LMFDB - Embedded newform 6534.2.a.bx.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:	$\Q(\zeta_{10})^+$
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			1.2
Root			$-0.618034$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +0.236068 q^{5} +1.00000 q^{7} +1.00000 q^{8} +O(q^{10})$	$q+1.00000 q^{2} +1.00000 q^{4} +0.236068 q^{5} +1.00000 q^{7} +1.00000 q^{8} +0.236068 q^{10} -3.61803 q^{13} +1.00000 q^{14} +1.00000 q^{16} -0.618034 q^{17} -2.85410 q^{19} +0.236068 q^{20} -1.76393 q^{23} -4.94427 q^{25} -3.61803 q^{26} +1.00000 q^{28} +2.61803 q^{29} -4.70820 q^{31} +1.00000 q^{32} -0.618034 q^{34} +0.236068 q^{35} +1.85410 q^{37} -2.85410 q^{38} +0.236068 q^{40} -1.52786 q^{41} -4.14590 q^{43} -1.76393 q^{46} -9.47214 q^{47} -6.00000 q^{49} -4.94427 q^{50} -3.61803 q^{52} -13.7984 q^{53} +1.00000 q^{56} +2.61803 q^{58} +0.381966 q^{59} +5.38197 q^{61} -4.70820 q^{62} +1.00000 q^{64} -0.854102 q^{65} +12.2361 q^{67} -0.618034 q^{68} +0.236068 q^{70} -3.38197 q^{71} -5.76393 q^{73} +1.85410 q^{74} -2.85410 q^{76} +6.00000 q^{79} +0.236068 q^{80} -1.52786 q^{82} +0.763932 q^{83} -0.145898 q^{85} -4.14590 q^{86} +10.1803 q^{89} -3.61803 q^{91} -1.76393 q^{92} -9.47214 q^{94} -0.673762 q^{95} +13.8541 q^{97} -6.00000 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	0.236068	0.105573	0.0527864	−	0.998606i	$-0.483190\pi$
$5$	0.236068	0.105573	0.0527864	+	0.998606i	$0.483190\pi$
$6$	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
$10$	0.236068	0.0746512
$11$	0	0
$11$	0	0
$12$	0	0
$13$	−3.61803	−1.00346	−0.501731	−	0.865024i	$-0.667303\pi$
$13$	−3.61803	−1.00346	−0.501731	+	0.865024i	$0.667303\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	−0.618034	−0.149895	−0.0749476	−	0.997187i	$-0.523879\pi$
$17$	−0.618034	−0.149895	−0.0749476	+	0.997187i	$0.523879\pi$
$18$	0	0
$19$	−2.85410	−0.654776	−0.327388	−	0.944890i	$-0.606168\pi$
$19$	−2.85410	−0.654776	−0.327388	+	0.944890i	$0.606168\pi$
$20$	0.236068	0.0527864
$21$	0	0
$22$	0	0
$23$	−1.76393	−0.367805	−0.183903	−	0.982944i	$-0.558873\pi$
$23$	−1.76393	−0.367805	−0.183903	+	0.982944i	$0.558873\pi$
$24$	0	0
$25$	−4.94427	−0.988854
$26$	−3.61803	−0.709555
$27$	0	0
$28$	1.00000	0.188982
$29$	2.61803	0.486157	0.243078	−	0.970007i	$-0.421843\pi$
$29$	2.61803	0.486157	0.243078	+	0.970007i	$0.421843\pi$
$30$	0	0
$31$	−4.70820	−0.845618	−0.422809	−	0.906219i	$-0.638956\pi$
$31$	−4.70820	−0.845618	−0.422809	+	0.906219i	$0.638956\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−0.618034	−0.105992
$35$	0.236068	0.0399028
$36$	0	0
$37$	1.85410	0.304812	0.152406	−	0.988318i	$-0.451298\pi$
$37$	1.85410	0.304812	0.152406	+	0.988318i	$0.451298\pi$
$38$	−2.85410	−0.462996
$39$	0	0
$40$	0.236068	0.0373256
$41$	−1.52786	−0.238612	−0.119306	−	0.992858i	$-0.538067\pi$
$41$	−1.52786	−0.238612	−0.119306	+	0.992858i	$0.538067\pi$
$42$	0	0
$43$	−4.14590	−0.632244	−0.316122	−	0.948719i	$-0.602381\pi$
$43$	−4.14590	−0.632244	−0.316122	+	0.948719i	$0.602381\pi$
$44$	0	0
$45$	0	0
$46$	−1.76393	−0.260078
$47$	−9.47214	−1.38165	−0.690827	−	0.723021i	$-0.742753\pi$
$47$	−9.47214	−1.38165	−0.690827	+	0.723021i	$0.742753\pi$
$48$	0	0
$49$	−6.00000	−0.857143
$50$	−4.94427	−0.699226
$51$	0	0
$52$	−3.61803	−0.501731
$53$	−13.7984	−1.89535	−0.947676	−	0.319233i	$-0.896575\pi$
$53$	−13.7984	−1.89535	−0.947676	+	0.319233i	$0.896575\pi$
$54$	0	0
$55$	0	0
$56$	1.00000	0.133631
$57$	0	0
$58$	2.61803	0.343765
$59$	0.381966	0.0497277	0.0248639	−	0.999691i	$-0.492085\pi$
$59$	0.381966	0.0497277	0.0248639	+	0.999691i	$0.492085\pi$
$60$	0	0
$61$	5.38197	0.689090	0.344545	−	0.938770i	$-0.388033\pi$
$61$	5.38197	0.689090	0.344545	+	0.938770i	$0.388033\pi$
$62$	−4.70820	−0.597942
$63$	0	0
$64$	1.00000	0.125000
$65$	−0.854102	−0.105938
$66$	0	0
$67$	12.2361	1.49487	0.747437	−	0.664333i	$-0.231284\pi$
$67$	12.2361	1.49487	0.747437	+	0.664333i	$0.231284\pi$
$68$	−0.618034	−0.0749476
$69$	0	0
$70$	0.236068	0.0282155
$71$	−3.38197	−0.401366	−0.200683	−	0.979656i	$-0.564316\pi$
$71$	−3.38197	−0.401366	−0.200683	+	0.979656i	$0.564316\pi$
$72$	0	0
$73$	−5.76393	−0.674617	−0.337309	−	0.941394i	$-0.609517\pi$
$73$	−5.76393	−0.674617	−0.337309	+	0.941394i	$0.609517\pi$
$74$	1.85410	0.215535
$75$	0	0
$76$	−2.85410	−0.327388
$77$	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	$0.390410\pi$
$80$	0.236068	0.0263932
$81$	0	0
$82$	−1.52786	−0.168724
$83$	0.763932	0.0838524	0.0419262	−	0.999121i	$-0.486651\pi$
$83$	0.763932	0.0838524	0.0419262	+	0.999121i	$0.486651\pi$
$84$	0	0
$85$	−0.145898	−0.0158249
$86$	−4.14590	−0.447064
$87$	0	0
$88$	0	0
$89$	10.1803	1.07911	0.539557	−	0.841949i	$-0.318592\pi$
$89$	10.1803	1.07911	0.539557	+	0.841949i	$0.318592\pi$
