LMFDB - Embedded newform 585.6.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,6,Mod(1,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, 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("585.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	585.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:	$93.8245345906$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	585.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

\(q-2.00000 q^{2} -28.0000 q^{4} -25.0000 q^{5} -168.000 q^{7} +120.000 q^{8} +50.0000 q^{10} -52.0000 q^{11} +169.000 q^{13} +336.000 q^{14} +656.000 q^{16} -1322.00 q^{17} +1700.00 q^{19} +700.000 q^{20} +104.000 q^{22} -1856.00 q^{23} +625.000 q^{25} -338.000 q^{26} +4704.00 q^{28} +4250.00 q^{29} +7192.00 q^{31} -5152.00 q^{32} +2644.00 q^{34} +4200.00 q^{35} -2298.00 q^{37} -3400.00 q^{38} -3000.00 q^{40} +6438.00 q^{41} +18956.0 q^{43} +1456.00 q^{44} +3712.00 q^{46} +968.000 q^{47} +11417.0 q^{49} -1250.00 q^{50} -4732.00 q^{52} -15366.0 q^{53} +1300.00 q^{55} -20160.0 q^{56} -8500.00 q^{58} +2940.00 q^{59} +26542.0 q^{61} -14384.0 q^{62} -10688.0 q^{64} -4225.00 q^{65} -43588.0 q^{67} +37016.0 q^{68} -8400.00 q^{70} +20688.0 q^{71} +24786.0 q^{73} +4596.00 q^{74} -47600.0 q^{76} +8736.00 q^{77} +51760.0 q^{79} -16400.0 q^{80} -12876.0 q^{82} -31436.0 q^{83} +33050.0 q^{85} -37912.0 q^{86} -6240.00 q^{88} -115690. q^{89} -28392.0 q^{91} +51968.0 q^{92} -1936.00 q^{94} -42500.0 q^{95} -127638. q^{97} -22834.0 q^{98} +O(q^{100})\)

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 $

$2$	−2.00000	−0.353553	−0.176777	−	0.984251i	$-0.556567\pi$
$2$	−2.00000	−0.353553	−0.176777	+	0.984251i	$0.556567\pi$
$3$	0	0
$3$	0	0
$4$	−28.0000	−0.875000
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	0	0
$7$	−168.000	−1.29588	−0.647939	−	0.761692i	$-0.724369\pi$
$7$	−168.000	−1.29588	−0.647939	+	0.761692i	$0.724369\pi$
$8$	120.000	0.662913
$9$	0	0
$10$	50.0000	0.158114
$11$	−52.0000	−0.129575	−0.0647876	−	0.997899i	$-0.520637\pi$
$11$	−52.0000	−0.129575	−0.0647876	+	0.997899i	$0.520637\pi$
$12$	0	0
$13$	169.000	0.277350
$13$	169.000	0.277350
$14$	336.000	0.458162
$15$	0	0
$16$	656.000	0.640625
$17$	−1322.00	−1.10945	−0.554727	−	0.832033i	$-0.687177\pi$
$17$	−1322.00	−1.10945	−0.554727	+	0.832033i	$0.687177\pi$
$18$	0	0
$19$	1700.00	1.08035	0.540176	−	0.841552i	$-0.318358\pi$
$19$	1700.00	1.08035	0.540176	+	0.841552i	$0.318358\pi$
$20$	700.000	0.391312
$21$	0	0
$22$	104.000	0.0458117
$23$	−1856.00	−0.731574	−0.365787	−	0.930699i	$-0.619200\pi$
$23$	−1856.00	−0.731574	−0.365787	+	0.930699i	$0.619200\pi$
$24$	0	0
$25$	625.000	0.200000
$26$	−338.000	−0.0980581
$27$	0	0
$28$	4704.00	1.13389
$29$	4250.00	0.938413	0.469206	−	0.883089i	$-0.344540\pi$
$29$	4250.00	0.938413	0.469206	+	0.883089i	$0.344540\pi$
$30$	0	0
$31$	7192.00	1.34414	0.672071	−	0.740486i	$-0.265405\pi$
$31$	7192.00	1.34414	0.672071	+	0.740486i	$0.265405\pi$
$32$	−5152.00	−0.889408
$33$	0	0
$34$	2644.00	0.392251
$35$	4200.00	0.579534
$36$	0	0
$37$	−2298.00	−0.275960	−0.137980	−	0.990435i	$-0.544061\pi$
$37$	−2298.00	−0.275960	−0.137980	+	0.990435i	$0.544061\pi$
$38$	−3400.00	−0.381962
$39$	0	0
$40$	−3000.00	−0.296464
$41$	6438.00	0.598124	0.299062	−	0.954234i	$-0.403326\pi$
$41$	6438.00	0.598124	0.299062	+	0.954234i	$0.403326\pi$
$42$	0	0
$43$	18956.0	1.56342	0.781710	−	0.623642i	$-0.214348\pi$
$43$	18956.0	1.56342	0.781710	+	0.623642i	$0.214348\pi$
$44$	1456.00	0.113378
$45$	0	0
$46$	3712.00	0.258651
$47$	968.000	0.0639191	0.0319596	−	0.999489i	$-0.489825\pi$
$47$	968.000	0.0639191	0.0319596	+	0.999489i	$0.489825\pi$
$48$	0	0
$49$	11417.0	0.679300
$50$	−1250.00	−0.0707107
$51$	0	0
$52$	−4732.00	−0.242681
$53$	−15366.0	−0.751400	−0.375700	−	0.926741i	$-0.622598\pi$
$53$	−15366.0	−0.751400	−0.375700	+	0.926741i	$0.622598\pi$
$54$	0	0
$55$	1300.00	0.0579478
$56$	−20160.0	−0.859054
$57$	0	0
$58$	−8500.00	−0.331779
$59$	2940.00	0.109956	0.0549778	−	0.998488i	$-0.482491\pi$
$59$	2940.00	0.109956	0.0549778	+	0.998488i	$0.482491\pi$
$60$	0	0
$61$	26542.0	0.913291	0.456645	−	0.889649i	$-0.349051\pi$
$61$	26542.0	0.913291	0.456645	+	0.889649i	$0.349051\pi$
$62$	−14384.0	−0.475226
$63$	0	0
$64$	−10688.0	−0.326172
$65$	−4225.00	−0.124035
$66$	0	0
$67$	−43588.0	−1.18626	−0.593130	−	0.805107i	$-0.702108\pi$
$67$	−43588.0	−1.18626	−0.593130	+	0.805107i	$0.702108\pi$
$68$	37016.0	0.970772
$69$	0	0
$70$	−8400.00	−0.204896
$71$	20688.0	0.487049	0.243524	−	0.969895i	$-0.421696\pi$
$71$	20688.0	0.487049	0.243524	+	0.969895i	$0.421696\pi$
$72$	0	0
$73$	24786.0	0.544376	0.272188	−	0.962244i	$-0.412253\pi$
$73$	24786.0	0.544376	0.272188	+	0.962244i	$0.412253\pi$
$74$	4596.00	0.0975665
$75$	0	0
$76$	−47600.0	−0.945307
$77$	8736.00	0.167914
$78$	0	0
$79$	51760.0	0.933096	0.466548	−	0.884496i	$-0.345497\pi$
