LMFDB - Embedded newform 588.6.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,6,Mod(1,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("588.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	588.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:	$94.3056860500$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 84)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	588.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+9.00000 q^{3} -69.0000 q^{5} +81.0000 q^{9} +O(q^{10})$

$q+9.00000 q^{3} -69.0000 q^{5} +81.0000 q^{9} +123.000 q^{11} -4.00000 q^{13} -621.000 q^{15} +1776.00 q^{17} -1396.00 q^{19} -1536.00 q^{23} +1636.00 q^{25} +729.000 q^{27} -3615.00 q^{29} +7295.00 q^{31} +1107.00 q^{33} +7640.00 q^{37} -36.0000 q^{39} +10032.0 q^{41} -9754.00 q^{43} -5589.00 q^{45} -17622.0 q^{47} +15984.0 q^{51} +4197.00 q^{53} -8487.00 q^{55} -12564.0 q^{57} -20133.0 q^{59} +34646.0 q^{61} +276.000 q^{65} -41386.0 q^{67} -13824.0 q^{69} +30762.0 q^{71} -80254.0 q^{73} +14724.0 q^{75} -98593.0 q^{79} +6561.00 q^{81} +73407.0 q^{83} -122544. q^{85} -32535.0 q^{87} -106554. q^{89} +65655.0 q^{93} +96324.0 q^{95} -161185. q^{97} +9963.00 q^{99} +O(q^{100})$

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0	0
$2$	0	0
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	0	0
$5$	−69.0000	−1.23431	−0.617155	−	0.786842i	$-0.711715\pi$
$5$	−69.0000	−1.23431	−0.617155	+	0.786842i	$0.711715\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	81.0000	0.333333
$10$	0	0
$11$	123.000	0.306495	0.153248	−	0.988188i	$-0.451027\pi$
$11$	123.000	0.306495	0.153248	+	0.988188i	$0.451027\pi$
$12$	0	0
$13$	−4.00000	−0.00656450	−0.00328225	−	0.999995i	$-0.501045\pi$
$13$	−4.00000	−0.00656450	−0.00328225	+	0.999995i	$0.501045\pi$
$14$	0	0
$15$	−621.000	−0.712629
$16$	0	0
$17$	1776.00	1.49046	0.745231	−	0.666807i	$-0.232339\pi$
$17$	1776.00	1.49046	0.745231	+	0.666807i	$0.232339\pi$
$18$	0	0
$19$	−1396.00	−0.887159	−0.443579	−	0.896235i	$-0.646292\pi$
$19$	−1396.00	−0.887159	−0.443579	+	0.896235i	$0.646292\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−1536.00	−0.605441	−0.302720	−	0.953079i	$-0.597895\pi$
$23$	−1536.00	−0.605441	−0.302720	+	0.953079i	$0.597895\pi$
$24$	0	0
$25$	1636.00	0.523520
$26$	0	0
$27$	729.000	0.192450
$28$	0	0
$29$	−3615.00	−0.798203	−0.399101	−	0.916907i	$-0.630678\pi$
$29$	−3615.00	−0.798203	−0.399101	+	0.916907i	$0.630678\pi$
$30$	0	0
$31$	7295.00	1.36339	0.681697	−	0.731635i	$-0.261242\pi$
$31$	7295.00	1.36339	0.681697	+	0.731635i	$0.261242\pi$
$32$	0	0
$33$	1107.00	0.176955
$34$	0	0
$35$	0	0
$36$	0	0
$37$	7640.00	0.917464	0.458732	−	0.888575i	$-0.348304\pi$
$37$	7640.00	0.917464	0.458732	+	0.888575i	$0.348304\pi$
$38$	0	0
$39$	−36.0000	−0.00379002
$40$	0	0
$41$	10032.0	0.932026	0.466013	−	0.884778i	$-0.345690\pi$
$41$	10032.0	0.932026	0.466013	+	0.884778i	$0.345690\pi$
$42$	0	0
$43$	−9754.00	−0.804473	−0.402237	−	0.915536i	$-0.631767\pi$
$43$	−9754.00	−0.804473	−0.402237	+	0.915536i	$0.631767\pi$
$44$	0	0
$45$	−5589.00	−0.411437
$46$	0	0
$47$	−17622.0	−1.16362	−0.581809	−	0.813325i	$-0.697655\pi$
$47$	−17622.0	−1.16362	−0.581809	+	0.813325i	$0.697655\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	15984.0	0.860518
$52$	0	0
$53$	4197.00	0.205234	0.102617	−	0.994721i	$-0.467278\pi$
$53$	4197.00	0.205234	0.102617	+	0.994721i	$0.467278\pi$
$54$	0	0
$55$	−8487.00	−0.378310
$56$	0	0
$57$	−12564.0	−0.512201
$58$	0	0
$59$	−20133.0	−0.752971	−0.376486	−	0.926422i	$-0.622868\pi$
$59$	−20133.0	−0.752971	−0.376486	+	0.926422i	$0.622868\pi$
$60$	0	0
$61$	34646.0	1.19214	0.596072	−	0.802931i	$-0.296727\pi$
$61$	34646.0	1.19214	0.596072	+	0.802931i	$0.296727\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	276.000	0.00810262
$66$	0	0
$67$	−41386.0	−1.12633	−0.563166	−	0.826344i	$-0.690417\pi$
$67$	−41386.0	−1.12633	−0.563166	+	0.826344i	$0.690417\pi$
$68$	0	0
$69$	−13824.0	−0.349551
$70$	0	0
$71$	30762.0	0.724217	0.362108	−	0.932136i	$-0.382057\pi$
$71$	30762.0	0.724217	0.362108	+	0.932136i	$0.382057\pi$
$72$	0	0
$73$	−80254.0	−1.76262	−0.881312	−	0.472535i	$-0.843339\pi$
$73$	−80254.0	−1.76262	−0.881312	+	0.472535i	$0.843339\pi$
$74$	0	0
$75$	14724.0	0.302254
$76$	0	0
$77$	0	0
$78$	0	0
$79$	−98593.0	−1.77737	−0.888686	−	0.458516i	$-0.848381\pi$
$79$	−98593.0	−1.77737	−0.888686	+	0.458516i	$0.848381\pi$
$80$	0	0
$81$	6561.00	0.111111
$82$	0	0
$83$	73407.0	1.16961	0.584807	−	0.811173i	$-0.301170\pi$