$90$	0	0
$91$	−3.61803	−0.379273
$92$	−1.76393	−0.183903
$93$	0	0
$94$	−9.47214	−0.976976
$95$	−0.673762	−0.0691265
$96$	0	0
$97$	13.8541	1.40667	0.703335	−	0.710858i	$-0.251693\pi$
$97$	13.8541	1.40667	0.703335	+	0.710858i	$0.251693\pi$
$98$	−6.00000	−0.606092
$99$	0	0
$100$	−4.94427	−0.494427
$101$	6.23607	0.620512	0.310256	−	0.950653i	$-0.399585\pi$
$101$	6.23607	0.620512	0.310256	+	0.950653i	$0.399585\pi$
$102$	0	0
$103$	−9.00000	−0.886796	−0.443398	−	0.896325i	$-0.646227\pi$
$103$	−9.00000	−0.886796	−0.443398	+	0.896325i	$0.646227\pi$
$104$	−3.61803	−0.354777
$105$	0	0
$106$	−13.7984	−1.34022
$107$	−9.70820	−0.938527	−0.469264	−	0.883058i	$-0.655481\pi$
$107$	−9.70820	−0.938527	−0.469264	+	0.883058i	$0.655481\pi$
$108$	0	0
$109$	−5.32624	−0.510161	−0.255081	−	0.966920i	$-0.582102\pi$
$109$	−5.32624	−0.510161	−0.255081	+	0.966920i	$0.582102\pi$
$110$	0	0
$111$	0	0
$112$	1.00000	0.0944911
$113$	−12.7082	−1.19549	−0.597744	−	0.801687i	$-0.703936\pi$
$113$	−12.7082	−1.19549	−0.597744	+	0.801687i	$0.703936\pi$
$114$	0	0
$115$	−0.416408	−0.0388302
$116$	2.61803	0.243078
$117$	0	0
$118$	0.381966	0.0351628
$119$	−0.618034	−0.0566551
$120$	0	0
$121$	0	0
$122$	5.38197	0.487260
$123$	0	0
$124$	−4.70820	−0.422809
$125$	−2.34752	−0.209969
$126$	0	0
$127$	4.32624	0.383892	0.191946	−	0.981406i	$-0.438520\pi$
$127$	4.32624	0.383892	0.191946	+	0.981406i	$0.438520\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	−0.854102	−0.0749097
$131$	−16.7639	−1.46467	−0.732336	−	0.680944i	$-0.761570\pi$
$131$	−16.7639	−1.46467	−0.732336	+	0.680944i	$0.761570\pi$
$132$	0	0
$133$	−2.85410	−0.247482
$134$	12.2361	1.05704
$135$	0	0
$136$	−0.618034	−0.0529960
$137$	−17.6180	−1.50521	−0.752605	−	0.658472i	$-0.771203\pi$
$137$	−17.6180	−1.50521	−0.752605	+	0.658472i	$0.771203\pi$
$138$	0	0
$139$	−9.00000	−0.763370	−0.381685	−	0.924292i	$-0.624656\pi$
$139$	−9.00000	−0.763370	−0.381685	+	0.924292i	$0.624656\pi$
$140$	0.236068	0.0199514
$141$	0	0
$142$	−3.38197	−0.283808
$143$	0	0
$144$	0	0
$145$	0.618034	0.0513249
$146$	−5.76393	−0.477026
$147$	0	0
$148$	1.85410	0.152406
$149$	−16.7639	−1.37335	−0.686677	−	0.726962i	$-0.740931\pi$
$149$	−16.7639	−1.37335	−0.686677	+	0.726962i	$0.740931\pi$
$150$	0	0
$151$	5.41641	0.440781	0.220391	−	0.975412i	$-0.429267\pi$
$151$	5.41641	0.440781	0.220391	+	0.975412i	$0.429267\pi$
$152$	−2.85410	−0.231498
$153$	0	0
$154$	0	0
$155$	−1.11146	−0.0892743
$156$	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
$160$	0.236068	0.0186628
$161$	−1.76393	−0.139017
$162$	0	0
$163$	19.8885	1.55779	0.778895	−	0.627154i	$-0.215780\pi$
$163$	19.8885	1.55779	0.778895	+	0.627154i	$0.215780\pi$
$164$	−1.52786	−0.119306
$165$	0	0
$166$	0.763932	0.0592926
$167$	24.9443	1.93025	0.965123	−	0.261797i	$-0.0843152\pi$
$167$	24.9443	1.93025	0.965123	+	0.261797i	$0.0843152\pi$
$168$	0	0
$169$	0.0901699	0.00693615
$170$	−0.145898	−0.0111899
$171$	0	0
$172$	−4.14590	−0.316122
$173$	11.0344	0.838933	0.419467	−	0.907771i	$-0.362217\pi$
$173$	11.0344	0.838933	0.419467	+	0.907771i	$0.362217\pi$
$174$	0	0
$175$	−4.94427	−0.373752
$176$	0	0
$177$	0	0
$178$	10.1803	0.763049
$179$	−13.4721	−1.00695	−0.503477	−	0.864008i	$-0.667946\pi$
$179$	−13.4721	−1.00695	−0.503477	+	0.864008i	$0.667946\pi$
$180$	0	0
$181$	−10.6180	−0.789232	−0.394616	−	0.918846i	$-0.629122\pi$
$181$	−10.6180	−0.789232	−0.394616	+	0.918846i	$0.629122\pi$
$182$	−3.61803	−0.268187
$183$	0	0
$184$	−1.76393	−0.130039
$185$	0.437694	0.0321799
$186$	0	0
$187$	0	0
$188$	−9.47214	−0.690827
$189$	0	0
$190$	−0.673762	−0.0488798
$191$	−9.09017	−0.657742	−0.328871	−	0.944375i	$-0.606668\pi$
$191$	−9.09017	−0.657742	−0.328871	+	0.944375i	$0.606668\pi$
$192$	0	0
$193$	18.1246	1.30464	0.652319	−	0.757944i	$-0.273796\pi$
$193$	18.1246	1.30464	0.652319	+	0.757944i	$0.273796\pi$
$194$	13.8541	0.994667
$195$	0	0
$196$	−6.00000	−0.428571
$197$	13.4721	0.959850	0.479925	−	0.877310i	$-0.340664\pi$
$197$	13.4721	0.959850	0.479925	+	0.877310i	$0.340664\pi$
$198$	0	0
$199$	19.1803	1.35966	0.679829	−	0.733371i	$-0.262054\pi$
$199$	19.1803	1.35966	0.679829	+	0.733371i	$0.262054\pi$
$200$	−4.94427	−0.349613
$201$	0	0
$202$	6.23607	0.438768
$203$	2.61803	0.183750
$204$	0	0
$205$	−0.360680	−0.0251910
$206$	−9.00000	−0.627060
$207$	0	0
$208$	−3.61803	−0.250866
$209$	0	0
$210$	0	0
$211$	−10.2361	−0.704680	−0.352340	−	0.935872i	$-0.614614\pi$
$211$	−10.2361	−0.704680	−0.352340	+	0.935872i	$0.614614\pi$
$212$	−13.7984	−0.947676
$213$	0	0
$214$	−9.70820	−0.663639
$215$	−0.978714	−0.0667477
$216$	0	0
$217$	−4.70820	−0.319614
$218$	−5.32624	−0.360738
$219$	0	0
$220$	0	0
$221$	2.23607	0.150414
$222$	0	0
$223$	−13.5623	−0.908199	−0.454100	−	0.890951i	$-0.650039\pi$
