\pi$
$600$	0	0
$601$	−40.3951	−1.64775	−0.823876	−	0.566771i	$-0.808193\pi$
$601$	−40.3951	−1.64775	−0.823876	+	0.566771i	$0.808193\pi$
$602$	−10.8541	−0.442380
$603$	0	0
$604$	−21.4164	−0.871421
$605$	0	0
$606$	0	0
$607$	2.12461	0.0862353	0.0431177	−	0.999070i	$-0.486271\pi$
$607$	2.12461	0.0862353	0.0431177	+	0.999070i	$0.486271\pi$
$608$	3.85410	0.156304
$609$	0	0
$610$	−32.2705	−1.30659
$611$	0.729490	0.0295120
$612$	0	0
$613$	11.0000	0.444286	0.222143	−	0.975014i	$-0.428695\pi$
$613$	11.0000	0.444286	0.222143	+	0.975014i	$0.428695\pi$
$614$	21.4721	0.866545
$615$	0	0
$616$	0	0
$617$	31.7984	1.28015	0.640077	−	0.768311i	$-0.278902\pi$
$617$	31.7984	1.28015	0.640077	+	0.768311i	$0.278902\pi$
$618$	0	0
$619$	−40.8885	−1.64345	−0.821725	−	0.569885i	$-0.806988\pi$
$619$	−40.8885	−1.64345	−0.821725	+	0.569885i	$0.806988\pi$
$620$	−36.8885	−1.48148
$621$	0	0
$622$	6.32624	0.253659
$623$	−12.1803	−0.487995
$624$	0	0
$625$	77.8328	3.11331
$626$	15.9443	0.637261
$627$	0	0
$628$	3.00000	0.119713
$629$	−7.85410	−0.313164
$630$	0	0
$631$	−26.8541	−1.06904	−0.534522	−	0.845154i	$-0.679509\pi$
$631$	−26.8541	−1.06904	−0.534522	+	0.845154i	$0.679509\pi$
$632$	6.00000	0.238667
$633$	0	0
$634$	−31.4164	−1.24770
$635$	47.9787	1.90398
$636$	0	0
$637$	8.29180	0.328533
$638$	0	0
$639$	0	0
$640$	−4.23607	−0.167445
$641$	−11.7984	−0.466008	−0.233004	−	0.972476i	$-0.574855\pi$
$641$	−11.7984	−0.466008	−0.233004	+	0.972476i	$0.574855\pi$
$642$	0	0
$643$	−31.6869	−1.24961	−0.624805	−	0.780781i	$-0.714822\pi$
$643$	−31.6869	−1.24961	−0.624805	+	0.780781i	$0.714822\pi$
$644$	−6.23607	−0.245736
$645$	0	0
$646$	6.23607	0.245355
$647$	6.36068	0.250064	0.125032	−	0.992153i	$-0.460097\pi$
$647$	6.36068	0.250064	0.125032	+	0.992153i	$0.460097\pi$
$648$	0	0
$649$	0	0
$650$	−17.8885	−0.701646
$651$	0	0
$652$	−15.8885	−0.622243
$653$	−1.65248	−0.0646664	−0.0323332	−	0.999477i	$-0.510294\pi$
$653$	−1.65248	−0.0646664	−0.0323332	+	0.999477i	$0.510294\pi$
$654$	0	0
$655$	89.9574	3.51493
$656$	−10.4721	−0.408868
$657$	0	0
$658$	−0.527864	−0.0205783
$659$	−13.3607	−0.520458	−0.260229	−	0.965547i	$-0.583798\pi$
$659$	−13.3607	−0.520458	−0.260229	+	0.965547i	$0.583798\pi$
$660$	0	0
$661$	42.2361	1.64279	0.821396	−	0.570358i	$-0.193195\pi$
$661$	42.2361	1.64279	0.821396	+	0.570358i	$0.193195\pi$
$662$	−20.1246	−0.782165