$83$	73407.0	1.16961	0.584807	+	0.811173i	$0.301170\pi$
$84$	0	0
$85$	−122544.	−1.83969
$86$	0	0
$87$	−32535.0	−0.460843
$88$	0	0
$89$	−106554.	−1.42592	−0.712959	−	0.701205i	$-0.752646\pi$
$89$	−106554.	−1.42592	−0.712959	+	0.701205i	$0.752646\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	65655.0	0.787155
$94$	0	0
$95$	96324.0	1.09503
$96$	0	0
$97$	−161185.	−1.73938	−0.869692	−	0.493595i	$-0.835682\pi$
$97$	−161185.	−1.73938	−0.869692	+	0.493595i	$0.835682\pi$
$98$	0	0
$99$	9963.00	0.102165
$100$	0	0
$101$	−69474.0	−0.677671	−0.338835	−	0.940846i	$-0.610033\pi$
$101$	−69474.0	−0.677671	−0.338835	+	0.940846i	$0.610033\pi$
$102$	0	0
$103$	36104.0	0.335322	0.167661	−	0.985845i	$-0.446379\pi$
$103$	36104.0	0.335322	0.167661	+	0.985845i	$0.446379\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−207291.	−1.75033	−0.875167	−	0.483821i	$-0.839249\pi$
$107$	−207291.	−1.75033	−0.875167	+	0.483821i	$0.839249\pi$
$108$	0	0
$109$	−2962.00	−0.0238791	−0.0119396	−	0.999929i	$-0.503801\pi$
$109$	−2962.00	−0.0238791	−0.0119396	+	0.999929i	$0.503801\pi$
$110$	0	0
$111$	68760.0	0.529698
$112$	0	0
$113$	−97104.0	−0.715387	−0.357693	−	0.933839i	$-0.616437\pi$
$113$	−97104.0	−0.715387	−0.357693	+	0.933839i	$0.616437\pi$
$114$	0	0
$115$	105984.	0.747301
$116$	0	0
$117$	−324.000	−0.00218817
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−145922.	−0.906061
$122$	0	0
$123$	90288.0	0.538105
$124$	0	0
$125$	102741.	0.588124
$126$	0	0
$127$	26981.0	0.148439	0.0742196	−	0.997242i	$-0.476353\pi$
$127$	26981.0	0.148439	0.0742196	+	0.997242i	$0.476353\pi$
$128$	0	0
$129$	−87786.0	−0.464463
$130$	0	0
$131$	308127.	1.56874	0.784371	−	0.620292i	$-0.212986\pi$
$131$	308127.	1.56874	0.784371	+	0.620292i	$0.212986\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	−50301.0	−0.237543
$136$	0	0
$137$	−196734.	−0.895526	−0.447763	−	0.894152i	$-0.647779\pi$
$137$	−196734.	−0.895526	−0.447763	+	0.894152i	$0.647779\pi$
$138$	0	0
$139$	182642.	0.801796	0.400898	−	0.916123i	$-0.368698\pi$
$139$	182642.	0.801796	0.400898	+	0.916123i	$0.368698\pi$
$140$	0	0
$141$	−158598.	−0.671815
$142$	0	0
$143$	−492.000	−0.00201199
$144$	0	0
$145$	249435.	0.985229
$146$	0	0
$147$	0	0
$148$	0	0
$149$	356322.	1.31485	0.657426	−	0.753519i	$-0.271645\pi$
$149$	356322.	1.31485	0.657426	+	0.753519i	$0.271645\pi$
$150$	0	0
$151$	−426001.	−1.52044	−0.760218	−	0.649668i	$-0.774908\pi$
$151$	−426001.	−1.52044	−0.760218	+	0.649668i	$0.774908\pi$
$152$	0	0
$153$	143856.	0.496820
$154$	0	0
$155$	−503355.	−1.68285
$156$	0	0
$157$	−163972.	−0.530910	−0.265455	−	0.964123i	$-0.585522\pi$
$157$	−163972.	−0.530910	−0.265455	+	0.964123i	$0.585522\pi$
$158$	0	0
$159$	37773.0	0.118492
$160$	0	0
$161$	0	0
$162$	0	0
$163$	−326608.	−0.962848	−0.481424	−	0.876488i	$-0.659880\pi$
$163$	−326608.	−0.962848	−0.481424	+	0.876488i	$0.659880\pi$
$164$	0	0
$165$	−76383.0	−0.218417
$166$	0	0
$167$	261942.	0.726798	0.363399	−	0.931634i	$-0.381616\pi$
$167$	261942.	0.726798	0.363399	+	0.931634i	$0.381616\pi$
$168$	0	0
$169$	−371277.	−0.999957
$170$	0	0
$171$	−113076.	−0.295720
$172$	0	0
$173$	408834.	1.03856	0.519280	−	0.854604i	$-0.326200\pi$
$173$	408834.	1.03856	0.519280	+	0.854604i	$0.326200\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−181197.	−0.434728
$178$	0	0
$179$	−298356.	−0.695989	−0.347994	−	0.937497i	$-0.613137\pi$
$179$	−298356.	−0.695989	−0.347994	+	0.937497i	$0.613137\pi$
$180$	0	0
$181$	103832.	0.235578	0.117789	−	0.993039i	$-0.462419\pi$
$181$	103832.	0.235578	0.117789	+	0.993039i	$0.462419\pi$
$182$	0	0
$183$	311814.	0.688284
$184$	0	0
$185$	−527160.	−1.13243
$186$	0	0
$187$	218448.	0.456819
$188$	0	0
$189$	0	0
$190$	0	0
$191$	315360.	0.625494	0.312747	−	0.949836i	$-0.398751\pi$
$191$	315360.	0.625494	0.312747	+	0.949836i	$0.398751\pi$
$192$	0	0
$193$	248333.	0.479889	0.239945	−	0.970787i	$-0.422871\pi$
$193$	248333.	0.479889	0.239945	+	0.970787i	$0.422871\pi$
$194$	0	0
$195$	2484.00	0.00467805
$196$	0	0
$197$	−394218.	−0.723721	−0.361860	−	0.932232i	$-0.617858\pi$
$197$	−394218.	−0.723721	−0.361860	+	0.932232i	$0.617858\pi$
$198$	0	0
$199$	−671596.	−1.20220	−0.601098	−	0.799175i	$-0.705270\pi$
$199$	−671596.	−1.20220	−0.601098	+	0.799175i	$0.705270\pi$
$200$	0	0
$201$	−372474.	−0.650288
$202$	0	0
$203$	0	0
$204$	0	0
$205$	−692208.	−1.15041
$206$	0	0
$207$	−124416.	−0.201814
$208$	0	0
$209$	−171708.	−0.271910
$210$	0	0