$223$	−13.5623	−0.908199	−0.454100	+	0.890951i	$0.650039\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	−12.7082	−0.845337
$227$	16.7984	1.11495	0.557474	−	0.830195i	$-0.311771\pi$
$227$	16.7984	1.11495	0.557474	+	0.830195i	$0.311771\pi$
$228$	0	0
$229$	−7.29180	−0.481855	−0.240928	−	0.970543i	$-0.577452\pi$
$229$	−7.29180	−0.481855	−0.240928	+	0.970543i	$0.577452\pi$
$230$	−0.416408	−0.0274571
$231$	0	0
$232$	2.61803	0.171882
$233$	11.6525	0.763379	0.381690	−	0.924291i	$-0.375342\pi$
$233$	11.6525	0.763379	0.381690	+	0.924291i	$0.375342\pi$
$234$	0	0
$235$	−2.23607	−0.145865
$236$	0.381966	0.0248639
$237$	0	0
$238$	−0.618034	−0.0400612
$239$	21.7082	1.40419	0.702093	−	0.712085i	$-0.252249\pi$
$239$	21.7082	1.40419	0.702093	+	0.712085i	$0.252249\pi$
$240$	0	0
$241$	27.4721	1.76964	0.884818	−	0.465937i	$-0.154283\pi$
$241$	27.4721	1.76964	0.884818	+	0.465937i	$0.154283\pi$
$242$	0	0
$243$	0	0
$244$	5.38197	0.344545
$245$	−1.41641	−0.0904910
$246$	0	0
$247$	10.3262	0.657043
$248$	−4.70820	−0.298971
$249$	0	0
$250$	−2.34752	−0.148470
$251$	−26.1803	−1.65249	−0.826244	−	0.563312i	$-0.809527\pi$
$251$	−26.1803	−1.65249	−0.826244	+	0.563312i	$0.809527\pi$
$252$	0	0
$253$	0	0
$254$	4.32624	0.271452
$255$	0	0
$256$	1.00000	0.0625000
$257$	10.0902	0.629408	0.314704	−	0.949190i	$-0.398095\pi$
$257$	10.0902	0.629408	0.314704	+	0.949190i	$0.398095\pi$
$258$	0	0
$259$	1.85410	0.115208
$260$	−0.854102	−0.0529692
$261$	0	0
$262$	−16.7639	−1.03568
$263$	−22.3607	−1.37882	−0.689409	−	0.724372i	$-0.742130\pi$
$263$	−22.3607	−1.37882	−0.689409	+	0.724372i	$0.742130\pi$
$264$	0	0
$265$	−3.25735	−0.200098
$266$	−2.85410	−0.174996
$267$	0	0
$268$	12.2361	0.747437
$269$	−25.9443	−1.58185	−0.790925	−	0.611913i	$-0.790400\pi$
$269$	−25.9443	−1.58185	−0.790925	+	0.611913i	$0.790400\pi$
$270$	0	0
$271$	−1.00000	−0.0607457	−0.0303728	−	0.999539i	$-0.509669\pi$
$271$	−1.00000	−0.0607457	−0.0303728	+	0.999539i	$0.509669\pi$
$272$	−0.618034	−0.0374738
$273$	0	0
$274$	−17.6180	−1.06434
$275$	0	0
$276$	0	0
$277$	−13.1246	−0.788581	−0.394291	−	0.918986i	$-0.629010\pi$
$277$	−13.1246	−0.788581	−0.394291	+	0.918986i	$0.629010\pi$
$278$	−9.00000	−0.539784
$279$	0	0
$280$	0.236068	0.0141078
$281$	−29.5066	−1.76021	−0.880107	−	0.474775i	$-0.842530\pi$
$281$	−29.5066	−1.76021	−0.880107	+	0.474775i	$0.842530\pi$
$282$	0	0
$283$	−21.9787	−1.30650	−0.653249	−	0.757143i	$-0.726595\pi$
$283$	−21.9787	−1.30650	−0.653249	+	0.757143i	$0.726595\pi$
$284$	−3.38197	−0.200683
$285$	0	0
$286$	0	0
$287$	−1.52786	−0.0901870
$288$	0	0
$289$	−16.6180	−0.977531
$290$	0.618034	0.0362922
$291$	0	0
$292$	−5.76393	−0.337309
$293$	22.7426	1.32864	0.664320	−	0.747448i	$-0.268721\pi$
$293$	22.7426	1.32864	0.664320	+	0.747448i	$0.268721\pi$
$294$	0	0
$295$	0.0901699	0.00524990
$296$	1.85410	0.107767
$297$	0	0
$298$	−16.7639	−0.971109
$299$	6.38197	0.369079
$300$	0	0
$301$	−4.14590	−0.238966
$302$	5.41641	0.311679
$303$	0	0
$304$	−2.85410	−0.163694
$305$	1.27051	0.0727492
$306$	0	0
$307$	12.5279	0.715003	0.357501	−	0.933913i	$-0.383629\pi$
$307$	12.5279	0.715003	0.357501	+	0.933913i	$0.383629\pi$
$308$	0	0
$309$	0	0
$310$	−1.11146	−0.0631265
$311$	−9.32624	−0.528842	−0.264421	−	0.964407i	$-0.585181\pi$
$311$	−9.32624	−0.528842	−0.264421	+	0.964407i	$0.585181\pi$
$312$	0	0
$313$	−1.94427	−0.109897	−0.0549484	−	0.998489i	$-0.517499\pi$
$313$	−1.94427	−0.109897	−0.0549484	+	0.998489i	$0.517499\pi$
$314$	3.00000	0.169300
$315$	0	0
$316$	6.00000	0.337526
$317$	−4.58359	−0.257440	−0.128720	−	0.991681i	$-0.541087\pi$
$317$	−4.58359	−0.257440	−0.128720	+	0.991681i	$0.541087\pi$
$318$	0	0
$319$	0	0
$320$	0.236068	0.0131966
$321$	0	0
$322$	−1.76393	−0.0983001
$323$	1.76393	0.0981478
$324$	0	0
$325$	17.8885	0.992278
$326$	19.8885	1.10152
$327$	0	0
$328$	−1.52786	−0.0843622
$329$	−9.47214	−0.522216
$330$	0	0
$331$	20.1246	1.10615	0.553074	−	0.833132i	$-0.313455\pi$
$331$	20.1246	1.10615	0.553074	+	0.833132i	$0.313455\pi$
$332$	0.763932	0.0419262
$333$	0	0
$334$	24.9443	1.36489
$335$	2.88854	0.157818
$336$	0	0
$337$	21.7426	1.18440	0.592199	−	0.805792i	$-0.298260\pi$
$337$	21.7426	1.18440	0.592199	+	0.805792i	$0.298260\pi$
$338$	0.0901699	0.00490460
$339$	0	0
$340$	−0.145898	−0.00791243
$341$	0	0
$342$	0	0
$343$	−13.0000	−0.701934
$344$	−4.14590	−0.223532
$345$	0	0
$346$	11.0344	0.593215
$347$	−27.0689	−1.45313	−0.726567	−	0.687096i	$-0.758885\pi$
$347$	−27.0689	−1.45313	−0.726567	+	0.687096i	$0.758885\pi$
$348$	0	0
$349$	12.5279	0.670601	0.335301	−	0.942111i	$-0.391162\pi$
$349$	12.5279	0.670601	0.335301	+	0.942111i	$0.391162\pi$
$350$	−4.94427	−0.264282
$351$	0	0
$352$	0	0
$353$	9.05573	0.481988	0.240994	−	0.970527i	$-0.422527\pi$