$663$	0	0
$664$	5.23607	0.203199
$665$	−16.3262	−0.633104
$666$	0	0
$667$	−2.38197	−0.0922301
$668$	7.05573	0.272994
$669$	0	0
$670$	−32.8885	−1.27060
$671$	0	0
$672$	0	0
$673$	−9.12461	−0.351728	−0.175864	−	0.984414i	$-0.556272\pi$
$673$	−9.12461	−0.351728	−0.175864	+	0.984414i	$0.556272\pi$
$674$	−20.7426	−0.798977
$675$	0	0
$676$	−11.0902	−0.426545
$677$	40.5066	1.55679	0.778397	−	0.627772i	$-0.216033\pi$
$677$	40.5066	1.55679	0.778397	+	0.627772i	$0.216033\pi$
$678$	0	0
$679$	7.14590	0.274234
$680$	−6.85410	−0.262843
$681$	0	0
$682$	0	0
$683$	1.23607	0.0472968	0.0236484	−	0.999720i	$-0.492472\pi$
$683$	1.23607	0.0472968	0.0236484	+	0.999720i	$0.492472\pi$
$684$	0	0
$685$	65.1591	2.48960
$686$	−13.0000	−0.496342
$687$	0	0
$688$	−10.8541	−0.413809
$689$	−14.9230	−0.568520
$690$	0	0
$691$	−4.61803	−0.175678	−0.0878391	−	0.996135i	$-0.527996\pi$
$691$	−4.61803	−0.175678	−0.0878391	+	0.996135i	$0.527996\pi$
$692$	−18.0344	−0.685567
$693$	0	0
$694$	31.0689	1.17936
$695$	38.1246	1.44615
$696$	0	0
$697$	−16.9443	−0.641810
$698$	21.4721	0.812732
$699$	0	0
$700$	12.9443	0.489247
$701$	14.8328	0.560228	0.280114	−	0.959967i	$-0.409628\pi$
$701$	14.8328	0.560228	0.280114	+	0.959967i	$0.409628\pi$
$702$	0	0
$703$	−18.7082	−0.705593
$704$	0	0
$705$	0	0
$706$	26.9443	1.01406
$707$	1.76393	0.0663395
$708$	0	0
$709$	−30.8885	−1.16004	−0.580022	−	0.814601i	$-0.696956\pi$
$709$	−30.8885	−1.16004	−0.580022	+	0.814601i	$0.696956\pi$
$710$	23.7984	0.893137
$711$	0	0
$712$	−12.1803	−0.456478
$713$	−54.3050	−2.03374
$714$	0	0
$715$	0	0
$716$	−4.52786	−0.169214
$717$	0	0
$718$	20.1246	0.751044
$719$	−24.4377	−0.911372	−0.455686	−	0.890141i	$-0.650606\pi$
$719$	−24.4377	−0.911372	−0.455686	+	0.890141i	$0.650606\pi$
$720$	0	0
$721$	−9.00000	−0.335178
$722$	−4.14590	−0.154294
$723$	0	0
$724$	−8.38197	−0.311513
$725$	4.94427	0.183626
$726$	0	0
$727$	8.27051	0.306736	0.153368	−	0.988169i	$-0.450988\pi$
$727$	8.27051	0.306736	0.153368	+	0.988169i	$0.450988\pi$
$728$	−1.38197	−0.0512191
$729$	0	0
$730$	43.3607	1.60485
$731$	−17.5623	−0.649565
$732$	0	0
$733$	9.72949	0.359367	0.179683	−	0.983724i	$-0.442493\pi$
$733$	9.72949	0.359367	0.179683	+	0.983724i	$0.442493\pi$
$734$	23.4164	0.864315
$735$	0	0
$736$	−6.23607	−0.229865
$737$	0	0
$738$	0	0
$739$	50.9574	1.87450	0.937250	−	0.348659i	$-0.113363\pi$