$211$	−511858.	−0.791486	−0.395743	−	0.918361i	$-0.629513\pi$
$211$	−511858.	−0.791486	−0.395743	+	0.918361i	$0.629513\pi$
$212$	0	0
$213$	276858.	0.418127
$214$	0	0
$215$	673026.	0.992969
$216$	0	0
$217$	0	0
$218$	0	0
$219$	−722286.	−1.01765
$220$	0	0
$221$	−7104.00	−0.00978413
$222$	0	0
$223$	808205.	1.08833	0.544163	−	0.838979i	$-0.316847\pi$
$223$	808205.	1.08833	0.544163	+	0.838979i	$0.316847\pi$
$224$	0	0
$225$	132516.	0.174507
$226$	0	0
$227$	190653.	0.245572	0.122786	−	0.992433i	$-0.460817\pi$
$227$	190653.	0.245572	0.122786	+	0.992433i	$0.460817\pi$
$228$	0	0
$229$	−992884.	−1.25115	−0.625576	−	0.780164i	$-0.715136\pi$
$229$	−992884.	−1.25115	−0.625576	+	0.780164i	$0.715136\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−1.20439e6	−1.45338	−0.726688	−	0.686968i	$-0.758941\pi$
$233$	−1.20439e6	−1.45338	−0.726688	+	0.686968i	$0.758941\pi$
$234$	0	0
$235$	1.21592e6	1.43627
$236$	0	0
$237$	−887337.	−1.02617
$238$	0	0
$239$	−1.63970e6	−1.85682	−0.928412	−	0.371553i	$-0.878826\pi$
$239$	−1.63970e6	−1.85682	−0.928412	+	0.371553i	$0.878826\pi$
$240$	0	0
$241$	−1.58563e6	−1.75857	−0.879286	−	0.476294i	$-0.841980\pi$
$241$	−1.58563e6	−1.75857	−0.879286	+	0.476294i	$0.841980\pi$
$242$	0	0
$243$	59049.0	0.0641500
$244$	0	0
$245$	0	0
$246$	0	0
$247$	5584.00	0.00582375
$248$	0	0
$249$	660663.	0.675276
$250$	0	0
$251$	−1.18862e6	−1.19086	−0.595428	−	0.803409i	$-0.703017\pi$
$251$	−1.18862e6	−1.19086	−0.595428	+	0.803409i	$0.703017\pi$
$252$	0	0
$253$	−188928.	−0.185565
$254$	0	0
$255$	−1.10290e6	−1.06215
$256$	0	0
$257$	−878586.	−0.829758	−0.414879	−	0.909877i	$-0.636176\pi$
$257$	−878586.	−0.829758	−0.414879	+	0.909877i	$0.636176\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−292815.	−0.266068
$262$	0	0
$263$	118842.	0.105945	0.0529725	−	0.998596i	$-0.483130\pi$
$263$	118842.	0.105945	0.0529725	+	0.998596i	$0.483130\pi$
$264$	0	0
$265$	−289593.	−0.253322
$266$	0	0
$267$	−958986.	−0.823255
$268$	0	0
$269$	304077.	0.256214	0.128107	−	0.991760i	$-0.459110\pi$
$269$	304077.	0.256214	0.128107	+	0.991760i	$0.459110\pi$
$270$	0	0
$271$	−128725.	−0.106473	−0.0532365	−	0.998582i	$-0.516954\pi$
$271$	−128725.	−0.106473	−0.0532365	+	0.998582i	$0.516954\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	201228.	0.160456
$276$	0	0
$277$	59240.0	0.0463891	0.0231945	−	0.999731i	$-0.492616\pi$
$277$	59240.0	0.0463891	0.0231945	+	0.999731i	$0.492616\pi$
$278$	0	0
$279$	590895.	0.454464
$280$	0	0
$281$	1.24959e6	0.944065	0.472032	−	0.881581i	$-0.343521\pi$
$281$	1.24959e6	0.944065	0.472032	+	0.881581i	$0.343521\pi$
$282$	0	0
$283$	64670.0	0.0479995	0.0239998	−	0.999712i	$-0.492360\pi$
$283$	64670.0	0.0479995	0.0239998	+	0.999712i	$0.492360\pi$
$284$	0	0
$285$	866916.	0.632215
$286$	0	0
$287$	0	0
$288$	0	0
$289$	1.73432e6	1.22147
$290$	0	0
$291$	−1.45066e6	−1.00423
$292$	0	0
$293$	2.77498e6	1.88839	0.944195	−	0.329388i	$-0.106842\pi$
$293$	2.77498e6	1.88839	0.944195	+	0.329388i	$0.106842\pi$
$294$	0	0
$295$	1.38918e6	0.929400
$296$	0	0
$297$	89667.0	0.0589850
$298$	0	0
$299$	6144.00	0.00397442
$300$	0	0
$301$	0	0
$302$	0	0
$303$	−625266.	−0.391254
$304$	0	0
$305$	−2.39057e6	−1.47147
$306$	0	0
$307$	−201304.	−0.121901	−0.0609504	−	0.998141i	$-0.519413\pi$
$307$	−201304.	−0.121901	−0.0609504	+	0.998141i	$0.519413\pi$
$308$	0	0
$309$	324936.	0.193598
$310$	0	0
$311$	1.61950e6	0.949465	0.474732	−	0.880130i	$-0.342545\pi$
$311$	1.61950e6	0.949465	0.474732	+	0.880130i	$0.342545\pi$
$312$	0	0
$313$	1.34661e6	0.776928	0.388464	−	0.921464i	$-0.373006\pi$
$313$	1.34661e6	0.776928	0.388464	+	0.921464i	$0.373006\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	1.18592e6	0.662838	0.331419	−	0.943484i	$-0.392473\pi$
$317$	1.18592e6	0.662838	0.331419	+	0.943484i	$0.392473\pi$
$318$	0	0
$319$	−444645.	−0.244645
$320$	0	0
$321$	−1.86562e6	−1.01056
$322$	0	0
$323$	−2.47930e6	−1.32228
$324$	0	0
$325$	−6544.00	−0.00343665
$326$	0	0
$327$	−26658.0	−0.0137866
$328$	0	0
$329$	0	0
$330$	0	0
$331$	3.28380e6	1.64743	0.823714	−	0.567006i	$-0.191898\pi$
$331$	3.28380e6	1.64743	0.823714	+	0.567006i	$0.191898\pi$
$332$	0	0
$333$	618840.	0.305821
$334$	0	0
$335$	2.85563e6	1.39024
$336$	0	0
$337$	−803047.	−0.385182	−0.192591	−	0.981279i	$-0.561689\pi$
$337$	−803047.	−0.385182	−0.192591	+	0.981279i	$0.561689\pi$
$338$	0	0
$339$	−873936.	−0.413029
$340$	0	0
$341$	897285.	0.417873
$342$	0	0
$343$	0	0
$344$	0	0
$345$	953856.	0.431455
$346$	0	0
$347$	1.00292e6	0.447141	0.223570	−	0.974688i	$-0.428229\pi$