$353$	9.05573	0.481988	0.240994	+	0.970527i	$0.422527\pi$
$354$	0	0
$355$	−0.798374	−0.0423733
$356$	10.1803	0.539557
$357$	0	0
$358$	−13.4721	−0.712025
$359$	−20.1246	−1.06214	−0.531068	−	0.847329i	$-0.678209\pi$
$359$	−20.1246	−1.06214	−0.531068	+	0.847329i	$0.678209\pi$
$360$	0	0
$361$	−10.8541	−0.571269
$362$	−10.6180	−0.558071
$363$	0	0
$364$	−3.61803	−0.189637
$365$	−1.36068	−0.0712212
$366$	0	0
$367$	−3.41641	−0.178335	−0.0891675	−	0.996017i	$-0.528421\pi$
$367$	−3.41641	−0.178335	−0.0891675	+	0.996017i	$0.528421\pi$
$368$	−1.76393	−0.0919513
$369$	0	0
$370$	0.437694	0.0227546
$371$	−13.7984	−0.716376
$372$	0	0
$373$	−34.1246	−1.76691	−0.883453	−	0.468520i	$-0.844787\pi$
$373$	−34.1246	−1.76691	−0.883453	+	0.468520i	$0.844787\pi$
$374$	0	0
$375$	0	0
$376$	−9.47214	−0.488488
$377$	−9.47214	−0.487840
$378$	0	0
$379$	5.70820	0.293211	0.146605	−	0.989195i	$-0.453165\pi$
$379$	5.70820	0.293211	0.146605	+	0.989195i	$0.453165\pi$
$380$	−0.673762	−0.0345633
$381$	0	0
$382$	−9.09017	−0.465094
$383$	32.8885	1.68053	0.840263	−	0.542179i	$-0.182401\pi$
$383$	32.8885	1.68053	0.840263	+	0.542179i	$0.182401\pi$
$384$	0	0
$385$	0	0
$386$	18.1246	0.922518
$387$	0	0
$388$	13.8541	0.703335
$389$	−10.3820	−0.526387	−0.263193	−	0.964743i	$-0.584776\pi$
$389$	−10.3820	−0.526387	−0.263193	+	0.964743i	$0.584776\pi$
$390$	0	0
$391$	1.09017	0.0551323
$392$	−6.00000	−0.303046
$393$	0	0
$394$	13.4721	0.678716
$395$	1.41641	0.0712672
$396$	0	0
$397$	16.8541	0.845883	0.422942	−	0.906157i	$-0.360998\pi$
$397$	16.8541	0.845883	0.422942	+	0.906157i	$0.360998\pi$
$398$	19.1803	0.961424
$399$	0	0
$400$	−4.94427	−0.247214
$401$	16.8885	0.843374	0.421687	−	0.906742i	$-0.361438\pi$
$401$	16.8885	0.843374	0.421687	+	0.906742i	$0.361438\pi$
$402$	0	0
$403$	17.0344	0.848546
$404$	6.23607	0.310256
$405$	0	0
$406$	2.61803	0.129931
$407$	0	0
$408$	0	0
$409$	9.70820	0.480040	0.240020	−	0.970768i	$-0.422846\pi$
$409$	9.70820	0.480040	0.240020	+	0.970768i	$0.422846\pi$
$410$	−0.360680	−0.0178127
$411$	0	0
$412$	−9.00000	−0.443398
$413$	0.381966	0.0187953
$414$	0	0
$415$	0.180340	0.00885254
$416$	−3.61803	−0.177389
$417$	0	0
$418$	0	0
$419$	13.4164	0.655434	0.327717	−	0.944776i	$-0.393721\pi$
$419$	13.4164	0.655434	0.327717	+	0.944776i	$0.393721\pi$
$420$	0	0
$421$	15.9787	0.778755	0.389377	−	0.921078i	$-0.372690\pi$
$421$	15.9787	0.778755	0.389377	+	0.921078i	$0.372690\pi$
$422$	−10.2361	−0.498284
$423$	0	0
$424$	−13.7984	−0.670108
$425$	3.05573	0.148225
$426$	0	0
$427$	5.38197	0.260452
$428$	−9.70820	−0.469264
$429$	0	0
$430$	−0.978714	−0.0471978
$431$	25.3262	1.21992	0.609961	−	0.792431i	$-0.291185\pi$
$431$	25.3262	1.21992	0.609961	+	0.792431i	$0.291185\pi$
$432$	0	0
$433$	−20.0902	−0.965472	−0.482736	−	0.875766i	$-0.660357\pi$
$433$	−20.0902	−0.965472	−0.482736	+	0.875766i	$0.660357\pi$
$434$	−4.70820	−0.226001
$435$	0	0
$436$	−5.32624	−0.255081
$437$	5.03444	0.240830
$438$	0	0
$439$	40.2705	1.92201	0.961003	−	0.276537i	$-0.0891868\pi$
$439$	40.2705	1.92201	0.961003	+	0.276537i	$0.0891868\pi$
$440$	0	0
$441$	0	0
$442$	2.23607	0.106359
$443$	−36.9787	−1.75691	−0.878456	−	0.477824i	$-0.841426\pi$
$443$	−36.9787	−1.75691	−0.878456	+	0.477824i	$0.841426\pi$
$444$	0	0
$445$	2.40325	0.113925
$446$	−13.5623	−0.642194
$447$	0	0
$448$	1.00000	0.0472456
$449$	−25.8541	−1.22013	−0.610065	−	0.792351i	$-0.708857\pi$
$449$	−25.8541	−1.22013	−0.610065	+	0.792351i	$0.708857\pi$
$450$	0	0
$451$	0	0
$452$	−12.7082	−0.597744
$453$	0	0
$454$	16.7984	0.788387
$455$	−0.854102	−0.0400409
$456$	0	0
$457$	1.85410	0.0867312	0.0433656	−	0.999059i	$-0.486192\pi$
$457$	1.85410	0.0867312	0.0433656	+	0.999059i	$0.486192\pi$
$458$	−7.29180	−0.340723
$459$	0	0
$460$	−0.416408	−0.0194151
$461$	−24.5066	−1.14139	−0.570693	−	0.821164i	$-0.693325\pi$
$461$	−24.5066	−1.14139	−0.570693	+	0.821164i	$0.693325\pi$
$462$	0	0
$463$	−22.1459	−1.02921	−0.514604	−	0.857428i	$-0.672061\pi$
$463$	−22.1459	−1.02921	−0.514604	+	0.857428i	$0.672061\pi$
$464$	2.61803	0.121539
$465$	0	0
$466$	11.6525	0.539791
$467$	−15.0344	−0.695711	−0.347855	−	0.937548i	$-0.613090\pi$
$467$	−15.0344	−0.695711	−0.347855	+	0.937548i	$0.613090\pi$
$468$	0	0
$469$	12.2361	0.565009
$470$	−2.23607	−0.103142
$471$	0	0
$472$	0.381966	0.0175814
$473$	0	0
$474$	0	0
$475$	14.1115	0.647478
$476$	−0.618034	−0.0283275
$477$	0	0
$478$	21.7082	0.992910
$479$	−0.326238	−0.0149062	−0.00745310	−	0.999972i	$-0.502372\pi$
$479$	−0.326238	−0.0149062	−0.00745310	+	0.999972i	$0.502372\pi$
$480$	0	0
$481$	−6.70820	−0.305868
$482$	27.4721	1.25132
$483$	0	0
$484$	0	0
$485$	3.27051	0.148506
$486$	0	0
$487$	−0.472136	−0.0213945	−0.0106973	−	0.999943i	$-0.503405\pi$