$79$	51760.0	0.933096	0.466548	+	0.884496i	$0.345497\pi$
$80$	−16400.0	−0.286496
$81$	0	0
$82$	−12876.0	−0.211469
$83$	−31436.0	−0.500878	−0.250439	−	0.968132i	$-0.580575\pi$
$83$	−31436.0	−0.500878	−0.250439	+	0.968132i	$0.580575\pi$
$84$	0	0
$85$	33050.0	0.496163
$86$	−37912.0	−0.552752
$87$	0	0
$88$	−6240.00	−0.0858970
$89$	−115690.	−1.54818	−0.774089	−	0.633077i	$-0.781792\pi$
$89$	−115690.	−1.54818	−0.774089	+	0.633077i	$0.781792\pi$
$90$	0	0
$91$	−28392.0	−0.359412
$92$	51968.0	0.640127
$93$	0	0
$94$	−1936.00	−0.0225988
$95$	−42500.0	−0.483148
$96$	0	0
$97$	−127638.	−1.37737	−0.688685	−	0.725061i	$-0.741812\pi$
$97$	−127638.	−1.37737	−0.688685	+	0.725061i	$0.741812\pi$
$98$	−22834.0	−0.240169
$99$	0	0
$100$	−17500.0	−0.175000
$101$	−149982.	−1.46297	−0.731485	−	0.681857i	$-0.761173\pi$
$101$	−149982.	−1.46297	−0.731485	+	0.681857i	$0.761173\pi$
$102$	0	0
$103$	76216.0	0.707869	0.353935	−	0.935270i	$-0.384844\pi$
$103$	76216.0	0.707869	0.353935	+	0.935270i	$0.384844\pi$
$104$	20280.0	0.183859
$105$	0	0
$106$	30732.0	0.265660
$107$	27348.0	0.230922	0.115461	−	0.993312i	$-0.463165\pi$
$107$	27348.0	0.230922	0.115461	+	0.993312i	$0.463165\pi$
$108$	0	0
$109$	162070.	1.30658	0.653291	−	0.757107i	$-0.273388\pi$
$109$	162070.	1.30658	0.653291	+	0.757107i	$0.273388\pi$
$110$	−2600.00	−0.0204876
$111$	0	0
$112$	−110208.	−0.830172
$113$	127174.	0.936919	0.468460	−	0.883485i	$-0.344809\pi$
$113$	127174.	0.936919	0.468460	+	0.883485i	$0.344809\pi$
$114$	0	0
$115$	46400.0	0.327170
$116$	−119000.	−0.821111
$117$	0	0
$118$	−5880.00	−0.0388752
$119$	222096.	1.43772
$120$	0	0
$121$	−158347.	−0.983210
$122$	−53084.0	−0.322897
$123$	0	0
$124$	−201376.	−1.17613
$125$	−15625.0	−0.0894427
$126$	0	0
$127$	−76528.0	−0.421028	−0.210514	−	0.977591i	$-0.567514\pi$
$127$	−76528.0	−0.421028	−0.210514	+	0.977591i	$0.567514\pi$
$128$	186240.	1.00473
$129$	0	0
$130$	8450.00	0.0438529
$131$	208308.	1.06054	0.530271	−	0.847828i	$-0.322090\pi$
$131$	208308.	1.06054	0.530271	+	0.847828i	$0.322090\pi$
$132$	0	0
$133$	−285600.	−1.40000
$134$	87176.0	0.419406
$135$	0	0
$136$	−158640.	−0.735471
$137$	−145962.	−0.664413	−0.332207	−	0.943207i	$-0.607793\pi$
$137$	−145962.	−0.664413	−0.332207	+	0.943207i	$0.607793\pi$
$138$	0	0
$139$	−236420.	−1.03788	−0.518940	−	0.854811i	$-0.673673\pi$
$139$	−236420.	−1.03788	−0.518940	+	0.854811i	$0.673673\pi$
$140$	−117600.	−0.507093
$141$	0	0
$142$	−41376.0	−0.172198
$143$	−8788.00	−0.0359377
$144$	0	0
$145$	−106250.	−0.419671
$146$	−49572.0	−0.192466
$147$	0	0
$148$	64344.0	0.241465
$149$	155530.	0.573916	0.286958	−	0.957943i	$-0.407356\pi$
$149$	155530.	0.573916	0.286958	+	0.957943i	$0.407356\pi$
$150$	0	0
$151$	−516768.	−1.84439	−0.922196	−	0.386723i	$-0.873607\pi$
$151$	−516768.	−1.84439	−0.922196	+	0.386723i	$0.873607\pi$
$152$	204000.	0.716178
$153$	0	0
$154$	−17472.0	−0.0593664
$155$	−179800.	−0.601119
$156$	0	0
$157$	394702.	1.27797	0.638984	−	0.769220i	$-0.279355\pi$
$157$	394702.	1.27797	0.638984	+	0.769220i	$0.279355\pi$
$158$	−103520.	−0.329899
$159$	0	0
$160$	128800.	0.397755
$161$	311808.	0.948031
$162$	0	0
$163$	−125444.	−0.369812	−0.184906	−	0.982756i	$-0.559198\pi$
$163$	−125444.	−0.369812	−0.184906	+	0.982756i	$0.559198\pi$
$164$	−180264.	−0.523359
$165$	0	0
$166$	62872.0	0.177087
$167$	9728.00	0.0269918	0.0134959	−	0.999909i	$-0.495704\pi$
$167$	9728.00	0.0269918	0.0134959	+	0.999909i	$0.495704\pi$
$168$	0	0
$169$	28561.0	0.0769231
$170$	−66100.0	−0.175420
$171$	0	0
$172$	−530768.	−1.36799
$173$	−107326.	−0.272640	−0.136320	−	0.990665i	$-0.543528\pi$
$173$	−107326.	−0.272640	−0.136320	+	0.990665i	$0.543528\pi$
$174$	0	0
$175$	−105000.	−0.259176
$176$	−34112.0	−0.0830091
$177$	0	0
$178$	231380.	0.547363
$179$	−14940.0	−0.0348512	−0.0174256	−	0.999848i	$-0.505547\pi$
$179$	−14940.0	−0.0348512	−0.0174256	+	0.999848i	$0.505547\pi$
$180$	0	0
$181$	−224618.	−0.509622	−0.254811	−	0.966991i	$-0.582013\pi$
$181$	−224618.	−0.509622	−0.254811	+	0.966991i	$0.582013\pi$
$182$	56784.0	0.127071
$183$	0	0
$184$	−222720.	−0.484970
$185$	57450.0	0.123413
$186$	0	0
$187$	68744.0	0.143758
$188$	−27104.0	−0.0559292
$189$	0	0
$190$	85000.0	0.170819
$191$	−147952.	−0.293452	−0.146726	−	0.989177i	$-0.546874\pi$
$191$	−147952.	−0.293452	−0.146726	+	0.989177i	$0.546874\pi$
$192$	0	0
$193$	139546.	0.269665	0.134832	−	0.990868i	$-0.456950\pi$
$193$	139546.	0.269665	0.134832	+	0.990868i	$0.456950\pi$
$194$	255276.	0.486974
$195$	0	0
$196$	−319676.	−0.594388
$197$	−915702.	−1.68108	−0.840540	−	0.541749i	$-0.817762\pi$
$197$	−915702.	−1.68108	−0.840540	+	0.541749i	$0.817762\pi$
$198$	0	0
$199$	−171560.	−0.307102	−0.153551	−	0.988141i	$-0.549071\pi$
$199$	−171560.	−0.307102	−0.153551	+	0.988141i	$0.549071\pi$
$200$	75000.0	0.132583
$201$	0	0