$347$	1.00292e6	0.447141	0.223570	+	0.974688i	$0.428229\pi$
$348$	0	0
$349$	−547078.	−0.240428	−0.120214	−	0.992748i	$-0.538358\pi$
$349$	−547078.	−0.240428	−0.120214	+	0.992748i	$0.538358\pi$
$350$	0	0
$351$	−2916.00	−0.00126334
$352$	0	0
$353$	4.05276e6	1.73107	0.865534	−	0.500850i	$-0.166979\pi$
$353$	4.05276e6	1.73107	0.865534	+	0.500850i	$0.166979\pi$
$354$	0	0
$355$	−2.12258e6	−0.893908
$356$	0	0
$357$	0	0
$358$	0	0
$359$	664206.	0.271999	0.135999	−	0.990709i	$-0.456576\pi$
$359$	664206.	0.271999	0.135999	+	0.990709i	$0.456576\pi$
$360$	0	0
$361$	−527283.	−0.212949
$362$	0	0
$363$	−1.31330e6	−0.523114
$364$	0	0
$365$	5.53753e6	2.17562
$366$	0	0
$367$	−300499.	−0.116460	−0.0582301	−	0.998303i	$-0.518546\pi$
$367$	−300499.	−0.116460	−0.0582301	+	0.998303i	$0.518546\pi$
$368$	0	0
$369$	812592.	0.310675
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−4.41940e6	−1.64472	−0.822359	−	0.568970i	$-0.807342\pi$
$373$	−4.41940e6	−1.64472	−0.822359	+	0.568970i	$0.807342\pi$
$374$	0	0
$375$	924669.	0.339553
$376$	0	0
$377$	14460.0	0.00523980
$378$	0	0
$379$	2.45794e6	0.878970	0.439485	−	0.898250i	$-0.355161\pi$
$379$	2.45794e6	0.878970	0.439485	+	0.898250i	$0.355161\pi$
$380$	0	0
$381$	242829.	0.0857014
$382$	0	0
$383$	−4.36645e6	−1.52101	−0.760503	−	0.649334i	$-0.775048\pi$
$383$	−4.36645e6	−1.52101	−0.760503	+	0.649334i	$0.775048\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−790074.	−0.268158
$388$	0	0
$389$	2.68305e6	0.898990	0.449495	−	0.893283i	$-0.351604\pi$
$389$	2.68305e6	0.898990	0.449495	+	0.893283i	$0.351604\pi$
$390$	0	0
$391$	−2.72794e6	−0.902386
$392$	0	0
$393$	2.77314e6	0.905714
$394$	0	0
$395$	6.80292e6	2.19383
$396$	0	0
$397$	3.57744e6	1.13919	0.569594	−	0.821926i	$-0.307100\pi$
$397$	3.57744e6	1.13919	0.569594	+	0.821926i	$0.307100\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	5.08447e6	1.57901	0.789505	−	0.613744i	$-0.210337\pi$
$401$	5.08447e6	1.57901	0.789505	+	0.613744i	$0.210337\pi$
$402$	0	0
$403$	−29180.0	−0.00894999
$404$	0	0
$405$	−452709.	−0.137146
$406$	0	0
$407$	939720.	0.281198
$408$	0	0
$409$	2.40338e6	0.710419	0.355210	−	0.934787i	$-0.384409\pi$
$409$	2.40338e6	0.710419	0.355210	+	0.934787i	$0.384409\pi$
$410$	0	0
$411$	−1.77061e6	−0.517032
$412$	0	0
$413$	0	0
$414$	0	0
$415$	−5.06508e6	−1.44366
$416$	0	0
$417$	1.64378e6	0.462917
$418$	0	0
$419$	−1.02058e6	−0.283995	−0.141997	−	0.989867i	$-0.545352\pi$
$419$	−1.02058e6	−0.283995	−0.141997	+	0.989867i	$0.545352\pi$
$420$	0	0
$421$	1.78337e6	0.490384	0.245192	−	0.969475i	$-0.421149\pi$
$421$	1.78337e6	0.490384	0.245192	+	0.969475i	$0.421149\pi$
$422$	0	0
$423$	−1.42738e6	−0.387873
$424$	0	0
$425$	2.90554e6	0.780286
$426$	0	0
$427$	0	0
$428$	0	0
$429$	−4428.00	−0.00116162
$430$	0	0
$431$	−3.73722e6	−0.969071	−0.484535	−	0.874772i	$-0.661011\pi$
$431$	−3.73722e6	−0.969071	−0.484535	+	0.874772i	$0.661011\pi$
$432$	0	0
$433$	−5.11914e6	−1.31213	−0.656065	−	0.754704i	$-0.727780\pi$
$433$	−5.11914e6	−1.31213	−0.656065	+	0.754704i	$0.727780\pi$
$434$	0	0
$435$	2.24492e6	0.568822
$436$	0	0
$437$	2.14426e6	0.537122
$438$	0	0
$439$	−4.46920e6	−1.10680	−0.553399	−	0.832916i	$-0.686669\pi$
$439$	−4.46920e6	−1.10680	−0.553399	+	0.832916i	$0.686669\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	3.19535e6	0.773587	0.386794	−	0.922166i	$-0.373583\pi$
$443$	3.19535e6	0.773587	0.386794	+	0.922166i	$0.373583\pi$
$444$	0	0
$445$	7.35223e6	1.76002
$446$	0	0
$447$	3.20690e6	0.759130
$448$	0	0
$449$	1.36033e6	0.318441	0.159221	−	0.987243i	$-0.449102\pi$
$449$	1.36033e6	0.318441	0.159221	+	0.987243i	$0.449102\pi$
$450$	0	0
$451$	1.23394e6	0.285661
$452$	0	0
$453$	−3.83401e6	−0.877824
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−101329.	−0.0226957	−0.0113478	−	0.999936i	$-0.503612\pi$
$457$	−101329.	−0.0226957	−0.0113478	+	0.999936i	$0.503612\pi$
$458$	0	0
$459$	1.29470e6	0.286839
$460$	0	0
$461$	−1.22239e6	−0.267890	−0.133945	−	0.990989i	$-0.542765\pi$
$461$	−1.22239e6	−0.267890	−0.133945	+	0.990989i	$0.542765\pi$
$462$	0	0
$463$	8.33742e6	1.80750	0.903751	−	0.428058i	$-0.140802\pi$
$463$	8.33742e6	1.80750	0.903751	+	0.428058i	$0.140802\pi$
$464$	0	0
$465$	−4.53020e6	−0.971593
$466$	0	0
$467$	−720156.	−0.152804	−0.0764019	−	0.997077i	$-0.524343\pi$
$467$	−720156.	−0.152804	−0.0764019	+	0.997077i	$0.524343\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	−1.47575e6	−0.306521
$472$	0	0