$487$	−0.472136	−0.0213945	−0.0106973	+	0.999943i	$0.503405\pi$
$488$	5.38197	0.243630
$489$	0	0
$490$	−1.41641	−0.0639868
$491$	16.4164	0.740862	0.370431	−	0.928860i	$-0.379210\pi$
$491$	16.4164	0.740862	0.370431	+	0.928860i	$0.379210\pi$
$492$	0	0
$493$	−1.61803	−0.0728726
$494$	10.3262	0.464599
$495$	0	0
$496$	−4.70820	−0.211405
$497$	−3.38197	−0.151702
$498$	0	0
$499$	−28.1246	−1.25903	−0.629515	−	0.776988i	$-0.716746\pi$
$499$	−28.1246	−1.25903	−0.629515	+	0.776988i	$0.716746\pi$
$500$	−2.34752	−0.104984
$501$	0	0
$502$	−26.1803	−1.16849
$503$	−8.52786	−0.380239	−0.190119	−	0.981761i	$-0.560887\pi$
$503$	−8.52786	−0.380239	−0.190119	+	0.981761i	$0.560887\pi$
$504$	0	0
$505$	1.47214	0.0655092
$506$	0	0
$507$	0	0
$508$	4.32624	0.191946
$509$	−33.9787	−1.50608	−0.753040	−	0.657975i	$-0.771413\pi$
$509$	−33.9787	−1.50608	−0.753040	+	0.657975i	$0.771413\pi$
$510$	0	0
$511$	−5.76393	−0.254981
$512$	1.00000	0.0441942
$513$	0	0
$514$	10.0902	0.445058
$515$	−2.12461	−0.0936216
$516$	0	0
$517$	0	0
$518$	1.85410	0.0814646
$519$	0	0
$520$	−0.854102	−0.0374548
$521$	−23.4721	−1.02833	−0.514166	−	0.857690i	$-0.671899\pi$
$521$	−23.4721	−1.02833	−0.514166	+	0.857690i	$0.671899\pi$
$522$	0	0
$523$	10.3475	0.452466	0.226233	−	0.974073i	$-0.427359\pi$
$523$	10.3475	0.452466	0.226233	+	0.974073i	$0.427359\pi$
$524$	−16.7639	−0.732336
$525$	0	0
$526$	−22.3607	−0.974972
$527$	2.90983	0.126754
$528$	0	0
$529$	−19.8885	−0.864719
$530$	−3.25735	−0.141490
$531$	0	0
$532$	−2.85410	−0.123741
$533$	5.52786	0.239438
$534$	0	0
$535$	−2.29180	−0.0990830
$536$	12.2361	0.528518
$537$	0	0
$538$	−25.9443	−1.11854
$539$	0	0
$540$	0	0
$541$	35.7082	1.53522	0.767608	−	0.640920i	$-0.221447\pi$
$541$	35.7082	1.53522	0.767608	+	0.640920i	$0.221447\pi$
$542$	−1.00000	−0.0429537
$543$	0	0
$544$	−0.618034	−0.0264980
$545$	−1.25735	−0.0538591
$546$	0	0
$547$	30.0344	1.28418	0.642090	−	0.766629i	$-0.278068\pi$
$547$	30.0344	1.28418	0.642090	+	0.766629i	$0.278068\pi$
$548$	−17.6180	−0.752605
$549$	0	0
$550$	0	0
$551$	−7.47214	−0.318324
$552$	0	0
$553$	6.00000	0.255146
$554$	−13.1246	−0.557611
$555$	0	0
$556$	−9.00000	−0.381685
$557$	−22.0344	−0.933629	−0.466815	−	0.884355i	$-0.654598\pi$
$557$	−22.0344	−0.933629	−0.466815	+	0.884355i	$0.654598\pi$
$558$	0	0
$559$	15.0000	0.634432
$560$	0.236068	0.00997569
$561$	0	0
$562$	−29.5066	−1.24466
$563$	−22.3050	−0.940042	−0.470021	−	0.882655i	$-0.655754\pi$
$563$	−22.3050	−0.940042	−0.470021	+	0.882655i	$0.655754\pi$
$564$	0	0
$565$	−3.00000	−0.126211
$566$	−21.9787	−0.923834
$567$	0	0
$568$	−3.38197	−0.141904
$569$	13.0689	0.547876	0.273938	−	0.961747i	$-0.411674\pi$
$569$	13.0689	0.547876	0.273938	+	0.961747i	$0.411674\pi$
$570$	0	0
$571$	−4.76393	−0.199364	−0.0996822	−	0.995019i	$-0.531783\pi$
$571$	−4.76393	−0.199364	−0.0996822	+	0.995019i	$0.531783\pi$
$572$	0	0
$573$	0	0
$574$	−1.52786	−0.0637718
$575$	8.72136	0.363706
$576$	0	0
$577$	−23.6525	−0.984665	−0.492333	−	0.870407i	$-0.663856\pi$
$577$	−23.6525	−0.984665	−0.492333	+	0.870407i	$0.663856\pi$
$578$	−16.6180	−0.691219
$579$	0	0
$580$	0.618034	0.0256625
$581$	0.763932	0.0316932
$582$	0	0
$583$	0	0
$584$	−5.76393	−0.238513
$585$	0	0
$586$	22.7426	0.939490
$587$	44.5623	1.83928	0.919642	−	0.392759i	$-0.128479\pi$
$587$	44.5623	1.83928	0.919642	+	0.392759i	$0.128479\pi$
$588$	0	0
$589$	13.4377	0.553691
$590$	0.0901699	0.00371224
$591$	0	0
$592$	1.85410	0.0762031
$593$	−6.43769	−0.264364	−0.132182	−	0.991225i	$-0.542198\pi$
$593$	−6.43769	−0.264364	−0.132182	+	0.991225i	$0.542198\pi$
$594$	0	0
$595$	−0.145898	−0.00598124
$596$	−16.7639	−0.686677
$597$	0	0
$598$	6.38197	0.260978
$599$	−6.27051	−0.256206	−0.128103	−	0.991761i	$-0.540889\pi$
$599$	−6.27051	−0.256206	−0.128103	+	0.991761i	$0.540889\pi$
$600$	0	0
$601$	33.3951	1.36222	0.681108	−	0.732183i	$-0.261499\pi$
$601$	33.3951	1.36222	0.681108	+	0.732183i	$0.261499\pi$
$602$	−4.14590	−0.168974
$603$	0	0
$604$	5.41641	0.220391
$605$	0	0
$606$	0	0
$607$	−38.1246	−1.54743	−0.773715	−	0.633534i	$-0.781604\pi$
$607$	−38.1246	−1.54743	−0.773715	+	0.633534i	$0.781604\pi$
$608$	−2.85410	−0.115749
$609$	0	0
$610$	1.27051	0.0514414
$611$	34.2705	1.38644
$612$	0	0
$613$	11.0000	0.444286	0.222143	−	0.975014i	$-0.428695\pi$
$613$	11.0000	0.444286	0.222143	+	0.975014i	$0.428695\pi$
$614$	12.5279	0.505583
$615$	0	0
$616$	0	0
$617$	7.20163	0.289927	0.144963	−	0.989437i	$-0.453694\pi$
$617$	7.20163	0.289927	0.144963	+	0.989437i	$0.453694\pi$
$618$	0	0
$619$	−5.11146	−0.205447	−0.102723	−	0.994710i	$-0.532756\pi$
$619$	−5.11146	−0.205447	−0.102723	+	0.994710i	$0.532756\pi$
$620$	−1.11146	−0.0446372
$621$	0	0
$622$	−9.32624	−0.373948
$623$	10.1803	0.407867
$624$	0	0
$625$	24.1672	0.966687