$739$	50.9574	1.87450	0.937250	+	0.348659i	$0.113363\pi$
$740$	20.5623	0.755885
$741$	0	0
$742$	10.7984	0.396421
$743$	−5.11146	−0.187521	−0.0937606	−	0.995595i	$-0.529889\pi$
$743$	−5.11146	−0.187521	−0.0937606	+	0.995595i	$0.529889\pi$
$744$	0	0
$745$	89.9574	3.29579
$746$	6.12461	0.224238
$747$	0	0
$748$	0	0
$749$	3.70820	0.135495
$750$	0	0
$751$	−10.3262	−0.376810	−0.188405	−	0.982091i	$-0.560332\pi$
$751$	−10.3262	−0.376810	−0.188405	+	0.982091i	$0.560332\pi$
$752$	−0.527864	−0.0192492
$753$	0	0
$754$	−0.527864	−0.0192237
$755$	90.7214	3.30169
$756$	0	0
$757$	37.6525	1.36850	0.684251	−	0.729246i	$-0.260129\pi$
$757$	37.6525	1.36850	0.684251	+	0.729246i	$0.260129\pi$
$758$	−7.70820	−0.279975
$759$	0	0
$760$	−16.3262	−0.592215
$761$	−17.1803	−0.622787	−0.311393	−	0.950281i	$-0.600796\pi$
$761$	−17.1803	−0.622787	−0.311393	+	0.950281i	$0.600796\pi$
$762$	0	0
$763$	10.3262	0.373835
$764$	2.09017	0.0756197
$765$	0	0
$766$	−2.88854	−0.104367
$767$	−3.61803	−0.130640
$768$	0	0
$769$	8.72949	0.314793	0.157397	−	0.987535i	$-0.449690\pi$
$769$	8.72949	0.314793	0.157397	+	0.987535i	$0.449690\pi$
$770$	0	0
$771$	0	0
$772$	−22.1246	−0.796282
$773$	3.20163	0.115154	0.0575772	−	0.998341i	$-0.481662\pi$
$773$	3.20163	0.115154	0.0575772	+	0.998341i	$0.481662\pi$
$774$	0	0
$775$	112.721	4.04907
$776$	7.14590	0.256523
$777$	0	0
$778$	−12.6180	−0.452378
$779$	−40.3607	−1.44607
$780$	0	0
$781$	0	0
$782$	−10.0902	−0.360824
$783$	0	0
$784$	−6.00000	−0.214286
$785$	−12.7082	−0.453575
$786$	0	0
$787$	−14.5279	−0.517862	−0.258931	−	0.965896i	$-0.583370\pi$
$787$	−14.5279	−0.517862	−0.258931	+	0.965896i	$0.583370\pi$
$788$	4.52786	0.161298
$789$	0	0
$790$	−25.4164	−0.904275
$791$	0.708204	0.0251808
$792$	0	0
$793$	−10.5279	−0.373855
$794$	10.1459	0.360064
$795$	0	0
$796$	−3.18034	−0.112724
$797$	24.7639	0.877183	0.438592	−	0.898686i	$-0.355477\pi$
$797$	24.7639	0.877183	0.438592	+	0.898686i	$0.355477\pi$
$798$	0	0
$799$	−0.854102	−0.0302160
$800$	12.9443	0.457649
$801$	0	0
$802$	−18.8885	−0.666978
$803$	0	0
$804$	0	0
$805$	26.4164	0.931056
$806$	−12.0344	−0.423895
$807$	0	0
$808$	1.76393	0.0620549
$809$	−13.3050	−0.467777	−0.233889	−	0.972263i	$-0.575145\pi$
$809$	−13.3050	−0.467777	−0.233889	+	0.972263i	$0.575145\pi$
$810$	0	0
$811$	−3.94427	−0.138502	−0.0692511	−	0.997599i	$-0.522061\pi$