$473$	−1.19974e6	−0.246567
$474$	0	0
$475$	−2.28386e6	−0.464445
$476$	0	0
$477$	339957.	0.0684113
$478$	0	0
$479$	−1.24610e6	−0.248150	−0.124075	−	0.992273i	$-0.539596\pi$
$479$	−1.24610e6	−0.248150	−0.124075	+	0.992273i	$0.539596\pi$
$480$	0	0
$481$	−30560.0	−0.00602269
$482$	0	0
$483$	0	0
$484$	0	0
$485$	1.11218e7	2.14694
$486$	0	0
$487$	−8.16097e6	−1.55926	−0.779631	−	0.626239i	$-0.784593\pi$
$487$	−8.16097e6	−1.55926	−0.779631	+	0.626239i	$0.784593\pi$
$488$	0	0
$489$	−2.93947e6	−0.555901
$490$	0	0
$491$	−8.86743e6	−1.65995	−0.829973	−	0.557803i	$-0.811644\pi$
$491$	−8.86743e6	−1.65995	−0.829973	+	0.557803i	$0.811644\pi$
$492$	0	0
$493$	−6.42024e6	−1.18969
$494$	0	0
$495$	−687447.	−0.126103
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−2.31979e6	−0.417059	−0.208529	−	0.978016i	$-0.566868\pi$
$499$	−2.31979e6	−0.417059	−0.208529	+	0.978016i	$0.566868\pi$
$500$	0	0
$501$	2.35748e6	0.419617
$502$	0	0
$503$	8.49978e6	1.49792	0.748958	−	0.662617i	$-0.230554\pi$
$503$	8.49978e6	1.49792	0.748958	+	0.662617i	$0.230554\pi$
$504$	0	0
$505$	4.79371e6	0.836456
$506$	0	0
$507$	−3.34149e6	−0.577325
$508$	0	0
$509$	6.49298e6	1.11084	0.555418	−	0.831572i	$-0.312558\pi$
$509$	6.49298e6	1.11084	0.555418	+	0.831572i	$0.312558\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	−1.01768e6	−0.170734
$514$	0	0
$515$	−2.49118e6	−0.413891
$516$	0	0
$517$	−2.16751e6	−0.356643
$518$	0	0
$519$	3.67951e6	0.599613
$520$	0	0
$521$	7.13365e6	1.15138	0.575688	−	0.817669i	$-0.304734\pi$
$521$	7.13365e6	1.15138	0.575688	+	0.817669i	$0.304734\pi$
$522$	0	0
$523$	−9.47732e6	−1.51506	−0.757532	−	0.652798i	$-0.773595\pi$
$523$	−9.47732e6	−1.51506	−0.757532	+	0.652798i	$0.773595\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	1.29559e7	2.03208
$528$	0	0
$529$	−4.07705e6	−0.633442
$530$	0	0
$531$	−1.63077e6	−0.250990
$532$	0	0
$533$	−40128.0	−0.00611828
$534$	0	0
$535$	1.43031e7	2.16045
$536$	0	0
$537$	−2.68520e6	−0.401829
$538$	0	0
$539$	0	0
$540$	0	0
$541$	788714.	0.115858	0.0579290	−	0.998321i	$-0.481550\pi$
$541$	788714.	0.115858	0.0579290	+	0.998321i	$0.481550\pi$
$542$	0	0
$543$	934488.	0.136011
$544$	0	0
$545$	204378.	0.0294743
$546$	0	0
$547$	671288.	0.0959269	0.0479635	−	0.998849i	$-0.484727\pi$
$547$	671288.	0.0959269	0.0479635	+	0.998849i	$0.484727\pi$
$548$	0	0
$549$	2.80633e6	0.397381
$550$	0	0
$551$	5.04654e6	0.708133
$552$	0	0
$553$	0	0
$554$	0	0
$555$	−4.74444e6	−0.653811
$556$	0	0
$557$	3.83364e6	0.523569	0.261784	−	0.965126i	$-0.415689\pi$
$557$	3.83364e6	0.523569	0.261784	+	0.965126i	$0.415689\pi$
$558$	0	0
$559$	39016.0	0.00528096
$560$	0	0
$561$	1.96603e6	0.263745
$562$	0	0
$563$	1.05975e7	1.40906	0.704532	−	0.709672i	$-0.251157\pi$
$563$	1.05975e7	1.40906	0.704532	+	0.709672i	$0.251157\pi$
$564$	0	0
$565$	6.70018e6	0.883009
$566$	0	0
$567$	0	0
$568$	0	0
$569$	8.14676e6	1.05488	0.527442	−	0.849591i	$-0.323151\pi$
$569$	8.14676e6	1.05488	0.527442	+	0.849591i	$0.323151\pi$
$570$	0	0
$571$	1.02484e7	1.31542	0.657709	−	0.753272i	$-0.271526\pi$
$571$	1.02484e7	1.31542	0.657709	+	0.753272i	$0.271526\pi$
$572$	0	0
$573$	2.83824e6	0.361129
$574$	0	0
$575$	−2.51290e6	−0.316960
$576$	0	0
$577$	−1.08217e7	−1.35318	−0.676589	−	0.736361i	$-0.736543\pi$
$577$	−1.08217e7	−1.35318	−0.676589	+	0.736361i	$0.736543\pi$
$578$	0	0
$579$	2.23500e6	0.277064
$580$	0	0
$581$	0	0
$582$	0	0
$583$	516231.	0.0629032
$584$	0	0
$585$	22356.0	0.00270087
$586$	0	0
$587$	−114531.	−0.0137192	−0.00685958	−	0.999976i	$-0.502183\pi$
$587$	−114531.	−0.0137192	−0.00685958	+	0.999976i	$0.502183\pi$
$588$	0	0
$589$	−1.01838e7	−1.20955
$590$	0	0
$591$	−3.54796e6	−0.417840
$592$	0	0
$593$	−1.46926e7	−1.71578	−0.857890	−	0.513834i	$-0.828225\pi$
$593$	−1.46926e7	−1.71578	−0.857890	+	0.513834i	$0.828225\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−6.04436e6	−0.694088
$598$	0	0
$599$	−1.06452e7	−1.21224	−0.606118	−	0.795374i	$-0.707274\pi$
$599$	−1.06452e7	−1.21224	−0.606118	+	0.795374i	$0.707274\pi$
$600$	0	0
$601$	−961477.	−0.108581	−0.0542904	−	0.998525i	$-0.517290\pi$
$601$	−961477.	−0.108581	−0.0542904	+	0.998525i	$0.517290\pi$
$602$	0	0
$603$	−3.35227e6	−0.375444
$604$	0	0
$605$	1.00686e7	1.11836
$606$	0	0
$607$	−6.48471e6	−0.714363	−0.357181	−	0.934035i	$-0.616262\pi$
$607$	−6.48471e6	−0.714363	−0.357181	+	0.934035i	$0.616262\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	70488.0	0.00763857
$612$	0	0
$613$	1.45529e7	1.56422	0.782112	−	0.623138i	$-0.214143\pi$