$202$	299964.	0.517238
$203$	−714000.	−1.21607
$204$	0	0
$205$	−160950.	−0.267489
$206$	−152432.	−0.250270
$207$	0	0
$208$	110864.	0.177677
$209$	−88400.0	−0.139987
$210$	0	0
$211$	−615148.	−0.951204	−0.475602	−	0.879661i	$-0.657770\pi$
$211$	−615148.	−0.951204	−0.475602	+	0.879661i	$0.657770\pi$
$212$	430248.	0.657475
$213$	0	0
$214$	−54696.0	−0.0816434
$215$	−473900.	−0.699183
$216$	0	0
$217$	−1.20826e6	−1.74185
$218$	−324140.	−0.461946
$219$	0	0
$220$	−36400.0	−0.0507043
$221$	−223418.	−0.307707
$222$	0	0
$223$	317616.	0.427701	0.213850	−	0.976866i	$-0.431399\pi$
$223$	317616.	0.427701	0.213850	+	0.976866i	$0.431399\pi$
$224$	865536.	1.15256
$225$	0	0
$226$	−254348.	−0.331251
$227$	−207852.	−0.267725	−0.133863	−	0.991000i	$-0.542738\pi$
$227$	−207852.	−0.267725	−0.133863	+	0.991000i	$0.542738\pi$
$228$	0	0
$229$	1.50283e6	1.89374	0.946872	−	0.321611i	$-0.104224\pi$
$229$	1.50283e6	1.89374	0.946872	+	0.321611i	$0.104224\pi$
$230$	−92800.0	−0.115672
$231$	0	0
$232$	510000.	0.622086
$233$	−1.51047e6	−1.82273	−0.911363	−	0.411605i	$-0.864968\pi$
$233$	−1.51047e6	−1.82273	−0.911363	+	0.411605i	$0.864968\pi$
$234$	0	0
$235$	−24200.0	−0.0285855
$236$	−82320.0	−0.0962111
$237$	0	0
$238$	−444192.	−0.508310
$239$	402840.	0.456182	0.228091	−	0.973640i	$-0.426752\pi$
$239$	402840.	0.456182	0.228091	+	0.973640i	$0.426752\pi$
$240$	0	0
$241$	214162.	0.237520	0.118760	−	0.992923i	$-0.462108\pi$
$241$	214162.	0.237520	0.118760	+	0.992923i	$0.462108\pi$
$242$	316694.	0.347617
$243$	0	0
$244$	−743176.	−0.799129
$245$	−285425.	−0.303792
$246$	0	0
$247$	287300.	0.299635
$248$	863040.	0.891049
$249$	0	0
$250$	31250.0	0.0316228
$251$	709948.	0.711283	0.355641	−	0.934623i	$-0.384262\pi$
$251$	709948.	0.711283	0.355641	+	0.934623i	$0.384262\pi$
$252$	0	0
$253$	96512.0	0.0947938
$254$	153056.	0.148856
$255$	0	0
$256$	−30464.0	−0.0290527
$257$	1.29692e6	1.22484	0.612420	−	0.790532i	$-0.290196\pi$
$257$	1.29692e6	1.22484	0.612420	+	0.790532i	$0.290196\pi$
$258$	0	0
$259$	386064.	0.357610
$260$	118300.	0.108530
$261$	0	0
$262$	−416616.	−0.374958
$263$	−2.15218e6	−1.91862	−0.959309	−	0.282359i	$-0.908883\pi$
$263$	−2.15218e6	−1.91862	−0.959309	+	0.282359i	$0.908883\pi$
$264$	0	0
$265$	384150.	0.336036
$266$	571200.	0.494976
$267$	0	0
$268$	1.22046e6	1.03798
$269$	−2.30567e6	−1.94275	−0.971374	−	0.237556i	$-0.923654\pi$
$269$	−2.30567e6	−1.94275	−0.971374	+	0.237556i	$0.923654\pi$
$270$	0	0
$271$	−297608.	−0.246162	−0.123081	−	0.992397i	$-0.539278\pi$
$271$	−297608.	−0.246162	−0.123081	+	0.992397i	$0.539278\pi$
$272$	−867232.	−0.710744
$273$	0	0
$274$	291924.	0.234906
$275$	−32500.0	−0.0259150
$276$	0	0
$277$	−223258.	−0.174827	−0.0874133	−	0.996172i	$-0.527860\pi$
$277$	−223258.	−0.174827	−0.0874133	+	0.996172i	$0.527860\pi$
$278$	472840.	0.366946
$279$	0	0
$280$	504000.	0.384181
$281$	−493802.	−0.373067	−0.186534	−	0.982449i	$-0.559725\pi$
$281$	−493802.	−0.373067	−0.186534	+	0.982449i	$0.559725\pi$
$282$	0	0
$283$	−430244.	−0.319337	−0.159668	−	0.987171i	$-0.551042\pi$
$283$	−430244.	−0.319337	−0.159668	+	0.987171i	$0.551042\pi$
$284$	−579264.	−0.426168
$285$	0	0
$286$	17576.0	0.0127059
$287$	−1.08158e6	−0.775096
$288$	0	0
$289$	327827.	0.230887
$290$	212500.	0.148376
$291$	0	0
$292$	−694008.	−0.476329
$293$	−869046.	−0.591390	−0.295695	−	0.955282i	$-0.595551\pi$
$293$	−869046.	−0.591390	−0.295695	+	0.955282i	$0.595551\pi$
$294$	0	0
$295$	−73500.0	−0.0491736
$296$	−275760.	−0.182937
$297$	0	0
$298$	−311060.	−0.202910
$299$	−313664.	−0.202902
$300$	0	0
$301$	−3.18461e6	−2.02600
$302$	1.03354e6	0.652091
$303$	0	0
$304$	1.11520e6	0.692100
$305$	−663550.	−0.408436
$306$	0	0
$307$	−282148.	−0.170856	−0.0854282	−	0.996344i	$-0.527226\pi$
$307$	−282148.	−0.170856	−0.0854282	+	0.996344i	$0.527226\pi$
$308$	−244608.	−0.146924
$309$	0	0
$310$	359600.	0.212528
$311$	−2.41519e6	−1.41596	−0.707980	−	0.706233i	$-0.750393\pi$
$311$	−2.41519e6	−1.41596	−0.707980	+	0.706233i	$0.750393\pi$
$312$	0	0
$313$	1.26315e6	0.728774	0.364387	−	0.931248i	$-0.381279\pi$
$313$	1.26315e6	0.728774	0.364387	+	0.931248i	$0.381279\pi$
$314$	−789404.	−0.451830
$315$	0	0
$316$	−1.44928e6	−0.816459
$317$	3.12146e6	1.74465	0.872327	−	0.488923i	$-0.162610\pi$
$317$	3.12146e6	1.74465	0.872327	+	0.488923i	$0.162610\pi$
$318$	0	0
$319$	−221000.	−0.121595
$320$	267200.	0.145868
$321$	0	0
$322$	−623616.	−0.335180
$323$	−2.24740e6	−1.19860
$324$	0	0
$325$	105625.	0.0554700
$326$	250888.	0.130748
$327$	0	0
$328$	772560.	0.396504
$329$	−162624.	−0.0828314
$330$	0	0
$331$	1.12521e6	0.564501	0.282250	−	0.959341i	$-0.408919\pi$
$331$	1.12521e6	0.564501	0.282250	+	0.959341i	$0.408919\pi$
$332$	880208.	0.438268
$333$	0	0
$334$	−19456.0	−0.00954305
$335$	1.08970e6	0.530512
$336$	0	0
$337$	2.51216e6	1.20496	0.602480	−	0.798134i	$-0.294179\pi$