$811$	−3.94427	−0.138502	−0.0692511	+	0.997599i	$0.522061\pi$
$812$	0.381966	0.0134044
$813$	0	0
$814$	0	0
$815$	67.3050	2.35759
$816$	0	0
$817$	−41.8328	−1.46354
$818$	−3.70820	−0.129654
$819$	0	0
$820$	44.3607	1.54914
$821$	33.5410	1.17059	0.585295	−	0.810821i	$-0.300979\pi$
$821$	33.5410	1.17059	0.585295	+	0.810821i	$0.300979\pi$
$822$	0	0
$823$	−20.9098	−0.728871	−0.364435	−	0.931229i	$-0.618738\pi$
$823$	−20.9098	−0.728871	−0.364435	+	0.931229i	$0.618738\pi$
$824$	−9.00000	−0.313530
$825$	0	0
$826$	2.61803	0.0910931
$827$	−10.5279	−0.366090	−0.183045	−	0.983105i	$-0.558595\pi$
$827$	−10.5279	−0.366090	−0.183045	+	0.983105i	$0.558595\pi$
$828$	0	0
$829$	11.9656	0.415581	0.207791	−	0.978173i	$-0.433373\pi$
$829$	11.9656	0.415581	0.207791	+	0.978173i	$0.433373\pi$
$830$	−22.1803	−0.769891
$831$	0	0
$832$	−1.38197	−0.0479111
$833$	−9.70820	−0.336369
$834$	0	0
$835$	−29.8885	−1.03434
$836$	0	0
$837$	0	0
$838$	−13.4164	−0.463462
$839$	−2.50658	−0.0865367	−0.0432683	−	0.999063i	$-0.513777\pi$
$839$	−2.50658	−0.0865367	−0.0432683	+	0.999063i	$0.513777\pi$
$840$	0	0
$841$	−28.8541	−0.994969
$842$	−30.9787	−1.06760
$843$	0	0
$844$	−5.76393	−0.198403
$845$	46.9787	1.61612
$846$	0	0
$847$	0	0
$848$	10.7984	0.370818
$849$	0	0
$850$	20.9443	0.718383
$851$	30.2705	1.03766
$852$	0	0
$853$	19.4934	0.667442	0.333721	−	0.942672i	$-0.391696\pi$
$853$	19.4934	0.667442	0.333721	+	0.942672i	$0.391696\pi$
$854$	7.61803	0.260684
$855$	0	0
$856$	3.70820	0.126744
$857$	−37.6312	−1.28546	−0.642728	−	0.766094i	$-0.722198\pi$
$857$	−37.6312	−1.28546	−0.642728	+	0.766094i	$0.722198\pi$
$858$	0	0
$859$	−7.65248	−0.261099	−0.130550	−	0.991442i	$-0.541674\pi$
$859$	−7.65248	−0.261099	−0.130550	+	0.991442i	$0.541674\pi$
$860$	45.9787	1.56786
$861$	0	0
$862$	9.67376	0.329490
$863$	−13.7639	−0.468530	−0.234265	−	0.972173i	$-0.575268\pi$
$863$	−13.7639	−0.468530	−0.234265	+	0.972173i	$0.575268\pi$
$864$	0	0
$865$	76.3951	2.59751
$866$	−8.90983	−0.302768
$867$	0	0
$868$	8.70820	0.295576
$869$	0	0
$870$	0	0
$871$	−10.7295	−0.363555
$872$	10.3262	0.349691
$873$	0	0
$874$	−24.0344	−0.812977
$875$	−33.6525	−1.13766
$876$	0	0
$877$	39.8885	1.34694	0.673470	−	0.739214i	$-0.264803\pi$
$877$	39.8885	1.34694	0.673470	+	0.739214i	$0.264803\pi$
$878$	6.72949	0.227109
$879$	0	0
$880$	0	0
$881$	−22.3475	−0.752907	−0.376454	−	0.926435i	$-0.622857\pi$