$613$	1.45529e7	1.56422	0.782112	+	0.623138i	$0.214143\pi$
$614$	0	0
$615$	−6.22987e6	−0.664188
$616$	0	0
$617$	−8.32057e6	−0.879913	−0.439957	−	0.898019i	$-0.645006\pi$
$617$	−8.32057e6	−0.879913	−0.439957	+	0.898019i	$0.645006\pi$
$618$	0	0
$619$	−1.28258e7	−1.34542	−0.672711	−	0.739905i	$-0.734870\pi$
$619$	−1.28258e7	−1.34542	−0.672711	+	0.739905i	$0.734870\pi$
$620$	0	0
$621$	−1.11974e6	−0.116517
$622$	0	0
$623$	0	0
$624$	0	0
$625$	−1.22016e7	−1.24945
$626$	0	0
$627$	−1.54537e6	−0.156987
$628$	0	0
$629$	1.35686e7	1.36744
$630$	0	0
$631$	−1.01905e7	−1.01887	−0.509437	−	0.860508i	$-0.670146\pi$
$631$	−1.01905e7	−1.01887	−0.509437	+	0.860508i	$0.670146\pi$
$632$	0	0
$633$	−4.60672e6	−0.456965
$634$	0	0
$635$	−1.86169e6	−0.183220
$636$	0	0
$637$	0	0
$638$	0	0
$639$	2.49172e6	0.241406
$640$	0	0
$641$	1.42014e7	1.36517	0.682584	−	0.730807i	$-0.260856\pi$
$641$	1.42014e7	1.36517	0.682584	+	0.730807i	$0.260856\pi$
$642$	0	0
$643$	−4.21242e6	−0.401795	−0.200897	−	0.979612i	$-0.564386\pi$
$643$	−4.21242e6	−0.401795	−0.200897	+	0.979612i	$0.564386\pi$
$644$	0	0
$645$	6.05723e6	0.573291
$646$	0	0
$647$	6.85645e6	0.643930	0.321965	−	0.946752i	$-0.395657\pi$
$647$	6.85645e6	0.643930	0.321965	+	0.946752i	$0.395657\pi$
$648$	0	0
$649$	−2.47636e6	−0.230782
$650$	0	0
$651$	0	0
$652$	0	0
$653$	−1.87954e7	−1.72492	−0.862458	−	0.506128i	$-0.831076\pi$
$653$	−1.87954e7	−1.72492	−0.862458	+	0.506128i	$0.831076\pi$
$654$	0	0
$655$	−2.12608e7	−1.93631
$656$	0	0
$657$	−6.50057e6	−0.587541
$658$	0	0
$659$	6.15770e6	0.552338	0.276169	−	0.961109i	$-0.410935\pi$
$659$	6.15770e6	0.552338	0.276169	+	0.961109i	$0.410935\pi$
$660$	0	0
$661$	−8.93533e6	−0.795439	−0.397720	−	0.917507i	$-0.630198\pi$
$661$	−8.93533e6	−0.795439	−0.397720	+	0.917507i	$0.630198\pi$
$662$	0	0
$663$	−63936.0	−0.00564887
$664$	0	0
$665$	0	0
$666$	0	0
$667$	5.55264e6	0.483265
$668$	0	0
$669$	7.27385e6	0.628346
$670$	0	0
$671$	4.26146e6	0.365386
$672$	0	0
$673$	1.67282e7	1.42368	0.711840	−	0.702342i	$-0.247862\pi$
$673$	1.67282e7	1.42368	0.711840	+	0.702342i	$0.247862\pi$
$674$	0	0
$675$	1.19264e6	0.100751
$676$	0	0
$677$	2.26083e7	1.89581	0.947907	−	0.318547i	$-0.103195\pi$
$677$	2.26083e7	1.89581	0.947907	+	0.318547i	$0.103195\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	1.71588e6	0.141781
$682$	0	0
$683$	−2.36947e7	−1.94357	−0.971784	−	0.235873i	$-0.924205\pi$
$683$	−2.36947e7	−1.94357	−0.971784	+	0.235873i	$0.924205\pi$
$684$	0	0
$685$	1.35746e7	1.10536
$686$	0	0
$687$	−8.93596e6	−0.722352
$688$	0	0
$689$	−16788.0	−0.00134726
$690$	0	0
$691$	2.22901e7	1.77589	0.887947	−	0.459946i	$-0.152131\pi$
$691$	2.22901e7	1.77589	0.887947	+	0.459946i	$0.152131\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	−1.26023e7	−0.989664
$696$	0	0
$697$	1.78168e7	1.38915
$698$	0	0
$699$	−1.08395e7	−0.839107
$700$	0	0
$701$	−1.14094e7	−0.876936	−0.438468	−	0.898747i	$-0.644479\pi$
$701$	−1.14094e7	−0.876936	−0.438468	+	0.898747i	$0.644479\pi$
$702$	0	0
$703$	−1.06654e7	−0.813936
$704$	0	0
$705$	1.09433e7	0.829228
$706$	0	0
$707$	0	0
$708$	0	0
$709$	1.00221e7	0.748757	0.374379	−	0.927276i	$-0.377856\pi$
$709$	1.00221e7	0.748757	0.374379	+	0.927276i	$0.377856\pi$
$710$	0	0
$711$	−7.98603e6	−0.592457
$712$	0	0
$713$	−1.12051e7	−0.825454
$714$	0	0
$715$	33948.0	0.00248341
$716$	0	0
$717$	−1.47573e7	−1.07204
$718$	0	0
$719$	−1.10208e7	−0.795045	−0.397522	−	0.917592i	$-0.630130\pi$
$719$	−1.10208e7	−0.795045	−0.397522	+	0.917592i	$0.630130\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	−1.42707e7	−1.01531
$724$	0	0
$725$	−5.91414e6	−0.417875
$726$	0	0
$727$	5.53991e6	0.388746	0.194373	−	0.980928i	$-0.437733\pi$
$727$	5.53991e6	0.388746	0.194373	+	0.980928i	$0.437733\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	0	0
$731$	−1.73231e7	−1.19904
$732$	0	0
$733$	−8.13347e6	−0.559134	−0.279567	−	0.960126i	$-0.590191\pi$
$733$	−8.13347e6	−0.559134	−0.279567	+	0.960126i	$0.590191\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−5.09048e6	−0.345215
$738$	0	0
$739$	−9.62947e6	−0.648621	−0.324311	−	0.945951i	$-0.605132\pi$
$739$	−9.62947e6	−0.648621	−0.324311	+	0.945951i	$0.605132\pi$
$740$	0	0
$741$	50256.0	0.00336235
$742$	0	0
$743$	−9.84625e6	−0.654333	−0.327166	−	0.944967i	$-0.606094\pi$
$743$	−9.84625e6	−0.654333	−0.327166	+	0.944967i	$0.606094\pi$
$744$	0	0
$745$	−2.45862e7	−1.62293
$746$	0	0
$747$	5.94597e6	0.389871