$626$	−1.94427	−0.0777087
$627$	0	0
$628$	3.00000	0.119713
$629$	−1.14590	−0.0456899
$630$	0	0
$631$	−20.1459	−0.801996	−0.400998	−	0.916079i	$-0.631336\pi$
$631$	−20.1459	−0.801996	−0.400998	+	0.916079i	$0.631336\pi$
$632$	6.00000	0.238667
$633$	0	0
$634$	−4.58359	−0.182038
$635$	1.02129	0.0405285
$636$	0	0
$637$	21.7082	0.860110
$638$	0	0
$639$	0	0
$640$	0.236068	0.00933141
$641$	12.7984	0.505505	0.252753	−	0.967531i	$-0.418664\pi$
$641$	12.7984	0.505505	0.252753	+	0.967531i	$0.418664\pi$
$642$	0	0
$643$	28.6869	1.13130	0.565651	−	0.824645i	$-0.308625\pi$
$643$	28.6869	1.13130	0.565651	+	0.824645i	$0.308625\pi$
$644$	−1.76393	−0.0695087
$645$	0	0
$646$	1.76393	0.0694010
$647$	−38.3607	−1.50811	−0.754057	−	0.656809i	$-0.771906\pi$
$647$	−38.3607	−1.50811	−0.754057	+	0.656809i	$0.771906\pi$
$648$	0	0
$649$	0	0
$650$	17.8885	0.701646
$651$	0	0
$652$	19.8885	0.778895
$653$	29.6525	1.16039	0.580196	−	0.814477i	$-0.302976\pi$
$653$	29.6525	1.16039	0.580196	+	0.814477i	$0.302976\pi$
$654$	0	0
$655$	−3.95743	−0.154629
$656$	−1.52786	−0.0596531
$657$	0	0
$658$	−9.47214	−0.369262
$659$	31.3607	1.22164	0.610819	−	0.791770i	$-0.290840\pi$
$659$	31.3607	1.22164	0.610819	+	0.791770i	$0.290840\pi$
$660$	0	0
$661$	37.7639	1.46885	0.734423	−	0.678692i	$-0.237453\pi$
$661$	37.7639	1.46885	0.734423	+	0.678692i	$0.237453\pi$
$662$	20.1246	0.782165
$663$	0	0
$664$	0.763932	0.0296463
$665$	−0.673762	−0.0261274
$666$	0	0
$667$	−4.61803	−0.178811
$668$	24.9443	0.965123
$669$	0	0
$670$	2.88854	0.111594
$671$	0	0
$672$	0	0
$673$	31.1246	1.19977	0.599883	−	0.800088i	$-0.295214\pi$
$673$	31.1246	1.19977	0.599883	+	0.800088i	$0.295214\pi$
$674$	21.7426	0.837495
$675$	0	0
$676$	0.0901699	0.00346807
$677$	2.49342	0.0958300	0.0479150	−	0.998851i	$-0.484742\pi$
$677$	2.49342	0.0958300	0.0479150	+	0.998851i	$0.484742\pi$
$678$	0	0
$679$	13.8541	0.531672
$680$	−0.145898	−0.00559493
$681$	0	0
$682$	0	0
$683$	−3.23607	−0.123825	−0.0619123	−	0.998082i	$-0.519720\pi$
$683$	−3.23607	−0.123825	−0.0619123	+	0.998082i	$0.519720\pi$
$684$	0	0
$685$	−4.15905	−0.158909
$686$	−13.0000	−0.496342
$687$	0	0
$688$	−4.14590	−0.158061
$689$	49.9230	1.90191
$690$	0	0
$691$	−2.38197	−0.0906143	−0.0453071	−	0.998973i	$-0.514427\pi$
$691$	−2.38197	−0.0906143	−0.0453071	+	0.998973i	$0.514427\pi$
$692$	11.0344	0.419467
$693$	0	0
$694$	−27.0689	−1.02752
$695$	−2.12461	−0.0805911
$696$	0	0
$697$	0.944272	0.0357668
$698$	12.5279	0.474187
$699$	0	0
$700$	−4.94427	−0.186876
$701$	−38.8328	−1.46670	−0.733348	−	0.679854i	$-0.762043\pi$
$701$	−38.8328	−1.46670	−0.733348	+	0.679854i	$0.762043\pi$
$702$	0	0
$703$	−5.29180	−0.199584
$704$	0	0
$705$	0	0
$706$	9.05573	0.340817
$707$	6.23607	0.234531
$708$	0	0
$709$	4.88854	0.183593	0.0917966	−	0.995778i	$-0.470739\pi$
$709$	4.88854	0.183593	0.0917966	+	0.995778i	$0.470739\pi$
$710$	−0.798374	−0.0299624
$711$	0	0
$712$	10.1803	0.381524
$713$	8.30495	0.311023
$714$	0	0
$715$	0	0
$716$	−13.4721	−0.503477
$717$	0	0
$718$	−20.1246	−0.751044
$719$	−44.5623	−1.66189	−0.830947	−	0.556352i	$-0.812201\pi$
$719$	−44.5623	−1.66189	−0.830947	+	0.556352i	$0.812201\pi$
$720$	0	0
$721$	−9.00000	−0.335178
$722$	−10.8541	−0.403948
$723$	0	0
$724$	−10.6180	−0.394616
$725$	−12.9443	−0.480738
$726$	0	0
$727$	−25.2705	−0.937231	−0.468616	−	0.883402i	$-0.655247\pi$
$727$	−25.2705	−0.937231	−0.468616	+	0.883402i	$0.655247\pi$
$728$	−3.61803	−0.134093
$729$	0	0
$730$	−1.36068	−0.0503610
$731$	2.56231	0.0947703
$732$	0	0
$733$	43.2705	1.59823	0.799116	−	0.601176i	$-0.205301\pi$
$733$	43.2705	1.59823	0.799116	+	0.601176i	$0.205301\pi$
$734$	−3.41641	−0.126102
$735$	0	0
$736$	−1.76393	−0.0650194
$737$	0	0
$738$	0	0
$739$	−42.9574	−1.58021	−0.790107	−	0.612969i	$-0.789975\pi$
$739$	−42.9574	−1.58021	−0.790107	+	0.612969i	$0.789975\pi$
$740$	0.437694	0.0160900
$741$	0	0
$742$	−13.7984	−0.506554
$743$	−40.8885	−1.50006	−0.750028	−	0.661407i	$-0.769960\pi$
$743$	−40.8885	−1.50006	−0.750028	+	0.661407i	$0.769960\pi$
$744$	0	0
$745$	−3.95743	−0.144989
$746$	−34.1246	−1.24939
$747$	0	0
$748$	0	0
$749$	−9.70820	−0.354730
$750$	0	0
$751$	5.32624	0.194357	0.0971786	−	0.995267i	$-0.469018\pi$
$751$	5.32624	0.194357	0.0971786	+	0.995267i	$0.469018\pi$
$752$	−9.47214	−0.345413
$753$	0	0
$754$	−9.47214	−0.344955
$755$	1.27864	0.0465345
$756$	0	0
$757$	6.34752	0.230705	0.115352	−	0.993325i	$-0.463200\pi$
$757$	6.34752	0.230705	0.115352	+	0.993325i	$0.463200\pi$
$758$	5.70820	0.207331
$759$	0	0
$760$	−0.673762	−0.0244399
$761$	5.18034	0.187787	0.0938936	−	0.995582i	$-0.470069\pi$
$761$	5.18034	0.187787	0.0938936	+	0.995582i	$0.470069\pi$
$762$	0	0
$763$	−5.32624	−0.192823
$764$	−9.09017	−0.328871
$765$	0	0
$766$	32.8885	1.18831