$881$	−22.3475	−0.752907	−0.376454	+	0.926435i	$0.622857\pi$
$882$	0	0
$883$	45.5410	1.53258	0.766289	−	0.642496i	$-0.222101\pi$
$883$	45.5410	1.53258	0.766289	+	0.642496i	$0.222101\pi$
$884$	−2.23607	−0.0752071
$885$	0	0
$886$	9.97871	0.335241
$887$	−22.6180	−0.759439	−0.379720	−	0.925102i	$-0.623980\pi$
$887$	−22.6180	−0.759439	−0.379720	+	0.925102i	$0.623980\pi$
$888$	0	0
$889$	−11.3262	−0.379870
$890$	51.5967	1.72953
$891$	0	0
$892$	6.56231	0.219722
$893$	−2.03444	−0.0680800
$894$	0	0
$895$	19.1803	0.641128
$896$	1.00000	0.0334077
$897$	0	0
$898$	−19.1459	−0.638907
$899$	3.32624	0.110936
$900$	0	0
$901$	17.4721	0.582081
$902$	0	0
$903$	0	0
$904$	0.708204	0.0235545
$905$	35.5066	1.18028
$906$	0	0
$907$	5.58359	0.185400	0.0927001	−	0.995694i	$-0.470450\pi$
$907$	5.58359	0.185400	0.0927001	+	0.995694i	$0.470450\pi$
$908$	−7.79837	−0.258798
$909$	0	0
$910$	5.85410	0.194062
$911$	44.3607	1.46973	0.734867	−	0.678211i	$-0.237244\pi$
$911$	44.3607	1.46973	0.734867	+	0.678211i	$0.237244\pi$
$912$	0	0
$913$	0	0
$914$	−4.85410	−0.160559
$915$	0	0
$916$	−20.7082	−0.684218
$917$	−21.2361	−0.701277
$918$	0	0
$919$	−42.1033	−1.38886	−0.694430	−	0.719560i	$-0.744344\pi$
$919$	−42.1033	−1.38886	−0.694430	+	0.719560i	$0.744344\pi$
$920$	26.4164	0.870923
$921$	0	0
$922$	13.5066	0.444815
$923$	7.76393	0.255553
$924$	0	0
$925$	−62.8328	−2.06593
$926$	−28.8541	−0.948205
$927$	0	0
$928$	0.381966	0.0125386
$929$	1.52786	0.0501276	0.0250638	−	0.999686i	$-0.492021\pi$
$929$	1.52786	0.0501276	0.0250638	+	0.999686i	$0.492021\pi$
$930$	0	0
$931$	−23.1246	−0.757879
$932$	−19.6525	−0.643738
$933$	0	0
$934$	14.0344	0.459221
$935$	0	0
$936$	0	0
$937$	−14.5623	−0.475730	−0.237865	−	0.971298i	$-0.576448\pi$
$937$	−14.5623	−0.475730	−0.237865	+	0.971298i	$0.576448\pi$
$938$	7.76393	0.253501
$939$	0	0
$940$	2.23607	0.0729325
$941$	−7.88854	−0.257159	−0.128580	−	0.991699i	$-0.541042\pi$
$941$	−7.88854	−0.257159	−0.128580	+	0.991699i	$0.541042\pi$
$942$	0	0
$943$	65.3050	2.12662
$944$	2.61803	0.0852097
$945$	0	0
$946$	0	0
$947$	−1.03444	−0.0336148	−0.0168074	−	0.999859i	$-0.505350\pi$
$947$	−1.03444	−0.0336148	−0.0168074	+	0.999859i	$0.505350\pi$
$948$	0	0
$949$	14.1459	0.459195
$950$	49.8885	1.61860
$951$	0	0
$952$	1.61803	0.0524408
$953$	25.1591	0.814982	0.407491	−	0.913209i	$-0.366404\pi$