$337$	2.51216e6	1.20496	0.602480	+	0.798134i	$0.294179\pi$
$338$	−57122.0	−0.0271964
$339$	0	0
$340$	−925400.	−0.434142
$341$	−373984.	−0.174167
$342$	0	0
$343$	905520.	0.415588
$344$	2.27472e6	1.03641
$345$	0	0
$346$	214652.	0.0963928
$347$	3.97887e6	1.77393	0.886964	−	0.461839i	$-0.152810\pi$
$347$	3.97887e6	1.77393	0.886964	+	0.461839i	$0.152810\pi$
$348$	0	0
$349$	−3.60697e6	−1.58518	−0.792591	−	0.609754i	$-0.791268\pi$
$349$	−3.60697e6	−1.58518	−0.792591	+	0.609754i	$0.791268\pi$
$350$	210000.	0.0916324
$351$	0	0
$352$	267904.	0.115245
$353$	2.70889e6	1.15706	0.578529	−	0.815662i	$-0.303627\pi$
$353$	2.70889e6	1.15706	0.578529	+	0.815662i	$0.303627\pi$
$354$	0	0
$355$	−517200.	−0.217815
$356$	3.23932e6	1.35466
$357$	0	0
$358$	29880.0	0.0123218
$359$	1.68176e6	0.688697	0.344348	−	0.938842i	$-0.388100\pi$
$359$	1.68176e6	0.688697	0.344348	+	0.938842i	$0.388100\pi$
$360$	0	0
$361$	413901.	0.167159
$362$	449236.	0.180179
$363$	0	0
$364$	794976.	0.314485
$365$	−619650.	−0.243453
$366$	0	0
$367$	−251728.	−0.0975588	−0.0487794	−	0.998810i	$-0.515533\pi$
$367$	−251728.	−0.0975588	−0.0487794	+	0.998810i	$0.515533\pi$
$368$	−1.21754e6	−0.468665
$369$	0	0
$370$	−114900.	−0.0436331
$371$	2.58149e6	0.973723
$372$	0	0
$373$	−1.31263e6	−0.488508	−0.244254	−	0.969711i	$-0.578543\pi$
$373$	−1.31263e6	−0.488508	−0.244254	+	0.969711i	$0.578543\pi$
$374$	−137488.	−0.0508260
$375$	0	0
$376$	116160.	0.0423728
$377$	718250.	0.260269
$378$	0	0
$379$	−3.42618e6	−1.22521	−0.612607	−	0.790387i	$-0.709879\pi$
$379$	−3.42618e6	−1.22521	−0.612607	+	0.790387i	$0.709879\pi$
$380$	1.19000e6	0.422754
$381$	0	0
$382$	295904.	0.103751
$383$	−4.70734e6	−1.63975	−0.819876	−	0.572541i	$-0.805958\pi$
$383$	−4.70734e6	−1.63975	−0.819876	+	0.572541i	$0.805958\pi$
$384$	0	0
$385$	−218400.	−0.0750932
$386$	−279092.	−0.0953409
$387$	0	0
$388$	3.57386e6	1.20520
$389$	4.48605e6	1.50311	0.751554	−	0.659672i	$-0.229305\pi$
$389$	4.48605e6	1.50311	0.751554	+	0.659672i	$0.229305\pi$
$390$	0	0
$391$	2.45363e6	0.811648
$392$	1.37004e6	0.450317
$393$	0	0
$394$	1.83140e6	0.594352
$395$	−1.29400e6	−0.417293
$396$	0	0
$397$	2.99646e6	0.954185	0.477092	−	0.878853i	$-0.341691\pi$
$397$	2.99646e6	0.954185	0.477092	+	0.878853i	$0.341691\pi$
$398$	343120.	0.108577
$399$	0	0
$400$	410000.	0.128125
$401$	5.57072e6	1.73002	0.865008	−	0.501758i	$-0.167313\pi$
$401$	5.57072e6	1.73002	0.865008	+	0.501758i	$0.167313\pi$
$402$	0	0
$403$	1.21545e6	0.372798
$404$	4.19950e6	1.28010
$405$	0	0
$406$	1.42800e6	0.429945
$407$	119496.	0.0357575
$408$	0	0
$409$	3.67345e6	1.08584	0.542920	−	0.839784i	$-0.317319\pi$
$409$	3.67345e6	1.08584	0.542920	+	0.839784i	$0.317319\pi$
$410$	321900.	0.0945717
$411$	0	0
$412$	−2.13405e6	−0.619386
$413$	−493920.	−0.142489
$414$	0	0
$415$	785900.	0.223999
$416$	−870688.	−0.246677
$417$	0	0
$418$	176800.	0.0494927
$419$	−4.29470e6	−1.19508	−0.597541	−	0.801838i	$-0.703856\pi$
$419$	−4.29470e6	−1.19508	−0.597541	+	0.801838i	$0.703856\pi$
$420$	0	0
$421$	2.52870e6	0.695332	0.347666	−	0.937618i	$-0.386974\pi$
$421$	2.52870e6	0.695332	0.347666	+	0.937618i	$0.386974\pi$
$422$	1.23030e6	0.336301
$423$	0	0
$424$	−1.84392e6	−0.498112
$425$	−826250.	−0.221891
$426$	0	0
$427$	−4.45906e6	−1.18351
$428$	−765744.	−0.202057
$429$	0	0
$430$	947800.	0.247198
$431$	981688.	0.254554	0.127277	−	0.991867i	$-0.459376\pi$
$431$	981688.	0.254554	0.127277	+	0.991867i	$0.459376\pi$
$432$	0	0
$433$	7.11511e6	1.82373	0.911867	−	0.410485i	$-0.134641\pi$
$433$	7.11511e6	1.82373	0.911867	+	0.410485i	$0.134641\pi$
$434$	2.41651e6	0.615835
$435$	0	0
$436$	−4.53796e6	−1.14326
$437$	−3.15520e6	−0.790357
$438$	0	0
$439$	4.17900e6	1.03493	0.517465	−	0.855704i	$-0.326876\pi$
$439$	4.17900e6	1.03493	0.517465	+	0.855704i	$0.326876\pi$
$440$	156000.	0.0384143
$441$	0	0
$442$	446836.	0.108791
$443$	1.21128e6	0.293249	0.146625	−	0.989192i	$-0.453159\pi$
$443$	1.21128e6	0.293249	0.146625	+	0.989192i	$0.453159\pi$
$444$	0	0
$445$	2.89225e6	0.692366
$446$	−635232.	−0.151215
$447$	0	0
$448$	1.79558e6	0.422679
$449$	5.20971e6	1.21954	0.609772	−	0.792577i	$-0.291261\pi$
$449$	5.20971e6	1.21954	0.609772	+	0.792577i	$0.291261\pi$
$450$	0	0
$451$	−334776.	−0.0775020
$452$	−3.56087e6	−0.819804
$453$	0	0
$454$	415704.	0.0946552
$455$	709800.	0.160734
$456$	0	0
$457$	−4.49688e6	−1.00721	−0.503606	−	0.863934i	$-0.667994\pi$
$457$	−4.49688e6	−1.00721	−0.503606	+	0.863934i	$0.667994\pi$
$458$	−3.00566e6	−0.669539
$459$	0	0
$460$	−1.29920e6	−0.286274
$461$	−600702.	−0.131646	−0.0658229	−	0.997831i	$-0.520967\pi$
$461$	−600702.	−0.131646	−0.0658229	+	0.997831i	$0.520967\pi$
$462$	0	0
$463$	1.70658e6	0.369976	0.184988	−	0.982741i	$-0.440775\pi$
$463$	1.70658e6	0.369976	0.184988	+	0.982741i	$0.440775\pi$
$464$	2.78800e6	0.601171
$465$	0	0