$767$	−1.38197	−0.0498999
$768$	0	0
$769$	42.2705	1.52431	0.762157	−	0.647392i	$-0.224141\pi$
$769$	42.2705	1.52431	0.762157	+	0.647392i	$0.224141\pi$
$770$	0	0
$771$	0	0
$772$	18.1246	0.652319
$773$	27.7984	0.999838	0.499919	−	0.866072i	$-0.333363\pi$
$773$	27.7984	0.999838	0.499919	+	0.866072i	$0.333363\pi$
$774$	0	0
$775$	23.2786	0.836193
$776$	13.8541	0.497333
$777$	0	0
$778$	−10.3820	−0.372212
$779$	4.36068	0.156238
$780$	0	0
$781$	0	0
$782$	1.09017	0.0389844
$783$	0	0
$784$	−6.00000	−0.214286
$785$	0.708204	0.0252769
$786$	0	0
$787$	−23.4721	−0.836691	−0.418346	−	0.908288i	$-0.637390\pi$
$787$	−23.4721	−0.836691	−0.418346	+	0.908288i	$0.637390\pi$
$788$	13.4721	0.479925
$789$	0	0
$790$	1.41641	0.0503935
$791$	−12.7082	−0.451852
$792$	0	0
$793$	−19.4721	−0.691476
$794$	16.8541	0.598130
$795$	0	0
$796$	19.1803	0.679829
$797$	29.2361	1.03559	0.517797	−	0.855503i	$-0.326752\pi$
$797$	29.2361	1.03559	0.517797	+	0.855503i	$0.326752\pi$
$798$	0	0
$799$	5.85410	0.207103
$800$	−4.94427	−0.174806
$801$	0	0
$802$	16.8885	0.596355
$803$	0	0
$804$	0	0
$805$	−0.416408	−0.0146764
$806$	17.0344	0.600013
$807$	0	0
$808$	6.23607	0.219384
$809$	49.3050	1.73347	0.866735	−	0.498769i	$-0.166214\pi$
$809$	49.3050	1.73347	0.866735	+	0.498769i	$0.166214\pi$
$810$	0	0
$811$	13.9443	0.489650	0.244825	−	0.969567i	$-0.421270\pi$
$811$	13.9443	0.489650	0.244825	+	0.969567i	$0.421270\pi$
$812$	2.61803	0.0918750
$813$	0	0
$814$	0	0
$815$	4.69505	0.164460
$816$	0	0
$817$	11.8328	0.413978
$818$	9.70820	0.339439
$819$	0	0
$820$	−0.360680	−0.0125955
$821$	−33.5410	−1.17059	−0.585295	−	0.810821i	$-0.699021\pi$
$821$	−33.5410	−1.17059	−0.585295	+	0.810821i	$0.699021\pi$
$822$	0	0
$823$	−32.0902	−1.11859	−0.559297	−	0.828968i	$-0.688929\pi$
$823$	−32.0902	−1.11859	−0.559297	+	0.828968i	$0.688929\pi$
$824$	−9.00000	−0.313530
$825$	0	0
$826$	0.381966	0.0132903
$827$	−19.4721	−0.677113	−0.338556	−	0.940946i	$-0.609939\pi$
$827$	−19.4721	−0.677113	−0.338556	+	0.940946i	$0.609939\pi$
$828$	0	0
$829$	41.0344	1.42519	0.712593	−	0.701578i	$-0.247521\pi$
$829$	41.0344	1.42519	0.712593	+	0.701578i	$0.247521\pi$
$830$	0.180340	0.00625969
$831$	0	0
$832$	−3.61803	−0.125433
$833$	3.70820	0.128482
$834$	0	0
$835$	5.88854	0.203781
$836$	0	0
$837$	0	0
$838$	13.4164	0.463462
$839$	35.5066	1.22582	0.612912	−	0.790151i	$-0.289998\pi$
$839$	35.5066	1.22582	0.612912	+	0.790151i	$0.289998\pi$
$840$	0	0
$841$	−22.1459	−0.763652
$842$	15.9787	0.550663
$843$	0	0
$844$	−10.2361	−0.352340
$845$	0.0212862	0.000732269 0
$846$	0	0
$847$	0	0
$848$	−13.7984	−0.473838
$849$	0	0
$850$	3.05573	0.104811
$851$	−3.27051	−0.112112
$852$	0	0
$853$	57.5066	1.96899	0.984494	−	0.175419i	$-0.0561280\pi$
$853$	57.5066	1.96899	0.984494	+	0.175419i	$0.0561280\pi$
$854$	5.38197	0.184167
$855$	0	0
$856$	−9.70820	−0.331820
$857$	40.6312	1.38793	0.693967	−	0.720006i	$-0.255861\pi$
$857$	40.6312	1.38793	0.693967	+	0.720006i	$0.255861\pi$
$858$	0	0
$859$	23.6525	0.807012	0.403506	−	0.914977i	$-0.367791\pi$
$859$	23.6525	0.807012	0.403506	+	0.914977i	$0.367791\pi$
$860$	−0.978714	−0.0333739
$861$	0	0
$862$	25.3262	0.862615
$863$	−18.2361	−0.620763	−0.310381	−	0.950612i	$-0.600457\pi$
$863$	−18.2361	−0.620763	−0.310381	+	0.950612i	$0.600457\pi$
$864$	0	0
$865$	2.60488	0.0885685
$866$	−20.0902	−0.682692
$867$	0	0
$868$	−4.70820	−0.159807
$869$	0	0
$870$	0	0
$871$	−44.2705	−1.50005
$872$	−5.32624	−0.180369
$873$	0	0
$874$	5.03444	0.170293
$875$	−2.34752	−0.0793608
$876$	0	0
$877$	4.11146	0.138834	0.0694170	−	0.997588i	$-0.477886\pi$
$877$	4.11146	0.138834	0.0694170	+	0.997588i	$0.477886\pi$
$878$	40.2705	1.35906
$879$	0	0
$880$	0	0
$881$	−53.6525	−1.80760	−0.903799	−	0.427957i	$-0.859233\pi$
$881$	−53.6525	−1.80760	−0.903799	+	0.427957i	$0.859233\pi$
$882$	0	0
$883$	−21.5410	−0.724913	−0.362457	−	0.932001i	$-0.618062\pi$
$883$	−21.5410	−0.724913	−0.362457	+	0.932001i	$0.618062\pi$
$884$	2.23607	0.0752071
$885$	0	0
$886$	−36.9787	−1.24232
$887$	−20.3820	−0.684359	−0.342180	−	0.939635i	$-0.611165\pi$
$887$	−20.3820	−0.684359	−0.342180	+	0.939635i	$0.611165\pi$
$888$	0	0
$889$	4.32624	0.145097
$890$	2.40325	0.0805572
$891$	0	0
$892$	−13.5623	−0.454100
$893$	27.0344	0.904673
$894$	0	0
$895$	−3.18034	−0.106307
$896$	1.00000	0.0334077
$897$	0	0
$898$	−25.8541	−0.862763
$899$	−12.3262	−0.411103
$900$	0	0
$901$	8.52786	0.284104
$902$	0	0
$903$	0	0
$904$	−12.7082	−0.422669
$905$	−2.50658	−0.0833215
$906$	0	0
$907$	32.4164	1.07637	0.538185	−	0.842827i	$-0.319110\pi$
$907$	32.4164	1.07637	0.538185	+	0.842827i	$0.319110\pi$
$908$	16.7984	0.557474
$909$	0	0
$910$	−0.854102	−0.0283132
$911$	−0.360680	−0.0119499	−0.00597493	−	0.999982i	$-0.501902\pi$