$953$	25.1591	0.814982	0.407491	+	0.913209i	$0.366404\pi$
$954$	0	0
$955$	−8.85410	−0.286512
$956$	8.29180	0.268176
$957$	0	0
$958$	15.3262	0.495168
$959$	−15.3820	−0.496710
$960$	0	0
$961$	44.8328	1.44622
$962$	6.70820	0.216281
$963$	0	0
$964$	18.5279	0.596742
$965$	93.7214	3.01700
$966$	0	0
$967$	−25.2705	−0.812645	−0.406322	−	0.913730i	$-0.633189\pi$
$967$	−25.2705	−0.812645	−0.406322	+	0.913730i	$0.633189\pi$
$968$	0	0
$969$	0	0
$970$	−30.2705	−0.971927
$971$	−48.0132	−1.54082	−0.770408	−	0.637551i	$-0.779947\pi$
$971$	−48.0132	−1.54082	−0.770408	+	0.637551i	$0.779947\pi$
$972$	0	0
$973$	−9.00000	−0.288527
$974$	8.47214	0.271465
$975$	0	0
$976$	7.61803	0.243847
$977$	−7.36068	−0.235489	−0.117745	−	0.993044i	$-0.537566\pi$
$977$	−7.36068	−0.235489	−0.117745	+	0.993044i	$0.537566\pi$
$978$	0	0
$979$	0	0
$980$	25.4164	0.811897
$981$	0	0
$982$	−10.4164	−0.332401
$983$	25.4164	0.810658	0.405329	−	0.914171i	$-0.367157\pi$
$983$	25.4164	0.810658	0.405329	+	0.914171i	$0.367157\pi$
$984$	0	0
$985$	−19.1803	−0.611136
$986$	0.618034	0.0196822
$987$	0	0
$988$	−5.32624	−0.169450
$989$	67.6869	2.15232
$990$	0	0
$991$	−21.5410	−0.684273	−0.342137	−	0.939650i	$-0.611151\pi$
$991$	−21.5410	−0.684273	−0.342137	+	0.939650i	$0.611151\pi$
$992$	8.70820	0.276486
$993$	0	0
$994$	−5.61803	−0.178193
$995$	13.4721	0.427095
$996$	0	0
$997$	−6.06888	−0.192203	−0.0961017	−	0.995372i	$-0.530637\pi$
$997$	−6.06888	−0.192203	−0.0961017	+	0.995372i	$0.530637\pi$
$998$	12.1246	0.383798
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6534.2.a.bx.1.1		2
3.2	odd	2		6534.2.a.bw.1.2		2
11.3	even	5		594.2.f.b.163.1	✓	4
11.4	even	5		594.2.f.b.379.1	yes	4
11.10	odd	2		6534.2.a.be.1.1		2
33.14	odd	10		594.2.f.i.163.1	yes	4
33.26	odd	10		594.2.f.i.379.1	yes	4
33.32	even	2		6534.2.a.cp.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
594.2.f.b.163.1	✓	4	11.3	even	5
594.2.f.b.379.1	yes	4	11.4	even	5
594.2.f.i.163.1	yes	4	33.14	odd	10
594.2.f.i.379.1	yes	4	33.26	odd	10
6534.2.a.be.1.1		2	11.10	odd	2
6534.2.a.bw.1.2		2	3.2	odd	2
6534.2.a.bx.1.1		2	1.1	even	1	trivial