$466$	3.02093e6	0.644431
$467$	−4.03181e6	−0.855476	−0.427738	−	0.903903i	$-0.640689\pi$
$467$	−4.03181e6	−0.855476	−0.427738	+	0.903903i	$0.640689\pi$
$468$	0	0
$469$	7.32278e6	1.53725
$470$	48400.0	0.0101065
$471$	0	0
$472$	352800.	0.0728909
$473$	−985712.	−0.202580
$474$	0	0
$475$	1.06250e6	0.216070
$476$	−6.21869e6	−1.25800
$477$	0	0
$478$	−805680.	−0.161285
$479$	7.41484e6	1.47660	0.738300	−	0.674472i	$-0.235629\pi$
$479$	7.41484e6	1.47660	0.738300	+	0.674472i	$0.235629\pi$
$480$	0	0
$481$	−388362.	−0.0765375
$482$	−428324.	−0.0839759
$483$	0	0
$484$	4.43372e6	0.860309
$485$	3.19095e6	0.615979
$486$	0	0
$487$	−4.94041e6	−0.943931	−0.471966	−	0.881617i	$-0.656455\pi$
$487$	−4.94041e6	−0.943931	−0.471966	+	0.881617i	$0.656455\pi$
$488$	3.18504e6	0.605432
$489$	0	0
$490$	570850.	0.107407
$491$	2.75587e6	0.515887	0.257944	−	0.966160i	$-0.416955\pi$
$491$	2.75587e6	0.515887	0.257944	+	0.966160i	$0.416955\pi$
$492$	0	0
$493$	−5.61850e6	−1.04113
$494$	−574600.	−0.105937
$495$	0	0
$496$	4.71795e6	0.861092
$497$	−3.47558e6	−0.631156
$498$	0	0
$499$	−2.60558e6	−0.468439	−0.234220	−	0.972184i	$-0.575253\pi$
$499$	−2.60558e6	−0.468439	−0.234220	+	0.972184i	$0.575253\pi$
$500$	437500.	0.0782624
$501$	0	0
$502$	−1.41990e6	−0.251476
$503$	4.90406e6	0.864244	0.432122	−	0.901815i	$-0.357765\pi$
$503$	4.90406e6	0.864244	0.432122	+	0.901815i	$0.357765\pi$
$504$	0	0
$505$	3.74955e6	0.654261
$506$	−193024.	−0.0335147
$507$	0	0
$508$	2.14278e6	0.368400
$509$	1.53429e6	0.262490	0.131245	−	0.991350i	$-0.458103\pi$
$509$	1.53429e6	0.262490	0.131245	+	0.991350i	$0.458103\pi$
$510$	0	0
$511$	−4.16405e6	−0.705446
$512$	−5.89875e6	−0.994455
$513$	0	0
$514$	−2.59384e6	−0.433047
$515$	−1.90540e6	−0.316569
$516$	0	0
$517$	−50336.0	−0.00828233
$518$	−772128.	−0.126434
$519$	0	0
$520$	−507000.	−0.0822242
$521$	−4.06380e6	−0.655901	−0.327950	−	0.944695i	$-0.606358\pi$
$521$	−4.06380e6	−0.655901	−0.327950	+	0.944695i	$0.606358\pi$
$522$	0	0
$523$	−6.45208e6	−1.03144	−0.515722	−	0.856756i	$-0.672476\pi$
$523$	−6.45208e6	−1.03144	−0.515722	+	0.856756i	$0.672476\pi$
$524$	−5.83262e6	−0.927974
$525$	0	0
$526$	4.30435e6	0.678334
$527$	−9.50782e6	−1.49126
$528$	0	0
$529$	−2.99161e6	−0.464799
$530$	−768300.	−0.118807
$531$	0	0
$532$	7.99680e6	1.22500
$533$	1.08802e6	0.165890
$534$	0	0
$535$	−683700.	−0.103272
$536$	−5.23056e6	−0.786387
$537$	0	0
$538$	4.61134e6	0.686865
$539$	−593684.	−0.0880204
$540$	0	0
$541$	−1.20603e7	−1.77160	−0.885798	−	0.464070i	$-0.846389\pi$
$541$	−1.20603e7	−1.77160	−0.885798	+	0.464070i	$0.846389\pi$
$542$	595216.	0.0870315
$543$	0	0
$544$	6.81094e6	0.986757
$545$	−4.05175e6	−0.584321
$546$	0	0
$547$	−5.95523e6	−0.851001	−0.425501	−	0.904958i	$-0.639902\pi$
$547$	−5.95523e6	−0.851001	−0.425501	+	0.904958i	$0.639902\pi$
$548$	4.08694e6	0.581362
$549$	0	0
$550$	65000.0	0.00916234
$551$	7.22500e6	1.01382
$552$	0	0
$553$	−8.69568e6	−1.20918
$554$	446516.	0.0618106
$555$	0	0
$556$	6.61976e6	0.908145
$557$	−1.12188e7	−1.53217	−0.766086	−	0.642738i	$-0.777799\pi$
$557$	−1.12188e7	−1.53217	−0.766086	+	0.642738i	$0.777799\pi$
$558$	0	0
$559$	3.20356e6	0.433615
$560$	2.75520e6	0.371264
$561$	0	0
$562$	987604.	0.131899
$563$	−5.29628e6	−0.704206	−0.352103	−	0.935961i	$-0.614533\pi$
$563$	−5.29628e6	−0.704206	−0.352103	+	0.935961i	$0.614533\pi$
$564$	0	0
$565$	−3.17935e6	−0.419003
$566$	860488.	0.112903
$567$	0	0
$568$	2.48256e6	0.322871
$569$	−3.66337e6	−0.474351	−0.237176	−	0.971467i	$-0.576222\pi$
$569$	−3.66337e6	−0.474351	−0.237176	+	0.971467i	$0.576222\pi$
$570$	0	0
$571$	−505348.	−0.0648635	−0.0324317	−	0.999474i	$-0.510325\pi$
$571$	−505348.	−0.0648635	−0.0324317	+	0.999474i	$0.510325\pi$
$572$	246064.	0.0314455
$573$	0	0
$574$	2.16317e6	0.274038
$575$	−1.16000e6	−0.146315
$576$	0	0
$577$	1.18889e7	1.48663	0.743315	−	0.668941i	$-0.233252\pi$
$577$	1.18889e7	1.48663	0.743315	+	0.668941i	$0.233252\pi$
$578$	−655654.	−0.0816310
$579$	0	0
$580$	2.97500e6	0.367212
$581$	5.28125e6	0.649077
$582$	0	0
$583$	799032.	0.0973627
$584$	2.97432e6	0.360874
$585$	0	0
$586$	1.73809e6	0.209088
$587$	3.79787e6	0.454930	0.227465	−	0.973786i	$-0.426956\pi$
$587$	3.79787e6	0.454930	0.227465	+	0.973786i	$0.426956\pi$
$588$	0	0
$589$	1.22264e7	1.45215
$590$	147000.	0.0173855
$591$	0	0
$592$	−1.50749e6	−0.176787
$593$	−7.78759e6	−0.909423	−0.454712	−	0.890639i	$-0.650258\pi$
$593$	−7.78759e6	−0.909423	−0.454712	+	0.890639i	$0.650258\pi$
$594$	0	0
$595$	−5.55240e6	−0.642966
$596$	−4.35484e6	−0.502177
$597$	0	0
$598$	627328.	0.0717368
$599$	1.10798e7	1.26173	0.630863	−	0.775894i	$-0.282701\pi$
$599$	1.10798e7	1.26173	0.630863	+	0.775894i	$0.282701\pi$
$600$	0	0
$601$	1.23129e7	1.39051	0.695256	−	0.718762i	$-0.255291\pi$
$601$	1.23129e7	1.39051	0.695256	+	0.718762i	$0.255291\pi$
$602$	6.36922e6	0.716300
$603$	0	0