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−3.11828e6	−0.201751	−0.100875	−	0.994899i	$-0.532164\pi$
$751$	−3.11828e6	−0.201751	−0.100875	+	0.994899i	$0.532164\pi$
$752$	0	0
$753$	−1.06976e7	−0.687541
$754$	0	0
$755$	2.93941e7	1.87669
$756$	0	0
$757$	−1.50476e6	−0.0954395	−0.0477197	−	0.998861i	$-0.515195\pi$
$757$	−1.50476e6	−0.0954395	−0.0477197	+	0.998861i	$0.515195\pi$
$758$	0	0
$759$	−1.70035e6	−0.107136
$760$	0	0
$761$	1.43614e7	0.898950	0.449475	−	0.893293i	$-0.351611\pi$
$761$	1.43614e7	0.898950	0.449475	+	0.893293i	$0.351611\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	−9.92606e6	−0.613230
$766$	0	0
$767$	80532.0	0.00494288
$768$	0	0
$769$	−1.03368e7	−0.630334	−0.315167	−	0.949036i	$-0.602061\pi$
$769$	−1.03368e7	−0.630334	−0.315167	+	0.949036i	$0.602061\pi$
$770$	0	0
$771$	−7.90727e6	−0.479061
$772$	0	0
$773$	−5.48615e6	−0.330232	−0.165116	−	0.986274i	$-0.552800\pi$
$773$	−5.48615e6	−0.330232	−0.165116	+	0.986274i	$0.552800\pi$
$774$	0	0
$775$	1.19346e7	0.713764
$776$	0	0
$777$	0	0
$778$	0	0
$779$	−1.40047e7	−0.826855
$780$	0	0
$781$	3.78373e6	0.221969
$782$	0	0
$783$	−2.63534e6	−0.153614
$784$	0	0
$785$	1.13141e7	0.655307
$786$	0	0
$787$	3.38827e6	0.195003	0.0975016	−	0.995235i	$-0.468915\pi$
$787$	3.38827e6	0.195003	0.0975016	+	0.995235i	$0.468915\pi$
$788$	0	0
$789$	1.06958e6	0.0611674
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−138584.	−0.00782582
$794$	0	0
$795$	−2.60634e6	−0.146256
$796$	0	0
$797$	7.52769e6	0.419774	0.209887	−	0.977726i	$-0.432690\pi$
$797$	7.52769e6	0.419774	0.209887	+	0.977726i	$0.432690\pi$
$798$	0	0
$799$	−3.12967e7	−1.73433
$800$	0	0
$801$	−8.63087e6	−0.475306
$802$	0	0
$803$	−9.87124e6	−0.540235
$804$	0	0
$805$	0	0
$806$	0	0
$807$	2.73669e6	0.147925
$808$	0	0
$809$	2.44330e6	0.131252	0.0656258	−	0.997844i	$-0.479096\pi$
$809$	2.44330e6	0.131252	0.0656258	+	0.997844i	$0.479096\pi$
$810$	0	0
$811$	1.29082e6	0.0689149	0.0344574	−	0.999406i	$-0.489030\pi$
$811$	1.29082e6	0.0689149	0.0344574	+	0.999406i	$0.489030\pi$
$812$	0	0
$813$	−1.15852e6	−0.0614722
$814$	0	0
$815$	2.25360e7	1.18845
$816$	0	0
$817$	1.36166e7	0.713696
$818$	0	0
$819$	0	0
$820$	0	0
$821$	2.80264e7	1.45114	0.725570	−	0.688148i	$-0.241576\pi$
$821$	2.80264e7	1.45114	0.725570	+	0.688148i	$0.241576\pi$
$822$	0	0
$823$	2.13490e7	1.09870	0.549349	−	0.835593i	$-0.314876\pi$
$823$	2.13490e7	1.09870	0.549349	+	0.835593i	$0.314876\pi$
$824$	0	0
$825$	1.81105e6	0.0926395
$826$	0	0
$827$	−2.96302e7	−1.50650	−0.753252	−	0.657732i	$-0.771516\pi$
$827$	−2.96302e7	−1.50650	−0.753252	+	0.657732i	$0.771516\pi$
$828$	0	0
$829$	1.19123e7	0.602018	0.301009	−	0.953621i	$-0.402677\pi$
$829$	1.19123e7	0.602018	0.301009	+	0.953621i	$0.402677\pi$
$830$	0	0
$831$	533160.	0.0267827
$832$	0	0
$833$	0	0
$834$	0	0
$835$	−1.80740e7	−0.897094
$836$	0	0
$837$	5.31806e6	0.262385
$838$	0	0
$839$	7.78879e6	0.382002	0.191001	−	0.981590i	$-0.438827\pi$
$839$	7.78879e6	0.382002	0.191001	+	0.981590i	$0.438827\pi$
$840$	0	0
$841$	−7.44292e6	−0.362872
$842$	0	0
$843$	1.12463e7	0.545056
$844$	0	0
$845$	2.56181e7	1.23426
$846$	0	0
$847$	0	0
$848$	0	0
$849$	582030.	0.0277125
$850$	0	0
$851$	−1.17350e7	−0.555470
$852$	0	0
$853$	1.39100e7	0.654568	0.327284	−	0.944926i	$-0.393867\pi$
$853$	1.39100e7	0.654568	0.327284	+	0.944926i	$0.393867\pi$
$854$	0	0
$855$	7.80224e6	0.365010
$856$	0	0
$857$	1.96059e7	0.911874	0.455937	−	0.890012i	$-0.349304\pi$
$857$	1.96059e7	0.911874	0.455937	+	0.890012i	$0.349304\pi$
$858$	0	0
$859$	−3.12047e7	−1.44290	−0.721451	−	0.692465i	$-0.756525\pi$
$859$	−3.12047e7	−1.44290	−0.721451	+	0.692465i	$0.756525\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	1.80441e7	0.824722	0.412361	−	0.911021i	$-0.364704\pi$
$863$	1.80441e7	0.824722	0.412361	+	0.911021i	$0.364704\pi$
$864$	0	0
$865$	−2.82095e7	−1.28190
$866$	0	0
$867$	1.56089e7	0.705219
$868$	0	0
$869$	−1.21269e7	−0.544756
$870$	0	0
$871$	165544.	0.00739381
$872$	0	0
$873$	−1.30560e7	−0.579794
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−2.61508e7	−1.14811	−0.574057	−	0.818815i	$-0.694631\pi$
$877$	−2.61508e7	−1.14811	−0.574057	+	0.818815i	$0.694631\pi$
$878$	0	0
$879$	2.49749e7	1.09026
$880$	0	0
$881$	−2.61559e7	−1.13535	−0.567676	−	0.823252i	$-0.692157\pi$
$881$	−2.61559e7	−1.13535	−0.567676	+	0.823252i	$0.692157\pi$
$882$	0	0
$883$	−2.65758e6	−0.114706	−0.0573529	−	0.998354i	$-0.518266\pi$
$883$	−2.65758e6	−0.114706	−0.0573529	+	0.998354i	$0.518266\pi$
$884$	0	0