6534.2.a.cp.1.2		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} -4.23607 q^{5} +1.00000 q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} -4.23607 q^{5} +1.00000 q^{7} +1.00000 q^{8} -4.23607 q^{10} -1.38197 q^{13} +1.00000 q^{14} +1.00000 q^{16} +1.61803 q^{17} +3.85410 q^{19} -4.23607 q^{20} -6.23607 q^{23} +12.9443 q^{25} -1.38197 q^{26} +1.00000 q^{28} +0.381966 q^{29} +8.70820 q^{31} +1.00000 q^{32} +1.61803 q^{34} -4.23607 q^{35} -4.85410 q^{37} +3.85410 q^{38} -4.23607 q^{40} -10.4721 q^{41} -10.8541 q^{43} -6.23607 q^{46} -0.527864 q^{47} -6.00000 q^{49} +12.9443 q^{50} -1.38197 q^{52} +10.7984 q^{53} +1.00000 q^{56} +0.381966 q^{58} +2.61803 q^{59} +7.61803 q^{61} +8.70820 q^{62} +1.00000 q^{64} +5.85410 q^{65} +7.76393 q^{67} +1.61803 q^{68} -4.23607 q^{70} -5.61803 q^{71} -10.2361 q^{73} -4.85410 q^{74} +3.85410 q^{76} +6.00000 q^{79} -4.23607 q^{80} -10.4721 q^{82} +5.23607 q^{83} -6.85410 q^{85} -10.8541 q^{86} -12.1803 q^{89} -1.38197 q^{91} -6.23607 q^{92} -0.527864 q^{94} -16.3262 q^{95} +7.14590 q^{97} -6.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{4} - 4 q^{5} + 2 q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^4 - 4 * q^5 + 2 * q^7 + 2 * q^8	\( 2 q + 2 q^{2} + 2 q^{4} - 4 q^{5} + 2 q^{7} + 2 q^{8} - 4 q^{10} - 5 q^{13} + 2 q^{14} + 2 q^{16} + q^{17} + q^{19} - 4 q^{20} - 8 q^{23} + 8 q^{25} - 5 q^{26} + 2 q^{28} + 3 q^{29} + 4 q^{31} + 2 q^{32} + q^{34} - 4 q^{35} - 3 q^{37} + q^{38} - 4 q^{40} - 12 q^{41} - 15 q^{43} - 8 q^{46} - 10 q^{47} - 12 q^{49} + 8 q^{50} - 5 q^{52} - 3 q^{53} + 2 q^{56} + 3 q^{58} + 3 q^{59} + 13 q^{61} + 4 q^{62} + 2 q^{64} + 5 q^{65} + 20 q^{67} + q^{68} - 4 q^{70} - 9 q^{71} - 16 q^{73} - 3 q^{74} + q^{76} + 12 q^{79} - 4 q^{80} - 12 q^{82} + 6 q^{83} - 7 q^{85} - 15 q^{86} - 2 q^{89} - 5 q^{91} - 8 q^{92} - 10 q^{94} - 17 q^{95} + 21 q^{97} - 12 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^4 - 4 * q^5 + 2 * q^7 + 2 * q^8 - 4 * q^10 - 5 * q^13 + 2 * q^14 + 2 * q^16 + q^17 + q^19 - 4 * q^20 - 8 * q^23 + 8 * q^25 - 5 * q^26 + 2 * q^28 + 3 * q^29 + 4 * q^31 + 2 * q^32 + q^34 - 4 * q^35 - 3 * q^37 + q^38 - 4 * q^40 - 12 * q^41 - 15 * q^43 - 8 * q^46 - 10 * q^47 - 12 * q^49 + 8 * q^50 - 5 * q^52 - 3 * q^53 + 2 * q^56 + 3 * q^58 + 3 * q^59 + 13 * q^61 + 4 * q^62 + 2 * q^64 + 5 * q^65 + 20 * q^67 + q^68 - 4 * q^70 - 9 * q^71 - 16 * q^73 - 3 * q^74 + q^76 + 12 * q^79 - 4 * q^80 - 12 * q^82 + 6 * q^83 - 7 * q^85 - 15 * q^86 - 2 * q^89 - 5 * q^91 - 8 * q^92 - 10 * q^94 - 17 * q^95 + 21 * q^97 - 12 * q^98

Introduction

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