$604$	1.44695e7	1.61384
$605$	3.95868e6	0.439705
$606$	0	0
$607$	−1.25030e7	−1.37735	−0.688673	−	0.725072i	$-0.741806\pi$
$607$	−1.25030e7	−1.37735	−0.688673	+	0.725072i	$0.741806\pi$
$608$	−8.75840e6	−0.960873
$609$	0	0
$610$	1.32710e6	0.144404
$611$	163592.	0.0177280
$612$	0	0
$613$	−9.93839e6	−1.06823	−0.534115	−	0.845412i	$-0.679355\pi$
$613$	−9.93839e6	−1.06823	−0.534115	+	0.845412i	$0.679355\pi$
$614$	564296.	0.0604068
$615$	0	0
$616$	1.04832e6	0.111312
$617$	−3.07364e6	−0.325043	−0.162521	−	0.986705i	$-0.551963\pi$
$617$	−3.07364e6	−0.325043	−0.162521	+	0.986705i	$0.551963\pi$
$618$	0	0
$619$	−1.36164e7	−1.42836	−0.714178	−	0.699964i	$-0.753199\pi$
$619$	−1.36164e7	−1.42836	−0.714178	+	0.699964i	$0.753199\pi$
$620$	5.03440e6	0.525979
$621$	0	0
$622$	4.83038e6	0.500617
$623$	1.94359e7	2.00625
$624$	0	0
$625$	390625.	0.0400000
$626$	−2.52629e6	−0.257660
$627$	0	0
$628$	−1.10517e7	−1.11822
$629$	3.03796e6	0.306165
$630$	0	0
$631$	−1.24109e7	−1.24088	−0.620442	−	0.784253i	$-0.713047\pi$
$631$	−1.24109e7	−1.24088	−0.620442	+	0.784253i	$0.713047\pi$
$632$	6.21120e6	0.618561
$633$	0	0
$634$	−6.24292e6	−0.616828
$635$	1.91320e6	0.188289
$636$	0	0
$637$	1.92947e6	0.188404
$638$	442000.	0.0429903
$639$	0	0
$640$	−4.65600e6	−0.449328
$641$	2.43440e6	0.234017	0.117008	−	0.993131i	$-0.462670\pi$
$641$	2.43440e6	0.234017	0.117008	+	0.993131i	$0.462670\pi$
$642$	0	0
$643$	2.81648e6	0.268645	0.134322	−	0.990938i	$-0.457114\pi$
$643$	2.81648e6	0.268645	0.134322	+	0.990938i	$0.457114\pi$
$644$	−8.73062e6	−0.829527
$645$	0	0
$646$	4.49480e6	0.423769
$647$	−2.01122e7	−1.88886	−0.944428	−	0.328719i	$-0.893383\pi$
$647$	−2.01122e7	−1.88886	−0.944428	+	0.328719i	$0.893383\pi$
$648$	0	0
$649$	−152880.	−0.0142475
$650$	−211250.	−0.0196116
$651$	0	0
$652$	3.51243e6	0.323585
$653$	−1.57962e7	−1.44967	−0.724836	−	0.688921i	$-0.758085\pi$
$653$	−1.57962e7	−1.44967	−0.724836	+	0.688921i	$0.758085\pi$
$654$	0	0
$655$	−5.20770e6	−0.474289
$656$	4.22333e6	0.383173
$657$	0	0
$658$	325248.	0.0292853
$659$	1.45108e7	1.30160	0.650801	−	0.759248i	$-0.274433\pi$
$659$	1.45108e7	1.30160	0.650801	+	0.759248i	$0.274433\pi$
$660$	0	0
$661$	1.16326e7	1.03556	0.517778	−	0.855515i	$-0.326759\pi$
$661$	1.16326e7	1.03556	0.517778	+	0.855515i	$0.326759\pi$
$662$	−2.25042e6	−0.199581
$663$	0	0
$664$	−3.77232e6	−0.332038
$665$	7.14000e6	0.626101
$666$	0	0
$667$	−7.88800e6	−0.686519
$668$	−272384.	−0.0236179
$669$	0	0
$670$	−2.17940e6	−0.187564
$671$	−1.38018e6	−0.118340
$672$	0	0
$673$	−2.12566e7	−1.80907	−0.904535	−	0.426398i	$-0.859782\pi$
$673$	−2.12566e7	−1.80907	−0.904535	+	0.426398i	$0.859782\pi$
$674$	−5.02432e6	−0.426018
$675$	0	0
$676$	−799708.	−0.0673077
$677$	−1.57430e7	−1.32013	−0.660063	−	0.751210i	$-0.729470\pi$
$677$	−1.57430e7	−1.32013	−0.660063	+	0.751210i	$0.729470\pi$
$678$	0	0
$679$	2.14432e7	1.78490
$680$	3.96600e6	0.328913
$681$	0	0
$682$	747968.	0.0615775
$683$	−5.96924e6	−0.489629	−0.244814	−	0.969570i	$-0.578727\pi$
$683$	−5.96924e6	−0.489629	−0.244814	+	0.969570i	$0.578727\pi$
$684$	0	0
$685$	3.64905e6	0.297135
$686$	−1.81104e6	−0.146932
$687$	0	0
$688$	1.24351e7	1.00157
$689$	−2.59685e6	−0.208401
$690$	0	0
$691$	−4.73795e6	−0.377481	−0.188741	−	0.982027i	$-0.560441\pi$
$691$	−4.73795e6	−0.377481	−0.188741	+	0.982027i	$0.560441\pi$
$692$	3.00513e6	0.238560
$693$	0	0
$694$	−7.95774e6	−0.627178
$695$	5.91050e6	0.464154
$696$	0	0
$697$	−8.51104e6	−0.663591
$698$	7.21394e6	0.560446
$699$	0	0
$700$	2.94000e6	0.226779
$701$	−1.50578e7	−1.15735	−0.578677	−	0.815557i	$-0.696431\pi$
$701$	−1.50578e7	−1.15735	−0.578677	+	0.815557i	$0.696431\pi$
$702$	0	0
$703$	−3.90660e6	−0.298133
$704$	555776.	0.0422638
$705$	0	0
$706$	−5.41779e6	−0.409082
$707$	2.51970e7	1.89583
$708$	0	0
$709$	−9.80053e6	−0.732207	−0.366104	−	0.930574i	$-0.619308\pi$
$709$	−9.80053e6	−0.732207	−0.366104	+	0.930574i	$0.619308\pi$
$710$	1.03440e6	0.0770092
$711$	0	0
$712$	−1.38828e7	−1.02631
$713$	−1.33484e7	−0.983340
$714$	0	0
$715$	219700.	0.0160718
$716$	418320.	0.0304948
$717$	0	0
$718$	−3.36352e6	−0.243491
$719$	2.26512e6	0.163406	0.0817032	−	0.996657i	$-0.473964\pi$
$719$	2.26512e6	0.163406	0.0817032	+	0.996657i	$0.473964\pi$
$720$	0	0
$721$	−1.28043e7	−0.917312
$722$	−827802.	−0.0590995
$723$	0	0
$724$	6.28930e6	0.445919
$725$	2.65625e6	0.187683
$726$	0	0
$727$	2.14597e7	1.50587	0.752934	−	0.658096i	$-0.228638\pi$
$727$	2.14597e7	1.50587	0.752934	+	0.658096i	$0.228638\pi$
$728$	−3.40704e6	−0.238259
$729$	0	0
$730$	1.23930e6	0.0860735
$731$	−2.50598e7	−1.73454
$732$	0	0
$733$	−2.22056e7	−1.52652	−0.763261	−	0.646090i	$-0.776403\pi$
$733$	−2.22056e7	−1.52652	−0.763261	+	0.646090i	$0.776403\pi$
$734$	503456.	0.0344922
$735$	0	0
$736$	9.56211e6	0.650668
$737$	2.26658e6	0.153710
$738$	0	0