$885$	1.25026e7	0.536589
$886$	0	0
$887$	−2.14425e7	−0.915095	−0.457547	−	0.889185i	$-0.651272\pi$
$887$	−2.14425e7	−0.915095	−0.457547	+	0.889185i	$0.651272\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	807003.	0.0340550
$892$	0	0
$893$	2.46003e7	1.03231
$894$	0	0
$895$	2.05866e7	0.859066
$896$	0	0
$897$	55296.0	0.00229463
$898$	0	0
$899$	−2.63714e7	−1.08826
$900$	0	0
$901$	7.45387e6	0.305893
$902$	0	0
$903$	0	0
$904$	0	0
$905$	−7.16441e6	−0.290776
$906$	0	0
$907$	−7.20614e6	−0.290860	−0.145430	−	0.989369i	$-0.546457\pi$
$907$	−7.20614e6	−0.290860	−0.145430	+	0.989369i	$0.546457\pi$
$908$	0	0
$909$	−5.62739e6	−0.225890
$910$	0	0
$911$	−2.30069e7	−0.918465	−0.459232	−	0.888316i	$-0.651876\pi$
$911$	−2.30069e7	−0.918465	−0.459232	+	0.888316i	$0.651876\pi$
$912$	0	0
$913$	9.02906e6	0.358481
$914$	0	0
$915$	−2.15152e7	−0.849556
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−1.42540e7	−0.556733	−0.278367	−	0.960475i	$-0.589793\pi$
$919$	−1.42540e7	−0.556733	−0.278367	+	0.960475i	$0.589793\pi$
$920$	0	0
$921$	−1.81174e6	−0.0703794
$922$	0	0
$923$	−123048.	−0.00475412
$924$	0	0
$925$	1.24990e7	0.480311
$926$	0	0
$927$	2.92442e6	0.111774
$928$	0	0
$929$	3.39933e7	1.29227	0.646136	−	0.763222i	$-0.276384\pi$
$929$	3.39933e7	1.29227	0.646136	+	0.763222i	$0.276384\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	1.45755e7	0.548174
$934$	0	0
$935$	−1.50729e7	−0.563856
$936$	0	0
$937$	−2.48240e7	−0.923682	−0.461841	−	0.886963i	$-0.652811\pi$
$937$	−2.48240e7	−0.923682	−0.461841	+	0.886963i	$0.652811\pi$
$938$	0	0
$939$	1.21195e7	0.448559
$940$	0	0
$941$	−3.44410e7	−1.26795	−0.633974	−	0.773354i	$-0.718577\pi$
$941$	−3.44410e7	−1.26795	−0.633974	+	0.773354i	$0.718577\pi$
$942$	0	0
$943$	−1.54092e7	−0.564286
$944$	0	0
$945$	0	0
$946$	0	0
$947$	6.29539e6	0.228112	0.114056	−	0.993474i	$-0.463616\pi$
$947$	6.29539e6	0.228112	0.114056	+	0.993474i	$0.463616\pi$
$948$	0	0
$949$	321016.	0.0115707
$950$	0	0
$951$	1.06733e7	0.382690
$952$	0	0
$953$	−1.79299e7	−0.639508	−0.319754	−	0.947501i	$-0.603600\pi$
$953$	−1.79299e7	−0.639508	−0.319754	+	0.947501i	$0.603600\pi$
$954$	0	0
$955$	−2.17598e7	−0.772053
$956$	0	0
$957$	−4.00181e6	−0.141246
$958$	0	0
$959$	0	0
$960$	0	0
$961$	2.45879e7	0.858840
$962$	0	0
$963$	−1.67906e7	−0.583445
$964$	0	0
$965$	−1.71350e7	−0.592332
$966$	0	0
$967$	−3.86476e7	−1.32910	−0.664549	−	0.747245i	$-0.731376\pi$
$967$	−3.86476e7	−1.32910	−0.664549	+	0.747245i	$0.731376\pi$
$968$	0	0
$969$	−2.23137e7	−0.763416
$970$	0	0
$971$	−3.88650e7	−1.32285	−0.661425	−	0.750011i	$-0.730048\pi$
$971$	−3.88650e7	−1.32285	−0.661425	+	0.750011i	$0.730048\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	−58896.0	−0.00198415
$976$	0	0
$977$	7.30910e6	0.244978	0.122489	−	0.992470i	$-0.460912\pi$
$977$	7.30910e6	0.244978	0.122489	+	0.992470i	$0.460912\pi$
$978$	0	0
$979$	−1.31061e7	−0.437037
$980$	0	0
$981$	−239922.	−0.00795972
$982$	0	0
$983$	−3.04655e7	−1.00560	−0.502799	−	0.864403i	$-0.667697\pi$
$983$	−3.04655e7	−1.00560	−0.502799	+	0.864403i	$0.667697\pi$
$984$	0	0
$985$	2.72010e7	0.893295
$986$	0	0
$987$	0	0
$988$	0	0
$989$	1.49821e7	0.487061
$990$	0	0
$991$	−1.01573e7	−0.328544	−0.164272	−	0.986415i	$-0.552528\pi$
$991$	−1.01573e7	−0.328544	−0.164272	+	0.986415i	$0.552528\pi$
$992$	0	0
$993$	2.95542e7	0.951142
$994$	0	0
$995$	4.63401e7	1.48388
$996$	0	0
$997$	−3.57915e6	−0.114036	−0.0570181	−	0.998373i	$-0.518159\pi$
$997$	−3.57915e6	−0.114036	−0.0570181	+	0.998373i	$0.518159\pi$
$998$	0	0
$999$	5.56956e6	0.176566

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.6.a.d.1.1		1
7.2	even	3		84.6.i.a.25.1	✓	2
7.3	odd	6		588.6.i.d.373.1		2
7.4	even	3		84.6.i.a.37.1	yes	2
7.5	odd	6		588.6.i.d.361.1		2
7.6	odd	2		588.6.a.c.1.1		1
21.2	odd	6		252.6.k.a.109.1		2
21.11	odd	6		252.6.k.a.37.1		2
28.11	odd	6		336.6.q.d.289.1		2
28.23	odd	6		336.6.q.d.193.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.6.i.a.25.1	✓	2	7.2	even	3
84.6.i.a.37.1	yes	2	7.4	even	3
252.6.k.a.37.1		2	21.11	odd	6
252.6.k.a.109.1		2	21.2	odd	6
336.6.q.d.193.1		2	28.23	odd	6
336.6.q.d.289.1		2	28.11	odd	6
588.6.a.c.1.1		1	7.6	odd	2
588.6.a.d.1.1		1	1.1	even	1	trivial
588.6.i.d.361.1		2	7.5	odd	6
588.6.i.d.373.1		2	7.3	odd	6

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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	588.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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