$911$	−0.360680	−0.0119499	−0.00597493	+	0.999982i	$0.501902\pi$
$912$	0	0
$913$	0	0
$914$	1.85410	0.0613282
$915$	0	0
$916$	−7.29180	−0.240928
$917$	−16.7639	−0.553594
$918$	0	0
$919$	45.1033	1.48782	0.743911	−	0.668279i	$-0.232969\pi$
$919$	45.1033	1.48782	0.743911	+	0.668279i	$0.232969\pi$
$920$	−0.416408	−0.0137286
$921$	0	0
$922$	−24.5066	−0.807081
$923$	12.2361	0.402755
$924$	0	0
$925$	−9.16718	−0.301415
$926$	−22.1459	−0.727759
$927$	0	0
$928$	2.61803	0.0859412
$929$	10.4721	0.343580	0.171790	−	0.985134i	$-0.445045\pi$
$929$	10.4721	0.343580	0.171790	+	0.985134i	$0.445045\pi$
$930$	0	0
$931$	17.1246	0.561236
$932$	11.6525	0.381690
$933$	0	0
$934$	−15.0344	−0.491942
$935$	0	0
$936$	0	0
$937$	5.56231	0.181713	0.0908563	−	0.995864i	$-0.471040\pi$
$937$	5.56231	0.181713	0.0908563	+	0.995864i	$0.471040\pi$
$938$	12.2361	0.399522
$939$	0	0
$940$	−2.23607	−0.0729325
$941$	27.8885	0.909141	0.454570	−	0.890711i	$-0.349793\pi$
$941$	27.8885	0.909141	0.454570	+	0.890711i	$0.349793\pi$
$942$	0	0
$943$	2.69505	0.0877628
$944$	0.381966	0.0124319
$945$	0	0
$946$	0	0
$947$	28.0344	0.910997	0.455498	−	0.890237i	$-0.349461\pi$
$947$	28.0344	0.910997	0.455498	+	0.890237i	$0.349461\pi$
$948$	0	0
$949$	20.8541	0.676953
$950$	14.1115	0.457836
$951$	0	0
$952$	−0.618034	−0.0200306
$953$	−44.1591	−1.43045	−0.715226	−	0.698893i	$-0.753676\pi$
$953$	−44.1591	−1.43045	−0.715226	+	0.698893i	$0.753676\pi$
$954$	0	0
$955$	−2.14590	−0.0694396
$956$	21.7082	0.702093
$957$	0	0
$958$	−0.326238	−0.0105403
$959$	−17.6180	−0.568916
$960$	0	0
$961$	−8.83282	−0.284930
$962$	−6.70820	−0.216281
$963$	0	0
$964$	27.4721	0.884818
$965$	4.27864	0.137734
$966$	0	0
$967$	8.27051	0.265962	0.132981	−	0.991119i	$-0.457545\pi$
$967$	8.27051	0.265962	0.132981	+	0.991119i	$0.457545\pi$
$968$	0	0
$969$	0	0
$970$	3.27051	0.105010
$971$	28.0132	0.898985	0.449492	−	0.893284i	$-0.351605\pi$
$971$	28.0132	0.898985	0.449492	+	0.893284i	$0.351605\pi$
$972$	0	0
$973$	−9.00000	−0.288527
$974$	−0.472136	−0.0151282
$975$	0	0
$976$	5.38197	0.172273
$977$	37.3607	1.19527	0.597637	−	0.801767i	$-0.296106\pi$
$977$	37.3607	1.19527	0.597637	+	0.801767i	$0.296106\pi$
$978$	0	0
$979$	0	0
$980$	−1.41641	−0.0452455
$981$	0	0
$982$	16.4164	0.523869
$983$	−1.41641	−0.0451764	−0.0225882	−	0.999745i	$-0.507191\pi$
$983$	−1.41641	−0.0451764	−0.0225882	+	0.999745i	$0.507191\pi$
$984$	0	0
$985$	3.18034	0.101334
$986$	−1.61803	−0.0515287
$987$	0	0
$988$	10.3262	0.328521
$989$	7.31308	0.232542
$990$	0	0
$991$	45.5410	1.44666	0.723329	−	0.690503i	$-0.242611\pi$
$991$	45.5410	1.44666	0.723329	+	0.690503i	$0.242611\pi$
$992$	−4.70820	−0.149486
$993$	0	0
$994$	−3.38197	−0.107269
$995$	4.52786	0.143543
$996$	0	0
$997$	52.0689	1.64904	0.824519	−	0.565834i	$-0.191446\pi$
$997$	52.0689	1.64904	0.824519	+	0.565834i	$0.191446\pi$
$998$	−28.1246	−0.890269
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6534.2.a.bx.1.2		2
3.2	odd	2		6534.2.a.bw.1.1		2
11.5	even	5		594.2.f.b.487.1	yes	4
11.9	even	5		594.2.f.b.433.1	✓	4
11.10	odd	2		6534.2.a.be.1.2		2
33.5	odd	10		594.2.f.i.487.1	yes	4
33.20	odd	10		594.2.f.i.433.1	yes	4
33.32	even	2		6534.2.a.cp.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
594.2.f.b.433.1	✓	4	11.9	even	5
594.2.f.b.487.1	yes	4	11.5	even	5
594.2.f.i.433.1	yes	4	33.20	odd	10
594.2.f.i.487.1	yes	4	33.5	odd	10
6534.2.a.be.1.2		2	11.10	odd	2
6534.2.a.bw.1.1		2	3.2	odd	2
6534.2.a.bx.1.2		2	1.1	even	1	trivial
6534.2.a.cp.1.1		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +0.236068 q^{5} +1.00000 q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +0.236068 q^{5} +1.00000 q^{7} +1.00000 q^{8} +0.236068 q^{10} -3.61803 q^{13} +1.00000 q^{14} +1.00000 q^{16} -0.618034 q^{17} -2.85410 q^{19} +0.236068 q^{20} -1.76393 q^{23} -4.94427 q^{25} -3.61803 q^{26} +1.00000 q^{28} +2.61803 q^{29} -4.70820 q^{31} +1.00000 q^{32} -0.618034 q^{34} +0.236068 q^{35} +1.85410 q^{37} -2.85410 q^{38} +0.236068 q^{40} -1.52786 q^{41} -4.14590 q^{43} -1.76393 q^{46} -9.47214 q^{47} -6.00000 q^{49} -4.94427 q^{50} -3.61803 q^{52} -13.7984 q^{53} +1.00000 q^{56} +2.61803 q^{58} +0.381966 q^{59} +5.38197 q^{61} -4.70820 q^{62} +1.00000 q^{64} -0.854102 q^{65} +12.2361 q^{67} -0.618034 q^{68} +0.236068 q^{70} -3.38197 q^{71} -5.76393 q^{73} +1.85410 q^{74} -2.85410 q^{76} +6.00000 q^{79} +0.236068 q^{80} -1.52786 q^{82} +0.763932 q^{83} -0.145898 q^{85} -4.14590 q^{86} +10.1803 q^{89} -3.61803 q^{91} -1.76393 q^{92} -9.47214 q^{94} -0.673762 q^{95} +13.8541 q^{97} -6.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{4} - 4 q^{5} + 2 q^{7} + 2 q^{8}+O(q^{10}) \) 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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