$739$	−7.73326e6	−0.520897	−0.260448	−	0.965488i	$-0.583870\pi$
$739$	−7.73326e6	−0.520897	−0.260448	+	0.965488i	$0.583870\pi$
$740$	−1.60860e6	−0.107986
$741$	0	0
$742$	−5.16298e6	−0.344263
$743$	1.76469e7	1.17272	0.586362	−	0.810049i	$-0.300560\pi$
$743$	1.76469e7	1.17272	0.586362	+	0.810049i	$0.300560\pi$
$744$	0	0
$745$	−3.88825e6	−0.256663
$746$	2.62527e6	0.172714
$747$	0	0
$748$	−1.92483e6	−0.125788
$749$	−4.59446e6	−0.299247
$750$	0	0
$751$	4.28731e6	0.277386	0.138693	−	0.990335i	$-0.455710\pi$
$751$	4.28731e6	0.277386	0.138693	+	0.990335i	$0.455710\pi$
$752$	635008.	0.0409482
$753$	0	0
$754$	−1.43650e6	−0.0920189
$755$	1.29192e7	0.824837
$756$	0	0
$757$	−1.32561e7	−0.840765	−0.420383	−	0.907347i	$-0.638104\pi$
$757$	−1.32561e7	−0.840765	−0.420383	+	0.907347i	$0.638104\pi$
$758$	6.85236e6	0.433179
$759$	0	0
$760$	−5.10000e6	−0.320285
$761$	9.95020e6	0.622831	0.311415	−	0.950274i	$-0.399197\pi$
$761$	9.95020e6	0.622831	0.311415	+	0.950274i	$0.399197\pi$
$762$	0	0
$763$	−2.72278e7	−1.69317
$764$	4.14266e6	0.256771
$765$	0	0
$766$	9.41467e6	0.579740
$767$	496860.	0.0304962
$768$	0	0
$769$	−915870.	−0.0558493	−0.0279247	−	0.999610i	$-0.508890\pi$
$769$	−915870.	−0.0558493	−0.0279247	+	0.999610i	$0.508890\pi$
$770$	436800.	0.0265495
$771$	0	0
$772$	−3.90729e6	−0.235957
$773$	−8.80201e6	−0.529826	−0.264913	−	0.964272i	$-0.585343\pi$
$773$	−8.80201e6	−0.529826	−0.264913	+	0.964272i	$0.585343\pi$
$774$	0	0
$775$	4.49500e6	0.268829
$776$	−1.53166e7	−0.913076
$777$	0	0
$778$	−8.97210e6	−0.531429
$779$	1.09446e7	0.646184
$780$	0	0
$781$	−1.07578e6	−0.0631094
$782$	−4.90726e6	−0.286961
$783$	0	0
$784$	7.48955e6	0.435177
$785$	−9.86755e6	−0.571525
$786$	0	0
$787$	−1.25325e7	−0.721273	−0.360637	−	0.932706i	$-0.617441\pi$
$787$	−1.25325e7	−0.721273	−0.360637	+	0.932706i	$0.617441\pi$
$788$	2.56397e7	1.47095
$789$	0	0
$790$	2.58800e6	0.147536
$791$	−2.13652e7	−1.21413
$792$	0	0
$793$	4.48560e6	0.253301
$794$	−5.99292e6	−0.337355
$795$	0	0
$796$	4.80368e6	0.268715
$797$	−8.76926e6	−0.489009	−0.244505	−	0.969648i	$-0.578625\pi$
$797$	−8.76926e6	−0.489009	−0.244505	+	0.969648i	$0.578625\pi$
$798$	0	0
$799$	−1.27970e6	−0.0709153
$800$	−3.22000e6	−0.177882
$801$	0	0
$802$	−1.11414e7	−0.611653
$803$	−1.28887e6	−0.0705376
$804$	0	0
$805$	−7.79520e6	−0.423972
$806$	−2.43090e6	−0.131804
$807$	0	0
$808$	−1.79978e7	−0.969822
$809$	−2.62017e6	−0.140753	−0.0703766	−	0.997520i	$-0.522420\pi$
$809$	−2.62017e6	−0.140753	−0.0703766	+	0.997520i	$0.522420\pi$
$810$	0	0
$811$	−2.82690e7	−1.50924	−0.754621	−	0.656161i	$-0.772179\pi$
$811$	−2.82690e7	−1.50924	−0.754621	+	0.656161i	$0.772179\pi$
$812$	1.99920e7	1.06406
$813$	0	0
$814$	−238992.	−0.0126422
$815$	3.13610e6	0.165385
$816$	0	0
$817$	3.22252e7	1.68904
$818$	−7.34690e6	−0.383902
$819$	0	0
$820$	4.50660e6	0.234053
$821$	3.17889e7	1.64596	0.822978	−	0.568074i	$-0.192311\pi$
$821$	3.17889e7	1.64596	0.822978	+	0.568074i	$0.192311\pi$
$822$	0	0
$823$	−2.90669e7	−1.49589	−0.747944	−	0.663762i	$-0.768959\pi$
$823$	−2.90669e7	−1.49589	−0.747944	+	0.663762i	$0.768959\pi$
$824$	9.14592e6	0.469255
$825$	0	0
$826$	987840.	0.0503775
$827$	1.46154e7	0.743099	0.371549	−	0.928413i	$-0.378827\pi$
$827$	1.46154e7	0.743099	0.371549	+	0.928413i	$0.378827\pi$
$828$	0	0
$829$	208430.	0.0105335	0.00526676	−	0.999986i	$-0.498324\pi$
$829$	208430.	0.0105335	0.00526676	+	0.999986i	$0.498324\pi$
$830$	−1.57180e6	−0.0791958
$831$	0	0
$832$	−1.80627e6	−0.0904638
$833$	−1.50933e7	−0.753652
$834$	0	0
$835$	−243200.	−0.0120711
$836$	2.47520e6	0.122488
$837$	0	0
$838$	8.58940e6	0.422525
$839$	8.12168e6	0.398328	0.199164	−	0.979966i	$-0.436177\pi$
$839$	8.12168e6	0.398328	0.199164	+	0.979966i	$0.436177\pi$
$840$	0	0
$841$	−2.44865e6	−0.119381
$842$	−5.05740e6	−0.245837
$843$	0	0
$844$	1.72241e7	0.832303
$845$	−714025.	−0.0344010
$846$	0	0
$847$	2.66023e7	1.27412
$848$	−1.00801e7	−0.481366
$849$	0	0
$850$	1.65250e6	0.0784502
$851$	4.26509e6	0.201885
$852$	0	0
$853$	−3.71033e7	−1.74598	−0.872991	−	0.487737i	$-0.837823\pi$
$853$	−3.71033e7	−1.74598	−0.872991	+	0.487737i	$0.837823\pi$
$854$	8.91811e6	0.418435
$855$	0	0
$856$	3.28176e6	0.153081
$857$	−3.11758e7	−1.44999	−0.724997	−	0.688752i	$-0.758159\pi$
$857$	−3.11758e7	−1.44999	−0.724997	+	0.688752i	$0.758159\pi$
$858$	0	0
$859$	−1.70113e7	−0.786601	−0.393301	−	0.919410i	$-0.628667\pi$
$859$	−1.70113e7	−0.786601	−0.393301	+	0.919410i	$0.628667\pi$
$860$	1.32692e7	0.611785
$861$	0	0
$862$	−1.96338e6	−0.0899985
$863$	−2.89381e7	−1.32264	−0.661321	−	0.750103i	$-0.730004\pi$
$863$	−2.89381e7	−1.32264	−0.661321	+	0.750103i	$0.730004\pi$
$864$	0	0
$865$	2.68315e6	0.121928
$866$	−1.42302e7	−0.644788
$867$	0	0
$868$	3.38312e7	1.52411
$869$	−2.69152e6	−0.120906
$870$	0	0
$871$	−7.36637e6	−0.329009
$872$	1.94484e7	0.866149
$873$	0	0
$874$	6.31040e6	0.279433
$875$	2.62500e6	0.115907
$876$	0	0
$877$	3.89173e7	1.70861	0.854307	−	0.519768i	$-0.173982\pi$
$877$	3.89173e7	1.70861	0.854307	+	0.519768i	$0.173982\pi$
$878$	−8.35800e6	−0.365903
$879$	0	0
$880$	852800.	0.0371228
$881$	−2.68616e7	−1.16598	−0.582991	−	0.812478i	$-0.698118\pi$
$881$	−2.68616e7	−1.16598	−0.582991	+	0.812478i	$0.698118\pi$
$882$	0	0
$883$	2.64941e7	1.14353	0.571765	−	0.820417i	$-0.306259\pi$
$883$	2.64941e7	1.14353	0.571765	+	0.820417i	$0.306259\pi$
$884$	6.25570e6	0.269244
$885$	0	0
$886$	−2.42257e6	−0.103679
$887$	3.19935e7	1.36538	0.682688	−	0.730710i	$-0.260811\pi$
$887$	3.19935e7	1.36538	0.682688	+	0.730710i	$0.260811\pi$
$888$	0	0
$889$	1.28567e7	0.545601
$890$	−5.78450e6	−0.244788
$891$	0	0
$892$	−8.89325e6	−0.374238
$893$	1.64560e6	0.0690551
$894$	0	0
$895$	373500.	0.0155859
$896$	−3.12883e7	−1.30200
$897$	0	0
$898$	−1.04194e7	−0.431174
$899$	3.05660e7	1.26136
$900$	0	0
$901$	2.03139e7	0.833643
$902$	669552.	0.0274011
$903$	0	0
$904$	1.52609e7	0.621096
$905$	5.61545e6	0.227910
$906$	0	0
$907$	−2.12847e6	−0.0859110	−0.0429555	−	0.999077i	$-0.513677\pi$
$907$	−2.12847e6	−0.0859110	−0.0429555	+	0.999077i	$0.513677\pi$
$908$	5.81986e6	0.234260
$909$	0	0
$910$	−1.41960e6	−0.0568280
$911$	−2.76348e7	−1.10322	−0.551608	−	0.834103i	$-0.685986\pi$
$911$	−2.76348e7	−1.10322	−0.551608	+	0.834103i	$0.685986\pi$
$912$	0	0
$913$	1.63467e6	0.0649013
$914$	8.99376e6	0.356103
$915$	0	0
$916$	−4.20792e7	−1.65703
$917$	−3.49957e7	−1.37433
$918$	0	0
$919$	−3.14009e7	−1.22646	−0.613230	−	0.789904i	$-0.710130\pi$
$919$	−3.14009e7	−1.22646	−0.613230	+	0.789904i	$0.710130\pi$
$920$	5.56800e6	0.216885
$921$	0	0
$922$	1.20140e6	0.0465438
$923$	3.49627e6	0.135083
$924$	0	0
$925$	−1.43625e6	−0.0551919
$926$	−3.41315e6	−0.130806
$927$	0	0
$928$	−2.18960e7	−0.834632
$929$	2.55910e7	0.972854	0.486427	−	0.873721i	$-0.338300\pi$
$929$	2.55910e7	0.972854	0.486427	+	0.873721i	$0.338300\pi$
$930$	0	0
$931$	1.94089e7	0.733883
$932$	4.22930e7	1.59488
$933$	0	0
$934$	8.06362e6	0.302457
$935$	−1.71860e6	−0.0642903
$936$	0	0
$937$	2.29463e7	0.853814	0.426907	−	0.904295i	$-0.359603\pi$
$937$	2.29463e7	0.853814	0.426907	+	0.904295i	$0.359603\pi$
$938$	−1.46456e7	−0.543499
$939$	0	0
$940$	677600.	0.0250123
$941$	−3.49096e7	−1.28520	−0.642600	−	0.766202i	$-0.722144\pi$
$941$	−3.49096e7	−1.28520	−0.642600	+	0.766202i	$0.722144\pi$
$942$	0	0
$943$	−1.19489e7	−0.437572
$944$	1.92864e6	0.0704403
$945$	0	0
$946$	1.97142e6	0.0716229
$947$	−5.00377e6	−0.181310	−0.0906552	−	0.995882i	$-0.528896\pi$
$947$	−5.00377e6	−0.181310	−0.0906552	+	0.995882i	$0.528896\pi$
$948$	0	0
$949$	4.18883e6	0.150983
$950$	−2.12500e6	−0.0763924
$951$	0	0
$952$	2.66515e7	0.953081
$953$	−1.50869e7	−0.538105	−0.269052	−	0.963126i	$-0.586710\pi$
$953$	−1.50869e7	−0.538105	−0.269052	+	0.963126i	$0.586710\pi$
$954$	0	0
$955$	3.69880e6	0.131236
$956$	−1.12795e7	−0.399159
$957$	0	0
$958$	−1.48297e7	−0.522057
$959$	2.45216e7	0.860999
$960$	0	0
$961$	2.30957e7	0.806720
$962$	776724.	0.0270601
$963$	0	0
$964$	−5.99654e6	−0.207830
$965$	−3.48865e6	−0.120598
$966$	0	0
$967$	−1.30422e7	−0.448522	−0.224261	−	0.974529i	$-0.571997\pi$
$967$	−1.30422e7	−0.448522	−0.224261	+	0.974529i	$0.571997\pi$
$968$	−1.90016e7	−0.651782
$969$	0	0
$970$	−6.38190e6	−0.217781
$971$	−3.60683e7	−1.22766	−0.613829	−	0.789439i	$-0.710372\pi$
$971$	−3.60683e7	−1.22766	−0.613829	+	0.789439i	$0.710372\pi$
$972$	0	0
$973$	3.97186e7	1.34497
$974$	9.88082e6	0.333730
$975$	0	0
$976$	1.74116e7	0.585077
$977$	8.89616e6	0.298171	0.149086	−	0.988824i	$-0.452367\pi$
$977$	8.89616e6	0.298171	0.149086	+	0.988824i	$0.452367\pi$
$978$	0	0
$979$	6.01588e6	0.200605
$980$	7.99190e6	0.265818
$981$	0	0
$982$	−5.51174e6	−0.182394
$983$	−4.07101e7	−1.34375	−0.671875	−	0.740665i	$-0.734511\pi$
$983$	−4.07101e7	−1.34375	−0.671875	+	0.740665i	$0.734511\pi$
$984$	0	0
$985$	2.28926e7	0.751802
$986$	1.12370e7	0.368093
$987$	0	0
$988$	−8.04440e6	−0.262181
$989$	−3.51823e7	−1.14376
$990$	0	0
$991$	1.37772e7	0.445631	0.222815	−	0.974861i	$-0.428475\pi$
$991$	1.37772e7	0.445631	0.222815	+	0.974861i	$0.428475\pi$
$992$	−3.70532e7	−1.19549
$993$	0	0
$994$	6.95117e6	0.223147
$995$	4.28900e6	0.137340
$996$	0	0
$997$	−5.76579e7	−1.83705	−0.918525	−	0.395363i	$-0.870619\pi$
$997$	−5.76579e7	−1.83705	−0.918525	+	0.395363i	$0.870619\pi$
$998$	5.21116e6	0.165618
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.6.a.b.1.1		1
3.2	odd	2		195.6.a.a.1.1	✓	1
15.14	odd	2		975.6.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.6.a.a.1.1	✓	1	3.2	odd	2
585.6.a.b.1.1		1	1.1	even	1	trivial
975.6.a.b.1.1		1	15.14	odd	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	585.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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